Properties

Label 570.2.m.b.493.3
Level $570$
Weight $2$
Character 570.493
Analytic conductor $4.551$
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] = [570,2,Mod(37,570)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(570, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 1, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("570.37");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 570.m (of order \(4\), 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: \(4.55147291521\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} + 108x^{16} + 1318x^{12} + 4652x^{8} + 5057x^{4} + 256 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{9} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 493.3
Root \(-1.20277 - 1.20277i\) of defining polynomial
Character \(\chi\) \(=\) 570.493
Dual form 570.2.m.b.37.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.707107 - 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(0.528178 - 2.17279i) q^{5} -1.00000 q^{6} +(0.904140 - 0.904140i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000i q^{9} +O(q^{10})\) \(q+(-0.707107 - 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(0.528178 - 2.17279i) q^{5} -1.00000 q^{6} +(0.904140 - 0.904140i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000i q^{9} +(-1.90987 + 1.16292i) q^{10} +2.66147 q^{11} +(0.707107 + 0.707107i) q^{12} +(-0.143663 + 0.143663i) q^{13} -1.27865 q^{14} +(-1.16292 - 1.90987i) q^{15} -1.00000 q^{16} +(3.29524 - 3.29524i) q^{17} +(-0.707107 + 0.707107i) q^{18} +(-4.05688 + 1.59427i) q^{19} +(2.17279 + 0.528178i) q^{20} -1.27865i q^{21} +(-1.88194 - 1.88194i) q^{22} +(1.75733 + 1.75733i) q^{23} -1.00000i q^{24} +(-4.44206 - 2.29524i) q^{25} +0.203169 q^{26} +(-0.707107 - 0.707107i) q^{27} +(0.904140 + 0.904140i) q^{28} -2.17494 q^{29} +(-0.528178 + 2.17279i) q^{30} -2.62167i q^{31} +(0.707107 + 0.707107i) q^{32} +(1.88194 - 1.88194i) q^{33} -4.66018 q^{34} +(-1.48696 - 2.44206i) q^{35} +1.00000 q^{36} +(0.984090 + 0.984090i) q^{37} +(3.99597 + 1.74133i) q^{38} +0.203169i q^{39} +(-1.16292 - 1.90987i) q^{40} -3.74005i q^{41} +(-0.904140 + 0.904140i) q^{42} +(-2.01084 - 2.01084i) q^{43} +2.66147i q^{44} +(-2.17279 - 0.528178i) q^{45} -2.48524i q^{46} +(3.24973 - 3.24973i) q^{47} +(-0.707107 + 0.707107i) q^{48} +5.36506i q^{49} +(1.51803 + 4.76399i) q^{50} -4.66018i q^{51} +(-0.143663 - 0.143663i) q^{52} +(2.54197 - 2.54197i) q^{53} +1.00000i q^{54} +(1.40573 - 5.78282i) q^{55} -1.27865i q^{56} +(-1.74133 + 3.99597i) q^{57} +(1.53792 + 1.53792i) q^{58} -2.19877 q^{59} +(1.90987 - 1.16292i) q^{60} -8.90579 q^{61} +(-1.85380 + 1.85380i) q^{62} +(-0.904140 - 0.904140i) q^{63} -1.00000i q^{64} +(0.236270 + 0.388028i) q^{65} -2.66147 q^{66} +(4.50928 + 4.50928i) q^{67} +(3.29524 + 3.29524i) q^{68} +2.48524 q^{69} +(-0.675353 + 2.77824i) q^{70} +2.55729i q^{71} +(-0.707107 - 0.707107i) q^{72} +(-5.25513 - 5.25513i) q^{73} -1.39171i q^{74} +(-4.76399 + 1.51803i) q^{75} +(-1.59427 - 4.05688i) q^{76} +(2.40634 - 2.40634i) q^{77} +(0.143663 - 0.143663i) q^{78} -4.22731 q^{79} +(-0.528178 + 2.17279i) q^{80} -1.00000 q^{81} +(-2.64461 + 2.64461i) q^{82} +(6.55477 + 6.55477i) q^{83} +1.27865 q^{84} +(-5.41940 - 8.90035i) q^{85} +2.84376i q^{86} +(-1.53792 + 1.53792i) q^{87} +(1.88194 - 1.88194i) q^{88} -4.94664 q^{89} +(1.16292 + 1.90987i) q^{90} +0.259782i q^{91} +(-1.75733 + 1.75733i) q^{92} +(-1.85380 - 1.85380i) q^{93} -4.59581 q^{94} +(1.32127 + 9.65682i) q^{95} +1.00000 q^{96} +(11.8481 + 11.8481i) q^{97} +(3.79367 - 3.79367i) q^{98} -2.66147i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 12 q^{5} - 20 q^{6} - 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 20 q + 12 q^{5} - 20 q^{6} - 4 q^{7} - 8 q^{11} - 20 q^{16} - 12 q^{17} - 4 q^{23} - 28 q^{25} + 24 q^{26} - 4 q^{28} - 12 q^{30} + 4 q^{35} + 20 q^{36} - 12 q^{38} + 4 q^{42} - 12 q^{43} - 44 q^{47} + 64 q^{55} + 12 q^{57} - 8 q^{58} - 24 q^{62} + 4 q^{63} + 8 q^{66} - 12 q^{68} - 4 q^{73} + 4 q^{76} + 88 q^{77} - 12 q^{80} - 20 q^{81} - 8 q^{82} + 76 q^{83} - 12 q^{85} + 8 q^{87} + 4 q^{92} - 24 q^{93} - 24 q^{95} + 20 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(211\) \(457\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 0.707107i −0.500000 0.500000i
\(3\) 0.707107 0.707107i 0.408248 0.408248i
\(4\) 1.00000i 0.500000i
\(5\) 0.528178 2.17279i 0.236208 0.971702i
\(6\) −1.00000 −0.408248
\(7\) 0.904140 0.904140i 0.341733 0.341733i −0.515286 0.857018i \(-0.672314\pi\)
0.857018 + 0.515286i \(0.172314\pi\)
\(8\) 0.707107 0.707107i 0.250000 0.250000i
\(9\) 1.00000i 0.333333i
\(10\) −1.90987 + 1.16292i −0.603955 + 0.367747i
\(11\) 2.66147 0.802462 0.401231 0.915977i \(-0.368582\pi\)
0.401231 + 0.915977i \(0.368582\pi\)
\(12\) 0.707107 + 0.707107i 0.204124 + 0.204124i
\(13\) −0.143663 + 0.143663i −0.0398448 + 0.0398448i −0.726748 0.686904i \(-0.758969\pi\)
0.686904 + 0.726748i \(0.258969\pi\)
\(14\) −1.27865 −0.341733
\(15\) −1.16292 1.90987i −0.300264 0.493128i
\(16\) −1.00000 −0.250000
\(17\) 3.29524 3.29524i 0.799214 0.799214i −0.183758 0.982972i \(-0.558826\pi\)
0.982972 + 0.183758i \(0.0588262\pi\)
\(18\) −0.707107 + 0.707107i −0.166667 + 0.166667i
\(19\) −4.05688 + 1.59427i −0.930713 + 0.365751i
\(20\) 2.17279 + 0.528178i 0.485851 + 0.118104i
\(21\) 1.27865i 0.279024i
\(22\) −1.88194 1.88194i −0.401231 0.401231i
\(23\) 1.75733 + 1.75733i 0.366428 + 0.366428i 0.866173 0.499745i \(-0.166573\pi\)
−0.499745 + 0.866173i \(0.666573\pi\)
\(24\) 1.00000i 0.204124i
\(25\) −4.44206 2.29524i −0.888411 0.459049i
\(26\) 0.203169 0.0398448
\(27\) −0.707107 0.707107i −0.136083 0.136083i
\(28\) 0.904140 + 0.904140i 0.170866 + 0.170866i
\(29\) −2.17494 −0.403876 −0.201938 0.979398i \(-0.564724\pi\)
−0.201938 + 0.979398i \(0.564724\pi\)
\(30\) −0.528178 + 2.17279i −0.0964317 + 0.396696i
\(31\) 2.62167i 0.470865i −0.971891 0.235432i \(-0.924349\pi\)
0.971891 0.235432i \(-0.0756507\pi\)
\(32\) 0.707107 + 0.707107i 0.125000 + 0.125000i
\(33\) 1.88194 1.88194i 0.327604 0.327604i
\(34\) −4.66018 −0.799214
\(35\) −1.48696 2.44206i −0.251342 0.412783i
\(36\) 1.00000 0.166667
\(37\) 0.984090 + 0.984090i 0.161783 + 0.161783i 0.783356 0.621573i \(-0.213506\pi\)
−0.621573 + 0.783356i \(0.713506\pi\)
\(38\) 3.99597 + 1.74133i 0.648232 + 0.282481i
\(39\) 0.203169i 0.0325332i
\(40\) −1.16292 1.90987i −0.183874 0.301978i
\(41\) 3.74005i 0.584098i −0.956403 0.292049i \(-0.905663\pi\)
0.956403 0.292049i \(-0.0943370\pi\)
\(42\) −0.904140 + 0.904140i −0.139512 + 0.139512i
\(43\) −2.01084 2.01084i −0.306650 0.306650i 0.536959 0.843609i \(-0.319573\pi\)
−0.843609 + 0.536959i \(0.819573\pi\)
\(44\) 2.66147i 0.401231i
\(45\) −2.17279 0.528178i −0.323901 0.0787361i
\(46\) 2.48524i 0.366428i
\(47\) 3.24973 3.24973i 0.474021 0.474021i −0.429192 0.903213i \(-0.641202\pi\)
0.903213 + 0.429192i \(0.141202\pi\)
\(48\) −0.707107 + 0.707107i −0.102062 + 0.102062i
\(49\) 5.36506i 0.766437i
\(50\) 1.51803 + 4.76399i 0.214681 + 0.673730i
\(51\) 4.66018i 0.652555i
\(52\) −0.143663 0.143663i −0.0199224 0.0199224i
\(53\) 2.54197 2.54197i 0.349166 0.349166i −0.510633 0.859799i \(-0.670589\pi\)
