Properties

Label 21.6.c.a.20.5
Level $21$
Weight $6$
Character 21.20
Analytic conductor $3.368$
Analytic rank $0$
Dimension $12$
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] = [21,6,Mod(20,21)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(21, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("21.20");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 21 = 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 21.c (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.36806021607\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 484x^{10} + 194194x^{8} - 39867800x^{6} + 5398720873x^{4} - 310089434788x^{2} + 9371104623076 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{7}\cdot 3^{10} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 20.5
Root \(6.98672 + 2.99433i\) of defining polynomial
Character \(\chi\) \(=\) 21.20
Dual form 21.6.c.a.20.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.99433i q^{2} +(-9.94100 + 12.0074i) q^{3} +23.0340 q^{4} +61.8023 q^{5} +(35.9539 + 29.7666i) q^{6} +(92.4210 + 90.9140i) q^{7} -164.790i q^{8} +(-45.3530 - 238.730i) q^{9} +O(q^{10})\) \(q-2.99433i q^{2} +(-9.94100 + 12.0074i) q^{3} +23.0340 q^{4} +61.8023 q^{5} +(35.9539 + 29.7666i) q^{6} +(92.4210 + 90.9140i) q^{7} -164.790i q^{8} +(-45.3530 - 238.730i) q^{9} -185.056i q^{10} +615.301i q^{11} +(-228.981 + 276.577i) q^{12} -322.895i q^{13} +(272.226 - 276.739i) q^{14} +(-614.377 + 742.083i) q^{15} +243.654 q^{16} -1537.42 q^{17} +(-714.836 + 135.802i) q^{18} -2171.63i q^{19} +1423.56 q^{20} +(-2010.39 + 205.956i) q^{21} +1842.41 q^{22} -793.329i q^{23} +(1978.69 + 1638.18i) q^{24} +694.530 q^{25} -966.853 q^{26} +(3317.37 + 1828.65i) q^{27} +(2128.83 + 2094.11i) q^{28} +513.596i q^{29} +(2222.04 + 1839.65i) q^{30} -161.215i q^{31} -6002.85i q^{32} +(-7388.14 - 6116.71i) q^{33} +4603.54i q^{34} +(5711.84 + 5618.70i) q^{35} +(-1044.66 - 5498.91i) q^{36} -8593.37 q^{37} -6502.57 q^{38} +(3877.11 + 3209.90i) q^{39} -10184.4i q^{40} +7004.53 q^{41} +(616.698 + 6019.78i) q^{42} -7726.50 q^{43} +14172.9i q^{44} +(-2802.92 - 14754.1i) q^{45} -2375.49 q^{46} -17604.2 q^{47} +(-2422.16 + 2925.64i) q^{48} +(276.290 + 16804.7i) q^{49} -2079.65i q^{50} +(15283.5 - 18460.3i) q^{51} -7437.56i q^{52} -7345.26i q^{53} +(5475.57 - 9933.29i) q^{54} +38027.1i q^{55} +(14981.7 - 15230.0i) q^{56} +(26075.5 + 21588.2i) q^{57} +1537.87 q^{58} +23416.6 q^{59} +(-14151.6 + 17093.1i) q^{60} -13344.8i q^{61} -482.731 q^{62} +(17512.3 - 26186.9i) q^{63} -10177.6 q^{64} -19955.7i q^{65} +(-18315.4 + 22122.5i) q^{66} +14471.1 q^{67} -35413.0 q^{68} +(9525.78 + 7886.48i) q^{69} +(16824.2 - 17103.1i) q^{70} -7370.42i q^{71} +(-39340.3 + 7473.71i) q^{72} -9422.68i q^{73} +25731.4i q^{74} +(-6904.32 + 8339.47i) q^{75} -50021.3i q^{76} +(-55939.5 + 56866.8i) q^{77} +(9611.48 - 11609.3i) q^{78} +27229.8 q^{79} +15058.4 q^{80} +(-54935.2 + 21654.3i) q^{81} -20973.8i q^{82} +15577.0 q^{83} +(-46307.4 + 4743.98i) q^{84} -95016.2 q^{85} +23135.7i q^{86} +(-6166.93 - 5105.66i) q^{87} +101395. q^{88} +90024.7 q^{89} +(-44178.5 + 8392.86i) q^{90} +(29355.7 - 29842.3i) q^{91} -18273.5i q^{92} +(1935.77 + 1602.64i) q^{93} +52712.7i q^{94} -134212. i q^{95} +(72078.4 + 59674.4i) q^{96} -84850.1i q^{97} +(50318.8 - 827.302i) q^{98} +(146891. - 27905.8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 196 q^{4} + 112 q^{7} - 492 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 196 q^{4} + 112 q^{7} - 492 q^{9} + 1392 q^{15} + 4868 q^{16} - 3804 q^{18} + 4116 q^{21} - 8752 q^{22} + 7812 q^{25} - 8204 q^{28} - 27876 q^{30} + 54864 q^{36} + 27464 q^{37} - 16080 q^{39} - 3444 q^{42} - 73840 q^{43} + 59144 q^{46} + 6972 q^{49} + 23760 q^{51} + 103968 q^{57} - 71512 q^{58} - 152676 q^{60} - 120624 q^{63} - 198788 q^{64} + 79344 q^{67} + 368760 q^{70} + 226644 q^{72} + 394644 q^{78} - 247104 q^{79} - 248868 q^{81} - 608076 q^{84} - 320112 q^{85} + 595456 q^{88} + 310128 q^{91} + 397272 q^{93} + 696576 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).

\(n\) \(8\) \(10\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.99433i 0.529327i −0.964341 0.264664i \(-0.914739\pi\)
0.964341 0.264664i \(-0.0852609\pi\)
\(3\) −9.94100 + 12.0074i −0.637716 + 0.770272i
\(4\) 23.0340 0.719813
\(5\) 61.8023 1.10555 0.552777 0.833329i \(-0.313568\pi\)
0.552777 + 0.833329i \(0.313568\pi\)
\(6\) 35.9539 + 29.7666i 0.407726 + 0.337560i
\(7\) 92.4210 + 90.9140i 0.712895 + 0.701271i
\(8\) 164.790i 0.910344i
\(9\) −45.3530 238.730i −0.186638 0.982429i
\(10\) 185.056i 0.585200i
\(11\) 615.301i 1.53323i 0.642110 + 0.766613i \(0.278059\pi\)
−0.642110 + 0.766613i \(0.721941\pi\)
\(12\) −228.981 + 276.577i −0.459036 + 0.554452i
\(13\) 322.895i 0.529911i −0.964261 0.264955i \(-0.914643\pi\)
0.964261 0.264955i \(-0.0853572\pi\)
\(14\) 272.226 276.739i 0.371202 0.377355i
\(15\) −614.377 + 742.083i −0.705029 + 0.851577i
\(16\) 243.654 0.237943
\(17\) −1537.42 −1.29024 −0.645120 0.764081i \(-0.723193\pi\)
−0.645120 + 0.764081i \(0.723193\pi\)
\(18\) −714.836 + 135.802i −0.520026 + 0.0987925i
\(19\) 2171.63i 1.38007i −0.723775 0.690036i \(-0.757595\pi\)
0.723775 0.690036i \(-0.242405\pi\)
\(20\) 1423.56 0.795792
\(21\) −2010.39 + 205.956i −0.994793 + 0.101912i
\(22\) 1842.41 0.811578
\(23\) 793.329i 0.312704i −0.987701 0.156352i \(-0.950027\pi\)
0.987701 0.156352i \(-0.0499735\pi\)
\(24\) 1978.69 + 1638.18i 0.701212 + 0.580540i
\(25\) 694.530 0.222250
\(26\) −966.853 −0.280496
\(27\) 3317.37 + 1828.65i 0.875759 + 0.482748i
\(28\) 2128.83 + 2094.11i 0.513151 + 0.504784i
\(29\) 513.596i 0.113404i 0.998391 + 0.0567018i \(0.0180584\pi\)
−0.998391 + 0.0567018i \(0.981942\pi\)
\(30\) 2222.04 + 1839.65i 0.450763 + 0.373191i
\(31\) 161.215i 0.0301302i −0.999887 0.0150651i \(-0.995204\pi\)
0.999887 0.0150651i \(-0.00479555\pi\)
\(32\) 6002.85i 1.03629i
\(33\) −7388.14 6116.71i −1.18100 0.977762i
\(34\) 4603.54i 0.682959i
\(35\) 5711.84 + 5618.70i 0.788144 + 0.775293i
\(36\) −1044.66 5498.91i −0.134344 0.707165i
\(37\) −8593.37 −1.03195 −0.515976 0.856603i \(-0.672571\pi\)
−0.515976 + 0.856603i \(0.672571\pi\)
\(38\) −6502.57 −0.730510
\(39\) 3877.11 + 3209.90i 0.408175 + 0.337932i
\(40\) 10184.4i 1.00643i
\(41\) 7004.53 0.650758 0.325379 0.945584i \(-0.394508\pi\)
0.325379 + 0.945584i \(0.394508\pi\)
\(42\) 616.698 + 6019.78i 0.0539448 + 0.526571i
\(43\) −7726.50 −0.637253 −0.318627 0.947880i \(-0.603222\pi\)
−0.318627 + 0.947880i \(0.603222\pi\)
\(44\) 14172.9i 1.10364i
\(45\) −2802.92 14754.1i −0.206338 1.08613i
\(46\) −2375.49 −0.165523
\(47\) −17604.2 −1.16244 −0.581221 0.813745i \(-0.697425\pi\)
−0.581221 + 0.813745i \(0.697425\pi\)
\(48\) −2422.16 + 2925.64i −0.151740 + 0.183281i
\(49\) 276.290 + 16804.7i 0.0164390 + 0.999865i
\(50\) 2079.65i 0.117643i
