Properties

Label 403.2.h.b.222.8
Level $403$
Weight $2$
Character 403.222
Analytic conductor $3.218$
Analytic rank $0$
Dimension $34$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [403,2,Mod(118,403)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(403, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("403.118");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 403 = 13 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 403.h (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: \(3.21797120146\)
Analytic rank: \(0\)
Dimension: \(34\)
Relative dimension: \(17\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 222.8
Character \(\chi\) \(=\) 403.222
Dual form 403.2.h.b.118.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.291491 q^{2} +(-0.965220 + 1.67181i) q^{3} -1.91503 q^{4} +(-0.817652 - 1.41622i) q^{5} +(0.281353 - 0.487317i) q^{6} +(-0.566002 + 0.980344i) q^{7} +1.14120 q^{8} +(-0.363299 - 0.629252i) q^{9} +O(q^{10})\) \(q-0.291491 q^{2} +(-0.965220 + 1.67181i) q^{3} -1.91503 q^{4} +(-0.817652 - 1.41622i) q^{5} +(0.281353 - 0.487317i) q^{6} +(-0.566002 + 0.980344i) q^{7} +1.14120 q^{8} +(-0.363299 - 0.629252i) q^{9} +(0.238338 + 0.412814i) q^{10} +(-1.40676 - 2.43657i) q^{11} +(1.84843 - 3.20157i) q^{12} +(-0.500000 - 0.866025i) q^{13} +(0.164984 - 0.285761i) q^{14} +3.15686 q^{15} +3.49742 q^{16} +(-0.697052 + 1.20733i) q^{17} +(0.105898 + 0.183421i) q^{18} +(4.07645 - 7.06061i) q^{19} +(1.56583 + 2.71210i) q^{20} +(-1.09263 - 1.89249i) q^{21} +(0.410056 + 0.710238i) q^{22} +1.36940 q^{23} +(-1.10151 + 1.90786i) q^{24} +(1.16289 - 2.01418i) q^{25} +(0.145745 + 0.252438i) q^{26} -4.38867 q^{27} +(1.08391 - 1.87739i) q^{28} +8.21183 q^{29} -0.920195 q^{30} +(-0.187632 - 5.56460i) q^{31} -3.30186 q^{32} +5.43131 q^{33} +(0.203184 - 0.351925i) q^{34} +1.85117 q^{35} +(0.695729 + 1.20504i) q^{36} +(0.953286 - 1.65114i) q^{37} +(-1.18825 + 2.05810i) q^{38} +1.93044 q^{39} +(-0.933102 - 1.61618i) q^{40} +(0.861909 + 1.49287i) q^{41} +(0.318492 + 0.551645i) q^{42} +(-0.941995 + 1.63158i) q^{43} +(2.69398 + 4.66612i) q^{44} +(-0.594104 + 1.02902i) q^{45} -0.399167 q^{46} -7.80087 q^{47} +(-3.37578 + 5.84702i) q^{48} +(2.85928 + 4.95242i) q^{49} +(-0.338972 + 0.587116i) q^{50} +(-1.34562 - 2.33068i) q^{51} +(0.957517 + 1.65847i) q^{52} +(-6.20206 - 10.7423i) q^{53} +1.27926 q^{54} +(-2.30047 + 3.98454i) q^{55} +(-0.645919 + 1.11876i) q^{56} +(7.86933 + 13.6301i) q^{57} -2.39367 q^{58} +(-1.48057 + 2.56443i) q^{59} -6.04549 q^{60} +1.73188 q^{61} +(0.0546929 + 1.62203i) q^{62} +0.822511 q^{63} -6.03237 q^{64} +(-0.817652 + 1.41622i) q^{65} -1.58318 q^{66} +(-3.58654 - 6.21208i) q^{67} +(1.33488 - 2.31207i) q^{68} +(-1.32177 + 2.28937i) q^{69} -0.539599 q^{70} +(-4.99209 - 8.64655i) q^{71} +(-0.414595 - 0.718100i) q^{72} +(-7.66699 - 13.2796i) q^{73} +(-0.277874 + 0.481292i) q^{74} +(2.24489 + 3.88826i) q^{75} +(-7.80653 + 13.5213i) q^{76} +3.18490 q^{77} -0.562705 q^{78} +(-4.12374 + 7.14253i) q^{79} +(-2.85967 - 4.95310i) q^{80} +(5.32592 - 9.22477i) q^{81} +(-0.251239 - 0.435158i) q^{82} +(-5.77267 - 9.99856i) q^{83} +(2.09243 + 3.62419i) q^{84} +2.27978 q^{85} +(0.274583 - 0.475591i) q^{86} +(-7.92622 + 13.7286i) q^{87} +(-1.60538 - 2.78061i) q^{88} -5.04840 q^{89} +(0.173176 - 0.299949i) q^{90} +1.13200 q^{91} -2.62244 q^{92} +(9.48406 + 5.05738i) q^{93} +2.27388 q^{94} -13.3325 q^{95} +(3.18702 - 5.52008i) q^{96} +16.6299 q^{97} +(-0.833455 - 1.44359i) q^{98} +(-1.02215 + 1.77041i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 34 q + 6 q^{2} - 2 q^{3} + 34 q^{4} - 5 q^{5} - 2 q^{7} + 36 q^{8} - 23 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 34 q + 6 q^{2} - 2 q^{3} + 34 q^{4} - 5 q^{5} - 2 q^{7} + 36 q^{8} - 23 q^{9} - 7 q^{10} - 5 q^{11} - 28 q^{12} - 17 q^{13} - 7 q^{14} + 8 q^{15} + 18 q^{16} - 8 q^{17} + 6 q^{18} + 3 q^{19} - 8 q^{20} + 13 q^{21} + 12 q^{22} - 14 q^{23} - 6 q^{24} - 26 q^{25} - 3 q^{26} + 28 q^{27} - 7 q^{28} - 18 q^{29} - 60 q^{30} - 9 q^{31} + 58 q^{32} - 14 q^{33} - 15 q^{34} + 50 q^{35} - 49 q^{36} - 6 q^{37} + 2 q^{38} + 4 q^{39} - 29 q^{40} - 5 q^{41} + 8 q^{42} - q^{43} - 22 q^{44} + 13 q^{45} + 34 q^{46} + 16 q^{47} - 49 q^{48} + 3 q^{49} - 35 q^{51} - 17 q^{52} + 30 q^{53} - 2 q^{54} + 21 q^{55} - 7 q^{56} + 34 q^{58} - 9 q^{59} - 38 q^{60} - 28 q^{61} - 62 q^{62} + 88 q^{63} + 56 q^{64} - 5 q^{65} + 140 q^{66} - 31 q^{67} - 39 q^{68} + 5 q^{69} + 56 q^{70} + q^{71} - 32 q^{72} - 10 q^{73} - 39 q^{74} - 2 q^{75} - 16 q^{76} + 76 q^{77} - 23 q^{79} - 22 q^{80} - 29 q^{81} - 10 q^{82} + 3 q^{83} + 52 q^{84} - 32 q^{85} + 4 q^{86} + 18 q^{87} - 10 q^{88} + 26 q^{89} + 35 q^{90} + 4 q^{91} - 94 q^{92} - 41 q^{93} + 70 q^{94} + 28 q^{95} - 23 q^{96} + 32 q^{97} - 38 q^{98} - 70 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/403\mathbb{Z}\right)^\times\).

\(n\) \(249\) \(313\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.291491 −0.206115 −0.103058 0.994675i \(-0.532863\pi\)
−0.103058 + 0.994675i \(0.532863\pi\)
\(3\) −0.965220 + 1.67181i −0.557270 + 0.965220i 0.440453 + 0.897776i \(0.354818\pi\)
−0.997723 + 0.0674442i \(0.978516\pi\)
\(4\) −1.91503 −0.957517
\(5\) −0.817652 1.41622i −0.365665 0.633351i 0.623217 0.782049i \(-0.285825\pi\)
−0.988883 + 0.148698i \(0.952492\pi\)
\(6\) 0.281353 0.487317i 0.114862 0.198946i
\(7\) −0.566002 + 0.980344i −0.213929 + 0.370535i −0.952941 0.303157i \(-0.901959\pi\)
0.739012 + 0.673692i \(0.235293\pi\)
\(8\) 1.14120 0.403474
\(9\) −0.363299 0.629252i −0.121100 0.209751i
\(10\) 0.238338 + 0.412814i 0.0753691 + 0.130543i
\(11\) −1.40676 2.43657i −0.424153 0.734654i 0.572188 0.820122i \(-0.306095\pi\)
−0.996341 + 0.0854682i \(0.972761\pi\)
\(12\) 1.84843 3.20157i 0.533595 0.924214i
\(13\) −0.500000 0.866025i −0.138675 0.240192i
\(14\) 0.164984 0.285761i 0.0440939 0.0763729i
\(15\) 3.15686 0.815097
\(16\) 3.49742 0.874354
\(17\) −0.697052 + 1.20733i −0.169060 + 0.292820i −0.938090 0.346393i \(-0.887406\pi\)
0.769030 + 0.639213i \(0.220740\pi\)
\(18\) 0.105898 + 0.183421i 0.0249605 + 0.0432328i
\(19\) 4.07645 7.06061i 0.935201 1.61982i 0.160925 0.986967i \(-0.448552\pi\)
0.774276 0.632849i \(-0.218114\pi\)
\(20\) 1.56583 + 2.71210i 0.350131 + 0.606444i
\(21\) −1.09263 1.89249i −0.238432 0.412976i
\(22\) 0.410056 + 0.710238i 0.0874243 + 0.151423i
\(23\) 1.36940 0.285539 0.142769 0.989756i \(-0.454399\pi\)
0.142769 + 0.989756i \(0.454399\pi\)
\(24\) −1.10151 + 1.90786i −0.224844 + 0.389441i
\(25\) 1.16289 2.01418i 0.232578 0.402837i
\(26\) 0.145745 + 0.252438i 0.0285830 + 0.0495073i
\(27\) −4.38867 −0.844599
\(28\) 1.08391 1.87739i 0.204840 0.354794i
\(29\) 8.21183 1.52490 0.762449 0.647048i \(-0.223997\pi\)
0.762449 + 0.647048i \(0.223997\pi\)
\(30\) −0.920195 −0.168004
\(31\) −0.187632 5.56460i −0.0336997 0.999432i
\(32\) −3.30186 −0.583691
\(33\) 5.43131 0.945470
\(34\) 0.203184 0.351925i 0.0348458 0.0603547i
\(35\) 1.85117 0.312905
\(36\) 0.695729 + 1.20504i 0.115955 + 0.200840i
\(37\) 0.953286 1.65114i 0.156719 0.271446i −0.776964 0.629544i \(-0.783242\pi\)
0.933684 + 0.358099i \(0.116575\pi\)
\(38\) −1.18825 + 2.05810i −0.192759 + 0.333868i
\(39\) 1.93044 0.309118
\(40\) −0.933102 1.61618i −0.147536 0.255540i
\(41\) 0.861909 + 1.49287i 0.134608 + 0.233147i 0.925447 0.378876i \(-0.123689\pi\)
