Properties

Label 1380.2.p.b.91.17
Level $1380$
Weight $2$
Character 1380.91
Analytic conductor $11.019$
Analytic rank $0$
Dimension $48$
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] = [1380,2,Mod(91,1380)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1380, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1380.91");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1380.p (of order \(2\), degree \(1\), 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: \(11.0193554789\)
Analytic rank: \(0\)
Dimension: \(48\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 91.17
Character \(\chi\) \(=\) 1380.91
Dual form 1380.2.p.b.91.18

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.698077 - 1.22991i) q^{2} -1.00000i q^{3} +(-1.02538 + 1.71715i) q^{4} +1.00000i q^{5} +(-1.22991 + 0.698077i) q^{6} -0.344556 q^{7} +(2.82774 + 0.0624257i) q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+(-0.698077 - 1.22991i) q^{2} -1.00000i q^{3} +(-1.02538 + 1.71715i) q^{4} +1.00000i q^{5} +(-1.22991 + 0.698077i) q^{6} -0.344556 q^{7} +(2.82774 + 0.0624257i) q^{8} -1.00000 q^{9} +(1.22991 - 0.698077i) q^{10} -1.11761 q^{11} +(1.71715 + 1.02538i) q^{12} -4.23633 q^{13} +(0.240526 + 0.423774i) q^{14} +1.00000 q^{15} +(-1.89720 - 3.52145i) q^{16} -3.31506i q^{17} +(0.698077 + 1.22991i) q^{18} +1.10641 q^{19} +(-1.71715 - 1.02538i) q^{20} +0.344556i q^{21} +(0.780176 + 1.37456i) q^{22} +(4.54924 + 1.51804i) q^{23} +(0.0624257 - 2.82774i) q^{24} -1.00000 q^{25} +(2.95729 + 5.21033i) q^{26} +1.00000i q^{27} +(0.353300 - 0.591654i) q^{28} +0.696902 q^{29} +(-0.698077 - 1.22991i) q^{30} +1.78017i q^{31} +(-3.00669 + 4.79164i) q^{32} +1.11761i q^{33} +(-4.07723 + 2.31416i) q^{34} -0.344556i q^{35} +(1.02538 - 1.71715i) q^{36} +8.80960i q^{37} +(-0.772359 - 1.36079i) q^{38} +4.23633i q^{39} +(-0.0624257 + 2.82774i) q^{40} -9.74007 q^{41} +(0.423774 - 0.240526i) q^{42} +8.82654 q^{43} +(1.14597 - 1.91910i) q^{44} -1.00000i q^{45} +(-1.30866 - 6.65488i) q^{46} +8.35120i q^{47} +(-3.52145 + 1.89720i) q^{48} -6.88128 q^{49} +(0.698077 + 1.22991i) q^{50} -3.31506 q^{51} +(4.34384 - 7.27442i) q^{52} +12.1249i q^{53} +(1.22991 - 0.698077i) q^{54} -1.11761i q^{55} +(-0.974314 - 0.0215091i) q^{56} -1.10641i q^{57} +(-0.486491 - 0.857130i) q^{58} +14.6024i q^{59} +(-1.02538 + 1.71715i) q^{60} -7.06741i q^{61} +(2.18946 - 1.24270i) q^{62} +0.344556 q^{63} +(7.99221 + 0.353047i) q^{64} -4.23633i q^{65} +(1.37456 - 0.780176i) q^{66} -2.20028 q^{67} +(5.69244 + 3.39919i) q^{68} +(1.51804 - 4.54924i) q^{69} +(-0.423774 + 0.240526i) q^{70} +16.5411i q^{71} +(-2.82774 - 0.0624257i) q^{72} +2.68382 q^{73} +(10.8350 - 6.14977i) q^{74} +1.00000i q^{75} +(-1.13449 + 1.89987i) q^{76} +0.385078 q^{77} +(5.21033 - 2.95729i) q^{78} -15.3762 q^{79} +(3.52145 - 1.89720i) q^{80} +1.00000 q^{81} +(6.79932 + 11.9795i) q^{82} +17.0787 q^{83} +(-0.591654 - 0.353300i) q^{84} +3.31506 q^{85} +(-6.16160 - 10.8559i) q^{86} -0.696902i q^{87} +(-3.16030 - 0.0697675i) q^{88} +11.9834i q^{89} +(-1.22991 + 0.698077i) q^{90} +1.45965 q^{91} +(-7.27139 + 6.25515i) q^{92} +1.78017 q^{93} +(10.2713 - 5.82978i) q^{94} +1.10641i q^{95} +(4.79164 + 3.00669i) q^{96} +9.50481i q^{97} +(4.80366 + 8.46339i) q^{98} +1.11761 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q - 4 q^{2} - 2 q^{4} - 2 q^{6} - 4 q^{8} - 48 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 48 q - 4 q^{2} - 2 q^{4} - 2 q^{6} - 4 q^{8} - 48 q^{9} + 2 q^{10} - 20 q^{14} + 48 q^{15} - 6 q^{16} + 4 q^{18} - 16 q^{19} - 28 q^{22} - 4 q^{23} + 2 q^{24} - 48 q^{25} - 20 q^{26} + 32 q^{29} - 4 q^{30} + 16 q^{32} + 28 q^{34} + 2 q^{36} - 2 q^{40} - 8 q^{41} + 26 q^{46} + 16 q^{48} + 40 q^{49} + 4 q^{50} - 16 q^{51} - 16 q^{52} + 2 q^{54} - 40 q^{56} - 8 q^{58} - 2 q^{60} + 24 q^{62} - 26 q^{64} + 48 q^{67} + 44 q^{68} - 8 q^{69} + 4 q^{72} - 20 q^{74} + 64 q^{76} + 32 q^{77} + 64 q^{79} - 16 q^{80} + 48 q^{81} - 20 q^{82} + 16 q^{85} + 40 q^{86} - 2 q^{90} - 28 q^{92} - 32 q^{94} - 2 q^{96} + 24 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1380\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(691\) \(1201\)
\(\chi(n)\) \(1\) \(1\) \(-1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.698077 1.22991i −0.493615 0.869681i
\(3\) 1.00000i 0.577350i
\(4\) −1.02538 + 1.71715i −0.512689 + 0.858574i
\(5\) 1.00000i 0.447214i
\(6\) −1.22991 + 0.698077i −0.502110 + 0.284989i
\(7\) −0.344556 −0.130230 −0.0651149 0.997878i \(-0.520741\pi\)
−0.0651149 + 0.997878i \(0.520741\pi\)
\(8\) 2.82774 + 0.0624257i 0.999756 + 0.0220708i
\(9\) −1.00000 −0.333333
\(10\) 1.22991 0.698077i 0.388933 0.220751i
\(11\) −1.11761 −0.336972 −0.168486 0.985704i \(-0.553888\pi\)
−0.168486 + 0.985704i \(0.553888\pi\)
\(12\) 1.71715 + 1.02538i 0.495698 + 0.296001i
\(13\) −4.23633 −1.17495 −0.587474 0.809243i \(-0.699878\pi\)
−0.587474 + 0.809243i \(0.699878\pi\)
\(14\) 0.240526 + 0.423774i 0.0642834 + 0.113258i
\(15\) 1.00000 0.258199
\(16\) −1.89720 3.52145i −0.474300 0.880363i
\(17\) 3.31506i 0.804019i −0.915635 0.402010i \(-0.868312\pi\)
0.915635 0.402010i \(-0.131688\pi\)
\(18\) 0.698077 + 1.22991i 0.164538 + 0.289894i
\(19\) 1.10641 0.253828 0.126914 0.991914i \(-0.459493\pi\)
0.126914 + 0.991914i \(0.459493\pi\)
\(20\) −1.71715 1.02538i −0.383966 0.229282i
\(21\) 0.344556i 0.0751882i
\(22\) 0.780176 + 1.37456i 0.166334 + 0.293058i
\(23\) 4.54924 + 1.51804i 0.948582 + 0.316533i
\(24\) 0.0624257 2.82774i 0.0127426 0.577210i
\(25\) −1.00000 −0.200000
\(26\) 2.95729 + 5.21033i 0.579971 + 1.02183i
\(27\) 1.00000i 0.192450i
\(28\) 0.353300 0.591654i 0.0667674 0.111812i
\(29\) 0.696902 0.129411 0.0647057 0.997904i \(-0.479389\pi\)
0.0647057 + 0.997904i \(0.479389\pi\)
\(30\) −0.698077 1.22991i −0.127451 0.224551i
\(31\) 1.78017i 0.319728i 0.987139 + 0.159864i \(0.0511056\pi\)
−0.987139 + 0.159864i \(0.948894\pi\)
\(32\) −3.00669 + 4.79164i −0.531514 + 0.847050i
\(33\) 1.11761i 0.194551i
\(34\) −4.07723 + 2.31416i −0.699240 + 0.396876i
\(35\) 0.344556i 0.0582406i
\(36\) 1.02538 1.71715i 0.170896 0.286191i
\(37\) 8.80960i 1.44829i 0.689649 + 0.724144i \(0.257765\pi\)
−0.689649 + 0.724144i \(0.742235\pi\)
\(38\) −0.772359 1.36079i −0.125293 0.220749i
\(39\) 4.23633i 0.678356i
\(40\) −0.0624257 + 2.82774i −0.00987037 + 0.447105i
\(41\) −9.74007 −1.52114 −0.760572 0.649254i \(-0.775081\pi\)
−0.760572 + 0.649254i \(0.775081\pi\)
\(42\) 0.423774 0.240526i 0.0653898 0.0371140i
\(43\) 8.82654 1.34603 0.673017 0.739627i \(-0.264998\pi\)
0.673017 + 0.739627i \(0.264998\pi\)
\(44\) 1.14597 1.91910i 0.172762 0.289315i
\(45\) 1.00000i 0.149071i
\(46\) −1.30866 6.65488i −0.192951 0.981208i
\(47\) 8.35120i 1.21815i 0.793113 + 0.609074i \(0.208459\pi\)
−0.793113 + 0.609074i \(0.791541\pi\)
\(48\) −3.52145 + 1.89720i −0.508278 + 0.273837i
\(49\) −6.88128 −0.983040
\(50\) 0.698077 + 1.22991i 0.0987229 + 0.173936i
