Properties

Label 170.2.n.a.19.1
Level $170$
Weight $2$
Character 170.19
Analytic conductor $1.357$
Analytic rank $0$
Dimension $20$
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] = [170,2,Mod(9,170)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(170, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([4, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("170.9");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 170 = 2 \cdot 5 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 170.n (of order \(8\), 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: \(1.35745683436\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(5\) over \(\Q(\zeta_{8})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - 16 x^{15} + 52 x^{14} + 992 x^{13} + 6181 x^{12} + 8952 x^{11} + 6244 x^{10} - 11448 x^{9} - 14520 x^{8} + 27936 x^{7} + 27880 x^{6} - 121104 x^{5} + 187460 x^{4} + \cdots + 2048 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 19.1
Root \(2.99334 + 1.23988i\) of defining polynomial
Character \(\chi\) \(=\) 170.19
Dual form 170.2.n.a.9.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} +(-1.23988 - 2.99334i) q^{3} -1.00000i q^{4} +(-2.18859 + 0.458323i) q^{5} +(2.99334 + 1.23988i) q^{6} +(1.49921 + 0.620992i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-5.30145 + 5.30145i) q^{9} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} +(-1.23988 - 2.99334i) q^{3} -1.00000i q^{4} +(-2.18859 + 0.458323i) q^{5} +(2.99334 + 1.23988i) q^{6} +(1.49921 + 0.620992i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-5.30145 + 5.30145i) q^{9} +(1.22349 - 1.87165i) q^{10} +(-4.11919 - 1.70622i) q^{11} +(-2.99334 + 1.23988i) q^{12} -1.78934 q^{13} +(-1.49921 + 0.620992i) q^{14} +(4.08551 + 5.98294i) q^{15} -1.00000 q^{16} +(-3.35446 + 2.39741i) q^{17} -7.49739i q^{18} +(-0.157527 - 0.157527i) q^{19} +(0.458323 + 2.18859i) q^{20} -5.25759i q^{21} +(4.11919 - 1.70622i) q^{22} +(2.07076 - 4.99927i) q^{23} +(1.23988 - 2.99334i) q^{24} +(4.57988 - 2.00616i) q^{25} +(1.26525 - 1.26525i) q^{26} +(13.4622 + 5.57623i) q^{27} +(0.620992 - 1.49921i) q^{28} +(-2.00418 - 4.83853i) q^{29} +(-7.11947 - 1.34168i) q^{30} +(-1.60817 + 0.666124i) q^{31} +(0.707107 - 0.707107i) q^{32} +14.4456i q^{33} +(0.676740 - 4.06719i) q^{34} +(-3.56577 - 0.671978i) q^{35} +(5.30145 + 5.30145i) q^{36} +(-3.91254 - 9.44570i) q^{37} +0.222777 q^{38} +(2.21857 + 5.35610i) q^{39} +(-1.87165 - 1.22349i) q^{40} +(0.657761 - 1.58798i) q^{41} +(3.71768 + 3.71768i) q^{42} +(3.65649 + 3.65649i) q^{43} +(-1.70622 + 4.11919i) q^{44} +(9.17295 - 14.0325i) q^{45} +(2.07076 + 4.99927i) q^{46} -5.48034 q^{47} +(1.23988 + 2.99334i) q^{48} +(-3.08775 - 3.08775i) q^{49} +(-1.81989 + 4.65704i) q^{50} +(11.3354 + 7.06855i) q^{51} +1.78934i q^{52} +(-1.42918 + 1.42918i) q^{53} +(-13.4622 + 5.57623i) q^{54} +(9.79722 + 1.84631i) q^{55} +(0.620992 + 1.49921i) q^{56} +(-0.276217 + 0.666847i) q^{57} +(4.83853 + 2.00418i) q^{58} +(1.74254 - 1.74254i) q^{59} +(5.98294 - 4.08551i) q^{60} +(-3.62231 + 8.74502i) q^{61} +(0.666124 - 1.60817i) q^{62} +(-11.2401 + 4.65582i) q^{63} +1.00000i q^{64} +(3.91614 - 0.820096i) q^{65} +(-10.2146 - 10.2146i) q^{66} -14.4344i q^{67} +(2.39741 + 3.35446i) q^{68} -17.5320 q^{69} +(2.99654 - 2.04622i) q^{70} +(7.59937 - 3.14776i) q^{71} -7.49739 q^{72} +(1.40695 - 0.582777i) q^{73} +(9.44570 + 3.91254i) q^{74} +(-11.6836 - 11.2217i) q^{75} +(-0.157527 + 0.157527i) q^{76} +(-5.11596 - 5.11596i) q^{77} +(-5.35610 - 2.21857i) q^{78} +(-2.76144 - 1.14383i) q^{79} +(2.18859 - 0.458323i) q^{80} -24.7186i q^{81} +(0.657761 + 1.58798i) q^{82} +(-10.0574 + 10.0574i) q^{83} -5.25759 q^{84} +(6.24277 - 6.78438i) q^{85} -5.17105 q^{86} +(-11.9984 + 11.9984i) q^{87} +(-1.70622 - 4.11919i) q^{88} +9.77020i q^{89} +(3.43622 + 16.4087i) q^{90} +(-2.68259 - 1.11117i) q^{91} +(-4.99927 - 2.07076i) q^{92} +(3.98787 + 3.98787i) q^{93} +(3.87519 - 3.87519i) q^{94} +(0.416961 + 0.272565i) q^{95} +(-2.99334 - 1.23988i) q^{96} +(4.59847 - 1.90475i) q^{97} +4.36674 q^{98} +(30.8831 - 12.7922i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q - 4 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 20 q - 4 q^{5} + 4 q^{10} - 8 q^{11} - 24 q^{13} + 8 q^{15} - 20 q^{16} + 8 q^{20} + 8 q^{22} + 16 q^{23} - 12 q^{25} - 12 q^{26} + 24 q^{27} - 12 q^{29} - 8 q^{30} + 8 q^{31} + 8 q^{34} - 8 q^{35} - 8 q^{37} - 8 q^{38} + 4 q^{40} + 4 q^{41} + 8 q^{42} + 16 q^{43} - 8 q^{44} - 12 q^{45} + 16 q^{46} + 40 q^{47} - 56 q^{49} + 8 q^{50} - 8 q^{51} + 44 q^{53} - 24 q^{54} - 72 q^{57} + 16 q^{59} + 16 q^{60} + 8 q^{61} - 8 q^{62} - 24 q^{63} - 8 q^{65} - 8 q^{66} + 20 q^{68} - 16 q^{69} - 16 q^{70} + 8 q^{71} - 28 q^{72} - 60 q^{73} + 28 q^{74} + 64 q^{75} + 8 q^{78} + 56 q^{79} + 4 q^{80} + 4 q^{82} + 16 q^{84} - 16 q^{85} + 48 q^{86} - 72 q^{87} - 8 q^{88} + 32 q^{90} - 24 q^{91} - 8 q^{92} + 72 q^{93} + 32 q^{94} + 8 q^{95} + 48 q^{97} - 36 q^{98} + 72 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/170\mathbb{Z}\right)^\times\).

\(n\) \(71\) \(137\)
\(\chi(n)\) \(e\left(\frac{7}{8}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 + 0.707107i −0.500000 + 0.500000i
\(3\) −1.23988 2.99334i −0.715846 1.72821i −0.684848 0.728686i \(-0.740132\pi\)
−0.0309978 0.999519i \(-0.509868\pi\)
\(4\) 1.00000i 0.500000i
\(5\) −2.18859 + 0.458323i −0.978769 + 0.204968i
\(6\) 2.99334 + 1.23988i 1.22203 + 0.506180i
\(7\) 1.49921 + 0.620992i 0.566647 + 0.234713i 0.647568 0.762008i \(-0.275786\pi\)
−0.0809209 + 0.996721i \(0.525786\pi\)
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) −5.30145 + 5.30145i −1.76715 + 1.76715i
\(10\) 1.22349 1.87165i 0.386900 0.591868i
\(11\) −4.11919 1.70622i −1.24198 0.514445i −0.337648 0.941272i \(-0.609631\pi\)
−0.904333 + 0.426827i \(0.859631\pi\)
\(12\) −2.99334 + 1.23988i −0.864103 + 0.357923i
\(13\) −1.78934 −0.496274 −0.248137 0.968725i \(-0.579818\pi\)
−0.248137 + 0.968725i \(0.579818\pi\)
\(14\) −1.49921 + 0.620992i −0.400680 + 0.165967i
\(15\) 4.08551 + 5.98294i 1.05487 + 1.54479i
\(16\) −1.00000 −0.250000
\(17\) −3.35446 + 2.39741i −0.813577 + 0.581457i
\(18\) 7.49739i 1.76715i
\(19\) −0.157527 0.157527i −0.0361392 0.0361392i 0.688806 0.724945i \(-0.258135\pi\)
−0.724945 + 0.688806i \(0.758135\pi\)
\(20\) 0.458323 + 2.18859i 0.102484 + 0.489384i
\(21\) 5.25759i 1.14730i
\(22\) 4.11919 1.70622i 0.878213 0.363768i
\(23\) 2.07076 4.99927i 0.431784 1.04242i −0.546928 0.837180i \(-0.684203\pi\)
0.978712 0.205239i \(-0.0657973\pi\)
\(24\) 1.23988 2.99334i 0.253090 0.611013i
\(25\) 4.57988 2.00616i 0.915976 0.401233i
\(26\) 1.26525 1.26525i 0.248137 0.248137i
\(27\) 13.4622 + 5.57623i 2.59080 + 1.07315i
\(28\) 0.620992 1.49921i 0.117356 0.283324i
\(29\) −2.00418 4.83853i −0.372168 0.898492i −0.993383 0.114852i \(-0.963361\pi\)
0.621215 0.783640i \(-0.286639\pi\)
\(30\) −7.11947 1.34168i −1.29983 0.244956i
\(31\) −1.60817 + 0.666124i −0.288835 + 0.119639i −0.522397 0.852703i \(-0.674962\pi\)
0.233561 + 0.972342i \(0.424962\pi\)
\(32\) 0.707107 0.707107i 0.125000 0.125000i
\(33\) 14.4456i 2.51466i
\(34\) 0.676740 4.06719i 0.116060 0.697517i
\(35\) −3.56577 0.671978i −0.602725 0.113585i
\(36\) 5.30145 + 5.30145i 0.883575 + 0.883575i
\(37\) −3.91254 9.44570i −0.643217 1.55286i −0.822315 0.569032i \(-0.807318\pi\)
0.179098 0.983831i \(-0.442682\pi\)
\(38\) 0.222777 0.0361392
\(39\) 2.21857 + 5.35610i 0.355256 + 0.857663i
\(40\) −1.87165 1.22349i −0.295934 0.193450i
\(41\) 0.657761 1.58798i 0.102725 0.248000i −0.864158 0.503221i \(-0.832148\pi\)
0.966883 + 0.255221i \(0.0821482\pi\)
\(42\) 3.71768 + 3.71768i 0.573651 + 0.573651i
\(43\) 3.65649 + 3.65649i 0.557609 + 0.557609i 0.928626 0.371017i \(-0.120991\pi\)
