Properties

Label 273.2.br.b.17.9
Level $273$
Weight $2$
Character 273.17
Analytic conductor $2.180$
Analytic rank $0$
Dimension $64$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [273,2,Mod(17,273)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(273, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("273.17");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 273.br (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.17991597518\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(32\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 17.9
Character \(\chi\) \(=\) 273.17
Dual form 273.2.br.b.257.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.52138 q^{2} +(-1.64324 + 0.547514i) q^{3} +0.314598 q^{4} +(1.84777 - 1.06681i) q^{5} +(2.49999 - 0.832977i) q^{6} +(-2.46764 + 0.954340i) q^{7} +2.56414 q^{8} +(2.40046 - 1.79939i) q^{9} +O(q^{10})\) \(q-1.52138 q^{2} +(-1.64324 + 0.547514i) q^{3} +0.314598 q^{4} +(1.84777 - 1.06681i) q^{5} +(2.49999 - 0.832977i) q^{6} +(-2.46764 + 0.954340i) q^{7} +2.56414 q^{8} +(2.40046 - 1.79939i) q^{9} +(-2.81117 + 1.62303i) q^{10} +(-0.983176 - 1.70291i) q^{11} +(-0.516959 + 0.172247i) q^{12} +(1.00389 + 3.46298i) q^{13} +(3.75422 - 1.45191i) q^{14} +(-2.45224 + 2.76471i) q^{15} -4.53022 q^{16} -2.98019 q^{17} +(-3.65201 + 2.73756i) q^{18} +(-1.80461 + 3.12568i) q^{19} +(0.581306 - 0.335617i) q^{20} +(3.53240 - 2.91927i) q^{21} +(1.49578 + 2.59078i) q^{22} +8.06678i q^{23} +(-4.21349 + 1.40390i) q^{24} +(-0.223820 + 0.387667i) q^{25} +(-1.52730 - 5.26850i) q^{26} +(-2.95933 + 4.27111i) q^{27} +(-0.776314 + 0.300234i) q^{28} +(-5.67051 - 3.27387i) q^{29} +(3.73078 - 4.20617i) q^{30} +(-2.68142 + 4.64436i) q^{31} +1.76392 q^{32} +(2.54796 + 2.25998i) q^{33} +4.53400 q^{34} +(-3.54153 + 4.39591i) q^{35} +(0.755179 - 0.566085i) q^{36} +3.66472i q^{37} +(2.74550 - 4.75534i) q^{38} +(-3.54566 - 5.14084i) q^{39} +(4.73795 - 2.73546i) q^{40} +(1.26089 + 0.727976i) q^{41} +(-5.37412 + 4.44133i) q^{42} +(0.823833 + 1.42692i) q^{43} +(-0.309305 - 0.535733i) q^{44} +(2.51589 - 5.88571i) q^{45} -12.2726i q^{46} +(7.14926 - 4.12763i) q^{47} +(7.44423 - 2.48036i) q^{48} +(5.17847 - 4.70993i) q^{49} +(0.340515 - 0.589789i) q^{50} +(4.89715 - 1.63169i) q^{51} +(0.315823 + 1.08945i) q^{52} +(-0.312061 - 0.180168i) q^{53} +(4.50226 - 6.49798i) q^{54} +(-3.63338 - 2.09773i) q^{55} +(-6.32736 + 2.44706i) q^{56} +(1.25405 - 6.12428i) q^{57} +(8.62700 + 4.98080i) q^{58} +12.2757i q^{59} +(-0.771469 + 0.869772i) q^{60} +(-1.10960 - 0.640630i) q^{61} +(4.07946 - 7.06584i) q^{62} +(-4.20623 + 6.73110i) q^{63} +6.37686 q^{64} +(5.54932 + 5.32783i) q^{65} +(-3.87642 - 3.43830i) q^{66} +(-5.03764 + 2.90848i) q^{67} -0.937561 q^{68} +(-4.41668 - 13.2556i) q^{69} +(5.38802 - 6.68786i) q^{70} +(-6.36642 - 11.0270i) q^{71} +(6.15510 - 4.61388i) q^{72} +(-1.00356 + 1.73822i) q^{73} -5.57543i q^{74} +(0.155536 - 0.759573i) q^{75} +(-0.567727 + 0.983332i) q^{76} +(4.05128 + 3.26388i) q^{77} +(5.39430 + 7.82118i) q^{78} +(-3.35196 - 5.80576i) q^{79} +(-8.37083 + 4.83290i) q^{80} +(2.52439 - 8.63872i) q^{81} +(-1.91830 - 1.10753i) q^{82} -0.817821i q^{83} +(1.11129 - 0.918398i) q^{84} +(-5.50671 + 3.17930i) q^{85} +(-1.25336 - 2.17089i) q^{86} +(11.1105 + 2.27506i) q^{87} +(-2.52100 - 4.36650i) q^{88} +15.4001i q^{89} +(-3.82763 + 8.95440i) q^{90} +(-5.78210 - 7.58731i) q^{91} +2.53779i q^{92} +(1.86336 - 9.09990i) q^{93} +(-10.8767 + 6.27969i) q^{94} +7.70073i q^{95} +(-2.89854 + 0.965771i) q^{96} +(9.24604 + 16.0146i) q^{97} +(-7.87842 + 7.16560i) q^{98} +(-5.42427 - 2.31865i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q - 6 q^{3} + 56 q^{4} - 6 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 64 q - 6 q^{3} + 56 q^{4} - 6 q^{7} - 6 q^{10} - 6 q^{12} - 12 q^{13} - 9 q^{15} + 16 q^{16} - 36 q^{18} - 12 q^{21} - 18 q^{22} - 12 q^{24} + 16 q^{25} + 18 q^{28} - 22 q^{30} + 36 q^{31} - 15 q^{33} - 24 q^{34} - 4 q^{36} - 9 q^{39} - 54 q^{40} + 39 q^{42} - 12 q^{43} - 6 q^{45} - 54 q^{48} + 2 q^{49} - 14 q^{51} - 48 q^{52} + 18 q^{54} + 42 q^{55} + 30 q^{58} - 9 q^{60} + 6 q^{61} + 3 q^{63} - 28 q^{64} - 9 q^{66} + 48 q^{67} - 39 q^{69} - 84 q^{70} - 123 q^{72} - 12 q^{73} + 18 q^{76} - 11 q^{78} + 4 q^{79} - 66 q^{82} + 27 q^{84} - 30 q^{85} - 30 q^{88} + 130 q^{91} + 84 q^{94} - 24 q^{96} - 12 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(92\) \(106\) \(157\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.52138 −1.07578 −0.537889 0.843016i \(-0.680778\pi\)
−0.537889 + 0.843016i \(0.680778\pi\)
\(3\) −1.64324 + 0.547514i −0.948723 + 0.316107i
\(4\) 0.314598 0.157299
\(5\) 1.84777 1.06681i 0.826350 0.477093i −0.0262514 0.999655i \(-0.508357\pi\)
0.852601 + 0.522562i \(0.175024\pi\)
\(6\) 2.49999 0.832977i 1.02062 0.340061i
\(7\) −2.46764 + 0.954340i −0.932679 + 0.360707i
\(8\) 2.56414 0.906559
\(9\) 2.40046 1.79939i 0.800152 0.599797i
\(10\) −2.81117 + 1.62303i −0.888969 + 0.513247i
\(11\) −0.983176 1.70291i −0.296439 0.513447i 0.678880 0.734249i \(-0.262466\pi\)
−0.975319 + 0.220802i \(0.929132\pi\)
\(12\) −0.516959 + 0.172247i −0.149233 + 0.0497234i
\(13\) 1.00389 + 3.46298i 0.278430 + 0.960456i
\(14\) 3.75422 1.45191i 1.00336 0.388041i
\(15\) −2.45224 + 2.76471i −0.633165 + 0.713845i
\(16\) −4.53022 −1.13256
\(17\) −2.98019 −0.722802 −0.361401 0.932411i \(-0.617701\pi\)
−0.361401 + 0.932411i \(0.617701\pi\)
\(18\) −3.65201 + 2.73756i −0.860787 + 0.645248i
\(19\) −1.80461 + 3.12568i −0.414006 + 0.717079i −0.995324 0.0965974i \(-0.969204\pi\)
0.581318 + 0.813677i \(0.302537\pi\)
\(20\) 0.581306 0.335617i 0.129984 0.0750463i
\(21\) 3.53240 2.91927i 0.770833 0.637038i
\(22\) 1.49578 + 2.59078i 0.318902 + 0.552355i
\(23\) 8.06678i 1.68204i 0.541004 + 0.841020i \(0.318045\pi\)
−0.541004 + 0.841020i \(0.681955\pi\)
\(24\) −4.21349 + 1.40390i −0.860074 + 0.286570i
\(25\) −0.223820 + 0.387667i −0.0447639 + 0.0775334i
\(26\) −1.52730 5.26850i −0.299529 1.03324i
\(27\) −2.95933 + 4.27111i −0.569523 + 0.821975i
\(28\) −0.776314 + 0.300234i −0.146710 + 0.0567388i
\(29\) −5.67051 3.27387i −1.05299 0.607942i −0.129503 0.991579i \(-0.541338\pi\)
−0.923484 + 0.383637i \(0.874672\pi\)
\(30\) 3.73078 4.20617i 0.681145 0.767939i
\(31\) −2.68142 + 4.64436i −0.481598 + 0.834152i −0.999777 0.0211203i \(-0.993277\pi\)
0.518179 + 0.855272i \(0.326610\pi\)
\(32\) 1.76392 0.311820
\(33\) 2.54796 + 2.25998i 0.443543 + 0.393413i
\(34\) 4.53400 0.777574
\(35\) −3.54153 + 4.39591i −0.598629 + 0.743045i
\(36\) 0.755179 0.566085i 0.125863 0.0943475i
\(37\) 3.66472i 0.602476i 0.953549 + 0.301238i \(0.0973998\pi\)
−0.953549 + 0.301238i \(0.902600\pi\)
\(38\) 2.74550 4.75534i 0.445379 0.771418i
\(39\) −3.54566 5.14084i −0.567760 0.823194i
\(40\) 4.73795 2.73546i 0.749135 0.432513i
\(41\) 1.26089 + 0.727976i 0.196918 + 0.113691i 0.595217 0.803565i \(-0.297066\pi\)
−0.398299 + 0.917256i \(0.630399\pi\)
\(42\) −5.37412 + 4.44133i −0.829245 + 0.685311i
\(43\) 0.823833 + 1.42692i 0.125633 + 0.217603i 0.921980 0.387237i \(-0.126570\pi\)
−0.796347 + 0.604840i \(0.793237\pi\)
\(44\) −0.309305 0.535733i −0.0466295 0.0807647i
\(45\) 2.51589 5.88571i 0.375047 0.877389i
\(46\) 12.2726i 1.80950i
\(47\) 7.14926 4.12763i 1.04283 0.602076i 0.122194 0.992506i \(-0.461007\pi\)
0.920633 + 0.390430i \(0.127674\pi\)
\(48\) 7.44423 2.48036i 1.07448 0.358009i
\(49\) 5.17847 4.70993i 0.739781 0.672847i
\(50\) 0.340515 0.589789i 0.0481560 0.0834087i
\(51\) 4.89715 1.63169i 0.685739 0.228483i
\(52\) 0.315823 + 1.08945i 0.0437968 + 0.151079i
\(53\) −0.312061 0.180168i −0.0428648 0.0247480i 0.478414 0.878134i \(-0.341212\pi\)
−0.521279 + 0.853386i \(0.674545\pi\)
\(54\) 4.50226 6.49798i 0.612681 0.884263i
