Properties

Label 378.2.bf.a.101.19
Level $378$
Weight $2$
Character 378.101
Analytic conductor $3.018$
Analytic rank $0$
Dimension $144$
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] = [378,2,Mod(5,378)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(378, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([5, 15]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("378.5");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 378.bf (of order \(18\), degree \(6\), 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: \(3.01834519640\)
Analytic rank: \(0\)
Dimension: \(144\)
Relative dimension: \(24\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 101.19
Character \(\chi\) \(=\) 378.101
Dual form 378.2.bf.a.131.19

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.642788 - 0.766044i) q^{2} +(0.433794 + 1.67685i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(-1.92601 + 1.61612i) q^{5} +(1.56338 + 0.745552i) q^{6} +(-2.53339 + 0.762832i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(-2.62365 + 1.45481i) q^{9} +O(q^{10})\) \(q+(0.642788 - 0.766044i) q^{2} +(0.433794 + 1.67685i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(-1.92601 + 1.61612i) q^{5} +(1.56338 + 0.745552i) q^{6} +(-2.53339 + 0.762832i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(-2.62365 + 1.45481i) q^{9} +2.51423i q^{10} +(-3.54893 + 4.22945i) q^{11} +(1.57605 - 0.718386i) q^{12} +(0.369054 - 1.01397i) q^{13} +(-1.04407 + 2.43103i) q^{14} +(-3.54548 - 2.52857i) q^{15} +(-0.939693 + 0.342020i) q^{16} +5.95585 q^{17} +(-0.571994 + 2.94497i) q^{18} -2.25110i q^{19} +(1.92601 + 1.61612i) q^{20} +(-2.37813 - 3.91721i) q^{21} +(0.958739 + 5.43728i) q^{22} +(0.623128 - 1.71203i) q^{23} +(0.462748 - 1.66909i) q^{24} +(0.229454 - 1.30130i) q^{25} +(-0.539521 - 0.934479i) q^{26} +(-3.57763 - 3.76837i) q^{27} +(1.19116 + 2.36244i) q^{28} +(2.98537 + 8.20224i) q^{29} +(-4.21599 + 1.09066i) q^{30} +(2.79075 - 0.492084i) q^{31} +(-0.342020 + 0.939693i) q^{32} +(-8.63166 - 4.11631i) q^{33} +(3.82834 - 4.56244i) q^{34} +(3.64653 - 5.56349i) q^{35} +(1.88830 + 2.33116i) q^{36} +(-3.16212 + 5.47695i) q^{37} +(-1.72444 - 1.44698i) q^{38} +(1.86037 + 0.178995i) q^{39} +(2.47604 - 0.436592i) q^{40} +(2.90079 + 1.05580i) q^{41} +(-4.52939 - 0.696183i) q^{42} +(0.312815 - 1.77406i) q^{43} +(4.78146 + 2.76058i) q^{44} +(2.70203 - 7.04211i) q^{45} +(-0.910952 - 1.57781i) q^{46} +(-1.02128 + 5.79199i) q^{47} +(-0.981149 - 1.42736i) q^{48} +(5.83618 - 3.86511i) q^{49} +(-0.849360 - 1.01223i) q^{50} +(2.58361 + 9.98705i) q^{51} +(-1.06265 - 0.187374i) q^{52} +(-1.83711 - 1.06065i) q^{53} +(-5.18639 + 0.318362i) q^{54} -13.8815i q^{55} +(2.57540 + 0.606066i) q^{56} +(3.77475 - 0.976514i) q^{57} +(8.20224 + 2.98537i) q^{58} +(10.0834 + 3.67006i) q^{59} +(-1.87449 + 3.93070i) q^{60} +(-5.35212 - 0.943723i) q^{61} +(1.41690 - 2.45414i) q^{62} +(5.53695 - 5.68702i) q^{63} +(0.500000 + 0.866025i) q^{64} +(0.927889 + 2.54935i) q^{65} +(-8.70160 + 3.96632i) q^{66} +(1.97593 - 1.65800i) q^{67} +(-1.03422 - 5.86536i) q^{68} +(3.14112 + 0.302223i) q^{69} +(-1.91794 - 6.36955i) q^{70} +(-10.0397 + 5.79644i) q^{71} +(2.99955 + 0.0519161i) q^{72} +(0.374428 - 0.216176i) q^{73} +(2.16302 + 5.94284i) q^{74} +(2.28161 - 0.179736i) q^{75} +(-2.21690 + 0.390899i) q^{76} +(5.76448 - 13.4221i) q^{77} +(1.33294 - 1.31007i) q^{78} +(-10.8017 - 9.06374i) q^{79} +(1.25712 - 2.17739i) q^{80} +(4.76703 - 7.63384i) q^{81} +(2.67338 - 1.54348i) q^{82} +(-6.41894 + 2.33630i) q^{83} +(-3.44474 + 3.02221i) q^{84} +(-11.4710 + 9.62535i) q^{85} +(-1.15793 - 1.37997i) q^{86} +(-12.4589 + 8.56410i) q^{87} +(5.18819 - 1.88835i) q^{88} +15.8030 q^{89} +(-3.65774 - 6.59646i) q^{90} +(-0.161473 + 2.85031i) q^{91} +(-1.79422 - 0.316370i) q^{92} +(2.03576 + 4.46620i) q^{93} +(3.78045 + 4.50537i) q^{94} +(3.63804 + 4.33565i) q^{95} +(-1.72409 - 0.165883i) q^{96} +(9.27207 + 1.63492i) q^{97} +(0.790577 - 6.95521i) q^{98} +(3.15807 - 16.2596i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144 q + 18 q^{6} - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 144 q + 18 q^{6} - 12 q^{9} + 12 q^{11} + 6 q^{14} + 12 q^{15} + 6 q^{21} - 6 q^{23} - 6 q^{29} - 18 q^{30} - 54 q^{35} + 6 q^{36} - 6 q^{39} + 24 q^{42} - 54 q^{47} + 18 q^{49} + 12 q^{50} + 18 q^{51} + 90 q^{53} - 54 q^{54} - 12 q^{56} - 6 q^{57} - 90 q^{59} - 36 q^{60} - 24 q^{63} + 72 q^{64} - 84 q^{65} - 36 q^{69} - 18 q^{70} - 72 q^{71} + 12 q^{72} + 18 q^{74} - 90 q^{75} - 78 q^{77} - 60 q^{78} + 36 q^{79} - 6 q^{84} - 72 q^{85} + 24 q^{86} + 90 q^{87} - 18 q^{91} - 42 q^{92} - 12 q^{93} + 78 q^{95} - 36 q^{98} - 108 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/378\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\)
\(\chi(n)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.642788 0.766044i 0.454519 0.541675i
\(3\) 0.433794 + 1.67685i 0.250451 + 0.968129i
\(4\) −0.173648 0.984808i −0.0868241 0.492404i
\(5\) −1.92601 + 1.61612i −0.861340 + 0.722750i −0.962256 0.272145i \(-0.912267\pi\)
0.100916 + 0.994895i \(0.467823\pi\)
\(6\) 1.56338 + 0.745552i 0.638247 + 0.304370i
\(7\) −2.53339 + 0.762832i −0.957533 + 0.288323i
\(8\) −0.866025 0.500000i −0.306186 0.176777i
\(9\) −2.62365 + 1.45481i −0.874548 + 0.484938i
\(10\) 2.51423i 0.795070i
\(11\) −3.54893 + 4.22945i −1.07004 + 1.27523i −0.110436 + 0.993883i \(0.535225\pi\)
−0.959607 + 0.281344i \(0.909220\pi\)
\(12\) 1.57605 0.718386i 0.454965 0.207380i
\(13\) 0.369054 1.01397i 0.102357 0.281224i −0.877934 0.478782i \(-0.841079\pi\)
0.980291 + 0.197557i \(0.0633008\pi\)
\(14\) −1.04407 + 2.43103i −0.279040 + 0.649721i
\(15\) −3.54548 2.52857i −0.915439 0.652875i
\(16\) −0.939693 + 0.342020i −0.234923 + 0.0855050i
\(17\) 5.95585 1.44450 0.722252 0.691630i \(-0.243107\pi\)
0.722252 + 0.691630i \(0.243107\pi\)
\(18\) −0.571994 + 2.94497i −0.134820 + 0.694135i
\(19\) 2.25110i 0.516437i −0.966086 0.258219i \(-0.916864\pi\)
0.966086 0.258219i \(-0.0831355\pi\)
\(20\) 1.92601 + 1.61612i 0.430670 + 0.361375i
\(21\) −2.37813 3.91721i −0.518949 0.854805i
\(22\) 0.958739 + 5.43728i 0.204404 + 1.15923i
\(23\) 0.623128 1.71203i 0.129931 0.356983i −0.857619 0.514285i \(-0.828057\pi\)
0.987551 + 0.157302i \(0.0502796\pi\)
\(24\) 0.462748 1.66909i 0.0944580 0.340702i
\(25\) 0.229454 1.30130i 0.0458907 0.260259i
\(26\) −0.539521 0.934479i −0.105809 0.183266i
\(27\) −3.57763 3.76837i −0.688515 0.725223i
\(28\) 1.19116 + 2.36244i 0.225108 + 0.446460i
\(29\) 2.98537 + 8.20224i 0.554370 + 1.52312i 0.827685 + 0.561194i \(0.189658\pi\)
−0.273315 + 0.961925i \(0.588120\pi\)
\(30\) −4.21599 + 1.09066i −0.769731 + 0.199126i
\(31\) 2.79075 0.492084i 0.501233 0.0883810i 0.0826855 0.996576i \(-0.473650\pi\)
0.418548 + 0.908195i \(0.362539\pi\)
\(32\) −0.342020 + 0.939693i −0.0604612 + 0.166116i
\(33\) −8.63166 4.11631i −1.50258 0.716557i
\(34\) 3.82834 4.56244i 0.656556 0.782452i
\(35\) 3.64653 5.56349i 0.616376 0.940401i
\(36\) 1.88830 + 2.33116i 0.314717 + 0.388527i
\(37\) −3.16212 + 5.47695i −0.519849 + 0.900405i 0.479885 + 0.877332i \(0.340678\pi\)
−0.999734 + 0.0230734i \(0.992655\pi\)
\(38\) −1.72444 1.44698i −0.279741 0.234731i
\(39\) 1.86037 + 0.178995i 0.297897 + 0.0286621i
\(40\) 2.47604 0.436592i 0.391496 0.0690313i
\(41\) 2.90079 + 1.05580i 0.453027 + 0.164888i 0.558448 0.829539i \(-0.311397\pi\)
−0.105421 + 0.994428i \(0.533619\pi\)
\(42\) −4.52939 0.696183i −0.698899 0.107423i
\(43\) 0.312815 1.77406i 0.0477038 0.270541i −0.951621 0.307273i \(-0.900584\pi\)
0.999325 + 0.0367315i \(0.0116946\pi\)
\(44\) 4.78146 + 2.76058i 0.720832 + 0.416173i
\(45\) 2.70203 7.04211i 0.402794 1.04978i
\(46\) −0.910952 1.57781i −0.134313 0.232636i
\(47\) −1.02128 + 5.79199i −0.148970 + 0.844849i 0.815124 + 0.579287i \(0.196669\pi\)
−0.964094 + 0.265562i \(0.914442\pi\)
\(48\) −0.981149 1.42736i −0.141617 0.206021i
\(49\) 5.83618 3.86511i 0.833739 0.552158i
\(50\) −0.849360 1.01223i −0.120118 0.143151i
\(51\) 2.58361 + 9.98705i 0.361778 + 1.39847i
