Properties

Label 1014.3.f.j.775.4
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 775.4
Root \(5.41254 + 5.41254i\) of defining polynomial
Character \(\chi\) \(=\) 1014.775
Dual form 1014.3.f.j.577.4

$q$-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 \(0.00297517\pi\)
0.00934664 + 0.999956i \(0.497025\pi\)
\(6\) 1.73205 + 1.73205i 0.288675 + 0.288675i
\(7\) 3.68049 3.68049i 0.525784 0.525784i −0.393528 0.919313i \(-0.628746\pi\)
0.919313 + 0.393528i \(0.128746\pi\)
\(8\) −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 −0.907473 0.420111i \(-0.861991\pi\)
0.420111 + 0.907473i \(0.361991\pi\)
\(12\) 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 0.871296 0.490759i \(-0.163280\pi\)
−0.490759 + 0.871296i \(0.663280\pi\)
\(20\) −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 \(0.0351934\pi\)
0.110338 + 0.993894i \(0.464807\pi\)
\(32\) −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 \(-0.404462\pi\)
0.955295 0.295655i \(-0.0955378\pi\)
\(38\) 14.4604i 0.380537i
\(39\) 0 0
\(40\) −20.1861 −0.504651
\(41\) −38.5116 38.5116i −0.939308 0.939308i 0.0589525 0.998261i \(-0.481224\pi\)
−0.998261 + 0.0589525i \(0.981224\pi\)
\(42\) 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 \(0.505613\pi\)
−0.999845 + 0.0176317i \(0.994387\pi\)
\(48\) −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 −0.0930750 0.995659i \(-0.529670\pi\)
0.995659 + 0.0930750i \(0.0296696\pi\)
\(60\) −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 0.441306 0.897357i \(-0.354515\pi\)
−0.897357 + 0.441306i \(0.854515\pi\)
\(68\) −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 \(-0.965920\pi\)
−0.106862 0.994274i \(-0.534080\pi\)
\(72\) −6.00000 + 6.00000i −0.0833333 + 0.0833333i
\(73\) 36.8385 36.8385i 0.504638 0.504638i −0.408238 0.912876i \(-0.633857\pi\)
0.912876 + 0.408238i \(0.133857\pi\)
\(74\) 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 \(-0.958333\pi\)
−0.130528 0.991445i \(-0.541667\pi\)
\(84\) 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 −0.478322 0.878184i \(-0.658755\pi\)
0.878184 + 0.478322i \(0.158755\pi\)
\(90\) 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 0.480478 0.877007i \(-0.340463\pi\)
−0.877007 + 0.480478i \(0.840463\pi\)
\(98\) −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 \(0.176752\pi\)
0.527183 + 0.849752i \(0.323248\pi\)
\(110\) −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 −0.824968 0.565179i \(-0.808807\pi\)
0.565179 + 0.824968i \(0.308807\pi\)
\(138\) 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 0.600792 0.799406i \(-0.294852\pi\)
−0.799406 + 0.600792i \(0.794852\pi\)
\(150\) −44.9201 + 44.9201i −0.299467 + 0.299467i
\(151\) 2.57635 2.57635i 0.0170619 0.0170619i −0.698524 0.715586i \(-0.746160\pi\)
0.715586 + 0.698524i \(0.246160\pi\)
\(152\) −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 −0.333069 0.942902i \(-0.608084\pi\)
0.942902 + 0.333069i \(0.108084\pi\)
\(164\) 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 −0.155774 0.987793i \(-0.549787\pi\)
0.987793 + 0.155774i \(0.0497872\pi\)
\(168\) 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 −0.657552 0.753409i \(-0.728408\pi\)
0.753409 + 0.657552i \(0.228408\pi\)
\(194\) 76.9267i 0.396529i
\(195\) 0 0
\(196\) −43.8160 −0.223551
\(197\) 66.9799 + 66.9799i 0.339999 + 0.339999i 0.856367 0.516368i \(-0.172716\pi\)
−0.516368 + 0.856367i \(0.672716\pi\)
\(198\) −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 \(-0.879432\pi\)
−0.369782 0.929119i \(-0.620568\pi\)
\(224\) −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 0.979456 0.201658i \(-0.0646329\pi\)
−0.201658 + 0.979456i \(0.564633\pi\)
\(228\) −25.0462 + 25.0462i −0.109852 + 0.109852i
\(229\) 174.256 174.256i 0.760945 0.760945i −0.215548 0.976493i \(-0.569154\pi\)
0.976493 + 0.215548i \(0.0691539\pi\)
\(230\) 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 0.0924720 0.995715i \(-0.470523\pi\)
−0.995715 + 0.0924720i \(0.970523\pi\)
\(240\) −34.9633 34.9633i −0.145680 0.145680i
\(241\) 84.9486 84.9486i 0.352484 0.352484i −0.508549 0.861033i \(-0.669818\pi\)
0.861033 + 0.508549i \(0.169818\pi\)
\(242\) −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 −0.486624 0.873612i \(-0.661772\pi\)