−0.371017 + 0.928626i \(0.620991\pi\)
\(44\) −1.70622 + 4.11919i −0.257223 + 0.620991i
\(45\) 9.17295 14.0325i 1.36742 2.09184i
\(46\) 2.07076 + 4.99927i 0.305318 + 0.737102i
\(47\) −5.48034 −0.799390 −0.399695 0.916648i \(-0.630884\pi\)
−0.399695 + 0.916648i \(0.630884\pi\)
\(48\) 1.23988 + 2.99334i 0.178962 + 0.432051i
\(49\) −3.08775 3.08775i −0.441108 0.441108i
\(50\) −1.81989 + 4.65704i −0.257372 + 0.658605i
\(51\) 11.3354 + 7.06855i 1.58727 + 0.989794i
\(52\) 1.78934i 0.248137i
\(53\) −1.42918 + 1.42918i −0.196313 + 0.196313i −0.798417 0.602105i \(-0.794329\pi\)
0.602105 + 0.798417i \(0.294329\pi\)
\(54\) −13.4622 + 5.57623i −1.83197 + 0.758828i
\(55\) 9.79722 + 1.84631i 1.32106 + 0.248956i
\(56\) 0.620992 + 1.49921i 0.0829836 + 0.200340i
\(57\) −0.276217 + 0.666847i −0.0365859 + 0.0883261i
\(58\) 4.83853 + 2.00418i 0.635330 + 0.263162i
\(59\) 1.74254 1.74254i 0.226859 0.226859i −0.584520 0.811379i \(-0.698717\pi\)
0.811379 + 0.584520i \(0.198717\pi\)
\(60\) 5.98294 4.08551i 0.772394 0.527437i
\(61\) −3.62231 + 8.74502i −0.463789 + 1.11969i 0.503041 + 0.864263i \(0.332215\pi\)
−0.966830 + 0.255423i \(0.917785\pi\)
\(62\) 0.666124 1.60817i 0.0845979 0.204237i
\(63\) −11.2401 + 4.65582i −1.41612 + 0.586578i
\(64\) 1.00000i 0.125000i
\(65\) 3.91614 0.820096i 0.485737 0.101720i
\(66\) −10.2146 10.2146i −1.25733 1.25733i
\(67\) 14.4344i 1.76345i −0.471767 0.881723i \(-0.656384\pi\)
0.471767 0.881723i \(-0.343616\pi\)
\(68\) 2.39741 + 3.35446i 0.290729 + 0.406789i
\(69\) −17.5320 −2.11061
\(70\) 2.99654 2.04622i 0.358155 0.244570i
\(71\) 7.59937 3.14776i 0.901879 0.373571i 0.116937 0.993139i \(-0.462692\pi\)
0.784942 + 0.619569i \(0.212692\pi\)
\(72\) −7.49739 −0.883575
\(73\) 1.40695 0.582777i 0.164671 0.0682089i −0.298825 0.954308i \(-0.596595\pi\)
0.463496 + 0.886099i \(0.346595\pi\)
\(74\) 9.44570 + 3.91254i 1.09804 + 0.454823i
\(75\) −11.6836 11.2217i −1.34911 1.29577i
\(76\) −0.157527 + 0.157527i −0.0180696 + 0.0180696i
\(77\) −5.11596 5.11596i −0.583018 0.583018i
\(78\) −5.35610 2.21857i −0.606459 0.251204i
\(79\) −2.76144 1.14383i −0.310687 0.128691i 0.221892 0.975071i \(-0.428777\pi\)
−0.532578 + 0.846381i \(0.678777\pi\)
\(80\) 2.18859 0.458323i 0.244692 0.0512421i
\(81\) 24.7186i 2.74652i
\(82\) 0.657761 + 1.58798i 0.0726376 + 0.175363i
\(83\) −10.0574 + 10.0574i −1.10394 + 1.10394i −0.110014 + 0.993930i \(0.535090\pi\)
−0.993930 + 0.110014i \(0.964910\pi\)
\(84\) −5.25759 −0.573651
\(85\) 6.24277 6.78438i 0.677123 0.735869i
\(86\) −5.17105 −0.557609
\(87\) −11.9984 + 11.9984i −1.28636 + 1.28636i
\(88\) −1.70622 4.11919i −0.181884 0.439107i
\(89\) 9.77020i 1.03564i 0.855490 + 0.517820i \(0.173256\pi\)
−0.855490 + 0.517820i \(0.826744\pi\)
\(90\) 3.43622 + 16.4087i 0.362210 + 1.72963i
\(91\) −2.68259 1.11117i −0.281212 0.116482i
\(92\) −4.99927 2.07076i −0.521210 0.215892i
\(93\) 3.98787 + 3.98787i 0.413523 + 0.413523i
\(94\) 3.87519 3.87519i 0.399695 0.399695i
\(95\) 0.416961 + 0.272565i 0.0427793 + 0.0279645i
\(96\) −2.99334 1.23988i −0.305506 0.126545i
\(97\) 4.59847 1.90475i 0.466903 0.193398i −0.136813 0.990597i \(-0.543686\pi\)
0.603716 + 0.797199i \(0.293686\pi\)
\(98\) 4.36674 0.441108
\(99\) 30.8831 12.7922i 3.10387 1.28567i
\(100\) −2.00616 4.57988i −0.200616 0.457988i
\(101\) 11.1039 1.10488 0.552438 0.833554i \(-0.313698\pi\)
0.552438 + 0.833554i \(0.313698\pi\)
\(102\) −13.0136 + 3.01712i −1.28853 + 0.298739i
\(103\) 3.86906i 0.381230i −0.981665 0.190615i \(-0.938952\pi\)
0.981665 0.190615i \(-0.0610481\pi\)
\(104\) −1.26525 1.26525i −0.124068 0.124068i
\(105\) 2.40968 + 11.5067i 0.235160 + 1.12294i
\(106\) 2.02116i 0.196313i
\(107\) 11.1802 4.63098i 1.08083 0.447694i 0.230029 0.973184i \(-0.426118\pi\)
0.850800 + 0.525490i \(0.176118\pi\)
\(108\) 5.57623 13.4622i 0.536573 1.29540i
\(109\) −4.89487 + 11.8173i −0.468843 + 1.13189i 0.495825 + 0.868422i \(0.334866\pi\)
−0.964669 + 0.263466i \(0.915134\pi\)
\(110\) −8.23322 + 5.62214i −0.785007 + 0.536050i
\(111\) −23.4231 + 23.4231i −2.22322 + 2.22322i
\(112\) −1.49921 0.620992i −0.141662 0.0586782i
\(113\) 1.96861 4.75264i 0.185191 0.447091i −0.803831 0.594858i \(-0.797208\pi\)
0.989022 + 0.147767i \(0.0472084\pi\)
\(114\) −0.276217 0.666847i −0.0258701 0.0624560i
\(115\) −2.24078 + 11.8904i −0.208954 + 1.10879i
\(116\) −4.83853 + 2.00418i −0.449246 + 0.186084i
\(117\) 9.48610 9.48610i 0.876991 0.876991i
\(118\) 2.46432i 0.226859i
\(119\) −6.51781 + 1.51112i −0.597487 + 0.138524i
\(120\) −1.34168 + 7.11947i −0.122478 + 0.649916i
\(121\) 6.27832 + 6.27832i 0.570756 + 0.570756i
\(122\) −3.62231 8.74502i −0.327948 0.791737i
\(123\) −5.56890 −0.502130
\(124\) 0.666124 + 1.60817i 0.0598197 + 0.144418i
\(125\) −9.10402 + 6.48974i −0.814289 + 0.580460i
\(126\) 4.65582 11.2401i 0.414773 1.00135i
\(127\) −0.920220 0.920220i −0.0816564 0.0816564i 0.665099 0.746755i \(-0.268389\pi\)
−0.746755 + 0.665099i \(0.768389\pi\)
\(128\) −0.707107 0.707107i −0.0625000 0.0625000i
\(129\) 6.41149 15.4787i 0.564501 1.36283i
\(130\) −2.18923 + 3.34902i −0.192008 + 0.293729i
\(131\) 1.58915 + 3.83655i 0.138845 + 0.335201i 0.977973 0.208733i \(-0.0669341\pi\)
−0.839128 + 0.543934i \(0.816934\pi\)
\(132\) 14.4456 1.25733
\(133\) −0.138343 0.333989i −0.0119958 0.0289605i
\(134\) 10.2067 + 10.2067i 0.881723 + 0.881723i
\(135\) −32.0190 6.03406i −2.75576 0.519329i
\(136\) −4.06719 0.676740i −0.348759 0.0580300i
\(137\) 21.1172i 1.80417i 0.431562 + 0.902083i \(0.357963\pi\)
−0.431562 + 0.902083i \(0.642037\pi\)
\(138\) 12.3970 12.3970i 1.05530 1.05530i
\(139\) 9.90569 4.10307i 0.840190 0.348018i 0.0792614 0.996854i \(-0.474744\pi\)
0.760928 + 0.648836i \(0.224744\pi\)
\(140\) −0.671978 + 3.56577i −0.0567925 + 0.301363i
\(141\) 6.79498 + 16.4045i 0.572240 + 1.38151i
\(142\) −3.14776 + 7.59937i −0.264154 + 0.637725i
\(143\) 7.37063 + 3.05301i 0.616363 + 0.255306i
\(144\) 5.30145 5.30145i 0.441788 0.441788i
\(145\) 6.60395 + 9.67101i 0.548428 + 0.803133i
\(146\) −0.582777 + 1.40695i −0.0482310 + 0.116440i
\(147\) −5.41425 + 13.0711i −0.446560 + 1.07809i
\(148\) −9.44570 + 3.91254i −0.776432 + 0.321609i
\(149\) 8.46929i 0.693831i −0.937896 0.346915i \(-0.887229\pi\)
0.937896 0.346915i \(-0.112771\pi\)
\(150\) 16.1965 0.326622i 1.32244 0.0266686i
\(151\) 1.27947 + 1.27947i 0.104121 + 0.104121i 0.757248 0.653127i \(-0.226543\pi\)
−0.653127 + 0.757248i \(0.726543\pi\)
\(152\) 0.222777i 0.0180696i
\(153\) 5.07378 30.4933i 0.410191 2.46524i
\(154\) 7.23507 0.583018
\(155\) 3.21432 2.19493i 0.258181 0.176301i
\(156\) 5.35610 2.21857i 0.428831 0.177628i
\(157\) −2.07703 −0.165765 −0.0828824 0.996559i \(-0.526413\pi\)
−0.0828824 + 0.996559i \(0.526413\pi\)
\(158\) 2.76144 1.14383i 0.219689 0.0909980i
\(159\) 6.05003 + 2.50600i 0.479798 + 0.198739i
\(160\) −1.22349 + 1.87165i −0.0967250 + 0.147967i
\(161\) 6.20901 6.20901i 0.489339 0.489339i
\(162\) 17.4787 + 17.4787i 1.37326 + 1.37326i
\(163\) −1.91410 0.792847i −0.149924 0.0621006i 0.306460 0.951884i \(-0.400856\pi\)
−0.456384 + 0.889783i \(0.650856\pi\)
\(164\) −1.58798 0.657761i −0.124000 0.0513625i
\(165\) −6.62077 31.6156i −0.515426 2.46127i
\(166\) 14.2233i 1.10394i
\(167\) −6.65999 16.0786i −0.515366 1.24420i −0.940723 0.339177i \(-0.889851\pi\)
0.425357 0.905026i \(-0.360149\pi\)
\(168\) 3.71768 3.71768i 0.286825 0.286825i
\(169\) −9.79826 −0.753712
\(170\) 0.382976 + 9.21159i 0.0293730 + 0.706496i
\(171\) 1.67025 0.127727
\(172\) 3.65649 3.65649i 0.278805 0.278805i
\(173\) 1.97254 + 4.76214i 0.149970 + 0.362059i 0.980955 0.194236i \(-0.0622226\pi\)
−0.830985 + 0.556295i \(0.812223\pi\)
\(174\) 16.9683i 1.28636i
\(175\) 8.11200 0.163588i 0.613210 0.0123661i
