Properties

Label 1710.2.t.c.1189.1
Level $1710$
Weight $2$
Character 1710.1189
Analytic conductor $13.654$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1710,2,Mod(919,1710)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1710, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1710.919");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1710.t (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(13.6544187456\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - 49 x^{16} - 8 x^{15} + 72 x^{13} + 2145 x^{12} - 648 x^{11} + 32 x^{10} - 7056 x^{9} - 11968 x^{8} + 10368 x^{7} + 9344 x^{6} + 18176 x^{5} + 56320 x^{4} + 28160 x^{3} + \cdots + 1024 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 570)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1189.1
Root \(0.320085 - 1.19457i\) of defining polynomial
Character \(\chi\) \(=\) 1710.1189
Dual form 1710.2.t.c.919.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-2.21950 - 0.271659i) q^{5} -4.03495i q^{7} -1.00000i q^{8} +O(q^{10})\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-2.21950 - 0.271659i) q^{5} -4.03495i q^{7} -1.00000i q^{8} +(1.78632 + 1.34502i) q^{10} +1.47054 q^{11} +(4.38320 - 2.53064i) q^{13} +(-2.01747 + 3.49437i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-0.0812933 - 0.0469347i) q^{17} +(-4.00172 - 1.72807i) q^{19} +(-0.874489 - 2.05798i) q^{20} +(-1.27352 - 0.735269i) q^{22} +(-2.22178 + 1.28274i) q^{23} +(4.85240 + 1.20590i) q^{25} -5.06128 q^{26} +(3.49437 - 2.01747i) q^{28} +(-2.10491 - 3.64581i) q^{29} +4.26558 q^{31} +(0.866025 - 0.500000i) q^{32} +(0.0469347 + 0.0812933i) q^{34} +(-1.09613 + 8.95558i) q^{35} -1.53807i q^{37} +(2.60156 + 3.49741i) q^{38} +(-0.271659 + 2.21950i) q^{40} +(3.88123 - 6.72248i) q^{41} +(3.97202 + 2.29325i) q^{43} +(0.735269 + 1.27352i) q^{44} +2.56549 q^{46} +(3.49530 - 2.01801i) q^{47} -9.28080 q^{49} +(-3.59936 - 3.47054i) q^{50} +(4.38320 + 2.53064i) q^{52} +(-9.22964 + 5.32873i) q^{53} +(-3.26387 - 0.399485i) q^{55} -4.03495 q^{56} +4.20982i q^{58} +(3.07599 - 5.32777i) q^{59} +(0.653722 + 1.13228i) q^{61} +(-3.69410 - 2.13279i) q^{62} -1.00000 q^{64} +(-10.4160 + 4.42603i) q^{65} +(-9.31187 + 5.37621i) q^{67} -0.0938694i q^{68} +(5.42707 - 7.20770i) q^{70} +(-4.33806 + 7.51373i) q^{71} +(-11.0108 - 6.35711i) q^{73} +(-0.769037 + 1.33201i) q^{74} +(-0.504306 - 4.32963i) q^{76} -5.93355i q^{77} +(-6.48112 + 11.2256i) q^{79} +(1.34502 - 1.78632i) q^{80} +(-6.72248 + 3.88123i) q^{82} -2.06328i q^{83} +(0.167681 + 0.126256i) q^{85} +(-2.29325 - 3.97202i) q^{86} -1.47054i q^{88} +(0.813846 + 1.40962i) q^{89} +(-10.2110 - 17.6860i) q^{91} +(-2.22178 - 1.28274i) q^{92} -4.03603 q^{94} +(8.41239 + 4.92257i) q^{95} +(-10.3479 - 5.97438i) q^{97} +(8.03741 + 4.64040i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 10 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 20 q + 10 q^{4} - 2 q^{10} - 12 q^{11} - 10 q^{14} - 10 q^{16} + 6 q^{19} + 14 q^{25} - 8 q^{29} + 40 q^{31} + 12 q^{34} - 2 q^{35} + 2 q^{40} + 14 q^{41} - 6 q^{44} + 44 q^{46} - 8 q^{49} + 8 q^{50} - 20 q^{56} - 8 q^{59} + 16 q^{61} - 20 q^{64} - 40 q^{65} + 8 q^{70} + 4 q^{71} - 26 q^{74} + 8 q^{79} - 16 q^{85} + 20 q^{86} + 2 q^{89} - 44 q^{91} - 32 q^{94} + 80 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1710\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(1027\) \(1351\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 0.500000i −0.612372 0.353553i
\(3\) 0 0
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) −2.21950 0.271659i −0.992593 0.121490i
\(6\) 0 0
\(7\) 4.03495i 1.52507i −0.646949 0.762533i \(-0.723955\pi\)
0.646949 0.762533i \(-0.276045\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 1.78632 + 1.34502i 0.564883 + 0.425331i
\(11\) 1.47054 0.443384 0.221692 0.975117i \(-0.428842\pi\)
0.221692 + 0.975117i \(0.428842\pi\)
\(12\) 0 0
\(13\) 4.38320 2.53064i 1.21568 0.701874i 0.251690 0.967808i \(-0.419014\pi\)
0.963991 + 0.265934i \(0.0856805\pi\)
\(14\) −2.01747 + 3.49437i −0.539192 + 0.933909i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −0.0812933 0.0469347i −0.0197165 0.0113833i 0.490109 0.871661i \(-0.336957\pi\)
−0.509826 + 0.860278i \(0.670290\pi\)
\(18\) 0 0
\(19\) −4.00172 1.72807i −0.918058 0.396447i
\(20\) −0.874489 2.05798i −0.195542 0.460178i
\(21\) 0 0
\(22\) −1.27352 0.735269i −0.271516 0.156760i
\(23\) −2.22178 + 1.28274i −0.463273 + 0.267471i −0.713419 0.700737i \(-0.752855\pi\)
0.250147 + 0.968208i \(0.419521\pi\)
\(24\) 0 0
\(25\) 4.85240 + 1.20590i 0.970481 + 0.241179i
\(26\) −5.06128 −0.992599
\(27\) 0 0
\(28\) 3.49437 2.01747i 0.660373 0.381267i
\(29\) −2.10491 3.64581i −0.390872 0.677011i 0.601693 0.798728i \(-0.294493\pi\)
−0.992565 + 0.121717i \(0.961160\pi\)
\(30\) 0 0
\(31\) 4.26558 0.766120 0.383060 0.923723i \(-0.374870\pi\)
0.383060 + 0.923723i \(0.374870\pi\)
\(32\) 0.866025 0.500000i 0.153093 0.0883883i
\(33\) 0 0
\(34\) 0.0469347 + 0.0812933i 0.00804924 + 0.0139417i
\(35\) −1.09613 + 8.95558i −0.185280 + 1.51377i
\(36\) 0 0
\(37\) 1.53807i 0.252858i −0.991976 0.126429i \(-0.959648\pi\)
0.991976 0.126429i \(-0.0403515\pi\)
\(38\) 2.60156 + 3.49741i 0.422028 + 0.567356i
\(39\) 0 0
\(40\) −0.271659 + 2.21950i −0.0429531 + 0.350935i
\(41\) 3.88123 6.72248i 0.606146 1.04987i −0.385724 0.922614i \(-0.626048\pi\)
0.991869 0.127261i \(-0.0406184\pi\)
\(42\) 0 0
\(43\) 3.97202 + 2.29325i 0.605727 + 0.349717i 0.771291 0.636482i \(-0.219611\pi\)
−0.165564 + 0.986199i \(0.552944\pi\)
\(44\) 0.735269 + 1.27352i 0.110846 + 0.191991i
\(45\) 0 0
\(46\) 2.56549 0.378261
\(47\) 3.49530 2.01801i 0.509842 0.294358i −0.222927 0.974835i \(-0.571561\pi\)
0.732769 + 0.680478i \(0.238228\pi\)
\(48\) 0 0
\(49\) −9.28080 −1.32583
\(50\) −3.59936 3.47054i −0.509026 0.490808i
\(51\) 0 0
\(52\) 4.38320 + 2.53064i 0.607840 + 0.350937i
\(53\) −9.22964 + 5.32873i −1.26779 + 0.731958i −0.974569 0.224087i \(-0.928060\pi\)
−0.293219 + 0.956045i \(0.594727\pi\)
\(54\) 0 0
\(55\) −3.26387 0.399485i −0.440100 0.0538666i
\(56\) −4.03495 −0.539192
\(57\) 0 0
\(58\) 4.20982i 0.552777i
