Properties

Label 380.2.d.b.379.9
Level $380$
Weight $2$
Character 380.379
Analytic conductor $3.034$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [380,2,Mod(379,380)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(380, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("380.379");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 380.d (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.03431527681\)
Analytic rank: \(0\)
Dimension: \(40\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 379.9
Character \(\chi\) \(=\) 380.379
Dual form 380.2.d.b.379.12

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.948256 - 1.04920i) q^{2} -1.76151i q^{3} +(-0.201622 + 1.98981i) q^{4} +(-1.85854 - 1.24332i) q^{5} +(-1.84816 + 1.67036i) q^{6} -4.29252 q^{7} +(2.27889 - 1.67531i) q^{8} -0.102903 q^{9} +O(q^{10})\) \(q+(-0.948256 - 1.04920i) q^{2} -1.76151i q^{3} +(-0.201622 + 1.98981i) q^{4} +(-1.85854 - 1.24332i) q^{5} +(-1.84816 + 1.67036i) q^{6} -4.29252 q^{7} +(2.27889 - 1.67531i) q^{8} -0.102903 q^{9} +(0.457886 + 3.12895i) q^{10} -0.376641i q^{11} +(3.50506 + 0.355158i) q^{12} +0.928582 q^{13} +(4.07040 + 4.50369i) q^{14} +(-2.19011 + 3.27382i) q^{15} +(-3.91870 - 0.802380i) q^{16} +5.96697i q^{17} +(0.0975780 + 0.107965i) q^{18} +(-3.61406 + 2.43692i) q^{19} +(2.84869 - 3.44746i) q^{20} +7.56129i q^{21} +(-0.395170 + 0.357152i) q^{22} +0.352652 q^{23} +(-2.95107 - 4.01428i) q^{24} +(1.90832 + 4.62150i) q^{25} +(-0.880533 - 0.974264i) q^{26} -5.10325i q^{27} +(0.865466 - 8.54130i) q^{28} -3.89105i q^{29} +(5.51167 - 0.806569i) q^{30} +1.06308 q^{31} +(2.87407 + 4.87234i) q^{32} -0.663455 q^{33} +(6.26051 - 5.65821i) q^{34} +(7.97780 + 5.33696i) q^{35} +(0.0207474 - 0.204757i) q^{36} -9.60143 q^{37} +(5.98386 + 1.48103i) q^{38} -1.63570i q^{39} +(-6.31834 + 0.280241i) q^{40} +6.82129i q^{41} +(7.93327 - 7.17004i) q^{42} -9.45416 q^{43} +(0.749444 + 0.0759391i) q^{44} +(0.191248 + 0.127941i) q^{45} +(-0.334405 - 0.370001i) q^{46} -2.56158 q^{47} +(-1.41340 + 6.90281i) q^{48} +11.4257 q^{49} +(3.03928 - 6.38457i) q^{50} +10.5108 q^{51} +(-0.187223 + 1.84770i) q^{52} +3.18648 q^{53} +(-5.35431 + 4.83919i) q^{54} +(-0.468284 + 0.700001i) q^{55} +(-9.78217 + 7.19129i) q^{56} +(4.29265 + 6.36618i) q^{57} +(-4.08247 + 3.68971i) q^{58} +3.98595 q^{59} +(-6.07272 - 5.01798i) q^{60} -3.22322 q^{61} +(-1.00807 - 1.11538i) q^{62} +0.441711 q^{63} +(2.38668 - 7.63569i) q^{64} +(-1.72580 - 1.15452i) q^{65} +(0.629125 + 0.696094i) q^{66} -8.75380i q^{67} +(-11.8731 - 1.20307i) q^{68} -0.621199i q^{69} +(-1.96548 - 13.4311i) q^{70} -10.1166 q^{71} +(-0.234504 + 0.172394i) q^{72} -5.09707i q^{73} +(9.10461 + 10.0738i) q^{74} +(8.14081 - 3.36152i) q^{75} +(-4.12034 - 7.68263i) q^{76} +1.61674i q^{77} +(-1.71617 + 1.55106i) q^{78} -14.4968 q^{79} +(6.28543 + 6.36344i) q^{80} -9.29812 q^{81} +(7.15687 - 6.46833i) q^{82} +3.49815 q^{83} +(-15.0455 - 1.52452i) q^{84} +(7.41883 - 11.0898i) q^{85} +(8.96496 + 9.91926i) q^{86} -6.85410 q^{87} +(-0.630990 - 0.858323i) q^{88} -10.4915i q^{89} +(-0.0471176 - 0.321977i) q^{90} -3.98595 q^{91} +(-0.0711025 + 0.701712i) q^{92} -1.87262i q^{93} +(2.42904 + 2.68760i) q^{94} +(9.74673 - 0.0356921i) q^{95} +(8.58266 - 5.06270i) q^{96} -9.74137 q^{97} +(-10.8345 - 11.9878i) q^{98} +0.0387573i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q - 4 q^{5} + 8 q^{6} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 40 q - 4 q^{5} + 8 q^{6} - 8 q^{9} - 8 q^{16} - 20 q^{20} - 40 q^{24} - 84 q^{25} - 24 q^{26} + 24 q^{30} + 24 q^{36} - 40 q^{44} - 12 q^{45} + 128 q^{49} - 120 q^{54} + 24 q^{61} + 72 q^{64} + 112 q^{66} + 32 q^{74} + 56 q^{76} + 96 q^{80} - 72 q^{81} + 44 q^{85} - 40 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.948256 1.04920i −0.670518 0.741893i
\(3\) 1.76151i 1.01701i −0.861060 0.508503i \(-0.830199\pi\)
0.861060 0.508503i \(-0.169801\pi\)
\(4\) −0.201622 + 1.98981i −0.100811 + 0.994906i
\(5\) −1.85854 1.24332i −0.831163 0.556028i
\(6\) −1.84816 + 1.67036i −0.754510 + 0.681921i
\(7\) −4.29252 −1.62242 −0.811209 0.584756i \(-0.801190\pi\)
−0.811209 + 0.584756i \(0.801190\pi\)
\(8\) 2.27889 1.67531i 0.805709 0.592311i
\(9\) −0.102903 −0.0343009
\(10\) 0.457886 + 3.12895i 0.144796 + 0.989461i
\(11\) 0.376641i 0.113562i −0.998387 0.0567808i \(-0.981916\pi\)
0.998387 0.0567808i \(-0.0180836\pi\)
\(12\) 3.50506 + 0.355158i 1.01182 + 0.102525i
\(13\) 0.928582 0.257542 0.128771 0.991674i \(-0.458897\pi\)
0.128771 + 0.991674i \(0.458897\pi\)
\(14\) 4.07040 + 4.50369i 1.08786 + 1.20366i
\(15\) −2.19011 + 3.27382i −0.565484 + 0.845298i
\(16\) −3.91870 0.802380i −0.979674 0.200595i
\(17\) 5.96697i 1.44720i 0.690219 + 0.723601i \(0.257514\pi\)
−0.690219 + 0.723601i \(0.742486\pi\)
\(18\) 0.0975780 + 0.107965i 0.0229994 + 0.0254476i
\(19\) −3.61406 + 2.43692i −0.829122 + 0.559068i
\(20\) 2.84869 3.44746i 0.636986 0.770875i
\(21\) 7.56129i 1.65001i
\(22\) −0.395170 + 0.357152i −0.0842505 + 0.0761450i
\(23\) 0.352652 0.0735331 0.0367666 0.999324i \(-0.488294\pi\)
0.0367666 + 0.999324i \(0.488294\pi\)
\(24\) −2.95107 4.01428i −0.602384 0.819411i
\(25\) 1.90832 + 4.62150i 0.381665 + 0.924301i
\(26\) −0.880533 0.974264i −0.172687 0.191069i
\(27\) 5.10325i 0.982122i
\(28\) 0.865466 8.54130i 0.163558 1.61415i
\(29\) 3.89105i 0.722549i −0.932459 0.361275i \(-0.882342\pi\)
0.932459 0.361275i \(-0.117658\pi\)
\(30\) 5.51167 0.806569i 1.00629 0.147259i
\(31\) 1.06308 0.190934 0.0954672 0.995433i \(-0.469565\pi\)
0.0954672 + 0.995433i \(0.469565\pi\)
\(32\) 2.87407 + 4.87234i 0.508069 + 0.861316i
\(33\) −0.663455 −0.115493
\(34\) 6.26051 5.65821i 1.07367 0.970375i
\(35\) 7.97780 + 5.33696i 1.34849 + 0.902111i
\(36\) 0.0207474 0.204757i 0.00345791 0.0341261i
\(37\) −9.60143 −1.57846 −0.789232 0.614095i \(-0.789521\pi\)
−0.789232 + 0.614095i \(0.789521\pi\)
\(38\) 5.98386 + 1.48103i 0.970710 + 0.240254i
\(39\) 1.63570i 0.261922i
\(40\) −6.31834 + 0.280241i −0.999018 + 0.0443099i
\(41\) 6.82129i 1.06531i 0.846334 + 0.532653i \(0.178805\pi\)
−0.846334 + 0.532653i \(0.821195\pi\)
\(42\) 7.93327 7.17004i 1.22413 1.10636i
\(43\) −9.45416 −1.44175 −0.720873 0.693067i \(-0.756259\pi\)
−0.720873 + 0.693067i \(0.756259\pi\)
\(44\) 0.749444 + 0.0759391i 0.112983 + 0.0114483i
\(45\) 0.191248 + 0.127941i 0.0285096 + 0.0190723i
\(46\) −0.334405 0.370001i −0.0493053 0.0545537i
\(47\) −2.56158 −0.373645 −0.186823 0.982394i \(-0.559819\pi\)
−0.186823 + 0.982394i \(0.559819\pi\)
\(48\) −1.41340 + 6.90281i −0.204006 + 0.996334i
\(49\) 11.4257 1.63224
\(50\) 3.03928 6.38457i 0.429819 0.902915i
\(51\) 10.5108 1.47181
\(52\) −0.187223 + 1.84770i −0.0259631 + 0.256230i
\(53\) 3.18648 0.437697 0.218848 0.975759i \(-0.429770\pi\)
0.218848 + 0.975759i \(0.429770\pi\)
\(54\) −5.35431 + 4.83919i −0.728629 + 0.658530i
\(55\) −0.468284 + 0.700001i −0.0631434 + 0.0943882i
\(56\) −9.78217 + 7.19129i −1.30720 + 0.960977i
\(57\) 4.29265 + 6.36618i 0.568576 + 0.843221i
\(58\) −4.08247 + 3.68971i −0.536054 + 0.484482i
\(59\) 3.98595 0.518927 0.259463 0.965753i \(-0.416454\pi\)