\(176\) 4.11919 + 1.70622i 0.310495 + 0.128611i
\(177\) −7.37654 3.05546i −0.554455 0.229663i
\(178\) −6.90857 6.90857i −0.517820 0.517820i
\(179\) −2.09869 + 2.09869i −0.156864 + 0.156864i −0.781175 0.624312i \(-0.785380\pi\)
0.624312 + 0.781175i \(0.285380\pi\)
\(180\) −14.0325 9.17295i −1.04592 0.683711i
\(181\) −10.0565 4.16552i −0.747491 0.309621i −0.0237737 0.999717i \(-0.507568\pi\)
−0.723717 + 0.690096i \(0.757568\pi\)
\(182\) 2.68259 1.11117i 0.198847 0.0823651i
\(183\) 30.6680 2.26705
\(184\) 4.99927 2.07076i 0.368551 0.152659i
\(185\) 12.8921 + 18.8796i 0.947848 + 1.38806i
\(186\) −5.63970 −0.413523
\(187\) 17.9082 4.15191i 1.30958 0.303618i
\(188\) 5.48034i 0.399695i
\(189\) 16.7198 + 16.7198i 1.21619 + 1.21619i
\(190\) −0.487568 + 0.102104i −0.0353719 + 0.00740739i
\(191\) 24.0385i 1.73937i −0.493611 0.869683i \(-0.664323\pi\)
0.493611 0.869683i \(-0.335677\pi\)
\(192\) 2.99334 1.23988i 0.216026 0.0894808i
\(193\) −6.71939 + 16.2220i −0.483672 + 1.16769i 0.474180 + 0.880428i \(0.342745\pi\)
−0.957852 + 0.287261i \(0.907255\pi\)
\(194\) −1.90475 + 4.59847i −0.136753 + 0.330151i
\(195\) −7.31037 10.7055i −0.523507 0.766637i
\(196\) −3.08775 + 3.08775i −0.220554 + 0.220554i
\(197\) −14.0551 5.82183i −1.00139 0.414788i −0.179082 0.983834i \(-0.557313\pi\)
−0.822306 + 0.569046i \(0.807313\pi\)
\(198\) −12.7922 + 30.8831i −0.909103 + 2.19477i
\(199\) −3.07405 7.42142i −0.217914 0.526091i 0.776684 0.629890i \(-0.216900\pi\)
−0.994598 + 0.103799i \(0.966900\pi\)
\(200\) 4.65704 + 1.81989i 0.329302 + 0.128686i
\(201\) −43.2071 + 17.8970i −3.04760 + 1.26236i
\(202\) −7.85162 + 7.85162i −0.552438 + 0.552438i
\(203\) 8.49854i 0.596481i
\(204\) 7.06855 11.3354i 0.494897 0.793637i
\(205\) −0.711766 + 3.77690i −0.0497119 + 0.263790i
\(206\) 2.73584 + 2.73584i 0.190615 + 0.190615i
\(207\) 15.5253 + 37.4814i 1.07908 + 2.60514i
\(208\) 1.78934 0.124068
\(209\) 0.380107 + 0.917660i 0.0262926 + 0.0634759i
\(210\) −9.84039 6.43259i −0.679051 0.443891i
\(211\) 3.61423 8.72553i 0.248814 0.600690i −0.749290 0.662242i \(-0.769605\pi\)
0.998104 + 0.0615519i \(0.0196050\pi\)
\(212\) 1.42918 + 1.42918i 0.0981564 + 0.0981564i
\(213\) −18.8446 18.8446i −1.29121 1.29121i
\(214\) −4.63098 + 11.1802i −0.316567 + 0.764262i
\(215\) −9.67841 6.32671i −0.660062 0.431478i
\(216\) 5.57623 + 13.4622i 0.379414 + 0.915987i
\(217\) −2.82463 −0.191749
\(218\) −4.89487 11.8173i −0.331522 0.800366i
\(219\) −3.48890 3.48890i −0.235758 0.235758i
\(220\) 1.84631 9.79722i 0.124478 0.660529i
\(221\) 6.00228 4.28978i 0.403757 0.288562i
\(222\) 33.1253i 2.22322i
\(223\) 1.52869 1.52869i 0.102369 0.102369i −0.654067 0.756436i \(-0.726939\pi\)
0.756436 + 0.654067i \(0.226939\pi\)
\(224\) 1.49921 0.620992i 0.100170 0.0414918i
\(225\) −13.6444 + 34.9156i −0.909629 + 2.32771i
\(226\) 1.96861 + 4.75264i 0.130950 + 0.316141i
\(227\) 0.146890 0.354624i 0.00974943 0.0235372i −0.918930 0.394421i \(-0.870945\pi\)
0.928679 + 0.370884i \(0.120945\pi\)
\(228\) 0.666847 + 0.276217i 0.0441631 + 0.0182929i
\(229\) −6.36165 + 6.36165i −0.420390 + 0.420390i −0.885338 0.464948i \(-0.846073\pi\)
0.464948 + 0.885338i \(0.346073\pi\)
\(230\) −6.82334 9.99228i −0.449918 0.658872i
\(231\) −8.97063 + 21.6570i −0.590224 + 1.42493i
\(232\) 2.00418 4.83853i 0.131581 0.317665i
\(233\) 11.4366 4.73720i 0.749238 0.310344i 0.0248072 0.999692i \(-0.492103\pi\)
0.724430 + 0.689348i \(0.242103\pi\)
\(234\) 13.4154i 0.876991i
\(235\) 11.9942 2.51177i 0.782418 0.163850i
\(236\) −1.74254 1.74254i −0.113429 0.113429i
\(237\) 9.68415i 0.629053i
\(238\) 3.54027 5.67731i 0.229481 0.368005i
\(239\) −8.64334 −0.559091 −0.279545 0.960132i \(-0.590184\pi\)
−0.279545 + 0.960132i \(0.590184\pi\)
\(240\) −4.08551 5.98294i −0.263719 0.386197i
\(241\) −20.1931 + 8.36424i −1.30075 + 0.538788i −0.922171 0.386781i \(-0.873587\pi\)
−0.378578 + 0.925569i \(0.623587\pi\)
\(242\) −8.87889 −0.570756
\(243\) −33.6047 + 13.9195i −2.15574 + 0.892937i
\(244\) 8.74502 + 3.62231i 0.559843 + 0.231894i
\(245\) 8.17303 + 5.34265i 0.522156 + 0.341329i
\(246\) 3.93780 3.93780i 0.251065 0.251065i
\(247\) 0.281870 + 0.281870i 0.0179349 + 0.0179349i
\(248\) −1.60817 0.666124i −0.102119 0.0422989i
\(249\) 42.5752 + 17.6352i 2.69810 + 1.11759i
\(250\) 1.84858 11.0265i 0.116914 0.697374i
\(251\) 21.7468i 1.37264i −0.727298 0.686322i \(-0.759224\pi\)
0.727298 0.686322i \(-0.240776\pi\)
\(252\) 4.65582 + 11.2401i 0.293289 + 0.708062i
\(253\) −17.0597 + 17.0597i −1.07254 + 1.07254i
\(254\) 1.30139 0.0816564
\(255\) −28.0482 10.2749i −1.75645 0.643439i
\(256\) 1.00000 0.0625000
\(257\) 13.9606 13.9606i 0.870840 0.870840i −0.121724 0.992564i \(-0.538842\pi\)
0.992564 + 0.121724i \(0.0388423\pi\)
\(258\) 6.41149 + 15.4787i 0.399162 + 0.963663i
\(259\) 16.5907i 1.03090i
\(260\) −0.820096 3.91614i −0.0508602 0.242869i
\(261\) 36.2763 + 15.0261i 2.24545 + 0.930095i
\(262\) −3.83655 1.58915i −0.237023 0.0981780i
\(263\) 13.2397 + 13.2397i 0.816392 + 0.816392i 0.985583 0.169191i \(-0.0541154\pi\)
−0.169191 + 0.985583i \(0.554115\pi\)
\(264\) −10.2146 + 10.2146i −0.628666 + 0.628666i
\(265\) 2.47286 3.78292i 0.151907 0.232383i
\(266\) 0.333989 + 0.138343i 0.0204782 + 0.00848234i
\(267\) 29.2455 12.1139i 1.78980 0.741358i
\(268\) −14.4344 −0.881723
\(269\) 9.51404 3.94085i 0.580081 0.240278i −0.0732956 0.997310i \(-0.523352\pi\)
0.653377 + 0.757033i \(0.273352\pi\)
\(270\) 26.9076 18.3741i 1.63754 1.11821i
\(271\) 18.9442 1.15078 0.575390 0.817879i \(-0.304850\pi\)
0.575390 + 0.817879i \(0.304850\pi\)
\(272\) 3.35446 2.39741i 0.203394 0.145364i
\(273\) 9.40763i 0.569376i
\(274\) −14.9321 14.9321i −0.902083 0.902083i
\(275\) −22.2883 + 0.449471i −1.34404 + 0.0271041i
\(276\) 17.5320i 1.05530i
\(277\) −21.1959 + 8.77965i −1.27354 + 0.527518i −0.914039 0.405626i \(-0.867053\pi\)
−0.359502 + 0.933144i \(0.617053\pi\)
\(278\) −4.10307 + 9.90569i −0.246086 + 0.594104i
\(279\) 4.99419 12.0570i 0.298994 0.721836i
\(280\) −2.04622 2.99654i −0.122285 0.179078i
\(281\) 16.9895 16.9895i 1.01351 1.01351i 0.0136041 0.999907i \(-0.495670\pi\)
0.999907 0.0136041i \(-0.00433046\pi\)
\(282\) −16.4045 6.79498i −0.976875 0.404635i
\(283\) −6.03994 + 14.5817i −0.359037 + 0.866792i 0.636399 + 0.771360i \(0.280423\pi\)
−0.995436 + 0.0954321i \(0.969577\pi\)
\(284\) −3.14776 7.59937i −0.186785 0.450940i
\(285\) 0.298896 1.58605i 0.0177051 0.0939498i
\(286\) −7.37063 + 3.05301i −0.435834 + 0.180528i
\(287\) 1.97224 1.97224i 0.116418 0.116418i
\(288\) 7.49739i 0.441788i
\(289\) 5.50486 16.0840i 0.323815 0.946120i
\(290\) −11.5081 2.16874i −0.675781 0.127353i
\(291\) −11.4031 11.4031i −0.668462 0.668462i
\(292\) −0.582777 1.40695i −0.0341044 0.0823354i
\(293\) 7.54899 0.441017 0.220508 0.975385i \(-0.429228\pi\)
0.220508 + 0.975385i \(0.429228\pi\)
\(294\) −5.41425 13.0711i −0.315765 0.762325i
\(295\) −3.01506 + 4.61235i −0.175543 + 0.268541i
\(296\) 3.91254 9.44570i 0.227412 0.549020i
\(297\) −45.9390 45.9390i −2.66565 2.66565i
\(298\) 5.98869 + 5.98869i 0.346915 + 0.346915i
\(299\) −3.70530 + 8.94539i −0.214283 + 0.517325i
\(300\) −11.2217 + 11.6836i −0.647887 + 0.674555i
\(301\) 3.21118 + 7.75248i 0.185090 + 0.446846i
\(302\) −1.80944 −0.104121
\(303\) −13.7675 33.2376i −0.790921 1.90945i
\(304\) 0.157527 + 0.157527i 0.00903480 + 0.00903480i
\(305\) 3.91971 20.7995i 0.224442 1.19097i
\(306\) 17.9743 + 25.1497i 1.02752 + 1.43771i
\(307\) 12.4976i 0.713278i 0.934242 + 0.356639i \(0.116077\pi\)
−0.934242 + 0.356639i \(0.883923\pi\)
\(308\) −5.11596 + 5.11596i −0.291509 + 0.291509i
\(309\) −11.5814 + 4.79717i −0.658843 + 0.272902i
\(310\) −0.720816 + 3.82492i −0.0409396 + 0.217241i
\(311\) −6.67803 16.1222i −0.378677 0.914206i −0.992214 0.124541i \(-0.960254\pi\)