0.859799 + 0.510633i \(0.170589\pi\)
\(54\) 1.00000i 0.136083i
\(55\) 1.40573 5.78282i 0.189548 0.779755i
\(56\) 1.27865i 0.170866i
\(57\) −1.74133 + 3.99597i −0.230645 + 0.529279i
\(58\) 1.53792 + 1.53792i 0.201938 + 0.201938i
\(59\) −2.19877 −0.286256 −0.143128 0.989704i \(-0.545716\pi\)
−0.143128 + 0.989704i \(0.545716\pi\)
\(60\) 1.90987 1.16292i 0.246564 0.150132i
\(61\) −8.90579 −1.14027 −0.570135 0.821551i \(-0.693109\pi\)
−0.570135 + 0.821551i \(0.693109\pi\)
\(62\) −1.85380 + 1.85380i −0.235432 + 0.235432i
\(63\) −0.904140 0.904140i −0.113911 0.113911i
\(64\) 1.00000i 0.125000i
\(65\) 0.236270 + 0.388028i 0.0293056 + 0.0481290i
\(66\) −2.66147 −0.327604
\(67\) 4.50928 + 4.50928i 0.550896 + 0.550896i 0.926700 0.375803i \(-0.122633\pi\)
−0.375803 + 0.926700i \(0.622633\pi\)
\(68\) 3.29524 + 3.29524i 0.399607 + 0.399607i
\(69\) 2.48524 0.299187
\(70\) −0.675353 + 2.77824i −0.0807202 + 0.332063i
\(71\) 2.55729i 0.303495i 0.988419 + 0.151748i \(0.0484901\pi\)
−0.988419 + 0.151748i \(0.951510\pi\)
\(72\) −0.707107 0.707107i −0.0833333 0.0833333i
\(73\) −5.25513 5.25513i −0.615066 0.615066i 0.329196 0.944262i \(-0.393222\pi\)
−0.944262 + 0.329196i \(0.893222\pi\)
\(74\) 1.39171i 0.161783i
\(75\) −4.76399 + 1.51803i −0.550098 + 0.175287i
\(76\) −1.59427 4.05688i −0.182876 0.465356i
\(77\) 2.40634 2.40634i 0.274228 0.274228i
\(78\) 0.143663 0.143663i 0.0162666 0.0162666i
\(79\) −4.22731 −0.475610 −0.237805 0.971313i \(-0.576428\pi\)
−0.237805 + 0.971313i \(0.576428\pi\)
\(80\) −0.528178 + 2.17279i −0.0590521 + 0.242926i
\(81\) −1.00000 −0.111111
\(82\) −2.64461 + 2.64461i −0.292049 + 0.292049i
\(83\) 6.55477 + 6.55477i 0.719479 + 0.719479i 0.968499 0.249019i \(-0.0801083\pi\)
−0.249019 + 0.968499i \(0.580108\pi\)
\(84\) 1.27865 0.139512
\(85\) −5.41940 8.90035i −0.587817 0.965379i
\(86\) 2.84376i 0.306650i
\(87\) −1.53792 + 1.53792i −0.164882 + 0.164882i
\(88\) 1.88194 1.88194i 0.200616 0.200616i
\(89\) −4.94664 −0.524343 −0.262171 0.965021i \(-0.584439\pi\)
−0.262171 + 0.965021i \(0.584439\pi\)
\(90\) 1.16292 + 1.90987i 0.122582 + 0.201318i
\(91\) 0.259782i 0.0272326i
\(92\) −1.75733 + 1.75733i −0.183214 + 0.183214i
\(93\) −1.85380 1.85380i −0.192230 0.192230i
\(94\) −4.59581 −0.474021
\(95\) 1.32127 + 9.65682i 0.135559 + 0.990769i
\(96\) 1.00000 0.102062
\(97\) 11.8481 + 11.8481i 1.20300 + 1.20300i 0.973251 + 0.229746i \(0.0737894\pi\)
0.229746 + 0.973251i \(0.426211\pi\)
\(98\) 3.79367 3.79367i 0.383219 0.383219i
\(99\) 2.66147i 0.267487i
\(100\) 2.29524 4.44206i 0.229524 0.444206i
\(101\) 3.64684 0.362874 0.181437 0.983403i \(-0.441925\pi\)
0.181437 + 0.983403i \(0.441925\pi\)
\(102\) −3.29524 + 3.29524i −0.326278 + 0.326278i
\(103\) 4.27174 4.27174i 0.420907 0.420907i −0.464609 0.885516i \(-0.653805\pi\)
0.885516 + 0.464609i \(0.153805\pi\)
\(104\) 0.203169i 0.0199224i
\(105\) −2.77824 0.675353i −0.271128 0.0659077i
\(106\) −3.59488 −0.349166
\(107\) 9.39155 + 9.39155i 0.907915 + 0.907915i 0.996104 0.0881885i \(-0.0281078\pi\)
−0.0881885 + 0.996104i \(0.528108\pi\)
\(108\) 0.707107 0.707107i 0.0680414 0.0680414i
\(109\) 12.0254 1.15182 0.575912 0.817512i \(-0.304647\pi\)
0.575912 + 0.817512i \(0.304647\pi\)
\(110\) −5.08307 + 3.09507i −0.484652 + 0.295103i
\(111\) 1.39171 0.132096
\(112\) −0.904140 + 0.904140i −0.0854332 + 0.0854332i
\(113\) −1.99650 + 1.99650i −0.187815 + 0.187815i −0.794751 0.606936i \(-0.792399\pi\)
0.606936 + 0.794751i \(0.292399\pi\)
\(114\) 4.05688 1.59427i 0.379962 0.149317i
\(115\) 4.74649 2.89013i 0.442612 0.269506i
\(116\) 2.17494i 0.201938i
\(117\) 0.143663 + 0.143663i 0.0132816 + 0.0132816i
\(118\) 1.55477 + 1.55477i 0.143128 + 0.143128i
\(119\) 5.95872i 0.546235i
\(120\) −2.17279 0.528178i −0.198348 0.0482158i
\(121\) −3.91659 −0.356054
\(122\) 6.29734 + 6.29734i 0.570135 + 0.570135i
\(123\) −2.64461 2.64461i −0.238457 0.238457i
\(124\) 2.62167 0.235432
\(125\) −7.33328 + 8.43937i −0.655909 + 0.754840i
\(126\) 1.27865i 0.113911i
\(127\) 12.5449 + 12.5449i 1.11318 + 1.11318i 0.992718 + 0.120462i \(0.0384377\pi\)
0.120462 + 0.992718i \(0.461562\pi\)
\(128\) −0.707107 + 0.707107i −0.0625000 + 0.0625000i
\(129\) −2.84376 −0.250379
\(130\) 0.107310 0.441445i 0.00941168 0.0387173i
\(131\) 20.6202 1.80159 0.900797 0.434240i \(-0.142983\pi\)
0.900797 + 0.434240i \(0.142983\pi\)
\(132\) 1.88194 + 1.88194i 0.163802 + 0.163802i
\(133\) −2.22655 + 5.10944i −0.193066 + 0.443044i
\(134\) 6.37709i 0.550896i
\(135\) −1.90987 + 1.16292i −0.164376 + 0.100088i
\(136\) 4.66018i 0.399607i
\(137\) −2.44206 + 2.44206i −0.208639 + 0.208639i −0.803689 0.595050i \(-0.797132\pi\)
0.595050 + 0.803689i \(0.297132\pi\)
\(138\) −1.75733 1.75733i −0.149594 0.149594i
\(139\) 16.1995i 1.37402i 0.726647 + 0.687011i \(0.241077\pi\)
−0.726647 + 0.687011i \(0.758923\pi\)
\(140\) 2.44206 1.48696i 0.206391 0.125671i
\(141\) 4.59581i 0.387037i
\(142\) 1.80828 1.80828i 0.151748 0.151748i
\(143\) −0.382353 + 0.382353i −0.0319740 + 0.0319740i
\(144\) 1.00000i 0.0833333i
\(145\) −1.14876 + 4.72570i −0.0953990 + 0.392448i
\(146\) 7.43187i 0.615066i
\(147\) 3.79367 + 3.79367i 0.312897 + 0.312897i
\(148\) −0.984090 + 0.984090i −0.0808917 + 0.0808917i
\(149\) 2.85261i 0.233695i −0.993150 0.116847i \(-0.962721\pi\)
0.993150 0.116847i \(-0.0372789\pi\)
\(150\) 4.44206 + 2.29524i 0.362692 + 0.187406i
\(151\) 18.6146i 1.51483i −0.652932 0.757417i \(-0.726461\pi\)
0.652932 0.757417i \(-0.273539\pi\)
\(152\) −1.74133 + 3.99597i −0.141240 + 0.324116i
\(153\) −3.29524 3.29524i −0.266405 0.266405i
\(154\) −3.40308 −0.274228
\(155\) −5.69634 1.38471i −0.457541 0.111222i
\(156\) −0.203169 −0.0162666
\(157\) −10.0694 + 10.0694i −0.803627 + 0.803627i −0.983661 0.180033i \(-0.942379\pi\)
0.180033 + 0.983661i \(0.442379\pi\)
\(158\) 2.98916 + 2.98916i 0.237805 + 0.237805i
\(159\) 3.59488i 0.285093i
\(160\) 1.90987 1.16292i 0.150989 0.0919368i
\(161\) 3.17774 0.250441
\(162\) 0.707107 + 0.707107i 0.0555556 + 0.0555556i
\(163\) 16.5520 + 16.5520i 1.29645 + 1.29645i 0.930719 + 0.365735i \(0.119182\pi\)
0.365735 + 0.930719i \(0.380818\pi\)
\(164\) 3.74005 0.292049
\(165\) −3.09507 5.08307i −0.240951 0.395716i
\(166\) 9.26984i 0.719479i
\(167\) 7.05038 + 7.05038i 0.545575 + 0.545575i 0.925158 0.379583i \(-0.123932\pi\)
−0.379583 + 0.925158i \(0.623932\pi\)
\(168\) −0.904140 0.904140i −0.0697559 0.0697559i
\(169\) 12.9587i 0.996825i
\(170\) −2.46140 + 10.1256i −0.188781 + 0.776598i
\(171\) 1.59427 + 4.05688i 0.121917 + 0.310238i
\(172\) 2.01084 2.01084i 0.153325 0.153325i
\(173\) 14.7696 14.7696i 1.12291 1.12291i 0.131609 0.991302i \(-0.457986\pi\)
0.991302 0.131609i \(-0.0420143\pi\)
\(174\) 2.17494 0.164882
\(175\) −6.09146 + 1.94102i −0.460471 + 0.146727i
\(176\) −2.66147 −0.200616
\(177\) −1.55477 + 1.55477i −0.116864 + 0.116864i
\(178\) 3.49780 + 3.49780i 0.262171 + 0.262171i
\(179\) 6.48791 0.484929 0.242465 0.970160i \(-0.422044\pi\)
0.242465 + 0.970160i \(0.422044\pi\)
\(180\) 0.528178 2.17279i 0.0393681 0.161950i
\(181\) 0.122571i 0.00911063i −0.999990 0.00455531i \(-0.998550\pi\)
0.999990 0.00455531i \(-0.00145001\pi\)
\(182\) 0.183694 0.183694i 0.0136163 0.0136163i
\(183\) −6.29734 + 6.29734i −0.465513 + 0.465513i
