Properties

Label 930.2.j.g.497.5
Level $930$
Weight $2$
Character 930.497
Analytic conductor $7.426$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [930,2,Mod(497,930)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(930, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("930.497");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.j (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.42608738798\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(20\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 497.5
Character \(\chi\) \(=\) 930.497
Dual form 930.2.j.g.683.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} +(-0.673165 - 1.59589i) q^{3} -1.00000i q^{4} +(-1.55932 - 1.60266i) q^{5} +(1.60446 + 0.652462i) q^{6} +(-0.700251 - 0.700251i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.09370 + 2.14859i) q^{9} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} +(-0.673165 - 1.59589i) q^{3} -1.00000i q^{4} +(-1.55932 - 1.60266i) q^{5} +(1.60446 + 0.652462i) q^{6} +(-0.700251 - 0.700251i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.09370 + 2.14859i) q^{9} +(2.23586 + 0.0306496i) q^{10} -4.42224i q^{11} +(-1.59589 + 0.673165i) q^{12} +(0.282488 - 0.282488i) q^{13} +0.990304 q^{14} +(-1.50799 + 3.56735i) q^{15} -1.00000 q^{16} +(-1.25971 + 1.25971i) q^{17} +(-0.0388113 - 2.99975i) q^{18} -5.10691i q^{19} +(-1.60266 + 1.55932i) q^{20} +(-0.646136 + 1.58890i) q^{21} +(3.12700 + 3.12700i) q^{22} +(-3.17479 - 3.17479i) q^{23} +(0.652462 - 1.60446i) q^{24} +(-0.137056 + 4.99812i) q^{25} +0.399498i q^{26} +(4.83830 + 1.89495i) q^{27} +(-0.700251 + 0.700251i) q^{28} +0.862782 q^{29} +(-1.45619 - 3.58880i) q^{30} +1.00000 q^{31} +(0.707107 - 0.707107i) q^{32} +(-7.05739 + 2.97689i) q^{33} -1.78149i q^{34} +(-0.0303525 + 2.21418i) q^{35} +(2.14859 + 2.09370i) q^{36} +(-1.12067 - 1.12067i) q^{37} +(3.61113 + 3.61113i) q^{38} +(-0.640978 - 0.260657i) q^{39} +(0.0306496 - 2.23586i) q^{40} +9.40638i q^{41} +(-0.666638 - 1.58041i) q^{42} +(-5.61274 + 5.61274i) q^{43} -4.42224 q^{44} +(6.70820 + 0.00516463i) q^{45} +4.48983 q^{46} +(-5.96081 + 5.96081i) q^{47} +(0.673165 + 1.59589i) q^{48} -6.01930i q^{49} +(-3.43729 - 3.63112i) q^{50} +(2.85834 + 1.16236i) q^{51} +(-0.282488 - 0.282488i) q^{52} +(7.34070 + 7.34070i) q^{53} +(-4.76113 + 2.08126i) q^{54} +(-7.08736 + 6.89568i) q^{55} -0.990304i q^{56} +(-8.15004 + 3.43779i) q^{57} +(-0.610079 + 0.610079i) q^{58} +0.852824 q^{59} +(3.56735 + 1.50799i) q^{60} -3.32914 q^{61} +(-0.707107 + 0.707107i) q^{62} +(2.97066 - 0.0384350i) q^{63} +1.00000i q^{64} +(-0.893220 - 0.0122445i) q^{65} +(2.88534 - 7.09531i) q^{66} +(7.00567 + 7.00567i) q^{67} +(1.25971 + 1.25971i) q^{68} +(-2.92945 + 7.20376i) q^{69} +(-1.54420 - 1.58712i) q^{70} -2.54520i q^{71} +(-2.99975 + 0.0388113i) q^{72} +(-8.92808 + 8.92808i) q^{73} +1.58487 q^{74} +(8.06869 - 3.14583i) q^{75} -5.10691 q^{76} +(-3.09668 + 3.09668i) q^{77} +(0.637553 - 0.268928i) q^{78} -2.12954i q^{79} +(1.55932 + 1.60266i) q^{80} +(-0.232848 - 8.99699i) q^{81} +(-6.65131 - 6.65131i) q^{82} +(3.12488 + 3.12488i) q^{83} +(1.58890 + 0.646136i) q^{84} +(3.98317 + 0.0546021i) q^{85} -7.93762i q^{86} +(-0.580794 - 1.37690i) q^{87} +(3.12700 - 3.12700i) q^{88} +2.60883 q^{89} +(-4.74707 + 4.73976i) q^{90} -0.395624 q^{91} +(-3.17479 + 3.17479i) q^{92} +(-0.673165 - 1.59589i) q^{93} -8.42986i q^{94} +(-8.18466 + 7.96330i) q^{95} +(-1.60446 - 0.652462i) q^{96} +(-11.2793 - 11.2793i) q^{97} +(4.25629 + 4.25629i) q^{98} +(9.50156 + 9.25884i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q - 4 q^{3} - 8 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 40 q - 4 q^{3} - 8 q^{7} + 8 q^{10} + 4 q^{12} - 20 q^{13} - 44 q^{15} - 40 q^{16} + 16 q^{18} - 32 q^{21} - 4 q^{22} + 8 q^{25} + 8 q^{27} - 8 q^{28} - 4 q^{30} + 40 q^{31} + 48 q^{33} + 64 q^{37} - 4 q^{40} - 20 q^{42} - 48 q^{43} - 4 q^{45} - 80 q^{46} + 4 q^{48} + 48 q^{51} + 20 q^{52} + 164 q^{55} + 40 q^{57} + 56 q^{58} + 24 q^{60} - 128 q^{61} + 56 q^{63} + 8 q^{66} - 4 q^{67} - 56 q^{70} - 16 q^{72} - 48 q^{73} - 48 q^{75} - 40 q^{76} - 36 q^{78} - 24 q^{81} - 16 q^{82} - 56 q^{85} - 12 q^{87} - 4 q^{88} - 28 q^{90} - 32 q^{91} - 4 q^{93} - 52 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(187\) \(311\) \(871\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 + 0.707107i −0.500000 + 0.500000i
\(3\) −0.673165 1.59589i −0.388652 0.921385i
\(4\) 1.00000i 0.500000i
\(5\) −1.55932 1.60266i −0.697348 0.716733i
\(6\) 1.60446 + 0.652462i 0.655018 + 0.266367i
\(7\) −0.700251 0.700251i −0.264670 0.264670i 0.562278 0.826948i \(-0.309925\pi\)
−0.826948 + 0.562278i \(0.809925\pi\)
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) −2.09370 + 2.14859i −0.697900 + 0.716196i
\(10\) 2.23586 + 0.0306496i 0.707040 + 0.00969227i
\(11\) 4.42224i 1.33336i −0.745346 0.666678i \(-0.767716\pi\)
0.745346 0.666678i \(-0.232284\pi\)
\(12\) −1.59589 + 0.673165i −0.460692 + 0.194326i
\(13\) 0.282488 0.282488i 0.0783480 0.0783480i −0.666847 0.745195i \(-0.732356\pi\)
0.745195 + 0.666847i \(0.232356\pi\)
\(14\) 0.990304 0.264670
\(15\) −1.50799 + 3.56735i −0.389361 + 0.921085i
\(16\) −1.00000 −0.250000
\(17\) −1.25971 + 1.25971i −0.305524 + 0.305524i −0.843170 0.537647i \(-0.819313\pi\)
0.537647 + 0.843170i \(0.319313\pi\)
\(18\) −0.0388113 2.99975i −0.00914792 0.707048i
\(19\) 5.10691i 1.17161i −0.810454 0.585803i \(-0.800779\pi\)
0.810454 0.585803i \(-0.199221\pi\)
\(20\) −1.60266 + 1.55932i −0.358366 + 0.348674i
\(21\) −0.646136 + 1.58890i −0.140998 + 0.346727i
\(22\) 3.12700 + 3.12700i 0.666678 + 0.666678i
\(23\) −3.17479 3.17479i −0.661990 0.661990i 0.293859 0.955849i \(-0.405060\pi\)
−0.955849 + 0.293859i \(0.905060\pi\)
\(24\) 0.652462 1.60446i 0.133183 0.327509i
\(25\) −0.137056 + 4.99812i −0.0274113 + 0.999624i
\(26\) 0.399498i 0.0783480i
\(27\) 4.83830 + 1.89495i 0.931132 + 0.364684i
\(28\) −0.700251 + 0.700251i −0.132335 + 0.132335i
\(29\) 0.862782 0.160215 0.0801073 0.996786i \(-0.474474\pi\)
0.0801073 + 0.996786i \(0.474474\pi\)
\(30\) −1.45619 3.58880i −0.265862 0.655223i
\(31\) 1.00000 0.179605
\(32\) 0.707107 0.707107i 0.125000 0.125000i
\(33\) −7.05739 + 2.97689i −1.22853 + 0.518211i
\(34\) 1.78149i 0.305524i
\(35\) −0.0303525 + 2.21418i −0.00513050 + 0.374265i
\(36\) 2.14859 + 2.09370i 0.358098 + 0.348950i
\(37\) −1.12067 1.12067i −0.184238 0.184238i 0.608962 0.793200i \(-0.291586\pi\)
−0.793200 + 0.608962i \(0.791586\pi\)
\(38\) 3.61113 + 3.61113i 0.585803 + 0.585803i
\(39\) −0.640978 0.260657i −0.102639 0.0417385i
\(40\) 0.0306496 2.23586i 0.00484613 0.353520i
\(41\) 9.40638i 1.46903i 0.678593 + 0.734515i \(0.262590\pi\)
−0.678593 + 0.734515i \(0.737410\pi\)
\(42\) −0.666638 1.58041i −0.102864 0.243863i
\(43\) −5.61274 + 5.61274i −0.855935 + 0.855935i −0.990856 0.134921i \(-0.956922\pi\)
0.134921 + 0.990856i \(0.456922\pi\)
\(44\) −4.42224 −0.666678
\(45\) 6.70820 + 0.00516463i 1.00000 + 0.000769898i
\(46\) 4.48983 0.661990
\(47\) −5.96081 + 5.96081i −0.869473 + 0.869473i −0.992414 0.122941i \(-0.960768\pi\)
0.122941 + 0.992414i \(0.460768\pi\)
\(48\) 0.673165 + 1.59589i 0.0971629 + 0.230346i
\(49\) 6.01930i 0.859900i
\(50\) −3.43729 3.63112i −0.486106 0.513518i
\(51\) 2.85834 + 1.16236i 0.400247 + 0.162763i
\(52\) −0.282488 0.282488i −0.0391740 0.0391740i
\(53\) 7.34070 + 7.34070i 1.00832 + 1.00832i 0.999965 + 0.00835762i \(0.00266034\pi\)
0.00835762 + 0.999965i \(0.497340\pi\)
