Properties

Label 128.4.k.a.5.2
Level $128$
Weight $4$
Character 128.5
Analytic conductor $7.552$
Analytic rank $0$
Dimension $752$
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] = [128,4,Mod(5,128)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(128, base_ring=CyclotomicField(32))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("128.5");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 128 = 2^{7} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 128.k (of order \(32\), degree \(16\), 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: \(7.55224448073\)
Analytic rank: \(0\)
Dimension: \(752\)
Relative dimension: \(47\) over \(\Q(\zeta_{32})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label 5.2
Character \(\chi\) \(=\) 128.5
Dual form 128.4.k.a.77.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.82184 + 0.192933i) q^{2} +(-9.75553 - 2.95931i) q^{3} +(7.92555 - 1.08885i) q^{4} +(-0.385980 - 0.0380157i) q^{5} +(28.0995 + 6.46853i) q^{6} +(8.69824 + 13.0178i) q^{7} +(-22.1546 + 4.60167i) q^{8} +(63.9633 + 42.7389i) q^{9} +O(q^{10})\) \(q+(-2.82184 + 0.192933i) q^{2} +(-9.75553 - 2.95931i) q^{3} +(7.92555 - 1.08885i) q^{4} +(-0.385980 - 0.0380157i) q^{5} +(28.0995 + 6.46853i) q^{6} +(8.69824 + 13.0178i) q^{7} +(-22.1546 + 4.60167i) q^{8} +(63.9633 + 42.7389i) q^{9} +(1.09651 + 0.0328059i) q^{10} +(-26.1023 + 48.8339i) q^{11} +(-80.5403 - 12.8318i) q^{12} +(-7.85581 - 79.7614i) q^{13} +(-27.0566 - 35.0561i) q^{14} +(3.65294 + 1.51310i) q^{15} +(61.6288 - 17.2595i) q^{16} +(47.9433 - 19.8588i) q^{17} +(-188.740 - 108.262i) q^{18} +(7.88262 - 9.60500i) q^{19} +(-3.10050 + 0.118980i) q^{20} +(-46.3322 - 152.737i) q^{21} +(64.2347 - 142.837i) q^{22} +(8.98677 + 45.1795i) q^{23} +(229.747 + 20.6705i) q^{24} +(-122.451 - 24.3569i) q^{25} +(37.5565 + 223.558i) q^{26} +(-322.900 - 393.455i) q^{27} +(83.1129 + 93.7024i) q^{28} +(-43.9891 + 23.5126i) q^{29} +(-10.5999 - 3.56494i) q^{30} +(-112.432 - 112.432i) q^{31} +(-170.577 + 60.5938i) q^{32} +(399.156 - 399.156i) q^{33} +(-131.457 + 65.2880i) q^{34} +(-2.86246 - 5.35529i) q^{35} +(553.481 + 269.083i) q^{36} +(20.0740 - 16.4743i) q^{37} +(-20.3904 + 28.6246i) q^{38} +(-159.401 + 801.363i) q^{39} +(8.72615 - 0.933930i) q^{40} +(173.362 - 34.4839i) q^{41} +(160.210 + 422.059i) q^{42} +(207.035 - 62.8034i) q^{43} +(-153.702 + 415.457i) q^{44} +(-23.0638 - 18.9280i) q^{45} +(-34.0758 - 125.756i) q^{46} +(-208.593 - 503.588i) q^{47} +(-652.298 - 14.0029i) q^{48} +(37.4558 - 90.4262i) q^{49} +(350.235 + 45.1066i) q^{50} +(-526.480 + 51.8538i) q^{51} +(-149.110 - 623.599i) q^{52} +(107.147 + 57.2712i) q^{53} +(987.083 + 1047.97i) q^{54} +(11.9314 - 17.8566i) q^{55} +(-252.609 - 248.378i) q^{56} +(-105.323 + 70.3748i) q^{57} +(119.594 - 74.8358i) q^{58} +(-7.03240 + 71.4012i) q^{59} +(30.5991 + 8.01462i) q^{60} +(-2.61145 + 8.60878i) q^{61} +(338.958 + 295.574i) q^{62} +1204.42i q^{63} +(469.649 - 203.896i) q^{64} +31.0849i q^{65} +(-1049.34 + 1203.36i) q^{66} +(250.224 - 824.876i) q^{67} +(358.354 - 209.595i) q^{68} +(46.0295 - 467.345i) q^{69} +(9.11062 + 14.5595i) q^{70} +(167.314 - 111.795i) q^{71} +(-1613.75 - 652.524i) q^{72} +(-136.148 + 203.760i) q^{73} +(-53.4672 + 50.3608i) q^{74} +(1122.49 + 599.984i) q^{75} +(52.0157 - 84.7079i) q^{76} +(-862.755 + 84.9740i) q^{77} +(295.195 - 2292.07i) q^{78} +(283.524 - 684.487i) q^{79} +(-24.4436 + 4.31896i) q^{80} +(1190.86 + 2874.98i) q^{81} +(-482.548 + 130.755i) q^{82} +(-777.382 - 637.981i) q^{83} +(-533.516 - 1160.07i) q^{84} +(-19.2601 + 5.84248i) q^{85} +(-572.103 + 217.165i) q^{86} +(498.718 - 99.2012i) q^{87} +(353.567 - 1202.01i) q^{88} +(56.7068 - 285.084i) q^{89} +(68.7341 + 48.9619i) q^{90} +(969.989 - 796.049i) q^{91} +(120.419 + 348.288i) q^{92} +(764.116 + 1429.56i) q^{93} +(685.775 + 1380.80i) q^{94} +(-3.40767 + 3.40767i) q^{95} +(1843.38 - 86.3359i) q^{96} +(-184.702 - 184.702i) q^{97} +(-88.2480 + 262.395i) q^{98} +(-3756.69 + 2007.99i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 752 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 752 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9} - 16 q^{10} - 16 q^{11} - 16 q^{12} - 16 q^{13} - 16 q^{14} - 16 q^{15} - 16 q^{16} - 16 q^{17} - 16 q^{18} - 16 q^{19} - 16 q^{20} - 16 q^{21} - 16 q^{22} - 16 q^{23} - 16 q^{24} - 16 q^{25} - 16 q^{26} - 16 q^{27} - 16 q^{28} - 16 q^{29} - 16 q^{30} - 16 q^{31} - 16 q^{32} - 16 q^{33} - 16 q^{34} - 16 q^{35} - 16 q^{36} - 16 q^{37} - 16 q^{38} - 16 q^{39} - 16 q^{40} - 16 q^{41} - 16 q^{42} - 16 q^{43} - 16 q^{44} - 16 q^{45} - 16 q^{46} - 16 q^{47} - 16 q^{48} - 16 q^{49} + 5696 q^{50} - 16 q^{51} + 6608 q^{52} - 16 q^{53} + 3440 q^{54} - 16 q^{55} - 800 q^{56} - 16 q^{57} - 4768 q^{58} - 16 q^{59} - 9808 q^{60} - 16 q^{61} - 5872 q^{62} - 12112 q^{64} - 10960 q^{66} - 16 q^{67} - 4144 q^{68} - 16 q^{69} - 4048 q^{70} - 16 q^{71} + 1280 q^{72} - 16 q^{73} + 5248 q^{74} - 16 q^{75} + 11888 q^{76} - 16 q^{77} + 14096 q^{78} - 16 q^{79} + 10016 q^{80} - 16 q^{81} - 16 q^{82} - 16 q^{83} - 16 q^{84} - 16 q^{85} - 16 q^{86} - 16 q^{87} - 16 q^{88} - 16 q^{89} - 16 q^{90} - 16 q^{91} - 16 q^{92} - 16 q^{93} - 16 q^{94} - 16 q^{95} - 16 q^{96} - 16 q^{97} - 16 q^{98} - 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{32}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.82184 + 0.192933i −0.997671 + 0.0682121i
\(3\) −9.75553 2.95931i −1.87745 0.569519i −0.995093 0.0989452i \(-0.968453\pi\)
−0.882361 0.470574i \(-0.844047\pi\)
\(4\) 7.92555 1.08885i 0.990694 0.136107i
\(5\) −0.385980 0.0380157i −0.0345231 0.00340023i 0.0807408 0.996735i \(-0.474271\pi\)
−0.115264 + 0.993335i \(0.536771\pi\)
\(6\) 28.0995 + 6.46853i 1.91193 + 0.440128i
\(7\) 8.69824 + 13.0178i 0.469661 + 0.702897i 0.988372 0.152052i \(-0.0485882\pi\)
−0.518712 + 0.854949i \(0.673588\pi\)
\(8\) −22.1546 + 4.60167i −0.979103 + 0.203367i
\(9\) 63.9633 + 42.7389i 2.36901 + 1.58292i
\(10\) 1.09651 + 0.0328059i 0.0346746 + 0.00103741i
\(11\) −26.1023 + 48.8339i −0.715466 + 1.33854i 0.216602 + 0.976260i \(0.430503\pi\)
−0.932068 + 0.362283i \(0.881997\pi\)
\(12\) −80.5403 12.8318i −1.93750 0.308686i
\(13\) −7.85581 79.7614i −0.167601 1.70168i −0.600002 0.799998i \(-0.704834\pi\)
0.432401 0.901681i \(-0.357666\pi\)
\(14\) −27.0566 35.0561i −0.516513 0.669223i
\(15\) 3.65294 + 1.51310i 0.0628790 + 0.0260453i
\(16\) 61.6288 17.2595i 0.962950 0.269680i
\(17\) 47.9433 19.8588i 0.683997 0.283321i −0.0134996 0.999909i \(-0.504297\pi\)
0.697497 + 0.716588i \(0.254297\pi\)
\(18\) −188.740 108.262i −2.47147 1.41764i
\(19\) 7.88262 9.60500i 0.0951788 0.115976i −0.723243 0.690594i \(-0.757349\pi\)
0.818422 + 0.574618i \(0.194849\pi\)
\(20\) −3.10050 + 0.118980i −0.0346646 + 0.00133023i
\(21\) −46.3322 152.737i −0.481453 1.58714i
\(22\) 64.2347 142.837i 0.622495 1.38423i
\(23\) 8.98677 + 45.1795i 0.0814727 + 0.409591i 0.999902 + 0.0140054i \(0.00445822\pi\)
−0.918429 + 0.395585i \(0.870542\pi\)
\(24\) 229.747 + 20.6705i 1.95404 + 0.175806i
\(25\) −122.451 24.3569i −0.979605 0.194856i
\(26\) 37.5565 + 223.558i 0.283286 + 1.68628i
\(27\) −322.900 393.455i −2.30156 2.80446i
\(28\) 83.1129 + 93.7024i 0.560959 + 0.632432i
\(29\) −43.9891 + 23.5126i −0.281675 + 0.150558i −0.606184 0.795324i \(-0.707301\pi\)
0.324510 + 0.945882i \(0.394801\pi\)
\(30\) −10.5999 3.56494i −0.0645092 0.0216956i
\(31\) −112.432 112.432i −0.651402 0.651402i 0.301928 0.953331i \(-0.402370\pi\)
−0.953331 + 0.301928i \(0.902370\pi\)
\(32\) −170.577 + 60.5938i −0.942312 + 0.334737i
\(33\) 399.156 399.156i 2.10558 2.10558i
\(34\) −131.457 + 65.2880i −0.663078 + 0.329318i
\(35\) −2.86246 5.35529i −0.0138241 0.0258631i
\(36\) 553.481 + 269.083i 2.56241 + 1.24575i
\(37\) 20.0740 16.4743i 0.0891931 0.0731989i −0.588740 0.808322i \(-0.700376\pi\)
0.677933 + 0.735124i \(0.262876\pi\)
\(38\) −20.3904 + 28.6246i −0.0870461 + 0.122198i
\(39\) −159.401 + 801.363i −0.654477 + 3.29028i
\(40\) 8.72615 0.933930i 0.0344931 0.00369168i
\(41\) 173.362 34.4839i 0.660358 0.131353i 0.146476 0.989214i \(-0.453207\pi\)
0.513882 + 0.857861i \(0.328207\pi\)