\(51\) 15283.5 18460.3i 0.822806 0.993835i
\(52\) 7437.56i 0.381437i
\(53\) 7345.26i 0.359184i −0.983741 0.179592i \(-0.942522\pi\)
0.983741 0.179592i \(-0.0574778\pi\)
\(54\) 5475.57 9933.29i 0.255532 0.463563i
\(55\) 38027.1i 1.69506i
\(56\) 14981.7 15230.0i 0.638397 0.648979i
\(57\) 26075.5 + 21588.2i 1.06303 + 0.880093i
\(58\) 1537.87 0.0600276
\(59\) 23416.6 0.875779 0.437889 0.899029i \(-0.355726\pi\)
0.437889 + 0.899029i \(0.355726\pi\)
\(60\) −14151.6 + 17093.1i −0.507489 + 0.612976i
\(61\) 13344.8i 0.459186i −0.973287 0.229593i \(-0.926260\pi\)
0.973287 0.229593i \(-0.0737395\pi\)
\(62\) −482.731 −0.0159487
\(63\) 17512.3 26186.9i 0.555895 0.831252i
\(64\) −10177.6 −0.310595
\(65\) 19955.7i 0.585845i
\(66\) −18315.4 + 22122.5i −0.517556 + 0.625136i
\(67\) 14471.1 0.393835 0.196918 0.980420i \(-0.436907\pi\)
0.196918 + 0.980420i \(0.436907\pi\)
\(68\) −35413.0 −0.928731
\(69\) 9525.78 + 7886.48i 0.240867 + 0.199416i
\(70\) 16824.2 17103.1i 0.410383 0.417186i
\(71\) 7370.42i 0.173519i −0.996229 0.0867593i \(-0.972349\pi\)
0.996229 0.0867593i \(-0.0276511\pi\)
\(72\) −39340.3 + 7473.71i −0.894348 + 0.169905i
\(73\) 9422.68i 0.206951i −0.994632 0.103475i \(-0.967004\pi\)
0.994632 0.103475i \(-0.0329963\pi\)
\(74\) 25731.4i 0.546240i
\(75\) −6904.32 + 8339.47i −0.141732 + 0.171193i
\(76\) 50021.3i 0.993394i
\(77\) −55939.5 + 56866.8i −1.07521 + 1.09303i
\(78\) 9611.48 11609.3i 0.178877 0.216058i
\(79\) 27229.8 0.490882 0.245441 0.969412i \(-0.421067\pi\)
0.245441 + 0.969412i \(0.421067\pi\)
\(80\) 15058.4 0.263059
\(81\) −54935.2 + 21654.3i −0.930333 + 0.366717i
\(82\) 20973.8i 0.344464i
\(83\) 15577.0 0.248192 0.124096 0.992270i \(-0.460397\pi\)
0.124096 + 0.992270i \(0.460397\pi\)
\(84\) −46307.4 + 4743.98i −0.716065 + 0.0733576i
\(85\) −95016.2 −1.42643
\(86\) 23135.7i 0.337315i
\(87\) −6166.93 5105.66i −0.0873516 0.0723192i
\(88\) 101395. 1.39576
\(89\) 90024.7 1.20472 0.602361 0.798224i \(-0.294227\pi\)
0.602361 + 0.798224i \(0.294227\pi\)
\(90\) −44178.5 + 8392.86i −0.574917 + 0.109220i
\(91\) 29355.7 29842.3i 0.371611 0.377771i
\(92\) 18273.5i 0.225089i
\(93\) 1935.77 + 1602.64i 0.0232085 + 0.0192145i
\(94\) 52712.7i 0.615313i
\(95\) 134212.i 1.52574i
\(96\) 72078.4 + 59674.4i 0.798228 + 0.660860i
\(97\) 84850.1i 0.915637i −0.889046 0.457818i \(-0.848631\pi\)
0.889046 0.457818i \(-0.151369\pi\)
\(98\) 50318.8 827.302i 0.529256 0.00870160i
\(99\) 146891. 27905.8i 1.50628 0.286158i
\(100\) 15997.8 0.159978
\(101\) −80893.8 −0.789063 −0.394532 0.918882i \(-0.629093\pi\)
−0.394532 + 0.918882i \(0.629093\pi\)
\(102\) −55276.3 45763.8i −0.526064 0.435533i
\(103\) 214822.i 1.99520i 0.0692543 + 0.997599i \(0.477938\pi\)
−0.0692543 + 0.997599i \(0.522062\pi\)
\(104\) −53209.8 −0.482401
\(105\) −124247. + 12728.5i −1.09980 + 0.112669i
\(106\) −21994.1 −0.190126
\(107\) 120007.i 1.01332i 0.862146 + 0.506660i \(0.169120\pi\)
−0.862146 + 0.506660i \(0.830880\pi\)
\(108\) 76412.4 + 42121.1i 0.630383 + 0.347488i
\(109\) 29204.1 0.235439 0.117719 0.993047i \(-0.462442\pi\)
0.117719 + 0.993047i \(0.462442\pi\)
\(110\) 113865. 0.897243
\(111\) 85426.7 103184.i 0.658091 0.794883i
\(112\) 22518.7 + 22151.6i 0.169629 + 0.166863i
\(113\) 64313.7i 0.473813i 0.971532 + 0.236907i \(0.0761335\pi\)
−0.971532 + 0.236907i \(0.923866\pi\)
\(114\) 64642.0 78078.6i 0.465857 0.562691i
\(115\) 49029.6i 0.345711i
\(116\) 11830.2i 0.0816293i
\(117\) −77084.8 + 14644.3i −0.520600 + 0.0989014i
\(118\) 70117.0i 0.463573i
\(119\) −142090. 139773.i −0.919805 0.904807i
\(120\) 122288. + 101243.i 0.775228 + 0.641819i
\(121\) −217545. −1.35078
\(122\) −39958.8 −0.243060
\(123\) −69632.0 + 84105.8i −0.414998 + 0.501260i
\(124\) 3713.44i 0.0216881i
\(125\) −150209. −0.859845
\(126\) −78412.2 52437.7i −0.440004 0.294250i
\(127\) −293422. −1.61430 −0.807149 0.590348i \(-0.798990\pi\)
−0.807149 + 0.590348i \(0.798990\pi\)
\(128\) 161616.i 0.871887i
\(129\) 76809.2 92774.9i 0.406386 0.490858i
\(130\) −59753.8 −0.310104
\(131\) 159323. 0.811147 0.405573 0.914063i \(-0.367072\pi\)
0.405573 + 0.914063i \(0.367072\pi\)
\(132\) −170178. 140892.i −0.850099 0.703805i
\(133\) 197432. 200704.i 0.967804 0.983847i
\(134\) 43331.2i 0.208468i
\(135\) 205021. + 113015.i 0.968199 + 0.533704i
\(136\) 253351.i 1.17456i
\(137\) 387950.i 1.76593i 0.469436 + 0.882967i \(0.344457\pi\)
−0.469436 + 0.882967i \(0.655543\pi\)
\(138\) 23614.7 28523.3i 0.105556 0.127498i
\(139\) 324317.i 1.42375i 0.702308 + 0.711874i \(0.252153\pi\)
−0.702308 + 0.711874i \(0.747847\pi\)
\(140\) 131566. + 129421.i 0.567316 + 0.558066i
\(141\) 175003. 211380.i 0.741308 0.895397i
\(142\) −22069.4 −0.0918481
\(143\) 198678. 0.812473
\(144\) −11050.4 58167.6i −0.0444092 0.233762i
\(145\) 31741.4i 0.125374i
\(146\) −28214.6 −0.109545
\(147\) −204527. 163738.i −0.780651 0.624967i
\(148\) −197940. −0.742812
\(149\) 318945.i 1.17693i −0.808523 0.588464i \(-0.799733\pi\)
0.808523 0.588464i \(-0.200267\pi\)
\(150\) 24971.1 + 20673.8i 0.0906169 + 0.0750226i
\(151\) 479410. 1.71106 0.855529 0.517754i \(-0.173232\pi\)
0.855529 + 0.517754i \(0.173232\pi\)
\(152\) −357862. −1.25634
\(153\) 69726.6 + 367029.i 0.240808 + 1.26757i
\(154\) 170278. + 167501.i 0.578570 + 0.569136i
\(155\) 9963.49i 0.0333106i
\(156\) 89305.4 + 73936.8i 0.293810 + 0.243248i
\(157\) 323801.i 1.04840i −0.851594 0.524202i \(-0.824364\pi\)
0.851594 0.524202i \(-0.175636\pi\)
\(158\) 81535.0i 0.259837i
\(159\) 88197.1 + 73019.2i 0.276670 + 0.229057i
\(160\) 370990.i 1.14568i
\(161\) 72124.7 73320.3i 0.219290 0.222925i
\(162\) 64839.9 + 164494.i 0.194113 + 0.492450i
\(163\) −21423.8 −0.0631579 −0.0315789 0.999501i \(-0.510054\pi\)
−0.0315789 + 0.999501i \(0.510054\pi\)
\(164\) 161342. 0.468424
\(165\) −456604. 378027.i −1.30566 1.08097i
\(166\) 46642.6i 0.131375i
\(167\) 436305. 1.21059 0.605297 0.796000i \(-0.293054\pi\)
0.605297 + 0.796000i \(0.293054\pi\)
\(168\) 33939.4 + 331292.i 0.0927749 + 0.905604i
\(169\) 267032. 0.719195
\(170\) 284509.i 0.755048i
\(171\) −518434. + 98489.9i −1.35582 + 0.257574i
\(172\) −177972. −0.458703
\(173\) −185581. −0.471431 −0.235715 0.971822i \(-0.575743\pi\)
−0.235715 + 0.971822i \(0.575743\pi\)
\(174\) −15288.0 + 18465.8i −0.0382805 + 0.0462376i
\(175\) 64189.2 + 63142.5i 0.158441 + 0.155857i
\(176\) 149921.i 0.364821i
\(177\) −232785. + 281172.i −0.558498 + 0.674588i
\(178\) 269563.i 0.637692i
\(179\) 170761.i 0.398341i −0.979965 0.199171i \(-0.936175\pi\)
0.979965 0.199171i \(-0.0638248\pi\)
\(180\) −64562.5 339846.i −0.148525 0.781809i
\(181\) 326285.i 0.740289i 0.928974 + 0.370144i \(0.120692\pi\)
−0.928974 + 0.370144i \(0.879308\pi\)
\(182\) −89357.5 87900.4i −0.199964 0.196704i
\(183\) 160236. + 132661.i 0.353698 + 0.292830i
\(184\) −130733. −0.284668
\(185\) −531090. −1.14088
