Properties

Label 930.2.h.d.371.3
Level $930$
Weight $2$
Character 930.371
Analytic conductor $7.426$
Analytic rank $0$
Dimension $16$
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] = [930,2,Mod(371,930)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(930, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("930.371");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.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: \(7.42608738798\)
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: \( x^{16} - 4x^{14} + 6x^{12} + 36x^{10} - 142x^{8} + 324x^{6} + 486x^{4} - 2916x^{2} + 6561 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{31}]\)
Coefficient ring index: \( 2^{5} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 371.3
Root \(1.60627 + 0.647994i\) of defining polynomial
Character \(\chi\) \(=\) 930.371
Dual form 930.2.h.d.371.11

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000i q^{2} +(-0.647994 - 1.60627i) q^{3} -1.00000 q^{4} +1.00000i q^{5} +(-1.60627 + 0.647994i) q^{6} +0.794255 q^{7} +1.00000i q^{8} +(-2.16021 + 2.08171i) q^{9} +O(q^{10})\) \(q-1.00000i q^{2} +(-0.647994 - 1.60627i) q^{3} -1.00000 q^{4} +1.00000i q^{5} +(-1.60627 + 0.647994i) q^{6} +0.794255 q^{7} +1.00000i q^{8} +(-2.16021 + 2.08171i) q^{9} +1.00000 q^{10} +6.29899 q^{11} +(0.647994 + 1.60627i) q^{12} -1.29599i q^{13} -0.794255i q^{14} +(1.60627 - 0.647994i) q^{15} +1.00000 q^{16} +3.58092 q^{17} +(2.08171 + 2.16021i) q^{18} -1.52616 q^{19} -1.00000i q^{20} +(-0.514672 - 1.27579i) q^{21} -6.29899i q^{22} -3.08645 q^{23} +(1.60627 - 0.647994i) q^{24} -1.00000 q^{25} -1.29599 q^{26} +(4.74359 + 2.12094i) q^{27} -0.794255 q^{28} +7.82280 q^{29} +(-0.647994 - 1.60627i) q^{30} +(4.83042 + 2.76894i) q^{31} -1.00000i q^{32} +(-4.08171 - 10.1179i) q^{33} -3.58092i q^{34} +0.794255i q^{35} +(2.16021 - 2.08171i) q^{36} -6.43954i q^{37} +1.52616i q^{38} +(-2.08171 + 0.839793i) q^{39} -1.00000 q^{40} -8.16341i q^{41} +(-1.27579 + 0.514672i) q^{42} -5.37138i q^{43} -6.29899 q^{44} +(-2.08171 - 2.16021i) q^{45} +3.08645i q^{46} -4.73191i q^{47} +(-0.647994 - 1.60627i) q^{48} -6.36916 q^{49} +1.00000i q^{50} +(-2.32041 - 5.75192i) q^{51} +1.29599i q^{52} -3.60528 q^{53} +(2.12094 - 4.74359i) q^{54} +6.29899i q^{55} +0.794255i q^{56} +(0.988943 + 2.45143i) q^{57} -7.82280i q^{58} +12.3268i q^{59} +(-1.60627 + 0.647994i) q^{60} -2.22360i q^{61} +(2.76894 - 4.83042i) q^{62} +(-1.71575 + 1.65341i) q^{63} -1.00000 q^{64} +1.29599 q^{65} +(-10.1179 + 4.08171i) q^{66} -2.25449 q^{67} -3.58092 q^{68} +(2.00000 + 4.95767i) q^{69} +0.794255 q^{70} +15.0300i q^{71} +(-2.08171 - 2.16021i) q^{72} -1.38168i q^{73} -6.43954 q^{74} +(0.647994 + 1.60627i) q^{75} +1.52616 q^{76} +5.00300 q^{77} +(0.839793 + 2.08171i) q^{78} -11.5702i q^{79} +1.00000i q^{80} +(0.332991 - 8.99384i) q^{81} -8.16341 q^{82} +9.77976 q^{83} +(0.514672 + 1.27579i) q^{84} +3.58092i q^{85} -5.37138 q^{86} +(-5.06913 - 12.5655i) q^{87} +6.29899i q^{88} -4.07539 q^{89} +(-2.16021 + 2.08171i) q^{90} -1.02934i q^{91} +3.08645 q^{92} +(1.31757 - 9.55322i) q^{93} -4.73191 q^{94} -1.52616i q^{95} +(-1.60627 + 0.647994i) q^{96} -2.73191 q^{97} +6.36916i q^{98} +(-13.6071 + 13.1126i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 16 q^{4} + 4 q^{7} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 16 q^{4} + 4 q^{7} - 8 q^{9} + 16 q^{10} + 16 q^{16} - 8 q^{18} + 20 q^{19} - 16 q^{25} - 4 q^{28} - 8 q^{31} - 24 q^{33} + 8 q^{36} + 8 q^{39} - 16 q^{40} + 8 q^{45} - 28 q^{49} + 16 q^{51} - 4 q^{63} - 16 q^{64} - 44 q^{66} - 24 q^{67} + 32 q^{69} + 4 q^{70} + 8 q^{72} - 20 q^{76} + 40 q^{78} + 8 q^{81} - 48 q^{82} + 16 q^{87} - 8 q^{90} + 12 q^{93} - 40 q^{94} - 8 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).

\(n\) \(187\) \(311\) \(871\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) −0.647994 1.60627i −0.374120 0.927380i
\(4\) −1.00000 −0.500000
\(5\) 1.00000i 0.447214i
\(6\) −1.60627 + 0.647994i −0.655757 + 0.264542i
\(7\) 0.794255 0.300200 0.150100 0.988671i \(-0.452040\pi\)
0.150100 + 0.988671i \(0.452040\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −2.16021 + 2.08171i −0.720069 + 0.693902i
\(10\) 1.00000 0.316228
\(11\) 6.29899 1.89922 0.949608 0.313440i \(-0.101481\pi\)
0.949608 + 0.313440i \(0.101481\pi\)
\(12\) 0.647994 + 1.60627i 0.187060 + 0.463690i
\(13\) 1.29599i 0.359442i −0.983718 0.179721i \(-0.942480\pi\)
0.983718 0.179721i \(-0.0575196\pi\)
\(14\) 0.794255i 0.212273i
\(15\) 1.60627 0.647994i 0.414737 0.167311i
\(16\) 1.00000 0.250000
\(17\) 3.58092 0.868500 0.434250 0.900792i \(-0.357013\pi\)
0.434250 + 0.900792i \(0.357013\pi\)
\(18\) 2.08171 + 2.16021i 0.490663 + 0.509166i
\(19\) −1.52616 −0.350125 −0.175063 0.984557i \(-0.556013\pi\)
−0.175063 + 0.984557i \(0.556013\pi\)
\(20\) 1.00000i 0.223607i
\(21\) −0.514672 1.27579i −0.112311 0.278400i
\(22\) 6.29899i 1.34295i
\(23\) −3.08645 −0.643569 −0.321784 0.946813i \(-0.604283\pi\)
−0.321784 + 0.946813i \(0.604283\pi\)
\(24\) 1.60627 0.647994i 0.327879 0.132271i
\(25\) −1.00000 −0.200000
\(26\) −1.29599 −0.254164
\(27\) 4.74359 + 2.12094i 0.912903 + 0.408176i
\(28\) −0.794255 −0.150100
\(29\) 7.82280 1.45266 0.726329 0.687347i \(-0.241225\pi\)
0.726329 + 0.687347i \(0.241225\pi\)
\(30\) −0.647994 1.60627i −0.118307 0.293263i
\(31\) 4.83042 + 2.76894i 0.867570 + 0.497316i
\(32\) 1.00000i 0.176777i
\(33\) −4.08171 10.1179i −0.710534 1.76130i
\(34\) 3.58092i 0.614123i
\(35\) 0.794255i 0.134254i
\(36\) 2.16021 2.08171i 0.360035 0.346951i
\(37\) 6.43954i 1.05865i −0.848418 0.529327i \(-0.822445\pi\)
0.848418 0.529327i \(-0.177555\pi\)
\(38\) 1.52616i 0.247576i
\(39\) −2.08171 + 0.839793i −0.333340 + 0.134474i
\(40\) −1.00000 −0.158114
\(41\) 8.16341i 1.27491i −0.770487 0.637456i \(-0.779987\pi\)
0.770487 0.637456i \(-0.220013\pi\)
\(42\) −1.27579 + 0.514672i −0.196858 + 0.0794157i
\(43\) 5.37138i 0.819128i −0.912281 0.409564i \(-0.865681\pi\)
0.912281 0.409564i \(-0.134319\pi\)
\(44\) −6.29899 −0.949608
\(45\) −2.08171 2.16021i −0.310323 0.322025i
\(46\) 3.08645i 0.455072i
\(47\) 4.73191i 0.690219i −0.938562 0.345110i \(-0.887842\pi\)
0.938562 0.345110i \(-0.112158\pi\)
\(48\) −0.647994 1.60627i −0.0935299 0.231845i
\(49\) −6.36916 −0.909880
\(50\) 1.00000i 0.141421i
\(51\) −2.32041 5.75192i −0.324923 0.805430i
\(52\) 1.29599i 0.179721i