\(52\) −1.06265 0.187374i −0.147363 0.0259841i
\(53\) −1.83711 1.06065i −0.252346 0.145692i 0.368492 0.929631i \(-0.379874\pi\)
−0.620838 + 0.783939i \(0.713207\pi\)
\(54\) −5.18639 + 0.318362i −0.705778 + 0.0433235i
\(55\) 13.8815i 1.87178i
\(56\) 2.57540 + 0.606066i 0.344152 + 0.0809889i
\(57\) 3.77475 0.976514i 0.499978 0.129342i
\(58\) 8.20224 + 2.98537i 1.07701 + 0.391999i
\(59\) 10.0834 + 3.67006i 1.31275 + 0.477802i 0.901128 0.433554i \(-0.142740\pi\)
0.411621 + 0.911355i \(0.364963\pi\)
\(60\) −1.87449 + 3.93070i −0.241996 + 0.507451i
\(61\) −5.35212 0.943723i −0.685269 0.120831i −0.179835 0.983697i \(-0.557556\pi\)
−0.505434 + 0.862865i \(0.668667\pi\)
\(62\) 1.41690 2.45414i 0.179947 0.311677i
\(63\) 5.53695 5.68702i 0.697590 0.716497i
\(64\) 0.500000 + 0.866025i 0.0625000 + 0.108253i
\(65\) 0.927889 + 2.54935i 0.115090 + 0.316208i
\(66\) −8.70160 + 3.96632i −1.07109 + 0.488220i
\(67\) 1.97593 1.65800i 0.241398 0.202557i −0.514060 0.857754i \(-0.671859\pi\)
0.755458 + 0.655197i \(0.227415\pi\)
\(68\) −1.03422 5.86536i −0.125418 0.711280i
\(69\) 3.14112 + 0.302223i 0.378147 + 0.0363833i
\(70\) −1.91794 6.36955i −0.229237 0.761306i
\(71\) −10.0397 + 5.79644i −1.19150 + 0.687911i −0.958646 0.284601i \(-0.908139\pi\)
−0.232851 + 0.972512i \(0.574805\pi\)
\(72\) 2.99955 + 0.0519161i 0.353500 + 0.00611837i
\(73\) 0.374428 0.216176i 0.0438235 0.0253015i −0.477928 0.878399i \(-0.658612\pi\)
0.521752 + 0.853097i \(0.325279\pi\)
\(74\) 2.16302 + 5.94284i 0.251446 + 0.690841i
\(75\) 2.28161 0.179736i 0.263458 0.0207541i
\(76\) −2.21690 + 0.390899i −0.254296 + 0.0448392i
\(77\) 5.76448 13.4221i 0.656924 1.52959i
\(78\) 1.33294 1.31007i 0.150926 0.148336i
\(79\) −10.8017 9.06374i −1.21529 1.01975i −0.999057 0.0434084i \(-0.986178\pi\)
−0.216233 0.976342i \(-0.569377\pi\)
\(80\) 1.25712 2.17739i 0.140550 0.243440i
\(81\) 4.76703 7.63384i 0.529670 0.848204i
\(82\) 2.67338 1.54348i 0.295226 0.170449i
\(83\) −6.41894 + 2.33630i −0.704570 + 0.256442i −0.669361 0.742938i \(-0.733432\pi\)
−0.0352090 + 0.999380i \(0.511210\pi\)
\(84\) −3.44474 + 3.02221i −0.375852 + 0.329750i
\(85\) −11.4710 + 9.62535i −1.24421 + 1.04402i
\(86\) −1.15793 1.37997i −0.124863 0.148806i
\(87\) −12.4589 + 8.56410i −1.33573 + 0.918168i
\(88\) 5.18819 1.88835i 0.553063 0.201298i
\(89\) 15.8030 1.67512 0.837559 0.546347i \(-0.183982\pi\)
0.837559 + 0.546347i \(0.183982\pi\)
\(90\) −3.65774 6.59646i −0.385560 0.695328i
\(91\) −0.161473 + 2.85031i −0.0169270 + 0.298794i
\(92\) −1.79422 0.316370i −0.187061 0.0329839i
\(93\) 2.03576 + 4.46620i 0.211099 + 0.463124i
\(94\) 3.78045 + 4.50537i 0.389924 + 0.464693i
\(95\) 3.63804 + 4.33565i 0.373255 + 0.444828i
\(96\) −1.72409 0.165883i −0.175964 0.0169304i
\(97\) 9.27207 + 1.63492i 0.941436 + 0.166001i 0.623245 0.782026i \(-0.285814\pi\)
0.318190 + 0.948027i \(0.396925\pi\)
\(98\) 0.790577 6.95521i 0.0798604 0.702583i
\(99\) 3.15807 16.2596i 0.317398 1.63415i
\(100\) −1.32137 −0.132137
\(101\) −6.40493 + 2.33120i −0.637314 + 0.231963i −0.640412 0.768032i \(-0.721236\pi\)
0.00309738 + 0.999995i \(0.499014\pi\)
\(102\) 9.31124 + 4.44039i 0.921950 + 0.439665i
\(103\) 4.98625 + 5.94238i 0.491309 + 0.585520i 0.953550 0.301235i \(-0.0973988\pi\)
−0.462241 + 0.886755i \(0.652954\pi\)
\(104\) −0.826595 + 0.693595i −0.0810543 + 0.0680126i
\(105\) 10.9110 + 3.70127i 1.06480 + 0.361207i
\(106\) −1.99338 + 0.725530i −0.193614 + 0.0704697i
\(107\) −15.5749 + 8.99215i −1.50568 + 0.869304i −0.505700 + 0.862710i \(0.668766\pi\)
−0.999978 + 0.00659411i \(0.997901\pi\)
\(108\) −3.08987 + 4.17764i −0.297323 + 0.401994i
\(109\) 3.60877 6.25057i 0.345657 0.598696i −0.639816 0.768529i \(-0.720989\pi\)
0.985473 + 0.169832i \(0.0543226\pi\)
\(110\) −10.6338 8.92284i −1.01390 0.850759i
\(111\) −10.5557 2.92653i −1.00191 0.277774i
\(112\) 2.11971 1.58330i 0.200294 0.149608i
\(113\) 1.36027 0.239852i 0.127963 0.0225634i −0.109300 0.994009i \(-0.534861\pi\)
0.237263 + 0.971445i \(0.423750\pi\)
\(114\) 1.67831 3.51932i 0.157188 0.329614i
\(115\) 1.56669 + 4.30444i 0.146094 + 0.401391i
\(116\) 7.55923 4.36432i 0.701857 0.405217i
\(117\) 0.506869 + 3.19720i 0.0468600 + 0.295581i
\(118\) 9.29293 5.36527i 0.855483 0.493913i
\(119\) −15.0885 + 4.54331i −1.38316 + 0.416484i
\(120\) 1.80619 + 3.96255i 0.164882 + 0.361730i
\(121\) −3.38321 19.1872i −0.307565 1.74429i
\(122\) −4.16321 + 3.49335i −0.376919 + 0.316273i
\(123\) −0.512073 + 5.32219i −0.0461721 + 0.479885i
\(124\) −0.969217 2.66290i −0.0870383 0.239136i
\(125\) −4.62447 8.00981i −0.413625 0.716419i
\(126\) −0.797427 7.89710i −0.0710404 0.703529i
\(127\) 8.72263 15.1080i 0.774008 1.34062i −0.161342 0.986899i \(-0.551582\pi\)
0.935350 0.353723i \(-0.115085\pi\)
\(128\) 0.984808 + 0.173648i 0.0870455 + 0.0153485i
\(129\) 3.11053 0.245034i 0.273867 0.0215740i
\(130\) 2.54935 + 0.927889i 0.223593 + 0.0813812i
\(131\) −18.3269 6.67046i −1.60123 0.582800i −0.621552 0.783373i \(-0.713498\pi\)
−0.979679 + 0.200572i \(0.935720\pi\)
\(132\) −2.55490 + 9.21531i −0.222376 + 0.802090i
\(133\) 1.71721 + 5.70292i 0.148901 + 0.494506i
\(134\) 2.57939i 0.222826i
\(135\) 12.9807 + 1.47606i 1.11720 + 0.127039i
\(136\) −5.15791 2.97792i −0.442287 0.255355i
\(137\) 15.8618 + 2.79686i 1.35516 + 0.238952i 0.803595 0.595177i \(-0.202918\pi\)
0.551570 + 0.834129i \(0.314029\pi\)
\(138\) 2.25059 2.21198i 0.191583 0.188296i
\(139\) 3.12282 + 3.72163i 0.264874 + 0.315664i 0.882046 0.471164i \(-0.156166\pi\)
−0.617172 + 0.786829i \(0.711722\pi\)
\(140\) −6.11218 2.62504i −0.516574 0.221856i
\(141\) −10.1553 + 0.799993i −0.855233 + 0.0673715i
\(142\) −2.01308 + 11.4168i −0.168934 + 0.958073i
\(143\) 2.97878 + 5.15940i 0.249098 + 0.431451i
\(144\) 1.96784 2.26442i 0.163987 0.188702i
\(145\) −19.0057 10.9729i −1.57833 0.911252i
\(146\) 0.0750772 0.425784i 0.00621343 0.0352381i
\(147\) 9.01290 + 8.10972i 0.743371 + 0.668879i
\(148\) 5.94284 + 2.16302i 0.488498 + 0.177799i
\(149\) −8.83668 + 1.55814i −0.723929 + 0.127648i −0.523458 0.852051i \(-0.675358\pi\)
−0.200471 + 0.979700i \(0.564247\pi\)
\(150\) 1.32891 1.86335i 0.108505 0.152142i
\(151\) −10.5742 8.87278i −0.860514 0.722057i 0.101565 0.994829i \(-0.467615\pi\)
−0.962079 + 0.272772i \(0.912060\pi\)
\(152\) −1.12555 + 1.94951i −0.0912941 + 0.158126i
\(153\) −15.6260 + 8.66465i −1.26329 + 0.700496i
\(154\) −6.57659 13.0434i −0.529957 1.05107i
\(155\) −4.57976 + 5.45794i −0.367855 + 0.438393i
\(156\) −0.146774 1.86318i −0.0117513 0.149174i
\(157\) −0.597998 + 1.64299i −0.0477255 + 0.131125i −0.961265 0.275624i \(-0.911115\pi\)
0.913540 + 0.406749i \(0.133338\pi\)
\(158\) −13.8865 + 2.44856i −1.10475 + 0.194797i
\(159\) 0.981630 3.54065i 0.0778483 0.280792i
\(160\) −0.859919 2.36261i −0.0679825 0.186780i
\(161\) −0.272638 + 4.81259i −0.0214869 + 0.379285i
\(162\) −2.78367 8.55869i −0.218706 0.672434i
\(163\) 12.1493 + 21.0432i 0.951606 + 1.64823i 0.741951 + 0.670454i \(0.233901\pi\)
0.209655 + 0.977775i \(0.432766\pi\)
\(164\) 0.536044 3.04006i 0.0418580 0.237389i
\(165\) 23.2771 6.02170i 1.81212 0.468789i
\(166\) −2.33630 + 6.41894i −0.181332 + 0.498206i
\(167\) 2.40743 + 13.6532i 0.186293 + 1.05652i 0.924283 + 0.381708i \(0.124664\pi\)
−0.737990 + 0.674811i \(0.764225\pi\)
\(168\) 0.100913 + 4.58146i 0.00778560 + 0.353468i
\(169\) 9.06665 + 7.60782i 0.697434 + 0.585217i
\(170\) 14.9744i 1.14848i
\(171\) 3.27493 + 5.90608i 0.250440 + 0.451650i
\(172\) −1.80143 −0.137358
\(173\) 21.0732 7.67002i 1.60217 0.583141i 0.622297 0.782781i \(-0.286199\pi\)
0.979869 + 0.199640i \(0.0639772\pi\)
\(174\) −1.44793 + 15.0490i −0.109768 + 1.14086i
\(175\) 0.411373 + 3.47173i 0.0310969 + 0.262438i
\(176\) 1.88835 5.18819i 0.142339 0.391074i
\(177\) −1.78001 + 18.5004i −0.133794 + 1.39058i
\(178\) 10.1580 12.1058i 0.761374 0.907370i
\(179\) 3.77729i 0.282328i −0.989986 0.141164i \(-0.954916\pi\)
0.989986 0.141164i \(-0.0450844\pi\)
\(180\) −7.40433 1.43813i −0.551886 0.107192i
\(181\) 17.0656 + 9.85285i 1.26848 + 0.732356i 0.974700 0.223517i \(-0.0717538\pi\)
