Properties

Label 273.2.i.e.79.3
Level $273$
Weight $2$
Character 273.79
Analytic conductor $2.180$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [273,2,Mod(79,273)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(273, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 2, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("273.79");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 273.i (of order \(3\), 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: \(2.17991597518\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - x^{9} + 7x^{8} - 8x^{7} + 41x^{6} - 40x^{5} + 59x^{4} - 10x^{3} + 18x^{2} - 4x + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 79.3
Root \(-0.281188 - 0.487032i\) of defining polynomial
Character \(\chi\) \(=\) 273.79
Dual form 273.2.i.e.235.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.0388377 + 0.0672688i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.996983 + 1.72683i) q^{4} +(1.10121 - 1.90736i) q^{5} -0.0776754 q^{6} +(2.64490 - 0.0672688i) q^{7} -0.310233 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.0388377 + 0.0672688i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.996983 + 1.72683i) q^{4} +(1.10121 - 1.90736i) q^{5} -0.0776754 q^{6} +(2.64490 - 0.0672688i) q^{7} -0.310233 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.0855372 + 0.148155i) q^{10} +(-1.45815 - 2.52558i) q^{11} +(-0.996983 + 1.72683i) q^{12} -1.00000 q^{13} +(-0.0981965 + 0.180532i) q^{14} +2.20243 q^{15} +(-1.98192 + 3.43278i) q^{16} +(0.196971 + 0.341163i) q^{17} +(-0.0388377 - 0.0672688i) q^{18} +(-0.0623756 + 0.108038i) q^{19} +4.39156 q^{20} +(1.38070 + 2.25691i) q^{21} +0.226524 q^{22} +(-1.69094 + 2.92879i) q^{23} +(-0.155116 - 0.268670i) q^{24} +(0.0746586 + 0.129313i) q^{25} +(0.0388377 - 0.0672688i) q^{26} -1.00000 q^{27} +(2.75308 + 4.50021i) q^{28} -0.642223 q^{29} +(-0.0855372 + 0.148155i) q^{30} +(-2.97890 - 5.15961i) q^{31} +(-0.464179 - 0.803982i) q^{32} +(1.45815 - 2.52558i) q^{33} -0.0305996 q^{34} +(2.78429 - 5.11884i) q^{35} -1.99397 q^{36} +(-2.09335 + 3.62579i) q^{37} +(-0.00484505 - 0.00839187i) q^{38} +(-0.500000 - 0.866025i) q^{39} +(-0.341633 + 0.591725i) q^{40} +0.434984 q^{41} +(-0.205443 + 0.00522513i) q^{42} -6.74934 q^{43} +(2.90749 - 5.03593i) q^{44} +(1.10121 + 1.90736i) q^{45} +(-0.131344 - 0.227495i) q^{46} +(4.73160 - 8.19538i) q^{47} -3.96384 q^{48} +(6.99095 - 0.355838i) q^{49} -0.0115983 q^{50} +(-0.196971 + 0.341163i) q^{51} +(-0.996983 - 1.72683i) q^{52} +(-6.21691 - 10.7680i) q^{53} +(0.0388377 - 0.0672688i) q^{54} -6.42292 q^{55} +(-0.820534 + 0.0208690i) q^{56} -0.124751 q^{57} +(0.0249424 - 0.0432016i) q^{58} +(3.66778 + 6.35277i) q^{59} +(2.19578 + 3.80321i) q^{60} +(1.19697 - 2.07321i) q^{61} +0.462775 q^{62} +(-1.26419 + 2.32418i) q^{63} -7.85556 q^{64} +(-1.10121 + 1.90736i) q^{65} +(0.113262 + 0.196176i) q^{66} +(-3.07024 - 5.31781i) q^{67} +(-0.392753 + 0.680269i) q^{68} -3.38187 q^{69} +(0.236203 + 0.386100i) q^{70} -14.0826 q^{71} +(0.155116 - 0.268670i) q^{72} +(3.77647 + 6.54105i) q^{73} +(-0.162602 - 0.281635i) q^{74} +(-0.0746586 + 0.129313i) q^{75} -0.248750 q^{76} +(-4.02654 - 6.58181i) q^{77} +0.0776754 q^{78} +(1.18736 - 2.05657i) q^{79} +(4.36503 + 7.56045i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-0.0168938 + 0.0292609i) q^{82} -9.78804 q^{83} +(-2.52076 + 4.63434i) q^{84} +0.867628 q^{85} +(0.262129 - 0.454020i) q^{86} +(-0.321111 - 0.556181i) q^{87} +(0.452365 + 0.783519i) q^{88} +(3.20182 - 5.54571i) q^{89} -0.171074 q^{90} +(-2.64490 + 0.0672688i) q^{91} -6.74335 q^{92} +(2.97890 - 5.15961i) q^{93} +(0.367529 + 0.636579i) q^{94} +(0.137378 + 0.237945i) q^{95} +(0.464179 - 0.803982i) q^{96} +14.9096 q^{97} +(-0.247575 + 0.484093i) q^{98} +2.91629 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q + 5 q^{3} - 6 q^{4} + 3 q^{5} + 4 q^{7} + 6 q^{8} - 5 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q + 5 q^{3} - 6 q^{4} + 3 q^{5} + 4 q^{7} + 6 q^{8} - 5 q^{9} + 2 q^{10} + q^{11} + 6 q^{12} - 10 q^{13} + 23 q^{14} + 6 q^{15} + 13 q^{17} + 7 q^{19} - 26 q^{20} + 2 q^{21} - 38 q^{22} + 4 q^{23} + 3 q^{24} - 16 q^{25} - 10 q^{27} - 4 q^{28} - 24 q^{29} - 2 q^{30} + 6 q^{31} - 21 q^{32} - q^{33} - 14 q^{34} - 3 q^{35} + 12 q^{36} - 11 q^{37} + 14 q^{38} - 5 q^{39} + 11 q^{40} - 20 q^{41} - 2 q^{42} + 20 q^{43} + 29 q^{44} + 3 q^{45} - q^{46} - 4 q^{47} + 22 q^{49} - 58 q^{50} - 13 q^{51} + 6 q^{52} + 9 q^{53} + 24 q^{55} + 42 q^{56} + 14 q^{57} - 34 q^{58} + 7 q^{59} - 13 q^{60} + 23 q^{61} + 48 q^{62} - 2 q^{63} - 26 q^{64} - 3 q^{65} - 19 q^{66} - 25 q^{67} + 20 q^{68} + 8 q^{69} + 73 q^{70} - 54 q^{71} - 3 q^{72} + 18 q^{73} - 15 q^{74} + 16 q^{75} - 4 q^{76} + 27 q^{77} - 8 q^{79} + 41 q^{80} - 5 q^{81} + 26 q^{82} - 24 q^{83} - 5 q^{84} + 20 q^{85} + 19 q^{86} - 12 q^{87} + 36 q^{88} + 29 q^{89} - 4 q^{90} - 4 q^{91} - 100 q^{92} - 6 q^{93} - 2 q^{94} + 33 q^{95} + 21 q^{96} - 26 q^{97} + 15 q^{98} - 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(106\) \(157\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.0388377 + 0.0672688i −0.0274624 + 0.0475663i −0.879430 0.476028i \(-0.842076\pi\)
0.851968 + 0.523595i \(0.175409\pi\)
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i
\(4\) 0.996983 + 1.72683i 0.498492 + 0.863413i
\(5\) 1.10121 1.90736i 0.492478 0.852996i −0.507485 0.861661i \(-0.669425\pi\)
0.999962 + 0.00866451i \(0.00275803\pi\)
\(6\) −0.0776754 −0.0317108
\(7\) 2.64490 0.0672688i 0.999677 0.0254252i
\(8\) −0.310233 −0.109684
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0.0855372 + 0.148155i 0.0270492 + 0.0468506i
\(11\) −1.45815 2.52558i −0.439647 0.761492i 0.558015 0.829831i \(-0.311563\pi\)
−0.997662 + 0.0683394i \(0.978230\pi\)
\(12\) −0.996983 + 1.72683i −0.287804 + 0.498492i
\(13\) −1.00000 −0.277350
\(14\) −0.0981965 + 0.180532i −0.0262441 + 0.0482491i
\(15\) 2.20243 0.568664
\(16\) −1.98192 + 3.43278i −0.495479 + 0.858196i
\(17\) 0.196971 + 0.341163i 0.0477724 + 0.0827443i 0.888923 0.458057i \(-0.151454\pi\)
−0.841150 + 0.540801i \(0.818121\pi\)
\(18\) −0.0388377 0.0672688i −0.00915413 0.0158554i
\(19\) −0.0623756 + 0.108038i −0.0143099 + 0.0247855i −0.873092 0.487556i \(-0.837888\pi\)
0.858782 + 0.512342i \(0.171222\pi\)
\(20\) 4.39156 0.981984
\(21\) 1.38070 + 2.25691i 0.301294 + 0.492499i
\(22\) 0.226524 0.0482951
\(23\) −1.69094 + 2.92879i −0.352585 + 0.610695i −0.986702 0.162543i \(-0.948031\pi\)
0.634117 + 0.773237i \(0.281364\pi\)
\(24\) −0.155116 0.268670i −0.0316630 0.0548419i
\(25\) 0.0746586 + 0.129313i 0.0149317 + 0.0258625i
\(26\) 0.0388377 0.0672688i 0.00761670 0.0131925i
\(27\) −1.00000 −0.192450
\(28\) 2.75308 + 4.50021i 0.520283 + 0.850459i
\(29\) −0.642223 −0.119258 −0.0596289 0.998221i \(-0.518992\pi\)
−0.0596289 + 0.998221i \(0.518992\pi\)
\(30\) −0.0855372 + 0.148155i −0.0156169 + 0.0270492i
\(31\) −2.97890 5.15961i −0.535026 0.926693i −0.999162 0.0409288i \(-0.986968\pi\)
0.464136 0.885764i \(-0.346365\pi\)
\(32\) −0.464179 0.803982i −0.0820560 0.142125i
\(33\) 1.45815 2.52558i 0.253831 0.439647i
\(34\) −0.0305996 −0.00524778
\(35\) 2.78429 5.11884i 0.470631 0.865242i
\(36\) −1.99397 −0.332328
\(37\) −2.09335 + 3.62579i −0.344145 + 0.596076i −0.985198 0.171420i \(-0.945164\pi\)
0.641053 + 0.767496i \(0.278498\pi\)
\(38\) −0.00484505 0.00839187i −0.000785970 0.00136134i
\(39\) −0.500000 0.866025i −0.0800641 0.138675i
\(40\) −0.341633 + 0.591725i −0.0540168 + 0.0935599i
\(41\) 0.434984 0.0679331 0.0339665 0.999423i \(-0.489186\pi\)
0.0339665 + 0.999423i \(0.489186\pi\)
\(42\) −0.205443 + 0.00522513i −0.0317006 + 0.000806255i
