Properties

Label 280.2.h.a.251.6
Level $280$
Weight $2$
Character 280.251
Analytic conductor $2.236$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [280,2,Mod(251,280)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(280, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("280.251");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 280.h (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.23581125660\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - x^{15} - 2x^{12} + 6x^{11} - 12x^{9} + 8x^{8} - 24x^{7} + 48x^{5} - 32x^{4} - 128x + 256 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 251.6
Root \(-0.470943 - 1.33350i\) of defining polynomial
Character \(\chi\) \(=\) 280.251
Dual form 280.2.h.a.251.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.470943 + 1.33350i) q^{2} -0.528177i q^{3} +(-1.55642 - 1.25600i) q^{4} -1.00000 q^{5} +(0.704322 + 0.248741i) q^{6} +(-2.17448 - 1.50719i) q^{7} +(2.40786 - 1.48398i) q^{8} +2.72103 q^{9} +O(q^{10})\) \(q+(-0.470943 + 1.33350i) q^{2} -0.528177i q^{3} +(-1.55642 - 1.25600i) q^{4} -1.00000 q^{5} +(0.704322 + 0.248741i) q^{6} +(-2.17448 - 1.50719i) q^{7} +(2.40786 - 1.48398i) q^{8} +2.72103 q^{9} +(0.470943 - 1.33350i) q^{10} +3.04781 q^{11} +(-0.663391 + 0.822067i) q^{12} +4.75069 q^{13} +(3.03389 - 2.18987i) q^{14} +0.528177i q^{15} +(0.844916 + 3.90975i) q^{16} -6.78894i q^{17} +(-1.28145 + 3.62848i) q^{18} +0.584285i q^{19} +(1.55642 + 1.25600i) q^{20} +(-0.796062 + 1.14851i) q^{21} +(-1.43535 + 4.06425i) q^{22} -5.80481i q^{23} +(-0.783804 - 1.27178i) q^{24} +1.00000 q^{25} +(-2.23730 + 6.33502i) q^{26} -3.02172i q^{27} +(1.49139 + 5.07698i) q^{28} -0.185682i q^{29} +(-0.704322 - 0.248741i) q^{30} -3.12589 q^{31} +(-5.61154 - 0.714577i) q^{32} -1.60978i q^{33} +(9.05303 + 3.19721i) q^{34} +(2.17448 + 1.50719i) q^{35} +(-4.23508 - 3.41762i) q^{36} +7.04672i q^{37} +(-0.779143 - 0.275165i) q^{38} -2.50920i q^{39} +(-2.40786 + 1.48398i) q^{40} +3.83583i q^{41} +(-1.15664 - 1.60243i) q^{42} -1.43554 q^{43} +(-4.74369 - 3.82806i) q^{44} -2.72103 q^{45} +(7.74069 + 2.73374i) q^{46} -2.95871 q^{47} +(2.06504 - 0.446265i) q^{48} +(2.45676 + 6.55472i) q^{49} +(-0.470943 + 1.33350i) q^{50} -3.58576 q^{51} +(-7.39409 - 5.96688i) q^{52} -0.535513i q^{53} +(4.02945 + 1.42306i) q^{54} -3.04781 q^{55} +(-7.47250 - 0.402212i) q^{56} +0.308606 q^{57} +(0.247606 + 0.0874456i) q^{58} +1.52116i q^{59} +(0.663391 - 0.822067i) q^{60} +13.2354 q^{61} +(1.47212 - 4.16837i) q^{62} +(-5.91683 - 4.10111i) q^{63} +(3.59560 - 7.14644i) q^{64} -4.75069 q^{65} +(2.14664 + 0.758117i) q^{66} -9.13242 q^{67} +(-8.52693 + 10.5665i) q^{68} -3.06597 q^{69} +(-3.03389 + 2.18987i) q^{70} -9.68233i q^{71} +(6.55186 - 4.03795i) q^{72} -12.4295i q^{73} +(-9.39678 - 3.31861i) q^{74} -0.528177i q^{75} +(0.733864 - 0.909396i) q^{76} +(-6.62742 - 4.59363i) q^{77} +(3.34601 + 1.18169i) q^{78} -2.81383i q^{79} +(-0.844916 - 3.90975i) q^{80} +6.56709 q^{81} +(-5.11507 - 1.80646i) q^{82} +13.4535i q^{83} +(2.68155 - 0.787716i) q^{84} +6.78894i q^{85} +(0.676056 - 1.91428i) q^{86} -0.0980728 q^{87} +(7.33871 - 4.52289i) q^{88} +3.10041i q^{89} +(1.28145 - 3.62848i) q^{90} +(-10.3303 - 7.16019i) q^{91} +(-7.29085 + 9.03475i) q^{92} +1.65102i q^{93} +(1.39338 - 3.94543i) q^{94} -0.584285i q^{95} +(-0.377423 + 2.96389i) q^{96} +13.5027i q^{97} +(-9.89769 + 0.189181i) q^{98} +8.29319 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + q^{2} + q^{4} - 16 q^{5} + q^{8} - 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + q^{2} + q^{4} - 16 q^{5} + q^{8} - 16 q^{9} - q^{10} - 4 q^{11} - 14 q^{12} + 7 q^{14} + 9 q^{16} - 15 q^{18} - q^{20} + 4 q^{21} + 6 q^{22} - 22 q^{24} + 16 q^{25} + 20 q^{26} - 3 q^{28} + 16 q^{31} - 19 q^{32} + 14 q^{34} + 15 q^{36} + 30 q^{38} - q^{40} + 20 q^{42} - 4 q^{43} - 20 q^{44} + 16 q^{45} + 6 q^{46} + 34 q^{48} - 8 q^{49} + q^{50} - 40 q^{51} + 38 q^{52} - 26 q^{54} + 4 q^{55} + q^{56} - 16 q^{57} + 18 q^{58} + 14 q^{60} + 8 q^{61} - 28 q^{62} - 28 q^{63} - 23 q^{64} - 46 q^{66} + 20 q^{67} - 12 q^{68} + 40 q^{69} - 7 q^{70} - 13 q^{72} - 28 q^{74} - 34 q^{76} + 4 q^{77} - 6 q^{78} - 9 q^{80} + 24 q^{81} + 16 q^{82} + 10 q^{84} - 24 q^{86} - 72 q^{87} - 44 q^{88} + 15 q^{90} - 32 q^{91} - 30 q^{92} + 58 q^{94} + 30 q^{96} - 39 q^{98} + 20 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/280\mathbb{Z}\right)^\times\).

\(n\) \(57\) \(71\) \(141\) \(241\)
\(\chi(n)\) \(1\) \(-1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.470943 + 1.33350i −0.333007 + 0.942924i
\(3\) 0.528177i 0.304943i −0.988308 0.152472i \(-0.951277\pi\)
0.988308 0.152472i \(-0.0487232\pi\)
\(4\) −1.55642 1.25600i −0.778212 0.628001i
\(5\) −1.00000 −0.447214
\(6\) 0.704322 + 0.248741i 0.287538 + 0.101548i
\(7\) −2.17448 1.50719i −0.821878 0.569664i
\(8\) 2.40786 1.48398i 0.851308 0.524666i
\(9\) 2.72103 0.907010
\(10\) 0.470943 1.33350i 0.148925 0.421689i
\(11\) 3.04781 0.918950 0.459475 0.888191i \(-0.348038\pi\)
0.459475 + 0.888191i \(0.348038\pi\)
\(12\) −0.663391 + 0.822067i −0.191505 + 0.237310i
\(13\) 4.75069 1.31760 0.658802 0.752317i \(-0.271064\pi\)
0.658802 + 0.752317i \(0.271064\pi\)
\(14\) 3.03389 2.18987i 0.810841 0.585266i
\(15\) 0.528177i 0.136375i
\(16\) 0.844916 + 3.90975i 0.211229 + 0.977437i
\(17\) 6.78894i 1.64656i −0.567635 0.823280i \(-0.692142\pi\)
0.567635 0.823280i \(-0.307858\pi\)
\(18\) −1.28145 + 3.62848i −0.302041 + 0.855242i
\(19\) 0.584285i 0.134044i 0.997751 + 0.0670221i \(0.0213498\pi\)
−0.997751 + 0.0670221i \(0.978650\pi\)
\(20\) 1.55642 + 1.25600i 0.348027 + 0.280851i
\(21\) −0.796062 + 1.14851i −0.173715 + 0.250626i
\(22\) −1.43535 + 4.06425i −0.306017 + 0.866500i
\(23\) 5.80481i 1.21039i −0.796079 0.605193i \(-0.793096\pi\)
0.796079 0.605193i \(-0.206904\pi\)
\(24\) −0.783804 1.27178i −0.159993 0.259600i
\(25\) 1.00000 0.200000
\(26\) −2.23730 + 6.33502i −0.438772 + 1.24240i
\(27\) 3.02172i 0.581529i
\(28\) 1.49139 + 5.07698i 0.281846 + 0.959460i
\(29\) 0.185682i 0.0344802i −0.999851 0.0172401i \(-0.994512\pi\)
0.999851 0.0172401i \(-0.00548797\pi\)
\(30\) −0.704322 0.248741i −0.128591 0.0454138i
\(31\) −3.12589 −0.561427 −0.280714 0.959792i \(-0.590571\pi\)
−0.280714 + 0.959792i \(0.590571\pi\)
\(32\) −5.61154 0.714577i −0.991989 0.126321i
\(33\) 1.60978i 0.280227i
\(34\) 9.05303 + 3.19721i 1.55258 + 0.548317i
\(35\) 2.17448 + 1.50719i 0.367555 + 0.254761i
\(36\) −4.23508 3.41762i −0.705846 0.569603i
\(37\) 7.04672i 1.15847i 0.815159 + 0.579237i \(0.196649\pi\)
−0.815159 + 0.579237i \(0.803351\pi\)
\(38\) −0.779143 0.275165i −0.126394 0.0446377i
\(39\) 2.50920i 0.401794i
\(40\) −2.40786 + 1.48398i −0.380716 + 0.234638i
\(41\) 3.83583i 0.599056i 0.954087 + 0.299528i \(0.0968292\pi\)
−0.954087 + 0.299528i \(0.903171\pi\)
\(42\) −1.15664 1.60243i −0.178473 0.247260i
\(43\) −1.43554 −0.218917 −0.109459 0.993991i \(-0.534912\pi\)
−0.109459 + 0.993991i \(0.534912\pi\)
\(44\) −4.74369 3.82806i −0.715138 0.577102i
\(45\) −2.72103 −0.405627
\(46\) 7.74069 + 2.73374i 1.14130 + 0.403067i
