Properties

Label 429.2.s.b.199.5
Level $429$
Weight $2$
Character 429.199
Analytic conductor $3.426$
Analytic rank $0$
Dimension $28$
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] = [429,2,Mod(166,429)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(429, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("429.166");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 429 = 3 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 429.s (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.42558224671\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(14\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 199.5
Character \(\chi\) \(=\) 429.199
Dual form 429.2.s.b.166.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.945010 - 0.545602i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.404638 - 0.700853i) q^{4} -1.08345i q^{5} +(0.945010 - 0.545602i) q^{6} +(-2.79805 + 1.61546i) q^{7} +3.06549i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.945010 - 0.545602i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.404638 - 0.700853i) q^{4} -1.08345i q^{5} +(0.945010 - 0.545602i) q^{6} +(-2.79805 + 1.61546i) q^{7} +3.06549i q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.591129 + 1.02387i) q^{10} +(0.866025 + 0.500000i) q^{11} +0.809275 q^{12} +(3.52518 - 0.757049i) q^{13} +3.52558 q^{14} +(0.938291 + 0.541723i) q^{15} +(0.863261 - 1.49521i) q^{16} +(2.05655 + 3.56204i) q^{17} +1.09120i q^{18} +(3.45345 - 1.99385i) q^{19} +(-0.759336 + 0.438403i) q^{20} -3.23091i q^{21} +(-0.545602 - 0.945010i) q^{22} +(-1.43078 + 2.47818i) q^{23} +(-2.65479 - 1.53275i) q^{24} +3.82615 q^{25} +(-3.74437 - 1.20792i) q^{26} +1.00000 q^{27} +(2.26440 + 1.30735i) q^{28} +(-2.58685 + 4.48056i) q^{29} +(-0.591129 - 1.02387i) q^{30} -8.59681i q^{31} +(3.67800 - 2.12350i) q^{32} +(-0.866025 + 0.500000i) q^{33} -4.48822i q^{34} +(1.75026 + 3.03154i) q^{35} +(-0.404638 + 0.700853i) q^{36} +(8.26769 + 4.77336i) q^{37} -4.35139 q^{38} +(-1.10697 + 3.43142i) q^{39} +3.32129 q^{40} +(5.76211 + 3.32675i) q^{41} +(-1.76279 + 3.05325i) q^{42} +(1.21027 + 2.09625i) q^{43} -0.809275i q^{44} +(-0.938291 + 0.541723i) q^{45} +(2.70420 - 1.56127i) q^{46} +5.83737i q^{47} +(0.863261 + 1.49521i) q^{48} +(1.71940 - 2.97810i) q^{49} +(-3.61575 - 2.08755i) q^{50} -4.11309 q^{51} +(-1.95700 - 2.16430i) q^{52} +13.3492 q^{53} +(-0.945010 - 0.545602i) q^{54} +(0.541723 - 0.938291i) q^{55} +(-4.95217 - 8.57741i) q^{56} +3.98770i q^{57} +(4.88920 - 2.82278i) q^{58} +(-11.7925 + 6.80838i) q^{59} -0.876806i q^{60} +(5.66826 + 9.81771i) q^{61} +(-4.69044 + 8.12407i) q^{62} +(2.79805 + 1.61546i) q^{63} -8.08738 q^{64} +(-0.820221 - 3.81934i) q^{65} +1.09120 q^{66} +(-11.5015 - 6.64039i) q^{67} +(1.66431 - 2.88267i) q^{68} +(-1.43078 - 2.47818i) q^{69} -3.81978i q^{70} +(0.489486 - 0.282605i) q^{71} +(2.65479 - 1.53275i) q^{72} -12.7075i q^{73} +(-5.20870 - 9.02173i) q^{74} +(-1.91307 + 3.31354i) q^{75} +(-2.79479 - 1.61357i) q^{76} -3.23091 q^{77} +(2.91828 - 2.63876i) q^{78} +1.87008 q^{79} +(-1.61998 - 0.935296i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.63016 - 6.28763i) q^{82} +2.40039i q^{83} +(-2.26440 + 1.30735i) q^{84} +(3.85928 - 2.22815i) q^{85} -2.64130i q^{86} +(-2.58685 - 4.48056i) q^{87} +(-1.53275 + 2.65479i) q^{88} +(-12.1719 - 7.02744i) q^{89} +1.18226 q^{90} +(-8.64066 + 7.81304i) q^{91} +2.31579 q^{92} +(7.44506 + 4.29841i) q^{93} +(3.18488 - 5.51637i) q^{94} +(-2.16022 - 3.74162i) q^{95} +4.24699i q^{96} +(-15.0115 + 8.66687i) q^{97} +(-3.24971 + 1.87622i) q^{98} -1.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28 q - 14 q^{3} + 18 q^{4} - 14 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 28 q - 14 q^{3} + 18 q^{4} - 14 q^{9} - 36 q^{12} - 6 q^{13} - 4 q^{14} + 6 q^{15} - 22 q^{16} + 2 q^{17} + 12 q^{19} + 18 q^{20} - 6 q^{22} + 2 q^{23} - 40 q^{25} - 18 q^{26} + 28 q^{27} - 18 q^{28} - 30 q^{32} + 2 q^{35} + 18 q^{36} + 20 q^{38} + 6 q^{39} + 20 q^{40} + 18 q^{41} + 2 q^{42} - 2 q^{43} - 6 q^{45} + 48 q^{46} - 22 q^{48} + 10 q^{49} + 24 q^{50} - 4 q^{51} - 28 q^{52} + 16 q^{53} - 12 q^{55} - 10 q^{56} - 48 q^{58} - 12 q^{59} - 4 q^{61} - 6 q^{62} - 32 q^{64} + 6 q^{65} + 12 q^{66} + 12 q^{67} - 22 q^{68} + 2 q^{69} - 18 q^{71} + 48 q^{74} + 20 q^{75} + 96 q^{76} - 24 q^{77} + 6 q^{78} - 48 q^{79} + 66 q^{80} - 14 q^{81} + 46 q^{82} + 18 q^{84} - 66 q^{85} + 12 q^{88} + 8 q^{91} + 72 q^{92} + 6 q^{93} + 50 q^{94} - 60 q^{95} - 36 q^{97} + 18 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).

\(n\) \(67\) \(79\) \(287\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.945010 0.545602i −0.668223 0.385799i 0.127180 0.991880i \(-0.459407\pi\)
−0.795403 + 0.606081i \(0.792741\pi\)
\(3\) −0.500000 + 0.866025i −0.288675 + 0.500000i
\(4\) −0.404638 0.700853i −0.202319 0.350427i
\(5\) 1.08345i 0.484531i −0.970210 0.242266i \(-0.922109\pi\)
0.970210 0.242266i \(-0.0778906\pi\)
\(6\) 0.945010 0.545602i 0.385799 0.222741i
\(7\) −2.79805 + 1.61546i −1.05757 + 0.610585i −0.924758 0.380556i \(-0.875732\pi\)
−0.132807 + 0.991142i \(0.542399\pi\)
\(8\) 3.06549i 1.08381i
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) −0.591129 + 1.02387i −0.186932 + 0.323775i
\(11\) 0.866025 + 0.500000i 0.261116 + 0.150756i
\(12\) 0.809275 0.233618
\(13\) 3.52518 0.757049i 0.977708 0.209968i
\(14\) 3.52558 0.942252
\(15\) 0.938291 + 0.541723i 0.242266 + 0.139872i
\(16\) 0.863261 1.49521i 0.215815 0.373803i
\(17\) 2.05655 + 3.56204i 0.498786 + 0.863922i 0.999999 0.00140167i \(-0.000446167\pi\)
−0.501213 + 0.865324i \(0.667113\pi\)
\(18\) 1.09120i 0.257199i
\(19\) 3.45345 1.99385i 0.792275 0.457420i −0.0484880 0.998824i \(-0.515440\pi\)
0.840763 + 0.541404i \(0.182107\pi\)
\(20\) −0.759336 + 0.438403i −0.169793 + 0.0980298i
\(21\) 3.23091i 0.705043i
\(22\) −0.545602 0.945010i −0.116323 0.201477i
\(23\) −1.43078 + 2.47818i −0.298338 + 0.516737i −0.975756 0.218862i \(-0.929766\pi\)
0.677418 + 0.735598i \(0.263099\pi\)
\(24\) −2.65479 1.53275i −0.541907 0.312870i
\(25\) 3.82615 0.765229
\(26\) −3.74437 1.20792i −0.734332 0.236893i
\(27\) 1.00000 0.192450
\(28\) 2.26440 + 1.30735i 0.427931 + 0.247066i
\(29\) −2.58685 + 4.48056i −0.480366 + 0.832018i −0.999746 0.0225248i \(-0.992830\pi\)
0.519380 + 0.854543i \(0.326163\pi\)
\(30\) −0.591129 1.02387i −0.107925 0.186932i
\(31\) 8.59681i 1.54403i −0.635602 0.772017i \(-0.719248\pi\)
0.635602 0.772017i \(-0.280752\pi\)
\(32\) 3.67800 2.12350i 0.650186 0.375385i
\(33\) −0.866025 + 0.500000i −0.150756 + 0.0870388i
\(34\) 4.48822i 0.769723i
\(35\) 1.75026 + 3.03154i 0.295848 + 0.512423i
\(36\) −0.404638 + 0.700853i −0.0674396 + 0.116809i
\(37\) 8.26769 + 4.77336i 1.35920 + 0.784735i 0.989516 0.144423i \(-0.0461325\pi\)
0.369684 + 0.929157i \(0.379466\pi\)
\(38\) −4.35139 −0.705888
\(39\) −1.10697 + 3.43142i −0.177256 + 0.549467i
\(40\) 3.32129 0.525142
\(41\) 5.76211 + 3.32675i 0.899890 + 0.519552i 0.877164 0.480190i \(-0.159432\pi\)
0.0227253 + 0.999742i \(0.492766\pi\)
\(42\) −1.76279 + 3.05325i −0.272005 + 0.471126i
\(43\) 1.21027 + 2.09625i 0.184564 + 0.319675i 0.943430 0.331573i \(-0.107579\pi\)
−0.758865 + 0.651248i \(0.774246\pi\)
\(44\) 0.809275i 0.122003i
\(45\) −0.938291 + 0.541723i −0.139872 + 0.0807552i
\(46\) 2.70420 1.56127i 0.398712 0.230197i
