Properties

Label 380.3.h.a.39.17
Level $380$
Weight $3$
Character 380.39
Analytic conductor $10.354$
Analytic rank $0$
Dimension $108$
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] = [380,3,Mod(39,380)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(380, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 0]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("380.39");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 380.h (of order \(2\), degree \(1\), 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: \(10.3542500457\)
Analytic rank: \(0\)
Dimension: \(108\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 39.17
Character \(\chi\) \(=\) 380.39
Dual form 380.3.h.a.39.18

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.70952 - 1.03804i) q^{2} +1.20444 q^{3} +(1.84495 + 3.54911i) q^{4} +(3.17819 - 3.85994i) q^{5} +(-2.05903 - 1.25026i) q^{6} +6.44137 q^{7} +(0.530130 - 7.98242i) q^{8} -7.54932 q^{9} +O(q^{10})\) \(q+(-1.70952 - 1.03804i) q^{2} +1.20444 q^{3} +(1.84495 + 3.54911i) q^{4} +(3.17819 - 3.85994i) q^{5} +(-2.05903 - 1.25026i) q^{6} +6.44137 q^{7} +(0.530130 - 7.98242i) q^{8} -7.54932 q^{9} +(-9.43996 + 3.29958i) q^{10} -4.38090i q^{11} +(2.22214 + 4.27470i) q^{12} -18.5880i q^{13} +(-11.0117 - 6.68640i) q^{14} +(3.82795 - 4.64908i) q^{15} +(-9.19233 + 13.0958i) q^{16} +10.0468i q^{17} +(12.9057 + 7.83649i) q^{18} -4.35890i q^{19} +(19.5629 + 4.15833i) q^{20} +7.75827 q^{21} +(-4.54754 + 7.48925i) q^{22} +16.8137 q^{23} +(0.638512 - 9.61437i) q^{24} +(-4.79828 - 24.5352i) q^{25} +(-19.2951 + 31.7766i) q^{26} -19.9327 q^{27} +(11.8840 + 22.8611i) q^{28} +14.9419 q^{29} +(-11.3699 + 3.97416i) q^{30} +10.3268i q^{31} +(29.3085 - 12.8457i) q^{32} -5.27654i q^{33} +(10.4289 - 17.1752i) q^{34} +(20.4719 - 24.8633i) q^{35} +(-13.9281 - 26.7933i) q^{36} -32.8822i q^{37} +(-4.52471 + 7.45164i) q^{38} -22.3882i q^{39} +(-29.1268 - 27.4159i) q^{40} +33.0801 q^{41} +(-13.2630 - 8.05339i) q^{42} -77.3574 q^{43} +(15.5483 - 8.08253i) q^{44} +(-23.9931 + 29.1399i) q^{45} +(-28.7434 - 17.4532i) q^{46} +77.0608 q^{47} +(-11.0716 + 15.7732i) q^{48} -7.50874 q^{49} +(-17.2657 + 46.9243i) q^{50} +12.1008i q^{51} +(65.9707 - 34.2939i) q^{52} -77.3006i q^{53} +(34.0755 + 20.6909i) q^{54} +(-16.9100 - 13.9233i) q^{55} +(3.41477 - 51.4177i) q^{56} -5.25005i q^{57} +(-25.5436 - 15.5103i) q^{58} -41.4208i q^{59} +(23.5624 + 5.00848i) q^{60} -5.37481 q^{61} +(10.7196 - 17.6539i) q^{62} -48.6279 q^{63} +(-63.4379 - 8.46344i) q^{64} +(-71.7485 - 59.0760i) q^{65} +(-5.47726 + 9.02038i) q^{66} -33.9875 q^{67} +(-35.6571 + 18.5358i) q^{68} +20.2511 q^{69} +(-60.8063 + 21.2538i) q^{70} +65.9277i q^{71} +(-4.00212 + 60.2618i) q^{72} -12.9194i q^{73} +(-34.1330 + 56.2129i) q^{74} +(-5.77926 - 29.5513i) q^{75} +(15.4702 - 8.04194i) q^{76} -28.2190i q^{77} +(-23.2398 + 38.2731i) q^{78} -49.5948i q^{79} +(21.3342 + 77.1029i) q^{80} +43.9360 q^{81} +(-56.5512 - 34.3384i) q^{82} -131.312 q^{83} +(14.3136 + 27.5349i) q^{84} +(38.7799 + 31.9305i) q^{85} +(132.244 + 80.3000i) q^{86} +17.9967 q^{87} +(-34.9701 - 2.32245i) q^{88} +146.244 q^{89} +(71.2652 - 24.9096i) q^{90} -119.732i q^{91} +(31.0203 + 59.6735i) q^{92} +12.4381i q^{93} +(-131.737 - 79.9922i) q^{94} +(-16.8251 - 13.8534i) q^{95} +(35.3005 - 15.4719i) q^{96} +58.5847i q^{97} +(12.8364 + 7.79437i) q^{98} +33.0728i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 108 q + 4 q^{5} + 324 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 108 q + 4 q^{5} + 324 q^{9} - 8 q^{10} + 8 q^{14} - 104 q^{16} - 16 q^{21} - 8 q^{24} - 76 q^{25} + 80 q^{26} - 88 q^{29} - 140 q^{30} - 88 q^{34} - 256 q^{36} + 44 q^{40} - 200 q^{41} - 8 q^{44} + 108 q^{45} + 272 q^{46} + 916 q^{49} - 276 q^{50} - 320 q^{54} - 328 q^{56} + 172 q^{60} + 200 q^{61} - 216 q^{64} - 192 q^{65} + 152 q^{66} - 592 q^{69} + 200 q^{70} - 232 q^{74} + 340 q^{80} + 1052 q^{81} + 208 q^{84} + 248 q^{85} - 1048 q^{86} + 760 q^{89} + 268 q^{90} - 320 q^{94} + 720 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/380\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(77\) \(191\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.70952 1.03804i −0.854762 0.519020i
\(3\) 1.20444 0.401481 0.200741 0.979644i \(-0.435665\pi\)
0.200741 + 0.979644i \(0.435665\pi\)
\(4\) 1.84495 + 3.54911i 0.461237 + 0.887277i
\(5\) 3.17819 3.85994i 0.635637 0.771988i
\(6\) −2.05903 1.25026i −0.343171 0.208377i
\(7\) 6.44137 0.920196 0.460098 0.887868i \(-0.347814\pi\)
0.460098 + 0.887868i \(0.347814\pi\)
\(8\) 0.530130 7.98242i 0.0662663 0.997802i
\(9\) −7.54932 −0.838813
\(10\) −9.43996 + 3.29958i −0.943996 + 0.329958i
\(11\) 4.38090i 0.398263i −0.979973 0.199132i \(-0.936188\pi\)
0.979973 0.199132i \(-0.0638122\pi\)
\(12\) 2.22214 + 4.27470i 0.185178 + 0.356225i
\(13\) 18.5880i 1.42984i −0.699204 0.714922i \(-0.746462\pi\)
0.699204 0.714922i \(-0.253538\pi\)
\(14\) −11.0117 6.68640i −0.786549 0.477600i
\(15\) 3.82795 4.64908i 0.255196 0.309939i
\(16\) −9.19233 + 13.0958i −0.574521 + 0.818490i
\(17\) 10.0468i 0.590987i 0.955345 + 0.295493i \(0.0954840\pi\)
−0.955345 + 0.295493i \(0.904516\pi\)
\(18\) 12.9057 + 7.83649i 0.716986 + 0.435360i
\(19\) 4.35890i 0.229416i
\(20\) 19.5629 + 4.15833i 0.978147 + 0.207917i
\(21\) 7.75827 0.369441
\(22\) −4.54754 + 7.48925i −0.206707 + 0.340421i
\(23\) 16.8137 0.731029 0.365514 0.930806i \(-0.380893\pi\)
0.365514 + 0.930806i \(0.380893\pi\)
\(24\) 0.638512 9.61437i 0.0266047 0.400599i
\(25\) −4.79828 24.5352i −0.191931 0.981408i
\(26\) −19.2951 + 31.7766i −0.742118 + 1.22218i
\(27\) −19.9327 −0.738249
\(28\) 11.8840 + 22.8611i 0.424428 + 0.816469i
\(29\) 14.9419 0.515239 0.257619 0.966246i \(-0.417062\pi\)
0.257619 + 0.966246i \(0.417062\pi\)
\(30\) −11.3699 + 3.97416i −0.378997 + 0.132472i
\(31\) 10.3268i 0.333123i 0.986031 + 0.166562i \(0.0532664\pi\)
−0.986031 + 0.166562i \(0.946734\pi\)
\(32\) 29.3085 12.8457i 0.915891 0.401427i
\(33\) 5.27654i 0.159895i
\(34\) 10.4289 17.1752i 0.306734 0.505153i
\(35\) 20.4719 24.8633i 0.584911 0.710380i
\(36\) −13.9281 26.7933i −0.386892 0.744259i
\(37\) 32.8822i 0.888708i −0.895851 0.444354i \(-0.853433\pi\)
0.895851 0.444354i \(-0.146567\pi\)
\(38\) −4.52471 + 7.45164i −0.119071 + 0.196096i
\(39\) 22.3882i 0.574056i
\(40\) −29.1268 27.4159i −0.728170 0.685397i
\(41\) 33.0801 0.806832 0.403416 0.915017i \(-0.367823\pi\)
0.403416 + 0.915017i \(0.367823\pi\)
\(42\) −13.2630 8.05339i −0.315785 0.191747i
\(43\) −77.3574 −1.79901 −0.899505 0.436911i \(-0.856072\pi\)
−0.899505 + 0.436911i \(0.856072\pi\)
\(44\) 15.5483 8.08253i 0.353370 0.183694i
\(45\) −23.9931 + 29.1399i −0.533180 + 0.647553i
\(46\) −28.7434 17.4532i −0.624856 0.379418i
\(47\) 77.0608 1.63959 0.819796 0.572655i \(-0.194087\pi\)
0.819796 + 0.572655i \(0.194087\pi\)
\(48\) −11.0716 + 15.7732i −0.230659 + 0.328608i
\(49\) −7.50874 −0.153240
\(50\) −17.2657 + 46.9243i −0.345315 + 0.938487i
\(51\) 12.1008i 0.237270i
\(52\) 65.9707 34.2939i 1.26867 0.659497i
