Properties

Label 136.3.j.b.115.9
Level $136$
Weight $3$
Character 136.115
Analytic conductor $3.706$
Analytic rank $0$
Dimension $64$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [136,3,Mod(115,136)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(136, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 2, 1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("136.115");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 136 = 2^{3} \cdot 17 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 136.j (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: \(3.70573159530\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(32\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 115.9
Character \(\chi\) \(=\) 136.115
Dual form 136.3.j.b.123.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.54442 + 1.27074i) q^{2} +(-4.05827 - 4.05827i) q^{3} +(0.770451 - 3.92510i) q^{4} +(3.34858 - 3.34858i) q^{5} +(11.4247 + 1.11067i) q^{6} +(-7.12993 - 7.12993i) q^{7} +(3.79787 + 7.04103i) q^{8} +23.9391i q^{9} +O(q^{10})\) \(q+(-1.54442 + 1.27074i) q^{2} +(-4.05827 - 4.05827i) q^{3} +(0.770451 - 3.92510i) q^{4} +(3.34858 - 3.34858i) q^{5} +(11.4247 + 1.11067i) q^{6} +(-7.12993 - 7.12993i) q^{7} +(3.79787 + 7.04103i) q^{8} +23.9391i q^{9} +(-0.916437 + 9.42676i) q^{10} +(1.68469 - 1.68469i) q^{11} +(-19.0558 + 12.8024i) q^{12} -4.79400i q^{13} +(20.0719 + 1.95132i) q^{14} -27.1788 q^{15} +(-14.8128 - 6.04819i) q^{16} +(-16.8443 - 2.29531i) q^{17} +(-30.4203 - 36.9719i) q^{18} +11.3212i q^{19} +(-10.5636 - 15.7234i) q^{20} +57.8703i q^{21} +(-0.461065 + 4.74266i) q^{22} +(6.50691 + 6.50691i) q^{23} +(13.1616 - 43.9872i) q^{24} +2.57409i q^{25} +(6.09191 + 7.40393i) q^{26} +(60.6268 - 60.6268i) q^{27} +(-33.4789 + 22.4924i) q^{28} +(3.53343 - 3.53343i) q^{29} +(41.9755 - 34.5372i) q^{30} +(-37.3287 + 37.3287i) q^{31} +(30.5628 - 9.48226i) q^{32} -13.6738 q^{33} +(28.9314 - 17.8598i) q^{34} -47.7502 q^{35} +(93.9633 + 18.4439i) q^{36} +(22.7670 - 22.7670i) q^{37} +(-14.3863 - 17.4847i) q^{38} +(-19.4553 + 19.4553i) q^{39} +(36.2949 + 10.8600i) q^{40} +(21.5376 - 21.5376i) q^{41} +(-73.5380 - 89.3760i) q^{42} +39.2822i q^{43} +(-5.31460 - 7.91054i) q^{44} +(80.1618 + 80.1618i) q^{45} +(-18.3180 - 1.78081i) q^{46} -53.6139i q^{47} +(35.5692 + 84.6595i) q^{48} +52.6718i q^{49} +(-3.27099 - 3.97546i) q^{50} +(59.0438 + 77.6738i) q^{51} +(-18.8169 - 3.69354i) q^{52} -90.9429 q^{53} +(-16.5923 + 170.674i) q^{54} -11.2826i q^{55} +(23.1235 - 77.2807i) q^{56} +(45.9445 - 45.9445i) q^{57} +(-0.967028 + 9.94715i) q^{58} -93.8058i q^{59} +(-20.9400 + 106.680i) q^{60} +(-45.9156 - 45.9156i) q^{61} +(10.2161 - 105.086i) q^{62} +(170.684 - 170.684i) q^{63} +(-35.1523 + 53.4819i) q^{64} +(-16.0531 - 16.0531i) q^{65} +(21.1181 - 17.3758i) q^{66} -18.2300 q^{67} +(-21.9870 + 64.3473i) q^{68} -52.8136i q^{69} +(73.7463 - 60.6780i) q^{70} +(-11.0862 + 11.0862i) q^{71} +(-168.556 + 90.9176i) q^{72} +(-16.7784 - 16.7784i) q^{73} +(-6.23088 + 64.0928i) q^{74} +(10.4463 - 10.4463i) q^{75} +(44.4369 + 8.72243i) q^{76} -24.0234 q^{77} +(5.32453 - 54.7698i) q^{78} +(-21.5651 - 21.5651i) q^{79} +(-69.8546 + 29.3490i) q^{80} -276.628 q^{81} +(-5.89442 + 60.6318i) q^{82} -31.5476i q^{83} +(227.147 + 44.5863i) q^{84} +(-64.0905 + 48.7185i) q^{85} +(-49.9173 - 60.6681i) q^{86} -28.6792 q^{87} +(18.2602 + 5.46371i) q^{88} +88.4664 q^{89} +(-225.668 - 21.9387i) q^{90} +(-34.1809 + 34.1809i) q^{91} +(30.5535 - 20.5270i) q^{92} +302.980 q^{93} +(68.1292 + 82.8022i) q^{94} +(37.9099 + 37.9099i) q^{95} +(-162.514 - 85.5506i) q^{96} +(-29.8391 - 29.8391i) q^{97} +(-66.9320 - 81.3472i) q^{98} +(40.3299 + 40.3299i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q - 8 q^{3} + 12 q^{4} + 26 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 64 q - 8 q^{3} + 12 q^{4} + 26 q^{6} - 30 q^{10} - 32 q^{11} - 14 q^{12} - 32 q^{14} - 124 q^{16} - 12 q^{17} + 84 q^{18} + 70 q^{20} - 38 q^{22} + 54 q^{24} + 160 q^{27} - 76 q^{28} + 56 q^{30} + 128 q^{33} + 54 q^{34} - 8 q^{35} - 360 q^{38} - 62 q^{40} - 88 q^{41} + 306 q^{44} - 280 q^{46} + 82 q^{48} - 164 q^{50} - 360 q^{51} - 204 q^{52} + 460 q^{54} - 328 q^{56} - 24 q^{57} + 194 q^{58} - 72 q^{62} + 204 q^{64} + 112 q^{65} - 8 q^{67} - 226 q^{68} - 36 q^{72} - 408 q^{73} - 250 q^{74} + 32 q^{75} + 508 q^{78} + 674 q^{80} + 80 q^{81} + 116 q^{82} + 1008 q^{84} - 324 q^{86} + 90 q^{88} - 8 q^{89} - 834 q^{90} + 384 q^{91} - 104 q^{92} + 154 q^{96} + 112 q^{97} - 216 q^{98} + 416 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/136\mathbb{Z}\right)^\times\).

\(n\) \(69\) \(103\) \(105\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.54442 + 1.27074i −0.772209 + 0.635369i
\(3\) −4.05827 4.05827i −1.35276 1.35276i −0.882564 0.470192i \(-0.844185\pi\)
−0.470192 0.882564i \(-0.655815\pi\)
\(4\) 0.770451 3.92510i 0.192613 0.981275i
\(5\) 3.34858 3.34858i 0.669715 0.669715i −0.287935 0.957650i \(-0.592969\pi\)
0.957650 + 0.287935i \(0.0929687\pi\)
\(6\) 11.4247 + 1.11067i 1.90411 + 0.185111i
\(7\) −7.12993 7.12993i −1.01856 1.01856i −0.999824 0.0187370i \(-0.994035\pi\)
−0.0187370 0.999824i \(-0.505965\pi\)
\(8\) 3.79787 + 7.04103i 0.474734 + 0.880129i
\(9\) 23.9391i 2.65990i
\(10\) −0.916437 + 9.42676i −0.0916437 + 0.942676i
\(11\) 1.68469 1.68469i 0.153153 0.153153i −0.626371 0.779525i \(-0.715461\pi\)
0.779525 + 0.626371i \(0.215461\pi\)
\(12\) −19.0558 + 12.8024i −1.58798 + 1.06687i
\(13\) 4.79400i 0.368769i −0.982854 0.184385i \(-0.940971\pi\)
0.982854 0.184385i \(-0.0590292\pi\)
\(14\) 20.0719 + 1.95132i 1.43370 + 0.139380i
\(15\) −27.1788 −1.81192
\(16\) −14.8128 6.04819i −0.925801 0.378012i
\(17\) −16.8443 2.29531i −0.990843 0.135018i
\(18\) −30.4203 36.9719i −1.69002 2.05400i
\(19\) 11.3212i 0.595853i 0.954589 + 0.297926i \(0.0962950\pi\)
−0.954589 + 0.297926i \(0.903705\pi\)
\(20\) −10.5636 15.7234i −0.528179 0.786170i
\(21\) 57.8703i 2.75573i
\(22\) −0.461065 + 4.74266i −0.0209575 + 0.215575i
\(23\) 6.50691 + 6.50691i 0.282909 + 0.282909i 0.834268 0.551359i \(-0.185891\pi\)
−0.551359 + 0.834268i \(0.685891\pi\)
\(24\) 13.1616 43.9872i 0.548400 1.83280i
\(25\) 2.57409i 0.102963i
\(26\) 6.09191 + 7.40393i 0.234304 + 0.284767i
\(27\) 60.6268 60.6268i 2.24544 2.24544i
\(28\) −33.4789 + 22.4924i −1.19568 + 0.803301i
\(29\) 3.53343 3.53343i 0.121842 0.121842i −0.643556 0.765399i \(-0.722542\pi\)
0.765399 + 0.643556i \(0.222542\pi\)
\(30\) 41.9755 34.5372i 1.39918 1.15124i
\(31\) −37.3287 + 37.3287i −1.20415 + 1.20415i −0.231259 + 0.972892i \(0.574285\pi\)
−0.972892 + 0.231259i \(0.925715\pi\)
\(32\) 30.5628 9.48226i 0.955089 0.296321i
\(33\) −13.6738 −0.414358
\(34\) 28.9314 17.8598i 0.850924 0.525289i
\(35\) −47.7502 −1.36429
\(36\) 93.9633 + 18.4439i 2.61009 + 0.512330i
\(37\) 22.7670 22.7670i 0.615326 0.615326i −0.329003 0.944329i \(-0.606713\pi\)
0.944329 + 0.329003i \(0.106713\pi\)
\(38\) −14.3863 17.4847i −0.378586 0.460123i
\(39\) −19.4553 + 19.4553i −0.498855 + 0.498855i
\(40\) 36.2949 + 10.8600i 0.907372 + 0.271499i
\(41\) 21.5376 21.5376i 0.525309 0.525309i −0.393861 0.919170i \(-0.628861\pi\)
0.919170 + 0.393861i \(0.128861\pi\)
\(42\) −73.5380 89.3760i −1.75091 2.12800i
\(43\) 39.2822i 0.913539i 0.889585 + 0.456769i \(0.150994\pi\)
−0.889585 + 0.456769i \(0.849006\pi\)
\(44\) −5.31460 7.91054i −0.120786 0.179785i
\(45\) 80.1618 + 80.1618i 1.78137 + 1.78137i
\(46\) −18.3180 1.78081i −0.398217 0.0387133i
\(47\) 53.6139i 1.14072i −0.821395 0.570360i \(-0.806804\pi\)
