Properties

Label 370.2.q.d.273.1
Level $370$
Weight $2$
Character 370.273
Analytic conductor $2.954$
Analytic rank $0$
Dimension $12$
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] = [370,2,Mod(97,370)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(370, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([3, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("370.97");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 370 = 2 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 370.q (of order \(12\), degree \(4\), 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: \(2.95446487479\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(3\) over \(\Q(\zeta_{12})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 2x^{11} - 4x^{10} + 6x^{8} + 44x^{7} + 56x^{6} + 32x^{5} + 92x^{4} - 16x^{3} + 36x^{2} - 24x + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 273.1
Root \(-0.208144 + 0.776804i\) of defining polynomial
Character \(\chi\) \(=\) 370.273
Dual form 370.2.q.d.267.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-2.78144 - 0.745286i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.02520 - 0.947920i) q^{5} +(2.03616 - 2.03616i) q^{6} +(-4.90683 - 1.31478i) q^{7} +1.00000 q^{8} +(4.58291 + 2.64594i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-2.78144 - 0.745286i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.02520 - 0.947920i) q^{5} +(2.03616 - 2.03616i) q^{6} +(-4.90683 - 1.31478i) q^{7} +1.00000 q^{8} +(4.58291 + 2.64594i) q^{9} +(1.83352 - 1.27992i) q^{10} -0.446393i q^{11} +(0.745286 + 2.78144i) q^{12} +(2.31524 + 4.01012i) q^{13} +(3.59205 - 3.59205i) q^{14} +(4.92652 + 4.14594i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.535731 - 0.309305i) q^{17} +(-4.58291 + 2.64594i) q^{18} +(1.21232 - 4.52445i) q^{19} +(0.191679 + 2.22784i) q^{20} +(12.6682 + 7.31397i) q^{21} +(0.386587 + 0.223196i) q^{22} +2.27723 q^{23} +(-2.78144 - 0.745286i) q^{24} +(3.20289 + 3.83946i) q^{25} -4.63048 q^{26} +(-4.66664 - 4.66664i) q^{27} +(1.31478 + 4.90683i) q^{28} +(-4.05041 + 4.05041i) q^{29} +(-6.05375 + 2.19352i) q^{30} +(0.176164 + 0.176164i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.332690 + 1.24162i) q^{33} +(0.535731 - 0.309305i) q^{34} +(8.69101 + 7.31397i) q^{35} -5.29189i q^{36} +(-3.72164 - 4.81138i) q^{37} +(3.31213 + 3.31213i) q^{38} +(-3.45103 - 12.8794i) q^{39} +(-2.02520 - 0.947920i) q^{40} +(-3.38733 + 1.95567i) q^{41} +(-12.6682 + 7.31397i) q^{42} +8.15549 q^{43} +(-0.386587 + 0.223196i) q^{44} +(-6.77317 - 9.70280i) q^{45} +(-1.13862 + 1.97214i) q^{46} +(-6.46505 + 6.46505i) q^{47} +(2.03616 - 2.03616i) q^{48} +(16.2861 + 9.40279i) q^{49} +(-4.92652 + 0.854057i) q^{50} +(1.25959 + 1.25959i) q^{51} +(2.31524 - 4.01012i) q^{52} +(8.08498 - 2.16636i) q^{53} +(6.37475 - 1.70811i) q^{54} +(-0.423145 + 0.904036i) q^{55} +(-4.90683 - 1.31478i) q^{56} +(-6.74402 + 11.6810i) q^{57} +(-1.48255 - 5.53296i) q^{58} +(-3.85140 + 1.03198i) q^{59} +(1.12723 - 6.33946i) q^{60} +(2.05254 - 7.66019i) q^{61} +(-0.240645 + 0.0644806i) q^{62} +(-19.0087 - 19.0087i) q^{63} +1.00000 q^{64} +(-0.887564 - 10.3160i) q^{65} +(-0.908926 - 0.908926i) q^{66} +(3.53962 - 13.2100i) q^{67} +0.618609i q^{68} +(-6.33399 - 1.69719i) q^{69} +(-10.6796 + 3.86965i) q^{70} +(7.60300 + 13.1688i) q^{71} +(4.58291 + 2.64594i) q^{72} +(0.847559 - 0.847559i) q^{73} +(6.02760 - 0.817343i) q^{74} +(-6.04718 - 13.0663i) q^{75} +(-4.52445 + 1.21232i) q^{76} +(-0.586908 + 2.19037i) q^{77} +(12.8794 + 3.45103i) q^{78} +(-2.81870 + 10.5195i) q^{79} +(1.83352 - 1.27992i) q^{80} +(1.56420 + 2.70927i) q^{81} -3.91135i q^{82} +(-9.97712 + 2.67336i) q^{83} -14.6279i q^{84} +(0.791768 + 1.13423i) q^{85} +(-4.07774 + 7.06286i) q^{86} +(14.2847 - 8.24727i) q^{87} -0.446393i q^{88} +(0.257339 + 0.960403i) q^{89} +(11.7895 - 1.01434i) q^{90} +(-6.08807 - 22.7210i) q^{91} +(-1.13862 - 1.97214i) q^{92} +(-0.358698 - 0.621284i) q^{93} +(-2.36637 - 8.83142i) q^{94} +(-6.74402 + 8.01375i) q^{95} +(0.745286 + 2.78144i) q^{96} +3.22099i q^{97} +(-16.2861 + 9.40279i) q^{98} +(1.18113 - 2.04578i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 6 q^{2} - 6 q^{4} + 2 q^{5} + 6 q^{6} - 4 q^{7} + 12 q^{8} + 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 6 q^{2} - 6 q^{4} + 2 q^{5} + 6 q^{6} - 4 q^{7} + 12 q^{8} + 18 q^{9} - 4 q^{10} - 6 q^{12} + 8 q^{14} - 10 q^{15} - 6 q^{16} - 12 q^{17} - 18 q^{18} - 8 q^{19} + 2 q^{20} + 54 q^{21} - 6 q^{22} - 4 q^{23} - 14 q^{25} + 18 q^{27} - 4 q^{28} + 4 q^{29} - 4 q^{30} - 2 q^{31} - 6 q^{32} + 20 q^{33} + 12 q^{34} + 6 q^{35} + 14 q^{37} + 16 q^{38} - 30 q^{39} + 2 q^{40} + 12 q^{41} - 54 q^{42} + 44 q^{43} + 6 q^{44} - 60 q^{45} + 2 q^{46} - 28 q^{47} + 6 q^{48} + 24 q^{49} + 10 q^{50} - 8 q^{51} + 8 q^{53} - 18 q^{54} - 4 q^{56} - 28 q^{57} - 14 q^{58} + 14 q^{60} + 24 q^{61} - 14 q^{62} + 8 q^{63} + 12 q^{64} - 10 q^{65} + 8 q^{66} + 18 q^{67} - 40 q^{69} - 30 q^{70} + 18 q^{72} - 28 q^{73} + 38 q^{74} - 30 q^{75} - 8 q^{76} + 10 q^{77} + 48 q^{78} - 56 q^{79} - 4 q^{80} + 4 q^{81} + 14 q^{83} - 28 q^{85} - 22 q^{86} + 18 q^{87} - 2 q^{89} + 18 q^{90} + 38 q^{91} + 2 q^{92} - 16 q^{94} - 28 q^{95} - 6 q^{96} - 24 q^{98} + 28 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/370\mathbb{Z}\right)^\times\).

\(n\) \(261\) \(297\)
\(\chi(n)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) −2.78144 0.745286i −1.60587 0.430291i −0.659060 0.752090i \(-0.729046\pi\)
−0.946808 + 0.321799i \(0.895712\pi\)
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) −2.02520 0.947920i −0.905698 0.423923i
\(6\) 2.03616 2.03616i 0.831258 0.831258i
\(7\) −4.90683 1.31478i −1.85461 0.496940i −0.854846 0.518881i \(-0.826349\pi\)
−0.999759 + 0.0219412i \(0.993015\pi\)
\(8\) 1.00000 0.353553
\(9\) 4.58291 + 2.64594i 1.52764 + 0.881981i
\(10\) 1.83352 1.27992i 0.579811 0.404745i
\(11\) 0.446393i 0.134592i −0.997733 0.0672962i \(-0.978563\pi\)
0.997733 0.0672962i \(-0.0214373\pi\)
\(12\) 0.745286 + 2.78144i 0.215145 + 0.802934i
\(13\) 2.31524 + 4.01012i 0.642133 + 1.11221i 0.984956 + 0.172806i \(0.0552834\pi\)
−0.342823 + 0.939400i \(0.611383\pi\)
\(14\) 3.59205 3.59205i 0.960014 0.960014i
\(15\) 4.92652 + 4.14594i 1.27202 + 1.07048i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −0.535731 0.309305i −0.129934 0.0750174i 0.433624 0.901094i \(-0.357235\pi\)
−0.563558 + 0.826076i \(0.690568\pi\)
\(18\) −4.58291 + 2.64594i −1.08020 + 0.623655i
\(19\) 1.21232 4.52445i 0.278126 1.03798i −0.675591 0.737276i \(-0.736112\pi\)
0.953717 0.300704i \(-0.0972217\pi\)
\(20\) 0.191679 + 2.22784i 0.0428606 + 0.498160i
\(21\) 12.6682 + 7.31397i 2.76442 + 1.59604i
\(22\) 0.386587 + 0.223196i 0.0824207 + 0.0475856i
\(23\) 2.27723 0.474836 0.237418 0.971408i \(-0.423699\pi\)
0.237418 + 0.971408i \(0.423699\pi\)
\(24\) −2.78144 0.745286i −0.567760 0.152131i
\(25\) 3.20289 + 3.83946i 0.640579 + 0.767892i
\(26\) −4.63048 −0.908113
\(27\) −4.66664 4.66664i −0.898096 0.898096i
\(28\) 1.31478 + 4.90683i 0.248470 + 0.927303i
\(29\) −4.05041 + 4.05041i −0.752142 + 0.752142i −0.974879 0.222737i \(-0.928501\pi\)
0.222737 + 0.974879i \(0.428501\pi\)
\(30\) −6.05375 + 2.19352i −1.10526 + 0.400480i
\(31\) 0.176164 + 0.176164i 0.0316400 + 0.0316400i 0.722750 0.691110i \(-0.242878\pi\)
−0.691110 + 0.722750i \(0.742878\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) −0.332690 + 1.24162i −0.0579139 + 0.216138i
\(34\) 0.535731 0.309305i 0.0918771 0.0530453i
\(35\) 8.69101 + 7.31397i 1.46905 + 1.23629i
\(36\) 5.29189i 0.881981i
\(37\) −3.72164 4.81138i −0.611834 0.790986i
\(38\) 3.31213 + 3.31213i 0.537298 + 0.537298i
\(39\) −3.45103 12.8794i −0.552608 2.06236i
\(40\) −2.02520 0.947920i −0.320213 0.149879i
\(41\) −3.38733 + 1.95567i −0.529012 + 0.305425i −0.740614 0.671931i \(-0.765465\pi\)
0.211602 + 0.977356i \(0.432132\pi\)
