Properties

Label 380.2.k.d.343.19
Level $380$
Weight $2$
Character 380.343
Analytic conductor $3.034$
Analytic rank $0$
Dimension $52$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [380,2,Mod(267,380)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(380, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("380.267");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 380.k (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.03431527681\)
Analytic rank: \(0\)
Dimension: \(52\)
Relative dimension: \(26\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 343.19
Character \(\chi\) \(=\) 380.343
Dual form 380.2.k.d.267.19

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.912296 - 1.08061i) q^{2} +(-1.34016 + 1.34016i) q^{3} +(-0.335432 - 1.97167i) q^{4} +(-2.21942 + 0.272360i) q^{5} +(0.225567 + 2.67081i) q^{6} +(0.697742 + 0.697742i) q^{7} +(-2.43662 - 1.43628i) q^{8} -0.592060i q^{9} +O(q^{10})\) \(q+(0.912296 - 1.08061i) q^{2} +(-1.34016 + 1.34016i) q^{3} +(-0.335432 - 1.97167i) q^{4} +(-2.21942 + 0.272360i) q^{5} +(0.225567 + 2.67081i) q^{6} +(0.697742 + 0.697742i) q^{7} +(-2.43662 - 1.43628i) q^{8} -0.592060i q^{9} +(-1.73045 + 2.64680i) q^{10} +4.74628i q^{11} +(3.09189 + 2.19282i) q^{12} +(3.30493 + 3.30493i) q^{13} +(1.39053 - 0.117439i) q^{14} +(2.60937 - 3.33938i) q^{15} +(-3.77497 + 1.32272i) q^{16} +(-1.03069 + 1.03069i) q^{17} +(-0.639785 - 0.540133i) q^{18} -1.00000 q^{19} +(1.28147 + 4.28460i) q^{20} -1.87017 q^{21} +(5.12887 + 4.33001i) q^{22} +(-6.40614 + 6.40614i) q^{23} +(5.19030 - 1.34062i) q^{24} +(4.85164 - 1.20896i) q^{25} +(6.58642 - 0.556264i) q^{26} +(-3.22703 - 3.22703i) q^{27} +(1.14167 - 1.60976i) q^{28} +1.98037i q^{29} +(-1.22805 - 5.86622i) q^{30} -9.29923i q^{31} +(-2.01454 + 5.28598i) q^{32} +(-6.36077 - 6.36077i) q^{33} +(0.173479 + 2.05407i) q^{34} +(-1.73862 - 1.35854i) q^{35} +(-1.16735 + 0.198596i) q^{36} +(-5.70256 + 5.70256i) q^{37} +(-0.912296 + 1.08061i) q^{38} -8.85828 q^{39} +(5.79906 + 2.52406i) q^{40} +9.41542 q^{41} +(-1.70615 + 2.02093i) q^{42} +(1.89635 - 1.89635i) q^{43} +(9.35809 - 1.59205i) q^{44} +(0.161254 + 1.31403i) q^{45} +(1.07824 + 12.7668i) q^{46} +(1.10706 + 1.10706i) q^{47} +(3.28640 - 6.83173i) q^{48} -6.02631i q^{49} +(3.11971 - 6.34566i) q^{50} -2.76258i q^{51} +(5.40766 - 7.62482i) q^{52} +(-0.00450773 - 0.00450773i) q^{53} +(-6.43116 + 0.543151i) q^{54} +(-1.29270 - 10.5340i) q^{55} +(-0.697982 - 2.70228i) q^{56} +(1.34016 - 1.34016i) q^{57} +(2.14001 + 1.80669i) q^{58} -3.02457 q^{59} +(-7.45943 - 4.02468i) q^{60} -0.724786 q^{61} +(-10.0488 - 8.48365i) q^{62} +(0.413105 - 0.413105i) q^{63} +(3.87422 + 6.99931i) q^{64} +(-8.23516 - 6.43490i) q^{65} +(-12.6764 + 1.07060i) q^{66} +(10.1252 + 10.1252i) q^{67} +(2.37791 + 1.68645i) q^{68} -17.1705i q^{69} +(-3.05419 + 0.639373i) q^{70} -9.29365i q^{71} +(-0.850361 + 1.44262i) q^{72} +(-4.54609 - 4.54609i) q^{73} +(0.959817 + 11.3647i) q^{74} +(-4.88177 + 8.12218i) q^{75} +(0.335432 + 1.97167i) q^{76} +(-3.31168 + 3.31168i) q^{77} +(-8.08137 + 9.57234i) q^{78} +0.319115 q^{79} +(8.01798 - 3.96383i) q^{80} +10.4256 q^{81} +(8.58965 - 10.1744i) q^{82} +(-2.15376 + 2.15376i) q^{83} +(0.627316 + 3.68736i) q^{84} +(2.00681 - 2.56825i) q^{85} +(-0.319181 - 3.77925i) q^{86} +(-2.65402 - 2.65402i) q^{87} +(6.81696 - 11.5649i) q^{88} +8.13569i q^{89} +(1.56706 + 1.02453i) q^{90} +4.61198i q^{91} +(14.7796 + 10.4820i) q^{92} +(12.4625 + 12.4625i) q^{93} +(2.20627 - 0.186333i) q^{94} +(2.21942 - 0.272360i) q^{95} +(-4.38426 - 9.78387i) q^{96} +(-8.29185 + 8.29185i) q^{97} +(-6.51209 - 5.49778i) q^{98} +2.81008 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 52 q + 2 q^{2} + 2 q^{3} + 4 q^{5} - 4 q^{6} + 4 q^{7} - 4 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 52 q + 2 q^{2} + 2 q^{3} + 4 q^{5} - 4 q^{6} + 4 q^{7} - 4 q^{8} + 2 q^{10} + 22 q^{12} - 2 q^{13} - 2 q^{15} + 16 q^{16} - 20 q^{17} - 2 q^{18} - 52 q^{19} - 12 q^{20} - 16 q^{21} - 36 q^{22} - 20 q^{23} - 16 q^{25} + 8 q^{27} - 24 q^{28} + 40 q^{30} + 2 q^{32} + 8 q^{33} + 20 q^{34} - 12 q^{35} - 4 q^{36} + 10 q^{37} - 2 q^{38} + 64 q^{39} - 36 q^{40} - 4 q^{41} - 60 q^{42} + 28 q^{43} - 8 q^{44} + 12 q^{45} - 8 q^{46} + 4 q^{47} - 2 q^{48} + 46 q^{50} + 74 q^{52} - 2 q^{53} + 24 q^{54} + 12 q^{56} - 2 q^{57} - 20 q^{58} - 28 q^{59} - 110 q^{60} - 4 q^{61} - 32 q^{62} - 44 q^{63} - 24 q^{64} + 10 q^{65} + 36 q^{66} - 6 q^{67} + 28 q^{68} + 124 q^{70} + 124 q^{72} + 8 q^{73} + 88 q^{74} - 2 q^{75} + 12 q^{77} - 40 q^{78} + 52 q^{79} - 120 q^{80} - 24 q^{81} - 80 q^{82} + 76 q^{83} - 40 q^{84} + 12 q^{85} - 8 q^{86} - 12 q^{87} + 20 q^{88} + 78 q^{90} + 8 q^{92} + 24 q^{93} + 32 q^{94} - 4 q^{95} - 4 q^{96} - 10 q^{97} - 122 q^{98} - 128 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(21\) \(77\) \(191\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{4}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.912296 1.08061i 0.645091 0.764106i
\(3\) −1.34016 + 1.34016i −0.773742 + 0.773742i −0.978759 0.205017i \(-0.934275\pi\)
0.205017 + 0.978759i \(0.434275\pi\)
\(4\) −0.335432 1.97167i −0.167716 0.985835i
\(5\) −2.21942 + 0.272360i −0.992554 + 0.121803i
\(6\) 0.225567 + 2.67081i 0.0920873 + 1.09035i
\(7\) 0.697742 + 0.697742i 0.263722 + 0.263722i 0.826564 0.562842i \(-0.190292\pi\)
−0.562842 + 0.826564i \(0.690292\pi\)
\(8\) −2.43662 1.43628i −0.861475 0.507800i
\(9\) 0.592060i 0.197353i
\(10\) −1.73045 + 2.64680i −0.547217 + 0.836991i
\(11\) 4.74628i 1.43106i 0.698584 + 0.715528i \(0.253814\pi\)
−0.698584 + 0.715528i \(0.746186\pi\)
\(12\) 3.09189 + 2.19282i 0.892551 + 0.633013i
\(13\) 3.30493 + 3.30493i 0.916623 + 0.916623i 0.996782 0.0801589i \(-0.0255428\pi\)
−0.0801589 + 0.996782i \(0.525543\pi\)
\(14\) 1.39053 0.117439i 0.371636 0.0313870i
\(15\) 2.60937 3.33938i 0.673737 0.862225i
\(16\) −3.77497 + 1.32272i −0.943743 + 0.330681i
\(17\) −1.03069 + 1.03069i −0.249979 + 0.249979i −0.820962 0.570983i \(-0.806562\pi\)
0.570983 + 0.820962i \(0.306562\pi\)
\(18\) −0.639785 0.540133i −0.150799 0.127311i
\(19\) −1.00000 −0.229416
\(20\) 1.28147 + 4.28460i 0.286545 + 0.958067i
\(21\) −1.87017 −0.408105
\(22\) 5.12887 + 4.33001i 1.09348 + 0.923161i
\(23\) −6.40614 + 6.40614i −1.33577 + 1.33577i −0.435662 + 0.900110i \(0.643486\pi\)
−0.900110 + 0.435662i \(0.856514\pi\)
\(24\) 5.19030 1.34062i 1.05947 0.273653i
\(25\) 4.85164 1.20896i 0.970328 0.241793i
\(26\) 6.58642 0.556264i 1.29170 0.109092i
\(27\) −3.22703 3.22703i −0.621042 0.621042i
\(28\) 1.14167 1.60976i 0.215756 0.304217i
\(29\) 1.98037i 0.367746i 0.982950 + 0.183873i \(0.0588636\pi\)
−0.982950 + 0.183873i \(0.941136\pi\)
\(30\) −1.22805 5.86622i −0.224210 1.07102i
\(31\) 9.29923i 1.67019i −0.550106 0.835095i \(-0.685413\pi\)
0.550106 0.835095i \(-0.314587\pi\)
\(32\) −2.01454 + 5.28598i −0.356124 + 0.934439i
\(33\) −6.36077 6.36077i −1.10727 1.10727i
\(34\) 0.173479 + 2.05407i 0.0297513 + 0.352269i
\(35\) −1.73862 1.35854i −0.293880 0.229636i
\(36\) −1.16735 + 0.198596i −0.194558 + 0.0330993i
\(37\) −5.70256 + 5.70256i −0.937496 + 0.937496i −0.998158 0.0606627i \(-0.980679\pi\)
0.0606627 + 0.998158i \(0.480679\pi\)
\(38\) −0.912296 + 1.08061i −0.147994 + 0.175298i
\(39\) −8.85828 −1.41846
\(40\) 5.79906 + 2.52406i 0.916912 + 0.399089i
\(41\) 9.41542 1.47044 0.735221 0.677828i \(-0.237078\pi\)
0.735221 + 0.677828i \(0.237078\pi\)
\(42\) −1.70615 + 2.02093i −0.263265 + 0.311836i
\(43\) 1.89635 1.89635i 0.289191 0.289191i −0.547569 0.836760i \(-0.684447\pi\)
0.836760 + 0.547569i \(0.184447\pi\)
\(44\) 9.35809 1.59205i 1.41079 0.240011i
\(45\) 0.161254 + 1.31403i 0.0240383 + 0.195884i
