Properties

Label 39.5.g.a.31.2
Level $39$
Weight $5$
Character 39.31
Analytic conductor $4.031$
Analytic rank $0$
Dimension $20$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [39,5,Mod(31,39)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(39, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 3]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("39.31");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 39 = 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 39.g (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.03142856027\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} + 5446 x^{16} - 1452 x^{15} + 106320 x^{13} + 8376897 x^{12} - 1643220 x^{11} + 1054152 x^{10} + \cdots + 2103506496 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{18}\cdot 3^{8} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 31.2
Root \(4.32919 - 4.32919i\) of defining polynomial
Character \(\chi\) \(=\) 39.31
Dual form 39.5.g.a.34.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-4.32919 + 4.32919i) q^{2} +5.19615 q^{3} -21.4837i q^{4} +(-26.0804 + 26.0804i) q^{5} +(-22.4951 + 22.4951i) q^{6} +(-16.9579 - 16.9579i) q^{7} +(23.7399 + 23.7399i) q^{8} +27.0000 q^{9} -225.814i q^{10} +(-69.5293 - 69.5293i) q^{11} -111.633i q^{12} +(-93.5895 - 140.720i) q^{13} +146.828 q^{14} +(-135.518 + 135.518i) q^{15} +138.190 q^{16} +166.635i q^{17} +(-116.888 + 116.888i) q^{18} +(-468.820 + 468.820i) q^{19} +(560.303 + 560.303i) q^{20} +(-88.1158 - 88.1158i) q^{21} +602.011 q^{22} +388.867i q^{23} +(123.356 + 123.356i) q^{24} -735.373i q^{25} +(1014.37 + 204.035i) q^{26} +140.296 q^{27} +(-364.318 + 364.318i) q^{28} -767.891 q^{29} -1173.36i q^{30} +(-66.8738 + 66.8738i) q^{31} +(-978.089 + 978.089i) q^{32} +(-361.285 - 361.285i) q^{33} +(-721.395 - 721.395i) q^{34} +884.537 q^{35} -580.060i q^{36} +(1532.33 + 1532.33i) q^{37} -4059.22i q^{38} +(-486.305 - 731.200i) q^{39} -1238.29 q^{40} +(802.986 - 802.986i) q^{41} +762.940 q^{42} +2798.62i q^{43} +(-1493.75 + 1493.75i) q^{44} +(-704.170 + 704.170i) q^{45} +(-1683.48 - 1683.48i) q^{46} +(33.8918 + 33.8918i) q^{47} +718.056 q^{48} -1825.86i q^{49} +(3183.56 + 3183.56i) q^{50} +865.862i q^{51} +(-3023.18 + 2010.65i) q^{52} -3139.54 q^{53} +(-607.368 + 607.368i) q^{54} +3626.70 q^{55} -805.159i q^{56} +(-2436.06 + 2436.06i) q^{57} +(3324.34 - 3324.34i) q^{58} +(-3959.16 - 3959.16i) q^{59} +(2911.42 + 2911.42i) q^{60} +504.230 q^{61} -579.018i q^{62} +(-457.863 - 457.863i) q^{63} -6257.62i q^{64} +(6110.87 + 1229.17i) q^{65} +3128.14 q^{66} +(4218.53 - 4218.53i) q^{67} +3579.94 q^{68} +2020.61i q^{69} +(-3829.33 + 3829.33i) q^{70} +(-3025.86 + 3025.86i) q^{71} +(640.978 + 640.978i) q^{72} +(3088.98 + 3088.98i) q^{73} -13267.5 q^{74} -3821.11i q^{75} +(10072.0 + 10072.0i) q^{76} +2358.14i q^{77} +(5270.81 + 1060.20i) q^{78} -9376.55 q^{79} +(-3604.05 + 3604.05i) q^{80} +729.000 q^{81} +6952.55i q^{82} +(6229.50 - 6229.50i) q^{83} +(-1893.05 + 1893.05i) q^{84} +(-4345.91 - 4345.91i) q^{85} +(-12115.7 - 12115.7i) q^{86} -3990.08 q^{87} -3301.24i q^{88} +(8558.42 + 8558.42i) q^{89} -6096.97i q^{90} +(-799.227 + 3973.39i) q^{91} +8354.30 q^{92} +(-347.486 + 347.486i) q^{93} -293.448 q^{94} -24454.0i q^{95} +(-5082.30 + 5082.30i) q^{96} +(2882.26 - 2882.26i) q^{97} +(7904.48 + 7904.48i) q^{98} +(-1877.29 - 1877.29i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 24 q^{5} - 24 q^{7} + 540 q^{9} + 372 q^{11} - 224 q^{13} + 480 q^{14} - 252 q^{15} - 2328 q^{16} - 840 q^{19} + 228 q^{20} + 936 q^{21} + 3536 q^{22} - 1404 q^{24} - 828 q^{26} - 1984 q^{28} - 5064 q^{29}+ \cdots + 10044 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/39\mathbb{Z}\right)^\times\).

\(n\) \(14\) \(28\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.32919 + 4.32919i −1.08230 + 1.08230i −0.0860014 + 0.996295i \(0.527409\pi\)
−0.996295 + 0.0860014i \(0.972591\pi\)
\(3\) 5.19615 0.577350
\(4\) 21.4837i 1.34273i
\(5\) −26.0804 + 26.0804i −1.04322 + 1.04322i −0.0441922 + 0.999023i \(0.514071\pi\)
−0.999023 + 0.0441922i \(0.985929\pi\)
\(6\) −22.4951 + 22.4951i −0.624864 + 0.624864i
\(7\) −16.9579 16.9579i −0.346080 0.346080i 0.512567 0.858647i \(-0.328694\pi\)
−0.858647 + 0.512567i \(0.828694\pi\)
\(8\) 23.7399 + 23.7399i 0.370937 + 0.370937i
\(9\) 27.0000 0.333333
\(10\) 225.814i 2.25814i
\(11\) −69.5293 69.5293i −0.574623 0.574623i 0.358794 0.933417i \(-0.383188\pi\)
−0.933417 + 0.358794i \(0.883188\pi\)
\(12\) 111.633i 0.775226i
\(13\) −93.5895 140.720i −0.553784 0.832660i
\(14\) 146.828 0.749121
\(15\) −135.518 + 135.518i −0.602301 + 0.602301i
\(16\) 138.190 0.539804
\(17\) 166.635i 0.576593i 0.957541 + 0.288296i \(0.0930888\pi\)
−0.957541 + 0.288296i \(0.906911\pi\)
\(18\) −116.888 + 116.888i −0.360765 + 0.360765i
\(19\) −468.820 + 468.820i −1.29867 + 1.29867i −0.369401 + 0.929270i \(0.620437\pi\)
−0.929270 + 0.369401i \(0.879563\pi\)
\(20\) 560.303 + 560.303i 1.40076 + 1.40076i
\(21\) −88.1158 88.1158i −0.199809 0.199809i
\(22\) 602.011 1.24382
\(23\) 388.867i 0.735098i 0.930004 + 0.367549i \(0.119803\pi\)
−0.930004 + 0.367549i \(0.880197\pi\)
\(24\) 123.356 + 123.356i 0.214160 + 0.214160i
\(25\) 735.373i 1.17660i
\(26\) 1014.37 + 204.035i 1.50054 + 0.301827i
\(27\) 140.296 0.192450
\(28\) −364.318 + 364.318i −0.464692 + 0.464692i
\(29\) −767.891 −0.913069 −0.456534 0.889706i \(-0.650909\pi\)
−0.456534 + 0.889706i \(0.650909\pi\)
\(30\) 1173.36i 1.30374i
\(31\) −66.8738 + 66.8738i −0.0695877 + 0.0695877i −0.741044 0.671456i \(-0.765669\pi\)
0.671456 + 0.741044i \(0.265669\pi\)
\(32\) −978.089 + 978.089i −0.955165 + 0.955165i
\(33\) −361.285 361.285i −0.331758 0.331758i
\(34\) −721.395 721.395i −0.624044 0.624044i
\(35\) 884.537 0.722071
\(36\) 580.060i 0.447577i
\(37\) 1532.33 + 1532.33i 1.11931 + 1.11931i 0.991843 + 0.127465i \(0.0406841\pi\)
0.127465 + 0.991843i \(0.459316\pi\)
\(38\) 4059.22i 2.81109i
\(39\) −486.305 731.200i −0.319727 0.480737i
\(40\) −1238.29 −0.773933
\(41\) 802.986 802.986i 0.477684 0.477684i −0.426707 0.904390i \(-0.640326\pi\)
0.904390 + 0.426707i \(0.140326\pi\)
\(42\) 762.940 0.432505
\(43\) 2798.62i 1.51358i 0.653655 + 0.756792i \(0.273235\pi\)
−0.653655 + 0.756792i \(0.726765\pi\)
\(44\) −1493.75 + 1493.75i −0.771564 + 0.771564i
\(45\) −704.170 + 704.170i −0.347738 + 0.347738i
\(46\) −1683.48 1683.48i −0.795594 0.795594i
\(47\) 33.8918 + 33.8918i 0.0153426 + 0.0153426i 0.714736 0.699394i \(-0.246547\pi\)
−0.699394 + 0.714736i \(0.746547\pi\)
\(48\) 718.056 0.311656
\(49\) 1825.86i 0.760458i
\(50\) 3183.56 + 3183.56i 1.27343 + 1.27343i
\(51\) 865.862i 0.332896i
\(52\) −3023.18 + 2010.65i −1.11804 + 0.743583i
\(53\) −3139.54 −1.11767 −0.558836 0.829278i \(-0.688752\pi\)
−0.558836 + 0.829278i \(0.688752\pi\)
\(54\) −607.368 + 607.368i −0.208288 + 0.208288i