\(59\) 3.07599 5.32777i 0.400460 0.693617i −0.593321 0.804966i \(-0.702184\pi\)
0.993781 + 0.111349i \(0.0355170\pi\)
\(60\) 0 0
\(61\) 0.653722 + 1.13228i 0.0837005 + 0.144974i 0.904837 0.425759i \(-0.139993\pi\)
−0.821136 + 0.570732i \(0.806659\pi\)
\(62\) −3.69410 2.13279i −0.469151 0.270864i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) −10.4160 + 4.42603i −1.29195 + 0.548982i
\(66\) 0 0
\(67\) −9.31187 + 5.37621i −1.13763 + 0.656808i −0.945842 0.324629i \(-0.894761\pi\)
−0.191784 + 0.981437i \(0.561427\pi\)
\(68\) 0.0938694i 0.0113833i
\(69\) 0 0
\(70\) 5.42707 7.20770i 0.648659 0.861485i
\(71\) −4.33806 + 7.51373i −0.514833 + 0.891716i 0.485019 + 0.874503i \(0.338813\pi\)
−0.999852 + 0.0172126i \(0.994521\pi\)
\(72\) 0 0
\(73\) −11.0108 6.35711i −1.28872 0.744044i −0.310296 0.950640i \(-0.600428\pi\)
−0.978426 + 0.206596i \(0.933761\pi\)
\(74\) −0.769037 + 1.33201i −0.0893987 + 0.154843i
\(75\) 0 0
\(76\) −0.504306 4.32963i −0.0578479 0.496642i
\(77\) 5.93355i 0.676190i
\(78\) 0 0
\(79\) −6.48112 + 11.2256i −0.729183 + 1.26298i 0.228046 + 0.973650i \(0.426766\pi\)
−0.957229 + 0.289332i \(0.906567\pi\)
\(80\) 1.34502 1.78632i 0.150377 0.199716i
\(81\) 0 0
\(82\) −6.72248 + 3.88123i −0.742374 + 0.428610i
\(83\) 2.06328i 0.226475i −0.993568 0.113237i \(-0.963878\pi\)
0.993568 0.113237i \(-0.0361221\pi\)
\(84\) 0 0
\(85\) 0.167681 + 0.126256i 0.0181875 + 0.0136944i
\(86\) −2.29325 3.97202i −0.247287 0.428314i
\(87\) 0 0
\(88\) 1.47054i 0.156760i
\(89\) 0.813846 + 1.40962i 0.0862675 + 0.149420i 0.905931 0.423426i \(-0.139173\pi\)
−0.819663 + 0.572846i \(0.805839\pi\)
\(90\) 0 0
\(91\) −10.2110 17.6860i −1.07040 1.85399i
\(92\) −2.22178 1.28274i −0.231636 0.133735i
\(93\) 0 0
\(94\) −4.03603 −0.416285
\(95\) 8.41239 + 4.92257i 0.863093 + 0.505045i
\(96\) 0 0
\(97\) −10.3479 5.97438i −1.05067 0.606607i −0.127836 0.991795i \(-0.540803\pi\)
−0.922838 + 0.385188i \(0.874136\pi\)
\(98\) 8.03741 + 4.64040i 0.811901 + 0.468751i
\(99\) 0 0
\(100\) 1.38186 + 4.80525i 0.138186 + 0.480525i
\(101\) 0.252103 + 0.436656i 0.0250852 + 0.0434489i 0.878295 0.478118i \(-0.158681\pi\)
−0.853210 + 0.521567i \(0.825348\pi\)
\(102\) 0 0
\(103\) 5.33797i 0.525966i −0.964800 0.262983i \(-0.915294\pi\)
0.964800 0.262983i \(-0.0847063\pi\)
\(104\) −2.53064 4.38320i −0.248150 0.429808i
\(105\) 0 0
\(106\) 10.6575 1.03514
\(107\) 17.9275i 1.73312i −0.499076 0.866558i \(-0.666327\pi\)
0.499076 0.866558i \(-0.333673\pi\)
\(108\) 0 0
\(109\) −4.43631 + 7.68392i −0.424922 + 0.735986i −0.996413 0.0846222i \(-0.973032\pi\)
0.571492 + 0.820608i \(0.306365\pi\)
\(110\) 2.62685 + 1.97790i 0.250460 + 0.188585i
\(111\) 0 0
\(112\) 3.49437 + 2.01747i 0.330187 + 0.190633i
\(113\) 15.8667i 1.49261i −0.665603 0.746306i \(-0.731826\pi\)
0.665603 0.746306i \(-0.268174\pi\)
\(114\) 0 0
\(115\) 5.27972 2.24349i 0.492336 0.209207i
\(116\) 2.10491 3.64581i 0.195436 0.338505i
\(117\) 0 0
\(118\) −5.32777 + 3.07599i −0.490461 + 0.283168i
\(119\) −0.189379 + 0.328014i −0.0173604 + 0.0300690i
\(120\) 0 0
\(121\) −8.83752 −0.803410
\(122\) 1.30744i 0.118370i
\(123\) 0 0
\(124\) 2.13279 + 3.69410i 0.191530 + 0.331740i
\(125\) −10.4423 3.99469i −0.933991 0.357296i
\(126\) 0 0
\(127\) −5.77290 + 3.33298i −0.512262 + 0.295755i −0.733763 0.679406i \(-0.762238\pi\)
0.221501 + 0.975160i \(0.428904\pi\)
\(128\) 0.866025 + 0.500000i 0.0765466 + 0.0441942i
\(129\) 0 0
\(130\) 11.2335 + 1.37494i 0.985247 + 0.120590i
\(131\) 3.53784 6.12771i 0.309102 0.535381i −0.669064 0.743205i \(-0.733305\pi\)
0.978166 + 0.207824i \(0.0666381\pi\)
\(132\) 0 0
\(133\) −6.97268 + 16.1467i −0.604608 + 1.40010i
\(134\) 10.7524 0.928867
\(135\) 0 0
\(136\) −0.0469347 + 0.0812933i −0.00402462 + 0.00697084i
\(137\) 16.3302 9.42826i 1.39519 0.805511i 0.401302 0.915946i \(-0.368558\pi\)
0.993883 + 0.110435i \(0.0352245\pi\)
\(138\) 0 0
\(139\) −9.99616 17.3139i −0.847864 1.46854i −0.883111 0.469164i \(-0.844555\pi\)
0.0352474 0.999379i \(-0.488778\pi\)
\(140\) −8.30383 + 3.52852i −0.701802 + 0.298214i
\(141\) 0 0
\(142\) 7.51373 4.33806i 0.630538 0.364042i
\(143\) 6.44566 3.72141i 0.539014 0.311200i
\(144\) 0 0
\(145\) 3.68144 + 8.66372i 0.305727 + 0.719483i
\(146\) 6.35711 + 11.0108i 0.526119 + 0.911264i
\(147\) 0 0
\(148\) 1.33201 0.769037i 0.109491 0.0632144i
\(149\) −6.10397 + 10.5724i −0.500056 + 0.866123i 0.499944 + 0.866058i \(0.333354\pi\)
−1.00000 6.51503e-5i \(0.999979\pi\)
\(150\) 0 0
\(151\) 19.9109 1.62032 0.810161 0.586207i \(-0.199380\pi\)
0.810161 + 0.586207i \(0.199380\pi\)
\(152\) −1.72807 + 4.00172i −0.140165 + 0.324582i
\(153\) 0 0
\(154\) −2.96677 + 5.13860i −0.239069 + 0.414080i
\(155\) −9.46747 1.15878i −0.760445 0.0930756i
\(156\) 0 0
\(157\) −14.0594 8.11721i −1.12206 0.647824i −0.180137 0.983641i \(-0.557654\pi\)
−0.941927 + 0.335817i \(0.890988\pi\)
\(158\) 11.2256 6.48112i 0.893063 0.515610i
\(159\) 0 0
\(160\) −2.05798 + 0.874489i −0.162697 + 0.0691344i
\(161\) 5.17581 + 8.96476i 0.407911 + 0.706522i
\(162\) 0 0
\(163\) 2.05750i 0.161156i 0.996748 + 0.0805780i \(0.0256766\pi\)
−0.996748 + 0.0805780i \(0.974323\pi\)
\(164\) 7.76245 0.606146
\(165\) 0 0
\(166\) −1.03164 + 1.78686i −0.0800709 + 0.138687i
\(167\) −18.8169 + 10.8639i −1.45609 + 0.840676i −0.998816 0.0486476i \(-0.984509\pi\)
−0.457278 + 0.889324i \(0.651176\pi\)
\(168\) 0 0
\(169\) 6.30829 10.9263i 0.485253 0.840483i
\(170\) −0.0820878 0.193181i −0.00629584 0.0148163i
\(171\) 0 0
\(172\) 4.58649i 0.349717i
\(173\) −20.0963 11.6026i −1.52790 0.882132i −0.999450 0.0331655i \(-0.989441\pi\)
−0.528447 0.848966i \(-0.677226\pi\)
\(174\) 0 0
\(175\) 4.86573 19.5792i 0.367815 1.48005i
\(176\) −0.735269 + 1.27352i −0.0554230 + 0.0959955i
\(177\) 0 0
\(178\) 1.62769i 0.122001i
\(179\) 6.37559 0.476534 0.238267 0.971200i \(-0.423421\pi\)
0.238267 + 0.971200i \(0.423421\pi\)
\(180\) 0 0
\(181\) 4.39603 + 7.61415i 0.326755 + 0.565955i 0.981866 0.189577i \(-0.0607116\pi\)
−0.655111 + 0.755532i \(0.727378\pi\)
\(182\) 20.4220i 1.51378i
\(183\) 0 0
\(184\) 1.28274 + 2.22178i 0.0945652 + 0.163792i