0.293779 + 0.955873i \(0.405087\pi\)
\(182\) 2.07967 + 1.95584i 0.154155 + 0.144976i
\(183\) −0.739237 9.38408i −0.0546460 0.693691i
\(184\) −1.39566 + 1.17110i −0.102889 + 0.0863344i
\(185\) −2.76111 15.6590i −0.203001 1.15128i
\(186\) 4.72987 + 1.31134i 0.346811 + 0.0961518i
\(187\) −21.1369 + 25.1900i −1.54568 + 1.84207i
\(188\) 5.88134 0.428941
\(189\) 11.9382 + 6.81763i 0.868374 + 0.495910i
\(190\) 5.65979 0.410604
\(191\) 2.19657 2.61777i 0.158939 0.189416i −0.680698 0.732564i \(-0.738323\pi\)
0.839637 + 0.543148i \(0.182768\pi\)
\(192\) −1.23530 + 1.21410i −0.0891499 + 0.0876202i
\(193\) 2.34561 + 13.3026i 0.168841 + 0.957542i 0.945016 + 0.327025i \(0.106046\pi\)
−0.776175 + 0.630517i \(0.782843\pi\)
\(194\) 7.21239 6.05191i 0.517819 0.434502i
\(195\) −3.87237 + 2.66182i −0.277306 + 0.190617i
\(196\) −4.81983 5.07634i −0.344273 0.362596i
\(197\) 4.36587 + 2.52063i 0.311055 + 0.179588i 0.647398 0.762152i \(-0.275857\pi\)
−0.336343 + 0.941739i \(0.609190\pi\)
\(198\) −10.4256 12.8707i −0.740917 0.914681i
\(199\) 1.63061i 0.115591i −0.998328 0.0577955i \(-0.981593\pi\)
0.998328 0.0577955i \(-0.0184071\pi\)
\(200\) −0.849360 + 1.01223i −0.0600588 + 0.0715753i
\(201\) 3.63736 + 2.59410i 0.256560 + 0.182974i
\(202\) −2.33120 + 6.40493i −0.164023 + 0.450649i
\(203\) −13.8201 18.5022i −0.969978 1.29860i
\(204\) 9.38669 4.27859i 0.657200 0.299562i
\(205\) −7.29326 + 2.65453i −0.509384 + 0.185400i
\(206\) 7.75722 0.540471
\(207\) 0.855819 + 5.39829i 0.0594836 + 0.375207i
\(208\) 1.07904i 0.0748182i
\(209\) 9.52091 + 7.98899i 0.658575 + 0.552610i
\(210\) 9.84878 5.97916i 0.679630 0.412601i
\(211\) 4.57458 + 25.9437i 0.314927 + 1.78604i 0.572627 + 0.819816i \(0.305924\pi\)
−0.257700 + 0.966225i \(0.582965\pi\)
\(212\) −0.725530 + 1.99338i −0.0498296 + 0.136906i
\(213\) −14.0749 14.3207i −0.964399 0.981235i
\(214\) −3.12294 + 17.7111i −0.213480 + 1.21070i
\(215\) 2.26460 + 3.92241i 0.154445 + 0.267506i
\(216\) 1.21413 + 5.05231i 0.0826112 + 0.343766i
\(217\) −6.69469 + 3.37552i −0.454465 + 0.229145i
\(218\) −2.46854 6.78227i −0.167191 0.459353i
\(219\) 0.524919 + 0.534083i 0.0354708 + 0.0360900i
\(220\) −13.6706 + 2.41049i −0.921671 + 0.162515i
\(221\) 2.19803 6.03904i 0.147856 0.406230i
\(222\) −9.02694 + 6.20502i −0.605848 + 0.416454i
\(223\) −3.26265 + 3.88827i −0.218483 + 0.260378i −0.864142 0.503248i \(-0.832138\pi\)
0.645659 + 0.763626i \(0.276583\pi\)
\(224\) 0.149645 2.64152i 0.00999855 0.176494i
\(225\) 1.29114 + 3.74795i 0.0860759 + 0.249863i
\(226\) 0.690627 1.19620i 0.0459398 0.0795701i
\(227\) 19.4169 + 16.2927i 1.28874 + 1.08138i 0.991975 + 0.126436i \(0.0403537\pi\)
0.296769 + 0.954949i \(0.404091\pi\)
\(228\) −1.61716 3.54784i −0.107099 0.234961i
\(229\) −23.9496 + 4.22295i −1.58263 + 0.279061i −0.894684 0.446700i \(-0.852599\pi\)
−0.687947 + 0.725761i \(0.741488\pi\)
\(230\) 4.30444 + 1.56669i 0.283826 + 0.103304i
\(231\) 25.0074 + 3.84374i 1.64537 + 0.252899i
\(232\) 1.51571 8.59604i 0.0995114 0.564357i
\(233\) −1.63962 0.946638i −0.107415 0.0620163i 0.445330 0.895367i \(-0.353086\pi\)
−0.552745 + 0.833350i \(0.686420\pi\)
\(234\) 2.77501 + 1.66684i 0.181408 + 0.108965i
\(235\) −7.39354 12.8060i −0.482301 0.835370i
\(236\) 1.86334 10.5675i 0.121293 0.687887i
\(237\) 10.5128 22.0447i 0.682879 1.43196i
\(238\) −6.21833 + 14.4788i −0.403074 + 0.938524i
\(239\) 7.92982 + 9.45039i 0.512937 + 0.611295i 0.958896 0.283759i \(-0.0915815\pi\)
−0.445958 + 0.895054i \(0.647137\pi\)
\(240\) 4.19648 + 1.16346i 0.270882 + 0.0751008i
\(241\) −12.1191 2.13693i −0.780661 0.137652i −0.230904 0.972976i \(-0.574168\pi\)
−0.549757 + 0.835325i \(0.685279\pi\)
\(242\) −16.8729 9.74158i −1.08463 0.626212i
\(243\) 14.8687 + 4.68207i 0.953827 + 0.300355i
\(244\) 5.43468i 0.347920i
\(245\) −4.99409 + 16.8762i −0.319061 + 1.07818i
\(246\) 3.74788 + 3.81331i 0.238956 + 0.243128i
\(247\) −2.28254 0.830778i −0.145235 0.0528611i
\(248\) −2.66290 0.969217i −0.169094 0.0615454i
\(249\) −6.70212 9.75011i −0.424730 0.617888i
\(250\) −9.10842 1.60606i −0.576067 0.101576i
\(251\) 0.281911 0.488285i 0.0177941 0.0308202i −0.856991 0.515331i \(-0.827669\pi\)
0.874785 + 0.484511i \(0.161002\pi\)
\(252\) −6.56210 4.46529i −0.413374 0.281287i
\(253\) 5.02951 + 8.71136i 0.316202 + 0.547679i
\(254\) −5.96663 16.3932i −0.374380 1.02860i
\(255\) −21.1163 15.0598i −1.32236 0.943081i
\(256\) 0.766044 0.642788i 0.0478778 0.0401742i
\(257\) −3.95416 22.4252i −0.246654 1.39884i −0.816620 0.577176i \(-0.804155\pi\)
0.569966 0.821668i \(-0.306956\pi\)
\(258\) 1.81170 2.54031i 0.112792 0.158153i
\(259\) 3.83290 16.2874i 0.238165 1.01205i
\(260\) 2.34950 1.35648i 0.145710 0.0841255i
\(261\) −19.7653 17.1766i −1.22344 1.06321i
\(262\) −16.8902 + 9.75155i −1.04348 + 0.602453i
\(263\) −5.95950 16.3736i −0.367479 1.00964i −0.976317 0.216345i \(-0.930586\pi\)
0.608838 0.793294i \(-0.291636\pi\)
\(264\) 5.41708 + 7.88066i 0.333398 + 0.485021i
\(265\) 5.25243 0.926146i 0.322654 0.0568927i
\(266\) 5.47249 + 2.35031i 0.335540 + 0.144107i
\(267\) 6.85526 + 26.4993i 0.419535 + 1.62173i
\(268\) −1.97593 1.65800i −0.120699 0.101279i
\(269\) 14.7766 25.5938i 0.900946 1.56048i 0.0746770 0.997208i \(-0.476207\pi\)
0.826269 0.563276i \(-0.190459\pi\)
\(270\) 9.47455 8.99499i 0.576603 0.547418i
\(271\) 10.8975 6.29170i 0.661979 0.382194i −0.131052 0.991376i \(-0.541835\pi\)
0.793031 + 0.609182i \(0.208502\pi\)
\(272\) −5.59666 + 2.03702i −0.339348 + 0.123512i
\(273\) −4.84958 + 0.965682i −0.293510 + 0.0584457i
\(274\) 12.3383 10.3530i 0.745383 0.625451i
\(275\) 4.68945 + 5.58867i 0.282784 + 0.337009i
\(276\) −0.247819 3.14588i −0.0149170 0.189360i
\(277\) −1.48811 + 0.541628i −0.0894120 + 0.0325433i −0.386339 0.922357i \(-0.626260\pi\)
0.296927 + 0.954900i \(0.404038\pi\)
\(278\) 4.85824 0.291378
\(279\) −6.60605 + 5.35108i −0.395494 + 0.320361i
\(280\) −5.93973 + 2.99486i −0.354967 + 0.178977i
\(281\) −25.2166 4.44638i −1.50430 0.265248i −0.640058 0.768327i \(-0.721090\pi\)
−0.864241 + 0.503078i \(0.832201\pi\)
\(282\) −5.91489 + 8.29366i −0.352226 + 0.493880i
\(283\) −1.81233 2.15985i −0.107732 0.128390i 0.709484 0.704721i \(-0.248928\pi\)
−0.817216 + 0.576332i \(0.804484\pi\)
\(284\) 7.45176 + 8.88066i 0.442181 + 0.526970i
\(285\) −5.69207 + 7.98123i −0.337169 + 0.472767i
\(286\) 5.86705 + 1.03452i 0.346926 + 0.0611725i
\(287\) −8.15424 0.461947i −0.481330 0.0272678i
\(288\) −0.469739 2.96300i −0.0276796 0.174596i
\(289\) 18.4721 1.08659
\(290\) −20.6224 + 7.50592i −1.21099 + 0.440763i
\(291\) 1.28066 + 16.2571i 0.0750737 + 0.953006i
\(292\) −0.277911 0.331201i −0.0162635 0.0193821i
\(293\) −14.6651 + 12.3054i −0.856742 + 0.718892i −0.961264 0.275631i \(-0.911113\pi\)
0.104522 + 0.994523i \(0.466669\pi\)
\(294\) 12.0058 1.69145i 0.700192 0.0986475i
\(295\) −25.3521 + 9.22740i −1.47605 + 0.537240i
\(296\) 5.47695 3.16212i 0.318341 0.183794i
\(297\) 28.6349 1.75772i 1.66156 0.101993i
\(298\) −4.48650 + 7.77084i −0.259896 + 0.450153i
\(299\) −1.50598 1.26366i −0.0870929 0.0730796i
\(300\) −0.573203 2.21574i −0.0330939 0.127926i
\(301\) 0.560826 + 4.73302i 0.0323255 + 0.272807i
\(302\) −13.5939 + 2.39697i −0.782241 + 0.137930i
\(303\) −6.68750 9.72884i −0.384187 0.558907i
\(304\) 0.769921 + 2.11534i 0.0441580 + 0.121323i
\(305\) 11.8334 6.83203i 0.677580 0.391201i
\(306\) −3.40671 + 17.5398i −0.194749 + 1.00268i
\(307\) 11.5754 6.68305i 0.660642 0.381422i −0.131880 0.991266i \(-0.542101\pi\)
0.792521 + 0.609844i \(0.208768\pi\)
\(308\) −14.2192 3.34618i −0.810213 0.190666i
\(309\) −7.80146 + 10.9390i −0.443810 + 0.622295i
\(310\) 1.23722 + 7.01660i 0.0702691 + 0.398516i
\(311\) 6.03746 5.06603i 0.342353 0.287268i −0.455358 0.890309i \(-0.650489\pi\)
0.797711 + 0.603040i \(0.206044\pi\)
\(312\) −1.52163 1.08520i −0.0861452 0.0614372i
\(313\) −10.4824 28.8003i −0.592502 1.62789i −0.765845 0.643025i \(-0.777679\pi\)
0.173343 0.984862i \(-0.444543\pi\)
\(314\) 0.874215 + 1.51418i 0.0493348 + 0.0854504i