\(42\) −12.6682 + 7.31397i −1.95474 + 1.12857i
\(43\) 8.15549 1.24370 0.621850 0.783136i \(-0.286381\pi\)
0.621850 + 0.783136i \(0.286381\pi\)
\(44\) −0.386587 + 0.223196i −0.0582803 + 0.0336481i
\(45\) −6.77317 9.70280i −1.00969 1.44641i
\(46\) −1.13862 + 1.97214i −0.167880 + 0.290776i
\(47\) −6.46505 + 6.46505i −0.943025 + 0.943025i −0.998462 0.0554376i \(-0.982345\pi\)
0.0554376 + 0.998462i \(0.482345\pi\)
\(48\) 2.03616 2.03616i 0.293894 0.293894i
\(49\) 16.2861 + 9.40279i 2.32659 + 1.34326i
\(50\) −4.92652 + 0.854057i −0.696715 + 0.120782i
\(51\) 1.25959 + 1.25959i 0.176377 + 0.176377i
\(52\) 2.31524 4.01012i 0.321066 0.556103i
\(53\) 8.08498 2.16636i 1.11056 0.297573i 0.343501 0.939152i \(-0.388387\pi\)
0.767057 + 0.641580i \(0.221721\pi\)
\(54\) 6.37475 1.70811i 0.867494 0.232444i
\(55\) −0.423145 + 0.904036i −0.0570568 + 0.121900i
\(56\) −4.90683 1.31478i −0.655702 0.175695i
\(57\) −6.74402 + 11.6810i −0.893267 + 1.54718i
\(58\) −1.48255 5.53296i −0.194669 0.726513i
\(59\) −3.85140 + 1.03198i −0.501410 + 0.134352i −0.500654 0.865647i \(-0.666907\pi\)
−0.000755498 1.00000i \(0.500240\pi\)
\(60\) 1.12723 6.33946i 0.145525 0.818421i
\(61\) 2.05254 7.66019i 0.262801 0.980787i −0.700782 0.713376i \(-0.747165\pi\)
0.963583 0.267411i \(-0.0861681\pi\)
\(62\) −0.240645 + 0.0644806i −0.0305619 + 0.00818904i
\(63\) −19.0087 19.0087i −2.39487 2.39487i
\(64\) 1.00000 0.125000
\(65\) −0.887564 10.3160i −0.110089 1.27954i
\(66\) −0.908926 0.908926i −0.111881 0.111881i
\(67\) 3.53962 13.2100i 0.432433 1.61386i −0.314701 0.949191i \(-0.601904\pi\)
0.747135 0.664673i \(-0.231429\pi\)
\(68\) 0.618609i 0.0750174i
\(69\) −6.33399 1.69719i −0.762523 0.204317i
\(70\) −10.6796 + 3.86965i −1.27646 + 0.462512i
\(71\) 7.60300 + 13.1688i 0.902310 + 1.56285i 0.824488 + 0.565879i \(0.191463\pi\)
0.0778211 + 0.996967i \(0.475204\pi\)
\(72\) 4.58291 + 2.64594i 0.540101 + 0.311827i
\(73\) 0.847559 0.847559i 0.0991993 0.0991993i −0.655765 0.754965i \(-0.727654\pi\)
0.754965 + 0.655765i \(0.227654\pi\)
\(74\) 6.02760 0.817343i 0.700694 0.0950142i
\(75\) −6.04718 13.0663i −0.698268 1.50877i
\(76\) −4.52445 + 1.21232i −0.518990 + 0.139063i
\(77\) −0.586908 + 2.19037i −0.0668844 + 0.249616i
\(78\) 12.8794 + 3.45103i 1.45831 + 0.390753i
\(79\) −2.81870 + 10.5195i −0.317128 + 1.18354i 0.604863 + 0.796329i \(0.293228\pi\)
−0.921992 + 0.387210i \(0.873439\pi\)
\(80\) 1.83352 1.27992i 0.204994 0.143099i
\(81\) 1.56420 + 2.70927i 0.173800 + 0.301030i
\(82\) 3.91135i 0.431936i
\(83\) −9.97712 + 2.67336i −1.09513 + 0.293440i −0.760781 0.649009i \(-0.775184\pi\)
−0.334351 + 0.942449i \(0.608517\pi\)
\(84\) 14.6279i 1.59604i
\(85\) 0.791768 + 1.13423i 0.0858793 + 0.123025i
\(86\) −4.07774 + 7.06286i −0.439715 + 0.761608i
\(87\) 14.2847 8.24727i 1.53148 0.884200i
\(88\) 0.446393i 0.0475856i
\(89\) 0.257339 + 0.960403i 0.0272779 + 0.101803i 0.978223 0.207558i \(-0.0665516\pi\)
−0.950945 + 0.309361i \(0.899885\pi\)
\(90\) 11.7895 1.01434i 1.24272 0.106921i
\(91\) −6.08807 22.7210i −0.638203 2.38181i
\(92\) −1.13862 1.97214i −0.118709 0.205610i
\(93\) −0.358698 0.621284i −0.0371953 0.0644241i
\(94\) −2.36637 8.83142i −0.244073 0.910892i
\(95\) −6.74402 + 8.01375i −0.691922 + 0.822193i
\(96\) 0.745286 + 2.78144i 0.0760654 + 0.283880i
\(97\) 3.22099i 0.327042i 0.986540 + 0.163521i \(0.0522852\pi\)
−0.986540 + 0.163521i \(0.947715\pi\)
\(98\) −16.2861 + 9.40279i −1.64515 + 0.949825i
\(99\) 1.18113 2.04578i 0.118708 0.205608i
\(100\) 1.72362 4.69352i 0.172362 0.469352i
\(101\) 0.484925i 0.0482518i 0.999709 + 0.0241259i \(0.00768026\pi\)
−0.999709 + 0.0241259i \(0.992320\pi\)
\(102\) −1.72063 + 0.461041i −0.170367 + 0.0456498i
\(103\) 0.657767i 0.0648117i −0.999475 0.0324059i \(-0.989683\pi\)
0.999475 0.0324059i \(-0.0103169\pi\)
\(104\) 2.31524 + 4.01012i 0.227028 + 0.393224i
\(105\) −18.7226 26.8207i −1.82714 2.61743i
\(106\) −2.16636 + 8.08498i −0.210416 + 0.785283i
\(107\) 17.7232 + 4.74891i 1.71336 + 0.459095i 0.976245 0.216668i \(-0.0695189\pi\)
0.737119 + 0.675763i \(0.236186\pi\)
\(108\) −1.70811 + 6.37475i −0.164363 + 0.613411i
\(109\) 1.33113 0.356675i 0.127499 0.0341632i −0.194505 0.980901i \(-0.562310\pi\)
0.322004 + 0.946738i \(0.395643\pi\)
\(110\) −0.571346 0.818472i −0.0544757 0.0780382i
\(111\) 6.76568 + 16.1563i 0.642170 + 1.53349i
\(112\) 3.59205 3.59205i 0.339416 0.339416i
\(113\) 10.0354 + 5.79397i 0.944055 + 0.545051i 0.891229 0.453553i \(-0.149844\pi\)
0.0528262 + 0.998604i \(0.483177\pi\)
\(114\) −6.74402 11.6810i −0.631635 1.09402i
\(115\) −4.61186 2.15863i −0.430058 0.201294i
\(116\) 5.53296 + 1.48255i 0.513722 + 0.137651i
\(117\) 24.5040i 2.26539i
\(118\) 1.03198 3.85140i 0.0950014 0.354550i
\(119\) 2.22207 + 2.22207i 0.203697 + 0.203697i
\(120\) 4.92652 + 4.14594i 0.449728 + 0.378471i
\(121\) 10.8007 0.981885
\(122\) 5.60765 + 5.60765i 0.507693 + 0.507693i
\(123\) 10.8792 2.91507i 0.980945 0.262843i
\(124\) 0.0644806 0.240645i 0.00579053 0.0216105i
\(125\) −2.84701 10.8118i −0.254644 0.967035i
\(126\) 25.9664 6.95766i 2.31327 0.619838i
\(127\) 4.94902 + 18.4700i 0.439154 + 1.63895i 0.730925 + 0.682458i \(0.239089\pi\)
−0.291771 + 0.956488i \(0.594245\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) −22.6840 6.07817i −1.99722 0.535153i
\(130\) 9.37767 + 4.38933i 0.822476 + 0.384970i
\(131\) −9.89179 + 2.65050i −0.864250 + 0.231575i −0.663600 0.748088i \(-0.730972\pi\)
−0.200650 + 0.979663i \(0.564305\pi\)
\(132\) 1.24162 0.332690i 0.108069 0.0289570i
\(133\) −11.8973 + 20.6068i −1.03163 + 1.78683i
\(134\) 9.67042 + 9.67042i 0.835397 + 0.835397i
\(135\) 5.02729 + 13.8745i 0.432681 + 1.19413i
\(136\) −0.535731 0.309305i −0.0459386 0.0265226i
\(137\) −6.63885 + 6.63885i −0.567195 + 0.567195i −0.931342 0.364147i \(-0.881361\pi\)
0.364147 + 0.931342i \(0.381361\pi\)
\(138\) 4.63680 4.63680i 0.394711 0.394711i
\(139\) 5.37396 9.30797i 0.455813 0.789492i −0.542921 0.839784i \(-0.682682\pi\)
0.998735 + 0.0502920i \(0.0160152\pi\)
\(140\) 1.98858 11.1836i 0.168066 0.945189i
\(141\) 22.8005 13.1639i 1.92015 1.10860i
\(142\) −15.2060 −1.27606
\(143\) 1.79009 1.03351i 0.149695 0.0864262i
\(144\) −4.58291 + 2.64594i −0.381909 + 0.220495i
\(145\) 12.0424 4.36343i 1.00006 0.362363i
\(146\) 0.310228 + 1.15779i 0.0256747 + 0.0958192i
\(147\) −38.2911 38.2911i −3.15820 3.15820i
\(148\) −2.30596 + 5.62873i −0.189549 + 0.462678i
\(149\) 5.11448i 0.418995i 0.977809 + 0.209497i \(0.0671828\pi\)
−0.977809 + 0.209497i \(0.932817\pi\)
\(150\) 14.3394 + 1.29615i 1.17080 + 0.105830i
\(151\) −11.0417 + 6.37493i −0.898561 + 0.518784i −0.876733 0.480978i \(-0.840282\pi\)
−0.0218277 + 0.999762i \(0.506949\pi\)
\(152\) 1.21232 4.52445i 0.0983324 0.366981i
\(153\) −1.63680 2.83503i −0.132328 0.229198i
\(154\) −1.60346 1.60346i −0.129211 0.129211i
\(155\) −0.189779 0.523758i −0.0152434 0.0420693i
\(156\) −9.42840 + 9.42840i −0.754876 + 0.754876i
\(157\) 2.30172 + 8.59015i 0.183698 + 0.685569i 0.994906 + 0.100811i \(0.0321438\pi\)
−0.811208 + 0.584758i \(0.801190\pi\)
\(158\) −7.70083 7.70083i −0.612645 0.612645i
\(159\) −24.1025 −1.91145
\(160\) 0.191679 + 2.22784i 0.0151535 + 0.176126i
\(161\) −11.1740 2.99406i −0.880633 0.235965i
\(162\) −3.12839 −0.245790
\(163\) −5.34325 3.08493i −0.418516 0.241630i 0.275926 0.961179i \(-0.411015\pi\)
−0.694442 + 0.719549i \(0.744349\pi\)
\(164\) 3.38733 + 1.95567i 0.264506 + 0.152713i
\(165\) 1.85072 2.19916i 0.144078 0.171205i
\(166\) 2.67336 9.97712i 0.207493 0.774375i
\(167\) −3.86637 + 2.23225i −0.299188 + 0.172736i −0.642078 0.766639i \(-0.721928\pi\)
0.342890 + 0.939376i \(0.388594\pi\)
\(168\) 12.6682 + 7.31397i 0.977371 + 0.564285i
\(169\) −4.22069 + 7.31045i −0.324668 + 0.562342i
\(170\) −1.37816 + 0.118574i −0.105700 + 0.00909422i
\(171\) 17.5274 17.5274i 1.34035 1.34035i
\(172\) −4.07774 7.06286i −0.310925 0.538538i
\(173\) 2.80128 + 10.4545i 0.212977 + 0.794843i 0.986869 + 0.161524i \(0.0516410\pi\)
