Properties

Label 507.2.q.a.16.12
Level $507$
Weight $2$
Character 507.16
Analytic conductor $4.048$
Analytic rank $0$
Dimension $360$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [507,2,Mod(16,507)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(507, base_ring=CyclotomicField(78))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("507.16");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 507 = 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 507.q (of order \(39\), degree \(24\), 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: \(4.04841538248\)
Analytic rank: \(0\)
Dimension: \(360\)
Relative dimension: \(15\) over \(\Q(\zeta_{39})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{39}]$

Embedding invariants

Embedding label 16.12
Character \(\chi\) \(=\) 507.16
Dual form 507.2.q.a.412.12

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.66608 + 0.134500i) q^{2} +(0.845190 + 0.534466i) q^{3} +(0.783635 + 0.127353i) q^{4} +(2.48154 + 2.19845i) q^{5} +(1.33627 + 1.00414i) q^{6} +(2.05375 - 2.13818i) q^{7} +(-1.95739 - 0.482453i) q^{8} +(0.428693 + 0.903450i) q^{9} +O(q^{10})\) \(q+(1.66608 + 0.134500i) q^{2} +(0.845190 + 0.534466i) q^{3} +(0.783635 + 0.127353i) q^{4} +(2.48154 + 2.19845i) q^{5} +(1.33627 + 1.00414i) q^{6} +(2.05375 - 2.13818i) q^{7} +(-1.95739 - 0.482453i) q^{8} +(0.428693 + 0.903450i) q^{9} +(3.83875 + 3.99656i) q^{10} +(0.456872 - 0.962837i) q^{11} +(0.594254 + 0.526463i) q^{12} +(-2.89957 - 2.14302i) q^{13} +(3.70930 - 3.28615i) q^{14} +(0.922374 + 3.18440i) q^{15} +(-4.70240 - 1.56989i) q^{16} +(1.39811 - 1.45559i) q^{17} +(0.592722 + 1.56288i) q^{18} +(-4.10438 + 7.10900i) q^{19} +(1.66464 + 2.03881i) q^{20} +(2.87859 - 0.709509i) q^{21} +(0.890687 - 1.54272i) q^{22} +(0.601302 + 1.04149i) q^{23} +(-1.39651 - 1.45392i) q^{24} +(0.722159 + 5.94752i) q^{25} +(-4.54268 - 3.96043i) q^{26} +(-0.120537 + 0.992709i) q^{27} +(1.88169 - 1.41400i) q^{28} +(-2.88783 - 0.233130i) q^{29} +(1.10845 + 5.42953i) q^{30} +(0.447434 - 3.68495i) q^{31} +(-3.91412 - 1.66765i) q^{32} +(0.900747 - 0.569598i) q^{33} +(2.52515 - 2.23709i) q^{34} +(9.79713 - 0.790906i) q^{35} +(0.220881 + 0.762570i) q^{36} +(1.93799 - 0.825698i) q^{37} +(-7.79440 + 11.2921i) q^{38} +(-1.30532 - 3.36097i) q^{39} +(-3.79669 - 5.50045i) q^{40} +(1.53005 + 0.967545i) q^{41} +(4.89139 - 0.794929i) q^{42} +(-7.39127 - 3.14913i) q^{43} +(0.480641 - 0.696329i) q^{44} +(-0.922374 + 3.18440i) q^{45} +(0.861738 + 1.81607i) q^{46} +(2.39336 - 6.31077i) q^{47} +(-3.13537 - 3.84013i) q^{48} +(-0.0720636 - 1.78824i) q^{49} +(0.403235 + 10.0062i) q^{50} +(1.95964 - 0.483007i) q^{51} +(-1.99928 - 2.04861i) q^{52} +(8.12976 + 2.00381i) q^{53} +(-0.334343 + 1.63772i) q^{54} +(3.25049 - 1.38491i) q^{55} +(-5.05156 + 3.19441i) q^{56} +(-7.26850 + 3.81480i) q^{57} +(-4.78001 - 0.776827i) q^{58} +(-13.7516 + 4.59097i) q^{59} +(0.317261 + 2.61288i) q^{60} +(2.40168 - 8.29157i) q^{61} +(1.24109 - 6.07924i) q^{62} +(2.81217 + 0.938839i) q^{63} +(2.48241 + 1.30287i) q^{64} +(-2.48407 - 11.6925i) q^{65} +(1.57733 - 0.827846i) q^{66} +(1.18066 - 0.191876i) q^{67} +(1.28098 - 0.962597i) q^{68} +(-0.0484240 + 1.20163i) q^{69} +16.4292 q^{70} +(0.451753 - 11.2101i) q^{71} +(-0.403246 - 1.97523i) q^{72} +(3.72647 + 5.39873i) q^{73} +(3.33990 - 1.11502i) q^{74} +(-2.56838 + 5.41275i) q^{75} +(-4.12169 + 5.04815i) q^{76} +(-1.12042 - 2.95430i) q^{77} +(-1.72271 - 5.77522i) q^{78} +(-3.90253 + 10.2901i) q^{79} +(-8.21784 - 14.2337i) q^{80} +(-0.632445 + 0.774605i) q^{81} +(2.41905 + 1.81780i) q^{82} +(3.42356 + 1.79682i) q^{83} +(2.34612 - 0.189399i) q^{84} +(6.66951 - 0.538419i) q^{85} +(-11.8909 - 6.24082i) q^{86} +(-2.31617 - 1.74049i) q^{87} +(-1.35880 + 1.66423i) q^{88} +(-8.58666 - 14.8725i) q^{89} +(-1.96505 + 5.18141i) q^{90} +(-10.5371 + 1.79858i) q^{91} +(0.338565 + 0.892722i) q^{92} +(2.34765 - 2.87534i) q^{93} +(4.83633 - 10.1923i) q^{94} +(-25.8140 + 8.61796i) q^{95} +(-2.41687 - 3.50144i) q^{96} +(0.209023 + 1.02386i) q^{97} +(0.120454 - 2.98904i) q^{98} +1.06573 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 360 q + q^{2} - 15 q^{3} + 15 q^{4} + 2 q^{5} - q^{6} + 2 q^{7} + 6 q^{8} + 15 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 360 q + q^{2} - 15 q^{3} + 15 q^{4} + 2 q^{5} - q^{6} + 2 q^{7} + 6 q^{8} + 15 q^{9} - q^{10} - 2 q^{11} + 30 q^{12} - 19 q^{13} + q^{15} + 15 q^{16} - 7 q^{17} - 2 q^{18} - 6 q^{19} + q^{20} + 4 q^{21} + 22 q^{22} + 46 q^{23} + 3 q^{24} + 28 q^{25} + 34 q^{26} + 30 q^{27} - 2 q^{28} + 36 q^{29} + q^{30} - 34 q^{31} - 190 q^{32} + 15 q^{33} - 51 q^{34} - 80 q^{35} + 15 q^{36} + q^{37} - 53 q^{38} + 5 q^{39} - 45 q^{40} + 9 q^{41} + 130 q^{42} + 78 q^{43} + 35 q^{44} - q^{45} - 318 q^{46} - 12 q^{47} - 15 q^{48} - 71 q^{49} + 48 q^{50} - 14 q^{51} - 63 q^{52} - 26 q^{53} - q^{54} - 61 q^{55} - 4 q^{56} - 38 q^{57} - 27 q^{58} + 208 q^{59} - 180 q^{60} - 3 q^{61} - 61 q^{62} + 2 q^{63} + 140 q^{64} + 45 q^{65} - 60 q^{66} - 80 q^{67} - 140 q^{68} + 6 q^{69} - 100 q^{70} + 84 q^{71} - 3 q^{72} + 134 q^{73} - 151 q^{74} - 12 q^{75} + 32 q^{76} + 82 q^{77} - 63 q^{78} + 4 q^{79} - 155 q^{80} + 15 q^{81} - 56 q^{82} + 106 q^{83} + 2 q^{84} - 19 q^{85} + q^{86} - 49 q^{87} + 8 q^{88} - 14 q^{89} + 2 q^{90} - 368 q^{91} + 36 q^{92} - 4 q^{93} - 59 q^{94} + 104 q^{95} + 75 q^{96} - 28 q^{97} + 101 q^{98} + 30 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).

\(n\) \(170\) \(340\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{39}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.66608 + 0.134500i 1.17810 + 0.0951058i 0.653961 0.756529i \(-0.273106\pi\)
0.524136 + 0.851634i \(0.324388\pi\)
\(3\) 0.845190 + 0.534466i 0.487971 + 0.308574i
\(4\) 0.783635 + 0.127353i 0.391817 + 0.0636765i
\(5\) 2.48154 + 2.19845i 1.10978 + 0.983176i 0.999942 0.0107736i \(-0.00342941\pi\)
0.109835 + 0.993950i \(0.464968\pi\)
\(6\) 1.33627 + 1.00414i 0.545530 + 0.409939i
\(7\) 2.05375 2.13818i 0.776244 0.808156i −0.209251 0.977862i \(-0.567102\pi\)
0.985495 + 0.169706i \(0.0542820\pi\)
\(8\) −1.95739 0.482453i −0.692042 0.170573i
\(9\) 0.428693 + 0.903450i 0.142898 + 0.301150i
\(10\) 3.83875 + 3.99656i 1.21392 + 1.26382i
\(11\) 0.456872 0.962837i 0.137752 0.290306i −0.822838 0.568277i \(-0.807610\pi\)
0.960590 + 0.277970i \(0.0896616\pi\)
\(12\) 0.594254 + 0.526463i 0.171546 + 0.151977i
\(13\) −2.89957 2.14302i −0.804195 0.594366i
\(14\) 3.70930 3.28615i 0.991351 0.878260i
\(15\) 0.922374 + 3.18440i 0.238156 + 0.822209i
\(16\) −4.70240 1.56989i −1.17560 0.392473i
\(17\) 1.39811 1.45559i 0.339092 0.353033i −0.529721 0.848172i \(-0.677703\pi\)
0.868814 + 0.495139i \(0.164883\pi\)
\(18\) 0.592722 + 1.56288i 0.139706 + 0.368374i
\(19\) −4.10438 + 7.10900i −0.941610 + 1.63092i −0.179210 + 0.983811i \(0.557354\pi\)
−0.762400 + 0.647106i \(0.775979\pi\)
\(20\) 1.66464 + 2.03881i 0.372224 + 0.455892i
\(21\) 2.87859 0.709509i 0.628160 0.154828i
\(22\) 0.890687 1.54272i 0.189895 0.328908i
\(23\) 0.601302 + 1.04149i 0.125380 + 0.217165i 0.921881 0.387472i \(-0.126652\pi\)
−0.796501 + 0.604637i \(0.793318\pi\)
\(24\) −1.39651 1.45392i −0.285062 0.296781i
\(25\) 0.722159 + 5.94752i 0.144432 + 1.18950i
\(26\) −4.54268 3.96043i −0.890892 0.776704i
\(27\) −0.120537 + 0.992709i −0.0231973 + 0.191047i
\(28\) 1.88169 1.41400i 0.355606 0.267221i
\(29\) −2.88783 0.233130i −0.536257 0.0432911i −0.190628 0.981662i \(-0.561052\pi\)
−0.345629 + 0.938371i \(0.612334\pi\)
\(30\) 1.10845 + 5.42953i 0.202374 + 0.991293i
\(31\) 0.447434 3.68495i 0.0803615 0.661836i −0.895749 0.444561i \(-0.853360\pi\)
0.976110 0.217276i \(-0.0697171\pi\)
\(32\) −3.91412 1.66765i −0.691925 0.294802i
\(33\) 0.900747 0.569598i 0.156800 0.0991543i
\(34\) 2.52515 2.23709i 0.433059 0.383657i
\(35\) 9.79713 0.790906i 1.65602 0.133687i
\(36\) 0.220881 + 0.762570i 0.0368135 + 0.127095i
\(37\) 1.93799 0.825698i 0.318603 0.135744i −0.226744 0.973954i \(-0.572808\pi\)
0.545347 + 0.838210i \(0.316398\pi\)
\(38\) −7.79440 + 11.2921i −1.26442 + 1.83183i
\(39\) −1.30532 3.36097i −0.209018 0.538187i
\(40\) −3.79669 5.50045i −0.600309 0.869697i
\(41\) 1.53005 + 0.967545i 0.238954 + 0.151105i 0.648576 0.761150i \(-0.275365\pi\)