\(46\) 1.07824 + 12.7668i 0.158978 + 1.88237i
\(47\) 1.10706 + 1.10706i 0.161482 + 0.161482i 0.783223 0.621741i \(-0.213574\pi\)
−0.621741 + 0.783223i \(0.713574\pi\)
\(48\) 3.28640 6.83173i 0.474351 0.986075i
\(49\) 6.02631i 0.860902i
\(50\) 3.11971 6.34566i 0.441194 0.897412i
\(51\) 2.76258i 0.386838i
\(52\) 5.40766 7.62482i 0.749907 1.05737i
\(53\) −0.00450773 0.00450773i −0.000619185 0.000619185i 0.706797 0.707416i \(-0.250139\pi\)
−0.707416 + 0.706797i \(0.750139\pi\)
\(54\) −6.43116 + 0.543151i −0.875170 + 0.0739135i
\(55\) −1.29270 10.5340i −0.174307 1.42040i
\(56\) −0.697982 2.70228i −0.0932717 0.361108i
\(57\) 1.34016 1.34016i 0.177509 0.177509i
\(58\) 2.14001 + 1.80669i 0.280997 + 0.237230i
\(59\) −3.02457 −0.393765 −0.196883 0.980427i \(-0.563082\pi\)
−0.196883 + 0.980427i \(0.563082\pi\)
\(60\) −7.45943 4.02468i −0.963009 0.519584i
\(61\) −0.724786 −0.0927993 −0.0463997 0.998923i \(-0.514775\pi\)
−0.0463997 + 0.998923i \(0.514775\pi\)
\(62\) −10.0488 8.48365i −1.27620 1.07742i
\(63\) 0.413105 0.413105i 0.0520463 0.0520463i
\(64\) 3.87422 + 6.99931i 0.484278 + 0.874914i
\(65\) −8.23516 6.43490i −1.02145 0.798151i
\(66\) −12.6764 + 1.07060i −1.56036 + 0.131782i
\(67\) 10.1252 + 10.1252i 1.23699 + 1.23699i 0.961226 + 0.275761i \(0.0889297\pi\)
0.275761 + 0.961226i \(0.411070\pi\)
\(68\) 2.37791 + 1.68645i 0.288364 + 0.204512i
\(69\) 17.1705i 2.06709i
\(70\) −3.05419 + 0.639373i −0.365046 + 0.0764197i
\(71\) 9.29365i 1.10295i −0.834190 0.551477i \(-0.814065\pi\)
0.834190 0.551477i \(-0.185935\pi\)
\(72\) −0.850361 + 1.44262i −0.100216 + 0.170015i
\(73\) −4.54609 4.54609i −0.532079 0.532079i 0.389112 0.921191i \(-0.372782\pi\)
−0.921191 + 0.389112i \(0.872782\pi\)
\(74\) 0.959817 + 11.3647i 0.111576 + 1.32112i
\(75\) −4.88177 + 8.12218i −0.563698 + 0.937869i
\(76\) 0.335432 + 1.97167i 0.0384767 + 0.226166i
\(77\) −3.31168 + 3.31168i −0.377401 + 0.377401i
\(78\) −8.08137 + 9.57234i −0.915035 + 1.08385i
\(79\) 0.319115 0.0359032 0.0179516 0.999839i \(-0.494286\pi\)
0.0179516 + 0.999839i \(0.494286\pi\)
\(80\) 8.01798 3.96383i 0.896438 0.443170i
\(81\) 10.4256 1.15840
\(82\) 8.58965 10.1744i 0.948568 1.12357i
\(83\) −2.15376 + 2.15376i −0.236406 + 0.236406i −0.815360 0.578954i \(-0.803461\pi\)
0.578954 + 0.815360i \(0.303461\pi\)
\(84\) 0.627316 + 3.68736i 0.0684458 + 0.402324i
\(85\) 2.00681 2.56825i 0.217669 0.278566i
\(86\) −0.319181 3.77925i −0.0344182 0.407527i
\(87\) −2.65402 2.65402i −0.284541 0.284541i
\(88\) 6.81696 11.5649i 0.726690 1.23282i
\(89\) 8.13569i 0.862381i 0.902261 + 0.431191i \(0.141906\pi\)
−0.902261 + 0.431191i \(0.858094\pi\)
\(90\) 1.56706 + 1.02453i 0.165183 + 0.107995i
\(91\) 4.61198i 0.483467i
\(92\) 14.7796 + 10.4820i 1.54088 + 1.09282i
\(93\) 12.4625 + 12.4625i 1.29230 + 1.29230i
\(94\) 2.20627 0.186333i 0.227560 0.0192188i
\(95\) 2.21942 0.272360i 0.227708 0.0279436i
\(96\) −4.38426 9.78387i −0.447466 0.998563i
\(97\) −8.29185 + 8.29185i −0.841910 + 0.841910i −0.989107 0.147197i \(-0.952975\pi\)
0.147197 + 0.989107i \(0.452975\pi\)
\(98\) −6.51209 5.49778i −0.657820 0.555360i
\(99\) 2.81008 0.282423
\(100\) −4.01107 9.16031i −0.401107 0.916031i
\(101\) 2.37691 0.236512 0.118256 0.992983i \(-0.462270\pi\)
0.118256 + 0.992983i \(0.462270\pi\)
\(102\) −2.98527 2.52029i −0.295585 0.249546i
\(103\) −3.18098 + 3.18098i −0.313432 + 0.313432i −0.846237 0.532806i \(-0.821138\pi\)
0.532806 + 0.846237i \(0.321138\pi\)
\(104\) −3.30607 12.7997i −0.324186 1.25511i
\(105\) 4.15070 0.509361i 0.405066 0.0497085i
\(106\) −0.00898348 0.000758711i −0.000872553 7.36925e-5i
\(107\) 11.3868 + 11.3868i 1.10080 + 1.10080i 0.994314 + 0.106490i \(0.0339613\pi\)
0.106490 + 0.994314i \(0.466039\pi\)
\(108\) −5.28018 + 7.44508i −0.508086 + 0.716403i
\(109\) 10.1057i 0.967951i 0.875082 + 0.483975i \(0.160808\pi\)
−0.875082 + 0.483975i \(0.839192\pi\)
\(110\) −12.5624 8.21320i −1.19778 0.783098i
\(111\) 15.2847i 1.45076i
\(112\) −3.55688 1.71104i −0.336093 0.161678i
\(113\) 4.33960 + 4.33960i 0.408236 + 0.408236i 0.881123 0.472887i \(-0.156788\pi\)
−0.472887 + 0.881123i \(0.656788\pi\)
\(114\) −0.225567 2.67081i −0.0211263 0.250144i
\(115\) 12.4731 15.9627i 1.16312 1.48853i
\(116\) 3.90465 0.664282i 0.362537 0.0616770i
\(117\) 1.95672 1.95672i 0.180899 0.180899i
\(118\) −2.75930 + 3.26838i −0.254014 + 0.300878i
\(119\) −1.43831 −0.131850
\(120\) −11.1543 + 4.38903i −1.01825 + 0.400662i
\(121\) −11.5271 −1.04792
\(122\) −0.661219 + 0.783210i −0.0598640 + 0.0709085i
\(123\) −12.6182 + 12.6182i −1.13774 + 1.13774i
\(124\) −18.3350 + 3.11926i −1.64653 + 0.280118i
\(125\) −10.4385 + 4.00459i −0.933652 + 0.358181i
\(126\) −0.0695310 0.823279i −0.00619432 0.0733435i
\(127\) −5.74713 5.74713i −0.509976 0.509976i 0.404543 0.914519i \(-0.367430\pi\)
−0.914519 + 0.404543i \(0.867430\pi\)
\(128\) 11.0980 + 2.19892i 0.980930 + 0.194359i
\(129\) 5.08283i 0.447518i
\(130\) −14.4665 + 3.02846i −1.26880 + 0.265614i
\(131\) 8.12224i 0.709644i −0.934934 0.354822i \(-0.884542\pi\)
0.934934 0.354822i \(-0.115458\pi\)
\(132\) −10.4077 + 14.6750i −0.905877 + 1.27729i
\(133\) −0.697742 0.697742i −0.0605019 0.0605019i
\(134\) 20.1785 1.70420i 1.74316 0.147221i
\(135\) 8.04104 + 6.28321i 0.692062 + 0.540773i
\(136\) 3.99175 1.03104i 0.342290 0.0884112i
\(137\) 4.96810 4.96810i 0.424453 0.424453i −0.462281 0.886734i \(-0.652969\pi\)
0.886734 + 0.462281i \(0.152969\pi\)
\(138\) −18.5546 15.6646i −1.57947 1.33346i
\(139\) 4.21496 0.357508 0.178754 0.983894i \(-0.442793\pi\)
0.178754 + 0.983894i \(0.442793\pi\)
\(140\) −2.09541 + 3.88368i −0.177095 + 0.328231i
\(141\) −2.96728 −0.249890
\(142\) −10.0428 8.47856i −0.842774 0.711505i
\(143\) −15.6861 + 15.6861i −1.31174 + 1.31174i
\(144\) 0.783132 + 2.23501i 0.0652610 + 0.186251i
\(145\) −0.539375 4.39528i −0.0447927 0.365008i
\(146\) −9.05992 + 0.765167i −0.749804 + 0.0633256i
\(147\) 8.07622 + 8.07622i 0.666116 + 0.666116i
\(148\) 13.1564 + 9.33075i 1.08145 + 0.766983i
\(149\) 7.03834i 0.576603i 0.957540 + 0.288302i \(0.0930906\pi\)
−0.957540 + 0.288302i \(0.906909\pi\)
\(150\) 4.32328 + 12.6851i 0.352995 + 1.03574i
\(151\) 16.8075i 1.36777i −0.729589 0.683886i \(-0.760289\pi\)
0.729589 0.683886i \(-0.239711\pi\)
\(152\) 2.43662 + 1.43628i 0.197636 + 0.116497i
\(153\) 0.610229 + 0.610229i 0.0493341 + 0.0493341i
\(154\) 0.557399 + 6.59986i 0.0449165 + 0.531832i
\(155\) 2.53274 + 20.6389i 0.203435 + 1.65775i
\(156\) 2.97135 + 17.4656i 0.237899 + 1.39837i
\(157\) 11.5208 11.5208i 0.919458 0.919458i −0.0775322 0.996990i \(-0.524704\pi\)
0.996990 + 0.0775322i \(0.0247040\pi\)
\(158\) 0.291127 0.344839i 0.0231608 0.0274339i
\(159\) 0.0120822 0.000958178
\(160\) 3.03142 12.2805i 0.239655 0.970858i
\(161\) −8.93967 −0.704544
\(162\) 9.51127 11.2660i 0.747276 0.885144i
\(163\) 8.50009 8.50009i 0.665778 0.665778i −0.290958 0.956736i \(-0.593974\pi\)
0.956736 + 0.290958i \(0.0939739\pi\)
\(164\) −3.15824 18.5641i −0.246617 1.44961i
\(165\) 15.8496 + 12.3848i 1.23389 + 0.964155i
\(166\) 0.362506 + 4.29223i 0.0281359 + 0.333142i
\(167\) 11.7917 + 11.7917i 0.912471 + 0.912471i 0.996466 0.0839953i \(-0.0267681\pi\)
−0.0839953 + 0.996466i \(0.526768\pi\)
\(168\) 4.55690 + 2.68608i 0.351572 + 0.207236i
\(169\) 8.84515i 0.680396i
\(170\) −0.944468 4.51158i −0.0724374 0.346023i
\(171\) 0.592060i 0.0452759i
\(172\) −4.37508 3.10288i −0.333597 0.236593i
\(173\) −14.0451 14.0451i −1.06783 1.06783i −0.997525 0.0703074i \(-0.977602\pi\)
−0.0703074 0.997525i \(-0.522398\pi\)
\(174\) −5.28921 + 0.446707i −0.400974 + 0.0338647i
\(175\) 4.22874 + 2.54165i 0.319663 + 0.192131i
\(176\) −6.27801 17.9170i −0.473223 1.35055i
\(177\) 4.05341 4.05341i 0.304673 0.304673i