\(315\) −1.47335 + 19.9016i −0.0830139 + 1.12133i
\(316\) −7.05034 + 12.2115i −0.396612 + 0.686953i
\(317\) 2.93349 + 0.517253i 0.164761 + 0.0290518i 0.255420 0.966830i \(-0.417786\pi\)
−0.0906589 + 0.995882i \(0.528897\pi\)
\(318\) −2.08132 3.02786i −0.116715 0.169794i
\(319\) −45.2859 16.4827i −2.53552 0.922854i
\(320\) −2.36261 0.859919i −0.132074 0.0480709i
\(321\) −21.8348 22.2159i −1.21870 1.23997i
\(322\) 3.51141 + 3.30232i 0.195683 + 0.184031i
\(323\) 13.4072i 0.745996i
\(324\) −8.34565 3.36900i −0.463647 0.187167i
\(325\) −1.23479 0.712907i −0.0684939 0.0395450i
\(326\) 23.9294 + 4.21940i 1.32533 + 0.233691i
\(327\) 12.0467 + 3.33990i 0.666186 + 0.184697i
\(328\) −1.98426 2.36475i −0.109562 0.130571i
\(329\) −1.83100 15.4525i −0.100946 0.851922i
\(330\) 10.3494 21.7020i 0.569714 1.19466i
\(331\) 0.0997327 0.565612i 0.00548180 0.0310889i −0.981944 0.189171i \(-0.939420\pi\)
0.987426 + 0.158082i \(0.0505311\pi\)
\(332\) 3.41544 + 5.91572i 0.187447 + 0.324667i
\(333\) 0.328330 18.9699i 0.0179924 1.03954i
\(334\) 12.0065 + 6.93193i 0.656964 + 0.379298i
\(335\) −1.12614 + 6.38667i −0.0615277 + 0.348941i
\(336\) 3.57447 + 2.86760i 0.195003 + 0.156441i
\(337\) 31.2126 + 11.3605i 1.70026 + 0.618844i 0.995855 0.0909532i \(-0.0289914\pi\)
0.704406 + 0.709798i \(0.251214\pi\)
\(338\) 11.6559 2.05524i 0.633995 0.111790i
\(339\) 0.992272 + 2.17692i 0.0538928 + 0.118234i
\(340\) 11.4710 + 9.62535i 0.622105 + 0.522008i
\(341\) −7.82293 + 13.5497i −0.423635 + 0.733758i
\(342\) 6.62941 + 1.28761i 0.358477 + 0.0696262i
\(343\) −11.8369 + 14.2439i −0.639133 + 0.769096i
\(344\) −1.15793 + 1.37997i −0.0624317 + 0.0744032i
\(345\) −6.53828 + 4.49434i −0.352009 + 0.241967i
\(346\) 7.67002 21.0732i 0.412343 1.13290i
\(347\) 11.2765 1.98835i 0.605353 0.106740i 0.137433 0.990511i \(-0.456115\pi\)
0.467920 + 0.883771i \(0.345004\pi\)
\(348\) 10.5975 + 10.7825i 0.568083 + 0.578001i
\(349\) 1.37121 + 3.76738i 0.0733994 + 0.201663i 0.970967 0.239214i \(-0.0768897\pi\)
−0.897567 + 0.440877i \(0.854667\pi\)
\(350\) 2.92392 + 1.91645i 0.156290 + 0.102439i
\(351\) −5.14134 + 2.23687i −0.274425 + 0.119395i
\(352\) −2.76058 4.78146i −0.147139 0.254853i
\(353\) −2.44462 + 13.8642i −0.130114 + 0.737914i 0.848024 + 0.529958i \(0.177792\pi\)
−0.978138 + 0.207956i \(0.933319\pi\)
\(354\) 13.0280 + 13.2554i 0.692429 + 0.704517i
\(355\) 9.96893 27.3894i 0.529096 1.45368i
\(356\) −2.74417 15.5629i −0.145441 0.824835i
\(357\) −14.1637 23.3303i −0.749625 1.23477i
\(358\) −2.89357 2.42799i −0.152930 0.128323i
\(359\) 28.7311i 1.51637i −0.652041 0.758184i \(-0.726087\pi\)
0.652041 0.758184i \(-0.273913\pi\)
\(360\) −5.86108 + 4.74764i −0.308906 + 0.250222i
\(361\) 13.9326 0.733292
\(362\) 18.5173 6.73975i 0.973248 0.354233i
\(363\) 30.7064 13.9964i 1.61167 0.734622i
\(364\) 2.83505 0.335931i 0.148597 0.0176076i
\(365\) −0.371788 + 1.02148i −0.0194603 + 0.0534666i
\(366\) −7.66379 5.46568i −0.400593 0.285696i
\(367\) 2.57350 3.06698i 0.134336 0.160095i −0.694683 0.719316i \(-0.744455\pi\)
0.829018 + 0.559221i \(0.188900\pi\)
\(368\) 1.82190i 0.0949733i
\(369\) −9.14664 + 1.45006i −0.476155 + 0.0754873i
\(370\) −13.7703 7.95030i −0.715885 0.413317i
\(371\) 5.46321 + 1.28565i 0.283636 + 0.0667477i
\(372\) 4.04484 2.78038i 0.209715 0.144156i
\(373\) 13.0328 10.9359i 0.674815 0.566237i −0.239671 0.970854i \(-0.577040\pi\)
0.914486 + 0.404617i \(0.132595\pi\)
\(374\) 5.71010 + 32.3836i 0.295262 + 1.67452i
\(375\) 11.4252 11.2291i 0.589994 0.579870i
\(376\) 3.78045 4.50537i 0.194962 0.232347i
\(377\) 9.41858 0.485082
\(378\) 12.8963 4.76288i 0.663315 0.244976i
\(379\) 28.7632 1.47747 0.738733 0.673998i \(-0.235424\pi\)
0.738733 + 0.673998i \(0.235424\pi\)
\(380\) 3.63804 4.33565i 0.186628 0.222414i
\(381\) 29.1177 + 8.07276i 1.49175 + 0.413580i
\(382\) −0.593401 3.36535i −0.0303611 0.172186i
\(383\) −2.44842 + 2.05447i −0.125109 + 0.104979i −0.703195 0.710997i \(-0.748244\pi\)
0.578087 + 0.815975i \(0.303800\pi\)
\(384\) 0.136022 + 1.72670i 0.00694135 + 0.0881154i
\(385\) 10.5892 + 35.1673i 0.539677 + 1.79229i
\(386\) 11.6981 + 6.75391i 0.595418 + 0.343765i
\(387\) 1.76021 + 5.10959i 0.0894767 + 0.259735i
\(388\) 9.41510i 0.477979i
\(389\) −5.19527 + 6.19149i −0.263411 + 0.313921i −0.881497 0.472189i \(-0.843464\pi\)
0.618086 + 0.786110i \(0.287908\pi\)
\(390\) −0.450035 + 4.67739i −0.0227884 + 0.236849i
\(391\) 3.71125 10.1966i 0.187686 0.515663i
\(392\) −6.98683 + 0.429193i −0.352888 + 0.0216775i
\(393\) 3.23523 33.6251i 0.163196 1.69616i
\(394\) 4.73724 1.72421i 0.238659 0.0868647i
\(395\) 35.4524 1.78380
\(396\) −16.5610 0.286637i −0.832221 0.0144040i
\(397\) 1.78165i 0.0894184i −0.999000 0.0447092i \(-0.985764\pi\)
0.999000 0.0447092i \(-0.0142361\pi\)
\(398\) −1.24912 1.04814i −0.0626128 0.0525383i
\(399\) −8.81802 + 5.35339i −0.441453 + 0.268005i
\(400\) 0.229454 + 1.30130i 0.0114727 + 0.0650648i
\(401\) 0.285143 0.783424i 0.0142394 0.0391223i −0.932369 0.361507i \(-0.882262\pi\)
0.946609 + 0.322385i \(0.104485\pi\)
\(402\) 4.32525 1.11893i 0.215724 0.0558069i
\(403\) 0.530980 3.01134i 0.0264500 0.150005i
\(404\) 3.40799 + 5.90282i 0.169554 + 0.293676i
\(405\) 3.15581 + 22.4070i 0.156814 + 1.11341i
\(406\) −23.0569 1.30619i −1.14429 0.0648254i
\(407\) −11.9423 32.8113i −0.591960 1.62640i
\(408\) 2.75605 9.94085i 0.136445 0.492145i
\(409\) −20.5179 + 3.61787i −1.01455 + 0.178892i −0.656113 0.754663i \(-0.727800\pi\)
−0.358434 + 0.933555i \(0.616689\pi\)
\(410\) −2.65453 + 7.29326i −0.131098 + 0.360189i
\(411\) 2.19084 + 27.8111i 0.108066 + 1.37182i
\(412\) 4.98625 5.94238i 0.245655 0.292760i
\(413\) −28.3449 1.60577i −1.39476 0.0790147i
\(414\) 4.68544 + 2.81436i 0.230277 + 0.138318i
\(415\) 8.58722 14.8735i 0.421530 0.730112i
\(416\) 0.826595 + 0.693595i 0.0405271 + 0.0340063i
\(417\) −4.88595 + 6.85091i −0.239266 + 0.335491i
\(418\) 12.2398 2.15822i 0.598670 0.105562i
\(419\) −8.07619 2.93949i −0.394548 0.143604i 0.137125 0.990554i \(-0.456214\pi\)
−0.531672 + 0.846950i \(0.678436\pi\)
\(420\) 1.75037 11.3879i 0.0854092 0.555674i
\(421\) −1.36643 + 7.74943i −0.0665959 + 0.377684i 0.933234 + 0.359268i \(0.116974\pi\)
−0.999830 + 0.0184164i \(0.994138\pi\)
\(422\) 22.8145 + 13.1720i 1.11059 + 0.641202i
\(423\) −5.74679 16.6819i −0.279418 0.811102i
\(424\) 1.06065 + 1.83711i 0.0515099 + 0.0892177i
\(425\) 1.36659 7.75032i 0.0662893 0.375946i
\(426\) −20.0174 + 1.57689i −0.969849 + 0.0764005i
\(427\) 14.2789 1.69194i 0.691006 0.0818789i
\(428\) 11.5601 + 13.7768i 0.558778 + 0.665925i
\(429\) −7.35936 + 7.23309i −0.355313 + 0.349217i
\(430\) 4.46040 + 0.786489i 0.215100 + 0.0379279i
\(431\) −28.3233 16.3525i −1.36429 0.787671i −0.374095 0.927390i \(-0.622047\pi\)
−0.990191 + 0.139720i \(0.955380\pi\)
\(432\) 4.65073 + 2.31749i 0.223758 + 0.111500i
\(433\) 0.976793i 0.0469417i 0.999725 + 0.0234708i \(0.00747169\pi\)
−0.999725 + 0.0234708i \(0.992528\pi\)
\(434\) −1.71747 + 7.29817i −0.0824412 + 0.350323i
\(435\) 10.1554 36.6296i 0.486914 1.75626i
\(436\) −6.78227 2.46854i −0.324812 0.118222i
\(437\) −3.85395 1.40272i −0.184359 0.0671013i
\(438\) 0.746543 0.0588095i 0.0356712 0.00281003i
\(439\) 21.9661 + 3.87322i 1.04839 + 0.184859i 0.671198 0.741278i \(-0.265780\pi\)
0.377188 + 0.926137i \(0.376891\pi\)
\(440\) −6.94074 + 12.0217i −0.330887 + 0.573113i
\(441\) −9.68904 + 18.6312i −0.461383 + 0.887201i
\(442\) −3.21331 5.56561i −0.152841 0.264729i
\(443\) −5.48324 15.0651i −0.260517 0.715764i −0.999133 0.0416374i \(-0.986743\pi\)
0.738616 0.674126i \(-0.235480\pi\)
\(444\) −1.04908 + 10.9035i −0.0497873 + 0.517459i
\(445\) −30.4369 + 25.5396i −1.44285 + 1.21069i
\(446\) 0.881400 + 4.99867i 0.0417355 + 0.236694i
\(447\) −6.44607 14.1419i −0.304889 0.668887i
\(448\) −1.92733 1.81257i −0.0910577 0.0856358i
\(449\) −24.1717 + 13.9556i −1.14073 + 0.658603i −0.946612 0.322374i \(-0.895519\pi\)
−0.194122 + 0.980977i \(0.562186\pi\)
\(450\) 3.70102 + 1.42007i 0.174468 + 0.0669425i
\(451\) −14.7602 + 8.52178i −0.695029 + 0.401275i