\(185\) −0.417831 + 3.41376i −0.0307196 + 0.250985i
\(186\) 0 0
\(187\) −0.119545 0.0690193i −0.00874200 0.00504719i
\(188\) 3.49530 + 2.01801i 0.254921 + 0.147179i
\(189\) 0 0
\(190\) −4.82406 8.46926i −0.349974 0.614425i
\(191\) −12.9659 −0.938177 −0.469088 0.883151i \(-0.655417\pi\)
−0.469088 + 0.883151i \(0.655417\pi\)
\(192\) 0 0
\(193\) 5.29710 + 3.05828i 0.381294 + 0.220140i 0.678381 0.734710i \(-0.262682\pi\)
−0.297087 + 0.954850i \(0.596015\pi\)
\(194\) 5.97438 + 10.3479i 0.428936 + 0.742939i
\(195\) 0 0
\(196\) −4.64040 8.03741i −0.331457 0.574101i
\(197\) 7.34941i 0.523624i 0.965119 + 0.261812i \(0.0843200\pi\)
−0.965119 + 0.261812i \(0.915680\pi\)
\(198\) 0 0
\(199\) 1.71780 + 2.97531i 0.121771 + 0.210914i 0.920466 0.390822i \(-0.127809\pi\)
−0.798695 + 0.601736i \(0.794476\pi\)
\(200\) 1.20590 4.85240i 0.0852698 0.343117i
\(201\) 0 0
\(202\) 0.504207i 0.0354759i
\(203\) −14.7107 + 8.49321i −1.03249 + 0.596106i
\(204\) 0 0
\(205\) −10.4406 + 13.8662i −0.729205 + 0.968458i
\(206\) −2.66899 + 4.62282i −0.185957 + 0.322087i
\(207\) 0 0
\(208\) 5.06128i 0.350937i
\(209\) −5.88469 2.54120i −0.407052 0.175778i
\(210\) 0 0
\(211\) 2.01970 3.49822i 0.139042 0.240827i −0.788092 0.615557i \(-0.788931\pi\)
0.927134 + 0.374730i \(0.122264\pi\)
\(212\) −9.22964 5.32873i −0.633894 0.365979i
\(213\) 0 0
\(214\) −8.96375 + 15.5257i −0.612749 + 1.06131i
\(215\) −8.19293 6.16891i −0.558754 0.420716i
\(216\) 0 0
\(217\) 17.2114i 1.16838i
\(218\) 7.68392 4.43631i 0.520421 0.300465i
\(219\) 0 0
\(220\) −1.28597 3.02634i −0.0867001 0.204035i
\(221\) −0.475100 −0.0319587
\(222\) 0 0
\(223\) 15.6334 + 9.02593i 1.04689 + 0.604421i 0.921776 0.387722i \(-0.126738\pi\)
0.125111 + 0.992143i \(0.460071\pi\)
\(224\) −2.01747 3.49437i −0.134798 0.233477i
\(225\) 0 0
\(226\) −7.93334 + 13.7409i −0.527718 + 0.914034i
\(227\) 26.8513i 1.78219i 0.453820 + 0.891093i \(0.350061\pi\)
−0.453820 + 0.891093i \(0.649939\pi\)
\(228\) 0 0
\(229\) 13.7131 0.906190 0.453095 0.891462i \(-0.350320\pi\)
0.453095 + 0.891462i \(0.350320\pi\)
\(230\) −5.69412 0.696938i −0.375459 0.0459548i
\(231\) 0 0
\(232\) −3.64581 + 2.10491i −0.239359 + 0.138194i
\(233\) −0.00572506 0.00330537i −0.000375061 0.000216542i 0.499812 0.866134i \(-0.333402\pi\)
−0.500188 + 0.865917i \(0.666736\pi\)
\(234\) 0 0
\(235\) −8.30605 + 3.52946i −0.541827 + 0.230237i
\(236\) 6.15198 0.400460
\(237\) 0 0
\(238\) 0.328014 0.189379i 0.0212620 0.0122756i
\(239\) −4.67499 −0.302400 −0.151200 0.988503i \(-0.548314\pi\)
−0.151200 + 0.988503i \(0.548314\pi\)
\(240\) 0 0
\(241\) 13.9044 + 24.0831i 0.895659 + 1.55133i 0.832987 + 0.553292i \(0.186629\pi\)
0.0626717 + 0.998034i \(0.480038\pi\)
\(242\) 7.65351 + 4.41876i 0.491986 + 0.284049i
\(243\) 0 0
\(244\) −0.653722 + 1.13228i −0.0418503 + 0.0724868i
\(245\) 20.5988 + 2.52121i 1.31601 + 0.161074i
\(246\) 0 0
\(247\) −21.9135 + 2.55244i −1.39432 + 0.162408i
\(248\) 4.26558i 0.270864i
\(249\) 0 0
\(250\) 7.04598 + 8.68068i 0.445627 + 0.549014i
\(251\) −3.03259 5.25259i −0.191415 0.331541i 0.754304 0.656525i \(-0.227974\pi\)
−0.945719 + 0.324984i \(0.894641\pi\)
\(252\) 0 0
\(253\) −3.26721 + 1.88633i −0.205408 + 0.118592i
\(254\) 6.66597 0.418260
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −1.11707 + 0.644941i −0.0696809 + 0.0402303i −0.534436 0.845209i \(-0.679476\pi\)
0.464755 + 0.885439i \(0.346142\pi\)
\(258\) 0 0
\(259\) −6.20604 −0.385625
\(260\) −9.04106 6.80751i −0.560703 0.422184i
\(261\) 0 0
\(262\) −6.12771 + 3.53784i −0.378571 + 0.218568i
\(263\) 24.4863 + 14.1372i 1.50989 + 0.871737i 0.999933 + 0.0115378i \(0.00367269\pi\)
0.509959 + 0.860199i \(0.329661\pi\)
\(264\) 0 0
\(265\) 21.9328 9.31984i 1.34732 0.572513i
\(266\) 14.1119 10.4971i 0.865255 0.643621i
\(267\) 0 0
\(268\) −9.31187 5.37621i −0.568813 0.328404i
\(269\) 13.8782 24.0377i 0.846169 1.46561i −0.0384337 0.999261i \(-0.512237\pi\)
0.884602 0.466346i \(-0.154430\pi\)
\(270\) 0 0
\(271\) −5.42826 + 9.40202i −0.329743 + 0.571132i −0.982461 0.186469i \(-0.940296\pi\)
0.652718 + 0.757601i \(0.273629\pi\)
\(272\) 0.0812933 0.0469347i 0.00492913 0.00284584i
\(273\) 0 0
\(274\) −18.8565 −1.13916
\(275\) 7.13565 + 1.77332i 0.430296 + 0.106935i
\(276\) 0 0
\(277\) 24.5237i 1.47349i −0.676173 0.736743i \(-0.736363\pi\)
0.676173 0.736743i \(-0.263637\pi\)
\(278\) 19.9923i 1.19906i
\(279\) 0 0
\(280\) 8.95558 + 1.09613i 0.535199 + 0.0655063i
\(281\) −3.29709 5.71073i −0.196688 0.340674i 0.750765 0.660570i \(-0.229685\pi\)
−0.947453 + 0.319896i \(0.896352\pi\)
\(282\) 0 0
\(283\) 20.4709 + 11.8189i 1.21687 + 0.702559i 0.964247 0.265006i \(-0.0853740\pi\)
0.252621 + 0.967565i \(0.418707\pi\)
\(284\) −8.67611 −0.514833
\(285\) 0 0
\(286\) −7.44281 −0.440103
\(287\) −27.1248 15.6605i −1.60113 0.924412i
\(288\) 0 0
\(289\) −8.49559 14.7148i −0.499741 0.865577i
\(290\) 1.14364 9.34372i 0.0671567 0.548682i
\(291\) 0 0
\(292\) 12.7142i 0.744044i
\(293\) 23.0123i 1.34439i 0.740374 + 0.672195i \(0.234648\pi\)
−0.740374 + 0.672195i \(0.765352\pi\)
\(294\) 0 0
\(295\) −8.27451 + 10.9894i −0.481761 + 0.639827i
\(296\) −1.53807 −0.0893987
\(297\) 0 0
\(298\) 10.5724 6.10397i 0.612442 0.353593i
\(299\) −6.49233 + 11.2451i −0.375461 + 0.650318i
\(300\) 0 0
\(301\) 9.25313 16.0269i 0.533341 0.923774i
\(302\) −17.2433 9.95543i −0.992241 0.572870i
\(303\) 0 0
\(304\) 3.49741 2.60156i 0.200590 0.149209i
\(305\) −1.14335 2.69069i −0.0654678 0.154068i
\(306\) 0 0
\(307\) 22.0807 + 12.7483i 1.26021 + 0.727584i 0.973116 0.230318i \(-0.0739765\pi\)
0.287097 + 0.957902i \(0.407310\pi\)
\(308\) 5.13860 2.96677i 0.292799 0.169048i
\(309\) 0 0
\(310\) 7.61968 + 5.73727i 0.432768 + 0.325855i
\(311\) 30.3172 1.71913 0.859565 0.511027i \(-0.170735\pi\)
0.859565 + 0.511027i \(0.170735\pi\)
\(312\) 0 0
\(313\) −6.54063 + 3.77623i −0.369698 + 0.213445i −0.673327 0.739345i \(-0.735135\pi\)
0.303628 + 0.952791i \(0.401802\pi\)
\(314\) 8.11721 + 14.0594i 0.458081 + 0.793419i
\(315\) 0 0
\(316\) −12.9622 −0.729183
\(317\) −12.1344 + 7.00579i −0.681535 + 0.393484i −0.800433 0.599422i \(-0.795397\pi\)
0.118898 + 0.992906i \(0.462064\pi\)