\(184\) 2.48524 0.183214
\(185\) 2.65800 1.61845i 0.195420 0.118991i
\(186\) 2.62167i 0.192230i
\(187\) 8.77018 8.77018i 0.641339 0.641339i
\(188\) 3.24973 + 3.24973i 0.237011 + 0.237011i
\(189\) −1.27865 −0.0930079
\(190\) 5.89413 7.76268i 0.427605 0.563164i
\(191\) −0.473897 −0.0342900 −0.0171450 0.999853i \(-0.505458\pi\)
−0.0171450 + 0.999853i \(0.505458\pi\)
\(192\) −0.707107 0.707107i −0.0510310 0.0510310i
\(193\) −8.37158 + 8.37158i −0.602600 + 0.602600i −0.941002 0.338402i \(-0.890114\pi\)
0.338402 + 0.941002i \(0.390114\pi\)
\(194\) 16.7558i 1.20300i
\(195\) 0.441445 + 0.107310i 0.0316125 + 0.00768460i
\(196\) −5.36506 −0.383219
\(197\) −9.45290 + 9.45290i −0.673491 + 0.673491i −0.958519 0.285028i \(-0.907997\pi\)
0.285028 + 0.958519i \(0.407997\pi\)
\(198\) −1.88194 + 1.88194i −0.133744 + 0.133744i
\(199\) 3.17530i 0.225091i −0.993647 0.112545i \(-0.964100\pi\)
0.993647 0.112545i \(-0.0359004\pi\)
\(200\) −4.76399 + 1.51803i −0.336865 + 0.107341i
\(201\) 6.37709 0.449805
\(202\) −2.57871 2.57871i −0.181437 0.181437i
\(203\) −1.96645 + 1.96645i −0.138018 + 0.138018i
\(204\) 4.66018 0.326278
\(205\) −8.12635 1.97541i −0.567569 0.137969i
\(206\) −6.04115 −0.420907
\(207\) 1.75733 1.75733i 0.122143 0.122143i
\(208\) 0.143663 0.143663i 0.00996120 0.00996120i
\(209\) −10.7973 + 4.24310i −0.746862 + 0.293501i
\(210\) 1.48696 + 2.44206i 0.102610 + 0.168518i
\(211\) 14.4553i 0.995142i 0.867423 + 0.497571i \(0.165775\pi\)
−0.867423 + 0.497571i \(0.834225\pi\)
\(212\) 2.54197 + 2.54197i 0.174583 + 0.174583i
\(213\) 1.80828 + 1.80828i 0.123901 + 0.123901i
\(214\) 13.2817i 0.907915i
\(215\) −5.43122 + 3.30706i −0.370406 + 0.225539i
\(216\) −1.00000 −0.0680414
\(217\) −2.37035 2.37035i −0.160910 0.160910i
\(218\) −8.50324 8.50324i −0.575912 0.575912i
\(219\) −7.43187 −0.502199
\(220\) 5.78282 + 1.40573i 0.389877 + 0.0947742i
\(221\) 0.946806i 0.0636890i
\(222\) −0.984090 0.984090i −0.0660478 0.0660478i
\(223\) 13.3101 13.3101i 0.891312 0.891312i −0.103335 0.994647i \(-0.532951\pi\)
0.994647 + 0.103335i \(0.0329513\pi\)
\(224\) 1.27865 0.0854332
\(225\) −2.29524 + 4.44206i −0.153016 + 0.296137i
\(226\) 2.82348 0.187815
\(227\) −21.0661 21.0661i −1.39820 1.39820i −0.805199 0.593005i \(-0.797942\pi\)
−0.593005 0.805199i \(-0.702058\pi\)
\(228\) −3.99597 1.74133i −0.264640 0.115322i
\(229\) 18.2167i 1.20379i 0.798574 + 0.601897i \(0.205588\pi\)
−0.798574 + 0.601897i \(0.794412\pi\)
\(230\) −5.39990 1.31265i −0.356059 0.0865533i
\(231\) 3.40308i 0.223906i
\(232\) −1.53792 + 1.53792i −0.100969 + 0.100969i
\(233\) −20.6479 20.6479i −1.35269 1.35269i −0.882642 0.470045i \(-0.844238\pi\)
−0.470045 0.882642i \(-0.655762\pi\)
\(234\) 0.203169i 0.0132816i
\(235\) −5.34455 8.77741i −0.348640 0.572575i
\(236\) 2.19877i 0.143128i
\(237\) −2.98916 + 2.98916i −0.194167 + 0.194167i
\(238\) −4.21345 + 4.21345i −0.273118 + 0.273118i
\(239\) 1.78480i 0.115449i 0.998333 + 0.0577247i \(0.0183846\pi\)
−0.998333 + 0.0577247i \(0.981615\pi\)
\(240\) 1.16292 + 1.90987i 0.0750660 + 0.123282i
\(241\) 6.17706i 0.397899i −0.980010 0.198950i \(-0.936247\pi\)
0.980010 0.198950i \(-0.0637530\pi\)
\(242\) 2.76945 + 2.76945i 0.178027 + 0.178027i
\(243\) −0.707107 + 0.707107i −0.0453609 + 0.0453609i
\(244\) 8.90579i 0.570135i
\(245\) 11.6572 + 2.83371i 0.744749 + 0.181039i
\(246\) 3.74005i 0.238457i
\(247\) 0.353785 0.811859i 0.0225108 0.0516574i
\(248\) −1.85380 1.85380i −0.117716 0.117716i
\(249\) 9.26984 0.587452
\(250\) 11.1529 0.782122i 0.705374 0.0494658i
\(251\) −3.89007 −0.245539 −0.122769 0.992435i \(-0.539178\pi\)
−0.122769 + 0.992435i \(0.539178\pi\)
\(252\) 0.904140 0.904140i 0.0569555 0.0569555i
\(253\) 4.67707 + 4.67707i 0.294045 + 0.294045i
\(254\) 17.7412i 1.11318i
\(255\) −10.1256 2.46140i −0.634090 0.154139i
\(256\) 1.00000 0.0625000
\(257\) −13.9017 13.9017i −0.867164 0.867164i 0.124994 0.992158i \(-0.460109\pi\)
−0.992158 + 0.124994i \(0.960109\pi\)
\(258\) 2.01084 + 2.01084i 0.125189 + 0.125189i
\(259\) 1.77951 0.110573
\(260\) −0.388028 + 0.236270i −0.0240645 + 0.0146528i
\(261\) 2.17494i 0.134625i
\(262\) −14.5807 14.5807i −0.900797 0.900797i
\(263\) −12.6517 12.6517i −0.780135 0.780135i 0.199718 0.979853i \(-0.435997\pi\)
−0.979853 + 0.199718i \(0.935997\pi\)
\(264\) 2.66147i 0.163802i
\(265\) −4.18055 6.86578i −0.256809 0.421761i
\(266\) 5.18732 2.03851i 0.318055 0.124989i
\(267\) −3.49780 + 3.49780i −0.214062 + 0.214062i
\(268\) −4.50928 + 4.50928i −0.275448 + 0.275448i
\(269\) −23.7972 −1.45094 −0.725470 0.688254i \(-0.758377\pi\)
−0.725470 + 0.688254i \(0.758377\pi\)
\(270\) 2.17279 + 0.528178i 0.132232 + 0.0321439i
\(271\) −13.5524 −0.823249 −0.411624 0.911354i \(-0.635038\pi\)
−0.411624 + 0.911354i \(0.635038\pi\)
\(272\) −3.29524 + 3.29524i −0.199803 + 0.199803i
\(273\) 0.183694 + 0.183694i 0.0111176 + 0.0111176i
\(274\) 3.45359 0.208639
\(275\) −11.8224 6.10871i −0.712917 0.368369i
\(276\) 2.48524i 0.149594i
\(277\) 11.8777 11.8777i 0.713662 0.713662i −0.253637 0.967299i \(-0.581627\pi\)
0.967299 + 0.253637i \(0.0816270\pi\)
\(278\) 11.4548 11.4548i 0.687011 0.687011i
\(279\) −2.62167 −0.156955
\(280\) −2.77824 0.675353i −0.166031 0.0403601i
\(281\) 16.4158i 0.979285i 0.871923 + 0.489643i \(0.162873\pi\)
−0.871923 + 0.489643i \(0.837127\pi\)
\(282\) −3.24973 + 3.24973i −0.193518 + 0.193518i
\(283\) 15.5488 + 15.5488i 0.924283 + 0.924283i 0.997329 0.0730457i \(-0.0232719\pi\)
−0.0730457 + 0.997329i \(0.523272\pi\)
\(284\) −2.55729 −0.151748
\(285\) 7.76268 + 5.89413i 0.459822 + 0.349138i
\(286\) 0.540729 0.0319740
\(287\) −3.38153 3.38153i −0.199605 0.199605i
\(288\) 0.707107 0.707107i 0.0416667 0.0416667i
\(289\) 4.71725i 0.277485i
\(290\) 4.15387 2.52928i 0.243923 0.148524i
\(291\) 16.7558 0.982242
\(292\) 5.25513 5.25513i 0.307533 0.307533i
\(293\) 19.2031 19.2031i 1.12186 1.12186i 0.130398 0.991462i \(-0.458375\pi\)
0.991462 0.130398i \(-0.0416254\pi\)
\(294\) 5.36506i 0.312897i
\(295\) −1.16134 + 4.77748i −0.0676161 + 0.278156i
\(296\) 1.39171 0.0808917
\(297\) −1.88194 1.88194i −0.109201 0.109201i
\(298\) −2.01710 + 2.01710i −0.116847 + 0.116847i
\(299\) −0.504924 −0.0292005
\(300\) −1.51803 4.76399i −0.0876433 0.275049i
\(301\) −3.63616 −0.209585
\(302\) −13.1625 + 13.1625i −0.757417 + 0.757417i
\(303\) 2.57871 2.57871i 0.148143 0.148143i
\(304\) 4.05688 1.59427i 0.232678 0.0914378i
\(305\) −4.70384 + 19.3504i −0.269341 + 1.10800i
\(306\) 4.66018i 0.266405i
\(307\) 15.2483 + 15.2483i 0.870269 + 0.870269i 0.992501 0.122233i \(-0.0390054\pi\)
−0.122233 + 0.992501i \(0.539005\pi\)
\(308\) 2.40634 + 2.40634i 0.137114 + 0.137114i
\(309\) 6.04115i 0.343669i
\(310\) 3.04878 + 5.00705i 0.173159 + 0.284381i
\(311\) 0.213974 0.0121334 0.00606668 0.999982i \(-0.498069\pi\)
0.00606668 + 0.999982i \(0.498069\pi\)
\(312\) 0.143663 + 0.143663i 0.00813329 + 0.00813329i
\(313\) −18.2399 18.2399i −1.03098 1.03098i −0.999504 0.0314771i \(-0.989979\pi\)
−0.0314771 0.999504i \(-0.510021\pi\)
\(314\) 14.2403 0.803627
\(315\) −2.44206 + 1.48696i −0.137594 + 0.0837808i
\(316\) 4.22731i 0.237805i
\(317\) −12.5740 12.5740i −0.706226 0.706226i 0.259513 0.965740i \(-0.416438\pi\)