0.613538 0.789665i \(-0.289746\pi\)
\(312\) −2.21857 + 5.35610i −0.125602 + 0.303230i
\(313\) −7.99415 3.31129i −0.451856 0.187165i 0.145137 0.989412i \(-0.453638\pi\)
−0.596993 + 0.802247i \(0.703638\pi\)
\(314\) 1.46868 1.46868i 0.0828824 0.0828824i
\(315\) 22.4662 15.3413i 1.26583 0.864385i
\(316\) −1.14383 + 2.76144i −0.0643453 + 0.155343i
\(317\) −1.60449 + 3.87358i −0.0901171 + 0.217562i −0.962512 0.271241i \(-0.912566\pi\)
0.872394 + 0.488802i \(0.162566\pi\)
\(318\) −6.05003 + 2.50600i −0.339269 + 0.140530i
\(319\) 23.3504i 1.30737i
\(320\) −0.458323 2.18859i −0.0256210 0.122346i
\(321\) −27.7242 27.7242i −1.54741 1.54741i
\(322\) 8.78087i 0.489339i
\(323\) 0.906076 + 0.150762i 0.0504154 + 0.00838864i
\(324\) −24.7186 −1.37326
\(325\) −8.19497 + 3.58971i −0.454575 + 0.199121i
\(326\) 1.91410 0.792847i 0.106012 0.0439118i
\(327\) 41.4421 2.29175
\(328\) 1.58798 0.657761i 0.0876813 0.0363188i
\(329\) −8.21617 3.40325i −0.452972 0.187627i
\(330\) 27.0372 + 17.6740i 1.48835 + 0.972923i
\(331\) −4.95608 + 4.95608i −0.272411 + 0.272411i −0.830070 0.557659i \(-0.811700\pi\)
0.557659 + 0.830070i \(0.311700\pi\)
\(332\) 10.0574 + 10.0574i 0.551972 + 0.551972i
\(333\) 70.8181 + 29.3338i 3.88081 + 1.60748i
\(334\) 16.0786 + 6.65999i 0.879784 + 0.364419i
\(335\) 6.61563 + 31.5911i 0.361450 + 1.72601i
\(336\) 5.25759i 0.286825i
\(337\) 0.581083 + 1.40286i 0.0316536 + 0.0764186i 0.938916 0.344147i \(-0.111832\pi\)
−0.907262 + 0.420565i \(0.861832\pi\)
\(338\) 6.92842 6.92842i 0.376856 0.376856i
\(339\) −16.6671 −0.905233
\(340\) −6.78438 6.24277i −0.367935 0.338562i
\(341\) 7.76089 0.420276
\(342\) −1.18104 + 1.18104i −0.0638635 + 0.0638635i
\(343\) −7.05866 17.0411i −0.381132 0.920134i
\(344\) 5.17105i 0.278805i
\(345\) 38.3704 8.03532i 2.06579 0.432607i
\(346\) −4.76214 1.97254i −0.256014 0.106045i
\(347\) 6.53872 + 2.70843i 0.351017 + 0.145396i 0.551223 0.834358i \(-0.314161\pi\)
−0.200206 + 0.979754i \(0.564161\pi\)
\(348\) 11.9984 + 11.9984i 0.643182 + 0.643182i
\(349\) 6.15710 6.15710i 0.329582 0.329582i −0.522845 0.852427i \(-0.675130\pi\)
0.852427 + 0.522845i \(0.175130\pi\)
\(350\) −5.62038 + 5.85173i −0.300422 + 0.312788i
\(351\) −24.0885 9.97777i −1.28575 0.532574i
\(352\) −4.11919 + 1.70622i −0.219553 + 0.0909420i
\(353\) −2.63910 −0.140465 −0.0702325 0.997531i \(-0.522374\pi\)
−0.0702325 + 0.997531i \(0.522374\pi\)
\(354\) 7.37654 3.05546i 0.392059 0.162396i
\(355\) −15.1892 + 10.3721i −0.806161 + 0.550496i
\(356\) 9.77020 0.517820
\(357\) 12.6046 + 17.6364i 0.667106 + 0.933418i
\(358\) 2.96800i 0.156864i
\(359\) −5.56265 5.56265i −0.293585 0.293585i 0.544909 0.838495i \(-0.316564\pi\)
−0.838495 + 0.544909i \(0.816564\pi\)
\(360\) 16.4087 3.43622i 0.864816 0.181105i
\(361\) 18.9504i 0.997388i
\(362\) 10.0565 4.16552i 0.528556 0.218935i
\(363\) 11.0088 26.5775i 0.577811 1.39496i
\(364\) −1.11117 + 2.68259i −0.0582410 + 0.140606i
\(365\) −2.81214 + 1.92030i −0.147194 + 0.100513i
\(366\) −21.6856 + 21.6856i −1.13352 + 1.13352i
\(367\) −21.5147 8.91170i −1.12306 0.465187i −0.257644 0.966240i \(-0.582946\pi\)
−0.865417 + 0.501053i \(0.832946\pi\)
\(368\) −2.07076 + 4.99927i −0.107946 + 0.260605i
\(369\) 4.93149 + 11.9057i 0.256723 + 0.619784i
\(370\) −22.4660 4.23377i −1.16795 0.220103i
\(371\) −3.03014 + 1.25513i −0.157317 + 0.0651629i
\(372\) 3.98787 3.98787i 0.206762 0.206762i
\(373\) 22.8229i 1.18173i −0.806772 0.590863i \(-0.798787\pi\)
0.806772 0.590863i \(-0.201213\pi\)
\(374\) −9.72715 + 15.5988i −0.502979 + 0.806597i
\(375\) 30.7139 + 19.2049i 1.58606 + 0.991738i
\(376\) −3.87519 3.87519i −0.199848 0.199848i
\(377\) 3.58617 + 8.65778i 0.184697 + 0.445898i
\(378\) −23.6454 −1.21619
\(379\) 7.07822 + 17.0883i 0.363583 + 0.877768i 0.994770 + 0.102137i \(0.0325681\pi\)
−0.631187 + 0.775631i \(0.717432\pi\)
\(380\) 0.272565 0.416961i 0.0139823 0.0213897i
\(381\) −1.61357 + 3.89550i −0.0826656 + 0.199572i
\(382\) 16.9978 + 16.9978i 0.869683 + 0.869683i
\(383\) −13.2517 13.2517i −0.677130 0.677130i 0.282220 0.959350i \(-0.408929\pi\)
−0.959350 + 0.282220i \(0.908929\pi\)
\(384\) −1.23988 + 2.99334i −0.0632724 + 0.152753i
\(385\) 13.5415 + 8.85200i 0.690140 + 0.451140i
\(386\) −6.71939 16.2220i −0.342008 0.825680i
\(387\) −38.7694 −1.97076
\(388\) −1.90475 4.59847i −0.0966989 0.233452i
\(389\) −1.12576 1.12576i −0.0570785 0.0570785i 0.677991 0.735070i \(-0.262851\pi\)
−0.735070 + 0.677991i \(0.762851\pi\)
\(390\) 12.7392 + 2.40072i 0.645072 + 0.121565i
\(391\) 5.03898 + 21.7343i 0.254832 + 1.09915i
\(392\) 4.36674i 0.220554i
\(393\) 9.51373 9.51373i 0.479904 0.479904i
\(394\) 14.0551 5.82183i 0.708088 0.293300i
\(395\) 6.56792 + 1.23774i 0.330468 + 0.0622775i
\(396\) −12.7922 30.8831i −0.642833 1.55194i
\(397\) 2.73922 6.61306i 0.137478 0.331900i −0.840114 0.542409i \(-0.817512\pi\)
0.977592 + 0.210509i \(0.0675122\pi\)
\(398\) 7.42142 + 3.07405i 0.372002 + 0.154088i
\(399\) −0.828214 + 0.828214i −0.0414626 + 0.0414626i
\(400\) −4.57988 + 2.00616i −0.228994 + 0.100308i
\(401\) 1.34092 3.23726i 0.0669621 0.161661i −0.886856 0.462046i \(-0.847115\pi\)
0.953818 + 0.300386i \(0.0971153\pi\)
\(402\) 17.8970 43.2071i 0.892620 2.15498i
\(403\) 2.87756 1.19192i 0.143341 0.0593739i
\(404\) 11.1039i 0.552438i
\(405\) 11.3291 + 54.0991i 0.562949 + 2.68820i
\(406\) 6.00938 + 6.00938i 0.298240 + 0.298240i
\(407\) 45.5843i 2.25953i
\(408\) 3.01712 + 13.0136i 0.149370 + 0.644267i
\(409\) −1.87972 −0.0929461 −0.0464730 0.998920i \(-0.514798\pi\)
−0.0464730 + 0.998920i \(0.514798\pi\)
\(410\) −2.16738 3.17397i −0.107039 0.156751i
\(411\) 63.2110 26.1829i 3.11797 1.29151i
\(412\) −3.86906 −0.190615
\(413\) 3.69452 1.53032i 0.181796 0.0753022i
\(414\) −37.4814 15.5253i −1.84211 0.763028i
\(415\) 17.4020 26.6211i 0.854233 1.30678i
\(416\) −1.26525 + 1.26525i −0.0620342 + 0.0620342i
\(417\) −24.5638 24.5638i −1.20289 1.20289i
\(418\) −0.917660 0.380107i −0.0448842 0.0185917i
\(419\) −30.1244 12.4779i −1.47167 0.609586i −0.504432 0.863451i \(-0.668298\pi\)
−0.967240 + 0.253865i \(0.918298\pi\)
\(420\) 11.5067 2.40968i 0.561471 0.117580i
\(421\) 27.3895i 1.33488i 0.744661 + 0.667442i \(0.232611\pi\)
−0.744661 + 0.667442i \(0.767389\pi\)
\(422\) 3.61423 + 8.72553i 0.175938 + 0.424752i
\(423\) 29.0538 29.0538i 1.41264 1.41264i
\(424\) −2.02116 −0.0981564
\(425\) −10.5534 + 17.7095i −0.511917 + 0.859035i
\(426\) 26.6503 1.29121
\(427\) −10.8612 + 10.8612i −0.525609 + 0.525609i
\(428\) −4.63098 11.1802i −0.223847 0.540415i
\(429\) 25.8482i 1.24796i
\(430\) 11.3173 2.37001i 0.545770 0.114292i
\(431\) −16.7310 6.93020i −0.805903 0.333816i −0.0585849 0.998282i \(-0.518659\pi\)
−0.747318 + 0.664466i \(0.768659\pi\)
\(432\) −13.4622 5.57623i −0.647701 0.268286i
\(433\) 22.9117 + 22.9117i 1.10107 + 1.10107i 0.994282 + 0.106786i \(0.0340559\pi\)
0.106786 + 0.994282i \(0.465944\pi\)
\(434\) 1.99732 1.99732i 0.0958743 0.0958743i
\(435\) 20.7605 31.7588i 0.995389 1.52272i
\(436\) 11.8173 + 4.89487i 0.565944 + 0.234422i
\(437\) −1.11372 + 0.461319i −0.0532766 + 0.0220679i
\(438\) 4.93405 0.235758
\(439\) −20.5501 + 8.51214i −0.980804 + 0.406262i −0.814723 0.579850i \(-0.803111\pi\)
−0.166081 + 0.986112i \(0.553111\pi\)
\(440\) 5.62214 + 8.23322i 0.268025 + 0.392503i
\(441\) 32.7392 1.55901
\(442\) −1.21092 + 7.27759i −0.0575975 + 0.346159i
\(443\) 9.63914i 0.457969i −0.973430 0.228985i \(-0.926459\pi\)
0.973430 0.228985i \(-0.0735406\pi\)
\(444\) 23.4231 + 23.4231i 1.11161 + 1.11161i
\(445\) −4.47791 21.3830i −0.212273 1.01365i
\(446\) 2.16190i 0.102369i
\(447\) −25.3514 + 10.5009i −1.19908 + 0.496676i
\(448\) −0.620992 + 1.49921i −0.0293391 + 0.0708309i
\(449\) −14.9247 + 36.0315i −0.704341 + 1.70043i 0.00933673 + 0.999956i \(0.497028\pi\)