\(47\) −2.95871 −0.431572 −0.215786 0.976441i \(-0.569231\pi\)
−0.215786 + 0.976441i \(0.569231\pi\)
\(48\) 2.06504 0.446265i 0.298062 0.0644128i
\(49\) 2.45676 + 6.55472i 0.350966 + 0.936388i
\(50\) −0.470943 + 1.33350i −0.0666014 + 0.188585i
\(51\) −3.58576 −0.502107
\(52\) −7.39409 5.96688i −1.02538 0.827457i
\(53\) 0.535513i 0.0735584i −0.999323 0.0367792i \(-0.988290\pi\)
0.999323 0.0367792i \(-0.0117098\pi\)
\(54\) 4.02945 + 1.42306i 0.548338 + 0.193653i
\(55\) −3.04781 −0.410967
\(56\) −7.47250 0.402212i −0.998555 0.0537479i
\(57\) 0.308606 0.0408759
\(58\) 0.247606 + 0.0874456i 0.0325123 + 0.0114822i
\(59\) 1.52116i 0.198038i 0.995086 + 0.0990188i \(0.0315704\pi\)
−0.995086 + 0.0990188i \(0.968430\pi\)
\(60\) 0.663391 0.822067i 0.0856435 0.106128i
\(61\) 13.2354 1.69461 0.847307 0.531103i \(-0.178222\pi\)
0.847307 + 0.531103i \(0.178222\pi\)
\(62\) 1.47212 4.16837i 0.186959 0.529383i
\(63\) −5.91683 4.10111i −0.745451 0.516691i
\(64\) 3.59560 7.14644i 0.449450 0.893305i
\(65\) −4.75069 −0.589250
\(66\) 2.14664 + 0.758117i 0.264233 + 0.0933177i
\(67\) −9.13242 −1.11570 −0.557851 0.829941i \(-0.688374\pi\)
−0.557851 + 0.829941i \(0.688374\pi\)
\(68\) −8.52693 + 10.5665i −1.03404 + 1.28137i
\(69\) −3.06597 −0.369099
\(70\) −3.03389 + 2.18987i −0.362619 + 0.261739i
\(71\) 9.68233i 1.14908i −0.818476 0.574540i \(-0.805181\pi\)
0.818476 0.574540i \(-0.194819\pi\)
\(72\) 6.55186 4.03795i 0.772145 0.475878i
\(73\) 12.4295i 1.45476i −0.686235 0.727380i \(-0.740738\pi\)
0.686235 0.727380i \(-0.259262\pi\)
\(74\) −9.39678 3.31861i −1.09235 0.385780i
\(75\) 0.528177i 0.0609886i
\(76\) 0.733864 0.909396i 0.0841800 0.104315i
\(77\) −6.62742 4.59363i −0.755264 0.523493i
\(78\) 3.34601 + 1.18169i 0.378861 + 0.133800i
\(79\) 2.81383i 0.316580i −0.987393 0.158290i \(-0.949402\pi\)
0.987393 0.158290i \(-0.0505982\pi\)
\(80\) −0.844916 3.90975i −0.0944645 0.437123i
\(81\) 6.56709 0.729676
\(82\) −5.11507 1.80646i −0.564865 0.199490i
\(83\) 13.4535i 1.47671i 0.674412 + 0.738355i \(0.264397\pi\)
−0.674412 + 0.738355i \(0.735603\pi\)
\(84\) 2.68155 0.787716i 0.292581 0.0859469i
\(85\) 6.78894i 0.736364i
\(86\) 0.676056 1.91428i 0.0729010 0.206422i
\(87\) −0.0980728 −0.0105145
\(88\) 7.33871 4.52289i 0.782309 0.482142i
\(89\) 3.10041i 0.328642i 0.986407 + 0.164321i \(0.0525434\pi\)
−0.986407 + 0.164321i \(0.947457\pi\)
\(90\) 1.28145 3.62848i 0.135077 0.382476i
\(91\) −10.3303 7.16019i −1.08291 0.750591i
\(92\) −7.29085 + 9.03475i −0.760124 + 0.941938i
\(93\) 1.65102i 0.171203i
\(94\) 1.39338 3.94543i 0.143717 0.406940i
\(95\) 0.584285i 0.0599464i
\(96\) −0.377423 + 2.96389i −0.0385206 + 0.302500i
\(97\) 13.5027i 1.37099i 0.728077 + 0.685495i \(0.240414\pi\)
−0.728077 + 0.685495i \(0.759586\pi\)
\(98\) −9.89769 + 0.189181i −0.999817 + 0.0191102i
\(99\) 8.29319 0.833497
\(100\) −1.55642 1.25600i −0.155642 0.125600i
\(101\) 1.29842 0.129198 0.0645988 0.997911i \(-0.479423\pi\)
0.0645988 + 0.997911i \(0.479423\pi\)
\(102\) 1.68869 4.78160i 0.167205 0.473449i
\(103\) 19.0846 1.88046 0.940232 0.340535i \(-0.110608\pi\)
0.940232 + 0.340535i \(0.110608\pi\)
\(104\) 11.4390 7.04993i 1.12169 0.691302i
\(105\) 0.796062 1.14851i 0.0776877 0.112083i
\(106\) 0.714105 + 0.252196i 0.0693600 + 0.0244955i
\(107\) −3.81102 −0.368425 −0.184213 0.982886i \(-0.558973\pi\)
−0.184213 + 0.982886i \(0.558973\pi\)
\(108\) −3.79528 + 4.70307i −0.365201 + 0.452553i
\(109\) 15.1487i 1.45098i 0.688233 + 0.725490i \(0.258387\pi\)
−0.688233 + 0.725490i \(0.741613\pi\)
\(110\) 1.43535 4.06425i 0.136855 0.387511i
\(111\) 3.72192 0.353269
\(112\) 4.05547 9.77513i 0.383206 0.923663i
\(113\) −16.6411 −1.56546 −0.782732 0.622359i \(-0.786175\pi\)
−0.782732 + 0.622359i \(0.786175\pi\)
\(114\) −0.145336 + 0.411525i −0.0136120 + 0.0385429i
\(115\) 5.80481i 0.541301i
\(116\) −0.233217 + 0.289000i −0.0216536 + 0.0268330i
\(117\) 12.9268 1.19508
\(118\) −2.02846 0.716378i −0.186734 0.0659479i
\(119\) −10.2322 + 14.7624i −0.937986 + 1.35327i
\(120\) 0.783804 + 1.27178i 0.0715512 + 0.116097i
\(121\) −1.71084 −0.155531
\(122\) −6.23311 + 17.6493i −0.564319 + 1.59789i
\(123\) 2.02600 0.182678
\(124\) 4.86522 + 3.92613i 0.436909 + 0.352577i
\(125\) −1.00000 −0.0894427
\(126\) 8.25530 5.95869i 0.735441 0.530842i
\(127\) 15.9073i 1.41154i 0.708440 + 0.705771i \(0.249399\pi\)
−0.708440 + 0.705771i \(0.750601\pi\)
\(128\) 7.83643 + 8.16029i 0.692649 + 0.721275i
\(129\) 0.758217i 0.0667573i
\(130\) 2.23730 6.33502i 0.196225 0.555618i
\(131\) 20.2439i 1.76872i −0.466806 0.884360i \(-0.654595\pi\)
0.466806 0.884360i \(-0.345405\pi\)
\(132\) −2.02189 + 2.50551i −0.175983 + 0.218076i
\(133\) 0.880629 1.27052i 0.0763602 0.110168i
\(134\) 4.30085 12.1780i 0.371537 1.05202i
\(135\) 3.02172i 0.260068i
\(136\) −10.0747 16.3468i −0.863895 1.40173i
\(137\) 6.38933 0.545877 0.272939 0.962031i \(-0.412004\pi\)
0.272939 + 0.962031i \(0.412004\pi\)
\(138\) 1.44390 4.08845i 0.122913 0.348032i
\(139\) 21.8128i 1.85014i 0.379801 + 0.925068i \(0.375992\pi\)
−0.379801 + 0.925068i \(0.624008\pi\)
\(140\) −1.49139 5.07698i −0.126045 0.429083i
\(141\) 1.56272i 0.131605i
\(142\) 12.9113 + 4.55983i 1.08350 + 0.382652i
\(143\) 14.4792 1.21081
\(144\) 2.29904 + 10.6385i 0.191587 + 0.886545i
\(145\) 0.185682i 0.0154200i
\(146\) 16.5747 + 5.85358i 1.37173 + 0.484446i
\(147\) 3.46205 1.29760i 0.285545 0.107025i
\(148\) 8.85070 10.9677i 0.727523 0.901539i
\(149\) 11.5156i 0.943396i −0.881760 0.471698i \(-0.843641\pi\)
0.881760 0.471698i \(-0.156359\pi\)
\(150\) 0.704322 + 0.248741i 0.0575076 + 0.0203096i
\(151\) 7.70970i 0.627407i 0.949521 + 0.313703i \(0.101570\pi\)
−0.949521 + 0.313703i \(0.898430\pi\)
\(152\) 0.867068 + 1.40688i 0.0703285 + 0.114113i
\(153\) 18.4729i 1.49345i
\(154\) 9.24673 6.67430i 0.745122 0.537830i
\(155\) 3.12589 0.251078
\(156\) −3.15157 + 3.90539i −0.252327 + 0.312681i
\(157\) −4.42111 −0.352843 −0.176422 0.984315i \(-0.556452\pi\)
−0.176422 + 0.984315i \(0.556452\pi\)
\(158\) 3.75223 + 1.32515i 0.298511 + 0.105424i
\(159\) −0.282846 −0.0224311
\(160\) 5.61154 + 0.714577i 0.443631 + 0.0564923i
\(161\) −8.74895 + 12.6225i −0.689514 + 0.994790i
\(162\) −3.09273 + 8.75719i −0.242988 + 0.688030i
\(163\) 17.5475 1.37443 0.687213 0.726456i \(-0.258834\pi\)
0.687213 + 0.726456i \(0.258834\pi\)
\(164\) 4.81781 5.97018i 0.376208 0.466193i
\(165\) 1.60978i 0.125321i
\(166\) −17.9402 6.33582i −1.39243 0.491755i
\(167\) 1.57597 0.121952 0.0609760 0.998139i \(-0.480579\pi\)
0.0609760 + 0.998139i \(0.480579\pi\)
\(168\) −0.212439 + 3.94680i −0.0163900 + 0.304502i
\(169\) 9.56903 0.736079
\(170\) −9.05303 3.19721i −0.694336 0.245215i
\(171\) 1.58986i 0.121579i
\(172\) 2.23430 + 1.80304i 0.170364 + 0.137480i
\(173\) −0.208914 −0.0158835 −0.00794173 0.999968i \(-0.502528\pi\)
−0.00794173 + 0.999968i \(0.502528\pi\)
\(174\) 0.0461867 0.130780i 0.00350141 0.00991439i
\(175\) −2.17448 1.50719i −0.164376 0.113933i
\(176\) 2.57514 + 11.9162i 0.194109 + 0.898215i
\(177\) 0.803439 0.0603902
\(178\) −4.13438 1.46012i −0.309885 0.109440i
