Properties

Label 325.2.m.c.199.2
Level $325$
Weight $2$
Character 325.199
Analytic conductor $2.595$
Analytic rank $0$
Dimension $8$
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] = [325,2,Mod(49,325)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(325, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("325.49");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 325 = 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 325.m (of order \(6\), degree \(2\), not 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: \(2.59513806569\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.22581504.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 4x^{7} + 5x^{6} + 2x^{5} - 11x^{4} + 4x^{3} + 20x^{2} - 32x + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 65)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 199.2
Root \(-1.27597 - 0.609843i\) of defining polynomial
Character \(\chi\) \(=\) 325.199
Dual form 325.2.m.c.49.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.109843 + 0.190254i) q^{2} +(1.38581 + 0.800098i) q^{3} +(0.975869 + 1.69025i) q^{4} +(-0.304444 + 0.175771i) q^{6} +(0.166123 + 0.287734i) q^{7} -0.868145 q^{8} +(-0.219687 - 0.380509i) q^{9} +O(q^{10})\) \(q+(-0.109843 + 0.190254i) q^{2} +(1.38581 + 0.800098i) q^{3} +(0.975869 + 1.69025i) q^{4} +(-0.304444 + 0.175771i) q^{6} +(0.166123 + 0.287734i) q^{7} -0.868145 q^{8} +(-0.219687 - 0.380509i) q^{9} +(4.65213 + 2.68591i) q^{11} +3.12316i q^{12} +(-0.619491 - 3.55193i) q^{13} -0.0729902 q^{14} +(-1.85638 + 3.21534i) q^{16} +(-4.38581 + 2.53215i) q^{17} +0.0965246 q^{18} +(1.96410 - 1.13397i) q^{19} +0.531659i q^{21} +(-1.02201 + 0.590059i) q^{22} +(-2.45880 - 1.41959i) q^{23} +(-1.20308 - 0.694601i) q^{24} +(0.743818 + 0.272296i) q^{26} -5.50367i q^{27} +(-0.324229 + 0.561581i) q^{28} +(-1.45174 + 2.51448i) q^{29} -5.46410i q^{31} +(-1.27597 - 2.21004i) q^{32} +(4.29798 + 7.44432i) q^{33} -1.11256i q^{34} +(0.428771 - 0.742653i) q^{36} +(-2.98601 + 5.17191i) q^{37} +0.498239i q^{38} +(1.98340 - 5.41796i) q^{39} +(3.23205 + 1.86603i) q^{41} +(-0.101151 - 0.0583993i) q^{42} +(4.38581 - 2.53215i) q^{43} +10.4844i q^{44} +(0.540166 - 0.311865i) q^{46} +8.34285 q^{47} +(-5.14517 + 2.97057i) q^{48} +(3.44481 - 5.96658i) q^{49} -8.10387 q^{51} +(5.39913 - 4.51332i) q^{52} -1.56063i q^{53} +(1.04710 + 0.604542i) q^{54} +(-0.144219 - 0.249795i) q^{56} +3.62916 q^{57} +(-0.318928 - 0.552399i) q^{58} +(-2.34461 + 1.35366i) q^{59} +(-7.05193 - 12.2143i) q^{61} +(1.03957 + 0.600196i) q^{62} +(0.0729902 - 0.126423i) q^{63} -6.86488 q^{64} -1.88842 q^{66} +(5.16612 - 8.94799i) q^{67} +(-8.55995 - 4.94209i) q^{68} +(-2.27162 - 3.93456i) q^{69} +(-11.0828 + 6.39866i) q^{71} +(0.190720 + 0.330337i) q^{72} +9.68922 q^{73} +(-0.655986 - 1.13620i) q^{74} +(3.83341 + 2.21322i) q^{76} +1.78477i q^{77} +(0.812927 + 0.972477i) q^{78} -4.51851 q^{79} +(3.74441 - 6.48552i) q^{81} +(-0.710039 + 0.409941i) q^{82} -4.26371 q^{83} +(-0.898640 + 0.518830i) q^{84} +1.11256i q^{86} +(-4.02367 + 2.32306i) q^{87} +(-4.03872 - 2.33176i) q^{88} +(2.79366 + 1.61292i) q^{89} +(0.919100 - 0.768307i) q^{91} -5.54133i q^{92} +(4.37182 - 7.57221i) q^{93} +(-0.916407 + 1.58726i) q^{94} -4.08359i q^{96} +(-1.25396 - 2.17191i) q^{97} +(0.756779 + 1.31078i) q^{98} -2.36023i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 2 q^{2} - 6 q^{3} - 2 q^{4} - 18 q^{6} - 10 q^{7} - 12 q^{8} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 2 q^{2} - 6 q^{3} - 2 q^{4} - 18 q^{6} - 10 q^{7} - 12 q^{8} + 4 q^{9} - 8 q^{13} - 4 q^{14} - 2 q^{16} - 18 q^{17} + 40 q^{18} - 12 q^{19} - 6 q^{22} - 6 q^{23} + 12 q^{24} + 10 q^{26} - 8 q^{28} + 8 q^{29} + 4 q^{32} + 18 q^{33} + 20 q^{36} + 2 q^{37} + 12 q^{41} + 42 q^{42} + 18 q^{43} - 42 q^{46} + 16 q^{47} + 6 q^{48} - 12 q^{49} - 8 q^{51} - 16 q^{52} - 18 q^{54} + 12 q^{56} + 28 q^{57} - 22 q^{58} + 12 q^{59} - 28 q^{61} - 12 q^{62} + 4 q^{63} + 8 q^{64} + 12 q^{66} + 30 q^{67} - 12 q^{68} + 16 q^{69} - 12 q^{72} + 16 q^{73} - 10 q^{74} + 54 q^{76} - 18 q^{78} + 16 q^{79} + 8 q^{81} + 6 q^{82} - 24 q^{83} + 30 q^{84} - 54 q^{87} - 42 q^{88} - 24 q^{89} + 28 q^{91} - 8 q^{93} - 32 q^{94} + 2 q^{97} - 24 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/325\mathbb{Z}\right)^\times\).

\(n\) \(27\) \(301\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.109843 + 0.190254i −0.0776710 + 0.134530i −0.902245 0.431224i \(-0.858082\pi\)
0.824574 + 0.565755i \(0.191415\pi\)
\(3\) 1.38581 + 0.800098i 0.800098 + 0.461937i 0.843505 0.537121i \(-0.180488\pi\)
−0.0434075 + 0.999057i \(0.513821\pi\)
\(4\) 0.975869 + 1.69025i 0.487934 + 0.845127i
\(5\) 0 0
\(6\) −0.304444 + 0.175771i −0.124289 + 0.0717582i
\(7\) 0.166123 + 0.287734i 0.0627887 + 0.108753i 0.895711 0.444637i \(-0.146667\pi\)
−0.832922 + 0.553390i \(0.813334\pi\)
\(8\) −0.868145 −0.306936
\(9\) −0.219687 0.380509i −0.0732290 0.126836i
\(10\) 0 0
\(11\) 4.65213 + 2.68591i 1.40267 + 0.809832i 0.994666 0.103149i \(-0.0328917\pi\)
0.408004 + 0.912980i \(0.366225\pi\)
\(12\) 3.12316i 0.901579i
\(13\) −0.619491 3.55193i −0.171816 0.985129i
\(14\) −0.0729902 −0.0195074
\(15\) 0 0
\(16\) −1.85638 + 3.21534i −0.464094 + 0.803835i
\(17\) −4.38581 + 2.53215i −1.06372 + 0.614136i −0.926458 0.376399i \(-0.877162\pi\)
−0.137258 + 0.990535i \(0.543829\pi\)
\(18\) 0.0965246 0.0227511
\(19\) 1.96410 1.13397i 0.450596 0.260152i −0.257486 0.966282i \(-0.582894\pi\)
0.708082 + 0.706130i \(0.249561\pi\)
\(20\) 0 0
\(21\) 0.531659i 0.116018i
\(22\) −1.02201 + 0.590059i −0.217894 + 0.125801i
\(23\) −2.45880 1.41959i −0.512695 0.296005i 0.221246 0.975218i \(-0.428988\pi\)
−0.733941 + 0.679213i \(0.762321\pi\)
\(24\) −1.20308 0.694601i −0.245578 0.141785i
\(25\) 0 0
\(26\) 0.743818 + 0.272296i 0.145875 + 0.0534016i
\(27\) 5.50367i 1.05918i
\(28\) −0.324229 + 0.561581i −0.0612735 + 0.106129i
\(29\) −1.45174 + 2.51448i −0.269581 + 0.466928i −0.968754 0.248025i \(-0.920219\pi\)
0.699173 + 0.714953i \(0.253552\pi\)
\(30\) 0 0
\(31\) 5.46410i 0.981382i −0.871334 0.490691i \(-0.836744\pi\)
0.871334 0.490691i \(-0.163256\pi\)
\(32\) −1.27597 2.21004i −0.225561 0.390683i
\(33\) 4.29798 + 7.44432i 0.748182 + 1.29589i
\(34\) 1.11256i 0.190802i
\(35\) 0 0
\(36\) 0.428771 0.742653i 0.0714619 0.123776i
\(37\) −2.98601 + 5.17191i −0.490896 + 0.850257i −0.999945 0.0104803i \(-0.996664\pi\)
0.509049 + 0.860738i \(0.329997\pi\)
\(38\) 0.498239i 0.0808250i
\(39\) 1.98340 5.41796i 0.317598 0.867568i
\(40\) 0 0
\(41\) 3.23205 + 1.86603i 0.504762 + 0.291424i 0.730678 0.682723i \(-0.239204\pi\)
−0.225916 + 0.974147i \(0.572538\pi\)
\(42\) −0.101151 0.0583993i −0.0156079 0.00901121i
\(43\) 4.38581 2.53215i 0.668830 0.386149i −0.126803 0.991928i \(-0.540472\pi\)
0.795633 + 0.605779i \(0.207138\pi\)