\(55\) 3626.70 1.19891
\(56\) 805.159i 0.256747i
\(57\) −2436.06 + 2436.06i −0.749788 + 0.749788i
\(58\) 3324.34 3324.34i 0.988211 0.988211i
\(59\) −3959.16 3959.16i −1.13736 1.13736i −0.988921 0.148440i \(-0.952575\pi\)
−0.148440 0.988921i \(-0.547425\pi\)
\(60\) 2911.42 + 2911.42i 0.808728 + 0.808728i
\(61\) 504.230 0.135509 0.0677546 0.997702i \(-0.478417\pi\)
0.0677546 + 0.997702i \(0.478417\pi\)
\(62\) 579.018i 0.150629i
\(63\) −457.863 457.863i −0.115360 0.115360i
\(64\) 6257.62i 1.52774i
\(65\) 6110.87 + 1229.17i 1.44636 + 0.290928i
\(66\) 3128.14 0.718122
\(67\) 4218.53 4218.53i 0.939748 0.939748i −0.0585372 0.998285i \(-0.518644\pi\)
0.998285 + 0.0585372i \(0.0186436\pi\)
\(68\) 3579.94 0.774209
\(69\) 2020.61i 0.424409i
\(70\) −3829.33 + 3829.33i −0.781495 + 0.781495i
\(71\) −3025.86 + 3025.86i −0.600249 + 0.600249i −0.940379 0.340130i \(-0.889529\pi\)
0.340130 + 0.940379i \(0.389529\pi\)
\(72\) 640.978 + 640.978i 0.123646 + 0.123646i
\(73\) 3088.98 + 3088.98i 0.579654 + 0.579654i 0.934808 0.355154i \(-0.115571\pi\)
−0.355154 + 0.934808i \(0.615571\pi\)
\(74\) −13267.5 −2.42285
\(75\) 3821.11i 0.679308i
\(76\) 10072.0 + 10072.0i 1.74377 + 1.74377i
\(77\) 2358.14i 0.397730i
\(78\) 5270.81 + 1060.20i 0.866339 + 0.174260i
\(79\) −9376.55 −1.50241 −0.751205 0.660069i \(-0.770527\pi\)
−0.751205 + 0.660069i \(0.770527\pi\)
\(80\) −3604.05 + 3604.05i −0.563132 + 0.563132i
\(81\) 729.000 0.111111
\(82\) 6952.55i 1.03399i
\(83\) 6229.50 6229.50i 0.904267 0.904267i −0.0915344 0.995802i \(-0.529177\pi\)
0.995802 + 0.0915344i \(0.0291772\pi\)
\(84\) −1893.05 + 1893.05i −0.268290 + 0.268290i
\(85\) −4345.91 4345.91i −0.601510 0.601510i
\(86\) −12115.7 12115.7i −1.63815 1.63815i
\(87\) −3990.08 −0.527160
\(88\) 3301.24i 0.426297i
\(89\) 8558.42 + 8558.42i 1.08047 + 1.08047i 0.996465 + 0.0840075i \(0.0267720\pi\)
0.0840075 + 0.996465i \(0.473228\pi\)
\(90\) 6096.97i 0.752712i
\(91\) −799.227 + 3973.39i −0.0965133 + 0.479820i
\(92\) 8354.30 0.987039
\(93\) −347.486 + 347.486i −0.0401765 + 0.0401765i
\(94\) −293.448 −0.0332105
\(95\) 24454.0i 2.70959i
\(96\) −5082.30 + 5082.30i −0.551465 + 0.551465i
\(97\) 2882.26 2882.26i 0.306330 0.306330i −0.537154 0.843484i \(-0.680501\pi\)
0.843484 + 0.537154i \(0.180501\pi\)
\(98\) 7904.48 + 7904.48i 0.823041 + 0.823041i
\(99\) −1877.29 1877.29i −0.191541 0.191541i
\(100\) −15798.5 −1.57985
\(101\) 5594.65i 0.548441i −0.961667 0.274220i \(-0.911580\pi\)
0.961667 0.274220i \(-0.0884198\pi\)
\(102\) −3748.48 3748.48i −0.360292 0.360292i
\(103\) 6792.74i 0.640281i 0.947370 + 0.320140i \(0.103730\pi\)
−0.947370 + 0.320140i \(0.896270\pi\)
\(104\) 1118.86 5562.48i 0.103445 0.514283i
\(105\) 4596.19 0.416888
\(106\) 13591.7 13591.7i 1.20965 1.20965i
\(107\) −8462.24 −0.739125 −0.369563 0.929206i \(-0.620492\pi\)
−0.369563 + 0.929206i \(0.620492\pi\)
\(108\) 3014.08i 0.258409i
\(109\) −12077.9 + 12077.9i −1.01657 + 1.01657i −0.0167121 + 0.999860i \(0.505320\pi\)
−0.999860 + 0.0167121i \(0.994680\pi\)
\(110\) −15700.7 + 15700.7i −1.29758 + 1.29758i
\(111\) 7962.24 + 7962.24i 0.646233 + 0.646233i
\(112\) −2343.41 2343.41i −0.186815 0.186815i
\(113\) 14864.2 1.16409 0.582043 0.813158i \(-0.302254\pi\)
0.582043 + 0.813158i \(0.302254\pi\)
\(114\) 21092.3i 1.62299i
\(115\) −10141.8 10141.8i −0.766866 0.766866i
\(116\) 16497.1i 1.22601i
\(117\) −2526.92 3799.43i −0.184595 0.277553i
\(118\) 34279.8 2.46192
\(119\) 2825.78 2825.78i 0.199547 0.199547i
\(120\) −6434.36 −0.446831
\(121\) 4972.34i 0.339618i
\(122\) −2182.90 + 2182.90i −0.146661 + 0.146661i
\(123\) 4172.44 4172.44i 0.275791 0.275791i
\(124\) 1436.70 + 1436.70i 0.0934376 + 0.0934376i
\(125\) 2878.56 + 2878.56i 0.184228 + 0.184228i
\(126\) 3964.35 0.249707
\(127\) 10995.6i 0.681728i 0.940113 + 0.340864i \(0.110720\pi\)
−0.940113 + 0.340864i \(0.889280\pi\)
\(128\) 11441.0 + 11441.0i 0.698301 + 0.698301i
\(129\) 14542.0i 0.873868i
\(130\) −31776.4 + 21133.8i −1.88026 + 1.25052i
\(131\) 14023.3 0.817160 0.408580 0.912722i \(-0.366024\pi\)
0.408580 + 0.912722i \(0.366024\pi\)
\(132\) −7761.74 + 7761.74i −0.445462 + 0.445462i
\(133\) 15900.4 0.898887
\(134\) 36525.6i 2.03417i
\(135\) −3658.98 + 3658.98i −0.200767 + 0.200767i
\(136\) −3955.91 + 3955.91i −0.213879 + 0.213879i
\(137\) 20682.4 + 20682.4i 1.10194 + 1.10194i 0.994176 + 0.107769i \(0.0343706\pi\)
0.107769 + 0.994176i \(0.465629\pi\)
\(138\) −8747.60 8747.60i −0.459336 0.459336i
\(139\) −12584.1 −0.651317 −0.325658 0.945487i \(-0.605586\pi\)
−0.325658 + 0.945487i \(0.605586\pi\)
\(140\) 19003.1i 0.969547i
\(141\) 176.107 + 176.107i 0.00885807 + 0.00885807i
\(142\) 26199.0i 1.29929i
\(143\) −3276.92 + 16291.4i −0.160248 + 0.796682i
\(144\) 3731.13 0.179935
\(145\) 20026.9 20026.9i 0.952527 0.952527i
\(146\) −26745.5 −1.25472
\(147\) 9487.44i 0.439051i
\(148\) 32920.2 32920.2i 1.50293 1.50293i
\(149\) −1317.22 + 1317.22i −0.0593315 + 0.0593315i −0.736150 0.676818i \(-0.763358\pi\)
0.676818 + 0.736150i \(0.263358\pi\)
\(150\) 16542.3 + 16542.3i 0.735213 + 0.735213i
\(151\) −6003.08 6003.08i −0.263282 0.263282i 0.563104 0.826386i \(-0.309607\pi\)
−0.826386 + 0.563104i \(0.809607\pi\)
\(152\) −22259.5 −0.963449
\(153\) 4499.15i 0.192198i
\(154\) −10208.8 10208.8i −0.430462 0.430462i
\(155\) 3488.19i 0.145190i
\(156\) −15708.9 + 10447.6i −0.645500 + 0.429308i
\(157\) −24232.6 −0.983107 −0.491553 0.870847i \(-0.663571\pi\)
−0.491553 + 0.870847i \(0.663571\pi\)
\(158\) 40592.8 40592.8i 1.62605 1.62605i
\(159\) −16313.5 −0.645288
\(160\) 51017.9i 1.99289i
\(161\) 6594.37 6594.37i 0.254403 0.254403i
\(162\) −3155.98 + 3155.98i −0.120255 + 0.120255i
\(163\) −24239.5 24239.5i −0.912322 0.912322i 0.0841325 0.996455i \(-0.473188\pi\)
−0.996455 + 0.0841325i \(0.973188\pi\)
\(164\) −17251.1 17251.1i −0.641401 0.641401i
\(165\) 18844.9 0.692191
\(166\) 53937.3i 1.95737i
\(167\) −17352.4 17352.4i −0.622195 0.622195i 0.323897 0.946092i \(-0.395007\pi\)
−0.946092 + 0.323897i \(0.895007\pi\)
\(168\) 4183.73i 0.148233i
\(169\) −11043.0 + 26339.8i −0.386646 + 0.922228i
\(170\) 37628.5 1.30202
\(171\) −12658.1 + 12658.1i −0.432890 + 0.432890i
\(172\) 60124.7 2.03234
\(173\) 2780.29i 0.0928961i 0.998921 + 0.0464480i \(0.0147902\pi\)
−0.998921 + 0.0464480i \(0.985210\pi\)
\(174\) 17273.8 17273.8i 0.570544 0.570544i
\(175\) −12470.4 + 12470.4i −0.407196 + 0.407196i
\(176\) −9608.25 9608.25i −0.310184 0.310184i
\(177\) −20572.4 20572.4i −0.656656 0.656656i
\(178\) −74102.0 −2.33878
\(179\) 2972.36i 0.0927674i −0.998924 0.0463837i \(-0.985230\pi\)
0.998924 0.0463837i \(-0.0147697\pi\)
\(180\) 15128.2 + 15128.2i 0.466919 + 0.466919i
\(181\) 44034.0i 1.34410i 0.740507 + 0.672049i \(0.234586\pi\)
−0.740507 + 0.672049i \(0.765414\pi\)
\(182\) −13741.5 20661.5i −0.414852 0.623764i
\(183\) 2620.05 0.0782362