\(54\) −4.76113 + 2.08126i −0.647908 + 0.283224i
\(55\) −7.08736 + 6.89568i −0.955659 + 0.929813i
\(56\) 0.990304i 0.132335i
\(57\) −8.15004 + 3.43779i −1.07950 + 0.455347i
\(58\) −0.610079 + 0.610079i −0.0801073 + 0.0801073i
\(59\) 0.852824 0.111028 0.0555141 0.998458i \(-0.482320\pi\)
0.0555141 + 0.998458i \(0.482320\pi\)
\(60\) 3.56735 + 1.50799i 0.460543 + 0.194680i
\(61\) −3.32914 −0.426253 −0.213126 0.977025i \(-0.568365\pi\)
−0.213126 + 0.977025i \(0.568365\pi\)
\(62\) −0.707107 + 0.707107i −0.0898027 + 0.0898027i
\(63\) 2.97066 0.0384350i 0.374268 0.00484236i
\(64\) 1.00000i 0.125000i
\(65\) −0.893220 0.0122445i −0.110790 0.00151874i
\(66\) 2.88534 7.09531i 0.355161 0.873372i
\(67\) 7.00567 + 7.00567i 0.855879 + 0.855879i 0.990850 0.134970i \(-0.0430939\pi\)
−0.134970 + 0.990850i \(0.543094\pi\)
\(68\) 1.25971 + 1.25971i 0.152762 + 0.152762i
\(69\) −2.92945 + 7.20376i −0.352664 + 0.867231i
\(70\) −1.54420 1.58712i −0.184567 0.189698i
\(71\) 2.54520i 0.302060i −0.988529 0.151030i \(-0.951741\pi\)
0.988529 0.151030i \(-0.0482589\pi\)
\(72\) −2.99975 + 0.0388113i −0.353524 + 0.00457396i
\(73\) −8.92808 + 8.92808i −1.04495 + 1.04495i −0.0460116 + 0.998941i \(0.514651\pi\)
−0.998941 + 0.0460116i \(0.985349\pi\)
\(74\) 1.58487 0.184238
\(75\) 8.06869 3.14583i 0.931692 0.363249i
\(76\) −5.10691 −0.585803
\(77\) −3.09668 + 3.09668i −0.352899 + 0.352899i
\(78\) 0.637553 0.268928i 0.0721886 0.0304501i
\(79\) 2.12954i 0.239592i −0.992799 0.119796i \(-0.961776\pi\)
0.992799 0.119796i \(-0.0382241\pi\)
\(80\) 1.55932 + 1.60266i 0.174337 + 0.179183i
\(81\) −0.232848 8.99699i −0.0258720 0.999665i
\(82\) −6.65131 6.65131i −0.734515 0.734515i
\(83\) 3.12488 + 3.12488i 0.343000 + 0.343000i 0.857494 0.514494i \(-0.172020\pi\)
−0.514494 + 0.857494i \(0.672020\pi\)
\(84\) 1.58890 + 0.646136i 0.173364 + 0.0704992i
\(85\) 3.98317 + 0.0546021i 0.432035 + 0.00592243i
\(86\) 7.93762i 0.855935i
\(87\) −0.580794 1.37690i −0.0622677 0.147619i
\(88\) 3.12700 3.12700i 0.333339 0.333339i
\(89\) 2.60883 0.276536 0.138268 0.990395i \(-0.455847\pi\)
0.138268 + 0.990395i \(0.455847\pi\)
\(90\) −4.74707 + 4.73976i −0.500385 + 0.499615i
\(91\) −0.395624 −0.0414727
\(92\) −3.17479 + 3.17479i −0.330995 + 0.330995i
\(93\) −0.673165 1.59589i −0.0698039 0.165486i
\(94\) 8.42986i 0.869473i
\(95\) −8.18466 + 7.96330i −0.839728 + 0.817017i
\(96\) −1.60446 0.652462i −0.163755 0.0665916i
\(97\) −11.2793 11.2793i −1.14524 1.14524i −0.987477 0.157762i \(-0.949572\pi\)
−0.157762 0.987477i \(-0.550428\pi\)
\(98\) 4.25629 + 4.25629i 0.429950 + 0.429950i
\(99\) 9.50156 + 9.25884i 0.954943 + 0.930548i
\(100\) 4.99812 + 0.137056i 0.499812 + 0.0137056i
\(101\) 3.97281i 0.395309i 0.980272 + 0.197655i \(0.0633325\pi\)
−0.980272 + 0.197655i \(0.936668\pi\)
\(102\) −2.84306 + 1.19924i −0.281505 + 0.118742i
\(103\) 4.23054 4.23054i 0.416848 0.416848i −0.467268 0.884116i \(-0.654762\pi\)
0.884116 + 0.467268i \(0.154762\pi\)
\(104\) 0.399498 0.0391740
\(105\) 3.55401 1.44207i 0.346836 0.140731i
\(106\) −10.3813 −1.00832
\(107\) −10.3058 + 10.3058i −0.996300 + 0.996300i −0.999993 0.00369355i \(-0.998824\pi\)
0.00369355 + 0.999993i \(0.498824\pi\)
\(108\) 1.89495 4.83830i 0.182342 0.465566i
\(109\) 6.25281i 0.598911i −0.954110 0.299455i \(-0.903195\pi\)
0.954110 0.299455i \(-0.0968050\pi\)
\(110\) 0.135540 9.88750i 0.0129232 0.942736i
\(111\) −1.03407 + 2.54287i −0.0981496 + 0.241358i
\(112\) 0.700251 + 0.700251i 0.0661675 + 0.0661675i
\(113\) −8.71474 8.71474i −0.819814 0.819814i 0.166267 0.986081i \(-0.446829\pi\)
−0.986081 + 0.166267i \(0.946829\pi\)
\(114\) 3.33207 8.19384i 0.312077 0.767423i
\(115\) −0.137612 + 10.0386i −0.0128324 + 0.936107i
\(116\) 0.862782i 0.0801073i
\(117\) 0.0155050 + 1.19839i 0.00143344 + 0.110791i
\(118\) −0.603038 + 0.603038i −0.0555141 + 0.0555141i
\(119\) 1.76422 0.161726
\(120\) −3.58880 + 1.45619i −0.327612 + 0.132931i
\(121\) −8.55620 −0.777836
\(122\) 2.35406 2.35406i 0.213126 0.213126i
\(123\) 15.0115 6.33204i 1.35354 0.570941i
\(124\) 1.00000i 0.0898027i
\(125\) 8.22402 7.57400i 0.735579 0.677439i
\(126\) −2.07340 + 2.12775i −0.184713 + 0.189555i
\(127\) −9.03363 9.03363i −0.801605 0.801605i 0.181742 0.983346i \(-0.441827\pi\)
−0.983346 + 0.181742i \(0.941827\pi\)
\(128\) −0.707107 0.707107i −0.0625000 0.0625000i
\(129\) 12.7356 + 5.17899i 1.12131 + 0.455985i
\(130\) 0.640260 0.622944i 0.0561545 0.0546358i
\(131\) 10.6882i 0.933831i −0.884302 0.466915i \(-0.845365\pi\)
0.884302 0.466915i \(-0.154635\pi\)
\(132\) 2.97689 + 7.05739i 0.259105 + 0.614267i
\(133\) −3.57612 + 3.57612i −0.310089 + 0.310089i
\(134\) −9.90752 −0.855879
\(135\) −4.50748 10.7090i −0.387942 0.921684i
\(136\) −1.78149 −0.152762
\(137\) −3.13371 + 3.13371i −0.267731 + 0.267731i −0.828185 0.560455i \(-0.810626\pi\)
0.560455 + 0.828185i \(0.310626\pi\)
\(138\) −3.02240 7.16526i −0.257283 0.609947i
\(139\) 21.5733i 1.82982i −0.403657 0.914911i \(-0.632261\pi\)
0.403657 0.914911i \(-0.367739\pi\)
\(140\) 2.21418 + 0.0303525i 0.187132 + 0.00256525i
\(141\) 13.5254 + 5.50016i 1.13904 + 0.463197i
\(142\) 1.79973 + 1.79973i 0.151030 + 0.151030i
\(143\) −1.24923 1.24923i −0.104466 0.104466i
\(144\) 2.09370 2.14859i 0.174475 0.179049i
\(145\) −1.34535 1.38275i −0.111725 0.114831i
\(146\) 12.6262i 1.04495i
\(147\) −9.60611 + 4.05198i −0.792298 + 0.334201i
\(148\) −1.12067 + 1.12067i −0.0921189 + 0.0921189i
\(149\) −6.21215 −0.508919 −0.254460 0.967083i \(-0.581898\pi\)
−0.254460 + 0.967083i \(0.581898\pi\)
\(150\) −3.48099 + 7.92986i −0.284221 + 0.647471i
\(151\) 14.5620 1.18504 0.592521 0.805555i \(-0.298133\pi\)
0.592521 + 0.805555i \(0.298133\pi\)
\(152\) 3.61113 3.61113i 0.292901 0.292901i
\(153\) −0.0691421 5.34403i −0.00558981 0.432040i
\(154\) 4.37936i 0.352899i
\(155\) −1.55932 1.60266i −0.125247 0.128729i
\(156\) −0.260657 + 0.640978i −0.0208693 + 0.0513193i
\(157\) −11.2599 11.2599i −0.898639 0.898639i 0.0966771 0.995316i \(-0.469179\pi\)
−0.995316 + 0.0966771i \(0.969179\pi\)
\(158\) 1.50581 + 1.50581i 0.119796 + 0.119796i
\(159\) 6.77342 16.6564i 0.537167 1.32094i
\(160\) −2.23586 0.0306496i −0.176760 0.00242307i
\(161\) 4.44630i 0.350418i
\(162\) 6.52648 + 6.19718i 0.512769 + 0.486897i
\(163\) −13.8251 + 13.8251i −1.08287 + 1.08287i −0.0866262 + 0.996241i \(0.527609\pi\)
−0.996241 + 0.0866262i \(0.972391\pi\)
\(164\) 9.40638 0.734515
\(165\) 15.7757 + 6.66869i 1.22813 + 0.519156i
\(166\) −4.41925 −0.343000
\(167\) 18.0679 18.0679i 1.39814 1.39814i 0.592759 0.805380i \(-0.298038\pi\)
0.805380 0.592759i \(-0.201962\pi\)
\(168\) −1.58041 + 0.666638i −0.121931 + 0.0514322i
\(169\) 12.8404i 0.987723i
\(170\) −2.85513 + 2.77791i −0.218979 + 0.213056i
\(171\) 10.9726 + 10.6923i 0.839099 + 0.817663i
\(172\) 5.61274 + 5.61274i 0.427968 + 0.427968i
\(173\) 8.14142 + 8.14142i 0.618980 + 0.618980i 0.945270 0.326290i \(-0.105798\pi\)
−0.326290 + 0.945270i \(0.605798\pi\)
\(174\) 1.38430 + 0.562933i 0.104943 + 0.0426758i
\(175\) 3.59591 3.40396i 0.271825 0.257316i
\(176\) 4.42224i 0.333339i
\(177\) −0.574091 1.36101i −0.0431513 0.102300i
\(178\) −1.84472 + 1.84472i −0.138268 + 0.138268i
\(179\) 12.7857 0.955645 0.477822 0.878456i \(-0.341426\pi\)
0.477822 + 0.878456i \(0.341426\pi\)
\(180\) 0.00516463 6.70820i 0.000384949 0.500000i
\(181\) 2.73755 0.203480 0.101740 0.994811i \(-0.467559\pi\)
0.101740 + 0.994811i \(0.467559\pi\)
\(182\) 0.279749 0.279749i 0.0207364 0.0207364i
\(183\) 2.24106 + 5.31292i 0.165664 + 0.392743i