−0.713678 + 0.700474i \(0.752972\pi\)
\(450\) −15.0410 34.3371i −0.709039 1.61867i
\(451\) −5.41888 + 5.41888i −0.255165 + 0.255165i
\(452\) −4.75264 1.96861i −0.223546 0.0925956i
\(453\) 2.24349 5.41626i 0.105408 0.254478i
\(454\) 0.146890 + 0.354624i 0.00689389 + 0.0166433i
\(455\) 6.38038 + 1.20240i 0.299117 + 0.0563693i
\(456\) −0.666847 + 0.276217i −0.0312280 + 0.0129351i
\(457\) −2.77769 + 2.77769i −0.129935 + 0.129935i −0.769083 0.639149i \(-0.779287\pi\)
0.639149 + 0.769083i \(0.279287\pi\)
\(458\) 8.99673i 0.420390i
\(459\) −58.5270 + 13.5692i −2.73181 + 0.633354i
\(460\) 11.8904 + 2.24078i 0.554395 + 0.104477i
\(461\) 26.6343 + 26.6343i 1.24048 + 1.24048i 0.959801 + 0.280681i \(0.0905603\pi\)
0.280681 + 0.959801i \(0.409440\pi\)
\(462\) −8.97063 21.6570i −0.417351 1.00758i
\(463\) −5.27399 −0.245103 −0.122551 0.992462i \(-0.539108\pi\)
−0.122551 + 0.992462i \(0.539108\pi\)
\(464\) 2.00418 + 4.83853i 0.0930419 + 0.224623i
\(465\) −10.5556 6.90010i −0.489503 0.319984i
\(466\) −4.73720 + 11.4366i −0.219447 + 0.529791i
\(467\) 4.54550 + 4.54550i 0.210340 + 0.210340i 0.804412 0.594072i \(-0.202480\pi\)
−0.594072 + 0.804412i \(0.702480\pi\)
\(468\) −9.48610 9.48610i −0.438495 0.438495i
\(469\) 8.96367 21.6402i 0.413904 0.999252i
\(470\) −6.70512 + 10.2573i −0.309284 + 0.473134i
\(471\) 2.57527 + 6.21725i 0.118662 + 0.286476i
\(472\) 2.46432 0.113429
\(473\) −8.82297 21.3005i −0.405681 0.979399i
\(474\) −6.84773 6.84773i −0.314527 0.314527i
\(475\) −1.03748 0.405430i −0.0476029 0.0186024i
\(476\) 1.51112 + 6.51781i 0.0692620 + 0.298743i
\(477\) 15.1534i 0.693829i
\(478\) 6.11176 6.11176i 0.279545 0.279545i
\(479\) −37.2765 + 15.4404i −1.70321 + 0.705492i −0.999985 0.00547848i \(-0.998256\pi\)
−0.703222 + 0.710970i \(0.748256\pi\)
\(480\) 7.11947 + 1.34168i 0.324958 + 0.0612391i
\(481\) 7.00086 + 16.9016i 0.319212 + 0.770646i
\(482\) 8.36424 20.1931i 0.380981 0.919769i
\(483\) −26.2841 10.8872i −1.19597 0.495387i
\(484\) 6.27832 6.27832i 0.285378 0.285378i
\(485\) −9.19118 + 6.27630i −0.417350 + 0.284992i
\(486\) 13.9195 33.6047i 0.631402 1.52434i
\(487\) 6.35893 15.3518i 0.288151 0.695657i −0.711827 0.702355i \(-0.752132\pi\)
0.999978 + 0.00669763i \(0.00213194\pi\)
\(488\) −8.74502 + 3.62231i −0.395869 + 0.163974i
\(489\) 6.71260i 0.303554i
\(490\) −9.55703 + 2.00138i −0.431742 + 0.0904131i
\(491\) 15.7923 + 15.7923i 0.712696 + 0.712696i 0.967098 0.254403i \(-0.0818789\pi\)
−0.254403 + 0.967098i \(0.581879\pi\)
\(492\) 5.56890i 0.251065i
\(493\) 18.3229 + 11.4258i 0.825222 + 0.514593i
\(494\) −0.398624 −0.0179349
\(495\) −61.7276 + 42.1514i −2.77445 + 1.89456i
\(496\) 1.60817 0.666124i 0.0722088 0.0299099i
\(497\) 13.3478 0.598729
\(498\) −42.5752 + 17.6352i −1.90784 + 0.790254i
\(499\) 18.1465 + 7.51654i 0.812350 + 0.336486i 0.749891 0.661561i \(-0.230106\pi\)
0.0624588 + 0.998048i \(0.480106\pi\)
\(500\) 6.48974 + 9.10402i 0.290230 + 0.407144i
\(501\) −39.8712 + 39.8712i −1.78132 + 1.78132i
\(502\) 15.3773 + 15.3773i 0.686322 + 0.686322i
\(503\) −11.7306 4.85898i −0.523042 0.216651i 0.105510 0.994418i \(-0.466352\pi\)
−0.628553 + 0.777767i \(0.716352\pi\)
\(504\) −11.2401 4.65582i −0.500676 0.207387i
\(505\) −24.3018 + 5.08915i −1.08142 + 0.226464i
\(506\) 24.1261i 1.07254i
\(507\) 12.1487 + 29.3295i 0.539542 + 1.30257i
\(508\) −0.920220 + 0.920220i −0.0408282 + 0.0408282i
\(509\) 2.65410 0.117641 0.0588204 0.998269i \(-0.481266\pi\)
0.0588204 + 0.998269i \(0.481266\pi\)
\(510\) 27.0986 12.5677i 1.19994 0.556505i
\(511\) 2.47121 0.109320
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) −1.24226 2.99907i −0.0548469 0.132412i
\(514\) 19.7433i 0.870840i
\(515\) 1.77328 + 8.46779i 0.0781399 + 0.373136i
\(516\) −15.4787 6.41149i −0.681413 0.282250i
\(517\) 22.5745 + 9.35068i 0.992827 + 0.411243i
\(518\) 11.7314 + 11.7314i 0.515449 + 0.515449i
\(519\) 11.8090 11.8090i 0.518357 0.518357i
\(520\) 3.34902 + 2.18923i 0.146864 + 0.0960042i
\(521\) −16.7528 6.93925i −0.733955 0.304014i −0.0157786 0.999876i \(-0.505023\pi\)
−0.718176 + 0.695862i \(0.755023\pi\)
\(522\) −36.2763 + 15.0261i −1.58777 + 0.657676i
\(523\) −33.8690 −1.48099 −0.740494 0.672063i \(-0.765408\pi\)
−0.740494 + 0.672063i \(0.765408\pi\)
\(524\) 3.83655 1.58915i 0.167600 0.0694224i
\(525\) −10.5476 24.0792i −0.460335 1.05090i
\(526\) −18.7237 −0.816392
\(527\) 3.79756 6.08992i 0.165425 0.265281i
\(528\) 14.4456i 0.628666i
\(529\) −4.44116 4.44116i −0.193094 0.193094i
\(530\) 0.926346 + 4.42350i 0.0402379 + 0.192145i
\(531\) 18.4759i 0.801787i
\(532\) −0.333989 + 0.138343i −0.0144803 + 0.00599792i
\(533\) −1.17696 + 2.84143i −0.0509797 + 0.123076i
\(534\) −12.1139 + 29.2455i −0.524219 + 1.26558i
\(535\) −22.3464 + 15.2595i −0.966118 + 0.659725i
\(536\) 10.2067 10.2067i 0.440862 0.440862i
\(537\) 8.88422 + 3.67997i 0.383383 + 0.158802i
\(538\) −3.94085 + 9.51404i −0.169902 + 0.410179i
\(539\) 7.45064 + 17.9874i 0.320922 + 0.774774i
\(540\) −6.03406 + 32.0190i −0.259664 + 1.37788i
\(541\) 4.21829 1.74727i 0.181359 0.0751212i −0.290156 0.956979i \(-0.593707\pi\)
0.471515 + 0.881858i \(0.343707\pi\)
\(542\) −13.3956 + 13.3956i −0.575390 + 0.575390i
\(543\) 35.2672i 1.51346i
\(544\) −0.676740 + 4.06719i −0.0290150 + 0.174379i
\(545\) 5.29676 28.1066i 0.226888 1.20395i
\(546\) −6.65220 6.65220i −0.284688 0.284688i
\(547\) −8.73921 21.0983i −0.373662 0.902099i −0.993123 0.117072i \(-0.962649\pi\)
0.619462 0.785027i \(-0.287351\pi\)
\(548\) 21.1172 0.902083
\(549\) −27.1578 65.5648i −1.15907 2.79824i
\(550\) 15.4424 16.0781i 0.658467 0.685571i
\(551\) −0.446486 + 1.07791i −0.0190210 + 0.0459207i
\(552\) −12.3970 12.3970i −0.527651 0.527651i
\(553\) −3.42967 3.42967i −0.145844 0.145844i
\(554\) 8.77965 21.1959i 0.373012 0.900530i
\(555\) 40.5283 61.9990i 1.72033 2.63171i
\(556\) −4.10307 9.90569i −0.174009 0.420095i
\(557\) −24.3785 −1.03295 −0.516476 0.856302i \(-0.672756\pi\)
−0.516476 + 0.856302i \(0.672756\pi\)
\(558\) 4.99419 + 12.0570i 0.211421 + 0.510415i
\(559\) −6.54270 6.54270i −0.276727 0.276727i
\(560\) 3.56577 + 0.671978i 0.150681 + 0.0283963i
\(561\) −34.6321 48.4574i −1.46217 2.04587i
\(562\) 24.0269i 1.01351i
\(563\) 13.5026 13.5026i 0.569068 0.569068i −0.362799 0.931867i \(-0.618179\pi\)
0.931867 + 0.362799i \(0.118179\pi\)
\(564\) 16.4045 6.79498i 0.690755 0.286120i
\(565\) −2.13024 + 11.3039i −0.0896198 + 0.475557i
\(566\) −6.03994 14.5817i −0.253878 0.612915i
\(567\) 15.3501 37.0584i 0.644643 1.55631i
\(568\) 7.59937 + 3.14776i 0.318863 + 0.132077i
\(569\) 32.8960 32.8960i 1.37907 1.37907i 0.532883 0.846189i \(-0.321108\pi\)
0.846189 0.532883i \(-0.178892\pi\)
\(570\) 0.910159 + 1.33286i 0.0381224 + 0.0558274i
\(571\) 3.84418 9.28068i 0.160874 0.388384i −0.822803 0.568327i \(-0.807591\pi\)
0.983677 + 0.179942i \(0.0575910\pi\)
\(572\) 3.05301 7.37063i 0.127653 0.308181i
\(573\) −71.9554 + 29.8049i −3.00598 + 1.24512i
\(574\) 2.78917i 0.116418i
\(575\) −0.545502 27.0503i −0.0227490 1.12808i
\(576\) −5.30145 5.30145i −0.220894 0.220894i
\(577\) 19.1206i 0.796002i −0.917385 0.398001i \(-0.869704\pi\)
0.917385 0.398001i \(-0.130296\pi\)
\(578\) 7.48061 + 15.2657i 0.311152 + 0.634968i
\(579\) 56.8893 2.36424
\(580\) 9.67101 6.60395i 0.401567 0.274214i
\(581\) −21.3237 + 8.83258i −0.884657 + 0.366437i
\(582\) 16.1264 0.668462
\(583\) 8.32555 3.44855i 0.344809 0.142825i
\(584\) 1.40695 + 0.582777i 0.0582199 + 0.0241155i
\(585\) −16.4135 + 25.1089i −0.678616 + 1.03813i
\(586\) −5.33794 + 5.33794i −0.220508 + 0.220508i
\(587\) 1.31962 + 1.31962i 0.0544667 + 0.0544667i 0.733815 0.679349i \(-0.237738\pi\)
−0.679349 + 0.733815i \(0.737738\pi\)
\(588\) 13.0711 + 5.41425i 0.539045 + 0.223280i