\(452\) −0.472416 1.29795i −0.0222206 0.0610506i
\(453\) 10.2913 21.5803i 0.483528 1.01393i
\(454\) 24.9619 4.40145i 1.17152 0.206570i
\(455\) −4.29544 5.75070i −0.201373 0.269597i
\(456\) −3.75729 1.04169i −0.175951 0.0487816i
\(457\) 2.65879 + 2.23099i 0.124373 + 0.104361i 0.702853 0.711335i \(-0.251909\pi\)
−0.578480 + 0.815697i \(0.696354\pi\)
\(458\) −12.1595 + 21.0609i −0.568176 + 0.984110i
\(459\) −21.3078 22.4438i −0.994563 1.04759i
\(460\) 3.96700 2.29035i 0.184962 0.106788i
\(461\) 32.5099 11.8326i 1.51414 0.551101i 0.554461 0.832209i \(-0.312924\pi\)
0.959676 + 0.281108i \(0.0907021\pi\)
\(462\) 19.0189 16.6861i 0.884841 0.776308i
\(463\) 3.16948 2.65951i 0.147298 0.123598i −0.566161 0.824295i \(-0.691572\pi\)
0.713459 + 0.700697i \(0.247127\pi\)
\(464\) −5.61066 6.68653i −0.260469 0.310414i
\(465\) −11.1388 5.31194i −0.516550 0.246335i
\(466\) −1.77910 + 0.647538i −0.0824151 + 0.0299966i
\(467\) 9.37807 0.433966 0.216983 0.976175i \(-0.430378\pi\)
0.216983 + 0.976175i \(0.430378\pi\)
\(468\) 3.06061 1.05436i 0.141477 0.0487376i
\(469\) −3.74103 + 5.70767i −0.172745 + 0.263556i
\(470\) −14.5624 2.56775i −0.671714 0.118441i
\(471\) −3.01445 0.290035i −0.138898 0.0133641i
\(472\) −6.89746 8.22008i −0.317481 0.378360i
\(473\) 6.39314 + 7.61905i 0.293957 + 0.350324i
\(474\) −10.1297 22.2233i −0.465273 1.02075i
\(475\) −2.92934 0.516522i −0.134408 0.0236997i
\(476\) 7.09438 + 14.0703i 0.325170 + 0.644913i
\(477\) 6.36297 + 0.110130i 0.291340 + 0.00504251i
\(478\) 12.3366 0.564263
\(479\) −10.7991 + 3.93054i −0.493421 + 0.179591i −0.576733 0.816933i \(-0.695673\pi\)
0.0833113 + 0.996524i \(0.473450\pi\)
\(480\) 3.58871 2.46684i 0.163801 0.112595i
\(481\) 4.38646 + 5.22758i 0.200005 + 0.238357i
\(482\) −9.42700 + 7.91019i −0.429388 + 0.360299i
\(483\) −8.18825 + 1.63050i −0.372578 + 0.0741903i
\(484\) −18.3082 + 6.66363i −0.832190 + 0.302892i
\(485\) −20.5004 + 11.8359i −0.930873 + 0.537440i
\(486\) 13.1441 8.38050i 0.596228 0.380147i
\(487\) −13.7343 + 23.7885i −0.622360 + 1.07796i 0.366685 + 0.930345i \(0.380493\pi\)
−0.989045 + 0.147614i \(0.952841\pi\)
\(488\) 4.16321 + 3.49335i 0.188460 + 0.158136i
\(489\) −30.0160 + 29.5009i −1.35737 + 1.33408i
\(490\) 9.71778 + 14.6735i 0.439005 + 0.662882i
\(491\) −12.3433 + 2.17646i −0.557047 + 0.0982224i −0.445082 0.895490i \(-0.646825\pi\)
−0.111965 + 0.993712i \(0.535714\pi\)
\(492\) 5.33025 0.419894i 0.240306 0.0189303i
\(493\) 17.7804 + 48.8513i 0.800790 + 2.20015i
\(494\) −2.10360 + 1.21452i −0.0946456 + 0.0546437i
\(495\) 20.1950 + 36.4201i 0.907697 + 1.63696i
\(496\) −2.45414 + 1.41690i −0.110194 + 0.0636207i
\(497\) 21.0129 22.3433i 0.942557 1.00223i
\(498\) −11.7771 1.13313i −0.527743 0.0507767i
\(499\) −7.48229 42.4342i −0.334953 1.89962i −0.427691 0.903925i \(-0.640673\pi\)
0.0927373 0.995691i \(-0.470438\pi\)
\(500\) −7.08509 + 5.94510i −0.316855 + 0.265873i
\(501\) −21.8501 + 9.95960i −0.976190 + 0.444962i
\(502\) −0.192839 0.529820i −0.00860681 0.0236470i
\(503\) 8.76699 + 15.1849i 0.390901 + 0.677060i 0.992569 0.121686i \(-0.0388302\pi\)
−0.601668 + 0.798747i \(0.705497\pi\)
\(504\) −7.63865 + 2.15663i −0.340252 + 0.0960639i
\(505\) 8.56849 14.8411i 0.381293 0.660418i
\(506\) 9.90619 + 1.74673i 0.440384 + 0.0776516i
\(507\) −8.82411 + 18.5036i −0.391892 + 0.821775i
\(508\) −16.3932 5.96663i −0.727330 0.264726i
\(509\) 21.0807 + 7.67273i 0.934384 + 0.340088i 0.763946 0.645281i \(-0.223260\pi\)
0.170438 + 0.985368i \(0.445482\pi\)
\(510\) −25.1098 + 6.49580i −1.11188 + 0.287639i
\(511\) −0.783668 + 0.833285i −0.0346674 + 0.0368624i
\(512\) 1.00000i 0.0441942i
\(513\) −8.48297 + 8.05359i −0.374532 + 0.355575i
\(514\) −19.7204 11.3856i −0.869828 0.502195i
\(515\) −19.2072 3.38674i −0.846369 0.149238i
\(516\) −0.781449 3.02072i −0.0344014 0.132980i
\(517\) −20.8725 24.8749i −0.917971 1.09399i
\(518\) −10.0132 13.4055i −0.439953 0.589005i
\(519\) 22.0029 + 32.0094i 0.965820 + 1.40506i
\(520\) 0.471102 2.67175i 0.0206592 0.117164i
\(521\) −15.6395 27.0884i −0.685179 1.18676i −0.973381 0.229195i \(-0.926391\pi\)
0.288202 0.957570i \(-0.406943\pi\)
\(522\) −25.8629 + 4.10019i −1.13199 + 0.179460i
\(523\) 5.01858 + 2.89748i 0.219447 + 0.126698i 0.605694 0.795697i \(-0.292895\pi\)
−0.386247 + 0.922395i \(0.626229\pi\)
\(524\) −3.38668 + 19.2068i −0.147948 + 0.839053i
\(525\) −5.64311 + 2.19583i −0.246286 + 0.0958337i
\(526\) −16.3736 5.95950i −0.713923 0.259847i
\(527\) 16.6213 2.93078i 0.724034 0.127667i
\(528\) 9.51896 + 0.915866i 0.414260 + 0.0398579i
\(529\) 15.0763 + 12.6505i 0.655490 + 0.550021i
\(530\) 2.66673 4.61891i 0.115835 0.200633i
\(531\) −31.7946 + 5.04056i −1.37977 + 0.218742i
\(532\) 5.31809 2.68142i 0.230568 0.116254i
\(533\) 2.14110 2.55166i 0.0927413 0.110525i
\(534\) 24.7061 + 11.7820i 1.06914 + 0.509856i
\(535\) 15.4650 42.4898i 0.668611 1.83699i
\(536\) −2.54021 + 0.447907i −0.109720 + 0.0193466i
\(537\) 6.33394 1.63857i 0.273330 0.0707093i
\(538\) −10.1078 27.7709i −0.435778 1.19729i
\(539\) −4.36490 + 38.4008i −0.188010 + 1.65404i
\(540\) −0.800435 13.0398i −0.0344453 0.561144i
\(541\) −10.9704 19.0013i −0.471655 0.816930i 0.527819 0.849357i \(-0.323010\pi\)
−0.999474 + 0.0324265i \(0.989677\pi\)
\(542\) 2.18509 12.3922i 0.0938574 0.532292i
\(543\) −9.11877 + 32.8906i −0.391324 + 1.41147i
\(544\) −2.03702 + 5.59666i −0.0873365 + 0.239955i
\(545\) 3.15112 + 17.8709i 0.134979 + 0.765505i
\(546\) −2.37750 + 4.33573i −0.101747 + 0.185552i
\(547\) 14.1134 + 11.8426i 0.603446 + 0.506352i 0.892551 0.450946i \(-0.148913\pi\)
−0.289105 + 0.957297i \(0.593358\pi\)
\(548\) 16.1065i 0.688035i
\(549\) 15.4150 5.31035i 0.657896 0.226640i
\(550\) 7.29549 0.311081
\(551\) 18.4641 6.72037i 0.786595 0.286297i
\(552\) −2.56918 1.83229i −0.109352 0.0779876i
\(553\) 34.2792 + 14.7221i 1.45770 + 0.626048i
\(554\) −0.541628 + 1.48811i −0.0230116 + 0.0632238i
\(555\) 25.0601 11.4228i 1.06374 0.484870i
\(556\) 3.12282 3.72163i 0.132437 0.157832i
\(557\) 1.18568i 0.0502389i 0.999684 + 0.0251194i \(0.00799660\pi\)
−0.999684 + 0.0251194i \(0.992003\pi\)
\(558\) −0.147120 + 8.50013i −0.00622808 + 0.359839i
\(559\) −1.68339 0.971908i −0.0712000 0.0411073i
\(560\) −1.52379 + 6.47516i −0.0643919 + 0.273625i
\(561\) −51.4088 24.5161i −2.17048 1.03507i
\(562\) −19.6151 + 16.4590i −0.827412 + 0.694281i
\(563\) −2.88559 16.3650i −0.121613 0.689702i −0.983262 0.182197i \(-0.941679\pi\)
0.861649 0.507505i \(-0.169432\pi\)
\(564\) 2.55129 + 9.86213i 0.107429 + 0.415270i
\(565\) −2.23227 + 2.66031i −0.0939122 + 0.111920i
\(566\) −2.81948 −0.118512
\(567\) −6.25343 + 22.9760i −0.262619 + 0.964899i
\(568\) 11.5929 0.486427
\(569\) −14.4079 + 17.1707i −0.604012 + 0.719833i −0.978234 0.207506i \(-0.933465\pi\)
0.374222 + 0.927339i \(0.377910\pi\)
\(570\) 2.45518 + 9.49061i 0.102836 + 0.397518i
\(571\) −5.46075 30.9694i −0.228525 1.29603i −0.855830 0.517257i \(-0.826953\pi\)
0.627305 0.778773i \(-0.284158\pi\)
\(572\) 4.56376 3.82945i 0.190820 0.160117i
\(573\) 5.34247 + 2.54775i 0.223185 + 0.106434i
\(574\) −5.59532 + 5.94958i −0.233544 + 0.248331i
\(575\) −2.08488 1.20370i −0.0869454 0.0501979i
\(576\) −2.57173 1.54474i −0.107155 0.0643640i
\(577\) 9.00385i 0.374835i −0.982280 0.187418i \(-0.939988\pi\)
0.982280 0.187418i \(-0.0600118\pi\)
\(578\) 11.8736 14.1505i 0.493878 0.588581i
\(579\) −21.2889 + 9.70382i −0.884738 + 0.403277i
\(580\) −7.50592 + 20.6224i −0.311666 + 0.856297i
\(581\) 14.4795 10.8153i 0.600711 0.448696i
\(582\) 13.2768 + 9.46880i 0.550342 + 0.392494i
\(583\) 11.0057 4.00576i 0.455811 0.165902i
\(584\) −0.432352 −0.0178909
\(585\) −6.14329 5.33869i −0.253994 0.220728i
\(586\) 19.1439i 0.790826i
\(587\) 11.6558 + 9.78039i 0.481087 + 0.403680i 0.850819 0.525458i \(-0.176106\pi\)
−0.369732 + 0.929138i \(0.620551\pi\)
\(588\) 6.42145 10.2842i 0.264816 0.424114i
\(589\) −1.10773 6.28225i −0.0456432 0.258856i
\(590\) −9.22740 + 25.3521i −0.379886 + 1.04373i
\(591\) −2.33283 + 8.41433i −0.0959600 + 0.346119i
\(592\) 1.09819 6.22816i 0.0451354 0.255976i