\(53\) −3.60528 −0.495223 −0.247611 0.968859i \(-0.579646\pi\)
−0.247611 + 0.968859i \(0.579646\pi\)
\(54\) 2.12094 4.74359i 0.288624 0.645520i
\(55\) 6.29899i 0.849355i
\(56\) 0.794255i 0.106137i
\(57\) 0.988943 + 2.45143i 0.130989 + 0.324699i
\(58\) 7.82280i 1.02718i
\(59\) 12.3268i 1.60482i 0.596776 + 0.802408i \(0.296448\pi\)
−0.596776 + 0.802408i \(0.703552\pi\)
\(60\) −1.60627 + 0.647994i −0.207369 + 0.0836557i
\(61\) 2.22360i 0.284702i −0.989816 0.142351i \(-0.954534\pi\)
0.989816 0.142351i \(-0.0454663\pi\)
\(62\) 2.76894 4.83042i 0.351655 0.613464i
\(63\) −1.71575 + 1.65341i −0.216165 + 0.208309i
\(64\) −1.00000 −0.125000
\(65\) 1.29599 0.160748
\(66\) −10.1179 + 4.08171i −1.24542 + 0.502423i
\(67\) −2.25449 −0.275430 −0.137715 0.990472i \(-0.543976\pi\)
−0.137715 + 0.990472i \(0.543976\pi\)
\(68\) −3.58092 −0.434250
\(69\) 2.00000 + 4.95767i 0.240772 + 0.596833i
\(70\) 0.794255 0.0949316
\(71\) 15.0300i 1.78373i 0.452298 + 0.891867i \(0.350604\pi\)
−0.452298 + 0.891867i \(0.649396\pi\)
\(72\) −2.08171 2.16021i −0.245332 0.254583i
\(73\) 1.38168i 0.161713i −0.996726 0.0808566i \(-0.974234\pi\)
0.996726 0.0808566i \(-0.0257656\pi\)
\(74\) −6.43954 −0.748581
\(75\) 0.647994 + 1.60627i 0.0748239 + 0.185476i
\(76\) 1.52616 0.175063
\(77\) 5.00300 0.570145
\(78\) 0.839793 + 2.08171i 0.0950878 + 0.235707i
\(79\) 11.5702i 1.30175i −0.759184 0.650876i \(-0.774402\pi\)
0.759184 0.650876i \(-0.225598\pi\)
\(80\) 1.00000i 0.111803i
\(81\) 0.332991 8.99384i 0.0369990 0.999315i
\(82\) −8.16341 −0.901498
\(83\) 9.77976 1.07347 0.536734 0.843752i \(-0.319658\pi\)
0.536734 + 0.843752i \(0.319658\pi\)
\(84\) 0.514672 + 1.27579i 0.0561553 + 0.139200i
\(85\) 3.58092i 0.388405i
\(86\) −5.37138 −0.579211
\(87\) −5.06913 12.5655i −0.543468 1.34717i
\(88\) 6.29899i 0.671474i
\(89\) −4.07539 −0.431991 −0.215995 0.976394i \(-0.569300\pi\)
−0.215995 + 0.976394i \(0.569300\pi\)
\(90\) −2.16021 + 2.08171i −0.227706 + 0.219431i
\(91\) 1.02934i 0.107905i
\(92\) 3.08645 0.321784
\(93\) 1.31757 9.55322i 0.136626 0.990623i
\(94\) −4.73191 −0.488059
\(95\) 1.52616i 0.156581i
\(96\) −1.60627 + 0.647994i −0.163939 + 0.0661356i
\(97\) −2.73191 −0.277383 −0.138691 0.990336i \(-0.544290\pi\)
−0.138691 + 0.990336i \(0.544290\pi\)
\(98\) 6.36916i 0.643382i
\(99\) −13.6071 + 13.1126i −1.36757 + 1.31787i
\(100\) 1.00000 0.100000
\(101\) 2.70318i 0.268976i 0.990915 + 0.134488i \(0.0429390\pi\)
−0.990915 + 0.134488i \(0.957061\pi\)
\(102\) −5.75192 + 2.32041i −0.569525 + 0.229755i
\(103\) 6.48383 0.638871 0.319435 0.947608i \(-0.396507\pi\)
0.319435 + 0.947608i \(0.396507\pi\)
\(104\) 1.29599 0.127082
\(105\) 1.27579 0.514672i 0.124504 0.0502269i
\(106\) 3.60528i 0.350175i
\(107\) 6.80067i 0.657445i −0.944426 0.328723i \(-0.893382\pi\)
0.944426 0.328723i \(-0.106618\pi\)
\(108\) −4.74359 2.12094i −0.456452 0.204088i
\(109\) 10.9677 1.05051 0.525256 0.850945i \(-0.323970\pi\)
0.525256 + 0.850945i \(0.323970\pi\)
\(110\) 6.29899 0.600585
\(111\) −10.3436 + 4.17278i −0.981775 + 0.396063i
\(112\) 0.794255 0.0750500
\(113\) 0.891745i 0.0838883i −0.999120 0.0419442i \(-0.986645\pi\)
0.999120 0.0419442i \(-0.0133552\pi\)
\(114\) 2.45143 0.988943i 0.229597 0.0926230i
\(115\) 3.08645i 0.287813i
\(116\) −7.82280 −0.726329
\(117\) 2.69787 + 2.79960i 0.249418 + 0.258823i
\(118\) 12.3268 1.13478
\(119\) 2.84416 0.260724
\(120\) 0.647994 + 1.60627i 0.0591535 + 0.146632i
\(121\) 28.6772 2.60702
\(122\) −2.22360 −0.201315
\(123\) −13.1126 + 5.28984i −1.18233 + 0.476969i
\(124\) −4.83042 2.76894i −0.433785 0.248658i
\(125\) 1.00000i 0.0894427i
\(126\) 1.65341 + 1.71575i 0.147297 + 0.152852i
\(127\) 6.07116i 0.538728i −0.963038 0.269364i \(-0.913186\pi\)
0.963038 0.269364i \(-0.0868135\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) −8.62789 + 3.48062i −0.759643 + 0.306452i
\(130\) 1.29599i 0.113666i
\(131\) 8.32683i 0.727518i 0.931493 + 0.363759i \(0.118507\pi\)
−0.931493 + 0.363759i \(0.881493\pi\)
\(132\) 4.08171 + 10.1179i 0.355267 + 0.880648i
\(133\) −1.21216 −0.105108
\(134\) 2.25449i 0.194758i
\(135\) −2.12094 + 4.74359i −0.182542 + 0.408263i
\(136\) 3.58092i 0.307061i
\(137\) 8.68407 0.741930 0.370965 0.928647i \(-0.379027\pi\)
0.370965 + 0.928647i \(0.379027\pi\)
\(138\) 4.95767 2.00000i 0.422025 0.170251i
\(139\) 5.62515i 0.477119i −0.971128 0.238559i \(-0.923325\pi\)
0.971128 0.238559i \(-0.0766752\pi\)
\(140\) 0.794255i 0.0671268i
\(141\) −7.60072 + 3.06625i −0.640096 + 0.258225i
\(142\) 15.0300 1.26129
\(143\) 8.16341i 0.682659i
\(144\) −2.16021 + 2.08171i −0.180017 + 0.173476i
\(145\) 7.82280i 0.649649i
\(146\) −1.38168 −0.114349
\(147\) 4.12718 + 10.2306i 0.340404 + 0.843805i
\(148\) 6.43954i 0.529327i
\(149\) 15.0300i 1.23131i −0.788017 0.615653i \(-0.788892\pi\)
0.788017 0.615653i \(-0.211108\pi\)
\(150\) 1.60627 0.647994i 0.131151 0.0529085i
\(151\) 4.80112i 0.390709i −0.980733 0.195355i \(-0.937414\pi\)
0.980733 0.195355i \(-0.0625858\pi\)
\(152\) 1.52616i 0.123788i
\(153\) −7.73553 + 7.45442i −0.625380 + 0.602655i
\(154\) 5.00300i 0.403153i
\(155\) −2.76894 + 4.83042i −0.222406 + 0.387989i
\(156\) 2.08171 0.839793i 0.166670 0.0672372i
\(157\) 19.8207 1.58186 0.790931 0.611905i \(-0.209596\pi\)
0.790931 + 0.611905i \(0.209596\pi\)
\(158\) −11.5702 −0.920477
\(159\) 2.33620 + 5.79105i 0.185273 + 0.459260i
\(160\) 1.00000 0.0790569
\(161\) −2.45143 −0.193199
\(162\) −8.99384 0.332991i −0.706623 0.0261622i
\(163\) −22.7132 −1.77903 −0.889516 0.456904i \(-0.848958\pi\)
−0.889516 + 0.456904i \(0.848958\pi\)
\(164\) 8.16341i 0.637456i
\(165\) 10.1179 4.08171i 0.787676 0.317760i
\(166\) 9.77976i 0.759056i
\(167\) −3.08645 −0.238837 −0.119418 0.992844i \(-0.538103\pi\)
−0.119418 + 0.992844i \(0.538103\pi\)
\(168\) 1.27579 0.514672i 0.0984291 0.0397078i
\(169\) 11.3204 0.870801
\(170\) 3.58092 0.274644
\(171\) 3.29682 3.17702i 0.252114 0.242953i
\(172\) 5.37138i 0.409564i
\(173\) 9.50385i 0.722564i 0.932457 + 0.361282i \(0.117661\pi\)
−0.932457 + 0.361282i \(0.882339\pi\)
\(174\) −12.5655 + 5.06913i −0.952591 + 0.384290i
\(175\) −0.794255 −0.0600400
\(176\) 6.29899 0.474804
\(177\) 19.8002 7.98771i 1.48828 0.600393i
\(178\) 4.07539i 0.305463i
\(179\) −23.1145 −1.72766 −0.863829 0.503785i \(-0.831940\pi\)
−0.863829 + 0.503785i \(0.831940\pi\)
\(180\) 2.08171 + 2.16021i 0.155161 + 0.161012i