−0.965740 + 0.259513i \(0.916438\pi\)
\(318\) −2.54197 + 2.54197i −0.142546 + 0.142546i
\(319\) −5.78853 −0.324096
\(320\) −2.17279 0.528178i −0.121463 0.0295260i
\(321\) 13.2817 0.741310
\(322\) −2.24700 2.24700i −0.125220 0.125220i
\(323\) −8.11490 + 18.6219i −0.451525 + 1.03615i
\(324\) 1.00000i 0.0555556i
\(325\) 0.967897 0.308417i 0.0536893 0.0171079i
\(326\) 23.4081i 1.29645i
\(327\) 8.50324 8.50324i 0.470230 0.470230i
\(328\) −2.64461 2.64461i −0.146024 0.146024i
\(329\) 5.87641i 0.323977i
\(330\) −1.40573 + 5.78282i −0.0773828 + 0.318334i
\(331\) 12.5316i 0.688802i −0.938823 0.344401i \(-0.888082\pi\)
0.938823 0.344401i \(-0.111918\pi\)
\(332\) −6.55477 + 6.55477i −0.359740 + 0.359740i
\(333\) 0.984090 0.984090i 0.0539278 0.0539278i
\(334\) 9.97075i 0.545575i
\(335\) 12.1794 7.41603i 0.665434 0.405181i
\(336\) 1.27865i 0.0697559i
\(337\) −10.1843 10.1843i −0.554774 0.554774i 0.373041 0.927815i \(-0.378315\pi\)
−0.927815 + 0.373041i \(0.878315\pi\)
\(338\) 9.16320 9.16320i 0.498412 0.498412i
\(339\) 2.82348i 0.153351i
\(340\) 8.90035 5.41940i 0.482689 0.293908i
\(341\) 6.97748i 0.377851i
\(342\) 1.74133 3.99597i 0.0941603 0.216077i
\(343\) 11.1797 + 11.1797i 0.603650 + 0.603650i
\(344\) −2.84376 −0.153325
\(345\) 1.31265 5.39990i 0.0706705 0.290721i
\(346\) −20.8873 −1.12291
\(347\) 3.39715 3.39715i 0.182369 0.182369i −0.610019 0.792387i \(-0.708838\pi\)
0.792387 + 0.610019i \(0.208838\pi\)
\(348\) −1.53792 1.53792i −0.0824409 0.0824409i
\(349\) 18.4982i 0.990188i −0.868840 0.495094i \(-0.835134\pi\)
0.868840 0.495094i \(-0.164866\pi\)
\(350\) 5.67982 + 2.93481i 0.303599 + 0.156872i
\(351\) 0.203169 0.0108444
\(352\) 1.88194 + 1.88194i 0.100308 + 0.100308i
\(353\) −2.03694 2.03694i −0.108415 0.108415i 0.650818 0.759234i \(-0.274426\pi\)
−0.759234 + 0.650818i \(0.774426\pi\)
\(354\) 2.19877 0.116864
\(355\) 5.55647 + 1.35071i 0.294907 + 0.0716881i
\(356\) 4.94664i 0.262171i
\(357\) −4.21345 4.21345i −0.223000 0.223000i
\(358\) −4.58765 4.58765i −0.242465 0.242465i
\(359\) 20.9321i 1.10475i 0.833595 + 0.552376i \(0.186279\pi\)
−0.833595 + 0.552376i \(0.813721\pi\)
\(360\) −1.90987 + 1.16292i −0.100659 + 0.0612912i
\(361\) 13.9166 12.9355i 0.732452 0.680818i
\(362\) −0.0866707 + 0.0866707i −0.00455531 + 0.00455531i
\(363\) −2.76945 + 2.76945i −0.145358 + 0.145358i
\(364\) −0.259782 −0.0136163
\(365\) −14.1939 + 8.64266i −0.742945 + 0.452378i
\(366\) 8.90579 0.465513
\(367\) 20.7061 20.7061i 1.08085 1.08085i 0.0844175 0.996430i \(-0.473097\pi\)
0.996430 0.0844175i \(-0.0269029\pi\)
\(368\) −1.75733 1.75733i −0.0916070 0.0916070i
\(369\) −3.74005 −0.194699
\(370\) −3.02390 0.735072i −0.157205 0.0382146i
\(371\) 4.59659i 0.238643i
\(372\) 1.85380 1.85380i 0.0961149 0.0961149i
\(373\) −7.00175 + 7.00175i −0.362537 + 0.362537i −0.864746 0.502209i \(-0.832521\pi\)
0.502209 + 0.864746i \(0.332521\pi\)
\(374\) −12.4029 −0.641339
\(375\) 0.782122 + 11.1529i 0.0403886 + 0.575936i
\(376\) 4.59581i 0.237011i
\(377\) 0.312458 0.312458i 0.0160924 0.0160924i
\(378\) 0.904140 + 0.904140i 0.0465040 + 0.0465040i
\(379\) −8.60331 −0.441922 −0.220961 0.975283i \(-0.570919\pi\)
−0.220961 + 0.975283i \(0.570919\pi\)
\(380\) −9.65682 + 1.32127i −0.495385 + 0.0677795i
\(381\) 17.7412 0.908908
\(382\) 0.335096 + 0.335096i 0.0171450 + 0.0171450i
\(383\) −1.41335 + 1.41335i −0.0722188 + 0.0722188i −0.742294 0.670075i \(-0.766262\pi\)
0.670075 + 0.742294i \(0.266262\pi\)
\(384\) 1.00000i 0.0510310i
\(385\) −3.95750 6.49945i −0.201693 0.331243i
\(386\) 11.8392 0.602600
\(387\) −2.01084 + 2.01084i −0.102217 + 0.102217i
\(388\) −11.8481 + 11.8481i −0.601498 + 0.601498i
\(389\) 14.9165i 0.756295i −0.925745 0.378148i \(-0.876561\pi\)
0.925745 0.378148i \(-0.123439\pi\)
\(390\) −0.236270 0.388028i −0.0119640 0.0196486i
\(391\) 11.5816 0.585708
\(392\) 3.79367 + 3.79367i 0.191609 + 0.191609i
\(393\) 14.5807 14.5807i 0.735498 0.735498i
\(394\) 13.3684 0.673491
\(395\) −2.23277 + 9.18507i −0.112343 + 0.462151i
\(396\) 2.66147 0.133744
\(397\) −20.0161 + 20.0161i −1.00458 + 1.00458i −0.00459066 + 0.999989i \(0.501461\pi\)
−0.999989 + 0.00459066i \(0.998539\pi\)
\(398\) −2.24527 + 2.24527i −0.112545 + 0.112545i
\(399\) 2.03851 + 5.18732i 0.102053 + 0.259691i
\(400\) 4.44206 + 2.29524i 0.222103 + 0.114762i
\(401\) 9.55630i 0.477219i 0.971116 + 0.238609i \(0.0766916\pi\)
−0.971116 + 0.238609i \(0.923308\pi\)
\(402\) −4.50928 4.50928i −0.224903 0.224903i
\(403\) 0.376635 + 0.376635i 0.0187615 + 0.0187615i
\(404\) 3.64684i 0.181437i
\(405\) −0.528178 + 2.17279i −0.0262454 + 0.107967i
\(406\) 2.78098 0.138018
\(407\) 2.61912 + 2.61912i 0.129825 + 0.129825i
\(408\) −3.29524 3.29524i −0.163139 0.163139i
\(409\) −37.3114 −1.84493 −0.922466 0.386079i \(-0.873829\pi\)
−0.922466 + 0.386079i \(0.873829\pi\)
\(410\) 4.34937 + 7.14303i 0.214800 + 0.352769i
\(411\) 3.45359i 0.170353i
\(412\) 4.27174 + 4.27174i 0.210454 + 0.210454i
\(413\) −1.98800 + 1.98800i −0.0978231 + 0.0978231i
\(414\) −2.48524 −0.122143
\(415\) 17.7042 10.7801i 0.869067 0.529173i
\(416\) −0.203169 −0.00996120
\(417\) 11.4548 + 11.4548i 0.560942 + 0.560942i
\(418\) 10.6351 + 4.63449i 0.520182 + 0.226680i
\(419\) 33.2272i 1.62326i 0.584175 + 0.811628i \(0.301418\pi\)
−0.584175 + 0.811628i \(0.698582\pi\)
\(420\) 0.675353 2.77824i 0.0329539 0.135564i
\(421\) 38.3380i 1.86848i 0.356646 + 0.934240i \(0.383920\pi\)
−0.356646 + 0.934240i \(0.616080\pi\)
\(422\) 10.2214 10.2214i 0.497571 0.497571i
\(423\) −3.24973 3.24973i −0.158007 0.158007i
\(424\) 3.59488i 0.174583i
\(425\) −22.2010 + 7.07427i −1.07691 + 0.343153i
\(426\) 2.55729i 0.123901i
\(427\) −8.05208 + 8.05208i −0.389668 + 0.389668i
\(428\) −9.39155 + 9.39155i −0.453958 + 0.453958i
\(429\) 0.540729i 0.0261066i
\(430\) 6.17889 + 1.50201i 0.297973 + 0.0724333i
\(431\) 21.2257i 1.02241i 0.859460 + 0.511203i \(0.170800\pi\)
−0.859460 + 0.511203i \(0.829200\pi\)
\(432\) 0.707107 + 0.707107i 0.0340207 + 0.0340207i
\(433\) −10.9862 + 10.9862i −0.527961 + 0.527961i −0.919964 0.392003i \(-0.871782\pi\)
0.392003 + 0.919964i \(0.371782\pi\)
\(434\) 3.35219i 0.160910i
\(435\) 2.52928 + 4.15387i 0.121270 + 0.199163i
\(436\) 12.0254i 0.575912i
\(437\) −9.93092 4.32761i −0.475061 0.207018i
\(438\) 5.25513 + 5.25513i 0.251100 + 0.251100i
\(439\) −1.43541 −0.0685084 −0.0342542 0.999413i \(-0.510906\pi\)
−0.0342542 + 0.999413i \(0.510906\pi\)
\(440\) −3.09507 5.08307i −0.147552 0.242326i
\(441\) 5.36506 0.255479
\(442\) 0.669493 0.669493i 0.0318445 0.0318445i
\(443\) 9.49661 + 9.49661i 0.451198 + 0.451198i 0.895752 0.444554i \(-0.146638\pi\)
−0.444554 + 0.895752i \(0.646638\pi\)
\(444\) 1.39171i 0.0660478i
\(445\) −2.61271 + 10.7480i −0.123854 + 0.509505i
\(446\) −18.8234 −0.891312
\(447\) −2.01710 2.01710i −0.0954056 0.0954056i
\(448\) −0.904140 0.904140i −0.0427166 0.0427166i
\(449\) 17.7665 0.838454 0.419227 0.907881i \(-0.362301\pi\)
0.419227 + 0.907881i \(0.362301\pi\)
\(450\) 4.76399 1.51803i 0.224577 0.0715605i
\(451\) 9.95402i 0.468716i
\(452\) −1.99650 1.99650i −0.0939076 0.0939076i
\(453\) −13.1625 13.1625i −0.618428 0.618428i
\(454\) 29.7919i 1.39820i
