Properties

Label 531.2.m.a.130.34
Level $531$
Weight $2$
Character 531.130
Analytic conductor $4.240$
Analytic rank $0$
Dimension $3248$
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] = [531,2,Mod(4,531)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(531, base_ring=CyclotomicField(174))
 
chi = DirichletCharacter(H, H._module([58, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("531.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 531 = 3^{2} \cdot 59 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 531.m (of order \(87\), degree \(56\), 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: \(4.24005634733\)
Analytic rank: \(0\)
Dimension: \(3248\)
Relative dimension: \(58\) over \(\Q(\zeta_{87})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{87}]$

Embedding invariants

Embedding label 130.34
Character \(\chi\) \(=\) 531.130
Dual form 531.2.m.a.241.34

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.437333 + 0.385280i) q^{2} +(1.25499 - 1.19374i) q^{3} +(-0.209280 - 1.64706i) q^{4} +(1.06633 + 0.155102i) q^{5} +(1.00877 - 0.0385391i) q^{6} +(0.439486 + 4.85504i) q^{7} +(1.19722 - 1.76576i) q^{8} +(0.149982 - 2.99625i) q^{9} +O(q^{10})\) \(q+(0.437333 + 0.385280i) q^{2} +(1.25499 - 1.19374i) q^{3} +(-0.209280 - 1.64706i) q^{4} +(1.06633 + 0.155102i) q^{5} +(1.00877 - 0.0385391i) q^{6} +(0.439486 + 4.85504i) q^{7} +(1.19722 - 1.76576i) q^{8} +(0.149982 - 2.99625i) q^{9} +(0.406583 + 0.478666i) q^{10} +(2.37991 - 2.42327i) q^{11} +(-2.22880 - 1.81721i) q^{12} +(4.40111 + 0.158994i) q^{13} +(-1.67835 + 2.29259i) q^{14} +(1.52338 - 1.07826i) q^{15} +(-2.01118 + 0.519482i) q^{16} +(-3.35498 + 1.55218i) q^{17} +(1.21999 - 1.25257i) q^{18} +(-5.54126 - 1.21972i) q^{19} +(0.0322998 - 1.78876i) q^{20} +(6.34719 + 5.56837i) q^{21} +(1.97445 - 0.142845i) q^{22} +(4.79758 + 1.81186i) q^{23} +(-0.605366 - 3.64517i) q^{24} +(-3.67982 - 1.09363i) q^{25} +(1.86349 + 1.76519i) q^{26} +(-3.38851 - 3.93929i) q^{27} +(7.90454 - 1.73992i) q^{28} +(1.38007 + 6.85717i) q^{29} +(1.08166 + 0.115367i) q^{30} +(1.84843 - 5.83185i) q^{31} +(-4.88488 - 2.47787i) q^{32} +(0.0940045 - 5.88217i) q^{33} +(-2.06527 - 0.613789i) q^{34} +(-0.284388 + 5.24522i) q^{35} +(-4.96638 + 0.380026i) q^{36} +(-3.46405 - 5.10909i) q^{37} +(-1.95344 - 2.66836i) q^{38} +(5.71313 - 5.05423i) q^{39} +(1.55050 - 1.69719i) q^{40} +(2.99388 + 2.45137i) q^{41} +(0.630449 + 4.88068i) q^{42} +(2.03601 - 0.525895i) q^{43} +(-4.48934 - 3.41271i) q^{44} +(0.624653 - 3.17172i) q^{45} +(1.40006 + 2.64080i) q^{46} +(-4.13373 + 0.601268i) q^{47} +(-1.90388 + 3.05277i) q^{48} +(-16.4920 + 3.01044i) q^{49} +(-1.18795 - 1.89604i) q^{50} +(-2.35756 + 5.95293i) q^{51} +(-0.659192 - 7.28214i) q^{52} +(1.51438 - 1.78287i) q^{53} +(0.0358249 - 3.02831i) q^{54} +(2.91362 - 2.21488i) q^{55} +(9.09900 + 5.03650i) q^{56} +(-8.41023 + 5.08407i) q^{57} +(-2.03838 + 3.53058i) q^{58} +(7.20781 + 2.65471i) q^{59} +(-2.09477 - 2.28343i) q^{60} +(-2.65106 - 2.33552i) q^{61} +(3.05528 - 1.83830i) q^{62} +(14.6128 - 0.588640i) q^{63} +(0.356051 + 0.893620i) q^{64} +(4.66836 + 0.852158i) q^{65} +(2.30739 - 2.53625i) q^{66} +(1.16421 + 2.40164i) q^{67} +(3.25866 + 5.20100i) q^{68} +(8.18379 - 3.45318i) q^{69} +(-2.14525 + 2.18434i) q^{70} +(-4.69360 + 11.7800i) q^{71} +(-5.11110 - 3.85199i) q^{72} +(-5.91434 - 0.643223i) q^{73} +(0.453489 - 3.56901i) q^{74} +(-5.92362 + 3.02025i) q^{75} +(-0.849277 + 9.38203i) q^{76} +(12.8110 + 10.4896i) q^{77} +(4.44583 - 0.00922613i) q^{78} +(-0.281412 + 15.5846i) q^{79} +(-2.22515 + 0.242000i) q^{80} +(-8.95501 - 0.898768i) q^{81} +(0.364860 + 2.22555i) q^{82} +(-12.4711 + 6.32603i) q^{83} +(7.84308 - 11.6195i) q^{84} +(-3.81825 + 1.13477i) q^{85} +(1.09303 + 0.554444i) q^{86} +(9.91764 + 6.95822i) q^{87} +(-1.42966 - 7.10354i) q^{88} +(7.68638 + 2.58984i) q^{89} +(1.49518 - 1.14643i) q^{90} +(1.16230 + 21.4374i) q^{91} +(1.98020 - 8.28107i) q^{92} +(-4.64195 - 9.52543i) q^{93} +(-2.03947 - 1.32969i) q^{94} +(-5.71961 - 2.16008i) q^{95} +(-9.08838 + 2.72157i) q^{96} +(-0.470665 - 0.642920i) q^{97} +(-8.37236 - 5.03748i) q^{98} +(-6.90379 - 7.49426i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3248 q - 29 q^{2} - 58 q^{3} + 29 q^{4} - 25 q^{5} - 66 q^{6} - 27 q^{7} - 116 q^{8} - 62 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3248 q - 29 q^{2} - 58 q^{3} + 29 q^{4} - 25 q^{5} - 66 q^{6} - 27 q^{7} - 116 q^{8} - 62 q^{9} - 116 q^{10} - 33 q^{11} - 58 q^{12} - 27 q^{13} - 33 q^{14} - 51 q^{15} + 29 q^{16} - 126 q^{17} - 78 q^{18} - 120 q^{19} - 31 q^{20} - 60 q^{21} - 29 q^{22} - 29 q^{23} - 16 q^{24} + 29 q^{25} - 92 q^{26} - 55 q^{27} - 132 q^{28} - 27 q^{29} - 64 q^{30} - 21 q^{31} - 49 q^{32} - 32 q^{33} - 17 q^{34} - 136 q^{35} - 70 q^{36} - 120 q^{37} - 33 q^{38} - 80 q^{39} - 17 q^{40} - 17 q^{41} - 68 q^{42} - 21 q^{43} - 104 q^{44} - 58 q^{45} - 116 q^{46} - 17 q^{47} + 106 q^{48} + 19 q^{49} - 5 q^{50} - 250 q^{51} - 21 q^{52} - 108 q^{53} + 175 q^{54} - 116 q^{55} - q^{56} + 63 q^{57} - 58 q^{58} - 17 q^{59} - 816 q^{60} - 27 q^{61} - 128 q^{62} + 95 q^{63} - 256 q^{64} - 59 q^{65} + 67 q^{66} - 15 q^{67} - 43 q^{68} - 302 q^{69} - 41 q^{70} - 134 q^{71} + 210 q^{72} - 144 q^{73} - 51 q^{74} - 47 q^{75} - 9 q^{76} - 85 q^{77} + 36 q^{78} - 39 q^{79} - 128 q^{80} - 22 q^{81} - 164 q^{82} - 35 q^{83} - 190 q^{84} - 17 q^{85} + 31 q^{86} - 75 q^{87} - 29 q^{88} - 36 q^{89} - 86 q^{90} - 136 q^{91} - 31 q^{92} - 41 q^{94} - 13 q^{95} - 30 q^{96} - 3 q^{97} - 156 q^{98} - 86 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/531\mathbb{Z}\right)^\times\).

\(n\) \(119\) \(415\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{26}{29}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.437333 + 0.385280i 0.309241 + 0.272434i 0.801475 0.598029i \(-0.204049\pi\)
−0.492233 + 0.870463i \(0.663819\pi\)
\(3\) 1.25499 1.19374i 0.724567 0.689205i
\(4\) −0.209280 1.64706i −0.104640 0.823528i
\(5\) 1.06633 + 0.155102i 0.476876 + 0.0693635i 0.378137 0.925750i \(-0.376565\pi\)
0.0987394 + 0.995113i \(0.468519\pi\)
\(6\) 1.00877 0.0385391i 0.411829 0.0157335i
\(7\) 0.439486 + 4.85504i 0.166110 + 1.83503i 0.470402 + 0.882452i \(0.344109\pi\)
−0.304292 + 0.952579i \(0.598420\pi\)
\(8\) 1.19722 1.76576i 0.423280 0.624291i
\(9\) 0.149982 2.99625i 0.0499941 0.998750i
\(10\) 0.406583 + 0.478666i 0.128573 + 0.151367i
\(11\) 2.37991 2.42327i 0.717571 0.730645i −0.254050 0.967191i \(-0.581763\pi\)
0.971620 + 0.236546i \(0.0760155\pi\)
\(12\) −2.22880 1.81721i −0.643398 0.524583i
\(13\) 4.40111 + 0.158994i 1.22065 + 0.0440971i 0.638911 0.769281i \(-0.279385\pi\)
0.581736 + 0.813378i \(0.302374\pi\)
\(14\) −1.67835 + 2.29259i −0.448557 + 0.612721i
\(15\) 1.52338 1.07826i 0.393334 0.278407i
\(16\) −2.01118 + 0.519482i −0.502796 + 0.129870i
\(17\) −3.35498 + 1.55218i −0.813703 + 0.376459i −0.782187 0.623044i \(-0.785896\pi\)
−0.0315162 + 0.999503i \(0.510034\pi\)
\(18\) 1.21999 1.25257i 0.287554 0.295234i
\(19\) −5.54126 1.21972i −1.27125 0.279824i −0.472418 0.881375i \(-0.656619\pi\)
−0.798834 + 0.601551i \(0.794550\pi\)
\(20\) 0.0322998 1.78876i 0.00722246 0.399979i
\(21\) 6.34719 + 5.56837i 1.38507 + 1.21512i
\(22\) 1.97445 0.142845i 0.420955 0.0304546i
\(23\) 4.79758 + 1.81186i 1.00036 + 0.377800i 0.798749 0.601665i \(-0.205496\pi\)
0.201616 + 0.979465i \(0.435381\pi\)
\(24\) −0.605366 3.64517i −0.123570 0.744067i
\(25\) −3.67982 1.09363i −0.735963 0.218725i
\(26\) 1.86349 + 1.76519i 0.365461 + 0.346183i
\(27\) −3.38851 3.93929i −0.652119 0.758117i
\(28\) 7.90454 1.73992i 1.49382 0.328814i
\(29\) 1.38007 + 6.85717i 0.256273 + 1.27335i 0.873602 + 0.486640i \(0.161778\pi\)
−0.617329 + 0.786705i \(0.711785\pi\)
\(30\) 1.08166 + 0.115367i 0.197483 + 0.0210630i
\(31\) 1.84843 5.83185i 0.331987 1.04743i −0.630519 0.776174i \(-0.717158\pi\)
0.962507 0.271258i \(-0.0874397\pi\)
\(32\) −4.88488 2.47787i −0.863532 0.438030i
\(33\) 0.0940045 5.88217i 0.0163641 1.02395i
\(34\) −2.06527 0.613789i −0.354191 0.105264i
\(35\) −0.284388 + 5.24522i −0.0480703 + 0.886604i
\(36\) −4.96638 + 0.380026i −0.827730 + 0.0633377i
\(37\) −3.46405 5.10909i −0.569487 0.839930i 0.428488 0.903548i \(-0.359047\pi\)
−0.997974 + 0.0636177i \(0.979736\pi\)
