Properties

Label 1110.2.e.c.739.8
Level $1110$
Weight $2$
Character 1110.739
Analytic conductor $8.863$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1110,2,Mod(739,1110)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1110, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1110.739");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1110.e (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: \(8.86339462436\)
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: \( x^{16} - 2 x^{15} + 2 x^{14} + 8 x^{13} + 138 x^{12} - 220 x^{11} + 196 x^{10} + 744 x^{9} + 4241 x^{8} - 3018 x^{7} + 658 x^{6} - 1584 x^{5} + 16372 x^{4} - 18840 x^{3} + 10952 x^{2} + \cdots + 64 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{6} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 739.8
Root \(-2.20888 + 2.20888i\) of defining polynomial
Character \(\chi\) \(=\) 1110.739
Dual form 1110.2.e.c.739.16

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} +(2.20888 + 0.347650i) q^{5} +1.00000i q^{6} +2.08112i q^{7} -1.00000 q^{8} -1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} +(2.20888 + 0.347650i) q^{5} +1.00000i q^{6} +2.08112i q^{7} -1.00000 q^{8} -1.00000 q^{9} +(-2.20888 - 0.347650i) q^{10} +6.52056 q^{11} -1.00000i q^{12} +1.53583 q^{13} -2.08112i q^{14} +(0.347650 - 2.20888i) q^{15} +1.00000 q^{16} -5.28561 q^{17} +1.00000 q^{18} -4.07548i q^{19} +(2.20888 + 0.347650i) q^{20} +2.08112 q^{21} -6.52056 q^{22} +1.43562 q^{23} +1.00000i q^{24} +(4.75828 + 1.53583i) q^{25} -1.53583 q^{26} +1.00000i q^{27} +2.08112i q^{28} +6.89042i q^{29} +(-0.347650 + 2.20888i) q^{30} +8.19513i q^{31} -1.00000 q^{32} -6.52056i q^{33} +5.28561 q^{34} +(-0.723502 + 4.59695i) q^{35} -1.00000 q^{36} +(-0.927865 - 6.01158i) q^{37} +4.07548i q^{38} -1.53583i q^{39} +(-2.20888 - 0.347650i) q^{40} +6.76262 q^{41} -2.08112 q^{42} -4.46572 q^{43} +6.52056 q^{44} +(-2.20888 - 0.347650i) q^{45} -1.43562 q^{46} +9.83376i q^{47} -1.00000i q^{48} +2.66892 q^{49} +(-4.75828 - 1.53583i) q^{50} +5.28561i q^{51} +1.53583 q^{52} +6.51769i q^{53} -1.00000i q^{54} +(14.4031 + 2.26687i) q^{55} -2.08112i q^{56} -4.07548 q^{57} -6.89042i q^{58} -11.0304i q^{59} +(0.347650 - 2.20888i) q^{60} -4.91211i q^{61} -8.19513i q^{62} -2.08112i q^{63} +1.00000 q^{64} +(3.39246 + 0.533931i) q^{65} +6.52056i q^{66} -11.8535i q^{67} -5.28561 q^{68} -1.43562i q^{69} +(0.723502 - 4.59695i) q^{70} -6.07887 q^{71} +1.00000 q^{72} -13.6398i q^{73} +(0.927865 + 6.01158i) q^{74} +(1.53583 - 4.75828i) q^{75} -4.07548i q^{76} +13.5701i q^{77} +1.53583i q^{78} +2.76246i q^{79} +(2.20888 + 0.347650i) q^{80} +1.00000 q^{81} -6.76262 q^{82} +15.8823i q^{83} +2.08112 q^{84} +(-11.6753 - 1.83754i) q^{85} +4.46572 q^{86} +6.89042 q^{87} -6.52056 q^{88} +7.15877i q^{89} +(2.20888 + 0.347650i) q^{90} +3.19625i q^{91} +1.43562 q^{92} +8.19513 q^{93} -9.83376i q^{94} +(1.41684 - 9.00224i) q^{95} +1.00000i q^{96} +19.0806 q^{97} -2.66892 q^{98} -6.52056 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 16 q^{2} + 16 q^{4} - 2 q^{5} - 16 q^{8} - 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 16 q^{2} + 16 q^{4} - 2 q^{5} - 16 q^{8} - 16 q^{9} + 2 q^{10} + 2 q^{11} + 6 q^{15} + 16 q^{16} - 38 q^{17} + 16 q^{18} - 2 q^{20} + 6 q^{21} - 2 q^{22} - 20 q^{23} - 4 q^{25} - 6 q^{30} - 16 q^{32} + 38 q^{34} - 10 q^{35} - 16 q^{36} - 4 q^{37} + 2 q^{40} - 6 q^{41} - 6 q^{42} - 2 q^{43} + 2 q^{44} + 2 q^{45} + 20 q^{46} - 18 q^{49} + 4 q^{50} + 20 q^{55} + 16 q^{57} + 6 q^{60} + 16 q^{64} + 12 q^{65} - 38 q^{68} + 10 q^{70} - 24 q^{71} + 16 q^{72} + 4 q^{74} - 2 q^{80} + 16 q^{81} + 6 q^{82} + 6 q^{84} + 2 q^{86} + 2 q^{87} - 2 q^{88} - 2 q^{90} - 20 q^{92} + 22 q^{93} - 16 q^{95} + 38 q^{97} + 18 q^{98} - 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).

\(n\) \(371\) \(631\) \(667\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 1.00000i 0.577350i
\(4\) 1.00000 0.500000
\(5\) 2.20888 + 0.347650i 0.987840 + 0.155474i
\(6\) 1.00000i 0.408248i
\(7\) 2.08112i 0.786591i 0.919412 + 0.393295i \(0.128665\pi\)
−0.919412 + 0.393295i \(0.871335\pi\)
\(8\) −1.00000 −0.353553
\(9\) −1.00000 −0.333333
\(10\) −2.20888 0.347650i −0.698508 0.109936i
\(11\) 6.52056 1.96602 0.983011 0.183545i \(-0.0587573\pi\)
0.983011 + 0.183545i \(0.0587573\pi\)
\(12\) 1.00000i 0.288675i
\(13\) 1.53583 0.425963 0.212981 0.977056i \(-0.431683\pi\)
0.212981 + 0.977056i \(0.431683\pi\)
\(14\) 2.08112i 0.556204i
\(15\) 0.347650 2.20888i 0.0897627 0.570330i
\(16\) 1.00000 0.250000
\(17\) −5.28561 −1.28195 −0.640974 0.767562i \(-0.721470\pi\)
−0.640974 + 0.767562i \(0.721470\pi\)
\(18\) 1.00000 0.235702
\(19\) 4.07548i 0.934979i −0.883998 0.467490i \(-0.845158\pi\)
0.883998 0.467490i \(-0.154842\pi\)
\(20\) 2.20888 + 0.347650i 0.493920 + 0.0777368i
\(21\) 2.08112 0.454138
\(22\) −6.52056 −1.39019
\(23\) 1.43562 0.299347 0.149673 0.988736i \(-0.452178\pi\)
0.149673 + 0.988736i \(0.452178\pi\)
\(24\) 1.00000i 0.204124i
\(25\) 4.75828 + 1.53583i 0.951656 + 0.307166i
\(26\) −1.53583 −0.301201
\(27\) 1.00000i 0.192450i
\(28\) 2.08112i 0.393295i
\(29\) 6.89042i 1.27952i 0.768575 + 0.639760i \(0.220966\pi\)
−0.768575 + 0.639760i \(0.779034\pi\)
\(30\) −0.347650 + 2.20888i −0.0634718 + 0.403284i
\(31\) 8.19513i 1.47189i 0.677042 + 0.735944i \(0.263261\pi\)
−0.677042 + 0.735944i \(0.736739\pi\)
\(32\) −1.00000 −0.176777
\(33\) 6.52056i 1.13508i
\(34\) 5.28561 0.906475
\(35\) −0.723502 + 4.59695i −0.122294 + 0.777026i
\(36\) −1.00000 −0.166667
\(37\) −0.927865 6.01158i −0.152540 0.988297i
\(38\) 4.07548i 0.661130i
\(39\) 1.53583i 0.245930i
\(40\) −2.20888 0.347650i −0.349254 0.0549682i
\(41\) 6.76262 1.05614 0.528072 0.849200i \(-0.322915\pi\)
0.528072 + 0.849200i \(0.322915\pi\)
\(42\) −2.08112 −0.321124
\(43\) −4.46572 −0.681016 −0.340508 0.940242i \(-0.610599\pi\)
−0.340508 + 0.940242i \(0.610599\pi\)
\(44\) 6.52056 0.983011
\(45\) −2.20888 0.347650i −0.329280 0.0518245i
\(46\) −1.43562 −0.211670
\(47\) 9.83376i 1.43440i 0.696867 + 0.717201i \(0.254577\pi\)