−0.773891 + 0.633318i \(0.781692\pi\)
\(174\) 16.4945i 1.25045i
\(175\) −10.6680 23.0507i −0.806425 1.74247i
\(176\) 0.386587 + 0.223196i 0.0291401 + 0.0168241i
\(177\) 11.4816 0.863008
\(178\) −0.960403 0.257339i −0.0719853 0.0192884i
\(179\) −17.2035 + 17.2035i −1.28585 + 1.28585i −0.348562 + 0.937286i \(0.613330\pi\)
−0.937286 + 0.348562i \(0.886670\pi\)
\(180\) −5.01628 + 10.7171i −0.373892 + 0.798809i
\(181\) 5.42208 + 9.39132i 0.403020 + 0.698051i 0.994089 0.108570i \(-0.0346271\pi\)
−0.591069 + 0.806621i \(0.701294\pi\)
\(182\) 22.7210 + 6.08807i 1.68419 + 0.451277i
\(183\) −11.4181 + 19.7767i −0.844047 + 1.46193i
\(184\) 2.27723 0.167880
\(185\) 2.97627 + 13.2718i 0.218820 + 0.975765i
\(186\) 0.717397 0.0526021
\(187\) −0.138071 + 0.239147i −0.0100968 + 0.0174881i
\(188\) 8.83142 + 2.36637i 0.644098 + 0.172585i
\(189\) 16.7628 + 29.0340i 1.21931 + 2.11191i
\(190\) −3.56810 9.84737i −0.258857 0.714403i
\(191\) −6.14580 + 6.14580i −0.444694 + 0.444694i −0.893586 0.448892i \(-0.851819\pi\)
0.448892 + 0.893586i \(0.351819\pi\)
\(192\) −2.78144 0.745286i −0.200733 0.0537864i
\(193\) 3.70441 0.266649 0.133325 0.991072i \(-0.457435\pi\)
0.133325 + 0.991072i \(0.457435\pi\)
\(194\) −2.78946 1.61050i −0.200272 0.115627i
\(195\) −5.21963 + 29.3548i −0.373786 + 2.10214i
\(196\) 18.8056i 1.34326i
\(197\) −1.20574 4.49989i −0.0859055 0.320604i 0.909579 0.415532i \(-0.136405\pi\)
−0.995484 + 0.0949282i \(0.969738\pi\)
\(198\) 1.18113 + 2.04578i 0.0839392 + 0.145387i
\(199\) 9.35671 9.35671i 0.663280 0.663280i −0.292872 0.956152i \(-0.594611\pi\)
0.956152 + 0.292872i \(0.0946110\pi\)
\(200\) 3.20289 + 3.83946i 0.226479 + 0.271491i
\(201\) −19.6905 + 34.1050i −1.38886 + 2.40558i
\(202\) −0.419957 0.242462i −0.0295481 0.0170596i
\(203\) 25.2000 14.5492i 1.76870 1.02116i
\(204\) 0.461041 1.72063i 0.0322793 0.120468i
\(205\) 8.71385 0.749722i 0.608602 0.0523628i
\(206\) 0.569643 + 0.328883i 0.0396889 + 0.0229144i
\(207\) 10.4363 + 6.02542i 0.725376 + 0.418796i
\(208\) −4.63048 −0.321066
\(209\) −2.01968 0.541172i −0.139704 0.0374337i
\(210\) 32.5887 2.80386i 2.24883 0.193485i
\(211\) −6.67374 −0.459439 −0.229720 0.973257i \(-0.573781\pi\)
−0.229720 + 0.973257i \(0.573781\pi\)
\(212\) −5.91862 5.91862i −0.406492 0.406492i
\(213\) −11.3328 42.2946i −0.776511 2.89798i
\(214\) −12.9743 + 12.9743i −0.886903 + 0.886903i
\(215\) −16.5165 7.73075i −1.12642 0.527233i
\(216\) −4.66664 4.66664i −0.317525 0.317525i
\(217\) −0.632790 1.09602i −0.0429566 0.0744030i
\(218\) −0.356675 + 1.33113i −0.0241571 + 0.0901554i
\(219\) −2.98911 + 1.72577i −0.201986 + 0.116616i
\(220\) 0.994490 0.0855639i 0.0670485 0.00576872i
\(221\) 2.86446i 0.192684i
\(222\) −17.3746 2.21889i −1.16611 0.148922i
\(223\) 3.72140 + 3.72140i 0.249203 + 0.249203i 0.820644 0.571440i \(-0.193615\pi\)
−0.571440 + 0.820644i \(0.693615\pi\)
\(224\) 1.31478 + 4.90683i 0.0878474 + 0.327851i
\(225\) 4.51957 + 26.0706i 0.301305 + 1.73804i
\(226\) −10.0354 + 5.79397i −0.667548 + 0.385409i
\(227\) 15.1690 8.75783i 1.00680 0.581278i 0.0965487 0.995328i \(-0.469220\pi\)
0.910254 + 0.414051i \(0.135886\pi\)
\(228\) 13.4880 0.893267
\(229\) 14.5294 8.38857i 0.960132 0.554332i 0.0639183 0.997955i \(-0.479640\pi\)
0.896214 + 0.443623i \(0.146307\pi\)
\(230\) 4.17536 2.91467i 0.275315 0.192187i
\(231\) 3.26491 5.65498i 0.214815 0.372070i
\(232\) −4.05041 + 4.05041i −0.265922 + 0.265922i
\(233\) 7.10588 7.10588i 0.465521 0.465521i −0.434939 0.900460i \(-0.643230\pi\)
0.900460 + 0.434939i \(0.143230\pi\)
\(234\) −21.2211 12.2520i −1.38727 0.800938i
\(235\) 19.2214 6.96469i 1.25387 0.454326i
\(236\) 2.81942 + 2.81942i 0.183529 + 0.183529i
\(237\) 15.6801 27.1587i 1.01853 1.76415i
\(238\) −3.03541 + 0.813335i −0.196756 + 0.0527207i
\(239\) 3.48667 0.934251i 0.225534 0.0604317i −0.144282 0.989537i \(-0.546087\pi\)
0.369816 + 0.929105i \(0.379421\pi\)
\(240\) −6.05375 + 2.19352i −0.390768 + 0.141591i
\(241\) 17.2137 + 4.61239i 1.10883 + 0.297110i 0.766356 0.642417i \(-0.222068\pi\)
0.342475 + 0.939527i \(0.388735\pi\)
\(242\) −5.40037 + 9.35371i −0.347149 + 0.601279i
\(243\) 2.79278 + 10.4228i 0.179157 + 0.668623i
\(244\) −7.66019 + 2.05254i −0.490393 + 0.131401i
\(245\) −24.0696 34.4805i −1.53775 2.20288i
\(246\) −2.91507 + 10.8792i −0.185858 + 0.693633i
\(247\) 20.9504 5.61364i 1.33304 0.357187i
\(248\) 0.176164 + 0.176164i 0.0111864 + 0.0111864i
\(249\) 29.7432 1.88490
\(250\) 10.7868 + 2.94031i 0.682216 + 0.185961i
\(251\) 4.01101 + 4.01101i 0.253173 + 0.253173i 0.822270 0.569097i \(-0.192707\pi\)
−0.569097 + 0.822270i \(0.692707\pi\)
\(252\) −6.95766 + 25.9664i −0.438292 + 1.63573i
\(253\) 1.01654i 0.0639093i
\(254\) −18.4700 4.94902i −1.15891 0.310529i
\(255\) −1.35693 3.74491i −0.0849743 0.234515i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −20.4160 11.7872i −1.27351 0.735264i −0.297867 0.954607i \(-0.596275\pi\)
−0.975648 + 0.219343i \(0.929608\pi\)
\(258\) 16.6059 16.6059i 1.03384 1.03384i
\(259\) 11.9355 + 28.5017i 0.741637 + 1.77101i
\(260\) −8.49010 + 5.92664i −0.526534 + 0.367554i
\(261\) −29.2798 + 7.84549i −1.81237 + 0.485624i
\(262\) 2.65050 9.89179i 0.163748 0.611117i
\(263\) −8.39907 2.25052i −0.517909 0.138773i −0.00960954 0.999954i \(-0.503059\pi\)
−0.508299 + 0.861181i \(0.669726\pi\)
\(264\) −0.332690 + 1.24162i −0.0204757 + 0.0764162i
\(265\) −18.4273 3.27659i −1.13198 0.201279i
\(266\) −11.8973 20.6068i −0.729471 1.26348i
\(267\) 2.86310i 0.175219i
\(268\) −13.2100 + 3.53962i −0.806932 + 0.216217i
\(269\) 13.4213i 0.818309i −0.912465 0.409154i \(-0.865824\pi\)
0.912465 0.409154i \(-0.134176\pi\)
\(270\) −14.5293 2.58349i −0.884226 0.157226i
\(271\) 5.78410 10.0183i 0.351359 0.608571i −0.635129 0.772406i \(-0.719053\pi\)
0.986488 + 0.163835i \(0.0523864\pi\)
\(272\) 0.535731 0.309305i 0.0324835 0.0187543i
\(273\) 67.7345i 4.09948i
\(274\) −2.42999 9.06883i −0.146801 0.547868i
\(275\) 1.71391 1.42975i 0.103353 0.0862171i
\(276\) 1.69719 + 6.33399i 0.102159 + 0.381262i
\(277\) −0.488351 0.845849i −0.0293422 0.0508221i 0.850981 0.525196i \(-0.176008\pi\)
−0.880324 + 0.474374i \(0.842675\pi\)
\(278\) 5.37396 + 9.30797i 0.322309 + 0.558255i
\(279\) 0.341224 + 1.27346i 0.0204285 + 0.0762403i
\(280\) 8.69101 + 7.31397i 0.519387 + 0.437094i
\(281\) −3.61332 13.4851i −0.215553 0.804454i −0.985971 0.166915i \(-0.946619\pi\)
0.770419 0.637538i \(-0.220047\pi\)
\(282\) 26.3277i 1.56779i
\(283\) −0.359942 + 0.207813i −0.0213963 + 0.0123532i −0.510660 0.859783i \(-0.670599\pi\)
0.489264 + 0.872136i \(0.337266\pi\)
\(284\) 7.60300 13.1688i 0.451155 0.781423i
\(285\) 24.7306 17.2636i 1.46492 1.02261i
\(286\) 2.06701i 0.122225i
\(287\) 19.1923 5.14256i 1.13289 0.303556i
\(288\) 5.29189i 0.311827i
\(289\) −8.30866 14.3910i −0.488745 0.846531i
\(290\) −2.24233 + 12.6107i −0.131674 + 0.740526i
\(291\) 2.40056 8.95901i 0.140723 0.525186i
\(292\) −1.15779 0.310228i −0.0677544 0.0181547i
\(293\) −0.438909 + 1.63803i −0.0256413 + 0.0956948i −0.977561 0.210654i \(-0.932441\pi\)
0.951919 + 0.306349i \(0.0991074\pi\)
\(294\) 52.3067 14.0155i 3.05059 0.817402i
\(295\) 8.77810 + 1.56085i 0.511081 + 0.0908763i
\(296\) −3.72164 4.81138i −0.216316 0.279656i
\(297\) −2.08316 + 2.08316i −0.120877 + 0.120877i
\(298\) −4.42927 2.55724i −0.256581 0.148137i
\(299\) 5.27234 + 9.13196i 0.304907 + 0.528115i
\(300\) −8.29218 + 11.7702i −0.478749 + 0.679551i
\(301\) −40.0176 10.7227i −2.30657 0.618045i
\(302\) 12.7499i 0.733672i
\(303\) 0.361407 1.34879i 0.0207623 0.0774860i
\(304\) 3.31213 + 3.31213i 0.189964 + 0.189964i
\(305\) −11.4181 + 13.5678i −0.653796 + 0.776890i
\(306\) 3.27361 0.187140
\(307\) 17.6114 + 17.6114i 1.00514 + 1.00514i 0.999987 + 0.00514878i \(0.00163891\pi\)
0.00514878 + 0.999987i \(0.498361\pi\)
\(308\) 2.19037 0.586908i 0.124808 0.0334422i
\(309\) −0.490224 + 1.82954i −0.0278879 + 0.104079i
