Properties

Label 624.2.bn.a.187.5
Level $624$
Weight $2$
Character 624.187
Analytic conductor $4.983$
Analytic rank $0$
Dimension $112$
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] = [624,2,Mod(187,624)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(624, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 1, 0, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("624.187");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 624.bn (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: \(4.98266508613\)
Analytic rank: \(0\)
Dimension: \(112\)
Relative dimension: \(56\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 187.5
Character \(\chi\) \(=\) 624.187
Dual form 624.2.bn.a.307.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.33764 - 0.459045i) q^{2} +(-0.707107 - 0.707107i) q^{3} +(1.57856 + 1.22807i) q^{4} -2.59977 q^{5} +(0.621260 + 1.27045i) q^{6} +(0.312171 + 0.312171i) q^{7} +(-1.54780 - 2.36735i) q^{8} +1.00000i q^{9} +O(q^{10})\) \(q+(-1.33764 - 0.459045i) q^{2} +(-0.707107 - 0.707107i) q^{3} +(1.57856 + 1.22807i) q^{4} -2.59977 q^{5} +(0.621260 + 1.27045i) q^{6} +(0.312171 + 0.312171i) q^{7} +(-1.54780 - 2.36735i) q^{8} +1.00000i q^{9} +(3.47756 + 1.19341i) q^{10} +3.08083 q^{11} +(-0.247828 - 1.98459i) q^{12} +(3.18261 + 1.69440i) q^{13} +(-0.274271 - 0.560872i) q^{14} +(1.83832 + 1.83832i) q^{15} +(0.983672 + 3.87716i) q^{16} -6.87394i q^{17} +(0.459045 - 1.33764i) q^{18} -5.01779 q^{19} +(-4.10389 - 3.19271i) q^{20} -0.441476i q^{21} +(-4.12103 - 1.41424i) q^{22} -1.76637i q^{23} +(-0.579510 + 2.76842i) q^{24} +1.75882 q^{25} +(-3.47937 - 3.72746i) q^{26} +(0.707107 - 0.707107i) q^{27} +(0.109410 + 0.876147i) q^{28} +(-5.32160 + 5.32160i) q^{29} +(-1.61513 - 3.30288i) q^{30} +(-1.73409 - 1.73409i) q^{31} +(0.463995 - 5.63779i) q^{32} +(-2.17847 - 2.17847i) q^{33} +(-3.15545 + 9.19485i) q^{34} +(-0.811573 - 0.811573i) q^{35} +(-1.22807 + 1.57856i) q^{36} -6.43566i q^{37} +(6.71199 + 2.30339i) q^{38} +(-1.05232 - 3.44857i) q^{39} +(4.02392 + 6.15457i) q^{40} +(-7.29029 - 7.29029i) q^{41} +(-0.202657 + 0.590536i) q^{42} +(1.90101 + 1.90101i) q^{43} +(4.86325 + 3.78348i) q^{44} -2.59977i q^{45} +(-0.810845 + 2.36277i) q^{46} +(1.14377 - 1.14377i) q^{47} +(2.04601 - 3.43713i) q^{48} -6.80510i q^{49} +(-2.35267 - 0.807380i) q^{50} +(-4.86061 + 4.86061i) q^{51} +(2.94307 + 6.58318i) q^{52} +(4.08570 + 4.08570i) q^{53} +(-1.27045 + 0.621260i) q^{54} -8.00945 q^{55} +(0.255840 - 1.22219i) q^{56} +(3.54811 + 3.54811i) q^{57} +(9.56123 - 4.67552i) q^{58} -13.7329 q^{59} +(0.644297 + 5.15947i) q^{60} +(5.28947 - 5.28947i) q^{61} +(1.52356 + 3.11562i) q^{62} +(-0.312171 + 0.312171i) q^{63} +(-3.20866 + 7.32834i) q^{64} +(-8.27406 - 4.40506i) q^{65} +(1.91399 + 3.91403i) q^{66} -15.7618 q^{67} +(8.44170 - 10.8509i) q^{68} +(-1.24901 + 1.24901i) q^{69} +(0.713043 + 1.45814i) q^{70} +(-11.1059 + 11.1059i) q^{71} +(2.36735 - 1.54780i) q^{72} +(0.621805 - 0.621805i) q^{73} +(-2.95426 + 8.60858i) q^{74} +(-1.24368 - 1.24368i) q^{75} +(-7.92085 - 6.16221i) q^{76} +(0.961744 + 0.961744i) q^{77} +(-0.175424 + 5.09600i) q^{78} -16.7040i q^{79} +(-2.55733 - 10.0797i) q^{80} -1.00000 q^{81} +(6.40520 + 13.0983i) q^{82} -7.48177 q^{83} +(0.542165 - 0.696894i) q^{84} +17.8707i q^{85} +(-1.67021 - 3.41551i) q^{86} +7.52588 q^{87} +(-4.76849 - 7.29338i) q^{88} +(11.0906 - 11.0906i) q^{89} +(-1.19341 + 3.47756i) q^{90} +(0.464574 + 1.52246i) q^{91} +(2.16924 - 2.78832i) q^{92} +2.45238i q^{93} +(-2.05499 + 1.00491i) q^{94} +13.0451 q^{95} +(-4.31462 + 3.65843i) q^{96} +(7.33233 - 7.33233i) q^{97} +(-3.12385 + 9.10276i) q^{98} +3.08083i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 112 q+O(q^{10}) \) Copy content Toggle raw display \( 112 q - 8 q^{10} + 32 q^{14} + 4 q^{20} - 8 q^{22} + 12 q^{24} + 112 q^{25} - 16 q^{26} - 8 q^{28} + 60 q^{32} - 24 q^{34} - 40 q^{38} + 40 q^{40} - 16 q^{43} - 4 q^{44} - 56 q^{46} - 56 q^{50} + 56 q^{52} + 32 q^{55} + 40 q^{56} + 40 q^{58} - 64 q^{59} + 44 q^{60} - 72 q^{64} + 24 q^{68} - 64 q^{70} - 64 q^{71} - 16 q^{73} - 16 q^{75} - 16 q^{76} + 24 q^{78} + 4 q^{80} - 112 q^{81} - 72 q^{82} + 80 q^{83} + 16 q^{86} - 16 q^{89} + 56 q^{91} - 24 q^{92} - 88 q^{94} + 40 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/624\mathbb{Z}\right)^\times\).

\(n\) \(79\) \(145\) \(209\) \(469\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{4}\right)\) \(1\) \(e\left(\frac{1}{4}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.33764 0.459045i −0.945853 0.324594i
\(3\) −0.707107 0.707107i −0.408248 0.408248i
\(4\) 1.57856 + 1.22807i 0.789278 + 0.614037i
\(5\) −2.59977 −1.16265 −0.581327 0.813670i \(-0.697466\pi\)
−0.581327 + 0.813670i \(0.697466\pi\)
\(6\) 0.621260 + 1.27045i 0.253628 + 0.518658i
\(7\) 0.312171 + 0.312171i 0.117989 + 0.117989i 0.763636 0.645647i \(-0.223412\pi\)
−0.645647 + 0.763636i \(0.723412\pi\)
\(8\) −1.54780 2.36735i −0.547228 0.836983i
\(9\) 1.00000i 0.333333i
\(10\) 3.47756 + 1.19341i 1.09970 + 0.377391i
\(11\) 3.08083 0.928904 0.464452 0.885598i \(-0.346251\pi\)
0.464452 + 0.885598i \(0.346251\pi\)
\(12\) −0.247828 1.98459i −0.0715418 0.572901i
\(13\) 3.18261 + 1.69440i 0.882697 + 0.469943i
\(14\) −0.274271 0.560872i −0.0733021 0.149899i
\(15\) 1.83832 + 1.83832i 0.474652 + 0.474652i
\(16\) 0.983672 + 3.87716i 0.245918 + 0.969291i
\(17\) 6.87394i 1.66718i −0.552387 0.833588i \(-0.686283\pi\)
0.552387 0.833588i \(-0.313717\pi\)
\(18\) 0.459045 1.33764i 0.108198 0.315284i
\(19\) −5.01779 −1.15116 −0.575580 0.817746i \(-0.695224\pi\)
−0.575580 + 0.817746i \(0.695224\pi\)
\(20\) −4.10389 3.19271i −0.917657 0.713912i
\(21\) 0.441476i 0.0963380i
\(22\) −4.12103 1.41424i −0.878607 0.301517i
\(23\) 1.76637i 0.368314i −0.982897 0.184157i \(-0.941044\pi\)
0.982897 0.184157i \(-0.0589555\pi\)
\(24\) −0.579510 + 2.76842i −0.118292 + 0.565102i
\(25\) 1.75882 0.351765
\(26\) −3.47937 3.72746i −0.682361 0.731015i
\(27\) 0.707107 0.707107i 0.136083 0.136083i
\(28\) 0.109410 + 0.876147i 0.0206766 + 0.165576i
\(29\) −5.32160 + 5.32160i −0.988196 + 0.988196i −0.999931 0.0117353i \(-0.996264\pi\)
0.0117353 + 0.999931i \(0.496264\pi\)
\(30\) −1.61513 3.30288i −0.294882 0.603020i
\(31\) −1.73409 1.73409i −0.311453 0.311453i 0.534020 0.845472i \(-0.320681\pi\)
−0.845472 + 0.534020i \(0.820681\pi\)
\(32\) 0.463995 5.63779i 0.0820234 0.996630i
\(33\) −2.17847 2.17847i −0.379224 0.379224i
\(34\) −3.15545 + 9.19485i −0.541155 + 1.57690i
\(35\) −0.811573 0.811573i −0.137181 0.137181i
\(36\) −1.22807 + 1.57856i −0.204679 + 0.263093i
\(37\) 6.43566i 1.05802i −0.848617 0.529008i \(-0.822564\pi\)
0.848617 0.529008i \(-0.177436\pi\)
\(38\) 6.71199 + 2.30339i 1.08883 + 0.373659i
\(39\) −1.05232 3.44857i −0.168506 0.552213i
\(40\) 4.02392 + 6.15457i 0.636237 + 0.973122i
\(41\) −7.29029 7.29029i −1.13855 1.13855i −0.988710 0.149842i \(-0.952124\pi\)
−0.149842 0.988710i \(-0.547876\pi\)
\(42\) −0.202657 + 0.590536i −0.0312707 + 0.0911216i
\(43\) 1.90101 + 1.90101i 0.289901 + 0.289901i 0.837041 0.547140i \(-0.184284\pi\)
−0.547140 + 0.837041i \(0.684284\pi\)
\(44\) 4.86325 + 3.78348i 0.733163 + 0.570381i
\(45\) 2.59977i 0.387551i
\(46\) −0.810845 + 2.36277i −0.119553 + 0.348371i
\(47\) 1.14377 1.14377i 0.166836 0.166836i −0.618751 0.785587i \(-0.712361\pi\)
0.785587 + 0.618751i \(0.212361\pi\)
\(48\) 2.04601 3.43713i 0.295316 0.496107i
\(49\) 6.80510i 0.972157i
\(50\) −2.35267 0.807380i −0.332718 0.114181i
\(51\) −4.86061 + 4.86061i −0.680622 + 0.680622i
