Properties

Label 378.4.g.b.109.3
Level $378$
Weight $4$
Character 378.109
Analytic conductor $22.303$
Analytic rank $0$
Dimension $6$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [378,4,Mod(109,378)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(378, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("378.109");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 378.g (of order \(3\), 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: \(22.3027219822\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.11184604443.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} + 43x^{4} - 210x^{3} + 1849x^{2} - 4515x + 11025 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 109.3
Root \(2.16527 + 3.75036i\) of defining polynomial
Character \(\chi\) \(=\) 378.109
Dual form 378.4.g.b.163.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(6.70319 + 11.6103i) q^{5} +(5.32531 - 17.7381i) q^{7} -8.00000 q^{8} +(-13.4064 + 23.2205i) q^{10} +(-21.8169 + 37.7881i) q^{11} -8.40639 q^{13} +(36.0486 - 8.51443i) q^{14} +(-8.00000 - 13.8564i) q^{16} +(-36.3086 + 62.8883i) q^{17} +(29.8496 + 51.7011i) q^{19} -53.6255 q^{20} -87.2678 q^{22} +(38.9919 + 67.5359i) q^{23} +(-27.3656 + 47.3986i) q^{25} +(-8.40639 - 14.5603i) q^{26} +(50.7961 + 53.9237i) q^{28} -59.0953 q^{29} +(-41.9845 + 72.7193i) q^{31} +(16.0000 - 27.7128i) q^{32} -145.234 q^{34} +(241.641 - 57.0738i) q^{35} +(1.78183 + 3.08622i) q^{37} +(-59.6993 + 103.402i) q^{38} +(-53.6255 - 92.8822i) q^{40} +50.0978 q^{41} -556.622 q^{43} +(-87.2678 - 151.152i) q^{44} +(-77.9838 + 135.072i) q^{46} +(1.82554 + 3.16193i) q^{47} +(-286.282 - 188.922i) q^{49} -109.462 q^{50} +(16.8128 - 29.1206i) q^{52} +(160.893 - 278.675i) q^{53} -584.973 q^{55} +(-42.6024 + 141.905i) q^{56} +(-59.0953 - 102.356i) q^{58} +(-427.740 + 740.867i) q^{59} +(-3.53933 - 6.13030i) q^{61} -167.938 q^{62} +64.0000 q^{64} +(-56.3496 - 97.6004i) q^{65} +(-243.423 + 421.621i) q^{67} +(-145.234 - 251.553i) q^{68} +(340.496 + 361.461i) q^{70} +564.619 q^{71} +(-91.9378 + 159.241i) q^{73} +(-3.56366 + 6.17243i) q^{74} -238.797 q^{76} +(554.108 + 588.225i) q^{77} +(656.542 + 1137.16i) q^{79} +(107.251 - 185.764i) q^{80} +(50.0978 + 86.7719i) q^{82} +941.530 q^{83} -973.534 q^{85} +(-556.622 - 964.097i) q^{86} +(174.536 - 302.305i) q^{88} +(-399.453 - 691.873i) q^{89} +(-44.7666 + 149.114i) q^{91} -311.935 q^{92} +(-3.65109 + 6.32387i) q^{94} +(-400.176 + 693.124i) q^{95} +524.765 q^{97} +(40.9401 - 684.777i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 6 q^{2} - 12 q^{4} + 5 q^{5} + 8 q^{7} - 48 q^{8} - 10 q^{10} - 29 q^{11} + 20 q^{13} + 20 q^{14} - 48 q^{16} - 38 q^{17} + 57 q^{19} - 40 q^{20} - 116 q^{22} - 14 q^{23} + 134 q^{25} + 20 q^{26}+ \cdots + 720 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/378\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 + 1.73205i 0.353553 + 0.612372i
\(3\) 0 0
\(4\) −2.00000 + 3.46410i −0.250000 + 0.433013i
\(5\) 6.70319 + 11.6103i 0.599552 + 1.03845i 0.992887 + 0.119059i \(0.0379878\pi\)
−0.393335 + 0.919395i \(0.628679\pi\)
\(6\) 0 0
\(7\) 5.32531 17.7381i 0.287539 0.957769i
\(8\) −8.00000 −0.353553
\(9\) 0 0
\(10\) −13.4064 + 23.2205i −0.423947 + 0.734298i
\(11\) −21.8169 + 37.7881i −0.598005 + 1.03578i 0.395110 + 0.918634i \(0.370706\pi\)
−0.993115 + 0.117142i \(0.962627\pi\)
\(12\) 0 0
\(13\) −8.40639 −0.179347 −0.0896735 0.995971i \(-0.528582\pi\)
−0.0896735 + 0.995971i \(0.528582\pi\)
\(14\) 36.0486 8.51443i 0.688172 0.162541i
\(15\) 0 0
\(16\) −8.00000 13.8564i −0.125000 0.216506i
\(17\) −36.3086 + 62.8883i −0.518007 + 0.897215i 0.481774 + 0.876296i \(0.339993\pi\)
−0.999781 + 0.0209196i \(0.993341\pi\)
\(18\) 0 0
\(19\) 29.8496 + 51.7011i 0.360420 + 0.624265i 0.988030 0.154263i \(-0.0493002\pi\)
−0.627610 + 0.778528i \(0.715967\pi\)
\(20\) −53.6255 −0.599552
\(21\) 0 0
\(22\) −87.2678 −0.845707
\(23\) 38.9919 + 67.5359i 0.353494 + 0.612270i 0.986859 0.161583i \(-0.0516600\pi\)
−0.633365 + 0.773853i \(0.718327\pi\)
\(24\) 0 0
\(25\) −27.3656 + 47.3986i −0.218925 + 0.379189i
\(26\) −8.40639 14.5603i −0.0634088 0.109827i
\(27\) 0 0
\(28\) 50.7961 + 53.9237i 0.342841 + 0.363950i
\(29\) −59.0953 −0.378404 −0.189202 0.981938i \(-0.560590\pi\)
−0.189202 + 0.981938i \(0.560590\pi\)
\(30\) 0 0
\(31\) −41.9845 + 72.7193i −0.243246 + 0.421315i −0.961637 0.274325i \(-0.911546\pi\)
0.718391 + 0.695640i \(0.244879\pi\)
\(32\) 16.0000 27.7128i 0.0883883 0.153093i
\(33\) 0 0
\(34\) −145.234 −0.732573
\(35\) 241.641 57.0738i 1.16699 0.275635i
\(36\) 0 0
\(37\) 1.78183 + 3.08622i 0.00791705 + 0.0137127i 0.869957 0.493128i \(-0.164147\pi\)
−0.862040 + 0.506841i \(0.830813\pi\)
\(38\) −59.6993 + 103.402i −0.254855 + 0.441422i
\(39\) 0 0
\(40\) −53.6255 92.8822i −0.211974 0.367149i
\(41\) 50.0978 0.190828 0.0954141 0.995438i \(-0.469582\pi\)
0.0954141 + 0.995438i \(0.469582\pi\)
\(42\) 0 0
\(43\) −556.622 −1.97405 −0.987023 0.160578i \(-0.948664\pi\)
−0.987023 + 0.160578i \(0.948664\pi\)
\(44\) −87.2678 151.152i −0.299003 0.517888i
\(45\) 0 0
\(46\) −77.9838 + 135.072i −0.249958 + 0.432940i
\(47\) 1.82554 + 3.16193i 0.00566559 + 0.00981310i 0.868844 0.495085i \(-0.164863\pi\)
−0.863179 + 0.504899i \(0.831530\pi\)
\(48\) 0 0
\(49\) −286.282 188.922i −0.834642 0.550793i
\(50\) −109.462 −0.309606
\(51\) 0 0
\(52\) 16.8128 29.1206i 0.0448368 0.0776596i
\(53\) 160.893 278.675i 0.416988 0.722244i −0.578647 0.815578i \(-0.696419\pi\)
0.995635 + 0.0933338i \(0.0297524\pi\)
\(54\) 0 0
\(55\) −584.973 −1.43414
\(56\) −42.6024 + 141.905i −0.101661 + 0.338622i
\(57\) 0 0
\(58\) −59.0953 102.356i −0.133786 0.231724i
\(59\) −427.740 + 740.867i −0.943847 + 1.63479i −0.185805 + 0.982587i \(0.559489\pi\)
−0.758042 + 0.652205i \(0.773844\pi\)
\(60\) 0 0
\(61\) −3.53933 6.13030i −0.00742894 0.0128673i 0.862287 0.506420i \(-0.169031\pi\)
−0.869716 + 0.493553i \(0.835698\pi\)
\(62\) −167.938 −0.344002