\(42\) 160.210 + 422.059i 0.588593 + 1.55060i
\(43\) 207.035 62.8034i 0.734245 0.222731i 0.0990501 0.995082i \(-0.468420\pi\)
0.635195 + 0.772352i \(0.280920\pi\)
\(44\) −153.702 + 415.457i −0.526624 + 1.42347i
\(45\) −23.0638 18.9280i −0.0764032 0.0627025i
\(46\) −34.0758 125.756i −0.109222 0.403079i
\(47\) −208.593 503.588i −0.647370 1.56289i −0.816531 0.577302i \(-0.804106\pi\)
0.169160 0.985589i \(-0.445894\pi\)
\(48\) −652.298 14.0029i −1.96148 0.0421072i
\(49\) 37.4558 90.4262i 0.109200 0.263633i
\(50\) 350.235 + 45.1066i 0.990615 + 0.127581i
\(51\) −526.480 + 51.8538i −1.44553 + 0.142372i
\(52\) −149.110 623.599i −0.397651 1.66303i
\(53\) 107.147 + 57.2712i 0.277694 + 0.148430i 0.604365 0.796708i \(-0.293427\pi\)
−0.326671 + 0.945138i \(0.605927\pi\)
\(54\) 987.083 + 1047.97i 2.48750 + 2.64094i
\(55\) 11.9314 17.8566i 0.0292515 0.0437779i
\(56\) −252.609 248.378i −0.602792 0.592695i
\(57\) −105.323 + 70.3748i −0.244744 + 0.163533i
\(58\) 119.594 74.8358i 0.270749 0.169421i
\(59\) −7.03240 + 71.4012i −0.0155176 + 0.157553i −0.999821 0.0189329i \(-0.993973\pi\)
0.984303 + 0.176486i \(0.0564731\pi\)
\(60\) 30.5991 + 8.01462i 0.0658388 + 0.0172447i
\(61\) −2.61145 + 8.60878i −0.00548133 + 0.0180695i −0.959638 0.281237i \(-0.909255\pi\)
0.954157 + 0.299307i \(0.0967553\pi\)
\(62\) 338.958 + 295.574i 0.694319 + 0.605451i
\(63\) 1204.42i 2.40861i
\(64\) 469.649 203.896i 0.917284 0.398234i
\(65\) 31.0849i 0.0593171i
\(66\) −1049.34 + 1203.36i −1.95705 + 2.24430i
\(67\) 250.224 824.876i 0.456264 1.50410i −0.363608 0.931552i \(-0.618455\pi\)
0.819871 0.572548i \(-0.194045\pi\)
\(68\) 358.354 209.595i 0.639070 0.373781i
\(69\) 46.0295 467.345i 0.0803087 0.815388i
\(70\) 9.11062 + 14.5595i 0.0155561 + 0.0248599i
\(71\) 167.314 111.795i 0.279669 0.186869i −0.407823 0.913061i \(-0.633712\pi\)
0.687491 + 0.726192i \(0.258712\pi\)
\(72\) −1613.75 652.524i −2.64142 1.06806i
\(73\) −136.148 + 203.760i −0.218286 + 0.326689i −0.924410 0.381400i \(-0.875442\pi\)
0.706124 + 0.708088i \(0.250442\pi\)
\(74\) −53.4672 + 50.3608i −0.0839923 + 0.0791125i
\(75\) 1122.49 + 599.984i 1.72819 + 0.923736i
\(76\) 52.0157 84.7079i 0.0785080 0.127851i
\(77\) −862.755 + 84.9740i −1.27688 + 0.125762i
\(78\) 295.195 2292.07i 0.428515 3.32726i
\(79\) 283.524 684.487i 0.403784 0.974820i −0.582955 0.812504i \(-0.698104\pi\)
0.986739 0.162316i \(-0.0518963\pi\)
\(80\) −24.4436 + 4.31896i −0.0341610 + 0.00603593i
\(81\) 1190.86 + 2874.98i 1.63355 + 3.94373i
\(82\) −482.548 + 130.755i −0.649860 + 0.176092i
\(83\) −777.382 637.981i −1.02806 0.843705i −0.0402189 0.999191i \(-0.512806\pi\)
−0.987838 + 0.155486i \(0.950306\pi\)
\(84\) −533.516 1160.07i −0.692992 1.50684i
\(85\) −19.2601 + 5.84248i −0.0245770 + 0.00745537i
\(86\) −572.103 + 217.165i −0.717342 + 0.272297i
\(87\) 498.718 99.2012i 0.614577 0.122247i
\(88\) 353.567 1202.01i 0.428300 1.45607i
\(89\) 56.7068 285.084i 0.0675383 0.339538i −0.932211 0.361914i \(-0.882123\pi\)
0.999750 + 0.0223765i \(0.00712327\pi\)
\(90\) 68.7341 + 48.9619i 0.0805024 + 0.0573448i
\(91\) 969.989 796.049i 1.11739 0.917018i
\(92\) 120.419 + 348.288i 0.136462 + 0.394690i
\(93\) 764.116 + 1429.56i 0.851991 + 1.59396i
\(94\) 685.775 + 1380.80i 0.752471 + 1.51509i
\(95\) −3.40767 + 3.40767i −0.00368021 + 0.00368021i
\(96\) 1843.38 86.3359i 1.95979 0.0917877i
\(97\) −184.702 184.702i −0.193336 0.193336i 0.603800 0.797136i \(-0.293653\pi\)
−0.797136 + 0.603800i \(0.793653\pi\)
\(98\) −88.2480 + 262.395i −0.0909632 + 0.270468i
\(99\) −3756.69 + 2007.99i −3.81376 + 2.03849i
\(100\) −997.010 59.7116i −0.997010 0.0597116i
\(101\) −841.984 1025.96i −0.829510 1.01076i −0.999679 0.0253464i \(-0.991931\pi\)
0.170168 0.985415i \(-0.445569\pi\)
\(102\) 1475.64 247.899i 1.43245 0.240643i
\(103\) 1332.82 + 265.115i 1.27502 + 0.253617i 0.785765 0.618525i \(-0.212270\pi\)
0.489253 + 0.872142i \(0.337270\pi\)
\(104\) 541.078 + 1730.93i 0.510164 + 1.63203i
\(105\) 12.0769 + 60.7146i 0.0112246 + 0.0564299i
\(106\) −313.401 140.938i −0.287172 0.129143i
\(107\) 17.7636 + 58.5586i 0.0160492 + 0.0529073i 0.964599 0.263720i \(-0.0849495\pi\)
−0.948550 + 0.316627i \(0.897450\pi\)
\(108\) −2987.58 2766.76i −2.66185 2.46511i
\(109\) 848.614 1034.04i 0.745711 0.908651i −0.252551 0.967584i \(-0.581270\pi\)
0.998262 + 0.0589323i \(0.0187696\pi\)
\(110\) −30.2234 + 52.6904i −0.0261971 + 0.0456712i
\(111\) −244.585 + 101.310i −0.209144 + 0.0866303i
\(112\) 760.743 + 652.146i 0.641817 + 0.550197i
\(113\) −173.778 71.9814i −0.144670 0.0599242i 0.309174 0.951006i \(-0.399948\pi\)
−0.453844 + 0.891081i \(0.649948\pi\)
\(114\) 283.628 218.907i 0.233019 0.179846i
\(115\) −1.75118 17.7800i −0.00141999 0.0144174i
\(116\) −323.036 + 234.248i −0.258561 + 0.187495i
\(117\) 2906.43 5437.55i 2.29658 4.29659i
\(118\) 6.06866 202.839i 0.00473445 0.158245i
\(119\) 675.540 + 451.381i 0.520392 + 0.347715i
\(120\) −87.8921 16.7124i −0.0668617 0.0127135i
\(121\) −963.958 1442.66i −0.724236 1.08390i
\(122\) 5.70816 24.7964i 0.00423600 0.0184013i
\(123\) −1793.29 176.624i −1.31460 0.129477i
\(124\) −1013.51 768.667i −0.734001 0.556680i
\(125\) 92.7309 + 28.1296i 0.0663528 + 0.0201279i
\(126\) −232.372 3398.67i −0.164296 2.40300i
\(127\) −2764.94 −1.93188 −0.965939 0.258771i \(-0.916683\pi\)
−0.965939 + 0.258771i \(0.916683\pi\)
\(128\) −1285.94 + 665.972i −0.887983 + 0.459876i
\(129\) −2205.59 −1.50536
\(130\) −5.99731 87.7167i −0.00404615 0.0591790i
\(131\) −415.091 125.916i −0.276845 0.0839799i 0.148809 0.988866i \(-0.452456\pi\)
−0.425654 + 0.904886i \(0.639956\pi\)
\(132\) 2728.91 3598.16i 1.79940 2.37257i
\(133\) 193.601 + 19.0681i 0.126221 + 0.0124317i
\(134\) −546.945 + 2375.95i −0.352603 + 1.53172i
\(135\) 109.676 + 164.141i 0.0699213 + 0.104645i
\(136\) −970.779 + 660.581i −0.612085 + 0.416503i
\(137\) −151.968 101.541i −0.0947698 0.0633232i 0.507282 0.861780i \(-0.330650\pi\)
−0.602052 + 0.798457i \(0.705650\pi\)
\(138\) −39.7215 + 1327.65i −0.0245023 + 0.818967i
\(139\) −435.105 + 814.024i −0.265504 + 0.496724i −0.978980 0.203956i \(-0.934620\pi\)
0.713476 + 0.700680i \(0.247120\pi\)
\(140\) −28.5177 39.3269i −0.0172156 0.0237409i
\(141\) 544.663 + 5530.06i 0.325312 + 3.30294i
\(142\) −450.563 + 347.749i −0.266271 + 0.205510i
\(143\) 4100.12 + 1698.32i 2.39768 + 0.993153i
\(144\) 4679.63 + 1529.97i 2.70812 + 0.885400i
\(145\) 17.8727 7.40313i 0.0102362 0.00423998i
\(146\) 344.875 601.245i 0.195494 0.340817i
\(147\) −633.000 + 771.313i −0.355163 + 0.432767i
\(148\) 141.159 152.426i 0.0784002 0.0846575i
\(149\) 516.585 + 1702.95i 0.284029 + 0.936317i 0.976618 + 0.214984i \(0.0689700\pi\)
−0.692589 + 0.721332i \(0.743530\pi\)
\(150\) −3283.25 1476.49i −1.78717 0.803701i
\(151\) −304.034 1528.48i −0.163854 0.823749i −0.972039 0.234820i \(-0.924550\pi\)
0.808185 0.588929i \(-0.200450\pi\)
\(152\) −130.437 + 249.068i −0.0696042 + 0.132908i
\(153\) 3915.35 + 778.811i 2.06887 + 0.411524i
\(154\) 2418.16 406.237i 1.26533 0.212568i
\(155\) 39.1225 + 47.6709i 0.0202735 + 0.0247033i
\(156\) −390.775 + 6524.81i −0.200558 + 3.34874i
\(157\) 333.186 178.092i 0.169371 0.0905304i −0.384533 0.923111i \(-0.625638\pi\)
0.553904 + 0.832581i \(0.313138\pi\)
\(158\) −667.998 + 1986.21i −0.336349 + 1.00009i
\(159\) −875.792 875.792i −0.436823 0.436823i
\(160\) 68.1427 16.9034i 0.0336697 0.00835207i
\(161\) −509.971 + 509.971i −0.249636 + 0.249636i
\(162\) −3915.08 7882.97i −1.89875 3.82312i
\(163\) 1097.56 + 2053.39i 0.527407 + 0.986709i 0.994721 + 0.102618i \(0.0327218\pi\)
−0.467314 + 0.884091i \(0.654778\pi\)
\(164\) 1336.45 462.070i 0.636335 0.220010i
\(165\) −169.240 + 138.892i −0.0798506 + 0.0655317i
\(166\) 2316.73 + 1650.30i 1.08321 + 0.771613i
\(167\) −126.626 + 636.593i −0.0586744 + 0.294976i −0.998970 0.0453838i \(-0.985549\pi\)
0.940295 + 0.340360i \(0.110549\pi\)
\(168\) 1729.31 + 3170.61i 0.794163 + 1.45606i
\(169\) −4145.38 + 824.568i −1.88684 + 0.375315i
\(170\) 53.2216 20.2024i 0.0240113 0.00911445i
\(171\) 914.705 277.473i 0.409060 0.124087i
\(172\) 1572.48 723.182i 0.697098 0.320594i
\(173\) 270.756 + 222.204i 0.118990 + 0.0976524i 0.692006 0.721891i \(-0.256727\pi\)