\(47\) 5.83737i 0.851468i 0.904848 + 0.425734i \(0.139984\pi\)
−0.904848 + 0.425734i \(0.860016\pi\)
\(48\) 0.863261 + 1.49521i 0.124601 + 0.215815i
\(49\) 1.71940 2.97810i 0.245629 0.425442i
\(50\) −3.61575 2.08755i −0.511344 0.295224i
\(51\) −4.11309 −0.575948
\(52\) −1.95700 2.16430i −0.271387 0.300135i
\(53\) 13.3492 1.83366 0.916829 0.399280i \(-0.130740\pi\)
0.916829 + 0.399280i \(0.130740\pi\)
\(54\) −0.945010 0.545602i −0.128600 0.0742470i
\(55\) 0.541723 0.938291i 0.0730459 0.126519i
\(56\) −4.95217 8.57741i −0.661761 1.14620i
\(57\) 3.98770i 0.528183i
\(58\) 4.88920 2.82278i 0.641983 0.370649i
\(59\) −11.7925 + 6.80838i −1.53525 + 0.886376i −0.536140 + 0.844129i \(0.680118\pi\)
−0.999107 + 0.0422468i \(0.986548\pi\)
\(60\) 0.876806i 0.113195i
\(61\) 5.66826 + 9.81771i 0.725746 + 1.25703i 0.958666 + 0.284533i \(0.0918386\pi\)
−0.232920 + 0.972496i \(0.574828\pi\)
\(62\) −4.69044 + 8.12407i −0.595686 + 1.03176i
\(63\) 2.79805 + 1.61546i 0.352522 + 0.203528i
\(64\) −8.08738 −1.01092
\(65\) −0.820221 3.81934i −0.101736 0.473730i
\(66\) 1.09120 0.134318
\(67\) −11.5015 6.64039i −1.40513 0.811252i −0.410217 0.911988i \(-0.634547\pi\)
−0.994913 + 0.100735i \(0.967880\pi\)
\(68\) 1.66431 2.88267i 0.201827 0.349575i
\(69\) −1.43078 2.47818i −0.172246 0.298338i
\(70\) 3.81978i 0.456551i
\(71\) 0.489486 0.282605i 0.0580913 0.0335390i −0.470673 0.882308i \(-0.655989\pi\)
0.528764 + 0.848769i \(0.322656\pi\)
\(72\) 2.65479 1.53275i 0.312870 0.180636i
\(73\) 12.7075i 1.48730i −0.668569 0.743650i \(-0.733093\pi\)
0.668569 0.743650i \(-0.266907\pi\)
\(74\) −5.20870 9.02173i −0.605499 1.04876i
\(75\) −1.91307 + 3.31354i −0.220903 + 0.382615i
\(76\) −2.79479 1.61357i −0.320584 0.185089i
\(77\) −3.23091 −0.368197
\(78\) 2.91828 2.63876i 0.330430 0.298781i
\(79\) 1.87008 0.210401 0.105200 0.994451i \(-0.466452\pi\)
0.105200 + 0.994451i \(0.466452\pi\)
\(80\) −1.61998 0.935296i −0.181119 0.104569i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −3.63016 6.28763i −0.400885 0.694352i
\(83\) 2.40039i 0.263477i 0.991285 + 0.131738i \(0.0420559\pi\)
−0.991285 + 0.131738i \(0.957944\pi\)
\(84\) −2.26440 + 1.30735i −0.247066 + 0.142644i
\(85\) 3.85928 2.22815i 0.418597 0.241677i
\(86\) 2.64130i 0.284819i
\(87\) −2.58685 4.48056i −0.277339 0.480366i
\(88\) −1.53275 + 2.65479i −0.163391 + 0.283002i
\(89\) −12.1719 7.02744i −1.29022 0.744907i −0.311524 0.950238i \(-0.600840\pi\)
−0.978693 + 0.205331i \(0.934173\pi\)
\(90\) 1.18226 0.124621
\(91\) −8.64066 + 7.81304i −0.905787 + 0.819029i
\(92\) 2.31579 0.241438
\(93\) 7.44506 + 4.29841i 0.772017 + 0.445724i
\(94\) 3.18488 5.51637i 0.328495 0.568970i
\(95\) −2.16022 3.74162i −0.221634 0.383882i
\(96\) 4.24699i 0.433457i
\(97\) −15.0115 + 8.66687i −1.52418 + 0.879987i −0.524592 + 0.851354i \(0.675782\pi\)
−0.999590 + 0.0286332i \(0.990885\pi\)
\(98\) −3.24971 + 1.87622i −0.328270 + 0.189527i
\(99\) 1.00000i 0.100504i
\(100\) −1.54820 2.68157i −0.154820 0.268157i
\(101\) 3.86014 6.68596i 0.384098 0.665278i −0.607545 0.794285i \(-0.707846\pi\)
0.991644 + 0.129007i \(0.0411791\pi\)
\(102\) 3.88691 + 2.24411i 0.384862 + 0.222200i
\(103\) 9.08848 0.895515 0.447757 0.894155i \(-0.352223\pi\)
0.447757 + 0.894155i \(0.352223\pi\)
\(104\) 2.32073 + 10.8064i 0.227566 + 1.05965i
\(105\) −3.50052 −0.341616
\(106\) −12.6152 7.28336i −1.22529 0.707423i
\(107\) −3.21702 + 5.57204i −0.311001 + 0.538669i −0.978579 0.205870i \(-0.933997\pi\)
0.667579 + 0.744539i \(0.267331\pi\)
\(108\) −0.404638 0.700853i −0.0389363 0.0674396i
\(109\) 8.47732i 0.811980i 0.913878 + 0.405990i \(0.133073\pi\)
−0.913878 + 0.405990i \(0.866927\pi\)
\(110\) −1.02387 + 0.591129i −0.0976218 + 0.0563620i
\(111\) −8.26769 + 4.77336i −0.784735 + 0.453067i
\(112\) 5.57825i 0.527095i
\(113\) 2.86486 + 4.96208i 0.269503 + 0.466793i 0.968734 0.248103i \(-0.0798072\pi\)
−0.699230 + 0.714896i \(0.746474\pi\)
\(114\) 2.17569 3.76841i 0.203772 0.352944i
\(115\) 2.68497 + 1.55017i 0.250375 + 0.144554i
\(116\) 4.18695 0.388748
\(117\) −2.41821 2.67437i −0.223564 0.247245i
\(118\) 14.8587 1.36785
\(119\) −11.5087 6.64452i −1.05500 0.609102i
\(120\) −1.66065 + 2.87632i −0.151595 + 0.262571i
\(121\) 0.500000 + 0.866025i 0.0454545 + 0.0787296i
\(122\) 12.3704i 1.11997i
\(123\) −5.76211 + 3.32675i −0.519552 + 0.299963i
\(124\) −6.02510 + 3.47859i −0.541070 + 0.312387i
\(125\) 9.56265i 0.855309i
\(126\) −1.76279 3.05325i −0.157042 0.272005i
\(127\) −0.674770 + 1.16874i −0.0598762 + 0.103709i −0.894410 0.447249i \(-0.852404\pi\)
0.834534 + 0.550957i \(0.185737\pi\)
\(128\) 0.286642 + 0.165493i 0.0253358 + 0.0146277i
\(129\) −2.42054 −0.213116
\(130\) −1.30872 + 4.05682i −0.114782 + 0.355807i
\(131\) 11.4747 1.00255 0.501273 0.865289i \(-0.332865\pi\)
0.501273 + 0.865289i \(0.332865\pi\)
\(132\) 0.700853 + 0.404638i 0.0610014 + 0.0352192i
\(133\) −6.44195 + 11.1578i −0.558588 + 0.967503i
\(134\) 7.24601 + 12.5505i 0.625960 + 1.08419i
\(135\) 1.08345i 0.0932481i
\(136\) −10.9194 + 6.30432i −0.936331 + 0.540591i
\(137\) −9.09749 + 5.25244i −0.777251 + 0.448746i −0.835455 0.549559i \(-0.814796\pi\)
0.0582043 + 0.998305i \(0.481463\pi\)
\(138\) 3.12254i 0.265808i
\(139\) 4.85985 + 8.41750i 0.412207 + 0.713963i 0.995131 0.0985634i \(-0.0314247\pi\)
−0.582924 + 0.812527i \(0.698091\pi\)
\(140\) 1.41644 2.45335i 0.119711 0.207346i
\(141\) −5.05531 2.91868i −0.425734 0.245798i
\(142\) −0.616759 −0.0517573
\(143\) 3.43142 + 1.10697i 0.286950 + 0.0925691i
\(144\) −1.72652 −0.143877
\(145\) 4.85444 + 2.80271i 0.403139 + 0.232752i
\(146\) −6.93323 + 12.0087i −0.573798 + 0.993848i
\(147\) 1.71940 + 2.97810i 0.141814 + 0.245629i
\(148\) 7.72592i 0.635067i
\(149\) 10.2722 5.93067i 0.841534 0.485860i −0.0162514 0.999868i \(-0.505173\pi\)
0.857785 + 0.514008i \(0.171840\pi\)
\(150\) 3.61575 2.08755i 0.295224 0.170448i
\(151\) 22.2043i 1.80696i −0.428632 0.903479i \(-0.641004\pi\)
0.428632 0.903479i \(-0.358996\pi\)
\(152\) 6.11212 + 10.5865i 0.495759 + 0.858679i
\(153\) 2.05655 3.56204i 0.166262 0.287974i
\(154\) 3.05325 + 1.76279i 0.246038 + 0.142050i
\(155\) −9.31418 −0.748133
\(156\) 2.85284 0.612661i 0.228410 0.0490521i
\(157\) −3.02291 −0.241255 −0.120627 0.992698i \(-0.538491\pi\)
−0.120627 + 0.992698i \(0.538491\pi\)
\(158\) −1.76725 1.02032i −0.140595 0.0811723i
\(159\) −6.67461 + 11.5608i −0.529331 + 0.916829i
\(160\) −2.30069 3.98492i −0.181886 0.315035i
\(161\) 9.24545i 0.728643i
\(162\) 0.945010 0.545602i 0.0742470 0.0428665i
\(163\) 10.1290 5.84800i 0.793368 0.458051i −0.0477791 0.998858i \(-0.515214\pi\)
0.841147 + 0.540807i \(0.181881\pi\)
\(164\) 5.38452i 0.420460i
\(165\) 0.541723 + 0.938291i 0.0421730 + 0.0730459i
\(166\) 1.30966 2.26839i 0.101649 0.176061i
\(167\) 18.8995 + 10.9116i 1.46249 + 0.844368i 0.999126 0.0418003i \(-0.0133093\pi\)
0.463363 + 0.886169i \(0.346643\pi\)
\(168\) 9.90434 0.764136
\(169\) 11.8538 5.33746i 0.911827 0.410574i
\(170\) −4.86274 −0.372955
\(171\) −3.45345 1.99385i −0.264092 0.152473i
\(172\) 0.979441 1.69644i 0.0746817 0.129352i
\(173\) −2.83167 4.90460i −0.215288 0.372890i 0.738074 0.674720i \(-0.235736\pi\)
−0.953362 + 0.301830i \(0.902402\pi\)
\(174\) 5.64556i 0.427989i
\(175\) −10.7058 + 6.18098i −0.809280 + 0.467238i
\(176\) 1.49521 0.863261i 0.112706 0.0650708i
\(177\) 13.6168i 1.02350i
\(178\) 7.66836 + 13.2820i 0.574768 + 0.995528i