\(589\) 0.358263 + 0.148397i 0.0147620 + 0.00611460i
\(590\) −1.12945 5.39339i −0.0464989 0.222042i
\(591\) 49.2902i 2.02753i
\(592\) 3.91254 + 9.44570i 0.160804 + 0.388216i
\(593\) −6.22387 + 6.22387i −0.255584 + 0.255584i −0.823255 0.567671i \(-0.807844\pi\)
0.567671 + 0.823255i \(0.307844\pi\)
\(594\) 64.9676 2.66565
\(595\) 13.5723 6.29448i 0.556408 0.258049i
\(596\) −8.46929 −0.346915
\(597\) −18.4034 + 18.4034i −0.753200 + 0.753200i
\(598\) −3.70530 8.94539i −0.151521 0.365804i
\(599\) 4.79224i 0.195806i 0.995196 + 0.0979028i \(0.0312134\pi\)
−0.995196 + 0.0979028i \(0.968787\pi\)
\(600\) −0.326622 16.1965i −0.0133343 0.661221i
\(601\) −12.0035 4.97202i −0.489634 0.202813i 0.124186 0.992259i \(-0.460368\pi\)
−0.613820 + 0.789446i \(0.710368\pi\)
\(602\) −7.75248 3.21118i −0.315968 0.130878i
\(603\) 76.5234 + 76.5234i 3.11628 + 3.11628i
\(604\) 1.27947 1.27947i 0.0520607 0.0520607i
\(605\) −16.6182 10.8632i −0.675625 0.441652i
\(606\) 33.2376 + 13.7675i 1.35019 + 0.559265i
\(607\) 35.5125 14.7098i 1.44141 0.597051i 0.481269 0.876573i \(-0.340176\pi\)
0.960139 + 0.279522i \(0.0901761\pi\)
\(608\) −0.222777 −0.00903480
\(609\) −25.4390 + 10.5372i −1.03084 + 0.426988i
\(610\) 11.9358 + 17.4791i 0.483266 + 0.707708i
\(611\) 9.80620 0.396716
\(612\) −30.4933 5.07378i −1.23262 0.205096i
\(613\) 20.7647i 0.838678i −0.907830 0.419339i \(-0.862262\pi\)
0.907830 0.419339i \(-0.137738\pi\)
\(614\) −8.83717 8.83717i −0.356639 0.356639i
\(615\) 12.1880 2.55235i 0.491470 0.102921i
\(616\) 7.23507i 0.291509i
\(617\) 44.8083 18.5602i 1.80391 0.747206i 0.819086 0.573671i \(-0.194481\pi\)
0.984828 0.173535i \(-0.0555190\pi\)
\(618\) 4.79717 11.5814i 0.192971 0.465872i
\(619\) 4.87259 11.7635i 0.195846 0.472814i −0.795198 0.606350i \(-0.792633\pi\)
0.991044 + 0.133536i \(0.0426331\pi\)
\(620\) −2.19493 3.21432i −0.0881507 0.129090i
\(621\) 55.7541 55.7541i 2.23734 2.23734i
\(622\) 16.1222 + 6.67803i 0.646441 + 0.267765i
\(623\) −6.06722 + 14.6476i −0.243078 + 0.586842i
\(624\) −2.21857 5.35610i −0.0888139 0.214416i
\(625\) 16.9506 18.3760i 0.678024 0.735040i
\(626\) 7.99415 3.31129i 0.319510 0.132346i
\(627\) 2.27558 2.27558i 0.0908779 0.0908779i
\(628\) 2.07703i 0.0828824i
\(629\) 35.7697 + 22.3053i 1.42623 + 0.889371i
\(630\) −5.03808 + 26.7340i −0.200722 + 1.06511i
\(631\) −28.6219 28.6219i −1.13942 1.13942i −0.988554 0.150867i \(-0.951794\pi\)
−0.150867 0.988554i \(-0.548206\pi\)
\(632\) −1.14383 2.76144i −0.0454990 0.109844i
\(633\) −30.5997 −1.21623
\(634\) −1.60449 3.87358i −0.0637224 0.153840i
\(635\) 2.43575 + 1.59223i 0.0966596 + 0.0631857i
\(636\) 2.50600 6.05003i 0.0993695 0.239899i
\(637\) 5.52504 + 5.52504i 0.218910 + 0.218910i
\(638\) −16.5112 16.5112i −0.653685 0.653685i
\(639\) −23.6000 + 56.9754i −0.933601 + 2.25391i
\(640\) 1.87165 + 1.22349i 0.0739836 + 0.0483625i
\(641\) 13.2912 + 32.0879i 0.524973 + 1.26740i 0.934781 + 0.355225i \(0.115596\pi\)
−0.409808 + 0.912172i \(0.634404\pi\)
\(642\) 39.2079 1.54741
\(643\) 5.51999 + 13.3264i 0.217687 + 0.525543i 0.994566 0.104107i \(-0.0331983\pi\)
−0.776879 + 0.629650i \(0.783198\pi\)
\(644\) −6.20901 6.20901i −0.244669 0.244669i
\(645\) −6.93790 + 36.8151i −0.273180 + 1.44960i
\(646\) −0.747298 + 0.534088i −0.0294020 + 0.0210134i
\(647\) 38.3237i 1.50666i 0.657644 + 0.753329i \(0.271553\pi\)
−0.657644 + 0.753329i \(0.728447\pi\)
\(648\) 17.4787 17.4787i 0.686629 0.686629i
\(649\) −10.1510 + 4.20467i −0.398461 + 0.165048i
\(650\) 3.25641 8.33303i 0.127727 0.326848i
\(651\) 3.50221 + 8.45509i 0.137263 + 0.331381i
\(652\) −0.792847 + 1.91410i −0.0310503 + 0.0749621i
\(653\) −28.2020 11.6817i −1.10363 0.457139i −0.244891 0.969551i \(-0.578752\pi\)
−0.858740 + 0.512412i \(0.828752\pi\)
\(654\) −29.3040 + 29.3040i −1.14588 + 1.14588i
\(655\) −5.23638 7.66830i −0.204602 0.299625i
\(656\) −0.657761 + 1.58798i −0.0256813 + 0.0620000i
\(657\) −4.36930 + 10.5484i −0.170463 + 0.411534i
\(658\) 8.21617 3.40325i 0.320300 0.132672i
\(659\) 32.1026i 1.25054i 0.780408 + 0.625271i \(0.215011\pi\)
−0.780408 + 0.625271i \(0.784989\pi\)
\(660\) −31.6156 + 6.62077i −1.23064 + 0.257713i
\(661\) −1.48757 1.48757i −0.0578597 0.0578597i 0.677585 0.735445i \(-0.263027\pi\)
−0.735445 + 0.677585i \(0.763027\pi\)
\(662\) 7.00895i 0.272411i
\(663\) −20.2829 12.6480i −0.787722 0.491209i
\(664\) −14.2233 −0.551972
\(665\) 0.455851 + 0.667561i 0.0176771 + 0.0258869i
\(666\) −70.8181 + 29.3338i −2.74414 + 1.13666i
\(667\) −28.3393 −1.09730
\(668\) −16.0786 + 6.65999i −0.622101 + 0.257683i
\(669\) −6.47129 2.68049i −0.250194 0.103634i
\(670\) −27.0162 17.6603i −1.04373 0.682278i
\(671\) 29.8419 29.8419i 1.15203 1.15203i
\(672\) −3.71768 3.71768i −0.143413 0.143413i
\(673\) 28.5802 + 11.8383i 1.10169 + 0.456334i 0.858067 0.513537i \(-0.171665\pi\)
0.243620 + 0.969871i \(0.421665\pi\)
\(674\) −1.40286 0.581083i −0.0540361 0.0223825i
\(675\) 72.8421 1.46895i 2.80369 0.0565398i
\(676\) 9.79826i 0.376856i
\(677\) −0.866714 2.09243i −0.0333105 0.0804188i 0.906349 0.422530i \(-0.138858\pi\)
−0.939659 + 0.342111i \(0.888858\pi\)
\(678\) 11.7854 11.7854i 0.452617 0.452617i
\(679\) 8.07689 0.309963
\(680\) 9.21159 0.382976i 0.353248 0.0146865i
\(681\) −1.24364 −0.0476562
\(682\) −5.48778 + 5.48778i −0.210138 + 0.210138i
\(683\) 2.62081 + 6.32720i 0.100283 + 0.242103i 0.966056 0.258333i \(-0.0831730\pi\)
−0.865773 + 0.500436i \(0.833173\pi\)
\(684\) 1.67025i 0.0638635i
\(685\) −9.67851 46.2170i −0.369797 1.76586i
\(686\) 17.0411 + 7.05866i 0.650633 + 0.269501i
\(687\) 26.9303 + 11.1549i 1.02745 + 0.425585i
\(688\) −3.65649 3.65649i −0.139402 0.139402i
\(689\) 2.55729 2.55729i 0.0974249 0.0974249i
\(690\) −21.4502 + 32.8138i −0.816594 + 1.24920i
\(691\) 21.4601 + 8.88906i 0.816380 + 0.338156i 0.751496 0.659737i \(-0.229332\pi\)
0.0648836 + 0.997893i \(0.479332\pi\)
\(692\) 4.76214 1.97254i 0.181030 0.0749849i
\(693\) 54.2441 2.06056
\(694\) −6.53872 + 2.70843i −0.248206 + 0.102810i
\(695\) −19.7990 + 13.5200i −0.751019 + 0.512841i
\(696\) −16.9683 −0.643182
\(697\) 1.60059 + 6.90373i 0.0606267 + 0.261497i
\(698\) 8.70745i 0.329582i
\(699\) −28.3601 28.3601i −1.07268 1.07268i
\(700\) −0.163588 8.11200i −0.00618305 0.306605i
\(701\) 44.0844i 1.66505i 0.553991 + 0.832523i \(0.313104\pi\)
−0.553991 + 0.832523i \(0.686896\pi\)
\(702\) 24.0885 9.97777i 0.909161 0.376587i
\(703\) −0.871624 + 2.10429i −0.0328739 + 0.0793646i
\(704\) 1.70622 4.11919i 0.0643057 0.155248i
\(705\) −22.3900 32.7885i −0.843256 1.23489i
\(706\) 1.86612 1.86612i 0.0702325 0.0702325i
\(707\) 16.6470 + 6.89541i 0.626075 + 0.259329i
\(708\) −3.05546 + 7.37654i −0.114831 + 0.277227i
\(709\) −7.50658 18.1225i −0.281916 0.680605i 0.717965 0.696080i \(-0.245074\pi\)
−0.999880 + 0.0154750i \(0.995074\pi\)
\(710\) 3.40621 18.0746i 0.127833 0.678328i
\(711\) 20.7036 8.57572i 0.776446 0.321615i
\(712\) −6.90857 + 6.90857i −0.258910 + 0.258910i
\(713\) 9.41904i 0.352746i
\(714\) −21.3836 3.55803i −0.800262 0.133156i
\(715\) −17.5306 3.30368i −0.655606 0.123551i
\(716\) 2.09869 + 2.09869i 0.0784318 + 0.0784318i
\(717\) 10.7167 + 25.8724i 0.400223 + 0.966224i
\(718\) 7.86678 0.293585
\(719\) −16.5133 39.8667i −0.615844 1.48678i −0.856489 0.516165i \(-0.827359\pi\)
0.240645 0.970613i \(-0.422641\pi\)
\(720\) −9.17295 + 14.0325i −0.341856 + 0.522960i
\(721\) 2.40265 5.80052i 0.0894795 0.216023i
\(722\) 13.3999 + 13.3999i 0.498694 + 0.498694i
\(723\) 50.0740 + 50.0740i 1.86227 + 1.86227i
\(724\) −4.16552 + 10.0565i −0.154810 + 0.373746i
\(725\) −18.8858 18.1392i −0.701401 0.673671i
\(726\) 11.0088 + 26.5775i 0.408574 + 0.986384i
\(727\) 32.8765 1.21932 0.609661 0.792663i \(-0.291306\pi\)
0.609661 + 0.792663i \(0.291306\pi\)
