Properties

Label 1014.3.f.h.775.3
Level $1014$
Weight $3$
Character 1014.775
Analytic conductor $27.629$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1014,3,Mod(577,1014)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1014, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 3]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1014.577");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1014.f (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: \(27.6294988061\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 2x^{7} + 2x^{6} + 82x^{5} + 5053x^{4} - 6736x^{3} + 6728x^{2} + 275384x + 5635876 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 78)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 775.3
Root \(5.41254 + 5.41254i\) of defining polynomial
Character \(\chi\) \(=\) 1014.775
Dual form 1014.3.f.h.577.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.00000 - 1.00000i) q^{2} +1.73205 q^{3} +2.00000i q^{4} +(-5.04651 - 5.04651i) q^{5} +(-1.73205 - 1.73205i) q^{6} +(-3.68049 + 3.68049i) q^{7} +(2.00000 - 2.00000i) q^{8} +3.00000 q^{9} +O(q^{10})\) \(q+(-1.00000 - 1.00000i) q^{2} +1.73205 q^{3} +2.00000i q^{4} +(-5.04651 - 5.04651i) q^{5} +(-1.73205 - 1.73205i) q^{6} +(-3.68049 + 3.68049i) q^{7} +(2.00000 - 2.00000i) q^{8} +3.00000 q^{9} +10.0930i q^{10} +(5.36098 - 5.36098i) q^{11} +3.46410i q^{12} +7.36098 q^{14} +(-8.74082 - 8.74082i) q^{15} -4.00000 q^{16} +16.1621i q^{17} +(-3.00000 - 3.00000i) q^{18} +(-7.23020 - 7.23020i) q^{19} +(10.0930 - 10.0930i) q^{20} +(-6.37479 + 6.37479i) q^{21} -10.7220 q^{22} -9.57467i q^{23} +(3.46410 - 3.46410i) q^{24} +25.9346i q^{25} +5.19615 q^{27} +(-7.36098 - 7.36098i) q^{28} -33.1759 q^{29} +17.4816i q^{30} +(-34.2312 - 34.2312i) q^{31} +(4.00000 + 4.00000i) q^{32} +(9.28549 - 9.28549i) q^{33} +(16.1621 - 16.1621i) q^{34} +37.1473 q^{35} +6.00000i q^{36} +(-46.2851 + 46.2851i) q^{37} +14.4604i q^{38} -20.1861 q^{40} +(38.5116 + 38.5116i) q^{41} +12.7496 q^{42} +47.0461i q^{43} +(10.7220 + 10.7220i) q^{44} +(-15.1395 - 15.1395i) q^{45} +(-9.57467 + 9.57467i) q^{46} +(47.8214 - 47.8214i) q^{47} -6.92820 q^{48} +21.9080i q^{49} +(25.9346 - 25.9346i) q^{50} +27.9936i q^{51} +67.5177 q^{53} +(-5.19615 - 5.19615i) q^{54} -54.1085 q^{55} +14.7220i q^{56} +(-12.5231 - 12.5231i) q^{57} +(33.1759 + 33.1759i) q^{58} +(-53.2525 + 53.2525i) q^{59} +(17.4816 - 17.4816i) q^{60} +70.5195 q^{61} +68.4624i q^{62} +(-11.0415 + 11.0415i) q^{63} -8.00000i q^{64} -18.5710 q^{66} +(30.5554 + 30.5554i) q^{67} -32.3242 q^{68} -16.5838i q^{69} +(-37.1473 - 37.1473i) q^{70} +(78.1807 + 78.1807i) q^{71} +(6.00000 - 6.00000i) q^{72} +(-36.8385 + 36.8385i) q^{73} +92.5703 q^{74} +44.9201i q^{75} +(14.4604 - 14.4604i) q^{76} +39.4621i q^{77} -13.3867 q^{79} +(20.1861 + 20.1861i) q^{80} +9.00000 q^{81} -77.0233i q^{82} +(93.1237 + 93.1237i) q^{83} +(-12.7496 - 12.7496i) q^{84} +(81.5623 - 81.5623i) q^{85} +(47.0461 - 47.0461i) q^{86} -57.4624 q^{87} -21.4439i q^{88} +(-35.5877 + 35.5877i) q^{89} +30.2791i q^{90} +19.1493 q^{92} +(-59.2902 - 59.2902i) q^{93} -95.6428 q^{94} +72.9747i q^{95} +(6.92820 + 6.92820i) q^{96} +(38.4633 + 38.4633i) q^{97} +(21.9080 - 21.9080i) q^{98} +(16.0829 - 16.0829i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 8 q^{2} - 6 q^{5} - 2 q^{7} + 16 q^{8} + 24 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 8 q^{2} - 6 q^{5} - 2 q^{7} + 16 q^{8} + 24 q^{9} - 12 q^{11} + 4 q^{14} + 6 q^{15} - 32 q^{16} - 24 q^{18} - 44 q^{19} + 12 q^{20} + 18 q^{21} + 24 q^{22} - 4 q^{28} - 72 q^{29} - 94 q^{31} + 32 q^{32} - 36 q^{33} + 60 q^{34} + 408 q^{35} - 46 q^{37} - 24 q^{40} - 30 q^{41} - 36 q^{42} - 24 q^{44} - 18 q^{45} + 144 q^{46} + 300 q^{47} + 208 q^{50} + 84 q^{53} - 792 q^{55} + 24 q^{57} + 72 q^{58} - 12 q^{59} - 12 q^{60} + 180 q^{61} - 6 q^{63} + 72 q^{66} - 74 q^{67} - 120 q^{68} - 408 q^{70} + 156 q^{71} + 48 q^{72} + 16 q^{73} + 92 q^{74} + 88 q^{76} - 96 q^{79} + 24 q^{80} + 72 q^{81} + 36 q^{84} + 234 q^{85} + 168 q^{86} - 60 q^{87} + 228 q^{89} - 288 q^{92} - 198 q^{93} - 600 q^{94} + 2 q^{97} - 32 q^{98} - 36 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times\).

\(n\) \(677\) \(847\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 1.00000i −0.500000 0.500000i
\(3\) 1.73205 0.577350
\(4\) 2.00000i 0.500000i
\(5\) −5.04651 5.04651i −1.00930 1.00930i −0.999956 0.00934664i \(-0.997025\pi\)
−0.00934664 0.999956i \(-0.502975\pi\)
\(6\) −1.73205 1.73205i −0.288675 0.288675i
\(7\) −3.68049 + 3.68049i −0.525784 + 0.525784i −0.919313 0.393528i \(-0.871254\pi\)
0.393528 + 0.919313i \(0.371254\pi\)
\(8\) 2.00000 2.00000i 0.250000 0.250000i
\(9\) 3.00000 0.333333
\(10\) 10.0930i 1.00930i
\(11\) 5.36098 5.36098i 0.487362 0.487362i −0.420111 0.907473i \(-0.638009\pi\)
0.907473 + 0.420111i \(0.138009\pi\)
\(12\) 3.46410i 0.288675i
\(13\) 0 0
\(14\) 7.36098 0.525784
\(15\) −8.74082 8.74082i −0.582721 0.582721i
\(16\) −4.00000 −0.250000
\(17\) 16.1621i 0.950712i 0.879794 + 0.475356i \(0.157681\pi\)
−0.879794 + 0.475356i \(0.842319\pi\)
\(18\) −3.00000 3.00000i −0.166667 0.166667i
\(19\) −7.23020 7.23020i −0.380537 0.380537i 0.490759 0.871296i \(-0.336720\pi\)
−0.871296 + 0.490759i \(0.836720\pi\)
\(20\) 10.0930 10.0930i 0.504651 0.504651i
\(21\) −6.37479 + 6.37479i −0.303562 + 0.303562i
\(22\) −10.7220 −0.487362
\(23\) 9.57467i 0.416290i −0.978098 0.208145i \(-0.933257\pi\)
0.978098 0.208145i \(-0.0667426\pi\)
\(24\) 3.46410 3.46410i 0.144338 0.144338i
\(25\) 25.9346i 1.03738i
\(26\) 0 0
\(27\) 5.19615 0.192450
\(28\) −7.36098 7.36098i −0.262892 0.262892i
\(29\) −33.1759 −1.14400 −0.571999 0.820254i \(-0.693832\pi\)
−0.571999 + 0.820254i \(0.693832\pi\)
\(30\) 17.4816i 0.582721i
\(31\) −34.2312 34.2312i −1.10423 1.10423i −0.993894 0.110338i \(-0.964807\pi\)
−0.110338 0.993894i \(-0.535193\pi\)
\(32\) 4.00000 + 4.00000i 0.125000 + 0.125000i
\(33\) 9.28549 9.28549i 0.281378 0.281378i
\(34\) 16.1621 16.1621i 0.475356 0.475356i
\(35\) 37.1473 1.06135
\(36\) 6.00000i 0.166667i
\(37\) −46.2851 + 46.2851i −1.25095 + 1.25095i −0.295655 + 0.955295i \(0.595538\pi\)
−0.955295 + 0.295655i \(0.904462\pi\)
\(38\) 14.4604i 0.380537i
\(39\) 0 0
\(40\) −20.1861 −0.504651
\(41\) 38.5116 + 38.5116i 0.939308 + 0.939308i 0.998261 0.0589525i \(-0.0187760\pi\)
−0.0589525 + 0.998261i \(0.518776\pi\)
\(42\) 12.7496 0.303562
\(43\) 47.0461i 1.09410i 0.837101 + 0.547048i \(0.184249\pi\)
−0.837101 + 0.547048i \(0.815751\pi\)
\(44\) 10.7220 + 10.7220i 0.243681 + 0.243681i
\(45\) −15.1395 15.1395i −0.336434 0.336434i