\(178\) 8.79150 + 7.42215i 0.658951 + 0.556314i
\(179\) 8.86640 0.662706 0.331353 0.943507i \(-0.392495\pi\)
0.331353 + 0.943507i \(0.392495\pi\)
\(180\) 2.53674 0.758706i 0.189078 0.0565506i
\(181\) 5.73740 0.426457 0.213229 0.977002i \(-0.431602\pi\)
0.213229 + 0.977002i \(0.431602\pi\)
\(182\) 4.98375 + 4.20749i 0.369420 + 0.311880i
\(183\) 0.971329 0.971329i 0.0718027 0.0718027i
\(184\) 24.8103 6.40834i 1.82904 0.472429i
\(185\) 11.1032 14.2095i 0.816325 1.04471i
\(186\) 24.8365 2.09760i 1.82110 0.153803i
\(187\) −4.89194 4.89194i −0.357734 0.357734i
\(188\) 1.81142 2.55411i 0.132111 0.186278i
\(189\) 4.50326i 0.327564i
\(190\) 1.73045 2.64680i 0.125540 0.192019i
\(191\) 3.42146i 0.247568i 0.992309 + 0.123784i \(0.0395030\pi\)
−0.992309 + 0.123784i \(0.960497\pi\)
\(192\) −14.5723 4.18812i −1.05166 0.302252i
\(193\) 14.1458 + 14.1458i 1.01824 + 1.01824i 0.999831 + 0.0184059i \(0.00585912\pi\)
0.0184059 + 0.999831i \(0.494141\pi\)
\(194\) 1.39563 + 16.5249i 0.100200 + 1.18642i
\(195\) 19.6602 2.41264i 1.40790 0.172773i
\(196\) −11.8819 + 2.02142i −0.848707 + 0.144387i
\(197\) −3.94287 + 3.94287i −0.280918 + 0.280918i −0.833475 0.552557i \(-0.813652\pi\)
0.552557 + 0.833475i \(0.313652\pi\)
\(198\) 2.56362 3.03660i 0.182189 0.215801i
\(199\) 22.6493 1.60557 0.802785 0.596269i \(-0.203351\pi\)
0.802785 + 0.596269i \(0.203351\pi\)
\(200\) −13.5580 4.02251i −0.958696 0.284434i
\(201\) −27.1387 −1.91422
\(202\) 2.16845 2.56851i 0.152571 0.180720i
\(203\) −1.38179 + 1.38179i −0.0969827 + 0.0969827i
\(204\) −5.44689 + 0.926658i −0.381359 + 0.0648790i
\(205\) −20.8968 + 2.56439i −1.45949 + 0.179105i
\(206\) 0.535402 + 6.33940i 0.0373032 + 0.441687i
\(207\) 3.79282 + 3.79282i 0.263619 + 0.263619i
\(208\) −16.8475 8.10451i −1.16817 0.561946i
\(209\) 4.74628i 0.328307i
\(210\) 3.23624 4.94997i 0.223322 0.341580i
\(211\) 23.7055i 1.63196i 0.578083 + 0.815978i \(0.303801\pi\)
−0.578083 + 0.815978i \(0.696199\pi\)
\(212\) −0.00737572 + 0.0103998i −0.000506567 + 0.000714261i
\(213\) 12.4550 + 12.4550i 0.853402 + 0.853402i
\(214\) 22.6928 1.91655i 1.55125 0.131013i
\(215\) −3.69231 + 4.72529i −0.251813 + 0.322262i
\(216\) 3.22813 + 12.4979i 0.219647 + 0.850377i
\(217\) 6.48846 6.48846i 0.440465 0.440465i
\(218\) 10.9203 + 9.21939i 0.739617 + 0.624416i
\(219\) 12.1850 0.823384
\(220\) −20.3359 + 6.08221i −1.37105 + 0.410062i
\(221\) −6.81272 −0.458273
\(222\) −16.5168 13.9442i −1.10853 0.935871i
\(223\) 12.4637 12.4637i 0.834631 0.834631i −0.153515 0.988146i \(-0.549059\pi\)
0.988146 + 0.153515i \(0.0490594\pi\)
\(224\) −5.09388 + 2.28262i −0.340349 + 0.152514i
\(225\) −0.715778 2.87246i −0.0477186 0.191497i
\(226\) 8.64842 0.730413i 0.575284 0.0485863i
\(227\) 0.871636 + 0.871636i 0.0578525 + 0.0578525i 0.735441 0.677589i \(-0.236975\pi\)
−0.677589 + 0.735441i \(0.736975\pi\)
\(228\) −3.09189 2.19282i −0.204765 0.145223i
\(229\) 10.1929i 0.673563i −0.941583 0.336782i \(-0.890662\pi\)
0.941583 0.336782i \(-0.109338\pi\)
\(230\) −5.87024 28.0413i −0.387072 1.84899i
\(231\) 8.87635i 0.584021i
\(232\) 2.84436 4.82542i 0.186742 0.316804i
\(233\) −5.24568 5.24568i −0.343656 0.343656i 0.514084 0.857740i \(-0.328132\pi\)
−0.857740 + 0.514084i \(0.828132\pi\)
\(234\) −0.329341 3.89955i −0.0215297 0.254922i
\(235\) −2.75856 2.15552i −0.179948 0.140610i
\(236\) 1.01454 + 5.96345i 0.0660408 + 0.388188i
\(237\) −0.427665 + 0.427665i −0.0277798 + 0.0277798i
\(238\) −1.31216 + 1.55425i −0.0850550 + 0.100747i
\(239\) −0.785993 −0.0508417 −0.0254208 0.999677i \(-0.508093\pi\)
−0.0254208 + 0.999677i \(0.508093\pi\)
\(240\) −5.43321 + 16.0576i −0.350712 + 1.03651i
\(241\) 18.3499 1.18202 0.591009 0.806665i \(-0.298730\pi\)
0.591009 + 0.806665i \(0.298730\pi\)
\(242\) −10.5162 + 12.4563i −0.676004 + 0.800723i
\(243\) −4.29096 + 4.29096i −0.275265 + 0.275265i
\(244\) 0.243117 + 1.42904i 0.0155639 + 0.0914848i
\(245\) 1.64133 + 13.3749i 0.104861 + 0.854492i
\(246\) 2.12381 + 25.1468i 0.135409 + 1.60330i
\(247\) −3.30493 3.30493i −0.210288 0.210288i
\(248\) −13.3563 + 22.6587i −0.848123 + 1.43883i
\(249\) 5.77276i 0.365834i
\(250\) −5.19565 + 14.9334i −0.328602 + 0.944469i
\(251\) 8.10035i 0.511290i −0.966771 0.255645i \(-0.917712\pi\)
0.966771 0.255645i \(-0.0822878\pi\)
\(252\) −0.953075 0.675938i −0.0600381 0.0425801i
\(253\) −30.4053 30.4053i −1.91156 1.91156i
\(254\) −11.4535 + 0.967319i −0.718656 + 0.0606950i
\(255\) 0.752417 + 6.13132i 0.0471182 + 0.383958i
\(256\) 12.5008 9.98649i 0.781300 0.624156i
\(257\) 8.11783 8.11783i 0.506376 0.506376i −0.407036 0.913412i \(-0.633438\pi\)
0.913412 + 0.407036i \(0.133438\pi\)
\(258\) 5.49255 + 4.63704i 0.341951 + 0.288690i
\(259\) −7.95784 −0.494476
\(260\) −9.92516 + 18.3955i −0.615532 + 1.14084i
\(261\) 1.17250 0.0725759
\(262\) −8.77697 7.40989i −0.542243 0.457784i
\(263\) −7.91763 + 7.91763i −0.488222 + 0.488222i −0.907745 0.419523i \(-0.862197\pi\)
0.419523 + 0.907745i \(0.362197\pi\)
\(264\) 6.36295 + 24.6346i 0.391613 + 1.51615i
\(265\) 0.0112323 + 0.00877682i 0.000689993 + 0.000539156i
\(266\) −1.39053 + 0.117439i −0.0852591 + 0.00720066i
\(267\) −10.9031 10.9031i −0.667261 0.667261i
\(268\) 16.5672 23.3598i 1.01200 1.42693i
\(269\) 17.7957i 1.08502i 0.840049 + 0.542510i \(0.182526\pi\)
−0.840049 + 0.542510i \(0.817474\pi\)
\(270\) 14.1255 2.95707i 0.859650 0.179962i
\(271\) 16.0644i 0.975843i 0.872888 + 0.487921i \(0.162245\pi\)
−0.872888 + 0.487921i \(0.837755\pi\)
\(272\) 2.52750 5.25414i 0.153252 0.318579i
\(273\) −6.18079 6.18079i −0.374079 0.374079i
\(274\) −0.836197 9.90095i −0.0505165 0.598138i
\(275\) 5.73807 + 23.0272i 0.346019 + 1.38859i
\(276\) −33.8546 + 5.75954i −2.03781 + 0.346684i
\(277\) −9.82279 + 9.82279i −0.590195 + 0.590195i −0.937684 0.347489i \(-0.887034\pi\)
0.347489 + 0.937684i \(0.387034\pi\)
\(278\) 3.84529 4.55472i 0.230625 0.273174i
\(279\) −5.50569 −0.329617
\(280\) 2.28511 + 5.80739i 0.136561 + 0.347058i
\(281\) 10.4171 0.621431 0.310715 0.950503i \(-0.399431\pi\)
0.310715 + 0.950503i \(0.399431\pi\)
\(282\) −2.70704 + 3.20648i −0.161202 + 0.190943i
\(283\) −9.74230 + 9.74230i −0.579120 + 0.579120i −0.934661 0.355541i \(-0.884297\pi\)
0.355541 + 0.934661i \(0.384297\pi\)
\(284\) −18.3240 + 3.11739i −1.08733 + 0.184983i
\(285\) −2.60937 + 3.33938i −0.154566 + 0.197808i
\(286\) 2.64018 + 31.2609i 0.156117 + 1.84850i
\(287\) 6.56954 + 6.56954i 0.387787 + 0.387787i
\(288\) 3.12962 + 1.19273i 0.184414 + 0.0702822i
\(289\) 14.8754i 0.875021i
\(290\) −5.24165 3.42694i −0.307800 0.201237i
\(291\) 22.2248i 1.30284i
\(292\) −7.43848 + 10.4883i −0.435304 + 0.613781i
\(293\) −17.9213 17.9213i −1.04697 1.04697i −0.998841 0.0481339i \(-0.984673\pi\)
−0.0481339 0.998841i \(-0.515327\pi\)
\(294\) 16.0951 1.35934i 0.938688 0.0792781i
\(295\) 6.71278 0.823773i 0.390833 0.0479619i
\(296\) 22.0854 5.70452i 1.28369 0.331569i
\(297\) 15.3164 15.3164i 0.888745 0.888745i
\(298\) 7.60569 + 6.42105i 0.440586 + 0.371961i
\(299\) −42.3437 −2.44880
\(300\) 17.6518 + 6.90080i 1.01913 + 0.398418i
\(301\) 2.64633 0.152532
\(302\) −18.1623 15.3334i −1.04512 0.882337i
\(303\) −3.18544 + 3.18544i −0.182999 + 0.182999i
\(304\) 3.77497 1.32272i 0.216509 0.0758634i
\(305\) 1.60860 0.197403i 0.0921083 0.0113033i
\(306\) 1.21613 0.102710i 0.0695215 0.00587152i
\(307\) −4.46875 4.46875i −0.255045 0.255045i 0.567990 0.823035i \(-0.307721\pi\)
−0.823035 + 0.567990i \(0.807721\pi\)
\(308\) 7.64038 + 5.41869i 0.435351 + 0.308759i
\(309\) 8.52605i 0.485030i
\(310\) 24.6132 + 16.0919i 1.39793 + 0.913956i
\(311\) 0.594436i 0.0337074i 0.999858 + 0.0168537i \(0.00536495\pi\)
−0.999858 + 0.0168537i \(0.994635\pi\)