\(310\) 0.548477 + 0.0975258i 0.0311514 + 0.00553909i
\(311\) 29.5971 7.93052i 1.67830 0.449699i 0.710969 0.703223i \(-0.248256\pi\)
0.967329 + 0.253524i \(0.0815898\pi\)
\(312\) −3.45103 12.8794i −0.195376 0.729154i
\(313\) −8.47539 + 14.6798i −0.479058 + 0.829752i −0.999712 0.0240156i \(-0.992355\pi\)
0.520654 + 0.853768i \(0.325688\pi\)
\(314\) −8.59015 2.30172i −0.484770 0.129894i
\(315\) 20.4777 + 56.5152i 1.15379 + 3.18427i
\(316\) 10.5195 2.81870i 0.591770 0.158564i
\(317\) 13.6013 3.64446i 0.763926 0.204693i 0.144240 0.989543i \(-0.453926\pi\)
0.619686 + 0.784849i \(0.287260\pi\)
\(318\) 12.0512 20.8734i 0.675800 1.17052i
\(319\) 1.80807 + 1.80807i 0.101233 + 0.101233i
\(320\) −2.02520 0.947920i −0.113212 0.0529903i
\(321\) −45.7568 26.4177i −2.55389 1.47449i
\(322\) 8.17992 8.17992i 0.455849 0.455849i
\(323\) −2.04891 + 2.04891i −0.114005 + 0.114005i
\(324\) 1.56420 2.70927i 0.0868998 0.150515i
\(325\) −7.98121 + 21.7333i −0.442718 + 1.20554i
\(326\) 5.34325 3.08493i 0.295935 0.170858i
\(327\) −3.96828 −0.219447
\(328\) −3.38733 + 1.95567i −0.187034 + 0.107984i
\(329\) 40.2230 23.2228i 2.21757 1.28031i
\(330\) 0.979171 + 2.70235i 0.0539016 + 0.148759i
\(331\) 4.20892 + 15.7079i 0.231343 + 0.863385i 0.979763 + 0.200160i \(0.0641462\pi\)
−0.748420 + 0.663225i \(0.769187\pi\)
\(332\) 7.30376 + 7.30376i 0.400846 + 0.400846i
\(333\) −4.32529 31.8974i −0.237024 1.74796i
\(334\) 4.46449i 0.244286i
\(335\) −19.6905 + 23.3977i −1.07581 + 1.27835i
\(336\) −12.6682 + 7.31397i −0.691106 + 0.399010i
\(337\) 2.86868 10.7060i 0.156267 0.583195i −0.842727 0.538341i \(-0.819051\pi\)
0.998994 0.0448539i \(-0.0142822\pi\)
\(338\) −4.22069 7.31045i −0.229575 0.397636i
\(339\) −23.5949 23.5949i −1.28150 1.28150i
\(340\) 0.586392 1.25281i 0.0318016 0.0679431i
\(341\) 0.0786384 0.0786384i 0.00425851 0.00425851i
\(342\) 6.41547 + 23.9429i 0.346909 + 1.29468i
\(343\) −42.4062 42.4062i −2.28972 2.28972i
\(344\) 8.15549 0.439715
\(345\) 11.2188 + 9.44127i 0.604001 + 0.508301i
\(346\) −10.4545 2.80128i −0.562039 0.150598i
\(347\) 12.5415 0.673262 0.336631 0.941637i \(-0.390713\pi\)
0.336631 + 0.941637i \(0.390713\pi\)
\(348\) −14.2847 8.24727i −0.765740 0.442100i
\(349\) −14.7799 8.53318i −0.791150 0.456770i 0.0492174 0.998788i \(-0.484327\pi\)
−0.840367 + 0.542018i \(0.817661\pi\)
\(350\) 25.2965 + 2.28658i 1.35215 + 0.122223i
\(351\) 7.90937 29.5182i 0.422171 1.57556i
\(352\) −0.386587 + 0.223196i −0.0206052 + 0.0118964i
\(353\) 8.29168 + 4.78720i 0.441322 + 0.254797i 0.704158 0.710043i \(-0.251325\pi\)
−0.262836 + 0.964840i \(0.584658\pi\)
\(354\) −5.74079 + 9.94334i −0.305119 + 0.528482i
\(355\) −2.91466 33.8765i −0.154694 1.79798i
\(356\) 0.703064 0.703064i 0.0372623 0.0372623i
\(357\) −4.52449 7.83665i −0.239461 0.414759i
\(358\) −6.29691 23.5004i −0.332802 1.24203i
\(359\) 32.6420i 1.72278i 0.507945 + 0.861389i \(0.330405\pi\)
−0.507945 + 0.861389i \(0.669595\pi\)
\(360\) −6.77317 9.70280i −0.356978 0.511383i
\(361\) −2.54645 1.47019i −0.134024 0.0773786i
\(362\) −10.8442 −0.569957
\(363\) −30.0416 8.04963i −1.57678 0.422496i
\(364\) −16.6329 + 16.6329i −0.871801 + 0.871801i
\(365\) −2.51990 + 0.913061i −0.131898 + 0.0477918i
\(366\) −11.4181 19.7767i −0.596832 1.03374i
\(367\) −17.0171 4.55973i −0.888287 0.238016i −0.214308 0.976766i \(-0.568750\pi\)
−0.673979 + 0.738750i \(0.735416\pi\)
\(368\) −1.13862 + 1.97214i −0.0593544 + 0.102805i
\(369\) −20.6984 −1.07752
\(370\) −12.9819 4.05840i −0.674896 0.210986i
\(371\) −42.5199 −2.20752
\(372\) −0.358698 + 0.621284i −0.0185976 + 0.0322121i
\(373\) 4.27448 + 1.14534i 0.221324 + 0.0593036i 0.367777 0.929914i \(-0.380119\pi\)
−0.146453 + 0.989218i \(0.546786\pi\)
\(374\) −0.138071 0.239147i −0.00713950 0.0123660i
\(375\) −0.139067 + 32.1942i −0.00718138 + 1.66250i
\(376\) −6.46505 + 6.46505i −0.333410 + 0.333410i
\(377\) −25.6203 6.86493i −1.31951 0.353562i
\(378\) −33.5256 −1.72437
\(379\) −12.8893 7.44164i −0.662079 0.382251i 0.130990 0.991384i \(-0.458185\pi\)
−0.793069 + 0.609132i \(0.791518\pi\)
\(380\) 10.3121 + 1.83362i 0.529000 + 0.0940626i
\(381\) 55.0617i 2.82089i
\(382\) −2.24952 8.39531i −0.115095 0.429542i
\(383\) 0.355835 + 0.616325i 0.0181823 + 0.0314927i 0.874973 0.484171i \(-0.160879\pi\)
−0.856791 + 0.515664i \(0.827545\pi\)
\(384\) 2.03616 2.03616i 0.103907 0.103907i
\(385\) 3.26491 3.87960i 0.166395 0.197723i
\(386\) −1.85221 + 3.20811i −0.0942748 + 0.163289i
\(387\) 37.3759 + 21.5790i 1.89992 + 1.09692i
\(388\) 2.78946 1.61050i 0.141613 0.0817605i
\(389\) −2.17814 + 8.12893i −0.110436 + 0.412153i −0.998905 0.0467836i \(-0.985103\pi\)
0.888469 + 0.458937i \(0.151770\pi\)
\(390\) −22.8122 19.1977i −1.15514 0.972114i
\(391\) −1.21998 0.704358i −0.0616972 0.0356209i
\(392\) 16.2861 + 9.40279i 0.822573 + 0.474913i
\(393\) 29.4888 1.48752
\(394\) 4.49989 + 1.20574i 0.226701 + 0.0607443i
\(395\) 15.6801 18.6323i 0.788952 0.937492i
\(396\) −2.36226 −0.118708
\(397\) −6.05500 6.05500i −0.303892 0.303892i 0.538643 0.842534i \(-0.318937\pi\)
−0.842534 + 0.538643i \(0.818937\pi\)
\(398\) 3.42479 + 12.7815i 0.171669 + 0.640679i
\(399\) 48.4496 48.4496i 2.42552 2.42552i
\(400\) −4.92652 + 0.854057i −0.246326 + 0.0427029i
\(401\) 8.60825 + 8.60825i 0.429876 + 0.429876i 0.888586 0.458710i \(-0.151688\pi\)
−0.458710 + 0.888586i \(0.651688\pi\)
\(402\) −19.6905 34.1050i −0.982073 1.70100i
\(403\) −0.298576 + 1.11430i −0.0148731 + 0.0555073i
\(404\) 0.419957 0.242462i 0.0208936 0.0120629i
\(405\) −0.599646 6.96955i −0.0297966 0.346320i
\(406\) 29.0985i 1.44413i
\(407\) −2.14777 + 1.66131i −0.106461 + 0.0823482i
\(408\) 1.25959 + 1.25959i 0.0623588 + 0.0623588i
\(409\) −3.16524 11.8128i −0.156511 0.584107i −0.998971 0.0453484i \(-0.985560\pi\)
0.842460 0.538758i \(-0.181106\pi\)
\(410\) −3.70765 + 7.92128i −0.183108 + 0.391204i
\(411\) 23.4134 13.5177i 1.15490 0.666781i
\(412\) −0.569643 + 0.328883i −0.0280643 + 0.0162029i
\(413\) 20.2550 0.996682
\(414\) −10.4363 + 6.02542i −0.512918 + 0.296133i
\(415\) 22.7398 + 4.04341i 1.11625 + 0.198483i
\(416\) 2.31524 4.01012i 0.113514 0.196612i
\(417\) −21.8845 + 21.8845i −1.07169 + 1.07169i
\(418\) 1.47851 1.47851i 0.0723163 0.0723163i
\(419\) −10.3821 5.99408i −0.507197 0.292830i 0.224484 0.974478i \(-0.427930\pi\)
−0.731681 + 0.681648i \(0.761264\pi\)
\(420\) −13.8661 + 29.6246i −0.676598 + 1.44553i
\(421\) 8.73028 + 8.73028i 0.425488 + 0.425488i 0.887088 0.461600i \(-0.152725\pi\)
−0.461600 + 0.887088i \(0.652725\pi\)
\(422\) 3.33687 5.77963i 0.162436 0.281348i
\(423\) −46.7349 + 12.5226i −2.27233 + 0.608868i
\(424\) 8.08498 2.16636i 0.392641 0.105208i
\(425\) −0.528328 3.04759i −0.0256277 0.147830i
\(426\) 42.2946 + 11.3328i 2.04918 + 0.549076i
\(427\) −20.1429 + 34.8886i −0.974785 + 1.68838i
\(428\) −4.74891 17.7232i −0.229547 0.856682i
\(429\) −5.74929 + 1.54052i −0.277578 + 0.0743768i
\(430\) 14.9533 10.4384i 0.721112 0.503382i
\(431\) −3.15682 + 11.7814i −0.152059 + 0.567490i 0.847281 + 0.531145i \(0.178238\pi\)
−0.999339 + 0.0363450i \(0.988428\pi\)
\(432\) 6.37475 1.70811i 0.306705 0.0821815i
\(433\) 10.7051 + 10.7051i 0.514455 + 0.514455i 0.915888 0.401433i \(-0.131488\pi\)
−0.401433 + 0.915888i \(0.631488\pi\)
\(434\) 1.26558 0.0607498
\(435\) −36.7472 + 3.16165i −1.76189 + 0.151590i
\(436\) −0.974454 0.974454i −0.0466679 0.0466679i
\(437\) 2.76074 10.3032i 0.132064 0.492870i
\(438\) 3.45153i 0.164921i
\(439\) 0.644478 + 0.172687i 0.0307593 + 0.00824192i 0.274166 0.961682i \(-0.411598\pi\)
−0.243407 + 0.969924i \(0.578265\pi\)
\(440\) −0.423145 + 0.904036i −0.0201726 + 0.0430982i
\(441\) 49.7585 + 86.1842i 2.36945 + 4.10401i
\(442\) 2.48069 + 1.43223i 0.117995 + 0.0681242i
\(443\) 19.3512 19.3512i 0.919404 0.919404i −0.0775819 0.996986i \(-0.524720\pi\)
0.996986 + 0.0775819i \(0.0247199\pi\)
\(444\) 10.6089 13.9374i 0.503477 0.661439i
\(445\) 0.389221 2.18895i 0.0184509 0.103766i
