Properties

Label 1710.2.t.c.1189.9
Level $1710$
Weight $2$
Character 1710.1189
Analytic conductor $13.654$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [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 1189.9
Root \(-1.19457 - 0.320085i\) of defining polynomial
Character \(\chi\) \(=\) 1710.1189
Dual form 1710.2.t.c.919.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(1.34502 + 1.78632i) q^{5} +4.03495i q^{7} +1.00000i q^{8} +O(q^{10})\) \(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(1.34502 + 1.78632i) q^{5} +4.03495i q^{7} +1.00000i q^{8} +(0.271659 + 2.21950i) q^{10} +1.47054 q^{11} +(-4.38320 + 2.53064i) q^{13} +(-2.01747 + 3.49437i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(0.0812933 + 0.0469347i) q^{17} +(-4.00172 - 1.72807i) q^{19} +(-0.874489 + 2.05798i) q^{20} +(1.27352 + 0.735269i) q^{22} +(2.22178 - 1.28274i) q^{23} +(-1.38186 + 4.80525i) q^{25} -5.06128 q^{26} +(-3.49437 + 2.01747i) q^{28} +(-2.10491 - 3.64581i) q^{29} +4.26558 q^{31} +(-0.866025 + 0.500000i) q^{32} +(0.0469347 + 0.0812933i) q^{34} +(-7.20770 + 5.42707i) q^{35} +1.53807i q^{37} +(-2.60156 - 3.49741i) q^{38} +(-1.78632 + 1.34502i) q^{40} +(3.88123 - 6.72248i) q^{41} +(-3.97202 - 2.29325i) q^{43} +(0.735269 + 1.27352i) q^{44} +2.56549 q^{46} +(-3.49530 + 2.01801i) q^{47} -9.28080 q^{49} +(-3.59936 + 3.47054i) q^{50} +(-4.38320 - 2.53064i) q^{52} +(9.22964 - 5.32873i) q^{53} +(1.97790 + 2.62685i) q^{55} -4.03495 q^{56} -4.20982i q^{58} +(3.07599 - 5.32777i) q^{59} +(0.653722 + 1.13228i) q^{61} +(3.69410 + 2.13279i) q^{62} -1.00000 q^{64} +(-10.4160 - 4.42603i) q^{65} +(9.31187 - 5.37621i) q^{67} +0.0938694i q^{68} +(-8.95558 + 1.09613i) q^{70} +(-4.33806 + 7.51373i) q^{71} +(11.0108 + 6.35711i) q^{73} +(-0.769037 + 1.33201i) q^{74} +(-0.504306 - 4.32963i) q^{76} +5.93355i q^{77} +(-6.48112 + 11.2256i) q^{79} +(-2.21950 + 0.271659i) q^{80} +(6.72248 - 3.88123i) q^{82} +2.06328i q^{83} +(0.0255005 + 0.208344i) q^{85} +(-2.29325 - 3.97202i) q^{86} +1.47054i q^{88} +(0.813846 + 1.40962i) q^{89} +(-10.2110 - 17.6860i) q^{91} +(2.22178 + 1.28274i) q^{92} -4.03603 q^{94} +(-2.29549 - 9.47263i) q^{95} +(10.3479 + 5.97438i) q^{97} +(-8.03741 - 4.64040i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 10 q^{4}+O(q^{10}) \) 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
\(5\) 1.34502 + 1.78632i 0.601509 + 0.798866i
\(6\) 0 0
\(7\) 4.03495i 1.52507i 0.646949 + 0.762533i \(0.276045\pi\)
−0.646949 + 0.762533i \(0.723955\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 0.271659 + 2.21950i 0.0859061 + 0.701869i
\(11\) 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 −0.963991 0.265934i \(-0.914320\pi\)
−0.251690 + 0.967808i \(0.580986\pi\)
\(14\) −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 0.509826 0.860278i \(-0.329710\pi\)
−0.490109 + 0.871661i \(0.663043\pi\)
\(18\) 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 −0.250147 0.968208i \(-0.580479\pi\)
0.713419 + 0.700737i \(0.247145\pi\)
\(24\) 0 0
\(25\) −1.38186 + 4.80525i −0.276373 + 0.961051i
\(26\) −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