\(318\) 0 0
\(319\) −3.09535 5.36131i −0.173307 0.300176i
\(320\) 2.21950 + 0.271659i 0.124074 + 0.0151862i
\(321\) 0 0
\(322\) 10.3516i 0.576873i
\(323\) 0.244207 + 0.328300i 0.0135880 + 0.0182671i
\(324\) 0 0
\(325\) 24.3207 6.99400i 1.34907 0.387957i
\(326\) 1.02875 1.78185i 0.0569773 0.0986875i
\(327\) 0 0
\(328\) −6.72248 3.88123i −0.371187 0.214305i
\(329\) −8.14258 14.1034i −0.448915 0.777544i
\(330\) 0 0
\(331\) −2.20541 −0.121220 −0.0606102 0.998162i \(-0.519305\pi\)
−0.0606102 + 0.998162i \(0.519305\pi\)
\(332\) 1.78686 1.03164i 0.0980665 0.0566187i
\(333\) 0 0
\(334\) 21.7279 1.18890
\(335\) 22.1282 9.40287i 1.20899 0.513734i
\(336\) 0 0
\(337\) 3.35026 + 1.93428i 0.182500 + 0.105367i 0.588467 0.808521i \(-0.299732\pi\)
−0.405966 + 0.913888i \(0.633065\pi\)
\(338\) −10.9263 + 6.30829i −0.594311 + 0.343126i
\(339\) 0 0
\(340\) −0.0255005 + 0.208344i −0.00138296 + 0.0112990i
\(341\) 6.27270 0.339685
\(342\) 0 0
\(343\) 9.20290i 0.496910i
\(344\) 2.29325 3.97202i 0.123644 0.214157i
\(345\) 0 0
\(346\) 11.6026 + 20.0963i 0.623761 + 1.08039i
\(347\) −10.6406 6.14337i −0.571219 0.329793i 0.186417 0.982471i \(-0.440312\pi\)
−0.757636 + 0.652677i \(0.773646\pi\)
\(348\) 0 0
\(349\) 23.1329 1.23828 0.619139 0.785282i \(-0.287482\pi\)
0.619139 + 0.785282i \(0.287482\pi\)
\(350\) −14.0034 + 14.5232i −0.748515 + 0.776298i
\(351\) 0 0
\(352\) 1.27352 0.735269i 0.0678791 0.0391900i
\(353\) 2.27216i 0.120935i −0.998170 0.0604674i \(-0.980741\pi\)
0.998170 0.0604674i \(-0.0192591\pi\)
\(354\) 0 0
\(355\) 11.6695 15.4983i 0.619353 0.822564i
\(356\) −0.813846 + 1.40962i −0.0431338 + 0.0747098i
\(357\) 0 0
\(358\) −5.52142 3.18779i −0.291816 0.168480i
\(359\) 10.3404 17.9101i 0.545746 0.945260i −0.452813 0.891605i \(-0.649580\pi\)
0.998560 0.0536549i \(-0.0170871\pi\)
\(360\) 0 0
\(361\) 13.0275 + 13.8305i 0.685660 + 0.727922i
\(362\) 8.79207i 0.462101i
\(363\) 0 0
\(364\) 10.2110 17.6860i 0.535202 0.926997i
\(365\) 22.7117 + 17.1008i 1.18878 + 0.895099i
\(366\) 0 0
\(367\) −31.7744 + 18.3450i −1.65861 + 0.957600i −0.685255 + 0.728304i \(0.740309\pi\)
−0.973357 + 0.229296i \(0.926358\pi\)
\(368\) 2.56549i 0.133735i
\(369\) 0 0
\(370\) 2.06873 2.74749i 0.107548 0.142835i
\(371\) 21.5012 + 37.2411i 1.11628 + 1.93346i
\(372\) 0 0
\(373\) 19.5380i 1.01164i −0.862640 0.505819i \(-0.831190\pi\)
0.862640 0.505819i \(-0.168810\pi\)
\(374\) 0.0690193 + 0.119545i 0.00356890 + 0.00618152i
\(375\) 0 0
\(376\) −2.01801 3.49530i −0.104071 0.180256i
\(377\) −18.4525 10.6536i −0.950352 0.548686i
\(378\) 0 0
\(379\) −3.46802 −0.178140 −0.0890701 0.996025i \(-0.528390\pi\)
−0.0890701 + 0.996025i \(0.528390\pi\)
\(380\) −0.0568730 + 9.74663i −0.00291752 + 0.499991i
\(381\) 0 0
\(382\) 11.2288 + 6.48293i 0.574514 + 0.331696i
\(383\) 21.7388 + 12.5509i 1.11080 + 0.641322i 0.939037 0.343816i \(-0.111720\pi\)
0.171765 + 0.985138i \(0.445053\pi\)
\(384\) 0 0
\(385\) −1.61190 + 13.1695i −0.0821501 + 0.671182i
\(386\) −3.05828 5.29710i −0.155662 0.269615i
\(387\) 0 0
\(388\) 11.9488i 0.606607i
\(389\) −7.02074 12.1603i −0.355965 0.616550i 0.631317 0.775525i \(-0.282515\pi\)
−0.987283 + 0.158974i \(0.949181\pi\)
\(390\) 0 0
\(391\) 0.240821 0.0121788
\(392\) 9.28080i 0.468751i
\(393\) 0 0
\(394\) 3.67471 6.36478i 0.185129 0.320653i
\(395\) 17.4344 23.1547i 0.877221 1.16504i
\(396\) 0 0
\(397\) −26.6267 15.3729i −1.33635 0.771544i −0.350089 0.936716i \(-0.613849\pi\)
−0.986265 + 0.165172i \(0.947182\pi\)
\(398\) 3.43559i 0.172211i
\(399\) 0 0
\(400\) −3.47054 + 3.59936i −0.173527 + 0.179968i
\(401\) 19.3518 33.5183i 0.966381 1.67382i 0.260525 0.965467i \(-0.416104\pi\)
0.705857 0.708355i \(-0.250562\pi\)
\(402\) 0 0
\(403\) 18.6969 10.7946i 0.931357 0.537719i
\(404\) −0.252103 + 0.436656i −0.0125426 + 0.0217244i
\(405\) 0 0
\(406\) 16.9864 0.843022
\(407\) 2.26180i 0.112113i
\(408\) 0 0
\(409\) −10.3920 17.9994i −0.513850 0.890014i −0.999871 0.0160671i \(-0.994885\pi\)
0.486021 0.873947i \(-0.338448\pi\)
\(410\) 15.9749 6.78818i 0.788946 0.335244i
\(411\) 0 0
\(412\) 4.62282 2.66899i 0.227750 0.131491i
\(413\) −21.4973 12.4115i −1.05781 0.610728i
\(414\) 0 0
\(415\) −0.560510 + 4.57947i −0.0275143 + 0.224797i
\(416\) 2.53064 4.38320i 0.124075 0.214904i
\(417\) 0 0
\(418\) 3.82569 + 5.14308i 0.187121 + 0.251556i
\(419\) −36.2672 −1.77177 −0.885883 0.463908i \(-0.846447\pi\)
−0.885883 + 0.463908i \(0.846447\pi\)
\(420\) 0 0
\(421\) 10.7212 18.5697i 0.522519 0.905030i −0.477137 0.878829i \(-0.658326\pi\)
0.999657 0.0262013i \(-0.00834109\pi\)
\(422\) −3.49822 + 2.01970i −0.170291 + 0.0983174i
\(423\) 0 0
\(424\) 5.32873 + 9.22964i 0.258786 + 0.448231i
\(425\) −0.337869 0.325778i −0.0163891 0.0158025i
\(426\) 0 0
\(427\) 4.56869 2.63773i 0.221094 0.127649i
\(428\) 15.5257 8.96375i 0.750461 0.433279i
\(429\) 0 0
\(430\) 4.01084 + 9.43890i 0.193420 + 0.455184i
\(431\) −2.91216 5.04400i −0.140274 0.242961i 0.787326 0.616537i \(-0.211465\pi\)
−0.927600 + 0.373576i \(0.878132\pi\)
\(432\) 0 0
\(433\) 27.3690 15.8015i 1.31527 0.759371i 0.332305 0.943172i \(-0.392174\pi\)
0.982963 + 0.183801i \(0.0588403\pi\)
\(434\) −8.60569 + 14.9055i −0.413086 + 0.715486i
\(435\) 0 0
\(436\) −8.87262 −0.424922
\(437\) 11.1076 1.29379i 0.531349 0.0618904i
\(438\) 0 0
\(439\) −0.932951 + 1.61592i −0.0445273 + 0.0771236i −0.887430 0.460942i \(-0.847512\pi\)
0.842903 + 0.538066i \(0.180845\pi\)
\(440\) −0.399485 + 3.26387i −0.0190447 + 0.155599i
\(441\) 0 0
\(442\) 0.411448 + 0.237550i 0.0195706 + 0.0112991i
\(443\) 13.6368 7.87318i 0.647902 0.374066i −0.139750 0.990187i \(-0.544630\pi\)
0.787652 + 0.616121i \(0.211297\pi\)
\(444\) 0 0
\(445\) −1.42340 3.34975i −0.0674755 0.158794i
\(446\) −9.02593 15.6334i −0.427390 0.740262i
\(447\) 0 0
\(448\) 4.03495i 0.190633i
\(449\) 29.7436 1.40369 0.701845 0.712330i \(-0.252360\pi\)
0.701845 + 0.712330i \(0.252360\pi\)
\(450\) 0 0
\(451\) 5.70749 9.88567i 0.268755 0.465498i
\(452\) 13.7409 7.93334i 0.646320 0.373153i
\(453\) 0 0
\(454\) 13.4257 23.2539i 0.630098 1.09136i
\(455\) 17.8588 + 42.0280i 0.837234 + 1.97030i
\(456\) 0 0