\(51\) −3.31506 −0.464201
\(52\) 4.34384 7.27442i 0.602383 1.00878i
\(53\) 12.1249i 1.66548i 0.553663 + 0.832741i \(0.313229\pi\)
−0.553663 + 0.832741i \(0.686771\pi\)
\(54\) 1.22991 0.698077i 0.167370 0.0949962i
\(55\) 1.11761i 0.150698i
\(56\) −0.974314 0.0215091i −0.130198 0.00287428i
\(57\) 1.10641i 0.146548i
\(58\) −0.486491 0.857130i −0.0638794 0.112547i
\(59\) 14.6024i 1.90107i 0.310623 + 0.950533i \(0.399462\pi\)
−0.310623 + 0.950533i \(0.600538\pi\)
\(60\) −1.02538 + 1.71715i −0.132376 + 0.221683i
\(61\) 7.06741i 0.904889i −0.891793 0.452444i \(-0.850552\pi\)
0.891793 0.452444i \(-0.149448\pi\)
\(62\) 2.18946 1.24270i 0.278061 0.157822i
\(63\) 0.344556 0.0434100
\(64\) 7.99221 + 0.353047i 0.999026 + 0.0441309i
\(65\) 4.23633i 0.525453i
\(66\) 1.37456 0.780176i 0.169197 0.0960331i
\(67\) −2.20028 −0.268807 −0.134403 0.990927i \(-0.542912\pi\)
−0.134403 + 0.990927i \(0.542912\pi\)
\(68\) 5.69244 + 3.39919i 0.690310 + 0.412212i
\(69\) 1.51804 4.54924i 0.182750 0.547664i
\(70\) −0.423774 + 0.240526i −0.0506507 + 0.0287484i
\(71\) 16.5411i 1.96306i 0.191301 + 0.981531i \(0.438729\pi\)
−0.191301 + 0.981531i \(0.561271\pi\)
\(72\) −2.82774 0.0624257i −0.333252 0.00735694i
\(73\) 2.68382 0.314118 0.157059 0.987589i \(-0.449799\pi\)
0.157059 + 0.987589i \(0.449799\pi\)
\(74\) 10.8350 6.14977i 1.25955 0.714897i
\(75\) 1.00000i 0.115470i
\(76\) −1.13449 + 1.89987i −0.130135 + 0.217930i
\(77\) 0.385078 0.0438838
\(78\) 5.21033 2.95729i 0.589953 0.334847i
\(79\) −15.3762 −1.72996 −0.864979 0.501808i \(-0.832669\pi\)
−0.864979 + 0.501808i \(0.832669\pi\)
\(80\) 3.52145 1.89720i 0.393710 0.212113i
\(81\) 1.00000 0.111111
\(82\) 6.79932 + 11.9795i 0.750859 + 1.32291i
\(83\) 17.0787 1.87463 0.937313 0.348489i \(-0.113305\pi\)
0.937313 + 0.348489i \(0.113305\pi\)
\(84\) −0.591654 0.353300i −0.0645547 0.0385482i
\(85\) 3.31506 0.359568
\(86\) −6.16160 10.8559i −0.664422 1.17062i
\(87\) 0.696902i 0.0747158i
\(88\) −3.16030 0.0697675i −0.336890 0.00743724i
\(89\) 11.9834i 1.27023i 0.772416 + 0.635117i \(0.219048\pi\)
−0.772416 + 0.635117i \(0.780952\pi\)
\(90\) −1.22991 + 0.698077i −0.129644 + 0.0735837i
\(91\) 1.45965 0.153013
\(92\) −7.27139 + 6.25515i −0.758094 + 0.652145i
\(93\) 1.78017 0.184595
\(94\) 10.2713 5.82978i 1.05940 0.601296i
\(95\) 1.10641i 0.113515i
\(96\) 4.79164 + 3.00669i 0.489044 + 0.306870i
\(97\) 9.50481i 0.965068i 0.875877 + 0.482534i \(0.160283\pi\)
−0.875877 + 0.482534i \(0.839717\pi\)
\(98\) 4.80366 + 8.46339i 0.485243 + 0.854931i
\(99\) 1.11761 0.112324
\(100\) 1.02538 1.71715i 0.102538 0.171715i
\(101\) 8.14918 0.810874 0.405437 0.914123i \(-0.367119\pi\)
0.405437 + 0.914123i \(0.367119\pi\)
\(102\) 2.31416 + 4.07723i 0.229136 + 0.403706i
\(103\) 3.46429 0.341347 0.170673 0.985328i \(-0.445406\pi\)
0.170673 + 0.985328i \(0.445406\pi\)
\(104\) −11.9792 0.264456i −1.17466 0.0259321i
\(105\) −0.344556 −0.0336252
\(106\) 14.9126 8.46410i 1.44844 0.822106i
\(107\) −12.1330 −1.17294 −0.586470 0.809971i \(-0.699483\pi\)
−0.586470 + 0.809971i \(0.699483\pi\)
\(108\) −1.71715 1.02538i −0.165233 0.0986671i
\(109\) 16.4638i 1.57695i −0.615069 0.788473i \(-0.710872\pi\)
0.615069 0.788473i \(-0.289128\pi\)
\(110\) −1.37456 + 0.780176i −0.131059 + 0.0743869i
\(111\) 8.80960 0.836170
\(112\) 0.653691 + 1.21334i 0.0617680 + 0.114650i
\(113\) 16.1919i 1.52320i −0.648045 0.761602i \(-0.724413\pi\)
0.648045 0.761602i \(-0.275587\pi\)
\(114\) −1.36079 + 0.772359i −0.127450 + 0.0723380i
\(115\) −1.51804 + 4.54924i −0.141558 + 0.424219i
\(116\) −0.714588 + 1.19668i −0.0663478 + 0.111109i
\(117\) 4.23633 0.391649
\(118\) 17.9597 10.1936i 1.65332 0.938394i
\(119\) 1.14222i 0.104707i
\(120\) 2.82774 + 0.0624257i 0.258136 + 0.00569866i
\(121\) −9.75095 −0.886450
\(122\) −8.69230 + 4.93359i −0.786964 + 0.446666i
\(123\) 9.74007i 0.878233i
\(124\) −3.05682 1.82535i −0.274510 0.163921i
\(125\) 1.00000i 0.0894427i
\(126\) −0.240526 0.423774i −0.0214278 0.0377528i
\(127\) 0.639825i 0.0567753i −0.999597 0.0283877i \(-0.990963\pi\)
0.999597 0.0283877i \(-0.00903729\pi\)
\(128\) −5.14495 10.0762i −0.454754 0.890617i
\(129\) 8.82654i 0.777133i
\(130\) −5.21033 + 2.95729i −0.456976 + 0.259371i
\(131\) 1.67592i 0.146425i −0.997316 0.0732127i \(-0.976675\pi\)
0.997316 0.0732127i \(-0.0233252\pi\)
\(132\) −1.91910 1.14597i −0.167036 0.0997440i
\(133\) −0.381220 −0.0330560
\(134\) 1.53596 + 2.70615i 0.132687 + 0.233776i
\(135\) −1.00000 −0.0860663
\(136\) 0.206945 9.37411i 0.0177454 0.803823i
\(137\) 10.2084i 0.872160i 0.899908 + 0.436080i \(0.143634\pi\)
−0.899908 + 0.436080i \(0.856366\pi\)
\(138\) −6.65488 + 1.30866i −0.566501 + 0.111400i
\(139\) 8.48317i 0.719533i −0.933042 0.359767i \(-0.882856\pi\)
0.933042 0.359767i \(-0.117144\pi\)
\(140\) 0.591654 + 0.353300i 0.0500039 + 0.0298593i
\(141\) 8.35120 0.703298
\(142\) 20.3441 11.5469i 1.70724 0.968997i
\(143\) 4.73456 0.395924
\(144\) 1.89720 + 3.52145i 0.158100 + 0.293454i
\(145\) 0.696902i 0.0578746i
\(146\) −1.87351 3.30087i −0.155053 0.273182i
\(147\) 6.88128i 0.567559i
\(148\) −15.1274 9.03317i −1.24346 0.742522i
\(149\) 8.00893i 0.656117i −0.944657 0.328058i \(-0.893606\pi\)
0.944657 0.328058i \(-0.106394\pi\)
\(150\) 1.22991 0.698077i 0.100422 0.0569977i
\(151\) 15.9200i 1.29555i −0.761832 0.647774i \(-0.775700\pi\)
0.761832 0.647774i \(-0.224300\pi\)
\(152\) 3.12864 + 0.0690684i 0.253766 + 0.00560219i
\(153\) 3.31506i 0.268006i
\(154\) −0.268814 0.473613i −0.0216617 0.0381649i
\(155\) −1.78017 −0.142987
\(156\) −7.27442 4.34384i −0.582419 0.347786i
\(157\) 11.4730i 0.915644i 0.889044 + 0.457822i \(0.151370\pi\)
−0.889044 + 0.457822i \(0.848630\pi\)
\(158\) 10.7338 + 18.9114i 0.853933 + 1.50451i
\(159\) 12.1249 0.961566
\(160\) −4.79164 3.00669i −0.378812 0.237700i
\(161\) −1.56747 0.523049i −0.123534 0.0412220i
\(162\) −0.698077 1.22991i −0.0548461 0.0966312i
\(163\) 11.6276i 0.910746i −0.890301 0.455373i \(-0.849506\pi\)
0.890301 0.455373i \(-0.150494\pi\)
\(164\) 9.98725 16.7251i 0.779874 1.30601i
\(165\) −1.11761 −0.0870057
\(166\) −11.9222 21.0053i −0.925343 1.63033i
\(167\) 18.3392i 1.41913i 0.704641 + 0.709564i \(0.251108\pi\)
−0.704641 + 0.709564i \(0.748892\pi\)
\(168\) −0.0215091 + 0.974314i −0.00165947 + 0.0751699i
\(169\) 4.94653 0.380502
\(170\) −2.31416 4.07723i −0.177488 0.312710i
\(171\) −1.10641 −0.0846093
\(172\) −9.05054 + 15.1565i −0.690097 + 1.15567i
\(173\) 7.02511 0.534109 0.267055 0.963681i \(-0.413950\pi\)
0.267055 + 0.963681i \(0.413950\pi\)
\(174\) −0.857130 + 0.486491i −0.0649788 + 0.0368808i
\(175\) 0.344556 0.0260460
\(176\) 2.12033 + 3.93561i 0.159826 + 0.296657i
\(177\) 14.6024 1.09758
\(178\) 14.7385 8.36531i 1.10470 0.627006i
\(179\) 3.75048i 0.280324i −0.990129 0.140162i \(-0.955238\pi\)
0.990129 0.140162i \(-0.0447624\pi\)
\(180\) 1.71715 + 1.02538i 0.127989 + 0.0764272i