\(35\) −7.20770 + 5.42707i −1.21832 + 0.917342i
\(36\) 0 0
\(37\) 1.53807i 0.252858i 0.991976 + 0.126429i \(0.0403515\pi\)
−0.991976 + 0.126429i \(0.959648\pi\)
\(38\) −2.60156 3.49741i −0.422028 0.567356i
\(39\) 0 0
\(40\) −1.78632 + 1.34502i −0.282442 + 0.212666i
\(41\) 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 0.165564 0.986199i \(-0.447056\pi\)
−0.771291 + 0.636482i \(0.780389\pi\)
\(44\) 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 −0.732769 0.680478i \(-0.761772\pi\)
0.222927 + 0.974835i \(0.428439\pi\)
\(48\) 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 0.293219 0.956045i \(-0.405273\pi\)
0.974569 + 0.224087i \(0.0719401\pi\)
\(54\) 0 0
\(55\) 1.97790 + 2.62685i 0.266700 + 0.354204i
\(56\) −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 0.191784 0.981437i \(-0.438573\pi\)
0.945842 + 0.324629i \(0.105239\pi\)
\(68\) 0.0938694i 0.0113833i
\(69\) 0 0
\(70\) −8.95558 + 1.09613i −1.07040 + 0.131013i
\(71\) −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 0.978426 0.206596i \(-0.0662386\pi\)
0.310296 + 0.950640i \(0.399572\pi\)
\(74\) −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 \(0.906567\pi\)
\(80\) −2.21950 + 0.271659i −0.248148 + 0.0303724i
\(81\) 0 0
\(82\) 6.72248 3.88123i 0.742374 0.428610i
\(83\) 2.06328i 0.226475i 0.993568 + 0.113237i \(0.0361221\pi\)
−0.993568 + 0.113237i \(0.963878\pi\)
\(84\) 0 0
\(85\) 0.0255005 + 0.208344i 0.00276592 + 0.0225980i
\(86\) −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
\(95\) −2.29549 9.47263i −0.235513 0.971871i
\(96\) 0 0
\(97\) 10.3479 + 5.97438i 1.05067 + 0.606607i 0.922838 0.385188i \(-0.125864\pi\)
0.127836 + 0.991795i \(0.459197\pi\)
\(98\) −8.03741 4.64040i −0.811901 0.468751i
\(99\) 0 0
\(100\) −4.85240 + 1.20590i −0.485240 + 0.120590i
\(101\) 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 \(0.0847063\pi\)
−0.964800 + 0.262983i \(0.915294\pi\)
\(104\) −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 \(0.333673\pi\)
−0.499076 + 0.866558i \(0.666327\pi\)
\(108\) 0 0
\(109\) −4.43631 + 7.68392i −0.424922 + 0.735986i −0.996413 0.0846222i \(-0.973032\pi\)
0.571492 + 0.820608i \(0.306365\pi\)
\(110\) 0.399485 + 3.26387i 0.0380894 + 0.311198i
\(111\) 0 0
\(112\) −3.49437 2.01747i −0.330187 0.190633i
\(113\) 15.8667i 1.49261i 0.665603 + 0.746306i \(0.268174\pi\)
−0.665603 + 0.746306i \(0.731826\pi\)
\(114\) 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 −0.221501 0.975160i \(-0.571096\pi\)
0.733763 + 0.679406i \(0.237762\pi\)
\(128\) −0.866025 0.500000i −0.0765466 0.0441942i
\(129\) 0 0
\(130\) −6.80751 9.04106i −0.597058 0.792953i
\(131\) 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 −0.993883 0.110435i \(-0.964775\pi\)
−0.401302 + 0.915946i \(0.631442\pi\)
\(138\) 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
\(155\) 5.73727 + 7.61968i 0.460828 + 0.612027i
\(156\) 0 0
\(157\) 14.0594 + 8.11721i 1.12206 + 0.647824i 0.941927 0.335817i \(-0.109012\pi\)
0.180137 + 0.983641i \(0.442346\pi\)
\(158\) −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 \(-0.974323\pi\)