−0.790840 + 0.612023i \(0.790356\pi\)
\(42\) 0.318492 + 0.551645i 0.0491444 + 0.0851207i
\(43\) −0.941995 + 1.63158i −0.143653 + 0.248814i −0.928870 0.370407i \(-0.879218\pi\)
0.785217 + 0.619221i \(0.212552\pi\)
\(44\) 2.69398 + 4.66612i 0.406133 + 0.703444i
\(45\) −0.594104 + 1.02902i −0.0885638 + 0.153397i
\(46\) −0.399167 −0.0588539
\(47\) −7.80087 −1.13787 −0.568937 0.822381i \(-0.692645\pi\)
−0.568937 + 0.822381i \(0.692645\pi\)
\(48\) −3.37578 + 5.84702i −0.487251 + 0.843944i
\(49\) 2.85928 + 4.95242i 0.408469 + 0.707489i
\(50\) −0.338972 + 0.587116i −0.0479378 + 0.0830307i
\(51\) −1.34562 2.33068i −0.188424 0.326360i
\(52\) 0.957517 + 1.65847i 0.132784 + 0.229988i
\(53\) −6.20206 10.7423i −0.851918 1.47557i −0.879475 0.475946i \(-0.842106\pi\)
0.0275564 0.999620i \(-0.491227\pi\)
\(54\) 1.27926 0.174085
\(55\) −2.30047 + 3.98454i −0.310196 + 0.537275i
\(56\) −0.645919 + 1.11876i −0.0863146 + 0.149501i
\(57\) 7.86933 + 13.6301i 1.04232 + 1.80535i
\(58\) −2.39367 −0.314305
\(59\) −1.48057 + 2.56443i −0.192754 + 0.333860i −0.946162 0.323693i \(-0.895075\pi\)
0.753408 + 0.657554i \(0.228409\pi\)
\(60\) −6.04549 −0.780469
\(61\) 1.73188 0.221744 0.110872 0.993835i \(-0.464636\pi\)
0.110872 + 0.993835i \(0.464636\pi\)
\(62\) 0.0546929 + 1.62203i 0.00694601 + 0.205998i
\(63\) 0.822511 0.103627
\(64\) −6.03237 −0.754047
\(65\) −0.817652 + 1.41622i −0.101417 + 0.175660i
\(66\) −1.58318 −0.194876
\(67\) −3.58654 6.21208i −0.438166 0.758926i 0.559382 0.828910i \(-0.311038\pi\)
−0.997548 + 0.0699841i \(0.977705\pi\)
\(68\) 1.33488 2.31207i 0.161878 0.280380i
\(69\) −1.32177 + 2.28937i −0.159122 + 0.275608i
\(70\) −0.539599 −0.0644945
\(71\) −4.99209 8.64655i −0.592452 1.02616i −0.993901 0.110275i \(-0.964827\pi\)
0.401449 0.915881i \(-0.368507\pi\)
\(72\) −0.414595 0.718100i −0.0488605 0.0846289i
\(73\) −7.66699 13.2796i −0.897353 1.55426i −0.830865 0.556475i \(-0.812154\pi\)
−0.0664887 0.997787i \(-0.521180\pi\)
\(74\) −0.277874 + 0.481292i −0.0323022 + 0.0559491i
\(75\) 2.24489 + 3.88826i 0.259217 + 0.448978i
\(76\) −7.80653 + 13.5213i −0.895470 + 1.55100i
\(77\) 3.18490 0.362954
\(78\) −0.562705 −0.0637138
\(79\) −4.12374 + 7.14253i −0.463957 + 0.803597i −0.999154 0.0411302i \(-0.986904\pi\)
0.535197 + 0.844727i \(0.320238\pi\)
\(80\) −2.85967 4.95310i −0.319721 0.553773i
\(81\) 5.32592 9.22477i 0.591769 1.02497i
\(82\) −0.251239 0.435158i −0.0277447 0.0480551i
\(83\) −5.77267 9.99856i −0.633633 1.09748i −0.986803 0.161925i \(-0.948230\pi\)
0.353170 0.935559i \(-0.385104\pi\)
\(84\) 2.09243 + 3.62419i 0.228303 + 0.395432i
\(85\) 2.27978 0.247277
\(86\) 0.274583 0.475591i 0.0296090 0.0512843i
\(87\) −7.92622 + 13.7286i −0.849780 + 1.47186i
\(88\) −1.60538 2.78061i −0.171135 0.296414i
\(89\) −5.04840 −0.535129 −0.267564 0.963540i \(-0.586219\pi\)
−0.267564 + 0.963540i \(0.586219\pi\)
\(90\) 0.173176 0.299949i 0.0182543 0.0316175i
\(91\) 1.13200 0.118666
\(92\) −2.62244 −0.273408
\(93\) 9.48406 + 5.05738i 0.983451 + 0.524426i
\(94\) 2.27388 0.234533
\(95\) −13.3325 −1.36788
\(96\) 3.18702 5.52008i 0.325274 0.563391i
\(97\) 16.6299 1.68851 0.844256 0.535940i \(-0.180043\pi\)
0.844256 + 0.535940i \(0.180043\pi\)
\(98\) −0.833455 1.44359i −0.0841917 0.145824i
\(99\) −1.02215 + 1.77041i −0.102729 + 0.177933i
\(100\) −2.22697 + 3.85723i −0.222697 + 0.385723i
\(101\) 3.81091 0.379200 0.189600 0.981861i \(-0.439281\pi\)
0.189600 + 0.981861i \(0.439281\pi\)
\(102\) 0.392235 + 0.679371i 0.0388370 + 0.0672677i
\(103\) 6.39130 + 11.0701i 0.629754 + 1.09077i 0.987601 + 0.156985i \(0.0501776\pi\)
−0.357847 + 0.933780i \(0.616489\pi\)
\(104\) −0.570598 0.988305i −0.0559517 0.0969113i
\(105\) −1.78679 + 3.09481i −0.174373 + 0.302022i
\(106\) 1.80784 + 3.13128i 0.175593 + 0.304136i
\(107\) −7.41980 + 12.8515i −0.717299 + 1.24240i 0.244767 + 0.969582i \(0.421288\pi\)
−0.962066 + 0.272816i \(0.912045\pi\)
\(108\) 8.40444 0.808718
\(109\) 20.1470 1.92974 0.964868 0.262736i \(-0.0846249\pi\)
0.964868 + 0.262736i \(0.0846249\pi\)
\(110\) 0.670567 1.16146i 0.0639361 0.110741i
\(111\) 1.84026 + 3.18743i 0.174670 + 0.302537i
\(112\) −1.97954 + 3.42867i −0.187049 + 0.323979i
\(113\) 0.857716 + 1.48561i 0.0806871 + 0.139754i 0.903545 0.428493i \(-0.140955\pi\)
−0.822858 + 0.568247i \(0.807622\pi\)
\(114\) −2.29384 3.97304i −0.214838 0.372110i
\(115\) −1.11969 1.93936i −0.104412 0.180846i
\(116\) −15.7259 −1.46012
\(117\) −0.363299 + 0.629252i −0.0335870 + 0.0581744i
\(118\) 0.431574 0.747508i 0.0397296 0.0688137i
\(119\) −0.789065 1.36670i −0.0723335 0.125285i
\(120\) 3.60259 0.328870
\(121\) 1.54208 2.67096i 0.140189 0.242814i
\(122\) −0.504827 −0.0457049
\(123\) −3.32773 −0.300051
\(124\) 0.359321 + 10.6564i 0.0322680 + 0.956973i
\(125\) −11.9799 −1.07151
\(126\) −0.239754 −0.0213590
\(127\) 2.27960 3.94838i 0.202282 0.350362i −0.746982 0.664845i \(-0.768498\pi\)
0.949263 + 0.314483i \(0.101831\pi\)
\(128\) 8.36210 0.739112
\(129\) −1.81846 3.14967i −0.160107 0.277313i
\(130\) 0.238338 0.412814i 0.0209036 0.0362062i
\(131\) 8.92638 15.4609i 0.779902 1.35083i −0.152096 0.988366i \(-0.548602\pi\)
0.931998 0.362463i \(-0.118064\pi\)
\(132\) −10.4011 −0.905304
\(133\) 4.61455 + 7.99264i 0.400132 + 0.693050i
\(134\) 1.04544 + 1.81076i 0.0903127 + 0.156426i
\(135\) 3.58840 + 6.21530i 0.308841 + 0.534928i
\(136\) −0.795473 + 1.37780i −0.0682112 + 0.118145i
\(137\) 6.63925 + 11.4995i 0.567230 + 0.982470i 0.996838 + 0.0794554i \(0.0253181\pi\)
−0.429609 + 0.903015i \(0.641349\pi\)
\(138\) 0.385283 0.667331i 0.0327975 0.0568069i
\(139\) 8.44477 0.716276 0.358138 0.933669i \(-0.383412\pi\)
0.358138 + 0.933669i \(0.383412\pi\)
\(140\) −3.54505 −0.299612
\(141\) 7.52955 13.0416i 0.634103 1.09830i
\(142\) 1.45515 + 2.52039i 0.122113 + 0.211506i
\(143\) −1.40676 + 2.43657i −0.117639 + 0.203756i
\(144\) −1.27061 2.20076i −0.105884 0.183396i
\(145\) −6.71442 11.6297i −0.557602 0.965796i
\(146\) 2.23486 + 3.87089i 0.184958 + 0.320357i
\(147\) −11.0394 −0.910510
\(148\) −1.82557 + 3.16199i −0.150061 + 0.259914i
\(149\) −1.70525 + 2.95359i −0.139700 + 0.241967i −0.927383 0.374113i \(-0.877947\pi\)
0.787683 + 0.616081i \(0.211280\pi\)
\(150\) −0.654364 1.13339i −0.0534286 0.0925411i
\(151\) 1.41358 0.115035 0.0575177 0.998344i \(-0.481681\pi\)
0.0575177 + 0.998344i \(0.481681\pi\)
\(152\) 4.65202 8.05754i 0.377329 0.653553i
\(153\) 1.01295 0.0818923
\(154\) −0.928371 −0.0748102
\(155\) −7.72726 + 4.81564i −0.620668 + 0.386801i
\(156\) −3.69686 −0.295985
\(157\) −5.16030 −0.411837 −0.205919 0.978569i \(-0.566018\pi\)
−0.205919 + 0.978569i \(0.566018\pi\)
\(158\) 1.20203 2.08198i 0.0956286 0.165634i
\(159\) 23.9454 1.89899
\(160\) 2.69977 + 4.67614i 0.213436 + 0.369681i
\(161\) −0.775081 + 1.34248i −0.0610849 + 0.105802i
\(162\) −1.55246 + 2.68894i −0.121973 + 0.211263i
\(163\) 6.88608 0.539359 0.269680 0.962950i \(-0.413082\pi\)
0.269680 + 0.962950i \(0.413082\pi\)
\(164\) −1.65058 2.85890i −0.128889 0.223242i
\(165\) −4.44093 7.69191i −0.345726 0.598814i
\(166\) 1.68268 + 2.91449i 0.130601 + 0.226208i
\(167\) 1.02734 1.77941i 0.0794981 0.137695i −0.823535 0.567265i \(-0.808002\pi\)
0.903034 + 0.429570i \(0.141335\pi\)
\(168\) −1.24691 2.15971i −0.0962010 0.166625i
\(169\) −0.500000 + 0.866025i −0.0384615 + 0.0666173i
\(170\) −0.664536 −0.0509676
\(171\) −5.92387 −0.453010