\(186\) 4798.83 5796.33i 0.0101708 0.0122849i
\(187\) 945977.i 1.97823i
\(188\) −405495. −0.836741
\(189\) 140345. + 470601.i 0.285787 + 0.958293i
\(190\) −401874. −0.807618
\(191\) 296995.i 0.589069i 0.955641 + 0.294534i \(0.0951646\pi\)
−0.955641 + 0.294534i \(0.904835\pi\)
\(192\) 101175. 122206.i 0.198071 0.239243i
\(193\) 414092. 0.800208 0.400104 0.916470i \(-0.368974\pi\)
0.400104 + 0.916470i \(0.368974\pi\)
\(194\) −254069. −0.484671
\(195\) 239615. + 198379.i 0.451260 + 0.373602i
\(196\) 6364.07 + 387080.i 0.0118330 + 0.719716i
\(197\) 216937.i 0.398262i −0.979973 0.199131i \(-0.936188\pi\)
0.979973 0.199131i \(-0.0638119\pi\)
\(198\) −83558.9 439840.i −0.151471 0.797317i
\(199\) 36716.3i 0.0657244i 0.999460 + 0.0328622i \(0.0104623\pi\)
−0.999460 + 0.0328622i \(0.989538\pi\)
\(200\) 114451.i 0.202323i
\(201\) −143857. + 173760.i −0.251155 + 0.303360i
\(202\) 242222.i 0.417672i
\(203\) −46693.1 + 47467.1i −0.0795266 + 0.0808448i
\(204\) 352040. 425216.i 0.592266 0.715375i
\(205\) 432896. 0.719448
\(206\) 643248. 1.05611
\(207\) −189392. + 35979.8i −0.307210 + 0.0583624i
\(208\) 78674.6i 0.126089i
\(209\) 1.33621e6 2.11596
\(210\) 38113.4 + 372036.i 0.0596389 + 0.582153i
\(211\) −587416. −0.908321 −0.454161 0.890920i \(-0.650061\pi\)
−0.454161 + 0.890920i \(0.650061\pi\)
\(212\) 169191.i 0.258545i
\(213\) 88499.2 + 73269.3i 0.133657 + 0.110656i
\(214\) 359340. 0.536378
\(215\) −477516. −0.704518
\(216\) 301342. 546669.i 0.439467 0.797242i
\(217\) 14656.7 14899.7i 0.0211294 0.0214797i
\(218\) 87446.7i 0.124624i
\(219\) 113141. + 93670.8i 0.159408 + 0.131976i
\(220\) 875916.i 1.22013i
\(221\) 496425.i 0.683712i
\(222\) −308965. 255795.i −0.420753 0.348346i
\(223\) 349812.i 0.471056i 0.971868 + 0.235528i \(0.0756819\pi\)
−0.971868 + 0.235528i \(0.924318\pi\)
\(224\) 545743. 554790.i 0.726722 0.738769i
\(225\) −31499.0 165805.i −0.0414802 0.218344i
\(226\) 192576. 0.250802
\(227\) −925060. −1.19153 −0.595766 0.803158i \(-0.703151\pi\)
−0.595766 + 0.803158i \(0.703151\pi\)
\(228\) 600624. + 497262.i 0.765183 + 0.633502i
\(229\) 136041.i 0.171428i 0.996320 + 0.0857142i \(0.0273172\pi\)
−0.996320 + 0.0857142i \(0.972683\pi\)
\(230\) −146811. −0.182994
\(231\) −126725. 1.23700e6i −0.156254 1.52524i
\(232\) 84635.4 0.103236
\(233\) 1.13764e6i 1.37283i −0.727212 0.686413i \(-0.759184\pi\)
0.727212 0.686413i \(-0.240816\pi\)
\(234\) 43849.7 + 230817.i 0.0523512 + 0.275567i
\(235\) −1.08798e6 −1.28514
\(236\) 539379. 0.630397
\(237\) −270692. + 326958.i −0.313043 + 0.378113i
\(238\) −418526. + 425464.i −0.478939 + 0.486878i
\(239\) 1.04427e6i 1.18254i 0.806473 + 0.591271i \(0.201374\pi\)
−0.806473 + 0.591271i \(0.798626\pi\)
\(240\) −149695. + 180811.i −0.167757 + 0.202627i
\(241\) 503492.i 0.558406i −0.960232 0.279203i \(-0.909930\pi\)
0.960232 0.279203i \(-0.0900702\pi\)
\(242\) 651400.i 0.715005i
\(243\) 286101. 874891.i 0.310816 0.950470i
\(244\) 307385.i 0.330528i
\(245\) 17075.4 + 1.03857e6i 0.0181742 + 1.10540i
\(246\) 251840. + 208501.i 0.265331 + 0.219670i
\(247\) −701208. −0.731315
\(248\) −26566.6 −0.0274288
\(249\) −154851. + 187038.i −0.158276 + 0.191175i
\(250\) 449774.i 0.455139i
\(251\) −1.68197e6 −1.68514 −0.842568 0.538590i \(-0.818957\pi\)
−0.842568 + 0.538590i \(0.818957\pi\)
\(252\) 403380. 603190.i 0.400141 0.598346i
\(253\) 488136. 0.479446
\(254\) 878601.i 0.854491i
\(255\) 944556. 1.14089e6i 0.909656 1.09874i
\(256\) −809614. −0.772108
\(257\) 953741. 0.900736 0.450368 0.892843i \(-0.351293\pi\)
0.450368 + 0.892843i \(0.351293\pi\)
\(258\) −277798. 229992.i −0.259825 0.215111i
\(259\) −794208. 781258.i −0.735673 0.723677i
\(260\) 459659.i 0.421699i
\(261\) 122611. 23293.1i 0.111411 0.0211654i
\(262\) 477064.i 0.429362i
\(263\) 1.64469e6i 1.46621i −0.680117 0.733104i \(-0.738071\pi\)
0.680117 0.733104i \(-0.261929\pi\)
\(264\) −1.00797e6 + 1.21749e6i −0.890099 + 1.07512i
\(265\) 453954.i 0.397098i
\(266\) −600974. 591174.i −0.520777 0.512285i
\(267\) −894935. + 1.08096e6i −0.768269 + 0.927963i
\(268\) 333328. 0.283488
\(269\) 76973.2 0.0648573 0.0324286 0.999474i \(-0.489676\pi\)
0.0324286 + 0.999474i \(0.489676\pi\)
\(270\) 338403. 613901.i 0.282504 0.512494i
\(271\) 1.79795e6i 1.48715i 0.668652 + 0.743576i \(0.266872\pi\)
−0.668652 + 0.743576i \(0.733128\pi\)
\(272\) −374599. −0.307004
\(273\) 66502.0 + 649146.i 0.0540043 + 0.527152i
\(274\) 1.16165e6 0.934756
\(275\) 427345.i 0.340759i
\(276\) 219417. + 181657.i 0.173379 + 0.143542i
\(277\) 1.16102e6 0.909160 0.454580 0.890706i \(-0.349789\pi\)
0.454580 + 0.890706i \(0.349789\pi\)
\(278\) 971111. 0.753628
\(279\) −38487.0 + 7311.60i −0.0296008 + 0.00562344i
\(280\) 925904. 941252.i 0.705783 0.717482i
\(281\) 1.50031e6i 1.13348i −0.823896 0.566741i \(-0.808204\pi\)
0.823896 0.566741i \(-0.191796\pi\)
\(282\) −632940. 524017.i −0.473958 0.392394i
\(283\) 775321.i 0.575460i 0.957712 + 0.287730i \(0.0929006\pi\)
−0.957712 + 0.287730i \(0.907099\pi\)
\(284\) 169770.i 0.124901i
\(285\) 1.61153e6 + 1.33420e6i 1.17524 + 0.972991i
\(286\) 594906.i 0.430064i
\(287\) 647366. + 636810.i 0.463922 + 0.456357i
\(288\) −1.43306e6 + 272247.i −1.01808 + 0.193412i
\(289\) 943804. 0.664718
\(290\) 95044.2 0.0663637
\(291\) 1.01883e6 + 843495.i 0.705289 + 0.583916i
\(292\) 217042.i 0.148966i
\(293\) 194034. 0.132041 0.0660206 0.997818i \(-0.478970\pi\)
0.0660206 + 0.997818i \(0.478970\pi\)
\(294\) −490286. + 612420.i −0.330812 + 0.413220i
\(295\) 1.44720e6 0.968221
\(296\) 1.41610e6i 0.939430i
\(297\) −1.12517e6 + 2.04118e6i −0.740162 + 1.34274i
\(298\) −955026. −0.622980
\(299\) −256162. −0.165705
\(300\) −159034. + 192091.i −0.102021 + 0.123227i
\(301\) −714091. 702447.i −0.454295 0.446887i
\(302\) 1.43551e6i 0.905710i
\(303\) 804165. 971320.i 0.503198 0.607793i
\(304\) 529126.i 0.328379i
\(305\) 824742.i 0.507655i
\(306\) 1.09900e6 208784.i 0.670958 0.127466i
\(307\) 394659.i 0.238988i −0.992835 0.119494i \(-0.961873\pi\)
0.992835 0.119494i \(-0.0381273\pi\)
\(308\) −1.28851e6 + 1.30987e6i −0.773947 + 0.786776i
\(309\) −2.57945e6 2.13555e6i −1.53685 1.27237i
\(310\) −29833.9 −0.0176322
\(311\) 2.29757e6 1.34700 0.673501 0.739186i \(-0.264790\pi\)
0.673501 + 0.739186i \(0.264790\pi\)
\(312\) 528958. 638908.i 0.307635 0.371580i
\(313\) 634859.i 0.366283i 0.983087 + 0.183141i \(0.0586266\pi\)
−0.983087 + 0.183141i \(0.941373\pi\)
\(314\) −969566. −0.554949
\(315\) 1.08230e6 1.61841e6i 0.614572 0.918994i
\(316\) 627212. 0.353343
\(317\) 192873.i 0.107801i 0.998546 + 0.0539005i \(0.0171654\pi\)
−0.998546 + 0.0539005i \(0.982835\pi\)
\(318\) 218643. 264091.i 0.121246 0.146449i
\(319\) −316016. −0.173873
\(320\) −628998. −0.343379
\(321\) −1.44096e6 1.19299e6i −0.780532 0.646210i
\(322\) −219545. 215965.i −0.118000 0.116076i
\(323\) 3.33871e6i 1.78062i