\(55\) −3.63338 2.09773i −0.489924 0.282858i
\(56\) −6.32736 + 2.44706i −0.845529 + 0.327002i
\(57\) 1.25405 6.12428i 0.166103 0.811180i
\(58\) 8.62700 + 4.98080i 1.13278 + 0.654011i
\(59\) 12.2757i 1.59816i 0.601227 + 0.799078i \(0.294679\pi\)
−0.601227 + 0.799078i \(0.705321\pi\)
\(60\) −0.771469 + 0.869772i −0.0995962 + 0.112287i
\(61\) −1.10960 0.640630i −0.142070 0.0820243i 0.427280 0.904119i \(-0.359472\pi\)
−0.569350 + 0.822095i \(0.692805\pi\)
\(62\) 4.07946 7.06584i 0.518092 0.897362i
\(63\) −4.20623 + 6.73110i −0.529935 + 0.848038i
\(64\) 6.37686 0.797107
\(65\) 5.54932 + 5.32783i 0.688308 + 0.660836i
\(66\) −3.87642 3.43830i −0.477154 0.423225i
\(67\) −5.03764 + 2.90848i −0.615446 + 0.355328i −0.775094 0.631846i \(-0.782297\pi\)
0.159648 + 0.987174i \(0.448964\pi\)
\(68\) −0.937561 −0.113696
\(69\) −4.41668 13.2556i −0.531705 1.59579i
\(70\) 5.38802 6.68786i 0.643992 0.799352i
\(71\) −6.36642 11.0270i −0.755556 1.30866i −0.945098 0.326788i \(-0.894034\pi\)
0.189542 0.981873i \(-0.439300\pi\)
\(72\) 6.15510 4.61388i 0.725386 0.543751i
\(73\) −1.00356 + 1.73822i −0.117458 + 0.203443i −0.918760 0.394818i \(-0.870808\pi\)
0.801302 + 0.598260i \(0.204141\pi\)
\(74\) 5.57543i 0.648130i
\(75\) 0.155536 0.759573i 0.0179597 0.0877079i
\(76\) −0.567727 + 0.983332i −0.0651228 + 0.112796i
\(77\) 4.05128 + 3.26388i 0.461686 + 0.371954i
\(78\) 5.39430 + 7.82118i 0.610784 + 0.885574i
\(79\) −3.35196 5.80576i −0.377125 0.653199i 0.613518 0.789681i \(-0.289754\pi\)
−0.990643 + 0.136482i \(0.956421\pi\)
\(80\) −8.37083 + 4.83290i −0.935888 + 0.540335i
\(81\) 2.52439 8.63872i 0.280488 0.959858i
\(82\) −1.91830 1.10753i −0.211840 0.122306i
\(83\) 0.817821i 0.0897675i −0.998992 0.0448838i \(-0.985708\pi\)
0.998992 0.0448838i \(-0.0142917\pi\)
\(84\) 1.11129 0.918398i 0.121251 0.100205i
\(85\) −5.50671 + 3.17930i −0.597287 + 0.344844i
\(86\) −1.25336 2.17089i −0.135154 0.234093i
\(87\) 11.1105 + 2.27506i 1.19117 + 0.243912i
\(88\) −2.52100 4.36650i −0.268739 0.465470i
\(89\) 15.4001i 1.63241i 0.577763 + 0.816205i \(0.303926\pi\)
−0.577763 + 0.816205i \(0.696074\pi\)
\(90\) −3.82763 + 8.95440i −0.403467 + 0.943876i
\(91\) −5.78210 7.58731i −0.606129 0.795366i
\(92\) 2.53779i 0.264583i
\(93\) 1.86336 9.09990i 0.193222 0.943616i
\(94\) −10.8767 + 6.27969i −1.12185 + 0.647701i
\(95\) 7.70073i 0.790078i
\(96\) −2.89854 + 0.965771i −0.295831 + 0.0985685i
\(97\) 9.24604 + 16.0146i 0.938793 + 1.62604i 0.767726 + 0.640778i \(0.221388\pi\)
0.171067 + 0.985259i \(0.445279\pi\)
\(98\) −7.87842 + 7.16560i −0.795841 + 0.723835i
\(99\) −5.42427 2.31865i −0.545160 0.233033i
\(100\) −0.0704132 + 0.121959i −0.00704132 + 0.0121959i
\(101\) −2.25160 3.89989i −0.224043 0.388054i 0.731989 0.681316i \(-0.238592\pi\)
−0.956032 + 0.293263i \(0.905259\pi\)
\(102\) −7.45044 + 2.48243i −0.737703 + 0.245797i
\(103\) −12.3721 + 7.14302i −1.21906 + 0.703822i −0.964716 0.263293i \(-0.915192\pi\)
−0.254340 + 0.967115i \(0.581858\pi\)
\(104\) 2.57412 + 8.87954i 0.252413 + 0.870711i
\(105\) 3.41276 9.16257i 0.333051 0.894175i
\(106\) 0.474763 + 0.274104i 0.0461130 + 0.0266234i
\(107\) 13.6102i 1.31575i −0.753129 0.657873i \(-0.771456\pi\)
0.753129 0.657873i \(-0.228544\pi\)
\(108\) −0.930999 + 1.34368i −0.0895855 + 0.129296i
\(109\) 5.53592 + 3.19617i 0.530245 + 0.306137i 0.741116 0.671377i \(-0.234297\pi\)
−0.210871 + 0.977514i \(0.567630\pi\)
\(110\) 5.52775 + 3.19145i 0.527050 + 0.304292i
\(111\) −2.00648 6.02200i −0.190447 0.571583i
\(112\) 11.1790 4.32338i 1.05631 0.408521i
\(113\) 8.99405 5.19271i 0.846089 0.488489i −0.0132406 0.999912i \(-0.504215\pi\)
0.859329 + 0.511423i \(0.170881\pi\)
\(114\) −1.90789 + 9.31736i −0.178690 + 0.872650i
\(115\) 8.60575 + 14.9056i 0.802490 + 1.38995i
\(116\) −1.78393 1.02995i −0.165634 0.0956288i
\(117\) 8.64105 + 6.50633i 0.798865 + 0.601510i
\(118\) 18.6760i 1.71926i
\(119\) 7.35402 2.84411i 0.674142 0.260719i
\(120\) −6.28787 + 7.08909i −0.574002 + 0.647143i
\(121\) 3.56673 6.17776i 0.324248 0.561614i
\(122\) 1.68813 + 0.974643i 0.152836 + 0.0882400i
\(123\) −2.47052 0.505882i −0.222759 0.0456138i
\(124\) −0.843571 + 1.46111i −0.0757549 + 0.131211i
\(125\) 11.6232i 1.03961i
\(126\) 6.39927 10.2406i 0.570092 0.912301i
\(127\) −5.54147 + 9.59811i −0.491726 + 0.851694i −0.999955 0.00952776i \(-0.996967\pi\)
0.508229 + 0.861222i \(0.330301\pi\)
\(128\) −13.2295 −1.16933
\(129\) −2.13501 1.89371i −0.187977 0.166732i
\(130\) −8.44262 8.10566i −0.740467 0.710913i
\(131\) −2.71371 4.70029i −0.237098 0.410666i 0.722782 0.691076i \(-0.242863\pi\)
−0.959880 + 0.280410i \(0.909530\pi\)
\(132\) 0.801583 + 0.710987i 0.0697689 + 0.0618835i
\(133\) 1.47016 9.43525i 0.127479 0.818140i
\(134\) 7.66417 4.42491i 0.662083 0.382254i
\(135\) −0.911698 + 11.0491i −0.0784664 + 0.950955i
\(136\) −7.64161 −0.655263
\(137\) −20.8080 −1.77774 −0.888872 0.458156i \(-0.848510\pi\)
−0.888872 + 0.458156i \(0.848510\pi\)
\(138\) 6.71944 + 20.1669i 0.571997 + 1.71672i
\(139\) 16.8386 9.72179i 1.42823 0.824591i 0.431252 0.902231i \(-0.358072\pi\)
0.996981 + 0.0776402i \(0.0247386\pi\)
\(140\) −1.11416 + 1.38295i −0.0941637 + 0.116880i
\(141\) −9.48800 + 10.6970i −0.799034 + 0.900849i
\(142\) 9.68575 + 16.7762i 0.812810 + 1.40783i
\(143\) 4.91013 5.11426i 0.410606 0.427676i
\(144\) −10.8746 + 8.15164i −0.906217 + 0.679304i
\(145\) −13.9704 −1.16018
\(146\) 1.52680 2.64449i 0.126358 0.218859i
\(147\) −5.93070 + 10.5748i −0.489156 + 0.872196i
\(148\) 1.15291i 0.0947688i
\(149\) −1.71483 + 2.97017i −0.140484 + 0.243326i −0.927679 0.373379i \(-0.878199\pi\)
0.787195 + 0.616704i \(0.211533\pi\)
\(150\) −0.236629 + 1.15560i −0.0193207 + 0.0943543i
\(151\) 0.857777 + 0.495238i 0.0698049 + 0.0403019i 0.534496 0.845171i \(-0.320501\pi\)
−0.464691 + 0.885473i \(0.653835\pi\)
\(152\) −4.62727 + 8.01466i −0.375321 + 0.650075i
\(153\) −7.15381 + 5.36252i −0.578351 + 0.433534i
\(154\) −6.16354 4.96561i −0.496672 0.400140i
\(155\) 11.4423i 0.919068i
\(156\) −1.11546 1.61730i −0.0893082 0.129488i
\(157\) −6.80298 3.92770i −0.542937 0.313465i 0.203332 0.979110i \(-0.434823\pi\)
−0.746268 + 0.665645i \(0.768156\pi\)
\(158\) 5.09960 + 8.83277i 0.405703 + 0.702698i
\(159\) 0.611434 + 0.125202i 0.0484899 + 0.00992914i
\(160\) 3.25933 1.88177i 0.257672 0.148767i
\(161\) −7.69846 19.9059i −0.606723 1.56880i
\(162\) −3.84055 + 13.1428i −0.301742 + 1.03259i
\(163\) −1.05396 0.608506i −0.0825528 0.0476619i 0.458155 0.888872i \(-0.348510\pi\)
−0.540708 + 0.841210i \(0.681844\pi\)
\(164\) 0.396674 + 0.229020i 0.0309750 + 0.0178835i
\(165\) 7.11903 + 1.45775i 0.554216 + 0.113485i
\(166\) 1.24422i 0.0965700i
\(167\) 6.12231 + 3.53472i 0.473759 + 0.273525i 0.717812 0.696237i \(-0.245144\pi\)
−0.244053 + 0.969762i \(0.578477\pi\)
\(168\) 9.05756 7.48542i 0.698806 0.577513i
\(169\) −10.9844 + 6.95292i −0.844953 + 0.534840i
\(170\) 8.37781 4.83693i 0.642548 0.370976i
\(171\) 1.29242 + 10.7503i 0.0988341 + 0.822092i
\(172\) 0.259176 + 0.448907i 0.0197620 + 0.0342288i
\(173\) 3.12542 5.41338i 0.237621 0.411572i −0.722410 0.691465i \(-0.756966\pi\)
0.960031 + 0.279893i \(0.0902991\pi\)
\(174\) −16.9033 3.46124i −1.28143 0.262396i
\(175\) 0.182339 1.17022i 0.0137836 0.0884604i
\(176\) 4.45401 + 7.71457i 0.335734 + 0.581508i
\(177\) −6.72110 20.1718i −0.505189 1.51621i
\(178\) 23.4294i 1.75611i
\(179\) 13.9037 8.02733i 1.03921 0.599991i 0.119604 0.992822i \(-0.461838\pi\)
0.919611 + 0.392831i \(0.128504\pi\)
\(180\) 0.791494 1.85163i 0.0589945 0.138013i
\(181\) 4.68253i 0.348050i −0.984741 0.174025i \(-0.944323\pi\)
0.984741 0.174025i \(-0.0556773\pi\)
\(182\) 8.79678 + 11.5432i 0.652061 + 0.855638i
\(183\) 2.17410 + 0.445184i 0.160714 + 0.0329089i