\(179\) −5.84685 −0.437014 −0.218507 0.975835i \(-0.570119\pi\)
−0.218507 + 0.975835i \(0.570119\pi\)
\(180\) 4.23508 + 3.41762i 0.315664 + 0.254734i
\(181\) −8.66680 −0.644198 −0.322099 0.946706i \(-0.604388\pi\)
−0.322099 + 0.946706i \(0.604388\pi\)
\(182\) 14.4131 10.4034i 1.06837 0.771149i
\(183\) 6.99061i 0.516761i
\(184\) −8.61422 13.9772i −0.635049 1.03041i
\(185\) 7.04672i 0.518085i
\(186\) −2.20163 0.777539i −0.161432 0.0570119i
\(187\) 20.6914i 1.51311i
\(188\) 4.60501 + 3.71615i 0.335855 + 0.271028i
\(189\) −4.55430 + 6.57067i −0.331276 + 0.477946i
\(190\) 0.779143 + 0.275165i 0.0565249 + 0.0199626i
\(191\) 12.9741i 0.938770i 0.882993 + 0.469385i \(0.155524\pi\)
−0.882993 + 0.469385i \(0.844476\pi\)
\(192\) −3.77459 1.89911i −0.272407 0.137057i
\(193\) −24.5869 −1.76980 −0.884901 0.465780i \(-0.845774\pi\)
−0.884901 + 0.465780i \(0.845774\pi\)
\(194\) −18.0058 6.35900i −1.29274 0.456550i
\(195\) 2.50920i 0.179688i
\(196\) 4.40898 13.2876i 0.314927 0.949116i
\(197\) 7.21194i 0.513829i −0.966434 0.256915i \(-0.917294\pi\)
0.966434 0.256915i \(-0.0827059\pi\)
\(198\) −3.90562 + 11.0589i −0.277560 + 0.785924i
\(199\) −6.32808 −0.448585 −0.224293 0.974522i \(-0.572007\pi\)
−0.224293 + 0.974522i \(0.572007\pi\)
\(200\) 2.40786 1.48398i 0.170262 0.104933i
\(201\) 4.82353i 0.340226i
\(202\) −0.611482 + 1.73144i −0.0430237 + 0.121823i
\(203\) −0.279858 + 0.403762i −0.0196422 + 0.0283385i
\(204\) 5.58097 + 4.50373i 0.390746 + 0.315324i
\(205\) 3.83583i 0.267906i
\(206\) −8.98777 + 25.4493i −0.626208 + 1.77313i
\(207\) 15.7951i 1.09783i
\(208\) 4.01393 + 18.5740i 0.278316 + 1.28787i
\(209\) 1.78079i 0.123180i
\(210\) 1.15664 + 1.60243i 0.0798155 + 0.110578i
\(211\) −10.2211 −0.703650 −0.351825 0.936066i \(-0.614439\pi\)
−0.351825 + 0.936066i \(0.614439\pi\)
\(212\) −0.672606 + 0.833486i −0.0461948 + 0.0572441i
\(213\) −5.11398 −0.350404
\(214\) 1.79477 5.08198i 0.122688 0.347397i
\(215\) 1.43554 0.0979028
\(216\) −4.48417 7.27587i −0.305109 0.495061i
\(217\) 6.79721 + 4.71131i 0.461424 + 0.319825i
\(218\) −20.2007 7.13417i −1.36816 0.483187i
\(219\) −6.56496 −0.443619
\(220\) 4.74369 + 3.82806i 0.319820 + 0.258088i
\(221\) 32.2521i 2.16951i
\(222\) −1.75281 + 4.96316i −0.117641 + 0.333106i
\(223\) 2.64553 0.177158 0.0885790 0.996069i \(-0.471767\pi\)
0.0885790 + 0.996069i \(0.471767\pi\)
\(224\) 11.1252 + 10.0115i 0.743334 + 0.668921i
\(225\) 2.72103 0.181402
\(226\) 7.83702 22.1909i 0.521311 1.47611i
\(227\) 16.2979i 1.08173i 0.841109 + 0.540866i \(0.181903\pi\)
−0.841109 + 0.540866i \(0.818097\pi\)
\(228\) −0.480322 0.387610i −0.0318101 0.0256701i
\(229\) 5.51840 0.364666 0.182333 0.983237i \(-0.441635\pi\)
0.182333 + 0.983237i \(0.441635\pi\)
\(230\) −7.74069 2.73374i −0.510406 0.180257i
\(231\) −2.42625 + 3.50045i −0.159635 + 0.230313i
\(232\) −0.275548 0.447096i −0.0180906 0.0293533i
\(233\) 18.6314 1.22058 0.610291 0.792177i \(-0.291053\pi\)
0.610291 + 0.792177i \(0.291053\pi\)
\(234\) −6.08777 + 17.2378i −0.397970 + 1.12687i
\(235\) 2.95871 0.193005
\(236\) 1.91057 2.36756i 0.124368 0.154115i
\(237\) −1.48620 −0.0965390
\(238\) −14.8669 20.5969i −0.963676 1.33510i
\(239\) 5.77674i 0.373666i 0.982392 + 0.186833i \(0.0598223\pi\)
−0.982392 + 0.186833i \(0.940178\pi\)
\(240\) −2.06504 + 0.446265i −0.133298 + 0.0288063i
\(241\) 1.42853i 0.0920200i 0.998941 + 0.0460100i \(0.0146506\pi\)
−0.998941 + 0.0460100i \(0.985349\pi\)
\(242\) 0.805710 2.28140i 0.0517930 0.146654i
\(243\) 12.5337i 0.804039i
\(244\) −20.5999 16.6237i −1.31877 1.06422i
\(245\) −2.45676 6.55472i −0.156957 0.418766i
\(246\) −0.954130 + 2.70166i −0.0608331 + 0.172252i
\(247\) 2.77576i 0.176617i
\(248\) −7.52672 + 4.63877i −0.477947 + 0.294562i
\(249\) 7.10581 0.450312
\(250\) 0.470943 1.33350i 0.0297851 0.0843377i
\(251\) 11.6354i 0.734419i −0.930138 0.367210i \(-0.880313\pi\)
0.930138 0.367210i \(-0.119687\pi\)
\(252\) 4.05811 + 13.8146i 0.255637 + 0.870239i
\(253\) 17.6920i 1.11228i
\(254\) −21.2123 7.49142i −1.33098 0.470054i
\(255\) 3.58576 0.224549
\(256\) −14.5722 + 6.60681i −0.910765 + 0.412926i
\(257\) 12.0011i 0.748611i 0.927305 + 0.374306i \(0.122119\pi\)
−0.927305 + 0.374306i \(0.877881\pi\)
\(258\) −1.01108 0.357077i −0.0629471 0.0222307i
\(259\) 10.6207 15.3230i 0.659941 0.952124i
\(260\) 7.39409 + 5.96688i 0.458562 + 0.370050i
\(261\) 0.505246i 0.0312739i
\(262\) 26.9952 + 9.53374i 1.66777 + 0.588996i
\(263\) 26.7775i 1.65117i 0.564277 + 0.825585i \(0.309155\pi\)
−0.564277 + 0.825585i \(0.690845\pi\)
\(264\) −2.38889 3.87614i −0.147026 0.238560i
\(265\) 0.535513i 0.0328963i
\(266\) 1.27951 + 1.77266i 0.0784516 + 0.108689i
\(267\) 1.63756 0.100217
\(268\) 14.2139 + 11.4703i 0.868253 + 0.700662i
\(269\) −19.0365 −1.16067 −0.580337 0.814376i \(-0.697079\pi\)
−0.580337 + 0.814376i \(0.697079\pi\)
\(270\) −4.02945 1.42306i −0.245224 0.0866045i
\(271\) −2.47835 −0.150549 −0.0752745 0.997163i \(-0.523983\pi\)
−0.0752745 + 0.997163i \(0.523983\pi\)
\(272\) 26.5430 5.73608i 1.60941 0.347801i
\(273\) −3.78184 + 5.45622i −0.228888 + 0.330226i
\(274\) −3.00901 + 8.52015i −0.181781 + 0.514721i
\(275\) 3.04781 0.183790
\(276\) 4.77194 + 3.85086i 0.287237 + 0.231795i
\(277\) 16.0967i 0.967159i −0.875301 0.483579i \(-0.839336\pi\)
0.875301 0.483579i \(-0.160664\pi\)
\(278\) −29.0873 10.2726i −1.74454 0.616109i
\(279\) −8.50565 −0.509220
\(280\) 7.47250 + 0.402212i 0.446567 + 0.0240368i
\(281\) 17.4111 1.03866 0.519328 0.854575i \(-0.326182\pi\)
0.519328 + 0.854575i \(0.326182\pi\)
\(282\) −2.08388 0.735954i −0.124093 0.0438254i
\(283\) 29.4211i 1.74890i 0.485114 + 0.874451i \(0.338778\pi\)
−0.485114 + 0.874451i \(0.661222\pi\)
\(284\) −12.1610 + 15.0698i −0.721624 + 0.894229i
\(285\) −0.308606 −0.0182802
\(286\) −6.81888 + 19.3080i −0.403209 + 1.14170i
\(287\) 5.78132 8.34095i 0.341261 0.492351i
\(288\) −15.2692 1.94439i −0.899744 0.114574i
\(289\) −29.0897 −1.71116
\(290\) −0.247606 0.0874456i −0.0145399 0.00513498i
\(291\) 7.13181 0.418074
\(292\) −15.6115 + 19.3456i −0.913591 + 1.13211i
\(293\) −23.7367 −1.38671 −0.693357 0.720594i \(-0.743869\pi\)
−0.693357 + 0.720594i \(0.743869\pi\)
\(294\) 0.0999211 + 5.22773i 0.00582752 + 0.304887i
\(295\) 1.52116i 0.0885651i
\(296\) 10.4572 + 16.9675i 0.607812 + 0.986218i
\(297\) 9.20962i 0.534396i
\(298\) 15.3560 + 5.42320i 0.889551 + 0.314158i
\(299\) 27.5768i 1.59481i
\(300\) −0.663391 + 0.822067i −0.0383009 + 0.0474621i
\(301\) 3.12155 + 2.16362i 0.179923 + 0.124709i
\(302\) −10.2809 3.63083i −0.591597 0.208931i
\(303\) 0.685795i 0.0393979i
\(304\) −2.28441 + 0.493672i −0.131020 + 0.0283140i
\(305\) −13.2354 −0.757855
\(306\) 24.6336 + 8.69969i 1.40821 + 0.497328i
\(307\) 3.27590i 0.186965i 0.995621 + 0.0934827i \(0.0298000\pi\)
−0.995621 + 0.0934827i \(0.970200\pi\)
\(308\) 4.54547 + 15.4737i 0.259002 + 0.881695i
\(309\) 10.0801i 0.573434i
\(310\) −1.47212 + 4.16837i −0.0836107 + 0.236747i
\(311\) 20.9116 1.18579 0.592893 0.805282i \(-0.297986\pi\)
0.592893 + 0.805282i \(0.297986\pi\)
