Properties

Label 170.2.n.b.9.5
Level $170$
Weight $2$
Character 170.9
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 9.5
Root \(2.99334 + 1.23988i\) of defining polynomial
Character \(\chi\) \(=\) 170.9
Dual form 170.2.n.b.19.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.707107 + 0.707107i) q^{2} +(1.23988 - 2.99334i) q^{3} +1.00000i q^{4} +(1.87165 + 1.22349i) q^{5} +(2.99334 - 1.23988i) q^{6} +(-1.49921 + 0.620992i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-5.30145 - 5.30145i) q^{9} +O(q^{10})\) \(q+(0.707107 + 0.707107i) q^{2} +(1.23988 - 2.99334i) q^{3} +1.00000i q^{4} +(1.87165 + 1.22349i) 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} +(0.458323 + 2.18859i) q^{10} +(-4.11919 + 1.70622i) q^{11} +(2.99334 + 1.23988i) q^{12} +1.78934 q^{13} +(-1.49921 - 0.620992i) q^{14} +(5.98294 - 4.08551i) q^{15} -1.00000 q^{16} +(3.35446 + 2.39741i) q^{17} -7.49739i q^{18} +(-0.157527 + 0.157527i) q^{19} +(-1.22349 + 1.87165i) q^{20} +5.25759i q^{21} +(-4.11919 - 1.70622i) q^{22} +(-2.07076 - 4.99927i) q^{23} +(1.23988 + 2.99334i) q^{24} +(2.00616 + 4.57988i) 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} +(-2.18859 + 0.458323i) 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} +(-3.43622 - 16.4087i) 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} +(4.08551 + 5.98294i) q^{60} +(-3.62231 - 8.74502i) q^{61} +(-0.666124 - 1.60817i) q^{62} +(11.2401 + 4.65582i) q^{63} -1.00000i q^{64} +(3.34902 + 2.18923i) q^{65} +(-10.2146 + 10.2146i) q^{66} -14.4344i q^{67} +(-2.39741 + 3.35446i) q^{68} -17.5320 q^{69} +(-2.04622 - 2.99654i) q^{70} +(7.59937 + 3.14776i) q^{71} +7.49739 q^{72} +(-1.40695 - 0.582777i) q^{73} +(9.44570 - 3.91254i) q^{74} +(16.1965 - 0.326622i) 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} +(-1.87165 - 1.22349i) q^{80} +24.7186i q^{81} +(-0.657761 + 1.58798i) q^{82} +(10.0574 + 10.0574i) q^{83} -5.25759 q^{84} +(3.34520 + 8.59126i) q^{85} -5.17105 q^{86} +(11.9984 + 11.9984i) q^{87} +(1.70622 - 4.11919i) q^{88} -9.77020i q^{89} +(9.17295 - 14.0325i) 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} +(-0.487568 + 0.102104i) 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 \( 20 q - 4 q^{5} + 8 q^{10} - 8 q^{11} + 24 q^{13} + 16 q^{15} - 20 q^{16} - 4 q^{20} - 8 q^{22} - 16 q^{23} + 8 q^{25} - 12 q^{26} - 24 q^{27} - 12 q^{29} + 8 q^{30} + 8 q^{31} + 8 q^{34} - 8 q^{35} + 8 q^{37} + 8 q^{38} - 4 q^{40} + 4 q^{41} - 8 q^{42} - 16 q^{43} - 8 q^{44} - 32 q^{45} + 16 q^{46} - 40 q^{47} - 56 q^{49} + 8 q^{50} - 8 q^{51} - 44 q^{53} - 24 q^{54} + 72 q^{57} + 16 q^{59} + 8 q^{60} + 8 q^{61} + 8 q^{62} + 24 q^{63} - 28 q^{65} - 8 q^{66} - 20 q^{68} - 16 q^{69} + 8 q^{71} + 28 q^{72} + 60 q^{73} + 28 q^{74} - 8 q^{78} + 56 q^{79} + 4 q^{80} - 4 q^{82} + 16 q^{84} + 84 q^{85} + 48 q^{86} + 72 q^{87} + 8 q^{88} - 12 q^{90} - 24 q^{91} + 8 q^{92} - 72 q^{93} + 32 q^{94} + 88 q^{95} - 48 q^{97} + 36 q^{98} + 72 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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 0.0309978 0.999519i \(-0.490132\pi\)
0.684848 0.728686i \(-0.259868\pi\)
\(4\) 1.00000i 0.500000i
\(5\) 1.87165 + 1.22349i 0.837028 + 0.547159i
\(6\) 2.99334 1.23988i 1.22203 0.506180i
\(7\) −1.49921 + 0.620992i −0.566647 + 0.234713i −0.647568 0.762008i \(-0.724214\pi\)
0.0809209 + 0.996721i \(0.474214\pi\)
\(8\) −0.707107 + 0.707107i −0.250000 + 0.250000i
\(9\) −5.30145 5.30145i −1.76715 1.76715i
\(10\) 0.458323 + 2.18859i 0.144934 + 0.692094i
\(11\) −4.11919 + 1.70622i −1.24198 + 0.514445i −0.904333 0.426827i \(-0.859631\pi\)
−0.337648 + 0.941272i \(0.609631\pi\)
\(12\) 2.99334 + 1.23988i 0.864103 + 0.357923i
\(13\) 1.78934 0.496274 0.248137 0.968725i \(-0.420182\pi\)
0.248137 + 0.968725i \(0.420182\pi\)
\(14\) −1.49921 0.620992i −0.400680 0.165967i
\(15\) 5.98294 4.08551i 1.54479 1.05487i
\(16\) −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 −0.724945 0.688806i \(-0.758135\pi\)
0.688806 + 0.724945i \(0.258135\pi\)
\(20\) −1.22349 + 1.87165i −0.273580 + 0.418514i
\(21\) 5.25759i 1.14730i
\(22\) −4.11919 1.70622i −0.878213 0.363768i
\(23\) −2.07076 4.99927i −0.431784 1.04242i −0.978712 0.205239i \(-0.934203\pi\)
0.546928 0.837180i \(-0.315797\pi\)
\(24\) 1.23988 + 2.99334i 0.253090 + 0.611013i
\(25\) 2.00616 + 4.57988i 0.401233 + 0.915976i
\(26\) 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 0.621215 + 0.783640i \(0.286639\pi\)
−0.993383 + 0.114852i \(0.963361\pi\)
\(30\) 7.11947 + 1.34168i 1.29983 + 0.244956i
\(31\) −1.60817 0.666124i −0.288835 0.119639i 0.233561 0.972342i \(-0.424962\pi\)
−0.522397 + 0.852703i \(0.674962\pi\)
\(32\) −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 −0.179098 0.983831i \(-0.557318\pi\)
0.822315 0.569032i \(-0.192682\pi\)
\(38\) −0.222777 −0.0361392
\(39\) 2.21857 5.35610i 0.355256 0.857663i
\(40\) −2.18859 + 0.458323i −0.346047 + 0.0724672i
\(41\) 0.657761 + 1.58798i 0.102725 + 0.248000i 0.966883 0.255221i \(-0.0821482\pi\)