\(179\) 0.920989 1.59520i 0.0688379 0.119231i −0.829552 0.558429i \(-0.811404\pi\)
0.898390 + 0.439199i \(0.144738\pi\)
\(180\) 0.759336 + 0.438403i 0.0565976 + 0.0326766i
\(181\) 3.75761 0.279301 0.139651 0.990201i \(-0.455402\pi\)
0.139651 + 0.990201i \(0.455402\pi\)
\(182\) 12.4283 2.66904i 0.921248 0.197842i
\(183\) −11.3365 −0.838019
\(184\) −7.59684 4.38604i −0.560047 0.323343i
\(185\) 5.17167 8.95759i 0.380229 0.658575i
\(186\) −4.69044 8.12407i −0.343919 0.595686i
\(187\) 4.11309i 0.300779i
\(188\) 4.09114 2.36202i 0.298377 0.172268i
\(189\) −2.79805 + 1.61546i −0.203528 + 0.117507i
\(190\) 4.71449i 0.342025i
\(191\) −5.69417 9.86259i −0.412015 0.713632i 0.583095 0.812404i \(-0.301842\pi\)
−0.995110 + 0.0987726i \(0.968508\pi\)
\(192\) 4.04369 7.00388i 0.291828 0.505461i
\(193\) 11.1931 + 6.46237i 0.805700 + 0.465171i 0.845461 0.534038i \(-0.179326\pi\)
−0.0397602 + 0.999209i \(0.512659\pi\)
\(194\) 18.9146 1.35799
\(195\) 3.71775 + 1.19934i 0.266234 + 0.0858862i
\(196\) −2.78294 −0.198782
\(197\) −13.8372 7.98893i −0.985861 0.569187i −0.0818268 0.996647i \(-0.526075\pi\)
−0.904035 + 0.427459i \(0.859409\pi\)
\(198\) −0.545602 + 0.945010i −0.0387742 + 0.0671589i
\(199\) 2.49054 + 4.31374i 0.176550 + 0.305793i 0.940696 0.339249i \(-0.110173\pi\)
−0.764147 + 0.645042i \(0.776840\pi\)
\(200\) 11.7290i 0.829367i
\(201\) 11.5015 6.64039i 0.811252 0.468377i
\(202\) −7.29574 + 4.21220i −0.513326 + 0.296369i
\(203\) 16.7158i 1.17322i
\(204\) 1.66431 + 2.88267i 0.116525 + 0.201827i
\(205\) 3.60435 6.24293i 0.251739 0.436025i
\(206\) −8.58871 4.95869i −0.598403 0.345488i
\(207\) 2.86156 0.198892
\(208\) 1.91120 5.92442i 0.132518 0.410785i
\(209\) 3.98770 0.275835
\(210\) 3.30802 + 1.90989i 0.228275 + 0.131795i
\(211\) −8.53766 + 14.7877i −0.587757 + 1.01802i 0.406769 + 0.913531i \(0.366655\pi\)
−0.994526 + 0.104493i \(0.966678\pi\)
\(212\) −5.40160 9.35585i −0.370984 0.642562i
\(213\) 0.565210i 0.0387275i
\(214\) 6.08022 3.51042i 0.415636 0.239967i
\(215\) 2.27117 1.31126i 0.154892 0.0894272i
\(216\) 3.06549i 0.208580i
\(217\) 13.8878 + 24.0543i 0.942764 + 1.63292i
\(218\) 4.62524 8.01115i 0.313261 0.542584i
\(219\) 11.0050 + 6.35375i 0.743650 + 0.429347i
\(220\) −0.876806 −0.0591142
\(221\) 9.94633 + 10.9999i 0.669062 + 0.739935i
\(222\) 10.4174 0.699170
\(223\) 14.8828 + 8.59260i 0.996628 + 0.575403i 0.907249 0.420595i \(-0.138178\pi\)
0.0893788 + 0.995998i \(0.471512\pi\)
\(224\) −6.86084 + 11.8833i −0.458409 + 0.793988i
\(225\) −1.91307 3.31354i −0.127538 0.220903i
\(226\) 6.25228i 0.415896i
\(227\) 8.31947 4.80325i 0.552183 0.318803i −0.197819 0.980239i \(-0.563386\pi\)
0.750002 + 0.661436i \(0.230053\pi\)
\(228\) 2.79479 1.61357i 0.185089 0.106861i
\(229\) 4.61591i 0.305028i −0.988301 0.152514i \(-0.951263\pi\)
0.988301 0.152514i \(-0.0487369\pi\)
\(230\) −1.69155 2.92985i −0.111538 0.193189i
\(231\) 1.61546 2.79805i 0.106289 0.184098i
\(232\) −13.7351 7.92997i −0.901754 0.520628i
\(233\) 1.75451 0.114942 0.0574709 0.998347i \(-0.481696\pi\)
0.0574709 + 0.998347i \(0.481696\pi\)
\(234\) 0.826094 + 3.84669i 0.0540035 + 0.251466i
\(235\) 6.32447 0.412563
\(236\) 9.54335 + 5.50985i 0.621219 + 0.358661i
\(237\) −0.935041 + 1.61954i −0.0607374 + 0.105200i
\(238\) 7.25053 + 12.5583i 0.469982 + 0.814032i
\(239\) 28.3540i 1.83407i 0.398807 + 0.917035i \(0.369424\pi\)
−0.398807 + 0.917035i \(0.630576\pi\)
\(240\) 1.61998 0.935296i 0.104569 0.0603731i
\(241\) −6.10023 + 3.52197i −0.392951 + 0.226870i −0.683438 0.730009i \(-0.739516\pi\)
0.290487 + 0.956879i \(0.406183\pi\)
\(242\) 1.09120i 0.0701452i
\(243\) −0.500000 0.866025i −0.0320750 0.0555556i
\(244\) 4.58718 7.94523i 0.293664 0.508641i
\(245\) −3.22660 1.86288i −0.206140 0.119015i
\(246\) 7.26033 0.462902
\(247\) 10.6646 9.64309i 0.678570 0.613575i
\(248\) 26.3535 1.67345
\(249\) −2.07880 1.20019i −0.131738 0.0760593i
\(250\) −5.21740 + 9.03679i −0.329977 + 0.571537i
\(251\) −7.80186 13.5132i −0.492449 0.852947i 0.507513 0.861644i \(-0.330565\pi\)
−0.999962 + 0.00869727i \(0.997232\pi\)
\(252\) 2.61470i 0.164711i
\(253\) −2.47818 + 1.43078i −0.155802 + 0.0899523i
\(254\) 1.27533 0.736312i 0.0800213 0.0462003i
\(255\) 4.45631i 0.279065i
\(256\) 7.90679 + 13.6950i 0.494175 + 0.855935i
\(257\) −1.24846 + 2.16240i −0.0778769 + 0.134887i −0.902334 0.431038i \(-0.858147\pi\)
0.824457 + 0.565925i \(0.191481\pi\)
\(258\) 2.28743 + 1.32065i 0.142409 + 0.0822200i
\(259\) −30.8446 −1.91659
\(260\) −2.34490 + 2.12030i −0.145425 + 0.131496i
\(261\) 5.17370 0.320244
\(262\) −10.8437 6.26059i −0.669924 0.386781i
\(263\) 3.33075 5.76902i 0.205383 0.355733i −0.744872 0.667207i \(-0.767489\pi\)
0.950255 + 0.311474i \(0.100823\pi\)
\(264\) −1.53275 2.65479i −0.0943339 0.163391i
\(265\) 14.4632i 0.888465i
\(266\) 12.1754 7.02948i 0.746523 0.431005i
\(267\) 12.1719 7.02744i 0.744907 0.430072i
\(268\) 10.7478i 0.656527i
\(269\) −9.47612 16.4131i −0.577769 1.00073i −0.995735 0.0922627i \(-0.970590\pi\)
0.417966 0.908463i \(-0.362743\pi\)
\(270\) −0.591129 + 1.02387i −0.0359750 + 0.0623105i
\(271\) −5.34468 3.08575i −0.324666 0.187446i 0.328804 0.944398i \(-0.393354\pi\)
−0.653471 + 0.756952i \(0.726688\pi\)
\(272\) 7.10135 0.430582
\(273\) −2.44596 11.3895i −0.148036 0.689327i
\(274\) 11.4630 0.692502
\(275\) 3.31354 + 1.91307i 0.199814 + 0.115363i
\(276\) −1.15789 + 2.00553i −0.0696970 + 0.120719i
\(277\) −0.446788 0.773859i −0.0268449 0.0464967i 0.852291 0.523068i \(-0.175213\pi\)
−0.879136 + 0.476571i \(0.841879\pi\)
\(278\) 10.6062i 0.636116i
\(279\) −7.44506 + 4.29841i −0.445724 + 0.257339i
\(280\) −9.29315 + 5.36540i −0.555372 + 0.320644i
\(281\) 6.13506i 0.365987i 0.983114 + 0.182993i \(0.0585787\pi\)
−0.983114 + 0.182993i \(0.941421\pi\)
\(282\) 3.18488 + 5.51637i 0.189657 + 0.328495i
\(283\) −7.61927 + 13.1970i −0.452918 + 0.784478i −0.998566 0.0535370i \(-0.982950\pi\)
0.545647 + 0.838015i \(0.316284\pi\)
\(284\) −0.396129 0.228705i −0.0235059 0.0135712i
\(285\) 4.32045 0.255921
\(286\) −2.63876 2.91828i −0.156033 0.172562i
\(287\) −21.4969 −1.26892
\(288\) −3.67800 2.12350i −0.216729 0.125128i
\(289\) 0.0412387 0.0714275i 0.00242580 0.00420162i
\(290\) −3.05833 5.29718i −0.179591 0.311061i
\(291\) 17.3337i 1.01612i
\(292\) −8.90609 + 5.14193i −0.521190 + 0.300909i
\(293\) −5.61984 + 3.24461i −0.328314 + 0.189552i −0.655092 0.755549i \(-0.727370\pi\)
0.326778 + 0.945101i \(0.394037\pi\)
\(294\) 3.75244i 0.218847i
\(295\) 7.37651 + 12.7765i 0.429477 + 0.743876i
\(296\) −14.6327 + 25.3445i −0.850507 + 1.47312i
\(297\) 0.866025 + 0.500000i 0.0502519 + 0.0290129i
\(298\) −12.9431 −0.749776
\(299\) −3.16764 + 9.81920i −0.183190 + 0.567859i
\(300\) 3.09641 0.178771
\(301\) −6.77280 3.91028i −0.390377 0.225385i
\(302\) −12.1147 + 20.9833i −0.697122 + 1.20745i
\(303\) 3.86014 + 6.68596i 0.221759 + 0.384098i
\(304\) 6.88485i 0.394873i
\(305\) 10.6370 6.14125i 0.609070 0.351647i
\(306\) −3.88691 + 2.24411i −0.222200 + 0.128287i
\(307\) 13.3662i 0.762850i −0.924400 0.381425i \(-0.875433\pi\)
0.924400 0.381425i \(-0.124567\pi\)
\(308\) 1.30735 + 2.26440i 0.0744932 + 0.129026i
\(309\) −4.54424 + 7.87086i −0.258513 + 0.447757i
\(310\) 8.80199 + 5.08183i 0.499919 + 0.288629i
\(311\) 21.8817 1.24080 0.620398 0.784287i \(-0.286971\pi\)
0.620398 + 0.784287i \(0.286971\pi\)
\(312\) −10.5190 3.39339i −0.595520 0.192113i