\(52\) 2.94307 + 6.58318i 0.408131 + 0.912923i
\(53\) 4.08570 + 4.08570i 0.561214 + 0.561214i 0.929652 0.368438i \(-0.120107\pi\)
−0.368438 + 0.929652i \(0.620107\pi\)
\(54\) −1.27045 + 0.621260i −0.172886 + 0.0845427i
\(55\) −8.00945 −1.07999
\(56\) 0.255840 1.22219i 0.0341880 0.163322i
\(57\) 3.54811 + 3.54811i 0.469959 + 0.469959i
\(58\) 9.56123 4.67552i 1.25545 0.613926i
\(59\) −13.7329 −1.78788 −0.893938 0.448192i \(-0.852068\pi\)
−0.893938 + 0.448192i \(0.852068\pi\)
\(60\) 0.644297 + 5.15947i 0.0831784 + 0.666085i
\(61\) 5.28947 5.28947i 0.677248 0.677248i −0.282129 0.959377i \(-0.591041\pi\)
0.959377 + 0.282129i \(0.0910406\pi\)
\(62\) 1.52356 + 3.11562i 0.193493 + 0.395684i
\(63\) −0.312171 + 0.312171i −0.0393298 + 0.0393298i
\(64\) −3.20866 + 7.32834i −0.401082 + 0.916042i
\(65\) −8.27406 4.40506i −1.02627 0.546381i
\(66\) 1.91399 + 3.91403i 0.235596 + 0.481784i
\(67\) −15.7618 −1.92561 −0.962804 0.270200i \(-0.912910\pi\)
−0.962804 + 0.270200i \(0.912910\pi\)
\(68\) 8.44170 10.8509i 1.02371 1.31586i
\(69\) −1.24901 + 1.24901i −0.150364 + 0.150364i
\(70\) 0.713043 + 1.45814i 0.0852250 + 0.174281i
\(71\) −11.1059 + 11.1059i −1.31802 + 1.31802i −0.402684 + 0.915339i \(0.631923\pi\)
−0.915339 + 0.402684i \(0.868077\pi\)
\(72\) 2.36735 1.54780i 0.278994 0.182409i
\(73\) 0.621805 0.621805i 0.0727768 0.0727768i −0.669781 0.742558i \(-0.733612\pi\)
0.742558 + 0.669781i \(0.233612\pi\)
\(74\) −2.95426 + 8.60858i −0.343425 + 1.00073i
\(75\) −1.24368 1.24368i −0.143607 0.143607i
\(76\) −7.92085 6.16221i −0.908584 0.706854i
\(77\) 0.961744 + 0.961744i 0.109601 + 0.109601i
\(78\) −0.175424 + 5.09600i −0.0198628 + 0.577008i
\(79\) 16.7040i 1.87935i −0.342066 0.939676i \(-0.611127\pi\)
0.342066 0.939676i \(-0.388873\pi\)
\(80\) −2.55733 10.0797i −0.285918 1.12695i
\(81\) −1.00000 −0.111111
\(82\) 6.40520 + 13.0983i 0.707336 + 1.44647i
\(83\) −7.48177 −0.821231 −0.410615 0.911809i \(-0.634686\pi\)
−0.410615 + 0.911809i \(0.634686\pi\)
\(84\) 0.542165 0.696894i 0.0591551 0.0760374i
\(85\) 17.8707i 1.93835i
\(86\) −1.67021 3.41551i −0.180104 0.368304i
\(87\) 7.52588 0.806859
\(88\) −4.76849 7.29338i −0.508323 0.777477i
\(89\) 11.0906 11.0906i 1.17560 1.17560i 0.194745 0.980854i \(-0.437612\pi\)
0.980854 0.194745i \(-0.0623881\pi\)
\(90\) −1.19341 + 3.47756i −0.125797 + 0.366567i
\(91\) 0.464574 + 1.52246i 0.0487006 + 0.159597i
\(92\) 2.16924 2.78832i 0.226158 0.290702i
\(93\) 2.45238i 0.254300i
\(94\) −2.05499 + 1.00491i −0.211956 + 0.103648i
\(95\) 13.0451 1.33840
\(96\) −4.31462 + 3.65843i −0.440359 + 0.373387i
\(97\) 7.33233 7.33233i 0.744486 0.744486i −0.228952 0.973438i \(-0.573530\pi\)
0.973438 + 0.228952i \(0.0735299\pi\)
\(98\) −3.12385 + 9.10276i −0.315556 + 0.919518i
\(99\) 3.08083i 0.309635i
\(100\) 2.77640 + 2.15997i 0.277640 + 0.215997i
\(101\) 4.68560 4.68560i 0.466234 0.466234i −0.434458 0.900692i \(-0.643060\pi\)
0.900692 + 0.434458i \(0.143060\pi\)
\(102\) 8.73298 4.27050i 0.864694 0.422843i
\(103\) 0.250872i 0.0247192i 0.999924 + 0.0123596i \(0.00393428\pi\)
−0.999924 + 0.0123596i \(0.996066\pi\)
\(104\) −0.914789 10.1569i −0.0897024 0.995969i
\(105\) 1.14774i 0.112008i
\(106\) −3.58967 7.34072i −0.348660 0.712993i
\(107\) 1.84416 1.84416i 0.178282 0.178282i −0.612325 0.790606i \(-0.709766\pi\)
0.790606 + 0.612325i \(0.209766\pi\)
\(108\) 1.98459 0.247828i 0.190967 0.0238473i
\(109\) 0.584695i 0.0560036i 0.999608 + 0.0280018i \(0.00891442\pi\)
−0.999608 + 0.0280018i \(0.991086\pi\)
\(110\) 10.7138 + 3.67670i 1.02152 + 0.350560i
\(111\) −4.55070 + 4.55070i −0.431933 + 0.431933i
\(112\) −0.903263 + 1.51741i −0.0853503 + 0.143382i
\(113\) 9.43859 0.887908 0.443954 0.896050i \(-0.353575\pi\)
0.443954 + 0.896050i \(0.353575\pi\)
\(114\) −3.11735 6.37483i −0.291966 0.597058i
\(115\) 4.59217i 0.428222i
\(116\) −14.9357 + 1.86512i −1.38675 + 0.173172i
\(117\) −1.69440 + 3.18261i −0.156648 + 0.294232i
\(118\) 18.3697 + 6.30403i 1.69107 + 0.580333i
\(119\) 2.14584 2.14584i 0.196709 0.196709i
\(120\) 1.50660 7.19727i 0.137533 0.657018i
\(121\) −1.50851 −0.137137
\(122\) −9.50351 + 4.64730i −0.860408 + 0.420747i
\(123\) 10.3100i 0.929624i
\(124\) −0.607769 4.86696i −0.0545792 0.437066i
\(125\) 8.42632 0.753673
\(126\) 0.560872 0.274271i 0.0499665 0.0244340i
\(127\) −5.82313 −0.516719 −0.258360 0.966049i \(-0.583182\pi\)
−0.258360 + 0.966049i \(0.583182\pi\)
\(128\) 7.65606 8.32975i 0.676707 0.736253i
\(129\) 2.68843i 0.236703i
\(130\) 9.04559 + 9.69055i 0.793350 + 0.849918i
\(131\) 6.85011 + 6.85011i 0.598497 + 0.598497i 0.939912 0.341415i \(-0.110906\pi\)
−0.341415 + 0.939912i \(0.610906\pi\)
\(132\) −0.763515 6.11417i −0.0664555 0.532170i
\(133\) −1.56641 1.56641i −0.135825 0.135825i
\(134\) 21.0836 + 7.23537i 1.82134 + 0.625041i
\(135\) −1.83832 + 1.83832i −0.158217 + 0.158217i
\(136\) −16.2730 + 10.6395i −1.39540 + 0.912326i
\(137\) −0.237416 + 0.237416i −0.0202838 + 0.0202838i −0.717176 0.696892i \(-0.754566\pi\)
0.696892 + 0.717176i \(0.254566\pi\)
\(138\) 2.24408 1.09738i 0.191029 0.0934148i
\(139\) 2.78720 2.78720i 0.236407 0.236407i −0.578953 0.815361i \(-0.696539\pi\)
0.815361 + 0.578953i \(0.196539\pi\)
\(140\) −0.284442 2.27778i −0.0240397 0.192508i
\(141\) −1.61753 −0.136221
\(142\) 19.9537 9.75754i 1.67448 0.818834i
\(143\) 9.80507 + 5.22016i 0.819941 + 0.436532i
\(144\) −3.87716 + 0.983672i −0.323097 + 0.0819727i
\(145\) 13.8350 13.8350i 1.14893 1.14893i
\(146\) −1.11719 + 0.546314i −0.0924591 + 0.0452133i
\(147\) −4.81193 + 4.81193i −0.396881 + 0.396881i
\(148\) 7.90346 10.1590i 0.649660 0.835068i
\(149\) −15.1865 −1.24413 −0.622064 0.782966i \(-0.713706\pi\)
−0.622064 + 0.782966i \(0.713706\pi\)
\(150\) 1.09269 + 2.23449i 0.0892175 + 0.182446i
\(151\) 12.1513 + 12.1513i 0.988862 + 0.988862i 0.999939 0.0110764i \(-0.00352578\pi\)
−0.0110764 + 0.999939i \(0.503526\pi\)
\(152\) 7.76651 + 11.8788i 0.629947 + 0.963501i
\(153\) 6.87394 0.555725
\(154\) −0.844982 1.72795i −0.0680906 0.139242i
\(155\) 4.50825 + 4.50825i 0.362112 + 0.362112i
\(156\) 2.57395 6.73608i 0.206081 0.539318i
\(157\) 4.75195 4.75195i 0.379247 0.379247i −0.491583 0.870831i \(-0.663582\pi\)
0.870831 + 0.491583i \(0.163582\pi\)
\(158\) −7.66791 + 22.3440i −0.610026 + 1.77759i
\(159\) 5.77806i 0.458230i
\(160\) −1.20628 + 14.6570i −0.0953649 + 1.15874i
\(161\) 0.551410 0.551410i 0.0434572 0.0434572i
\(162\) 1.33764 + 0.459045i 0.105095 + 0.0360660i
\(163\) 7.87339i 0.616692i −0.951274 0.308346i \(-0.900225\pi\)
0.951274 0.308346i \(-0.0997754\pi\)
\(164\) −2.55511 20.4611i −0.199521 1.59775i
\(165\) 5.66354 + 5.66354i 0.440906 + 0.440906i
\(166\) 10.0079 + 3.43447i 0.776764 + 0.266567i
\(167\) −1.90835 1.90835i −0.147672 0.147672i 0.629405 0.777077i \(-0.283299\pi\)
−0.777077 + 0.629405i \(0.783299\pi\)
\(168\) −1.04513 + 0.683315i −0.0806333 + 0.0527189i
\(169\) 7.25800 + 10.7852i 0.558308 + 0.829634i
\(170\) 8.20345 23.9045i 0.629176 1.83339i
\(171\) 5.01779i 0.383720i
\(172\) 0.666268 + 5.33542i 0.0508025 + 0.406822i
\(173\) −0.0223126 0.0223126i −0.00169639 0.00169639i 0.706258 0.707954i \(-0.250382\pi\)
−0.707954 + 0.706258i \(0.750382\pi\)
\(174\) −10.0669 3.45472i −0.763170 0.261901i
\(175\) 0.549054 + 0.549054i 0.0415045 + 0.0415045i
\(176\) 3.03052 + 11.9449i 0.228434 + 0.900378i
\(177\) 9.71065 + 9.71065i 0.729897 + 0.729897i
\(178\) −19.9263 + 9.74411i −1.49354 + 0.730352i
\(179\) 3.42532 3.42532i 0.256021 0.256021i −0.567413 0.823434i \(-0.692056\pi\)
0.823434 + 0.567413i \(0.192056\pi\)
\(180\) 3.19271 4.10389i 0.237971 0.305886i