−0.696867 + 0.717201i \(0.745423\pi\)
\(48\) 1.00000i 0.144338i
\(49\) 2.66892 0.381275
\(50\) −4.75828 1.53583i −0.672922 0.217199i
\(51\) 5.28561i 0.740133i
\(52\) 1.53583 0.212981
\(53\) 6.51769i 0.895273i 0.894216 + 0.447637i \(0.147734\pi\)
−0.894216 + 0.447637i \(0.852266\pi\)
\(54\) 1.00000i 0.136083i
\(55\) 14.4031 + 2.26687i 1.94212 + 0.305665i
\(56\) 2.08112i 0.278102i
\(57\) −4.07548 −0.539811
\(58\) 6.89042i 0.904757i
\(59\) 11.0304i 1.43603i −0.696027 0.718016i \(-0.745051\pi\)
0.696027 0.718016i \(-0.254949\pi\)
\(60\) 0.347650 2.20888i 0.0448814 0.285165i
\(61\) 4.91211i 0.628931i −0.949269 0.314465i \(-0.898175\pi\)
0.949269 0.314465i \(-0.101825\pi\)
\(62\) 8.19513i 1.04078i
\(63\) 2.08112i 0.262197i
\(64\) 1.00000 0.125000
\(65\) 3.39246 + 0.533931i 0.420783 + 0.0662260i
\(66\) 6.52056i 0.802625i
\(67\) 11.8535i 1.44813i −0.689731 0.724066i \(-0.742271\pi\)
0.689731 0.724066i \(-0.257729\pi\)
\(68\) −5.28561 −0.640974
\(69\) 1.43562i 0.172828i
\(70\) 0.723502 4.59695i 0.0864750 0.549440i
\(71\) −6.07887 −0.721430 −0.360715 0.932676i \(-0.617467\pi\)
−0.360715 + 0.932676i \(0.617467\pi\)
\(72\) 1.00000 0.117851
\(73\) 13.6398i 1.59642i −0.602379 0.798211i \(-0.705780\pi\)
0.602379 0.798211i \(-0.294220\pi\)
\(74\) 0.927865 + 6.01158i 0.107862 + 0.698832i
\(75\) 1.53583 4.75828i 0.177342 0.549439i
\(76\) 4.07548i 0.467490i
\(77\) 13.5701i 1.54646i
\(78\) 1.53583i 0.173899i
\(79\) 2.76246i 0.310801i 0.987852 + 0.155400i \(0.0496667\pi\)
−0.987852 + 0.155400i \(0.950333\pi\)
\(80\) 2.20888 + 0.347650i 0.246960 + 0.0388684i
\(81\) 1.00000 0.111111
\(82\) −6.76262 −0.746806
\(83\) 15.8823i 1.74331i 0.490117 + 0.871657i \(0.336954\pi\)
−0.490117 + 0.871657i \(0.663046\pi\)
\(84\) 2.08112 0.227069
\(85\) −11.6753 1.83754i −1.26636 0.199309i
\(86\) 4.46572 0.481551
\(87\) 6.89042 0.738731
\(88\) −6.52056 −0.695094
\(89\) 7.15877i 0.758828i 0.925227 + 0.379414i \(0.123874\pi\)
−0.925227 + 0.379414i \(0.876126\pi\)
\(90\) 2.20888 + 0.347650i 0.232836 + 0.0366455i
\(91\) 3.19625i 0.335058i
\(92\) 1.43562 0.149673
\(93\) 8.19513 0.849795
\(94\) 9.83376i 1.01427i
\(95\) 1.41684 9.00224i 0.145365 0.923610i
\(96\) 1.00000i 0.102062i
\(97\) 19.0806 1.93734 0.968671 0.248348i \(-0.0798877\pi\)
0.968671 + 0.248348i \(0.0798877\pi\)
\(98\) −2.66892 −0.269602
\(99\) −6.52056 −0.655341
\(100\) 4.75828 + 1.53583i 0.475828 + 0.153583i
\(101\) 1.62639 0.161832 0.0809161 0.996721i \(-0.474215\pi\)
0.0809161 + 0.996721i \(0.474215\pi\)
\(102\) 5.28561i 0.523353i
\(103\) −3.70274 −0.364842 −0.182421 0.983220i \(-0.558393\pi\)
−0.182421 + 0.983220i \(0.558393\pi\)
\(104\) −1.53583 −0.150601
\(105\) 4.59695 + 0.723502i 0.448616 + 0.0706065i
\(106\) 6.51769i 0.633054i
\(107\) 6.80165i 0.657541i −0.944410 0.328770i \(-0.893366\pi\)
0.944410 0.328770i \(-0.106634\pi\)
\(108\) 1.00000i 0.0962250i
\(109\) 17.9512i 1.71941i −0.510792 0.859704i \(-0.670648\pi\)
0.510792 0.859704i \(-0.329352\pi\)
\(110\) −14.4031 2.26687i −1.37328 0.216138i
\(111\) −6.01158 + 0.927865i −0.570594 + 0.0880690i
\(112\) 2.08112i 0.196648i
\(113\) 15.6346 1.47078 0.735392 0.677642i \(-0.236998\pi\)
0.735392 + 0.677642i \(0.236998\pi\)
\(114\) 4.07548 0.381704
\(115\) 3.17110 + 0.499091i 0.295707 + 0.0465405i
\(116\) 6.89042i 0.639760i
\(117\) −1.53583 −0.141988
\(118\) 11.0304i 1.01543i
\(119\) 11.0000i 1.00837i
\(120\) −0.347650 + 2.20888i −0.0317359 + 0.201642i
\(121\) 31.5177 2.86524
\(122\) 4.91211i 0.444721i
\(123\) 6.76262i 0.609765i
\(124\) 8.19513i 0.735944i
\(125\) 9.97653 + 5.04668i 0.892328 + 0.451388i
\(126\) 2.08112i 0.185401i
\(127\) 0.759690i 0.0674116i −0.999432 0.0337058i \(-0.989269\pi\)
0.999432 0.0337058i \(-0.0107309\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 4.46572i 0.393185i
\(130\) −3.39246 0.533931i −0.297539 0.0468288i
\(131\) 17.8737i 1.56163i −0.624763 0.780815i \(-0.714804\pi\)
0.624763 0.780815i \(-0.285196\pi\)
\(132\) 6.52056i 0.567542i
\(133\) 8.48158 0.735446
\(134\) 11.8535i 1.02398i
\(135\) −0.347650 + 2.20888i −0.0299209 + 0.190110i
\(136\) 5.28561 0.453237
\(137\) 7.88841i 0.673952i 0.941513 + 0.336976i \(0.109404\pi\)
−0.941513 + 0.336976i \(0.890596\pi\)
\(138\) 1.43562i 0.122208i
\(139\) −17.6834 −1.49989 −0.749943 0.661502i \(-0.769919\pi\)
−0.749943 + 0.661502i \(0.769919\pi\)
\(140\) −0.723502 + 4.59695i −0.0611471 + 0.388513i
\(141\) 9.83376 0.828152
\(142\) 6.07887 0.510128
\(143\) 10.0145 0.837452
\(144\) −1.00000 −0.0833333
\(145\) −2.39545 + 15.2201i −0.198932 + 1.26396i
\(146\) 13.6398i 1.12884i
\(147\) 2.66892i 0.220129i
\(148\) −0.927865 6.01158i −0.0762700 0.494149i
\(149\) −0.543289 −0.0445080 −0.0222540 0.999752i \(-0.507084\pi\)
−0.0222540 + 0.999752i \(0.507084\pi\)
\(150\) −1.53583 + 4.75828i −0.125400 + 0.388512i
\(151\) 7.98733 0.650000 0.325000 0.945714i \(-0.394636\pi\)
0.325000 + 0.945714i \(0.394636\pi\)
\(152\) 4.07548i 0.330565i
\(153\) 5.28561 0.427316
\(154\) 13.5701i 1.09351i
\(155\) −2.84903 + 18.1020i −0.228840 + 1.45399i
\(156\) 1.53583i 0.122965i
\(157\) 11.2296i 0.896216i 0.893979 + 0.448108i \(0.147902\pi\)
−0.893979 + 0.448108i \(0.852098\pi\)
\(158\) 2.76246i 0.219769i
\(159\) 6.51769 0.516886
\(160\) −2.20888 0.347650i −0.174627 0.0274841i
\(161\) 2.98769i 0.235463i
\(162\) −1.00000 −0.0785674
\(163\) −8.05362 −0.630808 −0.315404 0.948957i \(-0.602140\pi\)
−0.315404 + 0.948957i \(0.602140\pi\)
\(164\) 6.76262 0.528072
\(165\) 2.26687 14.4031i 0.176476 1.12128i
\(166\) 15.8823i 1.23271i
\(167\) −12.7129 −0.983753 −0.491876 0.870665i \(-0.663689\pi\)
−0.491876 + 0.870665i \(0.663689\pi\)
\(168\) −2.08112 −0.160562
\(169\) −10.6412 −0.818556
\(170\) 11.6753 + 1.83754i 0.895452 + 0.140933i
\(171\) 4.07548i 0.311660i
\(172\) −4.46572 −0.340508
\(173\) 1.56245i 0.118791i −0.998235 0.0593955i \(-0.981083\pi\)
0.998235 0.0593955i \(-0.0189173\pi\)
\(174\) −6.89042 −0.522362
\(175\) −3.19625 + 9.90257i −0.241614 + 0.748564i
\(176\) 6.52056 0.491506
\(177\) −11.0304 −0.829093
\(178\) 7.15877i 0.536572i
