Properties

Label 336.2.w.b.85.7
Level $336$
Weight $2$
Character 336.85
Analytic conductor $2.683$
Analytic rank $0$
Dimension $28$
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] = [336,2,Mod(85,336)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(336, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("336.85");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 336.w (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.68297350792\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(14\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 85.7
Character \(\chi\) \(=\) 336.85
Dual form 336.2.w.b.253.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.371814 - 1.36446i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(-1.72351 + 1.01465i) q^{4} +(0.116928 + 0.116928i) q^{5} +(1.22773 + 0.701908i) q^{6} -1.00000i q^{7} +(2.02528 + 1.97440i) q^{8} -1.00000i q^{9} +O(q^{10})\) \(q+(-0.371814 - 1.36446i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(-1.72351 + 1.01465i) q^{4} +(0.116928 + 0.116928i) q^{5} +(1.22773 + 0.701908i) q^{6} -1.00000i q^{7} +(2.02528 + 1.97440i) q^{8} -1.00000i q^{9} +(0.116068 - 0.203020i) q^{10} +(-0.842648 - 0.842648i) q^{11} +(0.501238 - 1.93617i) q^{12} +(5.06549 - 5.06549i) q^{13} +(-1.36446 + 0.371814i) q^{14} -0.165361 q^{15} +(1.94096 - 3.49752i) q^{16} -0.448406 q^{17} +(-1.36446 + 0.371814i) q^{18} +(1.66164 - 1.66164i) q^{19} +(-0.320168 - 0.0828854i) q^{20} +(0.707107 + 0.707107i) q^{21} +(-0.836452 + 1.46307i) q^{22} -2.66931i q^{23} +(-2.82820 + 0.0359761i) q^{24} -4.97266i q^{25} +(-8.79508 - 5.02824i) q^{26} +(0.707107 + 0.707107i) q^{27} +(1.01465 + 1.72351i) q^{28} +(0.858643 - 0.858643i) q^{29} +(0.0614837 + 0.225629i) q^{30} -1.40070 q^{31} +(-5.49391 - 1.34794i) q^{32} +1.19168 q^{33} +(0.166724 + 0.611833i) q^{34} +(0.116928 - 0.116928i) q^{35} +(1.01465 + 1.72351i) q^{36} +(5.76957 + 5.76957i) q^{37} +(-2.88506 - 1.64942i) q^{38} +7.16368i q^{39} +(0.00594906 + 0.467675i) q^{40} -5.42377i q^{41} +(0.701908 - 1.22773i) q^{42} +(3.30205 + 3.30205i) q^{43} +(2.30730 + 0.597317i) q^{44} +(0.116928 - 0.116928i) q^{45} +(-3.64218 + 0.992488i) q^{46} -12.4218 q^{47} +(1.10065 + 3.84559i) q^{48} -1.00000 q^{49} +(-6.78500 + 1.84890i) q^{50} +(0.317071 - 0.317071i) q^{51} +(-3.59071 + 13.8701i) q^{52} +(7.71727 + 7.71727i) q^{53} +(0.701908 - 1.22773i) q^{54} -0.197059i q^{55} +(1.97440 - 2.02528i) q^{56} +2.34991i q^{57} +(-1.49084 - 0.852330i) q^{58} +(-2.01752 - 2.01752i) q^{59} +(0.285002 - 0.167784i) q^{60} +(6.02230 - 6.02230i) q^{61} +(0.520800 + 1.91120i) q^{62} -1.00000 q^{63} +(0.203495 + 7.99741i) q^{64} +1.18460 q^{65} +(-0.443085 - 1.62601i) q^{66} +(-3.55703 + 3.55703i) q^{67} +(0.772832 - 0.454976i) q^{68} +(1.88749 + 1.88749i) q^{69} +(-0.203020 - 0.116068i) q^{70} +11.1040i q^{71} +(1.97440 - 2.02528i) q^{72} -8.39873i q^{73} +(5.72715 - 10.0176i) q^{74} +(3.51620 + 3.51620i) q^{75} +(-1.17787 + 4.54984i) q^{76} +(-0.842648 + 0.842648i) q^{77} +(9.77456 - 2.66356i) q^{78} +8.06582 q^{79} +(0.635912 - 0.182005i) q^{80} -1.00000 q^{81} +(-7.40053 + 2.01663i) q^{82} +(7.48793 - 7.48793i) q^{83} +(-1.93617 - 0.501238i) q^{84} +(-0.0524314 - 0.0524314i) q^{85} +(3.27777 - 5.73327i) q^{86} +1.21430i q^{87} +(-0.0428721 - 3.37032i) q^{88} +8.82635i q^{89} +(-0.203020 - 0.116068i) q^{90} +(-5.06549 - 5.06549i) q^{91} +(2.70842 + 4.60059i) q^{92} +(0.990445 - 0.990445i) q^{93} +(4.61858 + 16.9490i) q^{94} +0.388585 q^{95} +(4.83792 - 2.93164i) q^{96} -2.19995 q^{97} +(0.371814 + 1.36446i) q^{98} +(-0.842648 + 0.842648i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28 q+O(q^{10}) \) Copy content Toggle raw display \( 28 q - 4 q^{10} - 4 q^{11} - 8 q^{12} + 8 q^{15} + 4 q^{16} + 8 q^{19} - 28 q^{20} - 8 q^{22} - 16 q^{24} - 20 q^{26} + 4 q^{28} + 4 q^{29} + 8 q^{30} + 24 q^{33} + 12 q^{34} + 4 q^{36} + 4 q^{37} + 60 q^{38} - 56 q^{40} - 4 q^{42} + 20 q^{43} + 56 q^{44} - 44 q^{46} + 16 q^{48} - 28 q^{49} + 20 q^{50} - 8 q^{51} - 32 q^{52} + 20 q^{53} - 4 q^{54} - 12 q^{56} - 12 q^{58} - 12 q^{60} - 40 q^{61} - 60 q^{62} - 28 q^{63} + 60 q^{64} + 16 q^{65} + 24 q^{66} + 4 q^{67} - 108 q^{68} - 16 q^{69} - 4 q^{70} - 12 q^{72} + 28 q^{74} - 16 q^{75} - 8 q^{76} - 4 q^{77} + 12 q^{78} + 24 q^{79} - 72 q^{80} - 28 q^{81} + 36 q^{82} + 40 q^{83} + 48 q^{85} + 24 q^{86} + 4 q^{88} - 4 q^{90} + 52 q^{92} - 8 q^{94} + 40 q^{96} + 72 q^{97} - 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).

\(n\) \(85\) \(113\) \(127\) \(241\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.371814 1.36446i −0.262912 0.964820i
\(3\) −0.707107 + 0.707107i −0.408248 + 0.408248i
\(4\) −1.72351 + 1.01465i −0.861754 + 0.507326i
\(5\) 0.116928 + 0.116928i 0.0522919 + 0.0522919i 0.732769 0.680477i \(-0.238228\pi\)
−0.680477 + 0.732769i \(0.738228\pi\)
\(6\) 1.22773 + 0.701908i 0.501219 + 0.286553i
\(7\) 1.00000i 0.377964i
\(8\) 2.02528 + 1.97440i 0.716044 + 0.698056i
\(9\) 1.00000i 0.333333i
\(10\) 0.116068 0.203020i 0.0367041 0.0642004i
\(11\) −0.842648 0.842648i −0.254068 0.254068i 0.568568 0.822636i \(-0.307498\pi\)
−0.822636 + 0.568568i \(0.807498\pi\)
\(12\) 0.501238 1.93617i 0.144695 0.558925i
\(13\) 5.06549 5.06549i 1.40491 1.40491i 0.621495 0.783418i \(-0.286526\pi\)
0.783418 0.621495i \(-0.213474\pi\)
\(14\) −1.36446 + 0.371814i −0.364668 + 0.0993715i
\(15\) −0.165361 −0.0426961
\(16\) 1.94096 3.49752i 0.485241 0.874380i
\(17\) −0.448406 −0.108755 −0.0543773 0.998520i \(-0.517317\pi\)
−0.0543773 + 0.998520i \(0.517317\pi\)
\(18\) −1.36446 + 0.371814i −0.321607 + 0.0876374i
\(19\) 1.66164 1.66164i 0.381206 0.381206i −0.490330 0.871537i \(-0.663124\pi\)
0.871537 + 0.490330i \(0.163124\pi\)
\(20\) −0.320168 0.0828854i −0.0715918 0.0185337i
\(21\) 0.707107 + 0.707107i 0.154303 + 0.154303i
\(22\) −0.836452 + 1.46307i −0.178332 + 0.311927i
\(23\) 2.66931i 0.556590i −0.960496 0.278295i \(-0.910231\pi\)
0.960496 0.278295i \(-0.0897694\pi\)
\(24\) −2.82820 + 0.0359761i −0.577304 + 0.00734359i
\(25\) 4.97266i 0.994531i
\(26\) −8.79508 5.02824i −1.72486 0.986119i
\(27\) 0.707107 + 0.707107i 0.136083 + 0.136083i
\(28\) 1.01465 + 1.72351i 0.191751 + 0.325713i
\(29\) 0.858643 0.858643i 0.159446 0.159446i −0.622875 0.782321i \(-0.714036\pi\)
0.782321 + 0.622875i \(0.214036\pi\)
\(30\) 0.0614837 + 0.225629i 0.0112253 + 0.0411941i
\(31\) −1.40070 −0.251573 −0.125787 0.992057i \(-0.540145\pi\)
−0.125787 + 0.992057i \(0.540145\pi\)
\(32\) −5.49391 1.34794i −0.971195 0.238285i
\(33\) 1.19168 0.207445
\(34\) 0.166724 + 0.611833i 0.0285929 + 0.104929i
\(35\) 0.116928 0.116928i 0.0197645 0.0197645i
\(36\) 1.01465 + 1.72351i 0.169109 + 0.287251i
\(37\) 5.76957 + 5.76957i 0.948512 + 0.948512i 0.998738 0.0502262i \(-0.0159942\pi\)
−0.0502262 + 0.998738i \(0.515994\pi\)
\(38\) −2.88506 1.64942i −0.468019 0.267572i
\(39\) 7.16368i 1.14711i
\(40\) 0.00594906 + 0.467675i 0.000940629 + 0.0739459i
\(41\) 5.42377i 0.847051i −0.905884 0.423525i \(-0.860792\pi\)
0.905884 0.423525i \(-0.139208\pi\)
\(42\) 0.701908 1.22773i 0.108307 0.189443i
\(43\) 3.30205 + 3.30205i 0.503558 + 0.503558i 0.912542 0.408984i \(-0.134117\pi\)
−0.408984 + 0.912542i \(0.634117\pi\)
\(44\) 2.30730 + 0.597317i 0.347839 + 0.0900489i
\(45\) 0.116928 0.116928i 0.0174306 0.0174306i
\(46\) −3.64218 + 0.992488i −0.537009 + 0.146334i
\(47\) −12.4218 −1.81190 −0.905950 0.423385i \(-0.860842\pi\)
−0.905950 + 0.423385i \(0.860842\pi\)
\(48\) 1.10065 + 3.84559i 0.158865 + 0.555063i
\(49\) −1.00000 −0.142857
\(50\) −6.78500 + 1.84890i −0.959543 + 0.261474i