0.821395 0.570360i \(-0.193196\pi\)
\(48\) 35.5692 + 84.6595i 0.741024 + 1.76374i
\(49\) 52.6718i 1.07493i
\(50\) −3.27099 3.97546i −0.0654198 0.0795093i
\(51\) 59.0438 + 77.6738i 1.15772 + 1.52302i
\(52\) −18.8169 3.69354i −0.361864 0.0710296i
\(53\) −90.9429 −1.71590 −0.857952 0.513730i \(-0.828263\pi\)
−0.857952 + 0.513730i \(0.828263\pi\)
\(54\) −16.5923 + 170.674i −0.307265 + 3.16063i
\(55\) 11.2826i 0.205138i
\(56\) 23.1235 77.2807i 0.412920 1.38001i
\(57\) 45.9445 45.9445i 0.806044 0.806044i
\(58\) −0.967028 + 9.94715i −0.0166729 + 0.171503i
\(59\) 93.8058i 1.58993i −0.606656 0.794964i \(-0.707489\pi\)
0.606656 0.794964i \(-0.292511\pi\)
\(60\) −20.9400 + 106.680i −0.348999 + 1.77799i
\(61\) −45.9156 45.9156i −0.752714 0.752714i 0.222271 0.974985i \(-0.428653\pi\)
−0.974985 + 0.222271i \(0.928653\pi\)
\(62\) 10.2161 105.086i 0.164776 1.69494i
\(63\) 170.684 170.684i 2.70927 2.70927i
\(64\) −35.1523 + 53.4819i −0.549255 + 0.835655i
\(65\) −16.0531 16.0531i −0.246970 0.246970i
\(66\) 21.1181 17.3758i 0.319971 0.263270i
\(67\) −18.2300 −0.272089 −0.136044 0.990703i \(-0.543439\pi\)
−0.136044 + 0.990703i \(0.543439\pi\)
\(68\) −21.9870 + 64.3473i −0.323339 + 0.946283i
\(69\) 52.8136i 0.765414i
\(70\) 73.7463 60.6780i 1.05352 0.866829i
\(71\) −11.0862 + 11.0862i −0.156144 + 0.156144i −0.780855 0.624712i \(-0.785216\pi\)
0.624712 + 0.780855i \(0.285216\pi\)
\(72\) −168.556 + 90.9176i −2.34105 + 1.26274i
\(73\) −16.7784 16.7784i −0.229842 0.229842i 0.582785 0.812626i \(-0.301963\pi\)
−0.812626 + 0.582785i \(0.801963\pi\)
\(74\) −6.23088 + 64.0928i −0.0842011 + 0.866118i
\(75\) 10.4463 10.4463i 0.139284 0.139284i
\(76\) 44.4369 + 8.72243i 0.584696 + 0.114769i
\(77\) −24.0234 −0.311992
\(78\) 5.32453 54.7698i 0.0682632 0.702176i
\(79\) −21.5651 21.5651i −0.272977 0.272977i 0.557321 0.830297i \(-0.311829\pi\)
−0.830297 + 0.557321i \(0.811829\pi\)
\(80\) −69.8546 + 29.3490i −0.873183 + 0.366862i
\(81\) −276.628 −3.41516
\(82\) −5.89442 + 60.6318i −0.0718832 + 0.739413i
\(83\) 31.5476i 0.380092i −0.981775 0.190046i \(-0.939136\pi\)
0.981775 0.190046i \(-0.0608637\pi\)
\(84\) 227.147 + 44.5863i 2.70413 + 0.530789i
\(85\) −64.0905 + 48.7185i −0.754006 + 0.573159i
\(86\) −49.9173 60.6681i −0.580434 0.705443i
\(87\) −28.6792 −0.329646
\(88\) 18.2602 + 5.46371i 0.207502 + 0.0620876i
\(89\) 88.4664 0.994005 0.497002 0.867749i \(-0.334434\pi\)
0.497002 + 0.867749i \(0.334434\pi\)
\(90\) −225.668 21.9387i −2.50742 0.243763i
\(91\) −34.1809 + 34.1809i −0.375614 + 0.375614i
\(92\) 30.5535 20.5270i 0.332104 0.223120i
\(93\) 302.980 3.25785
\(94\) 68.1292 + 82.8022i 0.724779 + 0.880875i
\(95\) 37.9099 + 37.9099i 0.399052 + 0.399052i
\(96\) −162.514 85.5506i −1.69285 0.891152i
\(97\) −29.8391 29.8391i −0.307620 0.307620i 0.536366 0.843986i \(-0.319797\pi\)
−0.843986 + 0.536366i \(0.819797\pi\)
\(98\) −66.9320 81.3472i −0.682980 0.830074i
\(99\) 40.3299 + 40.3299i 0.407372 + 0.407372i
\(100\) 10.1035 + 1.98321i 0.101035 + 0.0198321i
\(101\) 49.1217i 0.486353i −0.969982 0.243177i \(-0.921811\pi\)
0.969982 0.243177i \(-0.0781895\pi\)
\(102\) −189.891 44.9315i −1.86168 0.440505i
\(103\) 155.870i 1.51330i 0.653820 + 0.756650i \(0.273166\pi\)
−0.653820 + 0.756650i \(0.726834\pi\)
\(104\) 33.7547 18.2070i 0.324564 0.175067i
\(105\) 193.783 + 193.783i 1.84555 + 1.84555i
\(106\) 140.454 115.565i 1.32504 1.09023i
\(107\) −62.5365 62.5365i −0.584454 0.584454i 0.351670 0.936124i \(-0.385614\pi\)
−0.936124 + 0.351670i \(0.885614\pi\)
\(108\) −191.256 284.676i −1.77089 2.63589i
\(109\) −109.883 109.883i −1.00810 1.00810i −0.999967 0.00813505i \(-0.997411\pi\)
−0.00813505 0.999967i \(-0.502589\pi\)
\(110\) 14.3372 + 17.4251i 0.130339 + 0.158410i
\(111\) −184.790 −1.66477
\(112\) 62.4911 + 148.737i 0.557956 + 1.32801i
\(113\) −78.4235 + 78.4235i −0.694014 + 0.694014i −0.963113 0.269099i \(-0.913274\pi\)
0.269099 + 0.963113i \(0.413274\pi\)
\(114\) −12.5741 + 129.341i −0.110299 + 1.13457i
\(115\) 43.5778 0.378937
\(116\) −11.1467 16.5914i −0.0960924 0.143029i
\(117\) 114.764 0.980888
\(118\) 119.203 + 144.875i 1.01019 + 1.22776i
\(119\) 103.734 + 136.464i 0.871710 + 1.14676i
\(120\) −103.222 191.367i −0.860181 1.59473i
\(121\) 115.324i 0.953088i
\(122\) 129.259 + 12.5662i 1.05950 + 0.103001i
\(123\) −174.811 −1.42123
\(124\) 117.759 + 175.279i 0.949669 + 1.41354i
\(125\) 92.3339 + 92.3339i 0.738671 + 0.738671i
\(126\) −46.7127 + 480.502i −0.370736 + 3.81351i
\(127\) −187.466 −1.47611 −0.738057 0.674739i \(-0.764256\pi\)
−0.738057 + 0.674739i \(0.764256\pi\)
\(128\) −13.6717 127.268i −0.106810 0.994279i
\(129\) 159.418 159.418i 1.23579 1.23579i
\(130\) 45.1919 + 4.39340i 0.347630 + 0.0337954i
\(131\) 33.8003 + 33.8003i 0.258018 + 0.258018i 0.824248 0.566230i \(-0.191598\pi\)
−0.566230 + 0.824248i \(0.691598\pi\)
\(132\) −10.5350 + 53.6711i −0.0798107 + 0.406599i
\(133\) 80.7194 80.7194i 0.606913 0.606913i
\(134\) 28.1547 23.1655i 0.210109 0.172877i
\(135\) 406.027i 3.00760i
\(136\) −47.8113 127.319i −0.351554 0.936168i
\(137\) 41.8673 0.305601 0.152800 0.988257i \(-0.451171\pi\)
0.152800 + 0.988257i \(0.451171\pi\)
\(138\) 67.1122 + 81.5662i 0.486320 + 0.591059i
\(139\) −19.5026 19.5026i −0.140306 0.140306i 0.633465 0.773771i \(-0.281632\pi\)
−0.773771 + 0.633465i \(0.781632\pi\)
\(140\) −36.7892 + 187.424i −0.262780 + 1.33875i
\(141\) −217.580 + 217.580i −1.54312 + 1.54312i
\(142\) 3.03407 31.2093i 0.0213667 0.219784i
\(143\) −8.07639 8.07639i −0.0564782 0.0564782i
\(144\) 144.788 354.605i 1.00547 2.46253i
\(145\) 23.6639i 0.163199i
\(146\) 47.2339 + 4.59192i 0.323520 + 0.0314515i
\(147\) 213.756 213.756i 1.45412 1.45412i
\(148\) −71.8220 106.904i −0.485284 0.722323i
\(149\) 3.45014i 0.0231553i 0.999933 + 0.0115776i \(0.00368536\pi\)
−0.999933 + 0.0115776i \(0.996315\pi\)
\(150\) −2.85895 + 29.4080i −0.0190597 + 0.196054i
\(151\) −55.4358 −0.367125 −0.183562 0.983008i \(-0.558763\pi\)
−0.183562 + 0.983008i \(0.558763\pi\)
\(152\) −79.7130 + 42.9965i −0.524428 + 0.282872i
\(153\) 54.9476 403.238i 0.359134 2.63554i
\(154\) 37.1022 30.5275i 0.240923 0.198230i
\(155\) 249.996i 1.61288i
\(156\) 61.3747 + 91.3535i 0.393428 + 0.585599i
\(157\) 249.307i 1.58794i −0.607957 0.793970i \(-0.708011\pi\)
0.607957 0.793970i \(-0.291989\pi\)
\(158\) 60.7092 + 5.90194i 0.384236 + 0.0373541i
\(159\) 369.071 + 369.071i 2.32120 + 2.32120i
\(160\) 70.5899 134.094i 0.441187 0.838088i
\(161\) 92.7876i 0.576321i
\(162\) 427.229 351.521i 2.63721 2.16988i
\(163\) 23.7173 23.7173i 0.145505 0.145505i −0.630602 0.776107i \(-0.717192\pi\)
0.776107 + 0.630602i \(0.217192\pi\)
\(164\) −67.9437 101.131i −0.414291 0.616653i
\(165\) −45.7878 + 45.7878i −0.277502 + 0.277502i
\(166\) 40.0888 + 48.7227i 0.241499 + 0.293510i
\(167\) 68.6999 68.6999i 0.411377 0.411377i −0.470841 0.882218i \(-0.656050\pi\)
0.882218 + 0.470841i \(0.156050\pi\)
\(168\) −407.467 + 219.784i −2.42540 + 1.30824i
\(169\) 146.018 0.864009
\(170\) 37.0741 156.684i 0.218083 0.921670i
\(171\) −271.019 −1.58491
\(172\) 154.186 + 30.2650i 0.896433 + 0.175959i
\(173\) 66.2063 66.2063i 0.382695 0.382695i −0.489377 0.872072i \(-0.662776\pi\)
0.872072 + 0.489377i \(0.162776\pi\)
\(174\) 44.2926 36.4437i 0.254555 0.209447i
\(175\) 18.3531 18.3531i 0.104875 0.104875i
\(176\) −35.1443 + 14.7656i −0.199683 + 0.0838957i
\(177\) −380.689 + 380.689i −2.15079 + 2.15079i
\(178\) −136.629 + 112.418i −0.767579 + 0.631560i
\(179\) 67.3735i 0.376388i 0.982132 + 0.188194i \(0.0602634\pi\)