\(172\) 1.80395 3.12454i 0.137550 0.238244i
\(173\) −2.86601 4.96407i −0.217898 0.377411i 0.736267 0.676691i \(-0.236587\pi\)
−0.954165 + 0.299280i \(0.903254\pi\)
\(174\) 2.31042 4.00177i 0.175153 0.303373i
\(175\) 1.31639 + 2.28006i 0.0995101 + 0.172357i
\(176\) −4.92001 8.52171i −0.370860 0.642348i
\(177\) −2.85816 4.95048i −0.214832 0.372101i
\(178\) 1.47156 0.110298
\(179\) −6.99568 + 12.1169i −0.522881 + 0.905657i 0.476764 + 0.879031i \(0.341810\pi\)
−0.999645 + 0.0266259i \(0.991524\pi\)
\(180\) 1.13773 1.97060i 0.0848013 0.146880i
\(181\) −2.67739 4.63737i −0.199009 0.344693i 0.749199 0.662345i \(-0.230439\pi\)
−0.948207 + 0.317652i \(0.897105\pi\)
\(182\) −0.329969 −0.0244589
\(183\) −1.67164 + 2.89537i −0.123572 + 0.214032i
\(184\) 1.56275 0.115207
\(185\) −3.11783 −0.229227
\(186\) −2.76452 1.47418i −0.202704 0.108092i
\(187\) 3.92233 0.286829
\(188\) 14.9389 1.08953
\(189\) 2.48399 4.30240i 0.180684 0.312954i
\(190\) 3.88629 0.281941
\(191\) −10.5506 18.2741i −0.763413 1.32227i −0.941082 0.338179i \(-0.890189\pi\)
0.177669 0.984090i \(-0.443144\pi\)
\(192\) 5.82257 10.0850i 0.420208 0.727821i
\(193\) 0.865511 1.49911i 0.0623008 0.107908i −0.833193 0.552983i \(-0.813490\pi\)
0.895493 + 0.445075i \(0.146823\pi\)
\(194\) −4.84747 −0.348028
\(195\) −1.57843 2.73392i −0.113034 0.195780i
\(196\) −5.47562 9.48406i −0.391116 0.677433i
\(197\) 0.647895 + 1.12219i 0.0461606 + 0.0799526i 0.888183 0.459491i \(-0.151968\pi\)
−0.842022 + 0.539443i \(0.818635\pi\)
\(198\) 0.297946 0.516057i 0.0211741 0.0366746i
\(199\) −11.5919 20.0777i −0.821727 1.42327i −0.904395 0.426696i \(-0.859677\pi\)
0.0826678 0.996577i \(-0.473656\pi\)
\(200\) 1.32708 2.29858i 0.0938391 0.162534i
\(201\) 13.8472 0.976707
\(202\) −1.11085 −0.0781588
\(203\) −4.64791 + 8.05042i −0.326219 + 0.565029i
\(204\) 2.57690 + 4.46332i 0.180419 + 0.312495i
\(205\) 1.40948 2.44130i 0.0984426 0.170508i
\(206\) −1.86301 3.22682i −0.129802 0.224823i
\(207\) −0.497500 0.861695i −0.0345786 0.0598920i
\(208\) −1.74871 3.02885i −0.121251 0.210013i
\(209\) −22.9383 −1.58667
\(210\) 0.520832 0.902107i 0.0359408 0.0622513i
\(211\) 6.96634 12.0660i 0.479582 0.830661i −0.520143 0.854079i \(-0.674122\pi\)
0.999726 + 0.0234180i \(0.00745486\pi\)
\(212\) 11.8771 + 20.5718i 0.815726 + 1.41288i
\(213\) 19.2738 1.32062
\(214\) 2.16280 3.74608i 0.147846 0.256077i
\(215\) 3.08090 0.210115
\(216\) −5.00833 −0.340774
\(217\) 5.56142 + 2.96563i 0.377534 + 0.201320i
\(218\) −5.87267 −0.397748
\(219\) 29.6013 2.00027
\(220\) 4.40548 7.63052i 0.297018 0.514450i
\(221\) 1.39410 0.0937775
\(222\) −0.536419 0.929105i −0.0360021 0.0623575i
\(223\) −6.55288 + 11.3499i −0.438814 + 0.760047i −0.997598 0.0692654i \(-0.977934\pi\)
0.558785 + 0.829313i \(0.311268\pi\)
\(224\) 1.86886 3.23696i 0.124868 0.216278i
\(225\) −1.68990 −0.112660
\(226\) −0.250016 0.433041i −0.0166308 0.0288055i
\(227\) 5.22178 + 9.04438i 0.346582 + 0.600297i 0.985640 0.168861i \(-0.0540091\pi\)
−0.639058 + 0.769158i \(0.720676\pi\)
\(228\) −15.0700 26.1021i −0.998037 1.72865i
\(229\) 1.11825 1.93687i 0.0738962 0.127992i −0.826710 0.562629i \(-0.809790\pi\)
0.900606 + 0.434637i \(0.143123\pi\)
\(230\) 0.326379 + 0.565306i 0.0215208 + 0.0372752i
\(231\) −3.07413 + 5.32456i −0.202263 + 0.350330i
\(232\) 9.37131 0.615257
\(233\) −15.5098 −1.01608 −0.508042 0.861333i \(-0.669630\pi\)
−0.508042 + 0.861333i \(0.669630\pi\)
\(234\) 0.105898 0.183421i 0.00692279 0.0119906i
\(235\) 6.37840 + 11.0477i 0.416081 + 0.720673i
\(236\) 2.83535 4.91097i 0.184565 0.319677i
\(237\) −7.96063 13.7882i −0.517099 0.895641i
\(238\) 0.230005 + 0.398381i 0.0149090 + 0.0258232i
\(239\) 5.42011 + 9.38790i 0.350598 + 0.607253i 0.986354 0.164637i \(-0.0526452\pi\)
−0.635757 + 0.771889i \(0.719312\pi\)
\(240\) 11.0408 0.712684
\(241\) −5.11607 + 8.86129i −0.329555 + 0.570806i −0.982424 0.186665i \(-0.940232\pi\)
0.652869 + 0.757471i \(0.273565\pi\)
\(242\) −0.449501 + 0.778559i −0.0288950 + 0.0500477i
\(243\) 3.69838 + 6.40578i 0.237251 + 0.410931i
\(244\) −3.31661 −0.212324
\(245\) 4.67580 8.09872i 0.298726 0.517408i
\(246\) 0.970002 0.0618450
\(247\) −8.15289 −0.518756
\(248\) −0.214125 6.35030i −0.0135969 0.403245i
\(249\) 22.2876 1.41242
\(250\) 3.49203 0.220855
\(251\) 6.99814 12.1211i 0.441719 0.765079i −0.556098 0.831116i \(-0.687702\pi\)
0.997817 + 0.0660372i \(0.0210356\pi\)
\(252\) −1.57514 −0.0992242
\(253\) −1.92641 3.33663i −0.121112 0.209772i
\(254\) −0.664482 + 1.15092i −0.0416933 + 0.0722149i
\(255\) −2.20049 + 3.81137i −0.137800 + 0.238677i
\(256\) 9.62727 0.601705
\(257\) 8.94601 + 15.4949i 0.558037 + 0.966548i 0.997660 + 0.0683661i \(0.0217786\pi\)
−0.439623 + 0.898182i \(0.644888\pi\)
\(258\) 0.530066 + 0.918101i 0.0330004 + 0.0571585i
\(259\) 1.07912 + 1.86910i 0.0670534 + 0.116140i
\(260\) 1.56583 2.71210i 0.0971087 0.168197i
\(261\) −2.98335 5.16731i −0.184665 0.319848i
\(262\) −2.60196 + 4.50672i −0.160750 + 0.278426i
\(263\) 0.564628 0.0348164 0.0174082 0.999848i \(-0.494459\pi\)
0.0174082 + 0.999848i \(0.494459\pi\)
\(264\) 6.19820 0.381473
\(265\) −10.1423 + 17.5669i −0.623034 + 1.07913i
\(266\) −1.34510 2.32978i −0.0824733 0.142848i
\(267\) 4.87281 8.43996i 0.298211 0.516517i
\(268\) 6.86835 + 11.8963i 0.419551 + 0.726684i
\(269\) −14.7514 25.5501i −0.899407 1.55782i −0.828253 0.560354i \(-0.810665\pi\)
−0.0711543 0.997465i \(-0.522668\pi\)
\(270\) −1.04599 1.81170i −0.0636567 0.110257i
\(271\) −4.38634 −0.266451 −0.133225 0.991086i \(-0.542533\pi\)
−0.133225 + 0.991086i \(0.542533\pi\)
\(272\) −2.43788 + 4.22253i −0.147818 + 0.256029i
\(273\) −1.09263 + 1.89249i −0.0661291 + 0.114539i
\(274\) −1.93528 3.35201i −0.116915 0.202502i
\(275\) −6.54360 −0.394594
\(276\) 2.53123 4.38422i 0.152362 0.263899i
\(277\) −11.7770 −0.707614 −0.353807 0.935318i \(-0.615113\pi\)
−0.353807 + 0.935318i \(0.615113\pi\)
\(278\) −2.46157 −0.147635
\(279\) −3.43337 + 2.13968i −0.205550 + 0.128099i
\(280\) 2.11255 0.126249
\(281\) −6.50230 −0.387895 −0.193947 0.981012i \(-0.562129\pi\)
−0.193947 + 0.981012i \(0.562129\pi\)
\(282\) −2.19480 + 3.80150i −0.130698 + 0.226376i
\(283\) −1.49693 −0.0889833 −0.0444917 0.999010i \(-0.514167\pi\)
−0.0444917 + 0.999010i \(0.514167\pi\)
\(284\) 9.56001 + 16.5584i 0.567282 + 0.982562i
\(285\) 12.8688 22.2893i 0.762279 1.32031i
\(286\) 0.410056 0.710238i 0.0242471 0.0419973i
\(287\) −1.95137 −0.115186
\(288\) 1.19956 + 2.07770i 0.0706848 + 0.122430i
\(289\) 7.52824 + 13.0393i 0.442838 + 0.767017i
\(290\) 1.95719 + 3.38996i 0.114930 + 0.199065i
\(291\) −16.0515 + 27.8020i −0.940957 + 1.62978i
\(292\) 14.6825 + 25.4309i 0.859231 + 1.48823i
\(293\) 1.44000 2.49415i 0.0841257 0.145710i −0.820893 0.571083i \(-0.806524\pi\)
0.905018 + 0.425373i \(0.139857\pi\)
\(294\) 3.21787 0.187670
\(295\) 4.84238 0.281934
\(296\) 1.08789 1.88427i 0.0632321 0.109521i
\(297\) 6.17378 + 10.6933i 0.358239 + 0.620488i
\(298\) 0.497066 0.860943i 0.0287943 0.0498731i
\(299\) −0.684698 1.18593i −0.0395971 0.0685842i
\(300\) −4.29903 7.44615i −0.248205 0.429903i
\(301\) −1.06634 1.84696i −0.0614629 0.106457i
\(302\) −0.412046 −0.0237106
\(303\) −3.67837 + 6.37112i −0.211317 + 0.366011i
\(304\) 14.2570 24.6939i 0.817697 1.41629i
\(305\) −1.41608 2.45272i −0.0810843 0.140442i
\(306\) −0.295266 −0.0168792
\(307\) −6.37233 + 11.0372i −0.363688 + 0.629926i −0.988565 0.150798i \(-0.951816\pi\)