\(51\) 0.317071 0.317071i 0.0443988 0.0443988i
\(52\) −3.59071 + 13.8701i −0.497941 + 1.92344i
\(53\) 7.71727 + 7.71727i 1.06005 + 1.06005i 0.998078 + 0.0619700i \(0.0197383\pi\)
0.0619700 + 0.998078i \(0.480262\pi\)
\(54\) 0.701908 1.22773i 0.0955175 0.167073i
\(55\) 0.197059i 0.0265714i
\(56\) 1.97440 2.02528i 0.263840 0.270639i
\(57\) 2.34991i 0.311254i
\(58\) −1.49084 0.852330i −0.195757 0.111916i
\(59\) −2.01752 2.01752i −0.262659 0.262659i 0.563475 0.826133i \(-0.309464\pi\)
−0.826133 + 0.563475i \(0.809464\pi\)
\(60\) 0.285002 0.167784i 0.0367936 0.0216609i
\(61\) 6.02230 6.02230i 0.771076 0.771076i −0.207219 0.978295i \(-0.566441\pi\)
0.978295 + 0.207219i \(0.0664412\pi\)
\(62\) 0.520800 + 1.91120i 0.0661417 + 0.242723i
\(63\) −1.00000 −0.125988
\(64\) 0.203495 + 7.99741i 0.0254369 + 0.999676i
\(65\) 1.18460 0.146931
\(66\) −0.443085 1.62601i −0.0545399 0.200148i
\(67\) −3.55703 + 3.55703i −0.434561 + 0.434561i −0.890177 0.455616i \(-0.849419\pi\)
0.455616 + 0.890177i \(0.349419\pi\)
\(68\) 0.772832 0.454976i 0.0937197 0.0551740i
\(69\) 1.88749 + 1.88749i 0.227227 + 0.227227i
\(70\) −0.203020 0.116068i −0.0242655 0.0138728i
\(71\) 11.1040i 1.31780i 0.752228 + 0.658902i \(0.228979\pi\)
−0.752228 + 0.658902i \(0.771021\pi\)
\(72\) 1.97440 2.02528i 0.232685 0.238681i
\(73\) 8.39873i 0.982997i −0.870878 0.491499i \(-0.836449\pi\)
0.870878 0.491499i \(-0.163551\pi\)
\(74\) 5.72715 10.0176i 0.665768 1.16452i
\(75\) 3.51620 + 3.51620i 0.406016 + 0.406016i
\(76\) −1.17787 + 4.54984i −0.135110 + 0.521902i
\(77\) −0.842648 + 0.842648i −0.0960286 + 0.0960286i
\(78\) 9.77456 2.66356i 1.10675 0.301588i
\(79\) 8.06582 0.907475 0.453738 0.891135i \(-0.350090\pi\)
0.453738 + 0.891135i \(0.350090\pi\)
\(80\) 0.635912 0.182005i 0.0710972 0.0203488i
\(81\) −1.00000 −0.111111
\(82\) −7.40053 + 2.01663i −0.817251 + 0.222700i
\(83\) 7.48793 7.48793i 0.821907 0.821907i −0.164475 0.986381i \(-0.552593\pi\)
0.986381 + 0.164475i \(0.0525929\pi\)
\(84\) −1.93617 0.501238i −0.211254 0.0546895i
\(85\) −0.0524314 0.0524314i −0.00568698 0.00568698i
\(86\) 3.27777 5.73327i 0.353451 0.618234i
\(87\) 1.21430i 0.130187i
\(88\) −0.0428721 3.37032i −0.00457019 0.359277i
\(89\) 8.82635i 0.935592i 0.883837 + 0.467796i \(0.154952\pi\)
−0.883837 + 0.467796i \(0.845048\pi\)
\(90\) −0.203020 0.116068i −0.0214001 0.0122347i
\(91\) −5.06549 5.06549i −0.531007 0.531007i
\(92\) 2.70842 + 4.60059i 0.282373 + 0.479644i
\(93\) 0.990445 0.990445i 0.102704 0.102704i
\(94\) 4.61858 + 16.9490i 0.476370 + 1.74816i
\(95\) 0.388585 0.0398680
\(96\) 4.83792 2.93164i 0.493768 0.299209i
\(97\) −2.19995 −0.223372 −0.111686 0.993744i \(-0.535625\pi\)
−0.111686 + 0.993744i \(0.535625\pi\)
\(98\) 0.371814 + 1.36446i 0.0375589 + 0.137831i
\(99\) −0.842648 + 0.842648i −0.0846893 + 0.0846893i
\(100\) 5.04551 + 8.57042i 0.504551 + 0.857042i
\(101\) −6.15886 6.15886i −0.612829 0.612829i 0.330853 0.943682i \(-0.392664\pi\)
−0.943682 + 0.330853i \(0.892664\pi\)
\(102\) −0.550523 0.314740i −0.0545099 0.0311639i
\(103\) 12.8752i 1.26863i 0.773073 + 0.634317i \(0.218718\pi\)
−0.773073 + 0.634317i \(0.781282\pi\)
\(104\) 20.2603 0.257721i 1.98669 0.0252717i
\(105\) 0.165361i 0.0161376i
\(106\) 7.66052 13.3993i 0.744056 1.30145i
\(107\) 1.60576 + 1.60576i 0.155235 + 0.155235i 0.780451 0.625217i \(-0.214989\pi\)
−0.625217 + 0.780451i \(0.714989\pi\)
\(108\) −1.93617 0.501238i −0.186308 0.0482316i
\(109\) −4.74644 + 4.74644i −0.454626 + 0.454626i −0.896887 0.442260i \(-0.854177\pi\)
0.442260 + 0.896887i \(0.354177\pi\)
\(110\) −0.268879 + 0.0732691i −0.0256366 + 0.00698594i
\(111\) −8.15941 −0.774457
\(112\) −3.49752 1.94096i −0.330485 0.183404i
\(113\) −16.0799 −1.51267 −0.756336 0.654183i \(-0.773013\pi\)
−0.756336 + 0.654183i \(0.773013\pi\)
\(114\) 3.20637 0.873731i 0.300304 0.0818324i
\(115\) 0.312118 0.312118i 0.0291052 0.0291052i
\(116\) −0.608656 + 2.35110i −0.0565122 + 0.218294i
\(117\) −5.06549 5.06549i −0.468304 0.468304i
\(118\) −2.00269 + 3.50297i −0.184362 + 0.322475i
\(119\) 0.448406i 0.0411053i
\(120\) −0.334903 0.326490i −0.0305723 0.0298043i
\(121\) 9.57989i 0.870899i
\(122\) −10.4564 5.97802i −0.946675 0.541224i
\(123\) 3.83519 + 3.83519i 0.345807 + 0.345807i
\(124\) 2.41412 1.42122i 0.216794 0.127630i
\(125\) 1.16608 1.16608i 0.104298 0.104298i
\(126\) 0.371814 + 1.36446i 0.0331238 + 0.121556i
\(127\) −3.72584 −0.330615 −0.165307 0.986242i \(-0.552862\pi\)
−0.165307 + 0.986242i \(0.552862\pi\)
\(128\) 10.8365 3.25121i 0.957820 0.287369i
\(129\) −4.66980 −0.411153
\(130\) −0.440450 1.61634i −0.0386300 0.141762i
\(131\) −0.420527 + 0.420527i −0.0367416 + 0.0367416i −0.725239 0.688497i \(-0.758271\pi\)
0.688497 + 0.725239i \(0.258271\pi\)
\(132\) −2.05388 + 1.20914i −0.178767 + 0.105242i
\(133\) −1.66164 1.66164i −0.144082 0.144082i
\(134\) 6.17599 + 3.53088i 0.533524 + 0.305022i
\(135\) 0.165361i 0.0142320i
\(136\) −0.908147 0.885333i −0.0778730 0.0759167i
\(137\) 15.0365i 1.28465i 0.766432 + 0.642326i \(0.222030\pi\)
−0.766432 + 0.642326i \(0.777970\pi\)
\(138\) 1.87361 3.27720i 0.159492 0.278974i
\(139\) −14.5884 14.5884i −1.23737 1.23737i −0.961070 0.276304i \(-0.910890\pi\)
−0.276304 0.961070i \(-0.589110\pi\)
\(140\) −0.0828854 + 0.320168i −0.00700510 + 0.0270592i
\(141\) 8.78351 8.78351i 0.739705 0.739705i
\(142\) 15.1510 4.12863i 1.27144 0.346467i
\(143\) −8.53684 −0.713886
\(144\) −3.49752 1.94096i −0.291460 0.161747i
\(145\) 0.200799 0.0166755
\(146\) −11.4597 + 3.12277i −0.948415 + 0.258442i
\(147\) 0.707107 0.707107i 0.0583212 0.0583212i
\(148\) −15.7980 4.08980i −1.29859 0.336180i
\(149\) 15.4379 + 15.4379i 1.26472 + 1.26472i 0.948778 + 0.315944i \(0.102321\pi\)
0.315944 + 0.948778i \(0.397679\pi\)
\(150\) 3.49034 6.10509i 0.284985 0.498478i
\(151\) 7.81338i 0.635844i 0.948117 + 0.317922i \(0.102985\pi\)
−0.948117 + 0.317922i \(0.897015\pi\)
\(152\) 6.64602 0.0845408i 0.539064 0.00685716i
\(153\) 0.448406i 0.0362515i
\(154\) 1.46307 + 0.836452i 0.117897 + 0.0674032i
\(155\) −0.163781 0.163781i −0.0131552 0.0131552i
\(156\) −7.26864 12.3467i −0.581957 0.988524i
\(157\) −12.5393 + 12.5393i −1.00074 + 1.00074i −0.000741791 1.00000i \(0.500236\pi\)
−1.00000 0.000741791i \(0.999764\pi\)
\(158\) −2.99898 11.0055i −0.238586 0.875550i
\(159\) −10.9139 −0.865526
\(160\) −0.484780 0.800006i −0.0383253 0.0632460i
\(161\) −2.66931 −0.210371
\(162\) 0.371814 + 1.36446i 0.0292125 + 0.107202i
\(163\) −4.28825 + 4.28825i −0.335881 + 0.335881i −0.854815 0.518933i \(-0.826329\pi\)
0.518933 + 0.854815i \(0.326329\pi\)
\(164\) 5.50324 + 9.34792i 0.429731 + 0.729950i
\(165\) 0.139341 + 0.139341i 0.0108477 + 0.0108477i
\(166\) −13.0011 7.43287i −1.00908 0.576902i
\(167\) 15.3880i 1.19076i −0.803444 0.595380i \(-0.797001\pi\)
0.803444 0.595380i \(-0.202999\pi\)
\(168\) 0.0359761 + 2.82820i 0.00277562 + 0.218200i
\(169\) 38.3183i 2.94756i
\(170\) −0.0520458 + 0.0910353i −0.00399173 + 0.00698209i
\(171\) −1.66164 1.66164i −0.127069 0.127069i
\(172\) −9.04154 2.34068i −0.689411 0.178475i
\(173\) −11.9143 + 11.9143i −0.905825 + 0.905825i −0.995932 0.0901075i \(-0.971279\pi\)
0.0901075 + 0.995932i \(0.471279\pi\)
\(174\) 1.65687 0.451496i 0.125607 0.0342278i
\(175\) −4.97266 −0.375897
\(176\) −4.58273 + 1.31163i −0.345436 + 0.0988677i
\(177\) 2.85320 0.214460
\(178\) 12.0432 3.28176i 0.902677 0.245978i
\(179\) 16.4795 16.4795i 1.23174 1.23174i 0.268444 0.963295i \(-0.413491\pi\)
0.963295 0.268444i \(-0.0865093\pi\)
\(180\) −0.0828854 + 0.320168i −0.00617791 + 0.0238639i
\(181\) 5.69994 + 5.69994i 0.423673 + 0.423673i 0.886466 0.462793i \(-0.153153\pi\)