\(38\) −1.95344 2.66836i −0.316890 0.432866i
\(39\) 5.71313 5.05423i 0.914832 0.809324i
\(40\) 1.55050 1.69719i 0.245155 0.268349i
\(41\) 2.99388 + 2.45137i 0.467566 + 0.382839i 0.837693 0.546142i \(-0.183904\pi\)
−0.370127 + 0.928981i \(0.620686\pi\)
\(42\) 0.630449 + 4.88068i 0.0972805 + 0.753105i
\(43\) 2.03601 0.525895i 0.310489 0.0801982i −0.0916085 0.995795i \(-0.529201\pi\)
0.402097 + 0.915597i \(0.368281\pi\)
\(44\) −4.48934 3.41271i −0.676793 0.514485i
\(45\) 0.624653 3.17172i 0.0931178 0.472812i
\(46\) 1.40006 + 2.64080i 0.206428 + 0.389365i
\(47\) −4.13373 + 0.601268i −0.602967 + 0.0877039i −0.438580 0.898692i \(-0.644518\pi\)
−0.164387 + 0.986396i \(0.552564\pi\)
\(48\) −1.90388 + 3.05277i −0.274802 + 0.440629i
\(49\) −16.4920 + 3.01044i −2.35600 + 0.430062i
\(50\) −1.18795 1.89604i −0.168002 0.268141i
\(51\) −2.35756 + 5.95293i −0.330125 + 0.833577i
\(52\) −0.659192 7.28214i −0.0914135 1.00985i
\(53\) 1.51438 1.78287i 0.208017 0.244896i −0.648253 0.761425i \(-0.724500\pi\)
0.856270 + 0.516529i \(0.172776\pi\)
\(54\) 0.0358249 3.02831i 0.00487515 0.412100i
\(55\) 2.91362 2.21488i 0.392872 0.298654i
\(56\) 9.09900 + 5.03650i 1.21590 + 0.673031i
\(57\) −8.41023 + 5.08407i −1.11396 + 0.673402i
\(58\) −2.03838 + 3.53058i −0.267653 + 0.463588i
\(59\) 7.20781 + 2.65471i 0.938377 + 0.345614i
\(60\) −2.09477 2.28343i −0.270434 0.294789i
\(61\) −2.65106 2.33552i −0.339433 0.299033i 0.474194 0.880421i \(-0.342740\pi\)
−0.813626 + 0.581388i \(0.802510\pi\)
\(62\) 3.05528 1.83830i 0.388021 0.233464i
\(63\) 14.6128 0.588640i 1.84104 0.0741617i
\(64\) 0.356051 + 0.893620i 0.0445064 + 0.111703i
\(65\) 4.66836 + 0.852158i 0.579039 + 0.105697i
\(66\) 2.30739 2.53625i 0.284021 0.312191i
\(67\) 1.16421 + 2.40164i 0.142231 + 0.293407i 0.958923 0.283667i \(-0.0915510\pi\)
−0.816692 + 0.577073i \(0.804195\pi\)
\(68\) 3.25866 + 5.20100i 0.395170 + 0.630714i
\(69\) 8.18379 3.45318i 0.985212 0.415714i
\(70\) −2.14525 + 2.18434i −0.256407 + 0.261079i
\(71\) −4.69360 + 11.7800i −0.557028 + 1.39803i 0.333346 + 0.942804i \(0.391822\pi\)
−0.890374 + 0.455230i \(0.849557\pi\)
\(72\) −5.11110 3.85199i −0.602349 0.453962i
\(73\) −5.91434 0.643223i −0.692221 0.0752835i −0.244755 0.969585i \(-0.578708\pi\)
−0.447465 + 0.894301i \(0.647673\pi\)
\(74\) 0.453489 3.56901i 0.0527171 0.414889i
\(75\) −5.92362 + 3.02025i −0.684001 + 0.348748i
\(76\) −0.849277 + 9.38203i −0.0974188 + 1.07619i
\(77\) 12.8110 + 10.4896i 1.45995 + 1.19540i
\(78\) 4.44583 0.00922613i 0.503392 0.00104465i
\(79\) −0.281412 + 15.5846i −0.0316613 + 1.75340i 0.464868 + 0.885380i \(0.346102\pi\)
−0.496529 + 0.868020i \(0.665392\pi\)
\(80\) −2.22515 + 0.242000i −0.248780 + 0.0270564i
\(81\) −8.95501 0.898768i −0.995001 0.0998631i
\(82\) 0.364860 + 2.22555i 0.0402920 + 0.245771i
\(83\) −12.4711 + 6.32603i −1.36889 + 0.694372i −0.974461 0.224557i \(-0.927907\pi\)
−0.394424 + 0.918928i \(0.629056\pi\)
\(84\) 7.84308 11.6195i 0.855750 1.26779i
\(85\) −3.81825 + 1.13477i −0.414148 + 0.123083i
\(86\) 1.09303 + 0.554444i 0.117865 + 0.0597873i
\(87\) 9.91764 + 6.95822i 1.06328 + 0.745999i
\(88\) −1.42966 7.10354i −0.152402 0.757240i
\(89\) 7.68638 + 2.58984i 0.814755 + 0.274523i 0.695670 0.718361i \(-0.255107\pi\)
0.119085 + 0.992884i \(0.462004\pi\)
\(90\) 1.49518 1.14643i 0.157606 0.120844i
\(91\) 1.16230 + 21.4374i 0.121842 + 2.24725i
\(92\) 1.98020 8.28107i 0.206451 0.863361i
\(93\) −4.64195 9.52543i −0.481348 0.987741i
\(94\) −2.03947 1.32969i −0.210356 0.137147i
\(95\) −5.71961 2.16008i −0.586820 0.221620i
\(96\) −9.08838 + 2.72157i −0.927579 + 0.277769i
\(97\) −0.470665 0.642920i −0.0477888 0.0652786i 0.782334 0.622859i \(-0.214029\pi\)
−0.830123 + 0.557580i \(0.811730\pi\)
\(98\) −8.37236 5.03748i −0.845736 0.508863i
\(99\) −6.90379 7.49426i −0.693857 0.753201i
\(100\) −1.03115 + 6.28974i −0.103115 + 0.628974i
\(101\) 11.2227 + 7.90863i 1.11670 + 0.786938i 0.979065 0.203546i \(-0.0652465\pi\)
0.137631 + 0.990484i \(0.456051\pi\)
\(102\) −3.32459 + 1.69509i −0.329183 + 0.167839i
\(103\) 1.98632 0.833286i 0.195718 0.0821061i −0.286806 0.957989i \(-0.592594\pi\)
0.482524 + 0.875883i \(0.339720\pi\)
\(104\) 5.54982 7.58096i 0.544205 0.743374i
\(105\) 5.90451 + 6.92217i 0.576222 + 0.675534i
\(106\) 1.34919 0.196246i 0.131045 0.0190611i
\(107\) −4.46552 16.0834i −0.431698 1.55484i −0.785103 0.619366i \(-0.787390\pi\)
0.353405 0.935471i \(-0.385024\pi\)
\(108\) −5.77909 + 6.40548i −0.556093 + 0.616367i
\(109\) −7.04706 + 13.2922i −0.674985 + 1.27316i 0.275174 + 0.961394i \(0.411264\pi\)
−0.950160 + 0.311763i \(0.899080\pi\)
\(110\) 2.12757 + 0.153922i 0.202856 + 0.0146759i
\(111\) −10.4463 2.27668i −0.991515 0.216093i
\(112\) −3.40599 9.53606i −0.321836 0.901073i
\(113\) −10.6621 1.55084i −1.00300 0.145891i −0.377416 0.926044i \(-0.623187\pi\)
−0.625589 + 0.780153i \(0.715141\pi\)
\(114\) −5.63687 1.01687i −0.527941 0.0952382i
\(115\) 4.83477 + 2.67615i 0.450844 + 0.249552i
\(116\) 11.0053 3.70813i 1.02182 0.344291i
\(117\) 1.13647 13.1630i 0.105067 1.21692i
\(118\) 2.12941 + 3.93802i 0.196028 + 0.362524i
\(119\) −9.01036 15.6064i −0.825978 1.43064i
\(120\) −0.0801465 3.98084i −0.00731634 0.363399i
\(121\) −0.00968142 0.536156i −0.000880129 0.0487414i
\(122\) −0.259565 2.04280i −0.0234999 0.184946i
\(123\) 6.68357 0.497476i 0.602637 0.0448559i
\(124\) −9.99223 1.82397i −0.897329 0.163798i
\(125\) −8.64405 3.99916i −0.773147 0.357696i
\(126\) 6.61746 + 5.37260i 0.589530 + 0.478629i
\(127\) 3.05604 5.76429i 0.271179 0.511498i −0.710097 0.704104i \(-0.751349\pi\)
0.981276 + 0.192605i \(0.0616938\pi\)
\(128\) −3.87332 + 10.8445i −0.342356 + 0.958526i
\(129\) 1.92739 3.09045i 0.169697 0.272099i
\(130\) 1.71331 + 2.17130i 0.150267 + 0.190436i
\(131\) 11.2937 + 0.407996i 0.986736 + 0.0356468i 0.524764 0.851248i \(-0.324154\pi\)
0.461972 + 0.886895i \(0.347142\pi\)
\(132\) −9.70793 + 1.07619i −0.844967 + 0.0936704i
\(133\) 3.48649 27.4391i 0.302317 2.37927i
\(134\) −0.416157 + 1.49886i −0.0359505 + 0.129482i
\(135\) −3.00227 4.72614i −0.258394 0.406761i
\(136\) −1.27586 + 7.78240i −0.109404 + 0.667335i
\(137\) −1.68671 5.32164i −0.144106 0.454659i 0.853708 0.520753i \(-0.174349\pi\)
−0.997813 + 0.0660939i \(0.978946\pi\)
\(138\) 4.90948 + 1.64286i 0.417923 + 0.139850i
\(139\) 2.49147 5.65075i 0.211323 0.479291i −0.777407 0.628998i \(-0.783465\pi\)
0.988730 + 0.149707i \(0.0478332\pi\)
\(140\) 8.69869 0.629319i 0.735174 0.0531871i
\(141\) −4.47002 + 5.68917i −0.376444 + 0.479115i
\(142\) −6.59129 + 3.34345i −0.553128 + 0.280576i
\(143\) 10.8595 10.2867i 0.908120 0.860217i
\(144\) 1.25485 + 6.10392i 0.104571 + 0.508660i
\(145\) 0.408050 + 7.52604i 0.0338867 + 0.625004i
\(146\) −2.33871 2.55998i −0.193553 0.211865i
\(147\) −17.1036 + 23.4652i −1.41068 + 1.93538i
\(148\) −7.69001 + 6.77472i −0.632115 + 0.556879i
\(149\) −4.91665 + 15.5122i −0.402787 + 1.27081i 0.509221 + 0.860636i \(0.329934\pi\)
−0.912008 + 0.410172i \(0.865469\pi\)
\(150\) −3.75424 0.961401i −0.306532 0.0784981i
\(151\) 4.97365 20.7994i 0.404750 1.69263i −0.276853 0.960912i \(-0.589291\pi\)
0.681603 0.731723i \(-0.261283\pi\)
\(152\) −8.78783 + 8.32427i −0.712787 + 0.675188i
\(153\) 4.14753 + 10.2852i 0.335308 + 0.831506i
\(154\) 1.56126 + 9.52327i 0.125810 + 0.767407i
\(155\) 2.87556 5.93197i 0.230970 0.476467i
\(156\) −9.52024 8.35209i −0.762229 0.668702i
\(157\) −10.1389 + 5.61208i −0.809168 + 0.447893i −0.833977 0.551799i \(-0.813941\pi\)
0.0248086 + 0.999692i \(0.492102\pi\)
\(158\) −6.12750 + 6.70722i −0.487478 + 0.533598i
\(159\) −0.227748 4.04525i −0.0180616 0.320809i
\(160\) −4.82456 3.39987i −0.381415 0.268784i
\(161\) −6.68820 + 24.0887i −0.527104 + 1.89846i
\(162\) −3.57004 3.84325i −0.280489 0.301954i
\(163\) −3.00119 0.326399i −0.235071 0.0255655i −0.0101748 0.999948i \(-0.503239\pi\)
−0.224896 + 0.974383i \(0.572204\pi\)
\(164\) 3.41098 5.44411i 0.266353 0.425114i
\(165\) 1.01257 6.25773i 0.0788287 0.487164i
\(166\) −7.89133 2.03830i −0.612486 0.158203i
\(167\) 12.1297 2.21414i 0.938622 0.171335i 0.311491 0.950249i \(-0.399172\pi\)
0.627131 + 0.778914i \(0.284229\pi\)
\(168\) 17.4314 4.54107i 1.34486 0.350351i
\(169\) 6.37834 + 0.461450i 0.490642 + 0.0354961i
\(170\) −2.10705 0.974827i −0.161604 0.0747658i
\(171\) −4.48568 + 16.4201i −0.343029 + 1.25567i