−0.409622 + 0.912255i \(0.634339\pi\)
\(42\) 4.89139 0.794929i 0.754759 0.122660i
\(43\) −7.39127 3.14913i −1.12716 0.480237i −0.253771 0.967264i \(-0.581671\pi\)
−0.873387 + 0.487027i \(0.838081\pi\)
\(44\) 0.480641 0.696329i 0.0724594 0.104976i
\(45\) −0.922374 + 3.18440i −0.137499 + 0.474703i
\(46\) 0.861738 + 1.81607i 0.127056 + 0.267766i
\(47\) 2.39336 6.31077i 0.349107 0.920520i −0.639336 0.768928i \(-0.720791\pi\)
0.988443 0.151592i \(-0.0484401\pi\)
\(48\) −3.13537 3.84013i −0.452551 0.554275i
\(49\) −0.0720636 1.78824i −0.0102948 0.255463i
\(50\) 0.403235 + 10.0062i 0.0570260 + 1.41509i
\(51\) 1.95964 0.483007i 0.274404 0.0676345i
\(52\) −1.99928 2.04861i −0.277250 0.284091i
\(53\) 8.12976 + 2.00381i 1.11671 + 0.275244i 0.754141 0.656713i \(-0.228054\pi\)
0.362569 + 0.931957i \(0.381900\pi\)
\(54\) −0.334343 + 1.63772i −0.0454983 + 0.222866i
\(55\) 3.25049 1.38491i 0.438296 0.186741i
\(56\) −5.05156 + 3.19441i −0.675043 + 0.426871i
\(57\) −7.26850 + 3.81480i −0.962737 + 0.505283i
\(58\) −4.78001 0.776827i −0.627646 0.102002i
\(59\) −13.7516 + 4.59097i −1.79031 + 0.597694i −0.999889 0.0148690i \(-0.995267\pi\)
−0.790422 + 0.612563i \(0.790139\pi\)
\(60\) 0.317261 + 2.61288i 0.0409582 + 0.337321i
\(61\) 2.40168 8.29157i 0.307504 1.06163i −0.646768 0.762687i \(-0.723880\pi\)
0.954272 0.298940i \(-0.0966331\pi\)
\(62\) 1.24109 6.07924i 0.157618 0.772065i
\(63\) 2.81217 + 0.938839i 0.354300 + 0.118283i
\(64\) 2.48241 + 1.30287i 0.310301 + 0.162859i
\(65\) −2.48407 11.6925i −0.308111 1.45028i
\(66\) 1.57733 0.827846i 0.194156 0.101901i
\(67\) 1.18066 0.191876i 0.144241 0.0234414i −0.0878621 0.996133i \(-0.528003\pi\)
0.232103 + 0.972691i \(0.425439\pi\)
\(68\) 1.28098 0.962597i 0.155342 0.116732i
\(69\) −0.0484240 + 1.20163i −0.00582956 + 0.144659i
\(70\) 16.4292 1.96366
\(71\) 0.451753 11.2101i 0.0536133 1.33040i −0.718772 0.695246i \(-0.755296\pi\)
0.772386 0.635154i \(-0.219063\pi\)
\(72\) −0.403246 1.97523i −0.0475230 0.232783i
\(73\) 3.72647 + 5.39873i 0.436151 + 0.631873i 0.978001 0.208602i \(-0.0668913\pi\)
−0.541850 + 0.840475i \(0.682276\pi\)
\(74\) 3.33990 1.11502i 0.388255 0.129619i
\(75\) −2.56838 + 5.41275i −0.296571 + 0.625011i
\(76\) −4.12169 + 5.04815i −0.472790 + 0.579063i
\(77\) −1.12042 2.95430i −0.127684 0.336674i
\(78\) −1.72271 5.77522i −0.195059 0.653915i
\(79\) −3.90253 + 10.2901i −0.439069 + 1.15773i 0.514749 + 0.857341i \(0.327885\pi\)
−0.953817 + 0.300387i \(0.902884\pi\)
\(80\) −8.21784 14.2337i −0.918783 1.59138i
\(81\) −0.632445 + 0.774605i −0.0702717 + 0.0860672i
\(82\) 2.41905 + 1.81780i 0.267140 + 0.200742i
\(83\) 3.42356 + 1.79682i 0.375785 + 0.197227i 0.642032 0.766678i \(-0.278092\pi\)
−0.266247 + 0.963905i \(0.585784\pi\)
\(84\) 2.34612 0.189399i 0.255983 0.0206651i
\(85\) 6.66951 0.538419i 0.723410 0.0583997i
\(86\) −11.8909 6.24082i −1.28223 0.672965i
\(87\) −2.31617 1.74049i −0.248319 0.186600i
\(88\) −1.35880 + 1.66423i −0.144849 + 0.177407i
\(89\) −8.58666 14.8725i −0.910185 1.57649i −0.813802 0.581142i \(-0.802606\pi\)
−0.0963822 0.995344i \(-0.530727\pi\)
\(90\) −1.96505 + 5.18141i −0.207135 + 0.546169i
\(91\) −10.5371 + 1.79858i −1.10459 + 0.188542i
\(92\) 0.338565 + 0.892722i 0.0352978 + 0.0930727i
\(93\) 2.34765 2.87534i 0.243440 0.298159i
\(94\) 4.83633 10.1923i 0.498829 1.05126i
\(95\) −25.8140 + 8.61796i −2.64846 + 0.884184i
\(96\) −2.41687 3.50144i −0.246671 0.357365i
\(97\) 0.209023 + 1.02386i 0.0212231 + 0.103957i 0.989022 0.147765i \(-0.0472080\pi\)
−0.967799 + 0.251723i \(0.919003\pi\)
\(98\) 0.120454 2.98904i 0.0121677 0.301939i
\(99\) 1.06573 0.107110
\(100\) −0.191525 + 4.75265i −0.0191525 + 0.475265i
\(101\) −3.68105 + 2.76613i −0.366279 + 0.275241i −0.767906 0.640563i \(-0.778701\pi\)
0.401627 + 0.915803i \(0.368445\pi\)
\(102\) 3.32987 0.541157i 0.329707 0.0535826i
\(103\) −8.82637 + 4.63244i −0.869688 + 0.456447i −0.839667 0.543102i \(-0.817250\pi\)
−0.0300211 + 0.999549i \(0.509557\pi\)
\(104\) 4.64168 + 5.59362i 0.455154 + 0.548500i
\(105\) 8.70315 + 4.56776i 0.849340 + 0.445768i
\(106\) 13.2753 + 4.43196i 1.28941 + 0.430470i
\(107\) −2.17078 + 10.6332i −0.209857 + 1.02795i 0.729230 + 0.684269i \(0.239879\pi\)
−0.939087 + 0.343680i \(0.888326\pi\)
\(108\) −0.220881 + 0.762570i −0.0212543 + 0.0733784i
\(109\) 0.926591 + 7.63117i 0.0887514 + 0.730933i 0.967363 + 0.253396i \(0.0815475\pi\)
−0.878611 + 0.477538i \(0.841529\pi\)
\(110\) 5.60185 1.87017i 0.534116 0.178314i
\(111\) 2.07927 + 0.337915i 0.197356 + 0.0320735i
\(112\) −13.0142 + 6.83040i −1.22973 + 0.645413i
\(113\) 6.87298 4.34621i 0.646556 0.408857i −0.170547 0.985350i \(-0.554553\pi\)
0.817103 + 0.576492i \(0.195579\pi\)
\(114\) −12.6230 + 5.37816i −1.18225 + 0.503711i
\(115\) −0.797501 + 3.90642i −0.0743673 + 0.364275i
\(116\) −2.23332 0.550463i −0.207358 0.0511092i
\(117\) 0.693086 3.53831i 0.0640758 0.327117i
\(118\) −23.5288 + 5.79934i −2.16600 + 0.533872i
\(119\) −0.240939 5.97883i −0.0220868 0.548079i
\(120\) −0.269119 6.67812i −0.0245671 0.609627i
\(121\) 6.23858 + 7.64087i 0.567143 + 0.694624i
\(122\) 5.11662 13.4914i 0.463237 1.22145i
\(123\) 0.776063 + 1.63552i 0.0699753 + 0.147470i
\(124\) 0.819914 2.83067i 0.0736305 0.254202i
\(125\) −1.86673 + 2.70442i −0.166965 + 0.241891i
\(126\) 4.55902 + 1.94242i 0.406150 + 0.173044i
\(127\) 14.3747 2.33612i 1.27555 0.207297i 0.515348 0.856981i \(-0.327663\pi\)
0.760205 + 0.649684i \(0.225099\pi\)
\(128\) 11.1525 + 7.05241i 0.985751 + 0.623351i
\(129\) −4.56393 6.61199i −0.401831 0.582153i
\(130\) −2.56602 19.8148i −0.225054 1.73787i
\(131\) 6.26603 9.07792i 0.547466 0.793141i −0.447401 0.894334i \(-0.647650\pi\)
0.994867 + 0.101192i \(0.0322657\pi\)
\(132\) 0.778397 0.331644i 0.0677508 0.0288659i
\(133\) 6.77094 + 23.3760i 0.587115 + 2.02696i
\(134\) 1.99288 0.160882i 0.172159 0.0138981i
\(135\) −2.48154 + 2.19845i −0.213577 + 0.189212i
\(136\) −3.43891 + 2.17463i −0.294884 + 0.186473i
\(137\) 11.8408 + 5.04491i 1.01163 + 0.431016i 0.833221 0.552940i \(-0.186494\pi\)
0.178411 + 0.983956i \(0.442904\pi\)
\(138\) −0.242297 + 1.99550i −0.0206257 + 0.169868i
\(139\) −3.46351 16.9654i −0.293771 1.43898i −0.811957 0.583717i \(-0.801598\pi\)
0.518186 0.855268i \(-0.326607\pi\)
\(140\) 7.77809 + 0.627913i 0.657369 + 0.0530683i
\(141\) 5.39573 4.05463i 0.454403 0.341461i
\(142\) 2.26042 18.6162i 0.189690 1.56224i
\(143\) −3.38811 + 1.81273i −0.283328 + 0.151588i
\(144\) −0.597564 4.92138i −0.0497970 0.410115i
\(145\) −6.65374 6.92727i −0.552563 0.575279i
\(146\) 5.48248 + 9.49593i 0.453733 + 0.785889i
\(147\) 0.894845 1.54992i 0.0738056 0.127835i
\(148\) 1.62383 0.400238i 0.133478 0.0328993i
\(149\) −7.10555 8.70272i −0.582109 0.712955i 0.396649 0.917970i \(-0.370173\pi\)
−0.978759 + 0.205016i \(0.934275\pi\)
\(150\) −5.00715 + 8.67263i −0.408832 + 0.708118i
\(151\) 3.64647 + 9.61495i 0.296745 + 0.782454i 0.997606 + 0.0691551i \(0.0220303\pi\)
−0.700860 + 0.713298i \(0.747200\pi\)
\(152\) 11.4636 11.9349i 0.929824 0.968050i
\(153\) 1.91441 + 0.639126i 0.154771 + 0.0516702i
\(154\) −1.46935 5.07280i −0.118404 0.408778i
\(155\) 9.21150 8.16067i 0.739885 0.655481i
\(156\) −0.594861 2.80001i −0.0476270 0.224180i
\(157\) 9.00568 + 7.97833i 0.718731 + 0.636740i 0.941063 0.338231i \(-0.109828\pi\)
−0.222332 + 0.974971i \(0.571367\pi\)
\(158\) −7.88594 + 16.6193i −0.627372 + 1.32216i
\(159\) 5.80023 + 6.03868i 0.459988 + 0.478898i
\(160\) −6.04678 12.7433i −0.478040 1.00745i
\(161\) 3.46181 + 0.853258i 0.272829 + 0.0672462i
\(162\) −1.15789 + 1.20549i −0.0909724 + 0.0947123i
\(163\) 1.53873 + 1.15628i 0.120523 + 0.0905672i 0.659295 0.751885i \(-0.270855\pi\)
−0.538772 + 0.842452i \(0.681111\pi\)
\(164\) 1.07578 + 0.953058i 0.0840043 + 0.0744213i
\(165\) 3.48747 + 0.566769i 0.271499 + 0.0441229i
\(166\) 5.46226 + 3.45412i 0.423953 + 0.268092i
\(167\) −1.69419 0.136769i −0.131100 0.0105835i 0.0147423 0.999891i \(-0.495307\pi\)
−0.145842 + 0.989308i \(0.546589\pi\)
\(168\) −5.97683 −0.461123
\(169\) 3.81497 + 12.4276i 0.293459 + 0.955972i
\(170\) 11.1844 0.857801
\(171\) −8.18215 0.660531i −0.625705 0.0505121i
\(172\) −5.39100 3.40906i −0.411060 0.259939i