\(181\) −4.71779 + 4.71779i −0.350671 + 0.350671i −0.860359 0.509688i \(-0.829761\pi\)
0.509688 + 0.860359i \(0.329761\pi\)
\(182\) 0.0774453 2.24976i 0.00574063 0.166764i
\(183\) −7.48044 −0.552970
\(184\) −4.18162 + 2.73398i −0.308273 + 0.201552i
\(185\) 16.7312i 1.23011i
\(186\) 1.12575 3.28040i 0.0825442 0.240530i
\(187\) 21.1774i 1.54865i
\(188\) 3.21014 0.400870i 0.234123 0.0292365i
\(189\) 0.441476 0.0321127
\(190\) −17.4496 5.98830i −1.26593 0.434437i
\(191\) 2.24769i 0.162637i 0.996688 + 0.0813185i \(0.0259131\pi\)
−0.996688 + 0.0813185i \(0.974087\pi\)
\(192\) 7.45078 2.91305i 0.537714 0.210231i
\(193\) −6.35227 6.35227i −0.457246 0.457246i 0.440504 0.897751i \(-0.354800\pi\)
−0.897751 + 0.440504i \(0.854800\pi\)
\(194\) −13.1739 + 6.44214i −0.945830 + 0.462519i
\(195\) 2.73580 + 8.96550i 0.195914 + 0.642033i
\(196\) 8.35716 10.7422i 0.596940 0.767302i
\(197\) 5.77122 0.411182 0.205591 0.978638i \(-0.434088\pi\)
0.205591 + 0.978638i \(0.434088\pi\)
\(198\) 1.41424 4.12103i 0.100506 0.292869i
\(199\) 11.5493i 0.818709i 0.912375 + 0.409355i \(0.134246\pi\)
−0.912375 + 0.409355i \(0.865754\pi\)
\(200\) −2.72230 4.16375i −0.192496 0.294421i
\(201\) 11.1453 + 11.1453i 0.786126 + 0.786126i
\(202\) −8.41854 + 4.11674i −0.592326 + 0.289653i
\(203\) −3.32249 −0.233193
\(204\) −13.6419 + 1.70356i −0.955126 + 0.119273i
\(205\) 18.9531 + 18.9531i 1.32374 + 1.32374i
\(206\) 0.115162 0.335576i 0.00802369 0.0233807i
\(207\) 1.76637 0.122771
\(208\) −3.43883 + 14.0062i −0.238440 + 0.971157i
\(209\) −15.4589 −1.06932
\(210\) 0.526864 1.53526i 0.0363570 0.105943i
\(211\) 1.67957 + 1.67957i 0.115627 + 0.115627i 0.762553 0.646926i \(-0.223946\pi\)
−0.646926 + 0.762553i \(0.723946\pi\)
\(212\) 1.43196 + 11.4670i 0.0983477 + 0.787560i
\(213\) 15.7061 1.07616
\(214\) −3.31337 + 1.62027i −0.226497 + 0.110759i
\(215\) −4.94219 4.94219i −0.337054 0.337054i
\(216\) −2.76842 0.579510i −0.188367 0.0394307i
\(217\) 1.08267i 0.0734962i
\(218\) 0.268402 0.782111i 0.0181784 0.0529712i
\(219\) −0.879366 −0.0594220
\(220\) −12.6434 9.83620i −0.852415 0.663156i
\(221\) 11.6472 21.8771i 0.783477 1.47161i
\(222\) 8.17616 3.99821i 0.548748 0.268342i
\(223\) 3.12370 + 3.12370i 0.209179 + 0.209179i 0.803918 0.594740i \(-0.202745\pi\)
−0.594740 + 0.803918i \(0.702745\pi\)
\(224\) 1.90480 1.61511i 0.127270 0.107914i
\(225\) 1.75882i 0.117255i
\(226\) −12.6254 4.33274i −0.839831 0.288210i
\(227\) 16.0224 1.06344 0.531721 0.846919i \(-0.321545\pi\)
0.531721 + 0.846919i \(0.321545\pi\)
\(228\) 1.24355 + 9.95823i 0.0823560 + 0.659500i
\(229\) 6.51126i 0.430276i −0.976584 0.215138i \(-0.930980\pi\)
0.976584 0.215138i \(-0.0690202\pi\)
\(230\) 2.10801 6.14266i 0.138998 0.405035i
\(231\) 1.36011i 0.0894888i
\(232\) 20.8348 + 4.36132i 1.36787 + 0.286335i
\(233\) −13.2251 −0.866405 −0.433202 0.901297i \(-0.642617\pi\)
−0.433202 + 0.901297i \(0.642617\pi\)
\(234\) 3.72746 3.47937i 0.243672 0.227454i
\(235\) −2.97354 + 2.97354i −0.193973 + 0.193973i
\(236\) −21.6782 16.8650i −1.41113 1.09782i
\(237\) −11.8115 + 11.8115i −0.767242 + 0.767242i
\(238\) −3.85540 + 1.88532i −0.249909 + 0.122207i
\(239\) 1.81466 + 1.81466i 0.117381 + 0.117381i 0.763357 0.645977i \(-0.223550\pi\)
−0.645977 + 0.763357i \(0.723550\pi\)
\(240\) −5.31915 + 8.93576i −0.343350 + 0.576801i
\(241\) −12.3236 12.3236i −0.793834 0.793834i 0.188281 0.982115i \(-0.439708\pi\)
−0.982115 + 0.188281i \(0.939708\pi\)
\(242\) 2.01784 + 0.692472i 0.129711 + 0.0445138i
\(243\) 0.707107 + 0.707107i 0.0453609 + 0.0453609i
\(244\) 14.8456 1.85386i 0.950391 0.118681i
\(245\) 17.6917i 1.13028i
\(246\) 4.73277 13.7911i 0.301750 0.879288i
\(247\) −15.9697 8.50215i −1.01612 0.540979i
\(248\) −1.42118 + 6.78923i −0.0902450 + 0.431116i
\(249\) 5.29041 + 5.29041i 0.335266 + 0.335266i
\(250\) −11.2714 3.86806i −0.712865 0.244638i
\(251\) −8.97239 8.97239i −0.566332 0.566332i 0.364767 0.931099i \(-0.381149\pi\)
−0.931099 + 0.364767i \(0.881149\pi\)
\(252\) −0.876147 + 0.109410i −0.0551921 + 0.00689219i
\(253\) 5.44189i 0.342129i
\(254\) 7.78925 + 2.67308i 0.488741 + 0.167724i
\(255\) 12.6365 12.6365i 0.791328 0.791328i
\(256\) −14.0648 + 7.62771i −0.879049 + 0.476732i
\(257\) 1.97467i 0.123176i −0.998102 0.0615881i \(-0.980383\pi\)
0.998102 0.0615881i \(-0.0196165\pi\)
\(258\) −1.23411 + 3.59615i −0.0768324 + 0.223886i
\(259\) 2.00902 2.00902i 0.124835 0.124835i
\(260\) −7.65132 17.1148i −0.474515 1.06141i
\(261\) −5.32160 5.32160i −0.329399 0.329399i
\(262\) −6.01846 12.3075i −0.371822 0.760359i
\(263\) 20.1922 1.24510 0.622551 0.782579i \(-0.286096\pi\)
0.622551 + 0.782579i \(0.286096\pi\)
\(264\) −1.78537 + 8.52903i −0.109882 + 0.524926i
\(265\) −10.6219 10.6219i −0.652498 0.652498i
\(266\) 1.37623 + 2.81434i 0.0843824 + 0.172558i
\(267\) −15.6845 −0.959873
\(268\) −24.8808 19.3566i −1.51984 1.18239i
\(269\) −18.9916 + 18.9916i −1.15794 + 1.15794i −0.173020 + 0.984918i \(0.555353\pi\)
−0.984918 + 0.173020i \(0.944647\pi\)
\(270\) 3.30288 1.61513i 0.201007 0.0982939i
\(271\) −5.60706 + 5.60706i −0.340605 + 0.340605i −0.856595 0.515990i \(-0.827424\pi\)
0.515990 + 0.856595i \(0.327424\pi\)
\(272\) 26.6514 6.76170i 1.61598 0.409989i
\(273\) 0.748038 1.40505i 0.0452733 0.0850372i
\(274\) 0.426562 0.208592i 0.0257696 0.0126015i
\(275\) 5.41863 0.326756
\(276\) −3.50552 + 0.437757i −0.211007 + 0.0263499i
\(277\) 7.97084 7.97084i 0.478922 0.478922i −0.425865 0.904787i \(-0.640030\pi\)
0.904787 + 0.425865i \(0.140030\pi\)
\(278\) −5.00772 + 2.44882i −0.300343 + 0.146870i
\(279\) 1.73409 1.73409i 0.103818 0.103818i
\(280\) −0.665126 + 3.17742i −0.0397489 + 0.189887i
\(281\) −8.08671 + 8.08671i −0.482413 + 0.482413i −0.905901 0.423489i \(-0.860805\pi\)
0.423489 + 0.905901i \(0.360805\pi\)
\(282\) 2.16368 + 0.742521i 0.128845 + 0.0442165i
\(283\) −22.7352 22.7352i −1.35147 1.35147i −0.884022 0.467445i \(-0.845174\pi\)
−0.467445 0.884022i \(-0.654826\pi\)
\(284\) −31.1700 + 3.89240i −1.84960 + 0.230972i
\(285\) −9.22429 9.22429i −0.546400 0.546400i
\(286\) −10.7193 11.4837i −0.633848 0.679043i
\(287\) 4.55163i 0.268674i
\(288\) 5.63779 + 0.463995i 0.332210 + 0.0273411i
\(289\) −30.2511 −1.77947
\(290\) −24.8570 + 12.1553i −1.45966 + 0.713784i
\(291\) −10.3695 −0.607870
\(292\) 1.74518 0.217932i 0.102129 0.0127535i
\(293\) 7.84277i 0.458180i 0.973405 + 0.229090i \(0.0735750\pi\)
−0.973405 + 0.229090i \(0.926425\pi\)
\(294\) 8.64552 4.22773i 0.504217 0.246566i
\(295\) 35.7025 2.07868
\(296\) −15.2354 + 9.96108i −0.885541 + 0.578976i
\(297\) 2.17847 2.17847i 0.126408 0.126408i
\(298\) 20.3141 + 6.97130i 1.17676 + 0.403837i
\(299\) 2.99295 5.62167i 0.173087 0.325110i
\(300\) −0.435886 3.49054i −0.0251659 0.201526i
\(301\) 1.18688i 0.0684105i
\(302\) −10.6761 21.8321i −0.614340 1.25630i
\(303\) −6.62644 −0.380679
\(304\) −4.93586 19.4548i −0.283091 1.11581i
\(305\) −13.7514 + 13.7514i −0.787405 + 0.787405i
\(306\) −9.19485 3.15545i −0.525635 0.180385i
\(307\) 19.3002i 1.10152i 0.834664 + 0.550760i \(0.185662\pi\)
−0.834664 + 0.550760i \(0.814338\pi\)
\(308\) 0.337074 + 2.69926i 0.0192066 + 0.153805i
\(309\) 0.177393 0.177393i 0.0100916 0.0100916i
\(310\) −3.96092 8.09991i −0.224965 0.460044i
\(311\) 25.4700i 1.44427i 0.691750 + 0.722137i \(0.256840\pi\)
−0.691750 + 0.722137i \(0.743160\pi\)
\(312\) −6.53518 + 7.82889i −0.369982 + 0.443223i
\(313\) 0.779174i 0.0440415i 0.999758 + 0.0220208i \(0.00700999\pi\)
−0.999758 + 0.0220208i \(0.992990\pi\)
\(314\) −8.53776 + 4.17504i −0.481814 + 0.235611i