\(312\) −3.72361 6.04182i −0.210808 0.342050i
\(313\) 13.8819i 0.784650i −0.919827 0.392325i \(-0.871671\pi\)
0.919827 0.392325i \(-0.128329\pi\)
\(314\) 2.08209 5.89554i 0.117499 0.332704i
\(315\) 5.91683 + 4.10111i 0.333376 + 0.231071i
\(316\) −3.53418 + 4.37951i −0.198813 + 0.246367i
\(317\) 5.93227i 0.333190i −0.986025 0.166595i \(-0.946723\pi\)
0.986025 0.166595i \(-0.0532772\pi\)
\(318\) 0.133204 0.377174i 0.00746973 0.0211509i
\(319\) 0.565923i 0.0316856i
\(320\) −3.59560 + 7.14644i −0.201000 + 0.399498i
\(321\) 2.01289i 0.112349i
\(322\) −12.7118 17.6112i −0.708398 0.981431i
\(323\) 3.96668 0.220712
\(324\) −10.2212 8.24828i −0.567843 0.458238i
\(325\) 4.75069 0.263521
\(326\) −8.26388 + 23.3995i −0.457694 + 1.29598i
\(327\) 8.00118 0.442466
\(328\) 5.69230 + 9.23615i 0.314305 + 0.509981i
\(329\) 6.43367 + 4.45934i 0.354700 + 0.245851i
\(330\) −2.14664 0.758117i −0.118169 0.0417330i
\(331\) −7.33151 −0.402976 −0.201488 0.979491i \(-0.564578\pi\)
−0.201488 + 0.979491i \(0.564578\pi\)
\(332\) 16.8976 20.9393i 0.927376 1.14919i
\(333\) 19.1743i 1.05075i
\(334\) −0.742192 + 2.10155i −0.0406109 + 0.114992i
\(335\) 9.13242 0.498957
\(336\) −5.16300 2.14201i −0.281665 0.116856i
\(337\) −16.5861 −0.903505 −0.451752 0.892143i \(-0.649201\pi\)
−0.451752 + 0.892143i \(0.649201\pi\)
\(338\) −4.50647 + 12.7603i −0.245120 + 0.694067i
\(339\) 8.78945i 0.477378i
\(340\) 8.52693 10.5665i 0.462438 0.573048i
\(341\) −9.52714 −0.515923
\(342\) −2.12007 0.748733i −0.114640 0.0404868i
\(343\) 4.53701 17.9559i 0.244976 0.969529i
\(344\) −3.45657 + 2.13031i −0.186366 + 0.114859i
\(345\) 3.06597 0.165066
\(346\) 0.0983868 0.278586i 0.00528931 0.0149769i
\(347\) 28.9802 1.55574 0.777870 0.628425i \(-0.216300\pi\)
0.777870 + 0.628425i \(0.216300\pi\)
\(348\) 0.152643 + 0.123180i 0.00818252 + 0.00660313i
\(349\) −10.2706 −0.549772 −0.274886 0.961477i \(-0.588640\pi\)
−0.274886 + 0.961477i \(0.588640\pi\)
\(350\) 3.03389 2.18987i 0.162168 0.117053i
\(351\) 14.3552i 0.766225i
\(352\) −17.1029 2.17790i −0.911589 0.116082i
\(353\) 24.6097i 1.30984i −0.755697 0.654921i \(-0.772702\pi\)
0.755697 0.654921i \(-0.227298\pi\)
\(354\) −0.378374 + 1.07138i −0.0201104 + 0.0569434i
\(355\) 9.68233i 0.513885i
\(356\) 3.89412 4.82555i 0.206388 0.255754i
\(357\) 7.79718 + 5.40442i 0.412671 + 0.286032i
\(358\) 2.75354 7.79676i 0.145529 0.412072i
\(359\) 5.06081i 0.267099i 0.991042 + 0.133550i \(0.0426375\pi\)
−0.991042 + 0.133550i \(0.957362\pi\)
\(360\) −6.55186 + 4.03795i −0.345314 + 0.212819i
\(361\) 18.6586 0.982032
\(362\) 4.08157 11.5571i 0.214523 0.607430i
\(363\) 0.903627i 0.0474281i
\(364\) 7.08511 + 24.1192i 0.371361 + 1.26419i
\(365\) 12.4295i 0.650589i
\(366\) 9.32196 + 3.29218i 0.487266 + 0.172085i
\(367\) 12.8106 0.668708 0.334354 0.942447i \(-0.391482\pi\)
0.334354 + 0.942447i \(0.391482\pi\)
\(368\) 22.6953 4.90458i 1.18308 0.255669i
\(369\) 10.4374i 0.543350i
\(370\) 9.39678 + 3.31861i 0.488515 + 0.172526i
\(371\) −0.807120 + 1.16447i −0.0419036 + 0.0604560i
\(372\) 2.07369 2.56970i 0.107516 0.133232i
\(373\) 12.4155i 0.642849i 0.946935 + 0.321425i \(0.104162\pi\)
−0.946935 + 0.321425i \(0.895838\pi\)
\(374\) 27.5919 + 9.74449i 1.42674 + 0.503875i
\(375\) 0.528177i 0.0272749i
\(376\) −7.12417 + 4.39067i −0.367401 + 0.226431i
\(377\) 0.882116i 0.0454313i
\(378\) −6.61715 9.16755i −0.340349 0.471528i
\(379\) 9.41586 0.483660 0.241830 0.970319i \(-0.422252\pi\)
0.241830 + 0.970319i \(0.422252\pi\)
\(380\) −0.733864 + 0.909396i −0.0376464 + 0.0466511i
\(381\) 8.40185 0.430440
\(382\) −17.3009 6.11005i −0.885189 0.312617i
\(383\) −28.8384 −1.47358 −0.736788 0.676124i \(-0.763658\pi\)
−0.736788 + 0.676124i \(0.763658\pi\)
\(384\) 4.31008 4.13902i 0.219948 0.211218i
\(385\) 6.62742 + 4.59363i 0.337765 + 0.234113i
\(386\) 11.5790 32.7865i 0.589357 1.66879i
\(387\) −3.90614 −0.198560
\(388\) 16.9594 21.0159i 0.860984 1.06692i
\(389\) 4.35382i 0.220747i −0.993890 0.110374i \(-0.964795\pi\)
0.993890 0.110374i \(-0.0352048\pi\)
\(390\) −3.34601 1.18169i −0.169432 0.0598373i
\(391\) −39.4085 −1.99297
\(392\) 15.6426 + 12.1371i 0.790071 + 0.613015i
\(393\) −10.6924 −0.539359
\(394\) 9.61709 + 3.39641i 0.484502 + 0.171109i
\(395\) 2.81383i 0.141579i
\(396\) −12.9077 10.4163i −0.648637 0.523437i
\(397\) 16.9988 0.853148 0.426574 0.904453i \(-0.359720\pi\)
0.426574 + 0.904453i \(0.359720\pi\)
\(398\) 2.98017 8.43847i 0.149382 0.422982i
\(399\) −0.671059 0.465128i −0.0335950 0.0232855i
\(400\) 0.844916 + 3.90975i 0.0422458 + 0.195487i
\(401\) 10.4337 0.521035 0.260518 0.965469i \(-0.416107\pi\)
0.260518 + 0.965469i \(0.416107\pi\)
\(402\) −6.43216 2.27161i −0.320807 0.113298i
\(403\) −14.8501 −0.739738
\(404\) −2.02089 1.63082i −0.100543 0.0811362i
\(405\) −6.56709 −0.326321
\(406\) −0.406618 0.563338i −0.0201801 0.0279580i
\(407\) 21.4771i 1.06458i
\(408\) −8.63402 + 5.32120i −0.427448 + 0.263439i
\(409\) 27.7527i 1.37228i −0.727469 0.686141i \(-0.759303\pi\)
0.727469 0.686141i \(-0.240697\pi\)
\(410\) 5.11507 + 1.80646i 0.252615 + 0.0892147i
\(411\) 3.37470i 0.166461i
\(412\) −29.7038 23.9703i −1.46340 1.18093i
\(413\) 2.29267 3.30773i 0.112815 0.162763i
\(414\) 21.0626 + 7.43858i 1.03517 + 0.365586i
\(415\) 13.4535i 0.660405i
\(416\) −26.6587 3.39473i −1.30705 0.166440i
\(417\) 11.5210 0.564186
\(418\) −2.37468 0.838652i −0.116149 0.0410198i
\(419\) 30.1125i 1.47109i −0.677476 0.735545i \(-0.736926\pi\)
0.677476 0.735545i \(-0.263074\pi\)
\(420\) −2.68155 + 0.787716i −0.130846 + 0.0384366i
\(421\) 27.1321i 1.32234i 0.750236 + 0.661170i \(0.229940\pi\)
−0.750236 + 0.661170i \(0.770060\pi\)
\(422\) 4.81356 13.6298i 0.234321 0.663489i
\(423\) −8.05074 −0.391440
\(424\) −0.794691 1.28944i −0.0385936 0.0626209i
\(425\) 6.78894i 0.329312i
\(426\) 2.40840 6.81948i 0.116687 0.330405i
\(427\) −28.7801 19.9482i −1.39277 0.965361i
\(428\) 5.93156 + 4.78665i 0.286713 + 0.231371i
\(429\) 7.64758i 0.369229i
\(430\) −0.676056 + 1.91428i −0.0326023 + 0.0923149i
\(431\) 3.80266i 0.183167i 0.995797 + 0.0915837i \(0.0291929\pi\)
−0.995797 + 0.0915837i \(0.970807\pi\)
\(432\) 11.8141 2.55309i 0.568408 0.122836i
\(433\) 6.04283i 0.290400i 0.989402 + 0.145200i \(0.0463825\pi\)
−0.989402 + 0.145200i \(0.953617\pi\)
\(434\) −9.48362 + 6.84529i −0.455228 + 0.328584i
\(435\) 0.0980728 0.00470223
\(436\) 19.0268 23.5778i 0.911217 1.12917i
\(437\) 3.39167 0.162245
\(438\) 3.09173 8.75435i 0.147728 0.418299i
\(439\) 20.7511 0.990398 0.495199 0.868780i \(-0.335095\pi\)
0.495199 + 0.868780i \(0.335095\pi\)
\(440\) −7.33871 + 4.52289i −0.349859 + 0.215621i
\(441\) 6.68492 + 17.8356i 0.318329 + 0.849313i
\(442\) 43.0081 + 15.1889i 2.04569 + 0.722464i
\(443\) 40.9174 1.94404 0.972022 0.234891i \(-0.0754733\pi\)
0.972022 + 0.234891i \(0.0754733\pi\)
\(444\) −5.79288 4.67474i −0.274918 0.221853i
\(445\) 3.10041i 0.146973i
\(446\) −1.24590 + 3.52781i −0.0589949 + 0.167047i
\(447\) −6.08228 −0.287682
\(448\) −18.5896 + 10.1206i −0.878277 + 0.478152i
\(449\) 9.64737 0.455288 0.227644 0.973744i \(-0.426898\pi\)