−0.982132 + 0.188194i \(0.939737\pi\)
\(180\) 376.404 252.882i 2.09113 1.40490i
\(181\) 19.0832 + 19.0832i 0.105432 + 0.105432i 0.757855 0.652423i \(-0.226247\pi\)
−0.652423 + 0.757855i \(0.726247\pi\)
\(182\) 9.35461 96.2244i 0.0513990 0.528706i
\(183\) 372.675i 2.03648i
\(184\) −21.1029 + 70.5278i −0.114690 + 0.383303i
\(185\) 152.474i 0.824186i
\(186\) −467.927 + 385.008i −2.51574 + 2.06993i
\(187\) −32.2443 + 24.5106i −0.172430 + 0.131073i
\(188\) −210.440 41.3069i −1.11936 0.219717i
\(189\) −864.529 −4.57423
\(190\) −106.722 10.3752i −0.561696 0.0546062i
\(191\) 138.978i 0.727632i −0.931471 0.363816i \(-0.881474\pi\)
0.931471 0.363816i \(-0.118526\pi\)
\(192\) 359.701 74.3865i 1.87344 0.387430i
\(193\) 82.3703 82.3703i 0.426789 0.426789i −0.460744 0.887533i \(-0.652417\pi\)
0.887533 + 0.460744i \(0.152417\pi\)
\(194\) 84.0017 + 8.16636i 0.432999 + 0.0420946i
\(195\) 130.295i 0.668181i
\(196\) 206.742 + 40.5810i 1.05481 + 0.207046i
\(197\) −13.2544 13.2544i −0.0672814 0.0672814i 0.672665 0.739947i \(-0.265149\pi\)
−0.739947 + 0.672665i \(0.765149\pi\)
\(198\) −113.535 11.0375i −0.573408 0.0557448i
\(199\) −45.2576 + 45.2576i −0.227425 + 0.227425i −0.811616 0.584191i \(-0.801412\pi\)
0.584191 + 0.811616i \(0.301412\pi\)
\(200\) −18.1242 + 9.77605i −0.0906211 + 0.0488803i
\(201\) 73.9820 + 73.9820i 0.368070 + 0.368070i
\(202\) 62.4208 + 75.8644i 0.309014 + 0.375566i
\(203\) −50.3862 −0.248208
\(204\) 350.368 171.909i 1.71749 0.842692i
\(205\) 144.241i 0.703614i
\(206\) −198.070 240.728i −0.961504 1.16858i
\(207\) −155.769 + 155.769i −0.752509 + 0.752509i
\(208\) −28.9950 + 71.0126i −0.139399 + 0.341407i
\(209\) 19.0727 + 19.0727i 0.0912569 + 0.0912569i
\(210\) −545.530 53.0345i −2.59776 0.252545i
\(211\) 164.401 164.401i 0.779153 0.779153i −0.200534 0.979687i \(-0.564268\pi\)
0.979687 + 0.200534i \(0.0642676\pi\)
\(212\) −70.0670 + 356.960i −0.330505 + 1.68377i
\(213\) 89.9815 0.422448
\(214\) 176.050 + 17.1150i 0.822664 + 0.0799766i
\(215\) 131.539 + 131.539i 0.611811 + 0.611811i
\(216\) 657.128 + 196.622i 3.04226 + 0.910288i
\(217\) 532.302 2.45300
\(218\) 309.338 + 30.0728i 1.41898 + 0.137949i
\(219\) 136.183i 0.621839i
\(220\) −44.2854 8.69270i −0.201297 0.0395123i
\(221\) −11.0037 + 80.7517i −0.0497905 + 0.365392i
\(222\) 285.392 234.819i 1.28555 1.05774i
\(223\) 64.6604 0.289957 0.144978 0.989435i \(-0.453689\pi\)
0.144978 + 0.989435i \(0.453689\pi\)
\(224\) −285.519 150.303i −1.27464 0.670996i
\(225\) −61.6212 −0.273872
\(226\) 21.4629 220.774i 0.0949687 0.976878i
\(227\) −260.063 + 260.063i −1.14565 + 1.14565i −0.158253 + 0.987399i \(0.550586\pi\)
−0.987399 + 0.158253i \(0.949414\pi\)
\(228\) −144.939 215.735i −0.635696 0.946205i
\(229\) −244.419 −1.06733 −0.533667 0.845695i \(-0.679186\pi\)
−0.533667 + 0.845695i \(0.679186\pi\)
\(230\) −67.3023 + 55.3759i −0.292619 + 0.240765i
\(231\) 97.4934 + 97.4934i 0.422049 + 0.422049i
\(232\) 38.2985 + 11.4595i 0.165080 + 0.0493943i
\(233\) −152.332 152.332i −0.653786 0.653786i 0.300116 0.953903i \(-0.402974\pi\)
−0.953903 + 0.300116i \(0.902974\pi\)
\(234\) −177.243 + 145.835i −0.757450 + 0.623226i
\(235\) −179.530 179.530i −0.763958 0.763958i
\(236\) −368.197 72.2728i −1.56016 0.306241i
\(237\) 175.034i 0.738541i
\(238\) −333.618 78.9397i −1.40176 0.331680i
\(239\) 126.163i 0.527878i 0.964539 + 0.263939i \(0.0850217\pi\)
−0.964539 + 0.263939i \(0.914978\pi\)
\(240\) 402.595 + 164.383i 1.67748 + 0.684929i
\(241\) −138.655 138.655i −0.575331 0.575331i 0.358283 0.933613i \(-0.383362\pi\)
−0.933613 + 0.358283i \(0.883362\pi\)
\(242\) −146.546 178.108i −0.605562 0.735983i
\(243\) 576.988 + 576.988i 2.37444 + 2.37444i
\(244\) −215.599 + 144.847i −0.883602 + 0.593637i
\(245\) 176.375 + 176.375i 0.719900 + 0.719900i
\(246\) 269.981 222.139i 1.09749 0.903004i
\(247\) 54.2738 0.219732
\(248\) −404.602 121.063i −1.63146 0.488157i
\(249\) −128.029 + 128.029i −0.514172 + 0.514172i
\(250\) −259.934 25.2699i −1.03974 0.101080i
\(251\) 345.825 1.37779 0.688895 0.724861i \(-0.258096\pi\)
0.688895 + 0.724861i \(0.258096\pi\)
\(252\) −538.448 801.455i −2.13670 3.18038i
\(253\) 21.9242 0.0866570
\(254\) 289.526 238.221i 1.13987 0.937876i
\(255\) 457.809 + 62.3838i 1.79533 + 0.244642i
\(256\) 182.839 + 179.181i 0.714214 + 0.699928i
\(257\) 447.501i 1.74125i −0.491948 0.870624i \(-0.663715\pi\)
0.491948 0.870624i \(-0.336285\pi\)
\(258\) −43.6294 + 448.785i −0.169106 + 1.73948i
\(259\) −324.655 −1.25349
\(260\) −75.3780 + 50.6418i −0.289915 + 0.194776i
\(261\) 84.5870 + 84.5870i 0.324088 + 0.324088i
\(262\) −95.1532 9.25047i −0.363180 0.0353071i
\(263\) 361.979 1.37635 0.688173 0.725547i \(-0.258413\pi\)
0.688173 + 0.725547i \(0.258413\pi\)
\(264\) −51.9315 96.2779i −0.196710 0.364689i
\(265\) −304.529 + 304.529i −1.14917 + 1.14917i
\(266\) −22.0913 + 227.238i −0.0830499 + 0.854277i
\(267\) −359.020 359.020i −1.34465 1.34465i
\(268\) −14.0453 + 71.5544i −0.0524078 + 0.266994i
\(269\) 76.8627 76.8627i 0.285735 0.285735i −0.549656 0.835391i \(-0.685241\pi\)
0.835391 + 0.549656i \(0.185241\pi\)
\(270\) 515.953 + 627.075i 1.91094 + 2.32250i
\(271\) 351.524i 1.29713i −0.761157 0.648567i \(-0.775368\pi\)
0.761157 0.648567i \(-0.224632\pi\)
\(272\) 235.629 + 135.878i 0.866285 + 0.499551i
\(273\) 277.430 1.01623
\(274\) −64.6606 + 53.2024i −0.235988 + 0.194169i
\(275\) 4.33653 + 4.33653i 0.0157692 + 0.0157692i
\(276\) −207.299 40.6903i −0.751082 0.147429i
\(277\) −143.565 + 143.565i −0.518286 + 0.518286i −0.917053 0.398766i \(-0.869438\pi\)
0.398766 + 0.917053i \(0.369438\pi\)
\(278\) 54.9027 + 5.33745i 0.197492 + 0.0191995i
\(279\) −893.614 893.614i −3.20292 3.20292i
\(280\) −181.349 336.211i −0.647676 1.20075i
\(281\) 101.471i 0.361107i 0.983565 + 0.180553i \(0.0577888\pi\)
−0.983565 + 0.180553i \(0.942211\pi\)
\(282\) 59.5471 612.520i 0.211160 2.17206i
\(283\) −148.615 + 148.615i −0.525142 + 0.525142i −0.919120 0.393978i \(-0.871099\pi\)
0.393978 + 0.919120i \(0.371099\pi\)
\(284\) 34.9730 + 52.0558i 0.123144 + 0.183295i
\(285\) 307.697i 1.07964i
\(286\) 22.7363 + 2.21034i 0.0794975 + 0.00772848i
\(287\) −307.124 −1.07012
\(288\) 226.997 + 731.646i 0.788183 + 2.54044i
\(289\) 278.463 + 77.3259i 0.963540 + 0.267564i
\(290\) 30.0706 + 36.5469i 0.103692 + 0.126024i
\(291\) 242.190i 0.832269i
\(292\) −78.7840 + 52.9301i −0.269808 + 0.181267i
\(293\) 82.6788i 0.282180i 0.989997 + 0.141090i \(0.0450607\pi\)
−0.989997 + 0.141090i \(0.954939\pi\)
\(294\) −58.5008 + 601.757i −0.198982 + 2.04679i
\(295\) −314.116 314.116i −1.06480 1.06480i
\(296\) 246.770 + 73.8372i 0.833682 + 0.249450i
\(297\) 204.274i 0.687792i
\(298\) −4.38422 5.32845i −0.0147121 0.0178807i
\(299\) 31.1941 31.1941i 0.104328 0.104328i
\(300\) −32.9545 49.0513i −0.109848 0.163504i
\(301\) 280.079 280.079i 0.930495 0.930495i
\(302\) 85.6161 70.4444i 0.283497 0.233260i
\(303\) −199.349 + 199.349i −0.657917 + 0.657917i
\(304\) 68.4728 167.699i 0.225240 0.551641i
\(305\) −307.503 −1.00821
\(306\) 427.548 + 692.591i 1.39721 + 2.26337i
\(307\) −217.880 −0.709707 −0.354853 0.934922i \(-0.615469\pi\)
−0.354853 + 0.934922i \(0.615469\pi\)
\(308\) −18.5089 + 94.2943i −0.0600937 + 0.306150i
\(309\) 632.562 632.562i 2.04713 2.04713i
\(310\) −317.679 386.098i −1.02477 1.24548i
\(311\) 361.855 361.855i 1.16352 1.16352i 0.179823 0.983699i \(-0.442448\pi\)
0.983699 0.179823i \(-0.0575524\pi\)
\(312\) −210.874 63.0967i −0.675880 0.202233i
\(313\) −189.814 + 189.814i −0.606435 + 0.606435i −0.942013 0.335577i \(-0.891069\pi\)