\(179\) 12.2571i 0.916135i 0.888917 + 0.458067i \(0.151458\pi\)
−0.888917 + 0.458067i \(0.848542\pi\)
\(180\) −2.20888 0.347650i −0.164640 0.0259123i
\(181\) −18.8971 −1.40461 −0.702305 0.711876i \(-0.747846\pi\)
−0.702305 + 0.711876i \(0.747846\pi\)
\(182\) 3.19625i 0.236922i
\(183\) −4.91211 −0.363113
\(184\) −1.43562 −0.105835
\(185\) 0.0403832 13.6014i 0.00296903 0.999996i
\(186\) −8.19513 −0.600896
\(187\) −34.4651 −2.52034
\(188\) 9.83376i 0.717201i
\(189\) −2.08112 −0.151379
\(190\) −1.41684 + 9.00224i −0.102788 + 0.653091i
\(191\) 8.66659i 0.627093i 0.949573 + 0.313546i \(0.101517\pi\)
−0.949573 + 0.313546i \(0.898483\pi\)
\(192\) 1.00000i 0.0721688i
\(193\) 14.0122 1.00862 0.504311 0.863522i \(-0.331747\pi\)
0.504311 + 0.863522i \(0.331747\pi\)
\(194\) −19.0806 −1.36991
\(195\) 0.533931 3.39246i 0.0382356 0.242939i
\(196\) 2.66892 0.190637
\(197\) 20.7652i 1.47946i −0.672903 0.739731i \(-0.734953\pi\)
0.672903 0.739731i \(-0.265047\pi\)
\(198\) 6.52056 0.463396
\(199\) 18.3572i 1.30131i 0.759373 + 0.650655i \(0.225506\pi\)
−0.759373 + 0.650655i \(0.774494\pi\)
\(200\) −4.75828 1.53583i −0.336461 0.108600i
\(201\) −11.8535 −0.836080
\(202\) −1.62639 −0.114433
\(203\) −14.3398 −1.00646
\(204\) 5.28561i 0.370067i
\(205\) 14.9378 + 2.35102i 1.04330 + 0.164202i
\(206\) 3.70274 0.257982
\(207\) −1.43562 −0.0997822
\(208\) 1.53583 0.106491
\(209\) 26.5744i 1.83819i
\(210\) −4.59695 0.723502i −0.317220 0.0499264i
\(211\) −1.37092 −0.0943781 −0.0471891 0.998886i \(-0.515026\pi\)
−0.0471891 + 0.998886i \(0.515026\pi\)
\(212\) 6.51769i 0.447637i
\(213\) 6.07887i 0.416518i
\(214\) 6.80165i 0.464952i
\(215\) −9.86422 1.55250i −0.672735 0.105880i
\(216\) 1.00000i 0.0680414i
\(217\) −17.0551 −1.15777
\(218\) 17.9512i 1.21581i
\(219\) −13.6398 −0.921694
\(220\) 14.4031 + 2.26687i 0.971058 + 0.152832i
\(221\) −8.11780 −0.546062
\(222\) 6.01158 0.927865i 0.403471 0.0622742i
\(223\) 10.4991i 0.703073i −0.936174 0.351537i \(-0.885659\pi\)
0.936174 0.351537i \(-0.114341\pi\)
\(224\) 2.08112i 0.139051i
\(225\) −4.75828 1.53583i −0.317219 0.102389i
\(226\) −15.6346 −1.04000
\(227\) −23.4274 −1.55493 −0.777465 0.628927i \(-0.783495\pi\)
−0.777465 + 0.628927i \(0.783495\pi\)
\(228\) −4.07548 −0.269905
\(229\) −17.8860 −1.18194 −0.590969 0.806694i \(-0.701254\pi\)
−0.590969 + 0.806694i \(0.701254\pi\)
\(230\) −3.17110 0.499091i −0.209096 0.0329091i
\(231\) 13.5701 0.892846
\(232\) 6.89042i 0.452379i
\(233\) 4.01113i 0.262778i −0.991331 0.131389i \(-0.958056\pi\)
0.991331 0.131389i \(-0.0419437\pi\)
\(234\) 1.53583 0.100400
\(235\) −3.41870 + 21.7216i −0.223012 + 1.41696i
\(236\) 11.0304i 0.718016i
\(237\) 2.76246 0.179441
\(238\) 11.0000i 0.713025i
\(239\) 8.70690i 0.563203i 0.959532 + 0.281601i \(0.0908655\pi\)
−0.959532 + 0.281601i \(0.909134\pi\)
\(240\) 0.347650 2.20888i 0.0224407 0.142582i
\(241\) 15.6443i 1.00774i −0.863781 0.503868i \(-0.831910\pi\)
0.863781 0.503868i \(-0.168090\pi\)
\(242\) −31.5177 −2.02603
\(243\) 1.00000i 0.0641500i
\(244\) 4.91211i 0.314465i
\(245\) 5.89533 + 0.927850i 0.376639 + 0.0592782i
\(246\) 6.76262i 0.431169i
\(247\) 6.25925i 0.398266i
\(248\) 8.19513i 0.520391i
\(249\) 15.8823 1.00650
\(250\) −9.97653 5.04668i −0.630971 0.319180i
\(251\) 9.35179i 0.590280i −0.955454 0.295140i \(-0.904634\pi\)
0.955454 0.295140i \(-0.0953662\pi\)
\(252\) 2.08112i 0.131098i
\(253\) 9.36102 0.588522
\(254\) 0.759690i 0.0476672i
\(255\) −1.83754 + 11.6753i −0.115071 + 0.731133i
\(256\) 1.00000 0.0625000
\(257\) 11.5996 0.723565 0.361782 0.932263i \(-0.382168\pi\)
0.361782 + 0.932263i \(0.382168\pi\)
\(258\) 4.46572i 0.278023i
\(259\) 12.5108 1.93100i 0.777386 0.119987i
\(260\) 3.39246 + 0.533931i 0.210392 + 0.0331130i
\(261\) 6.89042i 0.426507i
\(262\) 17.8737i 1.10424i
\(263\) 1.31327i 0.0809797i 0.999180 + 0.0404898i \(0.0128918\pi\)
−0.999180 + 0.0404898i \(0.987108\pi\)
\(264\) 6.52056i 0.401313i
\(265\) −2.26587 + 14.3968i −0.139191 + 0.884387i
\(266\) −8.48158 −0.520039
\(267\) 7.15877 0.438109
\(268\) 11.8535i 0.724066i
\(269\) −16.7383 −1.02055 −0.510277 0.860010i \(-0.670457\pi\)
−0.510277 + 0.860010i \(0.670457\pi\)
\(270\) 0.347650 2.20888i 0.0211573 0.134428i
\(271\) −27.8757 −1.69333 −0.846663 0.532130i \(-0.821392\pi\)
−0.846663 + 0.532130i \(0.821392\pi\)
\(272\) −5.28561 −0.320487
\(273\) 3.19625 0.193446
\(274\) 7.88841i 0.476556i
\(275\) 31.0266 + 10.0145i 1.87098 + 0.603896i
\(276\) 1.43562i 0.0864139i
\(277\) −18.0505 −1.08455 −0.542275 0.840201i \(-0.682437\pi\)
−0.542275 + 0.840201i \(0.682437\pi\)
\(278\) 17.6834 1.06058
\(279\) 8.19513i 0.490629i
\(280\) 0.723502 4.59695i 0.0432375 0.274720i
\(281\) 3.12679i 0.186528i −0.995641 0.0932642i \(-0.970270\pi\)
0.995641 0.0932642i \(-0.0297301\pi\)
\(282\) −9.83376 −0.585592
\(283\) 13.1469 0.781502 0.390751 0.920496i \(-0.372215\pi\)
0.390751 + 0.920496i \(0.372215\pi\)
\(284\) −6.07887 −0.360715
\(285\) −9.00224 1.41684i −0.533247 0.0839263i
\(286\) −10.0145 −0.592168
\(287\) 14.0738i 0.830753i
\(288\) 1.00000 0.0589256
\(289\) 10.9377 0.643392
\(290\) 2.39545 15.2201i 0.140666 0.893755i
\(291\) 19.0806i 1.11852i
\(292\) 13.6398i 0.798211i
\(293\) 17.8889i 1.04508i 0.852615 + 0.522540i \(0.175015\pi\)
−0.852615 + 0.522540i \(0.824985\pi\)
\(294\) 2.66892i 0.155655i
\(295\) 3.83470 24.3647i 0.223265 1.41857i
\(296\) 0.927865 + 6.01158i 0.0539310 + 0.349416i
\(297\) 6.52056i 0.378361i
\(298\) 0.543289 0.0314719
\(299\) 2.20486 0.127510
\(300\) 1.53583 4.75828i 0.0886712 0.274719i
\(301\) 9.29371i 0.535681i
\(302\) −7.98733 −0.459619
\(303\) 1.62639i 0.0934338i
\(304\) 4.07548i 0.233745i
\(305\) 1.70769 10.8502i 0.0977821 0.621283i
\(306\) −5.28561 −0.302158
\(307\) 21.1435i 1.20672i −0.797467 0.603362i \(-0.793827\pi\)
0.797467 0.603362i \(-0.206173\pi\)
\(308\) 13.5701i 0.773228i
\(309\) 3.70274i 0.210642i
\(310\) 2.84903 18.1020i 0.161814 1.02813i
\(311\) 25.3383i 1.43680i 0.695629 + 0.718401i \(0.255126\pi\)
−0.695629 + 0.718401i \(0.744874\pi\)
\(312\) 1.53583i 0.0869493i