\(181\) 9.93221i 0.738255i −0.929379 0.369128i \(-0.879657\pi\)
0.929379 0.369128i \(-0.120343\pi\)
\(182\) −1.01895 1.79525i −0.0755296 0.133073i
\(183\) −7.06741 −0.522438
\(184\) 12.7693 + 4.57661i 0.941364 + 0.337392i
\(185\) −8.80960 −0.647694
\(186\) −1.24270 2.18946i −0.0911188 0.160539i
\(187\) 3.70493i 0.270932i
\(188\) −14.3403 8.56314i −1.04587 0.624531i
\(189\) 0.344556i 0.0250627i
\(190\) 1.36079 0.772359i 0.0987220 0.0560328i
\(191\) −1.74084 −0.125963 −0.0629813 0.998015i \(-0.520061\pi\)
−0.0629813 + 0.998015i \(0.520061\pi\)
\(192\) 0.353047 7.99221i 0.0254790 0.576788i
\(193\) −8.74766 −0.629670 −0.314835 0.949146i \(-0.601949\pi\)
−0.314835 + 0.949146i \(0.601949\pi\)
\(194\) 11.6901 6.63509i 0.839301 0.476372i
\(195\) −4.23633 −0.303370
\(196\) 7.05591 11.8162i 0.503994 0.844013i
\(197\) −7.94495 −0.566054 −0.283027 0.959112i \(-0.591339\pi\)
−0.283027 + 0.959112i \(0.591339\pi\)
\(198\) −0.780176 1.37456i −0.0554447 0.0976859i
\(199\) 12.6767 0.898625 0.449313 0.893375i \(-0.351669\pi\)
0.449313 + 0.893375i \(0.351669\pi\)
\(200\) −2.82774 0.0624257i −0.199951 0.00441416i
\(201\) 2.20028i 0.155196i
\(202\) −5.68875 10.0228i −0.400259 0.705201i
\(203\) −0.240122 −0.0168532
\(204\) 3.39919 5.69244i 0.237991 0.398551i
\(205\) 9.74007i 0.680276i
\(206\) −2.41834 4.26078i −0.168494 0.296863i
\(207\) −4.54924 1.51804i −0.316194 0.105511i
\(208\) 8.03717 + 14.9181i 0.557278 + 1.03438i
\(209\) −1.23653 −0.0855328
\(210\) 0.240526 + 0.423774i 0.0165979 + 0.0292432i
\(211\) 14.8224i 1.02041i 0.860051 + 0.510207i \(0.170431\pi\)
−0.860051 + 0.510207i \(0.829569\pi\)
\(212\) −20.8202 12.4326i −1.42994 0.853874i
\(213\) 16.5411 1.13337
\(214\) 8.46975 + 14.9225i 0.578980 + 1.02008i
\(215\) 8.82654i 0.601965i
\(216\) −0.0624257 + 2.82774i −0.00424753 + 0.192403i
\(217\) 0.613368i 0.0416381i
\(218\) −20.2491 + 11.4930i −1.37144 + 0.778404i
\(219\) 2.68382i 0.181356i
\(220\) 1.91910 + 1.14597i 0.129386 + 0.0772614i
\(221\) 14.0437i 0.944680i
\(222\) −6.14977 10.8350i −0.412746 0.727201i
\(223\) 2.35237i 0.157526i 0.996893 + 0.0787630i \(0.0250970\pi\)
−0.996893 + 0.0787630i \(0.974903\pi\)
\(224\) 1.03597 1.65099i 0.0692189 0.110311i
\(225\) 1.00000 0.0666667
\(226\) −19.9146 + 11.3032i −1.32470 + 0.751876i
\(227\) −8.45514 −0.561187 −0.280594 0.959827i \(-0.590531\pi\)
−0.280594 + 0.959827i \(0.590531\pi\)
\(228\) 1.89987 + 1.13449i 0.125822 + 0.0751333i
\(229\) 22.5195i 1.48813i 0.668108 + 0.744065i \(0.267105\pi\)
−0.668108 + 0.744065i \(0.732895\pi\)
\(230\) 6.65488 1.30866i 0.438810 0.0862904i
\(231\) 0.385078i 0.0253363i
\(232\) 1.97066 + 0.0435046i 0.129380 + 0.00285622i
\(233\) −15.1809 −0.994536 −0.497268 0.867597i \(-0.665663\pi\)
−0.497268 + 0.867597i \(0.665663\pi\)
\(234\) −2.95729 5.21033i −0.193324 0.340610i
\(235\) −8.35120 −0.544772
\(236\) −25.0744 14.9729i −1.63221 0.974656i
\(237\) 15.3762i 0.998792i
\(238\) 1.40483 0.797358i 0.0910619 0.0516851i
\(239\) 5.81077i 0.375867i 0.982182 + 0.187934i \(0.0601790\pi\)
−0.982182 + 0.187934i \(0.939821\pi\)
\(240\) −1.89720 3.52145i −0.122464 0.227309i
\(241\) 4.01399i 0.258564i 0.991608 + 0.129282i \(0.0412672\pi\)
−0.991608 + 0.129282i \(0.958733\pi\)
\(242\) 6.80691 + 11.9928i 0.437565 + 0.770929i
\(243\) 1.00000i 0.0641500i
\(244\) 12.1358 + 7.24676i 0.776914 + 0.463926i
\(245\) 6.88128i 0.439629i
\(246\) 11.9795 6.79932i 0.763782 0.433509i
\(247\) −4.68712 −0.298234
\(248\) −0.111128 + 5.03385i −0.00705666 + 0.319650i
\(249\) 17.0787i 1.08232i
\(250\) −1.22991 + 0.698077i −0.0777866 + 0.0441502i
\(251\) 14.1494 0.893104 0.446552 0.894758i \(-0.352652\pi\)
0.446552 + 0.894758i \(0.352652\pi\)
\(252\) −0.353300 + 0.591654i −0.0222558 + 0.0372707i
\(253\) −5.08427 1.69657i −0.319645 0.106663i
\(254\) −0.786930 + 0.446647i −0.0493764 + 0.0280251i
\(255\) 3.31506i 0.207597i
\(256\) −8.80127 + 13.3618i −0.550079 + 0.835112i
\(257\) 3.78305 0.235980 0.117990 0.993015i \(-0.462355\pi\)
0.117990 + 0.993015i \(0.462355\pi\)
\(258\) −10.8559 + 6.16160i −0.675858 + 0.383604i
\(259\) 3.03540i 0.188610i
\(260\) 7.27442 + 4.34384i 0.451140 + 0.269394i
\(261\) −0.696902 −0.0431372
\(262\) −2.06123 + 1.16992i −0.127343 + 0.0722778i
\(263\) 11.5227 0.710520 0.355260 0.934768i \(-0.384392\pi\)
0.355260 + 0.934768i \(0.384392\pi\)
\(264\) −0.0697675 + 3.16030i −0.00429389 + 0.194503i
\(265\) −12.1249 −0.744826
\(266\) 0.266121 + 0.468868i 0.0163169 + 0.0287481i
\(267\) 11.9834 0.733370
\(268\) 2.25612 3.77820i 0.137814 0.230790i
\(269\) −25.4362 −1.55087 −0.775435 0.631428i \(-0.782469\pi\)
−0.775435 + 0.631428i \(0.782469\pi\)
\(270\) 0.698077 + 1.22991i 0.0424836 + 0.0748502i
\(271\) 6.86367i 0.416938i 0.978029 + 0.208469i \(0.0668480\pi\)
−0.978029 + 0.208469i \(0.933152\pi\)
\(272\) −11.6738 + 6.28932i −0.707829 + 0.381346i
\(273\) 1.45965i 0.0883423i
\(274\) 12.5554 7.12622i 0.758501 0.430511i
\(275\) 1.11761 0.0673943
\(276\) 6.25515 + 7.27139i 0.376516 + 0.437686i
\(277\) −16.6149 −0.998292 −0.499146 0.866518i \(-0.666353\pi\)
−0.499146 + 0.866518i \(0.666353\pi\)
\(278\) −10.4336 + 5.92190i −0.625764 + 0.355172i
\(279\) 1.78017i 0.106576i
\(280\) 0.0215091 0.974314i 0.00128542 0.0582264i
\(281\) 6.82628i 0.407221i −0.979052 0.203611i \(-0.934732\pi\)
0.979052 0.203611i \(-0.0652677\pi\)
\(282\) −5.82978 10.2713i −0.347158 0.611645i
\(283\) 0.162801 0.00967753 0.00483876 0.999988i \(-0.498460\pi\)
0.00483876 + 0.999988i \(0.498460\pi\)
\(284\) −28.4035 16.9608i −1.68544 1.00644i
\(285\) 1.10641 0.0655381
\(286\) −3.30509 5.82311i −0.195434 0.344327i
\(287\) 3.35600 0.198098
\(288\) 3.00669 4.79164i 0.177171 0.282350i
\(289\) 6.01041 0.353553
\(290\) 0.857130 0.486491i 0.0503324 0.0285677i
\(291\) 9.50481 0.557182
\(292\) −2.75193 + 4.60852i −0.161045 + 0.269693i
\(293\) 14.9580i 0.873854i 0.899497 + 0.436927i \(0.143933\pi\)
−0.899497 + 0.436927i \(0.856067\pi\)
\(294\) 8.46339 4.80366i 0.493595 0.280155i
\(295\) −14.6024 −0.850183
\(296\) −0.549945 + 24.9112i −0.0319649 + 1.44794i
\(297\) 1.11761i 0.0648502i
\(298\) −9.85029 + 5.59084i −0.570612 + 0.323869i
\(299\) −19.2721 6.43092i −1.11453 0.371910i
\(300\) −1.71715 1.02538i −0.0991396 0.0592002i
\(301\) −3.04123 −0.175294
\(302\) −19.5802 + 11.1134i −1.12671 + 0.639502i
\(303\) 8.14918i 0.468158i
\(304\) −2.09908 3.89617i −0.120391 0.223461i
\(305\) 7.06741 0.404678
\(306\) 4.07723 2.31416i 0.233080 0.132292i
\(307\) 8.69634i 0.496326i −0.968718 0.248163i \(-0.920173\pi\)
0.968718 0.248163i \(-0.0798269\pi\)
\(308\) −0.394851 + 0.661237i −0.0224987 + 0.0376775i
\(309\) 3.46429i 0.197077i
\(310\) 1.24270 + 2.18946i 0.0705803 + 0.124353i
\(311\) 5.74489i 0.325763i −0.986646 0.162881i \(-0.947921\pi\)
0.986646 0.162881i \(-0.0520788\pi\)
\(312\) −0.264456 + 11.9792i −0.0149719 + 0.678191i
\(313\) 0.954025i 0.0539247i −0.999636 0.0269623i \(-0.991417\pi\)
0.999636 0.0269623i \(-0.00858342\pi\)
