LMFDB - Embedded newform 1155.2.k.b.769.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1155,2,Mod(769,1155)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1155, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 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("1155.769");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1155 = 3 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1155.k (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.22272143346$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			769.4
Character	$\chi$	$=$	1155.769
Dual form			1155.2.k.b.769.3

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.52930 q^{2} +1.00000 q^{3} +4.39737 q^{4} +(-1.63381 + 1.52665i) q^{5} -2.52930 q^{6} +(-2.48590 + 0.905718i) q^{7} -6.06368 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.52930 q^{2} +1.00000 q^{3} +4.39737 q^{4} +(-1.63381 + 1.52665i) q^{5} -2.52930 q^{6} +(-2.48590 + 0.905718i) q^{7} -6.06368 q^{8} +1.00000 q^{9} +(4.13240 - 3.86136i) q^{10} +(-2.13976 + 2.53405i) q^{11} +4.39737 q^{12} -5.27466i q^{13} +(6.28758 - 2.29084i) q^{14} +(-1.63381 + 1.52665i) q^{15} +6.54214 q^{16} +5.11968i q^{17} -2.52930 q^{18} -4.28158 q^{19} +(-7.18448 + 6.71325i) q^{20} +(-2.48590 + 0.905718i) q^{21} +(5.41211 - 6.40938i) q^{22} +1.22635i q^{23} -6.06368 q^{24} +(0.338675 - 4.98852i) q^{25} +13.3412i q^{26} +1.00000 q^{27} +(-10.9314 + 3.98278i) q^{28} -8.66218i q^{29} +(4.13240 - 3.86136i) q^{30} -3.16260i q^{31} -4.41970 q^{32} +(-2.13976 + 2.53405i) q^{33} -12.9492i q^{34} +(2.67877 - 5.27487i) q^{35} +4.39737 q^{36} +3.79008i q^{37} +10.8294 q^{38} -5.27466i q^{39} +(9.90691 - 9.25713i) q^{40} +5.95804 q^{41} +(6.28758 - 2.29084i) q^{42} +7.87280 q^{43} +(-9.40934 + 11.1432i) q^{44} +(-1.63381 + 1.52665i) q^{45} -3.10180i q^{46} -6.85157 q^{47} +6.54214 q^{48} +(5.35935 - 4.50304i) q^{49} +(-0.856613 + 12.6175i) q^{50} +5.11968i q^{51} -23.1947i q^{52} -12.4608i q^{53} -2.52930 q^{54} +(-0.372642 - 7.40683i) q^{55} +(15.0737 - 5.49199i) q^{56} -4.28158 q^{57} +21.9093i q^{58} +1.69675i q^{59} +(-7.18448 + 6.71325i) q^{60} +7.32231 q^{61} +7.99918i q^{62} +(-2.48590 + 0.905718i) q^{63} -1.90553 q^{64} +(8.05257 + 8.61780i) q^{65} +(5.41211 - 6.40938i) q^{66} +1.64438i q^{67} +22.5131i q^{68} +1.22635i q^{69} +(-6.77541 + 13.3417i) q^{70} -4.95049 q^{71} -6.06368 q^{72} +13.6548i q^{73} -9.58626i q^{74} +(0.338675 - 4.98852i) q^{75} -18.8277 q^{76} +(3.02409 - 8.23741i) q^{77} +13.3412i q^{78} -2.01901i q^{79} +(-10.6886 + 9.98757i) q^{80} +1.00000 q^{81} -15.0697 q^{82} -3.14880i q^{83} +(-10.9314 + 3.98278i) q^{84} +(-7.81596 - 8.36459i) q^{85} -19.9127 