\(53\) 77.3006i 1.45850i −0.684246 0.729251i \(-0.739869\pi\)
0.684246 0.729251i \(-0.260131\pi\)
\(54\) 34.0755 + 20.6909i 0.631027 + 0.383166i
\(55\) −16.9100 13.9233i −0.307455 0.253151i
\(56\) 3.41477 51.4177i 0.0609780 0.918173i
\(57\) 5.25005i 0.0921061i
\(58\) −25.5436 15.5103i −0.440407 0.267419i
\(59\) 41.4208i 0.702047i −0.936367 0.351023i \(-0.885834\pi\)
0.936367 0.351023i \(-0.114166\pi\)
\(60\) 23.5624 + 5.00848i 0.392707 + 0.0834746i
\(61\) −5.37481 −0.0881116 −0.0440558 0.999029i \(-0.514028\pi\)
−0.0440558 + 0.999029i \(0.514028\pi\)
\(62\) 10.7196 17.6539i 0.172897 0.284741i
\(63\) −48.6279 −0.771872
\(64\) −63.4379 8.46344i −0.991218 0.132241i
\(65\) −71.7485 59.0760i −1.10382 0.908862i
\(66\) −5.47726 + 9.02038i −0.0829888 + 0.136672i
\(67\) −33.9875 −0.507276 −0.253638 0.967299i \(-0.581627\pi\)
−0.253638 + 0.967299i \(0.581627\pi\)
\(68\) −35.6571 + 18.5358i −0.524369 + 0.272585i
\(69\) 20.2511 0.293494
\(70\) −60.8063 + 21.2538i −0.868661 + 0.303626i
\(71\) 65.9277i 0.928560i 0.885689 + 0.464280i \(0.153687\pi\)
−0.885689 + 0.464280i \(0.846313\pi\)
\(72\) −4.00212 + 60.2618i −0.0555850 + 0.836969i
\(73\) 12.9194i 0.176979i −0.996077 0.0884893i \(-0.971796\pi\)
0.996077 0.0884893i \(-0.0282039\pi\)
\(74\) −34.1330 + 56.2129i −0.461257 + 0.759634i
\(75\) −5.77926 29.5513i −0.0770567 0.394017i
\(76\) 15.4702 8.04194i 0.203555 0.105815i
\(77\) 28.2190i 0.366480i
\(78\) −23.2398 + 38.2731i −0.297946 + 0.490681i
\(79\) 49.5948i 0.627782i −0.949459 0.313891i \(-0.898367\pi\)
0.949459 0.313891i \(-0.101633\pi\)
\(80\) 21.3342 + 77.1029i 0.266678 + 0.963786i
\(81\) 43.9360 0.542420
\(82\) −56.5512 34.3384i −0.689649 0.418762i
\(83\) −131.312 −1.58207 −0.791037 0.611768i \(-0.790459\pi\)
−0.791037 + 0.611768i \(0.790459\pi\)
\(84\) 14.3136 + 27.5349i 0.170400 + 0.327797i
\(85\) 38.7799 + 31.9305i 0.456235 + 0.375653i
\(86\) 132.244 + 80.3000i 1.53773 + 0.933721i
\(87\) 17.9967 0.206859
\(88\) −34.9701 2.32245i −0.397388 0.0263914i
\(89\) 146.244 1.64319 0.821596 0.570070i \(-0.193084\pi\)
0.821596 + 0.570070i \(0.193084\pi\)
\(90\) 71.2652 24.9096i 0.791836 0.276773i
\(91\) 119.732i 1.31574i
\(92\) 31.0203 + 59.6735i 0.337177 + 0.648625i
\(93\) 12.4381i 0.133743i
\(94\) −131.737 79.9922i −1.40146 0.850981i
\(95\) −16.8251 13.8534i −0.177106 0.145825i
\(96\) 35.3005 15.4719i 0.367713 0.161165i
\(97\) 58.5847i 0.603966i 0.953313 + 0.301983i \(0.0976485\pi\)
−0.953313 + 0.301983i \(0.902351\pi\)
\(98\) 12.8364 + 7.79437i 0.130983 + 0.0795344i
\(99\) 33.0728i 0.334068i
\(100\) 78.2255 62.2958i 0.782255 0.622958i
\(101\) 164.046 1.62421 0.812107 0.583508i \(-0.198320\pi\)
0.812107 + 0.583508i \(0.198320\pi\)
\(102\) 12.5611 20.6866i 0.123148 0.202809i
\(103\) −13.2411 −0.128554 −0.0642770 0.997932i \(-0.520474\pi\)
−0.0642770 + 0.997932i \(0.520474\pi\)
\(104\) −148.377 9.85405i −1.42670 0.0947505i
\(105\) 24.6572 29.9465i 0.234831 0.285204i
\(106\) −80.2411 + 132.147i −0.756991 + 1.24667i
\(107\) 55.1237 0.515174 0.257587 0.966255i \(-0.417073\pi\)
0.257587 + 0.966255i \(0.417073\pi\)
\(108\) −36.7748 70.7434i −0.340508 0.655031i
\(109\) 128.952 1.18304 0.591522 0.806289i \(-0.298527\pi\)
0.591522 + 0.806289i \(0.298527\pi\)
\(110\) 14.4551 + 41.3555i 0.131410 + 0.375959i
\(111\) 39.6047i 0.356800i
\(112\) −59.2112 + 84.3552i −0.528672 + 0.753171i
\(113\) 127.923i 1.13206i 0.824384 + 0.566032i \(0.191522\pi\)
−0.824384 + 0.566032i \(0.808478\pi\)
\(114\) −5.44976 + 8.97509i −0.0478049 + 0.0787288i
\(115\) 53.4369 64.8997i 0.464669 0.564345i
\(116\) 27.5671 + 53.0305i 0.237647 + 0.457159i
\(117\) 140.327i 1.19937i
\(118\) −42.9964 + 70.8098i −0.364376 + 0.600083i
\(119\) 64.7150i 0.543823i
\(120\) −35.0816 33.0209i −0.292347 0.275174i
\(121\) 101.808 0.841386
\(122\) 9.18836 + 5.57926i 0.0753144 + 0.0457316i
\(123\) 39.8431 0.323928
\(124\) −36.6510 + 19.0524i −0.295572 + 0.153649i
\(125\) −109.954 59.4564i −0.879634 0.475651i
\(126\) 83.1307 + 50.4777i 0.659767 + 0.400617i
\(127\) 7.74382 0.0609749 0.0304875 0.999535i \(-0.490294\pi\)
0.0304875 + 0.999535i \(0.490294\pi\)
\(128\) 99.6633 + 80.3195i 0.778620 + 0.627496i
\(129\) −93.1726 −0.722268
\(130\) 61.3325 + 175.470i 0.471789 + 1.34977i
\(131\) 161.434i 1.23232i 0.787622 + 0.616159i \(0.211312\pi\)
−0.787622 + 0.616159i \(0.788688\pi\)
\(132\) 18.7270 9.73495i 0.141871 0.0737496i
\(133\) 28.0773i 0.211107i
\(134\) 58.1024 + 35.2803i 0.433600 + 0.263286i
\(135\) −63.3499 + 76.9391i −0.469258 + 0.569919i
\(136\) 80.1975 + 5.32610i 0.589688 + 0.0391625i
\(137\) 70.5190i 0.514737i 0.966313 + 0.257369i \(0.0828554\pi\)
−0.966313 + 0.257369i \(0.917145\pi\)
\(138\) −34.6198 21.0214i −0.250868 0.152329i
\(139\) 215.827i 1.55271i 0.630295 + 0.776356i \(0.282934\pi\)
−0.630295 + 0.776356i \(0.717066\pi\)
\(140\) 126.012 + 26.7854i 0.900086 + 0.191324i
\(141\) 92.8154 0.658266
\(142\) 68.4356 112.705i 0.481941 0.793698i
\(143\) −81.4320 −0.569455
\(144\) 69.3958 98.8646i 0.481915 0.686560i
\(145\) 47.4882 57.6749i 0.327505 0.397758i
\(146\) −13.4109 + 22.0861i −0.0918554 + 0.151275i
\(147\) −9.04385 −0.0615228
\(148\) 116.702 60.6659i 0.788530 0.409905i
\(149\) −244.215 −1.63903 −0.819513 0.573061i \(-0.805756\pi\)
−0.819513 + 0.573061i \(0.805756\pi\)
\(150\) −20.7956 + 56.5177i −0.138637 + 0.376785i
\(151\) 173.692i 1.15028i 0.818056 + 0.575139i \(0.195052\pi\)
−0.818056 + 0.575139i \(0.804948\pi\)
\(152\) −34.7945 2.31078i −0.228911 0.0152025i
\(153\) 75.8462i 0.495727i
\(154\) −29.2924 + 48.2410i −0.190211 + 0.313254i
\(155\) 39.8609 + 32.8205i 0.257167 + 0.211745i
\(156\) 79.4581 41.3050i 0.509346 0.264776i
\(157\) 30.1229i 0.191866i 0.995388 + 0.0959328i \(0.0305834\pi\)
−0.995388 + 0.0959328i \(0.969417\pi\)
\(158\) −51.4813 + 84.7835i −0.325831 + 0.536604i
\(159\) 93.1042i 0.585561i
\(160\) 43.5644 153.955i 0.272278 0.962219i
\(161\) 108.303 0.672689
\(162\) −75.1097 45.6073i −0.463640 0.281527i
\(163\) 100.884 0.618918 0.309459 0.950913i \(-0.399852\pi\)
0.309459 + 0.950913i \(0.399852\pi\)
\(164\) 61.0311 + 117.405i 0.372141 + 0.715883i
\(165\) −20.3671 16.7698i −0.123437 0.101635i
\(166\) 224.481 + 136.307i 1.35230 + 0.821128i
\(167\) 158.441 0.948749 0.474375 0.880323i \(-0.342674\pi\)
0.474375 + 0.880323i \(0.342674\pi\)
\(168\) 4.11289 61.9297i 0.0244815 0.368629i
\(169\) −176.513 −1.04446
\(170\) −33.1501 94.8411i −0.195001 0.557889i
\(171\) 32.9067i 0.192437i
\(172\) −142.720 274.550i −0.829770 1.59622i
\(173\) 52.4672i 0.303279i 0.988436 + 0.151639i \(0.0484552\pi\)
−0.988436 + 0.151639i \(0.951545\pi\)
\(174\) −30.7658 18.6813i −0.176815 0.107364i
\(175\) −30.9075 158.040i −0.176614 0.903088i
\(176\) 57.3715 + 40.2707i 0.325975 + 0.228811i
\(177\) 49.8890i 0.281859i
\(178\) −250.008 151.807i −1.40454 0.852849i
\(179\) 30.3539i 0.169575i −0.996399 0.0847875i \(-0.972979\pi\)
0.996399 0.0847875i \(-0.0270211\pi\)
\(180\) −147.687 31.3926i −0.820482 0.174403i
\(181\) −300.899 −1.66242 −0.831212 0.555956i \(-0.812352\pi\)