−0.573017 + 0.819544i \(0.694227\pi\)
\(174\) −1388.16 + 376.149i −0.604807 + 0.163884i
\(175\) −748.030 1805.90i −0.323119 0.780077i
\(176\) −765.802 + 3460.09i −0.327980 + 1.48190i
\(177\) 279.903 675.746i 0.118863 0.286961i
\(178\) −105.015 + 815.403i −0.0442204 + 0.343354i
\(179\) 2337.44 230.217i 0.976023 0.0961299i 0.402588 0.915381i \(-0.368111\pi\)
0.573435 + 0.819251i \(0.305611\pi\)
\(180\) −203.403 124.901i −0.0842265 0.0517200i
\(181\) 2118.85 + 1132.55i 0.870126 + 0.465092i 0.845108 0.534595i \(-0.179536\pi\)
0.0250177 + 0.999687i \(0.492036\pi\)
\(182\) −2583.57 + 2433.47i −1.05224 + 0.991102i
\(183\) 50.9521 76.2552i 0.0205819 0.0308030i
\(184\) −406.999 959.579i −0.163067 0.384462i
\(185\) −8.37444 + 5.59562i −0.00332811 + 0.00222378i
\(186\) −2432.02 3886.57i −0.958734 1.53213i
\(187\) −281.648 + 2859.62i −0.110140 + 1.11827i
\(188\) −2201.55 3764.09i −0.854066 1.46024i
\(189\) 2313.27 7625.83i 0.890295 2.93491i
\(190\) 8.95845 10.2734i 0.00342060 0.00392267i
\(191\) 2507.13i 0.949790i −0.880043 0.474895i \(-0.842486\pi\)
0.880043 0.474895i \(-0.157514\pi\)
\(192\) −5185.07 + 599.275i −1.94896 + 0.225255i
\(193\) 2859.30i 1.06641i 0.845987 + 0.533204i \(0.179012\pi\)
−0.845987 + 0.533204i \(0.820988\pi\)
\(194\) 556.834 + 485.564i 0.206074 + 0.179698i
\(195\) 91.9899 303.250i 0.0337822 0.111365i
\(196\) 198.397 757.462i 0.0723021 0.276043i
\(197\) 193.329 1962.90i 0.0699193 0.709903i −0.894773 0.446522i \(-0.852662\pi\)
0.964692 0.263381i \(-0.0848375\pi\)
\(198\) 10213.4 6391.03i 3.66582 2.29389i
\(199\) 3439.28 2298.06i 1.22515 0.818618i 0.236908 0.971532i \(-0.423866\pi\)
0.988239 + 0.152914i \(0.0488659\pi\)
\(200\) 2824.92 23.8596i 0.998761 0.00843563i
\(201\) −4882.13 + 7306.62i −1.71323 + 2.56403i
\(202\) 2573.89 + 2732.65i 0.896525 + 0.951825i
\(203\) −688.711 368.124i −0.238118 0.127277i
\(204\) −4116.19 + 984.229i −1.41270 + 0.337793i
\(205\) −68.2254 + 6.71961i −0.0232442 + 0.00228936i
\(206\) −3812.16 490.966i −1.28935 0.166054i
\(207\) −1356.10 + 3273.92i −0.455340 + 1.09929i
\(208\) −1860.79 4780.01i −0.620300 1.59343i
\(209\) 263.295 + 635.651i 0.0871413 + 0.210378i
\(210\) −45.7929 168.997i −0.0150477 0.0555328i
\(211\) −797.468 654.465i −0.260189 0.213532i 0.495250 0.868751i \(-0.335076\pi\)
−0.755439 + 0.655219i \(0.772576\pi\)
\(212\) 911.559 + 337.239i 0.295312 + 0.109253i
\(213\) −1963.07 + 595.491i −0.631490 + 0.191560i
\(214\) −61.4238 161.816i −0.0196208 0.0516893i
\(215\) −82.2989 + 16.3703i −0.0261058 + 0.00519276i
\(216\) 8964.27 + 7230.95i 2.82380 + 2.27780i
\(217\) 485.663 2441.59i 0.151931 0.763807i
\(218\) −2195.15 + 3081.62i −0.681993 + 0.957401i
\(219\) 1931.18 1584.88i 0.595878 0.489024i
\(220\) 75.1198 154.515i 0.0230208 0.0473518i
\(221\) −1960.60 3668.02i −0.596760 1.11646i
\(222\) 670.634 333.070i 0.202748 0.100695i
\(223\) −1046.97 + 1046.97i −0.314395 + 0.314395i −0.846610 0.532214i \(-0.821360\pi\)
0.532214 + 0.846610i \(0.321360\pi\)
\(224\) −2272.52 1693.48i −0.677852 0.505135i
\(225\) −6791.35 6791.35i −2.01225 2.01225i
\(226\) 504.262 + 169.592i 0.148421 + 0.0499164i
\(227\) −3222.25 + 1722.33i −0.942152 + 0.503591i −0.869591 0.493773i \(-0.835617\pi\)
−0.0725614 + 0.997364i \(0.523117\pi\)
\(228\) −758.118 + 672.441i −0.220209 + 0.195322i
\(229\) −2372.67 2891.11i −0.684674 0.834278i 0.308463 0.951236i \(-0.400186\pi\)
−0.993137 + 0.116959i \(0.962686\pi\)
\(230\) 8.37191 + 49.8345i 0.00240012 + 0.0142869i
\(231\) 8668.10 + 1724.19i 2.46891 + 0.491098i
\(232\) 866.361 723.335i 0.245170 0.204695i
\(233\) −785.823 3950.60i −0.220948 1.11078i −0.918855 0.394594i \(-0.870885\pi\)
0.697907 0.716188i \(-0.254115\pi\)
\(234\) −7152.40 + 15904.6i −1.99815 + 4.44324i
\(235\) 61.3684 + 202.305i 0.0170350 + 0.0561570i
\(236\) 22.0097 + 573.551i 0.00607079 + 0.158199i
\(237\) −4791.53 + 5838.50i −1.31326 + 1.60022i
\(238\) −1993.35 1143.39i −0.542898 0.311408i
\(239\) 3876.09 1605.53i 1.04905 0.434532i 0.209499 0.977809i \(-0.432817\pi\)
0.839553 + 0.543277i \(0.182817\pi\)
\(240\) 251.242 + 30.2024i 0.0675732 + 0.00812315i
\(241\) 4773.42 + 1977.22i 1.27586 + 0.528480i 0.914742 0.404039i \(-0.132394\pi\)
0.361122 + 0.932519i \(0.382394\pi\)
\(242\) 2998.47 + 3884.99i 0.796484 + 1.03197i
\(243\) −1762.45 17894.5i −0.465273 4.72400i
\(244\) −11.3235 + 71.0728i −0.00297094 + 0.0186474i
\(245\) −17.8948 + 33.4788i −0.00466635 + 0.00873013i
\(246\) 5094.46 + 152.419i 1.32037 + 0.0395035i
\(247\) −828.033 553.274i −0.213305 0.142526i
\(248\) 3008.27 + 1973.52i 0.770263 + 0.505316i
\(249\) 5695.79 + 8524.35i 1.44962 + 2.16951i
\(250\) −267.099 61.4864i −0.0675712 0.0155550i
\(251\) 1062.82 + 104.678i 0.267268 + 0.0263236i 0.230763 0.973010i \(-0.425878\pi\)
0.0365046 + 0.999333i \(0.488378\pi\)
\(252\) 1311.43 + 9545.66i 0.327827 + 2.38619i
\(253\) −2440.87 740.429i −0.606546 0.183994i
\(254\) 7802.21 533.448i 1.92738 0.131777i
\(255\) 205.182 0.0503882
\(256\) 3500.22 2127.37i 0.854546 0.519376i
\(257\) −3806.73 −0.923958 −0.461979 0.886891i \(-0.652860\pi\)
−0.461979 + 0.886891i \(0.652860\pi\)
\(258\) 6223.83 425.532i 1.50185 0.102684i
\(259\) 389.068 + 118.023i 0.0933418 + 0.0283149i
\(260\) 33.8469 + 246.365i 0.00807345 + 0.0587651i
\(261\) −3818.59 376.098i −0.905612 0.0891950i
\(262\) 1195.61 + 275.231i 0.281928 + 0.0649002i
\(263\) −2904.58 4347.01i −0.681003 1.01919i −0.997505 0.0706016i \(-0.977508\pi\)
0.316501 0.948592i \(-0.397492\pi\)
\(264\) −7006.35 + 10679.9i −1.63337 + 2.48978i
\(265\) −39.1794 26.1788i −0.00908215 0.00606850i
\(266\) −549.990 16.4549i −0.126775 0.00379291i
\(267\) −1396.86 + 2613.34i −0.320173 + 0.599002i
\(268\) 1084.99 6810.06i 0.247300 1.55220i
\(269\) −128.210 1301.74i −0.0290600 0.295051i −0.998719 0.0505911i \(-0.983889\pi\)
0.969659 0.244460i \(-0.0786105\pi\)
\(270\) −341.155 442.020i −0.0768964 0.0996313i
\(271\) 5303.97 + 2196.98i 1.18890 + 0.492460i 0.887398 0.461004i \(-0.152511\pi\)
0.301506 + 0.953464i \(0.402511\pi\)
\(272\) 2611.93 2051.35i 0.582249 0.457284i
\(273\) −11818.5 + 4895.39i −2.62011 + 1.08528i
\(274\) 448.419 + 257.214i 0.0988685 + 0.0567112i
\(275\) 4385.68 5343.97i 0.961697 1.17183i
\(276\) −144.061 3754.09i −0.0314182 0.818730i
\(277\) 705.037 + 2324.20i 0.152930 + 0.504142i 0.999609 0.0279616i \(-0.00890162\pi\)
−0.846679 + 0.532104i \(0.821402\pi\)
\(278\) 1070.74 2380.99i 0.231003 0.513678i
\(279\) −2386.31 11996.8i −0.512059 2.57430i
\(280\) 88.0599 + 105.472i 0.0187949 + 0.0225113i
\(281\) −4405.88 876.385i −0.935349 0.186052i −0.296192 0.955129i \(-0.595717\pi\)
−0.639157 + 0.769076i \(0.720717\pi\)
\(282\) −2603.88 15499.9i −0.549855 3.27306i
\(283\) −827.644 1008.49i −0.173846 0.211832i 0.678797 0.734326i \(-0.262502\pi\)
−0.852643 + 0.522494i \(0.825002\pi\)
\(284\) 1204.32 1068.22i 0.251632 0.223194i
\(285\) 43.3280 23.1593i 0.00900537 0.00481347i
\(286\) −11897.5 4001.35i −2.45984 0.827289i
\(287\) 1956.85 + 1956.85i 0.402472 + 0.402472i
\(288\) −13500.3 3414.48i −2.76221 0.698611i
\(289\) −1569.83 + 1569.83i −0.319526 + 0.319526i
\(290\) −49.0057 + 24.3387i −0.00992315 + 0.00492834i
\(291\) 1255.28 + 2348.45i 0.252871 + 0.473089i
\(292\) −857.183 + 1763.15i −0.171791 + 0.353359i
\(293\) −4442.21 + 3645.63i −0.885723 + 0.726894i −0.962824 0.270129i \(-0.912934\pi\)
0.0771010 + 0.997023i \(0.475434\pi\)
\(294\) 1637.41 2298.65i 0.324816 0.455986i
\(295\) 5.42873 27.2921i 0.00107143 0.00538646i
\(296\) −368.921 + 457.355i −0.0724430 + 0.0898081i
\(297\) 27642.4 5498.41i 5.40059 1.07424i
\(298\) −1786.27 4705.79i −0.347235 0.914762i
\(299\) 3532.99 1071.72i 0.683337 0.207288i
\(300\) 9549.66 + 3532.98i 1.83783 + 0.679922i
\(301\) 2618.40 + 2148.87i 0.501403 + 0.411491i
\(302\) 1152.83 + 4254.47i 0.219662 + 0.810653i
\(303\) 5177.87 + 12500.5i 0.981719 + 2.37008i
\(304\) 320.019 727.995i 0.0603761 0.137347i
\(305\) 1.33523 3.22354i 0.000250673 0.000605178i
\(306\) −11198.7 1442.28i −2.09212 0.269443i
\(307\) −5483.52 + 540.080i −1.01942 + 0.100404i −0.593894 0.804544i \(-0.702410\pi\)
−0.425523 + 0.904947i \(0.639910\pi\)
\(308\) −6745.29 + 1612.88i −1.24788 + 0.298384i
\(309\) −12217.8 6530.57i −2.24935 1.20230i