0.873612 + 0.486624i \(0.161772\pi\)
\(272\) 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 −0.422177 0.906514i \(-0.638734\pi\)
0.906514 + 0.422177i \(0.138734\pi\)
\(282\) −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 −0.700406 0.713745i \(-0.746998\pi\)
0.713745 + 0.700406i \(0.246998\pi\)
\(294\) −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 −0.232296 0.972645i \(-0.574624\pi\)
0.972645 + 0.232296i \(0.0746240\pi\)
\(308\) −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 0.629346 0.777125i \(-0.283323\pi\)
−0.777125 + 0.629346i \(0.783323\pi\)
\(318\) 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 0.915503 0.402311i \(-0.131793\pi\)
−0.402311 + 0.915503i \(0.631793\pi\)
\(332\) 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 −0.0177827 0.999842i \(-0.505661\pi\)
0.999842 + 0.0177827i \(0.00566072\pi\)
\(350\) 190.904i 0.545441i
\(351\) 0 0
\(352\) 42.8878 0.121840
\(353\) 139.237 + 139.237i 0.394439 + 0.394439i 0.876266 0.481827i \(-0.160027\pi\)
−0.481827 + 0.876266i \(0.660027\pi\)
\(354\) 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 −0.627699 0.778456i \(-0.716003\pi\)
0.778456 + 0.627699i \(0.216003\pi\)
\(360\) −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 0.900313 0.435244i \(-0.143338\pi\)
−0.435244 + 0.900313i \(0.643338\pi\)
\(380\) −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 0.917173 0.398489i \(-0.130465\pi\)
−0.398489 + 0.917173i \(0.630465\pi\)
\(384\) 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 −0.586068 0.810262i \(-0.699325\pi\)
0.810262 + 0.586068i \(0.199325\pi\)
\(398\) 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 −0.999842 0.0177478i \(-0.994350\pi\)
0.0177478 + 0.999842i \(0.494350\pi\)
\(402\) 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 0.862697 0.505721i \(-0.168773\pi\)
−0.505721 + 0.862697i \(0.668773\pi\)
\(410\) 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 0.301230 0.953551i \(-0.402603\pi\)
−0.953551 + 0.301230i \(0.902603\pi\)
\(422\) −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 0.585270 0.810838i \(-0.300988\pi\)
−0.810838 + 0.585270i \(0.800988\pi\)
\(432\) −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 −0.681969 0.731381i \(-0.738876\pi\)
0.731381 + 0.681969i \(0.238876\pi\)
\(450\) −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 0.821651 0.569991i \(-0.193053\pi\)
−0.569991 + 0.821651i \(0.693053\pi\)
\(458\) 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 0.642629 0.766178i \(-0.277844\pi\)
−0.766178 + 0.642629i \(0.777844\pi\)
\(462\) −68.3503 + 68.3503i −0.147944 + 0.147944i
\(463\) 172.856 172.856i 0.373338 0.373338i −0.495353 0.868692i \(-0.664961\pi\)
0.868692 + 0.495353i \(0.164961\pi\)
\(464\) 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 −0.974492 0.224423i \(-0.927950\pi\)
0.224423 + 0.974492i \(0.427950\pi\)
\(480\) 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 \(-0.956564\pi\)
−0.136034 0.990704i \(-0.543436\pi\)
\(488\) −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 0.538931 0.842350i \(-0.318828\pi\)
−0.842350 + 0.538931i \(0.818828\pi\)
\(500\) −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 \(0.146413\pi\)
0.443920 + 0.896066i \(0.353587\pi\)
\(510\) −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 \(0.541157\pi\)
−0.991653 + 0.128938i \(0.958843\pi\)
\(542\) 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 −0.924995 0.379979i \(-0.875931\pi\)
0.379979 + 0.924995i \(0.375931\pi\)
\(558\) 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 0.849930 0.526895i \(-0.176644\pi\)
−0.526895 + 0.849930i \(0.676644\pi\)
\(578\) 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 0.0533553 0.998576i \(-0.483008\pi\)
−0.998576 + 0.0533553i \(0.983008\pi\)
\(588\) −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 −0.315898 0.948793i \(-0.602306\pi\)
0.948793 + 0.315898i \(0.102306\pi\)
\(594\) −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 0.809353 0.587323i \(-0.199818\pi\)
−0.587323 + 0.809353i \(0.699818\pi\)
\(614\) 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 0.718389 0.695641i \(-0.244880\pi\)
−0.695641 + 0.718389i \(0.744880\pi\)
\(618\) −189.461 + 189.461i −0.306571 + 0.306571i