\(43\) −6.74934 −1.02927 −0.514633 0.857411i \(-0.672072\pi\)
−0.514633 + 0.857411i \(0.672072\pi\)
\(44\) 2.90749 5.03593i 0.438321 0.759194i
\(45\) 1.10121 + 1.90736i 0.164159 + 0.284332i
\(46\) −0.131344 0.227495i −0.0193656 0.0335423i
\(47\) 4.73160 8.19538i 0.690175 1.19542i −0.281605 0.959530i \(-0.590867\pi\)
0.971780 0.235888i \(-0.0757999\pi\)
\(48\) −3.96384 −0.572130
\(49\) 6.99095 0.355838i 0.998707 0.0508340i
\(50\) −0.0115983 −0.00164024
\(51\) −0.196971 + 0.341163i −0.0275814 + 0.0477724i
\(52\) −0.996983 1.72683i −0.138257 0.239468i
\(53\) −6.21691 10.7680i −0.853959 1.47910i −0.877608 0.479380i \(-0.840862\pi\)
0.0236487 0.999720i \(-0.492472\pi\)
\(54\) 0.0388377 0.0672688i 0.00528514 0.00915413i
\(55\) −6.42292 −0.866066
\(56\) −0.820534 + 0.0208690i −0.109648 + 0.00278874i
\(57\) −0.124751 −0.0165237
\(58\) 0.0249424 0.0432016i 0.00327510 0.00567265i
\(59\) 3.66778 + 6.35277i 0.477504 + 0.827061i 0.999668 0.0257845i \(-0.00820837\pi\)
−0.522164 + 0.852845i \(0.674875\pi\)
\(60\) 2.19578 + 3.80321i 0.283474 + 0.490992i
\(61\) 1.19697 2.07321i 0.153256 0.265448i −0.779166 0.626817i \(-0.784357\pi\)
0.932423 + 0.361369i \(0.117691\pi\)
\(62\) 0.462775 0.0587724
\(63\) −1.26419 + 2.32418i −0.159273 + 0.292819i
\(64\) −7.85556 −0.981945
\(65\) −1.10121 + 1.90736i −0.136589 + 0.236579i
\(66\) 0.113262 + 0.196176i 0.0139416 + 0.0241475i
\(67\) −3.07024 5.31781i −0.375089 0.649674i 0.615251 0.788331i \(-0.289055\pi\)
−0.990340 + 0.138658i \(0.955721\pi\)
\(68\) −0.392753 + 0.680269i −0.0476283 + 0.0824947i
\(69\) −3.38187 −0.407130
\(70\) 0.236203 + 0.386100i 0.0282317 + 0.0461477i
\(71\) −14.0826 −1.67129 −0.835646 0.549269i \(-0.814906\pi\)
−0.835646 + 0.549269i \(0.814906\pi\)
\(72\) 0.155116 0.268670i 0.0182806 0.0316630i
\(73\) 3.77647 + 6.54105i 0.442003 + 0.765571i 0.997838 0.0657211i \(-0.0209348\pi\)
−0.555835 + 0.831293i \(0.687601\pi\)
\(74\) −0.162602 0.281635i −0.0189021 0.0327394i
\(75\) −0.0746586 + 0.129313i −0.00862084 + 0.0149317i
\(76\) −0.248750 −0.0285335
\(77\) −4.02654 6.58181i −0.458866 0.750067i
\(78\) 0.0776754 0.00879500
\(79\) 1.18736 2.05657i 0.133589 0.231382i −0.791469 0.611210i \(-0.790683\pi\)
0.925057 + 0.379827i \(0.124017\pi\)
\(80\) 4.36503 + 7.56045i 0.488025 + 0.845284i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −0.0168938 + 0.0292609i −0.00186561 + 0.00323132i
\(83\) −9.78804 −1.07438 −0.537189 0.843462i \(-0.680514\pi\)
−0.537189 + 0.843462i \(0.680514\pi\)
\(84\) −2.52076 + 4.63434i −0.275037 + 0.505648i
\(85\) 0.867628 0.0941074
\(86\) 0.262129 0.454020i 0.0282661 0.0489583i
\(87\) −0.321111 0.556181i −0.0344268 0.0596289i
\(88\) 0.452365 + 0.783519i 0.0482222 + 0.0835234i
\(89\) 3.20182 5.54571i 0.339392 0.587844i −0.644927 0.764244i \(-0.723112\pi\)
0.984318 + 0.176401i \(0.0564454\pi\)
\(90\) −0.171074 −0.0180328
\(91\) −2.64490 + 0.0672688i −0.277260 + 0.00705169i
\(92\) −6.74335 −0.703042
\(93\) 2.97890 5.15961i 0.308898 0.535026i
\(94\) 0.367529 + 0.636579i 0.0379077 + 0.0656581i
\(95\) 0.137378 + 0.237945i 0.0140946 + 0.0244126i
\(96\) 0.464179 0.803982i 0.0473751 0.0820560i
\(97\) 14.9096 1.51384 0.756919 0.653509i \(-0.226704\pi\)
0.756919 + 0.653509i \(0.226704\pi\)
\(98\) −0.247575 + 0.484093i −0.0250089 + 0.0489008i
\(99\) 2.91629 0.293098
\(100\) −0.148867 + 0.257845i −0.0148867 + 0.0257845i
\(101\) 9.99103 + 17.3050i 0.994145 + 1.72191i 0.590653 + 0.806926i \(0.298870\pi\)
0.403492 + 0.914983i \(0.367796\pi\)
\(102\) −0.0152998 0.0265000i −0.00151490 0.00262389i
\(103\) 7.33724 12.7085i 0.722960 1.25220i −0.236849 0.971547i \(-0.576115\pi\)
0.959808 0.280656i \(-0.0905520\pi\)
\(104\) 0.310233 0.0304208
\(105\) 5.82519 0.148155i 0.568480 0.0144584i
\(106\) 0.965802 0.0938070
\(107\) 2.51986 4.36453i 0.243604 0.421935i −0.718134 0.695905i \(-0.755003\pi\)
0.961738 + 0.273970i \(0.0883368\pi\)
\(108\) −0.996983 1.72683i −0.0959348 0.166164i
\(109\) 0.0613411 + 0.106246i 0.00587542 + 0.0101765i 0.868948 0.494903i \(-0.164796\pi\)
−0.863073 + 0.505080i \(0.831463\pi\)
\(110\) 0.249451 0.432062i 0.0237842 0.0411955i
\(111\) −4.18670 −0.397384
\(112\) −5.01105 + 9.21267i −0.473499 + 0.870516i
\(113\) −4.16138 −0.391470 −0.195735 0.980657i \(-0.562709\pi\)
−0.195735 + 0.980657i \(0.562709\pi\)
\(114\) 0.00484505 0.00839187i 0.000453780 0.000785970i
\(115\) 3.72417 + 6.45044i 0.347280 + 0.601507i
\(116\) −0.640285 1.10901i −0.0594490 0.102969i
\(117\) 0.500000 0.866025i 0.0462250 0.0800641i
\(118\) −0.569792 −0.0524536
\(119\) 0.543917 + 0.889092i 0.0498608 + 0.0815029i
\(120\) −0.683265 −0.0623733
\(121\) 1.24762 2.16095i 0.113420 0.196450i
\(122\) 0.0929752 + 0.161038i 0.00841758 + 0.0145797i
\(123\) 0.217492 + 0.376707i 0.0196106 + 0.0339665i
\(124\) 5.93983 10.2881i 0.533412 0.923897i
\(125\) 11.3410 1.01437
\(126\) −0.107247 0.175307i −0.00955430 0.0156175i
\(127\) 14.9711 1.32847 0.664237 0.747522i \(-0.268756\pi\)
0.664237 + 0.747522i \(0.268756\pi\)
\(128\) 1.23345 2.13640i 0.109023 0.188833i
\(129\) −3.37467 5.84510i −0.297123 0.514633i
\(130\) −0.0855372 0.148155i −0.00750210 0.0129940i
\(131\) −9.37108 + 16.2312i −0.818755 + 1.41812i 0.0878454 + 0.996134i \(0.472002\pi\)
−0.906600 + 0.421991i \(0.861331\pi\)
\(132\) 5.81499 0.506130
\(133\) −0.157709 + 0.289944i −0.0136751 + 0.0251414i
\(134\) 0.476964 0.0412034
\(135\) −1.10121 + 1.90736i −0.0947773 + 0.164159i
\(136\) −0.0611068 0.105840i −0.00523987 0.00907572i
\(137\) 6.79525 + 11.7697i 0.580557 + 1.00555i 0.995413 + 0.0956675i \(0.0304986\pi\)
−0.414856 + 0.909887i \(0.636168\pi\)
\(138\) 0.131344 0.227495i 0.0111808 0.0193656i
\(139\) −15.7292 −1.33413 −0.667066 0.744999i \(-0.732450\pi\)
−0.667066 + 0.744999i \(0.732450\pi\)
\(140\) 11.6152 0.295416i 0.981666 0.0249672i
\(141\) 9.46321 0.796946
\(142\) 0.546934 0.947317i 0.0458977 0.0794971i
\(143\) 1.45815 + 2.52558i 0.121936 + 0.211200i
\(144\) −1.98192 3.43278i −0.165160 0.286065i
\(145\) −0.707224 + 1.22495i −0.0587318 + 0.101726i
\(146\) −0.586678 −0.0485538
\(147\) 3.80364 + 5.87642i 0.313719 + 0.484679i
\(148\) −8.34815 −0.686213
\(149\) −1.67404 + 2.89953i −0.137143 + 0.237539i −0.926414 0.376506i \(-0.877125\pi\)
0.789271 + 0.614045i \(0.210459\pi\)
\(150\) −0.00579914 0.0100444i −0.000473498 0.000820122i
\(151\) 10.2238 + 17.7082i 0.832003 + 1.44107i 0.896448 + 0.443150i \(0.146139\pi\)
−0.0644447 + 0.997921i \(0.520528\pi\)
\(152\) 0.0193510 0.0335168i 0.00156957 0.00271857i
\(153\) −0.393942 −0.0318483
\(154\) 0.599132 0.0152380i 0.0482795 0.00122791i
\(155\) −13.1216 −1.05395
\(156\) 0.996983 1.72683i 0.0798225 0.138257i
\(157\) −5.10068 8.83464i −0.407079 0.705081i 0.587482 0.809237i \(-0.300119\pi\)
−0.994561 + 0.104156i \(0.966786\pi\)
\(158\) 0.0922287 + 0.159745i 0.00733732 + 0.0127086i
\(159\) 6.21691 10.7680i 0.493033 0.853959i
\(160\) −2.04464 −0.161643
\(161\) −4.27534 + 7.86009i −0.336944 + 0.619462i
\(162\) 0.0776754 0.00610275
\(163\) −7.79177 + 13.4957i −0.610299 + 1.05707i 0.380891 + 0.924620i \(0.375617\pi\)
−0.991190 + 0.132449i \(0.957716\pi\)
\(164\) 0.433672 + 0.751142i 0.0338641 + 0.0586543i
\(165\) −3.21146 5.56241i −0.250012 0.433033i
\(166\) 0.380145 0.658430i 0.0295050 0.0511041i
\(167\) 1.53310 0.118635 0.0593174 0.998239i \(-0.481108\pi\)
0.0593174 + 0.998239i \(0.481108\pi\)
\(168\) −0.428340 0.700168i −0.0330471 0.0540192i
\(169\) 1.00000 0.0769231
\(170\) −0.0336966 + 0.0583643i −0.00258442 + 0.00447634i
\(171\) −0.0623756 0.108038i −0.00476998 0.00826185i
\(172\) −6.72898 11.6549i −0.513080 0.888681i
\(173\) 6.99222 12.1109i 0.531609 0.920773i −0.467711 0.883882i \(-0.654921\pi\)
0.999319 0.0368914i \(-0.0117456\pi\)