\(46\) −9.57467 + 9.57467i −0.208145 + 0.208145i
\(47\) 47.8214 47.8214i 1.01748 1.01748i 0.0176317 0.999845i \(-0.494387\pi\)
0.999845 0.0176317i \(-0.00561265\pi\)
\(48\) −6.92820 −0.144338
\(49\) 21.9080i 0.447102i
\(50\) 25.9346 25.9346i 0.518692 0.518692i
\(51\) 27.9936i 0.548894i
\(52\) 0 0
\(53\) 67.5177 1.27392 0.636959 0.770897i \(-0.280192\pi\)
0.636959 + 0.770897i \(0.280192\pi\)
\(54\) −5.19615 5.19615i −0.0962250 0.0962250i
\(55\) −54.1085 −0.983791
\(56\) 14.7220i 0.262892i
\(57\) −12.5231 12.5231i −0.219703 0.219703i
\(58\) 33.1759 + 33.1759i 0.571999 + 0.571999i
\(59\) −53.2525 + 53.2525i −0.902584 + 0.902584i −0.995659 0.0930750i \(-0.970330\pi\)
0.0930750 + 0.995659i \(0.470330\pi\)
\(60\) 17.4816 17.4816i 0.291361 0.291361i
\(61\) 70.5195 1.15606 0.578028 0.816017i \(-0.303822\pi\)
0.578028 + 0.816017i \(0.303822\pi\)
\(62\) 68.4624i 1.10423i
\(63\) −11.0415 + 11.0415i −0.175261 + 0.175261i
\(64\) 8.00000i 0.125000i
\(65\) 0 0
\(66\) −18.5710 −0.281378
\(67\) 30.5554 + 30.5554i 0.456051 + 0.456051i 0.897357 0.441306i \(-0.145485\pi\)
−0.441306 + 0.897357i \(0.645485\pi\)
\(68\) −32.3242 −0.475356
\(69\) 16.5838i 0.240345i
\(70\) −37.1473 37.1473i −0.530676 0.530676i
\(71\) 78.1807 + 78.1807i 1.10114 + 1.10114i 0.994274 + 0.106862i \(0.0340804\pi\)
0.106862 + 0.994274i \(0.465920\pi\)
\(72\) 6.00000 6.00000i 0.0833333 0.0833333i
\(73\) −36.8385 + 36.8385i −0.504638 + 0.504638i −0.912876 0.408238i \(-0.866143\pi\)
0.408238 + 0.912876i \(0.366143\pi\)
\(74\) 92.5703 1.25095
\(75\) 44.9201i 0.598934i
\(76\) 14.4604 14.4604i 0.190269 0.190269i
\(77\) 39.4621i 0.512494i
\(78\) 0 0
\(79\) −13.3867 −0.169452 −0.0847259 0.996404i \(-0.527001\pi\)
−0.0847259 + 0.996404i \(0.527001\pi\)
\(80\) 20.1861 + 20.1861i 0.252326 + 0.252326i
\(81\) 9.00000 0.111111
\(82\) 77.0233i 0.939308i
\(83\) 93.1237 + 93.1237i 1.12197 + 1.12197i 0.991445 + 0.130528i \(0.0416671\pi\)
0.130528 + 0.991445i \(0.458333\pi\)
\(84\) −12.7496 12.7496i −0.151781 0.151781i
\(85\) 81.5623 81.5623i 0.959556 0.959556i
\(86\) 47.0461 47.0461i 0.547048 0.547048i
\(87\) −57.4624 −0.660488
\(88\) 21.4439i 0.243681i
\(89\) −35.5877 + 35.5877i −0.399862 + 0.399862i −0.878184 0.478322i \(-0.841245\pi\)
0.478322 + 0.878184i \(0.341245\pi\)
\(90\) 30.2791i 0.336434i
\(91\) 0 0
\(92\) 19.1493 0.208145
\(93\) −59.2902 59.2902i −0.637529 0.637529i
\(94\) −95.6428 −1.01748
\(95\) 72.9747i 0.768154i
\(96\) 6.92820 + 6.92820i 0.0721688 + 0.0721688i
\(97\) 38.4633 + 38.4633i 0.396529 + 0.396529i 0.877007 0.480478i \(-0.159537\pi\)
−0.480478 + 0.877007i \(0.659537\pi\)
\(98\) 21.9080 21.9080i 0.223551 0.223551i
\(99\) 16.0829 16.0829i 0.162454 0.162454i
\(100\) −51.8692 −0.518692
\(101\) 22.5497i 0.223264i 0.993750 + 0.111632i \(0.0356079\pi\)
−0.993750 + 0.111632i \(0.964392\pi\)
\(102\) 27.9936 27.9936i 0.274447 0.274447i
\(103\) 109.385i 1.06199i 0.847374 + 0.530996i \(0.178182\pi\)
−0.847374 + 0.530996i \(0.821818\pi\)
\(104\) 0 0
\(105\) 64.3410 0.612771
\(106\) −67.5177 67.5177i −0.636959 0.636959i
\(107\) −32.8750 −0.307243 −0.153621 0.988130i \(-0.549094\pi\)
−0.153621 + 0.988130i \(0.549094\pi\)
\(108\) 10.3923i 0.0962250i
\(109\) −150.086 150.086i −1.37693 1.37693i −0.849752 0.527183i \(-0.823248\pi\)
−0.527183 0.849752i \(-0.676752\pi\)
\(110\) 54.1085 + 54.1085i 0.491896 + 0.491896i
\(111\) −80.1682 + 80.1682i −0.722236 + 0.722236i
\(112\) 14.7220 14.7220i 0.131446 0.131446i
\(113\) −118.788 −1.05122 −0.525609 0.850726i \(-0.676163\pi\)
−0.525609 + 0.850726i \(0.676163\pi\)
\(114\) 25.0462i 0.219703i
\(115\) −48.3187 + 48.3187i −0.420163 + 0.420163i
\(116\) 66.3519i 0.571999i
\(117\) 0 0
\(118\) 106.505 0.902584
\(119\) −59.4844 59.4844i −0.499869 0.499869i
\(120\) −34.9633 −0.291361
\(121\) 63.5198i 0.524957i
\(122\) −70.5195 70.5195i −0.578028 0.578028i
\(123\) 66.7041 + 66.7041i 0.542310 + 0.542310i
\(124\) 68.4624 68.4624i 0.552116 0.552116i
\(125\) 4.71659 4.71659i 0.0377327 0.0377327i
\(126\) 22.0829 0.175261
\(127\) 66.4529i 0.523252i −0.965169 0.261626i \(-0.915741\pi\)
0.965169 0.261626i \(-0.0842586\pi\)
\(128\) −8.00000 + 8.00000i −0.0625000 + 0.0625000i
\(129\) 81.4863i 0.631677i
\(130\) 0 0
\(131\) −28.3277 −0.216242 −0.108121 0.994138i \(-0.534483\pi\)
−0.108121 + 0.994138i \(0.534483\pi\)
\(132\) 18.5710 + 18.5710i 0.140689 + 0.140689i
\(133\) 53.2214 0.400161
\(134\) 61.1108i 0.456051i
\(135\) −26.2225 26.2225i −0.194240 0.194240i
\(136\) 32.3242 + 32.3242i 0.237678 + 0.237678i
\(137\) 35.5910 35.5910i 0.259789 0.259789i −0.565179 0.824968i \(-0.691193\pi\)
0.824968 + 0.565179i \(0.191193\pi\)
\(138\) −16.5838 + 16.5838i −0.120173 + 0.120173i
\(139\) −148.284 −1.06679 −0.533396 0.845866i \(-0.679084\pi\)
−0.533396 + 0.845866i \(0.679084\pi\)
\(140\) 74.2946i 0.530676i
\(141\) 82.8291 82.8291i 0.587440 0.587440i
\(142\) 156.361i 1.10114i
\(143\) 0 0
\(144\) −12.0000 −0.0833333
\(145\) 167.423 + 167.423i 1.15464 + 1.15464i
\(146\) 73.6771 0.504638
\(147\) 37.9458i 0.258134i
\(148\) −92.5703 92.5703i −0.625475 0.625475i
\(149\) 29.5935 + 29.5935i 0.198614 + 0.198614i 0.799406 0.600792i \(-0.205148\pi\)
−0.600792 + 0.799406i \(0.705148\pi\)
\(150\) 44.9201 44.9201i 0.299467 0.299467i
\(151\) −2.57635 + 2.57635i −0.0170619 + 0.0170619i −0.715586 0.698524i \(-0.753840\pi\)
0.698524 + 0.715586i \(0.253840\pi\)
\(152\) −28.9208 −0.190269
\(153\) 48.4863i 0.316904i
\(154\) 39.4621 39.4621i 0.256247 0.256247i
\(155\) 345.497i 2.22901i
\(156\) 0 0
\(157\) 275.987 1.75788 0.878939 0.476934i \(-0.158252\pi\)
0.878939 + 0.476934i \(0.158252\pi\)
\(158\) 13.3867 + 13.3867i 0.0847259 + 0.0847259i
\(159\) 116.944 0.735497
\(160\) 40.3721i 0.252326i
\(161\) 35.2395 + 35.2395i 0.218879 + 0.218879i
\(162\) −9.00000 9.00000i −0.0555556 0.0555556i
\(163\) −99.4028 + 99.4028i −0.609833 + 0.609833i −0.942902 0.333069i \(-0.891916\pi\)
0.333069 + 0.942902i \(0.391916\pi\)
\(164\) −77.0233 + 77.0233i −0.469654 + 0.469654i
\(165\) −93.7187 −0.567992
\(166\) 186.247i 1.12197i
\(167\) −138.947 + 138.947i −0.832018 + 0.832018i −0.987793 0.155774i \(-0.950213\pi\)
0.155774 + 0.987793i \(0.450213\pi\)
\(168\) 25.4992i 0.151781i
\(169\) 0 0
\(170\) −163.125 −0.959556
\(171\) −21.6906 21.6906i −0.126846 0.126846i
\(172\) −94.0923 −0.547048
\(173\) 132.251i 0.764456i −0.924068 0.382228i \(-0.875157\pi\)
0.924068 0.382228i \(-0.124843\pi\)
\(174\) 57.4624 + 57.4624i 0.330244 + 0.330244i
\(175\) −95.4521 95.4521i −0.545441 0.545441i
\(176\) −21.4439 + 21.4439i −0.121840 + 0.121840i