\(181\) 9.81857i 0.729809i 0.931045 + 0.364904i \(0.118898\pi\)
−0.931045 + 0.364904i \(0.881102\pi\)
\(182\) −1.02934 −0.0763001
\(183\) −3.57170 + 1.44088i −0.264028 + 0.106513i
\(184\) 3.08645i 0.227536i
\(185\) 6.43954 0.473444
\(186\) −9.55322 1.31757i −0.700476 0.0966092i
\(187\) 22.5562 1.64947
\(188\) 4.73191i 0.345110i
\(189\) 3.76761 + 1.68457i 0.274054 + 0.122534i
\(190\) −1.52616 −0.110719
\(191\) 21.0336i 1.52194i 0.648789 + 0.760968i \(0.275276\pi\)
−0.648789 + 0.760968i \(0.724724\pi\)
\(192\) 0.647994 + 1.60627i 0.0467649 + 0.115923i
\(193\) 3.20932 0.231012 0.115506 0.993307i \(-0.463151\pi\)
0.115506 + 0.993307i \(0.463151\pi\)
\(194\) 2.73191i 0.196139i
\(195\) −0.839793 2.08171i −0.0601388 0.149074i
\(196\) 6.36916 0.454940
\(197\) 24.5350 1.74805 0.874023 0.485885i \(-0.161503\pi\)
0.874023 + 0.485885i \(0.161503\pi\)
\(198\) 13.1126 + 13.6071i 0.931875 + 0.967016i
\(199\) 23.0984i 1.63741i 0.574218 + 0.818703i \(0.305306\pi\)
−0.574218 + 0.818703i \(0.694694\pi\)
\(200\) 1.00000i 0.0707107i
\(201\) 1.46090 + 3.62132i 0.103044 + 0.255428i
\(202\) 2.70318 0.190195
\(203\) 6.21330 0.436088
\(204\) 2.32041 + 5.75192i 0.162462 + 0.402715i
\(205\) 8.16341 0.570158
\(206\) 6.48383i 0.451750i
\(207\) 6.66737 6.42508i 0.463414 0.446574i
\(208\) 1.29599i 0.0898606i
\(209\) −9.61326 −0.664963
\(210\) −0.514672 1.27579i −0.0355158 0.0880377i
\(211\) −10.3491 −0.712464 −0.356232 0.934397i \(-0.615939\pi\)
−0.356232 + 0.934397i \(0.615939\pi\)
\(212\) 3.60528 0.247611
\(213\) 24.1423 9.73936i 1.65420 0.667330i
\(214\) −6.80067 −0.464884
\(215\) 5.37138 0.366325
\(216\) −2.12094 + 4.74359i −0.144312 + 0.322760i
\(217\) 3.83659 + 2.19924i 0.260444 + 0.149294i
\(218\) 10.9677i 0.742824i
\(219\) −2.21935 + 0.895320i −0.149970 + 0.0605001i
\(220\) 6.29899i 0.424678i
\(221\) 4.64083i 0.312176i
\(222\) 4.17278 + 10.3436i 0.280059 + 0.694220i
\(223\) 4.29675i 0.287731i −0.989597 0.143866i \(-0.954047\pi\)
0.989597 0.143866i \(-0.0459533\pi\)
\(224\) 0.794255i 0.0530684i
\(225\) 2.16021 2.08171i 0.144014 0.138780i
\(226\) −0.891745 −0.0593180
\(227\) 15.1275i 1.00405i 0.864854 + 0.502024i \(0.167411\pi\)
−0.864854 + 0.502024i \(0.832589\pi\)
\(228\) −0.988943 2.45143i −0.0654943 0.162350i
\(229\) 13.6113i 0.899458i 0.893165 + 0.449729i \(0.148480\pi\)
−0.893165 + 0.449729i \(0.851520\pi\)
\(230\) −3.08645 −0.203514
\(231\) −3.24191 8.03617i −0.213302 0.528741i
\(232\) 7.82280i 0.513592i
\(233\) 7.43508i 0.487089i −0.969890 0.243544i \(-0.921690\pi\)
0.969890 0.243544i \(-0.0783101\pi\)
\(234\) 2.79960 2.69787i 0.183016 0.176365i
\(235\) 4.73191 0.308675
\(236\) 12.3268i 0.802408i
\(237\) −18.5849 + 7.49743i −1.20722 + 0.487011i
\(238\) 2.84416i 0.184360i
\(239\) −19.2752 −1.24681 −0.623406 0.781898i \(-0.714252\pi\)
−0.623406 + 0.781898i \(0.714252\pi\)
\(240\) 1.60627 0.647994i 0.103684 0.0418278i
\(241\) 1.24113i 0.0799480i 0.999201 + 0.0399740i \(0.0127275\pi\)
−0.999201 + 0.0399740i \(0.987272\pi\)
\(242\) 28.6772i 1.84344i
\(243\) −14.6623 + 5.29308i −0.940588 + 0.339551i
\(244\) 2.22360i 0.142351i
\(245\) 6.36916i 0.406911i
\(246\) 5.28984 + 13.1126i 0.337268 + 0.836032i
\(247\) 1.97789i 0.125850i
\(248\) −2.76894 + 4.83042i −0.175828 + 0.306732i
\(249\) −6.33723 15.7089i −0.401605 0.995513i
\(250\) −1.00000 −0.0632456
\(251\) 0.0663448 0.00418765 0.00209382 0.999998i \(-0.499334\pi\)
0.00209382 + 0.999998i \(0.499334\pi\)
\(252\) 1.71575 1.65341i 0.108082 0.104155i
\(253\) −19.4415 −1.22228
\(254\) −6.07116 −0.380938
\(255\) 5.75192 2.32041i 0.360199 0.145310i
\(256\) 1.00000 0.0625000
\(257\) 22.4615i 1.40111i −0.713598 0.700555i \(-0.752936\pi\)
0.713598 0.700555i \(-0.247064\pi\)
\(258\) 3.48062 + 8.62789i 0.216694 + 0.537149i
\(259\) 5.11463i 0.317808i
\(260\) −1.29599 −0.0803738
\(261\) −16.8989 + 16.2848i −1.04601 + 1.00800i
\(262\) 8.32683 0.514433
\(263\) 2.74243 0.169105 0.0845526 0.996419i \(-0.473054\pi\)
0.0845526 + 0.996419i \(0.473054\pi\)
\(264\) 10.1179 4.08171i 0.622712 0.251212i
\(265\) 3.60528i 0.221470i
\(266\) 1.21216i 0.0743223i
\(267\) 2.64083 + 6.54618i 0.161616 + 0.400620i
\(268\) 2.25449 0.137715
\(269\) −11.4441 −0.697761 −0.348880 0.937167i \(-0.613438\pi\)
−0.348880 + 0.937167i \(0.613438\pi\)
\(270\) 4.74359 + 2.12094i 0.288685 + 0.129076i
\(271\) 13.5481i 0.822989i −0.911412 0.411494i \(-0.865007\pi\)
0.911412 0.411494i \(-0.134993\pi\)
\(272\) 3.58092 0.217125
\(273\) −1.65341 + 0.667009i −0.100069 + 0.0403692i
\(274\) 8.68407i 0.524624i
\(275\) −6.29899 −0.379843
\(276\) −2.00000 4.95767i −0.120386 0.298417i
\(277\) 24.4043i 1.46631i 0.680059 + 0.733157i \(0.261954\pi\)
−0.680059 + 0.733157i \(0.738046\pi\)
\(278\) −5.62515 −0.337374
\(279\) −16.1988 + 4.07405i −0.969799 + 0.243907i
\(280\) −0.794255 −0.0474658
\(281\) 1.71830i 0.102505i −0.998686 0.0512526i \(-0.983679\pi\)
0.998686 0.0512526i \(-0.0163214\pi\)
\(282\) 3.06625 + 7.60072i 0.182592 + 0.452616i
\(283\) 8.16983 0.485646 0.242823 0.970071i \(-0.421927\pi\)
0.242823 + 0.970071i \(0.421927\pi\)
\(284\) 15.0300i 0.891867i
\(285\) −2.45143 + 0.988943i −0.145210 + 0.0585799i
\(286\) −8.16341 −0.482713
\(287\) 6.48383i 0.382728i
\(288\) 2.08171 + 2.16021i 0.122666 + 0.127291i
\(289\) −4.17702 −0.245707
\(290\) 7.82280 0.459371
\(291\) 1.77026 + 4.38818i 0.103774 + 0.257240i
\(292\) 1.38168i 0.0808566i
\(293\) 22.0128i 1.28600i 0.765865 + 0.643002i \(0.222311\pi\)
−0.765865 + 0.643002i \(0.777689\pi\)
\(294\) 10.2306 4.12718i 0.596660 0.240702i
\(295\) −12.3268 −0.717696
\(296\) 6.43954 0.374291
\(297\) 29.8798 + 13.3598i 1.73380 + 0.775214i
\(298\) −15.0300 −0.870665
\(299\) 4.00000i 0.231326i
\(300\) −0.647994 1.60627i −0.0374120 0.0927380i
\(301\) 4.26624i 0.245902i
\(302\) −4.80112 −0.276273
\(303\) 4.34203 1.75164i 0.249443 0.100629i
\(304\) −1.52616 −0.0875313
\(305\) 2.22360 0.127323
\(306\) 7.45442 + 7.73553i 0.426141 + 0.442211i
\(307\) −30.8507 −1.76074 −0.880371 0.474286i \(-0.842706\pi\)
−0.880371 + 0.474286i \(0.842706\pi\)
\(308\) −5.00300 −0.285072
\(309\) −4.20148 10.4148i −0.239014 0.592476i
\(310\) 4.83042 + 2.76894i 0.274350 + 0.157265i
\(311\) 18.0723i 1.02479i 0.858750 + 0.512394i \(0.171241\pi\)
−0.858750 + 0.512394i \(0.828759\pi\)
\(312\) −0.839793 2.08171i −0.0475439 0.117853i
\(313\) 20.8296i 1.17736i 0.808367 + 0.588678i \(0.200351\pi\)
