Properties

Label 336.3.bv.a.325.39
Level $336$
Weight $3$
Character 336.325
Analytic conductor $9.155$
Analytic rank $0$
Dimension $256$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [336,3,Mod(61,336)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(336, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 9, 0, 10]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("336.61");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 336.bv (of order \(12\), degree \(4\), 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: \(9.15533688251\)
Analytic rank: \(0\)
Dimension: \(256\)
Relative dimension: \(64\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 325.39
Character \(\chi\) \(=\) 336.325
Dual form 336.3.bv.a.61.39

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.682388 - 1.87999i) q^{2} +(-1.67303 + 0.448288i) q^{3} +(-3.06869 - 2.56576i) q^{4} +(-5.43160 - 1.45539i) q^{5} +(-0.298882 + 3.45118i) q^{6} +(3.99510 + 5.74797i) q^{7} +(-6.91763 + 4.01826i) q^{8} +(2.59808 - 1.50000i) q^{9} +O(q^{10})\) \(q+(0.682388 - 1.87999i) q^{2} +(-1.67303 + 0.448288i) q^{3} +(-3.06869 - 2.56576i) q^{4} +(-5.43160 - 1.45539i) q^{5} +(-0.298882 + 3.45118i) q^{6} +(3.99510 + 5.74797i) q^{7} +(-6.91763 + 4.01826i) q^{8} +(2.59808 - 1.50000i) q^{9} +(-6.44258 + 9.21819i) q^{10} +(-0.217255 + 0.0582132i) q^{11} +(6.28422 + 2.91694i) q^{12} +(-6.38974 - 6.38974i) q^{13} +(13.5323 - 3.58839i) q^{14} +9.73968 q^{15} +(2.83377 + 15.7471i) q^{16} +(27.4518 + 15.8493i) q^{17} +(-1.04708 - 5.90793i) q^{18} +(-6.66067 + 24.8579i) q^{19} +(12.9337 + 18.4023i) q^{20} +(-9.26068 - 7.82559i) q^{21} +(-0.0388119 + 0.448159i) q^{22} +(12.6487 - 7.30273i) q^{23} +(9.77208 - 9.82377i) q^{24} +(5.73350 + 3.31024i) q^{25} +(-16.3729 + 7.65234i) q^{26} +(-3.67423 + 3.67423i) q^{27} +(2.48816 - 27.8892i) q^{28} +(21.2144 - 21.2144i) q^{29} +(6.64624 - 18.3105i) q^{30} +(31.3113 + 18.0776i) q^{31} +(31.5380 + 5.41815i) q^{32} +(0.337378 - 0.194785i) q^{33} +(48.5293 - 40.7937i) q^{34} +(-13.3342 - 37.0351i) q^{35} +(-11.8213 - 2.06299i) q^{36} +(-13.0802 + 48.8160i) q^{37} +(42.1874 + 29.4847i) q^{38} +(13.5547 + 7.82580i) q^{39} +(43.4220 - 11.7577i) q^{40} -52.6739 q^{41} +(-21.0314 + 12.0699i) q^{42} +(18.6117 + 18.6117i) q^{43} +(0.816049 + 0.378784i) q^{44} +(-16.2948 + 4.36618i) q^{45} +(-5.09771 - 28.7627i) q^{46} +(6.34972 - 3.66601i) q^{47} +(-11.8002 - 25.0750i) q^{48} +(-17.0783 + 45.9274i) q^{49} +(10.1357 - 8.52003i) q^{50} +(-53.0329 - 14.2101i) q^{51} +(3.21363 + 36.0027i) q^{52} +(-32.3244 + 8.66131i) q^{53} +(4.40026 + 9.41476i) q^{54} +1.26476 q^{55} +(-50.7335 - 23.7090i) q^{56} -44.5740i q^{57} +(-25.4063 - 54.3591i) q^{58} +(13.9373 + 52.0148i) q^{59} +(-29.8881 - 24.9897i) q^{60} +(-26.4297 + 98.6370i) q^{61} +(55.3521 - 46.5289i) q^{62} +(19.0015 + 8.94102i) q^{63} +(31.7072 - 55.5937i) q^{64} +(25.4069 + 44.0061i) q^{65} +(-0.135971 - 0.767184i) q^{66} +(-29.2081 - 109.006i) q^{67} +(-43.5758 - 119.072i) q^{68} +(-17.8880 + 17.8880i) q^{69} +(-78.7247 - 0.204140i) q^{70} -54.0413i q^{71} +(-11.9451 + 20.8162i) q^{72} +(-71.4567 + 123.767i) q^{73} +(82.8477 + 57.9021i) q^{74} +(-11.0763 - 2.96788i) q^{75} +(84.2190 - 59.1918i) q^{76} +(-1.20256 - 1.01621i) q^{77} +(23.9619 - 20.1424i) q^{78} +(34.1574 + 59.1624i) q^{79} +(7.52626 - 89.6560i) q^{80} +(4.50000 - 7.79423i) q^{81} +(-35.9440 + 99.0262i) q^{82} +(65.3100 + 65.3100i) q^{83} +(8.33962 + 47.7750i) q^{84} +(-126.040 - 126.040i) q^{85} +(47.6902 - 22.2894i) q^{86} +(-25.9822 + 45.0025i) q^{87} +(1.26897 - 1.27568i) q^{88} +(31.3467 + 54.2940i) q^{89} +(-2.91102 + 33.6134i) q^{90} +(11.2004 - 62.2557i) q^{91} +(-57.5520 - 10.0437i) q^{92} +(-60.4888 - 16.2079i) q^{93} +(-2.55908 - 14.4390i) q^{94} +(72.3562 - 125.325i) q^{95} +(-55.1929 + 5.07334i) q^{96} +37.0194i q^{97} +(74.6889 + 63.4474i) q^{98} +(-0.477124 + 0.477124i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 256 q - 12 q^{4} - 24 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 256 q - 12 q^{4} - 24 q^{8} + 108 q^{10} + 32 q^{11} + 32 q^{14} - 4 q^{16} + 12 q^{18} + 48 q^{22} - 64 q^{29} - 96 q^{35} - 96 q^{37} + 60 q^{40} - 60 q^{42} - 192 q^{43} + 228 q^{44} + 180 q^{46} - 32 q^{50} + 720 q^{52} + 160 q^{53} - 56 q^{56} - 312 q^{58} + 384 q^{59} + 72 q^{60} - 96 q^{64} - 216 q^{66} - 320 q^{67} - 780 q^{68} - 828 q^{70} + 60 q^{72} - 88 q^{74} - 72 q^{78} - 612 q^{80} + 1152 q^{81} + 780 q^{82} - 72 q^{84} - 212 q^{86} - 464 q^{88} - 480 q^{91} - 488 q^{92} - 612 q^{94} + 768 q^{95} - 900 q^{96} - 196 q^{98} + 192 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).

\(n\) \(85\) \(113\) \(127\) \(241\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(1\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.682388 1.87999i 0.341194 0.939993i
\(3\) −1.67303 + 0.448288i −0.557678 + 0.149429i
\(4\) −3.06869 2.56576i −0.767174 0.641440i
\(5\) −5.43160 1.45539i −1.08632 0.291079i −0.329138 0.944282i \(-0.606758\pi\)
−0.757183 + 0.653203i \(0.773425\pi\)
\(6\) −0.298882 + 3.45118i −0.0498137 + 0.575197i
\(7\) 3.99510 + 5.74797i 0.570729 + 0.821139i
\(8\) −6.91763 + 4.01826i −0.864704 + 0.502282i
\(9\) 2.59808 1.50000i 0.288675 0.166667i
\(10\) −6.44258 + 9.21819i −0.644258 + 0.921819i
\(11\) −0.217255 + 0.0582132i −0.0197504 + 0.00529211i −0.268681 0.963229i \(-0.586588\pi\)
0.248930 + 0.968521i \(0.419921\pi\)
\(12\) 6.28422 + 2.91694i 0.523685 + 0.243078i
\(13\) −6.38974 6.38974i −0.491518 0.491518i 0.417266 0.908784i \(-0.362988\pi\)
−0.908784 + 0.417266i \(0.862988\pi\)
\(14\) 13.5323 3.58839i 0.966594 0.256313i
\(15\) 9.73968 0.649312
\(16\) 2.83377 + 15.7471i 0.177110 + 0.984191i
\(17\) 27.4518 + 15.8493i 1.61481 + 0.932313i 0.988233 + 0.152958i \(0.0488798\pi\)
0.626582 + 0.779356i \(0.284454\pi\)
\(18\) −1.04708 5.90793i −0.0581713 0.328218i
\(19\) −6.66067 + 24.8579i −0.350561 + 1.30831i 0.535418 + 0.844587i \(0.320154\pi\)
−0.885979 + 0.463725i \(0.846512\pi\)
\(20\) 12.9337 + 18.4023i 0.646687 + 0.920117i
\(21\) −9.26068 7.82559i −0.440985 0.372647i
\(22\) −0.0388119 + 0.448159i −0.00176418 + 0.0203709i
\(23\) 12.6487 7.30273i 0.549943 0.317510i −0.199156 0.979968i \(-0.563820\pi\)
0.749099 + 0.662458i \(0.230487\pi\)
\(24\) 9.77208 9.82377i 0.407170 0.409324i
\(25\) 5.73350 + 3.31024i 0.229340 + 0.132409i
\(26\) −16.3729 + 7.65234i −0.629727 + 0.294321i
\(27\) −3.67423 + 3.67423i −0.136083 + 0.136083i
\(28\) 2.48816 27.8892i 0.0888630 0.996044i
\(29\) 21.2144 21.2144i 0.731530 0.731530i −0.239393 0.970923i \(-0.576948\pi\)
0.970923 + 0.239393i \(0.0769484\pi\)
\(30\) 6.64624 18.3105i 0.221541 0.610349i
\(31\) 31.3113 + 18.0776i 1.01004 + 0.583148i 0.911204 0.411955i \(-0.135154\pi\)
0.0988381 + 0.995104i \(0.468487\pi\)
\(32\) 31.5380 + 5.41815i 0.985562 + 0.169317i
\(33\) 0.337378 0.194785i 0.0102236 0.00590258i
\(34\) 48.5293 40.7937i 1.42733 1.19981i
\(35\) −13.3342 37.0351i −0.380978 1.05815i
\(36\) −11.8213 2.06299i −0.328371 0.0573054i
\(37\) −13.0802 + 48.8160i −0.353519 + 1.31935i 0.528818 + 0.848735i \(0.322635\pi\)
−0.882338 + 0.470617i \(0.844031\pi\)
\(38\) 42.1874 + 29.4847i 1.11020 + 0.775913i
\(39\) 13.5547 + 7.82580i 0.347556 + 0.200662i
\(40\) 43.4220 11.7577i 1.08555 0.293943i
\(41\) −52.6739 −1.28473 −0.642365 0.766399i \(-0.722046\pi\)
−0.642365 + 0.766399i \(0.722046\pi\)
\(42\) −21.0314 + 12.0699i −0.500747 + 0.287378i
\(43\) 18.6117 + 18.6117i 0.432831 + 0.432831i 0.889590 0.456759i \(-0.150990\pi\)
−0.456759 + 0.889590i \(0.650990\pi\)
\(44\) 0.816049 + 0.378784i 0.0185466 + 0.00860873i
\(45\) −16.2948 + 4.36618i −0.362107 + 0.0970262i
\(46\) −5.09771 28.7627i −0.110820 0.625275i
\(47\) 6.34972 3.66601i 0.135100 0.0780003i −0.430926 0.902387i \(-0.641813\pi\)
0.566027 + 0.824387i \(0.308480\pi\)
\(48\) −11.8002 25.0750i −0.245837 0.522396i
\(49\) −17.0783 + 45.9274i −0.348538 + 0.937295i
\(50\) 10.1357 8.52003i 0.202713 0.170401i
\(51\) −53.0329 14.2101i −1.03986 0.278630i