\(177\) −92.2360 + 92.2360i −0.521107 + 0.521107i
\(178\) 71.1755 0.399862
\(179\) 35.4311i 0.197939i 0.995090 + 0.0989697i \(0.0315547\pi\)
−0.995090 + 0.0989697i \(0.968445\pi\)
\(180\) 30.2791 30.2791i 0.168217 0.168217i
\(181\) 121.119i 0.669163i 0.942367 + 0.334582i \(0.108595\pi\)
−0.942367 + 0.334582i \(0.891405\pi\)
\(182\) 0 0
\(183\) 122.143 0.667450
\(184\) −19.1493 19.1493i −0.104072 0.104072i
\(185\) 467.157 2.52517
\(186\) 118.580i 0.637529i
\(187\) 86.6447 + 86.6447i 0.463341 + 0.463341i
\(188\) 95.6428 + 95.6428i 0.508738 + 0.508738i
\(189\) −19.1244 + 19.1244i −0.101187 + 0.101187i
\(190\) 72.9747 72.9747i 0.384077 0.384077i
\(191\) 200.564 1.05007 0.525036 0.851080i \(-0.324052\pi\)
0.525036 + 0.851080i \(0.324052\pi\)
\(192\) 13.8564i 0.0721688i
\(193\) −18.5004 + 18.5004i −0.0958572 + 0.0958572i −0.753409 0.657552i \(-0.771592\pi\)
0.657552 + 0.753409i \(0.271592\pi\)
\(194\) 76.9267i 0.396529i
\(195\) 0 0
\(196\) −43.8160 −0.223551
\(197\) −66.9799 66.9799i −0.339999 0.339999i 0.516368 0.856367i \(-0.327284\pi\)
−0.856367 + 0.516368i \(0.827284\pi\)
\(198\) −32.1659 −0.162454
\(199\) 197.199i 0.990951i −0.868622 0.495475i \(-0.834994\pi\)
0.868622 0.495475i \(-0.165006\pi\)
\(200\) 51.8692 + 51.8692i 0.259346 + 0.259346i
\(201\) 52.9235 + 52.9235i 0.263301 + 0.263301i
\(202\) 22.5497 22.5497i 0.111632 0.111632i
\(203\) 122.104 122.104i 0.601496 0.601496i
\(204\) −55.9872 −0.274447
\(205\) 388.699i 1.89609i
\(206\) 109.385 109.385i 0.530996 0.530996i
\(207\) 28.7240i 0.138763i
\(208\) 0 0
\(209\) −77.5219 −0.370918
\(210\) −64.3410 64.3410i −0.306386 0.306386i
\(211\) −194.835 −0.923387 −0.461694 0.887039i \(-0.652758\pi\)
−0.461694 + 0.887039i \(0.652758\pi\)
\(212\) 135.035i 0.636959i
\(213\) 135.413 + 135.413i 0.635741 + 0.635741i
\(214\) 32.8750 + 32.8750i 0.153621 + 0.153621i
\(215\) 237.419 237.419i 1.10427 1.10427i
\(216\) 10.3923 10.3923i 0.0481125 0.0481125i
\(217\) 251.975 1.16118
\(218\) 300.172i 1.37693i
\(219\) −63.8062 + 63.8062i −0.291353 + 0.291353i
\(220\) 108.217i 0.491896i
\(221\) 0 0
\(222\) 160.336 0.722236
\(223\) 289.655 + 289.655i 1.29890 + 1.29890i 0.929119 + 0.369782i \(0.120568\pi\)
0.369782 + 0.929119i \(0.379432\pi\)
\(224\) −29.4439 −0.131446
\(225\) 77.8039i 0.345795i
\(226\) 118.788 + 118.788i 0.525609 + 0.525609i
\(227\) −176.560 176.560i −0.777798 0.777798i 0.201658 0.979456i \(-0.435367\pi\)
−0.979456 + 0.201658i \(0.935367\pi\)
\(228\) 25.0462 25.0462i 0.109852 0.109852i
\(229\) −174.256 + 174.256i −0.760945 + 0.760945i −0.976493 0.215548i \(-0.930846\pi\)
0.215548 + 0.976493i \(0.430846\pi\)
\(230\) 96.6374 0.420163
\(231\) 68.3503i 0.295889i
\(232\) −66.3519 + 66.3519i −0.286000 + 0.286000i
\(233\) 290.609i 1.24725i −0.781724 0.623624i \(-0.785660\pi\)
0.781724 0.623624i \(-0.214340\pi\)
\(234\) 0 0
\(235\) −482.663 −2.05388
\(236\) −106.505 106.505i −0.451292 0.451292i
\(237\) −23.1864 −0.0978330
\(238\) 118.969i 0.499869i
\(239\) 215.875 + 215.875i 0.903243 + 0.903243i 0.995715 0.0924720i \(-0.0294769\pi\)
−0.0924720 + 0.995715i \(0.529477\pi\)
\(240\) 34.9633 + 34.9633i 0.145680 + 0.145680i
\(241\) −84.9486 + 84.9486i −0.352484 + 0.352484i −0.861033 0.508549i \(-0.830182\pi\)
0.508549 + 0.861033i \(0.330182\pi\)
\(242\) 63.5198 63.5198i 0.262479 0.262479i
\(243\) 15.5885 0.0641500
\(244\) 141.039i 0.578028i
\(245\) 110.559 110.559i 0.451261 0.451261i
\(246\) 133.408i 0.542310i
\(247\) 0 0
\(248\) −136.925 −0.552116
\(249\) 161.295 + 161.295i 0.647771 + 0.647771i
\(250\) −9.43317 −0.0377327
\(251\) 174.494i 0.695196i 0.937644 + 0.347598i \(0.113003\pi\)
−0.937644 + 0.347598i \(0.886997\pi\)
\(252\) −22.0829 22.0829i −0.0876307 0.0876307i
\(253\) −51.3296 51.3296i −0.202884 0.202884i
\(254\) −66.4529 + 66.4529i −0.261626 + 0.261626i
\(255\) 141.270 141.270i 0.554000 0.554000i
\(256\) 16.0000 0.0625000
\(257\) 4.64878i 0.0180887i −0.999959 0.00904433i \(-0.997121\pi\)
0.999959 0.00904433i \(-0.00287894\pi\)
\(258\) 81.4863 81.4863i 0.315838 0.315838i
\(259\) 340.704i 1.31546i
\(260\) 0 0
\(261\) −99.5278 −0.381333
\(262\) 28.3277 + 28.3277i 0.108121 + 0.108121i
\(263\) 13.8431 0.0526355 0.0263177 0.999654i \(-0.491622\pi\)
0.0263177 + 0.999654i \(0.491622\pi\)
\(264\) 37.1420i 0.140689i
\(265\) −340.729 340.729i −1.28577 1.28577i
\(266\) −53.2214 53.2214i −0.200080 0.200080i
\(267\) −61.6398 + 61.6398i −0.230860 + 0.230860i
\(268\) −61.1108 + 61.1108i −0.228025 + 0.228025i
\(269\) −460.252 −1.71097 −0.855487 0.517825i \(-0.826742\pi\)
−0.855487 + 0.517825i \(0.826742\pi\)
\(270\) 52.4449i 0.194240i
\(271\) −104.874 + 104.874i −0.386988 + 0.386988i −0.873612 0.486624i \(-0.838228\pi\)
0.486624 + 0.873612i \(0.338228\pi\)
\(272\) 64.6484i 0.237678i
\(273\) 0 0
\(274\) −71.1821 −0.259789
\(275\) 139.035 + 139.035i 0.505582 + 0.505582i
\(276\) 33.1676 0.120173
\(277\) 373.291i 1.34762i −0.738904 0.673811i \(-0.764656\pi\)
0.738904 0.673811i \(-0.235344\pi\)
\(278\) 148.284 + 148.284i 0.533396 + 0.533396i
\(279\) −102.694 102.694i −0.368077 0.368077i
\(280\) 74.2946 74.2946i 0.265338 0.265338i
\(281\) −136.099 + 136.099i −0.484337 + 0.484337i −0.906514 0.422177i \(-0.861266\pi\)
0.422177 + 0.906514i \(0.361266\pi\)
\(282\) −165.658 −0.587440
\(283\) 380.695i 1.34521i −0.740001 0.672606i \(-0.765175\pi\)
0.740001 0.672606i \(-0.234825\pi\)
\(284\) −156.361 + 156.361i −0.550568 + 0.550568i
\(285\) 126.396i 0.443494i
\(286\) 0 0
\(287\) −283.483 −0.987747
\(288\) 12.0000 + 12.0000i 0.0416667 + 0.0416667i
\(289\) 27.7865 0.0961470
\(290\) 334.846i 1.15464i
\(291\) 66.6205 + 66.6205i 0.228936 + 0.228936i
\(292\) −73.6771 73.6771i −0.252319 0.252319i
\(293\) −3.90849 + 3.90849i −0.0133396 + 0.0133396i −0.713745 0.700406i \(-0.753002\pi\)
0.700406 + 0.713745i \(0.253002\pi\)
\(294\) 37.9458 37.9458i 0.129067 0.129067i
\(295\) 537.479 1.82196
\(296\) 185.141i 0.625475i
\(297\) 27.8565 27.8565i 0.0937928 0.0937928i
\(298\) 59.1870i 0.198614i
\(299\) 0 0
\(300\) −89.8402 −0.299467
\(301\) −173.153 173.153i −0.575259 0.575259i
\(302\) 5.15270 0.0170619
\(303\) 39.0572i 0.128902i
\(304\) 28.9208 + 28.9208i 0.0951343 + 0.0951343i
\(305\) −355.878 355.878i −1.16681 1.16681i
\(306\) 48.4863 48.4863i 0.158452 0.158452i
\(307\) −227.287 + 227.287i −0.740349 + 0.740349i −0.972645 0.232296i \(-0.925376\pi\)
0.232296 + 0.972645i \(0.425376\pi\)
\(308\) −78.9241 −0.256247
\(309\) 189.461i 0.613141i
\(310\) 345.497 345.497i 1.11450 1.11450i
\(311\) 308.864i 0.993132i −0.867999 0.496566i \(-0.834594\pi\)
0.867999 0.496566i \(-0.165406\pi\)
\(312\) 0 0