0.227644 + 0.973744i \(0.426898\pi\)
\(450\) −1.28145 + 3.62848i −0.0604082 + 0.171048i
\(451\) 11.6909i 0.550503i
\(452\) 25.9006 + 20.9013i 1.21826 + 0.983114i
\(453\) 4.07209 0.191323
\(454\) −21.7332 7.67540i −1.01999 0.360224i
\(455\) 10.3303 + 7.16019i 0.484292 + 0.335675i
\(456\) 0.743081 0.457965i 0.0347980 0.0214462i
\(457\) 8.31667 0.389037 0.194519 0.980899i \(-0.437686\pi\)
0.194519 + 0.980899i \(0.437686\pi\)
\(458\) −2.59886 + 7.35877i −0.121437 + 0.343853i
\(459\) −20.5142 −0.957523
\(460\) 7.29085 9.03475i 0.339938 0.421247i
\(461\) 14.8017 0.689385 0.344693 0.938716i \(-0.387983\pi\)
0.344693 + 0.938716i \(0.387983\pi\)
\(462\) −3.52521 4.88391i −0.164008 0.227220i
\(463\) 10.2328i 0.475556i −0.971319 0.237778i \(-0.923581\pi\)
0.971319 0.237778i \(-0.0764191\pi\)
\(464\) 0.725969 0.156885i 0.0337023 0.00728323i
\(465\) 1.65102i 0.0765644i
\(466\) −8.77432 + 24.8449i −0.406463 + 1.15092i
\(467\) 1.49149i 0.0690179i 0.999404 + 0.0345090i \(0.0109867\pi\)
−0.999404 + 0.0345090i \(0.989013\pi\)
\(468\) −20.1195 16.2360i −0.930026 0.750511i
\(469\) 19.8583 + 13.7643i 0.916971 + 0.635575i
\(470\) −1.39338 + 3.94543i −0.0642721 + 0.181989i
\(471\) 2.33513i 0.107597i
\(472\) 2.25737 + 3.66273i 0.103904 + 0.168591i
\(473\) −4.37524 −0.201174
\(474\) 0.699916 1.98184i 0.0321482 0.0910290i
\(475\) 0.584285i 0.0268089i
\(476\) 34.4674 10.1249i 1.57981 0.464076i
\(477\) 1.45715i 0.0667182i
\(478\) −7.70326 2.72052i −0.352339 0.124434i
\(479\) 33.0698 1.51100 0.755499 0.655150i \(-0.227395\pi\)
0.755499 + 0.655150i \(0.227395\pi\)
\(480\) 0.377423 2.96389i 0.0172269 0.135282i
\(481\) 33.4768i 1.52641i
\(482\) −1.90494 0.672759i −0.0867679 0.0306433i
\(483\) 6.66689 + 4.62099i 0.303354 + 0.210262i
\(484\) 2.66280 + 2.14882i 0.121036 + 0.0976737i
\(485\) 13.5027i 0.613126i
\(486\) 16.7137 + 5.90268i 0.758148 + 0.267751i
\(487\) 30.3143i 1.37367i −0.726811 0.686837i \(-0.758999\pi\)
0.726811 0.686837i \(-0.241001\pi\)
\(488\) 31.8689 19.6410i 1.44264 0.889107i
\(489\) 9.26819i 0.419122i
\(490\) 9.89769 0.189181i 0.447132 0.00854634i
\(491\) −24.0080 −1.08347 −0.541733 0.840551i \(-0.682232\pi\)
−0.541733 + 0.840551i \(0.682232\pi\)
\(492\) −3.15331 2.54466i −0.142162 0.114722i
\(493\) −1.26058 −0.0567738
\(494\) −3.70146 1.30722i −0.166537 0.0588148i
\(495\) −8.29319 −0.372751
\(496\) −2.64112 12.2215i −0.118590 0.548759i
\(497\) −14.5931 + 21.0541i −0.654590 + 0.944404i
\(498\) −3.34643 + 9.47557i −0.149957 + 0.424611i
\(499\) −36.6238 −1.63951 −0.819754 0.572716i \(-0.805890\pi\)
−0.819754 + 0.572716i \(0.805890\pi\)
\(500\) 1.55642 + 1.25600i 0.0696054 + 0.0561701i
\(501\) 0.832390i 0.0371884i
\(502\) 15.5157 + 5.47961i 0.692502 + 0.244567i
\(503\) 0.225539 0.0100563 0.00502815 0.999987i \(-0.498399\pi\)
0.00502815 + 0.999987i \(0.498399\pi\)
\(504\) −20.3329 1.09443i −0.905699 0.0487499i
\(505\) −1.29842 −0.0577789
\(506\) 23.5922 + 8.33191i 1.04880 + 0.370399i
\(507\) 5.05414i 0.224462i
\(508\) 19.9796 24.7585i 0.886450 1.09848i
\(509\) −11.4130 −0.505871 −0.252935 0.967483i \(-0.581396\pi\)
−0.252935 + 0.967483i \(0.581396\pi\)
\(510\) −1.68869 + 4.78160i −0.0747765 + 0.211733i
\(511\) −18.7336 + 27.0277i −0.828725 + 1.19564i
\(512\) −1.94746 22.5435i −0.0860665 0.996289i
\(513\) 1.76554 0.0779507
\(514\) −16.0035 5.65186i −0.705884 0.249293i
\(515\) −19.0846 −0.840969
\(516\) 0.952322 1.18011i 0.0419237 0.0519513i
\(517\) −9.01759 −0.396593
\(518\) 15.4314 + 21.3790i 0.678016 + 0.939339i
\(519\) 0.110344i 0.00484355i
\(520\) −11.4390 + 7.04993i −0.501633 + 0.309160i
\(521\) 18.6069i 0.815183i −0.913164 0.407591i \(-0.866369\pi\)
0.913164 0.407591i \(-0.133631\pi\)
\(522\) 0.673743 + 0.237942i 0.0294889 + 0.0104144i
\(523\) 35.5417i 1.55413i 0.629420 + 0.777065i \(0.283292\pi\)
−0.629420 + 0.777065i \(0.716708\pi\)
\(524\) −25.4264 + 31.5081i −1.11076 + 1.37644i
\(525\) −0.796062 + 1.14851i −0.0347430 + 0.0501252i
\(526\) −35.7077 12.6107i −1.55693 0.549852i
\(527\) 21.2215i 0.924424i
\(528\) 6.29385 1.36013i 0.273904 0.0591921i
\(529\) −10.6958 −0.465035
\(530\) −0.714105 0.252196i −0.0310187 0.0109547i
\(531\) 4.13911i 0.179622i
\(532\) −2.96641 + 0.871396i −0.128610 + 0.0377798i
\(533\) 18.2228i 0.789319i
\(534\) −0.771199 + 2.18368i −0.0333731 + 0.0944972i
\(535\) 3.81102 0.164765
\(536\) −21.9896 + 13.5523i −0.949806 + 0.585371i
\(537\) 3.08817i 0.133265i
\(538\) 8.96510 25.3851i 0.386513 1.09443i
\(539\) 7.48775 + 19.9775i 0.322520 + 0.860494i
\(540\) 3.79528 4.70307i 0.163323 0.202388i
\(541\) 40.2046i 1.72853i 0.503035 + 0.864266i \(0.332216\pi\)
−0.503035 + 0.864266i \(0.667784\pi\)
\(542\) 1.16716 3.30487i 0.0501339 0.141956i
\(543\) 4.57760i 0.196444i
\(544\) −4.85122 + 38.0964i −0.207994 + 1.63337i
\(545\) 15.1487i 0.648898i
\(546\) −5.49482 7.61265i −0.235156 0.325791i
\(547\) −6.38283 −0.272910 −0.136455 0.990646i \(-0.543571\pi\)
−0.136455 + 0.990646i \(0.543571\pi\)
\(548\) −9.94451 8.02501i −0.424808 0.342812i
\(549\) 36.0138 1.53703
\(550\) −1.43535 + 4.06425i −0.0612034 + 0.173300i
\(551\) 0.108491 0.00462188
\(552\) −7.38242 + 4.54983i −0.314217 + 0.193654i
\(553\) −4.24097 + 6.11863i −0.180344 + 0.260190i
\(554\) 21.4649 + 7.58065i 0.911957 + 0.322071i
\(555\) −3.72192 −0.157987
\(556\) 27.3969 33.9500i 1.16189 1.43980i
\(557\) 33.9096i 1.43680i 0.695631 + 0.718399i \(0.255125\pi\)
−0.695631 + 0.718399i \(0.744875\pi\)
\(558\) 4.00568 11.3422i 0.169574 0.480156i
\(559\) −6.81978 −0.288446
\(560\) −4.05547 + 9.77513i −0.171375 + 0.413075i
\(561\) −10.9287 −0.461411
\(562\) −8.19962 + 23.2176i −0.345880 + 0.979375i
\(563\) 13.9112i 0.586288i 0.956068 + 0.293144i \(0.0947016\pi\)
−0.956068 + 0.293144i \(0.905298\pi\)
\(564\) 1.96278 2.43226i 0.0826481 0.102417i
\(565\) 16.6411 0.700097
\(566\) −39.2329 13.8557i −1.64908 0.582397i
\(567\) −14.2800 9.89784i −0.599705 0.415670i
\(568\) −14.3684 23.3137i −0.602884 0.978222i
\(569\) −23.6948 −0.993336 −0.496668 0.867940i \(-0.665443\pi\)
−0.496668 + 0.867940i \(0.665443\pi\)
\(570\) 0.145336 0.411525i 0.00608745 0.0172369i
\(571\) 20.9646 0.877340 0.438670 0.898648i \(-0.355450\pi\)
0.438670 + 0.898648i \(0.355450\pi\)
\(572\) −22.5358 18.1859i −0.942269 0.760391i
\(573\) 6.85260 0.286271
\(574\) 8.39995 + 11.6375i 0.350607 + 0.485739i
\(575\) 5.80481i 0.242077i
\(576\) 9.78374 19.4457i 0.407656 0.810237i
\(577\) 11.5447i 0.480614i 0.970697 + 0.240307i \(0.0772481\pi\)
−0.970697 + 0.240307i \(0.922752\pi\)
\(578\) 13.6996 38.7911i 0.569829 1.61350i
\(579\) 12.9862i 0.539689i
\(580\) 0.233217 0.289000i 0.00968380 0.0120001i
\(581\) 20.2769 29.2544i 0.841229 1.21368i
\(582\) −3.35868 + 9.51024i −0.139222 + 0.394212i
\(583\) 1.63214i 0.0675965i
\(584\) −18.4451 29.9285i −0.763264 1.23845i
\(585\) −12.9268 −0.534456
\(586\) 11.1786 31.6528i 0.461786 1.30757i
\(587\) 8.38593i 0.346124i 0.984911 + 0.173062i \(0.0553661\pi\)
−0.984911 + 0.173062i \(0.944634\pi\)
\(588\) −7.01821 2.32872i −0.289426 0.0960348i
\(589\) 1.82641i 0.0752561i
\(590\) 2.02846 + 0.716378i 0.0835102 + 0.0294928i
