Properties

Label 273.2.by.c.202.4
Level $273$
Weight $2$
Character 273.202
Analytic conductor $2.180$
Analytic rank $0$
Dimension $32$
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] = [273,2,Mod(76,273)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(273, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 6, 7]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("273.76");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 273.by (of order \(12\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.17991597518\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 202.4
Character \(\chi\) \(=\) 273.202
Dual form 273.2.by.c.223.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.11595 + 0.299019i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.576113 + 0.332619i) q^{4} +(-0.549341 + 0.549341i) q^{5} +(1.11595 + 0.299019i) q^{6} +(0.347225 + 2.62287i) q^{7} +(2.17732 - 2.17732i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-1.11595 + 0.299019i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.576113 + 0.332619i) q^{4} +(-0.549341 + 0.549341i) q^{5} +(1.11595 + 0.299019i) q^{6} +(0.347225 + 2.62287i) q^{7} +(2.17732 - 2.17732i) q^{8} +(0.500000 + 0.866025i) q^{9} +(0.448776 - 0.777302i) q^{10} +(-0.824353 - 3.07653i) q^{11} +0.665238 q^{12} +(-2.63686 - 2.45905i) q^{13} +(-1.17177 - 2.82317i) q^{14} +(0.750414 - 0.201073i) q^{15} +(-1.11349 + 1.92862i) q^{16} +(-1.74975 - 3.03065i) q^{17} +(-0.816934 - 0.816934i) q^{18} +(-6.06267 - 1.62449i) q^{19} +(0.133761 - 0.499204i) q^{20} +(1.01073 - 2.44508i) q^{21} +(1.83988 + 3.18676i) q^{22} +(-4.89067 - 2.82363i) q^{23} +(-2.97428 + 0.796956i) q^{24} +4.39645i q^{25} +(3.67792 + 1.95572i) q^{26} -1.00000i q^{27} +(-1.07246 - 1.39557i) q^{28} +(4.54654 - 7.87483i) q^{29} +(-0.777302 + 0.448776i) q^{30} +(0.888029 - 0.888029i) q^{31} +(-0.928002 + 3.46335i) q^{32} +(-0.824353 + 3.07653i) q^{33} +(2.85886 + 2.85886i) q^{34} +(-1.63160 - 1.25010i) q^{35} +(-0.576113 - 0.332619i) q^{36} +(0.151142 + 0.564068i) q^{37} +7.25141 q^{38} +(1.05406 + 3.44804i) q^{39} +2.39219i q^{40} +(-0.704976 - 2.63101i) q^{41} +(-0.396799 + 3.03082i) q^{42} +(6.60921 - 3.81583i) q^{43} +(1.49823 + 1.49823i) q^{44} +(-0.750414 - 0.201073i) q^{45} +(6.30208 + 1.68864i) q^{46} +(-0.267009 - 0.267009i) q^{47} +(1.92862 - 1.11349i) q^{48} +(-6.75887 + 1.82145i) q^{49} +(-1.31462 - 4.90623i) q^{50} +3.49950i q^{51} +(2.33706 + 0.539622i) q^{52} -11.6025 q^{53} +(0.299019 + 1.11595i) q^{54} +(2.14292 + 1.23721i) q^{55} +(6.46685 + 4.95481i) q^{56} +(4.43818 + 4.43818i) q^{57} +(-2.71900 + 10.1474i) q^{58} +(-0.635122 + 2.37031i) q^{59} +(-0.365443 + 0.365443i) q^{60} +(6.70242 - 3.86964i) q^{61} +(-0.725461 + 1.25654i) q^{62} +(-2.09786 + 1.61214i) q^{63} -8.59639i q^{64} +(2.79940 - 0.0976783i) q^{65} -3.67976i q^{66} +(-6.90457 + 1.85007i) q^{67} +(2.01610 + 1.16400i) q^{68} +(2.82363 + 4.89067i) q^{69} +(2.19459 + 0.907181i) q^{70} +(-2.51079 + 9.37039i) q^{71} +(2.97428 + 0.796956i) q^{72} +(7.71628 + 7.71628i) q^{73} +(-0.337334 - 0.584279i) q^{74} +(2.19822 - 3.80744i) q^{75} +(4.03312 - 1.08067i) q^{76} +(7.78309 - 3.23042i) q^{77} +(-2.20731 - 3.53266i) q^{78} -10.8188 q^{79} +(-0.447786 - 1.67116i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(1.57344 + 2.72528i) q^{82} +(-10.3355 + 10.3355i) q^{83} +(0.230987 + 1.74483i) q^{84} +(2.62607 + 0.703654i) q^{85} +(-6.23456 + 6.23456i) q^{86} +(-7.87483 + 4.54654i) q^{87} +(-8.49348 - 4.90371i) q^{88} +(7.02589 - 1.88258i) q^{89} +0.897552 q^{90} +(5.53419 - 7.76999i) q^{91} +3.75677 q^{92} +(-1.21307 + 0.325041i) q^{93} +(0.377810 + 0.218129i) q^{94} +(4.22288 - 2.43808i) q^{95} +(2.53535 - 2.53535i) q^{96} +(0.704543 + 0.188782i) q^{97} +(6.99793 - 4.05368i) q^{98} +(2.25217 - 2.25217i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q - 2 q^{2} + 6 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} + 2 q^{8} + 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q - 2 q^{2} + 6 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} + 2 q^{8} + 16 q^{9} - 2 q^{10} - 4 q^{11} - 32 q^{12} - 6 q^{13} + 34 q^{14} + 4 q^{15} + 14 q^{16} + 8 q^{17} + 2 q^{18} - 2 q^{19} - 44 q^{20} + 2 q^{21} - 4 q^{22} - 18 q^{23} - 4 q^{24} + 28 q^{26} - 18 q^{28} - 18 q^{29} + 14 q^{31} - 8 q^{32} - 4 q^{33} + 66 q^{34} - 20 q^{35} + 6 q^{36} - 24 q^{37} - 24 q^{38} + 8 q^{39} + 16 q^{42} - 6 q^{43} - 20 q^{44} - 4 q^{45} - 58 q^{46} + 28 q^{47} + 60 q^{48} + 10 q^{49} + 70 q^{50} - 28 q^{52} - 80 q^{53} + 4 q^{54} - 60 q^{55} - 120 q^{56} + 16 q^{57} - 4 q^{58} + 42 q^{59} - 58 q^{60} - 36 q^{61} - 52 q^{62} + 2 q^{63} + 14 q^{65} + 26 q^{67} + 72 q^{68} - 2 q^{69} + 68 q^{70} - 4 q^{71} + 4 q^{72} - 12 q^{73} - 18 q^{74} - 16 q^{75} + 48 q^{76} - 28 q^{77} - 14 q^{78} - 4 q^{79} + 98 q^{80} - 16 q^{81} - 20 q^{82} + 36 q^{83} + 32 q^{84} - 10 q^{85} - 40 q^{86} + 96 q^{88} + 54 q^{89} - 4 q^{90} - 54 q^{91} - 4 q^{92} + 2 q^{93} + 60 q^{95} - 22 q^{96} + 40 q^{97} + 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(106\) \(157\)
\(\chi(n)\) \(1\) \(e\left(\frac{11}{12}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.11595 + 0.299019i −0.789098 + 0.211438i −0.630792 0.775952i \(-0.717270\pi\)
−0.158306 + 0.987390i \(0.550603\pi\)
\(3\) −0.866025 0.500000i −0.500000 0.288675i
\(4\) −0.576113 + 0.332619i −0.288056 + 0.166309i
\(5\) −0.549341 + 0.549341i −0.245673 + 0.245673i −0.819192 0.573519i \(-0.805578\pi\)
0.573519 + 0.819192i \(0.305578\pi\)
\(6\) 1.11595 + 0.299019i 0.455586 + 0.122074i
\(7\) 0.347225 + 2.62287i 0.131239 + 0.991351i
\(8\) 2.17732 2.17732i 0.769800 0.769800i
\(9\) 0.500000 + 0.866025i 0.166667 + 0.288675i
\(10\) 0.448776 0.777302i 0.141915 0.245805i
\(11\) −0.824353 3.07653i −0.248552 0.927608i −0.971565 0.236774i \(-0.923910\pi\)
0.723013 0.690834i \(-0.242757\pi\)
\(12\) 0.665238 0.192038
\(13\) −2.63686 2.45905i −0.731335 0.682019i
\(14\) −1.17177 2.82317i −0.313170 0.754524i
\(15\) 0.750414 0.201073i 0.193756 0.0519168i
\(16\) −1.11349 + 1.92862i −0.278373 + 0.482156i
\(17\) −1.74975 3.03065i −0.424376 0.735041i 0.571986 0.820263i \(-0.306173\pi\)
−0.996362 + 0.0852225i \(0.972840\pi\)
\(18\) −0.816934 0.816934i −0.192553 0.192553i
\(19\) −6.06267 1.62449i −1.39087 0.372683i −0.515814 0.856701i \(-0.672510\pi\)
−0.875058 + 0.484017i \(0.839177\pi\)
\(20\) 0.133761 0.499204i 0.0299099 0.111625i
\(21\) 1.01073 2.44508i 0.220559 0.533561i
\(22\) 1.83988 + 3.18676i 0.392263 + 0.679420i
\(23\) −4.89067 2.82363i −1.01978 0.588768i −0.105737 0.994394i \(-0.533720\pi\)
−0.914039 + 0.405626i \(0.867053\pi\)
\(24\) −2.97428 + 0.796956i −0.607122 + 0.162678i
\(25\) 4.39645i 0.879290i
\(26\) 3.67792 + 1.95572i 0.721299 + 0.383548i
\(27\) 1.00000i 0.192450i
\(28\) −1.07246 1.39557i −0.202675 0.263739i
\(29\) 4.54654 7.87483i 0.844271 1.46232i −0.0419819 0.999118i \(-0.513367\pi\)
0.886253 0.463202i \(-0.153299\pi\)
\(30\) −0.777302 + 0.448776i −0.141915 + 0.0819349i
\(31\) 0.888029 0.888029i 0.159495 0.159495i −0.622848 0.782343i \(-0.714025\pi\)
0.782343 + 0.622848i \(0.214025\pi\)
\(32\) −0.928002 + 3.46335i −0.164049 + 0.612239i
\(33\) −0.824353 + 3.07653i −0.143501 + 0.535555i
\(34\) 2.85886 + 2.85886i 0.490290 + 0.490290i
\(35\) −1.63160 1.25010i −0.275790 0.211306i
\(36\) −0.576113 0.332619i −0.0960188 0.0554365i
\(37\) 0.151142 + 0.564068i 0.0248475 + 0.0927322i 0.977236 0.212155i \(-0.0680480\pi\)
−0.952389 + 0.304887i \(0.901381\pi\)
\(38\) 7.25141 1.17633
\(39\) 1.05406 + 3.44804i 0.168785 + 0.552128i
\(40\) 2.39219i 0.378238i
\(41\) −0.704976 2.63101i −0.110099 0.410894i 0.888775 0.458344i \(-0.151557\pi\)
−0.998874 + 0.0474499i \(0.984891\pi\)
\(42\) −0.396799 + 3.03082i −0.0612275 + 0.467666i
\(43\) 6.60921 3.81583i 1.00790 0.581909i 0.0973205 0.995253i \(-0.468973\pi\)
0.910575 + 0.413344i \(0.135639\pi\)
\(44\) 1.49823 + 1.49823i 0.225867 + 0.225867i
\(45\) −0.750414 0.201073i −0.111865 0.0299742i