\(310\) −119.595 126.972i −0.0219114 0.0232629i
\(311\) −1049.37 + 1570.49i −0.191332 + 0.286348i −0.914716 0.404098i \(-0.867586\pi\)
0.723384 + 0.690446i \(0.242586\pi\)
\(312\) −156.146 18487.4i −0.0283334 3.35462i
\(313\) 6909.23 4616.60i 1.24771 0.833692i 0.256570 0.966526i \(-0.417408\pi\)
0.991138 + 0.132834i \(0.0424077\pi\)
\(314\) −905.839 + 566.829i −0.162801 + 0.101873i
\(315\) 45.7867 464.880i 0.00818981 0.0831525i
\(316\) 1501.78 5733.65i 0.267347 1.02071i
\(317\) −1770.60 + 5836.87i −0.313712 + 1.03417i 0.648351 + 0.761341i \(0.275459\pi\)
−0.962063 + 0.272827i \(0.912041\pi\)
\(318\) 2640.31 + 2302.38i 0.465602 + 0.406009i
\(319\) 2761.89i 0.484753i
\(320\) −189.026 + 60.8456i −0.0330216 + 0.0106293i
\(321\) 623.839i 0.108471i
\(322\) 1340.67 1537.45i 0.232026 0.266082i
\(323\) 187.175 617.034i 0.0322437 0.106293i
\(324\) 12568.6 + 21489.1i 2.15511 + 3.68469i
\(325\) −980.795 + 9958.18i −0.167399 + 1.69963i
\(326\) −3493.30 5582.57i −0.593484 0.948435i
\(327\) −11338.7 + 7576.29i −1.91753 + 1.28125i
\(328\) −3682.09 + 1561.73i −0.619845 + 0.262903i
\(329\) 4741.23 7095.76i 0.794506 1.18906i
\(330\) 450.772 424.583i 0.0751946 0.0708258i
\(331\) 3092.92 + 1653.20i 0.513602 + 0.274526i 0.707771 0.706442i \(-0.249701\pi\)
−0.194169 + 0.980968i \(0.562201\pi\)
\(332\) −6855.85 4209.90i −1.13332 0.695928i
\(333\) 1988.09 195.810i 0.327167 0.0322232i
\(334\) 234.499 1820.79i 0.0384168 0.298292i
\(335\) −127.940 + 308.873i −0.0208659 + 0.0503748i
\(336\) −5491.56 8613.31i −0.891634 1.39850i
\(337\) −2668.33 6441.92i −0.431315 1.04129i −0.978864 0.204513i \(-0.934439\pi\)
0.547549 0.836774i \(-0.315561\pi\)
\(338\) 11538.5 3126.58i 1.85684 0.503146i
\(339\) 1482.29 + 1216.48i 0.237483 + 0.194897i
\(340\) −146.285 + 67.2763i −0.0233336 + 0.0107311i
\(341\) 8425.26 2555.77i 1.33799 0.405874i
\(342\) −2527.62 + 959.460i −0.399643 + 0.151701i
\(343\) 6769.92 1346.62i 1.06572 0.211984i
\(344\) −4297.77 + 2344.09i −0.673606 + 0.367398i
\(345\) −35.5329 + 178.636i −0.00554501 + 0.0278766i
\(346\) −806.901 574.786i −0.125374 0.0893084i
\(347\) 5775.23 4739.61i 0.893460 0.733244i −0.0709991 0.997476i \(-0.522619\pi\)
0.964459 + 0.264233i \(0.0851187\pi\)
\(348\) 3844.60 1329.25i 0.592219 0.204757i
\(349\) 2308.49 + 4318.88i 0.354070 + 0.662419i 0.994400 0.105681i \(-0.0337024\pi\)
−0.640330 + 0.768100i \(0.721202\pi\)
\(350\) 2459.24 + 4951.65i 0.375577 + 0.756220i
\(351\) −28845.9 + 28845.9i −4.38655 + 4.38655i
\(352\) 1493.40 9911.56i 0.226133 1.50082i
\(353\) −5583.58 5583.58i −0.841880 0.841880i 0.147223 0.989103i \(-0.452966\pi\)
−0.989103 + 0.147223i \(0.952966\pi\)
\(354\) −659.468 + 1960.85i −0.0990122 + 0.294401i
\(355\) −68.8297 + 36.7902i −0.0102904 + 0.00550034i
\(356\) 139.018 2321.20i 0.0206965 0.345571i
\(357\) −5254.48 6402.60i −0.778981 0.949192i
\(358\) −6551.45 + 1100.60i −0.967192 + 0.162483i
\(359\) −1040.16 206.901i −0.152918 0.0304174i 0.118037 0.993009i \(-0.462340\pi\)
−0.270956 + 0.962592i \(0.587340\pi\)
\(360\) 598.068 + 313.209i 0.0875582 + 0.0458543i
\(361\) 1308.00 + 6575.78i 0.190699 + 0.958708i
\(362\) −6197.56 2787.07i −0.899824 0.404656i
\(363\) 5134.63 + 16926.6i 0.742420 + 2.44743i
\(364\) 6820.92 7365.31i 0.982179 1.06057i
\(365\) 60.2964 73.4714i 0.00864673 0.0105361i
\(366\) −129.066 + 225.010i −0.0184328 + 0.0321352i
\(367\) −6846.55 + 2835.93i −0.973806 + 0.403364i −0.812128 0.583480i \(-0.801691\pi\)
−0.161678 + 0.986844i \(0.551691\pi\)
\(368\) 1333.62 + 2629.25i 0.188912 + 0.372444i
\(369\) 12562.6 + 5203.61i 1.77232 + 0.734117i
\(370\) 22.5517 17.4057i 0.00316867 0.00244561i
\(371\) 186.442 + 1892.98i 0.0260906 + 0.264902i
\(372\) 7612.63 + 10498.1i 1.06101 + 1.46317i
\(373\) 2536.84 4746.09i 0.352151 0.658829i −0.642014 0.766693i \(-0.721901\pi\)
0.994166 + 0.107864i \(0.0344010\pi\)
\(374\) 243.050 8123.71i 0.0336037 1.12317i
\(375\) −821.395 548.839i −0.113111 0.0755784i
\(376\) 6938.63 + 10196.9i 0.951682 + 1.39858i
\(377\) 2220.97 + 3323.92i 0.303411 + 0.454086i
\(378\) −5056.40 + 21965.2i −0.688025 + 2.98880i
\(379\) −11867.1 1168.81i −1.60837 0.158411i −0.746446 0.665446i \(-0.768241\pi\)
−0.861925 + 0.507035i \(0.830741\pi\)
\(380\) −23.2972 + 30.7181i −0.00314506 + 0.00414686i
\(381\) 26973.4 + 8182.30i 3.62701 + 1.10024i
\(382\) 483.709 + 7074.73i 0.0647872 + 0.947577i
\(383\) 9102.11 1.21435 0.607175 0.794568i \(-0.292303\pi\)
0.607175 + 0.794568i \(0.292303\pi\)
\(384\) 14515.8 2691.43i 1.92906 0.357673i
\(385\) 336.237 0.0445096
\(386\) −551.653 8068.47i −0.0727419 1.06392i
\(387\) 15926.8 + 4831.34i 2.09200 + 0.634601i
\(388\) −1664.98 1262.75i −0.217852 0.165223i
\(389\) 11483.2 + 1131.00i 1.49672 + 0.147414i 0.812970 0.582306i \(-0.197849\pi\)
0.683747 + 0.729720i \(0.260349\pi\)
\(390\) −201.074 + 873.471i −0.0261071 + 0.113410i
\(391\) 1328.06 + 1987.59i 0.171773 + 0.257076i
\(392\) −413.705 + 2175.71i −0.0533042 + 0.280332i
\(393\) 3676.81 + 2456.76i 0.471935 + 0.315337i
\(394\) −166.834 + 5576.29i −0.0213325 + 0.713018i
\(395\) −135.456 + 253.420i −0.0172545 + 0.0322808i
\(396\) −27587.5 + 20004.9i −3.50081 + 2.53860i
\(397\) 920.830 + 9349.34i 0.116411 + 1.18194i 0.858922 + 0.512106i \(0.171135\pi\)
−0.742511 + 0.669834i \(0.766365\pi\)
\(398\) −9261.74 + 7148.30i −1.16645 + 0.900281i
\(399\) −1832.25 758.945i −0.229893 0.0952250i
\(400\) −7966.87 + 612.349i −0.995859 + 0.0765436i
\(401\) −7823.22 + 3240.49i −0.974247 + 0.403546i −0.812292 0.583252i \(-0.801780\pi\)
−0.161956 + 0.986798i \(0.551780\pi\)
\(402\) 12366.9 21560.0i 1.53434 2.67492i
\(403\) −8084.52 + 9851.02i −0.999302 + 1.21765i
\(404\) −7790.31 7214.51i −0.959362 0.888454i
\(405\) −350.352 1154.96i −0.0429855 0.141704i
\(406\) 2014.46 + 905.911i 0.246246 + 0.110738i
\(407\) 280.528 + 1410.31i 0.0341652 + 0.171760i
\(408\) 11425.3 3571.49i 1.38637 0.433370i
\(409\) −12085.0 2403.85i −1.46103 0.290618i −0.600342 0.799744i \(-0.704969\pi\)
−0.860692 + 0.509126i \(0.829969\pi\)
\(410\) 191.225 32.1246i 0.0230339 0.00386956i
\(411\) 1182.03 + 1440.31i 0.141862 + 0.172860i
\(412\) 10852.0 + 649.935i 1.29767 + 0.0777185i
\(413\) −990.658 + 529.518i −0.118032 + 0.0630893i
\(414\) 3195.05 9500.10i 0.379295 1.12779i
\(415\) 275.800 + 275.800i 0.0326229 + 0.0326229i
\(416\) 6173.06 + 13129.4i 0.727547 + 1.54741i
\(417\) 6653.63 6653.63i 0.781366 0.781366i
\(418\) −865.615 1742.91i −0.101289 0.203943i
\(419\) −7268.60 13598.6i −0.847481 1.58552i −0.810151 0.586222i \(-0.800615\pi\)
−0.0373301 0.999303i \(-0.511885\pi\)
\(420\) 161.825 + 468.047i 0.0188006 + 0.0543771i
\(421\) −6288.64 + 5160.96i −0.728004 + 0.597458i −0.923659 0.383215i \(-0.874817\pi\)
0.195655 + 0.980673i \(0.437317\pi\)
\(422\) 2376.59 + 1692.94i 0.274149 + 0.195286i
\(423\) 8180.50 41126.2i 0.940306 4.72724i
\(424\) −2637.34 775.765i −0.302076 0.0888549i
\(425\) −6354.38 + 1263.97i −0.725254 + 0.144262i
\(426\) 5424.58 2059.12i 0.616952 0.234190i
\(427\) −134.783 + 40.8859i −0.0152754 + 0.00463374i
\(428\) 204.548 + 444.768i 0.0231009 + 0.0502305i
\(429\) −34973.0 28701.6i −3.93592 3.23013i
\(430\) 229.076 62.0724i 0.0256907 0.00696139i
\(431\) −5562.73 13429.6i −0.621688 1.50089i −0.849721 0.527233i \(-0.823229\pi\)
0.228033 0.973653i \(-0.426771\pi\)
\(432\) −26690.8 18675.1i −2.97260 2.07987i
\(433\) −2139.71 + 5165.72i −0.237478 + 0.573322i −0.997021 0.0771349i \(-0.975423\pi\)
0.759543 + 0.650457i \(0.225423\pi\)
\(434\) −899.399 + 6983.48i −0.0994758 + 0.772391i
\(435\) −196.266 + 19.3305i −0.0216328 + 0.00213064i
\(436\) 5599.82 9119.35i 0.615098 1.00169i
\(437\) 504.789 + 269.815i 0.0552570 + 0.0295355i
\(438\) −5143.71 + 4844.87i −0.561133 + 0.528531i
\(439\) −7135.52 + 10679.1i −0.775763 + 1.16101i 0.207396 + 0.978257i \(0.433501\pi\)
−0.983159 + 0.182754i \(0.941499\pi\)
\(440\) −182.165 + 450.510i −0.0197372 + 0.0488118i
\(441\) 6260.51 4183.14i 0.676008 0.451694i
\(442\) 6240.17 + 9972.29i 0.671526 + 1.07315i
\(443\) −1303.01 + 13229.7i −0.139747 + 1.41887i 0.628047 + 0.778176i \(0.283855\pi\)
−0.767794 + 0.640697i \(0.778645\pi\)
\(444\) −1828.16 + 1069.26i −0.195407 + 0.114290i