0.335577 + 0.942013i \(0.391069\pi\)
\(314\) 316.803 + 385.033i 1.00893 + 1.22622i
\(315\) 1143.10i 3.62888i
\(316\) −101.260 + 68.0305i −0.320444 + 0.215286i
\(317\) 125.146 + 125.146i 0.394784 + 0.394784i 0.876389 0.481605i \(-0.159946\pi\)
−0.481605 + 0.876389i \(0.659946\pi\)
\(318\) −1038.99 101.007i −3.26727 0.317633i
\(319\) 11.9054i 0.0373211i
\(320\) 61.3781 + 296.798i 0.191806 + 0.927495i
\(321\) 507.580i 1.58125i
\(322\) 117.909 + 143.303i 0.366176 + 0.445040i
\(323\) 25.9857 190.698i 0.0804509 0.590397i
\(324\) −213.128 + 1085.79i −0.657803 + 3.35121i
\(325\) 12.3402 0.0379697
\(326\) −6.49095 + 66.7679i −0.0199109 + 0.204809i
\(327\) 891.870i 2.72743i
\(328\) 233.445 + 69.8500i 0.711721 + 0.212957i
\(329\) −382.263 + 382.263i −1.16189 + 1.16189i
\(330\) 12.5312 128.900i 0.0379734 0.390606i
\(331\) 387.195i 1.16977i −0.811115 0.584886i \(-0.801139\pi\)
0.811115 0.584886i \(-0.198861\pi\)
\(332\) −123.828 24.3059i −0.372975 0.0732105i
\(333\) 545.022 + 545.022i 1.63670 + 1.63670i
\(334\) −18.8018 + 193.401i −0.0562927 + 0.579045i
\(335\) −61.0444 + 61.0444i −0.182222 + 0.182222i
\(336\) 350.011 857.222i 1.04170 2.55126i
\(337\) −146.626 146.626i −0.435091 0.435091i 0.455265 0.890356i \(-0.349544\pi\)
−0.890356 + 0.455265i \(0.849544\pi\)
\(338\) −225.512 + 185.550i −0.667196 + 0.548965i
\(339\) 636.527 1.87766
\(340\) 141.846 + 289.097i 0.417195 + 0.850285i
\(341\) 125.774i 0.368840i
\(342\) 418.567 344.394i 1.22388 1.00700i
\(343\) 26.1797 26.1797i 0.0763256 0.0763256i
\(344\) −276.587 + 149.189i −0.804032 + 0.433688i
\(345\) −176.850 176.850i −0.512609 0.512609i
\(346\) −18.1193 + 186.381i −0.0523680 + 0.538673i
\(347\) 209.388 209.388i 0.603422 0.603422i −0.337797 0.941219i \(-0.609682\pi\)
0.941219 + 0.337797i \(0.109682\pi\)
\(348\) −22.0959 + 112.569i −0.0634940 + 0.323473i
\(349\) 449.548 1.28810 0.644051 0.764982i \(-0.277252\pi\)
0.644051 + 0.764982i \(0.277252\pi\)
\(350\) −5.02286 + 51.6667i −0.0143510 + 0.147619i
\(351\) −290.645 290.645i −0.828047 0.828047i
\(352\) 35.5142 67.4635i 0.100893 0.191658i
\(353\) 290.121 0.821872 0.410936 0.911664i \(-0.365202\pi\)
0.410936 + 0.911664i \(0.365202\pi\)
\(354\) 104.187 1071.70i 0.294313 3.02740i
\(355\) 74.2459i 0.209143i
\(356\) 68.1590 347.240i 0.191458 0.975392i
\(357\) 132.830 974.787i 0.372073 2.73050i
\(358\) −85.6141 104.053i −0.239145 0.290650i
\(359\) 17.2774 0.0481265 0.0240632 0.999710i \(-0.492340\pi\)
0.0240632 + 0.999710i \(0.492340\pi\)
\(360\) −259.978 + 868.866i −0.722160 + 2.41352i
\(361\) 232.830 0.644959
\(362\) −53.7223 5.22270i −0.148404 0.0144273i
\(363\) 468.014 468.014i 1.28930 1.28930i
\(364\) 107.829 + 160.498i 0.296232 + 0.440929i
\(365\) −112.368 −0.307857
\(366\) −473.573 575.566i −1.29391 1.57259i
\(367\) 436.568 + 436.568i 1.18956 + 1.18956i 0.977190 + 0.212368i \(0.0681174\pi\)
0.212368 + 0.977190i \(0.431883\pi\)
\(368\) −57.0306 135.741i −0.154974 0.368861i
\(369\) 515.591 + 515.591i 1.39727 + 1.39727i
\(370\) 193.755 + 235.484i 0.523662 + 0.636443i
\(371\) 648.416 + 648.416i 1.74775 + 1.74775i
\(372\) 233.431 1189.23i 0.627503 3.19684i
\(373\) 54.1812i 0.145258i 0.997359 + 0.0726289i \(0.0231389\pi\)
−0.997359 + 0.0726289i \(0.976861\pi\)
\(374\) 18.6522 78.8286i 0.0498722 0.210772i
\(375\) 749.431i 1.99848i
\(376\) 377.497 203.619i 1.00398 0.541539i
\(377\) −16.9392 16.9392i −0.0449317 0.0449317i
\(378\) 1335.19 1098.59i 3.53226 2.90632i
\(379\) −34.3158 34.3158i −0.0905429 0.0905429i 0.660385 0.750928i \(-0.270393\pi\)
−0.750928 + 0.660385i \(0.770393\pi\)
\(380\) 178.008 119.592i 0.468442 0.314717i
\(381\) 760.789 + 760.789i 1.99682 + 1.99682i
\(382\) 176.604 + 214.639i 0.462314 + 0.561883i
\(383\) 72.3226 0.188832 0.0944159 0.995533i \(-0.469902\pi\)
0.0944159 + 0.995533i \(0.469902\pi\)
\(384\) −461.003 + 571.970i −1.20053 + 1.48951i
\(385\) −80.4442 + 80.4442i −0.208946 + 0.208946i
\(386\) −22.5431 + 231.885i −0.0584017 + 0.600739i
\(387\) −940.379 −2.42992
\(388\) −140.111 + 94.1319i −0.361111 + 0.242608i
\(389\) −501.908 −1.29025 −0.645126 0.764076i \(-0.723195\pi\)
−0.645126 + 0.764076i \(0.723195\pi\)
\(390\) −165.571 201.230i −0.424541 0.515975i
\(391\) −94.6692 124.540i −0.242121 0.318516i
\(392\) −370.864 + 200.041i −0.946081 + 0.510308i
\(393\) 274.342i 0.698070i
\(394\) 37.3133 + 3.62747i 0.0947038 + 0.00920678i
\(395\) −144.425 −0.365633
\(396\) 189.371 127.227i 0.478209 0.321279i
\(397\) −160.196 160.196i −0.403517 0.403517i 0.475953 0.879471i \(-0.342103\pi\)
−0.879471 + 0.475953i \(0.842103\pi\)
\(398\) 12.3861 127.407i 0.0311208 0.320118i
\(399\) −655.162 −1.64201
\(400\) 15.5686 38.1294i 0.0389214 0.0953236i
\(401\) 305.319 305.319i 0.761393 0.761393i −0.215181 0.976574i \(-0.569034\pi\)
0.976574 + 0.215181i \(0.0690342\pi\)
\(402\) −208.271 20.2474i −0.518087 0.0503666i
\(403\) 178.954 + 178.954i 0.444054 + 0.444054i
\(404\) −192.807 37.8459i −0.477246 0.0936779i
\(405\) −926.309 + 926.309i −2.28718 + 2.28718i
\(406\) 77.8173 64.0276i 0.191668 0.157704i
\(407\) 76.7107i 0.188478i
\(408\) −322.663 + 710.725i −0.790840 + 1.74197i
\(409\) −562.929 −1.37636 −0.688178 0.725542i \(-0.741589\pi\)
−0.688178 + 0.725542i \(0.741589\pi\)
\(410\) 183.292 + 222.768i 0.447054 + 0.543337i
\(411\) −169.909 169.909i −0.413404 0.413404i
\(412\) 611.805 + 120.090i 1.48496 + 0.291481i
\(413\) −668.829 + 668.829i −1.61944 + 1.61944i
\(414\) 42.6309 438.515i 0.102973 1.05922i
\(415\) −105.640 105.640i −0.254553 0.254553i
\(416\) −45.4579 146.518i −0.109274 0.352207i
\(417\) 158.293i 0.379600i
\(418\) −53.6926 5.21981i −0.128451 0.0124876i
\(419\) 329.191 329.191i 0.785660 0.785660i −0.195120 0.980779i \(-0.562510\pi\)
0.980779 + 0.195120i \(0.0625095\pi\)
\(420\) 909.919 611.318i 2.16647 1.45552i
\(421\) 505.234i 1.20008i 0.799969 + 0.600041i \(0.204849\pi\)
−0.799969 + 0.600041i \(0.795151\pi\)
\(422\) −44.9933 + 462.815i −0.106619 + 1.09672i
\(423\) 1283.47 3.03420
\(424\) −345.390 640.332i −0.814598 1.51022i
\(425\) 5.90832 43.3588i 0.0139019 0.102021i
\(426\) −138.969 + 114.343i −0.326218 + 0.268410i
\(427\) 654.750i 1.53337i
\(428\) −293.643 + 197.281i −0.686083 + 0.460936i
\(429\) 65.5523i 0.152803i
\(430\) −370.304 35.9996i −0.861171 0.0837201i
\(431\) −81.7921 81.7921i −0.189773 0.189773i 0.605825 0.795598i \(-0.292843\pi\)
−0.795598 + 0.605825i \(0.792843\pi\)
\(432\) −1264.74 + 531.370i −2.92763 + 1.23002i
\(433\) 320.041i 0.739126i 0.929206 + 0.369563i \(0.120493\pi\)
−0.929206 + 0.369563i \(0.879507\pi\)
\(434\) −822.096 + 676.416i −1.89423 + 1.55856i
\(435\) −96.0344 + 96.0344i −0.220769 + 0.220769i
\(436\) −515.962 + 346.643i −1.18340 + 0.795052i
\(437\) −73.6661 + 73.6661i −0.168572 + 0.168572i
\(438\) −173.053 210.323i −0.395097 0.480190i
\(439\) −236.803 + 236.803i −0.539415 + 0.539415i −0.923357 0.383942i \(-0.874566\pi\)
0.383942 + 0.923357i \(0.374566\pi\)
\(440\) 79.4412 42.8499i 0.180548 0.0973862i
\(441\) −1260.91 −2.85922
\(442\) −85.6199 138.697i −0.193710 0.313794i
\(443\) 547.137 1.23507 0.617536 0.786542i \(-0.288131\pi\)
0.617536 + 0.786542i \(0.288131\pi\)
\(444\) −142.371 + 725.317i −0.320656 + 1.63360i
\(445\) 296.236 296.236i 0.665700 0.665700i
\(446\) −99.8627 + 82.1664i −0.223907 + 0.184230i
\(447\) 14.0016 14.0016i 0.0313234 0.0313234i
\(448\) 631.956 130.689i 1.41062 0.291716i
\(449\) −77.5113 + 77.5113i −0.172631 + 0.172631i −0.788134 0.615503i \(-0.788953\pi\)
0.615503 + 0.788134i \(0.288953\pi\)
\(450\) 95.1689 78.3044i 0.211486 0.174010i
\(451\) 72.5684i 0.160906i