\(46\) 6.30208 + 1.68864i 0.929191 + 0.248976i
\(47\) −0.267009 0.267009i −0.0389472 0.0389472i 0.687365 0.726312i \(-0.258767\pi\)
−0.726312 + 0.687365i \(0.758767\pi\)
\(48\) 1.92862 1.11349i 0.278373 0.160719i
\(49\) −6.75887 + 1.82145i −0.965553 + 0.260207i
\(50\) −1.31462 4.90623i −0.185915 0.693845i
\(51\) 3.49950i 0.490027i
\(52\) 2.33706 + 0.539622i 0.324092 + 0.0748321i
\(53\) −11.6025 −1.59372 −0.796862 0.604161i \(-0.793508\pi\)
−0.796862 + 0.604161i \(0.793508\pi\)
\(54\) 0.299019 + 1.11595i 0.0406913 + 0.151862i
\(55\) 2.14292 + 1.23721i 0.288951 + 0.166826i
\(56\) 6.46685 + 4.95481i 0.864169 + 0.662114i
\(57\) 4.43818 + 4.43818i 0.587852 + 0.587852i
\(58\) −2.71900 + 10.1474i −0.357022 + 1.33242i
\(59\) −0.635122 + 2.37031i −0.0826858 + 0.308588i −0.994866 0.101202i \(-0.967731\pi\)
0.912180 + 0.409790i \(0.134398\pi\)
\(60\) −0.365443 + 0.365443i −0.0471784 + 0.0471784i
\(61\) 6.70242 3.86964i 0.858157 0.495457i −0.00523788 0.999986i \(-0.501667\pi\)
0.863395 + 0.504529i \(0.168334\pi\)
\(62\) −0.725461 + 1.25654i −0.0921337 + 0.159580i
\(63\) −2.09786 + 1.61214i −0.264305 + 0.203110i
\(64\) 8.59639i 1.07455i
\(65\) 2.79940 0.0976783i 0.347223 0.0121155i
\(66\) 3.67976i 0.452947i
\(67\) −6.90457 + 1.85007i −0.843528 + 0.226023i −0.654607 0.755970i \(-0.727166\pi\)
−0.188921 + 0.981992i \(0.560499\pi\)
\(68\) 2.01610 + 1.16400i 0.244488 + 0.141155i
\(69\) 2.82363 + 4.89067i 0.339925 + 0.588768i
\(70\) 2.19459 + 0.907181i 0.262303 + 0.108429i
\(71\) −2.51079 + 9.37039i −0.297976 + 1.11206i 0.640849 + 0.767667i \(0.278582\pi\)
−0.938825 + 0.344394i \(0.888084\pi\)
\(72\) 2.97428 + 0.796956i 0.350522 + 0.0939221i
\(73\) 7.71628 + 7.71628i 0.903122 + 0.903122i 0.995705 0.0925826i \(-0.0295122\pi\)
−0.0925826 + 0.995705i \(0.529512\pi\)
\(74\) −0.337334 0.584279i −0.0392142 0.0679210i
\(75\) 2.19822 3.80744i 0.253829 0.439645i
\(76\) 4.03312 1.08067i 0.462630 0.123961i
\(77\) 7.78309 3.23042i 0.886965 0.368140i
\(78\) −2.20731 3.53266i −0.249929 0.399995i
\(79\) −10.8188 −1.21721 −0.608607 0.793472i \(-0.708271\pi\)
−0.608607 + 0.793472i \(0.708271\pi\)
\(80\) −0.447786 1.67116i −0.0500640 0.186841i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 1.57344 + 2.72528i 0.173757 + 0.300956i
\(83\) −10.3355 + 10.3355i −1.13447 + 1.13447i −0.145040 + 0.989426i \(0.546331\pi\)
−0.989426 + 0.145040i \(0.953669\pi\)
\(84\) 0.230987 + 1.74483i 0.0252028 + 0.190377i
\(85\) 2.62607 + 0.703654i 0.284837 + 0.0763220i
\(86\) −6.23456 + 6.23456i −0.672290 + 0.672290i
\(87\) −7.87483 + 4.54654i −0.844271 + 0.487440i
\(88\) −8.49348 4.90371i −0.905408 0.522737i
\(89\) 7.02589 1.88258i 0.744743 0.199553i 0.133558 0.991041i \(-0.457360\pi\)
0.611185 + 0.791488i \(0.290693\pi\)
\(90\) 0.897552 0.0946102
\(91\) 5.53419 7.76999i 0.580141 0.814516i
\(92\) 3.75677 0.391670
\(93\) −1.21307 + 0.325041i −0.125790 + 0.0337052i
\(94\) 0.377810 + 0.218129i 0.0389681 + 0.0224983i
\(95\) 4.22288 2.43808i 0.433258 0.250142i
\(96\) 2.53535 2.53535i 0.258763 0.258763i
\(97\) 0.704543 + 0.188782i 0.0715355 + 0.0191679i 0.294409 0.955679i \(-0.404877\pi\)
−0.222874 + 0.974847i \(0.571544\pi\)
\(98\) 6.99793 4.05368i 0.706898 0.409484i
\(99\) 2.25217 2.25217i 0.226352 0.226352i
\(100\) −1.46234 2.53285i −0.146234 0.253285i
\(101\) 5.71320 9.89554i 0.568484 0.984643i −0.428232 0.903669i \(-0.640863\pi\)
0.996716 0.0809746i \(-0.0258033\pi\)
\(102\) −1.04641 3.90527i −0.103610 0.386679i
\(103\) −19.3170 −1.90336 −0.951679 0.307094i \(-0.900643\pi\)
−0.951679 + 0.307094i \(0.900643\pi\)
\(104\) −11.0955 + 0.387150i −1.08800 + 0.0379631i
\(105\) 0.787950 + 1.89842i 0.0768961 + 0.185267i
\(106\) 12.9478 3.46936i 1.25760 0.336974i
\(107\) −4.59094 + 7.95175i −0.443823 + 0.768724i −0.997969 0.0636951i \(-0.979711\pi\)
0.554146 + 0.832419i \(0.313045\pi\)
\(108\) 0.332619 + 0.576113i 0.0320063 + 0.0554365i
\(109\) 1.79167 + 1.79167i 0.171610 + 0.171610i 0.787687 0.616076i \(-0.211279\pi\)
−0.616076 + 0.787687i \(0.711279\pi\)
\(110\) −2.76134 0.739899i −0.263284 0.0705466i
\(111\) 0.151142 0.564068i 0.0143457 0.0535390i
\(112\) −5.44516 2.25088i −0.514519 0.212688i
\(113\) 1.25451 + 2.17288i 0.118015 + 0.204407i 0.918981 0.394302i \(-0.129014\pi\)
−0.800966 + 0.598710i \(0.795680\pi\)
\(114\) −6.27990 3.62570i −0.588167 0.339578i
\(115\) 4.23779 1.13551i 0.395176 0.105887i
\(116\) 6.04906i 0.561641i
\(117\) 0.811171 3.51312i 0.0749928 0.324788i
\(118\) 2.83506i 0.260989i
\(119\) 7.34144 5.64167i 0.672989 0.517171i
\(120\) 1.19609 2.07170i 0.109188 0.189119i
\(121\) 0.740817 0.427711i 0.0673470 0.0388828i
\(122\) −6.32249 + 6.32249i −0.572411 + 0.572411i
\(123\) −0.704976 + 2.63101i −0.0635655 + 0.237230i
\(124\) −0.216230 + 0.806980i −0.0194180 + 0.0724689i
\(125\) −5.16186 5.16186i −0.461691 0.461691i
\(126\) 1.85905 2.42637i 0.165617 0.216158i
\(127\) −14.6248 8.44360i −1.29774 0.749249i −0.317724 0.948183i \(-0.602919\pi\)
−0.980013 + 0.198934i \(0.936252\pi\)
\(128\) 0.714478 + 2.66647i 0.0631515 + 0.235685i
\(129\) −7.63166 −0.671930
\(130\) −3.09479 + 0.946077i −0.271431 + 0.0829764i
\(131\) 9.18546i 0.802537i −0.915960 0.401269i \(-0.868569\pi\)
0.915960 0.401269i \(-0.131431\pi\)
\(132\) −0.548391 2.04662i −0.0477313 0.178136i
\(133\) 2.15571 16.4657i 0.186923 1.42775i
\(134\) 7.15197 4.12919i 0.617836 0.356708i
\(135\) 0.549341 + 0.549341i 0.0472798 + 0.0472798i
\(136\) −10.4085 2.78894i −0.892519 0.239150i
\(137\) 6.08217 + 1.62971i 0.519635 + 0.139236i 0.509098 0.860709i \(-0.329979\pi\)
0.0105372 + 0.999944i \(0.496646\pi\)
\(138\) −4.61344 4.61344i −0.392722 0.392722i
\(139\) 16.6243 9.59802i 1.41005 0.814093i 0.414658 0.909977i \(-0.363901\pi\)
0.995393 + 0.0958840i \(0.0305678\pi\)
\(140\) 1.35579 + 0.177502i 0.114585 + 0.0150017i
\(141\) 0.0977320 + 0.364741i 0.00823052 + 0.0307167i
\(142\) 11.2077i 0.940528i
\(143\) −5.39164 + 10.1395i −0.450872 + 0.847909i
\(144\) −2.22698 −0.185582
\(145\) 1.82837 + 6.82358i 0.151838 + 0.566667i
\(146\) −10.9183 6.30369i −0.903606 0.521697i
\(147\) 6.76408 + 1.80201i 0.557892 + 0.148627i
\(148\) −0.274694 0.274694i −0.0225797 0.0225797i
\(149\) −2.99088 + 11.1621i −0.245022 + 0.914435i 0.728350 + 0.685205i \(0.240287\pi\)
−0.973372 + 0.229230i \(0.926379\pi\)
\(150\) −1.31462 + 4.90623i −0.107338 + 0.400592i
\(151\) 8.90574 8.90574i 0.724738 0.724738i −0.244828 0.969567i \(-0.578732\pi\)
0.969567 + 0.244828i \(0.0787315\pi\)
\(152\) −16.7374 + 9.66336i −1.35759 + 0.783802i
\(153\) 1.74975 3.03065i 0.141459 0.245014i
\(154\) −7.71960 + 5.93228i −0.622063 + 0.478037i
\(155\) 0.975662i 0.0783671i
\(156\) −1.75414 1.63586i −0.140444 0.130973i
\(157\) 5.49387i 0.438459i −0.975673 0.219229i \(-0.929646\pi\)
0.975673 0.219229i \(-0.0703543\pi\)
\(158\) 12.0733 3.23503i 0.960501 0.257365i
\(159\) 10.0480 + 5.80124i 0.796862 + 0.460068i
\(160\) −1.39277 2.41235i −0.110108 0.190713i
\(161\) 5.70785 13.8080i 0.449841 1.08822i
\(162\) 0.299019 1.11595i 0.0234931 0.0876775i
\(163\) 10.2964 + 2.75892i 0.806480 + 0.216096i 0.638427 0.769682i \(-0.279585\pi\)
0.168053 + 0.985778i \(0.446252\pi\)
\(164\) 1.28127 + 1.28127i 0.100050 + 0.100050i
\(165\) −1.23721 2.14292i −0.0963169 0.166826i
\(166\) 8.44340 14.6244i 0.655335 1.13507i
\(167\) −12.5089 + 3.35175i −0.967967 + 0.259366i −0.707969 0.706243i \(-0.750389\pi\)
−0.259998 + 0.965609i \(0.583722\pi\)
\(168\) −3.12305 7.52442i −0.240949 0.580521i
\(169\) 0.906105 + 12.9684i 0.0697004 + 0.997568i
\(170\) −3.14098 −0.240902
\(171\) −1.62449 6.06267i −0.124228 0.463624i
\(172\) −2.53843 + 4.39670i −0.193554 + 0.335245i
\(173\) −0.498608 0.863615i −0.0379085 0.0656594i 0.846449 0.532470i \(-0.178736\pi\)
−0.884357 + 0.466811i \(0.845403\pi\)
\(174\) 7.42844 7.42844i 0.563149 0.563149i
\(175\) −11.5313 + 1.52656i −0.871684 + 0.115397i
\(176\) 6.85138 + 1.83582i 0.516442 + 0.138380i
\(177\) 1.73518 1.73518i 0.130424 0.130424i