0.624877 + 0.780723i \(0.285149\pi\)
\(308\) −6.09920 −0.347534
\(309\) −24.6761 −1.40377
\(310\) 2.25242 1.40371i 0.127929 0.0797256i
\(311\) −18.6991 −1.06033 −0.530165 0.847894i \(-0.677870\pi\)
−0.530165 + 0.847894i \(0.677870\pi\)
\(312\) 2.20301 0.124721
\(313\) −9.16560 + 15.8753i −0.518070 + 0.897324i 0.481709 + 0.876331i \(0.340016\pi\)
−0.999780 + 0.0209930i \(0.993317\pi\)
\(314\) 1.50418 0.0848859
\(315\) −0.672528 1.16485i −0.0378927 0.0656320i
\(316\) 7.89710 13.6782i 0.444247 0.769458i
\(317\) 13.8682 24.0204i 0.778915 1.34912i −0.153653 0.988125i \(-0.549104\pi\)
0.932568 0.360995i \(-0.117563\pi\)
\(318\) −6.97987 −0.391411
\(319\) −11.5520 20.0087i −0.646790 1.12027i
\(320\) 4.93239 + 8.54314i 0.275729 + 0.477576i
\(321\) −14.3235 24.8090i −0.799458 1.38470i
\(322\) 0.225929 0.391320i 0.0125905 0.0218074i
\(323\) 5.68299 + 9.84322i 0.316210 + 0.547692i
\(324\) −10.1993 + 17.6657i −0.566629 + 0.981430i
\(325\) −2.32578 −0.129011
\(326\) −2.00723 −0.111170
\(327\) −19.4463 + 33.6820i −1.07538 + 1.86262i
\(328\) 0.983607 + 1.70366i 0.0543106 + 0.0940688i
\(329\) 4.41530 7.64753i 0.243424 0.421622i
\(330\) 1.29449 + 2.24212i 0.0712593 + 0.123425i
\(331\) 10.5308 + 18.2399i 0.578826 + 1.00256i 0.995614 + 0.0935523i \(0.0298222\pi\)
−0.416789 + 0.909003i \(0.636844\pi\)
\(332\) 11.0549 + 19.1476i 0.606714 + 1.05086i
\(333\) −1.38531 −0.0759145
\(334\) −0.299461 + 0.518681i −0.0163858 + 0.0283810i
\(335\) −5.86509 + 10.1586i −0.320444 + 0.555026i
\(336\) −3.82139 6.61885i −0.208474 0.361088i
\(337\) 11.1487 0.607310 0.303655 0.952782i \(-0.401793\pi\)
0.303655 + 0.952782i \(0.401793\pi\)
\(338\) 0.145745 0.252438i 0.00792751 0.0137308i
\(339\) −3.31154 −0.179858
\(340\) −4.36586 −0.236772
\(341\) −13.2946 + 8.28521i −0.719943 + 0.448669i
\(342\) 1.72675 0.0933722
\(343\) −14.3975 −0.777390
\(344\) −1.07500 + 1.86196i −0.0579602 + 0.100390i
\(345\) 4.32299 0.232742
\(346\) 0.835415 + 1.44698i 0.0449122 + 0.0777902i
\(347\) −13.7745 + 23.8581i −0.739452 + 1.28077i 0.213290 + 0.976989i \(0.431582\pi\)
−0.952742 + 0.303780i \(0.901751\pi\)
\(348\) 15.1790 26.2908i 0.813678 1.40933i
\(349\) 22.8087 1.22092 0.610461 0.792046i \(-0.290984\pi\)
0.610461 + 0.792046i \(0.290984\pi\)
\(350\) −0.383717 0.664617i −0.0205105 0.0355253i
\(351\) 2.19433 + 3.80070i 0.117125 + 0.202866i
\(352\) 4.64491 + 8.04521i 0.247574 + 0.428811i
\(353\) 6.68667 11.5816i 0.355895 0.616429i −0.631375 0.775477i \(-0.717509\pi\)
0.987271 + 0.159048i \(0.0508426\pi\)
\(354\) 0.833127 + 1.44302i 0.0442802 + 0.0766956i
\(355\) −8.16358 + 14.1397i −0.433278 + 0.750459i
\(356\) 9.66785 0.512395
\(357\) 3.04649 0.161237
\(358\) 2.03918 3.53196i 0.107774 0.186670i
\(359\) −0.858901 1.48766i −0.0453311 0.0785157i 0.842470 0.538744i \(-0.181101\pi\)
−0.887801 + 0.460228i \(0.847768\pi\)
\(360\) −0.677989 + 1.17431i −0.0357332 + 0.0618917i
\(361\) −23.7348 41.1099i −1.24920 2.16368i
\(362\) 0.780433 + 1.35175i 0.0410187 + 0.0710464i
\(363\) 2.97689 + 5.15612i 0.156246 + 0.270626i
\(364\) −2.16782 −0.113625
\(365\) −12.5379 + 21.7162i −0.656262 + 1.13668i
\(366\) 0.487269 0.843975i 0.0254700 0.0441153i
\(367\) −1.41209 2.44580i −0.0737102 0.127670i 0.826814 0.562475i \(-0.190151\pi\)
−0.900525 + 0.434805i \(0.856817\pi\)
\(368\) 4.78935 0.249662
\(369\) 0.626261 1.08472i 0.0326018 0.0564680i
\(370\) 0.908818 0.0472472
\(371\) 14.0415 0.728999
\(372\) −18.1623 9.68505i −0.941671 0.502146i
\(373\) 31.7562 1.64427 0.822137 0.569289i \(-0.192782\pi\)
0.822137 + 0.569289i \(0.192782\pi\)
\(374\) −1.14332 −0.0591198
\(375\) 11.5632 20.0281i 0.597122 1.03425i
\(376\) −8.90232 −0.459102
\(377\) −4.10591 7.11165i −0.211465 0.366269i
\(378\) −0.724061 + 1.25411i −0.0372417 + 0.0645045i
\(379\) −4.14593 + 7.18096i −0.212962 + 0.368861i −0.952640 0.304100i \(-0.901644\pi\)
0.739678 + 0.672961i \(0.234978\pi\)
\(380\) 25.5321 1.30977
\(381\) 4.40063 + 7.62211i 0.225451 + 0.390492i
\(382\) 3.07540 + 5.32674i 0.157351 + 0.272540i
\(383\) −11.5934 20.0803i −0.592393 1.02605i −0.993909 0.110202i \(-0.964850\pi\)
0.401517 0.915852i \(-0.368483\pi\)
\(384\) −8.07126 + 13.9798i −0.411885 + 0.713406i
\(385\) −2.60415 4.51051i −0.132720 0.229877i
\(386\) −0.252288 + 0.436976i −0.0128411 + 0.0222415i
\(387\) 1.36890 0.0695852
\(388\) −31.8468 −1.61678
\(389\) −7.24532 + 12.5493i −0.367352 + 0.636273i −0.989151 0.146904i \(-0.953069\pi\)
0.621798 + 0.783177i \(0.286402\pi\)
\(390\) 0.460097 + 0.796912i 0.0232979 + 0.0403532i
\(391\) −0.954540 + 1.65331i −0.0482732 + 0.0836116i
\(392\) 3.26300 + 5.65169i 0.164807 + 0.285453i
\(393\) 17.2318 + 29.8464i 0.869231 + 1.50555i
\(394\) −0.188856 0.327107i −0.00951441 0.0164794i
\(395\) 13.4871 0.678612
\(396\) 1.95744 3.39039i 0.0983652 0.170373i
\(397\) 4.25232 7.36523i 0.213418 0.369650i −0.739364 0.673306i \(-0.764874\pi\)
0.952782 + 0.303655i \(0.0982072\pi\)
\(398\) 3.37893 + 5.85248i 0.169370 + 0.293358i
\(399\) −17.8162 −0.891927
\(400\) 4.06711 7.04444i 0.203355 0.352222i
\(401\) −22.7771 −1.13743 −0.568717 0.822533i \(-0.692560\pi\)
−0.568717 + 0.822533i \(0.692560\pi\)
\(402\) −4.03634 −0.201314
\(403\) −4.72527 + 2.94479i −0.235383 + 0.146691i
\(404\) −7.29802 −0.363090
\(405\) −17.4190 −0.865558
\(406\) 1.35482 2.34662i 0.0672387 0.116461i
\(407\) −5.36416 −0.265892
\(408\) −1.53561 2.65976i −0.0760241 0.131678i
\(409\) −11.3608 + 19.6775i −0.561755 + 0.972988i 0.435588 + 0.900146i \(0.356540\pi\)
−0.997343 + 0.0728423i \(0.976793\pi\)
\(410\) −0.410852 + 0.711616i −0.0202905 + 0.0351442i
\(411\) −25.6334 −1.26440
\(412\) −12.2396 21.1995i −0.603000 1.04443i
\(413\) −1.67602 2.90294i −0.0824713 0.142845i
\(414\) 0.145017 + 0.251176i 0.00712718 + 0.0123446i
\(415\) −9.44007 + 16.3507i −0.463395 + 0.802624i
\(416\) 1.65093 + 2.85949i 0.0809434 + 0.140198i
\(417\) −8.15106 + 14.1181i −0.399159 + 0.691364i
\(418\) 6.68629 0.327037
\(419\) 4.98063 0.243320 0.121660 0.992572i \(-0.461178\pi\)
0.121660 + 0.992572i \(0.461178\pi\)
\(420\) 3.42176 5.92666i 0.166965 0.289191i
\(421\) 11.2882 + 19.5518i 0.550154 + 0.952894i 0.998263 + 0.0589155i \(0.0187642\pi\)
−0.448109 + 0.893979i \(0.647902\pi\)
\(422\) −2.03062 + 3.51714i −0.0988492 + 0.171212i
\(423\) 2.83405 + 4.90871i 0.137796 + 0.238670i
\(424\) −7.07777 12.2591i −0.343727 0.595352i
\(425\) 1.62119 + 2.80798i 0.0786392 + 0.136207i
\(426\) −5.61815 −0.272200
\(427\) −0.980247 + 1.69784i −0.0474375 + 0.0821641i
\(428\) 14.2092 24.6110i 0.686826 1.18962i
\(429\) −2.71566 4.70366i −0.131113 0.227095i
\(430\) −0.898053 −0.0433080
\(431\) −6.94935 + 12.0366i −0.334739 + 0.579784i −0.983435 0.181263i \(-0.941981\pi\)
0.648696 + 0.761048i \(0.275315\pi\)
\(432\) −15.3490 −0.738479
\(433\) −13.2479 −0.636656 −0.318328 0.947981i \(-0.603121\pi\)
−0.318328 + 0.947981i \(0.603121\pi\)
\(434\) −1.62110 0.864454i −0.0778155 0.0414951i
\(435\) 25.9236 1.24294
\(436\) −38.5822 −1.84775
\(437\) 5.58227 9.66878i 0.267036 0.462520i
\(438\) −8.62852 −0.412286
\(439\) −8.77562 15.1998i −0.418837 0.725448i 0.576985 0.816755i \(-0.304229\pi\)
−0.995823 + 0.0913067i \(0.970896\pi\)
\(440\) −2.62529 + 4.54714i −0.125156 + 0.216776i
\(441\) 2.07755 3.59842i 0.0989309 0.171353i
\(442\) −0.406368 −0.0193290
\(443\) 11.0743 + 19.1812i 0.526156 + 0.911329i 0.999536 + 0.0304702i \(0.00970047\pi\)
