Properties

Label 731.2.f.c.259.10
Level $731$
Weight $2$
Character 731.259
Analytic conductor $5.837$
Analytic rank $0$
Dimension $56$
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] = [731,2,Mod(259,731)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(731, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([3, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("731.259");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 731 = 17 \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 731.f (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.83706438776\)
Analytic rank: \(0\)
Dimension: \(56\)
Relative dimension: \(28\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 259.10
Character \(\chi\) \(=\) 731.259
Dual form 731.2.f.c.302.19

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.47026i q^{2} +(-1.92339 + 1.92339i) q^{3} -0.161659 q^{4} +(2.97219 - 2.97219i) q^{5} +(2.82787 + 2.82787i) q^{6} +(-2.28989 - 2.28989i) q^{7} -2.70284i q^{8} -4.39883i q^{9} +O(q^{10})\) \(q-1.47026i q^{2} +(-1.92339 + 1.92339i) q^{3} -0.161659 q^{4} +(2.97219 - 2.97219i) q^{5} +(2.82787 + 2.82787i) q^{6} +(-2.28989 - 2.28989i) q^{7} -2.70284i q^{8} -4.39883i q^{9} +(-4.36988 - 4.36988i) q^{10} +(0.913013 + 0.913013i) q^{11} +(0.310933 - 0.310933i) q^{12} -1.35632 q^{13} +(-3.36672 + 3.36672i) q^{14} +11.4333i q^{15} -4.29718 q^{16} +(-3.90253 - 1.33050i) q^{17} -6.46741 q^{18} +0.817400i q^{19} +(-0.480482 + 0.480482i) q^{20} +8.80867 q^{21} +(1.34236 - 1.34236i) q^{22} +(3.47407 + 3.47407i) q^{23} +(5.19860 + 5.19860i) q^{24} -12.6678i q^{25} +1.99413i q^{26} +(2.69049 + 2.69049i) q^{27} +(0.370181 + 0.370181i) q^{28} +(-6.38622 + 6.38622i) q^{29} +16.8099 q^{30} +(0.763808 - 0.763808i) q^{31} +0.912300i q^{32} -3.51215 q^{33} +(-1.95618 + 5.73773i) q^{34} -13.6119 q^{35} +0.711112i q^{36} +(4.64772 - 4.64772i) q^{37} +1.20179 q^{38} +(2.60872 - 2.60872i) q^{39} +(-8.03333 - 8.03333i) q^{40} +(-4.87568 - 4.87568i) q^{41} -12.9510i q^{42} +1.00000i q^{43} +(-0.147597 - 0.147597i) q^{44} +(-13.0741 - 13.0741i) q^{45} +(5.10778 - 5.10778i) q^{46} -3.17925 q^{47} +(8.26515 - 8.26515i) q^{48} +3.48715i q^{49} -18.6249 q^{50} +(10.0651 - 4.94701i) q^{51} +0.219261 q^{52} -9.91351i q^{53} +(3.95571 - 3.95571i) q^{54} +5.42729 q^{55} +(-6.18918 + 6.18918i) q^{56} +(-1.57218 - 1.57218i) q^{57} +(9.38940 + 9.38940i) q^{58} +7.73520i q^{59} -1.84830i q^{60} +(0.831706 + 0.831706i) q^{61} +(-1.12299 - 1.12299i) q^{62} +(-10.0728 + 10.0728i) q^{63} -7.25305 q^{64} +(-4.03122 + 4.03122i) q^{65} +5.16377i q^{66} -3.55978 q^{67} +(0.630881 + 0.215088i) q^{68} -13.3640 q^{69} +20.0131i q^{70} +(3.04237 - 3.04237i) q^{71} -11.8893 q^{72} +(5.17099 - 5.17099i) q^{73} +(-6.83334 - 6.83334i) q^{74} +(24.3651 + 24.3651i) q^{75} -0.132140i q^{76} -4.18139i q^{77} +(-3.83549 - 3.83549i) q^{78} +(2.80138 + 2.80138i) q^{79} +(-12.7720 + 12.7720i) q^{80} +2.84680 q^{81} +(-7.16851 + 7.16851i) q^{82} -15.4276i q^{83} -1.42400 q^{84} +(-15.5536 + 7.64456i) q^{85} +1.47026 q^{86} -24.5663i q^{87} +(2.46772 - 2.46772i) q^{88} +18.0817 q^{89} +(-19.2224 + 19.2224i) q^{90} +(3.10581 + 3.10581i) q^{91} +(-0.561616 - 0.561616i) q^{92} +2.93819i q^{93} +4.67431i q^{94} +(2.42947 + 2.42947i) q^{95} +(-1.75471 - 1.75471i) q^{96} +(5.23314 - 5.23314i) q^{97} +5.12702 q^{98} +(4.01619 - 4.01619i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56 q - 4 q^{3} - 60 q^{4} - 2 q^{5} + 8 q^{6} + 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 56 q - 4 q^{3} - 60 q^{4} - 2 q^{5} + 8 q^{6} + 4 q^{7} + 4 q^{10} - 6 q^{11} - 14 q^{12} + 16 q^{13} + 6 q^{14} + 44 q^{16} + 8 q^{17} - 16 q^{18} + 12 q^{20} + 28 q^{21} + 14 q^{22} + 6 q^{23} + 62 q^{24} - 4 q^{27} + 34 q^{28} - 12 q^{29} - 96 q^{30} + 14 q^{31} - 44 q^{33} + 6 q^{34} - 32 q^{35} + 8 q^{37} + 72 q^{38} - 32 q^{39} - 84 q^{40} + 24 q^{41} + 4 q^{44} + 48 q^{45} - 4 q^{46} - 8 q^{47} + 38 q^{48} - 64 q^{50} + 28 q^{51} - 48 q^{52} + 34 q^{54} + 56 q^{55} - 26 q^{56} - 102 q^{57} + 76 q^{58} - 40 q^{61} + 34 q^{62} + 4 q^{63} - 204 q^{64} + 18 q^{65} - 20 q^{67} + 30 q^{68} - 16 q^{69} - 26 q^{71} + 144 q^{72} + 8 q^{73} - 80 q^{74} + 142 q^{75} - 32 q^{78} - 22 q^{79} - 32 q^{80} - 32 q^{81} + 100 q^{82} - 20 q^{84} - 2 q^{85} + 12 q^{86} + 34 q^{88} + 68 q^{89} - 10 q^{90} - 28 q^{91} + 68 q^{92} - 62 q^{95} + 62 q^{96} - 2 q^{97} - 32 q^{98} + 66 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/731\mathbb{Z}\right)^\times\).

\(n\) \(173\) \(562\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.47026i 1.03963i −0.854279 0.519815i \(-0.826001\pi\)
0.854279 0.519815i \(-0.173999\pi\)
\(3\) −1.92339 + 1.92339i −1.11047 + 1.11047i −0.117380 + 0.993087i \(0.537450\pi\)
−0.993087 + 0.117380i \(0.962550\pi\)
\(4\) −0.161659 −0.0808297
\(5\) 2.97219 2.97219i 1.32920 1.32920i 0.423137 0.906066i \(-0.360929\pi\)
0.906066 0.423137i \(-0.139071\pi\)
\(6\) 2.82787 + 2.82787i 1.15447 + 1.15447i
\(7\) −2.28989 2.28989i −0.865495 0.865495i 0.126474 0.991970i \(-0.459634\pi\)
−0.991970 + 0.126474i \(0.959634\pi\)
\(8\) 2.70284i 0.955597i
\(9\) 4.39883i 1.46628i
\(10\) −4.36988 4.36988i −1.38188 1.38188i
\(11\) 0.913013 + 0.913013i 0.275284 + 0.275284i 0.831223 0.555939i \(-0.187641\pi\)
−0.555939 + 0.831223i \(0.687641\pi\)
\(12\) 0.310933 0.310933i 0.0897587 0.0897587i
\(13\) −1.35632 −0.376174 −0.188087 0.982152i \(-0.560229\pi\)
−0.188087 + 0.982152i \(0.560229\pi\)
\(14\) −3.36672 + 3.36672i −0.899795 + 0.899795i
\(15\) 11.4333i 2.95207i
\(16\) −4.29718 −1.07430
\(17\) −3.90253 1.33050i −0.946503 0.322694i
\(18\) −6.46741 −1.52438
\(19\) 0.817400i 0.187524i 0.995595 + 0.0937622i \(0.0298893\pi\)
−0.995595 + 0.0937622i \(0.970111\pi\)
\(20\) −0.480482 + 0.480482i −0.107439 + 0.107439i
\(21\) 8.80867 1.92221
\(22\) 1.34236 1.34236i 0.286193 0.286193i
\(23\) 3.47407 + 3.47407i 0.724394 + 0.724394i 0.969497 0.245103i \(-0.0788219\pi\)
−0.245103 + 0.969497i \(0.578822\pi\)
\(24\) 5.19860 + 5.19860i 1.06116 + 1.06116i
\(25\) 12.6678i 2.53356i
\(26\) 1.99413i 0.391082i
\(27\) 2.69049 + 2.69049i 0.517784 + 0.517784i
\(28\) 0.370181 + 0.370181i 0.0699577 + 0.0699577i
\(29\) −6.38622 + 6.38622i −1.18589 + 1.18589i −0.207699 + 0.978193i \(0.566597\pi\)
−0.978193 + 0.207699i \(0.933403\pi\)
\(30\) 16.8099 3.06906
\(31\) 0.763808 0.763808i 0.137184 0.137184i −0.635180 0.772364i \(-0.719074\pi\)
0.772364 + 0.635180i \(0.219074\pi\)
\(32\) 0.912300i 0.161273i
\(33\) −3.51215 −0.611387
\(34\) −1.95618 + 5.73773i −0.335482 + 0.984013i
\(35\) −13.6119 −2.30084
\(36\) 0.711112i 0.118519i
\(37\) 4.64772 4.64772i 0.764080 0.764080i −0.212977 0.977057i \(-0.568316\pi\)
0.977057 + 0.212977i \(0.0683161\pi\)
\(38\) 1.20179 0.194956
\(39\) 2.60872 2.60872i 0.417729 0.417729i
\(40\) −8.03333 8.03333i −1.27018 1.27018i