\(44\) 10.4844i 1.58058i
\(45\) 0 0
\(46\) 0.540166 0.311865i 0.0796432 0.0459820i
\(47\) 8.34285 1.21693 0.608465 0.793581i \(-0.291786\pi\)
0.608465 + 0.793581i \(0.291786\pi\)
\(48\) −5.14517 + 2.97057i −0.742642 + 0.428764i
\(49\) 3.44481 5.96658i 0.492115 0.852368i
\(50\) 0 0
\(51\) −8.10387 −1.13477
\(52\) 5.39913 4.51332i 0.748724 0.625885i
\(53\) 1.56063i 0.214369i −0.994239 0.107184i \(-0.965817\pi\)
0.994239 0.107184i \(-0.0341835\pi\)
\(54\) 1.04710 + 0.604542i 0.142492 + 0.0822678i
\(55\) 0 0
\(56\) −0.144219 0.249795i −0.0192721 0.0333802i
\(57\) 3.62916 0.480694
\(58\) −0.318928 0.552399i −0.0418773 0.0725335i
\(59\) −2.34461 + 1.35366i −0.305242 + 0.176232i −0.644795 0.764355i \(-0.723057\pi\)
0.339553 + 0.940587i \(0.389724\pi\)
\(60\) 0 0
\(61\) −7.05193 12.2143i −0.902908 1.56388i −0.823702 0.567023i \(-0.808095\pi\)
−0.0792059 0.996858i \(-0.525238\pi\)
\(62\) 1.03957 + 0.600196i 0.132025 + 0.0762249i
\(63\) 0.0729902 0.126423i 0.00919590 0.0159278i
\(64\) −6.86488 −0.858111
\(65\) 0 0
\(66\) −1.88842 −0.232448
\(67\) 5.16612 8.94799i 0.631142 1.09317i −0.356176 0.934419i \(-0.615920\pi\)
0.987319 0.158752i \(-0.0507470\pi\)
\(68\) −8.55995 4.94209i −1.03805 0.599316i
\(69\) −2.27162 3.93456i −0.273471 0.473666i
\(70\) 0 0
\(71\) −11.0828 + 6.39866i −1.31529 + 0.759382i −0.982967 0.183785i \(-0.941165\pi\)
−0.332321 + 0.943166i \(0.607832\pi\)
\(72\) 0.190720 + 0.330337i 0.0224766 + 0.0389306i
\(73\) 9.68922 1.13404 0.567019 0.823705i \(-0.308097\pi\)
0.567019 + 0.823705i \(0.308097\pi\)
\(74\) −0.655986 1.13620i −0.0762569 0.132081i
\(75\) 0 0
\(76\) 3.83341 + 2.21322i 0.439722 + 0.253874i
\(77\) 1.78477i 0.203393i
\(78\) 0.812927 + 0.972477i 0.0920459 + 0.110111i
\(79\) −4.51851 −0.508372 −0.254186 0.967155i \(-0.581808\pi\)
−0.254186 + 0.967155i \(0.581808\pi\)
\(80\) 0 0
\(81\) 3.74441 6.48552i 0.416046 0.720613i
\(82\) −0.710039 + 0.409941i −0.0784107 + 0.0452704i
\(83\) −4.26371 −0.468003 −0.234001 0.972236i \(-0.575182\pi\)
−0.234001 + 0.972236i \(0.575182\pi\)
\(84\) −0.898640 + 0.518830i −0.0980496 + 0.0566090i
\(85\) 0 0
\(86\) 1.11256i 0.119970i
\(87\) −4.02367 + 2.32306i −0.431382 + 0.249059i
\(88\) −4.03872 2.33176i −0.430529 0.248566i
\(89\) 2.79366 + 1.61292i 0.296127 + 0.170969i 0.640702 0.767790i \(-0.278644\pi\)
−0.344575 + 0.938759i \(0.611977\pi\)
\(90\) 0 0
\(91\) 0.919100 0.768307i 0.0963478 0.0805405i
\(92\) 5.54133i 0.577724i
\(93\) 4.37182 7.57221i 0.453336 0.785201i
\(94\) −0.916407 + 1.58726i −0.0945202 + 0.163714i
\(95\) 0 0
\(96\) 4.08359i 0.416780i
\(97\) −1.25396 2.17191i −0.127320 0.220524i 0.795318 0.606193i \(-0.207304\pi\)
−0.922637 + 0.385669i \(0.873971\pi\)
\(98\) 0.756779 + 1.31078i 0.0764462 + 0.132409i
\(99\) 2.36023i 0.237213i
\(100\) 0 0
\(101\) 6.22336 10.7792i 0.619247 1.07257i −0.370376 0.928882i \(-0.620771\pi\)
0.989623 0.143686i \(-0.0458955\pi\)
\(102\) 0.890157 1.54180i 0.0881386 0.152661i
\(103\) 15.0247i 1.48043i 0.672370 + 0.740215i \(0.265276\pi\)
−0.672370 + 0.740215i \(0.734724\pi\)
\(104\) 0.537808 + 3.08359i 0.0527364 + 0.302371i
\(105\) 0 0
\(106\) 0.296916 + 0.171425i 0.0288390 + 0.0166502i
\(107\) −11.3140 6.53215i −1.09377 0.631487i −0.159190 0.987248i \(-0.550888\pi\)
−0.934577 + 0.355761i \(0.884222\pi\)
\(108\) 9.30260 5.37086i 0.895144 0.516811i
\(109\) 11.2325i 1.07587i −0.842985 0.537937i \(-0.819204\pi\)
0.842985 0.537937i \(-0.180796\pi\)
\(110\) 0 0
\(111\) −8.27607 + 4.77819i −0.785530 + 0.453526i
\(112\) −1.23355 −0.116560
\(113\) −15.8862 + 9.17191i −1.49445 + 0.862821i −0.999980 0.00637349i \(-0.997971\pi\)
−0.494470 + 0.869195i \(0.664638\pi\)
\(114\) −0.398640 + 0.690464i −0.0373360 + 0.0646679i
\(115\) 0 0
\(116\) −5.66682 −0.526151
\(117\) −1.21545 + 1.01603i −0.112368 + 0.0939325i
\(118\) 0.594763i 0.0547524i
\(119\) −1.45717 0.841298i −0.133579 0.0771216i
\(120\) 0 0
\(121\) 8.92820 + 15.4641i 0.811655 + 1.40583i
\(122\) 3.09843 0.280519
\(123\) 2.98601 + 5.17191i 0.269239 + 0.466336i
\(124\) 9.23572 5.33225i 0.829392 0.478850i
\(125\) 0 0
\(126\) 0.0160350 + 0.0277734i 0.00142851 + 0.00247425i
\(127\) −2.80589 1.61998i −0.248982 0.143750i 0.370316 0.928906i \(-0.379249\pi\)
−0.619298 + 0.785156i \(0.712583\pi\)
\(128\) 3.30600 5.72615i 0.292212 0.506125i
\(129\) 8.10387 0.713506
\(130\) 0 0
\(131\) 0.175664 0.0153478 0.00767390 0.999971i \(-0.497557\pi\)
0.00767390 + 0.999971i \(0.497557\pi\)
\(132\) −8.38853 + 14.5294i −0.730127 + 1.26462i
\(133\) 0.652566 + 0.376759i 0.0565846 + 0.0326692i
\(134\) 1.13493 + 1.96576i 0.0980430 + 0.169815i
\(135\) 0 0
\(136\) 3.80752 2.19827i 0.326492 0.188500i
\(137\) 8.99144 + 15.5736i 0.768190 + 1.33054i 0.938543 + 0.345162i \(0.112176\pi\)
−0.170353 + 0.985383i \(0.554491\pi\)
\(138\) 0.998090 0.0849631
\(139\) 5.99307 + 10.3803i 0.508325 + 0.880445i 0.999954 + 0.00964021i \(0.00306862\pi\)
−0.491628 + 0.870805i \(0.663598\pi\)
\(140\) 0 0
\(141\) 11.5616 + 6.67510i 0.973663 + 0.562144i
\(142\) 2.81140i 0.235928i
\(143\) 6.65821 18.1879i 0.556788 1.52095i
\(144\) 1.63129 0.135941
\(145\) 0 0
\(146\) −1.06430 + 1.84342i −0.0880819 + 0.152562i
\(147\) 9.54769 5.51236i 0.787481 0.454652i
\(148\) −11.6558 −0.958101
\(149\) −2.95350 + 1.70520i −0.241960 + 0.139696i −0.616077 0.787686i \(-0.711279\pi\)
0.374117 + 0.927381i \(0.377946\pi\)
\(150\) 0 0
\(151\) 7.96141i 0.647890i 0.946076 + 0.323945i \(0.105009\pi\)
−0.946076 + 0.323945i \(0.894991\pi\)
\(152\) −1.70512 + 0.984454i −0.138304 + 0.0798498i
\(153\) 1.92701 + 1.11256i 0.155790 + 0.0899451i
\(154\) −0.339560 0.196045i −0.0273625 0.0157978i
\(155\) 0 0
\(156\) 11.0933 1.93477i 0.888172 0.154906i
\(157\) 16.4329i 1.31148i 0.754985 + 0.655742i \(0.227644\pi\)
−0.754985 + 0.655742i \(0.772356\pi\)
\(158\) 0.496329 0.859667i 0.0394858 0.0683914i
\(159\) 1.24865 2.16273i 0.0990247 0.171516i
\(160\) 0 0
\(161\) 0.943307i 0.0743430i
\(162\) 0.822599 + 1.42478i 0.0646295 + 0.111942i
\(163\) 8.90361 + 15.4215i 0.697384 + 1.20791i 0.969370 + 0.245604i \(0.0789862\pi\)
−0.271986 + 0.962301i \(0.587680\pi\)
\(164\) 7.28398i 0.568784i
\(165\) 0 0
\(166\) 0.468341 0.811190i 0.0363503 0.0629605i
\(167\) 3.14683 5.45047i 0.243509 0.421770i −0.718202 0.695834i \(-0.755035\pi\)
0.961711 + 0.274064i \(0.0883682\pi\)
\(168\) 0.461557i 0.0356099i
\(169\) −12.2325 + 4.40078i −0.940959 + 0.338522i
\(170\) 0 0
\(171\) −0.862975 0.498239i −0.0659933 0.0381013i
\(172\) 8.55995 + 4.94209i 0.652690 + 0.376831i
\(173\) −13.8349 + 7.98756i −1.05184 + 0.607283i −0.923165 0.384404i \(-0.874407\pi\)
−0.128679 + 0.991686i \(0.541074\pi\)
\(174\) 1.02069i 0.0773786i
\(175\) 0 0
\(176\) −17.2722 + 9.97212i −1.30194 + 0.751677i
\(177\) −4.33225 −0.325632
\(178\) −0.613729 + 0.354337i −0.0460010 + 0.0265587i
\(179\) −11.8087 + 20.4533i −0.882625 + 1.52875i −0.0342123 + 0.999415i \(0.510892\pi\)