\(52\) 3.21363 + 36.0027i 0.0618005 + 0.692359i
\(53\) −32.3244 + 8.66131i −0.609895 + 0.163421i −0.550530 0.834815i \(-0.685574\pi\)
−0.0593651 + 0.998236i \(0.518908\pi\)
\(54\) 4.40026 + 9.41476i 0.0814862 + 0.174347i
\(55\) 1.26476 0.0229957
\(56\) −50.7335 23.7090i −0.905955 0.423375i
\(57\) 44.5740i 0.782001i
\(58\) −25.4063 54.3591i −0.438039 0.937226i
\(59\) 13.9373 + 52.0148i 0.236226 + 0.881607i 0.977592 + 0.210507i \(0.0675114\pi\)
−0.741367 + 0.671100i \(0.765822\pi\)
\(60\) −29.8881 24.9897i −0.498135 0.416495i
\(61\) −26.4297 + 98.6370i −0.433274 + 1.61700i 0.311890 + 0.950118i \(0.399038\pi\)
−0.745163 + 0.666882i \(0.767629\pi\)
\(62\) 55.3521 46.5289i 0.892775 0.750466i
\(63\) 19.0015 + 8.94102i 0.301612 + 0.141921i
\(64\) 31.7072 55.5937i 0.495425 0.868651i
\(65\) 25.4069 + 44.0061i 0.390876 + 0.677017i
\(66\) −0.135971 0.767184i −0.00206016 0.0116240i
\(67\) −29.2081 109.006i −0.435941 1.62696i −0.738803 0.673921i \(-0.764609\pi\)
0.302862 0.953035i \(-0.402058\pi\)
\(68\) −43.5758 119.072i −0.640820 1.75105i
\(69\) −17.8880 + 17.8880i −0.259246 + 0.259246i
\(70\) −78.7247 0.204140i −1.12464 0.00291629i
\(71\) 54.0413i 0.761145i −0.924751 0.380573i \(-0.875727\pi\)
0.924751 0.380573i \(-0.124273\pi\)
\(72\) −11.9451 + 20.8162i −0.165905 + 0.289114i
\(73\) −71.4567 + 123.767i −0.978858 + 1.69543i −0.312293 + 0.949986i \(0.601097\pi\)
−0.666566 + 0.745446i \(0.732236\pi\)
\(74\) 82.8477 + 57.9021i 1.11956 + 0.782460i
\(75\) −11.0763 2.96788i −0.147684 0.0395717i
\(76\) 84.2190 59.1918i 1.10814 0.778839i
\(77\) −1.20256 1.01621i −0.0156177 0.0131975i
\(78\) 23.9619 20.1424i 0.307204 0.258236i
\(79\) 34.1574 + 59.1624i 0.432372 + 0.748891i 0.997077 0.0764020i \(-0.0243432\pi\)
−0.564705 + 0.825293i \(0.691010\pi\)
\(80\) 7.52626 89.6560i 0.0940783 1.12070i
\(81\) 4.50000 7.79423i 0.0555556 0.0962250i
\(82\) −35.9440 + 99.0262i −0.438342 + 1.20764i
\(83\) 65.3100 + 65.3100i 0.786867 + 0.786867i 0.980979 0.194112i \(-0.0621825\pi\)
−0.194112 + 0.980979i \(0.562183\pi\)
\(84\) 8.33962 + 47.7750i 0.0992812 + 0.568750i
\(85\) −126.040 126.040i −1.48283 1.48283i
\(86\) 47.6902 22.2894i 0.554537 0.259179i
\(87\) −25.9822 + 45.0025i −0.298646 + 0.517270i
\(88\) 1.26897 1.27568i 0.0144201 0.0144964i
\(89\) 31.3467 + 54.2940i 0.352210 + 0.610045i 0.986636 0.162938i \(-0.0520971\pi\)
−0.634427 + 0.772983i \(0.718764\pi\)
\(90\) −2.91102 + 33.6134i −0.0323446 + 0.373483i
\(91\) 11.2004 62.2557i 0.123081 0.684128i
\(92\) −57.5520 10.0437i −0.625565 0.109170i
\(93\) −60.4888 16.2079i −0.650417 0.174279i
\(94\) −2.55908 14.4390i −0.0272243 0.153607i
\(95\) 72.3562 125.325i 0.761644 1.31921i
\(96\) −55.1929 + 5.07334i −0.574927 + 0.0528473i
\(97\) 37.0194i 0.381643i 0.981625 + 0.190822i \(0.0611152\pi\)
−0.981625 + 0.190822i \(0.938885\pi\)
\(98\) 74.6889 + 63.4474i 0.762132 + 0.647422i
\(99\) −0.477124 + 0.477124i −0.00481944 + 0.00481944i
\(100\) −9.10109 24.8689i −0.0910109 0.248689i
\(101\) −46.5756 173.822i −0.461144 1.72101i −0.669366 0.742933i \(-0.733434\pi\)
0.208222 0.978082i \(-0.433232\pi\)
\(102\) −62.9038 + 90.0043i −0.616704 + 0.882395i
\(103\) −64.3530 111.463i −0.624786 1.08216i −0.988582 0.150683i \(-0.951853\pi\)
0.363796 0.931479i \(-0.381481\pi\)
\(104\) 69.8775 + 18.5262i 0.671899 + 0.178137i
\(105\) 38.9110 + 55.9834i 0.370581 + 0.533175i
\(106\) −5.77466 + 66.6798i −0.0544779 + 0.629055i
\(107\) 9.07602 33.8722i 0.0848226 0.316562i −0.910458 0.413602i \(-0.864271\pi\)
0.995281 + 0.0970395i \(0.0309373\pi\)
\(108\) 20.7023 1.84790i 0.191688 0.0171102i
\(109\) 13.0283 + 48.6222i 0.119525 + 0.446075i 0.999586 0.0287872i \(-0.00916451\pi\)
−0.880060 + 0.474862i \(0.842498\pi\)
\(110\) 0.863059 2.37774i 0.00784599 0.0216158i
\(111\) 87.5345i 0.788599i
\(112\) −79.1924 + 79.1995i −0.707075 + 0.707138i
\(113\) 30.8100 0.272655 0.136327 0.990664i \(-0.456470\pi\)
0.136327 + 0.990664i \(0.456470\pi\)
\(114\) −83.7986 30.4168i −0.735075 0.266814i
\(115\) −79.3310 + 21.2567i −0.689835 + 0.184841i
\(116\) −119.531 + 10.6695i −1.03044 + 0.0919781i
\(117\) −26.1856 7.01642i −0.223809 0.0599694i
\(118\) 107.298 + 9.29229i 0.909303 + 0.0787482i
\(119\) 18.5714 + 221.112i 0.156062 + 1.85808i
\(120\) −67.3755 + 39.1366i −0.561463 + 0.326138i
\(121\) −104.745 + 60.4747i −0.865663 + 0.499791i
\(122\) 167.401 + 116.996i 1.37214 + 0.958985i
\(123\) 88.1251 23.6131i 0.716465 0.191976i
\(124\) −49.7021 135.812i −0.400823 1.09526i
\(125\) 73.0808 + 73.0808i 0.584647 + 0.584647i
\(126\) 29.7754 29.6214i 0.236313 0.235090i
\(127\) 48.2386 0.379831 0.189916 0.981800i \(-0.439179\pi\)
0.189916 + 0.981800i \(0.439179\pi\)
\(128\) −82.8787 97.5455i −0.647490 0.762074i
\(129\) −39.4814 22.7946i −0.306058 0.176703i
\(130\) 100.068 17.7355i 0.769756 0.136427i
\(131\) −33.5871 + 125.349i −0.256390 + 0.956860i 0.710922 + 0.703271i \(0.248278\pi\)
−0.967312 + 0.253589i \(0.918389\pi\)
\(132\) −1.53508 0.267894i −0.0116294 0.00202950i
\(133\) −169.493 + 61.0247i −1.27438 + 0.458832i
\(134\) −224.861 19.4736i −1.67807 0.145325i
\(135\) 25.3044 14.6095i 0.187440 0.108219i
\(136\) −253.588 + 0.668864i −1.86462 + 0.00491812i
\(137\) −11.7566 6.78766i −0.0858144 0.0495450i 0.456479 0.889734i \(-0.349110\pi\)
−0.542293 + 0.840189i \(0.682444\pi\)
\(138\) 21.4226 + 45.8356i 0.155236 + 0.332142i
\(139\) −36.6458 + 36.6458i −0.263639 + 0.263639i −0.826531 0.562892i \(-0.809689\pi\)
0.562892 + 0.826531i \(0.309689\pi\)
\(140\) −54.1045 + 147.862i −0.386461 + 1.05616i
\(141\) −8.97986 + 8.97986i −0.0636870 + 0.0636870i
\(142\) −101.597 36.8771i −0.715471 0.259698i
\(143\) 1.76017 + 1.01623i 0.0123089 + 0.00710652i
\(144\) 30.9829 + 36.6614i 0.215159 + 0.254593i
\(145\) −146.103 + 84.3527i −1.00761 + 0.581743i
\(146\) 183.918 + 218.794i 1.25971 + 1.49859i
\(147\) 7.98391 84.4941i 0.0543123 0.574790i
\(148\) 165.389 116.241i 1.11750 0.785411i
\(149\) 4.21037 15.7133i 0.0282575 0.105458i −0.950357 0.311162i \(-0.899282\pi\)
0.978614 + 0.205704i \(0.0659484\pi\)
\(150\) −13.1379 + 18.7980i −0.0875858 + 0.125320i
\(151\) 81.6294 + 47.1288i 0.540592 + 0.312111i 0.745319 0.666708i \(-0.232297\pi\)
−0.204727 + 0.978819i \(0.565631\pi\)
\(152\) −53.8097 198.722i −0.354011 1.30738i
\(153\) 95.0960 0.621542
\(154\) −2.73106 + 1.56735i −0.0177342 + 0.0101776i
\(155\) −143.761 143.761i −0.927487 0.927487i
\(156\) −21.5161 58.7930i −0.137923 0.376878i
\(157\) 176.242 47.2240i 1.12256 0.300790i 0.350642 0.936509i \(-0.385963\pi\)
0.771920 + 0.635720i \(0.219297\pi\)
\(158\) 134.533 23.8438i 0.851475 0.150910i
\(159\) 50.1971 28.9813i 0.315705 0.182272i
\(160\) −163.416 75.3294i −1.02135 0.470809i
\(161\) 92.5087 + 43.5292i 0.574588 + 0.270368i
\(162\) −11.5823 13.7786i −0.0714957 0.0850532i
\(163\) 102.638 + 27.5018i 0.629682 + 0.168723i 0.559525 0.828813i \(-0.310983\pi\)
0.0701567 + 0.997536i \(0.477650\pi\)
\(164\) 161.640 + 135.148i 0.985610 + 0.824076i
\(165\) −2.11599 + 0.566978i −0.0128242 + 0.00343623i
\(166\) 167.349 78.2151i 1.00812 0.471176i
\(167\) −26.7647 −0.160268 −0.0801340 0.996784i \(-0.525535\pi\)
−0.0801340 + 0.996784i \(0.525535\pi\)
\(168\) 95.5072 + 16.9227i 0.568495 + 0.100730i
\(169\) 87.3425i 0.516819i
\(170\) −322.963 + 150.946i −1.89978 + 0.887917i
\(171\) 19.9820 + 74.5738i 0.116854 + 0.436104i
\(172\) −9.36051 104.867i −0.0544215 0.609691i
\(173\) 22.1590 82.6984i 0.128086 0.478025i −0.871844 0.489783i \(-0.837076\pi\)
0.999931 + 0.0117577i \(0.00374268\pi\)
\(174\) 66.8741 + 79.5553i 0.384334 + 0.457214i
\(175\) 3.87876 + 46.1807i 0.0221643 + 0.263890i
\(176\) −1.53233 3.25616i −0.00870645 0.0185009i
\(177\) −46.6352 80.7745i −0.263476 0.456353i
\(178\) 123.463 21.8817i 0.693610 0.122931i
\(179\) 12.8834 + 48.0814i 0.0719742 + 0.268611i 0.992530 0.121999i \(-0.0389306\pi\)
−0.920556 + 0.390611i \(0.872264\pi\)
\(180\) 61.2063 + 28.4101i 0.340035 + 0.157834i
\(181\) 163.954 163.954i 0.905822 0.905822i −0.0901097 0.995932i \(-0.528722\pi\)
0.995932 + 0.0901097i \(0.0287218\pi\)