−0.473380 + 0.880858i \(0.656966\pi\)
\(444\) −3.52416 6.10402i −0.167249 0.289684i
\(445\) 4.12783 + 7.14962i 0.195678 + 0.338924i
\(446\) 1.91011 3.30840i 0.0904461 0.156657i
\(447\) −3.29189 5.70172i −0.155701 0.269682i
\(448\) 3.41434 5.91380i 0.161312 0.279401i
\(449\) −10.6095 −0.500692 −0.250346 0.968156i \(-0.580544\pi\)
−0.250346 + 0.968156i \(0.580544\pi\)
\(450\) 0.492592 0.0232210
\(451\) 2.42499 4.20021i 0.114188 0.197780i
\(452\) −1.64255 2.84499i −0.0772593 0.133817i
\(453\) −1.36442 + 2.36324i −0.0641058 + 0.111035i
\(454\) −1.52210 2.63636i −0.0714357 0.123730i
\(455\) −0.925585 1.60316i −0.0433921 0.0751573i
\(456\) 8.98045 + 15.5546i 0.420548 + 0.728411i
\(457\) 18.9407 0.886010 0.443005 0.896519i \(-0.353912\pi\)
0.443005 + 0.896519i \(0.353912\pi\)
\(458\) −0.325960 + 0.564580i −0.0152311 + 0.0263811i
\(459\) 3.05913 5.29856i 0.142788 0.247316i
\(460\) 2.14424 + 3.71394i 0.0999759 + 0.173163i
\(461\) 4.08386 0.190204 0.0951022 0.995468i \(-0.469682\pi\)
0.0951022 + 0.995468i \(0.469682\pi\)
\(462\) 0.896082 1.55206i 0.0416895 0.0722083i
\(463\) 30.8493 1.43369 0.716844 0.697233i \(-0.245586\pi\)
0.716844 + 0.697233i \(0.245586\pi\)
\(464\) 28.7202 1.33330
\(465\) −0.592327 17.5667i −0.0274685 0.814634i
\(466\) 4.52098 0.209430
\(467\) 36.9982 1.71207 0.856036 0.516916i \(-0.172920\pi\)
0.856036 + 0.516916i \(0.172920\pi\)
\(468\) 0.695729 1.20504i 0.0321601 0.0557029i
\(469\) 8.11996 0.374945
\(470\) −1.85924 3.22031i −0.0857605 0.148542i
\(471\) 4.98083 8.62705i 0.229504 0.397513i
\(472\) −1.68963 + 2.92652i −0.0777713 + 0.134704i
\(473\) 5.30063 0.243723
\(474\) 2.32045 + 4.01914i 0.106582 + 0.184605i
\(475\) −9.48091 16.4214i −0.435014 0.753466i
\(476\) 1.51109 + 2.61728i 0.0692605 + 0.119963i
\(477\) −4.50640 + 7.80531i −0.206334 + 0.357381i
\(478\) −1.57991 2.73649i −0.0722635 0.125164i
\(479\) −16.5043 + 28.5863i −0.754100 + 1.30614i 0.191721 + 0.981450i \(0.438593\pi\)
−0.945821 + 0.324690i \(0.894740\pi\)
\(480\) −10.4235 −0.475765
\(481\) −1.90657 −0.0869322
\(482\) 1.49129 2.58299i 0.0679263 0.117652i
\(483\) −1.49625 2.59158i −0.0680816 0.117921i
\(484\) −2.95313 + 5.11497i −0.134233 + 0.232499i
\(485\) −13.5975 23.5515i −0.617430 1.06942i
\(486\) −1.07804 1.86722i −0.0489010 0.0846990i
\(487\) −7.27231 12.5960i −0.329540 0.570780i 0.652881 0.757461i \(-0.273560\pi\)
−0.982421 + 0.186681i \(0.940227\pi\)
\(488\) 1.97641 0.0894681
\(489\) −6.64658 + 11.5122i −0.300569 + 0.520600i
\(490\) −1.36295 + 2.36070i −0.0615719 + 0.106646i
\(491\) 12.8216 + 22.2076i 0.578629 + 1.00221i 0.995637 + 0.0933116i \(0.0297453\pi\)
−0.417008 + 0.908903i \(0.636921\pi\)
\(492\) 6.37271 0.287304
\(493\) −5.72407 + 9.91438i −0.257799 + 0.446521i
\(494\) 2.37649 0.106923
\(495\) 3.34304 0.150258
\(496\) −0.656227 19.4617i −0.0294655 0.873858i
\(497\) 11.3021 0.506969
\(498\) −6.49662 −0.291121
\(499\) 12.8263 22.2157i 0.574183 0.994513i −0.421947 0.906620i \(-0.638653\pi\)
0.996130 0.0878930i \(-0.0280134\pi\)
\(500\) 22.9419 1.02599
\(501\) 1.98322 + 3.43504i 0.0886038 + 0.153466i
\(502\) −2.03989 + 3.53320i −0.0910449 + 0.157694i
\(503\) −11.6192 + 20.1251i −0.518076 + 0.897333i 0.481704 + 0.876334i \(0.340018\pi\)
−0.999779 + 0.0209992i \(0.993315\pi\)
\(504\) 0.938646 0.0418106
\(505\) −3.11600 5.39707i −0.138660 0.240166i
\(506\) 0.561530 + 0.972598i 0.0249630 + 0.0432373i
\(507\) −0.965220 1.67181i −0.0428669 0.0742477i
\(508\) −4.36551 + 7.56128i −0.193688 + 0.335477i
\(509\) 15.5178 + 26.8776i 0.687813 + 1.19133i 0.972544 + 0.232720i \(0.0747626\pi\)
−0.284730 + 0.958608i \(0.591904\pi\)
\(510\) 0.641423 1.11098i 0.0284027 0.0491949i
\(511\) 17.3581 0.767878
\(512\) −19.5305 −0.863132
\(513\) −17.8902 + 30.9867i −0.789870 + 1.36809i
\(514\) −2.60768 4.51664i −0.115020 0.199220i
\(515\) 10.4517 18.1029i 0.460558 0.797710i
\(516\) 3.48242 + 6.03173i 0.153305 + 0.265532i
\(517\) 10.9739 + 19.0074i 0.482632 + 0.835943i
\(518\) −0.314554 0.544824i −0.0138207 0.0239382i
\(519\) 11.0653 0.485713
\(520\) −0.933102 + 1.61618i −0.0409192 + 0.0708742i
\(521\) 7.58436 13.1365i 0.332277 0.575520i −0.650681 0.759351i \(-0.725517\pi\)
0.982958 + 0.183831i \(0.0588499\pi\)
\(522\) 0.869618 + 1.50622i 0.0380622 + 0.0659256i
\(523\) −7.86242 −0.343799 −0.171900 0.985114i \(-0.554991\pi\)
−0.171900 + 0.985114i \(0.554991\pi\)
\(524\) −17.0943 + 29.6082i −0.746769 + 1.29344i
\(525\) −5.08244 −0.221816
\(526\) −0.164584 −0.00717619
\(527\) 6.84909 + 3.65228i 0.298351 + 0.159096i
\(528\) 18.9956 0.826676
\(529\) −21.1248 −0.918468
\(530\) 2.95637 5.12059i 0.128417 0.222424i
\(531\) 2.15156 0.0933699
\(532\) −8.83702 15.3062i −0.383133 0.663606i
\(533\) 0.861909 1.49287i 0.0373334 0.0646634i
\(534\) −1.42038 + 2.46017i −0.0614659 + 0.106462i
\(535\) 24.2673 1.04917
\(536\) −4.09295 7.08920i −0.176789 0.306207i
\(537\) −13.5047 23.3909i −0.582772 1.00939i
\(538\) 4.29989 + 7.44763i 0.185381 + 0.321090i
\(539\) 8.04463 13.9337i 0.346507 0.600167i
\(540\) −6.87191 11.9025i −0.295720 0.512202i
\(541\) 14.6063 25.2989i 0.627976 1.08769i −0.359982 0.932959i \(-0.617217\pi\)
0.987957 0.154726i \(-0.0494496\pi\)
\(542\) 1.27858 0.0549196
\(543\) 10.3371 0.443606
\(544\) 2.30157 3.98643i 0.0986788 0.170917i
\(545\) −16.4733 28.5325i −0.705637 1.22220i
\(546\) 0.318492 0.551645i 0.0136302 0.0236082i
\(547\) 9.87380 + 17.1019i 0.422173 + 0.731226i 0.996152 0.0876447i \(-0.0279340\pi\)
−0.573978 + 0.818870i \(0.694601\pi\)
\(548\) −12.7144 22.0220i −0.543132 0.940732i
\(549\) −0.629190 1.08979i −0.0268532 0.0465110i
\(550\) 1.90740 0.0813318
\(551\) 33.4751 57.9805i 1.42609 2.47005i
\(552\) −1.50840 + 2.61262i −0.0642017 + 0.111201i
\(553\) −4.66809 8.08537i −0.198507 0.343825i
\(554\) 3.43290 0.145850
\(555\) 3.00939 5.21241i 0.127741 0.221255i
\(556\) −16.1720 −0.685847
\(557\) −5.44336 −0.230642 −0.115321 0.993328i \(-0.536790\pi\)
−0.115321 + 0.993328i \(0.536790\pi\)
\(558\) 1.00080 0.623697i 0.0423671 0.0264032i
\(559\) 1.88399 0.0796843
\(560\) 6.47432 0.273590
\(561\) −3.78591 + 6.55738i −0.159841 + 0.276853i
\(562\) 1.89536 0.0799509
\(563\) −12.0972 20.9529i −0.509834 0.883059i −0.999935 0.0113934i \(-0.996373\pi\)
0.490101 0.871666i \(-0.336960\pi\)
\(564\) −14.4193 + 24.9750i −0.607164 + 1.05164i
\(565\) 1.40263 2.42942i 0.0590090 0.102207i
\(566\) 0.436342 0.0183408
\(567\) 6.02897 + 10.4425i 0.253193 + 0.438543i
\(568\) −5.69695 9.86741i −0.239039 0.414027i
\(569\) 18.4093 + 31.8858i 0.771758 + 1.33672i 0.936599 + 0.350403i \(0.113955\pi\)
−0.164841 + 0.986320i \(0.552711\pi\)
\(570\) −3.75112 + 6.49714i −0.157117 + 0.272135i
\(571\) 16.2818 + 28.2008i 0.681370 + 1.18017i 0.974563 + 0.224115i \(0.0719490\pi\)
−0.293192 + 0.956053i \(0.594718\pi\)
\(572\) 2.69398 4.66612i 0.112641 0.195100i
\(573\) 40.7345 1.70171
\(574\) 0.568806 0.0237415
\(575\) 1.59246 2.75822i 0.0664100 0.115026i
\(576\) 2.19155 + 3.79588i 0.0913148 + 0.158162i
\(577\) −3.45823 + 5.98983i −0.143968 + 0.249360i −0.928987 0.370111i \(-0.879320\pi\)
0.785019 + 0.619471i \(0.212653\pi\)
\(578\) −2.19441 3.80083i −0.0912755 0.158094i
\(579\) 1.67082 + 2.89394i 0.0694367 + 0.120268i
\(580\) 12.8583 + 22.2713i 0.533914 + 0.924765i
\(581\) 13.0694 0.542209
\(582\) 4.67887 8.10404i 0.193945 0.335923i
\(583\) −17.4496 + 30.2235i −0.722687 + 1.25173i