\(455\) 0.564453 + 0.137211i 0.0264620 + 0.00643256i
\(456\) 1.59427 + 4.05688i 0.0746586 + 0.189981i
\(457\) 6.74008 6.74008i 0.315288 0.315288i −0.531666 0.846954i \(-0.678434\pi\)
0.846954 + 0.531666i \(0.178434\pi\)
\(458\) 12.8812 12.8812i 0.601897 0.601897i
\(459\) −4.66018 −0.217518
\(460\) 2.89013 + 4.74649i 0.134753 + 0.221306i
\(461\) −4.22763 −0.196900 −0.0984501 0.995142i \(-0.531388\pi\)
−0.0984501 + 0.995142i \(0.531388\pi\)
\(462\) −2.40634 + 2.40634i −0.111953 + 0.111953i
\(463\) 12.2736 + 12.2736i 0.570403 + 0.570403i 0.932241 0.361838i \(-0.117851\pi\)
−0.361838 + 0.932241i \(0.617851\pi\)
\(464\) 2.17494 0.100969
\(465\) −5.00705 + 3.04878i −0.232196 + 0.141384i
\(466\) 29.2005i 1.35269i
\(467\) 9.12358 9.12358i 0.422189 0.422189i −0.463768 0.885957i \(-0.653503\pi\)
0.885957 + 0.463768i \(0.153503\pi\)
\(468\) −0.143663 + 0.143663i −0.00664080 + 0.00664080i
\(469\) 8.15405 0.376519
\(470\) −2.42740 + 9.98573i −0.111968 + 0.460608i
\(471\) 14.2403i 0.656159i
\(472\) −1.55477 + 1.55477i −0.0715640 + 0.0715640i
\(473\) −5.35178 5.35178i −0.246075 0.246075i
\(474\) 4.22731 0.194167
\(475\) 21.6801 + 2.22968i 0.994753 + 0.102305i
\(476\) 5.95872 0.273118
\(477\) −2.54197 2.54197i −0.116389 0.116389i
\(478\) 1.26205 1.26205i 0.0577247 0.0577247i
\(479\) 36.9313i 1.68744i −0.536787 0.843718i \(-0.680362\pi\)
0.536787 0.843718i \(-0.319638\pi\)
\(480\) 0.528178 2.17279i 0.0241079 0.0991740i
\(481\) −0.282754 −0.0128925
\(482\) −4.36784 + 4.36784i −0.198950 + 0.198950i
\(483\) 2.24700 2.24700i 0.102242 0.102242i
\(484\) 3.91659i 0.178027i
\(485\) 32.0015 19.4856i 1.45311 0.884797i
\(486\) 1.00000 0.0453609
\(487\) 10.3862 + 10.3862i 0.470642 + 0.470642i 0.902122 0.431481i \(-0.142009\pi\)
−0.431481 + 0.902122i \(0.642009\pi\)
\(488\) −6.29734 + 6.29734i −0.285067 + 0.285067i
\(489\) 23.4081 1.05855
\(490\) −6.23913 10.2466i −0.281855 0.462894i
\(491\) −31.2661 −1.41102 −0.705509 0.708701i \(-0.749281\pi\)
−0.705509 + 0.708701i \(0.749281\pi\)
\(492\) 2.64461 2.64461i 0.119228 0.119228i
\(493\) −7.16696 + 7.16696i −0.322784 + 0.322784i
\(494\) −0.824235 + 0.323907i −0.0370841 + 0.0145733i
\(495\) −5.78282 1.40573i −0.259918 0.0631828i
\(496\) 2.62167i 0.117716i
\(497\) 2.31215 + 2.31215i 0.103714 + 0.103714i
\(498\) −6.55477 6.55477i −0.293726 0.293726i
\(499\) 31.8064i 1.42385i 0.702256 + 0.711925i \(0.252176\pi\)
−0.702256 + 0.711925i \(0.747824\pi\)
\(500\) −8.43937 7.33328i −0.377420 0.327954i
\(501\) 9.97075 0.445460
\(502\) 2.75069 + 2.75069i 0.122769 + 0.122769i
\(503\) −30.1365 30.1365i −1.34372 1.34372i −0.892324 0.451396i \(-0.850926\pi\)
−0.451396 0.892324i \(-0.649074\pi\)
\(504\) −1.27865 −0.0569555
\(505\) 1.92618 7.92383i 0.0857139 0.352606i
\(506\) 6.61437i 0.294045i
\(507\) 9.16320 + 9.16320i 0.406952 + 0.406952i
\(508\) −12.5449 + 12.5449i −0.556590 + 0.556590i
\(509\) 39.4733 1.74962 0.874811 0.484463i \(-0.160985\pi\)
0.874811 + 0.484463i \(0.160985\pi\)
\(510\) 5.41940 + 8.90035i 0.239975 + 0.394114i
\(511\) −9.50274 −0.420377
\(512\) −0.707107 0.707107i −0.0312500 0.0312500i
\(513\) 3.99597 + 1.74133i 0.176426 + 0.0768815i
\(514\) 19.6600i 0.867164i
\(515\) −7.02537 11.5378i −0.309575 0.508418i
\(516\) 2.84376i 0.125189i
\(517\) 8.64904 8.64904i 0.380384 0.380384i
\(518\) −1.25830 1.25830i −0.0552867 0.0552867i
\(519\) 20.8873i 0.916853i
\(520\) 0.441445 + 0.107310i 0.0193587 + 0.00470584i
\(521\) 43.0892i 1.88777i 0.330271 + 0.943886i \(0.392860\pi\)
−0.330271 + 0.943886i \(0.607140\pi\)
\(522\) 1.53792 1.53792i 0.0673127 0.0673127i
\(523\) 12.0200 12.0200i 0.525600 0.525600i −0.393658 0.919257i \(-0.628790\pi\)
0.919257 + 0.393658i \(0.128790\pi\)
\(524\) 20.6202i 0.900797i
\(525\) −2.93481 + 5.67982i −0.128085 + 0.247888i
\(526\) 17.8922i 0.780135i
\(527\) −8.63902 8.63902i −0.376322 0.376322i
\(528\) −1.88194 + 1.88194i −0.0819010 + 0.0819010i
\(529\) 16.8236i 0.731461i
\(530\) −1.89874 + 7.81093i −0.0824759 + 0.339285i
\(531\) 2.19877i 0.0954187i
\(532\) −5.10944 2.22655i −0.221522 0.0965330i
\(533\) 0.537305 + 0.537305i 0.0232733 + 0.0232733i
\(534\) 4.94664 0.214062
\(535\) 25.3663 15.4455i 1.09668 0.667766i
\(536\) 6.37709 0.275448
\(537\) 4.58765 4.58765i 0.197972 0.197972i
\(538\) 16.8271 + 16.8271i 0.725470 + 0.725470i
\(539\) 14.2789i 0.615037i
\(540\) −1.16292 1.90987i −0.0500440 0.0821879i
\(541\) −8.87532 −0.381580 −0.190790 0.981631i \(-0.561105\pi\)
−0.190790 + 0.981631i \(0.561105\pi\)
\(542\) 9.58298 + 9.58298i 0.411624 + 0.411624i
\(543\) −0.0866707 0.0866707i −0.00371940 0.00371940i
\(544\) 4.66018 0.199803
\(545\) 6.35155 26.1287i 0.272070 1.11923i
\(546\) 0.259782i 0.0111176i
\(547\) −13.9130 13.9130i −0.594877 0.594877i 0.344068 0.938945i \(-0.388195\pi\)
−0.938945 + 0.344068i \(0.888195\pi\)
\(548\) −2.44206 2.44206i −0.104319 0.104319i
\(549\) 8.90579i 0.380090i
\(550\) 4.04018 + 12.6792i 0.172274 + 0.540643i
\(551\) 8.82348 3.46745i 0.375893 0.147718i
\(552\) 1.75733 1.75733i 0.0747968 0.0747968i
\(553\) −3.82208 + 3.82208i −0.162531 + 0.162531i
\(554\) −16.7976 −0.713662
\(555\) 0.735072 3.02390i 0.0312021 0.128358i
\(556\) −16.1995 −0.687011
\(557\) 14.7010 14.7010i 0.622900 0.622900i −0.323372 0.946272i \(-0.604816\pi\)
0.946272 + 0.323372i \(0.104816\pi\)
\(558\) 1.85380 + 1.85380i 0.0784775 + 0.0784775i
\(559\) 0.577764 0.0244368
\(560\) 1.48696 + 2.44206i 0.0628356 + 0.103196i
\(561\) 12.4029i 0.523651i
\(562\) 11.6077 11.6077i 0.489643 0.489643i
\(563\) −9.68060 + 9.68060i −0.407989 + 0.407989i −0.881037 0.473048i \(-0.843154\pi\)
0.473048 + 0.881037i \(0.343154\pi\)
\(564\) 4.59581 0.193518
\(565\) 3.28348 + 5.39250i 0.138137 + 0.226864i
\(566\) 21.9894i 0.924283i
\(567\) −0.904140 + 0.904140i −0.0379703 + 0.0379703i
\(568\) 1.80828 + 1.80828i 0.0758738 + 0.0758738i
\(569\) 36.5026 1.53027 0.765133 0.643872i \(-0.222673\pi\)
0.765133 + 0.643872i \(0.222673\pi\)
\(570\) −1.32127 9.65682i −0.0553417 0.404480i
\(571\) −18.0651 −0.756000 −0.378000 0.925806i \(-0.623388\pi\)
−0.378000 + 0.925806i \(0.623388\pi\)
\(572\) −0.382353 0.382353i −0.0159870 0.0159870i
\(573\) −0.335096 + 0.335096i −0.0139988 + 0.0139988i
\(574\) 4.78220i 0.199605i
\(575\) −3.77265 11.8396i −0.157330 0.493747i
\(576\) −1.00000 −0.0416667
\(577\) 13.7843 13.7843i 0.573847 0.573847i −0.359354 0.933201i \(-0.617003\pi\)
0.933201 + 0.359354i \(0.117003\pi\)
\(578\) −3.33560 + 3.33560i −0.138743 + 0.138743i
\(579\) 11.8392i 0.492021i
\(580\) −4.72570 1.14876i −0.196224 0.0476995i
\(581\) 11.8529 0.491739
\(582\) −11.8481 11.8481i −0.491121 0.491121i
\(583\) 6.76536 6.76536i 0.280192 0.280192i
\(584\) −7.43187 −0.307533
\(585\) 0.388028 0.236270i 0.0160430 0.00976854i
\(586\) −27.1573 −1.12186
\(587\) −12.9491 + 12.9491i −0.534466 + 0.534466i −0.921898 0.387432i \(-0.873362\pi\)
0.387432 + 0.921898i \(0.373362\pi\)
\(588\) −3.79367 + 3.79367i −0.156448 + 0.156448i
\(589\) 4.17965 + 10.6358i 0.172219 + 0.438240i
\(590\) 4.19938 2.55699i 0.172886 0.105270i
\(591\) 13.3684i 0.549903i
\(592\) −0.984090 0.984090i −0.0404458 0.0404458i
\(593\) 1.56552 + 1.56552i 0.0642881 + 0.0642881i 0.738520 0.674232i \(-0.235525\pi\)
−0.674232 + 0.738520i \(0.735525\pi\)