\(184\) −9231.68 + 9231.68i −0.272675 + 0.272675i
\(185\) −79927.7 −2.33536
\(186\) 3008.67i 0.0869657i
\(187\) 11586.0 11586.0i 0.331323 0.331323i
\(188\) 728.122 728.122i 0.0206010 0.0206010i
\(189\) −2379.13 2379.13i −0.0666031 0.0666031i
\(190\) 105866. + 105866.i 2.93258 + 2.93258i
\(191\) −3688.96 −0.101120 −0.0505601 0.998721i \(-0.516101\pi\)
−0.0505601 + 0.998721i \(0.516101\pi\)
\(192\) 32515.5i 0.882040i
\(193\) 19216.9 + 19216.9i 0.515904 + 0.515904i 0.916329 0.400426i \(-0.131138\pi\)
−0.400426 + 0.916329i \(0.631138\pi\)
\(194\) 24955.7i 0.663079i
\(195\) 31753.0 + 6386.95i 0.835056 + 0.167967i
\(196\) −39226.2 −1.02109
\(197\) −15917.0 + 15917.0i −0.410136 + 0.410136i −0.881786 0.471650i \(-0.843659\pi\)
0.471650 + 0.881786i \(0.343659\pi\)
\(198\) 16254.3 0.414608
\(199\) 23311.0i 0.588646i −0.955706 0.294323i \(-0.904906\pi\)
0.955706 0.294323i \(-0.0950941\pi\)
\(200\) 17457.7 17457.7i 0.436443 0.436443i
\(201\) 21920.1 21920.1i 0.542564 0.542564i
\(202\) 24220.3 + 24220.3i 0.593576 + 0.593576i
\(203\) 13021.8 + 13021.8i 0.315995 + 0.315995i
\(204\) 18601.9 0.446990
\(205\) 41884.4i 0.996654i
\(206\) −29407.0 29407.0i −0.692974 0.692974i
\(207\) 10499.4i 0.245033i
\(208\) −12933.1 19446.0i −0.298935 0.449474i
\(209\) 65193.5 1.49249
\(210\) −19897.8 + 19897.8i −0.451196 + 0.451196i
\(211\) 10045.5 0.225636 0.112818 0.993616i \(-0.464012\pi\)
0.112818 + 0.993616i \(0.464012\pi\)
\(212\) 67448.9i 1.50073i
\(213\) −15722.8 + 15722.8i −0.346554 + 0.346554i
\(214\) 36634.6 36634.6i 0.799953 0.799953i
\(215\) −72989.0 72989.0i −1.57899 1.57899i
\(216\) 3330.62 + 3330.62i 0.0713868 + 0.0713868i
\(217\) 2268.08 0.0481658
\(218\) 104575.i 2.20047i
\(219\) 16050.8 + 16050.8i 0.334664 + 0.334664i
\(220\) 77915.0i 1.60981i
\(221\) 23448.8 15595.3i 0.480106 0.319308i
\(222\) −68940.0 −1.39883
\(223\) 24945.0 24945.0i 0.501620 0.501620i −0.410321 0.911941i \(-0.634583\pi\)
0.911941 + 0.410321i \(0.134583\pi\)
\(224\) 33172.7 0.661126
\(225\) 19855.1i 0.392199i
\(226\) −64349.9 + 64349.9i −1.25989 + 1.25989i
\(227\) 15576.9 15576.9i 0.302294 0.302294i −0.539617 0.841911i \(-0.681431\pi\)
0.841911 + 0.539617i \(0.181431\pi\)
\(228\) 52335.6 + 52335.6i 1.00676 + 1.00676i
\(229\) −24930.7 24930.7i −0.475405 0.475405i 0.428254 0.903658i \(-0.359129\pi\)
−0.903658 + 0.428254i \(0.859129\pi\)
\(230\) 87811.5 1.65995
\(231\) 12253.3i 0.229630i
\(232\) −18229.7 18229.7i −0.338691 0.338691i
\(233\) 22434.3i 0.413239i 0.978421 + 0.206619i \(0.0662462\pi\)
−0.978421 + 0.206619i \(0.933754\pi\)
\(234\) 27387.9 + 5508.94i 0.500181 + 0.100609i
\(235\) −1767.82 −0.0320113
\(236\) −85057.3 + 85057.3i −1.52717 + 1.52717i
\(237\) −48722.0 −0.867417
\(238\) 24466.7i 0.431938i
\(239\) −66829.7 + 66829.7i −1.16997 + 1.16997i −0.187751 + 0.982217i \(0.560120\pi\)
−0.982217 + 0.187751i \(0.939880\pi\)
\(240\) −18727.2 + 18727.2i −0.325124 + 0.325124i
\(241\) −34827.1 34827.1i −0.599629 0.599629i 0.340585 0.940214i \(-0.389375\pi\)
−0.940214 + 0.340585i \(0.889375\pi\)
\(242\) 21526.2 + 21526.2i 0.367567 + 0.367567i
\(243\) 3788.00 0.0641500
\(244\) 10832.7i 0.181952i
\(245\) 47619.1 + 47619.1i 0.793321 + 0.793321i
\(246\) 36126.5i 0.596975i
\(247\) 109849. + 22095.5i 1.80054 + 0.362168i
\(248\) −3175.16 −0.0516253
\(249\) 32369.4 32369.4i 0.522079 0.522079i
\(250\) −24923.6 −0.398778
\(251\) 4768.38i 0.0756873i −0.999284 0.0378437i \(-0.987951\pi\)
0.999284 0.0378437i \(-0.0120489\pi\)
\(252\) −9836.60 + 9836.60i −0.154897 + 0.154897i
\(253\) 27037.7 27037.7i 0.422404 0.422404i
\(254\) −47601.9 47601.9i −0.737832 0.737832i
\(255\) −22582.0 22582.0i −0.347282 0.347282i
\(256\) 1061.74 0.0162008
\(257\) 62743.6i 0.949956i 0.879998 + 0.474978i \(0.157544\pi\)
−0.879998 + 0.474978i \(0.842456\pi\)
\(258\) −62955.2 62955.2i −0.945785 0.945785i
\(259\) 51970.3i 0.774740i
\(260\) 26407.1 131284.i 0.390638 1.94207i
\(261\) −20733.1 −0.304356
\(262\) −60709.4 + 60709.4i −0.884409 + 0.884409i
\(263\) 45421.0 0.656667 0.328333 0.944562i \(-0.393513\pi\)
0.328333 + 0.944562i \(0.393513\pi\)
\(264\) 17153.8i 0.246123i
\(265\) 81880.4 81880.4i 1.16597 1.16597i
\(266\) −68835.8 + 68835.8i −0.972862 + 0.972862i
\(267\) 44470.9 + 44470.9i 0.623811 + 0.623811i
\(268\) −90629.6 90629.6i −1.26183 1.26183i
\(269\) 79205.8 1.09459 0.547296 0.836939i \(-0.315657\pi\)
0.547296 + 0.836939i \(0.315657\pi\)
\(270\) 31680.8i 0.434579i
\(271\) −16180.5 16180.5i −0.220320 0.220320i 0.588313 0.808633i \(-0.299792\pi\)
−0.808633 + 0.588313i \(0.799792\pi\)
\(272\) 23027.3i 0.311247i
\(273\) −4152.90 + 20646.3i −0.0557220 + 0.277024i
\(274\) −179076. −2.38526
\(275\) −51130.0 + 51130.0i −0.676099 + 0.676099i
\(276\) 43410.2 0.569867
\(277\) 2884.24i 0.0375899i −0.999823 0.0187950i \(-0.994017\pi\)
0.999823 0.0187950i \(-0.00598298\pi\)
\(278\) 54478.9 54478.9i 0.704918 0.704918i
\(279\) −1805.59 + 1805.59i −0.0231959 + 0.0231959i
\(280\) 20998.9 + 20998.9i 0.267843 + 0.267843i
\(281\) −103231. 103231.i −1.30736 1.30736i −0.923311 0.384052i \(-0.874528\pi\)
−0.384052 0.923311i \(-0.625472\pi\)
\(282\) −1524.80 −0.0191741
\(283\) 78581.6i 0.981178i 0.871391 + 0.490589i \(0.163218\pi\)
−0.871391 + 0.490589i \(0.836782\pi\)
\(284\) 65006.6 + 65006.6i 0.805973 + 0.805973i
\(285\) 127067.i 1.56438i
\(286\) −56341.9 84714.7i −0.688810 1.03568i
\(287\) −27233.9 −0.330633
\(288\) −26408.4 + 26408.4i −0.318388 + 0.318388i
\(289\) 55753.7 0.667541
\(290\) 173400.i 2.06183i
\(291\) 14976.6 14976.6i 0.176860 0.176860i
\(292\) 66362.7 66362.7i 0.778320 0.778320i
\(293\) −5490.45 5490.45i −0.0639547 0.0639547i 0.674406 0.738361i \(-0.264400\pi\)
−0.738361 + 0.674406i \(0.764400\pi\)
\(294\) 41072.9 + 41072.9i 0.475183 + 0.475183i
\(295\) 206513. 2.37303
\(296\) 72755.0i 0.830385i
\(297\) −9754.70 9754.70i −0.110586 0.110586i
\(298\) 11405.0i 0.128429i
\(299\) 54721.2 36393.9i 0.612087 0.407086i
\(300\) −82091.5 −0.912128
\(301\) 47458.7 47458.7i 0.523821 0.523821i
\(302\) 51976.9 0.569897
\(303\) 29070.6i 0.316642i
\(304\) −64786.2 + 64786.2i −0.701028 + 0.701028i
\(305\) −13150.5 + 13150.5i −0.141365 + 0.141365i
\(306\) −19477.7 19477.7i −0.208015 0.208015i
\(307\) 36642.5 + 36642.5i 0.388784 + 0.388784i 0.874254 0.485469i \(-0.161351\pi\)
−0.485469 + 0.874254i \(0.661351\pi\)
\(308\) 50661.6 0.534045
\(309\) 35296.1i 0.369666i
\(310\) 15101.0 + 15101.0i 0.157139 + 0.157139i
\(311\) 57004.6i 0.589371i −0.955594 0.294686i \(-0.904785\pi\)
0.955594 0.294686i \(-0.0952149\pi\)
\(312\) 5813.79 28903.5i 0.0597242 0.296921i
\(313\) −168911. −1.72413 −0.862064 0.506799i \(-0.830829\pi\)
−0.862064 + 0.506799i \(0.830829\pi\)
\(314\) 104907. 104907.i 1.06401 1.06401i
\(315\) 23882.5 0.240690
\(316\) 201443.i 2.01733i
\(317\) −57585.7 + 57585.7i −0.573055 + 0.573055i −0.932981 0.359926i \(-0.882802\pi\)
