Properties

Label 668.2.b.b.667.10
Level $668$
Weight $2$
Character 668.667
Analytic conductor $5.334$
Analytic rank $0$
Dimension $60$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [668,2,Mod(667,668)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(668, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("668.667");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 668 = 2^{2} \cdot 167 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 668.b (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: \(5.33400685502\)
Analytic rank: \(0\)
Dimension: \(60\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 667.10
Character \(\chi\) \(=\) 668.667
Dual form 668.2.b.b.667.11

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.30799 - 0.537726i) q^{2} -2.06566i q^{3} +(1.42170 + 1.40669i) q^{4} +1.78350i q^{5} +(-1.11076 + 2.70187i) q^{6} -0.540270i q^{7} +(-1.10317 - 2.60442i) q^{8} -1.26695 q^{9} +O(q^{10})\) \(q+(-1.30799 - 0.537726i) q^{2} -2.06566i q^{3} +(1.42170 + 1.40669i) q^{4} +1.78350i q^{5} +(-1.11076 + 2.70187i) q^{6} -0.540270i q^{7} +(-1.10317 - 2.60442i) q^{8} -1.26695 q^{9} +(0.959034 - 2.33281i) q^{10} +0.518196i q^{11} +(2.90574 - 2.93675i) q^{12} +4.59318i q^{13} +(-0.290517 + 0.706671i) q^{14} +3.68410 q^{15} +(0.0424712 + 3.99977i) q^{16} -4.49305i q^{17} +(1.65717 + 0.681274i) q^{18} -7.50492i q^{19} +(-2.50882 + 2.53560i) q^{20} -1.11602 q^{21} +(0.278648 - 0.677798i) q^{22} +8.08382 q^{23} +(-5.37986 + 2.27877i) q^{24} +1.81913 q^{25} +(2.46987 - 6.00786i) q^{26} -3.57988i q^{27} +(0.759991 - 0.768103i) q^{28} +2.47382 q^{29} +(-4.81879 - 1.98104i) q^{30} +3.56761i q^{31} +(2.09523 - 5.25452i) q^{32} +1.07042 q^{33} +(-2.41603 + 5.87688i) q^{34} +0.963572 q^{35} +(-1.80123 - 1.78221i) q^{36} +8.52951i q^{37} +(-4.03559 + 9.81640i) q^{38} +9.48796 q^{39} +(4.64499 - 1.96750i) q^{40} -10.7353i q^{41} +(1.45974 + 0.600110i) q^{42} +5.36699 q^{43} +(-0.728939 + 0.736721i) q^{44} -2.25961i q^{45} +(-10.5736 - 4.34688i) q^{46} -3.27968i q^{47} +(8.26218 - 0.0877311i) q^{48} +6.70811 q^{49} +(-2.37941 - 0.978194i) q^{50} -9.28111 q^{51} +(-6.46116 + 6.53014i) q^{52} -9.17750i q^{53} +(-1.92500 + 4.68247i) q^{54} -0.924203 q^{55} +(-1.40709 + 0.596009i) q^{56} -15.5026 q^{57} +(-3.23574 - 1.33024i) q^{58} -6.36471 q^{59} +(5.23770 + 5.18238i) q^{60} -12.5812 q^{61} +(1.91840 - 4.66642i) q^{62} +0.684498i q^{63} +(-5.56604 + 5.74623i) q^{64} -8.19194 q^{65} +(-1.40010 - 0.575591i) q^{66} +14.5036 q^{67} +(6.32030 - 6.38777i) q^{68} -16.6984i q^{69} +(-1.26035 - 0.518138i) q^{70} -3.96731 q^{71} +(1.39766 + 3.29969i) q^{72} -3.38016i q^{73} +(4.58654 - 11.1566i) q^{74} -3.75771i q^{75} +(10.5571 - 10.6698i) q^{76} +0.279966 q^{77} +(-12.4102 - 5.10192i) q^{78} -9.68909 q^{79} +(-7.13359 + 0.0757474i) q^{80} -11.1957 q^{81} +(-5.77267 + 14.0418i) q^{82} +6.57031 q^{83} +(-1.58664 - 1.56988i) q^{84} +8.01335 q^{85} +(-7.02000 - 2.88597i) q^{86} -5.11007i q^{87} +(1.34960 - 0.571657i) q^{88} -9.71328 q^{89} +(-1.21505 + 2.95556i) q^{90} +2.48156 q^{91} +(11.4928 + 11.3714i) q^{92} +7.36948 q^{93} +(-1.76357 + 4.28980i) q^{94} +13.3850 q^{95} +(-10.8541 - 4.32803i) q^{96} +15.8410 q^{97} +(-8.77417 - 3.60712i) q^{98} -0.656531i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 60 q - 2 q^{2} + 2 q^{4} - 8 q^{6} - 8 q^{8} - 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 60 q - 2 q^{2} + 2 q^{4} - 8 q^{6} - 8 q^{8} - 16 q^{9} + 18 q^{12} + 10 q^{14} + 10 q^{16} - 20 q^{18} + 20 q^{22} + 10 q^{24} - 188 q^{25} + 4 q^{29} + 18 q^{32} + 8 q^{33} + 30 q^{36} - 36 q^{38} + 14 q^{42} + 28 q^{44} - 28 q^{48} + 72 q^{49} - 40 q^{50} - 74 q^{54} + 50 q^{56} + 8 q^{57} - 22 q^{58} + 36 q^{61} + 104 q^{62} + 8 q^{64} + 24 q^{65} + 24 q^{66} + 90 q^{72} - 36 q^{76} - 84 q^{81} - 110 q^{84} - 16 q^{85} - 20 q^{88} + 28 q^{89} + 72 q^{93} + 90 q^{94} + 2 q^{96} - 4 q^{97} - 114 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/668\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(335\)
\(\chi(n)\) \(-1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.30799 0.537726i −0.924892 0.380230i
\(3\) 2.06566i 1.19261i −0.802758 0.596305i \(-0.796635\pi\)
0.802758 0.596305i \(-0.203365\pi\)
\(4\) 1.42170 + 1.40669i 0.710851 + 0.703343i
\(5\) 1.78350i 0.797605i 0.917037 + 0.398803i \(0.130574\pi\)
−0.917037 + 0.398803i \(0.869426\pi\)
\(6\) −1.11076 + 2.70187i −0.453466 + 1.10304i
\(7\) 0.540270i 0.204203i −0.994774 0.102102i \(-0.967443\pi\)
0.994774 0.102102i \(-0.0325567\pi\)
\(8\) −1.10317 2.60442i −0.390029 0.920803i
\(9\) −1.26695 −0.422318
\(10\) 0.959034 2.33281i 0.303273 0.737699i
\(11\) 0.518196i 0.156242i 0.996944 + 0.0781210i \(0.0248921\pi\)
−0.996944 + 0.0781210i \(0.975108\pi\)
\(12\) 2.90574 2.93675i 0.838813 0.847768i
\(13\) 4.59318i 1.27392i 0.770897 + 0.636960i \(0.219808\pi\)
−0.770897 + 0.636960i \(0.780192\pi\)
\(14\) −0.290517 + 0.706671i −0.0776440 + 0.188866i
\(15\) 3.68410 0.951232
\(16\) 0.0424712 + 3.99977i 0.0106178 + 0.999944i
\(17\) 4.49305i 1.08972i −0.838526 0.544862i \(-0.816582\pi\)
0.838526 0.544862i \(-0.183418\pi\)
\(18\) 1.65717 + 0.681274i 0.390599 + 0.160578i
\(19\) 7.50492i 1.72175i −0.508819 0.860874i \(-0.669918\pi\)
0.508819 0.860874i \(-0.330082\pi\)
\(20\) −2.50882 + 2.53560i −0.560990 + 0.566978i
\(21\) −1.11602 −0.243534
\(22\) 0.278648 0.677798i 0.0594079 0.144507i
\(23\) 8.08382 1.68559 0.842796 0.538233i \(-0.180908\pi\)
0.842796 + 0.538233i \(0.180908\pi\)
\(24\) −5.37986 + 2.27877i −1.09816 + 0.465152i
\(25\) 1.81913 0.363826
\(26\) 2.46987 6.00786i 0.484382 1.17824i
\(27\) 3.57988i 0.688949i
\(28\) 0.759991 0.768103i 0.143625 0.145158i
\(29\) 2.47382 0.459376 0.229688 0.973264i \(-0.426229\pi\)
0.229688 + 0.973264i \(0.426229\pi\)
\(30\) −4.81879 1.98104i −0.879787 0.361686i
\(31\) 3.56761i 0.640762i 0.947289 + 0.320381i \(0.103811\pi\)
−0.947289 + 0.320381i \(0.896189\pi\)
\(32\) 2.09523 5.25452i 0.370388 0.928877i
\(33\) 1.07042 0.186336
\(34\) −2.41603 + 5.87688i −0.414345 + 1.00788i
\(35\) 0.963572 0.162873
\(36\) −1.80123 1.78221i −0.300205 0.297034i
\(37\) 8.52951i 1.40224i 0.713042 + 0.701121i \(0.247317\pi\)
−0.713042 + 0.701121i \(0.752683\pi\)
\(38\) −4.03559 + 9.81640i −0.654659 + 1.59243i
\(39\) 9.48796 1.51929
\(40\) 4.64499 1.96750i 0.734437 0.311089i
\(41\) 10.7353i 1.67658i −0.545227 0.838288i \(-0.683557\pi\)
0.545227 0.838288i \(-0.316443\pi\)
\(42\) 1.45974 + 0.600110i 0.225243 + 0.0925990i
\(43\) 5.36699 0.818459 0.409229 0.912432i \(-0.365798\pi\)
0.409229 + 0.912432i \(0.365798\pi\)
\(44\) −0.728939 + 0.736721i −0.109892 + 0.111065i
\(45\) 2.25961i 0.336843i
\(46\) −10.5736 4.34688i −1.55899 0.640912i
\(47\) 3.27968i 0.478390i −0.970972 0.239195i \(-0.923117\pi\)