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) −56.3496 97.6004i −0.107528 0.186244i
\(66\) 0 0
\(67\) −243.423 + 421.621i −0.443863 + 0.768793i −0.997972 0.0636506i \(-0.979726\pi\)
0.554109 + 0.832444i \(0.313059\pi\)
\(68\) −145.234 251.553i −0.259004 0.448608i
\(69\) 0 0
\(70\) 340.496 + 361.461i 0.581386 + 0.617183i
\(71\) 564.619 0.943774 0.471887 0.881659i \(-0.343573\pi\)
0.471887 + 0.881659i \(0.343573\pi\)
\(72\) 0 0
\(73\) −91.9378 + 159.241i −0.147404 + 0.255312i −0.930267 0.366882i \(-0.880425\pi\)
0.782863 + 0.622194i \(0.213758\pi\)
\(74\) −3.56366 + 6.17243i −0.00559820 + 0.00969636i
\(75\) 0 0
\(76\) −238.797 −0.360420
\(77\) 554.108 + 588.225i 0.820083 + 0.870577i
\(78\) 0 0
\(79\) 656.542 + 1137.16i 0.935022 + 1.61950i 0.774595 + 0.632457i \(0.217954\pi\)
0.160426 + 0.987048i \(0.448713\pi\)
\(80\) 107.251 185.764i 0.149888 0.259614i
\(81\) 0 0
\(82\) 50.0978 + 86.7719i 0.0674680 + 0.116858i
\(83\) 941.530 1.24514 0.622568 0.782565i \(-0.286089\pi\)
0.622568 + 0.782565i \(0.286089\pi\)
\(84\) 0 0
\(85\) −973.534 −1.24229
\(86\) −556.622 964.097i −0.697931 1.20885i
\(87\) 0 0
\(88\) 174.536 302.305i 0.211427 0.366202i
\(89\) −399.453 691.873i −0.475752 0.824027i 0.523862 0.851803i \(-0.324491\pi\)
−0.999614 + 0.0277760i \(0.991157\pi\)
\(90\) 0 0
\(91\) −44.7666 + 149.114i −0.0515694 + 0.171773i
\(92\) −311.935 −0.353494
\(93\) 0 0
\(94\) −3.65109 + 6.32387i −0.00400618 + 0.00693891i
\(95\) −400.176 + 693.124i −0.432181 + 0.748559i
\(96\) 0 0
\(97\) 524.765 0.549297 0.274648 0.961545i \(-0.411439\pi\)
0.274648 + 0.961545i \(0.411439\pi\)
\(98\) 40.9401 684.777i 0.0421997 0.705846i
\(99\) 0 0
\(100\) −109.462 189.594i −0.109462 0.189594i
\(101\) 337.266 584.162i 0.332270 0.575508i −0.650687 0.759346i \(-0.725519\pi\)
0.982957 + 0.183838i \(0.0588522\pi\)
\(102\) 0 0
\(103\) −624.773 1082.14i −0.597676 1.03521i −0.993163 0.116734i \(-0.962757\pi\)
0.395487 0.918472i \(-0.370576\pi\)
\(104\) 67.2511 0.0634088
\(105\) 0 0
\(106\) 643.572 0.589710
\(107\) −886.082 1534.74i −0.800568 1.38662i −0.919243 0.393691i \(-0.871198\pi\)
0.118675 0.992933i \(-0.462135\pi\)
\(108\) 0 0
\(109\) 682.211 1181.62i 0.599486 1.03834i −0.393411 0.919363i \(-0.628705\pi\)
0.992897 0.118978i \(-0.0379617\pi\)
\(110\) −584.973 1013.20i −0.507045 0.878228i
\(111\) 0 0
\(112\) −288.389 + 68.1154i −0.243305 + 0.0574670i
\(113\) 780.182 0.649499 0.324749 0.945800i \(-0.394720\pi\)
0.324749 + 0.945800i \(0.394720\pi\)
\(114\) 0 0
\(115\) −522.740 + 905.413i −0.423876 + 0.734175i
\(116\) 118.191 204.712i 0.0946011 0.163854i
\(117\) 0 0
\(118\) −1710.96 −1.33480
\(119\) 922.167 + 978.946i 0.710377 + 0.754116i
\(120\) 0 0
\(121\) −286.459 496.161i −0.215221 0.372773i
\(122\) 7.07867 12.2606i 0.00525305 0.00909855i
\(123\) 0 0
\(124\) −167.938 290.877i −0.121623 0.210658i
\(125\) 942.051 0.674077
\(126\) 0 0
\(127\) 851.395 0.594875 0.297437 0.954741i \(-0.403868\pi\)
0.297437 + 0.954741i \(0.403868\pi\)
\(128\) 64.0000 + 110.851i 0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) 112.699 195.201i 0.0760337 0.131694i
\(131\) 751.502 + 1301.64i 0.501214 + 0.868129i 0.999999 + 0.00140275i \(0.000446511\pi\)
−0.498785 + 0.866726i \(0.666220\pi\)
\(132\) 0 0
\(133\) 1076.04 254.152i 0.701537 0.165698i
\(134\) −973.691 −0.627717
\(135\) 0 0
\(136\) 290.469 503.107i 0.183143 0.317214i
\(137\) −868.400 + 1504.11i −0.541551 + 0.937993i 0.457264 + 0.889331i \(0.348829\pi\)
−0.998815 + 0.0486627i \(0.984504\pi\)
\(138\) 0 0
\(139\) 3116.41 1.90166 0.950828 0.309720i \(-0.100235\pi\)
0.950828 + 0.309720i \(0.100235\pi\)
\(140\) −285.572 + 951.217i −0.172395 + 0.574232i
\(141\) 0 0
\(142\) 564.619 + 977.949i 0.333675 + 0.577941i
\(143\) 183.402 317.661i 0.107250 0.185763i
\(144\) 0 0
\(145\) −396.127 686.113i −0.226873 0.392956i
\(146\) −367.751 −0.208461
\(147\) 0 0
\(148\) −14.2546 −0.00791705
\(149\) 1475.41 + 2555.49i 0.811211 + 1.40506i 0.912017 + 0.410153i \(0.134525\pi\)
−0.100805 + 0.994906i \(0.532142\pi\)
\(150\) 0 0
\(151\) 644.154 1115.71i 0.347156 0.601292i −0.638587 0.769549i \(-0.720481\pi\)
0.985743 + 0.168258i \(0.0538142\pi\)
\(152\) −238.797 413.609i −0.127428 0.220711i
\(153\) 0 0
\(154\) −464.728 + 1547.97i −0.243174 + 0.809992i
\(155\) −1125.72 −0.583355
\(156\) 0 0
\(157\) 1666.45 2886.38i 0.847116 1.46725i −0.0366552 0.999328i \(-0.511670\pi\)
0.883771 0.467920i \(-0.154996\pi\)
\(158\) −1313.08 + 2274.33i −0.661160 + 1.14516i
\(159\) 0 0
\(160\) 429.004 0.211974
\(161\) 1405.60 331.993i 0.688057 0.162514i
\(162\) 0 0
\(163\) 1825.57 + 3161.97i 0.877235 + 1.51942i 0.854363 + 0.519677i \(0.173948\pi\)
0.0228725 + 0.999738i \(0.492719\pi\)
\(164\) −100.196 + 173.544i −0.0477070 + 0.0826310i
\(165\) 0 0
\(166\) 941.530 + 1630.78i 0.440222 + 0.762487i
\(167\) −3389.98 −1.57081 −0.785403 0.618985i \(-0.787544\pi\)
−0.785403 + 0.618985i \(0.787544\pi\)
\(168\) 0 0
\(169\) −2126.33 −0.967835
\(170\) −973.534 1686.21i −0.439216 0.760744i
\(171\) 0 0
\(172\) 1113.24 1928.19i 0.493512 0.854787i
\(173\) 314.750 + 545.164i 0.138324 + 0.239584i 0.926862 0.375402i \(-0.122495\pi\)
−0.788538 + 0.614986i \(0.789162\pi\)
\(174\) 0 0
\(175\) 695.032 + 737.826i 0.300226 + 0.318711i
\(176\) 698.142 0.299003
\(177\) 0 0
\(178\) 798.907 1383.75i 0.336408 0.582675i
\(179\) −121.747 + 210.872i −0.0508369 + 0.0880520i −0.890324 0.455327i \(-0.849522\pi\)
0.839487 + 0.543380i \(0.182856\pi\)
\(180\) 0 0
\(181\) 4216.08 1.73137 0.865687 0.500585i \(-0.166882\pi\)
0.865687 + 0.500585i \(0.166882\pi\)
\(182\) −303.039 + 71.5755i −0.123422 + 0.0291513i
\(183\) 0 0
\(184\) −311.935 540.287i −0.124979 0.216470i
\(185\) −23.8879 + 41.3750i −0.00949336 + 0.0164430i
\(186\) 0 0
\(187\) −1584.29 2744.06i −0.619542 1.07308i
\(188\) −14.6044 −0.00566559
\(189\) 0 0
\(190\) −1600.70 −0.611196
\(191\) 1900.44 + 3291.66i 0.719953 + 1.24700i 0.961018 + 0.276486i \(0.0891700\pi\)