−0.848412 + 0.529336i \(0.822441\pi\)
\(180\) 0 0
\(181\) 2.62590 0.195182 0.0975909 0.995227i \(-0.468886\pi\)
0.0975909 + 0.995227i \(0.468886\pi\)
\(182\) 0.0452168 + 0.259256i 0.00335169 + 0.0192174i
\(183\) 22.5689i 1.66834i
\(184\) 2.13459 + 1.23241i 0.157364 + 0.0908544i
\(185\) 0 0
\(186\) 0.960431 + 1.66351i 0.0704222 + 0.121975i
\(187\) −27.2045 −1.98939
\(188\) 8.14153 + 14.1015i 0.593782 + 1.02846i
\(189\) 1.58359 0.914288i 0.115189 0.0665046i
\(190\) 0 0
\(191\) 1.00791 + 1.74575i 0.0729298 + 0.126318i 0.900184 0.435509i \(-0.143432\pi\)
−0.827254 + 0.561828i \(0.810098\pi\)
\(192\) −9.51343 5.49258i −0.686572 0.396393i
\(193\) 11.4105 19.7636i 0.821348 1.42262i −0.0833298 0.996522i \(-0.526555\pi\)
0.904678 0.426095i \(-0.140111\pi\)
\(194\) 0.550955 0.0395563
\(195\) 0 0
\(196\) 13.4467 0.960480
\(197\) −0.321513 + 0.556877i −0.0229068 + 0.0396758i −0.877252 0.480031i \(-0.840625\pi\)
0.854345 + 0.519707i \(0.173959\pi\)
\(198\) 0.449045 + 0.259256i 0.0319122 + 0.0184245i
\(199\) −1.53342 2.65596i −0.108701 0.188276i 0.806543 0.591175i \(-0.201336\pi\)
−0.915244 + 0.402899i \(0.868003\pi\)
\(200\) 0 0
\(201\) 14.3185 8.26681i 1.00995 0.583096i
\(202\) 1.36719 + 2.36804i 0.0961952 + 0.166615i
\(203\) −0.964670 −0.0677065
\(204\) −7.90831 13.6976i −0.553693 0.959024i
\(205\) 0 0
\(206\) −2.85852 1.65037i −0.199163 0.114987i
\(207\) 1.24746i 0.0867045i
\(208\) 12.5707 + 4.60185i 0.871620 + 0.319081i
\(209\) 12.1830 0.842716
\(210\) 0 0
\(211\) 4.10020 7.10175i 0.282269 0.488904i −0.689674 0.724120i \(-0.742246\pi\)
0.971943 + 0.235215i \(0.0755796\pi\)
\(212\) 2.63786 1.52297i 0.181169 0.104598i
\(213\) −20.4782 −1.40314
\(214\) 2.48554 1.43503i 0.169908 0.0980964i
\(215\) 0 0
\(216\) 4.77798i 0.325101i
\(217\) 1.57221 0.907714i 0.106728 0.0616197i
\(218\) 2.13703 + 1.23381i 0.144738 + 0.0835643i
\(219\) 13.4274 + 7.75232i 0.907341 + 0.523854i
\(220\) 0 0
\(221\) 11.7110 + 14.0095i 0.787767 + 0.942378i
\(222\) 2.09941i 0.140903i
\(223\) −5.12210 + 8.87174i −0.343001 + 0.594095i −0.984989 0.172620i \(-0.944777\pi\)
0.641987 + 0.766715i \(0.278110\pi\)
\(224\) 0.423935 0.734278i 0.0283254 0.0490610i
\(225\) 0 0
\(226\) 4.02990i 0.268065i
\(227\) 3.52190 + 6.10012i 0.233757 + 0.404879i 0.958911 0.283708i \(-0.0915646\pi\)
−0.725154 + 0.688587i \(0.758231\pi\)
\(228\) 3.54159 + 6.13421i 0.234547 + 0.406248i
\(229\) 1.32899i 0.0878219i −0.999035 0.0439109i \(-0.986018\pi\)
0.999035 0.0439109i \(-0.0139818\pi\)
\(230\) 0 0
\(231\) −1.42799 + 2.47335i −0.0939547 + 0.162734i
\(232\) 1.26032 2.18294i 0.0827440 0.143317i
\(233\) 1.24746i 0.0817238i 0.999165 + 0.0408619i \(0.0130104\pi\)
−0.999165 + 0.0408619i \(0.986990\pi\)
\(234\) −0.0597962 0.342849i −0.00390900 0.0224127i
\(235\) 0 0
\(236\) −4.57606 2.64199i −0.297876 0.171979i
\(237\) −6.26180 3.61525i −0.406748 0.234836i
\(238\) 0.320121 0.184822i 0.0207504 0.0119802i
\(239\) 9.94207i 0.643099i −0.946893 0.321549i \(-0.895796\pi\)
0.946893 0.321549i \(-0.104204\pi\)
\(240\) 0 0
\(241\) −19.5608 + 11.2934i −1.26002 + 0.727475i −0.973079 0.230472i \(-0.925973\pi\)
−0.286944 + 0.957947i \(0.592640\pi\)
\(242\) −3.92282 −0.252168
\(243\) −3.92086 + 2.26371i −0.251523 + 0.145217i
\(244\) 13.7635 23.8391i 0.881119 1.52614i
\(245\) 0 0
\(246\) −1.31197 −0.0836483
\(247\) −5.24455 6.27387i −0.333702 0.399197i
\(248\) 4.74363i 0.301221i
\(249\) −5.90869 3.41139i −0.374448 0.216188i
\(250\) 0 0
\(251\) −3.38418 5.86157i −0.213608 0.369979i 0.739233 0.673449i \(-0.235188\pi\)
−0.952841 + 0.303470i \(0.901855\pi\)
\(252\) 0.284915 0.0179480
\(253\) −7.62577 13.2082i −0.479428 0.830394i
\(254\) 0.616417 0.355888i 0.0386774 0.0223304i
\(255\) 0 0
\(256\) −6.13860 10.6324i −0.383663 0.664523i
\(257\) 8.88007 + 5.12691i 0.553924 + 0.319808i 0.750703 0.660640i \(-0.229715\pi\)
−0.196779 + 0.980448i \(0.563048\pi\)
\(258\) −0.890157 + 1.54180i −0.0554187 + 0.0959881i
\(259\) −1.98418 −0.123291
\(260\) 0 0
\(261\) 1.27571 0.0789645
\(262\) −0.0192955 + 0.0334208i −0.00119208 + 0.00206474i
\(263\) −16.1574 9.32850i −0.996310 0.575220i −0.0891555 0.996018i \(-0.528417\pi\)
−0.907154 + 0.420798i \(0.861750\pi\)
\(264\) −3.73127 6.46275i −0.229644 0.397754i
\(265\) 0 0
\(266\) −0.143360 + 0.0827690i −0.00878998 + 0.00507489i
\(267\) 2.58098 + 4.47040i 0.157954 + 0.273584i
\(268\) 20.1658 1.23182
\(269\) 8.97894 + 15.5520i 0.547456 + 0.948221i 0.998448 + 0.0556934i \(0.0177369\pi\)
−0.450992 + 0.892528i \(0.648930\pi\)
\(270\) 0 0
\(271\) −26.7582 15.4488i −1.62544 0.938450i −0.985429 0.170086i \(-0.945595\pi\)
−0.640014 0.768363i \(-0.721071\pi\)
\(272\) 18.8025i 1.14007i
\(273\) 1.88842 0.329358i 0.114292 0.0199337i
\(274\) −3.95060 −0.238665
\(275\) 0 0
\(276\) 4.43361 7.67923i 0.266872 0.462235i
\(277\) 22.9536 13.2522i 1.37915 0.796250i 0.387089 0.922042i \(-0.373481\pi\)
0.992057 + 0.125792i \(0.0401472\pi\)
\(278\) −2.63320 −0.157929
\(279\) −2.07914 + 1.20039i −0.124475 + 0.0718656i
\(280\) 0 0
\(281\) 4.97766i 0.296942i 0.988917 + 0.148471i \(0.0474352\pi\)
−0.988917 + 0.148471i \(0.952565\pi\)
\(282\) −2.53993 + 1.46643i −0.151251 + 0.0873247i
\(283\) −10.9001 6.29317i −0.647943 0.374090i 0.139725 0.990190i \(-0.455378\pi\)
−0.787668 + 0.616100i \(0.788712\pi\)
\(284\) −21.6307 12.4885i −1.28355 0.741057i
\(285\) 0 0
\(286\) 2.72898 + 3.26458i 0.161368 + 0.193039i
\(287\) 1.23996i 0.0731926i
\(288\) −0.560626 + 0.971033i −0.0330352 + 0.0572187i
\(289\) 4.32355 7.48861i 0.254327 0.440507i
\(290\) 0 0
\(291\) 4.01315i 0.235255i
\(292\) 9.45541 + 16.3772i 0.553336 + 0.958406i
\(293\) 8.45880 + 14.6511i 0.494168 + 0.855925i 0.999977 0.00672072i \(-0.00213929\pi\)
−0.505809 + 0.862645i \(0.668806\pi\)
\(294\) 2.42199i 0.141253i
\(295\) 0 0
\(296\) 2.59229 4.48997i 0.150674 0.260974i
\(297\) 14.7824 25.6038i 0.857759 1.48568i
\(298\) 0.749222i 0.0434012i
\(299\) −3.51908 + 9.61292i −0.203514 + 0.555929i
\(300\) 0 0
\(301\) 1.45717 + 0.841298i 0.0839899 + 0.0484916i
\(302\) −1.51469 0.874509i −0.0871608 0.0503223i
\(303\) 17.2488 9.95859i 0.990917 0.572106i
\(304\) 8.42034i 0.482940i
\(305\) 0 0
\(306\) −0.423339 + 0.244415i −0.0242007 + 0.0139723i
\(307\) −4.30426 −0.245657 −0.122828 0.992428i \(-0.539197\pi\)
−0.122828 + 0.992428i \(0.539197\pi\)
\(308\) −3.01671 + 1.74170i −0.171893 + 0.0992425i
\(309\) −12.0213 + 20.8214i −0.683865 + 1.18449i
\(310\) 0 0
\(311\) 2.22512 0.126175 0.0630875 0.998008i \(-0.479905\pi\)
0.0630875 + 0.998008i \(0.479905\pi\)
\(312\) −1.72188 + 4.70357i −0.0974820 + 0.266287i
\(313\) 7.20887i 0.407469i 0.979026 + 0.203735i \(0.0653080\pi\)
−0.979026 + 0.203735i \(0.934692\pi\)
\(314\) −3.12642 1.80504i −0.176434 0.101864i
\(315\) 0 0
\(316\) −4.40948 7.63744i −0.248052 0.429639i
