Properties

Label 29.3.f.a.10.2
Level $29$
Weight $3$
Character 29.10
Analytic conductor $0.790$
Analytic rank $0$
Dimension $48$
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] = [29,3,Mod(2,29)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(29, base_ring=CyclotomicField(28))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("29.2");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 29 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 29.f (of order \(28\), degree \(12\), 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: \(0.790192766645\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(4\) over \(\Q(\zeta_{28})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label 10.2
Character \(\chi\) \(=\) 29.10
Dual form 29.3.f.a.3.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.29187 + 0.811733i) q^{2} +(2.15095 + 0.752648i) q^{3} +(-0.725528 + 1.50658i) q^{4} +(3.36294 + 0.767569i) q^{5} +(-3.38968 + 0.773673i) q^{6} +(-0.255710 + 0.123143i) q^{7} +(-0.968958 - 8.59974i) q^{8} +(-2.97640 - 2.37360i) q^{9} +O(q^{10})\) \(q+(-1.29187 + 0.811733i) q^{2} +(2.15095 + 0.752648i) q^{3} +(-0.725528 + 1.50658i) q^{4} +(3.36294 + 0.767569i) q^{5} +(-3.38968 + 0.773673i) q^{6} +(-0.255710 + 0.123143i) q^{7} +(-0.968958 - 8.59974i) q^{8} +(-2.97640 - 2.37360i) q^{9} +(-4.96753 + 1.73821i) q^{10} +(1.62739 - 14.4435i) q^{11} +(-2.69449 + 2.69449i) q^{12} +(-4.30976 + 3.43692i) q^{13} +(0.230383 - 0.366653i) q^{14} +(6.65579 + 4.18211i) q^{15} +(4.06213 + 5.09375i) q^{16} +(5.25353 + 5.25353i) q^{17} +(5.77183 + 0.650330i) q^{18} +(9.56906 + 27.3468i) q^{19} +(-3.59631 + 4.50963i) q^{20} +(-0.642701 + 0.0724150i) q^{21} +(9.62189 + 19.9801i) q^{22} +(-6.05686 - 26.5368i) q^{23} +(4.38841 - 19.2269i) q^{24} +(-11.8040 - 5.68451i) q^{25} +(2.77777 - 7.93841i) q^{26} +(-15.5273 - 24.7115i) q^{27} -0.474590i q^{28} +(2.32625 + 28.9065i) q^{29} -11.9931 q^{30} +(-12.9513 + 8.13783i) q^{31} +(23.2916 + 8.15007i) q^{32} +(14.3713 - 29.8423i) q^{33} +(-11.0513 - 2.52239i) q^{34} +(-0.954457 + 0.217849i) q^{35} +(5.73547 - 2.76205i) q^{36} +(3.05571 + 27.1202i) q^{37} +(-34.5602 - 27.5609i) q^{38} +(-11.8568 + 4.14889i) q^{39} +(3.34235 - 29.6642i) q^{40} +(-45.8791 + 45.8791i) q^{41} +(0.771502 - 0.615252i) q^{42} +(35.9543 - 57.2209i) q^{43} +(20.5795 + 12.9310i) q^{44} +(-8.18755 - 10.2669i) q^{45} +(29.3655 + 29.3655i) q^{46} +(17.2732 + 1.94622i) q^{47} +(4.90362 + 14.0137i) q^{48} +(-30.5008 + 38.2468i) q^{49} +(19.8635 - 2.23808i) q^{50} +(7.34599 + 15.2541i) q^{51} +(-2.05112 - 8.98655i) q^{52} +(1.31097 - 5.74372i) q^{53} +(40.1183 + 19.3199i) q^{54} +(16.5592 - 47.3235i) q^{55} +(1.30677 + 2.07972i) q^{56} +66.0236i q^{57} +(-26.4696 - 35.4551i) q^{58} -43.1476 q^{59} +(-11.1296 + 6.99321i) q^{60} +(104.863 + 36.6931i) q^{61} +(10.1256 - 21.0260i) q^{62} +(1.05339 + 0.240429i) q^{63} +(-62.1125 + 14.1768i) q^{64} +(-17.1315 + 8.25011i) q^{65} +(5.65820 + 50.2179i) q^{66} +(-67.4283 - 53.7723i) q^{67} +(-11.7264 + 4.10325i) q^{68} +(6.94493 - 61.6380i) q^{69} +(1.05620 - 1.05620i) q^{70} +(45.1943 - 36.0413i) q^{71} +(-17.5283 + 27.8962i) q^{72} +(-42.0399 - 26.4154i) q^{73} +(-25.9619 - 32.5552i) q^{74} +(-21.1113 - 21.1113i) q^{75} +(-48.1426 - 5.42437i) q^{76} +(1.36248 + 3.89374i) q^{77} +(11.9497 - 14.9844i) q^{78} +(96.9173 - 10.9200i) q^{79} +(9.75090 + 20.2479i) q^{80} +(-7.17507 - 31.4360i) q^{81} +(22.0280 - 96.5112i) q^{82} +(-0.956785 - 0.460763i) q^{83} +(0.357199 - 1.02082i) q^{84} +(13.6349 + 21.6998i) q^{85} +103.107i q^{86} +(-16.7528 + 63.9272i) q^{87} -125.787 q^{88} +(73.6381 - 46.2699i) q^{89} +(18.9112 + 6.61730i) q^{90} +(0.678813 - 1.40957i) q^{91} +(44.3742 + 10.1281i) q^{92} +(-33.9824 + 7.75627i) q^{93} +(-23.8944 + 11.5070i) q^{94} +(11.1896 + 99.3106i) q^{95} +(43.9648 + 35.0607i) q^{96} +(54.6355 - 19.1178i) q^{97} +(8.35675 - 74.1682i) q^{98} +(-39.1268 + 39.1268i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q - 16 q^{2} - 12 q^{3} - 14 q^{4} - 14 q^{5} - 14 q^{6} - 10 q^{7} + 28 q^{8} - 14 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 48 q - 16 q^{2} - 12 q^{3} - 14 q^{4} - 14 q^{5} - 14 q^{6} - 10 q^{7} + 28 q^{8} - 14 q^{9} - 20 q^{10} - 8 q^{11} - 68 q^{12} - 14 q^{13} + 26 q^{14} - 4 q^{15} + 18 q^{16} - 26 q^{17} - 34 q^{18} + 2 q^{19} + 46 q^{20} + 218 q^{21} + 154 q^{22} + 56 q^{23} + 154 q^{24} - 34 q^{25} + 110 q^{26} + 126 q^{27} - 170 q^{29} + 24 q^{30} - 88 q^{31} - 132 q^{32} - 224 q^{33} - 224 q^{34} - 210 q^{35} - 434 q^{36} - 56 q^{37} - 294 q^{38} - 232 q^{39} - 492 q^{40} - 34 q^{41} - 14 q^{42} + 176 q^{43} + 126 q^{44} + 114 q^{45} + 744 q^{46} + 208 q^{47} + 640 q^{48} + 506 q^{49} + 732 q^{50} + 322 q^{51} + 690 q^{52} - 14 q^{53} - 36 q^{54} + 284 q^{55} + 332 q^{56} - 508 q^{58} - 44 q^{59} - 316 q^{60} - 30 q^{61} - 504 q^{62} - 686 q^{63} - 896 q^{64} - 554 q^{65} - 608 q^{66} - 574 q^{67} - 796 q^{68} - 806 q^{69} - 1066 q^{70} + 224 q^{71} + 748 q^{72} - 22 q^{73} + 820 q^{74} + 768 q^{75} + 514 q^{76} + 436 q^{77} + 282 q^{78} + 564 q^{79} + 1162 q^{80} + 670 q^{81} - 18 q^{82} - 126 q^{83} + 572 q^{84} + 38 q^{85} - 118 q^{87} - 384 q^{88} - 160 q^{89} - 828 q^{90} - 434 q^{91} - 1022 q^{92} - 406 q^{93} - 2 q^{94} - 642 q^{95} - 1176 q^{96} + 604 q^{97} - 102 q^{98} + 316 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/29\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{23}{28}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.29187 + 0.811733i −0.645933 + 0.405867i −0.814776 0.579776i \(-0.803140\pi\)
0.168843 + 0.985643i \(0.445997\pi\)
\(3\) 2.15095 + 0.752648i 0.716982 + 0.250883i 0.664021 0.747714i \(-0.268849\pi\)
0.0529606 + 0.998597i \(0.483134\pi\)
\(4\) −0.725528 + 1.50658i −0.181382 + 0.376644i
\(5\) 3.36294 + 0.767569i 0.672588 + 0.153514i 0.545158 0.838334i \(-0.316470\pi\)
0.127431 + 0.991847i \(0.459327\pi\)
\(6\) −3.38968 + 0.773673i −0.564947 + 0.128945i
\(7\) −0.255710 + 0.123143i −0.0365299 + 0.0175919i −0.452060 0.891988i \(-0.649311\pi\)
0.415530 + 0.909580i \(0.363596\pi\)
\(8\) −0.968958 8.59974i −0.121120 1.07497i
\(9\) −2.97640 2.37360i −0.330711 0.263733i
\(10\) −4.96753 + 1.73821i −0.496753 + 0.173821i
\(11\) 1.62739 14.4435i 0.147945 1.31305i −0.671978 0.740571i \(-0.734555\pi\)
0.819923 0.572474i \(-0.194016\pi\)
\(12\) −2.69449 + 2.69449i −0.224541 + 0.224541i
\(13\) −4.30976 + 3.43692i −0.331520 + 0.264378i −0.775076 0.631869i \(-0.782288\pi\)
0.443556 + 0.896247i \(0.353717\pi\)
\(14\) 0.230383 0.366653i 0.0164559 0.0261895i
\(15\) 6.65579 + 4.18211i 0.443719 + 0.278807i
\(16\) 4.06213 + 5.09375i 0.253883 + 0.318359i
\(17\) 5.25353 + 5.25353i 0.309031 + 0.309031i 0.844534 0.535503i \(-0.179878\pi\)
−0.535503 + 0.844534i \(0.679878\pi\)
\(18\) 5.77183 + 0.650330i 0.320657 + 0.0361294i
\(19\) 9.56906 + 27.3468i 0.503635 + 1.43930i 0.862568 + 0.505942i \(0.168855\pi\)
−0.358933 + 0.933363i \(0.616859\pi\)
\(20\) −3.59631 + 4.50963i −0.179816 + 0.225482i
\(21\) −0.642701 + 0.0724150i −0.0306048 + 0.00344833i
\(22\) 9.62189 + 19.9801i 0.437359 + 0.908185i
\(23\) −6.05686 26.5368i −0.263342 1.15378i −0.917600 0.397505i \(-0.869876\pi\)
0.654258 0.756271i \(-0.272981\pi\)
\(24\) 4.38841 19.2269i 0.182850 0.801119i
\(25\) −11.8040 5.68451i −0.472160 0.227380i
\(26\) 2.77777 7.93841i 0.106837 0.305323i
\(27\) −15.5273 24.7115i −0.575084 0.915240i
\(28\) 0.474590i 0.0169496i
\(29\) 2.32625 + 28.9065i 0.0802155 + 0.996778i
\(30\) −11.9931 −0.399772
\(31\) −12.9513 + 8.13783i −0.417783 + 0.262511i −0.724479 0.689297i \(-0.757920\pi\)
0.306695 + 0.951808i \(0.400777\pi\)
\(32\) 23.2916 + 8.15007i 0.727862 + 0.254690i
\(33\) 14.3713 29.8423i 0.435494 0.904313i
\(34\) −11.0513 2.52239i −0.325039 0.0741880i
\(35\) −0.954457 + 0.217849i −0.0272702 + 0.00622425i
\(36\) 5.73547 2.76205i 0.159318 0.0767237i
\(37\) 3.05571 + 27.1202i 0.0825867 + 0.732977i 0.964955 + 0.262417i \(0.0845196\pi\)
−0.882368 + 0.470560i \(0.844052\pi\)
\(38\) −34.5602 27.5609i −0.909480 0.725286i
\(39\) −11.8568 + 4.14889i −0.304022 + 0.106382i
\(40\) 3.34235 29.6642i 0.0835587 0.741604i