−0.808367 + 0.588678i \(0.799649\pi\)
\(314\) 19.8207i 1.11855i
\(315\) −1.65341 1.71575i −0.0931588 0.0966718i
\(316\) 11.5702i 0.650876i
\(317\) 2.64083i 0.148324i −0.997246 0.0741619i \(-0.976372\pi\)
0.997246 0.0741619i \(-0.0236281\pi\)
\(318\) 5.79105 2.33620i 0.324746 0.131007i
\(319\) 49.2757 2.75891
\(320\) 1.00000i 0.0559017i
\(321\) −10.9237 + 4.40679i −0.609702 + 0.245963i
\(322\) 2.45143i 0.136613i
\(323\) −5.46506 −0.304084
\(324\) −0.332991 + 8.99384i −0.0184995 + 0.499658i
\(325\) 1.29599i 0.0718885i
\(326\) 22.7132i 1.25797i
\(327\) −7.10698 17.6170i −0.393017 0.974223i
\(328\) 8.16341 0.450749
\(329\) 3.75834i 0.207204i
\(330\) −4.08171 10.1179i −0.224691 0.556971i
\(331\) 21.4711i 1.18016i −0.807346 0.590078i \(-0.799097\pi\)
0.807346 0.590078i \(-0.200903\pi\)
\(332\) −9.77976 −0.536734
\(333\) 13.4052 + 13.9107i 0.734602 + 0.762304i
\(334\) 3.08645i 0.168883i
\(335\) 2.25449i 0.123176i
\(336\) −0.514672 1.27579i −0.0280777 0.0695999i
\(337\) 3.53220i 0.192411i 0.995361 + 0.0962057i \(0.0306707\pi\)
−0.995361 + 0.0962057i \(0.969329\pi\)
\(338\) 11.3204i 0.615749i
\(339\) −1.43238 + 0.577845i −0.0777964 + 0.0313843i
\(340\) 3.58092i 0.194203i
\(341\) 30.4268 + 17.4415i 1.64770 + 0.944510i
\(342\) −3.17702 3.29682i −0.171793 0.178272i
\(343\) −10.6185 −0.573346
\(344\) 5.37138 0.289605
\(345\) −4.95767 + 2.00000i −0.266912 + 0.107676i
\(346\) 9.50385 0.510930
\(347\) −24.4043 −1.31009 −0.655047 0.755588i \(-0.727351\pi\)
−0.655047 + 0.755588i \(0.727351\pi\)
\(348\) 5.06913 + 12.5655i 0.271734 + 0.673583i
\(349\) −21.1770 −1.13358 −0.566790 0.823862i \(-0.691815\pi\)
−0.566790 + 0.823862i \(0.691815\pi\)
\(350\) 0.794255i 0.0424547i
\(351\) 2.74872 6.14763i 0.146716 0.328136i
\(352\) 6.29899i 0.335737i
\(353\) −27.0512 −1.43979 −0.719894 0.694084i \(-0.755810\pi\)
−0.719894 + 0.694084i \(0.755810\pi\)
\(354\) −7.98771 19.8002i −0.424542 1.05237i
\(355\) −15.0300 −0.797710
\(356\) 4.07539 0.215995
\(357\) −1.84300 4.56849i −0.0975419 0.241790i
\(358\) 23.1145i 1.22164i
\(359\) 1.25811i 0.0664003i −0.999449 0.0332001i \(-0.989430\pi\)
0.999449 0.0332001i \(-0.0105699\pi\)
\(360\) 2.16021 2.08171i 0.113853 0.109716i
\(361\) −16.6708 −0.877412
\(362\) 9.81857 0.516053
\(363\) −18.5827 46.0634i −0.975338 2.41770i
\(364\) 1.02934i 0.0539523i
\(365\) 1.38168 0.0723204
\(366\) 1.44088 + 3.57170i 0.0753159 + 0.186696i
\(367\) 29.7449i 1.55267i 0.630320 + 0.776335i \(0.282924\pi\)
−0.630320 + 0.776335i \(0.717076\pi\)
\(368\) −3.08645 −0.160892
\(369\) 16.9938 + 17.6347i 0.884664 + 0.918024i
\(370\) 6.43954i 0.334776i
\(371\) −2.86351 −0.148666
\(372\) −1.31757 + 9.55322i −0.0683130 + 0.495311i
\(373\) −29.8006 −1.54302 −0.771509 0.636218i \(-0.780498\pi\)
−0.771509 + 0.636218i \(0.780498\pi\)
\(374\) 22.5562i 1.16635i
\(375\) −1.60627 + 0.647994i −0.0829474 + 0.0334623i
\(376\) 4.73191 0.244029
\(377\) 10.1383i 0.522147i
\(378\) 1.68457 3.76761i 0.0866448 0.193785i
\(379\) 33.2321 1.70702 0.853510 0.521076i \(-0.174469\pi\)
0.853510 + 0.521076i \(0.174469\pi\)
\(380\) 1.52616i 0.0782904i
\(381\) −9.75192 + 3.93408i −0.499606 + 0.201549i
\(382\) 21.0336 1.07617
\(383\) 15.7961 0.807141 0.403570 0.914949i \(-0.367769\pi\)
0.403570 + 0.914949i \(0.367769\pi\)
\(384\) 1.60627 0.647994i 0.0819696 0.0330678i
\(385\) 5.00300i 0.254976i
\(386\) 3.20932i 0.163350i
\(387\) 11.1816 + 11.6033i 0.568395 + 0.589828i
\(388\) 2.73191 0.138691
\(389\) −16.1854 −0.820631 −0.410315 0.911944i \(-0.634581\pi\)
−0.410315 + 0.911944i \(0.634581\pi\)
\(390\) −2.08171 + 0.839793i −0.105411 + 0.0425246i
\(391\) −11.0523 −0.558940
\(392\) 6.36916i 0.321691i
\(393\) 13.3751 5.39574i 0.674686 0.272179i
\(394\) 24.5350i 1.23605i
\(395\) 11.5702 0.582161
\(396\) 13.6071 13.1126i 0.683783 0.658935i
\(397\) −39.0049 −1.95760 −0.978799 0.204824i \(-0.934338\pi\)
−0.978799 + 0.204824i \(0.934338\pi\)
\(398\) 23.0984 1.15782
\(399\) 0.785472 + 1.94706i 0.0393228 + 0.0974747i
\(400\) −1.00000 −0.0500000
\(401\) −7.02927 −0.351025 −0.175513 0.984477i \(-0.556158\pi\)
−0.175513 + 0.984477i \(0.556158\pi\)
\(402\) 3.62132 1.46090i 0.180615 0.0728629i
\(403\) 3.58851 6.26017i 0.178756 0.311841i
\(404\) 2.70318i 0.134488i
\(405\) 8.99384 + 0.332991i 0.446907 + 0.0165464i
\(406\) 6.21330i 0.308361i
\(407\) 40.5626i 2.01061i
\(408\) 5.75192 2.32041i 0.284763 0.114878i
\(409\) 23.6737i 1.17059i −0.810820 0.585295i \(-0.800979\pi\)
0.810820 0.585295i \(-0.199021\pi\)
\(410\) 8.16341i 0.403162i
\(411\) −5.62723 13.9490i −0.277571 0.688051i
\(412\) −6.48383 −0.319435
\(413\) 9.79064i 0.481766i
\(414\) −6.42508 6.66737i −0.315775 0.327683i
\(415\) 9.77976i 0.480069i
\(416\) −1.29599 −0.0635411
\(417\) −9.03551 + 3.64506i −0.442471 + 0.178500i
\(418\) 9.61326i 0.470200i
\(419\) 21.7906i 1.06454i 0.846574 + 0.532271i \(0.178661\pi\)
−0.846574 + 0.532271i \(0.821339\pi\)
\(420\) −1.27579 + 0.514672i −0.0622520 + 0.0251134i
\(421\) −3.14981 −0.153512 −0.0767562 0.997050i \(-0.524456\pi\)
−0.0767562 + 0.997050i \(0.524456\pi\)
\(422\) 10.3491i 0.503788i
\(423\) 9.85044 + 10.2219i 0.478945 + 0.497006i
\(424\) 3.60528i 0.175088i
\(425\) −3.58092 −0.173700
\(426\) −9.73936 24.1423i −0.471873 1.16970i
\(427\) 1.76610i 0.0854677i
\(428\) 6.80067i 0.328723i
\(429\) −13.1126 + 5.28984i −0.633085 + 0.255396i
\(430\) 5.37138i 0.259031i
\(431\) 12.2481i 0.589969i −0.955502 0.294985i \(-0.904685\pi\)
0.955502 0.294985i \(-0.0953145\pi\)
\(432\) 4.74359 + 2.12094i 0.228226 + 0.102044i
\(433\) 38.5936i 1.85469i −0.374207 0.927345i \(-0.622085\pi\)
0.374207 0.927345i \(-0.377915\pi\)
\(434\) 2.19924 3.83659i 0.105567 0.184162i
\(435\) 12.5655 5.06913i 0.602471 0.243046i
\(436\) −10.9677 −0.525256
\(437\) 4.71041 0.225330
\(438\) 0.895320 + 2.21935i 0.0427800 + 0.106045i
\(439\) −8.54975 −0.408057 −0.204029 0.978965i \(-0.565404\pi\)
−0.204029 + 0.978965i \(0.565404\pi\)
\(440\) −6.29899 −0.300292
\(441\) 13.7587 13.2587i 0.655176 0.631368i
\(442\) −4.64083 −0.220742
\(443\) 27.6436i 1.31339i 0.754157 + 0.656694i \(0.228046\pi\)
−0.754157 + 0.656694i \(0.771954\pi\)
\(444\) 10.3436 4.17278i 0.490887 0.198032i
\(445\) 4.07539i 0.193192i
\(446\) −4.29675 −0.203457
\(447\) −24.1423 + 9.73936i −1.14189 + 0.460656i
\(448\) −0.794255 −0.0375250
\(449\) 16.7850 0.792133 0.396067 0.918222i \(-0.370375\pi\)
0.396067 + 0.918222i \(0.370375\pi\)