−0.864158 + 0.503221i \(0.832148\pi\)
\(42\) −3.71768 + 3.71768i −0.573651 + 0.573651i
\(43\) −3.65649 + 3.65649i −0.557609 + 0.557609i −0.928626 0.371017i \(-0.879009\pi\)
0.371017 + 0.928626i \(0.379009\pi\)
\(44\) −1.70622 4.11919i −0.257223 0.620991i
\(45\) −3.43622 16.4087i −0.512242 2.44607i
\(46\) 2.07076 4.99927i 0.305318 0.737102i
\(47\) 5.48034 0.799390 0.399695 0.916648i \(-0.369116\pi\)
0.399695 + 0.916648i \(0.369116\pi\)
\(48\) −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 \(-0.205671\pi\)
−0.602105 + 0.798417i \(0.705671\pi\)
\(54\) −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 0.811379 0.584520i \(-0.198717\pi\)
−0.584520 + 0.811379i \(0.698717\pi\)
\(60\) 4.08551 + 5.98294i 0.527437 + 0.772394i
\(61\) −3.62231 8.74502i −0.463789 1.11969i −0.966830 0.255423i \(-0.917785\pi\)
0.503041 0.864263i \(-0.332215\pi\)
\(62\) −0.666124 1.60817i −0.0845979 0.204237i
\(63\) 11.2401 + 4.65582i 1.41612 + 0.586578i
\(64\) 1.00000i 0.125000i
\(65\) 3.34902 + 2.18923i 0.415395 + 0.271541i
\(66\) −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
\(70\) −2.04622 2.99654i −0.244570 0.358155i
\(71\) 7.59937 + 3.14776i 0.901879 + 0.373571i 0.784942 0.619569i \(-0.212692\pi\)
0.116937 + 0.993139i \(0.462692\pi\)
\(72\) 7.49739 0.883575
\(73\) −1.40695 0.582777i −0.164671 0.0682089i 0.298825 0.954308i \(-0.403405\pi\)
−0.463496 + 0.886099i \(0.653405\pi\)
\(74\) 9.44570 3.91254i 1.09804 0.454823i
\(75\) 16.1965 0.326622i 1.87022 0.0377151i
\(76\) −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 −0.532578 0.846381i \(-0.678777\pi\)
0.221892 + 0.975071i \(0.428777\pi\)
\(80\) −1.87165 1.22349i −0.209257 0.136790i
\(81\) 24.7186i 2.74652i
\(82\) −0.657761 + 1.58798i −0.0726376 + 0.175363i
\(83\) 10.0574 + 10.0574i 1.10394 + 1.10394i 0.993930 + 0.110014i \(0.0350897\pi\)
0.110014 + 0.993930i \(0.464910\pi\)
\(84\) −5.25759 −0.573651
\(85\) 3.34520 + 8.59126i 0.362837 + 0.931852i
\(86\) −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 \(-0.826744\pi\)
0.855490 0.517820i \(-0.173256\pi\)
\(90\) 9.17295 14.0325i 0.966913 1.47916i
\(91\) −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
\(95\) −0.487568 + 0.102104i −0.0500235 + 0.0104756i
\(96\) −2.99334 + 1.23988i −0.305506 + 0.126545i
\(97\) −4.59847 1.90475i −0.466903 0.193398i 0.136813 0.990597i \(-0.456314\pi\)
−0.603716 + 0.797199i \(0.706314\pi\)
\(98\) −4.36674 −0.441108
\(99\) 30.8831 + 12.7922i 3.10387 + 1.28567i
\(100\) −4.57988 + 2.00616i −0.457988 + 0.200616i
\(101\) 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
\(105\) −6.43259 + 9.84039i −0.627757 + 0.960324i
\(106\) 2.02116i 0.196313i
\(107\) −11.1802 4.63098i −1.08083 0.447694i −0.230029 0.973184i \(-0.573882\pi\)
−0.850800 + 0.525490i \(0.823882\pi\)
\(108\) −5.57623 13.4622i −0.536573 1.29540i
\(109\) −4.89487 11.8173i −0.468843 1.13189i −0.964669 0.263466i \(-0.915134\pi\)
0.495825 0.868422i \(-0.334866\pi\)
\(110\) −5.62214 8.23322i −0.536050 0.785007i
\(111\) −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 \(-0.202792\pi\)
−0.989022 + 0.147767i \(0.952792\pi\)
\(114\) −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
\(125\) −1.84858 + 11.0265i −0.165342 + 0.986236i
\(126\) 4.65582 + 11.2401i 0.414773 + 1.00135i
\(127\) 0.920220 0.920220i 0.0816564 0.0816564i −0.665099 0.746755i \(-0.731611\pi\)
0.746755 + 0.665099i \(0.231611\pi\)
\(128\) 0.707107 0.707107i 0.0625000 0.0625000i
\(129\) 6.41149 + 15.4787i 0.564501 + 1.36283i
\(130\) 0.820096 + 3.91614i 0.0719272 + 0.343468i
\(131\) 1.58915 3.83655i 0.138845 0.335201i −0.839128 0.543934i \(-0.816934\pi\)
0.977973 + 0.208733i \(0.0669341\pi\)
\(132\) −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 0.760928 0.648836i \(-0.224744\pi\)
0.0792614 + 0.996854i \(0.474744\pi\)
\(140\) 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
\(145\) −9.67101 + 6.60395i −0.803133 + 0.548428i
\(146\) −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 \(0.112771\pi\)
−0.937896 + 0.346915i \(0.887229\pi\)
\(150\) 11.6836 + 11.2217i 0.953965 + 0.916250i
\(151\) 1.27947 1.27947i 0.104121 0.104121i −0.653127 0.757248i \(-0.726543\pi\)
0.757248 + 0.653127i \(0.226543\pi\)
\(152\) 0.222777i 0.0180696i
\(153\) −5.07378 30.4933i −0.410191 2.46524i
\(154\) 7.23507 0.583018
\(155\) −2.19493 3.21432i −0.176301 0.258181i
\(156\) 5.35610 + 2.21857i 0.428831 + 0.177628i
\(157\) 2.07703 0.165765 0.0828824 0.996559i \(-0.473587\pi\)
0.0828824 + 0.996559i \(0.473587\pi\)
\(158\) −2.76144 1.14383i −0.219689 0.0909980i
\(159\) 6.05003 2.50600i 0.479798 0.198739i
\(160\) −0.458323 2.18859i −0.0362336 0.173023i
\(161\) 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 \(-0.599144\pi\)
0.456384 + 0.889783i \(0.349144\pi\)
\(164\) −1.58798 + 0.657761i −0.124000 + 0.0513625i
\(165\) −17.6740 + 27.0372i −1.37592 + 2.10484i
\(166\) 14.2233i 1.10394i
\(167\) 6.65999 16.0786i 0.515366 1.24420i −0.425357 0.905026i \(-0.639851\pi\)
0.940723 0.339177i \(-0.110149\pi\)