−0.462793 + 0.886466i \(0.653153\pi\)
\(182\) −5.02824 + 8.79508i −0.372718 + 0.651935i
\(183\) 8.51681i 0.629581i
\(184\) 5.27029 5.40610i 0.388531 0.398543i
\(185\) 1.34925i 0.0991989i
\(186\) −1.71969 0.983163i −0.126093 0.0720890i
\(187\) 0.377849 + 0.377849i 0.0276310 + 0.0276310i
\(188\) 21.4090 12.6038i 1.56141 0.919223i
\(189\) 0.707107 0.707107i 0.0514344 0.0514344i
\(190\) −0.144481 0.530209i −0.0104818 0.0384654i
\(191\) −5.58350 −0.404008 −0.202004 0.979385i \(-0.564745\pi\)
−0.202004 + 0.979385i \(0.564745\pi\)
\(192\) −5.79892 5.51113i −0.418501 0.397732i
\(193\) −8.17034 −0.588114 −0.294057 0.955788i \(-0.595006\pi\)
−0.294057 + 0.955788i \(0.595006\pi\)
\(194\) 0.817974 + 3.00175i 0.0587271 + 0.215513i
\(195\) −0.837636 + 0.837636i −0.0599844 + 0.0599844i
\(196\) 1.72351 1.01465i 0.123108 0.0724751i
\(197\) −7.94570 7.94570i −0.566108 0.566108i 0.364928 0.931036i \(-0.381094\pi\)
−0.931036 + 0.364928i \(0.881094\pi\)
\(198\) 1.46307 + 0.836452i 0.103976 + 0.0594440i
\(199\) 2.13313i 0.151213i 0.997138 + 0.0756066i \(0.0240893\pi\)
−0.997138 + 0.0756066i \(0.975911\pi\)
\(200\) 9.81801 10.0710i 0.694238 0.712128i
\(201\) 5.03041i 0.354818i
\(202\) −6.11357 + 10.6935i −0.430150 + 0.752390i
\(203\) −0.858643 0.858643i −0.0602649 0.0602649i
\(204\) −0.224758 + 0.868192i −0.0157362 + 0.0607856i
\(205\) 0.634192 0.634192i 0.0442939 0.0442939i
\(206\) 17.5677 4.78719i 1.22400 0.333539i
\(207\) −2.66931 −0.185530
\(208\) −7.88472 27.5486i −0.546707 1.91015i
\(209\) −2.80035 −0.193705
\(210\) 0.225629 0.0614837i 0.0155699 0.00424278i
\(211\) 6.94940 6.94940i 0.478416 0.478416i −0.426208 0.904625i \(-0.640151\pi\)
0.904625 + 0.426208i \(0.140151\pi\)
\(212\) −21.1311 5.47044i −1.45129 0.375711i
\(213\) −7.85173 7.85173i −0.537992 0.537992i
\(214\) 1.59395 2.78804i 0.108960 0.190586i
\(215\) 0.772206i 0.0526640i
\(216\) 0.0359761 + 2.82820i 0.00244786 + 0.192435i
\(217\) 1.40070i 0.0950858i
\(218\) 8.24112 + 4.71154i 0.558159 + 0.319106i
\(219\) 5.93880 + 5.93880i 0.401307 + 0.401307i
\(220\) 0.199946 + 0.339632i 0.0134803 + 0.0228980i
\(221\) −2.27140 + 2.27140i −0.152791 + 0.152791i
\(222\) 3.03378 + 11.1332i 0.203614 + 0.747211i
\(223\) 9.83111 0.658340 0.329170 0.944271i \(-0.393231\pi\)
0.329170 + 0.944271i \(0.393231\pi\)
\(224\) −1.34794 + 5.49391i −0.0900633 + 0.367077i
\(225\) −4.97266 −0.331510
\(226\) 5.97874 + 21.9404i 0.397700 + 1.45946i
\(227\) 10.8974 10.8974i 0.723283 0.723283i −0.245989 0.969273i \(-0.579113\pi\)
0.969273 + 0.245989i \(0.0791129\pi\)
\(228\) −2.38434 4.05010i −0.157907 0.268224i
\(229\) 18.3016 + 18.3016i 1.20940 + 1.20940i 0.971221 + 0.238181i \(0.0765512\pi\)
0.238181 + 0.971221i \(0.423449\pi\)
\(230\) −0.541923 0.309823i −0.0357333 0.0204291i
\(231\) 1.19168i 0.0784070i
\(232\) 3.43430 0.0436860i 0.225473 0.00286812i
\(233\) 20.4162i 1.33751i 0.743483 + 0.668755i \(0.233172\pi\)
−0.743483 + 0.668755i \(0.766828\pi\)
\(234\) −5.02824 + 8.79508i −0.328706 + 0.574952i
\(235\) −1.45245 1.45245i −0.0947477 0.0947477i
\(236\) 5.52429 + 1.43013i 0.359601 + 0.0930938i
\(237\) −5.70339 + 5.70339i −0.370475 + 0.370475i
\(238\) 0.611833 0.166724i 0.0396593 0.0108071i
\(239\) 22.7723 1.47302 0.736510 0.676427i \(-0.236473\pi\)
0.736510 + 0.676427i \(0.236473\pi\)
\(240\) −0.320961 + 0.578355i −0.0207179 + 0.0373327i
\(241\) 7.04377 0.453729 0.226864 0.973926i \(-0.427153\pi\)
0.226864 + 0.973926i \(0.427153\pi\)
\(242\) −13.0714 + 3.56194i −0.840261 + 0.228970i
\(243\) 0.707107 0.707107i 0.0453609 0.0453609i
\(244\) −4.26895 + 16.4900i −0.273291 + 1.05566i
\(245\) −0.116928 0.116928i −0.00747027 0.00747027i
\(246\) 3.80699 6.65894i 0.242725 0.424558i
\(247\) 16.8340i 1.07112i
\(248\) −2.83681 2.76554i −0.180137 0.175612i
\(249\) 10.5895i 0.671084i
\(250\) −2.02464 1.15751i −0.128050 0.0732074i
\(251\) −0.962935 0.962935i −0.0607799 0.0607799i 0.676063 0.736843i \(-0.263685\pi\)
−0.736843 + 0.676063i \(0.763685\pi\)
\(252\) 1.72351 1.01465i 0.108571 0.0639170i
\(253\) −2.24929 + 2.24929i −0.141412 + 0.141412i
\(254\) 1.38532 + 5.08376i 0.0869226 + 0.318983i
\(255\) 0.0741491 0.00464340
\(256\) −8.46531 13.5771i −0.529082 0.848571i
\(257\) 14.1715 0.883994 0.441997 0.897016i \(-0.354270\pi\)
0.441997 + 0.897016i \(0.354270\pi\)
\(258\) 1.73630 + 6.37177i 0.108097 + 0.396689i
\(259\) 5.76957 5.76957i 0.358504 0.358504i
\(260\) −2.04166 + 1.20195i −0.126619 + 0.0745419i
\(261\) −0.858643 0.858643i −0.0531487 0.0531487i
\(262\) 0.730150 + 0.417435i 0.0451088 + 0.0257892i
\(263\) 20.3221i 1.25311i 0.779376 + 0.626557i \(0.215536\pi\)
−0.779376 + 0.626557i \(0.784464\pi\)
\(264\) 2.41349 + 2.35286i 0.148540 + 0.144808i
\(265\) 1.80473i 0.110864i
\(266\) −1.64942 + 2.88506i −0.101133 + 0.176895i
\(267\) −6.24117 6.24117i −0.381954 0.381954i
\(268\) 2.52143 9.73973i 0.154021 0.594949i
\(269\) 8.72963 8.72963i 0.532255 0.532255i −0.388988 0.921243i \(-0.627175\pi\)
0.921243 + 0.388988i \(0.127175\pi\)
\(270\) 0.225629 0.0614837i 0.0137314 0.00374178i
\(271\) 24.7011 1.50049 0.750244 0.661161i \(-0.229936\pi\)
0.750244 + 0.661161i \(0.229936\pi\)
\(272\) −0.870341 + 1.56831i −0.0527722 + 0.0950928i
\(273\) 7.16368 0.433566
\(274\) 20.5167 5.59077i 1.23946 0.337750i
\(275\) −4.19020 + 4.19020i −0.252678 + 0.252678i
\(276\) −5.16825 1.33796i −0.311092 0.0805358i
\(277\) 1.69928 + 1.69928i 0.102100 + 0.102100i 0.756311 0.654212i \(-0.226999\pi\)
−0.654212 + 0.756311i \(0.726999\pi\)
\(278\) −14.4812 + 25.3295i −0.868522 + 1.51916i
\(279\) 1.40070i 0.0838578i
\(280\) 0.467675 0.00594906i 0.0279489 0.000355525i
\(281\) 1.77758i 0.106042i −0.998593 0.0530208i \(-0.983115\pi\)
0.998593 0.0530208i \(-0.0168850\pi\)
\(282\) −15.2506 8.71893i −0.908159 0.519205i
\(283\) 12.6599 + 12.6599i 0.752553 + 0.752553i 0.974955 0.222402i \(-0.0713897\pi\)
−0.222402 + 0.974955i \(0.571390\pi\)
\(284\) −11.2667 19.1379i −0.668556 1.13562i
\(285\) −0.274771 + 0.274771i −0.0162760 + 0.0162760i
\(286\) 3.17412 + 11.6482i 0.187689 + 0.688772i
\(287\) −5.42377 −0.320155
\(288\) −1.34794 + 5.49391i −0.0794284 + 0.323732i
\(289\) −16.7989 −0.988172
\(290\) −0.0746600 0.273983i −0.00438418 0.0160888i
\(291\) 1.55560 1.55560i 0.0911911 0.0911911i
\(292\) 8.52178 + 14.4753i 0.498700 + 0.847102i
\(293\) 10.9894 + 10.9894i 0.642008 + 0.642008i 0.951049 0.309041i \(-0.100008\pi\)
−0.309041 + 0.951049i \(0.600008\pi\)
\(294\) −1.22773 0.701908i −0.0716028 0.0409361i
\(295\) 0.471810i 0.0274698i
\(296\) 0.293544 + 23.0764i 0.0170619 + 1.34129i
\(297\) 1.19168i 0.0691485i
\(298\) 15.3244 26.8044i 0.887718 1.55274i
\(299\) −13.5214 13.5214i −0.781961 0.781961i
\(300\) −9.62791 2.49248i −0.555868 0.143904i
\(301\) 3.30205 3.30205i 0.190327 0.190327i
\(302\) 10.6611 2.90512i 0.613475 0.167171i
\(303\) 8.70994 0.500373
\(304\) −2.58644 9.03681i −0.148342 0.518296i
\(305\) 1.40835 0.0806420
\(306\) 0.611833 0.166724i 0.0349762 0.00953096i
\(307\) −17.8158 + 17.8158i −1.01680 + 1.01680i −0.0169469 + 0.999856i \(0.505395\pi\)
−0.999856 + 0.0169469i \(0.994605\pi\)
\(308\) 0.597317 2.30730i 0.0340353 0.131471i
\(309\) −9.10416 9.10416i −0.517917 0.517917i
\(310\) −0.162577 + 0.284370i −0.00923377 + 0.0161511i
\(311\) 13.3582i 0.757476i −0.925504 0.378738i \(-0.876358\pi\)
0.925504 0.378738i \(-0.123642\pi\)
\(312\) −14.1440 + 14.5084i −0.800744 + 0.821378i
\(313\) 15.5358i 0.878137i 0.898454 + 0.439068i \(0.144691\pi\)
−0.898454 + 0.439068i \(0.855309\pi\)
\(314\) 21.7716 + 12.4471i 1.22864 + 0.702428i
\(315\) −0.116928 0.116928i −0.00658816 0.00658816i