\(41\) −45.8791 + 45.8791i −1.11900 + 1.11900i −0.127114 + 0.991888i \(0.540571\pi\)
−0.991888 + 0.127114i \(0.959429\pi\)
\(42\) 0.771502 0.615252i 0.0183691 0.0146489i
\(43\) 35.9543 57.2209i 0.836146 1.33072i −0.105605 0.994408i \(-0.533678\pi\)
0.941751 0.336311i \(-0.109179\pi\)
\(44\) 20.5795 + 12.9310i 0.467716 + 0.293885i
\(45\) −8.18755 10.2669i −0.181946 0.228153i
\(46\) 29.3655 + 29.3655i 0.638380 + 0.638380i
\(47\) 17.2732 + 1.94622i 0.367514 + 0.0414089i 0.293791 0.955870i \(-0.405083\pi\)
0.0737238 + 0.997279i \(0.476512\pi\)
\(48\) 4.90362 + 14.0137i 0.102159 + 0.291953i
\(49\) −30.5008 + 38.2468i −0.622465 + 0.780546i
\(50\) 19.8635 2.23808i 0.397270 0.0447616i
\(51\) 7.34599 + 15.2541i 0.144039 + 0.299100i
\(52\) −2.05112 8.98655i −0.0394447 0.172818i
\(53\) 1.31097 5.74372i 0.0247352 0.108372i −0.961053 0.276363i \(-0.910871\pi\)
0.985789 + 0.167991i \(0.0537279\pi\)
\(54\) 40.1183 + 19.3199i 0.742931 + 0.357777i
\(55\) 16.5592 47.3235i 0.301077 0.860427i
\(56\) 1.30677 + 2.07972i 0.0233352 + 0.0371378i
\(57\) 66.0236i 1.15831i
\(58\) −26.4696 35.4551i −0.456372 0.611295i
\(59\) −43.1476 −0.731315 −0.365658 0.930749i \(-0.619156\pi\)
−0.365658 + 0.930749i \(0.619156\pi\)
\(60\) −11.1296 + 6.99321i −0.185494 + 0.116554i
\(61\) 104.863 + 36.6931i 1.71906 + 0.601526i 0.996008 0.0892649i \(-0.0284518\pi\)
0.723055 + 0.690791i \(0.242737\pi\)
\(62\) 10.1256 21.0260i 0.163316 0.339129i
\(63\) 1.05339 + 0.240429i 0.0167204 + 0.00381633i
\(64\) −62.1125 + 14.1768i −0.970507 + 0.221512i
\(65\) −17.1315 + 8.25011i −0.263562 + 0.126925i
\(66\) 5.65820 + 50.2179i 0.0857303 + 0.760878i
\(67\) −67.4283 53.7723i −1.00639 0.802571i −0.0260070 0.999662i \(-0.508279\pi\)
−0.980385 + 0.197091i \(0.936851\pi\)
\(68\) −11.7264 + 4.10325i −0.172447 + 0.0603419i
\(69\) 6.94493 61.6380i 0.100651 0.893304i
\(70\) 1.05620 1.05620i 0.0150885 0.0150885i
\(71\) 45.1943 36.0413i 0.636540 0.507623i −0.251220 0.967930i \(-0.580832\pi\)
0.887760 + 0.460306i \(0.152260\pi\)
\(72\) −17.5283 + 27.8962i −0.243449 + 0.387447i
\(73\) −42.0399 26.4154i −0.575889 0.361855i 0.212379 0.977187i \(-0.431879\pi\)
−0.788268 + 0.615332i \(0.789022\pi\)
\(74\) −25.9619 32.5552i −0.350836 0.439935i
\(75\) −21.1113 21.1113i −0.281485 0.281485i
\(76\) −48.1426 5.42437i −0.633456 0.0713733i
\(77\) 1.36248 + 3.89374i 0.0176945 + 0.0505681i
\(78\) 11.9497 14.9844i 0.153201 0.192108i
\(79\) 96.9173 10.9200i 1.22680 0.138227i 0.525314 0.850909i \(-0.323948\pi\)
0.701488 + 0.712681i \(0.252519\pi\)
\(80\) 9.75090 + 20.2479i 0.121886 + 0.253099i
\(81\) −7.17507 31.4360i −0.0885811 0.388099i
\(82\) 22.0280 96.5112i 0.268635 1.17697i
\(83\) −0.956785 0.460763i −0.0115275 0.00555137i 0.428111 0.903726i \(-0.359179\pi\)
−0.439639 + 0.898175i \(0.644893\pi\)
\(84\) 0.357199 1.02082i 0.00425237 0.0121526i
\(85\) 13.6349 + 21.6998i 0.160410 + 0.255291i
\(86\) 103.107i 1.19892i
\(87\) −16.7528 + 63.9272i −0.192561 + 0.734796i
\(88\) −125.787 −1.42940
\(89\) 73.6381 46.2699i 0.827394 0.519886i −0.0505095 0.998724i \(-0.516085\pi\)
0.877904 + 0.478837i \(0.158942\pi\)
\(90\) 18.9112 + 6.61730i 0.210124 + 0.0735256i
\(91\) 0.678813 1.40957i 0.00745949 0.0154898i
\(92\) 44.3742 + 10.1281i 0.482328 + 0.110088i
\(93\) −33.9824 + 7.75627i −0.365403 + 0.0834007i
\(94\) −23.8944 + 11.5070i −0.254196 + 0.122414i
\(95\) 11.1896 + 99.3106i 0.117785 + 1.04537i
\(96\) 43.9648 + 35.0607i 0.457966 + 0.365216i
\(97\) 54.6355 19.1178i 0.563252 0.197091i −0.0336088 0.999435i \(-0.510700\pi\)
0.596861 + 0.802345i \(0.296414\pi\)
\(98\) 8.35675 74.1682i 0.0852729 0.756818i
\(99\) −39.1268 + 39.1268i −0.395220 + 0.395220i
\(100\) 17.1283 13.6594i 0.171283 0.136594i
\(101\) −43.1797 + 68.7201i −0.427522 + 0.680397i −0.989136 0.147002i \(-0.953038\pi\)
0.561614 + 0.827399i \(0.310181\pi\)
\(102\) −21.8723 13.7433i −0.214434 0.134738i
\(103\) 117.601 + 147.466i 1.14175 + 1.43171i 0.885217 + 0.465179i \(0.154010\pi\)
0.256537 + 0.966534i \(0.417419\pi\)
\(104\) 33.7326 + 33.7326i 0.324352 + 0.324352i
\(105\) −2.21695 0.249790i −0.0211138 0.00237895i
\(106\) 2.96878 + 8.48427i 0.0280073 + 0.0800403i
\(107\) 17.2592 21.6423i 0.161300 0.202264i −0.694613 0.719384i \(-0.744424\pi\)
0.855913 + 0.517119i \(0.172996\pi\)
\(108\) 48.4952 5.46409i 0.449029 0.0505935i
\(109\) −40.5822 84.2699i −0.372314 0.773118i 0.627672 0.778478i \(-0.284008\pi\)
−0.999986 + 0.00536026i \(0.998294\pi\)
\(110\) 17.0218 + 74.5773i 0.154743 + 0.677975i
\(111\) −13.8393 + 60.6338i −0.124678 + 0.546251i
\(112\) −1.66599 0.802297i −0.0148749 0.00716336i
\(113\) 49.3986 141.173i 0.437156 1.24932i −0.489035 0.872264i \(-0.662651\pi\)
0.926191 0.377055i \(-0.123063\pi\)
\(114\) −53.5935 85.2936i −0.470119 0.748189i
\(115\) 93.8909i 0.816443i
\(116\) −45.2377 17.4679i −0.389980 0.150585i
\(117\) 20.9854 0.179362
\(118\) 55.7409 35.0243i 0.472381 0.296816i
\(119\) −1.99031 0.696441i −0.0167253 0.00585245i
\(120\) 29.5159 61.2904i 0.245966 0.510753i
\(121\) −88.0000 20.0854i −0.727272 0.165995i
\(122\) −165.254 + 37.7181i −1.35454 + 0.309165i
\(123\) −133.214 + 64.1526i −1.08304 + 0.521566i
\(124\) −2.86373 25.4163i −0.0230946 0.204970i
\(125\) −102.755 81.9441i −0.822037 0.655553i
\(126\) −1.55600 + 0.544467i −0.0123492 + 0.00432117i
\(127\) −10.7711 + 95.5964i −0.0848120 + 0.752727i 0.877276 + 0.479987i \(0.159359\pi\)
−0.962088 + 0.272740i \(0.912070\pi\)
\(128\) −1.06196 + 1.06196i −0.00829659 + 0.00829659i
\(129\) 120.403 96.0181i 0.933356 0.744327i
\(130\) 15.4348 24.5643i 0.118729 0.188956i
\(131\) −86.3851 54.2793i −0.659428 0.414346i 0.160324 0.987064i \(-0.448746\pi\)
−0.819752 + 0.572718i \(0.805889\pi\)
\(132\) 34.5329 + 43.3029i 0.261613 + 0.328052i
\(133\) −5.81447 5.81447i −0.0437178 0.0437178i
\(134\) 130.757 + 14.7328i 0.975798 + 0.109946i
\(135\) −33.2495 95.0215i −0.246292 0.703863i
\(136\) 40.0885 50.2694i 0.294769 0.369628i
\(137\) −43.6939 + 4.92312i −0.318933 + 0.0359351i −0.269980 0.962866i \(-0.587017\pi\)
−0.0489532 + 0.998801i \(0.515589\pi\)
\(138\) 41.0617 + 85.2654i 0.297548 + 0.617865i
\(139\) 13.4998 + 59.1466i 0.0971211 + 0.425515i 0.999990 0.00439991i \(-0.00140054\pi\)
−0.902869 + 0.429915i \(0.858543\pi\)
\(140\) 0.364281 1.59602i 0.00260200 0.0114001i
\(141\) 35.6888 + 17.1868i 0.253112 + 0.121892i
\(142\) −29.1291 + 83.2462i −0.205135 + 0.586241i
\(143\) 42.6274 + 67.8412i 0.298094 + 0.474414i
\(144\) 24.8029i 0.172242i
\(145\) −14.3647 + 98.9966i −0.0990672 + 0.682735i
\(146\) 75.7522 0.518851
\(147\) −94.3919 + 59.3103i −0.642121 + 0.403472i
\(148\) −43.0756 15.0728i −0.291051 0.101843i
\(149\) −42.6095 + 88.4796i −0.285970 + 0.593823i −0.993625 0.112735i \(-0.964039\pi\)
0.707655 + 0.706558i \(0.249753\pi\)
\(150\) 44.4098 + 10.1362i 0.296065 + 0.0675750i
\(151\) 2.28538 0.521624i 0.0151350 0.00345446i −0.214947 0.976626i \(-0.568958\pi\)
0.230082 + 0.973171i \(0.426101\pi\)
\(152\) 225.903 108.789i 1.48621 0.715719i
\(153\) −3.16683 28.1064i −0.0206982 0.183702i
\(154\) −4.92082 3.92422i −0.0319534 0.0254820i
\(155\) −49.8008 + 17.4260i −0.321295 + 0.112426i
\(156\) 2.35186 20.8734i 0.0150760 0.133804i
\(157\) 55.3939 55.3939i 0.352828 0.352828i −0.508333 0.861161i \(-0.669738\pi\)
0.861161 + 0.508333i \(0.169738\pi\)
\(158\) −116.340 + 92.7781i −0.736330 + 0.587203i
\(159\) 7.14282 11.3677i 0.0449234 0.0714952i
\(160\) 72.0724 + 45.2861i 0.450453 + 0.283038i
\(161\) 4.81663 + 6.03986i 0.0299170 + 0.0375147i
\(162\) 34.7869 + 34.7869i 0.214734 + 0.214734i
\(163\) −59.0143 6.64931i −0.362051 0.0407933i −0.0709343 0.997481i \(-0.522598\pi\)
−0.291116 + 0.956688i \(0.594027\pi\)
\(164\) −35.8337 102.407i −0.218498 0.624432i
\(165\) 71.2359 89.3270i 0.431733 0.541376i
\(166\) 1.61005 0.181410i 0.00969913 0.00109283i
\(167\) 35.2685 + 73.2358i 0.211189 + 0.438538i 0.979474 0.201569i \(-0.0646042\pi\)
−0.768285 + 0.640107i \(0.778890\pi\)
\(168\) 1.24550 + 5.45690i 0.00741370 + 0.0324815i
\(169\) −30.8444 + 135.138i −0.182511 + 0.799635i
\(170\) −35.2288 16.9653i −0.207228 0.0997959i
\(171\) 36.4290 104.108i 0.213035 0.608819i