\(313\) 2.51660 0.00804026 0.00402013 0.999992i \(-0.498720\pi\)
0.00402013 + 0.999992i \(0.498720\pi\)
\(314\) −275.987 275.987i −0.878939 0.878939i
\(315\) 111.442 0.353784
\(316\) 26.7734i 0.0847259i
\(317\) 46.8460 + 46.8460i 0.147779 + 0.147779i 0.777125 0.629346i \(-0.216677\pi\)
−0.629346 + 0.777125i \(0.716677\pi\)
\(318\) −116.944 116.944i −0.367749 0.367749i
\(319\) −177.856 + 177.856i −0.557541 + 0.557541i
\(320\) −40.3721 + 40.3721i −0.126163 + 0.126163i
\(321\) −56.9412 −0.177387
\(322\) 70.4789i 0.218879i
\(323\) 116.855 116.855i 0.361781 0.361781i
\(324\) 18.0000i 0.0555556i
\(325\) 0 0
\(326\) 198.806 0.609833
\(327\) −259.956 259.956i −0.794974 0.794974i
\(328\) 154.047 0.469654
\(329\) 352.012i 1.06995i
\(330\) 93.7187 + 93.7187i 0.283996 + 0.283996i
\(331\) −169.867 169.867i −0.513192 0.513192i 0.402311 0.915503i \(-0.368207\pi\)
−0.915503 + 0.402311i \(0.868207\pi\)
\(332\) −186.247 + 186.247i −0.560986 + 0.560986i
\(333\) −138.855 + 138.855i −0.416983 + 0.416983i
\(334\) 277.894 0.832018
\(335\) 308.397i 0.920587i
\(336\) 25.4992 25.4992i 0.0758904 0.0758904i
\(337\) 5.72952i 0.0170015i −0.999964 0.00850077i \(-0.997294\pi\)
0.999964 0.00850077i \(-0.00270591\pi\)
\(338\) 0 0
\(339\) −205.746 −0.606921
\(340\) 163.125 + 163.125i 0.479778 + 0.479778i
\(341\) −367.025 −1.07632
\(342\) 43.3812i 0.126846i
\(343\) −260.976 260.976i −0.760863 0.760863i
\(344\) 94.0923 + 94.0923i 0.273524 + 0.273524i
\(345\) −83.6905 + 83.6905i −0.242581 + 0.242581i
\(346\) −132.251 + 132.251i −0.382228 + 0.382228i
\(347\) −102.971 −0.296747 −0.148373 0.988931i \(-0.547404\pi\)
−0.148373 + 0.988931i \(0.547404\pi\)
\(348\) 114.925i 0.330244i
\(349\) −342.739 + 342.739i −0.982059 + 0.982059i −0.999842 0.0177827i \(-0.994339\pi\)
0.0177827 + 0.999842i \(0.494339\pi\)
\(350\) 190.904i 0.545441i
\(351\) 0 0
\(352\) 42.8878 0.121840
\(353\) −139.237 139.237i −0.394439 0.394439i 0.481827 0.876266i \(-0.339973\pi\)
−0.876266 + 0.481827i \(0.839973\pi\)
\(354\) 184.472 0.521107
\(355\) 789.080i 2.22276i
\(356\) −71.1755 71.1755i −0.199931 0.199931i
\(357\) −103.030 103.030i −0.288600 0.288600i
\(358\) 35.4311 35.4311i 0.0989697 0.0989697i
\(359\) −54.1215 + 54.1215i −0.150756 + 0.150756i −0.778456 0.627699i \(-0.783997\pi\)
0.627699 + 0.778456i \(0.283997\pi\)
\(360\) −60.5582 −0.168217
\(361\) 256.448i 0.710383i
\(362\) 121.119 121.119i 0.334582 0.334582i
\(363\) 110.020i 0.303084i
\(364\) 0 0
\(365\) 371.812 1.01866
\(366\) −122.143 122.143i −0.333725 0.333725i
\(367\) −215.649 −0.587598 −0.293799 0.955867i \(-0.594920\pi\)
−0.293799 + 0.955867i \(0.594920\pi\)
\(368\) 38.2987i 0.104072i
\(369\) 115.535 + 115.535i 0.313103 + 0.313103i
\(370\) −467.157 467.157i −1.26259 1.26259i
\(371\) −248.498 + 248.498i −0.669806 + 0.669806i
\(372\) 118.580 118.580i 0.318764 0.318764i
\(373\) −631.387 −1.69273 −0.846363 0.532607i \(-0.821213\pi\)
−0.846363 + 0.532607i \(0.821213\pi\)
\(374\) 173.289i 0.463341i
\(375\) 8.16937 8.16937i 0.0217850 0.0217850i
\(376\) 191.286i 0.508738i
\(377\) 0 0
\(378\) 38.2488 0.101187
\(379\) −176.261 176.261i −0.465069 0.465069i 0.435244 0.900313i \(-0.356662\pi\)
−0.900313 + 0.435244i \(0.856662\pi\)
\(380\) −145.949 −0.384077
\(381\) 115.100i 0.302099i
\(382\) −200.564 200.564i −0.525036 0.525036i
\(383\) −198.656 198.656i −0.518684 0.518684i 0.398489 0.917173i \(-0.369535\pi\)
−0.917173 + 0.398489i \(0.869535\pi\)
\(384\) −13.8564 + 13.8564i −0.0360844 + 0.0360844i
\(385\) 199.146 199.146i 0.517262 0.517262i
\(386\) 37.0009 0.0958572
\(387\) 141.138i 0.364699i
\(388\) −76.9267 + 76.9267i −0.198265 + 0.198265i
\(389\) 265.150i 0.681620i 0.940132 + 0.340810i \(0.110701\pi\)
−0.940132 + 0.340810i \(0.889299\pi\)
\(390\) 0 0
\(391\) 154.747 0.395772
\(392\) 43.8160 + 43.8160i 0.111775 + 0.111775i
\(393\) −49.0650 −0.124847
\(394\) 133.960i 0.339999i
\(395\) 67.5561 + 67.5561i 0.171028 + 0.171028i
\(396\) 32.1659 + 32.1659i 0.0812270 + 0.0812270i
\(397\) −89.0047 + 89.0047i −0.224193 + 0.224193i −0.810262 0.586068i \(-0.800675\pi\)
0.586068 + 0.810262i \(0.300675\pi\)
\(398\) −197.199 + 197.199i −0.495475 + 0.495475i
\(399\) 92.1821 0.231033
\(400\) 103.738i 0.259346i
\(401\) 393.820 393.820i 0.982095 0.982095i −0.0177478 0.999842i \(-0.505650\pi\)
0.999842 + 0.0177478i \(0.00564959\pi\)
\(402\) 105.847i 0.263301i
\(403\) 0 0
\(404\) −45.0994 −0.111632
\(405\) −45.4186 45.4186i −0.112145 0.112145i
\(406\) −244.207 −0.601496
\(407\) 496.267i 1.21933i
\(408\) 55.9872 + 55.9872i 0.137223 + 0.137223i
\(409\) −146.003 146.003i −0.356977 0.356977i 0.505721 0.862697i \(-0.331227\pi\)
−0.862697 + 0.505721i \(0.831227\pi\)
\(410\) −388.699 + 388.699i −0.948047 + 0.948047i
\(411\) 61.6455 61.6455i 0.149989 0.149989i
\(412\) −218.770 −0.530996
\(413\) 391.990i 0.949129i
\(414\) −28.7240 + 28.7240i −0.0693817 + 0.0693817i
\(415\) 939.900i 2.26482i
\(416\) 0 0
\(417\) −256.835 −0.615912
\(418\) 77.5219 + 77.5219i 0.185459 + 0.185459i
\(419\) 335.412 0.800506 0.400253 0.916405i \(-0.368922\pi\)
0.400253 + 0.916405i \(0.368922\pi\)
\(420\) 128.682i 0.306386i
\(421\) 274.627 + 274.627i 0.652321 + 0.652321i 0.953551 0.301230i \(-0.0973973\pi\)
−0.301230 + 0.953551i \(0.597397\pi\)
\(422\) 194.835 + 194.835i 0.461694 + 0.461694i
\(423\) 143.464 143.464i 0.339159 0.339159i
\(424\) 135.035 135.035i 0.318480 0.318480i
\(425\) −419.158 −0.986254
\(426\) 270.826i 0.635741i
\(427\) −259.546 + 259.546i −0.607836 + 0.607836i
\(428\) 65.7500i 0.153621i
\(429\) 0 0
\(430\) −474.838 −1.10427
\(431\) 97.2197 + 97.2197i 0.225568 + 0.225568i 0.810838 0.585270i \(-0.199012\pi\)
−0.585270 + 0.810838i \(0.699012\pi\)
\(432\) −20.7846 −0.0481125
\(433\) 420.434i 0.970980i 0.874242 + 0.485490i \(0.161359\pi\)
−0.874242 + 0.485490i \(0.838641\pi\)
\(434\) −251.975 251.975i −0.580588 0.580588i
\(435\) 289.985 + 289.985i 0.666632 + 0.666632i
\(436\) 300.172 300.172i 0.688467 0.688467i
\(437\) −69.2268 + 69.2268i −0.158414 + 0.158414i
\(438\) 127.612 0.291353
\(439\) 745.361i 1.69786i 0.528505 + 0.848930i \(0.322753\pi\)
−0.528505 + 0.848930i \(0.677247\pi\)
\(440\) −108.217 + 108.217i −0.245948 + 0.245948i
\(441\) 65.7240i 0.149034i
\(442\) 0 0
\(443\) 661.917 1.49417 0.747084 0.664729i \(-0.231453\pi\)
0.747084 + 0.664729i \(0.231453\pi\)
\(444\) −160.336 160.336i −0.361118 0.361118i
\(445\) 359.188 0.807164
\(446\) 579.310i 1.29890i
\(447\) 51.2574 + 51.2574i 0.114670 + 0.114670i
\(448\) 29.4439 + 29.4439i 0.0657230 + 0.0657230i
\(449\) −22.1856 + 22.1856i −0.0494112 + 0.0494112i −0.731381 0.681969i \(-0.761124\pi\)