\(317\) 0.321644 0.0180653 0.00903266 0.999959i \(-0.497125\pi\)
0.00903266 + 0.999959i \(0.497125\pi\)
\(318\) 0.274313 + 0.475124i 0.0153827 + 0.0266436i
\(319\) −13.5073 + 7.79847i −0.756266 + 0.436630i
\(320\) 0 0
\(321\) −10.4527 18.1046i −0.583414 1.01050i
\(322\) 0.179468 + 0.103616i 0.0100014 + 0.00577430i
\(323\) −5.74278 + 9.94679i −0.319537 + 0.553454i
\(324\) 14.6162 0.812013
\(325\) 0 0
\(326\) −3.91201 −0.216666
\(327\) 8.98707 15.5661i 0.496986 0.860805i
\(328\) −2.80589 1.61998i −0.154929 0.0894485i
\(329\) 1.38594 + 2.40052i 0.0764094 + 0.132345i
\(330\) 0 0
\(331\) −14.4037 + 8.31600i −0.791701 + 0.457089i −0.840561 0.541717i \(-0.817775\pi\)
0.0488600 + 0.998806i \(0.484441\pi\)
\(332\) −4.16082 7.20676i −0.228355 0.395522i
\(333\) 2.62395 0.143791
\(334\) 0.691317 + 1.19740i 0.0378272 + 0.0655186i
\(335\) 0 0
\(336\) −1.70947 0.986961i −0.0932590 0.0538431i
\(337\) 24.2186i 1.31927i 0.751586 + 0.659636i \(0.229289\pi\)
−0.751586 + 0.659636i \(0.770711\pi\)
\(338\) 0.506387 2.81068i 0.0275438 0.152881i
\(339\) −29.3537 −1.59427
\(340\) 0 0
\(341\) 14.6761 25.4197i 0.794754 1.37655i
\(342\) 0.189584 0.109456i 0.0102515 0.00591873i
\(343\) 4.61478 0.249174
\(344\) −3.80752 + 2.19827i −0.205288 + 0.118523i
\(345\) 0 0
\(346\) 3.50952i 0.188673i
\(347\) 5.43309 3.13680i 0.291664 0.168392i −0.347028 0.937855i \(-0.612809\pi\)
0.638692 + 0.769463i \(0.279476\pi\)
\(348\) −7.85314 4.53401i −0.420972 0.243049i
\(349\) 6.12275 + 3.53497i 0.327743 + 0.189223i 0.654839 0.755769i \(-0.272737\pi\)
−0.327095 + 0.944991i \(0.606070\pi\)
\(350\) 0 0
\(351\) −19.5487 + 3.40948i −1.04343 + 0.181984i
\(352\) 13.7085i 0.730666i
\(353\) 10.8949 18.8705i 0.579878 1.00438i −0.415615 0.909541i \(-0.636434\pi\)
0.995493 0.0948371i \(-0.0302330\pi\)
\(354\) 0.475869 0.824229i 0.0252921 0.0438073i
\(355\) 0 0
\(356\) 6.29598i 0.333687i
\(357\) −1.34624 2.33176i −0.0712506 0.123410i
\(358\) −2.59422 4.49332i −0.137109 0.237479i
\(359\) 23.9737i 1.26528i −0.774444 0.632642i \(-0.781971\pi\)
0.774444 0.632642i \(-0.218029\pi\)
\(360\) 0 0
\(361\) −6.92820 + 12.0000i −0.364642 + 0.631579i
\(362\) −0.288438 + 0.499589i −0.0151600 + 0.0262578i
\(363\) 28.5737i 1.49973i
\(364\) 2.19556 + 0.803745i 0.115078 + 0.0421277i
\(365\) 0 0
\(366\) 4.29384 + 2.47905i 0.224443 + 0.129582i
\(367\) 5.53505 + 3.19566i 0.288927 + 0.166812i 0.637458 0.770485i \(-0.279986\pi\)
−0.348531 + 0.937297i \(0.613319\pi\)
\(368\) 9.12892 5.27059i 0.475878 0.274748i
\(369\) 1.63977i 0.0853628i
\(370\) 0 0
\(371\) 0.449045 0.259256i 0.0233133 0.0134599i
\(372\) 17.0653 0.884793
\(373\) −17.3899 + 10.0401i −0.900414 + 0.519855i −0.877335 0.479879i \(-0.840681\pi\)
−0.0230798 + 0.999734i \(0.507347\pi\)
\(374\) 2.98823 5.17577i 0.154518 0.267633i
\(375\) 0 0
\(376\) −7.24280 −0.373519
\(377\) 9.83062 + 3.59878i 0.506302 + 0.185346i
\(378\) 0.401714i 0.0206619i
\(379\) 4.73007 + 2.73091i 0.242968 + 0.140277i 0.616540 0.787324i \(-0.288534\pi\)
−0.373572 + 0.927601i \(0.621867\pi\)
\(380\) 0 0
\(381\) −2.59229 4.48997i −0.132807 0.230028i
\(382\) −0.442849 −0.0226581
\(383\) 2.83388 + 4.90842i 0.144804 + 0.250808i 0.929300 0.369326i \(-0.120411\pi\)
−0.784496 + 0.620134i \(0.787078\pi\)
\(384\) 9.16297 5.29024i 0.467596 0.269966i
\(385\) 0 0
\(386\) 2.50675 + 4.34181i 0.127590 + 0.220992i
\(387\) −1.92701 1.11256i −0.0979554 0.0565546i
\(388\) 2.44739 4.23901i 0.124247 0.215203i
\(389\) 10.6174 0.538325 0.269162 0.963095i \(-0.413253\pi\)
0.269162 + 0.963095i \(0.413253\pi\)
\(390\) 0 0
\(391\) 14.3784 0.727149
\(392\) −2.99059 + 5.17986i −0.151048 + 0.261622i
\(393\) 0.243436 + 0.140548i 0.0122797 + 0.00708971i
\(394\) −0.0706321 0.122338i −0.00355840 0.00616332i
\(395\) 0 0
\(396\) 3.98940 2.30328i 0.200475 0.115744i
\(397\) −14.0169 24.2780i −0.703487 1.21848i −0.967235 0.253884i \(-0.918292\pi\)
0.263748 0.964592i \(-0.415041\pi\)
\(398\) 0.673745 0.0337718
\(399\) 0.602888 + 1.04423i 0.0301822 + 0.0522770i
\(400\) 0 0
\(401\) 19.4979 + 11.2571i 0.973680 + 0.562155i 0.900356 0.435154i \(-0.143306\pi\)
0.0733241 + 0.997308i \(0.476639\pi\)
\(402\) 3.63222i 0.181159i
\(403\) −19.4081 + 3.38496i −0.966788 + 0.168617i
\(404\) 24.2927 1.20861
\(405\) 0 0
\(406\) 0.105963 0.183533i 0.00525884 0.00910857i
\(407\) −27.7826 + 16.0403i −1.37713 + 0.795087i
\(408\) 7.03533 0.348301
\(409\) 3.71328 2.14386i 0.183610 0.106007i −0.405378 0.914149i \(-0.632860\pi\)
0.588988 + 0.808142i \(0.299527\pi\)
\(410\) 0 0
\(411\) 28.7761i 1.41942i
\(412\) −25.3956 + 14.6622i −1.25115 + 0.722353i
\(413\) −0.778989 0.449749i −0.0383315 0.0221307i
\(414\) −0.237335 0.137025i −0.0116644 0.00673443i
\(415\) 0 0
\(416\) −7.05946 + 5.90125i −0.346119 + 0.289333i
\(417\) 19.1802i 0.939257i
\(418\) −1.33822 + 2.31787i −0.0654546 + 0.113371i
\(419\) 8.85578 15.3387i 0.432633 0.749343i −0.564466 0.825456i \(-0.690918\pi\)
0.997099 + 0.0761137i \(0.0242512\pi\)
\(420\) 0 0
\(421\) 12.8787i 0.627672i −0.949477 0.313836i \(-0.898386\pi\)
0.949477 0.313836i \(-0.101614\pi\)
\(422\) 0.900759 + 1.56016i 0.0438483 + 0.0759474i
\(423\) −1.83281 3.17453i −0.0891145 0.154351i
\(424\) 1.35485i 0.0657973i
\(425\) 0 0
\(426\) 2.24940 3.89607i 0.108984 0.188765i
\(427\) 2.34298 4.05816i 0.113385 0.196388i
\(428\) 25.4981i 1.23250i
\(429\) 23.7792 19.8778i 1.14807 0.959710i
\(430\) 0 0
\(431\) 8.22590 + 4.74923i 0.396228 + 0.228762i 0.684855 0.728679i \(-0.259866\pi\)
−0.288627 + 0.957442i \(0.593199\pi\)
\(432\) 17.6962 + 10.2169i 0.851408 + 0.491560i
\(433\) 1.20922 0.698141i 0.0581112 0.0335505i −0.470663 0.882313i \(-0.655985\pi\)
0.528774 + 0.848763i \(0.322652\pi\)
\(434\) 0.398826i 0.0191443i
\(435\) 0 0
\(436\) 18.9857 10.9614i 0.909251 0.524956i
\(437\) −6.43911 −0.308024
\(438\) −2.94983 + 1.70308i −0.140948 + 0.0813765i
\(439\) −2.08090 + 3.60422i −0.0993159 + 0.172020i −0.911402 0.411518i \(-0.864999\pi\)
0.812086 + 0.583538i \(0.198332\pi\)
\(440\) 0 0
\(441\) −3.02711 −0.144148
\(442\) −3.95174 + 0.689221i −0.187965 + 0.0327829i
\(443\) 9.54563i 0.453526i 0.973950 + 0.226763i \(0.0728144\pi\)
−0.973950 + 0.226763i \(0.927186\pi\)
\(444\) −16.1527 9.32578i −0.766574 0.442582i
\(445\) 0 0
\(446\) −1.12526 1.94900i −0.0532825 0.0922880i
\(447\) −5.45732 −0.258122
\(448\) −1.14042 1.97526i −0.0538796 0.0933223i
\(449\) −18.8075 + 10.8585i −0.887582 + 0.512446i −0.873151 0.487450i \(-0.837927\pi\)
−0.0144310 + 0.999896i \(0.504594\pi\)
\(450\) 0 0
\(451\) 10.0239 + 17.3620i 0.472009 + 0.817544i
\(452\) −31.0057 17.9012i −1.45839 0.842000i
\(453\) −6.36991 + 11.0330i −0.299284 + 0.518376i
\(454\) −1.54743 −0.0726246
\(455\) 0 0
\(456\) −3.15064 −0.147542
\(457\) 2.36130 4.08989i 0.110457 0.191317i −0.805498 0.592599i \(-0.798102\pi\)
0.915955 + 0.401282i \(0.131435\pi\)
\(458\) 0.252845 + 0.145980i 0.0118147 + 0.00682122i