\(728\) −1.11117 2.68259i −0.0411826 0.0994235i
\(729\) 30.8955 + 30.8955i 1.14428 + 1.14428i
\(730\) 0.630625 3.34634i 0.0233405 0.123853i
\(731\) −21.0316 3.49946i −0.777884 0.129432i
\(732\) 30.6680i 1.13352i
\(733\) 28.5557 28.5557i 1.05473 1.05473i 0.0563160 0.998413i \(-0.482065\pi\)
0.998413 0.0563160i \(-0.0179354\pi\)
\(734\) 21.5147 8.91170i 0.794124 0.328937i
\(735\) 5.85878 31.0889i 0.216104 1.14673i
\(736\) −2.07076 4.99927i −0.0763294 0.184275i
\(737\) −24.6283 + 59.4581i −0.907197 + 2.19017i
\(738\) −11.9057 4.93149i −0.438254 0.181531i
\(739\) 17.2306 17.2306i 0.633838 0.633838i −0.315191 0.949028i \(-0.602068\pi\)
0.949028 + 0.315191i \(0.102068\pi\)
\(740\) 18.8796 12.8921i 0.694028 0.473924i
\(741\) 0.494247 1.19322i 0.0181566 0.0438339i
\(742\) 1.25513 3.03014i 0.0460772 0.111240i
\(743\) −23.4641 + 9.71915i −0.860815 + 0.356561i −0.769026 0.639217i \(-0.779258\pi\)
−0.0917885 + 0.995779i \(0.529258\pi\)
\(744\) 5.63970i 0.206762i
\(745\) 3.88167 + 18.5358i 0.142213 + 0.679100i
\(746\) 16.1382 + 16.1382i 0.590863 + 0.590863i
\(747\) 106.638i 3.90167i
\(748\) −4.15191 17.9082i −0.151809 0.654788i
\(749\) 19.6372 0.717528
\(750\) −35.2979 + 8.13809i −1.28890 + 0.297161i
\(751\) 14.8511 6.15152i 0.541924 0.224472i −0.0948927 0.995488i \(-0.530251\pi\)
0.636817 + 0.771015i \(0.280251\pi\)
\(752\) 5.48034 0.199848
\(753\) −65.0955 + 26.9634i −2.37221 + 0.982602i
\(754\) −8.65778 3.58617i −0.315298 0.130601i
\(755\) −3.38664 2.21382i −0.123252 0.0805692i
\(756\) 16.7198 16.7198i 0.608095 0.608095i
\(757\) −23.3000 23.3000i −0.846853 0.846853i 0.142886 0.989739i \(-0.454362\pi\)
−0.989739 + 0.142886i \(0.954362\pi\)
\(758\) −17.0883 7.07822i −0.620676 0.257092i
\(759\) 72.2176 + 29.9135i 2.62133 + 1.08579i
\(760\) 0.102104 + 0.487568i 0.00370370 + 0.0176860i
\(761\) 3.29371i 0.119397i −0.998216 0.0596985i \(-0.980986\pi\)
0.998216 0.0596985i \(-0.0190139\pi\)
\(762\) −1.61357 3.89550i −0.0584534 0.141119i
\(763\) −14.6769 + 14.6769i −0.531338 + 0.531338i
\(764\) −24.0385 −0.869683
\(765\) 2.87132 + 69.0628i 0.103813 + 2.49697i
\(766\) 18.7407 0.677130
\(767\) −3.11799 + 3.11799i −0.112584 + 0.112584i
\(768\) −1.23988 2.99334i −0.0447404 0.108013i
\(769\) 11.8679i 0.427966i −0.976837 0.213983i \(-0.931356\pi\)
0.976837 0.213983i \(-0.0686437\pi\)
\(770\) −15.8346 + 3.31600i −0.570640 + 0.119500i
\(771\) −59.0984 24.4794i −2.12838 0.881603i
\(772\) 16.2220 + 6.71939i 0.583844 + 0.241836i
\(773\) −32.2433 32.2433i −1.15971 1.15971i −0.984538 0.175173i \(-0.943952\pi\)
−0.175173 0.984538i \(-0.556048\pi\)
\(774\) 27.4141 27.4141i 0.985379 0.985379i
\(775\) −6.02885 + 6.27702i −0.216563 + 0.225477i
\(776\) 4.59847 + 1.90475i 0.165075 + 0.0683764i
\(777\) −49.6617 + 20.5705i −1.78160 + 0.737964i
\(778\) 1.59207 0.0570785
\(779\) −0.353765 + 0.146534i −0.0126749 + 0.00525013i
\(780\) −10.7055 + 7.31037i −0.383319 + 0.261753i
\(781\) −36.6740 −1.31230
\(782\) −18.9316 11.8054i −0.676992 0.422160i
\(783\) 76.3130i 2.72721i
\(784\) 3.08775 + 3.08775i 0.110277 + 0.110277i
\(785\) 4.54577 0.951949i 0.162245 0.0339765i
\(786\) 13.4544i 0.479904i
\(787\) −8.98074 + 3.71995i −0.320129 + 0.132602i −0.536961 0.843607i \(-0.680428\pi\)
0.216832 + 0.976209i \(0.430428\pi\)
\(788\) −5.82183 + 14.0551i −0.207394 + 0.500694i
\(789\) 23.2152 56.0464i 0.826482 1.99530i
\(790\) −5.51944 + 3.76901i −0.196373 + 0.134095i
\(791\) 5.90271 5.90271i 0.209876 0.209876i
\(792\) 30.8831 + 12.7922i 1.09738 + 0.454551i
\(793\) 6.48154 15.6478i 0.230166 0.555670i
\(794\) 2.73922 + 6.61306i 0.0972113 + 0.234689i
\(795\) −14.3896 2.71176i −0.510347 0.0961761i
\(796\) −7.42142 + 3.07405i −0.263045 + 0.108957i
\(797\) 27.3910 27.3910i 0.970240 0.970240i −0.0293297 0.999570i \(-0.509337\pi\)
0.999570 + 0.0293297i \(0.00933729\pi\)
\(798\) 1.17127i 0.0414626i
\(799\) 18.3836 13.1386i 0.650365 0.464811i
\(800\) 1.81989 4.65704i 0.0643429 0.164651i
\(801\) −51.7962 51.7962i −1.83013 1.83013i
\(802\) 1.34092 + 3.23726i 0.0473494 + 0.114311i
\(803\) −6.78983 −0.239608
\(804\) 17.8970 + 43.2071i 0.631178 + 1.52380i
\(805\) −10.7433 + 16.4347i −0.378651 + 0.579248i
\(806\) −1.19192 + 2.87756i −0.0419837 + 0.101358i
\(807\) −23.5926 23.5926i −0.830498 0.830498i
\(808\) 7.85162 + 7.85162i 0.276219 + 0.276219i
\(809\) 7.24919 17.5011i 0.254868 0.615306i −0.743716 0.668495i \(-0.766939\pi\)
0.998584 + 0.0531895i \(0.0169387\pi\)
\(810\) −46.2647 30.2429i −1.62558 1.06263i
\(811\) −16.6667 40.2369i −0.585245 1.41291i −0.888002 0.459840i \(-0.847907\pi\)
0.302757 0.953068i \(-0.402093\pi\)
\(812\) −8.49854 −0.298240
\(813\) −23.4886 56.7065i −0.823781 1.98878i
\(814\) −32.2329 32.2329i −1.12976 1.12976i
\(815\) 4.55257 + 0.857943i 0.159470 + 0.0300524i
\(816\) −11.3354 7.06855i −0.396818 0.247449i
\(817\) 1.15199i 0.0403031i
\(818\) 1.32916 1.32916i 0.0464730 0.0464730i
\(819\) 20.1124 8.33085i 0.702786 0.291103i
\(820\) 3.77690 + 0.711766i 0.131895 + 0.0248559i
\(821\) −6.20858 14.9888i −0.216681 0.523114i 0.777741 0.628584i \(-0.216365\pi\)
−0.994422 + 0.105470i \(0.966365\pi\)
\(822\) −26.1829 + 63.2110i −0.913232 + 2.20474i
\(823\) 9.99366 + 4.13951i 0.348357 + 0.144294i 0.550000 0.835165i \(-0.314628\pi\)
−0.201642 + 0.979459i \(0.564628\pi\)
\(824\) 2.73584 2.73584i 0.0953074 0.0953074i
\(825\) 28.9803 + 66.1593i 1.00897 + 2.30337i
\(826\) −1.53032 + 3.69452i −0.0532467 + 0.128549i
\(827\) −16.7142 + 40.3516i −0.581210 + 1.40316i 0.310507 + 0.950571i \(0.399501\pi\)
−0.891717 + 0.452593i \(0.850499\pi\)
\(828\) 37.4814 15.5253i 1.30257 0.539542i
\(829\) 38.5554i 1.33909i 0.742774 + 0.669543i \(0.233510\pi\)
−0.742774 + 0.669543i \(0.766490\pi\)
\(830\) 6.51888 + 31.1291i 0.226274 + 1.08051i
\(831\) 52.5609 + 52.5609i 1.82332 + 1.82332i
\(832\) 1.78934i 0.0620342i
\(833\) 17.7604 + 2.95515i 0.615360 + 0.102390i
\(834\) 34.7384 1.20289
\(835\) 21.9452 + 32.1372i 0.759446 + 1.11215i
\(836\) 0.917660 0.380107i 0.0317379 0.0131463i
\(837\) −25.3639 −0.876706
\(838\) 30.1244 12.4779i 1.04063 0.431043i
\(839\) 39.2712 + 16.2667i 1.35579 + 0.561588i 0.937899 0.346908i \(-0.112768\pi\)
0.417894 + 0.908496i \(0.362768\pi\)
\(840\) −6.43259 + 9.84039i −0.221946 + 0.339526i
\(841\) 1.11149 1.11149i 0.0383273 0.0383273i
\(842\) −19.3673 19.3673i −0.667442 0.667442i
\(843\) −71.9205 29.7905i −2.47707 1.02604i
\(844\) −8.72553 3.61423i −0.300345 0.124407i
\(845\) 21.4444 4.49077i 0.737710 0.154487i
\(846\) 41.0882i 1.41264i
\(847\) 5.51372 + 13.3113i 0.189454 + 0.457382i
\(848\) 1.42918 1.42918i 0.0490782 0.0490782i
\(849\) 51.1368 1.75501
\(850\) −5.06006 19.9849i −0.173559 0.685476i
\(851\) −55.3235 −1.89647
\(852\) −18.8446 + 18.8446i −0.645607 + 0.645607i
\(853\) 2.19607 + 5.30178i 0.0751920 + 0.181530i 0.957006 0.290067i \(-0.0936777\pi\)
−0.881814 + 0.471597i \(0.843678\pi\)
\(854\) 15.3600i 0.525609i
\(855\) −3.65549 + 0.765512i −0.125015 + 0.0261800i
\(856\) 11.1802 + 4.63098i 0.382131 + 0.158284i
\(857\) 7.83237 + 3.24428i 0.267549 + 0.110822i 0.512425 0.858732i \(-0.328747\pi\)
−0.244876 + 0.969554i \(0.578747\pi\)
\(858\) 18.2774 + 18.2774i 0.623980 + 0.623980i
\(859\) −25.6691 + 25.6691i −0.875818 + 0.875818i −0.993099 0.117281i \(-0.962582\pi\)
0.117281 + 0.993099i \(0.462582\pi\)
\(860\) −6.32671 + 9.67841i −0.215739 + 0.330031i
\(861\) −8.34893 3.45824i −0.284531 0.117857i
\(862\) 16.7310 6.93020i 0.569860 0.236044i
\(863\) 37.1792 1.26560 0.632798 0.774317i \(-0.281906\pi\)
0.632798 + 0.774317i \(0.281906\pi\)
\(864\) 13.4622 5.57623i 0.457993 0.189707i
\(865\) −6.49970 9.51833i −0.220996 0.323633i
\(866\) −32.4021 −1.10107
\(867\) −54.9704 + 3.46440i −1.86689 + 0.117657i
\(868\) 2.82463i 0.0958743i