\(172\) 60.1218 + 95.6833i 0.349545 + 0.556298i
\(173\) 34.1362i 0.197319i −0.995121 0.0986597i \(-0.968544\pi\)
0.995121 0.0986597i \(-0.0314555\pi\)
\(174\) −30.2495 96.1842i −0.173847 0.552783i
\(175\) 3.71841 0.0212481
\(176\) 80.1822 50.3818i 0.455581 0.286260i
\(177\) −92.8081 32.4750i −0.524340 0.183474i
\(178\) −57.5717 + 119.549i −0.323437 + 0.671623i
\(179\) −71.0369 16.2137i −0.396854 0.0905793i 0.0194363 0.999811i \(-0.493813\pi\)
−0.416290 + 0.909232i \(0.636670\pi\)
\(180\) 21.4081 4.88626i 0.118934 0.0271459i
\(181\) 113.506 54.6618i 0.627107 0.301999i −0.0932070 0.995647i \(-0.529712\pi\)
0.720314 + 0.693648i \(0.243998\pi\)
\(182\) 0.267259 + 2.37199i 0.00146846 + 0.0130329i
\(183\) 197.937 + 157.850i 1.08162 + 0.862566i
\(184\) −222.341 + 77.8005i −1.20838 + 0.422829i
\(185\) −10.5404 + 93.5489i −0.0569753 + 0.505670i
\(186\) 37.6047 37.6047i 0.202176 0.202176i
\(187\) 84.4289 67.3298i 0.451491 0.360052i
\(188\) −15.4643 + 24.6113i −0.0822570 + 0.130911i
\(189\) 7.01352 + 4.40689i 0.0371086 + 0.0233169i
\(190\) −95.0691 119.213i −0.500364 0.627437i
\(191\) −107.857 107.857i −0.564698 0.564698i 0.365940 0.930638i \(-0.380747\pi\)
−0.930638 + 0.365940i \(0.880747\pi\)
\(192\) −144.271 16.2554i −0.751410 0.0846635i
\(193\) 66.7211 + 190.678i 0.345705 + 0.987969i 0.977151 + 0.212548i \(0.0681763\pi\)
−0.631445 + 0.775420i \(0.717538\pi\)
\(194\) −55.0632 + 69.0470i −0.283831 + 0.355913i
\(195\) −43.0584 + 4.85152i −0.220812 + 0.0248796i
\(196\) −35.4925 73.7008i −0.181084 0.376025i
\(197\) −76.3058 334.317i −0.387339 1.69704i −0.673769 0.738942i \(-0.735326\pi\)
0.286431 0.958101i \(-0.407531\pi\)
\(198\) 18.7861 82.3071i 0.0948791 0.415693i
\(199\) 267.208 + 128.681i 1.34275 + 0.646636i 0.960722 0.277513i \(-0.0895101\pi\)
0.382032 + 0.924149i \(0.375224\pi\)
\(200\) −37.4477 + 107.020i −0.187239 + 0.535098i
\(201\) −104.563 166.411i −0.520214 0.827915i
\(202\) 123.828i 0.613008i
\(203\) −4.15449 7.10522i −0.0204655 0.0350011i
\(204\) −28.3112 −0.138780
\(205\) −189.504 + 119.073i −0.924410 + 0.580845i
\(206\) −271.628 95.0466i −1.31858 0.461391i
\(207\) −44.9602 + 93.3608i −0.217199 + 0.451018i
\(208\) −35.0136 7.99162i −0.168335 0.0384213i
\(209\) 410.556 93.7067i 1.96438 0.448357i
\(210\) 3.06676 1.47688i 0.0146036 0.00703274i
\(211\) −23.1896 205.814i −0.109903 0.975420i −0.920748 0.390158i \(-0.872420\pi\)
0.810845 0.585262i \(-0.199008\pi\)
\(212\) 7.70221 + 6.14231i 0.0363312 + 0.0289731i
\(213\) 124.337 43.5074i 0.583741 0.204260i
\(214\) −4.72874 + 41.9688i −0.0220969 + 0.196116i
\(215\) 164.833 164.833i 0.766666 0.766666i
\(216\) −197.467 + 157.475i −0.914200 + 0.729050i
\(217\) 2.30965 3.67579i 0.0106435 0.0169391i
\(218\) 120.831 + 75.9234i 0.554273 + 0.348272i
\(219\) −70.5440 88.4594i −0.322119 0.403924i
\(220\) 59.2822 + 59.2822i 0.269465 + 0.269465i
\(221\) −40.6974 4.58549i −0.184151 0.0207488i
\(222\) −31.3400 89.5646i −0.141171 0.403444i
\(223\) −17.9820 + 22.5487i −0.0806367 + 0.101115i −0.820513 0.571627i \(-0.806312\pi\)
0.739877 + 0.672742i \(0.234884\pi\)
\(224\) −6.95951 + 0.784148i −0.0310692 + 0.00350066i
\(225\) 21.6407 + 44.9373i 0.0961808 + 0.199722i
\(226\) 50.7785 + 222.475i 0.224684 + 0.984403i
\(227\) −34.9328 + 153.050i −0.153889 + 0.674231i 0.837844 + 0.545910i \(0.183816\pi\)
−0.991733 + 0.128321i \(0.959041\pi\)
\(228\) −99.4695 47.9020i −0.436270 0.210096i
\(229\) −104.546 + 298.776i −0.456534 + 1.30470i 0.453902 + 0.891051i \(0.350031\pi\)
−0.910437 + 0.413648i \(0.864254\pi\)
\(230\) 76.2143 + 121.294i 0.331367 + 0.527367i
\(231\) 9.40070i 0.0406957i
\(232\) 246.335 48.0144i 1.06179 0.206959i
\(233\) 421.117 1.80737 0.903684 0.428200i \(-0.140852\pi\)
0.903684 + 0.428200i \(0.140852\pi\)
\(234\) −27.1103 + 17.0346i −0.115856 + 0.0727972i
\(235\) 56.5948 + 19.8034i 0.240829 + 0.0842697i
\(236\) 31.3048 65.0051i 0.132648 0.275445i
\(237\) 216.683 + 49.4564i 0.914273 + 0.208677i
\(238\) 3.13654 0.715895i 0.0131788 0.00300796i
\(239\) −187.354 + 90.2247i −0.783906 + 0.377509i −0.782628 0.622490i \(-0.786121\pi\)
−0.00127824 + 0.999999i \(0.500407\pi\)
\(240\) 5.73406 + 50.8912i 0.0238919 + 0.212047i
\(241\) 10.8085 + 8.61948i 0.0448485 + 0.0357655i 0.645658 0.763627i \(-0.276583\pi\)
−0.600809 + 0.799393i \(0.705155\pi\)
\(242\) 129.988 45.4848i 0.537141 0.187954i
\(243\) −21.1819 + 187.994i −0.0871682 + 0.773639i
\(244\) −131.362 + 131.362i −0.538368 + 0.538368i
\(245\) −131.929 + 105.210i −0.538487 + 0.429429i
\(246\) 120.020 191.011i 0.487886 0.776467i
\(247\) −135.229 84.9700i −0.547486 0.344008i
\(248\) 82.5325 + 103.493i 0.332792 + 0.417309i
\(249\) −1.71120 1.71120i −0.00687229 0.00687229i
\(250\) 199.262 + 22.4514i 0.797048 + 0.0898057i
\(251\) −20.8320 59.5343i −0.0829959 0.237189i 0.894905 0.446256i \(-0.147243\pi\)
−0.977901 + 0.209067i \(0.932957\pi\)
\(252\) −1.12649 + 1.41257i −0.00447018 + 0.00560543i
\(253\) −393.142 + 44.2964i −1.55392 + 0.175085i
\(254\) −63.6839 132.241i −0.250724 0.520634i
\(255\) 12.9956 + 56.9372i 0.0509629 + 0.223283i
\(256\) 57.2170 250.684i 0.223504 0.979234i
\(257\) −387.505 186.613i −1.50780 0.726120i −0.516325 0.856393i \(-0.672700\pi\)
−0.991478 + 0.130273i \(0.958415\pi\)
\(258\) −77.6033 + 221.778i −0.300788 + 0.859603i
\(259\) −4.12104 6.55859i −0.0159113 0.0253228i
\(260\) 31.7956i 0.122291i
\(261\) 61.6887 91.5590i 0.236355 0.350801i
\(262\) 155.658 0.594116
\(263\) 10.7365 6.74620i 0.0408232 0.0256509i −0.511466 0.859304i \(-0.670897\pi\)
0.552289 + 0.833653i \(0.313754\pi\)
\(264\) −270.561 94.6735i −1.02485 0.358612i
\(265\) 8.81741 18.3095i 0.0332733 0.0690926i
\(266\) 12.2313 + 2.79172i 0.0459824 + 0.0104952i
\(267\) 193.216 44.1004i 0.723657 0.165170i
\(268\) 129.933 62.5725i 0.484825 0.233479i
\(269\) −28.0878 249.286i −0.104416 0.926714i −0.931278 0.364310i \(-0.881305\pi\)
0.826862 0.562404i \(-0.190124\pi\)
\(270\) 120.086 + 95.7654i 0.444763 + 0.354687i
\(271\) 214.664 75.1142i 0.792119 0.277174i 0.0962629 0.995356i \(-0.469311\pi\)
0.695856 + 0.718182i \(0.255025\pi\)
\(272\) −5.41964 + 48.1007i −0.0199252 + 0.176841i
\(273\) 2.52100 2.52100i 0.00923444 0.00923444i
\(274\) 52.4503 41.8278i 0.191425 0.152656i
\(275\) −101.314 + 161.240i −0.368415 + 0.586328i
\(276\) 87.8235 + 55.1832i 0.318201 + 0.199939i
\(277\) −266.485 334.162i −0.962040 1.20636i −0.978448 0.206495i \(-0.933794\pi\)
0.0164075 0.999865i \(-0.494777\pi\)
\(278\) −65.4513 65.4513i −0.235436 0.235436i
\(279\) 57.8641 + 6.51972i 0.207398 + 0.0233682i
\(280\) 2.79827 + 7.99700i 0.00999383 + 0.0285607i
\(281\) −259.886 + 325.887i −0.924862 + 1.15974i 0.0619844 + 0.998077i \(0.480257\pi\)
−0.986846 + 0.161663i \(0.948314\pi\)
\(282\) −60.0563 + 6.76672i −0.212966 + 0.0239955i
\(283\) −202.446 420.383i −0.715356 1.48545i −0.867681 0.497121i \(-0.834390\pi\)
0.152325 0.988330i \(-0.451324\pi\)
\(284\) 21.5091 + 94.2376i 0.0757363 + 0.331823i
\(285\) −50.6777 + 222.033i −0.177816 + 0.779065i
\(286\) −110.138 53.0396i −0.385097 0.185453i
\(287\) 6.08202 17.3814i 0.0211917 0.0605624i
\(288\) −49.9800 79.5427i −0.173542 0.276190i
\(289\) 233.801i 0.809000i
\(290\) −61.8015 139.551i −0.213109 0.481209i
\(291\) 131.907 0.453288
\(292\) 70.2980 44.1712i 0.240747 0.151271i
\(293\) 285.468 + 99.8897i 0.974295 + 0.340921i 0.770039 0.637997i \(-0.220237\pi\)
0.204256 + 0.978917i \(0.434522\pi\)
\(294\) 73.7974 153.242i 0.251012 0.521231i
\(295\) −145.103 33.1188i −0.491874 0.112267i
\(296\) 230.265 52.5566i 0.777924 0.177556i
\(297\) −382.189 + 184.053i −1.28683 + 0.619706i
\(298\) −16.7760 148.891i −0.0562954 0.499635i
\(299\) 117.309 + 93.5504i 0.392336 + 0.312878i
\(300\) 47.1227 16.4889i 0.157076 0.0549632i
\(301\) −2.14749 + 19.0595i −0.00713451 + 0.0633205i
\(302\) −2.52899 + 2.52899i −0.00837414 + 0.00837414i
\(303\) −144.599 + 115.314i −0.477225 + 0.380575i
\(304\) −100.427 + 159.829i −0.330352 + 0.525752i
\(305\) 324.483 + 203.886i 1.06388 + 0.668479i
\(306\) 26.9060 + 33.7390i 0.0879280 + 0.110258i
\(307\) −271.866 271.866i −0.885558 0.885558i 0.108534 0.994093i \(-0.465384\pi\)
−0.994093 + 0.108534i \(0.965384\pi\)