0.681969 + 0.731381i \(0.261124\pi\)
\(450\) 77.8039 77.8039i 0.172897 0.172897i
\(451\) 412.920 0.915566
\(452\) 237.575i 0.525609i
\(453\) −4.46237 + 4.46237i −0.00985070 + 0.00985070i
\(454\) 353.120i 0.777798i
\(455\) 0 0
\(456\) −50.0923 −0.109852
\(457\) −115.008 115.008i −0.251659 0.251659i 0.569991 0.821651i \(-0.306947\pi\)
−0.821651 + 0.569991i \(0.806947\pi\)
\(458\) 348.513 0.760945
\(459\) 83.9807i 0.182965i
\(460\) −96.6374 96.6374i −0.210081 0.210081i
\(461\) 56.9560 + 56.9560i 0.123549 + 0.123549i 0.766178 0.642629i \(-0.222156\pi\)
−0.642629 + 0.766178i \(0.722156\pi\)
\(462\) 68.3503 68.3503i 0.147944 0.147944i
\(463\) −172.856 + 172.856i −0.373338 + 0.373338i −0.868692 0.495353i \(-0.835039\pi\)
0.495353 + 0.868692i \(0.335039\pi\)
\(464\) 132.704 0.286000
\(465\) 598.418i 1.28692i
\(466\) −290.609 + 290.609i −0.623624 + 0.623624i
\(467\) 649.970i 1.39180i −0.718139 0.695899i \(-0.755006\pi\)
0.718139 0.695899i \(-0.244994\pi\)
\(468\) 0 0
\(469\) −224.918 −0.479569
\(470\) 482.663 + 482.663i 1.02694 + 1.02694i
\(471\) 478.023 1.01491
\(472\) 213.010i 0.451292i
\(473\) 252.213 + 252.213i 0.533221 + 0.533221i
\(474\) 23.1864 + 23.1864i 0.0489165 + 0.0489165i
\(475\) 187.513 187.513i 0.394763 0.394763i
\(476\) 118.969 118.969i 0.249935 0.249935i
\(477\) 202.553 0.424640
\(478\) 431.750i 0.903243i
\(479\) 359.283 359.283i 0.750068 0.750068i −0.224423 0.974492i \(-0.572050\pi\)
0.974492 + 0.224423i \(0.0720499\pi\)
\(480\) 69.9266i 0.145680i
\(481\) 0 0
\(482\) 169.897 0.352484
\(483\) 61.0366 + 61.0366i 0.126370 + 0.126370i
\(484\) −127.040 −0.262479
\(485\) 388.212i 0.800436i
\(486\) −15.5885 15.5885i −0.0320750 0.0320750i
\(487\) 548.721 + 548.721i 1.12674 + 1.12674i 0.990704 + 0.136034i \(0.0434355\pi\)
0.136034 + 0.990704i \(0.456564\pi\)
\(488\) 141.039 141.039i 0.289014 0.289014i
\(489\) −172.171 + 172.171i −0.352087 + 0.352087i
\(490\) −221.118 −0.451261
\(491\) 125.014i 0.254610i −0.991864 0.127305i \(-0.959367\pi\)
0.991864 0.127305i \(-0.0406327\pi\)
\(492\) −133.408 + 133.408i −0.271155 + 0.271155i
\(493\) 536.193i 1.08761i
\(494\) 0 0
\(495\) −162.326 −0.327930
\(496\) 136.925 + 136.925i 0.276058 + 0.276058i
\(497\) −575.486 −1.15792
\(498\) 322.590i 0.647771i
\(499\) 151.406 + 151.406i 0.303419 + 0.303419i 0.842350 0.538931i \(-0.181172\pi\)
−0.538931 + 0.842350i \(0.681172\pi\)
\(500\) 9.43317 + 9.43317i 0.0188663 + 0.0188663i
\(501\) −240.663 + 240.663i −0.480366 + 0.480366i
\(502\) 174.494 174.494i 0.347598 0.347598i
\(503\) 526.512 1.04674 0.523372 0.852104i \(-0.324674\pi\)
0.523372 + 0.852104i \(0.324674\pi\)
\(504\) 44.1659i 0.0876307i
\(505\) 113.797 113.797i 0.225341 0.225341i
\(506\) 102.659i 0.202884i
\(507\) 0 0
\(508\) 132.906 0.261626
\(509\) −682.053 682.053i −1.33999 1.33999i −0.896066 0.443920i \(-0.853587\pi\)
−0.443920 0.896066i \(-0.646413\pi\)
\(510\) −282.540 −0.554000
\(511\) 271.168i 0.530661i
\(512\) −16.0000 16.0000i −0.0312500 0.0312500i
\(513\) −37.5692 37.5692i −0.0732344 0.0732344i
\(514\) −4.64878 + 4.64878i −0.00904433 + 0.00904433i
\(515\) 552.014 552.014i 1.07187 1.07187i
\(516\) −162.973 −0.315838
\(517\) 512.739i 0.991758i
\(518\) −340.704 + 340.704i −0.657729 + 0.657729i
\(519\) 229.065i 0.441359i
\(520\) 0 0
\(521\) −158.382 −0.303997 −0.151998 0.988381i \(-0.548571\pi\)
−0.151998 + 0.988381i \(0.548571\pi\)
\(522\) 99.5278 + 99.5278i 0.190666 + 0.190666i
\(523\) −229.478 −0.438773 −0.219386 0.975638i \(-0.570406\pi\)
−0.219386 + 0.975638i \(0.570406\pi\)
\(524\) 56.6554i 0.108121i
\(525\) −165.328 165.328i −0.314910 0.314910i
\(526\) −13.8431 13.8431i −0.0263177 0.0263177i
\(527\) 553.248 553.248i 1.04981 1.04981i
\(528\) −37.1420 + 37.1420i −0.0703446 + 0.0703446i
\(529\) 437.326 0.826703
\(530\) 681.458i 1.28577i
\(531\) −159.757 + 159.757i −0.300861 + 0.300861i
\(532\) 106.443i 0.200080i
\(533\) 0 0
\(534\) 123.280 0.230860
\(535\) 165.904 + 165.904i 0.310101 + 0.310101i
\(536\) 122.222 0.228025
\(537\) 61.3685i 0.114280i
\(538\) 460.252 + 460.252i 0.855487 + 0.855487i
\(539\) 117.448 + 117.448i 0.217900 + 0.217900i
\(540\) 52.4449 52.4449i 0.0971202 0.0971202i
\(541\) 606.240 606.240i 1.12059 1.12059i 0.128938 0.991653i \(-0.458843\pi\)
0.991653 0.128938i \(-0.0411569\pi\)
\(542\) 209.747 0.386988
\(543\) 209.783i 0.386341i
\(544\) −64.6484 + 64.6484i −0.118839 + 0.118839i
\(545\) 1514.82i 2.77949i
\(546\) 0 0
\(547\) −790.673 −1.44547 −0.722736 0.691124i \(-0.757116\pi\)
−0.722736 + 0.691124i \(0.757116\pi\)
\(548\) 71.1821 + 71.1821i 0.129894 + 0.129894i
\(549\) 211.558 0.385352
\(550\) 278.070i 0.505582i
\(551\) 239.869 + 239.869i 0.435334 + 0.435334i
\(552\) −33.1676 33.1676i −0.0600863 0.0600863i
\(553\) 49.2696 49.2696i 0.0890951 0.0890951i
\(554\) −373.291 + 373.291i −0.673811 + 0.673811i
\(555\) 809.140 1.45791
\(556\) 296.568i 0.533396i
\(557\) 303.574 303.574i 0.545016 0.545016i −0.379979 0.924995i \(-0.624069\pi\)
0.924995 + 0.379979i \(0.124069\pi\)
\(558\) 205.387i 0.368077i
\(559\) 0 0
\(560\) −148.589 −0.265338
\(561\) 150.073 + 150.073i 0.267510 + 0.267510i
\(562\) 272.197 0.484337
\(563\) 319.331i 0.567195i 0.958943 + 0.283598i \(0.0915280\pi\)
−0.958943 + 0.283598i \(0.908472\pi\)
\(564\) 165.658 + 165.658i 0.293720 + 0.293720i
\(565\) 599.464 + 599.464i 1.06100 + 1.06100i
\(566\) −380.695 + 380.695i −0.672606 + 0.672606i
\(567\) −33.1244 + 33.1244i −0.0584205 + 0.0584205i
\(568\) 312.723 0.550568
\(569\) 793.301i 1.39420i 0.716973 + 0.697101i \(0.245527\pi\)
−0.716973 + 0.697101i \(0.754473\pi\)
\(570\) 126.396 126.396i 0.221747 0.221747i
\(571\) 852.111i 1.49231i 0.665771 + 0.746156i \(0.268103\pi\)
−0.665771 + 0.746156i \(0.731897\pi\)
\(572\) 0 0
\(573\) 347.387 0.606259
\(574\) 283.483 + 283.483i 0.493873 + 0.493873i
\(575\) 248.315 0.431853
\(576\) 24.0000i 0.0416667i
\(577\) −186.391 186.391i −0.323035 0.323035i 0.526895 0.849930i \(-0.323356\pi\)
−0.849930 + 0.526895i \(0.823356\pi\)
\(578\) −27.7865 27.7865i −0.0480735 0.0480735i
\(579\) −32.0437 + 32.0437i −0.0553432 + 0.0553432i
\(580\) −334.846 + 334.846i −0.577320 + 0.577320i
\(581\) −685.482 −1.17983
\(582\) 133.241i 0.228936i
\(583\) 361.961 361.961i 0.620859 0.620859i
\(584\) 147.354i 0.252319i
\(585\) 0 0
\(586\) 7.81698 0.0133396
\(587\) 554.844 + 554.844i 0.945220 + 0.945220i 0.998576 0.0533553i \(-0.0169916\pi\)
−0.0533553 + 0.998576i \(0.516992\pi\)
\(588\) −75.8915 −0.129067
\(589\) 494.997i 0.840403i
\(590\) −537.479 537.479i −0.910981 0.910981i
\(591\) −116.013 116.013i −0.196299 0.196299i