\(452\) 247.399 + 368.242i 0.547342 + 0.814694i
\(453\) 224.974 + 224.974i 0.496630 + 0.496630i
\(454\) 71.1740 732.118i 0.156771 1.61259i
\(455\) 228.914i 0.503109i
\(456\) 497.988 + 149.005i 1.09208 + 0.326766i
\(457\) 156.295i 0.342001i −0.985271 0.171001i \(-0.945300\pi\)
0.985271 0.171001i \(-0.0547000\pi\)
\(458\) 377.486 310.593i 0.824204 0.678150i
\(459\) −1160.37 + 882.060i −2.52805 + 1.92170i
\(460\) 33.5745 171.047i 0.0729881 0.371841i
\(461\) −323.645 −0.702050 −0.351025 0.936366i \(-0.614167\pi\)
−0.351025 + 0.936366i \(0.614167\pi\)
\(462\) −274.459 26.6820i −0.594067 0.0577532i
\(463\) 107.360i 0.231879i −0.993256 0.115940i \(-0.963012\pi\)
0.993256 0.115940i \(-0.0369879\pi\)
\(464\) −73.7108 + 30.9691i −0.158860 + 0.0667438i
\(465\) 1014.55 1014.55i 2.18183 2.18183i
\(466\) 428.839 + 41.6902i 0.920255 + 0.0894640i
\(467\) 322.960i 0.691563i 0.938315 + 0.345782i \(0.112386\pi\)
−0.938315 + 0.345782i \(0.887614\pi\)
\(468\) 88.4199 450.460i 0.188931 0.962520i
\(469\) 129.978 + 129.978i 0.277139 + 0.277139i
\(470\) 505.405 + 49.1338i 1.07533 + 0.104540i
\(471\) −1011.75 + 1011.75i −2.14810 + 2.14810i
\(472\) 660.490 356.263i 1.39934 0.754794i
\(473\) 66.1782 + 66.1782i 0.139912 + 0.139912i
\(474\) −222.423 270.326i −0.469246 0.570308i
\(475\) −29.1418 −0.0613511
\(476\) 615.558 302.025i 1.29319 0.634507i
\(477\) 2177.09i 4.56413i
\(478\) −160.320 194.848i −0.335397 0.407632i
\(479\) 292.651 292.651i 0.610962 0.610962i −0.332234 0.943197i \(-0.607803\pi\)
0.943197 + 0.332234i \(0.107803\pi\)
\(480\) −830.662 + 257.717i −1.73055 + 0.536910i
\(481\) −109.145 109.145i −0.226913 0.226913i
\(482\) 390.334 + 37.9470i 0.809822 + 0.0787282i
\(483\) −376.557 + 376.557i −0.779621 + 0.779621i
\(484\) 452.657 + 88.8512i 0.935241 + 0.183577i
\(485\) −199.837 −0.412035
\(486\) −1624.31 157.910i −3.34220 0.324918i
\(487\) −399.978 399.978i −0.821309 0.821309i 0.164986 0.986296i \(-0.447242\pi\)
−0.986296 + 0.164986i \(0.947242\pi\)
\(488\) 148.912 497.675i 0.305147 1.01983i
\(489\) −192.502 −0.393665
\(490\) −496.524 48.2704i −1.01332 0.0985110i
\(491\) 279.523i 0.569293i −0.958633 0.284647i \(-0.908124\pi\)
0.958633 0.284647i \(-0.0918762\pi\)
\(492\) −134.683 + 686.151i −0.273747 + 1.39462i
\(493\) −67.6285 + 51.4079i −0.137178 + 0.104276i
\(494\) −83.8215 + 68.9678i −0.169679 + 0.139611i
\(495\) 270.095 0.545647
\(496\) 778.714 327.172i 1.56999 0.659620i
\(497\) 158.088 0.318084
\(498\) 35.0389 360.421i 0.0703592 0.723736i
\(499\) 158.690 158.690i 0.318016 0.318016i −0.529989 0.848005i \(-0.677804\pi\)
0.848005 + 0.529989i \(0.177804\pi\)
\(500\) 433.559 291.281i 0.867117 0.582562i
\(501\) −557.605 −1.11298
\(502\) −534.099 + 439.453i −1.06394 + 0.875405i
\(503\) −196.532 196.532i −0.390719 0.390719i 0.484224 0.874944i \(-0.339102\pi\)
−0.874944 + 0.484224i \(0.839102\pi\)
\(504\) 1850.03 + 553.555i 3.67069 + 1.09832i
\(505\) −164.488 164.488i −0.325718 0.325718i
\(506\) −33.8602 + 27.8599i −0.0669173 + 0.0550592i
\(507\) −592.578 592.578i −1.16879 1.16879i
\(508\) −144.434 + 735.824i −0.284318 + 1.44847i
\(509\) 239.733i 0.470989i 0.971876 + 0.235494i \(0.0756710\pi\)
−0.971876 + 0.235494i \(0.924329\pi\)
\(510\) −786.322 + 485.409i −1.54181 + 0.951782i
\(511\) 239.258i 0.468215i
\(512\) −510.072 44.3910i −0.996234 0.0867012i
\(513\) 686.368 + 686.368i 1.33795 + 1.33795i
\(514\) 568.656 + 691.128i 1.10634 + 1.34461i
\(515\) 521.942 + 521.942i 1.01348 + 1.01348i
\(516\) −502.906 748.553i −0.974625 1.45068i
\(517\) −90.3226 90.3226i −0.174705 0.174705i
\(518\) 501.403 412.551i 0.967959 0.796431i
\(519\) −537.366 −1.03539
\(520\) 52.0626 173.998i 0.100120 0.334611i
\(521\) −395.435 + 395.435i −0.758993 + 0.758993i −0.976139 0.217146i \(-0.930325\pi\)
0.217146 + 0.976139i \(0.430325\pi\)
\(522\) −238.126 23.1497i −0.456179 0.0443482i
\(523\) −233.873 −0.447176 −0.223588 0.974684i \(-0.571777\pi\)
−0.223588 + 0.974684i \(0.571777\pi\)
\(524\) 158.711 106.628i 0.302884 0.203489i
\(525\) −148.963 −0.283739
\(526\) −559.047 + 459.980i −1.06283 + 0.874487i
\(527\) 714.458 543.096i 1.35571 1.03054i
\(528\) 202.548 + 82.7020i 0.383613 + 0.156632i
\(529\) 444.320i 0.839925i
\(530\) 83.3434 857.297i 0.157252 1.61754i
\(531\) 2245.62 4.22905
\(532\) −254.641 379.022i −0.478649 0.712447i
\(533\) −103.251 103.251i −0.193718 0.193718i
\(534\) 1010.70 + 98.2566i 1.89269 + 0.184001i
\(535\) −418.817 −0.782835
\(536\) −69.2351 128.358i −0.129170 0.239473i
\(537\) 273.420 273.420i 0.509162 0.509162i
\(538\) −21.0358 + 216.380i −0.0390999 + 0.402194i
\(539\) 88.7355 + 88.7355i 0.164630 + 0.164630i
\(540\) −1593.69 312.824i −2.95129 0.579303i
\(541\) −178.648 + 178.648i −0.330218 + 0.330218i −0.852669 0.522451i \(-0.825018\pi\)
0.522451 + 0.852669i \(0.325018\pi\)
\(542\) 446.694 + 542.899i 0.824159 + 1.00166i
\(543\) 154.890i 0.285248i
\(544\) −536.575 + 89.5713i −0.986352 + 0.164653i
\(545\) −735.904 −1.35028
\(546\) −428.468 + 352.541i −0.784740 + 0.645680i
\(547\) −517.372 517.372i −0.945836 0.945836i 0.0527705 0.998607i \(-0.483195\pi\)
−0.998607 + 0.0527705i \(0.983195\pi\)
\(548\) 32.2567 164.333i 0.0588626 0.299879i
\(549\) 1099.18 1099.18i 2.00214 2.00214i
\(550\) −12.2080 1.18682i −0.0221964 0.00215786i
\(551\) 40.0027 + 40.0027i 0.0726001 + 0.0726001i
\(552\) 371.862 200.579i 0.673663 0.363368i
\(553\) 307.516i 0.556087i
\(554\) 39.2909 404.159i 0.0709222 0.729528i
\(555\) −618.782 + 618.782i −1.11492 + 1.11492i
\(556\) −91.5752 + 61.5237i −0.164704 + 0.110654i
\(557\) 678.176i 1.21755i 0.793343 + 0.608775i \(0.208339\pi\)
−0.793343 + 0.608775i \(0.791661\pi\)
\(558\) 2515.66 + 244.564i 4.50836 + 0.438287i
\(559\) 188.319 0.336885
\(560\) 707.315 + 288.803i 1.26306 + 0.515719i
\(561\) 230.327 + 31.3856i 0.410564 + 0.0559459i
\(562\) −128.943 156.714i −0.229436 0.278850i
\(563\) 995.695i 1.76855i −0.466965 0.884276i \(-0.654653\pi\)
0.466965 0.884276i \(-0.345347\pi\)
\(564\) 686.387 + 1021.66i 1.21700 + 1.81145i
\(565\) 525.214i 0.929583i
\(566\) 40.6729 418.374i 0.0718603 0.739178i
\(567\) 1972.34 + 1972.34i 3.47855 + 3.47855i
\(568\) −120.162 35.9543i −0.211553 0.0632998i
\(569\) 303.840i 0.533989i 0.963698 + 0.266995i \(0.0860306\pi\)
−0.963698 + 0.266995i \(0.913969\pi\)
\(570\) 391.002 + 475.213i 0.685969 + 0.833707i
\(571\) 127.417 127.417i 0.223148 0.223148i −0.586675 0.809823i \(-0.699563\pi\)
0.809823 + 0.586675i \(0.199563\pi\)
\(572\) −37.9231 + 25.4782i −0.0662991 + 0.0445422i
\(573\) −564.008 + 564.008i −0.984308 + 0.984308i
\(574\) 474.327 390.274i 0.826354 0.679920i
\(575\) −16.7493 + 16.7493i −0.0291293 + 0.0291293i
\(576\) −1280.31 841.514i −2.22276 1.46096i
\(577\) 737.054 1.27739 0.638695 0.769460i \(-0.279474\pi\)
0.638695 + 0.769460i \(0.279474\pi\)
\(578\) −528.324 + 234.430i −0.914056 + 0.405589i
\(579\) −668.561 −1.15468
\(580\) −92.8831 18.2319i −0.160143 0.0314343i
\(581\) −224.932 + 224.932i −0.387147 + 0.387147i
\(582\) −307.760 374.043i −0.528798 0.642685i
\(583\) −153.210 + 153.210i −0.262796 + 0.262796i
\(584\) 54.4151 181.860i 0.0931766 0.311404i
\(585\) 384.295 384.295i 0.656915 0.656915i
\(586\) −105.063 127.691i −0.179288 0.217902i
\(587\) 1045.64i 1.78133i 0.454658 + 0.890666i \(0.349762\pi\)
−0.454658 + 0.890666i \(0.650238\pi\)
\(588\) −674.326 1003.70i −1.14681 1.70698i
\(589\) −422.606 422.606i −0.717497 0.717497i
\(590\) 884.285 + 85.9671i 1.49879 + 0.145707i
\(591\) 107.580i 0.182031i
\(592\) −474.943 + 199.544i −0.802269 + 0.337068i
