Properties

Label 65.3.h.a.38.2
Level $65$
Weight $3$
Character 65.38
Analytic conductor $1.771$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [65,3,Mod(12,65)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(65, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([1, 2]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("65.12");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 65 = 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 65.h (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: \(1.77112171834\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 38.2
Character \(\chi\) \(=\) 65.38
Dual form 65.3.h.a.12.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.14254 - 2.14254i) q^{2} +(1.85789 + 1.85789i) q^{3} +5.18097i q^{4} +(1.93662 + 4.60972i) q^{5} -7.96121i q^{6} +(5.84982 + 5.84982i) q^{7} +(2.53029 - 2.53029i) q^{8} -2.09649i q^{9} +O(q^{10})\) \(q+(-2.14254 - 2.14254i) q^{2} +(1.85789 + 1.85789i) q^{3} +5.18097i q^{4} +(1.93662 + 4.60972i) q^{5} -7.96121i q^{6} +(5.84982 + 5.84982i) q^{7} +(2.53029 - 2.53029i) q^{8} -2.09649i q^{9} +(5.72722 - 14.0258i) q^{10} -8.13517i q^{11} +(-9.62568 + 9.62568i) q^{12} +(12.9699 - 0.884166i) q^{13} -25.0670i q^{14} +(-4.96631 + 12.1624i) q^{15} +9.88140 q^{16} +(-15.0817 + 15.0817i) q^{17} +(-4.49182 + 4.49182i) q^{18} -7.91139 q^{19} +(-23.8828 + 10.0336i) q^{20} +21.7366i q^{21} +(-17.4299 + 17.4299i) q^{22} +(-0.359560 - 0.359560i) q^{23} +9.40199 q^{24} +(-17.4990 + 17.8546i) q^{25} +(-29.6829 - 25.8942i) q^{26} +(20.6161 - 20.6161i) q^{27} +(-30.3078 + 30.3078i) q^{28} -39.6950i q^{29} +(36.6989 - 15.4179i) q^{30} +10.3309i q^{31} +(-31.2925 - 31.2925i) q^{32} +(15.1142 - 15.1142i) q^{33} +64.6265 q^{34} +(-15.6371 + 38.2949i) q^{35} +10.8619 q^{36} +(14.3950 + 14.3950i) q^{37} +(16.9505 + 16.9505i) q^{38} +(25.7393 + 22.4540i) q^{39} +(16.5641 + 6.76370i) q^{40} -38.9872i q^{41} +(46.5717 - 46.5717i) q^{42} +(-37.8080 - 37.8080i) q^{43} +42.1481 q^{44} +(9.66423 - 4.06011i) q^{45} +1.54074i q^{46} +(-56.8456 - 56.8456i) q^{47} +(18.3586 + 18.3586i) q^{48} +19.4408i q^{49} +(75.7465 - 0.761848i) q^{50} -56.0404 q^{51} +(4.58084 + 67.1967i) q^{52} +(49.5278 + 49.5278i) q^{53} -88.3415 q^{54} +(37.5008 - 15.7548i) q^{55} +29.6034 q^{56} +(-14.6985 - 14.6985i) q^{57} +(-85.0483 + 85.0483i) q^{58} -37.9923 q^{59} +(-63.0130 - 25.7303i) q^{60} -27.8752 q^{61} +(22.1345 - 22.1345i) q^{62} +(12.2641 - 12.2641i) q^{63} +94.5653i q^{64} +(29.1936 + 58.0753i) q^{65} -64.7658 q^{66} +(17.5028 + 17.5028i) q^{67} +(-78.1381 - 78.1381i) q^{68} -1.33605i q^{69} +(115.552 - 48.5453i) q^{70} +106.949i q^{71} +(-5.30472 - 5.30472i) q^{72} +(67.9236 - 67.9236i) q^{73} -61.6836i q^{74} +(-65.6830 + 0.660631i) q^{75} -40.9887i q^{76} +(47.5893 - 47.5893i) q^{77} +(-7.03903 - 103.256i) q^{78} -106.988i q^{79} +(19.1366 + 45.5505i) q^{80} +57.7363 q^{81} +(-83.5318 + 83.5318i) q^{82} +(-8.61976 + 8.61976i) q^{83} -112.617 q^{84} +(-98.7301 - 40.3149i) q^{85} +162.011i q^{86} +(73.7490 - 73.7490i) q^{87} +(-20.5843 - 20.5843i) q^{88} +70.4135 q^{89} +(-29.4050 - 12.0071i) q^{90} +(81.0438 + 70.6993i) q^{91} +(1.86287 - 1.86287i) q^{92} +(-19.1937 + 19.1937i) q^{93} +243.588i q^{94} +(-15.3214 - 36.4693i) q^{95} -116.276i q^{96} +(-33.7421 - 33.7421i) q^{97} +(41.6527 - 41.6527i) q^{98} -17.0553 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 4 q^{3}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 4 q^{3} + 16 q^{10} + 72 q^{12} - 36 q^{13} - 104 q^{16} - 48 q^{17} + 8 q^{22} - 104 q^{23} - 88 q^{25} + 88 q^{26} + 56 q^{27} - 24 q^{30} - 64 q^{35} + 256 q^{36} + 124 q^{38} - 368 q^{40} + 216 q^{42} + 8 q^{43} + 196 q^{48} - 296 q^{51} + 16 q^{52} + 220 q^{53} + 332 q^{55} + 584 q^{56} - 8 q^{61} - 596 q^{62} + 420 q^{65} - 360 q^{66} - 640 q^{68} - 184 q^{75} + 388 q^{77} - 636 q^{78} - 224 q^{81} - 1004 q^{82} - 52 q^{87} + 780 q^{88} + 452 q^{90} - 512 q^{91} + 812 q^{92} - 136 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/65\mathbb{Z}\right)^\times\).

\(n\) \(27\) \(41\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.14254 2.14254i −1.07127 1.07127i −0.997257 0.0740139i \(-0.976419\pi\)
−0.0740139 0.997257i \(-0.523581\pi\)
\(3\) 1.85789 + 1.85789i 0.619297 + 0.619297i 0.945351 0.326054i \(-0.105719\pi\)
−0.326054 + 0.945351i \(0.605719\pi\)
\(4\) 5.18097i 1.29524i
\(5\) 1.93662 + 4.60972i 0.387325 + 0.921943i
\(6\) 7.96121i 1.32687i
\(7\) 5.84982 + 5.84982i 0.835688 + 0.835688i 0.988288 0.152600i \(-0.0487645\pi\)
−0.152600 + 0.988288i \(0.548765\pi\)
\(8\) 2.53029 2.53029i 0.316286 0.316286i
\(9\) 2.09649i 0.232944i
\(10\) 5.72722 14.0258i 0.572722 1.40258i
\(11\) 8.13517i 0.739561i −0.929119 0.369780i \(-0.879433\pi\)
0.929119 0.369780i \(-0.120567\pi\)
\(12\) −9.62568 + 9.62568i −0.802140 + 0.802140i
\(13\) 12.9699 0.884166i 0.997684 0.0680128i
\(14\) 25.0670i 1.79050i
\(15\) −4.96631 + 12.1624i −0.331088 + 0.810825i
\(16\) 9.88140 0.617588
\(17\) −15.0817 + 15.0817i −0.887161 + 0.887161i −0.994249 0.107089i \(-0.965847\pi\)
0.107089 + 0.994249i \(0.465847\pi\)
\(18\) −4.49182 + 4.49182i −0.249546 + 0.249546i
\(19\) −7.91139 −0.416389 −0.208194 0.978087i \(-0.566759\pi\)
−0.208194 + 0.978087i \(0.566759\pi\)
\(20\) −23.8828 + 10.0336i −1.19414 + 0.501680i
\(21\) 21.7366i 1.03508i
\(22\) −17.4299 + 17.4299i −0.792270 + 0.792270i
\(23\) −0.359560 0.359560i −0.0156330 0.0156330i 0.699247 0.714880i \(-0.253519\pi\)
−0.714880 + 0.699247i \(0.753519\pi\)
\(24\) 9.40199 0.391749
\(25\) −17.4990 + 17.8546i −0.699959 + 0.714183i
\(26\) −29.6829 25.8942i −1.14165 0.995930i
\(27\) 20.6161 20.6161i 0.763558 0.763558i
\(28\) −30.3078 + 30.3078i −1.08242 + 1.08242i
\(29\) 39.6950i 1.36879i −0.729109 0.684397i \(-0.760065\pi\)
0.729109 0.684397i \(-0.239935\pi\)
\(30\) 36.6989 15.4179i 1.22330 0.513929i
\(31\) 10.3309i 0.333256i 0.986020 + 0.166628i \(0.0532879\pi\)
−0.986020 + 0.166628i \(0.946712\pi\)
\(32\) −31.2925 31.2925i −0.977890 0.977890i
\(33\) 15.1142 15.1142i 0.458007 0.458007i
\(34\) 64.6265 1.90078
\(35\) −15.6371 + 38.2949i −0.446775 + 1.09414i
\(36\) 10.8619 0.301719
\(37\) 14.3950 + 14.3950i 0.389053 + 0.389053i 0.874350 0.485297i \(-0.161288\pi\)
−0.485297 + 0.874350i \(0.661288\pi\)
\(38\) 16.9505 + 16.9505i 0.446065 + 0.446065i
\(39\) 25.7393 + 22.4540i 0.659983 + 0.575743i
\(40\) 16.5641 + 6.76370i 0.414103 + 0.169092i
\(41\) 38.9872i 0.950908i −0.879741 0.475454i \(-0.842284\pi\)
0.879741 0.475454i \(-0.157716\pi\)
\(42\) 46.5717 46.5717i 1.10885 1.10885i
\(43\) −37.8080 37.8080i −0.879256 0.879256i 0.114201 0.993458i \(-0.463569\pi\)
−0.993458 + 0.114201i \(0.963569\pi\)
\(44\) 42.1481 0.957911
\(45\) 9.66423 4.06011i 0.214761 0.0902247i
\(46\) 1.54074i 0.0334944i
\(47\) −56.8456 56.8456i −1.20948 1.20948i −0.971195 0.238285i \(-0.923415\pi\)
−0.238285 0.971195i \(-0.576585\pi\)
\(48\) 18.3586 + 18.3586i 0.382470 + 0.382470i
\(49\) 19.4408i 0.396750i
\(50\) 75.7465 0.761848i 1.51493 0.0152370i
\(51\) −56.0404 −1.09883
\(52\) 4.58084 + 67.1967i 0.0880931 + 1.29224i
