Properties

Label 966.2.k.b.229.1
Level $966$
Weight $2$
Character 966.229
Analytic conductor $7.714$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [966,2,Mod(229,966)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(966, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 5, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("966.229");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 966.k (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.71354883526\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 229.1
Character \(\chi\) \(=\) 966.229
Dual form 966.2.k.b.367.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.02969 + 3.51552i) q^{5} +1.00000i q^{6} +(2.03303 + 1.69316i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.02969 + 3.51552i) q^{5} +1.00000i q^{6} +(2.03303 + 1.69316i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(2.02969 + 3.51552i) q^{10} +(-4.89939 + 2.82867i) q^{11} +(0.866025 + 0.500000i) q^{12} -1.68666i q^{13} +(2.48284 - 0.914071i) q^{14} -4.05937i q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.577549 - 1.00034i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(3.27848 - 5.67849i) q^{19} +4.05937 q^{20} +(-2.60723 - 0.449810i) q^{21} +5.65733i q^{22} +(-3.50171 - 3.27690i) q^{23} +(0.866025 - 0.500000i) q^{24} +(-5.73924 - 9.94066i) q^{25} +(-1.46069 - 0.843329i) q^{26} +1.00000i q^{27} +(0.449810 - 2.60723i) q^{28} -6.42612 q^{29} +(-3.51552 - 2.02969i) q^{30} +(-2.49704 + 1.44167i) q^{31} +(0.500000 + 0.866025i) q^{32} +(2.82867 - 4.89939i) q^{33} -1.15510 q^{34} +(-10.0788 + 3.71055i) q^{35} -1.00000 q^{36} +(1.89767 + 1.09562i) q^{37} +(-3.27848 - 5.67849i) q^{38} +(0.843329 + 1.46069i) q^{39} +(2.02969 - 3.51552i) q^{40} -5.70186i q^{41} +(-1.69316 + 2.03303i) q^{42} +1.32493i q^{43} +(4.89939 + 2.82867i) q^{44} +(2.02969 + 3.51552i) q^{45} +(-4.58873 + 1.39412i) q^{46} +(3.82275 + 2.20707i) q^{47} -1.00000i q^{48} +(1.26639 + 6.88449i) q^{49} -11.4785 q^{50} +(1.00034 + 0.577549i) q^{51} +(-1.46069 + 0.843329i) q^{52} +(-1.85774 + 1.07256i) q^{53} +(0.866025 + 0.500000i) q^{54} -22.9652i q^{55} +(-2.03303 - 1.69316i) q^{56} +6.55695i q^{57} +(-3.21306 + 5.56519i) q^{58} +(6.54465 - 3.77855i) q^{59} +(-3.51552 + 2.02969i) q^{60} +(-5.20534 + 9.01591i) q^{61} +2.88334i q^{62} +(2.48284 - 0.914071i) q^{63} +1.00000 q^{64} +(5.92947 + 3.42338i) q^{65} +(-2.82867 - 4.89939i) q^{66} +(-4.92805 + 2.84521i) q^{67} +(-0.577549 + 1.00034i) q^{68} +(4.67101 + 1.08702i) q^{69} +(-1.82594 + 10.5837i) q^{70} -7.18784 q^{71} +(-0.500000 + 0.866025i) q^{72} +(-9.62590 + 5.55752i) q^{73} +(1.89767 - 1.09562i) q^{74} +(9.94066 + 5.73924i) q^{75} -6.55695 q^{76} +(-14.7500 - 2.54472i) q^{77} +1.68666 q^{78} +(-9.79501 - 5.65515i) q^{79} +(-2.02969 - 3.51552i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-4.93795 - 2.85093i) q^{82} -0.847910 q^{83} +(0.914071 + 2.48284i) q^{84} +4.68897 q^{85} +(1.14742 + 0.662464i) q^{86} +(5.56519 - 3.21306i) q^{87} +(4.89939 - 2.82867i) q^{88} +(6.80960 - 11.7946i) q^{89} +4.05937 q^{90} +(2.85579 - 3.42902i) q^{91} +(-1.08702 + 4.67101i) q^{92} +(1.44167 - 2.49704i) q^{93} +(3.82275 - 2.20707i) q^{94} +(13.3085 + 23.0511i) q^{95} +(-0.866025 - 0.500000i) q^{96} +4.92590 q^{97} +(6.59534 + 2.34552i) q^{98} +5.65733i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 16 q^{2} - 16 q^{4} - 32 q^{8} + 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 16 q^{2} - 16 q^{4} - 32 q^{8} + 16 q^{9} - 16 q^{16} - 16 q^{18} + 4 q^{23} - 40 q^{25} - 12 q^{26} + 24 q^{29} - 24 q^{31} + 16 q^{32} + 12 q^{35} - 32 q^{36} + 8 q^{39} - 4 q^{46} + 12 q^{47} + 24 q^{49} - 80 q^{50} - 12 q^{52} + 12 q^{58} - 12 q^{59} + 32 q^{64} + 24 q^{70} + 16 q^{71} - 16 q^{72} - 84 q^{73} + 12 q^{75} - 40 q^{77} + 16 q^{78} - 16 q^{81} - 36 q^{82} - 112 q^{85} - 48 q^{87} - 8 q^{92} - 8 q^{93} + 12 q^{94} + 24 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/966\mathbb{Z}\right)^\times\).

\(n\) \(323\) \(829\) \(925\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.353553 0.612372i
\(3\) −0.866025 + 0.500000i −0.500000 + 0.288675i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) −2.02969 + 3.51552i −0.907703 + 1.57219i −0.0904552 + 0.995901i \(0.528832\pi\)
−0.817248 + 0.576287i \(0.804501\pi\)
\(6\) 1.00000i 0.408248i
\(7\) 2.03303 + 1.69316i 0.768412 + 0.639956i
\(8\) −1.00000 −0.353553
\(9\) 0.500000 0.866025i 0.166667 0.288675i
\(10\) 2.02969 + 3.51552i 0.641843 + 1.11170i
\(11\) −4.89939 + 2.82867i −1.47722 + 0.852875i −0.999669 0.0257278i \(-0.991810\pi\)
−0.477554 + 0.878603i \(0.658476\pi\)
\(12\) 0.866025 + 0.500000i 0.250000 + 0.144338i
\(13\) 1.68666i 0.467795i −0.972261 0.233897i \(-0.924852\pi\)
0.972261 0.233897i \(-0.0751480\pi\)
\(14\) 2.48284 0.914071i 0.663566 0.244296i
\(15\) 4.05937i 1.04812i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −0.577549 1.00034i −0.140076 0.242619i 0.787449 0.616380i \(-0.211401\pi\)
−0.927525 + 0.373761i \(0.878068\pi\)
\(18\) −0.500000 0.866025i −0.117851 0.204124i
\(19\) 3.27848 5.67849i 0.752134 1.30273i −0.194653 0.980872i \(-0.562358\pi\)
0.946787 0.321862i \(-0.104309\pi\)
\(20\) 4.05937 0.907703
\(21\) −2.60723 0.449810i −0.568945 0.0981565i
\(22\) 5.65733i 1.20615i
\(23\) −3.50171 3.27690i −0.730156 0.683280i
\(24\) 0.866025 0.500000i 0.176777 0.102062i
\(25\) −5.73924 9.94066i −1.14785 1.98813i
\(26\) −1.46069 0.843329i −0.286465 0.165390i
\(27\) 1.00000i 0.192450i
\(28\) 0.449810 2.60723i 0.0850061 0.492721i
\(29\) −6.42612 −1.19330 −0.596651 0.802501i \(-0.703502\pi\)
−0.596651 + 0.802501i \(0.703502\pi\)
\(30\) −3.51552 2.02969i −0.641843 0.370568i
\(31\) −2.49704 + 1.44167i −0.448482 + 0.258931i −0.707189 0.707025i \(-0.750037\pi\)
0.258707 + 0.965956i \(0.416704\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) 2.82867 4.89939i 0.492408 0.852875i
\(34\) −1.15510 −0.198098
\(35\) −10.0788 + 3.71055i −1.70362 + 0.627198i
\(36\) −1.00000 −0.166667
\(37\) 1.89767 + 1.09562i 0.311975 + 0.180119i 0.647810 0.761802i \(-0.275685\pi\)
−0.335835 + 0.941921i \(0.609018\pi\)
\(38\) −3.27848 5.67849i −0.531839 0.921172i
\(39\) 0.843329 + 1.46069i 0.135041 + 0.233897i
\(40\) 2.02969 3.51552i 0.320921 0.555852i
\(41\) 5.70186i 0.890480i −0.895411 0.445240i \(-0.853118\pi\)
0.895411 0.445240i \(-0.146882\pi\)
\(42\) −1.69316 + 2.03303i −0.261261 + 0.313703i
\(43\) 1.32493i 0.202049i 0.994884 + 0.101025i \(0.0322121\pi\)
−0.994884 + 0.101025i \(0.967788\pi\)
\(44\) 4.89939 + 2.82867i 0.738611 + 0.426437i
\(45\) 2.02969 + 3.51552i 0.302568 + 0.524062i
\(46\) −4.58873 + 1.39412i −0.676571 + 0.205551i
\(47\) 3.82275 + 2.20707i 0.557606 + 0.321934i 0.752184 0.658953i \(-0.229000\pi\)
−0.194578 + 0.980887i \(0.562334\pi\)
\(48\) 1.00000i 0.144338i
\(49\) 1.26639 + 6.88449i 0.180913 + 0.983499i
\(50\) −11.4785 −1.62330
\(51\) 1.00034 + 0.577549i 0.140076 + 0.0808731i
\(52\) −1.46069 + 0.843329i −0.202561 + 0.116949i
\(53\) −1.85774 + 1.07256i −0.255180 + 0.147328i −0.622134 0.782911i \(-0.713734\pi\)
0.366954 + 0.930239i \(0.380401\pi\)
\(54\) 0.866025 + 0.500000i 0.117851 + 0.0680414i
\(55\) 22.9652i 3.09663i
\(56\) −2.03303 1.69316i −0.271675 0.226259i
\(57\) 6.55695i 0.868489i
\(58\) −3.21306 + 5.56519i −0.421896 + 0.730745i
\(59\) 6.54465 3.77855i 0.852041 0.491926i −0.00929818 0.999957i \(-0.502960\pi\)