\(591\) −3.80918 −0.156689
\(592\) −27.5509 + 5.95389i −1.13234 + 0.244703i
\(593\) 26.8713i 1.10347i 0.834018 + 0.551737i \(0.186035\pi\)
−0.834018 + 0.551737i \(0.813965\pi\)
\(594\) 12.2810 + 4.33721i 0.503895 + 0.177958i
\(595\) 10.2322 14.7624i 0.419480 0.605201i
\(596\) −14.4636 + 17.9232i −0.592454 + 0.734162i
\(597\) 3.34234i 0.136793i
\(598\) 36.7736 + 12.9871i 1.50378 + 0.531083i
\(599\) 34.0473i 1.39113i −0.718462 0.695566i \(-0.755153\pi\)
0.718462 0.695566i \(-0.244847\pi\)
\(600\) −0.783804 1.27178i −0.0319987 0.0519201i
\(601\) 24.5067i 0.999649i −0.866127 0.499825i \(-0.833398\pi\)
0.866127 0.499825i \(-0.166602\pi\)
\(602\) −4.35526 + 3.14363i −0.177507 + 0.128125i
\(603\) −24.8496 −1.01195
\(604\) 9.68340 11.9996i 0.394012 0.488256i
\(605\) 1.71084 0.0695556
\(606\) 0.914505 + 0.322970i 0.0371492 + 0.0131198i
\(607\) −36.7082 −1.48994 −0.744971 0.667097i \(-0.767537\pi\)
−0.744971 + 0.667097i \(0.767537\pi\)
\(608\) 0.417517 3.27874i 0.0169326 0.132971i
\(609\) 0.213258 + 0.147814i 0.00864164 + 0.00598974i
\(610\) 6.23311 17.6493i 0.252371 0.714600i
\(611\) −14.0559 −0.568641
\(612\) −23.2020 + 28.7517i −0.937886 + 1.16222i
\(613\) 41.6702i 1.68304i 0.540224 + 0.841521i \(0.318339\pi\)
−0.540224 + 0.841521i \(0.681661\pi\)
\(614\) −4.36840 1.54276i −0.176294 0.0622608i
\(615\) −2.02600 −0.0816961
\(616\) −22.7748 1.22587i −0.917622 0.0493916i
\(617\) 18.6715 0.751688 0.375844 0.926683i \(-0.377353\pi\)
0.375844 + 0.926683i \(0.377353\pi\)
\(618\) 13.4417 + 4.74713i 0.540705 + 0.190958i
\(619\) 19.0302i 0.764888i 0.923979 + 0.382444i \(0.124917\pi\)
−0.923979 + 0.382444i \(0.875083\pi\)
\(620\) −4.86522 3.92613i −0.195392 0.157677i
\(621\) −17.5405 −0.703875
\(622\) −9.84816 + 27.8855i −0.394875 + 1.11811i
\(623\) 4.67290 6.74178i 0.187216 0.270104i
\(624\) 9.81035 2.12007i 0.392728 0.0848705i
\(625\) 1.00000 0.0400000
\(626\) 18.5114 + 6.53758i 0.739866 + 0.261294i
\(627\) 0.940573 0.0375629
\(628\) 6.88113 + 5.55293i 0.274587 + 0.221586i
\(629\) 47.8398 1.90750
\(630\) −8.25530 + 5.95869i −0.328899 + 0.237400i
\(631\) 28.1199i 1.11944i −0.828683 0.559718i \(-0.810910\pi\)
0.828683 0.559718i \(-0.189090\pi\)
\(632\) −4.17567 6.77531i −0.166099 0.269507i
\(633\) 5.39855i 0.214573i
\(634\) 7.91067 + 2.79377i 0.314173 + 0.110955i
\(635\) 15.9073i 0.631261i
\(636\) 0.440228 + 0.355255i 0.0174562 + 0.0140868i
\(637\) 11.6713 + 31.1394i 0.462434 + 1.23379i
\(638\) 0.754657 + 0.266518i 0.0298771 + 0.0105515i
\(639\) 26.3459i 1.04223i
\(640\) −7.83643 8.16029i −0.309762 0.322564i
\(641\) −7.40297 −0.292400 −0.146200 0.989255i \(-0.546704\pi\)
−0.146200 + 0.989255i \(0.546704\pi\)
\(642\) −2.68418 0.947958i −0.105936 0.0374129i
\(643\) 10.9752i 0.432819i 0.976303 + 0.216409i \(0.0694346\pi\)
−0.976303 + 0.216409i \(0.930565\pi\)
\(644\) 29.4709 8.65722i 1.16132 0.341142i
\(645\) 0.758217i 0.0298548i
\(646\) −1.86808 + 5.28955i −0.0734987 + 0.208115i
\(647\) −37.3313 −1.46765 −0.733823 0.679340i \(-0.762266\pi\)
−0.733823 + 0.679340i \(0.762266\pi\)
\(648\) 15.8126 9.74543i 0.621179 0.382837i
\(649\) 4.63620i 0.181987i
\(650\) −2.23730 + 6.33502i −0.0877543 + 0.248480i
\(651\) 2.48841 3.59013i 0.0975283 0.140708i
\(652\) −27.3114 22.0397i −1.06960 0.863142i
\(653\) 27.0398i 1.05815i −0.848575 0.529074i \(-0.822539\pi\)
0.848575 0.529074i \(-0.177461\pi\)
\(654\) −3.76810 + 10.6695i −0.147344 + 0.417212i
\(655\) 20.2439i 0.790995i
\(656\) −14.9971 + 3.24095i −0.585539 + 0.126538i
\(657\) 33.8210i 1.31948i
\(658\) −8.97640 + 6.47918i −0.349937 + 0.252585i
\(659\) 16.0036 0.623410 0.311705 0.950179i \(-0.399100\pi\)
0.311705 + 0.950179i \(0.399100\pi\)
\(660\) 2.02189 2.50551i 0.0787020 0.0975267i
\(661\) −28.7776 −1.11932 −0.559659 0.828723i \(-0.689068\pi\)
−0.559659 + 0.828723i \(0.689068\pi\)
\(662\) 3.45273 9.77654i 0.134194 0.379976i
\(663\) −17.0348 −0.661578
\(664\) 19.9647 + 32.3941i 0.774780 + 1.25714i
\(665\) −0.880629 + 1.27052i −0.0341493 + 0.0492686i
\(666\) −25.5689 9.03003i −0.990775 0.349907i
\(667\) −1.07785 −0.0417344
\(668\) −2.45288 1.97942i −0.0949046 0.0765861i
\(669\) 1.39731i 0.0540231i
\(670\) −4.30085 + 12.1780i −0.166156 + 0.470479i
\(671\) 40.3389 1.55727
\(672\) 5.28784 5.87607i 0.203983 0.226674i
\(673\) 19.6820 0.758685 0.379342 0.925256i \(-0.376150\pi\)
0.379342 + 0.925256i \(0.376150\pi\)
\(674\) 7.81113 22.1176i 0.300874 0.851937i
\(675\) 3.02172i 0.116306i
\(676\) −14.8935 12.0187i −0.572826 0.462259i
\(677\) −41.7128 −1.60315 −0.801576 0.597893i \(-0.796005\pi\)
−0.801576 + 0.597893i \(0.796005\pi\)
\(678\) −11.7207 4.13933i −0.450131 0.158970i
\(679\) 20.3511 29.3614i 0.781004 1.12679i
\(680\) 10.0747 + 16.3468i 0.386346 + 0.626873i
\(681\) 8.60819 0.329866
\(682\) 4.48674 12.7044i 0.171806 0.486477i
\(683\) −22.1942 −0.849237 −0.424618 0.905372i \(-0.639592\pi\)
−0.424618 + 0.905372i \(0.639592\pi\)
\(684\) 1.99687 2.47449i 0.0763521 0.0946146i
\(685\) −6.38933 −0.244124
\(686\) 21.8075 + 14.5063i 0.832614 + 0.553854i
\(687\) 2.91469i 0.111202i
\(688\) −1.21291 5.61258i −0.0462417 0.213978i
\(689\) 2.54406i 0.0969208i
\(690\) −1.44390 + 4.08845i −0.0549682 + 0.155645i
\(691\) 7.35566i 0.279822i −0.990164 0.139911i \(-0.955318\pi\)
0.990164 0.139911i \(-0.0446817\pi\)
\(692\) 0.325159 + 0.262397i 0.0123607 + 0.00997483i
\(693\) −18.0334 12.4994i −0.685032 0.474813i
\(694\) −13.6481 + 38.6450i −0.518073 + 1.46695i
\(695\) 21.8128i 0.827406i
\(696\) −0.236146 + 0.145538i −0.00895109 + 0.00551661i
\(697\) 26.0412 0.986382
\(698\) 4.83687 13.6958i 0.183078 0.518393i
\(699\) 9.84066i 0.372208i
\(700\) 1.49139 + 5.07698i 0.0563691 + 0.191892i
\(701\) 10.2820i 0.388346i −0.980967 0.194173i \(-0.937798\pi\)
0.980967 0.194173i \(-0.0622024\pi\)
\(702\) 19.1426 + 6.76050i 0.722492 + 0.255159i
\(703\) −4.11730 −0.155287
\(704\) 10.9587 21.7810i 0.413022 0.820903i
\(705\) 1.56272i 0.0588555i
\(706\) 32.8169 + 11.5898i 1.23508 + 0.436187i
\(707\) −2.82339 1.95696i −0.106185 0.0735992i
\(708\) −1.25049 1.00912i −0.0469964 0.0379251i
\(709\) 10.8180i 0.406277i −0.979150 0.203139i \(-0.934886\pi\)
0.979150 0.203139i \(-0.0651142\pi\)
\(710\) −12.9113 4.55983i −0.484554 0.171127i
\(711\) 7.65651i 0.287142i
\(712\) 4.60094 + 7.46535i 0.172428 + 0.279776i
\(713\) 18.1452i 0.679544i
\(714\) −10.8788 + 7.85234i −0.407129 + 0.293866i
\(715\) −14.4792 −0.541491
\(716\) 9.10019 + 7.34366i 0.340090 + 0.274446i
\(717\) 3.05114 0.113947
\(718\) −6.74857 2.38335i −0.251854 0.0889459i
\(719\) −29.4274 −1.09746 −0.548729 0.836000i \(-0.684888\pi\)
−0.548729 + 0.836000i \(0.684888\pi\)
\(720\) −2.29904 10.6385i −0.0856802 0.396475i
\(721\) −41.4992 28.7641i −1.54551 1.07123i
\(722\) −8.78715 + 24.8812i −0.327024 + 0.925982i
\(723\) 0.754518 0.0280608
\(724\) 13.4892 + 10.8855i 0.501323 + 0.404557i
\(725\) 0.185682i 0.00689605i
\(726\) −1.20498 0.425557i −0.0447211 0.0157939i
\(727\) 31.0932 1.15318 0.576591 0.817033i \(-0.304383\pi\)
0.576591 + 0.817033i \(0.304383\pi\)
\(728\) −35.4995 1.91079i −1.31570 0.0708184i