\(184\) 20.6843i 1.52487i
\(185\) 3.90957 + 6.77157i 0.287437 + 0.497856i
\(186\) −2.83488 + 13.8444i −0.207864 + 1.01512i
\(187\) 2.93005 + 5.07499i 0.214266 + 0.371120i
\(188\) 2.24914 1.29854i 0.164036 0.0947060i
\(189\) 3.22646 13.3638i 0.234690 0.972070i
\(190\) 11.7157i 0.849949i
\(191\) −17.5596 10.1380i −1.27057 0.733562i −0.295472 0.955351i \(-0.595477\pi\)
−0.975095 + 0.221789i \(0.928810\pi\)
\(192\) −10.4787 + 3.49142i −0.756234 + 0.251971i
\(193\) 11.0346 6.37082i 0.794287 0.458582i −0.0471825 0.998886i \(-0.515024\pi\)
0.841470 + 0.540304i \(0.181691\pi\)
\(194\) −14.0667 24.3643i −1.00993 1.74926i
\(195\) −12.0359 5.71656i −0.861909 0.409371i
\(196\) 1.62914 1.48174i 0.116367 0.105838i
\(197\) 6.02585 10.4371i 0.429324 0.743611i −0.567490 0.823381i \(-0.692085\pi\)
0.996813 + 0.0797701i \(0.0254186\pi\)
\(198\) 8.25238 + 3.52754i 0.586471 + 0.250692i
\(199\) 0.787685i 0.0558375i −0.999610 0.0279188i \(-0.991112\pi\)
0.999610 0.0279188i \(-0.00888797\pi\)
\(200\) −0.573904 + 0.994031i −0.0405811 + 0.0702886i
\(201\) 6.68560 7.53750i 0.471566 0.531655i
\(202\) 3.42554 + 5.93322i 0.241020 + 0.417460i
\(203\) 17.1171 + 2.66713i 1.20139 + 0.187196i
\(204\) 1.54064 0.513328i 0.107866 0.0359401i
\(205\) 3.10646 0.216964
\(206\) 18.8226 10.8672i 1.31143 0.757157i
\(207\) 14.5153 + 19.3640i 1.00888 + 1.34589i
\(208\) −4.54786 15.6881i −0.315338 1.08777i
\(209\) 7.09700 0.490910
\(210\) −5.19210 + 13.9398i −0.358289 + 0.961934i
\(211\) 9.50759 16.4676i 0.654529 1.13368i −0.327482 0.944857i \(-0.606200\pi\)
0.982012 0.188821i \(-0.0604665\pi\)
\(212\) −0.0981737 0.0566806i −0.00674260 0.00389284i
\(213\) 16.4990 + 14.6342i 1.13049 + 1.00272i
\(214\) 20.7063i 1.41545i
\(215\) 3.04452 + 1.75775i 0.207634 + 0.119878i
\(216\) −7.58813 + 10.9517i −0.516307 + 0.745169i
\(217\) 2.18448 14.0196i 0.148292 0.951712i
\(218\) −8.42224 4.86258i −0.570426 0.329336i
\(219\) 0.697389 3.40576i 0.0471252 0.230140i
\(220\) −1.14305 0.659942i −0.0770646 0.0444933i
\(221\) −2.99179 10.3203i −0.201250 0.694220i
\(222\) 3.05262 + 9.16175i 0.204879 + 0.614896i
\(223\) −0.792230 + 1.37218i −0.0530516 + 0.0918881i −0.891332 0.453352i \(-0.850228\pi\)
0.838280 + 0.545240i \(0.183561\pi\)
\(224\) −4.35271 + 1.68338i −0.290828 + 0.112476i
\(225\) 0.160295 + 1.33332i 0.0106863 + 0.0888878i
\(226\) −13.6834 + 7.90009i −0.910204 + 0.525506i
\(227\) 11.2711i 0.748092i −0.927410 0.374046i \(-0.877970\pi\)
0.927410 0.374046i \(-0.122030\pi\)
\(228\) 0.394522 1.92669i 0.0261279 0.127598i
\(229\) 1.70730 + 2.95713i 0.112821 + 0.195412i 0.916907 0.399101i \(-0.130678\pi\)
−0.804085 + 0.594514i \(0.797345\pi\)
\(230\) −13.0926 22.6771i −0.863302 1.49528i
\(231\) −8.44423 3.14520i −0.555590 0.206939i
\(232\) −14.5400 8.39465i −0.954595 0.551136i
\(233\) −24.9375 + 14.3977i −1.63371 + 0.943222i −0.650772 + 0.759273i \(0.725555\pi\)
−0.982936 + 0.183948i \(0.941112\pi\)
\(234\) −13.1463 9.89860i −0.859402 0.647091i
\(235\) 8.80681 15.2539i 0.574493 0.995051i
\(236\) 3.86190i 0.251389i
\(237\) 8.68680 + 7.70500i 0.564268 + 0.500494i
\(238\) −11.1883 + 4.32698i −0.725227 + 0.280476i
\(239\) 12.4394 0.804638 0.402319 0.915500i \(-0.368204\pi\)
0.402319 + 0.915500i \(0.368204\pi\)
\(240\) 11.1092 12.5248i 0.717095 0.808469i
\(241\) 23.9445 1.54240 0.771202 0.636590i \(-0.219656\pi\)
0.771202 + 0.636590i \(0.219656\pi\)
\(242\) −5.42635 + 9.39872i −0.348819 + 0.604172i
\(243\) 0.581651 + 15.5776i 0.0373129 + 0.999304i
\(244\) −0.349079 0.201541i −0.0223475 0.0129023i
\(245\) 4.54403 14.2274i 0.290307 0.908952i
\(246\) 3.75860 + 0.769638i 0.239640 + 0.0490704i
\(247\) −12.6358 3.11147i −0.803995 0.197978i
\(248\) −6.87554 + 11.9088i −0.436597 + 0.756208i
\(249\) 0.447768 + 1.34387i 0.0283762 + 0.0851646i
\(250\) 17.6833i 1.11839i
\(251\) 4.84713 + 8.39547i 0.305948 + 0.529917i 0.977472 0.211065i \(-0.0676933\pi\)
−0.671524 + 0.740983i \(0.734360\pi\)
\(252\) −1.32327 + 2.11759i −0.0833582 + 0.133396i
\(253\) 13.7370 7.93107i 0.863639 0.498622i
\(254\) 8.43068 14.6024i 0.528988 0.916234i
\(255\) 7.30813 8.23935i 0.457653 0.515968i
\(256\) 7.37333 0.460833
\(257\) 3.37176 0.210325 0.105162 0.994455i \(-0.466464\pi\)
0.105162 + 0.994455i \(0.466464\pi\)
\(258\) 3.24817 + 2.88105i 0.202222 + 0.179367i
\(259\) −3.49739 9.04319i −0.217317 0.561916i
\(260\) 1.74580 + 1.67613i 0.108270 + 0.103949i
\(261\) −19.5028 + 2.34468i −1.20719 + 0.145132i
\(262\) 4.12859 + 7.15093i 0.255065 + 0.441786i
\(263\) −3.40506 + 1.96591i −0.209965 + 0.121223i −0.601295 0.799027i \(-0.705348\pi\)
0.391330 + 0.920250i \(0.372015\pi\)
\(264\) 6.53332 + 5.79491i 0.402098 + 0.356652i
\(265\) −0.768823 −0.0472284
\(266\) −2.23668 + 14.3546i −0.137140 + 0.880137i
\(267\) −8.43178 25.3061i −0.516017 1.54871i
\(268\) −1.58483 + 0.915003i −0.0968090 + 0.0558927i
\(269\) −9.95794 −0.607147 −0.303573 0.952808i \(-0.598180\pi\)
−0.303573 + 0.952808i \(0.598180\pi\)
\(270\) 1.38704 16.8099i 0.0844125 1.02302i
\(271\) 7.75422 0.471035 0.235518 0.971870i \(-0.424321\pi\)
0.235518 + 0.971870i \(0.424321\pi\)
\(272\) 13.5009 0.818613
\(273\) 13.6555 + 9.30197i 0.826470 + 0.562981i
\(274\) 31.6568 1.91246
\(275\) 0.880216 0.0530790
\(276\) −1.38948 4.17020i −0.0836367 0.251016i
\(277\) 25.0939 1.50775 0.753875 0.657018i \(-0.228183\pi\)
0.753875 + 0.657018i \(0.228183\pi\)
\(278\) −25.6180 + 14.7905i −1.53646 + 0.887077i
\(279\) 1.92038 + 15.9735i 0.114970 + 0.956309i
\(280\) −9.08098 + 11.2717i −0.542692 + 0.673615i
\(281\) −12.6834 −0.756631 −0.378315 0.925677i \(-0.623496\pi\)
−0.378315 + 0.925677i \(0.623496\pi\)
\(282\) 14.4349 16.2742i 0.859583 0.969114i
\(283\) 17.7369 10.2404i 1.05435 0.608727i 0.130484 0.991450i \(-0.458347\pi\)
0.923863 + 0.382723i \(0.125014\pi\)
\(284\) −2.00287 3.46906i −0.118848 0.205851i
\(285\) −4.21626 12.6541i −0.249749 0.749565i
\(286\) −7.47018 + 7.78073i −0.441721 + 0.460084i
\(287\) −3.80616 0.593061i −0.224671 0.0350073i
\(288\) 4.23421 3.17398i 0.249503 0.187029i
\(289\) −8.11848 −0.477558
\(290\) 21.2543 1.24810
\(291\) −23.9617 21.2535i −1.40466 1.24590i
\(292\) −0.315718 + 0.546839i −0.0184760 + 0.0320014i
\(293\) −0.806381 + 0.465564i −0.0471093 + 0.0271986i −0.523370 0.852106i \(-0.675325\pi\)
0.476260 + 0.879304i \(0.341992\pi\)
\(294\) 9.02285 16.0883i 0.526223 0.938290i
\(295\) 13.0959 + 22.6827i 0.762470 + 1.32064i
\(296\) 9.39683i 0.546180i
\(297\) 10.1829 + 0.840222i 0.590870 + 0.0487546i
\(298\) 2.60890 4.51876i 0.151130 0.261764i
\(299\) −27.9351 + 8.09820i −1.61553 + 0.468331i
\(300\) 0.0489312 0.238960i 0.00282505 0.0137964i
\(301\) −3.39469 2.73491i −0.195667 0.157637i
\(302\) −1.30500 0.753445i −0.0750946 0.0433559i
\(303\) 5.83516 + 5.17566i 0.335221 + 0.297334i
\(304\) 8.17529 14.1600i 0.468885 0.812133i
\(305\) −2.73373 −0.156533
\(306\) 10.8837 8.15843i 0.622178 0.466387i
\(307\) −30.5349 −1.74272 −0.871359 0.490646i \(-0.836761\pi\)
−0.871359 + 0.490646i \(0.836761\pi\)
\(308\) 1.27452 + 1.02681i 0.0726228 + 0.0585080i
\(309\) 16.4193 18.5116i 0.934064 1.05309i
\(310\) 17.4081i 0.988714i
\(311\) −7.99319 + 13.8446i −0.453252 + 0.785056i −0.998586 0.0531633i \(-0.983070\pi\)
0.545334 + 0.838219i \(0.316403\pi\)
\(312\) −9.09157 13.1818i −0.514709 0.746274i
\(313\) −18.2511 + 10.5373i −1.03161 + 0.595603i −0.917447 0.397859i \(-0.869753\pi\)
−0.114167 + 0.993462i \(0.536420\pi\)
\(314\) 10.3499 + 5.97553i 0.584079 + 0.337218i
\(315\) −0.591336 + 16.9248i −0.0333180 + 0.953605i
\(316\) −1.05452 1.82648i −0.0593214 0.102748i
\(317\) 0.601375 + 1.04161i 0.0337766 + 0.0585028i 0.882420 0.470463i \(-0.155913\pi\)
−0.848643 + 0.528966i \(0.822580\pi\)
\(318\) −0.930224 0.190479i −0.0521644 0.0106816i
\(319\) 12.8752i 0.720871i