0.259463 + 0.965753i \(0.416454\pi\)
\(60\) −6.07272 5.01798i −0.783985 0.647819i
\(61\) −3.22322 −0.412691 −0.206346 0.978479i \(-0.566157\pi\)
−0.206346 + 0.978479i \(0.566157\pi\)
\(62\) −1.00807 1.11538i −0.128025 0.141653i
\(63\) 0.441711 0.0556504
\(64\) 2.38668 7.63569i 0.298335 0.954461i
\(65\) −1.72580 1.15452i −0.214060 0.143201i
\(66\) 0.629125 + 0.696094i 0.0774400 + 0.0856833i
\(67\) 8.75380i 1.06945i −0.845027 0.534723i \(-0.820416\pi\)
0.845027 0.534723i \(-0.179584\pi\)
\(68\) −11.8731 1.20307i −1.43983 0.145894i
\(69\) 0.621199i 0.0747836i
\(70\) −1.96548 13.4311i −0.234920 1.60532i
\(71\) −10.1166 −1.20062 −0.600308 0.799769i \(-0.704956\pi\)
−0.600308 + 0.799769i \(0.704956\pi\)
\(72\) −0.234504 + 0.172394i −0.0276365 + 0.0203168i
\(73\) 5.09707i 0.596567i −0.954477 0.298283i \(-0.903586\pi\)
0.954477 0.298283i \(-0.0964141\pi\)
\(74\) 9.10461 + 10.0738i 1.05839 + 1.17105i
\(75\) 8.14081 3.36152i 0.940019 0.388155i
\(76\) −4.12034 7.68263i −0.472636 0.881258i
\(77\) 1.61674i 0.184244i
\(78\) −1.71617 + 1.55106i −0.194318 + 0.175623i
\(79\) −14.4968 −1.63102 −0.815509 0.578745i \(-0.803543\pi\)
−0.815509 + 0.578745i \(0.803543\pi\)
\(80\) 6.28543 + 6.36344i 0.702733 + 0.711454i
\(81\) −9.29812 −1.03312
\(82\) 7.15687 6.46833i 0.790344 0.714307i
\(83\) 3.49815 0.383972 0.191986 0.981398i \(-0.438507\pi\)
0.191986 + 0.981398i \(0.438507\pi\)
\(84\) −15.0455 1.52452i −1.64160 0.166339i
\(85\) 7.41883 11.0898i 0.804686 1.20286i
\(86\) 8.96496 + 9.91926i 0.966716 + 1.06962i
\(87\) −6.85410 −0.734837
\(88\) −0.630990 0.858323i −0.0672638 0.0914976i
\(89\) 10.4915i 1.11210i −0.831149 0.556050i \(-0.812316\pi\)
0.831149 0.556050i \(-0.187684\pi\)
\(90\) −0.0471176 0.321977i −0.00496664 0.0339394i
\(91\) −3.98595 −0.417841
\(92\) −0.0711025 + 0.701712i −0.00741295 + 0.0731585i
\(93\) 1.87262i 0.194181i
\(94\) 2.42904 + 2.68760i 0.250536 + 0.277205i
\(95\) 9.74673 0.0356921i 0.999993 0.00366193i
\(96\) 8.58266 5.06270i 0.875964 0.516709i
\(97\) −9.74137 −0.989086 −0.494543 0.869153i \(-0.664665\pi\)
−0.494543 + 0.869153i \(0.664665\pi\)
\(98\) −10.8345 11.9878i −1.09445 1.21095i
\(99\) 0.0387573i 0.00389526i
\(100\) −9.58068 + 2.86541i −0.958068 + 0.286541i
\(101\) −12.8341 −1.27704 −0.638519 0.769606i \(-0.720452\pi\)
−0.638519 + 0.769606i \(0.720452\pi\)
\(102\) −9.96697 11.0279i −0.986877 1.09193i
\(103\) 2.13005i 0.209881i 0.994479 + 0.104940i \(0.0334651\pi\)
−0.994479 + 0.104940i \(0.966535\pi\)
\(104\) 2.11614 1.55566i 0.207504 0.152545i
\(105\) 9.40109 14.0529i 0.917452 1.37143i
\(106\) −3.02160 3.34324i −0.293484 0.324724i
\(107\) 16.4182i 1.58721i 0.608433 + 0.793606i \(0.291799\pi\)
−0.608433 + 0.793606i \(0.708201\pi\)
\(108\) 10.1545 + 1.02893i 0.977118 + 0.0990087i
\(109\) 17.3936i 1.66600i −0.553273 0.833000i \(-0.686621\pi\)
0.553273 0.833000i \(-0.313379\pi\)
\(110\) 1.17849 0.172459i 0.112365 0.0164433i
\(111\) 16.9130i 1.60531i
\(112\) 16.8211 + 3.44423i 1.58944 + 0.325449i
\(113\) −12.0642 −1.13490 −0.567452 0.823406i \(-0.692071\pi\)
−0.567452 + 0.823406i \(0.692071\pi\)
\(114\) 2.60884 10.5406i 0.244340 0.987218i
\(115\) −0.655418 0.438459i −0.0611180 0.0408865i
\(116\) 7.74245 + 0.784521i 0.718868 + 0.0728409i
\(117\) −0.0955535 −0.00883392
\(118\) −3.77970 4.18204i −0.347950 0.384988i
\(119\) 25.6133i 2.34797i
\(120\) 0.493646 + 11.1298i 0.0450635 + 1.01601i
\(121\) 10.8581 0.987104
\(122\) 3.05644 + 3.38179i 0.276717 + 0.306173i
\(123\) 12.0157 1.08342
\(124\) −0.214340 + 2.11533i −0.0192483 + 0.189962i
\(125\) 2.19931 10.9619i 0.196712 0.980461i
\(126\) −0.418855 0.463441i −0.0373146 0.0412866i
\(127\) 4.18189i 0.371083i 0.982636 + 0.185541i \(0.0594039\pi\)
−0.982636 + 0.185541i \(0.940596\pi\)
\(128\) −10.2745 + 4.73649i −0.908147 + 0.418651i
\(129\) 16.6536i 1.46626i
\(130\) 0.425185 + 2.90549i 0.0372912 + 0.254828i
\(131\) 0.974860i 0.0851740i 0.999093 + 0.0425870i \(0.0135600\pi\)
−0.999093 + 0.0425870i \(0.986440\pi\)
\(132\) 0.133767 1.32015i 0.0116429 0.114904i
\(133\) 15.5134 10.4605i 1.34518 0.907043i
\(134\) −9.18445 + 8.30084i −0.793415 + 0.717083i
\(135\) −6.34496 + 9.48459i −0.546088 + 0.816303i
\(136\) 9.99651 + 13.5981i 0.857194 + 1.16602i
\(137\) 3.53192i 0.301753i −0.988553 0.150876i \(-0.951790\pi\)
0.988553 0.150876i \(-0.0482095\pi\)
\(138\) −0.651759 + 0.589056i −0.0554814 + 0.0501438i
\(139\) 7.20995i 0.611540i 0.952105 + 0.305770i \(0.0989139\pi\)
−0.952105 + 0.305770i \(0.901086\pi\)
\(140\) −12.2280 + 14.7983i −1.03346 + 1.25068i
\(141\) 4.51225i 0.380000i
\(142\) 9.59310 + 10.6143i 0.805035 + 0.890729i
\(143\) 0.349742i 0.0292469i
\(144\) 0.403244 + 0.0825670i 0.0336037 + 0.00688058i
\(145\) −4.83781 + 7.23166i −0.401758 + 0.600556i
\(146\) −5.34782 + 4.83333i −0.442589 + 0.400009i
\(147\) 20.1264i 1.66000i
\(148\) 1.93586 19.1050i 0.159127 1.57042i
\(149\) 3.91562 0.320780 0.160390 0.987054i \(-0.448725\pi\)
0.160390 + 0.987054i \(0.448725\pi\)
\(150\) −11.2465 5.35371i −0.918270 0.437129i
\(151\) 7.22811 0.588216 0.294108 0.955772i \(-0.404978\pi\)
0.294108 + 0.955772i \(0.404978\pi\)
\(152\) −4.15344 + 11.6081i −0.336888 + 0.941545i
\(153\) 0.614016i 0.0496403i
\(154\) 1.69627 1.53308i 0.136690 0.123539i
\(155\) −1.97577 1.32174i −0.158698 0.106165i
\(156\) 3.25474 + 0.329794i 0.260588 + 0.0264046i
\(157\) 23.7964i 1.89916i 0.313526 + 0.949580i \(0.398490\pi\)
−0.313526 + 0.949580i \(0.601510\pi\)
\(158\) 13.7467 + 15.2100i 1.09363 + 1.21004i
\(159\) 5.61301i 0.445140i
\(160\) 0.716291 12.6288i 0.0566278 0.998395i
\(161\) −1.51377 −0.119301
\(162\) 8.81699 + 9.75554i 0.692729 + 0.766468i
\(163\) 15.5139 1.21514 0.607571 0.794265i \(-0.292144\pi\)
0.607571 + 0.794265i \(0.292144\pi\)
\(164\) −13.5731 1.37532i −1.05988 0.107395i
\(165\) 1.23306 + 0.824885i 0.0959933 + 0.0642172i
\(166\) −3.31714 3.67025i −0.257460 0.284866i
\(167\) 4.46016i 0.345138i 0.984997 + 0.172569i \(0.0552067\pi\)
−0.984997 + 0.172569i \(0.944793\pi\)
\(168\) 12.6675 + 17.2314i 0.977319 + 1.32943i
\(169\) −12.1377 −0.933672
\(170\) −18.6704 + 2.73219i −1.43195 + 0.209549i
\(171\) 0.371896 0.250766i 0.0284396 0.0191765i
\(172\) 1.90617 18.8120i 0.145344 1.43440i
\(173\) 21.0522 1.60057 0.800283 0.599622i \(-0.204682\pi\)
0.800283 + 0.599622i \(0.204682\pi\)
\(174\) 6.49944 + 7.19129i 0.492721 + 0.545170i
\(175\) −8.19151 19.8379i −0.619220 1.49960i
\(176\) −0.302209 + 1.47594i −0.0227799 + 0.111253i
\(177\) 7.02128i 0.527752i
\(178\) −11.0077 + 9.94866i −0.825060 + 0.745684i
\(179\) 19.5988 1.46488 0.732440 0.680832i \(-0.238381\pi\)
0.732440 + 0.680832i \(0.238381\pi\)
\(180\) −0.293138 + 0.354752i −0.0218492 + 0.0264417i
\(181\) 17.6144i 1.30926i −0.755947 0.654632i \(-0.772823\pi\)
0.755947 0.654632i \(-0.227177\pi\)
\(182\) 3.77970 + 4.18204i 0.280170 + 0.309994i
\(183\) 5.67772i 0.419709i
\(184\) 0.803656 0.590802i 0.0592463 0.0435545i
\(185\) 17.8446 + 11.9376i 1.31196 + 0.877671i
\(186\) −1.96474 + 1.77572i −0.144062 + 0.130202i
\(187\) 2.24740 0.164346
\(188\) 0.516472 5.09707i 0.0376676 0.371742i
\(189\) 21.9058i 1.59341i
\(190\) −9.27984 10.1924i −0.673230 0.739433i