\(315\) 0.811573 0.811573i 0.0457270 0.0457270i
\(316\) 20.5138 26.3683i 1.15399 1.48333i
\(317\) 7.53592i 0.423259i −0.977350 0.211630i \(-0.932123\pi\)
0.977350 0.211630i \(-0.0678771\pi\)
\(318\) −2.65239 + 7.72895i −0.148739 + 0.433418i
\(319\) −16.3949 + 16.3949i −0.917939 + 0.917939i
\(320\) 8.34179 19.0520i 0.466320 1.06504i
\(321\) −2.60803 −0.145566
\(322\) −0.990709 + 0.484465i −0.0552101 + 0.0269982i
\(323\) 34.4920i 1.91918i
\(324\) −1.57856 1.22807i −0.0876975 0.0682263i
\(325\) 5.59765 + 2.98016i 0.310502 + 0.165309i
\(326\) −3.61424 + 10.5318i −0.200174 + 0.583300i
\(327\) 0.413442 0.413442i 0.0228634 0.0228634i
\(328\) −5.97476 + 28.5425i −0.329901 + 1.57600i
\(329\) 0.714103 0.0393698
\(330\) −4.97595 10.1756i −0.273917 0.560148i
\(331\) 13.2622i 0.728959i 0.931211 + 0.364480i \(0.118753\pi\)
−0.931211 + 0.364480i \(0.881247\pi\)
\(332\) −11.8104 9.18816i −0.648179 0.504266i
\(333\) 6.43566 0.352672
\(334\) 1.67666 + 3.42869i 0.0917428 + 0.187610i
\(335\) 40.9771 2.23882
\(336\) 1.71167 0.434268i 0.0933795 0.0236912i
\(337\) 3.21855i 0.175326i −0.996150 0.0876629i \(-0.972060\pi\)
0.996150 0.0876629i \(-0.0279398\pi\)
\(338\) −4.75767 17.7585i −0.258783 0.965935i
\(339\) −6.67409 6.67409i −0.362487 0.362487i
\(340\) −21.9465 + 28.2099i −1.19022 + 1.52990i
\(341\) −5.34244 5.34244i −0.289310 0.289310i
\(342\) −2.30339 + 6.71199i −0.124553 + 0.362943i
\(343\) 4.30955 4.30955i 0.232694 0.232694i
\(344\) 1.55797 7.44271i 0.0840002 0.401284i
\(345\) 3.24715 3.24715i 0.174821 0.174821i
\(346\) 0.0196037 + 0.0400887i 0.00105390 + 0.00215518i
\(347\) −6.19697 + 6.19697i −0.332671 + 0.332671i −0.853600 0.520929i \(-0.825586\pi\)
0.520929 + 0.853600i \(0.325586\pi\)
\(348\) 11.8800 + 9.24233i 0.636835 + 0.495441i
\(349\) 25.9541 1.38929 0.694646 0.719351i \(-0.255561\pi\)
0.694646 + 0.719351i \(0.255561\pi\)
\(350\) −0.482395 0.986476i −0.0257851 0.0527293i
\(351\) 3.44857 1.05232i 0.184071 0.0561687i
\(352\) 1.42949 17.3691i 0.0761919 0.925774i
\(353\) 23.8028 23.8028i 1.26689 1.26689i 0.319208 0.947685i \(-0.396583\pi\)
0.947685 0.319208i \(-0.103417\pi\)
\(354\) −8.53171 17.4470i −0.453455 0.927296i
\(355\) 28.8727 28.8727i 1.53241 1.53241i
\(356\) 31.1271 3.88705i 1.64974 0.206013i
\(357\) −3.03468 −0.160612
\(358\) −6.15422 + 3.00947i −0.325261 + 0.159055i
\(359\) −20.6184 20.6184i −1.08820 1.08820i −0.995714 0.0924811i \(-0.970520\pi\)
−0.0924811 0.995714i \(-0.529480\pi\)
\(360\) −6.15457 + 4.02392i −0.324374 + 0.212079i
\(361\) 6.17818 0.325168
\(362\) 8.47638 4.14502i 0.445509 0.217858i
\(363\) 1.06667 + 1.06667i 0.0559859 + 0.0559859i
\(364\) −1.13634 + 2.97382i −0.0595602 + 0.155870i
\(365\) −1.61655 + 1.61655i −0.0846143 + 0.0846143i
\(366\) 10.0061 + 3.43386i 0.523029 + 0.179491i
\(367\) 30.9160i 1.61380i −0.590687 0.806901i \(-0.701143\pi\)
0.590687 0.806901i \(-0.298857\pi\)
\(368\) 6.84851 1.73753i 0.357003 0.0905751i
\(369\) 7.29029 7.29029i 0.379517 0.379517i
\(370\) 7.68040 22.3804i 0.399285 1.16350i
\(371\) 2.55087i 0.132435i
\(372\) −3.01170 + 3.87122i −0.156149 + 0.200713i
\(373\) 7.25450 + 7.25450i 0.375624 + 0.375624i 0.869521 0.493897i \(-0.164428\pi\)
−0.493897 + 0.869521i \(0.664428\pi\)
\(374\) −9.72139 + 28.3277i −0.502681 + 1.46479i
\(375\) −5.95831 5.95831i −0.307686 0.307686i
\(376\) −4.47802 0.937378i −0.230936 0.0483416i
\(377\) −25.9535 + 7.91963i −1.33667 + 0.407882i
\(378\) −0.590536 0.202657i −0.0303739 0.0104236i
\(379\) 4.56879i 0.234683i −0.993092 0.117341i \(-0.962563\pi\)
0.993092 0.117341i \(-0.0374372\pi\)
\(380\) 20.5924 + 16.0204i 1.05637 + 0.821827i
\(381\) 4.11758 + 4.11758i 0.210950 + 0.210950i
\(382\) 1.03179 3.00660i 0.0527910 0.153831i
\(383\) 25.0640 + 25.0640i 1.28071 + 1.28071i 0.940262 + 0.340451i \(0.110580\pi\)
0.340451 + 0.940262i \(0.389420\pi\)
\(384\) −11.3037 + 0.476366i −0.576838 + 0.0243095i
\(385\) −2.50032 2.50032i −0.127428 0.127428i
\(386\) 5.58107 + 11.4130i 0.284069 + 0.580908i
\(387\) −1.90101 + 1.90101i −0.0966336 + 0.0966336i
\(388\) 20.5791 2.56985i 1.04475 0.130464i
\(389\) −9.29703 + 9.29703i −0.471378 + 0.471378i −0.902360 0.430982i \(-0.858167\pi\)
0.430982 + 0.902360i \(0.358167\pi\)
\(390\) 0.456061 13.2485i 0.0230936 0.670861i
\(391\) −12.1419 −0.614044
\(392\) −16.1100 + 10.5329i −0.813679 + 0.531992i
\(393\) 9.68752i 0.488671i
\(394\) −7.71981 2.64925i −0.388918 0.133467i
\(395\) 43.4267i 2.18504i
\(396\) −3.78348 + 4.86325i −0.190127 + 0.244388i
\(397\) −9.42160 −0.472856 −0.236428 0.971649i \(-0.575977\pi\)
−0.236428 + 0.971649i \(0.575977\pi\)
\(398\) 5.30166 15.4488i 0.265748 0.774379i
\(399\) 2.21523i 0.110900i
\(400\) 1.73011 + 6.81925i 0.0865053 + 0.340962i
\(401\) 22.1391 + 22.1391i 1.10557 + 1.10557i 0.993725 + 0.111849i \(0.0356772\pi\)
0.111849 + 0.993725i \(0.464323\pi\)
\(402\) −9.79216 20.0245i −0.488388 0.998732i
\(403\) −2.58069 8.45720i −0.128553 0.421283i
\(404\) 13.1507 1.64222i 0.654273 0.0817034i
\(405\) 2.59977 0.129184
\(406\) 4.44430 + 1.52517i 0.220567 + 0.0756932i
\(407\) 19.8271i 0.982795i
\(408\) 19.0300 + 3.98352i 0.942124 + 0.197214i
\(409\) 6.68243 + 6.68243i 0.330425 + 0.330425i 0.852748 0.522323i \(-0.174934\pi\)
−0.522323 + 0.852748i \(0.674934\pi\)
\(410\) −16.6521 34.0527i −0.822387 1.68174i
\(411\) 0.335757 0.0165617
\(412\) −0.308089 + 0.396016i −0.0151785 + 0.0195103i
\(413\) −4.28702 4.28702i −0.210950 0.210950i
\(414\) −2.36277 0.810845i −0.116124 0.0398509i
\(415\) 19.4509 0.954808
\(416\) 11.0294 17.1567i 0.540761 0.841176i
\(417\) −3.94170 −0.193026
\(418\) 20.6785 + 7.09635i 1.01142 + 0.347094i
\(419\) 8.15845 + 8.15845i 0.398567 + 0.398567i 0.877727 0.479161i \(-0.159059\pi\)
−0.479161 + 0.877727i \(0.659059\pi\)
\(420\) −1.40951 + 1.81177i −0.0687769 + 0.0884052i
\(421\) −24.2088 −1.17987 −0.589933 0.807452i \(-0.700846\pi\)
−0.589933 + 0.807452i \(0.700846\pi\)
\(422\) −1.47566 3.01766i −0.0718341 0.146898i
\(423\) 1.14377 + 1.14377i 0.0556120 + 0.0556120i
\(424\) 3.34844 15.9961i 0.162615 0.776839i
\(425\) 12.0901i 0.586454i
\(426\) −21.0090 7.20979i −1.01789 0.349316i
\(427\) 3.30244 0.159816
\(428\) 5.17587 0.646344i 0.250185 0.0312422i
\(429\) −3.24202 10.6244i −0.156526 0.512953i
\(430\) 4.34217 + 8.87955i 0.209398 + 0.428210i
\(431\) −0.871986 0.871986i −0.0420021 0.0420021i 0.685794 0.727796i \(-0.259455\pi\)
−0.727796 + 0.685794i \(0.759455\pi\)
\(432\) 3.43713 + 2.04601i 0.165369 + 0.0984385i
\(433\) 6.16927i 0.296476i 0.988952 + 0.148238i \(0.0473602\pi\)
−0.988952 + 0.148238i \(0.952640\pi\)
\(434\) −0.496993 + 1.44822i −0.0238564 + 0.0695167i
\(435\) −19.5656 −0.938098
\(436\) −0.718049 + 0.922974i −0.0343883 + 0.0442024i
\(437\) 8.86328i 0.423988i
\(438\) 1.17627 + 0.403669i 0.0562045 + 0.0192880i
\(439\) 13.5607i 0.647217i 0.946191 + 0.323608i \(0.104896\pi\)
−0.946191 + 0.323608i \(0.895104\pi\)
\(440\) 12.3970 + 18.9612i 0.591004 + 0.903937i
\(441\) 6.80510 0.324052
\(442\) −25.6223 + 23.9170i −1.21873 + 1.13762i
\(443\) 7.44734 7.44734i 0.353834 0.353834i −0.507700 0.861534i \(-0.669504\pi\)
0.861534 + 0.507700i \(0.169504\pi\)
\(444\) −12.7721 + 1.59494i −0.606138 + 0.0756923i
\(445\) −28.8330 + 28.8330i −1.36682 + 1.36682i
\(446\) −2.74447 5.61231i −0.129954 0.265751i
\(447\) 10.7385 + 10.7385i 0.507913 + 0.507913i
\(448\) −3.28934 + 1.28604i −0.155407 + 0.0607598i
\(449\) 15.0382 + 15.0382i 0.709697 + 0.709697i 0.966471 0.256775i \(-0.0826598\pi\)
−0.256775 + 0.966471i \(0.582660\pi\)
\(450\) 0.807380 2.35267i 0.0380602 0.110906i
\(451\) −22.4601 22.4601i −1.05761 1.05761i