\(178\) −7.27763 + 4.20174i −0.545482 + 0.314934i
\(179\) −4.88304 2.81922i −0.364975 0.210719i 0.306286 0.951940i \(-0.400914\pi\)
−0.671261 + 0.741221i \(0.734247\pi\)
\(180\) 0.499204 0.133761i 0.0372085 0.00996998i
\(181\) 21.5094 1.59878 0.799390 0.600813i \(-0.205156\pi\)
0.799390 + 0.600813i \(0.205156\pi\)
\(182\) −3.85252 + 10.3258i −0.285568 + 0.765397i
\(183\) −7.73929 −0.572104
\(184\) −16.7965 + 4.50062i −1.23826 + 0.331790i
\(185\) −0.392894 0.226838i −0.0288862 0.0166774i
\(186\) 1.25654 0.725461i 0.0921337 0.0531934i
\(187\) −7.88147 + 7.88147i −0.576350 + 0.576350i
\(188\) 0.242639 + 0.0650150i 0.0176963 + 0.00474171i
\(189\) 2.62287 0.347225i 0.190786 0.0252569i
\(190\) −3.98350 + 3.98350i −0.288993 + 0.288993i
\(191\) −4.39198 7.60714i −0.317793 0.550433i 0.662234 0.749297i \(-0.269608\pi\)
−0.980027 + 0.198863i \(0.936275\pi\)
\(192\) −4.29820 + 7.44469i −0.310196 + 0.537274i
\(193\) 0.249296 + 0.930384i 0.0179447 + 0.0669705i 0.974318 0.225178i \(-0.0722964\pi\)
−0.956373 + 0.292149i \(0.905630\pi\)
\(194\) −0.842685 −0.0605013
\(195\) −2.47319 1.31511i −0.177109 0.0941768i
\(196\) 3.28802 3.29749i 0.234859 0.235535i
\(197\) −16.6329 + 4.45678i −1.18505 + 0.317532i −0.796926 0.604076i \(-0.793542\pi\)
−0.388120 + 0.921609i \(0.626876\pi\)
\(198\) −1.83988 + 3.18676i −0.130754 + 0.226473i
\(199\) 1.12555 + 1.94951i 0.0797883 + 0.138197i 0.903159 0.429307i \(-0.141242\pi\)
−0.823370 + 0.567505i \(0.807909\pi\)
\(200\) 9.57249 + 9.57249i 0.676877 + 0.676877i
\(201\) 6.90457 + 1.85007i 0.487011 + 0.130494i
\(202\) −3.41670 + 12.7513i −0.240398 + 0.897179i
\(203\) 22.2333 + 9.19063i 1.56047 + 0.645056i
\(204\) −1.16400 2.01610i −0.0814961 0.141155i
\(205\) 1.83259 + 1.05805i 0.127994 + 0.0738973i
\(206\) 21.5568 5.77613i 1.50194 0.402442i
\(207\) 5.64726i 0.392512i
\(208\) 7.67872 2.34738i 0.532423 0.162762i
\(209\) 19.9911i 1.38282i
\(210\) −1.44698 1.88294i −0.0998510 0.129935i
\(211\) −10.3549 + 17.9352i −0.712859 + 1.23471i 0.250921 + 0.968008i \(0.419267\pi\)
−0.963780 + 0.266700i \(0.914067\pi\)
\(212\) 6.68434 3.85920i 0.459082 0.265051i
\(213\) 6.85960 6.85960i 0.470012 0.470012i
\(214\) 2.74555 10.2465i 0.187682 0.700440i
\(215\) −1.53452 + 5.72691i −0.104653 + 0.390572i
\(216\) −2.17732 2.17732i −0.148148 0.148148i
\(217\) 2.63753 + 2.02084i 0.179047 + 0.137183i
\(218\) −2.53516 1.46367i −0.171702 0.0991325i
\(219\) −2.82435 10.5406i −0.190852 0.712270i
\(220\) −1.64608 −0.110979
\(221\) −2.83869 + 12.2941i −0.190951 + 0.826993i
\(222\) 0.674667i 0.0452807i
\(223\) 5.92307 + 22.1052i 0.396638 + 1.48027i 0.818972 + 0.573834i \(0.194545\pi\)
−0.422333 + 0.906441i \(0.638789\pi\)
\(224\) −9.40613 1.23146i −0.628474 0.0822806i
\(225\) −3.80744 + 2.19822i −0.253829 + 0.146548i
\(226\) −2.04971 2.04971i −0.136345 0.136345i
\(227\) 15.1087 + 4.04837i 1.00280 + 0.268699i 0.722618 0.691248i \(-0.242939\pi\)
0.280182 + 0.959947i \(0.409605\pi\)
\(228\) −4.03312 1.08067i −0.267100 0.0715692i
\(229\) −3.61172 3.61172i −0.238669 0.238669i 0.577630 0.816299i \(-0.303978\pi\)
−0.816299 + 0.577630i \(0.803978\pi\)
\(230\) −4.38963 + 2.53435i −0.289444 + 0.167110i
\(231\) −8.35556 1.09392i −0.549755 0.0719747i
\(232\) −7.24678 27.0453i −0.475774 1.77561i
\(233\) 3.18656i 0.208758i 0.994538 + 0.104379i \(0.0332855\pi\)
−0.994538 + 0.104379i \(0.966714\pi\)
\(234\) 0.145259 + 4.16303i 0.00949587 + 0.272146i
\(235\) 0.293358 0.0191366
\(236\) −0.422507 1.57682i −0.0275029 0.102642i
\(237\) 9.36939 + 5.40942i 0.608607 + 0.351379i
\(238\) −6.50574 + 8.49107i −0.421704 + 0.550394i
\(239\) −1.61918 1.61918i −0.104736 0.104736i 0.652797 0.757533i \(-0.273596\pi\)
−0.757533 + 0.652797i \(0.773596\pi\)
\(240\) −0.447786 + 1.67116i −0.0289045 + 0.107873i
\(241\) 1.64242 6.12960i 0.105798 0.394842i −0.892637 0.450777i \(-0.851147\pi\)
0.998434 + 0.0559344i \(0.0178138\pi\)
\(242\) −0.698823 + 0.698823i −0.0449221 + 0.0449221i
\(243\) 0.866025 0.500000i 0.0555556 0.0320750i
\(244\) −2.57423 + 4.45870i −0.164798 + 0.285439i
\(245\) 2.71233 4.71353i 0.173284 0.301136i
\(246\) 3.14688i 0.200638i
\(247\) 11.9917 + 19.1920i 0.763016 + 1.22116i
\(248\) 3.86705i 0.245558i
\(249\) 14.1185 3.78305i 0.894725 0.239741i
\(250\) 7.30388 + 4.21690i 0.461938 + 0.266700i
\(251\) −10.7306 18.5859i −0.677308 1.17313i −0.975789 0.218716i \(-0.929813\pi\)
0.298481 0.954416i \(-0.403520\pi\)
\(252\) 0.672374 1.62656i 0.0423556 0.102464i
\(253\) −4.65534 + 17.3740i −0.292679 + 1.09229i
\(254\) 18.8453 + 5.04959i 1.18246 + 0.316839i
\(255\) −1.92242 1.92242i −0.120386 0.120386i
\(256\) 7.00174 + 12.1274i 0.437609 + 0.757961i
\(257\) 14.1914 24.5801i 0.885232 1.53327i 0.0397853 0.999208i \(-0.487333\pi\)
0.845447 0.534059i \(-0.179334\pi\)
\(258\) 8.51657 2.28201i 0.530219 0.142072i
\(259\) −1.42700 + 0.592283i −0.0886692 + 0.0368027i
\(260\) −1.58028 + 0.987406i −0.0980048 + 0.0612364i
\(261\) 9.09308 0.562847
\(262\) 2.74662 + 10.2505i 0.169687 + 0.633280i
\(263\) 6.33755 10.9770i 0.390790 0.676868i −0.601764 0.798674i \(-0.705535\pi\)
0.992554 + 0.121806i \(0.0388686\pi\)
\(264\) 4.90371 + 8.49348i 0.301803 + 0.522737i
\(265\) 6.37373 6.37373i 0.391535 0.391535i
\(266\) 2.51787 + 19.0195i 0.154381 + 1.16616i
\(267\) −7.02589 1.88258i −0.429977 0.115212i
\(268\) 3.36244 3.36244i 0.205394 0.205394i
\(269\) −5.62758 + 3.24908i −0.343120 + 0.198100i −0.661651 0.749812i \(-0.730144\pi\)
0.318531 + 0.947912i \(0.396810\pi\)
\(270\) −0.777302 0.448776i −0.0473051 0.0273116i
\(271\) 6.14616 1.64686i 0.373353 0.100040i −0.0672633 0.997735i \(-0.521427\pi\)
0.440616 + 0.897696i \(0.354760\pi\)
\(272\) 7.79332 0.472539
\(273\) −8.67774 + 3.96192i −0.525201 + 0.239786i
\(274\) −7.27473 −0.439482
\(275\) 13.5258 3.62423i 0.815636 0.218549i
\(276\) −3.25346 1.87839i −0.195835 0.113066i
\(277\) 15.6622 9.04260i 0.941053 0.543317i 0.0507626 0.998711i \(-0.483835\pi\)
0.890290 + 0.455394i \(0.150501\pi\)
\(278\) −15.6819 + 15.6819i −0.940538 + 0.940538i
\(279\) 1.21307 + 0.325041i 0.0726246 + 0.0194597i
\(280\) −6.27439 + 0.830628i −0.374967 + 0.0496395i
\(281\) −6.43538 + 6.43538i −0.383903 + 0.383903i −0.872506 0.488603i \(-0.837507\pi\)
0.488603 + 0.872506i \(0.337507\pi\)
\(282\) −0.218129 0.377810i −0.0129894 0.0224983i
\(283\) −7.33715 + 12.7083i −0.436148 + 0.755431i −0.997389 0.0722219i \(-0.976991\pi\)
0.561240 + 0.827653i \(0.310324\pi\)
\(284\) −1.67027 6.23354i −0.0991124 0.369892i
\(285\) −4.87616 −0.288839
\(286\) 2.98491 12.9274i 0.176502 0.764414i
\(287\) 6.65599 2.76261i 0.392891 0.163072i
\(288\) −3.46335 + 0.928002i −0.204080 + 0.0546830i
\(289\) 2.37677 4.11668i 0.139810 0.242158i
\(290\) −4.08075 7.06807i −0.239630 0.415051i
\(291\) −0.515761 0.515761i −0.0302344 0.0302344i
\(292\) −7.01203 1.87887i −0.410348 0.109952i
\(293\) −1.69762 + 6.33562i −0.0991763 + 0.370131i −0.997620 0.0689587i \(-0.978032\pi\)
0.898443 + 0.439090i \(0.144699\pi\)
\(294\) −8.08723 + 0.0116252i −0.471657 + 0.000677996i
\(295\) −0.953209 1.65101i −0.0554980 0.0961253i
\(296\) 1.55724 + 0.899074i 0.0905129 + 0.0522576i
\(297\) −3.07653 + 0.824353i −0.178518 + 0.0478338i
\(298\) 13.3507i 0.773385i
\(299\) 5.95258 + 19.4720i 0.344246 + 1.12609i
\(300\) 2.92468i 0.168857i
\(301\) 12.3033 + 16.0101i 0.709150 + 0.922809i
\(302\) −7.27540 + 12.6014i −0.418652 + 0.725127i
\(303\) −9.89554 + 5.71320i −0.568484 + 0.328214i
\(304\) 9.88377 9.88377i 0.566873 0.566873i
\(305\) −1.55616 + 5.80767i −0.0891055 + 0.332546i
\(306\) −1.04641 + 3.90527i −0.0598195 + 0.223249i
\(307\) −23.5768 23.5768i −1.34560 1.34560i −0.890377 0.455225i \(-0.849559\pi\)
−0.455225 0.890377i \(-0.650441\pi\)
\(308\) −3.40944 + 4.44988i −0.194271 + 0.253556i
\(309\) 16.7290 + 9.65849i 0.951679 + 0.549452i
\(310\) −0.291741 1.08879i −0.0165698 0.0618393i
\(311\) 2.90579 0.164772 0.0823861 0.996600i \(-0.473746\pi\)
0.0823861 + 0.996600i \(0.473746\pi\)
\(312\) 9.80253 + 5.21245i 0.554959 + 0.295097i