0.359926 + 0.932981i \(0.382802\pi\)
\(318\) 70624.3 70624.3i 0.698393 0.698393i
\(319\) 53390.9 + 53390.9i 0.524670 + 0.524670i
\(320\) 163201. + 163201.i 1.59376 + 1.59376i
\(321\) −43971.1 −0.426734
\(322\) 57096.5i 0.550678i
\(323\) −78122.0 78122.0i −0.748804 0.748804i
\(324\) 15661.6i 0.149192i
\(325\) −103481. + 68823.2i −0.979705 + 0.651580i
\(326\) 209874. 1.97481
\(327\) −62758.6 + 62758.6i −0.586918 + 0.586918i
\(328\) 38125.7 0.354381
\(329\) 1149.47i 0.0106195i
\(330\) −81583.1 + 81583.1i −0.749156 + 0.749156i
\(331\) −134787. + 134787.i −1.23025 + 1.23025i −0.266382 + 0.963868i \(0.585828\pi\)
−0.963868 + 0.266382i \(0.914172\pi\)
\(332\) −133833. 133833.i −1.21419 1.21419i
\(333\) 41373.0 + 41373.0i 0.373103 + 0.373103i
\(334\) 150243. 1.34680
\(335\) 220042.i 1.96072i
\(336\) −12176.7 12176.7i −0.107858 0.107858i
\(337\) 56729.9i 0.499520i 0.968308 + 0.249760i \(0.0803517\pi\)
−0.968308 + 0.249760i \(0.919648\pi\)
\(338\) −66222.5 161837.i −0.579659 1.41659i
\(339\) 77236.7 0.672085
\(340\) −93366.3 + 93366.3i −0.807667 + 0.807667i
\(341\) 9299.38 0.0799734
\(342\) 109599.i 0.937031i
\(343\) −71678.7 + 71678.7i −0.609259 + 0.609259i
\(344\) −66439.0 + 66439.0i −0.561444 + 0.561444i
\(345\) −52698.3 52698.3i −0.442750 0.442750i
\(346\) −12036.4 12036.4i −0.100541 0.100541i
\(347\) −183864. −1.52699 −0.763497 0.645811i \(-0.776519\pi\)
−0.763497 + 0.645811i \(0.776519\pi\)
\(348\) 85721.6i 0.707835i
\(349\) −72786.9 72786.9i −0.597588 0.597588i 0.342082 0.939670i \(-0.388868\pi\)
−0.939670 + 0.342082i \(0.888868\pi\)
\(350\) 107973.i 0.881413i
\(351\) −13130.2 19742.4i −0.106576 0.160246i
\(352\) 136012. 1.09772
\(353\) 106752. 106752.i 0.856695 0.856695i −0.134252 0.990947i \(-0.542863\pi\)
0.990947 + 0.134252i \(0.0428632\pi\)
\(354\) 178123. 1.42139
\(355\) 157831.i 1.25238i
\(356\) 183867. 183867.i 1.45078 1.45078i
\(357\) 14683.2 14683.2i 0.115209 0.115209i
\(358\) 12867.9 + 12867.9i 0.100402 + 0.100402i
\(359\) −26893.9 26893.9i −0.208672 0.208672i 0.595031 0.803703i \(-0.297140\pi\)
−0.803703 + 0.595031i \(0.797140\pi\)
\(360\) −33433.9 −0.257978
\(361\) 309264.i 2.37309i
\(362\) −190631. 190631.i −1.45471 1.45471i
\(363\) 25837.1i 0.196078i
\(364\) 85363.1 + 17170.3i 0.644269 + 0.129591i
\(365\) −161123. −1.20941
\(366\) −11342.7 + 11342.7i −0.0846748 + 0.0846748i
\(367\) 6492.32 0.0482023 0.0241012 0.999710i \(-0.492328\pi\)
0.0241012 + 0.999710i \(0.492328\pi\)
\(368\) 53737.5i 0.396809i
\(369\) 21680.6 21680.6i 0.159228 0.159228i
\(370\) 346022. 346022.i 2.52755 2.52755i
\(371\) 53240.0 + 53240.0i 0.386804 + 0.386804i
\(372\) 7465.29 + 7465.29i 0.0539462 + 0.0539462i
\(373\) −53286.9 −0.383004 −0.191502 0.981492i \(-0.561336\pi\)
−0.191502 + 0.981492i \(0.561336\pi\)
\(374\) 100316.i 0.717180i
\(375\) 14957.4 + 14957.4i 0.106364 + 0.106364i
\(376\) 1609.18i 0.0113823i
\(377\) 71866.5 + 108057.i 0.505643 + 0.760276i
\(378\) 20599.4 0.144168
\(379\) −92136.8 + 92136.8i −0.641438 + 0.641438i −0.950909 0.309471i \(-0.899848\pi\)
0.309471 + 0.950909i \(0.399848\pi\)
\(380\) −525363. −3.63825
\(381\) 57134.8i 0.393596i
\(382\) 15970.2 15970.2i 0.109442 0.109442i
\(383\) −15911.5 + 15911.5i −0.108471 + 0.108471i −0.759259 0.650788i \(-0.774439\pi\)
0.650788 + 0.759259i \(0.274439\pi\)
\(384\) 59449.0 + 59449.0i 0.403164 + 0.403164i
\(385\) −61501.3 61501.3i −0.414918 0.414918i
\(386\) −166387. −1.11672
\(387\) 75562.7i 0.504528i
\(388\) −61921.5 61921.5i −0.411319 0.411319i
\(389\) 215552.i 1.42447i 0.701941 + 0.712236i \(0.252317\pi\)
−0.701941 + 0.712236i \(0.747683\pi\)
\(390\) −165115. + 109814.i −1.08557 + 0.721988i
\(391\) −64799.0 −0.423852
\(392\) 43345.8 43345.8i 0.282082 0.282082i
\(393\) 72867.1 0.471788
\(394\) 137815.i 0.887778i
\(395\) 244544. 244544.i 1.56734 1.56734i
\(396\) −40331.2 + 40331.2i −0.257188 + 0.257188i
\(397\) 81274.7 + 81274.7i 0.515673 + 0.515673i 0.916259 0.400586i \(-0.131194\pi\)
−0.400586 + 0.916259i \(0.631194\pi\)
\(398\) 100917. + 100917.i 0.637089 + 0.637089i
\(399\) 82621.0 0.518973
\(400\) 101621.i 0.635132i
\(401\) 170564. + 170564.i 1.06072 + 1.06072i 0.998034 + 0.0626817i \(0.0199653\pi\)
0.0626817 + 0.998034i \(0.480035\pi\)
\(402\) 189793.i 1.17443i
\(403\) 15669.1 + 3151.77i 0.0964795 + 0.0194063i
\(404\) −120194. −0.736409
\(405\) −19012.6 + 19012.6i −0.115913 + 0.115913i
\(406\) −112748. −0.683999
\(407\) 213084.i 1.28636i
\(408\) −20555.5 + 20555.5i −0.123483 + 0.123483i
\(409\) −92288.1 + 92288.1i −0.551695 + 0.551695i −0.926930 0.375235i \(-0.877562\pi\)
0.375235 + 0.926930i \(0.377562\pi\)
\(410\) −181325. 181325.i −1.07867 1.07867i
\(411\) 107469. + 107469.i 0.636208 + 0.636208i
\(412\) 145933. 0.859725
\(413\) 134278.i 0.787235i
\(414\) −45453.9 45453.9i −0.265198 0.265198i
\(415\) 324935.i 1.88669i
\(416\) 229175. + 46097.4i 1.32428 + 0.266373i
\(417\) −65388.9 −0.376038
\(418\) −282235. + 282235.i −1.61532 + 1.61532i
\(419\) −20127.4 −0.114646 −0.0573232 0.998356i \(-0.518257\pi\)
−0.0573232 + 0.998356i \(0.518257\pi\)
\(420\) 98743.1i 0.559768i
\(421\) 171209. 171209.i 0.965965 0.965965i −0.0334748 0.999440i \(-0.510657\pi\)
0.999440 + 0.0334748i \(0.0106573\pi\)
\(422\) −43489.0 + 43489.0i −0.244205 + 0.244205i
\(423\) 915.080 + 915.080i 0.00511421 + 0.00511421i
\(424\) −74532.5 74532.5i −0.414586 0.414586i
\(425\) 122539. 0.678417
\(426\) 136134.i 0.750148i
\(427\) −8550.68 8550.68i −0.0468970 0.0468970i
\(428\) 181800.i 0.992446i
\(429\) −17027.4 + 84652.4i −0.0925195 + 0.459965i
\(430\) 631966. 3.41788
\(431\) 127549. 127549.i 0.686630 0.686630i −0.274856 0.961485i \(-0.588630\pi\)
0.961485 + 0.274856i \(0.0886301\pi\)
\(432\) 19387.5 0.103885
\(433\) 68957.0i 0.367792i 0.982946 + 0.183896i \(0.0588710\pi\)
−0.982946 + 0.183896i \(0.941129\pi\)
\(434\) −9818.93 + 9818.93i −0.0521297 + 0.0521297i
\(435\) 104063. 104063.i 0.549942 0.549942i
\(436\) 259478. + 259478.i 1.36498 + 1.36498i
\(437\) −182309. 182309.i −0.954651 0.954651i
\(438\) −138974. −0.724410
\(439\) 113397.i 0.588400i −0.955744 0.294200i \(-0.904947\pi\)
0.955744 0.294200i \(-0.0950531\pi\)
\(440\) 86097.7 + 86097.7i 0.444720 + 0.444720i
\(441\) 49298.2i 0.253486i
\(442\) −33999.4 + 169029.i −0.174031 + 0.865203i
\(443\) 92267.8 0.470157 0.235079 0.971976i \(-0.424465\pi\)
0.235079 + 0.971976i \(0.424465\pi\)
\(444\) 171058. 171058.i 0.867717 0.867717i
\(445\) −446414. −2.25433
\(446\) 215984.i 1.08580i
\(447\) −6844.47 + 6844.47i −0.0342551 + 0.0342551i
\(448\) −106116. + 106116.i −0.528719 + 0.528719i
\(449\) −17542.3 17542.3i −0.0870148 0.0870148i 0.662260 0.749274i \(-0.269598\pi\)
−0.749274 + 0.662260i \(0.769598\pi\)
\(450\) 85956.2 + 85956.2i 0.424475 + 0.424475i
\(451\) −111662. −0.548976
\(452\) 319338.i 1.56305i
