Properties

Label 384.3.u.a.235.42
Level $384$
Weight $3$
Character 384.235
Analytic conductor $10.463$
Analytic rank $0$
Dimension $1024$
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] = [384,3,Mod(19,384)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(384, base_ring=CyclotomicField(32))
 
chi = DirichletCharacter(H, H._module([16, 23, 0]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("384.19");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 384 = 2^{7} \cdot 3 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 384.u (of order \(32\), degree \(16\), 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: \(10.4632421514\)
Analytic rank: \(0\)
Dimension: \(1024\)
Relative dimension: \(64\) over \(\Q(\zeta_{32})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label 235.42
Character \(\chi\) \(=\) 384.235
Dual form 384.3.u.a.67.42

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.732561 + 1.86101i) q^{2} +(-1.09880 + 1.33889i) q^{3} +(-2.92671 + 2.72661i) q^{4} +(-1.79410 - 5.91435i) q^{5} +(-3.29663 - 1.06406i) q^{6} +(0.410318 - 2.06281i) q^{7} +(-7.21823 - 3.44922i) q^{8} +(-0.585271 - 2.94236i) q^{9} +O(q^{10})\) \(q+(0.732561 + 1.86101i) q^{2} +(-1.09880 + 1.33889i) q^{3} +(-2.92671 + 2.72661i) q^{4} +(-1.79410 - 5.91435i) q^{5} +(-3.29663 - 1.06406i) q^{6} +(0.410318 - 2.06281i) q^{7} +(-7.21823 - 3.44922i) q^{8} +(-0.585271 - 2.94236i) q^{9} +(9.69237 - 7.67146i) q^{10} +(9.51860 + 0.937500i) q^{11} +(-0.434764 - 6.91455i) q^{12} +(6.19805 + 1.88016i) q^{13} +(4.13948 - 0.747527i) q^{14} +(9.89005 + 4.09659i) q^{15} +(1.13124 - 15.9600i) q^{16} +(5.14803 + 12.4285i) q^{17} +(5.04700 - 3.24465i) q^{18} +(19.9617 - 10.6697i) q^{19} +(21.3769 + 12.4178i) q^{20} +(2.31102 + 2.81599i) q^{21} +(5.22826 + 18.4010i) q^{22} +(3.20682 + 2.14273i) q^{23} +(12.5495 - 5.87443i) q^{24} +(-10.9740 + 7.33261i) q^{25} +(1.04146 + 12.9120i) q^{26} +(4.58260 + 2.44945i) q^{27} +(4.42358 + 7.15601i) q^{28} +(4.99399 - 0.491865i) q^{29} +(-0.378727 + 21.4065i) q^{30} +(30.4590 - 30.4590i) q^{31} +(30.5303 - 9.58641i) q^{32} +(-11.7143 + 11.7143i) q^{33} +(-19.3582 + 18.6851i) q^{34} +(-12.9363 + 1.27412i) q^{35} +(9.73556 + 7.01561i) q^{36} +(-21.9329 - 11.7234i) q^{37} +(34.4796 + 29.3326i) q^{38} +(-9.32776 + 6.23261i) q^{39} +(-7.44970 + 48.8794i) q^{40} +(-20.7691 - 13.8774i) q^{41} +(-3.54761 + 6.36371i) q^{42} +(20.7622 + 25.2988i) q^{43} +(-30.4144 + 23.2097i) q^{44} +(-16.3521 + 8.74038i) q^{45} +(-1.63844 + 7.53760i) q^{46} +(-28.6184 - 69.0910i) q^{47} +(20.1257 + 19.0514i) q^{48} +(41.1833 + 17.0587i) q^{49} +(-21.6852 - 15.0512i) q^{50} +(-22.2970 - 6.76373i) q^{51} +(-23.2663 + 11.3970i) q^{52} +(43.1479 + 4.24969i) q^{53} +(-1.20141 + 10.3226i) q^{54} +(-11.5326 - 57.9783i) q^{55} +(-10.0768 + 13.4745i) q^{56} +(-7.64827 + 38.4505i) q^{57} +(4.57377 + 8.93354i) q^{58} +(-12.3809 - 40.8143i) q^{59} +(-40.1151 + 14.9767i) q^{60} +(-25.7782 + 31.4108i) q^{61} +(78.9977 + 34.3714i) q^{62} -6.30966 q^{63} +(40.2057 + 49.7946i) q^{64} -40.0307i q^{65} +(-30.3818 - 13.2189i) q^{66} +(99.4212 + 81.5929i) q^{67} +(-48.9543 - 22.3378i) q^{68} +(-6.39254 + 1.93916i) q^{69} +(-11.8478 - 23.1412i) q^{70} +(-47.2124 - 9.39114i) q^{71} +(-5.92422 + 23.2573i) q^{72} +(12.7678 - 2.53967i) q^{73} +(5.75011 - 49.4054i) q^{74} +(2.24069 - 22.7501i) q^{75} +(-29.3298 + 85.6548i) q^{76} +(5.83953 - 19.2504i) q^{77} +(-18.4321 - 12.7933i) q^{78} +(50.3282 - 121.503i) q^{79} +(-96.4224 + 21.9432i) q^{80} +(-8.31492 + 3.44415i) q^{81} +(10.6114 - 48.8175i) q^{82} +(-31.6094 - 59.1371i) q^{83} +(-14.4418 - 1.94033i) q^{84} +(64.2702 - 52.7452i) q^{85} +(-31.8717 + 57.1715i) q^{86} +(-4.82885 + 7.22688i) q^{87} +(-65.4738 - 39.5989i) q^{88} +(-18.6586 - 27.9246i) q^{89} +(-28.2448 - 24.0285i) q^{90} +(6.42157 - 12.0139i) q^{91} +(-15.2278 + 2.47259i) q^{92} +(7.31297 + 74.2498i) q^{93} +(107.614 - 103.873i) q^{94} +(-98.9177 - 98.9177i) q^{95} +(-20.7116 + 51.4104i) q^{96} +(31.4893 + 31.4893i) q^{97} +(-1.57706 + 89.1390i) q^{98} +(-2.81250 - 28.5558i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 1024 q+O(q^{10}) \) Copy content Toggle raw display \( 1024 q + 1248 q^{50} + 1056 q^{52} + 288 q^{54} + 1568 q^{56} + 576 q^{60} + 192 q^{62} - 192 q^{64} - 576 q^{66} - 960 q^{68} - 1344 q^{70} - 2464 q^{74} - 416 q^{76} - 1440 q^{78} - 1632 q^{80}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(133\) \(257\)
\(\chi(n)\) \(-1\) \(e\left(\frac{13}{32}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.732561 + 1.86101i 0.366281 + 0.930504i
\(3\) −1.09880 + 1.33889i −0.366267 + 0.446298i
\(4\) −2.92671 + 2.72661i −0.731677 + 0.681652i
\(5\) −1.79410 5.91435i −0.358820 1.18287i −0.931699 0.363231i \(-0.881674\pi\)
0.572879 0.819640i \(-0.305826\pi\)
\(6\) −3.29663 1.06406i −0.549439 0.177343i
\(7\) 0.410318 2.06281i 0.0586168 0.294687i −0.940346 0.340220i \(-0.889499\pi\)
0.998963 + 0.0455330i \(0.0144986\pi\)
\(8\) −7.21823 3.44922i −0.902279 0.431153i
\(9\) −0.585271 2.94236i −0.0650301 0.326928i
\(10\) 9.69237 7.67146i 0.969237 0.767146i
\(11\) 9.51860 + 0.937500i 0.865327 + 0.0852273i 0.520933 0.853598i \(-0.325584\pi\)
0.344395 + 0.938825i \(0.388084\pi\)
\(12\) −0.434764 6.91455i −0.0362304 0.576212i
\(13\) 6.19805 + 1.88016i 0.476773 + 0.144628i 0.519520 0.854458i \(-0.326111\pi\)
−0.0427467 + 0.999086i \(0.513611\pi\)
\(14\) 4.13948 0.747527i 0.295677 0.0533948i
\(15\) 9.89005 + 4.09659i 0.659336 + 0.273106i
\(16\) 1.13124 15.9600i 0.0707023 0.997497i
\(17\) 5.14803 + 12.4285i 0.302826 + 0.731086i 0.999901 + 0.0140876i \(0.00448436\pi\)
−0.697075 + 0.716998i \(0.745516\pi\)
\(18\) 5.04700 3.24465i 0.280389 0.180258i
\(19\) 19.9617 10.6697i 1.05061 0.561565i 0.146656 0.989187i \(-0.453149\pi\)
0.903957 + 0.427623i \(0.140649\pi\)
\(20\) 21.3769 + 12.4178i 1.06885 + 0.620889i
\(21\) 2.31102 + 2.81599i 0.110049 + 0.134095i
\(22\) 5.22826 + 18.4010i 0.237648 + 0.836408i
\(23\) 3.20682 + 2.14273i 0.139427 + 0.0931621i 0.623327 0.781961i \(-0.285780\pi\)
−0.483901 + 0.875123i \(0.660780\pi\)
\(24\) 12.5495 5.87443i 0.522898 0.244768i
\(25\) −10.9740 + 7.33261i −0.438961 + 0.293305i
\(26\) 1.04146 + 12.9120i 0.0400562 + 0.496614i
\(27\) 4.58260 + 2.44945i 0.169726 + 0.0907203i
\(28\) 4.42358 + 7.15601i 0.157985 + 0.255572i
\(29\) 4.99399 0.491865i 0.172207 0.0169609i −0.0115463 0.999933i \(-0.503675\pi\)
0.183753 + 0.982972i \(0.441175\pi\)
\(30\) −0.378727 + 21.4065i −0.0126242 + 0.713549i
\(31\) 30.4590 30.4590i 0.982550 0.982550i −0.0173007 0.999850i \(-0.505507\pi\)
0.999850 + 0.0173007i \(0.00550727\pi\)
\(32\) 30.5303 9.58641i 0.954073 0.299575i
\(33\) −11.7143 + 11.7143i −0.354978 + 0.354978i
\(34\) −19.3582 + 18.6851i −0.569359 + 0.549563i
\(35\) −12.9363 + 1.27412i −0.369609 + 0.0364033i
\(36\) 9.73556 + 7.01561i 0.270432 + 0.194878i
\(37\) −21.9329 11.7234i −0.592781 0.316848i 0.147588 0.989049i \(-0.452849\pi\)
−0.740369 + 0.672201i \(0.765349\pi\)
\(38\) 34.4796 + 29.3326i 0.907358 + 0.771910i
\(39\) −9.32776 + 6.23261i −0.239173 + 0.159810i
\(40\) −7.44970 + 48.8794i −0.186242 + 1.22199i
\(41\) −20.7691 13.8774i −0.506562 0.338474i 0.275885 0.961191i \(-0.411029\pi\)
−0.782448 + 0.622716i \(0.786029\pi\)
\(42\) −3.54761 + 6.36371i −0.0844669 + 0.151517i
\(43\) 20.7622 + 25.2988i 0.482841 + 0.588344i 0.956269 0.292489i \(-0.0944834\pi\)
−0.473427 + 0.880833i \(0.656983\pi\)
\(44\) −30.4144 + 23.2097i −0.691235 + 0.527493i
\(45\) −16.3521 + 8.74038i −0.363380 + 0.194231i
\(46\) −1.63844 + 7.53760i −0.0356184 + 0.163861i
\(47\) −28.6184 69.0910i −0.608903 1.47002i −0.864195 0.503157i \(-0.832172\pi\)
0.255292 0.966864i \(-0.417828\pi\)
\(48\) 20.1257 + 19.0514i 0.419285 + 0.396905i
\(49\) 41.1833 + 17.0587i 0.840475 + 0.348136i
\(50\) −21.6852 15.0512i −0.433704 0.301024i
\(51\) −22.2970 6.76373i −0.437197 0.132622i
\(52\) −23.2663 + 11.3970i −0.447430 + 0.219173i
\(53\) 43.1479 + 4.24969i 0.814111 + 0.0801829i 0.496498 0.868038i \(-0.334619\pi\)
0.317612 + 0.948221i \(0.397119\pi\)