\(593\) 10.0658 + 17.4345i 0.413354 + 0.715950i 0.995254 0.0973105i \(-0.0310240\pi\)
−0.581900 + 0.813260i \(0.697691\pi\)
\(594\) 17.0596 23.0654i 0.699966 0.946386i
\(595\) 21.7182 33.1353i 0.890358 1.35841i
\(596\) 3.06895 + 8.43186i 0.125709 + 0.345382i
\(597\) 2.73429 0.707350i 0.111907 0.0289499i
\(598\) −1.93605 + 0.341377i −0.0791708 + 0.0139599i
\(599\) −10.7363 + 29.4977i −0.438673 + 1.20524i 0.501683 + 0.865052i \(0.332714\pi\)
−0.940356 + 0.340192i \(0.889508\pi\)
\(600\) −2.06580 0.985150i −0.0843360 0.0402186i
\(601\) 23.7024 28.2474i 0.966841 1.15224i −0.0214676 0.999770i \(-0.506834\pi\)
0.988309 0.152467i \(-0.0487217\pi\)
\(602\) 3.98619 + 2.61271i 0.162465 + 0.106486i
\(603\) −2.77205 + 7.22462i −0.112887 + 0.294209i
\(604\) −6.90180 + 11.9543i −0.280830 + 0.486412i
\(605\) 37.5248 + 31.4871i 1.52560 + 1.28013i
\(606\) −11.7514 1.13066i −0.477367 0.0459297i
\(607\) 4.91217 0.866149i 0.199379 0.0351559i −0.0730667 0.997327i \(-0.523279\pi\)
0.272446 + 0.962171i \(0.412167\pi\)
\(608\) 2.11534 + 0.769921i 0.0857884 + 0.0312244i
\(609\) 25.0303 31.2003i 1.01428 1.26430i
\(610\) 2.37274 13.4565i 0.0960694 0.544837i
\(611\) 5.49599 + 3.17311i 0.222344 + 0.128370i
\(612\) 11.2464 + 13.8840i 0.454611 + 0.561229i
\(613\) 13.8525 + 23.9932i 0.559497 + 0.969078i 0.997538 + 0.0701228i \(0.0223391\pi\)
−0.438041 + 0.898955i \(0.644328\pi\)
\(614\) 2.32100 13.1630i 0.0936679 0.531217i
\(615\) −7.61502 11.0782i −0.307067 0.446715i
\(616\) −11.7032 + 8.74164i −0.471537 + 0.352211i
\(617\) −4.86311 5.79563i −0.195782 0.233323i 0.659218 0.751952i \(-0.270887\pi\)
−0.855000 + 0.518628i \(0.826443\pi\)
\(618\) 3.36504 + 13.0077i 0.135362 + 0.523246i
\(619\) 31.3178 + 5.52217i 1.25877 + 0.221955i 0.762942 0.646467i \(-0.223754\pi\)
0.495826 + 0.868422i \(0.334865\pi\)
\(620\) 6.17029 + 3.56242i 0.247805 + 0.143070i
\(621\) −8.68087 + 3.77683i −0.348351 + 0.151559i
\(622\) 7.88134i 0.316013i
\(623\) −40.0353 + 12.0551i −1.60398 + 0.482975i
\(624\) −1.80939 + 0.468083i −0.0724337 + 0.0187383i
\(625\) 28.0600 + 10.2130i 1.12240 + 0.408520i
\(626\) −28.8003 10.4824i −1.15109 0.418962i
\(627\) −9.26622 + 19.4307i −0.370057 + 0.775988i
\(628\) 1.72187 + 0.303612i 0.0687100 + 0.0121154i
\(629\) −18.8331 + 32.6199i −0.750924 + 1.30064i
\(630\) 14.2985 + 13.9212i 0.569666 + 0.554633i
\(631\) −0.274758 0.475894i −0.0109379 0.0189450i 0.860505 0.509443i \(-0.170148\pi\)
−0.871443 + 0.490498i \(0.836815\pi\)
\(632\) 4.82271 + 13.2503i 0.191837 + 0.527069i
\(633\) −41.5193 + 18.9251i −1.65024 + 0.752206i
\(634\) 2.28185 1.91470i 0.0906239 0.0760424i
\(635\) 7.61646 + 43.1951i 0.302250 + 1.71415i
\(636\) −3.65732 0.351889i −0.145022 0.0139533i
\(637\) −1.76523 7.34413i −0.0699410 0.290985i
\(638\) −41.7357 + 24.0961i −1.65233 + 0.953974i
\(639\) 17.9079 29.8138i 0.708427 1.17941i
\(640\) −2.17739 + 1.25712i −0.0860689 + 0.0496919i
\(641\) 0.734682 + 2.01852i 0.0290182 + 0.0797268i 0.953356 0.301849i \(-0.0976038\pi\)
−0.924338 + 0.381576i \(0.875382\pi\)
\(642\) −31.0535 + 2.44626i −1.22558 + 0.0965462i
\(643\) −26.2152 + 4.62245i −1.03383 + 0.182292i −0.664718 0.747094i \(-0.731448\pi\)
−0.369110 + 0.929386i \(0.620337\pi\)
\(644\) 4.78682 0.567201i 0.188627 0.0223508i
\(645\) −5.59492 + 5.49892i −0.220300 + 0.216520i
\(646\) −10.2705 8.61798i −0.404088 0.339070i
\(647\) 7.77791 13.4717i 0.305781 0.529628i −0.671654 0.740865i \(-0.734416\pi\)
0.977435 + 0.211237i \(0.0677491\pi\)
\(648\) −7.94529 + 4.22758i −0.312120 + 0.166075i
\(649\) −51.3077 + 29.6225i −2.01400 + 1.16279i
\(650\) −1.33983 + 0.487657i −0.0525524 + 0.0191275i
\(651\) −8.56435 9.76171i −0.335663 0.382592i
\(652\) 18.6138 15.6188i 0.728972 0.611681i
\(653\) 24.8305 + 29.5919i 0.971693 + 1.15802i 0.987416 + 0.158142i \(0.0505505\pi\)
−0.0157231 + 0.999876i \(0.505005\pi\)
\(654\) 10.3020 7.08148i 0.402840 0.276908i
\(655\) 46.0782 16.7711i 1.80042 0.655300i
\(656\) −3.08696 −0.120525
\(657\) −0.667870 + 1.11189i −0.0260561 + 0.0433791i
\(658\) −13.0142 8.53003i −0.507347 0.332535i
\(659\) −27.5899 4.86484i −1.07475 0.189507i −0.391857 0.920026i \(-0.628167\pi\)
−0.682893 + 0.730519i \(0.739278\pi\)
\(660\) −9.97225 21.8778i −0.388169 0.851594i
\(661\) 6.99910 + 8.34120i 0.272233 + 0.324435i 0.884789 0.465993i \(-0.154303\pi\)
−0.612555 + 0.790428i \(0.709858\pi\)
\(662\) −0.369177 0.439968i −0.0143485 0.0170998i
\(663\) 11.0801 + 1.06607i 0.430314 + 0.0414026i
\(664\) 6.72711 + 1.18617i 0.261063 + 0.0460324i
\(665\) −12.5240 8.20870i −0.485659 0.318320i
\(666\) −14.3207 12.4451i −0.554916 0.482238i
\(667\) 15.9027 0.615757
\(668\) 13.0278 4.74172i 0.504059 0.183463i
\(669\) −7.93536 3.78426i −0.306799 0.146308i
\(670\) 4.16860 + 4.96795i 0.161047 + 0.191929i
\(671\) 22.9857 19.2873i 0.887354 0.744578i
\(672\) 4.49434 0.894943i 0.173373 0.0345232i
\(673\) −3.26648 + 1.18890i −0.125914 + 0.0458288i −0.404208 0.914667i \(-0.632453\pi\)
0.278295 + 0.960496i \(0.410231\pi\)
\(674\) 28.7657 16.6079i 1.10801 0.639712i
\(675\) −5.72466 + 3.79088i −0.220342 + 0.145911i
\(676\) 5.91783 10.2500i 0.227609 0.394230i
\(677\) 7.82878 + 6.56912i 0.300884 + 0.252472i 0.780712 0.624891i \(-0.214856\pi\)
−0.479828 + 0.877363i \(0.659301\pi\)
\(678\) 2.30544 + 0.639172i 0.0885398 + 0.0245472i
\(679\) −24.7370 + 2.93114i −0.949318 + 0.112487i
\(680\) 14.7469 2.60028i 0.565518 0.0997160i
\(681\) −18.8975 + 39.6269i −0.724153 + 1.51850i
\(682\) 5.35120 + 14.7023i 0.204908 + 0.562980i
\(683\) −16.5794 + 9.57213i −0.634394 + 0.366267i −0.782452 0.622711i \(-0.786031\pi\)
0.148058 + 0.988979i \(0.452698\pi\)
\(684\) 5.24767 4.25076i 0.200650 0.162532i
\(685\) −35.0701 + 20.2477i −1.33996 + 0.773626i
\(686\) 3.30281 + 18.2234i 0.126102 + 0.695772i
\(687\) −17.4704 38.3279i −0.666539 1.46230i
\(688\) 0.312815 + 1.77406i 0.0119259 + 0.0676354i
\(689\) −1.75346 + 1.47133i −0.0668015 + 0.0560531i
\(690\) −0.759859 + 7.89752i −0.0289273 + 0.300653i
\(691\) −8.60953 23.6545i −0.327522 0.899859i −0.988737 0.149663i \(-0.952181\pi\)
0.661215 0.750196i \(-0.270041\pi\)
\(692\) −11.2128 19.4212i −0.426248 0.738282i
\(693\) 4.40272 + 43.6011i 0.167245 + 1.65627i
\(694\) 5.72522 9.91637i 0.217326 0.376420i
\(695\) −12.0292 2.12107i −0.456293 0.0804567i
\(696\) 15.0718 1.18729i 0.571294 0.0450041i
\(697\) 17.2767 + 6.28819i 0.654400 + 0.238182i
\(698\) 3.76738 + 1.37121i 0.142597 + 0.0519012i
\(699\) 0.876109 3.16005i 0.0331375 0.119524i
\(700\) 3.34755 1.00798i 0.126526 0.0380982i
\(701\) 14.4777i 0.546816i −0.961898 0.273408i \(-0.911849\pi\)
0.961898 0.273408i \(-0.0881509\pi\)
\(702\) −1.59125 + 5.37633i −0.0600579 + 0.202917i
\(703\) 12.3292 + 7.11824i 0.465003 + 0.268470i
\(704\) −5.43728 0.958739i −0.204925 0.0361338i
\(705\) 18.2664 17.9530i 0.687953 0.676149i
\(706\) 9.04918 + 10.7844i 0.340571 + 0.405876i
\(707\) 14.4479 10.7917i 0.543369 0.405865i
\(708\) 18.5285 1.45959i 0.696342 0.0548548i
\(709\) 2.28251 12.9448i 0.0857216 0.486151i −0.911477 0.411351i \(-0.865057\pi\)
0.997199 0.0748001i \(-0.0238319\pi\)
\(710\) −14.5736 25.2422i −0.546938 0.947324i
\(711\) 41.5260 + 8.06550i 1.55735 + 0.302480i
\(712\) −13.6858 7.90152i −0.512898 0.296122i
\(713\) 0.896531 5.08448i 0.0335753 0.190415i
\(714\) −26.9763 4.14636i −1.00956 0.155174i
\(715\) −14.0754 5.12302i −0.526389 0.191590i
\(716\) −3.71990 + 0.655919i −0.139019 + 0.0245128i
\(717\) −12.4070 + 17.3966i −0.463347 + 0.649689i
\(718\) −22.0093 18.4680i −0.821379 0.689219i
\(719\) −14.3697 + 24.8890i −0.535898 + 0.928202i 0.463222 + 0.886242i \(0.346693\pi\)
−0.999119 + 0.0419594i \(0.986640\pi\)
\(720\) −0.130529 + 7.54157i −0.00486454 + 0.281058i
\(721\) −17.1652 11.2507i −0.639264 0.418999i
\(722\) 8.95567 10.6730i 0.333296 0.397206i
\(723\) −1.67390 21.2489i −0.0622529 0.790255i
\(724\) 6.73975 18.5173i 0.250481 0.688190i
\(725\) 11.3585 2.00282i 0.421846 0.0743828i
\(726\) 9.01579 32.5192i 0.334607 1.20690i
\(727\) −4.22763 11.6153i −0.156794 0.430789i 0.836276 0.548308i \(-0.184728\pi\)