\(453\) −31192.9 31192.9i −0.152006 0.152006i
\(454\) 134871.i 0.654343i
\(455\) −82783.4 124472.i −0.399872 0.601240i
\(456\) −115664. −0.556248
\(457\) 104731. 104731.i 0.501466 0.501466i −0.410428 0.911893i \(-0.634621\pi\)
0.911893 + 0.410428i \(0.134621\pi\)
\(458\) 215859. 1.02906
\(459\) 23378.3i 0.110965i
\(460\) −217883. + 217883.i −1.02969 + 1.02969i
\(461\) −12382.8 + 12382.8i −0.0582663 + 0.0582663i −0.735640 0.677373i \(-0.763118\pi\)
0.677373 + 0.735640i \(0.263118\pi\)
\(462\) −53046.7 53046.7i −0.248527 0.248527i
\(463\) 156318. + 156318.i 0.729199 + 0.729199i 0.970460 0.241261i \(-0.0775611\pi\)
−0.241261 + 0.970460i \(0.577561\pi\)
\(464\) −106115. −0.492878
\(465\) 18125.2i 0.0838255i
\(466\) −97122.3 97122.3i −0.447247 0.447247i
\(467\) 3880.03i 0.0177911i 0.999960 + 0.00889553i \(0.00283157\pi\)
−0.999960 + 0.00889553i \(0.997168\pi\)
\(468\) −81625.8 + 54287.5i −0.372680 + 0.247861i
\(469\) −143075. −0.650455
\(470\) 7653.24 7653.24i 0.0346457 0.0346457i
\(471\) −125916. −0.567597
\(472\) 187980.i 0.843778i
\(473\) 194586. 194586.i 0.869740 0.869740i
\(474\) 210926. 210926.i 0.938803 0.938803i
\(475\) 344758. + 344758.i 1.52801 + 1.52801i
\(476\) −60708.3 60708.3i −0.267938 0.267938i
\(477\) −84767.6 −0.372557
\(478\) 578637.i 2.53250i
\(479\) 53446.0 + 53446.0i 0.232940 + 0.232940i 0.813919 0.580979i \(-0.197330\pi\)
−0.580979 + 0.813919i \(0.697330\pi\)
\(480\) 265097.i 1.15059i
\(481\) 72218.9 359040.i 0.312148 1.55186i
\(482\) 301546. 1.29795
\(483\) 34265.3 34265.3i 0.146879 0.146879i
\(484\) −106824. −0.456015
\(485\) 150341.i 0.639136i
\(486\) −16398.9 + 16398.9i −0.0694293 + 0.0694293i
\(487\) −39739.5 + 39739.5i −0.167558 + 0.167558i −0.785905 0.618347i \(-0.787803\pi\)
0.618347 + 0.785905i \(0.287803\pi\)
\(488\) 11970.4 + 11970.4i 0.0502653 + 0.0502653i
\(489\) −125952. 125952.i −0.526729 0.526729i
\(490\) −412304. −1.71722
\(491\) 183063.i 0.759342i 0.925122 + 0.379671i \(0.123963\pi\)
−0.925122 + 0.379671i \(0.876037\pi\)
\(492\) −89639.4 89639.4i −0.370313 0.370313i
\(493\) 127958.i 0.526469i
\(494\) −571212. + 379900.i −2.34069 + 1.55674i
\(495\) 97921.0 0.399637
\(496\) −9241.28 + 9241.28i −0.0375638 + 0.0375638i
\(497\) 102624. 0.415468
\(498\) 280266.i 1.13009i
\(499\) −57389.5 + 57389.5i −0.230479 + 0.230479i −0.812893 0.582414i \(-0.802108\pi\)
0.582414 + 0.812893i \(0.302108\pi\)
\(500\) 61842.1 61842.1i 0.247368 0.247368i
\(501\) −90165.7 90165.7i −0.359224 0.359224i
\(502\) 20643.2 + 20643.2i 0.0819161 + 0.0819161i
\(503\) −192555. −0.761061 −0.380530 0.924768i \(-0.624259\pi\)
−0.380530 + 0.924768i \(0.624259\pi\)
\(504\) 21739.3i 0.0855824i
\(505\) 145910. + 145910.i 0.572142 + 0.572142i
\(506\) 234102.i 0.914333i
\(507\) −57381.1 + 136865.i −0.223230 + 0.532449i
\(508\) 236226. 0.915377
\(509\) −84764.7 + 84764.7i −0.327175 + 0.327175i −0.851511 0.524336i \(-0.824313\pi\)
0.524336 + 0.851511i \(0.324313\pi\)
\(510\) 195524. 0.751724
\(511\) 104765.i 0.401213i
\(512\) −187652. + 187652.i −0.715835 + 0.715835i
\(513\) −65773.7 + 65773.7i −0.249929 + 0.249929i
\(514\) −271629. 271629.i −1.02813 1.02813i
\(515\) −177157. 177157.i −0.667951 0.667951i
\(516\) 312417. 1.17337
\(517\) 4712.95i 0.0176324i
\(518\) 224989. + 224989.i 0.838498 + 0.838498i
\(519\) 14446.8i 0.0536336i
\(520\) 115891. + 174252.i 0.428592 + 0.644424i
\(521\) 314076. 1.15707 0.578534 0.815658i \(-0.303625\pi\)
0.578534 + 0.815658i \(0.303625\pi\)
\(522\) 89757.2 89757.2i 0.329404 0.329404i
\(523\) −37022.8 −0.135352 −0.0676762 0.997707i \(-0.521558\pi\)
−0.0676762 + 0.997707i \(0.521558\pi\)
\(524\) 301272.i 1.09723i
\(525\) −64798.0 + 64798.0i −0.235095 + 0.235095i
\(526\) −196636. + 196636.i −0.710708 + 0.710708i
\(527\) −11143.5 11143.5i −0.0401238 0.0401238i
\(528\) −49925.9 49925.9i −0.179085 0.179085i
\(529\) 128624. 0.459631
\(530\) 708951.i 2.52386i
\(531\) −106897. 106897.i −0.379121 0.379121i
\(532\) 341600.i 1.20696i
\(533\) −188147. 37844.8i −0.662282 0.133214i
\(534\) −385045. −1.35030
\(535\) 220699. 220699.i 0.771067 0.771067i
\(536\) 200295. 0.697174
\(537\) 15444.8i 0.0535593i
\(538\) −342897. + 342897.i −1.18467 + 1.18467i
\(539\) −126951. + 126951.i −0.436976 + 0.436976i
\(540\) 78608.3 + 78608.3i 0.269576 + 0.269576i
\(541\) −38918.2 38918.2i −0.132971 0.132971i 0.637489 0.770460i \(-0.279973\pi\)
−0.770460 + 0.637489i \(0.779973\pi\)
\(542\) 140097. 0.476903
\(543\) 228807.i 0.776015i
\(544\) −162984. 162984.i −0.550741 0.550741i
\(545\) 629992.i 2.12101i
\(546\) −71403.2 107361.i −0.239515 0.360130i
\(547\) −383774. −1.28263 −0.641314 0.767279i \(-0.721610\pi\)
−0.641314 + 0.767279i \(0.721610\pi\)
\(548\) 444334. 444334.i 1.47962 1.47962i
\(549\) 13614.2 0.0451697
\(550\) 442702.i 1.46348i
\(551\) 360003. 360003.i 1.18578 1.18578i
\(552\) −47969.2 + 47969.2i −0.157429 + 0.157429i
\(553\) 159007. + 159007.i 0.519954 + 0.519954i
\(554\) 12486.4 + 12486.4i 0.0406835 + 0.0406835i
\(555\) −415316. −1.34832
\(556\) 270353.i 0.874543i
\(557\) 280053. + 280053.i 0.902672 + 0.902672i 0.995667 0.0929944i \(-0.0296439\pi\)
−0.0929944 + 0.995667i \(0.529644\pi\)
\(558\) 15633.5i 0.0502097i
\(559\) 393820. 261921.i 1.26030 0.838199i
\(560\) 122234. 0.389777
\(561\) 60202.8 60202.8i 0.191290 0.191290i
\(562\) 893810. 2.82991
\(563\) 50493.5i 0.159301i 0.996823 + 0.0796505i \(0.0253804\pi\)
−0.996823 + 0.0796505i \(0.974620\pi\)
\(564\) 3783.43 3783.43i 0.0118940 0.0118940i
\(565\) −387664. + 387664.i −1.21439 + 1.21439i
\(566\) −340194. 340194.i −1.06193 1.06193i
\(567\) −12362.3 12362.3i −0.0384533 0.0384533i
\(568\) −143667. −0.445309
\(569\) 301875.i 0.932400i −0.884679 0.466200i \(-0.845623\pi\)
0.884679 0.466200i \(-0.154377\pi\)
\(570\) 550096. + 550096.i 1.69312 + 1.69312i
\(571\) 290046.i 0.889601i −0.895630 0.444800i \(-0.853275\pi\)
0.895630 0.444800i \(-0.146725\pi\)
\(572\) 349999. + 70400.4i 1.06973 + 0.215171i
\(573\) −19168.4 −0.0583817
\(574\) 117901. 117901.i 0.357843 0.357843i
\(575\) 285962. 0.864914
\(576\) 168956.i 0.509246i
\(577\) 127765. 127765.i 0.383760 0.383760i −0.488695 0.872455i \(-0.662527\pi\)
0.872455 + 0.488695i \(0.162527\pi\)
\(578\) −241368. + 241368.i −0.722477 + 0.722477i
\(579\) 99853.9 + 99853.9i 0.297857 + 0.297857i
\(580\) −430252. 430252.i −1.27899 1.27899i
\(581\) −211278. −0.625897
\(582\) 129673.i 0.382829i
\(583\) 218290. + 218290.i 0.642240 + 0.642240i
\(584\) 146664.i 0.430030i
\(585\) 164994. + 33187.6i 0.482120 + 0.0969759i
\(586\) 47538.4 0.138436
\(587\) −432681. + 432681.i −1.25572 + 1.25572i −0.302598 + 0.953118i \(0.597854\pi\)
−0.953118 + 0.302598i \(0.902146\pi\)
\(588\) −203825. −0.589527
\(589\) 62703.6i 0.180743i
\(590\) −894031. + 894031.i −2.56832 + 2.56832i
\(591\) −82707.0 + 82707.0i −0.236792 + 0.236792i
\(592\) 211753. + 211753.i 0.604207 + 0.604207i