\(54\) −1.20141 + 10.3226i −0.0222484 + 0.191160i
\(55\) −11.5326 57.9783i −0.209684 1.05415i
\(56\) −10.0768 + 13.4745i −0.179944 + 0.240617i
\(57\) −7.64827 + 38.4505i −0.134180 + 0.674569i
\(58\) 4.57377 + 8.93354i 0.0788581 + 0.154027i
\(59\) −12.3809 40.8143i −0.209845 0.691767i −0.997167 0.0752244i \(-0.976033\pi\)
0.787321 0.616543i \(-0.211467\pi\)
\(60\) −40.1151 + 14.9767i −0.668584 + 0.249612i
\(61\) −25.7782 + 31.4108i −0.422593 + 0.514931i −0.940170 0.340705i \(-0.889334\pi\)
0.517577 + 0.855637i \(0.326834\pi\)
\(62\) 78.9977 + 34.3714i 1.27416 + 0.554378i
\(63\) −6.30966 −0.100153
\(64\) 40.2057 + 49.7946i 0.628214 + 0.778040i
\(65\) 40.0307i 0.615856i
\(66\) −30.3818 13.2189i −0.460330 0.200287i
\(67\) 99.4212 + 81.5929i 1.48390 + 1.21780i 0.919975 + 0.391977i \(0.128209\pi\)
0.563923 + 0.825827i \(0.309291\pi\)
\(68\) −48.9543 22.3378i −0.719916 0.328497i
\(69\) −6.39254 + 1.93916i −0.0926455 + 0.0281037i
\(70\) −11.8478 23.1412i −0.169254 0.330589i
\(71\) −47.2124 9.39114i −0.664964 0.132270i −0.148943 0.988846i \(-0.547587\pi\)
−0.516021 + 0.856576i \(0.672587\pi\)
\(72\) −5.92422 + 23.2573i −0.0822808 + 0.323019i
\(73\) 12.7678 2.53967i 0.174901 0.0347900i −0.106863 0.994274i \(-0.534081\pi\)
0.281764 + 0.959484i \(0.409081\pi\)
\(74\) 5.75011 49.4054i 0.0777042 0.667640i
\(75\) 2.24069 22.7501i 0.0298759 0.303335i
\(76\) −29.3298 + 85.6548i −0.385918 + 1.12704i
\(77\) 5.83953 19.2504i 0.0758381 0.250005i
\(78\) −18.4321 12.7933i −0.236309 0.164016i
\(79\) 50.3282 121.503i 0.637065 1.53801i −0.193506 0.981099i \(-0.561986\pi\)
0.830571 0.556913i \(-0.188014\pi\)
\(80\) −96.4224 + 21.9432i −1.20528 + 0.274290i
\(81\) −8.31492 + 3.44415i −0.102653 + 0.0425204i
\(82\) 10.6114 48.8175i 0.129408 0.595335i
\(83\) −31.6094 59.1371i −0.380837 0.712495i 0.616349 0.787473i \(-0.288611\pi\)
−0.997185 + 0.0749784i \(0.976111\pi\)
\(84\) −14.4418 1.94033i −0.171926 0.0230991i
\(85\) 64.2702 52.7452i 0.756120 0.620531i
\(86\) −31.8717 + 57.1715i −0.370601 + 0.664785i
\(87\) −4.82885 + 7.22688i −0.0555040 + 0.0830676i
\(88\) −65.4738 39.5989i −0.744021 0.449987i
\(89\) −18.6586 27.9246i −0.209647 0.313759i 0.711712 0.702471i \(-0.247920\pi\)
−0.921359 + 0.388712i \(0.872920\pi\)
\(90\) −28.2448 24.0285i −0.313831 0.266984i
\(91\) 6.42157 12.0139i 0.0705667 0.132021i
\(92\) −15.2278 + 2.47259i −0.165520 + 0.0268760i
\(93\) 7.31297 + 74.2498i 0.0786341 + 0.798385i
\(94\) 107.614 103.873i 1.14483 1.10503i
\(95\) −98.9177 98.9177i −1.04124 1.04124i
\(96\) −20.7116 + 51.4104i −0.215746 + 0.535525i
\(97\) 31.4893 + 31.4893i 0.324632 + 0.324632i 0.850541 0.525909i \(-0.176275\pi\)
−0.525909 + 0.850541i \(0.676275\pi\)
\(98\) −1.57706 + 89.1390i −0.0160925 + 0.909582i
\(99\) −2.81250 28.5558i −0.0284091 0.288442i
\(100\) 12.1246 51.3823i 0.121246 0.513823i
\(101\) 59.8985 112.062i 0.593055 1.10953i −0.389054 0.921215i \(-0.627198\pi\)
0.982109 0.188313i \(-0.0603019\pi\)
\(102\) −3.74658 46.4498i −0.0367312 0.455391i
\(103\) −10.0301 15.0111i −0.0973797 0.145739i 0.779580 0.626302i \(-0.215432\pi\)
−0.876960 + 0.480563i \(0.840432\pi\)
\(104\) −38.2539 34.9499i −0.367826 0.336057i
\(105\) 12.5085 18.7203i 0.119129 0.178289i
\(106\) 23.6997 + 83.4117i 0.223582 + 0.786903i
\(107\) −25.8010 + 21.1743i −0.241131 + 0.197891i −0.747195 0.664605i \(-0.768600\pi\)
0.506064 + 0.862496i \(0.331100\pi\)
\(108\) −20.0906 + 5.32612i −0.186024 + 0.0493159i
\(109\) 96.8055 + 181.110i 0.888124 + 1.66156i 0.740014 + 0.672591i \(0.234819\pi\)
0.148109 + 0.988971i \(0.452681\pi\)
\(110\) 99.4498 63.9350i 0.904089 0.581227i
\(111\) 39.7962 16.4841i 0.358525 0.148506i
\(112\) −32.4581 8.88218i −0.289805 0.0793051i
\(113\) −25.1499 + 60.7173i −0.222566 + 0.537321i −0.995237 0.0974851i \(-0.968920\pi\)
0.772671 + 0.634806i \(0.218920\pi\)
\(114\) −77.1595 + 13.9338i −0.676837 + 0.122226i
\(115\) 6.91950 22.8105i 0.0601695 0.198352i
\(116\) −13.2748 + 15.0562i −0.114438 + 0.129795i
\(117\) 1.90456 19.3373i 0.0162783 0.165276i
\(118\) 66.8860 52.9399i 0.566830 0.448643i
\(119\) 27.7498 5.51978i 0.233192 0.0463847i
\(120\) −57.2586 63.6831i −0.477155 0.530693i
\(121\) −28.9502 5.75855i −0.239258 0.0475913i
\(122\) −77.3399 24.9631i −0.633933 0.204615i
\(123\) 41.4015 12.5590i 0.336597 0.102106i
\(124\) −6.09490 + 172.195i −0.0491525 + 1.38867i
\(125\) −56.3833 46.2726i −0.451066 0.370180i
\(126\) −4.62221 11.7423i −0.0366842 0.0931931i
\(127\) 61.9840i 0.488063i −0.969767 0.244031i \(-0.921530\pi\)
0.969767 0.244031i \(-0.0784700\pi\)
\(128\) −63.2150 + 111.301i −0.493867 + 0.869537i
\(129\) −56.6859 −0.439426
\(130\) 74.4974 29.3249i 0.573057 0.225576i
\(131\) −69.3975 + 84.5611i −0.529752 + 0.645504i −0.967283 0.253699i \(-0.918353\pi\)
0.437532 + 0.899203i \(0.355853\pi\)
\(132\) 2.34404 66.2244i 0.0177579 0.501700i
\(133\) −13.8190 45.5550i −0.103902 0.342519i
\(134\) −79.0129 + 244.795i −0.589649 + 1.82683i
\(135\) 6.26527 31.4977i 0.0464094 0.233316i
\(136\) 5.70881 107.468i 0.0419765 0.790207i
\(137\) −5.20621 26.1734i −0.0380015 0.191047i 0.957122 0.289686i \(-0.0935509\pi\)
−0.995123 + 0.0986395i \(0.968551\pi\)
\(138\) −8.29172 10.4760i −0.0600849 0.0759132i
\(139\) 89.0877 + 8.77438i 0.640919 + 0.0631250i 0.413256 0.910615i \(-0.364392\pi\)
0.227663 + 0.973740i \(0.426892\pi\)
\(140\) 34.3868 39.0012i 0.245620 0.278580i
\(141\) 123.951 + 37.6003i 0.879088 + 0.266669i
\(142\) −17.1090 94.7423i −0.120486 0.667200i
\(143\) 57.2341 + 23.7072i 0.400239 + 0.165784i
\(144\) −47.6220 + 6.01240i −0.330708 + 0.0417528i
\(145\) −11.8688 28.6538i −0.0818537 0.197612i
\(146\) 14.0795 + 21.9005i 0.0964352 + 0.150003i
\(147\) −68.0920 + 36.3959i −0.463211 + 0.247591i
\(148\) 96.1561 25.4915i 0.649704 0.172240i
\(149\) 123.915 + 150.991i 0.831647 + 1.01336i 0.999620 + 0.0275728i \(0.00877782\pi\)
−0.167973 + 0.985792i \(0.553722\pi\)
\(150\) 43.9797 12.4959i 0.293198 0.0833062i
\(151\) −190.006 126.958i −1.25832 0.840782i −0.265938 0.963990i \(-0.585682\pi\)
−0.992381 + 0.123208i \(0.960682\pi\)
\(152\) −180.890 + 8.16436i −1.19007 + 0.0537129i
\(153\) 33.5559 22.4214i 0.219320 0.146545i
\(154\) 40.1029 3.23465i 0.260408 0.0210042i
\(155\) −234.792 125.499i −1.51479 0.809671i
\(156\) 10.3058 43.6742i 0.0660625 0.279963i
\(157\) −107.999 + 10.6370i −0.687895 + 0.0677517i −0.435924 0.899983i \(-0.643578\pi\)
−0.251970 + 0.967735i \(0.581078\pi\)
\(158\) 262.987 + 4.65281i 1.66447 + 0.0294481i
\(159\) −53.1008 + 53.1008i −0.333967 + 0.333967i
\(160\) −111.472 163.368i −0.696699 1.02105i
\(161\) 5.73585 5.73585i 0.0356264 0.0356264i
\(162\) −12.5008 12.9511i −0.0771653 0.0799449i
\(163\) −131.628 + 12.9642i −0.807533 + 0.0795351i −0.493354 0.869829i \(-0.664229\pi\)
−0.314179 + 0.949364i \(0.601729\pi\)
\(164\) 98.6233 16.0138i 0.601362 0.0976453i
\(165\) 90.2988 + 48.2657i 0.547266 + 0.292520i
\(166\) 86.8988 102.147i 0.523487 0.615343i
\(167\) 50.2187 33.5551i 0.300711 0.200928i −0.396056 0.918226i \(-0.629621\pi\)
0.696767 + 0.717298i \(0.254621\pi\)
\(168\) −6.96851 28.2977i −0.0414792 0.168438i
\(169\) −105.638 70.5847i −0.625074 0.417661i
\(170\) 145.241 + 80.9683i 0.854359 + 0.476284i
\(171\) −43.0771 52.4896i −0.251913 0.306957i
\(172\) −129.745 17.4319i −0.754330 0.101348i
\(173\) −234.498 + 125.342i −1.35548 + 0.724518i −0.979373 0.202060i \(-0.935237\pi\)
−0.376104 + 0.926577i \(0.622737\pi\)
\(174\) −16.9867 3.69240i −0.0976248 0.0212207i
\(175\) 10.6229 + 25.6460i 0.0607024 + 0.146549i
\(176\) 25.7303 150.856i 0.146195 0.857136i
\(177\) 68.2501 + 28.2701i 0.385594 + 0.159718i
\(178\) 38.2993 55.1803i 0.215165 0.310002i
\(179\) 59.6029 + 18.0804i 0.332977 + 0.101008i 0.452346 0.891842i \(-0.350587\pi\)
−0.119369 + 0.992850i \(0.538087\pi\)
\(180\) 24.0262 70.1663i 0.133479 0.389813i
\(181\) 39.6222 + 3.90245i 0.218907 + 0.0215605i 0.206876 0.978367i \(-0.433670\pi\)
0.0120312 + 0.999928i \(0.496170\pi\)
\(182\) 27.0622 + 3.14967i 0.148693 + 0.0173059i
\(183\) −13.7306 69.0285i −0.0750307 0.377205i
\(184\) −15.7568 26.5277i −0.0856349 0.144173i