\(452\) 14.8993 + 11.5913i 0.700806 + 0.545208i
\(453\) 17.1846i 0.807403i
\(454\) −21.4322 7.35500i −1.00586 0.345187i
\(455\) −1.20779 3.95805i −0.0566220 0.185556i
\(456\) 2.90786 13.8914i 0.136173 0.650522i
\(457\) −28.0523 28.0523i −1.31223 1.31223i −0.919769 0.392460i \(-0.871624\pi\)
−0.392460 0.919769i \(-0.628376\pi\)
\(458\) −2.98896 + 8.70972i −0.139665 + 0.406978i
\(459\) −4.86061 4.86061i −0.226874 0.226874i
\(460\) −5.63952 + 7.24899i −0.262944 + 0.337986i
\(461\) 17.7812i 0.828155i 0.910242 + 0.414078i \(0.135896\pi\)
−0.910242 + 0.414078i \(0.864104\pi\)
\(462\) −0.624353 + 1.81934i −0.0290475 + 0.0846433i
\(463\) −5.04088 + 5.04088i −0.234270 + 0.234270i −0.814472 0.580203i \(-0.802973\pi\)
0.580203 + 0.814472i \(0.302973\pi\)
\(464\) −25.8674 15.3980i −1.20086 0.714834i
\(465\) 6.37563i 0.295663i
\(466\) 17.6904 + 6.07092i 0.819492 + 0.281230i
\(467\) −23.4380 + 23.4380i −1.08458 + 1.08458i −0.0885031 + 0.996076i \(0.528208\pi\)
−0.996076 + 0.0885031i \(0.971792\pi\)
\(468\) −6.58318 + 2.94307i −0.304308 + 0.136044i
\(469\) −4.92037 4.92037i −0.227201 0.227201i
\(470\) 5.34252 2.61254i 0.246432 0.120507i
\(471\) −6.72028 −0.309654
\(472\) 21.2558 + 32.5106i 0.978376 + 1.49642i
\(473\) 5.85667 + 5.85667i 0.269290 + 0.269290i
\(474\) 21.2216 10.3775i 0.974741 0.476656i
\(475\) −8.82541 −0.404937
\(476\) 6.02258 0.752079i 0.276045 0.0344715i
\(477\) −4.08570 + 4.08570i −0.187071 + 0.187071i
\(478\) −1.59435 3.26037i −0.0729239 0.149126i
\(479\) 2.83070 2.83070i 0.129338 0.129338i −0.639474 0.768812i \(-0.720848\pi\)
0.768812 + 0.639474i \(0.220848\pi\)
\(480\) 11.2170 9.51109i 0.511985 0.434120i
\(481\) 10.9046 20.4822i 0.497207 0.933907i
\(482\) 10.8275 + 22.1417i 0.493177 + 1.00852i
\(483\) −0.779811 −0.0354826
\(484\) −2.38126 1.85256i −0.108239 0.0842071i
\(485\) −19.0624 + 19.0624i −0.865579 + 0.865579i
\(486\) −0.621260 1.27045i −0.0281809 0.0576287i
\(487\) −15.2061 + 15.2061i −0.689053 + 0.689053i −0.962023 0.272970i \(-0.911994\pi\)
0.272970 + 0.962023i \(0.411994\pi\)
\(488\) −20.7090 4.33499i −0.937454 0.196236i
\(489\) −5.56733 + 5.56733i −0.251763 + 0.251763i
\(490\) 8.12130 23.6651i 0.366883 1.06908i
\(491\) −21.3579 21.3579i −0.963868 0.963868i 0.0355015 0.999370i \(-0.488697\pi\)
−0.999370 + 0.0355015i \(0.988697\pi\)
\(492\) −12.6615 + 16.2749i −0.570823 + 0.733731i
\(493\) 36.5803 + 36.5803i 1.64750 + 1.64750i
\(494\) 17.4588 + 18.7036i 0.785507 + 0.841515i
\(495\) 8.00945i 0.359998i
\(496\) 5.01759 8.42915i 0.225296 0.378480i
\(497\) −6.93385 −0.311026
\(498\) −4.64812 9.50519i −0.208287 0.425938i
\(499\) 26.9120 1.20475 0.602374 0.798214i \(-0.294222\pi\)
0.602374 + 0.798214i \(0.294222\pi\)
\(500\) 13.3014 + 10.3481i 0.594857 + 0.462783i
\(501\) 2.69881i 0.120574i
\(502\) 7.88308 + 16.1205i 0.351839 + 0.719495i
\(503\) 15.6841 0.699319 0.349660 0.936877i \(-0.386297\pi\)
0.349660 + 0.936877i \(0.386297\pi\)
\(504\) 1.22219 + 0.255840i 0.0544408 + 0.0113960i
\(505\) −12.1815 + 12.1815i −0.542070 + 0.542070i
\(506\) −2.49807 + 7.27928i −0.111053 + 0.323604i
\(507\) 2.49414 12.7585i 0.110769 0.566625i
\(508\) −9.19213 7.15123i −0.407835 0.317285i
\(509\) 34.3940i 1.52449i −0.647290 0.762244i \(-0.724098\pi\)
0.647290 0.762244i \(-0.275902\pi\)
\(510\) −22.7038 + 11.1023i −1.00534 + 0.491620i
\(511\) 0.388219 0.0171738
\(512\) 22.3151 3.74676i 0.986196 0.165585i
\(513\) −3.54811 + 3.54811i −0.156653 + 0.156653i
\(514\) −0.906460 + 2.64139i −0.0399823 + 0.116507i
\(515\) 0.652211i 0.0287398i
\(516\) 3.30159 4.24383i 0.145344 0.186824i
\(517\) 3.52376 3.52376i 0.154975 0.154975i
\(518\) −3.60958 + 1.76512i −0.158596 + 0.0775547i
\(519\) 0.0315548i 0.00138510i
\(520\) 2.37824 + 26.4057i 0.104293 + 1.15797i
\(521\) 45.0314i 1.97286i −0.164183 0.986430i \(-0.552499\pi\)
0.164183 0.986430i \(-0.447501\pi\)
\(522\) 4.67552 + 9.56123i 0.204642 + 0.418484i
\(523\) 2.59835 2.59835i 0.113618 0.113618i −0.648012 0.761630i \(-0.724399\pi\)
0.761630 + 0.648012i \(0.224399\pi\)
\(524\) 2.40084 + 19.2257i 0.104881 + 0.839879i
\(525\) 0.776479i 0.0338883i
\(526\) −27.0098 9.26912i −1.17768 0.404153i
\(527\) −11.9201 + 11.9201i −0.519246 + 0.519246i
\(528\) 6.30339 10.5892i 0.274320 0.460836i
\(529\) 19.8799 0.864345
\(530\) 9.33234 + 19.0842i 0.405371 + 0.828965i
\(531\) 13.7329i 0.595958i
\(532\) −0.548997 4.39632i −0.0238020 0.190605i
\(533\) −10.8495 35.5548i −0.469942 1.54005i
\(534\) 20.9801 + 7.19987i 0.907899 + 0.311569i
\(535\) −4.79439 + 4.79439i −0.207280 + 0.207280i
\(536\) 24.3960 + 37.3136i 1.05375 + 1.61170i
\(537\) −4.84414 −0.209040
\(538\) 34.1219 16.6859i 1.47110 0.719380i
\(539\) 20.9653i 0.903041i
\(540\) −5.15947 + 0.644297i −0.222028 + 0.0277261i
\(541\) 27.3236 1.17474 0.587368 0.809320i \(-0.300164\pi\)
0.587368 + 0.809320i \(0.300164\pi\)
\(542\) 10.0741 4.92633i 0.432720 0.211604i
\(543\) 6.67197 0.286322
\(544\) −38.7539 3.18947i −1.66156 0.136747i
\(545\) 1.52008i 0.0651129i
\(546\) −1.64558 + 1.53606i −0.0704245 + 0.0657373i
\(547\) −4.06928 4.06928i −0.173990 0.173990i 0.614740 0.788730i \(-0.289261\pi\)
−0.788730 + 0.614740i \(0.789261\pi\)
\(548\) −0.666339 + 0.0832101i −0.0284646 + 0.00355456i
\(549\) 5.28947 + 5.28947i 0.225749 + 0.225749i
\(550\) −7.24817 2.48740i −0.309063 0.106063i
\(551\) 26.7026 26.7026i 1.13757 1.13757i
\(552\) 4.89007 + 1.02363i 0.208135 + 0.0435686i
\(553\) 5.21451 5.21451i 0.221744 0.221744i
\(554\) −14.3211 + 7.00313i −0.608445 + 0.297535i
\(555\) 11.8308 11.8308i 0.502189 0.502189i
\(556\) 7.82264 0.976863i 0.331754 0.0414282i
\(557\) −25.7141 −1.08954 −0.544771 0.838585i \(-0.683383\pi\)
−0.544771 + 0.838585i \(0.683383\pi\)
\(558\) −3.11562 + 1.52356i −0.131895 + 0.0644976i
\(559\) 2.82909 + 9.27123i 0.119658 + 0.392131i
\(560\) 2.34828 3.94492i 0.0992329 0.166703i
\(561\) −14.9747 + 14.9747i −0.632232 + 0.632232i
\(562\) 14.5293 7.10494i 0.612880 0.299704i
\(563\) 16.1382 16.1382i 0.680143 0.680143i −0.279889 0.960032i \(-0.590298\pi\)
0.960032 + 0.279889i \(0.0902977\pi\)
\(564\) −2.55337 1.98645i −0.107516 0.0836447i
\(565\) −24.5382 −1.03233
\(566\) 19.9750 + 40.8480i 0.839612 + 1.71697i
\(567\) −0.312171 0.312171i −0.0131099 0.0131099i
\(568\) 43.4810 + 9.10182i 1.82442 + 0.381904i
\(569\) 37.7402 1.58215 0.791075 0.611719i \(-0.209522\pi\)
0.791075 + 0.611719i \(0.209522\pi\)
\(570\) 8.10440 + 16.5731i 0.339456 + 0.694172i
\(571\) 30.6444 + 30.6444i 1.28243 + 1.28243i 0.939282 + 0.343147i \(0.111493\pi\)
0.343147 + 0.939282i \(0.388507\pi\)
\(572\) 9.06710 + 20.2817i 0.379114 + 0.848019i
\(573\) 1.58936 1.58936i 0.0663963 0.0663963i
\(574\) −2.08940 + 6.08844i −0.0872100 + 0.254126i
\(575\) 3.10674i 0.129560i
\(576\) −7.32834 3.20866i −0.305347 0.133694i
\(577\) −1.65091 + 1.65091i −0.0687281 + 0.0687281i −0.740635 0.671907i \(-0.765475\pi\)
0.671907 + 0.740635i \(0.265475\pi\)
\(578\) 40.4650 + 13.8866i 1.68312 + 0.577607i
\(579\) 8.98347i 0.373340i
\(580\) 38.8296 4.84890i 1.61231 0.201340i
\(581\) −2.33559 2.33559i −0.0968966 0.0968966i
\(582\) 13.8706 + 4.76006i 0.574956 + 0.197311i
\(583\) 12.5873 + 12.5873i 0.521314 + 0.521314i
\(584\) −2.43446 0.509601i −0.100739 0.0210875i
\(585\) 4.40506 8.27406i 0.182127 0.342090i
\(586\) 3.60019 10.4908i 0.148722 0.433371i
\(587\) 12.5683i 0.518747i 0.965777 + 0.259374i \(0.0835161\pi\)
−0.965777 + 0.259374i \(0.916484\pi\)
\(588\) −13.5053 + 1.68649i −0.556949 + 0.0695499i
\(589\) 8.70132 + 8.70132i 0.358532 + 0.358532i
\(590\) −47.7571 16.3891i −1.96613 0.674727i