\(445\) −32.7254 + 107.881i −0.00348614 + 0.0114923i
\(446\) 2752.38 3156.37i 0.292217 0.335108i
\(447\) 18141.9i 1.91965i
\(448\) 6739.40 + 4340.28i 0.710730 + 0.457721i
\(449\) 10209.4i 1.07308i −0.843875 0.536540i \(-0.819731\pi\)
0.843875 0.536540i \(-0.180269\pi\)
\(450\) 20474.4 + 17853.8i 2.14483 + 1.87031i
\(451\) −2841.17 + 9366.07i −0.296642 + 0.977896i
\(452\) −1455.67 381.273i −0.151480 0.0396761i
\(453\) −1557.24 + 15810.9i −0.161513 + 1.63987i
\(454\) 8760.39 5481.82i 0.905607 0.566684i
\(455\) −404.659 + 270.384i −0.0416938 + 0.0278589i
\(456\) 2009.55 2043.79i 0.206372 0.209888i
\(457\) 1619.57 2423.86i 0.165778 0.248104i −0.739275 0.673404i \(-0.764832\pi\)
0.905052 + 0.425300i \(0.139832\pi\)
\(458\) 7253.08 + 7700.47i 0.739987 + 0.785632i
\(459\) −23294.4 12451.1i −2.36883 1.26616i
\(460\) −33.2389 139.010i −0.00336907 0.0140899i
\(461\) 11950.2 1176.99i 1.20732 0.118911i 0.525737 0.850647i \(-0.323790\pi\)
0.681588 + 0.731736i \(0.261290\pi\)
\(462\) −24792.6 3193.03i −2.49666 0.321544i
\(463\) 493.558 1191.55i 0.0495412 0.119603i −0.897171 0.441682i \(-0.854382\pi\)
0.946713 + 0.322079i \(0.104382\pi\)
\(464\) −2305.18 + 2208.29i −0.230636 + 0.220942i
\(465\) −240.588 580.830i −0.0239935 0.0579255i
\(466\) 2979.67 + 10996.3i 0.296203 + 1.09312i
\(467\) 4300.71 + 3529.50i 0.426153 + 0.349734i 0.822893 0.568196i \(-0.192359\pi\)
−0.396740 + 0.917931i \(0.629859\pi\)
\(468\) 17114.4 46260.2i 1.69041 4.56919i
\(469\) 12914.6 3917.60i 1.27152 0.385710i
\(470\) −212.203 559.031i −0.0208260 0.0548642i
\(471\) −3777.44 + 751.380i −0.369544 + 0.0735069i
\(472\) −172.765 1614.22i −0.0168478 0.157417i
\(473\) −2337.15 + 11749.6i −0.227193 + 1.14218i
\(474\) 12394.5 17399.8i 1.20105 1.68607i
\(475\) −1199.18 + 984.142i −0.115836 + 0.0950642i
\(476\) 5845.52 + 2841.88i 0.562876 + 0.273650i
\(477\) 4405.76 + 8242.60i 0.422905 + 0.791200i
\(478\) −10627.9 + 5278.37i −1.01697 + 0.505078i
\(479\) 5664.97 5664.97i 0.540374 0.540374i −0.383265 0.923639i \(-0.625200\pi\)
0.923639 + 0.383265i \(0.125200\pi\)
\(480\) −714.791 36.7535i −0.0679699 0.00349492i
\(481\) −1471.71 1471.71i −0.139510 0.139510i
\(482\) −13851.3 4658.44i −1.30894 0.440220i
\(483\) 6484.20 3465.88i 0.610851 0.326507i
\(484\) −9210.75 10384.3i −0.865021 0.975236i
\(485\) 64.2696 + 78.3128i 0.00601718 + 0.00733196i
\(486\) 8425.80 + 50155.3i 0.786424 + 4.68126i
\(487\) −5214.12 1037.15i −0.485163 0.0965049i −0.0535525 0.998565i \(-0.517054\pi\)
−0.431610 + 0.902060i \(0.642054\pi\)
\(488\) 18.2407 202.741i 0.00169204 0.0188066i
\(489\) −4630.66 23279.9i −0.428232 2.15287i
\(490\) 44.0371 97.9243i 0.00405998 0.00902810i
\(491\) 2807.27 + 9254.34i 0.258026 + 0.850596i 0.986250 + 0.165258i \(0.0528457\pi\)
−0.728225 + 0.685338i \(0.759654\pi\)
\(492\) −14405.1 + 552.788i −1.31999 + 0.0506537i
\(493\) −1642.05 + 2000.84i −0.150008 + 0.182786i
\(494\) 2443.32 + 1401.49i 0.222531 + 0.127644i
\(495\) 1526.34 632.232i 0.138594 0.0574075i
\(496\) −8869.61 4988.55i −0.802938 0.451598i
\(497\) 2910.67 + 1205.64i 0.262699 + 0.108813i
\(498\) −17717.2 22955.5i −1.59423 2.06558i
\(499\) 136.914 + 1390.11i 0.0122828 + 0.124709i 0.999371 0.0354699i \(-0.0112928\pi\)
−0.987088 + 0.160179i \(0.948793\pi\)
\(500\) 765.573 + 121.972i 0.0684749 + 0.0109096i
\(501\) 3119.18 5835.58i 0.278153 0.520388i
\(502\) −3019.29 90.3328i −0.268441 0.00803137i
\(503\) 12627.0 + 8437.06i 1.11930 + 0.747893i 0.970530 0.240979i \(-0.0774685\pi\)
0.148770 + 0.988872i \(0.452469\pi\)
\(504\) −5542.32 26683.3i −0.489831 2.35827i
\(505\) 285.986 + 428.009i 0.0252004 + 0.0377151i
\(506\) 7030.59 + 1618.45i 0.617684 + 0.142191i
\(507\) 42880.6 + 4223.37i 3.75620 + 0.369953i
\(508\) −21913.7 + 3010.61i −1.91390 + 0.262941i
\(509\) −3045.86 923.952i −0.265237 0.0804586i 0.154865 0.987936i \(-0.450506\pi\)
−0.420102 + 0.907477i \(0.638006\pi\)
\(510\) −578.991 + 39.5864i −0.0502709 + 0.00343709i
\(511\) −3836.76 −0.332149
\(512\) −9466.61 + 6678.39i −0.817127 + 0.576457i
\(513\) −6324.44 −0.544309
\(514\) 10742.0 734.444i 0.921806 0.0630252i
\(515\) −504.364 152.997i −0.0431552 0.0130910i
\(516\) −17480.5 + 2401.56i −1.49135 + 0.204889i
\(517\) 30036.9 + 2958.38i 2.55517 + 0.251662i
\(518\) −1120.66 257.977i −0.0950558 0.0218819i
\(519\) −1983.80 2968.97i −0.167783 0.251105i
\(520\) −143.043 688.673i −0.0120631 0.0580775i
\(521\) −7820.83 5225.71i −0.657653 0.439429i 0.181452 0.983400i \(-0.441920\pi\)
−0.839104 + 0.543970i \(0.816920\pi\)
\(522\) 10848.0 + 324.556i 0.909586 + 0.0272135i
\(523\) −272.182 + 509.217i −0.0227566 + 0.0425746i −0.893043 0.449972i \(-0.851434\pi\)
0.870286 + 0.492547i \(0.163934\pi\)
\(524\) −3426.93 545.985i −0.285699 0.0455181i
\(525\) 1953.20 + 19831.2i 0.162371 + 1.64858i
\(526\) 9034.93 + 11706.2i 0.748939 + 0.970367i
\(527\) −7623.15 3157.61i −0.630113 0.261001i
\(528\) 17710.3 31488.8i 1.45974 2.59540i
\(529\) 9280.41 3844.07i 0.762753 0.315943i
\(530\) 115.609 + 66.3134i 0.00947494 + 0.00543485i
\(531\) −3501.42 + 4266.50i −0.286156 + 0.348682i
\(532\) 1555.16 59.6782i 0.126738 0.00486349i
\(533\) −4112.39 13556.7i −0.334198 1.10170i
\(534\) 3437.51 7643.91i 0.278568 0.619447i
\(535\) −4.63023 23.2778i −0.000374173 0.00188109i
\(536\) −1747.79 + 19426.2i −0.140845 + 1.56546i
\(537\) −23484.2 4671.30i −1.88719 0.375385i
\(538\) 612.938 + 3648.57i 0.0491183 + 0.292381i
\(539\) 3438.19 + 4189.44i 0.274755 + 0.334790i
\(540\) 1047.96 + 1181.49i 0.0835134 + 0.0941540i
\(541\) −9138.47 + 4884.61i −0.726235 + 0.388181i −0.792703 0.609608i \(-0.791327\pi\)
0.0664678 + 0.997789i \(0.478827\pi\)
\(542\) −15390.8 5176.20i −1.21973 0.410216i
\(543\) −17318.9 17318.9i −1.36874 1.36874i
\(544\) −6974.68 + 6292.50i −0.549701 + 0.495935i
\(545\) −366.858 + 366.858i −0.0288339 + 0.0288339i
\(546\) 32405.5 16094.2i 2.53997 1.26148i
\(547\) 4161.47 + 7785.56i 0.325286 + 0.608567i 0.990409 0.138167i \(-0.0441209\pi\)
−0.665123 + 0.746734i \(0.731621\pi\)
\(548\) −1314.99 639.302i −0.102507 0.0498351i
\(549\) −534.966 + 439.035i −0.0415880 + 0.0341304i
\(550\) −11344.7 + 15926.0i −0.879524 + 1.23470i
\(551\) −120.910 + 607.856i −0.00934835 + 0.0469973i
\(552\) 1130.80 + 10565.6i 0.0871924 + 0.814680i
\(553\) 11376.7 2262.96i 0.874839 0.174016i
\(554\) −2437.92 6422.48i −0.186962 0.492536i
\(555\) 98.2563 29.8057i 0.00751486 0.00227961i
\(556\) −2562.10 + 6925.36i −0.195426 + 0.528238i
\(557\) 3558.18 + 2920.12i 0.270673 + 0.222135i 0.759931 0.650003i \(-0.225233\pi\)
−0.489259 + 0.872139i \(0.662733\pi\)
\(558\) 9048.36 + 33392.6i 0.686465 + 2.53337i
\(559\) −6635.72 16020.0i −0.502077 1.21212i
\(560\) −268.840 280.635i −0.0202867 0.0211768i
\(561\) 11210.1 27063.6i 0.843656 2.03677i
\(562\) 12601.8 + 1622.98i 0.945861 + 0.121817i
\(563\) −5833.39 + 574.538i −0.436675 + 0.0430087i −0.313967 0.949434i \(-0.601658\pi\)
−0.122708 + 0.992443i \(0.539158\pi\)
\(564\) 10338.2 + 43235.7i 0.771836 + 3.22793i
\(565\) 64.3386 + 34.3897i 0.00479070 + 0.00256068i
\(566\) 2530.05 + 2686.11i 0.187890 + 0.199480i
\(567\) −27067.7 + 40509.6i −2.00482 + 3.00043i
\(568\) −3192.31 + 3246.70i −0.235821 + 0.239839i
\(569\) −13734.2 + 9176.89i −1.01189 + 0.676125i −0.946823 0.321755i \(-0.895727\pi\)
−0.0650701 + 0.997881i \(0.520727\pi\)
\(570\) −117.797 + 73.7113i −0.00865606 + 0.00541654i
\(571\) −144.244 + 1464.53i −0.0105717 + 0.107336i −0.999022 0.0442065i \(-0.985924\pi\)
0.988451 + 0.151543i \(0.0484240\pi\)
\(572\) 34344.9 + 8995.73i 2.51055 + 0.657571i
\(573\) −7419.38 + 24458.4i −0.540923 + 1.78319i
\(574\) −5899.47 5144.39i −0.428988 0.374081i
\(575\) 5751.15i 0.417112i
\(576\) 38754.6 + 7030.44i 2.80343 + 0.508568i
\(577\) 15853.9i 1.14386i 0.820302 + 0.571930i \(0.193805\pi\)
−0.820302 + 0.571930i \(0.806195\pi\)
\(578\) 4126.93 4732.68i 0.296986 0.340577i
\(579\) 8461.54 27894.0i 0.607339 2.00213i
\(580\) 133.590 78.1347i 0.00956387 0.00559374i
\(581\) 1543.27 15669.1i 0.110199 1.11887i
\(582\) −3995.28 6384.78i −0.284553 0.454738i
\(583\) −5593.56 + 3737.49i −0.397361 + 0.265508i
\(584\) 2078.66 5140.71i 0.147287 0.364254i
\(585\) −1328.54 + 1988.29i −0.0938943 + 0.140523i