\(172\) −1.29228 3.24337i −0.0985351 0.247304i
\(173\) 15.1418 + 6.35218i 1.15121 + 0.482947i 0.877836 0.478960i \(-0.158986\pi\)
0.273376 + 0.961907i \(0.411860\pi\)
\(174\) 1.65645 + 6.86413i 0.125575 + 0.520368i
\(175\) 3.69236 18.3463i 0.279117 1.38685i
\(176\) −3.52759 + 6.10997i −0.265902 + 0.460556i
\(177\) 12.2147 5.27261i 0.918115 0.396313i
\(178\) 2.36369 + 4.09404i 0.177166 + 0.306861i
\(179\) 12.8531 4.33073i 0.960689 0.323694i 0.205101 0.978741i \(-0.434248\pi\)
0.755588 + 0.655047i \(0.227351\pi\)
\(180\) −5.35473 0.365061i −0.399118 0.0272100i
\(181\) 3.45015 2.62274i 0.256448 0.194946i −0.469049 0.883172i \(-0.655403\pi\)
0.725497 + 0.688226i \(0.241610\pi\)
\(182\) −7.75110 + 9.82310i −0.574549 + 0.728136i
\(183\) −6.11503 + 0.233619i −0.452036 + 0.0172696i
\(184\) 8.94306 6.30219i 0.659291 0.464604i
\(185\) −2.90138 5.98525i −0.213314 0.440044i
\(186\) 1.63988 5.95424i 0.120242 0.436586i
\(187\) −4.22321 + 11.8241i −0.308831 + 0.864664i
\(188\) 1.85543 + 6.68265i 0.135321 + 0.487383i
\(189\) 17.6362 18.1826i 1.28284 1.32259i
\(190\) −1.66914 3.14833i −0.121092 0.228404i
\(191\) −5.26951 11.9515i −0.381288 0.864778i −0.997043 0.0768403i \(-0.975517\pi\)
0.615755 0.787937i \(-0.288851\pi\)
\(192\) 1.51359 + 0.696450i 0.109234 + 0.0502620i
\(193\) −14.1922 14.4508i −1.02158 1.04019i −0.999182 0.0404418i \(-0.987123\pi\)
−0.0223958 0.999749i \(-0.507129\pi\)
\(194\) 0.0418670 0.462508i 0.00300588 0.0332061i
\(195\) 6.87598 4.50335i 0.492399 0.322491i
\(196\) 8.40981 + 26.5332i 0.600701 + 1.89523i
\(197\) 6.13847 + 3.69339i 0.437348 + 0.263143i 0.717156 0.696912i \(-0.245443\pi\)
−0.279808 + 0.960056i \(0.590271\pi\)
\(198\) −0.131865 5.93738i −0.00937122 0.421951i
\(199\) −5.46113 8.05456i −0.387129 0.570973i 0.583331 0.812235i \(-0.301749\pi\)
−0.970460 + 0.241262i \(0.922439\pi\)
\(200\) −6.33662 + 5.18838i −0.448067 + 0.366874i
\(201\) 4.32799 + 1.62426i 0.305273 + 0.114567i
\(202\) 1.86100 + 7.78258i 0.130940 + 0.547580i
\(203\) −32.6853 + 9.71393i −2.29406 + 0.681784i
\(204\) 10.2982 + 2.63721i 0.721019 + 0.184641i
\(205\) 2.81225 + 3.07831i 0.196416 + 0.214999i
\(206\) 1.18973 + 0.400868i 0.0828926 + 0.0279298i
\(207\) 6.14835 14.1030i 0.427340 0.980226i
\(208\) −8.93402 + 1.96653i −0.619463 + 0.136354i
\(209\) −16.1434 + 10.5252i −1.11666 + 0.728040i
\(210\) −0.0847356 + 5.30219i −0.00584731 + 0.365886i
\(211\) −1.51492 6.33527i −0.104291 0.436138i 0.895672 0.444715i \(-0.146695\pi\)
−0.999963 + 0.00857706i \(0.997270\pi\)
\(212\) −3.25342 2.12116i −0.223446 0.145682i
\(213\) 8.17188 + 20.3867i 0.559928 + 1.39688i
\(214\) 4.24368 8.75426i 0.290092 0.598429i
\(215\) 2.25262 0.244987i 0.153628 0.0167080i
\(216\) −11.0126 + 1.26712i −0.749315 + 0.0862163i
\(217\) 29.1262 + 6.41116i 1.97722 + 0.435218i
\(218\) −8.20312 + 3.09801i −0.555585 + 0.209824i
\(219\) −8.19025 + 6.25293i −0.553446 + 0.422534i
\(220\) −4.25779 4.33536i −0.287060 0.292290i
\(221\) −15.0124 + 6.29789i −1.00984 + 0.423642i
\(222\) −3.69133 5.02040i −0.247746 0.336947i
\(223\) 8.73892 13.9478i 0.585201 0.934014i −0.414511 0.910044i \(-0.636048\pi\)
0.999713 0.0239701i \(-0.00763064\pi\)
\(224\) 9.88331 24.8052i 0.660357 1.65737i
\(225\) −3.82868 + 10.8616i −0.255246 + 0.724108i
\(226\) −4.06537 4.78613i −0.270425 0.318369i
\(227\) −1.01653 + 0.0367233i −0.0674698 + 0.00243741i −0.0698167 0.997560i \(-0.522241\pi\)
0.00234696 + 0.999997i \(0.499253\pi\)
\(228\) 10.1338 + 12.7881i 0.671130 + 0.846915i
\(229\) −9.15638 + 6.45251i −0.605070 + 0.426394i −0.837669 0.546179i \(-0.816082\pi\)
0.232598 + 0.972573i \(0.425277\pi\)
\(230\) 1.08333 + 3.03311i 0.0714329 + 0.199997i
\(231\) 28.5994 2.12874i 1.88171 0.140061i
\(232\) 13.7604 + 5.77264i 0.903413 + 0.378993i
\(233\) 5.13506 3.08966i 0.336409 0.202411i −0.337318 0.941391i \(-0.609520\pi\)
0.673727 + 0.738980i \(0.264692\pi\)
\(234\) 5.56845 5.31874i 0.364021 0.347697i
\(235\) −4.50117 −0.293624
\(236\) 2.86401 12.4272i 0.186431 0.808945i
\(237\) 18.2507 + 19.8943i 1.18551 + 1.29228i
\(238\) 2.07231 10.2967i 0.134328 0.667436i
\(239\) −0.195656 10.8354i −0.0126559 0.700885i −0.942738 0.333534i \(-0.891759\pi\)
0.930082 0.367351i \(-0.119735\pi\)
\(240\) −2.50365 + 2.95995i −0.161610 + 0.191064i
\(241\) 9.25340 11.7270i 0.596064 0.755402i −0.390173 0.920742i \(-0.627585\pi\)
0.986237 + 0.165340i \(0.0528721\pi\)
\(242\) 0.202336 0.238209i 0.0130067 0.0153126i
\(243\) −12.3113 + 9.56199i −0.789771 + 0.613402i
\(244\) −3.29192 + 4.85521i −0.210743 + 0.310823i
\(245\) −18.0528 + 0.652175i −1.15335 + 0.0416659i
\(246\) 3.11461 + 2.35748i 0.198580 + 0.150308i
\(247\) −24.1937 6.24916i −1.53941 0.397624i
\(248\) −8.08470 10.2459i −0.513379 0.650614i
\(249\) −8.09950 + 22.8263i −0.513285 + 1.44656i
\(250\) −2.23953 5.07935i −0.141640 0.321246i
\(251\) 4.19045 + 3.18549i 0.264499 + 0.201067i 0.729015 0.684498i \(-0.239979\pi\)
−0.464516 + 0.885565i \(0.653772\pi\)
\(252\) −4.02769 23.9449i −0.253721 1.50839i
\(253\) 15.8085 7.31377i 0.993869 0.459813i
\(254\) 3.55737 1.34349i 0.223210 0.0842978i
\(255\) −3.43724 + 5.98211i −0.215248 + 0.374614i
\(256\) −4.18887 + 2.31864i −0.261805 + 0.144915i
\(257\) 8.10987 18.3935i 0.505880 1.14736i −0.459894 0.887974i \(-0.652113\pi\)
0.965774 0.259384i \(-0.0835195\pi\)
\(258\) 2.03360 0.608973i 0.126607 0.0379130i
\(259\) 23.2824 19.0635i 1.44670 1.18455i
\(260\) 0.426557 7.86739i 0.0264540 0.487915i
\(261\) 20.7528 3.10658i 1.28456 0.192293i
\(262\) 4.78192 + 4.52967i 0.295428 + 0.279844i
\(263\) 11.0166 7.18256i 0.679311 0.442895i −0.159587 0.987184i \(-0.551016\pi\)
0.838898 + 0.544288i \(0.183200\pi\)
\(264\) −10.2740 7.20822i −0.632319 0.443635i
\(265\) 1.89135 1.66624i 0.116185 0.102356i
\(266\) 12.0965 10.6567i 0.741683 0.653406i
\(267\) 12.7379 5.92530i 0.779547 0.362623i
\(268\) 3.71198 2.42013i 0.226746 0.147833i
\(269\) −1.89010 1.79039i −0.115241 0.109162i 0.627909 0.778286i \(-0.283911\pi\)
−0.743151 + 0.669124i \(0.766669\pi\)
\(270\) 0.507896 3.22361i 0.0309096 0.196183i
\(271\) −0.195116 + 3.59871i −0.0118525 + 0.218606i 0.986607 + 0.163117i \(0.0521546\pi\)
−0.998459 + 0.0554893i \(0.982328\pi\)
\(272\) 5.94115 4.86457i 0.360235 0.294958i
\(273\) 27.0493 + 25.5162i 1.63710 + 1.54431i
\(274\) 1.31267 2.97719i 0.0793012 0.179859i
\(275\) −11.4078 + 6.31447i −0.687916 + 0.380777i
\(276\) −7.40029 12.7565i −0.445445 0.767849i
\(277\) −1.15171 + 0.434959i −0.0691998 + 0.0261342i −0.387664 0.921801i \(-0.626718\pi\)
0.318464 + 0.947935i \(0.396833\pi\)
\(278\) 3.26672 1.51135i 0.195925 0.0906446i
\(279\) −17.1964 6.41302i −1.02952 0.383938i
\(280\) 8.92134 + 6.78183i 0.533152 + 0.405292i
\(281\) 6.35131 + 14.4050i 0.378887 + 0.859332i 0.997297 + 0.0734766i \(0.0234094\pi\)
−0.618410 + 0.785856i \(0.712223\pi\)
\(282\) −4.14681 + 0.765852i −0.246939 + 0.0456058i
\(283\) 1.06497 + 1.34966i 0.0633061 + 0.0802289i 0.815665 0.578525i \(-0.196371\pi\)
−0.752359 + 0.658754i \(0.771084\pi\)
\(284\) 20.3847 + 5.26529i 1.20961 + 0.312438i
\(285\) −9.75661 + 4.11684i −0.577932 + 0.243861i
\(286\) 8.71249 0.314747i 0.515181 0.0186114i
\(287\) −10.5857 + 15.6127i −0.624854 + 0.921591i
\(288\) −8.15696 + 14.2647i −0.480653 + 0.840554i
\(289\) −2.15892 + 2.54168i −0.126995 + 0.149511i
\(290\) −2.72118 + 3.44860i −0.159793 + 0.202509i
\(291\) −1.35816 0.245005i −0.0796165 0.0143625i
\(292\) 0.178329 + 9.87586i 0.0104359 + 0.577941i
\(293\) −0.290033 + 1.44109i −0.0169439 + 0.0841892i −0.987910 0.155027i \(-0.950454\pi\)
0.970966 + 0.239216i \(0.0768904\pi\)
\(294\) −16.5206 + 3.67243i −0.963503 + 0.214180i
\(295\) 7.27413 + 3.94873i 0.423516 + 0.229904i
\(296\) −13.1687 −0.765413
\(297\) −17.6103 1.16388i −1.02186 0.0675353i
\(298\) −8.12676 + 4.88971i −0.470770 + 0.283253i
\(299\) 20.8266 + 8.73699i 1.20443 + 0.505273i
\(300\) 6.21422 + 9.12446i 0.358778 + 0.526801i
\(301\) 3.44804 + 9.65379i 0.198742 + 0.556435i
\(302\) 10.1888 7.18004i 0.586297 0.413165i
\(303\) 23.5251 3.47169i 1.35148 0.199443i
\(304\) 11.7781 0.425495i 0.675521 0.0244038i
\(305\) −2.46465 2.90161i −0.141125 0.166146i
\(306\) −2.14882 + 6.09600i −0.122840 + 0.348485i
\(307\) 0.730167 1.83258i 0.0416728 0.104591i −0.906667 0.421847i \(-0.861382\pi\)
0.948340 + 0.317256i \(0.102761\pi\)