\(591\) −4.08087 4.08087i −0.167865 0.167865i
\(592\) 24.9521 6.33058i 1.02552 0.260185i
\(593\) −16.6876 16.6876i −0.685276 0.685276i 0.275908 0.961184i \(-0.411021\pi\)
−0.961184 + 0.275908i \(0.911021\pi\)
\(594\) −3.91403 + 1.91399i −0.160595 + 0.0785321i
\(595\) −5.57871 + 5.57871i −0.228705 + 0.228705i
\(596\) −23.9728 18.6502i −0.981963 0.763940i
\(597\) 8.16660 8.16660i 0.334237 0.334237i
\(598\) −6.58408 + 6.14587i −0.269243 + 0.251323i
\(599\) 5.17898 0.211607 0.105804 0.994387i \(-0.466258\pi\)
0.105804 + 0.994387i \(0.466258\pi\)
\(600\) −1.01926 + 4.86917i −0.0416110 + 0.198783i
\(601\) 12.7711i 0.520946i 0.965481 + 0.260473i \(0.0838784\pi\)
−0.965481 + 0.260473i \(0.916122\pi\)
\(602\) 0.544830 1.58761i 0.0222056 0.0647063i
\(603\) 15.7618i 0.641869i
\(604\) 4.25882 + 34.1043i 0.173289 + 1.38768i
\(605\) 3.92177 0.159443
\(606\) 8.86378 + 3.04183i 0.360066 + 0.123566i
\(607\) 5.73009i 0.232577i 0.993215 + 0.116289i \(0.0370997\pi\)
−0.993215 + 0.116289i \(0.962900\pi\)
\(608\) −2.32823 + 28.2892i −0.0944220 + 1.14728i
\(609\) 2.34936 + 2.34936i 0.0952008 + 0.0952008i
\(610\) 24.7070 12.0819i 1.00036 0.489183i
\(611\) 5.57818 1.70217i 0.225669 0.0688622i
\(612\) 10.8509 + 8.44170i 0.438621 + 0.341236i
\(613\) 38.1340 1.54022 0.770109 0.637912i \(-0.220202\pi\)
0.770109 + 0.637912i \(0.220202\pi\)
\(614\) 8.85966 25.8167i 0.357547 1.04188i
\(615\) 26.8037i 1.08083i
\(616\) 0.788198 3.76536i 0.0317574 0.151711i
\(617\) −14.6535 14.6535i −0.589927 0.589927i 0.347685 0.937611i \(-0.386968\pi\)
−0.937611 + 0.347685i \(0.886968\pi\)
\(618\) −0.318720 + 0.155857i −0.0128208 + 0.00626948i
\(619\) −12.1900 −0.489959 −0.244980 0.969528i \(-0.578781\pi\)
−0.244980 + 0.969528i \(0.578781\pi\)
\(620\) 1.58006 + 12.6530i 0.0634568 + 0.508156i
\(621\) −1.24901 1.24901i −0.0501212 0.0501212i
\(622\) 11.6919 34.0697i 0.468803 1.36607i
\(623\) 6.92431 0.277417
\(624\) 12.3355 7.47228i 0.493816 0.299131i
\(625\) −30.7007 −1.22803
\(626\) 0.357676 1.04225i 0.0142956 0.0416568i
\(627\) 10.9311 + 10.9311i 0.436547 + 0.436547i
\(628\) 13.3370 1.66547i 0.532203 0.0664596i
\(629\) −44.2383 −1.76390
\(630\) −1.45814 + 0.713043i −0.0580937 + 0.0284083i
\(631\) 18.8694 + 18.8694i 0.751179 + 0.751179i 0.974699 0.223520i \(-0.0717548\pi\)
−0.223520 + 0.974699i \(0.571755\pi\)
\(632\) −39.5443 + 25.8544i −1.57299 + 1.02843i
\(633\) 2.37528i 0.0944087i
\(634\) −3.45933 + 10.0803i −0.137387 + 0.400341i
\(635\) 15.1388 0.600766
\(636\) 7.09588 9.12098i 0.281370 0.361670i
\(637\) 11.5306 21.6580i 0.456858 0.858120i
\(638\) 29.4565 14.4045i 1.16619 0.570279i
\(639\) −11.1059 11.1059i −0.439341 0.439341i
\(640\) −19.9040 + 21.6555i −0.786776 + 0.856007i
\(641\) 43.6031i 1.72222i 0.508419 + 0.861110i \(0.330230\pi\)
−0.508419 + 0.861110i \(0.669770\pi\)
\(642\) 3.48861 + 1.19721i 0.137684 + 0.0472499i
\(643\) 5.43518 0.214342 0.107171 0.994241i \(-0.465821\pi\)
0.107171 + 0.994241i \(0.465821\pi\)
\(644\) 1.54760 0.193259i 0.0609841 0.00761548i
\(645\) 6.98931i 0.275204i
\(646\) 15.8334 46.1378i 0.622956 1.81527i
\(647\) 20.5427i 0.807618i −0.914843 0.403809i \(-0.867686\pi\)
0.914843 0.403809i \(-0.132314\pi\)
\(648\) 1.54780 + 2.36735i 0.0608031 + 0.0929982i
\(649\) −42.3088 −1.66076
\(650\) −6.11961 6.55595i −0.240031 0.257145i
\(651\) −0.765561 + 0.765561i −0.0300047 + 0.0300047i
\(652\) 9.66910 12.4286i 0.378671 0.486741i
\(653\) 22.8348 22.8348i 0.893594 0.893594i −0.101265 0.994859i \(-0.532289\pi\)
0.994859 + 0.101265i \(0.0322891\pi\)
\(654\) −0.742825 + 0.363247i −0.0290467 + 0.0142041i
\(655\) −17.8087 17.8087i −0.695845 0.695845i
\(656\) 21.0944 35.4369i 0.823597 1.38358i
\(657\) 0.621805 + 0.621805i 0.0242589 + 0.0242589i
\(658\) −0.955212 0.327805i −0.0372380 0.0127792i
\(659\) −22.3109 22.3109i −0.869111 0.869111i 0.123263 0.992374i \(-0.460664\pi\)
−0.992374 + 0.123263i \(0.960664\pi\)
\(660\) 1.98497 + 15.8954i 0.0772647 + 0.618729i
\(661\) 3.35317i 0.130423i 0.997871 + 0.0652115i \(0.0207722\pi\)
−0.997871 + 0.0652115i \(0.979228\pi\)
\(662\) 6.08797 17.7401i 0.236616 0.689488i
\(663\) −23.7053 + 7.23359i −0.920636 + 0.280929i
\(664\) 11.5802 + 17.7119i 0.449401 + 0.687357i
\(665\) 4.07230 + 4.07230i 0.157917 + 0.157917i
\(666\) −8.60858 2.95426i −0.333576 0.114475i
\(667\) 9.39993 + 9.39993i 0.363967 + 0.363967i
\(668\) −0.668841 5.35602i −0.0258782 0.207231i
\(669\) 4.41759i 0.170794i
\(670\) −54.8125 18.8103i −2.11759 0.726706i
\(671\) 16.2960 16.2960i 0.629098 0.629098i
\(672\) −2.48895 0.204843i −0.0960134 0.00790197i
\(673\) 28.8339i 1.11147i 0.831361 + 0.555733i \(0.187562\pi\)
−0.831361 + 0.555733i \(0.812438\pi\)
\(674\) −1.47746 + 4.30526i −0.0569097 + 0.165832i
\(675\) 1.24368 1.24368i 0.0478691 0.0478691i
\(676\) −1.78792 + 25.9385i −0.0687660 + 0.997633i
\(677\) 2.94170 + 2.94170i 0.113059 + 0.113059i 0.761373 0.648314i \(-0.224526\pi\)
−0.648314 + 0.761373i \(0.724526\pi\)
\(678\) 5.86381 + 11.9912i 0.225198 + 0.460520i
\(679\) 4.57788 0.175683
\(680\) 42.3061 27.6602i 1.62237 1.06072i
\(681\) −11.3295 11.3295i −0.434149 0.434149i
\(682\) 4.69384 + 9.59869i 0.179736 + 0.367553i
\(683\) 7.51526 0.287563 0.143782 0.989609i \(-0.454074\pi\)
0.143782 + 0.989609i \(0.454074\pi\)
\(684\) 6.16221 7.92085i 0.235618 0.302861i
\(685\) 0.617229 0.617229i 0.0235831 0.0235831i
\(686\) −7.74290 + 3.78634i −0.295625 + 0.144563i
\(687\) −4.60416 + 4.60416i −0.175660 + 0.175660i
\(688\) −5.50054 + 9.24048i −0.209706 + 0.352290i
\(689\) 6.08037 + 19.9260i 0.231644 + 0.759121i
\(690\) −5.83411 + 2.85293i −0.222101 + 0.108609i
\(691\) 49.5404 1.88461 0.942303 0.334761i \(-0.108656\pi\)
0.942303 + 0.334761i \(0.108656\pi\)
\(692\) −0.00782015 0.0626231i −0.000297278 0.00238057i
\(693\) −0.961744 + 0.961744i −0.0365336 + 0.0365336i
\(694\) 11.1340 5.44462i 0.422641 0.206675i
\(695\) −7.24609 + 7.24609i −0.274860 + 0.274860i
\(696\) −11.6485 17.8164i −0.441536 0.675327i
\(697\) −50.1130 + 50.1130i −1.89817 + 1.89817i
\(698\) −34.7172 11.9141i −1.31407 0.450956i
\(699\) 9.35156 + 9.35156i 0.353708 + 0.353708i
\(700\) 0.192433 + 1.54099i 0.00727329 + 0.0582439i
\(701\) −0.00498862 0.00498862i −0.000188418 0.000188418i 0.707013 0.707201i \(-0.250042\pi\)
−0.707201 + 0.707013i \(0.750042\pi\)
\(702\) −5.09600 0.175424i −0.192336 0.00662093i
\(703\) 32.2927i 1.21794i
\(704\) −9.88532 + 22.5773i −0.372567 + 0.850915i
\(705\) 4.20522 0.158378
\(706\) −42.7660 + 20.9129i −1.60952 + 0.787069i
\(707\) 2.92541 0.110022
\(708\) 3.40341 + 27.2542i 0.127908 + 1.02427i
\(709\) 9.34496i 0.350957i 0.984483 + 0.175479i \(0.0561473\pi\)
−0.984483 + 0.175479i \(0.943853\pi\)
\(710\) −51.8752 + 25.3674i −1.94684 + 0.952021i
\(711\) 16.7040 0.626451
\(712\) −43.4212 9.08930i −1.62728 0.340636i
\(713\) −3.06306 + 3.06306i −0.114712 + 0.114712i
\(714\) 4.05931 + 1.39306i 0.151916 + 0.0521338i
\(715\) −25.4910 13.5712i −0.953308 0.507536i
\(716\) 9.61361 1.20051i 0.359278 0.0448653i
\(717\) 2.56632i 0.0958410i
\(718\) 18.1152 + 37.0447i 0.676052 + 1.38250i
\(719\) −4.52247 −0.168660 −0.0843299 0.996438i \(-0.526875\pi\)
−0.0843299 + 0.996438i \(0.526875\pi\)
\(720\) 10.0797 2.55733i 0.375650 0.0953059i
\(721\) −0.0783150 + 0.0783150i −0.00291660 + 0.00291660i
\(722\) −8.26418 2.83607i −0.307561 0.105547i
\(723\) 17.4282i 0.648163i
\(724\) −13.2411 + 1.65350i −0.492101 + 0.0614519i
\(725\) −9.35976 + 9.35976i −0.347613 + 0.347613i
\(726\) −0.937174 1.91648i −0.0347818 0.0711271i
\(727\) 33.8528i 1.25553i −0.778403 0.627765i \(-0.783970\pi\)