q^{86} -8.66218i q^{87} +(12.9748 - 15.3657i) q^{88} -4.88199i q^{89} +(4.13240 - 3.86136i) q^{90} +(4.77736 + 13.1123i) q^{91} +5.39270i q^{92} -3.16260i q^{93} +17.3297 q^{94} +(6.99530 - 6.53648i) q^{95} -4.41970 q^{96} +15.6959 q^{97} +(-13.5554 + 11.3896i) q^{98} +(-2.13976 + 2.53405i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 48 q^{3} + 48 q^{4} - 4 q^{5} + 48 q^{9}+O(q^{10}) $ 48 * q + 48 * q^3 + 48 * q^4 - 4 * q^5 + 48 * q^9	$ 48 q + 48 q^{3} + 48 q^{4} - 4 q^{5} + 48 q^{9} + 48 q^{12} - 4 q^{15} + 40 q^{16} - 18 q^{20} + 20 q^{25} + 48 q^{27} + 48 q^{36} - 20 q^{38} - 16 q^{44} - 4 q^{45} + 8 q^{47} + 40 q^{48} + 24 q^{49} - 8 q^{55} - 8 q^{56} - 18 q^{60} - 4 q^{64} - 14 q^{70} - 32 q^{71} + 20 q^{75} - 32 q^{77} - 46 q^{80} + 48 q^{81} - 32 q^{82} - 16 q^{86} + 68 q^{97}+O(q^{100}) $ 48 * q + 48 * q^3 + 48 * q^4 - 4 * q^5 + 48 * q^9 + 48 * q^12 - 4 * q^15 + 40 * q^16 - 18 * q^20 + 20 * q^25 + 48 * q^27 + 48 * q^36 - 20 * q^38 - 16 * q^44 - 4 * q^45 + 8 * q^47 + 40 * q^48 + 24 * q^49 - 8 * q^55 - 8 * q^56 - 18 * q^60 - 4 * q^64 - 14 * q^70 - 32 * q^71 + 20 * q^75 - 32 * q^77 - 46 * q^80 + 48 * q^81 - 32 * q^82 - 16 * q^86 + 68 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times$.

$n$	$211$	$232$	$386$	$661$
$\chi(n)$	$-1$	$-1$	$1$	$-1$

Coefficient data

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

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.52930			−1.78849			−0.894244	−	0.447581i	$-0.852286\pi$
$2$	−2.52930			−1.78849			−0.894244	+	0.447581i	$0.852286\pi$
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	4.39737			2.19869
$5$	−1.63381	+	1.52665i	−0.730662	+	0.682739i
$5$	−1.63381	+	1.52665i	−0.730662	+	0.682739i
$6$	−2.52930			−1.03258
$7$	−2.48590	+	0.905718i	−0.939580	+	0.342329i
$7$	−2.48590	+	0.905718i	−0.939580	+	0.342329i
$8$	−6.06368			−2.14384
$9$	1.00000			0.333333
$10$	4.13240	−	3.86136i	1.30678	−	1.22107i
$11$	−2.13976	+	2.53405i	−0.645163	+	0.764045i
$11$	−2.13976	+	2.53405i	−0.645163	+	0.764045i
$12$	4.39737			1.26941
$13$		−	5.27466i		−	1.46293i	−0.681880	−	0.731464i	$-0.738837\pi$
$13$		−	5.27466i		−	1.46293i	0.681880	−	0.731464i	$-0.261163\pi$
$14$	6.28758	−	2.29084i	1.68043	−	0.612251i
$15$	−1.63381	+	1.52665i	−0.421848	+	0.394180i
$16$	6.54214			1.63554
$17$			5.11968i			1.24171i	0.783927	+	0.620853i	$0.213213\pi$
$17$			5.11968i			1.24171i	−0.783927	+	0.620853i	$0.786787\pi$
$18$	−2.52930			−0.596162
$19$	−4.28158			−0.982263			−0.491131	−	0.871085i	$-0.663417\pi$
$19$	−4.28158			−0.982263			−0.491131	+	0.871085i	$0.663417\pi$
$20$	−7.18448	+	6.71325i	−1.60650	+	1.50113i
$21$	−2.48590	+	0.905718i	−0.542467	+	0.197644i