−0.241065 + 0.970509i \(0.577497\pi\)
\(192\) 0 0
\(193\) −1923.01 + 3330.75i −0.717209 + 1.24224i 0.244893 + 0.969550i \(0.421247\pi\)
−0.962101 + 0.272692i \(0.912086\pi\)
\(194\) 524.765 + 908.919i 0.194206 + 0.336374i
\(195\) 0 0
\(196\) 1227.01 613.867i 0.447161 0.223712i
\(197\) 4739.52 1.71410 0.857048 0.515237i \(-0.172296\pi\)
0.857048 + 0.515237i \(0.172296\pi\)
\(198\) 0 0
\(199\) 2073.53 3591.46i 0.738637 1.27936i −0.214472 0.976730i \(-0.568803\pi\)
0.953109 0.302627i \(-0.0978637\pi\)
\(200\) 218.925 379.189i 0.0774016 0.134063i
\(201\) 0 0
\(202\) 1349.07 0.469900
\(203\) −314.701 + 1048.24i −0.108806 + 0.362424i
\(204\) 0 0
\(205\) 335.815 + 581.649i 0.114411 + 0.198166i
\(206\) 1249.55 2164.28i 0.422621 0.732001i
\(207\) 0 0
\(208\) 67.2511 + 116.482i 0.0224184 + 0.0388298i
\(209\) −2604.91 −0.862131
\(210\) 0 0
\(211\) 226.994 0.0740612 0.0370306 0.999314i \(-0.488210\pi\)
0.0370306 + 0.999314i \(0.488210\pi\)
\(212\) 643.572 + 1114.70i 0.208494 + 0.361122i
\(213\) 0 0
\(214\) 1772.16 3069.48i 0.566087 0.980491i
\(215\) −3731.14 6462.53i −1.18354 2.04996i
\(216\) 0 0
\(217\) 1066.32 + 1131.98i 0.333580 + 0.354119i
\(218\) 2728.84 0.847801
\(219\) 0 0
\(220\) 1169.95 2026.41i 0.358535 0.621001i
\(221\) 305.224 528.664i 0.0929031 0.160913i
\(222\) 0 0
\(223\) −4919.61 −1.47732 −0.738658 0.674080i \(-0.764540\pi\)
−0.738658 + 0.674080i \(0.764540\pi\)
\(224\) −406.368 431.389i −0.121213 0.128676i
\(225\) 0 0
\(226\) 780.182 + 1351.32i 0.229633 + 0.397735i
\(227\) 751.565 1301.75i 0.219749 0.380617i −0.734982 0.678087i \(-0.762809\pi\)
0.954731 + 0.297470i \(0.0961427\pi\)
\(228\) 0 0
\(229\) 1870.02 + 3238.98i 0.539628 + 0.934662i 0.998924 + 0.0463793i \(0.0147683\pi\)
−0.459296 + 0.888283i \(0.651898\pi\)
\(230\) −2090.96 −0.599452
\(231\) 0 0
\(232\) 472.762 0.133786
\(233\) 617.169 + 1068.97i 0.173528 + 0.300560i 0.939651 0.342135i \(-0.111150\pi\)
−0.766123 + 0.642694i \(0.777817\pi\)
\(234\) 0 0
\(235\) −24.4739 + 42.3901i −0.00679364 + 0.0117669i
\(236\) −1710.96 2963.47i −0.471924 0.817396i
\(237\) 0 0
\(238\) −773.417 + 2576.19i −0.210644 + 0.701636i
\(239\) −407.673 −0.110335 −0.0551677 0.998477i \(-0.517569\pi\)
−0.0551677 + 0.998477i \(0.517569\pi\)
\(240\) 0 0
\(241\) −62.5169 + 108.282i −0.0167098 + 0.0289422i −0.874259 0.485459i \(-0.838652\pi\)
0.857550 + 0.514401i \(0.171986\pi\)
\(242\) 572.917 992.322i 0.152184 0.263590i
\(243\) 0 0
\(244\) 28.3147 0.00742894
\(245\) 274.429 4590.19i 0.0715618 1.19697i
\(246\) 0 0
\(247\) −250.927 434.619i −0.0646402 0.111960i
\(248\) 335.876 581.754i 0.0860006 0.148957i
\(249\) 0 0
\(250\) 942.051 + 1631.68i 0.238322 + 0.412786i
\(251\) −4144.15 −1.04214 −0.521068 0.853515i \(-0.674466\pi\)
−0.521068 + 0.853515i \(0.674466\pi\)
\(252\) 0 0
\(253\) −3402.74 −0.845566
\(254\) 851.395 + 1474.66i 0.210320 + 0.364285i
\(255\) 0 0
\(256\) −128.000 + 221.703i −0.0312500 + 0.0541266i
\(257\) −274.649 475.706i −0.0666619 0.115462i 0.830768 0.556619i \(-0.187902\pi\)
−0.897430 + 0.441157i \(0.854568\pi\)
\(258\) 0 0
\(259\) 64.2325 15.1712i 0.0154101 0.00363975i
\(260\) 450.797 0.107528
\(261\) 0 0
\(262\) −1503.00 + 2603.28i −0.354412 + 0.613860i
\(263\) −3079.75 + 5334.28i −0.722074 + 1.25067i 0.238093 + 0.971242i \(0.423478\pi\)
−0.960167 + 0.279427i \(0.909856\pi\)
\(264\) 0 0
\(265\) 4313.99 1.00002
\(266\) 1516.24 + 1609.60i 0.349499 + 0.371019i
\(267\) 0 0
\(268\) −973.691 1686.48i −0.221932 0.384397i
\(269\) 3198.75 5540.40i 0.725024 1.25578i −0.233940 0.972251i \(-0.575162\pi\)
0.958964 0.283528i \(-0.0915047\pi\)
\(270\) 0 0
\(271\) −3215.20 5568.89i −0.720700 1.24829i −0.960720 0.277521i \(-0.910487\pi\)
0.240020 0.970768i \(-0.422846\pi\)
\(272\) 1161.88 0.259004
\(273\) 0 0
\(274\) −3473.60 −0.765868
\(275\) −1194.07 2068.19i −0.261836 0.453514i
\(276\) 0 0
\(277\) −2033.41 + 3521.97i −0.441068 + 0.763953i −0.997769 0.0667605i \(-0.978734\pi\)
0.556701 + 0.830713i \(0.312067\pi\)
\(278\) 3116.41 + 5397.77i 0.672337 + 1.16452i
\(279\) 0 0
\(280\) −1933.13 + 456.591i −0.412595 + 0.0974518i
\(281\) 2270.90 0.482101 0.241050 0.970513i \(-0.422508\pi\)
0.241050 + 0.970513i \(0.422508\pi\)
\(282\) 0 0
\(283\) 3554.58 6156.71i 0.746635 1.29321i −0.202792 0.979222i \(-0.565001\pi\)
0.949427 0.313988i \(-0.101665\pi\)
\(284\) −1129.24 + 1955.90i −0.235944 + 0.408666i
\(285\) 0 0
\(286\) 733.607 0.151675
\(287\) 266.786 888.640i 0.0548706 0.182769i
\(288\) 0 0
\(289\) −180.128 311.991i −0.0366635 0.0635031i
\(290\) 792.255 1372.23i 0.160423 0.277862i
\(291\) 0 0
\(292\) −367.751 636.964i −0.0737021 0.127656i
\(293\) 1088.93 0.217119 0.108560 0.994090i \(-0.465376\pi\)
0.108560 + 0.994090i \(0.465376\pi\)
\(294\) 0 0
\(295\) −11468.9 −2.26354
\(296\) −14.2546 24.6897i −0.00279910 0.00484818i
\(297\) 0 0
\(298\) −2950.82 + 5110.98i −0.573613 + 0.993527i
\(299\) −327.781 567.733i −0.0633982 0.109809i
\(300\) 0 0
\(301\) −2964.18 + 9873.42i −0.567616 + 1.89068i
\(302\) 2576.62 0.490952
\(303\) 0 0
\(304\) 477.594 827.217i 0.0901049 0.156066i
\(305\) 47.4497 82.1852i 0.00890806 0.0154292i
\(306\) 0 0
\(307\) 1736.56 0.322836 0.161418 0.986886i \(-0.448393\pi\)
0.161418 + 0.986886i \(0.448393\pi\)
\(308\) −3145.89 + 743.035i −0.581992 + 0.137462i
\(309\) 0 0
\(310\) −1125.72 1949.81i −0.206247 0.357231i
\(311\) −1164.74 + 2017.38i −0.212367 + 0.367830i −0.952455 0.304680i \(-0.901451\pi\)
0.740088 + 0.672510i \(0.234784\pi\)
\(312\) 0 0
\(313\) −1744.00 3020.69i −0.314941 0.545494i 0.664484 0.747303i \(-0.268652\pi\)
−0.979425 + 0.201808i \(0.935318\pi\)
\(314\) 6665.80 1.19800
\(315\) 0 0
\(316\) −5252.33 −0.935022
\(317\) −1348.77 2336.14i −0.238974 0.413914i 0.721446 0.692470i \(-0.243478\pi\)
−0.960420 + 0.278556i \(0.910144\pi\)
\(318\) 0 0
\(319\) 1289.28 2233.10i 0.226288 0.391942i
\(320\) 429.004 + 743.057i 0.0749440 + 0.129807i
\(321\) 0 0
\(322\) 1980.63 + 2102.58i 0.342784 + 0.363890i