\(450\) −2.08171 2.16021i −0.0981326 0.101833i
\(451\) 51.4212i 2.42133i
\(452\) 0.891745i 0.0419442i
\(453\) −7.71189 + 3.11109i −0.362336 + 0.146172i
\(454\) 15.1275 0.709969
\(455\) 1.02934 0.0482564
\(456\) −2.45143 + 0.988943i −0.114799 + 0.0463115i
\(457\) 36.7242i 1.71788i −0.512072 0.858942i \(-0.671122\pi\)
0.512072 0.858942i \(-0.328878\pi\)
\(458\) 13.6113 0.636013
\(459\) 16.9864 + 7.59492i 0.792857 + 0.354501i
\(460\) 3.08645i 0.143906i
\(461\) 27.9560 1.30204 0.651021 0.759060i \(-0.274341\pi\)
0.651021 + 0.759060i \(0.274341\pi\)
\(462\) −8.03617 + 3.24191i −0.373876 + 0.150828i
\(463\) 19.2543i 0.894824i 0.894328 + 0.447412i \(0.147654\pi\)
−0.894328 + 0.447412i \(0.852346\pi\)
\(464\) 7.82280 0.363165
\(465\) 9.55322 + 1.31757i 0.443020 + 0.0611010i
\(466\) −7.43508 −0.344424
\(467\) 11.6732i 0.540170i 0.962836 + 0.270085i \(0.0870518\pi\)
−0.962836 + 0.270085i \(0.912948\pi\)
\(468\) −2.69787 2.79960i −0.124709 0.129412i
\(469\) −1.79064 −0.0826840
\(470\) 4.73191i 0.218267i
\(471\) −12.8437 31.8374i −0.591806 1.46699i
\(472\) −12.3268 −0.567388
\(473\) 33.8342i 1.55570i
\(474\) 7.49743 + 18.5849i 0.344368 + 0.853632i
\(475\) 1.52616 0.0700250
\(476\) −2.84416 −0.130362
\(477\) 7.78814 7.50513i 0.356595 0.343636i
\(478\) 19.2752i 0.881629i
\(479\) 36.8802i 1.68510i 0.538620 + 0.842549i \(0.318946\pi\)
−0.538620 + 0.842549i \(0.681054\pi\)
\(480\) −0.647994 1.60627i −0.0295767 0.0733159i
\(481\) −8.34557 −0.380525
\(482\) 1.24113 0.0565318
\(483\) 1.58851 + 3.93765i 0.0722797 + 0.179169i
\(484\) −28.6772 −1.30351
\(485\) 2.73191i 0.124049i
\(486\) 5.29308 + 14.6623i 0.240099 + 0.665096i
\(487\) 36.6545i 1.66098i 0.557037 + 0.830488i \(0.311938\pi\)
−0.557037 + 0.830488i \(0.688062\pi\)
\(488\) 2.22360 0.100658
\(489\) 14.7180 + 36.4835i 0.665571 + 1.64984i
\(490\) −6.36916 −0.287729
\(491\) 15.5310 0.700904 0.350452 0.936581i \(-0.386028\pi\)
0.350452 + 0.936581i \(0.386028\pi\)
\(492\) 13.1126 5.28984i 0.591164 0.238485i
\(493\) 28.0128 1.26163
\(494\) 1.97789 0.0889893
\(495\) −13.1126 13.6071i −0.589370 0.611595i
\(496\) 4.83042 + 2.76894i 0.216892 + 0.124329i
\(497\) 11.9377i 0.535477i
\(498\) −15.7089 + 6.33723i −0.703934 + 0.283978i
\(499\) 6.93560i 0.310480i −0.987877 0.155240i \(-0.950385\pi\)
0.987877 0.155240i \(-0.0496151\pi\)
\(500\) 1.00000i 0.0447214i
\(501\) 2.00000 + 4.95767i 0.0893534 + 0.221492i
\(502\) 0.0663448i 0.00296111i
\(503\) 14.1698i 0.631801i 0.948792 + 0.315901i \(0.102307\pi\)
−0.948792 + 0.315901i \(0.897693\pi\)
\(504\) −1.65341 1.71575i −0.0736485 0.0764258i
\(505\) −2.70318 −0.120290
\(506\) 19.4415i 0.864280i
\(507\) −7.33556 18.1836i −0.325784 0.807564i
\(508\) 6.07116i 0.269364i
\(509\) −10.7074 −0.474596 −0.237298 0.971437i \(-0.576262\pi\)
−0.237298 + 0.971437i \(0.576262\pi\)
\(510\) −2.32041 5.75192i −0.102750 0.254699i
\(511\) 1.09740i 0.0485463i
\(512\) 1.00000i 0.0441942i
\(513\) −7.23947 3.23690i −0.319630 0.142913i
\(514\) −22.4615 −0.990735
\(515\) 6.48383i 0.285712i
\(516\) 8.62789 3.48062i 0.379821 0.153226i
\(517\) 29.8062i 1.31088i
\(518\) −5.11463 −0.224724
\(519\) 15.2657 6.15844i 0.670092 0.270325i
\(520\) 1.29599i 0.0568328i
\(521\) 25.3540i 1.11078i 0.831590 + 0.555389i \(0.187431\pi\)
−0.831590 + 0.555389i \(0.812569\pi\)
\(522\) 16.2848 + 16.8989i 0.712766 + 0.739644i
\(523\) 22.4584i 0.982038i −0.871149 0.491019i \(-0.836625\pi\)
0.871149 0.491019i \(-0.163375\pi\)
\(524\) 8.32683i 0.363759i
\(525\) 0.514672 + 1.27579i 0.0224621 + 0.0556799i
\(526\) 2.74243i 0.119575i
\(527\) 17.2974 + 9.91534i 0.753485 + 0.431919i
\(528\) −4.08171 10.1179i −0.177634 0.440324i
\(529\) −13.4738 −0.585819
\(530\) −3.60528 −0.156603
\(531\) −25.6608 26.6285i −1.11359 1.15558i
\(532\) 1.21216 0.0525538
\(533\) −10.5797 −0.458257
\(534\) 6.54618 2.64083i 0.283281 0.114280i
\(535\) 6.80067 0.294019
\(536\) 2.25449i 0.0973792i
\(537\) 14.9781 + 37.1281i 0.646351 + 1.60220i
\(538\) 11.4441i 0.493391i
\(539\) −40.1193 −1.72806
\(540\) 2.12094 4.74359i 0.0912708 0.204131i
\(541\) −11.0924 −0.476898 −0.238449 0.971155i \(-0.576639\pi\)
−0.238449 + 0.971155i \(0.576639\pi\)
\(542\) −13.5481 −0.581941
\(543\) 15.7713 6.36238i 0.676810 0.273036i
\(544\) 3.58092i 0.153531i
\(545\) 10.9677i 0.469803i
\(546\) 0.667009 + 1.65341i 0.0285454 + 0.0707592i
\(547\) −21.5762 −0.922531 −0.461266 0.887262i \(-0.652604\pi\)
−0.461266 + 0.887262i \(0.652604\pi\)
\(548\) −8.68407 −0.370965
\(549\) 4.62888 + 4.80343i 0.197556 + 0.205005i
\(550\) 6.29899i 0.268590i
\(551\) −11.9389 −0.508612
\(552\) −4.95767 + 2.00000i −0.211012 + 0.0851257i
\(553\) 9.18970i 0.390786i
\(554\) 24.4043 1.03684
\(555\) −4.17278 10.3436i −0.177125 0.439063i
\(556\) 5.62515i 0.238559i
\(557\) −36.2557 −1.53620 −0.768101 0.640329i \(-0.778798\pi\)
−0.768101 + 0.640329i \(0.778798\pi\)
\(558\) 4.07405 + 16.1988i 0.172468 + 0.685751i
\(559\) −6.96124 −0.294429
\(560\) 0.794255i 0.0335634i
\(561\) −14.6163 36.2313i −0.617099 1.52969i
\(562\) −1.71830 −0.0724822
\(563\) 16.0128i 0.674860i −0.941351 0.337430i \(-0.890442\pi\)
0.941351 0.337430i \(-0.109558\pi\)
\(564\) 7.60072 3.06625i 0.320048 0.129112i
\(565\) 0.891745 0.0375160
\(566\) 8.16983i 0.343403i
\(567\) 0.264479 7.14340i 0.0111071 0.299994i
\(568\) −15.0300 −0.630645
\(569\) 20.8684 0.874848 0.437424 0.899255i \(-0.355891\pi\)
0.437424 + 0.899255i \(0.355891\pi\)
\(570\) 0.988943 + 2.45143i 0.0414223 + 0.102679i
\(571\) 9.02320i 0.377609i −0.982015 0.188805i \(-0.939539\pi\)
0.982015 0.188805i \(-0.0604613\pi\)
\(572\) 8.16341i 0.341329i
\(573\) 33.7856 13.6296i 1.41141 0.569386i
\(574\) −6.48383 −0.270630
\(575\) 3.08645 0.128714
\(576\) 2.16021 2.08171i 0.0900086 0.0867378i
\(577\) 22.4179 0.933270 0.466635 0.884450i \(-0.345466\pi\)
0.466635 + 0.884450i \(0.345466\pi\)
\(578\) 4.17702i 0.173741i
\(579\) −2.07962 5.15504i −0.0864261 0.214236i
\(580\) 7.82280i 0.324824i
\(581\) 7.76762 0.322255
\(582\) 4.38818 1.77026i 0.181896 0.0733796i
\(583\) −22.7096 −0.940535
\(584\) 1.38168 0.0571743
\(585\) −2.79960 + 2.69787i −0.115749 + 0.111543i
\(586\) 22.0128 0.909342
\(587\) −39.3627 −1.62467 −0.812336 0.583189i \(-0.801805\pi\)
−0.812336 + 0.583189i \(0.801805\pi\)
\(588\) −4.12718 10.2306i −0.170202 0.421902i
\(589\) −7.37200 4.22584i −0.303758 0.174123i
\(590\) 12.3268i 0.507487i
\(591\) −15.8985 39.4098i −0.653978 1.62110i