\(41\) −4.87568 4.87568i −0.761453 0.761453i 0.215132 0.976585i \(-0.430982\pi\)
−0.976585 + 0.215132i \(0.930982\pi\)
\(42\) 12.9510i 1.99839i
\(43\) 1.00000i 0.152499i
\(44\) −0.147597 0.147597i −0.0222511 0.0222511i
\(45\) −13.0741 13.0741i −1.94898 1.94898i
\(46\) 5.10778 5.10778i 0.753101 0.753101i
\(47\) −3.17925 −0.463741 −0.231870 0.972747i \(-0.574485\pi\)
−0.231870 + 0.972747i \(0.574485\pi\)
\(48\) 8.26515 8.26515i 1.19297 1.19297i
\(49\) 3.48715i 0.498165i
\(50\) −18.6249 −2.63396
\(51\) 10.0651 4.94701i 1.40940 0.692720i
\(52\) 0.219261 0.0304060
\(53\) 9.91351i 1.36173i −0.732411 0.680863i \(-0.761605\pi\)
0.732411 0.680863i \(-0.238395\pi\)
\(54\) 3.95571 3.95571i 0.538304 0.538304i
\(55\) 5.42729 0.731815
\(56\) −6.18918 + 6.18918i −0.827065 + 0.827065i
\(57\) −1.57218 1.57218i −0.208240 0.208240i
\(58\) 9.38940 + 9.38940i 1.23289 + 1.23289i
\(59\) 7.73520i 1.00704i 0.863985 + 0.503518i \(0.167961\pi\)
−0.863985 + 0.503518i \(0.832039\pi\)
\(60\) 1.84830i 0.238615i
\(61\) 0.831706 + 0.831706i 0.106489 + 0.106489i 0.758344 0.651855i \(-0.226009\pi\)
−0.651855 + 0.758344i \(0.726009\pi\)
\(62\) −1.12299 1.12299i −0.142620 0.142620i
\(63\) −10.0728 + 10.0728i −1.26906 + 1.26906i
\(64\) −7.25305 −0.906632
\(65\) −4.03122 + 4.03122i −0.500012 + 0.500012i
\(66\) 5.16377i 0.635616i
\(67\) −3.55978 −0.434896 −0.217448 0.976072i \(-0.569773\pi\)
−0.217448 + 0.976072i \(0.569773\pi\)
\(68\) 0.630881 + 0.215088i 0.0765055 + 0.0260832i
\(69\) −13.3640 −1.60883
\(70\) 20.0131i 2.39202i
\(71\) 3.04237 3.04237i 0.361063 0.361063i −0.503142 0.864204i \(-0.667823\pi\)
0.864204 + 0.503142i \(0.167823\pi\)
\(72\) −11.8893 −1.40117
\(73\) 5.17099 5.17099i 0.605219 0.605219i −0.336474 0.941693i \(-0.609234\pi\)
0.941693 + 0.336474i \(0.109234\pi\)
\(74\) −6.83334 6.83334i −0.794360 0.794360i
\(75\) 24.3651 + 24.3651i 2.81344 + 2.81344i
\(76\) 0.132140i 0.0151575i
\(77\) 4.18139i 0.476513i
\(78\) −3.83549 3.83549i −0.434284 0.434284i
\(79\) 2.80138 + 2.80138i 0.315180 + 0.315180i 0.846912 0.531732i \(-0.178459\pi\)
−0.531732 + 0.846912i \(0.678459\pi\)
\(80\) −12.7720 + 12.7720i −1.42796 + 1.42796i
\(81\) 2.84680 0.316311
\(82\) −7.16851 + 7.16851i −0.791629 + 0.791629i
\(83\) 15.4276i 1.69339i −0.532075 0.846697i \(-0.678588\pi\)
0.532075 0.846697i \(-0.321412\pi\)
\(84\) −1.42400 −0.155372
\(85\) −15.5536 + 7.64456i −1.68702 + 0.829169i
\(86\) 1.47026 0.158542
\(87\) 24.5663i 2.63379i
\(88\) 2.46772 2.46772i 0.263060 0.263060i
\(89\) 18.0817 1.91666 0.958330 0.285663i \(-0.0922137\pi\)
0.958330 + 0.285663i \(0.0922137\pi\)
\(90\) −19.2224 + 19.2224i −2.02622 + 2.02622i
\(91\) 3.10581 + 3.10581i 0.325577 + 0.325577i
\(92\) −0.561616 0.561616i −0.0585525 0.0585525i
\(93\) 2.93819i 0.304677i
\(94\) 4.67431i 0.482119i
\(95\) 2.42947 + 2.42947i 0.249258 + 0.249258i
\(96\) −1.75471 1.75471i −0.179089 0.179089i
\(97\) 5.23314 5.23314i 0.531345 0.531345i −0.389628 0.920972i \(-0.627396\pi\)
0.920972 + 0.389628i \(0.127396\pi\)
\(98\) 5.12702 0.517907
\(99\) 4.01619 4.01619i 0.403642 0.403642i
\(100\) 2.04787i 0.204787i
\(101\) −8.69769 −0.865453 −0.432726 0.901525i \(-0.642448\pi\)
−0.432726 + 0.901525i \(0.642448\pi\)
\(102\) −7.27338 14.7984i −0.720172 1.46526i
\(103\) 1.02408 0.100905 0.0504527 0.998726i \(-0.483934\pi\)
0.0504527 + 0.998726i \(0.483934\pi\)
\(104\) 3.66590i 0.359471i
\(105\) 26.1810 26.1810i 2.55501 2.55501i
\(106\) −14.5754 −1.41569
\(107\) −5.91535 + 5.91535i −0.571859 + 0.571859i −0.932648 0.360789i \(-0.882508\pi\)
0.360789 + 0.932648i \(0.382508\pi\)
\(108\) −0.434942 0.434942i −0.0418523 0.0418523i
\(109\) 3.40306 + 3.40306i 0.325954 + 0.325954i 0.851046 0.525092i \(-0.175969\pi\)
−0.525092 + 0.851046i \(0.675969\pi\)
\(110\) 7.97952i 0.760817i
\(111\) 17.8787i 1.69697i
\(112\) 9.84006 + 9.84006i 0.929799 + 0.929799i
\(113\) 11.3023 + 11.3023i 1.06323 + 1.06323i 0.997861 + 0.0653653i \(0.0208213\pi\)
0.0653653 + 0.997861i \(0.479179\pi\)
\(114\) −2.31150 + 2.31150i −0.216492 + 0.216492i
\(115\) 20.6512 1.92573
\(116\) 1.03239 1.03239i 0.0958552 0.0958552i
\(117\) 5.96620i 0.551575i
\(118\) 11.3727 1.04695
\(119\) 5.88966 + 11.9831i 0.539904 + 1.09848i
\(120\) 30.9024 2.82099
\(121\) 9.33282i 0.848438i
\(122\) 1.22282 1.22282i 0.110709 0.110709i
\(123\) 18.7556 1.69114
\(124\) −0.123477 + 0.123477i −0.0110885 + 0.0110885i
\(125\) −22.7901 22.7901i −2.03841 2.03841i
\(126\) 14.8096 + 14.8096i 1.31935 + 1.31935i
\(127\) 20.1385i 1.78700i −0.449062 0.893501i \(-0.648242\pi\)
0.449062 0.893501i \(-0.351758\pi\)
\(128\) 12.4885i 1.10383i
\(129\) −1.92339 1.92339i −0.169345 0.169345i
\(130\) 5.92694 + 5.92694i 0.519827 + 0.519827i
\(131\) 9.03788 9.03788i 0.789644 0.789644i −0.191792 0.981436i \(-0.561430\pi\)
0.981436 + 0.191792i \(0.0614299\pi\)
\(132\) 0.567772 0.0494182
\(133\) 1.87175 1.87175i 0.162302 0.162302i
\(134\) 5.23379i 0.452131i
\(135\) 15.9933 1.37648
\(136\) −3.59613 + 10.5479i −0.308365 + 0.904475i
\(137\) −2.27416 −0.194295 −0.0971474 0.995270i \(-0.530972\pi\)
−0.0971474 + 0.995270i \(0.530972\pi\)
\(138\) 19.6485i 1.67259i
\(139\) −2.33995 + 2.33995i −0.198472 + 0.198472i −0.799345 0.600873i \(-0.794820\pi\)
0.600873 + 0.799345i \(0.294820\pi\)
\(140\) 2.20050 0.185976
\(141\) 6.11492 6.11492i 0.514969 0.514969i
\(142\) −4.47306 4.47306i −0.375371 0.375371i
\(143\) −1.23833 1.23833i −0.103555 0.103555i
\(144\) 18.9026i 1.57521i
\(145\) 37.9621i 3.15258i
\(146\) −7.60270 7.60270i −0.629204 0.629204i
\(147\) −6.70714 6.70714i −0.553196 0.553196i
\(148\) −0.751346 + 0.751346i −0.0617603 + 0.0617603i
\(149\) 5.35347 0.438573 0.219287 0.975660i \(-0.429627\pi\)
0.219287 + 0.975660i \(0.429627\pi\)
\(150\) 35.8229 35.8229i 2.92493 2.92493i
\(151\) 21.6820i 1.76445i 0.470824 + 0.882227i \(0.343957\pi\)
−0.470824 + 0.882227i \(0.656043\pi\)
\(152\) 2.20930 0.179198
\(153\) −5.85265 + 17.1666i −0.473158 + 1.38784i
\(154\) −6.14772 −0.495398
\(155\) 4.54036i 0.364690i
\(156\) −0.421724 + 0.421724i −0.0337649 + 0.0337649i
\(157\) −8.65805 −0.690988 −0.345494 0.938421i \(-0.612289\pi\)
−0.345494 + 0.938421i \(0.612289\pi\)
\(158\) 4.11876 4.11876i 0.327671 0.327671i
\(159\) 19.0675 + 19.0675i 1.51215 + 1.51215i
\(160\) 2.71153 + 2.71153i 0.214365 + 0.214365i
\(161\) 15.9104i 1.25392i
\(162\) 4.18552i 0.328846i
\(163\) 7.87820 + 7.87820i 0.617068 + 0.617068i 0.944778 0.327710i \(-0.106277\pi\)
−0.327710 + 0.944778i \(0.606277\pi\)
\(164\) 0.788199 + 0.788199i 0.0615480 + 0.0615480i
\(165\) −10.4388 + 10.4388i −0.812657 + 0.812657i
\(166\) −22.6825 −1.76050
\(167\) −0.544219 + 0.544219i −0.0421129 + 0.0421129i −0.727850 0.685737i \(-0.759480\pi\)
0.685737 + 0.727850i \(0.259480\pi\)
\(168\) 23.8084i 1.83686i
\(169\) −11.1604 −0.858493
\(170\) 11.2395 + 22.8677i 0.862029 + 1.75388i
\(171\) 3.59560 0.274963
\(172\) 0.161659i 0.0123264i