\(174\) 0.0498849 0.00378176
\(175\) 0.206163 + 0.336996i 0.0155845 + 0.0254745i
\(176\) 11.5597 0.871345
\(177\) −3.66778 + 6.35277i −0.275687 + 0.477504i
\(178\) 0.248702 + 0.430765i 0.0186410 + 0.0322872i
\(179\) 10.9652 + 18.9923i 0.819577 + 1.41955i 0.905994 + 0.423290i \(0.139125\pi\)
−0.0864170 + 0.996259i \(0.527542\pi\)
\(180\) −2.19578 + 3.80321i −0.163664 + 0.283474i
\(181\) 0.955265 0.0710043 0.0355021 0.999370i \(-0.488697\pi\)
0.0355021 + 0.999370i \(0.488697\pi\)
\(182\) 0.0981965 0.180532i 0.00727881 0.0133819i
\(183\) 2.39394 0.176965
\(184\) 0.524584 0.908607i 0.0386729 0.0669834i
\(185\) 4.61045 + 7.98554i 0.338967 + 0.587108i
\(186\) 0.231387 + 0.400774i 0.0169661 + 0.0293862i
\(187\) 0.574424 0.994932i 0.0420061 0.0727566i
\(188\) 18.8693 1.37619
\(189\) −2.64490 + 0.0672688i −0.192388 + 0.00489309i
\(190\) −0.0213417 −0.00154829
\(191\) −9.84171 + 17.0463i −0.712121 + 1.23343i 0.251938 + 0.967743i \(0.418932\pi\)
−0.964059 + 0.265687i \(0.914401\pi\)
\(192\) −3.92778 6.80312i −0.283463 0.490973i
\(193\) −7.54753 13.0727i −0.543283 0.940993i −0.998713 0.0507219i \(-0.983848\pi\)
0.455430 0.890272i \(-0.349486\pi\)
\(194\) −0.579053 + 1.00295i −0.0415736 + 0.0720076i
\(195\) −2.20243 −0.157719
\(196\) 7.58433 + 11.7174i 0.541738 + 0.836956i
\(197\) −11.0323 −0.786015 −0.393008 0.919535i \(-0.628565\pi\)
−0.393008 + 0.919535i \(0.628565\pi\)
\(198\) −0.113262 + 0.196176i −0.00804918 + 0.0139416i
\(199\) −3.58851 6.21548i −0.254382 0.440603i 0.710345 0.703854i \(-0.248539\pi\)
−0.964728 + 0.263250i \(0.915206\pi\)
\(200\) −0.0231616 0.0401170i −0.00163777 0.00283670i
\(201\) 3.07024 5.31781i 0.216558 0.375089i
\(202\) −1.55211 −0.109206
\(203\) −1.69861 + 0.0432016i −0.119219 + 0.00303216i
\(204\) −0.785507 −0.0549965
\(205\) 0.479010 0.829670i 0.0334555 0.0579467i
\(206\) 0.569923 + 0.987135i 0.0397084 + 0.0687770i
\(207\) −1.69094 2.92879i −0.117528 0.203565i
\(208\) 1.98192 3.43278i 0.137421 0.238021i
\(209\) 0.363811 0.0251653
\(210\) −0.216271 + 0.397608i −0.0149241 + 0.0274375i
\(211\) 15.7119 1.08165 0.540825 0.841135i \(-0.318112\pi\)
0.540825 + 0.841135i \(0.318112\pi\)
\(212\) 12.3963 21.4711i 0.851383 1.47464i
\(213\) −7.04128 12.1958i −0.482460 0.835646i
\(214\) 0.195731 + 0.339017i 0.0133799 + 0.0231747i
\(215\) −7.43247 + 12.8734i −0.506890 + 0.877959i
\(216\) 0.310233 0.0211087
\(217\) −8.22596 13.4462i −0.558415 0.912790i
\(218\) −0.00952939 −0.000645412
\(219\) −3.77647 + 6.54105i −0.255190 + 0.442003i
\(220\) −6.40354 11.0913i −0.431727 0.747772i
\(221\) −0.196971 0.341163i −0.0132497 0.0229491i
\(222\) 0.162602 0.281635i 0.0109131 0.0189021i
\(223\) 6.20889 0.415778 0.207889 0.978152i \(-0.433341\pi\)
0.207889 + 0.978152i \(0.433341\pi\)
\(224\) −1.28179 2.09522i −0.0856431 0.139993i
\(225\) −0.149317 −0.00995449
\(226\) 0.161619 0.279932i 0.0107507 0.0186208i
\(227\) −11.8440 20.5143i −0.786111 1.36158i −0.928333 0.371750i \(-0.878758\pi\)
0.142221 0.989835i \(-0.454575\pi\)
\(228\) −0.124375 0.215424i −0.00823692 0.0142668i
\(229\) 4.52113 7.83083i 0.298765 0.517476i −0.677089 0.735901i \(-0.736759\pi\)
0.975854 + 0.218425i \(0.0700921\pi\)
\(230\) −0.578552 −0.0381486
\(231\) 3.68675 6.77799i 0.242570 0.445959i
\(232\) 0.199239 0.0130807
\(233\) −2.67224 + 4.62846i −0.175065 + 0.303221i −0.940184 0.340668i \(-0.889347\pi\)
0.765119 + 0.643889i \(0.222680\pi\)
\(234\) 0.0388377 + 0.0672688i 0.00253890 + 0.00439750i
\(235\) −10.4210 18.0497i −0.679792 1.17743i
\(236\) −7.31342 + 12.6672i −0.476063 + 0.824566i
\(237\) 2.37472 0.154255
\(238\) −0.0809327 + 0.00205840i −0.00524609 + 0.000133426i
\(239\) −27.2548 −1.76297 −0.881484 0.472215i \(-0.843455\pi\)
−0.881484 + 0.472215i \(0.843455\pi\)
\(240\) −4.36503 + 7.56045i −0.281761 + 0.488025i
\(241\) 7.83806 + 13.5759i 0.504894 + 0.874501i 0.999984 + 0.00565987i \(0.00180160\pi\)
−0.495090 + 0.868841i \(0.664865\pi\)
\(242\) 0.0969096 + 0.167852i 0.00622958 + 0.0107900i
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) 4.77344 0.305588
\(245\) 7.01982 13.7261i 0.448480 0.876928i
\(246\) −0.0337875 −0.00215422
\(247\) 0.0623756 0.108038i 0.00396886 0.00687427i
\(248\) 0.924153 + 1.60068i 0.0586838 + 0.101643i
\(249\) −4.89402 8.47669i −0.310146 0.537189i
\(250\) −0.440458 + 0.762896i −0.0278570 + 0.0482497i
\(251\) −18.2218 −1.15015 −0.575075 0.818101i \(-0.695027\pi\)
−0.575075 + 0.818101i \(0.695027\pi\)
\(252\) −5.27383 + 0.134132i −0.332220 + 0.00844951i
\(253\) 9.86253 0.620052
\(254\) −0.581445 + 1.00709i −0.0364831 + 0.0631906i
\(255\) 0.433814 + 0.751388i 0.0271665 + 0.0470537i
\(256\) −7.75975 13.4403i −0.484985 0.840018i
\(257\) −7.53068 + 13.0435i −0.469751 + 0.813632i −0.999402 0.0345833i \(-0.988990\pi\)
0.529651 + 0.848216i \(0.322323\pi\)
\(258\) 0.524258 0.0326389
\(259\) −5.29279 + 9.73066i −0.328878 + 0.604634i
\(260\) −4.39156 −0.272353
\(261\) 0.321111 0.556181i 0.0198763 0.0344268i
\(262\) −0.727902 1.26076i −0.0449699 0.0778902i
\(263\) 13.8958 + 24.0682i 0.856852 + 1.48411i 0.874916 + 0.484274i \(0.160916\pi\)
−0.0180644 + 0.999837i \(0.505750\pi\)
\(264\) −0.452365 + 0.783519i −0.0278411 + 0.0482222i
\(265\) −27.3846 −1.68222
\(266\) −0.0133792 0.0218697i −0.000820329 0.00134092i
\(267\) 6.40363 0.391896
\(268\) 6.12195 10.6035i 0.373958 0.647714i
\(269\) 4.00404 + 6.93521i 0.244131 + 0.422847i 0.961887 0.273448i \(-0.0881640\pi\)
−0.717756 + 0.696295i \(0.754831\pi\)
\(270\) −0.0855372 0.148155i −0.00520563 0.00901641i
\(271\) −10.1323 + 17.5496i −0.615490 + 1.06606i 0.374808 + 0.927103i \(0.377709\pi\)
−0.990298 + 0.138958i \(0.955625\pi\)
\(272\) −1.56152 −0.0946811
\(273\) −1.38070 2.25691i −0.0835640 0.136595i
\(274\) −1.05565 −0.0637740
\(275\) 0.217726 0.377113i 0.0131294 0.0227408i
\(276\) −3.37167 5.83991i −0.202951 0.351521i
\(277\) 14.7169 + 25.4905i 0.884256 + 1.53158i 0.846564 + 0.532286i \(0.178667\pi\)
0.0376912 + 0.999289i \(0.488000\pi\)
\(278\) 0.610885 1.05808i 0.0366385 0.0634597i
\(279\) 5.95780 0.356684
\(280\) −0.863778 + 1.58803i −0.0516206 + 0.0949031i
\(281\) −3.76735 −0.224741 −0.112371 0.993666i \(-0.535844\pi\)
−0.112371 + 0.993666i \(0.535844\pi\)
\(282\) −0.367529 + 0.636579i −0.0218860 + 0.0379077i
\(283\) −11.2203 19.4342i −0.666980 1.15524i −0.978744 0.205084i \(-0.934253\pi\)
0.311764 0.950160i \(-0.399080\pi\)
\(284\) −14.0401 24.3181i −0.833125 1.44301i
\(285\) −0.137378 + 0.237945i −0.00813755 + 0.0140946i
\(286\) −0.226524 −0.0133946
\(287\) 1.15049 0.0292609i 0.0679111 0.00172721i
\(288\) 0.928358 0.0547040
\(289\) 8.42240 14.5880i 0.495436 0.858120i
\(290\) −0.0549339 0.0951483i −0.00322583 0.00558730i
\(291\) 7.45479 + 12.9121i 0.437007 + 0.756919i
\(292\) −7.53016 + 13.0426i −0.440670 + 0.763262i
\(293\) 8.13635 0.475331 0.237665 0.971347i \(-0.423618\pi\)
0.237665 + 0.971347i \(0.423618\pi\)
\(294\) −0.543025 + 0.0276399i −0.0316698 + 0.00161199i
\(295\) 16.1560 0.940639
\(296\) 0.649426 1.12484i 0.0377471 0.0653800i
\(297\) 1.45815 + 2.52558i 0.0846102 + 0.146549i
\(298\) −0.130032 0.225222i −0.00753255 0.0130468i
\(299\) 1.69094 2.92879i 0.0977894 0.169376i
\(300\) −0.297734 −0.0171897
\(301\) −17.8513 + 0.454020i −1.02893 + 0.0261693i
\(302\) −1.58828 −0.0913951
\(303\) −9.99103 + 17.3050i −0.573970 + 0.994145i
\(304\) −0.247247 0.428244i −0.0141806 0.0245615i
\(305\) −2.63624 4.56610i −0.150951 0.261454i
\(306\) 0.0152998 0.0265000i 0.000874630 0.00151490i
\(307\) 18.9247 1.08009 0.540046 0.841636i \(-0.318407\pi\)
0.540046 + 0.841636i \(0.318407\pi\)
\(308\) 7.35126 13.5151i 0.418877 0.770093i
\(309\) 14.6745 0.834802
\(310\) 0.509613 0.882676i 0.0289441 0.0501326i