\(314\) 14.1108 8.00902i 0.796318 0.451975i
\(315\) 0.344556i 0.0194135i
\(316\) 15.7664 26.4032i 0.886931 1.48530i
\(317\) 3.33114 0.187095 0.0935476 0.995615i \(-0.470179\pi\)
0.0935476 + 0.995615i \(0.470179\pi\)
\(318\) −8.46410 14.9126i −0.474643 0.836255i
\(319\) −0.778864 −0.0436080
\(320\) −0.353047 + 7.99221i −0.0197359 + 0.446778i
\(321\) 12.1330i 0.677197i
\(322\) 0.450906 + 2.29298i 0.0251280 + 0.127783i
\(323\) 3.66781i 0.204082i
\(324\) −1.02538 + 1.71715i −0.0569654 + 0.0953972i
\(325\) 4.23633 0.234990
\(326\) −14.3010 + 8.11697i −0.792058 + 0.449558i
\(327\) −16.4638 −0.910451
\(328\) −27.5424 0.608031i −1.52077 0.0335729i
\(329\) 2.87746i 0.158639i
\(330\) 0.780176 + 1.37456i 0.0429473 + 0.0756672i
\(331\) 21.3748i 1.17486i −0.809274 0.587431i \(-0.800139\pi\)
0.809274 0.587431i \(-0.199861\pi\)
\(332\) −17.5121 + 29.3266i −0.961100 + 1.60951i
\(333\) 8.80960i 0.482763i
\(334\) 22.5556 12.8021i 1.23419 0.700502i
\(335\) 2.20028i 0.120214i
\(336\) 1.21334 0.653691i 0.0661930 0.0356618i
\(337\) 23.7780i 1.29527i 0.761950 + 0.647636i \(0.224242\pi\)
−0.761950 + 0.647636i \(0.775758\pi\)
\(338\) −3.45306 6.08381i −0.187821 0.330915i
\(339\) −16.1919 −0.879422
\(340\) −3.39919 + 5.69244i −0.184347 + 0.308716i
\(341\) 1.98953i 0.107739i
\(342\) 0.772359 + 1.36079i 0.0417644 + 0.0735831i
\(343\) 4.78288 0.258251
\(344\) 24.9591 + 0.551003i 1.34571 + 0.0297081i
\(345\) 4.54924 + 1.51804i 0.244923 + 0.0817285i
\(346\) −4.90406 8.64028i −0.263644 0.464504i
\(347\) 27.0291i 1.45100i −0.688223 0.725499i \(-0.741609\pi\)
0.688223 0.725499i \(-0.258391\pi\)
\(348\) 1.19668 + 0.714588i 0.0641490 + 0.0383059i
\(349\) −15.3747 −0.822986 −0.411493 0.911413i \(-0.634993\pi\)
−0.411493 + 0.911413i \(0.634993\pi\)
\(350\) −0.240526 0.423774i −0.0128567 0.0226517i
\(351\) 4.23633i 0.226119i
\(352\) 3.36031 5.35517i 0.179105 0.285432i
\(353\) −14.9106 −0.793611 −0.396806 0.917903i \(-0.629881\pi\)
−0.396806 + 0.917903i \(0.629881\pi\)
\(354\) −10.1936 17.9597i −0.541782 0.954545i
\(355\) −16.5411 −0.877908
\(356\) −20.5772 12.2875i −1.09059 0.651235i
\(357\) 1.14222 0.0604528
\(358\) −4.61277 + 2.61812i −0.243792 + 0.138372i
\(359\) 34.0479 1.79698 0.898491 0.438993i \(-0.144665\pi\)
0.898491 + 0.438993i \(0.144665\pi\)
\(360\) 0.0624257 2.82774i 0.00329012 0.149035i
\(361\) −17.7759 −0.935571
\(362\) −12.2158 + 6.93344i −0.642046 + 0.364414i
\(363\) 9.75095i 0.511792i
\(364\) −1.49670 + 2.50644i −0.0784482 + 0.131373i
\(365\) 2.68382i 0.140478i
\(366\) 4.93359 + 8.69230i 0.257883 + 0.454354i
\(367\) −7.09991 −0.370612 −0.185306 0.982681i \(-0.559328\pi\)
−0.185306 + 0.982681i \(0.559328\pi\)
\(368\) −3.28511 18.8999i −0.171248 0.985228i
\(369\) 9.74007 0.507048
\(370\) 6.14977 + 10.8350i 0.319711 + 0.563287i
\(371\) 4.17770i 0.216895i
\(372\) −1.82535 + 3.05682i −0.0946398 + 0.158489i
\(373\) 0.274698i 0.0142233i −0.999975 0.00711167i \(-0.997736\pi\)
0.999975 0.00711167i \(-0.00226373\pi\)
\(374\) 4.55675 2.58633i 0.235624 0.133736i
\(375\) −1.00000 −0.0516398
\(376\) −0.521330 + 23.6150i −0.0268855 + 1.21785i
\(377\) −2.95231 −0.152052
\(378\) −0.423774 + 0.240526i −0.0217966 + 0.0123713i
\(379\) 12.9574 0.665576 0.332788 0.943002i \(-0.392011\pi\)
0.332788 + 0.943002i \(0.392011\pi\)
\(380\) −1.89987 1.13449i −0.0974613 0.0581980i
\(381\) −0.639825 −0.0327792
\(382\) 1.21524 + 2.14108i 0.0621770 + 0.109547i
\(383\) 31.2410 1.59634 0.798170 0.602432i \(-0.205802\pi\)
0.798170 + 0.602432i \(0.205802\pi\)
\(384\) −10.0762 + 5.14495i −0.514198 + 0.262552i
\(385\) 0.385078i 0.0196254i
\(386\) 6.10654 + 10.7589i 0.310814 + 0.547612i
\(387\) −8.82654 −0.448678
\(388\) −16.3212 9.74603i −0.828582 0.494780i
\(389\) 33.0691i 1.67667i −0.545157 0.838334i \(-0.683530\pi\)
0.545157 0.838334i \(-0.316470\pi\)
\(390\) 2.95729 + 5.21033i 0.149748 + 0.263835i
\(391\) 5.03238 15.0810i 0.254499 0.762678i
\(392\) −19.4585 0.429569i −0.982801 0.0216965i
\(393\) −1.67592 −0.0845388
\(394\) 5.54619 + 9.77161i 0.279413 + 0.492287i
\(395\) 15.3762i 0.773661i
\(396\) −1.14597 + 1.91910i −0.0575872 + 0.0964384i
\(397\) 32.4640 1.62932 0.814661 0.579938i \(-0.196923\pi\)
0.814661 + 0.579938i \(0.196923\pi\)
\(398\) −8.84929 15.5912i −0.443575 0.781517i
\(399\) 0.381220i 0.0190849i
\(400\) 1.89720 + 3.52145i 0.0948600 + 0.176073i
\(401\) 28.3869i 1.41757i 0.705423 + 0.708786i \(0.250757\pi\)
−0.705423 + 0.708786i \(0.749243\pi\)
\(402\) 2.70615 1.53596i 0.134971 0.0766068i
\(403\) 7.54140i 0.375664i
\(404\) −8.35599 + 13.9934i −0.415726 + 0.696196i
\(405\) 1.00000i 0.0496904i
\(406\) 0.167623 + 0.295329i 0.00831901 + 0.0146569i
\(407\) 9.84568i 0.488032i
\(408\) −9.37411 0.206945i −0.464088 0.0102453i
\(409\) −35.5814 −1.75939 −0.879694 0.475541i \(-0.842252\pi\)
−0.879694 + 0.475541i \(0.842252\pi\)
\(410\) −11.9795 + 6.79932i −0.591623 + 0.335794i
\(411\) 10.2084 0.503542
\(412\) −3.55221 + 5.94870i −0.175005 + 0.293072i
\(413\) 5.03133i 0.247576i
\(414\) 1.30866 + 6.65488i 0.0643171 + 0.327069i
\(415\) 17.0787i 0.838358i
\(416\) 12.7374 20.2990i 0.624501 0.995239i
\(417\) −8.48317 −0.415423
\(418\) 0.863195 + 1.52083i 0.0422202 + 0.0743862i
\(419\) −38.1656 −1.86451 −0.932255 0.361802i \(-0.882162\pi\)
−0.932255 + 0.361802i \(0.882162\pi\)
\(420\) 0.353300 0.591654i 0.0172393 0.0288697i
\(421\) 16.9679i 0.826965i 0.910512 + 0.413483i \(0.135688\pi\)
−0.910512 + 0.413483i \(0.864312\pi\)
\(422\) 18.2303 10.3472i 0.887435 0.503692i
\(423\) 8.35120i 0.406049i
\(424\) −0.756904 + 34.2860i −0.0367585 + 1.66508i
\(425\) 3.31506i 0.160804i
\(426\) −11.5469 20.3441i −0.559451 0.985674i
\(427\) 2.43512i 0.117844i
\(428\) 12.4409 20.8341i 0.601353 1.00706i
\(429\) 4.73456i 0.228587i
\(430\) 10.8559 6.16160i 0.523517 0.297139i
\(431\) −23.2458 −1.11971 −0.559856 0.828590i \(-0.689144\pi\)
−0.559856 + 0.828590i \(0.689144\pi\)
\(432\) 3.52145 1.89720i 0.169426 0.0912791i
\(433\) 21.1065i 1.01432i −0.861853 0.507158i \(-0.830696\pi\)
0.861853 0.507158i \(-0.169304\pi\)
\(434\) −0.754390 + 0.428178i −0.0362119 + 0.0205532i
\(435\) 0.696902 0.0334139
\(436\) 28.2708 + 16.8816i 1.35393 + 0.808483i
\(437\) 5.03332 + 1.67957i 0.240776 + 0.0803449i
\(438\) −3.30087 + 1.87351i −0.157722 + 0.0895200i
\(439\) 15.7660i 0.752471i 0.926524 + 0.376235i \(0.122782\pi\)
−0.926524 + 0.376235i \(0.877218\pi\)
\(440\) 0.0697675 3.16030i 0.00332603 0.150662i
\(441\) 6.88128 0.327680
\(442\) 17.2725 9.80357i 0.821570 0.466308i
\(443\) 17.9865i 0.854563i −0.904119 0.427281i \(-0.859471\pi\)
0.904119 0.427281i \(-0.140529\pi\)
\(444\) −9.03317 + 15.1274i −0.428695 + 0.717914i
\(445\) −11.9834 −0.568066
\(446\) 2.89321 1.64213i 0.136997 0.0777572i
\(447\) −8.00893 −0.378809
\(448\) −2.75376 0.121644i −0.130103 0.00574716i
\(449\) 6.47433 0.305542 0.152771 0.988262i \(-0.451180\pi\)
0.152771 + 0.988262i \(0.451180\pi\)