\(182\) −109.397 63.5391i −0.601081 0.349116i
\(183\) 176.871i 0.966508i
\(184\) −58.1547 + 101.343i −0.316058 + 0.550779i
\(185\) 142.093 246.112i 0.768071 1.33034i
\(186\) −71.7475 + 102.658i −0.385739 + 0.551925i
\(187\) −6.88668 1.84528i −0.0368272 0.00986781i
\(188\) −28.8915 5.04198i −0.153678 0.0268190i
\(189\) −35.7983 6.44046i −0.189409 0.0340765i
\(190\) −186.233 221.549i −0.980176 1.16604i
\(191\) −15.2811 26.4676i −0.0800057 0.138574i 0.823246 0.567684i \(-0.192161\pi\)
−0.903252 + 0.429110i \(0.858827\pi\)
\(192\) −28.1252 + 107.224i −0.146485 + 0.558458i
\(193\) 85.6657 148.377i 0.443864 0.768794i −0.554109 0.832444i \(-0.686941\pi\)
0.997972 + 0.0636501i \(0.0202742\pi\)
\(194\) 69.5960 + 25.2616i 0.358742 + 0.130214i
\(195\) −62.2340 62.2340i −0.319149 0.319149i
\(196\) 170.247 97.1184i 0.868607 0.495502i
\(197\) 22.5141 + 22.5141i 0.114285 + 0.114285i 0.761937 0.647652i \(-0.224249\pi\)
−0.647652 + 0.761937i \(0.724249\pi\)
\(198\) 0.571403 + 1.22257i 0.00288587 + 0.00617460i
\(199\) −2.54529 + 4.40857i −0.0127904 + 0.0221536i −0.872350 0.488882i \(-0.837405\pi\)
0.859559 + 0.511036i \(0.170738\pi\)
\(200\) −52.9636 + 0.139697i −0.264818 + 0.000698484i
\(201\) 97.7321 + 169.277i 0.486230 + 0.842174i
\(202\) −358.566 31.0528i −1.77508 0.153727i
\(203\) 206.693 + 37.1860i 1.01819 + 0.183182i
\(204\) 126.282 + 179.676i 0.619029 + 0.880765i
\(205\) 286.104 + 76.6612i 1.39563 + 0.373957i
\(206\) −253.462 + 44.9220i −1.23040 + 0.218068i
\(207\) 21.9082 37.9461i 0.105837 0.183314i
\(208\) 82.5125 118.727i 0.396695 0.570801i
\(209\) 5.78824i 0.0276949i
\(210\) 131.800 34.9498i 0.627621 0.166427i
\(211\) 47.6523 47.6523i 0.225840 0.225840i −0.585112 0.810952i \(-0.698950\pi\)
0.810952 + 0.585112i \(0.198950\pi\)
\(212\) 121.417 + 56.3578i 0.572720 + 0.265839i
\(213\) 24.2261 + 90.4129i 0.113737 + 0.424474i
\(214\) −57.4858 40.1767i −0.268625 0.187742i
\(215\) −74.0041 128.179i −0.344205 0.596181i
\(216\) 10.6530 40.1810i 0.0493193 0.186023i
\(217\) 21.1823 + 252.198i 0.0976145 + 1.16220i
\(218\) 100.299 + 8.68621i 0.460089 + 0.0398450i
\(219\) 64.0663 239.099i 0.292540 1.09177i
\(220\) −3.88117 3.24508i −0.0176417 0.0147504i
\(221\) −74.1370 276.683i −0.335462 1.25196i
\(222\) −164.564 59.7325i −0.741278 0.269065i
\(223\) 26.1397i 0.117218i 0.998281 + 0.0586092i \(0.0186666\pi\)
−0.998281 + 0.0586092i \(0.981333\pi\)
\(224\) 94.8540 + 202.925i 0.423455 + 0.905917i
\(225\) 19.8614 0.0882730
\(226\) 21.0244 57.9224i 0.0930281 0.256294i
\(227\) −291.894 + 78.2127i −1.28588 + 0.344549i −0.836093 0.548588i \(-0.815165\pi\)
−0.449783 + 0.893138i \(0.648499\pi\)
\(228\) −114.366 + 136.784i −0.501606 + 0.599930i
\(229\) −90.5018 24.2499i −0.395204 0.105895i 0.0557431 0.998445i \(-0.482247\pi\)
−0.450948 + 0.892550i \(0.648914\pi\)
\(230\) −14.1722 + 163.647i −0.0616185 + 0.711507i
\(231\) 2.46748 + 1.16105i 0.0106817 + 0.00502620i
\(232\) −61.5083 + 231.998i −0.265122 + 0.999991i
\(233\) −295.697 + 170.721i −1.26909 + 0.732707i −0.974815 0.223014i \(-0.928410\pi\)
−0.294271 + 0.955722i \(0.595077\pi\)
\(234\) −31.0595 + 44.4407i −0.132733 + 0.189918i
\(235\) −39.8247 + 10.6710i −0.169467 + 0.0454084i
\(236\) 90.6881 195.377i 0.384271 0.827870i
\(237\) −83.6683 83.6683i −0.353031 0.353031i
\(238\) 428.360 + 115.970i 1.79983 + 0.487270i
\(239\) 376.540 1.57548 0.787741 0.616007i \(-0.211251\pi\)
0.787741 + 0.616007i \(0.211251\pi\)
\(240\) 27.6000 + 153.371i 0.115000 + 0.639047i
\(241\) −222.935 128.711i −0.925041 0.534072i −0.0398010 0.999208i \(-0.512672\pi\)
−0.885240 + 0.465135i \(0.846006\pi\)
\(242\) 42.2147 + 238.187i 0.174441 + 0.984243i
\(243\) −4.03459 + 15.0573i −0.0166032 + 0.0619642i
\(244\) 334.183 234.875i 1.36960 0.962601i
\(245\) 159.605 224.604i 0.651450 0.916751i
\(246\) 15.7433 181.787i 0.0639971 0.738973i
\(247\) 201.396 116.276i 0.815367 0.470752i
\(248\) −289.240 + 0.762900i −1.16629 + 0.00307621i
\(249\) −138.543 79.9881i −0.556399 0.321237i
\(250\) 187.260 87.5215i 0.749042 0.350086i
\(251\) 247.921 247.921i 0.987731 0.987731i −0.0121942 0.999926i \(-0.503882\pi\)
0.999926 + 0.0121942i \(0.00388164\pi\)
\(252\) −35.3694 76.1906i −0.140355 0.302344i
\(253\) −2.32287 + 2.32287i −0.00918131 + 0.00918131i
\(254\) 32.9174 90.6878i 0.129596 0.357039i
\(255\) 267.372 + 154.367i 1.04852 + 0.605363i
\(256\) −239.940 + 89.2470i −0.937264 + 0.348621i
\(257\) 63.2957 36.5438i 0.246287 0.142194i −0.371776 0.928322i \(-0.621251\pi\)
0.618063 + 0.786129i \(0.287918\pi\)
\(258\) −69.7952 + 58.6698i −0.270524 + 0.227402i
\(259\) −332.850 + 119.840i −1.28513 + 0.462704i
\(260\) 34.9429 200.229i 0.134396 0.770113i
\(261\) 23.2950 86.9381i 0.0892528 0.333096i
\(262\) 212.734 + 148.680i 0.811963 + 0.567479i
\(263\) 29.4953 + 17.0291i 0.112150 + 0.0647496i 0.555026 0.831833i \(-0.312708\pi\)
−0.442876 + 0.896583i \(0.646042\pi\)
\(264\) −1.55116 + 2.70312i −0.00587559 + 0.0102391i
\(265\) 188.179 0.710110
\(266\) −0.934257 + 360.286i −0.00351224 + 1.35446i
\(267\) −76.7833 76.7833i −0.287578 0.287578i
\(268\) −190.052 + 409.447i −0.709151 + 1.52779i
\(269\) 76.7758 20.5720i 0.285412 0.0764759i −0.113273 0.993564i \(-0.536133\pi\)
0.398685 + 0.917088i \(0.369467\pi\)
\(270\) −10.1983 57.5413i −0.0377713 0.213116i
\(271\) 313.145 180.794i 1.15552 0.667137i 0.205291 0.978701i \(-0.434186\pi\)
0.950225 + 0.311564i \(0.100853\pi\)
\(272\) −171.788 + 477.199i −0.631574 + 1.75441i
\(273\) 9.16985 + 109.177i 0.0335892 + 0.399915i
\(274\) −20.7832 + 17.4704i −0.0758512 + 0.0637605i
\(275\) −1.43833 0.385399i −0.00523028 0.00140145i
\(276\) 100.789 8.99649i 0.365177 0.0325960i
\(277\) −414.439 + 111.049i −1.49617 + 0.400897i −0.911815 0.410601i \(-0.865319\pi\)
−0.584354 + 0.811499i \(0.698652\pi\)
\(278\) 43.8870 + 93.9003i 0.157867 + 0.337771i
\(279\) 108.466 0.388765
\(280\) 241.058 + 202.615i 0.860922 + 0.723625i
\(281\) 212.095i 0.754786i 0.926053 + 0.377393i \(0.123179\pi\)
−0.926053 + 0.377393i \(0.876821\pi\)
\(282\) 10.7543 + 23.0098i 0.0381357 + 0.0815949i
\(283\) 20.4072 + 76.1607i 0.0721102 + 0.269119i 0.992563 0.121736i \(-0.0388461\pi\)
−0.920452 + 0.390855i \(0.872179\pi\)
\(284\) −138.657 + 165.836i −0.488229 + 0.583931i
\(285\) −64.8728 + 242.108i −0.227624 + 0.849503i
\(286\) 3.11162 2.61562i 0.0108798 0.00914554i
\(287\) −210.438 302.768i −0.733232 1.05494i
\(288\) 90.0653 33.2302i 0.312727 0.115383i
\(289\) 357.902 + 619.905i 1.23842 + 2.14500i
\(290\) 58.8829 + 332.233i 0.203045 + 1.14563i
\(291\) −16.5953 61.9347i −0.0570287 0.212834i
\(292\) 536.834 196.461i 1.83847 0.672812i
\(293\) 61.4463 61.4463i 0.209714 0.209714i −0.594432 0.804146i \(-0.702623\pi\)
0.804146 + 0.594432i \(0.202623\pi\)
\(294\) −153.400 72.6674i −0.521767 0.247168i
\(295\) 302.808i 1.02647i
\(296\) −105.671 390.251i −0.356998 1.31842i
\(297\) 0.584355 1.01213i 0.00196753 0.00340786i
\(298\) −26.6677 18.6380i −0.0894889 0.0625436i
\(299\) −127.484 34.1593i −0.426369 0.114245i
\(300\) 26.3748 + 37.5265i 0.0879161 + 0.125088i
\(301\) −32.6240 + 181.335i −0.108385 + 0.602443i
\(302\) 144.304 121.302i 0.477829 0.401663i
\(303\) 155.845 + 269.931i 0.514340 + 0.890862i
\(304\) −410.314 34.4442i −1.34972 0.113303i
\(305\) 287.111 497.291i 0.941349 1.63046i
\(306\) 64.8923 178.779i 0.212066 0.584245i
\(307\) 304.997 + 304.997i 0.993475 + 0.993475i 0.999979 0.00650363i \(-0.00207018\pi\)
−0.00650363 + 0.999979i \(0.502070\pi\)
\(308\) 1.08296 + 6.20391i 0.00351609 + 0.0201425i
\(309\) 157.632 + 157.632i 0.510136 + 0.510136i
\(310\) −368.368 + 172.167i −1.18828 + 0.555379i
\(311\) 68.9557 119.435i 0.221722 0.384035i −0.733609 0.679572i \(-0.762165\pi\)
0.955331 + 0.295538i \(0.0954988\pi\)
\(312\) −125.212 + 0.330260i −0.401322 + 0.00105853i
\(313\) 137.215 + 237.664i 0.438387 + 0.759309i 0.997565 0.0697385i \(-0.0222165\pi\)
−0.559178 + 0.829048i \(0.688883\pi\)
\(314\) 31.4851 363.558i 0.100271 1.15783i
\(315\) −90.1961 76.2187i −0.286337 0.241964i