\(168\) −3.71768 3.71768i −0.286825 0.286825i
\(169\) −9.79826 −0.753712
\(170\) −3.70952 + 8.44035i −0.284508 + 0.647345i
\(171\) 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 \(-0.937777\pi\)
0.830985 + 0.556295i \(0.187777\pi\)
\(174\) 16.9683i 1.28636i
\(175\) −5.85173 5.62038i −0.442349 0.424861i
\(176\) 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 0.624312 0.781175i \(-0.285380\pi\)
−0.781175 + 0.624312i \(0.785380\pi\)
\(180\) 16.4087 3.43622i 1.22303 0.256121i
\(181\) −10.0565 + 4.16552i −0.747491 + 0.309621i −0.723717 0.690096i \(-0.757568\pi\)
−0.0237737 + 0.999717i \(0.507568\pi\)
\(182\) −2.68259 1.11117i −0.198847 0.0823651i
\(183\) −30.6680 −2.26705
\(184\) 4.99927 + 2.07076i 0.368551 + 0.152659i
\(185\) 18.8796 12.8921i 1.38806 0.947848i
\(186\) −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
\(190\) −0.416961 0.272565i −0.0302496 0.0197739i
\(191\) 24.0385i 1.73937i 0.493611 + 0.869683i \(0.335677\pi\)
−0.493611 + 0.869683i \(0.664323\pi\)
\(192\) −2.99334 1.23988i −0.216026 0.0894808i
\(193\) 6.71939 + 16.2220i 0.483672 + 1.16769i 0.957852 + 0.287261i \(0.0927445\pi\)
−0.474180 + 0.880428i \(0.657255\pi\)
\(194\) −1.90475 4.59847i −0.136753 0.330151i
\(195\) 10.7055 7.31037i 0.766637 0.523507i
\(196\) −3.08775 3.08775i −0.220554 0.220554i
\(197\) 14.0551 5.82183i 1.00139 0.414788i 0.179082 0.983834i \(-0.442687\pi\)
0.822306 + 0.569046i \(0.192687\pi\)
\(198\) 12.7922 + 30.8831i 0.909103 + 2.19477i
\(199\) −3.07405 + 7.42142i −0.217914 + 0.526091i −0.994598 0.103799i \(-0.966900\pi\)
0.776684 + 0.629890i \(0.216900\pi\)
\(200\) −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
\(210\) −11.5067 + 2.40968i −0.794040 + 0.166283i
\(211\) 3.61423 + 8.72553i 0.248814 + 0.600690i 0.998104 0.0615519i \(-0.0196050\pi\)
−0.749290 + 0.662242i \(0.769605\pi\)
\(212\) −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
\(215\) −11.3173 + 2.37001i −0.771836 + 0.161634i
\(216\) 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 \(-0.273061\pi\)
−0.756436 + 0.654067i \(0.773061\pi\)
\(224\) 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 \(-0.129055\pi\)
−0.928679 + 0.370884i \(0.879055\pi\)
\(228\) −0.666847 + 0.276217i −0.0441631 + 0.0182929i
\(229\) −6.36165 6.36165i −0.420390 0.420390i 0.464948 0.885338i \(-0.346073\pi\)
−0.885338 + 0.464948i \(0.846073\pi\)
\(230\) 9.99228 6.82334i 0.658872 0.449918i
\(231\) −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 \(-0.507897\pi\)
−0.724430 + 0.689348i \(0.757897\pi\)
\(234\) 13.4154i 0.876991i
\(235\) 10.2573 + 6.70512i 0.669112 + 0.437394i
\(236\) −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 \(0.590184\pi\)
\(240\) −5.98294 + 4.08551i −0.386197 + 0.263719i
\(241\) −20.1931 8.36424i −1.30075 0.538788i −0.378578 0.925569i \(-0.623587\pi\)
−0.922171 + 0.386781i \(0.873587\pi\)
\(242\) 8.87889 0.570756
\(243\) 33.6047 + 13.9195i 2.15574 + 0.892937i
\(244\) 8.74502 3.62231i 0.559843 0.231894i
\(245\) −9.55703 + 2.00138i −0.610576 + 0.127863i
\(246\) 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
\(250\) −9.10402 + 6.48974i −0.575789 + 0.410447i
\(251\) 21.7468i 1.37264i 0.727298 + 0.686322i \(0.240776\pi\)
−0.727298 + 0.686322i \(0.759224\pi\)
\(252\) −4.65582 + 11.2401i −0.293289 + 0.708062i
\(253\) 17.0597 + 17.0597i 1.07254 + 1.07254i
\(254\) 1.30139 0.0816564
\(255\) 29.8642 + 0.638837i 1.87017 + 0.0400055i
\(256\) 1.00000 0.0625000
\(257\) −13.9606 13.9606i −0.870840 0.870840i 0.121724 0.992564i \(-0.461158\pi\)
−0.992564 + 0.121724i \(0.961158\pi\)
\(258\) −6.41149 + 15.4787i −0.399162 + 0.963663i
\(259\) 16.5907i 1.03090i
\(260\) −2.18923 + 3.34902i −0.135770 + 0.207698i
\(261\) 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 \(-0.945885\pi\)
0.169191 + 0.985583i \(0.445885\pi\)
\(264\) −10.2146 10.2146i −0.628666 0.628666i
\(265\) 0.926346 + 4.42350i 0.0569050 + 0.271734i
\(266\) 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 0.653377 0.757033i \(-0.273352\pi\)
−0.0732956 + 0.997310i \(0.523352\pi\)
\(270\) −18.3741 26.9076i −1.11821 1.63754i
\(271\) 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
\(275\) −16.0781 15.4424i −0.969544 0.931213i
\(276\) 17.5320i 1.05530i
\(277\) 21.1959 + 8.77965i 1.27354 + 0.527518i 0.914039 0.405626i \(-0.132947\pi\)
0.359502 + 0.933144i \(0.382947\pi\)
\(278\) 4.10307 + 9.90569i 0.246086 + 0.594104i
\(279\) 4.99419 + 12.0570i 0.298994 + 0.721836i
\(280\) 2.99654 2.04622i 0.179078 0.122285i
\(281\) 16.9895 + 16.9895i 1.01351 + 1.01351i 0.999907 + 0.0136041i \(0.00433046\pi\)
0.0136041 + 0.999907i \(0.495670\pi\)
\(282\) 16.4045 6.79498i 0.976875 0.404635i
\(283\) 6.03994 + 14.5817i 0.359037 + 0.866792i 0.995436 + 0.0954321i \(0.0304233\pi\)
−0.636399 + 0.771360i \(0.719577\pi\)
\(284\) −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 \(-0.570772\pi\)
−0.220508 + 0.975385i \(0.570772\pi\)
\(294\) −5.41425 + 13.0711i −0.315765 + 0.762325i
\(295\) 1.12945 + 5.39339i 0.0657593 + 0.314015i