\(311\) −5.80947 10.0623i −0.329425 0.570580i 0.652973 0.757381i \(-0.273521\pi\)
−0.982398 + 0.186801i \(0.940188\pi\)
\(312\) 0.155116 + 0.268670i 0.00878174 + 0.0152104i
\(313\) 5.85117 10.1345i 0.330727 0.572837i −0.651927 0.758282i \(-0.726039\pi\)
0.982655 + 0.185445i \(0.0593726\pi\)
\(314\) 0.792395 0.0447174
\(315\) 3.04090 + 4.97068i 0.171335 + 0.280066i
\(316\) 4.73512 0.266371
\(317\) 16.5034 28.5848i 0.926926 1.60548i 0.138492 0.990364i \(-0.455774\pi\)
0.788434 0.615119i \(-0.210892\pi\)
\(318\) 0.482901 + 0.836409i 0.0270798 + 0.0469035i
\(319\) 0.936454 + 1.62199i 0.0524314 + 0.0908138i
\(320\) −8.65065 + 14.9834i −0.483586 + 0.837595i
\(321\) 5.03973 0.281290
\(322\) −0.362695 0.592865i −0.0202122 0.0330391i
\(323\) −0.0491447 −0.00273448
\(324\) 0.996983 1.72683i 0.0553880 0.0959348i
\(325\) −0.0746586 0.129313i −0.00414132 0.00717297i
\(326\) −0.605229 1.04829i −0.0335205 0.0580593i
\(327\) −0.0613411 + 0.106246i −0.00339217 + 0.00587542i
\(328\) −0.134946 −0.00745116
\(329\) 11.9633 21.9942i 0.659558 1.21258i
\(330\) 0.498902 0.0274637
\(331\) −7.38730 + 12.7952i −0.406043 + 0.703286i −0.994442 0.105284i \(-0.966425\pi\)
0.588400 + 0.808570i \(0.299758\pi\)
\(332\) −9.75852 16.9022i −0.535568 0.927631i
\(333\) −2.09335 3.62579i −0.114715 0.198692i
\(334\) −0.0595421 + 0.103130i −0.00325800 + 0.00564302i
\(335\) −13.5239 −0.738892
\(336\) −10.4839 + 0.266643i −0.571945 + 0.0145465i
\(337\) −13.0713 −0.712041 −0.356020 0.934478i \(-0.615867\pi\)
−0.356020 + 0.934478i \(0.615867\pi\)
\(338\) −0.0388377 + 0.0672688i −0.00211249 + 0.00365894i
\(339\) −2.08069 3.60386i −0.113008 0.195735i
\(340\) 0.865010 + 1.49824i 0.0469118 + 0.0812536i
\(341\) −8.68734 + 15.0469i −0.470446 + 0.814836i
\(342\) 0.00969009 0.000523980
\(343\) 18.4664 1.41143i 0.997092 0.0762100i
\(344\) 2.09387 0.112894
\(345\) −3.72417 + 6.45044i −0.200502 + 0.347280i
\(346\) 0.543123 + 0.940717i 0.0291985 + 0.0505733i
\(347\) −3.18975 5.52481i −0.171235 0.296587i 0.767617 0.640909i \(-0.221442\pi\)
−0.938852 + 0.344322i \(0.888109\pi\)
\(348\) 0.640285 1.10901i 0.0343229 0.0594490i
\(349\) −10.3287 −0.552881 −0.276441 0.961031i \(-0.589155\pi\)
−0.276441 + 0.961031i \(0.589155\pi\)
\(350\) −0.0306762 0.000780203i −0.00163971 4.17036e-5i
\(351\) 1.00000 0.0533761
\(352\) −1.35368 + 2.34464i −0.0721515 + 0.124970i
\(353\) 15.0759 + 26.1122i 0.802407 + 1.38981i 0.918028 + 0.396516i \(0.129781\pi\)
−0.115620 + 0.993293i \(0.536886\pi\)
\(354\) −0.284896 0.493454i −0.0151420 0.0262268i
\(355\) −15.5079 + 26.8605i −0.823074 + 1.42561i
\(356\) 12.7686 0.676736
\(357\) −0.498018 + 0.915592i −0.0263579 + 0.0484583i
\(358\) −1.70345 −0.0900302
\(359\) 14.5886 25.2681i 0.769955 1.33360i −0.167631 0.985850i \(-0.553612\pi\)
0.937587 0.347752i \(-0.113055\pi\)
\(360\) −0.341633 0.591725i −0.0180056 0.0311866i
\(361\) 9.49222 + 16.4410i 0.499590 + 0.865316i
\(362\) −0.0371003 + 0.0642595i −0.00194995 + 0.00337741i
\(363\) 2.49525 0.130966
\(364\) −2.75308 4.50021i −0.144301 0.235875i
\(365\) 16.6348 0.870706
\(366\) −0.0929752 + 0.161038i −0.00485989 + 0.00841758i
\(367\) 2.24216 + 3.88353i 0.117040 + 0.202719i 0.918593 0.395204i \(-0.129326\pi\)
−0.801554 + 0.597923i \(0.795993\pi\)
\(368\) −6.70260 11.6092i −0.349397 0.605173i
\(369\) −0.217492 + 0.376707i −0.0113222 + 0.0196106i
\(370\) −0.716237 −0.0372354
\(371\) −17.1674 28.0621i −0.891289 1.45691i
\(372\) 11.8797 0.615932
\(373\) −11.9946 + 20.7752i −0.621055 + 1.07570i 0.368235 + 0.929733i \(0.379962\pi\)
−0.989290 + 0.145966i \(0.953371\pi\)
\(374\) 0.0446186 + 0.0772817i 0.00230717 + 0.00399614i
\(375\) 5.67050 + 9.82159i 0.292823 + 0.507185i
\(376\) −1.46790 + 2.54248i −0.0757011 + 0.131118i
\(377\) 0.642223 0.0330762
\(378\) 0.0981965 0.180532i 0.00505069 0.00928555i
\(379\) 20.2228 1.03878 0.519389 0.854538i \(-0.326160\pi\)
0.519389 + 0.854538i \(0.326160\pi\)
\(380\) −0.273926 + 0.474455i −0.0140521 + 0.0243390i
\(381\) 7.48557 + 12.9654i 0.383498 + 0.664237i
\(382\) −0.764459 1.32408i −0.0391131 0.0677459i
\(383\) 11.5409 19.9895i 0.589714 1.02141i −0.404555 0.914513i \(-0.632574\pi\)
0.994270 0.106901i \(-0.0340929\pi\)
\(384\) 2.46690 0.125888
\(385\) −16.9879 + 0.432062i −0.865786 + 0.0220199i
\(386\) 1.17251 0.0596794
\(387\) 3.37467 5.84510i 0.171544 0.297123i
\(388\) 14.8646 + 25.7462i 0.754635 + 1.30707i
\(389\) 16.6685 + 28.8706i 0.845124 + 1.46380i 0.885513 + 0.464615i \(0.153807\pi\)
−0.0403885 + 0.999184i \(0.512860\pi\)
\(390\) 0.0855372 0.148155i 0.00433134 0.00750210i
\(391\) −1.33226 −0.0673754
\(392\) −2.16882 + 0.110393i −0.109542 + 0.00557567i
\(393\) −18.7422 −0.945417
\(394\) 0.428467 0.742127i 0.0215859 0.0373878i
\(395\) −2.61508 4.52944i −0.131579 0.227901i
\(396\) 2.90749 + 5.03593i 0.146107 + 0.253065i
\(397\) 10.0940 17.4834i 0.506605 0.877465i −0.493366 0.869822i \(-0.664234\pi\)
0.999971 0.00764315i \(-0.00243291\pi\)
\(398\) 0.557477 0.0279438
\(399\) −0.329954 + 0.00839187i −0.0165184 + 0.000420119i
\(400\) −0.591869 −0.0295935
\(401\) 2.10744 3.65019i 0.105240 0.182282i −0.808596 0.588364i \(-0.799772\pi\)
0.913836 + 0.406083i \(0.133105\pi\)
\(402\) 0.238482 + 0.413063i 0.0118944 + 0.0206017i
\(403\) 2.97890 + 5.15961i 0.148390 + 0.257018i
\(404\) −19.9218 + 34.5055i −0.991146 + 1.71671i
\(405\) −2.20243 −0.109439
\(406\) 0.0630641 0.115942i 0.00312982 0.00575408i
\(407\) 12.2096 0.605210
\(408\) 0.0611068 0.105840i 0.00302524 0.00523987i
\(409\) −3.72314 6.44866i −0.184097 0.318866i 0.759175 0.650887i \(-0.225603\pi\)
−0.943272 + 0.332021i \(0.892269\pi\)
\(410\) 0.0372073 + 0.0644449i 0.00183754 + 0.00318271i
\(411\) −6.79525 + 11.7697i −0.335185 + 0.580557i
\(412\) 29.2604 1.44156
\(413\) 10.1282 + 16.5557i 0.498378 + 0.814653i
\(414\) 0.262688 0.0129104
\(415\) −10.7787 + 18.6693i −0.529107 + 0.916440i
\(416\) 0.464179 + 0.803982i 0.0227583 + 0.0394184i
\(417\) −7.86459 13.6219i −0.385131 0.667066i
\(418\) −0.0141296 + 0.0244731i −0.000691100 + 0.00119702i
\(419\) −12.2817 −0.600000 −0.300000 0.953939i \(-0.596987\pi\)
−0.300000 + 0.953939i \(0.596987\pi\)
\(420\) 6.06345 + 9.91138i 0.295866 + 0.483626i
\(421\) 26.9884 1.31533 0.657667 0.753309i \(-0.271544\pi\)
0.657667 + 0.753309i \(0.271544\pi\)
\(422\) −0.610212 + 1.05692i −0.0297047 + 0.0514500i
\(423\) 4.73160 + 8.19538i 0.230058 + 0.398473i
\(424\) 1.92869 + 3.34059i 0.0936655 + 0.162233i
\(425\) −0.0294112 + 0.0509416i −0.00142665 + 0.00247103i
\(426\) 1.09387 0.0529981
\(427\) 3.02640 5.56396i 0.146458 0.269259i
\(428\) 10.0490 0.485739
\(429\) −1.45815 + 2.52558i −0.0703999 + 0.121936i
\(430\) −0.577320 0.999947i −0.0278408 0.0482217i
\(431\) 10.1583 + 17.5948i 0.489310 + 0.847511i 0.999924 0.0122995i \(-0.00391516\pi\)
−0.510614 + 0.859810i \(0.670582\pi\)
\(432\) 1.98192 3.43278i 0.0953551 0.165160i
\(433\) −9.02891 −0.433902 −0.216951 0.976183i \(-0.569611\pi\)
−0.216951 + 0.976183i \(0.569611\pi\)
\(434\) 1.22399 0.0311303i 0.0587534 0.00149430i
\(435\) −1.41445 −0.0678176
\(436\) −0.122312 + 0.211851i −0.00585769 + 0.0101458i
\(437\) −0.210946 0.365370i −0.0100909 0.0174780i
\(438\) −0.293339 0.508078i −0.0140163 0.0242769i
\(439\) −5.01746 + 8.69049i −0.239470 + 0.414774i −0.960562 0.278065i \(-0.910307\pi\)
0.721092 + 0.692839i \(0.243640\pi\)
\(440\) 1.99260 0.0949935
\(441\) −3.18731 + 6.23226i −0.151777 + 0.296774i
\(442\) 0.0305996 0.00145547
\(443\) 16.8205 29.1339i 0.799165 1.38419i −0.120996 0.992653i \(-0.538609\pi\)
0.920161 0.391541i \(-0.128058\pi\)
\(444\) −4.17407 7.22971i −0.198093 0.343107i
\(445\) −7.05176 12.2140i −0.334286 0.579000i
\(446\) −0.241139 + 0.417665i −0.0114183 + 0.0197770i