\(313\) 15.2774 0.863532 0.431766 0.901986i \(-0.357891\pi\)
0.431766 + 0.901986i \(0.357891\pi\)
\(314\) 11.2296i 0.633720i
\(315\) 0.723502 4.59695i 0.0407647 0.259009i
\(316\) 2.76246i 0.155400i
\(317\) 26.3718i 1.48119i −0.671954 0.740593i \(-0.734545\pi\)
0.671954 0.740593i \(-0.265455\pi\)
\(318\) −6.51769 −0.365494
\(319\) 44.9294i 2.51556i
\(320\) 2.20888 + 0.347650i 0.123480 + 0.0194342i
\(321\) −6.80165 −0.379631
\(322\) 2.98769i 0.166498i
\(323\) 21.5414i 1.19860i
\(324\) 1.00000 0.0555556
\(325\) 7.30791 + 2.35878i 0.405370 + 0.130841i
\(326\) 8.05362 0.446049
\(327\) −17.9512 −0.992701
\(328\) −6.76262 −0.373403
\(329\) −20.4653 −1.12829
\(330\) −2.26687 + 14.4031i −0.124787 + 0.792865i
\(331\) 8.98662i 0.493950i −0.969022 0.246975i \(-0.920564\pi\)
0.969022 0.246975i \(-0.0794365\pi\)
\(332\) 15.8823i 0.871657i
\(333\) 0.927865 + 6.01158i 0.0508467 + 0.329432i
\(334\) 12.7129 0.695618
\(335\) 4.12085 26.1829i 0.225146 1.43052i
\(336\) 2.08112 0.113535
\(337\) 5.68375i 0.309614i 0.987945 + 0.154807i \(0.0494755\pi\)
−0.987945 + 0.154807i \(0.950524\pi\)
\(338\) 10.6412 0.578806
\(339\) 15.6346i 0.849157i
\(340\) −11.6753 1.83754i −0.633180 0.0996546i
\(341\) 53.4368i 2.89377i
\(342\) 4.07548i 0.220377i
\(343\) 20.1222i 1.08650i
\(344\) 4.46572 0.240775
\(345\) 0.499091 3.17110i 0.0268702 0.170726i
\(346\) 1.56245i 0.0839979i
\(347\) −11.6758 −0.626788 −0.313394 0.949623i \(-0.601466\pi\)
−0.313394 + 0.949623i \(0.601466\pi\)
\(348\) 6.89042 0.369366
\(349\) −0.886357 −0.0474456 −0.0237228 0.999719i \(-0.507552\pi\)
−0.0237228 + 0.999719i \(0.507552\pi\)
\(350\) 3.19625 9.90257i 0.170847 0.529315i
\(351\) 1.53583i 0.0819766i
\(352\) −6.52056 −0.347547
\(353\) −24.8083 −1.32042 −0.660208 0.751083i \(-0.729532\pi\)
−0.660208 + 0.751083i \(0.729532\pi\)
\(354\) 11.0304 0.586257
\(355\) −13.4275 2.11332i −0.712657 0.112163i
\(356\) 7.15877i 0.379414i
\(357\) −11.0000 −0.582182
\(358\) 12.2571i 0.647805i
\(359\) −5.29404 −0.279409 −0.139704 0.990193i \(-0.544615\pi\)
−0.139704 + 0.990193i \(0.544615\pi\)
\(360\) 2.20888 + 0.347650i 0.116418 + 0.0183227i
\(361\) 2.39045 0.125813
\(362\) 18.8971 0.993209
\(363\) 31.5177i 1.65425i
\(364\) 3.19625i 0.167529i
\(365\) 4.74188 30.1287i 0.248201 1.57701i
\(366\) 4.91211 0.256760
\(367\) 0.716886i 0.0374211i −0.999825 0.0187106i \(-0.994044\pi\)
0.999825 0.0187106i \(-0.00595610\pi\)
\(368\) 1.43562 0.0748366
\(369\) −6.76262 −0.352048
\(370\) −0.0403832 + 13.6014i −0.00209942 + 0.707104i
\(371\) −13.5641 −0.704214
\(372\) 8.19513 0.424897
\(373\) 1.21732i 0.0630305i −0.999503 0.0315153i \(-0.989967\pi\)
0.999503 0.0315153i \(-0.0100333\pi\)
\(374\) 34.4651 1.78215
\(375\) 5.04668 9.97653i 0.260609 0.515186i
\(376\) 9.83376i 0.507137i
\(377\) 10.5825i 0.545028i
\(378\) 2.08112 0.107041
\(379\) −33.1425 −1.70241 −0.851207 0.524830i \(-0.824129\pi\)
−0.851207 + 0.524830i \(0.824129\pi\)
\(380\) 1.41684 9.00224i 0.0726823 0.461805i
\(381\) −0.759690 −0.0389201
\(382\) 8.66659i 0.443421i
\(383\) 8.54131 0.436440 0.218220 0.975900i \(-0.429975\pi\)
0.218220 + 0.975900i \(0.429975\pi\)
\(384\) 1.00000i 0.0510310i
\(385\) −4.71764 + 29.9747i −0.240433 + 1.52765i
\(386\) −14.0122 −0.713204
\(387\) 4.46572 0.227005
\(388\) 19.0806 0.968671
\(389\) 23.0234i 1.16733i −0.811994 0.583666i \(-0.801618\pi\)
0.811994 0.583666i \(-0.198382\pi\)
\(390\) −0.533931 + 3.39246i −0.0270366 + 0.171784i
\(391\) −7.58810 −0.383747
\(392\) −2.66892 −0.134801
\(393\) −17.8737 −0.901607
\(394\) 20.7652i 1.04614i
\(395\) −0.960367 + 6.10193i −0.0483213 + 0.307021i
\(396\) −6.52056 −0.327670
\(397\) 16.8160i 0.843973i 0.906602 + 0.421987i \(0.138667\pi\)
−0.906602 + 0.421987i \(0.861333\pi\)
\(398\) 18.3572i 0.920166i
\(399\) 8.48158i 0.424610i
\(400\) 4.75828 + 1.53583i 0.237914 + 0.0767915i
\(401\) 19.6354i 0.980543i −0.871570 0.490271i \(-0.836898\pi\)
0.871570 0.490271i \(-0.163102\pi\)
\(402\) 11.8535 0.591197
\(403\) 12.5863i 0.626970i
\(404\) 1.62639 0.0809161
\(405\) 2.20888 + 0.347650i 0.109760 + 0.0172748i
\(406\) 14.3398 0.711674
\(407\) −6.05020 39.1988i −0.299897 1.94301i
\(408\) 5.28561i 0.261677i
\(409\) 32.0465i 1.58460i 0.610134 + 0.792298i \(0.291116\pi\)
−0.610134 + 0.792298i \(0.708884\pi\)
\(410\) −14.9378 2.35102i −0.737725 0.116109i
\(411\) 7.88841 0.389106
\(412\) −3.70274 −0.182421
\(413\) 22.9556 1.12957
\(414\) 1.43562 0.0705567
\(415\) −5.52149 + 35.0822i −0.271039 + 1.72212i
\(416\) −1.53583 −0.0753003
\(417\) 17.6834i 0.865960i
\(418\) 26.5744i 1.29980i
\(419\) 3.81945 0.186592 0.0932962 0.995638i \(-0.470260\pi\)
0.0932962 + 0.995638i \(0.470260\pi\)
\(420\) 4.59695 + 0.723502i 0.224308 + 0.0353033i
\(421\) 10.0113i 0.487920i 0.969785 + 0.243960i \(0.0784466\pi\)
−0.969785 + 0.243960i \(0.921553\pi\)
\(422\) 1.37092 0.0667354
\(423\) 9.83376i 0.478134i
\(424\) 6.51769i 0.316527i
\(425\) −25.1504 8.11780i −1.21997 0.393771i
\(426\) 6.07887i 0.294522i
\(427\) 10.2227 0.494711
\(428\) 6.80165i 0.328770i
\(429\) 10.0145i 0.483503i
\(430\) 9.86422 + 1.55250i 0.475695 + 0.0748684i
\(431\) 5.28491i 0.254565i 0.991866 + 0.127283i \(0.0406255\pi\)
−0.991866 + 0.127283i \(0.959374\pi\)
\(432\) 1.00000i 0.0481125i
\(433\) 23.3433i 1.12181i −0.827881 0.560904i \(-0.810454\pi\)
0.827881 0.560904i \(-0.189546\pi\)
\(434\) 17.0551 0.818670
\(435\) 15.2201 + 2.39545i 0.729748 + 0.114853i
\(436\) 17.9512i 0.859704i
\(437\) 5.85082i 0.279883i
\(438\) 13.6398 0.651736
\(439\) 20.3738i 0.972388i 0.873851 + 0.486194i \(0.161615\pi\)
−0.873851 + 0.486194i \(0.838385\pi\)
\(440\) −14.4031 2.26687i −0.686642 0.108069i
\(441\) −2.66892 −0.127092
\(442\) 8.11780 0.386124
\(443\) 4.11658i 0.195585i −0.995207 0.0977924i \(-0.968822\pi\)
0.995207 0.0977924i \(-0.0311781\pi\)
\(444\) −6.01158 + 0.927865i −0.285297 + 0.0440345i
\(445\) −2.48874 + 15.8128i −0.117978 + 0.749600i
\(446\) 10.4991i 0.497148i
\(447\) 0.543289i 0.0256967i
\(448\) 2.08112i 0.0983239i
\(449\) 13.0977i 0.618117i 0.951043 + 0.309058i \(0.100014\pi\)
−0.951043 + 0.309058i \(0.899986\pi\)