\(296\) 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
\(300\) 0.326622 + 16.1965i 0.0188576 + 0.935108i
\(301\) 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 0.613538 + 0.789665i \(0.289746\pi\)
−0.992214 + 0.124541i \(0.960254\pi\)
\(312\) 2.21857 + 5.35610i 0.125602 + 0.303230i
\(313\) 7.99415 3.31129i 0.451856 0.187165i −0.145137 0.989412i \(-0.546362\pi\)
0.596993 + 0.802247i \(0.296362\pi\)
\(314\) 1.46868 + 1.46868i 0.0828824 + 0.0828824i
\(315\) 15.3413 + 22.4662i 0.864385 + 1.26583i
\(316\) −1.14383 2.76144i −0.0643453 0.155343i
\(317\) 1.60449 + 3.87358i 0.0901171 + 0.217562i 0.962512 0.271241i \(-0.0874339\pi\)
−0.872394 + 0.488802i \(0.837434\pi\)
\(318\) 6.05003 + 2.50600i 0.339269 + 0.140530i
\(319\) 23.3504i 1.30737i
\(320\) 1.22349 1.87165i 0.0683949 0.104629i
\(321\) −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
\(325\) 3.58971 + 8.19497i 0.199121 + 0.454575i
\(326\) 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
\(330\) −31.6156 + 6.62077i −1.74038 + 0.364461i
\(331\) −4.95608 4.95608i −0.272411 0.272411i 0.557659 0.830070i \(-0.311700\pi\)
−0.830070 + 0.557659i \(0.811700\pi\)
\(332\) −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
\(335\) 17.6603 27.0162i 0.964886 1.47605i
\(336\) 5.25759i 0.286825i
\(337\) −0.581083 + 1.40286i −0.0316536 + 0.0764186i −0.938916 0.344147i \(-0.888168\pi\)
0.907262 + 0.420565i \(0.138168\pi\)
\(338\) −6.92842 6.92842i −0.376856 0.376856i
\(339\) −16.6671 −0.905233
\(340\) −8.59126 + 3.34520i −0.465926 + 0.181419i
\(341\) 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
\(345\) −32.8138 21.4502i −1.76664 1.15484i
\(346\) −4.76214 + 1.97254i −0.256014 + 0.106045i
\(347\) −6.53872 + 2.70843i −0.351017 + 0.145396i −0.551223 0.834358i \(-0.685839\pi\)
0.200206 + 0.979754i \(0.435839\pi\)
\(348\) −11.9984 + 11.9984i −0.643182 + 0.643182i
\(349\) 6.15710 + 6.15710i 0.329582 + 0.329582i 0.852427 0.522845i \(-0.175130\pi\)
−0.522845 + 0.852427i \(0.675130\pi\)
\(350\) −0.163588 8.11200i −0.00874415 0.433605i
\(351\) −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 \(-0.477626\pi\)
0.0702325 + 0.997531i \(0.477626\pi\)
\(354\) 7.37654 + 3.05546i 0.392059 + 0.162396i
\(355\) 10.3721 + 15.1892i 0.550496 + 0.806161i
\(356\) 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 −0.838495 0.544909i \(-0.816564\pi\)
0.544909 + 0.838495i \(0.316564\pi\)
\(360\) 14.0325 + 9.17295i 0.739578 + 0.483457i
\(361\) 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
\(365\) −1.92030 2.81214i −0.100513 0.147194i
\(366\) −21.6856 21.6856i −1.13352 1.13352i
\(367\) 21.5147 8.91170i 1.12306 0.465187i 0.257644 0.966240i \(-0.417054\pi\)
0.865417 + 0.501053i \(0.167054\pi\)
\(368\) 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 −0.631187 0.775631i \(-0.717432\pi\)
0.994770 0.102137i \(-0.0325681\pi\)
\(380\) −0.102104 0.487568i −0.00523782 0.0250117i
\(381\) −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 \(-0.591071\pi\)
0.959350 + 0.282220i \(0.0910707\pi\)
\(384\) −1.23988 2.99334i −0.0632724 0.152753i
\(385\) 15.8346 3.31600i 0.807007 0.168999i
\(386\) −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 −0.735070 0.677991i \(-0.762851\pi\)
0.677991 + 0.735070i \(0.262851\pi\)
\(390\) 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 \(-0.182488\pi\)
−0.977592 + 0.210509i \(0.932488\pi\)
\(398\) −7.42142 + 3.07405i −0.372002 + 0.154088i
\(399\) −0.828214 0.828214i −0.0414626 0.0414626i
\(400\) −2.00616 4.57988i −0.100308 0.228994i
\(401\) 1.34092 + 3.23726i 0.0669621 + 0.161661i 0.953818 0.300386i \(-0.0971153\pi\)
−0.886856 + 0.462046i \(0.847115\pi\)
\(402\) −17.8970 43.2071i −0.892620 2.15498i
\(403\) −2.87756 1.19192i −0.143341 0.0593739i
\(404\) 11.1039i 0.552438i
\(405\) −30.2429 + 46.2647i −1.50278 + 2.29891i
\(406\) 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 \(0.514798\pi\)
\(410\) −3.17397 + 2.16738i −0.156751 + 0.107039i
\(411\) 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
\(415\) 6.51888 + 31.1291i 0.319999 + 1.52807i
\(416\) −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 −0.967240 0.253865i \(-0.918298\pi\)
−0.504432 + 0.863451i \(0.668298\pi\)
\(420\) −9.84039 6.43259i −0.480162 0.313878i
\(421\) 27.3895i 1.33488i −0.744661 0.667442i \(-0.767389\pi\)
0.744661 0.667442i \(-0.232611\pi\)
\(422\) −3.61423 + 8.72553i −0.175938 + 0.424752i
\(423\) −29.0538 29.0538i −1.41264 1.41264i
\(424\) −2.02116 −0.0981564
\(425\) −4.25024 + 20.1726i −0.206167 + 0.978517i
\(426\) 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
\(430\) −9.67841 6.32671i −0.466735 0.305101i
\(431\) −16.7310 + 6.93020i −0.805903 + 0.333816i −0.747318 0.664466i \(-0.768659\pi\)
−0.0585849 + 0.998282i \(0.518659\pi\)
\(432\) 13.4622 5.57623i 0.647701 0.268286i
\(433\) −22.9117 + 22.9117i −1.10107 + 1.10107i −0.106786 + 0.994282i \(0.534056\pi\)
−0.994282 + 0.106786i \(0.965944\pi\)
\(434\) 1.99732 + 1.99732i 0.0958743 + 0.0958743i