0.996748 0.0805780i \(-0.0256766\pi\)
\(164\) 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 0.457278 0.889324i \(-0.348824\pi\)
0.998816 + 0.0486476i \(0.0154911\pi\)
\(168\) 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 \(0.0105588\pi\)
0.528447 + 0.848966i \(0.322774\pi\)
\(174\) 0 0
\(175\) −19.3889 5.57575i −1.46567 0.421487i
\(176\) −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
\(185\) −2.74749 + 2.06873i −0.201999 + 0.152096i
\(186\) 0 0
\(187\) 0.119545 + 0.0690193i 0.00874200 + 0.00504719i
\(188\) −3.49530 2.01801i −0.254921 0.147179i
\(189\) 0 0
\(190\) 2.74836 9.35128i 0.199387 0.678413i
\(191\) −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 0.297087 0.954850i \(-0.403985\pi\)
−0.678381 + 0.734710i \(0.737318\pi\)
\(194\) 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 \(-0.915680\pi\)
0.965119 0.261812i \(-0.0843200\pi\)
\(198\) 0 0
\(199\) 1.71780 + 2.97531i 0.121771 + 0.210914i 0.920466 0.390822i \(-0.127809\pi\)
−0.798695 + 0.601736i \(0.794476\pi\)
\(200\) −4.80525 1.38186i −0.339783 0.0977125i
\(201\) 0 0
\(202\) 0.504207i 0.0354759i
\(203\) 14.7107 8.49321i 1.03249 0.596106i
\(204\) 0 0
\(205\) 17.2288 2.10874i 1.20331 0.147281i
\(206\) −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
\(215\) −1.24596 10.1797i −0.0849739 0.694253i
\(216\) 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 −0.125111 0.992143i \(-0.539929\pi\)
−0.921776 + 0.387722i \(0.873262\pi\)
\(224\) −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 \(-0.649939\pi\)
0.453820 0.891093i \(-0.350061\pi\)
\(228\) 0 0
\(229\) 13.7131 0.906190 0.453095 0.891462i \(-0.350320\pi\)
0.453095 + 0.891462i \(0.350320\pi\)
\(230\) 3.45062 + 4.58278i 0.227527 + 0.302180i
\(231\) 0 0
\(232\) 3.64581 2.10491i 0.239359 0.138194i
\(233\) 0.00572506 + 0.00330537i 0.000375061 + 0.000216542i 0.500188 0.865917i \(-0.333264\pi\)
−0.499812 + 0.866134i \(0.666598\pi\)
\(234\) 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
\(245\) −12.4828 16.5785i −0.797498 1.05916i
\(246\) 0 0
\(247\) 21.9135 2.55244i 1.39432 0.162408i
\(248\) 4.26558i 0.270864i
\(249\) 0 0
\(250\) −11.0407 1.76166i −0.698274 0.111417i
\(251\) −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 −0.464755 0.885439i \(-0.653858\pi\)
0.534436 + 0.845209i \(0.320524\pi\)
\(258\) 0 0
\(259\) −6.20604 −0.385625
\(260\) −1.37494 11.2335i −0.0852704 0.696675i
\(261\) 0 0
\(262\) 6.12771 3.53784i 0.378571 0.218568i
\(263\) −24.4863 14.1372i −1.50989 0.871737i −0.999933 0.0115378i \(-0.996327\pi\)
−0.509959 0.860199i \(-0.670339\pi\)
\(264\) 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
\(275\) −2.03208 + 7.06631i −0.122539 + 0.426115i
\(276\) 0 0
\(277\) 24.5237i 1.47349i 0.676173 + 0.736743i \(0.263637\pi\)
−0.676173 + 0.736743i \(0.736363\pi\)
\(278\) 19.9923i 1.19906i
\(279\) 0 0
\(280\) −5.42707 7.20770i −0.324329 0.430742i
\(281\) −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 −0.252621 0.967565i \(-0.581293\pi\)
−0.964247 + 0.265006i \(0.914626\pi\)
\(284\) −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