\(313\) 0.960626i 0.0542978i −0.999631 0.0271489i \(-0.991357\pi\)
0.999631 0.0271489i \(-0.00864282\pi\)
\(314\) 1.64277 + 6.13090i 0.0927069 + 0.345987i
\(315\) 0.266825 2.03806i 0.0150339 0.114831i
\(316\) 6.23287 3.59855i 0.350626 0.202434i
\(317\) −23.7216 23.7216i −1.33234 1.33234i −0.903274 0.429064i \(-0.858844\pi\)
−0.429064 0.903274i \(-0.641156\pi\)
\(318\) −12.9478 3.46936i −0.726078 0.194552i
\(319\) −27.9751 7.49590i −1.56630 0.419690i
\(320\) 4.72235 + 4.72235i 0.263988 + 0.263988i
\(321\) 7.95175 4.59094i 0.443823 0.256241i
\(322\) −2.24083 + 17.1158i −0.124877 + 0.953829i
\(323\) 5.68489 + 21.2163i 0.316316 + 1.18051i
\(324\) 0.665238i 0.0369576i
\(325\) 10.8111 11.5928i 0.599692 0.643055i
\(326\) −12.3153 −0.682082
\(327\) −0.655795 2.44746i −0.0362656 0.135345i
\(328\) −7.26351 4.19359i −0.401060 0.231552i
\(329\) 0.607617 0.793041i 0.0334990 0.0437218i
\(330\) 2.02144 + 2.02144i 0.111277 + 0.111277i
\(331\) 3.27417 12.2194i 0.179965 0.671637i −0.815688 0.578492i \(-0.803641\pi\)
0.995653 0.0931447i \(-0.0296919\pi\)
\(332\) 2.51662 9.39217i 0.138118 0.515462i
\(333\) −0.412926 + 0.412926i −0.0226282 + 0.0226282i
\(334\) 12.9571 7.48078i 0.708981 0.409330i
\(335\) 2.77665 4.80929i 0.151704 0.262760i
\(336\) 3.59021 + 4.67189i 0.195862 + 0.254873i
\(337\) 12.8172i 0.698196i 0.937086 + 0.349098i \(0.113512\pi\)
−0.937086 + 0.349098i \(0.886488\pi\)
\(338\) −4.88896 14.2012i −0.265924 0.772441i
\(339\) 2.50903i 0.136272i
\(340\) −1.74696 + 0.468097i −0.0947423 + 0.0253861i
\(341\) −3.46410 2.00000i −0.187591 0.108306i
\(342\) 3.62570 + 6.27990i 0.196056 + 0.339578i
\(343\) −7.12427 17.0952i −0.384675 0.923052i
\(344\) 6.08209 22.6987i 0.327925 1.22383i
\(345\) −4.23779 1.13551i −0.228155 0.0611339i
\(346\) 0.814660 + 0.814660i 0.0437964 + 0.0437964i
\(347\) −9.29372 16.0972i −0.498913 0.864143i 0.501086 0.865397i \(-0.332934\pi\)
−0.999999 + 0.00125445i \(0.999601\pi\)
\(348\) 3.02453 5.23864i 0.162132 0.280820i
\(349\) 4.62637 1.23963i 0.247644 0.0663560i −0.132862 0.991135i \(-0.542417\pi\)
0.380506 + 0.924779i \(0.375750\pi\)
\(350\) 12.4119 5.15164i 0.663445 0.275367i
\(351\) −2.45905 + 2.63686i −0.131255 + 0.140745i
\(352\) 11.4201 0.608693
\(353\) −3.19876 11.9379i −0.170253 0.635392i −0.997312 0.0732769i \(-0.976654\pi\)
0.827059 0.562116i \(-0.190012\pi\)
\(354\) −1.41753 + 2.45524i −0.0753410 + 0.130494i
\(355\) −3.76826 6.52683i −0.199999 0.346408i
\(356\) −3.42152 + 3.42152i −0.181340 + 0.181340i
\(357\) −9.17871 + 1.21511i −0.485789 + 0.0643106i
\(358\) 6.29224 + 1.68600i 0.332555 + 0.0891079i
\(359\) 4.20137 4.20137i 0.221740 0.221740i −0.587491 0.809231i \(-0.699884\pi\)
0.809231 + 0.587491i \(0.199884\pi\)
\(360\) −2.07170 + 1.19609i −0.109188 + 0.0630397i
\(361\) 17.6626 + 10.1975i 0.929608 + 0.536710i
\(362\) −24.0035 + 6.43171i −1.26159 + 0.338043i
\(363\) −0.855422 −0.0448980
\(364\) −0.603871 + 6.31716i −0.0316514 + 0.331109i
\(365\) −8.47775 −0.443746
\(366\) 8.63668 2.31419i 0.451446 0.120965i
\(367\) 5.05707 + 2.91970i 0.263977 + 0.152407i 0.626147 0.779705i \(-0.284631\pi\)
−0.362170 + 0.932112i \(0.617964\pi\)
\(368\) 10.8914 6.28818i 0.567756 0.327794i
\(369\) 1.92603 1.92603i 0.100265 0.100265i
\(370\) 0.506280 + 0.135657i 0.0263202 + 0.00705249i
\(371\) −4.02867 30.4318i −0.209158 1.57994i
\(372\) 0.590750 0.590750i 0.0306290 0.0306290i
\(373\) −5.17801 8.96858i −0.268107 0.464375i 0.700266 0.713882i \(-0.253065\pi\)
−0.968373 + 0.249507i \(0.919731\pi\)
\(374\) 6.43864 11.1521i 0.332934 0.576659i
\(375\) 1.88937 + 7.05123i 0.0975667 + 0.364124i
\(376\) −1.16273 −0.0599632
\(377\) −31.3532 + 9.58469i −1.61477 + 0.493636i
\(378\) −2.82317 + 1.17177i −0.145208 + 0.0602695i
\(379\) 6.76845 1.81360i 0.347672 0.0931584i −0.0807572 0.996734i \(-0.525734\pi\)
0.428429 + 0.903575i \(0.359067\pi\)
\(380\) −1.62190 + 2.80922i −0.0832018 + 0.144110i
\(381\) 8.44360 + 14.6248i 0.432579 + 0.749249i
\(382\) 7.17592 + 7.17592i 0.367152 + 0.367152i
\(383\) −7.14098 1.91342i −0.364887 0.0977711i 0.0717170 0.997425i \(-0.477152\pi\)
−0.436604 + 0.899654i \(0.643819\pi\)
\(384\) 0.714478 2.66647i 0.0364605 0.136073i
\(385\) −2.50097 + 6.05017i −0.127461 + 0.308345i
\(386\) −0.556404 0.963720i −0.0283202 0.0490521i
\(387\) 6.60921 + 3.81583i 0.335965 + 0.193970i
\(388\) −0.468688 + 0.125585i −0.0237940 + 0.00637559i
\(389\) 10.2280i 0.518581i 0.965799 + 0.259290i \(0.0834886\pi\)
−0.965799 + 0.259290i \(0.916511\pi\)
\(390\) 3.15320 + 0.728068i 0.159669 + 0.0368672i
\(391\) 19.7626i 0.999436i
\(392\) −10.7504 + 18.6821i −0.542975 + 0.943590i
\(393\) −4.59273 + 7.95484i −0.231673 + 0.401269i
\(394\) 17.2289 9.94711i 0.867979 0.501128i
\(395\) 5.94323 5.94323i 0.299037 0.299037i
\(396\) −0.548391 + 2.04662i −0.0275577 + 0.102847i
\(397\) −7.30250 + 27.2533i −0.366502 + 1.36780i 0.498872 + 0.866676i \(0.333748\pi\)
−0.865373 + 0.501128i \(0.832919\pi\)
\(398\) −1.83900 1.83900i −0.0921810 0.0921810i
\(399\) −10.0997 + 13.1818i −0.505618 + 0.659916i
\(400\) −8.47910 4.89541i −0.423955 0.244770i
\(401\) −1.82731 6.81960i −0.0912514 0.340555i 0.905173 0.425043i \(-0.139741\pi\)
−0.996424 + 0.0844884i \(0.973074\pi\)
\(402\) −8.25838 −0.411891
\(403\) −4.52532 + 0.157900i −0.225422 + 0.00786558i
\(404\) 7.60126i 0.378177i
\(405\) −0.201073 0.750414i −0.00999139 0.0372884i
\(406\) −27.5595 3.60813i −1.36776 0.179068i
\(407\) 1.61078 0.929982i 0.0798432 0.0460975i
\(408\) 7.61953 + 7.61953i 0.377223 + 0.377223i
\(409\) −30.3999 8.14562i −1.50318 0.402775i −0.589014 0.808123i \(-0.700484\pi\)
−0.914163 + 0.405348i \(0.867150\pi\)
\(410\) −2.36146 0.632752i −0.116624 0.0312494i
\(411\) −4.45246 4.45246i −0.219624 0.219624i
\(412\) 11.1288 6.42519i 0.548274 0.316546i
\(413\) −6.43753 0.842810i −0.316770 0.0414720i
\(414\) 1.68864 + 6.30208i 0.0829919 + 0.309730i
\(415\) 11.3554i 0.557415i
\(416\) 10.9636 6.85037i 0.537534 0.335867i
\(417\) −19.1960 −0.940034
\(418\) −5.97772 22.3092i −0.292380 1.09118i
\(419\) −20.4187 11.7887i −0.997519 0.575918i −0.0900058 0.995941i \(-0.528689\pi\)
−0.907513 + 0.420023i \(0.862022\pi\)
\(420\) −1.08540 0.831617i −0.0529620 0.0405787i
\(421\) 4.63273 + 4.63273i 0.225785 + 0.225785i 0.810929 0.585144i \(-0.198962\pi\)
−0.585144 + 0.810929i \(0.698962\pi\)
\(422\) 6.19260 23.1111i 0.301451 1.12503i
\(423\) 0.0977320 0.364741i 0.00475189 0.0177343i
\(424\) −25.2624 + 25.2624i −1.22685 + 1.22685i
\(425\) 13.3241 7.69267i 0.646314 0.373149i
\(426\) −5.60384 + 9.70614i −0.271507 + 0.470264i
\(427\) 12.4768 + 16.2359i 0.603795 + 0.785711i
\(428\) 6.10813i 0.295248i
\(429\) 9.73905 6.08526i 0.470206 0.293799i
\(430\) 6.84981i 0.330327i
\(431\) 27.8082 7.45118i 1.33947 0.358911i 0.483234 0.875491i \(-0.339462\pi\)
0.856239 + 0.516580i \(0.172795\pi\)
\(432\) 1.92862 + 1.11349i 0.0927910 + 0.0535729i
\(433\) 1.92063 + 3.32663i 0.0922998 + 0.159868i 0.908478 0.417932i \(-0.137245\pi\)
−0.816179 + 0.577800i \(0.803912\pi\)
\(434\) −3.54763 1.46649i −0.170291 0.0703937i
\(435\) 1.82837 6.82358i 0.0876637 0.327165i
\(436\) −1.62814 0.436260i −0.0779739 0.0208930i
\(437\) 25.0636 + 25.0636i 1.19895 + 1.19895i
\(438\) 6.30369 + 10.9183i 0.301202 + 0.521697i
\(439\) −7.29107 + 12.6285i −0.347984 + 0.602726i −0.985891 0.167388i \(-0.946467\pi\)
0.637907 + 0.770113i \(0.279800\pi\)
\(440\) 7.35963 1.97201i 0.350857 0.0940118i
\(441\) −4.95686 4.94263i −0.236041 0.235363i
\(442\) −0.508333 14.5685i −0.0241789 0.692953i
\(443\) 32.2060 1.53015 0.765076 0.643940i \(-0.222701\pi\)
0.765076 + 0.643940i \(0.222701\pi\)
\(444\) 0.100545 + 0.375239i 0.00477166 + 0.0178081i
\(445\) −2.82543 + 4.89379i −0.133938 + 0.231988i
\(446\) −13.2197 22.8973i −0.625973 1.08422i
\(447\) 8.17122 8.17122i 0.386486 0.386486i
\(448\) 22.5472 2.98488i 1.06525 0.141022i
\(449\) −19.3546 5.18606i −0.913402 0.244745i −0.228639 0.973511i \(-0.573428\pi\)
−0.684763 + 0.728766i \(0.740094\pi\)