\(323\) −4335.19 −0.746800
\(324\) 0 0
\(325\) 230.046 398.451i 0.0392635 0.0680064i
\(326\) −3651.13 + 6323.94i −0.620299 + 1.07439i
\(327\) 0 0
\(328\) −400.782 −0.0674680
\(329\) 65.8084 15.5435i 0.0110278 0.00260468i
\(330\) 0 0
\(331\) 4985.88 + 8635.80i 0.827942 + 1.43404i 0.899650 + 0.436612i \(0.143822\pi\)
−0.0717073 + 0.997426i \(0.522845\pi\)
\(332\) −1883.06 + 3261.56i −0.311284 + 0.539160i
\(333\) 0 0
\(334\) −3389.98 5871.62i −0.555364 0.961918i
\(335\) −6526.84 −1.06448
\(336\) 0 0
\(337\) −8607.45 −1.39133 −0.695664 0.718367i \(-0.744890\pi\)
−0.695664 + 0.718367i \(0.744890\pi\)
\(338\) −2126.33 3682.92i −0.342181 0.592675i
\(339\) 0 0
\(340\) 1947.07 3372.42i 0.310572 0.537927i
\(341\) −1831.95 3173.03i −0.290925 0.503897i
\(342\) 0 0
\(343\) −4875.66 + 4072.04i −0.767525 + 0.641019i
\(344\) 4452.97 0.697931
\(345\) 0 0
\(346\) −629.501 + 1090.33i −0.0978097 + 0.169411i
\(347\) 2770.44 4798.54i 0.428602 0.742361i −0.568147 0.822927i \(-0.692340\pi\)
0.996749 + 0.0805663i \(0.0256729\pi\)
\(348\) 0 0
\(349\) −1450.89 −0.222535 −0.111267 0.993791i \(-0.535491\pi\)
−0.111267 + 0.993791i \(0.535491\pi\)
\(350\) −582.921 + 1941.66i −0.0890240 + 0.296531i
\(351\) 0 0
\(352\) 698.142 + 1209.22i 0.105713 + 0.183101i
\(353\) 2464.39 4268.45i 0.371576 0.643588i −0.618232 0.785995i \(-0.712151\pi\)
0.989808 + 0.142407i \(0.0454843\pi\)
\(354\) 0 0
\(355\) 3784.75 + 6555.38i 0.565841 + 0.980066i
\(356\) 3195.63 0.475752
\(357\) 0 0
\(358\) −486.988 −0.0718942
\(359\) −624.930 1082.41i −0.0918733 0.159129i 0.816426 0.577450i \(-0.195952\pi\)
−0.908299 + 0.418321i \(0.862619\pi\)
\(360\) 0 0
\(361\) 1647.50 2853.55i 0.240195 0.416030i
\(362\) 4216.08 + 7302.47i 0.612133 + 1.06025i
\(363\) 0 0
\(364\) −427.011 453.303i −0.0614876 0.0652734i
\(365\) −2465.11 −0.353506
\(366\) 0 0
\(367\) 1807.17 3130.11i 0.257040 0.445206i −0.708408 0.705803i \(-0.750586\pi\)
0.965448 + 0.260597i \(0.0839195\pi\)
\(368\) 623.870 1080.57i 0.0883736 0.153068i
\(369\) 0 0
\(370\) −95.5515 −0.0134256
\(371\) −4086.37 4337.97i −0.571843 0.607052i
\(372\) 0 0
\(373\) −2785.71 4824.98i −0.386698 0.669781i 0.605305 0.795994i \(-0.293051\pi\)
−0.992003 + 0.126213i \(0.959718\pi\)
\(374\) 3168.57 5488.13i 0.438083 0.758781i
\(375\) 0 0
\(376\) −14.6044 25.2955i −0.00200309 0.00346945i
\(377\) 496.778 0.0678657
\(378\) 0 0
\(379\) 2674.89 0.362533 0.181266 0.983434i \(-0.441980\pi\)
0.181266 + 0.983434i \(0.441980\pi\)
\(380\) −1600.70 2772.50i −0.216090 0.374279i
\(381\) 0 0
\(382\) −3800.88 + 6583.32i −0.509084 + 0.881759i
\(383\) 1675.22 + 2901.57i 0.223498 + 0.387111i 0.955868 0.293797i \(-0.0949189\pi\)
−0.732369 + 0.680907i \(0.761586\pi\)
\(384\) 0 0
\(385\) −3115.16 + 10376.3i −0.412372 + 1.37358i
\(386\) −7692.04 −1.01429
\(387\) 0 0
\(388\) −1049.53 + 1817.84i −0.137324 + 0.237852i
\(389\) 3529.71 6113.63i 0.460060 0.796847i −0.538904 0.842367i \(-0.681161\pi\)
0.998963 + 0.0455204i \(0.0144946\pi\)
\(390\) 0 0
\(391\) −5662.96 −0.732451
\(392\) 2290.26 + 1511.38i 0.295091 + 0.194735i
\(393\) 0 0
\(394\) 4739.52 + 8209.09i 0.606024 + 1.04966i
\(395\) −8801.85 + 15245.3i −1.12119 + 1.94195i
\(396\) 0 0
\(397\) −5510.26 9544.05i −0.696604 1.20655i −0.969637 0.244549i \(-0.921360\pi\)
0.273032 0.962005i \(-0.411973\pi\)
\(398\) 8294.13 1.04459
\(399\) 0 0
\(400\) 875.699 0.109462
\(401\) −1458.98 2527.02i −0.181690 0.314697i 0.760766 0.649026i \(-0.224823\pi\)
−0.942456 + 0.334330i \(0.891490\pi\)
\(402\) 0 0
\(403\) 352.938 611.307i 0.0436255 0.0755617i
\(404\) 1349.07 + 2336.65i 0.166135 + 0.287754i
\(405\) 0 0
\(406\) −2130.31 + 503.163i −0.260407 + 0.0615063i
\(407\) −155.496 −0.0189377
\(408\) 0 0
\(409\) 1400.02 2424.91i 0.169259 0.293165i −0.768901 0.639368i \(-0.779196\pi\)
0.938159 + 0.346204i \(0.112529\pi\)
\(410\) −671.630 + 1163.30i −0.0809011 + 0.140125i
\(411\) 0 0
\(412\) 4998.18 0.597676
\(413\) 10863.8 + 11532.7i 1.29436 + 1.37405i
\(414\) 0 0
\(415\) 6311.26 + 10931.4i 0.746524 + 1.29302i
\(416\) −134.502 + 232.965i −0.0158522 + 0.0274568i
\(417\) 0 0
\(418\) −2604.91 4511.84i −0.304810 0.527946i
\(419\) −7229.43 −0.842913 −0.421456 0.906849i \(-0.638481\pi\)
−0.421456 + 0.906849i \(0.638481\pi\)
\(420\) 0 0
\(421\) −10949.7 −1.26759 −0.633795 0.773501i \(-0.718504\pi\)
−0.633795 + 0.773501i \(0.718504\pi\)
\(422\) 226.994 + 393.165i 0.0261846 + 0.0453530i
\(423\) 0 0
\(424\) −1287.14 + 2229.40i −0.147428 + 0.255352i
\(425\) −1987.21 3441.95i −0.226809 0.392845i
\(426\) 0 0
\(427\) −127.588 + 30.1354i −0.0144600 + 0.00341535i
\(428\) 7088.66 0.800568
\(429\) 0 0
\(430\) 7462.28 12925.1i 0.836891 1.44954i
\(431\) −5046.99 + 8741.64i −0.564048 + 0.976960i 0.433089 + 0.901351i \(0.357423\pi\)
−0.997138 + 0.0756091i \(0.975910\pi\)
\(432\) 0 0
\(433\) 11040.9 1.22539 0.612694 0.790320i \(-0.290086\pi\)
0.612694 + 0.790320i \(0.290086\pi\)
\(434\) −894.321 + 2978.91i −0.0989143 + 0.329475i
\(435\) 0 0
\(436\) 2728.84 + 4726.50i 0.299743 + 0.519170i
\(437\) −2327.79 + 4031.84i −0.254813 + 0.441348i
\(438\) 0 0
\(439\) −566.206 980.697i −0.0615570 0.106620i 0.833605 0.552362i \(-0.186273\pi\)
−0.895162 + 0.445742i \(0.852940\pi\)
\(440\) 4679.78 0.507045
\(441\) 0 0
\(442\) 1220.90 0.131385
\(443\) 4719.63 + 8174.65i 0.506177 + 0.876725i 0.999974 + 0.00714780i \(0.00227523\pi\)
−0.493797 + 0.869577i \(0.664391\pi\)
\(444\) 0 0
\(445\) 5355.22 9275.52i 0.570476 0.988094i
\(446\) −4919.61 8521.01i −0.522310 0.904668i
\(447\) 0 0
\(448\) 340.820 1135.24i 0.0359424 0.119721i
\(449\) −8855.77 −0.930801 −0.465401 0.885100i \(-0.654090\pi\)
−0.465401 + 0.885100i \(0.654090\pi\)
\(450\) 0 0
\(451\) −1092.98 + 1893.10i −0.114116 + 0.197655i
\(452\) −1560.36 + 2702.63i −0.162375 + 0.281241i
\(453\) 0 0
\(454\) 3006.26 0.310772
\(455\) −2031.33 + 479.785i −0.209297 + 0.0494344i
\(456\) 0 0
\(457\) −2650.62 4591.01i −0.271315 0.469931i 0.697884 0.716211i \(-0.254125\pi\)