\(308\) 14.5958 23.2957i 0.831673 1.32740i
\(309\) 1.49808 3.41691i 0.0852230 0.194381i
\(310\) 3.54305 1.48635i 0.201232 0.0844190i
\(311\) −19.5839 19.9408i −1.11050 1.13074i −0.990436 0.137971i \(-0.955942\pi\)
−0.120067 0.992766i \(-0.538311\pi\)
\(312\) −2.08472 16.1390i −0.118024 0.913693i
\(313\) 14.1077 5.32794i 0.797413 0.301153i 0.0790947 0.996867i \(-0.474797\pi\)
0.718319 + 0.695714i \(0.244912\pi\)
\(314\) −6.59628 1.45195i −0.372250 0.0819383i
\(315\) 15.6733 + 1.63879i 0.883092 + 0.0923351i
\(316\) 25.7275 2.79804i 1.44729 0.157402i
\(317\) −7.96882 + 16.4388i −0.447573 + 0.923296i 0.548616 + 0.836075i \(0.315155\pi\)
−0.996189 + 0.0872213i \(0.972201\pi\)
\(318\) 1.45896 1.85687i 0.0818141 0.104128i
\(319\) 19.9013 + 12.9752i 1.11426 + 0.726470i
\(320\) 0.241065 + 1.00812i 0.0134759 + 0.0563554i
\(321\) −24.8035 14.8537i −1.38439 0.829054i
\(322\) −12.2059 + 7.95796i −0.680207 + 0.443480i
\(323\) 20.4841 4.50888i 1.13976 0.250881i
\(324\) 0.393785 + 14.9375i 0.0218769 + 0.829861i
\(325\) −16.0214 5.39823i −0.888707 0.299440i
\(326\) −1.18676 1.29904i −0.0657287 0.0719473i
\(327\) 7.02338 + 25.0938i 0.388394 + 1.38769i
\(328\) 7.91285 2.35167i 0.436914 0.129849i
\(329\) −4.73589 19.8052i −0.261098 1.09189i
\(330\) 2.85381 2.34659i 0.157097 0.129176i
\(331\) 8.98404 7.35606i 0.493808 0.404326i −0.353495 0.935437i \(-0.615007\pi\)
0.847302 + 0.531111i \(0.178225\pi\)
\(332\) 13.0293 + 19.2168i 0.715075 + 1.05466i
\(333\) −15.8277 + 9.61289i −0.867351 + 0.526783i
\(334\) 6.15777 + 3.70501i 0.336938 + 0.202729i
\(335\) 0.868929 + 2.74150i 0.0474747 + 0.149784i
\(336\) −15.6580 7.90177i −0.854215 0.431077i
\(337\) 0.944726 10.4365i 0.0514625 0.568510i −0.928769 0.370658i \(-0.879132\pi\)
0.980232 0.197852i \(-0.0633966\pi\)
\(338\) 2.61167 + 2.65926i 0.142056 + 0.144645i
\(339\) −15.2321 + 10.7814i −0.827293 + 0.585568i
\(340\) 2.66811 + 6.05140i 0.144699 + 0.328183i
\(341\) −9.73309 18.3585i −0.527076 0.994171i
\(342\) −8.28806 + 5.45278i −0.448167 + 0.294853i
\(343\) −12.7346 45.8659i −0.687603 2.47652i
\(344\) 1.50894 4.22472i 0.0813567 0.227782i
\(345\) 9.26219 2.41291i 0.498659 0.129906i
\(346\) 4.17465 + 8.61187i 0.224431 + 0.462977i
\(347\) 11.6098 8.18144i 0.623246 0.439203i −0.220914 0.975293i \(-0.570904\pi\)
0.844161 + 0.536090i \(0.180099\pi\)
\(348\) 9.38501 17.7911i 0.503089 0.953704i
\(349\) −7.45842 + 9.45219i −0.399240 + 0.505964i −0.942778 0.333421i \(-0.891797\pi\)
0.543538 + 0.839385i \(0.317084\pi\)
\(350\) 8.68325 6.60084i 0.464139 0.352830i
\(351\) −14.2869 17.8760i −0.762576 0.954150i
\(352\) −17.6301 + 5.94029i −0.939690 + 0.316618i
\(353\) −6.11091 10.5844i −0.325251 0.563351i 0.656312 0.754489i \(-0.272115\pi\)
−0.981563 + 0.191139i \(0.938782\pi\)
\(354\) 7.37334 + 2.40021i 0.391888 + 0.127570i
\(355\) −6.83202 + 11.8334i −0.362606 + 0.628052i
\(356\) 2.65701 13.2019i 0.140821 0.699700i
\(357\) −29.9378 8.82982i −1.58448 0.467323i
\(358\) 7.28965 + 3.05809i 0.385270 + 0.161625i
\(359\) −10.1857 25.5641i −0.537579 1.34922i −0.907458 0.420142i \(-0.861980\pi\)
0.369879 0.929080i \(-0.379399\pi\)
\(360\) −4.85266 4.90022i −0.255757 0.258264i
\(361\) 11.9739 + 5.53971i 0.630204 + 0.291564i
\(362\) 2.51935 + 0.182266i 0.132414 + 0.00957969i
\(363\) −0.652179 0.661311i −0.0342305 0.0347098i
\(364\) 35.0654 6.40080i 1.83792 0.335493i
\(365\) −6.20685 1.60321i −0.324882 0.0839158i
\(366\) −2.76432 2.25383i −0.144493 0.117810i
\(367\) −15.1721 + 24.2156i −0.791979 + 1.26404i 0.168504 + 0.985701i \(0.446106\pi\)
−0.960482 + 0.278341i \(0.910215\pi\)
\(368\) −10.5900 1.15174i −0.552044 0.0600384i
\(369\) 7.79393 8.60275i 0.405736 0.447841i
\(370\) 1.03713 3.73539i 0.0539176 0.194194i
\(371\) 9.32145 + 6.56884i 0.483945 + 0.341037i
\(372\) −14.7175 + 9.63904i −0.763065 + 0.499761i
\(373\) −21.5484 + 23.5871i −1.11573 + 1.22130i −0.142914 + 0.989735i \(0.545647\pi\)
−0.972821 + 0.231560i \(0.925617\pi\)
\(374\) −6.40254 + 3.54395i −0.331067 + 0.183253i
\(375\) −15.6221 + 5.29983i −0.806722 + 0.273682i
\(376\) −3.88728 + 8.01903i −0.200471 + 0.413550i
\(377\) 4.98359 + 30.3986i 0.256668 + 1.56561i
\(378\) 14.7183 1.15697i 0.757027 0.0595080i
\(379\) −18.3548 + 17.3866i −0.942823 + 0.893090i −0.994411 0.105579i \(-0.966331\pi\)
0.0515875 + 0.998668i \(0.483572\pi\)
\(380\) −2.36077 + 9.87259i −0.121105 + 0.506453i
\(381\) −3.04577 10.8822i −0.156040 0.557513i
\(382\) 2.30014 7.25701i 0.117685 0.371301i
\(383\) 21.9923 19.3747i 1.12376 0.990003i 0.123759 0.992312i \(-0.460505\pi\)
0.999997 + 0.00230922i \(0.000735048\pi\)
\(384\) 8.08451 + 18.2334i 0.412561 + 0.930470i
\(385\) 12.0338 + 13.1723i 0.613299 + 0.671323i
\(386\) −0.639115 11.7878i −0.0325301 0.599983i
\(387\) −1.27035 6.17927i −0.0645753 0.314110i
\(388\) −0.960424 + 0.909762i −0.0487581 + 0.0461862i
\(389\) −11.3850 + 5.77506i −0.577240 + 0.292807i −0.716656 0.697427i \(-0.754328\pi\)
0.139416 + 0.990234i \(0.455478\pi\)
\(390\) 4.74214 + 0.679718i 0.240128 + 0.0344188i
\(391\) −18.9081 + 1.36793i −0.956225 + 0.0691794i
\(392\) −14.4288 + 32.7251i −0.728764 + 1.65287i
\(393\) 14.6605 12.9697i 0.739524 0.654234i
\(394\) 1.26156 + 3.98027i 0.0635566 + 0.200523i
\(395\) −2.71727 + 16.5746i −0.136721 + 0.833959i
\(396\) −10.8986 + 12.9393i −0.547677 + 0.650226i
\(397\) 9.17202 33.0346i 0.460330 1.65796i −0.260977 0.965345i \(-0.584045\pi\)
0.721307 0.692615i \(-0.243542\pi\)
\(398\) 0.714932 5.62659i 0.0358363 0.282035i
\(399\) −28.3795 38.5976i −1.42075 1.93230i
\(400\) 7.96890 + 0.287884i 0.398445 + 0.0143942i
\(401\) −11.3940 14.4399i −0.568991 0.721093i 0.412849 0.910799i \(-0.364534\pi\)
−0.981841 + 0.189707i \(0.939246\pi\)
\(402\) 1.26698 + 2.37783i 0.0631910 + 0.118595i
\(403\) 9.06236 25.3727i 0.451428 1.26390i
\(404\) 10.6773 20.1395i 0.531214 1.00198i
\(405\) −9.40957 2.34732i −0.467565 0.116639i
\(406\) −18.0369 8.34478i −0.895159 0.414144i
\(407\) −20.6249 3.76485i −1.02234 0.186617i
\(408\) 7.68895 + 11.2898i 0.380660 + 0.558931i
\(409\) 0.325489 + 2.56163i 0.0160944 + 0.126665i 0.998047 0.0624603i \(-0.0198947\pi\)
−0.981953 + 0.189125i \(0.939435\pi\)
\(410\) 0.0438743 + 2.42975i 0.00216680 + 0.119997i
\(411\) −8.46945 4.66510i −0.417767 0.230112i
\(412\) −1.78817 3.09719i −0.0880966 0.152588i
\(413\) −9.72098 + 36.1609i −0.478338 + 1.77936i
\(414\) 8.12248 3.79887i 0.399198 0.186704i
\(415\) −14.2795 + 4.81132i −0.700953 + 0.236178i
\(416\) −21.1049 11.6820i −1.03475 0.572759i
\(417\) −3.61876 10.0658i −0.177211 0.492923i
\(418\) −11.1152 1.61675i −0.543662 0.0790778i
\(419\) 0.994596 + 2.78466i 0.0485892 + 0.136040i 0.963569 0.267460i \(-0.0861844\pi\)
−0.914980 + 0.403500i \(0.867794\pi\)
\(420\) 10.1655 11.1737i 0.496026 0.545223i
\(421\) −0.226230 0.0163669i −0.0110258 0.000797674i 0.0666438 0.997777i \(-0.478771\pi\)
−0.0776695 + 0.996979i \(0.524748\pi\)
\(422\) 1.77833 3.35429i 0.0865679 0.163284i
\(423\) 1.18156 + 12.4759i 0.0574495 + 0.606597i
\(424\) −1.33508 4.80852i −0.0648372 0.233522i
\(425\) 14.0432 2.04264i 0.681197 0.0990828i
\(426\) −4.28077 + 12.0643i −0.207404 + 0.584515i
\(427\) 10.1739 13.8974i 0.492351 0.672542i
\(428\) −25.5556 + 10.7209i −1.23528 + 0.518214i
\(429\) 1.34895 25.8731i 0.0651281 1.24916i
\(430\) 1.07953 + 0.760750i 0.0520598 + 0.0366866i
\(431\) 4.62043 28.1834i 0.222558 1.35755i −0.605027 0.796205i \(-0.706838\pi\)
0.827585 0.561340i \(-0.189714\pi\)
\(432\) 8.86130 + 6.16237i 0.426339 + 0.296487i
\(433\) 31.4767 + 18.9389i 1.51267 + 0.910145i 0.998627 + 0.0523817i \(0.0166813\pi\)
0.514045 + 0.857763i \(0.328146\pi\)
\(434\) 10.2678 + 14.0256i 0.492868 + 0.673249i
\(435\) 9.49621 + 8.95798i 0.455309 + 0.429502i
\(436\) 23.3677 + 8.82511i 1.11911 + 0.422646i
\(437\) −24.3746 15.8917i −1.16600 0.760204i
\(438\) −5.99100 0.420931i −0.286261 0.0201129i
\(439\) 2.15711 9.02088i 0.102953 0.430543i −0.896980 0.442070i \(-0.854244\pi\)
0.999934 + 0.0115275i \(0.00366941\pi\)
\(440\) −0.422711 7.79644i −0.0201520 0.371681i
\(441\) 6.54651 + 49.8657i 0.311738 + 2.37456i
\(442\) −8.99188 3.02972i −0.427700 0.144109i
\(443\) −1.09288 5.43021i −0.0519244 0.257997i 0.945856 0.324586i \(-0.105225\pi\)
−0.997780 + 0.0665892i \(0.978788\pi\)
\(444\) −1.56362 + 17.6820i −0.0742061 + 0.839152i
\(445\) 7.79451 + 3.95379i 0.369495 + 0.187428i