\(173\) −14.8210 + 14.8210i −1.12682 + 1.12682i −0.136127 + 0.990691i \(0.543465\pi\)
−0.990691 + 0.136127i \(0.956535\pi\)
\(174\) −36.1189 −2.73816
\(175\) −29.0078 + 29.0078i −2.19278 + 2.19278i
\(176\) −3.92338 3.92338i −0.295736 0.295736i
\(177\) −14.8778 14.8778i −1.11828 1.11828i
\(178\) 26.5848i 1.99262i
\(179\) 12.4339i 0.929357i −0.885479 0.464679i \(-0.846170\pi\)
0.885479 0.464679i \(-0.153830\pi\)
\(180\) 2.11356 + 2.11356i 0.157535 + 0.157535i
\(181\) 13.7427 + 13.7427i 1.02149 + 1.02149i 0.999764 + 0.0217250i \(0.00691584\pi\)
0.0217250 + 0.999764i \(0.493084\pi\)
\(182\) 4.56634 4.56634i 0.338479 0.338479i
\(183\) −3.19938 −0.236505
\(184\) 9.38984 9.38984i 0.692228 0.692228i
\(185\) 27.6278i 2.03123i
\(186\) 4.31990 0.316751
\(187\) −2.34830 4.77783i −0.171725 0.349389i
\(188\) 0.513955 0.0374840
\(189\) 12.3218i 0.896280i
\(190\) 3.57194 3.57194i 0.259136 0.259136i
\(191\) 17.7643 1.28538 0.642689 0.766128i \(-0.277819\pi\)
0.642689 + 0.766128i \(0.277819\pi\)
\(192\) 13.9504 13.9504i 1.00678 1.00678i
\(193\) 16.6413 + 16.6413i 1.19787 + 1.19787i 0.974803 + 0.223067i \(0.0716068\pi\)
0.223067 + 0.974803i \(0.428393\pi\)
\(194\) −7.69407 7.69407i −0.552402 0.552402i
\(195\) 15.5072i 1.11049i
\(196\) 0.563731i 0.0402665i
\(197\) 8.01451 + 8.01451i 0.571010 + 0.571010i 0.932411 0.361401i \(-0.117701\pi\)
−0.361401 + 0.932411i \(0.617701\pi\)
\(198\) −5.90483 5.90483i −0.419638 0.419638i
\(199\) 13.4150 13.4150i 0.950967 0.950967i −0.0478857 0.998853i \(-0.515248\pi\)
0.998853 + 0.0478857i \(0.0152483\pi\)
\(200\) −34.2390 −2.42106
\(201\) 6.84683 6.84683i 0.482938 0.482938i
\(202\) 12.7879i 0.899750i
\(203\) 29.2474 2.05277
\(204\) −1.62712 + 0.799730i −0.113922 + 0.0559923i
\(205\) −28.9829 −2.02425
\(206\) 1.50566i 0.104904i
\(207\) 15.2818 15.2818i 1.06216 1.06216i
\(208\) 5.82834 0.404122
\(209\) −0.746297 + 0.746297i −0.0516224 + 0.0516224i
\(210\) −38.4929 38.4929i −2.65626 2.65626i
\(211\) 19.6206 + 19.6206i 1.35074 + 1.35074i 0.884840 + 0.465896i \(0.154268\pi\)
0.465896 + 0.884840i \(0.345732\pi\)
\(212\) 1.60261i 0.110068i
\(213\) 11.7033i 0.801896i
\(214\) 8.69710 + 8.69710i 0.594521 + 0.594521i
\(215\) 2.97219 + 2.97219i 0.202702 + 0.202702i
\(216\) 7.27194 7.27194i 0.494793 0.494793i
\(217\) −3.49806 −0.237464
\(218\) 5.00338 5.00338i 0.338872 0.338872i
\(219\) 19.8916i 1.34415i
\(220\) −0.877372 −0.0591524
\(221\) 5.29306 + 1.80458i 0.356050 + 0.121389i
\(222\) 26.2863 1.76422
\(223\) 12.4157i 0.831416i −0.909498 0.415708i \(-0.863534\pi\)
0.909498 0.415708i \(-0.136466\pi\)
\(224\) 2.08906 2.08906i 0.139581 0.139581i
\(225\) −55.7235 −3.71490
\(226\) 16.6172 16.6172i 1.10536 1.10536i
\(227\) −8.67542 8.67542i −0.575808 0.575808i 0.357938 0.933745i \(-0.383480\pi\)
−0.933745 + 0.357938i \(0.883480\pi\)
\(228\) 0.254157 + 0.254157i 0.0168320 + 0.0168320i
\(229\) 20.9191i 1.38237i −0.722677 0.691186i \(-0.757088\pi\)
0.722677 0.691186i \(-0.242912\pi\)
\(230\) 30.3626i 2.00205i
\(231\) 8.04243 + 8.04243i 0.529153 + 0.529153i
\(232\) 17.2609 + 17.2609i 1.13323 + 1.13323i
\(233\) 9.79157 9.79157i 0.641467 0.641467i −0.309449 0.950916i \(-0.600145\pi\)
0.950916 + 0.309449i \(0.100145\pi\)
\(234\) 8.77185 0.573434
\(235\) −9.44932 + 9.44932i −0.616405 + 0.616405i
\(236\) 1.25047i 0.0813984i
\(237\) −10.7763 −0.699995
\(238\) 17.6182 8.65932i 1.14202 0.561300i
\(239\) −23.1829 −1.49958 −0.749789 0.661677i \(-0.769845\pi\)
−0.749789 + 0.661677i \(0.769845\pi\)
\(240\) 49.1311i 3.17140i
\(241\) −8.92637 + 8.92637i −0.574998 + 0.574998i −0.933521 0.358523i \(-0.883280\pi\)
0.358523 + 0.933521i \(0.383280\pi\)
\(242\) −13.7217 −0.882061
\(243\) −13.5469 + 13.5469i −0.869037 + 0.869037i
\(244\) −0.134453 0.134453i −0.00860748 0.00860748i
\(245\) 10.3645 + 10.3645i 0.662162 + 0.662162i
\(246\) 27.5756i 1.75816i
\(247\) 1.10865i 0.0705418i
\(248\) −2.06445 2.06445i −0.131092 0.131092i
\(249\) 29.6732 + 29.6732i 1.88046 + 1.88046i
\(250\) −33.5074 + 33.5074i −2.11919 + 2.11919i
\(251\) −4.25300 −0.268447 −0.134224 0.990951i \(-0.542854\pi\)
−0.134224 + 0.990951i \(0.542854\pi\)
\(252\) 1.62836 1.62836i 0.102577 0.102577i
\(253\) 6.34374i 0.398827i
\(254\) −29.6088 −1.85782
\(255\) 15.2121 44.6189i 0.952616 2.79415i
\(256\) 3.85516 0.240947
\(257\) 7.16627i 0.447020i −0.974702 0.223510i \(-0.928249\pi\)
0.974702 0.223510i \(-0.0717515\pi\)
\(258\) −2.82787 + 2.82787i −0.176056 + 0.176056i
\(259\) −21.2855 −1.32261
\(260\) 0.651685 0.651685i 0.0404158 0.0404158i
\(261\) 28.0919 + 28.0919i 1.73884 + 1.73884i
\(262\) −13.2880 13.2880i −0.820937 0.820937i
\(263\) 11.9151i 0.734718i 0.930079 + 0.367359i \(0.119738\pi\)
−0.930079 + 0.367359i \(0.880262\pi\)
\(264\) 9.49277i 0.584239i
\(265\) −29.4648 29.4648i −1.81001 1.81001i
\(266\) −2.75196 2.75196i −0.168734 0.168734i
\(267\) −34.7782 + 34.7782i −2.12839 + 2.12839i
\(268\) 0.575471 0.0351525
\(269\) 20.0497 20.0497i 1.22245 1.22245i 0.255693 0.966758i \(-0.417697\pi\)
0.966758 0.255693i \(-0.0823035\pi\)
\(270\) 23.5142i 1.43103i
\(271\) 9.04280 0.549311 0.274655 0.961543i \(-0.411436\pi\)
0.274655 + 0.961543i \(0.411436\pi\)
\(272\) 16.7699 + 5.71741i 1.01682 + 0.346669i
\(273\) −11.9473 −0.723085
\(274\) 3.34361i 0.201995i
\(275\) 11.5659 11.5659i 0.697447 0.697447i
\(276\) 2.16041 0.130041
\(277\) 15.1054 15.1054i 0.907598 0.907598i −0.0884795 0.996078i \(-0.528201\pi\)
0.996078 + 0.0884795i \(0.0282008\pi\)
\(278\) 3.44034 + 3.44034i 0.206338 + 0.206338i
\(279\) −3.35986 3.35986i −0.201149 0.201149i
\(280\) 36.7908i 2.19867i
\(281\) 5.57038i 0.332301i −0.986100 0.166151i \(-0.946866\pi\)
0.986100 0.166151i \(-0.0531338\pi\)
\(282\) −8.99051 8.99051i −0.535377 0.535377i
\(283\) −4.24562 4.24562i −0.252376 0.252376i 0.569568 0.821944i \(-0.307110\pi\)
−0.821944 + 0.569568i \(0.807110\pi\)
\(284\) −0.491827 + 0.491827i −0.0291846 + 0.0291846i
\(285\) −9.34560 −0.553586
\(286\) −1.82067 + 1.82067i −0.107658 + 0.107658i
\(287\) 22.3295i 1.31807i
\(288\) 4.01305 0.236471
\(289\) 13.4595 + 10.3847i 0.791737 + 0.610862i
\(290\) 55.8141 3.27752
\(291\) 20.1307i 1.18008i
\(292\) −0.835939 + 0.835939i −0.0489197 + 0.0489197i
\(293\) −10.9243 −0.638202 −0.319101 0.947721i \(-0.603381\pi\)
−0.319101 + 0.947721i \(0.603381\pi\)
\(294\) −9.86123 + 9.86123i −0.575119 + 0.575119i
\(295\) 22.9905 + 22.9905i 1.33856 + 1.33856i
\(296\) −12.5620 12.5620i −0.730152 0.730152i
\(297\) 4.91290i 0.285075i
\(298\) 7.87098i 0.455954i
\(299\) −4.71193 4.71193i −0.272498 0.272498i
\(300\) −3.93884 3.93884i −0.227409 0.227409i
\(301\) 2.28989 2.28989i 0.131987 0.131987i
\(302\) 31.8781 1.83438
\(303\) 16.7290 16.7290i 0.961057 0.961057i
\(304\) 3.51252i 0.201457i
\(305\) 4.94397 0.283091
\(306\) 25.2393 + 8.60490i 1.44283 + 0.491910i
\(307\) 5.22362 0.298128 0.149064 0.988828i \(-0.452374\pi\)
0.149064 + 0.988828i \(0.452374\pi\)