\(316\) 46.9777 269.191i 0.148664 0.851870i
\(317\) −273.757 73.3530i −0.863587 0.231397i −0.200274 0.979740i \(-0.564183\pi\)
−0.663313 + 0.748342i \(0.730850\pi\)
\(318\) −20.2306 114.146i −0.0636181 0.358951i
\(319\) −3.37396 + 5.84387i −0.0105767 + 0.0183194i
\(320\) −253.131 + 255.816i −0.791036 + 0.799426i
\(321\) 60.7379i 0.189215i
\(322\) 144.961 144.211i 0.450190 0.447861i
\(323\) −576.829 + 576.829i −1.78585 + 1.78585i
\(324\) −33.8072 + 12.3722i −0.104343 + 0.0381858i
\(325\) −15.4840 57.7871i −0.0476431 0.177806i
\(326\) 121.742 174.191i 0.373442 0.534330i
\(327\) −43.5935 75.5061i −0.133313 0.230905i
\(328\) 364.378 211.657i 1.11091 0.645297i
\(329\) 46.4399 + 21.8519i 0.141155 + 0.0664192i
\(330\) −0.378015 + 4.36493i −0.00114550 + 0.0132271i
\(331\) −107.835 + 402.446i −0.325785 + 1.21585i 0.587735 + 0.809054i \(0.300020\pi\)
−0.913520 + 0.406794i \(0.866647\pi\)
\(332\) −32.8467 367.986i −0.0989359 1.10839i
\(333\) 39.2406 + 146.448i 0.117840 + 0.439784i
\(334\) −18.2639 + 50.3173i −0.0546824 + 0.150651i
\(335\) 634.587i 1.89429i
\(336\) 96.9874 168.004i 0.288653 0.500013i
\(337\) −240.937 −0.714948 −0.357474 0.933923i \(-0.616362\pi\)
−0.357474 + 0.933923i \(0.616362\pi\)
\(338\) −164.203 59.6014i −0.485807 0.176336i
\(339\) −51.5461 + 13.8117i −0.152053 + 0.0407426i
\(340\) 63.3903 + 710.169i 0.186442 + 2.08873i
\(341\) −7.85488 2.10471i −0.0230348 0.00617216i
\(342\) 153.833 + 13.3224i 0.449805 + 0.0389543i
\(343\) −332.219 + 85.3189i −0.968569 + 0.248743i
\(344\) −203.536 53.9623i −0.591674 0.156867i
\(345\) 123.194 71.1263i 0.357085 0.206163i
\(346\) −140.351 98.0909i −0.405638 0.283500i
\(347\) −355.695 + 95.3081i −1.02506 + 0.274663i −0.731908 0.681404i \(-0.761370\pi\)
−0.293149 + 0.956067i \(0.594703\pi\)
\(348\) 195.197 71.4348i 0.560910 0.205272i
\(349\) −154.758 154.758i −0.443434 0.443434i 0.449731 0.893164i \(-0.351520\pi\)
−0.893164 + 0.449731i \(0.851520\pi\)
\(350\) 89.4659 + 24.2211i 0.255617 + 0.0692033i
\(351\) 46.9548 0.133774
\(352\) −7.16718 + 0.658807i −0.0203613 + 0.00187161i
\(353\) −221.682 127.988i −0.627994 0.362573i 0.151981 0.988383i \(-0.451435\pi\)
−0.779975 + 0.625811i \(0.784768\pi\)
\(354\) −183.678 + 32.5540i −0.518865 + 0.0919604i
\(355\) −78.6514 + 293.531i −0.221553 + 0.826848i
\(356\) 43.1120 247.040i 0.121101 0.693932i
\(357\) −130.192 361.602i −0.364685 1.01289i
\(358\) 99.1839 + 8.58960i 0.277050 + 0.0239933i
\(359\) 280.673 162.047i 0.781819 0.451383i −0.0552557 0.998472i \(-0.517597\pi\)
0.837074 + 0.547089i \(0.184264\pi\)
\(360\) 95.1770 95.6804i 0.264380 0.265779i
\(361\) −260.918 150.641i −0.722764 0.417288i
\(362\) −196.351 420.111i −0.542406 1.16053i
\(363\) 148.132 148.132i 0.408078 0.408078i
\(364\) −194.104 + 162.306i −0.533252 + 0.445896i
\(365\) 568.253 568.253i 1.55686 1.55686i
\(366\) −332.515 120.695i −0.908511 0.329767i
\(367\) −21.1759 12.2259i −0.0576999 0.0333131i 0.470873 0.882201i \(-0.343939\pi\)
−0.528572 + 0.848888i \(0.677273\pi\)
\(368\) 150.840 + 178.486i 0.409891 + 0.485015i
\(369\) −136.851 + 79.0108i −0.370869 + 0.214122i
\(370\) −365.725 435.077i −0.988447 1.17588i
\(371\) −178.924 151.197i −0.482276 0.407539i
\(372\) 144.036 + 204.937i 0.387194 + 0.550905i
\(373\) 163.526 610.286i 0.438406 1.63615i −0.294375 0.955690i \(-0.595112\pi\)
0.732781 0.680464i \(-0.238222\pi\)
\(374\) −8.16848 + 11.6877i −0.0218409 + 0.0312504i
\(375\) −155.028 89.5054i −0.413408 0.238681i
\(376\) −29.1940 + 50.8749i −0.0776437 + 0.135306i
\(377\) −271.108 −0.719121
\(378\) −36.5363 + 62.9055i −0.0966569 + 0.166417i
\(379\) 332.485 + 332.485i 0.877270 + 0.877270i 0.993251 0.115982i \(-0.0370013\pi\)
−0.115982 + 0.993251i \(0.537001\pi\)
\(380\) −543.592 + 198.934i −1.43050 + 0.523511i
\(381\) −80.7047 + 21.6248i −0.211823 + 0.0567579i
\(382\) −60.1864 + 10.6671i −0.157556 + 0.0279242i
\(383\) −660.811 + 381.519i −1.72535 + 0.996134i −0.818754 + 0.574144i \(0.805335\pi\)
−0.906600 + 0.421990i \(0.861332\pi\)
\(384\) 182.387 + 126.043i 0.474967 + 0.328238i
\(385\) 5.05286 + 7.26982i 0.0131243 + 0.0188827i
\(386\) −220.490 262.301i −0.571218 0.679536i
\(387\) 76.2723 + 20.4371i 0.197086 + 0.0528090i
\(388\) 94.9829 113.601i 0.244801 0.292787i
\(389\) −232.235 + 62.2271i −0.597004 + 0.159967i −0.544652 0.838662i \(-0.683338\pi\)
−0.0523518 + 0.998629i \(0.516672\pi\)
\(390\) −159.467 + 74.5314i −0.408889 + 0.191106i
\(391\) 462.973 1.18408
\(392\) −66.4068 386.334i −0.169405 0.985547i
\(393\) 224.769i 0.571931i
\(394\) 57.6896 26.9629i 0.146420 0.0684337i
\(395\) −99.4250 371.059i −0.251709 0.939390i
\(396\) 2.68833 0.239963i 0.00678872 0.000605966i
\(397\) 23.4795 87.6266i 0.0591422 0.220722i −0.930029 0.367485i \(-0.880219\pi\)
0.989172 + 0.146763i \(0.0468855\pi\)
\(398\) 6.55117 + 7.79346i 0.0164602 + 0.0195815i
\(399\) 256.210 178.078i 0.642131 0.446310i
\(400\) −35.8791 + 99.6662i −0.0896977 + 0.249165i
\(401\) 309.324 + 535.765i 0.771382 + 1.33607i 0.936806 + 0.349850i \(0.113768\pi\)
−0.165424 + 0.986223i \(0.552899\pi\)
\(402\) 384.930 68.2225i 0.957536 0.169708i
\(403\) −84.5600 315.582i −0.209826 0.783082i
\(404\) −303.060 + 652.910i −0.750149 + 1.61611i
\(405\) −35.7859 + 35.7859i −0.0883602 + 0.0883602i
\(406\) 210.954 363.205i 0.519591 0.894593i
\(407\) 11.3669i 0.0279286i
\(408\) 423.962 114.800i 1.03912 0.281372i
\(409\) −53.0052 + 91.8077i −0.129597 + 0.224469i −0.923521 0.383549i \(-0.874702\pi\)
0.793923 + 0.608018i \(0.208035\pi\)
\(410\) 339.356 485.558i 0.827697 1.18429i
\(411\) 22.7119 + 6.08565i 0.0552602 + 0.0148069i
\(412\) −88.5066 + 507.159i −0.214822 + 1.23097i
\(413\) −243.299 + 287.916i −0.589101 + 0.697133i
\(414\) −56.3882 67.0810i −0.136203 0.162031i
\(415\) −259.686 449.790i −0.625750 1.08383i
\(416\) −166.899 236.140i −0.401199 0.567644i
\(417\) 44.8818 77.7376i 0.107630 0.186421i
\(418\) −10.8818 3.94982i −0.0260330 0.00944934i
\(419\) −269.333 269.333i −0.642800 0.642800i 0.308443 0.951243i \(-0.400192\pi\)
−0.951243 + 0.308443i \(0.900192\pi\)
\(420\) 24.2339 271.632i 0.0576998 0.646743i
\(421\) 288.683 + 288.683i 0.685709 + 0.685709i 0.961281 0.275572i \(-0.0888671\pi\)
−0.275572 + 0.961281i \(0.588867\pi\)
\(422\) −57.0683 122.103i −0.135233 0.289343i
\(423\) 10.9980 19.0492i 0.0260001 0.0450335i
\(424\) 188.805 189.804i 0.445295 0.447650i
\(425\) 104.930 + 181.744i 0.246894 + 0.427633i
\(426\) 186.507 + 16.1520i 0.437809 + 0.0379155i
\(427\) −672.552 + 242.148i −1.57506 + 0.567090i
\(428\) −114.759 + 80.6564i −0.268129 + 0.188450i
\(429\) −3.40038 0.911129i −0.00792630 0.00212384i
\(430\) −291.474 + 51.6590i −0.677847 + 0.120137i
\(431\) −82.0819 + 142.170i −0.190445 + 0.329861i −0.945398 0.325918i \(-0.894327\pi\)
0.754953 + 0.655779i \(0.227660\pi\)
\(432\) −68.2703 47.4465i −0.158033 0.109830i
\(433\) 544.577i 1.25768i −0.777533 0.628842i \(-0.783529\pi\)
0.777533 0.628842i \(-0.216471\pi\)
\(434\) 488.584 + 132.274i 1.12577 + 0.304780i
\(435\) 206.621 206.621i 0.474991 0.474991i
\(436\) 84.7730 182.634i 0.194433 0.418885i
\(437\) 97.2821 + 363.062i 0.222613 + 0.830805i
\(438\) −405.784 283.602i −0.926448 0.647492i
\(439\) −276.890 479.588i −0.630730 1.09246i −0.987403 0.158226i \(-0.949422\pi\)
0.356673 0.934229i \(-0.383911\pi\)
\(440\) −8.74916 + 5.08215i −0.0198845 + 0.0115503i
\(441\) 24.5203 + 144.941i 0.0556017 + 0.328663i
\(442\) −570.751 49.4286i −1.29129 0.111829i
\(443\) −81.0497 + 302.482i −0.182956 + 0.682803i 0.812102 + 0.583515i \(0.198323\pi\)
−0.995059 + 0.0992878i \(0.968344\pi\)
\(444\) −224.592 + 268.617i −0.505839 + 0.604992i
\(445\) −91.2435 340.525i −0.205041 0.765225i
\(446\) 49.1423 + 17.8374i 0.110185 + 0.0399942i
\(447\) 28.1763i 0.0630343i
\(448\) 446.224 39.8503i 0.996036 0.0889516i
\(449\) 600.127 1.33659 0.668293 0.743899i \(-0.267025\pi\)
0.668293 + 0.743899i \(0.267025\pi\)
\(450\) 13.5532 37.3392i 0.0301182 0.0829760i
\(451\) 11.4436 3.06631i 0.0253739 0.00679892i
\(452\) −94.5464 79.0510i −0.209174 0.174892i