\(324\) −1.26538e6 + 498784.i −0.669665 + 0.263967i
\(325\) 224260.i 0.117772i
\(326\) 64149.9i 0.0334312i
\(327\) −290318. + 350664.i −0.150143 + 0.181352i
\(328\) 1.15427e6i 0.592413i
\(329\) −1.62700e6 1.60047e6i −0.828700 0.815187i
\(330\) −1.13194e6 + 1.36722e6i −0.572186 + 0.691121i
\(331\) −2.85474e6 −1.43218 −0.716088 0.698010i \(-0.754069\pi\)
−0.716088 + 0.698010i \(0.754069\pi\)
\(332\) 358800. 0.178652
\(333\) 389735. + 2.05150e6i 0.192601 + 1.01382i
\(334\) 1.30644e6i 0.640800i
\(335\) 894348. 0.435406
\(336\) −489840. + 50181.9i −0.236704 + 0.0242493i
\(337\) 3.37722e6 1.61989 0.809944 0.586507i \(-0.199497\pi\)
0.809944 + 0.586507i \(0.199497\pi\)
\(338\) 799581.i 0.380689i
\(339\) −772237. 639342.i −0.364965 0.302158i
\(340\) −2.18860e6 −1.02676
\(341\) 99196.0 0.0461964
\(342\) 294911. + 1.55236e6i 0.136341 + 0.717674i
\(343\) −1.50225e6 + 1.57823e6i −0.689457 + 0.724327i
\(344\) 1.27325e6i 0.580119i
\(345\) 588716. + 487403.i 0.266292 + 0.220466i
\(346\) 555690.i 0.249541i
\(347\) 547961.i 0.244301i 0.992512 + 0.122151i \(0.0389791\pi\)
−0.992512 + 0.122151i \(0.961021\pi\)
\(348\) −142049. 117604.i −0.0628768 0.0520563i
\(349\) 1206.49i 0.000530223i −1.00000 0.000265112i \(-0.999916\pi\)
1.00000 0.000265112i \(-8.43876e-5\pi\)
\(350\) 189069. 192203.i 0.0824994 0.0838669i
\(351\) 590461. 1.07116e6i 0.255813 0.464074i
\(352\) 3.69356e6 1.58887
\(353\) −1.15208e6 −0.492090 −0.246045 0.969258i \(-0.579131\pi\)
−0.246045 + 0.969258i \(0.579131\pi\)
\(354\) 841920. + 697033.i 0.357078 + 0.295628i
\(355\) 455509.i 0.191834i
\(356\) 2.07363e6 0.867174
\(357\) 3.09082e6 316640.i 1.28352 0.131491i
\(358\) −511313. −0.210853
\(359\) 2.10870e6i 0.863531i −0.901986 0.431766i \(-0.857891\pi\)
0.901986 0.431766i \(-0.142109\pi\)
\(360\) −2.43132e6 + 461893.i −0.988750 + 0.187839i
\(361\) −2.23988e6 −0.904599
\(362\) 977005. 0.391855
\(363\) 2.16261e6 2.61213e6i 0.861414 1.04047i
\(364\) 676179. 687387.i 0.267490 0.271924i
\(365\) 582344.i 0.228795i
\(366\) 397230. 479799.i 0.155003 0.187222i
\(367\) 3.37130e6i 1.30657i 0.757113 + 0.653284i \(0.226609\pi\)
−0.757113 + 0.653284i \(0.773391\pi\)
\(368\) 193298.i 0.0744059i
\(369\) −317676. 1.67219e6i −0.121456 0.639323i
\(370\) 1.59026e6i 0.603898i
\(371\) 667787. 678856.i 0.251885 0.256061i
\(372\) 44588.5 + 36915.3i 0.0167057 + 0.0138308i
\(373\) −65054.8 −0.0242107 −0.0121054 0.999927i \(-0.503853\pi\)
−0.0121054 + 0.999927i \(0.503853\pi\)
\(374\) −2.83256e6 −1.04713
\(375\) 1.49323e6 1.80361e6i 0.548337 0.662315i
\(376\) 2.90099e6i 1.05822i
\(377\) 165838. 0.0600938
\(378\) 1.40913e6 420239.i 0.507250 0.151275i
\(379\) −690875. −0.247059 −0.123530 0.992341i \(-0.539421\pi\)
−0.123530 + 0.992341i \(0.539421\pi\)
\(380\) 3.09144e6i 1.09825i
\(381\) 2.91691e6 3.52322e6i 1.02946 1.24345i
\(382\) 889301. 0.311810
\(383\) −2.44872e6 −0.852986 −0.426493 0.904491i \(-0.640251\pi\)
−0.426493 + 0.904491i \(0.640251\pi\)
\(384\) 1.94058e6 + 1.60663e6i 0.671590 + 0.556016i
\(385\) −3.45719e6 + 3.51450e6i −1.18870 + 1.20840i
\(386\) 1.23993e6i 0.423572i
\(387\) 350420. + 1.84455e6i 0.118936 + 0.626056i
\(388\) 1.95444e6i 0.659087i
\(389\) 3.72849e6i 1.24928i 0.780913 + 0.624640i \(0.214754\pi\)
−0.780913 + 0.624640i \(0.785246\pi\)
\(390\) 594012. 717484.i 0.197758 0.238864i
\(391\) 1.21968e6i 0.403463i
\(392\) 2.76925e6 45529.8i 0.910221 0.0149651i
\(393\) −1.58383e6 + 1.91304e6i −0.517281 + 0.624803i
\(394\) −649581. −0.210811
\(395\) 1.68287e6 0.542697
\(396\) 3.38349e6 642781.i 1.08424 0.205980i
\(397\) 3.19740e6i 1.01817i −0.860716 0.509086i \(-0.829984\pi\)
0.860716 0.509086i \(-0.170016\pi\)
\(398\) 109941. 0.0347897
\(399\) 447259. + 4.36583e6i 0.140646 + 1.37289i
\(400\) 169225. 0.0528828
\(401\) 6.01416e6i 1.86773i 0.357627 + 0.933865i \(0.383586\pi\)
−0.357627 + 0.933865i \(0.616414\pi\)
\(402\) 520293. + 430756.i 0.160577 + 0.132943i
\(403\) −52055.6 −0.0159663
\(404\) −1.86331e6 −0.567978
\(405\) −3.39512e6 + 1.33828e6i −1.02853 + 0.405425i
\(406\) 142132. + 139814.i 0.0427934 + 0.0420956i
\(407\) 5.28751e6i 1.58221i
\(408\) −3.04208e6 2.51856e6i −0.904732 0.749036i
\(409\) 5.69952e6i 1.68473i −0.538909 0.842364i \(-0.681163\pi\)
0.538909 0.842364i \(-0.318837\pi\)
\(410\) 1.29623e6i 0.380823i
\(411\) −4.65825e6 3.85661e6i −1.36025 1.12616i
\(412\) 4.94822e6i 1.43617i
\(413\) 2.16419e6 + 2.12890e6i 0.624338 + 0.614158i
\(414\) 107735. + 567100.i 0.0308928 + 0.162614i
\(415\) 962694. 0.274390
\(416\) −1.93829e6 −0.549143
\(417\) −3.89419e6 3.22404e6i −1.09667 0.907946i
\(418\) 4.00104e6i 1.12004i
\(419\) −2.40292e6 −0.668658 −0.334329 0.942456i \(-0.608510\pi\)
−0.334329 + 0.942456i \(0.608510\pi\)
\(420\) −2.86191e6 + 293189.i −0.791649 + 0.0811007i
\(421\) −1.84926e6 −0.508501 −0.254251 0.967138i \(-0.581829\pi\)
−0.254251 + 0.967138i \(0.581829\pi\)
\(422\) 1.75891e6i 0.480799i
\(423\) 798403. + 4.20265e6i 0.216956 + 1.14202i
\(424\) −1.21042e6 −0.326981
\(425\) −1.06778e6 −0.286755
\(426\) 219392. 264995.i 0.0585730 0.0707481i
\(427\) 1.21323e6 1.23334e6i 0.322014 0.327351i
\(428\) 2.76424e6i 0.729401i
\(429\) −1.97505e6 + 2.38559e6i −0.518127 + 0.625825i
\(430\) 1.42984e6i 0.372920i
\(431\) 670021.i 0.173738i −0.996220 0.0868691i \(-0.972314\pi\)
0.996220 0.0868691i \(-0.0276862\pi\)
\(432\) 808291. + 445557.i 0.208381 + 0.114867i
\(433\) 3.18314e6i 0.815898i −0.913005 0.407949i \(-0.866244\pi\)
0.913005 0.407949i \(-0.133756\pi\)
\(434\) −44614.5 43887.0i −0.0113698 0.0111844i
\(435\) −381131. 315542.i −0.0965719 0.0799528i
\(436\) 672688. 0.169472
\(437\) −1.72282e6 −0.431554
\(438\) 280481. 338782.i 0.0698583 0.0843792i
\(439\) 3.04218e6i 0.753396i −0.926336 0.376698i \(-0.877059\pi\)
0.926336 0.376698i \(-0.122941\pi\)
\(440\) 6.26647e6 1.54309
\(441\) 3.99927e6 828104.i 0.979228 0.202763i
\(442\) 1.48646e6 0.361907
\(443\) 4.06656e6i 0.984505i −0.870452 0.492253i \(-0.836174\pi\)
0.870452 0.492253i \(-0.163826\pi\)
\(444\) 1.96772e6 2.37673e6i 0.473703 0.572167i
\(445\) 5.56374e6 1.33188
\(446\) 1.04745e6 0.249343
\(447\) 3.82969e6 + 3.17063e6i 0.906555 + 0.750546i
\(448\) −940622. 925284.i −0.221422 0.217811i
\(449\) 3.30712e6i 0.774166i 0.922045 + 0.387083i \(0.126517\pi\)
−0.922045 + 0.387083i \(0.873483\pi\)
\(450\) −496475. + 94318.3i −0.115576 + 0.0219566i
\(451\) 4.30990e6i 0.997758i
\(452\) 1.48140e6i 0.341057i
\(453\) −4.76582e6 + 5.75645e6i −1.09117 + 1.31798i
\(454\) 2.76993e6i 0.630710i
\(455\) 1.81425e6 1.84432e6i 0.410836 0.417646i
\(456\) 3.55751e6 4.29698e6i 0.801187 0.967723i
\(457\) 797135. 0.178542 0.0892712 0.996007i \(-0.471546\pi\)
0.0892712 + 0.996007i \(0.471546\pi\)
\(458\) 407352. 0.0907416
\(459\) −5.10019e6 2.81140e6i −1.12994 0.622861i
\(460\) 1.12935e6i 0.248847i
\(461\) −4.32869e6 −0.948646 −0.474323 0.880351i \(-0.657307\pi\)