0.970972 0.239195i \(-0.0768835\pi\)
\(48\) 8.26218 0.0877311i 1.19254 0.0126629i
\(49\) 6.70811 0.958301
\(50\) −2.37941 0.978194i −0.336500 0.138337i
\(51\) −9.28111 −1.29962
\(52\) −6.46116 + 6.53014i −0.896002 + 0.905567i
\(53\) 9.17750i 1.26063i −0.776341 0.630314i \(-0.782926\pi\)
0.776341 0.630314i \(-0.217074\pi\)
\(54\) −1.92500 + 4.68247i −0.261959 + 0.637204i
\(55\) −0.924203 −0.124619
\(56\) −1.40709 + 0.596009i −0.188031 + 0.0796450i
\(57\) −15.5026 −2.05337
\(58\) −3.23574 1.33024i −0.424874 0.174669i
\(59\) −6.36471 −0.828615 −0.414308 0.910137i \(-0.635976\pi\)
−0.414308 + 0.910137i \(0.635976\pi\)
\(60\) 5.23770 + 5.18238i 0.676184 + 0.669042i
\(61\) −12.5812 −1.61086 −0.805428 0.592693i \(-0.798065\pi\)
−0.805428 + 0.592693i \(0.798065\pi\)
\(62\) 1.91840 4.66642i 0.243637 0.592636i
\(63\) 0.684498i 0.0862386i
\(64\) −5.56604 + 5.74623i −0.695755 + 0.718279i
\(65\) −8.19194 −1.01608
\(66\) −1.40010 0.575591i −0.172341 0.0708504i
\(67\) 14.5036 1.77189 0.885945 0.463790i \(-0.153511\pi\)
0.885945 + 0.463790i \(0.153511\pi\)
\(68\) 6.32030 6.38777i 0.766450 0.774631i
\(69\) 16.6984i 2.01025i
\(70\) −1.26035 0.518138i −0.150640 0.0619293i
\(71\) −3.96731 −0.470833 −0.235417 0.971895i \(-0.575645\pi\)
−0.235417 + 0.971895i \(0.575645\pi\)
\(72\) 1.39766 + 3.29969i 0.164716 + 0.388872i
\(73\) 3.38016i 0.395617i −0.980241 0.197809i \(-0.936618\pi\)
0.980241 0.197809i \(-0.0633825\pi\)
\(74\) 4.58654 11.1566i 0.533174 1.29692i
\(75\) 3.75771i 0.433903i
\(76\) 10.5571 10.6698i 1.21098 1.22391i
\(77\) 0.279966 0.0319051
\(78\) −12.4102 5.10192i −1.40518 0.577679i
\(79\) −9.68909 −1.09011 −0.545054 0.838401i \(-0.683491\pi\)
−0.545054 + 0.838401i \(0.683491\pi\)
\(80\) −7.13359 + 0.0757474i −0.797560 + 0.00846882i
\(81\) −11.1957 −1.24397
\(82\) −5.77267 + 14.0418i −0.637484 + 1.55065i
\(83\) 6.57031 0.721185 0.360593 0.932723i \(-0.382574\pi\)
0.360593 + 0.932723i \(0.382574\pi\)
\(84\) −1.58664 1.56988i −0.173117 0.171288i
\(85\) 8.01335 0.869169
\(86\) −7.02000 2.88597i −0.756986 0.311202i
\(87\) 5.11007i 0.547857i
\(88\) 1.34960 0.571657i 0.143868 0.0609389i
\(89\) −9.71328 −1.02961 −0.514803 0.857309i \(-0.672135\pi\)
−0.514803 + 0.857309i \(0.672135\pi\)
\(90\) −1.21505 + 2.95556i −0.128078 + 0.311543i
\(91\) 2.48156 0.260138
\(92\) 11.4928 + 11.3714i 1.19820 + 1.18555i
\(93\) 7.36948 0.764179
\(94\) −1.76357 + 4.28980i −0.181898 + 0.442459i
\(95\) 13.3850 1.37327
\(96\) −10.8541 4.32803i −1.10779 0.441728i
\(97\) 15.8410 1.60841 0.804203 0.594354i \(-0.202592\pi\)
0.804203 + 0.594354i \(0.202592\pi\)
\(98\) −8.77417 3.60712i −0.886325 0.364375i
\(99\) 0.656531i 0.0659838i
\(100\) 2.58626 + 2.55895i 0.258626 + 0.255895i
\(101\) 5.83864i 0.580966i −0.956880 0.290483i \(-0.906184\pi\)
0.956880 0.290483i \(-0.0938160\pi\)
\(102\) 12.1396 + 4.99069i 1.20200 + 0.494152i
\(103\) −4.34158 −0.427788 −0.213894 0.976857i \(-0.568615\pi\)
−0.213894 + 0.976857i \(0.568615\pi\)
\(104\) 11.9626 5.06705i 1.17303 0.496865i
\(105\) 1.99041i 0.194244i
\(106\) −4.93498 + 12.0041i −0.479328 + 1.16594i
\(107\) 2.50390i 0.242062i 0.992649 + 0.121031i \(0.0386200\pi\)
−0.992649 + 0.121031i \(0.961380\pi\)
\(108\) 5.03577 5.08953i 0.484567 0.489740i
\(109\) 9.09798i 0.871429i 0.900085 + 0.435714i \(0.143504\pi\)
−0.900085 + 0.435714i \(0.856496\pi\)
\(110\) 1.20885 + 0.496968i 0.115260 + 0.0473840i
\(111\) 17.6191 1.67233
\(112\) 2.16096 0.0229459i 0.204191 0.00216819i
\(113\) 15.7044i 1.47735i 0.674063 + 0.738674i \(0.264548\pi\)
−0.674063 + 0.738674i \(0.735452\pi\)
\(114\) 20.2774 + 8.33616i 1.89915 + 0.780753i
\(115\) 14.4175i 1.34444i
\(116\) 3.51703 + 3.47988i 0.326548 + 0.323099i
\(117\) 5.81935i 0.537999i
\(118\) 8.32501 + 3.42247i 0.766380 + 0.315064i
\(119\) −2.42746 −0.222525
\(120\) −4.06418 9.59497i −0.371007 0.875897i
\(121\) 10.7315 0.975588
\(122\) 16.4561 + 6.76523i 1.48987 + 0.612495i
\(123\) −22.1755 −1.99950
\(124\) −5.01851 + 5.07208i −0.450676 + 0.455486i
\(125\) 12.1619i 1.08779i
\(126\) 0.368072 0.895320i 0.0327905 0.0797614i
\(127\) 6.26428i 0.555865i −0.960601 0.277932i \(-0.910351\pi\)
0.960601 0.277932i \(-0.0896491\pi\)
\(128\) 10.3703 4.52303i 0.916610 0.399783i
\(129\) 11.0864i 0.976102i
\(130\) 10.7150 + 4.40502i 0.939769 + 0.386346i
\(131\) 0.822813 0.0718895 0.0359447 0.999354i \(-0.488556\pi\)
0.0359447 + 0.999354i \(0.488556\pi\)
\(132\) 1.52181 + 1.50574i 0.132457 + 0.131058i
\(133\) −4.05469 −0.351586
\(134\) −18.9706 7.79894i −1.63881 0.673725i
\(135\) 6.38472 0.549509
\(136\) −11.7018 + 4.95658i −1.00342 + 0.425023i
\(137\) 6.55510 0.560040 0.280020 0.959994i \(-0.409659\pi\)
0.280020 + 0.959994i \(0.409659\pi\)
\(138\) −8.97918 + 21.8415i −0.764358 + 1.85927i
\(139\) −6.87407 −0.583051 −0.291525 0.956563i \(-0.594163\pi\)
−0.291525 + 0.956563i \(0.594163\pi\)
\(140\) 1.36991 + 1.35544i 0.115779 + 0.114556i
\(141\) −6.77470 −0.570532
\(142\) 5.18922 + 2.13333i 0.435470 + 0.179025i
\(143\) −2.38017 −0.199040
\(144\) −0.0538091 5.06753i −0.00448409 0.422294i
\(145\) 4.41205i 0.366401i
\(146\) −1.81760 + 4.42123i −0.150425 + 0.365903i
\(147\) 13.8567i 1.14288i
\(148\) −11.9983 + 12.1264i −0.986257 + 0.996785i
\(149\) 18.8252i 1.54222i 0.636702 + 0.771110i \(0.280298\pi\)
−0.636702 + 0.771110i \(0.719702\pi\)
\(150\) −2.02062 + 4.91506i −0.164983 + 0.401313i
\(151\) 6.55785 0.533670 0.266835 0.963742i \(-0.414022\pi\)
0.266835 + 0.963742i \(0.414022\pi\)
\(152\) −19.5460 + 8.27919i −1.58539 + 0.671531i
\(153\) 5.69248i 0.460210i
\(154\) −0.366194 0.150545i −0.0295088 0.0121313i
\(155\) −6.36284 −0.511075
\(156\) 13.4890 + 13.3466i 1.07999 + 1.06858i
\(157\) 10.3627 0.827033 0.413517 0.910497i \(-0.364300\pi\)
0.413517 + 0.910497i \(0.364300\pi\)
\(158\) 12.6733 + 5.21008i 1.00823 + 0.414491i
\(159\) −18.9576 −1.50344
\(160\) 9.37144 + 3.73684i 0.740877 + 0.295423i
\(161\) 4.36745i 0.344203i
\(162\) 14.6439 + 6.02021i 1.15053 + 0.472993i
\(163\) −15.3264 −1.20045 −0.600227 0.799830i \(-0.704923\pi\)
−0.600227 + 0.799830i \(0.704923\pi\)
\(164\) 15.1012 15.2624i 1.17921 1.19180i
\(165\) 1.90909i 0.148622i
\(166\) −8.59393 3.53303i −0.667019 0.274216i
\(167\) −10.3001 7.80437i −0.797045 0.603920i
\(168\) 1.23115 + 2.90658i 0.0949854 + 0.224247i
\(169\) −8.09733 −0.622871
\(170\) −10.4814 4.30898i −0.803888 0.330484i
\(171\) 9.50839i 0.727125i
\(172\) 7.63026 + 7.54967i 0.581802 + 0.575657i
\(173\) 22.7705 1.73121 0.865605 0.500727i \(-0.166934\pi\)
0.865605 + 0.500727i \(0.166934\pi\)
\(174\) −2.74782 + 6.68394i −0.208311 + 0.506708i
\(175\) 0.982822i 0.0742944i
\(176\) −2.07267 + 0.0220084i −0.156233 + 0.00165895i
\(177\) 13.1473i 0.988215i
\(178\) 12.7049 + 5.22308i 0.952274 + 0.391487i
\(179\) 3.47751i 0.259922i 0.991519 + 0.129961i \(0.0414851\pi\)