\(450\) 4.75828 + 1.53583i 0.224307 + 0.0723998i
\(451\) 44.0961 2.07640
\(452\) 15.6346 0.735392
\(453\) 7.98733i 0.375278i
\(454\) 23.4274 1.09950
\(455\) −1.11118 + 7.06013i −0.0520927 + 0.330984i
\(456\) 4.07548 0.190852
\(457\) −12.4923 −0.584365 −0.292183 0.956363i \(-0.594382\pi\)
−0.292183 + 0.956363i \(0.594382\pi\)
\(458\) 17.8860 0.835756
\(459\) 5.28561i 0.246711i
\(460\) 3.17110 + 0.499091i 0.147853 + 0.0232702i
\(461\) 1.72410i 0.0802995i −0.999194 0.0401497i \(-0.987217\pi\)
0.999194 0.0401497i \(-0.0127835\pi\)
\(462\) −13.5701 −0.631338
\(463\) −17.2119 −0.799903 −0.399952 0.916536i \(-0.630973\pi\)
−0.399952 + 0.916536i \(0.630973\pi\)
\(464\) 6.89042i 0.319880i
\(465\) 18.1020 + 2.84903i 0.839461 + 0.132121i
\(466\) 4.01113i 0.185812i
\(467\) −0.918102 −0.0424847 −0.0212423 0.999774i \(-0.506762\pi\)
−0.0212423 + 0.999774i \(0.506762\pi\)
\(468\) −1.53583 −0.0709938
\(469\) 24.6685 1.13909
\(470\) 3.41870 21.7216i 0.157693 1.00194i
\(471\) 11.2296 0.517430
\(472\) 11.0304i 0.507714i
\(473\) −29.1190 −1.33889
\(474\) −2.76246 −0.126884
\(475\) 6.25925 19.3923i 0.287194 0.889779i
\(476\) 11.0000i 0.504185i
\(477\) 6.51769i 0.298424i
\(478\) 8.70690i 0.398244i
\(479\) 16.4565i 0.751918i −0.926636 0.375959i \(-0.877313\pi\)
0.926636 0.375959i \(-0.122687\pi\)
\(480\) −0.347650 + 2.20888i −0.0158680 + 0.100821i
\(481\) −1.42504 9.23277i −0.0649764 0.420978i
\(482\) 15.6443i 0.712577i
\(483\) 2.98769 0.135945
\(484\) 31.5177 1.43262
\(485\) 42.1467 + 6.63336i 1.91378 + 0.301206i
\(486\) 1.00000i 0.0453609i
\(487\) 0.244062 0.0110595 0.00552975 0.999985i \(-0.498240\pi\)
0.00552975 + 0.999985i \(0.498240\pi\)
\(488\) 4.91211i 0.222361i
\(489\) 8.05362i 0.364197i
\(490\) −5.89533 0.927850i −0.266324 0.0419160i
\(491\) 10.1056 0.456060 0.228030 0.973654i \(-0.426772\pi\)
0.228030 + 0.973654i \(0.426772\pi\)
\(492\) 6.76262i 0.304882i
\(493\) 36.4201i 1.64028i
\(494\) 6.25925i 0.281617i
\(495\) −14.4031 2.26687i −0.647372 0.101888i
\(496\) 8.19513i 0.367972i
\(497\) 12.6509i 0.567470i
\(498\) −15.8823 −0.711705
\(499\) 4.16552i 0.186474i −0.995644 0.0932370i \(-0.970279\pi\)
0.995644 0.0932370i \(-0.0297214\pi\)
\(500\) 9.97653 + 5.04668i 0.446164 + 0.225694i
\(501\) 12.7129i 0.567970i
\(502\) 9.35179i 0.417391i
\(503\) −30.4289 −1.35676 −0.678379 0.734712i \(-0.737317\pi\)
−0.678379 + 0.734712i \(0.737317\pi\)
\(504\) 2.08112i 0.0927006i
\(505\) 3.59250 + 0.565415i 0.159864 + 0.0251606i
\(506\) −9.36102 −0.416148
\(507\) 10.6412i 0.472593i
\(508\) 0.759690i 0.0337058i
\(509\) −11.3764 −0.504249 −0.252125 0.967695i \(-0.581129\pi\)
−0.252125 + 0.967695i \(0.581129\pi\)
\(510\) 1.83754 11.6753i 0.0813676 0.516989i
\(511\) 28.3862 1.25573
\(512\) −1.00000 −0.0441942
\(513\) 4.07548 0.179937
\(514\) −11.5996 −0.511637
\(515\) −8.17891 1.28726i −0.360406 0.0567233i
\(516\) 4.46572i 0.196592i
\(517\) 64.1216i 2.82007i
\(518\) −12.5108 + 1.93100i −0.549695 + 0.0848433i
\(519\) −1.56245 −0.0685840
\(520\) −3.39246 0.533931i −0.148769 0.0234144i
\(521\) −12.3545 −0.541259 −0.270630 0.962684i \(-0.587232\pi\)
−0.270630 + 0.962684i \(0.587232\pi\)
\(522\) 6.89042i 0.301586i
\(523\) 2.03723 0.0890820 0.0445410 0.999008i \(-0.485817\pi\)
0.0445410 + 0.999008i \(0.485817\pi\)
\(524\) 17.8737i 0.780815i
\(525\) 9.90257 + 3.19625i 0.432184 + 0.139496i
\(526\) 1.31327i 0.0572613i
\(527\) 43.3162i 1.88688i
\(528\) 6.52056i 0.283771i
\(529\) −20.9390 −0.910392
\(530\) 2.26587 14.3968i 0.0984232 0.625356i
\(531\) 11.0304i 0.478677i
\(532\) 8.48158 0.367723
\(533\) 10.3862 0.449878
\(534\) −7.15877 −0.309790
\(535\) 2.36459 15.0240i 0.102230 0.649545i
\(536\) 11.8535i 0.511992i
\(537\) 12.2571 0.528931
\(538\) 16.7383 0.721641
\(539\) 17.4029 0.749595
\(540\) −0.347650 + 2.20888i −0.0149605 + 0.0950550i
\(541\) 18.9129i 0.813129i −0.913622 0.406564i \(-0.866727\pi\)
0.913622 0.406564i \(-0.133273\pi\)
\(542\) 27.8757 1.19736
\(543\) 18.8971i 0.810952i
\(544\) 5.28561 0.226619
\(545\) 6.24071 39.6519i 0.267323 1.69850i
\(546\) −3.19625 −0.136787
\(547\) 14.2804 0.610588 0.305294 0.952258i \(-0.401245\pi\)
0.305294 + 0.952258i \(0.401245\pi\)
\(548\) 7.88841i 0.336976i
\(549\) 4.91211i 0.209644i
\(550\) −31.0266 10.0145i −1.32298 0.427019i
\(551\) 28.0818 1.19632
\(552\) 1.43562i 0.0611039i
\(553\) −5.74901 −0.244473
\(554\) 18.0505 0.766893
\(555\) −13.6014 0.0403832i −0.577348 0.00171417i
\(556\) −17.6834 −0.749943
\(557\) 2.04249 0.0865433 0.0432716 0.999063i \(-0.486222\pi\)
0.0432716 + 0.999063i \(0.486222\pi\)
\(558\) 8.19513i 0.346927i
\(559\) −6.85859 −0.290087
\(560\) −0.723502 + 4.59695i −0.0305735 + 0.194256i
\(561\) 34.4651i 1.45512i
\(562\) 3.12679i 0.131896i
\(563\) 5.77225 0.243271 0.121636 0.992575i \(-0.461186\pi\)
0.121636 + 0.992575i \(0.461186\pi\)
\(564\) 9.83376 0.414076
\(565\) 34.5350 + 5.43538i 1.45290 + 0.228668i
\(566\) −13.1469 −0.552606
\(567\) 2.08112i 0.0873990i
\(568\) 6.07887 0.255064
\(569\) 16.6017i 0.695978i −0.937499 0.347989i \(-0.886865\pi\)
0.937499 0.347989i \(-0.113135\pi\)
\(570\) 9.00224 + 1.41684i 0.377062 + 0.0593449i
\(571\) −7.10926 −0.297513 −0.148757 0.988874i \(-0.547527\pi\)
−0.148757 + 0.988874i \(0.547527\pi\)
\(572\) 10.0145 0.418726
\(573\) 8.66659 0.362052
\(574\) 14.0738i 0.587431i
\(575\) 6.83106 + 2.20486i 0.284875 + 0.0919491i
\(576\) −1.00000 −0.0416667
\(577\) 25.8359 1.07556 0.537782 0.843084i \(-0.319262\pi\)
0.537782 + 0.843084i \(0.319262\pi\)
\(578\) −10.9377 −0.454947
\(579\) 14.0122i 0.582328i
\(580\) −2.39545 + 15.2201i −0.0994658 + 0.631980i
\(581\) −33.0531 −1.37127
\(582\) 19.0806i 0.790916i
\(583\) 42.4990i 1.76013i
\(584\) 13.6398i 0.564420i
\(585\) −3.39246 0.533931i −0.140261 0.0220753i
\(586\) 17.8889i 0.738983i
\(587\) 8.21612 0.339116 0.169558 0.985520i \(-0.445766\pi\)
0.169558 + 0.985520i \(0.445766\pi\)
\(588\) 2.66892i 0.110065i
\(589\) 33.3991 1.37619
\(590\) −3.83470 + 24.3647i −0.157872 + 1.00308i
\(591\) −20.7652 −0.854167
\(592\) −0.927865 6.01158i −0.0381350 0.247074i