\(435\) 7.77697 + 37.1367i 0.372877 + 1.78057i
\(436\) 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 −0.166081 0.986112i \(-0.553111\pi\)
−0.814723 + 0.579850i \(0.803111\pi\)
\(440\) 8.23322 5.62214i 0.392503 0.268025i
\(441\) 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
\(445\) 11.9537 18.2864i 0.566660 0.866859i
\(446\) 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 −0.713678 0.700474i \(-0.752972\pi\)
0.00933673 0.999956i \(-0.497028\pi\)
\(450\) 34.3371 15.0410i 1.61867 0.709039i
\(451\) −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 \(-0.220713\pi\)
−0.639149 + 0.769083i \(0.720713\pi\)
\(458\) 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 0.280681 0.959801i \(-0.409440\pi\)
0.959801 0.280681i \(-0.0905603\pi\)
\(462\) 8.97063 21.6570i 0.417351 1.00758i
\(463\) 5.27399 0.245103 0.122551 0.992462i \(-0.460892\pi\)
0.122551 + 0.992462i \(0.460892\pi\)
\(464\) 2.00418 4.83853i 0.0930419 0.224623i
\(465\) −12.3430 + 2.58481i −0.572394 + 0.119867i
\(466\) −4.73720 11.4366i −0.219447 0.529791i
\(467\) −4.54550 + 4.54550i −0.210340 + 0.210340i −0.804412 0.594072i \(-0.797520\pi\)
0.594072 + 0.804412i \(0.297520\pi\)
\(468\) 9.48610 9.48610i 0.438495 0.438495i
\(469\) 8.96367 + 21.6402i 0.413904 + 0.999252i
\(470\) 2.51177 + 11.9942i 0.115859 + 0.553253i
\(471\) 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 −0.703222 0.710970i \(-0.748256\pi\)
−0.999985 + 0.00547848i \(0.998256\pi\)
\(480\) −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
\(485\) −6.27630 9.19118i −0.284992 0.417350i
\(486\) 13.9195 + 33.6047i 0.631402 + 1.52434i
\(487\) −6.35893 15.3518i −0.288151 0.695657i 0.711827 0.702355i \(-0.247868\pi\)
−0.999978 + 0.00669763i \(0.997868\pi\)
\(488\) 8.74502 + 3.62231i 0.395869 + 0.163974i
\(489\) 6.71260i 0.303554i
\(490\) −8.17303 5.34265i −0.369220 0.241356i
\(491\) 15.7923 15.7923i 0.712696 0.712696i −0.254403 0.967098i \(-0.581879\pi\)
0.967098 + 0.254403i \(0.0818789\pi\)
\(492\) 5.56890i 0.251065i
\(493\) −18.3229 + 11.4258i −0.825222 + 0.514593i
\(494\) −0.398624 −0.0179349
\(495\) 42.1514 + 61.7276i 1.89456 + 2.77445i
\(496\) 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 0.0624588 0.998048i \(-0.480106\pi\)
0.749891 + 0.661561i \(0.230106\pi\)
\(500\) −11.0265 1.84858i −0.493118 0.0826708i
\(501\) −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 \(-0.533648\pi\)
0.628553 + 0.777767i \(0.283648\pi\)
\(504\) −11.2401 + 4.65582i −0.500676 + 0.207387i
\(505\) 20.7826 + 13.5854i 0.924812 + 0.604543i
\(506\) 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 \(0.481266\pi\)
\(510\) 20.6654 + 21.5689i 0.915081 + 0.955087i
\(511\) 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
\(515\) 4.73374 7.24153i 0.208593 0.319100i
\(516\) −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
\(520\) −3.91614 + 0.820096i −0.171734 + 0.0359636i
\(521\) −16.7528 + 6.93925i −0.733955 + 0.304014i −0.718176 0.695862i \(-0.755023\pi\)
−0.0157786 + 0.999876i \(0.505023\pi\)
\(522\) 36.2763 + 15.0261i 1.58777 + 0.657676i
\(523\) 33.8690 1.48099 0.740494 0.672063i \(-0.234592\pi\)
0.740494 + 0.672063i \(0.234592\pi\)
\(524\) 3.83655 + 1.58915i 0.167600 + 0.0694224i
\(525\) −24.0792 + 10.5476i −1.05090 + 0.460335i
\(526\) −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
\(530\) −2.47286 + 3.78292i −0.107414 + 0.164319i
\(531\) 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
\(535\) −15.2595 22.3464i −0.659725 0.966118i
\(536\) 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 0.471515 0.881858i \(-0.343707\pi\)
−0.290156 + 0.956979i \(0.593707\pi\)
\(542\) 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 −0.619462 0.785027i \(-0.712649\pi\)
0.993123 0.117072i \(-0.0373510\pi\)
\(548\) −21.1172 −0.902083
\(549\) −27.1578 + 65.5648i −1.15907 + 2.79824i
\(550\) −0.449471 22.2883i −0.0191655 0.950378i
\(551\) −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
\(555\) −15.1821 72.4977i −0.644443 3.07736i
\(556\) −4.10307 + 9.90569i −0.174009 + 0.420095i
\(557\) 24.3785 1.03295 0.516476 0.856302i \(-0.327244\pi\)
0.516476 + 0.856302i \(0.327244\pi\)
\(558\) −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 \(-0.381821\pi\)
−0.931867 + 0.362799i \(0.881821\pi\)
\(564\) 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 0.846189 + 0.532883i \(0.178892\pi\)
0.532883 + 0.846189i \(0.321108\pi\)
\(570\) −1.33286 + 0.910159i −0.0558274 + 0.0381224i
\(571\) 3.84418 + 9.28068i 0.160874 + 0.388384i 0.983677 0.179942i \(-0.0575910\pi\)
−0.822803 + 0.568327i \(0.807591\pi\)
\(572\) −3.05301 7.37063i −0.127653 0.308181i
\(573\) 71.9554 + 29.8049i 3.00598 + 1.24512i
\(574\) 2.78917i 0.116418i
\(575\) 18.7418 19.5132i 0.781585 0.813757i
\(576\) −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
\(580\) −6.60395 9.67101i −0.274214 0.401567i
\(581\) −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
\(585\) −6.14858 29.3608i −0.254212 1.21392i
\(586\) −5.33794 5.33794i −0.220508 0.220508i