\(184\) 4.48983i 0.330995i
\(185\) −0.0485758 + 3.54355i −0.00357136 + 0.260527i
\(186\) 1.60446 + 0.652462i 0.117645 + 0.0478408i
\(187\) 5.57072 + 5.57072i 0.407372 + 0.407372i
\(188\) 5.96081 + 5.96081i 0.434737 + 0.434737i
\(189\) −2.06108 4.71497i −0.149922 0.342963i
\(190\) 0.156525 11.4183i 0.0113555 0.828372i
\(191\) 6.29907i 0.455785i 0.973686 + 0.227892i \(0.0731835\pi\)
−0.973686 + 0.227892i \(0.926817\pi\)
\(192\) 1.59589 0.673165i 0.115173 0.0485815i
\(193\) −8.56703 + 8.56703i −0.616668 + 0.616668i −0.944675 0.328007i \(-0.893623\pi\)
0.328007 + 0.944675i \(0.393623\pi\)
\(194\) 15.9513 1.14524
\(195\) 0.581743 + 1.43372i 0.0416595 + 0.102671i
\(196\) −6.01930 −0.429950
\(197\) −0.661707 + 0.661707i −0.0471447 + 0.0471447i −0.730286 0.683141i \(-0.760613\pi\)
0.683141 + 0.730286i \(0.260613\pi\)
\(198\) −13.2656 + 0.171633i −0.942746 + 0.0121974i
\(199\) 16.9809i 1.20375i 0.798592 + 0.601873i \(0.205579\pi\)
−0.798592 + 0.601873i \(0.794421\pi\)
\(200\) −3.63112 + 3.43729i −0.256759 + 0.243053i
\(201\) 6.46428 15.8962i 0.455955 1.12123i
\(202\) −2.80920 2.80920i −0.197655 0.197655i
\(203\) −0.604164 0.604164i −0.0424040 0.0424040i
\(204\) 1.16236 2.85834i 0.0813813 0.200124i
\(205\) 15.0753 14.6675i 1.05290 1.02442i
\(206\) 5.98289i 0.416848i
\(207\) 13.4684 0.174256i 0.936116 0.0121117i
\(208\) −0.282488 + 0.282488i −0.0195870 + 0.0195870i
\(209\) −22.5840 −1.56217
\(210\) −1.49337 + 3.53276i −0.103052 + 0.243784i
\(211\) −10.8572 −0.747442 −0.373721 0.927541i \(-0.621918\pi\)
−0.373721 + 0.927541i \(0.621918\pi\)
\(212\) 7.34070 7.34070i 0.504161 0.504161i
\(213\) −4.06185 + 1.71334i −0.278313 + 0.117396i
\(214\) 14.5746i 0.996300i
\(215\) 17.7474 + 0.243285i 1.21036 + 0.0165919i
\(216\) 2.08126 + 4.76113i 0.141612 + 0.323954i
\(217\) −0.700251 0.700251i −0.0475361 0.0475361i
\(218\) 4.42141 + 4.42141i 0.299455 + 0.299455i
\(219\) 20.2583 + 8.23812i 1.36893 + 0.556681i
\(220\) 6.89568 + 7.08736i 0.464906 + 0.477830i
\(221\) 0.711703i 0.0478743i
\(222\) −1.06688 2.52928i −0.0716043 0.169754i
\(223\) −0.145214 + 0.145214i −0.00972426 + 0.00972426i −0.711952 0.702228i \(-0.752189\pi\)
0.702228 + 0.711952i \(0.252189\pi\)
\(224\) −0.990304 −0.0661675
\(225\) −10.4519 10.7590i −0.696796 0.717269i
\(226\) 12.3245 0.819814
\(227\) 14.9233 14.9233i 0.990492 0.990492i −0.00946342 0.999955i \(-0.503012\pi\)
0.999955 + 0.00946342i \(0.00301234\pi\)
\(228\) 3.43779 + 8.15004i 0.227673 + 0.539750i
\(229\) 18.0957i 1.19579i −0.801573 0.597897i \(-0.796003\pi\)
0.801573 0.597897i \(-0.203997\pi\)
\(230\) −7.00108 7.19569i −0.461637 0.474470i
\(231\) 7.02651 + 2.85737i 0.462311 + 0.188001i
\(232\) 0.610079 + 0.610079i 0.0400537 + 0.0400537i
\(233\) −12.6901 12.6901i −0.831358 0.831358i 0.156344 0.987703i \(-0.450029\pi\)
−0.987703 + 0.156344i \(0.950029\pi\)
\(234\) −0.858356 0.836428i −0.0561125 0.0546790i
\(235\) 18.8480 + 0.258372i 1.22951 + 0.0168543i
\(236\) 0.852824i 0.0555141i
\(237\) −3.39850 + 1.43353i −0.220757 + 0.0931179i
\(238\) −1.24749 + 1.24749i −0.0808629 + 0.0808629i
\(239\) −10.4687 −0.677162 −0.338581 0.940937i \(-0.609947\pi\)
−0.338581 + 0.940937i \(0.609947\pi\)
\(240\) 1.50799 3.56735i 0.0973402 0.230271i
\(241\) −6.58071 −0.423901 −0.211950 0.977280i \(-0.567982\pi\)
−0.211950 + 0.977280i \(0.567982\pi\)
\(242\) 6.05015 6.05015i 0.388918 0.388918i
\(243\) −14.2014 + 6.42805i −0.911021 + 0.412360i
\(244\) 3.32914i 0.213126i
\(245\) −9.64690 + 9.38600i −0.616318 + 0.599649i
\(246\) −6.13730 + 15.0922i −0.391300 + 0.962241i
\(247\) −1.44264 1.44264i −0.0917929 0.0917929i
\(248\) 0.707107 + 0.707107i 0.0449013 + 0.0449013i
\(249\) 2.88339 7.09050i 0.182727 0.449342i
\(250\) −0.459629 + 11.1709i −0.0290695 + 0.706509i
\(251\) 2.94903i 0.186141i −0.995660 0.0930705i \(-0.970332\pi\)
0.995660 0.0930705i \(-0.0296682\pi\)
\(252\) −0.0384350 2.97066i −0.00242118 0.187134i
\(253\) −14.0397 + 14.0397i −0.882667 + 0.882667i
\(254\) 12.7755 0.801605
\(255\) −2.59419 6.39343i −0.162454 0.400372i
\(256\) 1.00000 0.0625000
\(257\) 3.32257 3.32257i 0.207256 0.207256i −0.595844 0.803100i \(-0.703182\pi\)
0.803100 + 0.595844i \(0.203182\pi\)
\(258\) −12.6675 + 5.34332i −0.788646 + 0.332661i
\(259\) 1.56951i 0.0975244i
\(260\) −0.0122445 + 0.893220i −0.000759369 + 0.0553952i
\(261\) −1.80641 + 1.85376i −0.111814 + 0.114745i
\(262\) 7.55769 + 7.55769i 0.466915 + 0.466915i
\(263\) −14.3978 14.3978i −0.887805 0.887805i 0.106507 0.994312i \(-0.466033\pi\)
−0.994312 + 0.106507i \(0.966033\pi\)
\(264\) −7.09531 2.88534i −0.436686 0.177581i
\(265\) 0.318184 23.2112i 0.0195459 1.42585i
\(266\) 5.05740i 0.310089i
\(267\) −1.75617 4.16340i −0.107476 0.254796i
\(268\) 7.00567 7.00567i 0.427940 0.427940i
\(269\) −24.5047 −1.49408 −0.747038 0.664781i \(-0.768525\pi\)
−0.747038 + 0.664781i \(0.768525\pi\)
\(270\) 10.7597 + 4.38513i 0.654813 + 0.266871i
\(271\) 25.1352 1.52686 0.763428 0.645893i \(-0.223515\pi\)
0.763428 + 0.645893i \(0.223515\pi\)
\(272\) 1.25971 1.25971i 0.0763809 0.0763809i
\(273\) 0.266320 + 0.631371i 0.0161184 + 0.0382123i
\(274\) 4.43173i 0.267731i
\(275\) 22.1029 + 0.606097i 1.33285 + 0.0365490i
\(276\) 7.20376 + 2.92945i 0.433615 + 0.176332i
\(277\) −11.6986 11.6986i −0.702902 0.702902i 0.262131 0.965032i \(-0.415575\pi\)
−0.965032 + 0.262131i \(0.915575\pi\)
\(278\) 15.2546 + 15.2546i 0.914911 + 0.914911i
\(279\) −2.09370 + 2.14859i −0.125346 + 0.128633i
\(280\) −1.58712 + 1.54420i −0.0948488 + 0.0922835i
\(281\) 8.51957i 0.508235i 0.967173 + 0.254118i \(0.0817850\pi\)
−0.967173 + 0.254118i \(0.918215\pi\)
\(282\) −13.4531 + 5.67468i −0.801119 + 0.337922i
\(283\) 14.1299 14.1299i 0.839937 0.839937i −0.148913 0.988850i \(-0.547577\pi\)
0.988850 + 0.148913i \(0.0475774\pi\)
\(284\) −2.54520 −0.151030
\(285\) 18.2181 + 7.70116i 1.07915 + 0.456177i
\(286\) 1.76667 0.104466
\(287\) 6.58682 6.58682i 0.388808 0.388808i
\(288\) 0.0388113 + 2.99975i 0.00228698 + 0.176762i
\(289\) 13.8263i 0.813311i
\(290\) 1.92906 + 0.0264440i 0.113278 + 0.00155284i
\(291\) −10.4076 + 25.5933i −0.610107 + 1.50031i
\(292\) 8.92808 + 8.92808i 0.522476 + 0.522476i
\(293\) 20.0654 + 20.0654i 1.17223 + 1.17223i 0.981676 + 0.190558i \(0.0610296\pi\)
0.190558 + 0.981676i \(0.438970\pi\)
\(294\) 3.92736 9.65772i 0.229048 0.563250i
\(295\) −1.32982 1.36679i −0.0774254 0.0795776i
\(296\) 1.58487i 0.0921189i
\(297\) 8.37993 21.3961i 0.486253 1.24153i
\(298\) 4.39266 4.39266i 0.254460 0.254460i
\(299\) −1.79368 −0.103731
\(300\) −3.14583 8.06869i −0.181625 0.465846i
\(301\) 7.86066 0.453081
\(302\) −10.2969 + 10.2969i −0.592521 + 0.592521i
\(303\) 6.34015 2.67436i 0.364232 0.153638i
\(304\) 5.10691i 0.292901i
\(305\) 5.19119 + 5.33549i 0.297246 + 0.305509i
\(306\) 3.82769 + 3.72991i 0.218815 + 0.213225i
\(307\) 3.42153 + 3.42153i 0.195277 + 0.195277i 0.797972 0.602695i \(-0.205906\pi\)
−0.602695 + 0.797972i \(0.705906\pi\)
\(308\) 3.09668 + 3.09668i 0.176450 + 0.176450i
\(309\) −9.59931 3.90361i −0.546086 0.222069i
\(310\) 2.23586 + 0.0306496i 0.126988 + 0.00174078i
\(311\) 13.5393i 0.767745i −0.923386 0.383872i \(-0.874590\pi\)
0.923386 0.383872i \(-0.125410\pi\)
\(312\) −0.268928 0.637553i −0.0152250 0.0360943i
\(313\) −14.6089 + 14.6089i −0.825742 + 0.825742i −0.986925 0.161183i \(-0.948469\pi\)
0.161183 + 0.986925i \(0.448469\pi\)
\(314\) 15.9239 0.898639
\(315\) −4.69381 4.70104i −0.264466 0.264874i
\(316\) −2.12954 −0.119796