\(446\) 9.19563 2.73290i 0.435426 0.129407i
\(447\) 12.3472 + 25.3368i 0.584001 + 1.19839i
\(448\) −4.18208 + 2.12137i −0.197585 + 0.100225i
\(449\) 1.37589 + 8.39256i 0.0649322 + 0.396069i 0.999218 + 0.0395437i \(0.0125904\pi\)
−0.934286 + 0.356525i \(0.883961\pi\)
\(450\) −5.85918 + 3.27503i −0.276204 + 0.154386i
\(451\) 13.0655 1.42096i 0.615231 0.0669104i
\(452\) −0.322962 + 17.8856i −0.0151909 + 0.841269i
\(453\) −18.5872 32.0403i −0.873303 1.50538i
\(454\) −0.458713 0.375590i −0.0215285 0.0176273i
\(455\) −2.08558 + 23.0396i −0.0977735 + 1.08011i
\(456\) −1.09161 + 20.9372i −0.0511193 + 0.980475i
\(457\) −1.46514 + 11.5308i −0.0685364 + 0.539389i 0.920392 + 0.390996i \(0.127870\pi\)
−0.988929 + 0.148392i \(0.952590\pi\)
\(458\) −6.49041 0.705875i −0.303277 0.0329834i
\(459\) 17.4829 + 7.95668i 0.816031 + 0.371386i
\(460\) 3.39595 8.52320i 0.158337 0.397396i
\(461\) −4.53440 + 4.61701i −0.211188 + 0.215036i −0.810907 0.585175i \(-0.801026\pi\)
0.599719 + 0.800210i \(0.295279\pi\)
\(462\) 13.3276 + 10.0878i 0.620058 + 0.469329i
\(463\) 21.0824 + 33.6487i 0.979782 + 1.56379i 0.816610 + 0.577190i \(0.195851\pi\)
0.163173 + 0.986598i \(0.447827\pi\)
\(464\) −6.33775 13.0741i −0.294223 0.606950i
\(465\) −3.47243 10.8772i −0.161030 0.504418i
\(466\) 3.43612 + 0.627226i 0.159175 + 0.0290557i
\(467\) −3.55599 8.92487i −0.164552 0.412994i 0.823460 0.567375i \(-0.192041\pi\)
−0.988011 + 0.154381i \(0.950662\pi\)
\(468\) −21.9180 + 0.882911i −1.01316 + 0.0408126i
\(469\) −11.1484 + 6.70775i −0.514784 + 0.309735i
\(470\) −1.96851 1.73421i −0.0908006 0.0799932i
\(471\) −6.02477 + 19.1462i −0.277607 + 0.882211i
\(472\) 13.3169 9.54901i 0.612960 0.439529i
\(473\) 3.57114 6.18540i 0.164201 0.284405i
\(474\) 0.316736 + 15.7321i 0.0145481 + 0.722599i
\(475\) 19.0569 + 10.5484i 0.874390 + 0.483995i
\(476\) −23.8189 + 18.1067i −1.09174 + 0.829918i
\(477\) −5.11479 4.80487i −0.234190 0.220000i
\(478\) 4.08911 4.81407i 0.187031 0.220190i
\(479\) 2.67087 + 29.5053i 0.122035 + 1.34813i 0.794166 + 0.607701i \(0.207908\pi\)
−0.672131 + 0.740433i \(0.734621\pi\)
\(480\) −10.1133 + 1.49246i −0.461607 + 0.0681211i
\(481\) −14.4333 23.0364i −0.658104 1.05037i
\(482\) 8.56499 1.56345i 0.390125 0.0712130i
\(483\) 20.3620 + 38.2149i 0.926503 + 1.73884i
\(484\) −0.881053 + 0.128153i −0.0400479 + 0.00582512i
\(485\) −0.402165 0.758564i −0.0182614 0.0344446i
\(486\) −9.06819 0.561533i −0.411341 0.0254716i
\(487\) 22.0700 + 16.7772i 1.00009 + 0.760246i 0.970939 0.239329i \(-0.0769273\pi\)
0.0291485 + 0.999575i \(0.490720\pi\)
\(488\) −7.29786 + 1.88501i −0.330359 + 0.0853305i
\(489\) −4.15608 + 3.17300i −0.187945 + 0.143488i
\(490\) −8.14636 6.67017i −0.368015 0.301328i
\(491\) −2.19963 + 2.40774i −0.0992680 + 0.108660i −0.785925 0.618322i \(-0.787813\pi\)
0.686657 + 0.726981i \(0.259077\pi\)
\(492\) −2.21811 10.9041i −0.100000 0.491595i
\(493\) −15.2737 20.8636i −0.687892 0.939648i
\(494\) −8.17304 12.0543i −0.367723 0.542350i
\(495\) −6.19933 9.06212i −0.278639 0.407312i
\(496\) −0.687986 + 12.6891i −0.0308915 + 0.569760i
\(497\) −59.2553 17.6104i −2.65796 0.789936i
\(498\) −12.3367 + 6.86214i −0.552822 + 0.307500i
\(499\) −16.3603 8.29884i −0.732390 0.371507i 0.0462905 0.998928i \(-0.485260\pi\)
−0.778680 + 0.627421i \(0.784111\pi\)
\(500\) −4.77782 + 15.0742i −0.213670 + 0.674138i
\(501\) 12.5795 17.2583i 0.562009 0.771046i
\(502\) 0.605312 + 3.00762i 0.0270164 + 0.134237i
\(503\) −9.96920 + 2.19439i −0.444505 + 0.0978428i −0.431582 0.902074i \(-0.642044\pi\)
−0.0129224 + 0.999917i \(0.504113\pi\)
\(504\) 16.4553 26.5075i 0.732977 1.18074i
\(505\) 10.7404 + 10.1738i 0.477941 + 0.452730i
\(506\) 9.73142 + 2.89214i 0.432614 + 0.128571i
\(507\) 8.55558 7.03495i 0.379967 0.312433i
\(508\) −10.1337 3.82711i −0.449610 0.169801i
\(509\) 31.1300 2.25214i 1.37981 0.0998245i 0.637797 0.770205i \(-0.279846\pi\)
0.742018 + 0.670380i \(0.233869\pi\)
\(510\) −3.80801 + 1.29187i −0.168622 + 0.0572051i
\(511\) 0.523602 28.9970i 0.0231628 1.28275i
\(512\) 19.7672 + 4.35109i 0.873595 + 0.192293i
\(513\) 13.9718 + 25.9617i 0.616868 + 1.14624i
\(514\) 10.6334 4.91953i 0.469019 0.216991i
\(515\) 2.24731 0.580473i 0.0990285 0.0255787i
\(516\) −5.49352 2.52774i −0.241839 0.111278i
\(517\) −8.38088 + 11.4481i −0.368591 + 0.503488i
\(518\) 17.5270 + 0.633178i 0.770090 + 0.0278203i
\(519\) 26.5856 10.1035i 1.16698 0.443493i
\(520\) 7.09375 7.22299i 0.311081 0.316749i
\(521\) 11.4017 + 13.4231i 0.499518 + 0.588078i 0.952918 0.303229i \(-0.0980649\pi\)
−0.453400 + 0.891307i \(0.649789\pi\)
\(522\) 10.2728 + 6.63703i 0.449627 + 0.290495i
\(523\) 14.3596 21.1788i 0.627901 0.926085i −0.372097 0.928194i \(-0.621361\pi\)
0.999998 + 0.00210925i \(0.000671395\pi\)
\(524\) −1.69156 18.6868i −0.0738960 0.816335i
\(525\) −17.2668 27.4320i −0.753584 1.19723i
\(526\) 7.58521 + 1.10330i 0.330731 + 0.0481061i
\(527\) 2.85064 + 22.4349i 0.124176 + 0.977278i
\(528\) 2.86662 + 11.8789i 0.124754 + 0.516965i
\(529\) 2.47586 + 2.18118i 0.107646 + 0.0948338i
\(530\) 1.46912 0.0638145
\(531\) 9.03522 21.1982i 0.392095 0.919925i
\(532\) −45.9233 −1.99103
\(533\) 12.7866 + 11.2647i 0.553851 + 0.487930i
\(534\) 7.85361 + 2.31633i 0.339859 + 0.100237i
\(535\) −2.26715 17.8427i −0.0980176 0.771408i
\(536\) 5.63453 + 0.819564i 0.243374 + 0.0353998i
\(537\) 10.9608 20.7783i 0.472992 0.896649i
\(538\) −0.136798 1.51122i −0.00589777 0.0651531i
\(539\) −31.9544 + 47.1292i −1.37637 + 2.03000i
\(540\) −7.15590 + 5.93399i −0.307941 + 0.255358i
\(541\) −11.4146 13.4383i −0.490750 0.577756i 0.459920 0.887961i \(-0.347878\pi\)
−0.950670 + 0.310205i \(0.899602\pi\)
\(542\) −1.47184 + 1.49866i −0.0632210 + 0.0643729i
\(543\) 1.19903 7.41007i 0.0514555 0.317997i
\(544\) 20.2348 + 0.731001i 0.867559 + 0.0313414i
\(545\) −9.57610 + 13.0808i −0.410195 + 0.560319i
\(546\) 1.99868 + 21.5806i 0.0855354 + 0.923566i
\(547\) −0.486692 + 0.125711i −0.0208095 + 0.00537501i −0.260479 0.965480i \(-0.583880\pi\)
0.239669 + 0.970855i \(0.422961\pi\)
\(548\) −8.41205 + 3.89183i −0.359345 + 0.166251i
\(549\) −7.39541 + 7.59293i −0.315628 + 0.324059i
\(550\) −7.42185 1.63367i −0.316469 0.0696600i
\(551\) 0.716518 39.6807i 0.0305247 1.69045i
\(552\) 3.70026 18.5848i 0.157494 0.791023i
\(553\) −75.7873 + 5.48293i −3.22280 + 0.233158i
\(554\) −0.671264 0.253511i −0.0285193 0.0107707i
\(555\) −10.7860 4.04791i −0.457841 0.171824i
\(556\) −9.82852 2.92099i −0.416822 0.123878i
\(557\) 15.5231 + 14.7043i 0.657736 + 0.623041i 0.941963 0.335716i \(-0.108978\pi\)
−0.284227 + 0.958757i \(0.591737\pi\)
\(558\) −5.04976 9.43008i −0.213774 0.399207i
\(559\) 9.04432 1.99081i 0.382534 0.0842021i
\(560\) −2.15284 10.6968i −0.0909741 0.452024i
\(561\) 8.81480 + 19.8805i 0.372161 + 0.839355i
\(562\) −2.77234 + 8.74683i −0.116944 + 0.368963i
\(563\) −18.7204 9.49598i −0.788970 0.400208i 0.0112327 0.999937i \(-0.496424\pi\)
−0.800203 + 0.599729i \(0.795275\pi\)
\(564\) 10.3059 + 6.17175i 0.433956 + 0.259877i
\(565\) −11.1287 3.30741i −0.468189 0.139144i
\(566\) −0.0542490 + 1.00056i −0.00228025 + 0.0420568i
\(567\) 0.427950 43.8719i 0.0179722 1.84245i
\(568\) 15.1815 + 22.3910i 0.637002 + 0.939507i
\(569\) 10.3040 + 14.0751i 0.431966 + 0.590057i 0.967001 0.254773i \(-0.0820006\pi\)
−0.535035 + 0.844830i \(0.679702\pi\)
\(570\) −5.85303 1.95860i −0.245156 0.0820366i
\(571\) 19.1576 20.9701i 0.801720 0.877571i −0.192894 0.981220i \(-0.561787\pi\)
0.994614 + 0.103649i \(0.0330518\pi\)
\(572\) −19.2155 15.7335i −0.803438 0.657849i
\(573\) −20.8801 8.70852i −0.872277 0.363804i
\(574\) −10.6448 + 2.74950i −0.444304 + 0.114762i
\(575\) −15.6727 11.9141i −0.653597 0.496852i
\(576\) 2.73091 0.932790i 0.113788 0.0388662i
\(577\) −5.80168 10.9431i −0.241527 0.455569i 0.732880 0.680358i \(-0.238176\pi\)
−0.974407 + 0.224789i \(0.927831\pi\)
\(578\) −1.92343 + 0.279770i −0.0800040 + 0.0116369i
\(579\) −35.0615 1.19378i −1.45711 0.0496118i
\(580\) 12.3104 2.24713i 0.511162 0.0933071i
\(581\) −36.1940 57.7676i −1.50158 2.39660i
\(582\) −0.499570 0.630419i −0.0207079 0.0261317i
\(583\) −0.716284 7.91284i −0.0296654 0.327716i
\(584\) −8.21652 + 9.67324i −0.340002 + 0.400281i
\(585\) 3.25345 13.8598i 0.134514 0.573030i
\(586\) −0.682063 + 0.518491i −0.0281758 + 0.0214187i