\(587\) −1.31962 + 1.31962i −0.0544667 + 0.0544667i −0.733815 0.679349i \(-0.762262\pi\)
0.679349 + 0.733815i \(0.262262\pi\)
\(588\) −13.0711 + 5.41425i −0.539045 + 0.223280i
\(589\) 0.358263 0.148397i 0.0147620 0.00611460i
\(590\) −3.01506 + 4.61235i −0.124128 + 0.189887i
\(591\) 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 \(-0.192156\pi\)
−0.567671 + 0.823255i \(0.692156\pi\)
\(594\) 64.9676 2.66565
\(595\) −10.3502 10.8027i −0.424319 0.442869i
\(596\) −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 \(-0.968787\pi\)
0.995196 0.0979028i \(-0.0312134\pi\)
\(600\) −11.2217 + 11.6836i −0.458125 + 0.476983i
\(601\) −12.0035 + 4.97202i −0.489634 + 0.202813i −0.613820 0.789446i \(-0.710368\pi\)
0.124186 + 0.992259i \(0.460368\pi\)
\(602\) 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
\(605\) 19.4323 4.06940i 0.790034 0.165445i
\(606\) 33.2376 13.7675i 1.35019 0.559265i
\(607\) −35.5125 14.7098i −1.44141 0.597051i −0.481269 0.876573i \(-0.659824\pi\)
−0.960139 + 0.279522i \(0.909824\pi\)
\(608\) 0.222777 0.00903480
\(609\) −25.4390 10.5372i −1.03084 0.426988i
\(610\) 17.4791 11.9358i 0.707708 0.483266i
\(611\) 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
\(615\) 10.4230 + 6.81347i 0.420297 + 0.274745i
\(616\) 7.23507i 0.291509i
\(617\) −44.8083 18.5602i −1.80391 0.747206i −0.984828 0.173535i \(-0.944481\pi\)
−0.819086 0.573671i \(-0.805519\pi\)
\(618\) −4.79717 11.5814i −0.192971 0.465872i
\(619\) 4.87259 + 11.7635i 0.195846 + 0.472814i 0.991044 0.133536i \(-0.0426331\pi\)
−0.795198 + 0.606350i \(0.792633\pi\)
\(620\) 3.21432 2.19493i 0.129090 0.0881507i
\(621\) 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 −0.150867 + 0.988554i \(0.548206\pi\)
−0.988554 + 0.150867i \(0.951794\pi\)
\(632\) 1.14383 2.76144i 0.0454990 0.109844i
\(633\) 30.5997 1.21623
\(634\) −1.60449 + 3.87358i −0.0637224 + 0.153840i
\(635\) 2.84821 0.596456i 0.113028 0.0236696i
\(636\) 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
\(640\) 2.18859 0.458323i 0.0865117 0.0181168i
\(641\) 13.2912 32.0879i 0.524973 1.26740i −0.409808 0.912172i \(-0.634404\pi\)
0.934781 0.355225i \(-0.115596\pi\)
\(642\) −39.2079 −1.54741
\(643\) −5.51999 + 13.3264i −0.217687 + 0.525543i −0.994566 0.104107i \(-0.966802\pi\)
0.776879 + 0.629650i \(0.216802\pi\)
\(644\) −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 \(-0.421248\pi\)
0.858740 + 0.512412i \(0.171248\pi\)
\(654\) −29.3040 29.3040i −1.14588 1.14588i
\(655\) 7.66830 5.23638i 0.299625 0.204602i
\(656\) −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 \(-0.784989\pi\)
0.780408 0.625271i \(-0.215011\pi\)
\(660\) −27.0372 17.6740i −1.05242 0.687961i
\(661\) −1.48757 + 1.48757i −0.0578597 + 0.0578597i −0.735445 0.677585i \(-0.763027\pi\)
0.677585 + 0.735445i \(0.263027\pi\)
\(662\) 7.00895i 0.272411i
\(663\) 20.2829 12.6480i 0.787722 0.491209i
\(664\) −14.2233 −0.551972
\(665\) 0.667561 0.455851i 0.0258869 0.0176771i
\(666\) −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
\(670\) 31.5911 6.61563i 1.22047 0.255584i
\(671\) 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 \(-0.828335\pi\)
−0.243620 + 0.969871i \(0.578335\pi\)
\(674\) −1.40286 + 0.581083i −0.0540361 + 0.0223825i
\(675\) −52.5459 50.4684i −2.02249 1.94253i
\(676\) 9.79826i 0.376856i
\(677\) 0.866714 2.09243i 0.0333105 0.0804188i −0.906349 0.422530i \(-0.861142\pi\)
0.939659 + 0.342111i \(0.111142\pi\)
\(678\) −11.7854 11.7854i −0.452617 0.452617i
\(679\) 8.07689 0.309963
\(680\) −8.44035 3.70952i −0.323672 0.142254i
\(681\) −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 \(-0.916827\pi\)
0.865773 + 0.500436i \(0.166827\pi\)
\(684\) 1.67025i 0.0638635i
\(685\) −25.8366 + 39.5241i −0.987167 + 1.51014i
\(686\) 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
\(690\) −8.03532 38.3704i −0.305899 1.46074i
\(691\) 21.4601 8.88906i 0.816380 0.338156i 0.0648836 0.997893i \(-0.479332\pi\)
0.751496 + 0.659737i \(0.229332\pi\)
\(692\) −4.76214 1.97254i −0.181030 0.0749849i
\(693\) −54.2441 −2.06056
\(694\) −6.53872 2.70843i −0.248206 0.102810i
\(695\) 13.5200 + 19.7990i 0.512841 + 0.751019i
\(696\) −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
\(700\) 5.62038 5.85173i 0.212430 0.221175i
\(701\) 44.0844i 1.66505i −0.553991 0.832523i \(-0.686896\pi\)
0.553991 0.832523i \(-0.313104\pi\)
\(702\) −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
\(705\) 32.7885 22.3900i 1.23489 0.843256i
\(706\) 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 −0.999880 0.0154750i \(-0.995074\pi\)
0.717965 + 0.696080i \(0.245074\pi\)
\(710\) −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 0.240645 + 0.970613i \(0.422641\pi\)
−0.856489 + 0.516165i \(0.827359\pi\)
\(720\) 3.43622 + 16.4087i 0.128061 + 0.611517i
\(721\) 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
\(725\) −26.1806 + 0.527963i −0.972323 + 0.0196080i
\(726\) 11.0088 26.5775i 0.408574 0.986384i
\(727\) −32.8765 −1.21932 −0.609661 0.792663i \(-0.708694\pi\)