\(290\) 7.52008 5.66228i 0.441595 0.332501i
\(291\) 0 0
\(292\) 12.7142i 0.744044i
\(293\) 23.0123i 1.34439i −0.740374 0.672195i \(-0.765352\pi\)
0.740374 0.672195i \(-0.234648\pi\)
\(294\) 0 0
\(295\) 13.6544 1.67124i 0.794987 0.0973034i
\(296\) −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 −0.287097 0.957902i \(-0.592690\pi\)
−0.973116 + 0.230318i \(0.926023\pi\)
\(308\) −5.13860 + 2.96677i −0.292799 + 0.169048i
\(309\) 0 0
\(310\) 1.15878 + 9.46747i 0.0658144 + 0.537716i
\(311\) 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 −0.303628 0.952791i \(-0.598198\pi\)
0.673327 + 0.739345i \(0.264865\pi\)
\(314\) 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 −0.118898 0.992906i \(-0.537936\pi\)
0.800433 + 0.599422i \(0.204603\pi\)
\(318\) 0 0
\(319\) −3.09535 5.36131i −0.173307 0.300176i
\(320\) −1.34502 1.78632i −0.0751887 0.0998582i
\(321\) 0 0
\(322\) 10.3516i 0.576873i
\(323\) −0.244207 0.328300i −0.0135880 0.0182671i
\(324\) 0 0
\(325\) −6.10339 24.5594i −0.338555 1.36231i
\(326\) 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 0.405966 0.913888i \(-0.366935\pi\)
−0.588467 + 0.808521i \(0.700268\pi\)
\(338\) 10.9263 6.30829i 0.594311 0.343126i
\(339\) 0 0
\(340\) −0.167681 + 0.126256i −0.00909376 + 0.00684719i
\(341\) 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 0.757636 0.652677i \(-0.226354\pi\)
−0.186417 + 0.982471i \(0.559688\pi\)
\(348\) 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 \(0.0192591\pi\)
−0.998170 + 0.0604674i \(0.980741\pi\)
\(354\) 0 0
\(355\) −19.2567 + 2.35694i −1.02204 + 0.125094i
\(356\) −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
\(365\) 3.45394 + 28.2193i 0.180787 + 1.47707i
\(366\) 0 0
\(367\) 31.7744 18.3450i 1.65861 0.957600i 0.685255 0.728304i \(-0.259691\pi\)
0.973357 0.229296i \(-0.0736424\pi\)
\(368\) 2.56549i 0.133735i
\(369\) 0 0
\(370\) −3.41376 + 0.417831i −0.177473 + 0.0217220i
\(371\) 21.5012 + 37.2411i 1.11628 + 1.93346i
\(372\) 0 0
\(373\) 19.5380i 1.01164i 0.862640 + 0.505819i \(0.168810\pi\)
−0.862640 + 0.505819i \(0.831190\pi\)
\(374\) 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 \(0.528390\pi\)
\(380\) 7.05579 6.72427i 0.361954 0.344948i
\(381\) 0 0
\(382\) −11.2288 6.48293i −0.574514 0.331696i
\(383\) −21.7388 12.5509i −1.11080 0.641322i −0.171765 0.985138i \(-0.554947\pi\)
−0.939037 + 0.343816i \(0.888280\pi\)
\(384\) 0 0
\(385\) −10.5992 + 7.98072i −0.540185 + 0.406735i
\(386\) −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
\(395\) −28.7698 + 3.52131i −1.44756 + 0.177176i
\(396\) 0 0
\(397\) 26.6267 + 15.3729i 1.33635 + 0.771544i 0.986265 0.165172i \(-0.0528179\pi\)
0.350089 + 0.936716i \(0.386151\pi\)
\(398\) 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
\(415\) −3.68568 + 2.77515i −0.180923 + 0.136227i
\(416\) 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 −0.982963 0.183801i \(-0.941160\pi\)
−0.332305 + 0.943172i \(0.607826\pi\)
\(434\) −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 \(0.180845\pi\)
\(440\) −2.62685 + 1.97790i −0.125230 + 0.0942926i
\(441\) 0 0
\(442\) −0.411448 0.237550i −0.0195706 0.0112991i