\(453\) −157.696 42.2545i −0.348115 0.0932771i
\(454\) −52.1459 + 602.128i −0.114859 + 1.32627i
\(455\) −151.443 + 321.847i −0.332841 + 0.707356i
\(456\) 179.110 + 308.347i 0.392785 + 0.676199i
\(457\) −622.494 + 359.397i −1.36213 + 0.786427i −0.989907 0.141716i \(-0.954738\pi\)
−0.372224 + 0.928143i \(0.621405\pi\)
\(458\) −107.347 + 153.594i −0.234382 + 0.335359i
\(459\) −159.099 + 42.6304i −0.346620 + 0.0928766i
\(460\) 297.982 + 138.314i 0.647787 + 0.300683i
\(461\) −431.586 431.586i −0.936196 0.936196i 0.0618874 0.998083i \(-0.480288\pi\)
−0.998083 + 0.0618874i \(0.980288\pi\)
\(462\) 3.86654 3.84653i 0.00836912 0.00832583i
\(463\) −104.170 −0.224988 −0.112494 0.993652i \(-0.535884\pi\)
−0.112494 + 0.993652i \(0.535884\pi\)
\(464\) 394.180 + 273.947i 0.849527 + 0.590403i
\(465\) 304.962 + 176.070i 0.655833 + 0.378645i
\(466\) 119.173 + 672.404i 0.255735 + 1.44293i
\(467\) −116.863 + 436.140i −0.250242 + 0.933918i 0.720433 + 0.693524i \(0.243943\pi\)
−0.970676 + 0.240393i \(0.922724\pi\)
\(468\) 62.3533 + 88.7173i 0.133233 + 0.189567i
\(469\) 509.874 603.377i 1.08715 1.28652i
\(470\) −7.11455 + 82.1515i −0.0151373 + 0.174790i
\(471\) −273.689 + 158.014i −0.581081 + 0.335487i
\(472\) −305.422 303.815i −0.647081 0.643677i
\(473\) −5.12693 2.96004i −0.0108392 0.00625800i
\(474\) −214.389 + 100.201i −0.452298 + 0.211394i
\(475\) −120.475 + 120.475i −0.253631 + 0.253631i
\(476\) 510.330 726.175i 1.07212 1.52558i
\(477\) −70.9894 + 70.9894i −0.148825 + 0.148825i
\(478\) 256.946 707.890i 0.537545 1.48094i
\(479\) 64.2885 + 37.1170i 0.134214 + 0.0774885i 0.565604 0.824677i \(-0.308643\pi\)
−0.431390 + 0.902166i \(0.641977\pi\)
\(480\) 307.170 + 52.7711i 0.639937 + 0.109940i
\(481\) 395.501 228.342i 0.822247 0.474725i
\(482\) −394.104 + 331.283i −0.817643 + 0.687309i
\(483\) −174.284 31.3553i −0.360836 0.0649178i
\(484\) 476.595 + 83.1727i 0.984700 + 0.171844i
\(485\) 53.8778 201.075i 0.111088 0.414587i
\(486\) 25.5543 + 17.8599i 0.0525810 + 0.0367487i
\(487\) 8.29449 + 4.78883i 0.0170318 + 0.00983332i 0.508492 0.861067i \(-0.330203\pi\)
−0.491460 + 0.870900i \(0.663537\pi\)
\(488\) −213.518 788.536i −0.437537 1.61585i
\(489\) −184.046 −0.376372
\(490\) −313.340 453.323i −0.639468 0.925148i
\(491\) −551.996 551.996i −1.12423 1.12423i −0.991099 0.133131i \(-0.957497\pi\)
−0.133131 0.991099i \(-0.542503\pi\)
\(492\) −331.015 153.647i −0.672794 0.312290i
\(493\) 918.607 246.140i 1.86330 0.499270i
\(494\) −81.1670 457.966i −0.164306 0.927057i
\(495\) 3.28595 1.89715i 0.00663829 0.00383262i
\(496\) −195.940 + 544.289i −0.395040 + 1.09736i
\(497\) 310.628 215.901i 0.625006 0.434407i
\(498\) −244.917 + 205.877i −0.491801 + 0.413407i
\(499\) 892.499 + 239.144i 1.78857 + 0.479247i 0.992103 0.125428i \(-0.0400305\pi\)
0.796472 + 0.604675i \(0.206697\pi\)
\(500\) −36.7550 411.770i −0.0735099 0.823541i
\(501\) 44.7783 11.9983i 0.0893778 0.0239487i
\(502\) −296.909 635.265i −0.591453 1.26547i
\(503\) −949.365 −1.88740 −0.943702 0.330796i \(-0.892683\pi\)
−0.943702 + 0.330796i \(0.892683\pi\)
\(504\) −167.373 + 14.5025i −0.332089 + 0.0287747i
\(505\) 1011.92i 2.00380i
\(506\) 2.78187 + 5.95207i 0.00549776 + 0.0117630i
\(507\) 39.1546 + 146.127i 0.0772279 + 0.288219i
\(508\) −148.029 123.768i −0.291396 0.243639i
\(509\) −196.046 + 731.655i −0.385160 + 1.43744i 0.452755 + 0.891635i \(0.350441\pi\)
−0.837915 + 0.545801i \(0.816225\pi\)
\(510\) 472.660 397.318i 0.926785 0.779054i
\(511\) −996.883 + 83.7291i −1.95085 + 0.163853i
\(512\) 4.05130 + 511.984i 0.00791269 + 0.999969i
\(513\) −66.8611 115.807i −0.130333 0.225744i
\(514\) −25.5096 143.932i −0.0496296 0.280023i
\(515\) 187.318 + 699.079i 0.363724 + 1.35744i
\(516\) 62.6710 + 171.250i 0.121455 + 0.331879i
\(517\) −1.16610 + 1.16610i −0.00225550 + 0.00225550i
\(518\) −1.83469 + 707.531i −0.00354188 + 1.36589i
\(519\) 148.291i 0.285724i
\(520\) −352.584 202.326i −0.678046 0.389089i
\(521\) 480.348 831.987i 0.921973 1.59690i 0.125613 0.992079i \(-0.459910\pi\)
0.796359 0.604824i \(-0.206757\pi\)
\(522\) −147.546 103.120i −0.282655 0.197547i
\(523\) 256.299 + 68.6751i 0.490056 + 0.131310i 0.495381 0.868676i \(-0.335028\pi\)
−0.00532540 + 0.999986i \(0.501695\pi\)
\(524\) 424.683 298.480i 0.810463 0.569619i
\(525\) −27.1915 75.5230i −0.0517934 0.143853i
\(526\) 52.1418 43.8303i 0.0991289 0.0833276i
\(527\) 573.035 + 992.526i 1.08735 + 1.88335i
\(528\) 4.02334 + 4.76073i 0.00761996 + 0.00901653i
\(529\) −157.840 + 273.387i −0.298375 + 0.516800i
\(530\) 128.411 353.774i 0.242285 0.667498i
\(531\) 114.232 + 114.232i 0.215127 + 0.215127i
\(532\) 676.696 + 247.611i 1.27198 + 0.465435i
\(533\) 336.572 + 336.572i 0.631468 + 0.631468i
\(534\) −196.748 + 91.9556i −0.368441 + 0.172201i
\(535\) −98.5946 + 170.771i −0.184289 + 0.319198i
\(536\) 640.065 + 636.698i 1.19415 + 1.18787i
\(537\) −43.1086 74.6663i −0.0802768 0.139043i
\(538\) 13.7158 158.376i 0.0254940 0.294378i
\(539\) 1.03676 10.9721i 0.00192350 0.0203565i
\(540\) −115.136 20.0929i −0.213215 0.0372091i
\(541\) 172.690 + 46.2722i 0.319206 + 0.0855309i 0.414864 0.909883i \(-0.363829\pi\)
−0.0956586 + 0.995414i \(0.530496\pi\)
\(542\) −126.204 712.080i −0.232850 1.31380i
\(543\) −200.802 + 347.799i −0.369800 + 0.640513i
\(544\) 779.901 + 648.594i 1.43364 + 1.19227i
\(545\) 283.058i 0.519372i
\(546\) 211.508 + 57.2617i 0.387378 + 0.104875i
\(547\) 407.815 407.815i 0.745548 0.745548i −0.228091 0.973640i \(-0.573249\pi\)
0.973640 + 0.228091i \(0.0732485\pi\)
\(548\) 18.6618 + 50.9938i 0.0340544 + 0.0930543i
\(549\) 79.2891 + 295.911i 0.144425 + 0.539000i
\(550\) −1.70604 + 2.44105i −0.00310189 + 0.00443826i
\(551\) 386.044 + 668.647i 0.700624 + 1.21352i
\(552\) 51.8638 195.621i 0.0939562 0.354385i
\(553\) −203.601 + 432.696i −0.368176 + 0.782451i
\(554\) −74.0382 + 854.917i −0.133643 + 1.54317i
\(555\) −127.397 + 475.453i −0.229544 + 0.856671i
\(556\) 206.479 18.4305i 0.371365 0.0331484i
\(557\) −123.888 462.355i −0.222420 0.830081i −0.983422 0.181332i \(-0.941959\pi\)
0.761002 0.648749i \(-0.224707\pi\)
\(558\) 74.0155 203.914i 0.132644 0.365437i
\(559\) 237.848i 0.425489i
\(560\) 545.408 314.924i 0.973943 0.562364i
\(561\) 12.3489 0.0220122
\(562\) 398.736 + 144.731i 0.709494 + 0.257528i
\(563\) −429.595 + 115.110i −0.763047 + 0.204458i −0.619298 0.785156i \(-0.712583\pi\)
−0.143749 + 0.989614i \(0.545916\pi\)
\(564\) 50.5966 4.51629i 0.0897103 0.00800761i
\(565\) −167.348 44.8407i −0.296190 0.0793640i
\(566\) 157.107 + 13.6059i 0.277574 + 0.0240386i
\(567\) 62.7790 5.27286i 0.110721 0.00929957i
\(568\) 217.152 + 373.838i 0.382310 + 0.658165i
\(569\) 418.540 241.644i 0.735571 0.424682i −0.0848860 0.996391i \(-0.527053\pi\)
0.820457 + 0.571709i \(0.193719\pi\)
\(570\) 410.892 + 287.172i 0.720863 + 0.503810i
\(571\) 72.2623 19.3626i 0.126554 0.0339100i −0.194986 0.980806i \(-0.562466\pi\)
0.321540 + 0.946896i \(0.395800\pi\)
\(572\) −2.79401 7.63467i −0.00488463 0.0133473i
\(573\) 37.4309 + 37.4309i 0.0653244 + 0.0653244i
\(574\) −712.800 + 189.014i −1.24181 + 0.329293i
\(575\) 96.6951 0.168165
\(576\) −1.01283 191.997i −0.00175839 0.333329i
\(577\) 36.7248 + 21.2031i 0.0636478 + 0.0367471i 0.531486 0.847067i \(-0.321634\pi\)
−0.467838 + 0.883814i \(0.654967\pi\)
\(578\) 1409.64 249.836i 2.43883 0.432242i
\(579\) −76.8057 + 286.643i −0.132652 + 0.495065i
\(580\) 664.775 + 116.013i 1.14616 + 0.200022i
\(581\) −114.480 + 636.320i −0.197040 + 1.09522i
\(582\) −127.761 11.0644i −0.219520 0.0190111i
\(583\) 6.51843 3.76342i 0.0111808 0.00645526i
\(584\) −3.01557 1143.30i −0.00516365 1.95771i
\(585\) 132.018 + 76.2208i 0.225672 + 0.130292i
\(586\) −73.5880 157.448i −0.125577 0.268683i
\(587\) −251.894 + 251.894i −0.429121 + 0.429121i −0.888329 0.459208i \(-0.848133\pi\)
0.459208 + 0.888329i \(0.348133\pi\)
\(588\) −241.292 + 238.802i −0.410360 + 0.406126i
\(589\) −657.926 + 657.926i −1.11702 + 1.11702i
\(590\) −569.275 206.632i −0.964873 0.350225i
\(591\) −47.7597 27.5741i −0.0808116 0.0466566i