\(593\) 405.674i 0.684105i −0.939681 0.342053i \(-0.888878\pi\)
0.939681 0.342053i \(-0.111122\pi\)
\(594\) 259.579 + 315.485i 0.437002 + 0.531119i
\(595\) 804.321 + 109.601i 1.35180 + 0.184204i
\(596\) 13.5421 + 2.65816i 0.0227217 + 0.00446000i
\(597\) 367.335 0.615301
\(598\) −8.53720 + 87.8163i −0.0142762 + 0.146850i
\(599\) 765.475i 1.27792i −0.769239 0.638961i \(-0.779365\pi\)
0.769239 0.638961i \(-0.220635\pi\)
\(600\) 113.227 + 33.8791i 0.188711 + 0.0564652i
\(601\) −2.71317 + 2.71317i −0.00451443 + 0.00451443i −0.709360 0.704846i \(-0.751016\pi\)
0.704846 + 0.709360i \(0.251016\pi\)
\(602\) −76.6520 + 788.466i −0.127329 + 1.30974i
\(603\) 436.408i 0.723728i
\(604\) −42.7106 + 217.591i −0.0707129 + 0.360250i
\(605\) 386.170 + 386.170i 0.638297 + 0.638297i
\(606\) 54.5578 561.198i 0.0900293 0.926070i
\(607\) −658.383 + 658.383i −1.08465 + 1.08465i −0.0885817 + 0.996069i \(0.528233\pi\)
−0.996069 + 0.0885817i \(0.971767\pi\)
\(608\) 107.351 + 346.008i 0.176564 + 0.569092i
\(609\) 204.481 + 204.481i 0.335765 + 0.335765i
\(610\) 474.914 390.756i 0.778547 0.640584i
\(611\) −257.025 −0.420663
\(612\) −1540.41 526.350i −2.51702 0.860048i
\(613\) 544.685i 0.888556i 0.895889 + 0.444278i \(0.146540\pi\)
−0.895889 + 0.444278i \(0.853460\pi\)
\(614\) 336.498 276.868i 0.548042 0.450925i
\(615\) −585.368 + 585.368i −0.951818 + 0.951818i
\(616\) −91.2379 169.150i −0.148113 0.274594i
\(617\) 563.768 + 563.768i 0.913724 + 0.913724i 0.996563 0.0828385i \(-0.0263986\pi\)
−0.0828385 + 0.996563i \(0.526399\pi\)
\(618\) −173.119 + 1780.76i −0.280129 + 2.88149i
\(619\) 451.241 451.241i 0.728984 0.728984i −0.241433 0.970417i \(-0.577617\pi\)
0.970417 + 0.241433i \(0.0776175\pi\)
\(620\) 981.259 + 192.610i 1.58268 + 0.310661i
\(621\) 788.986 1.27051
\(622\) −99.0325 + 1018.68i −0.159216 + 1.63775i
\(623\) −630.759 630.759i −1.01245 1.01245i
\(624\) 405.858 170.518i 0.650413 0.273267i
\(625\) 554.022 0.886435
\(626\) 51.9483 534.356i 0.0829845 0.853605i
\(627\) 154.804i 0.246897i
\(628\) −978.553 192.079i −1.55821 0.305858i
\(629\) −435.753 + 331.238i −0.692771 + 0.526611i
\(630\) 1452.58 + 1765.42i 2.30568 + 2.80225i
\(631\) 674.106 1.06831 0.534157 0.845385i \(-0.320629\pi\)
0.534157 + 0.845385i \(0.320629\pi\)
\(632\) 69.9392 233.743i 0.110663 0.369846i
\(633\) −1334.37 −2.10801
\(634\) −352.307 34.2500i −0.555689 0.0540222i
\(635\) −627.745 + 627.745i −0.988575 + 0.988575i
\(636\) 1732.99 1164.29i 2.72483 1.83064i
\(637\) 252.508 0.396403
\(638\) 15.1287 + 18.3870i 0.0237127 + 0.0288197i
\(639\) −265.393 265.393i −0.415326 0.415326i
\(640\) −471.946 380.385i −0.737416 0.594352i
\(641\) −256.865 256.865i −0.400726 0.400726i 0.477763 0.878489i \(-0.341448\pi\)
−0.878489 + 0.477763i \(0.841448\pi\)
\(642\) −645.001 783.915i −1.00467 1.22105i
\(643\) 51.7980 + 51.7980i 0.0805568 + 0.0805568i 0.746237 0.665680i \(-0.231859\pi\)
−0.665680 + 0.746237i \(0.731859\pi\)
\(644\) −364.201 71.4883i −0.565529 0.111007i
\(645\) 1067.64i 1.65526i
\(646\) 202.195 + 327.539i 0.312995 + 0.507026i
\(647\) 436.057i 0.673967i −0.941510 0.336984i \(-0.890593\pi\)
0.941510 0.336984i \(-0.109407\pi\)
\(648\) −1050.60 1947.74i −1.62129 3.00578i
\(649\) −158.033 158.033i −0.243503 0.243503i
\(650\) −19.0584 + 15.6811i −0.0293206 + 0.0241248i
\(651\) −2160.22 2160.22i −3.31832 3.31832i
\(652\) −74.8197 111.366i −0.114754 0.170806i
\(653\) −627.724 627.724i −0.961292 0.961292i 0.0379863 0.999278i \(-0.487906\pi\)
−0.999278 + 0.0379863i \(0.987906\pi\)
\(654\) −1133.33 1377.42i −1.73293 2.10615i
\(655\) 226.366 0.345597
\(656\) −449.297 + 188.769i −0.684904 + 0.287758i
\(657\) 401.660 401.660i 0.611355 0.611355i
\(658\) 104.618 1076.13i 0.158993 1.63546i
\(659\) −286.443 −0.434663 −0.217331 0.976098i \(-0.569735\pi\)
−0.217331 + 0.976098i \(0.569735\pi\)
\(660\) 144.445 + 214.999i 0.218855 + 0.325756i
\(661\) 866.938 1.31156 0.655778 0.754954i \(-0.272341\pi\)
0.655778 + 0.754954i \(0.272341\pi\)
\(662\) 492.023 + 597.991i 0.743237 + 0.903309i
\(663\) 372.368 283.056i 0.561641 0.426932i
\(664\) 222.128 119.814i 0.334530 0.180443i
\(665\) 540.590i 0.812917i
\(666\) −1534.32 149.161i −2.30379 0.223966i
\(667\) 45.9834 0.0689406
\(668\) −216.724 322.584i −0.324437 0.482910i
\(669\) −262.409 262.409i −0.392241 0.392241i
\(670\) 16.7066 171.849i 0.0249352 0.256492i
\(671\) −154.707 −0.230562
\(672\) 548.742 + 1768.68i 0.816580 + 2.63197i
\(673\) −599.909 + 599.909i −0.891395 + 0.891395i −0.994654 0.103259i \(-0.967073\pi\)
0.103259 + 0.994654i \(0.467073\pi\)
\(674\) 412.774 + 40.1285i 0.612424 + 0.0595378i
\(675\) 156.059 + 156.059i 0.231198 + 0.231198i
\(676\) 112.499 573.134i 0.166419 0.847831i
\(677\) 652.310 652.310i 0.963530 0.963530i −0.0358279 0.999358i \(-0.511407\pi\)
0.999358 + 0.0358279i \(0.0114068\pi\)
\(678\) −983.064 + 808.859i −1.44995 + 1.19301i
\(679\) 425.502i 0.626659i
\(680\) −586.436 266.237i −0.862406 0.391525i
\(681\) 2110.81 3.09957
\(682\) −159.826 194.248i −0.234349 0.284821i
\(683\) 20.9689 + 20.9689i 0.0307012 + 0.0307012i 0.722291 0.691590i \(-0.243089\pi\)
−0.691590 + 0.722291i \(0.743089\pi\)
\(684\) −208.807 + 1063.78i −0.305273 + 1.55523i
\(685\) 140.196 140.196i 0.204666 0.204666i
\(686\) −7.16485 + 73.6998i −0.0104444 + 0.107434i
\(687\) 991.919 + 991.919i 1.44384 + 1.44384i
\(688\) 237.586 581.879i 0.345329 0.845755i
\(689\) 435.980i 0.632772i
\(690\) 497.861 + 48.4003i 0.721537 + 0.0701454i
\(691\) 841.024 841.024i 1.21711 1.21711i 0.248473 0.968639i \(-0.420071\pi\)
0.968639 0.248473i \(-0.0799286\pi\)
\(692\) −208.858 310.875i −0.301817 0.449241i
\(693\) 575.098i 0.829868i
\(694\) −57.3051 + 589.458i −0.0825722 + 0.849364i
\(695\) −130.612 −0.187930
\(696\) −108.920 201.931i −0.156494 0.290131i
\(697\) −412.223 + 313.352i −0.591425 + 0.449572i
\(698\) −694.290 + 571.258i −0.994684 + 0.818420i
\(699\) 1236.41i 1.76883i
\(700\) −57.8974 86.1777i −0.0827106 0.123111i
\(701\) 276.797i 0.394861i −0.980317 0.197430i \(-0.936740\pi\)
0.980317 0.197430i \(-0.0632597\pi\)
\(702\) 818.210 + 79.5435i 1.16554 + 0.113310i
\(703\) 257.750 + 257.750i 0.366644 + 0.366644i
\(704\) 30.8797 + 149.321i 0.0438632 + 0.212104i
\(705\) 1457.16i 2.06690i
\(706\) −448.068 + 368.667i −0.634657 + 0.522192i
\(707\) −350.234 + 350.234i −0.495381 + 0.495381i
\(708\) 1200.94 + 1787.54i 1.69624 + 2.52478i
\(709\) 215.669 215.669i 0.304188 0.304188i −0.538462 0.842650i \(-0.680995\pi\)
0.842650 + 0.538462i \(0.180995\pi\)
\(710\) −94.3471 114.667i −0.132883 0.161502i
\(711\) 516.250 516.250i 0.726090 0.726090i
\(712\) 335.984 + 622.895i 0.471888 + 0.874853i
\(713\) −485.789 −0.681331
\(714\) 1033.55 + 1674.27i 1.44755 + 2.34492i
\(715\) −54.0888 −0.0756487
\(716\) 264.448 + 51.9080i 0.369340 + 0.0724972i
\(717\) 512.002 512.002i 0.714090 0.714090i
\(718\) −26.6835 + 21.9550i −0.0371637 + 0.0305781i
\(719\) −561.510 + 561.510i −0.780960 + 0.780960i −0.979993 0.199033i \(-0.936220\pi\)
0.199033 + 0.979993i \(0.436220\pi\)
\(720\) −702.587 1672.26i −0.975816 2.32258i
\(721\) 1111.34 1111.34i 1.54139 1.54139i
\(722\) −359.587 + 295.866i −0.498043 + 0.409787i
\(723\) 1125.40i 1.55656i
\(724\) 89.6063 60.2009i 0.123766 0.0831504i
\(725\) 9.09535 + 9.09535i 0.0125453 + 0.0125453i
\(726\) −128.086 + 1317.53i −0.176427 + 1.81478i
\(727\) 607.980i 0.836287i −0.908381 0.418143i \(-0.862681\pi\)
0.908381 0.418143i \(-0.137319\pi\)
\(728\) −370.483 110.854i −0.508906 0.152272i
\(729\) 2193.50i 3.00891i
\(730\) 173.543 142.790i 0.237730 0.195603i