\(443\) −13.6368 + 7.87318i −0.647902 + 0.374066i −0.787652 0.616121i \(-0.788703\pi\)
0.139750 + 0.990187i \(0.455370\pi\)
\(444\) 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 \(-0.903305\pi\)
0.954214 0.299125i \(-0.0966948\pi\)
\(458\) 11.8759 + 6.85657i 0.554926 + 0.320387i
\(459\) 0 0
\(460\) 0.696938 + 5.69412i 0.0324949 + 0.265490i
\(461\) −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 \(-0.851796\pi\)
0.893554 0.448956i \(-0.148204\pi\)
\(464\) 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 \(-0.788030\pi\)
0.786347 0.617785i \(-0.211970\pi\)
\(468\) 0 0
\(469\) 21.6927 + 37.5729i 1.00168 + 1.73496i
\(470\) −5.42852 7.20963i −0.250399 0.332555i
\(471\) 0 0
\(472\) 5.32777 + 3.07599i 0.245231 + 0.141584i
\(473\) −5.84101 3.37231i −0.268570 0.155059i
\(474\) 0 0
\(475\) 13.8337 16.8413i 0.634732 0.772733i
\(476\) −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
\(485\) 3.24599 + 26.5204i 0.147393 + 1.20423i
\(486\) 0 0
\(487\) 8.03640i 0.364164i 0.983283 + 0.182082i \(0.0582837\pi\)
−0.983283 + 0.182082i \(0.941716\pi\)
\(488\) −1.13228 + 0.653722i −0.0512559 + 0.0295926i
\(489\) 0 0
\(490\) −2.52121 20.5988i −0.113897 0.930558i
\(491\) −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 \(0.174521\pi\)
\(500\) −8.68068 7.04598i −0.388212 0.315106i
\(501\) 0 0
\(502\) 6.06517i 0.270702i
\(503\) 21.0518 12.1543i 0.938653 0.541932i 0.0491154 0.998793i \(-0.484360\pi\)
0.889538 + 0.456861i \(0.151026\pi\)
\(504\) 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
\(515\) −9.53531 + 7.17966i −0.420176 + 0.316373i
\(516\) 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 −0.959818 0.280622i \(-0.909459\pi\)
−0.236883 + 0.971538i \(0.576126\pi\)
\(524\) 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
\(530\) 14.3345 + 19.0376i 0.622649 + 0.826942i
\(531\) 0 0
\(532\) 17.4698 2.03485i 0.757413 0.0882218i
\(533\) 39.2880i 1.70175i
\(534\) 0 0
\(535\) −32.0242 + 24.1128i −1.38453 + 1.04249i
\(536\) 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
\(545\) −19.6928 + 2.41033i −0.843548 + 0.103247i
\(546\) 0 0
\(547\) 30.7554 17.7566i 1.31500 0.759218i 0.332084 0.943250i \(-0.392248\pi\)
0.982920 + 0.184032i \(0.0589150\pi\)
\(548\) −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 −0.668339 0.743857i \(-0.732994\pi\)
0.310030 + 0.950727i \(0.399661\pi\)
\(558\) 0 0
\(559\) 23.2135 0.981828
\(560\) −1.09613 8.95558i −0.0463199 0.378443i
\(561\) 0 0
\(562\) 6.59418i 0.278159i
\(563\) 11.5237i 0.485665i −0.970068 0.242833i \(-0.921923\pi\)
0.970068 0.242833i \(-0.0780766\pi\)
\(564\) 0 0
\(565\) −28.3429 + 21.3409i −1.19240 + 0.897820i
\(566\) −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
\(575\) 3.09372 + 12.4488i 0.129017 + 0.519150i
\(576\) 0 0
\(577\) 28.3094i 1.17854i 0.807938 + 0.589268i \(0.200584\pi\)
−0.807938 + 0.589268i \(0.799416\pi\)
\(578\) 16.9912i 0.706740i
\(579\) 0 0
\(580\) 9.34372 1.14364i 0.387977 0.0474869i
\(581\) −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 0.681281 0.732022i \(-0.261423\pi\)
−0.293309 + 0.956018i \(0.594757\pi\)