0.778403 0.627765i \(-0.216030\pi\)
\(728\) 2.88513 3.45627i 0.106930 0.128098i
\(729\) 1.00000i 0.0370370i
\(730\) 2.90444 1.42029i 0.107498 0.0525674i
\(731\) 13.0674 13.0674i 0.483315 0.483315i
\(732\) −11.8083 9.18653i −0.436447 0.339544i
\(733\) 33.7659i 1.24717i 0.781755 + 0.623585i \(0.214325\pi\)
−0.781755 + 0.623585i \(0.785675\pi\)
\(734\) −14.1918 + 41.3544i −0.523830 + 1.52642i
\(735\) 12.5099 12.5099i 0.461436 0.461436i
\(736\) −9.95844 0.819587i −0.367073 0.0302104i
\(737\) −48.5593 −1.78871
\(738\) −13.0983 + 6.40520i −0.482157 + 0.235779i
\(739\) 16.0669i 0.591032i −0.955338 0.295516i \(-0.904508\pi\)
0.955338 0.295516i \(-0.0954916\pi\)
\(740\) −20.5472 + 26.4112i −0.755330 + 0.970895i
\(741\) 5.28032 + 17.3042i 0.193977 + 0.635685i
\(742\) 1.17097 3.41215i 0.0429875 0.125264i
\(743\) 30.5825 30.5825i 1.12196 1.12196i 0.130519 0.991446i \(-0.458336\pi\)
0.991446 0.130519i \(-0.0416642\pi\)
\(744\) 5.80563 3.79578i 0.212845 0.139160i
\(745\) 39.4815 1.44649
\(746\) −6.37376 13.0340i −0.233360 0.477210i
\(747\) 7.48177i 0.273744i
\(748\) 26.0074 33.4297i 0.950926 1.22231i
\(749\) 1.15138 0.0420707
\(750\) 5.23493 + 10.7052i 0.191153 + 0.390899i
\(751\) −49.0740 −1.79074 −0.895368 0.445327i \(-0.853087\pi\)
−0.895368 + 0.445327i \(0.853087\pi\)
\(752\) 5.55968 + 3.30949i 0.202740 + 0.120685i
\(753\) 12.6889i 0.462408i
\(754\) 38.3519 + 1.32022i 1.39669 + 0.0480794i
\(755\) −31.5907 31.5907i −1.14970 1.14970i
\(756\) 0.696894 + 0.542165i 0.0253458 + 0.0197184i
\(757\) −19.2872 19.2872i −0.701004 0.701004i 0.263622 0.964626i \(-0.415083\pi\)
−0.964626 + 0.263622i \(0.915083\pi\)
\(758\) −2.09728 + 6.11139i −0.0761766 + 0.221976i
\(759\) −3.84800 + 3.84800i −0.139673 + 0.139673i
\(760\) −20.1912 30.8823i −0.732410 1.12022i
\(761\) 13.4163 13.4163i 0.486341 0.486341i −0.420808 0.907150i \(-0.638253\pi\)
0.907150 + 0.420808i \(0.138253\pi\)
\(762\) −3.61768 7.39798i −0.131055 0.268001i
\(763\) −0.182525 + 0.182525i −0.00660784 + 0.00660784i
\(764\) −2.76033 + 3.54810i −0.0998651 + 0.128366i
\(765\) −17.8707 −0.646116
\(766\) −22.0211 45.0322i −0.795655 1.62708i
\(767\) −43.7065 23.2691i −1.57815 0.840199i
\(768\) 15.3389 + 4.55169i 0.553495 + 0.164245i
\(769\) 37.1538 37.1538i 1.33980 1.33980i 0.443550 0.896250i \(-0.353719\pi\)
0.896250 0.443550i \(-0.146281\pi\)
\(770\) 2.19676 + 4.49228i 0.0791658 + 0.161891i
\(771\) −1.39630 + 1.39630i −0.0502865 + 0.0502865i
\(772\) −2.22636 17.8285i −0.0801283 0.641660i
\(773\) −19.0516 −0.685238 −0.342619 0.939474i \(-0.611314\pi\)
−0.342619 + 0.939474i \(0.611314\pi\)
\(774\) 3.41551 1.67021i 0.122768 0.0600345i
\(775\) −3.04997 3.04997i −0.109558 0.109558i
\(776\) −28.7071 6.00922i −1.03053 0.215719i
\(777\) −2.84119 −0.101927
\(778\) 16.7038 8.16831i 0.598861 0.292848i
\(779\) 36.5811 + 36.5811i 1.31065 + 1.31065i
\(780\) −6.69168 + 17.5123i −0.239601 + 0.627041i
\(781\) −34.2152 + 34.2152i −1.22432 + 1.22432i
\(782\) 16.2415 + 5.57370i 0.580796 + 0.199315i
\(783\) 7.52588i 0.268953i
\(784\) 26.3845 6.69399i 0.942303 0.239071i
\(785\) −12.3540 + 12.3540i −0.440933 + 0.440933i
\(786\) −4.44701 + 12.9584i −0.158620 + 0.462211i
\(787\) 30.5115i 1.08762i −0.839209 0.543809i \(-0.816982\pi\)
0.839209 0.543809i \(-0.183018\pi\)
\(788\) 9.11019 + 7.08748i 0.324537 + 0.252481i
\(789\) −14.2780 14.2780i −0.508311 0.508311i
\(790\) 19.9348 58.0893i 0.709250 2.06672i
\(791\) 2.94645 + 2.94645i 0.104764 + 0.104764i
\(792\) 7.29338 4.76849i 0.259159 0.169441i
\(793\) 25.7968 7.87183i 0.916072 0.279537i
\(794\) 12.6027 + 4.32494i 0.447253 + 0.153486i
\(795\) 15.0216i 0.532763i
\(796\) −14.1834 + 18.2312i −0.502718 + 0.646189i
\(797\) −26.4617 26.4617i −0.937323 0.937323i 0.0608252 0.998148i \(-0.480627\pi\)
−0.998148 + 0.0608252i \(0.980627\pi\)
\(798\) 1.01689 2.96318i 0.0359976 0.104895i
\(799\) −7.86220 7.86220i −0.278145 0.278145i
\(800\) 0.816085 9.91589i 0.0288530 0.350580i
\(801\) 11.0906 + 11.0906i 0.391866 + 0.391866i
\(802\) −19.4513 39.7770i −0.686848 1.40457i
\(803\) 1.91567 1.91567i 0.0676027 0.0676027i
\(804\) 3.90621 + 31.2806i 0.137761 + 1.10318i
\(805\) −1.43354 + 1.43354i −0.0505257 + 0.0505257i
\(806\) −0.430205 + 12.4973i −0.0151533 + 0.440200i
\(807\) 26.8582 0.945453
\(808\) −18.3448 3.84009i −0.645367 0.135094i
\(809\) 19.7169i 0.693211i 0.938011 + 0.346606i \(0.112666\pi\)
−0.938011 + 0.346606i \(0.887334\pi\)
\(810\) −3.47756 1.19341i −0.122189 0.0419323i
\(811\) 34.0528i 1.19576i −0.801587 0.597878i \(-0.796011\pi\)
0.801587 0.597878i \(-0.203989\pi\)
\(812\) −5.24474 4.08027i −0.184054 0.143189i
\(813\) 7.92958 0.278102
\(814\) −9.10155 + 26.5216i −0.319009 + 0.929580i
\(815\) 20.4690i 0.716999i
\(816\) −23.6266 14.0641i −0.827097 0.492343i
\(817\) −9.53884 9.53884i −0.333722 0.333722i
\(818\) −5.87114 12.0062i −0.205280 0.419787i
\(819\) −1.52246 + 0.464574i −0.0531991 + 0.0162335i
\(820\) 6.64272 + 53.1943i 0.231974 + 1.85763i
\(821\) 20.9843 0.732357 0.366179 0.930545i \(-0.380666\pi\)
0.366179 + 0.930545i \(0.380666\pi\)
\(822\) −0.449122 0.154128i −0.0156649 0.00537582i
\(823\) 31.0687i 1.08299i 0.840705 + 0.541494i \(0.182141\pi\)
−0.840705 + 0.541494i \(0.817859\pi\)
\(824\) 0.593901 0.388299i 0.0206895 0.0135270i
\(825\) −3.83155 3.83155i −0.133398 0.133398i
\(826\) 3.76655 + 7.70242i 0.131055 + 0.268001i
\(827\) 22.0032 0.765127 0.382563 0.923929i \(-0.375041\pi\)
0.382563 + 0.923929i \(0.375041\pi\)
\(828\) 2.78832 + 2.16924i 0.0969007 + 0.0753861i
\(829\) −26.4165 26.4165i −0.917483 0.917483i 0.0793628 0.996846i \(-0.474711\pi\)
−0.996846 + 0.0793628i \(0.974711\pi\)
\(830\) −26.0183 8.92885i −0.903108 0.309925i
\(831\) −11.2725 −0.391038
\(832\) −22.6291 + 17.8865i −0.784521 + 0.620102i
\(833\) −46.7778 −1.62076
\(834\) 5.27257 + 1.80942i 0.182574 + 0.0626550i
\(835\) 4.96127 + 4.96127i 0.171692 + 0.171692i
\(836\) −24.4028 18.9847i −0.843988 0.656600i
\(837\) −2.45238 −0.0847667
\(838\) −7.16797 14.6582i −0.247613 0.506358i
\(839\) −19.9383 19.9383i −0.688346 0.688346i 0.273520 0.961866i \(-0.411812\pi\)
−0.961866 + 0.273520i \(0.911812\pi\)
\(840\) 2.71709 1.77646i 0.0937486 0.0612938i
\(841\) 27.6388i 0.953062i
\(842\) 32.3827 + 11.1129i 1.11598 + 0.382977i
\(843\) 11.4363 0.393888
\(844\) 0.588660 + 4.71394i 0.0202625 + 0.162260i
\(845\) −18.8692 28.0392i −0.649119 0.964578i
\(846\) −1.00491 2.05499i −0.0345495 0.0706521i
\(847\) −0.470911 0.470911i −0.0161807 0.0161807i
\(848\) −11.8219 + 19.8599i −0.405967 + 0.681993i
\(849\) 32.1524i 1.10347i
\(850\) −5.54988 + 16.1721i −0.190359 + 0.554699i
\(851\) −11.3678 −0.389682
\(852\) 24.7929 + 19.2882i 0.849390 + 0.660803i
\(853\) 36.3083i 1.24317i 0.783346 + 0.621586i \(0.213511\pi\)
−0.783346 + 0.621586i \(0.786489\pi\)
\(854\) −4.41747 1.51597i −0.151163 0.0518754i
\(855\) 13.0451i 0.446133i
\(856\) −7.22014 1.51138i −0.246779 0.0516580i
\(857\) 18.0709 0.617289 0.308644 0.951178i \(-0.400125\pi\)
0.308644 + 0.951178i \(0.400125\pi\)
\(858\) −0.540449 + 15.6999i −0.0184506 + 0.535986i
\(859\) −2.21247 + 2.21247i −0.0754885 + 0.0754885i −0.743843 0.668354i \(-0.766999\pi\)
0.668354 + 0.743843i \(0.266999\pi\)
\(860\) −1.73215 13.8709i −0.0590657 0.472993i
\(861\) −3.21849 + 3.21849i −0.109686 + 0.109686i
\(862\) 0.766122 + 1.56668i 0.0260942 + 0.0533615i
\(863\) −8.59919 8.59919i −0.292720 0.292720i 0.545434 0.838154i \(-0.316365\pi\)
−0.838154 + 0.545434i \(0.816365\pi\)
\(864\) −3.65843 4.31462i −0.124462 0.146786i
\(865\) 0.0580077 + 0.0580077i 0.00197232 + 0.00197232i