−0.991519 + 0.129961i \(0.958515\pi\)
\(180\) 3.17856 3.21249i 0.236916 0.239445i
\(181\) −3.14064 −0.233442 −0.116721 0.993165i \(-0.537238\pi\)
−0.116721 + 0.993165i \(0.537238\pi\)
\(182\) −3.24587 1.33440i −0.240600 0.0989123i
\(183\) 25.9885i 1.92112i
\(184\) −8.91780 21.0537i −0.657429 1.55210i
\(185\) −15.2124 −1.11844
\(186\) −9.63924 3.96276i −0.706784 0.290564i
\(187\) 2.32828 0.170261
\(188\) 4.61347 4.66272i 0.336472 0.340064i
\(189\) −1.93411 −0.140685
\(190\) −17.5075 7.19747i −1.27013 0.522160i
\(191\) 19.5557i 1.41500i −0.706712 0.707501i \(-0.749823\pi\)
0.706712 0.707501i \(-0.250177\pi\)
\(192\) 11.8698 + 11.4976i 0.856626 + 0.829765i
\(193\) 16.7512i 1.20578i 0.797826 + 0.602888i \(0.205983\pi\)
−0.797826 + 0.602888i \(0.794017\pi\)
\(194\) −20.7199 8.51810i −1.48760 0.611564i
\(195\) 16.9218i 1.21179i
\(196\) 9.53693 + 9.43620i 0.681209 + 0.674014i
\(197\) 11.4841i 0.818211i 0.912487 + 0.409106i \(0.134159\pi\)
−0.912487 + 0.409106i \(0.865841\pi\)
\(198\) −0.353034 + 0.858739i −0.0250890 + 0.0610279i
\(199\) 1.93300i 0.137027i −0.997650 0.0685133i \(-0.978174\pi\)
0.997650 0.0685133i \(-0.0218255\pi\)
\(200\) −2.00681 4.73779i −0.141903 0.335012i
\(201\) 29.9594i 2.11317i
\(202\) −3.13959 + 7.63691i −0.220900 + 0.537331i
\(203\) 1.33653i 0.0938060i
\(204\) −13.1950 13.0556i −0.923833 0.914075i
\(205\) 19.1465 1.33725
\(206\) 5.67876 + 2.33458i 0.395658 + 0.162658i
\(207\) −10.2418 −0.711856
\(208\) −18.3717 + 0.195078i −1.27385 + 0.0135262i
\(209\) 3.88902 0.269009
\(210\) −1.07030 + 2.60345i −0.0738575 + 0.179655i
\(211\) 18.7643i 1.29179i 0.763428 + 0.645894i \(0.223515\pi\)
−0.763428 + 0.645894i \(0.776485\pi\)
\(212\) 12.9099 13.0477i 0.886653 0.896118i
\(213\) 8.19512i 0.561520i
\(214\) 1.34641 3.27509i 0.0920390 0.223881i
\(215\) 9.57202i 0.652807i
\(216\) −9.32354 + 3.94921i −0.634386 + 0.268710i
\(217\) 1.92748 0.130846
\(218\) 4.89222 11.9001i 0.331343 0.805978i
\(219\) −6.98226 −0.471817
\(220\) −1.31394 1.30006i −0.0885859 0.0876502i
\(221\) 20.6374 1.38822
\(222\) −23.0456 9.47423i −1.54672 0.635869i
\(223\) 24.5870i 1.64647i 0.567704 + 0.823233i \(0.307832\pi\)
−0.567704 + 0.823233i \(0.692168\pi\)
\(224\) −2.83886 1.13199i −0.189680 0.0756343i
\(225\) −2.30476 −0.153650
\(226\) 8.44468 20.5413i 0.561732 1.36639i
\(227\) −10.6020 −0.703681 −0.351841 0.936060i \(-0.614444\pi\)
−0.351841 + 0.936060i \(0.614444\pi\)
\(228\) −22.0401 21.8073i −1.45964 1.44422i
\(229\) −3.28643 −0.217174 −0.108587 0.994087i \(-0.534633\pi\)
−0.108587 + 0.994087i \(0.534633\pi\)
\(230\) 7.75265 18.8580i 0.511195 1.24346i
\(231\) 0.578315i 0.0380503i
\(232\) −2.72903 6.44287i −0.179170 0.422995i
\(233\) −10.5506 −0.691191 −0.345596 0.938384i \(-0.612323\pi\)
−0.345596 + 0.938384i \(0.612323\pi\)
\(234\) −3.12922 + 7.61168i −0.204563 + 0.497591i
\(235\) 5.84930 0.381566
\(236\) −9.04872 8.95315i −0.589022 0.582801i
\(237\) 20.0144i 1.30007i
\(238\) 3.17511 + 1.30531i 0.205812 + 0.0846106i
\(239\) 17.0884i 1.10536i −0.833394 0.552679i \(-0.813605\pi\)
0.833394 0.552679i \(-0.186395\pi\)
\(240\) 0.156468 + 14.7356i 0.0101000 + 0.951178i
\(241\) 7.23561i 0.466087i 0.972466 + 0.233043i \(0.0748684\pi\)
−0.972466 + 0.233043i \(0.925132\pi\)
\(242\) −14.0367 5.77059i −0.902314 0.370948i
\(243\) 12.3868i 0.794616i
\(244\) −17.8867 17.6978i −1.14508 1.13298i
\(245\) 11.9639i 0.764346i
\(246\) 29.0055 + 11.9244i 1.84932 + 0.760270i
\(247\) 34.4715 2.19337
\(248\) 9.29158 3.93567i 0.590016 0.249916i
\(249\) 13.5720i 0.860093i
\(250\) 6.53978 15.9077i 0.413612 1.00609i
\(251\) 5.10600i 0.322288i 0.986931 + 0.161144i \(0.0515184\pi\)
−0.986931 + 0.161144i \(0.948482\pi\)
\(252\) −0.962873 + 0.973152i −0.0606553 + 0.0613028i
\(253\) 4.18900i 0.263360i
\(254\) −3.36847 + 8.19365i −0.211356 + 0.514115i
\(255\) 16.5529i 1.03658i
\(256\) −15.9964 + 0.339751i −0.999775 + 0.0212344i
\(257\) 11.5441i 0.720102i −0.932933 0.360051i \(-0.882759\pi\)
0.932933 0.360051i \(-0.117241\pi\)
\(258\) −5.96144 + 14.5009i −0.371143 + 0.902789i
\(259\) 4.60824 0.286342
\(260\) −11.6465 11.5235i −0.722285 0.714656i
\(261\) −3.13421 −0.194003
\(262\) −1.07623 0.442448i −0.0664900 0.0273345i
\(263\) 27.4874i 1.69494i −0.530840 0.847472i \(-0.678123\pi\)
0.530840 0.847472i \(-0.321877\pi\)
\(264\) −1.18085 2.78782i −0.0726763 0.171579i
\(265\) 16.3681 1.00548
\(266\) 5.30351 + 2.18031i 0.325179 + 0.133683i
\(267\) 20.0643i 1.22792i
\(268\) 20.6197 + 20.4019i 1.25955 + 1.24625i
\(269\) 7.39493i 0.450877i 0.974257 + 0.225439i \(0.0723815\pi\)
−0.974257 + 0.225439i \(0.927619\pi\)
\(270\) −8.35118 3.43323i −0.508237 0.208940i
\(271\) 5.97777 0.363124 0.181562 0.983380i \(-0.441885\pi\)
0.181562 + 0.983380i \(0.441885\pi\)
\(272\) 17.9712 0.190825i 1.08966 0.0115705i
\(273\) 5.12606i 0.310243i
\(274\) −8.57404 3.52485i −0.517977 0.212944i
\(275\) 0.942667i 0.0568450i
\(276\) 23.4894 23.7402i 1.41390 1.42899i
\(277\) 5.16217i 0.310165i −0.987902 0.155082i \(-0.950436\pi\)
0.987902 0.155082i \(-0.0495643\pi\)
\(278\) 8.99124 + 3.69636i 0.539259 + 0.221693i
\(279\) 4.52000i 0.270605i
\(280\) −1.06298 2.50955i −0.0635253 0.149974i
\(281\) 7.39152 0.440941 0.220470 0.975394i \(-0.429241\pi\)
0.220470 + 0.975394i \(0.429241\pi\)
\(282\) 8.86127 + 3.64293i 0.527681 + 0.216933i
\(283\) 0.300267i 0.0178490i −0.999960 0.00892451i \(-0.997159\pi\)
0.999960 0.00892451i \(-0.00284080\pi\)
\(284\) −5.64033 5.58076i −0.334692 0.331157i
\(285\) 27.6489i 1.63778i
\(286\) 3.11325 + 1.27988i 0.184090 + 0.0756808i
\(287\) −5.79998 −0.342362
\(288\) −2.65456 + 6.65724i −0.156421 + 0.392282i
\(289\) −3.18747 −0.187498
\(290\) 2.37247 5.77094i 0.139317 0.338881i
\(291\) 32.7221i 1.91820i
\(292\) 4.75482 4.80557i 0.278255 0.281225i
\(293\) −19.2052 −1.12198 −0.560991 0.827822i \(-0.689580\pi\)
−0.560991 + 0.827822i \(0.689580\pi\)
\(294\) −7.45109 + 18.1245i −0.434557 + 1.05704i
\(295\) 11.3515i 0.660908i
\(296\) 22.2144 9.40947i 1.29119 0.546914i
\(297\) 1.85508 0.107643
\(298\) 10.1228 24.6233i 0.586398 1.42639i
\(299\) 37.1305i 2.14731i
\(300\) 5.28591 5.34234i 0.305182 0.308440i
\(301\) 2.89963i 0.167132i
\(302\) −8.57763 3.52633i −0.493587 0.202917i
\(303\) −12.0606 −0.692866
\(304\) 30.0180 0.318743i 1.72165 0.0182812i
\(305\) 22.4385i 1.28483i
\(306\) 3.06100 7.44574i 0.174986 0.425645i
\(307\) −1.74301 −0.0994789 −0.0497394 0.998762i \(-0.515839\pi\)
−0.0497394 + 0.998762i \(0.515839\pi\)
\(308\) 0.398028 + 0.393824i 0.0226798 + 0.0224402i
\(309\) 8.96822i 0.510184i
\(310\) 8.32256 + 3.42146i 0.472690 + 0.194326i
\(311\) 0.874002i 0.0495601i 0.999693 + 0.0247801i \(0.00788855\pi\)
−0.999693 + 0.0247801i \(0.992111\pi\)
\(312\) −10.4668 24.7107i −0.592566 1.39897i
\(313\) 10.2101i 0.577110i −0.957463 0.288555i \(-0.906825\pi\)