\(731\) 90.1647 661.682i 0.123344 0.905174i
\(732\) 1462.79 + 287.128i 1.99834 + 0.392252i
\(733\) −187.812 −0.256224 −0.128112 0.991760i \(-0.540892\pi\)
−0.128112 + 0.991760i \(0.540892\pi\)
\(734\) −1229.01 119.480i −1.67439 0.162779i
\(735\) 1431.56i 1.94770i
\(736\) 260.570 + 137.169i 0.354035 + 0.186371i
\(737\) −30.7118 + 30.7118i −0.0416713 + 0.0416713i
\(738\) −1451.47 141.107i −1.96676 0.191202i
\(739\) 462.811i 0.626266i 0.949709 + 0.313133i \(0.101379\pi\)
−0.949709 + 0.313133i \(0.898621\pi\)
\(740\) −598.477 117.474i −0.808753 0.158749i
\(741\) −220.258 220.258i −0.297244 0.297244i
\(742\) −1825.39 177.458i −2.46010 0.239162i
\(743\) 380.548 380.548i 0.512177 0.512177i −0.403016 0.915193i \(-0.632038\pi\)
0.915193 + 0.403016i \(0.132038\pi\)
\(744\) 1150.68 + 2133.29i 1.54661 + 2.86733i
\(745\) 11.5530 + 11.5530i 0.0155074 + 0.0155074i
\(746\) −68.8500 83.6783i −0.0922923 0.112169i
\(747\) 755.221 1.01101
\(748\) 71.3637 + 145.446i 0.0954061 + 0.194447i
\(749\) 891.762i 1.19060i
\(750\) 952.331 + 1157.44i 1.26977 + 1.54325i
\(751\) 531.659 531.659i 0.707935 0.707935i −0.258166 0.966101i \(-0.583118\pi\)
0.966101 + 0.258166i \(0.0831181\pi\)
\(752\) −324.267 + 794.172i −0.431206 + 1.05608i
\(753\) −1403.45 1403.45i −1.86381 1.86381i
\(754\) 47.6866 + 4.63593i 0.0632448 + 0.00614845i
\(755\) −185.631 + 185.631i −0.245869 + 0.245869i
\(756\) −666.077 + 3393.36i −0.881055 + 4.48858i
\(757\) −386.655 −0.510773 −0.255386 0.966839i \(-0.582203\pi\)
−0.255386 + 0.966839i \(0.582203\pi\)
\(758\) 96.6042 + 9.39153i 0.127446 + 0.0123899i
\(759\) −88.9744 88.9744i −0.117226 0.117226i
\(760\) −122.948 + 410.902i −0.161774 + 0.540661i
\(761\) −1437.86 −1.88943 −0.944717 0.327886i \(-0.893664\pi\)
−0.944717 + 0.327886i \(0.893664\pi\)
\(762\) −2141.74 208.212i −2.81068 0.273245i
\(763\) 1566.92i 2.05363i
\(764\) −545.501 107.075i −0.714007 0.140151i
\(765\) −1166.28 1534.27i −1.52454 2.00558i
\(766\) −111.696 + 91.9031i −0.145818 + 0.119978i
\(767\) −449.705 −0.586316
\(768\) −14.8419 1469.17i −0.0193254 1.91299i
\(769\) −1151.55 −1.49746 −0.748731 0.662874i \(-0.769336\pi\)
−0.748731 + 0.662874i \(0.769336\pi\)
\(770\) 22.0159 226.463i 0.0285921 0.294108i
\(771\) −1816.08 + 1816.08i −2.35548 + 2.35548i
\(772\) −259.849 386.774i −0.336592 0.501002i
\(773\) −100.104 −0.129501 −0.0647504 0.997901i \(-0.520625\pi\)
−0.0647504 + 0.997901i \(0.520625\pi\)
\(774\) 1452.34 1194.97i 1.87640 1.54389i
\(775\) −96.0873 96.0873i −0.123984 0.123984i
\(776\) 96.7730 323.423i 0.124707 0.416783i
\(777\) 1317.54 + 1317.54i 1.69567 + 1.69567i
\(778\) 775.155 637.793i 0.996343 0.819786i
\(779\) 243.832 + 243.832i 0.313007 + 0.313007i
\(780\) 511.422 + 100.386i 0.655669 + 0.128700i
\(781\) 37.3535i 0.0478278i
\(782\) 304.466 + 72.0419i 0.389343 + 0.0921252i
\(783\) 428.441i 0.547178i
\(784\) 318.569 780.217i 0.406338 0.995175i
\(785\) −834.822 834.822i −1.06347 1.06347i
\(786\) 348.616 + 423.698i 0.443532 + 0.539056i
\(787\) 523.093 + 523.093i 0.664667 + 0.664667i 0.956477 0.291809i \(-0.0942573\pi\)
−0.291809 + 0.956477i \(0.594257\pi\)
\(788\) −62.2369 + 41.8131i −0.0789808 + 0.0530623i
\(789\) −1469.01 1469.01i −1.86186 1.86186i
\(790\) 223.053 183.526i 0.282345 0.232312i
\(791\) 1118.31 1.41379
\(792\) −130.796 + 437.132i −0.165147 + 0.551934i
\(793\) −220.119 + 220.119i −0.277578 + 0.277578i
\(794\) 450.978 + 43.8425i 0.567982 + 0.0552173i
\(795\) 2471.72 3.10908
\(796\) 142.772 + 212.509i 0.179361 + 0.266971i
\(797\) −502.732 −0.630780 −0.315390 0.948962i \(-0.602135\pi\)
−0.315390 + 0.948962i \(0.602135\pi\)
\(798\) 1011.84 832.539i 1.26797 1.04328i
\(799\) −123.060 + 903.090i −0.154018 + 1.13028i
\(800\) 24.4082 + 78.6714i 0.0305102 + 0.0983392i
\(801\) 2117.80i 2.64395i
\(802\) −83.5595 + 859.519i −0.104189 + 1.07172i
\(803\) −56.5328 −0.0704020
\(804\) 347.386 233.387i 0.432073 0.290283i
\(805\) −310.706 310.706i −0.385971 0.385971i
\(806\) −503.782 48.9760i −0.625040 0.0607643i
\(807\) −623.859 −0.773059
\(808\) 345.867 186.558i 0.428054 0.230889i
\(809\) 818.125 818.125i 1.01128 1.01128i 0.0113442 0.999936i \(-0.496389\pi\)
0.999936 0.0113442i \(-0.00361106\pi\)
\(810\) 253.512 2607.70i 0.312978 3.21939i
\(811\) −222.437 222.437i −0.274275 0.274275i 0.556543 0.830819i \(-0.312127\pi\)
−0.830819 + 0.556543i \(0.812127\pi\)
\(812\) −38.8201 + 197.771i −0.0478080 + 0.243560i
\(813\) −1426.58 + 1426.58i −1.75471 + 1.75471i
\(814\) 97.4792 + 118.473i 0.119753 + 0.145545i
\(815\) 158.838i 0.194894i
\(816\) −404.819 1507.68i −0.496102 1.84764i
\(817\) −444.721 −0.544335
\(818\) 869.398 715.336i 1.06283 0.874493i
\(819\) −818.258 818.258i −0.999094 0.999094i
\(820\) −566.160 111.131i −0.690439 0.135525i
\(821\) 745.434 745.434i 0.907959 0.907959i −0.0881483 0.996107i \(-0.528095\pi\)
0.996107 + 0.0881483i \(0.0280949\pi\)
\(822\) 478.320 + 46.5006i 0.581898 + 0.0565701i
\(823\) 833.870 + 833.870i 1.01321 + 1.01321i 0.999912 + 0.0132956i \(0.00423225\pi\)
0.0132956 + 0.999912i \(0.495768\pi\)
\(824\) −1097.49 + 591.975i −1.33190 + 0.718416i
\(825\) 35.1976i 0.0426638i
\(826\) 183.045 1882.86i 0.221604 2.27949i
\(827\) −277.526 + 277.526i −0.335582 + 0.335582i −0.854702 0.519120i \(-0.826260\pi\)
0.519120 + 0.854702i \(0.326260\pi\)
\(828\) 491.398 + 731.423i 0.593476 + 0.883361i
\(829\) 1201.51i 1.44934i 0.689095 + 0.724671i \(0.258008\pi\)
−0.689095 + 0.724671i \(0.741992\pi\)
\(830\) 297.392 + 28.9114i 0.358303 + 0.0348330i
\(831\) 1165.25 1.40223
\(832\) 256.392 + 168.520i 0.308164 + 0.202548i
\(833\) 120.898 887.221i 0.145136 1.06509i
\(834\) −201.149 244.471i −0.241186 0.293130i
\(835\) 460.094i 0.551010i
\(836\) 89.5568 60.1676i 0.107125 0.0719709i
\(837\) 4526.24i 5.40769i
\(838\) −90.0930 + 926.725i −0.107510 + 1.10588i
\(839\) −652.995 652.995i −0.778302 0.778302i 0.201240 0.979542i \(-0.435503\pi\)
−0.979542 + 0.201240i \(0.935503\pi\)
\(840\) −628.470 + 2100.40i −0.748178 + 2.50047i
\(841\) 816.030i 0.970309i
\(842\) −642.020 780.293i −0.762494 0.926713i
\(843\) 411.796 411.796i 0.488489 0.488489i
\(844\) −518.628 771.955i −0.614489 0.914638i
\(845\) 488.951 488.951i 0.578640 0.578640i
\(846\) −1982.21 + 1630.95i −2.34304 + 1.92784i
\(847\) 822.250 822.250i 0.970779 0.970779i
\(848\) 1347.12 + 550.040i 1.58858 + 0.648632i
\(849\) 1206.24 1.42078
\(850\) 45.9727 + 74.4720i 0.0540855 + 0.0876141i
\(851\) 296.286 0.348162
\(852\) 69.3263 353.186i 0.0813689 0.414538i
\(853\) 771.856 771.856i 0.904872 0.904872i −0.0909806 0.995853i \(-0.529000\pi\)
0.995853 + 0.0909806i \(0.0290001\pi\)
\(854\) −832.015 1011.21i −0.974256 1.18408i
\(855\) −907.528 + 907.528i −1.06144 + 1.06144i
\(856\) 202.816 677.828i 0.236935 0.791855i
\(857\) 129.612 129.612i 0.151240 0.151240i −0.627432 0.778671i \(-0.715894\pi\)
0.778671 + 0.627432i \(0.215894\pi\)
\(858\) −83.2998 101.240i −0.0970860 0.117995i
\(859\) 1317.39i 1.53363i −0.641869 0.766815i \(-0.721841\pi\)
0.641869 0.766815i \(-0.278159\pi\)
\(860\) 617.649 414.960i 0.718197 0.482512i
\(861\) 1246.39 + 1246.39i 1.44761 + 1.44761i
\(862\) 230.257 + 22.3848i 0.267120 + 0.0259685i
\(863\) 1683.02i 1.95019i 0.221779 + 0.975097i \(0.428814\pi\)
−0.221779 + 0.975097i \(0.571186\pi\)
\(864\) 1278.05 2427.80i 1.47922 2.80996i
\(865\) 443.393i 0.512594i
\(866\) −406.689 494.278i −0.469617 0.570759i
\(867\) −816.269 1443.89i −0.941487 1.66538i
\(868\) 410.113 2089.34i 0.472480 2.40707i
\(869\) −72.6611 −0.0836146
\(870\) 26.2827 270.352i 0.0302100 0.310749i
\(871\) 87.3944i 0.100338i