\(173\) −16.5571 2.69079i −1.25881 0.204577i −0.505840 0.862627i \(-0.668817\pi\)
−0.752974 + 0.658050i \(0.771382\pi\)
\(174\) −3.62483 3.21132i −0.274797 0.243449i
\(175\) 14.2000 + 10.6706i 1.07342 + 0.806621i
\(176\) −3.65994 + 3.81040i −0.275879 + 0.287220i
\(177\) −14.0765 3.46954i −1.05805 0.260786i
\(178\) −12.3057 25.9338i −0.922353 1.94382i
\(179\) 8.00612 + 8.33525i 0.598405 + 0.623006i 0.949663 0.313273i \(-0.101425\pi\)
−0.351258 + 0.936279i \(0.614246\pi\)
\(180\) −1.12835 + 2.37794i −0.0841020 + 0.177241i
\(181\) 16.9245 + 14.9938i 1.25798 + 1.11448i 0.988460 + 0.151484i \(0.0484051\pi\)
0.269525 + 0.962993i \(0.413133\pi\)
\(182\) −17.7976 + 1.57933i −1.31925 + 0.117068i
\(183\) 6.46144 5.72434i 0.477644 0.423155i
\(184\) −0.674515 2.32869i −0.0497259 0.171674i
\(185\) 6.62444 + 2.21156i 0.487038 + 0.162597i
\(186\) 4.29810 4.47480i 0.315152 0.328108i
\(187\) −0.762738 2.01117i −0.0557769 0.147072i
\(188\) 2.67921 4.64053i 0.195402 0.338446i
\(189\) 1.87504 + 2.29650i 0.136389 + 0.167046i
\(190\) −44.1672 + 10.8862i −3.20423 + 0.789772i
\(191\) 4.26467 7.38663i 0.308581 0.534478i −0.669471 0.742838i \(-0.733479\pi\)
0.978052 + 0.208360i \(0.0668126\pi\)
\(192\) 1.40177 + 2.42793i 0.101164 + 0.175221i
\(193\) 10.3931 + 10.8204i 0.748115 + 0.778870i 0.981077 0.193615i \(-0.0620214\pi\)
−0.232962 + 0.972486i \(0.574842\pi\)
\(194\) 0.210540 + 1.73395i 0.0151159 + 0.124490i
\(195\) 4.14974 11.2101i 0.297169 0.802768i
\(196\) 0.171266 1.41050i 0.0122333 0.100750i
\(197\) −18.1526 + 13.6408i −1.29332 + 0.971867i −0.293446 + 0.955976i \(0.594802\pi\)
−0.999874 + 0.0158912i \(0.994941\pi\)
\(198\) 1.77560 + 0.143341i 0.126186 + 0.0101868i
\(199\) −4.70846 23.0635i −0.333774 1.63493i −0.707016 0.707198i \(-0.749959\pi\)
0.373242 0.927734i \(-0.378246\pi\)
\(200\) 1.45585 11.9900i 0.102944 0.847822i
\(201\) 1.10043 + 0.468851i 0.0776187 + 0.0330702i
\(202\) −6.50498 + 4.11350i −0.457689 + 0.289425i
\(203\) −6.42936 + 5.69591i −0.451252 + 0.399775i
\(204\) 1.59715 0.128935i 0.111823 0.00902728i
\(205\) 1.66978 + 5.76473i 0.116622 + 0.402626i
\(206\) −15.3285 + 6.53087i −1.06799 + 0.455027i
\(207\) −0.683157 + 0.989724i −0.0474827 + 0.0687906i
\(208\) 10.2706 + 14.6293i 0.712139 + 1.01436i
\(209\) 4.96963 + 7.19976i 0.343757 + 0.498018i
\(210\) 13.8858 + 8.78084i 0.958210 + 0.605935i
\(211\) −19.5968 + 3.18480i −1.34910 + 0.219250i −0.791658 0.610964i \(-0.790782\pi\)
−0.557444 + 0.830215i \(0.688218\pi\)
\(212\) 6.11557 + 2.60560i 0.420019 + 0.178954i
\(213\) 6.37326 9.23326i 0.436688 0.632652i
\(214\) −5.04686 + 17.4238i −0.344996 + 1.19107i
\(215\) −11.4185 24.0640i −0.778736 1.64115i
\(216\) 0.714873 1.88497i 0.0486410 0.128256i
\(217\) −6.96016 8.52465i −0.472487 0.578691i
\(218\) 0.517385 + 12.8388i 0.0350417 + 0.869551i
\(219\) 0.264142 + 6.55462i 0.0178491 + 0.442920i
\(220\) 2.72357 0.671300i 0.183623 0.0452590i
\(221\) −7.17328 + 1.22440i −0.482527 + 0.0823622i
\(222\) 3.41879 + 0.842656i 0.229454 + 0.0565553i
\(223\) 0.0904816 0.443208i 0.00605909 0.0296794i −0.976649 0.214842i \(-0.931076\pi\)
0.982708 + 0.185163i \(0.0592813\pi\)
\(224\) −11.6044 + 4.94415i −0.775348 + 0.330345i
\(225\) −5.06370 + 3.20209i −0.337580 + 0.213473i
\(226\) 12.0355 6.31672i 0.800590 0.420182i
\(227\) 4.92762 + 0.800816i 0.327058 + 0.0531520i 0.321723 0.946834i \(-0.395738\pi\)
0.00533435 + 0.999986i \(0.498302\pi\)
\(228\) −6.18168 + 2.06375i −0.409392 + 0.136675i
\(229\) −0.249718 2.05661i −0.0165018 0.135905i 0.982129 0.188206i \(-0.0602674\pi\)
−0.998631 + 0.0523015i \(0.983344\pi\)
\(230\) −1.85411 + 6.40114i −0.122257 + 0.422079i
\(231\) 0.632006 3.09577i 0.0415829 0.203687i
\(232\) 5.54014 + 1.84957i 0.363728 + 0.121430i
\(233\) −1.60701 0.843423i −0.105279 0.0552545i 0.411262 0.911517i \(-0.365088\pi\)
−0.516541 + 0.856263i \(0.672780\pi\)
\(234\) 1.63064 5.80189i 0.106598 0.379281i
\(235\) 19.8131 10.3987i 1.29246 0.678338i
\(236\) −11.3609 + 1.84633i −0.739534 + 0.120186i
\(237\) −8.79809 + 6.61134i −0.571498 + 0.429453i
\(238\) 0.402729 9.99363i 0.0261051 0.647791i
\(239\) 2.67774 0.173208 0.0866042 0.996243i \(-0.472398\pi\)
0.0866042 + 0.996243i \(0.472398\pi\)
\(240\) 0.661798 16.4224i 0.0427189 1.06006i
\(241\) 5.65507 + 27.7004i 0.364275 + 1.78434i 0.587136 + 0.809488i \(0.300255\pi\)
−0.222861 + 0.974850i \(0.571540\pi\)
\(242\) 9.36627 + 13.5694i 0.602087 + 0.872273i
\(243\) −0.948536 + 0.316668i −0.0608486 + 0.0203143i
\(244\) 2.93800 6.19170i 0.188086 0.396383i
\(245\) 3.75252 4.59601i 0.239740 0.293628i
\(246\) 1.07301 + 2.82929i 0.0684124 + 0.180389i
\(247\) 27.1356 11.8173i 1.72660 0.751914i
\(248\) −2.65362 + 6.99702i −0.168505 + 0.444311i
\(249\) 1.93322 + 3.34843i 0.122513 + 0.212198i
\(250\) −3.47386 + 4.25471i −0.219706 + 0.269092i
\(251\) −7.30383 5.48847i −0.461014 0.346429i 0.344722 0.938705i \(-0.387973\pi\)
−0.805735 + 0.592276i \(0.798230\pi\)
\(252\) 2.08415 + 1.09384i 0.131289 + 0.0689057i
\(253\) 1.27750 0.103130i 0.0803157 0.00648375i
\(254\) 24.2637 1.95877i 1.52244 0.122904i
\(255\) 5.92477 + 3.10956i 0.371024 + 0.194728i
\(256\) 13.1499 + 9.88150i 0.821868 + 0.617594i
\(257\) 3.16697 3.87883i 0.197550 0.241955i −0.666325 0.745662i \(-0.732133\pi\)
0.863875 + 0.503707i \(0.168031\pi\)
\(258\) −6.71456 11.6300i −0.418030 0.724050i
\(259\) 2.21464 5.83954i 0.137611 0.362851i
\(260\) −0.457524 9.47902i −0.0283744 0.587864i
\(261\) −1.02737 2.70895i −0.0635927 0.167680i
\(262\) 11.6607 14.2818i 0.720400 0.882330i
\(263\) 9.79656 20.6458i 0.604082 1.27308i −0.339085 0.940756i \(-0.610117\pi\)
0.943167 0.332320i \(-0.107831\pi\)
\(264\) −2.03792 + 0.680357i −0.125425 + 0.0418731i
\(265\) 15.7690 + 22.8454i 0.968684 + 1.40338i
\(266\) 8.13687 + 39.8570i 0.498903 + 2.44379i
\(267\) 0.691500 17.1594i 0.0423191 1.05014i
\(268\) 0.949643 0.0580087
\(269\) −1.12468 + 27.9085i −0.0685727 + 1.70161i 0.489648 + 0.871920i \(0.337125\pi\)
−0.558220 + 0.829693i \(0.688516\pi\)
\(270\) −4.43013 + 3.32903i −0.269609 + 0.202598i
\(271\) −6.12872 + 0.996014i −0.372293 + 0.0605036i −0.343680 0.939087i \(-0.611673\pi\)
−0.0286138 + 0.999591i \(0.509109\pi\)
\(272\) −8.85960 + 4.64988i −0.537192 + 0.281940i
\(273\) −9.86716 4.11160i −0.597187 0.248845i
\(274\) 19.0493 + 9.99783i 1.15081 + 0.603991i
\(275\) 6.05643 + 2.02193i 0.365216 + 0.121927i
\(276\) −0.190978 + 0.935471i −0.0114955 + 0.0563087i
\(277\) 5.21911 18.0184i 0.313586 1.08262i −0.636666 0.771140i \(-0.719687\pi\)
0.950251 0.311484i \(-0.100826\pi\)
\(278\) −3.48864 28.7315i −0.209235 1.72320i
\(279\) 3.52098 1.17548i 0.210796 0.0703739i
\(280\) −19.5584 3.17855i −1.16884 0.189954i
\(281\) 17.5767 9.22494i 1.04854 0.550314i 0.149759 0.988722i \(-0.452150\pi\)
0.898776 + 0.438409i \(0.144458\pi\)
\(282\) 9.53507 6.02961i 0.567805 0.359058i
\(283\) 12.0578 5.13734i 0.716760 0.305383i −0.00262269 0.999997i \(-0.500835\pi\)
0.719383 + 0.694613i \(0.244425\pi\)
\(284\) 1.78166 8.72713i 0.105722 0.517860i
\(285\) −26.4237 6.51286i −1.56521 0.385788i
\(286\) −5.88867 + 2.56445i −0.348204 + 0.151639i
\(287\) 5.21112 1.28443i 0.307603 0.0758173i
\(288\) −0.171314 4.25112i −0.0100948 0.250500i
\(289\) 0.520499 + 12.9161i 0.0306176 + 0.759768i
\(290\) −10.1539 12.4363i −0.596260 0.730286i
\(291\) −0.370555 + 0.977074i −0.0217223 + 0.0572771i
\(292\) 2.23265 + 4.70521i 0.130656 + 0.275351i
\(293\) −2.03172 + 7.01433i −0.118695 + 0.409781i −0.997758 0.0669233i \(-0.978682\pi\)
0.879063 + 0.476705i \(0.158169\pi\)
\(294\) 1.69935 2.46193i 0.0991080 0.143583i
\(295\) −44.2182 18.8396i −2.57448 1.09689i
\(296\) −4.19176 + 0.681227i −0.243641 + 0.0395955i
\(297\) 0.900747 + 0.569598i 0.0522667 + 0.0330514i
\(298\) −10.6679 15.4551i −0.617975 0.895292i
\(299\) 0.488405 4.30846i 0.0282452 0.249164i
\(300\) −2.70200 + 3.91453i −0.156000 + 0.226005i
\(301\) −21.9132 + 9.33634i −1.26306 + 0.538138i
\(302\) 4.78210 + 16.5097i 0.275179 + 0.950028i
\(303\) −4.58959 + 0.370510i −0.263665 + 0.0212853i
\(304\) 30.4608 26.9859i 1.74705 1.54775i
\(305\) 24.1885 15.2959i 1.38503 0.875838i
\(306\) 3.10361 + 1.32232i 0.177421 + 0.0755922i
\(307\) −3.41965 + 28.1634i −0.195170 + 1.60737i 0.485136 + 0.874439i \(0.338770\pi\)
−0.680306 + 0.732929i \(0.738153\pi\)