0.957463 0.288555i \(-0.0931748\pi\)
\(314\) −13.5544 5.57229i −0.764916 0.314463i
\(315\) −1.22080 −0.0687844
\(316\) −13.7750 13.6295i −0.774904 0.766720i
\(317\) −14.3483 −0.805882 −0.402941 0.915226i \(-0.632012\pi\)
−0.402941 + 0.915226i \(0.632012\pi\)
\(318\) 24.7965 + 10.1940i 1.39052 + 0.571651i
\(319\) 1.28192i 0.0717739i
\(320\) −10.2484 9.92703i −0.572903 0.554938i
\(321\) 5.17222 0.288685
\(322\) −2.34849 + 5.71260i −0.130876 + 0.318351i
\(323\) −33.7200 −1.87623
\(324\) −15.9169 15.7488i −0.884274 0.874934i
\(325\) 8.35560i 0.463485i
\(326\) 20.0468 + 8.24138i 1.11029 + 0.456448i
\(327\) 18.7933 1.03927
\(328\) −27.9593 + 11.8429i −1.54380 + 0.653913i
\(329\) −1.77191 −0.0976886
\(330\) 1.02657 2.49708i 0.0565106 0.137460i
\(331\) −33.1302 −1.82100 −0.910499 0.413510i \(-0.864303\pi\)
−0.910499 + 0.413510i \(0.864303\pi\)
\(332\) 9.34102 + 9.24236i 0.512655 + 0.507240i
\(333\) 10.8065i 0.592192i
\(334\) 9.27586 + 15.7467i 0.507552 + 0.861621i
\(335\) 25.8671i 1.41327i
\(336\) −0.0473985 4.46381i −0.00258580 0.243521i
\(337\) −12.9380 −0.704780 −0.352390 0.935853i \(-0.614631\pi\)
−0.352390 + 0.935853i \(0.614631\pi\)
\(338\) 10.5913 + 4.35414i 0.576089 + 0.236834i
\(339\) 32.4400 1.76190
\(340\) 11.3926 + 11.2723i 0.617850 + 0.611324i
\(341\) −1.84872 −0.100114
\(342\) 5.11291 12.4369i 0.276474 0.672512i
\(343\) 7.40608i 0.399891i
\(344\) −5.92069 13.9779i −0.319222 0.753639i
\(345\) 29.7816 1.60339
\(346\) −29.7837 12.2443i −1.60118 0.658258i
\(347\) 15.1845 0.815145 0.407573 0.913173i \(-0.366375\pi\)
0.407573 + 0.913173i \(0.366375\pi\)
\(348\) 7.18826 7.26499i 0.385331 0.389444i
\(349\) 33.3252i 1.78386i 0.452176 + 0.891929i \(0.350648\pi\)
−0.452176 + 0.891929i \(0.649352\pi\)
\(350\) −0.528489 + 1.28553i −0.0282489 + 0.0687143i
\(351\) 16.4431 0.877666
\(352\) 2.72287 + 1.08574i 0.145130 + 0.0578702i
\(353\) −2.39365 −0.127401 −0.0637005 0.997969i \(-0.520290\pi\)
−0.0637005 + 0.997969i \(0.520290\pi\)
\(354\) 7.06967 17.1967i 0.375748 0.913992i
\(355\) 7.07570i 0.375539i
\(356\) −13.8094 13.6635i −0.731896 0.724166i
\(357\) 5.01431i 0.265385i
\(358\) 1.86995 4.54857i 0.0988299 0.240399i
\(359\) 7.96139i 0.420186i 0.977681 + 0.210093i \(0.0673767\pi\)
−0.977681 + 0.210093i \(0.932623\pi\)
\(360\) −5.88499 + 2.49273i −0.310166 + 0.131378i
\(361\) −37.3239 −1.96441
\(362\) 4.10794 + 1.68880i 0.215909 + 0.0887616i
\(363\) 22.1676i 1.16350i
\(364\) 3.52804 + 3.49078i 0.184919 + 0.182966i
\(365\) 6.02851 0.315546
\(366\) 13.9747 33.9928i 0.730468 1.77683i
\(367\) 13.5783i 0.708779i −0.935098 0.354390i \(-0.884689\pi\)
0.935098 0.354390i \(-0.115311\pi\)
\(368\) 0.343330 + 32.3334i 0.0178973 + 1.68550i
\(369\) 13.6012i 0.708049i
\(370\) 19.8977 + 8.18008i 1.03443 + 0.425262i
\(371\) −4.95833 −0.257424
\(372\) 10.4772 + 10.3665i 0.543218 + 0.537480i
\(373\) 21.6358i 1.12026i −0.828405 0.560129i \(-0.810752\pi\)
0.828405 0.560129i \(-0.189248\pi\)
\(374\) −3.04538 1.25198i −0.157473 0.0647382i
\(375\) 25.1224 1.29731
\(376\) −8.54166 + 3.61803i −0.440503 + 0.186586i
\(377\) 11.3627i 0.585209i
\(378\) 2.52980 + 1.04002i 0.130119 + 0.0534928i
\(379\) −31.2090 −1.60310 −0.801550 0.597927i \(-0.795991\pi\)
−0.801550 + 0.597927i \(0.795991\pi\)
\(380\) 19.0295 + 18.8285i 0.976193 + 0.965883i
\(381\) −12.9399 −0.662930
\(382\) −10.5156 + 25.5788i −0.538026 + 1.30872i
\(383\) 31.0107i 1.58457i 0.610148 + 0.792287i \(0.291110\pi\)
−0.610148 + 0.792287i \(0.708890\pi\)
\(384\) −9.34305 21.4214i −0.476786 1.09316i
\(385\) 0.499319i 0.0254477i
\(386\) 9.00754 21.9105i 0.458472 1.11521i
\(387\) −6.79973 −0.345650
\(388\) 22.5211 + 22.2833i 1.14334 + 1.13126i
\(389\) 1.35231i 0.0685646i 0.999412 + 0.0342823i \(0.0109145\pi\)
−0.999412 + 0.0342823i \(0.989085\pi\)
\(390\) 9.09927 22.1336i 0.460759 1.12078i
\(391\) 36.3210i 1.83683i
\(392\) −7.40017 17.4708i −0.373765 0.882406i
\(393\) 1.69965i 0.0857361i
\(394\) 6.17532 15.0212i 0.311108 0.756757i
\(395\) 17.2805i 0.869476i
\(396\) 0.923533 0.933391i 0.0464093 0.0469047i
\(397\) 9.86238 0.494979 0.247489 0.968891i \(-0.420394\pi\)
0.247489 + 0.968891i \(0.420394\pi\)
\(398\) −1.03942 + 2.52835i −0.0521015 + 0.126735i
\(399\) 8.37561i 0.419305i
\(400\) 0.0772607 + 7.27611i 0.00386304 + 0.363806i
\(401\) 1.50263i 0.0750379i −0.999296 0.0375189i \(-0.988055\pi\)
0.999296 0.0375189i \(-0.0119455\pi\)
\(402\) −16.1100 + 39.1868i −0.803491 + 1.95446i
\(403\) −16.3867 −0.816280
\(404\) 8.21312 8.30080i 0.408618 0.412980i
\(405\) 19.9675i 0.992193i
\(406\) −0.718687 + 1.74818i −0.0356678 + 0.0867605i
\(407\) −4.41996 −0.219089
\(408\) 10.2386 + 24.1719i 0.506887 + 1.19669i
\(409\) −20.9361 −1.03523 −0.517613 0.855615i \(-0.673179\pi\)
−0.517613 + 0.855615i \(0.673179\pi\)
\(410\) −25.0435 10.2955i −1.23681 0.508461i
\(411\) 13.5406i 0.667910i
\(412\) −6.17243 6.10723i −0.304094 0.300882i
\(413\) 3.43867i 0.169206i
\(414\) 13.3963 + 5.50730i 0.658390 + 0.270669i
\(415\) 11.7181i 0.575221i
\(416\) 24.1350 + 9.62378i 1.18331 + 0.471844i
\(417\) 14.1995i 0.695352i
\(418\) −5.08682 2.09123i −0.248805 0.102285i
\(419\) 32.8545i 1.60505i 0.596620 + 0.802524i \(0.296510\pi\)
−0.596620 + 0.802524i \(0.703490\pi\)
\(420\) 2.79988 2.82977i 0.136620 0.138079i
\(421\) −12.8524 −0.626387 −0.313193 0.949689i \(-0.601399\pi\)
−0.313193 + 0.949689i \(0.601399\pi\)
\(422\) 10.0900 24.5436i 0.491176 1.19476i
\(423\) 4.15520i 0.202033i
\(424\) −23.9021 + 10.1243i −1.16079 + 0.491681i
\(425\) 8.17344i 0.396470i
\(426\) 4.40673 10.7192i 0.213507 0.519346i
\(427\) 6.79724i 0.328942i
\(428\) −3.52221 + 3.55980i −0.170252 + 0.172070i
\(429\) 4.91662i 0.237377i
\(430\) 5.14713 12.5202i 0.248216 0.603776i
\(431\) 0.316808i 0.0152601i −0.999971 0.00763005i \(-0.997571\pi\)
0.999971 0.00763005i \(-0.00242874\pi\)
\(432\) 14.3187 0.152042i 0.688910 0.00731513i
\(433\) 10.5211 0.505612 0.252806 0.967517i \(-0.418647\pi\)
0.252806 + 0.967517i \(0.418647\pi\)
\(434\) −2.52113 1.03645i −0.121018 0.0497514i
\(435\) 9.11380 0.436973
\(436\) −12.7980 + 12.9346i −0.612913 + 0.619456i
\(437\) 60.6684i 2.90216i
\(438\) 9.13276 + 3.75454i 0.436380 + 0.179399i
\(439\) −1.49302 −0.0712578 −0.0356289 0.999365i \(-0.511343\pi\)
−0.0356289 + 0.999365i \(0.511343\pi\)
\(440\) 1.01955 + 2.40702i 0.0486051 + 0.114750i
\(441\) −8.49886 −0.404708
\(442\) −26.9936 11.0973i −1.28395 0.527843i
\(443\) −15.3224 −0.727990 −0.363995 0.931401i \(-0.618588\pi\)
−0.363995 + 0.931401i \(0.618588\pi\)
\(444\) 25.0491 + 24.7845i 1.18878 + 1.17622i
\(445\) 17.3236i 0.821219i
\(446\) 13.2211 32.1596i 0.626035 1.52280i
\(447\) 38.8865 1.83927
\(448\) 3.10452 + 3.00717i 0.146675 + 0.142075i
\(449\) 35.9267 1.69549 0.847744 0.530406i \(-0.177961\pi\)
0.847744 + 0.530406i \(0.177961\pi\)