\(869\) 9.42328 + 9.42328i 0.319663 + 0.319663i
\(870\) 7.77697 + 37.1367i 0.263664 + 1.25905i
\(871\) 25.8281i 0.875152i
\(872\) −11.8173 + 4.89487i −0.400183 + 0.165761i
\(873\) −14.2806 + 34.4765i −0.483326 + 1.16685i
\(874\) 0.461319 1.11372i 0.0156043 0.0376722i
\(875\) −17.6789 + 4.07595i −0.597656 + 0.137792i
\(876\) −3.48890 + 3.48890i −0.117879 + 0.117879i
\(877\) −23.2054 9.61198i −0.783590 0.324573i −0.0452265 0.998977i \(-0.514401\pi\)
−0.738363 + 0.674403i \(0.764401\pi\)
\(878\) 8.51214 20.5501i 0.287271 0.693533i
\(879\) −9.35985 22.5967i −0.315700 0.762167i
\(880\) −9.79722 1.84631i −0.330264 0.0622391i
\(881\) 9.88865 4.09601i 0.333157 0.137998i −0.209833 0.977737i \(-0.567292\pi\)
0.542990 + 0.839739i \(0.317292\pi\)
\(882\) −23.1501 + 23.1501i −0.779504 + 0.779504i
\(883\) 3.61322i 0.121595i −0.998150 0.0607973i \(-0.980636\pi\)
0.998150 0.0607973i \(-0.0193643\pi\)
\(884\) −4.28978 6.00228i −0.144281 0.201878i
\(885\) 17.5446 + 3.30633i 0.589756 + 0.111141i
\(886\) 6.81590 + 6.81590i 0.228985 + 0.228985i
\(887\) −12.4793 30.1276i −0.419013 1.01159i −0.982634 0.185553i \(-0.940592\pi\)
0.563621 0.826033i \(-0.309408\pi\)
\(888\) −33.1253 −1.11161
\(889\) −0.808152 1.95105i −0.0271045 0.0654362i
\(890\) 18.2864 + 11.9537i 0.612962 + 0.400689i
\(891\) −42.1755 + 101.821i −1.41293 + 3.41112i
\(892\) −1.52869 1.52869i −0.0511844 0.0511844i
\(893\) 0.863303 + 0.863303i 0.0288893 + 0.0288893i
\(894\) 10.5009 25.3514i 0.351203 0.847879i
\(895\) 3.63130 5.55506i 0.121381 0.185685i
\(896\) −0.620992 1.49921i −0.0207459 0.0500850i
\(897\) 31.3707 1.04744
\(898\) −14.9247 36.0315i −0.498045 1.20239i
\(899\) 6.44612 + 6.44612i 0.214990 + 0.214990i
\(900\) 34.9156 + 13.6444i 1.16385 + 0.454814i
\(901\) 1.36780 8.22045i 0.0455681 0.273863i
\(902\) 7.66345i 0.255165i
\(903\) 19.2243 19.2243i 0.639745 0.639745i
\(904\) 4.75264 1.96861i 0.158071 0.0654750i
\(905\) 23.9187 + 4.50753i 0.795083 + 0.149835i
\(906\) 2.24349 + 5.41626i 0.0745350 + 0.179943i
\(907\) 6.13159 14.8030i 0.203596 0.491525i −0.788794 0.614658i \(-0.789294\pi\)
0.992390 + 0.123133i \(0.0392942\pi\)
\(908\) −0.354624 0.146890i −0.0117686 0.00487472i
\(909\) −58.8666 + 58.8666i −1.95248 + 1.95248i
\(910\) −5.36183 + 3.66139i −0.177743 + 0.121374i
\(911\) 13.9350 33.6421i 0.461687 1.11461i −0.506017 0.862524i \(-0.668883\pi\)
0.967704 0.252088i \(-0.0811174\pi\)
\(912\) 0.276217 0.666847i 0.00914647 0.0220815i
\(913\) 58.5885 24.2682i 1.93900 0.803159i
\(914\) 3.92824i 0.129935i
\(915\) −67.1199 + 14.0559i −2.21891 + 0.464673i
\(916\) 6.36165 + 6.36165i 0.210195 + 0.210195i
\(917\) 6.73863i 0.222529i
\(918\) 31.7900 50.9797i 1.04923 1.68258i
\(919\) 21.8170 0.719678 0.359839 0.933014i \(-0.382832\pi\)
0.359839 + 0.933014i \(0.382832\pi\)
\(920\) −9.99228 + 6.82334i −0.329436 + 0.224959i
\(921\) 37.4097 15.4956i 1.23269 0.510597i
\(922\) −37.6666 −1.24048
\(923\) −13.5979 + 5.63242i −0.447579 + 0.185393i
\(924\) 21.6570 + 8.97063i 0.712463 + 0.295112i
\(925\) −36.8686 35.4110i −1.21223 1.16431i
\(926\) 3.72927 3.72927i 0.122551 0.122551i
\(927\) 20.5116 + 20.5116i 0.673690 + 0.673690i
\(928\) −4.83853 2.00418i −0.158832 0.0657906i
\(929\) −44.7381 18.5311i −1.46781 0.607986i −0.501450 0.865186i \(-0.667200\pi\)
−0.966358 + 0.257200i \(0.917200\pi\)
\(930\) 12.3430 2.58481i 0.404743 0.0847591i
\(931\) 0.972811i 0.0318826i
\(932\) −4.73720 11.4366i −0.155172 0.374619i
\(933\) −39.9792 + 39.9792i −1.30886 + 1.30886i
\(934\) −6.42830 −0.210340
\(935\) −37.2908 + 17.2946i −1.21954 + 0.565593i
\(936\) 13.4154 0.438495
\(937\) 33.7018 33.7018i 1.10099 1.10099i 0.106699 0.994291i \(-0.465972\pi\)
0.994291 0.106699i \(-0.0340280\pi\)
\(938\) 8.96367 + 21.6402i 0.292674 + 0.706578i
\(939\) 28.0348i 0.914881i
\(940\) −2.51177 11.9942i −0.0819248 0.391209i
\(941\) −5.67849 2.35211i −0.185113 0.0766765i 0.288201 0.957570i \(-0.406943\pi\)
−0.473315 + 0.880893i \(0.656943\pi\)
\(942\) −6.21725 2.57527i −0.202569 0.0839068i
\(943\) −6.57665 6.57665i −0.214165 0.214165i
\(944\) −1.74254 + 1.74254i −0.0567147 + 0.0567147i
\(945\) −44.2560 28.9299i −1.43965 0.941088i
\(946\) 21.3005 + 8.82297i 0.692540 + 0.286859i
\(947\) 11.7699 4.87526i 0.382471 0.158425i −0.183160 0.983083i \(-0.558633\pi\)
0.565631 + 0.824658i \(0.308633\pi\)
\(948\) 9.68415 0.314527
\(949\) −2.51751 + 1.04279i −0.0817218 + 0.0338503i
\(950\) 1.02029 0.446928i 0.0331027 0.0145002i
\(951\) 13.5843 0.440502
\(952\) −5.67731 3.54027i −0.184003 0.114741i
\(953\) 24.9800i 0.809180i 0.914498 + 0.404590i \(0.132586\pi\)
−0.914498 + 0.404590i \(0.867414\pi\)
\(954\) 10.7151 + 10.7151i 0.346914 + 0.346914i
\(955\) 11.0174 + 52.6105i 0.356515 + 1.70244i
\(956\) 8.64334i 0.279545i
\(957\) 69.8956 28.9517i 2.25940 0.935876i
\(958\) 15.4404 37.2765i 0.498858 1.20435i
\(959\) −13.1136 + 31.6591i −0.423461 + 1.02233i
\(960\) −5.98294 + 4.08551i −0.193098 + 0.131859i
\(961\) −19.7778 + 19.7778i −0.637995 + 0.637995i
\(962\) −16.9016 7.00086i −0.544929 0.225717i
\(963\) −34.7203 + 83.8221i −1.11885 + 2.70113i
\(964\) 8.36424 + 20.1931i 0.269394 + 0.650375i
\(965\) 7.27108 38.5831i 0.234064 1.24203i
\(966\) 26.2841 10.8872i 0.845678 0.350291i
\(967\) −18.0041 + 18.0041i −0.578973 + 0.578973i −0.934620 0.355647i \(-0.884260\pi\)
0.355647 + 0.934620i \(0.384260\pi\)
\(968\) 8.87889i 0.285378i
\(969\) −0.672145 2.89912i −0.0215924 0.0931332i
\(970\) 2.06113 10.9372i 0.0661790 0.351171i
\(971\) 22.2438 + 22.2438i 0.713837 + 0.713837i 0.967336 0.253499i \(-0.0815814\pi\)
−0.253499 + 0.967336i \(0.581581\pi\)
\(972\) 13.9195 + 33.6047i 0.446469 + 1.07787i
\(973\) 17.3987 0.557776
\(974\) 6.35893 + 15.3518i 0.203753 + 0.491904i
\(975\) 20.9060 + 20.0795i 0.669528 + 0.643058i
\(976\) 3.62231 8.74502i 0.115947 0.279921i
\(977\) 1.83787 + 1.83787i 0.0587988 + 0.0587988i 0.735895 0.677096i \(-0.236762\pi\)
−0.677096 + 0.735895i \(0.736762\pi\)
\(978\) −4.74652 4.74652i −0.151777 0.151777i
\(979\) 16.6701 40.2453i 0.532780 1.28624i
\(980\) 5.34265 8.17303i 0.170665 0.261078i
\(981\) −36.6987 88.5986i −1.17170 2.82873i
\(982\) −22.3337 −0.712696
\(983\) 9.13417 + 22.0518i 0.291335 + 0.703345i 0.999998 0.00220274i \(-0.000701155\pi\)
−0.708663 + 0.705547i \(0.750701\pi\)
\(984\) −3.93780 3.93780i −0.125533 0.125533i
\(985\) 33.4293 + 6.29983i 1.06515 + 0.200729i
\(986\) −21.0355 + 4.87697i −0.669907 + 0.155314i
\(987\) 28.8134i 0.917141i
\(988\) 0.281870 0.281870i 0.00896747 0.00896747i
\(989\) 25.8515 10.7080i 0.822029 0.340496i
\(990\) 13.8425 73.4536i 0.439943 2.33451i
\(991\) 1.36367 + 3.29218i 0.0433183 + 0.104580i 0.944058 0.329780i \(-0.106975\pi\)
−0.900739 + 0.434360i \(0.856975\pi\)
\(992\) −0.666124 + 1.60817i −0.0211495 + 0.0510593i
\(993\) 20.9802 + 8.69027i 0.665785 + 0.275777i
\(994\) −9.43830 + 9.43830i −0.299365 + 0.299365i
\(995\) 10.1293 + 14.8336i 0.321119 + 0.470256i
\(996\) 17.6352 42.5752i 0.558794 1.34905i
\(997\) 6.90834 16.6782i 0.218789 0.528204i −0.775932 0.630816i \(-0.782720\pi\)
0.994721 + 0.102612i \(0.0327202\pi\)
\(998\) −18.1465 + 7.51654i −0.574418 + 0.237932i
\(999\) 148.977i 4.71343i
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 170.2.n.a.19.1 yes 20
5.2 odd 4 850.2.l.h.801.1 20
5.3 odd 4 850.2.l.i.801.5 20
5.4 even 2 170.2.n.b.19.5 yes 20
17.9 even 8 170.2.n.b.9.5 yes 20
85.9 even 8 inner 170.2.n.a.9.1 20
85.43 odd 8 850.2.l.i.451.5 20
85.77 odd 8 850.2.l.h.451.1 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
170.2.n.a.9.1 20 85.9 even 8 inner
170.2.n.a.19.1 yes 20 1.1 even 1 trivial
170.2.n.b.9.5 yes 20 17.9 even 8
170.2.n.b.19.5 yes 20 5.4 even 2
850.2.l.h.451.1 20 85.77 odd 8
850.2.l.h.801.1 20 5.2 odd 4
850.2.l.i.451.5 20 85.43 odd 8
850.2.l.i.801.5 20 5.3 odd 4