\(457\) 12.7891i 0.598250i 0.954214 + 0.299125i \(0.0966948\pi\)
−0.954214 + 0.299125i \(0.903305\pi\)
\(458\) −11.8759 6.85657i −0.554926 0.320387i
\(459\) 0 0
\(460\) 4.58278 + 3.45062i 0.213673 + 0.160886i
\(461\) −5.96303 + 10.3283i −0.277726 + 0.481035i −0.970819 0.239813i \(-0.922914\pi\)
0.693093 + 0.720848i \(0.256247\pi\)
\(462\) 0 0
\(463\) 19.3208i 0.897913i 0.893554 + 0.448956i \(0.148204\pi\)
−0.893554 + 0.448956i \(0.851796\pi\)
\(464\) 4.20982 0.195436
\(465\) 0 0
\(466\) 0.00330537 + 0.00572506i 0.000153118 + 0.000265208i
\(467\) 26.7009i 1.23557i 0.786347 + 0.617785i \(0.211970\pi\)
−0.786347 + 0.617785i \(0.788030\pi\)
\(468\) 0 0
\(469\) 21.6927 + 37.5729i 1.00168 + 1.73496i
\(470\) 8.95798 + 1.09642i 0.413201 + 0.0505742i
\(471\) 0 0
\(472\) −5.32777 3.07599i −0.245231 0.141584i
\(473\) 5.84101 + 3.37231i 0.268570 + 0.155059i
\(474\) 0 0
\(475\) −17.3341 13.2110i −0.795342 0.606161i
\(476\) −0.378758 −0.0173604
\(477\) 0 0
\(478\) 4.04866 + 2.33750i 0.185182 + 0.106915i
\(479\) 6.79124 + 11.7628i 0.310299 + 0.537454i 0.978427 0.206592i \(-0.0662373\pi\)
−0.668128 + 0.744047i \(0.732904\pi\)
\(480\) 0 0
\(481\) −3.89231 6.74168i −0.177474 0.307394i
\(482\) 27.8087i 1.26665i
\(483\) 0 0
\(484\) −4.41876 7.65351i −0.200853 0.347887i
\(485\) 21.3443 + 16.0713i 0.969195 + 0.729760i
\(486\) 0 0
\(487\) 8.03640i 0.364164i −0.983283 0.182082i \(-0.941716\pi\)
0.983283 0.182082i \(-0.0582837\pi\)
\(488\) 1.13228 0.653722i 0.0512559 0.0295926i
\(489\) 0 0
\(490\) −16.5785 12.4828i −0.748938 0.563916i
\(491\) −10.3390 + 17.9077i −0.466593 + 0.808163i −0.999272 0.0381546i \(-0.987852\pi\)
0.532679 + 0.846317i \(0.321185\pi\)
\(492\) 0 0
\(493\) 0.395174i 0.0177977i
\(494\) 20.2538 + 8.74626i 0.911263 + 0.393513i
\(495\) 0 0
\(496\) −2.13279 + 3.69410i −0.0957650 + 0.165870i
\(497\) 30.3175 + 17.5038i 1.35993 + 0.785154i
\(498\) 0 0
\(499\) −0.551160 + 0.954638i −0.0246733 + 0.0427355i −0.878098 0.478480i \(-0.841188\pi\)
0.853425 + 0.521216i \(0.174521\pi\)
\(500\) −1.76166 11.0407i −0.0787840 0.493754i
\(501\) 0 0
\(502\) 6.06517i 0.270702i
\(503\) −21.0518 + 12.1543i −0.938653 + 0.541932i −0.889538 0.456861i \(-0.848974\pi\)
−0.0491154 + 0.998793i \(0.515640\pi\)
\(504\) 0 0
\(505\) −0.440923 1.03765i −0.0196208 0.0461746i
\(506\) 3.77265 0.167715
\(507\) 0 0
\(508\) −5.77290 3.33298i −0.256131 0.147877i
\(509\) 4.96728 + 8.60358i 0.220171 + 0.381347i 0.954860 0.297057i \(-0.0960052\pi\)
−0.734689 + 0.678404i \(0.762672\pi\)
\(510\) 0 0
\(511\) −25.6506 + 44.4282i −1.13472 + 1.96539i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 1.28988 0.0568942
\(515\) −1.45011 + 11.8477i −0.0638994 + 0.522070i
\(516\) 0 0
\(517\) 5.13998 2.96757i 0.226056 0.130513i
\(518\) 5.37459 + 3.10302i 0.236146 + 0.136339i
\(519\) 0 0
\(520\) 4.42603 + 10.4160i 0.194094 + 0.456772i
\(521\) 20.9057 0.915895 0.457947 0.888979i \(-0.348585\pi\)
0.457947 + 0.888979i \(0.348585\pi\)
\(522\) 0 0
\(523\) 27.3676 15.8007i 1.19670 0.690916i 0.236883 0.971538i \(-0.423874\pi\)
0.959818 + 0.280622i \(0.0905408\pi\)
\(524\) 7.07568 0.309102
\(525\) 0 0
\(526\) −14.1372 24.4863i −0.616411 1.06766i
\(527\) −0.346763 0.200204i −0.0151052 0.00872101i
\(528\) 0 0
\(529\) −8.20913 + 14.2186i −0.356919 + 0.618202i
\(530\) −23.6543 2.89520i −1.02748 0.125759i
\(531\) 0 0
\(532\) −17.4698 + 2.03485i −0.757413 + 0.0882218i
\(533\) 39.2880i 1.70175i
\(534\) 0 0
\(535\) −4.87017 + 39.7902i −0.210556 + 1.72028i
\(536\) 5.37621 + 9.31187i 0.232217 + 0.402211i
\(537\) 0 0
\(538\) −24.0377 + 13.8782i −1.03634 + 0.598332i
\(539\) −13.6478 −0.587851
\(540\) 0 0
\(541\) −2.50615 4.34078i −0.107748 0.186625i 0.807110 0.590402i \(-0.201031\pi\)
−0.914858 + 0.403777i \(0.867697\pi\)
\(542\) 9.40202 5.42826i 0.403851 0.233164i
\(543\) 0 0
\(544\) −0.0938694 −0.00402462
\(545\) 11.9338 15.8493i 0.511189 0.678911i
\(546\) 0 0
\(547\) −30.7554 + 17.7566i −1.31500 + 0.759218i −0.982920 0.184032i \(-0.941085\pi\)
−0.332084 + 0.943250i \(0.607752\pi\)
\(548\) 16.3302 + 9.42826i 0.697593 + 0.402755i
\(549\) 0 0
\(550\) −5.29299 5.10356i −0.225694 0.217617i
\(551\) 2.12304 + 18.2270i 0.0904445 + 0.776495i
\(552\) 0 0
\(553\) 45.2948 + 26.1510i 1.92613 + 1.11205i
\(554\) −12.2618 + 21.2381i −0.520956 + 0.902322i
\(555\) 0 0
\(556\) 9.99616 17.3139i 0.423932 0.734271i
\(557\) 8.45640 4.88231i 0.358309 0.206870i −0.310030 0.950727i \(-0.600339\pi\)
0.668339 + 0.743857i \(0.267006\pi\)
\(558\) 0 0
\(559\) 23.2135 0.981828
\(560\) −7.20770 5.42707i −0.304581 0.229336i
\(561\) 0 0
\(562\) 6.59418i 0.278159i
\(563\) 11.5237i 0.485665i 0.970068 + 0.242833i \(0.0780766\pi\)
−0.970068 + 0.242833i \(0.921923\pi\)
\(564\) 0 0
\(565\) −4.31033 + 35.2162i −0.181337 + 1.48156i
\(566\) −11.8189 20.4709i −0.496784 0.860456i
\(567\) 0 0
\(568\) 7.51373 + 4.33806i 0.315269 + 0.182021i
\(569\) 1.93925 0.0812978 0.0406489 0.999173i \(-0.487057\pi\)
0.0406489 + 0.999173i \(0.487057\pi\)
\(570\) 0 0
\(571\) −38.0052 −1.59047 −0.795235 0.606301i \(-0.792652\pi\)
−0.795235 + 0.606301i \(0.792652\pi\)
\(572\) 6.44566 + 3.72141i 0.269507 + 0.155600i
\(573\) 0 0
\(574\) 15.6605 + 27.1248i 0.653658 + 1.13217i
\(575\) −12.3278 + 3.54516i −0.514106 + 0.147843i
\(576\) 0 0
\(577\) 28.3094i 1.17854i −0.807938 0.589268i \(-0.799416\pi\)
0.807938 0.589268i \(-0.200584\pi\)
\(578\) 16.9912i 0.706740i
\(579\) 0 0
\(580\) −5.66228 + 7.52008i −0.235113 + 0.312254i
\(581\) −8.32524 −0.345389
\(582\) 0 0
\(583\) −13.5725 + 7.83611i −0.562117 + 0.324539i
\(584\) −6.35711 + 11.0108i −0.263059 + 0.455632i
\(585\) 0 0
\(586\) 11.5061 19.9292i 0.475314 0.823267i
\(587\) −9.39980 5.42698i −0.387971 0.223995i 0.293309 0.956018i \(-0.405243\pi\)
−0.681281 + 0.732022i \(0.738577\pi\)
\(588\) 0 0
\(589\) −17.0696 7.37122i −0.703342 0.303726i
\(590\) 12.6606 5.37984i 0.521230 0.221484i
\(591\) 0 0
\(592\) 1.33201 + 0.769037i 0.0547453 + 0.0316072i
\(593\) 24.0190 13.8674i 0.986341 0.569464i 0.0821625 0.996619i \(-0.473817\pi\)
0.904179 + 0.427155i \(0.140484\pi\)
\(594\) 0 0
\(595\) 0.509436 0.676583i 0.0208848 0.0277372i
\(596\) −12.2079 −0.500056