\(185\) −29.9864 + 150.752i −0.162088 + 0.814874i
\(186\) −132.822 + 68.0021i −0.714099 + 0.365602i
\(187\) 37.3504 + 123.128i 0.199735 + 0.658437i
\(188\) 272.142 + 124.178i 1.44756 + 0.660521i
\(189\) 6.93306 8.44796i 0.0366829 0.0446982i
\(190\) 111.623 256.550i 0.587492 1.35026i
\(191\) −63.9722 −0.334933 −0.167467 0.985878i \(-0.553559\pi\)
−0.167467 + 0.985878i \(0.553559\pi\)
\(192\) −110.848 0.883177i −0.577332 0.00459988i
\(193\) 151.671i 0.785862i −0.919568 0.392931i \(-0.871461\pi\)
0.919568 0.392931i \(-0.128539\pi\)
\(194\) −35.5340 + 81.6698i −0.183165 + 0.420978i
\(195\) 53.5968 + 43.9857i 0.274855 + 0.225568i
\(196\) −167.044 + 62.3648i −0.852264 + 0.318188i
\(197\) −113.968 + 34.5718i −0.578517 + 0.175491i −0.565964 0.824430i \(-0.691496\pi\)
−0.0125532 + 0.999921i \(0.503996\pi\)
\(198\) 51.0823 26.1530i 0.257991 0.132086i
\(199\) 191.661 + 38.1237i 0.963118 + 0.191576i 0.651515 0.758636i \(-0.274134\pi\)
0.311604 + 0.950212i \(0.399134\pi\)
\(200\) 104.505 15.0766i 0.522525 0.0753831i
\(201\) −218.488 + 43.4600i −1.08701 + 0.216219i
\(202\) 252.428 + 29.3792i 1.24965 + 0.145442i
\(203\) 1.03450 10.5035i 0.00509606 0.0517412i
\(204\) 83.6990 40.9998i 0.410289 0.200979i
\(205\) −44.8143 + 147.733i −0.218606 + 0.720649i
\(206\) 20.5882 29.6627i 0.0999425 0.143994i
\(207\) 4.42781 10.6897i 0.0213904 0.0516410i
\(208\) 37.0187 96.7937i 0.177975 0.465355i
\(209\) 200.010 82.8468i 0.956985 0.396396i
\(210\) 44.0020 + 9.56469i 0.209533 + 0.0455462i
\(211\) 13.8322 + 25.8782i 0.0655554 + 0.122646i 0.912564 0.408933i \(-0.134099\pi\)
−0.847009 + 0.531579i \(0.821599\pi\)
\(212\) −137.868 + 105.210i −0.650323 + 0.496272i
\(213\) 64.4508 52.8934i 0.302586 0.248326i
\(214\) −58.3064 32.5044i −0.272460 0.151890i
\(215\) 112.377 168.183i 0.522682 0.782248i
\(216\) −24.6295 33.4871i −0.114026 0.155033i
\(217\) −50.3332 75.3290i −0.231950 0.347138i
\(218\) −266.132 + 312.830i −1.22079 + 1.43500i
\(219\) −10.6289 + 19.8853i −0.0485339 + 0.0908005i
\(220\) 191.837 + 138.241i 0.871985 + 0.628367i
\(221\) 8.54032 + 86.7113i 0.0386440 + 0.392359i
\(222\) 59.8303 + 61.9855i 0.269506 + 0.279214i
\(223\) 213.102 + 213.102i 0.955616 + 0.955616i 0.999056 0.0434403i \(-0.0138318\pi\)
−0.0434403 + 0.999056i \(0.513832\pi\)
\(224\) −7.24776 66.9116i −0.0323561 0.298713i
\(225\) 27.9979 + 27.9979i 0.124435 + 0.124435i
\(226\) −131.419 2.32510i −0.581501 0.0102880i
\(227\) −10.8142 109.798i −0.0476396 0.483693i −0.989171 0.146768i \(-0.953113\pi\)
0.941531 0.336925i \(-0.109387\pi\)
\(228\) −82.4550 133.387i −0.361645 0.585031i
\(229\) −101.713 + 190.291i −0.444160 + 0.830965i −1.00000 0.000324216i \(-0.999897\pi\)
0.555840 + 0.831289i \(0.312397\pi\)
\(230\) 47.5195 3.83286i 0.206607 0.0166646i
\(231\) 19.3577 + 28.9708i 0.0837995 + 0.125415i
\(232\) −37.7443 13.6750i −0.162691 0.0589439i
\(233\) −149.057 + 223.079i −0.639727 + 0.957420i 0.359973 + 0.932963i \(0.382786\pi\)
−0.999701 + 0.0244573i \(0.992214\pi\)
\(234\) 37.3820 10.6213i 0.159752 0.0453904i
\(235\) −357.284 + 293.216i −1.52036 + 1.24773i
\(236\) 147.520 + 85.6937i 0.625083 + 0.363109i
\(237\) 107.379 + 200.892i 0.453075 + 0.847644i
\(238\) 30.6008 + 47.5991i 0.128575 + 0.199996i
\(239\) 173.284 71.7767i 0.725039 0.300321i 0.0105275 0.999945i \(-0.496649\pi\)
0.714512 + 0.699624i \(0.246649\pi\)
\(240\) 76.5694 153.211i 0.319039 0.638377i
\(241\) −138.086 + 333.370i −0.572972 + 1.38328i 0.326041 + 0.945356i \(0.394285\pi\)
−0.899013 + 0.437922i \(0.855715\pi\)
\(242\) −10.4911 58.0950i −0.0433515 0.240062i
\(243\) 4.52509 14.9172i 0.0186218 0.0613878i
\(244\) −10.1997 162.217i −0.0418020 0.664825i
\(245\) 27.0041 274.177i 0.110221 1.11909i
\(246\) 53.7015 + 67.8483i 0.218299 + 0.275806i
\(247\) 143.784 28.6005i 0.582122 0.115791i
\(248\) −324.920 + 114.800i −1.31016 + 0.462905i
\(249\) 113.911 + 22.6583i 0.457473 + 0.0909970i
\(250\) 44.8094 138.827i 0.179238 0.555309i
\(251\) −283.173 + 85.8997i −1.12818 + 0.342230i −0.798579 0.601890i \(-0.794415\pi\)
−0.329602 + 0.944120i \(0.606915\pi\)
\(252\) 18.4665 17.2039i 0.0732798 0.0682696i
\(253\) 28.5156 + 23.4022i 0.112710 + 0.0924987i
\(254\) 115.353 45.4071i 0.454145 0.178768i
\(255\) 144.007i 0.564735i
\(256\) −253.441 36.1090i −0.990002 0.141051i
\(257\) −333.971 −1.29950 −0.649749 0.760149i \(-0.725126\pi\)
−0.649749 + 0.760149i \(0.725126\pi\)
\(258\) −41.5259 105.493i −0.160953 0.408887i
\(259\) −33.1825 + 40.4330i −0.128118 + 0.156112i
\(260\) 109.148 + 117.158i 0.419799 + 0.450608i
\(261\) −4.37008 14.4062i −0.0167436 0.0551963i
\(262\) −208.207 67.2032i −0.794683 0.256501i
\(263\) −16.2260 + 81.5734i −0.0616957 + 0.310165i −0.999295 0.0375535i \(-0.988044\pi\)
0.937599 + 0.347719i \(0.113044\pi\)
\(264\) 124.961 44.1512i 0.473339 0.167239i
\(265\) −52.2774 262.816i −0.197273 0.991759i
\(266\) 74.6550 59.0890i 0.280658 0.222139i
\(267\) 57.8901 + 5.70168i 0.216817 + 0.0213546i
\(268\) −513.448 + 32.2840i −1.91585 + 0.120463i
\(269\) 268.910 + 81.5729i 0.999665 + 0.303245i 0.747372 0.664406i \(-0.231315\pi\)
0.252293 + 0.967651i \(0.418815\pi\)
\(270\) 63.2071 11.4142i 0.234100 0.0422749i
\(271\) 333.176 + 138.006i 1.22943 + 0.509248i 0.900397 0.435070i \(-0.143276\pi\)
0.329036 + 0.944317i \(0.393276\pi\)
\(272\) 204.181 68.1029i 0.750667 0.250378i
\(273\) 9.02932 + 21.7987i 0.0330744 + 0.0798487i
\(274\) 44.8950 28.8624i 0.163851 0.105337i
\(275\) −111.332 + 59.5081i −0.404843 + 0.216393i
\(276\) 13.4218 23.1053i 0.0486297 0.0837148i
\(277\) 97.8660 + 119.250i 0.353307 + 0.430506i 0.919090 0.394049i \(-0.128926\pi\)
−0.565783 + 0.824554i \(0.691426\pi\)
\(278\) 48.9330 + 172.221i 0.176018 + 0.619499i
\(279\) −107.448 71.7945i −0.385119 0.257328i
\(280\) 97.7720 + 35.4234i 0.349186 + 0.126512i
\(281\) −193.066 + 129.003i −0.687068 + 0.459084i −0.849468 0.527641i \(-0.823077\pi\)
0.162399 + 0.986725i \(0.448077\pi\)
\(282\) 20.8276 + 258.219i 0.0738568 + 0.915671i
\(283\) 418.823 + 223.865i 1.47994 + 0.791043i 0.996440 0.0843021i \(-0.0268661\pi\)
0.483498 + 0.875346i \(0.339366\pi\)
\(284\) 163.783 101.245i 0.576700 0.356495i
\(285\) 241.131 23.7494i 0.846075 0.0833311i
\(286\) −2.19171 + 123.880i −0.00766333 + 0.433147i
\(287\) −37.1484 + 37.1484i −0.129437 + 0.129437i
\(288\) −46.0751 84.2204i −0.159983 0.292432i
\(289\) 76.3896 76.3896i 0.264324 0.264324i
\(290\) 44.6303 43.0785i 0.153898 0.148547i
\(291\) −76.7613 + 7.56033i −0.263785 + 0.0259805i
\(292\) −30.4429 + 42.2456i −0.104257 + 0.144677i
\(293\) 354.392 + 189.427i 1.20953 + 0.646507i 0.947871 0.318653i \(-0.103230\pi\)
0.261659 + 0.965160i \(0.415730\pi\)
\(294\) −117.615 100.058i −0.400050 0.340332i
\(295\) −219.177 + 146.450i −0.742975 + 0.496440i
\(296\) 117.880 + 160.273i 0.398244 + 0.541464i
\(297\) 41.3236 + 27.6115i 0.139137 + 0.0929681i
\(298\) −190.221 + 341.218i −0.638324 + 1.14503i
\(299\) 15.8474 + 19.3101i 0.0530012 + 0.0645822i
\(300\) 55.4728 + 72.6925i 0.184909 + 0.242308i
\(301\) 60.7056 32.4478i 0.201680 0.107800i
\(302\) 97.0789 446.608i 0.321453 1.47883i
\(303\) 84.2229 + 203.332i 0.277963 + 0.671063i
\(304\) −147.707 330.657i −0.485879 1.08769i
\(305\) 232.023 + 96.1071i 0.760732 + 0.315105i
\(306\) 66.3081 + 46.0229i 0.216693 + 0.150402i
\(307\) 568.899 + 172.574i 1.85309 + 0.562129i 0.999126 + 0.0418004i \(0.0133093\pi\)
0.853966 + 0.520329i \(0.174191\pi\)
\(308\) 35.3975 + 72.2623i 0.114927 + 0.234618i
\(309\) 31.1194 + 3.06499i 0.100710 + 0.00991907i
\(310\) 61.5551 528.886i 0.198565 1.70608i
\(311\) −53.5464 269.196i −0.172175 0.865582i −0.966219 0.257722i \(-0.917028\pi\)
0.794044 0.607860i \(-0.207972\pi\)
\(312\) 88.8276 12.8149i 0.284704 0.0410734i
\(313\) 27.6860 139.187i 0.0884537 0.444687i −0.911023 0.412355i \(-0.864706\pi\)
0.999477 0.0323324i \(-0.0102935\pi\)
\(314\) −98.9118 193.196i −0.315006 0.615273i
\(315\) 11.3201 + 37.3175i 0.0359370 + 0.118468i
\(316\) 183.995 + 492.829i 0.582262 + 1.55958i
\(317\) −53.4878 + 65.1750i −0.168731 + 0.205599i −0.850510 0.525959i \(-0.823707\pi\)