\(450\) 3.59161 3.59161i 0.169310 0.169310i
\(451\) −7.51321 + 4.33776i −0.353783 + 0.204257i
\(452\) −1.44548 0.834549i −0.0679897 0.0392539i
\(453\) −12.1655 + 3.25973i −0.571583 + 0.153155i
\(454\) −18.0711 −0.848120
\(455\) 1.22822 + 7.30854i 0.0575798 + 0.342630i
\(456\) 19.3267 0.905057
\(457\) 14.5061 3.88690i 0.678567 0.181822i 0.0969563 0.995289i \(-0.469089\pi\)
0.581611 + 0.813467i \(0.302423\pi\)
\(458\) 5.11049 + 2.95054i 0.238797 + 0.137870i
\(459\) −3.03065 + 1.74975i −0.141459 + 0.0816712i
\(460\) −2.06375 + 2.06375i −0.0962228 + 0.0962228i
\(461\) 29.9515 + 8.02549i 1.39498 + 0.373784i 0.876540 0.481329i \(-0.159846\pi\)
0.518441 + 0.855113i \(0.326512\pi\)
\(462\) 9.65151 1.27770i 0.449029 0.0594441i
\(463\) 3.61564 3.61564i 0.168033 0.168033i −0.618081 0.786114i \(-0.712090\pi\)
0.786114 + 0.618081i \(0.212090\pi\)
\(464\) 10.1251 + 17.5371i 0.470044 + 0.814141i
\(465\) 0.487831 0.844949i 0.0226226 0.0391835i
\(466\) −0.952840 3.55605i −0.0441395 0.164731i
\(467\) 17.6775 0.818017 0.409009 0.912530i \(-0.365875\pi\)
0.409009 + 0.912530i \(0.365875\pi\)
\(468\) 0.701203 + 2.29376i 0.0324131 + 0.106029i
\(469\) −7.24994 17.4674i −0.334771 0.806569i
\(470\) −0.327374 + 0.0877195i −0.0151006 + 0.00404620i
\(471\) −2.74694 + 4.75783i −0.126572 + 0.219229i
\(472\) 3.77806 + 6.54379i 0.173899 + 0.301202i
\(473\) −17.1878 17.1878i −0.790297 0.790297i
\(474\) −12.0733 3.23503i −0.554545 0.148590i
\(475\) 7.14198 26.6542i 0.327696 1.22298i
\(476\) −2.35297 + 5.69214i −0.107848 + 0.260899i
\(477\) −5.80124 10.0480i −0.265621 0.460068i
\(478\) 2.29110 + 1.32276i 0.104792 + 0.0605018i
\(479\) −19.1281 + 5.12537i −0.873987 + 0.234184i −0.667811 0.744331i \(-0.732769\pi\)
−0.206176 + 0.978515i \(0.566102\pi\)
\(480\) 2.78554i 0.127142i
\(481\) 0.988534 1.85904i 0.0450733 0.0847647i
\(482\) 7.33146i 0.333939i
\(483\) −11.8472 + 9.10417i −0.539064 + 0.414254i
\(484\) −0.284529 + 0.492819i −0.0129332 + 0.0224009i
\(485\) −0.490740 + 0.283329i −0.0222834 + 0.0128653i
\(486\) −0.816934 + 0.816934i −0.0370569 + 0.0370569i
\(487\) 10.1291 37.8022i 0.458992 1.71298i −0.217089 0.976152i \(-0.569656\pi\)
0.676080 0.736828i \(-0.263677\pi\)
\(488\) 6.16787 23.0188i 0.279206 1.04201i
\(489\) −7.53752 7.53752i −0.340859 0.340859i
\(490\) −1.61740 + 6.07111i −0.0730666 + 0.274265i
\(491\) 16.0715 + 9.27889i 0.725297 + 0.418750i 0.816699 0.577064i \(-0.195802\pi\)
−0.0914021 + 0.995814i \(0.529135\pi\)
\(492\) −0.468976 1.75024i −0.0211431 0.0789071i
\(493\) −31.8212 −1.43315
\(494\) −19.1210 17.8316i −0.860293 0.802282i
\(495\) 2.47443i 0.111217i
\(496\) 0.723862 + 2.70149i 0.0325023 + 0.121300i
\(497\) −25.4491 3.33183i −1.14155 0.149453i
\(498\) −14.6244 + 8.44340i −0.655335 + 0.378358i
\(499\) 3.54363 + 3.54363i 0.158635 + 0.158635i 0.781962 0.623327i \(-0.214219\pi\)
−0.623327 + 0.781962i \(0.714219\pi\)
\(500\) 4.69074 + 1.25688i 0.209776 + 0.0562094i
\(501\) 12.5089 + 3.35175i 0.558856 + 0.149745i
\(502\) 17.5323 + 17.5323i 0.782507 + 0.782507i
\(503\) 2.98438 1.72303i 0.133067 0.0768262i −0.431989 0.901879i \(-0.642188\pi\)
0.565056 + 0.825053i \(0.308855\pi\)
\(504\) −1.05756 + 8.07786i −0.0471077 + 0.359817i
\(505\) 2.29754 + 8.57453i 0.102239 + 0.381561i
\(506\) 20.7805i 0.923808i
\(507\) 5.69948 11.6840i 0.253123 0.518905i
\(508\) 11.2340 0.498428
\(509\) −7.93556 29.6159i −0.351737 1.31270i −0.884541 0.466463i \(-0.845528\pi\)
0.532803 0.846239i \(-0.321138\pi\)
\(510\) 2.72017 + 1.57049i 0.120451 + 0.0695424i
\(511\) −17.5595 + 22.9181i −0.776786 + 1.01384i
\(512\) −15.3439 15.3439i −0.678111 0.678111i
\(513\) −1.62449 + 6.06267i −0.0717229 + 0.267674i
\(514\) −8.48696 + 31.6738i −0.374344 + 1.39707i
\(515\) 10.6116 10.6116i 0.467604 0.467604i
\(516\) 4.39670 2.53843i 0.193554 0.111748i
\(517\) −0.601351 + 1.04157i −0.0264474 + 0.0458082i
\(518\) 1.41536 1.08766i 0.0621872 0.0477889i
\(519\) 0.997217i 0.0437729i
\(520\) 5.88252 6.30787i 0.257966 0.276619i
\(521\) 13.0906i 0.573510i −0.958004 0.286755i \(-0.907423\pi\)
0.958004 0.286755i \(-0.0925766\pi\)
\(522\) −10.1474 + 2.71900i −0.444141 + 0.119007i
\(523\) 29.9435 + 17.2879i 1.30934 + 0.755946i 0.981985 0.188957i \(-0.0605106\pi\)
0.327351 + 0.944903i \(0.393844\pi\)
\(524\) 3.05526 + 5.29186i 0.133469 + 0.231176i
\(525\) 10.7497 + 4.44361i 0.469154 + 0.193935i
\(526\) −3.79009 + 14.1448i −0.165256 + 0.616743i
\(527\) −4.24513 1.13748i −0.184921 0.0495494i
\(528\) −5.01556 5.01556i −0.218274 0.218274i
\(529\) 4.44578 + 7.70032i 0.193295 + 0.334797i
\(530\) −5.20691 + 9.01864i −0.226174 + 0.391745i
\(531\) −2.37031 + 0.635122i −0.102863 + 0.0275619i
\(532\) 4.23486 + 10.2031i 0.183604 + 0.442360i
\(533\) −4.61086 + 8.67118i −0.199719 + 0.375590i
\(534\) 8.40349 0.363654
\(535\) −1.84623 6.89022i −0.0798194 0.297890i
\(536\) −11.0053 + 19.0617i −0.475355 + 0.823340i
\(537\) 2.81922 + 4.88304i 0.121658 + 0.210719i
\(538\) 5.30857 5.30857i 0.228869 0.228869i
\(539\) 11.1754 + 19.2923i 0.481360 + 0.830979i
\(540\) −0.499204 0.133761i −0.0214823 0.00575617i
\(541\) 23.6775 23.6775i 1.01797 1.01797i 0.0181382 0.999835i \(-0.494226\pi\)
0.999835 0.0181382i \(-0.00577388\pi\)
\(542\) −6.36638 + 3.67563i −0.273460 + 0.157882i
\(543\) −18.6277 10.7547i −0.799390 0.461528i
\(544\) 12.1200 3.24754i 0.519640 0.139237i
\(545\) −1.96847 −0.0843201
\(546\) 8.49926 7.01612i 0.363735 0.300262i
\(547\) −9.25725 −0.395811 −0.197906 0.980221i \(-0.563414\pi\)
−0.197906 + 0.980221i \(0.563414\pi\)
\(548\) −4.04609 + 1.08415i −0.172840 + 0.0463124i
\(549\) 6.70242 + 3.86964i 0.286052 + 0.165152i
\(550\) −14.0104 + 8.08893i −0.597407 + 0.344913i
\(551\) −40.3567 + 40.3567i −1.71926 + 1.71926i
\(552\) 16.7965 + 4.50062i 0.714908 + 0.191559i
\(553\) −3.75657 28.3764i −0.159746 1.20669i
\(554\) −14.7744 + 14.7744i −0.627705 + 0.627705i
\(555\) 0.226838 + 0.392894i 0.00962872 + 0.0166774i
\(556\) −6.38496 + 11.0591i −0.270783 + 0.469009i
\(557\) 2.46966 + 9.21689i 0.104643 + 0.390532i 0.998304 0.0582092i \(-0.0185390\pi\)
−0.893662 + 0.448742i \(0.851872\pi\)
\(558\) −1.45092 −0.0614224
\(559\) −26.8109 6.19058i −1.13398 0.261834i
\(560\) 4.22775 1.75475i 0.178655 0.0741518i
\(561\) 10.7663 2.88482i 0.454553 0.121797i
\(562\) 5.25728 9.10588i 0.221765 0.384108i
\(563\) 1.08829 + 1.88498i 0.0458661 + 0.0794424i 0.888047 0.459753i \(-0.152062\pi\)
−0.842181 + 0.539195i \(0.818729\pi\)
\(564\) −0.177624 0.177624i −0.00747933 0.00747933i
\(565\) −1.88281 0.504497i −0.0792104 0.0212244i
\(566\) 4.38789 16.3758i 0.184437 0.688327i
\(567\) −2.44508 1.01073i −0.102684 0.0424466i
\(568\) 14.9356 + 25.8692i 0.626683 + 1.08545i
\(569\) 20.3648 + 11.7576i 0.853738 + 0.492906i 0.861910 0.507061i \(-0.169268\pi\)
−0.00817222 + 0.999967i \(0.502601\pi\)
\(570\) 5.44156 1.45806i 0.227922 0.0610715i
\(571\) 13.2414i 0.554134i 0.960851 + 0.277067i \(0.0893624\pi\)
−0.960851 + 0.277067i \(0.910638\pi\)
\(572\) −0.266400 7.63486i −0.0111388 0.319230i
\(573\) 8.78397i 0.366955i
\(574\) −6.60170 + 5.07321i −0.275550 + 0.211752i
\(575\) 12.4139 21.5016i 0.517697 0.896678i
\(576\) 7.44469 4.29820i 0.310196 0.179091i
\(577\) −1.10520 + 1.10520i −0.0460102 + 0.0460102i −0.729738 0.683727i \(-0.760358\pi\)
0.683727 + 0.729738i \(0.260358\pi\)
\(578\) −1.42140 + 5.30472i −0.0591223 + 0.220647i
\(579\) 0.249296 0.930384i 0.0103604 0.0386654i
\(580\) −3.32300 3.32300i −0.137980 0.137980i
\(581\) −30.6973 23.5198i −1.27354 0.975768i
\(582\) 0.729787 + 0.421343i 0.0302506 + 0.0174652i
\(583\) 9.56454 + 35.6954i 0.396123 + 1.47835i
\(584\) 33.6017 1.39045
\(585\) 1.48429 + 2.37551i 0.0613679 + 0.0982153i
\(586\) 7.57788i 0.313039i
\(587\) 6.57121 + 24.5241i 0.271223 + 1.01222i 0.958331 + 0.285662i \(0.0922133\pi\)
−0.687108 + 0.726556i \(0.741120\pi\)
\(588\) −4.49625 + 1.21170i −0.185422 + 0.0499696i
\(589\) −6.82642 + 3.94124i −0.281278 + 0.162396i
\(590\) 1.55742 + 1.55742i 0.0641179 + 0.0641179i
\(591\) 16.6329 + 4.45678i 0.684187 + 0.183327i