\(320\) 11.7830 6.80291i 0.658689 0.380294i
\(321\) 7.45177 + 22.3648i 0.415917 + 1.24828i
\(322\) 11.7123 + 30.2844i 0.652700 + 1.68769i
\(323\) 5.37808 9.31510i 0.299244 0.518306i
\(324\) 0.794168 2.71772i 0.0441204 0.150985i
\(325\) −1.56717 0.385905i −0.0869311 0.0214062i
\(326\) 1.60348 + 0.925770i 0.0888086 + 0.0512736i
\(327\) −10.8468 2.22106i −0.599828 0.122825i
\(328\) 3.23310 + 1.86663i 0.178518 + 0.103067i
\(329\) −13.7026 + 17.0083i −0.755450 + 0.937699i
\(330\) −10.8308 2.21778i −0.596214 0.122085i
\(331\) 4.19705 + 2.42317i 0.230690 + 0.133189i 0.610891 0.791715i \(-0.290812\pi\)
−0.380200 + 0.924904i \(0.624145\pi\)
\(332\) 0.257285i 0.0141203i
\(333\) 6.59425 + 8.79699i 0.361363 + 0.482072i
\(334\) −9.31437 5.37765i −0.509660 0.294252i
\(335\) −6.20561 + 10.7484i −0.339049 + 0.587250i
\(336\) −16.0026 + 13.2250i −0.873011 + 0.721481i
\(337\) −17.4614 −0.951181 −0.475590 0.879667i \(-0.657765\pi\)
−0.475590 + 0.879667i \(0.657765\pi\)
\(338\) 16.7114 10.5780i 0.908983 0.575369i
\(339\) −11.9363 + 13.4572i −0.648289 + 0.730896i
\(340\) −1.73240 + 1.00020i −0.0939527 + 0.0542436i
\(341\) 10.5452 0.571057
\(342\) −1.96627 16.3552i −0.106324 0.884389i
\(343\) −8.28370 + 16.5644i −0.447278 + 0.894395i
\(344\) 2.11242 + 3.65882i 0.113894 + 0.197270i
\(345\) −22.3023 19.7817i −1.20072 1.06501i
\(346\) −4.75495 + 8.23581i −0.255627 + 0.442760i
\(347\) 3.10439i 0.166652i 0.996522 + 0.0833262i \(0.0265544\pi\)
−0.996522 + 0.0833262i \(0.973446\pi\)
\(348\) 3.49534 + 0.715730i 0.187370 + 0.0383672i
\(349\) −6.68893 + 11.5856i −0.358050 + 0.620161i −0.987635 0.156771i \(-0.949892\pi\)
0.629585 + 0.776932i \(0.283225\pi\)
\(350\) −0.277408 + 1.78035i −0.0148281 + 0.0951638i
\(351\) −17.7616 5.96034i −0.948044 0.318140i
\(352\) −1.73424 3.00380i −0.0924355 0.160103i
\(353\) −6.07968 + 3.51011i −0.323589 + 0.186824i −0.652991 0.757366i \(-0.726486\pi\)
0.329402 + 0.944190i \(0.393153\pi\)
\(354\) 10.2254 + 30.6891i 0.543471 + 1.63110i
\(355\) −23.5274 13.5836i −1.24871 0.720941i
\(356\) 4.84485i 0.256777i
\(357\) −10.5272 + 8.69998i −0.557159 + 0.460452i
\(358\) −21.1529 + 12.2126i −1.11796 + 0.645457i
\(359\) −2.02933 3.51489i −0.107104 0.185509i 0.807492 0.589878i \(-0.200824\pi\)
−0.914596 + 0.404369i \(0.867491\pi\)
\(360\) 6.45109 15.0918i 0.340002 0.795406i
\(361\) 2.98676 + 5.17323i 0.157198 + 0.272275i
\(362\) 7.12391i 0.374424i
\(363\) −2.47857 + 12.1044i −0.130091 + 0.635314i
\(364\) −1.81904 2.38695i −0.0953435 0.125110i
\(365\) 4.28244i 0.224153i
\(366\) −3.30763 0.677294i −0.172893 0.0354027i
\(367\) 1.24170 0.716898i 0.0648164 0.0374218i −0.467242 0.884130i \(-0.654752\pi\)
0.532058 + 0.846708i \(0.321419\pi\)
\(368\) 36.5443i 1.90501i
\(369\) 4.33663 0.521361i 0.225756 0.0271410i
\(370\) −5.94794 10.3021i −0.309219 0.535582i
\(371\) 0.941994 + 0.146778i 0.0489059 + 0.00762033i
\(372\) 0.586210 2.86281i 0.0303936 0.148430i
\(373\) −14.0574 + 24.3481i −0.727865 + 1.26070i 0.229919 + 0.973210i \(0.426154\pi\)
−0.957784 + 0.287489i \(0.907179\pi\)
\(374\) −4.45772 7.72100i −0.230503 0.399243i
\(375\) −6.36388 19.0997i −0.328629 0.986305i
\(376\) 18.3317 10.5838i 0.945385 0.545818i
\(377\) 5.64474 22.9235i 0.290719 1.18062i
\(378\) −4.90867 + 20.3314i −0.252475 + 1.04573i
\(379\) 18.3318 + 10.5839i 0.941643 + 0.543658i 0.890475 0.455032i \(-0.150372\pi\)
0.0511683 + 0.998690i \(0.483706\pi\)
\(380\) 2.42263i 0.124279i
\(381\) 3.85085 18.8060i 0.197285 0.963461i
\(382\) 26.7148 + 15.4238i 1.36685 + 0.789150i
\(383\) 27.3258 + 15.7765i 1.39628 + 0.806144i 0.994001 0.109372i \(-0.0348841\pi\)
0.402281 + 0.915516i \(0.368217\pi\)
\(384\) 21.7391 7.24331i 1.10937 0.369634i
\(385\) 10.9678 + 1.70896i 0.558971 + 0.0870967i
\(386\) −16.7878 + 9.69245i −0.854477 + 0.493333i
\(387\) 4.54516 + 1.94287i 0.231044 + 0.0987614i
\(388\) 2.90879 + 5.03817i 0.147671 + 0.255774i
\(389\) 31.3731 + 18.1133i 1.59068 + 0.918379i 0.993191 + 0.116502i \(0.0371680\pi\)
0.597489 + 0.801877i \(0.296165\pi\)
\(390\) 18.3112 + 8.69706i 0.927223 + 0.440393i
\(391\) 24.0405i 1.21578i
\(392\) 13.2783 12.0769i 0.670656 0.609976i
\(393\) 7.03275 + 6.23790i 0.354755 + 0.314660i
\(394\) −9.16760 + 15.8788i −0.461857 + 0.799960i
\(395\) −12.3873 7.15183i −0.623274 0.359847i
\(396\) −1.70647 0.729442i −0.0857532 0.0366558i
\(397\) 6.48319 11.2292i 0.325382 0.563578i −0.656208 0.754580i \(-0.727840\pi\)
0.981590 + 0.191002i \(0.0611738\pi\)
\(398\) 1.19837i 0.0600688i
\(399\) 2.75010 + 16.3093i 0.137677 + 0.816486i
\(400\) 1.01395 1.75622i 0.0506976 0.0878109i
\(401\) 28.8738 1.44189 0.720944 0.692994i \(-0.243709\pi\)
0.720944 + 0.692994i \(0.243709\pi\)
\(402\) −10.1713 + 11.4674i −0.507300 + 0.571942i
\(403\) −18.7752 4.62325i −0.935258 0.230301i
\(404\) −0.708350 1.22690i −0.0352417 0.0610405i
\(405\) −4.55140 18.6555i −0.226161 0.926997i
\(406\) −26.0417 4.05772i −1.29243 0.201381i
\(407\) 6.24069 3.60306i 0.309339 0.178597i
\(408\) 12.5570 4.18389i 0.621663 0.207133i
\(409\) −14.9605 −0.739748 −0.369874 0.929082i \(-0.620599\pi\)
−0.369874 + 0.929082i \(0.620599\pi\)
\(410\) −4.72610 −0.233406
\(411\) 34.1924 11.3926i 1.68659 0.561958i
\(412\) −3.89223 + 2.24718i −0.191756 + 0.110711i
\(413\) −11.7152 30.2919i −0.576466 1.49057i
\(414\) −22.0833 29.4600i −1.08533 1.44788i
\(415\) −0.872462 1.51115i −0.0428275 0.0741794i
\(416\) 1.77079 + 6.10841i 0.0868200 + 0.299489i
\(417\) −22.3470 + 25.1946i −1.09434 + 1.23378i
\(418\) −10.7972 −0.528110
\(419\) −3.05253 + 5.28714i −0.149126 + 0.258294i −0.930905 0.365262i \(-0.880979\pi\)
0.781779 + 0.623556i \(0.214313\pi\)
\(420\) 1.07365 2.88253i 0.0523886 0.140653i
\(421\) 2.03050i 0.0989607i 0.998775 + 0.0494804i \(0.0157565\pi\)
−0.998775 + 0.0494804i \(0.984243\pi\)
\(422\) −14.4647 + 25.0535i −0.704129 + 1.21959i
\(423\) 9.73428 22.7725i 0.473297 1.10724i
\(424\) −0.800166 0.461976i −0.0388595 0.0224355i
\(425\) 0.667024 1.15532i 0.0323554 0.0560412i
\(426\) −25.1012 22.2642i −1.21616 1.07870i
\(427\) 3.34948 + 0.521903i 0.162093 + 0.0252567i
\(428\) 4.28174i 0.206966i
\(429\) −5.26839 + 11.0923i −0.254360 + 0.535541i
\(430\) −4.63187 2.67421i −0.223368 0.128962i
\(431\) −1.16281 2.01405i −0.0560106 0.0970132i 0.836661 0.547722i \(-0.184505\pi\)
−0.892671 + 0.450708i \(0.851171\pi\)
\(432\) 13.4064 19.3491i 0.645017 0.930933i
\(433\) −11.1370 + 6.42996i −0.535211 + 0.309004i −0.743136 0.669141i \(-0.766662\pi\)
0.207925 + 0.978145i \(0.433329\pi\)
\(434\) −3.32342 + 21.3291i −0.159529 + 1.02383i
\(435\) 22.9567 7.64900i 1.10069 0.366742i
\(436\) 1.74159 + 1.00551i 0.0834070 + 0.0481551i
\(437\) −25.2142 14.5574i −1.20616 0.696375i
\(438\) −1.06099 + 5.18146i −0.0506962 + 0.247580i
\(439\) 34.2942i 1.63677i 0.574669 + 0.818386i \(0.305131\pi\)
−0.574669 + 0.818386i \(0.694869\pi\)
\(440\) −9.31647 5.37887i −0.444145 0.256428i
\(441\) 3.95568 20.6241i 0.188366 0.982099i
\(442\) 4.55165 + 15.7011i 0.216500 + 0.746826i
\(443\) −2.84466 + 1.64237i −0.135154 + 0.0780311i −0.566052 0.824369i \(-0.691530\pi\)
0.430899 + 0.902400i \(0.358197\pi\)
\(444\) −0.631236 1.89451i −0.0299571 0.0899094i
\(445\) 16.4291 + 28.4560i 0.778812 + 1.34894i
\(446\) 1.20528 2.08761i 0.0570718 0.0988512i
\(447\) 1.19166 5.81958i 0.0563636 0.275257i
\(448\) −15.7358 + 6.08569i −0.743445 + 0.287522i
\(449\) 17.2112 + 29.8106i 0.812246 + 1.40685i 0.911289 + 0.411768i \(0.135089\pi\)
−0.0990430 + 0.995083i \(0.531578\pi\)
\(450\) −0.243869 2.02848i −0.0114961 0.0956235i
\(451\) 2.86291i 0.134809i
\(452\) 2.82951 1.63362i 0.133089 0.0768389i
\(453\) −1.68068 0.344148i −0.0789652 0.0161695i
\(454\) 17.1477i 0.804782i
\(455\) −18.7783 7.85122i −0.880339 0.368071i