\(594\) 2.66147i 0.109201i
\(595\) −12.9471 3.14727i −0.530778 0.129025i
\(596\) 2.85261 0.116847
\(597\) −2.24527 2.24527i −0.0918929 0.0918929i
\(598\) 0.357035 + 0.357035i 0.0146003 + 0.0146003i
\(599\) 31.2077 1.27511 0.637556 0.770404i \(-0.279946\pi\)
0.637556 + 0.770404i \(0.279946\pi\)
\(600\) −2.29524 + 4.44206i −0.0937029 + 0.181346i
\(601\) 27.0296i 1.10256i −0.834320 0.551281i \(-0.814139\pi\)
0.834320 0.551281i \(-0.185861\pi\)
\(602\) 2.57115 + 2.57115i 0.104792 + 0.104792i
\(603\) 4.50928 4.50928i 0.183632 0.183632i
\(604\) 18.6146 0.757417
\(605\) −2.06866 + 8.50995i −0.0841029 + 0.345979i
\(606\) −3.64684 −0.148143
\(607\) −10.1961 10.1961i −0.413847 0.413847i 0.469229 0.883076i \(-0.344532\pi\)
−0.883076 + 0.469229i \(0.844532\pi\)
\(608\) −3.99597 1.74133i −0.162058 0.0706202i
\(609\) 2.78098i 0.112691i
\(610\) 17.0089 10.3567i 0.688672 0.419331i
\(611\) 0.933728i 0.0377746i
\(612\) 3.29524 3.29524i 0.133202 0.133202i
\(613\) −22.4225 22.4225i −0.905634 0.905634i 0.0902818 0.995916i \(-0.471223\pi\)
−0.995916 + 0.0902818i \(0.971223\pi\)
\(614\) 21.5644i 0.870269i
\(615\) −7.14303 + 4.34937i −0.288035 + 0.175384i
\(616\) 3.40308i 0.137114i
\(617\) −1.22259 + 1.22259i −0.0492195 + 0.0492195i −0.731288 0.682069i \(-0.761081\pi\)
0.682069 + 0.731288i \(0.261081\pi\)
\(618\) −4.27174 + 4.27174i −0.171835 + 0.171835i
\(619\) 26.1462i 1.05090i 0.850823 + 0.525452i \(0.176104\pi\)
−0.850823 + 0.525452i \(0.823896\pi\)
\(620\) 1.38471 5.69634i 0.0556111 0.228770i
\(621\) 2.48524i 0.0997291i
\(622\) −0.151302 0.151302i −0.00606668 0.00606668i
\(623\) −4.47245 + 4.47245i −0.179185 + 0.179185i
\(624\) 0.203169i 0.00813329i
\(625\) 14.4637 + 20.3912i 0.578549 + 0.815648i
\(626\) 25.7952i 1.03098i
\(627\) −4.63449 + 10.6351i −0.185084 + 0.424727i
\(628\) −10.0694 10.0694i −0.401814 0.401814i
\(629\) 6.48563 0.258599
\(630\) 2.77824 + 0.675353i 0.110688 + 0.0269067i
\(631\) −33.3652 −1.32825 −0.664124 0.747623i \(-0.731195\pi\)
−0.664124 + 0.747623i \(0.731195\pi\)
\(632\) −2.98916 + 2.98916i −0.118902 + 0.118902i
\(633\) 10.2214 + 10.2214i 0.406265 + 0.406265i
\(634\) 17.7823i 0.706226i
\(635\) 33.8834 20.6315i 1.34462 0.818737i
\(636\) 3.59488 0.142546
\(637\) −0.770758 0.770758i −0.0305386 0.0305386i
\(638\) 4.09311 + 4.09311i 0.162048 + 0.162048i
\(639\) 2.55729 0.101165
\(640\) 1.16292 + 1.90987i 0.0459684 + 0.0754944i
\(641\) 31.2439i 1.23406i 0.786940 + 0.617029i \(0.211664\pi\)
−0.786940 + 0.617029i \(0.788336\pi\)
\(642\) −9.39155 9.39155i −0.370655 0.370655i
\(643\) −3.28874 3.28874i −0.129695 0.129695i 0.639279 0.768975i \(-0.279233\pi\)
−0.768975 + 0.639279i \(0.779233\pi\)
\(644\) 3.17774i 0.125220i
\(645\) −1.50201 + 6.17889i −0.0591416 + 0.243294i
\(646\) 18.9058 7.42959i 0.743838 0.292313i
\(647\) 24.2688 24.2688i 0.954105 0.954105i −0.0448869 0.998992i \(-0.514293\pi\)
0.998992 + 0.0448869i \(0.0142928\pi\)
\(648\) −0.707107 + 0.707107i −0.0277778 + 0.0277778i
\(649\) −5.85196 −0.229710
\(650\) −0.902490 0.466323i −0.0353986 0.0182907i
\(651\) −3.35219 −0.131382
\(652\) −16.5520 + 16.5520i −0.648227 + 0.648227i
\(653\) 0.820035 + 0.820035i 0.0320904 + 0.0320904i 0.722970 0.690879i \(-0.242776\pi\)
−0.690879 + 0.722970i \(0.742776\pi\)
\(654\) −12.0254 −0.470230
\(655\) 10.8911 44.8034i 0.425552 1.75061i
\(656\) 3.74005i 0.146024i
\(657\) −5.25513 + 5.25513i −0.205022 + 0.205022i
\(658\) −4.15525 + 4.15525i −0.161989 + 0.161989i
\(659\) −42.2189 −1.64461 −0.822307 0.569044i \(-0.807313\pi\)
−0.822307 + 0.569044i \(0.807313\pi\)
\(660\) 5.08307 3.09507i 0.197858 0.120475i
\(661\) 26.8163i 1.04303i 0.853241 + 0.521517i \(0.174634\pi\)
−0.853241 + 0.521517i \(0.825366\pi\)
\(662\) −8.86121 + 8.86121i −0.344401 + 0.344401i
\(663\) 0.669493 + 0.669493i 0.0260009 + 0.0260009i
\(664\) 9.26984 0.359740
\(665\) 9.92573 + 7.53651i 0.384903 + 0.292253i
\(666\) −1.39171 −0.0539278
\(667\) −3.82208 3.82208i −0.147992 0.147992i
\(668\) −7.05038 + 7.05038i −0.272788 + 0.272788i
\(669\) 18.8234i 0.727753i
\(670\) −13.8561 3.36824i −0.535307 0.130126i
\(671\) −23.7025 −0.915023
\(672\) 0.904140 0.904140i 0.0348780 0.0348780i
\(673\) −23.1618 + 23.1618i −0.892824 + 0.892824i −0.994788 0.101964i \(-0.967487\pi\)
0.101964 + 0.994788i \(0.467487\pi\)
\(674\) 14.4028i 0.554774i
\(675\) 1.51803 + 4.76399i 0.0584289 + 0.183366i
\(676\) −12.9587 −0.498412
\(677\) −18.0408 18.0408i −0.693364 0.693364i 0.269606 0.962971i \(-0.413106\pi\)
−0.962971 + 0.269606i \(0.913106\pi\)
\(678\) 1.99650 1.99650i 0.0766753 0.0766753i
\(679\) 21.4248 0.822207
\(680\) −10.1256 2.46140i −0.388299 0.0943905i
\(681\) −29.7919 −1.14163
\(682\) −4.93382 + 4.93382i −0.188926 + 0.188926i
\(683\) −20.2075 + 20.2075i −0.773220 + 0.773220i −0.978668 0.205448i \(-0.934135\pi\)
0.205448 + 0.978668i \(0.434135\pi\)
\(684\) −4.05688 + 1.59427i −0.155119 + 0.0609585i
\(685\) 4.01624 + 6.59592i 0.153453 + 0.252017i
\(686\) 15.8106i 0.603650i
\(687\) 12.8812 + 12.8812i 0.491447 + 0.491447i
\(688\) 2.01084 + 2.01084i 0.0766625 + 0.0766625i
\(689\) 0.730371i 0.0278249i
\(690\) −4.74649 + 2.89013i −0.180696 + 0.110025i
\(691\) −5.06618 −0.192727 −0.0963633 0.995346i \(-0.530721\pi\)
−0.0963633 + 0.995346i \(0.530721\pi\)
\(692\) 14.7696 + 14.7696i 0.561455 + 0.561455i
\(693\) −2.40634 2.40634i −0.0914093 0.0914093i
\(694\) −4.80430 −0.182369
\(695\) 35.1981 + 8.55620i 1.33514 + 0.324555i
\(696\) 2.17494i 0.0824409i
\(697\) −12.3244 12.3244i −0.466819 0.466819i
\(698\) −13.0802 + 13.0802i −0.495094 + 0.495094i
\(699\) −29.2005 −1.10446
\(700\) −1.94102 6.09146i −0.0733637 0.230236i
\(701\) 31.7812 1.20036 0.600180 0.799865i \(-0.295096\pi\)
0.600180 + 0.799865i \(0.295096\pi\)
\(702\) −0.143663 0.143663i −0.00542219 0.00542219i
\(703\) −5.56124 2.42343i −0.209746 0.0914014i
\(704\) 2.66147i 0.100308i
\(705\) −9.98573 2.42740i −0.376084 0.0914213i
\(706\) 2.88067i 0.108415i
\(707\) 3.29726 3.29726i 0.124006 0.124006i
\(708\) −1.55477 1.55477i −0.0584318 0.0584318i
\(709\) 40.1995i 1.50972i −0.655884 0.754861i \(-0.727704\pi\)
0.655884 0.754861i \(-0.272296\pi\)
\(710\) −2.97392 4.88411i −0.111609 0.183297i
\(711\) 4.22731i 0.158537i
\(712\) −3.49780 + 3.49780i −0.131086 + 0.131086i
\(713\) 4.60712 4.60712i 0.172538 0.172538i
\(714\) 5.95872i 0.223000i
\(715\) 0.628823 + 1.03272i 0.0235167 + 0.0386217i
\(716\) 6.48791i 0.242465i
\(717\) 1.26205 + 1.26205i 0.0471320 + 0.0471320i
\(718\) 14.8012 14.8012i 0.552376 0.552376i
\(719\) 9.60719i 0.358288i −0.983823 0.179144i \(-0.942667\pi\)
0.983823 0.179144i \(-0.0573328\pi\)
\(720\) 2.17279 + 0.528178i 0.0809752 + 0.0196840i
\(721\) 7.72450i 0.287676i
\(722\) −18.9873 0.693705i −0.706635 0.0258170i
\(723\) −4.36784 4.36784i −0.162442 0.162442i
\(724\) 0.122571 0.00455531
\(725\) 9.66121 + 4.99202i 0.358808 + 0.185399i
\(726\) 3.91659 0.145358
\(727\) 7.58566 7.58566i 0.281337 0.281337i −0.552305 0.833642i \(-0.686252\pi\)
0.833642 + 0.552305i \(0.186252\pi\)
\(728\) 0.183694 + 0.183694i 0.00680814 + 0.00680814i
\(729\) 1.00000i 0.0370370i
\(730\) 16.1479 + 3.92535i 0.597661 + 0.145284i
\(731\) −13.2524 −0.490158
\(732\) −6.29734 6.29734i −0.232757 0.232757i