\(313\) −18.9378 −1.07043 −0.535214 0.844717i \(-0.679769\pi\)
−0.535214 + 0.844717i \(0.679769\pi\)
\(314\) 2.85668 + 1.64931i 0.161212 + 0.0930757i
\(315\) 1.75026 3.03154i 0.0986159 0.170808i
\(316\) −0.756706 1.31065i −0.0425680 0.0737300i
\(317\) 15.1134i 0.848852i −0.905463 0.424426i \(-0.860476\pi\)
0.905463 0.424426i \(-0.139524\pi\)
\(318\) 12.6152 7.28336i 0.707423 0.408431i
\(319\) −4.48056 + 2.58685i −0.250863 + 0.144836i
\(320\) 8.76223i 0.489824i
\(321\) −3.21702 5.57204i −0.179556 0.311001i
\(322\) −5.04433 + 8.73704i −0.281110 + 0.486896i
\(323\) 14.2043 + 8.20088i 0.790351 + 0.456309i
\(324\) 0.809275 0.0449597
\(325\) 13.4878 2.89658i 0.748171 0.160673i
\(326\) −12.7627 −0.706862
\(327\) −7.34157 4.23866i −0.405990 0.234398i
\(328\) −10.1981 + 17.6637i −0.563098 + 0.975314i
\(329\) −9.43002 16.3333i −0.519894 0.900482i
\(330\) 1.18226i 0.0650812i
\(331\) −10.3752 + 5.99012i −0.570272 + 0.329247i −0.757258 0.653116i \(-0.773461\pi\)
0.186986 + 0.982363i \(0.440128\pi\)
\(332\) 1.68232 0.971288i 0.0923293 0.0533064i
\(333\) 9.54671i 0.523157i
\(334\) −11.9068 20.6232i −0.651512 1.12845i
\(335\) −7.19450 + 12.4612i −0.393077 + 0.680830i
\(336\) −4.83090 2.78912i −0.263547 0.152159i
\(337\) 1.33145 0.0725285 0.0362643 0.999342i \(-0.488454\pi\)
0.0362643 + 0.999342i \(0.488454\pi\)
\(338\) −14.1140 1.42347i −0.767703 0.0774267i
\(339\) −5.72972 −0.311195
\(340\) −3.12322 1.80319i −0.169380 0.0977917i
\(341\) 4.29841 7.44506i 0.232772 0.403173i
\(342\) 2.17569 + 3.76841i 0.117648 + 0.203772i
\(343\) 11.5059i 0.621261i
\(344\) −6.42603 + 3.71007i −0.346468 + 0.200033i
\(345\) −2.68497 + 1.55017i −0.144554 + 0.0834584i
\(346\) 6.17986i 0.332231i
\(347\) 17.7364 + 30.7204i 0.952141 + 1.64916i 0.740779 + 0.671749i \(0.234457\pi\)
0.211363 + 0.977408i \(0.432210\pi\)
\(348\) −2.09347 + 3.62600i −0.112222 + 0.194374i
\(349\) −4.49438 2.59483i −0.240579 0.138898i 0.374864 0.927080i \(-0.377689\pi\)
−0.615443 + 0.788182i \(0.711023\pi\)
\(350\) 13.4894 0.721039
\(351\) 3.52518 0.757049i 0.188160 0.0404083i
\(352\) 4.24699 0.226366
\(353\) 6.65401 + 3.84169i 0.354157 + 0.204473i 0.666515 0.745492i \(-0.267785\pi\)
−0.312358 + 0.949965i \(0.601119\pi\)
\(354\) −7.42933 + 12.8680i −0.394864 + 0.683925i
\(355\) −0.306187 0.530331i −0.0162507 0.0281471i
\(356\) 11.3743i 0.602835i
\(357\) 11.5087 6.64452i 0.609102 0.351665i
\(358\) −1.74069 + 1.00499i −0.0919981 + 0.0531151i
\(359\) 3.37413i 0.178080i −0.996028 0.0890400i \(-0.971620\pi\)
0.996028 0.0890400i \(-0.0283799\pi\)
\(360\) −1.66065 2.87632i −0.0875237 0.151595i
\(361\) −1.54914 + 2.68319i −0.0815338 + 0.141221i
\(362\) −3.55098 2.05016i −0.186635 0.107754i
\(363\) −1.00000 −0.0524864
\(364\) 8.97213 + 2.89438i 0.470267 + 0.151707i
\(365\) −13.7679 −0.720644
\(366\) 10.7131 + 6.18522i 0.559984 + 0.323307i
\(367\) 13.1719 22.8143i 0.687566 1.19090i −0.285058 0.958510i \(-0.592013\pi\)
0.972623 0.232388i \(-0.0746539\pi\)
\(368\) 2.47027 + 4.27864i 0.128772 + 0.223039i
\(369\) 6.65351i 0.346368i
\(370\) −9.77455 + 5.64334i −0.508155 + 0.293383i
\(371\) −37.3519 + 21.5651i −1.93921 + 1.11960i
\(372\) 6.95719i 0.360713i
\(373\) −7.68103 13.3039i −0.397708 0.688851i 0.595734 0.803182i \(-0.296861\pi\)
−0.993443 + 0.114330i \(0.963528\pi\)
\(374\) 2.24411 3.88691i 0.116040 0.200987i
\(375\) 8.28149 + 4.78132i 0.427655 + 0.246906i
\(376\) −17.8944 −0.922833
\(377\) −5.72711 + 17.7531i −0.294961 + 0.914333i
\(378\) 3.52558 0.181336
\(379\) −12.1978 7.04243i −0.626561 0.361745i 0.152858 0.988248i \(-0.451152\pi\)
−0.779419 + 0.626503i \(0.784486\pi\)
\(380\) −1.74822 + 3.02800i −0.0896816 + 0.155333i
\(381\) −0.674770 1.16874i −0.0345695 0.0598762i
\(382\) 12.4270i 0.635820i
\(383\) 11.6525 6.72757i 0.595414 0.343763i −0.171821 0.985128i \(-0.554965\pi\)
0.767235 + 0.641366i \(0.221632\pi\)
\(384\) −0.286642 + 0.165493i −0.0146277 + 0.00844528i
\(385\) 3.50052i 0.178403i
\(386\) −7.05176 12.2140i −0.358925 0.621676i
\(387\) 1.21027 2.09625i 0.0615214 0.106558i
\(388\) 12.1484 + 7.01388i 0.616742 + 0.356076i
\(389\) −5.93346 −0.300838 −0.150419 0.988622i \(-0.548062\pi\)
−0.150419 + 0.988622i \(0.548062\pi\)
\(390\) −2.85895 3.16180i −0.144769 0.160104i
\(391\) −11.7698 −0.595227
\(392\) 9.12932 + 5.27082i 0.461100 + 0.266216i
\(393\) −5.73733 + 9.93734i −0.289410 + 0.501273i
\(394\) 8.71754 + 15.0992i 0.439183 + 0.760688i
\(395\) 2.02613i 0.101946i
\(396\) −0.700853 + 0.404638i −0.0352192 + 0.0203338i
\(397\) 28.0879 16.2165i 1.40969 0.813884i 0.414331 0.910126i \(-0.364016\pi\)
0.995358 + 0.0962421i \(0.0306823\pi\)
\(398\) 5.43537i 0.272450i
\(399\) −6.44195 11.1578i −0.322501 0.558588i
\(400\) 3.30296 5.72090i 0.165148 0.286045i
\(401\) −17.2287 9.94698i −0.860359 0.496729i 0.00377329 0.999993i \(-0.498799\pi\)
−0.864133 + 0.503264i \(0.832132\pi\)
\(402\) −14.4920 −0.722797
\(403\) −6.50821 30.3053i −0.324197 1.50961i
\(404\) −6.24783 −0.310841
\(405\) 0.938291 + 0.541723i 0.0466241 + 0.0269184i
\(406\) −9.12016 + 15.7966i −0.452626 + 0.783971i
\(407\) 4.77336 + 8.26769i 0.236606 + 0.409814i
\(408\) 12.6086i 0.624221i
\(409\) 16.3827 9.45857i 0.810073 0.467696i −0.0369081 0.999319i \(-0.511751\pi\)
0.846981 + 0.531623i \(0.178418\pi\)
\(410\) −6.81230 + 3.93308i −0.336436 + 0.194241i
\(411\) 10.5049i 0.518167i
\(412\) −3.67754 6.36969i −0.181180 0.313812i
\(413\) 21.9973 38.1004i 1.08242 1.87480i
\(414\) −2.70420 1.56127i −0.132904 0.0767323i
\(415\) 2.60069 0.127663
\(416\) 11.3580 10.2701i 0.556873 0.503535i
\(417\) −9.71970 −0.475976
\(418\) −3.76841 2.17569i −0.184319 0.106417i
\(419\) 13.1214 22.7270i 0.641023 1.11028i −0.344181 0.938903i \(-0.611844\pi\)
0.985205 0.171382i \(-0.0548232\pi\)
\(420\) 1.41644 + 2.45335i 0.0691153 + 0.119711i
\(421\) 2.62866i 0.128113i −0.997946 0.0640565i \(-0.979596\pi\)
0.997946 0.0640565i \(-0.0204038\pi\)
\(422\) 16.1363 9.31632i 0.785505 0.453511i
\(423\) 5.05531 2.91868i 0.245798 0.141911i
\(424\) 40.9219i 1.98734i
\(425\) 7.86865 + 13.6289i 0.381685 + 0.661098i
\(426\) 0.308379 0.534129i 0.0149410 0.0258786i
\(427\) −31.7202 18.3137i −1.53505 0.886260i
\(428\) 5.20690 0.251685
\(429\) −2.67437 + 2.41821i −0.129120 + 0.116752i
\(430\) −2.86170 −0.138004
\(431\) −25.4067 14.6686i −1.22380 0.706559i −0.258072 0.966126i \(-0.583087\pi\)
−0.965725 + 0.259566i \(0.916420\pi\)
\(432\) 0.863261 1.49521i 0.0415337 0.0719384i
\(433\) 7.62347 + 13.2042i 0.366361 + 0.634556i 0.988994 0.147959i \(-0.0472703\pi\)
−0.622633 + 0.782514i \(0.713937\pi\)
\(434\) 30.3088i 1.45487i
\(435\) −4.85444 + 2.80271i −0.232752 + 0.134380i
\(436\) 5.94136 3.43024i 0.284539 0.164279i
\(437\) 11.4110i 0.545863i
\(438\) −6.93323 12.0087i −0.331283 0.573798i
\(439\) −12.4511 + 21.5659i −0.594258 + 1.02928i 0.399394 + 0.916780i \(0.369221\pi\)
−0.993651 + 0.112505i \(0.964113\pi\)
\(440\) 2.87632 + 1.66065i 0.137123 + 0.0791682i
\(441\) −3.43881 −0.163753
\(442\) −3.39780 15.8218i −0.161617 0.752565i
\(443\) −18.5762 −0.882580 −0.441290 0.897364i \(-0.645479\pi\)
−0.441290 + 0.897364i \(0.645479\pi\)
\(444\) 6.69084 + 3.86296i 0.317533 + 0.183328i
\(445\) −7.61384 + 13.1876i −0.360931 + 0.625151i
\(446\) −9.37628 16.2402i −0.443979 0.768995i
\(447\) 11.8613i 0.561023i
\(448\) 22.6289 13.0648i 1.06912 0.617254i
\(449\) −0.904836 + 0.522408i −0.0427019 + 0.0246539i −0.521199 0.853435i \(-0.674515\pi\)