\(191\) 23.4244i 1.69493i −0.530849 0.847467i \(-0.678127\pi\)
0.530849 0.847467i \(-0.321873\pi\)
\(192\) −13.4503 4.20415i −0.970693 0.303408i
\(193\) −19.0446 −1.37086 −0.685431 0.728137i \(-0.740386\pi\)
−0.685431 + 0.728137i \(0.740386\pi\)
\(194\) 9.23731 + 10.2206i 0.663200 + 0.733796i
\(195\) −2.03370 + 3.04001i −0.145636 + 0.217700i
\(196\) −2.30367 + 22.7350i −0.164548 + 1.62393i
\(197\) 19.5602i 1.39361i −0.717262 0.696803i \(-0.754605\pi\)
0.717262 0.696803i \(-0.245395\pi\)
\(198\) 0.0406640 0.0367519i 0.00288987 0.00261184i
\(199\) 20.7395i 1.47018i 0.677969 + 0.735091i \(0.262860\pi\)
−0.677969 + 0.735091i \(0.737140\pi\)
\(200\) 12.0913 + 7.33487i 0.854984 + 0.518654i
\(201\) −15.4199 −1.08763
\(202\) 12.1700 + 13.4654i 0.856276 + 0.947425i
\(203\) 16.7024i 1.17228i
\(204\) −2.11922 + 20.9146i −0.148375 + 1.46431i
\(205\) 8.48103 12.6776i 0.592341 0.885444i
\(206\) 2.23484 2.01984i 0.155709 0.140729i
\(207\) −0.0362888 −0.00252225
\(208\) −3.63883 0.745075i −0.252308 0.0516617i
\(209\) 0.917845 + 1.36120i 0.0634887 + 0.0941563i
\(210\) −23.6589 + 3.46221i −1.63262 + 0.238915i
\(211\) 0.0749824 0.00516200 0.00258100 0.999997i \(-0.499178\pi\)
0.00258100 + 0.999997i \(0.499178\pi\)
\(212\) −0.642465 + 6.34050i −0.0441247 + 0.435467i
\(213\) 17.8204i 1.22103i
\(214\) 17.2259 15.5687i 1.17754 1.06425i
\(215\) 17.5709 + 11.7545i 1.19833 + 0.801651i
\(216\) −8.54953 11.6298i −0.581722 0.791305i
\(217\) −4.56328 −0.309776
\(218\) −18.2492 + 16.4935i −1.23599 + 1.11708i
\(219\) −8.97852 −0.606712
\(220\) −1.29845 1.07293i −0.0875417 0.0723371i
\(221\) 5.54082i 0.372716i
\(222\) 17.7450 16.0378i 1.19097 1.07639i
\(223\) 1.00367i 0.0672104i 0.999435 + 0.0336052i \(0.0106989\pi\)
−0.999435 + 0.0336052i \(0.989301\pi\)
\(224\) −12.3370 20.9146i −0.824301 1.39742i
\(225\) −0.196371 0.475565i −0.0130914 0.0317043i
\(226\) 11.4399 + 12.6577i 0.760974 + 0.841978i
\(227\) 6.78069i 0.450050i −0.974353 0.225025i \(-0.927754\pi\)
0.974353 0.225025i \(-0.0722464\pi\)
\(228\) −13.5330 + 7.25801i −0.896244 + 0.480673i
\(229\) −18.5264 −1.22426 −0.612129 0.790758i \(-0.709687\pi\)
−0.612129 + 0.790758i \(0.709687\pi\)
\(230\) 0.161475 + 1.10343i 0.0106473 + 0.0727582i
\(231\) 2.84789 0.187378
\(232\) −6.51870 8.86727i −0.427974 0.582165i
\(233\) 10.1129i 0.662519i −0.943540 0.331259i \(-0.892527\pi\)
0.943540 0.331259i \(-0.107473\pi\)
\(234\) 0.0906091 + 0.100254i 0.00592331 + 0.00655383i
\(235\) 4.76080 + 3.18486i 0.310560 + 0.207758i
\(236\) −0.803656 + 7.93129i −0.0523136 + 0.516283i
\(237\) 25.5362i 1.65875i
\(238\) −26.8734 + 24.2880i −1.74194 + 1.57435i
\(239\) 18.2687i 1.18171i 0.806780 + 0.590853i \(0.201208\pi\)
−0.806780 + 0.590853i \(0.798792\pi\)
\(240\) 11.2092 11.0718i 0.723553 0.714683i
\(241\) 13.1021i 0.843981i 0.906600 + 0.421991i \(0.138668\pi\)
−0.906600 + 0.421991i \(0.861332\pi\)
\(242\) −10.2963 11.3923i −0.661871 0.732326i
\(243\) 1.06893i 0.0685718i
\(244\) 0.649873 6.41360i 0.0416038 0.410589i
\(245\) −21.2351 14.2058i −1.35666 0.907573i
\(246\) −11.3940 12.6069i −0.726455 0.803784i
\(247\) −3.35595 + 2.26288i −0.213534 + 0.143984i
\(248\) 2.42264 1.78098i 0.153838 0.113093i
\(249\) 6.16202i 0.390502i
\(250\) −13.5867 + 8.08717i −0.859297 + 0.511478i
\(251\) 12.8628i 0.811891i −0.913897 0.405946i \(-0.866942\pi\)
0.913897 0.405946i \(-0.133058\pi\)
\(252\) −0.0890587 + 0.878922i −0.00561017 + 0.0553669i
\(253\) 0.132823i 0.00835053i
\(254\) 4.38762 3.96550i 0.275304 0.248818i
\(255\) −19.5348 13.0683i −1.22332 0.818370i
\(256\) 14.7124 + 6.28857i 0.919523 + 0.393035i
\(257\) 27.1520 1.69369 0.846847 0.531836i \(-0.178498\pi\)
0.846847 + 0.531836i \(0.178498\pi\)
\(258\) 17.4728 15.7918i 1.08781 0.983156i
\(259\) 41.2143 2.56093
\(260\) 2.64524 3.20125i 0.164051 0.198533i
\(261\) 0.400399i 0.0247841i
\(262\) 1.02282 0.924417i 0.0631900 0.0571107i
\(263\) 18.6447 1.14968 0.574841 0.818265i \(-0.305064\pi\)
0.574841 + 0.818265i \(0.305064\pi\)
\(264\) −1.51194 + 1.11149i −0.0930536 + 0.0684076i
\(265\) −5.92220 3.96181i −0.363798 0.243372i
\(266\) −25.6858 6.35733i −1.57490 0.389793i
\(267\) −18.4809 −1.13101
\(268\) 17.4184 + 1.76496i 1.06400 + 0.107812i
\(269\) 4.51225i 0.275116i 0.990494 + 0.137558i \(0.0439254\pi\)
−0.990494 + 0.137558i \(0.956075\pi\)
\(270\) 15.9678 2.33671i 0.971772 0.142208i
\(271\) 12.8691i 0.781741i −0.920446 0.390871i \(-0.872174\pi\)
0.920446 0.390871i \(-0.127826\pi\)
\(272\) 4.78777 23.3827i 0.290301 1.41779i
\(273\) 7.02128i 0.424947i
\(274\) −3.70568 + 3.34917i −0.223868 + 0.202331i
\(275\) 1.74065 0.718753i 0.104965 0.0433424i
\(276\) 1.23607 + 0.125247i 0.0744026 + 0.00753901i
\(277\) 4.35925i 0.261922i 0.991388 + 0.130961i \(0.0418063\pi\)
−0.991388 + 0.130961i \(0.958194\pi\)
\(278\) 7.56465 6.83688i 0.453697 0.410049i
\(279\) −0.109394 −0.00654922
\(280\) 27.1216 1.20294i 1.62083 0.0718893i
\(281\) 7.22169i 0.430810i −0.976525 0.215405i \(-0.930893\pi\)
0.976525 0.215405i \(-0.0691071\pi\)
\(282\) 4.73423 4.27876i 0.281919 0.254797i
\(283\) 4.15031 0.246710 0.123355 0.992363i \(-0.460635\pi\)
0.123355 + 0.992363i \(0.460635\pi\)
\(284\) 2.03973 20.1301i 0.121035 1.19450i
\(285\) −0.0628719 17.1689i −0.00372421 1.01700i
\(286\) −0.366948 + 0.331645i −0.0216981 + 0.0196106i
\(287\) 29.2805i 1.72837i
\(288\) −0.295750 0.501376i −0.0174272 0.0295439i
\(289\) −18.6047 −1.09439
\(290\) 12.1749 1.78166i 0.714935 0.104622i
\(291\) 17.1595i 1.00591i
\(292\) 10.1422 + 1.02768i 0.593528 + 0.0601405i
\(293\) 4.82841 0.282079 0.141039 0.990004i \(-0.454956\pi\)
0.141039 + 0.990004i \(0.454956\pi\)
\(294\) −21.1166 + 19.0850i −1.23154 + 1.11306i
\(295\) −7.40804 4.95580i −0.431313 0.288538i
\(296\) −21.8806 + 16.0854i −1.27178 + 0.934942i
\(297\) −1.92209 −0.111531
\(298\) −3.71301 4.10825i −0.215089 0.237985i
\(299\) 0.327467 0.0189379
\(300\) 5.04743 + 16.8764i 0.291413 + 0.974361i
\(301\) 40.5821 2.33911
\(302\) −6.85410 7.58370i −0.394409 0.436393i
\(303\) 22.6073i 1.29875i
\(304\) 16.1177 6.64972i 0.924415 0.381387i
\(305\) 5.99048 + 4.00749i 0.343014 + 0.229468i
\(306\) −0.644223 + 0.582245i −0.0368278 + 0.0332847i
\(307\) 0.488437i 0.0278766i 0.999903 + 0.0139383i \(0.00443684\pi\)
−0.999903 + 0.0139383i \(0.995563\pi\)
\(308\) −3.21700 0.325970i −0.183306 0.0185739i
\(309\) 3.75210 0.213450
\(310\) 0.486769 + 3.32632i 0.0276466 + 0.188922i
\(311\) 2.59142i 0.146946i 0.997297 + 0.0734730i \(0.0234083\pi\)
−0.997297 + 0.0734730i \(0.976592\pi\)
\(312\) −2.74031 3.72759i −0.155139 0.211033i
\(313\) 9.45632i 0.534503i −0.963627 0.267251i \(-0.913885\pi\)
0.963627 0.267251i \(-0.0861154\pi\)
\(314\) 24.9671 22.5651i 1.40897 1.27342i
\(315\) −0.820937 0.549187i −0.0462545 0.0309432i
\(316\) 2.92287 28.8459i 0.164425 1.62271i
\(317\) −23.7528 −1.33409 −0.667045 0.745018i \(-0.732441\pi\)
−0.667045 + 0.745018i \(0.732441\pi\)
\(318\) −5.88914 + 5.32257i −0.330247 + 0.298475i
\(319\) −1.46553 −0.0820538
\(320\) −13.9293 + 11.2238i −0.778673 + 0.627430i
\(321\) 28.9208 1.61420
\(322\) 1.43544 + 1.58824i 0.0799938 + 0.0885090i