\(588\) 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 −0.904179 0.427155i \(-0.859516\pi\)
−0.0821625 + 0.996619i \(0.526183\pi\)
\(594\) 0 0
\(595\) −0.840656 + 0.102893i −0.0344635 + 0.00421821i
\(596\) −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
\(605\) −11.8866 15.7866i −0.483259 0.641817i
\(606\) 0 0
\(607\) 12.9882i 0.527176i 0.964635 + 0.263588i \(0.0849059\pi\)
−0.964635 + 0.263588i \(0.915094\pi\)
\(608\) 4.32963 0.504306i 0.175590 0.0204523i
\(609\) 0 0
\(610\) −2.33551 + 1.75853i −0.0945621 + 0.0712009i
\(611\) 10.2137 17.6907i 0.413204 0.715690i
\(612\) 0 0
\(613\) 23.2303 + 13.4120i 0.938264 + 0.541707i 0.889416 0.457099i \(-0.151112\pi\)
0.0488484 + 0.998806i \(0.484445\pi\)
\(614\) −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 −0.239398 0.970922i \(-0.576950\pi\)
0.721144 + 0.692785i \(0.243617\pi\)
\(618\) 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
\(625\) −21.1809 13.2804i −0.847236 0.531216i
\(626\) 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
\(640\) −0.271659 2.21950i −0.0107383 0.0877336i
\(641\) 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 0.990226 0.139470i \(-0.0445399\pi\)
0.374328 + 0.927296i \(0.377873\pi\)
\(644\) −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 \(0.218956\pi\)
−0.772600 + 0.634893i \(0.781044\pi\)
\(648\) 0 0
\(649\) 4.52336 7.83470i 0.177558 0.307539i
\(650\) 6.99400 24.3207i 0.274327 0.953938i
\(651\) 0 0
\(652\) 1.78185 1.02875i 0.0697826 0.0402890i
\(653\) 25.3382i 0.991559i 0.868448 + 0.495780i \(0.165118\pi\)
−0.868448 + 0.495780i \(0.834882\pi\)
\(654\) 0 0
\(655\) 15.7045 1.92217i 0.613625 0.0751054i
\(656\) 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
\(665\) 38.2216 9.26219i 1.48217 0.359172i
\(666\) 0 0
\(667\) −9.35330 5.40013i −0.362161 0.209094i
\(668\) 18.8169 + 10.8639i 0.728047 + 0.420338i
\(669\) 0 0
\(670\) 14.4622 + 19.2072i 0.558723 + 0.742040i
\(671\) 0.961324 + 1.66506i 0.0371115 + 0.0642790i
\(672\) 0 0
\(673\) 11.3374i 0.437025i 0.975834 + 0.218512i \(0.0701204\pi\)
−0.975834 + 0.218512i \(0.929880\pi\)
\(674\) −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 \(-0.798252\pi\)
0.805776 0.592220i \(-0.201748\pi\)
\(678\) 0 0
\(679\) −24.1063 + 41.7534i −0.925116 + 1.60235i
\(680\) −0.208344 + 0.0255005i −0.00798961 + 0.000977899i
\(681\) 0 0
\(682\) 5.43231 + 3.13635i 0.208014 + 0.120097i
\(683\) 10.5683i 0.404386i 0.979346 + 0.202193i \(0.0648069\pi\)
−0.979346 + 0.202193i \(0.935193\pi\)
\(684\) 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
\(700\) −4.86573 19.5792i −0.183907 0.740024i
\(701\) −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
\(725\) 20.4278 5.07661i 0.758668 0.188541i
\(726\) 0 0
\(727\) −34.0238 19.6436i −1.26187 0.728543i −0.288436 0.957499i \(-0.593135\pi\)
−0.973437 + 0.228957i \(0.926469\pi\)
\(728\) 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 \(0.315324\pi\)
−0.548171 + 0.836366i \(0.684676\pi\)
\(734\) 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 −0.483826 0.875164i \(-0.660753\pi\)
−0.999827 + 0.0185770i \(0.994086\pi\)