−0.993071 + 0.117520i \(0.962506\pi\)
\(728\) 1.56499 2.38770i 0.0580025 0.0884942i
\(729\) −1.40118 + 26.9636i −0.0518954 + 0.998653i
\(730\) 0.543517 + 0.941400i 0.0201165 + 0.0348428i
\(731\) 1.86308 10.5660i 0.0689083 0.390799i
\(732\) −9.11314 + 2.35753i −0.336831 + 0.0871370i
\(733\) −0.871846 + 2.39538i −0.0322024 + 0.0884753i −0.954752 0.297403i \(-0.903879\pi\)
0.922550 + 0.385879i \(0.126102\pi\)
\(734\) −0.695227 3.94283i −0.0256613 0.145532i
\(735\) −30.4653 1.05354i −1.12373 0.0388603i
\(736\) 1.39566 + 1.17110i 0.0514447 + 0.0431672i
\(737\) 14.2412i 0.524582i
\(738\) −4.76853 + 7.93882i −0.175532 + 0.292232i
\(739\) 17.7262 0.652069 0.326034 0.945358i \(-0.394287\pi\)
0.326034 + 0.945358i \(0.394287\pi\)
\(740\) −14.9417 + 5.43833i −0.549267 + 0.199917i
\(741\) 0.402935 4.18787i 0.0148022 0.153845i
\(742\) 4.49655 3.35866i 0.165074 0.123300i
\(743\) −12.0106 + 32.9989i −0.440627 + 1.21061i 0.498453 + 0.866917i \(0.333902\pi\)
−0.939081 + 0.343697i \(0.888321\pi\)
\(744\) 0.470079 4.88573i 0.0172339 0.179119i
\(745\) 14.5014 17.2821i 0.531291 0.633168i
\(746\) 17.0132i 0.622896i
\(747\) 13.4421 15.4680i 0.491822 0.565944i
\(748\) 28.4776 + 16.4416i 1.04125 + 0.601164i
\(749\) 32.5978 34.6616i 1.19110 1.26651i
\(750\) −1.25806 15.9701i −0.0459378 0.583147i
\(751\) −12.5109 + 10.4979i −0.456530 + 0.383074i −0.841852 0.539708i \(-0.818535\pi\)
0.385322 + 0.922782i \(0.374090\pi\)
\(752\) −1.02128 5.79199i −0.0372424 0.211212i
\(753\) 0.941071 + 0.260908i 0.0342945 + 0.00950800i
\(754\) 6.05415 7.21505i 0.220479 0.262757i
\(755\) 34.7055 1.26306
\(756\) 4.64102 12.9407i 0.168792 0.470648i
\(757\) −2.55127 −0.0927273 −0.0463637 0.998925i \(-0.514763\pi\)
−0.0463637 + 0.998925i \(0.514763\pi\)
\(758\) 18.4886 22.0339i 0.671537 0.800307i
\(759\) −12.4259 + 12.2127i −0.451030 + 0.443292i
\(760\) −0.982812 5.57380i −0.0356503 0.202183i
\(761\) 20.2148 16.9622i 0.732786 0.614881i −0.198104 0.980181i \(-0.563478\pi\)
0.930890 + 0.365301i \(0.119034\pi\)
\(762\) 24.9006 17.1164i 0.902054 0.620062i
\(763\) −4.37430 + 18.5881i −0.158360 + 0.672933i
\(764\) −2.95944 1.70863i −0.107069 0.0618161i
\(765\) 16.0929 41.9418i 0.581838 1.51641i
\(766\) 3.19619i 0.115483i
\(767\) 7.44266 8.86981i 0.268739 0.320270i
\(768\) 1.41016 + 1.00570i 0.0508849 + 0.0362902i
\(769\) 3.98342 10.9444i 0.143646 0.394664i −0.846917 0.531726i \(-0.821544\pi\)
0.990562 + 0.137062i \(0.0437660\pi\)
\(770\) 33.7463 + 14.4933i 1.21613 + 0.522301i
\(771\) 35.8883 16.3584i 1.29249 0.589135i
\(772\) 12.6932 4.61995i 0.456838 0.166275i
\(773\) −31.7996 −1.14375 −0.571876 0.820340i \(-0.693784\pi\)
−0.571876 + 0.820340i \(0.693784\pi\)
\(774\) 5.04562 + 1.93598i 0.181361 + 0.0695873i
\(775\) 3.74450i 0.134506i
\(776\) −7.21239 6.05191i −0.258910 0.217251i
\(777\) 28.9743 0.638197i 1.03945 0.0228952i
\(778\) 1.40350 + 7.95962i 0.0503178 + 0.285366i
\(779\) 2.37671 6.52996i 0.0851546 0.233960i
\(780\) 3.29382 + 3.35132i 0.117938 + 0.119996i
\(781\) 11.1145 63.0337i 0.397710 2.25552i
\(782\) −5.42549 9.39722i −0.194015 0.336044i
\(783\) 20.2285 40.5945i 0.722908 1.45073i
\(784\) −4.16227 + 5.62810i −0.148652 + 0.201004i
\(785\) −1.50351 4.13085i −0.0536625 0.147436i
\(786\) −23.6787 24.0921i −0.844593 0.859338i
\(787\) 31.9833 5.63951i 1.14008 0.201027i 0.428439 0.903570i \(-0.359064\pi\)
0.711641 + 0.702544i \(0.247952\pi\)
\(788\) 1.72421 4.73724i 0.0614226 0.168757i
\(789\) 24.8709 17.0960i 0.885426 0.608632i
\(790\) 22.7884 27.1581i 0.810773 0.966242i
\(791\) −3.26313 + 1.64530i −0.116024 + 0.0585000i
\(792\) −10.8648 + 12.5022i −0.386063 + 0.444247i
\(793\) −2.93213 + 5.07860i −0.104123 + 0.180346i
\(794\) −1.36482 1.14522i −0.0484357 0.0406424i
\(795\) 3.83148 + 8.40578i 0.135889 + 0.298122i
\(796\) −1.60584 + 0.283153i −0.0569174 + 0.0100361i
\(797\) −5.75945 2.09627i −0.204010 0.0742537i 0.237994 0.971267i \(-0.423510\pi\)
−0.442004 + 0.897013i \(0.645732\pi\)
\(798\) −1.56718 + 10.1961i −0.0554775 + 0.360938i
\(799\) −6.08261 + 34.4962i −0.215187 + 1.22039i
\(800\) 1.14434 + 0.660685i 0.0404585 + 0.0233587i
\(801\) −41.4615 + 22.9905i −1.46497 + 0.812329i
\(802\) −0.416851 0.722008i −0.0147195 0.0254950i
\(803\) −0.414513 + 2.35082i −0.0146278 + 0.0829586i
\(804\) 1.92307 4.03257i 0.0678215 0.142218i
\(805\) −7.25261 9.70973i −0.255621 0.342223i
\(806\) −1.96551 2.34241i −0.0692322 0.0825077i
\(807\) 49.3270 + 13.6757i 1.73639 + 0.481407i
\(808\) 6.71243 + 1.18358i 0.236143 + 0.0416383i
\(809\) −10.1637 5.86803i −0.357337 0.206309i 0.310575 0.950549i \(-0.399478\pi\)
−0.667912 + 0.744240i \(0.732812\pi\)
\(810\) 19.1932 + 11.9854i 0.674382 + 0.421125i
\(811\) 16.3722i 0.574907i −0.957795 0.287453i \(-0.907191\pi\)
0.957795 0.287453i \(-0.0928086\pi\)
\(812\) −15.8213 + 16.8230i −0.555217 + 0.590370i
\(813\) 15.2775 + 15.5442i 0.535806 + 0.545160i
\(814\) −32.8113 11.9423i −1.15004 0.418579i
\(815\) −57.4080 20.8948i −2.01091 0.731913i
\(816\) −5.84357 8.50111i −0.204566 0.297599i
\(817\) −3.99358 0.704176i −0.139718 0.0246360i
\(818\) −10.4172 + 18.0432i −0.364230 + 0.630865i
\(819\) −3.72302 7.71311i −0.130093 0.269518i
\(820\) 3.88066 + 6.72151i 0.135519 + 0.234725i
\(821\) −7.33250 20.1459i −0.255906 0.703096i −0.999409 0.0343636i \(-0.989060\pi\)
0.743504 0.668732i \(-0.233163\pi\)
\(822\) 22.7128 + 16.1983i 0.792199 + 0.564982i
\(823\) −20.3850 + 17.1051i −0.710578 + 0.596246i −0.924761 0.380548i \(-0.875735\pi\)
0.214183 + 0.976793i \(0.431291\pi\)
\(824\) −1.34703 7.63937i −0.0469259 0.266130i
\(825\) −7.33710 + 10.2878i −0.255445 + 0.358176i
\(826\) −19.4498 + 20.6813i −0.676747 + 0.719594i
\(827\) −1.62462 + 0.937977i −0.0564937 + 0.0326167i −0.527981 0.849256i \(-0.677051\pi\)
0.471487 + 0.881873i \(0.343717\pi\)
\(828\) 5.16767 1.78022i 0.179589 0.0618670i
\(829\) −20.8924 + 12.0622i −0.725622 + 0.418938i −0.816818 0.576895i \(-0.804264\pi\)
0.0911965 + 0.995833i \(0.470931\pi\)
\(830\) −5.87401 16.1387i −0.203890 0.560183i
\(831\) −1.55376 2.26038i −0.0538995 0.0784118i
\(832\) 1.06265 0.187374i 0.0368408 0.00649602i
\(833\) 34.7594 23.0200i 1.20434 0.797595i
\(834\) 2.10748 + 8.14654i 0.0729759 + 0.282091i
\(835\) −26.7020 22.4056i −0.924060 0.775379i
\(836\) 6.21433 10.7635i 0.214927 0.372265i
\(837\) −11.8386 8.75607i −0.409202 0.302654i
\(838\) −7.44306 + 4.29725i −0.257116 + 0.148446i
\(839\) 7.89023 2.87181i 0.272401 0.0991458i −0.202208 0.979343i \(-0.564812\pi\)
0.474609 + 0.880197i \(0.342589\pi\)
\(840\) −7.59855 8.66088i −0.262175 0.298829i
\(841\) −36.1490 + 30.3326i −1.24652 + 1.04595i
\(842\) 5.05808 + 6.02799i 0.174313 + 0.207738i
\(843\) −3.48293 44.2133i −0.119959 1.52279i
\(844\) 24.7552 9.01017i 0.852110 0.310143i
\(845\) −29.7576 −1.02369
\(846\) −16.4731 6.32063i −0.566355 0.217308i
\(847\) 23.2076 + 46.0278i 0.797422 + 1.58154i
\(848\) 2.08908 + 0.368361i 0.0717393 + 0.0126496i
\(849\) 2.83556 3.97593i 0.0973163 0.136454i
\(850\) −5.05866 6.02868i −0.173511 0.206782i
\(851\) 7.40630 + 8.82648i 0.253885 + 0.302568i
\(852\) −11.6590 + 16.3479i −0.399431 + 0.560068i
\(853\) 5.55474 + 0.979451i 0.190191 + 0.0335358i 0.267932 0.963438i \(-0.413660\pi\)
−0.0777413 + 0.996974i \(0.524771\pi\)
\(854\) 7.88222 12.0259i 0.269724 0.411516i
\(855\) −15.8525 6.08253i −0.542144 0.208018i
\(856\) 17.9843 0.614690
\(857\) 12.4436 4.52910i 0.425065 0.154711i −0.120625 0.992698i \(-0.538490\pi\)
0.545690 + 0.837987i \(0.316268\pi\)
\(858\) 0.810360 + 10.2869i 0.0276652 + 0.351190i
\(859\) 24.0348 + 28.6436i 0.820058 + 0.977307i 0.999980 0.00637407i \(-0.00202894\pi\)
−0.179922 + 0.983681i \(0.557584\pi\)
\(860\) 3.46957 2.91132i 0.118312 0.0992751i
\(861\) −2.76265 13.8738i −0.0941508 0.472819i
\(862\) −30.7326 + 11.1857i −1.04676 + 0.380988i
\(863\) −5.31021 + 3.06585i −0.180762 + 0.104363i −0.587651 0.809115i \(-0.699947\pi\)
0.406889 + 0.913478i \(0.366614\pi\)
\(864\) 4.76473 2.07301i 0.162099 0.0705253i
\(865\) −28.1917 + 48.8294i −0.958545 + 1.66025i