−0.831212 + 0.555956i \(0.812352\pi\)
\(182\) −124.287 + 204.685i −0.682894 + 1.12464i
\(183\) −6.47365 −0.0353751
\(184\) 8.91343 134.214i 0.0484425 0.729422i
\(185\) −126.923 104.506i −0.686072 0.564896i
\(186\) 12.9112 21.2632i 0.0694151 0.114318i
\(187\) 44.0139 0.235368
\(188\) 142.173 + 273.497i 0.756241 + 1.45477i
\(189\) −128.394 −0.679334
\(190\) 14.3825 + 41.1478i 0.0756976 + 0.216567i
\(191\) 240.190i 1.25754i −0.777593 0.628768i \(-0.783559\pi\)
0.777593 0.628768i \(-0.216441\pi\)
\(192\) −76.4074 10.1937i −0.397955 0.0530924i
\(193\) 81.0689i 0.420046i 0.977696 + 0.210023i \(0.0673539\pi\)
−0.977696 + 0.210023i \(0.932646\pi\)
\(194\) 60.8132 100.152i 0.313470 0.516247i
\(195\) −86.4170 71.1538i −0.443164 0.364891i
\(196\) −13.8532 26.6493i −0.0706798 0.135966i
\(197\) 265.088i 1.34563i 0.739812 + 0.672813i \(0.234914\pi\)
−0.739812 + 0.672813i \(0.765086\pi\)
\(198\) 34.3308 56.5387i 0.173388 0.285549i
\(199\) 78.0268i 0.392094i 0.980594 + 0.196047i \(0.0628106\pi\)
−0.980594 + 0.196047i \(0.937189\pi\)
\(200\) −198.394 + 25.2950i −0.991970 + 0.126475i
\(201\) −40.9360 −0.203662
\(202\) −280.440 170.286i −1.38832 0.843000i
\(203\) 96.2465 0.474120
\(204\) −42.9469 + 22.3253i −0.210524 + 0.109438i
\(205\) 105.135 127.687i 0.512852 0.622864i
\(206\) 22.6359 + 13.7447i 0.109883 + 0.0667221i
\(207\) −126.932 −0.613196
\(208\) 243.425 + 170.867i 1.17031 + 0.821476i
\(209\) −19.0959 −0.0913679
\(210\) −73.2377 + 25.5990i −0.348751 + 0.121900i
\(211\) 225.442i 1.06845i −0.845343 0.534224i \(-0.820604\pi\)
0.845343 0.534224i \(-0.179396\pi\)
\(212\) 274.348 142.616i 1.29410 0.672715i
\(213\) 79.4062i 0.372799i
\(214\) −94.2353 57.2205i −0.440352 0.267386i
\(215\) −245.856 + 298.595i −1.14352 + 1.38881i
\(216\) −10.5669 + 159.111i −0.0489210 + 0.736626i
\(217\) 66.5188i 0.306538i
\(218\) −220.446 133.857i −1.01122 0.614024i
\(219\) 15.5607i 0.0710536i
\(220\) 18.2172 85.7032i 0.0828056 0.389560i
\(221\) 186.749 0.845019
\(222\) −41.1113 + 67.7053i −0.185186 + 0.304979i
\(223\) 213.433 0.957099 0.478550 0.878060i \(-0.341163\pi\)
0.478550 + 0.878060i \(0.341163\pi\)
\(224\) 188.787 82.7436i 0.842799 0.369391i
\(225\) 36.2237 + 185.224i 0.160994 + 0.823218i
\(226\) 132.789 218.688i 0.587563 0.967645i
\(227\) 33.4439 0.147330 0.0736650 0.997283i \(-0.476530\pi\)
0.0736650 + 0.997283i \(0.476530\pi\)
\(228\) 18.6330 9.68607i 0.0817236 0.0424827i
\(229\) −44.7554 −0.195439 −0.0977193 0.995214i \(-0.531155\pi\)
−0.0977193 + 0.995214i \(0.531155\pi\)
\(230\) −158.720 + 55.4780i −0.690088 + 0.241209i
\(231\) 33.9882i 0.147135i
\(232\) 7.92116 119.273i 0.0341430 0.514106i
\(233\) 215.494i 0.924866i −0.886654 0.462433i \(-0.846977\pi\)
0.886654 0.462433i \(-0.153023\pi\)
\(234\) 145.664 239.892i 0.622498 1.02518i
\(235\) 244.914 297.450i 1.04219 1.26575i
\(236\) 147.007 76.4192i 0.622910 0.323810i
\(237\) 59.7341i 0.252043i
\(238\) 67.1767 110.632i 0.282255 0.464840i
\(239\) 305.842i 1.27968i 0.768510 + 0.639838i \(0.220998\pi\)
−0.768510 + 0.639838i \(0.779002\pi\)
\(240\) 25.6959 + 92.8661i 0.107066 + 0.386942i
\(241\) −149.888 −0.621943 −0.310971 0.950419i \(-0.600654\pi\)
−0.310971 + 0.950419i \(0.600654\pi\)
\(242\) −174.043 105.680i −0.719185 0.436696i
\(243\) 232.313 0.956020
\(244\) −9.91624 19.0758i −0.0406403 0.0781794i
\(245\) −23.8642 + 28.9833i −0.0974047 + 0.118299i
\(246\) −68.1128 41.3587i −0.276881 0.168125i
\(247\) −81.0231 −0.328029
\(248\) 82.4329 + 5.47456i 0.332391 + 0.0220748i
\(249\) −158.158 −0.635173
\(250\) 126.251 + 215.779i 0.505006 + 0.863116i
\(251\) 79.7048i 0.317549i −0.987315 0.158774i \(-0.949246\pi\)
0.987315 0.158774i \(-0.0507543\pi\)
\(252\) −89.7160 172.586i −0.356016 0.684864i
\(253\) 73.6589i 0.291142i
\(254\) −13.2382 8.03839i −0.0521191 0.0316472i
\(255\) 46.7082 + 38.4585i 0.183170 + 0.150818i
\(256\) −87.0020 240.763i −0.339852 0.940479i
\(257\) 112.477i 0.437653i 0.975764 + 0.218827i \(0.0702230\pi\)
−0.975764 + 0.218827i \(0.929777\pi\)
\(258\) 159.281 + 96.7169i 0.617368 + 0.374872i
\(259\) 211.806i 0.817785i
\(260\) 77.2950 363.635i 0.297289 1.39860i
\(261\) −112.801 −0.432189
\(262\) 167.575 275.975i 0.639598 1.05334i
\(263\) −399.362 −1.51849 −0.759244 0.650806i \(-0.774431\pi\)
−0.759244 + 0.650806i \(0.774431\pi\)
\(264\) −42.1196 2.79726i −0.159544 0.0105957i
\(265\) −298.376 245.676i −1.12595 0.927078i
\(266\) −29.1453 + 47.9988i −0.109569 + 0.180447i
\(267\) 176.143 0.659711
\(268\) −62.7051 120.625i −0.233974 0.450094i
\(269\) −49.1692 −0.182785 −0.0913925 0.995815i \(-0.529132\pi\)
−0.0913925 + 0.995815i \(0.529132\pi\)
\(270\) 188.164 65.7696i 0.696904 0.243591i
\(271\) 477.297i 1.76124i 0.473819 + 0.880622i \(0.342875\pi\)
−0.473819 + 0.880622i \(0.657125\pi\)
\(272\) −131.571 92.3533i −0.483717 0.339534i
\(273\) 144.211i 0.528244i
\(274\) 73.2015 120.554i 0.267159 0.439978i
\(275\) −107.486 + 21.0208i −0.390859 + 0.0764391i
\(276\) 37.3622 + 71.8734i 0.135370 + 0.260411i
\(277\) 373.269i 1.34754i 0.738940 + 0.673771i \(0.235327\pi\)
−0.738940 + 0.673771i \(0.764673\pi\)
\(278\) 224.037 368.961i 0.805888 1.32720i
\(279\) 77.9604i 0.279428i
\(280\) −187.617 176.596i −0.670059 0.630699i
\(281\) 308.449 1.09768 0.548842 0.835926i \(-0.315069\pi\)
0.548842 + 0.835926i \(0.315069\pi\)
\(282\) −158.670 96.3461i −0.562661 0.341653i
\(283\) 178.424 0.630472 0.315236 0.949013i \(-0.397916\pi\)
0.315236 + 0.949013i \(0.397916\pi\)
\(284\) −233.985 + 121.633i −0.823890 + 0.428286i
\(285\) −20.2649 16.6856i −0.0711048 0.0585461i
\(286\) 139.210 + 84.5297i 0.486748 + 0.295558i
\(287\) 213.081 0.742443
\(288\) −221.259 + 96.9759i −0.768261 + 0.336722i
\(289\) 188.062 0.650735
\(290\) −141.051 + 49.3021i −0.486383 + 0.170007i
\(291\) 70.5619i 0.242481i
\(292\) 45.8525 23.8357i 0.157029 0.0816291i
\(293\) 383.511i 1.30891i −0.756100 0.654456i \(-0.772898\pi\)
0.756100 0.654456i \(-0.227102\pi\)
\(294\) 15.4607 + 9.38788i 0.0525874 + 0.0319316i
\(295\) −159.882 131.643i −0.541972 0.446247i
\(296\) −262.479 17.4318i −0.886754 0.0588914i
\(297\) 87.3232i 0.294017i
\(298\) 417.491 + 253.505i 1.40098 + 0.850687i
\(299\) 312.532i 1.04526i
\(300\) 94.2182 75.0318i 0.314061 0.250106i
\(301\) −498.288 −1.65544
\(302\) 180.299 296.931i 0.597017 0.983214i
\(303\) 197.584 0.652092
\(304\) 57.0834 + 40.0685i 0.187774 + 0.131804i
\(305\) −17.0821 + 20.7464i −0.0560070 + 0.0680211i
\(306\) −78.7314 + 129.661i −0.257292 + 0.423729i
\(307\) 89.1480 0.290384 0.145192 0.989403i \(-0.453620\pi\)
0.145192 + 0.989403i \(0.453620\pi\)
\(308\) 100.152 52.0626i 0.325170 0.169034i
\(309\) −15.9481 −0.0516120
\(310\) −34.0742 97.4847i −0.109917 0.314467i
\(311\) 494.211i 1.58910i 0.607198 + 0.794551i \(0.292294\pi\)
−0.607198 + 0.794551i \(0.707706\pi\)
\(312\) −178.712 11.8687i −0.572794 0.0380405i
\(313\) 193.158i 0.617117i 0.951205 + 0.308559i \(0.0998466\pi\)
−0.951205 + 0.308559i \(0.900153\pi\)
\(314\) 31.2688 51.4959i 0.0995821 0.164000i
\(315\) −154.549 + 187.701i −0.490630 + 0.595876i