\(733\) 16.6371 + 16.6371i 0.614504 + 0.614504i 0.944116 0.329612i \(-0.106918\pi\)
−0.329612 + 0.944116i \(0.606918\pi\)
\(734\) −29.2828 −1.08085
\(735\) 10.2466 6.23913i 0.377951 0.230134i
\(736\) 2.48524i 0.0916070i
\(737\) 12.0013 + 12.0013i 0.442074 + 0.442074i
\(738\) 2.64461 + 2.64461i 0.0973496 + 0.0973496i
\(739\) 18.7582i 0.690030i 0.938597 + 0.345015i \(0.112126\pi\)
−0.938597 + 0.345015i \(0.887874\pi\)
\(740\) 1.61845 + 2.65800i 0.0594954 + 0.0977099i
\(741\) −0.323907 0.824235i −0.0118990 0.0302790i
\(742\) −3.25028 + 3.25028i −0.119321 + 0.119321i
\(743\) −18.3052 + 18.3052i −0.671553 + 0.671553i −0.958074 0.286521i \(-0.907501\pi\)
0.286521 + 0.958074i \(0.407501\pi\)
\(744\) −2.62167 −0.0961149
\(745\) −6.19813 1.50669i −0.227082 0.0552007i
\(746\) 9.90197 0.362537
\(747\) 6.55477 6.55477i 0.239826 0.239826i
\(748\) 8.77018 + 8.77018i 0.320669 + 0.320669i
\(749\) 16.9826 0.620529
\(750\) 7.33328 8.43937i 0.267774 0.308162i
\(751\) 32.7384i 1.19464i −0.802002 0.597321i \(-0.796232\pi\)
0.802002 0.597321i \(-0.203768\pi\)
\(752\) −3.24973 + 3.24973i −0.118505 + 0.118505i
\(753\) −2.75069 + 2.75069i −0.100241 + 0.100241i
\(754\) −0.441882 −0.0160924
\(755\) −40.4456 9.83182i −1.47197 0.357816i
\(756\) 1.27865i 0.0465040i
\(757\) 18.8701 18.8701i 0.685844 0.685844i −0.275466 0.961311i \(-0.588832\pi\)
0.961311 + 0.275466i \(0.0888322\pi\)
\(758\) 6.08346 + 6.08346i 0.220961 + 0.220961i
\(759\) 6.61437 0.240086
\(760\) 7.76268 + 5.89413i 0.281582 + 0.213803i
\(761\) 6.60459 0.239416 0.119708 0.992809i \(-0.461804\pi\)
0.119708 + 0.992809i \(0.461804\pi\)
\(762\) −12.5449 12.5449i −0.454454 0.454454i
\(763\) 10.8726 10.8726i 0.393616 0.393616i
\(764\) 0.473897i 0.0171450i
\(765\) −8.90035 + 5.41940i −0.321793 + 0.195939i
\(766\) 1.99878 0.0722188
\(767\) 0.315881 0.315881i 0.0114058 0.0114058i
\(768\) 0.707107 0.707107i 0.0255155 0.0255155i
\(769\) 5.37624i 0.193872i 0.995291 + 0.0969360i \(0.0309042\pi\)
−0.995291 + 0.0969360i \(0.969096\pi\)
\(770\) −1.79743 + 7.39418i −0.0647749 + 0.266468i
\(771\) −19.6600 −0.708036
\(772\) −8.37158 8.37158i −0.301300 0.301300i
\(773\) −1.67948 + 1.67948i −0.0604066 + 0.0604066i −0.736665 0.676258i \(-0.763600\pi\)
0.676258 + 0.736665i \(0.263600\pi\)
\(774\) 2.84376 0.102217
\(775\) −6.01736 + 11.6456i −0.216150 + 0.418322i
\(776\) 16.7558 0.601498
\(777\) 1.25830 1.25830i 0.0451414 0.0451414i
\(778\) −10.5475 + 10.5475i −0.378148 + 0.378148i
\(779\) 5.96266 + 15.1729i 0.213634 + 0.543627i
\(780\) −0.107310 + 0.441445i −0.00384230 + 0.0158063i
\(781\) 6.80615i 0.243543i
\(782\) −8.18945 8.18945i −0.292854 0.292854i
\(783\) 1.53792 + 1.53792i 0.0549606 + 0.0549606i
\(784\) 5.36506i 0.191609i
\(785\) 16.5603 + 27.1972i 0.591063 + 0.970710i
\(786\) −20.6202 −0.735498
\(787\) −33.8233 33.8233i −1.20567 1.20567i −0.972415 0.233257i \(-0.925062\pi\)
−0.233257 0.972415i \(-0.574938\pi\)
\(788\) −9.45290 9.45290i −0.336745 0.336745i
\(789\) −17.8922 −0.636978
\(790\) 8.07364 4.91602i 0.287247 0.174904i
\(791\) 3.61024i 0.128365i
\(792\) −1.88194 1.88194i −0.0668719 0.0668719i
\(793\) 1.27943 1.27943i 0.0454338 0.0454338i
\(794\) 28.3071 1.00458
\(795\) −7.81093 1.89874i −0.277025 0.0673413i
\(796\) 3.17530 0.112545
\(797\) −19.1081 19.1081i −0.676844 0.676844i 0.282441 0.959285i \(-0.408856\pi\)
−0.959285 + 0.282441i \(0.908856\pi\)
\(798\) 2.22655 5.10944i 0.0788189 0.180872i
\(799\) 21.4173i 0.757688i
\(800\) −1.51803 4.76399i −0.0536703 0.168432i
\(801\) 4.94664i 0.174781i
\(802\) 6.75733 6.75733i 0.238609 0.238609i
\(803\) −13.9863 13.9863i −0.493568 0.493568i
\(804\) 6.37709i 0.224903i
\(805\) 1.67841 6.90457i 0.0591562 0.243354i
\(806\) 0.532642i 0.0187615i
\(807\) −16.8271 + 16.8271i −0.592344 + 0.592344i
\(808\) 2.57871 2.57871i 0.0907186 0.0907186i
\(809\) 9.60569i 0.337718i 0.985640 + 0.168859i \(0.0540082\pi\)
−0.985640 + 0.168859i \(0.945992\pi\)
\(810\) 1.90987 1.16292i 0.0671062 0.0408608i
\(811\) 28.5091i 1.00109i −0.865711 0.500545i \(-0.833133\pi\)
0.865711 0.500545i \(-0.166867\pi\)
\(812\) −1.96645 1.96645i −0.0690089 0.0690089i
\(813\) −9.58298 + 9.58298i −0.336090 + 0.336090i
\(814\) 3.70400i 0.129825i
\(815\) 44.7065 27.2217i 1.56600 0.953534i
\(816\) 4.66018i 0.163139i
\(817\) 11.3636 + 4.95191i 0.397561 + 0.173246i
\(818\) 26.3832 + 26.3832i 0.922466 + 0.922466i
\(819\) 0.259782 0.00907752
\(820\) 1.97541 8.12635i 0.0689844 0.283785i
\(821\) 13.9024 0.485196 0.242598 0.970127i \(-0.422000\pi\)
0.242598 + 0.970127i \(0.422000\pi\)
\(822\) 2.44206 2.44206i 0.0851765 0.0851765i
\(823\) 21.8340 + 21.8340i 0.761085 + 0.761085i 0.976518 0.215434i \(-0.0691165\pi\)
−0.215434 + 0.976518i \(0.569117\pi\)
\(824\) 6.04115i 0.210454i
\(825\) −12.6792 + 4.04018i −0.441433 + 0.140661i
\(826\) 2.81146 0.0978231
\(827\) 10.5045 + 10.5045i 0.365278 + 0.365278i 0.865752 0.500473i \(-0.166841\pi\)
−0.500473 + 0.865752i \(0.666841\pi\)
\(828\) 1.75733 + 1.75733i 0.0610713 + 0.0610713i
\(829\) −22.5926 −0.784674 −0.392337 0.919822i \(-0.628333\pi\)
−0.392337 + 0.919822i \(0.628333\pi\)
\(830\) −20.1414 4.89613i −0.699120 0.169947i
\(831\) 16.7976i 0.582703i
\(832\) 0.143663 + 0.143663i 0.00498060 + 0.00498060i
\(833\) 17.6792 + 17.6792i 0.612547 + 0.612547i
\(834\) 16.1995i 0.560942i
\(835\) 19.0429 11.5952i 0.659006 0.401267i
\(836\) −4.24310 10.7973i −0.146751 0.373431i
\(837\) −1.85380 + 1.85380i −0.0640766 + 0.0640766i
\(838\) 23.4952 23.4952i 0.811628 0.811628i
\(839\) −8.89881 −0.307221 −0.153610 0.988131i \(-0.549090\pi\)
−0.153610 + 0.988131i \(0.549090\pi\)
\(840\) −2.44206 + 1.48696i −0.0842589 + 0.0513051i
\(841\) −24.2696 −0.836884
\(842\) 27.1090 27.1090i 0.934240 0.934240i
\(843\) 11.6077 + 11.6077i 0.399792 + 0.399792i
\(844\) −14.4553 −0.497571
\(845\) 28.1566 + 6.84451i 0.968617 + 0.235458i
\(846\) 4.59581i 0.158007i
\(847\) −3.54115 + 3.54115i −0.121675 + 0.121675i
\(848\) −2.54197 + 2.54197i −0.0872915 + 0.0872915i
\(849\) 21.9894 0.754674
\(850\) 20.7008 + 10.6962i 0.710030 + 0.366878i
\(851\) 3.45873i 0.118564i
\(852\) −1.80828 + 1.80828i −0.0619507 + 0.0619507i
\(853\) −4.21663 4.21663i −0.144375 0.144375i 0.631225 0.775600i \(-0.282552\pi\)
−0.775600 + 0.631225i \(0.782552\pi\)
\(854\) 11.3874 0.389668
\(855\) 9.65682 1.32127i 0.330256 0.0451863i
\(856\) 13.2817 0.453958
\(857\) 1.84086 + 1.84086i 0.0628825 + 0.0628825i 0.737849 0.674966i \(-0.235842\pi\)
−0.674966 + 0.737849i \(0.735842\pi\)
\(858\) 0.382353 0.382353i 0.0130533 0.0130533i
\(859\) 14.0924i 0.480826i 0.970671 + 0.240413i \(0.0772829\pi\)
−0.970671 + 0.240413i \(0.922717\pi\)
\(860\) −3.30706 5.43122i −0.112770 0.185203i
\(861\) −4.78220 −0.162977
\(862\) 15.0089 15.0089i 0.511203 0.511203i
\(863\) −2.40643 + 2.40643i −0.0819160 + 0.0819160i −0.746878 0.664962i \(-0.768448\pi\)
0.664962 + 0.746878i \(0.268448\pi\)
\(864\) 1.00000i 0.0340207i
\(865\) −24.2903 39.8922i −0.825894 1.35638i
\(866\) 15.5368 0.527961
\(867\) −3.33560 3.33560i −0.113283 0.113283i
\(868\) 2.37035 2.37035i 0.0804550 0.0804550i
\(869\) −11.2509 −0.381659
\(870\) 1.14876 4.72570i 0.0389465 0.160216i
\(871\) −1.29563 −0.0439007
\(872\) 8.50324 8.50324i 0.287956 0.287956i