\(592\) 185.141 185.141i 0.312737 0.312737i
\(593\) −375.307 + 375.307i −0.632895 + 0.632895i −0.948793 0.315898i \(-0.897694\pi\)
0.315898 + 0.948793i \(0.397694\pi\)
\(594\) −55.7129 −0.0937928
\(595\) 600.378i 1.00904i
\(596\) −59.1870 + 59.1870i −0.0993070 + 0.0993070i
\(597\) 341.559i 0.572126i
\(598\) 0 0
\(599\) 320.645 0.535300 0.267650 0.963516i \(-0.413753\pi\)
0.267650 + 0.963516i \(0.413753\pi\)
\(600\) 89.8402 + 89.8402i 0.149734 + 0.149734i
\(601\) −58.4208 −0.0972059 −0.0486030 0.998818i \(-0.515477\pi\)
−0.0486030 + 0.998818i \(0.515477\pi\)
\(602\) 346.306i 0.575259i
\(603\) 91.6662 + 91.6662i 0.152017 + 0.152017i
\(604\) −5.15270 5.15270i −0.00853096 0.00853096i
\(605\) 320.554 320.554i 0.529841 0.529841i
\(606\) 39.0572 39.0572i 0.0644509 0.0644509i
\(607\) −655.852 −1.08048 −0.540240 0.841511i \(-0.681667\pi\)
−0.540240 + 0.841511i \(0.681667\pi\)
\(608\) 57.8416i 0.0951343i
\(609\) 211.490 211.490i 0.347274 0.347274i
\(610\) 711.755i 1.16681i
\(611\) 0 0
\(612\) −96.9726 −0.158452
\(613\) −136.104 136.104i −0.222030 0.222030i 0.587323 0.809353i \(-0.300182\pi\)
−0.809353 + 0.587323i \(0.800182\pi\)
\(614\) 454.574 0.740349
\(615\) 673.247i 1.09471i
\(616\) 78.9241 + 78.9241i 0.128124 + 0.128124i
\(617\) −14.0356 14.0356i −0.0227481 0.0227481i 0.695641 0.718389i \(-0.255120\pi\)
−0.718389 + 0.695641i \(0.755120\pi\)
\(618\) 189.461 189.461i 0.306571 0.306571i
\(619\) −319.972 + 319.972i −0.516917 + 0.516917i −0.916637 0.399720i \(-0.869107\pi\)
0.399720 + 0.916637i \(0.369107\pi\)
\(620\) −690.993 −1.11450
\(621\) 49.7514i 0.0801150i
\(622\) −308.864 + 308.864i −0.496566 + 0.496566i
\(623\) 261.961i 0.420482i
\(624\) 0 0
\(625\) 600.761 0.961217
\(626\) −2.51660 2.51660i −0.00402013 0.00402013i
\(627\) −134.272 −0.214150
\(628\) 551.974i 0.878939i
\(629\) −748.065 748.065i −1.18929 1.18929i
\(630\) −111.442 111.442i −0.176892 0.176892i
\(631\) 309.780 309.780i 0.490935 0.490935i −0.417666 0.908601i \(-0.637152\pi\)
0.908601 + 0.417666i \(0.137152\pi\)
\(632\) −26.7734 + 26.7734i −0.0423630 + 0.0423630i
\(633\) −337.464 −0.533118
\(634\) 93.6921i 0.147779i
\(635\) −335.356 + 335.356i −0.528119 + 0.528119i
\(636\) 233.888i 0.367749i
\(637\) 0 0
\(638\) 355.711 0.557541
\(639\) 234.542 + 234.542i 0.367045 + 0.367045i
\(640\) 80.7442 0.126163
\(641\) 619.237i 0.966048i 0.875607 + 0.483024i \(0.160462\pi\)
−0.875607 + 0.483024i \(0.839538\pi\)
\(642\) 56.9412 + 56.9412i 0.0886934 + 0.0886934i
\(643\) 285.392 + 285.392i 0.443845 + 0.443845i 0.893302 0.449457i \(-0.148382\pi\)
−0.449457 + 0.893302i \(0.648382\pi\)
\(644\) −70.4789 + 70.4789i −0.109439 + 0.109439i
\(645\) 411.222 411.222i 0.637553 0.637553i
\(646\) −233.711 −0.361781
\(647\) 250.092i 0.386540i −0.981146 0.193270i \(-0.938091\pi\)
0.981146 0.193270i \(-0.0619094\pi\)
\(648\) 18.0000 18.0000i 0.0277778 0.0277778i
\(649\) 570.971i 0.879770i
\(650\) 0 0
\(651\) 436.434 0.670405
\(652\) −198.806 198.806i −0.304917 0.304917i
\(653\) −391.661 −0.599787 −0.299894 0.953973i \(-0.596951\pi\)
−0.299894 + 0.953973i \(0.596951\pi\)
\(654\) 519.913i 0.794974i
\(655\) 142.956 + 142.956i 0.218254 + 0.218254i
\(656\) −154.047 154.047i −0.234827 0.234827i
\(657\) −110.516 + 110.516i −0.168213 + 0.168213i
\(658\) 352.012 352.012i 0.534973 0.534973i
\(659\) −611.987 −0.928661 −0.464330 0.885662i \(-0.653705\pi\)
−0.464330 + 0.885662i \(0.653705\pi\)
\(660\) 187.437i 0.283996i
\(661\) 428.563 428.563i 0.648356 0.648356i −0.304239 0.952596i \(-0.598402\pi\)
0.952596 + 0.304239i \(0.0984023\pi\)
\(662\) 339.733i 0.513192i
\(663\) 0 0
\(664\) 372.495 0.560986
\(665\) −268.582 268.582i −0.403883 0.403883i
\(666\) 277.711 0.416983
\(667\) 317.649i 0.476235i
\(668\) −277.894 277.894i −0.416009 0.416009i
\(669\) 501.697 + 501.697i 0.749920 + 0.749920i
\(670\) −308.397 + 308.397i −0.460293 + 0.460293i
\(671\) 378.053 378.053i 0.563418 0.563418i
\(672\) −50.9984 −0.0758904
\(673\) 785.253i 1.16680i 0.812187 + 0.583398i \(0.198277\pi\)
−0.812187 + 0.583398i \(0.801723\pi\)
\(674\) −5.72952 + 5.72952i −0.00850077 + 0.00850077i
\(675\) 134.760i 0.199645i
\(676\) 0 0
\(677\) −622.197 −0.919051 −0.459525 0.888165i \(-0.651980\pi\)
−0.459525 + 0.888165i \(0.651980\pi\)
\(678\) 205.746 + 205.746i 0.303461 + 0.303461i
\(679\) −283.128 −0.416978
\(680\) 326.249i 0.479778i
\(681\) −305.811 305.811i −0.449062 0.449062i
\(682\) 367.025 + 367.025i 0.538161 + 0.538161i
\(683\) 597.755 597.755i 0.875191 0.875191i −0.117842 0.993032i \(-0.537598\pi\)
0.993032 + 0.117842i \(0.0375975\pi\)
\(684\) 43.3812 43.3812i 0.0634228 0.0634228i
\(685\) −359.221 −0.524411
\(686\) 521.952i 0.760863i
\(687\) −301.821 + 301.821i −0.439332 + 0.439332i
\(688\) 188.185i 0.273524i
\(689\) 0 0
\(690\) 167.381 0.242581
\(691\) 471.479 + 471.479i 0.682314 + 0.682314i 0.960521 0.278207i \(-0.0897402\pi\)
−0.278207 + 0.960521i \(0.589740\pi\)
\(692\) 264.502 0.382228
\(693\) 118.386i 0.170831i
\(694\) 102.971 + 102.971i 0.148373 + 0.148373i
\(695\) 748.317 + 748.317i 1.07672 + 1.07672i
\(696\) −114.925 + 114.925i −0.165122 + 0.165122i
\(697\) −622.429 + 622.429i −0.893012 + 0.893012i
\(698\) 685.477 0.982059
\(699\) 503.349i 0.720099i
\(700\) 190.904 190.904i 0.272720 0.272720i
\(701\) 299.776i 0.427640i −0.976873 0.213820i \(-0.931409\pi\)
0.976873 0.213820i \(-0.0685907\pi\)
\(702\) 0 0
\(703\) 669.302 0.952065
\(704\) −42.8878 42.8878i −0.0609202 0.0609202i
\(705\) −835.996 −1.18581
\(706\) 278.474i 0.394439i
\(707\) −82.9940 82.9940i −0.117389 0.117389i
\(708\) −184.472 184.472i −0.260554 0.260554i
\(709\) −242.444 + 242.444i −0.341951 + 0.341951i −0.857101 0.515149i \(-0.827737\pi\)
0.515149 + 0.857101i \(0.327737\pi\)
\(710\) −789.080 + 789.080i −1.11138 + 1.11138i
\(711\) −40.1601 −0.0564839
\(712\) 142.351i 0.199931i
\(713\) −327.752 + 327.752i −0.459681 + 0.459681i
\(714\) 206.060i 0.288600i
\(715\) 0 0
\(716\) −70.8623 −0.0989697
\(717\) 373.907 + 373.907i 0.521488 + 0.521488i
\(718\) 108.243 0.150756
\(719\) 637.194i 0.886223i −0.896466 0.443112i \(-0.853875\pi\)
0.896466 0.443112i \(-0.146125\pi\)
\(720\) 60.5582 + 60.5582i 0.0841086 + 0.0841086i
\(721\) −402.591 402.591i −0.558379 0.558379i
\(722\) −256.448 + 256.448i −0.355192 + 0.355192i
\(723\) −147.135 + 147.135i −0.203507 + 0.203507i
\(724\) −242.237 −0.334582
\(725\) 860.406i 1.18677i
\(726\) 110.020 110.020i 0.151542 0.151542i
\(727\) 617.181i 0.848943i 0.905441 + 0.424471i \(0.139540\pi\)
−0.905441 + 0.424471i \(0.860460\pi\)
\(728\) 0 0
\(729\) 27.0000 0.0370370