\(53\) 49.5278 + 49.5278i 0.934486 + 0.934486i 0.997982 0.0634958i \(-0.0202250\pi\)
−0.0634958 + 0.997982i \(0.520225\pi\)
\(54\) −88.3415 −1.63595
\(55\) 37.5008 15.7548i 0.681833 0.286450i
\(56\) 29.6034 0.528633
\(57\) −14.6985 14.6985i −0.257868 0.257868i
\(58\) −85.0483 + 85.0483i −1.46635 + 1.46635i
\(59\) −37.9923 −0.643937 −0.321969 0.946750i \(-0.604345\pi\)
−0.321969 + 0.946750i \(0.604345\pi\)
\(60\) −63.0130 25.7303i −1.05022 0.428839i
\(61\) −27.8752 −0.456971 −0.228486 0.973547i \(-0.573377\pi\)
−0.228486 + 0.973547i \(0.573377\pi\)
\(62\) 22.1345 22.1345i 0.357007 0.357007i
\(63\) 12.2641 12.2641i 0.194668 0.194668i
\(64\) 94.5653i 1.47758i
\(65\) 29.1936 + 58.0753i 0.449132 + 0.893466i
\(66\) −64.7658 −0.981300
\(67\) 17.5028 + 17.5028i 0.261235 + 0.261235i 0.825556 0.564320i \(-0.190862\pi\)
−0.564320 + 0.825556i \(0.690862\pi\)
\(68\) −78.1381 78.1381i −1.14909 1.14909i
\(69\) 1.33605i 0.0193630i
\(70\) 115.552 48.5453i 1.65074 0.693504i
\(71\) 106.949i 1.50633i 0.657831 + 0.753165i \(0.271474\pi\)
−0.657831 + 0.753165i \(0.728526\pi\)
\(72\) −5.30472 5.30472i −0.0736767 0.0736767i
\(73\) 67.9236 67.9236i 0.930460 0.930460i −0.0672743 0.997735i \(-0.521430\pi\)
0.997735 + 0.0672743i \(0.0214303\pi\)
\(74\) 61.6836i 0.833562i
\(75\) −65.6830 + 0.660631i −0.875773 + 0.00880841i
\(76\) 40.9887i 0.539325i
\(77\) 47.5893 47.5893i 0.618042 0.618042i
\(78\) −7.03903 103.256i −0.0902440 1.32380i
\(79\) 106.988i 1.35428i −0.735853 0.677141i \(-0.763219\pi\)
0.735853 0.677141i \(-0.236781\pi\)
\(80\) 19.1366 + 45.5505i 0.239207 + 0.569381i
\(81\) 57.7363 0.712794
\(82\) −83.5318 + 83.5318i −1.01868 + 1.01868i
\(83\) −8.61976 + 8.61976i −0.103853 + 0.103853i −0.757124 0.653271i \(-0.773396\pi\)
0.653271 + 0.757124i \(0.273396\pi\)
\(84\) −112.617 −1.34068
\(85\) −98.7301 40.3149i −1.16153 0.474293i
\(86\) 162.011i 1.88384i
\(87\) 73.7490 73.7490i 0.847690 0.847690i
\(88\) −20.5843 20.5843i −0.233913 0.233913i
\(89\) 70.4135 0.791163 0.395581 0.918431i \(-0.370543\pi\)
0.395581 + 0.918431i \(0.370543\pi\)
\(90\) −29.4050 12.0071i −0.326722 0.133412i
\(91\) 81.0438 + 70.6993i 0.890591 + 0.776916i
\(92\) 1.86287 1.86287i 0.0202486 0.0202486i
\(93\) −19.1937 + 19.1937i −0.206384 + 0.206384i
\(94\) 243.588i 2.59136i
\(95\) −15.3214 36.4693i −0.161278 0.383887i
\(96\) 116.276i 1.21121i
\(97\) −33.7421 33.7421i −0.347856 0.347856i 0.511454 0.859310i \(-0.329107\pi\)
−0.859310 + 0.511454i \(0.829107\pi\)
\(98\) 41.6527 41.6527i 0.425027 0.425027i
\(99\) −17.0553 −0.172276
\(100\) −92.5040 90.6618i −0.925040 0.906618i
\(101\) 129.417 1.28136 0.640681 0.767807i \(-0.278652\pi\)
0.640681 + 0.767807i \(0.278652\pi\)
\(102\) 120.069 + 120.069i 1.17715 + 1.17715i
\(103\) −91.5406 91.5406i −0.888744 0.888744i 0.105659 0.994402i \(-0.466305\pi\)
−0.994402 + 0.105659i \(0.966305\pi\)
\(104\) 30.5804 35.0548i 0.294042 0.337065i
\(105\) −100.200 + 42.0957i −0.954283 + 0.400911i
\(106\) 212.231i 2.00218i
\(107\) −113.834 + 113.834i −1.06387 + 1.06387i −0.0660525 + 0.997816i \(0.521040\pi\)
−0.997816 + 0.0660525i \(0.978960\pi\)
\(108\) 106.811 + 106.811i 0.988993 + 0.988993i
\(109\) 1.96303 0.0180095 0.00900474 0.999959i \(-0.497134\pi\)
0.00900474 + 0.999959i \(0.497134\pi\)
\(110\) −114.102 46.5919i −1.03729 0.423563i
\(111\) 53.4885i 0.481878i
\(112\) 57.8044 + 57.8044i 0.516111 + 0.516111i
\(113\) 152.551 + 152.551i 1.35001 + 1.35001i 0.885646 + 0.464361i \(0.153716\pi\)
0.464361 + 0.885646i \(0.346284\pi\)
\(114\) 62.9843i 0.552494i
\(115\) 0.961137 2.35380i 0.00835772 0.0204678i
\(116\) 205.659 1.77292
\(117\) −1.85365 27.1913i −0.0158431 0.232404i
\(118\) 81.4001 + 81.4001i 0.689832 + 0.689832i
\(119\) −176.451 −1.48278
\(120\) 18.2081 + 43.3405i 0.151734 + 0.361171i
\(121\) 54.8190 0.453050
\(122\) 59.7239 + 59.7239i 0.489540 + 0.489540i
\(123\) 72.4340 72.4340i 0.588894 0.588894i
\(124\) −53.5243 −0.431648
\(125\) −116.193 46.0878i −0.929547 0.368702i
\(126\) −52.5527 −0.417085
\(127\) −32.1405 + 32.1405i −0.253075 + 0.253075i −0.822230 0.569155i \(-0.807270\pi\)
0.569155 + 0.822230i \(0.307270\pi\)
\(128\) 77.4402 77.4402i 0.605001 0.605001i
\(129\) 140.486i 1.08904i
\(130\) 61.8803 186.977i 0.476002 1.43829i
\(131\) −69.7160 −0.532184 −0.266092 0.963948i \(-0.585732\pi\)
−0.266092 + 0.963948i \(0.585732\pi\)
\(132\) 78.3065 + 78.3065i 0.593231 + 0.593231i
\(133\) −46.2802 46.2802i −0.347971 0.347971i
\(134\) 75.0008i 0.559708i
\(135\) 134.960 + 55.1087i 0.999702 + 0.408212i
\(136\) 76.3222i 0.561193i
\(137\) 66.6819 + 66.6819i 0.486729 + 0.486729i 0.907273 0.420543i \(-0.138160\pi\)
−0.420543 + 0.907273i \(0.638160\pi\)
\(138\) −2.86253 + 2.86253i −0.0207430 + 0.0207430i
\(139\) 2.94331i 0.0211749i 0.999944 + 0.0105875i \(0.00337015\pi\)
−0.999944 + 0.0105875i \(0.996630\pi\)
\(140\) −198.405 81.0155i −1.41718 0.578682i
\(141\) 211.226i 1.49805i
\(142\) 229.144 229.144i 1.61369 1.61369i
\(143\) −7.19284 105.512i −0.0502996 0.737848i
\(144\) 20.7163i 0.143863i
\(145\) 182.983 76.8743i 1.26195 0.530168i
\(146\) −291.058 −1.99355
\(147\) −36.1188 + 36.1188i −0.245706 + 0.245706i
\(148\) −74.5799 + 74.5799i −0.503918 + 0.503918i
\(149\) 143.091 0.960343 0.480171 0.877175i \(-0.340574\pi\)
0.480171 + 0.877175i \(0.340574\pi\)
\(150\) 142.144 + 139.313i 0.947627 + 0.928754i
\(151\) 116.794i 0.773468i 0.922191 + 0.386734i \(0.126397\pi\)
−0.922191 + 0.386734i \(0.873603\pi\)
\(152\) −20.0181 + 20.0181i −0.131698 + 0.131698i
\(153\) 31.6187 + 31.6187i 0.206658 + 0.206658i
\(154\) −203.924 −1.32418
\(155\) −47.6227 + 20.0071i −0.307243 + 0.129078i
\(156\) −116.333 + 133.355i −0.745727 + 0.854838i
\(157\) −151.195 + 151.195i −0.963027 + 0.963027i −0.999340 0.0363137i \(-0.988438\pi\)
0.0363137 + 0.999340i \(0.488438\pi\)
\(158\) −229.227 + 229.227i −1.45080 + 1.45080i
\(159\) 184.034i 1.15745i
\(160\) 83.6477 204.851i 0.522798 1.28032i
\(161\) 4.20672i 0.0261287i
\(162\) −123.702 123.702i −0.763595 0.763595i
\(163\) −170.294 + 170.294i −1.04475 + 1.04475i −0.0457966 + 0.998951i \(0.514583\pi\)
−0.998951 + 0.0457966i \(0.985417\pi\)
\(164\) 201.992 1.23166
\(165\) 98.9430 + 40.4018i 0.599655 + 0.244859i
\(166\) 36.9364 0.222508
\(167\) −115.052 115.052i −0.688931 0.688931i 0.273064 0.961996i \(-0.411963\pi\)
−0.961996 + 0.273064i \(0.911963\pi\)
\(168\) 54.9999 + 54.9999i 0.327381 + 0.327381i
\(169\) 167.437 22.9351i 0.990749 0.135711i
\(170\) 125.157 + 297.910i 0.736218 + 1.75241i
\(171\) 16.5862i 0.0969951i
\(172\) 195.882 195.882i 1.13885 1.13885i
\(173\) −178.343 178.343i −1.03088 1.03088i −0.999508 0.0313760i \(-0.990011\pi\)
−0.0313760 0.999508i \(-0.509989\pi\)
\(174\) −316.021 −1.81621
\(175\) −206.812 + 2.08009i −1.18178 + 0.0118862i
\(176\) 80.3869i 0.456744i
\(177\) −70.5855 70.5855i −0.398788 0.398788i
\(178\) −150.864 150.864i −0.847550 0.847550i
\(179\) 109.444i 0.611417i 0.952125 + 0.305709i \(0.0988934\pi\)
−0.952125 + 0.305709i \(0.901107\pi\)
\(180\) 21.0353 + 50.0701i 0.116863 + 0.278167i
\(181\) −176.025 −0.972516 −0.486258 0.873815i \(-0.661639\pi\)
−0.486258 + 0.873815i \(0.661639\pi\)