\(456\) 3.21556 15.7035i 0.150582 0.735383i
\(457\) 11.3831i 0.532480i −0.963907 0.266240i \(-0.914219\pi\)
0.963907 0.266240i \(-0.0857813\pi\)
\(458\) −2.59745 4.49891i −0.121371 0.210220i
\(459\) 8.81936 12.7287i 0.411652 0.594125i
\(460\) 2.70735 + 4.68927i 0.126231 + 0.218638i
\(461\) −8.28378 + 4.78265i −0.385814 + 0.222750i −0.680345 0.732892i \(-0.738170\pi\)
0.294531 + 0.955642i \(0.404837\pi\)
\(462\) 12.8469 + 4.78505i 0.597691 + 0.222621i
\(463\) 8.59018i 0.399220i 0.979875 + 0.199610i \(0.0639674\pi\)
−0.979875 + 0.199610i \(0.936033\pi\)
\(464\) 25.6887 + 14.8314i 1.19257 + 0.688529i
\(465\) −6.26482 18.8024i −0.290524 0.871942i
\(466\) 37.9394 21.9043i 1.75751 1.01470i
\(467\) −5.74246 9.94623i −0.265729 0.460257i 0.702025 0.712152i \(-0.252279\pi\)
−0.967754 + 0.251895i \(0.918946\pi\)
\(468\) 2.71846 + 2.04688i 0.125661 + 0.0946170i
\(469\) 9.65538 11.9847i 0.445844 0.553402i
\(470\) −13.3985 + 23.2069i −0.618027 + 1.07045i
\(471\) 13.3294 + 2.72942i 0.614185 + 0.125765i
\(472\) 31.4765i 1.44882i
\(473\) 1.61995 2.80583i 0.0744852 0.129012i
\(474\) −13.2159 11.7222i −0.607027 0.538420i
\(475\) −0.807814 1.39918i −0.0370651 0.0641986i
\(476\) 2.31356 0.894753i 0.106042 0.0410109i
\(477\) −1.07328 + 0.129033i −0.0491422 + 0.00590800i
\(478\) −18.9251 −0.865612
\(479\) 10.0631 5.80991i 0.459793 0.265461i −0.252164 0.967684i \(-0.581142\pi\)
0.711957 + 0.702223i \(0.247809\pi\)
\(480\) −4.32555 + 4.87672i −0.197433 + 0.222591i
\(481\) −12.6908 + 3.67899i −0.578652 + 0.167747i
\(482\) −36.4288 −1.65928
\(483\) 23.5491 + 28.4951i 1.07152 + 1.29657i
\(484\) 1.12209 1.94351i 0.0510039 0.0883414i
\(485\) 34.1692 + 19.7276i 1.55154 + 0.895784i
\(486\) −0.884912 23.6995i −0.0401404 1.07503i
\(487\) 17.9245i 0.812236i 0.913821 + 0.406118i \(0.133118\pi\)
−0.913821 + 0.406118i \(0.866882\pi\)
\(488\) −2.84518 1.64266i −0.128795 0.0743599i
\(489\) 2.06508 + 0.422860i 0.0933861 + 0.0191224i
\(490\) −6.91319 + 21.6452i −0.312306 + 0.977831i
\(491\) −22.9168 13.2310i −1.03422 0.597107i −0.116029 0.993246i \(-0.537017\pi\)
−0.918191 + 0.396139i \(0.870350\pi\)
\(492\) −0.777221 0.159149i −0.0350398 0.00717501i
\(493\) 16.8992 + 9.75675i 0.761101 + 0.439422i
\(494\) 19.2238 + 4.73373i 0.864921 + 0.212981i
\(495\) −12.4964 + 1.50235i −0.561671 + 0.0675256i
\(496\) 12.1474 21.0400i 0.545436 0.944724i
\(497\) 26.2335 + 21.1348i 1.17673 + 0.948027i
\(498\) −0.681226 2.04454i −0.0305265 0.0916182i
\(499\) 17.9158 10.3437i 0.802023 0.463048i −0.0421553 0.999111i \(-0.513422\pi\)
0.844178 + 0.536063i \(0.180089\pi\)
\(500\) 3.65665i 0.163530i
\(501\) −11.9957 2.45633i −0.535929 0.109741i
\(502\) −7.37432 12.7727i −0.329132 0.570074i
\(503\) −7.35956 12.7471i −0.328147 0.568367i 0.653997 0.756497i \(-0.273091\pi\)
−0.982144 + 0.188130i \(0.939757\pi\)
\(504\) −10.7853 + 17.2595i −0.480417 + 0.768797i
\(505\) −8.32091 4.80408i −0.370276 0.213779i
\(506\) −20.8992 + 12.0662i −0.929084 + 0.536407i
\(507\) 14.2431 17.4394i 0.632560 0.774511i
\(508\) −1.74334 + 3.01955i −0.0773480 + 0.133971i
\(509\) 42.1320i 1.86747i −0.357965 0.933735i \(-0.616529\pi\)
0.357965 0.933735i \(-0.383471\pi\)
\(510\) −11.1184 + 12.5352i −0.492333 + 0.555067i
\(511\) 0.817571 5.24702i 0.0361672 0.232115i
\(512\) 15.2413 0.673576
\(513\) −8.00967 16.9576i −0.353636 0.748696i
\(514\) −5.12973 −0.226263
\(515\) −15.2405 + 26.3974i −0.671578 + 1.16321i
\(516\) −0.671671 0.595758i −0.0295687 0.0262268i
\(517\) −14.0580 8.11637i −0.618269 0.356958i
\(518\) 5.32086 + 13.7581i 0.233785 + 0.604498i
\(519\) −2.17190 + 10.6067i −0.0953358 + 0.465581i
\(520\) 14.2292 + 13.6613i 0.623992 + 0.599087i
\(521\) 8.45049 14.6367i 0.370223 0.641244i −0.619377 0.785094i \(-0.712615\pi\)
0.989600 + 0.143849i \(0.0459481\pi\)
\(522\) 29.6712 3.56714i 1.29867 0.156130i
\(523\) 17.4693i 0.763880i −0.924187 0.381940i \(-0.875256\pi\)
0.924187 0.381940i \(-0.124744\pi\)
\(524\) −0.853729 1.47870i −0.0372953 0.0645974i
\(525\) 0.341086 + 2.02278i 0.0148862 + 0.0882816i
\(526\) 5.18039 2.99090i 0.225876 0.130409i
\(527\) 7.99114 13.8411i 0.348100 0.602926i
\(528\) −11.5428 10.2382i −0.502337 0.445562i
\(529\) −42.0730 −1.82926
\(530\) 1.16967 0.0508073
\(531\) 22.0887 + 29.4672i 0.958569 + 1.27877i
\(532\) 0.462511 2.96831i 0.0200524 0.128693i
\(533\) −1.25516 + 5.09725i −0.0543671 + 0.220786i
\(534\) 12.8279 + 38.5001i 0.555119 + 1.66606i
\(535\) −14.5195 25.1486i −0.627734 1.08727i
\(536\) −12.9172 + 7.45775i −0.557938 + 0.322126i
\(537\) −18.4521 + 20.8033i −0.796266 + 0.897729i
\(538\) 15.1498 0.653155
\(539\) −13.1119 4.18778i −0.564771 0.180380i
\(540\) −0.286818 + 3.47603i −0.0123427 + 0.149584i
\(541\) −29.2962 + 16.9141i −1.25954 + 0.727196i −0.972985 0.230868i \(-0.925844\pi\)
−0.286555 + 0.958064i \(0.592510\pi\)
\(542\) −11.7971 −0.506730
\(543\) 2.56375 + 7.69450i 0.110021 + 0.330203i
\(544\) −5.25681 −0.225384
\(545\) 13.6388 0.584224
\(546\) −20.7752 14.1518i −0.889099 0.605643i
\(547\) 32.5242 1.39064 0.695318 0.718702i \(-0.255264\pi\)
0.695318 + 0.718702i \(0.255264\pi\)
\(548\) −6.54614 −0.279637
\(549\) −3.81630 + 0.458806i −0.162876 + 0.0195814i
\(550\) −1.33914 −0.0571013
\(551\) 20.4661 11.8161i 0.871886 0.503384i
\(552\) −11.3250 33.9893i −0.482022 1.44668i
\(553\) 13.8121 + 11.1276i 0.587350 + 0.473194i
\(554\) −38.1774 −1.62200
\(555\) −10.1319 8.98675i −0.430074 0.381466i
\(556\) 5.29740 3.05846i 0.224660 0.129707i
\(557\) −0.0426284 0.0738346i −0.00180622 0.00312847i 0.865121 0.501563i \(-0.167242\pi\)
−0.866927 + 0.498435i \(0.833908\pi\)
\(558\) −2.92162 24.3018i −0.123682 1.02878i
\(559\) −4.11435 + 4.28539i −0.174019 + 0.181253i
\(560\) 16.0439 19.9145i 0.677980 0.841540i
\(561\) −7.59340 6.73518i −0.320593 0.284359i
\(562\) 19.2963 0.813967
\(563\) −20.5016 −0.864038 −0.432019 0.901865i \(-0.642199\pi\)
−0.432019 + 0.901865i \(0.642199\pi\)
\(564\) −2.98491 + 3.36525i −0.125687 + 0.141703i
\(565\) 11.0793 19.1899i 0.466110 0.807326i
\(566\) −26.9845 + 15.5795i −1.13424 + 0.654856i
\(567\) 2.01500 + 23.7264i 0.0846222 + 0.996413i
\(568\) −16.3244 28.2747i −0.684956 1.18638i
\(569\) 19.3818i 0.812528i 0.913756 + 0.406264i \(0.133169\pi\)
−0.913756 + 0.406264i \(0.866831\pi\)
\(570\) 6.41453 + 19.2517i 0.268675 + 0.806366i
\(571\) 0.256292 0.443910i 0.0107255 0.0185771i −0.860613 0.509260i \(-0.829919\pi\)
0.871338 + 0.490683i \(0.163253\pi\)
\(572\) 1.54472 1.60894i 0.0645879 0.0672730i
\(573\) 34.4053 + 7.04507i 1.43730 + 0.294312i
\(574\) 5.79062 + 0.902272i 0.241696 + 0.0376601i
\(575\) −3.12722 1.80550i −0.130414 0.0752947i
\(576\) 15.3074 11.4745i 0.637807 0.478102i
\(577\) 4.27288 7.40085i 0.177882 0.308101i −0.763273 0.646077i \(-0.776409\pi\)
0.941155 + 0.337975i \(0.109742\pi\)
\(578\) 12.3513 0.513746
\(579\) −14.6443 + 16.5104i −0.608598 + 0.686147i
\(580\) −4.39507 −0.182495
\(581\) 0.780480 + 2.01809i 0.0323798 + 0.0837243i
\(582\) 36.4548 + 32.3346i 1.51110 + 1.34031i
\(583\) 0.708549i 0.0293451i
\(584\) −2.57326 + 4.45702i −0.106482 + 0.184433i
\(585\) 22.9077 + 2.80384i 0.947119 + 0.115924i
\(586\) 1.22681 0.708300i 0.0506791 0.0292596i
\(587\) −17.7192 10.2302i −0.731351 0.422245i 0.0875655 0.996159i \(-0.472091\pi\)
−0.818916 + 0.573913i \(0.805425\pi\)
\(588\) −1.86579 + 3.32682i −0.0769438 + 0.137196i
\(589\) −9.67785 16.7625i −0.398769 0.690688i
\(590\) −19.9238 34.5090i −0.820249 1.42071i
\(591\) −4.18745 + 20.4498i −0.172249 + 0.841193i
\(592\) 16.6020i 0.682337i
\(593\) 0.0584810 0.0337640i 0.00240153 0.00138652i −0.498799 0.866718i \(-0.666225\pi\)
0.501200 + 0.865331i \(0.332892\pi\)
\(594\) −15.4920 1.27830i −0.635645 0.0524491i
\(595\) 10.5544 13.1006i 0.432690 0.537074i
\(596\) −0.539481 + 0.934409i −0.0220980 + 0.0382749i