\(744\) 0 0
\(745\) −27.0956 + 3.31640i −0.992705 + 0.121503i
\(746\) −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
\(755\) 26.7804 + 35.5671i 0.974639 + 1.29442i
\(756\) 0 0
\(757\) 11.2784 + 6.51161i 0.409922 + 0.236668i 0.690756 0.723088i \(-0.257278\pi\)
−0.280834 + 0.959756i \(0.590611\pi\)
\(758\) −3.00339 1.73401i −0.109088 0.0629820i
\(759\) 0 0
\(760\) 9.47263 2.29549i 0.343608 0.0832662i
\(761\) −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 \(-0.491608\pi\)
\(770\) −13.1695 + 1.61190i −0.474597 + 0.0580889i
\(771\) 0 0
\(772\) 6.11656i 0.220140i
\(773\) 11.4692 6.62172i 0.412517 0.238167i −0.279354 0.960188i \(-0.590120\pi\)
0.691871 + 0.722022i \(0.256787\pi\)
\(774\) 0 0
\(775\) −5.89445 + 20.4972i −0.211735 + 0.736280i
\(776\) −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
\(785\) 4.41023 + 36.0324i 0.157408 + 1.28605i
\(786\) 0 0
\(787\) 21.7913i 0.776775i −0.921496 0.388388i \(-0.873032\pi\)
0.921496 0.388388i \(-0.126968\pi\)
\(788\) 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 \(-0.915272\pi\)
0.964782 0.263049i \(-0.0847283\pi\)
\(798\) 0 0
\(799\) −0.378860 −0.0134031
\(800\) −1.20590 4.85240i −0.0426349 0.171558i
\(801\) 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
\(815\) 3.67535 2.76737i 0.128742 0.0969369i
\(816\) 0 0
\(817\) 11.9320 + 16.0409i 0.417448 + 0.561199i
\(818\) 20.7839i 0.726694i
\(819\) 0 0
\(820\) 10.4406 + 13.8662i 0.364602 + 0.484229i
\(821\) −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 −0.668671 0.743559i \(-0.733136\pi\)
0.309605 + 0.950865i \(0.399803\pi\)
\(824\) −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 −0.672286 0.740292i \(-0.734687\pi\)
0.304968 + 0.952363i \(0.401354\pi\)
\(828\) 0 0
\(829\) 33.0048 1.14631 0.573153 0.819449i \(-0.305720\pi\)
0.573153 + 0.819449i \(0.305720\pi\)
\(830\) −4.57947 + 0.560510i −0.158956 + 0.0194556i
\(831\) 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
\(845\) 28.0026 3.42741i 0.963317 0.117906i
\(846\) 0 0
\(847\) 35.6589i 1.22525i
\(848\) 10.6575i 0.365979i
\(849\) 0 0
\(850\) −0.455492 + 0.113197i −0.0156233 + 0.00388262i
\(851\) 1.97295 + 3.41726i 0.0676320 + 0.117142i
\(852\) 0 0
\(853\) −19.4891 11.2520i −0.667295 0.385263i 0.127756 0.991806i \(-0.459223\pi\)
−0.795051 + 0.606543i \(0.792556\pi\)
\(854\) −5.27547 −0.180523
\(855\) 0 0
\(856\) −17.9275 −0.612749
\(857\) −1.71631 0.990914i −0.0586281 0.0338490i 0.470399 0.882454i \(-0.344110\pi\)
−0.529028 + 0.848605i \(0.677443\pi\)
\(858\) 0 0
\(859\) −16.4673 28.5223i −0.561858 0.973167i −0.997334 0.0729670i \(-0.976753\pi\)
0.435476 0.900200i \(-0.356580\pi\)
\(860\) 8.19293 6.16891i 0.279377 0.210358i
\(861\) 0 0
\(862\) 5.82431i 0.198377i
\(863\) 1.13901i 0.0387723i 0.999812 + 0.0193862i \(0.00617119\pi\)
−0.999812 + 0.0193862i \(0.993829\pi\)
\(864\) 0 0
\(865\) 6.30392 + 51.5042i 0.214340 + 1.75120i
\(866\) −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 0.123782 0.992309i \(-0.460498\pi\)
−0.797474 + 0.603353i \(0.793831\pi\)
\(878\) −1.61592 + 0.932951i −0.0545346 + 0.0314856i
\(879\) 0 0