\(308\) −6.85474 0.772343i −0.0222556 0.00250761i
\(309\) 141.962 + 405.704i 0.459424 + 1.31296i
\(310\) 50.1906 62.9370i 0.161905 0.203023i
\(311\) −124.784 + 14.0597i −0.401233 + 0.0452081i −0.310276 0.950647i \(-0.600421\pi\)
−0.0909576 + 0.995855i \(0.528993\pi\)
\(312\) 47.1682 + 97.9457i 0.151180 + 0.313928i
\(313\) 13.5770 + 59.4846i 0.0433769 + 0.190047i 0.991975 0.126438i \(-0.0403545\pi\)
−0.948598 + 0.316485i \(0.897497\pi\)
\(314\) −26.5964 + 116.527i −0.0847020 + 0.371104i
\(315\) 3.35793 + 1.61709i 0.0106601 + 0.00513363i
\(316\) −53.8645 + 153.936i −0.170457 + 0.487139i
\(317\) 239.824 + 381.678i 0.756543 + 1.20403i 0.973686 + 0.227892i \(0.0731833\pi\)
−0.217143 + 0.976140i \(0.569674\pi\)
\(318\) 20.4837i 0.0644140i
\(319\) 421.297 + 13.4431i 1.32068 + 0.0421413i
\(320\) −219.762 −0.686757
\(321\) 53.4125 33.5613i 0.166394 0.104552i
\(322\) −11.1252 3.89288i −0.0345503 0.0120897i
\(323\) −93.3958 + 193.938i −0.289151 + 0.600429i
\(324\) 52.5665 + 11.9980i 0.162242 + 0.0370307i
\(325\) 70.4096 16.0705i 0.216645 0.0494478i
\(326\) 81.6360 39.3138i 0.250417 0.120594i
\(327\) −23.8646 211.804i −0.0729804 0.647719i
\(328\) 439.003 + 350.093i 1.33842 + 1.06736i
\(329\) −4.65658 + 1.62941i −0.0141537 + 0.00495261i
\(330\) −19.5175 + 173.223i −0.0591441 + 0.524918i
\(331\) 295.773 295.773i 0.893575 0.893575i −0.101283 0.994858i \(-0.532295\pi\)
0.994858 + 0.101283i \(0.0322946\pi\)
\(332\) 1.38835 1.10717i 0.00418178 0.00333486i
\(333\) 55.2773 87.9734i 0.165998 0.264184i
\(334\) −105.010 65.9822i −0.314402 0.197552i
\(335\) −185.483 232.589i −0.553682 0.694295i
\(336\) −2.97960 2.97960i −0.00886785 0.00886785i
\(337\) −90.2891 10.1731i −0.267920 0.0301873i −0.0230176 0.999735i \(-0.507327\pi\)
−0.244902 + 0.969548i \(0.578756\pi\)
\(338\) −69.8493 199.618i −0.206655 0.590586i
\(339\) 212.507 266.476i 0.626865 0.786064i
\(340\) −42.5848 + 4.79815i −0.125249 + 0.0141122i
\(341\) 96.4620 + 200.305i 0.282880 + 0.587406i
\(342\) 37.4466 + 164.064i 0.109493 + 0.479720i
\(343\) 6.18411 27.0944i 0.0180295 0.0789923i
\(344\) −526.923 253.753i −1.53175 0.737654i
\(345\) 70.6668 201.954i 0.204831 0.585374i
\(346\) 27.7095 + 44.0994i 0.0800853 + 0.127455i
\(347\) 392.579i 1.13135i 0.824628 + 0.565676i \(0.191385\pi\)
−0.824628 + 0.565676i \(0.808615\pi\)
\(348\) −84.1566 71.6204i −0.241829 0.205806i
\(349\) −487.106 −1.39572 −0.697860 0.716234i \(-0.745864\pi\)
−0.697860 + 0.716234i \(0.745864\pi\)
\(350\) −4.80368 + 3.01836i −0.0137248 + 0.00862387i
\(351\) 151.850 + 53.1346i 0.432621 + 0.151381i
\(352\) 155.620 323.148i 0.442103 0.918035i
\(353\) 98.6003 + 22.5049i 0.279321 + 0.0637532i 0.359886 0.932996i \(-0.382815\pi\)
−0.0805655 + 0.996749i \(0.525673\pi\)
\(354\) 146.257 33.3821i 0.413154 0.0942998i
\(355\) 179.650 86.5149i 0.506056 0.243704i
\(356\) 16.2825 + 144.511i 0.0457374 + 0.405931i
\(357\) −3.75688 2.99601i −0.0105235 0.00839219i
\(358\) 104.931 36.7170i 0.293104 0.102562i
\(359\) 3.96158 35.1600i 0.0110350 0.0979386i −0.986987 0.160798i \(-0.948593\pi\)
0.998022 + 0.0628592i \(0.0200219\pi\)
\(360\) −80.3590 + 80.3590i −0.223219 + 0.223219i
\(361\) −374.039 + 298.286i −1.03612 + 0.826277i
\(362\) −102.264 + 162.753i −0.282498 + 0.449593i
\(363\) −174.166 109.436i −0.479796 0.301476i
\(364\) 1.63113 + 2.04537i 0.00448111 + 0.00561914i
\(365\) −121.102 121.102i −0.331787 0.331787i
\(366\) −383.840 43.2484i −1.04874 0.118165i
\(367\) −76.1146 217.523i −0.207397 0.592706i 0.792455 0.609930i \(-0.208803\pi\)
−0.999852 + 0.0172247i \(0.994517\pi\)
\(368\) 110.568 138.648i 0.300457 0.376761i
\(369\) 245.453 27.6559i 0.665184 0.0749482i
\(370\) −62.3199 129.409i −0.168432 0.349753i
\(371\) 0.372074 + 1.63016i 0.00100289 + 0.00439397i
\(372\) 12.9698 56.8245i 0.0348651 0.152754i
\(373\) 402.935 + 194.043i 1.08026 + 0.520224i 0.887398 0.461003i \(-0.152510\pi\)
0.192857 + 0.981227i \(0.438225\pi\)
\(374\) −54.4170 + 155.515i −0.145500 + 0.415815i
\(375\) −159.345 253.595i −0.424919 0.676254i
\(376\) 150.431i 0.400082i
\(377\) −109.375 116.585i −0.290119 0.309244i
\(378\) −12.6377 −0.0334332
\(379\) −215.124 + 135.171i −0.567609 + 0.356653i −0.785061 0.619419i \(-0.787368\pi\)
0.217452 + 0.976071i \(0.430226\pi\)
\(380\) −157.737 55.1946i −0.415098 0.145249i
\(381\) −95.1185 + 197.516i −0.249655 + 0.518414i
\(382\) 226.888 + 51.7858i 0.593949 + 0.135565i
\(383\) −215.485 + 49.1830i −0.562624 + 0.128415i −0.494368 0.869253i \(-0.664601\pi\)
−0.0682557 + 0.997668i \(0.521743\pi\)
\(384\) −3.08351 + 1.48494i −0.00802998 + 0.00386703i
\(385\) 1.59322 + 14.1402i 0.00413824 + 0.0367279i
\(386\) −240.974 192.171i −0.624286 0.497851i
\(387\) −242.834 + 84.9712i −0.627477 + 0.219564i
\(388\) −10.8372 + 96.1830i −0.0279310 + 0.247894i
\(389\) 408.712 408.712i 1.05067 1.05067i 0.0520279 0.998646i \(-0.483432\pi\)
0.998646 0.0520279i \(-0.0165685\pi\)
\(390\) 51.6876 41.2195i 0.132532 0.105691i
\(391\) 107.592 171.232i 0.275172 0.437933i
\(392\) 358.466 + 225.239i 0.914455 + 0.574590i
\(393\) −144.956 181.769i −0.368846 0.462518i
\(394\) 369.953 + 369.953i 0.938968 + 0.938968i
\(395\) 334.309 + 37.6676i 0.846352 + 0.0953610i
\(396\) −30.5599 87.3351i −0.0771714 0.220543i
\(397\) −173.996 + 218.184i −0.438277 + 0.549582i −0.951088 0.308919i \(-0.900033\pi\)
0.512811 + 0.858501i \(0.328604\pi\)
\(398\) −449.651 + 50.6635i −1.12978 + 0.127295i
\(399\) −8.13036 16.8829i −0.0203768 0.0423129i
\(400\) −18.9939 83.2179i −0.0474849 0.208045i
\(401\) −71.9206 + 315.105i −0.179353 + 0.785797i 0.802576 + 0.596549i \(0.203462\pi\)
−0.981929 + 0.189248i \(0.939395\pi\)
\(402\) 270.163 + 130.103i 0.672046 + 0.323640i
\(403\) 27.8478 79.5846i 0.0691014 0.197480i
\(404\) −72.2040 114.912i −0.178723 0.284435i
\(405\) 111.225i 0.274629i
\(406\) 11.1346 + 5.80665i 0.0274251 + 0.0143021i
\(407\) 396.683 0.974650
\(408\) 124.063 77.9542i 0.304077 0.191064i
\(409\) 138.542 + 48.4780i 0.338734 + 0.118528i 0.494285 0.869300i \(-0.335430\pi\)
−0.155552 + 0.987828i \(0.549715\pi\)
\(410\) 148.158 307.653i 0.361361 0.750374i
\(411\) −97.6885 22.2968i −0.237685 0.0542500i
\(412\) −307.492 + 70.1830i −0.746340 + 0.170347i
\(413\) 11.0333 5.31334i 0.0267149 0.0128652i
\(414\) −17.7015 157.105i −0.0427573 0.379481i
\(415\) −2.86394 2.28392i −0.00690107 0.00550342i
\(416\) −128.392 + 44.9264i −0.308635 + 0.107996i
\(417\) −15.4792 + 137.382i −0.0371204 + 0.329453i
\(418\) −454.318 + 454.318i −1.08689 + 1.08689i
\(419\) 554.089 441.871i 1.32241 1.05459i 0.328485 0.944509i \(-0.393462\pi\)
0.993923 0.110076i \(-0.0351093\pi\)
\(420\) 1.98479 3.15877i 0.00472568 0.00752088i
\(421\) −408.042 256.390i −0.969220 0.609001i −0.0483331 0.998831i \(-0.515391\pi\)
−0.920887 + 0.389830i \(0.872534\pi\)
\(422\) 197.024 + 247.060i 0.466880 + 0.585449i
\(423\) −46.7923 46.7923i −0.110620 0.110620i
\(424\) −50.6648 5.70855i −0.119492 0.0134636i
\(425\) −32.1490 91.8764i −0.0756446 0.216180i
\(426\) −125.310 + 157.134i −0.294155 + 0.368859i
\(427\) −31.3329 + 3.53037i −0.0733792 + 0.00826786i
\(428\) 20.0837 + 41.7043i 0.0469246 + 0.0974400i
\(429\) 40.6287 + 178.006i 0.0947057 + 0.414933i
\(430\) −79.1418 + 346.743i −0.184051 + 0.806379i
\(431\) 158.220 + 76.1946i 0.367099 + 0.176786i 0.608334 0.793681i \(-0.291838\pi\)
−0.241235 + 0.970467i \(0.577552\pi\)
\(432\) 62.8004 179.473i 0.145371 0.415447i
\(433\) 2.79964 + 4.45560i 0.00646568 + 0.0102901i 0.849941 0.526877i \(-0.176637\pi\)
−0.843476 + 0.537167i \(0.819494\pi\)
\(434\) 6.62344i 0.0152614i
\(435\) −105.407 + 202.125i −0.242316 + 0.464654i
\(436\) 156.402 0.358721
\(437\) 667.739 419.568i 1.52801 0.960110i
\(438\) 162.939 + 57.0148i 0.372006 + 0.130171i
\(439\) −232.675 + 483.154i −0.530010 + 1.10058i 0.448386 + 0.893840i \(0.351999\pi\)
−0.978396 + 0.206738i \(0.933715\pi\)
\(440\) −423.015 96.5504i −0.961398 0.219433i
\(441\) 181.565 41.4410i 0.411712 0.0939705i
\(442\) 56.2977 27.1116i 0.127370 0.0613384i
\(443\) 49.1601 + 436.308i 0.110971 + 0.984894i 0.918596 + 0.395198i \(0.129324\pi\)
−0.807625 + 0.589696i \(0.799247\pi\)
\(444\) −81.3086 64.8415i −0.183128 0.146039i