\(323\) −14.5410 21.5650i −0.809085 1.19991i
\(324\) 1.87471 18.5015i 0.104150 1.02786i
\(325\) 1.77203 + 4.29145i 0.0982948 + 0.238047i
\(326\) −14.7111 16.2771i −0.814775 0.901506i
\(327\) −30.6388 −1.69433
\(328\) 11.4278 + 15.5450i 0.630993 + 0.858327i
\(329\) 10.9956 0.606209
\(330\) −0.303787 2.07592i −0.0167229 0.114276i
\(331\) −17.7390 −0.975021 −0.487511 0.873117i \(-0.662095\pi\)
−0.487511 + 0.873117i \(0.662095\pi\)
\(332\) −0.705305 + 6.96066i −0.0387086 + 0.382016i
\(333\) 0.988012 0.0541427
\(334\) 4.67958 4.22938i 0.256055 0.231421i
\(335\) −10.8838 + 16.2693i −0.594643 + 0.888885i
\(336\) 6.06703 29.6304i 0.330983 1.61647i
\(337\) −4.34489 −0.236681 −0.118341 0.992973i \(-0.537757\pi\)
−0.118341 + 0.992973i \(0.537757\pi\)
\(338\) 11.5097 + 12.7349i 0.626044 + 0.692685i
\(339\) 21.2512i 1.15420i
\(340\) 20.5709 + 16.9980i 1.11561 + 0.921848i
\(341\) 0.400399i 0.0216828i
\(342\) −0.615755 0.152401i −0.0332962 0.00824093i
\(343\) −18.9974 −1.02576
\(344\) −21.5450 + 15.8386i −1.16163 + 0.853962i
\(345\) −0.772348 + 1.15452i −0.0415818 + 0.0621574i
\(346\) −19.9628 22.0878i −1.07321 1.18745i
\(347\) −23.7679 −1.27593 −0.637964 0.770067i \(-0.720223\pi\)
−0.637964 + 0.770067i \(0.720223\pi\)
\(348\) 1.38194 13.6384i 0.0740796 0.731093i
\(349\) 14.9933 0.802570 0.401285 0.915953i \(-0.368564\pi\)
0.401285 + 0.915953i \(0.368564\pi\)
\(350\) −13.0462 + 27.4059i −0.697347 + 1.46491i
\(351\) 4.73879i 0.252938i
\(352\) 1.83512 1.08249i 0.0978124 0.0576971i
\(353\) 3.27604i 0.174366i 0.996192 + 0.0871831i \(0.0277865\pi\)
−0.996192 + 0.0871831i \(0.972213\pi\)
\(354\) −7.36669 + 6.65797i −0.391535 + 0.353867i
\(355\) 18.8020 + 12.5781i 0.997909 + 0.667577i
\(356\) 20.8762 + 2.11533i 1.10644 + 0.112112i
\(357\) −45.1180 −2.38790
\(358\) −18.5846 20.5629i −0.982228 1.08678i
\(359\) 1.83814i 0.0970133i −0.998823 0.0485067i \(-0.984554\pi\)
0.998823 0.0485067i \(-0.0154462\pi\)
\(360\) 0.650174 0.0288375i 0.0342672 0.00151987i
\(361\) 7.12282 17.6144i 0.374885 0.927071i
\(362\) −18.4809 + 16.7029i −0.971335 + 0.877886i
\(363\) 19.1267i 1.00389i
\(364\) 0.803656 7.93129i 0.0421230 0.415713i
\(365\) −6.33728 + 9.47309i −0.331708 + 0.495844i
\(366\) 5.95704 5.38393i 0.311380 0.281423i
\(367\) 9.82842 0.513040 0.256520 0.966539i \(-0.417424\pi\)
0.256520 + 0.966539i \(0.417424\pi\)
\(368\) −1.38194 0.282961i −0.0720385 0.0147504i
\(369\) 0.701928i 0.0365409i
\(370\) −4.39636 30.0424i −0.228556 1.56183i
\(371\) −13.6780 −0.710128
\(372\) 3.72616 + 0.377561i 0.193192 + 0.0195756i
\(373\) −8.37248 −0.433510 −0.216755 0.976226i \(-0.569547\pi\)
−0.216755 + 0.976226i \(0.569547\pi\)
\(374\) −2.13111 2.35797i −0.110197 0.121928i
\(375\) −19.3094 3.87409i −0.997135 0.200057i
\(376\) −5.83757 + 4.29145i −0.301050 + 0.221314i
\(377\) 3.61316i 0.186087i
\(378\) 22.9835 20.7723i 1.18214 1.06841i
\(379\) −32.6382 −1.67651 −0.838256 0.545277i \(-0.816425\pi\)
−0.838256 + 0.545277i \(0.816425\pi\)
\(380\) −1.89414 + 19.4013i −0.0971671 + 0.995268i
\(381\) 7.36642 0.377393
\(382\) −24.5768 + 22.2124i −1.25746 + 1.13648i
\(383\) 6.10267i 0.311832i −0.987770 0.155916i \(-0.950167\pi\)
0.987770 0.155916i \(-0.0498329\pi\)
\(384\) 8.34336 + 18.0986i 0.425770 + 0.923591i
\(385\) 2.01012 3.00477i 0.102445 0.153137i
\(386\) 18.0592 + 19.9815i 0.919188 + 1.01703i
\(387\) 0.972857 0.0494531
\(388\) 1.96407 19.3835i 0.0997108 0.984047i
\(389\) 3.65867 0.185502 0.0927510 0.995689i \(-0.470434\pi\)
0.0927510 + 0.995689i \(0.470434\pi\)
\(390\) 5.11803 0.748965i 0.259162 0.0379253i
\(391\) 2.10427i 0.106417i
\(392\) 26.0379 19.1416i 1.31511 0.966795i
\(393\) 1.71722 0.0866224
\(394\) −20.5225 + 18.5481i −1.03391 + 0.934439i
\(395\) 26.9428 + 18.0241i 1.35564 + 0.906892i
\(396\) −0.0771198 0.00781433i −0.00387541 0.000392685i
\(397\) 30.1641i 1.51389i 0.653478 + 0.756946i \(0.273309\pi\)
−0.653478 + 0.756946i \(0.726691\pi\)
\(398\) 21.7597 19.6663i 1.09072 0.985783i
\(399\) −18.4263 27.3269i −0.922468 1.36806i
\(400\) −3.76994 19.6415i −0.188497 0.982074i
\(401\) 34.6456i 1.73012i −0.501670 0.865059i \(-0.667281\pi\)
0.501670 0.865059i \(-0.332719\pi\)
\(402\) 14.6220 + 16.1785i 0.729278 + 0.806908i
\(403\) 0.987155 0.0491737
\(404\) 2.58763 25.5374i 0.128739 1.27053i
\(405\) 17.2809 + 11.5605i 0.858695 + 0.574447i
\(406\) 17.5241 15.8381i 0.869705 0.786033i
\(407\) 3.61629i 0.179253i
\(408\) 23.9531 17.6089i 1.18585 0.871771i
\(409\) 30.5268i 1.50945i 0.656041 + 0.754726i \(0.272230\pi\)
−0.656041 + 0.754726i \(0.727770\pi\)
\(410\) −21.3435 + 3.12337i −1.05408 + 0.154252i
\(411\) −6.22150 −0.306884
\(412\) −4.23841 0.429466i −0.208811 0.0211583i
\(413\) −17.1098 −0.841917
\(414\) 0.0344111 + 0.0380741i 0.00169121 + 0.00187124i
\(415\) −6.50145 4.34931i −0.319144 0.213499i
\(416\) 2.66881 + 4.52437i 0.130849 + 0.221825i
\(417\) 12.7004 0.621940
\(418\) 0.557815 2.25377i 0.0272836 0.110235i
\(419\) 6.46767i 0.315966i 0.987442 + 0.157983i \(0.0504992\pi\)
−0.987442 + 0.157983i \(0.949501\pi\)
\(420\) 26.0672 + 21.5398i 1.27195 + 1.05103i
\(421\) 21.2039i 1.03341i −0.856162 0.516707i \(-0.827158\pi\)
0.856162 0.516707i \(-0.172842\pi\)
\(422\) −0.0711025 0.0786712i −0.00346122 0.00382965i
\(423\) 0.263594 0.0128164
\(424\) 7.26164 5.33834i 0.352656 0.259253i
\(425\) −27.5764 + 11.3869i −1.33765 + 0.552346i
\(426\) 18.6971 16.8983i 0.905877 0.818726i
\(427\) 13.8357 0.669558
\(428\) −32.6692 3.31028i −1.57913 0.160008i
\(429\) −0.616072 −0.0297443
\(430\) −4.32893 29.5816i −0.208759 1.42655i
\(431\) −7.73794 −0.372723 −0.186362 0.982481i \(-0.559670\pi\)
−0.186362 + 0.982481i \(0.559670\pi\)
\(432\) −4.09475 + 19.9981i −0.197009 + 0.962159i
\(433\) −23.8336 −1.14537 −0.572684 0.819776i \(-0.694098\pi\)
−0.572684 + 0.819776i \(0.694098\pi\)
\(434\) 4.32716 + 4.78777i 0.207710 + 0.229820i
\(435\) 12.7386 + 8.52182i 0.610769 + 0.408590i
\(436\) 34.6099 + 3.50692i 1.65751 + 0.167951i
\(437\) −1.27451 + 0.859387i −0.0609679 + 0.0411100i
\(438\) 8.51393 + 9.42022i 0.406811 + 0.450115i
\(439\) −10.4173 −0.497193 −0.248596 0.968607i \(-0.579969\pi\)
−0.248596 + 0.968607i \(0.579969\pi\)
\(440\) 0.105550 + 2.37975i 0.00503190 + 0.113450i
\(441\) −1.17573 −0.0559873
\(442\) 5.81340 5.25411i 0.276515 0.249913i
\(443\) 5.03629 0.239282 0.119641 0.992817i \(-0.461826\pi\)
0.119641 + 0.992817i \(0.461826\pi\)
\(444\) −33.6536 3.41003i −1.59713 0.161833i
\(445\) −13.0443 + 19.4989i −0.618360 + 0.924337i
\(446\) 1.05304 0.951732i 0.0498630 0.0450658i
\(447\) 6.89739i 0.326235i
\(448\) −10.2449 + 32.7763i −0.484024 + 1.54854i
\(449\) 27.3757i 1.29194i −0.763363 0.645970i \(-0.776453\pi\)
0.763363 0.645970i \(-0.223547\pi\)
\(450\) −0.312750 + 0.656989i −0.0147432 + 0.0309708i
\(451\) 2.56918 0.120978
\(452\) 2.43241 24.0055i 0.114411 1.12912i
\(453\) 12.7324i 0.598219i
\(454\) −7.11427 + 6.42983i −0.333889 + 0.301767i
\(455\) 7.40804 + 4.95580i 0.347294 + 0.232332i
\(456\) 20.4478 + 7.31631i 0.957556 + 0.342618i
\(457\) 8.86333i 0.414609i −0.978276 0.207305i \(-0.933531\pi\)
0.978276 0.207305i \(-0.0664691\pi\)
\(458\) 17.5677 + 19.4378i 0.820887 + 0.908268i