\(316\) 176.017 91.4998i 0.557017 0.289556i
\(317\) 619.732i 1.95499i 0.210954 + 0.977496i \(0.432343\pi\)
−0.210954 + 0.977496i \(0.567657\pi\)
\(318\) −96.6459 + 159.164i −0.303918 + 0.500516i
\(319\) 65.4590i 0.205201i
\(320\) −234.286 + 217.968i −0.732143 + 0.681151i
\(321\) 66.3933 0.206833
\(322\) −185.147 112.423i −0.574990 0.349139i
\(323\) 43.7929 0.135582
\(324\) 81.0596 + 155.934i 0.250184 + 0.481277i
\(325\) −456.060 + 89.1903i −1.40326 + 0.274432i
\(326\) −172.463 104.721i −0.529028 0.321231i
\(327\) 155.315 0.474970
\(328\) 17.5368 264.059i 0.0534657 0.805058i
\(329\) 496.377 1.50875
\(330\) 17.4104 + 49.8103i 0.0527587 + 0.150940i
\(331\) 155.301i 0.469186i 0.972094 + 0.234593i \(0.0753757\pi\)
−0.972094 + 0.234593i \(0.924624\pi\)
\(332\) −242.264 466.041i −0.729711 1.40374i
\(333\) 248.238i 0.745460i
\(334\) −270.859 164.468i −0.810955 0.492420i
\(335\) −108.018 + 131.190i −0.322443 + 0.391611i
\(336\) −71.3166 + 101.601i −0.212252 + 0.302384i
\(337\) 182.187i 0.540615i −0.962774 0.270308i \(-0.912875\pi\)
0.962774 0.270308i \(-0.0871254\pi\)
\(338\) 301.753 + 183.228i 0.892761 + 0.542093i
\(339\) 154.076i 0.454502i
\(340\) −41.7778 + 196.544i −0.122876 + 0.578071i
\(341\) 45.2407 0.132671
\(342\) 34.1585 56.2548i 0.0998785 0.164488i
\(343\) −363.994 −1.06121
\(344\) −41.0095 + 617.499i −0.119214 + 1.79505i
\(345\) 64.3618 78.1681i 0.186556 0.226574i
\(346\) 54.4631 89.6940i 0.157408 0.259231i
\(347\) −37.0704 −0.106831 −0.0534156 0.998572i \(-0.517011\pi\)
−0.0534156 + 0.998572i \(0.517011\pi\)
\(348\) 33.2030 + 63.8722i 0.0954109 + 0.183541i
\(349\) −244.060 −0.699311 −0.349656 0.936878i \(-0.613701\pi\)
−0.349656 + 0.936878i \(0.613701\pi\)
\(350\) −111.215 + 302.257i −0.317757 + 0.863592i
\(351\) 370.509i 1.05558i
\(352\) −56.2755 128.398i −0.159874 0.364766i
\(353\) 48.4139i 0.137150i −0.997646 0.0685750i \(-0.978155\pi\)
0.997646 0.0685750i \(-0.0218452\pi\)
\(354\) −51.7867 + 85.2864i −0.146290 + 0.240922i
\(355\) 254.477 + 209.531i 0.716837 + 0.590227i
\(356\) 269.813 + 519.036i 0.757901 + 1.45797i
\(357\) 77.9456i 0.218335i
\(358\) −31.5086 + 51.8908i −0.0880128 + 0.144946i
\(359\) 191.649i 0.533842i −0.963718 0.266921i \(-0.913994\pi\)
0.963718 0.266921i \(-0.0860062\pi\)
\(360\) 219.887 + 206.971i 0.610798 + 0.574920i
\(361\) −19.0000 −0.0526316
\(362\) 514.394 + 312.345i 1.42098 + 0.862831i
\(363\) 122.622 0.337801
\(364\) 424.942 220.899i 1.16742 0.606867i
\(365\) −49.8683 41.0604i −0.136625 0.112494i
\(366\) 11.0669 + 6.71991i 0.0302373 + 0.0183604i
\(367\) 276.491 0.753381 0.376690 0.926339i \(-0.377062\pi\)
0.376690 + 0.926339i \(0.377062\pi\)
\(368\) −154.557 + 220.189i −0.419991 + 0.598340i
\(369\) −249.732 −0.676781
\(370\) 108.497 + 310.406i 0.293236 + 0.838936i
\(371\) 497.922i 1.34211i
\(372\) −44.1440 + 22.9476i −0.118667 + 0.0616871i
\(373\) 671.067i 1.79911i −0.436811 0.899553i \(-0.643892\pi\)
0.436811 0.899553i \(-0.356108\pi\)
\(374\) −75.2428 45.6881i −0.201184 0.122161i
\(375\) −132.434 71.6119i −0.353157 0.190965i
\(376\) 40.8523 615.132i 0.108650 1.63599i
\(377\) 277.740i 0.736711i
\(378\) 219.493 + 133.278i 0.580669 + 0.352588i
\(379\) 291.027i 0.767880i −0.923358 0.383940i \(-0.874567\pi\)
0.923358 0.383940i \(-0.125433\pi\)
\(380\) 18.1258 85.2728i 0.0476993 0.224402i
\(381\) 9.32699 0.0244803
\(382\) −249.326 + 410.610i −0.652686 + 1.07490i
\(383\) −60.6356 −0.158318 −0.0791588 0.996862i \(-0.525223\pi\)
−0.0791588 + 0.996862i \(0.525223\pi\)
\(384\) 120.039 + 96.7403i 0.312601 + 0.251928i
\(385\) −108.924 89.6852i −0.282918 0.232948i
\(386\) 84.1527 138.589i 0.218012 0.359039i
\(387\) 583.995 1.50903
\(388\) −207.923 + 108.086i −0.535885 + 0.278571i
\(389\) 435.068 1.11843 0.559214 0.829024i \(-0.311103\pi\)
0.559214 + 0.829024i \(0.311103\pi\)
\(390\) 73.8716 + 211.343i 0.189414 + 0.541906i
\(391\) 168.923i 0.432028i
\(392\) −3.98061 + 59.9379i −0.0101546 + 0.152903i
\(393\) 194.438i 0.494753i
\(394\) 275.172 453.175i 0.698407 1.15019i
\(395\) −191.433 157.621i −0.484640 0.399041i
\(396\) −117.379 + 61.0176i −0.296411 + 0.154085i
\(397\) 169.633i 0.427286i 0.976912 + 0.213643i \(0.0685330\pi\)
−0.976912 + 0.213643i \(0.931467\pi\)
\(398\) 80.9949 133.389i 0.203505 0.335147i
\(399\) 33.8175i 0.0847557i
\(400\) 365.417 + 162.698i 0.913541 + 0.406746i
\(401\) 8.07776 0.0201441 0.0100720 0.999949i \(-0.496794\pi\)
0.0100720 + 0.999949i \(0.496794\pi\)
\(402\) 69.9811 + 42.4932i 0.174082 + 0.105704i
\(403\) 191.955 0.476314
\(404\) 302.656 + 582.216i 0.749148 + 1.44113i
\(405\) 139.637 169.590i 0.344782 0.418742i
\(406\) −164.536 99.9076i −0.405260 0.246078i
\(407\) −144.054 −0.353940
\(408\) 96.5934 + 6.41498i 0.236748 + 0.0157230i
\(409\) −101.139 −0.247284 −0.123642 0.992327i \(-0.539457\pi\)
−0.123642 + 0.992327i \(0.539457\pi\)
\(410\) −312.275 + 109.150i −0.761646 + 0.266221i
\(411\) 84.9361i 0.206657i
\(412\) −24.4291 46.9940i −0.0592939 0.114063i
\(413\) 266.807i 0.646021i
\(414\) 216.993 + 131.760i 0.524137 + 0.318261i
\(415\) −417.334 + 506.857i −1.00563 + 1.22134i
\(416\) −238.775 544.786i −0.573978 1.30958i
\(417\) 259.951i 0.623385i
\(418\) 32.6449 + 19.8223i 0.0780978 + 0.0474217i
\(419\) 598.543i 1.42850i 0.699889 + 0.714251i \(0.253233\pi\)
−0.699889 + 0.714251i \(0.746767\pi\)
\(420\) 151.774 + 32.2615i 0.361368 + 0.0768130i
\(421\) 625.523 1.48580 0.742901 0.669401i \(-0.233449\pi\)
0.742901 + 0.669401i \(0.233449\pi\)
\(422\) −234.018 + 385.399i −0.554545 + 0.913269i
\(423\) −581.757 −1.37531
\(424\) −617.046 40.9794i −1.45530 0.0966495i
\(425\) 246.500 48.2072i 0.579999 0.113429i
\(426\) 82.4268 135.747i 0.193490 0.318655i
\(427\) −34.6211 −0.0810799
\(428\) 101.700 + 195.640i 0.237618 + 0.457102i
\(429\) −98.0803 −0.228625
\(430\) 730.250 255.247i 1.69826 0.593598i
\(431\) 594.626i 1.37964i −0.723980 0.689821i \(-0.757689\pi\)
0.723980 0.689821i \(-0.242311\pi\)
\(432\) 183.228 261.036i 0.424139 0.604249i
\(433\) 263.306i 0.608098i 0.952656 + 0.304049i \(0.0983386\pi\)
−0.952656 + 0.304049i \(0.901661\pi\)
\(434\) 69.0492 113.716i 0.159099 0.262017i
\(435\) 57.1969 69.4662i 0.131487 0.159692i
\(436\) 237.910 + 457.664i 0.545664 + 1.04969i
\(437\) 73.2890i 0.167709i
\(438\) −16.1527 + 26.6015i −0.0368782 + 0.0607339i
\(439\) 316.778i 0.721590i −0.932645 0.360795i \(-0.882505\pi\)
0.932645 0.360795i \(-0.117495\pi\)
\(440\) −120.106 + 127.602i −0.272968 + 0.290003i
\(441\) 56.6858 0.128539
\(442\) −319.252 193.853i −0.722290 0.438582i
\(443\) 291.631 0.658309 0.329155 0.944276i \(-0.393236\pi\)
0.329155 + 0.944276i \(0.393236\pi\)
\(444\) 140.562 73.0687i 0.316580 0.164569i
\(445\) 464.791 564.494i 1.04447 1.26853i
\(446\) −364.869 221.552i −0.818092 0.496753i
\(447\) −294.143 −0.658038
\(448\) −408.627 54.5162i −0.912114 0.121688i
\(449\) −15.5790 −0.0346971 −0.0173486 0.999850i \(-0.505522\pi\)
−0.0173486 + 0.999850i \(0.505522\pi\)
\(450\) 130.345 354.247i 0.289655 0.787215i
\(451\) 144.921i 0.321332i