\(592\) 6.43954i 0.264663i
\(593\) 44.4651i 1.82596i −0.408002 0.912981i \(-0.633774\pi\)
0.408002 0.912981i \(-0.366226\pi\)
\(594\) 13.3598 29.8798i 0.548159 1.22598i
\(595\) 2.84416i 0.116599i
\(596\) 15.0300i 0.615653i
\(597\) 37.1023 14.9677i 1.51850 0.612585i
\(598\) 4.00000 0.163572
\(599\) 23.7096i 0.968746i −0.874862 0.484373i \(-0.839048\pi\)
0.874862 0.484373i \(-0.160952\pi\)
\(600\) −1.60627 + 0.647994i −0.0655757 + 0.0264542i
\(601\) 7.38511i 0.301245i 0.988591 + 0.150622i \(0.0481278\pi\)
−0.988591 + 0.150622i \(0.951872\pi\)
\(602\) −4.26624 −0.173879
\(603\) 4.87017 4.69319i 0.198329 0.191121i
\(604\) 4.80112i 0.195355i
\(605\) 28.6772i 1.16590i
\(606\) −1.75164 4.34203i −0.0711557 0.176383i
\(607\) 29.5461 1.19924 0.599620 0.800285i \(-0.295318\pi\)
0.599620 + 0.800285i \(0.295318\pi\)
\(608\) 1.52616i 0.0618940i
\(609\) −4.02618 9.98023i −0.163149 0.404419i
\(610\) 2.22360i 0.0900308i
\(611\) −6.13249 −0.248094
\(612\) 7.73553 7.45442i 0.312690 0.301327i
\(613\) 11.5459i 0.466333i 0.972437 + 0.233166i \(0.0749087\pi\)
−0.972437 + 0.233166i \(0.925091\pi\)
\(614\) 30.8507i 1.24503i
\(615\) −5.28984 13.1126i −0.213307 0.528753i
\(616\) 5.00300i 0.201577i
\(617\) 21.5662i 0.868222i −0.900859 0.434111i \(-0.857062\pi\)
0.900859 0.434111i \(-0.142938\pi\)
\(618\) −10.4148 + 4.20148i −0.418944 + 0.169008i
\(619\) 4.82819i 0.194061i 0.995281 + 0.0970307i \(0.0309345\pi\)
−0.995281 + 0.0970307i \(0.969065\pi\)
\(620\) 2.76894 4.83042i 0.111203 0.193994i
\(621\) −14.6408 6.54618i −0.587516 0.262689i
\(622\) 18.0723 0.724635
\(623\) −3.23690 −0.129684
\(624\) −2.08171 + 0.839793i −0.0833350 + 0.0336186i
\(625\) 1.00000 0.0400000
\(626\) 20.8296 0.832517
\(627\) 6.22934 + 15.4415i 0.248776 + 0.616674i
\(628\) −19.8207 −0.790931
\(629\) 23.0595i 0.919441i
\(630\) −1.71575 + 1.65341i −0.0683573 + 0.0658732i
\(631\) 24.1393i 0.960969i 0.877003 + 0.480485i \(0.159539\pi\)
−0.877003 + 0.480485i \(0.840461\pi\)
\(632\) 11.5702 0.460239
\(633\) 6.70618 + 16.6235i 0.266547 + 0.660725i
\(634\) −2.64083 −0.104881
\(635\) 6.07116 0.240927
\(636\) −2.33620 5.79105i −0.0926363 0.229630i
\(637\) 8.25436i 0.327049i
\(638\) 49.2757i 1.95085i
\(639\) −31.2881 32.4679i −1.23774 1.28441i
\(640\) −1.00000 −0.0395285
\(641\) 11.4554 0.452462 0.226231 0.974074i \(-0.427360\pi\)
0.226231 + 0.974074i \(0.427360\pi\)
\(642\) 4.40679 + 10.9237i 0.173922 + 0.431124i
\(643\) 14.1156i 0.556667i −0.960485 0.278333i \(-0.910218\pi\)
0.960485 0.278333i \(-0.0897820\pi\)
\(644\) 2.45143 0.0965997
\(645\) −3.48062 8.62789i −0.137049 0.339723i
\(646\) 5.46506i 0.215020i
\(647\) 19.0908 0.750536 0.375268 0.926916i \(-0.377551\pi\)
0.375268 + 0.926916i \(0.377551\pi\)
\(648\) 8.99384 + 0.332991i 0.353311 + 0.0130811i
\(649\) 77.6465i 3.04789i
\(650\) 1.29599 0.0508328
\(651\) 1.04649 7.58769i 0.0410151 0.297385i
\(652\) 22.7132 0.889516
\(653\) 0.725491i 0.0283907i 0.999899 + 0.0141953i \(0.00451867\pi\)
−0.999899 + 0.0141953i \(0.995481\pi\)
\(654\) −17.6170 + 7.10698i −0.688880 + 0.277905i
\(655\) −8.32683 −0.325356
\(656\) 8.16341i 0.318728i
\(657\) 2.87625 + 2.98471i 0.112213 + 0.116445i
\(658\) −3.75834 −0.146515
\(659\) 18.6136i 0.725084i −0.931967 0.362542i \(-0.881909\pi\)
0.931967 0.362542i \(-0.118091\pi\)
\(660\) −10.1179 + 4.08171i −0.393838 + 0.158880i
\(661\) −10.9605 −0.426314 −0.213157 0.977018i \(-0.568375\pi\)
−0.213157 + 0.977018i \(0.568375\pi\)
\(662\) −21.4711 −0.834496
\(663\) −7.45442 + 3.00723i −0.289506 + 0.116791i
\(664\) 9.77976i 0.379528i
\(665\) 1.21216i 0.0470055i
\(666\) 13.9107 13.4052i 0.539030 0.519442i
\(667\) −24.1447 −0.934886
\(668\) 3.08645 0.119418
\(669\) −6.90173 + 2.78427i −0.266836 + 0.107646i
\(670\) −2.25449 −0.0870986
\(671\) 14.0064i 0.540712i
\(672\) −1.27579 + 0.514672i −0.0492146 + 0.0198539i
\(673\) 23.7514i 0.915547i −0.889069 0.457774i \(-0.848647\pi\)
0.889069 0.457774i \(-0.151353\pi\)
\(674\) 3.53220 0.136055
\(675\) −4.74359 2.12094i −0.182581 0.0816351i
\(676\) −11.3204 −0.435401
\(677\) 25.3141 0.972898 0.486449 0.873709i \(-0.338292\pi\)
0.486449 + 0.873709i \(0.338292\pi\)
\(678\) 0.577845 + 1.43238i 0.0221920 + 0.0550103i
\(679\) −2.16983 −0.0832704
\(680\) −3.58092 −0.137322
\(681\) 24.2988 9.80253i 0.931134 0.375634i
\(682\) 17.4415 30.4268i 0.667869 1.16510i
\(683\) 37.8027i 1.44648i 0.690597 + 0.723240i \(0.257348\pi\)
−0.690597 + 0.723240i \(0.742652\pi\)
\(684\) −3.29682 + 3.17702i −0.126057 + 0.121476i
\(685\) 8.68407i 0.331801i
\(686\) 10.6185i 0.405417i
\(687\) 21.8634 8.82003i 0.834140 0.336505i
\(688\) 5.37138i 0.204782i
\(689\) 4.67240i 0.178004i
\(690\) 2.00000 + 4.95767i 0.0761387 + 0.188735i
\(691\) −0.703178 −0.0267502 −0.0133751 0.999911i \(-0.504258\pi\)
−0.0133751 + 0.999911i \(0.504258\pi\)
\(692\) 9.50385i 0.361282i
\(693\) −10.8075 + 10.4148i −0.410544 + 0.395625i
\(694\) 24.4043i 0.926376i
\(695\) 5.62515 0.213374
\(696\) 12.5655 5.06913i 0.476295 0.192145i
\(697\) 29.2325i 1.10726i
\(698\) 21.1770i 0.801562i
\(699\) −11.9428 + 4.81789i −0.451716 + 0.182229i
\(700\) 0.794255 0.0300200
\(701\) 0.102385i 0.00386702i 0.999998 + 0.00193351i \(0.000615456\pi\)
−0.999998 + 0.00193351i \(0.999385\pi\)
\(702\) −6.14763 2.74872i −0.232027 0.103744i
\(703\) 9.82777i 0.370661i
\(704\) −6.29899 −0.237402
\(705\) −3.06625 7.60072i −0.115482 0.286260i
\(706\) 27.0512i 1.01808i
\(707\) 2.14701i 0.0807467i
\(708\) −19.8002 + 7.98771i −0.744138 + 0.300197i
\(709\) 2.82812i 0.106212i −0.998589 0.0531061i \(-0.983088\pi\)
0.998589 0.0531061i \(-0.0169121\pi\)
\(710\) 15.0300i 0.564066i
\(711\) 24.0858 + 24.9941i 0.903288 + 0.937351i
\(712\) 4.07539i 0.152732i
\(713\) −14.9088 8.54618i −0.558341 0.320057i
\(714\) −4.56849 + 1.84300i −0.170971 + 0.0689725i
\(715\) 8.16341 0.305294
\(716\) 23.1145 0.863829
\(717\) 12.4902 + 30.9612i 0.466457 + 1.15627i
\(718\) −1.25811 −0.0469521
\(719\) 39.6781 1.47974 0.739871 0.672749i \(-0.234886\pi\)
0.739871 + 0.672749i \(0.234886\pi\)
\(720\) −2.08171 2.16021i −0.0775806 0.0805062i
\(721\) 5.14981 0.191789
\(722\) 16.6708i 0.620424i
\(723\) 1.99359 0.804243i 0.0741423 0.0299101i
\(724\) 9.81857i 0.364904i
\(725\) −7.82280 −0.290532
\(726\) −46.0634 + 18.5827i −1.70957 + 0.689668i
\(727\) −43.5862 −1.61652 −0.808261 0.588825i \(-0.799591\pi\)
−0.808261 + 0.588825i \(0.799591\pi\)