\(182\) −22.1634 325.116i −0.121777 1.78635i
\(183\) −51.7891 51.7891i −0.283001 0.283001i
\(184\) −1.81958 −0.00988902
\(185\) −38.4791 + 94.2343i −0.207995 + 0.509375i
\(186\) 82.2468 0.442187
\(187\) 122.692 + 122.692i 0.656109 + 0.656109i
\(188\) 294.515 294.515i 1.56657 1.56657i
\(189\) 241.200 1.27619
\(190\) −45.3103 + 110.964i −0.238475 + 0.584019i
\(191\) 268.857 1.40763 0.703815 0.710384i \(-0.251479\pi\)
0.703815 + 0.710384i \(0.251479\pi\)
\(192\) −175.692 + 175.692i −0.915062 + 0.915062i
\(193\) −185.483 + 185.483i −0.961053 + 0.961053i −0.999269 0.0382165i \(-0.987832\pi\)
0.0382165 + 0.999269i \(0.487832\pi\)
\(194\) 144.588i 0.745297i
\(195\) −53.6590 + 162.136i −0.275175 + 0.831466i
\(196\) −100.722 −0.513888
\(197\) −21.7152 21.7152i −0.110229 0.110229i 0.649841 0.760070i \(-0.274835\pi\)
−0.760070 + 0.649841i \(0.774835\pi\)
\(198\) 36.5417 + 36.5417i 0.184554 + 0.184554i
\(199\) 66.5114i 0.334228i −0.985938 0.167114i \(-0.946555\pi\)
0.985938 0.167114i \(-0.0534448\pi\)
\(200\) 0.899723 + 89.4546i 0.00449861 + 0.447273i
\(201\) 65.0364i 0.323564i
\(202\) −277.282 277.282i −1.37269 1.37269i
\(203\) 232.209 232.209i 1.14389 1.14389i
\(204\) 290.344i 1.42325i
\(205\) 179.720 75.5035i 0.876683 0.368310i
\(206\) 392.259i 1.90417i
\(207\) −0.753814 + 0.753814i −0.00364161 + 0.00364161i
\(208\) 128.161 8.73680i 0.616158 0.0420038i
\(209\) 64.3605i 0.307945i
\(210\) 304.874 + 124.490i 1.45178 + 0.592812i
\(211\) 21.9873 0.104205 0.0521027 0.998642i \(-0.483408\pi\)
0.0521027 + 0.998642i \(0.483408\pi\)
\(212\) −256.602 + 256.602i −1.21039 + 1.21039i
\(213\) −198.700 + 198.700i −0.932866 + 0.932866i
\(214\) 487.788 2.27938
\(215\) 101.064 247.504i 0.470067 1.15118i
\(216\) 104.329i 0.483005i
\(217\) −60.4341 + 60.4341i −0.278498 + 0.278498i
\(218\) −4.20588 4.20588i −0.0192930 0.0192930i
\(219\) 252.389 1.15246
\(220\) 81.6250 + 194.291i 0.371023 + 0.883140i
\(221\) −182.274 + 208.943i −0.824768 + 0.945445i
\(222\) 114.601 114.601i 0.516222 0.516222i
\(223\) 57.1409 57.1409i 0.256237 0.256237i −0.567285 0.823522i \(-0.692006\pi\)
0.823522 + 0.567285i \(0.192006\pi\)
\(224\) 366.111i 1.63442i
\(225\) 37.4319 + 36.6865i 0.166364 + 0.163051i
\(226\) 653.693i 2.89245i
\(227\) 176.929 + 176.929i 0.779424 + 0.779424i 0.979733 0.200309i \(-0.0641945\pi\)
−0.200309 + 0.979733i \(0.564195\pi\)
\(228\) 76.1525 76.1525i 0.334002 0.334002i
\(229\) −110.421 −0.482189 −0.241094 0.970502i \(-0.577506\pi\)
−0.241094 + 0.970502i \(0.577506\pi\)
\(230\) −7.10240 + 2.98384i −0.0308800 + 0.0129732i
\(231\) 176.831 0.765503
\(232\) −100.440 100.440i −0.432930 0.432930i
\(233\) −5.66668 5.66668i −0.0243205 0.0243205i 0.694842 0.719162i \(-0.255474\pi\)
−0.719162 + 0.694842i \(0.755474\pi\)
\(234\) −54.2870 + 62.2300i −0.231996 + 0.265940i
\(235\) 151.954 372.130i 0.646611 1.58353i
\(236\) 196.837i 0.834056i
\(237\) 198.772 198.772i 0.838702 0.838702i
\(238\) 378.053 + 378.053i 1.58846 + 1.58846i
\(239\) −215.554 −0.901901 −0.450950 0.892549i \(-0.648915\pi\)
−0.450950 + 0.892549i \(0.648915\pi\)
\(240\) −49.0742 + 120.181i −0.204476 + 0.500756i
\(241\) 72.6956i 0.301642i 0.988561 + 0.150821i \(0.0481917\pi\)
−0.988561 + 0.150821i \(0.951808\pi\)
\(242\) −117.452 117.452i −0.485339 0.485339i
\(243\) −78.2768 78.2768i −0.322127 0.322127i
\(244\) 144.421i 0.591889i
\(245\) −89.6164 + 37.6494i −0.365781 + 0.153671i
\(246\) −310.386 −1.26173
\(247\) −102.610 + 6.99498i −0.415425 + 0.0283198i
\(248\) 26.1402 + 26.1402i 0.105404 + 0.105404i
\(249\) −32.0291 −0.128631
\(250\) 150.204 + 347.694i 0.600817 + 1.39078i
\(251\) 1.33457 0.00531702 0.00265851 0.999996i \(-0.499154\pi\)
0.00265851 + 0.999996i \(0.499154\pi\)
\(252\) 63.5400 + 63.5400i 0.252143 + 0.252143i
\(253\) −2.92508 + 2.92508i −0.0115616 + 0.0115616i
\(254\) 137.725 0.542224
\(255\) −108.529 258.330i −0.425604 1.01306i
\(256\) 46.4233 0.181341
\(257\) −17.9322 + 17.9322i −0.0697753 + 0.0697753i −0.741133 0.671358i \(-0.765711\pi\)
0.671358 + 0.741133i \(0.265711\pi\)
\(258\) −300.998 + 300.998i −1.16666 + 1.16666i
\(259\) 168.416i 0.650254i
\(260\) −300.886 + 151.251i −1.15726 + 0.581735i
\(261\) −83.2203 −0.318852
\(262\) 149.370 + 149.370i 0.570113 + 0.570113i
\(263\) −131.362 131.362i −0.499473 0.499473i 0.411801 0.911274i \(-0.364900\pi\)
−0.911274 + 0.411801i \(0.864900\pi\)
\(264\) 76.4868i 0.289723i
\(265\) −132.392 + 324.226i −0.499594 + 1.22349i
\(266\) 198.315i 0.745543i
\(267\) 130.820 + 130.820i 0.489964 + 0.489964i
\(268\) −90.6814 + 90.6814i −0.338363 + 0.338363i
\(269\) 299.295i 1.11262i 0.830975 + 0.556310i \(0.187783\pi\)
−0.830975 + 0.556310i \(0.812217\pi\)
\(270\) −171.084 407.230i −0.633645 1.50826i
\(271\) 388.157i 1.43231i −0.697940 0.716156i \(-0.745900\pi\)
0.697940 0.716156i \(-0.254100\pi\)
\(272\) −149.029 + 149.029i −0.547900 + 0.547900i
\(273\) 19.2188 + 281.922i 0.0703985 + 1.03268i
\(274\) 285.738i 1.04284i
\(275\) 145.250 + 142.357i 0.528181 + 0.517663i
\(276\) 6.92202 0.0250798
\(277\) −136.515 + 136.515i −0.492833 + 0.492833i −0.909198 0.416365i \(-0.863304\pi\)
0.416365 + 0.909198i \(0.363304\pi\)
\(278\) 6.30617 6.30617i 0.0226841 0.0226841i
\(279\) 21.6587 0.0776298
\(280\) 57.3307 + 136.463i 0.204752 + 0.487370i
\(281\) 16.8095i 0.0598205i 0.999553 + 0.0299102i \(0.00952214\pi\)
−0.999553 + 0.0299102i \(0.990478\pi\)
\(282\) −452.560 + 452.560i −1.60482 + 1.60482i
\(283\) 172.741 + 172.741i 0.610391 + 0.610391i 0.943048 0.332657i \(-0.107945\pi\)
−0.332657 + 0.943048i \(0.607945\pi\)
\(284\) −554.103 −1.95107
\(285\) 39.2905 96.2213i 0.137861 0.337619i
\(286\) −210.654 + 241.476i −0.736551 + 0.844320i
\(287\) 228.068 228.068i 0.794663 0.794663i
\(288\) −65.6044 + 65.6044i −0.227793 + 0.227793i
\(289\) 165.917i 0.574108i
\(290\) −556.755 227.342i −1.91984 0.783938i
\(291\) 125.378i 0.430852i
\(292\) 351.910 + 351.910i 1.20517 + 1.20517i
\(293\) 41.8279 41.8279i 0.142757 0.142757i −0.632116 0.774874i \(-0.717814\pi\)
0.774874 + 0.632116i \(0.217814\pi\)
\(294\) 154.772 0.526436
\(295\) −73.5768 175.134i −0.249413 0.593674i
\(296\) 72.8468 0.246104
\(297\) −167.715 167.715i −0.564697 0.564697i
\(298\) −306.579 306.579i −1.02879 1.02879i
\(299\) −4.98137 4.34554i −0.0166601 0.0145336i
\(300\) −3.42271 340.302i −0.0114090 1.13434i
\(301\) 442.340i 1.46957i
\(302\) 250.235 250.235i 0.828593 0.828593i
\(303\) 240.443 + 240.443i 0.793543 + 0.793543i
\(304\) −78.1756 −0.257157
\(305\) −53.9838 128.497i −0.176996 0.421302i
\(306\) 135.489i 0.442774i
\(307\) 74.7402 + 74.7402i 0.243453 + 0.243453i 0.818277 0.574824i \(-0.194929\pi\)
−0.574824 + 0.818277i \(0.694929\pi\)
\(308\) 246.559 + 246.559i 0.800515 + 0.800515i
\(309\) 340.145i 1.10079i
\(310\) 144.900 + 59.1675i 0.467418 + 0.190863i
\(311\) 86.8500 0.279260 0.139630 0.990204i \(-0.455409\pi\)
0.139630 + 0.990204i \(0.455409\pi\)
\(312\) 121.943 8.31292i 0.390842 0.0266440i
\(313\) −219.953 219.953i −0.702726 0.702726i 0.262269 0.964995i \(-0.415529\pi\)
−0.964995 + 0.262269i \(0.915529\pi\)
\(314\) 647.884 2.06333
\(315\) 80.2849 + 32.7831i 0.254873 + 0.104073i
\(316\) 554.303 1.75412