\(450\) −0.698077 1.22991i −0.0329076 0.0579787i
\(451\) 10.8856 0.512582
\(452\) 27.8039 + 16.6028i 1.30778 + 0.780930i
\(453\) −15.9200 −0.747985
\(454\) 5.90234 + 10.3991i 0.277010 + 0.488054i
\(455\) 1.45965i 0.0684296i
\(456\) 0.0690684 3.12864i 0.00323442 0.146512i
\(457\) 27.2895i 1.27655i 0.769809 + 0.638274i \(0.220351\pi\)
−0.769809 + 0.638274i \(0.779649\pi\)
\(458\) 27.6970 15.7203i 1.29420 0.734562i
\(459\) 3.31506 0.154734
\(460\) −6.25515 7.27139i −0.291648 0.339030i
\(461\) 21.5131 1.00197 0.500983 0.865457i \(-0.332972\pi\)
0.500983 + 0.865457i \(0.332972\pi\)
\(462\) −0.473613 + 0.268814i −0.0220345 + 0.0125064i
\(463\) 24.6597i 1.14603i −0.819544 0.573016i \(-0.805773\pi\)
0.819544 0.573016i \(-0.194227\pi\)
\(464\) −1.32216 2.45411i −0.0613799 0.113929i
\(465\) 1.78017i 0.0825534i
\(466\) 10.5975 + 18.6713i 0.490918 + 0.864929i
\(467\) −10.2882 −0.476082 −0.238041 0.971255i \(-0.576505\pi\)
−0.238041 + 0.971255i \(0.576505\pi\)
\(468\) −4.34384 + 7.27442i −0.200794 + 0.336260i
\(469\) 0.758118 0.0350066
\(470\) 5.82978 + 10.2713i 0.268908 + 0.473778i
\(471\) 11.4730 0.528647
\(472\) −0.911563 + 41.2917i −0.0419581 + 1.90060i
\(473\) −9.86461 −0.453575
\(474\) 18.9114 10.7338i 0.868630 0.493018i
\(475\) −1.10641 −0.0507656
\(476\) −1.96136 1.17121i −0.0898990 0.0536823i
\(477\) 12.1249i 0.555160i
\(478\) 7.14674 4.05636i 0.326884 0.185534i
\(479\) −33.9683 −1.55205 −0.776026 0.630700i \(-0.782768\pi\)
−0.776026 + 0.630700i \(0.782768\pi\)
\(480\) −3.00669 + 4.79164i −0.137236 + 0.218707i
\(481\) 37.3204i 1.70166i
\(482\) 4.93686 2.80207i 0.224868 0.127631i
\(483\) −0.523049 + 1.56747i −0.0237996 + 0.0713222i
\(484\) 9.99841 16.7438i 0.454473 0.761083i
\(485\) −9.50481 −0.431591
\(486\) −1.22991 + 0.698077i −0.0557900 + 0.0316654i
\(487\) 10.1278i 0.458936i −0.973316 0.229468i \(-0.926301\pi\)
0.973316 0.229468i \(-0.0736987\pi\)
\(488\) 0.441188 19.9848i 0.0199716 0.904668i
\(489\) −11.6276 −0.525819
\(490\) −8.46339 + 4.80366i −0.382337 + 0.217007i
\(491\) 17.7630i 0.801631i 0.916159 + 0.400816i \(0.131273\pi\)
−0.916159 + 0.400816i \(0.868727\pi\)
\(492\) −16.7251 9.98725i −0.754028 0.450260i
\(493\) 2.31027i 0.104049i
\(494\) 3.27197 + 5.76476i 0.147213 + 0.259369i
\(495\) 1.11761i 0.0502328i
\(496\) 6.26879 3.37734i 0.281477 0.151647i
\(497\) 5.69932i 0.255649i
\(498\) −21.0053 + 11.9222i −0.941269 + 0.534247i
\(499\) 14.1094i 0.631623i −0.948822 0.315811i \(-0.897723\pi\)
0.948822 0.315811i \(-0.102277\pi\)
\(500\) 1.71715 + 1.02538i 0.0767932 + 0.0458563i
\(501\) 18.3392 0.819334
\(502\) −9.87739 17.4026i −0.440850 0.776716i
\(503\) −8.15173 −0.363467 −0.181734 0.983348i \(-0.558171\pi\)
−0.181734 + 0.983348i \(0.558171\pi\)
\(504\) 0.974314 + 0.0215091i 0.0433994 + 0.000958093i
\(505\) 8.14918i 0.362634i
\(506\) 1.46257 + 7.43755i 0.0650191 + 0.330639i
\(507\) 4.94653i 0.219683i
\(508\) 1.09868 + 0.656063i 0.0487458 + 0.0291081i
\(509\) 39.1703 1.73619 0.868096 0.496397i \(-0.165344\pi\)
0.868096 + 0.496397i \(0.165344\pi\)
\(510\) −4.07723 + 2.31416i −0.180543 + 0.102473i
\(511\) −0.924727 −0.0409075
\(512\) 22.5778 + 1.49724i 0.997808 + 0.0661694i
\(513\) 1.10641i 0.0488492i
\(514\) −2.64086 4.65282i −0.116483 0.205227i
\(515\) 3.46429i 0.152655i
\(516\) 15.1565 + 9.05054i 0.667227 + 0.398428i
\(517\) 9.33337i 0.410481i
\(518\) −3.73328 + 2.11894i −0.164031 + 0.0931009i
\(519\) 7.02511i 0.308368i
\(520\) 0.264456 11.9792i 0.0115972 0.525325i
\(521\) 26.2040i 1.14802i −0.818850 0.574008i \(-0.805388\pi\)
0.818850 0.574008i \(-0.194612\pi\)
\(522\) 0.486491 + 0.857130i 0.0212931 + 0.0375156i
\(523\) 13.1813 0.576376 0.288188 0.957574i \(-0.406947\pi\)
0.288188 + 0.957574i \(0.406947\pi\)
\(524\) 2.87780 + 1.71845i 0.125717 + 0.0750707i
\(525\) 0.344556i 0.0150376i
\(526\) −8.04372 14.1719i −0.350723 0.617925i
\(527\) 5.90136 0.257067
\(528\) 3.93561 2.12033i 0.171275 0.0922754i
\(529\) 18.3911 + 13.8118i 0.799614 + 0.600515i
\(530\) 8.46410 + 14.9126i 0.367657 + 0.647761i
\(531\) 14.6024i 0.633689i
\(532\) 0.390895 0.654612i 0.0169474 0.0283810i
\(533\) 41.2622 1.78726
\(534\) −8.36531 14.7385i −0.362002 0.637798i
\(535\) 12.1330i 0.524555i
\(536\) −6.22181 0.137354i −0.268741 0.00593278i
\(537\) −3.75048 −0.161845
\(538\) 17.7564 + 31.2843i 0.765532 + 1.34876i
\(539\) 7.69058 0.331257
\(540\) 1.02538 1.71715i 0.0441252 0.0738943i
\(541\) 0.429117 0.0184492 0.00922459 0.999957i \(-0.497064\pi\)
0.00922459 + 0.999957i \(0.497064\pi\)
\(542\) 8.44172 4.79136i 0.362603 0.205807i
\(543\) −9.93221 −0.426232
\(544\) 15.8845 + 9.96736i 0.681044 + 0.427347i
\(545\) 16.4638 0.705232
\(546\) −1.79525 + 1.01895i −0.0768296 + 0.0436070i
\(547\) 5.27276i 0.225447i −0.993626 0.112724i \(-0.964043\pi\)
0.993626 0.112724i \(-0.0359574\pi\)
\(548\) −17.5293 10.4674i −0.748814 0.447147i
\(549\) 7.06741i 0.301630i
\(550\) −0.780176 1.37456i −0.0332668 0.0586115i
\(551\) 0.771060 0.0328482
\(552\) 4.57661 12.7693i 0.194793 0.543497i
\(553\) 5.29796 0.225292
\(554\) 11.5985 + 20.4349i 0.492772 + 0.868195i
\(555\) 8.80960i 0.373946i
\(556\) 14.5669 + 8.69846i 0.617773 + 0.368897i
\(557\) 18.8981i 0.800739i −0.916354 0.400369i \(-0.868882\pi\)
0.916354 0.400369i \(-0.131118\pi\)
\(558\) −2.18946 + 1.24270i −0.0926871 + 0.0526075i
\(559\) −37.3922 −1.58152
\(560\) −1.21334 + 0.653691i −0.0512729 + 0.0276235i
\(561\) 3.70493 0.156422
\(562\) −8.39573 + 4.76526i −0.354153 + 0.201010i
\(563\) 27.0492 1.13999 0.569994 0.821649i \(-0.306946\pi\)
0.569994 + 0.821649i \(0.306946\pi\)
\(564\) −8.56314 + 14.3403i −0.360573 + 0.603834i
\(565\) 16.1919 0.681198
\(566\) −0.113648 0.200232i −0.00477697 0.00841636i
\(567\) −0.344556 −0.0144700
\(568\) −1.03259 + 46.7738i −0.0433264 + 1.96258i
\(569\) 13.1945i 0.553143i 0.960993 + 0.276571i \(0.0891982\pi\)
−0.960993 + 0.276571i \(0.910802\pi\)
\(570\) −0.772359 1.36079i −0.0323506 0.0569972i
\(571\) −1.70748 −0.0714558 −0.0357279 0.999362i \(-0.511375\pi\)
−0.0357279 + 0.999362i \(0.511375\pi\)
\(572\) −4.85472 + 8.12995i −0.202986 + 0.339930i
\(573\) 1.74084i 0.0727246i
\(574\) −2.34274 4.12759i −0.0977842 0.172282i
\(575\) −4.54924 1.51804i −0.189716 0.0633066i
\(576\) −7.99221 0.353047i −0.333009 0.0147103i
\(577\) −37.2727 −1.55168 −0.775842 0.630927i \(-0.782675\pi\)
−0.775842 + 0.630927i \(0.782675\pi\)
\(578\) −4.19572 7.39228i −0.174519 0.307479i
\(579\) 8.74766i 0.363540i
\(580\) −1.19668 0.714588i −0.0496896 0.0296717i
\(581\) −5.88455 −0.244132
\(582\) −6.63509 11.6901i −0.275033 0.484570i
\(583\) 13.5509i 0.561220i
\(584\) 7.58915 + 0.167539i 0.314041 + 0.00693283i
\(585\) 4.23633i 0.175151i
\(586\) 18.3970 10.4418i 0.759974 0.431347i
\(587\) 14.5005i 0.598498i 0.954175 + 0.299249i \(0.0967362\pi\)
−0.954175 + 0.299249i \(0.903264\pi\)
\(588\) −11.8162 7.05591i −0.487291 0.290981i
\(589\) 1.96960i 0.0811559i
\(590\) 10.1936 + 17.9597i 0.419663 + 0.739387i