\(447\) −3.34809 −0.158359
\(448\) −20.7771 + 0.528435i −0.981628 + 0.0249662i
\(449\) 1.21577 0.0573759 0.0286879 0.999588i \(-0.490867\pi\)
0.0286879 + 0.999588i \(0.490867\pi\)
\(450\) 0.00579914 0.0100444i 0.000273374 0.000473498i
\(451\) −0.634270 1.09859i −0.0298666 0.0517305i
\(452\) −4.14883 7.18599i −0.195145 0.338000i
\(453\) −10.2238 + 17.7082i −0.480357 + 0.832003i
\(454\) 1.83997 0.0863540
\(455\) −2.78429 + 5.11884i −0.130529 + 0.239975i
\(456\) 0.0387019 0.00181238
\(457\) 14.2167 24.6241i 0.665029 1.15186i −0.314248 0.949341i \(-0.601752\pi\)
0.979277 0.202524i \(-0.0649144\pi\)
\(458\) 0.351181 + 0.608263i 0.0164096 + 0.0284222i
\(459\) −0.196971 0.341163i −0.00919381 0.0159241i
\(460\) −7.42586 + 12.8620i −0.346233 + 0.599692i
\(461\) 30.9864 1.44318 0.721590 0.692320i \(-0.243412\pi\)
0.721590 + 0.692320i \(0.243412\pi\)
\(462\) 0.312763 + 0.511245i 0.0145510 + 0.0237853i
\(463\) −14.7992 −0.687779 −0.343889 0.939010i \(-0.611745\pi\)
−0.343889 + 0.939010i \(0.611745\pi\)
\(464\) 1.27283 2.20461i 0.0590898 0.102346i
\(465\) −6.56081 11.3637i −0.304250 0.526977i
\(466\) −0.207568 0.359518i −0.00961538 0.0166543i
\(467\) 0.914979 1.58479i 0.0423402 0.0733353i −0.844079 0.536219i \(-0.819852\pi\)
0.886419 + 0.462884i \(0.153185\pi\)
\(468\) 1.99397 0.0921711
\(469\) −8.47818 13.8585i −0.391486 0.639927i
\(470\) 1.61891 0.0746748
\(471\) 5.10068 8.83464i 0.235027 0.407079i
\(472\) −1.13786 1.97084i −0.0523745 0.0907152i
\(473\) 9.84152 + 17.0460i 0.452514 + 0.783777i
\(474\) −0.0922287 + 0.159745i −0.00423621 + 0.00733732i
\(475\) −0.0186275 −0.000854689
\(476\) −0.993031 + 1.82566i −0.0455155 + 0.0836790i
\(477\) 12.4338 0.569306
\(478\) 1.05851 1.83340i 0.0484153 0.0838578i
\(479\) −4.67330 8.09439i −0.213528 0.369842i 0.739288 0.673389i \(-0.235162\pi\)
−0.952816 + 0.303547i \(0.901829\pi\)
\(480\) −1.02232 1.77071i −0.0466623 0.0808215i
\(481\) 2.09335 3.62579i 0.0954486 0.165322i
\(482\) −1.21765 −0.0554623
\(483\) −8.94471 + 0.227495i −0.406998 + 0.0103514i
\(484\) 4.97544 0.226156
\(485\) 16.4186 28.4379i 0.745531 1.29130i
\(486\) 0.0388377 + 0.0672688i 0.00176171 + 0.00305138i
\(487\) −11.6870 20.2424i −0.529587 0.917272i −0.999404 0.0345080i \(-0.989014\pi\)
0.469817 0.882764i \(-0.344320\pi\)
\(488\) −0.371340 + 0.643179i −0.0168098 + 0.0291154i
\(489\) −15.5835 −0.704712
\(490\) 0.650705 + 1.00530i 0.0293959 + 0.0454150i
\(491\) −21.4726 −0.969044 −0.484522 0.874779i \(-0.661007\pi\)
−0.484522 + 0.874779i \(0.661007\pi\)
\(492\) −0.433672 + 0.751142i −0.0195514 + 0.0338641i
\(493\) −0.126499 0.219103i −0.00569723 0.00986790i
\(494\) 0.00484505 + 0.00839187i 0.000217989 + 0.000377568i
\(495\) 3.21146 5.56241i 0.144344 0.250012i
\(496\) 23.6157 1.06038
\(497\) −37.2469 + 0.947317i −1.67075 + 0.0424930i
\(498\) 0.760290 0.0340694
\(499\) 11.0957 19.2184i 0.496714 0.860333i −0.503279 0.864124i \(-0.667873\pi\)
0.999993 + 0.00379076i \(0.00120664\pi\)
\(500\) 11.3068 + 19.5839i 0.505655 + 0.875819i
\(501\) 0.766550 + 1.32770i 0.0342469 + 0.0593174i
\(502\) 0.707693 1.22576i 0.0315859 0.0547083i
\(503\) 17.3231 0.772399 0.386200 0.922415i \(-0.373788\pi\)
0.386200 + 0.922415i \(0.373788\pi\)
\(504\) 0.392194 0.721037i 0.0174697 0.0321176i
\(505\) 44.0090 1.95838
\(506\) −0.383038 + 0.663441i −0.0170281 + 0.0294936i
\(507\) 0.500000 + 0.866025i 0.0222058 + 0.0384615i
\(508\) 14.9260 + 25.8526i 0.662233 + 1.14702i
\(509\) 13.4306 23.2625i 0.595303 1.03109i −0.398202 0.917298i \(-0.630366\pi\)
0.993504 0.113796i \(-0.0363011\pi\)
\(510\) −0.0673933 −0.00298423
\(511\) 10.4284 + 17.0463i 0.461325 + 0.754086i
\(512\) 6.13928 0.271321
\(513\) 0.0623756 0.108038i 0.00275395 0.00476998i
\(514\) −0.584948 1.01316i −0.0258010 0.0446886i
\(515\) −16.1597 27.9895i −0.712083 1.23336i
\(516\) 6.72898 11.6549i 0.296227 0.513080i
\(517\) −27.5975 −1.21374
\(518\) −0.449010 0.733956i −0.0197284 0.0322482i
\(519\) 13.9844 0.613849
\(520\) 0.341633 0.591725i 0.0149816 0.0259489i
\(521\) 5.10145 + 8.83598i 0.223499 + 0.387111i 0.955868 0.293797i \(-0.0949188\pi\)
−0.732369 + 0.680908i \(0.761585\pi\)
\(522\) 0.0249424 + 0.0432016i 0.00109170 + 0.00189088i
\(523\) −5.95733 + 10.3184i −0.260496 + 0.451192i −0.966374 0.257141i \(-0.917219\pi\)
0.705878 + 0.708334i \(0.250553\pi\)
\(524\) −37.3712 −1.63257
\(525\) −0.188766 + 0.347040i −0.00823841 + 0.0151461i
\(526\) −2.15872 −0.0941248
\(527\) 1.17351 2.03258i 0.0511190 0.0885408i
\(528\) 5.77985 + 10.0110i 0.251536 + 0.435673i
\(529\) 5.78146 + 10.0138i 0.251368 + 0.435382i
\(530\) 1.06355 1.84213i 0.0461978 0.0800170i
\(531\) −7.33555 −0.318336
\(532\) −0.657917 + 0.0167331i −0.0285243 + 0.000725472i
\(533\) −0.434984 −0.0188412
\(534\) −0.248702 + 0.430765i −0.0107624 + 0.0186410i
\(535\) −5.54981 9.61256i −0.239939 0.415587i
\(536\) 0.952488 + 1.64976i 0.0411412 + 0.0712587i
\(537\) −10.9652 + 18.9923i −0.473183 + 0.819577i
\(538\) −0.622031 −0.0268177
\(539\) −11.0925 17.1374i −0.477789 0.738158i
\(540\) −4.39156 −0.188983
\(541\) −9.98434 + 17.2934i −0.429260 + 0.743501i −0.996808 0.0798401i \(-0.974559\pi\)
0.567547 + 0.823341i \(0.307892\pi\)
\(542\) −0.787026 1.36317i −0.0338057 0.0585532i
\(543\) 0.477632 + 0.827283i 0.0204972 + 0.0355021i
\(544\) 0.182859 0.316722i 0.00784004 0.0135793i
\(545\) 0.270199 0.0115740
\(546\) 0.205443 0.00522513i 0.00879216 0.000223615i
\(547\) −16.7640 −0.716778 −0.358389 0.933572i \(-0.616674\pi\)
−0.358389 + 0.933572i \(0.616674\pi\)
\(548\) −13.5495 + 23.4684i −0.578806 + 1.00252i
\(549\) 1.19697 + 2.07321i 0.0510855 + 0.0884826i
\(550\) 0.0169120 + 0.0292924i 0.000721129 + 0.00124903i
\(551\) 0.0400590 0.0693843i 0.00170657 0.00295587i
\(552\) 1.04917 0.0446556
\(553\) 3.00210 5.51929i 0.127662 0.234704i
\(554\) −2.28629 −0.0971351
\(555\) −4.61045 + 7.98554i −0.195703 + 0.338967i
\(556\) −15.6817 27.1616i −0.665054 1.15191i
\(557\) −11.6898 20.2474i −0.495314 0.857909i 0.504671 0.863311i \(-0.331614\pi\)
−0.999985 + 0.00540254i \(0.998280\pi\)
\(558\) −0.231387 + 0.400774i −0.00979540 + 0.0169661i
\(559\) 6.74934 0.285467
\(560\) 12.0536 + 19.7030i 0.509359 + 0.832603i
\(561\) 1.14885 0.0485044
\(562\) 0.146315 0.253425i 0.00617193 0.0106901i
\(563\) −21.0019 36.3763i −0.885124 1.53308i −0.845571 0.533863i \(-0.820740\pi\)
−0.0395532 0.999217i \(-0.512593\pi\)
\(564\) 9.43466 + 16.3413i 0.397271 + 0.688093i
\(565\) −4.58257 + 7.93725i −0.192790 + 0.333922i
\(566\) 1.74309 0.0732675
\(567\) −1.38070 2.25691i −0.0579841 0.0947814i
\(568\) 4.36887 0.183314
\(569\) −6.28982 + 10.8943i −0.263683 + 0.456712i −0.967218 0.253948i \(-0.918271\pi\)
0.703535 + 0.710661i \(0.251604\pi\)
\(570\) −0.0106709 0.0184825i −0.000446953 0.000774146i
\(571\) 4.39938 + 7.61995i 0.184108 + 0.318885i 0.943276 0.332011i \(-0.107727\pi\)
−0.759167 + 0.650895i \(0.774394\pi\)
\(572\) −2.90749 + 5.03593i −0.121568 + 0.210563i
\(573\) −19.6834 −0.822287
\(574\) −0.0427139 + 0.0785284i −0.00178284 + 0.00327771i
\(575\) −0.504972 −0.0210588
\(576\) 3.92778 6.80312i 0.163658 0.283463i
\(577\) −0.706850 1.22430i −0.0294266 0.0509683i 0.850937 0.525268i \(-0.176035\pi\)
−0.880364 + 0.474299i \(0.842701\pi\)
\(578\) 0.654213 + 1.13313i 0.0272117 + 0.0471320i
\(579\) 7.54753 13.0727i 0.313664 0.543283i
\(580\) −2.82036 −0.117109
\(581\) −25.8884 + 0.658430i −1.07403 + 0.0273163i
\(582\) −1.15811 −0.0480051
\(583\) −18.1303 + 31.4027i −0.750882 + 1.30057i
\(584\) −1.17159 2.02925i −0.0484806 0.0839708i
\(585\) −1.10121 1.90736i −0.0455296 0.0788595i
\(586\) −0.315997 + 0.547323i −0.0130537 + 0.0226097i
\(587\) −24.3046 −1.00316 −0.501580 0.865111i \(-0.667248\pi\)