\(593\) 351836. + 351836.i 1.00053 + 1.00053i 1.00000 0.000531251i \(0.000169102\pi\)
0.000531251 1.00000i \(0.499831\pi\)
\(594\) 84459.8 0.239374
\(595\) 147395.i 0.416341i
\(596\) 28298.7 + 28298.7i 0.0796663 + 0.0796663i
\(597\) 121127.i 0.339855i
\(598\) −79342.4 + 394454.i −0.221872 + 1.10305i
\(599\) −484810. −1.35119 −0.675597 0.737271i \(-0.736114\pi\)
−0.675597 + 0.737271i \(0.736114\pi\)
\(600\) 90712.9 90712.9i 0.251980 0.251980i
\(601\) 214570. 0.594046 0.297023 0.954870i \(-0.404006\pi\)
0.297023 + 0.954870i \(0.404006\pi\)
\(602\) 410915.i 1.13386i
\(603\) 113900. 113900.i 0.313249 0.313249i
\(604\) −128968. + 128968.i −0.353516 + 0.353516i
\(605\) 129681. + 129681.i 0.354294 + 0.354294i
\(606\) 125852. + 125852.i 0.342701 + 0.342701i
\(607\) −2800.08 −0.00759964 −0.00379982 0.999993i \(-0.501210\pi\)
−0.00379982 + 0.999993i \(0.501210\pi\)
\(608\) 917096.i 2.48089i
\(609\) 67663.3 + 67663.3i 0.182440 + 0.182440i
\(610\) 113862.i 0.305998i
\(611\) 1597.32 7941.17i 0.00427869 0.0212717i
\(612\) 96658.4 0.258070
\(613\) −92722.6 + 92722.6i −0.246754 + 0.246754i −0.819637 0.572883i \(-0.805825\pi\)
0.572883 + 0.819637i \(0.305825\pi\)
\(614\) −317265. −0.841560
\(615\) 217638.i 0.575418i
\(616\) −55982.2 + 55982.2i −0.147533 + 0.147533i
\(617\) 260927. 260927.i 0.685407 0.685407i −0.275806 0.961213i \(-0.588945\pi\)
0.961213 + 0.275806i \(0.0889447\pi\)
\(618\) −152803. 152803.i −0.400089 0.400089i
\(619\) 103595. + 103595.i 0.270369 + 0.270369i 0.829249 0.558880i \(-0.188769\pi\)
−0.558880 + 0.829249i \(0.688769\pi\)
\(620\) −74939.2 −0.194951
\(621\) 54556.5i 0.141470i
\(622\) 246783. + 246783.i 0.637874 + 0.637874i
\(623\) 290266.i 0.747859i
\(624\) −67202.5 101045.i −0.172590 0.259504i
\(625\) 309460. 0.792218
\(626\) 731248. 731248.i 1.86602 1.86602i
\(627\) 338755. 0.861690
\(628\) 520606.i 1.32005i
\(629\) −255341. + 255341.i −0.645385 + 0.645385i
\(630\) −103392. + 103392.i −0.260498 + 0.260498i
\(631\) −300176. 300176.i −0.753907 0.753907i 0.221299 0.975206i \(-0.428970\pi\)
−0.975206 + 0.221299i \(0.928970\pi\)
\(632\) −222599. 222599.i −0.557299 0.557299i
\(633\) 52198.2 0.130271
\(634\) 498599.i 1.24043i
\(635\) −286769. 286769.i −0.711189 0.711189i
\(636\) 350475.i 0.866449i
\(637\) −256934. + 170881.i −0.633203 + 0.421130i
\(638\) −462279. −1.13570
\(639\) −81698.1 + 81698.1i −0.200083 + 0.200083i
\(640\) −596770. −1.45696
\(641\) 466494.i 1.13535i 0.823253 + 0.567675i \(0.192157\pi\)
−0.823253 + 0.567675i \(0.807843\pi\)
\(642\) 190359. 190359.i 0.461853 0.461853i
\(643\) 439463. 439463.i 1.06292 1.06292i 0.0650372 0.997883i \(-0.479283\pi\)
0.997883 0.0650372i \(-0.0207166\pi\)
\(644\) −141671. 141671.i −0.341594 0.341594i
\(645\) −379262. 379262.i −0.911633 0.911633i
\(646\) 676409. 1.62086
\(647\) 562437.i 1.34358i −0.740740 0.671792i \(-0.765525\pi\)
0.740740 0.671792i \(-0.234475\pi\)
\(648\) 17306.4 + 17306.4i 0.0412152 + 0.0412152i
\(649\) 550555.i 1.30711i
\(650\) 150042. 745938.i 0.355128 1.76553i
\(651\) 11785.3 0.0278085
\(652\) −520754. + 520754.i −1.22500 + 1.22500i
\(653\) 37629.2 0.0882467 0.0441234 0.999026i \(-0.485951\pi\)
0.0441234 + 0.999026i \(0.485951\pi\)
\(654\) 543387.i 1.27044i
\(655\) −365733. + 365733.i −0.852474 + 0.852474i
\(656\) 110965. 110965.i 0.257856 0.257856i
\(657\) 83402.4 + 83402.4i 0.193218 + 0.193218i
\(658\) 4976.27 + 4976.27i 0.0114935 + 0.0114935i
\(659\) 18033.4 0.0415248 0.0207624 0.999784i \(-0.493391\pi\)
0.0207624 + 0.999784i \(0.493391\pi\)
\(660\) 404858.i 0.929426i
\(661\) 536607. + 536607.i 1.22816 + 1.22816i 0.964661 + 0.263495i \(0.0848754\pi\)
0.263495 + 0.964661i \(0.415125\pi\)
\(662\) 1.16704e6i 2.66299i
\(663\) 121844. 81035.7i 0.277189 0.184353i
\(664\) 295776. 0.670852
\(665\) −414689. + 414689.i −0.937733 + 0.937733i
\(666\) −358223. −0.807616
\(667\) 298607.i 0.671195i
\(668\) −372794. + 372794.i −0.835440 + 0.835440i
\(669\) 129618. 129618.i 0.289610 0.289610i
\(670\) −952601. 952601.i −2.12208 2.12208i
\(671\) −35058.7 35058.7i −0.0778666 0.0778666i
\(672\) 172370. 0.381701
\(673\) 75975.6i 0.167743i 0.996477 + 0.0838715i \(0.0267285\pi\)
−0.996477 + 0.0838715i \(0.973271\pi\)
\(674\) −245594. 245594.i −0.540628 0.540628i
\(675\) 103170.i 0.226436i
\(676\) 565875. + 237244.i 1.23830 + 0.519162i
\(677\) 438381. 0.956478 0.478239 0.878230i \(-0.341275\pi\)
0.478239 + 0.878230i \(0.341275\pi\)
\(678\) −334372. + 334372.i −0.727395 + 0.727395i
\(679\) −97754.1 −0.212029
\(680\) 206343.i 0.446244i
\(681\) 80940.0 80940.0i 0.174530 0.174530i
\(682\) −40258.7 + 40258.7i −0.0865549 + 0.0865549i
\(683\) −14323.9 14323.9i −0.0307057 0.0307057i 0.691587 0.722293i \(-0.256912\pi\)
−0.722293 + 0.691587i \(0.756912\pi\)
\(684\) 271944. + 271944.i 0.581255 + 0.581255i
\(685\) −1.07881e6 −2.29913
\(686\) 620620.i 1.31880i
\(687\) −129544. 129544.i −0.274475 0.274475i
\(688\) 386741.i 0.817039i
\(689\) 293828. + 441795.i 0.618949 + 0.930641i
\(690\) 456282. 0.958374
\(691\) 64315.1 64315.1i 0.134697 0.134697i −0.636544 0.771241i \(-0.719637\pi\)
0.771241 + 0.636544i \(0.219637\pi\)
\(692\) 59730.8 0.124734
\(693\) 63669.9i 0.132577i
\(694\) 795981. 795981.i 1.65266 1.65266i
\(695\) 328198. 328198.i 0.679464 0.679464i
\(696\) −94724.2 94724.2i −0.195543 0.195543i
\(697\) 133806. + 133806.i 0.275429 + 0.275429i
\(698\) 630216. 1.29354
\(699\) 116572.i 0.238583i
\(700\) 267910. + 267910.i 0.546755 + 0.546755i
\(701\) 77204.1i 0.157110i 0.996910 + 0.0785551i \(0.0250307\pi\)
−0.996910 + 0.0785551i \(0.974969\pi\)
\(702\) 142312. + 28625.3i 0.288780 + 0.0580865i
\(703\) −1.43678e6 −2.90723
\(704\) −435088. + 435088.i −0.877873 + 0.877873i
\(705\) −9185.89 −0.0184817
\(706\) 924298.i 1.85440i
\(707\) −94873.4 + 94873.4i −0.189804 + 0.189804i
\(708\) −441971. + 441971.i −0.881712 + 0.881712i
\(709\) 561910. + 561910.i 1.11783 + 1.11783i 0.992060 + 0.125766i \(0.0401389\pi\)
0.125766 + 0.992060i \(0.459861\pi\)
\(710\) 683279. + 683279.i 1.35544 + 1.35544i
\(711\) −253167. −0.500804
\(712\) 406353.i 0.801574i
\(713\) −26005.0 26005.0i −0.0511538 0.0511538i
\(714\) 127133.i 0.249380i
\(715\) −339421. 510348.i −0.663937 0.998285i
\(716\) −63857.3 −0.124562
\(717\) −347258. + 347258.i −0.675481 + 0.675481i
\(718\) 232857. 0.451690
\(719\) 324777.i 0.628243i −0.949383 0.314121i \(-0.898290\pi\)
0.949383 0.314121i \(-0.101710\pi\)
\(720\) −97309.2 + 97309.2i −0.187711 + 0.187711i
\(721\) 115191. 115191.i 0.221588 0.221588i
\(722\) 1.33886e6 + 1.33886e6i 2.56839 + 2.56839i
\(723\) −180967. 180967.i −0.346196 0.346196i
\(724\) 946013. 1.80476
\(725\) 564686.i 1.07431i
\(726\) 111853. + 111853.i 0.212215 + 0.212215i
\(727\) 922269.i 1.74497i −0.488638 0.872487i \(-0.662506\pi\)
0.488638 0.872487i \(-0.337494\pi\)
\(728\) −113302. + 75354.5i −0.213783 + 0.142183i