\(619\) 319.972 319.972i 0.516917 0.516917i −0.399720 0.916637i \(-0.630893\pi\)
0.916637 + 0.399720i \(0.130893\pi\)
\(620\) −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 −0.908601 0.417666i \(-0.862848\pi\)
0.417666 + 0.908601i \(0.362848\pi\)
\(632\) 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 0.449457 0.893302i \(-0.351618\pi\)
−0.893302 + 0.449457i \(0.851618\pi\)
\(644\) 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 −0.952596 0.304239i \(-0.901598\pi\)
0.304239 + 0.952596i \(0.401598\pi\)
\(662\) 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 −0.993032 0.117842i \(-0.962402\pi\)
0.117842 + 0.993032i \(0.462402\pi\)
\(684\) −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 0.278207 0.960521i \(-0.410260\pi\)
−0.960521 + 0.278207i \(0.910260\pi\)
\(692\) 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 −0.515149 0.857101i \(-0.672263\pi\)
0.857101 + 0.515149i \(0.172263\pi\)
\(710\) 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 \(0.106369\pi\)
0.327985 + 0.944683i \(0.393631\pi\)
\(734\) −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 −0.603821 0.797120i \(-0.706356\pi\)
0.797120 + 0.603821i \(0.206356\pi\)
\(740\) 934.314i 1.26259i
\(741\) 0 0
\(742\) 496.996 0.669806
\(743\) 741.898 + 741.898i 0.998517 + 0.998517i 0.999999 0.00148231i \(-0.000471834\pi\)
−0.00148231 + 0.999999i \(0.500472\pi\)
\(744\) −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 −0.877802 0.479023i \(-0.840991\pi\)
0.479023 + 0.877802i \(0.340991\pi\)
\(762\) 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 0.474937 0.880020i \(-0.342471\pi\)
−0.880020 + 0.474937i \(0.842471\pi\)
\(770\) −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 \(0.0314197\pi\)
0.0985477 + 0.995132i \(0.468580\pi\)
\(774\) −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 −0.838058 0.545581i \(-0.816309\pi\)
0.545581 + 0.838058i \(0.316309\pi\)
\(788\) −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 0.100324 0.994955i \(-0.468012\pi\)
−0.994955 + 0.100324i \(0.968012\pi\)
\(812\) −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 0.904339 0.426815i \(-0.140364\pi\)
−0.426815 + 0.904339i \(0.640364\pi\)
\(822\) −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 \(0.520486\pi\)
−0.997930 + 0.0643137i \(0.979514\pi\)
\(828\) 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 −0.563458 0.826144i \(-0.690530\pi\)
0.826144 + 0.563458i \(0.190530\pi\)
\(840\) −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 −0.990039 0.140791i \(-0.955036\pi\)
0.140791 + 0.990039i \(0.455036\pi\)
\(854\) 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 0.390058 0.920790i \(-0.372455\pi\)
−0.920790 + 0.390058i \(0.872455\pi\)
\(864\) −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 0.564985 0.825101i \(-0.308882\pi\)
−0.825101 + 0.564985i \(0.808882\pi\)
\(878\) −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 0.399725 0.916635i \(-0.369105\pi\)
−0.916635 + 0.399725i \(0.869105\pi\)
\(930\) −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 0.427904 0.903824i \(-0.359252\pi\)
−0.903824 + 0.427904i \(0.859252\pi\)
\(942\) 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 −0.452077 0.891979i \(-0.649317\pi\)
0.891979 + 0.452077i \(0.149317\pi\)
\(948\) 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 \(-0.911111\pi\)
−0.275638 0.961262i \(-0.588889\pi\)
\(968\) −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 0.614851 0.788643i \(-0.289216\pi\)
−0.788643 + 0.614851i \(0.789216\pi\)
\(978\) 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 −0.403261 0.915085i \(-0.632123\pi\)
0.915085 + 0.403261i \(0.132123\pi\)
\(984\) 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.j.775.4 8
13.4 even 6 78.3.l.c.37.1 yes 8
13.5 odd 4 inner 1014.3.f.j.577.4 8
13.8 odd 4 1014.3.f.h.577.3 8
13.11 odd 12 78.3.l.c.19.1 8
13.12 even 2 1014.3.f.h.775.3 8
39.11 even 12 234.3.bb.d.19.2 8
39.17 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 13.11 odd 12
78.3.l.c.37.1 yes 8 13.4 even 6
234.3.bb.d.19.2 8 39.11 even 12
234.3.bb.d.37.2 8 39.17 odd 6
1014.3.f.h.577.3 8 13.8 odd 4
1014.3.f.h.775.3 8 13.12 even 2
1014.3.f.j.577.4 8 13.5 odd 4 inner
1014.3.f.j.775.4 8 1.1 even 1 trivial