\(592\) −805.775 67.6416i −1.36111 0.114259i
\(593\) −454.362 + 262.326i −0.766209 + 0.442371i −0.831520 0.555494i \(-0.812529\pi\)
0.0653118 + 0.997865i \(0.479196\pi\)
\(594\) −1.50404 1.78925i −0.00253205 0.00301220i
\(595\) 220.933 1228.02i 0.371315 2.06390i
\(596\) −53.2369 + 37.4165i −0.0893236 + 0.0627794i
\(597\) 2.28204 8.51670i 0.00382252 0.0142658i
\(598\) −151.213 + 216.359i −0.252864 + 0.361804i
\(599\) 705.307 + 407.209i 1.17747 + 0.679815i 0.955429 0.295221i \(-0.0953934\pi\)
0.222045 + 0.975036i \(0.428727\pi\)
\(600\) 88.5472 23.9767i 0.147579 0.0399611i
\(601\) 286.337 0.476434 0.238217 0.971212i \(-0.423437\pi\)
0.238217 + 0.971212i \(0.423437\pi\)
\(602\) 318.646 + 185.074i 0.529312 + 0.307431i
\(603\) −239.394 239.394i −0.397005 0.397005i
\(604\) −129.575 354.065i −0.214528 0.586201i
\(605\) 656.949 176.029i 1.08587 0.290957i
\(606\) 613.814 108.788i 1.01289 0.179519i
\(607\) 409.425 236.382i 0.674506 0.389426i −0.123276 0.992372i \(-0.539340\pi\)
0.797782 + 0.602946i \(0.206007\pi\)
\(608\) −344.748 + 747.881i −0.567020 + 1.23007i
\(609\) −362.474 + 30.4445i −0.595196 + 0.0499910i
\(610\) −738.980 879.111i −1.21144 1.44117i
\(611\) −63.9979 17.1482i −0.104743 0.0280658i
\(612\) −291.820 243.993i −0.476831 0.398682i
\(613\) 156.420 41.9127i 0.255172 0.0683730i −0.128965 0.991649i \(-0.541166\pi\)
0.384137 + 0.923276i \(0.374499\pi\)
\(614\) 781.516 365.264i 1.27283 0.594892i
\(615\) −513.027 −0.834190
\(616\) 12.4023 + 2.19753i 0.0201335 + 0.00356741i
\(617\) 1138.03i 1.84446i −0.386646 0.922228i \(-0.626367\pi\)
0.386646 0.922228i \(-0.373633\pi\)
\(618\) 403.912 188.780i 0.653579 0.305469i
\(619\) 137.681 + 513.834i 0.222425 + 0.830103i 0.983420 + 0.181344i \(0.0580448\pi\)
−0.760994 + 0.648759i \(0.775289\pi\)
\(620\) 72.3023 + 810.012i 0.116617 + 1.30647i
\(621\) −19.6423 + 73.3062i −0.0316302 + 0.118045i
\(622\) −177.481 211.137i −0.285339 0.339448i
\(623\) −186.847 + 397.090i −0.299915 + 0.637383i
\(624\) −84.8225 + 235.623i −0.135933 + 0.377601i
\(625\) −373.341 646.645i −0.597345 1.03463i
\(626\) 540.439 95.7839i 0.863320 0.153009i
\(627\) 2.59480 + 9.68391i 0.00413843 + 0.0154448i
\(628\) −661.999 307.279i −1.05414 0.489298i
\(629\) −1132.78 + 1132.78i −1.80092 + 1.80092i
\(630\) −204.839 + 117.557i −0.325141 + 0.186598i
\(631\) 321.327i 0.509234i −0.967042 0.254617i \(-0.918051\pi\)
0.967042 0.254617i \(-0.0819495\pi\)
\(632\) −474.018 272.010i −0.750029 0.430396i
\(633\) −58.3619 + 101.086i −0.0921988 + 0.159693i
\(634\) −324.711 + 464.604i −0.512163 + 0.732814i
\(635\) −262.013 70.2061i −0.412618 0.110561i
\(636\) −228.398 39.8588i −0.359117 0.0626711i
\(637\) 402.591 184.338i 0.632010 0.289385i
\(638\) 8.68405 + 10.3308i 0.0136114 + 0.0161925i
\(639\) −81.0620 140.403i −0.126858 0.219724i
\(640\) 308.197 + 650.449i 0.481558 + 1.01633i
\(641\) 279.724 484.496i 0.436387 0.755844i −0.561021 0.827802i \(-0.689591\pi\)
0.997408 + 0.0719574i \(0.0229246\pi\)
\(642\) 114.186 + 41.4468i 0.177860 + 0.0645588i
\(643\) −165.322 165.322i −0.257111 0.257111i 0.566767 0.823878i \(-0.308194\pi\)
−0.823878 + 0.566767i \(0.808194\pi\)
\(644\) −172.195 370.933i −0.267384 0.575983i
\(645\) 181.272 + 181.272i 0.281042 + 0.281042i
\(646\) 690.810 + 1478.05i 1.06936 + 2.28801i
\(647\) −332.374 + 575.688i −0.513715 + 0.889781i 0.486158 + 0.873871i \(0.338398\pi\)
−0.999873 + 0.0159103i \(0.994935\pi\)
\(648\) 0.189906 + 71.9997i 0.000293065 + 0.111111i
\(649\) −6.05590 10.4891i −0.00933112 0.0161620i
\(650\) −119.205 10.3235i −0.183392 0.0158823i
\(651\) −148.496 412.440i −0.228105 0.633549i
\(652\) −244.402 347.739i −0.374850 0.533343i
\(653\) 55.0427 + 14.7487i 0.0842921 + 0.0225860i 0.300719 0.953713i \(-0.402774\pi\)
−0.216427 + 0.976299i \(0.569440\pi\)
\(654\) −171.698 + 30.4307i −0.262535 + 0.0465301i
\(655\) 364.863 631.961i 0.557043 0.964827i
\(656\) −149.266 829.459i −0.227539 1.26442i
\(657\) 428.740i 0.652572i
\(658\) 72.7713 72.3949i 0.110595 0.110023i
\(659\) 777.357 777.357i 1.17960 1.17960i 0.199755 0.979846i \(-0.435985\pi\)
0.979846 0.199755i \(-0.0640148\pi\)
\(660\) 7.94806 + 3.68924i 0.0120425 + 0.00558975i
\(661\) −1.60777 6.00029i −0.00243233 0.00907759i 0.964699 0.263355i \(-0.0848290\pi\)
−0.967131 + 0.254277i \(0.918162\pi\)
\(662\) 683.007 + 477.352i 1.03173 + 0.721076i
\(663\) 248.067 + 429.665i 0.374159 + 0.648062i
\(664\) −714.223 189.358i −1.07564 0.285177i
\(665\) 1009.43 84.7831i 1.51794 0.127493i
\(666\) 302.098 + 26.1625i 0.453600 + 0.0392830i
\(667\) 113.411 423.257i 0.170032 0.634568i
\(668\) 82.1328 + 68.6719i 0.122953 + 0.102802i
\(669\) −11.7181 43.7326i −0.0175159 0.0653701i
\(670\) 1193.01 + 433.034i 1.78062 + 0.646320i
\(671\) 22.9679i 0.0342294i
\(672\) −249.663 296.979i −0.371522 0.441933i
\(673\) −740.367 −1.10010 −0.550050 0.835132i \(-0.685391\pi\)
−0.550050 + 0.835132i \(0.685391\pi\)
\(674\) −164.413 + 452.959i −0.243936 + 0.672046i
\(675\) −33.2288 + 8.90363i −0.0492279 + 0.0131906i
\(676\) −224.100 + 268.027i −0.331508 + 0.396490i
\(677\) 929.578 + 249.080i 1.37308 + 0.367917i 0.868604 0.495506i \(-0.165017\pi\)
0.504480 + 0.863423i \(0.331684\pi\)
\(678\) −9.20856 + 106.331i −0.0135819 + 0.156830i
\(679\) −212.786 + 147.896i −0.313382 + 0.217815i
\(680\) 1378.36 + 365.438i 2.02701 + 0.537409i
\(681\) 453.286 261.705i 0.665618 0.384295i
\(682\) −9.31689 + 13.3308i −0.0136611 + 0.0195467i
\(683\) 1260.57 337.769i 1.84564 0.494537i 0.846364 0.532606i \(-0.178787\pi\)
0.999275 + 0.0380683i \(0.0121204\pi\)
\(684\) 130.020 280.113i 0.190087 0.409522i
\(685\) 53.9783 + 53.9783i 0.0788004 + 0.0788004i
\(686\) −66.3040 + 682.788i −0.0966530 + 0.995318i
\(687\) 162.283 0.236220
\(688\) −240.339 + 345.821i −0.349329 + 0.502647i
\(689\) 261.888 + 151.201i 0.380099 + 0.219450i
\(690\) −49.6501 280.139i −0.0719567 0.405999i
\(691\) 46.2219 172.503i 0.0668914 0.249642i −0.924381 0.381470i \(-0.875418\pi\)
0.991273 + 0.131828i \(0.0420846\pi\)
\(692\) −280.183 + 196.921i −0.404889 + 0.284569i
\(693\) −4.64865 0.836337i −0.00670801 0.00120684i
\(694\) −63.5438 + 733.738i −0.0915617 + 1.05726i
\(695\) 252.380 145.711i 0.363136 0.209657i
\(696\) −1.09649 415.714i −0.00157541 0.597290i
\(697\) −1446.00 834.846i −2.07460 1.19777i
\(698\) −396.549 + 185.338i −0.568121 + 0.265528i
\(699\) 418.179 418.179i 0.598253 0.598253i
\(700\) 106.586 151.666i 0.152265 0.216666i
\(701\) −458.612 + 458.612i −0.654225 + 0.654225i −0.954008 0.299782i \(-0.903086\pi\)
0.299782 + 0.954008i \(0.403086\pi\)
\(702\) 32.0414 88.2744i 0.0456430 0.125747i
\(703\) −1126.34 650.294i −1.60219 0.925028i
\(704\) −3.65224 + 13.9238i −0.00518785 + 0.0197781i
\(705\) 61.8443 35.7058i 0.0877224 0.0506465i
\(706\) −391.889 + 329.421i −0.555083 + 0.466603i
\(707\) 813.052 962.153i 1.15000 1.36090i
\(708\) −64.1388 + 367.527i −0.0905915 + 0.519106i
\(709\) 6.64532 24.8007i 0.00937281 0.0349798i −0.961081 0.276267i \(-0.910903\pi\)
0.970454 + 0.241287i \(0.0775694\pi\)
\(710\) 498.163 + 348.165i 0.701639 + 0.490374i
\(711\) 177.487 + 102.472i 0.249630 + 0.144124i
\(712\) −435.012 249.627i −0.610972 0.350599i
\(713\) 528.063 0.740621
\(714\) −768.649 1.99318i −1.07654 0.00279157i
\(715\) −8.08151 8.08151i −0.0113028 0.0113028i
\(716\) 83.8302 180.603i 0.117081 0.252239i
\(717\) −629.964 + 168.798i −0.878611 + 0.235423i
\(718\) −113.118 638.240i −0.157545 0.888913i
\(719\) 25.7848 14.8869i 0.0358620 0.0207049i −0.481962 0.876192i \(-0.660076\pi\)
0.517824 + 0.855487i \(0.326742\pi\)
\(720\) −114.930 244.222i −0.159625 0.339198i
\(721\) 383.587 815.203i 0.532021 1.13066i
\(722\) −461.250 + 387.726i −0.638850 + 0.537017i
\(723\) 430.677 + 115.400i 0.595680 + 0.159612i
\(724\) −923.790 + 82.4582i −1.27595 + 0.113893i
\(725\) 191.857 51.4080i 0.264631 0.0709075i
\(726\) −177.403 379.570i −0.244357 0.522824i
\(727\) 145.182 0.199700 0.0998500 0.995003i \(-0.468164\pi\)
0.0998500 + 0.995003i \(0.468164\pi\)
\(728\) 172.679 + 475.668i 0.237197 + 0.653390i