0.478497 + 0.878089i \(0.341182\pi\)
\(450\) 4.17510i 0.196816i
\(451\) 3.32675 + 5.76211i 0.156651 + 0.271327i
\(452\) 2.31846 4.01569i 0.109051 0.188882i
\(453\) 19.2295 + 11.1021i 0.903479 + 0.521624i
\(454\) −10.4826 −0.491975
\(455\) 8.46500 + 9.36168i 0.396845 + 0.438882i
\(456\) −12.2242 −0.572453
\(457\) −22.6264 13.0634i −1.05842 0.611079i −0.133425 0.991059i \(-0.542597\pi\)
−0.924995 + 0.379980i \(0.875931\pi\)
\(458\) −2.51845 + 4.36208i −0.117679 + 0.203826i
\(459\) 2.05655 + 3.56204i 0.0959913 + 0.166262i
\(460\) 2.50903i 0.116984i
\(461\) −11.5901 + 6.69153i −0.539804 + 0.311656i −0.744999 0.667065i \(-0.767550\pi\)
0.205196 + 0.978721i \(0.434217\pi\)
\(462\) −3.05325 + 1.76279i −0.142050 + 0.0820125i
\(463\) 23.7960i 1.10589i 0.833216 + 0.552947i \(0.186497\pi\)
−0.833216 + 0.552947i \(0.813503\pi\)
\(464\) 4.46626 + 7.73578i 0.207341 + 0.359125i
\(465\) 4.65709 8.06631i 0.215967 0.374066i
\(466\) −1.65803 0.957263i −0.0768067 0.0443444i
\(467\) −24.1995 −1.11982 −0.559911 0.828553i \(-0.689165\pi\)
−0.559911 + 0.828553i \(0.689165\pi\)
\(468\) −0.895840 + 2.77696i −0.0414102 + 0.128365i
\(469\) 42.9091 1.98136
\(470\) −5.97668 3.45064i −0.275684 0.159166i
\(471\) 1.51146 2.61792i 0.0696442 0.120627i
\(472\) −20.8710 36.1497i −0.960667 1.66392i
\(473\) 2.42054i 0.111296i
\(474\) 1.76725 1.02032i 0.0811723 0.0468648i
\(475\) 13.2134 7.62875i 0.606272 0.350031i
\(476\) 10.7545i 0.492932i
\(477\) −6.67461 11.5608i −0.305610 0.529331i
\(478\) 15.4700 26.7948i 0.707582 1.22557i
\(479\) −5.08360 2.93502i −0.232276 0.134104i 0.379346 0.925255i \(-0.376149\pi\)
−0.611621 + 0.791151i \(0.709482\pi\)
\(480\) 4.60139 0.210024
\(481\) 32.7588 + 10.5679i 1.49367 + 0.481854i
\(482\) 7.68637 0.350105
\(483\) 8.00679 + 4.62272i 0.364322 + 0.210341i
\(484\) 0.404638 0.700853i 0.0183926 0.0318570i
\(485\) 9.39007 + 16.2641i 0.426381 + 0.738514i
\(486\) 1.09120i 0.0494980i
\(487\) 21.1621 12.2179i 0.958945 0.553647i 0.0630971 0.998007i \(-0.479902\pi\)
0.895848 + 0.444360i \(0.146569\pi\)
\(488\) −30.0961 + 17.3760i −1.36239 + 0.786574i
\(489\) 11.6960i 0.528912i
\(490\) 2.03278 + 3.52088i 0.0918317 + 0.159057i
\(491\) −5.95863 + 10.3206i −0.268909 + 0.465764i −0.968580 0.248701i \(-0.919996\pi\)
0.699671 + 0.714465i \(0.253330\pi\)
\(492\) 4.66313 + 2.69226i 0.210230 + 0.121376i
\(493\) −21.2799 −0.958399
\(494\) −15.3394 + 3.29421i −0.690153 + 0.148214i
\(495\) −1.08345 −0.0486972
\(496\) −12.8541 7.42130i −0.577164 0.333226i
\(497\) −0.913072 + 1.58149i −0.0409569 + 0.0709394i
\(498\) 1.30966 + 2.26839i 0.0586871 + 0.101649i
\(499\) 17.6126i 0.788446i −0.919015 0.394223i \(-0.871014\pi\)
0.919015 0.394223i \(-0.128986\pi\)
\(500\) −6.70201 + 3.86941i −0.299723 + 0.173045i
\(501\) −18.8995 + 10.9116i −0.844368 + 0.487496i
\(502\) 17.0268i 0.759945i
\(503\) −6.91415 11.9757i −0.308287 0.533968i 0.669701 0.742631i \(-0.266422\pi\)
−0.977988 + 0.208663i \(0.933089\pi\)
\(504\) −4.95217 + 8.57741i −0.220587 + 0.382068i
\(505\) −7.24387 4.18225i −0.322348 0.186108i
\(506\) 3.12254 0.138814
\(507\) −1.30450 + 12.9344i −0.0579348 + 0.574436i
\(508\) 1.09215 0.0484563
\(509\) −15.9091 9.18515i −0.705160 0.407124i 0.104106 0.994566i \(-0.466802\pi\)
−0.809266 + 0.587442i \(0.800135\pi\)
\(510\) 2.43137 4.21126i 0.107663 0.186478i
\(511\) 20.5284 + 35.5563i 0.908124 + 1.57292i
\(512\) 17.9178i 0.791863i
\(513\) 3.45345 1.99385i 0.152473 0.0880305i
\(514\) 2.35962 1.36233i 0.104078 0.0600896i
\(515\) 9.84687i 0.433905i
\(516\) 0.979441 + 1.69644i 0.0431175 + 0.0746817i
\(517\) −2.91868 + 5.05531i −0.128364 + 0.222332i
\(518\) 29.1485 + 16.8289i 1.28071 + 0.739418i
\(519\) 5.66334 0.248593
\(520\) 11.7081 2.51438i 0.513436 0.110263i
\(521\) 29.1227 1.27589 0.637945 0.770082i \(-0.279785\pi\)
0.637945 + 0.770082i \(0.279785\pi\)
\(522\) −4.88920 2.82278i −0.213994 0.123550i
\(523\) −7.21022 + 12.4885i −0.315281 + 0.546082i −0.979497 0.201458i \(-0.935432\pi\)
0.664216 + 0.747540i \(0.268765\pi\)
\(524\) −4.64308 8.04205i −0.202834 0.351318i
\(525\) 12.3620i 0.539520i
\(526\) −6.29518 + 3.63452i −0.274483 + 0.158473i
\(527\) 30.6222 17.6797i 1.33392 0.770142i
\(528\) 1.72652i 0.0751372i
\(529\) 7.40574 + 12.8271i 0.321989 + 0.557701i
\(530\) −7.89112 + 13.6678i −0.342768 + 0.593692i
\(531\) 11.7925 + 6.80838i 0.511749 + 0.295459i
\(532\) 10.4266 0.452052
\(533\) 22.8310 + 7.36520i 0.988919 + 0.319022i
\(534\) −15.3367 −0.663685
\(535\) 6.03700 + 3.48546i 0.261002 + 0.150690i
\(536\) 20.3560 35.2577i 0.879247 1.52290i
\(537\) 0.920989 + 1.59520i 0.0397436 + 0.0688379i
\(538\) 20.6807i 0.891610i
\(539\) 2.97810 1.71940i 0.128276 0.0740600i
\(540\) −0.759336 + 0.438403i −0.0326766 + 0.0188659i
\(541\) 14.9509i 0.642789i −0.946945 0.321395i \(-0.895848\pi\)
0.946945 0.321395i \(-0.104152\pi\)
\(542\) 3.36718 + 5.83213i 0.144633 + 0.250512i
\(543\) −1.87881 + 3.25419i −0.0806273 + 0.139651i
\(544\) 15.1280 + 8.73414i 0.648606 + 0.374473i
\(545\) 9.18471 0.393430
\(546\) −3.90270 + 12.0978i −0.167020 + 0.517736i
\(547\) −27.9053 −1.19314 −0.596572 0.802560i \(-0.703471\pi\)
−0.596572 + 0.802560i \(0.703471\pi\)
\(548\) 7.36237 + 4.25067i 0.314505 + 0.181580i
\(549\) 5.66826 9.81771i 0.241915 0.419010i
\(550\) −2.08755 3.61575i −0.0890135 0.154176i
\(551\) 20.6311i 0.878916i
\(552\) 7.59684 4.38604i 0.323343 0.186682i
\(553\) −5.23259 + 3.02104i −0.222512 + 0.128468i
\(554\) 0.975073i 0.0414269i
\(555\) 5.17167 + 8.95759i 0.219525 + 0.380229i
\(556\) 3.93296 6.81208i 0.166794 0.288897i
\(557\) −28.0832 16.2138i −1.18992 0.687002i −0.231633 0.972803i \(-0.574407\pi\)
−0.958289 + 0.285801i \(0.907740\pi\)
\(558\) 9.38087 0.397124
\(559\) 5.85337 + 6.47341i 0.247571 + 0.273796i
\(560\) 6.04372 0.255394
\(561\) −3.56204 2.05655i −0.150390 0.0868274i
\(562\) 3.34730 5.79769i 0.141197 0.244561i
\(563\) −10.0899 17.4762i −0.425238 0.736534i 0.571205 0.820808i \(-0.306476\pi\)
−0.996443 + 0.0842739i \(0.973143\pi\)
\(564\) 4.72404i 0.198918i
\(565\) 5.37614 3.10392i 0.226176 0.130583i
\(566\) 14.4006 8.31417i 0.605301 0.349471i
\(567\) 3.23091i 0.135686i
\(568\) 0.866323 + 1.50052i 0.0363501 + 0.0629602i
\(569\) −9.12870 + 15.8114i −0.382695 + 0.662848i −0.991447 0.130514i \(-0.958337\pi\)
0.608751 + 0.793361i \(0.291671\pi\)
\(570\) −4.08287 2.35724i −0.171012 0.0987341i
\(571\) 2.44991 0.102525 0.0512627 0.998685i \(-0.483675\pi\)
0.0512627 + 0.998685i \(0.483675\pi\)
\(572\) −0.612661 2.85284i −0.0256166 0.119283i
\(573\) 11.3883 0.475754
\(574\) 20.3148 + 11.7288i 0.847923 + 0.489549i
\(575\) −5.47437 + 9.48189i −0.228297 + 0.395422i
\(576\) 4.04369 + 7.00388i 0.168487 + 0.291828i
\(577\) 20.4700i 0.852176i 0.904682 + 0.426088i \(0.140109\pi\)
−0.904682 + 0.426088i \(0.859891\pi\)
\(578\) −0.0779419 + 0.0449998i −0.00324195 + 0.00187174i
\(579\) −11.1931 + 6.46237i −0.465171 + 0.268567i
\(580\) 4.53633i 0.188361i
\(581\) −3.87773 6.71642i −0.160875 0.278644i
\(582\) −9.45731 + 16.3805i −0.392018 + 0.678995i
\(583\) 11.5608 + 6.67461i 0.478798 + 0.276434i
\(584\) 38.9547 1.61196
\(585\) −2.89753 + 2.62000i −0.119798 + 0.108324i
\(586\) 7.08107 0.292516
\(587\) −22.3926 12.9284i −0.924240 0.533610i −0.0392548 0.999229i \(-0.512498\pi\)
−0.884985 + 0.465619i \(0.845832\pi\)
\(588\) 1.39147 2.41010i 0.0573833 0.0993908i