\(587\) 15.5910 + 8.62997i 0.643509 + 0.356197i 0.772100 0.635501i \(-0.219206\pi\)
−0.128591 + 0.991698i \(0.541045\pi\)
\(588\) 42.2279 + 23.2598i 1.74145 + 0.959216i
\(589\) −17.3559 + 30.0612i −0.715136 + 1.23865i
\(590\) 1.65985 + 4.52949i 0.0683349 + 0.186476i
\(591\) 12.1126 2.69256i 0.498247 0.110757i
\(592\) 9.62092 + 8.47581i 0.395417 + 0.348354i
\(593\) 11.6507 7.01001i 0.478438 0.287866i −0.255836 0.966720i \(-0.582351\pi\)
0.734273 + 0.678854i \(0.237523\pi\)
\(594\) −7.25316 7.29392i −0.297601 0.299273i
\(595\) −7.18741 18.0390i −0.294655 0.739529i
\(596\) 26.5784 + 4.85160i 1.08869 + 0.198729i
\(597\) −16.4687 3.58921i −0.674018 0.146897i
\(598\) 5.74196 + 11.8450i 0.234806 + 0.484380i
\(599\) 19.6843 + 31.4173i 0.804280 + 1.28368i 0.955445 + 0.295168i \(0.0953756\pi\)
−0.151165 + 0.988508i \(0.548303\pi\)
\(600\) −1.75882 + 14.0756i −0.0718034 + 0.574634i
\(601\) −1.18820 + 1.20985i −0.0484675 + 0.0493506i −0.737268 0.675600i \(-0.763885\pi\)
0.688801 + 0.724951i \(0.258137\pi\)
\(602\) −2.21147 + 5.55038i −0.0901329 + 0.226217i
\(603\) 7.37051 3.12805i 0.300150 0.127384i
\(604\) −35.2987 3.83897i −1.43629 0.156205i
\(605\) 0.0728351 0.573219i 0.00296117 0.0233047i
\(606\) 11.6259 + 7.54548i 0.472269 + 0.306514i
\(607\) −0.264404 + 2.92089i −0.0107318 + 0.118555i −0.999528 0.0307156i \(-0.990221\pi\)
0.988796 + 0.149271i \(0.0476927\pi\)
\(608\) 24.0461 + 19.6887i 0.975196 + 0.798483i
\(609\) −29.4237 + 51.2085i −1.19231 + 2.07507i
\(610\) 0.0400606 2.21855i 0.00162201 0.0898265i
\(611\) −18.2886 + 1.98900i −0.739877 + 0.0804665i
\(612\) 16.0722 8.98369i 0.649682 0.363144i
\(613\) 3.15779 + 19.2616i 0.127542 + 0.777970i 0.970698 + 0.240302i \(0.0772465\pi\)
−0.843156 + 0.537668i \(0.819305\pi\)
\(614\) 1.02538 0.520129i 0.0413811 0.0209907i
\(615\) 7.20403 + 0.506159i 0.290495 + 0.0204103i
\(616\) 33.8596 10.0629i 1.36424 0.405447i
\(617\) −10.7611 5.45859i −0.433224 0.219754i 0.222222 0.974996i \(-0.428669\pi\)
−0.655447 + 0.755242i \(0.727520\pi\)
\(618\) 1.97163 0.917145i 0.0793106 0.0368930i
\(619\) −1.10482 5.48951i −0.0444063 0.220642i 0.951912 0.306371i \(-0.0991148\pi\)
−0.996318 + 0.0857290i \(0.972678\pi\)
\(620\) −10.3721 3.49476i −0.416553 0.140353i
\(621\) −9.11917 25.0386i −0.365940 1.00476i
\(622\) −0.881920 16.2661i −0.0353618 0.652210i
\(623\) −9.19572 + 38.4559i −0.368419 + 1.54070i
\(624\) −8.86456 + 13.1328i −0.354866 + 0.525734i
\(625\) 7.48181 + 4.87797i 0.299272 + 0.195119i
\(626\) 8.22251 + 3.10533i 0.328637 + 0.124114i
\(627\) −7.69552 + 32.4799i −0.307329 + 1.29712i
\(628\) 11.3653 + 15.5248i 0.453524 + 0.619505i
\(629\) 19.5521 + 11.7641i 0.779592 + 0.469065i
\(630\) 6.22307 + 6.75532i 0.247933 + 0.269139i
\(631\) −5.95625 + 36.3315i −0.237114 + 1.44633i 0.552901 + 0.833247i \(0.313521\pi\)
−0.790016 + 0.613087i \(0.789928\pi\)
\(632\) 27.1817 + 19.1550i 1.08123 + 0.761945i
\(633\) −9.46385 6.14227i −0.376154 0.244133i
\(634\) −9.81858 + 4.11901i −0.389946 + 0.163587i
\(635\) 4.15278 5.67263i 0.164798 0.225111i
\(636\) −6.61510 + 1.22170i −0.262306 + 0.0484437i
\(637\) −73.0617 + 10.6271i −2.89481 + 0.421062i
\(638\) 3.70440 + 13.3420i 0.146659 + 0.528216i
\(639\) 34.5920 + 15.8300i 1.36844 + 0.626225i
\(640\) −5.81222 + 10.9630i −0.229748 + 0.433351i
\(641\) −11.0290 0.797908i −0.435619 0.0315155i −0.147394 0.989078i \(-0.547088\pi\)
−0.288226 + 0.957562i \(0.593065\pi\)
\(642\) −5.12452 16.0523i −0.202249 0.633534i
\(643\) −7.83701 21.9420i −0.309061 0.865308i −0.990996 0.133894i \(-0.957252\pi\)
0.681934 0.731413i \(-0.261139\pi\)
\(644\) 41.0752 + 5.97455i 1.61859 + 0.235430i
\(645\) 2.53456 2.99650i 0.0997982 0.117987i
\(646\) 10.6955 + 5.92022i 0.420810 + 0.232928i
\(647\) 18.4892 6.22972i 0.726884 0.244916i 0.0685563 0.997647i \(-0.478161\pi\)
0.658328 + 0.752732i \(0.271264\pi\)
\(648\) −12.3081 + 14.7364i −0.483508 + 0.578900i
\(649\) 23.5870 11.1485i 0.925873 0.437618i
\(650\) −4.92685 8.53355i −0.193247 0.334713i
\(651\) 44.2062 26.7231i 1.73258 1.04736i
\(652\) 0.0904919 + 5.01143i 0.00354393 + 0.196263i
\(653\) 4.08633 + 32.1598i 0.159910 + 1.25851i 0.846864 + 0.531809i \(0.178488\pi\)
−0.686954 + 0.726701i \(0.741053\pi\)
\(654\) −6.59659 + 13.6803i −0.257947 + 0.534943i
\(655\) 11.9795 + 2.18673i 0.468078 + 0.0854426i
\(656\) −7.29468 3.37488i −0.284810 0.131767i
\(657\) −2.81430 + 17.6244i −0.109796 + 0.687591i
\(658\) 5.55938 10.4861i 0.216727 0.408791i
\(659\) 14.4382 40.4241i 0.562434 1.57470i −0.235449 0.971887i \(-0.575656\pi\)
0.797883 0.602812i \(-0.205953\pi\)
\(660\) −10.5188 0.358144i −0.409442 0.0139408i
\(661\) 16.7365 + 21.2104i 0.650974 + 0.824990i 0.993418 0.114548i \(-0.0365421\pi\)
−0.342444 + 0.939538i \(0.611255\pi\)
\(662\) 6.76317 + 0.244326i 0.262858 + 0.00949600i
\(663\) −11.3224 + 25.8247i −0.439724 + 1.00295i
\(664\) −3.76040 + 29.5947i −0.145932 + 1.14850i
\(665\) 7.97358 28.7183i 0.309202 1.11365i
\(666\) −10.6256 1.89405i −0.411734 0.0733931i
\(667\) −5.80326 + 35.3983i −0.224703 + 1.37063i
\(668\) −6.18531 19.5149i −0.239317 0.755053i
\(669\) −5.68279 27.9363i −0.219709 1.08008i
\(670\) −0.676235 + 1.53373i −0.0261252 + 0.0592532i
\(671\) −11.9689 + 0.865905i −0.462054 + 0.0334279i
\(672\) −17.2075 42.9283i −0.663795 1.65600i
\(673\) −28.3620 + 14.3867i −1.09327 + 0.554566i −0.904076 0.427373i \(-0.859439\pi\)
−0.189198 + 0.981939i \(0.560589\pi\)
\(674\) 4.43412 4.20022i 0.170796 0.161787i
\(675\) 8.16098 + 18.2016i 0.314116 + 0.700581i
\(676\) −0.574827 10.6021i −0.0221087 0.407772i
\(677\) −21.6333 23.6801i −0.831437 0.910100i 0.165665 0.986182i \(-0.447023\pi\)
−0.997102 + 0.0760826i \(0.975759\pi\)
\(678\) −10.8154 1.15354i −0.415362 0.0443013i
\(679\) 2.91455 2.56765i 0.111850 0.0985373i
\(680\) −2.56755 + 8.10069i −0.0984609 + 0.310647i
\(681\) −1.23190 + 1.25956i −0.0472065 + 0.0482665i
\(682\) 2.81659 11.7788i 0.107853 0.451032i
\(683\) −5.56100 + 5.26766i −0.212786 + 0.201562i −0.786668 0.617377i \(-0.788195\pi\)
0.573882 + 0.818938i \(0.305437\pi\)
\(684\) 27.9835 + 3.95178i 1.06998 + 0.151100i
\(685\) −0.973195 5.93623i −0.0371839 0.226812i
\(686\) 12.1020 24.9650i 0.462055 0.953170i
\(687\) −3.78852 + 19.0281i −0.144541 + 0.725968i
\(688\) −3.82160 + 2.11534i −0.145697 + 0.0806466i
\(689\) 6.94843 7.60582i 0.264714 0.289759i
\(690\) 4.98031 + 2.51330i 0.189597 + 0.0956795i
\(691\) 8.91425 + 6.28188i 0.339114 + 0.238974i 0.733067 0.680156i \(-0.238088\pi\)
−0.393953 + 0.919131i \(0.628893\pi\)
\(692\) 7.29350 26.2688i 0.277257 0.998591i
\(693\) 33.3508 36.8118i 1.26689 1.39836i
\(694\) 8.22950 + 0.895012i 0.312387 + 0.0339742i
\(695\) 3.53316 5.63912i 0.134020 0.213904i
\(696\) 24.1601 9.18169i 0.915787 0.348031i
\(697\) −13.8494 3.57725i −0.524583 0.135498i
\(698\) −6.90356 + 1.26017i −0.261303 + 0.0476981i
\(699\) 2.75619 10.0074i 0.104249 0.378515i
\(700\) −30.9901 2.24202i −1.17132 0.0847404i
\(701\) 15.6127 + 7.22322i 0.589685 + 0.272817i 0.691956 0.721939i \(-0.256749\pi\)
−0.102272 + 0.994757i \(0.532611\pi\)
\(702\) 0.639152 13.3222i 0.0241233 0.502814i
\(703\) 12.9635 + 32.5360i 0.488929 + 1.22712i
\(704\) 3.01286 + 1.26393i 0.113551 + 0.0476361i
\(705\) −5.64890 + 5.37321i −0.212750 + 0.202367i
\(706\) 1.40546 6.98332i 0.0528952 0.262821i
\(707\) −33.4645 + 57.9622i −1.25856 + 2.17989i
\(708\) −11.2406 19.0149i −0.422447 0.714624i
\(709\) −10.7611 18.6388i −0.404143 0.699996i 0.590078 0.807346i \(-0.299097\pi\)
−0.994221 + 0.107350i \(0.965764\pi\)
\(710\) −7.54704 + 2.54289i −0.283235 + 0.0954331i
\(711\) 46.6530 + 3.18059i 1.74962 + 0.119281i
\(712\) 13.7753 10.4717i 0.516252 0.392444i
\(713\) 19.4345 24.6297i 0.727828 0.922388i
\(714\) −9.69084 15.3960i −0.362671 0.576182i
\(715\) 13.1753 9.28465i 0.492728 0.347226i
\(716\) −9.82286 20.2635i −0.367098 0.757283i
\(717\) −13.1802 13.3647i −0.492223 0.499115i
\(718\) 5.39482 15.1044i 0.201333 0.563690i
\(719\) −7.33467 26.4171i −0.273537 0.985191i −0.964886 0.262670i \(-0.915397\pi\)
0.691349 0.722521i \(-0.257017\pi\)
\(720\) 0.391358 + 6.70340i 0.0145851 + 0.249821i
\(721\) 4.91859 + 9.27745i 0.183178 + 0.345510i
\(722\) 3.10223 + 7.03600i 0.115453 + 0.261853i
\(723\) −2.38605 25.7633i −0.0887383 0.958149i
\(724\) −5.04184 5.13371i −0.187379 0.190793i