\(729\) 27.0000i 0.0370370i
\(730\) −680.539 1456.08i −0.932245 1.99463i
\(731\) 215.943 + 805.910i 0.295408 + 1.10248i
\(732\) −453.808 + 542.763i −0.619957 + 0.741480i
\(733\) −102.901 + 384.032i −0.140383 + 0.523918i 0.859534 + 0.511078i \(0.170754\pi\)
−0.999918 + 0.0128395i \(0.995913\pi\)
\(734\) −37.4347 + 31.4675i −0.0510009 + 0.0428713i
\(735\) −166.338 + 447.319i −0.226310 + 0.608597i
\(736\) 438.482 161.781i 0.595763 0.219811i
\(737\) 12.6912 + 21.9818i 0.0172200 + 0.0298260i
\(738\) 55.1540 + 311.194i 0.0747344 + 0.421672i
\(739\) 136.737 + 510.311i 0.185030 + 0.690542i 0.994624 + 0.103552i \(0.0330207\pi\)
−0.809594 + 0.586990i \(0.800313\pi\)
\(740\) −1067.51 + 390.667i −1.44257 + 0.527929i
\(741\) −284.816 + 284.816i −0.384368 + 0.384368i
\(742\) −406.344 + 233.200i −0.547634 + 0.314286i
\(743\) 900.097i 1.21144i −0.795679 0.605718i \(-0.792886\pi\)
0.795679 0.605718i \(-0.207114\pi\)
\(744\) 483.567 130.939i 0.649955 0.175994i
\(745\) −45.7381 + 79.2207i −0.0613934 + 0.106336i
\(746\) −1035.74 723.877i −1.38839 0.970344i
\(747\) 267.645 + 71.7154i 0.358294 + 0.0960045i
\(748\) 16.3986 + 23.3321i 0.0219232 + 0.0311927i
\(749\) 230.956 83.1540i 0.308352 0.111020i
\(750\) −274.058 + 230.373i −0.365411 + 0.307164i
\(751\) −473.285 819.754i −0.630207 1.09155i −0.987509 0.157562i \(-0.949637\pi\)
0.357302 0.933989i \(-0.383697\pi\)
\(752\) 75.7225 + 89.6008i 0.100695 + 0.119150i
\(753\) −303.639 + 525.919i −0.403240 + 0.698432i
\(754\) −185.001 + 509.680i −0.245360 + 0.675968i
\(755\) −374.788 374.788i −0.496408 0.496408i
\(756\) 93.3295 + 111.614i 0.123452 + 0.147637i
\(757\) 789.374 + 789.374i 1.04277 + 1.04277i 0.999044 + 0.0437228i \(0.0139218\pi\)
0.0437228 + 0.999044i \(0.486078\pi\)
\(758\) 851.951 398.184i 1.12395 0.525308i
\(759\) 2.84493 4.92756i 0.00374826 0.00649217i
\(760\) 3.05353 + 1157.69i 0.00401781 + 1.52328i
\(761\) −504.141 873.198i −0.662472 1.14744i −0.979964 0.199174i \(-0.936174\pi\)
0.317492 0.948261i \(-0.397159\pi\)
\(762\) −14.4176 + 166.480i −0.0189208 + 0.218478i
\(763\) −227.430 + 269.137i −0.298073 + 0.352735i
\(764\) −21.0165 + 120.429i −0.0275086 + 0.157629i
\(765\) −516.524 138.402i −0.675194 0.180918i
\(766\) 266.322 + 1502.66i 0.347679 + 1.96170i
\(767\) 243.305 421.417i 0.317217 0.549435i
\(768\) 361.418 256.875i 0.470597 0.334473i
\(769\) 1084.70i 1.41053i −0.708944 0.705264i \(-0.750828\pi\)
0.708944 0.705264i \(-0.249172\pi\)
\(770\) 17.1152 4.53846i 0.0222275 0.00589411i
\(771\) −89.5136 + 89.5136i −0.116101 + 0.116101i
\(772\) −643.582 + 235.527i −0.833655 + 0.305087i
\(773\) −309.352 1154.52i −0.400197 1.49356i −0.812745 0.582620i \(-0.802028\pi\)
0.412548 0.910936i \(-0.364639\pi\)
\(774\) 90.4687 129.445i 0.116885 0.167241i
\(775\) 119.682 + 207.296i 0.154429 + 0.267478i
\(776\) −148.754 256.087i −0.191693 0.330008i
\(777\) 503.146 349.709i 0.647549 0.450076i
\(778\) −41.4880 + 479.061i −0.0533265 + 0.615759i
\(779\) 350.843 1309.36i 0.450376 1.68083i
\(780\) 31.2997 + 350.655i 0.0401278 + 0.449557i
\(781\) 3.14592 + 11.7407i 0.00402806 + 0.0150329i
\(782\) 315.927 870.384i 0.403999 1.11302i
\(783\) 155.893i 0.199097i
\(784\) −771.618 138.786i −0.984207 0.177023i
\(785\) −1026.01 −1.30702
\(786\) −422.563 153.380i −0.537611 0.195139i
\(787\) 1024.84 274.604i 1.30221 0.348925i 0.459923 0.887959i \(-0.347877\pi\)
0.842284 + 0.539033i \(0.181210\pi\)
\(788\) −11.3232 126.855i −0.0143695 0.160983i
\(789\) −56.9806 15.2679i −0.0722187 0.0193510i
\(790\) −765.432 66.2886i −0.968902 0.0839096i
\(791\) 123.089 + 177.095i 0.155612 + 0.223887i
\(792\) 1.38336 5.21778i 0.00174667 0.00658810i
\(793\) 799.144 461.386i 1.00775 0.581823i
\(794\) −148.715 103.936i −0.187298 0.130902i
\(795\) −314.830 + 84.3584i −0.396012 + 0.106111i
\(796\) 19.1220 6.99795i 0.0240226 0.00879139i
\(797\) −345.273 345.273i −0.433216 0.433216i 0.456505 0.889721i \(-0.349101\pi\)
−0.889721 + 0.456505i \(0.849101\pi\)
\(798\) −159.949 603.190i −0.200437 0.755877i
\(799\) 232.415 0.290883
\(800\) 162.888 + 135.463i 0.203609 + 0.169329i
\(801\) 162.882 + 94.0400i 0.203348 + 0.117403i
\(802\) 1218.31 215.926i 1.51909 0.269234i
\(803\) 8.31944 31.0486i 0.0103604 0.0386657i
\(804\) 134.414 770.216i 0.167182 0.957981i
\(805\) −439.118 371.070i −0.545489 0.460956i
\(806\) −650.993 56.3778i −0.807683 0.0699476i
\(807\) −119.226 + 68.8353i −0.147740 + 0.0852978i
\(808\) 1020.66 + 1015.29i 1.26319 + 1.25654i
\(809\) 305.931 + 176.630i 0.378160 + 0.218331i 0.677017 0.735967i \(-0.263272\pi\)
−0.298857 + 0.954298i \(0.596606\pi\)
\(810\) 42.8571 + 91.6968i 0.0529100 + 0.113206i
\(811\) 796.093 796.093i 0.981619 0.981619i −0.0182149 0.999834i \(-0.505798\pi\)
0.999834 + 0.0182149i \(0.00579832\pi\)
\(812\) −538.867 644.437i −0.663630 0.793642i
\(813\) −442.854 + 442.854i −0.544715 + 0.544715i
\(814\) −21.3697 7.75666i −0.0262527 0.00952907i
\(815\) −517.464 298.758i −0.634925 0.366574i
\(816\) 73.4847 875.380i 0.0900548 1.07277i
\(817\) −586.616 + 338.683i −0.718012 + 0.414545i
\(818\) 136.427 + 162.298i 0.166781 + 0.198408i
\(819\) −64.2841 178.546i −0.0784909 0.218004i
\(820\) −681.270 969.323i −0.830817 1.18210i
\(821\) 86.5633 323.059i 0.105436 0.393494i −0.892958 0.450140i \(-0.851374\pi\)
0.998394 + 0.0566461i \(0.0180407\pi\)
\(822\) 26.9393 38.5454i 0.0327729 0.0468922i
\(823\) 929.795 + 536.818i 1.12976 + 0.652269i 0.943875 0.330302i \(-0.107150\pi\)
0.185888 + 0.982571i \(0.440484\pi\)
\(824\) 893.056 + 512.470i 1.08381 + 0.621930i
\(825\) 2.57914 0.00312623
\(826\) 375.254 + 653.868i 0.454302 + 0.791608i
\(827\) 112.114 + 112.114i 0.135567 + 0.135567i 0.771634 0.636067i \(-0.219440\pi\)
−0.636067 + 0.771634i \(0.719440\pi\)
\(828\) −164.590 + 60.2338i −0.198780 + 0.0727462i
\(829\) 707.751 189.641i 0.853741 0.228759i 0.194697 0.980864i \(-0.437628\pi\)
0.659044 + 0.752104i \(0.270961\pi\)
\(830\) −1022.80 + 181.275i −1.23230 + 0.218404i
\(831\) 643.588 371.576i 0.774474 0.447143i
\(832\) −557.830 + 152.628i −0.670468 + 0.183448i
\(833\) −1196.75 + 990.113i −1.43668 + 1.18861i
\(834\) −115.519 137.424i −0.138512 0.164777i
\(835\) 145.375 + 38.9532i 0.174102 + 0.0466506i
\(836\) −14.8512 + 17.7623i −0.0177646 + 0.0212468i
\(837\) −181.466 + 48.6238i −0.216806 + 0.0580929i
\(838\) −690.133 + 322.553i −0.823547 + 0.384908i
\(839\) 801.988 0.955886 0.477943 0.878391i \(-0.341383\pi\)
0.477943 + 0.878391i \(0.341383\pi\)
\(840\) −494.128 230.918i −0.588247 0.274902i
\(841\) 59.0986i 0.0702718i
\(842\) 739.715 345.727i 0.878521 0.410602i
\(843\) −95.0796 354.842i −0.112787 0.420927i
\(844\) −268.494 + 23.9660i −0.318121 + 0.0283958i
\(845\) −127.118 + 474.410i −0.150435 + 0.561432i
\(846\) −28.3072 33.6751i −0.0334601 0.0398051i
\(847\) −766.075 360.470i −0.904457 0.425585i
\(848\) −227.990 484.471i −0.268856 0.571310i
\(849\) −68.2838 118.271i −0.0804285 0.139306i
\(850\) 413.280 73.2470i 0.486211 0.0861730i
\(851\) 191.043 + 712.980i 0.224492 + 0.837815i
\(852\) 157.635 339.608i 0.185018 0.398601i
\(853\) 147.448 147.448i 0.172858 0.172858i −0.615376 0.788234i \(-0.710996\pi\)
0.788234 + 0.615376i \(0.210996\pi\)
\(854\) −3.70716 + 1429.63i −0.00434093 + 1.67404i
\(855\) 434.137i 0.507763i
\(856\) 73.3226 + 270.785i 0.0856572 + 0.316337i
\(857\) −144.361 + 250.041i −0.168450 + 0.291764i −0.937875 0.346973i \(-0.887209\pi\)
0.769425 + 0.638737i \(0.220543\pi\)
\(858\) −4.03329 + 5.77092i −0.00470080 + 0.00672602i
\(859\) 802.102 + 214.923i 0.933762 + 0.250201i 0.693458 0.720497i \(-0.256086\pi\)
0.240304 + 0.970698i \(0.422753\pi\)
\(860\) −101.780 + 583.219i −0.118349 + 0.678161i
\(861\) 487.796 + 412.204i 0.566546 + 0.478751i
\(862\) 211.266 + 251.328i 0.245088 + 0.291564i
\(863\) −280.131 485.200i −0.324601 0.562225i 0.656831 0.754038i \(-0.271897\pi\)
−0.981431 + 0.191813i \(0.938563\pi\)
\(864\) −135.785 + 95.9703i −0.157159 + 0.111077i
\(865\) −240.717 + 416.935i −0.278286 + 0.482005i
\(866\) −1023.80 371.613i −1.18221 0.429114i