\(308\) 0.675960i 0.0385164i
\(309\) −1.96970 + 1.96970i −0.112052 + 0.112052i
\(310\) −6.67550 −0.379143
\(311\) −4.74739 + 4.74739i −0.269200 + 0.269200i −0.828778 0.559578i \(-0.810963\pi\)
0.559578 + 0.828778i \(0.310963\pi\)
\(312\) −7.05093 7.05093i −0.399181 0.399181i
\(313\) −1.23502 1.23502i −0.0698075 0.0698075i 0.671341 0.741149i \(-0.265719\pi\)
−0.741149 + 0.671341i \(0.765719\pi\)
\(314\) 12.7296i 0.718371i
\(315\) 59.8766i 3.37366i
\(316\) −0.452870 0.452870i −0.0254759 0.0254759i
\(317\) −10.6869 10.6869i −0.600234 0.600234i 0.340141 0.940375i \(-0.389525\pi\)
−0.940375 + 0.340141i \(0.889525\pi\)
\(318\) 28.0342 28.0342i 1.57208 1.57208i
\(319\) −11.6614 −0.652913
\(320\) −21.5574 + 21.5574i −1.20510 + 1.20510i
\(321\) 22.7550i 1.27006i
\(322\) −23.3925 −1.30361
\(323\) 1.08755 3.18993i 0.0605130 0.177493i
\(324\) −0.460211 −0.0255673
\(325\) 17.1815i 0.953059i
\(326\) 11.5830 11.5830i 0.641522 0.641522i
\(327\) −13.0908 −0.723923
\(328\) −13.1782 + 13.1782i −0.727642 + 0.727642i
\(329\) 7.28011 + 7.28011i 0.401365 + 0.401365i
\(330\) 15.3477 + 15.3477i 0.844863 + 0.844863i
\(331\) 7.29874i 0.401175i −0.979676 0.200587i \(-0.935715\pi\)
0.979676 0.200587i \(-0.0642851\pi\)
\(332\) 2.49401i 0.136877i
\(333\) −20.4445 20.4445i −1.12035 1.12035i
\(334\) 0.800143 + 0.800143i 0.0437819 + 0.0437819i
\(335\) −10.5803 + 10.5803i −0.578065 + 0.578065i
\(336\) −37.8525 −2.06502
\(337\) 7.33362 7.33362i 0.399487 0.399487i −0.478565 0.878052i \(-0.658843\pi\)
0.878052 + 0.478565i \(0.158843\pi\)
\(338\) 16.4087i 0.892515i
\(339\) −43.4772 −2.36136
\(340\) 2.51438 1.23581i 0.136361 0.0670215i
\(341\) 1.39473 0.0755290
\(342\) 5.28646i 0.285859i
\(343\) −8.04402 + 8.04402i −0.434336 + 0.434336i
\(344\) 2.70284 0.145727
\(345\) −39.7202 + 39.7202i −2.13846 + 2.13846i
\(346\) 21.7907 + 21.7907i 1.17147 + 1.17147i
\(347\) 23.0790 + 23.0790i 1.23895 + 1.23895i 0.960432 + 0.278513i \(0.0898417\pi\)
0.278513 + 0.960432i \(0.410158\pi\)
\(348\) 3.97138i 0.212888i
\(349\) 26.0155i 1.39258i 0.717762 + 0.696289i \(0.245167\pi\)
−0.717762 + 0.696289i \(0.754833\pi\)
\(350\) 42.6490 + 42.6490i 2.27968 + 2.27968i
\(351\) −3.64915 3.64915i −0.194777 0.194777i
\(352\) −0.832942 + 0.832942i −0.0443959 + 0.0443959i
\(353\) −6.51294 −0.346649 −0.173324 0.984865i \(-0.555451\pi\)
−0.173324 + 0.984865i \(0.555451\pi\)
\(354\) −21.8742 + 21.8742i −1.16260 + 1.16260i
\(355\) 18.0850i 0.959850i
\(356\) −2.92308 −0.154923
\(357\) −34.3761 11.7199i −1.81938 0.620285i
\(358\) −18.2811 −0.966187
\(359\) 4.95878i 0.261714i 0.991401 + 0.130857i \(0.0417729\pi\)
−0.991401 + 0.130857i \(0.958227\pi\)
\(360\) −35.3373 + 35.3373i −1.86244 + 1.86244i
\(361\) 18.3319 0.964835
\(362\) 20.2054 20.2054i 1.06197 1.06197i
\(363\) 17.9506 + 17.9506i 0.942163 + 0.942163i
\(364\) −0.502083 0.502083i −0.0263163 0.0263163i
\(365\) 30.7383i 1.60892i
\(366\) 4.70392i 0.245878i
\(367\) −8.91874 8.91874i −0.465554 0.465554i 0.434916 0.900471i \(-0.356778\pi\)
−0.900471 + 0.434916i \(0.856778\pi\)
\(368\) −14.9287 14.9287i −0.778213 0.778213i
\(369\) −21.4473 + 21.4473i −1.11650 + 1.11650i
\(370\) −40.6199 −2.11173
\(371\) −22.7008 + 22.7008i −1.17857 + 1.17857i
\(372\) 0.474986i 0.0246269i
\(373\) 11.9670 0.619630 0.309815 0.950797i \(-0.399733\pi\)
0.309815 + 0.950797i \(0.399733\pi\)
\(374\) −7.02464 + 3.45260i −0.363235 + 0.178530i
\(375\) 87.6684 4.52718
\(376\) 8.59298i 0.443149i
\(377\) 8.66173 8.66173i 0.446102 0.446102i
\(378\) −18.1162 −0.931799
\(379\) −10.9563 + 10.9563i −0.562788 + 0.562788i −0.930098 0.367310i \(-0.880279\pi\)
0.367310 + 0.930098i \(0.380279\pi\)
\(380\) −0.392746 0.392746i −0.0201474 0.0201474i
\(381\) 38.7341 + 38.7341i 1.98441 + 1.98441i
\(382\) 26.1181i 1.33632i
\(383\) 2.27975i 0.116490i 0.998302 + 0.0582448i \(0.0185504\pi\)
−0.998302 + 0.0582448i \(0.981450\pi\)
\(384\) −24.0201 24.0201i −1.22577 1.22577i
\(385\) −12.4279 12.4279i −0.633383 0.633383i
\(386\) 24.4671 24.4671i 1.24534 1.24534i
\(387\) 4.39883 0.223605
\(388\) −0.845986 + 0.845986i −0.0429484 + 0.0429484i
\(389\) 8.35299i 0.423514i −0.977322 0.211757i \(-0.932082\pi\)
0.977322 0.211757i \(-0.0679185\pi\)
\(390\) −22.7996 −1.15450
\(391\) −8.93542 18.1799i −0.451884 0.919399i
\(392\) 9.42520 0.476045
\(393\) 34.7667i 1.75375i
\(394\) 11.7834 11.7834i 0.593639 0.593639i
\(395\) 16.6525 0.837877
\(396\) −0.649254 + 0.649254i −0.0326262 + 0.0326262i
\(397\) 25.2836 + 25.2836i 1.26895 + 1.26895i 0.946633 + 0.322313i \(0.104460\pi\)
0.322313 + 0.946633i \(0.395540\pi\)
\(398\) −19.7236 19.7236i −0.988654 0.988654i
\(399\) 7.20021i 0.360461i
\(400\) 54.4359i 2.72179i
\(401\) 4.37041 + 4.37041i 0.218248 + 0.218248i 0.807760 0.589512i \(-0.200680\pi\)
−0.589512 + 0.807760i \(0.700680\pi\)
\(402\) −10.0666 10.0666i −0.502077 0.502077i
\(403\) −1.03596 + 1.03596i −0.0516050 + 0.0516050i
\(404\) 1.40606 0.0699542
\(405\) 8.46121 8.46121i 0.420441 0.420441i
\(406\) 43.0013i 2.13412i
\(407\) 8.48684 0.420677
\(408\) −13.3710 27.2044i −0.661961 1.34682i
\(409\) 12.2954 0.607971 0.303985 0.952677i \(-0.401683\pi\)
0.303985 + 0.952677i \(0.401683\pi\)
\(410\) 42.6123i 2.10447i
\(411\) 4.37409 4.37409i 0.215758 0.215758i
\(412\) −0.165552 −0.00815616
\(413\) 17.7127 17.7127i 0.871586 0.871586i
\(414\) −22.4682 22.4682i −1.10425 1.10425i
\(415\) −45.8536 45.8536i −2.25086 2.25086i
\(416\) 1.23737i 0.0606669i
\(417\) 9.00127i 0.440794i
\(418\) 1.09725 + 1.09725i 0.0536682 + 0.0536682i
\(419\) −20.3827 20.3827i −0.995760 0.995760i 0.00423101 0.999991i \(-0.498653\pi\)
−0.999991 + 0.00423101i \(0.998653\pi\)
\(420\) −4.23241 + 4.23241i −0.206520 + 0.206520i
\(421\) −25.0164 −1.21922 −0.609612 0.792700i \(-0.708675\pi\)
−0.609612 + 0.792700i \(0.708675\pi\)
\(422\) 28.8473 28.8473i 1.40426 1.40426i
\(423\) 13.9850i 0.679972i
\(424\) −26.7946 −1.30126
\(425\) −16.8545 + 49.4365i −0.817564 + 2.39802i
\(426\) 17.2069 0.833675
\(427\) 3.80902i 0.184332i
\(428\) 0.956272 0.956272i 0.0462232 0.0462232i
\(429\) 4.76358 0.229988
\(430\) 4.36988 4.36988i 0.210734 0.210734i
\(431\) −19.5830 19.5830i −0.943281 0.943281i 0.0551942 0.998476i \(-0.482422\pi\)
−0.998476 + 0.0551942i \(0.982422\pi\)
\(432\) −11.5615 11.5615i −0.556254 0.556254i
\(433\) 8.03109i 0.385949i 0.981204 + 0.192975i \(0.0618135\pi\)
−0.981204 + 0.192975i \(0.938186\pi\)
\(434\) 5.14306i 0.246875i
\(435\) −73.0158 73.0158i −3.50084 3.50084i
\(436\) −0.550137 0.550137i −0.0263468 0.0263468i
\(437\) −2.83971 + 2.83971i −0.135842 + 0.135842i
\(438\) 29.2458 1.39742
\(439\) 13.2986 13.2986i 0.634708 0.634708i −0.314537 0.949245i \(-0.601849\pi\)
0.949245 + 0.314537i \(0.101849\pi\)
\(440\) 14.6691i 0.699320i
\(441\) 15.3394 0.730447
\(442\) 2.65320 7.78217i 0.126200 0.370160i
\(443\) 11.1117 0.527934 0.263967 0.964532i \(-0.414969\pi\)
0.263967 + 0.964532i \(0.414969\pi\)