\(591\) 7.94495i 0.326812i
\(592\) 31.0226 16.7136i 1.27502 0.686923i
\(593\) 32.2207 1.32315 0.661574 0.749880i \(-0.269889\pi\)
0.661574 + 0.749880i \(0.269889\pi\)
\(594\) −1.37456 + 0.780176i −0.0563990 + 0.0320110i
\(595\) −1.14222 −0.0468265
\(596\) 13.7525 + 8.21218i 0.563325 + 0.336384i
\(597\) 12.6767i 0.518821i
\(598\) 5.54392 + 28.1923i 0.226708 + 1.15287i
\(599\) 0.676848i 0.0276553i −0.999904 0.0138276i \(-0.995598\pi\)
0.999904 0.0138276i \(-0.00440161\pi\)
\(600\) −0.0624257 + 2.82774i −0.00254852 + 0.115442i
\(601\) −11.7698 −0.480100 −0.240050 0.970760i \(-0.577164\pi\)
−0.240050 + 0.970760i \(0.577164\pi\)
\(602\) 2.12301 + 3.74046i 0.0865276 + 0.152450i
\(603\) 2.20028 0.0896022
\(604\) 27.3369 + 16.3240i 1.11232 + 0.664213i
\(605\) 9.75095i 0.396433i
\(606\) −10.0228 + 5.68875i −0.407148 + 0.231090i
\(607\) 3.30282i 0.134057i 0.997751 + 0.0670286i \(0.0213519\pi\)
−0.997751 + 0.0670286i \(0.978648\pi\)
\(608\) −3.32664 + 5.30152i −0.134913 + 0.215005i
\(609\) 0.240122i 0.00973022i
\(610\) −4.93359 8.69230i −0.199755 0.351941i
\(611\) 35.3785i 1.43126i
\(612\) −5.69244 3.39919i −0.230103 0.137404i
\(613\) 21.2125i 0.856763i 0.903598 + 0.428382i \(0.140916\pi\)
−0.903598 + 0.428382i \(0.859084\pi\)
\(614\) −10.6958 + 6.07071i −0.431646 + 0.244994i
\(615\) −9.74007 −0.392758
\(616\) 1.08890 + 0.0240388i 0.0438731 + 0.000968550i
\(617\) 28.3728i 1.14225i −0.820864 0.571124i \(-0.806508\pi\)
0.820864 0.571124i \(-0.193492\pi\)
\(618\) −4.26078 + 2.41834i −0.171394 + 0.0972799i
\(619\) −4.37548 −0.175866 −0.0879328 0.996126i \(-0.528026\pi\)
−0.0879328 + 0.996126i \(0.528026\pi\)
\(620\) 1.82535 3.05682i 0.0733077 0.122765i
\(621\) −1.51804 + 4.54924i −0.0609168 + 0.182555i
\(622\) −7.06572 + 4.01037i −0.283310 + 0.160801i
\(623\) 4.12894i 0.165422i
\(624\) 14.9181 8.03717i 0.597200 0.321744i
\(625\) 1.00000 0.0400000
\(626\) −1.17337 + 0.665982i −0.0468972 + 0.0266180i
\(627\) 1.23653i 0.0493824i
\(628\) −19.7008 11.7641i −0.786148 0.469440i
\(629\) 29.2043 1.16445
\(630\) 0.423774 0.240526i 0.0168836 0.00958280i
\(631\) −38.6015 −1.53670 −0.768351 0.640028i \(-0.778923\pi\)
−0.768351 + 0.640028i \(0.778923\pi\)
\(632\) −43.4799 0.959870i −1.72954 0.0381816i
\(633\) 14.8224 0.589137
\(634\) −2.32539 4.09701i −0.0923530 0.162713i
\(635\) 0.639825 0.0253907
\(636\) −12.4326 + 20.8202i −0.492984 + 0.825576i
\(637\) 29.1514 1.15502
\(638\) 0.543707 + 0.957936i 0.0215255 + 0.0379250i
\(639\) 16.5411i 0.654354i
\(640\) 10.0762 5.14495i 0.398296 0.203372i
\(641\) 42.8647i 1.69306i 0.532345 + 0.846528i \(0.321311\pi\)
−0.532345 + 0.846528i \(0.678689\pi\)
\(642\) 14.9225 8.46975i 0.588945 0.334275i
\(643\) 26.5465 1.04689 0.523446 0.852059i \(-0.324646\pi\)
0.523446 + 0.852059i \(0.324646\pi\)
\(644\) 2.50540 2.15525i 0.0987265 0.0849287i
\(645\) 8.82654 0.347545
\(646\) −4.51109 + 2.56041i −0.177487 + 0.100738i
\(647\) 35.0008i 1.37602i 0.725701 + 0.688011i \(0.241516\pi\)
−0.725701 + 0.688011i \(0.758484\pi\)
\(648\) 2.82774 + 0.0624257i 0.111084 + 0.00245231i
\(649\) 16.3197i 0.640605i
\(650\) −2.95729 5.21033i −0.115994 0.204366i
\(651\) −0.613368 −0.0240398
\(652\) 19.9664 + 11.9227i 0.781943 + 0.466929i
\(653\) 27.3819 1.07154 0.535768 0.844365i \(-0.320022\pi\)
0.535768 + 0.844365i \(0.320022\pi\)
\(654\) 11.4930 + 20.2491i 0.449412 + 0.791801i
\(655\) 1.67592 0.0654835
\(656\) 18.4789 + 34.2992i 0.721478 + 1.33916i
\(657\) −2.68382 −0.104706
\(658\) −3.53902 + 2.00868i −0.137965 + 0.0783067i
\(659\) −25.7125 −1.00162 −0.500808 0.865558i \(-0.666964\pi\)
−0.500808 + 0.865558i \(0.666964\pi\)
\(660\) 1.14597 1.91910i 0.0446069 0.0747009i
\(661\) 1.18452i 0.0460726i −0.999735 0.0230363i \(-0.992667\pi\)
0.999735 0.0230363i \(-0.00733333\pi\)
\(662\) −26.2891 + 14.9212i −1.02176 + 0.579930i
\(663\) 14.0437 0.545411
\(664\) 48.2940 + 1.06615i 1.87417 + 0.0413745i
\(665\) 0.381220i 0.0147831i
\(666\) −10.8350 + 6.14977i −0.419850 + 0.238299i
\(667\) 3.17037 + 1.05792i 0.122757 + 0.0409630i
\(668\) −31.4911 18.8046i −1.21843 0.727571i
\(669\) 2.35237 0.0909477
\(670\) −2.70615 + 1.53596i −0.104548 + 0.0593394i
\(671\) 7.89859i 0.304922i
\(672\) −1.65099 1.03597i −0.0636882 0.0399636i
\(673\) −30.4877 −1.17522 −0.587608 0.809146i \(-0.699930\pi\)
−0.587608 + 0.809146i \(0.699930\pi\)
\(674\) 29.2449 16.5989i 1.12647 0.639365i
\(675\) 1.00000i 0.0384900i
\(676\) −5.07206 + 8.49393i −0.195079 + 0.326689i
\(677\) 28.5320i 1.09657i −0.836290 0.548287i \(-0.815280\pi\)
0.836290 0.548287i \(-0.184720\pi\)
\(678\) 11.3032 + 19.9146i 0.434096 + 0.764817i
\(679\) 3.27494i 0.125681i
\(680\) 9.37411 + 0.206945i 0.359481 + 0.00793596i
\(681\) 8.45514i 0.324002i
\(682\) −2.44695 + 1.38885i −0.0936987 + 0.0531817i
\(683\) 8.20988i 0.314142i 0.987587 + 0.157071i \(0.0502052\pi\)
−0.987587 + 0.157071i \(0.949795\pi\)
\(684\) 1.13449 1.89987i 0.0433783 0.0726434i
\(685\) −10.2084 −0.390042
\(686\) −3.33881 5.88253i −0.127477 0.224596i
\(687\) 22.5195 0.859172
\(688\) −16.7457 31.0822i −0.638424 1.18500i
\(689\) 51.3651i 1.95685i
\(690\) −1.30866 6.65488i −0.0498198 0.253347i
\(691\) 5.68367i 0.216217i −0.994139 0.108109i \(-0.965521\pi\)
0.994139 0.108109i \(-0.0344794\pi\)
\(692\) −7.20339 + 12.0632i −0.273832 + 0.458572i
\(693\) −0.385078 −0.0146279
\(694\) −33.2435 + 18.8684i −1.26191 + 0.716234i
\(695\) 8.48317 0.321785
\(696\) 0.0435046 1.97066i 0.00164904 0.0746976i
\(697\) 32.2889i 1.22303i
\(698\) 10.7327 + 18.9095i 0.406238 + 0.715735i
\(699\) 15.1809i 0.574196i
\(700\) −0.353300 + 0.591654i −0.0133535 + 0.0223624i
\(701\) 27.0506i 1.02169i 0.859674 + 0.510843i \(0.170667\pi\)
−0.859674 + 0.510843i \(0.829333\pi\)
\(702\) −5.21033 + 2.95729i −0.196651 + 0.111616i
\(703\) 9.74702i 0.367616i
\(704\) −8.93216 0.394568i −0.336643 0.0148709i
\(705\) 8.35120i 0.314524i
\(706\) 10.4087 + 18.3388i 0.391738 + 0.690188i
\(707\) −2.80785 −0.105600
\(708\) −14.9729 + 25.0744i −0.562718 + 0.942355i
\(709\) 32.4076i 1.21709i −0.793518 0.608547i \(-0.791753\pi\)
0.793518 0.608547i \(-0.208247\pi\)
\(710\) 11.5469 + 20.3441i 0.433349 + 0.763500i
\(711\) 15.3762 0.576653
\(712\) −0.748070 + 33.8858i −0.0280351 + 1.26992i
\(713\) −2.70237 + 8.09842i −0.101204 + 0.303288i
\(714\) −0.797358 1.40483i −0.0298404 0.0525746i
\(715\) 4.73456i 0.177063i
\(716\) 6.44013 + 3.84566i 0.240679 + 0.143719i
\(717\) 5.81077 0.217007
\(718\) −23.7681 41.8760i −0.887016 1.56280i
\(719\) 12.2149i 0.455538i 0.973715 + 0.227769i \(0.0731431\pi\)
−0.973715 + 0.227769i \(0.926857\pi\)
\(720\) −3.52145 + 1.89720i −0.131237 + 0.0707045i
\(721\) −1.19364 −0.0444535
\(722\) 12.4089 + 21.8628i 0.461812 + 0.813648i
\(723\) 4.01399 0.149282
\(724\) 17.0551 + 10.1843i 0.633847 + 0.378495i
\(725\) −0.696902 −0.0258823
\(726\) 11.9928 6.80691i 0.445096 0.252628i
\(727\) 22.7019 0.841966 0.420983 0.907068i \(-0.361685\pi\)