\(593\) 26.1388i 1.07339i 0.843776 + 0.536696i \(0.180328\pi\)
−0.843776 + 0.536696i \(0.819672\pi\)
\(594\) 6.52056i 0.267542i
\(595\) 3.82415 24.2977i 0.156775 0.996107i
\(596\) −0.543289 −0.0222540
\(597\) 18.3572 0.751312
\(598\) −2.20486 −0.0901635
\(599\) 15.3216 0.626024 0.313012 0.949749i \(-0.398662\pi\)
0.313012 + 0.949749i \(0.398662\pi\)
\(600\) −1.53583 + 4.75828i −0.0627000 + 0.194256i
\(601\) −31.7252 −1.29410 −0.647049 0.762449i \(-0.723997\pi\)
−0.647049 + 0.762449i \(0.723997\pi\)
\(602\) 9.29371i 0.378783i
\(603\) 11.8535i 0.482711i
\(604\) 7.98733 0.325000
\(605\) 69.6187 + 10.9571i 2.83040 + 0.445470i
\(606\) 1.62639i 0.0660677i
\(607\) −10.9926 −0.446176 −0.223088 0.974798i \(-0.571614\pi\)
−0.223088 + 0.974798i \(0.571614\pi\)
\(608\) 4.07548i 0.165283i
\(609\) 14.3398i 0.581079i
\(610\) −1.70769 + 10.8502i −0.0691424 + 0.439313i
\(611\) 15.1030i 0.611002i
\(612\) 5.28561 0.213658
\(613\) 1.14926i 0.0464181i 0.999731 + 0.0232091i \(0.00738834\pi\)
−0.999731 + 0.0232091i \(0.992612\pi\)
\(614\) 21.1435i 0.853283i
\(615\) 2.35102 14.9378i 0.0948023 0.602350i
\(616\) 13.5701i 0.546755i
\(617\) 18.8902i 0.760491i 0.924886 + 0.380245i \(0.124160\pi\)
−0.924886 + 0.380245i \(0.875840\pi\)
\(618\) 3.70274i 0.148946i
\(619\) −44.0915 −1.77219 −0.886093 0.463507i \(-0.846591\pi\)
−0.886093 + 0.463507i \(0.846591\pi\)
\(620\) −2.84903 + 18.1020i −0.114420 + 0.726995i
\(621\) 1.43562i 0.0576093i
\(622\) 25.3383i 1.01597i
\(623\) −14.8983 −0.596887
\(624\) 1.53583i 0.0614824i
\(625\) 20.2824 + 14.6158i 0.811298 + 0.584633i
\(626\) −15.2774 −0.610610
\(627\) −26.5744 −1.06128
\(628\) 11.2296i 0.448108i
\(629\) 4.90433 + 31.7749i 0.195548 + 1.26695i
\(630\) −0.723502 + 4.59695i −0.0288250 + 0.183147i
\(631\) 25.3338i 1.00852i −0.863552 0.504261i \(-0.831765\pi\)
0.863552 0.504261i \(-0.168235\pi\)
\(632\) 2.76246i 0.109885i
\(633\) 1.37092i 0.0544892i
\(634\) 26.3718i 1.04736i
\(635\) 0.264106 1.67806i 0.0104807 0.0665919i
\(636\) 6.51769 0.258443
\(637\) 4.09901 0.162409
\(638\) 44.9294i 1.77877i
\(639\) 6.07887 0.240477
\(640\) −2.20888 0.347650i −0.0873135 0.0137421i
\(641\) 24.8092 0.979904 0.489952 0.871749i \(-0.337014\pi\)
0.489952 + 0.871749i \(0.337014\pi\)
\(642\) 6.80165 0.268440
\(643\) 7.91150 0.311999 0.156000 0.987757i \(-0.450140\pi\)
0.156000 + 0.987757i \(0.450140\pi\)
\(644\) 2.98769i 0.117732i
\(645\) −1.55250 + 9.86422i −0.0611298 + 0.388403i
\(646\) 21.5414i 0.847535i
\(647\) −7.28378 −0.286355 −0.143177 0.989697i \(-0.545732\pi\)
−0.143177 + 0.989697i \(0.545732\pi\)
\(648\) −1.00000 −0.0392837
\(649\) 71.9242i 2.82327i
\(650\) −7.30791 2.35878i −0.286640 0.0925188i
\(651\) 17.0551i 0.668441i
\(652\) −8.05362 −0.315404
\(653\) 10.3228 0.403961 0.201980 0.979390i \(-0.435262\pi\)
0.201980 + 0.979390i \(0.435262\pi\)
\(654\) 17.9512 0.701946
\(655\) 6.21377 39.4807i 0.242792 1.54264i
\(656\) 6.76262 0.264036
\(657\) 13.6398i 0.532140i
\(658\) 20.4653 0.797819
\(659\) −37.2866 −1.45248 −0.726240 0.687442i \(-0.758734\pi\)
−0.726240 + 0.687442i \(0.758734\pi\)
\(660\) 2.26687 14.4031i 0.0882378 0.560641i
\(661\) 38.1635i 1.48439i −0.670184 0.742195i \(-0.733785\pi\)
0.670184 0.742195i \(-0.266215\pi\)
\(662\) 8.98662i 0.349275i
\(663\) 8.11780i 0.315269i
\(664\) 15.8823i 0.616355i
\(665\) 18.7348 + 2.94862i 0.726503 + 0.114342i
\(666\) −0.927865 6.01158i −0.0359540 0.232944i
\(667\) 9.89200i 0.383020i
\(668\) −12.7129 −0.491876
\(669\) −10.4991 −0.405919
\(670\) −4.12085 + 26.1829i −0.159203 + 1.01153i
\(671\) 32.0297i 1.23649i
\(672\) −2.08112 −0.0802811
\(673\) 36.4380i 1.40458i −0.711890 0.702291i \(-0.752160\pi\)
0.711890 0.702291i \(-0.247840\pi\)
\(674\) 5.68375i 0.218930i
\(675\) −1.53583 + 4.75828i −0.0591141 + 0.183146i
\(676\) −10.6412 −0.409278
\(677\) 11.3104i 0.434694i −0.976094 0.217347i \(-0.930260\pi\)
0.976094 0.217347i \(-0.0697403\pi\)
\(678\) 15.6346i 0.600445i
\(679\) 39.7091i 1.52390i
\(680\) 11.6753 + 1.83754i 0.447726 + 0.0704664i
\(681\) 23.4274i 0.897739i
\(682\) 53.4368i 2.04620i
\(683\) 1.49065 0.0570380 0.0285190 0.999593i \(-0.490921\pi\)
0.0285190 + 0.999593i \(0.490921\pi\)
\(684\) 4.07548i 0.155830i
\(685\) −2.74240 + 17.4245i −0.104782 + 0.665757i
\(686\) 20.1222i 0.768270i
\(687\) 17.8860i 0.682392i
\(688\) −4.46572 −0.170254
\(689\) 10.0101i 0.381353i
\(690\) −0.499091 + 3.17110i −0.0190001 + 0.120722i
\(691\) 41.8658 1.59265 0.796325 0.604869i \(-0.206775\pi\)
0.796325 + 0.604869i \(0.206775\pi\)
\(692\) 1.56245i 0.0593955i
\(693\) 13.5701i 0.515485i
\(694\) 11.6758 0.443206
\(695\) −39.0605 6.14763i −1.48165 0.233193i
\(696\) −6.89042 −0.261181
\(697\) −35.7446 −1.35392
\(698\) 0.886357 0.0335491
\(699\) −4.01113 −0.151715
\(700\) −3.19625 + 9.90257i −0.120807 + 0.374282i
\(701\) 18.0848i 0.683052i −0.939872 0.341526i \(-0.889056\pi\)
0.939872 0.341526i \(-0.110944\pi\)
\(702\) 1.53583i 0.0579662i
\(703\) −24.5001 + 3.78149i −0.924038 + 0.142622i
\(704\) 6.52056 0.245753
\(705\) 21.7216 + 3.41870i 0.818082 + 0.128756i
\(706\) 24.8083 0.933674
\(707\) 3.38473i 0.127296i
\(708\) −11.0304 −0.414547
\(709\) 30.5559i 1.14755i 0.819013 + 0.573775i \(0.194522\pi\)
−0.819013 + 0.573775i \(0.805478\pi\)
\(710\) 13.4275 + 2.11332i 0.503925 + 0.0793114i
\(711\) 2.76246i 0.103600i
\(712\) 7.15877i 0.268286i
\(713\) 11.7651i 0.440605i
\(714\) 11.0000 0.411665
\(715\) 22.1207 + 3.48153i 0.827269 + 0.130202i
\(716\) 12.2571i 0.458067i
\(717\) 8.70690 0.325165
\(718\) 5.29404 0.197572
\(719\) 42.0288 1.56741 0.783704 0.621134i \(-0.213328\pi\)
0.783704 + 0.621134i \(0.213328\pi\)
\(720\) −2.20888 0.347650i −0.0823200 0.0129561i
\(721\) 7.70587i 0.286982i
\(722\) −2.39045 −0.0889635
\(723\) −15.6443 −0.581816
\(724\) −18.8971 −0.702305
\(725\) −10.5825 + 32.7866i −0.393025 + 1.21766i
\(726\) 31.5177i 1.16973i
\(727\) −43.0285 −1.59584 −0.797919 0.602765i \(-0.794066\pi\)
−0.797919 + 0.602765i \(0.794066\pi\)
\(728\) 3.19625i 0.118461i
\(729\) −1.00000 −0.0370370
\(730\) −4.74188 + 30.1287i −0.175505 + 1.11511i
\(731\) 23.6040 0.873027