\(445\) 283.156 99.0805i 0.636305 0.222653i
\(446\) 4.92679 43.7265i 0.0110466 0.0980414i
\(447\) −158.245 + 158.245i −0.354015 + 0.354015i
\(448\) 14.1370 11.2739i 0.0315558 0.0251649i
\(449\) 27.2504 43.3687i 0.0606912 0.0965896i −0.815000 0.579461i \(-0.803263\pi\)
0.875691 + 0.482871i \(0.160406\pi\)
\(450\) −64.4340 40.4866i −0.143187 0.0899701i
\(451\) 587.991 + 737.318i 1.30375 + 1.63485i
\(452\) 176.848 + 176.848i 0.391256 + 0.391256i
\(453\) 5.30833 + 0.598106i 0.0117182 + 0.00132032i
\(454\) −79.1076 226.077i −0.174246 0.497966i
\(455\) 3.36475 4.21927i 0.00739506 0.00927311i
\(456\) 567.786 63.9741i 1.24514 0.140294i
\(457\) 141.198 + 293.202i 0.308968 + 0.641579i 0.996410 0.0846606i \(-0.0269806\pi\)
−0.687442 + 0.726240i \(0.741266\pi\)
\(458\) −107.467 470.843i −0.234644 1.02804i
\(459\) 48.2496 211.395i 0.105119 0.460556i
\(460\) 141.454 + 68.1205i 0.307508 + 0.148088i
\(461\) −3.04533 + 8.70305i −0.00660592 + 0.0188786i −0.947139 0.320823i \(-0.896040\pi\)
0.940533 + 0.339702i \(0.110326\pi\)
\(462\) −7.63086 12.1444i −0.0165170 0.0262867i
\(463\) 107.108i 0.231334i 0.993288 + 0.115667i \(0.0369005\pi\)
−0.993288 + 0.115667i \(0.963099\pi\)
\(464\) −137.793 + 129.271i −0.296968 + 0.278602i
\(465\) −120.234 −0.258569
\(466\) −544.026 + 341.834i −1.16744 + 0.733550i
\(467\) −666.211 233.117i −1.42658 0.499180i −0.496980 0.867762i \(-0.665558\pi\)
−0.929595 + 0.368582i \(0.879843\pi\)
\(468\) −15.2255 + 31.6161i −0.0325331 + 0.0675558i
\(469\) 23.8638 + 5.44675i 0.0508822 + 0.0116135i
\(470\) −89.1880 + 20.3566i −0.189762 + 0.0433119i
\(471\) 160.841 77.4572i 0.341489 0.164453i
\(472\) 41.8082 + 371.058i 0.0885768 + 0.786140i
\(473\) −767.959 612.427i −1.62359 1.29477i
\(474\) −320.070 + 111.997i −0.675254 + 0.236282i
\(475\) 42.4999 377.197i 0.0894735 0.794099i
\(476\) 2.49327 2.49327i 0.00523796 0.00523796i
\(477\) −17.5353 + 13.9839i −0.0367615 + 0.0293163i
\(478\) 168.797 268.639i 0.353132 0.562007i
\(479\) −268.422 168.661i −0.560380 0.352110i 0.221868 0.975077i \(-0.428784\pi\)
−0.782249 + 0.622966i \(0.785927\pi\)
\(480\) 120.939 + 151.653i 0.251957 + 0.315944i
\(481\) −106.379 106.379i −0.221162 0.221162i
\(482\) −20.9598 2.36160i −0.0434851 0.00489959i
\(483\) 5.81442 + 16.6166i 0.0120381 + 0.0344030i
\(484\) 94.1067 118.006i 0.194435 0.243814i
\(485\) 198.410 22.3555i 0.409093 0.0460937i
\(486\) −125.237 260.057i −0.257689 0.535097i
\(487\) −60.5532 265.301i −0.124339 0.544765i −0.998274 0.0587228i \(-0.981297\pi\)
0.873935 0.486042i \(-0.161560\pi\)
\(488\) 213.943 937.347i 0.438409 1.92079i
\(489\) −121.932 58.7193i −0.249349 0.120080i
\(490\) 85.0325 243.009i 0.173536 0.495936i
\(491\) −21.2173 33.7671i −0.0432123 0.0687720i 0.824420 0.565979i \(-0.191502\pi\)
−0.867632 + 0.497207i \(0.834359\pi\)
\(492\) 247.242i 0.502524i
\(493\) −139.640 + 164.082i −0.283246 + 0.332824i
\(494\) 243.671 0.493260
\(495\) −161.614 + 101.549i −0.326492 + 0.205149i
\(496\) −94.0619 32.9137i −0.189641 0.0663582i
\(497\) −7.11838 + 14.7815i −0.0143227 + 0.0297414i
\(498\) 3.59968 + 0.821603i 0.00722827 + 0.00164981i
\(499\) −733.757 + 167.475i −1.47046 + 0.335622i −0.881362 0.472442i \(-0.843372\pi\)
−0.589094 + 0.808064i \(0.700515\pi\)
\(500\) 198.006 95.3549i 0.396013 0.190710i
\(501\) 20.7398 + 184.071i 0.0413969 + 0.367407i
\(502\) 75.2381 + 60.0004i 0.149877 + 0.119523i
\(503\) −475.580 + 166.413i −0.945487 + 0.330840i −0.758611 0.651544i \(-0.774122\pi\)
−0.186875 + 0.982384i \(0.559836\pi\)
\(504\) 1.04694 9.29182i 0.00207725 0.0184361i
\(505\) −197.958 + 197.958i −0.391997 + 0.391997i
\(506\) 471.929 376.351i 0.932667 0.743777i
\(507\) −168.056 + 267.460i −0.331472 + 0.527534i
\(508\) −136.208 85.5854i −0.268127 0.168475i
\(509\) −156.669 196.457i −0.307798 0.385967i 0.603741 0.797181i \(-0.293676\pi\)
−0.911539 + 0.411214i \(0.865105\pi\)
\(510\) −63.0063 63.0063i −0.123542 0.123542i
\(511\) 14.0029 + 1.57775i 0.0274029 + 0.00308757i
\(512\) 127.588 + 364.624i 0.249195 + 0.712157i
\(513\) 527.199 661.086i 1.02768 1.28867i
\(514\) 652.085 73.4723i 1.26865 0.142942i
\(515\) 282.293 + 586.188i 0.548142 + 1.13823i
\(516\) 57.3028 + 251.060i 0.111052 + 0.486550i
\(517\) 56.2205 246.318i 0.108744 0.476437i
\(518\) 10.6477 + 5.12764i 0.0205553 + 0.00989892i
\(519\) 25.6926 73.4252i 0.0495040 0.141474i
\(520\) 87.5486 + 139.333i 0.168363 + 0.267948i
\(521\) 240.735i 0.462063i 0.972946 + 0.231031i \(0.0742100\pi\)
−0.972946 + 0.231031i \(0.925790\pi\)
\(522\) −5.37205 + 168.357i −0.0102913 + 0.322522i
\(523\) −250.645 −0.479245 −0.239623 0.970866i \(-0.577024\pi\)
−0.239623 + 0.970866i \(0.577024\pi\)
\(524\) 144.451 90.7644i 0.275669 0.173215i
\(525\) 7.99809 + 2.79865i 0.0152345 + 0.00533077i
\(526\) −8.39402 + 17.4304i −0.0159582 + 0.0331376i
\(527\) −110.792 25.2876i −0.210232 0.0479841i
\(528\) 210.387 48.0195i 0.398461 0.0909461i
\(529\) −190.906 + 91.9355i −0.360881 + 0.173791i
\(530\) 3.47155 + 30.8109i 0.00655009 + 0.0581337i
\(531\) 128.424 + 102.415i 0.241854 + 0.192872i
\(532\) 12.9785 4.54138i 0.0243957 0.00853642i
\(533\) 40.0451 355.410i 0.0751315 0.666811i
\(534\) −213.812 + 213.812i −0.400397 + 0.400397i
\(535\) 74.6535 59.5342i 0.139539 0.111279i
\(536\) −397.092 + 631.969i −0.740844 + 1.17905i
\(537\) −140.593 88.3405i −0.261812 0.164508i
\(538\) 238.639 + 299.244i 0.443568 + 0.556216i
\(539\) 502.780 + 502.780i 0.932802 + 0.932802i
\(540\) 167.281 + 18.8480i 0.309779 + 0.0349037i
\(541\) 288.943 + 825.753i 0.534091 + 1.52635i 0.822458 + 0.568826i \(0.192602\pi\)
−0.288367 + 0.957520i \(0.593112\pi\)
\(542\) −216.345 + 271.287i −0.399160 + 0.500530i
\(543\) 285.287 32.1441i 0.525391 0.0591973i
\(544\) 79.5463 + 165.180i 0.146225 + 0.303639i
\(545\) −71.7927 314.544i −0.131730 0.577145i
\(546\) −1.21041 + 5.30317i −0.00221688 + 0.00971277i
\(547\) 885.756 + 426.558i 1.61930 + 0.779813i 0.999986 0.00533110i \(-0.00169695\pi\)
0.619313 + 0.785144i \(0.287411\pi\)
\(548\) 24.2841 69.3999i 0.0443140 0.126642i
\(549\) −225.019 358.115i −0.409870 0.652305i
\(550\) 290.541i 0.528256i
\(551\) −768.241 + 340.224i −1.39427 + 0.617466i
\(552\) −536.800 −0.972464
\(553\) −23.4380 + 14.7271i −0.0423833 + 0.0266312i
\(554\) 615.513 + 215.377i 1.11103 + 0.388768i
\(555\) −93.0813 + 193.285i −0.167714 + 0.348262i
\(556\) −98.9034 22.5741i −0.177884 0.0406008i
\(557\) −697.102 + 159.109i −1.25153 + 0.285653i −0.796399 0.604771i \(-0.793264\pi\)
−0.455130 + 0.890425i \(0.650407\pi\)
\(558\) −80.0450 + 38.5476i −0.143450 + 0.0690818i
\(559\) 41.7093 + 370.180i 0.0746141 + 0.662219i
\(560\) −4.98680 3.97684i −0.00890499 0.00710150i
\(561\) 232.277 81.2774i 0.414042 0.144880i
\(562\) 71.2048 631.960i 0.126699 1.12448i
\(563\) 509.988 509.988i 0.905840 0.905840i −0.0900931 0.995933i \(-0.528716\pi\)
0.995933 + 0.0900931i \(0.0287165\pi\)
\(564\) −51.7865 + 41.2984i −0.0918201 + 0.0732241i
\(565\) 274.485 436.840i 0.485814 0.773168i
\(566\) 602.771 + 378.746i 1.06497 + 0.669163i
\(567\) 5.70587 + 7.15494i 0.0100633 + 0.0126189i
\(568\) −353.737 353.737i −0.622776 0.622776i
\(569\) 19.5814 + 2.20630i 0.0344137 + 0.00387750i 0.129155 0.991624i \(-0.458774\pi\)
−0.0947408 + 0.995502i \(0.530202\pi\)
\(570\) −114.763 327.974i −0.201339 0.575393i
\(571\) 153.514 192.500i 0.268851 0.337128i −0.629019 0.777390i \(-0.716543\pi\)
0.897869 + 0.440262i \(0.145115\pi\)
\(572\) −133.135 + 15.0007i −0.232754 + 0.0262251i
\(573\) −150.816 313.174i −0.263205 0.546551i
\(574\) 6.25192 + 27.3914i 0.0108918 + 0.0477203i
\(575\) −79.3537 + 347.671i −0.138007 + 0.604646i
\(576\) 218.521 + 105.234i 0.379377 + 0.182699i
\(577\) 305.351 872.644i 0.529205 1.51238i −0.300279 0.953852i \(-0.597080\pi\)
0.829484 0.558530i \(-0.188635\pi\)
\(578\) 189.784 + 302.039i 0.328346 + 0.522559i
\(579\) 460.355i 0.795087i
\(580\) −138.724 93.4664i −0.239179 0.161149i
\(581\) 0.301399 0.000518759
\(582\) −170.406 + 107.073i −0.292794 + 0.183975i
\(583\) −80.8260 28.2822i −0.138638 0.0485116i
\(584\) −186.431 + 387.128i −0.319231 + 0.662890i
\(585\) 70.5727 + 16.1078i 0.120637 + 0.0275346i
\(586\) −449.871 + 102.680i −0.767697 + 0.175222i