\(872\) 356.368 1191.01i 0.408679 1.36584i
\(873\) 714.321 714.321i 0.818237 0.818237i
\(874\) 20.1609 207.381i 0.0230674 0.237279i
\(875\) 1316.67i 1.50476i
\(876\) 534.531 + 104.922i 0.610195 + 0.119774i
\(877\) −742.665 742.665i −0.846824 0.846824i 0.142911 0.989736i \(-0.454354\pi\)
−0.989736 + 0.142911i \(0.954354\pi\)
\(878\) 64.8083 666.638i 0.0738135 0.759269i
\(879\) 335.533 335.533i 0.381721 0.381721i
\(880\) −68.2394 + 167.127i −0.0775448 + 0.189917i
\(881\) −653.470 653.470i −0.741737 0.741737i 0.231175 0.972912i \(-0.425743\pi\)
−0.972912 + 0.231175i \(0.925743\pi\)
\(882\) 1947.38 1602.29i 2.20791 1.81666i
\(883\) −1133.04 −1.28317 −0.641583 0.767054i \(-0.721722\pi\)
−0.641583 + 0.767054i \(0.721722\pi\)
\(884\) 308.481 + 105.406i 0.348960 + 0.119237i
\(885\) 2549.53i 2.88083i
\(886\) −845.008 + 695.268i −0.953734 + 0.784727i
\(887\) 80.3118 80.3118i 0.0905431 0.0905431i −0.660385 0.750928i \(-0.729607\pi\)
0.750928 + 0.660385i \(0.229607\pi\)
\(888\) −701.807 1301.11i −0.790324 1.46521i
\(889\) 1336.62 + 1336.62i 1.50351 + 1.50351i
\(890\) −81.0739 + 833.952i −0.0910943 + 0.937024i
\(891\) −466.031 + 466.031i −0.523043 + 0.523043i
\(892\) 49.8177 253.799i 0.0558494 0.284527i
\(893\) 606.974 0.679702
\(894\) −3.83195 + 39.4166i −0.00428630 + 0.0440902i
\(895\) 225.605 + 225.605i 0.252073 + 0.252073i
\(896\) −809.932 + 1004.89i −0.903942 + 1.12153i
\(897\) −253.188 −0.282261
\(898\) 21.2133 218.206i 0.0236228 0.242991i
\(899\) 263.796i 0.293433i
\(900\) −47.4761 + 241.869i −0.0527513 + 0.268744i
\(901\) 1531.87 + 208.742i 1.70019 + 0.231678i
\(902\) 92.2154 + 112.076i 0.102234 + 0.124253i
\(903\) −2273.27 −2.51747
\(904\) −850.025 254.340i −0.940294 0.281350i
\(905\) 127.803 0.141219
\(906\) −633.335 61.5707i −0.699046 0.0679588i
\(907\) 970.143 970.143i 1.06962 1.06962i 0.0722295 0.997388i \(-0.476989\pi\)
0.997388 0.0722295i \(-0.0230114\pi\)
\(908\) 820.407 + 1221.14i 0.903532 + 1.34487i
\(909\) 1175.93 1.29365
\(910\) −290.890 353.539i −0.319660 0.388505i
\(911\) 258.283 + 258.283i 0.283516 + 0.283516i 0.834509 0.550994i \(-0.185751\pi\)
−0.550994 + 0.834509i \(0.685751\pi\)
\(912\) −958.448 + 402.686i −1.05093 + 0.441541i
\(913\) −53.1479 53.1479i −0.0582124 0.0582124i
\(914\) 198.610 + 241.384i 0.217297 + 0.264097i
\(915\) 1247.93 + 1247.93i 1.36386 + 1.36386i
\(916\) −188.313 + 959.370i −0.205582 + 1.04735i
\(917\) 481.988i 0.525614i
\(918\) 671.235 2836.80i 0.731193 3.09020i
\(919\) 1752.37i 1.90683i 0.301669 + 0.953413i \(0.402456\pi\)
−0.301669 + 0.953413i \(0.597544\pi\)
\(920\) 165.503 + 306.832i 0.179894 + 0.333514i
\(921\) 884.215 + 884.215i 0.960060 + 0.960060i
\(922\) 499.843 411.268i 0.542129 0.446060i
\(923\) 53.1472 + 53.1472i 0.0575809 + 0.0575809i
\(924\) 457.785 307.557i 0.495439 0.332854i
\(925\) 58.6043 + 58.6043i 0.0633560 + 0.0633560i
\(926\) 136.427 + 165.809i 0.147329 + 0.179059i
\(927\) −3731.38 −4.02523
\(928\) 74.4867 141.496i 0.0802658 0.152475i
\(929\) 874.077 874.077i 0.940880 0.940880i −0.0574676 0.998347i \(-0.518303\pi\)
0.998347 + 0.0574676i \(0.0183026\pi\)
\(930\) −277.662 + 2856.12i −0.298561 + 3.07109i
\(931\) −596.308 −0.640503
\(932\) −715.283 + 480.554i −0.767472 + 0.515616i
\(933\) −2937.01 −3.14792
\(934\) −410.398 498.785i −0.439398 0.534031i
\(935\) −25.8971 + 190.048i −0.0276974 + 0.203260i
\(936\) 435.859 + 808.056i 0.465661 + 0.863308i
\(937\) 617.566i 0.659089i 0.944140 + 0.329545i \(0.106895\pi\)
−0.944140 + 0.329545i \(0.893105\pi\)
\(938\) −365.909 35.5724i −0.390095 0.0379237i
\(939\) 1540.63 1.64072
\(940\) −842.993 + 566.354i −0.896801 + 0.602505i
\(941\) −810.618 810.618i −0.861443 0.861443i 0.130063 0.991506i \(-0.458482\pi\)
−0.991506 + 0.130063i \(0.958482\pi\)
\(942\) 276.896 2848.24i 0.293945 3.02361i
\(943\) 280.287 0.297229
\(944\) −567.356 + 1389.53i −0.601012 + 1.47196i
\(945\) −2894.94 + 2894.94i −3.06343 + 3.06343i
\(946\) −186.302 18.1116i −0.196936 0.0191455i
\(947\) −1016.09 1016.09i −1.07296 1.07296i −0.997120 0.0758381i \(-0.975837\pi\)
−0.0758381 0.997120i \(-0.524163\pi\)
\(948\) 687.027 + 134.855i 0.724712 + 0.142252i
\(949\) −80.4358 + 80.4358i −0.0847584 + 0.0847584i
\(950\) 45.0070 37.0315i 0.0473758 0.0389806i
\(951\) 1015.76i 1.06809i
\(952\) −566.883 + 1248.67i −0.595465 + 1.31162i
\(953\) 1007.10 1.05677 0.528384 0.849006i \(-0.322798\pi\)
0.528384 + 0.849006i \(0.322798\pi\)
\(954\) 2766.51 + 3362.33i 2.89990 + 3.52446i
\(955\) −465.377 465.377i −0.487306 0.487306i
\(956\) 495.201 + 97.2022i 0.517993 + 0.101676i
\(957\) −48.3155 + 48.3155i −0.0504864 + 0.0504864i
\(958\) −80.0927 + 823.858i −0.0836040 + 0.859977i
\(959\) −298.511 298.511i −0.311273 0.311273i
\(960\) 955.399 1453.58i 0.995207 1.51414i
\(961\) 1825.86i 1.89996i
\(962\) 307.261 + 29.8708i 0.319398 + 0.0310507i
\(963\) 1497.07 1497.07i 1.55459 1.55459i
\(964\) −651.060 + 437.407i −0.675373 + 0.453741i
\(965\) 551.646i 0.571654i
\(966\) 103.056 1060.07i 0.106683 1.09738i
\(967\) −1356.69 −1.40299 −0.701496 0.712674i \(-0.747484\pi\)
−0.701496 + 0.712674i \(0.747484\pi\)
\(968\) −811.998 + 437.985i −0.838841 + 0.452464i
\(969\) −879.361 + 668.447i −0.907493 + 0.689832i
\(970\) 308.632 253.940i 0.318177 0.261794i
\(971\) 274.508i 0.282707i −0.989959 0.141353i \(-0.954855\pi\)
0.989959 0.141353i \(-0.0451454\pi\)
\(972\) 2709.28 1820.20i 2.78732 1.87263i
\(973\) 278.104i 0.285821i
\(974\) 1126.00 + 109.466i 1.15606 + 0.112388i
\(975\) −50.0797 50.0797i −0.0513638 0.0513638i
\(976\) 402.432 + 957.845i 0.412328 + 0.981398i
\(977\) 1035.39i 1.05976i 0.848072 + 0.529882i \(0.177764\pi\)
−0.848072 + 0.529882i \(0.822236\pi\)
\(978\) 297.304 244.620i 0.303992 0.250123i
\(979\) 149.038 149.038i 0.152235 0.152235i
\(980\) 828.180 556.403i 0.845082 0.567758i
\(981\) 2630.50 2630.50i 2.68145 2.68145i
\(982\) 355.200 + 431.700i 0.361711 + 0.439613i
\(983\) 92.8187 92.8187i 0.0944239 0.0944239i −0.658317 0.752741i \(-0.728731\pi\)
0.752741 + 0.658317i \(0.228731\pi\)
\(984\) −663.911 1230.85i −0.674706 1.25086i
\(985\) −88.7670 −0.0901187
\(986\) 39.1207 165.333i 0.0396762 0.167681i
\(987\) 3102.65 3.14352
\(988\) 41.8153 213.030i 0.0423232 0.215618i
\(989\) −255.606 + 255.606i −0.258448 + 0.258448i
\(990\) −417.140 + 343.220i −0.421353 + 0.346687i
\(991\) −85.6124 + 85.6124i −0.0863899 + 0.0863899i −0.748981 0.662591i \(-0.769457\pi\)
0.662591 + 0.748981i \(0.269457\pi\)
\(992\) −786.910 + 1494.83i −0.793256 + 1.50689i
\(993\) −1571.34 + 1571.34i −1.58242 + 1.58242i
\(994\) −244.153 + 200.888i −0.245627 + 0.202100i
\(995\) 303.097i 0.304620i
\(996\) 403.886 + 601.165i 0.405508 + 0.603580i
\(997\) 1012.05 + 1012.05i 1.01510 + 1.01510i 0.999884 + 0.0152111i \(0.00484204\pi\)
0.0152111 + 0.999884i \(0.495158\pi\)
\(998\) −43.4302 + 446.737i −0.0435172 + 0.447632i
\(999\) 2760.58i 2.76335i
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 136.3.j.b.115.9 64
4.3 odd 2 544.3.n.b.47.31 64
8.3 odd 2 inner 136.3.j.b.115.24 yes 64
8.5 even 2 544.3.n.b.47.32 64
17.4 even 4 inner 136.3.j.b.123.24 yes 64
68.55 odd 4 544.3.n.b.463.32 64
136.21 even 4 544.3.n.b.463.31 64
136.123 odd 4 inner 136.3.j.b.123.9 yes 64
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
136.3.j.b.115.9 64 1.1 even 1 trivial
136.3.j.b.115.24 yes 64 8.3 odd 2 inner
136.3.j.b.123.9 yes 64 136.123 odd 4 inner
136.3.j.b.123.24 yes 64 17.4 even 4 inner
544.3.n.b.47.31 64 4.3 odd 2
544.3.n.b.47.32 64 8.5 even 2
544.3.n.b.463.31 64 136.21 even 4
544.3.n.b.463.32 64 68.55 odd 4