\(732\) −4.91211 −0.181557
\(733\) 34.2793i 1.26613i −0.774097 0.633067i \(-0.781796\pi\)
0.774097 0.633067i \(-0.218204\pi\)
\(734\) 0.716886i 0.0264607i
\(735\) 0.927850 5.89533i 0.0342243 0.217452i
\(736\) −1.43562 −0.0529175
\(737\) 77.2913i 2.84706i
\(738\) 6.76262 0.248935
\(739\) 8.98532 0.330530 0.165265 0.986249i \(-0.447152\pi\)
0.165265 + 0.986249i \(0.447152\pi\)
\(740\) 0.0403832 13.6014i 0.00148452 0.499998i
\(741\) −6.25925 −0.229939
\(742\) 13.5641 0.497954
\(743\) 3.60771i 0.132354i −0.997808 0.0661771i \(-0.978920\pi\)
0.997808 0.0661771i \(-0.0210802\pi\)
\(744\) −8.19513 −0.300448
\(745\) −1.20006 0.188874i −0.0439668 0.00691982i
\(746\) 1.21732i 0.0445693i
\(747\) 15.8823i 0.581105i
\(748\) −34.4651 −1.26017
\(749\) 14.1551 0.517216
\(750\) −5.04668 + 9.97653i −0.184279 + 0.364291i
\(751\) 13.5278 0.493635 0.246817 0.969062i \(-0.420615\pi\)
0.246817 + 0.969062i \(0.420615\pi\)
\(752\) 9.83376i 0.358600i
\(753\) −9.35179 −0.340798
\(754\) 10.5825i 0.385393i
\(755\) 17.6430 + 2.77679i 0.642096 + 0.101058i
\(756\) −2.08112 −0.0756897
\(757\) 11.9133 0.432995 0.216497 0.976283i \(-0.430537\pi\)
0.216497 + 0.976283i \(0.430537\pi\)
\(758\) 33.1425 1.20379
\(759\) 9.36102i 0.339783i
\(760\) −1.41684 + 9.00224i −0.0513942 + 0.326546i
\(761\) 32.0203 1.16074 0.580368 0.814354i \(-0.302909\pi\)
0.580368 + 0.814354i \(0.302909\pi\)
\(762\) 0.759690 0.0275207
\(763\) 37.3586 1.35247
\(764\) 8.66659i 0.313546i
\(765\) 11.6753 + 1.83754i 0.422120 + 0.0664364i
\(766\) −8.54131 −0.308610
\(767\) 16.9408i 0.611696i
\(768\) 1.00000i 0.0360844i
\(769\) 34.1223i 1.23048i 0.788339 + 0.615241i \(0.210941\pi\)
−0.788339 + 0.615241i \(0.789059\pi\)
\(770\) 4.71764 29.9747i 0.170012 1.08021i
\(771\) 11.5996i 0.417750i
\(772\) 14.0122 0.504311
\(773\) 48.7174i 1.75224i 0.482090 + 0.876122i \(0.339878\pi\)
−0.482090 + 0.876122i \(0.660122\pi\)
\(774\) −4.46572 −0.160517
\(775\) −12.5863 + 38.9947i −0.452114 + 1.40073i
\(776\) −19.0806 −0.684954
\(777\) −1.93100 12.5108i −0.0692743 0.448824i
\(778\) 23.0234i 0.825429i
\(779\) 27.5609i 0.987473i
\(780\) 0.533931 3.39246i 0.0191178 0.121470i
\(781\) −39.6377 −1.41835
\(782\) 7.58810 0.271350
\(783\) −6.89042 −0.246244
\(784\) 2.66892 0.0953187
\(785\) −3.90395 + 24.8047i −0.139338 + 0.885318i
\(786\) 17.8737 0.637532
\(787\) 9.85605i 0.351330i −0.984450 0.175665i \(-0.943792\pi\)
0.984450 0.175665i \(-0.0562076\pi\)
\(788\) 20.7652i 0.739731i
\(789\) 1.31327 0.0467536
\(790\) 0.960367 6.10193i 0.0341683 0.217097i
\(791\) 32.5376i 1.15690i
\(792\) 6.52056 0.231698
\(793\) 7.54416i 0.267901i
\(794\) 16.8160i 0.596779i
\(795\) 14.3968 + 2.26587i 0.510601 + 0.0803622i
\(796\) 18.3572i 0.650655i
\(797\) 40.2825 1.42688 0.713439 0.700717i \(-0.247137\pi\)
0.713439 + 0.700717i \(0.247137\pi\)
\(798\) 8.48158i 0.300245i
\(799\) 51.9774i 1.83883i
\(800\) −4.75828 1.53583i −0.168231 0.0542998i
\(801\) 7.15877i 0.252943i
\(802\) 19.6354i 0.693349i
\(803\) 88.9393i 3.13860i
\(804\) −11.8535 −0.418040
\(805\) −1.03867 + 6.59945i −0.0366083 + 0.232600i
\(806\) 12.5863i 0.443334i
\(807\) 16.7383i 0.589217i
\(808\) −1.62639 −0.0572163
\(809\) 10.5881i 0.372257i 0.982525 + 0.186128i \(0.0595940\pi\)
−0.982525 + 0.186128i \(0.940406\pi\)
\(810\) −2.20888 0.347650i −0.0776120 0.0122152i
\(811\) 14.1487 0.496829 0.248414 0.968654i \(-0.420091\pi\)
0.248414 + 0.968654i \(0.420091\pi\)
\(812\) −14.3398 −0.503229
\(813\) 27.8757i 0.977642i
\(814\) 6.05020 + 39.1988i 0.212059 + 1.37392i
\(815\) −17.7895 2.79984i −0.623138 0.0980740i
\(816\) 5.28561i 0.185033i
\(817\) 18.1999i 0.636736i
\(818\) 32.0465i 1.12048i
\(819\) 3.19625i 0.111686i
\(820\) 14.9378 + 2.35102i 0.521650 + 0.0821012i
\(821\) −52.6633 −1.83796 −0.918981 0.394301i \(-0.870987\pi\)
−0.918981 + 0.394301i \(0.870987\pi\)
\(822\) −7.88841 −0.275140
\(823\) 2.21515i 0.0772153i 0.999254 + 0.0386077i \(0.0122923\pi\)
−0.999254 + 0.0386077i \(0.987708\pi\)
\(824\) 3.70274 0.128991
\(825\) 10.0145 31.0266i 0.348659 1.08021i
\(826\) −22.9556 −0.798726
\(827\) −34.6262 −1.20407 −0.602036 0.798469i \(-0.705644\pi\)
−0.602036 + 0.798469i \(0.705644\pi\)
\(828\) −1.43562 −0.0498911
\(829\) 21.2800i 0.739084i −0.929214 0.369542i \(-0.879515\pi\)
0.929214 0.369542i \(-0.120485\pi\)
\(830\) 5.52149 35.0822i 0.191654 1.21772i
\(831\) 18.0505i 0.626165i
\(832\) 1.53583 0.0532453
\(833\) −14.1069 −0.488775
\(834\) 17.6834i 0.612326i
\(835\) −28.0812 4.41963i −0.971790 0.152948i
\(836\) 26.5744i 0.919095i
\(837\) −8.19513 −0.283265
\(838\) −3.81945 −0.131941
\(839\) −30.1498 −1.04089 −0.520443 0.853896i \(-0.674233\pi\)
−0.520443 + 0.853896i \(0.674233\pi\)
\(840\) −4.59695 0.723502i −0.158610 0.0249632i
\(841\) −18.4780 −0.637171
\(842\) 10.0113i 0.345012i
\(843\) −3.12679 −0.107692
\(844\) −1.37092 −0.0471891
\(845\) −23.5052 3.69942i −0.808602 0.127264i
\(846\) 9.83376i 0.338092i
\(847\) 65.5922i 2.25378i
\(848\) 6.51769i 0.223818i
\(849\) 13.1469i 0.451201i
\(850\) 25.1504 + 8.11780i 0.862652 + 0.278438i
\(851\) −1.33206 8.63032i −0.0456623 0.295843i
\(852\) 6.07887i 0.208259i
\(853\) −48.4265 −1.65809 −0.829046 0.559180i \(-0.811116\pi\)
−0.829046 + 0.559180i \(0.811116\pi\)
\(854\) −10.2227 −0.349814
\(855\) −1.41684 + 9.00224i −0.0484549 + 0.307870i
\(856\) 6.80165i 0.232476i
\(857\) −1.36575 −0.0466531 −0.0233265 0.999728i \(-0.507426\pi\)
−0.0233265 + 0.999728i \(0.507426\pi\)
\(858\) 10.0145i 0.341889i
\(859\) 24.4949i 0.835754i −0.908504 0.417877i \(-0.862774\pi\)
0.908504 0.417877i \(-0.137226\pi\)
\(860\) −9.86422 1.55250i −0.336367 0.0529400i
\(861\) 14.0738 0.479635
\(862\) 5.28491i 0.180005i
\(863\) 24.3928i 0.830341i −0.909744 0.415170i \(-0.863722\pi\)
0.909744 0.415170i \(-0.136278\pi\)
\(864\) 1.00000i 0.0340207i
\(865\) 0.543186 3.45126i 0.0184689 0.117347i
\(866\) 23.3433i 0.793238i
\(867\) 10.9377i 0.371463i
\(868\) −17.0551 −0.578887
\(869\) 18.0128i 0.611041i
\(870\) −15.2201 2.39545i −0.516010 0.0812135i
\(871\) 18.2049i 0.616850i
\(872\) 17.9512i 0.607903i