\(317\) −1.18936 + 1.18936i −0.0668012 + 0.0668012i −0.739718 0.672917i \(-0.765041\pi\)
0.672917 + 0.739718i \(0.265041\pi\)
\(318\) 6.98833 + 16.5674i 0.391886 + 0.929053i
\(319\) 3.81543i 0.213623i
\(320\) 1.60266 1.55932i 0.0895916 0.0871685i
\(321\) 23.3844 + 9.50938i 1.30519 + 0.530762i
\(322\) −3.14401 3.14401i −0.175209 0.175209i
\(323\) 6.43321 + 6.43321i 0.357953 + 0.357953i
\(324\) −8.99699 + 0.232848i −0.499833 + 0.0129360i
\(325\) 1.37319 + 1.45062i 0.0761709 + 0.0804661i
\(326\) 19.5517i 1.08287i
\(327\) −9.97877 + 4.20917i −0.551827 + 0.232768i
\(328\) −6.65131 + 6.65131i −0.367257 + 0.367257i
\(329\) 8.34812 0.460247
\(330\) −15.8706 + 6.43961i −0.873645 + 0.354489i
\(331\) −13.6823 −0.752048 −0.376024 0.926610i \(-0.622709\pi\)
−0.376024 + 0.926610i \(0.622709\pi\)
\(332\) 3.12488 3.12488i 0.171500 0.171500i
\(333\) 4.75422 0.0615110i 0.260530 0.00337078i
\(334\) 25.5519i 1.39814i
\(335\) 0.303662 22.1518i 0.0165908 1.21028i
\(336\) 0.646136 1.58890i 0.0352496 0.0866818i
\(337\) −0.457008 0.457008i −0.0248948 0.0248948i 0.694550 0.719445i \(-0.255604\pi\)
−0.719445 + 0.694550i \(0.755604\pi\)
\(338\) −9.07953 9.07953i −0.493862 0.493862i
\(339\) −8.04127 + 19.7742i −0.436742 + 1.07399i
\(340\) 0.0546021 3.98317i 0.00296122 0.216018i
\(341\) 4.42224i 0.239478i
\(342\) −15.3194 + 0.198206i −0.828381 + 0.0107177i
\(343\) −9.11677 + 9.11677i −0.492260 + 0.492260i
\(344\) −7.93762 −0.427968
\(345\) 16.1131 6.53804i 0.867502 0.351996i
\(346\) −11.5137 −0.618980
\(347\) 9.05827 9.05827i 0.486273 0.486273i −0.420855 0.907128i \(-0.638270\pi\)
0.907128 + 0.420855i \(0.138270\pi\)
\(348\) −1.37690 + 0.580794i −0.0738097 + 0.0311338i
\(349\) 0.0529227i 0.00283289i −0.999999 0.00141644i \(-0.999549\pi\)
0.999999 0.00141644i \(-0.000450868\pi\)
\(350\) −0.135728 + 4.94966i −0.00725495 + 0.264570i
\(351\) 1.90206 0.831460i 0.101524 0.0443800i
\(352\) −3.12700 3.12700i −0.166669 0.166669i
\(353\) −2.59840 2.59840i −0.138299 0.138299i 0.634568 0.772867i \(-0.281178\pi\)
−0.772867 + 0.634568i \(0.781178\pi\)
\(354\) 1.36832 + 0.556436i 0.0727255 + 0.0295742i
\(355\) −4.07910 + 3.96877i −0.216496 + 0.210641i
\(356\) 2.60883i 0.138268i
\(357\) −1.18761 2.81549i −0.0628550 0.149012i
\(358\) −9.04082 + 9.04082i −0.477822 + 0.477822i
\(359\) −21.5350 −1.13658 −0.568288 0.822830i \(-0.692394\pi\)
−0.568288 + 0.822830i \(0.692394\pi\)
\(360\) 4.73976 + 4.74707i 0.249807 + 0.250192i
\(361\) −7.08053 −0.372660
\(362\) −1.93574 + 1.93574i −0.101740 + 0.101740i
\(363\) 5.75973 + 13.6547i 0.302307 + 0.716686i
\(364\) 0.395624i 0.0207364i
\(365\) 28.2304 + 0.386989i 1.47765 + 0.0202559i
\(366\) −5.34147 2.17214i −0.279203 0.113539i
\(367\) 20.7979 + 20.7979i 1.08564 + 1.08564i 0.995972 + 0.0896685i \(0.0285807\pi\)
0.0896685 + 0.995972i \(0.471419\pi\)
\(368\) 3.17479 + 3.17479i 0.165497 + 0.165497i
\(369\) −20.2104 19.6941i −1.05211 1.02524i
\(370\) −2.47132 2.54002i −0.128478 0.132049i
\(371\) 10.2807i 0.533745i
\(372\) −1.59589 + 0.673165i −0.0827428 + 0.0349020i
\(373\) 13.2229 13.2229i 0.684658 0.684658i −0.276388 0.961046i \(-0.589138\pi\)
0.961046 + 0.276388i \(0.0891376\pi\)
\(374\) −7.87819 −0.407372
\(375\) −17.6234 8.02604i −0.910066 0.414463i
\(376\) −8.42986 −0.434737
\(377\) 0.243725 0.243725i 0.0125525 0.0125525i
\(378\) 4.79139 + 1.87658i 0.246443 + 0.0965208i
\(379\) 8.35532i 0.429184i −0.976704 0.214592i \(-0.931158\pi\)
0.976704 0.214592i \(-0.0688422\pi\)
\(380\) 7.96330 + 8.18466i 0.408508 + 0.419864i
\(381\) −8.33551 + 20.4977i −0.427041 + 1.05013i
\(382\) −4.45412 4.45412i −0.227892 0.227892i
\(383\) −5.02031 5.02031i −0.256526 0.256526i 0.567114 0.823640i \(-0.308060\pi\)
−0.823640 + 0.567114i \(0.808060\pi\)
\(384\) −0.652462 + 1.60446i −0.0332958 + 0.0818773i
\(385\) 9.79163 + 0.134226i 0.499028 + 0.00684078i
\(386\) 12.1156i 0.616668i
\(387\) −0.308069 23.8109i −0.0156600 1.21037i
\(388\) −11.2793 + 11.2793i −0.572620 + 0.572620i
\(389\) −28.9564 −1.46815 −0.734073 0.679071i \(-0.762383\pi\)
−0.734073 + 0.679071i \(0.762383\pi\)
\(390\) −1.42515 0.602438i −0.0721652 0.0305056i
\(391\) 7.99861 0.404507
\(392\) 4.25629 4.25629i 0.214975 0.214975i
\(393\) −17.0571 + 7.19490i −0.860417 + 0.362935i
\(394\) 0.935795i 0.0471447i
\(395\) −3.41294 + 3.32063i −0.171724 + 0.167079i
\(396\) 9.25884 9.50156i 0.465274 0.477472i
\(397\) −18.5427 18.5427i −0.930629 0.930629i 0.0671160 0.997745i \(-0.478620\pi\)
−0.997745 + 0.0671160i \(0.978620\pi\)
\(398\) −12.0073 12.0073i −0.601873 0.601873i
\(399\) 8.11439 + 3.29976i 0.406228 + 0.165195i
\(400\) 0.137056 4.99812i 0.00685282 0.249906i
\(401\) 21.3665i 1.06699i −0.845803 0.533496i \(-0.820878\pi\)
0.845803 0.533496i \(-0.179122\pi\)
\(402\) 6.66939 + 15.8113i 0.332639 + 0.788594i
\(403\) 0.282488 0.282488i 0.0140717 0.0140717i
\(404\) 3.97281 0.197655
\(405\) −14.0561 + 14.4023i −0.698451 + 0.715658i
\(406\) 0.854417 0.0424040
\(407\) −4.95589 + 4.95589i −0.245654 + 0.245654i
\(408\) 1.19924 + 2.84306i 0.0593711 + 0.140752i
\(409\) 12.6304i 0.624535i −0.949994 0.312267i \(-0.898911\pi\)
0.949994 0.312267i \(-0.101089\pi\)
\(410\) −0.288302 + 21.0313i −0.0142382 + 1.03866i
\(411\) 7.11053 + 2.89153i 0.350737 + 0.142629i
\(412\) −4.23054 4.23054i −0.208424 0.208424i
\(413\) −0.597191 0.597191i −0.0293858 0.0293858i
\(414\) −9.40036 + 9.64679i −0.462002 + 0.474114i
\(415\) 0.135448 9.88080i 0.00664889 0.485030i
\(416\) 0.399498i 0.0195870i
\(417\) −34.4285 + 14.5224i −1.68597 + 0.711163i
\(418\) 15.9693 15.9693i 0.781083 0.781083i
\(419\) −27.4856 −1.34276 −0.671381 0.741113i \(-0.734298\pi\)
−0.671381 + 0.741113i \(0.734298\pi\)
\(420\) −1.44207 3.55401i −0.0703657 0.173418i
\(421\) −12.5192 −0.610147 −0.305073 0.952329i \(-0.598681\pi\)
−0.305073 + 0.952329i \(0.598681\pi\)
\(422\) 7.67721 7.67721i 0.373721 0.373721i
\(423\) −0.327174 25.2875i −0.0159077 1.22952i
\(424\) 10.3813i 0.504161i
\(425\) −6.12351 6.46882i −0.297034 0.313784i
\(426\) 1.66065 4.08367i 0.0804586 0.197855i
\(427\) 2.33123 + 2.33123i 0.112816 + 0.112816i
\(428\) 10.3058 + 10.3058i 0.498150 + 0.498150i
\(429\) −1.15269 + 2.83456i −0.0556523 + 0.136854i
\(430\) −12.7213 + 12.3773i −0.613477 + 0.596885i
\(431\) 9.08020i 0.437378i 0.975795 + 0.218689i \(0.0701780\pi\)
−0.975795 + 0.218689i \(0.929822\pi\)
\(432\) −4.83830 1.89495i −0.232783 0.0911709i
\(433\) −6.99720 + 6.99720i −0.336264 + 0.336264i −0.854959 0.518695i \(-0.826418\pi\)
0.518695 + 0.854959i \(0.326418\pi\)
\(434\) 0.990304 0.0475361
\(435\) −1.30107 + 3.07784i −0.0623813 + 0.147571i
\(436\) −6.25281 −0.299455
\(437\) −16.2134 + 16.2134i −0.775591 + 0.775591i
\(438\) −20.1500 + 8.49952i −0.962803 + 0.406123i
\(439\) 37.6408i 1.79650i −0.439486 0.898249i \(-0.644840\pi\)
0.439486 0.898249i \(-0.355160\pi\)
\(440\) −9.88750 0.135540i −0.471368 0.00646162i
\(441\) 12.9330 + 12.6026i 0.615856 + 0.600124i
\(442\) −0.503250 0.503250i −0.0239372 0.0239372i
\(443\) −14.9275 14.9275i −0.709225 0.709225i 0.257147 0.966372i \(-0.417218\pi\)
−0.966372 + 0.257147i \(0.917218\pi\)
\(444\) 2.54287 + 1.03407i 0.120679 + 0.0490748i
\(445\) −4.06800 4.18108i −0.192842 0.198202i
\(446\) 0.205364i 0.00972426i
\(447\) 4.18180 + 9.91388i 0.197792 + 0.468911i
\(448\) 0.700251 0.700251i 0.0330837 0.0330837i
\(449\) −20.5392 −0.969305 −0.484653 0.874707i \(-0.661054\pi\)
−0.484653 + 0.874707i \(0.661054\pi\)
\(450\) 14.9984 + 0.217151i 0.707033 + 0.0102366i
\(451\) 41.5972 1.95874