\(316\) −13.9015 + 8.18399i −0.782021 + 0.460386i
\(317\) −7.90981 + 7.90981i −0.444259 + 0.444259i −0.893441 0.449181i \(-0.851716\pi\)
0.449181 + 0.893441i \(0.351716\pi\)
\(318\) 4.05793 + 14.8915i 0.227557 + 0.835076i
\(319\) −1.44707 −0.0810202
\(320\) −0.911329 + 0.958917i −0.0509448 + 0.0536051i
\(321\) −2.27089 −0.126748
\(322\) 0.992488 + 3.64218i 0.0553092 + 0.202971i
\(323\) −0.745090 + 0.745090i −0.0414579 + 0.0414579i
\(324\) 1.72351 1.01465i 0.0957505 0.0563695i
\(325\) −25.1889 25.1889i −1.39723 1.39723i
\(326\) 7.44558 + 4.25672i 0.412372 + 0.235758i
\(327\) 6.71248i 0.371201i
\(328\) 10.7087 10.9846i 0.591288 0.606525i
\(329\) 12.4218i 0.684834i
\(330\) 0.138317 0.241935i 0.00761409 0.0133181i
\(331\) −7.23397 7.23397i −0.397615 0.397615i 0.479776 0.877391i \(-0.340718\pi\)
−0.877391 + 0.479776i \(0.840718\pi\)
\(332\) −5.30787 + 20.5031i −0.291307 + 1.12526i
\(333\) 5.76957 5.76957i 0.316171 0.316171i
\(334\) −20.9964 + 5.72148i −1.14887 + 0.313065i
\(335\) −0.831835 −0.0454480
\(336\) 3.84559 1.10065i 0.209794 0.0600455i
\(337\) −10.6952 −0.582602 −0.291301 0.956631i \(-0.594088\pi\)
−0.291301 + 0.956631i \(0.594088\pi\)
\(338\) −52.2838 + 14.2473i −2.84387 + 0.774950i
\(339\) 11.3702 11.3702i 0.617546 0.617546i
\(340\) 0.143565 + 0.0371664i 0.00778593 + 0.00201563i
\(341\) 1.18030 + 1.18030i 0.0639167 + 0.0639167i
\(342\) −1.64942 + 2.88506i −0.0891905 + 0.156006i
\(343\) 1.00000i 0.0539949i
\(344\) 0.168001 + 13.2071i 0.00905803 + 0.712081i
\(345\) 0.441402i 0.0237643i
\(346\) 20.6864 + 11.8267i 1.11211 + 0.635805i
\(347\) 21.2763 + 21.2763i 1.14217 + 1.14217i 0.988052 + 0.154121i \(0.0492547\pi\)
0.154121 + 0.988052i \(0.450745\pi\)
\(348\) −1.23210 2.09287i −0.0660473 0.112189i
\(349\) −3.09709 + 3.09709i −0.165783 + 0.165783i −0.785123 0.619340i \(-0.787400\pi\)
0.619340 + 0.785123i \(0.287400\pi\)
\(350\) 1.84890 + 6.78500i 0.0988280 + 0.362673i
\(351\) 7.16368 0.382369
\(352\) 3.49359 + 5.76527i 0.186209 + 0.307290i
\(353\) 24.0364 1.27933 0.639665 0.768654i \(-0.279073\pi\)
0.639665 + 0.768654i \(0.279073\pi\)
\(354\) −1.06086 3.89309i −0.0563841 0.206915i
\(355\) −1.29837 + 1.29837i −0.0689105 + 0.0689105i
\(356\) −8.95567 15.2123i −0.474650 0.806250i
\(357\) −0.317071 0.317071i −0.0167812 0.0167812i
\(358\) −28.6130 16.3584i −1.51225 0.864567i
\(359\) 25.2131i 1.33070i −0.746532 0.665349i \(-0.768283\pi\)
0.746532 0.665349i \(-0.231717\pi\)
\(360\) 0.467675 0.00594906i 0.0246486 0.000313543i
\(361\) 13.4779i 0.709363i
\(362\) 5.65803 9.89667i 0.297380 0.520157i
\(363\) 6.77401 + 6.77401i 0.355543 + 0.355543i
\(364\) 13.8701 + 3.59071i 0.726991 + 0.188204i
\(365\) 0.982049 0.982049i 0.0514028 0.0514028i
\(366\) 11.6209 3.16667i 0.607432 0.165524i
\(367\) 9.37796 0.489526 0.244763 0.969583i \(-0.421290\pi\)
0.244763 + 0.969583i \(0.421290\pi\)
\(368\) −9.33598 5.18104i −0.486672 0.270081i
\(369\) −5.42377 −0.282350
\(370\) 1.84100 0.501670i 0.0957091 0.0260806i
\(371\) 7.71727 7.71727i 0.400661 0.400661i
\(372\) −0.702084 + 2.71200i −0.0364014 + 0.140611i
\(373\) 11.0512 + 11.0512i 0.572209 + 0.572209i 0.932745 0.360536i \(-0.117406\pi\)
−0.360536 + 0.932745i \(0.617406\pi\)
\(374\) 0.375070 0.656049i 0.0193944 0.0339235i
\(375\) 1.64909i 0.0851588i
\(376\) −25.1575 24.5255i −1.29740 1.26481i
\(377\) 8.69889i 0.448016i
\(378\) −1.22773 0.701908i −0.0631477 0.0361022i
\(379\) 19.6856 + 19.6856i 1.01118 + 1.01118i 0.999937 + 0.0112441i \(0.00357920\pi\)
0.0112441 + 0.999937i \(0.496421\pi\)
\(380\) −0.669730 + 0.394279i −0.0343564 + 0.0202261i
\(381\) 2.63456 2.63456i 0.134973 0.134973i
\(382\) 2.07602 + 7.61847i 0.106219 + 0.389795i
\(383\) 1.50314 0.0768067 0.0384034 0.999262i \(-0.487773\pi\)
0.0384034 + 0.999262i \(0.487773\pi\)
\(384\) −5.36361 + 9.96151i −0.273710 + 0.508346i
\(385\) −0.197059 −0.0100430
\(386\) 3.03785 + 11.1481i 0.154622 + 0.567424i
\(387\) 3.30205 3.30205i 0.167853 0.167853i
\(388\) 3.79164 2.23219i 0.192491 0.113322i
\(389\) −24.4743 24.4743i −1.24090 1.24090i −0.959630 0.281266i \(-0.909246\pi\)
−0.281266 0.959630i \(-0.590754\pi\)
\(390\) 1.45437 + 0.831477i 0.0736447 + 0.0421035i
\(391\) 1.19694i 0.0605317i
\(392\) −2.02528 1.97440i −0.102292 0.0997222i
\(393\) 0.594714i 0.0299994i
\(394\) −7.88728 + 13.7959i −0.397356 + 0.695029i
\(395\) 0.943122 + 0.943122i 0.0474536 + 0.0474536i
\(396\) 0.597317 2.30730i 0.0300163 0.115946i
\(397\) −16.2293 + 16.2293i −0.814527 + 0.814527i −0.985309 0.170782i \(-0.945371\pi\)
0.170782 + 0.985309i \(0.445371\pi\)
\(398\) 2.91057 0.793126i 0.145894 0.0397558i
\(399\) 2.34991 0.117643
\(400\) −17.3920 9.65175i −0.869598 0.482587i
\(401\) −8.45753 −0.422349 −0.211174 0.977448i \(-0.567729\pi\)
−0.211174 + 0.977448i \(0.567729\pi\)
\(402\) −6.86379 + 1.87038i −0.342335 + 0.0932858i
\(403\) −7.09523 + 7.09523i −0.353439 + 0.353439i
\(404\) 16.8639 + 4.36575i 0.839012 + 0.217204i
\(405\) −0.116928 0.116928i −0.00581021 0.00581021i
\(406\) −0.852330 + 1.49084i −0.0423004 + 0.0739892i
\(407\) 9.72343i 0.481973i
\(408\) 1.26818 0.0161319i 0.0627844 0.000798649i
\(409\) 2.90076i 0.143433i −0.997425 0.0717166i \(-0.977152\pi\)
0.997425 0.0717166i \(-0.0228477\pi\)
\(410\) −1.10113 0.629529i −0.0543810 0.0310902i
\(411\) −10.6324 10.6324i −0.524457 0.524457i
\(412\) −13.0639 22.1906i −0.643610 1.09325i
\(413\) −2.01752 + 2.01752i −0.0992757 + 0.0992757i
\(414\) 0.992488 + 3.64218i 0.0487781 + 0.179003i
\(415\) 1.75110 0.0859581
\(416\) −34.6573 + 21.0013i −1.69921 + 1.02968i
\(417\) 20.6312 1.01031
\(418\) 1.04121 + 3.82097i 0.0509273 + 0.186890i
\(419\) 8.22993 8.22993i 0.402058 0.402058i −0.476900 0.878958i \(-0.658239\pi\)
0.878958 + 0.476900i \(0.158239\pi\)
\(420\) −0.167784 0.285002i −0.00818703 0.0139067i
\(421\) 12.1183 + 12.1183i 0.590609 + 0.590609i 0.937796 0.347187i \(-0.112863\pi\)
−0.347187 + 0.937796i \(0.612863\pi\)
\(422\) −12.0661 6.89830i −0.587367 0.335804i
\(423\) 12.4218i 0.603967i
\(424\) 0.392638 + 30.8666i 0.0190682 + 1.49901i
\(425\) 2.22977i 0.108160i
\(426\) −7.79400 + 13.6328i −0.377620 + 0.660509i
\(427\) −6.02230 6.02230i −0.291439 0.291439i
\(428\) −4.39682 1.13825i −0.212529 0.0550196i
\(429\) 6.03646 6.03646i 0.291443 0.291443i
\(430\) 1.05364 0.287117i 0.0508113 0.0138460i
\(431\) 23.4181 1.12801 0.564005 0.825771i \(-0.309260\pi\)
0.564005 + 0.825771i \(0.309260\pi\)
\(432\) 3.84559 1.10065i 0.185021 0.0529551i
\(433\) −17.2436 −0.828673 −0.414336 0.910124i \(-0.635986\pi\)
−0.414336 + 0.910124i \(0.635986\pi\)
\(434\) 1.91120 0.520800i 0.0917406 0.0249992i
\(435\) −0.141987 + 0.141987i −0.00680773 + 0.00680773i
\(436\) 3.36455 12.9965i 0.161133 0.622420i
\(437\) −4.43544 4.43544i −0.212176 0.212176i
\(438\) 5.89513 10.3114i 0.281680 0.492697i
\(439\) 15.7763i 0.752961i −0.926424 0.376481i \(-0.877134\pi\)
0.926424 0.376481i \(-0.122866\pi\)
\(440\) 0.389072 0.399098i 0.0185483 0.0190263i
\(441\) 1.00000i 0.0476190i
\(442\) 3.94377 + 2.25470i 0.187586 + 0.107245i
\(443\) −2.04057 2.04057i −0.0969506 0.0969506i 0.656968 0.753919i \(-0.271839\pi\)
−0.753919 + 0.656968i \(0.771839\pi\)
\(444\) 14.0628 8.27895i 0.667391 0.392902i
\(445\) −1.03205 + 1.03205i −0.0489238 + 0.0489238i
\(446\) −3.65534 13.4142i −0.173085 0.635179i
\(447\) −21.8325 −1.03264
\(448\) 7.99741 0.203495i 0.377842 0.00961424i
\(449\) −30.1235 −1.42162 −0.710809 0.703385i \(-0.751671\pi\)
−0.710809 + 0.703385i \(0.751671\pi\)
\(450\) 1.84890 + 6.78500i 0.0871581 + 0.319848i
\(451\) −4.57033 + 4.57033i −0.215208 + 0.215208i
\(452\) 27.7139 16.3155i 1.30355 0.767418i
\(453\) −5.52489 5.52489i −0.259582 0.259582i