\(589\) −17.1407 29.6886i −0.706272 1.22330i
\(590\) 16.0985i 0.662766i
\(591\) 13.8372 7.98893i 0.569187 0.328620i
\(592\) 14.2744 8.24131i 0.586673 0.338716i
\(593\) 3.99700i 0.164137i 0.996627 + 0.0820686i \(0.0261527\pi\)
−0.996627 + 0.0820686i \(0.973847\pi\)
\(594\) −0.545602 0.945010i −0.0223863 0.0387742i
\(595\) −7.19898 + 12.4690i −0.295129 + 0.511179i
\(596\) −8.31306 4.79955i −0.340516 0.196597i
\(597\) −4.98108 −0.203862
\(598\) 8.35083 7.55097i 0.341491 0.308782i
\(599\) −41.2173 −1.68409 −0.842047 0.539404i \(-0.818650\pi\)
−0.842047 + 0.539404i \(0.818650\pi\)
\(600\) −10.1576 5.86451i −0.414683 0.239418i
\(601\) 17.1849 29.7652i 0.700988 1.21415i −0.267131 0.963660i \(-0.586076\pi\)
0.968120 0.250488i \(-0.0805909\pi\)
\(602\) 4.26691 + 7.39050i 0.173906 + 0.301214i
\(603\) 13.2808i 0.540835i
\(604\) −15.5619 + 8.98469i −0.633206 + 0.365582i
\(605\) 0.938291 0.541723i 0.0381470 0.0220242i
\(606\) 8.42439i 0.342218i
\(607\) 22.0492 + 38.1904i 0.894951 + 1.55010i 0.833865 + 0.551968i \(0.186123\pi\)
0.0610857 + 0.998133i \(0.480544\pi\)
\(608\) 8.46786 14.6668i 0.343417 0.594816i
\(609\) 14.4763 + 8.35789i 0.586609 + 0.338679i
\(610\) −13.4027 −0.542659
\(611\) 4.41917 + 20.5778i 0.178781 + 0.832487i
\(612\) −3.32862 −0.134552
\(613\) −17.4807 10.0925i −0.706039 0.407632i 0.103554 0.994624i \(-0.466979\pi\)
−0.809593 + 0.586992i \(0.800312\pi\)
\(614\) −7.29263 + 12.6312i −0.294307 + 0.509754i
\(615\) 3.60435 + 6.24293i 0.145342 + 0.251739i
\(616\) 9.90434i 0.399057i
\(617\) −21.0976 + 12.1807i −0.849359 + 0.490377i −0.860434 0.509561i \(-0.829808\pi\)
0.0110758 + 0.999939i \(0.496474\pi\)
\(618\) 8.58871 4.95869i 0.345488 0.199468i
\(619\) 1.80436i 0.0725232i 0.999342 + 0.0362616i \(0.0115450\pi\)
−0.999342 + 0.0362616i \(0.988455\pi\)
\(620\) 3.76887 + 6.52787i 0.151361 + 0.262166i
\(621\) −1.43078 + 2.47818i −0.0574152 + 0.0994460i
\(622\) −20.6784 11.9387i −0.829128 0.478697i
\(623\) 45.4101 1.81932
\(624\) 4.17510 + 4.61736i 0.167138 + 0.184842i
\(625\) 8.77013 0.350805
\(626\) 17.8964 + 10.3325i 0.715284 + 0.412970i
\(627\) −1.99385 + 3.45345i −0.0796266 + 0.137917i
\(628\) 1.22318 + 2.11862i 0.0488104 + 0.0845420i
\(629\) 39.2665i 1.56566i
\(630\) −3.30802 + 1.90989i −0.131795 + 0.0760918i
\(631\) 6.92607 3.99877i 0.275722 0.159188i −0.355763 0.934576i \(-0.615779\pi\)
0.631485 + 0.775388i \(0.282446\pi\)
\(632\) 5.73272i 0.228035i
\(633\) −8.53766 14.7877i −0.339342 0.587757i
\(634\) −8.24589 + 14.2823i −0.327486 + 0.567222i
\(635\) 1.26626 + 0.731077i 0.0502501 + 0.0290119i
\(636\) 10.8032 0.428375
\(637\) 3.80664 11.8000i 0.150825 0.467533i
\(638\) 5.64556 0.223510
\(639\) −0.489486 0.282605i −0.0193638 0.0111797i
\(640\) 0.179303 0.310561i 0.00708756 0.0122760i
\(641\) −23.4892 40.6844i −0.927766 1.60694i −0.787051 0.616887i \(-0.788393\pi\)
−0.140715 0.990050i \(-0.544940\pi\)
\(642\) 7.02084i 0.277090i
\(643\) −21.7416 + 12.5525i −0.857404 + 0.495023i −0.863142 0.504961i \(-0.831507\pi\)
0.00573777 + 0.999984i \(0.498174\pi\)
\(644\) −6.47970 + 3.74106i −0.255336 + 0.147418i
\(645\) 2.62252i 0.103262i
\(646\) −8.94883 15.4998i −0.352087 0.609832i
\(647\) −5.06789 + 8.77784i −0.199239 + 0.345093i −0.948282 0.317429i \(-0.897180\pi\)
0.749043 + 0.662522i \(0.230514\pi\)
\(648\) −2.65479 1.53275i −0.104290 0.0602119i
\(649\) −13.6168 −0.534505
\(650\) −14.3265 4.62170i −0.561933 0.181278i
\(651\) −27.7756 −1.08861
\(652\) −8.19718 4.73265i −0.321027 0.185345i
\(653\) −9.06830 + 15.7068i −0.354870 + 0.614653i −0.987096 0.160132i \(-0.948808\pi\)
0.632226 + 0.774784i \(0.282141\pi\)
\(654\) 4.62524 + 8.01115i 0.180861 + 0.313261i
\(655\) 12.4322i 0.485765i
\(656\) 9.94841 5.74371i 0.388420 0.224254i
\(657\) −11.0050 + 6.35375i −0.429347 + 0.247883i
\(658\) 20.5801i 0.802297i
\(659\) −4.52144 7.83137i −0.176130 0.305067i 0.764421 0.644717i \(-0.223025\pi\)
−0.940552 + 0.339650i \(0.889691\pi\)
\(660\) 0.438403 0.759336i 0.0170648 0.0295571i
\(661\) 7.51960 + 4.34144i 0.292478 + 0.168862i 0.639059 0.769158i \(-0.279324\pi\)
−0.346581 + 0.938020i \(0.612657\pi\)
\(662\) 13.0729 0.508092
\(663\) −14.4994 + 3.11381i −0.563109 + 0.120930i
\(664\) −7.35837 −0.285560
\(665\) 12.0889 + 6.97950i 0.468786 + 0.270653i
\(666\) −5.20870 + 9.02173i −0.201833 + 0.349585i
\(667\) −7.40242 12.8214i −0.286623 0.496445i
\(668\) 17.6610i 0.683327i
\(669\) −14.8828 + 8.59260i −0.575403 + 0.332209i
\(670\) 13.5977 7.85066i 0.525326 0.303297i
\(671\) 11.3365i 0.437641i
\(672\) −6.86084 11.8833i −0.264663 0.458409i
\(673\) 9.82195 17.0121i 0.378608 0.655769i −0.612252 0.790663i \(-0.709736\pi\)
0.990860 + 0.134894i \(0.0430694\pi\)
\(674\) −1.25823 0.726440i −0.0484652 0.0279814i
\(675\) 3.82615 0.147268
\(676\) −8.53725 6.14800i −0.328356 0.236462i
\(677\) 12.4044 0.476741 0.238371 0.971174i \(-0.423387\pi\)
0.238371 + 0.971174i \(0.423387\pi\)
\(678\) 5.41464 + 3.12614i 0.207948 + 0.120059i
\(679\) 28.0019 48.5007i 1.07461 1.86129i
\(680\) 6.83039 + 11.8306i 0.261933 + 0.453682i
\(681\) 9.60650i 0.368122i
\(682\) −8.12407 + 4.69044i −0.311087 + 0.179606i
\(683\) 19.0470 10.9968i 0.728815 0.420781i −0.0891737 0.996016i \(-0.528423\pi\)
0.817988 + 0.575235i \(0.195089\pi\)
\(684\) 3.22714i 0.123393i
\(685\) 5.69073 + 9.85663i 0.217432 + 0.376602i
\(686\) −6.27764 + 10.8732i −0.239681 + 0.415140i
\(687\) 3.99749 + 2.30795i 0.152514 + 0.0880539i
\(688\) 4.17911 0.159327
\(689\) 47.0584 10.1060i 1.79278 0.385009i
\(690\) 3.38310 0.128792
\(691\) 21.0345 + 12.1443i 0.800189 + 0.461989i 0.843537 0.537071i \(-0.180469\pi\)
−0.0433481 + 0.999060i \(0.513802\pi\)
\(692\) −2.29160 + 3.96917i −0.0871136 + 0.150885i
\(693\) 1.61546 + 2.79805i 0.0613661 + 0.106289i
\(694\) 38.7081i 1.46934i
\(695\) 9.11990 5.26538i 0.345938 0.199727i
\(696\) 13.7351 7.92997i 0.520628 0.300585i
\(697\) 27.3665i 1.03658i
\(698\) 2.83149 + 4.90429i 0.107173 + 0.185630i
\(699\) −0.877254 + 1.51945i −0.0331808 + 0.0574709i
\(700\) 8.66391 + 5.00211i 0.327465 + 0.189062i
\(701\) −36.4133 −1.37531 −0.687657 0.726036i \(-0.741361\pi\)
−0.687657 + 0.726036i \(0.741361\pi\)
\(702\) −3.74437 1.20792i −0.141322 0.0455902i
\(703\) 38.0694 1.43581
\(704\) −7.00388 4.04369i −0.263968 0.152402i
\(705\) −3.16223 + 5.47715i −0.119097 + 0.206281i
\(706\) −4.19207 7.26088i −0.157771 0.273267i
\(707\) 24.9436i 0.938099i
\(708\) −9.54335 + 5.50985i −0.358661 + 0.207073i
\(709\) 38.8080 22.4058i 1.45746 0.841467i 0.458578 0.888654i \(-0.348359\pi\)
0.998886 + 0.0471869i \(0.0150256\pi\)
\(710\) 0.668224i 0.0250780i
\(711\) −0.935041 1.61954i −0.0350668 0.0607374i
\(712\) 21.5425 37.3128i 0.807341 1.39836i
\(713\) 21.3045 + 12.3001i 0.797858 + 0.460644i
\(714\) −14.5011 −0.542688
\(715\) 1.19934 3.71775i 0.0448526 0.139036i
\(716\) −1.49067 −0.0557088
\(717\) −24.5553 14.1770i −0.917035 0.529450i
\(718\) −1.84093 + 3.18859i −0.0687030 + 0.118997i
\(719\) −10.6646 18.4716i −0.397721 0.688874i 0.595723 0.803190i \(-0.296866\pi\)
−0.993444 + 0.114316i \(0.963532\pi\)
\(720\) 1.87059i 0.0697129i
\(721\) −25.4301 + 14.6821i −0.947065 + 0.546788i
\(722\) 2.92791 1.69043i 0.108965 0.0629113i
\(723\) 7.04394i 0.261967i
\(724\) −1.52047 2.63353i −0.0565079 0.0978745i
\(725\) −9.89767 + 17.1433i −0.367590 + 0.636685i
\(726\) 0.945010 + 0.545602i 0.0350726 + 0.0202492i