\(452\) −454.013 + 236.012i −1.00445 + 0.522149i
\(453\) 209.202i 0.461815i
\(454\) −57.1732 34.7161i −0.125932 0.0764672i
\(455\) −462.159 380.531i −1.01573 0.836331i
\(456\) −41.9081 2.78321i −0.0919037 0.00610353i
\(457\) 422.833i 0.925237i 0.886558 + 0.462618i \(0.153090\pi\)
−0.886558 + 0.462618i \(0.846910\pi\)
\(458\) 76.5105 + 46.4579i 0.167054 + 0.101437i
\(459\) 200.259i 0.436295i
\(460\) 328.924 + 69.9168i 0.715053 + 0.151993i
\(461\) 548.488 1.18978 0.594889 0.803808i \(-0.297196\pi\)
0.594889 + 0.803808i \(0.297196\pi\)
\(462\) −35.2811 + 58.1036i −0.0763660 + 0.125765i
\(463\) 366.269 0.791078 0.395539 0.918449i \(-0.370558\pi\)
0.395539 + 0.918449i \(0.370558\pi\)
\(464\) −137.351 + 195.677i −0.296015 + 0.421718i
\(465\) 48.0102 + 39.5305i 0.103248 + 0.0850118i
\(466\) −223.691 + 368.392i −0.480024 + 0.790540i
\(467\) −223.999 −0.479656 −0.239828 0.970815i \(-0.577091\pi\)
−0.239828 + 0.970815i \(0.577091\pi\)
\(468\) −498.034 + 258.895i −1.06418 + 0.553195i
\(469\) −218.926 −0.466793
\(470\) −727.451 + 254.268i −1.54777 + 0.540997i
\(471\) 36.2814i 0.0770305i
\(472\) −330.638 21.9584i −0.700504 0.0465220i
\(473\) 338.895i 0.716480i
\(474\) −62.0064 + 102.117i −0.130815 + 0.215437i
\(475\) −106.947 + 20.9152i −0.225151 + 0.0440320i
\(476\) −229.680 + 119.396i −0.482522 + 0.250831i
\(477\) 583.567i 1.22341i
\(478\) 317.476 522.845i 0.664177 1.09382i
\(479\) 763.448i 1.59384i −0.604087 0.796918i \(-0.706462\pi\)
0.604087 0.796918i \(-0.293538\pi\)
\(480\) 52.4709 185.430i 0.109314 0.386313i
\(481\) −611.214 −1.27071
\(482\) 256.238 + 155.590i 0.531613 + 0.322801i
\(483\) 130.445 0.270072
\(484\) 187.830 + 361.327i 0.388078 + 0.746543i
\(485\) 226.133 + 186.193i 0.466254 + 0.383903i
\(486\) −397.145 241.150i −0.817170 0.496193i
\(487\) −630.562 −1.29479 −0.647394 0.762155i \(-0.724141\pi\)
−0.647394 + 0.762155i \(0.724141\pi\)
\(488\) −2.84935 + 42.9039i −0.00583883 + 0.0879179i
\(489\) 121.509 0.248484
\(490\) 70.8822 24.7757i 0.144657 0.0505626i
\(491\) 441.165i 0.898503i −0.893405 0.449251i \(-0.851691\pi\)
0.893405 0.449251i \(-0.148309\pi\)
\(492\) 73.5085 + 141.408i 0.149407 + 0.287414i
\(493\) 150.118i 0.304499i
\(494\) 138.511 + 84.1052i 0.280387 + 0.170253i
\(495\) 127.659 + 105.111i 0.257897 + 0.212346i
\(496\) −135.238 94.9275i −0.272658 0.191386i
\(497\) 424.665i 0.854457i
\(498\) 270.375 + 164.174i 0.542922 + 0.329667i
\(499\) 181.530i 0.363788i 0.983318 + 0.181894i \(0.0582228\pi\)
−0.983318 + 0.181894i \(0.941777\pi\)
\(500\) 8.15719 499.933i 0.0163144 0.999867i
\(501\) 190.833 0.380905
\(502\) −82.7367 + 136.257i −0.164814 + 0.271429i
\(503\) −863.536 −1.71677 −0.858386 0.513005i \(-0.828532\pi\)
−0.858386 + 0.513005i \(0.828532\pi\)
\(504\) −25.7791 + 388.168i −0.0511491 + 0.770176i
\(505\) 521.368 633.207i 1.03241 1.25387i
\(506\) −76.4609 + 125.922i −0.151108 + 0.248857i
\(507\) −212.600 −0.419329
\(508\) 14.2869 + 27.4836i 0.0281239 + 0.0541017i
\(509\) 774.848 1.52229 0.761147 0.648579i \(-0.224636\pi\)
0.761147 + 0.648579i \(0.224636\pi\)
\(510\) −39.9275 114.231i −0.0782892 0.223982i
\(511\) 83.2189i 0.162855i
\(512\) −101.189 + 501.901i −0.197635 + 0.980276i
\(513\) 86.8847i 0.169366i
\(514\) 116.756 192.282i 0.227151 0.374090i
\(515\) −42.0825 + 51.1097i −0.0817137 + 0.0992422i
\(516\) −171.899 330.680i −0.333137 0.640852i
\(517\) 337.596i 0.652990i
\(518\) −219.863 + 362.088i −0.424447 + 0.699012i
\(519\) 63.1938i 0.121761i
\(520\) −509.606 + 541.408i −0.980011 + 1.04117i
\(521\) 279.159 0.535813 0.267906 0.963445i \(-0.413668\pi\)
0.267906 + 0.963445i \(0.413668\pi\)
\(522\) 192.837 + 117.092i 0.369419 + 0.224315i
\(523\) 328.355 0.627830 0.313915 0.949451i \(-0.398359\pi\)
0.313915 + 0.949451i \(0.398359\pi\)
\(524\) −572.946 + 297.837i −1.09341 + 0.568391i
\(525\) −37.2263 190.351i −0.0709073 0.362573i
\(526\) 682.720 + 414.554i 1.29795 + 0.788125i
\(527\) −103.751 −0.196871
\(528\) 69.1008 + 48.5038i 0.130873 + 0.0918632i
\(529\) −246.301 −0.465597
\(530\) 255.060 + 729.714i 0.481245 + 1.37682i
\(531\) 312.698i 0.588886i
\(532\) 99.6493 51.8011i 0.187311 0.0973706i
\(533\) 614.892i 1.15364i
\(534\) −301.120 182.843i −0.563896 0.342403i
\(535\) 175.193 212.774i 0.327464 0.397709i
\(536\) −18.0178 + 271.302i −0.0336153 + 0.506161i
\(537\) 36.5596i 0.0680812i
\(538\) 84.0559 + 51.0395i 0.156238 + 0.0948690i
\(539\) 32.8950i 0.0610297i
\(540\) −389.942 82.8869i −0.722116 0.153494i
\(541\) −520.625 −0.962337 −0.481169 0.876628i \(-0.659788\pi\)
−0.481169 + 0.876628i \(0.659788\pi\)
\(542\) 495.454 815.952i 0.914121 1.50545i
\(543\) −362.415 −0.667432
\(544\) 129.057 + 294.456i 0.237238 + 0.541279i
\(545\) 409.833 497.747i 0.751987 0.913296i
\(546\) −149.696 + 246.531i −0.274169 + 0.451523i
\(547\) 972.376 1.77765 0.888827 0.458244i \(-0.151521\pi\)
0.888827 + 0.458244i \(0.151521\pi\)
\(548\) −250.279 + 130.104i −0.456714 + 0.237416i
\(549\) 40.5761 0.0739091
\(550\) 205.571 + 75.6394i 0.373765 + 0.137526i
\(551\) 65.1303i 0.118204i
\(552\) 10.7357 161.653i 0.0194488 0.292849i
\(553\) 319.458i 0.577682i
\(554\) 387.468 638.113i 0.699401 1.15183i
\(555\) −152.872 125.871i −0.275445 0.226795i
\(556\) −765.993 + 398.189i −1.37769 + 0.716168i
\(557\) 704.353i 1.26455i −0.774745 0.632274i \(-0.782122\pi\)
0.774745 0.632274i \(-0.217878\pi\)
\(558\) −80.9259 + 133.275i −0.145029 + 0.238844i
\(559\) 1437.92i 2.57230i
\(560\) 137.422 + 496.648i 0.245396 + 0.886872i
\(561\) 53.0122 0.0944960
\(562\) −527.302 320.183i −0.938260 0.569720i
\(563\) −741.155 −1.31644 −0.658220 0.752826i \(-0.728690\pi\)
−0.658220 + 0.752826i \(0.728690\pi\)
\(564\) 171.240 + 329.412i 0.303616 + 0.584064i
\(565\) 493.776 + 406.563i 0.873939 + 0.719581i
\(566\) −305.020 185.211i −0.538904 0.327228i
\(567\) 283.008 0.499132
\(568\) 526.263 + 34.9503i 0.926519 + 0.0615322i
\(569\) 355.408 0.624618 0.312309 0.949980i \(-0.398897\pi\)
0.312309 + 0.949980i \(0.398897\pi\)
\(570\) 17.3230 + 49.5602i 0.0303912 + 0.0869478i
\(571\) 1057.10i 1.85131i −0.378364 0.925657i \(-0.623513\pi\)
0.378364 0.925657i \(-0.376487\pi\)
\(572\) −150.238 289.011i −0.262654 0.505264i
\(573\) 289.295i 0.504877i
\(574\) −364.268 221.187i −0.634612 0.385343i
\(575\) −80.6766 412.527i −0.140307 0.717438i
\(576\) 478.913 + 63.8932i 0.831446 + 0.110926i
\(577\) 270.911i 0.469516i −0.972054 0.234758i \(-0.924570\pi\)
0.972054 0.234758i \(-0.0754297\pi\)
\(578\) −321.497 195.216i −0.556224 0.337744i
\(579\) 97.6429i 0.168641i
\(580\) 292.308 + 62.1335i 0.503979 + 0.107127i
\(581\) −845.831 −1.45582
\(582\) 73.2461 120.627i 0.125852 0.207263i
\(583\) −338.646 −0.580868
\(584\) −103.128 6.84898i −0.176590 0.0117277i
\(585\) 541.652 + 445.984i 0.925901 + 0.762365i
\(586\) −398.100 + 655.621i −0.679351 + 1.11881i
\(587\) 727.172 1.23879 0.619397 0.785078i \(-0.287377\pi\)
0.619397 + 0.785078i \(0.287377\pi\)
\(588\) −16.6854 32.0976i −0.0283766 0.0545878i
\(589\) 45.0135 0.0764237
\(590\) 136.671 + 391.010i 0.231646 + 0.662729i
\(591\) 319.284i 0.540244i