\(450\) 3.01461 + 1.23933i 0.142110 + 0.0584224i
\(451\) 5.56301 0.261952
\(452\) −22.0912 + 22.3270i −1.03908 + 1.05017i
\(453\) 13.5463i 0.636460i
\(454\) 13.8674 + 5.70098i 0.650829 + 0.267560i
\(455\) 4.42586i 0.207488i
\(456\) 17.1020 + 40.3754i 0.800874 + 1.89075i
\(457\) 33.6351i 1.57338i −0.617345 0.786692i \(-0.711792\pi\)
0.617345 0.786692i \(-0.288208\pi\)
\(458\) 4.29864 + 1.76720i 0.200862 + 0.0825758i
\(459\) −16.0846 −0.750764
\(460\) −20.2809 + 20.4974i −0.945600 + 0.955694i
\(461\) 3.45927 0.161114 0.0805572 0.996750i \(-0.474330\pi\)
0.0805572 + 0.996750i \(0.474330\pi\)
\(462\) −0.310975 + 0.756433i −0.0144679 + 0.0351925i
\(463\) −32.0716 −1.49050 −0.745248 0.666787i \(-0.767669\pi\)
−0.745248 + 0.666787i \(0.767669\pi\)
\(464\) 0.105066 + 9.89471i 0.00487757 + 0.459351i
\(465\) 13.1435i 0.609513i
\(466\) 13.8001 + 5.67332i 0.639277 + 0.262811i
\(467\) 7.44867i 0.344683i −0.985037 0.172342i \(-0.944867\pi\)
0.985037 0.172342i \(-0.0551333\pi\)
\(468\) 8.18600 8.27338i 0.378398 0.382437i
\(469\) 7.83584i 0.361825i
\(470\) −7.65085 3.14532i −0.352908 0.145083i
\(471\) 21.4058i 0.986328i
\(472\) 7.02134 + 16.5764i 0.323184 + 0.762991i
\(473\) 2.78116i 0.127878i
\(474\) 10.7623 26.1787i 0.494327 1.20243i
\(475\) 13.6524i 0.626417i
\(476\) −3.45112 3.41467i −0.158182 0.156511i
\(477\) 11.6275i 0.532386i
\(478\) −9.18889 + 22.3516i −0.420290 + 1.02234i
\(479\) −23.6642 −1.08124 −0.540622 0.841266i \(-0.681811\pi\)
−0.540622 + 0.841266i \(0.681811\pi\)
\(480\) 7.71905 19.3582i 0.352325 0.883577i
\(481\) −39.1776 −1.78634
\(482\) 3.89078 9.46414i 0.177220 0.431080i
\(483\) −9.02166 −0.410500
\(484\) 15.2570 + 15.0958i 0.693498 + 0.686173i
\(485\) 28.2524i 1.28287i
\(486\) 6.66073 16.2019i 0.302137 0.734934i
\(487\) −13.8961 −0.629691 −0.314846 0.949143i \(-0.601953\pi\)
−0.314846 + 0.949143i \(0.601953\pi\)
\(488\) 13.8792 + 32.7667i 0.628280 + 1.48328i
\(489\) 31.6591i 1.43167i
\(490\) 6.43330 15.6487i 0.290627 0.706937i
\(491\) 37.1343i 1.67585i 0.545789 + 0.837923i \(0.316230\pi\)
−0.545789 + 0.837923i \(0.683770\pi\)
\(492\) −31.5270 31.1940i −1.42135 1.40634i
\(493\) 11.1150i 0.500594i
\(494\) −45.0885 18.5362i −2.02863 0.833983i
\(495\) 1.17092 0.0526290
\(496\) −14.2697 + 0.151521i −0.640726 + 0.00680349i
\(497\) 2.14342i 0.0961456i
\(498\) −7.29803 + 17.7522i −0.327033 + 0.795493i
\(499\) 7.40457 0.331474 0.165737 0.986170i \(-0.447000\pi\)
0.165737 + 0.986170i \(0.447000\pi\)
\(500\) −17.1080 + 17.2906i −0.765093 + 0.773260i
\(501\) −16.1212 + 21.2765i −0.720241 + 0.950564i
\(502\) 2.74563 6.67862i 0.122543 0.298082i
\(503\) 12.1896i 0.543506i 0.962367 + 0.271753i \(0.0876034\pi\)
−0.962367 + 0.271753i \(0.912397\pi\)
\(504\) 1.78272 0.755116i 0.0794088 0.0336355i
\(505\) 10.4132 0.463381
\(506\) 2.25254 5.47920i 0.100137 0.243580i
\(507\) 16.7263i 0.742842i
\(508\) 8.81187 8.90594i 0.390964 0.395137i
\(509\) −17.5006 −0.775701 −0.387850 0.921722i \(-0.626782\pi\)
−0.387850 + 0.921722i \(0.626782\pi\)
\(510\) −8.90090 + 21.6510i −0.394138 + 0.958725i
\(511\) −1.82620 −0.0807863
\(512\) 21.1059 + 8.15728i 0.932758 + 0.360504i
\(513\) −26.8668 −1.18620
\(514\) −6.20757 + 15.0996i −0.273804 + 0.666017i
\(515\) 7.74320i 0.341206i
\(516\) 15.5951 15.7615i 0.686534 0.693863i
\(517\) 1.69952 0.0747446
\(518\) −6.02755 2.47797i −0.264836 0.108876i
\(519\) 47.0362i 2.06466i
\(520\) 9.03708 + 21.3353i 0.396302 + 0.935614i
\(521\) 4.99086i 0.218653i 0.994006 + 0.109327i \(0.0348695\pi\)
−0.994006 + 0.109327i \(0.965131\pi\)
\(522\) 4.09954 + 1.68535i 0.179432 + 0.0737657i
\(523\) 2.24632i 0.0982245i 0.998793 + 0.0491123i \(0.0156392\pi\)
−0.998793 + 0.0491123i \(0.984361\pi\)
\(524\) 1.16979 + 1.15744i 0.0511027 + 0.0505629i
\(525\) −2.03018 −0.0886042
\(526\) −14.7807 + 35.9534i −0.644468 + 1.56764i
\(527\) 16.0295 0.698254
\(528\) 0.0454620 + 4.28143i 0.00197848 + 0.186325i
\(529\) 42.3481 1.84122
\(530\) −21.4094 8.80154i −0.929963 0.382314i
\(531\) 8.06380 0.349939
\(532\) −5.76456 5.70367i −0.249925 0.247285i
\(533\) 49.3093 2.13582
\(534\) 10.7891 26.2441i 0.466891 1.13569i
\(535\) −4.46571 −0.193069
\(536\) −15.9998 37.7734i −0.691088 1.63156i
\(537\) 7.18336 0.309985
\(538\) 3.97645 9.67254i 0.171437 0.417013i
\(539\) 3.47612i 0.149727i
\(540\) 9.07717 + 8.98130i 0.390619 + 0.386493i
\(541\) 21.4088i 0.920437i −0.887806 0.460219i \(-0.847771\pi\)
0.887806 0.460219i \(-0.152229\pi\)
\(542\) −7.81890 3.21440i −0.335850 0.138070i
\(543\) 6.48750i 0.278405i
\(544\) −23.6088 9.41397i −1.01222 0.403621i
\(545\) −16.2262 −0.695056
\(546\) −2.75642 + 6.70486i −0.117964 + 0.286942i
\(547\) −13.1954 −0.564193 −0.282096 0.959386i \(-0.591030\pi\)
−0.282096 + 0.959386i \(0.591030\pi\)
\(548\) 9.31940 + 9.22097i 0.398105 + 0.393900i
\(549\) 15.9398 0.680294
\(550\) 0.506896 1.23300i 0.0216141 0.0525754i
\(551\) 18.5658i 0.790930i
\(552\) −43.4898 + 18.4212i −1.85105 + 0.784056i
\(553\) 5.23473i 0.222603i
\(554\) −2.77583 + 6.75209i −0.117934 + 0.286869i
\(555\) 31.4236i 1.33386i
\(556\) −9.77287 9.66965i −0.414462 0.410084i
\(557\) −10.0693 −0.426652 −0.213326 0.976981i \(-0.568430\pi\)
−0.213326 + 0.976981i \(0.568430\pi\)
\(558\) −2.43052 + 5.91214i −0.102892 + 0.250281i
\(559\) 24.6516i 1.04265i
\(560\) 0.0409241 + 3.85407i 0.00172936 + 0.162864i
\(561\) 4.80944i 0.203055i
\(562\) −9.66807 3.97461i −0.407823 0.167659i
\(563\) 28.5277i 1.20230i 0.799136 + 0.601150i \(0.205291\pi\)
−0.799136 + 0.601150i \(0.794709\pi\)
\(564\) −9.63160 9.52987i −0.405563 0.401280i
\(565\) −28.0088 −1.17834
\(566\) −0.161461 + 0.392748i −0.00678673 + 0.0165084i
\(567\) 6.04870i 0.254021i
\(568\) 4.37661 + 10.3326i 0.183638 + 0.433545i
\(569\) 24.3518i 1.02088i 0.859913 + 0.510441i \(0.170518\pi\)
−0.859913 + 0.510441i \(0.829482\pi\)
\(570\) −14.8675 + 36.1646i −0.622733 + 1.51477i
\(571\) 45.4580 1.90236 0.951179 0.308640i \(-0.0998737\pi\)
0.951179 + 0.308640i \(0.0998737\pi\)
\(572\) −3.38389 3.34815i −0.141488 0.139993i
\(573\) −40.3955 −1.68754
\(574\) 7.58635 + 3.11880i 0.316648 + 0.130176i
\(575\) 14.7055 0.613263
\(576\) 7.05192 7.28021i 0.293830 0.303342i
\(577\) 29.7141 1.23702 0.618508 0.785779i \(-0.287737\pi\)
0.618508 + 0.785779i \(0.287737\pi\)
\(578\) 4.16920 + 1.71399i 0.173416 + 0.0712925i
\(579\) 34.6022 1.43802
\(580\) −6.20637 + 6.27262i −0.257705 + 0.260456i
\(581\) 3.54974i 0.147268i
\(582\) −17.5955 + 42.8003i −0.729357 + 1.77413i
\(583\) 4.75575 0.196963
\(584\) −8.80336 + 3.72888i −0.364286 + 0.154302i
\(585\) 10.3788 0.429111
\(586\) 25.1204 + 10.3272i 1.03771 + 0.426611i
\(587\) −27.3517 −1.12893 −0.564463 0.825458i \(-0.690917\pi\)
−0.564463 + 0.825458i \(0.690917\pi\)
\(588\) 19.4920 19.7001i 0.803836 0.812417i
\(589\) 26.7747 1.10323