\(454\) −18.9208 10.8172i −0.887998 0.507678i
\(455\) 1.18460i 0.0555347i
\(456\) −4.63967 + 4.75923i −0.217272 + 0.222871i
\(457\) 15.3037i 0.715876i −0.933745 0.357938i \(-0.883480\pi\)
0.933745 0.357938i \(-0.116520\pi\)
\(458\) 18.1670 31.7766i 0.848888 1.48482i
\(459\) −0.317071 0.317071i −0.0147996 0.0147996i
\(460\) −0.221247 + 0.854629i −0.0103157 + 0.0398473i
\(461\) 3.13603 3.13603i 0.146060 0.146060i −0.630296 0.776355i \(-0.717066\pi\)
0.776355 + 0.630296i \(0.217066\pi\)
\(462\) −1.62601 + 0.443085i −0.0756486 + 0.0206142i
\(463\) 26.1517 1.21537 0.607686 0.794178i \(-0.292098\pi\)
0.607686 + 0.794178i \(0.292098\pi\)
\(464\) −1.33653 4.66972i −0.0620467 0.216786i
\(465\) 0.231622 0.0107412
\(466\) 27.8571 7.59103i 1.29046 0.351647i
\(467\) 8.99017 8.99017i 0.416015 0.416015i −0.467812 0.883828i \(-0.654958\pi\)
0.883828 + 0.467812i \(0.154958\pi\)
\(468\) 13.8701 + 3.59071i 0.641146 + 0.165980i
\(469\) 3.55703 + 3.55703i 0.164249 + 0.164249i
\(470\) −1.44177 + 2.52186i −0.0665041 + 0.116325i
\(471\) 17.7332i 0.817102i
\(472\) −0.102647 8.06943i −0.00472472 0.371426i
\(473\) 5.56493i 0.255876i
\(474\) 9.90266 + 5.66146i 0.454844 + 0.260039i
\(475\) −8.26276 8.26276i −0.379122 0.379122i
\(476\) −0.454976 0.772832i −0.0208538 0.0354227i
\(477\) 7.71727 7.71727i 0.353349 0.353349i
\(478\) −8.46707 31.0720i −0.387275 1.42120i
\(479\) −24.8217 −1.13413 −0.567066 0.823672i \(-0.691922\pi\)
−0.567066 + 0.823672i \(0.691922\pi\)
\(480\) 0.908481 + 0.222898i 0.0414663 + 0.0101739i
\(481\) 58.4514 2.66515
\(482\) −2.61897 9.61095i −0.119291 0.437767i
\(483\) 1.88749 1.88749i 0.0858838 0.0858838i
\(484\) 9.72025 + 16.5110i 0.441830 + 0.750501i
\(485\) −0.257237 0.257237i −0.0116805 0.0116805i
\(486\) −1.22773 0.701908i −0.0556911 0.0318392i
\(487\) 12.6249i 0.572087i 0.958217 + 0.286043i \(0.0923401\pi\)
−0.958217 + 0.286043i \(0.907660\pi\)
\(488\) 24.0872 0.306402i 1.09038 0.0138702i
\(489\) 6.06450i 0.274246i
\(490\) −0.116068 + 0.203020i −0.00524344 + 0.00917149i
\(491\) 13.7916 + 13.7916i 0.622407 + 0.622407i 0.946146 0.323739i \(-0.104940\pi\)
−0.323739 + 0.946146i \(0.604940\pi\)
\(492\) −10.5014 2.71860i −0.473438 0.122564i
\(493\) −0.385021 + 0.385021i −0.0173405 + 0.0173405i
\(494\) −22.9694 + 6.25913i −1.03344 + 0.281611i
\(495\) −0.197059 −0.00885712
\(496\) −2.71871 + 4.89898i −0.122074 + 0.219971i
\(497\) 11.1040 0.498083
\(498\) 14.4490 3.93733i 0.647475 0.176436i
\(499\) −26.6980 + 26.6980i −1.19516 + 1.19516i −0.219567 + 0.975597i \(0.570465\pi\)
−0.975597 + 0.219567i \(0.929535\pi\)
\(500\) −0.826588 + 3.19293i −0.0369661 + 0.142792i
\(501\) 10.8810 + 10.8810i 0.486126 + 0.486126i
\(502\) −0.955855 + 1.67192i −0.0426619 + 0.0746215i
\(503\) 29.5574i 1.31790i −0.752186 0.658951i \(-0.771001\pi\)
0.752186 0.658951i \(-0.228999\pi\)
\(504\) −2.02528 1.97440i −0.0902130 0.0879467i
\(505\) 1.44029i 0.0640920i
\(506\) 3.90539 + 2.23275i 0.173616 + 0.0992580i
\(507\) 27.0951 + 27.0951i 1.20334 + 1.20334i
\(508\) 6.42151 3.78043i 0.284909 0.167729i
\(509\) 13.2978 13.2978i 0.589413 0.589413i −0.348060 0.937472i \(-0.613159\pi\)
0.937472 + 0.348060i \(0.113159\pi\)
\(510\) −0.0275697 0.101174i −0.00122081 0.00448004i
\(511\) −8.39873 −0.371538
\(512\) −15.3779 + 16.5988i −0.679616 + 0.733568i
\(513\) 2.34991 0.103751
\(514\) −5.26917 19.3365i −0.232413 0.852895i
\(515\) −1.50548 + 1.50548i −0.0663392 + 0.0663392i
\(516\) 8.04845 4.73822i 0.354313 0.208589i
\(517\) 10.4672 + 10.4672i 0.460345 + 0.460345i
\(518\) −10.0176 5.72715i −0.440146 0.251636i
\(519\) 16.8493i 0.739603i
\(520\) 2.39914 + 2.33887i 0.105209 + 0.102566i
\(521\) 13.4541i 0.589435i 0.955584 + 0.294717i \(0.0952255\pi\)
−0.955584 + 0.294717i \(0.904774\pi\)
\(522\) −0.852330 + 1.49084i −0.0373055 + 0.0652523i
\(523\) 4.26642 + 4.26642i 0.186558 + 0.186558i 0.794206 0.607648i \(-0.207887\pi\)
−0.607648 + 0.794206i \(0.707887\pi\)
\(524\) 0.298093 1.15147i 0.0130223 0.0503022i
\(525\) 3.51620 3.51620i 0.153459 0.153459i
\(526\) 27.7287 7.55604i 1.20903 0.329459i
\(527\) 0.628083 0.0273597
\(528\) 2.31302 4.16794i 0.100661 0.181386i
\(529\) 15.8748 0.690207
\(530\) 2.46249 0.671025i 0.106964 0.0291474i
\(531\) −2.01752 + 2.01752i −0.0875529 + 0.0875529i
\(532\) 4.54984 + 1.17787i 0.197260 + 0.0510669i
\(533\) −27.4740 27.4740i −1.19003 1.19003i
\(534\) −6.19528 + 10.8364i −0.268096 + 0.468937i
\(535\) 0.375517i 0.0162350i
\(536\) −14.2270 + 0.180974i −0.614512 + 0.00781691i
\(537\) 23.3056i 1.00571i
\(538\) −15.1570 8.66544i −0.653467 0.373594i
\(539\) 0.842648 + 0.842648i 0.0362954 + 0.0362954i
\(540\) −0.167784 0.285002i −0.00722028 0.0122645i
\(541\) −22.8454 + 22.8454i −0.982202 + 0.982202i −0.999844 0.0176425i \(-0.994384\pi\)
0.0176425 + 0.999844i \(0.494384\pi\)
\(542\) −9.18423 33.7038i −0.394496 1.44770i
\(543\) −8.06094 −0.345928
\(544\) 2.46350 + 0.604427i 0.105622 + 0.0259146i
\(545\) −1.10999 −0.0475465
\(546\) −2.66356 9.77456i −0.113990 0.418313i
\(547\) −31.0153 + 31.0153i −1.32612 + 1.32612i −0.417391 + 0.908727i \(0.637055\pi\)
−0.908727 + 0.417391i \(0.862945\pi\)
\(548\) −15.2568 25.9155i −0.651737 1.10705i
\(549\) −6.02230 6.02230i −0.257025 0.257025i
\(550\) 7.27533 + 4.15939i 0.310221 + 0.177357i
\(551\) 2.85351i 0.121564i
\(552\) 0.0960316 + 7.54935i 0.00408737 + 0.321322i
\(553\) 8.06582i 0.342993i
\(554\) 1.68678 2.95041i 0.0716645 0.125351i
\(555\) −0.954065 0.954065i −0.0404978 0.0404978i
\(556\) 39.9454 + 10.3411i 1.69406 + 0.438561i
\(557\) 17.9517 17.9517i 0.760638 0.760638i −0.215799 0.976438i \(-0.569236\pi\)
0.976438 + 0.215799i \(0.0692358\pi\)
\(558\) 1.91120 0.520800i 0.0809076 0.0220472i
\(559\) 33.4530 1.41491
\(560\) −0.182005 0.635912i −0.00769113 0.0268722i
\(561\) −0.534359 −0.0225606
\(562\) −2.42544 + 0.660930i −0.102311 + 0.0278796i
\(563\) −14.0454 + 14.0454i −0.591943 + 0.591943i −0.938156 0.346213i \(-0.887467\pi\)
0.346213 + 0.938156i \(0.387467\pi\)
\(564\) −6.22625 + 24.0507i −0.262173 + 1.01272i
\(565\) −1.88020 1.88020i −0.0791005 0.0791005i
\(566\) 12.5668 21.9811i 0.528223 0.923934i
\(567\) 1.00000i 0.0419961i
\(568\) −21.9238 + 22.4887i −0.919901 + 0.943606i
\(569\) 25.5548i 1.07131i −0.844436 0.535657i \(-0.820064\pi\)
0.844436 0.535657i \(-0.179936\pi\)
\(570\) 0.477078 + 0.272751i 0.0199826 + 0.0114243i
\(571\) −24.6646 24.6646i −1.03218 1.03218i −0.999465 0.0327177i \(-0.989584\pi\)
−0.0327177 0.999465i \(-0.510416\pi\)
\(572\) 14.7133 8.66192i 0.615195 0.362173i
\(573\) 3.94813 3.94813i 0.164936 0.164936i
\(574\) 2.01663 + 7.40053i 0.0841727 + 0.308892i
\(575\) −13.2736 −0.553547
\(576\) 7.99741 0.203495i 0.333225 0.00847897i
\(577\) −23.4856 −0.977720 −0.488860 0.872362i \(-0.662587\pi\)
−0.488860 + 0.872362i \(0.662587\pi\)
\(578\) 6.24608 + 22.9215i 0.259803 + 0.953408i
\(579\) 5.77730 5.77730i 0.240097 0.240097i
\(580\) −0.346079 + 0.203741i −0.0143702 + 0.00845989i
\(581\) −7.48793 7.48793i −0.310651 0.310651i
\(582\) −2.70095 1.54417i −0.111958 0.0640077i
\(583\) 13.0059i 0.538648i
\(584\) 16.5824 17.0098i 0.686187 0.703869i
\(585\) 1.18460i 0.0489770i
\(586\) 10.9086 19.0806i 0.450630 0.788214i
\(587\) −20.3478 20.3478i −0.839842 0.839842i 0.148996 0.988838i \(-0.452396\pi\)
−0.988838 + 0.148996i \(0.952396\pi\)
\(588\) −0.501238 + 1.93617i −0.0206707 + 0.0798464i
\(589\) −2.32746 + 2.32746i −0.0959013 + 0.0959013i
\(590\) −0.643767 + 0.175426i −0.0265035 + 0.00722216i
\(591\) 11.2369 0.462225
\(592\) 31.3777 8.98066i 1.28962 0.369103i
\(593\) 3.34815 0.137492 0.0687459 0.997634i \(-0.478100\pi\)