−0.969199 + 0.246280i \(0.920792\pi\)
\(458\) −3740.05 + 6477.96i −0.381574 + 0.660906i
\(459\) 0 0
\(460\) −2090.96 3621.65i −0.211938 0.367088i
\(461\) 8217.88 0.830249 0.415124 0.909765i \(-0.363738\pi\)
0.415124 + 0.909765i \(0.363738\pi\)
\(462\) 0 0
\(463\) −14957.4 −1.50136 −0.750682 0.660664i \(-0.770275\pi\)
−0.750682 + 0.660664i \(0.770275\pi\)
\(464\) 472.762 + 818.849i 0.0473005 + 0.0819269i
\(465\) 0 0
\(466\) −1234.34 + 2137.94i −0.122703 + 0.212528i
\(467\) −121.131 209.805i −0.0120027 0.0207893i 0.859962 0.510359i \(-0.170487\pi\)
−0.871964 + 0.489569i \(0.837154\pi\)
\(468\) 0 0
\(469\) 6182.46 + 6563.12i 0.608698 + 0.646177i
\(470\) −97.8958 −0.00960765
\(471\) 0 0
\(472\) 3421.92 5926.94i 0.333700 0.577986i
\(473\) 12143.8 21033.7i 1.18049 2.04467i
\(474\) 0 0
\(475\) −3267.41 −0.315619
\(476\) −5235.50 + 1236.59i −0.504136 + 0.119073i
\(477\) 0 0
\(478\) −407.673 706.110i −0.0390095 0.0675664i
\(479\) −4879.07 + 8450.79i −0.465408 + 0.806110i −0.999220 0.0394932i \(-0.987426\pi\)
0.533812 + 0.845603i \(0.320759\pi\)
\(480\) 0 0
\(481\) −14.9787 25.9439i −0.00141990 0.00245934i
\(482\) −250.067 −0.0236312
\(483\) 0 0
\(484\) 2291.67 0.215221
\(485\) 3517.60 + 6092.66i 0.329332 + 0.570419i
\(486\) 0 0
\(487\) 6608.98 11447.1i 0.614952 1.06513i −0.375441 0.926846i \(-0.622509\pi\)
0.990393 0.138282i \(-0.0441580\pi\)
\(488\) 28.3147 + 49.0424i 0.00262653 + 0.00454928i
\(489\) 0 0
\(490\) 8224.88 4114.87i 0.758290 0.379369i
\(491\) −13789.5 −1.26744 −0.633720 0.773562i \(-0.718473\pi\)
−0.633720 + 0.773562i \(0.718473\pi\)
\(492\) 0 0
\(493\) 2145.67 3716.41i 0.196016 0.339510i
\(494\) 501.855 869.238i 0.0457075 0.0791678i
\(495\) 0 0
\(496\) 1343.50 0.121623
\(497\) 3006.77 10015.3i 0.271372 0.903917i
\(498\) 0 0
\(499\) 995.188 + 1723.72i 0.0892800 + 0.154638i 0.907207 0.420684i \(-0.138210\pi\)
−0.817927 + 0.575322i \(0.804877\pi\)
\(500\) −1884.10 + 3263.36i −0.168519 + 0.291884i
\(501\) 0 0
\(502\) −4144.15 7177.87i −0.368451 0.638176i
\(503\) 221.800 0.0196612 0.00983059 0.999952i \(-0.496871\pi\)
0.00983059 + 0.999952i \(0.496871\pi\)
\(504\) 0 0
\(505\) 9043.04 0.796852
\(506\) −3402.74 5893.71i −0.298953 0.517801i
\(507\) 0 0
\(508\) −1702.79 + 2949.32i −0.148719 + 0.257588i
\(509\) −2603.26 4508.99i −0.226695 0.392647i 0.730132 0.683306i \(-0.239459\pi\)
−0.956827 + 0.290659i \(0.906125\pi\)
\(510\) 0 0
\(511\) 2335.04 + 2478.81i 0.202145 + 0.214591i
\(512\) −512.000 −0.0441942
\(513\) 0 0
\(514\) 549.298 951.411i 0.0471371 0.0816439i
\(515\) 8375.94 14507.6i 0.716676 1.24132i
\(516\) 0 0
\(517\) −159.311 −0.0135522
\(518\) 90.5098 + 96.0827i 0.00767717 + 0.00814986i
\(519\) 0 0
\(520\) 450.797 + 780.803i 0.0380168 + 0.0658471i
\(521\) −6123.38 + 10606.0i −0.514914 + 0.891858i 0.484936 + 0.874550i \(0.338843\pi\)
−0.999850 + 0.0173079i \(0.994490\pi\)
\(522\) 0 0
\(523\) 6370.75 + 11034.5i 0.532646 + 0.922569i 0.999273 + 0.0381155i \(0.0121355\pi\)
−0.466628 + 0.884454i \(0.654531\pi\)
\(524\) −6012.02 −0.501214
\(525\) 0 0
\(526\) −12319.0 −1.02117
\(527\) −3048.80 5280.67i −0.252007 0.436489i
\(528\) 0 0
\(529\) 3042.77 5270.23i 0.250084 0.433157i
\(530\) 4313.99 + 7472.05i 0.353562 + 0.612387i
\(531\) 0 0
\(532\) −1271.67 + 4235.81i −0.103635 + 0.345199i
\(533\) −421.141 −0.0342245
\(534\) 0 0
\(535\) 11879.2 20575.3i 0.959964 1.66271i
\(536\) 1947.38 3372.97i 0.156929 0.271810i
\(537\) 0 0
\(538\) 12795.0 1.02534
\(539\) 13384.8 6696.35i 1.06962 0.535125i
\(540\) 0 0
\(541\) 1757.33 + 3043.78i 0.139655 + 0.241890i 0.927366 0.374155i \(-0.122067\pi\)
−0.787711 + 0.616045i \(0.788734\pi\)
\(542\) 6430.40 11137.8i 0.509612 0.882673i
\(543\) 0 0
\(544\) 1161.88 + 2012.43i 0.0915717 + 0.158607i
\(545\) 18292.0 1.43769
\(546\) 0 0
\(547\) 8362.90 0.653696 0.326848 0.945077i \(-0.394013\pi\)
0.326848 + 0.945077i \(0.394013\pi\)
\(548\) −3473.60 6016.45i −0.270775 0.468997i
\(549\) 0 0
\(550\) 2388.13 4136.37i 0.185146 0.320683i
\(551\) −1763.97 3055.29i −0.136384 0.236225i
\(552\) 0 0
\(553\) 23667.4 5590.08i 1.81997 0.429863i
\(554\) −8133.65 −0.623765
\(555\) 0 0
\(556\) −6232.81 + 10795.5i −0.475414 + 0.823441i
\(557\) 6241.84 10811.2i 0.474821 0.822414i −0.524763 0.851248i \(-0.675846\pi\)
0.999584 + 0.0288343i \(0.00917952\pi\)
\(558\) 0 0
\(559\) 4679.18 0.354039
\(560\) −2723.97 2891.69i −0.205551 0.218207i
\(561\) 0 0
\(562\) 2270.90 + 3933.31i 0.170448 + 0.295225i
\(563\) 5609.22 9715.46i 0.419894 0.727278i −0.576034 0.817426i \(-0.695400\pi\)
0.995928 + 0.0901473i \(0.0287338\pi\)
\(564\) 0 0
\(565\) 5229.71 + 9058.13i 0.389408 + 0.674475i
\(566\) 14218.3 1.05590
\(567\) 0 0
\(568\) −4516.95 −0.333675
\(569\) 10878.7 + 18842.5i 0.801511 + 1.38826i 0.918621 + 0.395139i \(0.129304\pi\)
−0.117110 + 0.993119i \(0.537363\pi\)
\(570\) 0 0
\(571\) −1353.09 + 2343.62i −0.0991683 + 0.171765i −0.911341 0.411653i \(-0.864952\pi\)
0.812172 + 0.583418i \(0.198285\pi\)
\(572\) 733.607 + 1270.64i 0.0536252 + 0.0928817i
\(573\) 0 0
\(574\) 1805.96 426.554i 0.131323 0.0310174i
\(575\) −4268.14 −0.309555
\(576\) 0 0
\(577\) 3842.52 6655.44i 0.277238 0.480190i −0.693460 0.720496i \(-0.743914\pi\)
0.970697 + 0.240306i \(0.0772477\pi\)
\(578\) 360.256 623.982i 0.0259250 0.0449035i
\(579\) 0 0
\(580\) 3169.02 0.226873
\(581\) 5013.94 16701.0i 0.358026 1.19255i
\(582\) 0 0
\(583\) 7020.39 + 12159.7i 0.498722 + 0.863812i
\(584\) 735.502 1273.93i 0.0521153 0.0902663i
\(585\) 0 0
\(586\) 1088.93 + 1886.08i 0.0767632 + 0.132958i
\(587\) −24730.3 −1.73889 −0.869445 0.494030i \(-0.835523\pi\)
−0.869445 + 0.494030i \(0.835523\pi\)
\(588\) 0 0
\(589\) −5012.89 −0.350683
\(590\) −11468.9 19864.7i −0.800283 1.38613i
\(591\) 0 0
\(592\) 28.5092 49.3795i 0.00197926 0.00342818i
\(593\) 8612.12 + 14916.6i 0.596387 + 1.03297i 0.993350 + 0.115138i \(0.0367309\pi\)
−0.396963 + 0.917835i \(0.629936\pi\)
\(594\) 0 0
\(595\) −5184.37 + 17268.7i −0.357207 + 1.18983i