\(586\) 11831.8 11144.4i 0.834077 0.785618i
\(587\) −9459.43 5056.17i −0.665132 0.355520i 0.104030 0.994574i \(-0.466826\pi\)
−0.769162 + 0.639054i \(0.779326\pi\)
\(588\) −4177.03 + 6802.33i −0.292956 + 0.477080i
\(589\) −1966.18 + 193.651i −0.137546 + 0.0135471i
\(590\) −10.0535 + 78.0613i −0.000701516 + 0.00544700i
\(591\) −7694.85 + 18577.0i −0.535573 + 1.29299i
\(592\) 952.798 1361.76i 0.0661482 0.0945405i
\(593\) 2064.50 + 4984.15i 0.142966 + 0.345151i 0.979101 0.203372i \(-0.0651902\pi\)
−0.836135 + 0.548523i \(0.815190\pi\)
\(594\) −76941.5 + 20848.8i −5.31473 + 1.44013i
\(595\) −243.585 199.905i −0.0167832 0.0137736i
\(596\) 5948.48 + 12934.3i 0.408824 + 0.888945i
\(597\) −40352.7 + 12240.9i −2.76638 + 0.839171i
\(598\) −9762.75 + 3705.85i −0.667606 + 0.253417i
\(599\) 25019.5 4976.69i 1.70663 0.339469i 0.757135 0.653258i \(-0.226598\pi\)
0.949493 + 0.313789i \(0.101598\pi\)
\(600\) −27629.2 8127.06i −1.87993 0.552976i
\(601\) 3547.76 17835.8i 0.240792 1.21054i −0.651346 0.758781i \(-0.725795\pi\)
0.892138 0.451763i \(-0.149205\pi\)
\(602\) −7803.31 5558.59i −0.528304 0.376331i
\(603\) 51259.4 42067.5i 3.46177 2.84100i
\(604\) −4073.93 11783.0i −0.274447 0.793781i
\(605\) 317.224 + 593.485i 0.0213174 + 0.0398820i
\(606\) −17022.9 34275.4i −1.14110 2.29759i
\(607\) 12929.1 12929.1i 0.864539 0.864539i −0.127322 0.991861i \(-0.540638\pi\)
0.991861 + 0.127322i \(0.0406383\pi\)
\(608\) −762.587 + 2116.03i −0.0508668 + 0.141145i
\(609\) 5629.35 + 5629.35i 0.374570 + 0.374570i
\(610\) −3.14589 + 9.35392i −0.000208809 + 0.000620868i
\(611\) −38528.2 + 20593.8i −2.55104 + 1.36356i
\(612\) 31879.3 + 1909.27i 2.10563 + 0.126108i
\(613\) 5081.30 + 6191.58i 0.334799 + 0.407954i 0.913012 0.407932i \(-0.133750\pi\)
−0.578213 + 0.815886i \(0.696250\pi\)
\(614\) 15369.4 2581.97i 1.01019 0.169707i
\(615\) 685.460 + 136.347i 0.0449438 + 0.00893987i
\(616\) 18722.9 5852.67i 1.22463 0.382810i
\(617\) −2531.19 12725.2i −0.165157 0.830302i −0.971167 0.238400i \(-0.923377\pi\)
0.806010 0.591902i \(-0.201623\pi\)
\(618\) 35736.7 + 16071.0i 2.32612 + 1.04607i
\(619\) −5183.81 17088.7i −0.336599 1.10962i −0.947993 0.318292i \(-0.896891\pi\)
0.611394 0.791326i \(-0.290609\pi\)
\(620\) 361.974 + 335.219i 0.0234471 + 0.0217141i
\(621\) 14874.3 18124.4i 0.961167 1.17119i
\(622\) 2658.14 4634.12i 0.171353 0.298732i
\(623\) 4204.43 1741.53i 0.270380 0.111995i
\(624\) 4007.44 + 52138.2i 0.257093 + 3.34487i
\(625\) 14383.5 + 5957.85i 0.920545 + 0.381302i
\(626\) −18606.0 + 14360.3i −1.18793 + 0.916859i
\(627\) −687.499 6980.29i −0.0437895 0.444603i
\(628\) 2446.77 1774.27i 0.155473 0.112740i
\(629\) 635.254 1188.48i 0.0402690 0.0753381i
\(630\) −39.5120 + 1320.65i −0.00249872 + 0.0835175i
\(631\) −20601.7 13765.6i −1.29975 0.868466i −0.303321 0.952889i \(-0.598095\pi\)
−0.996430 + 0.0844230i \(0.973095\pi\)
\(632\) −3131.56 + 16469.2i −0.197100 + 1.03656i
\(633\) 5842.96 + 8744.61i 0.366883 + 0.549079i
\(634\) 3870.21 16812.3i 0.242438 1.05316i
\(635\) 1067.21 + 105.111i 0.0666944 + 0.00656882i
\(636\) −7894.75 5987.53i −0.492212 0.373304i
\(637\) −7506.77 2277.15i −0.466921 0.141639i
\(638\) 532.860 + 7793.61i 0.0330660 + 0.483624i
\(639\) 15479.9 0.958336
\(640\) 521.663 208.166i 0.0322196 0.0128570i
\(641\) −3955.08 −0.243707 −0.121854 0.992548i \(-0.538884\pi\)
−0.121854 + 0.992548i \(0.538884\pi\)
\(642\) 120.359 + 1760.37i 0.00739906 + 0.108219i
\(643\) −12419.9 3767.55i −0.761733 0.231069i −0.114564 0.993416i \(-0.536547\pi\)
−0.647169 + 0.762347i \(0.724047\pi\)
\(644\) −3486.52 + 4597.08i −0.213335 + 0.281290i
\(645\) 851.314 + 83.8471i 0.0519697 + 0.00511857i
\(646\) −409.132 + 1777.28i −0.0249181 + 0.108245i
\(647\) −4297.44 6431.58i −0.261128 0.390806i 0.677619 0.735413i \(-0.263012\pi\)
−0.938747 + 0.344608i \(0.888012\pi\)
\(648\) −39612.6 58214.0i −2.40143 3.52911i
\(649\) −3303.24 2207.15i −0.199790 0.133495i
\(650\) 846.384 28289.6i 0.0510737 1.70709i
\(651\) −11963.3 + 22381.8i −0.720245 + 1.34748i
\(652\) 10934.6 + 15079.1i 0.656797 + 0.905743i
\(653\) 1194.25 + 12125.4i 0.0715691 + 0.726653i 0.962276 + 0.272075i \(0.0877099\pi\)
−0.890707 + 0.454578i \(0.849790\pi\)
\(654\) 30534.3 23566.7i 1.82567 1.40907i
\(655\) 155.430 + 64.3812i 0.00927199 + 0.00384058i
\(656\) 10088.9 5117.36i 0.600468 0.304572i
\(657\) −17416.9 + 7214.33i −1.03424 + 0.428398i
\(658\) −12010.0 + 20937.8i −0.711547 + 1.24049i
\(659\) −2158.98 + 2630.73i −0.127621 + 0.155506i −0.832900 0.553423i \(-0.813321\pi\)
0.705280 + 0.708929i \(0.250821\pi\)
\(660\) −1190.09 + 1285.07i −0.0701882 + 0.0757901i
\(661\) −936.209 3086.27i −0.0550897 0.181606i 0.925078 0.379778i \(-0.124000\pi\)
−0.980167 + 0.198172i \(0.936500\pi\)
\(662\) −9046.68 4068.34i −0.531132 0.238853i
\(663\) 8271.86 + 41585.5i 0.484544 + 2.43597i
\(664\) 20158.3 + 10556.9i 1.17815 + 0.617001i
\(665\) −74.0013 14.7198i −0.00431526 0.000858358i
\(666\) −5572.30 + 936.113i −0.324207 + 0.0544649i
\(667\) −1457.61 1776.10i −0.0846160 0.103105i
\(668\) −310.427 + 5183.23i −0.0179802 + 0.300217i
\(669\) 13312.0 7115.43i 0.769316 0.411208i
\(670\) 301.433 896.275i 0.0173811 0.0516808i
\(671\) −352.236 352.236i −0.0202651 0.0202651i
\(672\) 17158.1 + 23245.9i 0.984952 + 1.33442i
\(673\) 2686.46 2686.46i 0.153871 0.153871i −0.625973 0.779845i \(-0.715298\pi\)
0.779845 + 0.625973i \(0.215298\pi\)
\(674\) 8772.46 + 17663.3i 0.501339 + 1.00944i
\(675\) 29956.0 + 56043.7i 1.70816 + 3.19574i
\(676\) −31956.6 + 11048.9i −1.81820 + 0.628634i
\(677\) 23740.7 19483.5i 1.34775 1.10607i 0.363062 0.931765i \(-0.381731\pi\)
0.984691 0.174308i \(-0.0557688\pi\)
\(678\) −4417.47 3146.73i −0.250224 0.178244i
\(679\) 797.837 4011.00i 0.0450930 0.226698i
\(680\) 399.814 218.066i 0.0225473 0.0122977i
\(681\) 36531.7 7266.61i 2.05565 0.408895i
\(682\) −23281.6 + 8837.50i −1.30718 + 0.496195i
\(683\) −12250.3 + 3716.10i −0.686305 + 0.208188i −0.614131 0.789204i \(-0.710493\pi\)
−0.0721734 + 0.997392i \(0.522993\pi\)
\(684\) 6947.42 3195.10i 0.388364 0.178608i
\(685\) 54.7963 + 44.9701i 0.00305643 + 0.00250835i
\(686\) −18843.8 + 5106.09i −1.04878 + 0.284186i
\(687\) 14591.0 + 35225.7i 0.810306 + 1.95625i
\(688\) 11675.4 7443.82i 0.646976 0.412490i
\(689\) 3726.31 8996.10i 0.206039 0.497423i
\(690\) 65.8034 510.938i 0.00363057 0.0281899i
\(691\) −19246.4 + 1895.61i −1.05958 + 0.104359i −0.612763 0.790267i \(-0.709942\pi\)
−0.446816 + 0.894626i \(0.647442\pi\)
\(692\) 2387.84 + 1466.28i 0.131174 + 0.0805483i
\(693\) −58816.3 31438.0i −3.22402 1.72328i
\(694\) −15382.3 + 14488.6i −0.841363 + 0.792480i
\(695\) 198.887 297.656i 0.0108550 0.0162457i
\(696\) −10592.4 + 4492.69i −0.576873 + 0.244677i
\(697\) 7626.75 5096.03i 0.414468 0.276938i
\(698\) −7347.43 11741.8i −0.398430 0.636724i
\(699\) −4024.92 + 40865.7i −0.217792 + 2.21128i
\(700\) −7894.92 13498.3i −0.426285 0.728840i
\(701\) 5376.21 17723.0i 0.289667 0.954905i −0.684488 0.729025i \(-0.739974\pi\)
0.974155 0.225881i \(-0.0725260\pi\)
\(702\) 75833.2 86963.8i 4.07712 4.67555i
\(703\) 322.671i 0.0173112i
\(704\) −2301.88 + 28257.0i −0.123232 + 1.51275i
\(705\) 2155.20i 0.115134i
\(706\) 16833.2 + 14678.7i 0.897346 + 0.782493i
\(707\) 6032.01 19884.9i 0.320873 1.05778i
\(708\) 1482.60 5660.43i 0.0786999 0.300469i
\(709\) −564.286 + 5729.29i −0.0298903 + 0.303481i 0.968603 + 0.248612i \(0.0799743\pi\)
−0.998494 + 0.0548695i \(0.982526\pi\)
\(710\) 187.128 117.096i 0.00989126 0.00618946i
\(711\) 47389.3 31664.5i 2.49963 1.67020i
\(712\) 55.5488 + 6576.86i 0.00292385 + 0.346177i
\(713\) 4069.24 6090.05i 0.213737 0.319880i
\(714\) 16062.6 + 17053.3i 0.841913 + 0.893845i
\(715\) −1518.00 811.387i −0.0793985 0.0424394i
\(716\) 18274.8 4369.72i 0.953856 0.228078i
\(717\) −42564.6 + 4192.25i −2.21702 + 0.218357i
\(718\) 2975.09 + 383.160i 0.154637 + 0.0199156i
\(719\) −7302.95 + 17630.9i −0.378796 + 0.914494i 0.613396 + 0.789775i \(0.289803\pi\)
−0.992192 + 0.124719i \(0.960197\pi\)
\(720\) −1748.08 768.438i −0.0904821 0.0397750i
\(721\) 8141.98 + 19656.5i 0.420559 + 1.01532i
\(722\) −4959.66 18303.4i −0.255650 0.943467i
\(723\) −40716.1 33414.8i −2.09440 1.71883i