−0.609661 + 0.792663i \(0.708694\pi\)
\(728\) 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 −0.998413 0.0563160i \(-0.982065\pi\)
−0.0563160 0.998413i \(-0.517935\pi\)
\(734\) 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 0.949028 0.315191i \(-0.102068\pi\)
−0.315191 + 0.949028i \(0.602068\pi\)
\(740\) 12.8921 + 18.8796i 0.473924 + 0.694028i
\(741\) 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 \(-0.220742\pi\)
0.0917885 + 0.995779i \(0.470742\pi\)
\(744\) 5.63970i 0.206762i
\(745\) −10.3621 + 15.8516i −0.379636 + 0.580756i
\(746\) 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
\(750\) 8.13809 + 35.2979i 0.297161 + 1.28890i
\(751\) 14.8511 + 6.15152i 0.541924 + 0.224472i 0.636817 0.771015i \(-0.280251\pi\)
−0.0948927 + 0.995488i \(0.530251\pi\)
\(752\) −5.48034 −0.199848
\(753\) 65.0955 + 26.9634i 2.37221 + 0.982602i
\(754\) −8.65778 + 3.58617i −0.315298 + 0.130601i
\(755\) 3.96012 0.829307i 0.144124 0.0301816i
\(756\) 16.7198 + 16.7198i 0.608095 + 0.608095i
\(757\) 23.3000 23.3000i 0.846853 0.846853i −0.142886 0.989739i \(-0.545638\pi\)
0.989739 + 0.142886i \(0.0456382\pi\)
\(758\) 17.0883 7.07822i 0.620676 0.257092i
\(759\) 72.2176 29.9135i 2.62133 1.08579i
\(760\) 0.272565 0.416961i 0.00988696 0.0151248i
\(761\) 3.29371i 0.119397i 0.998216 + 0.0596985i \(0.0190139\pi\)
−0.998216 + 0.0596985i \(0.980986\pi\)
\(762\) 1.61357 3.89550i 0.0584534 0.141119i
\(763\) 14.6769 + 14.6769i 0.531338 + 0.531338i
\(764\) −24.0385 −0.869683
\(765\) 27.8117 63.2805i 1.00554 2.28791i
\(766\) 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 \(0.0686437\pi\)
−0.976837 + 0.213983i \(0.931356\pi\)
\(770\) 13.5415 + 8.85200i 0.488003 + 0.319004i
\(771\) −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 0.175173 0.984538i \(-0.443952\pi\)
0.984538 0.175173i \(-0.0560483\pi\)
\(774\) 27.4141 + 27.4141i 0.985379 + 0.985379i
\(775\) −0.175477 8.70157i −0.00630333 0.312569i
\(776\) 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
\(780\) 7.31037 + 10.7055i 0.261753 + 0.383319i
\(781\) −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
\(785\) 3.88747 + 2.54121i 0.138750 + 0.0906998i
\(786\) 13.4544i 0.479904i
\(787\) 8.98074 + 3.71995i 0.320129 + 0.132602i 0.536961 0.843607i \(-0.319572\pi\)
−0.216832 + 0.976209i \(0.569572\pi\)
\(788\) 5.82183 + 14.0551i 0.207394 + 0.500694i
\(789\) 23.2152 + 56.0464i 0.826482 + 1.99530i
\(790\) −3.76901 5.51944i −0.134095 0.196373i
\(791\) 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 \(-0.490663\pi\)
−0.999570 + 0.0293297i \(0.990663\pi\)
\(798\) 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
\(805\) 4.02447 + 19.2178i 0.141844 + 0.677337i
\(806\) −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 0.998584 0.0531895i \(-0.0169387\pi\)
−0.743716 + 0.668495i \(0.766939\pi\)
\(810\) −54.0991 + 11.3291i −1.90085 + 0.398065i
\(811\) −16.6667 + 40.2369i −0.585245 + 1.41291i 0.302757 + 0.953068i \(0.402093\pi\)
−0.888002 + 0.459840i \(0.847907\pi\)
\(812\) 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 −0.994422 0.105470i \(-0.966365\pi\)
0.777741 + 0.628584i \(0.216365\pi\)
\(822\) 26.1829 + 63.2110i 0.913232 + 2.20474i
\(823\) −9.99366 + 4.13951i −0.348357 + 0.144294i −0.550000 0.835165i \(-0.685372\pi\)
0.201642 + 0.979459i \(0.435372\pi\)
\(824\) 2.73584 + 2.73584i 0.0953074 + 0.0953074i
\(825\) −66.1593 + 28.9803i −2.30337 + 1.00897i
\(826\) −1.53032 3.69452i −0.0532467 0.128549i
\(827\) 16.7142 + 40.3516i 0.581210 + 1.40316i 0.891717 + 0.452593i \(0.149501\pi\)
−0.310507 + 0.950571i \(0.600499\pi\)
\(828\) −37.4814 15.5253i −1.30257 0.539542i
\(829\) 38.5554i 1.33909i −0.742774 0.669543i \(-0.766490\pi\)
0.742774 0.669543i \(-0.233510\pi\)
\(830\) −17.4020 + 26.6211i −0.604034 + 0.924033i
\(831\) 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
\(835\) 32.1372 21.9452i 1.11215 0.759446i
\(836\) 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 0.417894 0.908496i \(-0.362768\pi\)
0.937899 + 0.346908i \(0.112768\pi\)
\(840\) −2.40968 11.5067i −0.0831417 0.397020i
\(841\) 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
\(845\) −18.3389 11.9880i −0.630879 0.412401i
\(846\) 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
\(850\) −17.2696 + 11.2588i −0.592342 + 0.386175i
\(851\) −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 \(-0.906322\pi\)
0.881814 + 0.471597i \(0.156322\pi\)
\(854\) 15.3600i 0.525609i
\(855\) 3.12612 + 2.04352i 0.106911 + 0.0698870i
\(856\) 11.1802 4.63098i 0.382131 0.158284i
\(857\) −7.83237 + 3.24428i −0.267549 + 0.110822i −0.512425 0.858732i \(-0.671253\pi\)
0.244876 + 0.969554i \(0.421253\pi\)
\(858\) −18.2774 + 18.2774i −0.623980 + 0.623980i
\(859\) −25.6691 25.6691i −0.875818 0.875818i 0.117281 0.993099i \(-0.462582\pi\)
−0.993099 + 0.117281i \(0.962582\pi\)
\(860\) −2.37001 11.3173i −0.0808168 0.385918i
\(861\) −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 \(-0.718094\pi\)
−0.632798 + 0.774317i \(0.718094\pi\)