\(446\) −5.08353 + 1.36213i −0.240712 + 0.0644986i
\(447\) 3.81175 14.2257i 0.180290 0.672850i
\(448\) −4.90683 1.31478i −0.231826 0.0621175i
\(449\) −1.19693 + 4.46699i −0.0564865 + 0.210810i −0.988401 0.151868i \(-0.951471\pi\)
0.931914 + 0.362679i \(0.118138\pi\)
\(450\) −24.8376 9.12122i −1.17085 0.429978i
\(451\) 0.872999 + 1.51208i 0.0411079 + 0.0712010i
\(452\) 11.5879i 0.545051i
\(453\) 35.4630 9.50229i 1.66620 0.446456i
\(454\) 17.5157i 0.822051i
\(455\) −9.20810 + 51.7856i −0.431682 + 2.42775i
\(456\) −6.74402 + 11.6810i −0.315818 + 0.547012i
\(457\) −2.44032 + 1.40892i −0.114154 + 0.0659066i −0.555990 0.831189i \(-0.687661\pi\)
0.441836 + 0.897096i \(0.354327\pi\)
\(458\) 16.7771i 0.783944i
\(459\) 1.05665 + 3.94348i 0.0493203 + 0.184066i
\(460\) 0.436496 + 5.07330i 0.0203518 + 0.236544i
\(461\) 4.84955 + 18.0988i 0.225866 + 0.842943i 0.982056 + 0.188591i \(0.0603920\pi\)
−0.756190 + 0.654352i \(0.772941\pi\)
\(462\) 3.26491 + 5.65498i 0.151897 + 0.263094i
\(463\) 0.661825 + 1.14631i 0.0307576 + 0.0532738i 0.880994 0.473127i \(-0.156875\pi\)
−0.850237 + 0.526400i \(0.823541\pi\)
\(464\) −1.48255 5.53296i −0.0688257 0.256861i
\(465\) 0.137510 + 1.59824i 0.00637685 + 0.0741168i
\(466\) 2.60093 + 9.70681i 0.120486 + 0.449659i
\(467\) 12.6461i 0.585190i −0.956236 0.292595i \(-0.905481\pi\)
0.956236 0.292595i \(-0.0945188\pi\)
\(468\) 21.2211 12.2520i 0.980945 0.566349i
\(469\) −34.7366 + 60.1655i −1.60399 + 2.77819i
\(470\) −3.57910 + 20.1286i −0.165092 + 0.928461i
\(471\) 25.6085i 1.17998i
\(472\) −3.85140 + 1.03198i −0.177275 + 0.0475007i
\(473\) 3.64055i 0.167393i
\(474\) 15.6801 + 27.1587i 0.720211 + 1.24744i
\(475\) 21.2544 9.83667i 0.975219 0.451338i
\(476\) 0.813335 3.03541i 0.0372791 0.139128i
\(477\) 42.7848 + 11.4641i 1.95898 + 0.524907i
\(478\) −0.934251 + 3.48667i −0.0427316 + 0.159477i
\(479\) −30.2014 + 8.09245i −1.37994 + 0.369753i −0.871099 0.491108i \(-0.836592\pi\)
−0.508840 + 0.860861i \(0.669925\pi\)
\(480\) 1.12723 6.33946i 0.0514509 0.289356i
\(481\) 10.6777 26.0637i 0.486862 1.18840i
\(482\) −12.6013 + 12.6013i −0.573973 + 0.573973i
\(483\) 28.8484 + 16.6556i 1.31265 + 0.757857i
\(484\) −5.40037 9.35371i −0.245471 0.425169i
\(485\) 3.05324 6.52316i 0.138641 0.296201i
\(486\) −10.4228 2.79278i −0.472788 0.126683i
\(487\) 43.1104i 1.95352i 0.214340 + 0.976759i \(0.431240\pi\)
−0.214340 + 0.976759i \(0.568760\pi\)
\(488\) 2.05254 7.66019i 0.0929142 0.346761i
\(489\) 12.5628 + 12.5628i 0.568109 + 0.568109i
\(490\) 41.8958 3.60463i 1.89266 0.162840i
\(491\) 25.3117 1.14230 0.571150 0.820846i \(-0.306498\pi\)
0.571150 + 0.820846i \(0.306498\pi\)
\(492\) −7.96413 7.96413i −0.359051 0.359051i
\(493\) 3.42274 0.917120i 0.154152 0.0413050i
\(494\) −5.61364 + 20.9504i −0.252570 + 0.942603i
\(495\) −4.33126 + 3.02350i −0.194676 + 0.135896i
\(496\) −0.240645 + 0.0644806i −0.0108053 + 0.00289526i
\(497\) −19.9925 74.6131i −0.896788 3.34686i
\(498\) −14.8716 + 25.7584i −0.666413 + 1.15426i
\(499\) 23.7843 + 6.37299i 1.06473 + 0.285294i 0.748327 0.663330i \(-0.230858\pi\)
0.316405 + 0.948624i \(0.397524\pi\)
\(500\) −7.93977 + 7.87147i −0.355077 + 0.352023i
\(501\) 12.4177 3.32732i 0.554784 0.148654i
\(502\) −5.47915 + 1.46813i −0.244546 + 0.0655260i
\(503\) −14.7528 + 25.5527i −0.657797 + 1.13934i 0.323388 + 0.946266i \(0.395178\pi\)
−0.981185 + 0.193071i \(0.938155\pi\)
\(504\) −19.0087 19.0087i −0.846714 0.846714i
\(505\) 0.459670 0.982071i 0.0204550 0.0437016i
\(506\) 0.880349 + 0.508270i 0.0391363 + 0.0225953i
\(507\) 17.1880 17.1880i 0.763345 0.763345i
\(508\) 13.5210 13.5210i 0.599896 0.599896i
\(509\) −2.86541 + 4.96304i −0.127007 + 0.219983i −0.922516 0.385959i \(-0.873870\pi\)
0.795509 + 0.605942i \(0.207204\pi\)
\(510\) 3.92165 + 0.697316i 0.173654 + 0.0308777i
\(511\) −5.27318 + 3.04447i −0.233272 + 0.134680i
\(512\) 1.00000 0.0441942
\(513\) −26.7715 + 15.4565i −1.18199 + 0.682422i
\(514\) 20.4160 11.7872i 0.900511 0.519910i
\(515\) −0.623511 + 1.33211i −0.0274752 + 0.0586999i
\(516\) 6.07817 + 22.6840i 0.267577 + 0.998609i
\(517\) 2.88595 + 2.88595i 0.126924 + 0.126924i
\(518\) −30.6510 3.91441i −1.34673 0.171989i
\(519\) 31.1664i 1.36805i
\(520\) −0.887564 10.3160i −0.0389223 0.452385i
\(521\) −24.8121 + 14.3253i −1.08704 + 0.627602i −0.932786 0.360430i \(-0.882630\pi\)
−0.154252 + 0.988032i \(0.549297\pi\)
\(522\) 7.84549 29.2798i 0.343388 1.28154i
\(523\) 4.18923 + 7.25595i 0.183182 + 0.317281i 0.942962 0.332899i \(-0.108027\pi\)
−0.759780 + 0.650180i \(0.774694\pi\)
\(524\) 7.24129 + 7.24129i 0.316337 + 0.316337i
\(525\) 12.4931 + 72.0649i 0.545244 + 3.14517i
\(526\) 6.14854 6.14854i 0.268089 0.268089i
\(527\) −0.0398883 0.148865i −0.00173756 0.00648467i
\(528\) −0.908926 0.908926i −0.0395559 0.0395559i
\(529\) −17.8142 −0.774531
\(530\) 12.0512 14.3202i 0.523472 0.622029i
\(531\) −20.3812 5.46112i −0.884467 0.236992i
\(532\) 23.7946 1.03163
\(533\) −15.6850 9.05572i −0.679391 0.392247i
\(534\) 2.47952 + 1.43155i 0.107299 + 0.0619492i
\(535\) −31.3915 26.4177i −1.35717 1.14214i
\(536\) 3.53962 13.2100i 0.152888 0.570587i
\(537\) 60.6720 35.0290i 2.61819 1.51161i
\(538\) 11.6232 + 6.71063i 0.501110 + 0.289316i
\(539\) 4.19734 7.27000i 0.180792 0.313141i
\(540\) 9.50202 11.2910i 0.408902 0.485888i
\(541\) −26.1818 + 26.1818i −1.12564 + 1.12564i −0.134764 + 0.990878i \(0.543028\pi\)
−0.990878 + 0.134764i \(0.956972\pi\)
\(542\) 5.78410 + 10.0183i 0.248448 + 0.430325i
\(543\) −8.08200 30.1624i −0.346832 1.29439i
\(544\) 0.618609i 0.0265226i
\(545\) −3.03390 0.539465i −0.129958 0.0231081i
\(546\) −58.6598 33.8672i −2.51041 1.44938i
\(547\) −9.02187 −0.385747 −0.192874 0.981224i \(-0.561781\pi\)
−0.192874 + 0.981224i \(0.561781\pi\)
\(548\) 9.06883 + 2.42999i 0.387401 + 0.103804i
\(549\) 29.6750 29.6750i 1.26650 1.26650i
\(550\) 0.381245 + 2.19916i 0.0162563 + 0.0937726i
\(551\) 13.4155 + 23.2363i 0.571518 + 0.989898i
\(552\) −6.33399 1.69719i −0.269593 0.0722371i
\(553\) 27.6617 47.9115i 1.17630 2.03740i
\(554\) 0.976702 0.0414961
\(555\) 1.61299 39.1331i 0.0684676 1.66111i
\(556\) −10.7479 −0.455813
\(557\) −3.54864 + 6.14642i −0.150361 + 0.260432i −0.931360 0.364099i \(-0.881377\pi\)
0.780999 + 0.624532i \(0.214710\pi\)
\(558\) −1.27346 0.341224i −0.0539101 0.0144452i
\(559\) 18.8819 + 32.7045i 0.798621 + 1.38325i
\(560\) −10.6796 + 3.86965i −0.451295 + 0.163523i
\(561\) 0.562270 0.562270i 0.0237391 0.0237391i
\(562\) 13.4851 + 3.61332i 0.568835 + 0.152419i
\(563\) −21.2351 −0.894954 −0.447477 0.894295i \(-0.647677\pi\)
−0.447477 + 0.894295i \(0.647677\pi\)
\(564\) −22.8005 13.1639i −0.960074 0.554299i
\(565\) −14.8316 21.2468i −0.623970 0.893858i
\(566\) 0.415625i 0.0174700i
\(567\) −4.11315 15.3505i −0.172736 0.644660i
\(568\) 7.60300 + 13.1688i 0.319015 + 0.552550i
\(569\) 5.61604 5.61604i 0.235437 0.235437i −0.579521 0.814957i \(-0.696760\pi\)
0.814957 + 0.579521i \(0.196760\pi\)
\(570\) 2.58537 + 30.0492i 0.108289 + 1.25862i
\(571\) −9.35867 + 16.2097i −0.391648 + 0.678354i −0.992667 0.120880i \(-0.961428\pi\)
0.601019 + 0.799235i \(0.294762\pi\)
\(572\) −1.79009 1.03351i −0.0748473 0.0432131i
\(573\) 21.6746 12.5138i 0.905468 0.522772i
\(574\) −5.14256 + 19.1923i −0.214646 + 0.801071i
\(575\) 7.29373 + 8.74334i 0.304170 + 0.364623i
\(576\) 4.58291 + 2.64594i 0.190954 + 0.110248i
\(577\) 32.6054 + 18.8248i 1.35738 + 0.783685i 0.989270 0.146097i \(-0.0466711\pi\)
0.368112 + 0.929782i \(0.380004\pi\)
\(578\) 16.6173 0.691190
\(579\) −10.3036 2.76085i −0.428204 0.114737i
\(580\) −9.80002 8.24727i −0.406924 0.342449i
\(581\) 52.4709 2.17686
\(582\) 6.55845 + 6.55845i 0.271856 + 0.271856i
\(583\) −0.967049 3.60908i −0.0400511 0.149473i
\(584\) 0.847559 0.847559i 0.0350723 0.0350723i
\(585\) 23.2278 49.6255i 0.960352 2.05176i
\(586\) −1.19912 1.19912i −0.0495353 0.0495353i