\(587\) −507.435 + 244.368i −0.864456 + 0.416300i −0.812923 0.582371i \(-0.802125\pi\)
−0.0515328 + 0.998671i \(0.516411\pi\)
\(588\) −20.8715 185.240i −0.0354958 0.315034i
\(589\) −346.475 276.305i −0.588243 0.469108i
\(590\) 214.337 74.9998i 0.363283 0.127118i
\(591\) 87.4939 776.530i 0.148044 1.31393i
\(592\) −125.731 + 125.731i −0.212383 + 0.212383i
\(593\) 40.7023 32.4590i 0.0686380 0.0547370i −0.588570 0.808446i \(-0.700309\pi\)
0.657208 + 0.753709i \(0.271737\pi\)
\(594\) 344.336 548.007i 0.579690 0.922571i
\(595\) −6.15874 3.86979i −0.0103508 0.00650386i
\(596\) −102.387 128.389i −0.171790 0.215418i
\(597\) 477.899 + 477.899i 0.800500 + 0.800500i
\(598\) −227.485 25.6314i −0.380409 0.0428618i
\(599\) −211.707 605.024i −0.353434 1.01006i −0.974127 0.226002i \(-0.927434\pi\)
0.620693 0.784054i \(-0.286851\pi\)
\(600\) −161.096 + 202.008i −0.268493 + 0.336680i
\(601\) 333.408 37.5661i 0.554756 0.0625060i 0.169864 0.985468i \(-0.445667\pi\)
0.384892 + 0.922962i \(0.374239\pi\)
\(602\) −12.6969 26.3655i −0.0210913 0.0437964i
\(603\) 73.0597 + 320.095i 0.121160 + 0.530838i
\(604\) −0.872245 + 3.82156i −0.00144411 + 0.00632708i
\(605\) −280.522 135.092i −0.463672 0.223293i
\(606\) 93.1986 266.346i 0.153793 0.439515i
\(607\) −54.8088 87.2277i −0.0902945 0.143703i 0.798523 0.601965i \(-0.205615\pi\)
−0.888817 + 0.458262i \(0.848472\pi\)
\(608\) 714.938i 1.17589i
\(609\) −3.58835 18.4098i −0.00589220 0.0302296i
\(610\) −584.690 −0.958508
\(611\) −81.1322 + 50.9787i −0.132786 + 0.0834349i
\(612\) 44.6420 + 15.6209i 0.0729444 + 0.0255243i
\(613\) 356.350 739.969i 0.581322 1.20713i −0.378261 0.925699i \(-0.623478\pi\)
0.959582 0.281428i \(-0.0908080\pi\)
\(614\) 571.898 + 130.532i 0.931430 + 0.212593i
\(615\) −497.233 + 113.490i −0.808509 + 0.184537i
\(616\) 32.1650 15.4899i 0.0522159 0.0251459i
\(617\) 12.5149 + 111.073i 0.0202835 + 0.180021i 0.999769 0.0214938i \(-0.00684223\pi\)
−0.979486 + 0.201515i \(0.935414\pi\)
\(618\) −512.719 408.880i −0.829643 0.661618i
\(619\) −86.4870 + 30.2631i −0.139721 + 0.0488903i −0.399233 0.916849i \(-0.630724\pi\)
0.259513 + 0.965740i \(0.416438\pi\)
\(620\) 9.87823 87.6717i 0.0159326 0.141406i
\(621\) −561.718 + 561.718i −0.904539 + 0.904539i
\(622\) 149.791 119.454i 0.240821 0.192049i
\(623\) −13.1321 + 20.8997i −0.0210789 + 0.0335468i
\(624\) −69.2974 43.5425i −0.111054 0.0697796i
\(625\) −78.4444 98.3662i −0.125511 0.157386i
\(626\) −65.8253 65.8253i −0.105152 0.105152i
\(627\) 953.611 + 107.446i 1.52091 + 0.171366i
\(628\) 43.2653 + 123.645i 0.0688937 + 0.196887i
\(629\) −126.423 + 158.530i −0.200991 + 0.252035i
\(630\) −5.65064 + 0.636675i −0.00896928 + 0.00101059i
\(631\) 106.650 + 221.460i 0.169017 + 0.350967i 0.968222 0.250091i \(-0.0804605\pi\)
−0.799206 + 0.601058i \(0.794746\pi\)
\(632\) −187.818 822.883i −0.297180 1.30203i
\(633\) 105.026 460.147i 0.165917 0.726931i
\(634\) −619.641 298.404i −0.977352 0.470668i
\(635\) −109.600 + 313.217i −0.172598 + 0.493256i
\(636\) 11.9440 + 19.0088i 0.0187799 + 0.0298881i
\(637\) 269.663i 0.423333i
\(638\) −555.172 + 324.614i −0.870175 + 0.508800i
\(639\) −220.064 −0.344388
\(640\) −4.38645 + 2.75619i −0.00685383 + 0.00430655i
\(641\) 916.494 + 320.695i 1.42979 + 0.500305i 0.930551 0.366161i \(-0.119328\pi\)
0.499237 + 0.866466i \(0.333614\pi\)
\(642\) −41.7590 + 86.7134i −0.0650451 + 0.135068i
\(643\) 48.0847 + 10.9750i 0.0747817 + 0.0170684i 0.259748 0.965676i \(-0.416360\pi\)
−0.184966 + 0.982745i \(0.559218\pi\)
\(644\) −12.5941 + 2.87452i −0.0195561 + 0.00446355i
\(645\) 478.609 230.486i 0.742029 0.357342i
\(646\) −36.7714 326.355i −0.0569216 0.505193i
\(647\) −71.4194 56.9551i −0.110386 0.0880295i 0.566742 0.823896i \(-0.308204\pi\)
−0.677127 + 0.735866i \(0.736775\pi\)
\(648\) −263.390 + 92.1640i −0.406465 + 0.142228i
\(649\) −70.2180 + 623.202i −0.108194 + 0.960250i
\(650\) −77.9148 + 77.9148i −0.119869 + 0.119869i
\(651\) 7.73450 6.16806i 0.0118810 0.00947475i
\(652\) 52.8342 84.0852i 0.0810341 0.128965i
\(653\) 207.926 + 130.649i 0.318416 + 0.200074i 0.681751 0.731585i \(-0.261219\pi\)
−0.363334 + 0.931659i \(0.618362\pi\)
\(654\) 202.758 + 254.251i 0.310028 + 0.388762i
\(655\) −248.845 248.845i −0.379916 0.379916i
\(656\) −420.063 47.3298i −0.640340 0.0721490i
\(657\) 62.4279 + 178.409i 0.0950196 + 0.271551i
\(658\) 4.69303 5.88488i 0.00713227 0.00894359i
\(659\) −259.653 + 29.2559i −0.394011 + 0.0443943i −0.306747 0.951791i \(-0.599241\pi\)
−0.0872632 + 0.996185i \(0.527812\pi\)
\(660\) 82.8942 + 172.132i 0.125597 + 0.260805i
\(661\) 217.845 + 954.443i 0.329569 + 1.44394i 0.819953 + 0.572431i \(0.194000\pi\)
−0.490383 + 0.871507i \(0.663143\pi\)
\(662\) −142.010 + 622.188i −0.214517 + 0.939862i
\(663\) −84.0865 40.4939i −0.126827 0.0610768i
\(664\) −3.03536 + 8.67457i −0.00457133 + 0.0130641i
\(665\) −15.0907 24.0167i −0.0226928 0.0361154i
\(666\) 158.520i 0.238018i
\(667\) 752.999 236.814i 1.12893 0.355044i
\(668\) −135.924 −0.203478
\(669\) −55.6495 + 34.9669i −0.0831831 + 0.0522674i
\(670\) 428.420 + 149.911i 0.639432 + 0.223747i
\(671\) 700.629 1454.87i 1.04416 2.16821i
\(672\) −15.5597 3.55140i −0.0231543 0.00528482i
\(673\) 593.737 135.517i 0.882225 0.201362i 0.242671 0.970109i \(-0.421976\pi\)
0.639554 + 0.768747i \(0.279119\pi\)
\(674\) 124.899 60.1483i 0.185310 0.0892408i
\(675\) 42.8112 + 379.960i 0.0634239 + 0.562903i
\(676\) −181.217 144.516i −0.268073 0.213781i
\(677\) 559.076 195.629i 0.825814 0.288965i 0.115907 0.993260i \(-0.463023\pi\)
0.709907 + 0.704295i \(0.248737\pi\)
\(678\) −58.2238 + 516.750i −0.0858758 + 0.762168i
\(679\) −11.6166 + 11.6166i −0.0171084 + 0.0171084i
\(680\) 173.401 138.282i 0.255001 0.203357i
\(681\) −190.332 + 302.911i −0.279488 + 0.444803i
\(682\) −287.210 180.466i −0.421130 0.264613i
\(683\) 217.747 + 273.046i 0.318809 + 0.399774i 0.915252 0.402881i \(-0.131991\pi\)
−0.596443 + 0.802656i \(0.703420\pi\)
\(684\) 130.416 + 130.416i 0.190667 + 0.190667i
\(685\) −150.719 16.9819i −0.220027 0.0247911i
\(686\) 14.0043 + 40.0221i 0.0204145 + 0.0583413i
\(687\) −449.747 + 563.965i −0.654653 + 0.820909i
\(688\) 437.520 49.2967i 0.635930 0.0716521i
\(689\) 14.0907 + 29.2597i 0.0204510 + 0.0424670i
\(690\) 72.6408 + 318.260i 0.105277 + 0.461247i
\(691\) 181.564 795.482i 0.262755 1.15120i −0.655494 0.755200i \(-0.727540\pi\)
0.918249 0.396004i \(-0.129603\pi\)
\(692\) 51.4288 + 24.7668i 0.0743191 + 0.0357902i
\(693\) 5.18690 14.8233i 0.00748471 0.0213901i
\(694\) −318.669 507.159i −0.459178 0.730777i
\(695\) 209.269i 0.301106i
\(696\) 565.991 + 82.1272i 0.813205 + 0.117999i
\(697\) −482.054 −0.691613
\(698\) 629.276 395.400i 0.901541 0.566476i
\(699\) 905.799 + 316.953i 1.29585 + 0.453437i
\(700\) −2.69781 + 5.60206i −0.00385402 + 0.00800295i
\(701\) −924.382 210.984i −1.31866 0.300976i −0.495414 0.868657i \(-0.664984\pi\)
−0.823249 + 0.567681i \(0.807841\pi\)
\(702\) −239.301 + 54.6189i −0.340885 + 0.0778047i
\(703\) −712.409 + 343.078i −1.01338 + 0.488020i
\(704\) 103.681 + 920.193i 0.147274 + 1.30709i
\(705\) 106.827 + 85.1920i 0.151528 + 0.120840i
\(706\) −145.646 + 50.9638i −0.206298 + 0.0721867i
\(707\) 2.57905 22.8897i 0.00364788 0.0323758i
\(708\) 116.261 116.261i 0.164210 0.164210i
\(709\) −268.833 + 214.387i −0.379172 + 0.302380i −0.794467 0.607307i \(-0.792250\pi\)
0.415295 + 0.909687i \(0.363678\pi\)
\(710\) −161.857 + 257.593i −0.227967 + 0.362808i
\(711\) −314.384 197.541i −0.442172 0.277835i
\(712\) −469.261 588.435i −0.659075 0.826454i
\(713\) 294.397 + 294.397i 0.412898 + 0.412898i
\(714\) 7.28535 + 0.820862i 0.0102036 + 0.00114967i
\(715\) 91.2808 + 260.865i 0.127665 + 0.364847i
\(716\) 75.9664 95.2589i 0.106098 0.133043i
\(717\) −470.895 + 53.0571i −0.656757 + 0.0739987i
\(718\) 23.4227 + 48.6377i 0.0326221 + 0.0677405i
\(719\) −258.798 1133.87i −0.359942 1.57701i −0.753334 0.657639i \(-0.771555\pi\)
0.393391 0.919371i \(-0.371302\pi\)
\(720\) 19.0379 83.4107i 0.0264416 0.115848i
\(721\) −48.2311 23.2269i −0.0668947 0.0322148i
\(722\) 241.079 688.965i 0.333905 0.954246i
\(723\) 16.7610 + 26.6750i 0.0231826 + 0.0368949i