\(444\) 2.89026i 0.137166i
\(445\) 53.7423 53.7423i 2.54763 2.54763i
\(446\) −18.2543 −0.864365
\(447\) −10.2968 + 10.2968i −0.487021 + 0.487021i
\(448\) 16.6087 + 16.6087i 0.784686 + 0.784686i
\(449\) −2.96686 2.96686i −0.140015 0.140015i 0.633625 0.773640i \(-0.281566\pi\)
−0.773640 + 0.633625i \(0.781566\pi\)
\(450\) 81.9279i 3.86212i
\(451\) 8.90311i 0.419231i
\(452\) −1.82711 1.82711i −0.0859403 0.0859403i
\(453\) −41.7028 41.7028i −1.95937 1.95937i
\(454\) −12.7551 + 12.7551i −0.598627 + 0.598627i
\(455\) 18.4621 0.865516
\(456\) −4.24933 + 4.24933i −0.198993 + 0.198993i
\(457\) 21.7030i 1.01522i −0.861586 0.507611i \(-0.830529\pi\)
0.861586 0.507611i \(-0.169471\pi\)
\(458\) −30.7565 −1.43716
\(459\) −6.92002 14.0794i −0.322999 0.657171i
\(460\) −3.33845 −0.155656
\(461\) 23.6671i 1.10229i −0.834410 0.551144i \(-0.814191\pi\)
0.834410 0.551144i \(-0.185809\pi\)
\(462\) 11.8244 11.8244i 0.550123 0.550123i
\(463\) 6.72203 0.312399 0.156199 0.987726i \(-0.450076\pi\)
0.156199 + 0.987726i \(0.450076\pi\)
\(464\) 27.4428 27.4428i 1.27400 1.27400i
\(465\) 8.73286 + 8.73286i 0.404977 + 0.404977i
\(466\) −14.3961 14.3961i −0.666888 0.666888i
\(467\) 8.78313i 0.406435i 0.979134 + 0.203217i \(0.0651398\pi\)
−0.979134 + 0.203217i \(0.934860\pi\)
\(468\) 0.964491i 0.0445836i
\(469\) 8.15149 + 8.15149i 0.376401 + 0.376401i
\(470\) 13.8929 + 13.8929i 0.640833 + 0.640833i
\(471\) 16.6528 16.6528i 0.767320 0.767320i
\(472\) 20.9070 0.962321
\(473\) −0.913013 + 0.913013i −0.0419804 + 0.0419804i
\(474\) 15.8439i 0.727735i
\(475\) 10.3547 0.475104
\(476\) −0.952118 1.93717i −0.0436403 0.0887901i
\(477\) −43.6078 −1.99666
\(478\) 34.0849i 1.55901i
\(479\) −19.2013 + 19.2013i −0.877329 + 0.877329i −0.993258 0.115929i \(-0.963016\pi\)
0.115929 + 0.993258i \(0.463016\pi\)
\(480\) −10.4306 −0.476091
\(481\) −6.30377 + 6.30377i −0.287427 + 0.287427i
\(482\) 13.1241 + 13.1241i 0.597785 + 0.597785i
\(483\) 30.6019 + 30.6019i 1.39244 + 1.39244i
\(484\) 1.50874i 0.0685789i
\(485\) 31.1077i 1.41253i
\(486\) 19.9175 + 19.9175i 0.903477 + 0.903477i
\(487\) 1.12237 + 1.12237i 0.0508593 + 0.0508593i 0.732079 0.681220i \(-0.238550\pi\)
−0.681220 + 0.732079i \(0.738550\pi\)
\(488\) 2.24797 2.24797i 0.101761 0.101761i
\(489\) −30.3056 −1.37047
\(490\) 15.2385 15.2385i 0.688403 0.688403i
\(491\) 15.2206i 0.686897i 0.939172 + 0.343448i \(0.111595\pi\)
−0.939172 + 0.343448i \(0.888405\pi\)
\(492\) −3.03202 −0.136694
\(493\) 33.4193 16.4256i 1.50513 0.739770i
\(494\) −1.63000 −0.0733374
\(495\) 23.8737i 1.07304i
\(496\) −3.28222 + 3.28222i −0.147376 + 0.147376i
\(497\) −13.9333 −0.624996
\(498\) 43.6272 43.6272i 1.95498 1.95498i
\(499\) −15.6355 15.6355i −0.699942 0.699942i 0.264456 0.964398i \(-0.414808\pi\)
−0.964398 + 0.264456i \(0.914808\pi\)
\(500\) 3.68424 + 3.68424i 0.164764 + 0.164764i
\(501\) 2.09349i 0.0935301i
\(502\) 6.25301i 0.279086i
\(503\) −26.2035 26.2035i −1.16835 1.16835i −0.982595 0.185759i \(-0.940526\pi\)
−0.185759 0.982595i \(-0.559474\pi\)
\(504\) 27.2252 + 27.2252i 1.21271 + 1.21271i
\(505\) −25.8512 + 25.8512i −1.15036 + 1.15036i
\(506\) 9.32693 0.414633
\(507\) 21.4658 21.4658i 0.953329 0.953329i
\(508\) 3.25557i 0.144443i
\(509\) −14.9145 −0.661075 −0.330537 0.943793i \(-0.607230\pi\)
−0.330537 + 0.943793i \(0.607230\pi\)
\(510\) −65.6014 22.3657i −2.90488 0.990368i
\(511\) −23.6820 −1.04763
\(512\) 19.3088i 0.853338i
\(513\) −2.19920 + 2.19920i −0.0970972 + 0.0970972i
\(514\) −10.5363 −0.464735
\(515\) 3.04375 3.04375i 0.134124 0.134124i
\(516\) 0.310933 + 0.310933i 0.0136881 + 0.0136881i
\(517\) −2.90269 2.90269i −0.127660 0.127660i
\(518\) 31.2951i 1.37503i
\(519\) 57.0129i 2.50259i
\(520\) 10.8957 + 10.8957i 0.477809 + 0.477809i
\(521\) 10.1428 + 10.1428i 0.444364 + 0.444364i 0.893475 0.449112i \(-0.148260\pi\)
−0.449112 + 0.893475i \(0.648260\pi\)
\(522\) 41.3023 41.3023i 1.80775 1.80775i
\(523\) 5.55041 0.242703 0.121351 0.992610i \(-0.461277\pi\)
0.121351 + 0.992610i \(0.461277\pi\)
\(524\) −1.46106 + 1.46106i −0.0638266 + 0.0638266i
\(525\) 111.586i 4.87003i
\(526\) 17.5183 0.763835
\(527\) −3.99703 + 1.96454i −0.174113 + 0.0855766i
\(528\) 15.0924 0.656811
\(529\) 1.13833i 0.0494924i
\(530\) −43.3209 + 43.3209i −1.88174 + 1.88174i
\(531\) 34.0258 1.47659
\(532\) −0.302586 + 0.302586i −0.0131188 + 0.0131188i
\(533\) 6.61296 + 6.61296i 0.286439 + 0.286439i
\(534\) 51.1329 + 51.1329i 2.21274 + 2.21274i
\(535\) 35.1631i 1.52023i
\(536\) 9.62150i 0.415585i
\(537\) 23.9153 + 23.9153i 1.03202 + 1.03202i
\(538\) −29.4782 29.4782i −1.27090 1.27090i
\(539\) −3.18381 + 3.18381i −0.137137 + 0.137137i
\(540\) −2.58546 −0.111260
\(541\) 29.3762 29.3762i 1.26298 1.26298i 0.313340 0.949641i \(-0.398552\pi\)
0.949641 0.313340i \(-0.101448\pi\)
\(542\) 13.2952i 0.571080i
\(543\) −52.8651 −2.26866
\(544\) 1.21382 3.56028i 0.0520420 0.152646i
\(545\) 20.2291 0.866518
\(546\) 17.5657i 0.751741i
\(547\) −21.0425 + 21.0425i −0.899712 + 0.899712i −0.995410 0.0956981i \(-0.969492\pi\)
0.0956981 + 0.995410i \(0.469492\pi\)
\(548\) 0.367640 0.0157048
\(549\) 3.65853 3.65853i 0.156142 0.156142i
\(550\) −17.0048 17.0048i −0.725087 0.725087i
\(551\) −5.22010 5.22010i −0.222384 0.222384i
\(552\) 36.1206i 1.53739i
\(553\) 12.8297i 0.545574i
\(554\) −22.2089 22.2089i −0.943566 0.943566i
\(555\) 53.1389 + 53.1389i 2.25562 + 2.25562i
\(556\) 0.378275 0.378275i 0.0160424 0.0160424i
\(557\) −24.2276 −1.02656 −0.513278 0.858223i \(-0.671569\pi\)
−0.513278 + 0.858223i \(0.671569\pi\)
\(558\) −4.93986 + 4.93986i −0.209121 + 0.209121i
\(559\) 1.35632i 0.0573660i
\(560\) 58.4930 2.47178
\(561\) 13.7063 + 4.67292i 0.578680 + 0.197291i
\(562\) −8.18990 −0.345470
\(563\) 40.7601i 1.71783i −0.512117 0.858916i \(-0.671138\pi\)
0.512117 0.858916i \(-0.328862\pi\)
\(564\) −0.988534 + 0.988534i −0.0416248 + 0.0416248i
\(565\) 67.1848 2.82649
\(566\) −6.24216 + 6.24216i −0.262378 + 0.262378i
\(567\) −6.51884 6.51884i −0.273765 0.273765i
\(568\) −8.22302 8.22302i −0.345030 0.345030i
\(569\) 3.33703i 0.139895i −0.997551 0.0699477i \(-0.977717\pi\)
0.997551 0.0699477i \(-0.0222832\pi\)
\(570\) 13.7405i 0.575524i
\(571\) 10.5154 + 10.5154i 0.440055 + 0.440055i 0.892031 0.451975i \(-0.149280\pi\)
−0.451975 + 0.892031i \(0.649280\pi\)
\(572\) 0.200188 + 0.200188i 0.00837028 + 0.00837028i
\(573\) −34.1675 + 34.1675i −1.42737 + 1.42737i
\(574\) 32.8301 1.37030
\(575\) 44.0088 44.0088i 1.83529 1.83529i
\(576\) 31.9049i 1.32937i
\(577\) −6.20640 −0.258376 −0.129188 0.991620i \(-0.541237\pi\)
−0.129188 + 0.991620i \(0.541237\pi\)
\(578\) 15.2681 19.7890i 0.635070 0.823113i
\(579\) −64.0155 −2.66039
\(580\) 6.13693i 0.254822i
\(581\) −35.3273 + 35.3273i −1.46563 + 1.46563i
\(582\) 29.5973 1.22685
\(583\) 9.05116 9.05116i 0.374861 0.374861i
\(584\) −13.9763 13.9763i −0.578345 0.578345i