\(312\) 21.5842 + 12.7229i 1.22197 + 0.720294i
\(313\) 14.2529 + 14.2529i 0.805624 + 0.805624i 0.983968 0.178344i \(-0.0570740\pi\)
−0.178344 + 0.983968i \(0.557074\pi\)
\(314\) −1.93910 22.9598i −0.109430 1.29570i
\(315\) −0.804339 + 1.02937i −0.0453194 + 0.0579982i
\(316\) −0.107041 0.629190i −0.00602155 0.0353947i
\(317\) −8.72134 + 8.72134i −0.489840 + 0.489840i −0.908256 0.418416i \(-0.862585\pi\)
0.418416 + 0.908256i \(0.362585\pi\)
\(318\) 0.0110225 0.0130561i 0.000618112 0.000732150i
\(319\) −9.39940 −0.526265
\(320\) −10.5049 14.4792i −0.587240 0.809413i
\(321\) −30.5203 −1.70348
\(322\) −8.15562 + 9.66028i −0.454495 + 0.538347i
\(323\) 1.03069 1.03069i 0.0573491 0.0573491i
\(324\) −3.49710 20.5559i −0.194283 1.14200i
\(325\) 20.0299 + 12.0388i 1.11106 + 0.667792i
\(326\) −1.43068 16.9399i −0.0792379 0.938213i
\(327\) −13.5433 13.5433i −0.748944 0.748944i
\(328\) −22.9418 13.5231i −1.26675 0.746690i
\(329\) 1.54489i 0.0851725i
\(330\) 27.8427 5.82867i 1.53269 0.320858i
\(331\) 12.5175i 0.688023i −0.938966 0.344011i \(-0.888214\pi\)
0.938966 0.344011i \(-0.111786\pi\)
\(332\) 4.96894 + 3.52406i 0.272706 + 0.193408i
\(333\) 3.37626 + 3.37626i 0.185018 + 0.185018i
\(334\) 23.4998 1.98470i 1.28585 0.108598i
\(335\) −25.2297 19.7143i −1.37845 1.07711i
\(336\) 7.05985 2.47372i 0.385146 0.134953i
\(337\) −10.1313 + 10.1313i −0.551887 + 0.551887i −0.926985 0.375098i \(-0.877609\pi\)
0.375098 + 0.926985i \(0.377609\pi\)
\(338\) 9.55815 + 8.06939i 0.519895 + 0.438917i
\(339\) −11.6315 −0.631738
\(340\) −5.73689 3.09530i −0.311127 0.167866i
\(341\) 44.1367 2.39014
\(342\) 0.639785 + 0.540133i 0.0345956 + 0.0292071i
\(343\) 9.08901 9.08901i 0.490760 0.490760i
\(344\) −7.34437 + 1.89700i −0.395982 + 0.102279i
\(345\) 4.67657 + 38.1085i 0.251778 + 2.05169i
\(346\) −27.9906 + 2.36398i −1.50479 + 0.127089i
\(347\) −0.483917 0.483917i −0.0259781 0.0259781i 0.693998 0.719976i \(-0.255847\pi\)
−0.719976 + 0.693998i \(0.755847\pi\)
\(348\) −4.34261 + 6.12309i −0.232788 + 0.328232i
\(349\) 12.0418i 0.644582i −0.946641 0.322291i \(-0.895547\pi\)
0.946641 0.322291i \(-0.104453\pi\)
\(350\) 6.60439 2.25088i 0.353019 0.120314i
\(351\) 21.3302i 1.13852i
\(352\) −25.0887 9.56157i −1.33723 0.509633i
\(353\) −19.3284 19.3284i −1.02875 1.02875i −0.999574 0.0291749i \(-0.990712\pi\)
−0.0291749 0.999574i \(-0.509288\pi\)
\(354\) −0.682242 8.07806i −0.0362608 0.429344i
\(355\) 2.53122 + 20.6265i 0.134343 + 1.09474i
\(356\) 16.0409 2.72897i 0.850166 0.144635i
\(357\) 1.92757 1.92757i 0.102018 0.102018i
\(358\) 8.08878 9.58112i 0.427505 0.506378i
\(359\) −23.7453 −1.25323 −0.626614 0.779330i \(-0.715560\pi\)
−0.626614 + 0.779330i \(0.715560\pi\)
\(360\) 1.49439 3.43339i 0.0787614 0.180956i
\(361\) 1.00000 0.0526316
\(362\) 5.23420 6.19988i 0.275104 0.325859i
\(363\) 15.4482 15.4482i 0.810820 0.810820i
\(364\) 9.09331 1.54701i 0.476619 0.0810852i
\(365\) 11.3278 + 8.85150i 0.592926 + 0.463308i
\(366\) −0.163488 1.93577i −0.00854563 0.101184i
\(367\) −13.2536 13.2536i −0.691835 0.691835i 0.270801 0.962635i \(-0.412712\pi\)
−0.962635 + 0.270801i \(0.912712\pi\)
\(368\) 15.7094 32.6565i 0.818910 1.70234i
\(369\) 5.57449i 0.290196i
\(370\) −5.22552 24.9615i −0.271662 1.29769i
\(371\) 0.00629047i 0.000326585i
\(372\) 20.3915 28.7522i 1.05725 1.49073i
\(373\) −8.99990 8.99990i −0.465997 0.465997i 0.434618 0.900615i \(-0.356883\pi\)
−0.900615 + 0.434618i \(0.856883\pi\)
\(374\) −9.74916 + 0.823378i −0.504117 + 0.0425758i
\(375\) 8.62253 19.3561i 0.445266 0.999546i
\(376\) −1.10744 4.28754i −0.0571120 0.221113i
\(377\) −6.54500 + 6.54500i −0.337085 + 0.337085i
\(378\) −4.86627 4.10831i −0.250294 0.211309i
\(379\) 1.33948 0.0688044 0.0344022 0.999408i \(-0.489047\pi\)
0.0344022 + 0.999408i \(0.489047\pi\)
\(380\) −1.28147 4.28460i −0.0657380 0.219796i
\(381\) 15.4042 0.789179
\(382\) 3.69726 + 3.12138i 0.189168 + 0.159704i
\(383\) 2.40611 2.40611i 0.122946 0.122946i −0.642956 0.765903i \(-0.722292\pi\)
0.765903 + 0.642956i \(0.222292\pi\)
\(384\) −17.8200 + 11.9261i −0.909371 + 0.608603i
\(385\) 6.44803 8.25197i 0.328622 0.420559i
\(386\) 28.1912 2.38092i 1.43490 0.121186i
\(387\) −1.12275 1.12275i −0.0570727 0.0570727i
\(388\) 19.1302 + 13.5674i 0.971186 + 0.688783i
\(389\) 26.3685i 1.33693i −0.743742 0.668467i \(-0.766951\pi\)
0.743742 0.668467i \(-0.233049\pi\)
\(390\) 15.3288 23.4461i 0.776205 1.18724i
\(391\) 13.2055i 0.667830i
\(392\) −8.65545 + 14.6838i −0.437166 + 0.741645i
\(393\) 10.8851 + 10.8851i 0.549081 + 0.549081i
\(394\) 0.663637 + 7.85777i 0.0334336 + 0.395869i
\(395\) −0.708250 + 0.0869143i −0.0356359 + 0.00437313i
\(396\) −0.942591 5.54055i −0.0473670 0.278423i
\(397\) 15.2631 15.2631i 0.766032 0.766032i −0.211373 0.977405i \(-0.567793\pi\)
0.977405 + 0.211373i \(0.0677935\pi\)
\(398\) 20.6629 24.4751i 1.03574 1.22683i
\(399\) 1.87017 0.0936257
\(400\) −16.7157 + 10.9812i −0.835783 + 0.549059i
\(401\) −13.0632 −0.652343 −0.326171 0.945311i \(-0.605759\pi\)
−0.326171 + 0.945311i \(0.605759\pi\)
\(402\) −24.7585 + 29.3263i −1.23484 + 1.46267i
\(403\) 30.7333 30.7333i 1.53094 1.53094i
\(404\) −0.797293 4.68649i −0.0396668 0.233161i
\(405\) −23.1389 + 2.83953i −1.14978 + 0.141097i
\(406\) 0.232574 + 2.75378i 0.0115424 + 0.136668i
\(407\) −27.0659 27.0659i −1.34161 1.34161i
\(408\) −3.96782 + 6.73135i −0.196437 + 0.333251i
\(409\) 30.5100i 1.50862i 0.656517 + 0.754312i \(0.272029\pi\)
−0.656517 + 0.754312i \(0.727971\pi\)
\(410\) −16.2929 + 24.9207i −0.804650 + 1.23075i
\(411\) 13.3161i 0.656834i
\(412\) 7.33885 + 5.20485i 0.361559 + 0.256424i
\(413\) −2.11037 2.11037i −0.103844 0.103844i
\(414\) 7.55872 0.638381i 0.371491 0.0313747i
\(415\) 4.19349 5.36669i 0.205850 0.263440i
\(416\) −24.1277 + 10.8119i −1.18296 + 0.530097i
\(417\) −5.64872 + 5.64872i −0.276619 + 0.276619i
\(418\) −5.12887 4.33001i −0.250861 0.211788i
\(419\) −9.78783 −0.478167 −0.239083 0.970999i \(-0.576847\pi\)
−0.239083 + 0.970999i \(0.576847\pi\)
\(420\) −2.39657 8.01295i −0.116941 0.390992i
\(421\) 26.7931 1.30582 0.652909 0.757437i \(-0.273549\pi\)
0.652909 + 0.757437i \(0.273549\pi\)
\(422\) 25.6164 + 21.6264i 1.24699 + 1.05276i
\(423\) 0.655447 0.655447i 0.0318689 0.0318689i
\(424\) 0.00450928 + 0.0174580i 0.000218990 + 0.000847834i
\(425\) −3.75447 + 6.24660i −0.182118 + 0.303005i
\(426\) 24.8216 2.09634i 1.20261 0.101568i
\(427\) −0.505714 0.505714i −0.0244732 0.0244732i
\(428\) 18.6315 26.2705i 0.900589 1.26983i
\(429\) 42.0438i 2.02989i
\(430\) 1.73771 + 8.30080i 0.0838000 + 0.400300i
\(431\) 2.45196i 0.118107i 0.998255 + 0.0590534i \(0.0188082\pi\)
−0.998255 + 0.0590534i \(0.981192\pi\)
\(432\) 16.4504 + 7.91346i 0.791470 + 0.380737i
\(433\) 20.7659 + 20.7659i 0.997948 + 0.997948i 0.999998 0.00205006i \(-0.000652555\pi\)
−0.00205006 + 0.999998i \(0.500653\pi\)
\(434\) −1.09209 12.9309i −0.0524222 0.620702i
\(435\) 6.61323 + 5.16753i 0.317080 + 0.247764i
\(436\) 19.9251 3.38978i 0.954240 0.162341i
\(437\) 6.40614 6.40614i 0.306447 0.306447i
\(438\) 11.1163 13.1672i 0.531157 0.629153i
\(439\) −24.9711 −1.19180 −0.595902 0.803057i \(-0.703205\pi\)
−0.595902 + 0.803057i \(0.703205\pi\)
\(440\) −11.9799 + 27.5239i −0.571118 + 1.31215i
\(441\) −3.56794 −0.169902
\(442\) −6.21521 + 7.36188i −0.295628 + 0.350169i
\(443\) −14.4843 + 14.4843i −0.688170 + 0.688170i −0.961827 0.273657i \(-0.911767\pi\)
0.273657 + 0.961827i \(0.411767\pi\)
\(444\) −30.1364 + 5.12698i −1.43021 + 0.243316i
\(445\) −2.21584 18.0565i −0.105041 0.855960i
\(446\) −2.09781 24.8390i −0.0993340 1.17616i
\(447\) −9.43250 9.43250i −0.446142 0.446142i
\(448\) −2.18051 + 7.58693i −0.103019 + 0.358449i
\(449\) 33.6613i 1.58857i 0.607543 + 0.794286i \(0.292155\pi\)