\(724\) 18026.2 + 6668.96i 0.925331 + 0.342334i
\(725\) 5959.18 1807.70i 0.305267 0.0926017i
\(726\) −17754.8 46773.5i −0.907635 2.39109i
\(727\) −31945.9 + 6354.43i −1.62972 + 0.324172i −0.923435 0.383754i \(-0.874631\pi\)
−0.706286 + 0.707926i \(0.749631\pi\)
\(728\) −17826.5 + 22099.7i −0.907548 + 1.12509i
\(729\) −19370.1 + 97380.3i −0.984105 + 4.94743i
\(730\) −155.972 + 218.958i −0.00790791 + 0.0111013i
\(731\) 8678.74 7122.46i 0.439117 0.360374i
\(732\) 320.793 659.844i 0.0161979 0.0333177i
\(733\) 13789.1 + 25797.6i 0.694831 + 1.29994i 0.943508 + 0.331351i \(0.107504\pi\)
−0.248676 + 0.968587i \(0.579996\pi\)
\(734\) 18772.7 9323.47i 0.944023 0.468849i
\(735\) 273.647 273.647i 0.0137328 0.0137328i
\(736\) −4270.53 7162.03i −0.213878 0.358690i
\(737\) 33750.5 + 33750.5i 1.68686 + 1.68686i
\(738\) −36453.7 12260.0i −1.81826 0.611514i
\(739\) 8084.62 4321.32i 0.402433 0.215105i −0.257747 0.966212i \(-0.582980\pi\)
0.660180 + 0.751108i \(0.270480\pi\)
\(740\) −60.2793 + 53.4669i −0.00299447 + 0.00265606i
\(741\) 6440.59 + 7847.88i 0.319300 + 0.389068i
\(742\) −891.329 5305.71i −0.0440993 0.262505i
\(743\) 34942.2 + 6950.44i 1.72531 + 0.343186i 0.955479 0.295060i \(-0.0953395\pi\)
0.769833 + 0.638246i \(0.220340\pi\)
\(744\) −23507.0 28155.1i −1.15835 1.38739i
\(745\) −134.652 676.943i −0.00662185 0.0332903i
\(746\) −6242.87 + 13882.1i −0.306391 + 0.681315i
\(747\) −22457.3 74031.7i −1.09996 3.62608i
\(748\) 881.486 + 22970.7i 0.0430886 + 1.12285i
\(749\) −607.795 + 740.600i −0.0296507 + 0.0361294i
\(750\) 2423.73 + 1390.26i 0.118003 + 0.0676868i
\(751\) 1771.93 733.956i 0.0860965 0.0356624i −0.339220 0.940707i \(-0.610163\pi\)
0.425316 + 0.905045i \(0.360163\pi\)
\(752\) −21547.0 27435.3i −1.04487 1.33040i
\(753\) −10058.6 4166.39i −0.486792 0.201636i
\(754\) −6908.52 8951.06i −0.333678 0.432332i
\(755\) 59.2447 + 601.521i 0.00285581 + 0.0289955i
\(756\) 10030.5 62957.7i 0.482550 3.02877i
\(757\) 8428.07 15767.8i 0.404654 0.757055i −0.594229 0.804296i \(-0.702543\pi\)
0.998884 + 0.0472408i \(0.0150428\pi\)
\(758\) 33712.6 + 1008.63i 1.61543 + 0.0483313i
\(759\) 21620.8 + 14446.6i 1.03397 + 0.690879i
\(760\) 59.8145 91.1765i 0.00285487 0.00435174i
\(761\) −20736.2 31034.0i −0.987764 1.47829i −0.874676 0.484708i \(-0.838926\pi\)
−0.113088 0.993585i \(-0.536074\pi\)
\(762\) −77693.3 17885.1i −3.69361 0.850273i
\(763\) 20842.4 + 2052.80i 0.988919 + 0.0974000i
\(764\) −2729.90 19870.4i −0.129273 0.940951i
\(765\) −1481.64 449.450i −0.0700245 0.0212417i
\(766\) −25684.7 + 1756.10i −1.21152 + 0.0828335i
\(767\) 5750.30 0.270706
\(768\) −40442.0 + 10395.4i −1.90016 + 0.488425i
\(769\) 5098.88 0.239103 0.119551 0.992828i \(-0.461854\pi\)
0.119551 + 0.992828i \(0.461854\pi\)
\(770\) −948.806 + 64.8711i −0.0444059 + 0.00303610i
\(771\) 37136.7 + 11265.3i 1.73469 + 0.526212i
\(772\) 3113.35 + 22661.5i 0.145145 + 1.05648i
\(773\) −35544.2 3500.80i −1.65386 0.162891i −0.772398 0.635139i \(-0.780943\pi\)
−0.881466 + 0.472248i \(0.843443\pi\)
\(774\) −45875.0 10560.5i −2.13041 0.490423i
\(775\) 11028.9 + 16505.9i 0.511188 + 0.765046i
\(776\) 4941.92 + 3242.05i 0.228614 + 0.149978i
\(777\) −3446.30 2302.75i −0.159119 0.106320i
\(778\) −32622.0 976.004i −1.50329 0.0449761i
\(779\) 1035.33 1936.97i 0.0476183 0.0890875i
\(780\) 398.877 2503.59i 0.0183104 0.114927i
\(781\) 1092.14 + 11088.7i 0.0500382 + 0.508047i
\(782\) −4131.06 5352.43i −0.188908 0.244760i
\(783\) 23455.3 + 9715.48i 1.07053 + 0.443427i
\(784\) 747.642 6219.33i 0.0340580 0.283315i
\(785\) −135.374 + 56.0736i −0.00615502 + 0.00254949i
\(786\) −10849.4 6223.22i −0.492345 0.282411i
\(787\) −5448.24 + 6638.70i −0.246771 + 0.300691i −0.881634 0.471933i \(-0.843556\pi\)
0.634863 + 0.772624i \(0.281056\pi\)
\(788\) −605.070 15767.6i −0.0273537 0.712813i
\(789\) 15471.6 + 51002.9i 0.698102 + 2.30133i
\(790\) 333.341 741.244i 0.0150123 0.0333826i
\(791\) −574.525 2888.33i −0.0258252 0.129832i
\(792\) 73987.8 61773.3i 3.31950 2.77149i
\(793\) 707.164 + 140.664i 0.0316672 + 0.00629900i
\(794\) −4402.23 26204.7i −0.196762 1.17125i
\(795\) 304.744 + 371.332i 0.0135952 + 0.0165658i
\(796\) 24756.0 21958.2i 1.10233 0.977750i
\(797\) −4023.33 + 2150.52i −0.178813 + 0.0955774i −0.558374 0.829589i \(-0.688575\pi\)
0.379562 + 0.925166i \(0.376075\pi\)
\(798\) 5316.75 + 1788.12i 0.235853 + 0.0793216i
\(799\) −20001.3 20001.3i −0.885599 0.885599i
\(800\) 22363.1 3265.02i 0.988319 0.144295i
\(801\) 15811.3 15811.3i 0.697461 0.697461i
\(802\) 21450.7 10653.5i 0.944451 0.469062i
\(803\) −6396.61 11967.2i −0.281110 0.525920i
\(804\) −30737.7 + 63224.9i −1.34830 + 2.77335i
\(805\) 216.225 177.452i 0.00946701 0.00776937i
\(806\) 20912.6 29357.8i 0.913916 1.28298i
\(807\) −2601.50 + 13078.6i −0.113478 + 0.570494i
\(808\) 23374.9 + 18855.2i 1.01773 + 0.820944i
\(809\) −27339.6 + 5438.19i −1.18815 + 0.236337i −0.749303 0.662227i \(-0.769611\pi\)
−0.438842 + 0.898564i \(0.644611\pi\)
\(810\) 1211.47 + 3191.50i 0.0525513 + 0.138442i
\(811\) −11247.2 + 3411.81i −0.486983 + 0.147725i −0.524222 0.851582i \(-0.675644\pi\)
0.0372389 + 0.999306i \(0.488144\pi\)
\(812\) −5859.25 2167.68i −0.253226 0.0936831i
\(813\) −45241.5 37128.8i −1.95165 1.60168i
\(814\) −1063.70 3925.54i −0.0458018 0.169030i
\(815\) −345.574 834.290i −0.0148527 0.0358575i
\(816\) −31551.4 + 12282.5i −1.35358 + 0.526927i
\(817\) 1028.75 2483.63i 0.0440532 0.106354i
\(818\) 34565.6 + 4451.68i 1.47745 + 0.190281i
\(819\) 96065.9 9461.67i 4.09867 0.403684i
\(820\) −533.407 + 127.544i −0.0227163 + 0.00543174i
\(821\) 16018.3 + 8561.96i 0.680929 + 0.363964i 0.775318 0.631571i \(-0.217590\pi\)
−0.0943890 + 0.995535i \(0.530090\pi\)
\(822\) −3613.39 3836.27i −0.153323 0.162780i
\(823\) 41.7282 62.4506i 0.00176738 0.00264507i −0.830585 0.556892i \(-0.811994\pi\)
0.832352 + 0.554247i \(0.186994\pi\)
\(824\) −30748.0 + 259.701i −1.29995 + 0.0109795i
\(825\) −58599.1 + 39154.7i −2.47292 + 1.65235i
\(826\) 2693.32 1685.35i 0.113453 0.0709935i
\(827\) 3493.66 35471.7i 0.146900 1.49150i −0.585525 0.810655i \(-0.699111\pi\)
0.732425 0.680848i \(-0.238389\pi\)
\(828\) −7183.03 + 27424.2i −0.301483 + 1.15103i
\(829\) 12089.3 39853.0i 0.506487 1.66967i −0.214505 0.976723i \(-0.568814\pi\)
0.720993 0.692942i \(-0.243686\pi\)
\(830\) −831.475 725.053i −0.0347722 0.0303217i
\(831\) 24760.2i 1.03360i
\(832\) −19952.5 35858.1i −0.831404 1.49418i
\(833\) 5079.15i 0.211263i
\(834\) −17491.8 + 20059.2i −0.726247 + 0.832845i
\(835\) 73.0757 240.898i 0.00302861 0.00998399i
\(836\) 2778.89 + 4751.20i 0.114964 + 0.196559i
\(837\) −7932.66 + 80541.6i −0.327590 + 3.32608i
\(838\) 23134.4 + 36970.7i 0.953659 + 1.52402i
\(839\) −29446.8 + 19675.7i −1.21170 + 0.809632i −0.986353 0.164647i \(-0.947352\pi\)
−0.225347 + 0.974279i \(0.572352\pi\)
\(840\) −546.947 1289.53i −0.0224660 0.0529680i
\(841\) −12167.6 + 18210.1i −0.498897 + 0.746653i
\(842\) 16749.8 15776.7i 0.685555 0.645725i
\(843\) 40388.3 + 21588.0i 1.65011 + 0.882004i
\(844\) −7032.99 4318.67i −0.286831 0.176131i
\(845\) 1631.38 160.677i 0.0664156 0.00654137i
\(846\) −15149.5 + 117630.i −0.615661 + 4.78037i
\(847\) 10395.6 25097.3i 0.421722 1.01813i
\(848\) 7591.81 + 1680.25i 0.307434 + 0.0680426i
\(849\) 5089.68 + 12287.6i 0.205745 + 0.496712i
\(850\) 17687.2 4792.68i 0.713724 0.193397i
\(851\) 924.702 + 758.883i 0.0372484 + 0.0305690i
\(852\) −14910.0 + 6857.09i −0.599541 + 0.275728i
\(853\) −1419.24 + 430.523i −0.0569684 + 0.0172812i −0.318640 0.947876i \(-0.603226\pi\)
0.261672 + 0.965157i \(0.415726\pi\)
\(854\) 372.447 141.377i 0.0149237 0.00566491i
\(855\) −363.606 + 72.3257i −0.0145439 + 0.00289297i
\(856\) −663.012 1215.60i −0.0264734 0.0485378i
\(857\) 2459.07 12362.6i 0.0980167 0.492763i −0.900326 0.435216i \(-0.856672\pi\)
0.998343 0.0575472i \(-0.0183280\pi\)
\(858\) 104226. + 74243.7i 4.14709 + 2.95413i
\(859\) 12210.6 10021.0i 0.485007 0.398035i −0.359864 0.933005i \(-0.617177\pi\)
0.844871 + 0.534970i \(0.179677\pi\)
\(860\) −634.440 + 219.355i −0.0251561 + 0.00869760i
\(861\) −13299.2 24881.1i −0.526407 0.984838i
\(862\) 18288.2 + 36823.0i 0.722618 + 1.45498i