0.0687459 + 0.997634i \(0.478100\pi\)
\(594\) −1.62601 + 0.443085i −0.0667158 + 0.0181800i
\(595\) −0.0524314 + 0.0524314i −0.00214948 + 0.00214948i
\(596\) −42.2714 10.9433i −1.73151 0.448254i
\(597\) −1.50835 1.50835i −0.0617325 0.0617325i
\(598\) −13.4220 + 23.4768i −0.548865 + 0.960039i
\(599\) 1.10888i 0.0453078i −0.999743 0.0226539i \(-0.992788\pi\)
0.999743 0.0226539i \(-0.00721158\pi\)
\(600\) 0.178897 + 14.0637i 0.00730343 + 0.574146i
\(601\) 33.3043i 1.35851i 0.733901 + 0.679256i \(0.237697\pi\)
−0.733901 + 0.679256i \(0.762303\pi\)
\(602\) −5.73327 3.27777i −0.233671 0.133592i
\(603\) 3.55703 + 3.55703i 0.144854 + 0.144854i
\(604\) −7.92786 13.4664i −0.322580 0.547941i
\(605\) 1.12016 1.12016i 0.0455410 0.0455410i
\(606\) −3.23848 11.8844i −0.131554 0.482770i
\(607\) −20.3798 −0.827193 −0.413596 0.910460i \(-0.635727\pi\)
−0.413596 + 0.910460i \(0.635727\pi\)
\(608\) −11.3687 + 6.88910i −0.461062 + 0.279390i
\(609\) 1.21430 0.0492061
\(610\) −0.523645 1.92164i −0.0212018 0.0778050i
\(611\) −62.9222 + 62.9222i −2.54556 + 2.54556i
\(612\) −0.454976 0.772832i −0.0183913 0.0312399i
\(613\) −16.5645 16.5645i −0.669033 0.669033i 0.288460 0.957492i \(-0.406857\pi\)
−0.957492 + 0.288460i \(0.906857\pi\)
\(614\) 30.9332 + 17.6848i 1.24836 + 0.713702i
\(615\) 0.896883i 0.0361658i
\(616\) −3.37032 + 0.0428721i −0.135794 + 0.00172737i
\(617\) 0.0743739i 0.00299418i 0.999999 + 0.00149709i \(0.000476539\pi\)
−0.999999 + 0.00149709i \(0.999523\pi\)
\(618\) −9.03721 + 15.8073i −0.363530 + 0.635864i
\(619\) −15.5469 15.5469i −0.624884 0.624884i 0.321892 0.946776i \(-0.395681\pi\)
−0.946776 + 0.321892i \(0.895681\pi\)
\(620\) 0.448460 + 0.116098i 0.0180106 + 0.00466260i
\(621\) 1.88749 1.88749i 0.0757424 0.0757424i
\(622\) −18.2268 + 4.96678i −0.730828 + 0.199150i
\(623\) 8.82635 0.353620
\(624\) 25.0551 + 13.9044i 1.00301 + 0.556623i
\(625\) −24.5906 −0.983623
\(626\) 21.1980 5.77644i 0.847244 0.230873i
\(627\) 1.98015 1.98015i 0.0790795 0.0790795i
\(628\) 8.88854 34.3345i 0.354691 1.37010i
\(629\) −2.58711 2.58711i −0.103155 0.103155i
\(630\) −0.116068 + 0.203020i −0.00462428 + 0.00808849i
\(631\) 28.4423i 1.13227i 0.824313 + 0.566134i \(0.191562\pi\)
−0.824313 + 0.566134i \(0.808438\pi\)
\(632\) 16.3355 + 15.9251i 0.649792 + 0.633468i
\(633\) 9.82794i 0.390625i
\(634\) 13.7336 + 7.85165i 0.545431 + 0.311829i
\(635\) −0.435655 0.435655i −0.0172885 0.0172885i
\(636\) 18.8101 11.0738i 0.745870 0.439103i
\(637\) −5.06549 + 5.06549i −0.200702 + 0.200702i
\(638\) 0.538040 + 1.97447i 0.0213012 + 0.0781699i
\(639\) 11.1040 0.439268
\(640\) 1.64725 + 0.886934i 0.0651133 + 0.0350591i
\(641\) −17.6510 −0.697171 −0.348585 0.937277i \(-0.613338\pi\)
−0.348585 + 0.937277i \(0.613338\pi\)
\(642\) 0.844347 + 3.09854i 0.0333237 + 0.122289i
\(643\) −33.7930 + 33.7930i −1.33266 + 1.33266i −0.429685 + 0.902979i \(0.641375\pi\)
−0.902979 + 0.429685i \(0.858625\pi\)
\(644\) 4.60059 2.70842i 0.181288 0.106727i
\(645\) −0.546032 0.546032i −0.0215000 0.0215000i
\(646\) 1.29368 + 0.739611i 0.0508992 + 0.0290996i
\(647\) 36.6980i 1.44275i 0.692547 + 0.721373i \(0.256488\pi\)
−0.692547 + 0.721373i \(0.743512\pi\)
\(648\) −2.02528 1.97440i −0.0795604 0.0775617i
\(649\) 3.40012i 0.133466i
\(650\) −25.0037 + 43.7349i −0.980726 + 1.71542i
\(651\) −0.990445 0.990445i −0.0388186 0.0388186i
\(652\) 3.03976 11.7419i 0.119046 0.459849i
\(653\) 25.5329 25.5329i 0.999179 0.999179i −0.000820971 1.00000i \(-0.500261\pi\)
1.00000 0.000820971i \(0.000261323\pi\)
\(654\) −9.15891 + 2.49579i −0.358142 + 0.0975932i
\(655\) −0.0983429 −0.00384257
\(656\) −18.9698 10.5273i −0.740645 0.411024i
\(657\) −8.39873 −0.327666
\(658\) 16.9490 4.61858i 0.660741 0.180051i
\(659\) −8.93401 + 8.93401i −0.348020 + 0.348020i −0.859371 0.511352i \(-0.829145\pi\)
0.511352 + 0.859371i \(0.329145\pi\)
\(660\) −0.381539 0.0987732i −0.0148514 0.00384474i
\(661\) −15.8744 15.8744i −0.617442 0.617442i 0.327433 0.944875i \(-0.393817\pi\)
−0.944875 + 0.327433i \(0.893817\pi\)
\(662\) −7.18078 + 12.5602i −0.279089 + 0.488165i
\(663\) 3.21224i 0.124753i
\(664\) 29.9493 0.380970i 1.16226 0.0147845i
\(665\) 0.388585i 0.0150687i
\(666\) −10.0176 5.72715i −0.388173 0.221923i
\(667\) −2.29199 2.29199i −0.0887462 0.0887462i
\(668\) 15.6135 + 26.5214i 0.604103 + 1.02614i
\(669\) −6.95164 + 6.95164i −0.268766 + 0.268766i
\(670\) 0.309288 + 1.13501i 0.0119488 + 0.0438492i
\(671\) −10.1493 −0.391811
\(672\) −2.93164 4.83792i −0.113090 0.186627i
\(673\) 17.4999 0.674572 0.337286 0.941402i \(-0.390491\pi\)
0.337286 + 0.941402i \(0.390491\pi\)
\(674\) 3.97661 + 14.5931i 0.153173 + 0.562106i
\(675\) 3.51620 3.51620i 0.135339 0.135339i
\(676\) 38.8797 + 66.0419i 1.49537 + 2.54007i
\(677\) −22.5939 22.5939i −0.868353 0.868353i 0.123937 0.992290i \(-0.460448\pi\)
−0.992290 + 0.123937i \(0.960448\pi\)
\(678\) −19.7418 11.2866i −0.758181 0.433460i
\(679\) 2.19995i 0.0844265i
\(680\) −0.00266760 0.209708i −0.000102298 0.00804195i
\(681\) 15.4112i 0.590558i
\(682\) 1.17162 2.04932i 0.0448636 0.0784726i
\(683\) 18.1651 + 18.1651i 0.695067 + 0.695067i 0.963342 0.268275i \(-0.0864537\pi\)
−0.268275 + 0.963342i \(0.586454\pi\)
\(684\) 4.54984 + 1.17787i 0.173967 + 0.0450368i
\(685\) −1.75819 + 1.75819i −0.0671768 + 0.0671768i
\(686\) 1.36446 0.371814i 0.0520954 0.0141959i
\(687\) −25.8823 −0.987473
\(688\) 17.9582 5.13983i 0.684648 0.195954i
\(689\) 78.1834 2.97855
\(690\) 0.602275 0.164119i 0.0229282 0.00624792i
\(691\) 31.4362 31.4362i 1.19589 1.19589i 0.220505 0.975386i \(-0.429230\pi\)
0.975386 0.220505i \(-0.0707705\pi\)
\(692\) 8.44551 32.6232i 0.321050 1.24015i
\(693\) 0.842648 + 0.842648i 0.0320095 + 0.0320095i
\(694\) 21.1199 36.9416i 0.801700 1.40228i
\(695\) 3.41160i 0.129409i
\(696\) −2.39752 + 2.45930i −0.0908779 + 0.0932197i
\(697\) 2.43205i 0.0921206i
\(698\) 5.37740 + 3.07432i 0.203538 + 0.116365i
\(699\) −14.4364 14.4364i −0.546036 0.546036i
\(700\) 8.57042 5.04551i 0.323931 0.190702i
\(701\) −8.84023 + 8.84023i −0.333891 + 0.333891i −0.854062 0.520171i \(-0.825868\pi\)
0.520171 + 0.854062i \(0.325868\pi\)
\(702\) −2.66356 9.77456i −0.100529 0.368917i
\(703\) 19.1739 0.723157
\(704\) 6.56752 6.91047i 0.247523 0.260448i
\(705\) 2.05408 0.0773611
\(706\) −8.93708 32.7968i −0.336351 1.23432i
\(707\) −6.15886 + 6.15886i −0.231628 + 0.231628i
\(708\) −4.91752 + 2.89501i −0.184812 + 0.108801i
\(709\) 17.9508 + 17.9508i 0.674156 + 0.674156i 0.958671 0.284515i \(-0.0918327\pi\)
−0.284515 + 0.958671i \(0.591833\pi\)
\(710\) 2.25433 + 1.28883i 0.0846036 + 0.0483688i
\(711\) 8.06582i 0.302492i
\(712\) −17.4267 + 17.8758i −0.653095 + 0.669924i
\(713\) 3.73891i 0.140023i
\(714\) −0.314740 + 0.550523i −0.0117788 + 0.0206028i
\(715\) −0.998197 0.998197i −0.0373305 0.0373305i
\(716\) −11.6816 + 45.1236i −0.436564 + 1.68635i
\(717\) −16.1025 + 16.1025i −0.601358 + 0.601358i
\(718\) −34.4023 + 9.37460i −1.28388 + 0.349857i
\(719\) −50.0437 −1.86631 −0.933157 0.359470i \(-0.882958\pi\)
−0.933157 + 0.359470i \(0.882958\pi\)
\(720\) −0.182005 0.635912i −0.00678294 0.0236991i
\(721\) 12.8752 0.479498
\(722\) 18.3901 5.01127i 0.684408 0.186500i
\(723\) −4.98070 + 4.98070i −0.185234 + 0.185234i
\(724\) −15.6074 4.04045i −0.580043 0.150162i
\(725\) −4.26974 4.26974i −0.158574 0.158574i
\(726\) 6.72420 11.7615i 0.249558 0.436512i
\(727\) 47.5239i 1.76256i −0.472592 0.881281i \(-0.656682\pi\)
0.472592 0.881281i \(-0.343318\pi\)
\(728\) −0.257721 20.2603i −0.00955179 0.750897i
\(729\) 1.00000i 0.0370370i
\(730\) −1.70511 0.974828i −0.0631088 0.0360800i
\(731\) −1.48066 1.48066i −0.0547642 0.0547642i