\(585\) 17.7327 + 17.7327i 0.733155 + 0.733155i
\(586\) 16.0615i 0.663494i
\(587\) 28.5144i 1.17692i 0.808527 + 0.588458i \(0.200265\pi\)
−0.808527 + 0.588458i \(0.799735\pi\)
\(588\) 1.08427 + 1.08427i 0.0447146 + 0.0447146i
\(589\) 0.624336 + 0.624336i 0.0257253 + 0.0257253i
\(590\) 33.8019 33.8019i 1.39160 1.39160i
\(591\) −30.8300 −1.26818
\(592\) −19.9721 + 19.9721i −0.820848 + 0.820848i
\(593\) 36.4712i 1.49769i −0.662744 0.748846i \(-0.730608\pi\)
0.662744 0.748846i \(-0.269392\pi\)
\(594\) 7.22323 0.296373
\(595\) 53.1210 + 18.1107i 2.17775 + 0.742466i
\(596\) −0.865438 −0.0354497
\(597\) 51.6046i 2.11204i
\(598\) −6.92776 + 6.92776i −0.283297 + 0.283297i
\(599\) 17.5141 0.715606 0.357803 0.933797i \(-0.383526\pi\)
0.357803 + 0.933797i \(0.383526\pi\)
\(600\) 65.8548 65.8548i 2.68851 2.68851i
\(601\) 8.37503 + 8.37503i 0.341625 + 0.341625i 0.856978 0.515353i \(-0.172339\pi\)
−0.515353 + 0.856978i \(0.672339\pi\)
\(602\) −3.36672 3.36672i −0.137217 0.137217i
\(603\) 15.6589i 0.637678i
\(604\) 3.50509i 0.142620i
\(605\) −27.7389 27.7389i −1.12775 1.12775i
\(606\) −24.5960 24.5960i −0.999143 0.999143i
\(607\) 27.9449 27.9449i 1.13425 1.13425i 0.144787 0.989463i \(-0.453750\pi\)
0.989463 0.144787i \(-0.0462496\pi\)
\(608\) −0.745715 −0.0302427
\(609\) −56.2541 + 56.2541i −2.27953 + 2.27953i
\(610\) 7.26892i 0.294310i
\(611\) 4.31206 0.174447
\(612\) 0.946135 2.77514i 0.0382452 0.112178i
\(613\) 28.4140 1.14763 0.573815 0.818985i \(-0.305463\pi\)
0.573815 + 0.818985i \(0.305463\pi\)
\(614\) 7.68007i 0.309942i
\(615\) 55.7452 55.7452i 2.24786 2.24786i
\(616\) −11.3016 −0.455355
\(617\) −3.44087 + 3.44087i −0.138524 + 0.138524i −0.772969 0.634444i \(-0.781229\pi\)
0.634444 + 0.772969i \(0.281229\pi\)
\(618\) 2.89597 + 2.89597i 0.116493 + 0.116493i
\(619\) 15.1093 + 15.1093i 0.607296 + 0.607296i 0.942239 0.334943i \(-0.108717\pi\)
−0.334943 + 0.942239i \(0.608717\pi\)
\(620\) 0.733991i 0.0294778i
\(621\) 18.6939i 0.750160i
\(622\) 6.97989 + 6.97989i 0.279868 + 0.279868i
\(623\) −41.4051 41.4051i −1.65886 1.65886i
\(624\) −11.2101 + 11.2101i −0.448765 + 0.448765i
\(625\) −72.1341 −2.88536
\(626\) −1.81580 + 1.81580i −0.0725740 + 0.0725740i
\(627\) 2.87083i 0.114650i
\(628\) 1.39966 0.0558523
\(629\) −24.3217 + 11.9541i −0.969768 + 0.476640i
\(630\) 88.0340 3.50736
\(631\) 3.12241i 0.124301i −0.998067 0.0621507i \(-0.980204\pi\)
0.998067 0.0621507i \(-0.0197959\pi\)
\(632\) 7.57168 7.57168i 0.301185 0.301185i
\(633\) −75.4758 −2.99990
\(634\) −15.7124 + 15.7124i −0.624021 + 0.624021i
\(635\) −59.8553 59.8553i −2.37529 2.37529i
\(636\) −3.08244 3.08244i −0.122227 0.122227i
\(637\) 4.72968i 0.187397i
\(638\) 17.1453i 0.678788i
\(639\) −13.3828 13.3828i −0.529417 0.529417i
\(640\) 37.1180 + 37.1180i 1.46722 + 1.46722i
\(641\) 21.2253 21.2253i 0.838350 0.838350i −0.150292 0.988642i \(-0.548021\pi\)
0.988642 + 0.150292i \(0.0480213\pi\)
\(642\) −33.4557 −1.32039
\(643\) −28.0083 + 28.0083i −1.10454 + 1.10454i −0.110682 + 0.993856i \(0.535303\pi\)
−0.993856 + 0.110682i \(0.964697\pi\)
\(644\) 2.57207i 0.101354i
\(645\) −11.4333 −0.450187
\(646\) −4.69002 1.59898i −0.184526 0.0629111i
\(647\) −27.1090 −1.06576 −0.532882 0.846190i \(-0.678891\pi\)
−0.532882 + 0.846190i \(0.678891\pi\)
\(648\) 7.69442i 0.302265i
\(649\) −7.06233 + 7.06233i −0.277221 + 0.277221i
\(650\) 25.2613 0.990829
\(651\) 6.72813 6.72813i 0.263696 0.263696i
\(652\) −1.27358 1.27358i −0.0498774 0.0498774i
\(653\) 8.45209 + 8.45209i 0.330756 + 0.330756i 0.852873 0.522118i \(-0.174858\pi\)
−0.522118 + 0.852873i \(0.674858\pi\)
\(654\) 19.2469i 0.752612i
\(655\) 53.7246i 2.09919i
\(656\) 20.9517 + 20.9517i 0.818026 + 0.818026i
\(657\) −22.7463 22.7463i −0.887418 0.887418i
\(658\) 10.7036 10.7036i 0.417271 0.417271i
\(659\) 21.1848 0.825242 0.412621 0.910903i \(-0.364613\pi\)
0.412621 + 0.910903i \(0.364613\pi\)
\(660\) 1.68752 1.68752i 0.0656868 0.0656868i
\(661\) 9.03316i 0.351349i 0.984448 + 0.175675i \(0.0562107\pi\)
−0.984448 + 0.175675i \(0.943789\pi\)
\(662\) −10.7310 −0.417073
\(663\) −13.6515 + 6.70970i −0.530181 + 0.260583i
\(664\) −41.6982 −1.61820
\(665\) 11.1264i 0.431463i
\(666\) −30.0587 + 30.0587i −1.16475 + 1.16475i
\(667\) −44.3724 −1.71811
\(668\) 0.0879781 0.0879781i 0.00340397 0.00340397i
\(669\) 23.8802 + 23.8802i 0.923260 + 0.923260i
\(670\) 15.5558 + 15.5558i 0.600974 + 0.600974i
\(671\) 1.51872i 0.0586294i
\(672\) 8.03615i 0.310001i
\(673\) 27.8567 + 27.8567i 1.07380 + 1.07380i 0.997051 + 0.0767481i \(0.0244537\pi\)
0.0767481 + 0.997051i \(0.475546\pi\)
\(674\) −10.7823 10.7823i −0.415319 0.415319i
\(675\) 34.0825 34.0825i 1.31184 1.31184i
\(676\) 1.80418 0.0693917
\(677\) −18.9507 + 18.9507i −0.728333 + 0.728333i −0.970288 0.241955i \(-0.922211\pi\)
0.241955 + 0.970288i \(0.422211\pi\)
\(678\) 63.9227i 2.45494i
\(679\) −23.9666 −0.919753
\(680\) 20.6620 + 42.0387i 0.792351 + 1.61211i
\(681\) 33.3723 1.27883
\(682\) 2.05062i 0.0785221i
\(683\) −25.6754 + 25.6754i −0.982443 + 0.982443i −0.999849 0.0174057i \(-0.994459\pi\)
0.0174057 + 0.999849i \(0.494459\pi\)
\(684\) −0.581263 −0.0222251
\(685\) −6.75924 + 6.75924i −0.258257 + 0.258257i
\(686\) 11.8268 + 11.8268i 0.451549 + 0.451549i
\(687\) 40.2355 + 40.2355i 1.53508 + 1.53508i
\(688\) 4.29718i 0.163829i
\(689\) 13.4458i 0.512246i
\(690\) 58.3989 + 58.3989i 2.22321 + 2.22321i
\(691\) −21.6577 21.6577i −0.823896 0.823896i 0.162768 0.986664i \(-0.447958\pi\)
−0.986664 + 0.162768i \(0.947958\pi\)
\(692\) 2.39595 2.39595i 0.0910803 0.0910803i
\(693\) −18.3932 −0.698700
\(694\) 33.9321 33.9321i 1.28804 1.28804i
\(695\) 13.9096i 0.527620i
\(696\) −66.3988 −2.51684
\(697\) 12.5404 + 25.5146i 0.475002 + 0.966434i
\(698\) 38.2495 1.44777
\(699\) 37.6659i 1.42466i
\(700\) 4.68938 4.68938i 0.177242 0.177242i
\(701\) 15.8083 0.597070 0.298535 0.954399i \(-0.403502\pi\)
0.298535 + 0.954399i \(0.403502\pi\)
\(702\) −5.36519 + 5.36519i −0.202496 + 0.202496i
\(703\) 3.79904 + 3.79904i 0.143284 + 0.143284i
\(704\) −6.62213 6.62213i −0.249581 0.249581i
\(705\) 36.3494i 1.36900i
\(706\) 9.57570i 0.360386i
\(707\) 19.9167 + 19.9167i 0.749045 + 0.749045i
\(708\) 2.40513 + 2.40513i 0.0903903 + 0.0903903i
\(709\) 18.9139 18.9139i 0.710325 0.710325i −0.256278 0.966603i \(-0.582496\pi\)
0.966603 + 0.256278i \(0.0824962\pi\)
\(710\) −26.5896 −0.997889
\(711\) 12.3228 12.3228i 0.462141 0.462141i
\(712\) 48.8720i 1.83155i
\(713\) 5.30704 0.198750
\(714\) −17.2313 + 50.5418i −0.644867 + 1.89148i
\(715\) −7.36111 −0.275290
\(716\) 2.01006i 0.0751196i
\(717\) 44.5897 44.5897i 1.66523 1.66523i
\(718\) 7.29069 0.272086
\(719\) 3.51866 3.51866i 0.131224 0.131224i −0.638444 0.769668i \(-0.720422\pi\)
0.769668 + 0.638444i \(0.220422\pi\)
\(720\) 56.1820 + 56.1820i 2.09378 + 2.09378i
\(721\) −2.34502 2.34502i −0.0873332 0.0873332i
\(722\) 26.9526i 1.00307i
\(723\) 34.3377i 1.27703i