−0.474323 + 0.880351i \(0.657307\pi\)
\(462\) −3.70398e6 + 379455.i −0.807352 + 0.0827095i
\(463\) 5.38489e6 1.16741 0.583706 0.811965i \(-0.301602\pi\)
0.583706 + 0.811965i \(0.301602\pi\)
\(464\) 125140.i 0.0269836i
\(465\) 119635. + 99047.1i 0.0256582 + 0.0212427i
\(466\) −3.40647e6 −0.726674
\(467\) 677568. 0.143767 0.0718837 0.997413i \(-0.477099\pi\)
0.0718837 + 0.997413i \(0.477099\pi\)
\(468\) −1.77557e6 + 337316.i −0.374734 + 0.0711905i
\(469\) 1.33743e6 + 1.31563e6i 0.280763 + 0.276185i
\(470\) 3.25777e6i 0.680261i
\(471\) 3.88799e6 + 3.21891e6i 0.807557 + 0.668584i
\(472\) 3.85882e6i 0.797259i
\(473\) 4.75413e6i 0.977053i
\(474\) 979019. + 810539.i 0.200145 + 0.165702i
\(475\) 1.50826e6i 0.306720i
\(476\) −3.27290e6 3.21953e6i −0.662088 0.651292i
\(477\) −1.75353e6 + 333130.i −0.352873 + 0.0670374i
\(478\) 3.12687e6 0.625951
\(479\) 7.87592e6 1.56842 0.784210 0.620495i \(-0.213068\pi\)
0.784210 + 0.620495i \(0.213068\pi\)
\(480\) 4.45461e6 + 3.68802e6i 0.882484 + 0.730617i
\(481\) 2.77476e6i 0.546842i
\(482\) −1.50762e6 −0.295579
\(483\) 163391. + 1.59490e6i 0.0318683 + 0.311076i
\(484\) −5.01092e6 −0.972309
\(485\) 5.24394e6i 1.01229i
\(486\) −2.61971e6 856679.i −0.503110 0.164523i
\(487\) 6.38336e6 1.21963 0.609813 0.792545i \(-0.291244\pi\)
0.609813 + 0.792545i \(0.291244\pi\)
\(488\) −2.19909e6 −0.418017
\(489\) 212974. 257243.i 0.0402768 0.0486488i
\(490\) 3.10982e6 51129.2i 0.585121 0.00962009i
\(491\) 837734.i 0.156820i 0.996921 + 0.0784102i \(0.0249844\pi\)
−0.996921 + 0.0784102i \(0.975016\pi\)
\(492\) −1.60390e6 + 1.93729e6i −0.298721 + 0.360814i
\(493\) 789613.i 0.146318i
\(494\) 2.09965e6i 0.387105i
\(495\) 9.07821e6 1.72464e6i 1.66528 0.316363i
\(496\) 39280.8i 0.00716928i
\(497\) 670074. 681182.i 0.121684 0.123701i
\(498\) 560054. + 463674.i 0.101194 + 0.0837798i
\(499\) −4.80919e6 −0.864611 −0.432306 0.901727i \(-0.642300\pi\)
−0.432306 + 0.901727i \(0.642300\pi\)
\(500\) −3.45991e6 −0.618927
\(501\) −4.33731e6 + 5.23886e6i −0.772015 + 0.932487i
\(502\) 5.03638e6i 0.891988i
\(503\) −2.58231e6 −0.455081 −0.227540 0.973769i \(-0.573068\pi\)
−0.227540 + 0.973769i \(0.573068\pi\)
\(504\) −4.31534e6 2.88586e6i −0.756725 0.506056i
\(505\) −4.99943e6 −0.872352
\(506\) 1.46164e6i 0.253784i
\(507\) −2.65456e6 + 3.20635e6i −0.458642 + 0.553975i
\(508\) −6.75869e6 −1.16199
\(509\) 5.81775e6 0.995315 0.497658 0.867374i \(-0.334194\pi\)
0.497658 + 0.867374i \(0.334194\pi\)
\(510\) −3.41621e6 2.82831e6i −0.581592 0.481506i
\(511\) 856653. 870853.i 0.145129 0.147534i
\(512\) 2.74747e6i 0.463189i
\(513\) 3.97115e6 7.20410e6i 0.666227 1.20861i
\(514\) 2.85581e6i 0.476784i
\(515\) 1.32765e7i 2.20580i
\(516\) 1.76922e6 2.13698e6i 0.292522 0.353326i
\(517\) 1.08319e7i 1.78229i
\(518\) −2.33934e6 + 2.37812e6i −0.383062 + 0.389412i
\(519\) 1.84486e6 2.22833e6i 0.300639 0.363130i
\(520\) −3.28849e6 −0.533320
\(521\) −7.44578e6 −1.20175 −0.600877 0.799341i \(-0.705182\pi\)
−0.600877 + 0.799341i \(0.705182\pi\)
\(522\) −69747.2 367137.i −0.0112034 0.0589728i
\(523\) 2.68003e6i 0.428435i 0.976786 + 0.214218i \(0.0687202\pi\)
−0.976786 + 0.214218i \(0.931280\pi\)
\(524\) 3.66984e6 0.583874
\(525\) −1.39628e6 + 143042.i −0.221092 + 0.0226499i
\(526\) −4.92475e6 −0.776103
\(527\) 247856.i 0.0388752i
\(528\) −1.80015e6 1.49036e6i −0.281011 0.232652i
\(529\) 5.80697e6 0.902216
\(530\) −1.35929e6 −0.210195
\(531\) −1.06201e6 5.59026e6i −0.163453 0.860390i
\(532\) 4.54764e6 4.62302e6i 0.696638 0.708185i
\(533\) 2.26173e6i 0.344844i
\(534\) 3.23674e6 + 2.67973e6i 0.491196 + 0.406666i
\(535\) 7.41670e6i 1.12028i
\(536\) 2.38469e6i 0.358525i
\(537\) 2.05038e6 + 1.69753e6i 0.306831 + 0.254028i
\(538\) 230483.i 0.0343307i
\(539\) −1.03400e7 + 170002.i −1.53302 + 0.0252047i
\(540\) 4.72246e6 + 2.60318e6i 0.696922 + 0.384167i
\(541\) −7.33897e6 −1.07806 −0.539029 0.842288i \(-0.681209\pi\)
−0.539029 + 0.842288i \(0.681209\pi\)
\(542\) 5.38366e6 0.787190
\(543\) −3.91782e6 3.24360e6i −0.570224 0.472094i
\(544\) 9.22891e6i 1.33707i
\(545\) 1.80488e6 0.260290
\(546\) 1.94375e6 199129.i 0.279036 0.0285859i
\(547\) −3.63983e6 −0.520131 −0.260066 0.965591i \(-0.583744\pi\)
−0.260066 + 0.965591i \(0.583744\pi\)
\(548\) 8.93604e6i 1.27114i
\(549\) −3.18582e6 + 605228.i −0.451118 + 0.0857015i
\(550\) 1.27961e6 0.180373
\(551\) 1.11534e6 0.156505
\(552\) 1.29961e6 1.56975e6i 0.181537 0.219272i
\(553\) 2.51661e6 + 2.47557e6i 0.349947 + 0.344241i
\(554\) 3.47647e6i 0.481243i
\(555\) 5.27957e6 6.37699e6i 0.727556 0.878786i
\(556\) 7.47032e6i 1.02483i
\(557\) 1.12162e7i 1.53183i −0.642944 0.765913i \(-0.722287\pi\)
0.642944 0.765913i \(-0.277713\pi\)
\(558\) 21893.3 + 115243.i 0.00297664 + 0.0156685i
\(559\) 2.49485e6i 0.337687i
\(560\) 1.39171e6 + 1.36902e6i 0.187534 + 0.184476i
\(561\) 1.13587e7 + 9.40395e6i 1.52377 + 1.26155i
\(562\) −4.49241e6 −0.599983
\(563\) 1.46722e7 1.95085 0.975426 0.220326i \(-0.0707120\pi\)
0.975426 + 0.220326i \(0.0707120\pi\)
\(564\) 4.03103e6 4.86892e6i 0.533603 0.644518i
\(565\) 3.97474e6i 0.523826i
\(566\) 2.32156e6 0.304607
\(567\) −7.04584e6 2.99307e6i −0.920397 0.390984i
\(568\) −1.21457e6 −0.157962
\(569\) 5.12118e6i 0.663116i 0.943435 + 0.331558i \(0.107574\pi\)
−0.943435 + 0.331558i \(0.892426\pi\)
\(570\) 3.99503e6 4.82544e6i 0.515030 0.622085i
\(571\) 4.08710e6 0.524596 0.262298 0.964987i \(-0.415520\pi\)
0.262298 + 0.964987i \(0.415520\pi\)
\(572\) 4.57634e6 0.584828
\(573\) −3.56613e6 2.95243e6i −0.453743 0.375658i
\(574\) 1.90682e6 1.93842e6i 0.241562 0.245566i
\(575\) 550991.i 0.0694984i
\(576\) 461583. + 2.42969e6i 0.0579688 + 0.305137i
\(577\) 2.58345e6i 0.323043i 0.986869 + 0.161521i \(0.0516401\pi\)
−0.986869 + 0.161521i \(0.948360\pi\)
\(578\) 2.82606e6i 0.351853i
\(579\) −4.11648e6 + 4.97214e6i −0.510305 + 0.616378i
\(580\) 731133.i 0.0902456i
\(581\) 1.43964e6 + 1.41617e6i 0.176935 + 0.174050i
\(582\) 2.52570e6 3.05070e6i 0.309082 0.373329i
\(583\) 4.51955e6 0.550711
\(584\) −1.55276e6 −0.188396
\(585\) −4.76402e6 + 905049.i −0.575551 + 0.109341i
\(586\) 581002.i 0.0698929i
\(587\) −9.72773e6 −1.16524 −0.582621 0.812744i \(-0.697973\pi\)
−0.582621 + 0.812744i \(0.697973\pi\)
\(588\) −4.71107e6 3.77155e6i −0.561923 0.449859i
\(589\) −350100. −0.0415819
\(590\) 4.33340e6i 0.512505i
\(591\) 2.60484e6 + 2.15657e6i 0.306770 + 0.253978i
\(592\) −2.09381e6 −0.245546
\(593\) 9.57397e6 1.11803 0.559017 0.829156i \(-0.311179\pi\)
0.559017 + 0.829156i \(0.311179\pi\)
\(594\) 6.11197e6 + 3.36912e6i 0.710747 + 0.391788i
\(595\) −8.78149e6 8.63830e6i −1.01689 1.00031i
\(596\) 7.34658e6i 0.847169i
\(597\) −440866. 364997.i −0.0506257 0.0419135i
\(598\) 767032.i 0.0877123i
\(599\) 5.71115e6i 0.650364i −0.945651 0.325182i \(-0.894574\pi\)
0.945651 0.325182i \(-0.105426\pi\)