−0.607543 + 0.794286i \(0.707845\pi\)
\(450\) −3.75701 1.84706i −0.177107 0.0870711i
\(451\) 44.6882i 2.10428i
\(452\) 7.10063 10.0119i 0.333985 0.470921i
\(453\) 22.5247 + 22.5247i 1.05830 + 1.05830i
\(454\) 1.73709 0.146708i 0.0815256 0.00688535i
\(455\) −1.25612 10.2359i −0.0588878 0.479867i
\(456\) −5.19030 + 1.34062i −0.243058 + 0.0627803i
\(457\) 7.29974 7.29974i 0.341468 0.341468i −0.515451 0.856919i \(-0.672376\pi\)
0.856919 + 0.515451i \(0.172376\pi\)
\(458\) −11.0145 9.29890i −0.514674 0.434509i
\(459\) 6.65212 0.310495
\(460\) −35.6570 19.2385i −1.66252 0.896999i
\(461\) −0.951158 −0.0442999 −0.0221499 0.999755i \(-0.507051\pi\)
−0.0221499 + 0.999755i \(0.507051\pi\)
\(462\) −9.59187 8.09786i −0.446254 0.376747i
\(463\) −13.1374 + 13.1374i −0.610549 + 0.610549i −0.943089 0.332540i \(-0.892094\pi\)
0.332540 + 0.943089i \(0.392094\pi\)
\(464\) −2.61949 7.47585i −0.121607 0.347058i
\(465\) −31.0537 24.2651i −1.44008 1.12527i
\(466\) −10.4541 + 0.882918i −0.484279 + 0.0409004i
\(467\) 19.9319 + 19.9319i 0.922339 + 0.922339i 0.997194 0.0748550i \(-0.0238494\pi\)
−0.0748550 + 0.997194i \(0.523849\pi\)
\(468\) −4.51435 3.20165i −0.208676 0.147997i
\(469\) 14.1295i 0.652441i
\(470\) −4.84589 + 1.01445i −0.223524 + 0.0467932i
\(471\) 30.8794i 1.42285i
\(472\) 7.36972 + 4.34411i 0.339219 + 0.199954i
\(473\) 9.00060 + 9.00060i 0.413848 + 0.413848i
\(474\) 0.0719817 + 0.852296i 0.00330623 + 0.0391473i
\(475\) −4.85164 + 1.20896i −0.222608 + 0.0554710i
\(476\) 0.482456 + 2.83587i 0.0221133 + 0.129982i
\(477\) −0.00266885 + 0.00266885i −0.000122198 + 0.000122198i
\(478\) −0.717058 + 0.849352i −0.0327975 + 0.0388484i
\(479\) −29.5471 −1.35004 −0.675021 0.737799i \(-0.735865\pi\)
−0.675021 + 0.737799i \(0.735865\pi\)
\(480\) 12.3952 + 20.5204i 0.565763 + 0.936625i
\(481\) −37.6932 −1.71866
\(482\) 16.7405 19.8290i 0.762509 0.903188i
\(483\) 11.9806 11.9806i 0.545135 0.545135i
\(484\) 3.86657 + 22.7277i 0.175753 + 1.03308i
\(485\) 16.1447 20.6615i 0.733094 0.938189i
\(486\) 0.722225 + 8.55147i 0.0327608 + 0.387902i
\(487\) 28.7952 + 28.7952i 1.30483 + 1.30483i 0.925092 + 0.379742i \(0.123987\pi\)
0.379742 + 0.925092i \(0.376013\pi\)
\(488\) 1.76603 + 1.04099i 0.0799443 + 0.0471235i
\(489\) 22.7830i 1.03028i
\(490\) 15.9504 + 10.4282i 0.720567 + 0.471100i
\(491\) 2.85127i 0.128676i −0.997928 0.0643380i \(-0.979506\pi\)
0.997928 0.0643380i \(-0.0204936\pi\)
\(492\) 29.1114 + 20.6463i 1.31244 + 0.930809i
\(493\) −2.04115 2.04115i −0.0919288 0.0919288i
\(494\) −6.58642 + 0.556264i −0.296337 + 0.0250275i
\(495\) −6.23674 + 0.765354i −0.280321 + 0.0344001i
\(496\) 12.3003 + 35.1043i 0.552300 + 1.57623i
\(497\) 6.48457 6.48457i 0.290873 0.290873i
\(498\) −6.23810 5.26647i −0.279536 0.235996i
\(499\) −12.2247 −0.547252 −0.273626 0.961836i \(-0.588223\pi\)
−0.273626 + 0.961836i \(0.588223\pi\)
\(500\) 11.3972 + 19.2381i 0.509696 + 0.860354i
\(501\) −31.6056 −1.41203
\(502\) −8.75331 7.38992i −0.390680 0.329828i
\(503\) 22.0965 22.0965i 0.985234 0.985234i −0.0146587 0.999893i \(-0.504666\pi\)
0.999893 + 0.0146587i \(0.00466618\pi\)
\(504\) −1.59991 + 0.413247i −0.0712657 + 0.0184075i
\(505\) −5.27536 + 0.647377i −0.234751 + 0.0288079i
\(506\) −60.5949 + 5.11761i −2.69377 + 0.227506i
\(507\) −11.8539 11.8539i −0.526451 0.526451i
\(508\) −9.40368 + 13.2592i −0.417221 + 0.588283i
\(509\) 5.44703i 0.241435i −0.992687 0.120718i \(-0.961480\pi\)
0.992687 0.120718i \(-0.0385196\pi\)
\(510\) 7.31198 + 4.78051i 0.323780 + 0.211684i
\(511\) 6.34399i 0.280642i
\(512\) 0.612936 22.6191i 0.0270882 0.999633i
\(513\) 3.22703 + 3.22703i 0.142477 + 0.142477i
\(514\) −1.36634 16.1781i −0.0602666 0.713584i
\(515\) 6.19356 7.92631i 0.272921 0.349275i
\(516\) 10.0217 1.70495i 0.441179 0.0750560i
\(517\) −5.25443 + 5.25443i −0.231089 + 0.231089i
\(518\) −7.25990 + 8.59931i −0.318982 + 0.377832i
\(519\) 37.6455 1.65245
\(520\) 10.8237 + 27.5074i 0.474649 + 1.20628i
\(521\) −14.5598 −0.637877 −0.318938 0.947775i \(-0.603326\pi\)
−0.318938 + 0.947775i \(0.603326\pi\)
\(522\) 1.06967 1.26701i 0.0468180 0.0554557i
\(523\) −1.82937 + 1.82937i −0.0799929 + 0.0799929i −0.745971 0.665978i \(-0.768014\pi\)
0.665978 + 0.745971i \(0.268014\pi\)
\(524\) −16.0144 + 2.72446i −0.699592 + 0.119019i
\(525\) −9.07340 + 2.26097i −0.395996 + 0.0986768i
\(526\) 1.33264 + 15.7791i 0.0581060 + 0.688001i
\(527\) 9.58461 + 9.58461i 0.417512 + 0.417512i
\(528\) 32.4253 + 15.5982i 1.41113 + 0.678823i
\(529\) 59.0772i 2.56857i
\(530\) 0.0197315 0.00413064i 0.000857080 0.000179424i
\(531\) 1.79072i 0.0777108i
\(532\) −1.14167 + 1.60976i −0.0494978 + 0.0697921i
\(533\) 31.1173 + 31.1173i 1.34784 + 1.34784i
\(534\) −21.7289 + 1.83514i −0.940301 + 0.0794143i
\(535\) −28.3734 22.1708i −1.22669 0.958526i
\(536\) −10.1287 39.2137i −0.437491 1.69378i
\(537\) −11.8824 + 11.8824i −0.512763 + 0.512763i
\(538\) 19.2301 + 16.2349i 0.829071 + 0.699936i
\(539\) 28.6025 1.23200
\(540\) 9.69119 17.9619i 0.417043 0.772956i
\(541\) −36.8551 −1.58452 −0.792262 0.610181i \(-0.791097\pi\)
−0.792262 + 0.610181i \(0.791097\pi\)
\(542\) 17.3593 + 14.6555i 0.745647 + 0.629507i
\(543\) −7.68903 + 7.68903i −0.329968 + 0.329968i
\(544\) −3.37184 7.52457i −0.144566 0.322613i
\(545\) −2.75239 22.4288i −0.117900 0.960744i
\(546\) −12.3177 + 1.04031i −0.527150 + 0.0445211i
\(547\) −7.80179 7.80179i −0.333580 0.333580i 0.520364 0.853944i \(-0.325796\pi\)
−0.853944 + 0.520364i \(0.825796\pi\)
\(548\) −11.4619 8.12899i −0.489629 0.347253i
\(549\) 0.429116i 0.0183142i
\(550\) 30.1182 + 14.8070i 1.28425 + 0.631374i
\(551\) 1.98037i 0.0843668i
\(552\) −24.6616 + 41.8380i −1.04967 + 1.78074i
\(553\) 0.222660 + 0.222660i 0.00946846 + 0.00946846i
\(554\) 1.65331 + 19.5759i 0.0702423 + 0.831700i
\(555\) 4.16295 + 33.9231i 0.176707 + 1.43996i
\(556\) −1.41383 8.31051i −0.0599599 0.352444i
\(557\) −1.76844 + 1.76844i −0.0749310 + 0.0749310i −0.743579 0.668648i \(-0.766873\pi\)
0.668648 + 0.743579i \(0.266873\pi\)
\(558\) −5.02282 + 5.94950i −0.212633 + 0.251863i
\(559\) 12.5346 0.530158
\(560\) 8.36022 + 2.82875i 0.353284 + 0.119537i
\(561\) 13.1120 0.553587
\(562\) 9.50346 11.2568i 0.400879 0.474839i
\(563\) 6.91763 6.91763i 0.291543 0.291543i −0.546146 0.837690i \(-0.683906\pi\)
0.837690 + 0.546146i \(0.183906\pi\)
\(564\) 0.995323 + 5.85051i 0.0419107 + 0.246351i
\(565\) −10.8133 8.44946i −0.454920 0.355472i
\(566\) 1.63976 + 19.4155i 0.0689242 + 0.816094i
\(567\) 7.27441 + 7.27441i 0.305497 + 0.305497i
\(568\) −13.3482 + 22.6451i −0.560080 + 0.950167i
\(569\) 8.71597i 0.365392i −0.983169 0.182696i \(-0.941518\pi\)
0.983169 0.182696i \(-0.0584825\pi\)
\(570\) 1.22805 + 5.86622i 0.0514374 + 0.245709i
\(571\) 44.1078i 1.84586i 0.384973 + 0.922928i \(0.374211\pi\)
−0.384973 + 0.922928i \(0.625789\pi\)
\(572\) 36.1895 + 25.6662i 1.51316 + 1.07316i
\(573\) −4.58530 4.58530i −0.191554 0.191554i
\(574\) 13.0925 1.10574i 0.546469 0.0461527i
\(575\) −23.3355 + 38.8251i −0.973157 + 1.61912i
\(576\) 4.14401 2.29377i 0.172667 0.0955738i
\(577\) −9.97337 + 9.97337i −0.415197 + 0.415197i −0.883544 0.468348i \(-0.844850\pi\)
0.468348 + 0.883544i \(0.344850\pi\)
\(578\) 16.0744 + 13.5707i 0.668609 + 0.564468i
\(579\) −37.9153 −1.57570
\(580\) −8.48512 + 2.53779i −0.352325 + 0.105376i
\(581\) −3.00553 −0.124691
\(582\) −24.0163 20.2756i −0.995510 0.840451i
\(583\) 0.0213949 0.0213949i 0.000886088 0.000886088i
\(584\) 4.54765 + 17.6065i 0.188183 + 0.728563i
\(585\) −3.80984 + 4.87571i −0.157518 + 0.201586i
\(586\) −35.7155 + 3.01640i −1.47539 + 0.124606i
\(587\) −5.10277 5.10277i −0.210614 0.210614i 0.593914 0.804528i \(-0.297582\pi\)