\(724\) −2.22164 2.22164i −0.0825666 0.0825666i
\(725\) 80.8994 + 80.8994i 3.00453 + 3.00453i
\(726\) 26.3920 26.3920i 0.979500 0.979500i
\(727\) −25.2428 −0.936204 −0.468102 0.883674i \(-0.655062\pi\)
−0.468102 + 0.883674i \(0.655062\pi\)
\(728\) 8.39448 8.39448i 0.311120 0.311120i
\(729\) 43.5716i 1.61376i
\(730\) −45.1933 −1.67268
\(731\) 1.33050 3.90253i 0.0492104 0.144340i
\(732\) 0.517210 0.0191166
\(733\) 9.86420i 0.364343i 0.983267 + 0.182171i \(0.0583125\pi\)
−0.983267 + 0.182171i \(0.941687\pi\)
\(734\) −13.1129 + 13.1129i −0.484004 + 0.484004i
\(735\) −39.8698 −1.47062
\(736\) −3.16940 + 3.16940i −0.116825 + 0.116825i
\(737\) −3.25012 3.25012i −0.119720 0.119720i
\(738\) 31.5330 + 31.5330i 1.16075 + 1.16075i
\(739\) 30.7198i 1.13005i 0.825075 + 0.565024i \(0.191133\pi\)
−0.825075 + 0.565024i \(0.808867\pi\)
\(740\) 4.46629i 0.164184i
\(741\) 2.13237 + 2.13237i 0.0783344 + 0.0783344i
\(742\) 33.3760 + 33.3760i 1.22527 + 1.22527i
\(743\) −12.9858 + 12.9858i −0.476403 + 0.476403i −0.903979 0.427577i \(-0.859367\pi\)
0.427577 + 0.903979i \(0.359367\pi\)
\(744\) 7.94145 0.291148
\(745\) 15.9115 15.9115i 0.582953 0.582953i
\(746\) 17.5947i 0.644186i
\(747\) −67.8632 −2.48298
\(748\) 0.379624 + 0.772380i 0.0138804 + 0.0282410i
\(749\) 27.0910 0.989882
\(750\) 128.895i 4.70659i
\(751\) 21.4129 21.4129i 0.781368 0.781368i −0.198694 0.980062i \(-0.563670\pi\)
0.980062 + 0.198694i \(0.0636699\pi\)
\(752\) 13.6618 0.498195
\(753\) 8.18017 8.18017i 0.298102 0.298102i
\(754\) −12.7350 12.7350i −0.463781 0.463781i
\(755\) 64.4429 + 64.4429i 2.34532 + 2.34532i
\(756\) 1.99194i 0.0724460i
\(757\) 26.9588i 0.979835i 0.871769 + 0.489917i \(0.162973\pi\)
−0.871769 + 0.489917i \(0.837027\pi\)
\(758\) 16.1086 + 16.1086i 0.585091 + 0.585091i
\(759\) −12.2015 12.2015i −0.442885 0.442885i
\(760\) 6.56645 6.56645i 0.238190 0.238190i
\(761\) −46.1263 −1.67208 −0.836039 0.548670i \(-0.815134\pi\)
−0.836039 + 0.548670i \(0.815134\pi\)
\(762\) 56.9491 56.9491i 2.06305 2.06305i
\(763\) 15.5852i 0.564224i
\(764\) −2.87176 −0.103897
\(765\) 33.6271 + 68.4174i 1.21579 + 2.47364i
\(766\) 3.35182 0.121106
\(767\) 10.4914i 0.378821i
\(768\) −7.41496 + 7.41496i −0.267564 + 0.267564i
\(769\) 12.5039 0.450900 0.225450 0.974255i \(-0.427615\pi\)
0.225450 + 0.974255i \(0.427615\pi\)
\(770\) −18.2722 + 18.2722i −0.658484 + 0.658484i
\(771\) 13.7835 + 13.7835i 0.496401 + 0.496401i
\(772\) −2.69023 2.69023i −0.0968234 0.0968234i
\(773\) 33.6746i 1.21119i 0.795773 + 0.605595i \(0.207065\pi\)
−0.795773 + 0.605595i \(0.792935\pi\)
\(774\) 6.46741i 0.232466i
\(775\) −9.67576 9.67576i −0.347564 0.347564i
\(776\) −14.1443 14.1443i −0.507751 0.507751i
\(777\) 40.9402 40.9402i 1.46872 1.46872i
\(778\) −12.2811 −0.440297
\(779\) 3.98538 3.98538i 0.142791 0.142791i
\(780\) 2.50688i 0.0897608i
\(781\) 5.55544 0.198789
\(782\) −26.7292 + 13.1374i −0.955834 + 0.469792i
\(783\) −34.3641 −1.22807
\(784\) 14.9849i 0.535177i
\(785\) −25.7334 + 25.7334i −0.918463 + 0.918463i
\(786\) 51.1160 1.82325
\(787\) 2.38770 2.38770i 0.0851123 0.0851123i −0.663269 0.748381i \(-0.730831\pi\)
0.748381 + 0.663269i \(0.230831\pi\)
\(788\) −1.29562 1.29562i −0.0461545 0.0461545i
\(789\) −22.9174 22.9174i −0.815881 0.815881i
\(790\) 24.4834i 0.871081i
\(791\) 51.7617i 1.84044i
\(792\) −10.8551 10.8551i −0.385719 0.385719i
\(793\) −1.12806 1.12806i −0.0400584 0.0400584i
\(794\) 37.1734 37.1734i 1.31923 1.31923i
\(795\) 113.344 4.01991
\(796\) −2.16867 + 2.16867i −0.0768664 + 0.0768664i
\(797\) 15.6916i 0.555827i 0.960606 + 0.277913i \(0.0896428\pi\)
−0.960606 + 0.277913i \(0.910357\pi\)
\(798\) 10.5862 0.374746
\(799\) 12.4071 + 4.22999i 0.438932 + 0.149646i
\(800\) 11.5568 0.408596
\(801\) 79.5385i 2.81035i
\(802\) 6.42564 6.42564i 0.226897 0.226897i
\(803\) 9.44236 0.333214
\(804\) −1.10685 + 1.10685i −0.0390357 + 0.0390357i
\(805\) −47.2888 47.2888i −1.66671 1.66671i
\(806\) 1.52313 + 1.52313i 0.0536501 + 0.0536501i
\(807\) 77.1266i 2.71498i
\(808\) 23.5084i 0.827024i
\(809\) 1.94966 + 1.94966i 0.0685465 + 0.0685465i 0.740549 0.672002i \(-0.234566\pi\)
−0.672002 + 0.740549i \(0.734566\pi\)
\(810\) −12.4402 12.4402i −0.437103 0.437103i
\(811\) −3.02126 + 3.02126i −0.106091 + 0.106091i −0.758160 0.652069i \(-0.773901\pi\)
0.652069 + 0.758160i \(0.273901\pi\)
\(812\) −4.72812 −0.165925
\(813\) −17.3928 + 17.3928i −0.609992 + 0.609992i
\(814\) 12.4779i 0.437349i
\(815\) 46.8310 1.64042
\(816\) −43.2518 + 21.2582i −1.51412 + 0.744187i
\(817\) −0.817400 −0.0285972
\(818\) 18.0775i 0.632064i
\(819\) 13.6619 13.6619i 0.477386 0.477386i
\(820\) 4.68535 0.163620
\(821\) −14.2140 + 14.2140i −0.496073 + 0.496073i −0.910213 0.414140i \(-0.864082\pi\)
0.414140 + 0.910213i \(0.364082\pi\)
\(822\) −6.43105 6.43105i −0.224309 0.224309i
\(823\) −34.0421 34.0421i −1.18663 1.18663i −0.977993 0.208639i \(-0.933097\pi\)
−0.208639 0.977993i \(-0.566903\pi\)
\(824\) 2.76792i 0.0964250i
\(825\) 44.4912i 1.54899i
\(826\) −26.0423 26.0423i −0.906126 0.906126i
\(827\) 31.9868 + 31.9868i 1.11229 + 1.11229i 0.992840 + 0.119450i \(0.0381132\pi\)
0.119450 + 0.992840i \(0.461887\pi\)
\(828\) −2.47045 + 2.47045i −0.0858541 + 0.0858541i
\(829\) 36.4960 1.26756 0.633780 0.773514i \(-0.281503\pi\)
0.633780 + 0.773514i \(0.281503\pi\)
\(830\) −67.4166 + 67.4166i −2.34007 + 2.34007i
\(831\) 58.1072i 2.01572i
\(832\) 9.83742 0.341051
\(833\) 4.63966 13.6087i 0.160755 0.471515i
\(834\) −13.2342 −0.458262
\(835\) 3.23504i 0.111953i
\(836\) 0.120646 0.120646i 0.00417262 0.00417262i
\(837\) 4.11003 0.142063
\(838\) −29.9678 + 29.9678i −1.03522 + 1.03522i
\(839\) 28.9206 + 28.9206i 0.998450 + 0.998450i 0.999999 0.00154859i \(-0.000492930\pi\)
−0.00154859 + 0.999999i \(0.500493\pi\)
\(840\) −70.7630 70.7630i −2.44155 2.44155i
\(841\) 52.5677i 1.81268i
\(842\) 36.7806i 1.26754i
\(843\) 10.7140 + 10.7140i 0.369009 + 0.369009i
\(844\) −3.17185 3.17185i −0.109179 0.109179i
\(845\) −33.1708 + 33.1708i −1.14111 + 1.14111i
\(846\) 20.5615 0.706919
\(847\) −21.3711 + 21.3711i −0.734319 + 0.734319i
\(848\) 42.6002i 1.46290i
\(849\) 16.3319 0.560511
\(850\) 72.6844 + 24.7805i 2.49305 + 0.849964i
\(851\) 32.2930 1.10699
\(852\) 1.89195i 0.0648170i
\(853\) −15.9773 + 15.9773i −0.547053 + 0.547053i −0.925587 0.378534i \(-0.876428\pi\)
0.378534 + 0.925587i \(0.376428\pi\)
\(854\) −5.60025 −0.191637
\(855\) 10.6868 10.6868i 0.365481 0.365481i
\(856\) 15.9882 + 15.9882i 0.546466 + 0.546466i
\(857\) −9.51312 9.51312i −0.324962 0.324962i 0.525705 0.850667i \(-0.323802\pi\)
−0.850667 + 0.525705i \(0.823802\pi\)
\(858\) 7.00370i 0.239102i
\(859\) 20.1251i 0.686661i −0.939215 0.343330i \(-0.888445\pi\)
0.939215 0.343330i \(-0.111555\pi\)
\(860\) −0.480482 0.480482i −0.0163843 0.0163843i
\(861\) −42.9482 42.9482i −1.46367 1.46367i
\(862\) −28.7921 + 28.7921i −0.980663 + 0.980663i