\(600\) 1.37426e6 + 1.13776e6i 0.155844 + 0.129025i
\(601\) 1.49010e6i 0.168279i 0.996454 + 0.0841395i \(0.0268141\pi\)
−0.996454 + 0.0841395i \(0.973186\pi\)
\(602\) −2.10336e6 + 2.13822e6i −0.236549 + 0.240470i
\(603\) −656308. 3.45469e6i −0.0735046 0.386915i
\(604\) 1.10427e7 1.23164
\(605\) −1.34448e7 −1.49336
\(606\) −2.90845e6 2.40793e6i −0.321721 0.266356i
\(607\) 1.13768e7i 1.25328i −0.779308 0.626641i \(-0.784429\pi\)
0.779308 0.626641i \(-0.215571\pi\)
\(608\) −1.30360e7 −1.43016
\(609\) −105778. 1.03253e6i −0.0115572 0.112813i
\(610\) −2.46955e6 −0.268716
\(611\) 5.68431e6i 0.615991i
\(612\) 1.60608e6 + 8.45414e6i 0.173336 + 0.912412i
\(613\) 8.50093e6 0.913724 0.456862 0.889537i \(-0.348973\pi\)
0.456862 + 0.889537i \(0.348973\pi\)
\(614\) −1.18174e6 −0.126503
\(615\) −4.30342e6 + 5.19794e6i −0.458803 + 0.554170i
\(616\) 9.37106e6 + 9.21826e6i 0.995032 + 0.978807i
\(617\) 1.82563e7i 1.93064i 0.261073 + 0.965319i \(0.415924\pi\)
−0.261073 + 0.965319i \(0.584076\pi\)
\(618\) −6.39453e6 + 7.72370e6i −0.673499 + 0.813494i
\(619\) 1.24791e7i 1.30905i −0.756041 0.654524i \(-0.772869\pi\)
0.756041 0.654524i \(-0.227131\pi\)
\(620\) 229499.i 0.0239774i
\(621\) 1.45072e6 2.63177e6i 0.150957 0.273854i
\(622\) 6.87968e6i 0.713005i
\(623\) 8.32017e6 + 8.18450e6i 0.858840 + 0.844836i
\(624\) 944674. + 782104.i 0.0971226 + 0.0804087i
\(625\) −1.14537e7 −1.17285
\(626\) 1.90098e6 0.193883
\(627\) −1.32832e7 + 1.60443e7i −1.34938 + 1.62987i
\(628\) 7.45843e6i 0.754655i
\(629\) 1.32116e7 1.33146
\(630\) −4.84606e6 3.24077e6i −0.486449 0.325310i
\(631\) −1.52412e7 −1.52387 −0.761933 0.647656i \(-0.775749\pi\)
−0.761933 + 0.647656i \(0.775749\pi\)
\(632\) 4.48720e6i 0.446871i
\(633\) 5.83950e6 7.05331e6i 0.579250 0.699654i
\(634\) 577525. 0.0570620
\(635\) −1.81342e7 −1.78469
\(636\) 2.03153e6 + 1.68193e6i 0.199150 + 0.164878i
\(637\) 5.42616e6 89212.6i 0.529839 0.00871119i
\(638\) 946256.i 0.0920358i
\(639\) −1.75954e6 + 334271.i −0.170470 + 0.0323852i
\(640\) 9.98827e6i 0.963918i
\(641\) 3.06269e6i 0.294414i −0.989106 0.147207i \(-0.952972\pi\)
0.989106 0.147207i \(-0.0470283\pi\)
\(642\) −3.57220e6 + 4.31472e6i −0.342056 + 0.413157i
\(643\) 4.16015e6i 0.396809i 0.980120 + 0.198404i \(0.0635760\pi\)
−0.980120 + 0.198404i \(0.936424\pi\)
\(644\) 1.66132e6 1.68886e6i 0.157848 0.160465i
\(645\) 4.74699e6 5.73370e6i 0.449282 0.542670i
\(646\) 9.99718e6 0.942532
\(647\) −1.44997e7 −1.36175 −0.680877 0.732398i \(-0.738401\pi\)
−0.680877 + 0.732398i \(0.738401\pi\)
\(648\) 3.56840e6 + 9.05276e6i 0.333838 + 0.846922i
\(649\) 1.44083e7i 1.34277i
\(650\) −671508. −0.0623402
\(651\) 33203.2 + 324106.i 0.00307063 + 0.0299733i
\(652\) −493476. −0.0454619
\(653\) 5.47090e6i 0.502084i −0.967976 0.251042i \(-0.919227\pi\)
0.967976 0.251042i \(-0.0807732\pi\)
\(654\) 1.05000e6 + 869308.i 0.0959945 + 0.0794747i
\(655\) 9.84652e6 0.896766
\(656\) 1.70668e6 0.154843
\(657\) −2.24948e6 + 427347.i −0.203314 + 0.0386249i
\(658\) −4.79232e6 + 4.87176e6i −0.431501 + 0.438653i
\(659\) 1.88834e7i 1.69381i −0.531741 0.846907i \(-0.678462\pi\)
0.531741 0.846907i \(-0.321538\pi\)
\(660\) −1.05174e7 8.70748e6i −0.939831 0.778095i
\(661\) 4.64223e6i 0.413260i −0.978419 0.206630i \(-0.933750\pi\)
0.978419 0.206630i \(-0.0662496\pi\)
\(662\) 8.54802e6i 0.758089i
\(663\) −5.96075e6 4.93496e6i −0.526644 0.436014i
\(664\) 2.56693e6i 0.225940i
\(665\) 1.22017e7 1.24040e7i 1.06996 1.08770i
\(666\) 6.14285e6 1.16699e6i 0.536642 0.101949i
\(667\) 407451. 0.0354618
\(668\) 1.00498e7 0.871401
\(669\) −4.20031e6 3.47748e6i −0.362841 0.300400i
\(670\) 2.67797e6i 0.230472i
\(671\) 8.21109e6 0.704036
\(672\) 1.23632e6 + 1.20681e7i 0.105611 + 1.03090i
\(673\) 629529. 0.0535770 0.0267885 0.999641i \(-0.491472\pi\)
0.0267885 + 0.999641i \(0.491472\pi\)
\(674\) 1.01125e7i 0.857451i
\(675\) 2.30401e6 + 1.27005e6i 0.194637 + 0.107291i
\(676\) 6.15082e6 0.517685
\(677\) 6.49528e6 0.544661 0.272331 0.962204i \(-0.412206\pi\)
0.272331 + 0.962204i \(0.412206\pi\)
\(678\) −1.91440e6 + 2.31233e6i −0.159940 + 0.193186i
\(679\) 7.71406e6 7.84193e6i 0.642109 0.652753i
\(680\) 1.56577e7i 1.29854i
\(681\) 9.19603e6 1.11075e7i 0.759858 0.917803i
\(682\) 297025.i 0.0244530i
\(683\) 8.25581e6i 0.677186i 0.940933 + 0.338593i \(0.109951\pi\)
−0.940933 + 0.338593i \(0.890049\pi\)
\(684\) −1.19416e7 + 2.26862e6i −0.975938 + 0.185405i
\(685\) 2.39762e7i 1.95233i
\(686\) 4.72573e6 + 4.49823e6i 0.383406 + 0.364948i
\(687\) −1.63350e6 1.35239e6i −0.132046 0.109322i
\(688\) −1.88259e6 −0.151630
\(689\) −2.37175e6 −0.190336
\(690\) 1.45944e6 1.76281e6i 0.116698 0.140955i
\(691\) 2.21202e7i 1.76235i −0.472787 0.881177i \(-0.656752\pi\)
0.472787 0.881177i \(-0.343248\pi\)
\(692\) −4.27467e6 −0.339342
\(693\) 1.61128e7 + 1.07754e7i 1.27450 + 0.852313i
\(694\) 1.64077e6 0.129315
\(695\) 2.00436e7i 1.57403i
\(696\) −841360. + 1.01625e6i −0.0658353 + 0.0795199i
\(697\) −1.07689e7 −0.839633
\(698\) −3612.61 −0.000280661
\(699\) 1.36600e7 + 1.13093e7i 1.05745 + 0.875472i
\(700\) 1.47853e6 + 1.45442e6i 0.114048 + 0.112188i
\(701\) 4.20151e6i 0.322932i −0.986878 0.161466i \(-0.948378\pi\)
0.986878 0.161466i \(-0.0516222\pi\)
\(702\) −3.20741e6 1.76803e6i −0.245647 0.135409i
\(703\) 1.86616e7i 1.42417i
\(704\) 6.26227e6i 0.476212i
\(705\) 1.08156e7 1.30638e7i 0.819556 0.989910i
\(706\) 3.44969e6i 0.260476i
\(707\) −7.47629e6 7.35438e6i −0.562519 0.553347i
\(708\) −5.36197e6 + 6.47651e6i −0.402014 + 0.485577i
\(709\) 1.27013e7 0.948928 0.474464 0.880275i \(-0.342642\pi\)
0.474464 + 0.880275i \(0.342642\pi\)
\(710\) −1.36394e6 −0.101543
\(711\) −1.23495e6 6.50058e6i −0.0916172 0.482257i
\(712\) 1.48351e7i 1.09671i
\(713\) −127897. −0.00942185
\(714\) −948124. 9.25492e6i −0.0696017 0.679403i
\(715\) 1.22787e7 0.898233
\(716\) 3.93330e6i 0.286731i
\(717\) −1.25389e7 1.03810e7i −0.910879 0.754125i
\(718\) −6.31413e6 −0.457091
\(719\) −1.21200e7 −0.874337 −0.437169 0.899380i \(-0.644019\pi\)
−0.437169 + 0.899380i \(0.644019\pi\)
\(720\) −682943. 3.59489e6i −0.0490968 0.258437i
\(721\) −1.95303e7 + 1.98541e7i −1.39917 + 1.42237i
\(722\) 6.70692e6i 0.478829i
\(723\) 6.04560e6 + 5.00521e6i 0.430124 + 0.356104i
\(724\) 7.51566e6i 0.532869i
\(725\) 356708.i 0.0252039i
\(726\) −7.82158e6 6.47556e6i −0.550748 0.455970i
\(727\) 3.77140e6i 0.264647i −0.991207 0.132323i \(-0.957756\pi\)
0.991207 0.132323i \(-0.0422437\pi\)
\(728\) −4.91770e6 4.83751e6i −0.343901 0.338294i
\(729\) 7.66100e6 + 1.21326e7i 0.533908 + 0.845542i
\(730\) −1.74373e6 −0.121108
\(731\) 1.18789e7 0.822209
\(732\) 3.69088e6 + 3.05572e6i 0.254596 + 0.210783i
\(733\) 1.16976e7i 0.804148i 0.915607 + 0.402074i \(0.131711\pi\)
−0.915607 + 0.402074i \(0.868289\pi\)
\(734\) 1.00948e7 0.691601
\(735\) −1.26402e7 1.01194e7i −0.863052 0.690935i
\(736\) −4.76224e6 −0.324053