\(459\) 30.4509 1.42133
\(460\) 1.00460 1.21575i 0.0468396 0.0566848i
\(461\) −6.71485 −0.312742 −0.156371 0.987698i \(-0.549980\pi\)
−0.156371 + 0.987698i \(0.549980\pi\)
\(462\) −2.70053 2.98800i −0.125640 0.139014i
\(463\) −7.43802 −0.345674 −0.172837 0.984950i \(-0.555293\pi\)
−0.172837 + 0.984950i \(0.555293\pi\)
\(464\) −3.12210 + 15.2478i −0.144940 + 0.707863i
\(465\) −2.32826 + 3.48033i −0.107970 + 0.161397i
\(466\) −10.6104 + 9.58962i −0.491518 + 0.444231i
\(467\) 31.0421 1.43646 0.718228 0.695808i \(-0.244953\pi\)
0.718228 + 0.695808i \(0.244953\pi\)
\(468\) 0.0192657 0.190133i 0.000890557 0.00878892i
\(469\) 37.5758i 1.73509i
\(470\) −1.17291 8.01507i −0.0541025 0.369708i
\(471\) 41.9175 1.93146
\(472\) 9.08355 6.67770i 0.418104 0.307366i
\(473\) 3.56082i 0.163727i
\(474\) 26.7925 24.2148i 1.23062 1.11222i
\(475\) −18.1590 12.0519i −0.833194 0.552981i
\(476\) 50.9656 + 5.16421i 2.33601 + 0.236701i
\(477\) −0.327897 −0.0150134
\(478\) 19.1675 17.3234i 0.876699 0.792355i
\(479\) 21.0127i 0.960093i 0.877243 + 0.480046i \(0.159380\pi\)
−0.877243 + 0.480046i \(0.840620\pi\)
\(480\) −22.2457 1.26175i −1.01537 0.0575908i
\(481\) −8.91571 −0.406521
\(482\) 13.7467 12.4242i 0.626144 0.565905i
\(483\) 2.66651i 0.121330i
\(484\) −2.18924 + 21.6057i −0.0995110 + 0.982075i
\(485\) 18.1047 + 12.1116i 0.822092 + 0.549960i
\(486\) 1.12152 1.01362i 0.0508730 0.0459786i
\(487\) 23.9504i 1.08530i 0.839960 + 0.542648i \(0.182578\pi\)
−0.839960 + 0.542648i \(0.817422\pi\)
\(488\) −7.34537 + 5.39989i −0.332509 + 0.244442i
\(489\) 27.3278i 1.23581i
\(490\) 5.23167 + 35.7505i 0.236343 + 1.61504i
\(491\) 31.9941i 1.44387i 0.691959 + 0.721937i \(0.256748\pi\)
−0.691959 + 0.721937i \(0.743252\pi\)
\(492\) −2.42264 + 23.9091i −0.109221 + 1.07790i
\(493\) 23.2177 1.04567
\(494\) 5.55650 + 1.37525i 0.249999 + 0.0618756i
\(495\) 0.0481877 0.0720320i 0.00216587 0.00323760i
\(496\) −4.16588 0.852992i −0.187054 0.0383005i
\(497\) 43.4256 1.94790
\(498\) −6.46516 + 5.84317i −0.289711 + 0.261839i
\(499\) 29.7730i 1.33282i −0.745584 0.666412i \(-0.767829\pi\)
0.745584 0.666412i \(-0.232171\pi\)
\(500\) 21.3687 + 6.58636i 0.955636 + 0.294551i
\(501\) 7.85660 0.351007
\(502\) −13.4956 + 12.1972i −0.602337 + 0.544388i
\(503\) −24.3841 −1.08723 −0.543617 0.839333i \(-0.682946\pi\)
−0.543617 + 0.839333i \(0.682946\pi\)
\(504\) 1.00661 0.740003i 0.0448380 0.0329623i
\(505\) 23.8526 + 15.9568i 1.06143 + 0.710069i
\(506\) −0.139358 + 0.125950i −0.00619520 + 0.00559918i
\(507\) 21.3807i 0.949550i
\(508\) −8.32117 0.843161i −0.369192 0.0374092i
\(509\) 28.9266i 1.28215i 0.767478 + 0.641075i \(0.221511\pi\)
−0.767478 + 0.641075i \(0.778489\pi\)
\(510\) 4.81277 + 32.8879i 0.213113 + 1.45630i
\(511\) 21.8793i 0.967881i
\(512\) −7.35316 21.3993i −0.324967 0.945725i
\(513\) 12.4362 + 18.4434i 0.549073 + 0.814298i
\(514\) −25.7470 28.4877i −1.13565 1.25654i
\(515\) 2.64833 3.95879i 0.116700 0.174445i
\(516\) −33.1374 3.35772i −1.45879 0.147816i
\(517\) 0.964797i 0.0424317i
\(518\) −39.0817 43.2418i −1.71715 1.89994i
\(519\) 37.0835i 1.62779i
\(520\) −5.86710 + 0.260226i −0.257289 + 0.0114117i
\(521\) 8.62409i 0.377828i −0.981994 0.188914i \(-0.939503\pi\)
0.981994 0.188914i \(-0.0604968\pi\)
\(522\) 0.420097 0.379680i 0.0183871 0.0166182i
\(523\) 33.0172i 1.44374i −0.692028 0.721870i \(-0.743283\pi\)
0.692028 0.721870i \(-0.256717\pi\)
\(524\) −1.93979 0.196553i −0.0847400 0.00858647i
\(525\) −34.9445 + 14.4294i −1.52510 + 0.629750i
\(526\) −17.6800 19.5620i −0.770883 0.852942i
\(527\) 6.34335i 0.276321i
\(528\) 2.59988 + 0.532343i 0.113145 + 0.0231673i
\(529\) −22.8756 −0.994593
\(530\) 1.45905 + 9.97035i 0.0633769 + 0.433084i
\(531\) −0.410165 −0.0177996
\(532\) 17.6866 + 32.9778i 0.766813 + 1.42977i
\(533\) 6.33413i 0.274361i
\(534\) 17.5246 + 19.3901i 0.758364 + 0.839091i
\(535\) 20.4131 30.5139i 0.882535 1.31923i
\(536\) −14.6653 19.9489i −0.633445 0.861663i
\(537\) 34.5233i 1.48979i
\(538\) 4.73423 4.27876i 0.204107 0.184471i
\(539\) 4.30338i 0.185360i
\(540\) −17.5933 14.5376i −0.757093 0.625598i
\(541\) −31.2615 −1.34404 −0.672018 0.740535i \(-0.734572\pi\)
−0.672018 + 0.740535i \(0.734572\pi\)
\(542\) −13.5022 + 12.2032i −0.579969 + 0.524172i
\(543\) −31.0278 −1.33153
\(544\) −29.0731 + 17.1495i −1.24650 + 0.735279i
\(545\) −21.6257 + 32.3266i −0.926344 + 1.38472i
\(546\) 7.36669 6.65797i 0.315265 0.284935i
\(547\) 21.1292i 0.903419i −0.892165 0.451709i \(-0.850814\pi\)
0.892165 0.451709i \(-0.149186\pi\)
\(548\) 7.02786 + 0.712114i 0.300215 + 0.0304200i
\(549\) 0.331678 0.0141557
\(550\) −2.40469 1.14472i −0.102536 0.0488109i
\(551\) 9.48218 + 14.0625i 0.403954 + 0.599081i
\(552\) −1.04070 1.41564i −0.0442952 0.0602538i
\(553\) 62.2277 2.64619
\(554\) 4.57371 4.13369i 0.194318 0.175624i
\(555\) 21.0282 31.4334i 0.892597 1.33427i
\(556\) −14.3464 1.45369i −0.608425 0.0616500i
\(557\) 8.78169i 0.372092i −0.982541 0.186046i \(-0.940433\pi\)
0.982541 0.186046i \(-0.0595674\pi\)
\(558\) 0.103733 + 0.114775i 0.00439137 + 0.00485882i
\(559\) −8.77896 −0.371310
\(560\) −26.9803 27.3152i −1.14013 1.15428i
\(561\) 3.95881i 0.167141i
\(562\) −7.57696 + 6.84801i −0.319615 + 0.288866i
\(563\) 17.0044i 0.716649i −0.933597 0.358325i \(-0.883348\pi\)
0.933597 0.358325i \(-0.116652\pi\)
\(564\) −8.97852 0.909768i −0.378064 0.0383082i
\(565\) 22.4218 + 14.9996i 0.943291 + 0.631039i
\(566\) −3.93556 4.35449i −0.165424 0.183033i
\(567\) 39.9123 1.67616
\(568\) −23.0546 + 16.9484i −0.967348 + 0.711139i
\(569\) 15.9943i 0.670515i 0.942127 + 0.335258i \(0.108823\pi\)
−0.942127 + 0.335258i \(0.891177\pi\)
\(570\) −17.9539 + 16.3465i −0.752008 + 0.684679i
\(571\) 40.0149i 1.67457i −0.546765 0.837286i \(-0.684141\pi\)
0.546765 0.837286i \(-0.315859\pi\)
\(572\) 0.695920 + 0.0705157i 0.0290979 + 0.00294841i
\(573\) −41.2623 −1.72376
\(574\) −30.7210 + 27.7654i −1.28227 + 1.15891i
\(575\) 0.672975 + 1.62978i 0.0280650 + 0.0679667i
\(576\) −0.245596 + 0.785732i −0.0102331 + 0.0327388i
\(577\) 14.6674i 0.610613i 0.952254 + 0.305306i \(0.0987589\pi\)
−0.952254 + 0.305306i \(0.901241\pi\)
\(578\) 17.6420 + 19.5200i 0.733811 + 0.811923i
\(579\) 33.5472i 1.39418i
\(580\) −13.4142 11.0844i −0.556995 0.460254i
\(581\) −15.0159 −0.622964
\(582\) 18.0036 16.2716i 0.746275 0.674478i
\(583\) 1.20016i 0.0497055i
\(584\) −8.53917 11.6157i −0.353353 0.480659i
\(585\) 0.177590 + 0.118803i 0.00734243 + 0.00491191i
\(586\) −4.57857 5.06594i −0.189139 0.209272i
\(587\) 0.410556 0.0169454 0.00847272 0.999964i \(-0.497303\pi\)
0.00847272 + 0.999964i \(0.497303\pi\)
\(588\) 40.0478 + 4.05793i 1.65154 + 0.167346i
\(589\) −3.84203 + 2.59064i −0.158308 + 0.106745i
\(590\) 1.82511 + 12.4719i 0.0751387 + 0.513458i
\(591\) −34.4554 −1.41731
\(592\) 37.6251 + 7.70399i 1.54638 + 0.316632i
\(593\) 20.4734i 0.840742i −0.907352 0.420371i \(-0.861900\pi\)
0.907352 0.420371i \(-0.138100\pi\)
\(594\) 1.82264 + 2.01665i 0.0747837 + 0.0827443i
\(595\) −31.8455 + 47.6033i −1.30554 + 1.95154i
\(596\) −0.789476 + 7.79135i −0.0323382 + 0.319146i
\(597\) 36.5327 1.49518