\(308\) −0.501759 2.45778i −0.0285904 0.140045i
\(309\) −9.93584 0.802104i −0.565230 0.0456301i
\(310\) 16.4447 12.3574i 0.933997 0.701853i
\(311\) −3.12388 + 25.7274i −0.177139 + 1.45887i 0.584777 + 0.811194i \(0.301182\pi\)
−0.761916 + 0.647676i \(0.775741\pi\)
\(312\) 0.933500 + 7.20849i 0.0528490 + 0.408101i
\(313\) −0.413236 3.40331i −0.0233575 0.192366i 0.976360 0.216153i \(-0.0693509\pi\)
−0.999717 + 0.0237864i \(0.992428\pi\)
\(314\) 13.9311 + 14.5038i 0.786177 + 0.818497i
\(315\) 4.91450 + 8.51216i 0.276901 + 0.479606i
\(316\) −4.36863 + 7.56669i −0.245755 + 0.425660i
\(317\) 0.488964 0.120519i 0.0274629 0.00676901i −0.225560 0.974229i \(-0.572421\pi\)
0.253023 + 0.967460i \(0.418575\pi\)
\(318\) 8.85145 + 10.8411i 0.496365 + 0.607936i
\(319\) −1.54384 + 2.67400i −0.0864382 + 0.149715i
\(320\) 3.29589 + 8.69056i 0.184246 + 0.485817i
\(321\) −7.51780 + 7.82686i −0.419603 + 0.436853i
\(322\) 5.65288 + 1.88721i 0.315023 + 0.105170i
\(323\) 4.60940 + 15.9135i 0.256474 + 0.885450i
\(324\) −0.594254 + 0.526463i −0.0330141 + 0.0292480i
\(325\) 10.6517 18.7928i 0.590848 1.04244i
\(326\) 2.40814 + 2.13342i 0.133374 + 0.118159i
\(327\) −3.29545 + 6.94502i −0.182239 + 0.384060i
\(328\) −2.52811 2.63204i −0.139592 0.145330i
\(329\) −8.57819 18.0782i −0.472931 0.996681i
\(330\) 5.73418 + 1.41335i 0.315656 + 0.0778022i
\(331\) −15.5731 + 16.2133i −0.855977 + 0.891166i −0.995076 0.0991124i \(-0.968400\pi\)
0.139100 + 0.990278i \(0.455579\pi\)
\(332\) 2.45399 + 1.84405i 0.134680 + 0.101206i
\(333\) 1.57678 + 1.39690i 0.0864069 + 0.0765498i
\(334\) −2.80426 0.455736i −0.153442 0.0249368i
\(335\) 3.35168 + 2.11948i 0.183122 + 0.115799i
\(336\) −14.6501 1.18268i −0.799230 0.0645205i
\(337\) −23.1748 −1.26241 −0.631205 0.775616i \(-0.717439\pi\)
−0.631205 + 0.775616i \(0.717439\pi\)
\(338\) 4.68453 + 21.2186i 0.254805 + 1.15414i
\(339\) 8.13188 0.441663
\(340\) 5.29503 + 0.427459i 0.287163 + 0.0231822i
\(341\) −3.34359 2.11436i −0.181065 0.114499i
\(342\) −13.5433 2.20100i −0.732337 0.119016i
\(343\) 11.5624 + 10.2434i 0.624311 + 0.553092i
\(344\) 12.9483 + 9.73001i 0.698125 + 0.524607i
\(345\) −2.76189 + 2.87543i −0.148695 + 0.154808i
\(346\) −27.2236 6.71001i −1.46355 0.360732i
\(347\) −14.1353 29.7896i −0.758825 1.59919i −0.799972 0.600037i \(-0.795152\pi\)
0.0411470 0.999153i \(-0.486899\pi\)
\(348\) −1.59337 1.65888i −0.0854138 0.0889251i
\(349\) 2.48942 5.24635i 0.133256 0.280831i −0.825844 0.563899i \(-0.809301\pi\)
0.959100 + 0.283068i \(0.0913522\pi\)
\(350\) 22.2231 + 19.6880i 1.18788 + 1.05237i
\(351\) 2.47689 2.62011i 0.132207 0.139851i
\(352\) −3.39393 + 3.00676i −0.180897 + 0.160261i
\(353\) 9.17390 + 31.6720i 0.488278 + 1.68573i 0.704762 + 0.709444i \(0.251054\pi\)
−0.216485 + 0.976286i \(0.569459\pi\)
\(354\) −22.9859 7.67382i −1.22169 0.407859i
\(355\) 25.7660 26.8252i 1.36752 1.42374i
\(356\) −4.83475 12.7482i −0.256241 0.675652i
\(357\) 2.99184 5.18202i 0.158345 0.274262i
\(358\) 12.2178 + 14.9640i 0.645728 + 0.790874i
\(359\) 22.5375 5.55500i 1.18948 0.293181i 0.405578 0.914061i \(-0.367070\pi\)
0.783906 + 0.620879i \(0.213224\pi\)
\(360\) 3.34177 5.78812i 0.176127 0.305061i
\(361\) −24.1919 41.9017i −1.27326 2.20535i
\(362\) 26.1808 + 27.2571i 1.37603 + 1.43260i
\(363\) 1.18900 + 9.79229i 0.0624063 + 0.513962i
\(364\) −8.48631 + 0.0674914i −0.444804 + 0.00353751i
\(365\) −2.62145 + 21.5896i −0.137213 + 1.13005i
\(366\) 11.5352 8.66815i 0.602955 0.453091i
\(367\) 3.87379 + 0.312725i 0.202210 + 0.0163241i 0.181157 0.983454i \(-0.442016\pi\)
0.0210535 + 0.999778i \(0.493298\pi\)
\(368\) −1.19254 5.84146i −0.0621656 0.304507i
\(369\) −0.218208 + 1.79710i −0.0113594 + 0.0935535i
\(370\) 10.7394 + 4.57563i 0.558314 + 0.237876i
\(371\) 20.9810 13.2676i 1.08928 0.688818i
\(372\) 2.20588 1.95424i 0.114370 0.101323i
\(373\) −12.0854 + 0.975637i −0.625760 + 0.0505165i −0.389279 0.921120i \(-0.627276\pi\)
−0.236480 + 0.971636i \(0.575994\pi\)
\(374\) −1.00028 3.45337i −0.0517233 0.178569i
\(375\) −3.02316 + 1.28805i −0.156115 + 0.0665145i
\(376\) −7.72939 + 11.1980i −0.398613 + 0.577490i
\(377\) 7.87386 + 6.86465i 0.405525 + 0.353547i
\(378\) 2.81508 + 4.07835i 0.144792 + 0.209768i
\(379\) 6.49518 + 4.10730i 0.333635 + 0.210978i 0.690770 0.723075i \(-0.257272\pi\)
−0.357135 + 0.934053i \(0.616246\pi\)
\(380\) −21.3262 + 3.46585i −1.09401 + 0.177794i
\(381\) 13.3980 + 5.70834i 0.686399 + 0.292447i
\(382\) 8.09879 11.7331i 0.414370 0.600319i
\(383\) 5.06878 17.4994i 0.259002 0.894180i −0.720620 0.693330i \(-0.756143\pi\)
0.979622 0.200849i \(-0.0643702\pi\)
\(384\) 5.65671 + 11.9213i 0.288668 + 0.608354i
\(385\) 3.71452 9.79438i 0.189309 0.499168i
\(386\) 15.8605 + 19.4256i 0.807277 + 0.988735i
\(387\) −0.323503 8.02765i −0.0164446 0.408069i
\(388\) 0.0334057 + 0.828954i 0.00169592 + 0.0420838i
\(389\) 12.5972 3.10494i 0.638705 0.157427i 0.0933519 0.995633i \(-0.470242\pi\)
0.545353 + 0.838207i \(0.316396\pi\)
\(390\) 8.42156 18.1187i 0.426442 0.917477i
\(391\) 2.35667 + 0.580866i 0.119182 + 0.0293756i
\(392\) −0.721686 + 3.53505i −0.0364506 + 0.178547i
\(393\) 10.1478 4.32359i 0.511890 0.218096i
\(394\) −32.0784 + 20.2852i −1.61609 + 1.02195i
\(395\) −32.3066 + 16.9558i −1.62552 + 0.853138i
\(396\) 0.835146 + 0.135724i 0.0419677 + 0.00682041i
\(397\) −6.32629 + 2.11203i −0.317508 + 0.106000i −0.470955 0.882157i \(-0.656091\pi\)
0.153447 + 0.988157i \(0.450962\pi\)
\(398\) −4.74262 39.0590i −0.237726 1.95785i
\(399\) −6.77094 + 23.3760i −0.338971 + 1.17026i
\(400\) 5.94107 29.1013i 0.297054 1.45506i
\(401\) 20.3713 + 6.80094i 1.01729 + 0.339623i 0.775935 0.630813i \(-0.217279\pi\)
0.241359 + 0.970436i \(0.422407\pi\)
\(402\) 1.77035 + 0.929153i 0.0882972 + 0.0463419i
\(403\) −9.19427 + 9.72590i −0.457999 + 0.484481i
\(404\) −3.23688 + 1.69884i −0.161041 + 0.0845207i
\(405\) −3.27237 + 0.531811i −0.162605 + 0.0264259i
\(406\) −11.4779 + 8.62510i −0.569640 + 0.428057i
\(407\) 0.0903980 2.24320i 0.00448086 0.111191i
\(408\) −4.06880 −0.201436
\(409\) 0.398236 9.88211i 0.0196915 0.488639i −0.959013 0.283363i \(-0.908550\pi\)
0.978704 0.205276i \(-0.0658092\pi\)
\(410\) 2.00662 + 9.82910i 0.0991001 + 0.485425i
\(411\) 7.31143 + 10.5924i 0.360646 + 0.522486i
\(412\) −7.50660 + 2.50607i −0.369824 + 0.123465i
\(413\) −18.4261 + 38.8322i −0.906689 + 1.91081i
\(414\) −1.27131 + 1.55708i −0.0624816 + 0.0765261i
\(415\) 4.54547 + 11.9854i 0.223128 + 0.588341i
\(416\) 7.77545 + 13.2235i 0.381223 + 0.648335i
\(417\) 6.14009 16.1901i 0.300682 0.792832i
\(418\) 7.31145 + 12.6638i 0.357615 + 0.619407i
\(419\) −14.6008 + 17.8827i −0.713294 + 0.873627i −0.996340 0.0854797i \(-0.972758\pi\)
0.283046 + 0.959106i \(0.408655\pi\)
\(420\) 6.23837 + 4.68783i 0.304401 + 0.228743i
\(421\) 4.25779 + 2.23466i 0.207512 + 0.108911i 0.565278 0.824901i \(-0.308769\pi\)
−0.357766 + 0.933811i \(0.616461\pi\)
\(422\) −33.0783 + 2.67035i −1.61022 + 0.129991i
\(423\) 6.72748 0.543098i 0.327101 0.0264063i
\(424\) −14.9464 7.84447i −0.725861 0.380961i
\(425\) 9.66681 + 7.26413i 0.468909 + 0.352362i
\(426\) 11.8602 14.5262i 0.574630 0.703794i
\(427\) −12.7964 22.1640i −0.619262 1.07259i
\(428\) −3.05527 + 8.05608i −0.147682 + 0.389405i
\(429\) −3.83243 0.278728i −0.185032 0.0134571i
\(430\) −15.7876 41.6284i −0.761343 2.00750i
\(431\) 5.83605 7.14787i 0.281113 0.344301i −0.614677 0.788779i \(-0.710714\pi\)
0.895790 + 0.444478i \(0.146611\pi\)
\(432\) 2.12526 4.47888i 0.102251 0.215490i
\(433\) −16.4506 + 5.49201i −0.790565 + 0.263929i −0.683143 0.730284i \(-0.739388\pi\)
−0.107421 + 0.994214i \(0.534259\pi\)
\(434\) −10.4496 15.1389i −0.501598 0.726690i
\(435\) −1.92128 9.41106i −0.0921184 0.451226i
\(436\) −0.245743 + 6.09805i −0.0117690 + 0.292044i
\(437\) −9.87190 −0.472237
\(438\) −0.441514 + 10.9561i −0.0210964 + 0.523501i
\(439\) −12.3830 + 9.30524i −0.591010 + 0.444115i −0.853700 0.520765i \(-0.825647\pi\)
0.262690 + 0.964880i \(0.415390\pi\)
\(440\) −7.03064 + 1.14259i −0.335173 + 0.0544708i
\(441\) 1.58469 0.831711i 0.0754615 0.0396053i
\(442\) −12.1159 + 1.07515i −0.576296 + 0.0511396i
\(443\) −30.3297 15.9183i −1.44101 0.756300i −0.450374 0.892840i \(-0.648709\pi\)
−0.990635 + 0.136540i \(0.956402\pi\)