\(727\) 42.5295 1.57733 0.788667 0.614821i \(-0.210772\pi\)
0.788667 + 0.614821i \(0.210772\pi\)
\(728\) −23.9508 26.4879i −0.887675 0.981705i
\(729\) 1.00000 0.0370370
\(730\) 13.0108 + 7.51178i 0.481551 + 0.278023i
\(731\) −4.97795 + 8.62206i −0.184116 + 0.318898i
\(732\) 4.58718 + 7.94523i 0.169547 + 0.293664i
\(733\) 44.3019i 1.63633i 0.574985 + 0.818164i \(0.305008\pi\)
−0.574985 + 0.818164i \(0.694992\pi\)
\(734\) −24.8951 + 14.3732i −0.918894 + 0.530524i
\(735\) 3.22660 1.86288i 0.119015 0.0687134i
\(736\) 12.1530i 0.447966i
\(737\) −6.64039 11.5015i −0.244602 0.423663i
\(738\) −3.63016 + 6.28763i −0.133628 + 0.231451i
\(739\) −13.6402 7.87517i −0.501762 0.289693i 0.227679 0.973736i \(-0.426886\pi\)
−0.729441 + 0.684044i \(0.760220\pi\)
\(740\) −8.37061 −0.307710
\(741\) 3.01888 + 14.0573i 0.110901 + 0.516409i
\(742\) 47.0638 1.72777
\(743\) 29.4252 + 16.9886i 1.07951 + 0.623253i 0.930763 0.365623i \(-0.119144\pi\)
0.148743 + 0.988876i \(0.452477\pi\)
\(744\) −13.1767 + 22.8228i −0.483082 + 0.836723i
\(745\) −6.42556 11.1294i −0.235414 0.407750i
\(746\) 16.7631i 0.613742i
\(747\) 2.07880 1.20019i 0.0760593 0.0439128i
\(748\) 2.88267 1.66431i 0.105401 0.0608533i
\(749\) 20.7878i 0.759570i
\(750\) −5.21740 9.03679i −0.190512 0.329977i
\(751\) 13.3092 23.0523i 0.485661 0.841189i −0.514203 0.857668i \(-0.671912\pi\)
0.999864 + 0.0164790i \(0.00524567\pi\)
\(752\) 8.72811 + 5.03917i 0.318281 + 0.183760i
\(753\) 15.6037 0.568631
\(754\) 15.0983 13.6522i 0.549848 0.497182i
\(755\) −24.0571 −0.875528
\(756\) 2.26440 + 1.30735i 0.0823553 + 0.0475479i
\(757\) −2.72942 + 4.72749i −0.0992024 + 0.171824i −0.911355 0.411622i \(-0.864962\pi\)
0.812152 + 0.583445i \(0.198296\pi\)
\(758\) 7.68472 + 13.3103i 0.279122 + 0.483453i
\(759\) 2.86156i 0.103868i
\(760\) 11.4699 6.62215i 0.416057 0.240211i
\(761\) 26.6966 15.4133i 0.967752 0.558732i 0.0692016 0.997603i \(-0.477955\pi\)
0.898550 + 0.438871i \(0.144621\pi\)
\(762\) 1.47262i 0.0533475i
\(763\) −13.6947 23.7200i −0.495783 0.858722i
\(764\) −4.60815 + 7.98155i −0.166717 + 0.288762i
\(765\) −3.85928 2.22815i −0.139532 0.0805591i
\(766\) −14.6823 −0.530493
\(767\) −36.4162 + 32.9282i −1.31491 + 1.18897i
\(768\) −15.8136 −0.570624
\(769\) −16.4285 9.48498i −0.592426 0.342037i 0.173630 0.984811i \(-0.444450\pi\)
−0.766056 + 0.642774i \(0.777784\pi\)
\(770\) 1.90989 3.30802i 0.0688276 0.119213i
\(771\) −1.24846 2.16240i −0.0449623 0.0778769i
\(772\) 10.4597i 0.376452i
\(773\) 29.1506 16.8301i 1.04848 0.605338i 0.126254 0.991998i \(-0.459705\pi\)
0.922222 + 0.386660i \(0.126371\pi\)
\(774\) −2.28743 + 1.32065i −0.0822200 + 0.0474698i
\(775\) 32.8927i 1.18154i
\(776\) −26.5682 46.0175i −0.953743 1.65193i
\(777\) 15.4223 26.7122i 0.553272 0.958295i
\(778\) 5.60718 + 3.23731i 0.201027 + 0.116063i
\(779\) 26.5322 0.950613
\(780\) −0.663785 3.09090i −0.0237673 0.110672i
\(781\) 0.565210 0.0202248
\(782\) 11.1226 + 6.42165i 0.397744 + 0.229638i
\(783\) −2.58685 + 4.48056i −0.0924465 + 0.160122i
\(784\) −2.96859 5.14175i −0.106021 0.183634i
\(785\) 3.27516i 0.116895i
\(786\) 10.8437 6.26059i 0.386781 0.223308i
\(787\) −4.64159 + 2.67982i −0.165455 + 0.0955254i −0.580441 0.814302i \(-0.697120\pi\)
0.414986 + 0.909828i \(0.363786\pi\)
\(788\) 12.9305i 0.460629i
\(789\) 3.33075 + 5.76902i 0.118578 + 0.205383i
\(790\) −1.10546 + 1.91471i −0.0393305 + 0.0681225i
\(791\) −16.0321 9.25611i −0.570034 0.329109i
\(792\) 3.06549 0.108927
\(793\) 27.4141 + 30.3180i 0.973503 + 1.07662i
\(794\) −35.3911 −1.25598
\(795\) 12.5255 + 7.23158i 0.444232 + 0.256478i
\(796\) 2.01553 3.49100i 0.0714386 0.123735i
\(797\) −2.96256 5.13131i −0.104939 0.181760i 0.808774 0.588119i \(-0.200132\pi\)
−0.913713 + 0.406359i \(0.866798\pi\)
\(798\) 14.0590i 0.497682i
\(799\) −20.7930 + 12.0048i −0.735602 + 0.424700i
\(800\) 14.0726 8.12481i 0.497541 0.287255i
\(801\) 14.0549i 0.496605i
\(802\) 10.8542 + 18.8000i 0.383274 + 0.663851i
\(803\) 6.35375 11.0050i 0.224219 0.388359i
\(804\) −9.30787 5.37390i −0.328263 0.189523i
\(805\) −10.0169 −0.353051
\(806\) −10.3843 + 32.1897i −0.365771 + 1.13383i
\(807\) 18.9522 0.667150
\(808\) 20.4957 + 11.8332i 0.721037 + 0.416291i
\(809\) 23.7269 41.0962i 0.834194 1.44487i −0.0604908 0.998169i \(-0.519267\pi\)
0.894685 0.446698i \(-0.147400\pi\)
\(810\) −0.591129 1.02387i −0.0207702 0.0359750i
\(811\) 14.9271i 0.524161i 0.965046 + 0.262081i \(0.0844086\pi\)
−0.965046 + 0.262081i \(0.915591\pi\)
\(812\) −11.7153 + 6.76384i −0.411127 + 0.237364i
\(813\) 5.34468 3.08575i 0.187446 0.108222i
\(814\) 10.4174i 0.365130i
\(815\) −6.33599 10.9743i −0.221940 0.384412i
\(816\) −3.55067 + 6.14995i −0.124298 + 0.215291i
\(817\) 8.35920 + 4.82618i 0.292451 + 0.168847i
\(818\) −20.6424 −0.721746
\(819\) 11.0866 + 3.57651i 0.387398 + 0.124973i
\(820\) −5.83383 −0.203726
\(821\) −36.8360 21.2673i −1.28558 0.742232i −0.307721 0.951477i \(-0.599566\pi\)
−0.977863 + 0.209244i \(0.932900\pi\)
\(822\) −5.73148 + 9.92721i −0.199908 + 0.346251i
\(823\) −14.6807 25.4277i −0.511736 0.886352i −0.999907 0.0136047i \(-0.995669\pi\)
0.488172 0.872748i \(-0.337664\pi\)
\(824\) 27.8607i 0.970572i
\(825\) −3.31354 + 1.91307i −0.115363 + 0.0666047i
\(826\) −41.5753 + 24.0035i −1.44659 + 0.835189i
\(827\) 1.84784i 0.0642556i 0.999484 + 0.0321278i \(0.0102284\pi\)
−0.999484 + 0.0321278i \(0.989772\pi\)
\(828\) −1.15789 2.00553i −0.0402396 0.0696970i
\(829\) 15.1977 26.3232i 0.527839 0.914244i −0.471634 0.881794i \(-0.656336\pi\)
0.999473 0.0324499i \(-0.0103309\pi\)
\(830\) −2.45768 1.41894i −0.0853072 0.0492522i
\(831\) 0.893576 0.0309978
\(832\) −28.5094 + 6.12254i −0.988387 + 0.212261i
\(833\) 14.1441 0.490065
\(834\) 9.18521 + 5.30308i 0.318058 + 0.183631i
\(835\) 11.8222 20.4766i 0.409123 0.708622i
\(836\) −1.61357 2.79479i −0.0558066 0.0966598i
\(837\) 8.59681i 0.297149i
\(838\) −24.7997 + 14.3181i −0.856693 + 0.494612i
\(839\) −13.9637 + 8.06193i −0.482079 + 0.278329i −0.721283 0.692641i \(-0.756447\pi\)
0.239203 + 0.970970i \(0.423114\pi\)
\(840\) 10.7308i 0.370248i
\(841\) 1.11641 + 1.93368i 0.0384969 + 0.0666786i
\(842\) −1.43420 + 2.48411i −0.0494258 + 0.0856081i
\(843\) −5.31312 3.06753i −0.182993 0.105651i
\(844\) 13.8186 0.475657
\(845\) −5.78285 12.8429i −0.198936 0.441809i
\(846\) −6.36976 −0.218997
\(847\) −2.79805 1.61546i −0.0961423 0.0555078i
\(848\) 11.5239 19.9599i 0.395731 0.685427i
\(849\) −7.61927 13.1970i −0.261493 0.452918i
\(850\) 17.1726i 0.589015i
\(851\) −23.6585 + 13.6592i −0.811002 + 0.468232i
\(852\) 0.396129 0.228705i 0.0135712 0.00783531i
\(853\) 55.1988i 1.88997i 0.327112 + 0.944986i \(0.393925\pi\)
−0.327112 + 0.944986i \(0.606075\pi\)
\(854\) 19.9839 + 34.6132i 0.683836 + 1.18444i
\(855\) −2.16022 + 3.74162i −0.0738781 + 0.127961i
\(856\) −17.0810 9.86173i −0.583817 0.337067i
\(857\) −4.48302 −0.153137 −0.0765686 0.997064i \(-0.524396\pi\)
−0.0765686 + 0.997064i \(0.524396\pi\)
\(858\) 3.84669 0.826094i 0.131324 0.0282024i
\(859\) −3.35158 −0.114355 −0.0571773 0.998364i \(-0.518210\pi\)
−0.0571773 + 0.998364i \(0.518210\pi\)
\(860\) −1.83800 1.06117i −0.0626753 0.0361856i
\(861\) 10.7485 18.6169i 0.366306 0.634461i
\(862\) 16.0064 + 27.7239i 0.545179 + 0.944278i
\(863\) 28.5494i 0.971832i 0.874006 + 0.485916i \(0.161514\pi\)
−0.874006 + 0.485916i \(0.838486\pi\)
\(864\) 3.67800 2.12350i 0.125128 0.0722428i