0.861339 + 0.508031i \(0.169626\pi\)
\(60\) −3.51552 + 2.02969i −0.453851 + 0.262031i
\(61\) −5.20534 + 9.01591i −0.666476 + 1.15437i 0.312407 + 0.949948i \(0.398865\pi\)
−0.978883 + 0.204421i \(0.934469\pi\)
\(62\) 2.88334i 0.366184i
\(63\) 2.48284 0.914071i 0.312808 0.115162i
\(64\) 1.00000 0.125000
\(65\) 5.92947 + 3.42338i 0.735461 + 0.424618i
\(66\) −2.82867 4.89939i −0.348185 0.603074i
\(67\) −4.92805 + 2.84521i −0.602057 + 0.347598i −0.769851 0.638224i \(-0.779669\pi\)
0.167793 + 0.985822i \(0.446336\pi\)
\(68\) −0.577549 + 1.00034i −0.0700381 + 0.121310i
\(69\) 4.67101 + 1.08702i 0.562324 + 0.130862i
\(70\) −1.82594 + 10.5837i −0.218242 + 1.26500i
\(71\) −7.18784 −0.853040 −0.426520 0.904478i \(-0.640261\pi\)
−0.426520 + 0.904478i \(0.640261\pi\)
\(72\) −0.500000 + 0.866025i −0.0589256 + 0.102062i
\(73\) −9.62590 + 5.55752i −1.12663 + 0.650458i −0.943084 0.332554i \(-0.892090\pi\)
−0.183542 + 0.983012i \(0.558756\pi\)
\(74\) 1.89767 1.09562i 0.220600 0.127363i
\(75\) 9.94066 + 5.73924i 1.14785 + 0.662711i
\(76\) −6.55695 −0.752134
\(77\) −14.7500 2.54472i −1.68092 0.289998i
\(78\) 1.68666 0.190976
\(79\) −9.79501 5.65515i −1.10202 0.636254i −0.165272 0.986248i \(-0.552850\pi\)
−0.936752 + 0.349994i \(0.886184\pi\)
\(80\) −2.02969 3.51552i −0.226926 0.393047i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −4.93795 2.85093i −0.545306 0.314832i
\(83\) −0.847910 −0.0930702 −0.0465351 0.998917i \(-0.514818\pi\)
−0.0465351 + 0.998917i \(0.514818\pi\)
\(84\) 0.914071 + 2.48284i 0.0997333 + 0.270900i
\(85\) 4.68897 0.508591
\(86\) 1.14742 + 0.662464i 0.123730 + 0.0714353i
\(87\) 5.56519 3.21306i 0.596651 0.344476i
\(88\) 4.89939 2.82867i 0.522277 0.301537i
\(89\) 6.80960 11.7946i 0.721817 1.25022i −0.238454 0.971154i \(-0.576641\pi\)
0.960271 0.279069i \(-0.0900259\pi\)
\(90\) 4.05937 0.427895
\(91\) 2.85579 3.42902i 0.299368 0.359459i
\(92\) −1.08702 + 4.67101i −0.113330 + 0.486987i
\(93\) 1.44167 2.49704i 0.149494 0.258931i
\(94\) 3.82275 2.20707i 0.394287 0.227642i
\(95\) 13.3085 + 23.0511i 1.36543 + 2.36499i
\(96\) −0.866025 0.500000i −0.0883883 0.0510310i
\(97\) 4.92590 0.500149 0.250075 0.968227i \(-0.419545\pi\)
0.250075 + 0.968227i \(0.419545\pi\)
\(98\) 6.59534 + 2.34552i 0.666230 + 0.236933i
\(99\) 5.65733i 0.568583i
\(100\) −5.73924 + 9.94066i −0.573924 + 0.994066i
\(101\) −6.94536 + 4.00991i −0.691089 + 0.399001i −0.804020 0.594602i \(-0.797310\pi\)
0.112931 + 0.993603i \(0.463976\pi\)
\(102\) 1.00034 0.577549i 0.0990489 0.0571859i
\(103\) 3.81453 6.60696i 0.375857 0.651003i −0.614598 0.788841i \(-0.710682\pi\)
0.990455 + 0.137837i \(0.0440150\pi\)
\(104\) 1.68666i 0.165390i
\(105\) 6.87318 8.25281i 0.670754 0.805391i
\(106\) 2.14513i 0.208353i
\(107\) 6.14656 + 3.54872i 0.594210 + 0.343067i 0.766761 0.641933i \(-0.221867\pi\)
−0.172550 + 0.985001i \(0.555201\pi\)
\(108\) 0.866025 0.500000i 0.0833333 0.0481125i
\(109\) −15.1271 + 8.73364i −1.44891 + 0.836531i −0.998417 0.0562469i \(-0.982087\pi\)
−0.450497 + 0.892778i \(0.648753\pi\)
\(110\) −19.8884 11.4826i −1.89629 1.09482i
\(111\) −2.19124 −0.207983
\(112\) −2.48284 + 0.914071i −0.234606 + 0.0863715i
\(113\) 8.83766i 0.831377i 0.909507 + 0.415688i \(0.136459\pi\)
−0.909507 + 0.415688i \(0.863541\pi\)
\(114\) 5.67849 + 3.27848i 0.531839 + 0.307057i
\(115\) 18.6274 5.65923i 1.73701 0.527726i
\(116\) 3.21306 + 5.56519i 0.298325 + 0.516715i
\(117\) −1.46069 0.843329i −0.135041 0.0779658i
\(118\) 7.55711i 0.695688i
\(119\) 0.519575 3.01161i 0.0476293 0.276074i
\(120\) 4.05937i 0.370568i
\(121\) 10.5027 18.1912i 0.954791 1.65375i
\(122\) 5.20534 + 9.01591i 0.471269 + 0.816262i
\(123\) 2.85093 + 4.93795i 0.257060 + 0.445240i
\(124\) 2.49704 + 1.44167i 0.224241 + 0.129466i
\(125\) 26.2986 2.35222
\(126\) 0.449810 2.60723i 0.0400722 0.232271i
\(127\) −6.74682 −0.598683 −0.299342 0.954146i \(-0.596767\pi\)
−0.299342 + 0.954146i \(0.596767\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) −0.662464 1.14742i −0.0583267 0.101025i
\(130\) 5.92947 3.42338i 0.520049 0.300251i
\(131\) 4.79326 + 2.76739i 0.418789 + 0.241788i 0.694559 0.719436i \(-0.255600\pi\)
−0.275770 + 0.961224i \(0.588933\pi\)
\(132\) −5.65733 −0.492408
\(133\) 16.2798 5.99352i 1.41164 0.519704i
\(134\) 5.69042i 0.491578i
\(135\) −3.51552 2.02969i −0.302568 0.174687i
\(136\) 0.577549 + 1.00034i 0.0495244 + 0.0857789i
\(137\) −15.9415 + 9.20385i −1.36198 + 0.786338i −0.989887 0.141859i \(-0.954692\pi\)
−0.372090 + 0.928197i \(0.621359\pi\)
\(138\) 3.27690 3.50171i 0.278948 0.298085i
\(139\) 20.4754i 1.73670i 0.495950 + 0.868351i \(0.334820\pi\)
−0.495950 + 0.868351i \(0.665180\pi\)
\(140\) 8.25281 + 6.87318i 0.697489 + 0.580890i
\(141\) −4.41413 −0.371737
\(142\) −3.59392 + 6.22486i −0.301595 + 0.522378i
\(143\) 4.77099 + 8.26360i 0.398970 + 0.691037i
\(144\) 0.500000 + 0.866025i 0.0416667 + 0.0721688i
\(145\) 13.0430 22.5912i 1.08316 1.87609i
\(146\) 11.1150i 0.919887i
\(147\) −4.53897 5.32895i −0.374368 0.439524i
\(148\) 2.19124i 0.180119i
\(149\) −13.7082 7.91446i −1.12302 0.648378i −0.180852 0.983510i \(-0.557886\pi\)
−0.942171 + 0.335132i \(0.891219\pi\)
\(150\) 9.94066 5.73924i 0.811652 0.468607i
\(151\) 7.74316 + 13.4115i 0.630129 + 1.09142i 0.987525 + 0.157463i \(0.0503314\pi\)
−0.357396 + 0.933953i \(0.616335\pi\)
\(152\) −3.27848 + 5.67849i −0.265919 + 0.460586i
\(153\) −1.15510 −0.0933842
\(154\) −9.57879 + 11.5015i −0.771881 + 0.926818i
\(155\) 11.7045i 0.940130i
\(156\) 0.843329 1.46069i 0.0675203 0.116949i
\(157\) 2.07407 + 3.59239i 0.165529 + 0.286704i 0.936843 0.349750i \(-0.113734\pi\)
−0.771314 + 0.636455i \(0.780400\pi\)
\(158\) −9.79501 + 5.65515i −0.779249 + 0.449900i
\(159\) 1.07256 1.85774i 0.0850599 0.147328i
\(160\) −4.05937 −0.320921
\(161\) −1.57073 12.5910i −0.123791 0.992308i
\(162\) −1.00000 −0.0785674
\(163\) 10.4256 18.0576i 0.816593 1.41438i −0.0915851 0.995797i \(-0.529193\pi\)
0.908178 0.418584i \(-0.137473\pi\)
\(164\) −4.93795 + 2.85093i −0.385589 + 0.222620i
\(165\) 11.4826 + 19.8884i 0.893919 + 1.54831i
\(166\) −0.423955 + 0.734312i −0.0329053 + 0.0569936i
\(167\) 10.9872i 0.850212i −0.905144 0.425106i \(-0.860237\pi\)
0.905144 0.425106i \(-0.139763\pi\)
\(168\) 2.60723 + 0.449810i 0.201153 + 0.0347036i
\(169\) 10.1552 0.781168
\(170\) 2.34449 4.06077i 0.179814 0.311447i
\(171\) −3.27848 5.67849i −0.250711 0.434245i
\(172\) 1.14742 0.662464i 0.0874900 0.0505124i
\(173\) 1.79243 + 1.03486i 0.136276 + 0.0786789i 0.566588 0.824001i \(-0.308263\pi\)
−0.430312 + 0.902680i \(0.641596\pi\)
\(174\) 6.42612i 0.487163i
\(175\) 5.16313 29.9271i 0.390296 2.26228i
\(176\) 5.65733i 0.426437i
\(177\) −3.77855 + 6.54465i −0.284014 + 0.491926i
\(178\) −6.80960 11.7946i −0.510401 0.884041i
\(179\) 2.79957 + 4.84900i 0.209250 + 0.362431i 0.951478 0.307715i \(-0.0995645\pi\)
−0.742229 + 0.670147i \(0.766231\pi\)
\(180\) 2.02969 3.51552i 0.151284 0.262031i
\(181\) −22.5958 −1.67954 −0.839768 0.542946i \(-0.817309\pi\)
−0.839768 + 0.542946i \(0.817309\pi\)
\(182\) −1.54172 4.18769i −0.114280 0.310413i
\(183\) 10.4107i 0.769580i
\(184\) 3.50171 + 3.27690i 0.258149 + 0.241576i
\(185\) −7.70334 + 4.44753i −0.566361 + 0.326989i
\(186\) −1.44167 2.49704i −0.105708 0.183092i
\(187\) 5.65928 + 3.26739i 0.413848 + 0.238935i
\(188\) 4.41413i 0.321934i