\(724\) 210.665i 0.290973i
\(725\) 136.861 354.437i 0.188773 0.488878i
\(726\) 313.831 0.432275
\(727\) 606.627 381.169i 0.834425 0.524304i −0.0457500 0.998953i \(-0.514568\pi\)
0.880175 + 0.474649i \(0.157425\pi\)
\(728\) −12.7797 4.47180i −0.0175545 0.00614259i
\(729\) −312.968 + 649.884i −0.429311 + 0.891474i
\(730\) 254.750 + 58.1451i 0.348973 + 0.0796508i
\(731\) 489.499 111.725i 0.669629 0.152838i
\(732\) −381.421 + 183.683i −0.521067 + 0.250933i
\(733\) −5.44223 48.3011i −0.00742460 0.0658951i 0.989454 0.144850i \(-0.0462701\pi\)
−0.996878 + 0.0789554i \(0.974842\pi\)
\(734\) 274.900 + 219.226i 0.374524 + 0.298673i
\(735\) −362.959 + 127.005i −0.493822 + 0.172796i
\(736\) 75.2034 667.449i 0.102179 0.906860i
\(737\) −886.392 + 886.392i −1.20270 + 1.20270i
\(738\) −294.643 + 234.970i −0.399245 + 0.318387i
\(739\) 266.443 424.041i 0.360545 0.573804i −0.616364 0.787462i \(-0.711395\pi\)
0.976909 + 0.213658i \(0.0685378\pi\)
\(740\) −133.291 83.7524i −0.180123 0.113179i
\(741\) −226.918 284.546i −0.306232 0.384002i
\(742\) −1.80393 1.80393i −0.00243117 0.00243117i
\(743\) −353.124 39.7875i −0.475267 0.0535498i −0.128918 0.991655i \(-0.541150\pi\)
−0.346350 + 0.938106i \(0.612579\pi\)
\(744\) 99.6295 + 284.725i 0.133911 + 0.382694i
\(745\) −211.208 + 264.846i −0.283500 + 0.355498i
\(746\) −678.050 + 76.3979i −0.908914 + 0.102410i
\(747\) 1.75411 + 3.64244i 0.00234820 + 0.00487609i
\(748\) 40.1818 + 176.048i 0.0537190 + 0.235358i
\(749\) −1.74823 + 7.65949i −0.00233408 + 0.0102263i
\(750\) 411.704 + 198.266i 0.548938 + 0.264355i
\(751\) −225.087 + 643.260i −0.299716 + 0.856539i 0.691273 + 0.722594i \(0.257050\pi\)
−0.990989 + 0.133945i \(0.957235\pi\)
\(752\) 60.2523 + 95.8910i 0.0801228 + 0.127515i
\(753\) 143.734i 0.190882i
\(754\) 235.934 + 61.8290i 0.312909 + 0.0820013i
\(755\) 8.08599 0.0107099
\(756\) −11.7278 + 7.36908i −0.0155130 + 0.00974746i
\(757\) −546.623 191.272i −0.722091 0.252671i −0.0558840 0.998437i \(-0.517798\pi\)
−0.666207 + 0.745767i \(0.732083\pi\)
\(758\) 168.188 349.246i 0.221884 0.460747i
\(759\) −878.966 200.618i −1.15806 0.264319i
\(760\) 843.203 192.456i 1.10948 0.253231i
\(761\) 918.062 442.116i 1.20639 0.580966i 0.280899 0.959737i \(-0.409367\pi\)
0.925490 + 0.378771i \(0.123653\pi\)
\(762\) −37.4496 332.375i −0.0491465 0.436187i
\(763\) 20.7545 + 16.5512i 0.0272012 + 0.0216922i
\(764\) 240.749 84.2416i 0.315116 0.110264i
\(765\) 10.9237 96.9508i 0.0142794 0.126733i
\(766\) 238.454 238.454i 0.311298 0.311298i
\(767\) 185.956 148.295i 0.242446 0.193344i
\(768\) 311.747 496.143i 0.405921 0.646019i
\(769\) 165.357 + 103.901i 0.215028 + 0.135111i 0.635240 0.772315i \(-0.280901\pi\)
−0.420211 + 0.907426i \(0.638044\pi\)
\(770\) −13.5363 16.9740i −0.0175796 0.0220442i
\(771\) −693.049 693.049i −0.898896 0.898896i
\(772\) −335.679 37.8219i −0.434817 0.0489921i
\(773\) 269.245 + 769.458i 0.348312 + 0.995418i 0.976154 + 0.217078i \(0.0696525\pi\)
−0.627842 + 0.778341i \(0.716062\pi\)
\(774\) 244.735 306.888i 0.316195 0.396496i
\(775\) 199.137 22.4373i 0.256951 0.0289514i
\(776\) −217.348 451.327i −0.280087 0.581607i
\(777\) −3.92781 17.2089i −0.00505510 0.0221478i
\(778\) −196.236 + 859.766i −0.252231 + 1.10510i
\(779\) −1693.66 815.626i −2.17415 1.04702i
\(780\) 23.9309 68.3907i 0.0306807 0.0876803i
\(781\) −447.013 711.417i −0.572360 0.910906i
\(782\) 308.545i 0.394559i
\(783\) 678.204 506.325i 0.866160 0.646647i
\(784\) −318.718 −0.406527
\(785\) 228.805 143.768i 0.291472 0.183144i
\(786\) 334.812 + 117.156i 0.425970 + 0.149053i
\(787\) 354.355 735.826i 0.450261 0.934976i −0.545064 0.838394i \(-0.683495\pi\)
0.995325 0.0965819i \(-0.0307910\pi\)
\(788\) 559.036 + 127.596i 0.709437 + 0.161924i
\(789\) 28.1712 6.42988i 0.0357049 0.00814941i
\(790\) −462.459 + 222.708i −0.585391 + 0.281909i
\(791\) 4.75282 + 42.1824i 0.00600862 + 0.0533280i
\(792\) 374.393 + 298.568i 0.472718 + 0.376980i
\(793\) −578.044 + 202.266i −0.728934 + 0.255065i
\(794\) 47.6722 423.103i 0.0600406 0.532875i
\(795\) 32.7464 32.7464i 0.0411905 0.0411905i
\(796\) −387.734 + 309.208i −0.487103 + 0.388452i
\(797\) −398.246 + 633.804i −0.499681 + 0.795238i −0.997397 0.0721022i \(-0.977029\pi\)
0.497716 + 0.867340i \(0.334172\pi\)
\(798\) 24.2077 + 15.2107i 0.0303355 + 0.0190610i
\(799\) 80.5206 + 100.970i 0.100777 + 0.126370i
\(800\) −228.605 228.605i −0.285756 0.285756i
\(801\) −329.002 37.0697i −0.410739 0.0462792i
\(802\) −162.869 465.453i −0.203079 0.580366i
\(803\) −449.947 + 564.215i −0.560332 + 0.702634i
\(804\) 326.574 36.7961i 0.406187 0.0457662i
\(805\) 11.5620 + 24.0088i 0.0143628 + 0.0298246i
\(806\) 28.6258 + 125.418i 0.0355158 + 0.155605i
\(807\) 127.209 557.341i 0.157632 0.690633i
\(808\) 632.815 + 304.748i 0.783187 + 0.377163i
\(809\) −332.410 + 949.974i −0.410890 + 1.17426i 0.533605 + 0.845734i \(0.320837\pi\)
−0.944496 + 0.328524i \(0.893449\pi\)
\(810\) 90.2850 + 143.688i 0.111463 + 0.177392i
\(811\) 477.481i 0.588755i 0.955689 + 0.294378i \(0.0951124\pi\)
−0.955689 + 0.294378i \(0.904888\pi\)
\(812\) 13.7188 1.10401i 0.0168950 0.00135962i
\(813\) 518.265 0.637473
\(814\) −512.461 + 322.000i −0.629559 + 0.395578i
\(815\) −193.358 67.6588i −0.237249 0.0830169i
\(816\) −47.8602 + 99.3828i −0.0586522 + 0.121793i
\(817\) 1908.86 + 435.684i 2.33642 + 0.533273i
\(818\) −218.329 + 49.8322i −0.266906 + 0.0609195i
\(819\) −5.36617 + 2.58421i −0.00655210 + 0.00315533i
\(820\) −41.9023 371.893i −0.0511003 0.453528i
\(821\) −287.826 229.534i −0.350580 0.279578i 0.432327 0.901717i \(-0.357693\pi\)
−0.782907 + 0.622139i \(0.786264\pi\)
\(822\) 144.299 50.4925i 0.175547 0.0614264i
\(823\) −133.488 + 1184.74i −0.162196 + 1.43953i 0.604030 + 0.796962i \(0.293561\pi\)
−0.766226 + 0.642571i \(0.777868\pi\)
\(824\) 1154.22 1154.22i 1.40076 1.40076i
\(825\) −339.278 + 270.565i −0.411246 + 0.327958i
\(826\) −9.94048 + 15.8202i −0.0120345 + 0.0191528i
\(827\) 1156.66 + 726.779i 1.39862 + 0.878814i 0.999278 0.0379859i \(-0.0120942\pi\)
0.399347 + 0.916800i \(0.369237\pi\)
\(828\) −108.035 135.472i −0.130477 0.163613i
\(829\) 1047.04 + 1047.04i 1.26302 + 1.26302i 0.949622 + 0.313398i \(0.101467\pi\)
0.313398 + 0.949622i \(0.398533\pi\)
\(830\) 5.55376 + 0.625759i 0.00669128 + 0.000753927i
\(831\) −321.689 919.333i −0.387110 1.10630i
\(832\) 218.965 274.574i 0.263179 0.330017i
\(833\) −361.167 + 40.6938i −0.433574 + 0.0488521i
\(834\) −91.5203 190.044i −0.109737 0.227870i
\(835\) 62.3924 + 273.359i 0.0747214 + 0.327376i
\(836\) −156.694 + 686.520i −0.187433 + 0.821197i
\(837\) 402.196 + 193.687i 0.480521 + 0.231407i
\(838\) −357.127 + 1020.61i −0.426166 + 1.21791i
\(839\) 613.856 + 976.947i 0.731652 + 1.16442i 0.980622 + 0.195907i \(0.0627651\pi\)
−0.248970 + 0.968511i \(0.580092\pi\)
\(840\) 19.3072i 0.0229848i
\(841\) −830.177 + 134.488i −0.987131 + 0.159914i
\(842\) 735.255 0.873224
\(843\) −804.279 + 505.362i −0.954068 + 0.599480i
\(844\) 326.898 + 114.387i 0.387320 + 0.135529i
\(845\) −207.456 + 430.787i −0.245510 + 0.509807i
\(846\) 98.4323 + 22.4665i 0.116350 + 0.0265562i
\(847\) 24.9758 5.70057i 0.0294874 0.00673031i
\(848\) 34.5824 16.6540i 0.0407811 0.0196392i
\(849\) −119.049 1056.59i −0.140223 1.24451i
\(850\) 116.111 + 92.5957i 0.136602 + 0.108936i
\(851\) 701.175 245.352i 0.823943 0.288310i
\(852\) −24.6628 + 218.889i −0.0289470 + 0.256912i
\(853\) −338.738 + 338.738i −0.397114 + 0.397114i −0.877214 0.480100i \(-0.840600\pi\)
0.480100 + 0.877214i \(0.340600\pi\)
\(854\) 37.6122 29.9948i 0.0440424 0.0351227i
\(855\) 202.419 322.147i 0.236747 0.376781i
\(856\) −202.842 127.454i −0.236964 0.148895i
\(857\) −455.913 571.697i −0.531987 0.667091i 0.441119 0.897449i \(-0.354582\pi\)
−0.973106 + 0.230358i \(0.926010\pi\)
\(858\) −196.980 196.980i −0.229581 0.229581i
\(859\) 152.501 + 17.1827i 0.177533 + 0.0200031i 0.200283 0.979738i \(-0.435814\pi\)
−0.0227505 + 0.999741i \(0.507242\pi\)
\(860\) 128.742 + 367.925i 0.149701 + 0.427820i
\(861\) 26.1642 32.8089i 0.0303881 0.0381055i
\(862\) −266.248 + 29.9990i −0.308873 + 0.0348016i
\(863\) 163.086 + 338.651i 0.188975 + 0.392411i 0.973833 0.227265i \(-0.0729784\pi\)