$22$	5.41211	−	6.40938i	1.15387	−	1.36648i
$23$			1.22635i			0.255711i	0.991793	+	0.127855i	$0.0408093\pi$
$23$			1.22635i			0.255711i	−0.991793	+	0.127855i	$0.959191\pi$
$24$	−6.06368			−1.23774
$25$	0.338675	−	4.98852i	0.0677351	−	0.997703i
$26$			13.3412i			2.61643i
$27$	1.00000			0.192450
$28$	−10.9314	+	3.98278i	−2.06584	+	0.752675i
$29$		−	8.66218i		−	1.60853i	−0.594274	−	0.804263i	$-0.702560\pi$
$29$		−	8.66218i		−	1.60853i	0.594274	−	0.804263i	$-0.297440\pi$
$30$	4.13240	−	3.86136i	0.754470	−	0.704985i
$31$		−	3.16260i		−	0.568020i	−0.958821	−	0.284010i	$-0.908335\pi$
$31$		−	3.16260i		−	0.568020i	0.958821	−	0.284010i	$-0.0916649\pi$
$32$	−4.41970			−0.781300
$33$	−2.13976	+	2.53405i	−0.372485	+	0.441122i
$34$		−	12.9492i		−	2.22077i
$35$	2.67877	−	5.27487i	0.452794	−	0.891615i
$36$	4.39737			0.732896
$37$			3.79008i			0.623085i	0.950232	+	0.311543i	$0.100846\pi$
$37$			3.79008i			0.623085i	−0.950232	+	0.311543i	$0.899154\pi$
$38$	10.8294			1.75676
$39$		−	5.27466i		−	0.844622i
$40$	9.90691	−	9.25713i	1.56642	−	1.46368i
$41$	5.95804			0.930489			0.465245	−	0.885182i	$-0.345966\pi$
$41$	5.95804			0.930489			0.465245	+	0.885182i	$0.345966\pi$
$42$	6.28758	−	2.29084i	0.970195	−	0.353484i
$43$	7.87280			1.20059			0.600296	−	0.799778i	$-0.295050\pi$
$43$	7.87280			1.20059			0.600296	+	0.799778i	$0.295050\pi$
$44$	−9.40934	+	11.1432i	−1.41851	+	1.67990i
$45$	−1.63381	+	1.52665i	−0.243554	+	0.227580i
$46$		−	3.10180i		−	0.457335i
$47$	−6.85157			−0.999404			−0.499702	−	0.866198i	$-0.666557\pi$
$47$	−6.85157			−0.999404			−0.499702	+	0.866198i	$0.666557\pi$
$48$	6.54214			0.944277
$49$	5.35935	−	4.50304i	0.765621	−	0.643291i
$50$	−0.856613	+	12.6175i	−0.121143	+	1.78438i
$51$			5.11968i			0.716899i
$52$		−	23.1947i		−	3.21652i
$53$		−	12.4608i		−	1.71162i	−0.517289	−	0.855811i	$-0.673059\pi$
$53$		−	12.4608i		−	1.71162i	0.517289	−	0.855811i	$-0.326941\pi$
$54$	−2.52930			−0.344195
$55$	−0.372642	−	7.40683i	−0.0502470	−	0.998737i
$56$	15.0737	−	5.49199i	2.01431	−	0.733898i
$57$	−4.28158			−0.567110
$58$			21.9093i			2.87683i
$59$			1.69675i			0.220898i	0.993882	+	0.110449i	$0.0352289\pi$
$59$			1.69675i			0.220898i	−0.993882	+	0.110449i	$0.964771\pi$
$60$	−7.18448	+	6.71325i	−0.927512	+	0.866677i
$61$	7.32231			0.937525			0.468763	−	0.883324i	$-0.344700\pi$
$61$	7.32231			0.937525			0.468763	+	0.883324i	$0.344700\pi$
$62$			7.99918i			1.01590i
$63$	−2.48590	+	0.905718i	−0.313193	+	0.114110i
$64$	−1.90553			−0.238191
$65$	8.05257	+	8.61780i	0.998798	+	1.06891i
$66$	5.41211	−	6.40938i	0.666185	−	0.788940i
$67$			1.64438i			0.200893i	0.994942	+	0.100446i	$0.0320271\pi$
$67$			1.64438i			0.200893i	−0.994942	+	0.100446i	$0.967973\pi$