\(598\) −0.310522 0.343576i −0.0126982 0.0140499i
\(599\) −35.7972 −1.46263 −0.731317 0.682038i \(-0.761094\pi\)
−0.731317 + 0.682038i \(0.761094\pi\)
\(600\) 12.9204 21.2989i 0.527474 0.869524i
\(601\) 36.5899i 1.49253i 0.665647 + 0.746267i \(0.268156\pi\)
−0.665647 + 0.746267i \(0.731844\pi\)
\(602\) −38.4822 42.5786i −1.56842 1.73537i
\(603\) 0.900789i 0.0366830i
\(604\) −1.45735 + 14.3826i −0.0592986 + 0.585219i
\(605\) −20.1803 13.5001i −0.820444 0.548858i
\(606\) 23.7195 21.4375i 0.963537 0.870838i
\(607\) 24.9730i 1.01362i 0.862057 + 0.506812i \(0.169176\pi\)
−0.862057 + 0.506812i \(0.830824\pi\)
\(608\) −22.2606 10.6050i −0.902786 0.430090i
\(609\) 29.4213 1.19221
\(610\) −1.47587 10.0853i −0.0597561 0.408342i
\(611\) −2.37864 −0.0962295
\(612\) 1.22178 + 0.123799i 0.0493874 + 0.00500429i
\(613\) 19.7446i 0.797478i 0.917065 + 0.398739i \(0.130552\pi\)
−0.917065 + 0.398739i \(0.869448\pi\)
\(614\) 0.512466 0.463163i 0.0206814 0.0186917i
\(615\) −22.3317 14.9394i −0.900501 0.602414i
\(616\) 2.70853 + 3.68437i 0.109130 + 0.148447i
\(617\) 32.3305i 1.30158i −0.759259 0.650788i \(-0.774439\pi\)
0.759259 0.650788i \(-0.225561\pi\)
\(618\) −3.55795 3.93669i −0.143122 0.158357i
\(619\) 7.95921i 0.319908i 0.987124 + 0.159954i \(0.0511345\pi\)
−0.987124 + 0.159954i \(0.948865\pi\)
\(620\) 3.02838 3.66492i 0.121623 0.147187i
\(621\) 1.79967i 0.0722185i
\(622\) 2.71891 2.45733i 0.109018 0.0985300i
\(623\) 45.0351i 1.80429i
\(624\) −1.31245 + 6.40982i −0.0525402 + 0.256598i
\(625\) −17.7166 + 17.6386i −0.708664 + 0.705546i
\(626\) −9.92153 + 8.96701i −0.396544 + 0.358394i
\(627\) 2.39776 1.61679i 0.0957575 0.0645683i
\(628\) −47.3503 4.79788i −1.88948 0.191456i
\(629\) 57.2914i 2.28436i
\(630\) 0.202253 + 1.38209i 0.00805796 + 0.0550639i
\(631\) 37.9642i 1.51133i 0.654957 + 0.755666i \(0.272687\pi\)
−0.654957 + 0.755666i \(0.727313\pi\)
\(632\) −33.0366 + 24.2866i −1.31413 + 0.966070i
\(633\) 0.132082i 0.00524979i
\(634\) 22.5237 + 24.9213i 0.894531 + 0.989752i
\(635\) 5.19942 7.77220i 0.206333 0.308430i
\(636\) 11.1688 + 1.13171i 0.442873 + 0.0448751i
\(637\) 10.6097 0.420371
\(638\) 1.38969 + 1.53762i 0.0550185 + 0.0608751i
\(639\) 1.04102 0.0411822
\(640\) 24.9845 + 3.97153i 0.987600 + 0.156989i
\(641\) 22.7859i 0.899988i 0.893032 + 0.449994i \(0.148574\pi\)
−0.893032 + 0.449994i \(0.851426\pi\)
\(642\) −27.4243 30.3436i −1.08235 1.19757i
\(643\) −17.9394 −0.707461 −0.353731 0.935347i \(-0.615087\pi\)
−0.353731 + 0.935347i \(0.615087\pi\)
\(644\) 0.305209 3.01211i 0.0120269 0.118694i
\(645\) 20.7057 30.9513i 0.815284 1.21870i
\(646\) −8.83723 + 35.7055i −0.347696 + 1.40481i
\(647\) 21.4626 0.843781 0.421891 0.906647i \(-0.361367\pi\)
0.421891 + 0.906647i \(0.361367\pi\)
\(648\) −21.1894 + 15.5772i −0.832398 + 0.611931i
\(649\) 1.50127i 0.0589301i
\(650\) 2.82222 5.92860i 0.110697 0.232539i
\(651\) 8.03825i 0.315044i
\(652\) −3.12794 + 30.8697i −0.122500 + 1.20895i
\(653\) 11.7812i 0.461035i −0.973068 0.230518i \(-0.925958\pi\)
0.973068 0.230518i \(-0.0740420\pi\)
\(654\) 29.0535 + 32.1461i 1.13608 + 1.25701i
\(655\) 1.21206 1.81181i 0.0473591 0.0707935i
\(656\) 5.47326 26.7306i 0.213695 1.04365i
\(657\) 0.524502i 0.0204628i
\(658\) −10.4267 11.5366i −0.406474 0.449743i
\(659\) 24.3327 0.947866 0.473933 0.880561i \(-0.342834\pi\)
0.473933 + 0.880561i \(0.342834\pi\)
\(660\) −1.88998 + 2.28723i −0.0735673 + 0.0890305i
\(661\) 7.73106i 0.300703i 0.988633 + 0.150352i \(0.0480406\pi\)
−0.988633 + 0.150352i \(0.951959\pi\)
\(662\) 16.8211 + 18.6116i 0.653769 + 0.723362i
\(663\) 9.76018 0.379054
\(664\) 7.97191 5.86049i 0.309370 0.227431i
\(665\) −41.8380 + 0.153209i −1.62241 + 0.00594119i
\(666\) −0.936888 1.03662i −0.0363037 0.0401681i
\(667\) 1.37219i 0.0531313i
\(668\) −8.87488 0.899267i −0.343380 0.0347937i
\(669\) 1.76796 0.0683534
\(670\) 27.3902 4.00824i 1.05818 0.154852i
\(671\) 1.21400i 0.0468658i
\(672\) −36.8412 + 21.7317i −1.42118 + 0.838319i
\(673\) 4.63946 0.178838 0.0894190 0.995994i \(-0.471499\pi\)
0.0894190 + 0.995994i \(0.471499\pi\)
\(674\) 4.12007 + 4.55864i 0.158699 + 0.175592i
\(675\) 23.5847 9.73866i 0.907776 0.374841i
\(676\) 2.44724 24.1518i 0.0941244 0.928915i
\(677\) −3.39362 −0.130427 −0.0652137 0.997871i \(-0.520773\pi\)
−0.0652137 + 0.997871i \(0.520773\pi\)
\(678\) 22.2966 20.1515i 0.856296 0.773915i
\(679\) 41.8150 1.60471
\(680\) −1.67219 37.7013i −0.0641254 1.44578i
\(681\) −11.9442 −0.457704
\(682\) −0.420097 + 0.379680i −0.0160863 + 0.0145387i
\(683\) 9.59176i 0.367018i 0.983018 + 0.183509i \(0.0587457\pi\)
−0.983018 + 0.183509i \(0.941254\pi\)
\(684\) 0.423994 + 0.790562i 0.0162118 + 0.0302279i
\(685\) −4.39130 + 6.56421i −0.167783 + 0.250806i
\(686\) 18.0144 + 19.9320i 0.687792 + 0.761006i
\(687\) 32.6343i 1.24508i
\(688\) 37.0480 + 7.58582i 1.41244 + 0.289207i
\(689\) 2.95891 0.112725
\(690\) 1.94370 0.284438i 0.0739955 0.0108284i
\(691\) 21.3675i 0.812856i −0.913683 0.406428i \(-0.866774\pi\)
0.913683 0.406428i \(-0.133226\pi\)
\(692\) −4.24458 + 41.8898i −0.161355 + 1.59241i
\(693\) 0.166366i 0.00631974i
\(694\) 22.5380 + 24.9372i 0.855532 + 0.946602i
\(695\) 8.96426 13.4000i 0.340034 0.508290i
\(696\) −15.6197 + 11.4827i −0.592065 + 0.435252i
\(697\) −40.7024 −1.54171
\(698\) −14.2174 15.7308i −0.538138 0.595421i
\(699\) −17.8139 −0.673785
\(700\) 41.1252 12.2998i 1.55439 0.464889i
\(701\) 17.7323 0.669739 0.334869 0.942265i \(-0.391308\pi\)
0.334869 + 0.942265i \(0.391308\pi\)
\(702\) −4.97192 + 4.49358i −0.187653 + 0.169599i
\(703\) 34.7001 23.3979i 1.30874 0.882470i
\(704\) −2.87591 0.898921i −0.108390 0.0338794i
\(705\) 5.61015 8.38618i 0.211291 0.315842i
\(706\) 3.43721 3.10653i 0.129361 0.116916i
\(707\) 55.0904 2.07189
\(708\) 13.9710 + 1.41564i 0.525063 + 0.0532032i
\(709\) 1.60751 0.0603715 0.0301857 0.999544i \(-0.490390\pi\)
0.0301857 + 0.999544i \(0.490390\pi\)
\(710\) −4.63224 31.6543i −0.173845 1.18796i
\(711\) 1.49176 0.0559453
\(712\) −17.5766 23.9091i −0.658710 0.896030i
\(713\) 0.374897 0.0140400
\(714\) 42.7834 + 47.3376i 1.60113 + 1.77156i
\(715\) −0.434840 + 0.650009i −0.0162621 + 0.0243089i
\(716\) −3.95154 + 38.9978i −0.147676 + 1.45742i
\(717\) 32.1804 1.20180
\(718\) −1.92857 + 1.74303i −0.0719735 + 0.0650492i
\(719\) 37.3717i 1.39373i −0.717203 0.696864i \(-0.754578\pi\)
0.717203 0.696864i \(-0.245422\pi\)
\(720\) −0.646787 0.654814i −0.0241043 0.0244035i
\(721\) 9.14329i 0.340514i
\(722\) −25.2352 + 9.22969i −0.939155 + 0.343493i
\(723\) 23.0794 0.858334
\(724\) 35.0492 + 3.55144i 1.30259 + 0.131988i
\(725\) 17.9825 7.42537i 0.667853 0.275771i
\(726\) −20.0676 + 18.1370i −0.744779 + 0.673127i
\(727\) 10.1249 0.375514 0.187757 0.982216i \(-0.439878\pi\)
0.187757 + 0.982216i \(0.439878\pi\)
\(728\) −9.08355 + 6.67770i −0.336659 + 0.247492i
\(729\) −26.0114 −0.963386
\(730\) 15.9485 2.33388i 0.590280 0.0863806i
\(731\) 56.4126i 2.08650i
\(732\) −11.2976 1.14475i −0.417571 0.0423113i
\(733\) 26.6032i 0.982613i −0.870987 0.491307i \(-0.836519\pi\)
0.870987 0.491307i \(-0.163481\pi\)
\(734\) −9.31986 10.3119i −0.344002 0.380621i