\(729\) 19683.0 0.0370370
\(730\) 697533. 697533.i 1.30894 1.30894i
\(731\) −466348. −0.872722
\(732\) 56288.4i 0.105050i
\(733\) 295621. 295621.i 0.550209 0.550209i −0.376292 0.926501i \(-0.622801\pi\)
0.926501 + 0.376292i \(0.122801\pi\)
\(734\) −28106.5 + 28106.5i −0.0521692 + 0.0521692i
\(735\) 247436. + 247436.i 0.458024 + 0.458024i
\(736\) −380346. 380346.i −0.702140 0.702140i
\(737\) −586623. −1.08000
\(738\) 187719.i 0.344663i
\(739\) 369186. + 369186.i 0.676015 + 0.676015i 0.959096 0.283081i \(-0.0913566\pi\)
−0.283081 + 0.959096i \(0.591357\pi\)
\(740\) 1.71714e6i 3.13576i
\(741\) 570791. + 114812.i 1.03954 + 0.209098i
\(742\) −460972. −0.837272
\(743\) −671107. + 671107.i −1.21567 + 1.21567i −0.246530 + 0.969135i \(0.579290\pi\)
−0.969135 + 0.246530i \(0.920710\pi\)
\(744\) −16498.6 −0.0298059
\(745\) 68707.2i 0.123791i
\(746\) 230689. 230689.i 0.414523 0.414523i
\(747\) 168196. 168196.i 0.301422 0.301422i
\(748\) −248911. 248911.i −0.444878 0.444878i
\(749\) 143502. + 143502.i 0.255796 + 0.255796i
\(750\) −129507. −0.230235
\(751\) 167627.i 0.297210i 0.988897 + 0.148605i \(0.0474784\pi\)
−0.988897 + 0.148605i \(0.952522\pi\)
\(752\) 4683.51 + 4683.51i 0.00828201 + 0.00828201i
\(753\) 24777.2i 0.0436981i
\(754\) −778924. 156676.i −1.37010 0.275588i
\(755\) 313125. 0.549319
\(756\) −51112.5 + 51112.5i −0.0894300 + 0.0894300i
\(757\) −578076. −1.00877 −0.504386 0.863478i \(-0.668281\pi\)
−0.504386 + 0.863478i \(0.668281\pi\)
\(758\) 797754.i 1.38845i
\(759\) 140492. 140492.i 0.243875 0.243875i
\(760\) 580537. 580537.i 1.00508 1.00508i
\(761\) −762616. 762616.i −1.31685 1.31685i −0.916254 0.400597i \(-0.868803\pi\)
−0.400597 0.916254i \(-0.631197\pi\)
\(762\) −247347. 247347.i −0.425987 0.425987i
\(763\) 409632. 0.703630
\(764\) 79252.6i 0.135777i
\(765\) −117340. 117340.i −0.200503 0.200503i
\(766\) 137768.i 0.234795i
\(767\) −186595. + 927666.i −0.317183 + 1.57689i
\(768\) 5516.94 0.00935354
\(769\) 698760. 698760.i 1.18161 1.18161i 0.202287 0.979326i \(-0.435163\pi\)
0.979326 0.202287i \(-0.0648374\pi\)
\(770\) 532501. 0.898129
\(771\) 326026.i 0.548457i
\(772\) 412850. 412850.i 0.692720 0.692720i
\(773\) −311294. + 311294.i −0.520968 + 0.520968i −0.917864 0.396895i \(-0.870088\pi\)
0.396895 + 0.917864i \(0.370088\pi\)
\(774\) −327125. 327125.i −0.546049 0.546049i
\(775\) 49177.2 + 49177.2i 0.0818766 + 0.0818766i
\(776\) 136849. 0.227258
\(777\) 270046.i 0.447296i
\(778\) −933166. 933166.i −1.54170 1.54170i
\(779\) 752912.i 1.24071i
\(780\) 137215. 682172.i 0.225535 1.12126i
\(781\) 420771. 0.689833
\(782\) 280527. 280527.i 0.458734 0.458734i
\(783\) −107732. −0.175720
\(784\) 252315.i 0.410498i
\(785\) 631996. 631996.i 1.02559 1.02559i
\(786\) −315455. + 315455.i −0.510614 + 0.510614i
\(787\) −528223. 528223.i −0.852841 0.852841i 0.137642 0.990482i \(-0.456048\pi\)
−0.990482 + 0.137642i \(0.956048\pi\)
\(788\) 341955. + 341955.i 0.550702 + 0.550702i
\(789\) 236014. 0.379127
\(790\) 2.11735e6i 3.39265i
\(791\) −252066. 252066.i −0.402866 0.402866i
\(792\) 89133.6i 0.142099i
\(793\) −47190.6 70955.0i −0.0750428 0.112833i
\(794\) −703706. −1.11622
\(795\) 425463. 425463.i 0.673175 0.673175i
\(796\) −500805. −0.790393
\(797\) 550495.i 0.866636i −0.901241 0.433318i \(-0.857343\pi\)
0.901241 0.433318i \(-0.142657\pi\)
\(798\) −357682. + 357682.i −0.561682 + 0.561682i
\(799\) −5647.58 + 5647.58i −0.00884644 + 0.00884644i
\(800\) 719260. + 719260.i 1.12384 + 1.12384i
\(801\) 231077. + 231077.i 0.360158 + 0.360158i
\(802\) −1.47681e6 −2.29602
\(803\) 429549.i 0.666165i
\(804\) −470925. 470925.i −0.728517 0.728517i
\(805\) 343967.i 0.530793i
\(806\) −81479.2 + 54190.0i −0.125423 + 0.0834160i
\(807\) 411565. 0.631963
\(808\) 132817. 132817.i 0.203437 0.203437i
\(809\) 705446. 1.07787 0.538936 0.842347i \(-0.318827\pi\)
0.538936 + 0.842347i \(0.318827\pi\)
\(810\) 164618.i 0.250904i
\(811\) 476089. 476089.i 0.723846 0.723846i −0.245540 0.969386i \(-0.578965\pi\)
0.969386 + 0.245540i \(0.0789654\pi\)
\(812\) 279757. 279757.i 0.424296 0.424296i
\(813\) −84076.5 84076.5i −0.127202 0.127202i
\(814\) 922481. + 922481.i 1.39222 + 1.39222i
\(815\) 1.26435e6 1.90350
\(816\) 119653.i 0.179699i
\(817\) −1.31205e6 1.31205e6i −1.96565 1.96565i
\(818\) 799064.i 1.19419i
\(819\) −21579.1 + 107282.i −0.0321711 + 0.159940i
\(820\) 899831. 1.33824
\(821\) 162224. 162224.i 0.240675 0.240675i −0.576455 0.817129i \(-0.695564\pi\)
0.817129 + 0.576455i \(0.195564\pi\)
\(822\) −930506. −1.37713
\(823\) 1.34448e6i 1.98497i 0.122378 + 0.992484i \(0.460948\pi\)
−0.122378 + 0.992484i \(0.539052\pi\)
\(824\) −161259. + 161259.i −0.237504 + 0.237504i
\(825\) −265679. + 265679.i −0.390346 + 0.390346i
\(826\) −581314. 581314.i −0.852022 0.852022i
\(827\) −542193. 542193.i −0.792762 0.792762i 0.189180 0.981942i \(-0.439417\pi\)
−0.981942 + 0.189180i \(0.939417\pi\)
\(828\) 225566. 0.329013
\(829\) 485612.i 0.706611i 0.935508 + 0.353305i \(0.114942\pi\)
−0.935508 + 0.353305i \(0.885058\pi\)
\(830\) −1.40671e6 1.40671e6i −2.04196 2.04196i
\(831\) 14986.9i 0.0217026i
\(832\) −880569. + 585648.i −1.27209 + 0.846038i
\(833\) 304253. 0.438474
\(834\) 283081. 283081.i 0.406985 0.406985i
\(835\) 905114. 1.29817
\(836\) 1.40060e6i 2.00401i
\(837\) −9382.13 + 9382.13i −0.0133922 + 0.0133922i
\(838\) 87135.4 87135.4i 0.124081 0.124081i
\(839\) 702797. + 702797.i 0.998404 + 0.998404i 0.999999 0.00159522i \(-0.000507774\pi\)
−0.00159522 + 0.999999i \(0.500508\pi\)
\(840\) 109113. + 109113.i 0.154639 + 0.154639i
\(841\) −117625. −0.166305
\(842\) 1.48239e6i 2.09092i
\(843\) −536403. 536403.i −0.754807 0.754807i
\(844\) 215815.i 0.302969i
\(845\) −398945. 974957.i −0.558727 1.36544i
\(846\) −7923.10 −0.0110702
\(847\) −84320.5 + 84320.5i −0.117535 + 0.117535i
\(848\) −433853. −0.603324
\(849\) 408322.i 0.566484i
\(850\) −530494. + 530494.i −0.734248 + 0.734248i
\(851\) −595874. + 595874.i −0.822801 + 0.822801i
\(852\) 337784. + 337784.i 0.465329 + 0.465329i
\(853\) 528758. + 528758.i 0.726706 + 0.726706i 0.969962 0.243256i \(-0.0782154\pi\)
−0.243256 + 0.969962i \(0.578215\pi\)
\(854\) 74034.9 0.101513
\(855\) 660259.i 0.903196i
\(856\) −200893. 200893.i −0.274169 0.274169i
\(857\) 427769.i 0.582435i 0.956657 + 0.291217i \(0.0940603\pi\)
−0.956657 + 0.291217i \(0.905940\pi\)
\(858\) −292761. 440191.i −0.397685 0.597952i
\(859\) −110526. −0.149788 −0.0748941 0.997191i \(-0.523862\pi\)
−0.0748941 + 0.997191i \(0.523862\pi\)
\(860\) −1.56807e6 + 1.56807e6i −2.12016 + 2.12016i
\(861\) −141512. −0.190891
\(862\) 1.10437e6i 1.48627i
\(863\) 115225. 115225.i 0.154713 0.154713i −0.625506 0.780219i \(-0.715108\pi\)
0.780219 + 0.625506i \(0.215108\pi\)
\(864\) −137222. + 137222.i −0.183822 + 0.183822i
\(865\) −72510.9 72510.9i −0.0969106 0.0969106i