−0.804528 + 0.593914i \(0.797582\pi\)
\(588\) 13.2146 18.6327i 0.544962 0.768399i
\(589\) 9.29923i 0.383168i
\(590\) 5.23387 8.00542i 0.215475 0.329578i
\(591\) 10.5682i 0.434716i
\(592\) 13.9841 29.0699i 0.574742 1.19477i
\(593\) 3.54561 + 3.54561i 0.145601 + 0.145601i 0.776150 0.630549i \(-0.217170\pi\)
−0.630549 + 0.776150i \(0.717170\pi\)
\(594\) −2.57795 30.5240i −0.105774 1.25242i
\(595\) 3.19221 0.391739i 0.130868 0.0160597i
\(596\) 13.8773 2.36089i 0.568436 0.0967057i
\(597\) −30.3537 + 30.3537i −1.24230 + 1.24230i
\(598\) −38.6300 + 45.7570i −1.57970 + 1.87114i
\(599\) 30.4232 1.24306 0.621529 0.783391i \(-0.286512\pi\)
0.621529 + 0.783391i \(0.286512\pi\)
\(600\) 23.5607 12.7791i 0.961862 0.521704i
\(601\) 26.2371 1.07023 0.535117 0.844778i \(-0.320268\pi\)
0.535117 + 0.844778i \(0.320268\pi\)
\(602\) 2.41423 2.85965i 0.0983968 0.116550i
\(603\) 5.99471 5.99471i 0.244123 0.244123i
\(604\) −33.1388 + 5.63777i −1.34840 + 0.229397i
\(605\) 25.5835 3.13953i 1.04012 0.127640i
\(606\) 0.536152 + 6.34829i 0.0217797 + 0.257881i
\(607\) −0.273256 0.273256i −0.0110911 0.0110911i 0.701539 0.712631i \(-0.252496\pi\)
−0.712631 + 0.701539i \(0.752496\pi\)
\(608\) 2.01454 5.28598i 0.0817005 0.214375i
\(609\) 3.70364i 0.150079i
\(610\) 1.25421 1.91836i 0.0507813 0.0776722i
\(611\) 7.31754i 0.296036i
\(612\) 0.998481 1.40786i 0.0403612 0.0569095i
\(613\) −6.40183 6.40183i −0.258567 0.258567i 0.565904 0.824471i \(-0.308527\pi\)
−0.824471 + 0.565904i \(0.808527\pi\)
\(614\) −8.90579 + 0.752149i −0.359408 + 0.0303543i
\(615\) 24.5683 31.4417i 0.990690 1.26785i
\(616\) 12.8258 3.31281i 0.516765 0.133477i
\(617\) 21.3006 21.3006i 0.857530 0.857530i −0.133517 0.991047i \(-0.542627\pi\)
0.991047 + 0.133517i \(0.0426269\pi\)
\(618\) −9.21333 7.77828i −0.370615 0.312888i
\(619\) −21.5289 −0.865320 −0.432660 0.901557i \(-0.642425\pi\)
−0.432660 + 0.901557i \(0.642425\pi\)
\(620\) 39.8435 11.9167i 1.60015 0.478585i
\(621\) 41.3456 1.65914
\(622\) 0.642353 + 0.542302i 0.0257560 + 0.0217443i
\(623\) −5.67661 + 5.67661i −0.227429 + 0.227429i
\(624\) 33.4397 11.7171i 1.33866 0.469058i
\(625\) 22.0768 11.7309i 0.883073 0.469236i
\(626\) 28.4048 2.39896i 1.13528 0.0958817i
\(627\) 6.36077 + 6.36077i 0.254025 + 0.254025i
\(628\) −26.5796 18.8507i −1.06064 0.752226i
\(629\) 11.7551i 0.468708i
\(630\) 0.378547 + 1.80826i 0.0150817 + 0.0720429i
\(631\) 33.6642i 1.34015i 0.742294 + 0.670074i \(0.233738\pi\)
−0.742294 + 0.670074i \(0.766262\pi\)
\(632\) −0.777562 0.458337i −0.0309297 0.0182317i
\(633\) −31.7692 31.7692i −1.26271 1.26271i
\(634\) 1.46792 + 17.3808i 0.0582985 + 0.690280i
\(635\) 14.3206 + 11.1900i 0.568295 + 0.444062i
\(636\) −0.00405275 0.0238221i −0.000160702 0.000944606i
\(637\) 19.9166 19.9166i 0.789122 0.789122i
\(638\) −8.57503 + 10.1571i −0.339489 + 0.402123i
\(639\) −5.50240 −0.217671
\(640\) −25.2299 1.85769i −0.997300 0.0734315i
\(641\) −11.4028 −0.450383 −0.225192 0.974314i \(-0.572301\pi\)
−0.225192 + 0.974314i \(0.572301\pi\)
\(642\) −27.8435 + 32.9805i −1.09890 + 1.30164i
\(643\) 31.2371 31.2371i 1.23187 1.23187i 0.268629 0.963244i \(-0.413430\pi\)
0.963244 0.268629i \(-0.0865704\pi\)
\(644\) 2.99865 + 17.6261i 0.118163 + 0.694565i
\(645\) −1.38436 11.2809i −0.0545092 0.444186i
\(646\) −0.173479 2.05407i −0.00682543 0.0808161i
\(647\) 26.4732 + 26.4732i 1.04077 + 1.04077i 0.999133 + 0.0416381i \(0.0132576\pi\)
0.0416381 + 0.999133i \(0.486742\pi\)
\(648\) −25.4033 14.9741i −0.997937 0.588238i
\(649\) 14.3554i 0.563500i
\(650\) 31.2824 10.6615i 1.22700 0.418180i
\(651\) 17.3912i 0.681613i
\(652\) −19.6106 13.9082i −0.768010 0.544686i
\(653\) −17.1865 17.1865i −0.672558 0.672558i 0.285747 0.958305i \(-0.407758\pi\)
−0.958305 + 0.285747i \(0.907758\pi\)
\(654\) −26.9904 + 2.27951i −1.05541 + 0.0891359i
\(655\) 2.21218 + 18.0267i 0.0864369 + 0.704360i
\(656\) −35.5429 + 12.4540i −1.38772 + 0.486247i
\(657\) −2.69155 + 2.69155i −0.105008 + 0.105008i
\(658\) 1.66942 + 1.40940i 0.0650808 + 0.0549440i
\(659\) 46.1104 1.79621 0.898104 0.439783i \(-0.144945\pi\)
0.898104 + 0.439783i \(0.144945\pi\)
\(660\) 19.1022 35.4045i 0.743554 1.37812i
\(661\) 8.33816 0.324317 0.162158 0.986765i \(-0.448154\pi\)
0.162158 + 0.986765i \(0.448154\pi\)
\(662\) −13.5265 11.4196i −0.525722 0.443837i
\(663\) 9.13013 9.13013i 0.354585 0.354585i
\(664\) 8.34128 2.15450i 0.323704 0.0836107i
\(665\) 1.73862 + 1.35854i 0.0674208 + 0.0526821i
\(666\) 6.72856 0.568269i 0.260726 0.0220200i
\(667\) −12.6865 12.6865i −0.491225 0.491225i
\(668\) 19.2941 27.2047i 0.746510 1.05258i
\(669\) 33.4067i 1.29158i
\(670\) −44.3204 + 9.27816i −1.71225 + 0.358447i
\(671\) 3.44003i 0.132801i
\(672\) 3.76754 9.88570i 0.145336 0.381349i
\(673\) −0.923216 0.923216i −0.0355873 0.0355873i 0.689089 0.724677i \(-0.258011\pi\)
−0.724677 + 0.689089i \(0.758011\pi\)
\(674\) 1.70523 + 20.1907i 0.0656831 + 0.777718i
\(675\) −19.5577 11.7550i −0.752777 0.452451i
\(676\) 17.4397 2.96695i 0.670759 0.114113i
\(677\) 3.76247 3.76247i 0.144603 0.144603i −0.631099 0.775702i \(-0.717396\pi\)
0.775702 + 0.631099i \(0.217396\pi\)
\(678\) −10.6114 + 12.5691i −0.407528 + 0.482715i
\(679\) −11.5711 −0.444060
\(680\) −8.57855 + 3.37551i −0.328972 + 0.129445i
\(681\) −2.33626 −0.0895259
\(682\) 40.2657 47.6945i 1.54185 1.82632i
\(683\) −13.9942 + 13.9942i −0.535473 + 0.535473i −0.922196 0.386723i \(-0.873607\pi\)
0.386723 + 0.922196i \(0.373607\pi\)
\(684\) 1.16735 0.198596i 0.0446346 0.00759351i
\(685\) −9.67317 + 12.3794i −0.369593 + 0.472993i
\(686\) −1.52980 18.1135i −0.0584081 0.691578i
\(687\) 13.6601 + 13.6601i 0.521164 + 0.521164i
\(688\) −4.65032 + 9.66702i −0.177292 + 0.368552i
\(689\) 0.0297955i 0.00113512i
\(690\) 45.4469 + 29.7127i 1.73013 + 1.13114i
\(691\) 10.1227i 0.385087i −0.981288 0.192544i \(-0.938326\pi\)
0.981288 0.192544i \(-0.0616737\pi\)
\(692\) −22.9812 + 32.4036i −0.873614 + 1.23180i
\(693\) 1.96071 + 1.96071i 0.0744812 + 0.0744812i
\(694\) −0.964402 + 0.0814497i −0.0366082 + 0.00309179i
\(695\) −9.35475 + 1.14799i −0.354846 + 0.0435456i
\(696\) 2.65493 + 10.2787i 0.100635 + 0.389614i
\(697\) −9.70437 + 9.70437i −0.367579 + 0.367579i
\(698\) −13.0125 10.9857i −0.492529 0.415814i
\(699\) 14.0601 0.531802
\(700\) 3.59284 9.19023i 0.135797 0.347358i
\(701\) −21.0307 −0.794320 −0.397160 0.917749i \(-0.630004\pi\)
−0.397160 + 0.917749i \(0.630004\pi\)
\(702\) −23.0496 19.4595i −0.869952 0.734450i
\(703\) 5.70256 5.70256i 0.215076 0.215076i
\(704\) −33.2207 + 18.3881i −1.25205 + 0.693029i
\(705\) 6.58565 0.808171i 0.248030 0.0304375i
\(706\) −38.5198 + 3.25323i −1.44971 + 0.122437i
\(707\) 1.65847 + 1.65847i 0.0623732 + 0.0623732i
\(708\) −9.35163 6.63234i −0.351456 0.249259i
\(709\) 24.7345i 0.928924i 0.885593 + 0.464462i \(0.153752\pi\)
−0.885593 + 0.464462i \(0.846248\pi\)
\(710\) 24.5984 + 16.0822i 0.923162 + 0.603555i
\(711\) 0.188935i 0.00708562i
\(712\) 11.6851 19.8236i 0.437917 0.742920i
\(713\) 59.5721 + 59.5721i 2.23099 + 2.23099i
\(714\) −0.324435 3.84146i −0.0121417 0.143763i
\(715\) 30.5418 39.0863i 1.14220 1.46175i
\(716\) −2.97408 17.4816i −0.111147 0.653319i
\(717\) 1.05336 1.05336i 0.0393383 0.0393383i
\(718\) −21.6627 + 25.6594i −0.808446 + 0.957599i
\(719\) 26.9815 1.00624 0.503120 0.864216i \(-0.332185\pi\)
0.503120 + 0.864216i \(0.332185\pi\)
\(720\) −2.34682 4.74712i −0.0874610 0.176915i
\(721\) −4.43901 −0.165317
\(722\) 0.912296 1.08061i 0.0339521 0.0402161i
\(723\) −24.5918 + 24.5918i −0.914578 + 0.914578i
\(724\) −1.92451 11.3123i −0.0715238 0.420417i
\(725\) 2.39420 + 9.60806i 0.0889183 + 0.356834i
\(726\) −2.60014 30.7868i −0.0965001 1.14261i