\(459\) 13.9361 + 24.1381i 0.650482 + 1.12667i
\(460\) 0 0
\(461\) 1.54283 0.890753i 0.0718568 0.0414865i −0.463641 0.886023i \(-0.653457\pi\)
0.535498 + 0.844537i \(0.320124\pi\)
\(462\) −0.313710 0.543362i −0.0145951 0.0252795i
\(463\) −6.80200 −0.316116 −0.158058 0.987430i \(-0.550523\pi\)
−0.158058 + 0.987430i \(0.550523\pi\)
\(464\) −5.38995 9.33566i −0.250222 0.433397i
\(465\) 0 0
\(466\) −0.237335 0.137025i −0.0109943 0.00634758i
\(467\) 18.2374i 0.843927i 0.906613 + 0.421963i \(0.138659\pi\)
−0.906613 + 0.421963i \(0.861341\pi\)
\(468\) −2.90348 1.06290i −0.134213 0.0491325i
\(469\) 3.43285 0.158514
\(470\) 0 0
\(471\) −13.1479 + 22.7728i −0.605823 + 1.04932i
\(472\) 2.03546 1.17517i 0.0936897 0.0540918i
\(473\) 27.2045 1.25086
\(474\) 1.37564 0.794223i 0.0631850 0.0364799i
\(475\) 0 0
\(476\) 3.28398i 0.150521i
\(477\) −0.593832 + 0.342849i −0.0271897 + 0.0156980i
\(478\) 1.89152 + 1.09207i 0.0865162 + 0.0499502i
\(479\) −30.4674 17.5904i −1.39209 0.803724i −0.398544 0.917149i \(-0.630485\pi\)
−0.993547 + 0.113425i \(0.963818\pi\)
\(480\) 0 0
\(481\) 20.2201 + 7.40214i 0.921957 + 0.337508i
\(482\) 4.96204i 0.226015i
\(483\) 0.754738 1.30724i 0.0343418 0.0594817i
\(484\) −17.4255 + 30.1819i −0.792069 + 1.37190i
\(485\) 0 0
\(486\) 0.994615i 0.0451166i
\(487\) −5.15200 8.92352i −0.233459 0.404363i 0.725364 0.688365i \(-0.241671\pi\)
−0.958824 + 0.284002i \(0.908338\pi\)
\(488\) 6.12210 + 10.6038i 0.277134 + 0.480011i
\(489\) 28.4950i 1.28859i
\(490\) 0 0
\(491\) 4.66599 8.08174i 0.210573 0.364724i −0.741321 0.671151i \(-0.765800\pi\)
0.951894 + 0.306427i \(0.0991336\pi\)
\(492\) −5.82790 + 10.0942i −0.262742 + 0.455083i
\(493\) 14.7041i 0.662238i
\(494\) 1.76971 0.308654i 0.0796230 0.0138870i
\(495\) 0 0
\(496\) 17.5689 + 10.1434i 0.788869 + 0.455454i
\(497\) −3.68222 2.12593i −0.165170 0.0953611i
\(498\) 1.29806 0.749437i 0.0581676 0.0335831i
\(499\) 23.9421i 1.07179i 0.844283 + 0.535897i \(0.180026\pi\)
−0.844283 + 0.535897i \(0.819974\pi\)
\(500\) 0 0
\(501\) 8.72181 5.03554i 0.389662 0.224971i
\(502\) 1.48692 0.0663645
\(503\) 36.4980 21.0721i 1.62737 0.939560i 0.642490 0.766294i \(-0.277901\pi\)
0.984875 0.173266i \(-0.0554320\pi\)
\(504\) −0.0633661 + 0.109753i −0.00282255 + 0.00488880i
\(505\) 0 0
\(506\) 3.35056 0.148951
\(507\) −20.4729 3.68852i −0.909235 0.163813i
\(508\) 6.32355i 0.280562i
\(509\) 29.0640 + 16.7801i 1.28824 + 0.743765i 0.978340 0.207005i \(-0.0663715\pi\)
0.309899 + 0.950770i \(0.399705\pi\)
\(510\) 0 0
\(511\) 1.60960 + 2.78792i 0.0712047 + 0.123330i
\(512\) 15.9211 0.703621
\(513\) −6.24102 10.8098i −0.275548 0.477263i
\(514\) −1.95084 + 1.12632i −0.0860477 + 0.0496796i
\(515\) 0 0
\(516\) 7.90831 + 13.6976i 0.348144 + 0.603003i
\(517\) 38.8120 + 22.4081i 1.70695 + 0.985508i
\(518\) 0.217949 0.377499i 0.00957614 0.0165864i
\(519\) −25.5633 −1.12210
\(520\) 0 0
\(521\) 12.4649 0.546098 0.273049 0.962000i \(-0.411968\pi\)
0.273049 + 0.962000i \(0.411968\pi\)
\(522\) −0.140128 + 0.242710i −0.00613326 + 0.0106231i
\(523\) 4.90132 + 2.82978i 0.214320 + 0.123738i 0.603317 0.797501i \(-0.293845\pi\)
−0.388998 + 0.921239i \(0.627179\pi\)
\(524\) 0.171425 + 0.296916i 0.00748872 + 0.0129708i
\(525\) 0 0
\(526\) 3.54958 2.04935i 0.154769 0.0893558i
\(527\) 13.8359 + 23.9645i 0.602702 + 1.04391i
\(528\) −31.9147 −1.38891
\(529\) −7.46953 12.9376i −0.324762 0.562505i
\(530\) 0 0
\(531\) 1.03016 + 0.594763i 0.0447051 + 0.0258105i
\(532\) 1.47067i 0.0637616i
\(533\) 4.62577 12.6360i 0.200364 0.547327i
\(534\) −1.13402 −0.0490737
\(535\) 0 0
\(536\) −4.48494 + 7.76815i −0.193720 + 0.335533i
\(537\) −32.7293 + 18.8963i −1.41237 + 0.815433i
\(538\) −3.94511 −0.170086
\(539\) 32.0514 18.5049i 1.38055 0.797061i
\(540\) 0 0
\(541\) 15.4750i 0.665321i −0.943047 0.332660i \(-0.892054\pi\)
0.943047 0.332660i \(-0.107946\pi\)
\(542\) 5.87842 3.39391i 0.252500 0.145781i
\(543\) 3.63900 + 2.10098i 0.156165 + 0.0901616i
\(544\) 11.1923 + 6.46187i 0.479866 + 0.277051i
\(545\) 0 0
\(546\) −0.144769 + 0.395458i −0.00619552 + 0.0169240i
\(547\) 25.1765i 1.07647i −0.842795 0.538234i \(-0.819092\pi\)
0.842795 0.538234i \(-0.180908\pi\)
\(548\) −17.5489 + 30.3956i −0.749653 + 1.29844i
\(549\) −3.09843 + 5.36665i −0.132238 + 0.229043i
\(550\) 0 0
\(551\) 6.58493i 0.280528i
\(552\) 1.97210 + 3.41577i 0.0839380 + 0.145385i
\(553\) −0.750630 1.30013i −0.0319200 0.0552871i
\(554\) 5.82269i 0.247382i
\(555\) 0 0
\(556\) −11.6969 + 20.2596i −0.496059 + 0.859199i
\(557\) −21.1744 + 36.6752i −0.897190 + 1.55398i −0.0661194 + 0.997812i \(0.521062\pi\)
−0.831071 + 0.556167i \(0.812272\pi\)
\(558\) 0.527420i 0.0223275i
\(559\) −11.7110 14.0095i −0.495322 0.592537i
\(560\) 0 0
\(561\) −37.7002 21.7662i −1.59171 0.918971i
\(562\) −0.947022 0.546763i −0.0399477 0.0230638i
\(563\) −20.6032 + 11.8953i −0.868322 + 0.501326i −0.866790 0.498673i \(-0.833821\pi\)
−0.00153173 + 0.999999i \(0.500488\pi\)
\(564\) 26.0561i 1.09716i
\(565\) 0 0
\(566\) 2.39461 1.38253i 0.100653 0.0581119i
\(567\) 2.48814 0.104492
\(568\) 9.62148 5.55497i 0.403709 0.233081i
\(569\) 13.3710 23.1593i 0.560543 0.970889i −0.436906 0.899507i \(-0.643926\pi\)
0.997449 0.0713817i \(-0.0227408\pi\)
\(570\) 0 0
\(571\) 16.7159 0.699539 0.349769 0.936836i \(-0.386260\pi\)
0.349769 + 0.936836i \(0.386260\pi\)
\(572\) 37.2398 6.49498i 1.55707 0.271569i
\(573\) 3.22571i 0.134756i
\(574\) −0.235908 0.136202i −0.00984661 0.00568494i
\(575\) 0 0
\(576\) 1.50812 + 2.61215i 0.0628385 + 0.108840i
\(577\) 20.6768 0.860786 0.430393 0.902642i \(-0.358375\pi\)
0.430393 + 0.902642i \(0.358375\pi\)
\(578\) 0.949828 + 1.64515i 0.0395076 + 0.0684292i
\(579\) 31.6257 18.2591i 1.31432 0.758822i
\(580\) 0 0
\(581\) −0.708301 1.22681i −0.0293853 0.0508968i
\(582\) 0.763519 + 0.440818i 0.0316489 + 0.0182725i
\(583\) 4.19170 7.26023i 0.173602 0.300688i
\(584\) −8.41165 −0.348076
\(585\) 0 0
\(586\) −3.71657 −0.153530
\(587\) 10.3986 18.0109i 0.429196 0.743388i −0.567606 0.823300i \(-0.692130\pi\)
0.996802 + 0.0799116i \(0.0254638\pi\)
\(588\) 18.6346 + 10.7587i 0.768478 + 0.443681i
\(589\) −6.19615 10.7321i −0.255308 0.442206i
\(590\) 0 0
\(591\) −0.891111 + 0.514483i −0.0366554 + 0.0211630i
\(592\) −11.0863 19.2021i −0.455644 0.789199i
\(593\) 21.8475 0.897169 0.448585 0.893740i \(-0.351928\pi\)
0.448585 + 0.893740i \(0.351928\pi\)
\(594\) 3.24749 + 5.62482i 0.133246 + 0.230789i
\(595\) 0 0
\(596\) −5.76446 3.32811i −0.236121 0.136325i
\(597\) 4.90755i 0.200853i
\(598\) −1.44235 1.72544i −0.0589822 0.0705583i
\(599\) 3.58040 0.146291 0.0731456 0.997321i \(-0.476696\pi\)
0.0731456 + 0.997321i \(0.476696\pi\)
\(600\) 0 0
\(601\) −10.6743 + 18.4885i −0.435414 + 0.754160i −0.997329 0.0730352i \(-0.976731\pi\)
0.561915 + 0.827195i \(0.310065\pi\)
\(602\) −0.320121 + 0.184822i −0.0130472 + 0.00753278i