\(444\) 1.58636 + 0.529604i 0.0752851 + 0.0251339i
\(445\) 11.3884 55.7841i 0.539862 2.64442i
\(446\) 0.210361 0.726251i 0.00996089 0.0343890i
\(447\) −1.35423 11.1531i −0.0640531 0.527525i
\(448\) 7.88401 2.63207i 0.372484 0.124354i
\(449\) 3.20522 + 0.520899i 0.151264 + 0.0245827i 0.235572 0.971857i \(-0.424304\pi\)
−0.0843078 + 0.996440i \(0.526868\pi\)
\(450\) −8.86722 + 4.65387i −0.418005 + 0.219386i
\(451\) 1.63063 1.03115i 0.0767832 0.0485547i
\(452\) 5.93941 2.53055i 0.279366 0.119027i
\(453\) −2.05690 + 10.0754i −0.0966417 + 0.473382i
\(454\) 8.10210 + 1.99699i 0.380251 + 0.0937234i
\(455\) −30.1023 18.7021i −1.41122 0.876768i
\(456\) 16.0678 3.96035i 0.752442 0.185460i
\(457\) −1.35956 33.7372i −0.0635976 1.57816i −0.644769 0.764378i \(-0.723046\pi\)
0.581171 0.813781i \(-0.302595\pi\)
\(458\) −0.139436 3.46007i −0.00651543 0.161679i
\(459\) 1.27645 + 1.56337i 0.0595797 + 0.0729719i
\(460\) −1.12244 + 2.95964i −0.0523342 + 0.137994i
\(461\) −15.5379 32.7454i −0.723671 1.52510i −0.846332 0.532655i \(-0.821194\pi\)
0.122662 0.992449i \(-0.460857\pi\)
\(462\) 1.46935 5.07280i 0.0683605 0.236008i
\(463\) 9.17000 13.2850i 0.426166 0.617408i −0.549809 0.835290i \(-0.685299\pi\)
0.975975 + 0.217882i \(0.0699149\pi\)
\(464\) 13.2137 + 5.62985i 0.613433 + 0.261359i
\(465\) 12.1471 1.97409i 0.563307 0.0915462i
\(466\) −2.56397 1.62135i −0.118773 0.0751078i
\(467\) −7.24403 10.4948i −0.335214 0.485641i 0.618740 0.785596i \(-0.287644\pi\)
−0.953953 + 0.299955i \(0.903028\pi\)
\(468\) 0.993740 2.68448i 0.0459357 0.124090i
\(469\) 2.01452 2.91853i 0.0930217 0.134765i
\(470\) 34.4089 14.6602i 1.58716 0.676227i
\(471\) 3.34736 + 11.5564i 0.154238 + 0.532492i
\(472\) 29.1323 2.35180i 1.34092 0.108250i
\(473\) −6.40896 + 5.67784i −0.294684 + 0.261068i
\(474\) −15.5476 + 9.83168i −0.714123 + 0.451584i
\(475\) −45.2449 19.2771i −2.07598 0.884492i
\(476\) 0.572615 4.71591i 0.0262457 0.216153i
\(477\) 1.67483 + 8.20386i 0.0766852 + 0.375629i
\(478\) 4.46133 + 0.360155i 0.204056 + 0.0164731i
\(479\) −16.9465 + 12.7345i −0.774307 + 0.581854i −0.912751 0.408516i \(-0.866046\pi\)
0.138444 + 0.990370i \(0.455790\pi\)
\(480\) 1.70019 14.0023i 0.0776027 0.639116i
\(481\) −7.38880 1.75897i −0.336900 0.0802019i
\(482\) 5.69611 + 46.9117i 0.259451 + 2.13677i
\(483\) 2.46985 + 2.57138i 0.112382 + 0.117002i
\(484\) 3.91568 + 6.78215i 0.177985 + 0.308280i
\(485\) −1.73221 + 3.00028i −0.0786557 + 0.136236i
\(486\) −1.62293 + 0.400016i −0.0736176 + 0.0181451i
\(487\) 22.3360 + 27.3566i 1.01214 + 1.23965i 0.970647 + 0.240507i \(0.0773136\pi\)
0.0414919 + 0.999139i \(0.486789\pi\)
\(488\) −8.70133 + 15.0711i −0.393891 + 0.682239i
\(489\) 0.682529 + 1.79968i 0.0308650 + 0.0813844i
\(490\) 6.87017 7.15261i 0.310363 0.323122i
\(491\) 21.6699 + 7.23449i 0.977950 + 0.326488i 0.760324 0.649544i \(-0.225040\pi\)
0.217627 + 0.976032i \(0.430169\pi\)
\(492\) 0.399862 + 1.38048i 0.0180272 + 0.0622370i
\(493\) −4.37686 + 3.87756i −0.197124 + 0.174636i
\(494\) 46.7996 16.0388i 2.10561 0.721619i
\(495\) 2.64466 + 2.34296i 0.118868 + 0.105308i
\(496\) −7.88898 + 16.6257i −0.354226 + 0.746515i
\(497\) −23.0415 23.9888i −1.03355 1.07604i
\(498\) 2.77054 + 5.83878i 0.124151 + 0.261642i
\(499\) −29.5591 7.28566i −1.32325 0.326151i −0.486470 0.873697i \(-0.661716\pi\)
−0.836775 + 0.547546i \(0.815562\pi\)
\(500\) −1.80725 + 1.88155i −0.0808226 + 0.0841453i
\(501\) −1.35881 1.02108i −0.0607073 0.0456185i
\(502\) −11.4306 10.1266i −0.510171 0.451972i
\(503\) −22.7827 3.70256i −1.01583 0.165089i −0.370373 0.928883i \(-0.620770\pi\)
−0.645460 + 0.763794i \(0.723334\pi\)
\(504\) −5.05156 3.19441i −0.225014 0.142290i
\(505\) −15.2159 1.22835i −0.677097 0.0546610i
\(506\) 2.14229 0.0952363
\(507\) −3.41777 + 12.5427i −0.151788 + 0.557040i
\(508\) 11.5621 0.512983
\(509\) 18.7358 + 1.51251i 0.830450 + 0.0670409i 0.488377 0.872633i \(-0.337589\pi\)
0.342073 + 0.939673i \(0.388871\pi\)
\(510\) 9.45291 + 5.97766i 0.418582 + 0.264695i
\(511\) 19.1967 + 3.11976i 0.849211 + 0.138010i
\(512\) 0.826128 + 0.731886i 0.0365101 + 0.0323451i
\(513\) −6.56244 4.93135i −0.289739 0.217725i
\(514\) 5.79813 6.03649i 0.255744 0.266258i
\(515\) −32.0871 7.90877i −1.41393 0.348502i
\(516\) −2.73440 5.76262i −0.120375 0.253685i
\(517\) −4.98278 5.18763i −0.219143 0.228152i
\(518\) 4.47519 9.43127i 0.196629 0.414386i
\(519\) −12.5558 11.1234i −0.551137 0.488265i
\(520\) −0.778804 + 24.0853i −0.0341528 + 1.05621i
\(521\) 16.9416 15.0089i 0.742224 0.657553i −0.204768 0.978810i \(-0.565644\pi\)
0.946992 + 0.321258i \(0.104106\pi\)
\(522\) −1.34733 4.65152i −0.0589710 0.203591i
\(523\) −41.3721 13.8120i −1.80907 0.603958i −0.999865 0.0164368i \(-0.994768\pi\)
−0.809209 0.587521i \(-0.800104\pi\)
\(524\) 6.06638 6.31577i 0.265011 0.275906i
\(525\) 6.29862 + 16.6081i 0.274894 + 0.724836i
\(526\) 19.0987 33.0800i 0.832744 1.44235i
\(527\) −4.73821 5.80326i −0.206400 0.252794i
\(528\) −5.12988 + 1.26440i −0.223249 + 0.0550260i
\(529\) 10.7769 18.6661i 0.468560 0.811569i
\(530\) 23.1998 + 40.1832i 1.00773 + 1.74545i
\(531\) −10.0429 10.4558i −0.435827 0.453744i
\(532\) 2.32894 + 19.1805i 0.100972 + 0.831582i
\(533\) −2.36302 6.08438i −0.102354 0.263544i
\(534\) 3.46003 28.4959i 0.149730 1.23314i
\(535\) −28.7634 + 21.6143i −1.24355 + 0.934467i
\(536\) −2.40359 0.194038i −0.103819 0.00838115i
\(537\) 2.31178 + 11.3239i 0.0997609 + 0.488661i
\(538\) −5.62750 + 46.3466i −0.242619 + 1.99814i
\(539\) −1.75471 0.747611i −0.0755806 0.0322019i
\(540\) −2.22460 + 1.40675i −0.0957314 + 0.0605369i
\(541\) −20.6169 + 18.2650i −0.886390 + 0.785273i −0.977581 0.210561i \(-0.932471\pi\)
0.0911912 + 0.995833i \(0.470933\pi\)
\(542\) −10.3449 + 0.835127i −0.444352 + 0.0358718i
\(543\) 6.29073 + 21.7181i 0.269961 + 0.932013i
\(544\) −7.89980 + 3.36579i −0.338701 + 0.144307i
\(545\) −14.4774 + 20.9741i −0.620142 + 0.898431i
\(546\) −15.8865 8.17738i −0.679878 0.349960i
\(547\) −20.9568 30.3611i −0.896046 1.29815i −0.953993 0.299827i \(-0.903071\pi\)
0.0579472 0.998320i \(-0.481544\pi\)
\(548\) 8.63641 + 5.46134i 0.368929 + 0.233297i
\(549\) 8.52061 1.38473i 0.363651 0.0590990i
\(550\) 9.81854 + 4.18329i 0.418664 + 0.178376i
\(551\) 13.5101 19.5728i 0.575549 0.833827i
\(552\) 0.674515 2.32869i 0.0287093 0.0991158i
\(553\) 13.9873 + 29.4776i 0.594800 + 1.25352i
\(554\) 11.1189 29.3182i 0.472398 1.24561i
\(555\) 4.41690 + 5.40972i 0.187487 + 0.229630i
\(556\) −0.553532 13.7357i −0.0234750 0.582525i
\(557\) 0.619326 + 15.3684i 0.0262417 + 0.651180i 0.957774 + 0.287522i \(0.0928314\pi\)
−0.931532 + 0.363658i \(0.881528\pi\)
\(558\) 6.02434 1.48487i 0.255031 0.0628594i
\(559\) 14.6829 + 24.9707i 0.621019 + 1.05615i
\(560\) −47.3116 11.6613i −1.99928 0.492778i
\(561\) 0.430246 2.10748i 0.0181650 0.0889780i
\(562\) 30.5249 13.0054i 1.28761 0.548601i
\(563\) 18.0632 11.4224i 0.761271 0.481399i −0.0965619 0.995327i \(-0.530785\pi\)
0.857833 + 0.513928i \(0.171810\pi\)
\(564\) 4.74465 2.49019i 0.199786 0.104856i
\(565\) 26.6105 + 4.32462i 1.11951 + 0.181938i
\(566\) 20.7802 6.93745i 0.873457 0.291603i
\(567\) 0.357360 + 2.94312i 0.0150077 + 0.123600i
\(568\) −6.29263 + 21.7247i −0.264033 + 0.911548i
\(569\) 5.61750 27.5163i 0.235498 1.15354i −0.674289 0.738468i \(-0.735550\pi\)
0.909786 0.415077i \(-0.136245\pi\)
\(570\) −43.1480 14.4049i −1.80727 0.603356i
\(571\) −35.8740 18.8281i −1.50128 0.787933i −0.504150 0.863616i \(-0.668194\pi\)
−0.997132 + 0.0756830i \(0.975886\pi\)
\(572\) −2.88589 + 0.989030i −0.120665 + 0.0413534i
\(573\) 7.55236 3.96378i 0.315504 0.165589i
\(574\) 8.85491 1.43906i 0.369597 0.0600653i
\(575\) −5.76002 + 4.32837i −0.240209 + 0.180506i
\(576\) −0.112887 + 2.80126i −0.00470363 + 0.116719i
\(577\) −17.6949 −0.736647 −0.368324 0.929698i \(-0.620068\pi\)
−0.368324 + 0.929698i \(0.620068\pi\)
\(578\) −0.870015 + 21.5892i −0.0361878 + 0.897992i
\(579\) 3.00104 + 14.7001i 0.124719 + 0.610915i
\(580\) −4.33189 6.27582i −0.179872 0.260589i
\(581\) 10.8731 3.62996i 0.451091 0.150596i
\(582\) −0.748792 + 1.57804i −0.0310384 + 0.0654121i
\(583\) 5.64360 6.91216i 0.233734 0.286272i
\(584\) −4.68953 12.3653i −0.194054 0.511678i