\(725\) 2.42077 26.7424i 0.0899051 0.993189i
\(726\) −0.0304293 0.540485i −0.00112934 0.0200593i
\(727\) −15.1774 47.8852i −0.562898 1.77596i −0.628147 0.778095i \(-0.716186\pi\)
0.0652481 0.997869i \(-0.479216\pi\)
\(728\) 39.2449 + 23.6129i 1.45451 + 0.875151i
\(729\) −4.03603 + 26.6966i −0.149482 + 0.988764i
\(730\) −2.09678 3.09252i −0.0776052 0.114459i
\(731\) −6.01450 + 4.92463i −0.222454 + 0.182144i
\(732\) 1.66454 + 10.0229i 0.0615232 + 0.370458i
\(733\) 4.39657 + 18.3861i 0.162391 + 0.679108i 0.992577 + 0.121621i \(0.0388091\pi\)
−0.830186 + 0.557487i \(0.811766\pi\)
\(734\) −15.9651 + 4.74475i −0.589281 + 0.175132i
\(735\) −21.8775 + 22.3688i −0.806964 + 0.825085i
\(736\) −18.9460 20.7385i −0.698360 0.764432i
\(737\) 8.59054 + 2.89449i 0.316436 + 0.106620i
\(738\) 6.72302 0.759419i 0.247478 0.0279546i
\(739\) 30.3257 6.67518i 1.11555 0.245551i 0.381313 0.924446i \(-0.375472\pi\)
0.734235 + 0.678896i \(0.237541\pi\)
\(740\) −9.25083 + 6.03134i −0.340067 + 0.221716i
\(741\) −37.8227 + 21.0384i −1.38945 + 0.772863i
\(742\) 1.54573 + 6.46414i 0.0567456 + 0.237306i
\(743\) 25.0336 + 16.3213i 0.918392 + 0.598771i 0.915979 0.401226i \(-0.131416\pi\)
0.00241295 + 0.999997i \(0.499232\pi\)
\(744\) −22.3771 3.20743i −0.820383 0.117590i
\(745\) −7.64872 + 15.7785i −0.280227 + 0.578079i
\(746\) −18.5115 + 2.01325i −0.677754 + 0.0737102i
\(747\) 17.0839 + 38.3154i 0.625067 + 1.40189i
\(748\) 20.3588 + 4.48131i 0.744391 + 0.163853i
\(749\) 76.1227 28.7487i 2.78146 1.05045i
\(750\) −8.87399 3.70110i −0.324032 0.135145i
\(751\) 21.6866 + 22.0817i 0.791354 + 0.805773i 0.984498 0.175398i \(-0.0561211\pi\)
−0.193143 + 0.981171i \(0.561868\pi\)
\(752\) 8.00134 3.35666i 0.291779 0.122405i
\(753\) 9.06160 1.00454i 0.330223 0.0366075i
\(754\) −9.53248 + 15.2144i −0.347153 + 0.554075i
\(755\) 8.52957 21.4076i 0.310423 0.779102i
\(756\) −33.6387 25.2425i −1.22343 0.918063i
\(757\) −25.3638 29.8606i −0.921862 1.08530i −0.996115 0.0880607i \(-0.971933\pi\)
0.0742528 0.997239i \(-0.476343\pi\)
\(758\) −14.7259 + 0.531987i −0.534868 + 0.0193226i
\(759\) 11.1087 28.0498i 0.403220 1.01814i
\(760\) −10.6618 + 7.51339i −0.386744 + 0.272539i
\(761\) 15.8629 + 44.4128i 0.575030 + 1.60996i 0.776255 + 0.630418i \(0.217117\pi\)
−0.201226 + 0.979545i \(0.564493\pi\)
\(762\) 2.86069 5.93263i 0.103632 0.214916i
\(763\) −67.6310 28.3720i −2.44841 1.02713i
\(764\) −18.5819 + 11.1804i −0.672271 + 0.404492i
\(765\) 2.82738 + 11.6106i 0.102224 + 0.419783i
\(766\) 17.0827 0.617222
\(767\) 31.3002 + 12.8297i 1.13019 + 0.463252i
\(768\) −2.48914 + 7.91027i −0.0898190 + 0.285437i
\(769\) 4.95773 24.6335i 0.178780 0.888307i −0.784566 0.620045i \(-0.787114\pi\)
0.963346 0.268261i \(-0.0864491\pi\)
\(770\) 0.187741 + 10.3971i 0.00676571 + 0.374685i
\(771\) −11.7793 32.7647i −0.424220 1.17999i
\(772\) −20.8311 + 26.3996i −0.749728 + 0.950144i
\(773\) 18.0100 21.2030i 0.647775 0.762620i −0.336032 0.941851i \(-0.609085\pi\)
0.983807 + 0.179231i \(0.0573609\pi\)
\(774\) 1.82519 3.19184i 0.0656050 0.114728i
\(775\) −13.1797 + 19.4387i −0.473430 + 0.698257i
\(776\) −1.69873 + 0.0613683i −0.0609809 + 0.00220299i
\(777\) 6.46236 51.7175i 0.231836 1.85536i
\(778\) −7.20403 1.86078i −0.258277 0.0667121i
\(779\) −13.5999 17.2354i −0.487266 0.617521i
\(780\) −8.85627 10.3827i −0.317105 0.371759i
\(781\) 17.3759 + 39.4094i 0.621760 + 1.41018i
\(782\) −8.79619 6.68669i −0.314551 0.239116i
\(783\) 22.3360 28.6721i 0.798224 1.02466i
\(784\) 31.6046 14.6218i 1.12873 0.522208i
\(785\) −11.6818 + 4.41176i −0.416940 + 0.157463i
\(786\) 11.4085 0.0236752i 0.406927 0.000844468i
\(787\) 5.35186 2.96238i 0.190773 0.105597i −0.386010 0.922495i \(-0.626147\pi\)
0.576783 + 0.816897i \(0.304308\pi\)
\(788\) 4.79857 10.8834i 0.170942 0.387704i
\(789\) 5.25156 22.1649i 0.186961 0.789091i
\(790\) −7.57422 + 6.20171i −0.269479 + 0.220647i
\(791\) 2.84356 52.4464i 0.101105 1.86478i
\(792\) −21.4984 + 3.21820i −0.763913 + 0.114354i
\(793\) −11.2962 10.7004i −0.401141 0.379981i
\(794\) 16.7388 10.9133i 0.594039 0.387300i
\(795\) 0.384572 4.34889i 0.0136393 0.154239i
\(796\) −12.1234 + 10.6804i −0.429703 + 0.378558i
\(797\) 17.7266 15.6167i 0.627908 0.553173i −0.286442 0.958098i \(-0.592472\pi\)
0.914350 + 0.404925i \(0.132702\pi\)
\(798\) 2.45959 27.8141i 0.0870687 0.984608i
\(799\) 12.9353 8.43354i 0.457619 0.298357i
\(800\) 15.2656 + 14.4603i 0.539720 + 0.511250i
\(801\) 8.91264 22.6419i 0.314912 0.800011i
\(802\) 0.580405 10.7049i 0.0204948 0.378004i
\(803\) −15.6343 + 12.8012i −0.551723 + 0.451746i
\(804\) 1.76949 7.46836i 0.0624051 0.263389i
\(805\) −10.8680 + 24.6491i −0.383047 + 0.868766i
\(806\) 13.7389 7.60478i 0.483931 0.267867i
\(807\) −4.50931 + 0.00935785i −0.158735 + 0.000329412i
\(808\) 27.4007 10.3482i 0.963954 0.364049i
\(809\) −17.9862 + 8.32132i −0.632363 + 0.292562i −0.709766 0.704438i \(-0.751199\pi\)
0.0774031 + 0.997000i \(0.475337\pi\)
\(810\) −3.21074 4.65188i −0.112814 0.163450i
\(811\) −24.2714 18.4506i −0.852283 0.647889i 0.0850294 0.996378i \(-0.472902\pi\)
−0.937313 + 0.348490i \(0.886695\pi\)
\(812\) 22.8398 + 51.8016i 0.801519 + 1.81788i
\(813\) 4.05104 + 4.74925i 0.142076 + 0.166563i
\(814\) −7.56942 9.59285i −0.265308 0.336229i
\(815\) −3.14962 0.813536i −0.110326 0.0284969i
\(816\) 1.64905 13.1971i 0.0577283 0.461993i
\(817\) −11.9235 + 0.430748i −0.417151 + 0.0150700i
\(818\) −0.844600 + 1.24569i −0.0295307 + 0.0435546i
\(819\) 64.4061 0.267316i 2.25053 0.00934078i
\(820\) 4.48161 5.27616i 0.156505 0.184251i
\(821\) −29.6536 + 37.5805i −1.03492 + 1.31157i −0.0859146 + 0.996303i \(0.527381\pi\)
−0.949003 + 0.315266i \(0.897906\pi\)
\(822\) −1.90660 5.30331i −0.0665003 0.184974i
\(823\) −1.01785 56.3685i −0.0354800 1.96488i −0.203439 0.979088i \(-0.565212\pi\)
0.167959 0.985794i \(-0.446282\pi\)
\(824\) 0.906674 4.50500i 0.0315855 0.156939i
\(825\) −6.77881 + 21.5425i −0.236008 + 0.750013i
\(826\) −18.1834 + 12.0690i −0.632681 + 0.419936i
\(827\) 14.4164 0.501309 0.250655 0.968077i \(-0.419354\pi\)
0.250655 + 0.968077i \(0.419354\pi\)
\(828\) −24.5151 7.17520i −0.851960 0.249355i
\(829\) 6.87987 4.13948i 0.238948 0.143770i −0.391044 0.920372i \(-0.627886\pi\)
0.629992 + 0.776602i \(0.283058\pi\)
\(830\) −8.09860 3.39746i −0.281107 0.117927i
\(831\) −0.926159 + 1.92071i −0.0321281 + 0.0666288i
\(832\) 1.42494 + 3.98953i 0.0494008 + 0.138312i
\(833\) 50.6577 35.6985i 1.75518 1.23688i
\(834\) 2.29554 5.79633i 0.0794881 0.200711i
\(835\) 13.2776 0.479666i 0.459491 0.0165995i
\(836\) 20.7140 + 24.3864i 0.716410 + 0.843422i
\(837\) −29.2368 + 12.4798i −1.01057 + 0.431365i
\(838\) −0.637906 + 1.60102i −0.0220361 + 0.0553064i
\(839\) −29.6788 + 47.3690i −1.02463 + 1.63536i −0.289822 + 0.957081i \(0.593596\pi\)
−0.734804 + 0.678279i \(0.762726\pi\)
\(840\) 19.2919 2.13864i 0.665633 0.0737900i
\(841\) −18.3741 + 7.70814i −0.633589 + 0.265798i
\(842\) −0.0926320 0.0943197i −0.00319231 0.00325047i
\(843\) 25.1666 + 10.4963i 0.866785 + 0.361513i
\(844\) −10.1175 + 3.82100i −0.348259 + 0.131524i
\(845\) 6.72983 + 1.48135i 0.231513 + 0.0509599i
\(846\) −4.28997 + 5.91134i −0.147492 + 0.203236i
\(847\) 2.59880 0.282637i 0.0892959 0.00971151i
\(848\) −2.11953 + 4.37237i −0.0727851 + 0.150148i
\(849\) 2.94767 + 0.422505i 0.101164 + 0.0145003i
\(850\) 6.92856 + 4.51726i 0.237648 + 0.154941i
\(851\) −7.36208 30.7877i −0.252369 1.05539i
\(852\) 31.8679 17.7261i 1.09178 0.607285i
\(853\) 18.4515 12.0300i 0.631767 0.411898i −0.189950 0.981794i \(-0.560833\pi\)
0.821717 + 0.569896i \(0.193016\pi\)
\(854\) 9.80379 2.15798i 0.335479 0.0738444i
\(855\) −7.32998 + 16.8134i −0.250680 + 0.575006i
\(856\) −33.7456 11.3702i −1.15340 0.388626i
\(857\) −23.7414 25.9876i −0.810990 0.887719i 0.184475 0.982837i \(-0.440941\pi\)
−0.995466 + 0.0951185i \(0.969677\pi\)
\(858\) 10.5583 10.7954i 0.360456 0.368550i
\(859\) 35.9608 10.6874i 1.22697 0.364649i 0.394589 0.918858i \(-0.370887\pi\)
0.832378 + 0.554209i \(0.186979\pi\)
\(860\) −0.874937 3.65892i −0.0298351 0.124768i
\(861\) 5.35260 + 32.2303i 0.182416 + 1.09841i
\(862\) 12.8792 10.5454i 0.438666 0.359176i
\(863\) −32.4704 47.8903i −1.10531 1.63020i −0.696448 0.717607i \(-0.745237\pi\)
−0.408858 0.912598i \(-0.634073\pi\)
\(864\) 6.79140 + 27.6392i 0.231048 + 0.940306i