\(603\) −4.53972 −0.184872
\(604\) −13.4568 + 7.76929i −0.547550 + 0.316128i
\(605\) 0 0
\(606\) 4.37554i 0.177744i
\(607\) 2.85767 1.64988i 0.115989 0.0669665i −0.440883 0.897565i \(-0.645335\pi\)
0.556872 + 0.830598i \(0.312001\pi\)
\(608\) −5.01226 2.89383i −0.203274 0.117360i
\(609\) −1.33685 0.771830i −0.0541718 0.0312761i
\(610\) 0 0
\(611\) −5.16832 29.6332i −0.209088 1.19883i
\(612\) 4.34285i 0.175549i
\(613\) −4.94318 + 8.56183i −0.199653 + 0.345809i −0.948416 0.317029i \(-0.897315\pi\)
0.748763 + 0.662838i \(0.230648\pi\)
\(614\) 0.472795 0.818904i 0.0190804 0.0330483i
\(615\) 0 0
\(616\) 1.54944i 0.0624286i
\(617\) −22.8584 39.5920i −0.920246 1.59391i −0.799033 0.601287i \(-0.794655\pi\)
−0.121213 0.992626i \(-0.538679\pi\)
\(618\) −2.64091 4.57419i −0.106233 0.184001i
\(619\) 19.9143i 0.800425i −0.916422 0.400212i \(-0.868936\pi\)
0.916422 0.400212i \(-0.131064\pi\)
\(620\) 0 0
\(621\) −7.81295 + 13.5324i −0.313523 + 0.543038i
\(622\) −0.244415 + 0.423339i −0.00980014 + 0.0169743i
\(623\) 1.07177i 0.0429397i
\(624\) 13.7386 + 16.4351i 0.549986 + 0.657930i
\(625\) 0 0
\(626\) −1.37152 0.791847i −0.0548169 0.0316486i
\(627\) 16.8833 + 9.74760i 0.674255 + 0.389282i
\(628\) −27.7757 + 16.0363i −1.10837 + 0.639918i
\(629\) 30.2440i 1.20591i
\(630\) 0 0
\(631\) 12.6403 7.29790i 0.503204 0.290525i −0.226832 0.973934i \(-0.572837\pi\)
0.730036 + 0.683409i \(0.239503\pi\)
\(632\) 3.92272 0.156038
\(633\) 11.3642 6.56112i 0.451686 0.260781i
\(634\) −0.0353305 + 0.0611942i −0.00140315 + 0.00243033i
\(635\) 0 0
\(636\) 4.87409 0.193270
\(637\) −23.3269 8.53948i −0.924246 0.338346i
\(638\) 3.42644i 0.135654i
\(639\) 4.86950 + 2.81140i 0.192634 + 0.111217i
\(640\) 0 0
\(641\) −7.08183 12.2661i −0.279716 0.484482i 0.691598 0.722282i \(-0.256907\pi\)
−0.971314 + 0.237801i \(0.923573\pi\)
\(642\) 4.59265 0.181257
\(643\) −8.38581 14.5246i −0.330704 0.572796i 0.651946 0.758265i \(-0.273953\pi\)
−0.982650 + 0.185469i \(0.940620\pi\)
\(644\) 1.59443 0.920544i 0.0628293 0.0362745i
\(645\) 0 0
\(646\) −1.26161 2.18518i −0.0496376 0.0859748i
\(647\) 2.59087 + 1.49584i 0.101858 + 0.0588075i 0.550063 0.835123i \(-0.314604\pi\)
−0.448206 + 0.893930i \(0.647937\pi\)
\(648\) −3.25069 + 5.63037i −0.127699 + 0.221182i
\(649\) −14.5432 −0.570872
\(650\) 0 0
\(651\) 2.90504 0.113858
\(652\) −17.3775 + 30.0987i −0.680556 + 1.17876i
\(653\) 10.1016 + 5.83217i 0.395307 + 0.228230i 0.684457 0.729053i \(-0.260039\pi\)
−0.289150 + 0.957284i \(0.593373\pi\)
\(654\) 1.97434 + 3.41966i 0.0772028 + 0.133719i
\(655\) 0 0
\(656\) −11.9998 + 6.92810i −0.468514 + 0.270497i
\(657\) −2.12859 3.68683i −0.0830444 0.143837i
\(658\) −0.608946 −0.0237392
\(659\) −0.905237 1.56792i −0.0352630 0.0610773i 0.847855 0.530228i \(-0.177894\pi\)
−0.883118 + 0.469150i \(0.844560\pi\)
\(660\) 0 0
\(661\) 10.6872 + 6.17028i 0.415686 + 0.239996i 0.693230 0.720717i \(-0.256187\pi\)
−0.277544 + 0.960713i \(0.589520\pi\)
\(662\) 3.65383i 0.142010i
\(663\) 5.02027 + 28.7844i 0.194971 + 1.11789i
\(664\) 3.70152 0.143647
\(665\) 0 0
\(666\) −0.288223 + 0.499217i −0.0111684 + 0.0193443i
\(667\) 7.13907 4.12174i 0.276426 0.159594i
\(668\) 12.2836 0.475265
\(669\) −14.1965 + 8.19636i −0.548869 + 0.316890i
\(670\) 0 0
\(671\) 75.7634i 2.92481i
\(672\) 1.17499 0.678380i 0.0453262 0.0261691i
\(673\) 8.02481 + 4.63313i 0.309334 + 0.178594i 0.646628 0.762805i \(-0.276178\pi\)
−0.337295 + 0.941399i \(0.609512\pi\)
\(674\) −4.60770 2.66025i −0.177482 0.102469i
\(675\) 0 0
\(676\) −19.3757 16.3814i −0.745220 0.630053i
\(677\) 13.8984i 0.534158i −0.963675 0.267079i \(-0.913941\pi\)
0.963675 0.267079i \(-0.0860585\pi\)
\(678\) 3.22431 5.58467i 0.123829 0.214478i
\(679\) 0.416622 0.721611i 0.0159885 0.0276929i
\(680\) 0 0
\(681\) 11.2715i 0.431924i
\(682\) 3.22414 + 5.58438i 0.123459 + 0.213837i
\(683\) −18.8756 32.6935i −0.722255 1.25098i −0.960094 0.279678i \(-0.909772\pi\)
0.237838 0.971305i \(-0.423561\pi\)
\(684\) 1.94486i 0.0743637i
\(685\) 0 0
\(686\) −0.506903 + 0.877981i −0.0193536 + 0.0335215i
\(687\) 1.06332 1.84172i 0.0405681 0.0702661i
\(688\) 18.8025i 0.716838i
\(689\) −5.54324 + 0.966794i −0.211181 + 0.0368319i
\(690\) 0 0
\(691\) −1.43146 0.826456i −0.0544554 0.0314399i 0.472525 0.881317i \(-0.343343\pi\)
−0.526981 + 0.849877i \(0.676676\pi\)
\(692\) −27.0020 15.5896i −1.02646 0.592628i
\(693\) 0.679120 0.392090i 0.0257976 0.0148943i
\(694\) 1.37823i 0.0523168i
\(695\) 0 0
\(696\) 3.49312 2.01676i 0.132407 0.0764450i
\(697\) −18.9002 −0.715897
\(698\) −1.34509 + 0.776587i −0.0509123 + 0.0293943i
\(699\) −0.998090 + 1.72874i −0.0377512 + 0.0653871i
\(700\) 0 0
\(701\) −20.4819 −0.773590 −0.386795 0.922166i \(-0.626418\pi\)
−0.386795 + 0.922166i \(0.626418\pi\)
\(702\) 1.49863 4.09373i 0.0565620 0.154508i
\(703\) 13.5442i 0.510830i
\(704\) −31.9363 18.4384i −1.20365 0.694925i
\(705\) 0 0
\(706\) 2.39347 + 4.14561i 0.0900794 + 0.156022i
\(707\) 4.13538 0.155527
\(708\) −4.22770 7.32260i −0.158887 0.275200i
\(709\) −19.0021 + 10.9709i −0.713639 + 0.412020i −0.812407 0.583091i \(-0.801843\pi\)
0.0987679 + 0.995110i \(0.468510\pi\)
\(710\) 0 0
\(711\) 0.992658 + 1.71933i 0.0372276 + 0.0644801i
\(712\) −2.42530 1.40025i −0.0908919 0.0524764i
\(713\) −7.75678 + 13.4351i −0.290494 + 0.503150i
\(714\) 0.591503 0.0221364
\(715\) 0 0
\(716\) −46.0950 −1.72265
\(717\) 7.95463 13.7778i 0.297071 0.514542i
\(718\) 4.56110 + 2.63335i 0.170219 + 0.0982759i
\(719\) −19.4237 33.6429i −0.724384 1.25467i −0.959227 0.282636i \(-0.908791\pi\)
0.234844 0.972033i \(-0.424542\pi\)
\(720\) 0 0
\(721\) −4.32312 + 2.49596i −0.161002 + 0.0929543i
\(722\) −1.52204 2.63624i −0.0566443 0.0981108i
\(723\) −36.1434 −1.34419
\(724\) 2.56254 + 4.43844i 0.0952359 + 0.164953i
\(725\) 0 0
\(726\) −5.43628 3.13864i −0.201759 0.116486i
\(727\) 30.6598i 1.13711i −0.822645 0.568555i \(-0.807503\pi\)
0.822645 0.568555i \(-0.192497\pi\)
\(728\) −0.797912 + 0.667002i −0.0295726 + 0.0247207i
\(729\) −29.7112 −1.10042
\(730\) 0 0
\(731\) −12.8236 + 22.2110i −0.474296 + 0.821505i
\(732\) 38.1473 22.0243i 1.40996 0.814043i
\(733\) 24.3858 0.900709 0.450355 0.892850i \(-0.351298\pi\)
0.450355 + 0.892850i \(0.351298\pi\)
\(734\) −1.21598 + 0.702045i −0.0448826 + 0.0259130i
\(735\) 0 0
\(736\) 7.24539i 0.267069i
\(737\) 48.0669 27.7515i 1.77057 1.02224i
\(738\) 0.311973 + 0.180117i 0.0114839 + 0.00663021i
\(739\) 33.1504 + 19.1394i 1.21946 + 0.704054i 0.964802 0.262977i \(-0.0847044\pi\)
0.254656 + 0.967032i \(0.418038\pi\)
\(740\) 0 0
\(741\) −2.24823 12.8905i −0.0825909 0.473546i
\(742\) 0.113910i 0.00418178i
\(743\) 20.0040 34.6479i 0.733874 1.27111i −0.221342 0.975196i \(-0.571044\pi\)
0.955216 0.295910i \(-0.0956230\pi\)
\(744\) −3.79537 + 6.57377i −0.139145 + 0.241006i
\(745\) 0 0