\(737\) 8.90409e6i 0.603838i
\(738\) −5.00709e6 + 951227.i −0.338411 + 0.0642900i
\(739\) −1.02243e6 −0.0688689 −0.0344344 0.999407i \(-0.510963\pi\)
−0.0344344 + 0.999407i \(0.510963\pi\)
\(740\) −1.22331e7 −0.821219
\(741\) 6.97071e6 8.41965e6i 0.466371 0.563312i
\(742\) −2.03272e6 1.99957e6i −0.135540 0.133330i
\(743\) 1.29463e7i 0.860345i −0.902747 0.430173i \(-0.858453\pi\)
0.902747 0.430173i \(-0.141547\pi\)
\(744\) 264099. 318995.i 0.0174918 0.0211277i
\(745\) 1.97116e7i 1.30116i
\(746\) 194795.i 0.0128154i
\(747\) −706463. 3.71870e6i −0.0463221 0.243831i
\(748\) 2.17896e7i 1.42395i
\(749\) −1.09103e7 + 1.10912e7i −0.710612 + 0.722391i
\(750\) −5.40059e6 4.47120e6i −0.350581 0.290249i
\(751\) −2.90253e7 −1.87792 −0.938959 0.344028i \(-0.888208\pi\)
−0.938959 + 0.344028i \(0.888208\pi\)
\(752\) −4.28933e6 −0.276596
\(753\) 1.67205e7 2.01960e7i 1.07464 1.29801i
\(754\) 496572.i 0.0318093i
\(755\) 2.96287e7 1.89167
\(756\) 3.23271e6 + 1.08398e7i 0.205713 + 0.689792i
\(757\) −1.29941e7 −0.824148 −0.412074 0.911150i \(-0.635195\pi\)
−0.412074 + 0.911150i \(0.635195\pi\)
\(758\) 2.06870e6i 0.130775i
\(759\) −4.85256e6 + 5.86122e6i −0.305750 + 0.369304i
\(760\) −2.21167e7 −1.38895
\(761\) −1.68382e7 −1.05398 −0.526991 0.849871i \(-0.676680\pi\)
−0.526991 + 0.849871i \(0.676680\pi\)
\(762\) −1.05497e7 8.73418e6i −0.658191 0.544922i
\(763\) 2.69908e6 + 2.65506e6i 0.167843 + 0.165106i
\(764\) 6.84099e6i 0.424019i
\(765\) 4.30927e6 + 2.26832e7i 0.266226 + 1.40137i
\(766\) 7.33226e6i 0.451509i
\(767\) 7.56111e6i 0.464085i
\(768\) 8.04838e6 9.72132e6i 0.492385 0.594733i
\(769\) 2.53765e7i 1.54745i 0.633525 + 0.773723i \(0.281608\pi\)
−0.633525 + 0.773723i \(0.718392\pi\)
\(770\) 1.05236e7 + 1.03520e7i 0.639640 + 0.629210i
\(771\) −9.48114e6 + 1.14519e7i −0.574413 + 0.693812i
\(772\) 9.53819e6 0.576000
\(773\) 3.00362e6 0.180799 0.0903996 0.995906i \(-0.471186\pi\)
0.0903996 + 0.995906i \(0.471186\pi\)
\(774\) 5.52318e6 1.04927e6i 0.331388 0.0629558i
\(775\) 111969.i 0.00669643i
\(776\) −1.39824e7 −0.833544
\(777\) 1.72761e7 1.76985e6i 1.02658 0.105168i
\(778\) 1.11643e7 0.661277
\(779\) 1.52112e7i 0.898093i
\(780\) 5.51929e6 + 4.56947e6i 0.324823 + 0.268924i
\(781\) 4.53503e6 0.266043
\(782\) 3.65212e6 0.213564
\(783\) −939186. + 1.70379e6i −0.0547454 + 0.0993142i
\(784\) 67319.1 + 4.09454e6i 0.00391155 + 0.237911i
\(785\) 2.00117e7i 1.15907i
\(786\) 5.72828e6 + 4.74249e6i 0.330725 + 0.273811i
\(787\) 9.42926e6i 0.542676i 0.962484 + 0.271338i \(0.0874662\pi\)
−0.962484 + 0.271338i \(0.912534\pi\)
\(788\) 4.99694e6i 0.286674i
\(789\) 1.97484e7 + 1.63499e7i 1.12938 + 0.935023i
\(790\) 5.03905e6i 0.287264i
\(791\) −5.84701e6 + 5.94393e6i −0.332271 + 0.337779i
\(792\) −4.59858e6 2.42061e7i −0.260502 1.37124i
\(793\) −4.30898e6 −0.243328
\(794\) −9.57407e6 −0.538946
\(795\) 5.45079e6 + 4.51276e6i 0.305873 + 0.253235i
\(796\) 845725.i 0.0473093i
\(797\) −6.70033e6 −0.373637 −0.186819 0.982394i \(-0.559818\pi\)
−0.186819 + 0.982394i \(0.559818\pi\)
\(798\) 1.30727e7 1.33924e6i 0.726706 0.0744477i
\(799\) 2.70651e7 1.49983
\(800\) 4.16916e6i 0.230316i
\(801\) −4.08289e6 2.14916e7i −0.224847 1.18355i
\(802\) 1.80084e7 0.988640
\(803\) 5.79778e6 0.317302
\(804\) −3.31361e6 + 4.00238e6i −0.180784 + 0.218363i
\(805\) 4.45748e6 4.53137e6i 0.242437 0.246456i
\(806\) 155872.i 0.00845141i
\(807\) −765190. + 924244.i −0.0413605 + 0.0499577i
\(808\) 1.33305e7i 0.718318i
\(809\) 2.51823e7i 1.35277i 0.736547 + 0.676386i \(0.236455\pi\)
−0.736547 + 0.676386i \(0.763545\pi\)
\(810\) 4.00726e6 + 1.01661e7i 0.214603 + 0.544430i
\(811\) 2.59174e6i 0.138369i −0.997604 0.0691846i \(-0.977960\pi\)
0.997604 0.0691846i \(-0.0220397\pi\)
\(812\) −1.07553e6 + 1.09336e6i −0.0572442 + 0.0581931i
\(813\) −2.15887e7 1.78735e7i −1.14551 0.948380i
\(814\) −1.58325e7 −0.837509
\(815\) −1.32404e6 −0.0698245
\(816\) 3.72388e6 4.49794e6i 0.195781 0.236476i
\(817\) 1.67791e7i 0.879455i
\(818\) −1.70662e7 −0.891772
\(819\) −8.45562e6 5.65465e6i −0.440490 0.294575i
\(820\) 9.97134e6 0.517868
\(821\) 2.39963e7i 1.24247i −0.783623 0.621237i \(-0.786630\pi\)
0.783623 0.621237i \(-0.213370\pi\)
\(822\) −1.15480e7 + 1.39483e7i −0.596109 + 0.720017i
\(823\) −1.47240e7 −0.757748 −0.378874 0.925448i \(-0.623689\pi\)
−0.378874 + 0.925448i \(0.623689\pi\)
\(824\) 3.54005e7 1.81632
\(825\) −5.13128e6 4.24824e6i −0.262477 0.217307i
\(826\) 6.37462e6 6.48029e6i 0.325090 0.330479i
\(827\) 2.95165e7i 1.50072i 0.661028 + 0.750361i \(0.270121\pi\)
−0.661028 + 0.750361i \(0.729879\pi\)
\(828\) −4.36245e6 + 828760.i −0.221133 + 0.0420100i
\(829\) 3.36080e7i 1.69846i −0.528019 0.849232i \(-0.677065\pi\)
0.528019 0.849232i \(-0.322935\pi\)
\(830\) 2.88262e6i 0.145242i
\(831\) −1.15417e7 + 1.39408e7i −0.579785 + 0.700300i
\(832\) 3.28629e6i 0.164588i
\(833\) −424774. 2.58359e7i −0.0212102 1.29007i
\(834\) −9.65382e6 + 1.16605e7i −0.480600 + 0.580498i
\(835\) 2.69647e7 1.33838
\(836\) 3.07782e7 1.52310
\(837\) 294806. 534811.i 0.0145453 0.0263868i
\(838\) 7.19513e6i 0.353939i
\(839\) 6.45947e6 0.316805 0.158402 0.987375i \(-0.449366\pi\)
0.158402 + 0.987375i \(0.449366\pi\)
\(840\) 2.09753e6 + 2.04746e7i 0.102568 + 1.00119i
\(841\) 2.02474e7 0.987140
\(842\) 5.53728e6i 0.269164i
\(843\) 1.80147e7 + 1.49146e7i 0.873089 + 0.722839i
\(844\) −1.35305e7 −0.653821
\(845\) 1.65032e7 0.795108
\(846\) 1.25841e7 2.39068e6i 0.604501 0.114841i
\(847\) −2.01057e7 1.97779e7i −0.962965 0.947263i
\(848\) 1.78970e6i 0.0854655i
\(849\) −9.30955e6 7.70746e6i −0.443261 0.366980i
\(850\) 3.19730e6i 0.151787i
\(851\) 6.81737e6i 0.322696i
\(852\) 2.03849e6 + 1.68769e6i 0.0962077 + 0.0796513i
\(853\) 4.03008e7i 1.89645i −0.317602 0.948224i \(-0.602877\pi\)
0.317602 0.948224i \(-0.397123\pi\)
\(854\) −3.69303e6 3.63281e6i −0.173276 0.170451i
\(855\) −3.20404e7 + 6.08691e6i −1.49893 + 0.284762i
\(856\) 1.97759e7 0.922469
\(857\) −9.87862e6 −0.459456 −0.229728 0.973255i \(-0.573784\pi\)
−0.229728 + 0.973255i \(0.573784\pi\)
\(858\) 7.14324e6 + 5.91396e6i 0.331266 + 0.274258i
\(859\) 4.71083e6i 0.217829i 0.994051 + 0.108914i \(0.0347374\pi\)
−0.994051 + 0.108914i \(0.965263\pi\)
\(860\) −1.09991e7 −0.507121
\(861\) −1.40819e7 + 1.44262e6i −0.647369 + 0.0663200i
\(862\) −2.00626e6 −0.0919643
\(863\) 8.17467e6i 0.373632i 0.982395 + 0.186816i \(0.0598167\pi\)
−0.982395 + 0.186816i \(0.940183\pi\)
\(864\) 1.09771e7 1.99137e7i 0.500269 0.907543i
\(865\) −1.14693e7 −0.521192
\(866\) −9.53136e6 −0.431877
\(867\) −9.38236e6 + 1.13326e7i −0.423901 + 0.512014i
\(868\) 337603. 343200.i 0.0152092 0.0154614i
\(869\) 1.67545e7i 0.752633i
\(870\) −944835. + 1.14123e6i −0.0423212 + 0.0511181i
\(871\) 4.67264e6i 0.208698i
\(872\) 4.81254e6i 0.214330i
\(873\) −2.02563e7 + 3.84821e6i −0.899548 + 0.170892i