\(452\) −8.71474 + 8.71474i −0.409907 + 0.409907i
\(453\) −9.80265 23.2393i −0.460569 1.09188i
\(454\) 21.1047i 0.990492i
\(455\) 0.616904 + 0.634052i 0.0289209 + 0.0297248i
\(456\) −8.19384 3.33207i −0.383712 0.156038i
\(457\) 1.21507 + 1.21507i 0.0568387 + 0.0568387i 0.734955 0.678116i \(-0.237203\pi\)
−0.678116 + 0.734955i \(0.737203\pi\)
\(458\) 12.7956 + 12.7956i 0.597897 + 0.597897i
\(459\) −8.48192 + 3.70776i −0.395902 + 0.173063i
\(460\) 10.0386 + 0.137612i 0.468053 + 0.00641618i
\(461\) 5.57688i 0.259741i 0.991531 + 0.129871i \(0.0414562\pi\)
−0.991531 + 0.129871i \(0.958544\pi\)
\(462\) −6.98896 + 2.94803i −0.325156 + 0.137155i
\(463\) −15.0409 + 15.0409i −0.699009 + 0.699009i −0.964197 0.265188i \(-0.914566\pi\)
0.265188 + 0.964197i \(0.414566\pi\)
\(464\) −0.862782 −0.0400537
\(465\) −1.50799 + 3.56735i −0.0699313 + 0.165432i
\(466\) 17.9466 0.831358
\(467\) −23.1199 + 23.1199i −1.06986 + 1.06986i −0.0724925 + 0.997369i \(0.523095\pi\)
−0.997369 + 0.0724925i \(0.976905\pi\)
\(468\) 1.19839 0.0155050i 0.0553957 0.000716721i
\(469\) 9.81146i 0.453051i
\(470\) −13.5102 + 13.1448i −0.623180 + 0.606326i
\(471\) −10.3898 + 25.5493i −0.478735 + 1.17725i
\(472\) 0.603038 + 0.603038i 0.0277571 + 0.0277571i
\(473\) 24.8209 + 24.8209i 1.14127 + 1.14127i
\(474\) 1.38945 3.41677i 0.0638193 0.156937i
\(475\) 25.5250 + 0.699935i 1.17117 + 0.0321152i
\(476\) 1.76422i 0.0808629i
\(477\) −31.1413 + 0.402913i −1.42586 + 0.0184481i
\(478\) 7.40247 7.40247i 0.338581 0.338581i
\(479\) −35.0571 −1.60180 −0.800900 0.598799i \(-0.795645\pi\)
−0.800900 + 0.598799i \(0.795645\pi\)
\(480\) 1.45619 + 3.58880i 0.0664655 + 0.163806i
\(481\) −0.633153 −0.0288693
\(482\) 4.65326 4.65326i 0.211950 0.211950i
\(483\) 7.09578 2.99309i 0.322869 0.136190i
\(484\) 8.55620i 0.388918i
\(485\) −0.488903 + 35.6649i −0.0221999 + 1.61946i
\(486\) 5.49660 14.5872i 0.249331 0.661690i
\(487\) 9.20945 + 9.20945i 0.417320 + 0.417320i 0.884279 0.466959i \(-0.154650\pi\)
−0.466959 + 0.884279i \(0.654650\pi\)
\(488\) −2.35406 2.35406i −0.106563 0.106563i
\(489\) 31.3699 + 12.7567i 1.41860 + 0.576879i
\(490\) 0.184489 13.4583i 0.00833438 0.607984i
\(491\) 32.9660i 1.48774i 0.668326 + 0.743868i \(0.267011\pi\)
−0.668326 + 0.743868i \(0.732989\pi\)
\(492\) −6.33204 15.0115i −0.285470 0.676771i
\(493\) −1.08685 + 1.08685i −0.0489494 + 0.0489494i
\(494\) 2.04020 0.0917929
\(495\) 0.0228392 29.6653i 0.00102655 1.33335i
\(496\) −1.00000 −0.0449013
\(497\) −1.78228 + 1.78228i −0.0799461 + 0.0799461i
\(498\) 2.97488 + 7.05261i 0.133308 + 0.316035i
\(499\) 28.0406i 1.25527i 0.778508 + 0.627635i \(0.215977\pi\)
−0.778508 + 0.627635i \(0.784023\pi\)
\(500\) −7.57400 8.22402i −0.338720 0.367789i
\(501\) −40.9970 16.6717i −1.83161 0.744835i
\(502\) 2.08528 + 2.08528i 0.0930705 + 0.0930705i
\(503\) −26.9938 26.9938i −1.20360 1.20360i −0.973065 0.230530i \(-0.925954\pi\)
−0.230530 0.973065i \(-0.574046\pi\)
\(504\) 2.12775 + 2.07340i 0.0947777 + 0.0923565i
\(505\) 6.36708 6.19487i 0.283331 0.275668i
\(506\) 19.8551i 0.882667i
\(507\) 20.4918 8.64370i 0.910073 0.383880i
\(508\) −9.03363 + 9.03363i −0.400802 + 0.400802i
\(509\) −30.0807 −1.33330 −0.666652 0.745369i \(-0.732273\pi\)
−0.666652 + 0.745369i \(0.732273\pi\)
\(510\) 6.35521 + 2.68647i 0.281413 + 0.118959i
\(511\) 12.5038 0.553135
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) 9.67735 24.7088i 0.427265 1.09092i
\(514\) 4.69882i 0.207256i
\(515\) −13.3769 0.183373i −0.589456 0.00808040i
\(516\) 5.17899 12.7356i 0.227992 0.560653i
\(517\) 26.3601 + 26.3601i 1.15932 + 1.15932i
\(518\) −1.10981 1.10981i −0.0487622 0.0487622i
\(519\) 7.51225 18.4733i 0.329751 0.810887i
\(520\) −0.622944 0.640260i −0.0273179 0.0280773i
\(521\) 24.4421i 1.07083i −0.844589 0.535415i \(-0.820155\pi\)
0.844589 0.535415i \(-0.179845\pi\)
\(522\) −0.0334857 2.58813i −0.00146563 0.113279i
\(523\) −6.56960 + 6.56960i −0.287269 + 0.287269i −0.835999 0.548731i \(-0.815111\pi\)
0.548731 + 0.835999i \(0.315111\pi\)
\(524\) −10.6882 −0.466915
\(525\) −7.85298 3.44724i −0.342732 0.150450i
\(526\) 20.3615 0.887805
\(527\) −1.25971 + 1.25971i −0.0548737 + 0.0548737i
\(528\) 7.05739 2.97689i 0.307133 0.129553i
\(529\) 2.84140i 0.123539i
\(530\) 16.1878 + 16.6378i 0.703152 + 0.722698i
\(531\) −1.78556 + 1.83237i −0.0774866 + 0.0795180i
\(532\) 3.57612 + 3.57612i 0.155044 + 0.155044i
\(533\) 2.65718 + 2.65718i 0.115095 + 0.115095i
\(534\) 4.18577 + 1.70216i 0.181136 + 0.0736598i
\(535\) 32.5868 + 0.446706i 1.40885 + 0.0193128i
\(536\) 9.90752i 0.427940i
\(537\) −8.60685 20.4044i −0.371413 0.880517i
\(538\) 17.3274 17.3274i 0.747038 0.747038i
\(539\) −26.6188 −1.14655
\(540\) −10.7090 + 4.50748i −0.460842 + 0.193971i
\(541\) −11.5909 −0.498330 −0.249165 0.968461i \(-0.580156\pi\)
−0.249165 + 0.968461i \(0.580156\pi\)
\(542\) −17.7733 + 17.7733i −0.763428 + 0.763428i
\(543\) −1.84282 4.36881i −0.0790830 0.187484i
\(544\) 1.78149i 0.0763809i
\(545\) −10.0212 + 9.75012i −0.429259 + 0.417649i
\(546\) −0.634764 0.258130i −0.0271654 0.0110469i
\(547\) 1.55467 + 1.55467i 0.0664731 + 0.0664731i 0.739562 0.673089i \(-0.235033\pi\)
−0.673089 + 0.739562i \(0.735033\pi\)
\(548\) 3.13371 + 3.13371i 0.133865 + 0.133865i
\(549\) 6.97022 7.15294i 0.297482 0.305280i
\(550\) −16.0577 + 15.2005i −0.684702 + 0.648153i
\(551\) 4.40615i 0.187708i
\(552\) −7.16526 + 3.02240i −0.304974 + 0.128642i
\(553\) −1.49121 + 1.49121i −0.0634129 + 0.0634129i
\(554\) 16.5443 0.702902
\(555\) 5.68780 2.30787i 0.241434 0.0979637i
\(556\) −21.5733 −0.914911
\(557\) 13.8257 13.8257i 0.585812 0.585812i −0.350682 0.936494i \(-0.614050\pi\)
0.936494 + 0.350682i \(0.114050\pi\)
\(558\) −0.0388113 2.99975i −0.00164301 0.126989i
\(559\) 3.17106i 0.134122i
\(560\) 0.0303525 2.21418i 0.00128263 0.0935662i
\(561\) 5.14022 12.6402i 0.217020 0.533672i
\(562\) −6.02425 6.02425i −0.254118 0.254118i
\(563\) −20.7731 20.7731i −0.875481 0.875481i 0.117582 0.993063i \(-0.462486\pi\)
−0.993063 + 0.117582i \(0.962486\pi\)
\(564\) 5.50016 13.5254i 0.231599 0.569521i
\(565\) −0.377742 + 27.5558i −0.0158917 + 1.15928i
\(566\) 19.9827i 0.839937i
\(567\) −6.13710 + 6.46320i −0.257734 + 0.271429i
\(568\) 1.79973 1.79973i 0.0755149 0.0755149i
\(569\) −7.64700 −0.320579 −0.160290 0.987070i \(-0.551243\pi\)
−0.160290 + 0.987070i \(0.551243\pi\)
\(570\) −18.3277 + 7.43662i −0.767663 + 0.311486i
\(571\) 11.8402 0.495498 0.247749 0.968824i \(-0.420309\pi\)
0.247749 + 0.968824i \(0.420309\pi\)
\(572\) −1.24923 + 1.24923i −0.0522328 + 0.0522328i
\(573\) 10.0526 4.24031i 0.419953 0.177142i
\(574\) 9.31517i 0.388808i
\(575\) 16.3031 15.4329i 0.679887 0.643595i
\(576\) −2.14859 2.09370i −0.0895244 0.0872375i
\(577\) 1.73481 + 1.73481i 0.0722212 + 0.0722212i 0.742295 0.670074i \(-0.233737\pi\)
−0.670074 + 0.742295i \(0.733737\pi\)
\(578\) −9.77666 9.77666i −0.406655 0.406655i
\(579\) 19.4390 + 7.90497i 0.807858 + 0.328519i
\(580\) −1.38275 + 1.34535i −0.0574155 + 0.0558627i
\(581\) 4.37640i 0.181564i
\(582\) −10.7379 25.4565i −0.445099 1.05521i
\(583\) 32.4623 32.4623i 1.34445 1.34445i
\(584\) −12.6262 −0.522476
\(585\) 1.89644 1.89352i 0.0784083 0.0782876i
\(586\) −28.3768 −1.17223
\(587\) −6.61726 + 6.61726i −0.273124 + 0.273124i −0.830356 0.557233i \(-0.811863\pi\)
0.557233 + 0.830356i \(0.311863\pi\)
\(588\) 4.05198 + 9.60611i 0.167101 + 0.396149i
\(589\) 5.10691i 0.210427i
\(590\) 1.90679 + 0.0261388i 0.0785015 + 0.00107612i
\(591\) 1.50145 + 0.610571i 0.0617612 + 0.0251155i