\(863\) −11047.6 + 11047.6i −0.435763 + 0.435763i −0.890583 0.454820i \(-0.849703\pi\)
0.454820 + 0.890583i \(0.349703\pi\)
\(864\) 78920.2 + 47548.5i 3.10755 + 1.87226i
\(865\) −96.0593 96.0593i −0.00377585 0.00377585i
\(866\) 5041.28 14989.7i 0.197817 0.588186i
\(867\) 19960.1 10668.9i 0.781870 0.417918i
\(868\) 1190.61 19879.8i 0.0465577 0.777378i
\(869\) 26025.5 + 31712.2i 1.01594 + 1.23793i
\(870\) 550.102 92.4139i 0.0214370 0.00360129i
\(871\) −67759.0 13478.1i −2.63597 0.524326i
\(872\) −14042.4 + 26813.7i −0.545338 + 1.04132i
\(873\) −3920.18 19708.1i −0.151979 0.764052i
\(874\) −1476.49 663.985i −0.0571430 0.0256975i
\(875\) 440.409 + 1451.83i 0.0170155 + 0.0560925i
\(876\) 13580.0 14663.8i 0.523773 0.565576i
\(877\) 21323.2 25982.4i 0.821019 1.00041i −0.178844 0.983877i \(-0.557236\pi\)
0.999863 0.0165374i \(-0.00526427\pi\)
\(878\) 18075.0 31511.3i 0.694761 1.21122i
\(879\) 54124.7 22419.2i 2.07688 0.860274i
\(880\) 427.122 1306.41i 0.0163617 0.0500445i
\(881\) −31161.2 12907.4i −1.19166 0.493600i −0.303362 0.952875i \(-0.598109\pi\)
−0.888294 + 0.459275i \(0.848109\pi\)
\(882\) −16859.1 + 13012.0i −0.643622 + 0.496754i
\(883\) −775.920 7878.05i −0.0295717 0.300246i −0.998582 0.0532276i \(-0.983049\pi\)
0.969011 0.247019i \(-0.0794509\pi\)
\(884\) −19532.7 26936.3i −0.743164 1.02485i
\(885\) −133.726 + 250.184i −0.00507926 + 0.00950263i
\(886\) 1124.44 37583.4i 0.0426369 1.42510i
\(887\) 27065.3 + 18084.5i 1.02454 + 0.684574i 0.949873 0.312635i \(-0.101212\pi\)
0.0746636 + 0.997209i \(0.476212\pi\)
\(888\) 4952.48 3369.99i 0.187156 0.127353i
\(889\) −24050.1 35993.5i −0.907327 1.35791i
\(890\) 71.5319 310.737i 0.00269411 0.0117033i
\(891\) −171480. 16889.4i −6.44760 0.635033i
\(892\) −7157.80 + 9437.79i −0.268678 + 0.354261i
\(893\) −6481.22 1966.06i −0.242873 0.0736748i
\(894\) 3500.18 + 51193.6i 0.130943 + 1.91518i
\(895\) −910.955 −0.0340222
\(896\) −19854.9 10947.3i −0.740296 0.408175i
\(897\) −37637.7 −1.40099
\(898\) 1969.74 + 28809.4i 0.0731970 + 1.07058i
\(899\) 7589.38 + 2302.21i 0.281557 + 0.0854095i
\(900\) −61220.0 46430.4i −2.26741 1.71965i
\(901\) 6274.31 + 617.966i 0.231995 + 0.0228495i
\(902\) 6210.29 26977.7i 0.229246 0.995853i
\(903\) −19184.8 28712.0i −0.707009 1.05811i
\(904\) 4181.22 + 795.046i 0.153833 + 0.0292509i
\(905\) −774.779 517.691i −0.0284580 0.0190150i
\(906\) 1343.83 44916.2i 0.0492778 1.64707i
\(907\) −11785.7 + 22049.4i −0.431462 + 0.807209i −0.999879 0.0155312i \(-0.995056\pi\)
0.568417 + 0.822741i \(0.307556\pi\)
\(908\) −23662.8 + 17159.0i −0.864843 + 0.627138i
\(909\) −10007.6 101609.i −0.365162 3.70755i
\(910\) 1089.72 841.053i 0.0396964 0.0306381i
\(911\) −6120.90 2535.36i −0.222606 0.0922066i 0.268593 0.963254i \(-0.413441\pi\)
−0.491199 + 0.871047i \(0.663441\pi\)
\(912\) −5276.32 + 6154.94i −0.191575 + 0.223476i
\(913\) 51446.5 21309.8i 1.86488 0.772457i
\(914\) −4102.53 + 7152.21i −0.148468 + 0.258834i
\(915\) −22.5654 + 27.4960i −0.000815288 + 0.000993431i
\(916\) −21952.7 20330.1i −0.791853 0.733326i
\(917\) −1971.40 6498.84i −0.0709939 0.234035i
\(918\) 68135.4 + 30640.8i 2.44968 + 1.10163i
\(919\) 1985.40 + 9981.29i 0.0712648 + 0.358272i 0.999920 0.0126725i \(-0.00403390\pi\)
−0.928655 + 0.370945i \(0.879034\pi\)
\(920\) 120.614 + 385.851i 0.00432233 + 0.0138273i
\(921\) 55092.9 + 10958.7i 1.97109 + 0.392074i
\(922\) −33494.5 + 5626.87i −1.19640 + 0.200988i
\(923\) −10231.3 12466.9i −0.364863 0.444587i
\(924\) 70576.9 + 4226.90i 2.51278 + 0.150492i
\(925\) −2859.34 + 1528.35i −0.101637 + 0.0543262i
\(926\) −1162.85 + 3457.60i −0.0412674 + 0.122704i
\(927\) 73920.9 + 73920.9i 2.61907 + 2.61907i
\(928\) 6078.79 6676.17i 0.215028 0.236160i
\(929\) −23243.0 + 23243.0i −0.820860 + 0.820860i −0.986231 0.165372i \(-0.947118\pi\)
0.165372 + 0.986231i \(0.447118\pi\)
\(930\) 790.961 + 1592.59i 0.0278889 + 0.0561539i
\(931\) −573.294 1072.56i −0.0201815 0.0377569i
\(932\) −10529.7 30455.0i −0.370077 1.07037i
\(933\) 14884.7 12215.5i 0.522297 0.428638i
\(934\) −12816.9 9129.94i −0.449016 0.319851i
\(935\) 217.421 1093.05i 0.00760472 0.0382315i
\(936\) −39368.9 + 133841.i −1.37480 + 4.67385i
\(937\) 44598.1 8871.11i 1.55492 0.309292i 0.658526 0.752558i \(-0.271180\pi\)
0.896390 + 0.443266i \(0.146180\pi\)
\(938\) −35687.1 + 13546.5i −1.24224 + 0.471545i
\(939\) −81065.1 + 24590.8i −2.81732 + 0.854624i
\(940\) 706.659 + 1536.55i 0.0245199 + 0.0533158i
\(941\) 21095.8 + 17312.9i 0.730822 + 0.599770i 0.924449 0.381305i \(-0.124525\pi\)
−0.193627 + 0.981075i \(0.562025\pi\)
\(942\) 10514.4 2849.07i 0.363669 0.0985431i
\(943\) 3115.94 + 7522.54i 0.107602 + 0.259775i
\(944\) 798.951 + 4521.75i 0.0275462 + 0.155901i
\(945\) −1182.78 + 2855.48i −0.0407151 + 0.0982949i
\(946\) 4328.17 33606.5i 0.148753 1.15501i
\(947\) −7856.75 + 773.823i −0.269599 + 0.0265532i −0.231913 0.972736i \(-0.574499\pi\)
−0.0376857 + 0.999290i \(0.511999\pi\)
\(948\) −31618.3 + 51490.6i −1.08324 + 1.76407i
\(949\) 17321.7 + 9258.65i 0.592504 + 0.316700i
\(950\) 3194.02 3008.45i 0.109082 0.102744i
\(951\) 34546.2 51702.1i 1.17796 1.76294i
\(952\) −17043.4 6891.55i −0.580231 0.234618i
\(953\) −23242.7 + 15530.3i −0.790035 + 0.527885i −0.883886 0.467701i \(-0.845082\pi\)
0.0938511 + 0.995586i \(0.470082\pi\)
\(954\) −14022.6 22409.3i −0.475890 0.760510i
\(955\) −95.3104 + 967.703i −0.00322950 + 0.0327897i
\(956\) 28972.0 16945.2i 0.980147 0.573271i
\(957\) −8173.29 + 26943.7i −0.276076 + 0.910101i
\(958\) −14892.7 + 17078.6i −0.502255 + 0.575976i
\(959\) 2861.52i 0.0963538i
\(960\) 2024.11 34.1942i 0.0680500 0.00114960i
\(961\) 4508.87i 0.151350i
\(962\) 4436.87 + 3868.99i 0.148701 + 0.129669i
\(963\) −1366.52 + 4504.80i −0.0457272 + 0.150743i
\(964\) 39984.9 + 10473.0i 1.33592 + 0.349909i
\(965\) 108.698 1103.63i 0.00362603 0.0368157i
\(966\) −17628.7 + 11031.2i −0.587157 + 0.367414i
\(967\) −11967.2 + 7996.20i −0.397971 + 0.265916i −0.738412 0.674350i \(-0.764424\pi\)
0.340441 + 0.940266i \(0.389424\pi\)
\(968\) 27994.7 + 27525.8i 0.929530 + 0.913959i
\(969\) −3651.99 + 5465.59i −0.121072 + 0.181197i
\(970\) −196.468 208.586i −0.00650330 0.00690443i
\(971\) 8993.85 + 4807.31i 0.297247 + 0.158882i 0.613278 0.789867i \(-0.289851\pi\)
−0.316031 + 0.948749i \(0.602351\pi\)
\(972\) −33452.9 139905.i −1.10391 4.61671i
\(973\) −14381.5 + 1416.45i −0.473843 + 0.0466694i
\(974\) 14913.5 + 1920.70i 0.490616 + 0.0631861i
\(975\) 39037.5 94244.9i 1.28226 3.09564i
\(976\) −12.3569 + 575.621i −0.000405260 + 0.0188783i
\(977\) 19221.0 + 46403.6i 0.629411 + 1.51953i 0.840357 + 0.542034i \(0.182346\pi\)
−0.210946 + 0.977498i \(0.567654\pi\)
\(978\) 17558.4 + 64798.7i 0.574087 + 2.11864i
\(979\) 12441.6 + 10210.6i 0.406165 + 0.333331i
\(980\) −105.373 + 284.823i −0.00343470 + 0.00928401i
\(981\) 98473.8 29871.7i 3.20492 0.972202i
\(982\) −9707.15 25572.7i −0.315446 0.831015i
\(983\) −8243.26 + 1639.69i −0.267466 + 0.0532023i −0.327001 0.945024i \(-0.606038\pi\)
0.0595351 + 0.998226i \(0.481038\pi\)
\(984\) 40542.4 4339.11i 1.31346 0.140575i
\(985\) −149.242 + 750.290i −0.00482766 + 0.0242703i
\(986\) 4247.57 5962.86i 0.137191 0.192592i
\(987\) −67251.8 + 55192.1i −2.16884 + 1.77992i
\(988\) −7165.05 3483.40i −0.230719 0.112168i
\(989\) 4698.01 + 8789.35i 0.151049 + 0.282594i
\(990\) −4185.12 + 2078.54i −0.134355 + 0.0667276i
\(991\) 24250.7 24250.7i 0.777346 0.777346i −0.202033 0.979379i \(-0.564755\pi\)
0.979379 + 0.202033i \(0.0647548\pi\)
\(992\) 25991.1 + 12365.6i 0.831872 + 0.395776i
\(993\) −25280.8 25280.8i −0.807916 0.807916i
\(994\) −8446.04 2840.55i −0.269509 0.0906407i
\(995\) −1414.86 + 756.257i −0.0450794 + 0.0240954i
\(996\) 54424.1 + 61358.4i 1.73142 + 1.95202i
\(997\) −27518.0 33530.8i −0.874126 1.06513i −0.997350 0.0727470i \(-0.976823\pi\)
0.123224 0.992379i \(-0.460677\pi\)
\(998\) −654.548 3896.26i −0.0207609 0.123581i
\(999\) −12963.8 2578.66i −0.410567 0.0816669i
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 128.4.k.a.5.2 752
128.77 even 32 inner 128.4.k.a.77.2 yes 752
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
128.4.k.a.5.2 752 1.1 even 1 trivial
128.4.k.a.77.2 yes 752 128.77 even 32 inner