−0.784858 + 0.619676i \(0.787264\pi\)
\(864\) −160.254 702.118i −0.185479 0.812636i
\(865\) 26.2019 114.798i 0.0302913 0.132715i
\(866\) −7.23351 3.48348i −0.00835279 0.00402249i
\(867\) 175.970 502.893i 0.202964 0.580038i
\(868\) 3.86213 + 6.14655i 0.00444946 + 0.00708128i
\(869\) 1417.60i 1.63130i
\(870\) −27.8991 346.681i −0.0320679 0.398483i
\(871\) 475.410 0.545821
\(872\) −685.377 + 430.651i −0.785982 + 0.493865i
\(873\) −207.995 72.7806i −0.238253 0.0833683i
\(874\) −522.052 + 1084.05i −0.597313 + 1.24033i
\(875\) 36.3662 + 8.30035i 0.0415614 + 0.00948612i
\(876\) 184.452 42.1001i 0.210562 0.0480594i
\(877\) −57.8702 + 27.8688i −0.0659866 + 0.0317775i −0.466586 0.884476i \(-0.654516\pi\)
0.400599 + 0.916253i \(0.368802\pi\)
\(878\) −91.6075 813.039i −0.104337 0.926013i
\(879\) 538.845 + 429.715i 0.613021 + 0.488868i
\(880\) 308.320 107.886i 0.350363 0.122597i
\(881\) 45.7401 405.955i 0.0519184 0.460789i −0.940675 0.339308i \(-0.889807\pi\)
0.992594 0.121481i \(-0.0387643\pi\)
\(882\) −200.918 + 200.918i −0.227799 + 0.227799i
\(883\) 215.197 171.614i 0.243711 0.194353i −0.494015 0.869454i \(-0.664471\pi\)
0.737726 + 0.675100i \(0.235900\pi\)
\(884\) 36.4355 57.9867i 0.0412166 0.0655959i
\(885\) −287.181 180.448i −0.324499 0.203896i
\(886\) −417.674 523.747i −0.471415 0.591136i
\(887\) −519.628 519.628i −0.585826 0.585826i 0.350672 0.936498i \(-0.385953\pi\)
−0.936498 + 0.350672i \(0.885953\pi\)
\(888\) 534.845 + 60.2626i 0.602303 + 0.0678632i
\(889\) −9.01777 25.7713i −0.0101437 0.0289891i
\(890\) −285.372 + 357.846i −0.320643 + 0.402074i
\(891\) −465.723 + 52.4744i −0.522697 + 0.0588938i
\(892\) −20.9249 43.4509i −0.0234584 0.0487118i
\(893\) 112.065 + 490.990i 0.125493 + 0.549820i
\(894\) 75.9785 332.884i 0.0849871 0.372353i
\(895\) −226.448 109.051i −0.253014 0.121845i
\(896\) 0.140781 0.402328i 0.000157121 0.000449027i
\(897\) 181.914 + 289.514i 0.202802 + 0.322758i
\(898\) 78.1466i 0.0870229i
\(899\) −265.365 355.446i −0.295178 0.395380i
\(900\) −83.4024 −0.0926694
\(901\) 37.0620 23.2876i 0.0411343 0.0258464i
\(902\) −1358.11 475.223i −1.50567 0.526855i
\(903\) −18.9642 + 39.3796i −0.0210013 + 0.0436097i
\(904\) −1261.92 288.024i −1.39593 0.318611i
\(905\) 423.672 96.7004i 0.468146 0.106851i
\(906\) −7.34316 + 3.53628i −0.00810503 + 0.00390318i
\(907\) −71.1673 631.627i −0.0784645 0.696391i −0.969944 0.243330i \(-0.921760\pi\)
0.891479 0.453062i \(-0.149668\pi\)
\(908\) −205.237 163.671i −0.226032 0.180255i
\(909\) 291.634 102.047i 0.320830 0.112263i
\(910\) −0.921891 + 8.18201i −0.00101307 + 0.00899122i
\(911\) 1005.04 1005.04i 1.10323 1.10323i 0.109207 0.994019i \(-0.465169\pi\)
0.994019 0.109207i \(-0.0348310\pi\)
\(912\) −336.308 + 268.196i −0.368758 + 0.294075i
\(913\) −8.21210 + 13.0695i −0.00899463 + 0.0143149i
\(914\) −420.411 264.162i −0.459968 0.289017i
\(915\) 544.491 + 682.770i 0.595072 + 0.746196i
\(916\) −374.278 374.278i −0.408600 0.408600i
\(917\) 28.7736 + 3.24201i 0.0313780 + 0.00353545i
\(918\) 109.265 + 312.260i 0.119025 + 0.340153i
\(919\) 390.750 489.985i 0.425190 0.533172i −0.522383 0.852711i \(-0.674957\pi\)
0.947573 + 0.319539i \(0.103528\pi\)
\(920\) −807.438 + 90.9764i −0.877650 + 0.0988874i
\(921\) −380.150 789.389i −0.412758 0.857100i
\(922\) −3.13040 13.7152i −0.00339523 0.0148755i
\(923\) −70.9057 + 310.658i −0.0768209 + 0.336574i
\(924\) −14.1629 6.82047i −0.0153278 0.00738146i
\(925\) 118.095 337.497i 0.127671 0.364861i
\(926\) −86.9427 138.369i −0.0938906 0.149426i
\(927\) 718.056i 0.774601i
\(928\) −181.408 + 692.238i −0.195483 + 0.745946i
\(929\) 314.415 0.338445 0.169222 0.985578i \(-0.445874\pi\)
0.169222 + 0.985578i \(0.445874\pi\)
\(930\) 155.327 97.5982i 0.167018 0.104944i
\(931\) −1337.79 468.113i −1.43694 0.502807i
\(932\) −305.532 + 634.444i −0.327824 + 0.680734i
\(933\) −278.985 63.6764i −0.299019 0.0682491i
\(934\) 1049.88 239.629i 1.12407 0.256562i
\(935\) 335.610 161.621i 0.358941 0.172857i
\(936\) −20.3340 180.469i −0.0217243 0.192809i
\(937\) 1133.62 + 904.034i 1.20984 + 0.964818i 0.999917 0.0128995i \(-0.00410614\pi\)
0.209926 + 0.977717i \(0.432678\pi\)
\(938\) −35.2501 + 12.3345i −0.0375800 + 0.0131498i
\(939\) −15.5677 + 138.167i −0.0165790 + 0.147143i
\(940\) −70.8965 + 70.8965i −0.0754218 + 0.0754218i
\(941\) −774.360 + 617.532i −0.822912 + 0.656250i −0.941620 0.336679i \(-0.890696\pi\)
0.118708 + 0.992929i \(0.462125\pi\)
\(942\) −144.911 + 230.625i −0.153833 + 0.244824i
\(943\) 1495.37 + 939.603i 1.58576 + 0.996397i
\(944\) −175.271 219.783i −0.185669 0.232821i
\(945\) 20.2035 + 20.2035i 0.0213793 + 0.0213793i
\(946\) 1489.23 + 167.796i 1.57424 + 0.177374i
\(947\) −223.766 639.488i −0.236290 0.675278i −0.999573 0.0292137i \(-0.990700\pi\)
0.763283 0.646064i \(-0.223586\pi\)
\(948\) −231.719 + 290.567i −0.244430 + 0.306505i
\(949\) 271.969 30.6436i 0.286585 0.0322904i
\(950\) 251.279 + 521.787i 0.264504 + 0.549249i
\(951\) 228.579 + 1001.47i 0.240357 + 1.05307i
\(952\) −4.06068 + 17.7910i −0.00426542 + 0.0186880i
\(953\) 109.037 + 52.5095i 0.114415 + 0.0550992i 0.490216 0.871601i \(-0.336918\pi\)
−0.375801 + 0.926700i \(0.622632\pi\)
\(954\) 11.3020 32.2993i 0.0118470 0.0338567i
\(955\) −279.930 445.506i −0.293120 0.466498i
\(956\) 347.723i 0.363727i
\(957\) 896.070 + 346.004i 0.936332 + 0.361551i
\(958\) 483.673 0.504878
\(959\) 10.5667 6.63949i 0.0110184 0.00692335i
\(960\) −472.697 165.404i −0.492392 0.172295i
\(961\) −315.451 + 655.040i −0.328253 + 0.681624i
\(962\) 223.779 + 51.0761i 0.232618 + 0.0530936i
\(963\) −102.740 + 23.4498i −0.106688 + 0.0243508i
\(964\) −20.8277 + 10.0301i −0.0216055 + 0.0104047i
\(965\) 78.0206 + 692.452i 0.0808504 + 0.717567i
\(966\) −20.9997 16.7467i −0.0217388 0.0173362i
\(967\) −929.620 + 325.288i −0.961345 + 0.336389i −0.764917 0.644129i \(-0.777220\pi\)
−0.196428 + 0.980518i \(0.562934\pi\)
\(968\) −87.4611 + 776.239i −0.0903524 + 0.801900i
\(969\) −346.857 + 346.857i −0.357953 + 0.357953i
\(970\) −238.173 + 189.936i −0.245539 + 0.195811i
\(971\) 13.1141 20.8709i 0.0135058 0.0214943i −0.839903 0.542736i \(-0.817388\pi\)
0.853409 + 0.521242i \(0.174531\pi\)
\(972\) −267.859 168.307i −0.275576 0.173156i
\(973\) −10.7356 13.4620i −0.0110335 0.0138355i
\(974\) 293.580 + 293.580i 0.301417 + 0.301417i
\(975\) 163.543 + 18.4268i 0.167736 + 0.0188993i
\(976\) 239.061 + 683.197i 0.244939 + 0.699997i
\(977\) 778.385 976.064i 0.796709 0.999042i −0.203093 0.979159i \(-0.565099\pi\)
0.999802 0.0198824i \(-0.00632919\pi\)
\(978\) 205.184 23.1187i 0.209800 0.0236387i
\(979\) −548.461 1138.89i −0.560226 1.16332i
\(980\) −62.7885 275.094i −0.0640699 0.280709i
\(981\) −79.2339 + 347.147i −0.0807685 + 0.353870i
\(982\) 54.8197 + 26.3998i 0.0558245 + 0.0268837i
\(983\) −470.193 + 1343.73i −0.478324 + 1.36697i 0.411809 + 0.911270i \(0.364897\pi\)
−0.890133 + 0.455701i \(0.849389\pi\)
\(984\) 680.775 + 1083.45i 0.691844 + 1.10106i
\(985\) 1182.86i 1.20087i
\(986\) 47.2055 325.323i 0.0478757 0.329942i
\(987\) −11.2424 −0.0113905
\(988\) 226.126 142.084i 0.228873 0.143810i
\(989\) −1736.23 607.534i −1.75554 0.614291i
\(990\) 126.353 262.374i 0.127629 0.265025i
\(991\) −598.205 136.536i −0.603638 0.137776i −0.0902298 0.995921i \(-0.528760\pi\)
−0.513408 + 0.858145i \(0.671617\pi\)
\(992\) −367.980 + 83.9890i −0.370947 + 0.0846663i
\(993\) 858.806 413.579i 0.864860 0.416494i
\(994\) −2.80262 24.8739i −0.00281953 0.0250241i
\(995\) 799.834 + 637.846i 0.803853 + 0.641051i
\(996\) 3.81958 1.33653i 0.00383491 0.00134189i
\(997\) −157.753 + 1400.10i −0.158228 + 1.40431i 0.624053 + 0.781382i \(0.285485\pi\)
−0.782280 + 0.622927i \(0.785943\pi\)
\(998\) 811.971 811.971i 0.813598 0.813598i
\(999\) 622.733 496.613i 0.623356 0.497110i
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 29.3.f.a.10.2 yes 48
3.2 odd 2 261.3.s.a.10.3 48
29.3 odd 28 inner 29.3.f.a.3.2 48
87.32 even 28 261.3.s.a.235.3 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
29.3.f.a.3.2 48 29.3 odd 28 inner
29.3.f.a.10.2 yes 48 1.1 even 1 trivial
261.3.s.a.10.3 48 3.2 odd 2
261.3.s.a.235.3 48 87.32 even 28