\(584\) −8.74954 15.1546i −0.362059 0.627104i
\(585\) 1.18821 0.0491264
\(586\) −0.419747 + 0.727023i −0.0173396 + 0.0300330i
\(587\) 16.0678 0.663190 0.331595 0.943422i \(-0.392413\pi\)
0.331595 + 0.943422i \(0.392413\pi\)
\(588\) 21.1407 0.871829
\(589\) −40.0544 21.3590i −1.65041 0.880082i
\(590\) −1.41151 −0.0581109
\(591\) −2.50145 −0.102896
\(592\) 3.33404 5.77472i 0.137028 0.237340i
\(593\) 23.0992 0.948571 0.474286 0.880371i \(-0.342706\pi\)
0.474286 + 0.880371i \(0.342706\pi\)
\(594\) −1.79960 3.11700i −0.0738385 0.127892i
\(595\) −1.29036 + 2.23497i −0.0528997 + 0.0916249i
\(596\) 3.26562 5.65622i 0.133765 0.231688i
\(597\) 44.7549 1.83170
\(598\) 0.199583 + 0.345688i 0.00816157 + 0.0141362i
\(599\) −20.7219 35.8914i −0.846674 1.46648i −0.884159 0.467186i \(-0.845268\pi\)
0.0374848 0.999297i \(-0.488065\pi\)
\(600\) 2.56186 + 4.43727i 0.104587 + 0.181151i
\(601\) 7.37467 12.7733i 0.300819 0.521034i −0.675503 0.737358i \(-0.736073\pi\)
0.976322 + 0.216324i \(0.0694066\pi\)
\(602\) 0.310829 + 0.538371i 0.0126684 + 0.0219424i
\(603\) −2.60597 + 4.51368i −0.106123 + 0.183811i
\(604\) −2.70705 −0.110148
\(605\) −5.04353 −0.205049
\(606\) 1.07221 1.85712i 0.0435556 0.0754404i
\(607\) −12.7808 22.1371i −0.518759 0.898516i −0.999762 0.0217977i \(-0.993061\pi\)
0.481004 0.876718i \(-0.340272\pi\)
\(608\) −13.4598 + 23.3131i −0.545869 + 0.945472i
\(609\) −8.97251 15.5408i −0.363584 0.629747i
\(610\) 0.412773 + 0.714944i 0.0167127 + 0.0289472i
\(611\) 3.90043 + 6.75575i 0.157795 + 0.273308i
\(612\) −1.93984 −0.0784133
\(613\) 5.26219 9.11438i 0.212538 0.368126i −0.739970 0.672640i \(-0.765160\pi\)
0.952508 + 0.304513i \(0.0984938\pi\)
\(614\) 1.85747 3.21724i 0.0749616 0.129837i
\(615\) 2.72092 + 4.71278i 0.109718 + 0.190038i
\(616\) 3.63460 0.146442
\(617\) 7.20070 12.4720i 0.289889 0.502103i −0.683894 0.729581i \(-0.739715\pi\)
0.973783 + 0.227479i \(0.0730482\pi\)
\(618\) 7.19284 0.289339
\(619\) −35.5923 −1.43057 −0.715287 0.698831i \(-0.753704\pi\)
−0.715287 + 0.698831i \(0.753704\pi\)
\(620\) 14.7980 9.22210i 0.594300 0.370369i
\(621\) −6.00982 −0.241166
\(622\) 5.45063 0.218550
\(623\) 2.85740 4.94916i 0.114479 0.198284i
\(624\) 6.75155 0.270278
\(625\) 3.98093 + 6.89517i 0.159237 + 0.275807i
\(626\) 2.67169 4.62750i 0.106782 0.184952i
\(627\) 22.1405 38.3484i 0.884205 1.53149i
\(628\) 9.88215 0.394341
\(629\) 1.32898 + 2.30186i 0.0529899 + 0.0917811i
\(630\) 0.196036 + 0.339544i 0.00781025 + 0.0135278i
\(631\) −5.77319 9.99946i −0.229827 0.398072i 0.727930 0.685652i \(-0.240483\pi\)
−0.957757 + 0.287580i \(0.907149\pi\)
\(632\) −4.70600 + 8.15103i −0.187195 + 0.324230i
\(633\) 13.4481 + 23.2928i 0.534514 + 0.925805i
\(634\) −4.04245 + 7.00173i −0.160546 + 0.278074i
\(635\) −7.45568 −0.295869
\(636\) −45.8562 −1.81832
\(637\) 2.85928 4.95242i 0.113289 0.196222i
\(638\) 3.36731 + 5.83236i 0.133313 + 0.230905i
\(639\) −3.62724 + 6.28256i −0.143491 + 0.248534i
\(640\) −6.83729 11.8425i −0.270268 0.468117i
\(641\) 13.1940 + 22.8527i 0.521132 + 0.902628i 0.999698 + 0.0245760i \(0.00782357\pi\)
−0.478566 + 0.878052i \(0.658843\pi\)
\(642\) 4.17516 + 7.23159i 0.164780 + 0.285408i
\(643\) −45.7510 −1.80425 −0.902123 0.431480i \(-0.857992\pi\)
−0.902123 + 0.431480i \(0.857992\pi\)
\(644\) 1.48431 2.57089i 0.0584898 0.101307i
\(645\) −2.97374 + 5.15067i −0.117091 + 0.202808i
\(646\) −1.65654 2.86921i −0.0651756 0.112888i
\(647\) 19.9093 0.782715 0.391358 0.920239i \(-0.372006\pi\)
0.391358 + 0.920239i \(0.372006\pi\)
\(648\) 6.07792 10.5273i 0.238763 0.413550i
\(649\) 8.33123 0.327029
\(650\) 0.677943 0.0265911
\(651\) −10.3260 + 6.43516i −0.404707 + 0.252214i
\(652\) −13.1871 −0.516445
\(653\) −45.8704 −1.79505 −0.897523 0.440968i \(-0.854635\pi\)
−0.897523 + 0.440968i \(0.854635\pi\)
\(654\) 5.66842 9.81799i 0.221653 0.383914i
\(655\) −29.1947 −1.14073
\(656\) 3.01446 + 5.22119i 0.117695 + 0.203853i
\(657\) −5.57082 + 9.64894i −0.217338 + 0.376441i
\(658\) −1.28702 + 2.22919i −0.0501733 + 0.0869027i
\(659\) 26.7938 1.04374 0.521868 0.853026i \(-0.325235\pi\)
0.521868 + 0.853026i \(0.325235\pi\)
\(660\) 8.50452 + 14.7303i 0.331038 + 0.573375i
\(661\) −2.62929 4.55406i −0.102267 0.177132i 0.810351 0.585945i \(-0.199276\pi\)
−0.912618 + 0.408812i \(0.865943\pi\)
\(662\) −3.06964 5.31676i −0.119305 0.206642i
\(663\) −1.34562 + 2.33068i −0.0522594 + 0.0905159i
\(664\) −6.58775 11.4103i −0.255654 0.442806i
\(665\) 7.54620 13.0704i 0.292629 0.506848i
\(666\) 0.403805 0.0156471
\(667\) 11.2453 0.435418
\(668\) −1.96739 + 3.40763i −0.0761208 + 0.131845i
\(669\) −12.6499 21.9103i −0.489075 0.847103i
\(670\) 1.70962 2.96115i 0.0660484 0.114399i
\(671\) −2.43633 4.21985i −0.0940535 0.162906i
\(672\) 3.60772 + 6.24875i 0.139171 + 0.241051i
\(673\) 15.2603 + 26.4316i 0.588240 + 1.01886i 0.994463 + 0.105088i \(0.0335124\pi\)
−0.406223 + 0.913774i \(0.633154\pi\)
\(674\) −3.24975 −0.125176
\(675\) −5.10353 + 8.83958i −0.196435 + 0.340236i
\(676\) 0.957517 1.65847i 0.0368276 0.0637872i
\(677\) −24.8548 43.0498i −0.955247 1.65454i −0.733802 0.679364i \(-0.762256\pi\)
−0.221446 0.975173i \(-0.571078\pi\)
\(678\) 0.965283 0.0370715
\(679\) −9.41256 + 16.3030i −0.361221 + 0.625653i
\(680\) 2.60168 0.0997699
\(681\) −20.1607 −0.772558
\(682\) 3.87525 2.41506i 0.148391 0.0924776i
\(683\) 45.0893 1.72529 0.862647 0.505806i \(-0.168805\pi\)
0.862647 + 0.505806i \(0.168805\pi\)
\(684\) 11.3444 0.433764
\(685\) 10.8572 18.8052i 0.414832 0.718511i
\(686\) 4.19673 0.160232
\(687\) 2.15872 + 3.73901i 0.0823603 + 0.142652i
\(688\) −3.29455 + 5.70633i −0.125604 + 0.217552i
\(689\) −6.20206 + 10.7423i −0.236280 + 0.409248i
\(690\) −1.26011 −0.0479716
\(691\) −5.02895 8.71039i −0.191310 0.331359i 0.754375 0.656444i \(-0.227940\pi\)
−0.945685 + 0.325085i \(0.894607\pi\)
\(692\) 5.48850 + 9.50636i 0.208641 + 0.361378i
\(693\) −1.15707 2.00411i −0.0439535 0.0761297i
\(694\) 4.01513 6.95441i 0.152412 0.263986i
\(695\) −6.90489 11.9596i −0.261917 0.453654i
\(696\) −9.04537 + 15.6670i −0.342864 + 0.593858i
\(697\) −2.40318 −0.0910269
\(698\) −6.64853 −0.251651
\(699\) 14.9704 25.9295i 0.566233 0.980744i
\(700\) −2.52094 4.36640i −0.0952826 0.165034i
\(701\) 10.5481 18.2698i 0.398395 0.690041i −0.595133 0.803627i \(-0.702901\pi\)
0.993528 + 0.113586i \(0.0362339\pi\)
\(702\) −0.639628 1.10787i −0.0241412 0.0418138i
\(703\) −7.77204 13.4616i −0.293128 0.507712i
\(704\) 8.48608 + 14.6983i 0.319831 + 0.553964i
\(705\) −24.6262 −0.927477
\(706\) −1.94910 + 3.37594i −0.0733554 + 0.127055i
\(707\) −2.15698 + 3.73600i −0.0811217 + 0.140507i
\(708\) 5.47347 + 9.48033i 0.205706 + 0.356293i
\(709\) 46.8510 1.75953 0.879763 0.475413i \(-0.157701\pi\)
0.879763 + 0.475413i \(0.157701\pi\)
\(710\) 2.37961 4.12160i 0.0893052 0.154681i
\(711\) 5.99260 0.224740
\(712\) −5.76121 −0.215911
\(713\) −0.256942 7.62015i −0.00962257 0.285377i
\(714\) −0.888022 −0.0332334
\(715\) 4.60095 0.172066
\(716\) 13.3970 23.2042i 0.500668 0.867182i
\(717\) −20.9264 −0.781510
\(718\) 0.250362 + 0.433639i 0.00934342 + 0.0161833i
\(719\) −23.4679 + 40.6476i −0.875206 + 1.51590i −0.0186624 + 0.999826i \(0.505941\pi\)
−0.856543 + 0.516075i \(0.827393\pi\)
\(720\) −2.07783 + 3.59891i −0.0774362 + 0.134123i
\(721\) −14.4700 −0.538889
\(722\) 6.91848 + 11.9832i 0.257479 + 0.445967i
\(723\) −9.87627 17.1062i −0.367302 0.636186i