\(596\) −11803.3 −0.811211
\(597\) 0 0
\(598\) 655.562 1135.47i 0.0448293 0.0776466i
\(599\) 4841.41 8385.56i 0.330241 0.571995i −0.652318 0.757946i \(-0.726203\pi\)
0.982559 + 0.185951i \(0.0595366\pi\)
\(600\) 0 0
\(601\) 16084.7 1.09169 0.545847 0.837885i \(-0.316208\pi\)
0.545847 + 0.837885i \(0.316208\pi\)
\(602\) −20065.5 + 4739.31i −1.35848 + 0.320864i
\(603\) 0 0
\(604\) 2576.62 + 4462.83i 0.173578 + 0.300646i
\(605\) 3840.37 6651.72i 0.258072 0.446993i
\(606\) 0 0
\(607\) −3883.60 6726.59i −0.259688 0.449792i 0.706470 0.707743i \(-0.250286\pi\)
−0.966158 + 0.257950i \(0.916953\pi\)
\(608\) 1910.38 0.127428
\(609\) 0 0
\(610\) 189.799 0.0125979
\(611\) −15.3462 26.5804i −0.00101611 0.00175995i
\(612\) 0 0
\(613\) 14001.4 24251.2i 0.922531 1.59787i 0.127047 0.991897i \(-0.459450\pi\)
0.795484 0.605974i \(-0.207217\pi\)
\(614\) 1736.56 + 3007.81i 0.114140 + 0.197696i
\(615\) 0 0
\(616\) −4432.86 4705.80i −0.289943 0.307795i
\(617\) 10440.8 0.681247 0.340624 0.940200i \(-0.389362\pi\)
0.340624 + 0.940200i \(0.389362\pi\)
\(618\) 0 0
\(619\) 14166.3 24536.7i 0.919857 1.59324i 0.120227 0.992746i \(-0.461638\pi\)
0.799630 0.600493i \(-0.205029\pi\)
\(620\) 2251.44 3899.61i 0.145839 0.252600i
\(621\) 0 0
\(622\) −4658.95 −0.300332
\(623\) −14399.7 + 3401.12i −0.926025 + 0.218720i
\(624\) 0 0
\(625\) 9735.45 + 16862.3i 0.623069 + 1.07919i
\(626\) 3488.00 6041.39i 0.222697 0.385723i
\(627\) 0 0
\(628\) 6665.80 + 11545.5i 0.423558 + 0.733624i
\(629\) −258.783 −0.0164044
\(630\) 0 0
\(631\) −6567.27 −0.414325 −0.207162 0.978307i \(-0.566423\pi\)
−0.207162 + 0.978307i \(0.566423\pi\)
\(632\) −5252.33 9097.31i −0.330580 0.572581i
\(633\) 0 0
\(634\) 2697.55 4672.29i 0.168980 0.292682i
\(635\) 5707.07 + 9884.93i 0.356658 + 0.617750i
\(636\) 0 0
\(637\) 2406.60 + 1588.15i 0.149691 + 0.0987831i
\(638\) 5157.12 0.320019
\(639\) 0 0
\(640\) −858.009 + 1486.11i −0.0529934 + 0.0917872i
\(641\) −3966.30 + 6869.84i −0.244399 + 0.423311i −0.961962 0.273182i \(-0.911924\pi\)
0.717564 + 0.696493i \(0.245257\pi\)
\(642\) 0 0
\(643\) −21042.2 −1.29055 −0.645274 0.763951i \(-0.723257\pi\)
−0.645274 + 0.763951i \(0.723257\pi\)
\(644\) −1661.15 + 5533.14i −0.101644 + 0.338566i
\(645\) 0 0
\(646\) −4335.19 7508.77i −0.264034 0.457320i
\(647\) −14683.0 + 25431.7i −0.892193 + 1.54532i −0.0549522 + 0.998489i \(0.517501\pi\)
−0.837241 + 0.546834i \(0.815833\pi\)
\(648\) 0 0
\(649\) −18664.0 32326.9i −1.12885 1.95523i
\(650\) 920.183 0.0555270
\(651\) 0 0
\(652\) −14604.5 −0.877235
\(653\) 12269.9 + 21252.2i 0.735314 + 1.27360i 0.954585 + 0.297937i \(0.0962987\pi\)
−0.219271 + 0.975664i \(0.570368\pi\)
\(654\) 0 0
\(655\) −10074.9 + 17450.3i −0.601008 + 1.04098i
\(656\) −400.782 694.175i −0.0238535 0.0413155i
\(657\) 0 0
\(658\) 92.7304 + 98.4400i 0.00549393 + 0.00583220i
\(659\) −4246.88 −0.251039 −0.125520 0.992091i \(-0.540060\pi\)
−0.125520 + 0.992091i \(0.540060\pi\)
\(660\) 0 0
\(661\) −10274.9 + 17796.7i −0.604611 + 1.04722i 0.387502 + 0.921869i \(0.373338\pi\)
−0.992113 + 0.125348i \(0.959995\pi\)
\(662\) −9971.77 + 17271.6i −0.585444 + 1.01402i
\(663\) 0 0
\(664\) −7532.24 −0.440222
\(665\) 10163.7 + 10789.5i 0.592677 + 0.629169i
\(666\) 0 0
\(667\) −2304.24 3991.06i −0.133764 0.231686i
\(668\) 6779.96 11743.2i 0.392701 0.680179i
\(669\) 0 0
\(670\) −6526.84 11304.8i −0.376349 0.651856i
\(671\) 308.870 0.0177702
\(672\) 0 0
\(673\) −6712.91 −0.384493 −0.192246 0.981347i \(-0.561577\pi\)
−0.192246 + 0.981347i \(0.561577\pi\)
\(674\) −8607.45 14908.5i −0.491909 0.852011i
\(675\) 0 0
\(676\) 4252.67 7365.83i 0.241959 0.419085i
\(677\) 12236.0 + 21193.3i 0.694632 + 1.20314i 0.970305 + 0.241886i \(0.0777661\pi\)
−0.275673 + 0.961252i \(0.588901\pi\)
\(678\) 0 0
\(679\) 2794.53 9308.34i 0.157944 0.526099i
\(680\) 7788.27 0.439216
\(681\) 0 0
\(682\) 3663.90 6346.05i 0.205715 0.356309i
\(683\) −10284.1 + 17812.5i −0.576148 + 0.997918i 0.419768 + 0.907632i \(0.362112\pi\)
−0.995916 + 0.0902863i \(0.971222\pi\)
\(684\) 0 0
\(685\) −23284.2 −1.29875
\(686\) −11928.6 4372.85i −0.663904 0.243376i
\(687\) 0 0
\(688\) 4452.97 + 7712.77i 0.246756 + 0.427394i
\(689\) −1352.53 + 2342.65i −0.0747856 + 0.129532i
\(690\) 0 0
\(691\) 3635.32 + 6296.55i 0.200136 + 0.346646i 0.948572 0.316561i \(-0.102528\pi\)
−0.748436 + 0.663207i \(0.769195\pi\)
\(692\) −2518.00 −0.138324
\(693\) 0 0
\(694\) 11081.8 0.606135
\(695\) 20889.9 + 36182.3i 1.14014 + 1.97478i
\(696\) 0 0
\(697\) −1818.98 + 3150.56i −0.0988504 + 0.171214i
\(698\) −1450.89 2513.02i −0.0786779 0.136274i
\(699\) 0 0
\(700\) −3945.97 + 932.009i −0.213062 + 0.0503238i
\(701\) 3876.20 0.208848 0.104424 0.994533i \(-0.466700\pi\)
0.104424 + 0.994533i \(0.466700\pi\)
\(702\) 0 0
\(703\) −106.374 + 184.245i −0.00570692 + 0.00988467i
\(704\) −1396.28 + 2418.44i −0.0747507 + 0.129472i
\(705\) 0 0
\(706\) 9857.56 0.525487
\(707\) −8565.90 9093.32i −0.455663 0.483719i
\(708\) 0 0
\(709\) −10514.6 18211.8i −0.556960 0.964682i −0.997748 0.0670713i \(-0.978634\pi\)
0.440789 0.897611i \(-0.354699\pi\)
\(710\) −7569.50 + 13110.8i −0.400110 + 0.693011i
\(711\) 0 0
\(712\) 3195.63 + 5534.99i 0.168204 + 0.291338i
\(713\) −6548.22 −0.343945
\(714\) 0 0
\(715\) 4917.51 0.257209
\(716\) −486.988 843.488i −0.0254184 0.0440260i
\(717\) 0 0
\(718\) 1249.86 2164.82i 0.0649642 0.112521i
\(719\) 5169.58 + 8953.98i 0.268140 + 0.464433i 0.968382 0.249474i \(-0.0802576\pi\)
−0.700241 + 0.713906i \(0.746924\pi\)
\(720\) 0 0
\(721\) −22522.2 + 5319.58i −1.16334 + 0.274773i
\(722\) 6590.00 0.339687
\(723\) 0 0
\(724\) −8432.16 + 14604.9i −0.432844 + 0.749707i
\(725\) 1617.18 2801.03i 0.0828421 0.143487i
\(726\) 0 0
\(727\) 9537.43 0.486552 0.243276 0.969957i \(-0.421778\pi\)
0.243276 + 0.969957i \(0.421778\pi\)
\(728\) 358.133 1192.91i 0.0182325 0.0607309i
\(729\) 0 0
\(730\) −2465.11 4269.69i −0.124983 0.216477i
\(731\) 20210.1 35005.0i 1.02257 1.77114i