\(592\) 1.12067 + 1.12067i 0.0460594 + 0.0460594i
\(593\) 31.9338 + 31.9338i 1.31137 + 1.31137i 0.920409 + 0.390957i \(0.127856\pi\)
0.390957 + 0.920409i \(0.372144\pi\)
\(594\) 9.20384 + 21.0548i 0.377638 + 0.863891i
\(595\) −2.75098 2.82745i −0.112779 0.115914i
\(596\) 6.21215i 0.254460i
\(597\) 27.0996 11.4310i 1.10911 0.467838i
\(598\) 1.26832 1.26832i 0.0518655 0.0518655i
\(599\) 41.0791 1.67845 0.839223 0.543787i \(-0.183010\pi\)
0.839223 + 0.543787i \(0.183010\pi\)
\(600\) 7.92986 + 3.48099i 0.323735 + 0.142111i
\(601\) 23.6759 0.965761 0.482880 0.875686i \(-0.339591\pi\)
0.482880 + 0.875686i \(0.339591\pi\)
\(602\) −5.55832 + 5.55832i −0.226540 + 0.226540i
\(603\) −29.7201 + 0.384524i −1.21029 + 0.0156590i
\(604\) 14.5620i 0.592521i
\(605\) 13.3418 + 13.7127i 0.542423 + 0.557501i
\(606\) −2.59211 + 6.37422i −0.105297 + 0.258935i
\(607\) 5.00888 + 5.00888i 0.203304 + 0.203304i 0.801414 0.598110i \(-0.204081\pi\)
−0.598110 + 0.801414i \(0.704081\pi\)
\(608\) −3.61113 3.61113i −0.146451 0.146451i
\(609\) −0.557475 + 1.37088i −0.0225900 + 0.0555508i
\(610\) −7.44348 0.102037i −0.301378 0.00413135i
\(611\) 3.36771i 0.136243i
\(612\) −5.34403 + 0.0691421i −0.216020 + 0.00279490i
\(613\) 15.0946 15.0946i 0.609664 0.609664i −0.333194 0.942858i \(-0.608127\pi\)
0.942858 + 0.333194i \(0.108127\pi\)
\(614\) −4.83877 −0.195277
\(615\) −33.5558 14.1847i −1.35310 0.571983i
\(616\) −4.37936 −0.176450
\(617\) 26.1869 26.1869i 1.05425 1.05425i 0.0558042 0.998442i \(-0.482228\pi\)
0.998442 0.0558042i \(-0.0177723\pi\)
\(618\) 9.54800 4.02747i 0.384077 0.162009i
\(619\) 33.2037i 1.33457i 0.744803 + 0.667284i \(0.232543\pi\)
−0.744803 + 0.667284i \(0.767457\pi\)
\(620\) −1.60266 + 1.55932i −0.0643645 + 0.0626237i
\(621\) −9.34452 21.3767i −0.374983 0.857816i
\(622\) 9.57375 + 9.57375i 0.383872 + 0.383872i
\(623\) −1.82684 1.82684i −0.0731907 0.0731907i
\(624\) 0.640978 + 0.260657i 0.0256597 + 0.0104346i
\(625\) −24.9624 1.37005i −0.998497 0.0548020i
\(626\) 20.6601i 0.825742i
\(627\) 15.2027 + 36.0414i 0.607139 + 1.43936i
\(628\) −11.2599 + 11.2599i −0.449319 + 0.449319i
\(629\) 2.82344 0.112578
\(630\) 6.64316 + 0.00511456i 0.264670 + 0.000203769i
\(631\) −13.2694 −0.528248 −0.264124 0.964489i \(-0.585083\pi\)
−0.264124 + 0.964489i \(0.585083\pi\)
\(632\) 1.50581 1.50581i 0.0598981 0.0598981i
\(633\) 7.30870 + 17.3269i 0.290495 + 0.688682i
\(634\) 1.68201i 0.0668012i
\(635\) −0.391564 + 28.5642i −0.0155387 + 1.13353i
\(636\) −16.6564 6.77342i −0.660470 0.268583i
\(637\) −1.70038 1.70038i −0.0673714 0.0673714i
\(638\) 2.69792 + 2.69792i 0.106812 + 0.106812i
\(639\) 5.46858 + 5.32888i 0.216334 + 0.210807i
\(640\) −0.0306496 + 2.23586i −0.00121153 + 0.0883800i
\(641\) 39.1022i 1.54445i 0.635352 + 0.772223i \(0.280855\pi\)
−0.635352 + 0.772223i \(0.719145\pi\)
\(642\) −23.2594 + 9.81111i −0.917975 + 0.387214i
\(643\) 10.7210 10.7210i 0.422794 0.422794i −0.463371 0.886165i \(-0.653360\pi\)
0.886165 + 0.463371i \(0.153360\pi\)
\(644\) 4.44630 0.175209
\(645\) −11.5587 28.4866i −0.455122 1.12166i
\(646\) −9.09793 −0.357953
\(647\) 19.5198 19.5198i 0.767401 0.767401i −0.210247 0.977648i \(-0.567427\pi\)
0.977648 + 0.210247i \(0.0674268\pi\)
\(648\) 6.19718 6.52648i 0.243448 0.256384i
\(649\) 3.77139i 0.148040i
\(650\) −1.99674 0.0547538i −0.0783185 0.00214762i
\(651\) −0.646136 + 1.58890i −0.0253241 + 0.0622741i
\(652\) 13.8251 + 13.8251i 0.541434 + 0.541434i
\(653\) −0.461992 0.461992i −0.0180792 0.0180792i 0.698009 0.716089i \(-0.254069\pi\)
−0.716089 + 0.698009i \(0.754069\pi\)
\(654\) 4.07972 10.0324i 0.159530 0.392298i
\(655\) −17.1296 + 16.6663i −0.669307 + 0.651205i
\(656\) 9.40638i 0.367257i
\(657\) −0.490040 37.8755i −0.0191183 1.47766i
\(658\) −5.90301 + 5.90301i −0.230123 + 0.230123i
\(659\) 16.5140 0.643295 0.321647 0.946860i \(-0.395763\pi\)
0.321647 + 0.946860i \(0.395763\pi\)
\(660\) 6.66869 15.7757i 0.259578 0.614067i
\(661\) 41.4148 1.61085 0.805425 0.592697i \(-0.201937\pi\)
0.805425 + 0.592697i \(0.201937\pi\)
\(662\) 9.67486 9.67486i 0.376024 0.376024i
\(663\) 1.13580 0.479093i 0.0441107 0.0186064i
\(664\) 4.41925i 0.171500i
\(665\) 11.3076 + 0.155007i 0.438491 + 0.00601093i
\(666\) −3.31825 + 3.40524i −0.128579 + 0.131950i
\(667\) −2.73915 2.73915i −0.106060 0.106060i
\(668\) −18.0679 18.0679i −0.699070 0.699070i
\(669\) 0.329498 + 0.133992i 0.0127391 + 0.00518043i
\(670\) 15.4490 + 15.8784i 0.596846 + 0.613437i
\(671\) 14.7222i 0.568346i
\(672\) 0.666638 + 1.58041i 0.0257161 + 0.0609657i
\(673\) −30.2179 + 30.2179i −1.16481 + 1.16481i −0.181405 + 0.983409i \(0.558064\pi\)
−0.983409 + 0.181405i \(0.941936\pi\)
\(674\) 0.646306 0.0248948
\(675\) −10.1343 + 23.9227i −0.390070 + 0.920785i
\(676\) 12.8404 0.493862
\(677\) 9.35727 9.35727i 0.359629 0.359629i −0.504047 0.863676i \(-0.668156\pi\)
0.863676 + 0.504047i \(0.168156\pi\)
\(678\) −8.29642 19.6685i −0.318622 0.755364i
\(679\) 15.7967i 0.606221i
\(680\) 2.77791 + 2.85513i 0.106528 + 0.109489i
\(681\) −33.8616 13.7700i −1.29758 0.527668i
\(682\) 3.12700 + 3.12700i 0.119739 + 0.119739i
\(683\) 10.0475 + 10.0475i 0.384455 + 0.384455i 0.872704 0.488249i \(-0.162364\pi\)
−0.488249 + 0.872704i \(0.662364\pi\)
\(684\) 10.6923 10.9726i 0.408832 0.419549i
\(685\) 9.90872 + 0.135831i 0.378593 + 0.00518983i
\(686\) 12.8931i 0.492260i
\(687\) −28.8786 + 12.1814i −1.10179 + 0.464748i
\(688\) 5.61274 5.61274i 0.213984 0.213984i
\(689\) 4.14731 0.158000
\(690\) −6.77062 + 16.0168i −0.257753 + 0.609749i
\(691\) −20.4686 −0.778664 −0.389332 0.921098i \(-0.627294\pi\)
−0.389332 + 0.921098i \(0.627294\pi\)
\(692\) 8.14142 8.14142i 0.309490 0.309490i
\(693\) −0.169969 13.1370i −0.00645658 0.499033i
\(694\) 12.8103i 0.486273i
\(695\) −34.5747 + 33.6396i −1.31149 + 1.27602i
\(696\) 0.562933 1.38430i 0.0213379 0.0524717i
\(697\) −11.8493 11.8493i −0.448823 0.448823i
\(698\) 0.0374220 + 0.0374220i 0.00141644 + 0.00141644i
\(699\) −11.7095 + 28.7945i −0.442892 + 1.08911i
\(700\) −3.40396 3.59591i −0.128658 0.135913i
\(701\) 14.9733i 0.565535i −0.959189 0.282767i \(-0.908748\pi\)
0.959189 0.282767i \(-0.0912524\pi\)
\(702\) −0.757029 + 1.93289i −0.0285722 + 0.0729523i
\(703\) −5.72319 + 5.72319i −0.215854 + 0.215854i
\(704\) 4.42224 0.166669
\(705\) −12.2754 30.2531i −0.462320 1.13940i
\(706\) 3.67469 0.138299
\(707\) 2.78196 2.78196i 0.104627 0.104627i
\(708\) −1.36101 + 0.574091i −0.0511499 + 0.0215757i
\(709\) 6.59112i 0.247535i −0.992311 0.123767i \(-0.960502\pi\)
0.992311 0.123767i \(-0.0394976\pi\)
\(710\) 0.0780094 5.69070i 0.00292764 0.213568i
\(711\) 4.57551 + 4.45862i 0.171595 + 0.167211i
\(712\) 1.84472 + 1.84472i 0.0691339 + 0.0691339i
\(713\) −3.17479 3.17479i −0.118897 0.118897i
\(714\) 2.83062 + 1.15109i 0.105933 + 0.0430783i
\(715\) −0.0541479 + 3.95003i −0.00202502 + 0.147723i
\(716\) 12.7857i 0.477822i
\(717\) 7.04714 + 16.7068i 0.263180 + 0.623927i
\(718\) 15.2276 15.2276i 0.568288 0.568288i
\(719\) 25.2777 0.942699 0.471349 0.881947i \(-0.343767\pi\)
0.471349 + 0.881947i \(0.343767\pi\)
\(720\) −6.70820 0.00516463i −0.250000 0.000192474i
\(721\) −5.92488 −0.220654
\(722\) 5.00669 5.00669i 0.186330 0.186330i
\(723\) 4.42990 + 10.5021i 0.164750 + 0.390576i
\(724\) 2.73755i 0.101740i
\(725\) −0.118250 + 4.31229i −0.00439169 + 0.160154i
\(726\) −13.7281 5.58259i −0.509497 0.207190i
\(727\) 2.42912 + 2.42912i 0.0900911 + 0.0900911i 0.750716 0.660625i \(-0.229709\pi\)