0.681779 + 0.731558i \(0.261207\pi\)
\(318\) −137.721 59.9215i −0.433084 0.188432i
\(319\) 47.9969 0.150461
\(320\) 222.370 327.127i 0.694905 1.02227i
\(321\) 57.8112i 0.180097i
\(322\) 14.8763 + 6.47260i 0.0461998 + 0.0201012i
\(323\) 235.372 + 193.164i 0.728705 + 0.598032i
\(324\) 14.9445 32.7515i 0.0461250 0.101085i
\(325\) −81.8041 + 24.8150i −0.251705 + 0.0763538i
\(326\) −120.552 235.464i −0.369792 0.722281i
\(327\) −348.857 69.3920i −1.06684 0.212208i
\(328\) 102.049 + 171.808i 0.311126 + 0.523804i
\(329\) −154.264 + 30.6850i −0.468887 + 0.0932675i
\(330\) −23.6735 + 203.405i −0.0717380 + 0.616377i
\(331\) 36.0939 366.467i 0.109045 1.10715i −0.772488 0.635029i \(-0.780988\pi\)
0.881533 0.472123i \(-0.156512\pi\)
\(332\) 253.755 + 86.8905i 0.764323 + 0.261718i
\(333\) −21.6576 + 71.3957i −0.0650380 + 0.214401i
\(334\) 99.2345 + 68.8763i 0.297109 + 0.206216i
\(335\) 304.197 734.398i 0.908052 2.19223i
\(336\) 47.5573 33.6982i 0.141540 0.100292i
\(337\) −334.766 + 138.665i −0.993372 + 0.411468i −0.819363 0.573276i \(-0.805672\pi\)
−0.174010 + 0.984744i \(0.555672\pi\)
\(338\) 53.9729 248.300i 0.159683 0.734615i
\(339\) −53.6592 100.389i −0.158287 0.296134i
\(340\) −44.2847 + 329.609i −0.130249 + 0.969439i
\(341\) 318.483 261.372i 0.933967 0.766487i
\(342\) 66.1270 118.619i 0.193354 0.346839i
\(343\) 109.343 163.643i 0.318784 0.477093i
\(344\) −62.6051 254.226i −0.181991 0.739029i
\(345\) 22.9377 + 34.3287i 0.0664861 + 0.0995035i
\(346\) −405.046 344.582i −1.17065 0.995901i
\(347\) −153.797 + 287.733i −0.443218 + 0.829203i −0.999999 0.00145674i \(-0.999536\pi\)
0.556781 + 0.830659i \(0.312036\pi\)
\(348\) −5.57223 34.3173i −0.0160122 0.0986131i
\(349\) −10.7530 109.177i −0.0308107 0.312827i −0.998221 0.0596144i \(-0.981013\pi\)
0.967411 0.253212i \(-0.0814871\pi\)
\(350\) −39.9455 + 38.5566i −0.114130 + 0.110162i
\(351\) 23.7978 + 23.7978i 0.0678001 + 0.0678001i
\(352\) 299.593 62.6270i 0.851117 0.177918i
\(353\) −27.6535 27.6535i −0.0783385 0.0783385i 0.666852 0.745190i \(-0.267641\pi\)
−0.745190 + 0.666852i \(0.767641\pi\)
\(354\) −2.61355 + 147.724i −0.00738292 + 0.417298i
\(355\) 29.1613 + 296.080i 0.0821445 + 0.834027i
\(356\) 130.748 + 30.8524i 0.367268 + 0.0866640i
\(357\) −23.1011 + 43.2192i −0.0647091 + 0.121062i
\(358\) 10.0151 + 124.167i 0.0279752 + 0.346834i
\(359\) −254.305 380.595i −0.708371 1.06015i −0.994780 0.102045i \(-0.967461\pi\)
0.286408 0.958108i \(-0.407539\pi\)
\(360\) 148.181 6.68804i 0.411613 0.0185779i
\(361\) 84.0639 125.811i 0.232864 0.348506i
\(362\) 21.7632 + 76.5961i 0.0601194 + 0.211592i
\(363\) 39.5206 32.4337i 0.108872 0.0893490i
\(364\) 13.9632 + 52.6703i 0.0383603 + 0.144699i
\(365\) −37.9272 70.9568i −0.103910 0.194402i
\(366\) 118.404 76.1204i 0.323508 0.207979i
\(367\) −438.598 + 181.673i −1.19509 + 0.495023i −0.889410 0.457111i \(-0.848884\pi\)
−0.305681 + 0.952134i \(0.598884\pi\)
\(368\) 37.8255 48.7568i 0.102787 0.132491i
\(369\) −28.6768 + 69.2320i −0.0777150 + 0.187621i
\(370\) −302.517 + 54.6299i −0.817614 + 0.147648i
\(371\) 26.4706 87.2620i 0.0713494 0.235207i
\(372\) −223.853 197.368i −0.601755 0.530559i
\(373\) 33.8114 343.293i 0.0906472 0.920356i −0.837076 0.547087i \(-0.815737\pi\)
0.927723 0.373269i \(-0.121763\pi\)
\(374\) −201.780 + 159.708i −0.539520 + 0.427027i
\(375\) 123.908 24.6468i 0.330421 0.0657249i
\(376\) −31.7358 + 597.426i −0.0844038 + 1.58890i
\(377\) 31.8778 + 6.34089i 0.0845565 + 0.0168193i
\(378\) 20.8006 + 6.71384i 0.0550281 + 0.0177615i
\(379\) −440.712 + 133.688i −1.16283 + 0.352740i −0.811976 0.583691i \(-0.801608\pi\)
−0.350852 + 0.936431i \(0.614108\pi\)
\(380\) 559.213 + 19.7936i 1.47161 + 0.0520884i
\(381\) 82.9899 + 68.1081i 0.217821 + 0.178761i
\(382\) −46.8636 119.053i −0.122680 0.311657i
\(383\) 5.91781i 0.0154512i −0.999970 0.00772561i \(-0.997541\pi\)
0.999970 0.00772561i \(-0.00245916\pi\)
\(384\) −79.5592 206.936i −0.207185 0.538895i
\(385\) −124.330 −0.322935
\(386\) 282.262 111.109i 0.731248 0.287846i
\(387\) 62.2865 75.8964i 0.160947 0.196115i
\(388\) −178.019 6.30107i −0.458812 0.0162399i
\(389\) −79.7046 262.751i −0.204896 0.675452i −0.997812 0.0661202i \(-0.978938\pi\)
0.792916 0.609331i \(-0.208562\pi\)
\(390\) −42.5949 + 131.966i −0.109218 + 0.338375i
\(391\) −10.1220 + 50.8866i −0.0258874 + 0.130145i
\(392\) −238.431 265.184i −0.608243 0.676489i
\(393\) −36.9642 185.832i −0.0940565 0.472854i
\(394\) −147.827 186.769i −0.375195 0.474034i
\(395\) −808.905 79.6702i −2.04786 0.201697i
\(396\) 86.0918 + 75.9059i 0.217404 + 0.191682i
\(397\) 581.987 + 176.544i 1.46596 + 0.444695i 0.919601 0.392854i \(-0.128512\pi\)
0.546362 + 0.837549i \(0.316012\pi\)
\(398\) 69.4546 + 384.610i 0.174509 + 0.966356i
\(399\) 76.1776 + 31.5538i 0.190921 + 0.0790822i
\(400\) 104.614 + 183.440i 0.261535 + 0.458600i
\(401\) −120.551 291.037i −0.300627 0.725777i −0.999940 0.0109619i \(-0.996511\pi\)
0.699313 0.714816i \(-0.253489\pi\)
\(402\) −240.936 374.772i −0.599342 0.932267i
\(403\) 246.054 131.519i 0.610557 0.326350i
\(404\) 130.244 + 491.293i 0.322387 + 1.21607i
\(405\) 35.2877 + 42.9982i 0.0871301 + 0.106168i
\(406\) 20.3049 5.76921i 0.0500120 0.0142099i
\(407\) −197.780 132.152i −0.485945 0.324698i
\(408\) 137.616 + 125.730i 0.337293 + 0.308161i
\(409\) 42.7801 28.5847i 0.104597 0.0698893i −0.502172 0.864768i \(-0.667465\pi\)
0.606769 + 0.794879i \(0.292465\pi\)
\(410\) −307.762 + 24.8237i −0.750638 + 0.0605455i
\(411\) 40.7640 + 21.7888i 0.0991824 + 0.0530141i
\(412\) 70.2846 + 16.5850i 0.170594 + 0.0402549i
\(413\) −89.2720 + 8.79253i −0.216155 + 0.0212894i
\(414\) 23.1372 + 0.409348i 0.0558870 + 0.000988764i
\(415\) −293.047 + 293.047i −0.706138 + 0.706138i
\(416\) 207.252 2.01519i 0.498203 0.00484420i
\(417\) −109.638 + 109.638i −0.262920 + 0.262920i
\(418\) 300.698 + 311.530i 0.719374 + 0.745287i
\(419\) 650.353 64.0541i 1.55215 0.152874i 0.714719 0.699411i \(-0.246554\pi\)
0.837435 + 0.546537i \(0.184054\pi\)
\(420\) 14.4342 + 88.8948i 0.0343671 + 0.211654i
\(421\) −692.783 370.300i −1.64557 0.879573i −0.992496 0.122275i \(-0.960981\pi\)
−0.653069 0.757298i \(-0.726519\pi\)
\(422\) −38.0267 + 44.6992i −0.0901106 + 0.105922i
\(423\) −186.541 + 124.643i −0.440995 + 0.294663i
\(424\) −296.793 179.502i −0.699984 0.423354i
\(425\) −147.628 98.6417i −0.347359 0.232098i
\(426\) 145.649 + 81.1959i 0.341900 + 0.190601i
\(427\) 54.2172 + 66.0638i 0.126972 + 0.154716i
\(428\) 17.7779 132.320i 0.0415372 0.309159i
\(429\) −94.6303 + 50.5809i −0.220583 + 0.117904i
\(430\) 395.314 + 85.9291i 0.919334 + 0.199835i
\(431\) 177.832 + 429.325i 0.412604 + 0.996115i 0.984436 + 0.175744i \(0.0562330\pi\)
−0.571832 + 0.820371i \(0.693767\pi\)
\(432\) 44.2771 70.3672i 0.102493 0.162887i
\(433\) −415.141 171.957i −0.958754 0.397129i −0.152240 0.988344i \(-0.548649\pi\)
−0.806514 + 0.591215i \(0.798649\pi\)
\(434\) 103.316 148.854i 0.238055 0.342981i
\(435\) 51.4058 + 15.5938i 0.118174 + 0.0358477i
\(436\) −777.138 266.107i −1.78243 0.610336i
\(437\) 86.8758 + 8.55652i 0.198800 + 0.0195801i
\(438\) −44.7931 5.21330i −0.102267 0.0119025i
\(439\) −75.2068 378.090i −0.171314 0.861253i −0.966850 0.255347i \(-0.917810\pi\)
0.795536 0.605907i \(-0.207190\pi\)
\(440\) −116.735 + 458.280i −0.265307 + 1.04154i
\(441\) 26.0893 131.160i 0.0591594 0.297415i
\(442\) −155.114 + 79.4150i −0.350937 + 0.179672i
\(443\) 90.2214 + 297.420i 0.203660 + 0.671377i 0.997959 + 0.0638507i \(0.0203381\pi\)
−0.794299 + 0.607526i \(0.792162\pi\)
\(444\) −71.5262 + 156.753i −0.161095 + 0.353047i
\(445\) −131.680 + 160.453i −0.295911 + 0.360568i
\(446\) −240.475 + 552.696i −0.539181 + 1.23923i
\(447\) −338.320 −0.756867
\(448\) 119.214 62.5050i 0.266102 0.139520i
\(449\) 296.652i 0.660695i 0.943859 + 0.330347i \(0.107166\pi\)
−0.943859 + 0.330347i \(0.892834\pi\)
\(450\) −31.5942 + 72.6146i −0.0702093 + 0.161366i
\(451\) −184.682 151.565i −0.409495 0.336064i
\(452\) −91.9457 246.276i −0.203420 0.544858i
\(453\) 378.762 114.896i 0.836120 0.253634i
\(454\) 196.413 100.559i 0.432629 0.221496i