\(592\) −1.25617 0.336590i −0.0516283 0.0138338i
\(593\) 13.5799 + 13.5799i 0.557660 + 0.557660i 0.928641 0.370981i \(-0.120978\pi\)
−0.370981 + 0.928641i \(0.620978\pi\)
\(594\) 3.18676 1.83988i 0.130754 0.0754911i
\(595\) −0.933753 + 7.13216i −0.0382801 + 0.292390i
\(596\) −1.98964 7.42545i −0.0814989 0.304158i
\(597\) 2.25111i 0.0921316i
\(598\) −12.4653 19.9499i −0.509743 0.815810i
\(599\) −6.33246 −0.258737 −0.129369 0.991597i \(-0.541295\pi\)
−0.129369 + 0.991597i \(0.541295\pi\)
\(600\) −3.50377 13.0763i −0.143041 0.533836i
\(601\) 20.1592 + 11.6389i 0.822309 + 0.474760i 0.851212 0.524822i \(-0.175868\pi\)
−0.0289030 + 0.999582i \(0.509201\pi\)
\(602\) −18.5172 14.1876i −0.754706 0.578245i
\(603\) −5.05450 5.05450i −0.205835 0.205835i
\(604\) −2.16849 + 8.09292i −0.0882347 + 0.329296i
\(605\) −0.172002 + 0.641921i −0.00699288 + 0.0260978i
\(606\) 9.33461 9.33461i 0.379192 0.379192i
\(607\) 9.09221 5.24939i 0.369041 0.213066i −0.303998 0.952673i \(-0.598322\pi\)
0.673040 + 0.739607i \(0.264988\pi\)
\(608\) 11.2523 19.4896i 0.456343 0.790409i
\(609\) −14.6593 19.0760i −0.594025 0.772998i
\(610\) 6.94641i 0.281252i
\(611\) 0.0474768 + 1.36066i 0.00192071 + 0.0550462i
\(612\) 2.32800i 0.0941036i
\(613\) −8.40441 + 2.25196i −0.339451 + 0.0909556i −0.424518 0.905420i \(-0.639556\pi\)
0.0850667 + 0.996375i \(0.472890\pi\)
\(614\) 33.3606 + 19.2607i 1.34632 + 0.777300i
\(615\) −1.05805 1.83259i −0.0426646 0.0738973i
\(616\) 9.91264 23.9800i 0.399392 0.966180i
\(617\) 7.98973 29.8181i 0.321654 1.20043i −0.595978 0.803000i \(-0.703236\pi\)
0.917633 0.397430i \(-0.130098\pi\)
\(618\) −21.5568 5.77613i −0.867143 0.232350i
\(619\) 2.31233 + 2.31233i 0.0929403 + 0.0929403i 0.752048 0.659108i \(-0.229066\pi\)
−0.659108 + 0.752048i \(0.729066\pi\)
\(620\) −0.324524 0.562091i −0.0130332 0.0225741i
\(621\) −2.82363 + 4.89067i −0.113308 + 0.196256i
\(622\) −3.24272 + 0.868885i −0.130021 + 0.0348391i
\(623\) 7.37733 + 17.7743i 0.295566 + 0.712112i
\(624\) −7.82366 1.80647i −0.313197 0.0723165i
\(625\) −16.3110 −0.652440
\(626\) 0.287245 + 1.07201i 0.0114806 + 0.0428462i
\(627\) 9.99557 17.3128i 0.399184 0.691408i
\(628\) 1.82737 + 3.16509i 0.0729198 + 0.126301i
\(629\) 1.44503 1.44503i 0.0576173 0.0576173i
\(630\) 0.311652 + 2.35416i 0.0124165 + 0.0937919i
\(631\) 5.07213 + 1.35907i 0.201918 + 0.0541039i 0.358361 0.933583i \(-0.383336\pi\)
−0.156442 + 0.987687i \(0.550003\pi\)
\(632\) −23.5561 + 23.5561i −0.937011 + 0.937011i
\(633\) 17.9352 10.3549i 0.712859 0.411569i
\(634\) 33.5654 + 19.3790i 1.33305 + 0.769638i
\(635\) 12.6724 3.39556i 0.502889 0.134749i
\(636\) −7.71841 −0.306055
\(637\) 22.3013 + 11.8175i 0.883608 + 0.468227i
\(638\) 33.4603 1.32471
\(639\) −9.37039 + 2.51079i −0.370687 + 0.0993253i
\(640\) −1.85729 1.07231i −0.0734160 0.0423867i
\(641\) −28.4420 + 16.4210i −1.12339 + 0.648589i −0.942264 0.334871i \(-0.891307\pi\)
−0.181126 + 0.983460i \(0.557974\pi\)
\(642\) −7.50099 + 7.50099i −0.296041 + 0.296041i
\(643\) 35.7163 + 9.57017i 1.40852 + 0.377411i 0.881395 0.472380i \(-0.156605\pi\)
0.527120 + 0.849791i \(0.323272\pi\)
\(644\) 1.30444 + 9.85351i 0.0514023 + 0.388283i
\(645\) 4.19239 4.19239i 0.165075 0.165075i
\(646\) −12.6881 21.9765i −0.499208 0.864653i
\(647\) −24.0363 + 41.6322i −0.944966 + 1.63673i −0.189147 + 0.981949i \(0.560572\pi\)
−0.755819 + 0.654780i \(0.772761\pi\)
\(648\) 0.796956 + 2.97428i 0.0313074 + 0.116841i
\(649\) 7.81588 0.306800
\(650\) −8.59821 + 16.1698i −0.337249 + 0.634231i
\(651\) −1.27375 3.06886i −0.0499221 0.120278i
\(652\) −6.84958 + 1.83534i −0.268250 + 0.0718775i
\(653\) 17.6801 30.6228i 0.691876 1.19836i −0.279347 0.960190i \(-0.590118\pi\)
0.971223 0.238174i \(-0.0765488\pi\)
\(654\) 1.46367 + 2.53516i 0.0572341 + 0.0991325i
\(655\) 5.04595 + 5.04595i 0.197162 + 0.197162i
\(656\) 5.85921 + 1.56997i 0.228764 + 0.0612970i
\(657\) −2.82435 + 10.5406i −0.110189 + 0.411229i
\(658\) −0.440938 + 1.06669i −0.0171895 + 0.0415837i
\(659\) 14.6210 + 25.3243i 0.569554 + 0.986496i 0.996610 + 0.0822711i \(0.0262173\pi\)
−0.427056 + 0.904225i \(0.640449\pi\)
\(660\) 1.42555 + 0.823040i 0.0554894 + 0.0320368i
\(661\) −21.1225 + 5.65976i −0.821570 + 0.220139i −0.645033 0.764155i \(-0.723156\pi\)
−0.176537 + 0.984294i \(0.556490\pi\)
\(662\) 14.6153i 0.568038i
\(663\) 8.60545 9.22769i 0.334208 0.358374i
\(664\) 45.0073i 1.74662i
\(665\) 7.86105 + 10.2295i 0.304838 + 0.396682i
\(666\) 0.337334 0.584279i 0.0130714 0.0226403i
\(667\) −44.4713 + 25.6755i −1.72193 + 0.994159i
\(668\) 6.09168 6.09168i 0.235694 0.235694i
\(669\) 5.92307 22.1052i 0.228999 0.854637i
\(670\) −1.66054 + 6.19721i −0.0641521 + 0.239419i
\(671\) −17.4302 17.4302i −0.672886 0.672886i
\(672\) 7.53022 + 5.76954i 0.290484 + 0.222565i
\(673\) −6.52213 3.76555i −0.251409 0.145151i 0.369000 0.929429i \(-0.379700\pi\)
−0.620409 + 0.784278i \(0.713034\pi\)
\(674\) −3.83258 14.3034i −0.147625 0.550945i
\(675\) 4.39645 0.169219
\(676\) −4.83555 7.16986i −0.185983 0.275764i
\(677\) 30.7509i 1.18185i −0.806726 0.590926i \(-0.798763\pi\)
0.806726 0.590926i \(-0.201237\pi\)
\(678\) 0.750245 + 2.79995i 0.0288130 + 0.107532i
\(679\) −0.250514 + 1.91347i −0.00961386 + 0.0734323i
\(680\) 7.24989 4.18573i 0.278021 0.160515i
\(681\) −11.0603 11.0603i −0.423833 0.423833i
\(682\) 4.46380 + 1.19607i 0.170928 + 0.0458000i
\(683\) 14.8258 + 3.97256i 0.567293 + 0.152006i 0.531055 0.847338i \(-0.321796\pi\)
0.0362380 + 0.999343i \(0.488463\pi\)
\(684\) 2.95245 + 2.95245i 0.112890 + 0.112890i
\(685\) −4.23646 + 2.44592i −0.161867 + 0.0934538i
\(686\) 13.0621 + 16.9471i 0.498714 + 0.647044i
\(687\) 1.32198 + 4.93371i 0.0504368 + 0.188233i
\(688\) 16.9956i 0.647951i
\(689\) 30.5942 + 28.5311i 1.16555 + 1.08695i
\(690\) 5.06871 0.192962
\(691\) −12.7049 47.4152i −0.483316 1.80376i −0.587528 0.809204i \(-0.699899\pi\)
0.104212 0.994555i \(-0.466768\pi\)
\(692\) 0.574509 + 0.331693i 0.0218396 + 0.0126091i
\(693\) 6.68917 + 5.12514i 0.254100 + 0.194688i
\(694\) 15.1847 + 15.1847i 0.576404 + 0.576404i
\(695\) −3.85980 + 14.4050i −0.146411 + 0.546412i
\(696\) −7.24678 + 27.0453i −0.274688 + 1.02515i
\(697\) −6.74013 + 6.74013i −0.255301 + 0.255301i
\(698\) −4.79214 + 2.76674i −0.181385 + 0.104723i
\(699\) 1.59328 2.75964i 0.0602633 0.104379i
\(700\) 6.13557 4.71500i 0.231903 0.178210i
\(701\) 40.9218i 1.54559i 0.634653 + 0.772797i \(0.281143\pi\)
−0.634653 + 0.772797i \(0.718857\pi\)
\(702\) 1.95572 3.67792i 0.0738138 0.138814i
\(703\) 3.66529i 0.138239i
\(704\) −26.4470 + 7.08646i −0.996760 + 0.267081i
\(705\) −0.254056 0.146679i −0.00956829 0.00552425i
\(706\) 7.13933 + 12.3657i 0.268692 + 0.465389i
\(707\) 27.9385 + 11.5490i 1.05073 + 0.434344i
\(708\) −0.422507 + 1.57682i −0.0158788 + 0.0592604i
\(709\) −20.0521 5.37294i −0.753071 0.201785i −0.138191 0.990406i \(-0.544129\pi\)
−0.614880 + 0.788621i \(0.710796\pi\)
\(710\) 6.15685 + 6.15685i 0.231062 + 0.231062i
\(711\) −5.40942 9.36939i −0.202869 0.351379i
\(712\) 11.1986 19.3966i 0.419687 0.726919i
\(713\) −6.85053 + 1.83559i −0.256554 + 0.0687435i
\(714\) 9.87967 4.10061i 0.369737 0.153462i
\(715\) −2.60820 8.53191i −0.0975413 0.319075i
\(716\) 3.75090 0.140178
\(717\) 0.592662 + 2.21184i 0.0221333 + 0.0826028i
\(718\) −3.43224 + 5.94482i −0.128090 + 0.221859i
\(719\) −6.50138 11.2607i −0.242461 0.419954i 0.718954 0.695058i \(-0.244621\pi\)
−0.961415 + 0.275103i \(0.911288\pi\)
\(720\) 1.22337 1.22337i 0.0455925 0.0455925i
\(721\) −6.70734 50.6659i −0.249794 1.88690i
\(722\) −22.7598 6.09847i −0.847033 0.226962i
\(723\) −4.48718 + 4.48718i −0.166880 + 0.166880i
\(724\) −12.3918 + 7.15442i −0.460539 + 0.265892i
\(725\) 34.6213 + 19.9886i 1.28580 + 0.742359i
\(726\) 0.954610 0.255787i 0.0354289 0.00949315i
\(727\) −9.09604 −0.337353 −0.168677 0.985671i \(-0.553949\pi\)
−0.168677 + 0.985671i \(0.553949\pi\)
\(728\) −4.86806 28.9675i −0.180422 1.07361i
\(729\) −1.00000 −0.0370370