\(189\) −1.69316 + 2.03303i −0.123160 + 0.147881i
\(190\) 26.6171 1.93101
\(191\) 4.57461 + 2.64115i 0.331007 + 0.191107i 0.656288 0.754510i \(-0.272126\pi\)
−0.325281 + 0.945617i \(0.605459\pi\)
\(192\) −0.866025 + 0.500000i −0.0625000 + 0.0360844i
\(193\) −13.3588 23.1381i −0.961587 1.66552i −0.718517 0.695510i \(-0.755179\pi\)
−0.243071 0.970009i \(-0.578155\pi\)
\(194\) 2.46295 4.26595i 0.176829 0.306278i
\(195\) −6.84677 −0.490307
\(196\) 5.32895 4.53897i 0.380639 0.324212i
\(197\) 14.1605 1.00889 0.504447 0.863443i \(-0.331696\pi\)
0.504447 + 0.863443i \(0.331696\pi\)
\(198\) 4.89939 + 2.82867i 0.348185 + 0.201025i
\(199\) −11.6374 20.1566i −0.824955 1.42886i −0.901954 0.431832i \(-0.857867\pi\)
0.0769991 0.997031i \(-0.475466\pi\)
\(200\) 5.73924 + 9.94066i 0.405826 + 0.702911i
\(201\) 2.84521 4.92805i 0.200686 0.347598i
\(202\) 8.01981i 0.564272i
\(203\) −13.0645 10.8805i −0.916947 0.763660i
\(204\) 1.15510i 0.0808731i
\(205\) 20.0450 + 11.5730i 1.40000 + 0.808292i
\(206\) −3.81453 6.60696i −0.265771 0.460329i
\(207\) −4.58873 + 1.39412i −0.318939 + 0.0968978i
\(208\) 1.46069 + 0.843329i 0.101281 + 0.0584743i
\(209\) 37.0948i 2.56590i
\(210\) −3.71055 10.0788i −0.256052 0.695500i
\(211\) −2.59509 −0.178653 −0.0893266 0.996002i \(-0.528471\pi\)
−0.0893266 + 0.996002i \(0.528471\pi\)
\(212\) 1.85774 + 1.07256i 0.127590 + 0.0736640i
\(213\) 6.22486 3.59392i 0.426520 0.246251i
\(214\) 6.14656 3.54872i 0.420170 0.242585i
\(215\) −4.65780 2.68918i −0.317660 0.183401i
\(216\) 1.00000i 0.0680414i
\(217\) −7.51753 1.29695i −0.510323 0.0880429i
\(218\) 17.4673i 1.18303i
\(219\) 5.55752 9.62590i 0.375542 0.650458i
\(220\) −19.8884 + 11.4826i −1.34088 + 0.774157i
\(221\) −1.68724 + 0.974128i −0.113496 + 0.0655269i
\(222\) −1.09562 + 1.89767i −0.0735332 + 0.127363i
\(223\) 11.5831i 0.775664i 0.921730 + 0.387832i \(0.126776\pi\)
−0.921730 + 0.387832i \(0.873224\pi\)
\(224\) −0.449810 + 2.60723i −0.0300542 + 0.174203i
\(225\) −11.4785 −0.765232
\(226\) 7.65364 + 4.41883i 0.509112 + 0.293936i
\(227\) 3.86164 + 6.68855i 0.256306 + 0.443935i 0.965249 0.261330i \(-0.0841612\pi\)
−0.708943 + 0.705265i \(0.750828\pi\)
\(228\) 5.67849 3.27848i 0.376067 0.217122i
\(229\) −11.0002 + 19.0529i −0.726912 + 1.25905i 0.231271 + 0.972889i \(0.425712\pi\)
−0.958182 + 0.286158i \(0.907622\pi\)
\(230\) 4.41263 18.9614i 0.290961 1.25028i
\(231\) 14.0462 5.17120i 0.924174 0.340240i
\(232\) 6.42612 0.421896
\(233\) −11.7283 + 20.3141i −0.768350 + 1.33082i 0.170108 + 0.985425i \(0.445588\pi\)
−0.938457 + 0.345395i \(0.887745\pi\)
\(234\) −1.46069 + 0.843329i −0.0954882 + 0.0551301i
\(235\) −15.5180 + 8.95930i −1.01228 + 0.584440i
\(236\) −6.54465 3.77855i −0.426020 0.245963i
\(237\) 11.3103 0.734683
\(238\) −2.34835 1.95577i −0.152221 0.126774i
\(239\) 14.2154 0.919516 0.459758 0.888044i \(-0.347936\pi\)
0.459758 + 0.888044i \(0.347936\pi\)
\(240\) 3.51552 + 2.02969i 0.226926 + 0.131016i
\(241\) 8.10166 + 14.0325i 0.521874 + 0.903912i 0.999676 + 0.0254449i \(0.00810022\pi\)
−0.477802 + 0.878467i \(0.658566\pi\)
\(242\) −10.5027 18.1912i −0.675139 1.16938i
\(243\) 0.866025 + 0.500000i 0.0555556 + 0.0320750i
\(244\) 10.4107 0.666476
\(245\) −26.7729 9.52133i −1.71046 0.608295i
\(246\) 5.70186 0.363537
\(247\) −9.57766 5.52967i −0.609412 0.351844i
\(248\) 2.49704 1.44167i 0.158562 0.0915460i
\(249\) 0.734312 0.423955i 0.0465351 0.0268671i
\(250\) 13.1493 22.7752i 0.831634 1.44043i
\(251\) 10.0678 0.635475 0.317737 0.948179i \(-0.397077\pi\)
0.317737 + 0.948179i \(0.397077\pi\)
\(252\) −2.03303 1.69316i −0.128069 0.106659i
\(253\) 26.4255 + 6.14966i 1.66136 + 0.386626i
\(254\) −3.37341 + 5.84292i −0.211667 + 0.366617i
\(255\) −4.06077 + 2.34449i −0.254295 + 0.146817i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −17.1515 9.90240i −1.06988 0.617695i −0.141730 0.989905i \(-0.545267\pi\)
−0.928148 + 0.372211i \(0.878600\pi\)
\(258\) −1.32493 −0.0824864
\(259\) 2.00295 + 5.44049i 0.124457 + 0.338055i
\(260\) 6.84677i 0.424618i
\(261\) −3.21306 + 5.56519i −0.198884 + 0.344476i
\(262\) 4.79326 2.76739i 0.296128 0.170970i
\(263\) −11.6562 + 6.72970i −0.718750 + 0.414971i −0.814293 0.580455i \(-0.802875\pi\)
0.0955421 + 0.995425i \(0.469542\pi\)
\(264\) −2.82867 + 4.89939i −0.174092 + 0.301537i
\(265\) 8.70787i 0.534920i
\(266\) 2.94938 17.0955i 0.180838 1.04819i
\(267\) 13.6192i 0.833482i
\(268\) 4.92805 + 2.84521i 0.301029 + 0.173799i
\(269\) −14.9189 + 8.61345i −0.909624 + 0.525171i −0.880310 0.474399i \(-0.842665\pi\)
−0.0293136 + 0.999570i \(0.509332\pi\)
\(270\) −3.51552 + 2.02969i −0.213948 + 0.123523i
\(271\) 17.3001 + 9.98824i 1.05091 + 0.606743i 0.922904 0.385031i \(-0.125809\pi\)
0.128005 + 0.991773i \(0.459143\pi\)
\(272\) 1.15510 0.0700381
\(273\) −0.758675 + 4.39751i −0.0459171 + 0.266150i
\(274\) 18.4077i 1.11205i
\(275\) 56.2376 + 32.4688i 3.39126 + 1.95794i
\(276\) −1.39412 4.58873i −0.0839160 0.276209i
\(277\) −4.94088 8.55786i −0.296869 0.514192i 0.678549 0.734555i \(-0.262609\pi\)
−0.975418 + 0.220363i \(0.929276\pi\)
\(278\) 17.7322 + 10.2377i 1.06351 + 0.614017i
\(279\) 2.88334i 0.172621i
\(280\) 10.0788 3.71055i 0.602321 0.221748i
\(281\) 19.4586i 1.16080i −0.814331 0.580400i \(-0.802896\pi\)
0.814331 0.580400i \(-0.197104\pi\)
\(282\) −2.20707 + 3.82275i −0.131429 + 0.227642i
\(283\) 15.2174 + 26.3573i 0.904581 + 1.56678i 0.821479 + 0.570239i \(0.193149\pi\)
0.0831017 + 0.996541i \(0.473517\pi\)
\(284\) 3.59392 + 6.22486i 0.213260 + 0.369377i
\(285\) −23.0511 13.3085i −1.36543 0.788330i
\(286\) 9.54198 0.564229
\(287\) 9.65418 11.5920i 0.569868 0.684256i
\(288\) 1.00000 0.0589256
\(289\) 7.83287 13.5669i 0.460757 0.798055i
\(290\) −13.0430 22.5912i −0.765912 1.32660i
\(291\) −4.26595 + 2.46295i −0.250075 + 0.144381i
\(292\) 9.62590 + 5.55752i 0.563313 + 0.325229i
\(293\) −15.7604 −0.920733 −0.460367 0.887729i \(-0.652282\pi\)
−0.460367 + 0.887729i \(0.652282\pi\)
\(294\) −6.88449 + 1.26639i −0.401512 + 0.0738575i
\(295\) 30.6771i 1.78609i
\(296\) −1.89767 1.09562i −0.110300 0.0636816i
\(297\) −2.82867 4.89939i −0.164136 0.284292i
\(298\) −13.7082 + 7.91446i −0.794097 + 0.458472i
\(299\) −5.52701 + 5.90618i −0.319635 + 0.341563i
\(300\) 11.4785i 0.662711i
\(301\) −2.24332 + 2.69361i −0.129303 + 0.155257i
\(302\) 15.4863 0.891137
\(303\) 4.00991 6.94536i 0.230363 0.399001i
\(304\) 3.27848 + 5.67849i 0.188033 + 0.325684i
\(305\) −21.1304 36.5989i −1.20992 2.09565i
\(306\) −0.577549 + 1.00034i −0.0330163 + 0.0571859i
\(307\) 7.88200i 0.449849i −0.974376 0.224925i \(-0.927786\pi\)
0.974376 0.224925i \(-0.0722136\pi\)
\(308\) 5.17120 + 14.0462i 0.294656 + 0.800358i
\(309\) 7.62906i 0.434002i
\(310\) −10.1364 5.85226i −0.575710 0.332386i
\(311\) 15.8777 9.16702i 0.900345 0.519814i 0.0230326 0.999735i \(-0.492668\pi\)
0.877312 + 0.479921i \(0.159335\pi\)
\(312\) −0.843329 1.46069i −0.0477441 0.0826952i
\(313\) −6.20167 + 10.7416i −0.350539 + 0.607152i −0.986344 0.164698i \(-0.947335\pi\)
0.635805 + 0.771850i \(0.280668\pi\)
\(314\) 4.14814 0.234093
\(315\) −1.82594 + 10.5837i −0.102880 + 0.596326i
\(316\) 11.3103i 0.636254i
\(317\) 1.83984 3.18670i 0.103336 0.178983i −0.809721 0.586815i \(-0.800382\pi\)
0.913057 + 0.407832i \(0.133715\pi\)
\(318\) −1.07256 1.85774i −0.0601464 0.104177i
\(319\) 31.4841 18.1774i 1.76277 1.01774i