\(455\) −82.5755 16.4253i −0.181485 0.0360995i
\(456\) 187.831 251.164i 0.411910 0.550797i
\(457\) −577.018 + 114.776i −1.26262 + 0.251151i −0.780613 0.625015i \(-0.785093\pi\)
−0.482009 + 0.876166i \(0.660093\pi\)
\(458\) −428.644 49.8883i −0.935904 0.108927i
\(459\) −6.85150 + 69.5645i −0.0149270 + 0.151557i
\(460\) 41.9440 + 85.6265i 0.0911825 + 0.186145i
\(461\) 173.646 572.435i 0.376673 1.24172i −0.539857 0.841757i \(-0.681522\pi\)
0.916530 0.399967i \(-0.130978\pi\)
\(462\) −39.7343 + 57.2477i −0.0860049 + 0.123913i
\(463\) −44.7061 + 107.930i −0.0965575 + 0.233110i −0.964777 0.263071i \(-0.915265\pi\)
0.868219 + 0.496181i \(0.165265\pi\)
\(464\) −2.20076 80.2603i −0.00474301 0.172975i
\(465\) 426.020 176.463i 0.916171 0.379490i
\(466\) −524.345 113.977i −1.12520 0.244585i
\(467\) −18.9064 35.3714i −0.0404849 0.0757418i 0.860865 0.508833i \(-0.169923\pi\)
−0.901350 + 0.433091i \(0.857423\pi\)
\(468\) 47.1511 + 61.7875i 0.100750 + 0.132025i
\(469\) 209.105 171.608i 0.445852 0.365901i
\(470\) −807.409 450.111i −1.71789 0.957682i
\(471\) 104.428 156.288i 0.221716 0.331821i
\(472\) −51.4095 + 337.311i −0.108918 + 0.714643i
\(473\) 173.909 + 260.274i 0.367673 + 0.550261i
\(474\) −295.200 + 346.998i −0.622784 + 0.732064i
\(475\) −140.823 + 263.461i −0.296469 + 0.554655i
\(476\) −66.1653 + 91.8176i −0.139003 + 0.192894i
\(477\) −12.7491 129.444i −0.0267276 0.271370i
\(478\) 260.519 + 269.903i 0.545018 + 0.564650i
\(479\) 224.838 + 224.838i 0.469390 + 0.469390i 0.901717 0.432327i \(-0.142307\pi\)
−0.432327 + 0.901717i \(0.642307\pi\)
\(480\) 341.218 + 30.2603i 0.710871 + 0.0630422i
\(481\) −113.899 113.899i −0.236797 0.236797i
\(482\) −721.561 12.7660i −1.49701 0.0264855i
\(483\) 1.37713 + 13.9822i 0.00285120 + 0.0289487i
\(484\) 100.430 62.0821i 0.207500 0.128269i
\(485\) 129.744 242.734i 0.267513 0.500482i
\(486\) 31.0760 2.50655i 0.0639424 0.00515751i
\(487\) 84.8125 + 126.931i 0.174153 + 0.260638i 0.908270 0.418385i \(-0.137404\pi\)
−0.734117 + 0.679023i \(0.762404\pi\)
\(488\) 294.416 137.816i 0.603311 0.282409i
\(489\) 127.275 190.481i 0.260277 0.389531i
\(490\) 530.029 150.597i 1.08169 0.307341i
\(491\) −563.701 + 462.617i −1.14807 + 0.942194i −0.998913 0.0466203i \(-0.985155\pi\)
−0.149154 + 0.988814i \(0.547655\pi\)
\(492\) −86.9266 + 149.642i −0.176680 + 0.304151i
\(493\) 31.8224 + 59.5355i 0.0645484 + 0.120762i
\(494\) 158.556 + 246.632i 0.320964 + 0.499255i
\(495\) −163.843 + 67.8661i −0.330996 + 0.137103i
\(496\) −451.669 520.581i −0.910622 1.04956i
\(497\) −38.7442 + 93.5367i −0.0779561 + 0.188203i
\(498\) 41.2794 + 228.587i 0.0828903 + 0.459011i
\(499\) 110.997 365.908i 0.222439 0.733283i −0.772697 0.634775i \(-0.781093\pi\)
0.995136 0.0985081i \(-0.0314070\pi\)
\(500\) 291.184 18.3087i 0.582369 0.0366174i
\(501\) −10.2537 + 104.108i −0.0204665 + 0.207800i
\(502\) −367.302 464.061i −0.731677 0.924425i
\(503\) 391.796 77.9331i 0.778918 0.154937i 0.210409 0.977613i \(-0.432520\pi\)
0.568509 + 0.822677i \(0.307520\pi\)
\(504\) 45.5446 + 21.7634i 0.0903662 + 0.0431814i
\(505\) −770.240 153.210i −1.52523 0.303387i
\(506\) −22.6622 + 70.2114i −0.0447870 + 0.138758i
\(507\) 210.580 63.8788i 0.415345 0.125994i
\(508\) 169.006 + 181.409i 0.332689 + 0.357104i
\(509\) −583.969 479.251i −1.14729 0.941553i −0.148409 0.988926i \(-0.547415\pi\)
−0.998877 + 0.0473728i \(0.984915\pi\)
\(510\) −267.999 + 105.494i −0.525488 + 0.206851i
\(511\) 27.3795i 0.0535803i
\(512\) −118.462 498.107i −0.231370 0.972866i
\(513\) 117.611 0.229262
\(514\) −244.654 621.523i −0.475981 1.20919i
\(515\) −70.7860 + 86.2530i −0.137449 + 0.167482i
\(516\) 165.903 154.560i 0.321518 0.299535i
\(517\) −207.635 684.479i −0.401614 1.32394i
\(518\) −99.5543 32.1333i −0.192190 0.0620333i
\(519\) 89.8473 451.693i 0.173116 0.870314i
\(520\) −138.075 + 288.950i −0.265528 + 0.555674i
\(521\) −47.2217 237.400i −0.0906367 0.455661i −0.999275 0.0380769i \(-0.987877\pi\)
0.908638 0.417584i \(-0.137123\pi\)
\(522\) 23.6088 18.6862i 0.0452275 0.0357973i
\(523\) −451.337 44.4528i −0.862977 0.0849959i −0.343164 0.939276i \(-0.611499\pi\)
−0.519814 + 0.854280i \(0.673999\pi\)
\(524\) −27.4586 436.705i −0.0524019 0.833407i
\(525\) −46.0097 13.9569i −0.0876376 0.0265846i
\(526\) −163.695 + 29.5609i −0.311208 + 0.0561994i
\(527\) 535.363 + 221.755i 1.01587 + 0.420787i
\(528\) 173.708 + 200.211i 0.328992 + 0.379187i
\(529\) −196.747 474.990i −0.371923 0.897901i
\(530\) 450.807 289.818i 0.850579 0.546826i
\(531\) −112.844 + 60.3163i −0.212512 + 0.113590i
\(532\) 164.655 + 95.6473i 0.309501 + 0.179788i
\(533\) −102.636 125.062i −0.192563 0.234638i
\(534\) 31.7972 + 111.911i 0.0595453 + 0.209571i
\(535\) 171.522 + 114.607i 0.320602 + 0.214219i
\(536\) −436.213 931.882i −0.813831 1.73859i
\(537\) −89.6995 + 59.9353i −0.167038 + 0.111611i
\(538\) 45.1851 + 560.201i 0.0839871 + 1.04127i
\(539\) 376.015 + 200.984i 0.697616 + 0.372883i
\(540\) 67.5451 + 109.267i 0.125083 + 0.202347i
\(541\) 16.3930 1.61457i 0.0303012 0.00298441i −0.0828552 0.996562i \(-0.526404\pi\)
0.113156 + 0.993577i \(0.463904\pi\)
\(542\) −12.7586 + 721.142i −0.0235398 + 1.33052i
\(543\) −48.7619 + 48.7619i −0.0898010 + 0.0898010i
\(544\) 276.315 + 330.094i 0.507933 + 0.606790i
\(545\) 897.471 897.471i 1.64674 1.64674i
\(546\) −33.9531 + 32.7725i −0.0621851 + 0.0600230i
\(547\) 591.269 58.2349i 1.08093 0.106462i 0.458162 0.888869i \(-0.348508\pi\)
0.622768 + 0.782406i \(0.286008\pi\)
\(548\) 86.6016 + 62.4066i 0.158032 + 0.113881i
\(549\) 107.509 + 57.4648i 0.195827 + 0.104672i
\(550\) −192.302 163.596i −0.349641 0.297447i
\(551\) 94.4403 63.1030i 0.171398 0.114524i
\(552\) 52.8314 + 8.05202i 0.0957091 + 0.0145870i
\(553\) −229.986 153.672i −0.415889 0.277888i
\(554\) −150.233 + 269.487i −0.271178 + 0.486439i
\(555\) −168.891 205.795i −0.304309 0.370801i
\(556\) −284.658 + 217.227i −0.511975 + 0.390696i
\(557\) −322.522 + 172.392i −0.579034 + 0.309500i −0.734789 0.678296i \(-0.762719\pi\)
0.155755 + 0.987796i \(0.450219\pi\)
\(558\) 54.8979 252.556i 0.0983834 0.452609i
\(559\) 81.1193 + 195.839i 0.145115 + 0.350339i
\(560\) 5.70079 + 207.904i 0.0101800 + 0.371258i
\(561\) −205.896 85.2848i −0.367015 0.152023i
\(562\) −381.508 264.796i −0.678840 0.471166i
\(563\) 30.7507 + 9.32812i 0.0546193 + 0.0165686i 0.317476 0.948266i \(-0.397165\pi\)
−0.262857 + 0.964835i \(0.584665\pi\)
\(564\) −465.291 + 227.922i −0.824984 + 0.404117i
\(565\) 404.225 + 39.8127i 0.715442 + 0.0704649i
\(566\) −109.802 + 943.427i −0.193997 + 1.66683i
\(567\) 3.69286 + 18.5653i 0.00651298 + 0.0327430i
\(568\) 308.398 + 230.634i 0.542954 + 0.406045i
\(569\) −215.309 + 1082.43i −0.378399 + 1.90234i 0.0499956 + 0.998749i \(0.484079\pi\)
−0.428395 + 0.903592i \(0.640921\pi\)
\(570\) 220.841 + 431.350i 0.387441 + 0.756754i
\(571\) 295.215 + 973.195i 0.517015 + 1.70437i 0.693842 + 0.720127i \(0.255916\pi\)
−0.176828 + 0.984242i \(0.556584\pi\)
\(572\) −232.148 + 86.6710i −0.405853 + 0.151523i
\(573\) 70.2928 85.6520i 0.122675 0.149480i
\(574\) −96.3469 41.9200i −0.167852 0.0730314i
\(575\) −50.9035 −0.0885279
\(576\) 122.982 147.443i 0.213511 0.255977i
\(577\) 605.035i 1.04859i 0.851538 + 0.524294i \(0.175671\pi\)
−0.851538 + 0.524294i \(0.824329\pi\)
\(578\) 198.122 + 86.2017i 0.342771 + 0.149138i
\(579\) 203.072 + 166.657i 0.350728 + 0.287835i
\(580\) 112.864 + 51.4997i 0.194593 + 0.0887926i
\(581\) −134.958 + 40.9391i −0.232286 + 0.0704632i
\(582\) −70.3022 137.315i −0.120794 0.235937i
\(583\) 406.723 + 80.9023i 0.697638 + 0.138769i
\(584\) −100.921 25.7070i −0.172810 0.0440189i
\(585\) −117.784 + 23.4288i −0.201341 + 0.0400492i
\(586\) −92.9106 + 798.294i −0.158550 + 1.36228i
\(587\) 22.6391 229.858i 0.0385674 0.391582i −0.956451 0.291892i \(-0.905715\pi\)
0.995019 0.0996893i \(-0.0317849\pi\)
\(588\) 100.048 292.180i 0.170150 0.496905i
\(589\) 283.023 933.003i 0.480515 1.58405i
\(590\) −433.105 300.608i −0.734077 0.509505i
\(591\) 78.9402 190.578i 0.133570 0.322468i
\(592\) −211.916 + 336.786i −0.357966 + 0.568895i