−0.660625 + 0.750716i \(0.729709\pi\)
\(728\) −0.279749 0.279749i −0.0103682 0.0103682i
\(729\) 19.8183 + 18.3367i 0.734012 + 0.679137i
\(730\) −20.2356 + 19.6883i −0.748952 + 0.728696i
\(731\) 14.1408i 0.523017i
\(732\) 5.31292 2.24106i 0.196371 0.0828319i
\(733\) 17.1919 17.1919i 0.634998 0.634998i −0.314319 0.949317i \(-0.601776\pi\)
0.949317 + 0.314319i \(0.101776\pi\)
\(734\) −29.4126 −1.08564
\(735\) 21.4729 + 9.07703i 0.792041 + 0.334811i
\(736\) −4.48983 −0.165497
\(737\) 30.9808 30.9808i 1.14119 1.14119i
\(738\) 28.2168 0.365074i 1.03867 0.0134386i
\(739\) 44.8879i 1.65123i 0.564235 + 0.825614i \(0.309171\pi\)
−0.564235 + 0.825614i \(0.690829\pi\)
\(740\) 3.54355 + 0.0485758i 0.130264 + 0.00178568i
\(741\) −1.33115 + 3.27342i −0.0489011 + 0.120252i
\(742\) 7.26953 + 7.26953i 0.266873 + 0.266873i
\(743\) −14.7333 14.7333i −0.540514 0.540514i 0.383166 0.923680i \(-0.374834\pi\)
−0.923680 + 0.383166i \(0.874834\pi\)
\(744\) 0.652462 1.60446i 0.0239204 0.0588224i
\(745\) 9.68672 + 9.95599i 0.354894 + 0.364759i
\(746\) 18.7001i 0.684658i
\(747\) −13.2566 + 0.171517i −0.485035 + 0.00627547i
\(748\) 5.57072 5.57072i 0.203686 0.203686i
\(749\) 14.4333 0.527381
\(750\) 18.1369 6.78633i 0.662265 0.247802i
\(751\) 19.0621 0.695585 0.347792 0.937572i \(-0.386931\pi\)
0.347792 + 0.937572i \(0.386931\pi\)
\(752\) 5.96081 5.96081i 0.217368 0.217368i
\(753\) −4.70631 + 1.98518i −0.171507 + 0.0723440i
\(754\) 0.344680i 0.0125525i
\(755\) −22.7068 23.3380i −0.826387 0.849358i
\(756\) −4.71497 + 2.06108i −0.171482 + 0.0749609i
\(757\) 31.8979 + 31.8979i 1.15935 + 1.15935i 0.984616 + 0.174734i \(0.0559067\pi\)
0.174734 + 0.984616i \(0.444093\pi\)
\(758\) 5.90811 + 5.90811i 0.214592 + 0.214592i
\(759\) 31.8567 + 12.9547i 1.15633 + 0.470226i
\(760\) −11.4183 0.156525i −0.414186 0.00567776i
\(761\) 37.7081i 1.36692i 0.729990 + 0.683458i \(0.239525\pi\)
−0.729990 + 0.683458i \(0.760475\pi\)
\(762\) −8.60000 20.3882i −0.311545 0.738586i
\(763\) −4.37854 + 4.37854i −0.158514 + 0.158514i
\(764\) 6.29907 0.227892
\(765\) −8.45687 + 8.44386i −0.305759 + 0.305288i
\(766\) 7.09980 0.256526
\(767\) 0.240912 0.240912i 0.00869884 0.00869884i
\(768\) −0.673165 1.59589i −0.0242907 0.0575865i
\(769\) 40.7512i 1.46953i −0.678323 0.734764i \(-0.737293\pi\)
0.678323 0.734764i \(-0.262707\pi\)
\(770\) −7.01864 + 6.82882i −0.252934 + 0.246093i
\(771\) −7.53908 3.06580i −0.271513 0.110412i
\(772\) 8.56703 + 8.56703i 0.308334 + 0.308334i
\(773\) 22.9415 + 22.9415i 0.825149 + 0.825149i 0.986841 0.161692i \(-0.0516951\pi\)
−0.161692 + 0.986841i \(0.551695\pi\)
\(774\) 17.0547 + 16.6190i 0.613017 + 0.597357i
\(775\) −0.137056 + 4.99812i −0.00492321 + 0.179538i
\(776\) 15.9513i 0.572620i
\(777\) 2.50475 1.05654i 0.0898575 0.0379030i
\(778\) 20.4752 20.4752i 0.734073 0.734073i
\(779\) 48.0375 1.72112
\(780\) 1.43372 0.581743i 0.0513354 0.0208298i
\(781\) −11.2555 −0.402753
\(782\) −5.65587 + 5.65587i −0.202253 + 0.202253i
\(783\) 4.17440 + 1.63493i 0.149181 + 0.0584276i
\(784\) 6.01930i 0.214975i
\(785\) −0.488062 + 35.6036i −0.0174197 + 1.27075i
\(786\) 6.97363 17.1488i 0.248741 0.611676i
\(787\) −8.35326 8.35326i −0.297761 0.297761i 0.542375 0.840136i \(-0.317525\pi\)
−0.840136 + 0.542375i \(0.817525\pi\)
\(788\) 0.661707 + 0.661707i 0.0235723 + 0.0235723i
\(789\) −13.2851 + 32.6693i −0.472963 + 1.16306i
\(790\) 0.0652697 4.76135i 0.00232219 0.169401i
\(791\) 12.2050i 0.433960i
\(792\) 0.171633 + 13.2656i 0.00609871 + 0.471373i
\(793\) −0.940441 + 0.940441i −0.0333960 + 0.0333960i
\(794\) 26.2233 0.930629
\(795\) −37.2565 + 15.1171i −1.32135 + 0.536150i
\(796\) 16.9809 0.601873
\(797\) 16.8402 16.8402i 0.596509 0.596509i −0.342873 0.939382i \(-0.611400\pi\)
0.939382 + 0.342873i \(0.111400\pi\)
\(798\) −8.07102 + 3.40446i −0.285711 + 0.120517i
\(799\) 15.0177i 0.531289i
\(800\) 3.43729 + 3.63112i 0.121527 + 0.128379i
\(801\) −5.46211 + 5.60530i −0.192994 + 0.198054i
\(802\) 15.1084 + 15.1084i 0.533496 + 0.533496i
\(803\) 39.4821 + 39.4821i 1.39329 + 1.39329i
\(804\) −15.8962 6.46428i −0.560617 0.227978i
\(805\) 7.12592 6.93319i 0.251156 0.244363i
\(806\) 0.399498i 0.0140717i
\(807\) 16.4957 + 39.1067i 0.580675 + 1.37662i
\(808\) −2.80920 + 2.80920i −0.0988274 + 0.0988274i
\(809\) −37.7696 −1.32791 −0.663954 0.747774i \(-0.731123\pi\)
−0.663954 + 0.747774i \(0.731123\pi\)
\(810\) −0.244862 20.1231i −0.00860356 0.707054i
\(811\) −20.1953 −0.709154 −0.354577 0.935027i \(-0.615375\pi\)
−0.354577 + 0.935027i \(0.615375\pi\)
\(812\) −0.604164 + 0.604164i −0.0212020 + 0.0212020i
\(813\) −16.9201 40.1129i −0.593415 1.40682i
\(814\) 7.00869i 0.245654i
\(815\) 43.7148 + 0.599252i 1.53126 + 0.0209909i
\(816\) −2.85834 1.16236i −0.100062 0.0406906i
\(817\) 28.6638 + 28.6638i 1.00282 + 1.00282i
\(818\) 8.93107 + 8.93107i 0.312267 + 0.312267i
\(819\) 0.828318 0.850033i 0.0289438 0.0297026i
\(820\) −14.6675 15.0753i −0.512212 0.526451i
\(821\) 33.8991i 1.18309i −0.806273 0.591543i \(-0.798519\pi\)
0.806273 0.591543i \(-0.201481\pi\)
\(822\) −7.07253 + 2.98328i −0.246683 + 0.104054i
\(823\) 16.1065 16.1065i 0.561436 0.561436i −0.368279 0.929715i \(-0.620053\pi\)
0.929715 + 0.368279i \(0.120053\pi\)
\(824\) 5.98289 0.208424
\(825\) −13.9116 35.6817i −0.484340 1.24228i
\(826\) 0.844556 0.0293858
\(827\) 19.0742 19.0742i 0.663275 0.663275i −0.292875 0.956151i \(-0.594612\pi\)
0.956151 + 0.292875i \(0.0946121\pi\)
\(828\) −0.174256 13.4684i −0.00605583 0.468058i
\(829\) 16.1596i 0.561247i −0.959818 0.280623i \(-0.909459\pi\)
0.959818 0.280623i \(-0.0905412\pi\)
\(830\) 6.89101 + 7.08256i 0.239190 + 0.245839i
\(831\) −10.7946 + 26.5447i −0.374459 + 0.920827i
\(832\) 0.282488 + 0.282488i 0.00979350 + 0.00979350i
\(833\) 7.58255 + 7.58255i 0.262720 + 0.262720i
\(834\) 14.0757 34.6135i 0.487403 1.19857i
\(835\) −57.1305 0.783157i −1.97708 0.0271023i
\(836\) 22.5840i 0.781083i
\(837\) 4.83830 + 1.89495i 0.167236 + 0.0654991i
\(838\) 19.4353 19.4353i 0.671381 0.671381i
\(839\) −3.57570 −0.123447 −0.0617234 0.998093i \(-0.519660\pi\)
−0.0617234 + 0.998093i \(0.519660\pi\)
\(840\) 3.53276 + 1.49337i 0.121892 + 0.0515261i
\(841\) −28.2556 −0.974331
\(842\) 8.85239 8.85239i 0.305073 0.305073i
\(843\) 13.5963 5.73507i 0.468280 0.197526i
\(844\) 10.8572i 0.373721i
\(845\) 20.5788 20.0223i 0.707933 0.688787i
\(846\) 18.1123 + 17.6496i 0.622713 + 0.606805i
\(847\) 5.99149 + 5.99149i 0.205870 + 0.205870i
\(848\) −7.34070 7.34070i −0.252081 0.252081i
\(849\) −32.0615 13.0380i −1.10035 0.447462i
\(850\) 8.90412 + 0.244165i 0.305409 + 0.00837480i
\(851\) 7.11582i 0.243927i
\(852\) 1.71334 + 4.06185i 0.0586980 + 0.139157i
\(853\) 13.5352 13.5352i 0.463435 0.463435i −0.436345 0.899780i \(-0.643727\pi\)
0.899780 + 0.436345i \(0.143727\pi\)
\(854\) −3.29686 −0.112816
\(855\) 0.0263753 34.2582i 0.000902017 1.17161i
\(856\) −14.5746 −0.498150
\(857\) 20.5962 20.5962i 0.703553 0.703553i −0.261618 0.965171i \(-0.584256\pi\)
0.965171 + 0.261618i \(0.0842562\pi\)
\(858\) −1.18926 2.81941i −0.0406008 0.0962531i
\(859\) 21.4891i 0.733197i 0.930379 + 0.366599i \(0.119478\pi\)
−0.930379 + 0.366599i \(0.880522\pi\)
\(860\) 0.243285 17.7474i 0.00829595 0.605181i
\(861\) −14.9458 6.07780i −0.509352 0.207131i
\(862\) −6.42067 6.42067i −0.218689 0.218689i
\(863\) −38.3646 38.3646i −1.30595 1.30595i −0.924315 0.381630i \(-0.875363\pi\)
−0.381630 0.924315i \(-0.624637\pi\)
\(864\) 4.76113 2.08126i 0.161977 0.0708060i
\(865\) 0.352891 25.7430i 0.0119986 0.875288i