\(320\) −2.02969 + 3.51552i −0.113463 + 0.196523i
\(321\) −7.09744 −0.396140
\(322\) −11.6895 4.93520i −0.651429 0.275028i
\(323\) −7.57393 −0.421424
\(324\) −0.500000 + 0.866025i −0.0277778 + 0.0481125i
\(325\) −16.7665 + 9.68014i −0.930038 + 0.536957i
\(326\) −10.4256 18.0576i −0.577419 1.00012i
\(327\) 8.73364 15.1271i 0.482971 0.836531i
\(328\) 5.70186i 0.314832i
\(329\) 4.03483 + 10.9596i 0.222447 + 0.604221i
\(330\) 22.9652 1.26419
\(331\) −2.45413 + 4.25068i −0.134891 + 0.233638i −0.925556 0.378611i \(-0.876402\pi\)
0.790665 + 0.612249i \(0.209735\pi\)
\(332\) 0.423955 + 0.734312i 0.0232676 + 0.0403006i
\(333\) 1.89767 1.09562i 0.103992 0.0600396i
\(334\) −9.51516 5.49358i −0.520647 0.300595i
\(335\) 23.0995i 1.26206i
\(336\) 1.69316 2.03303i 0.0923697 0.110911i
\(337\) 17.4280i 0.949365i −0.880157 0.474682i \(-0.842563\pi\)
0.880157 0.474682i \(-0.157437\pi\)
\(338\) 5.07759 8.79465i 0.276185 0.478366i
\(339\) −4.41883 7.65364i −0.239998 0.415688i
\(340\) −2.34449 4.06077i −0.127148 0.220226i
\(341\) 8.15599 14.1266i 0.441672 0.764998i
\(342\) −6.55695 −0.354559
\(343\) −9.08197 + 16.1406i −0.490380 + 0.871509i
\(344\) 1.32493i 0.0714353i
\(345\) −13.3021 + 14.2147i −0.716163 + 0.765295i
\(346\) 1.79243 1.03486i 0.0963615 0.0556344i
\(347\) 5.46035 + 9.45761i 0.293127 + 0.507711i 0.974547 0.224181i \(-0.0719708\pi\)
−0.681420 + 0.731892i \(0.738637\pi\)
\(348\) −5.56519 3.21306i −0.298325 0.172238i
\(349\) 35.9929i 1.92665i 0.268332 + 0.963327i \(0.413528\pi\)
−0.268332 + 0.963327i \(0.586472\pi\)
\(350\) −23.3361 19.4350i −1.24737 1.03884i
\(351\) 1.68666 0.0900271
\(352\) −4.89939 2.82867i −0.261139 0.150768i
\(353\) −4.71527 + 2.72237i −0.250969 + 0.144897i −0.620208 0.784438i \(-0.712952\pi\)
0.369239 + 0.929334i \(0.379618\pi\)
\(354\) 3.77855 + 6.54465i 0.200828 + 0.347844i
\(355\) 14.5891 25.2690i 0.774307 1.34114i
\(356\) −13.6192 −0.721817
\(357\) 1.05584 + 2.86792i 0.0558811 + 0.151786i
\(358\) 5.59914 0.295924
\(359\) 11.5930 + 6.69322i 0.611855 + 0.353255i 0.773691 0.633563i \(-0.218408\pi\)
−0.161836 + 0.986818i \(0.551742\pi\)
\(360\) −2.02969 3.51552i −0.106974 0.185284i
\(361\) −11.9968 20.7791i −0.631411 1.09364i
\(362\) −11.2979 + 19.5686i −0.593805 + 1.02850i
\(363\) 21.0054i 1.10250i
\(364\) −4.39751 0.758675i −0.230492 0.0397654i
\(365\) 45.1200i 2.36169i
\(366\) −9.01591 5.20534i −0.471269 0.272087i
\(367\) 6.26456 + 10.8505i 0.327007 + 0.566393i 0.981917 0.189314i \(-0.0606265\pi\)
−0.654909 + 0.755708i \(0.727293\pi\)
\(368\) 4.58873 1.39412i 0.239204 0.0726733i
\(369\) −4.93795 2.85093i −0.257060 0.148413i
\(370\) 8.89505i 0.462432i
\(371\) −5.59285 0.964899i −0.290366 0.0500951i
\(372\) −2.88334 −0.149494
\(373\) −8.52214 4.92026i −0.441260 0.254761i 0.262872 0.964831i \(-0.415330\pi\)
−0.704132 + 0.710069i \(0.748664\pi\)
\(374\) 5.65928 3.26739i 0.292635 0.168953i
\(375\) −22.7752 + 13.1493i −1.17611 + 0.679026i
\(376\) −3.82275 2.20707i −0.197143 0.113821i
\(377\) 10.8387i 0.558220i
\(378\) 0.914071 + 2.48284i 0.0470147 + 0.127703i
\(379\) 10.2772i 0.527903i 0.964536 + 0.263951i \(0.0850258\pi\)
−0.964536 + 0.263951i \(0.914974\pi\)
\(380\) 13.3085 23.0511i 0.682714 1.18250i
\(381\) 5.84292 3.37341i 0.299342 0.172825i
\(382\) 4.57461 2.64115i 0.234057 0.135133i
\(383\) −8.84461 + 15.3193i −0.451939 + 0.782781i −0.998506 0.0546341i \(-0.982601\pi\)
0.546568 + 0.837415i \(0.315934\pi\)
\(384\) 1.00000i 0.0510310i
\(385\) 38.8839 46.6889i 1.98170 2.37948i
\(386\) −26.7176 −1.35989
\(387\) 1.14742 + 0.662464i 0.0583267 + 0.0336749i
\(388\) −2.46295 4.26595i −0.125037 0.216571i
\(389\) −27.8127 + 16.0577i −1.41016 + 0.814156i −0.995403 0.0957759i \(-0.969467\pi\)
−0.414757 + 0.909932i \(0.636133\pi\)
\(390\) −3.42338 + 5.92947i −0.173350 + 0.300251i
\(391\) −1.25562 + 5.39548i −0.0634995 + 0.272861i
\(392\) −1.26639 6.88449i −0.0639625 0.347719i
\(393\) −5.53478 −0.279193
\(394\) 7.08025 12.2634i 0.356698 0.617819i
\(395\) 39.7616 22.9563i 2.00062 1.15506i
\(396\) 4.89939 2.82867i 0.246204 0.142146i
\(397\) −16.1963 9.35091i −0.812867 0.469309i 0.0350835 0.999384i \(-0.488830\pi\)
−0.847950 + 0.530075i \(0.822164\pi\)
\(398\) −23.2748 −1.16666
\(399\) −11.1020 + 13.3305i −0.555795 + 0.667357i
\(400\) 11.4785 0.573924
\(401\) −14.8691 8.58467i −0.742527 0.428698i 0.0804605 0.996758i \(-0.474361\pi\)
−0.822987 + 0.568060i \(0.807694\pi\)
\(402\) −2.84521 4.92805i −0.141906 0.245789i
\(403\) 2.43160 + 4.21165i 0.121127 + 0.209797i
\(404\) 6.94536 + 4.00991i 0.345545 + 0.199500i
\(405\) 4.05937 0.201712
\(406\) −15.9550 + 5.87393i −0.791834 + 0.291518i
\(407\) −12.3966 −0.614475
\(408\) −1.00034 0.577549i −0.0495244 0.0285930i
\(409\) −8.69664 + 5.02101i −0.430021 + 0.248273i −0.699356 0.714774i \(-0.746530\pi\)
0.269334 + 0.963047i \(0.413196\pi\)
\(410\) 20.0450 11.5730i 0.989951 0.571548i
\(411\) 9.20385 15.9415i 0.453992 0.786338i
\(412\) −7.62906 −0.375857
\(413\) 19.7032 + 3.39926i 0.969529 + 0.167267i
\(414\) −1.08702 + 4.67101i −0.0534243 + 0.229568i
\(415\) 1.72099 2.98084i 0.0844801 0.146324i
\(416\) 1.46069 0.843329i 0.0716161 0.0413476i
\(417\) −10.2377 17.7322i −0.501343 0.868351i
\(418\) 32.1251 + 18.5474i 1.57129 + 0.907184i
\(419\) 36.7063 1.79322 0.896610 0.442821i \(-0.146022\pi\)
0.896610 + 0.442821i \(0.146022\pi\)
\(420\) −10.5837 1.82594i −0.516433 0.0890970i
\(421\) 1.74437i 0.0850155i 0.999096 + 0.0425077i \(0.0135347\pi\)
−0.999096 + 0.0425077i \(0.986465\pi\)
\(422\) −1.29754 + 2.24741i −0.0631634 + 0.109402i
\(423\) 3.82275 2.20707i 0.185869 0.107311i
\(424\) 1.85774 1.07256i 0.0902196 0.0520883i
\(425\) −6.62939 + 11.4824i −0.321573 + 0.556980i
\(426\) 7.18784i 0.348252i
\(427\) −25.8480 + 9.51610i −1.25087 + 0.460516i
\(428\) 7.09744i 0.343067i
\(429\) −8.26360 4.77099i −0.398970 0.230346i
\(430\) −4.65780 + 2.68918i −0.224619 + 0.129684i
\(431\) −12.3926 + 7.15487i −0.596931 + 0.344638i −0.767833 0.640650i \(-0.778665\pi\)
0.170903 + 0.985288i \(0.445332\pi\)
\(432\) −0.866025 0.500000i −0.0416667 0.0240563i
\(433\) 17.9359 0.861943 0.430972 0.902365i \(-0.358171\pi\)
0.430972 + 0.902365i \(0.358171\pi\)
\(434\) −4.88196 + 5.86190i −0.234342 + 0.281380i
\(435\) 26.0860i 1.25073i
\(436\) 15.1271 + 8.73364i 0.724457 + 0.418265i
\(437\) −30.0881 + 9.14115i −1.43931 + 0.437281i
\(438\) −5.55752 9.62590i −0.265548 0.459943i
\(439\) −28.0581 16.1994i −1.33914 0.773154i −0.352462 0.935826i \(-0.614655\pi\)
−0.986680 + 0.162672i \(0.947989\pi\)
\(440\) 22.9652i 1.09482i
\(441\) 6.59534 + 2.34552i 0.314064 + 0.111691i
\(442\) 1.94826i 0.0926691i
\(443\) −19.0976 + 33.0780i −0.907355 + 1.57159i −0.0896309 + 0.995975i \(0.528569\pi\)
−0.817724 + 0.575610i \(0.804765\pi\)
\(444\) 1.09562 + 1.89767i 0.0519958 + 0.0900594i
\(445\) 27.6427 + 47.8786i 1.31039 + 2.26966i
\(446\) 10.0313 + 5.79156i 0.474995 + 0.274239i
\(447\) 15.8289 0.748682
\(448\) 2.03303 + 1.69316i 0.0960515 + 0.0799945i
\(449\) 14.0922 0.665052 0.332526 0.943094i \(-0.392099\pi\)
0.332526 + 0.943094i \(0.392099\pi\)
\(450\) −5.73924 + 9.94066i −0.270551 + 0.468607i
\(451\) 16.1286 + 27.9356i 0.759468 + 1.31544i
\(452\) 7.65364 4.41883i 0.359997 0.207844i
\(453\) −13.4115 7.74316i −0.630129 0.363805i
\(454\) 7.72328 0.362471
\(455\) 6.25843 + 16.9994i 0.293400 + 0.796944i
\(456\) 6.55695i 0.307057i