\(585\) 9.49871 7.25673i 0.392723 0.300029i
\(586\) −4.32844 + 11.4132i −0.178806 + 0.471474i
\(587\) −14.9739 25.9355i −0.618037 1.07047i −0.989843 0.142161i \(-0.954595\pi\)
0.371806 0.928310i \(-0.378739\pi\)
\(588\) 0.898619 1.10061i 0.0370584 0.0453883i
\(589\) 24.3599 + 18.3053i 1.00373 + 0.754255i
\(590\) −71.1372 37.3357i −2.92867 1.53709i
\(591\) −22.6329 + 1.82712i −0.930995 + 0.0751577i
\(592\) −10.4094 + 0.840336i −0.427825 + 0.0345376i
\(593\) 5.07935 + 2.66585i 0.208584 + 0.109473i 0.565780 0.824556i \(-0.308575\pi\)
−0.357196 + 0.934029i \(0.616267\pi\)
\(594\) 1.42411 + 1.07015i 0.0584318 + 0.0439087i
\(595\) 12.5463 15.3664i 0.514347 0.629960i
\(596\) −4.45984 7.72467i −0.182682 0.316415i
\(597\) 8.34714 22.0096i 0.341626 0.900793i
\(598\) 1.39321 7.11255i 0.0569725 0.290854i
\(599\) −16.3344 43.0704i −0.667407 1.75981i −0.649971 0.759959i \(-0.725219\pi\)
−0.0174362 0.999848i \(-0.505550\pi\)
\(600\) 7.63873 9.35574i 0.311850 0.381947i
\(601\) 6.06212 12.7756i 0.247279 0.521129i −0.741420 0.671041i \(-0.765848\pi\)
0.988699 + 0.149911i \(0.0478988\pi\)
\(602\) −37.7649 + 12.6078i −1.53918 + 0.513855i
\(603\) 0.679491 + 0.984413i 0.0276710 + 0.0400884i
\(604\) 1.63301 + 7.99900i 0.0664461 + 0.325475i
\(605\) −1.31681 + 32.6763i −0.0535359 + 1.32848i
\(606\) −7.69647 −0.312648
\(607\) 0.926586 22.9930i 0.0376090 0.933257i −0.864732 0.502234i \(-0.832512\pi\)
0.902341 0.431023i \(-0.141847\pi\)
\(608\) 27.9204 20.9808i 1.13232 0.850884i
\(609\) −8.47830 + 1.37786i −0.343558 + 0.0558336i
\(610\) 42.3572 22.2308i 1.71499 0.900098i
\(611\) −20.4638 + 13.1695i −0.827876 + 0.532780i
\(612\) 1.41881 + 0.744647i 0.0573519 + 0.0301006i
\(613\) −30.0969 10.0478i −1.21560 0.405828i −0.364687 0.931130i \(-0.618824\pi\)
−0.850916 + 0.525303i \(0.823952\pi\)
\(614\) −9.48538 + 46.4625i −0.382799 + 1.87507i
\(615\) −1.66978 + 5.76473i −0.0673319 + 0.232457i
\(616\) 0.767784 + 6.32327i 0.0309349 + 0.254772i
\(617\) 3.09716 1.03398i 0.124687 0.0416266i −0.253640 0.967299i \(-0.581628\pi\)
0.378327 + 0.925672i \(0.376500\pi\)
\(618\) −16.4460 2.67274i −0.661556 0.107513i
\(619\) 26.4507 13.8824i 1.06314 0.557980i 0.159909 0.987132i \(-0.448880\pi\)
0.903232 + 0.429152i \(0.141188\pi\)
\(620\) 8.25773 5.22187i 0.331639 0.209716i
\(621\) −1.10637 + 0.471381i −0.0443971 + 0.0189159i
\(622\) −8.66497 + 42.4438i −0.347434 + 1.70184i
\(623\) −49.4350 12.1846i −1.98057 0.488167i
\(624\) 0.861752 + 17.8538i 0.0344977 + 0.714726i
\(625\) 18.5076 4.56172i 0.740306 0.182469i
\(626\) −0.230740 5.72577i −0.00922224 0.228848i
\(627\) 0.352261 + 8.74126i 0.0140679 + 0.349092i
\(628\) 6.04109 + 7.39900i 0.241066 + 0.295252i
\(629\) 1.50764 3.97533i 0.0601137 0.158507i
\(630\) 7.04307 + 14.8430i 0.280603 + 0.591357i
\(631\) −13.3073 + 45.9421i −0.529755 + 1.82893i 0.0289786 + 0.999580i \(0.490775\pi\)
−0.558734 + 0.829347i \(0.688713\pi\)
\(632\) 12.6033 18.2590i 0.501331 0.726304i
\(633\) −18.2652 7.78208i −0.725977 0.309310i
\(634\) 0.830863 0.135028i 0.0329978 0.00536266i
\(635\) 40.8073 + 25.8050i 1.61939 + 1.02404i
\(636\) 3.77622 + 5.47080i 0.149737 + 0.216931i
\(637\) −3.62327 + 5.33955i −0.143559 + 0.211561i
\(638\) −2.93181 + 4.24746i −0.116071 + 0.168159i
\(639\) 10.3215 4.39757i 0.408311 0.173965i
\(640\) 12.1710 + 42.0190i 0.481099 + 1.66095i
\(641\) 15.1865 1.22598i 0.599830 0.0484233i 0.223177 0.974778i \(-0.428357\pi\)
0.376653 + 0.926355i \(0.377075\pi\)
\(642\) −13.5780 + 12.0290i −0.535880 + 0.474748i
\(643\) −10.6824 + 6.75515i −0.421273 + 0.266397i −0.728239 0.685324i \(-0.759661\pi\)
0.306965 + 0.951721i \(0.400686\pi\)
\(644\) 2.60413 + 1.10951i 0.102617 + 0.0437210i
\(645\) 3.21057 26.4415i 0.126416 1.04113i
\(646\) 5.53927 + 27.1331i 0.217940 + 1.06754i
\(647\) 10.0700 + 0.812931i 0.395891 + 0.0319596i 0.276809 0.960925i \(-0.410723\pi\)
0.119082 + 0.992884i \(0.462005\pi\)
\(648\) 1.61165 1.21108i 0.0633117 0.0475757i
\(649\) −1.86238 + 15.3381i −0.0731048 + 0.602072i
\(650\) 20.2742 29.8777i 0.795219 1.17190i
\(651\) −1.32653 10.9249i −0.0519906 0.428181i
\(652\) 1.05855 + 1.10207i 0.0414560 + 0.0431603i
\(653\) 0.984412 + 1.70505i 0.0385230 + 0.0667238i 0.884644 0.466267i \(-0.154401\pi\)
−0.846121 + 0.532991i \(0.821068\pi\)
\(654\) −6.42459 + 11.1277i −0.251222 + 0.435128i
\(655\) 35.5067 8.75162i 1.38736 0.341954i
\(656\) −5.67596 6.95179i −0.221609 0.271422i
\(657\) −3.27997 + 5.68108i −0.127964 + 0.221640i
\(658\) −11.8604 31.2734i −0.462368 1.21917i
\(659\) 30.0002 31.2335i 1.16864 1.21668i 0.196954 0.980413i \(-0.436895\pi\)
0.971687 0.236272i \(-0.0759255\pi\)
\(660\) 2.66072 + 0.888280i 0.103568 + 0.0345762i
\(661\) 4.12934 + 14.2562i 0.160613 + 0.554500i 0.999941 + 0.0108746i \(0.00346157\pi\)
−0.839328 + 0.543625i \(0.817051\pi\)
\(662\) −28.1268 + 24.9182i −1.09318 + 0.968472i
\(663\) −6.71718 2.79902i −0.260874 0.108705i
\(664\) −5.83436 5.16880i −0.226417 0.200588i
\(665\) −34.5886 + 72.8940i −1.34129 + 2.82671i
\(666\) 2.43916 + 2.53943i 0.0945154 + 0.0984009i
\(667\) −1.49366 3.14782i −0.0578347 0.121884i
\(668\) −1.31021 0.322937i −0.0506934 0.0124948i
\(669\) 0.313354 0.326236i 0.0121150 0.0126130i
\(670\) 5.29911 + 3.98202i 0.204722 + 0.153839i
\(671\) −6.88618 6.10062i −0.265838 0.235512i
\(672\) −12.4504 2.02338i −0.480283 0.0780536i
\(673\) 29.1728 + 18.4478i 1.12453 + 0.711109i 0.961307 0.275481i \(-0.0888370\pi\)
0.163222 + 0.986589i \(0.447811\pi\)
\(674\) −38.6111 3.11701i −1.48724 0.120063i
\(675\) −5.99120 −0.230601
\(676\) 1.40685 + 10.2246i 0.0541095 + 0.393253i
\(677\) 18.0232 0.692688 0.346344 0.938108i \(-0.387423\pi\)
0.346344 + 0.938108i \(0.387423\pi\)
\(678\) 13.5484 + 1.09374i 0.520322 + 0.0420047i
\(679\) 2.61848 + 1.65583i 0.100488 + 0.0635448i
\(680\) −13.3146 2.16383i −0.510592 0.0829792i
\(681\) 3.73677 + 3.31049i 0.143193 + 0.126858i
\(682\) −5.28631 3.97240i −0.202423 0.152111i
\(683\) 24.1237 25.1154i 0.923068 0.961015i −0.0762814 0.997086i \(-0.524305\pi\)
0.999349 + 0.0360709i \(0.0114842\pi\)
\(684\) −6.32770 1.55964i −0.241945 0.0596342i
\(685\) 18.2925 + 38.5506i 0.698921 + 1.47294i
\(686\) 17.8862 + 18.6215i 0.682897 + 0.710971i
\(687\) 0.888131 1.87170i 0.0338843 0.0714097i
\(688\) 29.8129 + 26.4119i 1.13661 + 1.00695i
\(689\) −19.2786 23.2324i −0.734456 0.885083i
\(690\) −4.98827 + 4.41922i −0.189900 + 0.168237i
\(691\) −3.22966 11.1501i −0.122862 0.424169i 0.875380 0.483435i \(-0.160611\pi\)
−0.998242 + 0.0592664i \(0.981124\pi\)
\(692\) −12.6321 4.21720i −0.480199 0.160314i
\(693\) 2.18875 2.27873i 0.0831437 0.0865617i
\(694\) −19.5439 51.5331i −0.741877 1.95617i
\(695\) 28.7027 49.7145i 1.08876 1.88578i
\(696\) 3.69394 + 4.52426i 0.140018 + 0.171491i
\(697\) 3.54753 0.874388i 0.134372 0.0331198i
\(698\) 4.85321 8.40601i 0.183697 0.318172i
\(699\) −0.907447 1.57174i −0.0343228 0.0594488i
\(700\) 9.76867 + 10.1703i 0.369221 + 0.384400i
\(701\) −5.79340 47.7129i −0.218814 1.80209i −0.526044 0.850457i \(-0.676325\pi\)
0.307230 0.951635i \(-0.400598\pi\)
\(702\) 4.47911 4.03218i 0.169053 0.152185i
\(703\) −2.08434 + 17.1661i −0.0786126 + 0.647433i
\(704\) 2.38859 1.79491i 0.0900235 0.0676483i
\(705\) 22.3036 + 1.80053i 0.840002 + 0.0678120i
\(706\) 11.0246 + 54.0020i 0.414916 + 2.03239i
\(707\) −1.64547 + 13.5517i −0.0618844 + 0.509664i
\(708\) −10.5890 4.51153i −0.397957 0.169554i
\(709\) −15.3602 + 9.71321i −0.576865 + 0.364787i −0.790813 0.612058i \(-0.790342\pi\)
0.213948 + 0.976845i \(0.431368\pi\)
\(710\) 46.5362 41.2275i 1.74647 1.54724i
\(711\) −10.9696 + 0.885557i −0.411392 + 0.0332110i
\(712\) 9.63215 + 33.2540i 0.360980 + 1.24625i
\(713\) 4.10686 1.74977i 0.153803 0.0655295i
\(714\) 5.68163 8.23127i 0.212630 0.308047i
\(715\) −12.3929 2.95023i −0.463468 0.110332i
\(716\) 5.21235 + 7.55140i 0.194795 + 0.282209i
\(717\) 2.26320 + 1.43116i 0.0845206 + 0.0534476i
\(718\) 38.2964 6.22378i 1.42921 0.232269i
\(719\) 8.39730 + 3.57775i 0.313166 + 0.133428i 0.542831 0.839842i \(-0.317353\pi\)
−0.229664 + 0.973270i \(0.573763\pi\)
\(720\) 9.33653 13.5263i 0.347952 0.504096i
\(721\) −8.22217 + 28.3862i −0.306209 + 1.05716i
\(722\) −34.6699 73.0654i −1.29028 2.71921i
\(723\) −10.0253 + 26.4345i −0.372845 + 0.983111i