\(727\) −29.4984 29.4984i −1.09404 1.09404i −0.995093 0.0989427i \(-0.968454\pi\)
−0.0989427 0.995093i \(-0.531546\pi\)
\(728\) 6.62408 11.2376i 0.245505 0.416495i
\(729\) 19.7758i 0.732437i
\(730\) 19.8994 4.16579i 0.736508 0.154183i
\(731\) 3.90910i 0.144583i
\(732\) −2.24096 1.58933i −0.0828281 0.0587432i
\(733\) −19.4831 19.4831i −0.719625 0.719625i 0.248904 0.968528i \(-0.419930\pi\)
−0.968528 + 0.248904i \(0.919930\pi\)
\(734\) −26.4133 + 2.23076i −0.974931 + 0.0823390i
\(735\) −20.1242 15.7249i −0.742291 0.580021i
\(736\) −20.9573 46.7682i −0.772497 1.72390i
\(737\) −48.0569 + 48.0569i −1.77020 + 1.77020i
\(738\) −6.02384 5.08558i −0.221741 0.187203i
\(739\) 37.1086 1.36506 0.682532 0.730856i \(-0.260879\pi\)
0.682532 + 0.730856i \(0.260879\pi\)
\(740\) −31.7409 17.1256i −1.16682 0.629548i
\(741\) 8.85828 0.325417
\(742\) −0.00679754 0.00573877i −0.000249545 0.000210677i
\(743\) 12.3911 12.3911i 0.454586 0.454586i −0.442288 0.896873i \(-0.645833\pi\)
0.896873 + 0.442288i \(0.145833\pi\)
\(744\) −12.4667 48.2658i −0.457053 1.76951i
\(745\) −1.91696 15.6210i −0.0702322 0.572310i
\(746\) −17.9359 + 1.51480i −0.656681 + 0.0554609i
\(747\) 1.27515 + 1.27515i 0.0466554 + 0.0466554i
\(748\) −8.00437 + 11.2862i −0.292669 + 0.412664i
\(749\) 15.8901i 0.580612i
\(750\) −13.0501 26.9761i −0.476522 0.985028i
\(751\) 4.32457i 0.157806i −0.996882 0.0789029i \(-0.974858\pi\)
0.996882 0.0789029i \(-0.0251417\pi\)
\(752\) −5.64347 2.71479i −0.205796 0.0989983i
\(753\) 10.8558 + 10.8558i 0.395606 + 0.395606i
\(754\) 1.10161 + 13.0436i 0.0401183 + 0.475019i
\(755\) 4.57769 + 37.3028i 0.166599 + 1.35759i
\(756\) −8.87895 + 1.51054i −0.322924 + 0.0549378i
\(757\) 4.02457 4.02457i 0.146275 0.146275i −0.630177 0.776452i \(-0.717017\pi\)
0.776452 + 0.630177i \(0.217017\pi\)
\(758\) 1.22200 1.44745i 0.0443851 0.0525739i
\(759\) 81.4959 2.95812
\(760\) −5.79906 2.52406i −0.210354 0.0915572i
\(761\) 35.1030 1.27248 0.636241 0.771490i \(-0.280488\pi\)
0.636241 + 0.771490i \(0.280488\pi\)
\(762\) 14.0532 16.6459i 0.509092 0.603016i
\(763\) −7.05117 + 7.05117i −0.255270 + 0.255270i
\(764\) 6.74599 1.14767i 0.244061 0.0415212i
\(765\) −1.52056 1.18815i −0.0549759 0.0429577i
\(766\) −0.404980 4.79515i −0.0146325 0.173256i
\(767\) −9.99599 9.99599i −0.360934 0.360934i
\(768\) −3.36958 + 30.1366i −0.121589 + 1.08746i
\(769\) 50.0247i 1.80394i 0.431802 + 0.901968i \(0.357878\pi\)
−0.431802 + 0.901968i \(0.642122\pi\)
\(770\) −3.03464 14.4960i −0.109361 0.522401i
\(771\) 21.7584i 0.783609i
\(772\) 23.1459 32.6358i 0.833039 1.17459i
\(773\) −0.732635 0.732635i −0.0263510 0.0263510i 0.693809 0.720160i \(-0.255931\pi\)
−0.720160 + 0.693809i \(0.755931\pi\)
\(774\) −2.23754 + 0.188974i −0.0804267 + 0.00679254i
\(775\) −11.2424 45.1165i −0.403840 1.62063i
\(776\) 32.1135 8.29470i 1.15281 0.297762i
\(777\) 10.6648 10.6648i 0.382597 0.382597i
\(778\) −28.4940 24.0558i −1.02156 0.862443i
\(779\) −9.41542 −0.337342
\(780\) −11.3516 37.9542i −0.406453 1.35898i
\(781\) 44.1102 1.57839
\(782\) −14.2700 12.0473i −0.510293 0.430811i
\(783\) 6.39072 6.39072i 0.228386 0.228386i
\(784\) 7.97115 + 22.7491i 0.284684 + 0.812470i
\(785\) −22.4316 + 28.7072i −0.800619 + 1.02460i
\(786\) 21.6930 1.83211i 0.773763 0.0653491i
\(787\) 13.7218 + 13.7218i 0.489128 + 0.489128i 0.908031 0.418903i \(-0.137585\pi\)
−0.418903 + 0.908031i \(0.637585\pi\)
\(788\) 9.09661 + 6.45147i 0.324053 + 0.229824i
\(789\) 21.2218i 0.755516i
\(790\) −0.552213 + 0.844633i −0.0196469 + 0.0300507i
\(791\) 6.05585i 0.215321i
\(792\) −6.84709 4.03605i −0.243301 0.143415i
\(793\) −2.39537 2.39537i −0.0850620 0.0850620i
\(794\) −2.56898 30.4179i −0.0911697 1.07949i
\(795\) −0.0268154 + 0.00329070i −0.000951044 + 0.000116709i
\(796\) −7.59732 44.6570i −0.269280 1.58283i
\(797\) −23.8669 + 23.8669i −0.845410 + 0.845410i −0.989556 0.144146i \(-0.953956\pi\)
0.144146 + 0.989556i \(0.453956\pi\)
\(798\) 1.70615 2.02093i 0.0603971 0.0715400i
\(799\) −2.28208 −0.0807341
\(800\) −3.38327 + 28.0812i −0.119617 + 0.992820i
\(801\) 4.81681 0.170194
\(802\) −11.9175 + 14.1162i −0.420820 + 0.498459i
\(803\) 21.5770 21.5770i 0.761435 0.761435i
\(804\) 9.10320 + 53.5086i 0.321045 + 1.88710i
\(805\) 19.8409 2.43481i 0.699298 0.0858158i
\(806\) −5.17282 61.2486i −0.182205 2.15739i
\(807\) −23.8490 23.8490i −0.839526 0.839526i
\(808\) −5.79163 3.41390i −0.203749 0.120101i
\(809\) 55.6290i 1.95581i −0.209043 0.977906i \(-0.567035\pi\)
0.209043 0.977906i \(-0.432965\pi\)
\(810\) −18.0411 + 27.5946i −0.633899 + 0.969574i
\(811\) 10.2643i 0.360427i −0.983628 0.180213i \(-0.942321\pi\)
0.983628 0.180213i \(-0.0576788\pi\)
\(812\) 3.18793 + 2.26094i 0.111875 + 0.0793434i
\(813\) −21.5289 21.5289i −0.755050 0.755050i
\(814\) −53.9398 + 4.55556i −1.89059 + 0.159672i
\(815\) −16.5502 + 21.1803i −0.579727 + 0.741915i
\(816\) 3.65413 + 10.4286i 0.127920 + 0.365076i
\(817\) −1.89635 + 1.89635i −0.0663449 + 0.0663449i
\(818\) 32.9694 + 27.8342i 1.15275 + 0.973199i
\(819\) 2.73057 0.0954137
\(820\) 12.0656 + 40.3414i 0.421348 + 1.40878i
\(821\) 1.32813 0.0463522 0.0231761 0.999731i \(-0.492622\pi\)
0.0231761 + 0.999731i \(0.492622\pi\)
\(822\) 14.3895 + 12.1482i 0.501891 + 0.423718i
\(823\) −13.3218 + 13.3218i −0.464370 + 0.464370i −0.900085 0.435715i \(-0.856496\pi\)
0.435715 + 0.900085i \(0.356496\pi\)
\(824\) 12.3196 3.18207i 0.429174 0.110853i
\(825\) −38.5501 23.1702i −1.34214 0.806684i
\(826\) −4.20576 + 0.355203i −0.146337 + 0.0123591i
\(827\) 0.0744113 + 0.0744113i 0.00258753 + 0.00258753i 0.708399 0.705812i \(-0.249418\pi\)
−0.705812 + 0.708399i \(0.749418\pi\)
\(828\) 6.20595 8.75042i 0.215672 0.304098i
\(829\) 27.2990i 0.948132i 0.880489 + 0.474066i \(0.157214\pi\)
−0.880489 + 0.474066i \(0.842786\pi\)
\(830\) −1.97359 9.42753i −0.0685042 0.327234i
\(831\) 26.3282i 0.913317i
\(832\) −10.3282 + 35.9363i −0.358066 + 1.24587i
\(833\) 6.21126 + 6.21126i 0.215207 + 0.215207i
\(834\) 0.950754 + 11.2574i 0.0329219 + 0.389810i
\(835\) −29.3824 22.9592i −1.01682 0.794535i
\(836\) −9.35809 + 1.59205i −0.323656 + 0.0550624i
\(837\) −30.0088 + 30.0088i −1.03726 + 1.03726i
\(838\) −8.92939 + 10.5768i −0.308461 + 0.365370i
\(839\) 35.2499 1.21696 0.608482 0.793568i \(-0.291779\pi\)
0.608482 + 0.793568i \(0.291779\pi\)
\(840\) −10.8452 4.72043i −0.374197 0.162870i
\(841\) 25.0781 0.864763
\(842\) 24.4433 28.9529i 0.842370 0.997783i
\(843\) −13.9606 + 13.9606i −0.480827 + 0.480827i
\(844\) 46.7395 7.95160i 1.60884 0.273705i
\(845\) −2.40907 19.6311i −0.0828745 0.675330i
\(846\) −0.110320 1.30624i −0.00379290 0.0449096i
\(847\) −8.04296 8.04296i −0.276359 0.276359i
\(848\) 0.0229790 + 0.0110541i 0.000789104 + 0.000379598i
\(849\) 26.1125i 0.896179i
\(850\) 3.32495 + 9.75586i 0.114045 + 0.334623i
\(851\) 73.0628i 2.50456i
\(852\) 20.3793 28.7349i 0.698184 0.984443i
\(853\) −2.90863 2.90863i −0.0995897 0.0995897i 0.655556 0.755146i \(-0.272434\pi\)
−0.755146 + 0.655556i \(0.772434\pi\)
\(854\) −1.00784 + 0.0851183i −0.0344875 + 0.00291269i
\(855\) −0.161254 1.31403i −0.00551476 0.0449388i
\(856\) −11.3907 44.0999i −0.389327 1.50730i
\(857\) −1.96804 + 1.96804i −0.0672271 + 0.0672271i −0.739921 0.672694i \(-0.765137\pi\)
0.672694 + 0.739921i \(0.265137\pi\)
\(858\) −45.4329 38.3564i −1.55106 1.30947i
\(859\) −41.5822 −1.41876 −0.709382 0.704824i \(-0.751026\pi\)
−0.709382 + 0.704824i \(0.751026\pi\)
\(860\) 10.5552 + 5.69500i 0.359930 + 0.194198i
\(861\) −17.6085 −0.600095
\(862\) 2.64961 + 2.23692i 0.0902462 + 0.0761896i
\(863\) −0.751986 + 0.751986i −0.0255979 + 0.0255979i −0.719790 0.694192i \(-0.755762\pi\)
0.694192 + 0.719790i \(0.255762\pi\)
\(864\) 23.5590 10.5570i 0.801493 0.359157i