\(317\) 180.080 + 180.080i 0.568076 + 0.568076i 0.931589 0.363513i \(-0.118423\pi\)
−0.363513 + 0.931589i \(0.618423\pi\)
\(318\) 394.301 394.301i 1.23994 1.23994i
\(319\) −322.926 −1.01231
\(320\) −435.919 + 183.137i −1.36225 + 0.572304i
\(321\) −422.982 −1.31770
\(322\) −9.01308 + 9.01308i −0.0279909 + 0.0279909i
\(323\) 119.317 119.317i 0.369404 0.369404i
\(324\) 299.130i 0.923242i
\(325\) −211.174 + 247.044i −0.649765 + 0.760135i
\(326\) 729.723 2.23842
\(327\) 3.64710 + 3.64710i 0.0111532 + 0.0111532i
\(328\) −98.6489 98.6489i −0.300759 0.300759i
\(329\) 665.072i 2.02150i
\(330\) −125.427 298.552i −0.380082 0.904703i
\(331\) 163.850i 0.495015i −0.968886 0.247508i \(-0.920388\pi\)
0.968886 0.247508i \(-0.0796115\pi\)
\(332\) −44.6588 44.6588i −0.134514 0.134514i
\(333\) 30.1789 30.1789i 0.0906274 0.0906274i
\(334\) 493.006i 1.47606i
\(335\) −46.7866 + 114.579i −0.139661 + 0.342027i
\(336\) 214.788i 0.639251i
\(337\) −79.9086 + 79.9086i −0.237117 + 0.237117i −0.815655 0.578538i \(-0.803623\pi\)
0.578538 + 0.815655i \(0.303623\pi\)
\(338\) −407.879 309.600i −1.20674 0.915977i
\(339\) 566.845i 1.67211i
\(340\) 208.870 511.518i 0.614325 1.50447i
\(341\) 84.0439 0.246463
\(342\) 35.5366 35.5366i 0.103908 0.103908i
\(343\) 172.916 172.916i 0.504129 0.504129i
\(344\) −191.330 −0.556193
\(345\) 6.15879 2.58742i 0.0178516 0.00749975i
\(346\) 764.214i 2.20871i
\(347\) −96.4247 + 96.4247i −0.277881 + 0.277881i −0.832263 0.554382i \(-0.812955\pi\)
0.554382 + 0.832263i \(0.312955\pi\)
\(348\) 382.092 + 382.092i 1.09796 + 1.09796i
\(349\) −207.740 −0.595243 −0.297622 0.954684i \(-0.596193\pi\)
−0.297622 + 0.954684i \(0.596193\pi\)
\(350\) 447.560 + 438.646i 1.27874 + 1.25328i
\(351\) 249.160 285.616i 0.709858 0.813721i
\(352\) −254.570 + 254.570i −0.723209 + 0.723209i
\(353\) 147.867 147.867i 0.418886 0.418886i −0.465934 0.884820i \(-0.654281\pi\)
0.884820 + 0.465934i \(0.154281\pi\)
\(354\) 302.465i 0.854421i
\(355\) −493.007 + 207.121i −1.38875 + 0.583439i
\(356\) 364.810i 1.02475i
\(357\) −327.826 327.826i −0.918280 0.918280i
\(358\) 234.488 234.488i 0.654994 0.654994i
\(359\) 17.3232 0.0482541 0.0241270 0.999709i \(-0.492319\pi\)
0.0241270 + 0.999709i \(0.492319\pi\)
\(360\) 14.1800 34.7265i 0.0393890 0.0964626i
\(361\) −298.410 −0.826620
\(362\) 377.142 + 377.142i 1.04183 + 1.04183i
\(363\) 101.848 + 101.848i 0.280572 + 0.280572i
\(364\) −366.291 + 419.886i −1.00630 + 1.15353i
\(365\) 444.651 + 181.566i 1.21822 + 0.497442i
\(366\) 221.921i 0.606341i
\(367\) 375.328 375.328i 1.02269 1.02269i 0.0229563 0.999736i \(-0.492692\pi\)
0.999736 0.0229563i \(-0.00730785\pi\)
\(368\) −3.55296 3.55296i −0.00965477 0.00965477i
\(369\) −81.7364 −0.221508
\(370\) 284.344 119.458i 0.768497 0.322859i
\(371\) 579.457i 1.56188i
\(372\) −99.4423 99.4423i −0.267318 0.267318i
\(373\) −20.6902 20.6902i −0.0554698 0.0554698i 0.678828 0.734298i \(-0.262488\pi\)
−0.734298 + 0.678828i \(0.762488\pi\)
\(374\) 525.747i 1.40574i
\(375\) −130.249 301.501i −0.347329 0.804002i
\(376\) −287.671 −0.765083
\(377\) −35.0970 514.841i −0.0930955 1.36562i
\(378\) −516.782 516.782i −1.36715 1.36715i
\(379\) −550.791 −1.45327 −0.726637 0.687021i \(-0.758918\pi\)
−0.726637 + 0.687021i \(0.758918\pi\)
\(380\) 188.946 79.3797i 0.497227 0.208894i
\(381\) −119.427 −0.313457
\(382\) −576.038 576.038i −1.50795 1.50795i
\(383\) −265.558 + 265.558i −0.693363 + 0.693363i −0.962970 0.269607i \(-0.913106\pi\)
0.269607 + 0.962970i \(0.413106\pi\)
\(384\) 287.751 0.749351
\(385\) 311.536 + 127.211i 0.809183 + 0.330417i
\(386\) 794.811 2.05910
\(387\) −79.2642 + 79.2642i −0.204817 + 0.204817i
\(388\) 174.817 174.817i 0.450559 0.450559i
\(389\) 262.682i 0.675275i 0.941276 + 0.337638i \(0.109628\pi\)
−0.941276 + 0.337638i \(0.890372\pi\)
\(390\) 462.350 232.416i 1.18551 0.595939i
\(391\) 10.8456 0.0277380
\(392\) 49.1907 + 49.1907i 0.125487 + 0.125487i
\(393\) −129.525 129.525i −0.329579 0.329579i
\(394\) 93.0513i 0.236171i
\(395\) 493.186 207.196i 1.24857 0.524547i
\(396\) 88.3631i 0.223139i
\(397\) 546.439 + 546.439i 1.37642 + 1.37642i 0.850588 + 0.525833i \(0.176246\pi\)
0.525833 + 0.850588i \(0.323754\pi\)
\(398\) −142.503 + 142.503i −0.358049 + 0.358049i
\(399\) 171.967i 0.430995i
\(400\) −172.915 + 176.428i −0.432286 + 0.441070i
\(401\) 318.719i 0.794810i −0.917643 0.397405i \(-0.869911\pi\)
0.917643 0.397405i \(-0.130089\pi\)
\(402\) 139.343 139.343i 0.346625 0.346625i
\(403\) 9.13426 + 133.991i 0.0226657 + 0.332484i
\(404\) 670.509i 1.65967i
\(405\) 111.813 + 266.148i 0.276083 + 0.657156i
\(406\) −995.034 −2.45082
\(407\) 117.105 117.105i 0.287728 0.287728i
\(408\) −141.798 + 141.798i −0.347545 + 0.347545i
\(409\) 213.233 0.521352 0.260676 0.965426i \(-0.416055\pi\)
0.260676 + 0.965426i \(0.416055\pi\)
\(410\) −546.827 223.288i −1.33373 0.544606i
\(411\) 247.775i 0.602860i
\(412\) 474.270 474.270i 1.15114 1.15114i
\(413\) −222.248 222.248i −0.538131 0.538131i
\(414\) 3.23016 0.00780231
\(415\) −56.4279 23.0414i −0.135971 0.0555215i
\(416\) −433.528 378.192i −1.04213 0.909116i
\(417\) −5.46835 + 5.46835i −0.0131135 + 0.0131135i
\(418\) 137.895 137.895i 0.329893 0.329893i
\(419\) 246.659i 0.588685i 0.955700 + 0.294343i \(0.0951007\pi\)
−0.955700 + 0.294343i \(0.904899\pi\)
\(420\) −218.097 519.132i −0.519278 1.23603i
\(421\) 587.204i 1.39478i 0.716690 + 0.697392i \(0.245656\pi\)
−0.716690 + 0.697392i \(0.754344\pi\)
\(422\) −47.1088 47.1088i −0.111632 0.111632i
\(423\) −119.176 + 119.176i −0.281741 + 0.281741i
\(424\) 250.639 0.591130
\(425\) −5.36278 533.193i −0.0126183 1.25457i
\(426\) 851.448 1.99870
\(427\) −163.065 163.065i −0.381885 0.381885i
\(428\) −589.771 589.771i −1.37797 1.37797i
\(429\) 182.667 209.394i 0.425797 0.488097i
\(430\) −746.823 + 313.753i −1.73680 + 0.729659i
\(431\) 159.391i 0.369817i 0.982756 + 0.184909i \(0.0591989\pi\)
−0.982756 + 0.184909i \(0.940801\pi\)
\(432\) 203.716 203.716i 0.471564 0.471564i
\(433\) 535.308 + 535.308i 1.23628 + 1.23628i 0.961511 + 0.274767i \(0.0886009\pi\)
0.274767 + 0.961511i \(0.411399\pi\)
\(434\) 258.965 0.596694
\(435\) 482.786 + 197.138i 1.10985 + 0.453191i
\(436\) 10.1704i 0.0233267i
\(437\) 2.84462 + 2.84462i 0.00650942 + 0.00650942i
\(438\) −540.754 540.754i −1.23460 1.23460i
\(439\) 48.6760i 0.110879i 0.998462 + 0.0554396i \(0.0176560\pi\)
−0.998462 + 0.0554396i \(0.982344\pi\)
\(440\) 55.0238 134.752i 0.125054 0.306254i
\(441\) 40.7574 0.0924204
\(442\) 838.199 57.1405i 1.89638 0.129277i
\(443\) 51.4871 + 51.4871i 0.116224 + 0.116224i 0.762827 0.646603i \(-0.223811\pi\)
−0.646603 + 0.762827i \(0.723811\pi\)
\(444\) −277.123 −0.624150
\(445\) 136.364 + 324.586i 0.306437 + 0.729407i
\(446\) −244.853 −0.548999
\(447\) 265.847 + 265.847i 0.594737 + 0.594737i
\(448\) −553.190 + 553.190i −1.23480 + 1.23480i
\(449\) −208.122 −0.463524 −0.231762 0.972773i \(-0.574449\pi\)
−0.231762 + 0.972773i \(0.574449\pi\)
\(450\) −1.59721 158.802i −0.00354935 0.352893i
\(451\) −317.168 −0.703254
\(452\) −790.362 + 790.362i −1.74859 + 1.74859i
\(453\) −216.990 + 216.990i −0.479006 + 0.479006i