\(730\) −371.812 371.812i −0.509332 0.509332i
\(731\) −760.364 −1.04017
\(732\) 244.287i 0.333725i
\(733\) −932.866 932.866i −1.27267 1.27267i −0.944683 0.327985i \(-0.893631\pi\)
−0.327985 0.944683i \(-0.606369\pi\)
\(734\) 215.649 + 215.649i 0.293799 + 0.293799i
\(735\) 191.494 191.494i 0.260536 0.260536i
\(736\) 38.2987 38.2987i 0.0520362 0.0520362i
\(737\) 327.614 0.444523
\(738\) 231.070i 0.313103i
\(739\) −142.848 + 142.848i −0.193299 + 0.193299i −0.797120 0.603821i \(-0.793644\pi\)
0.603821 + 0.797120i \(0.293644\pi\)
\(740\) 934.314i 1.26259i
\(741\) 0 0
\(742\) 496.996 0.669806
\(743\) −741.898 741.898i −0.998517 0.998517i 0.00148231 0.999999i \(-0.499528\pi\)
−0.999999 + 0.00148231i \(0.999528\pi\)
\(744\) −237.161 −0.318764
\(745\) 298.688i 0.400923i
\(746\) 631.387 + 631.387i 0.846363 + 0.846363i
\(747\) 279.371 + 279.371i 0.373991 + 0.373991i
\(748\) −173.289 + 173.289i −0.231670 + 0.231670i
\(749\) 120.996 120.996i 0.161543 0.161543i
\(750\) −16.3387 −0.0217850
\(751\) 1468.78i 1.95576i 0.209162 + 0.977881i \(0.432926\pi\)
−0.209162 + 0.977881i \(0.567074\pi\)
\(752\) −191.286 + 191.286i −0.254369 + 0.254369i
\(753\) 302.233i 0.401371i
\(754\) 0 0
\(755\) 26.0032 0.0344413
\(756\) −38.2488 38.2488i −0.0505936 0.0505936i
\(757\) −855.727 −1.13042 −0.565210 0.824947i \(-0.691205\pi\)
−0.565210 + 0.824947i \(0.691205\pi\)
\(758\) 352.522i 0.465069i
\(759\) −88.9055 88.9055i −0.117135 0.117135i
\(760\) 145.949 + 145.949i 0.192039 + 0.192039i
\(761\) 303.471 303.471i 0.398779 0.398779i −0.479023 0.877802i \(-0.659009\pi\)
0.877802 + 0.479023i \(0.159009\pi\)
\(762\) −115.100 + 115.100i −0.151050 + 0.151050i
\(763\) 1104.78 1.44794
\(764\) 401.127i 0.525036i
\(765\) 244.687 244.687i 0.319852 0.319852i
\(766\) 397.312i 0.518684i
\(767\) 0 0
\(768\) 27.7128 0.0360844
\(769\) 311.509 + 311.509i 0.405083 + 0.405083i 0.880020 0.474937i \(-0.157529\pi\)
−0.474937 + 0.880020i \(0.657529\pi\)
\(770\) −398.292 −0.517262
\(771\) 8.05193i 0.0104435i
\(772\) −37.0009 37.0009i −0.0479286 0.0479286i
\(773\) −845.415 845.415i −1.09368 1.09368i −0.995132 0.0985477i \(-0.968580\pi\)
−0.0985477 0.995132i \(-0.531420\pi\)
\(774\) 141.138 141.138i 0.182349 0.182349i
\(775\) 887.773 887.773i 1.14551 1.14551i
\(776\) 153.853 0.198265
\(777\) 590.116i 0.759481i
\(778\) 265.150 265.150i 0.340810 0.340810i
\(779\) 556.894i 0.714883i
\(780\) 0 0
\(781\) 838.250 1.07330
\(782\) −154.747 154.747i −0.197886 0.197886i
\(783\) −172.387 −0.220163
\(784\) 87.6320i 0.111775i
\(785\) −1392.77 1392.77i −1.77423 1.77423i
\(786\) 49.0650 + 49.0650i 0.0624237 + 0.0624237i
\(787\) 230.179 230.179i 0.292477 0.292477i −0.545581 0.838058i \(-0.683691\pi\)
0.838058 + 0.545581i \(0.183691\pi\)
\(788\) 133.960 133.960i 0.170000 0.170000i
\(789\) 23.9770 0.0303891
\(790\) 135.112i 0.171028i
\(791\) 437.197 437.197i 0.552714 0.552714i
\(792\) 64.3317i 0.0812270i
\(793\) 0 0
\(794\) 178.009 0.224193
\(795\) −590.160 590.160i −0.742340 0.742340i
\(796\) 394.398 0.495475
\(797\) 2.59745i 0.00325903i −0.999999 0.00162952i \(-0.999481\pi\)
0.999999 0.00162952i \(-0.000518691\pi\)
\(798\) −92.1821 92.1821i −0.115516 0.115516i
\(799\) 772.894 + 772.894i 0.967327 + 0.967327i
\(800\) −103.738 + 103.738i −0.129673 + 0.129673i
\(801\) −106.763 + 106.763i −0.133287 + 0.133287i
\(802\) −787.640 −0.982095
\(803\) 394.981i 0.491882i
\(804\) −105.847 + 105.847i −0.131651 + 0.131651i
\(805\) 355.673i 0.441830i
\(806\) 0 0
\(807\) −797.180 −0.987831
\(808\) 45.0994 + 45.0994i 0.0558161 + 0.0558161i
\(809\) −112.480 −0.139036 −0.0695179 0.997581i \(-0.522146\pi\)
−0.0695179 + 0.997581i \(0.522146\pi\)
\(810\) 90.8373i 0.112145i
\(811\) 725.545 + 725.545i 0.894630 + 0.894630i 0.994955 0.100324i \(-0.0319881\pi\)
−0.100324 + 0.994955i \(0.531988\pi\)
\(812\) 244.207 + 244.207i 0.300748 + 0.300748i
\(813\) −181.647 + 181.647i −0.223428 + 0.223428i
\(814\) 496.267 496.267i 0.609665 0.609665i
\(815\) 1003.28 1.23101
\(816\) 111.974i 0.137223i
\(817\) 340.153 340.153i 0.416344 0.416344i
\(818\) 292.007i 0.356977i
\(819\) 0 0
\(820\) 777.398 0.948047
\(821\) −392.048 392.048i −0.477525 0.477525i 0.426815 0.904339i \(-0.359636\pi\)
−0.904339 + 0.426815i \(0.859636\pi\)
\(822\) −123.291 −0.149989
\(823\) 111.028i 0.134907i 0.997722 + 0.0674534i \(0.0214874\pi\)
−0.997722 + 0.0674534i \(0.978513\pi\)
\(824\) 218.770 + 218.770i 0.265498 + 0.265498i
\(825\) 240.816 + 240.816i 0.291898 + 0.291898i
\(826\) −391.990 + 391.990i −0.474564 + 0.474564i
\(827\) 878.475 878.475i 1.06224 1.06224i 0.0643137 0.997930i \(-0.479514\pi\)
0.997930 0.0643137i \(-0.0204858\pi\)
\(828\) 57.4480 0.0693817
\(829\) 826.511i 0.996998i 0.866890 + 0.498499i \(0.166115\pi\)
−0.866890 + 0.498499i \(0.833885\pi\)
\(830\) −939.900 + 939.900i −1.13241 + 1.13241i
\(831\) 646.559i 0.778050i
\(832\) 0 0
\(833\) −354.079 −0.425065
\(834\) 256.835 + 256.835i 0.307956 + 0.307956i
\(835\) 1402.40 1.67952
\(836\) 155.044i 0.185459i
\(837\) −177.871 177.871i −0.212510 0.212510i
\(838\) −335.412 335.412i −0.400253 0.400253i
\(839\) −220.394 + 220.394i −0.262686 + 0.262686i −0.826144 0.563458i \(-0.809470\pi\)
0.563458 + 0.826144i \(0.309470\pi\)
\(840\) 128.682 128.682i 0.153193 0.153193i
\(841\) 259.643 0.308732
\(842\) 549.254i 0.652321i
\(843\) −235.730 + 235.730i −0.279632 + 0.279632i
\(844\) 389.670i 0.461694i
\(845\) 0 0
\(846\) −286.928 −0.339159
\(847\) −233.784 233.784i −0.276014 0.276014i
\(848\) −270.071 −0.318480
\(849\) 659.383i 0.776658i
\(850\) 419.158 + 419.158i 0.493127 + 0.493127i
\(851\) 443.165 + 443.165i 0.520758 + 0.520758i
\(852\) −270.826 + 270.826i −0.317871 + 0.317871i
\(853\) 724.409 724.409i 0.849249 0.849249i −0.140791 0.990039i \(-0.544964\pi\)
0.990039 + 0.140791i \(0.0449645\pi\)
\(854\) 519.092 0.607836
\(855\) 218.924i 0.256051i
\(856\) −65.7500 + 65.7500i −0.0768107 + 0.0768107i
\(857\) 49.0244i 0.0572047i −0.999591 0.0286023i \(-0.990894\pi\)
0.999591 0.0286023i \(-0.00910565\pi\)
\(858\) 0 0
\(859\) −584.617 −0.680578 −0.340289 0.940321i \(-0.610525\pi\)
−0.340289 + 0.940321i \(0.610525\pi\)
\(860\) 474.838 + 474.838i 0.552137 + 0.552137i
\(861\) −491.008 −0.570276
\(862\) 194.439i 0.225568i
\(863\) 458.022 + 458.022i 0.530732 + 0.530732i 0.920790 0.390058i \(-0.127545\pi\)
−0.390058 + 0.920790i \(0.627545\pi\)
\(864\) 20.7846 + 20.7846i 0.0240563 + 0.0240563i
\(865\) −667.406 + 667.406i −0.771568 + 0.771568i
\(866\) 420.434 420.434i 0.485490 0.485490i
\(867\) 48.1276 0.0555105
\(868\) 503.950i 0.580588i
\(869\) −71.7658 + 71.7658i −0.0825843 + 0.0825843i