\(590\) −6.10398 + 14.8477i −0.251297 + 0.611268i
\(591\) 23.7223 0.975807
\(592\) −34.1161 + 0.362259i −1.40216 + 0.0148887i
\(593\) 4.66771i 0.191680i 0.995397 + 0.0958399i \(0.0305537\pi\)
−0.995397 + 0.0958399i \(0.969446\pi\)
\(594\) −2.42644 0.997526i −0.0995580 0.0409290i
\(595\) 4.32937i 0.177487i
\(596\) −26.4811 + 26.7638i −1.08471 + 1.09629i
\(597\) −3.99292 −0.163419
\(598\) 19.9660 48.5664i 0.816471 1.98603i
\(599\) 5.99780i 0.245064i 0.992465 + 0.122532i \(0.0391013\pi\)
−0.992465 + 0.122532i \(0.960899\pi\)
\(600\) −9.78666 + 4.14538i −0.399539 + 0.169234i
\(601\) 30.3224 1.23688 0.618438 0.785834i \(-0.287766\pi\)
0.618438 + 0.785834i \(0.287766\pi\)
\(602\) −1.55920 + 3.79270i −0.0635484 + 0.154579i
\(603\) −18.3753 −0.748301
\(604\) 9.32330 + 9.22483i 0.379360 + 0.375353i
\(605\) 19.1396i 0.778134i
\(606\) 15.7753 + 6.48532i 0.640826 + 0.263448i
\(607\) −3.36426 −0.136551 −0.0682755 0.997667i \(-0.521750\pi\)
−0.0682755 + 0.997667i \(0.521750\pi\)
\(608\) −39.4348 15.7245i −1.59929 0.637714i
\(609\) −2.76082 −0.111874
\(610\) −12.0658 + 29.3495i −0.488529 + 1.18833i
\(611\) 15.0641 0.609430
\(612\) −8.00754 + 8.09301i −0.323685 + 0.327141i
\(613\) −27.9675 −1.12960 −0.564798 0.825229i \(-0.691046\pi\)
−0.564798 + 0.825229i \(0.691046\pi\)
\(614\) 2.27985 + 0.937262i 0.0920072 + 0.0378248i
\(615\) 39.5501i 1.59481i
\(616\) −0.308849 0.729150i −0.0124439 0.0293783i
\(617\) 11.3852 0.458352 0.229176 0.973385i \(-0.426397\pi\)
0.229176 + 0.973385i \(0.426397\pi\)
\(618\) 4.82245 11.7304i 0.193987 0.471866i
\(619\) −3.17429 −0.127586 −0.0637928 0.997963i \(-0.520320\pi\)
−0.0637928 + 0.997963i \(0.520320\pi\)
\(620\) −9.04605 8.95051i −0.363298 0.359461i
\(621\) 28.9391i 1.16129i
\(622\) 0.469974 1.14319i 0.0188442 0.0458378i
\(623\) 5.24780i 0.210249i
\(624\) 0.402965 + 37.9497i 0.0161315 + 1.51920i
\(625\) −12.5951 −0.503804
\(626\) −5.49025 + 13.3548i −0.219434 + 0.533765i
\(627\) 8.03340i 0.320823i
\(628\) 14.7327 + 14.5771i 0.587897 + 0.581688i
\(629\) 38.3235 1.52806
\(630\) 1.59680 + 0.656456i 0.0636181 + 0.0261539i
\(631\) 34.1130i 1.35802i −0.734130 0.679009i \(-0.762410\pi\)
0.734130 0.679009i \(-0.237590\pi\)
\(632\) 10.6887 + 25.2345i 0.425173 + 1.00377i
\(633\) 38.7607 1.54060
\(634\) 18.7675 + 7.71547i 0.745354 + 0.306420i
\(635\) 11.1723 0.443361
\(636\) −26.9521 26.6674i −1.06872 1.05743i
\(637\) 30.8116i 1.22080i
\(638\) 0.689323 1.67675i 0.0272906 0.0663831i
\(639\) 5.02640 0.198841
\(640\) 8.06683 + 18.4953i 0.318869 + 0.731092i
\(641\) 32.5524i 1.28574i 0.765974 + 0.642871i \(0.222257\pi\)
−0.765974 + 0.642871i \(0.777743\pi\)
\(642\) −6.76523 2.78123i −0.267002 0.109767i
\(643\) 48.8264 1.92552 0.962762 0.270349i \(-0.0871392\pi\)
0.962762 + 0.270349i \(0.0871392\pi\)
\(644\) 6.14363 6.20921i 0.242093 0.244677i
\(645\) 19.7726 0.778544
\(646\) 44.1056 + 18.1321i 1.73531 + 0.713398i
\(647\) −40.4496 −1.59024 −0.795120 0.606453i \(-0.792592\pi\)
−0.795120 + 0.606453i \(0.792592\pi\)
\(648\) 12.3507 + 29.1583i 0.485182 + 1.14545i
\(649\) 3.29817i 0.129465i
\(650\) 4.49302 10.9291i 0.176231 0.428674i
\(651\) 3.98151i 0.156048i
\(652\) −21.7895 21.5594i −0.853343 0.844330i
\(653\) −15.3926 −0.602358 −0.301179 0.953568i \(-0.597380\pi\)
−0.301179 + 0.953568i \(0.597380\pi\)
\(654\) −24.5816 10.1057i −0.961217 0.395163i
\(655\) 1.46749i 0.0573394i
\(656\) 42.9389 0.455943i 1.67648 0.0178016i
\(657\) 4.28250i 0.167076i
\(658\) 2.31765 + 0.952803i 0.0903515 + 0.0371441i
\(659\) 27.8761 1.08590 0.542949 0.839765i \(-0.317308\pi\)
0.542949 + 0.839765i \(0.317308\pi\)
\(660\) −2.68549 + 2.71416i −0.104532 + 0.105648i
\(661\) 15.8624i 0.616975i −0.951228 0.308488i \(-0.900177\pi\)
0.951228 0.308488i \(-0.0998228\pi\)
\(662\) 43.3341 + 17.8150i 1.68423 + 0.692398i
\(663\) 42.6298i 1.65561i
\(664\) −7.24815 17.1119i −0.281283 0.664069i
\(665\) 7.23153i 0.280427i
\(666\) −5.81093 + 14.1348i −0.225169 + 0.547714i
\(667\) 19.9979 0.774322
\(668\) −3.66536 25.5845i −0.141817 0.989893i
\(669\) 50.7884 1.96359
\(670\) 13.9094 33.8340i 0.537367 1.30712i
\(671\) 6.51953i 0.251684i
\(672\) −2.33831 + 5.86413i −0.0902022 + 0.226214i
\(673\) 32.9504i 1.27014i 0.772453 + 0.635072i \(0.219030\pi\)
−0.772453 + 0.635072i \(0.780970\pi\)
\(674\) 16.9229 + 6.95712i 0.651846 + 0.267978i
\(675\) 6.51228i 0.250658i
\(676\) −11.5120 11.3904i −0.442769 0.438092i
\(677\) −25.6134 −0.984403 −0.492201 0.870481i \(-0.663808\pi\)
−0.492201 + 0.870481i \(0.663808\pi\)
\(678\) −42.4314 17.4438i −1.62957 0.669927i
\(679\) 8.55841i 0.328442i
\(680\) −8.84006 20.8701i −0.339001 0.800334i
\(681\) 21.9002i 0.839217i
\(682\) 2.41812 + 0.994107i 0.0925947 + 0.0380663i
\(683\) −28.8668 −1.10456 −0.552279 0.833659i \(-0.686242\pi\)
−0.552279 + 0.833659i \(0.686242\pi\)
\(684\) −13.3753 + 13.5181i −0.511418 + 0.516877i
\(685\) 11.6910i 0.446691i
\(686\) −3.98244 + 9.68712i −0.152050 + 0.369856i
\(687\) 6.78865i 0.259003i
\(688\) 0.227943 + 21.4668i 0.00869023 + 0.818412i
\(689\) 42.1540 1.60594
\(690\) −38.9542 16.0144i −1.48296 0.609656i
\(691\) −25.9720 −0.988022 −0.494011 0.869456i \(-0.664470\pi\)
−0.494011 + 0.869456i \(0.664470\pi\)
\(692\) 32.3729 + 32.0310i 1.23063 + 1.21763i
\(693\) −0.354704 −0.0134741
\(694\) −19.8612 8.16508i −0.753921 0.309942i
\(695\) 12.2599i 0.465044i
\(696\) −13.3088 + 5.63726i −0.504468 + 0.213680i
\(697\) −48.2343 −1.82701
\(698\) 17.9198 43.5892i 0.678275 1.64988i
\(699\) 21.7939i 0.824321i
\(700\) 1.38252 1.39728i 0.0522544 0.0528122i
\(701\) −7.67525 −0.289890 −0.144945 0.989440i \(-0.546301\pi\)
−0.144945 + 0.989440i \(0.546301\pi\)
\(702\) −21.5074 8.84186i −0.811746 0.333715i
\(703\) 64.0133 2.41431
\(704\) −2.97768 2.88430i −0.112225 0.108706i
\(705\) 12.0827i 0.455060i
\(706\) 3.13088 + 1.28713i 0.117832 + 0.0484416i
\(707\) −3.15444 −0.118635
\(708\) −18.4942 + 18.6916i −0.695054 + 0.702473i
\(709\) 23.7497i 0.891940i 0.895048 + 0.445970i \(0.147141\pi\)
−0.895048 + 0.445970i \(0.852859\pi\)
\(710\) −3.80479 + 9.25498i −0.142791 + 0.347333i
\(711\) 12.2756 0.460372
\(712\) 10.7154 + 25.2975i 0.401576 + 0.948064i
\(713\) 28.8399i 1.08006i
\(714\) 2.69632 6.55869i 0.100907 0.245453i
\(715\) 4.24503i 0.158755i
\(716\) −4.89177 + 4.94399i −0.182814 + 0.184765i
\(717\) −35.2989 −1.31826
\(718\) 4.28105 10.4135i 0.159767 0.388627i
\(719\) 9.19104 0.342768 0.171384 0.985204i \(-0.445176\pi\)
0.171384 + 0.985204i \(0.445176\pi\)
\(720\) 9.03794 0.0959685i 0.336824 0.00357653i
\(721\) 2.34563i 0.0873556i
\(722\) 48.8194 + 20.0700i 1.81687 + 0.746928i
\(723\) 14.9463 0.555860
\(724\) −4.46506 4.41790i −0.165942 0.164190i
\(725\) 4.50020 0.167133
\(726\) −11.9201 + 28.9951i −0.442396 + 1.07611i
\(727\) −10.8951 −0.404078 −0.202039 0.979377i \(-0.564757\pi\)