\(457\) −3.70638 2.13988i −0.173377 0.100099i 0.410800 0.911725i \(-0.365249\pi\)
−0.584177 + 0.811626i \(0.698583\pi\)
\(458\) 11.0002 + 19.0529i 0.514004 + 0.890281i
\(459\) 1.00034 0.577549i 0.0466921 0.0269577i
\(460\) −14.2147 13.3021i −0.662765 0.620216i
\(461\) 7.14597i 0.332821i 0.986057 + 0.166410i \(0.0532177\pi\)
−0.986057 + 0.166410i \(0.946782\pi\)
\(462\) 2.54472 14.7500i 0.118391 0.686232i
\(463\) 2.83540 0.131772 0.0658861 0.997827i \(-0.479013\pi\)
0.0658861 + 0.997827i \(0.479013\pi\)
\(464\) 3.21306 5.56519i 0.149163 0.258357i
\(465\) 5.85226 + 10.1364i 0.271392 + 0.470065i
\(466\) 11.7283 + 20.3141i 0.543305 + 0.941032i
\(467\) 12.7367 22.0606i 0.589384 1.02084i −0.404929 0.914348i \(-0.632704\pi\)
0.994313 0.106495i \(-0.0339628\pi\)
\(468\) 1.68666i 0.0779658i
\(469\) −14.8363 2.55961i −0.685075 0.118192i
\(470\) 17.9186i 0.826523i
\(471\) −3.59239 2.07407i −0.165529 0.0955680i
\(472\) −6.54465 + 3.77855i −0.301242 + 0.173922i
\(473\) −3.74778 6.49134i −0.172323 0.298472i
\(474\) 5.65515 9.79501i 0.259750 0.449900i
\(475\) −75.2639 −3.45334
\(476\) −2.86792 + 1.05584i −0.131451 + 0.0483944i
\(477\) 2.14513i 0.0982187i
\(478\) 7.10768 12.3109i 0.325098 0.563086i
\(479\) 9.60900 + 16.6433i 0.439046 + 0.760450i 0.997616 0.0690070i \(-0.0219831\pi\)
−0.558570 + 0.829457i \(0.688650\pi\)
\(480\) 3.51552 2.02969i 0.160461 0.0926420i
\(481\) 1.84794 3.20072i 0.0842586 0.145940i
\(482\) 16.2033 0.738041
\(483\) 7.65579 + 10.1187i 0.348350 + 0.460419i
\(484\) −21.0054 −0.954791
\(485\) −9.99802 + 17.3171i −0.453987 + 0.786328i
\(486\) 0.866025 0.500000i 0.0392837 0.0226805i
\(487\) −15.1812 26.2947i −0.687927 1.19152i −0.972507 0.232872i \(-0.925188\pi\)
0.284580 0.958652i \(-0.408146\pi\)
\(488\) 5.20534 9.01591i 0.235635 0.408131i
\(489\) 20.8511i 0.942921i
\(490\) −21.6322 + 18.4254i −0.977242 + 0.832374i
\(491\) 8.50669 0.383902 0.191951 0.981405i \(-0.438519\pi\)
0.191951 + 0.981405i \(0.438519\pi\)
\(492\) 2.85093 4.93795i 0.128530 0.222620i
\(493\) 3.71140 + 6.42834i 0.167153 + 0.289518i
\(494\) −9.57766 + 5.52967i −0.430919 + 0.248791i
\(495\) −19.8884 11.4826i −0.893919 0.516105i
\(496\) 2.88334i 0.129466i
\(497\) −14.6131 12.1702i −0.655486 0.545908i
\(498\) 0.847910i 0.0379958i
\(499\) −6.28157 + 10.8800i −0.281202 + 0.487056i −0.971681 0.236297i \(-0.924066\pi\)
0.690479 + 0.723352i \(0.257400\pi\)
\(500\) −13.1493 22.7752i −0.588054 1.01854i
\(501\) 5.49358 + 9.51516i 0.245435 + 0.425106i
\(502\) 5.03391 8.71899i 0.224674 0.389147i
\(503\) −5.00925 −0.223351 −0.111676 0.993745i \(-0.535622\pi\)
−0.111676 + 0.993745i \(0.535622\pi\)
\(504\) −2.48284 + 0.914071i −0.110594 + 0.0407159i
\(505\) 32.5554i 1.44870i
\(506\) 18.5385 19.8103i 0.824137 0.880676i
\(507\) −8.79465 + 5.07759i −0.390584 + 0.225504i
\(508\) 3.37341 + 5.84292i 0.149671 + 0.259238i
\(509\) 16.2344 + 9.37291i 0.719575 + 0.415447i 0.814596 0.580028i \(-0.196958\pi\)
−0.0950210 + 0.995475i \(0.530292\pi\)
\(510\) 4.68897i 0.207631i
\(511\) −28.9795 4.99965i −1.28198 0.221172i
\(512\) −1.00000 −0.0441942
\(513\) 5.67849 + 3.27848i 0.250711 + 0.144748i
\(514\) −17.1515 + 9.90240i −0.756518 + 0.436776i
\(515\) 15.4846 + 26.8201i 0.682333 + 1.18184i
\(516\) −0.662464 + 1.14742i −0.0291633 + 0.0505124i
\(517\) −24.9722 −1.09828
\(518\) 5.71307 + 0.985641i 0.251018 + 0.0433066i
\(519\) −2.06972 −0.0908505
\(520\) −5.92947 3.42338i −0.260025 0.150125i
\(521\) −2.62697 4.55004i −0.115090 0.199341i 0.802726 0.596348i \(-0.203382\pi\)
−0.917816 + 0.397007i \(0.870049\pi\)
\(522\) 3.21306 + 5.56519i 0.140632 + 0.243582i
\(523\) 9.66808 16.7456i 0.422755 0.732234i −0.573452 0.819239i \(-0.694396\pi\)
0.996208 + 0.0870049i \(0.0277296\pi\)
\(524\) 5.53478i 0.241788i
\(525\) 10.4921 + 28.4992i 0.457915 + 1.24381i
\(526\) 13.4594i 0.586857i
\(527\) 2.88433 + 1.66527i 0.125643 + 0.0725402i
\(528\) 2.82867 + 4.89939i 0.123102 + 0.213219i
\(529\) 1.52388 + 22.9495i 0.0662555 + 0.997803i
\(530\) −7.54124 4.35393i −0.327570 0.189123i
\(531\) 7.55711i 0.327951i
\(532\) −13.3305 11.1020i −0.577948 0.481332i
\(533\) −9.61708 −0.416562
\(534\) 11.7946 + 6.80960i 0.510401 + 0.294680i
\(535\) −24.9512 + 14.4056i −1.07873 + 0.622807i
\(536\) 4.92805 2.84521i 0.212859 0.122894i
\(537\) −4.84900 2.79957i −0.209250 0.120810i
\(538\) 17.2269i 0.742705i
\(539\) −25.6785 30.1476i −1.10605 1.29855i
\(540\) 4.05937i 0.174687i
\(541\) −4.36382 + 7.55835i −0.187615 + 0.324959i −0.944455 0.328642i \(-0.893409\pi\)
0.756840 + 0.653601i \(0.226742\pi\)
\(542\) 17.3001 9.98824i 0.743105 0.429032i
\(543\) 19.5686 11.2979i 0.839768 0.484840i
\(544\) 0.577549 1.00034i 0.0247622 0.0428894i
\(545\) 70.9062i 3.03729i
\(546\) 3.42902 + 2.85579i 0.146748 + 0.122216i
\(547\) −25.3827 −1.08529 −0.542643 0.839963i \(-0.682577\pi\)
−0.542643 + 0.839963i \(0.682577\pi\)
\(548\) 15.9415 + 9.20385i 0.680988 + 0.393169i
\(549\) 5.20534 + 9.01591i 0.222159 + 0.384790i
\(550\) 56.2376 32.4688i 2.39798 1.38447i
\(551\) −21.0679 + 36.4907i −0.897522 + 1.55455i
\(552\) −4.67101 1.08702i −0.198812 0.0462668i
\(553\) −10.3384 28.0816i −0.439634 1.19415i
\(554\) −9.88176 −0.419836
\(555\) 4.44753 7.70334i 0.188787 0.326989i
\(556\) 17.7322 10.2377i 0.752014 0.434176i
\(557\) −0.975085 + 0.562966i −0.0413157 + 0.0238536i −0.520516 0.853852i \(-0.674260\pi\)
0.479200 + 0.877706i \(0.340927\pi\)
\(558\) 2.49704 + 1.44167i 0.105708 + 0.0610307i
\(559\) 2.23470 0.0945177
\(560\) 1.82594 10.5837i 0.0771602 0.447244i
\(561\) −6.53478 −0.275898
\(562\) −16.8516 9.72928i −0.710842 0.410405i
\(563\) −21.1487 36.6307i −0.891313 1.54380i −0.838302 0.545206i \(-0.816452\pi\)
−0.0530108 0.998594i \(-0.516882\pi\)
\(564\) 2.20707 + 3.82275i 0.0929343 + 0.160967i
\(565\) −31.0689 17.9377i −1.30708 0.754643i
\(566\) 30.4348 1.27927
\(567\) 0.449810 2.60723i 0.0188902 0.109494i
\(568\) 7.18784 0.301595
\(569\) 25.2638 + 14.5861i 1.05911 + 0.611479i 0.925187 0.379512i \(-0.123908\pi\)
0.133926 + 0.990991i \(0.457242\pi\)
\(570\) −23.0511 + 13.3085i −0.965503 + 0.557434i
\(571\) 11.9062 6.87403i 0.498257 0.287669i −0.229736 0.973253i \(-0.573786\pi\)
0.727994 + 0.685584i \(0.240453\pi\)
\(572\) 4.77099 8.26360i 0.199485 0.345518i
\(573\) −5.28230 −0.220671
\(574\) −5.21190 14.1568i −0.217540 0.590892i
\(575\) −12.4774 + 53.6162i −0.520343 + 2.23595i
\(576\) 0.500000 0.866025i 0.0208333 0.0360844i
\(577\) 24.2748 14.0150i 1.01057 0.583454i 0.0992124 0.995066i \(-0.468368\pi\)
0.911359 + 0.411613i \(0.135034\pi\)
\(578\) −7.83287 13.5669i −0.325805 0.564310i
\(579\) 23.1381 + 13.3588i 0.961587 + 0.555173i
\(580\) −26.0860 −1.08316
\(581\) −1.72382 1.43565i −0.0715163 0.0595608i
\(582\) 4.92590i 0.204185i
\(583\) 6.06785 10.5098i 0.251305 0.435272i
\(584\) 9.62590 5.55752i 0.398323 0.229972i
\(585\) 5.92947 3.42338i 0.245154 0.141539i
\(586\) −7.88021 + 13.6489i −0.325528 + 0.563832i
\(587\) 1.89303i 0.0781337i 0.999237 + 0.0390668i \(0.0124385\pi\)
−0.999237 + 0.0390668i \(0.987561\pi\)
\(588\) −2.34552 + 6.59534i −0.0967276 + 0.271987i
\(589\) 18.9059i 0.779004i
\(590\) 26.5672 + 15.3386i 1.09375 + 0.631478i
\(591\) −12.2634 + 7.08025i −0.504447 + 0.291243i
\(592\) −1.89767 + 1.09562i −0.0779937 + 0.0450297i
\(593\) 6.51640 + 3.76224i 0.267596 + 0.154497i 0.627795 0.778379i \(-0.283958\pi\)
−0.360198 + 0.932876i \(0.617291\pi\)