\(735\) −25.0235 + 37.4057i −0.923007 + 1.37973i
\(736\) 1.01355 + 1.71824i 0.0373599 + 0.0633353i
\(737\) −3.29704 −0.121448
\(738\) −0.736460 + 0.665608i −0.0271095 + 0.0245014i
\(739\) 15.5478i 0.571934i 0.958239 + 0.285967i \(0.0923147\pi\)
−0.958239 + 0.285967i \(0.907685\pi\)
\(740\) −27.3515 + 33.1005i −1.00546 + 1.21680i
\(741\) 3.98608 + 5.91152i 0.146432 + 0.217165i
\(742\) 12.9703 + 14.3509i 0.476153 + 0.526839i
\(743\) 37.6670i 1.38187i −0.722918 0.690934i \(-0.757199\pi\)
0.722918 0.690934i \(-0.242801\pi\)
\(744\) −3.13721 4.26749i −0.115016 0.156454i
\(745\) −7.27733 4.86836i −0.266621 0.178363i
\(746\) 7.93925 + 8.78436i 0.290677 + 0.321618i
\(747\) −0.359969 −0.0131706
\(748\) −0.453126 + 4.47191i −0.0165679 + 0.163509i
\(749\) 70.4756i 2.57512i
\(750\) 14.2456 + 23.9330i 0.520176 + 0.873910i
\(751\) 4.74210 0.173042 0.0865208 0.996250i \(-0.472425\pi\)
0.0865208 + 0.996250i \(0.472425\pi\)
\(752\) 10.0381 + 2.05536i 0.366051 + 0.0749514i
\(753\) −22.6579 −0.825698
\(754\) −3.79091 + 3.42620i −0.138057 + 0.124775i
\(755\) −13.4337 8.98684i −0.488903 0.327065i
\(756\) −43.5884 4.41669i −1.58529 0.160634i
\(757\) 15.0862i 0.548316i −0.961685 0.274158i \(-0.911601\pi\)
0.961685 0.274158i \(-0.0883992\pi\)
\(758\) 30.9494 + 34.2439i 1.12413 + 1.24379i
\(759\) −0.233969 −0.00849254
\(760\) 22.1519 16.4101i 0.803535 0.595258i
\(761\) −24.9280 −0.903638 −0.451819 0.892110i \(-0.649225\pi\)
−0.451819 + 0.892110i \(0.649225\pi\)
\(762\) −6.98525 7.72882i −0.253049 0.279986i
\(763\) 74.6621i 2.70295i
\(764\) 46.6102 + 4.72288i 1.68630 + 0.170868i
\(765\) −0.763417 + 1.14117i −0.0276014 + 0.0412592i
\(766\) −6.40289 + 5.78689i −0.231346 + 0.209089i
\(767\) 3.70128 0.133646
\(768\) 11.0773 25.9159i 0.399719 0.935161i
\(769\) 27.1950 0.980678 0.490339 0.871532i \(-0.336873\pi\)
0.490339 + 0.871532i \(0.336873\pi\)
\(770\) −5.05869 + 0.740281i −0.182303 + 0.0266779i
\(771\) 47.8284i 1.72250i
\(772\) 3.83982 37.8952i 0.138198 1.36388i
\(773\) −11.1297 −0.400308 −0.200154 0.979764i \(-0.564144\pi\)
−0.200154 + 0.979764i \(0.564144\pi\)
\(774\) −0.922518 1.02072i −0.0331592 0.0366889i
\(775\) 2.02870 + 4.91302i 0.0728730 + 0.176481i
\(776\) −22.1995 + 16.3198i −0.796916 + 0.585847i
\(777\) 72.5992i 2.60448i
\(778\) −3.46936 3.83866i −0.124382 0.137623i
\(779\) −16.6230 24.6525i −0.595579 0.883269i
\(780\) −5.63902 4.65961i −0.201909 0.166841i
\(781\) 3.81032i 0.136344i
\(782\) 2.20779 1.99538i 0.0789502 0.0713547i
\(783\) −19.8570 −0.709631
\(784\) −44.7738 9.16775i −1.59907 0.327420i
\(785\) 29.5865 44.2265i 1.05599 1.57851i
\(786\) −1.62837 1.80170i −0.0580819 0.0642646i
\(787\) 13.2771i 0.473278i 0.971598 + 0.236639i \(0.0760459\pi\)
−0.971598 + 0.236639i \(0.923954\pi\)
\(788\) 38.9211 + 3.94377i 1.38651 + 0.140491i
\(789\) 32.8428i 1.16923i
\(790\) −6.63788 45.3598i −0.236165 1.61383i
\(791\) 51.7858 1.84129
\(792\) 0.0649305 + 0.0883237i 0.00230721 + 0.00313845i
\(793\) −2.99303 −0.106285
\(794\) 31.6480 28.6033i 1.12315 1.01509i
\(795\) −6.97875 + 10.4320i −0.247511 + 0.369984i
\(796\) −41.2676 4.18153i −1.46269 0.148210i
\(797\) −19.5604 −0.692866 −0.346433 0.938075i \(-0.612607\pi\)
−0.346433 + 0.938075i \(0.612607\pi\)
\(798\) −11.1985 + 45.2457i −0.396422 + 1.60168i
\(799\) 15.2849i 0.540740i
\(800\) −17.0329 + 22.5805i −0.602203 + 0.798343i
\(801\) 1.07961i 0.0381460i
\(802\) −36.3500 + 32.8529i −1.28356 + 1.16008i
\(803\) −1.91976 −0.0677470
\(804\) 3.10899 30.6826i 0.109645 1.08209i
\(805\) 2.81339 + 1.88209i 0.0991590 + 0.0663350i
\(806\) −0.936076 1.03572i −0.0329719 0.0364816i
\(807\) 7.94835 0.279795
\(808\) −29.2474 + 21.5010i −1.02892 + 0.756403i
\(809\) 6.76217 0.237745 0.118873 0.992910i \(-0.462072\pi\)
0.118873 + 0.992910i \(0.462072\pi\)
\(810\) −4.25748 29.0934i −0.149593 1.02224i
\(811\) −6.17322 −0.216771 −0.108385 0.994109i \(-0.534568\pi\)
−0.108385 + 0.994109i \(0.534568\pi\)
\(812\) −33.2346 3.36757i −1.16631 0.118178i
\(813\) −22.6690 −0.795035
\(814\) 3.79419 3.42917i 0.132986 0.120192i
\(815\) −28.8332 19.2887i −1.00998 0.675654i
\(816\) −41.1888 8.43369i −1.44190 0.295238i
\(817\) 34.1679 23.0390i 1.19538 0.806034i
\(818\) 32.0285 28.9472i 1.11985 1.01211i
\(819\) 0.410165 0.0143323
\(820\) 23.5161 + 19.4317i 0.821218 + 0.678586i
\(821\) 50.4086 1.75927 0.879636 0.475647i \(-0.157786\pi\)
0.879636 + 0.475647i \(0.157786\pi\)
\(822\) 5.89958 + 6.52757i 0.205771 + 0.227675i
\(823\) 42.0362 1.46529 0.732644 0.680612i \(-0.238286\pi\)
0.732644 + 0.680612i \(0.238286\pi\)
\(824\) 3.56850 + 4.85416i 0.124315 + 0.169103i
\(825\) −1.26609 3.06616i −0.0440795 0.106750i
\(826\) 16.2244 + 17.9515i 0.564520 + 0.624612i
\(827\) 36.2488i 1.26050i 0.776394 + 0.630248i \(0.217047\pi\)
−0.776394 + 0.630248i \(0.782953\pi\)
\(828\) 0.00731663 0.0722080i 0.000254271 0.00250940i
\(829\) 30.0656i 1.04422i 0.852878 + 0.522110i \(0.174855\pi\)
−0.852878 + 0.522110i \(0.825145\pi\)
\(830\) 1.60175 + 10.9456i 0.0555977 + 0.379926i
\(831\) 7.67885 0.266376
\(832\) 2.21623 7.09036i 0.0768339 0.245814i
\(833\) 68.1767i 2.36218i
\(834\) −12.0432 13.3252i −0.417022 0.461413i
\(835\) 5.54540 8.28938i 0.191906 0.286866i
\(836\) −2.89359 + 1.55189i −0.100077 + 0.0536732i
\(837\) 5.42516i 0.187521i
\(838\) 6.78585 6.13300i 0.234413 0.211861i
\(839\) −20.6881 −0.714231 −0.357116 0.934060i \(-0.616240\pi\)
−0.357116 + 0.934060i \(0.616240\pi\)
\(840\) −2.11898 47.7748i −0.0731118 1.64839i
\(841\) 13.8598 0.477923
\(842\) −22.2470 + 20.1067i −0.766682 + 0.692922i
\(843\) −12.7210 −0.438136
\(844\) −0.0151181 + 0.149201i −0.000520387 + 0.00513570i
\(845\) 22.5584 + 15.0911i 0.776034 + 0.519148i
\(846\) −0.249954 0.276561i −0.00859360 0.00950837i
\(847\) −46.6087 −1.60150
\(848\) −12.4869 2.55677i −0.428800 0.0877998i
\(849\) 7.31080i 0.250906i
\(850\) 38.0965 + 18.1353i 1.30670 + 0.622036i
\(851\) −3.38597 −0.116069
\(852\) −35.4593 3.59299i −1.21481 0.123094i
\(853\) 10.3551i 0.354553i −0.984161 0.177276i \(-0.943271\pi\)
0.984161 0.177276i \(-0.0567286\pi\)
\(854\) −13.1198 14.5164i −0.448951 0.496741i
\(855\) −1.00296 + 0.00367281i −0.0343006 + 0.000125608i
\(856\) 27.5056 + 37.4154i 0.940123 + 1.27883i
\(857\) −8.93791 −0.305313 −0.152657 0.988279i \(-0.548783\pi\)
−0.152657 + 0.988279i \(0.548783\pi\)
\(858\) 0.584194 + 0.646380i 0.0199441 + 0.0220671i
\(859\) 18.8257i 0.642325i 0.947024 + 0.321162i \(0.104073\pi\)
−0.947024 + 0.321162i \(0.895927\pi\)
\(860\) −26.9320 + 32.5928i −0.918372 + 1.11141i
\(861\) −51.5778 −1.75777
\(862\) 7.33754 + 8.11861i 0.249918 + 0.276521i
\(863\) 14.2058i 0.483573i 0.970330 + 0.241786i \(0.0777333\pi\)
−0.970330 + 0.241786i \(0.922267\pi\)
\(864\) 24.8648 14.6671i 0.845917 0.498986i
\(865\) −39.1262 26.1745i −1.33033 0.889961i
\(866\) 22.6003 + 25.0061i 0.767990 + 0.849741i
\(867\) 32.7723i 1.11300i
\(868\) 0.920058 9.08007i 0.0312288 0.308198i
\(869\) 5.46009i 0.185221i
\(870\) −3.13840 21.4462i −0.106402 0.727093i
\(871\) 8.12862i 0.275428i
\(872\) −29.1396 39.6380i −0.986791 1.34231i
\(873\) 1.00241 0.0339265
\(874\) 2.11022 + 0.522287i 0.0713793 + 0.0176666i