\(730\) 9.46076 2.53500i 0.350159 0.0938247i
\(731\) −23.1289 13.3535i −0.855453 0.493896i
\(732\) 4.45870 2.57423i 0.164798 0.0951463i
\(733\) −24.5299 + 24.5299i −0.906033 + 0.906033i −0.995949 0.0899161i \(-0.971340\pi\)
0.0899161 + 0.995949i \(0.471340\pi\)
\(734\) −6.51649 1.74609i −0.240528 0.0644493i
\(735\) −4.70571 + 2.72587i −0.173573 + 0.100545i
\(736\) 14.3178 14.3178i 0.527760 0.527760i
\(737\) 11.3836 + 19.7170i 0.419321 + 0.726285i
\(738\) −1.57344 + 2.72528i −0.0579191 + 0.100319i
\(739\) −12.5301 46.7628i −0.460926 1.72020i −0.670056 0.742311i \(-0.733730\pi\)
0.209130 0.977888i \(-0.432937\pi\)
\(740\) 0.301802 0.0110945
\(741\) −0.789153 22.6166i −0.0289903 0.830843i
\(742\) 13.5955 + 32.7558i 0.499106 + 1.20250i
\(743\) −11.2679 + 3.01923i −0.413379 + 0.110765i −0.459514 0.888171i \(-0.651976\pi\)
0.0461346 + 0.998935i \(0.485310\pi\)
\(744\) −1.93353 + 3.34897i −0.0708865 + 0.122779i
\(745\) −4.48879 7.77482i −0.164457 0.284847i
\(746\) 8.46019 + 8.46019i 0.309749 + 0.309749i
\(747\) −14.1185 3.78305i −0.516570 0.138414i
\(748\) 1.91909 7.16214i 0.0701689 0.261874i
\(749\) −22.4505 9.28039i −0.820322 0.339098i
\(750\) −4.21690 7.30388i −0.153979 0.266700i
\(751\) −12.9544 7.47922i −0.472712 0.272921i 0.244662 0.969608i \(-0.421323\pi\)
−0.717374 + 0.696688i \(0.754656\pi\)
\(752\) 0.812272 0.217648i 0.0296205 0.00793679i
\(753\) 21.4611i 0.782088i
\(754\) 32.1227 20.0713i 1.16984 0.730952i
\(755\) 9.78458i 0.356097i
\(756\) −1.39557 + 1.07246i −0.0507565 + 0.0390048i
\(757\) 13.2377 22.9284i 0.481134 0.833348i −0.518632 0.854998i \(-0.673558\pi\)
0.999766 + 0.0216496i \(0.00689182\pi\)
\(758\) −7.01097 + 4.04778i −0.254650 + 0.147022i
\(759\) 12.7186 12.7186i 0.461657 0.461657i
\(760\) 3.88608 14.5031i 0.140963 0.526081i
\(761\) −10.6129 + 39.6079i −0.384718 + 1.43579i 0.453893 + 0.891056i \(0.350035\pi\)
−0.838611 + 0.544731i \(0.816632\pi\)
\(762\) −13.7957 13.7957i −0.499767 0.499767i
\(763\) −4.07719 + 5.32141i −0.147604 + 0.192648i
\(764\) 5.06055 + 2.92171i 0.183084 + 0.105704i
\(765\) 0.703654 + 2.62607i 0.0254407 + 0.0949458i
\(766\) 8.54114 0.308604
\(767\) 7.50344 4.68838i 0.270934 0.169288i
\(768\) 14.0035i 0.505307i
\(769\) 0.837092 + 3.12407i 0.0301863 + 0.112657i 0.979375 0.202050i \(-0.0647604\pi\)
−0.949189 + 0.314707i \(0.898094\pi\)
\(770\) 0.981851 7.49955i 0.0353834 0.270265i
\(771\) −24.5801 + 14.1914i −0.885232 + 0.511089i
\(772\) −0.453085 0.453085i −0.0163069 0.0163069i
\(773\) −20.3857 5.46232i −0.733221 0.196466i −0.127158 0.991882i \(-0.540585\pi\)
−0.606063 + 0.795417i \(0.707252\pi\)
\(774\) −8.51657 2.28201i −0.306122 0.0820251i
\(775\) 3.90417 + 3.90417i 0.140242 + 0.140242i
\(776\) 1.94506 1.12298i 0.0698234 0.0403126i
\(777\) 1.53196 + 0.200566i 0.0549586 + 0.00719525i
\(778\) −3.05836 11.4140i −0.109648 0.409211i
\(779\) 17.0962i 0.612533i
\(780\) 1.86227 0.0649793i 0.0666798 0.00232663i
\(781\) 30.8980 1.10562
\(782\) −5.90937 22.0541i −0.211319 0.788652i
\(783\) −7.87483 4.54654i −0.281424 0.162480i
\(784\) 4.01305 15.0635i 0.143323 0.537982i
\(785\) 3.01801 + 3.01801i 0.107718 + 0.107718i
\(786\) 2.74662 10.2505i 0.0979688 0.365625i
\(787\) 12.5317 46.7690i 0.446707 1.66713i −0.264682 0.964336i \(-0.585267\pi\)
0.711389 0.702798i \(-0.248066\pi\)
\(788\) 8.10003 8.10003i 0.288552 0.288552i
\(789\) −10.9770 + 6.33755i −0.390790 + 0.225623i
\(790\) −4.85523 + 8.40951i −0.172741 + 0.299197i
\(791\) −5.26358 + 4.04490i −0.187151 + 0.143820i
\(792\) 9.80742i 0.348492i
\(793\) −27.1890 6.27789i −0.965511 0.222934i
\(794\) 32.5970i 1.15682i
\(795\) −8.70667 + 2.33295i −0.308794 + 0.0827411i
\(796\) −1.29689 0.748760i −0.0459671 0.0265391i
\(797\) −22.9487 39.7483i −0.812884 1.40796i −0.910837 0.412765i \(-0.864563\pi\)
0.0979535 0.995191i \(-0.468770\pi\)
\(798\) 7.32920 17.7303i 0.259451 0.627646i
\(799\) −0.342013 + 1.27641i −0.0120995 + 0.0451561i
\(800\) −15.2264 4.07991i −0.538336 0.144247i
\(801\) 5.14331 + 5.14331i 0.181730 + 0.181730i
\(802\) 4.07838 + 7.06395i 0.144012 + 0.249437i
\(803\) 17.3784 30.1003i 0.613271 1.06222i
\(804\) −4.59318 + 1.23074i −0.161989 + 0.0434048i
\(805\) 4.44976 + 10.7209i 0.156834 + 0.377861i
\(806\) 5.00283 1.52937i 0.176217 0.0538696i
\(807\) 6.49817 0.228746
\(808\) −9.10633 33.9853i −0.320359 1.19560i
\(809\) 22.7833 39.4619i 0.801019 1.38740i −0.117928 0.993022i \(-0.537625\pi\)
0.918946 0.394383i \(-0.129042\pi\)
\(810\) 0.448776 + 0.777302i 0.0157684 + 0.0273116i
\(811\) 15.7365 15.7365i 0.552584 0.552584i −0.374602 0.927186i \(-0.622221\pi\)
0.927186 + 0.374602i \(0.122221\pi\)
\(812\) −15.8659 + 2.10038i −0.556783 + 0.0737090i
\(813\) −6.14616 1.64686i −0.215555 0.0577579i
\(814\) −1.51947 + 1.51947i −0.0532573 + 0.0532573i
\(815\) −7.17186 + 4.14067i −0.251219 + 0.145041i
\(816\) −6.74921 3.89666i −0.236270 0.136410i
\(817\) −46.2683 + 12.3975i −1.61872 + 0.433735i
\(818\) 36.3605 1.27132
\(819\) 9.49610 + 0.907752i 0.331821 + 0.0317194i
\(820\) −1.40771 −0.0491592
\(821\) −51.3616 + 13.7623i −1.79253 + 0.480307i −0.992772 0.120014i \(-0.961706\pi\)
−0.799759 + 0.600322i \(0.795039\pi\)
\(822\) 6.30010 + 3.63736i 0.219741 + 0.126868i
\(823\) 0.0980900 0.0566323i 0.00341920 0.00197408i −0.498289 0.867011i \(-0.666038\pi\)
0.501709 + 0.865037i \(0.332705\pi\)
\(824\) −42.0593 + 42.0593i −1.46521 + 1.46521i
\(825\) −13.5258 3.62423i −0.470908 0.126179i
\(826\) 7.43600 0.984405i 0.258731 0.0342518i
\(827\) 5.18917 5.18917i 0.180445 0.180445i −0.611105 0.791550i \(-0.709275\pi\)
0.791550 + 0.611105i \(0.209275\pi\)
\(828\) 1.87839 + 3.25346i 0.0652784 + 0.113066i
\(829\) 2.19576 3.80317i 0.0762620 0.132090i −0.825372 0.564589i \(-0.809035\pi\)
0.901634 + 0.432499i \(0.142368\pi\)
\(830\) 3.39548 + 12.6721i 0.117859 + 0.439855i
\(831\) −18.0852 −0.627369
\(832\) −21.1390 + 22.6675i −0.732863 + 0.785855i
\(833\) 17.3465 + 17.2967i 0.601021 + 0.599295i
\(834\) 21.4219 5.73997i 0.741779 0.198759i
\(835\) 5.03040 8.71291i 0.174084 0.301523i
\(836\) −6.64943 11.5171i −0.229975 0.398329i
\(837\) −0.888029 0.888029i −0.0306948 0.0306948i
\(838\) 26.3114 + 7.05011i 0.908911 + 0.243542i
\(839\) −0.0267890 + 0.0999778i −0.000924858 + 0.00345162i −0.966387 0.257093i \(-0.917235\pi\)
0.965462 + 0.260544i \(0.0839021\pi\)
\(840\) 5.84910 + 2.41785i 0.201813 + 0.0834238i
\(841\) −26.8420 46.4917i −0.925587 1.60316i
\(842\) −6.55517 3.78463i −0.225906 0.130427i
\(843\) 8.79089 2.35551i 0.302774 0.0811282i
\(844\) 13.7769i 0.474220i
\(845\) −7.62183 6.62631i −0.262199 0.227952i
\(846\) 0.436257i 0.0149988i
\(847\) 1.37906 + 1.79455i 0.0473850 + 0.0616616i
\(848\) 12.9193 22.3768i 0.443650 0.768424i
\(849\) 12.7083 7.33715i 0.436148 0.251810i
\(850\) −12.5688 + 12.5688i −0.431107 + 0.431107i
\(851\) 0.853536 3.18544i 0.0292588 0.109195i
\(852\) −1.67027 + 6.23354i −0.0572225 + 0.213557i
\(853\) −30.7045 30.7045i −1.05130 1.05130i −0.998611 0.0526924i \(-0.983220\pi\)
−0.0526924 0.998611i \(-0.516780\pi\)
\(854\) −18.7784 14.3877i −0.642583 0.492338i
\(855\) 4.22288 + 2.43808i 0.144419 + 0.0833805i
\(856\) 7.31756 + 27.3095i 0.250109 + 0.933419i
\(857\) −46.5367 −1.58966 −0.794831 0.606831i \(-0.792441\pi\)
−0.794831 + 0.606831i \(0.792441\pi\)
\(858\) −9.04872 + 9.70302i −0.308918 + 0.331255i
\(859\) 34.8981i 1.19071i −0.803464 0.595354i \(-0.797012\pi\)
0.803464 0.595354i \(-0.202988\pi\)
\(860\) −1.02082 3.80975i −0.0348097 0.129912i
\(861\) −7.14557 0.935507i −0.243520 0.0318820i
\(862\) −28.8046 + 16.6303i −0.981088 + 0.566431i
\(863\) 33.6057 + 33.6057i 1.14395 + 1.14395i 0.987720 + 0.156232i \(0.0499348\pi\)
0.156232 + 0.987720i \(0.450065\pi\)
\(864\) 3.46335 + 0.928002i 0.117826 + 0.0315713i
\(865\) 0.748326 + 0.200513i 0.0254438 + 0.00681766i
\(866\) −3.13806 3.13806i −0.106636 0.106636i
\(867\) −4.11668 + 2.37677i −0.139810 + 0.0807193i
\(868\) −2.19168 0.286938i −0.0743905 0.00973931i
\(869\) 8.91854 + 33.2844i 0.302541 + 1.12910i