\(587\) 15.7920 + 27.3526i 0.651806 + 1.12896i 0.982684 + 0.185288i \(0.0593219\pi\)
−0.330878 + 0.943674i \(0.607345\pi\)
\(588\) −14.0155 + 52.3067i −0.577991 + 2.15709i
\(589\) 1.01061 0.583479i 0.0416416 0.0240418i
\(590\) −5.74079 + 6.82163i −0.236345 + 0.280842i
\(591\) 13.4148i 0.551811i
\(592\) 6.02760 0.817343i 0.247733 0.0335926i
\(593\) 8.14760 + 8.14760i 0.334582 + 0.334582i 0.854323 0.519742i \(-0.173972\pi\)
−0.519742 + 0.854323i \(0.673972\pi\)
\(594\) −0.762488 2.84564i −0.0312852 0.116758i
\(595\) −2.39380 6.60649i −0.0981362 0.270840i
\(596\) 4.42927 2.55724i 0.181430 0.104749i
\(597\) −32.9986 + 19.0517i −1.35054 + 0.779736i
\(598\) −10.5447 −0.431204
\(599\) 29.2107 16.8648i 1.19352 0.689078i 0.234416 0.972136i \(-0.424682\pi\)
0.959103 + 0.283058i \(0.0913489\pi\)
\(600\) −6.04718 13.0663i −0.246875 0.533430i
\(601\) −13.5899 + 23.5384i −0.554344 + 0.960152i 0.443610 + 0.896220i \(0.353697\pi\)
−0.997954 + 0.0639322i \(0.979636\pi\)
\(602\) 29.2949 29.2949i 1.19397 1.19397i
\(603\) 51.1748 51.1748i 2.08400 2.08400i
\(604\) 11.0417 + 6.37493i 0.449280 + 0.259392i
\(605\) −21.8737 10.2382i −0.889291 0.416243i
\(606\) 0.987383 + 0.987383i 0.0401097 + 0.0401097i
\(607\) −6.74092 + 11.6756i −0.273606 + 0.473899i −0.969782 0.243972i \(-0.921550\pi\)
0.696177 + 0.717870i \(0.254883\pi\)
\(608\) −4.52445 + 1.21232i −0.183491 + 0.0491662i
\(609\) −80.9358 + 21.6867i −3.27969 + 0.878789i
\(610\) −6.04102 16.6722i −0.244594 0.675039i
\(611\) −40.8938 10.9574i −1.65438 0.443291i
\(612\) −1.63680 + 2.83503i −0.0661639 + 0.114599i
\(613\) −6.95722 25.9647i −0.281000 1.04870i −0.951713 0.306988i \(-0.900679\pi\)
0.670714 0.741716i \(-0.265988\pi\)
\(614\) −24.0576 + 6.44622i −0.970886 + 0.260148i
\(615\) −24.7958 4.40900i −0.999865 0.177788i
\(616\) −0.586908 + 2.19037i −0.0236472 + 0.0882526i
\(617\) −42.1875 + 11.3041i −1.69841 + 0.455086i −0.972537 0.232747i \(-0.925229\pi\)
−0.725868 + 0.687834i \(0.758562\pi\)
\(618\) −1.33932 1.33932i −0.0538753 0.0538753i
\(619\) −13.5911 −0.546272 −0.273136 0.961975i \(-0.588061\pi\)
−0.273136 + 0.961975i \(0.588061\pi\)
\(620\) −0.358698 + 0.426232i −0.0144057 + 0.0171179i
\(621\) −10.6270 10.6270i −0.426448 0.426448i
\(622\) −7.93052 + 29.5971i −0.317985 + 1.18674i
\(623\) 5.05088i 0.202359i
\(624\) 12.8794 + 3.45103i 0.515590 + 0.138152i
\(625\) −4.48293 + 24.5948i −0.179317 + 0.983791i
\(626\) −8.47539 14.6798i −0.338745 0.586723i
\(627\) 5.21431 + 3.01048i 0.208239 + 0.120227i
\(628\) 6.28843 6.28843i 0.250936 0.250936i
\(629\) 0.505616 + 3.72873i 0.0201602 + 0.148674i
\(630\) −59.1825 10.5233i −2.35789 0.419260i
\(631\) 43.6140 11.6863i 1.73625 0.465226i 0.754639 0.656140i \(-0.227812\pi\)
0.981607 + 0.190915i \(0.0611453\pi\)
\(632\) −2.81870 + 10.5195i −0.112122 + 0.418444i
\(633\) 18.5626 + 4.97384i 0.737798 + 0.197693i
\(634\) −3.64446 + 13.6013i −0.144740 + 0.540177i
\(635\) 7.48530 42.0967i 0.297045 1.67056i
\(636\) 12.0512 + 20.8734i 0.477863 + 0.827683i
\(637\) 87.0789i 3.45019i
\(638\) −2.46987 + 0.661800i −0.0977832 + 0.0262009i
\(639\) 80.4684i 3.18328i
\(640\) 1.83352 1.27992i 0.0724764 0.0505932i
\(641\) 16.8051 29.1073i 0.663763 1.14967i −0.315857 0.948807i \(-0.602292\pi\)
0.979619 0.200864i \(-0.0643748\pi\)
\(642\) 45.7568 26.4177i 1.80588 1.04262i
\(643\) 35.8527i 1.41389i 0.707267 + 0.706946i \(0.249928\pi\)
−0.707267 + 0.706946i \(0.750072\pi\)
\(644\) 2.99406 + 11.1740i 0.117982 + 0.440316i
\(645\) 40.1782 + 33.8122i 1.58201 + 1.33135i
\(646\) −0.749954 2.79887i −0.0295066 0.110120i
\(647\) −21.5009 37.2407i −0.845289 1.46408i −0.885370 0.464888i \(-0.846095\pi\)
0.0400802 0.999196i \(-0.487239\pi\)
\(648\) 1.56420 + 2.70927i 0.0614475 + 0.106430i
\(649\) 0.460668 + 1.71924i 0.0180828 + 0.0674860i
\(650\) −14.8310 17.7786i −0.581718 0.697333i
\(651\) 0.943219 + 3.52014i 0.0369677 + 0.137965i
\(652\) 6.16985i 0.241630i
\(653\) −18.4727 + 10.6652i −0.722891 + 0.417361i −0.815816 0.578312i \(-0.803712\pi\)
0.0929248 + 0.995673i \(0.470378\pi\)
\(654\) 1.98414 3.43664i 0.0775861 0.134383i
\(655\) 22.5453 + 4.00883i 0.880919 + 0.156638i
\(656\) 3.91135i 0.152713i
\(657\) 6.12688 1.64169i 0.239032 0.0640485i
\(658\) 46.4455i 1.81063i
\(659\) −12.6462 21.9038i −0.492624 0.853250i 0.507340 0.861746i \(-0.330629\pi\)
−0.999964 + 0.00849583i \(0.997296\pi\)
\(660\) −2.82989 0.503188i −0.110153 0.0195866i
\(661\) 5.58323 20.8369i 0.217163 0.810462i −0.768231 0.640172i \(-0.778863\pi\)
0.985394 0.170290i \(-0.0544704\pi\)
\(662\) −15.7079 4.20892i −0.610505 0.163584i
\(663\) −2.13484 + 7.96734i −0.0829104 + 0.309426i
\(664\) −9.97712 + 2.67336i −0.387187 + 0.103747i
\(665\) 43.6280 30.4552i 1.69182 1.18100i
\(666\) 29.7866 + 12.2029i 1.15421 + 0.472852i
\(667\) −9.22371 + 9.22371i −0.357144 + 0.357144i
\(668\) 3.86637 + 2.23225i 0.149594 + 0.0863682i
\(669\) −7.57736 13.1244i −0.292958 0.507418i
\(670\) −10.4178 28.7514i −0.402474 1.11076i
\(671\) −3.41945 0.916240i −0.132007 0.0353710i
\(672\) 14.6279i 0.564285i
\(673\) 0.927847 3.46277i 0.0357659 0.133480i −0.945734 0.324941i \(-0.894656\pi\)
0.981500 + 0.191460i \(0.0613224\pi\)
\(674\) 7.83737 + 7.83737i 0.301884 + 0.301884i
\(675\) 2.97063 32.8642i 0.114340 1.26494i
\(676\) 8.44138 0.324668
\(677\) 3.73268 + 3.73268i 0.143459 + 0.143459i 0.775189 0.631730i \(-0.217655\pi\)
−0.631730 + 0.775189i \(0.717655\pi\)
\(678\) 32.2312 8.63632i 1.23783 0.331676i
\(679\) 4.23489 15.8048i 0.162520 0.606534i
\(680\) 0.791768 + 1.13423i 0.0303629 + 0.0434959i
\(681\) −48.7189 + 13.0542i −1.86691 + 0.500237i
\(682\) 0.0287837 + 0.107422i 0.00110218 + 0.00411341i
\(683\) 14.7455 25.5399i 0.564220 0.977257i −0.432902 0.901441i \(-0.642510\pi\)
0.997122 0.0758164i \(-0.0241563\pi\)
\(684\) −23.9429 6.41547i −0.915479 0.245302i
\(685\) 19.7381 7.15192i 0.754154 0.273261i
\(686\) 57.9279 15.5217i 2.21170 0.592623i
\(687\) −46.6647 + 12.5038i −1.78037 + 0.477048i
\(688\) −4.07774 + 7.06286i −0.155463 + 0.269269i
\(689\) 27.4060 + 27.4060i 1.04409 + 1.04409i
\(690\) −13.7858 + 4.99515i −0.524816 + 0.190162i
\(691\) 30.8171 + 17.7923i 1.17234 + 0.676850i 0.954230 0.299075i \(-0.0966780\pi\)
0.218109 + 0.975925i \(0.430011\pi\)
\(692\) 7.65324 7.65324i 0.290933 0.290933i
\(693\) −8.48534 + 8.48534i −0.322331 + 0.322331i
\(694\) −6.27074 + 10.8612i −0.238034 + 0.412287i
\(695\) −19.7066 + 13.7564i −0.747513 + 0.521812i
\(696\) 14.2847 8.24727i 0.541460 0.312612i
\(697\) 2.41960 0.0916488
\(698\) 14.7799 8.53318i 0.559427 0.322986i
\(699\) −25.0605 + 14.4687i −0.947875 + 0.547256i
\(700\) −14.6285 + 20.7641i −0.552904 + 0.784809i
\(701\) −7.84329 29.2716i −0.296237 1.10557i −0.940230 0.340540i \(-0.889390\pi\)
0.643993 0.765031i \(-0.277277\pi\)
\(702\) 21.6088 + 21.6088i 0.815572 + 0.815572i
\(703\) −26.2807 + 11.0054i −0.991195 + 0.415077i
\(704\) 0.446393i 0.0168241i
\(705\) −58.6539 + 5.04646i −2.20903 + 0.190061i
\(706\) −8.29168 + 4.78720i −0.312061 + 0.180169i
\(707\) 0.637569 2.37944i 0.0239783 0.0894881i
\(708\) −5.74079 9.94334i −0.215752 0.373694i
\(709\) 19.6226 + 19.6226i 0.736941 + 0.736941i 0.971985 0.235043i \(-0.0755233\pi\)
−0.235043 + 0.971985i \(0.575523\pi\)
\(710\) 30.7952 + 14.4141i 1.15572 + 0.540950i
\(711\) −40.7519 + 40.7519i −1.52832 + 1.52832i
\(712\) 0.257339 + 0.960403i 0.00964420 + 0.0359926i
\(713\) 0.401167 + 0.401167i 0.0150238 + 0.0150238i
\(714\) 9.04898 0.338650
\(715\) −4.60497 + 0.396202i −0.172216 + 0.0148171i
\(716\) 23.5004 + 6.29691i 0.878250 + 0.235326i
\(717\) −10.3943 −0.388181
\(718\) −28.2688 16.3210i −1.05498 0.609094i
\(719\) 17.6288 + 10.1780i 0.657443 + 0.379575i 0.791302 0.611425i \(-0.209404\pi\)
−0.133859 + 0.991000i \(0.542737\pi\)
\(720\) 11.7895 1.01434i 0.439367 0.0378023i
\(721\) −0.864819 + 3.22755i −0.0322075 + 0.120200i
\(722\) 2.54645 1.47019i 0.0947690 0.0547149i
\(723\) −44.4414 25.6582i −1.65279 0.954240i
\(724\) 5.42208 9.39132i 0.201510 0.349026i