\(875\) −9.44056 + 47.0541i −0.319149 + 1.59072i
\(876\) 1.81027 17.8656i 0.0611633 0.603621i
\(877\) 52.5843 1.77565 0.887824 0.460184i \(-0.152217\pi\)
0.887824 + 0.460184i \(0.152217\pi\)
\(878\) 9.87831 + 10.9298i 0.333377 + 0.368864i
\(879\) 8.50527i 0.286876i
\(880\) 2.39673 2.36735i 0.0807938 0.0798034i
\(881\) 7.17014 0.241568 0.120784 0.992679i \(-0.461459\pi\)
0.120784 + 0.992679i \(0.461459\pi\)
\(882\) 1.11490 + 1.23357i 0.0375405 + 0.0415366i
\(883\) 23.0586 0.775985 0.387992 0.921663i \(-0.373169\pi\)
0.387992 + 0.921663i \(0.373169\pi\)
\(884\) −11.0252 1.11715i −0.370817 0.0375739i
\(885\) −8.72968 + 13.0493i −0.293445 + 0.438648i
\(886\) −4.77569 5.28406i −0.160443 0.177521i
\(887\) 34.1642i 1.14712i −0.819163 0.573560i \(-0.805562\pi\)
0.819163 0.573560i \(-0.194438\pi\)
\(888\) 28.3344 + 38.5428i 0.950842 + 1.29341i
\(889\) 17.9508i 0.602052i
\(890\) 32.8275 4.80393i 1.10038 0.161028i
\(891\) 3.50205i 0.117323i
\(892\) −1.99711 0.202361i −0.0668680 0.00677555i
\(893\) 9.25771 6.24238i 0.309798 0.208893i
\(894\) −7.23671 + 6.54049i −0.242032 + 0.218747i
\(895\) −36.4250 24.3675i −1.21755 0.814515i
\(896\) 44.1035 20.3315i 1.47340 0.679227i
\(897\) 0.576834i 0.0192599i
\(898\) −28.7225 + 25.9592i −0.958482 + 0.866269i
\(899\) 4.13649i 0.137960i
\(900\) 0.985877 0.294858i 0.0328626 0.00982859i
\(901\) 19.0136i 0.633436i
\(902\) −2.43624 2.69557i −0.0811178 0.0897526i
\(903\) 71.4856i 2.37889i
\(904\) −27.4930 + 20.2113i −0.914403 + 0.672216i
\(905\) −21.9002 + 32.7369i −0.727988 + 1.08821i
\(906\) −13.3587 + 12.0735i −0.443814 + 0.401116i
\(907\) 40.1696i 1.33381i −0.745142 0.666906i \(-0.767618\pi\)
0.745142 0.666906i \(-0.232382\pi\)
\(908\) 13.4923 + 1.36714i 0.447757 + 0.0453700i
\(909\) 1.32066 0.0438035
\(910\) −1.82511 12.4719i −0.0605019 0.413438i
\(911\) 53.5926 1.77560 0.887802 0.460226i \(-0.152232\pi\)
0.887802 + 0.460226i \(0.152232\pi\)
\(912\) −11.7135 28.3915i −0.387873 0.940136i
\(913\) 1.31755i 0.0436045i
\(914\) −9.29936 + 8.40470i −0.307596 + 0.278003i
\(915\) 7.05921 10.5523i 0.233370 0.348847i
\(916\) 3.73533 36.8640i 0.123419 1.21802i
\(917\) 4.18460i 0.138188i
\(918\) −28.8753 31.9490i −0.953026 1.05447i
\(919\) 36.0060i 1.18773i 0.804566 + 0.593864i \(0.202398\pi\)
−0.804566 + 0.593864i \(0.797602\pi\)
\(920\) −2.22818 + 0.0988276i −0.0734609 + 0.00325825i
\(921\) 0.860384 0.0283506
\(922\) 6.36740 + 7.04519i 0.209699 + 0.232021i
\(923\) −9.39407 −0.309210
\(924\) −0.574198 + 5.66677i −0.0188897 + 0.186423i
\(925\) −18.3226 44.3730i −0.602444 1.45898i
\(926\) 7.05314 + 7.80393i 0.231781 + 0.256453i
\(927\) 0.219188i 0.00719908i
\(928\) 18.9585 11.1832i 0.622343 0.367105i
\(929\) 13.0488 0.428118 0.214059 0.976821i \(-0.431331\pi\)
0.214059 + 0.976821i \(0.431331\pi\)
\(930\) 5.85933 0.857446i 0.192135 0.0281167i
\(931\) −41.2931 + 27.8435i −1.35333 + 0.912535i
\(932\) 20.1228 + 2.03899i 0.659143 + 0.0667892i
\(933\) 4.56481 0.149445
\(934\) −29.4358 32.5692i −0.963170 1.06570i
\(935\) −4.17688 2.79424i −0.136599 0.0913813i
\(936\) −0.217756 + 0.160082i −0.00711757 + 0.00523243i
\(937\) 22.0684i 0.720943i 0.932770 + 0.360471i \(0.117384\pi\)
−0.932770 + 0.360471i \(0.882616\pi\)
\(938\) 39.4244 35.6315i 1.28725 1.16341i
\(939\) −16.6574 −0.543593
\(940\) −7.29716 + 8.83096i −0.238007 + 0.288034i
\(941\) 32.6150i 1.06322i 0.846990 + 0.531609i \(0.178413\pi\)
−0.846990 + 0.531609i \(0.821587\pi\)
\(942\) −39.7485 43.9796i −1.29508 1.43293i
\(943\) 2.40554i 0.0783353i
\(944\) −15.6197 3.19825i −0.508379 0.104094i
\(945\) 27.2359 40.7128i 0.885983 1.32439i
\(946\) 3.73600 3.37657i 0.121468 0.109782i
\(947\) −51.3144 −1.66749 −0.833747 0.552147i \(-0.813809\pi\)
−0.833747 + 0.552147i \(0.813809\pi\)
\(948\) −50.8122 5.14866i −1.65030 0.167221i
\(949\) 4.73305i 0.153641i
\(950\) 4.57457 + 30.4807i 0.148419 + 0.988925i
\(951\) 41.8407i 1.35678i
\(952\) −42.9102 58.3699i −1.39073 1.89178i
\(953\) −34.2291 −1.10879 −0.554394 0.832254i \(-0.687050\pi\)
−0.554394 + 0.832254i \(0.687050\pi\)
\(954\) 0.310930 + 0.344028i 0.0100667 + 0.0111383i
\(955\) −29.1240 + 43.5352i −0.942431 + 1.40877i
\(956\) −36.3513 3.68338i −1.17568 0.119129i
\(957\) 2.58153i 0.0834492i
\(958\) 22.0464 19.9254i 0.712286 0.643760i
\(959\) 15.1608i 0.489569i
\(960\) 19.7708 + 24.5366i 0.638100 + 0.791915i
\(961\) −29.8699 −0.963544
\(962\) 8.45437 + 9.35432i 0.272580 + 0.301595i
\(963\) 1.68948i 0.0544427i
\(964\) −26.0707 2.64167i −0.839681 0.0850826i
\(965\) 35.3952 + 23.6785i 1.13941 + 0.762239i
\(966\) 2.79769 2.52853i 0.0900141 0.0813542i
\(967\) 41.3727 1.33046 0.665229 0.746640i \(-0.268334\pi\)
0.665229 + 0.746640i \(0.268334\pi\)
\(968\) 24.7445 18.1907i 0.795319 0.584673i
\(969\) −37.9868 + 25.6141i −1.22031 + 0.822844i
\(970\) −4.46043 30.4803i −0.143216 0.978662i
\(971\) −30.6284 −0.982914 −0.491457 0.870902i \(-0.663535\pi\)
−0.491457 + 0.870902i \(0.663535\pi\)
\(972\) −2.12697 0.215520i −0.0682225 0.00691279i
\(973\) 30.9488i 0.992174i
\(974\) 25.1287 22.7111i 0.805174 0.727711i
\(975\) 7.55941 3.12145i 0.242095 0.0999664i
\(976\) 12.6308 + 2.58625i 0.404303 + 0.0827838i
\(977\) 31.8746 1.01976 0.509879 0.860246i \(-0.329690\pi\)
0.509879 + 0.860246i \(0.329690\pi\)
\(978\) −28.6722 + 25.9138i −0.916836 + 0.828631i
\(979\) −3.95154 −0.126292
\(980\) 32.5483 39.3896i 1.03972 1.25826i
\(981\) 1.78984i 0.0571453i
\(982\) 33.5681 30.3386i 1.07120 0.968143i
\(983\) 11.0853i 0.353566i 0.984250 + 0.176783i \(0.0565690\pi\)
−0.984250 + 0.176783i \(0.943431\pi\)
\(984\) 27.3826 20.1301i 0.872924 0.641723i
\(985\) −24.3195 + 36.3534i −0.774885 + 1.15831i
\(986\) −22.0164 24.3600i −0.701144 0.775779i
\(987\) 19.3689i 0.616518i
\(988\) −3.82608 7.13395i −0.121724 0.226961i
\(989\) −3.33403 −0.106016
\(990\) −0.121270 + 0.0177464i −0.00385421 + 0.000564019i
\(991\) 17.2353 0.547497 0.273749 0.961801i \(-0.411736\pi\)
0.273749 + 0.961801i \(0.411736\pi\)
\(992\) 3.05537 + 5.17968i 0.0970080 + 0.164455i
\(993\) 31.2473i 0.991602i
\(994\) −41.1785 45.5619i −1.30610 1.44514i
\(995\) 25.7857 38.5451i 0.817463 1.22196i
\(996\) 12.2612 + 1.24240i 0.388513 + 0.0393669i
\(997\) 11.4664i 0.363145i −0.983378 0.181572i \(-0.941881\pi\)
0.983378 0.181572i \(-0.0581187\pi\)
\(998\) −31.2377 + 28.2324i −0.988812 + 0.893682i
\(999\) 48.9985i 1.55024i
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.d.b.379.9 40
4.3 odd 2 inner 380.2.d.b.379.11 yes 40
5.4 even 2 inner 380.2.d.b.379.32 yes 40
19.18 odd 2 inner 380.2.d.b.379.31 yes 40
20.19 odd 2 inner 380.2.d.b.379.30 yes 40
76.75 even 2 inner 380.2.d.b.379.29 yes 40
95.94 odd 2 inner 380.2.d.b.379.10 yes 40
380.379 even 2 inner 380.2.d.b.379.12 yes 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
380.2.d.b.379.9 40 1.1 even 1 trivial
380.2.d.b.379.10 yes 40 95.94 odd 2 inner
380.2.d.b.379.11 yes 40 4.3 odd 2 inner
380.2.d.b.379.12 yes 40 380.379 even 2 inner
380.2.d.b.379.29 yes 40 76.75 even 2 inner
380.2.d.b.379.30 yes 40 20.19 odd 2 inner
380.2.d.b.379.31 yes 40 19.18 odd 2 inner
380.2.d.b.379.32 yes 40 5.4 even 2 inner