−0.501580 + 0.865111i \(0.667248\pi\)
\(588\) −6.35539 + 12.4269i −0.262092 + 0.512477i
\(589\) 0.743243 0.0306248
\(590\) −0.627462 + 1.08680i −0.0258322 + 0.0447427i
\(591\) −5.51613 9.55421i −0.226903 0.393008i
\(592\) −8.29770 14.3720i −0.341033 0.590687i
\(593\) 13.3532 23.1283i 0.548348 0.949767i −0.450040 0.893009i \(-0.648590\pi\)
0.998388 0.0567584i \(-0.0180765\pi\)
\(594\) −0.226524 −0.00929439
\(595\) 2.29478 0.0583643i 0.0940770 0.00239270i
\(596\) −6.67597 −0.273459
\(597\) 3.58851 6.21548i 0.146868 0.254382i
\(598\) 0.131344 + 0.227495i 0.00537106 + 0.00930295i
\(599\) 16.8268 + 29.1449i 0.687526 + 1.19083i 0.972636 + 0.232335i \(0.0746364\pi\)
−0.285110 + 0.958495i \(0.592030\pi\)
\(600\) 0.0231616 0.0401170i 0.000945567 0.00163777i
\(601\) −12.5737 −0.512890 −0.256445 0.966559i \(-0.582551\pi\)
−0.256445 + 0.966559i \(0.582551\pi\)
\(602\) 0.662762 1.21847i 0.0270122 0.0496611i
\(603\) 6.14047 0.250059
\(604\) −20.3860 + 35.3095i −0.829493 + 1.43672i
\(605\) −2.74780 4.75933i −0.111714 0.193494i
\(606\) −0.776057 1.34417i −0.0315252 0.0546032i
\(607\) −10.7209 + 18.5691i −0.435146 + 0.753695i −0.997308 0.0733326i \(-0.976637\pi\)
0.562162 + 0.827027i \(0.309970\pi\)
\(608\) 0.115814 0.00469687
\(609\) −0.886720 1.44944i −0.0359317 0.0587343i
\(610\) 0.409542 0.0165819
\(611\) −4.73160 + 8.19538i −0.191420 + 0.331549i
\(612\) −0.392753 0.680269i −0.0158761 0.0274982i
\(613\) −15.3631 26.6096i −0.620509 1.07475i −0.989391 0.145276i \(-0.953593\pi\)
0.368882 0.929476i \(-0.379740\pi\)
\(614\) −0.734993 + 1.27304i −0.0296619 + 0.0513759i
\(615\) 0.958020 0.0386311
\(616\) 1.24916 + 2.04190i 0.0503302 + 0.0822703i
\(617\) 0.216739 0.00872559 0.00436279 0.999990i \(-0.498611\pi\)
0.00436279 + 0.999990i \(0.498611\pi\)
\(618\) −0.569923 + 0.987135i −0.0229257 + 0.0397084i
\(619\) −15.2490 26.4121i −0.612909 1.06159i −0.990747 0.135718i \(-0.956666\pi\)
0.377838 0.925872i \(-0.376668\pi\)
\(620\) −13.0820 22.6588i −0.525387 0.909997i
\(621\) 1.69094 2.92879i 0.0678550 0.117528i
\(622\) 0.902505 0.0361871
\(623\) 8.09542 14.8832i 0.324336 0.596283i
\(624\) 3.96384 0.158680
\(625\) 12.1156 20.9848i 0.484622 0.839391i
\(626\) 0.454492 + 0.787202i 0.0181651 + 0.0314629i
\(627\) 0.181905 + 0.315069i 0.00726460 + 0.0125827i
\(628\) 10.1706 17.6160i 0.405851 0.702954i
\(629\) −1.64932 −0.0657626
\(630\) −0.452474 + 0.0115080i −0.0180270 + 0.000458489i
\(631\) −14.0505 −0.559343 −0.279671 0.960096i \(-0.590226\pi\)
−0.279671 + 0.960096i \(0.590226\pi\)
\(632\) −0.368358 + 0.638015i −0.0146525 + 0.0253789i
\(633\) 7.85593 + 13.6069i 0.312245 + 0.540825i
\(634\) 1.28191 + 2.22034i 0.0509112 + 0.0881808i
\(635\) 16.4864 28.5553i 0.654244 1.13318i
\(636\) 24.7926 0.983092
\(637\) −6.99095 + 0.355838i −0.276992 + 0.0140988i
\(638\) −0.145479 −0.00575956
\(639\) 7.04128 12.1958i 0.278549 0.482460i
\(640\) −2.71658 4.70526i −0.107382 0.185992i
\(641\) 9.08657 + 15.7384i 0.358898 + 0.621629i 0.987777 0.155874i \(-0.0498193\pi\)
−0.628879 + 0.777503i \(0.716486\pi\)
\(642\) −0.195731 + 0.339017i −0.00772490 + 0.0133799i
\(643\) −7.27895 −0.287054 −0.143527 0.989646i \(-0.545844\pi\)
−0.143527 + 0.989646i \(0.545844\pi\)
\(644\) −17.8354 + 0.453617i −0.702815 + 0.0178750i
\(645\) −14.8649 −0.585306
\(646\) 0.00190867 0.00330591i 7.50955e−5 0.000130069i
\(647\) −8.88985 15.3977i −0.349496 0.605345i 0.636664 0.771141i \(-0.280314\pi\)
−0.986160 + 0.165797i \(0.946980\pi\)
\(648\) 0.155116 + 0.268670i 0.00609355 + 0.0105543i
\(649\) 10.6963 18.5265i 0.419867 0.727230i
\(650\) 0.0115983 0.000454922
\(651\) 7.53180 13.8470i 0.295195 0.542707i
\(652\) −31.0731 −1.21692
\(653\) −4.06627 + 7.04298i −0.159125 + 0.275613i −0.934554 0.355823i \(-0.884201\pi\)
0.775428 + 0.631436i \(0.217534\pi\)
\(654\) −0.00476470 0.00825270i −0.000186314 0.000322706i
\(655\) 20.6391 + 35.7480i 0.806437 + 1.39679i
\(656\) −0.862103 + 1.49321i −0.0336595 + 0.0582999i
\(657\) −7.55295 −0.294669
\(658\) 1.01490 + 1.65896i 0.0395648 + 0.0646731i
\(659\) 10.0958 0.393278 0.196639 0.980476i \(-0.436997\pi\)
0.196639 + 0.980476i \(0.436997\pi\)
\(660\) 6.40354 11.0913i 0.249257 0.431727i
\(661\) −12.1727 21.0838i −0.473464 0.820064i 0.526074 0.850439i \(-0.323663\pi\)
−0.999539 + 0.0303745i \(0.990330\pi\)
\(662\) −0.573811 0.993870i −0.0223018 0.0386279i
\(663\) 0.196971 0.341163i 0.00764971 0.0132497i
\(664\) 3.03657 0.117842
\(665\) 0.379356 + 0.620099i 0.0147108 + 0.0240464i
\(666\) 0.325204 0.0126014
\(667\) 1.08596 1.88094i 0.0420485 0.0728301i
\(668\) 1.52848 + 2.64740i 0.0591385 + 0.102431i
\(669\) 3.10445 + 5.37706i 0.120025 + 0.207889i
\(670\) 0.525239 0.909740i 0.0202917 0.0351463i
\(671\) −6.98143 −0.269515
\(672\) 1.17362 2.15767i 0.0452735 0.0832340i
\(673\) −39.4811 −1.52189 −0.760943 0.648819i \(-0.775263\pi\)
−0.760943 + 0.648819i \(0.775263\pi\)
\(674\) 0.507660 0.879294i 0.0195543 0.0338691i
\(675\) −0.0746586 0.129313i −0.00287361 0.00497724i
\(676\) 0.996983 + 1.72683i 0.0383455 + 0.0664164i
\(677\) −8.99151 + 15.5738i −0.345572 + 0.598548i −0.985457 0.169922i \(-0.945648\pi\)
0.639886 + 0.768470i \(0.278982\pi\)
\(678\) 0.323237 0.0124138
\(679\) 39.4343 1.00295i 1.51335 0.0384897i
\(680\) −0.269167 −0.0103221
\(681\) 11.8440 20.5143i 0.453862 0.786111i
\(682\) −0.674793 1.16878i −0.0258391 0.0447547i
\(683\) −7.66325 13.2731i −0.293226 0.507882i 0.681345 0.731963i \(-0.261395\pi\)
−0.974571 + 0.224080i \(0.928062\pi\)
\(684\) 0.124375 0.215424i 0.00475559 0.00823692i
\(685\) 29.9321 1.14365
\(686\) −0.622247 + 1.29703i −0.0237575 + 0.0495208i
\(687\) 9.04226 0.344984
\(688\) 13.3766 23.1690i 0.509980 0.883311i
\(689\) 6.21691 + 10.7680i 0.236846 + 0.410229i
\(690\) −0.289276 0.501041i −0.0110125 0.0190743i
\(691\) 12.6299 21.8757i 0.480466 0.832191i −0.519283 0.854602i \(-0.673801\pi\)
0.999749 + 0.0224112i \(0.00713432\pi\)
\(692\) 27.8845 1.06001
\(693\) 7.71329 0.196176i 0.293004 0.00745209i
\(694\) 0.495530 0.0188101
\(695\) −17.3212 + 30.0012i −0.657030 + 1.13801i
\(696\) 0.0996193 + 0.172546i 0.00377606 + 0.00654033i
\(697\) 0.0856792 + 0.148401i 0.00324533 + 0.00562108i
\(698\) 0.401142 0.694798i 0.0151834 0.0262985i
\(699\) −5.34449 −0.202147
\(700\) −0.376392 + 0.691987i −0.0142263 + 0.0261547i
\(701\) 37.6169 1.42077 0.710385 0.703813i \(-0.248521\pi\)
0.710385 + 0.703813i \(0.248521\pi\)
\(702\) −0.0388377 + 0.0672688i −0.00146583 + 0.00253890i
\(703\) −0.261148 0.452322i −0.00984939 0.0170596i
\(704\) 11.4546 + 19.8399i 0.431710 + 0.747743i
\(705\) 10.4210 18.0497i 0.392478 0.679792i
\(706\) −2.34205 −0.0881441
\(707\) 27.5893 + 45.0978i 1.03760 + 1.69608i
\(708\) −14.6268 −0.549710
\(709\) −5.36331 + 9.28953i −0.201423 + 0.348876i −0.948987 0.315314i \(-0.897890\pi\)
0.747564 + 0.664190i \(0.231223\pi\)
\(710\) −1.20458 2.08640i −0.0452071 0.0783011i
\(711\) 1.18736 + 2.05657i 0.0445295 + 0.0771274i
\(712\) −0.993308 + 1.72046i −0.0372258 + 0.0644770i
\(713\) 20.1485 0.754569
\(714\) −0.0422490 0.0690606i −0.00158113 0.00258453i
\(715\) 6.42292 0.240203
\(716\) −21.8642 + 37.8700i −0.817105 + 1.41527i
\(717\) −13.6274 23.6034i −0.508925 0.881484i
\(718\) 1.13317 + 1.96271i 0.0422896 + 0.0732478i
\(719\) −6.17034 + 10.6873i −0.230115 + 0.398571i −0.957842 0.287296i \(-0.907244\pi\)
0.727727 + 0.685867i \(0.240577\pi\)
\(720\) −8.73006 −0.325350
\(721\) 18.5513 34.1061i 0.690888 1.27018i
\(722\) −1.47462 −0.0548798
\(723\) −7.83806 + 13.5759i −0.291500 + 0.504894i
\(724\) 0.952383 + 1.64958i 0.0353950 + 0.0613060i
\(725\) −0.0479475 0.0830475i −0.00178072 0.00308431i
\(726\) −0.0969096 + 0.167852i −0.00359665 + 0.00622958i
\(727\) 46.5464 1.72631 0.863155 0.504939i \(-0.168485\pi\)