\(728\) 1.02934 0.0381500
\(729\) 18.0032 + 20.1217i 0.666785 + 0.745250i
\(730\) 1.38168i 0.0511382i
\(731\) 19.2345i 0.711413i
\(732\) 3.57170 1.44088i 0.132014 0.0532564i
\(733\) −13.3668 −0.493715 −0.246857 0.969052i \(-0.579398\pi\)
−0.246857 + 0.969052i \(0.579398\pi\)
\(734\) 29.7449 1.09790
\(735\) −10.2306 + 4.12718i −0.377361 + 0.152233i
\(736\) 3.08645i 0.113768i
\(737\) −14.2010 −0.523101
\(738\) 17.6347 16.9938i 0.649141 0.625552i
\(739\) 42.2685i 1.55487i 0.628961 + 0.777436i \(0.283480\pi\)
−0.628961 + 0.777436i \(0.716520\pi\)
\(740\) −6.43954 −0.236722
\(741\) 3.17702 1.28166i 0.116711 0.0470829i
\(742\) 2.86351i 0.105123i
\(743\) 42.1504 1.54635 0.773174 0.634193i \(-0.218668\pi\)
0.773174 + 0.634193i \(0.218668\pi\)
\(744\) 9.55322 + 1.31757i 0.350238 + 0.0483046i
\(745\) 15.0300 0.550657
\(746\) 29.8006i 1.09108i
\(747\) −21.1263 + 20.3586i −0.772971 + 0.744882i
\(748\) −22.5562 −0.824735
\(749\) 5.40146i 0.197365i
\(750\) 0.647994 + 1.60627i 0.0236614 + 0.0586527i
\(751\) 44.3804 1.61946 0.809732 0.586799i \(-0.199612\pi\)
0.809732 + 0.586799i \(0.199612\pi\)
\(752\) 4.73191i 0.172555i
\(753\) −0.0429910 0.106568i −0.00156668 0.00388354i
\(754\) −10.1383 −0.369214
\(755\) 4.80112 0.174730
\(756\) −3.76761 1.68457i −0.137027 0.0612671i
\(757\) 14.4419i 0.524900i 0.964946 + 0.262450i \(0.0845305\pi\)
−0.964946 + 0.262450i \(0.915470\pi\)
\(758\) 33.2321i 1.20705i
\(759\) 12.5980 + 31.2283i 0.457278 + 1.13352i
\(760\) 1.52616 0.0553596
\(761\) 1.05668 0.0383045 0.0191522 0.999817i \(-0.493903\pi\)
0.0191522 + 0.999817i \(0.493903\pi\)
\(762\) 3.93408 + 9.75192i 0.142517 + 0.353275i
\(763\) 8.71111 0.315363
\(764\) 21.0336i 0.760968i
\(765\) −7.45442 7.73553i −0.269515 0.279679i
\(766\) 15.7961i 0.570735i
\(767\) 15.9754 0.576839
\(768\) −0.647994 1.60627i −0.0233825 0.0579613i
\(769\) 17.2930 0.623600 0.311800 0.950148i \(-0.399068\pi\)
0.311800 + 0.950148i \(0.399068\pi\)
\(770\) 5.00300 0.180296
\(771\) −36.0793 + 14.5549i −1.29936 + 0.524183i
\(772\) −3.20932 −0.115506
\(773\) 24.1216 0.867595 0.433798 0.901010i \(-0.357173\pi\)
0.433798 + 0.901010i \(0.357173\pi\)
\(774\) 11.6033 11.1816i 0.417072 0.401916i
\(775\) −4.83042 2.76894i −0.173514 0.0994631i
\(776\) 2.73191i 0.0980697i
\(777\) −8.21548 + 3.31425i −0.294729 + 0.118898i
\(778\) 16.1854i 0.580274i
\(779\) 12.4587i 0.446378i
\(780\) 0.839793 + 2.08171i 0.0300694 + 0.0745371i
\(781\) 94.6738i 3.38770i
\(782\) 11.0523i 0.395230i
\(783\) 37.1081 + 16.5917i 1.32614 + 0.592940i
\(784\) −6.36916 −0.227470
\(785\) 19.8207i 0.707431i
\(786\) −5.39574 13.3751i −0.192460 0.477075i
\(787\) 46.7835i 1.66765i 0.552029 + 0.833825i \(0.313854\pi\)
−0.552029 + 0.833825i \(0.686146\pi\)
\(788\) −24.5350 −0.874023
\(789\) −1.77708 4.40508i −0.0632656 0.156825i
\(790\) 11.5702i 0.411650i
\(791\) 0.708272i 0.0251833i
\(792\) −13.1126 13.6071i −0.465938 0.483508i
\(793\) −2.88176 −0.102334
\(794\) 39.0049i 1.38423i
\(795\) −5.79105 + 2.33620i −0.205387 + 0.0828564i
\(796\) 23.0984i 0.818703i
\(797\) −7.31843 −0.259232 −0.129616 0.991564i \(-0.541374\pi\)
−0.129616 + 0.991564i \(0.541374\pi\)
\(798\) 1.94706 0.785472i 0.0689250 0.0278054i
\(799\) 16.9446i 0.599456i
\(800\) 1.00000i 0.0353553i
\(801\) 8.80369 8.48377i 0.311063 0.299759i
\(802\) 7.02927i 0.248212i
\(803\) 8.70318i 0.307128i
\(804\) −1.46090 3.62132i −0.0515219 0.127714i
\(805\) 2.45143i 0.0864014i
\(806\) −6.26017 3.58851i −0.220505 0.126400i
\(807\) 7.41573 + 18.3824i 0.261046 + 0.647090i
\(808\) −2.70318 −0.0950975
\(809\) 27.5875 0.969925 0.484963 0.874535i \(-0.338833\pi\)
0.484963 + 0.874535i \(0.338833\pi\)
\(810\) 0.332991 8.99384i 0.0117001 0.316011i
\(811\) −25.5390 −0.896795 −0.448398 0.893834i \(-0.648005\pi\)
−0.448398 + 0.893834i \(0.648005\pi\)
\(812\) −6.21330 −0.218044
\(813\) −21.7619 + 8.77909i −0.763224 + 0.307896i
\(814\) −40.5626 −1.42172
\(815\) 22.7132i 0.795608i
\(816\) −2.32041 5.75192i −0.0812308 0.201358i
\(817\) 8.19758i 0.286797i
\(818\) −23.6737 −0.827732
\(819\) 2.14279 + 2.22360i 0.0748753 + 0.0776988i
\(820\) −8.16341 −0.285079
\(821\) 24.0504 0.839365 0.419683 0.907671i \(-0.362141\pi\)
0.419683 + 0.907671i \(0.362141\pi\)
\(822\) −13.9490 + 5.62723i −0.486526 + 0.196272i
\(823\) 7.84558i 0.273480i −0.990607 0.136740i \(-0.956338\pi\)
0.990607 0.136740i \(-0.0436624\pi\)
\(824\) 6.48383i 0.225875i
\(825\) 4.08171 + 10.1179i 0.142107 + 0.352259i
\(826\) 9.79064 0.340660
\(827\) −45.8205 −1.59334 −0.796668 0.604417i \(-0.793406\pi\)
−0.796668 + 0.604417i \(0.793406\pi\)
\(828\) −6.66737 + 6.42508i −0.231707 + 0.223287i
\(829\) 9.33400i 0.324183i −0.986776 0.162092i \(-0.948176\pi\)
0.986776 0.162092i \(-0.0518240\pi\)
\(830\) 9.77976 0.339460
\(831\) 39.2000 15.8139i 1.35983 0.548577i
\(832\) 1.29599i 0.0449303i
\(833\) −22.8074 −0.790231
\(834\) 3.64506 + 9.03551i 0.126218 + 0.312874i
\(835\) 3.08645i 0.106811i
\(836\) 9.61326 0.332482
\(837\) 17.0408 + 23.3797i 0.589015 + 0.808122i
\(838\) 21.7906 0.752745
\(839\) 23.8271i 0.822603i 0.911499 + 0.411301i \(0.134926\pi\)
−0.911499 + 0.411301i \(0.865074\pi\)
\(840\) 0.514672 + 1.27579i 0.0177579 + 0.0440188i
\(841\) 32.1963 1.11022
\(842\) 3.14981i 0.108550i
\(843\) −2.76006 + 1.11345i −0.0950614 + 0.0383492i
\(844\) 10.3491 0.356232
\(845\) 11.3204i 0.389434i
\(846\) 10.2219 9.85044i 0.351436 0.338665i
\(847\) 22.7770 0.782628
\(848\) −3.60528 −0.123806
\(849\) −5.29400 13.1230i −0.181690 0.450379i
\(850\) 3.58092i 0.122825i
\(851\) 19.8753i 0.681317i
\(852\) −24.1423 + 9.73936i −0.827100 + 0.333665i
\(853\) 39.6514 1.35764 0.678818 0.734306i \(-0.262492\pi\)
0.678818 + 0.734306i \(0.262492\pi\)
\(854\) −1.76610 −0.0604348
\(855\) 3.17702 + 3.29682i 0.108652 + 0.112749i
\(856\) 6.80067 0.232442
\(857\) 34.0801i 1.16415i −0.813134 0.582077i \(-0.802240\pi\)
0.813134 0.582077i \(-0.197760\pi\)
\(858\) 5.28984 + 13.1126i 0.180592 + 0.447658i
\(859\) 10.1514i 0.346363i 0.984890 + 0.173181i \(0.0554047\pi\)
−0.984890 + 0.173181i \(0.944595\pi\)
\(860\) −5.37138 −0.183162
\(861\) −10.4148 + 4.20148i −0.354935 + 0.143186i
\(862\) −12.2481 −0.417171
\(863\) −19.1946 −0.653390 −0.326695 0.945130i \(-0.605935\pi\)
−0.326695 + 0.945130i \(0.605935\pi\)
\(864\) 2.12094 4.74359i 0.0721559 0.161380i
\(865\) −9.50385 −0.323140
\(866\) −38.5936 −1.31146