\(597\) 0.431269 + 1.29435i 0.0176507 + 0.0529744i
\(598\) 42.4999 12.3204i 1.73795 0.503820i
\(599\) 21.1111 + 12.1885i 0.862578 + 0.498009i 0.864875 0.501988i \(-0.167398\pi\)
−0.00229705 + 0.999997i \(0.500731\pi\)
\(600\) 0.398815 1.94765i 0.0162815 0.0795124i
\(601\) 2.07893 + 1.20027i 0.0848014 + 0.0489601i 0.541801 0.840507i \(-0.317743\pi\)
−0.457000 + 0.889467i \(0.651076\pi\)
\(602\) 5.16462 + 4.16083i 0.210494 + 0.169583i
\(603\) −6.85914 + 16.0464i −0.279326 + 0.653459i
\(604\) 0.269855 + 0.155801i 0.0109802 + 0.00633945i
\(605\) 15.2201i 0.618786i
\(606\) −8.87750 7.87415i −0.360624 0.319865i
\(607\) 5.55033 + 3.20449i 0.225281 + 0.130066i 0.608393 0.793636i \(-0.291814\pi\)
−0.383112 + 0.923702i \(0.625148\pi\)
\(608\) −3.18319 + 5.51344i −0.129095 + 0.223600i
\(609\) −29.5878 + 4.98915i −1.19896 + 0.202171i
\(610\) 4.15905 0.168395
\(611\) 21.4710 + 20.6140i 0.868623 + 0.833954i
\(612\) −2.25058 + 1.68704i −0.0909741 + 0.0681945i
\(613\) 3.63524 2.09881i 0.146826 0.0847701i −0.424787 0.905293i \(-0.639651\pi\)
0.571613 + 0.820523i \(0.306318\pi\)
\(614\) 46.4552 1.87478
\(615\) −5.10465 + 1.70083i −0.205839 + 0.0685840i
\(616\) 10.3880 + 8.36904i 0.418546 + 0.337198i
\(617\) −7.73717 13.4012i −0.311487 0.539511i 0.667198 0.744881i \(-0.267494\pi\)
−0.978684 + 0.205370i \(0.934160\pi\)
\(618\) −24.9801 + 28.1631i −1.00485 + 1.13289i
\(619\) 17.9155 31.0306i 0.720087 1.24723i −0.240878 0.970555i \(-0.577435\pi\)
0.960965 0.276671i \(-0.0892313\pi\)
\(620\) 3.59973i 0.144569i
\(621\) −34.4541 23.8723i −1.38260 0.957961i
\(622\) 12.1607 21.0629i 0.487599 0.844546i
\(623\) −14.6970 38.0019i −0.588821 1.52251i
\(624\) 16.0626 + 23.2892i 0.643021 + 0.932313i
\(625\) 11.2807 + 19.5388i 0.451228 + 0.781551i
\(626\) 27.7669 16.0312i 1.10979 0.640736i
\(627\) −11.6621 + 3.88571i −0.465738 + 0.155180i
\(628\) −2.14020 1.23565i −0.0854034 0.0493077i
\(629\) 10.9215i 0.435470i
\(630\) 0.899647 25.7491i 0.0358428 1.02587i
\(631\) −29.8930 + 17.2587i −1.19002 + 0.687060i −0.958312 0.285725i \(-0.907766\pi\)
−0.231710 + 0.972785i \(0.574432\pi\)
\(632\) −8.59488 14.8868i −0.341886 0.592164i
\(633\) −6.60697 + 32.2658i −0.262603 + 1.28245i
\(634\) −0.914921 1.58469i −0.0363361 0.0629361i
\(635\) 23.6469i 0.938397i
\(636\) 0.192356 + 0.0393882i 0.00762741 + 0.00156184i
\(637\) 21.5090 + 13.2046i 0.852218 + 0.523187i
\(638\) 19.5880i 0.775497i
\(639\) −35.1242 15.0141i −1.38949 0.593948i
\(640\) −24.4451 + 14.1134i −0.966276 + 0.557880i
\(641\) 24.2596i 0.958197i −0.877761 0.479098i \(-0.840964\pi\)
0.877761 0.479098i \(-0.159036\pi\)
\(642\) −11.3370 34.0253i −0.447435 1.34287i
\(643\) 3.39247 + 5.87593i 0.133786 + 0.231724i 0.925133 0.379643i \(-0.123953\pi\)
−0.791347 + 0.611367i \(0.790620\pi\)
\(644\) −2.42192 6.26236i −0.0954370 0.246771i
\(645\) −5.96526 1.22149i −0.234882 0.0480961i
\(646\) −8.18210 + 14.1718i −0.321920 + 0.557583i
\(647\) 17.2893 + 29.9460i 0.679714 + 1.17730i 0.975067 + 0.221910i \(0.0712292\pi\)
−0.295354 + 0.955388i \(0.595437\pi\)
\(648\) 6.47288 22.1509i 0.254279 0.870168i
\(649\) 20.9044 12.0692i 0.820569 0.473756i
\(650\) 2.38426 + 0.587109i 0.0935185 + 0.0230283i
\(651\) 4.08630 + 24.2335i 0.160155 + 0.949787i
\(652\) −0.331575 0.191435i −0.0129855 0.00749717i
\(653\) 24.3380i 0.952418i −0.879332 0.476209i \(-0.842011\pi\)
0.879332 0.476209i \(-0.157989\pi\)
\(654\) 16.5021 + 3.37908i 0.645282 + 0.132133i
\(655\) −10.0287 5.79005i −0.391852 0.226236i
\(656\) −5.71212 3.29789i −0.223021 0.128761i
\(657\) 0.718728 + 5.97831i 0.0280402 + 0.233236i
\(658\) 20.8469 25.8761i 0.812697 1.00876i
\(659\) 41.4269 23.9179i 1.61376 0.931707i 0.625277 0.780403i \(-0.284986\pi\)
0.988487 0.151305i \(-0.0483475\pi\)
\(660\) 2.23964 + 0.458604i 0.0871777 + 0.0178511i
\(661\) 24.3076 + 42.1021i 0.945458 + 1.63758i 0.754832 + 0.655918i \(0.227718\pi\)
0.190625 + 0.981663i \(0.438948\pi\)
\(662\) −6.38530 3.68656i −0.248172 0.143282i
\(663\) 10.5667 + 15.3207i 0.410378 + 0.595006i
\(664\) 2.09701i 0.0813796i
\(665\) −7.34912 19.0026i −0.284986 0.736889i
\(666\) −10.0324 13.3836i −0.388746 0.518603i
\(667\) 26.4096 45.7428i 1.02258 1.77117i
\(668\) 1.92607 + 1.11202i 0.0745218 + 0.0430252i
\(669\) 0.550533 2.68858i 0.0212848 0.103946i
\(670\) 9.44110 16.3525i 0.364742 0.631751i
\(671\) 2.51941i 0.0972608i
\(672\) 6.23087 5.14936i 0.240361 0.198641i
\(673\) 0.594127 1.02906i 0.0229019 0.0396673i −0.854347 0.519702i \(-0.826043\pi\)
0.877249 + 0.480035i \(0.159376\pi\)
\(674\) 26.5654 1.02326
\(675\) −0.993412 2.10319i −0.0382364 0.0809519i
\(676\) −3.45567 + 2.18738i −0.132910 + 0.0841298i
\(677\) −2.75441 4.77077i −0.105860 0.183356i 0.808229 0.588868i \(-0.200426\pi\)
−0.914089 + 0.405513i \(0.867093\pi\)
\(678\) 18.1596 20.4736i 0.697415 0.786282i
\(679\) −38.0993 30.6944i −1.46212 1.17794i
\(680\) −14.1200 + 8.15217i −0.541476 + 0.312621i
\(681\) 6.17111 + 18.5212i 0.236477 + 0.709733i
\(682\) −16.0433 −0.614331
\(683\) 20.4839 0.783796 0.391898 0.920009i \(-0.371819\pi\)
0.391898 + 0.920009i \(0.371819\pi\)
\(684\) 0.406594 + 3.38201i 0.0155465 + 0.129314i
\(685\) −38.4484 + 22.1982i −1.46904 + 0.848150i
\(686\) 12.6027 25.2008i 0.481172 0.962171i
\(687\) −4.42456 3.92449i −0.168808 0.149729i
\(688\) −3.73215 6.46427i −0.142287 0.246448i
\(689\) 0.310642 1.26153i 0.0118345 0.0480604i
\(690\) 33.9303 + 30.0954i 1.29170 + 1.14571i
\(691\) −20.8027 −0.791374 −0.395687 0.918386i \(-0.629493\pi\)
−0.395687 + 0.918386i \(0.629493\pi\)
\(692\) 0.983250 1.70304i 0.0373776 0.0647398i
\(693\) 15.5979 + 0.544976i 0.592516 + 0.0207019i
\(694\) 4.72296i 0.179281i
\(695\) 20.7427 35.9273i 0.786814 1.36280i
\(696\) 28.4888 + 5.83357i 1.07987 + 0.221121i
\(697\) −3.75769 2.16951i −0.142333 0.0821759i
\(698\) 10.1764 17.6261i 0.385183 0.667156i
\(699\) 33.0953 37.3124i 1.25178 1.41128i
\(700\) 0.0573636 0.368149i 0.00216814 0.0139147i
\(701\) 39.6765i 1.49856i 0.662253 + 0.749280i \(0.269600\pi\)
−0.662253 + 0.749280i \(0.730400\pi\)
\(702\) 27.0221 + 9.06795i 1.01989 + 0.342248i
\(703\) −11.4547 6.61338i −0.432023 0.249428i
\(704\) −6.26957 10.8592i −0.236293 0.409272i
\(705\) −6.11999 + 29.8875i −0.230492 + 1.12563i
\(706\) 9.24951 5.34021i 0.348110 0.200981i
\(707\) 9.27796 + 7.47472i 0.348934 + 0.281116i
\(708\) −2.11445 6.34603i −0.0794658 0.238498i
\(709\) 7.07562 + 4.08511i 0.265730 + 0.153420i 0.626946 0.779063i \(-0.284305\pi\)
−0.361215 + 0.932482i \(0.617638\pi\)
\(710\) 35.7942 + 20.6658i 1.34333 + 0.775573i
\(711\) −18.4931 7.90500i −0.693544 0.296461i
\(712\) 39.4880i 1.47988i
\(713\) −37.4650 21.6305i −1.40308 0.810067i
\(714\) 16.0159 13.2360i 0.599380 0.495344i
\(715\) 3.61686 14.6882i 0.135263 0.549307i
\(716\) 4.37409 2.52538i 0.163467 0.0943780i
\(717\) −20.4409 + 6.81074i −0.763379 + 0.254352i
\(718\) 3.08738 + 5.34749i 0.115220 + 0.199567i
\(719\) −20.3828 + 35.3041i −0.760151 + 1.31662i 0.182621 + 0.983183i \(0.441542\pi\)
−0.942772 + 0.333437i \(0.891791\pi\)
\(720\) −11.3975 + 26.6636i −0.424761 + 0.993693i
\(721\) 23.7129 29.4335i 0.883115 1.09616i
\(722\) −4.54400 7.87045i −0.169110 0.292908i
\(723\) −39.3466 + 13.1100i −1.46331 + 0.487565i
\(724\) 1.47311i 0.0547479i
\(725\) 2.53834 1.46551i 0.0942716 0.0544278i
\(726\) 3.77085 18.4153i 0.139950 0.683457i
\(727\) 40.4086i 1.49867i −0.662191 0.749335i \(-0.730373\pi\)
0.662191 0.749335i \(-0.269627\pi\)
\(728\) −14.8261 19.4549i −0.549492 0.721047i
\(729\) −9.48474 25.2792i −0.351287 0.936268i
\(730\) 6.51522i 0.241139i
\(731\) −2.45518 4.25249i −0.0908080 0.157284i
\(732\) 0.683967 + 0.140054i 0.0252801 + 0.00517655i
\(733\) 16.9577 + 29.3717i 0.626348 + 1.08487i 0.988278 + 0.152662i \(0.0487846\pi\)