\(732\) 0 0
\(733\) 6617.25 + 11461.4i 0.333443 + 0.577540i 0.983184 0.182615i \(-0.0584562\pi\)
−0.649742 + 0.760155i \(0.725123\pi\)
\(734\) 7228.69 0.363509
\(735\) 0 0
\(736\) 2495.48 0.124979
\(737\) −10621.5 18397.0i −0.530865 0.919485i
\(738\) 0 0
\(739\) −18675.7 + 32347.2i −0.929628 + 1.61016i −0.145685 + 0.989331i \(0.546539\pi\)
−0.783943 + 0.620833i \(0.786795\pi\)
\(740\) −95.5515 165.500i −0.00474668 0.00822149i
\(741\) 0 0
\(742\) 3427.22 11415.8i 0.169565 0.564806i
\(743\) −23.0684 −0.00113903 −0.000569515 1.00000i \(-0.500181\pi\)
−0.000569515 1.00000i \(0.500181\pi\)
\(744\) 0 0
\(745\) −19779.9 + 34259.9i −0.972727 + 1.68481i
\(746\) 5571.41 9649.97i 0.273437 0.473607i
\(747\) 0 0
\(748\) 12674.3 0.619542
\(749\) −31942.0 + 7544.48i −1.55826 + 0.368050i
\(750\) 0 0
\(751\) 9842.85 + 17048.3i 0.478257 + 0.828365i 0.999689 0.0249278i \(-0.00793559\pi\)
−0.521433 + 0.853292i \(0.674602\pi\)
\(752\) 29.2087 50.5910i 0.00141640 0.00245327i
\(753\) 0 0
\(754\) 496.778 + 860.445i 0.0239941 + 0.0415591i
\(755\) 17271.6 0.832552
\(756\) 0 0
\(757\) 5562.94 0.267092 0.133546 0.991043i \(-0.457364\pi\)
0.133546 + 0.991043i \(0.457364\pi\)
\(758\) 2674.89 + 4633.05i 0.128175 + 0.222005i
\(759\) 0 0
\(760\) 3201.40 5545.00i 0.152799 0.264655i
\(761\) −4584.56 7940.68i −0.218384 0.378252i 0.735930 0.677057i \(-0.236745\pi\)
−0.954314 + 0.298806i \(0.903412\pi\)
\(762\) 0 0
\(763\) −17326.8 18393.7i −0.822114 0.872733i
\(764\) −15203.5 −0.719953
\(765\) 0 0
\(766\) −3350.45 + 5803.14i −0.158037 + 0.273729i
\(767\) 3595.75 6228.02i 0.169276 0.293195i
\(768\) 0 0
\(769\) −12864.9 −0.603277 −0.301638 0.953422i \(-0.597534\pi\)
−0.301638 + 0.953422i \(0.597534\pi\)
\(770\) −21087.5 + 4980.71i −0.986935 + 0.233107i
\(771\) 0 0
\(772\) −7692.04 13323.0i −0.358604 0.621121i
\(773\) −460.408 + 797.450i −0.0214227 + 0.0371052i −0.876538 0.481333i \(-0.840153\pi\)
0.855115 + 0.518438i \(0.173486\pi\)
\(774\) 0 0
\(775\) −2297.86 3980.01i −0.106505 0.184473i
\(776\) −4198.12 −0.194206
\(777\) 0 0
\(778\) 14118.8 0.650623
\(779\) 1495.40 + 2590.11i 0.0687782 + 0.119127i
\(780\) 0 0
\(781\) −12318.3 + 21335.9i −0.564382 + 0.977538i
\(782\) −5662.96 9808.54i −0.258960 0.448533i
\(783\) 0 0
\(784\) −327.521 + 5478.22i −0.0149199 + 0.249554i
\(785\) 44682.1 2.03156
\(786\) 0 0
\(787\) 2159.63 3740.60i 0.0978179 0.169426i −0.812963 0.582315i \(-0.802147\pi\)
0.910781 + 0.412889i \(0.135480\pi\)
\(788\) −9479.04 + 16418.2i −0.428524 + 0.742225i
\(789\) 0 0
\(790\) −35207.4 −1.58560
\(791\) 4154.71 13839.0i 0.186757 0.622070i
\(792\) 0 0
\(793\) 29.7530 + 51.5337i 0.00133236 + 0.00230771i
\(794\) 11020.5 19088.1i 0.492574 0.853163i
\(795\) 0 0
\(796\) 8294.13 + 14365.9i 0.369319 + 0.639679i
\(797\) −20369.7 −0.905308 −0.452654 0.891686i \(-0.649523\pi\)
−0.452654 + 0.891686i \(0.649523\pi\)
\(798\) 0 0
\(799\) −265.132 −0.0117393
\(800\) 875.699 + 1516.76i 0.0387008 + 0.0670317i
\(801\) 0 0
\(802\) 2917.95 5054.04i 0.128474 0.222524i
\(803\) −4011.60 6948.30i −0.176297 0.305355i
\(804\) 0 0
\(805\) 13276.6 + 14094.0i 0.581289 + 0.617080i
\(806\) 1411.75 0.0616958
\(807\) 0 0
\(808\) −2698.13 + 4673.30i −0.117475 + 0.203473i
\(809\) 18244.3 31600.1i 0.792876 1.37330i −0.131304 0.991342i \(-0.541916\pi\)
0.924179 0.381959i \(-0.124750\pi\)
\(810\) 0 0
\(811\) −5722.53 −0.247775 −0.123887 0.992296i \(-0.539536\pi\)
−0.123887 + 0.992296i \(0.539536\pi\)
\(812\) −3001.81 3186.64i −0.129733 0.137720i
\(813\) 0 0
\(814\) −155.496 269.327i −0.00669550 0.0115969i
\(815\) −24474.2 + 42390.6i −1.05190 + 1.82194i
\(816\) 0 0
\(817\) −16614.9 28777.9i −0.711485 1.23233i
\(818\) 5600.10 0.239368
\(819\) 0 0
\(820\) −2686.52 −0.114411
\(821\) 15351.2 + 26589.1i 0.652572 + 1.13029i 0.982497 + 0.186280i \(0.0596432\pi\)
−0.329925 + 0.944007i \(0.607023\pi\)
\(822\) 0 0
\(823\) 2340.54 4053.94i 0.0991326 0.171703i −0.812193 0.583388i \(-0.801727\pi\)
0.911326 + 0.411686i \(0.135060\pi\)
\(824\) 4998.18 + 8657.10i 0.211311 + 0.366001i
\(825\) 0 0
\(826\) −9111.38 + 30349.2i −0.383808 + 1.27843i
\(827\) 10970.9 0.461300 0.230650 0.973037i \(-0.425915\pi\)
0.230650 + 0.973037i \(0.425915\pi\)
\(828\) 0 0
\(829\) −9850.98 + 17062.4i −0.412713 + 0.714839i −0.995185 0.0980110i \(-0.968752\pi\)
0.582473 + 0.812850i \(0.302085\pi\)
\(830\) −12622.5 + 21862.8i −0.527872 + 0.914301i
\(831\) 0 0
\(832\) −538.009 −0.0224184
\(833\) 22275.5 11144.3i 0.926530 0.463539i
\(834\) 0 0
\(835\) −22723.7 39358.6i −0.941779 1.63121i
\(836\) 5209.82 9023.68i 0.215533 0.373314i
\(837\) 0 0
\(838\) −7229.43 12521.7i −0.298015 0.516177i
\(839\) −22274.4 −0.916564 −0.458282 0.888807i \(-0.651535\pi\)
−0.458282 + 0.888807i \(0.651535\pi\)
\(840\) 0 0
\(841\) −20896.7 −0.856810
\(842\) −10949.7 18965.4i −0.448160 0.776237i
\(843\) 0 0
\(844\) −453.988 + 786.330i −0.0185153 + 0.0320694i
\(845\) −14253.2 24687.3i −0.580267 1.00505i
\(846\) 0 0
\(847\) −10326.4 + 2439.03i −0.418915 + 0.0989446i
\(848\) −5148.58 −0.208494
\(849\) 0 0
\(850\) 3974.42 6883.91i 0.160378 0.277784i
\(851\) −138.954 + 240.675i −0.00559726 + 0.00969474i
\(852\) 0 0
\(853\) 28462.2 1.14247 0.571234 0.820787i \(-0.306465\pi\)
0.571234 + 0.820787i \(0.306465\pi\)
\(854\) −179.784 190.854i −0.00720385 0.00764740i
\(855\) 0 0
\(856\) 7088.66 + 12277.9i 0.283044 + 0.490246i
\(857\) 15320.4 26535.7i 0.610658 1.05769i −0.380472 0.924793i \(-0.624238\pi\)
0.991130 0.132898i \(-0.0424284\pi\)
\(858\) 0 0
\(859\) −2623.56 4544.14i −0.104208 0.180494i 0.809206 0.587525i \(-0.199897\pi\)
−0.913414 + 0.407031i \(0.866564\pi\)
\(860\) 29849.1 1.18354
\(861\) 0 0
\(862\) −20187.9 −0.797685
\(863\) 8166.76 + 14145.2i 0.322132 + 0.557949i 0.980928 0.194373i \(-0.0622672\pi\)
−0.658796 + 0.752322i \(0.728934\pi\)
\(864\) 0 0
\(865\) −4219.67 + 7308.67i −0.165865 + 0.287286i
\(866\) 11040.9 + 19123.5i 0.433240 + 0.750394i
\(867\) 0 0