\(724\) 11.3531 + 13.9050i 0.421934 + 0.516775i
\(725\) −0.698931 17.3438i −0.0259576 0.644132i
\(726\) 0.663906 + 16.4747i 0.0246399 + 0.611432i
\(727\) −18.6516 + 4.59719i −0.691748 + 0.170501i −0.569490 0.821998i \(-0.692859\pi\)
−0.122257 + 0.992498i \(0.539013\pi\)
\(728\) 21.4930 + 1.56316i 0.796584 + 0.0579345i
\(729\) −0.970942 0.239316i −0.0359608 0.00886354i
\(730\) −7.27135 + 35.6174i −0.269125 + 1.31826i
\(731\) −14.9177 + 6.35583i −0.551750 + 0.235079i
\(732\) 5.79242 3.66291i 0.214094 0.135385i
\(733\) −27.8157 + 14.5988i −1.02740 + 0.539219i −0.892219 0.451603i \(-0.850852\pi\)
−0.135176 + 0.990822i \(0.543160\pi\)
\(734\) 6.41198 + 1.04205i 0.236671 + 0.0384627i
\(735\) 5.62801 1.87890i 0.207592 0.0693044i
\(736\) −0.616734 5.07926i −0.0227331 0.187224i
\(737\) 0.354666 1.22445i 0.0130643 0.0451031i
\(738\) −0.605262 + 2.96477i −0.0222800 + 0.109135i
\(739\) 45.0165 + 15.0287i 1.65596 + 0.552840i 0.982480 0.186367i \(-0.0596715\pi\)
0.673478 + 0.739207i \(0.264800\pi\)
\(740\) 4.90949 + 2.57670i 0.180476 + 0.0947213i
\(741\) 29.2507 + 4.51523i 1.07455 + 0.165871i
\(742\) 36.7405 19.2829i 1.34879 0.707898i
\(743\) 20.9418 3.40337i 0.768280 0.124858i 0.236375 0.971662i \(-0.424041\pi\)
0.531905 + 0.846804i \(0.321476\pi\)
\(744\) −5.98248 + 4.49554i −0.219328 + 0.164815i
\(745\) 1.49981 37.2173i 0.0549486 1.36354i
\(746\) −20.2665 −0.742010
\(747\) −0.155686 + 3.86330i −0.00569625 + 0.141351i
\(748\) −0.341579 1.67316i −0.0124894 0.0611769i
\(749\) 18.2774 + 26.4794i 0.667842 + 0.967537i
\(750\) −5.21007 + 1.73938i −0.190245 + 0.0635131i
\(751\) 5.77771 12.1763i 0.210831 0.444318i −0.770294 0.637689i \(-0.779891\pi\)
0.981126 + 0.193371i \(0.0619420\pi\)
\(752\) −21.1617 + 25.9184i −0.771689 + 0.945147i
\(753\) −3.23972 8.54245i −0.118062 0.311304i
\(754\) 12.1952 + 12.4961i 0.444123 + 0.455081i
\(755\) −12.0891 + 31.8764i −0.439969 + 1.16010i
\(756\) 1.17688 + 2.03841i 0.0428026 + 0.0741363i
\(757\) 28.1127 34.4318i 1.02177 1.25144i 0.0542848 0.998525i \(-0.482712\pi\)
0.967488 0.252918i \(-0.0813904\pi\)
\(758\) 10.2691 + 7.71670i 0.372989 + 0.280283i
\(759\) 1.13485 + 0.595615i 0.0411924 + 0.0216195i
\(760\) 54.6858 4.41469i 1.98366 0.160138i
\(761\) −23.3923 + 1.88842i −0.847970 + 0.0684552i −0.496809 0.867860i \(-0.665495\pi\)
−0.351161 + 0.936315i \(0.614213\pi\)
\(762\) 21.5543 + 11.3126i 0.780831 + 0.409812i
\(763\) 18.2198 + 13.6913i 0.659600 + 0.495658i
\(764\) 4.28265 5.24530i 0.154941 0.189768i
\(765\) 3.34560 + 5.79476i 0.120961 + 0.209510i
\(766\) 10.7987 28.4737i 0.390172 1.02880i
\(767\) 49.7123 + 16.1582i 1.79501 + 0.583437i
\(768\) 5.83283 + 15.3799i 0.210474 + 0.554975i
\(769\) 27.8479 34.1075i 1.00422 1.22995i 0.0311343 0.999515i \(-0.490088\pi\)
0.973088 0.230434i \(-0.0740145\pi\)
\(770\) 7.50603 15.8186i 0.270499 0.570064i
\(771\) 4.74979 1.58571i 0.171060 0.0571081i
\(772\) 6.76642 + 9.80285i 0.243529 + 0.352812i
\(773\) 9.20246 + 45.0766i 0.330989 + 1.62129i 0.715805 + 0.698300i \(0.246060\pi\)
−0.384816 + 0.922993i \(0.625735\pi\)
\(774\) 0.540736 13.4182i 0.0194364 0.482308i
\(775\) 22.2394 0.798863
\(776\) 0.0848263 2.10494i 0.00304509 0.0755631i
\(777\) 4.99283 3.75187i 0.179117 0.134597i
\(778\) 21.4056 3.47875i 0.767428 0.124719i
\(779\) −13.1582 + 6.90595i −0.471441 + 0.247431i
\(780\) 4.67952 8.25610i 0.167554 0.295616i
\(781\) −10.5872 5.55657i −0.378838 0.198830i
\(782\) 3.84827 + 1.28474i 0.137614 + 0.0459422i
\(783\) 0.579520 2.83868i 0.0207104 0.101446i
\(784\) −2.46847 + 8.52214i −0.0881596 + 0.304362i
\(785\) 4.80795 + 39.5970i 0.171603 + 1.41328i
\(786\) 17.4886 5.83856i 0.623799 0.208255i
\(787\) 5.44842 + 0.885454i 0.194215 + 0.0315630i 0.256741 0.966480i \(-0.417351\pi\)
−0.0625255 + 0.998043i \(0.519915\pi\)
\(788\) −15.9622 + 8.37761i −0.568630 + 0.298440i
\(789\) 19.3144 12.2137i 0.687612 0.434820i
\(790\) −56.1059 + 23.9045i −1.99616 + 0.850483i
\(791\) 4.82240 23.6217i 0.171465 0.839891i
\(792\) −2.08606 0.514167i −0.0741248 0.0182701i
\(793\) −24.7328 + 18.8951i −0.878288 + 0.670986i
\(794\) −10.8242 + 2.66792i −0.384136 + 0.0946810i
\(795\) 1.11775 + 27.7367i 0.0396425 + 0.983720i
\(796\) −0.752497 18.6730i −0.0266716 0.661848i
\(797\) 16.1229 + 19.7469i 0.571102 + 0.699473i 0.976707 0.214575i \(-0.0688368\pi\)
−0.405606 + 0.914048i \(0.632939\pi\)
\(798\) −14.4250 + 38.0356i −0.510640 + 1.34645i
\(799\) −5.83970 12.3069i −0.206594 0.435387i
\(800\) 7.09176 24.4836i 0.250732 0.865626i
\(801\) 9.75556 14.1334i 0.344696 0.499378i
\(802\) 33.0255 + 14.0709i 1.16617 + 0.496859i
\(803\) 6.90062 1.12146i 0.243518 0.0395755i
\(804\) 0.802629 + 0.507552i 0.0283065 + 0.0179000i
\(805\) 6.71475 + 9.72799i 0.236664 + 0.342867i
\(806\) −16.6265 + 14.9675i −0.585644 + 0.527208i
\(807\) −15.8667 + 22.9869i −0.558535 + 0.809178i
\(808\) 8.53979 3.63847i 0.300429 0.128001i
\(809\) 0.251853 + 0.869496i 0.00885467 + 0.0305699i 0.964824 0.262897i \(-0.0846780\pi\)
−0.955969 + 0.293467i \(0.905191\pi\)
\(810\) −5.52355 + 0.445907i −0.194078 + 0.0156676i
\(811\) −33.6818 + 29.8395i −1.18273 + 1.04781i −0.184846 + 0.982767i \(0.559179\pi\)
−0.997883 + 0.0650392i \(0.979283\pi\)
\(812\) −5.76366 + 3.64472i −0.202265 + 0.127904i
\(813\) −5.71227 2.43377i −0.200338 0.0853561i
\(814\) 0.452321 3.72520i 0.0158538 0.130568i
\(815\) 1.27639 + 6.25219i 0.0447101 + 0.219005i
\(816\) −9.97325 0.805124i −0.349134 0.0281850i
\(817\) 52.7238 39.6193i 1.84457 1.38610i
\(818\) 1.99264 16.4108i 0.0696709 0.573791i
\(819\) −6.14211 8.74874i −0.214623 0.305706i
\(820\) 0.574338 + 4.73010i 0.0200567 + 0.165182i
\(821\) 6.75366 + 7.03131i 0.235704 + 0.245394i 0.828541 0.559929i \(-0.189171\pi\)
−0.592836 + 0.805323i \(0.701992\pi\)
\(822\) 10.7568 + 18.6312i 0.375185 + 0.649839i
\(823\) 0.620399 1.07456i 0.0216257 0.0374569i −0.855010 0.518612i \(-0.826449\pi\)
0.876636 + 0.481155i \(0.159782\pi\)
\(824\) 19.5116 4.80917i 0.679718 0.167536i
\(825\) 4.03818 + 4.94587i 0.140591 + 0.172193i
\(826\) −35.9223 + 62.2192i −1.24990 + 2.16488i
\(827\) 5.40318 + 14.2470i 0.187887 + 0.495417i 0.995551 0.0942258i \(-0.0300376\pi\)
−0.807664 + 0.589643i \(0.799268\pi\)
\(828\) −0.661390 + 0.688580i −0.0229849 + 0.0239298i
\(829\) −0.121826 0.0406714i −0.00423118 0.00141258i 0.314552 0.949240i \(-0.398146\pi\)
−0.318783 + 0.947828i \(0.603274\pi\)
\(830\) 5.96108 + 20.5800i 0.206912 + 0.714343i
\(831\) 14.0414 12.4396i 0.487090 0.431524i
\(832\) −4.40584 9.09759i −0.152745 0.315402i
\(833\) −2.70370 2.39527i −0.0936775 0.0829911i
\(834\) 12.4075 26.1482i 0.429635 0.905437i
\(835\) −3.90351 4.06398i −0.135086 0.140640i
\(836\) 2.97747 + 6.27488i 0.102978 + 0.217021i
\(837\) 3.60415 + 0.888343i 0.124578 + 0.0307056i
\(838\) −26.7313 + 27.8302i −0.923417 + 0.961379i
\(839\) −18.1960 13.6734i −0.628194 0.472057i 0.238335 0.971183i \(-0.423398\pi\)
−0.866530 + 0.499126i \(0.833655\pi\)
\(840\) −14.8317 13.1398i −0.511743 0.453365i
\(841\) −20.3392 3.30545i −0.701353 0.113981i
\(842\) 6.79326 + 4.29580i 0.234111 + 0.148043i
\(843\) 19.7860 + 1.59729i 0.681467 + 0.0550137i
\(844\) −15.7623 −0.542562
\(845\) −17.8545 + 39.2266i −0.614214 + 1.34944i
\(846\) 11.2816 0.387868
\(847\) 29.1500 + 2.35323i 1.00161 + 0.0808580i
\(848\) −35.0836 22.1855i −1.20478 0.761855i
\(849\) 12.9368 + 2.10244i 0.443991 + 0.0721556i
\(850\) 15.1287 + 13.4028i 0.518909 + 0.459713i
\(851\) 2.02527 + 1.52189i 0.0694253 + 0.0521697i
\(852\) 6.17019 6.42385i 0.211387 0.220077i
\(853\) 28.1881 + 6.94775i 0.965143 + 0.237886i 0.690236 0.723584i \(-0.257507\pi\)
0.274907 + 0.961471i \(0.411353\pi\)
\(854\) −18.3388 38.6482i −0.627541 1.32251i
\(855\) −18.8522 19.6272i −0.644730 0.671235i
\(856\) 9.37908 19.7660i 0.320571 0.675588i
\(857\) −5.65438 5.00934i −0.193150 0.171116i 0.561005 0.827812i \(-0.310415\pi\)
−0.754155 + 0.656697i \(0.771953\pi\)
\(858\) −6.34766 0.979846i −0.216705 0.0334514i
\(859\) −15.5464 + 13.7730i −0.530438 + 0.469927i −0.885319 0.464984i \(-0.846060\pi\)
0.354881 + 0.934912i \(0.384521\pi\)
\(860\) −5.88332 20.3116i −0.200619 0.692619i
\(861\) 5.09087 + 1.69958i 0.173496 + 0.0579216i
\(862\) 10.6847 11.1240i 0.363923 0.378884i
\(863\) 5.73473 + 15.1212i 0.195212 + 0.514733i 0.996504 0.0835407i \(-0.0266228\pi\)