\(873\) 11.8481 11.8481i 0.400999 0.400999i
\(874\) 3.96214 + 10.0823i 0.134021 + 0.341039i
\(875\) 1.00006 + 14.2607i 0.0338081 + 0.482099i
\(876\) 7.43187i 0.251100i
\(877\) 1.38678 + 1.38678i 0.0468281 + 0.0468281i 0.730133 0.683305i \(-0.239458\pi\)
−0.683305 + 0.730133i \(0.739458\pi\)
\(878\) 1.01499 + 1.01499i 0.0342542 + 0.0342542i
\(879\) 27.1573i 0.915994i
\(880\) −1.40573 + 5.78282i −0.0473871 + 0.194939i
\(881\) 8.63628 0.290964 0.145482 0.989361i \(-0.453527\pi\)
0.145482 + 0.989361i \(0.453527\pi\)
\(882\) −3.79367 3.79367i −0.127740 0.127740i
\(883\) −17.5459 17.5459i −0.590468 0.590468i 0.347290 0.937758i \(-0.387102\pi\)
−0.937758 + 0.347290i \(0.887102\pi\)
\(884\) −0.946806 −0.0318445
\(885\) 2.55699 + 4.19938i 0.0859524 + 0.141161i
\(886\) 13.4302i 0.451198i
\(887\) −19.8938 19.8938i −0.667970 0.667970i 0.289276 0.957246i \(-0.406585\pi\)
−0.957246 + 0.289276i \(0.906585\pi\)
\(888\) 0.984090 0.984090i 0.0330239 0.0330239i
\(889\) 22.6847 0.760821
\(890\) 9.44746 5.75254i 0.316680 0.192825i
\(891\) −2.66147 −0.0891625
\(892\) 13.3101 + 13.3101i 0.445656 + 0.445656i
\(893\) −8.00281 + 18.3647i −0.267804 + 0.614551i
\(894\) 2.85261i 0.0954056i
\(895\) 3.42677 14.0969i 0.114544 0.471207i
\(896\) 1.27865i 0.0427166i
\(897\) −0.357035 + 0.357035i −0.0119211 + 0.0119211i
\(898\) −12.5628 12.5628i −0.419227 0.419227i
\(899\) 5.70197i 0.190171i
\(900\) −4.44206 2.29524i −0.148069 0.0765081i
\(901\) 16.7528i 0.558116i
\(902\) −7.03855 + 7.03855i −0.234358 + 0.234358i
\(903\) −2.57115 + 2.57115i −0.0855626 + 0.0855626i
\(904\) 2.82348i 0.0939076i
\(905\) −0.266321 0.0647393i −0.00885282 0.00215201i
\(906\) 18.6146i 0.618428i
\(907\) −19.4964 19.4964i −0.647367 0.647367i 0.304989 0.952356i \(-0.401347\pi\)
−0.952356 + 0.304989i \(0.901347\pi\)
\(908\) 21.0661 21.0661i 0.699102 0.699102i
\(909\) 3.64684i 0.120958i
\(910\) −0.302105 0.496151i −0.0100147 0.0164473i
\(911\) 47.2989i 1.56708i −0.621341 0.783541i \(-0.713412\pi\)
0.621341 0.783541i \(-0.286588\pi\)
\(912\) 1.74133 3.99597i 0.0576612 0.132320i
\(913\) 17.4453 + 17.4453i 0.577355 + 0.577355i
\(914\) −9.53191 −0.315288
\(915\) 10.3567 + 17.0089i 0.342382 + 0.562298i
\(916\) −18.2167 −0.601897
\(917\) 18.6435 18.6435i 0.615664 0.615664i
\(918\) 3.29524 + 3.29524i 0.108759 + 0.108759i
\(919\) 42.1995i 1.39203i −0.718026 0.696016i \(-0.754954\pi\)
0.718026 0.696016i \(-0.245046\pi\)
\(920\) 1.31265 5.39990i 0.0432767 0.178029i
\(921\) 21.5644 0.710571
\(922\) 2.98938 + 2.98938i 0.0984501 + 0.0984501i
\(923\) −0.367387 0.367387i −0.0120927 0.0120927i
\(924\) 3.40308 0.111953
\(925\) −2.11266 6.63011i −0.0694637 0.217997i
\(926\) 17.3575i 0.570403i
\(927\) −4.27174 4.27174i −0.140302 0.140302i
\(928\) −1.53792 1.53792i −0.0504846 0.0504846i
\(929\) 15.8786i 0.520960i −0.965479 0.260480i \(-0.916119\pi\)
0.965479 0.260480i \(-0.0838809\pi\)
\(930\) 5.69634 + 1.38471i 0.186790 + 0.0454063i
\(931\) −8.55337 21.7654i −0.280325 0.713333i
\(932\) 20.6479 20.6479i 0.676344 0.676344i
\(933\) 0.151302 0.151302i 0.00495342 0.00495342i
\(934\) −12.9027 −0.422189
\(935\) −14.4236 23.6880i −0.471701 0.774680i
\(936\) 0.203169 0.00664080
\(937\) −7.52072 + 7.52072i −0.245691 + 0.245691i −0.819200 0.573508i \(-0.805582\pi\)
0.573508 + 0.819200i \(0.305582\pi\)
\(938\) −5.76578 5.76578i −0.188259 0.188259i
\(939\) −25.7952 −0.841793
\(940\) 8.77741 5.34455i 0.286288 0.174320i
\(941\) 17.9276i 0.584422i −0.956354 0.292211i \(-0.905609\pi\)
0.956354 0.292211i \(-0.0943909\pi\)
\(942\) 10.0694 10.0694i 0.328079 0.328079i
\(943\) 6.57249 6.57249i 0.214030 0.214030i
\(944\) 2.19877 0.0715640
\(945\) −0.675353 + 2.77824i −0.0219692 + 0.0903760i
\(946\) 7.56856i 0.246075i
\(947\) −6.90093 + 6.90093i −0.224250 + 0.224250i −0.810285 0.586035i \(-0.800688\pi\)
0.586035 + 0.810285i \(0.300688\pi\)
\(948\) −2.98916 2.98916i −0.0970834 0.0970834i
\(949\) 1.50993 0.0490144
\(950\) −13.7535 16.9068i −0.446224 0.548529i
\(951\) −17.7823 −0.576632
\(952\) −4.21345 4.21345i −0.136559 0.136559i
\(953\) −42.1375 + 42.1375i −1.36497 + 1.36497i −0.497511 + 0.867458i \(0.665752\pi\)
−0.867458 + 0.497511i \(0.834248\pi\)
\(954\) 3.59488i 0.116389i
\(955\) −0.250302 + 1.02968i −0.00809958 + 0.0333197i
\(956\) −1.78480 −0.0577247
\(957\) −4.09311 + 4.09311i −0.132312 + 0.132312i
\(958\) −26.1144 + 26.1144i −0.843718 + 0.843718i
\(959\) 4.41592i 0.142598i
\(960\) −1.90987 + 1.16292i −0.0616409 + 0.0375330i
\(961\) 24.1269 0.778286
\(962\) 0.199937 + 0.199937i 0.00644623 + 0.00644623i
\(963\) 9.39155 9.39155i 0.302638 0.302638i
\(964\) 6.17706 0.198950
\(965\) 13.7680 + 22.6114i 0.443209 + 0.727887i
\(966\) −3.17774 −0.102242
\(967\) −9.16729 + 9.16729i −0.294800 + 0.294800i −0.838973 0.544173i \(-0.816844\pi\)
0.544173 + 0.838973i \(0.316844\pi\)
\(968\) −2.76945 + 2.76945i −0.0890135 + 0.0890135i
\(969\) 7.42959 + 18.9058i 0.238673 + 0.607341i
\(970\) −36.4069 8.85004i −1.16895 0.284158i
\(971\) 47.1525i 1.51319i 0.653881 + 0.756597i \(0.273140\pi\)
−0.653881 + 0.756597i \(0.726860\pi\)
\(972\) −0.707107 0.707107i −0.0226805 0.0226805i
\(973\) 14.6466 + 14.6466i 0.469548 + 0.469548i
\(974\) 14.6882i 0.470642i
\(975\) 0.466323 0.902490i 0.0149343 0.0289028i
\(976\) 8.90579 0.285067
\(977\) 26.5454 + 26.5454i 0.849262 + 0.849262i 0.990041 0.140779i \(-0.0449606\pi\)
−0.140779 + 0.990041i \(0.544961\pi\)
\(978\) −16.5520 16.5520i −0.529275 0.529275i
\(979\) −13.1653 −0.420765
\(980\) −2.83371 + 11.6572i −0.0905195 + 0.372374i
\(981\) 12.0254i 0.383941i
\(982\) 22.1084 + 22.1084i 0.705509 + 0.705509i
\(983\) −30.2846 + 30.2846i −0.965928 + 0.965928i −0.999438 0.0335108i \(-0.989331\pi\)
0.0335108 + 0.999438i \(0.489331\pi\)
\(984\) −3.74005 −0.119228
\(985\) 15.5464 + 25.5320i 0.495349 + 0.813517i
\(986\) 10.1356 0.322784
\(987\) −4.15525 4.15525i −0.132263 0.132263i
\(988\) 0.811859 + 0.353785i 0.0258287 + 0.0112554i
\(989\) 7.06740i 0.224730i
\(990\) 3.09507 + 5.08307i 0.0983677 + 0.161551i
\(991\) 3.31607i 0.105339i −0.998612 0.0526693i \(-0.983227\pi\)
0.998612 0.0526693i \(-0.0167729\pi\)
\(992\) 1.85380 1.85380i 0.0588581 0.0588581i
\(993\) −8.86121 8.86121i −0.281202 0.281202i
\(994\) 3.26988i 0.103714i
\(995\) −6.89926 1.67712i −0.218721 0.0531683i
\(996\) 9.26984i 0.293726i
\(997\) −36.9548 + 36.9548i −1.17037 + 1.17037i −0.188247 + 0.982122i \(0.560281\pi\)
−0.982122 + 0.188247i \(0.939719\pi\)
\(998\) 22.4905 22.4905i 0.711925 0.711925i
\(999\) 1.39171i 0.0440319i
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 570.2.m.b.493.3 yes 20
3.2 odd 2 1710.2.p.c.1063.8 20
5.2 odd 4 inner 570.2.m.b.37.8 yes 20
15.2 even 4 1710.2.p.c.37.3 20
19.18 odd 2 inner 570.2.m.b.493.8 yes 20
57.56 even 2 1710.2.p.c.1063.3 20
95.37 even 4 inner 570.2.m.b.37.3 20
285.227 odd 4 1710.2.p.c.37.8 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
570.2.m.b.37.3 20 95.37 even 4 inner
570.2.m.b.37.8 yes 20 5.2 odd 4 inner
570.2.m.b.493.3 yes 20 1.1 even 1 trivial
570.2.m.b.493.8 yes 20 19.18 odd 2 inner
1710.2.p.c.37.3 20 15.2 even 4
1710.2.p.c.37.8 20 285.227 odd 4
1710.2.p.c.1063.3 20 57.56 even 2
1710.2.p.c.1063.8 20 3.2 odd 2