\(597\) 0 0
\(598\) 11.2451 6.49233i 0.459844 0.265491i
\(599\) −15.6071 27.0323i −0.637690 1.10451i −0.985938 0.167109i \(-0.946557\pi\)
0.348248 0.937402i \(-0.386777\pi\)
\(600\) 0 0
\(601\) 42.3271 1.72656 0.863280 0.504726i \(-0.168406\pi\)
0.863280 + 0.504726i \(0.168406\pi\)
\(602\) −16.0269 + 9.25313i −0.653207 + 0.377129i
\(603\) 0 0
\(604\) 9.95543 + 17.2433i 0.405081 + 0.701620i
\(605\) 19.6149 + 2.40079i 0.797459 + 0.0976060i
\(606\) 0 0
\(607\) 12.9882i 0.527176i −0.964635 0.263588i \(-0.915094\pi\)
0.964635 0.263588i \(-0.0849059\pi\)
\(608\) −4.32963 + 0.504306i −0.175590 + 0.0204523i
\(609\) 0 0
\(610\) −0.355179 + 2.90188i −0.0143808 + 0.117494i
\(611\) 10.2137 17.6907i 0.413204 0.715690i
\(612\) 0 0
\(613\) −23.2303 13.4120i −0.938264 0.541707i −0.0488484 0.998806i \(-0.515555\pi\)
−0.889416 + 0.457099i \(0.848888\pi\)
\(614\) −12.7483 22.0807i −0.514480 0.891105i
\(615\) 0 0
\(616\) −5.93355 −0.239069
\(617\) −11.9663 + 6.90877i −0.481747 + 0.278136i −0.721144 0.692785i \(-0.756383\pi\)
0.239398 + 0.970922i \(0.423050\pi\)
\(618\) 0 0
\(619\) 36.2091 1.45537 0.727684 0.685912i \(-0.240597\pi\)
0.727684 + 0.685912i \(0.240597\pi\)
\(620\) −3.73020 8.77846i −0.149808 0.352551i
\(621\) 0 0
\(622\) −26.2555 15.1586i −1.05275 0.607804i
\(623\) 5.68775 3.28383i 0.227875 0.131564i
\(624\) 0 0
\(625\) 22.0916 + 11.7030i 0.883665 + 0.468120i
\(626\) 7.55247 0.301857
\(627\) 0 0
\(628\) 16.2344i 0.647824i
\(629\) −0.0721890 + 0.125035i −0.00287837 + 0.00498547i
\(630\) 0 0
\(631\) −1.00438 1.73963i −0.0399836 0.0692536i 0.845341 0.534227i \(-0.179397\pi\)
−0.885325 + 0.464973i \(0.846064\pi\)
\(632\) 11.2256 + 6.48112i 0.446532 + 0.257805i
\(633\) 0 0
\(634\) 14.0116 0.556471
\(635\) 13.7184 5.82932i 0.544399 0.231329i
\(636\) 0 0
\(637\) −40.6796 + 23.4864i −1.61178 + 0.930564i
\(638\) 6.19071i 0.245093i
\(639\) 0 0
\(640\) −1.78632 1.34502i −0.0706104 0.0531664i
\(641\) 8.04795 13.9395i 0.317875 0.550575i −0.662170 0.749354i \(-0.730364\pi\)
0.980044 + 0.198779i \(0.0636975\pi\)
\(642\) 0 0
\(643\) −34.6016 19.9773i −1.36455 0.787826i −0.374328 0.927296i \(-0.622127\pi\)
−0.990226 + 0.139470i \(0.955460\pi\)
\(644\) −5.17581 + 8.96476i −0.203955 + 0.353261i
\(645\) 0 0
\(646\) −0.0473389 0.406420i −0.00186252 0.0159904i
\(647\) 32.2985i 1.26979i −0.772600 0.634893i \(-0.781044\pi\)
0.772600 0.634893i \(-0.218956\pi\)
\(648\) 0 0
\(649\) 4.52336 7.83470i 0.177558 0.307539i
\(650\) −24.5594 6.10339i −0.963298 0.239394i
\(651\) 0 0
\(652\) −1.78185 + 1.02875i −0.0697826 + 0.0402890i
\(653\) 25.3382i 0.991559i −0.868448 0.495780i \(-0.834882\pi\)
0.868448 0.495780i \(-0.165118\pi\)
\(654\) 0 0
\(655\) −9.51690 + 12.6394i −0.371856 + 0.493862i
\(656\) 3.88123 + 6.72248i 0.151536 + 0.262469i
\(657\) 0 0
\(658\) 16.2852i 0.634862i
\(659\) −2.44914 4.24204i −0.0954051 0.165247i 0.814372 0.580343i \(-0.197081\pi\)
−0.909778 + 0.415096i \(0.863748\pi\)
\(660\) 0 0
\(661\) −24.1271 41.7893i −0.938435 1.62542i −0.768391 0.639980i \(-0.778942\pi\)
−0.170044 0.985437i \(-0.554391\pi\)
\(662\) 1.90994 + 1.10271i 0.0742320 + 0.0428579i
\(663\) 0 0
\(664\) −2.06328 −0.0800709
\(665\) 19.8623 33.9436i 0.770227 1.31627i
\(666\) 0 0
\(667\) 9.35330 + 5.40013i 0.362161 + 0.209094i
\(668\) −18.8169 10.8639i −0.728047 0.420338i
\(669\) 0 0
\(670\) −23.8650 2.92099i −0.921987 0.112848i
\(671\) 0.961324 + 1.66506i 0.0371115 + 0.0642790i
\(672\) 0 0
\(673\) 11.3374i 0.437025i −0.975834 0.218512i \(-0.929880\pi\)
0.975834 0.218512i \(-0.0701204\pi\)
\(674\) −1.93428 3.35026i −0.0745055 0.129047i
\(675\) 0 0
\(676\) 12.6166 0.485253
\(677\) 30.8182i 1.18444i 0.805776 + 0.592220i \(0.201748\pi\)
−0.805776 + 0.592220i \(0.798252\pi\)
\(678\) 0 0
\(679\) −24.1063 + 41.7534i −0.925116 + 1.60235i
\(680\) 0.126256 0.167681i 0.00484169 0.00643026i
\(681\) 0 0
\(682\) −5.43231 3.13635i −0.208014 0.120097i
\(683\) 10.5683i 0.404386i −0.979346 0.202193i \(-0.935193\pi\)
0.979346 0.202193i \(-0.0648069\pi\)
\(684\) 0 0
\(685\) −38.8063 + 16.4898i −1.48271 + 0.630043i
\(686\) 4.60145 7.96995i 0.175684 0.304294i
\(687\) 0 0
\(688\) −3.97202 + 2.29325i −0.151432 + 0.0874292i
\(689\) −26.9702 + 46.7138i −1.02748 + 1.77965i
\(690\) 0 0
\(691\) −0.570970 −0.0217207 −0.0108604 0.999941i \(-0.503457\pi\)
−0.0108604 + 0.999941i \(0.503457\pi\)
\(692\) 23.2053i 0.882132i
\(693\) 0 0
\(694\) 6.14337 + 10.6406i 0.233199 + 0.403913i
\(695\) 17.4831 + 41.1438i 0.663171 + 1.56067i
\(696\) 0 0
\(697\) −0.631035 + 0.364328i −0.0239022 + 0.0137999i
\(698\) −20.0337 11.5665i −0.758287 0.437797i
\(699\) 0 0
\(700\) 19.3889 5.57575i 0.732833 0.210743i
\(701\) −3.36247 + 5.82398i −0.126999 + 0.219969i −0.922513 0.385967i \(-0.873868\pi\)
0.795514 + 0.605936i \(0.207201\pi\)
\(702\) 0 0
\(703\) −2.65790 + 6.15494i −0.100245 + 0.232138i
\(704\) −1.47054 −0.0554230
\(705\) 0 0
\(706\) −1.13608 + 1.96775i −0.0427569 + 0.0740571i
\(707\) 1.76188 1.01722i 0.0662625 0.0382566i
\(708\) 0 0
\(709\) −15.4517 26.7632i −0.580302 1.00511i −0.995443 0.0953554i \(-0.969601\pi\)
0.415141 0.909757i \(-0.363732\pi\)
\(710\) −17.8552 + 7.58716i −0.670095 + 0.284741i
\(711\) 0 0
\(712\) 1.40962 0.813846i 0.0528278 0.0305002i
\(713\) −9.47717 + 5.47164i −0.354923 + 0.204915i
\(714\) 0 0
\(715\) −15.3171 + 6.50866i −0.572828 + 0.243410i
\(716\) 3.18779 + 5.52142i 0.119133 + 0.206345i
\(717\) 0 0
\(718\) −17.9101 + 10.3404i −0.668400 + 0.385901i
\(719\) 11.7185 20.2970i 0.437025 0.756949i −0.560434 0.828199i \(-0.689366\pi\)
0.997458 + 0.0712504i \(0.0226989\pi\)
\(720\) 0 0
\(721\) −21.5384 −0.802133
\(722\) −4.36691 18.4914i −0.162520 0.688177i
\(723\) 0 0
\(724\) −4.39603 + 7.61415i −0.163377 + 0.282978i
\(725\) −5.81740 20.2293i −0.216053 0.751296i
\(726\) 0 0
\(727\) 34.0238 + 19.6436i 1.26187 + 0.728543i 0.973437 0.228957i \(-0.0735314\pi\)
0.288436 + 0.957499i \(0.406865\pi\)
\(728\) −17.6860 + 10.2110i −0.655486 + 0.378445i
\(729\) 0 0
\(730\) −11.1184 26.1656i −0.411512 0.968432i
\(731\) −0.215266 0.372851i −0.00796189 0.0137904i
\(732\) 0 0
\(733\) 45.2875i 1.67273i −0.548171 0.836366i \(-0.684676\pi\)