\(729\) 13.0812 0.484490
\(730\) −16.5747 5.85358i −0.613456 0.216651i
\(731\) 9.74577i 0.360460i
\(732\) −8.78023 + 10.8804i −0.324527 + 0.402150i
\(733\) 10.0076 0.369639 0.184820 0.982772i \(-0.440830\pi\)
0.184820 + 0.982772i \(0.440830\pi\)
\(734\) −6.03307 + 17.0829i −0.222685 + 0.630541i
\(735\) −3.46205 + 1.29760i −0.127700 + 0.0478629i
\(736\) −4.14798 + 32.5739i −0.152897 + 1.20069i
\(737\) −27.8339 −1.02527
\(738\) −13.9182 4.91543i −0.512338 0.180939i
\(739\) 40.1592 1.47728 0.738641 0.674099i \(-0.235468\pi\)
0.738641 + 0.674099i \(0.235468\pi\)
\(740\) −8.85070 + 10.9677i −0.325358 + 0.403180i
\(741\) 1.46609 0.0538582
\(742\) −1.17270 1.62469i −0.0430513 0.0596442i
\(743\) 41.3554i 1.51718i 0.651567 + 0.758591i \(0.274112\pi\)
−0.651567 + 0.758591i \(0.725888\pi\)
\(744\) 2.45009 + 3.97544i 0.0898246 + 0.145747i
\(745\) 11.5156i 0.421899i
\(746\) −16.5560 5.84699i −0.606158 0.214073i
\(747\) 36.6073i 1.33939i
\(748\) −25.9885 + 32.2046i −0.950233 + 1.17752i
\(749\) 8.28700 + 5.74393i 0.302800 + 0.209878i
\(750\) −0.704322 0.248741i −0.0257182 0.00908275i
\(751\) 10.4171i 0.380126i −0.981772 0.190063i \(-0.939131\pi\)
0.981772 0.190063i \(-0.0608693\pi\)
\(752\) −2.49986 11.5678i −0.0911605 0.421835i
\(753\) −6.14554 −0.223956
\(754\) 1.17630 + 0.415427i 0.0428383 + 0.0151290i
\(755\) 7.70970i 0.280585i
\(756\) 15.3412 4.50655i 0.557954 0.163902i
\(757\) 31.7145i 1.15268i −0.817209 0.576341i \(-0.804480\pi\)
0.817209 0.576341i \(-0.195520\pi\)
\(758\) −4.43434 + 12.5560i −0.161062 + 0.456055i
\(759\) −9.34449 −0.339183
\(760\) −0.867068 1.40688i −0.0314519 0.0510329i
\(761\) 11.9199i 0.432095i −0.976383 0.216047i \(-0.930683\pi\)
0.976383 0.216047i \(-0.0693166\pi\)
\(762\) −3.95680 + 11.2038i −0.143340 + 0.405872i
\(763\) 22.8319 32.9406i 0.826571 1.19253i
\(764\) 16.2955 20.1932i 0.589549 0.730563i
\(765\) 18.4729i 0.667890i
\(766\) 13.5813 38.4560i 0.490711 1.38947i
\(767\) 7.22653i 0.260935i
\(768\) 3.48957 + 7.69672i 0.125919 + 0.277731i
\(769\) 9.56458i 0.344908i −0.985018 0.172454i \(-0.944830\pi\)
0.985018 0.172454i \(-0.0551695\pi\)
\(770\) −9.24673 + 6.67430i −0.333229 + 0.240525i
\(771\) 6.33873 0.228284
\(772\) 38.2676 + 30.8812i 1.37728 + 1.11144i
\(773\) −30.6270 −1.10158 −0.550788 0.834645i \(-0.685673\pi\)
−0.550788 + 0.834645i \(0.685673\pi\)
\(774\) 1.83957 5.20882i 0.0661219 0.187227i
\(775\) −3.12589 −0.112285
\(776\) 20.0377 + 32.5126i 0.719313 + 1.16714i
\(777\) −8.09325 5.60963i −0.290344 0.201244i
\(778\) 5.80580 + 2.05040i 0.208148 + 0.0735105i
\(779\) −2.24122 −0.0803001
\(780\) 3.15157 3.90539i 0.112844 0.139835i
\(781\) 29.5099i 1.05595i
\(782\) 18.5592 52.5511i 0.663675 1.87922i
\(783\) −0.561078 −0.0200513
\(784\) −23.5515 + 15.1435i −0.841126 + 0.540839i
\(785\) 4.42111 0.157796
\(786\) 5.03550 14.2582i 0.179610 0.508574i
\(787\) 26.7295i 0.952804i −0.879228 0.476402i \(-0.841941\pi\)
0.879228 0.476402i \(-0.158059\pi\)
\(788\) −9.05821 + 11.2248i −0.322685 + 0.399868i
\(789\) 14.1432 0.503513
\(790\) −3.75223 1.32515i −0.133498 0.0471469i
\(791\) 36.1858 + 25.0813i 1.28662 + 0.891789i
\(792\) 19.9689 12.3069i 0.709562 0.437308i
\(793\) 62.8771 2.23283
\(794\) −8.00549 + 22.6679i −0.284104 + 0.804454i
\(795\) 0.282846 0.0100315
\(796\) 9.84918 + 7.94808i 0.349095 + 0.281712i
\(797\) −1.38276 −0.0489799 −0.0244899 0.999700i \(-0.507796\pi\)
−0.0244899 + 0.999700i \(0.507796\pi\)
\(798\) 0.936277 0.675806i 0.0331438 0.0239233i
\(799\) 20.0865i 0.710610i
\(800\) −5.61154 0.714577i −0.198398 0.0252641i
\(801\) 8.43630i 0.298082i
\(802\) −4.91369 + 13.9133i −0.173508 + 0.491297i
\(803\) 37.8827i 1.33685i
\(804\) 6.05837 7.50746i 0.213662 0.264768i
\(805\) 8.74895 12.6225i 0.308360 0.444883i
\(806\) 6.99358 19.8026i 0.246338 0.697517i
\(807\) 10.0546i 0.353939i
\(808\) 3.12641 1.92683i 0.109987 0.0677856i
\(809\) 3.98813 0.140215 0.0701075 0.997539i \(-0.477666\pi\)
0.0701075 + 0.997539i \(0.477666\pi\)
\(810\) 3.09273 8.75719i 0.108667 0.307696i
\(811\) 19.2038i 0.674338i 0.941444 + 0.337169i \(0.109469\pi\)
−0.941444 + 0.337169i \(0.890531\pi\)
\(812\) 0.942704 0.276923i 0.0330824 0.00971811i
\(813\) 1.30901i 0.0459089i
\(814\) −28.6396 10.1145i −1.00382 0.354513i
\(815\) −17.5475 −0.614662
\(816\) −3.02967 14.0194i −0.106060 0.490778i
\(817\) 0.838763i 0.0293446i
\(818\) 37.0081 + 13.0699i 1.29396 + 0.456980i
\(819\) −28.1090 19.4831i −0.982209 0.680794i
\(820\) −4.81781 + 5.97018i −0.168245 + 0.208488i
\(821\) 39.4413i 1.37651i 0.725468 + 0.688256i \(0.241623\pi\)
−0.725468 + 0.688256i \(0.758377\pi\)
\(822\) 4.50014 + 1.58929i 0.156961 + 0.0554329i
\(823\) 0.408196i 0.0142288i 0.999975 + 0.00711440i \(0.00226460\pi\)
−0.999975 + 0.00711440i \(0.997735\pi\)
\(824\) 45.9531 28.3212i 1.60085 0.986616i
\(825\) 1.60978i 0.0560455i
\(826\) 3.33113 + 4.61502i 0.115905 + 0.160577i
\(827\) 33.9219 1.17958 0.589790 0.807557i \(-0.299211\pi\)
0.589790 + 0.807557i \(0.299211\pi\)
\(828\) −19.8386 + 24.5838i −0.689440 + 0.854347i
\(829\) −16.5466 −0.574686 −0.287343 0.957828i \(-0.592772\pi\)
−0.287343 + 0.957828i \(0.592772\pi\)
\(830\) 17.9402 + 6.33582i 0.622712 + 0.219920i
\(831\) −8.50192 −0.294928
\(832\) 17.0816 33.9505i 0.592197 1.17702i
\(833\) 44.4996 16.6788i 1.54182 0.577887i
\(834\) −5.42574 + 15.3632i −0.187878 + 0.531985i
\(835\) −1.57597 −0.0545386
\(836\) 2.23668 2.77167i 0.0773572 0.0958602i
\(837\) 9.44556i 0.326486i
\(838\) 40.1549 + 14.1813i 1.38713 + 0.489884i
\(839\) 33.4148 1.15361 0.576804 0.816883i \(-0.304300\pi\)
0.576804 + 0.816883i \(0.304300\pi\)
\(840\) 0.212439 3.94680i 0.00732985 0.136178i
\(841\) 28.9655 0.998811
\(842\) −36.1806 12.7777i −1.24687 0.440349i
\(843\) 9.19612i 0.316731i
\(844\) 15.9084 + 12.8377i 0.547589 + 0.441893i
\(845\) −9.56903 −0.329185
\(846\) 3.79144 10.7356i 0.130352 0.369098i
\(847\) 3.72020 + 2.57856i 0.127828 + 0.0886005i
\(848\) 2.09372 0.452464i 0.0718987 0.0155377i
\(849\) 15.5395 0.533315
\(850\) 9.05303 + 3.19721i 0.310516 + 0.109663i
\(851\) 40.9049 1.40220
\(852\) 7.95953 + 6.42317i 0.272689 + 0.220054i
\(853\) 12.1851 0.417211 0.208606 0.978000i \(-0.433107\pi\)
0.208606 + 0.978000i \(0.433107\pi\)
\(854\) 40.1546 28.9837i 1.37406 0.991801i
\(855\) 1.58986i 0.0543720i
\(856\) −9.17641 + 5.65548i −0.313643 + 0.193300i
\(857\) 16.0726i 0.549031i −0.961583 0.274515i \(-0.911483\pi\)
0.961583 0.274515i \(-0.0885174\pi\)
\(858\) 10.1980 + 3.60158i 0.348155 + 0.122956i
\(859\) 21.5250i 0.734425i −0.930137 0.367212i \(-0.880312\pi\)
0.930137 0.367212i \(-0.119688\pi\)
\(860\) −2.23430 1.80304i −0.0761891 0.0614831i
\(861\) −4.40550 3.05356i −0.150139 0.104065i
\(862\) −5.07083 1.79084i −0.172713 0.0609961i
\(863\) 3.22755i 0.109867i −0.998490 0.0549336i \(-0.982505\pi\)
0.998490 0.0549336i \(-0.0174947\pi\)
\(864\) −2.15925 + 16.9565i −0.0734591 + 0.576871i
\(865\) 0.208914 0.00710330
\(866\) −8.05809 2.84583i −0.273825 0.0967052i
\(867\) 15.3645i 0.521807i
\(868\) −4.66192 15.8701i −0.158236 0.538667i
\(869\) 8.57602i 0.290922i