\(592\) 430.620 + 302.264i 0.727398 + 0.510581i
\(593\) 148.946i 0.251174i −0.992083 0.125587i \(-0.959919\pi\)
0.992083 0.125587i \(-0.0400815\pi\)
\(594\) 90.6449 149.281i 0.152601 0.251315i
\(595\) 249.796 + 205.676i 0.419825 + 0.345674i
\(596\) −450.564 866.745i −0.755979 1.45427i
\(597\) 93.9788i 0.157418i
\(598\) −324.421 + 534.281i −0.542509 + 0.893447i
\(599\) 145.115i 0.242262i 0.992637 + 0.121131i \(0.0386522\pi\)
−0.992637 + 0.121131i \(0.961348\pi\)
\(600\) −238.954 + 30.4664i −0.398257 + 0.0507773i
\(601\) −785.811 −1.30751 −0.653753 0.756708i \(-0.726807\pi\)
−0.653753 + 0.756708i \(0.726807\pi\)
\(602\) 851.835 + 517.242i 1.41501 + 0.859207i
\(603\) 256.582 0.425509
\(604\) −616.452 + 320.453i −1.02062 + 0.530551i
\(605\) 323.564 392.972i 0.534816 0.649540i
\(606\) −337.774 205.100i −0.557383 0.338448i
\(607\) −383.971 −0.632572 −0.316286 0.948664i \(-0.602436\pi\)
−0.316286 + 0.948664i \(0.602436\pi\)
\(608\) −55.9929 127.753i −0.0920936 0.210120i
\(609\) 115.923 0.190350
\(610\) 50.7379 17.7346i 0.0831769 0.0290731i
\(611\) 1432.41i 2.34436i
\(612\) 269.187 139.932i 0.439847 0.228648i
\(613\) 303.034i 0.494345i 0.968971 + 0.247173i \(0.0795015\pi\)
−0.968971 + 0.247173i \(0.920499\pi\)
\(614\) −152.401 92.5391i −0.248209 0.150715i
\(615\) 126.629 153.792i 0.205900 0.250068i
\(616\) −225.256 14.9597i −0.365675 0.0242853i
\(617\) 847.375i 1.37338i −0.726951 0.686690i \(-0.759063\pi\)
0.726951 0.686690i \(-0.240937\pi\)
\(618\) 27.2637 + 16.5548i 0.0441160 + 0.0267877i
\(619\) 316.706i 0.511642i 0.966724 + 0.255821i \(0.0823458\pi\)
−0.966724 + 0.255821i \(0.917654\pi\)
\(620\) −42.9423 + 202.023i −0.0692618 + 0.325843i
\(621\) −335.142 −0.539681
\(622\) 513.010 844.865i 0.824775 1.35830i
\(623\) 942.013 1.51206
\(624\) 293.192 + 205.800i 0.469859 + 0.329807i
\(625\) −578.953 + 235.454i −0.926325 + 0.376726i
\(626\) 200.505 330.208i 0.320296 0.527488i
\(627\) −22.9999 −0.0366825
\(628\) −106.909 + 55.5752i −0.170238 + 0.0884956i
\(629\) 330.360 0.525214
\(630\) 459.046 160.452i 0.728644 0.254685i
\(631\) 319.937i 0.507032i 0.967331 + 0.253516i \(0.0815871\pi\)
−0.967331 + 0.253516i \(0.918413\pi\)
\(632\) −395.886 26.2917i −0.626402 0.0416008i
\(633\) 271.533i 0.428962i
\(634\) 643.307 1059.45i 1.01468 1.67105i
\(635\) 24.6113 29.8907i 0.0387579 0.0470719i
\(636\) 330.437 171.772i 0.519555 0.270082i
\(637\) 139.572i 0.219109i
\(638\) −67.9490 + 111.904i −0.106503 + 0.175398i
\(639\) 497.709i 0.778888i
\(640\) 626.777 129.424i 0.979339 0.202225i
\(641\) 262.847 0.410057 0.205029 0.978756i \(-0.434271\pi\)
0.205029 + 0.978756i \(0.434271\pi\)
\(642\) −113.501 68.9189i −0.176793 0.107350i
\(643\) −385.615 −0.599713 −0.299856 0.953984i \(-0.596939\pi\)
−0.299856 + 0.953984i \(0.596939\pi\)
\(644\) 199.813 + 384.379i 0.310269 + 0.596862i
\(645\) −296.120 + 359.641i −0.459101 + 0.557583i
\(646\) −74.8650 45.4587i −0.115890 0.0703695i
\(647\) −101.900 −0.157496 −0.0787482 0.996895i \(-0.525092\pi\)
−0.0787482 + 0.996895i \(0.525092\pi\)
\(648\) 23.2918 350.715i 0.0359441 0.541228i
\(649\) −181.460 −0.279600
\(650\) 872.229 + 320.935i 1.34189 + 0.493747i
\(651\) 80.1182i 0.123069i
\(652\) 186.125 + 358.047i 0.285468 + 0.549152i
\(653\) 500.908i 0.767088i −0.923523 0.383544i \(-0.874703\pi\)
0.923523 0.383544i \(-0.125297\pi\)
\(654\) −265.515 161.223i −0.405987 0.246519i
\(655\) 623.124 + 513.066i 0.951335 + 0.783307i
\(656\) −304.083 + 433.212i −0.463542 + 0.660384i
\(657\) 97.5329i 0.148452i
\(658\) −848.569 515.259i −1.28962 0.783069i
\(659\) 552.028i 0.837675i −0.908061 0.418837i \(-0.862438\pi\)
0.908061 0.418837i \(-0.137562\pi\)
\(660\) 21.9416 103.225i 0.0332449 0.156401i
\(661\) 29.9077 0.0452461 0.0226231 0.999744i \(-0.492798\pi\)
0.0226231 + 0.999744i \(0.492798\pi\)
\(662\) 161.208 265.490i 0.243517 0.401042i
\(663\) 224.929 0.339259
\(664\) −69.6126 + 1048.19i −0.104838 + 1.57860i
\(665\) −108.377 89.2348i −0.162972 0.134188i
\(666\) 257.681 424.369i 0.386908 0.637191i
\(667\) 251.228 0.376654
\(668\) 292.316 + 562.325i 0.437598 + 0.841803i
\(669\) 257.068 0.384257
\(670\) 320.840 112.144i 0.478866 0.167380i
\(671\) 23.5465i 0.0350916i
\(672\) 227.383 99.6600i 0.338368 0.148304i
\(673\) 540.570i 0.803225i 0.915810 + 0.401612i \(0.131550\pi\)
−0.915810 + 0.401612i \(0.868450\pi\)
\(674\) −189.118 + 311.454i −0.280590 + 0.462097i
\(675\) 95.6427 + 489.053i 0.141693 + 0.724524i
\(676\) −325.657 626.464i −0.481742 0.926722i
\(677\) 257.178i 0.379880i −0.981796 0.189940i \(-0.939171\pi\)
0.981796 0.189940i \(-0.0608293\pi\)
\(678\) 159.937 263.397i 0.235896 0.388491i
\(679\) 377.366i 0.555767i
\(680\) 275.441 292.630i 0.405060 0.430339i
\(681\) 40.2813 0.0591502
\(682\) −77.3401 46.9616i −0.113402 0.0688587i
\(683\) −1357.92 −1.98817 −0.994086 0.108593i \(-0.965365\pi\)
−0.994086 + 0.108593i \(0.965365\pi\)
\(684\) −116.789 + 60.7112i −0.170745 + 0.0887590i
\(685\) 272.199 + 224.122i 0.397371 + 0.327186i
\(686\) 622.256 + 377.840i 0.907079 + 0.550787i
\(687\) −53.9054 −0.0784649
\(688\) 711.095 1013.06i 1.03357 1.47247i
\(689\) −1436.86 −2.08543
\(690\) −191.170 + 66.8202i −0.277057 + 0.0968408i
\(691\) 1073.44i 1.55346i 0.629834 + 0.776730i \(0.283123\pi\)
−0.629834 + 0.776730i \(0.716877\pi\)
\(692\) −186.212 + 96.7993i −0.269092 + 0.139883i
\(693\) 213.034i 0.307408i
\(694\) 63.3728 + 38.4806i 0.0913153 + 0.0554475i
\(695\) 833.079 + 685.938i 1.19867 + 0.986961i
\(696\) 9.54060 143.657i 0.0137078 0.206404i
\(697\) 332.348i 0.476827i
\(698\) 417.226 + 253.343i 0.597745 + 0.362956i
\(699\) 259.550i 0.371316i
\(700\) 503.880 401.270i 0.719828 0.573243i
\(701\) −543.051 −0.774680 −0.387340 0.921937i \(-0.626606\pi\)
−0.387340 + 0.921937i \(0.626606\pi\)
\(702\) 384.603 633.394i 0.547867 0.902271i
\(703\) −143.330 −0.203884
\(704\) −37.0775 + 277.915i −0.0526669 + 0.394766i
\(705\) 294.985 358.262i 0.418418 0.508173i
\(706\) −50.2556 + 82.7648i −0.0711835 + 0.117231i
\(707\) 1056.68 1.49460
\(708\) 177.061 92.0426i 0.250087 0.130004i
\(709\) 428.058 0.603748 0.301874 0.953348i \(-0.402388\pi\)
0.301874 + 0.953348i \(0.402388\pi\)
\(710\) −217.534 622.355i −0.306386 0.876556i
\(711\) 374.407i 0.526592i
\(712\) 77.5284 1167.38i 0.108888 1.63958i
\(713\) 173.631i 0.243522i
\(714\) 80.9106 133.250i 0.113320 0.186624i
\(715\) −258.806 + 314.323i −0.361967 + 0.439612i
\(716\) 107.729 56.0014i 0.150460 0.0782143i
\(717\) 368.370i 0.513766i
\(718\) −198.939 + 327.629i −0.277074 + 0.456308i
\(719\) 566.186i 0.787463i 0.919226 + 0.393731i \(0.128816\pi\)
−0.919226 + 0.393731i \(0.871184\pi\)
\(720\) −161.059 582.074i −0.223693 0.808436i
\(721\) −85.2906 −0.118295
\(722\) 32.4810 + 19.7228i 0.0449875 + 0.0273168i
\(723\) −180.532 −0.249698
\(724\) −555.142 1067.92i −0.766771 1.47503i
\(725\) −71.6955 366.603i −0.0988903 0.505660i
\(726\) −209.625 127.286i −0.288739 0.175325i
\(727\) −1178.55 −1.62112 −0.810560 0.585656i \(-0.800837\pi\)
−0.810560 + 0.585656i \(0.800837\pi\)