\(594\) −5.65733 −0.232123
\(595\) 9.53281 + 7.93920i 0.390807 + 0.325475i
\(596\) 15.8289i 0.648378i
\(597\) 20.1566 + 11.6374i 0.824955 + 0.476288i
\(598\) 2.35140 + 7.73962i 0.0961558 + 0.316496i
\(599\) 23.1928 + 40.1711i 0.947631 + 1.64135i 0.750395 + 0.660990i \(0.229863\pi\)
0.197236 + 0.980356i \(0.436803\pi\)
\(600\) −9.94066 5.73924i −0.405826 0.234304i
\(601\) 5.74340i 0.234278i 0.993116 + 0.117139i \(0.0373723\pi\)
−0.993116 + 0.117139i \(0.962628\pi\)
\(602\) 1.21108 + 3.28958i 0.0493598 + 0.134073i
\(603\) 5.69042i 0.231732i
\(604\) 7.74316 13.4115i 0.315065 0.545708i
\(605\) 42.6344 + 73.8449i 1.73333 + 3.00222i
\(606\) −4.00991 6.94536i −0.162891 0.282136i
\(607\) 20.9112 + 12.0731i 0.848761 + 0.490033i 0.860233 0.509902i \(-0.170318\pi\)
−0.0114715 + 0.999934i \(0.503652\pi\)
\(608\) 6.55695 0.265919
\(609\) 16.7544 + 2.89053i 0.678923 + 0.117130i
\(610\) −42.2608 −1.71109
\(611\) 3.72257 6.44767i 0.150599 0.260845i
\(612\) 0.577549 + 1.00034i 0.0233460 + 0.0404365i
\(613\) 2.02156 1.16715i 0.0816501 0.0471407i −0.458619 0.888633i \(-0.651656\pi\)
0.540269 + 0.841492i \(0.318322\pi\)
\(614\) −6.82601 3.94100i −0.275475 0.159046i
\(615\) −23.1459 −0.933335
\(616\) 14.7500 + 2.54472i 0.594294 + 0.102530i
\(617\) 3.06512i 0.123397i 0.998095 + 0.0616986i \(0.0196518\pi\)
−0.998095 + 0.0616986i \(0.980348\pi\)
\(618\) 6.60696 + 3.81453i 0.265771 + 0.153443i
\(619\) −4.41751 7.65135i −0.177555 0.307534i 0.763488 0.645822i \(-0.223485\pi\)
−0.941042 + 0.338289i \(0.890152\pi\)
\(620\) −10.1364 + 5.85226i −0.407088 + 0.235033i
\(621\) 3.27690 3.50171i 0.131497 0.140519i
\(622\) 18.3340i 0.735128i
\(623\) 33.8143 12.4489i 1.35474 0.498755i
\(624\) −1.68666 −0.0675203
\(625\) −24.6816 + 42.7498i −0.987264 + 1.70999i
\(626\) 6.20167 + 10.7416i 0.247869 + 0.429321i
\(627\) −18.5474 32.1251i −0.740713 1.28295i
\(628\) 2.07407 3.59239i 0.0827643 0.143352i
\(629\) 2.53110i 0.100921i
\(630\) 8.25281 + 6.87318i 0.328800 + 0.273834i
\(631\) 5.70623i 0.227162i −0.993529 0.113581i \(-0.963768\pi\)
0.993529 0.113581i \(-0.0362321\pi\)
\(632\) 9.79501 + 5.65515i 0.389624 + 0.224950i
\(633\) 2.24741 1.29754i 0.0893266 0.0515727i
\(634\) −1.83984 3.18670i −0.0730696 0.126560i
\(635\) 13.6939 23.7186i 0.543427 0.941242i
\(636\) −2.14513 −0.0850599
\(637\) 11.6118 2.13597i 0.460076 0.0846302i
\(638\) 36.3547i 1.43930i
\(639\) −3.59392 + 6.22486i −0.142173 + 0.246251i
\(640\) 2.02969 + 3.51552i 0.0802303 + 0.138963i
\(641\) 5.46662 3.15616i 0.215919 0.124661i −0.388140 0.921600i \(-0.626882\pi\)
0.604059 + 0.796940i \(0.293549\pi\)
\(642\) −3.54872 + 6.14656i −0.140057 + 0.242585i
\(643\) −29.5677 −1.16604 −0.583019 0.812458i \(-0.698129\pi\)
−0.583019 + 0.812458i \(0.698129\pi\)
\(644\) −10.1187 + 7.65579i −0.398734 + 0.301680i
\(645\) 5.37837 0.211773
\(646\) −3.78696 + 6.55921i −0.148996 + 0.258069i
\(647\) 38.1119 22.0039i 1.49833 0.865063i 0.498335 0.866984i \(-0.333945\pi\)
0.999998 + 0.00192095i \(0.000611456\pi\)
\(648\) 0.500000 + 0.866025i 0.0196419 + 0.0340207i
\(649\) −21.3765 + 37.0252i −0.839102 + 1.45337i
\(650\) 19.3603i 0.759372i
\(651\) 7.15885 2.63557i 0.280577 0.103296i
\(652\) −20.8511 −0.816593
\(653\) −8.76586 + 15.1829i −0.343035 + 0.594154i −0.984995 0.172585i \(-0.944788\pi\)
0.641960 + 0.766738i \(0.278122\pi\)
\(654\) −8.73364 15.1271i −0.341512 0.591517i
\(655\) −19.4576 + 11.2339i −0.760271 + 0.438943i
\(656\) 4.93795 + 2.85093i 0.192795 + 0.111310i
\(657\) 11.1150i 0.433639i
\(658\) 11.5087 + 1.98552i 0.448655 + 0.0774036i
\(659\) 46.8252i 1.82405i −0.410132 0.912026i \(-0.634517\pi\)
0.410132 0.912026i \(-0.365483\pi\)
\(660\) 11.4826 19.8884i 0.446960 0.774157i
\(661\) −19.0305 32.9619i −0.740202 1.28207i −0.952403 0.304842i \(-0.901396\pi\)
0.212201 0.977226i \(-0.431937\pi\)
\(662\) 2.45413 + 4.25068i 0.0953824 + 0.165207i
\(663\) 0.974128 1.68724i 0.0378320 0.0655269i
\(664\) 0.847910 0.0329053
\(665\) −11.9726 + 69.3970i −0.464279 + 2.69110i
\(666\) 2.19124i 0.0849088i
\(667\) 22.5024 + 21.0578i 0.871296 + 0.815360i
\(668\) −9.51516 + 5.49358i −0.368153 + 0.212553i
\(669\) −5.79156 10.0313i −0.223915 0.387832i
\(670\) −20.0048 11.5498i −0.772852 0.446206i
\(671\) 58.8967i 2.27368i
\(672\) −0.914071 2.48284i −0.0352610 0.0957775i
\(673\) −45.8997 −1.76930 −0.884651 0.466254i \(-0.845603\pi\)
−0.884651 + 0.466254i \(0.845603\pi\)
\(674\) −15.0931 8.71401i −0.581365 0.335651i
\(675\) 9.94066 5.73924i 0.382616 0.220904i
\(676\) −5.07759 8.79465i −0.195292 0.338256i
\(677\) 7.26567 12.5845i 0.279242 0.483662i −0.691954 0.721941i \(-0.743250\pi\)
0.971197 + 0.238279i \(0.0765834\pi\)
\(678\) −8.83766 −0.339408
\(679\) 10.0145 + 8.34035i 0.384320 + 0.320073i
\(680\) −4.68897 −0.179814
\(681\) −6.68855 3.86164i −0.256306 0.147978i
\(682\) −8.15599 14.1266i −0.312309 0.540935i
\(683\) −23.3505 40.4443i −0.893482 1.54756i −0.835672 0.549229i \(-0.814921\pi\)
−0.0578106 0.998328i \(-0.518412\pi\)
\(684\) −3.27848 + 5.67849i −0.125356 + 0.217122i
\(685\) 74.7236i 2.85504i
\(686\) 9.43716 + 15.9355i 0.360312 + 0.608420i
\(687\) 22.0003i 0.839365i
\(688\) −1.14742 0.662464i −0.0437450 0.0252562i
\(689\) 1.80905 + 3.13336i 0.0689192 + 0.119372i
\(690\) 5.65923 + 18.6274i 0.215443 + 0.709131i
\(691\) −0.0941465 0.0543555i −0.00358150 0.00206778i 0.498208 0.867057i \(-0.333992\pi\)
−0.501790 + 0.864990i \(0.667325\pi\)
\(692\) 2.06972i 0.0786789i
\(693\) −9.57879 + 11.5015i −0.363868 + 0.436906i
\(694\) 10.9207 0.414544
\(695\) −71.9817 41.5587i −2.73042 1.57641i
\(696\) −5.56519 + 3.21306i −0.210948 + 0.121791i
\(697\) −5.70382 + 3.29310i −0.216048 + 0.124735i
\(698\) 31.1707 + 17.9964i 1.17983 + 0.681175i
\(699\) 23.4567i 0.887214i
\(700\) −28.4992 + 10.4921i −1.07717 + 0.396566i
\(701\) 21.6443i 0.817495i −0.912648 0.408747i \(-0.865966\pi\)
0.912648 0.408747i \(-0.134034\pi\)
\(702\) 0.843329 1.46069i 0.0318294 0.0551301i
\(703\) 12.4429 7.18392i 0.469294 0.270947i
\(704\) −4.89939 + 2.82867i −0.184653 + 0.106609i
\(705\) 8.95930 15.5180i 0.337427 0.584440i
\(706\) 5.44473i 0.204915i
\(707\) −20.9095 3.60739i −0.786384 0.135670i
\(708\) 7.55711 0.284014
\(709\) 13.6161 + 7.86128i 0.511365 + 0.295237i 0.733394 0.679803i \(-0.237935\pi\)
−0.222030 + 0.975040i \(0.571268\pi\)
\(710\) −14.5891 25.2690i −0.547518 0.948328i
\(711\) −9.79501 + 5.65515i −0.367341 + 0.212085i
\(712\) −6.80960 + 11.7946i −0.255201 + 0.442021i
\(713\) 13.4681 + 3.13426i 0.504384 + 0.117379i
\(714\) 3.01161 + 0.519575i 0.112707 + 0.0194446i
\(715\) −38.7344 −1.44859
\(716\) 2.79957 4.84900i 0.104625 0.181216i
\(717\) −12.3109 + 7.10768i −0.459758 + 0.265441i
\(718\) 11.5930 6.69322i 0.432647 0.249789i
\(719\) 19.1661 + 11.0655i 0.714775 + 0.412675i 0.812826 0.582506i \(-0.197928\pi\)
−0.0980518 + 0.995181i \(0.531261\pi\)
\(720\) −4.05937 −0.151284
\(721\) 18.9417 6.97350i 0.705426 0.259707i
\(722\) −23.9936 −0.892950
\(723\) −14.0325 8.10166i −0.521874 0.301304i
\(724\) 11.2979 + 19.5686i 0.419884 + 0.727260i
\(725\) 36.8811 + 63.8799i 1.36973 + 2.37244i
\(726\) 18.1912 + 10.5027i 0.675139 + 0.389792i
\(727\) −5.61811 −0.208364 −0.104182 0.994558i \(-0.533222\pi\)
−0.104182 + 0.994558i \(0.533222\pi\)
\(728\) −2.85579 + 3.42902i −0.105843 + 0.127088i
\(729\) −1.00000 −0.0370370
\(730\) −39.0751 22.5600i −1.44623 0.834984i