\(864\) 13.4622 + 5.57623i 0.457993 + 0.189707i
\(865\) −9.51833 + 6.49970i −0.323633 + 0.220996i
\(866\) −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
\(870\) −20.7605 + 31.7588i −0.703846 + 1.07672i
\(871\) 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
\(875\) −4.07595 17.6789i −0.137792 0.597656i
\(876\) −3.48890 3.48890i −0.117879 0.117879i
\(877\) 23.2054 9.61198i 0.783590 0.324573i 0.0452265 0.998977i \(-0.485599\pi\)
0.738363 + 0.674403i \(0.235599\pi\)
\(878\) −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 0.542990 0.839739i \(-0.317292\pi\)
−0.209833 + 0.977737i \(0.567292\pi\)
\(882\) 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 −0.563621 0.826033i \(-0.690592\pi\)
0.982634 0.185553i \(-0.0594078\pi\)
\(888\) 33.1253 1.11161
\(889\) −0.808152 + 1.95105i −0.0271045 + 0.0654362i
\(890\) 21.3830 4.47791i 0.716760 0.150100i
\(891\) −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
\(895\) −1.36030 6.49574i −0.0454699 0.217129i
\(896\) −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 \(-0.210706\pi\)
−0.992390 + 0.123133i \(0.960706\pi\)
\(908\) 0.354624 0.146890i 0.0117686 0.00487472i
\(909\) −58.8666 58.8666i −1.95248 1.95248i
\(910\) −3.66139 5.36183i −0.121374 0.177743i
\(911\) 13.9350 + 33.6421i 0.461687 + 1.11461i 0.967704 + 0.252088i \(0.0811174\pi\)
−0.506017 + 0.862524i \(0.668883\pi\)
\(912\) −0.276217 0.666847i −0.00914647 0.0220815i
\(913\) −58.5885 24.2682i −1.93900 0.803159i
\(914\) 3.92824i 0.129935i
\(915\) −57.3999 37.5219i −1.89758 1.24044i
\(916\) 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 \(0.382832\pi\)
\(920\) 6.82334 + 9.99228i 0.224959 + 0.329436i
\(921\) 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
\(925\) 51.1094 1.03068i 1.68047 0.0338886i
\(926\) 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 −0.966358 0.257200i \(-0.917200\pi\)
−0.501450 + 0.865186i \(0.667200\pi\)
\(930\) −10.5556 6.90010i −0.346131 0.226263i
\(931\) 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
\(935\) −28.4381 29.6813i −0.930024 0.970683i
\(936\) 13.4154 0.438495
\(937\) −33.7018 33.7018i −1.10099 1.10099i −0.994291 0.106699i \(-0.965972\pi\)
−0.106699 0.994291i \(-0.534028\pi\)
\(938\) −8.96367 + 21.6402i −0.292674 + 0.706578i
\(939\) 28.0348i 0.914881i
\(940\) −6.70512 + 10.2573i −0.218697 + 0.334556i
\(941\) −5.67849 + 2.35211i −0.185113 + 0.0766765i −0.473315 0.880893i \(-0.656943\pi\)
0.288201 + 0.957570i \(0.406943\pi\)
\(942\) 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
\(945\) 51.7502 10.8372i 1.68344 0.352536i
\(946\) 21.3005 8.82297i 0.692540 0.286859i
\(947\) −11.7699 4.87526i −0.382471 0.158425i 0.183160 0.983083i \(-0.441367\pi\)
−0.565631 + 0.824658i \(0.691367\pi\)
\(948\) −9.68415 −0.314527
\(949\) −2.51751 1.04279i −0.0817218 0.0338503i
\(950\) −0.446928 1.02029i −0.0145002 0.0331027i
\(951\) 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
\(955\) −29.4108 + 44.9917i −0.951710 + 1.45590i
\(956\) 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
\(960\) −4.08551 5.98294i −0.131859 0.193098i
\(961\) −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 \(-0.115740\pi\)
−0.355647 + 0.934620i \(0.615740\pi\)
\(968\) 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 −0.253499 0.967336i \(-0.581581\pi\)
0.967336 + 0.253499i \(0.0815814\pi\)
\(972\) −13.9195 + 33.6047i −0.446469 + 1.07787i
\(973\) −17.3987 −0.557776
\(974\) 6.35893 15.3518i 0.203753 0.491904i
\(975\) 28.9811 0.584439i 0.928139 0.0187170i
\(976\) 3.62231 + 8.74502i 0.115947 + 0.279921i
\(977\) −1.83787 + 1.83787i −0.0587988 + 0.0587988i −0.735895 0.677096i \(-0.763238\pi\)
0.677096 + 0.735895i \(0.263238\pi\)
\(978\) 4.74652 4.74652i 0.151777 0.151777i
\(979\) 16.6701 + 40.2453i 0.532780 + 1.28624i
\(980\) −2.00138 9.55703i −0.0639317 0.305288i
\(981\) −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 \(-0.999299\pi\)
0.708663 + 0.705547i \(0.249299\pi\)
\(984\) −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 −0.900739 0.434360i \(-0.856975\pi\)
0.944058 + 0.329780i \(0.106975\pi\)
\(992\) 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
\(995\) −14.8336 + 10.1293i −0.470256 + 0.321119i
\(996\) 17.6352 + 42.5752i 0.558794 + 1.34905i
\(997\) −6.90834 16.6782i −0.218789 0.528204i 0.775932 0.630816i \(-0.217280\pi\)
−0.994721 + 0.102612i \(0.967280\pi\)
\(998\) 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.b.9.5 yes 20
5.2 odd 4 850.2.l.h.451.1 20
5.3 odd 4 850.2.l.i.451.5 20
5.4 even 2 170.2.n.a.9.1 20
17.2 even 8 170.2.n.a.19.1 yes 20
85.2 odd 8 850.2.l.h.801.1 20
85.19 even 8 inner 170.2.n.b.19.5 yes 20
85.53 odd 8 850.2.l.i.801.5 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
170.2.n.a.9.1 20 5.4 even 2
170.2.n.a.19.1 yes 20 17.2 even 8
170.2.n.b.9.5 yes 20 1.1 even 1 trivial
170.2.n.b.19.5 yes 20 85.19 even 8 inner
850.2.l.h.451.1 20 5.2 odd 4
850.2.l.h.801.1 20 85.2 odd 8
850.2.l.i.451.5 20 5.3 odd 4
850.2.l.i.801.5 20 85.53 odd 8