0.548171 0.836366i \(-0.315324\pi\)
\(734\) 36.6899 1.35425
\(735\) 0 0
\(736\) −1.28274 + 2.22178i −0.0472826 + 0.0818959i
\(737\) −13.6935 + 7.90592i −0.504405 + 0.291218i
\(738\) 0 0
\(739\) 15.7422 27.2663i 0.579086 1.00301i −0.416499 0.909136i \(-0.636743\pi\)
0.995585 0.0938695i \(-0.0299237\pi\)
\(740\) −3.16532 + 1.34503i −0.116359 + 0.0494442i
\(741\) 0 0
\(742\) 43.0023i 1.57866i
\(743\) 40.4415 + 23.3489i 1.48365 + 0.856587i 0.999827 0.0185770i \(-0.00591359\pi\)
0.483826 + 0.875164i \(0.339247\pi\)
\(744\) 0 0
\(745\) 16.4199 21.8073i 0.601577 0.798956i
\(746\) −9.76898 + 16.9204i −0.357668 + 0.619499i
\(747\) 0 0
\(748\) 0.138039i 0.00504719i
\(749\) −72.3365 −2.64312
\(750\) 0 0
\(751\) −14.8807 25.7741i −0.543004 0.940510i −0.998730 0.0503901i \(-0.983954\pi\)
0.455726 0.890120i \(-0.349380\pi\)
\(752\) 4.03603i 0.147179i
\(753\) 0 0
\(754\) 10.6536 + 18.4525i 0.387980 + 0.672000i
\(755\) −44.1922 5.40896i −1.60832 0.196852i
\(756\) 0 0
\(757\) −11.2784 6.51161i −0.409922 0.236668i 0.280834 0.959756i \(-0.409389\pi\)
−0.690756 + 0.723088i \(0.742722\pi\)
\(758\) 3.00339 + 1.73401i 0.109088 + 0.0629820i
\(759\) 0 0
\(760\) 4.92257 8.41239i 0.178560 0.305150i
\(761\) −43.4538 −1.57520 −0.787600 0.616187i \(-0.788676\pi\)
−0.787600 + 0.616187i \(0.788676\pi\)
\(762\) 0 0
\(763\) 31.0042 + 17.9003i 1.12243 + 0.648034i
\(764\) −6.48293 11.2288i −0.234544 0.406242i
\(765\) 0 0
\(766\) −12.5509 21.7388i −0.453483 0.785456i
\(767\) 31.1369i 1.12429i
\(768\) 0 0
\(769\) −23.6418 40.9487i −0.852544 1.47665i −0.878905 0.476996i \(-0.841725\pi\)
0.0263617 0.999652i \(-0.491608\pi\)
\(770\) 7.98072 10.5992i 0.287605 0.381969i
\(771\) 0 0
\(772\) 6.11656i 0.220140i
\(773\) −11.4692 + 6.62172i −0.412517 + 0.238167i −0.691871 0.722022i \(-0.743213\pi\)
0.279354 + 0.960188i \(0.409880\pi\)
\(774\) 0 0
\(775\) 20.6983 + 5.14385i 0.743505 + 0.184772i
\(776\) −5.97438 + 10.3479i −0.214468 + 0.371469i
\(777\) 0 0
\(778\) 14.0415i 0.503411i
\(779\) −27.1485 + 20.1944i −0.972696 + 0.723541i
\(780\) 0 0
\(781\) −6.37928 + 11.0492i −0.228269 + 0.395373i
\(782\) −0.208557 0.120411i −0.00745799 0.00430587i
\(783\) 0 0
\(784\) 4.64040 8.03741i 0.165729 0.287050i
\(785\) 28.9999 + 21.8356i 1.03505 + 0.779345i
\(786\) 0 0
\(787\) 21.7913i 0.776775i 0.921496 + 0.388388i \(0.126968\pi\)
−0.921496 + 0.388388i \(0.873032\pi\)
\(788\) −6.36478 + 3.67471i −0.226736 + 0.130906i
\(789\) 0 0
\(790\) −26.6760 + 11.3353i −0.949089 + 0.403293i
\(791\) −64.0212 −2.27633
\(792\) 0 0
\(793\) 5.73079 + 3.30867i 0.203506 + 0.117494i
\(794\) 15.3729 + 26.6267i 0.545564 + 0.944945i
\(795\) 0 0
\(796\) −1.71780 + 2.97531i −0.0608857 + 0.105457i
\(797\) 14.8524i 0.526099i 0.964782 + 0.263049i \(0.0847283\pi\)
−0.964782 + 0.263049i \(0.915272\pi\)
\(798\) 0 0
\(799\) −0.378860 −0.0134031
\(800\) 4.80525 1.38186i 0.169891 0.0488563i
\(801\) 0 0
\(802\) −33.5183 + 19.3518i −1.18357 + 0.683335i
\(803\) −16.1919 9.34838i −0.571399 0.329897i
\(804\) 0 0
\(805\) −9.05237 21.3034i −0.319054 0.750846i
\(806\) −21.5893 −0.760450
\(807\) 0 0
\(808\) 0.436656 0.252103i 0.0153615 0.00886897i
\(809\) −0.338772 −0.0119106 −0.00595530 0.999982i \(-0.501896\pi\)
−0.00595530 + 0.999982i \(0.501896\pi\)
\(810\) 0 0
\(811\) −2.04652 3.54467i −0.0718629 0.124470i 0.827855 0.560942i \(-0.189561\pi\)
−0.899718 + 0.436472i \(0.856228\pi\)
\(812\) −14.7107 8.49321i −0.516243 0.298053i
\(813\) 0 0
\(814\) −1.13090 + 1.95877i −0.0396380 + 0.0686550i
\(815\) 0.558939 4.56664i 0.0195788 0.159962i
\(816\) 0 0
\(817\) −11.9320 16.0409i −0.417448 0.561199i
\(818\) 20.7839i 0.726694i
\(819\) 0 0
\(820\) −17.2288 2.10874i −0.601656 0.0736404i
\(821\) −17.2054 29.8007i −0.600474 1.04005i −0.992749 0.120203i \(-0.961645\pi\)
0.392275 0.919848i \(-0.371688\pi\)
\(822\) 0 0
\(823\) 10.3009 5.94720i 0.359065 0.207306i −0.309605 0.950865i \(-0.600197\pi\)
0.668671 + 0.743559i \(0.266864\pi\)
\(824\) −5.33797 −0.185957
\(825\) 0 0
\(826\) 12.4115 + 21.4973i 0.431850 + 0.747986i
\(827\) 10.5632 6.09865i 0.367318 0.212071i −0.304968 0.952363i \(-0.598646\pi\)
0.672286 + 0.740292i \(0.265313\pi\)
\(828\) 0 0
\(829\) 33.0048 1.14631 0.573153 0.819449i \(-0.305720\pi\)
0.573153 + 0.819449i \(0.305720\pi\)
\(830\) 2.77515 3.68568i 0.0963268 0.127932i
\(831\) 0 0
\(832\) −4.38320 + 2.53064i −0.151960 + 0.0877342i
\(833\) 0.754467 + 0.435592i 0.0261407 + 0.0150924i
\(834\) 0 0
\(835\) 44.7154 19.0008i 1.54744 0.657549i
\(836\) −0.741602 6.36689i −0.0256488 0.220203i
\(837\) 0 0
\(838\) 31.4083 + 18.1336i 1.08498 + 0.626414i
\(839\) 8.97119 15.5386i 0.309720 0.536451i −0.668581 0.743639i \(-0.733098\pi\)
0.978301 + 0.207189i \(0.0664314\pi\)
\(840\) 0 0
\(841\) 5.63869 9.76650i 0.194438 0.336776i
\(842\) −18.5697 + 10.7212i −0.639953 + 0.369477i
\(843\) 0 0
\(844\) 4.03940 0.139042
\(845\) −16.9695 + 22.5372i −0.583769 + 0.775304i
\(846\) 0 0
\(847\) 35.6589i 1.22525i
\(848\) 10.6575i 0.365979i
\(849\) 0 0
\(850\) 0.129715 + 0.451066i 0.00444918 + 0.0154714i
\(851\) 1.97295 + 3.41726i 0.0676320 + 0.117142i
\(852\) 0 0
\(853\) 19.4891 + 11.2520i 0.667295 + 0.385263i 0.795051 0.606543i \(-0.207444\pi\)
−0.127756 + 0.991806i \(0.540777\pi\)
\(854\) −5.27547 −0.180523
\(855\) 0 0
\(856\) −17.9275 −0.612749
\(857\) 1.71631 + 0.990914i 0.0586281 + 0.0338490i 0.529028 0.848605i \(-0.322557\pi\)
−0.470399 + 0.882454i \(0.655890\pi\)
\(858\) 0 0
\(859\) −16.4673 28.5223i −0.561858 0.973167i −0.997334 0.0729670i \(-0.976753\pi\)
0.435476 0.900200i \(-0.356580\pi\)
\(860\) 1.24596 10.1797i 0.0424870 0.347126i
\(861\) 0 0
\(862\) 5.82431i 0.198377i
\(863\) 1.13901i 0.0387723i −0.999812 0.0193862i \(-0.993829\pi\)
0.999812 0.0193862i \(-0.00617119\pi\)
\(864\) 0 0
\(865\) 41.4520 + 31.2114i 1.40941 + 1.06122i
\(866\) −31.6030 −1.07391
\(867\) 0 0
\(868\) 14.9055 8.60569i 0.505925 0.292096i
\(869\) −9.53074 + 16.5077i −0.323308 + 0.559986i
\(870\) 0 0
\(871\) −27.2105 + 47.1300i −0.921993 + 1.59694i
\(872\) 7.68392 + 4.43631i 0.260210 + 0.150232i
\(873\) 0 0
\(874\) −10.2664 4.43335i −0.347265 0.149960i