\(724\) 5.12728 + 8.88071i 0.190554 + 0.330049i
\(725\) 9.54945 16.5401i 0.354658 0.614285i
\(726\) −0.867735 1.50296i −0.0322047 0.0557801i
\(727\) 6.30816 10.9261i 0.233957 0.405225i −0.725012 0.688736i \(-0.758166\pi\)
0.958969 + 0.283511i \(0.0914993\pi\)
\(728\) 1.29184 0.0478787
\(729\) 17.6766 0.654687
\(730\) 3.65467 6.33008i 0.135266 0.234287i
\(731\) −1.31324 2.27460i −0.0485719 0.0841290i
\(732\) 3.20126 5.54474i 0.118322 0.204939i
\(733\) −9.01199 15.6092i −0.332865 0.576540i 0.650207 0.759757i \(-0.274682\pi\)
−0.983072 + 0.183217i \(0.941349\pi\)
\(734\) 0.411610 + 0.712929i 0.0151928 + 0.0263147i
\(735\) 9.02635 + 15.6341i 0.332942 + 0.576672i
\(736\) −4.52155 −0.166667
\(737\) −10.0908 + 17.4777i −0.371699 + 0.643801i
\(738\) −0.182549 + 0.316185i −0.00671973 + 0.0116389i
\(739\) −9.68707 16.7785i −0.356345 0.617207i 0.631002 0.775781i \(-0.282644\pi\)
−0.987347 + 0.158574i \(0.949310\pi\)
\(740\) 5.97074 0.219489
\(741\) 7.86933 13.6301i 0.289087 0.500714i
\(742\) −4.09297 −0.150258
\(743\) −3.68643 −0.135242 −0.0676210 0.997711i \(-0.521541\pi\)
−0.0676210 + 0.997711i \(0.521541\pi\)
\(744\) 10.8232 + 5.77146i 0.396797 + 0.211592i
\(745\) 5.57722 0.204334
\(746\) −9.25665 −0.338910
\(747\) −4.19441 + 7.26493i −0.153465 + 0.265810i
\(748\) −7.51138 −0.274643
\(749\) −8.39924 14.5479i −0.306901 0.531569i
\(750\) −3.37057 + 5.83800i −0.123076 + 0.213174i
\(751\) 6.66112 11.5374i 0.243068 0.421006i −0.718519 0.695507i \(-0.755180\pi\)
0.961587 + 0.274502i \(0.0885130\pi\)
\(752\) −27.2829 −0.994905
\(753\) 13.5095 + 23.3991i 0.492313 + 0.852711i
\(754\) 1.19684 + 2.07298i 0.0435862 + 0.0754935i
\(755\) −1.15582 2.00193i −0.0420645 0.0728578i
\(756\) −4.75693 + 8.23924i −0.173008 + 0.299658i
\(757\) −2.09062 3.62106i −0.0759848 0.131610i 0.825529 0.564359i \(-0.190877\pi\)
−0.901514 + 0.432750i \(0.857543\pi\)
\(758\) 1.20850 2.09318i 0.0438947 0.0760279i
\(759\) 7.43762 0.269969
\(760\) −15.2150 −0.551904
\(761\) −11.2827 + 19.5422i −0.408997 + 0.708404i −0.994778 0.102066i \(-0.967455\pi\)
0.585780 + 0.810470i \(0.300788\pi\)
\(762\) −1.28274 2.22177i −0.0464689 0.0804864i
\(763\) −11.4033 + 19.7510i −0.412826 + 0.715035i
\(764\) 20.2047 + 34.9956i 0.730980 + 1.26609i
\(765\) −0.828243 1.43456i −0.0299452 0.0518666i
\(766\) 3.37936 + 5.85322i 0.122101 + 0.211485i
\(767\) 2.96115 0.106921
\(768\) −9.29244 + 16.0950i −0.335312 + 0.580777i
\(769\) −1.72255 + 2.98354i −0.0621166 + 0.107589i −0.895411 0.445240i \(-0.853118\pi\)
0.833295 + 0.552829i \(0.186452\pi\)
\(770\) 0.759084 + 1.31477i 0.0273555 + 0.0473811i
\(771\) −34.5395 −1.24391
\(772\) −1.65748 + 2.87084i −0.0596541 + 0.103324i
\(773\) 0.757611 0.0272494 0.0136247 0.999907i \(-0.495663\pi\)
0.0136247 + 0.999907i \(0.495663\pi\)
\(774\) −0.399022 −0.0143426
\(775\) −11.4263 6.09309i −0.410446 0.218870i
\(776\) 18.9780 0.681270
\(777\) −4.16636 −0.149467
\(778\) 2.11195 3.65800i 0.0757169 0.131146i
\(779\) 14.0541 0.503540
\(780\) 3.02274 + 5.23554i 0.108232 + 0.187463i
\(781\) −14.0453 + 24.3272i −0.502580 + 0.870494i
\(782\) 0.278240 0.481925i 0.00994983 0.0172336i
\(783\) −36.0390 −1.28793
\(784\) 10.0001 + 17.3207i 0.357147 + 0.618596i
\(785\) 4.21934 + 7.30810i 0.150595 + 0.260837i
\(786\) −5.02292 8.69996i −0.179162 0.310317i
\(787\) 0.895768 1.55151i 0.0319307 0.0553055i −0.849618 0.527398i \(-0.823168\pi\)
0.881549 + 0.472092i \(0.156501\pi\)
\(788\) −1.24074 2.14903i −0.0441996 0.0765559i
\(789\) −0.544990 + 0.943950i −0.0194022 + 0.0336055i
\(790\) −3.93138 −0.139872
\(791\) −1.94188 −0.0690451
\(792\) −1.16647 + 2.02038i −0.0414486 + 0.0717912i
\(793\) −0.865940 1.49985i −0.0307504 0.0532613i
\(794\) −1.23951 + 2.14690i −0.0439886 + 0.0761905i
\(795\) −19.5790 33.9118i −0.694396 1.20273i
\(796\) 22.1989 + 38.4495i 0.786817 + 1.36281i
\(797\) 10.7412 + 18.6043i 0.380473 + 0.658999i 0.991130 0.132896i \(-0.0424278\pi\)
−0.610657 + 0.791895i \(0.709094\pi\)
\(798\) 5.19327 0.183840
\(799\) 5.43761 9.41821i 0.192369 0.333192i
\(800\) −3.83969 + 6.65055i −0.135754 + 0.235132i
\(801\) 1.83408 + 3.17671i 0.0648039 + 0.112244i
\(802\) 6.63932 0.234442
\(803\) −21.5712 + 37.3624i −0.761230 + 1.31849i
\(804\) −26.5179 −0.935213
\(805\) 2.53499 0.0893465
\(806\) 1.37737 0.858381i 0.0485159 0.0302352i
\(807\) 56.9533 2.00485
\(808\) 4.34900 0.152997
\(809\) −25.1129 + 43.4969i −0.882923 + 1.52927i −0.0348480 + 0.999393i \(0.511095\pi\)
−0.848075 + 0.529876i \(0.822239\pi\)
\(810\) 5.07748 0.178405
\(811\) −23.2923 40.3435i −0.817904 1.41665i −0.907224 0.420649i \(-0.861803\pi\)
0.0893194 0.996003i \(-0.471531\pi\)
\(812\) 8.90090 15.4168i 0.312360 0.541024i
\(813\) 4.23378 7.33312i 0.148485 0.257184i
\(814\) 1.56360 0.0548043
\(815\) −5.63042 9.75217i −0.197225 0.341604i
\(816\) −4.70618 8.15135i −0.164749 0.285354i
\(817\) 7.67998 + 13.3021i 0.268689 + 0.465382i
\(818\) 3.31157 5.73580i 0.115786 0.200548i
\(819\) −0.411256 0.712315i −0.0143704 0.0248903i
\(820\) −2.69921 + 4.67517i −0.0942604 + 0.163264i
\(821\) 17.4667 0.609591 0.304796 0.952418i \(-0.401412\pi\)
0.304796 + 0.952418i \(0.401412\pi\)
\(822\) 7.47189 0.260612
\(823\) −18.2339 + 31.5820i −0.635594 + 1.10088i 0.350795 + 0.936452i \(0.385911\pi\)
−0.986389 + 0.164429i \(0.947422\pi\)
\(824\) 7.29373 + 12.6331i 0.254089 + 0.440095i
\(825\) 6.31602 10.9397i 0.219895 0.380870i
\(826\) 0.488543 + 0.846182i 0.0169986 + 0.0294424i
\(827\) 9.06299 + 15.6976i 0.315151 + 0.545858i 0.979470 0.201592i \(-0.0646114\pi\)
−0.664318 + 0.747450i \(0.731278\pi\)
\(828\) 0.952729 + 1.65018i 0.0331096 + 0.0573476i
\(829\) 38.6065 1.34086 0.670429 0.741974i \(-0.266110\pi\)
0.670429 + 0.741974i \(0.266110\pi\)
\(830\) 2.75169 4.76607i 0.0955127 0.165433i
\(831\) 11.3674 19.6890i 0.394332 0.683003i
\(832\) 3.01619 + 5.22419i 0.104567 + 0.181116i
\(833\) −7.97228 −0.276223
\(834\) 2.37596 4.11528i 0.0822728 0.142501i
\(835\) −3.36004 −0.116279
\(836\) 43.9275 1.51926
\(837\) 0.823453 + 24.4212i 0.0284627 + 0.844120i
\(838\) −1.45181 −0.0501519
\(839\) 16.7944 0.579806 0.289903 0.957056i \(-0.406377\pi\)
0.289903 + 0.957056i \(0.406377\pi\)
\(840\) −2.03907 + 3.53178i −0.0703548 + 0.121858i
\(841\) 38.4341 1.32532
\(842\) −3.29041 5.69916i −0.113395 0.196406i
\(843\) 6.27615 10.8706i 0.216162 0.374403i
\(844\) −13.3408 + 23.1069i −0.459208 + 0.795372i
\(845\) 1.63530 0.0562562
\(846\) −0.826098 1.43084i −0.0284018 0.0491934i
\(847\) 1.74564 + 3.02353i 0.0599808 + 0.103890i
\(848\) −21.6912 37.5702i −0.744879 1.29017i
\(849\) 1.44487 2.50258i 0.0495877 0.0858885i
\(850\) −0.472561 0.818500i −0.0162087 0.0280743i
\(851\) 1.30543 2.26106i 0.0447494 0.0775083i
\(852\) −36.9100 −1.26452
\(853\) −30.0012 −1.02722 −0.513610 0.858024i \(-0.671692\pi\)
−0.513610 + 0.858024i \(0.671692\pi\)
\(854\) 0.285733 0.494904i 0.00977758 0.0169353i
\(855\) 4.84367 + 8.38948i 0.165650 + 0.286914i
\(856\) −8.46744 + 14.6660i −0.289411 + 0.501275i
\(857\) 15.9138 + 27.5636i 0.543607 + 0.941554i 0.998693 + 0.0511070i \(0.0162750\pi\)
−0.455087 + 0.890447i \(0.650392\pi\)
\(858\) 0.791589 + 1.37107i 0.0270244 + 0.0468076i
\(859\) 17.2106 + 29.8097i 0.587219 + 1.01709i 0.994595 + 0.103833i \(0.0331108\pi\)
−0.407375 + 0.913261i \(0.633556\pi\)
\(860\) −5.90002 −0.201189
\(861\) 1.88350 3.26232i 0.0641895 0.111179i