\(593\) 918.531 380.468i 1.54896 0.641599i 0.565830 0.824522i \(-0.308556\pi\)
0.983127 + 0.182923i \(0.0585560\pi\)
\(594\) −21.1132 + 97.1306i −0.0355442 + 0.163520i
\(595\) −82.4319 154.219i −0.138541 0.259192i
\(596\) −774.358 104.039i −1.29926 0.174562i
\(597\) −261.640 + 214.723i −0.438259 + 0.359670i
\(598\) −24.3270 + 43.6379i −0.0406807 + 0.0729731i
\(599\) 279.293 417.991i 0.466265 0.697815i −0.521589 0.853197i \(-0.674661\pi\)
0.987855 + 0.155381i \(0.0496607\pi\)
\(600\) −94.6442 + 156.487i −0.157740 + 0.260812i
\(601\) −490.297 733.781i −0.815802 1.22093i −0.972411 0.233273i \(-0.925056\pi\)
0.156610 0.987661i \(-0.449944\pi\)
\(602\) 104.856 + 89.2036i 0.174180 + 0.148179i
\(603\) 181.887 340.286i 0.301637 0.564322i
\(604\) 902.257 146.503i 1.49380 0.242554i
\(605\) 17.8814 + 181.553i 0.0295560 + 0.300087i
\(606\) −316.704 + 305.693i −0.522614 + 0.504443i
\(607\) 388.096 + 388.096i 0.639368 + 0.639368i 0.950399 0.311032i \(-0.100675\pi\)
−0.311032 + 0.950399i \(0.600675\pi\)
\(608\) 507.152 517.111i 0.834131 0.850511i
\(609\) 12.9263 + 12.9263i 0.0212254 + 0.0212254i
\(610\) −8.88505 + 502.202i −0.0145657 + 0.823281i
\(611\) −47.4765 482.037i −0.0777029 0.788931i
\(612\) −37.0742 + 157.115i −0.0605788 + 0.256723i
\(613\) −280.264 + 524.337i −0.457201 + 0.855362i 0.542680 + 0.839939i \(0.317409\pi\)
−0.999881 + 0.0154230i \(0.995091\pi\)
\(614\) 95.5924 + 1185.15i 0.155688 + 1.93021i
\(615\) −148.557 222.331i −0.241556 0.361514i
\(616\) −108.550 + 118.812i −0.176217 + 0.192876i
\(617\) 434.803 650.729i 0.704706 1.05467i −0.290501 0.956875i \(-0.593822\pi\)
0.995207 0.0977920i \(-0.0311780\pi\)
\(618\) 17.0929 + 60.1588i 0.0276584 + 0.0973443i
\(619\) 275.569 226.153i 0.445184 0.365353i −0.384931 0.922945i \(-0.625775\pi\)
0.830115 + 0.557592i \(0.188275\pi\)
\(620\) 1029.35 272.887i 1.66025 0.440140i
\(621\) 9.44706 + 17.6742i 0.0152127 + 0.0284609i
\(622\) 461.750 296.853i 0.742363 0.477255i
\(623\) −65.2589 + 27.0311i −0.104749 + 0.0433886i
\(624\) 88.9203 + 155.921i 0.142500 + 0.249874i
\(625\) −298.785 + 721.330i −0.478056 + 1.15413i
\(626\) 279.310 50.4391i 0.446182 0.0805736i
\(627\) −108.848 + 358.824i −0.173602 + 0.572287i
\(628\) 287.080 325.603i 0.457134 0.518477i
\(629\) 32.7921 332.944i 0.0521338 0.529323i
\(630\) −61.1556 + 48.4043i −0.0970723 + 0.0768322i
\(631\) −546.705 + 108.746i −0.866410 + 0.172340i −0.608234 0.793758i \(-0.708122\pi\)
−0.258176 + 0.966098i \(0.583122\pi\)
\(632\) −782.371 + 703.443i −1.23793 + 1.11304i
\(633\) −49.8470 9.91518i −0.0787472 0.0156638i
\(634\) −160.474 51.7965i −0.253114 0.0816980i
\(635\) −366.595 + 111.205i −0.577315 + 0.175127i
\(636\) 10.6256 300.196i 0.0167069 0.472006i
\(637\) 223.183 + 183.162i 0.350366 + 0.287538i
\(638\) 35.1607 + 89.3227i 0.0551108 + 0.140004i
\(639\) 144.412i 0.225997i
\(640\) 771.686 + 174.191i 1.20576 + 0.272174i
\(641\) 1228.19 1.91605 0.958026 0.286681i \(-0.0925518\pi\)
0.958026 + 0.286681i \(0.0925518\pi\)
\(642\) 107.587 42.3502i 0.167581 0.0659661i
\(643\) 674.019 821.295i 1.04824 1.27729i 0.0885974 0.996068i \(-0.471762\pi\)
0.959644 0.281218i \(-0.0907384\pi\)
\(644\) −1.14775 + 32.4265i −0.00178222 + 0.0503518i
\(645\) 101.700 + 335.260i 0.157675 + 0.519784i
\(646\) −187.057 + 579.533i −0.289561 + 0.897111i
\(647\) −177.389 + 891.796i −0.274172 + 1.37836i 0.560749 + 0.827986i \(0.310513\pi\)
−0.834921 + 0.550370i \(0.814487\pi\)
\(648\) 71.8986 + 3.81932i 0.110955 + 0.00589401i
\(649\) −79.5852 400.102i −0.122627 0.616490i
\(650\) −106.107 134.060i −0.163242 0.206246i
\(651\) 156.164 + 15.3808i 0.239883 + 0.0236264i
\(652\) 349.888 396.840i 0.536638 0.608650i
\(653\) 715.553 + 217.061i 1.09579 + 0.332405i 0.785892 0.618364i \(-0.212204\pi\)
0.309901 + 0.950769i \(0.399704\pi\)
\(654\) −126.420 700.061i −0.193303 1.07043i
\(655\) 624.630 + 258.730i 0.953634 + 0.395008i
\(656\) −244.978 + 315.775i −0.373442 + 0.481364i
\(657\) −14.9452 36.0810i −0.0227477 0.0549178i
\(658\) −170.113 264.608i −0.258530 0.402140i
\(659\) −998.841 + 533.892i −1.51569 + 0.810154i −0.998942 0.0459824i \(-0.985358\pi\)
−0.516750 + 0.856137i \(0.672858\pi\)
\(660\) −395.880 + 104.950i −0.599818 + 0.159015i
\(661\) −196.235 239.113i −0.296875 0.361744i 0.603114 0.797655i \(-0.293926\pi\)
−0.899990 + 0.435911i \(0.856426\pi\)
\(662\) 708.440 201.289i 1.07015 0.304062i
\(663\) −125.481 83.8439i −0.189263 0.126461i
\(664\) 24.1872 + 535.893i 0.0364265 + 0.807068i
\(665\) −244.636 + 163.460i −0.367873 + 0.245805i
\(666\) −148.734 + 11.9966i −0.223324 + 0.0180130i
\(667\) 17.0688 + 9.12344i 0.0255903 + 0.0136783i
\(668\) −55.4840 + 235.132i −0.0830599 + 0.351995i
\(669\) −519.478 + 51.1642i −0.776500 + 0.0764786i
\(670\) 1589.56 + 28.1229i 2.37248 + 0.0419744i
\(671\) −274.820 + 274.820i −0.409568 + 0.409568i
\(672\) 97.5514 + 63.8186i 0.145166 + 0.0949681i
\(673\) 674.938 674.938i 1.00288 1.00288i 0.00288393 0.999996i \(-0.499082\pi\)
0.999996 0.00288393i \(-0.000917985\pi\)
\(674\) −503.293 521.423i −0.746726 0.773625i
\(675\) −68.2504 + 6.72208i −0.101112 + 0.00995864i
\(676\) 501.627 81.4510i 0.742052 0.120490i
\(677\) −295.202 157.789i −0.436044 0.233070i 0.238743 0.971083i \(-0.423265\pi\)
−0.674787 + 0.738012i \(0.735765\pi\)
\(678\) 147.517 173.402i 0.217576 0.255755i
\(679\) 77.8770 52.0357i 0.114694 0.0766358i
\(680\) −645.847 + 159.045i −0.949775 + 0.233889i
\(681\) 158.891 + 106.167i 0.233320 + 0.155899i
\(682\) 719.724 + 401.228i 1.05531 + 0.588311i
\(683\) 776.493 + 946.159i 1.13689 + 1.38530i 0.911637 + 0.410997i \(0.134819\pi\)
0.225249 + 0.974301i \(0.427681\pi\)
\(684\) 269.193 + 36.1675i 0.393557 + 0.0528764i
\(685\) −145.458 + 77.7490i −0.212348 + 0.113502i
\(686\) 384.641 + 83.6093i 0.560702 + 0.121879i
\(687\) −143.017 345.274i −0.208177 0.502583i
\(688\) 427.255 302.745i 0.621010 0.440036i
\(689\) 259.443 + 107.465i 0.376550 + 0.155972i
\(690\) −47.0827 + 67.8352i −0.0682359 + 0.0983118i
\(691\) 639.709 + 194.054i 0.925772 + 0.280830i 0.716951 0.697124i \(-0.245537\pi\)
0.208822 + 0.977954i \(0.433037\pi\)
\(692\) 344.549 1006.22i 0.497903 1.45408i
\(693\) −60.0591 5.91531i −0.0866654 0.00853579i
\(694\) −648.140 75.4347i −0.933919 0.108695i
\(695\) −107.937 542.638i −0.155306 0.780775i
\(696\) 59.7829 35.5095i 0.0858950 0.0510195i
\(697\) 65.5553 329.569i 0.0940536 0.472839i
\(698\) 195.301 99.9898i 0.279801 0.143252i
\(699\) −134.895 444.690i −0.192983 0.636180i
\(700\) −101.017 46.0938i −0.144310 0.0658483i
\(701\) −419.939 + 511.698i −0.599058 + 0.729954i −0.980952 0.194252i \(-0.937772\pi\)
0.381894 + 0.924206i \(0.375272\pi\)
\(702\) −26.8546 + 61.7213i −0.0382544 + 0.0879221i
\(703\) −562.902 −0.800714
\(704\) 336.020 + 511.668i 0.477301 + 0.726801i
\(705\) 800.551i 1.13553i
\(706\) 31.2055 71.7213i 0.0442005 0.101588i
\(707\) −206.585 169.540i −0.292200 0.239802i
\(708\) −276.830 + 103.353i −0.391002 + 0.145978i
\(709\) 485.733 147.346i 0.685096 0.207822i 0.0714988 0.997441i \(-0.477222\pi\)
0.613597 + 0.789619i \(0.289722\pi\)
\(710\) −529.644 + 271.166i −0.745978 + 0.381924i
\(711\) −386.960 76.9712i −0.544248 0.108258i
\(712\) 38.3640 + 265.924i 0.0538820 + 0.373488i
\(713\) 162.942 32.4112i 0.228530 0.0454575i
\(714\) −97.3543 11.3307i −0.136351 0.0158694i
\(715\) 37.5287 381.036i 0.0524878 0.532917i
\(716\) −223.738 + 109.598i −0.312484 + 0.153070i
\(717\) −94.3037 + 310.878i −0.131525 + 0.433581i
\(718\) 521.996 752.074i 0.727014 1.04746i
\(719\) −155.195 + 374.675i −0.215849 + 0.521105i −0.994302 0.106597i \(-0.966005\pi\)
0.778453 + 0.627702i \(0.216005\pi\)
\(720\) 120.998 + 270.866i 0.168053 + 0.376203i
\(721\) −35.0806 + 14.5308i −0.0486554 + 0.0201537i
\(722\) 295.717 + 64.2798i 0.409580 + 0.0890301i
\(723\) −294.617 551.190i −0.407493 0.762365i
\(724\) −126.603 + 96.6129i −0.174866 + 0.133443i
\(725\) −51.1976 + 42.0168i −0.0706173 + 0.0579541i
\(726\) 89.3106 + 49.7884i 0.123017 + 0.0685791i
\(727\) 245.974 368.126i 0.338341 0.506363i −0.622815 0.782369i \(-0.714011\pi\)
0.961156 + 0.276006i \(0.0890110\pi\)