\(875\) −16.1184 + 42.1343i −0.544901 + 1.42440i
\(876\) 0 0
\(877\) 19.9508 + 11.5186i 0.673692 + 0.388956i 0.797474 0.603353i \(-0.206169\pi\)
−0.123782 + 0.992309i \(0.539502\pi\)
\(878\) 1.61592 0.932951i 0.0545346 0.0314856i
\(879\) 0 0
\(880\) 1.97790 2.62685i 0.0666749 0.0885511i
\(881\) 6.22555 0.209744 0.104872 0.994486i \(-0.466557\pi\)
0.104872 + 0.994486i \(0.466557\pi\)
\(882\) 0 0
\(883\) −28.2402 + 16.3045i −0.950360 + 0.548691i −0.893193 0.449674i \(-0.851540\pi\)
−0.0571672 + 0.998365i \(0.518207\pi\)
\(884\) −0.237550 0.411448i −0.00798967 0.0138385i
\(885\) 0 0
\(886\) −15.7464 −0.529009
\(887\) 3.26261 1.88367i 0.109548 0.0632474i −0.444225 0.895915i \(-0.646521\pi\)
0.553773 + 0.832668i \(0.313188\pi\)
\(888\) 0 0
\(889\) 13.4484 + 23.2933i 0.451045 + 0.781234i
\(890\) −0.442177 + 3.61267i −0.0148218 + 0.121097i
\(891\) 0 0
\(892\) 18.0519i 0.604421i
\(893\) −17.4745 + 2.03539i −0.584762 + 0.0681118i
\(894\) 0 0
\(895\) −14.1506 1.73199i −0.473004 0.0578939i
\(896\) 2.01747 3.49437i 0.0673991 0.116739i
\(897\) 0 0
\(898\) −25.7588 14.8718i −0.859581 0.496279i
\(899\) −8.97866 15.5515i −0.299455 0.518671i
\(900\) 0 0
\(901\) 1.00041 0.0333285
\(902\) −9.88567 + 5.70749i −0.329157 + 0.190039i
\(903\) 0 0
\(904\) −15.8667 −0.527718
\(905\) −7.68856 18.0939i −0.255576 0.601461i
\(906\) 0 0
\(907\) −8.85151 5.11042i −0.293910 0.169689i 0.345794 0.938310i \(-0.387610\pi\)
−0.639704 + 0.768622i \(0.720943\pi\)
\(908\) −23.2539 + 13.4257i −0.771709 + 0.445547i
\(909\) 0 0
\(910\) 5.54782 45.3267i 0.183909 1.50257i
\(911\) 18.6042 0.616383 0.308192 0.951324i \(-0.400276\pi\)
0.308192 + 0.951324i \(0.400276\pi\)
\(912\) 0 0
\(913\) 3.03414i 0.100415i
\(914\) 6.39456 11.0757i 0.211513 0.366352i
\(915\) 0 0
\(916\) 6.85657 + 11.8759i 0.226548 + 0.392392i
\(917\) −24.7250 14.2750i −0.816492 0.471402i
\(918\) 0 0
\(919\) 35.5145 1.17152 0.585758 0.810486i \(-0.300797\pi\)
0.585758 + 0.810486i \(0.300797\pi\)
\(920\) −2.24349 5.27972i −0.0739657 0.174067i
\(921\) 0 0
\(922\) 10.3283 5.96303i 0.340143 0.196382i
\(923\) 43.9123i 1.44539i
\(924\) 0 0
\(925\) 1.85476 7.46335i 0.0609841 0.245393i
\(926\) 9.66039 16.7323i 0.317460 0.549857i
\(927\) 0 0
\(928\) −3.64581 2.10491i −0.119680 0.0690971i
\(929\) −2.13612 + 3.69987i −0.0700838 + 0.121389i −0.898938 0.438076i \(-0.855660\pi\)
0.828854 + 0.559465i \(0.188993\pi\)
\(930\) 0 0
\(931\) 37.1392 + 16.0379i 1.21719 + 0.525621i
\(932\) 0.00661073i 0.000216542i
\(933\) 0 0
\(934\) 13.3504 23.1237i 0.436840 0.756629i
\(935\) 0.246581 + 0.185664i 0.00806406 + 0.00607187i
\(936\) 0 0
\(937\) 44.5676 25.7311i 1.45596 0.840599i 0.457152 0.889389i \(-0.348870\pi\)
0.998809 + 0.0487891i \(0.0155362\pi\)
\(938\) 43.3854i 1.41658i
\(939\) 0 0
\(940\) −7.20963 5.42852i −0.235152 0.177059i
\(941\) 30.2442 + 52.3845i 0.985934 + 1.70769i 0.637712 + 0.770275i \(0.279881\pi\)
0.348222 + 0.937412i \(0.386786\pi\)
\(942\) 0 0
\(943\) 19.9145i 0.648505i
\(944\) 3.07599 + 5.32777i 0.100115 + 0.173404i
\(945\) 0 0
\(946\) −3.37231 5.84101i −0.109643 0.189908i
\(947\) −10.0415 5.79749i −0.326306 0.188393i 0.327894 0.944715i \(-0.393661\pi\)
−0.654200 + 0.756322i \(0.726995\pi\)
\(948\) 0 0
\(949\) −64.3503 −2.08890
\(950\) 8.40627 + 20.1081i 0.272736 + 0.652392i
\(951\) 0 0
\(952\) 0.328014 + 0.189379i 0.0106310 + 0.00613781i
\(953\) 22.5443 + 13.0160i 0.730282 + 0.421629i 0.818525 0.574470i \(-0.194792\pi\)
−0.0882433 + 0.996099i \(0.528125\pi\)
\(954\) 0 0
\(955\) 28.7778 + 3.52229i 0.931227 + 0.113979i
\(956\) −2.33750 4.04866i −0.0756000 0.130943i
\(957\) 0 0
\(958\) 13.5825i 0.438830i
\(959\) −38.0425 65.8916i −1.22846 2.12775i
\(960\) 0 0
\(961\) −12.8049 −0.413060
\(962\) 7.78462i 0.250986i
\(963\) 0 0
\(964\) −13.9044 + 24.0831i −0.447829 + 0.775663i
\(965\) −10.9261 8.22688i −0.351725 0.264833i
\(966\) 0 0
\(967\) 14.9595 + 8.63685i 0.481064 + 0.277743i 0.720860 0.693081i \(-0.243747\pi\)
−0.239796 + 0.970823i \(0.577080\pi\)
\(968\) 8.83752i 0.284049i
\(969\) 0 0
\(970\) −10.4491 24.5903i −0.335499 0.789547i
\(971\) −5.47052 + 9.47522i −0.175557 + 0.304074i −0.940354 0.340198i \(-0.889506\pi\)
0.764797 + 0.644272i \(0.222839\pi\)
\(972\) 0 0
\(973\) −69.8605 + 40.3340i −2.23963 + 1.29305i
\(974\) −4.01820 + 6.95973i −0.128752 + 0.223004i
\(975\) 0 0
\(976\) −1.30744 −0.0418503
\(977\) 9.01488i 0.288412i −0.989548 0.144206i \(-0.953937\pi\)
0.989548 0.144206i \(-0.0460627\pi\)
\(978\) 0 0
\(979\) 1.19679 + 2.07290i 0.0382496 + 0.0662503i
\(980\) 8.11595 + 19.0997i 0.259255 + 0.610117i
\(981\) 0 0
\(982\) 17.9077 10.3390i 0.571457 0.329931i
\(983\) 12.8956 + 7.44527i 0.411305 + 0.237467i 0.691350 0.722520i \(-0.257016\pi\)
−0.280045 + 0.959987i \(0.590349\pi\)
\(984\) 0 0
\(985\) 1.99653 16.3121i 0.0636149 0.519745i
\(986\) 0.197587 0.342231i 0.00629245 0.0108988i
\(987\) 0 0
\(988\) −13.1672 17.7014i −0.418905 0.563157i
\(989\) −11.7666 −0.374156
\(990\) 0 0
\(991\) −23.1717 + 40.1346i −0.736075 + 1.27492i 0.218176 + 0.975910i \(0.429989\pi\)
−0.954250 + 0.299009i \(0.903344\pi\)
\(992\) 3.69410 2.13279i 0.117288 0.0677161i
\(993\) 0 0
\(994\) −17.5038 30.3175i −0.555188 0.961613i
\(995\) −3.00439 7.07037i −0.0952454 0.224146i
\(996\) 0 0
\(997\) 26.1990 15.1260i 0.829730 0.479045i −0.0240304 0.999711i \(-0.507650\pi\)
0.853760 + 0.520667i \(0.174317\pi\)
\(998\) 0.954638 0.551160i 0.0302185 0.0174467i
\(999\) 0 0
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 1710.2.t.c.1189.1 20
3.2 odd 2 570.2.q.c.49.10 yes 20
5.4 even 2 inner 1710.2.t.c.1189.9 20
15.14 odd 2 570.2.q.c.49.2 20
19.7 even 3 inner 1710.2.t.c.919.9 20
57.26 odd 6 570.2.q.c.349.2 yes 20
95.64 even 6 inner 1710.2.t.c.919.1 20
285.254 odd 6 570.2.q.c.349.10 yes 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
570.2.q.c.49.2 20 15.14 odd 2
570.2.q.c.49.10 yes 20 3.2 odd 2
570.2.q.c.349.2 yes 20 57.26 odd 6
570.2.q.c.349.10 yes 20 285.254 odd 6
1710.2.t.c.919.1 20 95.64 even 6 inner
1710.2.t.c.919.9 20 19.7 even 3 inner
1710.2.t.c.1189.1 20 1.1 even 1 trivial
1710.2.t.c.1189.9 20 5.4 even 2 inner