\(866\) 2.83197 8.25226i 0.0962344 0.280423i
\(867\) 21.3907 + 21.3907i 0.726467 + 0.726467i
\(868\) 1.32959 1.70905i 0.0451294 0.0580089i
\(869\) 51.4623i 1.74574i
\(870\) 26.1717 + 8.98148i 0.887303 + 0.304501i
\(871\) −50.1636 26.7068i −1.69973 0.904926i
\(872\) 1.38418 0.904989i 0.0468741 0.0306468i
\(873\) 7.33233 + 7.33233i 0.248162 + 0.248162i
\(874\) 4.06865 11.8559i 0.137624 0.401031i
\(875\) 2.63045 + 2.63045i 0.0889255 + 0.0889255i
\(876\) −1.38813 1.07993i −0.0469005 0.0364873i
\(877\) 24.8875i 0.840391i 0.907434 + 0.420195i \(0.138038\pi\)
−0.907434 + 0.420195i \(0.861962\pi\)
\(878\) 6.22497 18.1393i 0.210083 0.612172i
\(879\) 5.54568 5.54568i 0.187051 0.187051i
\(880\) −7.87868 31.0540i −0.265590 1.04683i
\(881\) 39.7663i 1.33976i 0.742469 + 0.669880i \(0.233655\pi\)
−0.742469 + 0.669880i \(0.766345\pi\)
\(882\) −9.10276 3.12385i −0.306506 0.105185i
\(883\) −0.270023 + 0.270023i −0.00908699 + 0.00908699i −0.711636 0.702549i \(-0.752045\pi\)
0.702549 + 0.711636i \(0.252045\pi\)
\(884\) 45.2524 20.2305i 1.52200 0.680426i
\(885\) −25.2455 25.2455i −0.848618 0.848618i
\(886\) −13.3805 + 6.54319i −0.449527 + 0.219823i
\(887\) 28.6599 0.962304 0.481152 0.876637i \(-0.340218\pi\)
0.481152 + 0.876637i \(0.340218\pi\)
\(888\) 17.8166 + 3.72953i 0.597887 + 0.125155i
\(889\) −1.81781 1.81781i −0.0609674 0.0609674i
\(890\) 51.8038 25.3325i 1.73647 0.849147i
\(891\) −3.08083 −0.103212
\(892\) 1.09480 + 8.76708i 0.0366567 + 0.293543i
\(893\) −5.73919 + 5.73919i −0.192055 + 0.192055i
\(894\) −9.43477 19.2937i −0.315546 0.645277i
\(895\) −8.90507 + 8.90507i −0.297664 + 0.297664i
\(896\) 4.99030 0.210304i 0.166714 0.00702577i
\(897\) −6.09146 + 1.85879i −0.203388 + 0.0620632i
\(898\) −13.2125 27.0189i −0.440906 0.901632i
\(899\) 18.4563 0.615552
\(900\) −2.15997 + 2.77640i −0.0719988 + 0.0925467i
\(901\) 28.0849 28.0849i 0.935643 0.935643i
\(902\) 19.7333 + 40.3537i 0.657047 + 1.34363i
\(903\) 0.839249 0.839249i 0.0279285 0.0279285i
\(904\) −14.6090 22.3444i −0.485888 0.743164i
\(905\) 12.2652 12.2652i 0.407709 0.407709i
\(906\) −7.88851 + 22.9868i −0.262078 + 0.763685i
\(907\) 7.92876 + 7.92876i 0.263270 + 0.263270i 0.826381 0.563111i \(-0.190396\pi\)
−0.563111 + 0.826381i \(0.690396\pi\)
\(908\) 25.2922 + 19.6767i 0.839351 + 0.652993i
\(909\) 4.68560 + 4.68560i 0.155411 + 0.155411i
\(910\) −0.201340 + 5.84887i −0.00667436 + 0.193888i
\(911\) 0.271475i 0.00899435i −0.999990 0.00449718i \(-0.998568\pi\)
0.999990 0.00449718i \(-0.00143150\pi\)
\(912\) −10.2664 + 17.2468i −0.339955 + 0.571098i
\(913\) −23.0500 −0.762845
\(914\) 24.6465 + 50.4010i 0.815235 + 1.66712i
\(915\) 19.4475 0.642913
\(916\) 7.99631 10.2784i 0.264205 0.339607i
\(917\) 4.27681i 0.141233i
\(918\) 4.27050 + 8.73298i 0.140948 + 0.288231i
\(919\) −30.8639 −1.01811 −0.509054 0.860735i \(-0.670005\pi\)
−0.509054 + 0.860735i \(0.670005\pi\)
\(920\) 10.8713 7.10774i 0.358415 0.234335i
\(921\) 13.6473 13.6473i 0.449694 0.449694i
\(922\) 8.16239 23.7849i 0.268814 0.783313i
\(923\) −54.1634 + 16.5278i −1.78281 + 0.544020i
\(924\) 1.67032 2.14701i 0.0549494 0.0706315i
\(925\) 11.3192i 0.372173i
\(926\) 9.05687 4.42889i 0.297627 0.145542i
\(927\) −0.250872 −0.00823972
\(928\) 27.5329 + 32.4713i 0.903811 + 1.06592i
\(929\) 24.5772 24.5772i 0.806351 0.806351i −0.177728 0.984080i \(-0.556875\pi\)
0.984080 + 0.177728i \(0.0568748\pi\)
\(930\) −2.92670 + 8.52829i −0.0959704 + 0.279654i
\(931\) 34.1465i 1.11911i
\(932\) −20.8765 16.2414i −0.683834 0.532004i
\(933\) 18.0100 18.0100i 0.589622 0.589622i
\(934\) 42.1106 20.5924i 1.37790 0.673805i
\(935\) 55.0565i 1.80054i
\(936\) 10.1569 0.914789i 0.331990 0.0299008i
\(937\) 38.5662i 1.25990i 0.776634 + 0.629952i \(0.216925\pi\)
−0.776634 + 0.629952i \(0.783075\pi\)
\(938\) 4.32300 + 8.84035i 0.141151 + 0.288648i
\(939\) 0.550959 0.550959i 0.0179799 0.0179799i
\(940\) −8.34563 + 1.04217i −0.272204 + 0.0339919i
\(941\) 17.9469i 0.585052i 0.956258 + 0.292526i \(0.0944958\pi\)
−0.956258 + 0.292526i \(0.905504\pi\)
\(942\) 8.98930 + 3.08491i 0.292887 + 0.100512i
\(943\) −12.8774 + 12.8774i −0.419345 + 0.419345i
\(944\) −13.5087 53.2448i −0.439671 1.73297i
\(945\) −1.14774 −0.0373359
\(946\) −5.14563 10.5226i −0.167299 0.342119i
\(947\) 16.7657i 0.544812i −0.962182 0.272406i \(-0.912181\pi\)
0.962182 0.272406i \(-0.0878193\pi\)
\(948\) −33.1506 + 4.13973i −1.07668 + 0.134452i
\(949\) 3.03255 0.925375i 0.0984408 0.0300389i
\(950\) 11.8052 + 4.05126i 0.383011 + 0.131440i
\(951\) −5.32870 + 5.32870i −0.172795 + 0.172795i
\(952\) −8.40128 1.75863i −0.272287 0.0569975i
\(953\) 44.7508 1.44962 0.724810 0.688949i \(-0.241927\pi\)
0.724810 + 0.688949i \(0.241927\pi\)
\(954\) 7.34072 3.58967i 0.237664 0.116220i
\(955\) 5.84348i 0.189091i
\(956\) 0.636006 + 5.09308i 0.0205699 + 0.164722i
\(957\) 23.1859 0.749494
\(958\) −5.08587 + 2.48703i −0.164317 + 0.0803523i
\(959\) −0.148229 −0.00478656
\(960\) −19.3703 + 7.57328i −0.625175 + 0.244426i
\(961\) 24.9858i 0.805995i
\(962\) −23.9886 + 22.3920i −0.773425 + 0.721949i
\(963\) 1.84416 + 1.84416i 0.0594272 + 0.0594272i
\(964\) −4.31921 34.5878i −0.139112 1.11400i
\(965\) 16.5145 + 16.5145i 0.531620 + 0.531620i
\(966\) 1.04311 + 0.357969i 0.0335614 + 0.0115175i
\(967\) −25.6036 + 25.6036i −0.823355 + 0.823355i −0.986588 0.163233i \(-0.947808\pi\)
0.163233 + 0.986588i \(0.447808\pi\)
\(968\) 2.33486 + 3.57116i 0.0750452 + 0.114781i
\(969\) 24.3895 24.3895i 0.783504 0.783504i
\(970\) 34.2491 16.7481i 1.09967 0.537749i
\(971\) 6.12175 6.12175i 0.196456 0.196456i −0.602023 0.798479i \(-0.705638\pi\)
0.798479 + 0.602023i \(0.205638\pi\)
\(972\) 0.247828 + 1.98459i 0.00794909 + 0.0636556i
\(973\) 1.74017 0.0557871
\(974\) 27.3205 13.3600i 0.875406 0.428081i
\(975\) −1.85085 6.06543i −0.0592745 0.194249i
\(976\) 25.7113 + 15.3050i 0.822997 + 0.489902i
\(977\) 22.5001 22.5001i 0.719842 0.719842i −0.248730 0.968573i \(-0.580013\pi\)
0.968573 + 0.248730i \(0.0800133\pi\)
\(978\) 10.0027 4.89142i 0.319852 0.156410i
\(979\) 34.1682 34.1682i 1.09202 1.09202i
\(980\) −21.7267 + 27.9274i −0.694035 + 0.892107i
\(981\) −0.584695 −0.0186679
\(982\) 18.7649 + 38.3734i 0.598812 + 1.22454i
\(983\) −38.2746 38.2746i −1.22077 1.22077i −0.967359 0.253411i \(-0.918447\pi\)
−0.253411 0.967359i \(-0.581553\pi\)
\(984\) 24.4074 15.9578i 0.778079 0.508716i
\(985\) −15.0039 −0.478063
\(986\) −32.1393 65.7233i −1.02352 2.09306i
\(987\) −0.504947 0.504947i −0.0160726 0.0160726i
\(988\) −14.7677 33.0330i −0.469823 1.05092i
\(989\) 3.35789 3.35789i 0.106775 0.106775i
\(990\) −3.67670 + 10.7138i −0.116853 + 0.340506i
\(991\) 21.6332i 0.687200i 0.939116 + 0.343600i \(0.111646\pi\)
−0.939116 + 0.343600i \(0.888354\pi\)
\(992\) −10.5811 + 8.97186i −0.335950 + 0.284857i
\(993\) 9.37783 9.37783i 0.297596 0.297596i
\(994\) 9.27499 + 3.18295i 0.294185 + 0.100957i
\(995\) 30.0256i 0.951876i
\(996\) 1.85419 + 14.8482i 0.0587523 + 0.470484i
\(997\) 14.0786 + 14.0786i 0.445873 + 0.445873i 0.893980 0.448107i \(-0.147902\pi\)
−0.448107 + 0.893980i \(0.647902\pi\)
\(998\) −35.9986 12.3538i −1.13951 0.391054i
\(999\) −4.55070 4.55070i −0.143978 0.143978i
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 624.2.bn.a.187.5 yes 112
13.8 odd 4 624.2.r.a.619.33 yes 112
16.3 odd 4 624.2.r.a.499.33 112
208.99 even 4 inner 624.2.bn.a.307.5 yes 112
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
624.2.r.a.499.33 112 16.3 odd 4
624.2.r.a.619.33 yes 112 13.8 odd 4
624.2.bn.a.187.5 yes 112 1.1 even 1 trivial
624.2.bn.a.307.5 yes 112 208.99 even 4 inner