0.863155 + 0.504939i \(0.168485\pi\)
\(728\) 0.820534 0.0208690i 0.0304110 0.000773457i
\(729\) 1.00000 0.0370370
\(730\) −0.646058 + 1.11900i −0.0239117 + 0.0414162i
\(731\) −1.32942 2.30263i −0.0491705 0.0851658i
\(732\) 2.38672 + 4.13392i 0.0882157 + 0.152794i
\(733\) −18.9421 + 32.8088i −0.699644 + 1.21182i 0.268946 + 0.963155i \(0.413325\pi\)
−0.968590 + 0.248664i \(0.920009\pi\)
\(734\) −0.348321 −0.0128568
\(735\) 15.3971 0.783708i 0.567929 0.0289075i
\(736\) 3.13959 0.115727
\(737\) −8.95371 + 15.5083i −0.329814 + 0.571255i
\(738\) −0.0168938 0.0292609i −0.000621868 0.00107711i
\(739\) −9.48912 16.4356i −0.349063 0.604595i 0.637020 0.770847i \(-0.280167\pi\)
−0.986083 + 0.166252i \(0.946833\pi\)
\(740\) −9.19309 + 15.9229i −0.337945 + 0.585337i
\(741\) 0.124751 0.00458285
\(742\) 2.55445 0.0649684i 0.0937767 0.00238507i
\(743\) 20.2127 0.741534 0.370767 0.928726i \(-0.379095\pi\)
0.370767 + 0.928726i \(0.379095\pi\)
\(744\) −0.924153 + 1.60068i −0.0338811 + 0.0586838i
\(745\) 3.68696 + 6.38600i 0.135080 + 0.233965i
\(746\) −0.931682 1.61372i −0.0341113 0.0590825i
\(747\) 4.89402 8.47669i 0.179063 0.310146i
\(748\) 2.29077 0.0837587
\(749\) 6.37118 11.7132i 0.232798 0.427992i
\(750\) −0.880916 −0.0321665
\(751\) 23.5767 40.8361i 0.860328 1.49013i −0.0112854 0.999936i \(-0.503592\pi\)
0.871613 0.490195i \(-0.163074\pi\)
\(752\) 18.7553 + 32.4851i 0.683935 + 1.18461i
\(753\) −9.11090 15.7805i −0.332020 0.575075i
\(754\) −0.0249424 + 0.0432016i −0.000908350 + 0.00157331i
\(755\) 45.0344 1.63897
\(756\) −2.75308 4.50021i −0.100129 0.163671i
\(757\) −14.7288 −0.535327 −0.267664 0.963512i \(-0.586252\pi\)
−0.267664 + 0.963512i \(0.586252\pi\)
\(758\) −0.785408 + 1.36037i −0.0285273 + 0.0494107i
\(759\) 4.93127 + 8.54120i 0.178994 + 0.310026i
\(760\) −0.0426191 0.0738184i −0.00154596 0.00267767i
\(761\) −20.8747 + 36.1560i −0.756706 + 1.31065i 0.187815 + 0.982204i \(0.439859\pi\)
−0.944522 + 0.328450i \(0.893474\pi\)
\(762\) −1.16289 −0.0421270
\(763\) 0.169388 + 0.276883i 0.00613226 + 0.0100238i
\(764\) −39.2481 −1.41995
\(765\) −0.433814 + 0.751388i −0.0156846 + 0.0271665i
\(766\) 0.896446 + 1.55269i 0.0323899 + 0.0561010i
\(767\) −3.66778 6.35277i −0.132436 0.229385i
\(768\) 7.75975 13.4403i 0.280006 0.484985i
\(769\) −34.0121 −1.22651 −0.613254 0.789886i \(-0.710140\pi\)
−0.613254 + 0.789886i \(0.710140\pi\)
\(770\) 0.630708 1.15954i 0.0227291 0.0417869i
\(771\) −15.0614 −0.542422
\(772\) 15.0495 26.0665i 0.541644 0.938155i
\(773\) 8.50125 + 14.7246i 0.305769 + 0.529607i 0.977432 0.211249i \(-0.0677532\pi\)
−0.671663 + 0.740856i \(0.734420\pi\)
\(774\) 0.262129 + 0.454020i 0.00942203 + 0.0163194i
\(775\) 0.444801 0.770419i 0.0159777 0.0276743i
\(776\) −4.62544 −0.166044
\(777\) −11.0734 + 0.281635i −0.397256 + 0.0101036i
\(778\) −2.58946 −0.0928366
\(779\) −0.0271324 + 0.0469947i −0.000972119 + 0.00168376i
\(780\) −2.19578 3.80321i −0.0786216 0.136177i
\(781\) 20.5344 + 35.5666i 0.734779 + 1.27267i
\(782\) 0.0517420 0.0896197i 0.00185029 0.00320479i
\(783\) 0.642223 0.0229512
\(784\) −12.6340 + 24.7037i −0.451213 + 0.882273i
\(785\) −22.4678 −0.801909
\(786\) 0.727902 1.26076i 0.0259634 0.0449699i
\(787\) 15.5647 + 26.9589i 0.554822 + 0.960980i 0.997917 + 0.0645052i \(0.0205469\pi\)
−0.443096 + 0.896474i \(0.646120\pi\)
\(788\) −10.9990 19.0508i −0.391822 0.678656i
\(789\) −13.8958 + 24.0682i −0.494704 + 0.856852i
\(790\) 0.406254 0.0144539
\(791\) −11.0064 + 0.279932i −0.391344 + 0.00995322i
\(792\) −0.904729 −0.0321482
\(793\) −1.19697 + 2.07321i −0.0425057 + 0.0736220i
\(794\) 0.784057 + 1.35803i 0.0278251 + 0.0481946i
\(795\) −13.6923 23.7158i −0.485616 0.841111i
\(796\) 7.15536 12.3935i 0.253615 0.439274i
\(797\) 10.5797 0.374752 0.187376 0.982288i \(-0.440002\pi\)
0.187376 + 0.982288i \(0.440002\pi\)
\(798\) 0.0122501 0.0225215i 0.000433650 0.000797254i
\(799\) 3.72795 0.131885
\(800\) 0.0693100 0.120048i 0.00245048 0.00424435i
\(801\) 3.20182 + 5.54571i 0.113131 + 0.195948i
\(802\) 0.163696 + 0.283530i 0.00578030 + 0.0100118i
\(803\) 11.0133 19.0756i 0.388651 0.673163i
\(804\) 12.2439 0.431809
\(805\) 10.2839 + 16.8102i 0.362461 + 0.592483i
\(806\) −0.462775 −0.0163005
\(807\) −4.00404 + 6.93521i −0.140949 + 0.244131i
\(808\) −3.09955 5.36857i −0.109042 0.188866i
\(809\) 9.51307 + 16.4771i 0.334462 + 0.579305i 0.983381 0.181552i \(-0.0581122\pi\)
−0.648920 + 0.760857i \(0.724779\pi\)
\(810\) 0.0855372 0.148155i 0.00300547 0.00520563i
\(811\) −24.9894 −0.877497 −0.438748 0.898610i \(-0.644578\pi\)
−0.438748 + 0.898610i \(0.644578\pi\)
\(812\) −1.76809 2.89014i −0.0620478 0.101424i
\(813\) −20.2645 −0.710707
\(814\) −0.474194 + 0.821329i −0.0166205 + 0.0287876i
\(815\) 17.1608 + 29.7234i 0.601117 + 1.04117i
\(816\) −0.780760 1.35232i −0.0273321 0.0473405i
\(817\) 0.420994 0.729183i 0.0147287 0.0255109i
\(818\) 0.578392 0.0202230
\(819\) 1.26419 2.32418i 0.0441744 0.0812135i
\(820\) 1.91026 0.0667092
\(821\) −22.8500 + 39.5774i −0.797471 + 1.38126i 0.123788 + 0.992309i \(0.460496\pi\)
−0.921258 + 0.388951i \(0.872837\pi\)
\(822\) −0.527823 0.914217i −0.0184100 0.0318870i
\(823\) 5.18997 + 8.98930i 0.180911 + 0.313347i 0.942191 0.335076i \(-0.108762\pi\)
−0.761280 + 0.648423i \(0.775429\pi\)
\(824\) −2.27625 + 3.94258i −0.0792970 + 0.137346i
\(825\) 0.435453 0.0151605
\(826\) −1.50704 + 0.0383292i −0.0524366 + 0.00133364i
\(827\) −9.56239 −0.332517 −0.166258 0.986082i \(-0.553169\pi\)
−0.166258 + 0.986082i \(0.553169\pi\)
\(828\) 3.37167 5.83991i 0.117174 0.202951i
\(829\) 8.93681 + 15.4790i 0.310388 + 0.537608i 0.978446 0.206501i \(-0.0662076\pi\)
−0.668058 + 0.744109i \(0.732874\pi\)
\(830\) −0.837241 1.45014i −0.0290611 0.0503353i
\(831\) −14.7169 + 25.4905i −0.510525 + 0.884256i
\(832\) 7.85556 0.272343
\(833\) 1.49841 + 2.31497i 0.0519169 + 0.0802089i
\(834\) 1.22177 0.0423064
\(835\) 1.68827 2.92417i 0.0584250 0.101195i
\(836\) 0.362713 + 0.628238i 0.0125447 + 0.0217281i
\(837\) 2.97890 + 5.15961i 0.102966 + 0.178342i
\(838\) 0.476992 0.826175i 0.0164774 0.0285397i
\(839\) 33.6620 1.16214 0.581071 0.813853i \(-0.302634\pi\)
0.581071 + 0.813853i \(0.302634\pi\)
\(840\) −1.80716 + 0.0459625i −0.0623531 + 0.00158586i
\(841\) −28.5876 −0.985778
\(842\) −1.04817 + 1.81548i −0.0361222 + 0.0625655i
\(843\) −1.88367 3.26262i −0.0648772 0.112371i
\(844\) 15.6645 + 27.1316i 0.539193 + 0.933910i
\(845\) 1.10121 1.90736i 0.0378829 0.0656151i
\(846\) −0.735058 −0.0252718
\(847\) 3.15447 5.79940i 0.108389 0.199270i
\(848\) 49.2857 1.69248
\(849\) 11.2203 19.4342i 0.385081 0.666980i
\(850\) −0.00228452 0.00395691i −7.83585e−5 0.000135721i
\(851\) −7.07945 12.2620i −0.242681 0.420335i
\(852\) 14.0401 24.3181i 0.481005 0.833125i
\(853\) −45.2796 −1.55035 −0.775173 0.631749i \(-0.782337\pi\)
−0.775173 + 0.631749i \(0.782337\pi\)
\(854\) 0.256742 + 0.419674i 0.00878555 + 0.0143609i
\(855\) −0.274755 −0.00939643
\(856\) −0.781744 + 1.35402i −0.0267195 + 0.0462795i
\(857\) 22.2861 + 38.6006i 0.761278 + 1.31857i 0.942192 + 0.335074i \(0.108761\pi\)
−0.180914 + 0.983499i \(0.557905\pi\)
\(858\) −0.113262 0.196176i −0.00386670 0.00669732i
\(859\) 19.9505 34.5552i 0.680701 1.17901i −0.294066 0.955785i \(-0.595009\pi\)
0.974767 0.223224i \(-0.0716582\pi\)
\(860\) −29.6402 −1.01072
\(861\) 0.600584 + 0.981721i 0.0204679 + 0.0334570i
\(862\) −1.57811 −0.0537505
\(863\) 1.55523 2.69373i 0.0529406 0.0916957i −0.838341 0.545147i \(-0.816474\pi\)
0.891281 + 0.453451i \(0.149807\pi\)
\(864\) 0.464179 + 0.803982i 0.0157917 + 0.0273520i
\(865\) −15.3998 26.6733i −0.523611 0.906920i
\(866\) 0.350662 0.607364i 0.0119160 0.0206391i