\(867\) −876.678 876.678i −1.01116 1.01116i
\(868\) 582.078 828.268i 0.670596 0.954226i
\(869\) −10.8649 10.8649i −0.0125027 0.0125027i
\(870\) −247.449 529.441i −0.284424 0.608553i
\(871\) −509.888 + 883.152i −0.585405 + 1.01395i
\(872\) −285.501 283.999i −0.327410 0.325687i
\(873\) 55.5291 + 96.1792i 0.0636072 + 0.110171i
\(874\) 748.935 + 64.8599i 0.856905 + 0.0742104i
\(875\) −128.101 + 712.032i −0.146401 + 0.813751i
\(876\) −810.069 + 569.342i −0.924737 + 0.649934i
\(877\) 836.787 + 224.216i 0.954147 + 0.255663i 0.702121 0.712058i \(-0.252237\pi\)
0.252026 + 0.967720i \(0.418903\pi\)
\(878\) −1090.57 + 193.285i −1.24210 + 0.220142i
\(879\) −75.2560 + 130.347i −0.0856155 + 0.148290i
\(880\) 3.58405 + 19.9163i 0.00407278 + 0.0226322i
\(881\) 1043.70i 1.18467i 0.805691 + 0.592337i \(0.201794\pi\)
−0.805691 + 0.592337i \(0.798206\pi\)
\(882\) 289.219 + 52.8077i 0.327912 + 0.0598727i
\(883\) −737.560 + 737.560i −0.835289 + 0.835289i −0.988235 0.152945i \(-0.951124\pi\)
0.152945 + 0.988235i \(0.451124\pi\)
\(884\) −482.398 + 1039.27i −0.545699 + 1.17565i
\(885\) 135.745 + 506.608i 0.153384 + 0.572438i
\(886\) 513.354 + 358.782i 0.579406 + 0.404946i
\(887\) −780.535 1351.93i −0.879972 1.52416i −0.851370 0.524566i \(-0.824228\pi\)
−0.0286025 0.999591i \(-0.509106\pi\)
\(888\) 351.736 + 605.531i 0.396100 + 0.681904i
\(889\) 192.718 + 277.274i 0.216781 + 0.311894i
\(890\) −702.446 60.8338i −0.789265 0.0683526i
\(891\) −0.523919 + 1.95529i −0.000588012 + 0.00219449i
\(892\) 67.0682 80.2148i 0.0751886 0.0899269i
\(893\) 48.8362 + 182.259i 0.0546878 + 0.204098i
\(894\) 52.9711 + 19.2272i 0.0592518 + 0.0215069i
\(895\) 279.910i 0.312748i
\(896\) 229.580 866.088i 0.256227 0.966617i
\(897\) 228.599 0.254848
\(898\) 409.519 1128.23i 0.456035 1.25638i
\(899\) 1047.75 280.745i 1.16547 0.312286i
\(900\) −60.9486 50.9596i −0.0677207 0.0566218i
\(901\) −1024.64 274.552i −1.13723 0.304719i
\(902\) 2.04437 23.6063i 0.00226649 0.0261711i
\(903\) −26.7095 318.005i −0.0295786 0.352165i
\(904\) −213.132 + 123.803i −0.235766 + 0.136950i
\(905\) −1129.15 + 651.915i −1.24768 + 0.720348i
\(906\) −187.048 + 267.632i −0.206454 + 0.295400i
\(907\) 843.102 225.909i 0.929550 0.249072i 0.237887 0.971293i \(-0.423545\pi\)
0.691663 + 0.722220i \(0.256878\pi\)
\(908\) 1096.41 + 508.918i 1.20750 + 0.560483i
\(909\) −381.741 381.741i −0.419957 0.419957i
\(910\) 501.726 + 504.334i 0.551347 + 0.554214i
\(911\) 292.574 0.321157 0.160578 0.987023i \(-0.448664\pi\)
0.160578 + 0.987023i \(0.448664\pi\)
\(912\) 701.910 126.312i 0.769638 0.138501i
\(913\) −17.9908 10.3870i −0.0197051 0.0113768i
\(914\) 250.879 + 1415.53i 0.274485 + 1.54872i
\(915\) −257.417 + 960.693i −0.281330 + 1.04994i
\(916\) 215.503 + 306.621i 0.235265 + 0.334739i
\(917\) −854.684 + 307.723i −0.932044 + 0.335576i
\(918\) −28.4225 + 328.194i −0.0309613 + 0.357509i
\(919\) 1113.06 642.623i 1.21116 0.699264i 0.248148 0.968722i \(-0.420178\pi\)
0.963012 + 0.269458i \(0.0868446\pi\)
\(920\) 463.368 465.819i 0.503661 0.506325i
\(921\) −646.996 373.543i −0.702493 0.405585i
\(922\) −1105.89 + 516.867i −1.19944 + 0.560593i
\(923\) −345.310 + 345.310i −0.374117 + 0.374117i
\(924\) −4.59295 9.89386i −0.00497073 0.0107076i
\(925\) −236.588 + 236.588i −0.255771 + 0.255771i
\(926\) −71.0841 + 195.837i −0.0767647 + 0.211488i
\(927\) −334.388 193.059i −0.360720 0.208262i
\(928\) 784.001 554.115i 0.844828 0.597107i
\(929\) 178.728 103.188i 0.192387 0.111075i −0.400712 0.916204i \(-0.631237\pi\)
0.593100 + 0.805129i \(0.297904\pi\)
\(930\) 539.112 453.177i 0.579690 0.487287i
\(931\) −1027.91 730.440i −1.10409 0.784576i
\(932\) 1345.43 + 234.797i 1.44360 + 0.251929i
\(933\) −61.8240 + 230.730i −0.0662636 + 0.247299i
\(934\) 740.190 + 517.317i 0.792495 + 0.553873i
\(935\) 34.7201 + 20.0457i 0.0371338 + 0.0214392i
\(936\) 209.336 56.6837i 0.223650 0.0605595i
\(937\) −430.745 −0.459707 −0.229853 0.973225i \(-0.573825\pi\)
−0.229853 + 0.973225i \(0.573825\pi\)
\(938\) −786.409 1370.29i −0.838389 1.46087i
\(939\) −336.107 336.107i −0.357942 0.357942i
\(940\) 149.589 + 69.4345i 0.159137 + 0.0738664i
\(941\) −549.626 + 147.272i −0.584087 + 0.156506i −0.538750 0.842466i \(-0.681103\pi\)
−0.0453378 + 0.998972i \(0.514436\pi\)
\(942\) 110.303 + 622.359i 0.117094 + 0.660678i
\(943\) −666.256 + 384.663i −0.706528 + 0.407914i
\(944\) −779.585 + 366.870i −0.825832 + 0.388633i
\(945\) 185.069 + 87.0827i 0.195840 + 0.0921510i
\(946\) −9.06338 + 7.61867i −0.00958074 + 0.00805356i
\(947\) 322.726 + 86.4742i 0.340788 + 0.0913139i 0.425154 0.905121i \(-0.360220\pi\)
−0.0843662 + 0.996435i \(0.526887\pi\)
\(948\) 42.0798 + 471.425i 0.0443879 + 0.497284i
\(949\) 1247.43 334.247i 1.31446 0.352209i
\(950\) 144.280 + 308.701i 0.151874 + 0.324948i
\(951\) 490.888 0.516181
\(952\) −1016.96 1454.95i −1.06823 1.52831i
\(953\) 185.513i 0.194662i −0.995252 0.0973310i \(-0.968969\pi\)
0.995252 0.0973310i \(-0.0310305\pi\)
\(954\) 85.0168 + 181.901i 0.0891161 + 0.190672i
\(955\) 44.4800 + 166.002i 0.0465759 + 0.173824i
\(956\) −1155.49 966.111i −1.20867 1.01058i
\(957\) 3.02501 11.2895i 0.00316093 0.0117968i
\(958\) 113.649 95.5333i 0.118632 0.0997216i
\(959\) −7.95341 94.6938i −0.00829344 0.0987422i
\(960\) 308.818 541.465i 0.321685 0.564026i
\(961\) 173.099 + 299.815i 0.180123 + 0.311983i
\(962\) −159.396 899.354i −0.165692 0.934879i
\(963\) −27.2280 101.616i −0.0282742 0.105521i
\(964\) 353.876 + 966.973i 0.367091 + 1.00308i
\(965\) −681.249 + 681.249i −0.705958 + 0.705958i
\(966\) −177.877 + 306.254i −0.184137 + 0.317034i
\(967\) 1398.42i 1.44614i 0.690776 + 0.723069i \(0.257269\pi\)
−0.690776 + 0.723069i \(0.742731\pi\)
\(968\) 481.586 839.235i 0.497506 0.866979i
\(969\) 706.469 1223.64i 0.729070 1.26279i
\(970\) −341.252 238.500i −0.351806 0.245877i
\(971\) −545.569 146.185i −0.561863 0.150551i −0.0333007 0.999445i \(-0.510602\pi\)
−0.528562 + 0.848895i \(0.677269\pi\)
\(972\) 51.0143 35.8544i 0.0524838 0.0368873i
\(973\) −357.043 64.2354i −0.366951 0.0660179i
\(974\) 14.6630 12.3257i 0.0150544 0.0126547i
\(975\) 51.8105 + 89.7384i 0.0531390 + 0.0920394i
\(976\) −1628.14 136.676i −1.66817 0.140037i
\(977\) −80.7105 + 139.795i −0.0826106 + 0.143086i −0.904371 0.426748i \(-0.859659\pi\)
0.821760 + 0.569834i \(0.192992\pi\)
\(978\) −125.591 + 346.003i −0.128416 + 0.353787i
\(979\) −9.97083 9.97083i −0.0101847 0.0101847i
\(980\) −1066.06 + 279.732i −1.08782 + 0.285441i
\(981\) 106.782 + 106.782i 0.108850 + 0.108850i
\(982\) −1414.42 + 661.070i −1.44035 + 0.673187i
\(983\) −824.636 + 1428.31i −0.838897 + 1.45301i 0.0519208 + 0.998651i \(0.483466\pi\)
−0.890818 + 0.454361i \(0.849868\pi\)
\(984\) −514.734 + 517.456i −0.523103 + 0.525870i
\(985\) −89.5209 155.055i −0.0908841 0.157416i
\(986\) 164.106 1894.93i 0.166436 1.92184i
\(987\) −87.4914 15.7405i −0.0886438 0.0159479i
\(988\) −916.357 159.918i −0.927487 0.161860i
\(989\) 371.331 + 99.4977i 0.375461 + 0.100604i
\(990\) −1.32431 7.47213i −0.00133769 0.00754761i
\(991\) −454.076 + 786.483i −0.458200 + 0.793626i −0.998866 0.0476118i \(-0.984839\pi\)
0.540666 + 0.841237i \(0.318172\pi\)
\(992\) 889.548 + 739.780i 0.896722 + 0.745746i
\(993\) 721.646i 0.726733i
\(994\) −193.921 731.304i −0.195092 0.735718i
\(995\) 20.2412 20.2412i 0.0203429 0.0203429i
\(996\) 219.917 + 600.928i 0.220800 + 0.603341i
\(997\) −228.030 851.021i −0.228717 0.853582i −0.980881 0.194607i \(-0.937657\pi\)
0.752165 0.658975i \(-0.229010\pi\)
\(998\) 1058.62 1514.70i 1.06074 1.51773i
\(999\) −131.302 227.421i −0.131433 0.227649i
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 336.3.bv.a.325.39 yes 256
7.5 odd 6 inner 336.3.bv.a.229.5 yes 256
16.13 even 4 inner 336.3.bv.a.157.5 yes 256
112.61 odd 12 inner 336.3.bv.a.61.39 256
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
336.3.bv.a.61.39 256 112.61 odd 12 inner
336.3.bv.a.157.5 yes 256 16.13 even 4 inner
336.3.bv.a.229.5 yes 256 7.5 odd 6 inner
336.3.bv.a.325.39 yes 256 1.1 even 1 trivial