−0.202039 + 0.979377i \(0.564757\pi\)
\(728\) −2.73758 6.46303i −0.101461 0.239536i
\(729\) −8.00006 −0.296298
\(730\) −7.88526 3.24168i −0.291846 0.119980i
\(731\) 24.1141i 0.891894i
\(732\) −36.5576 + 36.9479i −1.35121 + 1.36563i
\(733\) −11.2934 −0.417132 −0.208566 0.978008i \(-0.566880\pi\)
−0.208566 + 0.978008i \(0.566880\pi\)
\(734\) −7.30138 + 17.7603i −0.269499 + 0.655544i
\(735\) 24.7134 0.911566
\(736\) 16.9375 42.4766i 0.624323 1.56571i
\(737\) 7.51569i 0.276844i
\(738\) 7.31370 17.7903i 0.269221 0.654869i
\(739\) 20.9399 0.770288 0.385144 0.922856i \(-0.374152\pi\)
0.385144 + 0.922856i \(0.374152\pi\)
\(740\) −21.6274 21.3990i −0.795041 0.786643i
\(741\) 71.2064i 2.61583i
\(742\) 6.48548 + 2.66622i 0.238089 + 0.0978802i
\(743\) 13.2550i 0.486281i −0.969991 0.243140i \(-0.921822\pi\)
0.969991 0.243140i \(-0.0781775\pi\)
\(744\) −8.12977 19.1932i −0.298052 0.703659i
\(745\) −33.5747 −1.23008
\(746\) −11.6341 + 28.2995i −0.425955 + 1.03612i
\(747\) −8.32428 −0.304570
\(748\) 3.31012 + 3.27516i 0.121030 + 0.119752i
\(749\) 1.35278 0.0494297
\(750\) −32.8600 13.5090i −1.19988 0.493277i
\(751\) −11.2524 −0.410607 −0.205304 0.978698i \(-0.565818\pi\)
−0.205304 + 0.978698i \(0.565818\pi\)
\(752\) 13.1180 0.139292i 0.478363 0.00507945i
\(753\) 10.5473 0.384364
\(754\) 6.11002 14.8624i 0.222514 0.541255i
\(755\) 11.6959i 0.425658i
\(756\) −2.74972 2.72068i −0.100006 0.0989501i
\(757\) 22.1035 0.803365 0.401682 0.915779i \(-0.368426\pi\)
0.401682 + 0.915779i \(0.368426\pi\)
\(758\) 40.8213 + 16.7819i 1.48270 + 0.609546i
\(759\) 8.65306 0.314086
\(760\) −14.7659 34.8603i −0.535616 1.26451i
\(761\) 15.1012 0.547416 0.273708 0.961813i \(-0.411750\pi\)
0.273708 + 0.961813i \(0.411750\pi\)
\(762\) 16.9253 + 6.95811i 0.613139 + 0.252066i
\(763\) 4.91537 0.177948
\(764\) 27.5087 27.8024i 0.995231 1.00586i
\(765\) −10.1525 −0.367066
\(766\) 16.6753 40.5619i 0.602502 1.46556i
\(767\) 29.2343i 1.05559i
\(768\) 0.701810 + 33.0431i 0.0253244 + 1.19234i
\(769\) 1.26472i 0.0456069i 0.999740 + 0.0228034i \(0.00725919\pi\)
−0.999740 + 0.0228034i \(0.992741\pi\)
\(770\) 0.268497 0.653107i 0.00967596 0.0235363i
\(771\) −23.8462 −0.858801
\(772\) −23.5636 + 23.8152i −0.848074 + 0.857127i
\(773\) 10.4883i 0.377237i 0.982050 + 0.188619i \(0.0604010\pi\)
−0.982050 + 0.188619i \(0.939599\pi\)
\(774\) 8.89401 + 3.65639i 0.319689 + 0.131426i
\(775\) 6.48996i 0.233126i
\(776\) −17.4752 41.2566i −0.627325 1.48103i
\(777\) 9.51906i 0.341494i
\(778\) 0.727170 1.76881i 0.0260703 0.0634149i
\(779\) −80.5678 −2.88664
\(780\) −23.8036 + 24.0577i −0.852306 + 0.861404i
\(781\) 2.05585i 0.0735640i
\(782\) −19.5307 + 47.5077i −0.698417 + 1.69887i
\(783\) 8.85598i 0.316487i
\(784\) 0.284902 + 26.8309i 0.0101751 + 0.958247i
\(785\) 18.4819i 0.659646i
\(786\) −0.913947 + 2.22314i −0.0325994 + 0.0792966i
\(787\) −9.95211 −0.354754 −0.177377 0.984143i \(-0.556761\pi\)
−0.177377 + 0.984143i \(0.556761\pi\)
\(788\) −16.1546 + 16.3270i −0.575483 + 0.581626i
\(789\) −56.7796 −2.02141
\(790\) −9.29217 + 22.6028i −0.330601 + 0.804171i
\(791\) 8.48464 0.301679
\(792\) −1.70988 + 0.724263i −0.0607581 + 0.0257356i
\(793\) 57.7877i 2.05210i
\(794\) −12.8999 5.30326i −0.457802 0.188206i
\(795\) 33.8109i 1.19915i
\(796\) 2.71912 2.74814i 0.0963766 0.0974054i
\(797\) 35.5770i 1.26020i 0.776514 + 0.630100i \(0.216986\pi\)
−0.776514 + 0.630100i \(0.783014\pi\)
\(798\) 4.50378 10.9553i 0.159432 0.387812i
\(799\) −14.7357 −0.521313
\(800\) 3.81150 9.55866i 0.134757 0.337950i
\(801\) 12.3063 0.434821
\(802\) −0.808004 + 1.96544i −0.0285316 + 0.0694019i
\(803\) 1.75158 0.0618121
\(804\) 42.1435 42.5933i 1.48629 1.50215i
\(805\) 7.78934 0.274538
\(806\) 21.4337 + 8.81155i 0.754971 + 0.310374i
\(807\) 15.2754 0.537720
\(808\) −15.2063 + 6.44099i −0.534955 + 0.226593i
\(809\) −18.5473 −0.652087 −0.326043 0.945355i \(-0.605716\pi\)
−0.326043 + 0.945355i \(0.605716\pi\)
\(810\) −10.7370 + 26.1174i −0.377261 + 0.917672i
\(811\) −9.80190 −0.344191 −0.172096 0.985080i \(-0.555054\pi\)
−0.172096 + 0.985080i \(0.555054\pi\)
\(812\) 1.88008 1.90015i 0.0659778 0.0666821i
\(813\) 12.3481i 0.433065i
\(814\) 5.78128 + 2.37673i 0.202634 + 0.0833042i
\(815\) 27.3346i 0.957488i
\(816\) −0.394180 37.1224i −0.0137991 1.29954i
\(817\) 40.2789i 1.40918i
\(818\) 27.3844 + 11.2579i 0.957472 + 0.393623i
\(819\) −3.14402 −0.109861
\(820\) 27.2205 + 26.9330i 0.950583 + 0.940543i
\(821\) 40.0684i 1.39840i −0.714928 0.699198i \(-0.753541\pi\)
0.714928 0.699198i \(-0.246459\pi\)
\(822\) −7.28114 + 17.7111i −0.253959 + 0.617744i
\(823\) 31.7996 1.10846 0.554232 0.832362i \(-0.313012\pi\)
0.554232 + 0.832362i \(0.313012\pi\)
\(824\) 4.78949 + 11.3073i 0.166850 + 0.393909i
\(825\) 1.94723 0.0677938
\(826\) 1.84906 4.49776i 0.0643370 0.156497i
\(827\) 30.3420 1.05509 0.527547 0.849526i \(-0.323112\pi\)
0.527547 + 0.849526i \(0.323112\pi\)
\(828\) −14.5608 14.4070i −0.506024 0.500679i
\(829\) 44.3374i 1.53990i −0.638103 0.769951i \(-0.720281\pi\)
0.638103 0.769951i \(-0.279719\pi\)
\(830\) 6.30115 15.3273i 0.218716 0.532017i
\(831\) −10.6633 −0.369905
\(832\) −26.3935 25.5659i −0.915029 0.886337i
\(833\) 30.1398i 1.04428i
\(834\) 7.63543 18.5729i 0.264393 0.643125i
\(835\) 13.9191 18.3702i 0.481690 0.635727i
\(836\) 5.52903 + 5.47063i 0.191226 + 0.189206i
\(837\) 12.7716 0.441453
\(838\) 17.6667 42.9735i 0.610287 1.48450i
\(839\) 9.67347i 0.333965i 0.985960 + 0.166983i \(0.0534024\pi\)
−0.985960 + 0.166983i \(0.946598\pi\)
\(840\) −5.18388 + 2.19576i −0.178861 + 0.0757608i
\(841\) −22.8802 −0.788973
\(842\) 16.8109 + 6.91106i 0.579340 + 0.238171i
\(843\) 15.2684i 0.525870i
\(844\) −26.3955 + 26.6772i −0.908569 + 0.918268i
\(845\) 14.4416i 0.496805i
\(846\) 2.23436 5.43498i 0.0768188 0.186858i
\(847\) 5.79790i 0.199218i
\(848\) 36.7080 0.389780i 1.26056 0.0133851i
\(849\) −0.620250 −0.0212869
\(850\) −4.39507 + 10.6908i −0.150750 + 0.366692i
\(851\) 68.9510i 2.36361i
\(852\) −11.5280 + 11.6510i −0.394941 + 0.399157i
\(853\) 30.3335 1.03860 0.519300 0.854592i \(-0.326193\pi\)
0.519300 + 0.854592i \(0.326193\pi\)
\(854\) 3.65505 8.89076i 0.125073 0.304236i
\(855\) −16.9582 −0.579959
\(856\) 6.52123 2.76222i 0.222891 0.0944109i
\(857\) −53.7671 −1.83665 −0.918325 0.395828i \(-0.870458\pi\)
−0.918325 + 0.395828i \(0.870458\pi\)
\(858\) 2.64380 6.43092i 0.0902577 0.219548i
\(859\) 7.22281i 0.246439i 0.992379 + 0.123220i \(0.0393219\pi\)
−0.992379 + 0.123220i \(0.960678\pi\)
\(860\) −13.4648 + 13.6086i −0.459147 + 0.464048i
\(861\) 11.9808i 0.408304i
\(862\) −0.170356 + 0.414383i −0.00580234 + 0.0141139i
\(863\) 53.3262i 1.81524i 0.419789 + 0.907622i \(0.362104\pi\)
−0.419789 + 0.907622i \(0.637896\pi\)
\(864\) −18.8106 7.50068i −0.639949 0.255178i