\(868\) −6053.94 + 1429.90i −0.236733 + 0.0559146i
\(869\) −57294.9 −2.23659
\(870\) 0 0
\(871\) 2046.31 3544.31i 0.0796055 0.137881i
\(872\) −5457.69 + 9453.00i −0.211950 + 0.367109i
\(873\) 0 0
\(874\) −9311.14 −0.360359
\(875\) 5016.71 16710.2i 0.193824 0.645610i
\(876\) 0 0
\(877\) −2357.53 4083.35i −0.0907731 0.157224i 0.817064 0.576548i \(-0.195600\pi\)
−0.907837 + 0.419324i \(0.862267\pi\)
\(878\) 1132.41 1961.39i 0.0435274 0.0753917i
\(879\) 0 0
\(880\) 4679.78 + 8105.62i 0.179268 + 0.310501i
\(881\) −31965.3 −1.22240 −0.611202 0.791475i \(-0.709314\pi\)
−0.611202 + 0.791475i \(0.709314\pi\)
\(882\) 0 0
\(883\) 20209.4 0.770217 0.385109 0.922871i \(-0.374164\pi\)
0.385109 + 0.922871i \(0.374164\pi\)
\(884\) 1220.90 + 2114.65i 0.0464516 + 0.0804565i
\(885\) 0 0
\(886\) −9439.27 + 16349.3i −0.357921 + 0.619938i
\(887\) 8313.28 + 14399.0i 0.314693 + 0.545064i 0.979372 0.202065i \(-0.0647651\pi\)
−0.664679 + 0.747129i \(0.731432\pi\)
\(888\) 0 0
\(889\) 4533.94 15102.2i 0.171050 0.569753i
\(890\) 21420.9 0.806775
\(891\) 0 0
\(892\) 9839.22 17042.0i 0.369329 0.639697i
\(893\) −108.984 + 188.765i −0.00408398 + 0.00707367i
\(894\) 0 0
\(895\) −3264.37 −0.121917
\(896\) 2307.11 544.923i 0.0860215 0.0203176i
\(897\) 0 0
\(898\) −8855.77 15338.6i −0.329088 0.569997i
\(899\) 2481.09 4297.37i 0.0920455 0.159427i
\(900\) 0 0
\(901\) 11683.6 + 20236.6i 0.432006 + 0.748256i
\(902\) −4371.92 −0.161385
\(903\) 0 0
\(904\) −6241.46 −0.229633
\(905\) 28261.2 + 48949.8i 1.03805 + 1.79795i
\(906\) 0 0
\(907\) 9941.67 17219.5i 0.363956 0.630390i −0.624652 0.780903i \(-0.714759\pi\)
0.988608 + 0.150513i \(0.0480927\pi\)
\(908\) 3006.26 + 5206.99i 0.109875 + 0.190308i
\(909\) 0 0
\(910\) −2862.34 3038.58i −0.104270 0.110690i
\(911\) −4520.76 −0.164412 −0.0822060 0.996615i \(-0.526197\pi\)
−0.0822060 + 0.996615i \(0.526197\pi\)
\(912\) 0 0
\(913\) −20541.3 + 35578.6i −0.744598 + 1.28968i
\(914\) 5301.24 9182.02i 0.191849 0.332291i
\(915\) 0 0
\(916\) −14960.2 −0.539628
\(917\) 27090.6 6398.61i 0.975585 0.230426i
\(918\) 0 0
\(919\) −262.053 453.889i −0.00940623 0.0162921i 0.861284 0.508124i \(-0.169661\pi\)
−0.870690 + 0.491832i \(0.836327\pi\)
\(920\) 4181.92 7243.30i 0.149863 0.259570i
\(921\) 0 0
\(922\) 8217.88 + 14233.8i 0.293537 + 0.508421i
\(923\) −4746.41 −0.169263
\(924\) 0 0
\(925\) −195.043 −0.00693295
\(926\) −14957.4 25907.1i −0.530812 0.919394i
\(927\) 0 0
\(928\) −945.525 + 1637.70i −0.0334465 + 0.0579311i
\(929\) −2348.23 4067.25i −0.0829310 0.143641i 0.821577 0.570098i \(-0.193095\pi\)
−0.904508 + 0.426457i \(0.859761\pi\)
\(930\) 0 0
\(931\) 1222.05 20440.3i 0.0430193 0.719555i
\(932\) −4937.35 −0.173528
\(933\) 0 0
\(934\) 242.262 419.610i 0.00848720 0.0147003i
\(935\) 21239.5 36788.0i 0.742896 1.28673i
\(936\) 0 0
\(937\) 28172.9 0.982250 0.491125 0.871089i \(-0.336586\pi\)
0.491125 + 0.871089i \(0.336586\pi\)
\(938\) −5185.20 + 17271.5i −0.180493 + 0.601208i
\(939\) 0 0
\(940\) −97.8958 169.560i −0.00339682 0.00588346i
\(941\) −2698.64 + 4674.19i −0.0934891 + 0.161928i −0.908977 0.416846i \(-0.863135\pi\)
0.815488 + 0.578774i \(0.196469\pi\)
\(942\) 0 0
\(943\) 1953.41 + 3383.40i 0.0674567 + 0.116838i
\(944\) 13687.7 0.471924
\(945\) 0 0
\(946\) 48575.1 1.66947
\(947\) −8835.13 15302.9i −0.303171 0.525108i 0.673681 0.739022i \(-0.264712\pi\)
−0.976852 + 0.213914i \(0.931379\pi\)
\(948\) 0 0
\(949\) 772.865 1338.64i 0.0264365 0.0457894i
\(950\) −3267.41 5659.32i −0.111588 0.193276i
\(951\) 0 0
\(952\) −7377.33 7831.57i −0.251156 0.266620i
\(953\) −54328.8 −1.84668 −0.923338 0.383989i \(-0.874550\pi\)
−0.923338 + 0.383989i \(0.874550\pi\)
\(954\) 0 0
\(955\) −25478.0 + 44129.3i −0.863298 + 1.49528i
\(956\) 815.346 1412.22i 0.0275838 0.0477766i
\(957\) 0 0
\(958\) −19516.3 −0.658186
\(959\) 22055.7 + 23413.7i 0.742664 + 0.788391i
\(960\) 0 0
\(961\) 11370.1 + 19693.6i 0.381662 + 0.661058i
\(962\) 29.9575 51.8879i 0.00100402 0.00173901i
\(963\) 0 0
\(964\) −250.067 433.130i −0.00835491 0.0144711i
\(965\) −51561.2 −1.72002
\(966\) 0 0
\(967\) 37517.1 1.24764 0.623821 0.781567i \(-0.285579\pi\)
0.623821 + 0.781567i \(0.285579\pi\)
\(968\) 2291.67 + 3969.29i 0.0760920 + 0.131795i
\(969\) 0 0
\(970\) −7035.20 + 12185.3i −0.232873 + 0.403347i
\(971\) −26650.0 46159.1i −0.880781 1.52556i −0.850474 0.526018i \(-0.823685\pi\)
−0.0303077 0.999541i \(-0.509649\pi\)
\(972\) 0 0
\(973\) 16595.8 55279.2i 0.546801 1.82135i
\(974\) 26435.9 0.869674
\(975\) 0 0
\(976\) −56.6293 + 98.0849i −0.00185723 + 0.00321682i
\(977\) −12188.1 + 21110.4i −0.399111 + 0.691281i −0.993616 0.112811i \(-0.964015\pi\)
0.594505 + 0.804092i \(0.297348\pi\)
\(978\) 0 0
\(979\) 34859.4 1.13801
\(980\) 15352.0 + 10131.0i 0.500411 + 0.330229i
\(981\) 0 0
\(982\) −13789.5 23884.2i −0.448108 0.776146i
\(983\) 220.918 382.641i 0.00716804 0.0124154i −0.862419 0.506195i \(-0.831052\pi\)
0.869587 + 0.493779i \(0.164385\pi\)
\(984\) 0 0
\(985\) 31769.9 + 55027.1i 1.02769 + 1.78001i
\(986\) 8582.67 0.277209
\(987\) 0 0
\(988\) 2007.42 0.0646402
\(989\) −21703.7 37591.9i −0.697814 1.20865i
\(990\) 0 0
\(991\) −22694.0 + 39307.2i −0.727447 + 1.25998i 0.230512 + 0.973070i \(0.425960\pi\)
−0.957959 + 0.286906i \(0.907373\pi\)
\(992\) 1343.50 + 2327.02i 0.0430003 + 0.0744787i
\(993\) 0 0
\(994\) 20353.8 4807.41i 0.649479 0.153402i
\(995\) 55597.2 1.77141
\(996\) 0 0
\(997\) 19853.0 34386.3i 0.630641 1.09230i −0.356780 0.934189i \(-0.616125\pi\)
0.987421 0.158114i \(-0.0505414\pi\)
\(998\) −1990.38 + 3447.43i −0.0631305 + 0.109345i
\(999\) 0 0
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 378.4.g.b.109.3 yes 6
3.2 odd 2 378.4.g.a.109.1 6
7.2 even 3 inner 378.4.g.b.163.3 yes 6
21.2 odd 6 378.4.g.a.163.1 yes 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
378.4.g.a.109.1 6 3.2 odd 2
378.4.g.a.163.1 yes 6 21.2 odd 6
378.4.g.b.109.3 yes 6 1.1 even 1 trivial
378.4.g.b.163.3 yes 6 7.2 even 3 inner