\(865\) 15.1609 + 9.12202i 0.515487 + 0.310158i
\(866\) 6.46901 + 20.4099i 0.219826 + 0.693558i
\(867\) 0.324680 + 5.76696i 0.0110267 + 0.195856i
\(868\) 4.46401 49.3142i 0.151518 1.67383i
\(869\) 37.0959 + 37.7718i 1.25839 + 1.28132i
\(870\) 0.701676 + 7.57632i 0.0237890 + 0.256861i
\(871\) 4.74195 + 10.7550i 0.160675 + 0.364418i
\(872\) 15.0339 + 28.3570i 0.509113 + 0.960290i
\(873\) −1.99694 + 1.31380i −0.0675861 + 0.0444655i
\(874\) −4.53707 16.3410i −0.153469 0.552744i
\(875\) 15.6171 43.7247i 0.527956 1.47817i
\(876\) 12.0130 + 12.1812i 0.405881 + 0.411564i
\(877\) −1.57920 3.25771i −0.0533257 0.110005i 0.871501 0.490393i \(-0.163147\pi\)
−0.924827 + 0.380388i \(0.875790\pi\)
\(878\) 4.41894 3.11404i 0.149132 0.105094i
\(879\) 1.35629 + 2.15477i 0.0457466 + 0.0726785i
\(880\) −4.70923 + 5.96809i −0.158748 + 0.201184i
\(881\) −0.711886 + 0.541162i −0.0239841 + 0.0182322i −0.617098 0.786887i \(-0.711692\pi\)
0.593114 + 0.805119i \(0.297899\pi\)
\(882\) −16.3493 + 24.3301i −0.550508 + 0.819239i
\(883\) −2.93936 + 0.990384i −0.0989172 + 0.0333291i −0.368325 0.929697i \(-0.620069\pi\)
0.269408 + 0.963026i \(0.413172\pi\)
\(884\) 13.5148 + 23.4083i 0.454551 + 0.787306i
\(885\) 13.8427 3.72780i 0.465317 0.125309i
\(886\) 1.61420 2.79588i 0.0542301 0.0939294i
\(887\) 7.41286 36.8323i 0.248899 1.23671i −0.636280 0.771458i \(-0.719528\pi\)
0.885179 0.465250i \(-0.154036\pi\)
\(888\) −16.5265 + 15.7199i −0.554593 + 0.527526i
\(889\) 29.3289 + 12.3038i 0.983661 + 0.412657i
\(890\) 1.88548 + 4.73219i 0.0632014 + 0.158624i
\(891\) −23.4901 + 19.5615i −0.786948 + 0.655334i
\(892\) −24.8017 11.4745i −0.830422 0.384194i
\(893\) 23.6395 + 1.71023i 0.791064 + 0.0572306i
\(894\) −4.36194 + 15.8377i −0.145885 + 0.529693i
\(895\) 14.3774 2.62443i 0.480582 0.0877251i
\(896\) −54.3526 14.0391i −1.81579 0.469013i
\(897\) 36.5667 13.8967i 1.22093 0.463996i
\(898\) −2.63176 + 4.20045i −0.0878231 + 0.140171i
\(899\) 42.5410 + 4.62661i 1.41882 + 0.154306i
\(900\) 18.6910 + 4.03293i 0.623032 + 0.134431i
\(901\) −2.31339 + 8.33209i −0.0770703 + 0.277582i
\(902\) 6.26145 + 4.41245i 0.208483 + 0.146919i
\(903\) 15.8513 + 7.99932i 0.527499 + 0.266201i
\(904\) −15.5032 + 16.9700i −0.515630 + 0.564414i
\(905\) 4.08578 2.26157i 0.135816 0.0751772i
\(906\) 4.21568 21.1736i 0.140057 0.703444i
\(907\) −8.96020 + 18.4839i −0.297518 + 0.613749i −0.994662 0.103182i \(-0.967097\pi\)
0.697144 + 0.716931i \(0.254454\pi\)
\(908\) 0.273226 + 1.66660i 0.00906732 + 0.0553082i
\(909\) 25.3794 32.4397i 0.841782 1.07596i
\(910\) −9.78878 + 9.27243i −0.324495 + 0.307378i
\(911\) 2.33401 9.76067i 0.0773293 0.323385i −0.920381 0.391024i \(-0.872121\pi\)
0.997710 + 0.0676382i \(0.0215464\pi\)
\(912\) 14.2734 14.5940i 0.472641 0.483254i
\(913\) −14.3505 + 45.2764i −0.474933 + 1.49843i
\(914\) −5.08335 + 4.47831i −0.168142 + 0.148129i
\(915\) −6.55686 0.699337i −0.216763 0.0231194i
\(916\) 12.5439 + 13.7307i 0.414462 + 0.453675i
\(917\) 2.98259 + 55.0106i 0.0984938 + 1.81661i
\(918\) 4.58029 + 10.2155i 0.151172 + 0.337163i
\(919\) −7.45297 + 7.05982i −0.245851 + 0.232882i −0.800695 0.599072i \(-0.795536\pi\)
0.554845 + 0.831954i \(0.312778\pi\)
\(920\) 10.5137 5.33311i 0.346627 0.175828i
\(921\) −1.27127 3.17149i −0.0418898 0.104504i
\(922\) −3.76189 + 0.272159i −0.123891 + 0.00896307i
\(923\) −22.5300 + 51.0990i −0.741584 + 1.68194i
\(924\) −9.49144 46.6594i −0.312246 1.53498i
\(925\) 7.15964 + 22.5889i 0.235408 + 0.742719i
\(926\) −3.74415 + 22.8383i −0.123041 + 0.750514i
\(927\) −2.19882 6.07649i −0.0722186 0.199578i
\(928\) 10.2497 36.9161i 0.336463 1.21183i
\(929\) 0.699402 5.50436i 0.0229466 0.180592i −0.976433 0.215823i \(-0.930757\pi\)
0.999379 + 0.0352303i \(0.0112165\pi\)
\(930\) 2.67217 6.09482i 0.0876238 0.199857i
\(931\) 95.0584 + 3.43408i 3.11541 + 0.112547i
\(932\) −6.16352 7.81113i −0.201893 0.255862i
\(933\) −48.3816 1.64731i −1.58394 0.0539304i
\(934\) 1.88342 5.27320i 0.0616275 0.172544i
\(935\) −6.33725 + 11.9533i −0.207250 + 0.390916i
\(936\) −21.8821 17.7657i −0.715237 0.580689i
\(937\) 0.0918176 + 0.0424793i 0.00299955 + 0.00138774i 0.421388 0.906880i \(-0.361543\pi\)
−0.418389 + 0.908268i \(0.637405\pi\)
\(938\) −7.45992 1.36173i −0.243575 0.0444620i
\(939\) 11.3448 23.5274i 0.370223 0.767786i
\(940\) 0.942005 + 7.41368i 0.0307248 + 0.241807i
\(941\) 0.887938 + 49.1739i 0.0289460 + 1.60302i 0.612179 + 0.790719i \(0.290293\pi\)
−0.583233 + 0.812305i \(0.698212\pi\)
\(942\) −10.0115 + 6.05205i −0.326192 + 0.197186i
\(943\) 9.92184 + 17.1851i 0.323100 + 0.559625i
\(944\) −15.8753 1.59478i −0.516697 0.0519058i
\(945\) 21.6261 16.6532i 0.703497 0.541728i
\(946\) 3.94489 1.32919i 0.128259 0.0432157i
\(947\) 11.9957 + 6.63988i 0.389807 + 0.215767i 0.667017 0.745042i \(-0.267571\pi\)
−0.277210 + 0.960809i \(0.589410\pi\)
\(948\) 28.9476 34.2234i 0.940174 1.11153i
\(949\) −25.9274 3.77124i −0.841638 0.122420i
\(950\) 4.27011 + 11.9554i 0.138541 + 0.387885i
\(951\) 9.62287 + 30.1432i 0.312043 + 0.977459i
\(952\) −38.3445 2.77409i −1.24275 0.0899087i
\(953\) 17.3116 32.6531i 0.560777 1.05774i −0.427349 0.904087i \(-0.640552\pi\)
0.988125 0.153650i \(-0.0491029\pi\)
\(954\) −0.385646 4.07196i −0.0124857 0.131834i
\(955\) −3.76533 13.5615i −0.121843 0.438839i
\(956\) −17.8056 + 2.58990i −0.575874 + 0.0837632i
\(957\) 40.4648 7.47321i 1.30804 0.241575i
\(958\) −10.1998 + 13.9327i −0.329540 + 0.450145i
\(959\) 25.0955 10.5278i 0.810375 0.339962i
\(960\) 1.50596 + 0.977404i 0.0486046 + 0.0315456i
\(961\) −5.25373 3.70231i −0.169475 0.119429i
\(962\) 2.56331 15.6355i 0.0826443 0.504108i
\(963\) −48.8595 + 10.9676i −1.57447 + 0.353426i
\(964\) −21.2516 12.7866i −0.684467 0.411830i
\(965\) −12.8922 17.6105i −0.415015 0.566902i
\(966\) −5.81850 + 24.5577i −0.187207 + 0.790132i
\(967\) −54.2802 20.4996i −1.74553 0.659222i −0.745560 0.666439i \(-0.767818\pi\)
−0.999974 + 0.00721663i \(0.997703\pi\)
\(968\) −0.958315 0.624800i −0.0308014 0.0200818i
\(969\) 20.3248 30.1112i 0.652926 0.967310i
\(970\) 0.116380 0.486691i 0.00373672 0.0156267i
\(971\) 2.34672 + 43.2827i 0.0753098 + 1.38901i 0.755105 + 0.655604i \(0.227586\pi\)
−0.679795 + 0.733402i \(0.737931\pi\)
\(972\) 18.3256 + 18.2763i 0.587795 + 0.586212i
\(973\) 28.5296 + 9.61273i 0.914616 + 0.308170i
\(974\) 3.18802 + 15.8404i 0.102151 + 0.507558i
\(975\) −26.5507 + 12.3506i −0.850303 + 0.395536i
\(976\) 6.54502 + 3.31998i 0.209501 + 0.106270i
\(977\) −40.6355 + 12.0767i −1.30005 + 0.386368i −0.859396 0.511311i \(-0.829160\pi\)
−0.440650 + 0.897679i \(0.645252\pi\)
\(978\) −3.04009 0.213598i −0.0972113 0.00683012i
\(979\) 24.5688 12.4626i 0.785223 0.398307i
\(980\) 4.85226 + 29.5975i 0.155000 + 0.945457i
\(981\) 38.7697 + 23.1083i 1.23782 + 0.737792i
\(982\) −1.88963 + 0.205509i −0.0603004 + 0.00655807i
\(983\) 0.491522 27.2205i 0.0156771 0.868198i −0.892846 0.450363i \(-0.851295\pi\)
0.908523 0.417835i \(-0.137211\pi\)
\(984\) 7.12325 12.3972i 0.227081 0.395208i
\(985\) 5.97276 + 4.89045i 0.190308 + 0.155823i
\(986\) 1.35864 15.0090i 0.0432679 0.477983i
\(987\) −29.5856 19.2018i −0.941721 0.611200i
\(988\) −5.22945 + 41.1563i −0.166371 + 1.30936i
\(989\) 10.7208 + 1.16595i 0.340901 + 0.0370752i
\(990\) 0.780286 6.35164i 0.0247991 0.201868i
\(991\) −0.214147 + 0.537468i −0.00680260 + 0.0170732i −0.932339 0.361586i \(-0.882235\pi\)
0.925536 + 0.378659i \(0.123615\pi\)
\(992\) −23.4799 + 23.9077i −0.745488 + 0.759071i
\(993\) 2.49365 19.9564i 0.0791335 0.633296i
\(994\) −19.1294 30.5315i −0.606746 0.968401i
\(995\) −4.57407 9.43582i −0.145008 0.299136i
\(996\) 39.2913 + 8.56323i 1.24499 + 0.271336i
\(997\) −37.3738 6.82219i −1.18364 0.216061i −0.448379 0.893844i \(-0.647998\pi\)
−0.735262 + 0.677783i \(0.762941\pi\)
\(998\) −3.95754 9.93268i −0.125274 0.314413i
\(999\) −8.38824 + 30.9581i −0.265392 + 0.979471i
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 531.2.m.a.130.34 3248
9.7 even 3 inner 531.2.m.a.484.34 yes 3248
59.5 even 29 inner 531.2.m.a.418.34 yes 3248
531.241 even 87 inner 531.2.m.a.241.34 yes 3248
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
531.2.m.a.130.34 3248 1.1 even 1 trivial
531.2.m.a.241.34 yes 3248 531.241 even 87 inner
531.2.m.a.418.34 yes 3248 59.5 even 29 inner
531.2.m.a.484.34 yes 3248 9.7 even 3 inner