\(731\) 1.32538 0.765211i 0.0490211 0.0283023i
\(732\) −9.01591 + 5.20534i −0.333238 + 0.192395i
\(733\) 13.2866 23.0130i 0.490751 0.850006i −0.509192 0.860653i \(-0.670056\pi\)
0.999943 + 0.0106469i \(0.00338909\pi\)
\(734\) 12.5291 0.462458
\(735\) 27.9467 5.14076i 1.03083 0.189620i
\(736\) 1.08702 4.67101i 0.0400683 0.172176i
\(737\) 16.0963 27.8796i 0.592915 1.02696i
\(738\) −4.93795 + 2.85093i −0.181769 + 0.104944i
\(739\) −9.73154 16.8555i −0.357981 0.620041i 0.629643 0.776885i \(-0.283201\pi\)
−0.987623 + 0.156844i \(0.949868\pi\)
\(740\) 7.70334 + 4.44753i 0.283180 + 0.163494i
\(741\) 11.0593 0.406275
\(742\) −3.63205 + 4.36110i −0.133337 + 0.160101i
\(743\) 45.3501i 1.66373i −0.554975 0.831867i \(-0.687272\pi\)
0.554975 0.831867i \(-0.312728\pi\)
\(744\) −1.44167 + 2.49704i −0.0528541 + 0.0915460i
\(745\) 55.6468 32.1277i 2.03874 1.17707i
\(746\) −8.52214 + 4.92026i −0.312018 + 0.180144i
\(747\) −0.423955 + 0.734312i −0.0155117 + 0.0268671i
\(748\) 6.53478i 0.238935i
\(749\) 6.48756 + 17.6218i 0.237050 + 0.643885i
\(750\) 26.2986i 0.960288i
\(751\) 29.0897 + 16.7950i 1.06150 + 0.612857i 0.925847 0.377900i \(-0.123354\pi\)
0.135652 + 0.990756i \(0.456687\pi\)
\(752\) −3.82275 + 2.20707i −0.139401 + 0.0804834i
\(753\) −8.71899 + 5.03391i −0.317737 + 0.183446i
\(754\) 9.38657 + 5.41934i 0.341839 + 0.197361i
\(755\) −62.8647 −2.28788
\(756\) 2.60723 + 0.449810i 0.0948242 + 0.0163594i
\(757\) 12.3995i 0.450669i 0.974281 + 0.225335i \(0.0723475\pi\)
−0.974281 + 0.225335i \(0.927652\pi\)
\(758\) 8.90029 + 5.13858i 0.323273 + 0.186642i
\(759\) −25.9600 + 7.88698i −0.942287 + 0.286279i
\(760\) −13.3085 23.0511i −0.482752 0.836150i
\(761\) −3.23071 1.86525i −0.117113 0.0676152i 0.440299 0.897851i \(-0.354872\pi\)
−0.557412 + 0.830236i \(0.688206\pi\)
\(762\) 6.74682i 0.244411i
\(763\) −45.5413 7.85695i −1.64871 0.284441i
\(764\) 5.28230i 0.191107i
\(765\) 2.34449 4.06077i 0.0847651 0.146817i
\(766\) 8.84461 + 15.3193i 0.319569 + 0.553510i
\(767\) −6.37313 11.0386i −0.230120 0.398580i
\(768\) 0.866025 + 0.500000i 0.0312500 + 0.0180422i
\(769\) 22.5407 0.812837 0.406418 0.913687i \(-0.366778\pi\)
0.406418 + 0.913687i \(0.366778\pi\)
\(770\) −20.9918 57.0188i −0.756493 2.05482i
\(771\) 19.8048 0.713252
\(772\) −13.3588 + 23.1381i −0.480794 + 0.832759i
\(773\) −1.13116 1.95922i −0.0406850 0.0704684i 0.844966 0.534820i \(-0.179621\pi\)
−0.885651 + 0.464352i \(0.846287\pi\)
\(774\) 1.14742 0.662464i 0.0412432 0.0238118i
\(775\) 28.6623 + 16.5482i 1.02958 + 0.594428i
\(776\) −4.92590 −0.176829
\(777\) −4.45485 3.71013i −0.159817 0.133100i
\(778\) 32.1153i 1.15139i
\(779\) −32.3779 18.6934i −1.16006 0.669761i
\(780\) 3.42338 + 5.92947i 0.122577 + 0.212309i
\(781\) 35.2161 20.3320i 1.26013 0.727536i
\(782\) 4.04481 + 3.78514i 0.144642 + 0.135356i
\(783\) 6.42612i 0.229651i
\(784\) −6.59534 2.34552i −0.235548 0.0837685i
\(785\) −16.8388 −0.601003
\(786\) −2.76739 + 4.79326i −0.0987095 + 0.170970i
\(787\) −5.09861 8.83105i −0.181746 0.314793i 0.760729 0.649069i \(-0.224841\pi\)
−0.942475 + 0.334276i \(0.891508\pi\)
\(788\) −7.08025 12.2634i −0.252224 0.436864i
\(789\) 6.72970 11.6562i 0.239583 0.414971i
\(790\) 45.9127i 1.63350i
\(791\) −14.9636 + 17.9672i −0.532045 + 0.638840i
\(792\) 5.65733i 0.201025i
\(793\) 15.2068 + 8.77963i 0.540008 + 0.311774i
\(794\) −16.1963 + 9.35091i −0.574784 + 0.331852i
\(795\) 4.35393 + 7.54124i 0.154418 + 0.267460i
\(796\) −11.6374 + 20.1566i −0.412477 + 0.714432i
\(797\) −42.3104 −1.49871 −0.749355 0.662168i \(-0.769636\pi\)
−0.749355 + 0.662168i \(0.769636\pi\)
\(798\) 5.99352 + 16.2798i 0.212168 + 0.576300i
\(799\) 5.09876i 0.180381i
\(800\) 5.73924 9.94066i 0.202913 0.351455i
\(801\) −6.80960 11.7946i −0.240606 0.416741i
\(802\) −14.8691 + 8.58467i −0.525046 + 0.303135i
\(803\) 31.4407 54.4569i 1.10952 1.92174i
\(804\) −5.69042 −0.200686
\(805\) 47.4519 + 20.0338i 1.67246 + 0.706098i
\(806\) 4.86320 0.171299
\(807\) 8.61345 14.9189i 0.303208 0.525171i
\(808\) 6.94536 4.00991i 0.244337 0.141068i
\(809\) 5.12273 + 8.87283i 0.180106 + 0.311952i 0.941916 0.335848i \(-0.109023\pi\)
−0.761811 + 0.647800i \(0.775689\pi\)
\(810\) 2.02969 3.51552i 0.0713159 0.123523i
\(811\) 0.00263642i 9.25771e-5i −1.00000 4.62885e-5i \(-0.999985\pi\)
1.00000 4.62885e-5i \(-1.47341e-5\pi\)
\(812\) −2.89053 + 16.7544i −0.101438 + 0.587965i
\(813\) −19.9765 −0.700606
\(814\) −6.19828 + 10.7357i −0.217250 + 0.376288i
\(815\) 42.3212 + 73.3025i 1.48245 + 2.56767i
\(816\) −1.00034 + 0.577549i −0.0350191 + 0.0202183i
\(817\) 7.52358 + 4.34374i 0.263217 + 0.151968i
\(818\) 10.0420i 0.351111i
\(819\) −1.54172 4.18769i −0.0538722 0.146330i
\(820\) 23.1459i 0.808292i
\(821\) 15.5493 26.9322i 0.542675 0.939941i −0.456074 0.889942i \(-0.650745\pi\)
0.998749 0.0499989i \(-0.0159218\pi\)
\(822\) −9.20385 15.9415i −0.321021 0.556025i
\(823\) 11.5987 + 20.0896i 0.404306 + 0.700278i 0.994240 0.107173i \(-0.0341799\pi\)
−0.589935 + 0.807451i \(0.700847\pi\)
\(824\) −3.81453 + 6.60696i −0.132886 + 0.230164i
\(825\) −64.9376 −2.26084
\(826\) 12.7954 15.3638i 0.445210 0.534575i
\(827\) 50.8112i 1.76688i −0.468547 0.883439i \(-0.655222\pi\)
0.468547 0.883439i \(-0.344778\pi\)
\(828\) 3.50171 + 3.27690i 0.121693 + 0.113880i
\(829\) 32.1953 18.5880i 1.11819 0.645587i 0.177252 0.984166i \(-0.443279\pi\)
0.940938 + 0.338578i \(0.109946\pi\)
\(830\) −1.72099 2.98084i −0.0597365 0.103467i
\(831\) 8.55786 + 4.94088i 0.296869 + 0.171397i
\(832\) 1.68666i 0.0584743i
\(833\) 6.15546 5.24296i 0.213274 0.181658i
\(834\) −20.4754 −0.709006
\(835\) 38.6256 + 22.3005i 1.33669 + 0.771740i
\(836\) 32.1251 18.5474i 1.11107 0.641476i
\(837\) −1.44167 2.49704i −0.0498313 0.0863104i
\(838\) 18.3532 31.7886i 0.633999 1.09812i
\(839\) 32.6237 1.12629 0.563147 0.826357i \(-0.309590\pi\)
0.563147 + 0.826357i \(0.309590\pi\)
\(840\) −6.87318 + 8.25281i −0.237147 + 0.284749i
\(841\) 12.2951 0.423968
\(842\) 1.51067 + 0.872186i 0.0520611 + 0.0300575i
\(843\) 9.72928 + 16.8516i 0.335094 + 0.580400i
\(844\) 1.29754 + 2.24741i 0.0446633 + 0.0773591i
\(845\) −20.6118 + 35.7007i −0.709069 + 1.22814i
\(846\) 4.41413i 0.151761i
\(847\) 52.1530 19.2004i 1.79200 0.659734i
\(848\) 2.14513i 0.0736640i
\(849\) −26.3573 15.2174i −0.904581 0.522260i
\(850\) 6.62939 + 11.4824i 0.227386 + 0.393845i
\(851\) −3.05484 10.0550i −0.104719 0.344681i
\(852\) −6.22486 3.59392i −0.213260 0.123126i
\(853\) 19.3294i 0.661828i 0.943661 + 0.330914i \(0.107357\pi\)
−0.943661 + 0.330914i \(0.892643\pi\)
\(854\) −4.68283 + 27.1431i −0.160243 + 0.928817i
\(855\) 26.6171 0.910285
\(856\) −6.14656 3.54872i −0.210085 0.121293i
\(857\) 0.785476 0.453495i 0.0268314 0.0154911i −0.486524 0.873667i \(-0.661736\pi\)
0.513356 + 0.858176i \(0.328402\pi\)
\(858\) −8.26360 + 4.77099i −0.282115 + 0.162879i
\(859\) −40.8309 23.5737i −1.39313 0.804324i −0.399470 0.916746i \(-0.630806\pi\)
−0.993661 + 0.112422i \(0.964139\pi\)
\(860\) 5.37837i 0.183401i
\(861\) −2.56475 + 14.8661i −0.0874065 + 0.506635i
\(862\) 14.3097i 0.487392i
\(863\) −7.34726 + 12.7258i −0.250104 + 0.433192i −0.963554 0.267513i \(-0.913798\pi\)
0.713450 + 0.700706i \(0.247131\pi\)
\(864\) −0.866025 + 0.500000i −0.0294628 + 0.0170103i
\(865\) −7.27613 + 4.20088i −0.247396 + 0.142834i
\(866\) 8.96794 15.5329i 0.304743 0.527830i
\(867\) 15.6657i 0.532037i