\(746\) 4.41134i 0.161511i
\(747\) 0.936681 + 1.62238i 0.0342714 + 0.0593598i
\(748\) −26.5480 45.9825i −0.970691 1.68129i
\(749\) 4.34057i 0.158601i
\(750\) 0 0
\(751\) 12.8010 22.1720i 0.467115 0.809067i −0.532179 0.846632i \(-0.678627\pi\)
0.999294 + 0.0375648i \(0.0119601\pi\)
\(752\) −15.4875 + 26.8251i −0.564770 + 0.978211i
\(753\) 10.8307i 0.394693i
\(754\) −1.76451 + 1.47502i −0.0642597 + 0.0537169i
\(755\) 0 0
\(756\) 3.09076 + 1.78445i 0.112410 + 0.0648998i
\(757\) −1.60083 0.924239i −0.0581831 0.0335920i 0.470626 0.882333i \(-0.344028\pi\)
−0.528809 + 0.848741i \(0.677361\pi\)
\(758\) −1.03914 + 0.599945i −0.0377431 + 0.0217910i
\(759\) 24.4055i 0.885862i
\(760\) 0 0
\(761\) 22.7006 13.1062i 0.822896 0.475099i −0.0285179 0.999593i \(-0.509079\pi\)
0.851414 + 0.524494i \(0.175745\pi\)
\(762\) 1.13898 0.0412610
\(763\) 3.23196 1.86597i 0.117005 0.0675528i
\(764\) −1.96718 + 3.40725i −0.0711699 + 0.123270i
\(765\) 0 0
\(766\) −1.24513 −0.0449884
\(767\) 6.26058 + 7.48932i 0.226056 + 0.270424i
\(768\) 19.6459i 0.708911i
\(769\) 38.4078 + 22.1747i 1.38502 + 0.799641i 0.992749 0.120208i \(-0.0383562\pi\)
0.392271 + 0.919850i \(0.371690\pi\)
\(770\) 0 0
\(771\) 8.20406 + 14.2099i 0.295462 + 0.511755i
\(772\) 44.5408 1.60306
\(773\) 11.6319 + 20.1471i 0.418371 + 0.724640i 0.995776 0.0918181i \(-0.0292678\pi\)
−0.577405 + 0.816458i \(0.695935\pi\)
\(774\) 0.423339 0.244415i 0.0152166 0.00878531i
\(775\) 0 0
\(776\) 1.08861 + 1.88554i 0.0390790 + 0.0676868i
\(777\) −2.74970 1.58754i −0.0986448 0.0569526i
\(778\) −1.16625 + 2.02001i −0.0418122 + 0.0724209i
\(779\) 8.46410 0.303258
\(780\) 0 0
\(781\) −68.7449 −2.45989
\(782\) −1.57938 + 2.73556i −0.0564784 + 0.0978235i
\(783\) 13.8389 + 7.98989i 0.494562 + 0.285535i
\(784\) 12.7897 + 22.1524i 0.456776 + 0.791159i
\(785\) 0 0
\(786\) −0.0534798 + 0.0308766i −0.00190756 + 0.00110133i
\(787\) 23.9567 + 41.4942i 0.853963 + 1.47911i 0.877604 + 0.479387i \(0.159141\pi\)
−0.0236408 + 0.999721i \(0.507526\pi\)
\(788\) −1.25502 −0.0447081
\(789\) −14.9274 25.8551i −0.531430 0.920464i
\(790\) 0 0
\(791\) −5.27814 3.04734i −0.187669 0.108351i
\(792\) 2.04903i 0.0728090i
\(793\) −39.0158 + 32.6147i −1.38549 + 1.15818i
\(794\) 6.15865 0.218562
\(795\) 0 0
\(796\) 2.99284 5.18374i 0.106078 0.183733i
\(797\) −17.9225 + 10.3476i −0.634849 + 0.366530i −0.782627 0.622490i \(-0.786121\pi\)
0.147779 + 0.989020i \(0.452788\pi\)
\(798\) −0.264893 −0.00937712
\(799\) −36.5902 + 21.1253i −1.29447 + 0.747361i
\(800\) 0 0
\(801\) 1.41735i 0.0500795i
\(802\) −4.28344 + 2.47305i −0.151254 + 0.0873263i
\(803\) 45.0755 + 26.0244i 1.59068 + 0.918380i
\(804\) 27.9460 + 16.1346i 0.985580 + 0.569025i
\(805\) 0 0
\(806\) 1.48785 4.06430i 0.0524073 0.143159i
\(807\) 28.7361i 1.01156i
\(808\) −5.40278 + 9.35788i −0.190069 + 0.329209i
\(809\) 7.94574 13.7624i 0.279357 0.483861i −0.691868 0.722024i \(-0.743212\pi\)
0.971225 + 0.238163i \(0.0765453\pi\)
\(810\) 0 0
\(811\) 23.8796i 0.838525i 0.907865 + 0.419263i \(0.137711\pi\)
−0.907865 + 0.419263i \(0.862289\pi\)
\(812\) −0.941391 1.63054i −0.0330363 0.0572206i
\(813\) −24.7212 42.8183i −0.867009 1.50170i
\(814\) 7.04768i 0.247021i
\(815\) 0 0
\(816\) 15.0438 26.0567i 0.526640 0.912167i
\(817\) 5.74278 9.94679i 0.200915 0.347994i
\(818\) 0.941956i 0.0329347i
\(819\) −0.494262 0.180939i −0.0172709 0.00632250i
\(820\) 0 0
\(821\) 13.7782 + 7.95484i 0.480862 + 0.277626i 0.720776 0.693169i \(-0.243786\pi\)
−0.239914 + 0.970794i \(0.577119\pi\)
\(822\) −5.47478 3.16087i −0.190955 0.110248i
\(823\) 12.8271 7.40573i 0.447124 0.258147i −0.259491 0.965746i \(-0.583555\pi\)
0.706615 + 0.707598i \(0.250221\pi\)
\(824\) 13.0436i 0.454397i
\(825\) 0 0
\(826\) 0.171134 0.0988040i 0.00595450 0.00343783i
\(827\) 33.9498 1.18055 0.590275 0.807202i \(-0.299019\pi\)
0.590275 + 0.807202i \(0.299019\pi\)
\(828\) −2.10853 + 1.21736i −0.0732763 + 0.0423061i
\(829\) −11.6573 + 20.1910i −0.404875 + 0.701264i −0.994307 0.106554i \(-0.966018\pi\)
0.589432 + 0.807818i \(0.299352\pi\)
\(830\) 0 0
\(831\) 42.4124 1.47127
\(832\) 4.25274 + 24.3836i 0.147437 + 0.845350i
\(833\) 34.8910i 1.20890i
\(834\) −3.64911 2.10682i −0.126358 0.0729530i
\(835\) 0 0
\(836\) 11.8890 + 20.5924i 0.411190 + 0.712202i
\(837\) −30.0726 −1.03946
\(838\) 1.94550 + 3.36970i 0.0672061 + 0.116404i
\(839\) 12.8111 7.39649i 0.442288 0.255355i −0.262280 0.964992i \(-0.584474\pi\)
0.704568 + 0.709637i \(0.251141\pi\)
\(840\) 0 0
\(841\) 10.2849 + 17.8140i 0.354652 + 0.614276i
\(842\) 2.45024 + 1.41465i 0.0844408 + 0.0487519i
\(843\) −3.98261 + 6.89809i −0.137169 + 0.237583i
\(844\) 16.0050 0.550915
\(845\) 0 0
\(846\) 0.805291 0.0276865
\(847\) −2.96636 + 5.13789i −0.101925 + 0.176540i
\(848\) 5.01794 + 2.89711i 0.172317 + 0.0994872i
\(849\) −10.0703 17.4423i −0.345612 0.598617i
\(850\) 0 0
\(851\) 14.6840 8.47780i 0.503360 0.290615i
\(852\) −19.9841 34.6134i −0.684643 1.18584i
\(853\) 16.3452 0.559650 0.279825 0.960051i \(-0.409724\pi\)
0.279825 + 0.960051i \(0.409724\pi\)
\(854\) 0.514722 + 0.891525i 0.0176134 + 0.0305073i
\(855\) 0 0
\(856\) 9.82220 + 5.67085i 0.335716 + 0.193826i
\(857\) 34.1418i 1.16626i −0.812378 0.583132i \(-0.801827\pi\)
0.812378 0.583132i \(-0.198173\pi\)
\(858\) 1.16986 + 6.70754i 0.0399383 + 0.228992i
\(859\) 45.1996 1.54219 0.771096 0.636719i \(-0.219709\pi\)
0.771096 + 0.636719i \(0.219709\pi\)
\(860\) 0 0
\(861\) −0.992090 + 1.71835i −0.0338103 + 0.0585612i
\(862\) −1.80712 + 1.04334i −0.0615508 + 0.0355364i
\(863\) 4.75058 0.161712 0.0808559 0.996726i \(-0.474235\pi\)
0.0808559 + 0.996726i \(0.474235\pi\)
\(864\) −12.1633 + 7.02250i −0.413805 + 0.238910i
\(865\) 0 0
\(866\) 0.306745i 0.0104236i
\(867\) 11.9832 6.91853i 0.406972 0.234966i
\(868\) 3.06854 + 1.77162i 0.104153 + 0.0601327i
\(869\) −21.0207 12.1363i −0.713079 0.411696i
\(870\) 0 0
\(871\) −34.9830 12.8065i −1.18535 0.433933i
\(872\) 9.75140i 0.330224i
\(873\) −0.550955 + 0.954282i −0.0186470 + 0.0322975i
\(874\) 0.707294 1.22507i 0.0239246 0.0414386i
\(875\) 0 0
\(876\) 30.2610i 1.02242i
\(877\) 1.12753 + 1.95294i 0.0380741 + 0.0659462i 0.884434 0.466664i \(-0.154544\pi\)
−0.846360 + 0.532611i \(0.821211\pi\)
\(878\) −0.457146 0.791801i −0.0154279 0.0267220i
\(879\) 27.0715i 0.913098i
\(880\) 0 0
\(881\) −1.49152 + 2.58339i −0.0502507 + 0.0870367i −0.890057 0.455850i \(-0.849335\pi\)
0.839806 + 0.542887i \(0.182669\pi\)
\(882\) 0.332509 0.575922i 0.0111961 0.0193923i
\(883\) 28.2874i 0.951947i −0.879460 0.475973i \(-0.842096\pi\)
0.879460 0.475973i \(-0.157904\pi\)
\(884\) −12.2512 + 33.4660i −0.412051 + 1.12558i
\(885\) 0 0
\(886\) −1.81610 1.04852i −0.0610130 0.0352259i
\(887\) −24.2328 13.9908i −0.813658 0.469766i 0.0345665 0.999402i \(-0.488995\pi\)
−0.848225 + 0.529637i \(0.822328\pi\)
\(888\) 7.18483 4.14816i 0.241107 0.139203i