\(880\) −3.26387 + 0.399485i −0.110025 + 0.0134666i
\(881\) 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 0.0571672 0.998365i \(-0.481793\pi\)
0.893193 + 0.449674i \(0.148460\pi\)
\(884\) −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 −0.553773 0.832668i \(-0.686812\pi\)
0.444225 + 0.895915i \(0.353479\pi\)
\(888\) 0 0
\(889\) 13.4484 + 23.2933i 0.451045 + 0.781234i
\(890\) −2.90758 + 2.18927i −0.0974621 + 0.0733846i
\(891\) 0 0
\(892\) 18.0519i 0.604421i
\(893\) 17.4745 2.03539i 0.584762 0.0681118i
\(894\) 0 0
\(895\) 8.57527 + 11.3888i 0.286640 + 0.380687i
\(896\) 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 0.639704 0.768622i \(-0.279057\pi\)
−0.345794 + 0.938310i \(0.612390\pi\)
\(908\) 23.2539 13.4257i 0.771709 0.445547i
\(909\) 0 0
\(910\) 36.4802 27.4679i 1.20931 0.910553i
\(911\) 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
\(925\) −7.39083 2.12541i −0.243009 0.0698830i
\(926\) 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
\(935\) 0.0374995 + 0.306377i 0.00122636 + 0.0100196i
\(936\) 0 0
\(937\) −44.5676 + 25.7311i −1.45596 + 0.840599i −0.998809 0.0487891i \(-0.984464\pi\)
−0.457152 + 0.889389i \(0.651130\pi\)
\(938\) 43.3854i 1.41658i
\(939\) 0 0
\(940\) −1.09642 8.95798i −0.0357614 0.292177i
\(941\) 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 0.654200 0.756322i \(-0.273005\pi\)
−0.327894 + 0.944715i \(0.606339\pi\)
\(948\) 0 0
\(949\) −64.3503 −2.08890
\(950\) 20.4010 7.66818i 0.661894 0.248789i
\(951\) 0 0
\(952\) −0.328014 0.189379i −0.0106310 0.00613781i
\(953\) −22.5443 13.0160i −0.730282 0.421629i 0.0882433 0.996099i \(-0.471875\pi\)
−0.818525 + 0.574470i \(0.805208\pi\)
\(954\) 0 0
\(955\) −17.4393 23.1612i −0.564322 0.749477i
\(956\) −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
\(965\) −1.66162 13.5757i −0.0534894 0.437019i
\(966\) 0 0
\(967\) −14.9595 8.63685i −0.481064 0.277743i 0.239796 0.970823i \(-0.422920\pi\)
−0.720860 + 0.693081i \(0.756253\pi\)
\(968\) 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 \(0.0460627\pi\)
−0.989548 + 0.144206i \(0.953937\pi\)
\(978\) 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 0.280045 0.959987i \(-0.409651\pi\)
−0.691350 + 0.722520i \(0.742984\pi\)
\(984\) 0 0
\(985\) 13.1284 9.88508i 0.418305 0.314965i
\(986\) 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 −0.853760 0.520667i \(-0.825683\pi\)
0.0240304 + 0.999711i \(0.492350\pi\)
\(998\) −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.1189.9 20
3.2 odd 2 570.2.q.c.49.2 20
5.4 even 2 inner 1710.2.t.c.1189.1 20
15.14 odd 2 570.2.q.c.49.10 yes 20
19.7 even 3 inner 1710.2.t.c.919.1 20
57.26 odd 6 570.2.q.c.349.10 yes 20
95.64 even 6 inner 1710.2.t.c.919.9 20
285.254 odd 6 570.2.q.c.349.2 yes 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
570.2.q.c.49.2 20 3.2 odd 2
570.2.q.c.49.10 yes 20 15.14 odd 2
570.2.q.c.349.2 yes 20 285.254 odd 6
570.2.q.c.349.10 yes 20 57.26 odd 6
1710.2.t.c.919.1 20 19.7 even 3 inner
1710.2.t.c.919.9 20 95.64 even 6 inner
1710.2.t.c.1189.1 20 5.4 even 2 inner
1710.2.t.c.1189.9 20 1.1 even 1 trivial