\(725\) −28.5244 2.57835i −1.05937 0.0957577i
\(726\) 21.9920 21.9920i 0.816200 0.816200i
\(727\) 9.26823 + 16.0530i 0.343739 + 0.595374i 0.985124 0.171845i \(-0.0549730\pi\)
−0.641384 + 0.767220i \(0.721640\pi\)
\(728\) −6.08807 22.7210i −0.225639 0.842095i
\(729\) 40.4570i 1.49841i
\(730\) 0.469215 2.63883i 0.0173664 0.0976674i
\(731\) −4.36915 2.52253i −0.161599 0.0932991i
\(732\) 22.8361 0.844047
\(733\) −38.1401 10.2196i −1.40874 0.377470i −0.527262 0.849703i \(-0.676781\pi\)
−0.881474 + 0.472233i \(0.843448\pi\)
\(734\) 12.4574 12.4574i 0.459811 0.459811i
\(735\) 41.2504 + 113.844i 1.52154 + 4.19921i
\(736\) −1.13862 1.97214i −0.0419699 0.0726940i
\(737\) −5.89687 1.58006i −0.217214 0.0582023i
\(738\) 10.3492 17.9254i 0.380960 0.659841i
\(739\) −38.8698 −1.42985 −0.714925 0.699201i \(-0.753539\pi\)
−0.714925 + 0.699201i \(0.753539\pi\)
\(740\) 10.0056 9.21345i 0.367814 0.338693i
\(741\) −62.4561 −2.29438
\(742\) 21.2599 36.8233i 0.780477 1.35183i
\(743\) −21.7441 5.82632i −0.797715 0.213747i −0.163134 0.986604i \(-0.552160\pi\)
−0.634580 + 0.772857i \(0.718827\pi\)
\(744\) −0.358698 0.621284i −0.0131505 0.0227774i
\(745\) 4.84812 10.3579i 0.177621 0.379483i
\(746\) −3.12913 + 3.12913i −0.114566 + 0.114566i
\(747\) −52.7978 14.1471i −1.93177 0.517616i
\(748\) 0.276143 0.0100968
\(749\) −80.7208 46.6042i −2.94947 1.70288i
\(750\) −27.8115 16.2175i −1.01553 0.592181i
\(751\) 10.9028i 0.397850i −0.980015 0.198925i \(-0.936255\pi\)
0.980015 0.198925i \(-0.0637451\pi\)
\(752\) −2.36637 8.83142i −0.0862927 0.322049i
\(753\) −8.16706 14.1458i −0.297624 0.515500i
\(754\) 18.7553 18.7553i 0.683029 0.683029i
\(755\) 28.4046 2.44387i 1.03375 0.0889417i
\(756\) 16.7628 29.0340i 0.609657 1.05596i
\(757\) 11.1831 + 6.45657i 0.406457 + 0.234668i 0.689266 0.724508i \(-0.257933\pi\)
−0.282809 + 0.959176i \(0.591266\pi\)
\(758\) 12.8893 7.44164i 0.468161 0.270293i
\(759\) −0.757612 + 2.82745i −0.0274996 + 0.102630i
\(760\) −6.74402 + 8.01375i −0.244631 + 0.290689i
\(761\) 18.0185 + 10.4030i 0.653169 + 0.377107i 0.789669 0.613533i \(-0.210252\pi\)
−0.136500 + 0.990640i \(0.543586\pi\)
\(762\) 47.6848 + 27.5308i 1.72744 + 0.997337i
\(763\) −7.00056 −0.253437
\(764\) 8.39531 + 2.24952i 0.303732 + 0.0813847i
\(765\) 0.627481 + 7.29307i 0.0226866 + 0.263681i
\(766\) −0.711671 −0.0257137
\(767\) −13.0553 13.0553i −0.471399 0.471399i
\(768\) 0.745286 + 2.78144i 0.0268932 + 0.100367i
\(769\) 35.9160 35.9160i 1.29516 1.29516i 0.363615 0.931549i \(-0.381542\pi\)
0.931549 0.363615i \(-0.118458\pi\)
\(770\) 1.72738 + 4.76729i 0.0622506 + 0.171801i
\(771\) 48.0011 + 48.0011i 1.72872 + 1.72872i
\(772\) −1.85221 3.20811i −0.0666623 0.115463i
\(773\) −3.68870 + 13.7664i −0.132673 + 0.495143i −0.999997 0.00260185i \(-0.999172\pi\)
0.867323 + 0.497745i \(0.165838\pi\)
\(774\) −37.3759 + 21.5790i −1.34345 + 0.775640i
\(775\) −0.112140 + 1.24061i −0.00402820 + 0.0445641i
\(776\) 3.22099i 0.115627i
\(777\) −11.9561 88.1714i −0.428921 3.16313i
\(778\) −5.95079 5.95079i −0.213346 0.213346i
\(779\) 4.74182 + 17.6967i 0.169893 + 0.634050i
\(780\) 28.0318 10.1571i 1.00370 0.363681i
\(781\) 5.87845 3.39392i 0.210347 0.121444i
\(782\) 1.21998 0.704358i 0.0436265 0.0251878i
\(783\) 37.8036 1.35099
\(784\) −16.2861 + 9.40279i −0.581647 + 0.335814i
\(785\) 3.48132 19.5787i 0.124254 0.698792i
\(786\) −14.7444 + 25.5381i −0.525916 + 0.910913i
\(787\) −19.9261 + 19.9261i −0.710290 + 0.710290i −0.966596 0.256306i \(-0.917495\pi\)
0.256306 + 0.966596i \(0.417495\pi\)
\(788\) −3.29415 + 3.29415i −0.117349 + 0.117349i
\(789\) 21.6843 + 12.5194i 0.771980 + 0.445703i
\(790\) 8.29597 + 22.8955i 0.295157 + 0.814586i
\(791\) −41.6244 41.6244i −1.47999 1.47999i
\(792\) 1.18113 2.04578i 0.0419696 0.0726935i
\(793\) 35.4704 9.50426i 1.25959 0.337506i
\(794\) 8.27128 2.21628i 0.293537 0.0786529i
\(795\) 48.8124 + 22.8472i 1.73120 + 0.810308i
\(796\) −12.7815 3.42479i −0.453028 0.121389i
\(797\) −0.792040 + 1.37185i −0.0280555 + 0.0485935i −0.879712 0.475506i \(-0.842265\pi\)
0.851657 + 0.524100i \(0.175598\pi\)
\(798\) 17.7338 + 66.1834i 0.627770 + 2.34287i
\(799\) 5.46320 1.46386i 0.193274 0.0517876i
\(800\) 1.72362 4.69352i 0.0609393 0.165941i
\(801\) −1.36181 + 5.08234i −0.0481172 + 0.179576i
\(802\) −11.7591 + 3.15084i −0.415228 + 0.111260i
\(803\) −0.378344 0.378344i −0.0133515 0.0133515i
\(804\) 39.3810 1.38886
\(805\) 19.7914 + 16.6556i 0.697557 + 0.587033i
\(806\) −0.815726 0.815726i −0.0287327 0.0287327i
\(807\) −10.0027 + 37.3305i −0.352111 + 1.31410i
\(808\) 0.484925i 0.0170596i
\(809\) −27.0254 7.24144i −0.950163 0.254595i −0.249731 0.968315i \(-0.580342\pi\)
−0.700431 + 0.713720i \(0.747009\pi\)
\(810\) 6.33563 + 2.96547i 0.222611 + 0.104196i
\(811\) −12.7965 22.1641i −0.449344 0.778287i 0.548999 0.835823i \(-0.315009\pi\)
−0.998343 + 0.0575357i \(0.981676\pi\)
\(812\) −25.2000 14.5492i −0.884348 0.510578i
\(813\) −23.5547 + 23.5547i −0.826099 + 0.826099i
\(814\) −0.364856 2.69068i −0.0127882 0.0943082i
\(815\) 7.89690 + 11.3126i 0.276616 + 0.396262i
\(816\) −1.72063 + 0.461041i −0.0602340 + 0.0161397i
\(817\) 9.88709 36.8991i 0.345905 1.29094i
\(818\) 11.8128 + 3.16524i 0.413026 + 0.110670i
\(819\) 32.2173 120.237i 1.12577 4.20141i
\(820\) −5.00620 7.17155i −0.174824 0.250442i
\(821\) 12.1905 + 21.1146i 0.425452 + 0.736904i 0.996463 0.0840385i \(-0.0267819\pi\)
−0.571011 + 0.820943i \(0.693449\pi\)
\(822\) 27.0355i 0.942971i
\(823\) 5.95521 1.59569i 0.207586 0.0556224i −0.153528 0.988144i \(-0.549063\pi\)
0.361113 + 0.932522i \(0.382397\pi\)
\(824\) 0.657767i 0.0229144i
\(825\) −5.83271 + 2.69942i −0.203069 + 0.0939816i
\(826\) −10.1275 + 17.5413i −0.352380 + 0.610341i
\(827\) 2.03545 1.17517i 0.0707796 0.0408646i −0.464193 0.885734i \(-0.653655\pi\)
0.534972 + 0.844870i \(0.320322\pi\)
\(828\) 12.0508i 0.418796i
\(829\) 11.7310 + 43.7806i 0.407434 + 1.52056i 0.799522 + 0.600636i \(0.205086\pi\)
−0.392088 + 0.919928i \(0.628247\pi\)
\(830\) −14.8716 + 17.6716i −0.516201 + 0.613389i
\(831\) 0.727922 + 2.71664i 0.0252513 + 0.0942393i
\(832\) 2.31524 + 4.01012i 0.0802666 + 0.139026i
\(833\) −5.81665 10.0747i −0.201535 0.349069i
\(834\) −8.01027 29.8947i −0.277373 1.03517i
\(835\) 9.94617 0.855748i 0.344201 0.0296144i
\(836\) 0.541172 + 2.01968i 0.0187168 + 0.0698522i
\(837\) 1.64419i 0.0568316i
\(838\) 10.3821 5.99408i 0.358642 0.207062i
\(839\) 13.1457 22.7690i 0.453839 0.786073i −0.544781 0.838578i \(-0.683387\pi\)
0.998621 + 0.0525054i \(0.0167207\pi\)
\(840\) −18.7226 26.8207i −0.645990 0.925402i
\(841\) 3.81158i 0.131434i
\(842\) −11.9258 + 3.19550i −0.410990 + 0.110124i
\(843\) 40.2010i 1.38460i
\(844\) 3.33687 + 5.77963i 0.114860 + 0.198943i
\(845\) 15.4775 10.8043i 0.532441 0.371678i
\(846\) 12.5226 46.7349i 0.430535 1.60678i
\(847\) −52.9973 14.2006i −1.82101 0.487938i
\(848\) −2.16636 + 8.08498i −0.0743932 + 0.277639i
\(849\) 1.15604 0.309760i 0.0396751 0.0106309i
\(850\) 2.90345 + 1.06625i 0.0995876 + 0.0365721i
\(851\) −8.47503 10.9566i −0.290520 0.375588i
\(852\) −30.9618 + 30.9618i −1.06073 + 1.06073i
\(853\) −46.4734 26.8314i −1.59122 0.918691i −0.993098 0.117285i \(-0.962581\pi\)
−0.598121 0.801406i \(-0.704086\pi\)
\(854\) −20.1429 34.8886i −0.689277 1.19386i
\(855\) −52.1111 + 18.8820i −1.78216 + 0.645750i
\(856\) 17.7232 + 4.74891i 0.605766 + 0.162314i
\(857\) 1.21914i 0.0416450i −0.999783 0.0208225i \(-0.993372\pi\)
0.999783 0.0208225i \(-0.00662848\pi\)
\(858\) 1.54052 5.74929i 0.0525924 0.196277i
\(859\) 30.9991 + 30.9991i 1.05768 + 1.05768i 0.998232 + 0.0594446i \(0.0189330\pi\)
0.0594446 + 0.998232i \(0.481067\pi\)
\(860\) 1.56323 + 18.1691i 0.0533058 + 0.619561i
\(861\) −57.2150 −1.94988
\(862\) −8.62459 8.62459i −0.293755 0.293755i
\(863\) 38.3228 10.2686i 1.30452 0.349546i 0.461363 0.887211i \(-0.347360\pi\)
0.843158 + 0.537666i \(0.180694\pi\)