−0.361930 + 0.932205i \(0.617882\pi\)
\(734\) −1.88910 + 1.09067i −0.0697281 + 0.0402575i
\(735\) 0.322762 + 25.8668i 0.0119052 + 0.954112i
\(736\) 14.2292i 0.524494i
\(737\) 9.90577 + 5.71910i 0.364884 + 0.210666i
\(738\) −6.59766 + 0.793188i −0.242863 + 0.0291977i
\(739\) 22.6528 13.0786i 0.833297 0.481104i −0.0216835 0.999765i \(-0.506903\pi\)
0.854980 + 0.518661i \(0.173569\pi\)
\(740\) 1.22994 + 2.13032i 0.0452136 + 0.0783122i
\(741\) 22.4672 1.80538i 0.825352 0.0663222i
\(742\) −1.43313 0.223305i −0.0526119 0.00819779i
\(743\) −24.6858 + 42.7570i −0.905633 + 1.56860i −0.0855687 + 0.996332i \(0.527271\pi\)
−0.820065 + 0.572271i \(0.806063\pi\)
\(744\) 4.77791 23.3334i 0.175167 0.855444i
\(745\) 7.31760i 0.268096i
\(746\) 21.3867 37.0428i 0.783021 1.35623i
\(747\) −1.47158 1.96314i −0.0538423 0.0718277i
\(748\) 0.921788 + 1.59658i 0.0337039 + 0.0583769i
\(749\) 12.9888 + 33.5850i 0.474599 + 1.22717i
\(750\) 9.68188 + 29.0579i 0.353532 + 1.06105i
\(751\) 17.6920 0.645592 0.322796 0.946469i \(-0.395377\pi\)
0.322796 + 0.946469i \(0.395377\pi\)
\(752\) −32.3878 + 18.6991i −1.18106 + 0.681885i
\(753\) −12.5616 11.1419i −0.457771 0.406033i
\(754\) −8.58780 + 34.8753i −0.312749 + 1.27008i
\(755\) 2.11330 0.0769110
\(756\) 1.01504 4.20421i 0.0369166 0.152906i
\(757\) −0.495303 + 0.857890i −0.0180021 + 0.0311806i −0.874886 0.484329i \(-0.839064\pi\)
0.856884 + 0.515509i \(0.172397\pi\)
\(758\) −27.8897 16.1021i −1.01300 0.584856i
\(759\) −18.2308 + 20.5538i −0.661736 + 0.746057i
\(760\) 19.7457i 0.716253i
\(761\) 6.68767 + 3.86113i 0.242428 + 0.139966i 0.616292 0.787518i \(-0.288634\pi\)
−0.373864 + 0.927483i \(0.621967\pi\)
\(762\) −5.85861 + 28.6111i −0.212235 + 1.03647i
\(763\) −16.7109 2.60382i −0.604974 0.0942648i
\(764\) −5.52421 3.18940i −0.199859 0.115389i
\(765\) −7.49782 + 17.5405i −0.271084 + 0.634178i
\(766\) −41.5729 24.0021i −1.50209 0.867232i
\(767\) −42.5104 + 12.3235i −1.53496 + 0.444975i
\(768\) −12.1161 + 4.03700i −0.437203 + 0.145673i
\(769\) −5.63630 + 9.76236i −0.203250 + 0.352040i −0.949574 0.313544i \(-0.898484\pi\)
0.746324 + 0.665583i \(0.231817\pi\)
\(770\) −16.6862 2.59998i −0.601329 0.0936968i
\(771\) −5.54060 + 1.84609i −0.199540 + 0.0664852i
\(772\) 3.47146 2.00425i 0.124941 0.0721345i
\(773\) 13.2843i 0.477801i 0.971044 + 0.238901i \(0.0767871\pi\)
−0.971044 + 0.238901i \(0.923213\pi\)
\(774\) −6.91492 2.95584i −0.248552 0.106245i
\(775\) −1.20031 2.07900i −0.0431164 0.0746798i
\(776\) 23.7081 + 41.0637i 0.851072 + 1.47410i
\(777\) 10.6983 + 12.9452i 0.383800 + 0.464408i
\(778\) −47.7304 27.5572i −1.71122 0.987972i
\(779\) −4.55084 + 2.62743i −0.163051 + 0.0941373i
\(780\) −3.78647 1.79842i −0.135577 0.0643937i
\(781\) −12.5186 + 21.6829i −0.447952 + 0.775876i
\(782\) 36.5748i 1.30791i
\(783\) 30.7640 14.5309i 1.09941 0.519292i
\(784\) −23.4596 + 21.3370i −0.837844 + 0.762037i
\(785\) −16.7605 −0.598207
\(786\) −10.6995 9.49021i −0.381638 0.338505i
\(787\) −15.0454 −0.536310 −0.268155 0.963376i \(-0.586414\pi\)
−0.268155 + 0.963376i \(0.586414\pi\)
\(788\) 1.89572 3.28348i 0.0675322 0.116969i
\(789\) 4.51895 5.09477i 0.160879 0.181379i
\(790\) 18.8458 + 10.8806i 0.670505 + 0.387116i
\(791\) −17.2384 + 21.3971i −0.612928 + 0.760794i
\(792\) −13.9086 5.94533i −0.494220 0.211258i
\(793\) 1.10456 4.48566i 0.0392241 0.159290i
\(794\) −9.86340 + 17.0839i −0.350039 + 0.606285i
\(795\) 1.26336 0.420942i 0.0448067 0.0149293i
\(796\) 0.247804i 0.00878319i
\(797\) 5.94719 + 10.3008i 0.210660 + 0.364875i 0.951921 0.306342i \(-0.0991052\pi\)
−0.741261 + 0.671217i \(0.765772\pi\)
\(798\) −4.18395 24.8126i −0.148110 0.878358i
\(799\) −21.3061 + 12.3011i −0.753757 + 0.435182i
\(800\) −0.394800 + 0.683813i −0.0139583 + 0.0241764i
\(801\) 27.7108 + 36.9673i 0.979114 + 1.30618i
\(802\) −43.9280 −1.55115
\(803\) 3.94670 0.139276
\(804\) 2.10328 2.37128i 0.0741769 0.0836288i
\(805\) −35.4609 28.5688i −1.24983 1.00692i
\(806\) 28.5642 + 7.03373i 1.00613 + 0.247753i
\(807\) 16.3633 5.45211i 0.576014 0.191923i
\(808\) −5.77342 9.99985i −0.203108 0.351794i
\(809\) −31.9163 + 18.4269i −1.12212 + 0.647856i −0.941941 0.335778i \(-0.891001\pi\)
−0.180178 + 0.983634i \(0.557667\pi\)
\(810\) 6.92441 + 28.3820i 0.243299 + 0.997243i
\(811\) 45.9924 1.61501 0.807506 0.589859i \(-0.200817\pi\)
0.807506 + 0.589859i \(0.200817\pi\)
\(812\) 5.38502 + 0.839073i 0.188977 + 0.0294457i
\(813\) −12.7420 + 4.24554i −0.446882 + 0.148898i
\(814\) −9.49446 + 5.48163i −0.332781 + 0.192131i
\(815\) −2.59665 −0.0909567
\(816\) −22.1852 + 7.39194i −0.776638 + 0.258770i
\(817\) −5.94679 −0.208052
\(818\) 22.7606 0.795805
\(819\) −27.5322 7.80875i −0.962054 0.272860i
\(820\) 0.977286 0.0341283
\(821\) −10.3729 −0.362018 −0.181009 0.983481i \(-0.557936\pi\)
−0.181009 + 0.983481i \(0.557936\pi\)
\(822\) −52.0197 + 17.3325i −1.81439 + 0.604542i
\(823\) 0.365784 0.0127504 0.00637521 0.999980i \(-0.497971\pi\)
0.00637521 + 0.999980i \(0.497971\pi\)
\(824\) −31.7237 + 18.3157i −1.10515 + 0.638057i
\(825\) −1.44640 + 0.481931i −0.0503573 + 0.0167787i
\(826\) 17.8232 + 46.0855i 0.620150 + 1.60352i
\(827\) 52.0422 1.80968 0.904842 0.425747i \(-0.139989\pi\)
0.904842 + 0.425747i \(0.139989\pi\)
\(828\) 4.56648 + 6.09187i 0.158696 + 0.211707i
\(829\) 28.9084 16.6902i 1.00403 0.579676i 0.0945909 0.995516i \(-0.469846\pi\)
0.909438 + 0.415840i \(0.136512\pi\)
\(830\) 1.32735 + 2.29903i 0.0460729 + 0.0798006i
\(831\) −41.2353 + 13.7393i −1.43044 + 0.476610i
\(832\) 6.40169 + 22.0829i 0.221939 + 0.765587i
\(833\) −15.4328 + 14.0365i −0.534715 + 0.486335i
\(834\) 33.9984 38.3305i 1.17727 1.32728i
\(835\) 15.0835 0.521988
\(836\) 2.23270 0.0772196
\(837\) −11.9014 25.1968i −0.411371 0.870930i
\(838\) 4.64406 8.04375i 0.160426 0.277867i
\(839\) −22.2197 + 12.8285i −0.767108 + 0.442890i −0.831842 0.555013i \(-0.812713\pi\)
0.0647343 + 0.997903i \(0.479380\pi\)
\(840\) 8.75078 23.4941i 0.301931 0.810623i
\(841\) 6.93645 + 12.0143i 0.239188 + 0.414286i
\(842\) 3.08917i 0.106460i
\(843\) 20.8419 6.94436i 0.717833 0.239176i
\(844\) 2.99107 5.18068i 0.102957 0.178327i
\(845\) −12.8792 + 24.5657i −0.443059 + 0.845087i
\(846\) −14.8095 + 34.6456i −0.509163 + 1.19114i
\(847\) −2.90571 + 18.6483i −0.0998414 + 0.640764i
\(848\) 1.41370 + 0.816203i 0.0485468 + 0.0280285i
\(849\) −23.5391 + 26.5385i −0.807860 + 0.910801i
\(850\) −1.01480 + 1.75768i −0.0348073 + 0.0602880i
\(851\) −29.5625 −1.01339
\(852\) 5.19054 + 4.60390i 0.177825 + 0.157727i
\(853\) −45.2420 −1.54906 −0.774529 0.632539i \(-0.782013\pi\)
−0.774529 + 0.632539i \(0.782013\pi\)
\(854\) −5.09583 0.794013i −0.174376 0.0271706i
\(855\) 13.8566 + 18.4853i 0.473886 + 0.632183i
\(856\) 34.8984i 1.19280i
\(857\) 15.7123 27.2145i 0.536722 0.929629i −0.462356 0.886694i \(-0.652996\pi\)
0.999078 0.0429347i \(-0.0136707\pi\)
\(858\) 8.01522 16.8756i 0.273635 0.576124i
\(859\) 28.0376 16.1875i 0.956632 0.552312i 0.0614972 0.998107i \(-0.480412\pi\)
0.895135 + 0.445796i \(0.147079\pi\)
\(860\) 0.957799 + 0.552986i 0.0326607 + 0.0188567i
\(861\) 6.57913 1.10939i 0.224216 0.0378078i
\(862\) 1.76908 + 3.06413i 0.0602550 + 0.104365i
\(863\) 19.7814 + 34.2625i 0.673368 + 1.16631i 0.976943 + 0.213500i \(0.0684864\pi\)
−0.303575 + 0.952808i \(0.598180\pi\)
\(864\) −5.22002 + 7.53389i −0.177589 + 0.256308i
\(865\) 13.3369i 0.453469i
\(866\) 16.9436 9.78241i 0.575768 0.332420i
\(867\) 13.3406 4.44498i 0.453070 0.150960i
\(868\) 0.687233 4.41054i 0.0233262 0.149703i
\(869\) −6.59113 + 11.4162i −0.223589 + 0.387267i
\(870\) −34.9259 + 11.6370i −1.18410 + 0.394533i
\(871\) −15.1293 14.5254i −0.512635 0.492175i
\(872\) 14.1949 + 8.19541i 0.480699 + 0.277531i
\(873\) 51.0113 + 21.8051i 1.72647 + 0.737992i