\(870\) 579.970i 0.666632i
\(871\) 0 0
\(872\) −600.344 −0.688467
\(873\) 115.390 + 115.390i 0.132176 + 0.132176i
\(874\) 138.454 0.158414
\(875\) 34.7187i 0.0396785i
\(876\) −127.612 127.612i −0.145676 0.145676i
\(877\) 228.121 + 228.121i 0.260116 + 0.260116i 0.825101 0.564985i \(-0.191118\pi\)
−0.564985 + 0.825101i \(0.691118\pi\)
\(878\) 745.361 745.361i 0.848930 0.848930i
\(879\) −6.76970 + 6.76970i −0.00770160 + 0.00770160i
\(880\) 216.434 0.245948
\(881\) 1259.45i 1.42957i −0.699345 0.714785i \(-0.746525\pi\)
0.699345 0.714785i \(-0.253475\pi\)
\(882\) 65.7240 65.7240i 0.0745170 0.0745170i
\(883\) 213.692i 0.242007i −0.992652 0.121003i \(-0.961389\pi\)
0.992652 0.121003i \(-0.0386112\pi\)
\(884\) 0 0
\(885\) 930.940 1.05191
\(886\) −661.917 661.917i −0.747084 0.747084i
\(887\) −267.572 −0.301660 −0.150830 0.988560i \(-0.548195\pi\)
−0.150830 + 0.988560i \(0.548195\pi\)
\(888\) 320.673i 0.361118i
\(889\) 244.579 + 244.579i 0.275117 + 0.275117i
\(890\) −359.188 359.188i −0.403582 0.403582i
\(891\) 48.2488 48.2488i 0.0541513 0.0541513i
\(892\) −579.310 + 579.310i −0.649450 + 0.649450i
\(893\) −691.517 −0.774375
\(894\) 102.515i 0.114670i
\(895\) 178.804 178.804i 0.199781 0.199781i
\(896\) 58.8878i 0.0657230i
\(897\) 0 0
\(898\) 44.3712 0.0494112
\(899\) 1135.65 + 1135.65i 1.26324 + 1.26324i
\(900\) −155.608 −0.172897
\(901\) 1091.23i 1.21113i
\(902\) −412.920 412.920i −0.457783 0.457783i
\(903\) −299.909 299.909i −0.332126 0.332126i
\(904\) −237.575 + 237.575i −0.262805 + 0.262805i
\(905\) 611.226 611.226i 0.675388 0.675388i
\(906\) 8.92473 0.00985070
\(907\) 49.8286i 0.0549378i 0.999623 + 0.0274689i \(0.00874473\pi\)
−0.999623 + 0.0274689i \(0.991255\pi\)
\(908\) 353.120 353.120i 0.388899 0.388899i
\(909\) 67.6491i 0.0744215i
\(910\) 0 0
\(911\) −465.226 −0.510676 −0.255338 0.966852i \(-0.582187\pi\)
−0.255338 + 0.966852i \(0.582187\pi\)
\(912\) 50.0923 + 50.0923i 0.0549258 + 0.0549258i
\(913\) 998.468 1.09361
\(914\) 230.017i 0.251659i
\(915\) −616.398 616.398i −0.673659 0.673659i
\(916\) −348.513 348.513i −0.380472 0.380472i
\(917\) 104.260 104.260i 0.113697 0.113697i
\(918\) 83.9807 83.9807i 0.0914823 0.0914823i
\(919\) 668.804 0.727752 0.363876 0.931447i \(-0.381453\pi\)
0.363876 + 0.931447i \(0.381453\pi\)
\(920\) 193.275i 0.210081i
\(921\) −393.673 + 393.673i −0.427440 + 0.427440i
\(922\) 113.912i 0.123549i
\(923\) 0 0
\(924\) −136.701 −0.147944
\(925\) −1200.39 1200.39i −1.29772 1.29772i
\(926\) 345.711 0.373338
\(927\) 328.156i 0.353997i
\(928\) −132.704 132.704i −0.143000 0.143000i
\(929\) 480.209 + 480.209i 0.516910 + 0.516910i 0.916635 0.399725i \(-0.130895\pi\)
−0.399725 + 0.916635i \(0.630895\pi\)
\(930\) 598.418 598.418i 0.643460 0.643460i
\(931\) 158.399 158.399i 0.170139 0.170139i
\(932\) 581.218 0.623624
\(933\) 534.968i 0.573385i
\(934\) −649.970 + 649.970i −0.695899 + 0.695899i
\(935\) 874.507i 0.935302i
\(936\) 0 0
\(937\) −210.517 −0.224671 −0.112336 0.993670i \(-0.535833\pi\)
−0.112336 + 0.993670i \(0.535833\pi\)
\(938\) 224.918 + 224.918i 0.239784 + 0.239784i
\(939\) 4.35888 0.00464205
\(940\) 965.325i 1.02694i
\(941\) 447.841 + 447.841i 0.475920 + 0.475920i 0.903824 0.427904i \(-0.140748\pi\)
−0.427904 + 0.903824i \(0.640748\pi\)
\(942\) −478.023 478.023i −0.507456 0.507456i
\(943\) 368.736 368.736i 0.391025 0.391025i
\(944\) 213.010 213.010i 0.225646 0.225646i
\(945\) 193.023 0.204257
\(946\) 504.427i 0.533221i
\(947\) −416.587 + 416.587i −0.439902 + 0.439902i −0.891979 0.452077i \(-0.850683\pi\)
0.452077 + 0.891979i \(0.350683\pi\)
\(948\) 46.3729i 0.0489165i
\(949\) 0 0
\(950\) −375.025 −0.394763
\(951\) 81.1397 + 81.1397i 0.0853204 + 0.0853204i
\(952\) −237.938 −0.249935
\(953\) 384.832i 0.403811i −0.979405 0.201906i \(-0.935287\pi\)
0.979405 0.201906i \(-0.0647135\pi\)
\(954\) −202.553 202.553i −0.212320 0.212320i
\(955\) −1012.15 1012.15i −1.05984 1.05984i
\(956\) −431.750 + 431.750i −0.451622 + 0.451622i
\(957\) −308.055 + 308.055i −0.321896 + 0.321896i
\(958\) −718.565 −0.750068
\(959\) 261.985i 0.273186i
\(960\) −69.9266 + 69.9266i −0.0728402 + 0.0728402i
\(961\) 1382.55i 1.43866i
\(962\) 0 0
\(963\) −98.6250 −0.102414
\(964\) −169.897 169.897i −0.176242 0.176242i
\(965\) 186.725 0.193498
\(966\) 122.073i 0.126370i
\(967\) 1196.08 + 1196.08i 1.23690 + 1.23690i 0.961262 + 0.275638i \(0.0888891\pi\)
0.275638 + 0.961262i \(0.411111\pi\)
\(968\) 127.040 + 127.040i 0.131239 + 0.131239i
\(969\) 202.399 202.399i 0.208874 0.208874i
\(970\) −388.212 + 388.212i −0.400218 + 0.400218i
\(971\) 299.923 0.308881 0.154440 0.988002i \(-0.450643\pi\)
0.154440 + 0.988002i \(0.450643\pi\)
\(972\) 31.1769i 0.0320750i
\(973\) 545.758 545.758i 0.560902 0.560902i
\(974\) 1097.44i 1.12674i
\(975\) 0 0
\(976\) −282.078 −0.289014
\(977\) 169.795 + 169.795i 0.173792 + 0.173792i 0.788643 0.614851i \(-0.210784\pi\)
−0.614851 + 0.788643i \(0.710784\pi\)
\(978\) 344.341 0.352087
\(979\) 381.570i 0.389755i
\(980\) 221.118 + 221.118i 0.225631 + 0.225631i
\(981\) −450.258 450.258i −0.458978 0.458978i
\(982\) −125.014 + 125.014i −0.127305 + 0.127305i
\(983\) −503.122 + 503.122i −0.511823 + 0.511823i −0.915085 0.403261i \(-0.867877\pi\)
0.403261 + 0.915085i \(0.367877\pi\)
\(984\) 266.816 0.271155
\(985\) 676.030i 0.686325i
\(986\) −536.193 + 536.193i −0.543806 + 0.543806i
\(987\) 609.703i 0.617734i
\(988\) 0 0
\(989\) 450.451 0.455461
\(990\) 162.326 + 162.326i 0.163965 + 0.163965i
\(991\) −536.965 −0.541842 −0.270921 0.962602i \(-0.587328\pi\)
−0.270921 + 0.962602i \(0.587328\pi\)
\(992\) 273.850i 0.276058i
\(993\) −294.217 294.217i −0.296291 0.296291i
\(994\) 575.486 + 575.486i 0.578960 + 0.578960i
\(995\) −995.169 + 995.169i −1.00017 + 1.00017i
\(996\) −322.590 + 322.590i −0.323886 + 0.323886i
\(997\) −1019.21 −1.02228 −0.511139 0.859498i \(-0.670776\pi\)
−0.511139 + 0.859498i \(0.670776\pi\)
\(998\) 302.812i 0.303419i
\(999\) −240.505 + 240.505i −0.240745 + 0.240745i
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 1014.3.f.h.775.3 8
13.2 odd 12 78.3.l.c.19.1 8
13.5 odd 4 inner 1014.3.f.h.577.3 8
13.8 odd 4 1014.3.f.j.577.4 8
13.9 even 3 78.3.l.c.37.1 yes 8
13.12 even 2 1014.3.f.j.775.4 8
39.2 even 12 234.3.bb.d.19.2 8
39.35 odd 6 234.3.bb.d.37.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
78.3.l.c.19.1 8 13.2 odd 12
78.3.l.c.37.1 yes 8 13.9 even 3
234.3.bb.d.19.2 8 39.2 even 12
234.3.bb.d.37.2 8 39.35 odd 6
1014.3.f.h.577.3 8 13.5 odd 4 inner
1014.3.f.h.775.3 8 1.1 even 1 trivial
1014.3.f.j.577.4 8 13.8 odd 4
1014.3.f.j.775.4 8 13.12 even 2