0.420983 + 0.907068i \(0.361685\pi\)
\(728\) 4.12752 + 0.0911199i 0.152976 + 0.00337713i
\(729\) −1.00000 −0.0370370
\(730\) 3.30087 1.87351i 0.122171 0.0693419i
\(731\) 29.2605i 1.08224i
\(732\) 7.24676 12.1358i 0.267848 0.448552i
\(733\) 22.3687i 0.826205i 0.910685 + 0.413103i \(0.135555\pi\)
−0.910685 + 0.413103i \(0.864445\pi\)
\(734\) 4.95628 + 8.73228i 0.182940 + 0.322314i
\(735\) −6.88128 −0.253820
\(736\) −20.9521 + 17.2340i −0.772303 + 0.635254i
\(737\) 2.45905 0.0905802
\(738\) −6.79932 11.9795i −0.250286 0.440970i
\(739\) 3.85801i 0.141919i −0.997479 0.0709596i \(-0.977394\pi\)
0.997479 0.0709596i \(-0.0226061\pi\)
\(740\) 9.03317 15.1274i 0.332066 0.556094i
\(741\) 4.68712i 0.172186i
\(742\) −5.13821 + 2.91635i −0.188630 + 0.107063i
\(743\) −8.11201 −0.297601 −0.148800 0.988867i \(-0.547541\pi\)
−0.148800 + 0.988867i \(0.547541\pi\)
\(744\) 5.03385 + 0.111128i 0.184550 + 0.00407416i
\(745\) 8.00893 0.293424
\(746\) −0.337855 + 0.191760i −0.0123698 + 0.00702085i
\(747\) −17.0787 −0.624875
\(748\) −6.36192 3.79896i −0.232615 0.138904i
\(749\) 4.18049 0.152752
\(750\) 0.698077 + 1.22991i 0.0254902 + 0.0449101i
\(751\) 46.8539 1.70972 0.854861 0.518858i \(-0.173643\pi\)
0.854861 + 0.518858i \(0.173643\pi\)
\(752\) 29.4084 15.8439i 1.07241 0.577768i
\(753\) 14.1494i 0.515634i
\(754\) 2.06094 + 3.63109i 0.0750550 + 0.132236i
\(755\) 15.9200 0.579387
\(756\) 0.591654 + 0.353300i 0.0215182 + 0.0128494i
\(757\) 18.3340i 0.666359i −0.942863 0.333179i \(-0.891879\pi\)
0.942863 0.333179i \(-0.108121\pi\)
\(758\) −9.04524 15.9365i −0.328538 0.578838i
\(759\) −1.69657 + 5.08427i −0.0615817 + 0.184547i
\(760\) −0.0690684 + 3.12864i −0.00250537 + 0.113488i
\(761\) 44.7295 1.62144 0.810722 0.585431i \(-0.199075\pi\)
0.810722 + 0.585431i \(0.199075\pi\)
\(762\) 0.446647 + 0.786930i 0.0161803 + 0.0285075i
\(763\) 5.67270i 0.205366i
\(764\) 1.78502 2.98928i 0.0645797 0.108148i
\(765\) −3.31506 −0.119856
\(766\) −21.8086 38.4237i −0.787977 1.38831i
\(767\) 61.8605i 2.23365i
\(768\) 13.3618 + 8.80127i 0.482152 + 0.317588i
\(769\) 35.2621i 1.27158i −0.771861 0.635791i \(-0.780674\pi\)
0.771861 0.635791i \(-0.219326\pi\)
\(770\) 0.473613 0.268814i 0.0170678 0.00968739i
\(771\) 3.78305i 0.136243i
\(772\) 8.96966 15.0210i 0.322825 0.540619i
\(773\) 26.9995i 0.971106i 0.874207 + 0.485553i \(0.161382\pi\)
−0.874207 + 0.485553i \(0.838618\pi\)
\(774\) 6.16160 + 10.8559i 0.221474 + 0.390207i
\(775\) 1.78017i 0.0639456i
\(776\) −0.593345 + 26.8771i −0.0212998 + 0.964832i
\(777\) −3.03540 −0.108894
\(778\) −40.6721 + 23.0847i −1.45817 + 0.827628i
\(779\) −10.7765 −0.386109
\(780\) 4.34384 7.27442i 0.155535 0.260466i
\(781\) 18.4864i 0.661496i
\(782\) −22.0613 + 4.33828i −0.788910 + 0.155136i
\(783\) 0.696902i 0.0249053i
\(784\) 13.0552 + 24.2321i 0.466256 + 0.865433i
\(785\) −11.4730 −0.409488
\(786\) 1.16992 + 2.06123i 0.0417296 + 0.0735218i
\(787\) −29.4507 −1.04980 −0.524902 0.851163i \(-0.675898\pi\)
−0.524902 + 0.851163i \(0.675898\pi\)
\(788\) 8.14658 13.6427i 0.290210 0.486000i
\(789\) 11.5227i 0.410219i
\(790\) −18.9114 + 10.7338i −0.672838 + 0.381890i
\(791\) 5.57901i 0.198367i
\(792\) 3.16030 + 0.0697675i 0.112297 + 0.00247908i
\(793\) 29.9399i 1.06320i
\(794\) −22.6624 39.9279i −0.804257 1.41699i
\(795\) 12.1249i 0.430025i
\(796\) −12.9984 + 21.7677i −0.460715 + 0.771537i
\(797\) 36.0729i 1.27777i −0.769303 0.638884i \(-0.779396\pi\)
0.769303 0.638884i \(-0.220604\pi\)
\(798\) 0.468868 0.266121i 0.0165977 0.00942057i
\(799\) 27.6847 0.979414
\(800\) 3.00669 4.79164i 0.106303 0.169410i
\(801\) 11.9834i 0.423411i
\(802\) 34.9134 19.8162i 1.23284 0.699735i
\(803\) −2.99946 −0.105849
\(804\) −3.77820 2.25612i −0.133247 0.0795671i
\(805\) 0.523049 1.56747i 0.0184351 0.0552459i
\(806\) −9.27527 + 5.26447i −0.326707 + 0.185433i
\(807\) 25.4362i 0.895395i
\(808\) 23.0438 + 0.508718i 0.810676 + 0.0178966i
\(809\) −55.4940 −1.95106 −0.975532 0.219858i \(-0.929440\pi\)
−0.975532 + 0.219858i \(0.929440\pi\)
\(810\) 1.22991 0.698077i 0.0432148 0.0245279i
\(811\) 34.6894i 1.21811i 0.793127 + 0.609056i \(0.208451\pi\)
−0.793127 + 0.609056i \(0.791549\pi\)
\(812\) 0.246216 0.412325i 0.00864047 0.0144698i
\(813\) 6.86367 0.240719
\(814\) −12.1093 + 6.87304i −0.424432 + 0.240900i
\(815\) 11.6276 0.407298
\(816\) 6.28932 + 11.6738i 0.220170 + 0.408665i
\(817\) 9.76577 0.341661
\(818\) 24.8385 + 43.7621i 0.868459 + 1.53011i
\(819\) −1.45965 −0.0510044
\(820\) 16.7251 + 9.98725i 0.584068 + 0.348770i
\(821\) 39.8207 1.38975 0.694875 0.719130i \(-0.255460\pi\)
0.694875 + 0.719130i \(0.255460\pi\)
\(822\) −7.12622 12.5554i −0.248556 0.437921i
\(823\) 43.6703i 1.52225i 0.648605 + 0.761126i \(0.275353\pi\)
−0.648605 + 0.761126i \(0.724647\pi\)
\(824\) 9.79611 + 0.216261i 0.341264 + 0.00753380i
\(825\) 1.11761i 0.0389101i
\(826\) −6.18810 + 3.51225i −0.215312 + 0.122207i
\(827\) 25.7183 0.894311 0.447156 0.894456i \(-0.352437\pi\)
0.447156 + 0.894456i \(0.352437\pi\)
\(828\) 7.27139 6.25515i 0.252698 0.217382i
\(829\) 16.0133 0.556165 0.278083 0.960557i \(-0.410301\pi\)
0.278083 + 0.960557i \(0.410301\pi\)
\(830\) 21.0053 11.9222i 0.729104 0.413826i
\(831\) 16.6149i 0.576364i
\(832\) −33.8577 1.49563i −1.17380 0.0518515i
\(833\) 22.8118i 0.790383i
\(834\) 5.92190 + 10.4336i 0.205059 + 0.361285i
\(835\) −18.3392 −0.634653
\(836\) 1.26791 2.12331i 0.0438517 0.0734363i
\(837\) −1.78017 −0.0615317
\(838\) 26.6425 + 46.9404i 0.920350 + 1.62153i
\(839\) 5.08265 0.175473 0.0877363 0.996144i \(-0.472037\pi\)
0.0877363 + 0.996144i \(0.472037\pi\)
\(840\) −0.974314 0.0215091i −0.0336170 0.000742136i
\(841\) −28.5143 −0.983253
\(842\) 20.8691 11.8449i 0.719196 0.408202i
\(843\) −6.82628 −0.235109
\(844\) −25.4522 15.1985i −0.876102 0.523155i
\(845\) 4.94653i 0.170166i
\(846\) −10.2713 + 5.82978i −0.353133 + 0.200432i
\(847\) 3.35975 0.115442
\(848\) 42.6972 23.0033i 1.46623 0.789938i
\(849\) 0.162801i 0.00558732i
\(850\) 4.07723 2.31416i 0.139848 0.0793751i
\(851\) −13.3733 + 40.0769i −0.458431 + 1.37382i
\(852\) −16.9608 + 28.4035i −0.581069 + 0.973087i
\(853\) 37.7514 1.29258 0.646292 0.763090i \(-0.276319\pi\)
0.646292 + 0.763090i \(0.276319\pi\)
\(854\) 2.99498 1.69990i 0.102486 0.0581693i
\(855\) 1.10641i 0.0378384i
\(856\) −34.3089 0.757410i −1.17265 0.0258877i
\(857\) 23.3670 0.798201 0.399101 0.916907i \(-0.369322\pi\)
0.399101 + 0.916907i \(0.369322\pi\)
\(858\) −5.82311 + 3.30509i −0.198798 + 0.112834i
\(859\) 44.0917i 1.50439i 0.658940 + 0.752196i \(0.271005\pi\)
−0.658940 + 0.752196i \(0.728995\pi\)
\(860\) −15.1565 9.05054i −0.516832 0.308621i
\(861\) 3.35600i 0.114372i
\(862\) 16.2274 + 28.5904i 0.552706 + 0.973792i
\(863\) 7.36620i 0.250748i 0.992110 + 0.125374i \(0.0400131\pi\)
−0.992110 + 0.125374i \(0.959987\pi\)
\(864\) −4.79164 3.00669i −0.163015 0.102290i
\(865\) 7.02511i 0.238861i