\(874\) 38.3603 + 22.1473i 1.29756 + 0.749145i
\(875\) −11.0925 28.6819i −0.374995 0.969625i
\(876\) 0.219397 1.07145i 0.00741274 0.0362008i
\(877\) −7.68921 4.43937i −0.259646 0.149907i 0.364527 0.931193i \(-0.381231\pi\)
−0.624173 + 0.781286i \(0.714564\pi\)
\(878\) 52.1745i 1.76080i
\(879\) 1.07017 1.20654i 0.0360960 0.0406955i
\(880\) 16.4600 + 9.50319i 0.554867 + 0.320352i
\(881\) −16.6075 + 28.7650i −0.559520 + 0.969116i 0.438017 + 0.898967i \(0.355681\pi\)
−0.997536 + 0.0701495i \(0.977652\pi\)
\(882\) −6.01810 + 31.3771i −0.202640 + 1.05652i
\(883\) 43.5385 1.46519 0.732594 0.680666i \(-0.238310\pi\)
0.732594 + 0.680666i \(0.238310\pi\)
\(884\) −0.941212 3.24675i −0.0316564 0.109200i
\(885\) −33.9387 30.1029i −1.14084 1.01190i
\(886\) 4.32781 2.49866i 0.145396 0.0839442i
\(887\) −39.7300 −1.33400 −0.667001 0.745057i \(-0.732422\pi\)
−0.667001 + 0.745057i \(0.732422\pi\)
\(888\) −5.14490 15.4412i −0.172651 0.518174i
\(889\) 4.51448 28.9731i 0.151411 0.971727i
\(890\) −24.9948 43.2923i −0.837829 1.45116i
\(891\) −17.1929 + 4.19457i −0.575983 + 0.140524i
\(892\) −0.249234 + 0.431686i −0.00834497 + 0.0144539i
\(893\) 29.7950i 0.997053i
\(894\) −1.81297 + 8.85380i −0.0606347 + 0.296115i
\(895\) 17.1273 29.6654i 0.572503 0.991605i
\(896\) 32.6455 12.6254i 1.09061 0.421785i
\(897\) 41.4701 28.6021i 1.38465 0.954996i
\(898\) −26.1848 45.3533i −0.873796 1.51346i
\(899\) 30.4101 17.5573i 1.01423 0.585567i
\(900\) 0.0504284 + 0.419459i 0.00168095 + 0.0139820i
\(901\) 0.929999 + 0.536935i 0.0309828 + 0.0178879i
\(902\) 4.35558i 0.145025i
\(903\) 7.07568 + 2.63546i 0.235464 + 0.0877026i
\(904\) 23.0620 13.3148i 0.767030 0.442845i
\(905\) −4.99538 8.65226i −0.166052 0.287611i
\(906\) 2.55695 + 0.523580i 0.0849491 + 0.0173948i
\(907\) −14.6547 25.3827i −0.486602 0.842819i 0.513280 0.858221i \(-0.328430\pi\)
−0.999881 + 0.0154026i \(0.995097\pi\)
\(908\) 3.54588i 0.117674i
\(909\) −12.4223 5.31001i −0.412022 0.176122i
\(910\) 28.5689 + 11.9447i 0.947049 + 0.395962i
\(911\) 30.7193i 1.01778i 0.860833 + 0.508888i \(0.169943\pi\)
−0.860833 + 0.508888i \(0.830057\pi\)
\(912\) −5.68113 + 27.7443i −0.188121 + 0.918707i
\(913\) −1.39268 + 0.804062i −0.0460909 + 0.0266106i
\(914\) 17.3181i 0.572830i
\(915\) 4.49217 1.49676i 0.148507 0.0494812i
\(916\) 0.537113 + 0.930307i 0.0177467 + 0.0307382i
\(917\) 11.1821 + 9.00881i 0.369267 + 0.297497i
\(918\) −13.4176 + 19.3652i −0.442847 + 0.639147i
\(919\) −2.25759 + 3.91025i −0.0744709 + 0.128987i −0.900856 0.434118i \(-0.857060\pi\)
0.826385 + 0.563105i \(0.190393\pi\)
\(920\) 22.0663 + 38.2200i 0.727505 + 1.26008i
\(921\) 50.1761 16.7183i 1.65336 0.550886i
\(922\) 12.6028 7.27622i 0.415051 0.239630i
\(923\) 31.7949 33.1167i 1.04654 1.09005i
\(924\) −2.65654 0.989474i −0.0873938 0.0325513i
\(925\) −1.42069 0.820235i −0.0467120 0.0269692i
\(926\) 13.0689i 0.429472i
\(927\) −16.8455 + 39.4087i −0.553280 + 1.29435i
\(928\) −10.0023 5.77484i −0.328342 0.189569i
\(929\) 2.56569 + 1.48130i 0.0841775 + 0.0485999i 0.541498 0.840702i \(-0.317857\pi\)
−0.457320 + 0.889302i \(0.651191\pi\)
\(930\) 9.53118 + 28.6056i 0.312540 + 0.938016i
\(931\) 5.37661 + 24.6858i 0.176211 + 0.809045i
\(932\) −7.84528 + 4.52947i −0.256981 + 0.148368i
\(933\) 5.55459 27.1264i 0.181849 0.888077i
\(934\) 8.73647 + 15.1320i 0.285866 + 0.495134i
\(935\) 10.8281 + 6.25163i 0.354118 + 0.204450i
\(936\) 22.1568 + 16.6831i 0.724219 + 0.545305i
\(937\) 45.7524i 1.49466i 0.664450 + 0.747332i \(0.268666\pi\)
−0.664450 + 0.747332i \(0.731334\pi\)
\(938\) −14.6895 + 18.2333i −0.479630 + 0.595338i
\(939\) 24.2216 27.3080i 0.790442 0.891163i
\(940\) 2.77061 4.79883i 0.0903672 0.156521i
\(941\) 18.3277 + 10.5815i 0.597465 + 0.344947i 0.768044 0.640397i \(-0.221230\pi\)
−0.170579 + 0.985344i \(0.554564\pi\)
\(942\) −20.2790 4.15248i −0.660727 0.135295i
\(943\) −5.87243 + 10.1713i −0.191232 + 0.331224i
\(944\) 55.6116i 1.81000i
\(945\) −8.29486 28.1352i −0.269832 0.915239i
\(946\) −2.46455 + 4.26873i −0.0801296 + 0.138789i
\(947\) −53.1830 −1.72822 −0.864108 0.503307i \(-0.832116\pi\)
−0.864108 + 0.503307i \(0.832116\pi\)
\(948\) 2.73285 + 2.42398i 0.0887588 + 0.0787272i
\(949\) −7.02686 1.73032i −0.228102 0.0561685i
\(950\) 1.22899 + 2.12868i 0.0398738 + 0.0690634i
\(951\) −1.55850 1.38236i −0.0505378 0.0448260i
\(952\) 18.8567 7.29270i 0.611150 0.236358i
\(953\) 14.8320 8.56324i 0.480455 0.277391i −0.240151 0.970735i \(-0.577197\pi\)
0.720606 + 0.693345i \(0.243864\pi\)
\(954\) 1.63287 0.196308i 0.0528661 0.00635570i
\(955\) −43.2615 −1.39991
\(956\) 3.91341 0.126569
\(957\) −7.04933 21.1569i −0.227873 0.683907i
\(958\) −15.3097 + 8.83908i −0.494635 + 0.285578i
\(959\) 51.3465 19.8579i 1.65806 0.641244i
\(960\) −15.6376 + 17.6302i −0.504700 + 0.569011i
\(961\) 1.11994 + 1.93980i 0.0361273 + 0.0625742i
\(962\) 19.3076 5.59714i 0.622501 0.180459i
\(963\) −24.4900 32.6707i −0.789181 1.05280i
\(964\) 7.53291 0.242619
\(965\) 13.5930 23.5437i 0.437573 0.757898i
\(966\) −35.8272 43.3519i −1.15272 1.39482i
\(967\) 7.67083i 0.246677i 0.992365 + 0.123339i \(0.0393601\pi\)
−0.992365 + 0.123339i \(0.960640\pi\)
\(968\) 9.14558 15.8406i 0.293950 0.509137i
\(969\) −3.73731 + 18.2515i −0.120060 + 0.586322i
\(970\) −51.9843 30.0132i −1.66912 0.963665i
\(971\) −12.3165 + 21.3327i −0.395254 + 0.684600i −0.993134 0.116986i \(-0.962677\pi\)
0.597880 + 0.801586i \(0.296010\pi\)
\(972\) 0.182986 + 4.90068i 0.00586928 + 0.157190i
\(973\) −32.2737 + 40.0596i −1.03465 + 1.28425i
\(974\) 27.2700i 0.873786i
\(975\) 2.78652 0.223915i 0.0892402 0.00717101i
\(976\) 5.02676 + 2.90220i 0.160903 + 0.0928971i
\(977\) 18.1969 + 31.5180i 0.582170 + 1.00835i 0.995222 + 0.0976409i \(0.0311297\pi\)
−0.413051 + 0.910708i \(0.635537\pi\)
\(978\) −3.14177 0.643332i −0.100463 0.0205715i
\(979\) 26.2250 15.1410i 0.838156 0.483910i
\(980\) 1.42954 4.47590i 0.0456650 0.142977i
\(981\) 19.0399 2.28903i 0.607897 0.0730829i
\(982\) 34.8651 + 20.1294i 1.11259 + 0.642355i
\(983\) −21.2666 12.2783i −0.678301 0.391617i 0.120914 0.992663i \(-0.461418\pi\)
−0.799214 + 0.601046i \(0.794751\pi\)
\(984\) −6.33475 1.29715i −0.201945 0.0413516i
\(985\) 25.7138i 0.819310i
\(986\) −25.7101 14.8437i −0.818776 0.472720i
\(987\) 13.2044 35.4511i 0.420300 1.12842i
\(988\) −3.97519 0.978863i −0.126468 0.0311418i
\(989\) −11.5107 + 6.64568i −0.366018 + 0.211320i
\(990\) 19.0118 2.28565i 0.604234 0.0726426i
\(991\) 14.8307 + 25.6876i 0.471113 + 0.815992i 0.999454 0.0330404i \(-0.0105190\pi\)
−0.528341 + 0.849032i \(0.677186\pi\)
\(992\) −4.72981 + 8.19228i −0.150172 + 0.260105i
\(993\) −8.22346 1.68389i −0.260964 0.0534368i
\(994\) −39.9112 32.1541i −1.26590 1.01987i
\(995\) −0.840313 1.45546i −0.0266397 0.0461413i
\(996\) 0.140867 + 0.422780i 0.00446355 + 0.0133963i
\(997\) 5.32946i 0.168786i −0.996433 0.0843929i \(-0.973105\pi\)
0.996433 0.0843929i \(-0.0268951\pi\)
\(998\) −27.2568 + 15.7367i −0.862799 + 0.498137i
\(999\) −15.6524 10.8451i −0.495220 0.343124i
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.br.b.17.9 yes 64
3.2 odd 2 inner 273.2.br.b.17.24 yes 64
7.5 odd 6 273.2.y.b.173.24 yes 64
13.10 even 6 273.2.y.b.101.9 64
21.5 even 6 273.2.y.b.173.9 yes 64
39.23 odd 6 273.2.y.b.101.24 yes 64
91.75 odd 6 inner 273.2.br.b.257.24 yes 64
273.257 even 6 inner 273.2.br.b.257.9 yes 64
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
273.2.y.b.101.9 64 13.10 even 6
273.2.y.b.101.24 yes 64 39.23 odd 6
273.2.y.b.173.9 yes 64 21.5 even 6
273.2.y.b.173.24 yes 64 7.5 odd 6
273.2.br.b.17.9 yes 64 1.1 even 1 trivial
273.2.br.b.17.24 yes 64 3.2 odd 2 inner
273.2.br.b.257.9 yes 64 273.257 even 6 inner
273.2.br.b.257.24 yes 64 91.75 odd 6 inner