\(728\) −87.7911 + 64.5698i −0.120592 + 0.0886948i
\(729\) 15.0004 + 22.4497i 0.0205767 + 0.0307952i
\(730\) 104.267 122.563i 0.142832 0.167895i
\(731\) −207.540 + 388.281i −0.283913 + 0.531164i
\(732\) 228.399 + 164.588i 0.312020 + 0.224847i
\(733\) 87.3918 + 887.303i 0.119225 + 1.21051i 0.849587 + 0.527449i \(0.176851\pi\)
−0.730362 + 0.683060i \(0.760649\pi\)
\(734\) −659.396 683.148i −0.898360 0.930720i
\(735\) 337.422 + 337.422i 0.459078 + 0.459078i
\(736\) 118.446 + 34.6763i 0.160932 + 0.0471146i
\(737\) 869.857 + 869.857i 1.18027 + 1.18027i
\(738\) −149.849 2.65116i −0.203047 0.00359235i
\(739\) −81.4924 827.406i −0.110274 1.11963i −0.877937 0.478776i \(-0.841081\pi\)
0.767663 0.640854i \(-0.221419\pi\)
\(740\) −323.279 522.967i −0.436864 0.706712i
\(741\) −119.697 + 223.938i −0.161535 + 0.302210i
\(742\) 181.787 14.6627i 0.244995 0.0197610i
\(743\) −290.143 434.229i −0.390502 0.584427i 0.583179 0.812344i \(-0.301809\pi\)
−0.973681 + 0.227917i \(0.926809\pi\)
\(744\) 203.318 561.177i 0.273276 0.754270i
\(745\) 670.699 1003.77i 0.900268 1.34735i
\(746\) 663.640 188.560i 0.889598 0.252761i
\(747\) −155.502 + 127.617i −0.208169 + 0.170840i
\(748\) −445.035 258.519i −0.594966 0.345614i
\(749\) 33.0919 + 61.9107i 0.0441815 + 0.0826577i
\(750\) 136.638 + 212.539i 0.182184 + 0.283385i
\(751\) −805.661 + 333.716i −1.07278 + 0.444362i −0.847972 0.530040i \(-0.822177\pi\)
−0.224812 + 0.974402i \(0.572177\pi\)
\(752\) −1135.06 + 378.591i −1.50939 + 0.503445i
\(753\) 196.141 473.526i 0.260479 0.628852i
\(754\) 11.5520 + 63.9700i 0.0153209 + 0.0848408i
\(755\) −409.985 + 1351.54i −0.543026 + 1.79012i
\(756\) 2.74321 + 43.6284i 0.00362859 + 0.0577096i
\(757\) 73.5319 746.581i 0.0971359 0.986237i −0.815855 0.578257i \(-0.803733\pi\)
0.912991 0.407980i \(-0.133767\pi\)
\(758\) −571.644 722.234i −0.754148 0.952815i
\(759\) −62.6660 + 12.4650i −0.0825639 + 0.0164230i
\(760\) 372.822 + 1055.20i 0.490555 + 1.38842i
\(761\) 362.998 + 72.2047i 0.477001 + 0.0948814i 0.427735 0.903904i \(-0.359312\pi\)
0.0492661 + 0.998786i \(0.484312\pi\)
\(762\) −65.9545 + 204.338i −0.0865545 + 0.268161i
\(763\) 413.316 125.378i 0.541699 0.164323i
\(764\) 187.228 174.427i 0.245063 0.228308i
\(765\) −192.811 158.236i −0.252040 0.206844i
\(766\) 11.0131 4.33516i 0.0143774 0.00565948i
\(767\) 276.247i 0.360166i
\(768\) 326.827 299.653i 0.425556 0.390174i
\(769\) 1070.85 1.39253 0.696264 0.717786i \(-0.254844\pi\)
0.696264 + 0.717786i \(0.254844\pi\)
\(770\) −91.0794 231.379i −0.118285 0.300493i
\(771\) 366.968 447.152i 0.475963 0.579963i
\(772\) 413.548 + 443.898i 0.535684 + 0.574997i
\(773\) 351.401 + 1158.41i 0.454594 + 1.49859i 0.822518 + 0.568739i \(0.192568\pi\)
−0.367925 + 0.929856i \(0.619932\pi\)
\(774\) 186.873 + 60.3171i 0.241437 + 0.0779290i
\(775\) −110.914 + 557.603i −0.143115 + 0.719487i
\(776\) −118.684 335.911i −0.152943 0.432875i
\(777\) −17.6745 88.8556i −0.0227471 0.114357i
\(778\) 430.593 340.812i 0.553461 0.438062i
\(779\) −562.654 55.4165i −0.722277 0.0711380i
\(780\) −276.794 + 17.4039i −0.354864 + 0.0223127i
\(781\) −440.592 133.652i −0.564138 0.171130i
\(782\) −102.115 + 18.4405i −0.130582 + 0.0235812i
\(783\) 24.0902 + 9.97851i 0.0307666 + 0.0127439i
\(784\) 318.844 637.986i 0.406689 0.813758i
\(785\) 256.673 + 619.663i 0.326972 + 0.789379i
\(786\) 318.756 204.924i 0.405542 0.260717i
\(787\) 48.7848 26.0760i 0.0619883 0.0331334i −0.440111 0.897943i \(-0.645061\pi\)
0.502100 + 0.864810i \(0.332561\pi\)
\(788\) 239.287 411.927i 0.303664 0.522750i
\(789\) −91.3890 111.358i −0.115829 0.141138i
\(790\) −444.306 1563.74i −0.562412 1.97942i
\(791\) 114.929 + 76.7928i 0.145295 + 0.0970832i
\(792\) −78.1940 + 215.823i −0.0987299 + 0.272504i
\(793\) −218.832 + 146.219i −0.275954 + 0.184387i
\(794\) 97.7916 + 1212.41i 0.123163 + 1.52697i
\(795\) 409.325 + 218.789i 0.514874 + 0.275206i
\(796\) −664.883 + 411.006i −0.835280 + 0.516339i
\(797\) −807.823 + 79.5636i −1.01358 + 0.0998289i −0.591146 0.806565i \(-0.701324\pi\)
−0.422434 + 0.906394i \(0.638824\pi\)
\(798\) −2.91713 + 164.882i −0.00365555 + 0.206619i
\(799\) 711.366 711.366i 0.890320 0.890320i
\(800\) −264.747 + 329.069i −0.330934 + 0.411336i
\(801\) −71.2437 + 71.2437i −0.0889434 + 0.0889434i
\(802\) 453.311 437.549i 0.565225 0.545573i
\(803\) 123.912 12.2043i 0.154312 0.0151984i
\(804\) 520.953 722.926i 0.647952 0.899162i
\(805\) −44.2145 23.6331i −0.0549248 0.0293579i
\(806\) 425.008 + 361.564i 0.527305 + 0.448591i
\(807\) −404.696 + 270.409i −0.501482 + 0.335080i
\(808\) −818.889 + 602.288i −1.01348 + 0.745406i
\(809\) −557.825 372.727i −0.689524 0.460725i 0.160799 0.986987i \(-0.448593\pi\)
−0.850322 + 0.526262i \(0.823593\pi\)
\(810\) −54.1696 + 97.1695i −0.0668761 + 0.119962i
\(811\) −900.666 1097.46i −1.11056 1.35322i −0.929101 0.369826i \(-0.879417\pi\)
−0.181461 0.983398i \(-0.558083\pi\)
\(812\) 25.6111 + 33.5612i 0.0315408 + 0.0413316i
\(813\) −550.870 + 294.446i −0.677577 + 0.362172i
\(814\) 101.051 464.879i 0.124141 0.571105i
\(815\) 312.828 + 755.235i 0.383839 + 0.926668i
\(816\) −133.172 + 348.209i −0.163201 + 0.426726i
\(817\) 684.379 + 283.479i 0.837673 + 0.346976i
\(818\) 84.5355 + 58.6740i 0.103344 + 0.0717287i
\(819\) −39.1076 11.8632i −0.0477504 0.0144849i
\(820\) −271.651 554.562i −0.331282 0.676296i
\(821\) −1103.21 108.657i −1.34374 0.132347i −0.599565 0.800326i \(-0.704660\pi\)
−0.744180 + 0.667979i \(0.767160\pi\)
\(822\) −10.6870 + 91.8237i −0.0130013 + 0.111708i
\(823\) 239.470 + 1203.90i 0.290973 + 1.46282i 0.798924 + 0.601432i \(0.205403\pi\)
−0.507951 + 0.861386i \(0.669597\pi\)
\(824\) 20.6230 + 142.950i 0.0250279 + 0.173483i
\(825\) 42.6565 214.449i 0.0517049 0.259938i
\(826\) −81.7602 159.695i −0.0989833 0.193335i
\(827\) 70.9418 + 233.864i 0.0857821 + 0.282786i 0.989328 0.145706i \(-0.0465453\pi\)
−0.903546 + 0.428491i \(0.859045\pi\)
\(828\) 16.1876 + 43.3585i 0.0195503 + 0.0523653i
\(829\) −624.740 + 761.247i −0.753606 + 0.918272i −0.998687 0.0512309i \(-0.983686\pi\)
0.245081 + 0.969503i \(0.421186\pi\)
\(830\) −760.038 330.688i −0.915709 0.398420i
\(831\) −267.198 −0.321538
\(832\) 155.575 + 384.222i 0.186990 + 0.461806i
\(833\) 599.663i 0.719884i
\(834\) −284.353 123.720i −0.340951 0.148346i
\(835\) −288.554 236.810i −0.345573 0.283605i
\(836\) −359.480 + 787.817i −0.430000 + 0.942365i
\(837\) 214.189 64.9736i 0.255901 0.0776268i
\(838\) 595.628 + 1163.39i 0.710774 + 1.38829i
\(839\) 1147.37 + 228.226i 1.36754 + 0.272021i 0.823634 0.567122i \(-0.191943\pi\)
0.543910 + 0.839143i \(0.316943\pi\)
\(840\) −154.860 + 91.9830i −0.184357 + 0.109504i
\(841\) −800.142 + 159.158i −0.951418 + 0.189249i
\(842\) 181.626 1560.54i 0.215708 1.85338i
\(843\) 39.4205 400.243i 0.0467622 0.474785i
\(844\) −111.042 38.0230i −0.131567 0.0450510i
\(845\) −227.939 + 751.414i −0.269750 + 0.889247i
\(846\) −368.613 255.846i −0.435713 0.302418i
\(847\) −23.7575 + 57.3557i −0.0280490 + 0.0677163i
\(848\) 116.635 683.831i 0.137542 0.806404i
\(849\) −759.935 + 314.775i −0.895094 + 0.370760i
\(850\) 75.4267 346.998i 0.0887373 0.408233i
\(851\) −45.2148 84.5909i −0.0531314 0.0994018i
\(852\) −44.4092 + 330.536i −0.0521235 + 0.387953i
\(853\) −444.361 + 364.677i −0.520939 + 0.427523i −0.857764 0.514044i \(-0.828147\pi\)
0.336825 + 0.941567i \(0.390647\pi\)
\(854\) −83.2279 + 149.294i −0.0974566 + 0.174818i
\(855\) −233.158 + 348.945i −0.272699 + 0.408123i
\(856\) 259.273 63.8478i 0.302888 0.0745886i
\(857\) 886.709 + 1327.05i 1.03467 + 1.54849i 0.820464 + 0.571698i \(0.193715\pi\)
0.214202 + 0.976789i \(0.431285\pi\)
\(858\) −163.454 139.054i −0.190506 0.162068i
\(859\) 17.0396 31.8789i 0.0198366 0.0371116i −0.871808 0.489848i \(-0.837052\pi\)
0.891644 + 0.452737i \(0.149552\pi\)
\(860\) 129.677 + 798.630i 0.150787 + 0.928640i
\(861\) −8.91903 90.5564i −0.0103589 0.105176i
\(862\) −668.705 + 645.455i −0.775760 + 0.748788i
\(863\) −302.307 302.307i −0.350298 0.350298i 0.509922 0.860220i \(-0.329674\pi\)
−0.860220 + 0.509922i \(0.829674\pi\)