\(866\) −25.9592 + 14.7340i −0.882130 + 0.500681i
\(867\) 6.01041i 0.204124i
\(868\) 1.05324 + 0.628934i 0.0357494 + 0.0213474i
\(869\) 17.1846 0.582947
\(870\) −0.486491 0.857130i −0.0164936 0.0290594i
\(871\) 9.32111 0.315834
\(872\) 1.02776 46.5553i 0.0348045 1.57656i
\(873\) 9.50481i 0.321689i
\(874\) −1.44791 7.36302i −0.0489764 0.249058i
\(875\) 0.344556i 0.0116481i
\(876\) 4.60852 + 2.75193i 0.155708 + 0.0929792i
\(877\) −22.1457 −0.747807 −0.373904 0.927468i \(-0.621981\pi\)
−0.373904 + 0.927468i \(0.621981\pi\)
\(878\) 19.3908 11.0059i 0.654409 0.371431i
\(879\) 14.9580 0.504520
\(880\) −3.93561 + 2.12033i −0.132669 + 0.0714762i
\(881\) 27.8954i 0.939821i 0.882714 + 0.469910i \(0.155714\pi\)
−0.882714 + 0.469910i \(0.844286\pi\)
\(882\) −4.80366 8.46339i −0.161748 0.284977i
\(883\) 17.3820i 0.584952i −0.956273 0.292476i \(-0.905521\pi\)
0.956273 0.292476i \(-0.0944791\pi\)
\(884\) −24.1151 14.4001i −0.811078 0.484327i
\(885\) 14.6024i 0.490853i
\(886\) −22.1218 + 12.5559i −0.743197 + 0.421825i
\(887\) 19.8802i 0.667513i 0.942659 + 0.333756i \(0.108316\pi\)
−0.942659 + 0.333756i \(0.891684\pi\)
\(888\) 24.9112 + 0.549945i 0.835966 + 0.0184549i
\(889\) 0.220456i 0.00739384i
\(890\) 8.36531 + 14.7385i 0.280406 + 0.494036i
\(891\) −1.11761 −0.0374413
\(892\) −4.03936 2.41206i −0.135248 0.0807619i
\(893\) 9.23985i 0.309200i
\(894\) 5.59084 + 9.85029i 0.186986 + 0.329443i
\(895\) 3.75048 0.125365
\(896\) 1.77272 + 3.47181i 0.0592226 + 0.115985i
\(897\) −6.43092 + 19.2721i −0.214722 + 0.643476i
\(898\) −4.51958 7.96287i −0.150820 0.265724i
\(899\) 1.24060i 0.0413765i
\(900\) −1.02538 + 1.71715i −0.0341793 + 0.0572383i
\(901\) 40.1947 1.33908
\(902\) −7.59897 13.3883i −0.253018 0.445783i
\(903\) 3.04123i 0.101206i
\(904\) 1.01079 45.7864i 0.0336184 1.52283i
\(905\) 9.93221 0.330158
\(906\) 11.1134 + 19.5802i 0.369217 + 0.650508i
\(907\) −7.49646 −0.248916 −0.124458 0.992225i \(-0.539719\pi\)
−0.124458 + 0.992225i \(0.539719\pi\)
\(908\) 8.66972 14.5187i 0.287715 0.481821i
\(909\) −8.14918 −0.270291
\(910\) 1.79525 1.01895i 0.0595119 0.0337779i
\(911\) 41.7614 1.38362 0.691808 0.722081i \(-0.256814\pi\)
0.691808 + 0.722081i \(0.256814\pi\)
\(912\) −3.89617 + 2.09908i −0.129015 + 0.0695075i
\(913\) −19.0872 −0.631696
\(914\) 33.5637 19.0501i 1.11019 0.630123i
\(915\) 7.06741i 0.233641i
\(916\) −38.6693 23.0910i −1.27767 0.762948i
\(917\) 0.577447i 0.0190690i
\(918\) −2.31416 4.07723i −0.0763788 0.134569i
\(919\) −31.3223 −1.03323 −0.516613 0.856219i \(-0.672807\pi\)
−0.516613 + 0.856219i \(0.672807\pi\)
\(920\) −4.57661 + 12.7693i −0.150886 + 0.420991i
\(921\) −8.69634 −0.286554
\(922\) −15.0178 26.4593i −0.494585 0.871390i
\(923\) 70.0735i 2.30650i
\(924\) 0.661237 + 0.394851i 0.0217531 + 0.0129896i
\(925\) 8.80960i 0.289658i
\(926\) −30.3293 + 17.2143i −0.996682 + 0.565698i
\(927\) −3.46429 −0.113782
\(928\) −2.09537 + 3.33930i −0.0687840 + 0.109618i
\(929\) −39.0276 −1.28045 −0.640226 0.768186i \(-0.721159\pi\)
−0.640226 + 0.768186i \(0.721159\pi\)
\(930\) 2.18946 1.24270i 0.0717951 0.0407496i
\(931\) −7.61352 −0.249523
\(932\) 15.5662 26.0679i 0.509888 0.853883i
\(933\) −5.74489 −0.188079
\(934\) 7.18197 + 12.6536i 0.235001 + 0.414040i
\(935\) −3.70493 −0.121164
\(936\) 11.9792 + 0.264456i 0.391554 + 0.00864402i
\(937\) 6.62490i 0.216426i 0.994128 + 0.108213i \(0.0345128\pi\)
−0.994128 + 0.108213i \(0.965487\pi\)
\(938\) −0.529225 0.932420i −0.0172798 0.0304446i
\(939\) −0.954025 −0.0311334
\(940\) 8.56314 14.3403i 0.279299 0.467728i
\(941\) 33.1946i 1.08211i −0.840987 0.541056i \(-0.818025\pi\)
0.840987 0.541056i \(-0.181975\pi\)
\(942\) −8.00902 14.1108i −0.260948 0.459754i
\(943\) −44.3099 14.7858i −1.44293 0.481492i
\(944\) 51.4216 27.7036i 1.67363 0.901675i
\(945\) 0.344556 0.0112084
\(946\) 6.88626 + 12.1326i 0.223891 + 0.394466i
\(947\) 4.95185i 0.160914i −0.996758 0.0804568i \(-0.974362\pi\)
0.996758 0.0804568i \(-0.0256379\pi\)
\(948\) −26.4032 15.7664i −0.857537 0.512070i
\(949\) −11.3696 −0.369072
\(950\) 0.772359 + 1.36079i 0.0250586 + 0.0441498i
\(951\) 3.33114i 0.108019i
\(952\) −0.0713040 + 3.22990i −0.00231098 + 0.104682i
\(953\) 0.385951i 0.0125022i 0.999980 + 0.00625109i \(0.00198980\pi\)
−0.999980 + 0.00625109i \(0.998010\pi\)
\(954\) −14.9126 + 8.46410i −0.482812 + 0.274035i
\(955\) 1.74084i 0.0563322i
\(956\) −9.97795 5.95823i −0.322710 0.192703i
\(957\) 0.778864i 0.0251771i
\(958\) 23.7125 + 41.7781i 0.766116 + 1.34979i
\(959\) 3.51735i 0.113581i
\(960\) 7.99221 + 0.353047i 0.257947 + 0.0113945i
\(961\) 27.8310 0.897774
\(962\) −45.9009 + 26.0525i −1.47990 + 0.839966i
\(963\) 12.1330 0.390980
\(964\) −6.89261 4.11586i −0.221996 0.132563i
\(965\) 8.74766i 0.281597i
\(966\) 2.29298 0.450906i 0.0737753 0.0145077i
\(967\) 14.9587i 0.481038i 0.970644 + 0.240519i \(0.0773176\pi\)
−0.970644 + 0.240519i \(0.922682\pi\)
\(968\) −27.5731 0.608710i −0.886234 0.0195647i
\(969\) −3.66781 −0.117827
\(970\) 6.63509 + 11.6901i 0.213040 + 0.375347i
\(971\) −11.6718 −0.374566 −0.187283 0.982306i \(-0.559968\pi\)
−0.187283 + 0.982306i \(0.559968\pi\)
\(972\) 1.71715 + 1.02538i 0.0550776 + 0.0328890i
\(973\) 2.92293i 0.0937047i
\(974\) −12.4564 + 7.07001i −0.399128 + 0.226538i
\(975\) 4.23633i 0.135671i
\(976\) −24.8875 + 13.4083i −0.796631 + 0.429189i
\(977\) 32.1540i 1.02870i −0.857581 0.514349i \(-0.828034\pi\)
0.857581 0.514349i \(-0.171966\pi\)
\(978\) 8.11697 + 14.3010i 0.259552 + 0.457295i
\(979\) 13.3927i 0.428033i
\(980\) 11.8162 + 7.05591i 0.377454 + 0.225393i
\(981\) 16.4638i 0.525649i
\(982\) 21.8469 12.3999i 0.697163 0.395697i
\(983\) −6.87025 −0.219127 −0.109563 0.993980i \(-0.534945\pi\)
−0.109563 + 0.993980i \(0.534945\pi\)
\(984\) −0.608031 + 27.5424i −0.0193833 + 0.878019i
\(985\) 7.94495i 0.253147i
\(986\) −2.84143 + 1.61275i −0.0904897 + 0.0513603i
\(987\) −2.87746 −0.0915904
\(988\) 4.80607 8.04849i 0.152902 0.256056i
\(989\) 40.1540 + 13.3990i 1.27682 + 0.426064i
\(990\) 1.37456 0.780176i 0.0436865 0.0247956i
\(991\) 38.9553i 1.23746i −0.785605 0.618728i \(-0.787648\pi\)
0.785605 0.618728i \(-0.212352\pi\)
\(992\) −8.52993 5.35243i −0.270826 0.169940i
\(993\) −21.3748 −0.678307
\(994\) −7.00967 + 3.97856i −0.222333 + 0.126192i
\(995\) 12.6767i 0.401877i
\(996\) 29.3266 + 17.5121i 0.929249 + 0.554891i
\(997\) 56.0474 1.77504 0.887520 0.460770i \(-0.152427\pi\)
0.887520 + 0.460770i \(0.152427\pi\)
\(998\) −17.3533 + 9.84943i −0.549310 + 0.311778i
\(999\) −8.80960 −0.278723
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 1380.2.p.b.91.17 yes 48
4.3 odd 2 1380.2.p.a.91.18 yes 48
23.22 odd 2 1380.2.p.a.91.17 48
92.91 even 2 inner 1380.2.p.b.91.18 yes 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1380.2.p.a.91.17 48 23.22 odd 2
1380.2.p.a.91.18 yes 48 4.3 odd 2
1380.2.p.b.91.17 yes 48 1.1 even 1 trivial
1380.2.p.b.91.18 yes 48 92.91 even 2 inner