\(863\) 35.6708 1.21425 0.607123 0.794607i \(-0.292323\pi\)
0.607123 + 0.794607i \(0.292323\pi\)
\(864\) −2.45453 + 2.45453i −0.0835049 + 0.0835049i
\(865\) 88.1015i 2.99554i
\(866\) 11.8078 0.401244
\(867\) −45.8616 + 5.91418i −1.55754 + 0.200856i
\(868\) 0.565495 0.0191941
\(869\) 5.11539i 0.173528i
\(870\) −107.352 + 107.352i −3.63958 + 3.63958i
\(871\) 4.82818 0.163597
\(872\) 9.19792 9.19792i 0.311481 0.311481i
\(873\) −23.0197 23.0197i −0.779098 0.779098i
\(874\) 4.17510 + 4.17510i 0.141225 + 0.141225i
\(875\) 104.374i 3.52847i
\(876\) 3.21567i 0.108647i
\(877\) 16.9503 + 16.9503i 0.572371 + 0.572371i 0.932790 0.360419i \(-0.117366\pi\)
−0.360419 + 0.932790i \(0.617366\pi\)
\(878\) −19.5524 19.5524i −0.659861 0.659861i
\(879\) 21.0116 21.0116i 0.708703 0.708703i
\(880\) −23.3221 −0.786187
\(881\) −22.8512 + 22.8512i −0.769878 + 0.769878i −0.978085 0.208207i \(-0.933237\pi\)
0.208207 + 0.978085i \(0.433237\pi\)
\(882\) 22.5529i 0.759394i
\(883\) 29.5980 0.996052 0.498026 0.867162i \(-0.334058\pi\)
0.498026 + 0.867162i \(0.334058\pi\)
\(884\) −0.855673 0.291727i −0.0287794 0.00981184i
\(885\) −88.4390 −2.97285
\(886\) 16.3371i 0.548856i
\(887\) 32.6533 32.6533i 1.09639 1.09639i 0.101560 0.994829i \(-0.467616\pi\)
0.994829 0.101560i \(-0.0323835\pi\)
\(888\) 48.3232 1.62162
\(889\) −46.1148 + 46.1148i −1.54664 + 1.54664i
\(890\) −79.0151 79.0151i −2.64859 2.64859i
\(891\) 2.59916 + 2.59916i 0.0870751 + 0.0870751i
\(892\) 2.00711i 0.0672031i
\(893\) 2.59872i 0.0869627i
\(894\) 15.1389 + 15.1389i 0.506322 + 0.506322i
\(895\) −36.9560 36.9560i −1.23530 1.23530i
\(896\) 28.5971 28.5971i 0.955364 0.955364i
\(897\) 18.1257 0.605201
\(898\) −4.36205 + 4.36205i −0.145563 + 0.145563i
\(899\) 9.75569i 0.325371i
\(900\) 9.00822 0.300274
\(901\) −13.1899 + 38.6878i −0.439420 + 1.28888i
\(902\) −13.0899 −0.435845
\(903\) 8.80867i 0.293134i
\(904\) 30.5481 30.5481i 1.01602 1.01602i
\(905\) 81.6919 2.71553
\(906\) −61.3139 + 61.3139i −2.03702 + 2.03702i
\(907\) 6.19267 + 6.19267i 0.205624 + 0.205624i 0.802405 0.596780i \(-0.203554\pi\)
−0.596780 + 0.802405i \(0.703554\pi\)
\(908\) 1.40246 + 1.40246i 0.0465423 + 0.0465423i
\(909\) 38.2596i 1.26899i
\(910\) 27.1440i 0.899816i
\(911\) 2.83118 + 2.83118i 0.0938011 + 0.0938011i 0.752450 0.658649i \(-0.228872\pi\)
−0.658649 + 0.752450i \(0.728872\pi\)
\(912\) 6.75593 + 6.75593i 0.223711 + 0.223711i
\(913\) 14.0856 14.0856i 0.466164 0.466164i
\(914\) −31.9090 −1.05546
\(915\) −9.50917 + 9.50917i −0.314364 + 0.314364i
\(916\) 3.38177i 0.111737i
\(917\) −41.3914 −1.36687
\(918\) −20.7004 + 10.1742i −0.683214 + 0.335799i
\(919\) −23.6469 −0.780038 −0.390019 0.920807i \(-0.627532\pi\)
−0.390019 + 0.920807i \(0.627532\pi\)
\(920\) 55.8167i 1.84022i
\(921\) −10.0470 + 10.0470i −0.331061 + 0.331061i
\(922\) −34.7968 −1.14597
\(923\) −4.12641 + 4.12641i −0.135822 + 0.135822i
\(924\) −1.30013 1.30013i −0.0427712 0.0427712i
\(925\) −58.8763 58.8763i −1.93584 1.93584i
\(926\) 9.88311i 0.324779i
\(927\) 4.50475i 0.147955i
\(928\) −5.82615 5.82615i −0.191253 0.191253i
\(929\) −35.5615 35.5615i −1.16674 1.16674i −0.982970 0.183766i \(-0.941171\pi\)
−0.183766 0.982970i \(-0.558829\pi\)
\(930\) 12.8396 12.8396i 0.421026 0.421026i
\(931\) −2.85040 −0.0934181
\(932\) −1.58290 + 1.58290i −0.0518495 + 0.0518495i
\(933\) 18.2621i 0.597875i
\(934\) 12.9135 0.422542
\(935\) −21.1802 7.22102i −0.692666 0.236152i
\(936\) 16.1256 0.527083
\(937\) 36.0462i 1.17758i 0.808287 + 0.588789i \(0.200395\pi\)
−0.808287 + 0.588789i \(0.799605\pi\)
\(938\) 11.9848 11.9848i 0.391317 0.391317i
\(939\) 4.75085 0.155038
\(940\) 1.52757 1.52757i 0.0498238 0.0498238i
\(941\) 3.51654 + 3.51654i 0.114636 + 0.114636i 0.762098 0.647462i \(-0.224170\pi\)
−0.647462 + 0.762098i \(0.724170\pi\)
\(942\) −24.4839 24.4839i −0.797728 0.797728i
\(943\) 33.8769i 1.10318i
\(944\) 33.2396i 1.08186i
\(945\) −36.6227 36.6227i −1.19134 1.19134i
\(946\) 1.34236 + 1.34236i 0.0436440 + 0.0436440i
\(947\) −5.37400 + 5.37400i −0.174632 + 0.174632i −0.789011 0.614379i \(-0.789407\pi\)
0.614379 + 0.789011i \(0.289407\pi\)
\(948\) 1.74209 0.0565803
\(949\) −7.01350 + 7.01350i −0.227668 + 0.227668i
\(950\) 15.2240i 0.493932i
\(951\) 41.1099 1.33308
\(952\) 32.3882 15.9188i 1.04971 0.515931i
\(953\) −54.4092 −1.76249 −0.881244 0.472662i \(-0.843293\pi\)
−0.881244 + 0.472662i \(0.843293\pi\)
\(954\) 64.1148i 2.07579i
\(955\) 52.7987 52.7987i 1.70853 1.70853i
\(956\) 3.74773 0.121210
\(957\) 22.4294 22.4294i 0.725039 0.725039i
\(958\) 28.2308 + 28.2308i 0.912097 + 0.912097i
\(959\) 5.20757 + 5.20757i 0.168161 + 0.168161i
\(960\) 82.9265i 2.67644i
\(961\) 29.8332i 0.962361i
\(962\) 9.26816 + 9.26816i 0.298818 + 0.298818i
\(963\) 26.0206 + 26.0206i 0.838503 + 0.838503i
\(964\) 1.44303 1.44303i 0.0464769 0.0464769i
\(965\) 98.9224 3.18442
\(966\) 44.9927 44.9927i 1.44762 1.44762i
\(967\) 0.142538i 0.00458372i −0.999997 0.00229186i \(-0.999270\pi\)
0.999997 0.00229186i \(-0.000729522\pi\)
\(968\) −25.2251 −0.810764
\(969\) 4.04369 + 8.22725i 0.129902 + 0.264297i
\(970\) −45.7364 −1.46851
\(971\) 38.4708i 1.23459i 0.786733 + 0.617293i \(0.211771\pi\)
−0.786733 + 0.617293i \(0.788229\pi\)
\(972\) 2.18999 2.18999i 0.0702440 0.0702440i
\(973\) 10.7165 0.343554
\(974\) 1.65017 1.65017i 0.0528748 0.0528748i
\(975\) −33.0467 33.0467i −1.05834 1.05834i
\(976\) −3.57400 3.57400i −0.114401 0.114401i
\(977\) 2.52641i 0.0808272i −0.999183 0.0404136i \(-0.987132\pi\)
0.999183 0.0404136i \(-0.0128675\pi\)
\(978\) 44.5571i 1.42478i
\(979\) 16.5089 + 16.5089i 0.527625 + 0.527625i
\(980\) −1.67551 1.67551i −0.0535223 0.0535223i
\(981\) 14.9695 14.9695i 0.477939 0.477939i
\(982\) 22.3782 0.714118
\(983\) −23.3424 + 23.3424i −0.744508 + 0.744508i −0.973442 0.228934i \(-0.926476\pi\)
0.228934 + 0.973442i \(0.426476\pi\)
\(984\) 50.6934i 1.61605i
\(985\) 47.6412 1.51798
\(986\) −24.1498 49.1350i −0.769087 1.56478i
\(987\) −28.0049 −0.891407
\(988\) 0.179224i 0.00570187i
\(989\) −3.47407 + 3.47407i −0.110469 + 0.110469i
\(990\) −35.1005 −1.11557
\(991\) −29.4543 + 29.4543i −0.935648 + 0.935648i −0.998051 0.0624028i \(-0.980124\pi\)
0.0624028 + 0.998051i \(0.480124\pi\)
\(992\) 0.696822 + 0.696822i 0.0221241 + 0.0221241i
\(993\) 14.0383 + 14.0383i 0.445492 + 0.445492i
\(994\) 20.4856i 0.649764i
\(995\) 79.7440i 2.52806i
\(996\) −4.79694 4.79694i −0.151997 0.151997i
\(997\) −32.4123 32.4123i −1.02651 1.02651i −0.999639 0.0268686i \(-0.991446\pi\)
−0.0268686 0.999639i \(-0.508554\pi\)
\(998\) −22.9882 + 22.9882i −0.727680 + 0.727680i
\(999\) 25.0092 0.791257
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 731.2.f.c.259.10 56
17.13 even 4 inner 731.2.f.c.302.19 yes 56
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
731.2.f.c.259.10 56 1.1 even 1 trivial
731.2.f.c.302.19 yes 56 17.13 even 4 inner