\(870\) −0.0461867 + 0.130780i −0.00156588 + 0.00443385i
\(871\) −43.3853 −1.47005
\(872\) 22.4803 + 36.4759i 0.761281 + 1.23523i
\(873\) 36.7412i 1.24350i
\(874\) −1.59728 + 4.52277i −0.0540289 + 0.152985i
\(875\) 2.17448 + 1.50719i 0.0735110 + 0.0509523i
\(876\) 10.2179 + 8.24561i 0.345230 + 0.278593i
\(877\) 27.5777i 0.931233i −0.884987 0.465616i \(-0.845833\pi\)
0.884987 0.465616i \(-0.154167\pi\)
\(878\) −9.77261 + 27.6716i −0.329810 + 0.933870i
\(879\) 12.5372i 0.422869i
\(880\) −2.57514 11.9162i −0.0868081 0.401694i
\(881\) 20.1792i 0.679856i 0.940452 + 0.339928i \(0.110403\pi\)
−0.940452 + 0.339928i \(0.889597\pi\)
\(882\) −26.9319 + 0.514768i −0.906844 + 0.0173331i
\(883\) 4.97245 0.167336 0.0836681 0.996494i \(-0.473336\pi\)
0.0836681 + 0.996494i \(0.473336\pi\)
\(884\) −40.5088 + 50.1980i −1.36246 + 1.68834i
\(885\) −0.803439 −0.0270073
\(886\) −19.2698 + 54.5632i −0.647381 + 1.83309i
\(887\) −5.11354 −0.171696 −0.0858480 0.996308i \(-0.527360\pi\)
−0.0858480 + 0.996308i \(0.527360\pi\)
\(888\) 8.96186 5.52325i 0.300740 0.185348i
\(889\) 23.9753 34.5901i 0.804105 1.16012i
\(890\) 4.13438 + 1.46012i 0.138585 + 0.0489432i
\(891\) 20.0152 0.670536
\(892\) −4.11757 3.32280i −0.137867 0.111255i
\(893\) 1.72873i 0.0578498i
\(894\) 2.86441 8.11070i 0.0958002 0.271262i
\(895\) 5.84685 0.195439
\(896\) −4.74108 29.5554i −0.158388 0.987377i
\(897\) −14.5654 −0.486326
\(898\) −4.54337 + 12.8647i −0.151614 + 0.429302i
\(899\) 0.580422i 0.0193581i
\(900\) −4.23508 3.41762i −0.141169 0.113921i
\(901\) −3.63557 −0.121118
\(902\) −15.5898 5.50575i −0.519082 0.183321i
\(903\) 1.14278 1.64873i 0.0380292 0.0548663i
\(904\) −40.0695 + 24.6951i −1.33269 + 0.821347i
\(905\) 8.66680 0.288094
\(906\) −1.91772 + 5.43011i −0.0637120 + 0.180403i
\(907\) −26.8798 −0.892530 −0.446265 0.894901i \(-0.647246\pi\)
−0.446265 + 0.894901i \(0.647246\pi\)
\(908\) 20.4702 25.3665i 0.679329 0.841817i
\(909\) 3.53304 0.117183
\(910\) −14.4131 + 10.4034i −0.477788 + 0.344868i
\(911\) 43.0775i 1.42722i −0.700543 0.713610i \(-0.747059\pi\)
0.700543 0.713610i \(-0.252941\pi\)
\(912\) 0.260746 + 1.20657i 0.00863417 + 0.0399536i
\(913\) 41.0036i 1.35702i
\(914\) −3.91668 + 11.0902i −0.129552 + 0.366833i
\(915\) 6.99061i 0.231103i
\(916\) −8.58898 6.93113i −0.283788 0.229011i
\(917\) −30.5114 + 44.0201i −1.00758 + 1.45367i
\(918\) 9.66105 27.3557i 0.318862 0.902872i
\(919\) 6.42394i 0.211906i −0.994371 0.105953i \(-0.966211\pi\)
0.994371 0.105953i \(-0.0337893\pi\)
\(920\) 8.61422 + 13.9772i 0.284003 + 0.460814i
\(921\) 1.73025 0.0570138
\(922\) −6.97078 + 19.7381i −0.229570 + 0.650038i
\(923\) 45.9977i 1.51403i
\(924\) 8.17285 2.40081i 0.268867 0.0789809i
\(925\) 7.04672i 0.231695i
\(926\) 13.6453 + 4.81905i 0.448414 + 0.158364i
\(927\) 51.9298 1.70560
\(928\) −0.132684 + 1.04196i −0.00435556 + 0.0342040i
\(929\) 8.92552i 0.292837i 0.989223 + 0.146418i \(0.0467746\pi\)
−0.989223 + 0.146418i \(0.953225\pi\)
\(930\) 2.20163 + 0.777539i 0.0721945 + 0.0254965i
\(931\) −3.82983 + 1.43545i −0.125517 + 0.0470450i
\(932\) −28.9983 23.4011i −0.949872 0.766527i
\(933\) 11.0450i 0.361597i
\(934\) −1.98890 0.702407i −0.0650787 0.0229835i
\(935\) 20.6914i 0.676682i
\(936\) 31.1259 19.1831i 1.01738 0.627018i
\(937\) 23.5181i 0.768304i −0.923270 0.384152i \(-0.874494\pi\)
0.923270 0.384152i \(-0.125506\pi\)
\(938\) −27.7067 + 19.9988i −0.904657 + 0.652983i
\(939\) −7.33209 −0.239274
\(940\) −4.60501 3.71615i −0.150199 0.121207i
\(941\) 0.932766 0.0304073 0.0152037 0.999884i \(-0.495160\pi\)
0.0152037 + 0.999884i \(0.495160\pi\)
\(942\) −3.11389 1.09971i −0.101456 0.0358306i
\(943\) 22.2663 0.725089
\(944\) −5.94733 + 1.28525i −0.193569 + 0.0418313i
\(945\) 4.55430 6.57067i 0.148151 0.213744i
\(946\) 2.06049 5.83437i 0.0669924 0.189692i
\(947\) 18.3452 0.596140 0.298070 0.954544i \(-0.403657\pi\)
0.298070 + 0.954544i \(0.403657\pi\)
\(948\) 2.31316 + 1.86667i 0.0751278 + 0.0606266i
\(949\) 59.0486i 1.91680i
\(950\) −0.779143 0.275165i −0.0252787 0.00892754i
\(951\) −3.13329 −0.101604
\(952\) −2.73060 + 50.7304i −0.0884991 + 1.64418i
\(953\) −47.3388 −1.53345 −0.766727 0.641973i \(-0.778116\pi\)
−0.766727 + 0.641973i \(0.778116\pi\)
\(954\) 1.94310 + 0.686234i 0.0629102 + 0.0222176i
\(955\) 12.9741i 0.419831i
\(956\) 7.25560 8.99106i 0.234663 0.290792i
\(957\) −0.298908 −0.00966231
\(958\) −15.5740 + 44.0984i −0.503173 + 1.42476i
\(959\) −13.8935 9.62993i −0.448644 0.310967i
\(960\) 3.77459 + 1.89911i 0.121824 + 0.0612937i
\(961\) −21.2288 −0.684800
\(962\) −44.6412 15.7657i −1.43929 0.508306i
\(963\) −10.3699 −0.334165
\(964\) 1.79424 2.22341i 0.0577886 0.0716111i
\(965\) 24.5869 0.791479
\(966\) −9.30180 + 6.71405i −0.299281 + 0.216021i
\(967\) 6.55903i 0.210924i 0.994423 + 0.105462i \(0.0336322\pi\)
−0.994423 + 0.105462i \(0.966368\pi\)
\(968\) −4.11947 + 2.53886i −0.132405 + 0.0816019i
\(969\) 2.09511i 0.0673046i
\(970\) 18.0058 + 6.35900i 0.578131 + 0.204175i
\(971\) 40.6590i 1.30481i 0.757871 + 0.652404i \(0.226240\pi\)
−0.757871 + 0.652404i \(0.773760\pi\)
\(972\) −15.7424 + 19.5078i −0.504938 + 0.625713i
\(973\) 32.8760 47.4316i 1.05396 1.52059i
\(974\) 40.4241 + 14.2763i 1.29527 + 0.457443i
\(975\) 2.50920i 0.0803588i
\(976\) 11.1828 + 51.7469i 0.357952 + 1.65638i
\(977\) 5.28576 0.169106 0.0845532 0.996419i \(-0.473054\pi\)
0.0845532 + 0.996419i \(0.473054\pi\)
\(978\) 12.3591 + 4.36479i 0.395200 + 0.139571i
\(979\) 9.44946i 0.302006i
\(980\) −4.40898 + 13.2876i −0.140840 + 0.424458i
\(981\) 41.2200i 1.31605i
\(982\) 11.3064 32.0146i 0.360802 1.02163i
\(983\) −11.2577 −0.359066 −0.179533 0.983752i \(-0.557459\pi\)
−0.179533 + 0.983752i \(0.557459\pi\)
\(984\) 4.87832 3.00654i 0.155515 0.0958450i
\(985\) 7.21194i 0.229791i
\(986\) 0.593663 1.68098i 0.0189061 0.0535334i
\(987\) 2.35532 3.39811i 0.0749706 0.108163i
\(988\) 3.48636 4.32026i 0.110916 0.137446i
\(989\) 8.33301i 0.264974i
\(990\) 3.90562 11.0589i 0.124129 0.351476i
\(991\) 14.3170i 0.454796i 0.973802 + 0.227398i \(0.0730218\pi\)
−0.973802 + 0.227398i \(0.926978\pi\)
\(992\) 17.5411 + 2.23369i 0.556930 + 0.0709198i
\(993\) 3.87233i 0.122885i
\(994\) −21.2030 29.3751i −0.672518 0.931722i
\(995\) 6.32808 0.200614
\(996\) −11.0597 8.92492i −0.350439 0.282797i
\(997\) −18.4076 −0.582974 −0.291487 0.956575i \(-0.594150\pi\)
−0.291487 + 0.956575i \(0.594150\pi\)
\(998\) 17.2478 48.8378i 0.545968 1.54593i
\(999\) 21.2932 0.673687
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 280.2.h.a.251.6 yes 16
4.3 odd 2 1120.2.h.a.111.9 16
7.6 odd 2 280.2.h.b.251.6 yes 16
8.3 odd 2 280.2.h.b.251.5 yes 16
8.5 even 2 1120.2.h.b.111.9 16
28.27 even 2 1120.2.h.b.111.8 16
56.13 odd 2 1120.2.h.a.111.8 16
56.27 even 2 inner 280.2.h.a.251.5 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
280.2.h.a.251.5 16 56.27 even 2 inner
280.2.h.a.251.6 yes 16 1.1 even 1 trivial
280.2.h.b.251.5 yes 16 8.3 odd 2
280.2.h.b.251.6 yes 16 7.6 odd 2
1120.2.h.a.111.8 16 56.13 odd 2
1120.2.h.a.111.9 16 4.3 odd 2
1120.2.h.b.111.8 16 28.27 even 2
1120.2.h.b.111.9 16 8.5 even 2