\(732\) −8.64160 14.6788i −0.319403 0.542544i
\(733\) 10.4370 10.4370i 0.385498 0.385498i −0.487580 0.873078i \(-0.662120\pi\)
0.873078 + 0.487580i \(0.162120\pi\)
\(734\) −3.48686 12.7959i −0.128702 0.472304i
\(735\) 0.165361 0.00609945
\(736\) −3.59809 + 14.6650i −0.132627 + 0.540558i
\(737\) 5.99465 0.220816
\(738\) 2.01663 + 7.40053i 0.0742333 + 0.272417i
\(739\) −12.4092 + 12.4092i −0.456480 + 0.456480i −0.897498 0.441018i \(-0.854617\pi\)
0.441018 + 0.897498i \(0.354617\pi\)
\(740\) −1.36902 2.32545i −0.0503262 0.0854851i
\(741\) 11.9035 + 11.9035i 0.437284 + 0.437284i
\(742\) −13.3993 7.66052i −0.491904 0.281227i
\(743\) 47.1053i 1.72812i 0.503385 + 0.864062i \(0.332088\pi\)
−0.503385 + 0.864062i \(0.667912\pi\)
\(744\) 3.96146 0.0503918i 0.145234 0.00184745i
\(745\) 3.61025i 0.132269i
\(746\) 10.9699 19.1879i 0.401638 0.702519i
\(747\) −7.48793 7.48793i −0.273969 0.273969i
\(748\) −1.03461 0.267841i −0.0378291 0.00979323i
\(749\) 1.60576 1.60576i 0.0586732 0.0586732i
\(750\) 2.25012 0.613156i 0.0821629 0.0223893i
\(751\) −16.2432 −0.592722 −0.296361 0.955076i \(-0.595773\pi\)
−0.296361 + 0.955076i \(0.595773\pi\)
\(752\) −24.1102 + 43.4454i −0.879208 + 1.58429i
\(753\) 1.36180 0.0496266
\(754\) −11.8693 + 3.23437i −0.432254 + 0.117789i
\(755\) −0.913605 + 0.913605i −0.0332495 + 0.0332495i
\(756\) −0.501238 + 1.93617i −0.0182298 + 0.0704179i
\(757\) 4.11102 + 4.11102i 0.149418 + 0.149418i 0.777858 0.628440i \(-0.216306\pi\)
−0.628440 + 0.777858i \(0.716306\pi\)
\(758\) 19.5408 34.1796i 0.709756 1.24146i
\(759\) 3.18098i 0.115462i
\(760\) 0.786993 + 0.767222i 0.0285472 + 0.0278301i
\(761\) 45.8114i 1.66066i 0.557272 + 0.830330i \(0.311848\pi\)
−0.557272 + 0.830330i \(0.688152\pi\)
\(762\) −4.57433 2.61519i −0.165710 0.0947385i
\(763\) 4.74644 + 4.74644i 0.171833 + 0.171833i
\(764\) 9.62321 5.66531i 0.348156 0.204964i
\(765\) −0.0524314 + 0.0524314i −0.00189566 + 0.00189566i
\(766\) −0.558887 2.05097i −0.0201934 0.0741046i
\(767\) −20.4394 −0.738026
\(768\) 15.5864 + 3.61460i 0.562424 + 0.130431i
\(769\) 48.3860 1.74484 0.872422 0.488753i \(-0.162548\pi\)
0.872422 + 0.488753i \(0.162548\pi\)
\(770\) 0.0732691 + 0.268879i 0.00264044 + 0.00968972i
\(771\) −10.0208 + 10.0208i −0.360889 + 0.360889i
\(772\) 14.0817 8.29005i 0.506810 0.298365i
\(773\) 12.3922 + 12.3922i 0.445715 + 0.445715i 0.893927 0.448212i \(-0.147939\pi\)
−0.448212 + 0.893927i \(0.647939\pi\)
\(774\) −5.73327 3.27777i −0.206078 0.117817i
\(775\) 6.96520i 0.250198i
\(776\) −4.45552 4.34359i −0.159944 0.155926i
\(777\) 8.15941i 0.292717i
\(778\) −24.2943 + 42.4941i −0.870994 + 1.52349i
\(779\) −9.01235 9.01235i −0.322901 0.322901i
\(780\) 0.593765 2.29358i 0.0212602 0.0821234i
\(781\) 9.35678 9.35678i 0.334812 0.334812i
\(782\) 1.63317 0.445038i 0.0584022 0.0159145i
\(783\) 1.21430 0.0433957
\(784\) −1.94096 + 3.49752i −0.0693202 + 0.124911i
\(785\) −2.93239 −0.104661
\(786\) −0.811465 + 0.221123i −0.0289440 + 0.00788720i
\(787\) 15.5433 15.5433i 0.554059 0.554059i −0.373551 0.927610i \(-0.621860\pi\)
0.927610 + 0.373551i \(0.121860\pi\)
\(788\) 21.7566 + 5.63237i 0.775047 + 0.200645i
\(789\) −14.3699 14.3699i −0.511581 0.511581i
\(790\) 0.936187 1.63752i 0.0333080 0.0582603i
\(791\) 16.0799i 0.571736i
\(792\) −3.37032 + 0.0428721i −0.119759 + 0.00152340i
\(793\) 61.0117i 2.16659i
\(794\) 28.1786 + 16.1100i 1.00002 + 0.571723i
\(795\) −1.27614 1.27614i −0.0452600 0.0452600i
\(796\) −2.16438 3.67646i −0.0767144 0.130309i
\(797\) −9.99655 + 9.99655i −0.354096 + 0.354096i −0.861631 0.507535i \(-0.830557\pi\)
0.507535 + 0.861631i \(0.330557\pi\)
\(798\) −0.873731 3.20637i −0.0309297 0.113504i
\(799\) 5.57000 0.197052
\(800\) −6.70286 + 27.3193i −0.236982 + 0.965884i
\(801\) 8.82635 0.311864
\(802\) 3.14463 + 11.5400i 0.111041 + 0.407491i
\(803\) −7.07717 + 7.07717i −0.249748 + 0.249748i
\(804\) 5.10411 + 8.66995i 0.180008 + 0.305766i
\(805\) −0.312118 0.312118i −0.0110007 0.0110007i
\(806\) 12.3193 + 7.04306i 0.433928 + 0.248081i
\(807\) 12.3456i 0.434584i
\(808\) −0.313350 24.6334i −0.0110236 0.866601i
\(809\) 55.0628i 1.93590i −0.251133 0.967952i \(-0.580803\pi\)
0.251133 0.967952i \(-0.419197\pi\)
\(810\) −0.116068 + 0.203020i −0.00407823 + 0.00713338i
\(811\) 12.2961 + 12.2961i 0.431773 + 0.431773i 0.889231 0.457458i \(-0.151240\pi\)
−0.457458 + 0.889231i \(0.651240\pi\)
\(812\) 2.35110 + 0.608656i 0.0825075 + 0.0213596i
\(813\) −17.4663 + 17.4663i −0.612571 + 0.612571i
\(814\) −13.2672 + 3.61531i −0.465017 + 0.126716i
\(815\) −1.00283 −0.0351277
\(816\) −0.493539 1.72439i −0.0172773 0.0603656i
\(817\) 10.9736 0.383919
\(818\) −3.95797 + 1.07854i −0.138387 + 0.0377103i
\(819\) −5.06549 + 5.06549i −0.177002 + 0.177002i
\(820\) −0.449552 + 1.73652i −0.0156990 + 0.0606419i
\(821\) 24.4022 + 24.4022i 0.851643 + 0.851643i 0.990336 0.138692i \(-0.0442899\pi\)
−0.138692 + 0.990336i \(0.544290\pi\)
\(822\) −10.5542 + 18.4607i −0.368120 + 0.643892i
\(823\) 20.7268i 0.722492i −0.932471 0.361246i \(-0.882351\pi\)
0.932471 0.361246i \(-0.117649\pi\)
\(824\) −25.4208 + 26.0759i −0.885576 + 0.908397i
\(825\) 5.92583i 0.206311i
\(826\) 3.50297 + 2.00269i 0.121884 + 0.0696824i
\(827\) 17.1915 + 17.1915i 0.597808 + 0.597808i 0.939729 0.341921i \(-0.111077\pi\)
−0.341921 + 0.939729i \(0.611077\pi\)
\(828\) 4.60059 2.70842i 0.159881 0.0941242i
\(829\) 6.26159 6.26159i 0.217474 0.217474i −0.589959 0.807433i \(-0.700856\pi\)
0.807433 + 0.589959i \(0.200856\pi\)
\(830\) −0.651083 2.38931i −0.0225994 0.0829341i
\(831\) −2.40314 −0.0833640
\(832\) 41.5416 + 39.4800i 1.44020 + 1.36872i
\(833\) 0.448406 0.0155364
\(834\) −7.67095 28.1504i −0.265623 0.974769i
\(835\) 1.79929 1.79929i 0.0622671 0.0622671i
\(836\) 4.82643 2.84138i 0.166926 0.0982713i
\(837\) −0.990445 0.990445i −0.0342348 0.0342348i
\(838\) −14.2894 8.16942i −0.493620 0.282208i
\(839\) 22.4991i 0.776754i 0.921501 + 0.388377i \(0.126964\pi\)
−0.921501 + 0.388377i \(0.873036\pi\)
\(840\) −0.326490 + 0.334903i −0.0112650 + 0.0115552i
\(841\) 27.5255i 0.949154i
\(842\) 12.0292 21.0407i 0.414553 0.725110i
\(843\) 1.25694 + 1.25694i 0.0432913 + 0.0432913i
\(844\) −4.92613 + 19.0286i −0.169565 + 0.654990i
\(845\) 4.48049 4.48049i 0.154134 0.154134i
\(846\) 16.9490 4.61858i 0.582719 0.158790i
\(847\) −9.57989 −0.329169
\(848\) 41.9702 12.0124i 1.44126 0.412506i
\(849\) −17.9038 −0.614457
\(850\) 3.04244 0.829060i 0.104355 0.0284365i
\(851\) 15.4008 15.4008i 0.527933 0.527933i
\(852\) 21.4993 + 5.56575i 0.736554 + 0.190680i
\(853\) 7.92257 + 7.92257i 0.271264 + 0.271264i 0.829609 0.558345i \(-0.188563\pi\)
−0.558345 + 0.829609i \(0.688563\pi\)
\(854\) −5.97802 + 10.4564i −0.204563 + 0.357809i
\(855\) 0.388585i 0.0132893i
\(856\) 0.0816977 + 6.42252i 0.00279237 + 0.219517i
\(857\) 8.87592i 0.303196i −0.988442 0.151598i \(-0.951558\pi\)
0.988442 0.151598i \(-0.0484419\pi\)
\(858\) −10.4809 5.99207i −0.357814 0.204566i
\(859\) 20.6928 + 20.6928i 0.706030 + 0.706030i 0.965698 0.259668i \(-0.0836130\pi\)
−0.259668 + 0.965698i \(0.583613\pi\)
\(860\) −0.783520 1.33090i −0.0267178 0.0453834i
\(861\) 3.83519 3.83519i 0.130703 0.130703i
\(862\) −8.70718 31.9531i −0.296568 1.08833i
\(863\) 45.9301 1.56348 0.781740 0.623605i \(-0.214333\pi\)
0.781740 + 0.623605i \(0.214333\pi\)
\(864\) −2.93164 4.83792i −0.0997364 0.164589i
\(865\) −2.78623 −0.0947346
\(866\) 6.41140 + 23.5282i 0.217868 + 0.799520i
\(867\) 11.8786 11.8786i 0.403420 0.403420i
\(868\) −1.42122 2.41412i −0.0482395 0.0819406i
\(869\) −6.79664 6.79664i −0.230560 0.230560i
\(870\) 0.246528 + 0.140943i 0.00835807 + 0.00477840i