\(865\) −5.31386 + 3.06796i −0.180677 + 0.104314i
\(866\) 16.6375i 0.565366i
\(867\) 0.0412387 + 0.0714275i 0.00140054 + 0.00242580i
\(868\) 11.2390 19.4666i 0.381478 0.660739i
\(869\) 1.61954 + 0.935041i 0.0549391 + 0.0317191i
\(870\) 6.11665 0.207374
\(871\) −45.5719 14.7014i −1.54414 0.498137i
\(872\) −25.9871 −0.880036
\(873\) 15.0115 + 8.66687i 0.508061 + 0.293329i
\(874\) 6.22587 10.7835i 0.210593 0.364758i
\(875\) 15.4480 + 26.7568i 0.522239 + 0.904545i
\(876\) 10.2839i 0.347460i
\(877\) −24.1954 + 13.9692i −0.817022 + 0.471708i −0.849388 0.527768i \(-0.823029\pi\)
0.0323664 + 0.999476i \(0.489696\pi\)
\(878\) 23.5328 13.5867i 0.794193 0.458527i
\(879\) 6.48923i 0.218876i
\(880\) −0.935296 1.61998i −0.0315288 0.0546095i
\(881\) −20.6746 + 35.8095i −0.696546 + 1.20645i 0.273111 + 0.961983i \(0.411947\pi\)
−0.969657 + 0.244470i \(0.921386\pi\)
\(882\) 3.24971 + 1.87622i 0.109423 + 0.0631756i
\(883\) −37.9003 −1.27545 −0.637723 0.770266i \(-0.720124\pi\)
−0.637723 + 0.770266i \(0.720124\pi\)
\(884\) 3.68467 11.4219i 0.123929 0.384160i
\(885\) −14.7530 −0.495917
\(886\) 17.5547 + 10.1352i 0.589760 + 0.340498i
\(887\) 11.2642 19.5102i 0.378216 0.655089i −0.612587 0.790403i \(-0.709871\pi\)
0.990803 + 0.135314i \(0.0432044\pi\)
\(888\) −14.6327 25.3445i −0.491040 0.850507i
\(889\) 4.36025i 0.146238i
\(890\) 14.3903 8.30825i 0.482364 0.278493i
\(891\) −0.866025 + 0.500000i −0.0290129 + 0.0167506i
\(892\) 13.9076i 0.465660i
\(893\) 11.6388 + 20.1590i 0.389478 + 0.674596i
\(894\) 6.47157 11.2091i 0.216442 0.374888i
\(895\) −1.72831 0.997841i −0.0577710 0.0333541i
\(896\) −1.06939 −0.0357257
\(897\) −6.91985 7.65286i −0.231047 0.255522i
\(898\) 1.14011 0.0380458
\(899\) 38.5185 + 22.2387i 1.28466 + 0.741701i
\(900\) −1.54820 + 2.68157i −0.0516068 + 0.0893856i
\(901\) 27.4533 + 47.5505i 0.914602 + 1.58414i
\(902\) 7.26033i 0.241742i
\(903\) 6.77280 3.91028i 0.225385 0.130126i
\(904\) −15.2112 + 8.78220i −0.505917 + 0.292091i
\(905\) 4.07117i 0.135330i
\(906\) −12.1147 20.9833i −0.402484 0.697122i
\(907\) −16.6527 + 28.8433i −0.552943 + 0.957725i 0.445118 + 0.895472i \(0.353162\pi\)
−0.998060 + 0.0622526i \(0.980172\pi\)
\(908\) −6.73275 3.88715i −0.223434 0.129000i
\(909\) −7.72028 −0.256065
\(910\) −2.89176 13.4654i −0.0958608 0.446373i
\(911\) 17.5218 0.580524 0.290262 0.956947i \(-0.406258\pi\)
0.290262 + 0.956947i \(0.406258\pi\)
\(912\) 5.96245 + 3.44242i 0.197436 + 0.113990i
\(913\) −1.20019 + 2.07880i −0.0397206 + 0.0687982i
\(914\) 14.2548 + 24.6900i 0.471507 + 0.816673i
\(915\) 12.2825i 0.406047i
\(916\) −3.23507 + 1.86777i −0.106890 + 0.0617128i
\(917\) −32.1067 + 18.5368i −1.06026 + 0.612140i
\(918\) 4.48822i 0.148133i
\(919\) −27.3561 47.3821i −0.902393 1.56299i −0.824379 0.566039i \(-0.808475\pi\)
−0.0780145 0.996952i \(-0.524858\pi\)
\(920\) −4.75203 + 8.23076i −0.156670 + 0.271360i
\(921\) 11.5755 + 6.68311i 0.381425 + 0.220216i
\(922\) 14.6036 0.480946
\(923\) 1.51158 1.36680i 0.0497543 0.0449887i
\(924\) −2.61470 −0.0860173
\(925\) 31.6334 + 18.2636i 1.04010 + 0.600502i
\(926\) 12.9831 22.4875i 0.426653 0.738984i
\(927\) −4.54424 7.87086i −0.149252 0.258513i
\(928\) 21.9727i 0.721288i
\(929\) 6.67428 3.85340i 0.218976 0.126426i −0.386500 0.922289i \(-0.626316\pi\)
0.605476 + 0.795863i \(0.292983\pi\)
\(930\) −8.80199 + 5.08183i −0.288629 + 0.166640i
\(931\) 13.7129i 0.449423i
\(932\) −0.709940 1.22965i −0.0232549 0.0402786i
\(933\) −10.9408 + 18.9501i −0.358187 + 0.620398i
\(934\) 22.8688 + 13.2033i 0.748290 + 0.432025i
\(935\) 4.45631 0.145737
\(936\) 8.19825 7.41301i 0.267968 0.242302i
\(937\) −40.3770 −1.31906 −0.659530 0.751678i \(-0.729245\pi\)
−0.659530 + 0.751678i \(0.729245\pi\)
\(938\) −40.5495 23.4112i −1.32399 0.764404i
\(939\) 9.46890 16.4006i 0.309006 0.535214i
\(940\) −2.55912 4.43252i −0.0834692 0.144573i
\(941\) 16.4105i 0.534966i 0.963563 + 0.267483i \(0.0861919\pi\)
−0.963563 + 0.267483i \(0.913808\pi\)
\(942\) −2.85668 + 1.64931i −0.0930757 + 0.0537373i
\(943\) −16.4886 + 9.51970i −0.536943 + 0.310004i
\(944\) 23.5096i 0.765174i
\(945\) 1.75026 + 3.03154i 0.0569359 + 0.0986159i
\(946\) 1.32065 2.28743i 0.0429380 0.0743708i
\(947\) −22.2938 12.8713i −0.724451 0.418262i 0.0919380 0.995765i \(-0.470694\pi\)
−0.816389 + 0.577503i \(0.804027\pi\)
\(948\) 1.51341 0.0491533
\(949\) −9.62020 44.7962i −0.312285 1.45415i
\(950\) −16.6490 −0.540166
\(951\) 13.0886 + 7.55669i 0.424426 + 0.245043i
\(952\) 20.3687 35.2797i 0.660154 1.14342i
\(953\) 12.2543 + 21.2250i 0.396955 + 0.687547i 0.993349 0.115146i \(-0.0367335\pi\)
−0.596393 + 0.802692i \(0.703400\pi\)
\(954\) 14.5667i 0.471615i
\(955\) −10.6856 + 6.16932i −0.345777 + 0.199634i
\(956\) 19.8720 11.4731i 0.642707 0.371067i
\(957\) 5.17370i 0.167242i
\(958\) 3.20270 + 5.54724i 0.103475 + 0.179223i
\(959\) 16.9702 29.3932i 0.547996 0.949156i
\(960\) −7.58831 4.38112i −0.244912 0.141400i
\(961\) −42.9052 −1.38404
\(962\) −25.1915 27.8600i −0.812206 0.898242i
\(963\) 6.43403 0.207334
\(964\) 4.93677 + 2.85024i 0.159003 + 0.0918002i
\(965\) 7.00162 12.1272i 0.225390 0.390387i
\(966\) −5.04433 8.73704i −0.162299 0.281110i
\(967\) 15.1247i 0.486379i −0.969979 0.243189i \(-0.921806\pi\)
0.969979 0.243189i \(-0.0781936\pi\)
\(968\) −2.65479 + 1.53275i −0.0853283 + 0.0492643i
\(969\) −14.2043 + 8.20088i −0.456309 + 0.263450i
\(970\) 20.4930i 0.657989i
\(971\) −19.7020 34.1249i −0.632269 1.09512i −0.987087 0.160186i \(-0.948791\pi\)
0.354818 0.934935i \(-0.384543\pi\)
\(972\) −0.404638 + 0.700853i −0.0129788 + 0.0224799i
\(973\) −27.1962 15.7018i −0.871871 0.503375i
\(974\) −26.6645 −0.854386
\(975\) −4.23541 + 13.1291i −0.135642 + 0.420468i
\(976\) 19.5728 0.626509
\(977\) 38.0554 + 21.9713i 1.21750 + 0.702924i 0.964383 0.264511i \(-0.0852105\pi\)
0.253118 + 0.967435i \(0.418544\pi\)
\(978\) 6.38136 11.0528i 0.204053 0.353431i
\(979\) −7.02744 12.1719i −0.224598 0.389015i
\(980\) 3.01517i 0.0963160i
\(981\) 7.34157 4.23866i 0.234398 0.135330i
\(982\) 11.2619 6.50208i 0.359383 0.207490i
\(983\) 26.1389i 0.833703i 0.908975 + 0.416851i \(0.136866\pi\)
−0.908975 + 0.416851i \(0.863134\pi\)
\(984\) −10.1981 17.6637i −0.325105 0.563098i
\(985\) −8.65556 + 14.9919i −0.275789 + 0.477681i
\(986\) 20.1097 + 11.6104i 0.640424 + 0.369749i
\(987\) 18.8600 0.600322
\(988\) −11.0737 3.57234i −0.352301 0.113651i
\(989\) −6.92651 −0.220250
\(990\) 1.02387 + 0.591129i 0.0325406 + 0.0187873i
\(991\) −10.3362 + 17.9028i −0.328339 + 0.568700i −0.982182 0.187930i \(-0.939822\pi\)
0.653843 + 0.756630i \(0.273155\pi\)
\(992\) −18.2553 31.6191i −0.579607 1.00391i
\(993\) 11.9802i 0.380181i
\(994\) 1.72572 0.996348i 0.0547367 0.0316022i
\(995\) 4.67370 2.69836i 0.148166 0.0855438i
\(996\) 1.94258i 0.0615529i
\(997\) 6.18669 + 10.7157i 0.195935 + 0.339369i 0.947206 0.320624i \(-0.103893\pi\)
−0.751272 + 0.659993i \(0.770559\pi\)
\(998\) −9.60944 + 16.6440i −0.304181 + 0.526858i
\(999\) 8.26769 + 4.77336i 0.261578 + 0.151022i
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 429.2.s.b.199.5 yes 28
13.6 odd 12 5577.2.a.bg.1.8 14
13.7 odd 12 5577.2.a.bf.1.7 14
13.10 even 6 inner 429.2.s.b.166.5 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
429.2.s.b.166.5 28 13.10 even 6 inner
429.2.s.b.199.5 yes 28 1.1 even 1 trivial
5577.2.a.bf.1.7 14 13.7 odd 12
5577.2.a.bg.1.8 14 13.6 odd 12