\(866\) 9.89553i 0.336264i
\(867\) 22.0652 9.30736i 0.749372 0.316095i
\(868\) −0.700251 + 0.700251i −0.0237681 + 0.0237681i
\(869\) −9.41734 −0.319462
\(870\) −1.25637 3.09636i −0.0425950 0.104976i
\(871\) 3.95803 0.134113
\(872\) 4.42141 4.42141i 0.149728 0.149728i
\(873\) 47.8500 0.619092i 1.61948 0.0209531i
\(874\) 22.9292i 0.775591i
\(875\) −11.0626 0.455173i −0.373983 0.0153877i
\(876\) 8.23812 20.2583i 0.278340 0.684463i
\(877\) −15.3051 15.3051i −0.516818 0.516818i 0.399789 0.916607i \(-0.369083\pi\)
−0.916607 + 0.399789i \(0.869083\pi\)
\(878\) 26.6161 + 26.6161i 0.898249 + 0.898249i
\(879\) 18.5148 45.5294i 0.624488 1.53567i
\(880\) 7.08736 6.89568i 0.238915 0.232453i
\(881\) 36.8177i 1.24042i −0.784436 0.620209i \(-0.787048\pi\)
0.784436 0.620209i \(-0.212952\pi\)
\(882\) −18.0564 + 0.233617i −0.607990 + 0.00786629i
\(883\) −23.4905 + 23.4905i −0.790519 + 0.790519i −0.981579 0.191059i \(-0.938808\pi\)
0.191059 + 0.981579i \(0.438808\pi\)
\(884\) 0.711703 0.0239372
\(885\) −1.28605 + 3.04232i −0.0432301 + 0.102267i
\(886\) 21.1106 0.709225
\(887\) 17.6666 17.6666i 0.593186 0.593186i −0.345305 0.938491i \(-0.612224\pi\)
0.938491 + 0.345305i \(0.112224\pi\)
\(888\) −2.52928 + 1.06688i −0.0848769 + 0.0358022i
\(889\) 12.6516i 0.424321i
\(890\) 5.83298 + 0.0799598i 0.195522 + 0.00268026i
\(891\) −39.7868 + 1.02971i −1.33291 + 0.0344966i
\(892\) 0.145214 + 0.145214i 0.00486213 + 0.00486213i
\(893\) 30.4413 + 30.4413i 1.01868 + 1.01868i
\(894\) −9.96715 4.05319i −0.333351 0.135559i
\(895\) −19.9369 20.4911i −0.666417 0.684942i
\(896\) 0.990304i 0.0330837i
\(897\) 1.20744 + 2.86250i 0.0403153 + 0.0955762i
\(898\) 14.5234 14.5234i 0.484653 0.484653i
\(899\) 0.862782 0.0287754
\(900\) −10.7590 + 10.4519i −0.358635 + 0.348398i
\(901\) −18.4943 −0.616133
\(902\) −29.4137 + 29.4137i −0.979369 + 0.979369i
\(903\) −5.29151 12.5447i −0.176091 0.417462i
\(904\) 12.3245i 0.409907i
\(905\) −4.26871 4.38737i −0.141897 0.145841i
\(906\) 23.3642 + 9.50118i 0.776224 + 0.315655i
\(907\) −28.4548 28.4548i −0.944825 0.944825i 0.0537306 0.998555i \(-0.482889\pi\)
−0.998555 + 0.0537306i \(0.982889\pi\)
\(908\) −14.9233 14.9233i −0.495246 0.495246i
\(909\) −8.53593 8.31787i −0.283119 0.275886i
\(910\) −0.884560 0.0121257i −0.0293229 0.000401965i
\(911\) 8.59612i 0.284802i 0.989809 + 0.142401i \(0.0454823\pi\)
−0.989809 + 0.142401i \(0.954518\pi\)
\(912\) 8.15004 3.43779i 0.269875 0.113837i
\(913\) 13.8190 13.8190i 0.457341 0.457341i
\(914\) −1.71837 −0.0568387
\(915\) 5.02030 11.8762i 0.165966 0.392615i
\(916\) −18.0957 −0.597897
\(917\) −7.48441 + 7.48441i −0.247157 + 0.247157i
\(918\) 3.37584 8.61940i 0.111419 0.284483i
\(919\) 43.3194i 1.42897i 0.699648 + 0.714487i \(0.253340\pi\)
−0.699648 + 0.714487i \(0.746660\pi\)
\(920\) −7.19569 + 7.00108i −0.237235 + 0.230819i
\(921\) 3.15711 7.76361i 0.104030 0.255820i
\(922\) −3.94345 3.94345i −0.129871 0.129871i
\(923\) −0.718987 0.718987i −0.0236658 0.0236658i
\(924\) 2.85737 7.02651i 0.0940005 0.231155i
\(925\) 5.75486 5.44767i 0.189219 0.179118i
\(926\) 21.2710i 0.699009i
\(927\) 0.232204 + 17.9472i 0.00762657 + 0.589462i
\(928\) 0.610079 0.610079i 0.0200268 0.0200268i
\(929\) −49.6565 −1.62918 −0.814588 0.580040i \(-0.803037\pi\)
−0.814588 + 0.580040i \(0.803037\pi\)
\(930\) −1.45619 3.58880i −0.0477502 0.117682i
\(931\) −30.7400 −1.00746
\(932\) −12.6901 + 12.6901i −0.415679 + 0.415679i
\(933\) −21.6072 + 9.11419i −0.707388 + 0.298385i
\(934\) 32.6965i 1.06986i
\(935\) 0.241464 17.6145i 0.00789671 0.576056i
\(936\) −0.836428 + 0.858356i −0.0273395 + 0.0280562i
\(937\) −10.7151 10.7151i −0.350048 0.350048i 0.510079 0.860128i \(-0.329616\pi\)
−0.860128 + 0.510079i \(0.829616\pi\)
\(938\) 6.93775 + 6.93775i 0.226526 + 0.226526i
\(939\) 33.1482 + 13.4799i 1.08175 + 0.439900i
\(940\) 0.258372 18.8480i 0.00842717 0.614753i
\(941\) 41.4459i 1.35110i 0.737316 + 0.675549i \(0.236093\pi\)
−0.737316 + 0.675549i \(0.763907\pi\)
\(942\) −10.7194 25.4127i −0.349257 0.827992i
\(943\) 29.8633 29.8633i 0.972482 0.972482i
\(944\) −0.852824 −0.0277571
\(945\) −4.34262 + 10.6554i −0.141265 + 0.346619i
\(946\) −35.1020 −1.14127
\(947\) −9.07927 + 9.07927i −0.295037 + 0.295037i −0.839066 0.544029i \(-0.816898\pi\)
0.544029 + 0.839066i \(0.316898\pi\)
\(948\) 1.43353 + 3.39850i 0.0465590 + 0.110378i
\(949\) 5.04414i 0.163740i
\(950\) −18.5438 + 17.5539i −0.601640 + 0.569525i
\(951\) 2.69872 + 1.09745i 0.0875120 + 0.0355872i
\(952\) 1.24749 + 1.24749i 0.0404315 + 0.0404315i
\(953\) −2.70424 2.70424i −0.0875989 0.0875989i 0.661950 0.749548i \(-0.269729\pi\)
−0.749548 + 0.661950i \(0.769729\pi\)
\(954\) 21.7354 22.3052i 0.703708 0.722156i
\(955\) 10.0953 9.82226i 0.326676 0.317841i
\(956\) 10.4687i 0.338581i
\(957\) −6.08899 + 2.56841i −0.196829 + 0.0830249i
\(958\) 24.7891 24.7891i 0.800900 0.800900i
\(959\) 4.38876 0.141720
\(960\) −3.56735 1.50799i −0.115136 0.0486701i
\(961\) 1.00000 0.0322581
\(962\) 0.447707 0.447707i 0.0144347 0.0144347i
\(963\) −0.565660 43.7202i −0.0182281 1.40886i
\(964\) 6.58071i 0.211950i
\(965\) 27.0888 + 0.371339i 0.872018 + 0.0119538i
\(966\) −2.90104 + 7.13391i −0.0933395 + 0.229530i
\(967\) 8.01011 + 8.01011i 0.257588 + 0.257588i 0.824072 0.566485i \(-0.191697\pi\)
−0.566485 + 0.824072i \(0.691697\pi\)
\(968\) −6.05015 6.05015i −0.194459 0.194459i
\(969\) 5.93605 14.5973i 0.190693 0.468932i
\(970\) −24.8732 25.5646i −0.798630 0.820830i
\(971\) 23.2223i 0.745238i −0.927984 0.372619i \(-0.878460\pi\)
0.927984 0.372619i \(-0.121540\pi\)
\(972\) 6.42805 + 14.2014i 0.206180 + 0.455511i
\(973\) −15.1067 + 15.1067i −0.484299 + 0.484299i
\(974\) −13.0241 −0.417320
\(975\) 1.39065 3.16796i 0.0445363 0.101456i
\(976\) 3.32914 0.106563
\(977\) −36.1374 + 36.1374i −1.15614 + 1.15614i −0.170840 + 0.985299i \(0.554648\pi\)
−0.985299 + 0.170840i \(0.945352\pi\)
\(978\) −31.2022 + 13.1615i −0.997737 + 0.420858i
\(979\) 11.5369i 0.368720i
\(980\) 9.38600 + 9.64690i 0.299825 + 0.308159i
\(981\) 13.4347 + 13.0915i 0.428937 + 0.417980i
\(982\) −23.3105 23.3105i −0.743868 0.743868i
\(983\) 6.21084 + 6.21084i 0.198095 + 0.198095i 0.799183 0.601088i \(-0.205266\pi\)
−0.601088 + 0.799183i \(0.705266\pi\)
\(984\) 15.0922 + 6.13730i 0.481120 + 0.195650i
\(985\) 2.09230 + 0.0286818i 0.0666663 + 0.000913877i
\(986\) 1.53704i 0.0489494i
\(987\) −5.61966 13.3226i −0.178876 0.424064i
\(988\) −1.44264 + 1.44264i −0.0458965 + 0.0458965i
\(989\) 35.6386 1.13324
\(990\) 20.9604 + 20.9927i 0.666164 + 0.667191i
\(991\) −29.2313 −0.928564 −0.464282 0.885687i \(-0.653688\pi\)
−0.464282 + 0.885687i \(0.653688\pi\)
\(992\) 0.707107 0.707107i 0.0224507 0.0224507i
\(993\) 9.21045 + 21.8354i 0.292285 + 0.692926i
\(994\) 2.52052i 0.0799461i
\(995\) 27.2147 26.4787i 0.862764 0.839430i
\(996\) −7.09050 2.88339i −0.224671 0.0913637i
\(997\) 33.1147 + 33.1147i 1.04875 + 1.04875i 0.998749 + 0.0500044i \(0.0159235\pi\)
0.0500044 + 0.998749i \(0.484076\pi\)
\(998\) −19.8277 19.8277i −0.627635 0.627635i
\(999\) −3.29854 7.54579i −0.104361 0.238738i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 930.2.j.g.497.5 40
3.2 odd 2 inner 930.2.j.g.497.19 yes 40
5.3 odd 4 inner 930.2.j.g.683.19 yes 40
15.8 even 4 inner 930.2.j.g.683.5 yes 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
930.2.j.g.497.5 40 1.1 even 1 trivial
930.2.j.g.497.19 yes 40 3.2 odd 2 inner
930.2.j.g.683.5 yes 40 15.8 even 4 inner
930.2.j.g.683.19 yes 40 5.3 odd 4 inner