\(864\) 163.390 + 30.8518i 0.189108 + 0.0357082i
\(865\) 1162.03 + 1162.03i 1.34338 + 1.34338i
\(866\) 15.8973 898.549i 0.0183572 1.03759i
\(867\) 18.3405 + 186.215i 0.0211540 + 0.214780i
\(868\) 352.703 + 83.2270i 0.406340 + 0.0958837i
\(869\) 592.963 1109.36i 0.682351 1.27659i
\(870\) 8.63774 + 107.090i 0.00992843 + 0.123092i
\(871\) 462.810 + 692.644i 0.531355 + 0.795229i
\(872\) −74.0745 1641.20i −0.0849478 1.88211i
\(873\) 74.2230 111.083i 0.0850206 0.127242i
\(874\) 47.7181 + 167.945i 0.0545973 + 0.192156i
\(875\) −118.586 + 97.3213i −0.135527 + 0.111224i
\(876\) −23.1117 87.1793i −0.0263832 0.0995198i
\(877\) 598.268 + 1119.28i 0.682176 + 1.27626i 0.949836 + 0.312748i \(0.101249\pi\)
−0.267661 + 0.963513i \(0.586251\pi\)
\(878\) 648.536 416.935i 0.738651 0.474869i
\(879\) −643.029 + 266.351i −0.731546 + 0.303016i
\(880\) −938.378 + 118.473i −1.06634 + 0.134628i
\(881\) −618.700 + 1493.67i −0.702270 + 1.69543i 0.0161980 + 0.999869i \(0.494844\pi\)
−0.718468 + 0.695560i \(0.755156\pi\)
\(882\) 263.202 47.5302i 0.298415 0.0538891i
\(883\) −62.8748 + 207.270i −0.0712059 + 0.234734i −0.985319 0.170726i \(-0.945389\pi\)
0.914113 + 0.405460i \(0.132889\pi\)
\(884\) −261.423 230.493i −0.295727 0.260738i
\(885\) 44.7520 454.374i 0.0505672 0.513417i
\(886\) −487.409 + 385.781i −0.550123 + 0.435419i
\(887\) −1322.27 + 263.015i −1.49072 + 0.296522i −0.872161 0.489218i \(-0.837282\pi\)
−0.618556 + 0.785741i \(0.712282\pi\)
\(888\) −344.116 18.2797i −0.387518 0.0205853i
\(889\) −127.861 25.4331i −0.143826 0.0286087i
\(890\) −395.068 127.517i −0.443897 0.143277i
\(891\) −82.3753 + 24.9883i −0.0924526 + 0.0280452i
\(892\) −1204.73 42.6421i −1.35060 0.0478051i
\(893\) −1308.45 1073.82i −1.46523 1.20249i
\(894\) −247.840 629.616i −0.277226 0.704268i
\(895\) 384.951i 0.430113i
\(896\) 203.654 + 176.069i 0.227292 + 0.196506i
\(897\) −43.2672 −0.0482355
\(898\) −552.072 + 217.316i −0.614779 + 0.242000i
\(899\) 137.130 167.094i 0.152537 0.185866i
\(900\) −158.281 5.60243i −0.175868 0.00622493i
\(901\) 169.310 + 558.139i 0.187913 + 0.619466i
\(902\) 146.772 454.726i 0.162719 0.504131i
\(903\) −23.2592 + 116.932i −0.0257577 + 0.129493i
\(904\) 390.966 351.524i 0.432484 0.388854i
\(905\) −48.0058 241.341i −0.0530450 0.266675i
\(906\) 491.290 + 620.712i 0.542262 + 0.685112i
\(907\) −1048.62 103.280i −1.15614 0.113869i −0.498282 0.867015i \(-0.666036\pi\)
−0.657854 + 0.753146i \(0.728536\pi\)
\(908\) 331.026 + 291.861i 0.364567 + 0.321433i
\(909\) −364.784 110.656i −0.401303 0.121734i
\(910\) −29.9240 165.706i −0.0328835 0.182095i
\(911\) 773.241 + 320.287i 0.848782 + 0.351577i 0.764310 0.644849i \(-0.223080\pi\)
0.0844719 + 0.996426i \(0.473080\pi\)
\(912\) 605.016 + 165.563i 0.663394 + 0.181538i
\(913\) −245.437 592.536i −0.268824 0.648999i
\(914\) −636.300 989.755i −0.696171 1.08288i
\(915\) −383.625 + 205.052i −0.419262 + 0.224100i
\(916\) −221.165 834.257i −0.241447 0.910761i
\(917\) 145.958 + 177.850i 0.159169 + 0.193948i
\(918\) −134.479 + 38.2095i −0.146492 + 0.0416226i
\(919\) −79.4937 53.1160i −0.0865002 0.0577976i 0.511568 0.859243i \(-0.329065\pi\)
−0.598068 + 0.801445i \(0.704065\pi\)
\(920\) −128.625 + 140.785i −0.139810 + 0.153027i
\(921\) −856.165 + 572.071i −0.929604 + 0.621141i
\(922\) 1192.51 96.1864i 1.29340 0.104324i
\(923\) −274.968 146.974i −0.297907 0.159235i
\(924\) −135.646 32.0084i −0.146803 0.0346411i
\(925\) 326.655 32.1727i 0.353141 0.0347813i
\(926\) −233.609 4.13305i −0.252277 0.00446334i
\(927\) −38.2977 + 38.2977i −0.0413136 + 0.0413136i
\(928\) 147.753 62.8912i 0.159217 0.0677707i
\(929\) −1021.29 + 1021.29i −1.09935 + 1.09935i −0.104861 + 0.994487i \(0.533440\pi\)
−0.994487 + 0.104861i \(0.966560\pi\)
\(930\) 640.485 + 663.556i 0.688693 + 0.713501i
\(931\) 1004.10 98.8951i 1.07852 0.106225i
\(932\) −172.003 1059.30i −0.184553 1.13659i
\(933\) 419.262 + 224.100i 0.449369 + 0.240193i
\(934\) 51.9764 61.0968i 0.0556493 0.0654141i
\(935\) 661.211 441.807i 0.707177 0.472521i
\(936\) −80.4461 + 133.012i −0.0859467 + 0.142107i
\(937\) 402.970 + 269.256i 0.430064 + 0.287360i 0.751702 0.659503i \(-0.229233\pi\)
−0.321638 + 0.946863i \(0.604233\pi\)
\(938\) 472.545 + 263.432i 0.503780 + 0.280845i
\(939\) 155.935 + 190.008i 0.166065 + 0.202351i
\(940\) 246.183 1832.33i 0.261897 1.94929i
\(941\) 305.824 163.466i 0.324999 0.173715i −0.300826 0.953679i \(-0.597262\pi\)
0.625825 + 0.779964i \(0.284762\pi\)
\(942\) 367.353 + 79.8513i 0.389971 + 0.0847678i
\(943\) −36.8670 89.0049i −0.0390955 0.0943848i
\(944\) −665.400 + 151.428i −0.704873 + 0.160411i
\(945\) −62.4028 25.8481i −0.0660347 0.0273525i
\(946\) −356.972 + 514.313i −0.377349 + 0.543671i
\(947\) −622.871 188.946i −0.657731 0.199520i −0.0562612 0.998416i \(-0.517918\pi\)
−0.601470 + 0.798896i \(0.705418\pi\)
\(948\) −862.019 295.171i −0.909303 0.311362i
\(949\) 83.9104 + 8.26445i 0.0884198 + 0.00870859i
\(950\) −593.465 69.0712i −0.624700 0.0727066i
\(951\) −28.4900 143.229i −0.0299579 0.150609i
\(952\) −219.344 55.8723i −0.230403 0.0586893i
\(953\) −126.035 + 633.619i −0.132251 + 0.664868i 0.856603 + 0.515976i \(0.172571\pi\)
−0.988853 + 0.148892i \(0.952429\pi\)
\(954\) 231.556 118.552i 0.242721 0.124268i
\(955\) 114.773 + 378.354i 0.120181 + 0.396182i
\(956\) −311.446 + 682.548i −0.325780 + 0.713962i
\(957\) −52.7391 + 64.2628i −0.0551088 + 0.0671502i
\(958\) −253.718 + 583.132i −0.264841 + 0.608698i
\(959\) −56.1268 −0.0585264
\(960\) 193.648 + 657.177i 0.201717 + 0.684559i
\(961\) 894.506i 0.930807i
\(962\) 128.529 295.406i 0.133606 0.307075i
\(963\) 77.4030 + 63.5230i 0.0803769 + 0.0659636i
\(964\) −504.830 1352.18i −0.523683 1.40268i
\(965\) −897.038 + 272.113i −0.929573 + 0.281983i
\(966\) −25.0122 + 12.8057i −0.0258926 + 0.0132564i
\(967\) −458.093 91.1203i −0.473726 0.0942299i −0.0475472 0.998869i \(-0.515140\pi\)
−0.426179 + 0.904639i \(0.640140\pi\)
\(968\) 189.106 + 141.422i 0.195358 + 0.146097i
\(969\) −517.253 + 102.888i −0.533801 + 0.106180i
\(970\) 546.775 + 63.6372i 0.563686 + 0.0656054i
\(971\) 139.433 1415.69i 0.143597 1.45797i −0.605678 0.795710i \(-0.707098\pi\)
0.749275 0.662259i \(-0.230402\pi\)
\(972\) 27.4298 + 55.9965i 0.0282199 + 0.0576096i
\(973\) 54.6541 180.170i 0.0561707 0.185170i
\(974\) −174.089 + 250.822i −0.178736 + 0.257517i
\(975\) 56.6618 136.794i 0.0581147 0.140301i
\(976\) 472.154 + 446.952i 0.483764 + 0.457942i
\(977\) −267.943 + 110.985i −0.274250 + 0.113598i −0.515570 0.856847i \(-0.672420\pi\)
0.241320 + 0.970446i \(0.422420\pi\)
\(978\) 447.723 + 97.3214i 0.457795 + 0.0995107i
\(979\) −151.424 283.295i −0.154673 0.289372i
\(980\) 668.541 + 876.067i 0.682184 + 0.893946i
\(981\) 476.233 390.835i 0.485457 0.398404i
\(982\) −1273.88 710.156i −1.29723 0.723173i
\(983\) 320.790 480.096i 0.326338 0.488399i −0.631632 0.775268i \(-0.717615\pi\)
0.957970 + 0.286869i \(0.0926146\pi\)
\(984\) −342.164 52.1492i −0.347728 0.0529971i
\(985\) 408.939 + 612.021i 0.415167 + 0.621341i
\(986\) −87.4842 + 102.835i −0.0887263 + 0.104295i
\(987\) 128.422 240.260i 0.130113 0.243424i
\(988\) −342.832 + 475.748i −0.346996 + 0.481526i
\(989\) 12.3721 + 125.616i 0.0125097 + 0.127014i
\(990\) −246.325 255.198i −0.248813 0.257775i
\(991\) −1124.75 1124.75i −1.13496 1.13496i −0.989340 0.145623i \(-0.953482\pi\)
−0.145623 0.989340i \(-0.546518\pi\)
\(992\) 637.932 1221.92i 0.643076 1.23177i
\(993\) 451.001 + 451.001i 0.454180 + 0.454180i
\(994\) −202.455 3.58188i −0.203677 0.00360350i
\(995\) −118.381 1201.95i −0.118976 1.20799i
\(996\) −395.164 + 244.276i −0.396751 + 0.245257i
\(997\) −168.625 + 315.475i −0.169132 + 0.316425i −0.952180 0.305537i \(-0.901164\pi\)
0.783048 + 0.621962i \(0.213664\pi\)
\(998\) 762.270 61.4837i 0.763798 0.0616069i
\(999\) −71.7938 107.447i −0.0718656 0.107555i
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 384.3.u.a.235.42 yes 1024
128.67 odd 32 inner 384.3.u.a.67.42 1024
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
384.3.u.a.67.42 1024 128.67 odd 32 inner
384.3.u.a.235.42 yes 1024 1.1 even 1 trivial