\(865\) 40.6112i 1.38082i
\(866\) −13.7615 5.65747i −0.467636 0.192249i
\(867\) 6.58424i 0.223612i
\(868\) 2.74030 + 2.71135i 0.0930117 + 0.0920293i
\(869\) 5.02085i 0.170321i
\(870\) −11.9208 4.90073i −0.404153 0.166150i
\(871\) 66.6175i 2.25725i
\(872\) 23.6950 10.0366i 0.802414 0.339882i
\(873\) −20.0698 −0.679259
\(874\) −32.6230 + 79.3540i −1.10349 + 2.68419i
\(875\) 6.57072 0.222131
\(876\) −9.92669 9.82184i −0.335392 0.331849i
\(877\) −29.9090 −1.00996 −0.504978 0.863132i \(-0.668499\pi\)
−0.504978 + 0.863132i \(0.668499\pi\)
\(878\) 1.95286 + 0.802834i 0.0659058 + 0.0270943i
\(879\) 39.6715i 1.33809i
\(880\) −0.0392520 3.69660i −0.00132319 0.124612i
\(881\) 52.0568i 1.75384i −0.480639 0.876919i \(-0.659595\pi\)
0.480639 0.876919i \(-0.340405\pi\)
\(882\) 11.1165 + 4.57006i 0.374311 + 0.153882i
\(883\) 9.28366i 0.312420i 0.987724 + 0.156210i \(0.0499277\pi\)
−0.987724 + 0.156210i \(0.950072\pi\)
\(884\) 29.3402 + 29.0303i 0.986818 + 0.976395i
\(885\) −23.4483 −0.788205
\(886\) 20.0417 + 8.23927i 0.673313 + 0.276804i
\(887\) 18.5360 0.622377 0.311189 0.950348i \(-0.399273\pi\)
0.311189 + 0.950348i \(0.399273\pi\)
\(888\) −19.4368 45.8875i −0.652255 1.53988i
\(889\) −3.38440 −0.113509
\(890\) −9.31536 + 22.6592i −0.312252 + 0.759539i
\(891\) 5.80157i 0.194360i
\(892\) −34.5861 + 34.9553i −1.15803 + 1.17039i
\(893\) −24.6137 −0.823666
\(894\) −50.8633 20.9103i −1.70112 0.699343i
\(895\) −6.20214 −0.207315
\(896\) −2.44366 5.60274i −0.0816370 0.187174i
\(897\) 76.6989 2.56090
\(898\) −46.9920 19.3187i −1.56814 0.644675i
\(899\) 8.82563i 0.294351i
\(900\) −3.27667 3.24207i −0.109222 0.108069i
\(901\) −41.2350 −1.37374
\(902\) −7.27639 2.99137i −0.242277 0.0996019i
\(903\) −5.98964 −0.199323
\(904\) 40.9010 17.3246i 1.36035 0.576208i
\(905\) 5.60133i 0.186195i
\(906\) −7.28419 + 17.7185i −0.242001 + 0.588657i
\(907\) 43.9327i 1.45876i −0.684108 0.729381i \(-0.739808\pi\)
0.684108 0.729381i \(-0.260192\pi\)
\(908\) −15.0729 14.9137i −0.500212 0.494929i
\(909\) 7.39728i 0.245352i
\(910\) 2.37990 5.78900i 0.0788929 0.191904i
\(911\) 0.963872i 0.0319345i −0.999873 0.0159672i \(-0.994917\pi\)
0.999873 0.0159672i \(-0.00508275\pi\)
\(912\) −0.658415 62.0070i −0.0218023 2.05326i
\(913\) 3.40471i 0.112679i
\(914\) −18.0865 + 43.9946i −0.598248 + 1.45521i
\(915\) −46.3504 −1.53230
\(916\) −4.67233 4.62298i −0.154378 0.152747i
\(917\) 0.444541i 0.0146800i
\(918\) 21.0386 + 8.64910i 0.694376 + 0.285463i
\(919\) 13.1544i 0.433924i −0.976180 0.216962i \(-0.930385\pi\)
0.976180 0.216962i \(-0.0696147\pi\)
\(920\) 37.5492 15.9049i 1.23796 0.524369i
\(921\) 3.60047i 0.118640i
\(922\) −4.52471 1.86014i −0.149013 0.0612605i
\(923\) 18.2226i 0.599804i
\(924\) 0.813507 0.822191i 0.0267624 0.0270481i
\(925\) 15.5163i 0.510172i
\(926\) 41.9496 + 17.2458i 1.37855 + 0.566731i
\(927\) 5.50058 0.180663
\(928\) 5.18322 12.9987i 0.170147 0.426704i
\(929\) 29.8819 0.980392 0.490196 0.871612i \(-0.336925\pi\)
0.490196 + 0.871612i \(0.336925\pi\)
\(930\) 7.06758 17.1916i 0.231755 0.563734i
\(931\) 50.3438i 1.64995i
\(932\) −14.9998 14.8413i −0.491334 0.486144i
\(933\) 1.80539 0.0591059
\(934\) −4.00534 + 9.74282i −0.131059 + 0.318795i
\(935\) 4.15249i 0.135801i
\(936\) −15.1561 + 6.41972i −0.495391 + 0.209835i
\(937\) 15.5508i 0.508021i −0.967201 0.254010i \(-0.918250\pi\)
0.967201 0.254010i \(-0.0817498\pi\)
\(938\) −4.21353 + 10.2492i −0.137577 + 0.334649i
\(939\) −21.0906 −0.688267
\(940\) 8.31596 + 8.22812i 0.271237 + 0.268372i
\(941\) 44.2590i 1.44280i −0.692517 0.721402i \(-0.743498\pi\)
0.692517 0.721402i \(-0.256502\pi\)
\(942\) −11.5105 + 27.9987i −0.375031 + 0.912247i
\(943\) 86.7825i 2.82603i
\(944\) −0.270317 25.4574i −0.00879808 0.828569i
\(945\) 3.44948i 0.112211i
\(946\) 1.49550 3.63774i 0.0486229 0.118273i
\(947\) 22.8331i 0.741976i −0.928638 0.370988i \(-0.879019\pi\)
0.928638 0.370988i \(-0.120981\pi\)
\(948\) −28.1539 + 28.4545i −0.914398 + 0.924159i
\(949\) 15.5257 0.503985
\(950\) −7.34127 + 17.8573i −0.238182 + 0.579368i
\(951\) 29.6388i 0.961103i
\(952\) 2.67789 + 6.32213i 0.0867911 + 0.204902i
\(953\) 27.2403i 0.882398i 0.897409 + 0.441199i \(0.145447\pi\)
−0.897409 + 0.441199i \(0.854553\pi\)
\(954\) 6.25240 15.2087i 0.202429 0.492399i
\(955\) 34.8776 1.12861
\(956\) 24.0381 24.2947i 0.777446 0.785745i
\(957\) 2.64802 0.0855983
\(958\) 30.9526 + 12.7248i 1.00003 + 0.411121i
\(959\) 3.54153i 0.114362i
\(960\) −20.5059 + 21.1697i −0.661825 + 0.683249i
\(961\) 18.2721 0.589424
\(962\) 51.2441 + 21.0668i 1.65218 + 0.679221i
\(963\) 3.17233i 0.102227i
\(964\) −10.1782 + 10.2869i −0.327819 + 0.331318i
\(965\) −29.8757 −0.961733
\(966\) 11.8003 + 4.85118i 0.379668 + 0.156084i
\(967\) 46.0430i 1.48064i 0.672252 + 0.740322i \(0.265327\pi\)
−0.672252 + 0.740322i \(0.734673\pi\)
\(968\) −11.8386 27.9493i −0.380507 0.898325i
\(969\) 69.6540i 2.23761i
\(970\) 15.1920 36.9539i 0.487787 1.18652i
\(971\) 37.9258 1.21710 0.608548 0.793517i \(-0.291752\pi\)
0.608548 + 0.793517i \(0.291752\pi\)
\(972\) −17.4244 + 17.6104i −0.558888 + 0.564854i
\(973\) 3.71385i 0.119061i
\(974\) 18.1760 + 7.47228i 0.582397 + 0.239427i
\(975\) 17.2598 0.552757
\(976\) −0.534339 50.3219i −0.0171038 1.61077i
\(977\) 59.3446i 1.89860i −0.314370 0.949301i \(-0.601793\pi\)
0.314370 0.949301i \(-0.398207\pi\)
\(978\) 17.0239 41.4099i 0.544364 1.32414i
\(979\) 5.03339i 0.160868i
\(980\) −16.8295 + 17.0091i −0.537597 + 0.543336i
\(981\) 11.5267i 0.368020i
\(982\) 19.9681 48.5714i 0.637206 1.54998i
\(983\) −25.7569 −0.821517 −0.410758 0.911744i \(-0.634736\pi\)
−0.410758 + 0.911744i \(0.634736\pi\)
\(984\) 24.4633 + 57.7545i 0.779863 + 1.84115i
\(985\) −20.4820 −0.652609
\(986\) −5.97681 + 14.5383i −0.190341 + 0.462995i
\(987\) 3.66017i 0.116504i
\(988\) 49.0082 + 48.4905i 1.55916 + 1.54269i
\(989\) 43.3858 1.37959
\(990\) −1.53156 0.629635i −0.0486762 0.0200111i
\(991\) 46.6075 1.48054 0.740268 0.672311i \(-0.234698\pi\)
0.740268 + 0.672311i \(0.234698\pi\)
\(992\) 18.7461 + 7.47497i 0.595190 + 0.237331i
\(993\) 68.4357i 2.17174i
\(994\) 1.15257 2.80358i 0.0365574 0.0889243i
\(995\) 3.44750 0.109293
\(996\) 19.0916 19.2954i 0.604940 0.611398i
\(997\) 10.4926 0.332305 0.166153 0.986100i \(-0.446866\pi\)
0.166153 + 0.986100i \(0.446866\pi\)
\(998\) −9.68514 3.98163i −0.306578 0.126036i
\(999\) 30.5346 0.966074
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 668.2.b.b.667.10 yes 60
4.3 odd 2 inner 668.2.b.b.667.12 yes 60
167.166 odd 2 inner 668.2.b.b.667.9 60
668.667 even 2 inner 668.2.b.b.667.11 yes 60
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
668.2.b.b.667.9 60 167.166 odd 2 inner
668.2.b.b.667.10 yes 60 1.1 even 1 trivial
668.2.b.b.667.11 yes 60 668.667 even 2 inner
668.2.b.b.667.12 yes 60 4.3 odd 2 inner