\(874\) 5.15868e6i 0.228433i
\(875\) −1.38824e7 1.36561e7i −0.612979 0.602984i
\(876\) 2.60610e6 + 2.15762e6i 0.114744 + 0.0949978i
\(877\) −1.16202e7 −0.510169 −0.255084 0.966919i \(-0.582103\pi\)
−0.255084 + 0.966919i \(0.582103\pi\)
\(878\) −9.10927e6 −0.398793
\(879\) −1.92889e6 + 2.32984e6i −0.0842047 + 0.101708i
\(880\) 9.26544e6i 0.403329i
\(881\) −4.28179e7 −1.85860 −0.929300 0.369327i \(-0.879588\pi\)
−0.929300 + 0.369327i \(0.879588\pi\)
\(882\) −2.47961e6 1.19751e7i −0.107328 0.518332i
\(883\) 2.20297e7 0.950839 0.475420 0.879759i \(-0.342296\pi\)
0.475420 + 0.879759i \(0.342296\pi\)
\(884\) 1.14347e7i 0.492145i
\(885\) −1.43866e7 + 1.73771e7i −0.617449 + 0.745793i
\(886\) −1.21766e7 −0.521125
\(887\) 1.86327e7 0.795181 0.397590 0.917563i \(-0.369847\pi\)
0.397590 + 0.917563i \(0.369847\pi\)
\(888\) −1.70036e7 1.40774e7i −0.723617 0.599089i
\(889\) −2.71184e7 2.66762e7i −1.15082 1.13206i
\(890\) 1.66596e7i 0.705003i
\(891\) −1.33239e7 3.38017e7i −0.562260 1.42641i
\(892\) 8.05757e6i 0.339072i
\(893\) 3.82298e7i 1.60426i
\(894\) 9.49391e6 1.14673e7i 0.397284 0.479864i
\(895\) 1.05534e7i 0.440388i
\(896\) 1.46932e7 1.49367e7i 0.611429 0.621564i
\(897\) 2.54651e6 3.07583e6i 0.105673 0.127638i
\(898\) 9.90260e6 0.409787
\(899\) 82799.6 0.00341687
\(900\) −725549. 3.81916e6i −0.0298580 0.157167i
\(901\) 1.12927e7i 0.463434i
\(902\) 1.29052e7 0.528141
\(903\) 1.55333e7 1.59132e6i 0.633935 0.0649437i
\(904\) 1.05982e7 0.431333
\(905\) 2.01652e7i 0.818429i
\(906\) 1.72367e7 + 1.42704e7i 0.697643 + 0.577585i
\(907\) 5.81361e6 0.234654 0.117327 0.993093i \(-0.462567\pi\)
0.117327 + 0.993093i \(0.462567\pi\)
\(908\) −2.13078e7 −0.857679
\(909\) 3.66878e6 + 1.93118e7i 0.147269 + 0.775198i
\(910\) −5.52250e6 5.43245e6i −0.221071 0.217467i
\(911\) 2.69096e7i 1.07426i 0.843498 + 0.537132i \(0.180492\pi\)
−0.843498 + 0.537132i \(0.819508\pi\)
\(912\) 6.35340e6 + 5.26004e6i 0.252941 + 0.209412i
\(913\) 9.58454e6i 0.380535i
\(914\) 2.38688e6i 0.0945073i
\(915\) 9.90297e6 + 8.19876e6i 0.391032 + 0.323739i
\(916\) 3.13358e6i 0.123396i
\(917\) 1.47248e7 + 1.44847e7i 0.578262 + 0.568833i
\(918\) −8.41825e6 + 1.52716e7i −0.329697 + 0.598107i
\(919\) 1.86255e7 0.727476 0.363738 0.931501i \(-0.381500\pi\)
0.363738 + 0.931501i \(0.381500\pi\)
\(920\) −8.07958e6 −0.314716
\(921\) 4.73881e6 + 3.92331e6i 0.184086 + 0.152406i
\(922\) 1.29615e7i 0.502144i
\(923\) −2.37987e6 −0.0919494
\(924\) −2.91898e6 2.84930e7i −0.112474 1.09789i
\(925\) −5.96835e6 −0.229351
\(926\) 1.61241e7i 0.617943i
\(927\) 5.12845e7 9.74283e6i 1.96014 0.372380i
\(928\) 3.08304e6 0.117519
\(929\) 2.43516e7 0.925740 0.462870 0.886426i \(-0.346820\pi\)
0.462870 + 0.886426i \(0.346820\pi\)
\(930\) 296579. 358227.i 0.0112443 0.0135816i
\(931\) 3.64936e7 600000.i 1.37989 0.0226870i
\(932\) 2.62044e7i 0.988177i
\(933\) −2.28402e7 + 2.75878e7i −0.859004 + 1.03756i
\(934\) 2.02886e6i 0.0761000i
\(935\) 5.84636e7i 2.18704i
\(936\) 2.41322e6 + 1.27028e7i 0.0900343 + 0.473924i
\(937\) 6.06143e6i 0.225541i 0.993621 + 0.112771i \(0.0359725\pi\)
−0.993621 + 0.112771i \(0.964027\pi\)
\(938\) 3.93941e6 4.00471e6i 0.146192 0.148616i
\(939\) −7.62298e6 6.31114e6i −0.282137 0.233584i
\(940\) −2.50606e7 −0.925063
\(941\) −1.76788e6 −0.0650847 −0.0325424 0.999470i \(-0.510360\pi\)
−0.0325424 + 0.999470i \(0.510360\pi\)
\(942\) 9.63845e6 1.16419e7i 0.353900 0.427462i
\(943\) 5.55690e6i 0.203495i
\(944\) 5.70555e6 0.208386
\(945\) 8.67366e6 + 2.90842e7i 0.315953 + 1.05944i
\(946\) −1.42354e7 −0.517180
\(947\) 4.74165e7i 1.71812i −0.511872 0.859061i \(-0.671048\pi\)
0.511872 0.859061i \(-0.328952\pi\)
\(948\) −6.23512e6 + 7.53116e6i −0.225332 + 0.272170i
\(949\) −3.04253e6 −0.109665
\(950\) −4.51623e6 −0.162355
\(951\) −2.31589e6 1.91735e6i −0.0830362 0.0687464i
\(952\) −2.30332e7 + 2.34150e7i −0.823685 + 0.837339i
\(953\) 3.22073e7i 1.14874i −0.818596 0.574370i \(-0.805247\pi\)
0.818596 0.574370i \(-0.194753\pi\)
\(954\) 997498. + 5.25066e6i 0.0354847 + 0.186785i
\(955\) 1.83550e7i 0.651247i
\(956\) 2.40536e7i 0.851209i
\(957\) 3.14152e6 3.79452e6i 0.110882 0.133930i
\(958\) 2.35831e7i 0.830207i
\(959\) −3.52701e7 + 3.58547e7i −1.23840 + 1.25893i
\(960\) 6.25287e6 7.55260e6i 0.218978 0.264496i
\(961\) 2.86032e7 0.999092
\(962\) 8.30852e6 0.289458
\(963\) 2.86493e7 5.44267e6i 0.995515 0.189124i
\(964\) 1.15974e7i 0.401948i
\(965\) 2.55918e7 0.884674
\(966\) 4.77566e6 489245.i 0.164661 0.0168688i
\(967\) 2.97124e7 1.02181 0.510906 0.859637i \(-0.329310\pi\)
0.510906 + 0.859637i \(0.329310\pi\)
\(968\) 3.58491e7i 1.22967i
\(969\) −4.00890e7 3.31901e7i −1.37156 1.13553i
\(970\) −1.57021e7 −0.535830
\(971\) 1.54497e7 0.525861 0.262931 0.964815i \(-0.415311\pi\)
0.262931 + 0.964815i \(0.415311\pi\)
\(972\) 6.59005e6 2.01523e7i 0.223729 0.684161i
\(973\) −2.94850e7 + 2.99737e7i −0.998432 + 1.01498i
\(974\) 1.91139e7i 0.645581i
\(975\) 2.69277e6 + 2.22937e6i 0.0907168 + 0.0751053i
\(976\) 3.25152e6i 0.109260i
\(977\) 2.78966e7i 0.935008i −0.883991 0.467504i \(-0.845153\pi\)
0.883991 0.467504i \(-0.154847\pi\)
\(978\) −770270. 637714.i −0.0257511 0.0213196i
\(979\) 5.53923e7i 1.84711i
\(980\) 393314. + 2.39225e7i 0.0130820 + 0.795684i
\(981\) −1.32449e6 6.97191e6i −0.0439418 0.231302i
\(982\) 2.50845e6 0.0830093
\(983\) 3.66294e6 0.120905 0.0604527 0.998171i \(-0.480746\pi\)
0.0604527 + 0.998171i \(0.480746\pi\)
\(984\) 1.38598e7 + 1.14746e7i 0.456319 + 0.377791i
\(985\) 1.34072e7i 0.440300i
\(986\) −2.36436e6 −0.0774499
\(987\) 3.53914e7 3.62568e6i 1.15639 0.118467i
\(988\) −1.61516e7 −0.526410
\(989\) 6.12966e6i 0.199272i
\(990\) −5.16414e6 2.71831e7i −0.167460 0.881478i
\(991\) 5.89627e6 0.190719 0.0953594 0.995443i \(-0.469600\pi\)
0.0953594 + 0.995443i \(0.469600\pi\)
\(992\) −967752. −0.0312237
\(993\) 2.83789e7 3.42778e7i 0.913320 1.10316i
\(994\) −2.03968e6 2.00642e6i −0.0654781 0.0644104i
\(995\) 2.26916e6i 0.0726619i
\(996\) −3.56684e6 + 4.30824e6i −0.113929 + 0.137611i
\(997\) 1.33192e7i 0.424366i 0.977230 + 0.212183i \(0.0680572\pi\)
−0.977230 + 0.212183i \(0.931943\pi\)
\(998\) 1.44003e7i 0.457662i
\(999\) −2.85074e7 1.57142e7i −0.903741 0.498173i
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 21.6.c.a.20.5 12
3.2 odd 2 inner 21.6.c.a.20.8 yes 12
4.3 odd 2 336.6.k.d.209.9 12
7.6 odd 2 inner 21.6.c.a.20.6 yes 12
12.11 even 2 336.6.k.d.209.3 12
21.20 even 2 inner 21.6.c.a.20.7 yes 12
28.27 even 2 336.6.k.d.209.4 12
84.83 odd 2 336.6.k.d.209.10 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
21.6.c.a.20.5 12 1.1 even 1 trivial
21.6.c.a.20.6 yes 12 7.6 odd 2 inner
21.6.c.a.20.7 yes 12 21.20 even 2 inner
21.6.c.a.20.8 yes 12 3.2 odd 2 inner
336.6.k.d.209.3 12 12.11 even 2
336.6.k.d.209.4 12 28.27 even 2
336.6.k.d.209.9 12 4.3 odd 2
336.6.k.d.209.10 12 84.83 odd 2