\(864\) −1.70811 + 6.37475i −0.0581111 + 0.216873i
\(865\) 4.23689 23.8279i 0.144059 0.810174i
\(866\) −14.6235 + 3.91835i −0.496926 + 0.133151i
\(867\) 12.3847 + 46.2202i 0.420605 + 1.56972i
\(868\) −0.632790 + 1.09602i −0.0214783 + 0.0372015i
\(869\) 4.69584 + 1.25825i 0.159295 + 0.0426831i
\(870\) 15.6355 33.4048i 0.530093 1.13253i
\(871\) 61.1689 16.3902i 2.07263 0.555359i
\(872\) 1.33113 0.356675i 0.0450777 0.0120785i
\(873\) −8.52256 + 14.7615i −0.288445 + 0.499601i
\(874\) 7.54248 + 7.54248i 0.255128 + 0.255128i
\(875\) −0.245332 + 56.7947i −0.00829373 + 1.92001i
\(876\) 2.98911 + 1.72577i 0.100993 + 0.0583082i
\(877\) −30.1718 + 30.1718i −1.01883 + 1.01883i −0.0190116 + 0.999819i \(0.506052\pi\)
−0.999819 + 0.0190116i \(0.993948\pi\)
\(878\) −0.471791 + 0.471791i −0.0159222 + 0.0159222i
\(879\) 2.44160 4.22898i 0.0823532 0.142640i
\(880\) −0.571346 0.818472i −0.0192601 0.0275907i
\(881\) −43.6201 + 25.1841i −1.46960 + 0.848474i −0.999419 0.0340967i \(-0.989145\pi\)
−0.470181 + 0.882570i \(0.655811\pi\)
\(882\) −99.5170 −3.35091
\(883\) 4.96366 2.86577i 0.167041 0.0964409i −0.414149 0.910209i \(-0.635921\pi\)
0.581190 + 0.813768i \(0.302587\pi\)
\(884\) −2.48069 + 1.43223i −0.0834348 + 0.0481711i
\(885\) −23.2525 10.8836i −0.781625 0.365849i
\(886\) 7.08304 + 26.4343i 0.237959 + 0.888076i
\(887\) 16.5303 + 16.5303i 0.555033 + 0.555033i 0.927889 0.372856i \(-0.121622\pi\)
−0.372856 + 0.927889i \(0.621622\pi\)
\(888\) 6.76568 + 16.1563i 0.227041 + 0.542169i
\(889\) 97.1358i 3.25783i
\(890\) 1.70107 + 1.43155i 0.0570202 + 0.0479857i
\(891\) 1.20940 0.698246i 0.0405163 0.0233921i
\(892\) 1.36213 5.08353i 0.0456074 0.170209i
\(893\) 21.4131 + 37.0885i 0.716561 + 1.24112i
\(894\) 10.4139 + 10.4139i 0.348293 + 0.348293i
\(895\) 51.1480 18.5330i 1.70969 0.619490i
\(896\) 3.59205 3.59205i 0.120002 0.120002i
\(897\) −7.85880 29.3294i −0.262398 0.979282i
\(898\) −3.27007 3.27007i −0.109124 0.109124i
\(899\) −1.42707 −0.0475956
\(900\) 20.3180 16.9494i 0.677266 0.564978i
\(901\) −5.00144 1.34013i −0.166622 0.0446463i
\(902\) −1.74600 −0.0581354
\(903\) 103.315 + 59.6490i 3.43811 + 1.98500i
\(904\) 10.0354 + 5.79397i 0.333774 + 0.192705i
\(905\) −2.07859 24.1590i −0.0690948 0.803073i
\(906\) −9.50229 + 35.4630i −0.315692 + 1.17818i
\(907\) 4.86415 2.80832i 0.161511 0.0932487i −0.417066 0.908876i \(-0.636942\pi\)
0.578577 + 0.815628i \(0.303608\pi\)
\(908\) −15.1690 8.75783i −0.503401 0.290639i
\(909\) −1.28308 + 2.22236i −0.0425572 + 0.0737112i
\(910\) −40.2436 33.8672i −1.33406 1.12269i
\(911\) 32.1621 32.1621i 1.06558 1.06558i 0.0678858 0.997693i \(-0.478375\pi\)
0.997693 0.0678858i \(-0.0216254\pi\)
\(912\) −6.74402 11.6810i −0.223317 0.386796i
\(913\) 1.19337 + 4.45371i 0.0394948 + 0.147396i
\(914\) 2.81784i 0.0932060i
\(915\) 41.8706 29.2283i 1.38420 0.966259i
\(916\) −14.5294 8.38857i −0.480066 0.277166i
\(917\) 52.0221 1.71792
\(918\) −3.94348 1.05665i −0.130154 0.0348747i
\(919\) 11.6186 11.6186i 0.383263 0.383263i −0.489013 0.872276i \(-0.662643\pi\)
0.872276 + 0.489013i \(0.162643\pi\)
\(920\) −4.61186 2.15863i −0.152048 0.0711680i
\(921\) −35.8596 62.1107i −1.18161 2.04662i
\(922\) −18.0988 4.84955i −0.596051 0.159711i
\(923\) −35.2055 + 60.9778i −1.15880 + 2.00711i
\(924\) −6.52981 −0.214815
\(925\) 6.55310 29.6994i 0.215465 0.976512i
\(926\) −1.32365 −0.0434978
\(927\) 1.74041 3.01448i 0.0571627 0.0990087i
\(928\) 5.53296 + 1.48255i 0.181628 + 0.0486671i
\(929\) −3.00479 5.20445i −0.0985839 0.170752i 0.812515 0.582941i \(-0.198098\pi\)
−0.911099 + 0.412188i \(0.864765\pi\)
\(930\) −1.45287 0.680035i −0.0476416 0.0222992i
\(931\) 62.2865 62.2865i 2.04136 2.04136i
\(932\) −9.70681 2.60093i −0.317957 0.0851963i
\(933\) −88.2332 −2.88863
\(934\) 10.9518 + 6.32303i 0.358354 + 0.206896i
\(935\) 0.506314 0.353440i 0.0165582 0.0115587i
\(936\) 24.5040i 0.800938i
\(937\) −13.9036 51.8890i −0.454212 1.69514i −0.690395 0.723432i \(-0.742563\pi\)
0.236184 0.971708i \(-0.424103\pi\)
\(938\) −34.7366 60.1655i −1.13419 1.96447i
\(939\) 34.5145 34.5145i 1.12634 1.12634i
\(940\) −15.6423 13.1639i −0.510195 0.429358i
\(941\) −2.75738 + 4.77592i −0.0898880 + 0.155691i −0.907464 0.420131i \(-0.861984\pi\)
0.817576 + 0.575821i \(0.195318\pi\)
\(942\) 22.1776 + 12.8042i 0.722585 + 0.417185i
\(943\) −7.71373 + 4.45352i −0.251194 + 0.145027i
\(944\) 1.03198 3.85140i 0.0335881 0.125352i
\(945\) −6.42614 74.6895i −0.209042 2.42965i
\(946\) 3.15281 + 1.82028i 0.102507 + 0.0591823i
\(947\) 0.892850 + 0.515487i 0.0290137 + 0.0167511i 0.514437 0.857528i \(-0.328001\pi\)
−0.485423 + 0.874279i \(0.661334\pi\)
\(948\) −31.3602 −1.01853
\(949\) 5.36112 + 1.43651i 0.174029 + 0.0466310i
\(950\) −2.10839 + 23.3252i −0.0684052 + 0.756769i
\(951\) −40.5475 −1.31484
\(952\) 2.22207 + 2.22207i 0.0720178 + 0.0720178i
\(953\) 7.28070 + 27.1719i 0.235845 + 0.880186i 0.977766 + 0.209698i \(0.0672482\pi\)
−0.741921 + 0.670487i \(0.766085\pi\)
\(954\) −31.3206 + 31.3206i −1.01404 + 1.01404i
\(955\) 18.2722 6.62076i 0.591275 0.214243i
\(956\) −2.55242 2.55242i −0.0825512 0.0825512i
\(957\) −3.68152 6.37658i −0.119007 0.206126i
\(958\) 8.09245 30.2014i 0.261455 0.975764i
\(959\) 41.3043 23.8470i 1.33378 0.770061i
\(960\) 4.92652 + 4.14594i 0.159003 + 0.133810i
\(961\) 30.9379i 0.997998i
\(962\) 17.2330 + 22.2790i 0.555614 + 0.718305i
\(963\) 68.6583 + 68.6583i 2.21248 + 2.21248i
\(964\) −4.61239 17.2137i −0.148555 0.554415i
\(965\) −7.50219 3.51149i −0.241504 0.113039i
\(966\) −28.8484 + 16.6556i −0.928181 + 0.535886i
\(967\) −14.3102 + 8.26199i −0.460184 + 0.265688i −0.712122 0.702056i \(-0.752266\pi\)
0.251937 + 0.967744i \(0.418932\pi\)
\(968\) 10.8007 0.347149
\(969\) 7.22596 4.17191i 0.232131 0.134021i
\(970\) 4.12260 + 5.90576i 0.132369 + 0.189623i
\(971\) 18.6691 32.3359i 0.599121 1.03771i −0.393830 0.919183i \(-0.628850\pi\)
0.992951 0.118525i \(-0.0378167\pi\)
\(972\) 7.63002 7.63002i 0.244733 0.244733i
\(973\) −38.6070 + 38.6070i −1.23768 + 1.23768i
\(974\) −37.3347 21.5552i −1.19628 0.690673i
\(975\) 38.3968 54.5016i 1.22968 1.74545i
\(976\) 5.60765 + 5.60765i 0.179496 + 0.179496i
\(977\) 4.43992 7.69016i 0.142046 0.246030i −0.786221 0.617945i \(-0.787965\pi\)
0.928267 + 0.371915i \(0.121299\pi\)
\(978\) −17.1611 + 4.59830i −0.548752 + 0.147038i
\(979\) 0.428717 0.114874i 0.0137019 0.00367140i
\(980\) −17.8262 + 38.0851i −0.569437 + 1.21658i
\(981\) 7.04418 + 1.88748i 0.224903 + 0.0602627i
\(982\) −12.6558 + 21.9205i −0.403864 + 0.699513i
\(983\) 1.63912 + 6.11727i 0.0522797 + 0.195111i 0.987127 0.159940i \(-0.0511302\pi\)
−0.934847 + 0.355051i \(0.884464\pi\)
\(984\) 10.8792 2.91507i 0.346816 0.0929291i
\(985\) −1.82366 + 10.2561i −0.0581067 + 0.326787i
\(986\) −0.917120 + 3.42274i −0.0292070 + 0.109002i
\(987\) −129.186 + 34.6152i −4.11202 + 1.10181i
\(988\) −15.3368 15.3368i −0.487927 0.487927i
\(989\) 18.5719 0.590553
\(990\) −0.452794 5.26273i −0.0143908 0.167261i
\(991\) 17.9411 + 17.9411i 0.569916 + 0.569916i 0.932105 0.362188i \(-0.117970\pi\)
−0.362188 + 0.932105i \(0.617970\pi\)
\(992\) 0.0644806 0.240645i 0.00204726 0.00764048i
\(993\) 46.8275i 1.48603i
\(994\) 74.6131 + 19.9925i 2.36659 + 0.634125i
\(995\) −27.8186 + 10.0798i −0.881910 + 0.319552i
\(996\) −14.8716 25.7584i −0.471225 0.816186i
\(997\) 17.0886 + 9.86613i 0.541203 + 0.312464i 0.745566 0.666431i \(-0.232179\pi\)
−0.204363 + 0.978895i \(0.565512\pi\)
\(998\) −17.4113 + 17.4113i −0.551146 + 0.551146i
\(999\) −5.08544 + 39.8206i −0.160896 + 1.25987i
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 370.2.q.d.273.1 yes 12
5.2 odd 4 370.2.r.d.347.1 yes 12
37.8 odd 12 370.2.r.d.193.1 yes 12
185.82 even 12 inner 370.2.q.d.267.1 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
370.2.q.d.267.1 12 185.82 even 12 inner
370.2.q.d.273.1 yes 12 1.1 even 1 trivial
370.2.r.d.193.1 yes 12 37.8 odd 12
370.2.r.d.347.1 yes 12 5.2 odd 4