\(867\) 2.70668 + 6.70942i 0.0919238 + 0.227864i
\(868\) −3.83659 2.19924i −0.130222 0.0746471i
\(869\) 72.8807i 2.47231i
\(870\) −5.06913 12.5655i −0.171860 0.426012i
\(871\) 2.92179i 0.0990012i
\(872\) 10.9677i 0.371412i
\(873\) 5.90148 5.68703i 0.199735 0.192477i
\(874\) 4.71041i 0.159332i
\(875\) 0.794255i 0.0268507i
\(876\) 2.21935 0.895320i 0.0749849 0.0302501i
\(877\) −26.3591 −0.890085 −0.445042 0.895510i \(-0.646811\pi\)
−0.445042 + 0.895510i \(0.646811\pi\)
\(878\) 8.54975i 0.288540i
\(879\) 35.3585 14.2642i 1.19261 0.481119i
\(880\) 6.29899i 0.212339i
\(881\) −32.7893 −1.10470 −0.552351 0.833612i \(-0.686269\pi\)
−0.552351 + 0.833612i \(0.686269\pi\)
\(882\) −13.2587 13.7587i −0.446445 0.463280i
\(883\) 1.72114i 0.0579210i −0.999581 0.0289605i \(-0.990780\pi\)
0.999581 0.0289605i \(-0.00921970\pi\)
\(884\) 4.64083i 0.156088i
\(885\) 7.98771 + 19.8002i 0.268504 + 0.665577i
\(886\) 27.6436 0.928706
\(887\) 15.2809i 0.513083i 0.966533 + 0.256542i \(0.0825831\pi\)
−0.966533 + 0.256542i \(0.917417\pi\)
\(888\) −4.17278 10.3436i −0.140029 0.347110i
\(889\) 4.82205i 0.161726i
\(890\) −4.07539 −0.136607
\(891\) 2.09751 56.6521i 0.0702691 1.89792i
\(892\) 4.29675i 0.143866i
\(893\) 7.22164i 0.241663i
\(894\) 9.73936 + 24.1423i 0.325733 + 0.807438i
\(895\) 23.1145i 0.772632i
\(896\) 0.794255i 0.0265342i
\(897\) 6.42508 2.59198i 0.214527 0.0865436i
\(898\) 16.7850i 0.560123i
\(899\) 37.7875 + 21.6608i 1.26028 + 0.722430i
\(900\) −2.16021 + 2.08171i −0.0720069 + 0.0693902i
\(901\) −12.9102 −0.430101
\(902\) −51.4212 −1.71214
\(903\) −6.85274 + 2.76450i −0.228045 + 0.0919968i
\(904\) 0.891745 0.0296590
\(905\) −9.81857 −0.326380
\(906\) 3.11109 + 7.71189i 0.103359 + 0.256210i
\(907\) 13.9605 0.463550 0.231775 0.972769i \(-0.425547\pi\)
0.231775 + 0.972769i \(0.425547\pi\)
\(908\) 15.1275i 0.502024i
\(909\) −5.62723 5.83942i −0.186643 0.193682i
\(910\) 1.02934i 0.0341224i
\(911\) 26.5887 0.880922 0.440461 0.897772i \(-0.354815\pi\)
0.440461 + 0.897772i \(0.354815\pi\)
\(912\) 0.988943 + 2.45143i 0.0327472 + 0.0811748i
\(913\) 61.6026 2.03875
\(914\) −36.7242 −1.21473
\(915\) −1.44088 3.57170i −0.0476340 0.118077i
\(916\) 13.6113i 0.449729i
\(917\) 6.61362i 0.218401i
\(918\) 7.59492 16.9864i 0.250670 0.560635i
\(919\) 44.6090 1.47152 0.735758 0.677244i \(-0.236826\pi\)
0.735758 + 0.677244i \(0.236826\pi\)
\(920\) 3.08645 0.101757
\(921\) 19.9911 + 49.5545i 0.658728 + 1.63288i
\(922\) 27.9560i 0.920682i
\(923\) 19.4787 0.641150
\(924\) 3.24191 + 8.03617i 0.106651 + 0.264371i
\(925\) 6.43954i 0.211731i
\(926\) 19.2543 0.632736
\(927\) −14.0064 + 13.4974i −0.460031 + 0.443314i
\(928\) 7.82280i 0.256796i
\(929\) −14.3336 −0.470269 −0.235135 0.971963i \(-0.575553\pi\)
−0.235135 + 0.971963i \(0.575553\pi\)
\(930\) 1.31757 9.55322i 0.0432050 0.313262i
\(931\) 9.72036 0.318572
\(932\) 7.43508i 0.243544i
\(933\) 29.0291 11.7108i 0.950369 0.383393i
\(934\) 11.6732 0.381958
\(935\) 22.5562i 0.737666i
\(936\) −2.79960 + 2.69787i −0.0915079 + 0.0881826i
\(937\) −50.3617 −1.64524 −0.822622 0.568588i \(-0.807490\pi\)
−0.822622 + 0.568588i \(0.807490\pi\)
\(938\) 1.79064i 0.0584665i
\(939\) 33.4579 13.4974i 1.09186 0.440472i
\(940\) −4.73191 −0.154338
\(941\) −37.3281 −1.21686 −0.608431 0.793607i \(-0.708201\pi\)
−0.608431 + 0.793607i \(0.708201\pi\)
\(942\) −31.8374 + 12.8437i −1.03732 + 0.418470i
\(943\) 25.1960i 0.820493i
\(944\) 12.3268i 0.401204i
\(945\) −1.68457 + 3.76761i −0.0547990 + 0.122561i
\(946\) −33.8342 −1.10005
\(947\) −47.7740 −1.55245 −0.776223 0.630459i \(-0.782867\pi\)
−0.776223 + 0.630459i \(0.782867\pi\)
\(948\) 18.5849 7.49743i 0.603609 0.243505i
\(949\) −1.79064 −0.0581266
\(950\) 1.52616i 0.0495152i
\(951\) −4.24188 + 1.71124i −0.137553 + 0.0554908i
\(952\) 2.84416i 0.0921798i
\(953\) 45.3985 1.47060 0.735300 0.677741i \(-0.237041\pi\)
0.735300 + 0.677741i \(0.237041\pi\)
\(954\) −7.50513 7.78814i −0.242988 0.252150i
\(955\) −21.0336 −0.680631
\(956\) 19.2752 0.623406
\(957\) −31.9304 79.1502i −1.03216 2.55856i
\(958\) 36.8802 1.19154
\(959\) 6.89736 0.222727
\(960\) −1.60627 + 0.647994i −0.0518421 + 0.0209139i
\(961\) 15.6660 + 26.7503i 0.505354 + 0.862912i
\(962\) 8.34557i 0.269072i
\(963\) 14.1570 + 14.6909i 0.456203 + 0.473406i
\(964\) 1.24113i 0.0399740i
\(965\) 3.20932i 0.103312i
\(966\) 3.93765 1.58851i 0.126692 0.0511094i
\(967\) 35.4621i 1.14038i −0.821511 0.570192i \(-0.806869\pi\)
0.821511 0.570192i \(-0.193131\pi\)
\(968\) 28.6772i 0.921722i
\(969\) 3.54132 + 8.77836i 0.113764 + 0.282001i
\(970\) −2.73191 −0.0877162
\(971\) 54.7208i 1.75607i 0.478592 + 0.878037i \(0.341147\pi\)
−0.478592 + 0.878037i \(0.658853\pi\)
\(972\) 14.6623 5.29308i 0.470294 0.169776i
\(973\) 4.46780i 0.143231i
\(974\) 36.6545 1.17449
\(975\) 2.08171 0.839793i 0.0666680 0.0268949i
\(976\) 2.22360i 0.0711756i
\(977\) 2.00206i 0.0640514i −0.999487 0.0320257i \(-0.989804\pi\)
0.999487 0.0320257i \(-0.0101958\pi\)
\(978\) 36.4835 14.7180i 1.16661 0.470630i
\(979\) −25.6708 −0.820443
\(980\) 6.36916i 0.203455i
\(981\) −23.6924 + 22.8315i −0.756441 + 0.728952i
\(982\) 15.5310i 0.495614i
\(983\) −22.3957 −0.714312 −0.357156 0.934045i \(-0.616253\pi\)
−0.357156 + 0.934045i \(0.616253\pi\)
\(984\) −5.28984 13.1126i −0.168634 0.418016i
\(985\) 24.5350i 0.781750i
\(986\) 28.0128i 0.892110i
\(987\) −6.03690 + 2.43538i −0.192157 + 0.0775190i
\(988\) 1.97789i 0.0629249i
\(989\) 16.5785i 0.527165i
\(990\) −13.6071 + 13.1126i −0.432463 + 0.416747i
\(991\) 38.3858i 1.21937i −0.792645 0.609683i \(-0.791297\pi\)
0.792645 0.609683i \(-0.208703\pi\)
\(992\) 2.76894 4.83042i 0.0879138 0.153366i
\(993\) −34.4883 + 13.9131i −1.09445 + 0.441519i
\(994\) 11.9377 0.378639
\(995\) −23.0984 −0.732270
\(996\) 6.33723 + 15.7089i 0.200803 + 0.497757i
\(997\) 2.99996 0.0950097 0.0475048 0.998871i \(-0.484873\pi\)
0.0475048 + 0.998871i \(0.484873\pi\)
\(998\) −6.93560 −0.219542
\(999\) 13.6579 30.5465i 0.432117 0.966449i
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 930.2.h.d.371.3 16
3.2 odd 2 inner 930.2.h.d.371.14 yes 16
31.30 odd 2 inner 930.2.h.d.371.6 yes 16
93.92 even 2 inner 930.2.h.d.371.11 yes 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
930.2.h.d.371.3 16 1.1 even 1 trivial
930.2.h.d.371.6 yes 16 31.30 odd 2 inner
930.2.h.d.371.11 yes 16 93.92 even 2 inner
930.2.h.d.371.14 yes 16 3.2 odd 2 inner