\(454\) 758.157i 1.66995i
\(455\) −168.953 + 510.507i −0.371325 + 1.12199i
\(456\) −74.3828 −0.163120
\(457\) −132.896 132.896i −0.290800 0.290800i 0.546596 0.837396i \(-0.315923\pi\)
−0.837396 + 0.546596i \(0.815923\pi\)
\(458\) 236.582 + 236.582i 0.516555 + 0.516555i
\(459\) 621.852i 1.35480i
\(460\) 12.1950 + 4.97963i 0.0265108 + 0.0108253i
\(461\) 493.512i 1.07052i −0.844686 0.535262i \(-0.820213\pi\)
0.844686 0.535262i \(-0.179787\pi\)
\(462\) −378.868 378.868i −0.820061 0.820061i
\(463\) 255.494 255.494i 0.551823 0.551823i −0.375144 0.926967i \(-0.622407\pi\)
0.926967 + 0.375144i \(0.122407\pi\)
\(464\) 392.243i 0.845351i
\(465\) −125.649 51.3067i −0.270212 0.110337i
\(466\) 24.2822i 0.0521077i
\(467\) 399.519 399.519i 0.855502 0.855502i −0.135302 0.990804i \(-0.543201\pi\)
0.990804 + 0.135302i \(0.0432006\pi\)
\(468\) 140.877 9.60369i 0.301020 0.0205207i
\(469\) 204.776i 0.436623i
\(470\) −1122.87 + 471.738i −2.38909 + 1.00370i
\(471\) −561.808 −1.19280
\(472\) −96.1314 + 96.1314i −0.203668 + 0.203668i
\(473\) −307.575 + 307.575i −0.650263 + 0.650263i
\(474\) −851.757 −1.79695
\(475\) 138.441 141.254i 0.291455 0.297378i
\(476\) 914.187i 1.92056i
\(477\) 103.835 103.835i 0.217683 0.217683i
\(478\) 461.834 + 461.834i 0.966180 + 0.966180i
\(479\) 52.5979 0.109808 0.0549039 0.998492i \(-0.482515\pi\)
0.0549039 + 0.998492i \(0.482515\pi\)
\(480\) 535.999 225.183i 1.11666 0.469130i
\(481\) 199.429 + 173.974i 0.414613 + 0.361692i
\(482\) 155.753 155.753i 0.323140 0.323140i
\(483\) 7.81562 7.81562i 0.0161814 0.0161814i
\(484\) 284.016i 0.586810i
\(485\) 90.1957 220.887i 0.185971 0.455437i
\(486\) 335.423i 0.690171i
\(487\) −96.3440 96.3440i −0.197832 0.197832i 0.601238 0.799070i \(-0.294674\pi\)
−0.799070 + 0.601238i \(0.794674\pi\)
\(488\) −70.5323 + 70.5323i −0.144533 + 0.144533i
\(489\) −632.774 −1.29402
\(490\) 272.672 + 111.341i 0.556474 + 0.227228i
\(491\) −444.562 −0.905421 −0.452710 0.891658i \(-0.649543\pi\)
−0.452710 + 0.891658i \(0.649543\pi\)
\(492\) 375.279 + 375.279i 0.762761 + 0.762761i
\(493\) 598.670 + 598.670i 1.21434 + 1.21434i
\(494\) 234.833 + 204.859i 0.475371 + 0.414694i
\(495\) −33.0297 78.6202i −0.0667267 0.158829i
\(496\) 102.084i 0.205815i
\(497\) −625.635 + 625.635i −1.25882 + 1.25882i
\(498\) 68.6238 + 68.6238i 0.137799 + 0.137799i
\(499\) 604.573 1.21157 0.605785 0.795629i \(-0.292859\pi\)
0.605785 + 0.795629i \(0.292859\pi\)
\(500\) 238.780 601.995i 0.477560 1.20399i
\(501\) 427.506i 0.853306i
\(502\) −2.85938 2.85938i −0.00569597 0.00569597i
\(503\) 289.710 + 289.710i 0.575964 + 0.575964i 0.933789 0.357825i \(-0.116482\pi\)
−0.357825 + 0.933789i \(0.616482\pi\)
\(504\) 62.0634i 0.123142i
\(505\) 250.633 + 596.578i 0.496303 + 1.18134i
\(506\) 12.5342 0.0247712
\(507\) 353.689 + 268.468i 0.697612 + 0.529522i
\(508\) −166.519 166.519i −0.327794 0.327794i
\(509\) 725.956 1.42624 0.713119 0.701043i \(-0.247282\pi\)
0.713119 + 0.701043i \(0.247282\pi\)
\(510\) −320.955 + 786.012i −0.629324 + 1.54120i
\(511\) 794.682 1.55515
\(512\) −409.225 409.225i −0.799267 0.799267i
\(513\) −163.102 + 163.102i −0.317937 + 0.317937i
\(514\) 76.8412 0.149496
\(515\) 244.697 599.256i 0.475139 1.16360i
\(516\) 727.856 1.41057
\(517\) −462.448 + 462.448i −0.894484 + 0.894484i
\(518\) 360.838 360.838i 0.696598 0.696598i
\(519\) 662.683i 1.27685i
\(520\) 220.815 + 73.0790i 0.424644 + 0.140537i
\(521\) −238.823 −0.458394 −0.229197 0.973380i \(-0.573610\pi\)
−0.229197 + 0.973380i \(0.573610\pi\)
\(522\) 178.303 + 178.303i 0.341577 + 0.341577i
\(523\) 192.082 + 192.082i 0.367270 + 0.367270i 0.866481 0.499211i \(-0.166377\pi\)
−0.499211 + 0.866481i \(0.666377\pi\)
\(524\) 361.197i 0.689307i
\(525\) −388.098 380.369i −0.739235 0.724513i
\(526\) 562.895i 1.07014i
\(527\) −155.808 155.808i −0.295652 0.295652i
\(528\) 149.350 149.350i 0.282860 0.282860i
\(529\) 528.741i 0.999511i
\(530\) 978.323 411.011i 1.84589 0.775492i
\(531\) 79.6505i 0.150001i
\(532\) 239.777 239.777i 0.450708 0.450708i
\(533\) −34.4712 505.660i −0.0646739 0.948706i
\(534\) 560.577i 1.04977i
\(535\) −745.196 304.289i −1.39289 0.568764i
\(536\) 88.5740 0.165250
\(537\) −203.334 + 203.334i −0.378649 + 0.378649i
\(538\) 641.252 641.252i 1.19192 1.19192i
\(539\) 158.154 0.293421
\(540\) −285.517 + 699.223i −0.528734 + 1.29486i
\(541\) 574.763i 1.06241i −0.847244 0.531205i \(-0.821740\pi\)
0.847244 0.531205i \(-0.178260\pi\)
\(542\) −831.642 + 831.642i −1.53439 + 1.53439i
\(543\) −327.036 327.036i −0.602276 0.602276i
\(544\) 943.889 1.73509
\(545\) 3.80166 + 9.04903i 0.00697552 + 0.0166037i
\(546\) 562.853 645.207i 1.03087 1.18170i
\(547\) −73.3806 + 73.3806i −0.134151 + 0.134151i −0.770994 0.636843i \(-0.780240\pi\)
0.636843 + 0.770994i \(0.280240\pi\)
\(548\) −345.477 + 345.477i −0.630433 + 0.630433i
\(549\) 58.4402i 0.106448i
\(550\) −6.19776 616.210i −0.0112687 1.12038i
\(551\) 314.043i 0.569951i
\(552\) −3.38058 3.38058i −0.00612423 0.00612423i
\(553\) 625.862 625.862i 1.13176 1.13176i
\(554\) 584.977 1.05592
\(555\) −246.567 + 103.587i −0.444265 + 0.186643i
\(556\) −15.2492 −0.0274267
\(557\) 14.5118 + 14.5118i 0.0260535 + 0.0260535i 0.720014 0.693960i \(-0.244136\pi\)
−0.693960 + 0.720014i \(0.744136\pi\)
\(558\) −46.4047 46.4047i −0.0831626 0.0831626i
\(559\) −523.795 456.938i −0.937021 0.817420i
\(560\) −154.517 + 378.407i −0.275923 + 0.675728i
\(561\) 455.898i 0.812652i
\(562\) 36.0152 36.0152i 0.0640839 0.0640839i
\(563\) −366.360 366.360i −0.650729 0.650729i 0.302440 0.953168i \(-0.402199\pi\)
−0.953168 + 0.302440i \(0.902199\pi\)
\(564\) 1094.35 1.94034
\(565\) −407.783 + 998.649i −0.721739 + 1.76752i
\(566\) 740.208i 1.30779i
\(567\) 337.747 + 337.747i 0.595674 + 0.595674i
\(568\) 270.613 + 270.613i 0.476431 + 0.476431i
\(569\) 125.290i 0.220194i 0.993921 + 0.110097i \(0.0351161\pi\)
−0.993921 + 0.110097i \(0.964884\pi\)
\(570\) −290.340 + 121.977i −0.509368 + 0.213994i
\(571\) 74.4532 0.130391 0.0651955 0.997873i \(-0.479233\pi\)
0.0651955 + 0.997873i \(0.479233\pi\)
\(572\) 546.657 37.2659i 0.955693 0.0651502i
\(573\) 499.507 + 499.507i 0.871740 + 0.871740i
\(574\) −977.292 −1.70260
\(575\) 12.7117 0.127853i 0.0221073 0.000222353i
\(576\) 198.255 0.344193
\(577\) −733.284 733.284i −1.27086 1.27086i −0.945640 0.325216i \(-0.894563\pi\)
−0.325216 0.945640i \(-0.605437\pi\)
\(578\) −355.484 + 355.484i −0.615025 + 0.615025i
\(579\) −689.215 −1.19035
\(580\) 398.284 + 948.030i 0.686696 + 1.63453i
\(581\) −100.848 −0.173577
\(582\) −268.628 + 268.628i −0.461560 + 0.461560i
\(583\) 402.917 402.917i 0.691109 0.691109i
\(584\) 343.732i 0.588583i
\(585\) 121.754 61.2040i 0.208127 0.104622i
\(586\) −179.236 −0.305863
\(587\) −176.214 176.214i −0.300195 0.300195i 0.540895 0.841090i \(-0.318086\pi\)
−0.841090 + 0.540895i \(0.818086\pi\)
\(588\) −187.131 187.131i −0.318249 0.318249i
\(589\) 81.7321i 0.138764i
\(590\) −217.590 + 532.873i −0.368797 + 0.903174i
\(591\) 80.6887i 0.136529i
\(592\) 142.242 + 142.242i 0.240274 + 0.240274i
\(593\) −324.274 + 324.274i −0.546836 + 0.546836i −0.925524 0.378689i \(-0.876375\pi\)