\(870\) 8.16150i 0.276701i
\(871\) 22.7559 + 12.1003i 0.771053 + 0.410004i
\(872\) 7.80207 0.264212
\(873\) 0.188782 + 0.704543i 0.00638929 + 0.0238452i
\(874\) −35.4643 20.4753i −1.19960 0.692587i
\(875\) 11.7465 15.3312i 0.397106 0.518289i
\(876\) 5.13316 + 5.13316i 0.173433 + 0.173433i
\(877\) 0.133090 0.496699i 0.00449413 0.0167723i −0.963642 0.267195i \(-0.913903\pi\)
0.968136 + 0.250423i \(0.0805697\pi\)
\(878\) 4.36033 16.2730i 0.147154 0.549186i
\(879\) 4.63800 4.63800i 0.156436 0.156436i
\(880\) −4.77224 + 2.75525i −0.160872 + 0.0928796i
\(881\) −18.3777 + 31.8310i −0.619159 + 1.07242i 0.370480 + 0.928840i \(0.379193\pi\)
−0.989639 + 0.143575i \(0.954140\pi\)
\(882\) 7.00956 + 4.03355i 0.236024 + 0.135817i
\(883\) 25.7950i 0.868071i −0.900896 0.434036i \(-0.857089\pi\)
0.900896 0.434036i \(-0.142911\pi\)
\(884\) −2.45386 8.02701i −0.0825321 0.269978i
\(885\) 1.90642i 0.0640835i
\(886\) −35.9403 + 9.63019i −1.20744 + 0.323532i
\(887\) 32.5539 + 18.7950i 1.09305 + 0.631074i 0.934388 0.356258i \(-0.115948\pi\)
0.158665 + 0.987332i \(0.449281\pi\)
\(888\) −0.899074 1.55724i −0.0301710 0.0522576i
\(889\) 17.0684 41.2906i 0.572455 1.38484i
\(890\) 1.68971 6.30610i 0.0566393 0.211381i
\(891\) 3.07653 + 0.824353i 0.103068 + 0.0276169i
\(892\) −10.7650 10.7650i −0.360438 0.360438i
\(893\) 1.18503 + 2.05254i 0.0396557 + 0.0686856i
\(894\) −6.67535 + 11.5620i −0.223257 + 0.386693i
\(895\) 4.23117 1.13374i 0.141432 0.0378967i
\(896\) −6.74571 + 2.79985i −0.225358 + 0.0935363i
\(897\) 4.58090 19.8395i 0.152952 0.662422i
\(898\) 23.1496 0.772512
\(899\) −2.95562 11.0305i −0.0985756 0.367889i
\(900\) 1.46234 2.53285i 0.0487447 0.0844283i
\(901\) 20.3014 + 35.1631i 0.676338 + 1.17145i
\(902\) 7.08732 7.08732i 0.235982 0.235982i
\(903\) −2.64990 20.0168i −0.0881833 0.666119i
\(904\) 7.46254 + 1.99958i 0.248200 + 0.0665051i
\(905\) −11.8160 + 11.8160i −0.392777 + 0.392777i
\(906\) 12.6014 7.27540i 0.418652 0.241709i
\(907\) −25.7384 14.8601i −0.854631 0.493421i 0.00757996 0.999971i \(-0.497587\pi\)
−0.862211 + 0.506550i \(0.830921\pi\)
\(908\) −10.0509 + 2.69312i −0.333550 + 0.0893745i
\(909\) 11.4264 0.378989
\(910\) −3.55602 7.78872i −0.117881 0.258194i
\(911\) −35.4837 −1.17563 −0.587814 0.808996i \(-0.700011\pi\)
−0.587814 + 0.808996i \(0.700011\pi\)
\(912\) −13.5015 + 3.61771i −0.447079 + 0.119794i
\(913\) 40.3175 + 23.2773i 1.33431 + 0.770366i
\(914\) −15.0259 + 8.67519i −0.497012 + 0.286950i
\(915\) 4.25151 4.25151i 0.140551 0.140551i
\(916\) 3.28209 + 0.879433i 0.108443 + 0.0290573i
\(917\) 24.0922 3.18942i 0.795596 0.105324i
\(918\) 2.85886 2.85886i 0.0943563 0.0943563i
\(919\) 0.276560 + 0.479016i 0.00912288 + 0.0158013i 0.870551 0.492079i \(-0.163763\pi\)
−0.861428 + 0.507880i \(0.830429\pi\)
\(920\) 6.75466 11.6994i 0.222694 0.385718i
\(921\) 8.62972 + 32.2066i 0.284359 + 1.06124i
\(922\) −35.8242 −1.17981
\(923\) 29.6629 18.5343i 0.976367 0.610063i
\(924\) 5.17760 2.14899i 0.170331 0.0706967i
\(925\) −2.47990 + 0.664486i −0.0815384 + 0.0218482i
\(926\) −2.95374 + 5.11603i −0.0970659 + 0.168123i
\(927\) −9.65849 16.7290i −0.317226 0.549452i
\(928\) 23.0541 + 23.0541i 0.756788 + 0.756788i
\(929\) 0.202032 + 0.0541344i 0.00662846 + 0.00177609i 0.262132 0.965032i \(-0.415574\pi\)
−0.255503 + 0.966808i \(0.582241\pi\)
\(930\) −0.291741 + 1.08879i −0.00956657 + 0.0357029i
\(931\) 43.9357 0.0631567i 1.43994 0.00206988i
\(932\) −1.05991 1.83582i −0.0347185 0.0601341i
\(933\) −2.51649 1.45290i −0.0823861 0.0475656i
\(934\) −19.7273 + 5.28590i −0.645496 + 0.172960i
\(935\) 8.65924i 0.283187i
\(936\) −5.88301 9.41538i −0.192292 0.307751i
\(937\) 7.20471i 0.235368i −0.993051 0.117684i \(-0.962453\pi\)
0.993051 0.117684i \(-0.0375470\pi\)
\(938\) 13.3137 + 17.3249i 0.434707 + 0.565678i
\(939\) −0.480313 + 0.831926i −0.0156744 + 0.0271489i
\(940\) −0.169007 + 0.0975764i −0.00551241 + 0.00318259i
\(941\) −27.6042 + 27.6042i −0.899870 + 0.899870i −0.995424 0.0955544i \(-0.969538\pi\)
0.0955544 + 0.995424i \(0.469538\pi\)
\(942\) 1.64277 6.13090i 0.0535244 0.199756i
\(943\) −3.98118 + 14.8580i −0.129645 + 0.483842i
\(944\) −3.86423 3.86423i −0.125770 0.125770i
\(945\) −1.25010 + 1.63160i −0.0406659 + 0.0530758i
\(946\) 24.3203 + 14.0413i 0.790721 + 0.456523i
\(947\) 10.3004 + 38.4417i 0.334719 + 1.24919i 0.904174 + 0.427164i \(0.140487\pi\)
−0.569455 + 0.822022i \(0.692846\pi\)
\(948\) −7.19710 −0.233751
\(949\) −1.37203 39.3215i −0.0445380 1.27643i
\(950\) 31.8804i 1.03434i
\(951\) 8.68271 + 32.4043i 0.281556 + 1.05078i
\(952\) 3.70094 28.2684i 0.119948 0.916185i
\(953\) 32.2352 18.6110i 1.04420 0.602870i 0.123181 0.992384i \(-0.460690\pi\)
0.921020 + 0.389514i \(0.127357\pi\)
\(954\) 9.47846 + 9.47846i 0.306877 + 0.306877i
\(955\) 6.59162 + 1.76622i 0.213300 + 0.0571535i
\(956\) 1.47140 + 0.394261i 0.0475885 + 0.0127513i
\(957\) 20.4792 + 20.4792i 0.661998 + 0.661998i
\(958\) 19.8135 11.4393i 0.640145 0.369588i
\(959\) −2.16264 + 16.5186i −0.0698352 + 0.533414i
\(960\) −1.72850 6.45086i −0.0557872 0.208200i
\(961\) 29.4228i 0.949123i
\(962\) −0.547271 + 2.37019i −0.0176447 + 0.0764179i
\(963\) −9.18189 −0.295882
\(964\) 1.09260 + 4.07764i 0.0351903 + 0.131332i
\(965\) −0.648047 0.374150i −0.0208614 0.0120443i
\(966\) 10.4985 13.7023i 0.337785 0.440866i
\(967\) 3.64583 + 3.64583i 0.117242 + 0.117242i 0.763294 0.646052i \(-0.223581\pi\)
−0.646052 + 0.763294i \(0.723581\pi\)
\(968\) 0.681733 2.54426i 0.0219117 0.0817757i
\(969\) 5.68489 21.2163i 0.182625 0.681566i
\(970\) 0.462922 0.462922i 0.0148635 0.0148635i
\(971\) 25.7260 14.8529i 0.825587 0.476653i −0.0267525 0.999642i \(-0.508517\pi\)
0.852339 + 0.522989i \(0.175183\pi\)
\(972\) −0.332619 + 0.576113i −0.0106688 + 0.0184788i
\(973\) 30.9467 + 40.2705i 0.992105 + 1.29101i
\(974\) 45.2142i 1.44876i
\(975\) −15.1591 + 4.63414i −0.485480 + 0.148411i
\(976\) 17.2353i 0.551687i
\(977\) 44.1801 11.8380i 1.41345 0.378732i 0.530293 0.847815i \(-0.322082\pi\)
0.883154 + 0.469083i \(0.155415\pi\)
\(978\) 10.6654 + 6.15766i 0.341041 + 0.196900i
\(979\) −11.5836 20.0634i −0.370214 0.641230i
\(980\) 0.00520036 + 3.61769i 0.000166119 + 0.115563i
\(981\) −0.655795 + 2.44746i −0.0209379 + 0.0781414i
\(982\) −20.7096 5.54912i −0.660870 0.177080i
\(983\) 36.4493 + 36.4493i 1.16255 + 1.16255i 0.983915 + 0.178637i \(0.0571687\pi\)
0.178637 + 0.983915i \(0.442831\pi\)
\(984\) 4.19359 + 7.26351i 0.133687 + 0.231552i
\(985\) 6.68886 11.5854i 0.213125 0.369143i
\(986\) 35.5109 9.51512i 1.13090 0.303023i
\(987\) −0.922732 + 0.382985i −0.0293709 + 0.0121906i
\(988\) −13.2922 7.06807i −0.422882 0.224865i
\(989\) −43.0980 −1.37044
\(990\) −0.739899 2.76134i −0.0235155 0.0877612i
\(991\) −1.36323 + 2.36118i −0.0433043 + 0.0750052i −0.886865 0.462028i \(-0.847122\pi\)
0.843561 + 0.537034i \(0.180455\pi\)
\(992\) 2.25146 + 3.89965i 0.0714840 + 0.123814i
\(993\) −8.94519 + 8.94519i −0.283867 + 0.283867i
\(994\) 29.3963 3.89159i 0.932393 0.123434i
\(995\) −1.68926 0.452636i −0.0535532 0.0143495i
\(996\) −6.87555 + 6.87555i −0.217860 + 0.217860i
\(997\) 9.41930 5.43824i 0.298312 0.172231i −0.343372 0.939199i \(-0.611569\pi\)
0.641684 + 0.766969i \(0.278236\pi\)
\(998\) −5.01414 2.89492i −0.158720 0.0916370i
\(999\) 0.564068 0.151142i 0.0178463 0.00478191i
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 273.2.by.c.202.4 32
3.2 odd 2 819.2.fm.f.748.5 32
7.6 odd 2 273.2.by.d.202.4 yes 32
13.2 odd 12 273.2.by.d.223.4 yes 32
21.20 even 2 819.2.fm.e.748.5 32
39.2 even 12 819.2.fm.e.496.5 32
91.41 even 12 inner 273.2.by.c.223.4 yes 32
273.41 odd 12 819.2.fm.f.496.5 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
273.2.by.c.202.4 32 1.1 even 1 trivial
273.2.by.c.223.4 yes 32 91.41 even 12 inner
273.2.by.d.202.4 yes 32 7.6 odd 2
273.2.by.d.223.4 yes 32 13.2 odd 12
819.2.fm.e.496.5 32 39.2 even 12
819.2.fm.e.748.5 32 21.20 even 2
819.2.fm.f.496.5 32 273.41 odd 12
819.2.fm.f.748.5 32 3.2 odd 2