\(862\) 2.02567 3.50857i 0.0689947 0.119502i
\(863\) 12.8493 + 22.2556i 0.437395 + 0.757590i 0.997488 0.0708399i \(-0.0225679\pi\)
−0.560093 + 0.828430i \(0.689235\pi\)
\(864\) 14.4908 0.492985
\(865\) −4.68680 + 8.11777i −0.159356 + 0.276012i
\(866\) 3.86165 0.131224
\(867\) −29.0656 −0.987120
\(868\) −10.6503 5.67928i −0.361495 0.192767i
\(869\) 23.2044 0.787155
\(870\) −7.55648 −0.256189
\(871\) −3.58654 + 6.21208i −0.121525 + 0.210488i
\(872\) 22.9917 0.778598
\(873\) −6.04163 10.4644i −0.204478 0.354166i
\(874\) −1.62718 + 2.81836i −0.0550402 + 0.0953324i
\(875\) 6.78063 11.7444i 0.229227 0.397033i
\(876\) −56.6875 −1.91529
\(877\) −14.2678 24.7126i −0.481790 0.834485i 0.517991 0.855386i \(-0.326680\pi\)
−0.999782 + 0.0209007i \(0.993347\pi\)
\(878\) 2.55801 + 4.43061i 0.0863287 + 0.149526i
\(879\) 2.77983 + 4.81481i 0.0937615 + 0.162400i
\(880\) −8.04572 + 13.9356i −0.271221 + 0.469769i
\(881\) −10.3155 17.8670i −0.347539 0.601956i 0.638272 0.769811i \(-0.279649\pi\)
−0.985812 + 0.167855i \(0.946316\pi\)
\(882\) −0.605586 + 1.04891i −0.0203912 + 0.0353185i
\(883\) 7.77337 0.261595 0.130797 0.991409i \(-0.458246\pi\)
0.130797 + 0.991409i \(0.458246\pi\)
\(884\) −2.66975 −0.0897936
\(885\) −4.67396 + 8.09554i −0.157114 + 0.272129i
\(886\) −3.22806 5.59116i −0.108449 0.187839i
\(887\) 18.9906 32.8927i 0.637642 1.10443i −0.348306 0.937381i \(-0.613243\pi\)
0.985949 0.167048i \(-0.0534236\pi\)
\(888\) 2.10010 + 3.63748i 0.0704747 + 0.122066i
\(889\) 2.58051 + 4.46958i 0.0865476 + 0.149905i
\(890\) −1.20323 2.08405i −0.0403322 0.0698574i
\(891\) −29.9691 −1.00400
\(892\) 12.5490 21.7355i 0.420171 0.727758i
\(893\) −31.7998 + 55.0789i −1.06414 + 1.84314i
\(894\) 0.959556 + 1.66200i 0.0320923 + 0.0555856i
\(895\) 22.8801 0.764798
\(896\) −4.73296 + 8.19773i −0.158117 + 0.273867i
\(897\) 2.64354 0.0882651
\(898\) 3.09257 0.103200
\(899\) −1.54080 45.6956i −0.0513886 1.52403i
\(900\) 3.23622 0.107874
\(901\) 17.2926 0.576101
\(902\) −0.706862 + 1.22432i −0.0235359 + 0.0407655i
\(903\) 4.11702 0.137006
\(904\) 0.978822 + 1.69537i 0.0325551 + 0.0563872i
\(905\) −4.37834 + 7.58351i −0.145541 + 0.252084i
\(906\) 0.397715 0.688862i 0.0132132 0.0228859i
\(907\) −16.9654 −0.563328 −0.281664 0.959513i \(-0.590886\pi\)
−0.281664 + 0.959513i \(0.590886\pi\)
\(908\) −9.99988 17.3203i −0.331858 0.574794i
\(909\) −1.38450 2.39802i −0.0459209 0.0795374i
\(910\) 0.269800 + 0.467307i 0.00894377 + 0.0154911i
\(911\) 19.5816 33.9164i 0.648769 1.12370i −0.334649 0.942343i \(-0.608618\pi\)
0.983417 0.181357i \(-0.0580490\pi\)
\(912\) 27.5223 + 47.6701i 0.911356 + 1.57851i
\(913\) −16.2415 + 28.1311i −0.537514 + 0.931002i
\(914\) −5.52105 −0.182620
\(915\) 5.46730 0.180743
\(916\) −2.14149 + 3.70917i −0.0707568 + 0.122554i
\(917\) 10.1047 + 17.5018i 0.333686 + 0.577962i
\(918\) −0.891708 + 1.54448i −0.0294307 + 0.0509755i
\(919\) −12.0832 20.9287i −0.398587 0.690373i 0.594965 0.803752i \(-0.297166\pi\)
−0.993552 + 0.113379i \(0.963833\pi\)
\(920\) −1.27779 2.21319i −0.0421274 0.0729667i
\(921\) −12.3014 21.3066i −0.405345 0.702078i
\(922\) −1.19041 −0.0392040
\(923\) −4.99209 + 8.64655i −0.164317 + 0.284605i
\(924\) 5.88707 10.1967i 0.193670 0.335447i
\(925\) −2.21713 3.84018i −0.0728988 0.126264i
\(926\) −8.99229 −0.295505
\(927\) 4.64391 8.04348i 0.152526 0.264183i
\(928\) −27.1143 −0.890070
\(929\) −57.8571 −1.89823 −0.949116 0.314928i \(-0.898020\pi\)
−0.949116 + 0.314928i \(0.898020\pi\)
\(930\) 0.172658 + 5.12052i 0.00566167 + 0.167908i
\(931\) 46.6229 1.52800
\(932\) 29.7019 0.972916
\(933\) 18.0488 31.2614i 0.590890 1.02345i
\(934\) −10.7846 −0.352884
\(935\) −3.20710 5.55486i −0.104883 0.181663i
\(936\) −0.414595 + 0.718100i −0.0135515 + 0.0234718i
\(937\) 24.3080 42.1026i 0.794107 1.37543i −0.129298 0.991606i \(-0.541272\pi\)
0.923405 0.383828i \(-0.125394\pi\)
\(938\) −2.36689 −0.0772818
\(939\) −17.6936 30.6463i −0.577410 1.00010i
\(940\) −12.2148 21.1567i −0.398404 0.690056i
\(941\) −5.76439 9.98421i −0.187914 0.325476i 0.756641 0.653831i \(-0.226839\pi\)
−0.944554 + 0.328355i \(0.893506\pi\)
\(942\) −1.45187 + 2.51471i −0.0473043 + 0.0819335i
\(943\) 1.18029 + 2.04433i 0.0384357 + 0.0665726i
\(944\) −5.17819 + 8.96888i −0.168536 + 0.291912i
\(945\) −8.12417 −0.264279
\(946\) −1.54508 −0.0502350
\(947\) 15.4749 26.8033i 0.502867 0.870990i −0.497128 0.867677i \(-0.665612\pi\)
0.999995 0.00331313i \(-0.00105460\pi\)
\(948\) 15.2449 + 26.4049i 0.495131 + 0.857591i
\(949\) −7.66699 + 13.2796i −0.248881 + 0.431075i
\(950\) 2.76360 + 4.78669i 0.0896630 + 0.155301i
\(951\) 26.7717 + 46.3699i 0.868132 + 1.50365i
\(952\) −0.900478 1.55967i −0.0291847 0.0505493i
\(953\) 17.1203 0.554582 0.277291 0.960786i \(-0.410563\pi\)
0.277291 + 0.960786i \(0.410563\pi\)
\(954\) 1.31357 2.27518i 0.0425285 0.0736616i
\(955\) −17.2534 + 29.8838i −0.558307 + 0.967016i
\(956\) −10.3797 17.9781i −0.335703 0.581455i
\(957\) 44.6010 1.44175
\(958\) 4.81085 8.33263i 0.155431 0.269215i
\(959\) −15.0313 −0.485386
\(960\) −19.0433 −0.614621
\(961\) −30.9296 + 2.08819i −0.997729 + 0.0673610i
\(962\) 0.555748 0.0179180
\(963\) 10.7824 0.347458
\(964\) 9.79744 16.9697i 0.315554 0.546556i
\(965\) −2.83075 −0.0911250
\(966\) 0.436142 + 0.755421i 0.0140326 + 0.0243053i
\(967\) −8.02352 + 13.8971i −0.258019 + 0.446902i −0.965711 0.259619i \(-0.916403\pi\)
0.707692 + 0.706521i \(0.249736\pi\)
\(968\) 1.75981 3.04808i 0.0565625 0.0979692i
\(969\) −21.9413 −0.704857
\(970\) 3.96354 + 6.86506i 0.127262 + 0.220424i
\(971\) 22.1664 + 38.3933i 0.711352 + 1.23210i 0.964350 + 0.264631i \(0.0852503\pi\)
−0.252997 + 0.967467i \(0.581416\pi\)
\(972\) −7.08251 12.2673i −0.227172 0.393473i
\(973\) −4.77976 + 8.27878i −0.153232 + 0.265406i
\(974\) 2.11981 + 3.67162i 0.0679232 + 0.117646i
\(975\) 2.24489 3.88826i 0.0718939 0.124524i
\(976\) 6.05711 0.193883
\(977\) −23.3962 −0.748510 −0.374255 0.927326i \(-0.622102\pi\)
−0.374255 + 0.927326i \(0.622102\pi\)
\(978\) 1.93742 3.35570i 0.0619517 0.107304i
\(979\) 7.10186 + 12.3008i 0.226976 + 0.393135i
\(980\) −8.95431 + 15.5093i −0.286035 + 0.495427i
\(981\) −7.31939 12.6776i −0.233690 0.404763i
\(982\) −3.73737 6.47331i −0.119264 0.206572i
\(983\) 9.74672 + 16.8818i 0.310872 + 0.538446i 0.978551 0.206003i \(-0.0660456\pi\)
−0.667679 + 0.744449i \(0.732712\pi\)
\(984\) −3.79759 −0.121063
\(985\) 1.05951 1.83512i 0.0337587 0.0584718i
\(986\) 1.66851 2.88995i 0.0531363 0.0920348i
\(987\) 8.52348 + 14.7631i 0.271305 + 0.469915i
\(988\) 15.6131 0.496718
\(989\) −1.28996 + 2.23428i −0.0410185 + 0.0710461i
\(990\) −0.974465 −0.0309705
\(991\) −3.38191 −0.107430 −0.0537150 0.998556i \(-0.517106\pi\)
−0.0537150 + 0.998556i \(0.517106\pi\)
\(992\) 0.619533 + 18.3735i 0.0196702 + 0.583360i
\(993\) −40.6582 −1.29025
\(994\) −3.29446 −0.104494
\(995\) −18.9563 + 32.8332i −0.600954 + 1.04088i
\(996\) −42.6815 −1.35241
\(997\) 18.0332 + 31.2344i 0.571117 + 0.989204i 0.996452 + 0.0841675i \(0.0268231\pi\)
−0.425335 + 0.905036i \(0.639844\pi\)
\(998\) −3.73874 + 6.47569i −0.118348 + 0.204984i
\(999\) −4.18365 + 7.24630i −0.132365 + 0.229263i
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 403.2.h.b.222.8 yes 34
31.25 even 3 inner 403.2.h.b.118.8 34
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
403.2.h.b.118.8 34 31.25 even 3 inner
403.2.h.b.222.8 yes 34 1.1 even 1 trivial