\(868\) 2.63557 + 7.15885i 0.0894572 + 0.242987i
\(869\) 63.9861 2.17058
\(870\) 22.5912 + 13.0430i 0.765912 + 0.442199i
\(871\) 4.79890 + 8.31194i 0.162604 + 0.281639i
\(872\) 15.1271 8.73364i 0.512268 0.295758i
\(873\) 2.46295 4.26595i 0.0833582 0.144381i
\(874\) −7.12757 + 30.6276i −0.241094 + 1.03599i
\(875\) 53.4657 + 44.5278i 1.80747 + 1.50531i
\(876\) −11.1150 −0.375542
\(877\) 9.56932 16.5746i 0.323133 0.559683i −0.658000 0.753018i \(-0.728597\pi\)
0.981133 + 0.193335i \(0.0619305\pi\)
\(878\) −28.0581 + 16.1994i −0.946916 + 0.546702i
\(879\) 13.6489 7.88021i 0.460367 0.265793i
\(880\) 19.8884 + 11.4826i 0.670439 + 0.387078i
\(881\) 0.0981784 0.00330771 0.00165386 0.999999i \(-0.499474\pi\)
0.00165386 + 0.999999i \(0.499474\pi\)
\(882\) 5.32895 4.53897i 0.179435 0.152835i
\(883\) −27.4328 −0.923186 −0.461593 0.887092i \(-0.652722\pi\)
−0.461593 + 0.887092i \(0.652722\pi\)
\(884\) 1.68724 + 0.974128i 0.0567480 + 0.0327635i
\(885\) −15.3386 26.5672i −0.515600 0.893045i
\(886\) 19.0976 + 33.0780i 0.641597 + 1.11128i
\(887\) −29.6506 17.1188i −0.995571 0.574793i −0.0886359 0.996064i \(-0.528251\pi\)
−0.906935 + 0.421271i \(0.861584\pi\)
\(888\) 2.19124 0.0735332
\(889\) −13.7165 11.4235i −0.460035 0.383131i
\(890\) 55.2854 1.85317
\(891\) 4.89939 + 2.82867i 0.164136 + 0.0947639i
\(892\) 10.0313 5.79156i 0.335872 0.193916i
\(893\) 25.0656 14.4716i 0.838788 0.484275i
\(894\) 7.91446 13.7082i 0.264699 0.458472i
\(895\) −22.7290 −0.759746
\(896\) 2.48284 0.914071i 0.0829457 0.0305370i
\(897\) 1.83344 7.87840i 0.0612167 0.263052i
\(898\) 7.04610 12.2042i 0.235131 0.407259i
\(899\) 16.0463 9.26434i 0.535174 0.308983i
\(900\) 5.73924 + 9.94066i 0.191308 + 0.331355i
\(901\) 2.14587 + 1.23892i 0.0714892 + 0.0412743i
\(902\) 32.2573 1.07405
\(903\) 0.595965 3.45440i 0.0198325 0.114955i
\(904\) 8.83766i 0.293936i
\(905\) 45.8624 79.4361i 1.52452 2.64054i
\(906\) −13.4115 + 7.74316i −0.445569 + 0.257249i
\(907\) −28.9373 + 16.7069i −0.960846 + 0.554745i −0.896433 0.443179i \(-0.853851\pi\)
−0.0644125 + 0.997923i \(0.520517\pi\)
\(908\) 3.86164 6.68855i 0.128153 0.221967i
\(909\) 8.01981i 0.266000i
\(910\) 17.8511 + 3.07974i 0.591759 + 0.102092i
\(911\) 15.0207i 0.497659i −0.968547 0.248830i \(-0.919954\pi\)
0.968547 0.248830i \(-0.0800460\pi\)
\(912\) −5.67849 3.27848i −0.188033 0.108561i
\(913\) 4.15424 2.39845i 0.137485 0.0793773i
\(914\) −3.70638 + 2.13988i −0.122596 + 0.0707809i
\(915\) 36.5989 + 21.1304i 1.20992 + 0.698550i
\(916\) 22.0003 0.726912
\(917\) 5.05918 + 13.7419i 0.167069 + 0.453799i
\(918\) 1.15510i 0.0381239i
\(919\) 41.5218 + 23.9726i 1.36968 + 0.790784i 0.990887 0.134698i \(-0.0430064\pi\)
0.378792 + 0.925482i \(0.376340\pi\)
\(920\) −18.6274 + 5.65923i −0.614126 + 0.186579i
\(921\) 3.94100 + 6.82601i 0.129860 + 0.224925i
\(922\) 6.18859 + 3.57298i 0.203810 + 0.117670i
\(923\) 12.1234i 0.399048i
\(924\) −11.5015 9.57879i −0.378372 0.315119i
\(925\) 25.1521i 0.826996i
\(926\) 1.41770 2.45553i 0.0465885 0.0806937i
\(927\) −3.81453 6.60696i −0.125286 0.217001i
\(928\) −3.21306 5.56519i −0.105474 0.182686i
\(929\) 35.9751 + 20.7702i 1.18030 + 0.681449i 0.956085 0.293090i \(-0.0946836\pi\)
0.224219 + 0.974539i \(0.428017\pi\)
\(930\) 11.7045 0.383807
\(931\) 43.2453 + 15.3795i 1.41731 + 0.504041i
\(932\) 23.4567 0.768350
\(933\) −9.16702 + 15.8777i −0.300115 + 0.519814i
\(934\) −12.7367 22.0606i −0.416757 0.721845i
\(935\) −22.9731 + 13.2635i −0.751301 + 0.433764i
\(936\) 1.46069 + 0.843329i 0.0477441 + 0.0275651i
\(937\) 1.07710 0.0351873 0.0175937 0.999845i \(-0.494399\pi\)
0.0175937 + 0.999845i \(0.494399\pi\)
\(938\) −9.63482 + 11.5688i −0.314588 + 0.377734i
\(939\) 12.4033i 0.404768i
\(940\) 15.5180 + 8.95930i 0.506140 + 0.292220i
\(941\) 8.11695 + 14.0590i 0.264605 + 0.458309i 0.967460 0.253024i \(-0.0814251\pi\)
−0.702855 + 0.711333i \(0.748092\pi\)
\(942\) −3.59239 + 2.07407i −0.117046 + 0.0675768i
\(943\) −18.6844 + 19.9662i −0.608448 + 0.650190i
\(944\) 7.55711i 0.245963i
\(945\) −3.71055 10.0788i −0.120704 0.327862i
\(946\) −7.49555 −0.243701
\(947\) −2.86317 + 4.95916i −0.0930405 + 0.161151i −0.908789 0.417256i \(-0.862992\pi\)
0.815749 + 0.578407i \(0.196325\pi\)
\(948\) −5.65515 9.79501i −0.183671 0.318127i
\(949\) 9.37363 + 16.2356i 0.304281 + 0.527030i
\(950\) −37.6319 + 65.1804i −1.22094 + 2.11473i
\(951\) 3.67969i 0.119322i
\(952\) −0.519575 + 3.01161i −0.0168395 + 0.0976069i
\(953\) 6.77880i 0.219587i 0.993954 + 0.109793i \(0.0350189\pi\)
−0.993954 + 0.109793i \(0.964981\pi\)
\(954\) 1.85774 + 1.07256i 0.0601464 + 0.0347255i
\(955\) −18.5700 + 10.7214i −0.600912 + 0.346936i
\(956\) −7.10768 12.3109i −0.229879 0.398162i
\(957\) −18.1774 + 31.4841i −0.587591 + 1.01774i
\(958\) 19.2180 0.620905
\(959\) −47.9932 8.27996i −1.54978 0.267374i
\(960\) 4.05937i 0.131016i
\(961\) −11.3432 + 19.6470i −0.365909 + 0.633773i
\(962\) −1.84794 3.20072i −0.0595798 0.103195i
\(963\) 6.14656 3.54872i 0.198070 0.114356i
\(964\) 8.10166 14.0325i 0.260937 0.451956i
\(965\) 108.457 3.49134
\(966\) 12.5910 1.57073i 0.405108 0.0505375i
\(967\) −14.4508 −0.464705 −0.232353 0.972632i \(-0.574642\pi\)
−0.232353 + 0.972632i \(0.574642\pi\)
\(968\) −10.5027 + 18.1912i −0.337570 + 0.584688i
\(969\) 6.55921 3.78696i 0.210712 0.121655i
\(970\) 9.99802 + 17.3171i 0.321017 + 0.556018i
\(971\) −8.92641 + 15.4610i −0.286462 + 0.496167i −0.972963 0.230962i \(-0.925813\pi\)
0.686501 + 0.727129i \(0.259146\pi\)
\(972\) 1.00000i 0.0320750i
\(973\) −34.6682 + 41.6271i −1.11141 + 1.33450i
\(974\) −30.3625 −0.972876
\(975\) 9.68014 16.7665i 0.310013 0.536957i
\(976\) −5.20534 9.01591i −0.166619 0.288592i
\(977\) −39.1189 + 22.5853i −1.25152 + 0.722568i −0.971412 0.237400i \(-0.923705\pi\)
−0.280112 + 0.959967i \(0.590372\pi\)
\(978\) 18.0576 + 10.4256i 0.577419 + 0.333373i
\(979\) 77.0484i 2.46248i
\(980\) 5.14076 + 27.9467i 0.164215 + 0.892725i
\(981\) 17.4673i 0.557687i
\(982\) 4.25335 7.36701i 0.135730 0.235091i
\(983\) −10.9144 18.9044i −0.348117 0.602956i 0.637798 0.770204i \(-0.279845\pi\)
−0.985915 + 0.167248i \(0.946512\pi\)
\(984\) −2.85093 4.93795i −0.0908843 0.157416i
\(985\) −28.7414 + 49.7815i −0.915776 + 1.58617i
\(986\) 7.42281 0.236390
\(987\) −8.97405 7.47385i −0.285647 0.237895i
\(988\) 11.0593i 0.351844i
\(989\) 4.34165 4.63950i 0.138056 0.147528i
\(990\) −19.8884 + 11.4826i −0.632096 + 0.364941i
\(991\) −10.9207 18.9151i −0.346906 0.600859i 0.638792 0.769379i \(-0.279434\pi\)
−0.985698 + 0.168520i \(0.946101\pi\)
\(992\) −2.49704 1.44167i −0.0792812 0.0457730i
\(993\) 4.90826i 0.155759i
\(994\) −17.8462 + 6.57020i −0.566048 + 0.208394i
\(995\) 94.4812 2.99525
\(996\) −0.734312 0.423955i −0.0232676 0.0134335i
\(997\) 49.4147 28.5296i 1.56498 0.903542i 0.568240 0.822863i \(-0.307624\pi\)
0.996740 0.0806791i \(-0.0257089\pi\)
\(998\) 6.28157 + 10.8800i 0.198840 + 0.344400i
\(999\) −1.09562 + 1.89767i −0.0346639 + 0.0600396i
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 966.2.k.b.229.1 32
7.3 odd 6 inner 966.2.k.b.367.8 yes 32
23.22 odd 2 inner 966.2.k.b.229.8 yes 32
161.45 even 6 inner 966.2.k.b.367.1 yes 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
966.2.k.b.229.1 32 1.1 even 1 trivial
966.2.k.b.229.8 yes 32 23.22 odd 2 inner
966.2.k.b.367.1 yes 32 161.45 even 6 inner
966.2.k.b.367.8 yes 32 7.3 odd 6 inner