0.378689 + 0.925524i \(0.376375\pi\)
\(594\) 718.673i 1.20989i
\(595\) −341.719 813.388i −0.574317 1.36704i
\(596\) 741.351i 1.24388i
\(597\) 123.571 123.571i 0.206986 0.206986i
\(598\) 1.36227 + 19.9833i 0.00227805 + 0.0334169i
\(599\) 505.327i 0.843618i 0.906685 + 0.421809i \(0.138605\pi\)
−0.906685 + 0.421809i \(0.861395\pi\)
\(600\) −164.525 + 167.868i −0.274209 + 0.279781i
\(601\) 153.252 0.254995 0.127497 0.991839i \(-0.459306\pi\)
0.127497 + 0.991839i \(0.459306\pi\)
\(602\) −947.732 + 947.732i −1.57431 + 1.57431i
\(603\) 36.6944 36.6944i 0.0608531 0.0608531i
\(604\) −605.105 −1.00183
\(605\) 106.164 + 252.700i 0.175477 + 0.417686i
\(606\) 1030.32i 1.70020i
\(607\) 85.7922 85.7922i 0.141338 0.141338i −0.632897 0.774236i \(-0.718135\pi\)
0.774236 + 0.632897i \(0.218135\pi\)
\(608\) 247.567 + 247.567i 0.407182 + 0.407182i
\(609\) 862.837 1.41681
\(610\) −159.648 + 390.973i −0.261717 + 0.640939i
\(611\) −787.542 687.020i −1.28894 1.12442i
\(612\) −163.816 + 163.816i −0.267673 + 0.267673i
\(613\) 196.289 196.289i 0.320210 0.320210i −0.528637 0.848848i \(-0.677297\pi\)
0.848848 + 0.528637i \(0.177297\pi\)
\(614\) 320.268i 0.521609i
\(615\) 474.177 + 193.623i 0.771020 + 0.314834i
\(616\) 240.829i 0.390956i
\(617\) −305.676 305.676i −0.495423 0.495423i 0.414587 0.910010i \(-0.363926\pi\)
−0.910010 + 0.414587i \(0.863926\pi\)
\(618\) −728.774 + 728.774i −1.17925 + 1.17925i
\(619\) −782.801 −1.26462 −0.632311 0.774715i \(-0.717893\pi\)
−0.632311 + 0.774715i \(0.717893\pi\)
\(620\) −103.656 246.732i −0.167188 0.397955i
\(621\) −14.8254 −0.0238735
\(622\) −186.080 186.080i −0.299164 0.299164i
\(623\) 411.906 + 411.906i 0.661166 + 0.661166i
\(624\) 254.341 + 221.877i 0.407597 + 0.355572i
\(625\) −12.5711 624.874i −0.0201137 0.999798i
\(626\) 942.518i 1.50562i
\(627\) −119.575 + 119.575i −0.190709 + 0.190709i
\(628\) −783.338 783.338i −1.24735 1.24735i
\(629\) −434.202 −0.690305
\(630\) −101.775 242.253i −0.161547 0.384529i
\(631\) 109.969i 0.174278i 0.996196 + 0.0871390i \(0.0277724\pi\)
−0.996196 + 0.0871390i \(0.972228\pi\)
\(632\) −270.711 270.711i −0.428340 0.428340i
\(633\) 40.8500 + 40.8500i 0.0645340 + 0.0645340i
\(634\) 771.658i 1.21713i
\(635\) −210.403 85.9146i −0.331343 0.135299i
\(636\) −953.477 −1.49918
\(637\) 17.1889 + 252.145i 0.0269841 + 0.395832i
\(638\) 691.882 + 691.882i 1.08445 + 1.08445i
\(639\) 224.219 0.350890
\(640\) 506.950 + 207.005i 0.792109 + 0.323445i
\(641\) 1036.39 1.61683 0.808413 0.588616i \(-0.200327\pi\)
0.808413 + 0.588616i \(0.200327\pi\)
\(642\) 906.256 + 906.256i 1.41161 + 1.41161i
\(643\) −510.295 + 510.295i −0.793616 + 0.793616i −0.982080 0.188464i \(-0.939649\pi\)
0.188464 + 0.982080i \(0.439649\pi\)
\(644\) 21.7949 0.0338430
\(645\) 647.602 272.069i 1.00403 0.421812i
\(646\) −511.285 −0.791463
\(647\) 821.330 821.330i 1.26944 1.26944i 0.323068 0.946376i \(-0.395286\pi\)
0.946376 0.323068i \(-0.104714\pi\)
\(648\) 146.089 146.089i 0.225447 0.225447i
\(649\) 309.074i 0.476231i
\(650\) 981.750 76.8535i 1.51039 0.118236i
\(651\) −224.560 −0.344946
\(652\) −882.288 882.288i −1.35320 1.35320i
\(653\) −804.144 804.144i −1.23146 1.23146i −0.963403 0.268058i \(-0.913618\pi\)
−0.268058 0.963403i \(-0.586382\pi\)
\(654\) 15.6281i 0.0238962i
\(655\) −135.014 321.371i −0.206128 0.490643i
\(656\) 385.249i 0.587269i
\(657\) −142.401 142.401i −0.216745 0.216745i
\(658\) −1424.95 + 1424.95i −2.16557 + 2.16557i
\(659\) 74.8778i 0.113623i −0.998385 0.0568117i \(-0.981907\pi\)
0.998385 0.0568117i \(-0.0180935\pi\)
\(660\) −209.321 + 512.621i −0.317153 + 0.776699i
\(661\) 374.898i 0.567168i −0.958947 0.283584i \(-0.908477\pi\)
0.958947 0.283584i \(-0.0915234\pi\)
\(662\) −351.056 + 351.056i −0.530295 + 0.530295i
\(663\) −726.838 + 49.5490i −1.09629 + 0.0747345i
\(664\) 43.6209i 0.0656942i
\(665\) 123.711 302.966i 0.186032 0.455588i
\(666\) −129.319 −0.194173
\(667\) −14.2727 + 14.2727i −0.0213984 + 0.0213984i
\(668\) 596.079 596.079i 0.892334 0.892334i
\(669\) 212.323 0.317373
\(670\) 345.733 145.248i 0.516019 0.216789i
\(671\) 226.770i 0.337958i
\(672\) 680.193 680.193i 1.01219 1.01219i
\(673\) 151.987 + 151.987i 0.225835 + 0.225835i 0.810950 0.585115i \(-0.198951\pi\)
−0.585115 + 0.810950i \(0.698951\pi\)
\(674\) 342.415 0.508034
\(675\) 7.33069 + 728.851i 0.0108603 + 1.07978i
\(676\) 118.826 + 867.484i 0.175778 + 1.28326i
\(677\) 523.082 523.082i 0.772646 0.772646i −0.205922 0.978568i \(-0.566019\pi\)
0.978568 + 0.205922i \(0.0660193\pi\)
\(678\) 1214.49 1214.49i 1.79128 1.79128i
\(679\) 394.770i 0.581399i
\(680\) −351.824 + 147.807i −0.517388 + 0.217364i
\(681\) 657.430i 0.965389i
\(682\) −180.068 180.068i −0.264029 0.264029i
\(683\) −465.705 + 465.705i −0.681853 + 0.681853i −0.960417 0.278565i \(-0.910141\pi\)
0.278565 + 0.960417i \(0.410141\pi\)
\(684\) −85.9325 −0.125632
\(685\) −178.247 + 436.523i −0.260215 + 0.637259i
\(686\) −740.960 −1.08012
\(687\) −205.150 205.150i −0.298618 0.298618i
\(688\) −373.596 373.596i −0.543018 0.543018i
\(689\) 686.161 + 598.579i 0.995879 + 0.868765i
\(690\) −18.7391 7.65182i −0.0271581 0.0110896i
\(691\) 446.872i 0.646704i 0.946279 + 0.323352i \(0.104810\pi\)
−0.946279 + 0.323352i \(0.895190\pi\)
\(692\) 923.990 923.990i 1.33525 1.33525i
\(693\) −99.7705 99.7705i −0.143969 0.143969i
\(694\) 413.188 0.595372
\(695\) −13.5678 + 5.70008i −0.0195221 + 0.00820156i
\(696\) 373.212i 0.536224i
\(697\) 587.995 + 587.995i 0.843608 + 0.843608i
\(698\) 445.091 + 445.091i 0.637667 + 0.637667i
\(699\) 21.0561i 0.0301232i
\(700\) −10.7769 1071.49i −0.0153955 1.53070i
\(701\) −605.527 −0.863804 −0.431902 0.901921i \(-0.642157\pi\)
−0.431902 + 0.901921i \(0.642157\pi\)
\(702\) −1145.78 + 78.1086i −1.63217 + 0.111266i
\(703\) −113.884 113.884i −0.161997 0.161997i
\(704\) 769.304 1.09276
\(705\) 973.690 409.064i 1.38112 0.580233i
\(706\) −633.622 −0.897481
\(707\) 757.069 + 757.069i 1.07082 + 1.07082i
\(708\) 365.702 365.702i 0.516528 0.516528i
\(709\) 331.454 0.467496 0.233748 0.972297i \(-0.424901\pi\)
0.233748 + 0.972297i \(0.424901\pi\)
\(710\) 1500.05 + 612.523i 2.11275 + 0.862708i
\(711\) −224.300 −0.315471
\(712\) 178.166 178.166i 0.250234 0.250234i
\(713\) 3.71459 3.71459i 0.00520980 0.00520980i
\(714\) 1404.76i 1.96745i
\(715\) 472.452 237.494i 0.660772 0.332160i
\(716\) −567.025 −0.791934
\(717\) −400.476 400.476i −0.558544 0.558544i
\(718\) −37.1157 37.1157i −0.0516932 0.0516932i
\(719\) 142.878i 0.198718i 0.995052 + 0.0993591i \(0.0316792\pi\)
−0.995052 + 0.0993591i \(0.968321\pi\)
\(720\) 95.4962 40.1196i 0.132634 0.0557217i
\(721\) 1070.99i 1.48543i
\(722\) 639.356 + 639.356i 0.885534 + 0.885534i
\(723\) −135.060 + 135.060i −0.186806 + 0.186806i
\(724\) 911.983i 1.25965i
\(725\) 708.738 + 694.623i 0.977569 + 0.958100i
\(726\) 436.426i 0.601138i
\(727\) −218.258 + 218.258i −0.300218 + 0.300218i −0.841099 0.540881i \(-0.818091\pi\)
0.540881 + 0.841099i \(0.318091\pi\)
\(728\) 383.954 26.1743i 0.527409 0.0359538i
\(729\) 810.486i 1.11178i
\(730\) −563.670 1341.70i −0.772151 1.83794i
\(731\) 1140.42 1.56008
\(732\) 268.318 268.318i 0.366555 0.366555i