\(865\) 34.9974 + 27.3467i 1.18995 + 0.929816i
\(866\) 41.3846 3.49518i 1.40630 0.118771i
\(867\) −19.9354 19.9354i −0.677041 0.677041i
\(868\) −14.9695 10.6167i −0.508100 0.360353i
\(869\) 1.51461i 0.0513795i
\(870\) 11.6173 2.43200i 0.393863 0.0824525i
\(871\) 66.9260i 2.26770i
\(872\) 14.5146 24.6237i 0.491526 0.833865i
\(873\) 4.90927 + 4.90927i 0.166154 + 0.166154i
\(874\) −1.07824 12.7668i −0.0364719 0.431844i
\(875\) −10.0776 4.48924i −0.340685 0.151764i
\(876\) −4.08723 24.0247i −0.138095 0.811721i
\(877\) 15.6200 15.6200i 0.527449 0.527449i −0.392362 0.919811i \(-0.628342\pi\)
0.919811 + 0.392362i \(0.128342\pi\)
\(878\) −22.7810 + 26.9840i −0.768822 + 0.910665i
\(879\) 48.0349 1.62018
\(880\) 18.8134 + 38.0556i 0.634201 + 1.28285i
\(881\) 23.1977 0.781552 0.390776 0.920486i \(-0.372207\pi\)
0.390776 + 0.920486i \(0.372207\pi\)
\(882\) −3.25501 + 3.85554i −0.109602 + 0.129823i
\(883\) 31.0012 31.0012i 1.04327 1.04327i 0.0442526 0.999020i \(-0.485909\pi\)
0.999020 0.0442526i \(-0.0140907\pi\)
\(884\) 2.28521 + 13.4324i 0.0768598 + 0.451782i
\(885\) −7.89222 + 10.1002i −0.265294 + 0.339514i
\(886\) 2.43790 + 28.8659i 0.0819029 + 0.969767i
\(887\) 15.0265 + 15.0265i 0.504541 + 0.504541i 0.912846 0.408305i \(-0.133880\pi\)
−0.408305 + 0.912846i \(0.633880\pi\)
\(888\) −21.9530 + 37.2430i −0.736696 + 1.24979i
\(889\) 8.02003i 0.268983i
\(890\) −21.5335 14.0784i −0.721805 0.471910i
\(891\) 49.4830i 1.65774i
\(892\) −28.7550 20.3936i −0.962790 0.682828i
\(893\) −1.10706 1.10706i −0.0370465 0.0370465i
\(894\) −18.7981 + 1.58762i −0.628702 + 0.0530978i
\(895\) −19.6783 + 2.41486i −0.657772 + 0.0807198i
\(896\) 6.20923 + 9.27780i 0.207436 + 0.309949i
\(897\) 56.7474 56.7474i 1.89474 1.89474i
\(898\) 36.3747 + 30.7090i 1.21384 + 1.02477i
\(899\) 18.4159 0.614206
\(900\) −5.42345 + 2.37480i −0.180782 + 0.0791598i
\(901\) 0.00929214 0.000309566
\(902\) 48.2905 + 40.7688i 1.60790 + 1.35745i
\(903\) −3.54650 + 3.54650i −0.118020 + 0.118020i
\(904\) −4.34109 16.8068i −0.144383 0.558987i
\(905\) −12.7337 + 1.56264i −0.423282 + 0.0519439i
\(906\) 44.8896 3.79120i 1.49136 0.125954i
\(907\) −31.8884 31.8884i −1.05884 1.05884i −0.998157 0.0606790i \(-0.980673\pi\)
−0.0606790 0.998157i \(-0.519327\pi\)
\(908\) 1.42620 2.01095i 0.0473303 0.0667359i
\(909\) 1.40727i 0.0466763i
\(910\) −12.2070 7.98081i −0.404657 0.264561i
\(911\) 26.4093i 0.874979i 0.899224 + 0.437489i \(0.144132\pi\)
−0.899224 + 0.437489i \(0.855868\pi\)
\(912\) −3.28640 + 6.83173i −0.108824 + 0.226221i
\(913\) −10.2223 10.2223i −0.338310 0.338310i
\(914\) −1.22864 14.5477i −0.0406399 0.481195i
\(915\) −1.89123 + 2.42034i −0.0625223 + 0.0800139i
\(916\) −20.0970 + 3.41902i −0.664022 + 0.112967i
\(917\) 5.66723 5.66723i 0.187148 0.187148i
\(918\) 6.06870 7.18835i 0.200297 0.237251i
\(919\) −0.693031 −0.0228610 −0.0114305 0.999935i \(-0.503639\pi\)
−0.0114305 + 0.999935i \(0.503639\pi\)
\(920\) −53.3191 + 20.9801i −1.75788 + 0.691694i
\(921\) 11.9777 0.394678
\(922\) −0.867738 + 1.02783i −0.0285774 + 0.0338498i
\(923\) 30.7149 30.7149i 1.01099 1.01099i
\(924\) −17.5012 + 2.97742i −0.575749 + 0.0979498i
\(925\) −20.7726 + 34.5610i −0.682999 + 1.13636i
\(926\) 2.21121 + 26.1817i 0.0726648 + 0.860384i
\(927\) 1.88333 + 1.88333i 0.0618567 + 0.0618567i
\(928\) −10.4682 3.98955i −0.343636 0.130963i
\(929\) 39.3217i 1.29010i −0.764139 0.645051i \(-0.776836\pi\)
0.764139 0.645051i \(-0.223164\pi\)
\(930\) −54.5513 + 11.4199i −1.78881 + 0.374474i
\(931\) 6.02631i 0.197504i
\(932\) −8.58318 + 12.1023i −0.281152 + 0.396425i
\(933\) −0.796640 0.796640i −0.0260808 0.0260808i
\(934\) 39.7224 3.35481i 1.29976 0.109773i
\(935\) 12.1896 + 9.52488i 0.398643 + 0.311497i
\(936\) −7.57816 + 1.95739i −0.247700 + 0.0639792i
\(937\) 27.9936 27.9936i 0.914512 0.914512i −0.0821109 0.996623i \(-0.526166\pi\)
0.996623 + 0.0821109i \(0.0261662\pi\)
\(938\) 15.2685 + 12.8903i 0.498534 + 0.420883i
\(939\) −38.2025 −1.24669
\(940\) −3.32466 + 6.16200i −0.108438 + 0.200982i
\(941\) −29.0330 −0.946448 −0.473224 0.880942i \(-0.656910\pi\)
−0.473224 + 0.880942i \(0.656910\pi\)
\(942\) 33.3685 + 28.1711i 1.08721 + 0.917865i
\(943\) −60.3165 + 60.3165i −1.96418 + 1.96418i
\(944\) 11.4177 4.00067i 0.371613 0.130211i
\(945\) 1.22651 + 9.99463i 0.0398984 + 0.325125i
\(946\) 17.9374 1.51492i 0.583194 0.0492543i
\(947\) −3.93345 3.93345i −0.127820 0.127820i 0.640303 0.768123i \(-0.278809\pi\)
−0.768123 + 0.640303i \(0.778809\pi\)
\(948\) 0.986668 + 0.699762i 0.0320455 + 0.0227272i
\(949\) 30.0490i 0.975432i
\(950\) −3.11971 + 6.34566i −0.101217 + 0.205880i
\(951\) 23.3760i 0.758019i
\(952\) 3.50462 + 2.06581i 0.113585 + 0.0669533i
\(953\) −20.9223 20.9223i −0.677740 0.677740i 0.281748 0.959488i \(-0.409086\pi\)
−0.959488 + 0.281748i \(0.909086\pi\)
\(954\) 0.000449202 0.00531876i 1.45435e−5 0.000172201i
\(955\) −0.931869 7.59365i −0.0301546 0.245725i
\(956\) 0.263648 + 1.54972i 0.00852697 + 0.0501215i
\(957\) 12.5967 12.5967i 0.407194 0.407194i
\(958\) −26.9557 + 31.9289i −0.870899 + 1.03157i
\(959\) 6.93290 0.223875
\(960\) 33.4827 + 5.32628i 1.08065 + 0.171905i
\(961\) −55.4756 −1.78954
\(962\) −34.3873 + 40.7316i −1.10869 + 1.31324i
\(963\) 6.74167 6.74167i 0.217247 0.217247i
\(964\) −6.15514 36.1799i −0.198244 1.16528i
\(965\) −35.2482 27.5427i −1.13468 0.886630i
\(966\) −2.01649 23.8762i −0.0648795 0.768203i
\(967\) 30.9050 + 30.9050i 0.993839 + 0.993839i 0.999981 0.00614252i \(-0.00195524\pi\)
−0.00614252 + 0.999981i \(0.501955\pi\)
\(968\) 28.0872 + 16.5561i 0.902757 + 0.532134i
\(969\) 2.76258i 0.0887468i
\(970\) −7.59820 36.2955i −0.243964 1.16538i
\(971\) 5.36484i 0.172166i 0.996288 + 0.0860829i \(0.0274350\pi\)
−0.996288 + 0.0860829i \(0.972565\pi\)
\(972\) 9.89968 + 7.02103i 0.317532 + 0.225200i
\(973\) 2.94095 + 2.94095i 0.0942826 + 0.0942826i
\(974\) 57.3861 4.84661i 1.83877 0.155295i
\(975\) −42.9772 + 10.7093i −1.37637 + 0.342973i
\(976\) 2.73604 0.958692i 0.0875787 0.0306870i
\(977\) −21.3158 + 21.3158i −0.681953 + 0.681953i −0.960440 0.278487i \(-0.910167\pi\)
0.278487 + 0.960440i \(0.410167\pi\)
\(978\) 24.6195 + 20.7848i 0.787244 + 0.664625i
\(979\) −38.6142 −1.23412
\(980\) 25.8204 7.72254i 0.824801 0.246687i
\(981\) 5.98318 0.191028
\(982\) −3.08111 2.60120i −0.0983222 0.0830077i
\(983\) 0.756505 0.756505i 0.0241288 0.0241288i −0.694939 0.719068i \(-0.744569\pi\)
0.719068 + 0.694939i \(0.244569\pi\)
\(984\) 48.8689 12.6225i 1.55788 0.402391i
\(985\) 7.67700 9.82476i 0.244610 0.313043i
\(986\) −4.06782 + 0.343553i −0.129546 + 0.0109409i
\(987\) −2.07040 2.07040i −0.0659015 0.0659015i
\(988\) −5.40766 + 7.62482i −0.172040 + 0.242578i
\(989\) 24.2966i 0.772586i
\(990\) −4.86270 + 7.43771i −0.154547 + 0.236386i
\(991\) 11.1144i 0.353061i 0.984295 + 0.176530i \(0.0564874\pi\)
−0.984295 + 0.176530i \(0.943513\pi\)
\(992\) 49.1556 + 18.7337i 1.56069 + 0.594795i
\(993\) 16.7754 + 16.7754i 0.532352 + 0.532352i
\(994\) −1.09144 12.9231i −0.0346184 0.409897i
\(995\) −50.2684 + 6.16878i −1.59361 + 0.195564i
\(996\) −11.3820 + 1.93637i −0.360652 + 0.0613563i
\(997\) −34.7183 + 34.7183i −1.09954 + 1.09954i −0.105075 + 0.994464i \(0.533508\pi\)
−0.994464 + 0.105075i \(0.966492\pi\)
\(998\) −11.1525 + 13.2101i −0.353027 + 0.418159i
\(999\) 36.8046 1.16445
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 380.2.k.d.343.19 yes 52
4.3 odd 2 380.2.k.c.343.20 yes 52
5.2 odd 4 380.2.k.c.267.20 52
20.7 even 4 inner 380.2.k.d.267.19 yes 52
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
380.2.k.c.267.20 52 5.2 odd 4
380.2.k.c.343.20 yes 52 4.3 odd 2
380.2.k.d.267.19 yes 52 20.7 even 4 inner
380.2.k.d.343.19 yes 52 1.1 even 1 trivial