\(866\) −298528. 298528.i −0.398060 0.398060i
\(867\) 289705. 0.385405
\(868\) 48726.7i 0.0646737i
\(869\) 651945. + 651945.i 0.863319 + 0.863319i
\(870\) 901014.i 1.19040i
\(871\) −988440. 198819.i −1.30291 0.262073i
\(872\) −573457. −0.754168
\(873\) 77820.9 77820.9i 0.102110 0.102110i
\(874\) 1.57850e6 2.06643
\(875\) 97628.6i 0.127515i
\(876\) 344831. 344831.i 0.449363 0.449363i
\(877\) 352595. 352595.i 0.458435 0.458435i −0.439707 0.898141i \(-0.644918\pi\)
0.898141 + 0.439707i \(0.144918\pi\)
\(878\) 490917. + 490917.i 0.636823 + 0.636823i
\(879\) −28529.2 28529.2i −0.0369243 0.0369243i
\(880\) 501174. 0.647177
\(881\) 776892.i 1.00094i 0.865753 + 0.500471i \(0.166840\pi\)
−0.865753 + 0.500471i \(0.833160\pi\)
\(882\) 213421. + 213421.i 0.274347 + 0.274347i
\(883\) 990585.i 1.27049i 0.772312 + 0.635244i \(0.219100\pi\)
−0.772312 + 0.635244i \(0.780900\pi\)
\(884\) −335045. 503768.i −0.428745 0.644653i
\(885\) 1.07307e6 1.37007
\(886\) −399445. + 399445.i −0.508849 + 0.508849i
\(887\) 951592. 1.20949 0.604747 0.796418i \(-0.293274\pi\)
0.604747 + 0.796418i \(0.293274\pi\)
\(888\) 378046.i 0.479423i
\(889\) 186462. 186462.i 0.235932 0.235932i
\(890\) 1.93261e6 1.93261e6i 2.43985 2.43985i
\(891\) −50686.9 50686.9i −0.0638470 0.0638470i
\(892\) −535912. 535912.i −0.673540 0.673540i
\(893\) −31778.4 −0.0398500
\(894\) 59262.0i 0.0741483i
\(895\) 77520.3 + 77520.3i 0.0967764 + 0.0967764i
\(896\) 388030.i 0.483336i
\(897\) 284340. 189108.i 0.353389 0.235031i
\(898\) 151887. 0.188352
\(899\) 51351.8 51351.8i 0.0635384 0.0635384i
\(900\) −426560. −0.526617
\(901\) 523158.i 0.644442i
\(902\) 483406. 483406.i 0.594154 0.594154i
\(903\) 246603. 246603.i 0.302428 0.302428i
\(904\) 352875. + 352875.i 0.431802 + 0.431802i
\(905\) −1.14842e6 1.14842e6i −1.40218 1.40218i
\(906\) 270080. 0.329030
\(907\) 122762.i 0.149228i −0.997212 0.0746141i \(-0.976227\pi\)
0.997212 0.0746141i \(-0.0237725\pi\)
\(908\) −334650. 334650.i −0.405900 0.405900i
\(909\) 151055.i 0.182814i
\(910\) 897246. + 180476.i 1.08350 + 0.217940i
\(911\) 93939.2 0.113191 0.0565953 0.998397i \(-0.481976\pi\)
0.0565953 + 0.998397i \(0.481976\pi\)
\(912\) −336639. + 336639.i −0.404739 + 0.404739i
\(913\) −866266. −1.03923
\(914\) 906796.i 1.08547i
\(915\) −68332.0 + 68332.0i −0.0816172 + 0.0816172i
\(916\) −535604. + 535604.i −0.638341 + 0.638341i
\(917\) −237805. 237805.i −0.282802 0.282802i
\(918\) −101209. 101209.i −0.120097 0.120097i
\(919\) 217922. 0.258030 0.129015 0.991643i \(-0.458818\pi\)
0.129015 + 0.991643i \(0.458818\pi\)
\(920\) 481531.i 0.568917i
\(921\) 190400. + 190400.i 0.224465 + 0.224465i
\(922\) 107215.i 0.126123i
\(923\) 708986. + 142609.i 0.832212 + 0.167395i
\(924\) 263246. 0.308331
\(925\) 1.12684e6 1.12684e6i 1.31697 1.31697i
\(926\) −1.35346e6 −1.57842
\(927\) 183404.i 0.213427i
\(928\) 751065. 751065.i 0.872131 0.872131i
\(929\) −489424. + 489424.i −0.567092 + 0.567092i −0.931313 0.364221i \(-0.881335\pi\)
0.364221 + 0.931313i \(0.381335\pi\)
\(930\) 78467.2 + 78467.2i 0.0907240 + 0.0907240i
\(931\) 856000. + 856000.i 0.987584 + 0.987584i
\(932\) 481972. 0.554868
\(933\) 296204.i 0.340274i
\(934\) −16797.4 16797.4i −0.0192552 0.0192552i
\(935\) 604337.i 0.691283i
\(936\) 30209.3 150187.i 0.0344818 0.171428i
\(937\) 74994.8 0.0854185 0.0427093 0.999088i \(-0.486401\pi\)
0.0427093 + 0.999088i \(0.486401\pi\)
\(938\) 619397. 619397.i 0.703985 0.703985i
\(939\) −877688. −0.995426
\(940\) 37979.4i 0.0429826i
\(941\) −746527. + 746527.i −0.843075 + 0.843075i −0.989258 0.146183i \(-0.953301\pi\)
0.146183 + 0.989258i \(0.453301\pi\)
\(942\) 545115. 545115.i 0.614308 0.614308i
\(943\) 312255. + 312255.i 0.351144 + 0.351144i
\(944\) −547115. 547115.i −0.613953 0.613953i
\(945\) 124097. 0.138963
\(946\) 1.68480e6i 1.88263i
\(947\) −392710. 392710.i −0.437897 0.437897i 0.453407 0.891304i \(-0.350208\pi\)
−0.891304 + 0.453407i \(0.850208\pi\)
\(948\) 1.04673e6i 1.16471i
\(949\) 145584. 723776.i 0.161652 0.803659i
\(950\) −2.98504e6 −3.30752
\(951\) −299224. + 299224.i −0.330854 + 0.330854i
\(952\) 134168. 0.148039
\(953\) 920738.i 1.01380i −0.862006 0.506898i \(-0.830792\pi\)
0.862006 0.506898i \(-0.169208\pi\)
\(954\) 366975. 366975.i 0.403218 0.403218i
\(955\) 96209.5 96209.5i 0.105490 0.105490i
\(956\) 1.43575e6 + 1.43575e6i 1.57095 + 1.57095i
\(957\) 277427. + 277427.i 0.302918 + 0.302918i
\(958\) −462756. −0.504221
\(959\) 701460.i 0.762721i
\(960\) 848018. + 848018.i 0.920158 + 0.920158i
\(961\) 914577.i 0.990315i
\(962\) 1.24170e6 + 1.86700e6i 1.34173 + 2.01741i
\(963\) −228481. −0.246375
\(964\) −748214. + 748214.i −0.805141 + 0.805141i
\(965\) −1.00237e6 −1.07640
\(966\) 296682.i 0.317934i
\(967\) −683545. + 683545.i −0.730994 + 0.730994i −0.970817 0.239823i \(-0.922911\pi\)
0.239823 + 0.970817i \(0.422911\pi\)
\(968\) 118043. 118043.i 0.125977 0.125977i
\(969\) −405934. 405934.i −0.432322 0.432322i
\(970\) −650853. 650853.i −0.691734 0.691734i
\(971\) −107226. −0.113726 −0.0568632 0.998382i \(-0.518110\pi\)
−0.0568632 + 0.998382i \(0.518110\pi\)
\(972\) 81380.1i 0.0861362i
\(973\) 213400. + 213400.i 0.225407 + 0.225407i
\(974\) 344080.i 0.362695i
\(975\) −537705. + 357616.i −0.565633 + 0.376190i
\(976\) 69679.4 0.0731484
\(977\) −730243. + 730243.i −0.765030 + 0.765030i −0.977227 0.212197i \(-0.931938\pi\)
0.212197 + 0.977227i \(0.431938\pi\)
\(978\) 1.09054e6 1.14015
\(979\) 1.19012e6i 1.24173i
\(980\) 1.02303e6 1.02303e6i 1.06522 1.06522i
\(981\) −326103. + 326103.i −0.338857 + 0.338857i
\(982\) −792514. 792514.i −0.821833 0.821833i
\(983\) 180212. + 180212.i 0.186500 + 0.186500i 0.794181 0.607681i \(-0.207900\pi\)
−0.607681 + 0.794181i \(0.707900\pi\)
\(984\) 198107. 0.204602
\(985\) 830241.i 0.855720i
\(986\) 553953. + 553953.i 0.569795 + 0.569795i
\(987\) 5972.82i 0.00613119i
\(988\) 474693. 2.35996e6i 0.486294 2.41763i
\(989\) −1.08829e6 −1.11263
\(990\) −423918. + 423918.i −0.432525 + 0.432525i
\(991\) −662719. −0.674811 −0.337405 0.941359i \(-0.609549\pi\)
−0.337405 + 0.941359i \(0.609549\pi\)
\(992\) 130817.i 0.132936i
\(993\) −700376. + 700376.i −0.710285 + 0.710285i
\(994\) −444280. + 444280.i −0.449659 + 0.449659i
\(995\) 607959. + 607959.i 0.614084 + 0.614084i
\(996\) −695415. 695415.i −0.701012 0.701012i
\(997\) 464482. 0.467281 0.233641 0.972323i \(-0.424936\pi\)
0.233641 + 0.972323i \(0.424936\pi\)
\(998\) 496899.i 0.498893i
\(999\) 214980. + 214980.i 0.215411 + 0.215411i
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 39.5.g.a.31.2 20
3.2 odd 2 117.5.j.b.109.9 20
13.8 odd 4 inner 39.5.g.a.34.2 yes 20
39.8 even 4 117.5.j.b.73.9 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
39.5.g.a.31.2 20 1.1 even 1 trivial
39.5.g.a.34.2 yes 20 13.8 odd 4 inner
117.5.j.b.73.9 20 39.8 even 4
117.5.j.b.109.9 20 3.2 odd 2