−0.801292 + 0.598274i \(0.795854\pi\)
\(864\) 2.12729 3.68457i 0.0723718 0.125352i
\(865\) −35.1715 43.0773i −1.19587 1.46467i
\(866\) −28.1467 + 6.93753i −0.956463 + 0.235747i
\(867\) −6.46327 + 11.1947i −0.219504 + 0.380192i
\(868\) −4.36858 7.56661i −0.148279 0.256827i
\(869\) 8.12475 + 8.45877i 0.275613 + 0.286944i
\(870\) −1.93522 15.9380i −0.0656102 0.540349i
\(871\) −3.83460 1.97382i −0.129930 0.0668803i
\(872\) 1.86798 15.3842i 0.0632578 0.520975i
\(873\) −0.835402 + 0.627764i −0.0282741 + 0.0212466i
\(874\) −16.4474 1.32777i −0.556341 0.0449125i
\(875\) 1.94875 + 9.54560i 0.0658797 + 0.322700i
\(876\) −0.627760 + 5.17007i −0.0212100 + 0.174680i
\(877\) 12.1777 + 5.18843i 0.411212 + 0.175201i 0.587658 0.809109i \(-0.300050\pi\)
−0.176446 + 0.984310i \(0.556460\pi\)
\(878\) −21.8827 + 13.8378i −0.738505 + 0.467002i
\(879\) −5.46611 + 4.84255i −0.184367 + 0.163335i
\(880\) −17.4593 + 1.40946i −0.588552 + 0.0475128i
\(881\) −9.01060 31.1082i −0.303575 1.04806i −0.956764 0.290866i \(-0.906056\pi\)
0.653189 0.757195i \(-0.273431\pi\)
\(882\) 2.75209 1.17256i 0.0926677 0.0394820i
\(883\) −4.59024 + 6.65012i −0.154474 + 0.223794i −0.892578 0.450892i \(-0.851106\pi\)
0.738104 + 0.674687i \(0.235721\pi\)
\(884\) −5.77716 + 0.0459455i −0.194307 + 0.00154532i
\(885\) −27.3037 39.5562i −0.917803 1.32967i
\(886\) −48.3908 30.6005i −1.62572 1.02804i
\(887\) −42.1062 + 6.84293i −1.41379 + 0.229763i −0.818850 0.574008i \(-0.805388\pi\)
−0.594939 + 0.803771i \(0.702824\pi\)
\(888\) −3.90692 1.66458i −0.131108 0.0558598i
\(889\) 24.5271 35.5336i 0.822611 1.19176i
\(890\) 26.4770 91.4091i 0.887510 3.06404i
\(891\) 0.456872 + 0.962837i 0.0153058 + 0.0322563i
\(892\) 0.127348 0.335790i 0.00426394 0.0112431i
\(893\) 35.0400 + 42.9162i 1.17257 + 1.43614i
\(894\) −0.756170 18.7642i −0.0252901 0.627567i
\(895\) 1.54284 + 38.2853i 0.0515716 + 1.27974i
\(896\) 37.9838 9.36215i 1.26895 0.312768i
\(897\) 2.71552 3.38043i 0.0906685 0.112869i
\(898\) 5.27009 + 1.29896i 0.175865 + 0.0433469i
\(899\) −2.15119 + 10.5372i −0.0717461 + 0.351435i
\(900\) −4.37589 + 1.86439i −0.145863 + 0.0621464i
\(901\) 14.2831 9.03206i 0.475838 0.300901i
\(902\) 2.85544 1.49865i 0.0950759 0.0498997i
\(903\) −23.5108 3.82087i −0.782390 0.127151i
\(904\) −15.5500 + 5.19134i −0.517184 + 0.172661i
\(905\) 9.03563 + 74.4151i 0.300354 + 2.47364i
\(906\) −4.78210 + 16.5097i −0.158875 + 0.548499i
\(907\) 0.494586 2.42264i 0.0164224 0.0804425i −0.970754 0.240078i \(-0.922827\pi\)
0.987176 + 0.159636i \(0.0510320\pi\)
\(908\) 3.75947 + 1.25509i 0.124762 + 0.0416518i
\(909\) −4.07710 2.13983i −0.135229 0.0709737i
\(910\) −47.6375 35.2080i −1.57917 1.16713i
\(911\) 28.2983 14.8521i 0.937564 0.492072i 0.0745308 0.997219i \(-0.476254\pi\)
0.863033 + 0.505147i \(0.168562\pi\)
\(912\) 40.1682 6.52797i 1.33010 0.216163i
\(913\) 3.29418 2.47541i 0.109021 0.0819243i
\(914\) 2.27251 56.3917i 0.0751679 1.86527i
\(915\) 28.6190 0.946114
\(916\) 0.0662282 1.64344i 0.00218824 0.0543007i
\(917\) −6.54135 32.0417i −0.216014 1.05811i
\(918\) 1.91640 + 2.77639i 0.0632507 + 0.0916344i
\(919\) −46.0135 + 15.3615i −1.51784 + 0.506731i −0.948881 0.315633i \(-0.897783\pi\)
−0.568963 + 0.822363i \(0.692655\pi\)
\(920\) 3.44568 7.26163i 0.113601 0.239409i
\(921\) −17.9426 + 21.9757i −0.591229 + 0.724124i
\(922\) −21.4831 56.6463i −0.707508 1.86555i
\(923\) −25.3334 + 31.5364i −0.833859 + 1.03803i
\(924\) 0.889518 2.34547i 0.0292630 0.0771601i
\(925\) 6.31039 + 10.9299i 0.207484 + 0.359373i
\(926\) 17.0648 20.9006i 0.560784 0.686836i
\(927\) −7.96897 5.98830i −0.261735 0.196681i
\(928\) 10.9145 + 5.72839i 0.358287 + 0.188044i
\(929\) 2.42601 0.195848i 0.0795949 0.00642556i −0.0406050 0.999175i \(-0.512929\pi\)
0.120200 + 0.992750i \(0.461646\pi\)
\(930\) 20.5035 1.65521i 0.672336 0.0542766i
\(931\) 13.0084 + 6.82732i 0.426332 + 0.223756i
\(932\) −1.15190 0.865593i −0.0377316 0.0283534i
\(933\) −16.3907 + 20.0750i −0.536608 + 0.657225i
\(934\) −10.6576 18.4595i −0.348727 0.604013i
\(935\) 2.52870 6.66764i 0.0826974 0.218055i
\(936\) −3.06371 + 6.59147i −0.100140 + 0.215449i
\(937\) 2.84619 + 7.50478i 0.0929809 + 0.245171i 0.973436 0.228959i \(-0.0735321\pi\)
−0.880455 + 0.474129i \(0.842763\pi\)
\(938\) 3.74889 4.59156i 0.122406 0.149920i
\(939\) 1.46969 3.09730i 0.0479615 0.101077i
\(940\) 16.8505 5.62554i 0.549604 0.183485i
\(941\) 7.11026 + 10.3010i 0.231788 + 0.335803i 0.921569 0.388216i \(-0.126908\pi\)
−0.689781 + 0.724018i \(0.742293\pi\)
\(942\) 4.02264 + 19.7042i 0.131065 + 0.641997i
\(943\) −0.0876621 + 2.17531i −0.00285467 + 0.0708379i
\(944\) 71.8730 2.33927
\(945\) −0.395774 + 9.82103i −0.0128745 + 0.319478i
\(946\) −11.4415 + 8.59774i −0.371996 + 0.279537i
\(947\) 6.73039 1.09380i 0.218708 0.0355436i −0.0500696 0.998746i \(-0.515944\pi\)
0.268778 + 0.963202i \(0.413380\pi\)
\(948\) −7.73646 + 4.06041i −0.251269 + 0.131876i
\(949\) 0.764402 23.6399i 0.0248135 0.767382i
\(950\) −72.7889 38.2026i −2.36158 1.23946i
\(951\) 0.477680 + 0.159473i 0.0154898 + 0.00517127i
\(952\) −2.41290 + 11.8192i −0.0782025 + 0.383061i
\(953\) −5.62101 + 19.4060i −0.182082 + 0.628621i 0.816595 + 0.577211i \(0.195859\pi\)
−0.998678 + 0.0514104i \(0.983628\pi\)
\(954\) 1.68698 + 13.8936i 0.0546181 + 0.449820i
\(955\) 26.8221 8.95452i 0.867941 0.289761i
\(956\) 2.09837 + 0.341018i 0.0678660 + 0.0110293i
\(957\) −2.73400 + 1.43491i −0.0883776 + 0.0463842i
\(958\) −29.9471 + 18.9374i −0.967547 + 0.611840i
\(959\) 35.1050 14.9569i 1.13360 0.482982i
\(960\) −1.85915 + 9.10672i −0.0600038 + 0.293918i
\(961\) 16.7205 + 4.12124i 0.539372 + 0.132943i
\(962\) −12.0738 3.92437i −0.389274 0.126527i
\(963\) −10.5372 + 2.59718i −0.339555 + 0.0836928i
\(964\) 0.903784 + 22.4272i 0.0291089 + 0.722330i
\(965\) 2.00284 + 49.7000i 0.0644738 + 1.59990i
\(966\) 3.76911 + 4.61633i 0.121269 + 0.148528i
\(967\) −16.3423 + 43.0911i −0.525532 + 1.38571i 0.365091 + 0.930972i \(0.381038\pi\)
−0.890623 + 0.454743i \(0.849731\pi\)
\(968\) −8.52497 17.9660i −0.274003 0.577449i
\(969\) −4.60940 + 15.9135i −0.148075 + 0.511215i
\(970\) −3.28954 + 4.76572i −0.105621 + 0.153018i
\(971\) 37.3576 + 15.9166i 1.19886 + 0.510787i 0.896772 0.442493i \(-0.145906\pi\)
0.302089 + 0.953280i \(0.402316\pi\)
\(972\) −0.783635 + 0.127353i −0.0251351 + 0.00408485i
\(973\) −43.3882 27.4370i −1.39096 0.879591i
\(974\) 33.5341 + 48.5825i 1.07450 + 1.55668i
\(975\) 19.0468 10.1905i 0.609986 0.326359i
\(976\) −24.3105 + 35.2199i −0.778161 + 1.12736i
\(977\) 8.99495 3.83239i 0.287774 0.122609i −0.243256 0.969962i \(-0.578215\pi\)
0.531030 + 0.847353i \(0.321805\pi\)
\(978\) 0.895092 + 3.09021i 0.0286219 + 0.0988142i
\(979\) −18.2428 + 1.47271i −0.583044 + 0.0470682i
\(980\) 3.52592 3.12370i 0.112632 0.0997828i
\(981\) −6.49716 + 4.10855i −0.207438 + 0.131176i
\(982\) 35.1308 + 14.9678i 1.12107 + 0.477643i
\(983\) 1.07036 8.81524i 0.0341393 0.281163i −0.965635 0.259903i \(-0.916309\pi\)
0.999774 0.0212594i \(-0.00676758\pi\)
\(984\) −0.729997 3.57576i −0.0232715 0.113991i
\(985\) −75.0350 6.05745i −2.39081 0.193006i
\(986\) −7.81373 + 5.87164i −0.248840 + 0.186991i
\(987\) 2.41195 19.8642i 0.0767733 0.632285i
\(988\) 22.7694 5.80461i 0.724391 0.184669i
\(989\) −1.16462 9.59148i −0.0370326 0.304991i
\(990\) 4.09108 + 4.25927i 0.130023 + 0.135368i
\(991\) 15.6360 + 27.0823i 0.496694 + 0.860299i 0.999993 0.00381360i \(-0.00121391\pi\)
−0.503299 + 0.864112i \(0.667881\pi\)
\(992\) −7.89652 + 13.6772i −0.250715 + 0.434250i
\(993\) −21.8277 + 5.38005i −0.692682 + 0.170731i
\(994\) −35.1625 43.0663i −1.11529 1.36598i
\(995\) 39.0198 67.5843i 1.23701 2.14257i
\(996\) 1.08850 + 2.87015i 0.0344906 + 0.0909442i
\(997\) 1.60292 1.66882i 0.0507650 0.0528520i −0.695336 0.718685i \(-0.744744\pi\)
0.746101 + 0.665833i \(0.231924\pi\)
\(998\) −48.2679 16.1142i −1.52789 0.510086i
\(999\) 0.586080 + 2.02338i 0.0185427 + 0.0640170i
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 507.2.q.a.16.12 360
169.74 even 39 inner 507.2.q.a.412.12 yes 360
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
507.2.q.a.16.12 360 1.1 even 1 trivial
507.2.q.a.412.12 yes 360 169.74 even 39 inner