\(728\) −955.751 63.4736i −1.31285 0.0871890i
\(729\) −115.616 −0.158596
\(730\) 42.6287 + 121.959i 0.0583955 + 0.167067i
\(731\) 777.192i 1.06319i
\(732\) −11.9435 22.9757i −0.0163163 0.0313875i
\(733\) 999.534i 1.36362i −0.731529 0.681810i \(-0.761193\pi\)
0.731529 0.681810i \(-0.238807\pi\)
\(734\) −472.668 287.008i −0.643961 0.391019i
\(735\) −28.7430 + 34.9087i −0.0391062 + 0.0474949i
\(736\) 492.783 215.982i 0.669543 0.293454i
\(737\) 148.896i 0.202029i
\(738\) 426.923 + 259.232i 0.578487 + 0.351263i
\(739\) 855.820i 1.15808i −0.815300 0.579039i \(-0.803428\pi\)
0.815300 0.579039i \(-0.196572\pi\)
\(740\) 136.735 643.272i 0.184777 0.869287i
\(741\) −97.5878 −0.131697
\(742\) −516.863 + 851.210i −0.696580 + 1.14718i
\(743\) −972.675 −1.30912 −0.654559 0.756011i \(-0.727146\pi\)
−0.654559 + 0.756011i \(0.727146\pi\)
\(744\) 99.2858 + 6.59379i 0.133449 + 0.00886263i
\(745\) −776.160 + 942.655i −1.04183 + 1.26531i
\(746\) −696.594 + 1147.20i −0.933772 + 1.53781i
\(747\) 991.317 1.32706
\(748\) 81.2033 + 156.210i 0.108561 + 0.208837i
\(749\) 355.072 0.474061
\(750\) 152.063 + 259.894i 0.202750 + 0.346525i
\(751\) 1107.31i 1.47445i −0.675647 0.737225i \(-0.736136\pi\)
0.675647 0.737225i \(-0.263864\pi\)
\(752\) −708.369 + 1009.18i −0.941980 + 1.34199i
\(753\) 95.9999i 0.127490i
\(754\) −288.305 + 474.804i −0.382368 + 0.629713i
\(755\) 670.441 + 552.025i 0.888001 + 0.731159i
\(756\) −236.880 455.684i −0.313334 0.602757i
\(757\) 620.597i 0.819811i −0.912128 0.409906i \(-0.865562\pi\)
0.912128 0.409906i \(-0.134438\pi\)
\(758\) −302.097 + 497.517i −0.398545 + 0.656355i
\(759\) 88.7180i 0.116888i
\(760\) −119.503 + 126.961i −0.157241 + 0.167054i
\(761\) −925.617 −1.21632 −0.608159 0.793816i \(-0.708092\pi\)
−0.608159 + 0.793816i \(0.708092\pi\)
\(762\) −15.9447 9.68178i −0.0209248 0.0127058i
\(763\) 830.627 1.08863
\(764\) 852.459 443.137i 1.11578 0.580023i
\(765\) −292.762 241.053i −0.382695 0.315102i
\(766\) 103.658 + 62.9422i 0.135324 + 0.0821700i
\(767\) −769.928 −1.00382
\(768\) −104.789 289.985i −0.136444 0.377585i
\(769\) −262.821 −0.341770 −0.170885 0.985291i \(-0.554663\pi\)
−0.170885 + 0.985291i \(0.554663\pi\)
\(770\) 93.1108 + 266.386i 0.120923 + 0.345956i
\(771\) 135.472i 0.175710i
\(772\) −287.722 + 149.568i −0.372697 + 0.193741i
\(773\) 62.4348i 0.0807694i 0.999184 + 0.0403847i \(0.0128583\pi\)
−0.999184 + 0.0403847i \(0.987142\pi\)
\(774\) −998.354 606.210i −1.28986 0.783217i
\(775\) 253.371 49.5509i 0.326930 0.0639367i
\(776\) 467.647 + 31.0575i 0.602638 + 0.0400226i
\(777\) 255.109i 0.328325i
\(778\) −743.760 451.618i −0.955989 0.580486i
\(779\) 144.193i 0.185100i
\(780\) 93.0975 437.978i 0.119356 0.561511i
\(781\) 288.823 0.369811
\(782\) 175.349 288.778i 0.224231 0.369281i
\(783\) −297.833 −0.380374
\(784\) 69.0228 98.3332i 0.0880393 0.125425i
\(785\) 116.273 + 95.7362i 0.148118 + 0.121957i
\(786\) 201.834 332.396i 0.256786 0.422896i
\(787\) −703.356 −0.893718 −0.446859 0.894605i \(-0.647457\pi\)
−0.446859 + 0.894605i \(0.647457\pi\)
\(788\) −940.828 + 489.074i −1.19394 + 0.620653i
\(789\) −481.009 −0.609644
\(790\) 163.642 + 468.173i 0.207142 + 0.592623i
\(791\) 824.000i 1.04172i
\(792\) 264.001 + 17.5329i 0.333334 + 0.0221375i
\(793\) 99.9068i 0.125986i
\(794\) 176.085 289.991i 0.221770 0.365228i
\(795\) −359.377 295.902i −0.452046 0.372204i
\(796\) −276.925 + 143.955i −0.347896 + 0.180848i
\(797\) 594.908i 0.746435i 0.927744 + 0.373217i \(0.121745\pi\)
−0.927744 + 0.373217i \(0.878255\pi\)
\(798\) −35.1039 + 57.8119i −0.0439899 + 0.0724459i
\(799\) 774.213i 0.968977i
\(800\) −455.801 657.454i −0.569752 0.821817i
\(801\) −1104.04 −1.37833
\(802\) −13.8091 8.38504i −0.0172184 0.0104552i
\(803\) −56.5987 −0.0704841
\(804\) −75.5248 145.286i −0.0939363 0.180704i
\(805\) 344.207 418.043i 0.427586 0.519308i
\(806\) −328.151 199.256i −0.407135 0.247216i
\(807\) −59.2215 −0.0733848
\(808\) 86.9656 1309.48i 0.107631 1.62064i
\(809\) 1546.99 1.91222 0.956112 0.293001i \(-0.0946538\pi\)
0.956112 + 0.293001i \(0.0946538\pi\)
\(810\) −414.754 + 144.970i −0.512042 + 0.178976i
\(811\) 1456.80i 1.79630i −0.439686 0.898152i \(-0.644910\pi\)
0.439686 0.898152i \(-0.355090\pi\)
\(812\) 177.570 + 341.589i 0.218682 + 0.420676i
\(813\) 574.878i 0.707107i
\(814\) 246.263 + 149.533i 0.302534 + 0.183702i
\(815\) 320.627 389.405i 0.393407 0.477797i
\(816\) −158.470 111.234i −0.194203 0.136317i
\(817\) 337.193i 0.412721i
\(818\) 172.900 + 104.986i 0.211369 + 0.128345i
\(819\) 903.895i 1.10366i
\(820\) 647.144 + 137.558i 0.789200 + 0.167754i
\(821\) 576.233 0.701867 0.350934 0.936400i \(-0.385864\pi\)
0.350934 + 0.936400i \(0.385864\pi\)
\(822\) 88.1671 145.200i 0.107259 0.176643i
\(823\) −12.5467 −0.0152451 −0.00762255 0.999971i \(-0.502426\pi\)
−0.00762255 + 0.999971i \(0.502426\pi\)
\(824\) −7.01949 + 105.696i −0.00851880 + 0.128271i
\(825\) −129.461 + 25.3183i −0.156923 + 0.0306889i
\(826\) −276.956 + 456.112i −0.335297 + 0.552194i
\(827\) −1258.03 −1.52120 −0.760600 0.649221i \(-0.775095\pi\)
−0.760600 + 0.649221i \(0.775095\pi\)
\(828\) −234.182 450.494i −0.282829 0.544075i
\(829\) 592.821 0.715104 0.357552 0.933893i \(-0.383611\pi\)
0.357552 + 0.933893i \(0.383611\pi\)
\(830\) 1239.58 433.275i 1.49347 0.522018i
\(831\) 449.582i 0.541013i
\(832\) −157.318 + 1179.18i −0.189084 + 1.41729i
\(833\) 75.4386i 0.0905625i
\(834\) 269.840 444.393i 0.323549 0.532846i
\(835\) 503.555 611.573i 0.603060 0.732423i
\(836\) −35.2309 67.7734i −0.0421423 0.0810686i
\(837\) 205.841i 0.245928i
\(838\) 621.311 1023.22i 0.741421 1.22103i
\(839\) 1194.78i 1.42405i −0.702152 0.712027i \(-0.747777\pi\)
0.702152 0.712027i \(-0.252223\pi\)
\(840\) −225.974 212.700i −0.269016 0.253214i
\(841\) −617.739 −0.734529
\(842\) −1069.35 649.317i −1.27001 0.771161i
\(843\) 371.510 0.440700
\(844\) 800.120 415.930i 0.948009 0.492808i
\(845\) −560.991 + 681.330i −0.663895 + 0.806307i
\(846\) 994.527 + 603.886i 1.17556 + 0.713814i
\(847\) 655.781 0.774240
\(848\) 1012.32 + 710.573i 1.19377 + 0.837940i
\(849\) 214.901 0.253123
\(850\) −471.438 173.465i −0.554633 0.204076i
\(851\) 552.870i 0.649671i
\(852\) −281.821 + 146.500i −0.330776 + 0.171949i
\(853\) 566.396i 0.664005i 0.943279 + 0.332002i \(0.107724\pi\)
−0.943279 + 0.332002i \(0.892276\pi\)
\(854\) 59.1857 + 35.9381i 0.0693040 + 0.0420821i
\(855\) 127.018 + 104.584i 0.148559 + 0.122320i
\(856\) 29.2227 440.020i 0.0341387 0.514042i
\(857\) 1029.47i 1.20125i −0.799530 0.600626i \(-0.794918\pi\)
0.799530 0.600626i \(-0.205082\pi\)
\(858\) 167.671 + 101.811i 0.195420 + 0.118661i
\(859\) 274.430i 0.319476i −0.987159 0.159738i \(-0.948935\pi\)
0.987159 0.159738i \(-0.0510650\pi\)
\(860\) −1513.34 321.678i −1.75969 0.374044i
\(861\) 256.644 0.298077
\(862\) −617.245 + 1016.53i −0.716062 + 1.17927i
\(863\) 1475.75 1.71002 0.855012 0.518608i \(-0.173550\pi\)
0.855012 + 0.518608i \(0.173550\pi\)
\(864\) −584.198 + 256.049i −0.676156 + 0.296353i
\(865\) 202.520 + 166.751i 0.234128 + 0.192775i