\(867\) 16.8448 0.572080
\(868\) 15.0182 27.6105i 0.509750 0.937161i
\(869\) −6.92538 −0.234927
\(870\) 0.0549339 0.0951483i 0.00186243 0.00322583i
\(871\) 3.07024 + 5.31781i 0.104031 + 0.180187i
\(872\) −0.0190300 0.0329610i −0.000644438 0.00111620i
\(873\) −7.45479 + 12.9121i −0.252306 + 0.437007i
\(874\) 0.0327707 0.00110848
\(875\) 29.9957 0.762896i 1.01404 0.0257906i
\(876\) −15.0603 −0.508841
\(877\) 2.32137 4.02073i 0.0783872 0.135771i −0.824167 0.566347i \(-0.808356\pi\)
0.902554 + 0.430576i \(0.141690\pi\)
\(878\) −0.389733 0.675037i −0.0131528 0.0227814i
\(879\) 4.06817 + 7.04629i 0.137216 + 0.237665i
\(880\) 12.7297 22.0485i 0.429118 0.743254i
\(881\) −42.8058 −1.44216 −0.721082 0.692850i \(-0.756355\pi\)
−0.721082 + 0.692850i \(0.756355\pi\)
\(882\) −0.295449 0.456453i −0.00994829 0.0153696i
\(883\) −9.60368 −0.323190 −0.161595 0.986857i \(-0.551664\pi\)
−0.161595 + 0.986857i \(0.551664\pi\)
\(884\) 0.392753 0.680269i 0.0132097 0.0228799i
\(885\) 8.07801 + 13.9915i 0.271539 + 0.470320i
\(886\) 1.30654 + 2.26299i 0.0438939 + 0.0760266i
\(887\) 5.24687 9.08785i 0.176173 0.305140i −0.764394 0.644750i \(-0.776962\pi\)
0.940567 + 0.339610i \(0.110295\pi\)
\(888\) 1.29885 0.0435866
\(889\) 39.5971 1.00709i 1.32805 0.0337768i
\(890\) 1.09550 0.0367211
\(891\) −1.45815 + 2.52558i −0.0488497 + 0.0846102i
\(892\) 6.19016 + 10.7217i 0.207262 + 0.358988i
\(893\) 0.590273 + 1.02238i 0.0197527 + 0.0342127i
\(894\) 0.130032 0.225222i 0.00434892 0.00753255i
\(895\) 48.3001 1.61449
\(896\) 3.11863 5.73352i 0.104186 0.191544i
\(897\) 3.38187 0.112918
\(898\) −0.0472178 + 0.0817837i −0.00157568 + 0.00272916i
\(899\) 1.91312 + 3.31362i 0.0638061 + 0.110515i
\(900\) −0.148867 0.257845i −0.00496223 0.00859483i
\(901\) 2.44910 4.24197i 0.0815914 0.141320i
\(902\) 0.0985343 0.00328083
\(903\) −9.31885 15.2327i −0.310112 0.506912i
\(904\) 1.29100 0.0429380
\(905\) 1.05195 1.82203i 0.0349680 0.0605664i
\(906\) −0.794139 1.37549i −0.0263835 0.0456976i
\(907\) −27.1740 47.0667i −0.902298 1.56283i −0.824504 0.565856i \(-0.808546\pi\)
−0.0777940 0.996969i \(-0.524788\pi\)
\(908\) 23.6165 40.9049i 0.783740 1.35748i
\(909\) −19.9821 −0.662763
\(910\) −0.236203 0.386100i −0.00783006 0.0127991i
\(911\) 29.9548 0.992445 0.496223 0.868195i \(-0.334720\pi\)
0.496223 + 0.868195i \(0.334720\pi\)
\(912\) 0.247247 0.428244i 0.00818715 0.0141806i
\(913\) 14.2724 + 24.7205i 0.472347 + 0.818129i
\(914\) 1.10429 + 1.91268i 0.0365266 + 0.0632659i
\(915\) 2.63624 4.56610i 0.0871514 0.150951i
\(916\) 18.0300 0.595727
\(917\) −23.6937 + 43.5602i −0.782434 + 1.43848i
\(918\) 0.0305996 0.00100994
\(919\) −15.4047 + 26.6817i −0.508153 + 0.880147i 0.491803 + 0.870707i \(0.336338\pi\)
−0.999955 + 0.00943982i \(0.996995\pi\)
\(920\) −1.15536 2.00114i −0.0380910 0.0659756i
\(921\) 9.46237 + 16.3893i 0.311796 + 0.540046i
\(922\) −1.20344 + 2.08442i −0.0396332 + 0.0686467i
\(923\) 14.0826 0.463533
\(924\) 15.3800 0.391167i 0.505966 0.0128685i
\(925\) −0.625147 −0.0205547
\(926\) 0.574768 0.995528i 0.0188881 0.0327151i
\(927\) 7.33724 + 12.7085i 0.240987 + 0.417401i
\(928\) 0.298106 + 0.516335i 0.00978582 + 0.0169495i
\(929\) 9.94398 17.2235i 0.326252 0.565084i −0.655513 0.755184i \(-0.727548\pi\)
0.981765 + 0.190099i \(0.0608810\pi\)
\(930\) 1.01923 0.0334218
\(931\) −0.397621 + 0.777482i −0.0130315 + 0.0254809i
\(932\) −10.6567 −0.349073
\(933\) 5.80947 10.0623i 0.190193 0.329425i
\(934\) 0.0710713 + 0.123099i 0.00232552 + 0.00402793i
\(935\) −1.26513 2.19126i −0.0413741 0.0716620i
\(936\) −0.155116 + 0.268670i −0.00507014 + 0.00878174i
\(937\) −50.6240 −1.65382 −0.826908 0.562338i \(-0.809902\pi\)
−0.826908 + 0.562338i \(0.809902\pi\)
\(938\) 1.26152 0.0320848i 0.0411901 0.00104761i
\(939\) 11.7023 0.381891
\(940\) 20.7791 35.9905i 0.677741 1.17388i
\(941\) −10.5585 18.2878i −0.344197 0.596167i 0.641011 0.767532i \(-0.278515\pi\)
−0.985208 + 0.171365i \(0.945182\pi\)
\(942\) 0.396197 + 0.686234i 0.0129088 + 0.0223587i
\(943\) −0.735531 + 1.27398i −0.0239522 + 0.0414864i
\(944\) −29.0769 −0.946373
\(945\) −2.78429 + 5.11884i −0.0905729 + 0.166516i
\(946\) −1.52889 −0.0497084
\(947\) −16.5481 + 28.6621i −0.537741 + 0.931394i 0.461285 + 0.887252i \(0.347389\pi\)
−0.999025 + 0.0441420i \(0.985945\pi\)
\(948\) 2.36756 + 4.10073i 0.0768947 + 0.133186i
\(949\) −3.77647 6.54105i −0.122590 0.212331i
\(950\) 0.000723449 0.00125305i 2.34718e−5 4.06543e-5i
\(951\) 33.0069 1.07032
\(952\) −0.168741 0.275826i −0.00546893 0.00893956i
\(953\) −3.06989 −0.0994436 −0.0497218 0.998763i \(-0.515833\pi\)
−0.0497218 + 0.998763i \(0.515833\pi\)
\(954\) −0.482901 + 0.836409i −0.0156345 + 0.0270798i
\(955\) 21.6756 + 37.5433i 0.701408 + 1.21487i
\(956\) −27.1726 47.0643i −0.878824 1.52217i
\(957\) −0.936454 + 1.62199i −0.0302713 + 0.0524314i
\(958\) 0.726000 0.0234560
\(959\) 18.7645 + 30.6726i 0.605936 + 0.990469i
\(960\) −17.3013 −0.558397
\(961\) −2.24770 + 3.89314i −0.0725066 + 0.125585i
\(962\) 0.162602 + 0.281635i 0.00524249 + 0.00908027i
\(963\) 2.51986 + 4.36453i 0.0812015 + 0.140645i
\(964\) −15.6288 + 27.0699i −0.503370 + 0.871863i
\(965\) −33.2457 −1.07022
\(966\) 0.332088 0.610535i 0.0106848 0.0196437i
\(967\) 10.0334 0.322651 0.161325 0.986901i \(-0.448423\pi\)
0.161325 + 0.986901i \(0.448423\pi\)
\(968\) −0.387054 + 0.670397i −0.0124404 + 0.0215474i
\(969\) −0.0245723 0.0425605i −0.000789377 0.00136724i
\(970\) 1.27532 + 2.20892i 0.0409481 + 0.0709242i
\(971\) 9.73484 16.8612i 0.312406 0.541103i −0.666477 0.745526i \(-0.732198\pi\)
0.978883 + 0.204423i \(0.0655318\pi\)
\(972\) 1.99397 0.0639565
\(973\) −41.6021 + 1.05808i −1.33370 + 0.0339206i
\(974\) 1.81558 0.0581749
\(975\) 0.0746586 0.129313i 0.00239099 0.00414132i
\(976\) 4.74460 + 8.21788i 0.151871 + 0.263048i
\(977\) −0.934264 1.61819i −0.0298898 0.0517706i 0.850694 0.525662i \(-0.176182\pi\)
−0.880583 + 0.473891i \(0.842849\pi\)
\(978\) 0.605229 1.04829i 0.0193531 0.0335205i
\(979\) −18.6749 −0.596851
\(980\) 30.7012 1.56269i 0.980714 0.0499182i
\(981\) −0.122682 −0.00391694
\(982\) 0.833946 1.44444i 0.0266123 0.0460938i
\(983\) −16.1431 27.9608i −0.514886 0.891810i −0.999851 0.0172756i \(-0.994501\pi\)
0.484964 0.874534i \(-0.338833\pi\)
\(984\) −0.0674732 0.116867i −0.00215097 0.00372558i
\(985\) −12.1489 + 21.0424i −0.387095 + 0.670468i
\(986\) 0.0196517 0.000625839
\(987\) 25.0292 0.636579i 0.796688 0.0202625i
\(988\) 0.248750 0.00791378
\(989\) 11.4127 19.7674i 0.362903 0.628567i
\(990\) 0.249451 + 0.432062i 0.00792808 + 0.0137318i
\(991\) −28.4183 49.2219i −0.902736 1.56358i −0.823928 0.566695i \(-0.808222\pi\)
−0.0788081 0.996890i \(-0.525111\pi\)
\(992\) −2.76549 + 4.78996i −0.0878043 + 0.152082i
\(993\) −14.7746 −0.468858
\(994\) 1.38286 2.54235i 0.0438616 0.0806383i
\(995\) −15.8068 −0.501111
\(996\) 9.75852 16.9022i 0.309210 0.535568i
\(997\) 12.0568 + 20.8830i 0.381843 + 0.661371i 0.991326 0.131428i \(-0.0419563\pi\)
−0.609483 + 0.792799i \(0.708623\pi\)
\(998\) 0.861866 + 1.49280i 0.0272819 + 0.0472536i
\(999\) 2.09335 3.62579i 0.0662307 0.114715i
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 273.2.i.e.79.3 10
3.2 odd 2 819.2.j.g.352.3 10
7.2 even 3 1911.2.a.t.1.3 5
7.4 even 3 inner 273.2.i.e.235.3 yes 10
7.5 odd 6 1911.2.a.u.1.3 5
21.2 odd 6 5733.2.a.bq.1.3 5
21.5 even 6 5733.2.a.bp.1.3 5
21.11 odd 6 819.2.j.g.235.3 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
273.2.i.e.79.3 10 1.1 even 1 trivial
273.2.i.e.235.3 yes 10 7.4 even 3 inner
819.2.j.g.235.3 10 21.11 odd 6
819.2.j.g.352.3 10 3.2 odd 2
1911.2.a.t.1.3 5 7.2 even 3
1911.2.a.u.1.3 5 7.5 odd 6
5733.2.a.bp.1.3 5 21.5 even 6
5733.2.a.bq.1.3 5 21.2 odd 6