\(873\) −19.0806 −0.645781
\(874\) 5.85082i 0.197907i
\(875\) −10.5028 + 20.7624i −0.355058 + 0.701897i
\(876\) −13.6398 −0.460847
\(877\) 1.49594i 0.0505142i −0.999681 0.0252571i \(-0.991960\pi\)
0.999681 0.0252571i \(-0.00804045\pi\)
\(878\) 20.3738i 0.687582i
\(879\) 17.8889 0.603377
\(880\) 14.4031 + 2.26687i 0.485529 + 0.0764162i
\(881\) −19.4185 −0.654224 −0.327112 0.944986i \(-0.606075\pi\)
−0.327112 + 0.944986i \(0.606075\pi\)
\(882\) 2.66892 0.0898673
\(883\) −33.5516 −1.12910 −0.564551 0.825398i \(-0.690951\pi\)
−0.564551 + 0.825398i \(0.690951\pi\)
\(884\) −8.11780 −0.273031
\(885\) −24.3647 3.83470i −0.819011 0.128902i
\(886\) 4.11658i 0.138299i
\(887\) 7.43914i 0.249782i −0.992170 0.124891i \(-0.960142\pi\)
0.992170 0.124891i \(-0.0398581\pi\)
\(888\) 6.01158 0.927865i 0.201735 0.0311371i
\(889\) 1.58101 0.0530254
\(890\) 2.48874 15.8128i 0.0834228 0.530048i
\(891\) 6.52056 0.218447
\(892\) 10.4991i 0.351537i
\(893\) 40.0773 1.34114
\(894\) 0.543289i 0.0181703i
\(895\) −4.26116 + 27.0743i −0.142435 + 0.904995i
\(896\) 2.08112i 0.0695255i
\(897\) 2.20486i 0.0736182i
\(898\) 13.0977i 0.437075i
\(899\) −56.4679 −1.88331
\(900\) −4.75828 1.53583i −0.158609 0.0511944i
\(901\) 34.4500i 1.14769i
\(902\) −44.0961 −1.46824
\(903\) −9.29371 −0.309275
\(904\) −15.6346 −0.520000
\(905\) −41.7414 6.56957i −1.38753 0.218380i
\(906\) 7.98733i 0.265361i
\(907\) 34.3902 1.14191 0.570953 0.820983i \(-0.306574\pi\)
0.570953 + 0.820983i \(0.306574\pi\)
\(908\) −23.4274 −0.777465
\(909\) −1.62639 −0.0539441
\(910\) 1.11118 7.06013i 0.0368351 0.234041i
\(911\) 0.581529i 0.0192669i −0.999954 0.00963346i \(-0.996934\pi\)
0.999954 0.00963346i \(-0.00306647\pi\)
\(912\) −4.07548 −0.134953
\(913\) 103.562i 3.42739i
\(914\) 12.4923 0.413209
\(915\) −10.8502 1.70769i −0.358698 0.0564545i
\(916\) −17.8860 −0.590969
\(917\) 37.1973 1.22836
\(918\) 5.28561i 0.174451i
\(919\) 0.382311i 0.0126113i −0.999980 0.00630564i \(-0.997993\pi\)
0.999980 0.00630564i \(-0.00200716\pi\)
\(920\) −3.17110 0.499091i −0.104548 0.0164545i
\(921\) −21.1435 −0.696702
\(922\) 1.72410i 0.0567803i
\(923\) −9.33612 −0.307302
\(924\) 13.5701 0.446423
\(925\) 4.81773 30.0298i 0.158406 0.987374i
\(926\) 17.2119 0.565617
\(927\) 3.70274 0.121614
\(928\) 6.89042i 0.226189i
\(929\) 11.2764 0.369967 0.184983 0.982742i \(-0.440777\pi\)
0.184983 + 0.982742i \(0.440777\pi\)
\(930\) −18.1020 2.84903i −0.593589 0.0934234i
\(931\) 10.8771i 0.356484i
\(932\) 4.01113i 0.131389i
\(933\) 25.3383 0.829538
\(934\) 0.918102 0.0300412
\(935\) −76.1293 11.9818i −2.48969 0.391846i
\(936\) 1.53583 0.0502002
\(937\) 31.5133i 1.02949i −0.857342 0.514747i \(-0.827886\pi\)
0.857342 0.514747i \(-0.172114\pi\)
\(938\) −24.6685 −0.805457
\(939\) 15.2774i 0.498561i
\(940\) −3.41870 + 21.7216i −0.111506 + 0.708480i
\(941\) 28.8572 0.940719 0.470360 0.882475i \(-0.344124\pi\)
0.470360 + 0.882475i \(0.344124\pi\)
\(942\) −11.2296 −0.365879
\(943\) 9.70852 0.316153
\(944\) 11.0304i 0.359008i
\(945\) −4.59695 0.723502i −0.149539 0.0235355i
\(946\) 29.1190 0.946740
\(947\) −4.66293 −0.151525 −0.0757625 0.997126i \(-0.524139\pi\)
−0.0757625 + 0.997126i \(0.524139\pi\)
\(948\) 2.76246 0.0897204
\(949\) 20.9485i 0.680016i
\(950\) −6.25925 + 19.3923i −0.203077 + 0.629169i
\(951\) −26.3718 −0.855163
\(952\) 11.0000i 0.356512i
\(953\) 3.87816i 0.125626i 0.998025 + 0.0628130i \(0.0200072\pi\)
−0.998025 + 0.0628130i \(0.979993\pi\)
\(954\) 6.51769i 0.211018i
\(955\) −3.01294 + 19.1434i −0.0974964 + 0.619467i
\(956\) 8.70690i 0.281601i
\(957\) 44.9294 1.45236
\(958\) 16.4565i 0.531687i
\(959\) −16.4168 −0.530125
\(960\) 0.347650 2.20888i 0.0112203 0.0712912i
\(961\) −36.1601 −1.16645
\(962\) 1.42504 + 9.23277i 0.0459452 + 0.297676i
\(963\) 6.80165i 0.219180i
\(964\) 15.6443i 0.503868i
\(965\) 30.9513 + 4.87134i 0.996357 + 0.156814i
\(966\) −2.98769 −0.0961275
\(967\) −7.25231 −0.233219 −0.116609 0.993178i \(-0.537203\pi\)
−0.116609 + 0.993178i \(0.537203\pi\)
\(968\) −31.5177 −1.01302
\(969\) 21.5414 0.692010
\(970\) −42.1467 6.63336i −1.35325 0.212984i
\(971\) −25.7900 −0.827640 −0.413820 0.910359i \(-0.635806\pi\)
−0.413820 + 0.910359i \(0.635806\pi\)
\(972\) 1.00000i 0.0320750i
\(973\) 36.8013i 1.17980i
\(974\) −0.244062 −0.00782025
\(975\) 2.35878 7.30791i 0.0755413 0.234040i
\(976\) 4.91211i 0.157233i
\(977\) 22.9259 0.733464 0.366732 0.930327i \(-0.380477\pi\)
0.366732 + 0.930327i \(0.380477\pi\)
\(978\) 8.05362i 0.257526i
\(979\) 46.6792i 1.49187i
\(980\) 5.89533 + 0.927850i 0.188319 + 0.0296391i
\(981\) 17.9512i 0.573136i
\(982\) −10.1056 −0.322483
\(983\) 6.33377i 0.202016i 0.994886 + 0.101008i \(0.0322068\pi\)
−0.994886 + 0.101008i \(0.967793\pi\)
\(984\) 6.76262i 0.215584i
\(985\) 7.21902 45.8679i 0.230017 1.46147i
\(986\) 36.4201i 1.15985i
\(987\) 20.4653i 0.651417i
\(988\) 6.25925i 0.199133i
\(989\) −6.41105 −0.203860
\(990\) 14.4031 + 2.26687i 0.457761 + 0.0720458i
\(991\) 29.5353i 0.938219i 0.883140 + 0.469109i \(0.155425\pi\)
−0.883140 + 0.469109i \(0.844575\pi\)
\(992\) 8.19513i 0.260195i
\(993\) −8.98662 −0.285182
\(994\) 12.6509i 0.401262i
\(995\) −6.38189 + 40.5489i −0.202319 + 1.28549i
\(996\) 15.8823 0.503251
\(997\) 55.4664 1.75664 0.878319 0.478074i \(-0.158665\pi\)
0.878319 + 0.478074i \(0.158665\pi\)
\(998\) 4.16552i 0.131857i
\(999\) 6.01158 0.927865i 0.190198 0.0293563i
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 1110.2.e.c.739.8 16
3.2 odd 2 3330.2.e.f.739.1 16
5.4 even 2 1110.2.e.d.739.9 yes 16
15.14 odd 2 3330.2.e.e.739.15 16
37.36 even 2 1110.2.e.d.739.1 yes 16
111.110 odd 2 3330.2.e.e.739.16 16
185.184 even 2 inner 1110.2.e.c.739.16 yes 16
555.554 odd 2 3330.2.e.f.739.2 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1110.2.e.c.739.8 16 1.1 even 1 trivial
1110.2.e.c.739.16 yes 16 185.184 even 2 inner
1110.2.e.d.739.1 yes 16 37.36 even 2
1110.2.e.d.739.9 yes 16 5.4 even 2
3330.2.e.e.739.15 16 15.14 odd 2
3330.2.e.e.739.16 16 111.110 odd 2
3330.2.e.f.739.1 16 3.2 odd 2
3330.2.e.f.739.2 16 555.554 odd 2