\(866\) 273.322 450.129i 0.315615 0.519779i
\(867\) 226.511 0.261258
\(868\) −236.083 + 122.724i −0.271984 + 0.141387i
\(869\) −217.270 −0.250023
\(870\) −169.888 + 59.3816i −0.195274 + 0.0682547i
\(871\) 631.758i 0.725325i
\(872\) 68.3613 1029.35i 0.0783960 1.18044i
\(873\) 442.274i 0.506614i
\(874\) −76.0769 + 125.289i −0.0870445 + 0.143352i
\(875\) −708.256 382.981i −0.809436 0.437692i
\(876\) 55.2267 28.7087i 0.0630442 0.0327725i
\(877\) 1390.07i 1.58503i 0.609851 + 0.792516i \(0.291229\pi\)
−0.609851 + 0.792516i \(0.708771\pi\)
\(878\) −328.828 + 541.540i −0.374520 + 0.616788i
\(879\) 461.917i 0.525503i
\(880\) 337.780 93.4630i 0.383841 0.106208i
\(881\) 601.667 0.682936 0.341468 0.939893i \(-0.389076\pi\)
0.341468 + 0.939893i \(0.389076\pi\)
\(882\) −96.9058 58.8421i −0.109871 0.0667144i
\(883\) 822.025 0.930946 0.465473 0.885062i \(-0.345884\pi\)
0.465473 + 0.885062i \(0.345884\pi\)
\(884\) 344.543 + 662.793i 0.389754 + 0.749766i
\(885\) −192.568 158.556i −0.217592 0.179160i
\(886\) −498.550 302.724i −0.562698 0.341675i
\(887\) 1146.80 1.29289 0.646446 0.762959i \(-0.276254\pi\)
0.646446 + 0.762959i \(0.276254\pi\)
\(888\) −316.142 20.9957i −0.356015 0.0236438i
\(889\) 49.8808 0.0561089
\(890\) −1380.54 + 482.544i −1.55117 + 0.542185i
\(891\) 192.479i 0.216026i
\(892\) 393.773 + 757.497i 0.441450 + 0.849212i
\(893\) 335.900i 0.376148i
\(894\) 502.845 + 305.332i 0.562466 + 0.341535i
\(895\) −117.164 96.4704i −0.130910 0.107788i
\(896\) 641.968 + 517.368i 0.716482 + 0.577420i
\(897\) 376.427i 0.419651i
\(898\) 26.6327 + 16.1716i 0.0296578 + 0.0180085i
\(899\) 154.302i 0.171638i
\(900\) −590.549 + 470.291i −0.656166 + 0.522545i
\(901\) 776.622 0.861955
\(902\) −150.433 + 247.745i −0.166777 + 0.274662i
\(903\) −600.159 −0.664628
\(904\) 1021.14 + 67.8159i 1.12957 + 0.0750176i
\(905\) −956.312 + 1161.45i −1.05670 + 1.28337i
\(906\) 217.160 357.636i 0.239691 0.394742i
\(907\) −329.375 −0.363148 −0.181574 0.983377i \(-0.558119\pi\)
−0.181574 + 0.983377i \(0.558119\pi\)
\(908\) 61.7023 + 118.696i 0.0679541 + 0.130723i
\(909\) −1238.43 −1.36241
\(910\) 395.066 + 1130.27i 0.434138 + 1.24205i
\(911\) 1242.65i 1.36405i 0.731327 + 0.682027i \(0.238901\pi\)
−0.731327 + 0.682027i \(0.761099\pi\)
\(912\) 68.7538 + 48.2602i 0.0753879 + 0.0529169i
\(913\) 575.265i 0.630082i
\(914\) 438.917 722.844i 0.480216 0.790857i
\(915\) −20.5745 + 24.9879i −0.0224858 + 0.0273092i
\(916\) −82.5715 158.842i −0.0901435 0.173408i
\(917\) 1039.85i 1.13397i
\(918\) −207.877 + 342.348i −0.226446 + 0.372929i
\(919\) 1254.84i 1.36544i 0.730682 + 0.682718i \(0.239202\pi\)
−0.730682 + 0.682718i \(0.760798\pi\)
\(920\) −489.728 460.961i −0.532313 0.501045i
\(921\) 107.374 0.116584
\(922\) −937.654 569.352i −1.01698 0.617519i
\(923\) 1225.46 1.32770
\(924\) 120.628 62.7064i 0.130549 0.0678641i
\(925\) −806.771 + 157.778i −0.872185 + 0.170571i
\(926\) −626.146 380.202i −0.676184 0.410585i
\(927\) 99.9610 0.107833
\(928\) 437.926 191.939i 0.471903 0.206831i
\(929\) 1699.39 1.82927 0.914635 0.404281i \(-0.132478\pi\)
0.914635 + 0.404281i \(0.132478\pi\)
\(930\) −41.0404 117.415i −0.0441295 0.126252i
\(931\) 32.7298i 0.0351556i
\(932\) 764.810 397.575i 0.820612 0.426582i
\(933\) 595.249i 0.637994i
\(934\) 382.932 + 232.520i 0.409992 + 0.248951i
\(935\) 139.884 169.891i 0.149609 0.181702i
\(936\) 1120.14 + 74.3913i 1.19674 + 0.0794779i
\(937\) 80.2211i 0.0856148i 0.999083 + 0.0428074i \(0.0136302\pi\)
−0.999083 + 0.0428074i \(0.986370\pi\)
\(938\) 374.259 + 227.254i 0.398997 + 0.242275i
\(939\) 232.648i 0.247761i
\(940\) 1507.54 + 320.445i 1.60376 + 0.340899i
\(941\) −1490.89 −1.58437 −0.792185 0.610281i \(-0.791057\pi\)
−0.792185 + 0.610281i \(0.791057\pi\)
\(942\) 37.6615 62.0239i 0.0399803 0.0658427i
\(943\) 556.197 0.589817
\(944\) 542.440 + 380.753i 0.574618 + 0.403341i
\(945\) −408.060 + 495.593i −0.431810 + 0.524437i
\(946\) 351.786 579.349i 0.371867 0.612420i
\(947\) −641.294 −0.677184 −0.338592 0.940933i \(-0.609951\pi\)
−0.338592 + 0.940933i \(0.609951\pi\)
\(948\) 212.003 110.206i 0.223632 0.116251i
\(949\) −240.146 −0.253052
\(950\) 204.538 + 75.2596i 0.215304 + 0.0792207i
\(951\) 746.433i 0.784893i
\(952\) 516.582 + 34.3074i 0.542628 + 0.0360372i
\(953\) 1570.96i 1.64844i 0.566273 + 0.824218i \(0.308385\pi\)
−0.566273 + 0.824218i \(0.691615\pi\)
\(954\) 605.765 997.622i 0.634974 1.04572i
\(955\) −927.117 763.367i −0.970803 0.799337i
\(956\) −1085.47 + 564.263i −1.13543 + 0.590234i
\(957\) 78.8417i 0.0823842i
\(958\) −792.489 + 1305.13i −0.827233 + 1.36235i
\(959\) 454.239i 0.473659i
\(960\) −282.184 + 262.530i −0.293942 + 0.273469i
\(961\) 854.357 0.889029
\(962\) 1044.88 + 634.464i 1.08616 + 0.659526i
\(963\) −416.146 −0.432135
\(964\) −276.536 531.970i −0.286863 0.551836i
\(965\) 312.921 + 257.652i 0.324270 + 0.266997i
\(966\) −222.999 135.407i −0.230848 0.140173i
\(967\) −549.309 −0.568055 −0.284028 0.958816i \(-0.591671\pi\)
−0.284028 + 0.958816i \(0.591671\pi\)
\(968\) 53.9714 812.672i 0.0557555 0.839537i
\(969\) 52.7460 0.0544335
\(970\) −193.305 553.037i −0.199283 0.570141i
\(971\) 1755.93i 1.80837i 0.427136 + 0.904187i \(0.359522\pi\)
−0.427136 + 0.904187i \(0.640478\pi\)
\(972\) 428.605 + 824.504i 0.440952 + 0.848255i
\(973\) 1390.22i 1.42880i
\(974\) 1077.96 + 654.548i 1.10674 + 0.672021i
\(975\) −549.299 + 107.425i −0.563383 + 0.110179i
\(976\) 49.4070 70.3876i 0.0506219 0.0721184i
\(977\) 993.873i 1.01727i −0.860982 0.508635i \(-0.830150\pi\)
0.860982 0.508635i \(-0.169850\pi\)
\(978\) −207.722 126.131i −0.212395 0.128968i
\(979\) 640.681i 0.654423i
\(980\) −146.893 31.2238i −0.149891 0.0318611i
\(981\) −973.498 −0.992353
\(982\) −457.946 + 754.182i −0.466341 + 0.768006i
\(983\) 237.419 0.241525 0.120763 0.992681i \(-0.461466\pi\)
0.120763 + 0.992681i \(0.461466\pi\)
\(984\) 21.1220 318.044i 0.0214655 0.323216i
\(985\) 1023.23 + 842.500i 1.03881 + 0.855330i
\(986\) 155.828 256.630i 0.158041 0.260274i
\(987\) 597.859 0.605733
\(988\) −149.483 287.560i −0.151299 0.291052i
\(989\) −1300.66 −1.31513
\(990\) −109.126 312.206i −0.110229 0.315359i
\(991\) 235.754i 0.237895i 0.992901 + 0.118948i \(0.0379520\pi\)
−0.992901 + 0.118948i \(0.962048\pi\)
\(992\) 132.655 + 302.664i 0.133724 + 0.305104i
\(993\) 187.051i 0.188369i
\(994\) 440.819 725.975i 0.443480 0.730357i
\(995\) 301.179 + 247.983i 0.302692 + 0.249230i
\(996\) −291.794 561.320i −0.292965 0.563575i
\(997\) 1880.76i 1.88642i −0.332202 0.943208i \(-0.607792\pi\)
0.332202 0.943208i \(-0.392208\pi\)
\(998\) 188.436 310.331i 0.188813 0.310952i
\(999\) 655.431i 0.656088i
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 380.3.h.a.39.17 108
4.3 odd 2 inner 380.3.h.a.39.91 yes 108
5.4 even 2 inner 380.3.h.a.39.92 yes 108
20.19 odd 2 inner 380.3.h.a.39.18 yes 108
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
380.3.h.a.39.17 108 1.1 even 1 trivial
380.3.h.a.39.18 yes 108 20.19 odd 2 inner
380.3.h.a.39.91 yes 108 4.3 odd 2 inner
380.3.h.a.39.92 yes 108 5.4 even 2 inner