\(733\) 541.958 541.958i 0.739370 0.739370i −0.233086 0.972456i \(-0.574882\pi\)
0.972456 + 0.233086i \(0.0748824\pi\)
\(734\) −1608.31 −2.19116
\(735\) −236.446 96.5490i −0.321695 0.131359i
\(736\) 22.5030i 0.0305748i
\(737\) 142.388 142.388i 0.193199 0.193199i
\(738\) 175.124 + 175.124i 0.237295 + 0.237295i
\(739\) 192.974 0.261128 0.130564 0.991440i \(-0.458321\pi\)
0.130564 + 0.991440i \(0.458321\pi\)
\(740\) −488.225 199.359i −0.659764 0.269404i
\(741\) −203.634 177.642i −0.274809 0.239733i
\(742\) 1241.51 1241.51i 1.67320 1.67320i
\(743\) −547.384 + 547.384i −0.736722 + 0.736722i −0.971942 0.235220i \(-0.924419\pi\)
0.235220 + 0.971942i \(0.424419\pi\)
\(744\) 97.1313i 0.130553i
\(745\) 277.113 + 659.610i 0.371964 + 0.885382i
\(746\) 88.6594i 0.118846i
\(747\) 18.0713 + 18.0713i 0.0241918 + 0.0241918i
\(748\) −635.666 + 635.666i −0.849821 + 0.849821i
\(749\) −1331.82 −1.77813
\(750\) −366.915 + 925.041i −0.489220 + 1.23339i
\(751\) 1416.39 1.88601 0.943004 0.332780i \(-0.107987\pi\)
0.943004 + 0.332780i \(0.107987\pi\)
\(752\) −561.714 561.714i −0.746960 0.746960i
\(753\) 2.47949 + 2.47949i 0.00329281 + 0.00329281i
\(754\) −1027.87 + 1178.26i −1.36322 + 1.56268i
\(755\) −538.385 + 226.185i −0.713093 + 0.299583i
\(756\) 1249.65i 1.65298i
\(757\) −130.692 + 130.692i −0.172644 + 0.172644i −0.788140 0.615496i \(-0.788956\pi\)
0.615496 + 0.788140i \(0.288956\pi\)
\(758\) 1180.09 + 1180.09i 1.55685 + 1.55685i
\(759\) −10.8690 −0.0143201
\(760\) −131.045 53.5102i −0.172428 0.0704082i
\(761\) 527.493i 0.693158i 0.938021 + 0.346579i \(0.112657\pi\)
−0.938021 + 0.346579i \(0.887343\pi\)
\(762\) 255.877 + 255.877i 0.335797 + 0.335797i
\(763\) 11.4834 + 11.4834i 0.0150503 + 0.0150503i
\(764\) 1392.94i 1.82322i
\(765\) −84.5198 + 206.987i −0.110483 + 0.270571i
\(766\) 1137.94 1.48556
\(767\) −492.756 + 33.5915i −0.642446 + 0.0437960i
\(768\) 86.2495 + 86.2495i 0.112304 + 0.112304i
\(769\) 1162.78 1.51206 0.756032 0.654535i \(-0.227136\pi\)
0.756032 + 0.654535i \(0.227136\pi\)
\(770\) −394.924 940.032i −0.512888 1.22082i
\(771\) −66.6323 −0.0864232
\(772\) −960.984 960.984i −1.24480 1.24480i
\(773\) −51.0887 + 51.0887i −0.0660915 + 0.0660915i −0.739380 0.673288i \(-0.764881\pi\)
0.673288 + 0.739380i \(0.264881\pi\)
\(774\) 339.654 0.438829
\(775\) −184.454 180.781i −0.238006 0.233266i
\(776\) −170.754 −0.220044
\(777\) −312.898 + 312.898i −0.402700 + 0.402700i
\(778\) 562.807 562.807i 0.723403 0.723403i
\(779\) 308.443i 0.395948i
\(780\) −840.022 278.006i −1.07695 0.356418i
\(781\) 870.052 1.11402
\(782\) −23.2371 23.2371i −0.0297149 0.0297149i
\(783\) −818.355 818.355i −1.04515 1.04515i
\(784\) 192.102i 0.245028i
\(785\) −989.775 404.159i −1.26086 0.514852i
\(786\) 555.024i 0.706138i
\(787\) −42.2712 42.2712i −0.0537118 0.0537118i 0.679741 0.733453i \(-0.262092\pi\)
−0.733453 + 0.679741i \(0.762092\pi\)
\(788\) 112.506 112.506i 0.142774 0.142774i
\(789\) 488.110i 0.618644i
\(790\) −1500.60 612.745i −1.89949 0.775627i
\(791\) 1784.79i 2.25637i
\(792\) −43.1548 + 43.1548i −0.0544884 + 0.0544884i
\(793\) −361.539 + 24.6463i −0.455913 + 0.0310799i
\(794\) 2341.54i 2.94904i
\(795\) −848.346 + 356.405i −1.06710 + 0.448308i
\(796\) 344.594 0.432907
\(797\) 58.3327 58.3327i 0.0731903 0.0731903i −0.669564 0.742754i \(-0.733519\pi\)
0.742754 + 0.669564i \(0.233519\pi\)
\(798\) −368.447 + 368.447i −0.461713 + 0.461713i
\(799\) 1714.66 2.14601
\(800\) 1106.30 11.1270i 1.38288 0.0139088i
\(801\) 147.621i 0.184296i
\(802\) −682.869 + 682.869i −0.851457 + 0.851457i
\(803\) −552.570 552.570i −0.688132 0.688132i
\(804\) −336.952 −0.419095
\(805\) 19.3918 8.14683i 0.0240892 0.0101203i
\(806\) 267.511 306.652i 0.331900 0.380462i
\(807\) −556.057 + 556.057i −0.689042 + 0.689042i
\(808\) 327.463 327.463i 0.405276 0.405276i
\(809\) 1297.47i 1.60380i 0.597461 + 0.801898i \(0.296176\pi\)
−0.597461 + 0.801898i \(0.703824\pi\)
\(810\) 330.668 809.798i 0.408233 0.999751i
\(811\) 1185.64i 1.46195i −0.682405 0.730974i \(-0.739066\pi\)
0.682405 0.730974i \(-0.260934\pi\)
\(812\) 1203.07 + 1203.07i 1.48161 + 1.48161i
\(813\) 721.152 721.152i 0.887026 0.887026i
\(814\) −501.807 −0.616470
\(815\) −1114.80 455.211i −1.36785 0.558542i
\(816\) −553.758 −0.678625
\(817\) 299.114 + 299.114i 0.366113 + 0.366113i
\(818\) −456.860 456.860i −0.558509 0.558509i
\(819\) 148.221 169.908i 0.180978 0.207457i
\(820\) 391.182 + 931.125i 0.477051 + 1.13552i
\(821\) 378.986i 0.461615i −0.972999 0.230807i \(-0.925863\pi\)
0.972999 0.230807i \(-0.0741367\pi\)
\(822\) 530.869 530.869i 0.645826 0.645826i
\(823\) −879.804 879.804i −1.06902 1.06902i −0.997434 0.0715868i \(-0.977194\pi\)
−0.0715868 0.997434i \(-0.522806\pi\)
\(824\) −463.248 −0.562194
\(825\) 5.37435 + 534.342i 0.00651436 + 0.647688i
\(826\) 952.352i 1.15297i
\(827\) 695.484 + 695.484i 0.840972 + 0.840972i 0.988985 0.148014i \(-0.0472880\pi\)
−0.148014 + 0.988985i \(0.547288\pi\)
\(828\) −3.90549 3.90549i −0.00471678 0.00471678i
\(829\) 59.4731i 0.0717407i 0.999356 + 0.0358704i \(0.0114203\pi\)
−0.999356 + 0.0358704i \(0.988580\pi\)
\(830\) 71.5319 + 170.266i 0.0861830 + 0.205140i
\(831\) −507.259 −0.610420
\(832\) 83.6114 + 1226.50i 0.100494 + 1.47416i
\(833\) −293.200 293.200i −0.351981 0.351981i
\(834\) 23.4323 0.0280963
\(835\) 307.544 753.166i 0.368316 0.901996i
\(836\) −333.450 −0.398864
\(837\) 212.983 + 212.983i 0.254460 + 0.254460i
\(838\) 528.478 528.478i 0.630641 0.630641i
\(839\) −1394.24 −1.66179 −0.830893 0.556432i \(-0.812170\pi\)
−0.830893 + 0.556432i \(0.812170\pi\)
\(840\) −147.020 + 360.048i −0.175024 + 0.428629i
\(841\) −734.696 −0.873598
\(842\) 1258.11 1258.11i 1.49419 1.49419i
\(843\) −31.2303 + 31.2303i −0.0370466 + 0.0370466i
\(844\) 113.916i 0.134971i
\(845\) 429.986 + 727.418i 0.508859 + 0.860850i
\(846\) 510.680 0.603641
\(847\) 320.681 + 320.681i 0.378608 + 0.378608i
\(848\) 489.404 + 489.404i 0.577127 + 0.577127i
\(849\) 641.866i 0.756026i
\(850\) −1130.90 + 1153.88i −1.33047 + 1.35750i
\(851\) 10.3517i 0.0121642i
\(852\) −1029.46 1029.46i −1.20829 1.20829i
\(853\) −500.786 + 500.786i −0.587088 + 0.587088i −0.936842 0.349754i \(-0.886265\pi\)
0.349754 + 0.936842i \(0.386265\pi\)
\(854\) 698.748i 0.818206i
\(855\) −76.4575 + 32.1211i −0.0894240 + 0.0375686i
\(856\) 576.065i 0.672973i
\(857\) 183.439 183.439i 0.214048 0.214048i −0.591937 0.805984i \(-0.701636\pi\)
0.805984 + 0.591937i \(0.201636\pi\)
\(858\) −840.006 + 57.2637i −0.979028 + 0.0667409i
\(859\) 76.4724i 0.0890249i 0.999009 + 0.0445125i \(0.0141734\pi\)
−0.999009 + 0.0445125i \(0.985827\pi\)
\(860\) 1282.31 + 523.612i 1.49106 + 0.608851i
\(861\) 847.451 0.984264
\(862\) 341.503 341.503i 0.396175 0.396175i
\(863\) 1133.00 1133.00i 1.31286 1.31286i 0.393557 0.919300i \(-0.371245\pi\)
0.919300 0.393557i \(-0.128755\pi\)
\(864\) −1290.25 −1.49335
\(865\) 476.727 1167.49i 0.551130 1.34970i
\(866\) 2293.84i 2.64878i
\(867\) 308.256 308.256i 0.355543 0.355543i
\(868\) −313.108 313.108i −0.360723 0.360723i
\(869\) −870.368 −1.00157
\(870\) −612.013 1456.77i −0.703463 1.67444i
\(871\) 242.484 + 211.534i 0.278398 + 0.242863i