\(866\) 0.748267 + 0.627871i 0.0254272 + 0.0213359i
\(867\) 8.01309 + 30.9749i 0.272139 + 1.05196i
\(868\) 4.48676 + 6.00683i 0.152290 + 0.203885i
\(869\) 76.6693 13.5189i 2.60083 0.458596i
\(870\) −21.5322 31.3245i −0.730008 1.06200i
\(871\) −0.951936 2.61542i −0.0322551 0.0886202i
\(872\) −6.25057 + 3.60877i −0.211671 + 0.122208i
\(873\) −26.7051 + 9.19970i −0.903831 + 0.311363i
\(874\) −3.55182 + 2.05064i −0.120142 + 0.0693640i
\(875\) 17.8257 + 16.7643i 0.602620 + 0.566738i
\(876\) 0.434818 0.609687i 0.0146911 0.0205994i
\(877\) 3.88182 + 22.0149i 0.131080 + 0.743391i 0.977510 + 0.210891i \(0.0676364\pi\)
−0.846430 + 0.532500i \(0.821252\pi\)
\(878\) 17.0866 14.3374i 0.576645 0.483863i
\(879\) −26.9960 19.2531i −0.910552 0.649389i
\(880\) 4.74774 + 13.0443i 0.160046 + 0.439724i
\(881\) −5.65245 9.79033i −0.190436 0.329845i 0.754959 0.655772i \(-0.227657\pi\)
−0.945395 + 0.325927i \(0.894323\pi\)
\(882\) 8.04435 + 19.3982i 0.270867 + 0.653170i
\(883\) −2.61482 + 4.52900i −0.0879957 + 0.152413i −0.906664 0.421854i \(-0.861380\pi\)
0.818668 + 0.574267i \(0.194713\pi\)
\(884\) −6.32898 1.11597i −0.212867 0.0375341i
\(885\) −26.4705 38.5088i −0.889797 1.29446i
\(886\) −15.0651 5.48324i −0.506121 0.184213i
\(887\) 27.7731 + 10.1086i 0.932528 + 0.339413i 0.763211 0.646149i \(-0.223622\pi\)
0.169317 + 0.985562i \(0.445844\pi\)
\(888\) 7.67826 + 7.81231i 0.257666 + 0.262164i
\(889\) −10.5730 + 44.9285i −0.354606 + 1.50685i
\(890\) 39.7325i 1.33184i
\(891\) 15.3691 + 47.2539i 0.514883 + 1.58306i
\(892\) 4.39575 + 2.53789i 0.147181 + 0.0849748i
\(893\) 13.0383 + 2.29901i 0.436312 + 0.0769335i
\(894\) −14.9767 4.15223i −0.500897 0.138871i
\(895\) 6.10454 + 7.27511i 0.204052 + 0.243180i
\(896\) −2.62737 + 0.311323i −0.0877743 + 0.0104006i
\(897\) 1.46569 3.07346i 0.0489380 0.102620i
\(898\) −4.84671 + 27.4871i −0.161737 + 0.917256i
\(899\) 12.3676 + 21.4214i 0.412483 + 0.714442i
\(900\) 3.46681 1.92235i 0.115560 0.0640783i
\(901\) −10.9415 6.31709i −0.364515 0.210453i
\(902\) −2.95958 + 16.7846i −0.0985434 + 0.558867i
\(903\) −7.69327 + 2.99358i −0.256016 + 0.0996200i
\(904\) −1.29795 0.472416i −0.0431693 0.0157123i
\(905\) −48.7920 + 8.60335i −1.62190 + 0.285985i
\(906\) −9.91631 21.7551i −0.329447 0.722765i
\(907\) 5.90232 + 4.95264i 0.195983 + 0.164450i 0.735499 0.677526i \(-0.236948\pi\)
−0.539515 + 0.841976i \(0.681392\pi\)
\(908\) 12.6735 21.9511i 0.420584 0.728473i
\(909\) 13.4128 15.4342i 0.444874 0.511921i
\(910\) −7.16634 0.405981i −0.237562 0.0134581i
\(911\) 19.4607 23.1923i 0.644761 0.768397i −0.340353 0.940298i \(-0.610546\pi\)
0.985114 + 0.171901i \(0.0549909\pi\)
\(912\) −3.21312 + 2.20866i −0.106397 + 0.0731362i
\(913\) 12.8991 35.4399i 0.426897 1.17289i
\(914\) 3.41808 0.602699i 0.113060 0.0199355i
\(915\) 16.5896 + 16.8792i 0.548434 + 0.558008i
\(916\) 8.31759 + 22.8524i 0.274821 + 0.755064i
\(917\) 51.5178 + 2.91854i 1.70127 + 0.0963785i
\(918\) −30.8893 + 1.89611i −1.01950 + 0.0625810i
\(919\) 6.70923 + 11.6207i 0.221317 + 0.383333i 0.955208 0.295935i \(-0.0956311\pi\)
−0.733891 + 0.679267i \(0.762298\pi\)
\(920\) 0.795429 4.51110i 0.0262245 0.148727i
\(921\) 16.2278 + 16.5111i 0.534724 + 0.544059i
\(922\) 11.8326 32.5099i 0.389687 1.07066i
\(923\) 2.17220 + 12.3192i 0.0714989 + 0.405491i
\(924\) −0.557156 25.2950i −0.0183291 0.832144i
\(925\) 6.40157 + 5.37156i 0.210482 + 0.176616i
\(926\) 4.13746i 0.135965i
\(927\) −21.7272 8.33662i −0.713615 0.273811i
\(928\) −8.72864 −0.286532
\(929\) −32.2528 + 11.7390i −1.05818 + 0.385146i −0.811744 0.584014i \(-0.801481\pi\)
−0.246435 + 0.969159i \(0.579259\pi\)
\(930\) −11.2291 + 5.11838i −0.368216 + 0.167838i
\(931\) −8.70074 13.1378i −0.285155 0.430574i
\(932\) −0.647538 + 1.77910i −0.0212108 + 0.0582763i
\(933\) 11.1140 + 7.92629i 0.363855 + 0.259495i
\(934\) 6.02811 7.18402i 0.197246 0.235068i
\(935\) 82.6759i 2.70379i
\(936\) 1.15964 3.02229i 0.0379040 0.0987867i
\(937\) −13.4150 7.74515i −0.438249 0.253023i 0.264606 0.964357i \(-0.414758\pi\)
−0.702854 + 0.711334i \(0.748092\pi\)
\(938\) 1.96764 + 6.53462i 0.0642458 + 0.213363i
\(939\) 43.7465 30.0708i 1.42761 0.981325i
\(940\) −11.3276 + 9.50495i −0.369464 + 0.310017i
\(941\) −0.467308 2.65024i −0.0152338 0.0863953i 0.976243 0.216679i \(-0.0695224\pi\)
−0.991477 + 0.130283i \(0.958411\pi\)
\(942\) −2.15983 + 2.12277i −0.0703711 + 0.0691636i
\(943\) 3.61513 4.30834i 0.117725 0.140299i
\(944\) −10.7305 −0.349250
\(945\) −34.0112 + 6.16263i −1.10638 + 0.200470i
\(946\) 9.94596 0.323371
\(947\) 28.6809 34.1805i 0.932003 1.11072i −0.0616347 0.998099i \(-0.519631\pi\)
0.993638 0.112620i \(-0.0359242\pi\)
\(948\) −23.5353 6.52505i −0.764391 0.211924i
\(949\) −0.0810115 0.459439i −0.00262974 0.0149140i
\(950\) −2.27863 + 1.91199i −0.0739284 + 0.0620333i
\(951\) 0.405175 + 5.14340i 0.0131387 + 0.166786i
\(952\) 15.3387 + 3.60963i 0.497130 + 0.116989i
\(953\) 19.2307 + 11.1028i 0.622942 + 0.359656i 0.778014 0.628247i \(-0.216227\pi\)
−0.155072 + 0.987903i \(0.549561\pi\)
\(954\) 4.17440 4.80352i 0.135151 0.155520i
\(955\) 8.59180i 0.278024i
\(956\) 7.92982 9.45039i 0.256469 0.305647i
\(957\) 7.99426 83.0876i 0.258418 2.68584i
\(958\) −3.93054 + 10.7991i −0.126990 + 0.348902i
\(959\) −42.3177 + 5.01432i −1.36651 + 0.161921i
\(960\) 0.417068 4.33476i 0.0134608 0.139904i
\(961\) −21.5843 + 7.85606i −0.696269 + 0.253421i
\(962\) 6.82412 0.220019
\(963\) 27.7810 46.2507i 0.895230 1.49041i
\(964\) 12.3061i 0.396352i
\(965\) −26.0163 21.8302i −0.837493 0.702740i
\(966\) −4.01427 + 7.32063i −0.129157 + 0.235537i
\(967\) −7.58590 43.0218i −0.243946 1.38349i −0.822927 0.568147i \(-0.807661\pi\)
0.578981 0.815341i \(-0.303451\pi\)
\(968\) −6.66363 + 18.3082i −0.214177 + 0.588447i
\(969\) 22.4818 5.81596i 0.722221 0.186836i
\(970\) −4.11056 + 23.3121i −0.131982 + 0.748508i
\(971\) −10.2335 17.7249i −0.328408 0.568820i 0.653788 0.756678i \(-0.273179\pi\)
−0.982196 + 0.187858i \(0.939846\pi\)
\(972\) 2.02902 15.4558i 0.0650808 0.495746i
\(973\) −10.7503 7.04617i −0.344639 0.225890i
\(974\) 9.39481 + 25.8120i 0.301029 + 0.827071i
\(975\) 0.659793 2.37981i 0.0211303 0.0762151i
\(976\) 5.35212 0.943723i 0.171317 0.0302078i
\(977\) −10.4740 + 28.7771i −0.335094 + 0.920662i 0.651671 + 0.758502i \(0.274068\pi\)
−0.986764 + 0.162160i \(0.948154\pi\)
\(978\) 3.30514 + 41.9564i 0.105687 + 1.34162i
\(979\) −56.0839 + 66.8381i −1.79245 + 2.13616i
\(980\) 17.4870 + 1.98770i 0.558603 + 0.0634946i
\(981\) −0.374707 + 21.6494i −0.0119635 + 0.691211i
\(982\) −6.26687 + 10.8545i −0.199984 + 0.346382i
\(983\) −14.5651 12.2216i −0.464554 0.389807i 0.380249 0.924884i \(-0.375838\pi\)
−0.844803 + 0.535077i \(0.820283\pi\)
\(984\) 3.10456 4.35311i 0.0989698 0.138772i
\(985\) −12.4824 + 2.20098i −0.397721 + 0.0701290i
\(986\) 48.8513 + 17.7804i 1.55574 + 0.566244i
\(987\) 25.1172 9.77350i 0.799489 0.311094i
\(988\) −0.421797 + 2.39213i −0.0134191 + 0.0761038i
\(989\) −2.84232 1.64101i −0.0903805 0.0521812i
\(990\) 40.8805 + 7.94012i 1.29927 + 0.252354i
\(991\) 9.30306 + 16.1134i 0.295522 + 0.511858i 0.975106 0.221739i \(-0.0711733\pi\)
−0.679585 + 0.733597i \(0.737840\pi\)
\(992\) −0.492084 + 2.79075i −0.0156237 + 0.0886064i
\(993\) 0.991710 0.0781226i 0.0314710 0.00247915i
\(994\) −3.60913 30.4588i −0.114475 0.966095i
\(995\) 2.63526 + 3.14058i 0.0835434 + 0.0995631i
\(996\) −8.43817 + 8.29339i −0.267374 + 0.262786i
\(997\) −47.0895 8.30315i −1.49134 0.262963i −0.632240 0.774772i \(-0.717864\pi\)
−0.859099 + 0.511809i \(0.828976\pi\)
\(998\) −37.3160 21.5444i −1.18122 0.681976i
\(999\) 31.9520 7.67846i 1.01092 0.242936i
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 378.2.bf.a.101.19 yes 144
7.5 odd 6 378.2.ba.a.47.12 144
27.23 odd 18 378.2.ba.a.185.12 yes 144
189.131 even 18 inner 378.2.bf.a.131.19 yes 144
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
378.2.ba.a.47.12 144 7.5 odd 6
378.2.ba.a.185.12 yes 144 27.23 odd 18
378.2.bf.a.101.19 yes 144 1.1 even 1 trivial
378.2.bf.a.131.19 yes 144 189.131 even 18 inner