\(889\) 1.07647i 0.0361035i
\(890\) 0 0
\(891\) 34.8390 20.1143i 1.16715 0.673855i
\(892\) −19.9940 −0.669448
\(893\) 16.3862 9.46058i 0.548343 0.316586i
\(894\) 0.599451 1.03828i 0.0200486 0.0347252i
\(895\) 0 0
\(896\) 2.19681 0.0733903
\(897\) −12.5681 + 10.5061i −0.419635 + 0.350787i
\(898\) 4.77095i 0.159209i
\(899\) 13.7394 + 7.93244i 0.458234 + 0.264562i
\(900\) 0 0
\(901\) 3.95174 + 6.84461i 0.131651 + 0.228027i
\(902\) −4.40426 −0.146646
\(903\) 1.34624 + 2.33176i 0.0448001 + 0.0775960i
\(904\) 13.7915 7.96255i 0.458700 0.264830i
\(905\) 0 0
\(906\) −1.39938 2.42381i −0.0464914 0.0805255i
\(907\) −14.3344 8.27600i −0.475967 0.274800i 0.242767 0.970085i \(-0.421945\pi\)
−0.718734 + 0.695285i \(0.755278\pi\)
\(908\) −6.87383 + 11.9058i −0.228116 + 0.395109i
\(909\) −5.46876 −0.181387
\(910\) 0 0
\(911\) 7.04863 0.233532 0.116766 0.993159i \(-0.462747\pi\)
0.116766 + 0.993159i \(0.462747\pi\)
\(912\) −6.73710 + 11.6690i −0.223088 + 0.386399i
\(913\) −19.8353 11.4519i −0.656454 0.379004i
\(914\) 0.518746 + 0.898494i 0.0171586 + 0.0297196i
\(915\) 0 0
\(916\) 2.24632 1.29692i 0.0742206 0.0428513i
\(917\) 0.0291818 + 0.0505443i 0.000963668 + 0.00166912i
\(918\) −6.12316 −0.202094
\(919\) 8.27188 + 14.3273i 0.272864 + 0.472615i 0.969594 0.244719i \(-0.0786957\pi\)
−0.696730 + 0.717334i \(0.745362\pi\)
\(920\) 0 0
\(921\) −5.96488 3.44383i −0.196550 0.113478i
\(922\) 0.391374i 0.0128892i
\(923\) 29.5933 + 35.4015i 0.974076 + 1.16525i
\(924\) −5.57412 −0.183375
\(925\) 0 0
\(926\) 0.747155 1.29411i 0.0245530 0.0425271i
\(927\) 5.71704 3.30074i 0.187772 0.108410i
\(928\) 7.40948 0.243228
\(929\) 29.3035 16.9184i 0.961416 0.555074i 0.0648073 0.997898i \(-0.479357\pi\)
0.896609 + 0.442824i \(0.146023\pi\)
\(930\) 0 0
\(931\) 15.6253i 0.512098i
\(932\) −2.10853 + 1.21736i −0.0690670 + 0.0398759i
\(933\) 3.08359 + 1.78031i 0.100952 + 0.0582848i
\(934\) −3.46975 2.00326i −0.113534 0.0655487i
\(935\) 0 0
\(936\) 1.05518 0.882066i 0.0344898 0.0288312i
\(937\) 30.4606i 0.995104i 0.867434 + 0.497552i \(0.165768\pi\)
−0.867434 + 0.497552i \(0.834232\pi\)
\(938\) −0.377076 + 0.653115i −0.0123120 + 0.0213250i
\(939\) −5.76780 + 9.99012i −0.188225 + 0.326015i
\(940\) 0 0
\(941\) 38.2101i 1.24561i 0.782375 + 0.622807i \(0.214008\pi\)
−0.782375 + 0.622807i \(0.785992\pi\)
\(942\) −2.88842 5.00289i −0.0941098 0.163003i
\(943\) −5.29798 9.17637i −0.172526 0.298824i
\(944\) 10.0516i 0.327153i
\(945\) 0 0
\(946\) −2.98823 + 5.17577i −0.0971558 + 0.168279i
\(947\) −26.2241 + 45.4215i −0.852169 + 1.47600i 0.0270773 + 0.999633i \(0.491380\pi\)
−0.879247 + 0.476367i \(0.841953\pi\)
\(948\) 14.1120i 0.458338i
\(949\) −6.00239 34.4155i −0.194846 1.11717i
\(950\) 0 0
\(951\) 0.445737 + 0.257347i 0.0144540 + 0.00834504i
\(952\) 1.26503 + 0.730368i 0.0410000 + 0.0236714i
\(953\) −34.4245 + 19.8750i −1.11512 + 0.643814i −0.940150 0.340760i \(-0.889316\pi\)
−0.174969 + 0.984574i \(0.555982\pi\)
\(954\) 0.150639i 0.00487711i
\(955\) 0 0
\(956\) 16.8046 9.70215i 0.543500 0.313790i
\(957\) −24.9581 −0.806782
\(958\) 6.69329 3.86437i 0.216250 0.124852i
\(959\) −2.98737 + 5.17428i −0.0964673 + 0.167086i
\(960\) 0 0
\(961\) 1.14359 0.0368901
\(962\) −3.62933 + 3.03389i −0.117014 + 0.0978164i
\(963\) 5.74011i 0.184972i
\(964\) −38.1776 22.0418i −1.22962 0.709920i
\(965\) 0 0
\(966\) 0.165806 + 0.287184i 0.00533472 + 0.00924001i
\(967\) −25.7857 −0.829214 −0.414607 0.910001i \(-0.636081\pi\)
−0.414607 + 0.910001i \(0.636081\pi\)
\(968\) −7.75097 13.4251i −0.249126 0.431498i
\(969\) −15.9168 + 9.18958i −0.511322 + 0.295212i
\(970\) 0 0
\(971\) 27.7626 + 48.0863i 0.890945 + 1.54316i 0.838744 + 0.544525i \(0.183290\pi\)
0.0522005 + 0.998637i \(0.483377\pi\)
\(972\) −7.65249 4.41817i −0.245454 0.141713i
\(973\) −1.99118 + 3.44882i −0.0638342 + 0.110564i
\(974\) 2.26365 0.0725321
\(975\) 0 0
\(976\) 52.3642 1.67614
\(977\) −20.2580 + 35.0879i −0.648112 + 1.12256i 0.335461 + 0.942054i \(0.391108\pi\)
−0.983573 + 0.180509i \(0.942226\pi\)
\(978\) −5.42130 3.12999i −0.173354 0.100086i
\(979\) 8.66430 + 15.0070i 0.276912 + 0.479626i
\(980\) 0 0
\(981\) −4.27405 + 2.46762i −0.136460 + 0.0787852i
\(982\) 1.02506 + 1.77545i 0.0327109 + 0.0566569i
\(983\) −34.8059 −1.11014 −0.555068 0.831805i \(-0.687308\pi\)
−0.555068 + 0.831805i \(0.687308\pi\)
\(984\) −2.59229 4.48997i −0.0826390 0.143135i
\(985\) 0 0
\(986\) 2.79751 + 1.61514i 0.0890910 + 0.0514367i
\(987\) 4.43555i 0.141185i
\(988\) 5.48645 14.9871i 0.174547 0.476803i
\(989\) −14.3784 −0.457208
\(990\) 0 0
\(991\) −21.9427 + 38.0059i −0.697034 + 1.20730i 0.272456 + 0.962168i \(0.412164\pi\)
−0.969490 + 0.245130i \(0.921169\pi\)
\(992\) −12.0759 + 6.97201i −0.383410 + 0.221362i
\(993\) −26.6145 −0.844584
\(994\) 0.808936 0.467040i 0.0256579 0.0148136i
\(995\) 0 0
\(996\) 13.3163i 0.421942i
\(997\) 4.75567 2.74569i 0.150614 0.0869568i −0.422799 0.906223i \(-0.638952\pi\)
0.573413 + 0.819267i \(0.305619\pi\)
\(998\) −4.55508 2.62988i −0.144189 0.0832474i
\(999\) 28.4645 + 16.4340i 0.900577 + 0.519949i
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 325.2.m.c.199.2 8
5.2 odd 4 65.2.m.a.56.2 yes 8
5.3 odd 4 325.2.n.d.251.3 8
5.4 even 2 325.2.m.b.199.3 8
13.10 even 6 325.2.m.b.49.3 8
15.2 even 4 585.2.bu.c.316.3 8
20.7 even 4 1040.2.da.b.641.2 8
65.2 even 12 845.2.e.n.146.2 8
65.7 even 12 845.2.a.m.1.2 4
65.12 odd 4 845.2.m.g.316.3 8
65.17 odd 12 845.2.c.g.506.4 8
65.22 odd 12 845.2.c.g.506.5 8
65.23 odd 12 325.2.n.d.101.3 8
65.32 even 12 845.2.a.l.1.3 4
65.33 even 12 4225.2.a.bi.1.3 4
65.37 even 12 845.2.e.m.146.3 8
65.42 odd 12 845.2.m.g.361.3 8
65.47 even 4 845.2.e.m.191.3 8
65.49 even 6 inner 325.2.m.c.49.2 8
65.57 even 4 845.2.e.n.191.2 8
65.58 even 12 4225.2.a.bl.1.2 4
65.62 odd 12 65.2.m.a.36.2 8
195.32 odd 12 7605.2.a.cj.1.2 4
195.62 even 12 585.2.bu.c.361.3 8
195.137 odd 12 7605.2.a.cf.1.3 4
260.127 even 12 1040.2.da.b.881.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
65.2.m.a.36.2 8 65.62 odd 12
65.2.m.a.56.2 yes 8 5.2 odd 4
325.2.m.b.49.3 8 13.10 even 6
325.2.m.b.199.3 8 5.4 even 2
325.2.m.c.49.2 8 65.49 even 6 inner
325.2.m.c.199.2 8 1.1 even 1 trivial
325.2.n.d.101.3 8 65.23 odd 12
325.2.n.d.251.3 8 5.3 odd 4
585.2.bu.c.316.3 8 15.2 even 4
585.2.bu.c.361.3 8 195.62 even 12
845.2.a.l.1.3 4 65.32 even 12
845.2.a.m.1.2 4 65.7 even 12
845.2.c.g.506.4 8 65.17 odd 12
845.2.c.g.506.5 8 65.22 odd 12
845.2.e.m.146.3 8 65.37 even 12
845.2.e.m.191.3 8 65.47 even 4
845.2.e.n.146.2 8 65.2 even 12
845.2.e.n.191.2 8 65.57 even 4
845.2.m.g.316.3 8 65.12 odd 4
845.2.m.g.361.3 8 65.42 odd 12
1040.2.da.b.641.2 8 20.7 even 4
1040.2.da.b.881.2 8 260.127 even 12
4225.2.a.bi.1.3 4 65.33 even 12
4225.2.a.bl.1.2 4 65.58 even 12
7605.2.a.cf.1.3 4 195.137 odd 12
7605.2.a.cj.1.2 4 195.32 odd 12