\(872\) 4.96704 4.96704i 0.00569614 0.00569614i
\(873\) −70.7399 + 70.7399i −0.0810308 + 0.0810308i
\(874\) 12.1894i 0.0139467i
\(875\) −410.105 949.316i −0.468692 1.08493i
\(876\) 1307.62i 1.49272i
\(877\) 125.284 + 125.284i 0.142856 + 0.142856i 0.774918 0.632062i \(-0.217791\pi\)
−0.632062 + 0.774918i \(0.717791\pi\)
\(878\) 104.290 104.290i 0.118782 0.118782i
\(879\) 155.423 0.176818
\(880\) 370.561 155.679i 0.421092 0.176908i
\(881\) 508.152 0.576790 0.288395 0.957512i \(-0.406878\pi\)
0.288395 + 0.957512i \(0.406878\pi\)
\(882\) −87.3244 87.3244i −0.0990073 0.0990073i
\(883\) 164.059 + 164.059i 0.185797 + 0.185797i 0.793876 0.608079i \(-0.208060\pi\)
−0.608079 + 0.793876i \(0.708060\pi\)
\(884\) −1082.53 944.356i −1.22458 1.06828i
\(885\) 188.682 462.077i 0.213200 0.522121i
\(886\) 220.627i 0.249014i
\(887\) −999.858 + 999.858i −1.12724 + 1.12724i −0.136611 + 0.990625i \(0.543621\pi\)
−0.990625 + 0.136611i \(0.956379\pi\)
\(888\) 135.341 + 135.341i 0.152411 + 0.152411i
\(889\) −376.032 −0.422983
\(890\) 403.273 987.606i 0.453116 1.10967i
\(891\) 469.695i 0.527154i
\(892\) 296.045 + 296.045i 0.331889 + 0.331889i
\(893\) 449.727 + 449.727i 0.503614 + 0.503614i
\(894\) 1139.18i 1.27425i
\(895\) −504.505 + 211.951i −0.563692 + 0.236817i
\(896\) 906.022 1.01119
\(897\) −1.18129 17.3284i −0.00131693 0.0193181i
\(898\) 445.911 + 445.911i 0.496560 + 0.496560i
\(899\) 410.087 0.456159
\(900\) −190.072 + 193.934i −0.211191 + 0.215482i
\(901\) −1493.93 −1.65808
\(902\) 679.545 + 679.545i 0.753376 + 0.753376i
\(903\) 821.819 821.819i 0.910099 0.910099i
\(904\) 771.994 0.853976
\(905\) −340.895 811.428i −0.376679 0.896605i
\(906\) 929.819 1.02629
\(907\) −781.132 + 781.132i −0.861226 + 0.861226i −0.991481 0.130255i \(-0.958420\pi\)
0.130255 + 0.991481i \(0.458420\pi\)
\(908\) −916.666 + 916.666i −1.00954 + 1.00954i
\(909\) 271.323i 0.298485i
\(910\) 1455.77 731.794i 1.59975 0.804169i
\(911\) −484.480 −0.531811 −0.265906 0.963999i \(-0.585671\pi\)
−0.265906 + 0.963999i \(0.585671\pi\)
\(912\) −145.242 145.242i −0.159256 0.159256i
\(913\) 70.1232 + 70.1232i 0.0768053 + 0.0768053i
\(914\) 569.469i 0.623052i
\(915\) 138.437 339.029i 0.151297 0.370524i
\(916\) 572.090i 0.624552i
\(917\) −407.826 407.826i −0.444740 0.444740i
\(918\) 1332.34 1332.34i 1.45135 1.45135i
\(919\) 1462.32i 1.59121i 0.605816 + 0.795605i \(0.292847\pi\)
−0.605816 + 0.795605i \(0.707153\pi\)
\(920\) −3.52384 8.38774i −0.00383026 0.00911711i
\(921\) 277.718i 0.301540i
\(922\) −1057.37 + 1057.37i −1.14682 + 1.14682i
\(923\) 94.5611 + 1387.12i 0.102450 + 1.50284i
\(924\) 916.158i 0.991513i
\(925\) −508.913 + 5.11858i −0.550176 + 0.00553360i
\(926\) −1094.81 −1.18230
\(927\) −191.914 + 191.914i −0.207027 + 0.207027i
\(928\) −1242.16 + 1242.16i −1.33853 + 1.33853i
\(929\) −93.0218 −0.100131 −0.0500656 0.998746i \(-0.515943\pi\)
−0.0500656 + 0.998746i \(0.515943\pi\)
\(930\) 159.281 + 379.134i 0.171270 + 0.407671i
\(931\) 153.803i 0.165202i
\(932\) 29.3589 29.3589i 0.0315010 0.0315010i
\(933\) 161.358 + 161.358i 0.172945 + 0.172945i
\(934\) −1711.97 −1.83295
\(935\) −327.968 + 803.186i −0.350768 + 0.859023i
\(936\) −73.4920 64.1115i −0.0785171 0.0684952i
\(937\) −714.871 + 714.871i −0.762936 + 0.762936i −0.976852 0.213916i \(-0.931378\pi\)
0.213916 + 0.976852i \(0.431378\pi\)
\(938\) 438.741 438.741i 0.467741 0.467741i
\(939\) 817.298i 0.870391i
\(940\) 1928.00 + 787.267i 2.05106 + 0.837519i
\(941\) 891.314i 0.947199i 0.880740 + 0.473599i \(0.157046\pi\)
−0.880740 + 0.473599i \(0.842954\pi\)
\(942\) 1203.70 + 1203.70i 1.27781 + 1.27781i
\(943\) −14.0182 + 14.0182i −0.0148656 + 0.0148656i
\(944\) −375.417 −0.397688
\(945\) 467.114 + 1111.87i 0.494301 + 1.17658i
\(946\) 1317.98 1.39322
\(947\) 256.254 + 256.254i 0.270596 + 0.270596i 0.829340 0.558744i \(-0.188717\pi\)
−0.558744 + 0.829340i \(0.688717\pi\)
\(948\) 1029.83 + 1029.83i 1.08632 + 1.08632i
\(949\) 820.906 941.018i 0.865023 0.991589i
\(950\) −599.260 + 6.02728i −0.630800 + 0.00634450i
\(951\) 669.138i 0.703615i
\(952\) −446.471 + 446.471i −0.468982 + 0.468982i
\(953\) 263.391 + 263.391i 0.276381 + 0.276381i 0.831663 0.555281i \(-0.187389\pi\)
−0.555281 + 0.831663i \(0.687389\pi\)
\(954\) −444.940 −0.466394
\(955\) 520.675 + 1239.36i 0.545209 + 1.29775i
\(956\) 1116.78i 1.16818i
\(957\) −599.961 599.961i −0.626918 0.626918i
\(958\) −112.693 112.693i −0.117634 0.117634i
\(959\) 780.155i 0.813508i
\(960\) −1150.14 469.641i −1.19806 0.489209i
\(961\) 854.272 0.888940
\(962\) −54.5385 800.030i −0.0566929 0.831632i
\(963\) 238.652 + 238.652i 0.247821 + 0.247821i
\(964\) −376.634 −0.390699
\(965\) −1214.24 495.814i −1.25828 0.513797i
\(966\) −33.4906 −0.0346694
\(967\) −480.135 480.135i −0.496521 0.496521i 0.413832 0.910353i \(-0.364190\pi\)
−0.910353 + 0.413832i \(0.864190\pi\)
\(968\) 138.708 138.708i 0.143293 0.143293i
\(969\) 443.357 0.457541
\(970\) −666.508 + 280.012i −0.687121 + 0.288672i
\(971\) −330.493 −0.340364 −0.170182 0.985413i \(-0.554435\pi\)
−0.170182 + 0.985413i \(0.554435\pi\)
\(972\) 405.550 405.550i 0.417233 0.417233i
\(973\) −17.2178 + 17.2178i −0.0176956 + 0.0176956i
\(974\) 412.842i 0.423863i
\(975\) −851.318 + 66.6430i −0.873146 + 0.0683518i
\(976\) −275.447 −0.282220
\(977\) 562.631 + 562.631i 0.575876 + 0.575876i 0.933764 0.357888i \(-0.116503\pi\)
−0.357888 + 0.933764i \(0.616503\pi\)
\(978\) 1355.75 + 1355.75i 1.38624 + 1.38624i
\(979\) 572.826i 0.585113i
\(980\) −195.061 464.300i −0.199042 0.473776i
\(981\) 4.11548i 0.00419519i
\(982\) 952.492 + 952.492i 0.969951 + 0.969951i
\(983\) 610.708 610.708i 0.621270 0.621270i −0.324586 0.945856i \(-0.605225\pi\)
0.945856 + 0.324586i \(0.105225\pi\)
\(984\) 366.557i 0.372518i
\(985\) 58.0467 142.155i 0.0589306 0.144320i
\(986\) 2565.35i 2.60178i
\(987\) 1235.63 1235.63i 1.25191 1.25191i
\(988\) −36.2408 531.619i −0.0366810 0.538076i
\(989\) 27.1885i 0.0274909i
\(990\) −97.6795 + 239.215i −0.0986661 + 0.241631i
\(991\) 5.75936 0.00581166 0.00290583 0.999996i \(-0.499075\pi\)
0.00290583 + 0.999996i \(0.499075\pi\)
\(992\) 323.281 323.281i 0.325888 0.325888i
\(993\) 304.415 304.415i 0.306561 0.306561i
\(994\) 2680.90 2.69708
\(995\) 306.599 128.808i 0.308139 0.129455i
\(996\) 165.942i 0.166609i
\(997\) 609.083 609.083i 0.610916 0.610916i −0.332269 0.943185i \(-0.607814\pi\)
0.943185 + 0.332269i \(0.107814\pi\)
\(998\) −1295.32 1295.32i −1.29792 1.29792i
\(999\) 593.535 0.594129
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 65.3.h.a.38.2 yes 24
5.2 odd 4 inner 65.3.h.a.12.11 yes 24
5.3 odd 4 325.3.h.b.207.2 24
5.4 even 2 325.3.h.b.168.11 24
13.12 even 2 inner 65.3.h.a.38.11 yes 24
65.12 odd 4 inner 65.3.h.a.12.2 24
65.38 odd 4 325.3.h.b.207.11 24
65.64 even 2 325.3.h.b.168.2 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
65.3.h.a.12.2 24 65.12 odd 4 inner
65.3.h.a.12.11 yes 24 5.2 odd 4 inner
65.3.h.a.38.2 yes 24 1.1 even 1 trivial
65.3.h.a.38.11 yes 24 13.12 even 2 inner
325.3.h.b.168.2 24 65.64 even 2
325.3.h.b.168.11 24 5.4 even 2
325.3.h.b.207.2 24 5.3 odd 4
325.3.h.b.207.11 24 65.38 odd 4