\(871\) 36.0362i 1.22104i
\(872\) −18.9842 + 0.241489i −0.642887 + 0.00817784i
\(873\) 2.19995i 0.0744572i
\(874\) −4.40283 + 7.70114i −0.148928 + 0.260495i
\(875\) −1.16608 1.16608i −0.0394209 0.0394209i
\(876\) −16.2614 4.20976i −0.549421 0.142235i
\(877\) 1.95490 1.95490i 0.0660123 0.0660123i −0.673330 0.739342i \(-0.735137\pi\)
0.739342 + 0.673330i \(0.235137\pi\)
\(878\) −21.5261 + 5.86585i −0.726472 + 0.197963i
\(879\) −15.5414 −0.524197
\(880\) −0.689216 0.382484i −0.0232335 0.0128935i
\(881\) −11.8155 −0.398075 −0.199037 0.979992i \(-0.563782\pi\)
−0.199037 + 0.979992i \(0.563782\pi\)
\(882\) 1.36446 0.371814i 0.0459438 0.0125196i
\(883\) 22.8916 22.8916i 0.770362 0.770362i −0.207808 0.978170i \(-0.566633\pi\)
0.978170 + 0.207808i \(0.0666328\pi\)
\(884\) 1.61010 6.21945i 0.0541534 0.209183i
\(885\) 0.333620 + 0.333620i 0.0112145 + 0.0112145i
\(886\) −2.02557 + 3.54300i −0.0680504 + 0.119029i
\(887\) 2.71951i 0.0913123i −0.998957 0.0456562i \(-0.985462\pi\)
0.998957 0.0456562i \(-0.0145379\pi\)
\(888\) −16.5251 16.1099i −0.554545 0.540614i
\(889\) 3.72584i 0.124961i
\(890\) 1.79192 + 1.02446i 0.0600654 + 0.0343400i
\(891\) 0.842648 + 0.842648i 0.0282298 + 0.0282298i
\(892\) −16.9440 + 9.97515i −0.567327 + 0.333993i
\(893\) −20.6405 + 20.6405i −0.690708 + 0.690708i
\(894\) 8.11762 + 29.7896i 0.271494 + 0.996312i
\(895\) 3.85385 0.128820
\(896\) −3.25121 10.8365i −0.108615 0.362022i
\(897\) 19.1221 0.638469
\(898\) 11.2004 + 41.1024i 0.373761 + 1.37161i
\(899\) −1.20270 + 1.20270i −0.0401124 + 0.0401124i
\(900\) 8.57042 5.04551i 0.285681 0.168184i
\(901\) −3.46047 3.46047i −0.115285 0.115285i
\(902\) 7.93535 + 4.53672i 0.264218 + 0.151056i
\(903\) 4.66980i 0.155401i
\(904\) −32.5663 31.7482i −1.08314 1.05593i
\(905\) 1.33297i 0.0443094i
\(906\) −5.48427 + 9.59274i −0.182203 + 0.318697i
\(907\) −19.6178 19.6178i −0.651399 0.651399i 0.301931 0.953330i \(-0.402369\pi\)
−0.953330 + 0.301931i \(0.902369\pi\)
\(908\) −7.72467 + 29.8387i −0.256352 + 0.990232i
\(909\) −6.15886 + 6.15886i −0.204276 + 0.204276i
\(910\) −1.61634 + 0.440450i −0.0535810 + 0.0146008i
\(911\) 40.6590 1.34709 0.673547 0.739145i \(-0.264770\pi\)
0.673547 + 0.739145i \(0.264770\pi\)
\(912\) 8.21887 + 4.56110i 0.272154 + 0.151033i
\(913\) −12.6194 −0.417640
\(914\) −20.8813 + 5.69013i −0.690692 + 0.188213i
\(915\) −0.995856 + 0.995856i −0.0329220 + 0.0329220i
\(916\) −50.1126 12.9732i −1.65577 0.428647i
\(917\) 0.420527 + 0.420527i 0.0138870 + 0.0138870i
\(918\) −0.314740 + 0.550523i −0.0103880 + 0.0181700i
\(919\) 52.2631i 1.72400i −0.506907 0.862001i \(-0.669211\pi\)
0.506907 0.862001i \(-0.330789\pi\)
\(920\) 1.24837 0.0158799i 0.0411576 0.000523545i
\(921\) 25.1954i 0.830216i
\(922\) −5.44501 3.11297i −0.179322 0.102520i
\(923\) 56.2473 + 56.2473i 1.85140 + 1.85140i
\(924\) 1.20914 + 2.05388i 0.0397779 + 0.0675676i
\(925\) 28.6901 28.6901i 0.943324 0.943324i
\(926\) −9.72356 35.6829i −0.319536 1.17261i
\(927\) 12.8752 0.422878
\(928\) −5.87471 + 3.55991i −0.192847 + 0.116860i
\(929\) 8.53368 0.279981 0.139991 0.990153i \(-0.455293\pi\)
0.139991 + 0.990153i \(0.455293\pi\)
\(930\) −0.0861203 0.316039i −0.00282400 0.0103633i
\(931\) −1.66164 + 1.66164i −0.0544580 + 0.0544580i
\(932\) −20.7153 35.1875i −0.678553 1.15260i
\(933\) 9.44570 + 9.44570i 0.309238 + 0.309238i
\(934\) −15.6094 8.92407i −0.510755 0.292004i
\(935\) 0.0883623i 0.00288976i
\(936\) −0.257721 20.2603i −0.00842389 0.662229i
\(937\) 9.87941i 0.322746i 0.986893 + 0.161373i \(0.0515923\pi\)
−0.986893 + 0.161373i \(0.948408\pi\)
\(938\) 3.53088 6.17599i 0.115287 0.201653i
\(939\) −10.9855 10.9855i −0.358498 0.358498i
\(940\) 3.97705 + 1.02958i 0.129717 + 0.0335813i
\(941\) 15.4288 15.4288i 0.502963 0.502963i −0.409394 0.912358i \(-0.634260\pi\)
0.912358 + 0.409394i \(0.134260\pi\)
\(942\) −24.1962 + 6.59345i −0.788356 + 0.214826i
\(943\) −14.4777 −0.471460
\(944\) −10.9723 + 3.14038i −0.357117 + 0.102211i
\(945\) 0.165361 0.00537921
\(946\) −7.59313 + 2.06912i −0.246874 + 0.0672728i
\(947\) 10.3348 10.3348i 0.335837 0.335837i −0.518961 0.854798i \(-0.673681\pi\)
0.854798 + 0.518961i \(0.173681\pi\)
\(948\) 4.04289 15.6168i 0.131307 0.507210i
\(949\) −42.5437 42.5437i −1.38103 1.38103i
\(950\) −8.20201 + 14.3464i −0.266108 + 0.465460i
\(951\) 11.1862i 0.362736i
\(952\) −0.885333 + 0.908147i −0.0286938 + 0.0294332i
\(953\) 21.8196i 0.706807i −0.935471 0.353404i \(-0.885024\pi\)
0.935471 0.353404i \(-0.114976\pi\)
\(954\) −13.3993 7.66052i −0.433818 0.248019i
\(955\) −0.652869 0.652869i −0.0211263 0.0211263i
\(956\) −39.2483 + 23.1060i −1.26938 + 0.747300i
\(957\) 1.02323 1.02323i 0.0330764 0.0330764i
\(958\) 9.22905 + 33.8682i 0.298177 + 1.09423i
\(959\) 15.0365 0.485553
\(960\) −0.0336503 1.32246i −0.00108606 0.0426823i
\(961\) −29.0380 −0.936711
\(962\) −21.7330 79.7546i −0.700701 2.57139i
\(963\) 1.60576 1.60576i 0.0517449 0.0517449i
\(964\) −12.1400 + 7.14697i −0.391003 + 0.230188i
\(965\) −0.955344 0.955344i −0.0307536 0.0307536i
\(966\) −3.27720 1.87361i −0.105442 0.0602825i
\(967\) 17.9595i 0.577540i −0.957399 0.288770i \(-0.906754\pi\)
0.957399 0.288770i \(-0.0932463\pi\)
\(968\) 18.9145 19.4019i 0.607936 0.623602i
\(969\) 1.05372i 0.0338502i
\(970\) −0.255345 + 0.446634i −0.00819865 + 0.0143405i
\(971\) −35.0162 35.0162i −1.12372 1.12372i −0.991177 0.132548i \(-0.957684\pi\)
−0.132548 0.991177i \(-0.542316\pi\)
\(972\) −0.501238 + 1.93617i −0.0160772 + 0.0621027i
\(973\) −14.5884 + 14.5884i −0.467683 + 0.467683i
\(974\) 17.2261 4.69410i 0.551960 0.150409i
\(975\) 35.6225 1.14083
\(976\) −9.37404 32.7522i −0.300056 1.04837i
\(977\) 42.2799 1.35265 0.676327 0.736601i \(-0.263571\pi\)
0.676327 + 0.736601i \(0.263571\pi\)
\(978\) −8.27477 + 2.25486i −0.264598 + 0.0721026i
\(979\) 7.43750 7.43750i 0.237704 0.237704i
\(980\) 0.320168 + 0.0828854i 0.0102274 + 0.00264768i
\(981\) 4.74644 + 4.74644i 0.151542 + 0.151542i
\(982\) 13.6902 23.9460i 0.436872 0.764149i
\(983\) 31.1172i 0.992484i 0.868184 + 0.496242i \(0.165287\pi\)
−0.868184 + 0.496242i \(0.834713\pi\)
\(984\) 0.195126 + 15.3395i 0.00622040 + 0.489005i
\(985\) 1.85815i 0.0592057i
\(986\) 0.668503 + 0.382190i 0.0212895 + 0.0121714i
\(987\) −8.78351 8.78351i −0.279582 0.279582i
\(988\) 17.0807 + 29.0136i 0.543409 + 0.923045i
\(989\) 8.81421 8.81421i 0.280276 0.280276i
\(990\) 0.0732691 + 0.268879i 0.00232865 + 0.00854553i
\(991\) 4.94685 0.157142 0.0785709 0.996909i \(-0.474964\pi\)
0.0785709 + 0.996909i \(0.474964\pi\)
\(992\) 7.69533 + 1.88807i 0.244327 + 0.0599462i
\(993\) 10.2304 0.324651
\(994\) −4.12863 15.1510i −0.130952 0.480561i
\(995\) −0.249423 + 0.249423i −0.00790722 + 0.00790722i
\(996\) −10.7447 18.2511i −0.340458 0.578309i
\(997\) −22.2296 22.2296i −0.704018 0.704018i 0.261252 0.965271i \(-0.415864\pi\)
−0.965271 + 0.261252i \(0.915864\pi\)
\(998\) 46.3550 + 26.5017i 1.46734 + 0.838895i
\(999\) 8.15941i 0.258152i
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 336.2.w.b.85.7 28
4.3 odd 2 1344.2.w.b.1009.11 28
8.3 odd 2 2688.2.w.c.2017.4 28
8.5 even 2 2688.2.w.d.2017.11 28
16.3 odd 4 1344.2.w.b.337.11 28
16.5 even 4 2688.2.w.d.673.11 28
16.11 odd 4 2688.2.w.c.673.4 28
16.13 even 4 inner 336.2.w.b.253.7 yes 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
336.2.w.b.85.7 28 1.1 even 1 trivial
336.2.w.b.253.7 yes 28 16.13 even 4 inner
1344.2.w.b.337.11 28 16.3 odd 4
1344.2.w.b.1009.11 28 4.3 odd 2
2688.2.w.c.673.4 28 16.11 odd 4
2688.2.w.c.2017.4 28 8.3 odd 2
2688.2.w.d.673.11 28 16.5 even 4
2688.2.w.d.2017.11 28 8.5 even 2