$68$			22.5131i			2.73012i
$69$			1.22635i			0.147635i
$70$	−6.77541	+	13.3417i	−0.809817	+	1.59464i
$71$	−4.95049			−0.587515			−0.293758	−	0.955880i	$-0.594906\pi$
$71$	−4.95049			−0.587515			−0.293758	+	0.955880i	$0.594906\pi$
$72$	−6.06368			−0.714612
$73$			13.6548i			1.59817i	0.601218	+	0.799085i	$0.294682\pi$
$73$			13.6548i			1.59817i	−0.601218	+	0.799085i	$0.705318\pi$
$74$		−	9.58626i		−	1.11438i
$75$	0.338675	−	4.98852i	0.0391069	−	0.576024i
$76$	−18.8277			−2.15969
$77$	3.02409	−	8.23741i	0.344627	−	0.938740i
$78$			13.3412i			1.51060i
$79$		−	2.01901i		−	0.227157i	−0.993529	−	0.113578i	$-0.963769\pi$
$79$		−	2.01901i		−	0.227157i	0.993529	−	0.113578i	$-0.0362313\pi$
$80$	−10.6886	+	9.98757i	−1.19502	+	1.11664i
$81$	1.00000			0.111111
$82$	−15.0697			−1.66417
$83$		−	3.14880i		−	0.345626i	−0.984955	−	0.172813i	$-0.944714\pi$
$83$		−	3.14880i		−	0.345626i	0.984955	−	0.172813i	$-0.0552856\pi$
$84$	−10.9314	+	3.98278i	−1.19271	+	0.434557i
$85$	−7.81596	−	8.36459i	−0.847760	−	0.907267i
$86$	−19.9127			−2.14724
$87$		−	8.66218i		−	0.928683i
$88$	12.9748	−	15.3657i	1.38312	−	1.63799i
$89$		−	4.88199i		−	0.517489i	−0.965946	−	0.258745i	$-0.916691\pi$
$89$		−	4.88199i		−	0.517489i	0.965946	−	0.258745i	$-0.0833088\pi$
$90$	4.13240	−	3.86136i	0.435593	−	0.407023i
$91$	4.77736	+	13.1123i	0.500803	+	1.37454i
$92$			5.39270i			0.562228i
$93$		−	3.16260i		−	0.327947i
$94$	17.3297			1.78742
$95$	6.99530	−	6.53648i	0.717703	−	0.670629i
$96$	−4.41970			−0.451084
$97$	15.6959			1.59368			0.796838	−	0.604193i	$-0.206505\pi$
$97$	15.6959			1.59368			0.796838	+	0.604193i	$0.206505\pi$
$98$	−13.5554	+	11.3896i	−1.36930	+	1.15052i
$99$	−2.13976	+	2.53405i	−0.215054	+	0.254682i
$100$	1.48928	−	21.9364i	0.148928	−	2.19364i
$101$	3.17273			0.315699			0.157849	−	0.987463i	$-0.449544\pi$
$101$	3.17273			0.315699			0.157849	+	0.987463i	$0.449544\pi$
$102$		−	12.9492i		−	1.28216i
$103$	8.09081			0.797211			0.398605	−	0.917123i	$-0.369494\pi$
$103$	8.09081			0.797211			0.398605	+	0.917123i	$0.369494\pi$
$104$			31.9839i			3.13628i
$105$	2.67877	−	5.27487i	0.261421	−	0.514774i
$106$			31.5171i			3.06121i
$107$	−11.5492			−1.11650			−0.558250	−	0.829673i	$-0.688527\pi$
$107$	−11.5492			−1.11650			−0.558250	+	0.829673i	$0.688527\pi$
$108$	4.39737			0.423137
$109$		−	12.2689i		−	1.17515i	−0.809171	−	0.587573i	$-0.800083\pi$
$109$		−	12.2689i		−	1.17515i	0.809171	−	0.587573i	$-0.199917\pi$
$110$	0.942524	+	18.7341i	0.0898661	+	1.78623i
$111$			3.79008i			0.359738i
$112$	−16.2631	+	5.92534i	−1.53672	+	0.559892i
$113$		−	5.43099i		−	0.510904i	−0.966822	−	0.255452i	$-0.917776\pi$
$113$		−	5.43099i		−	0.510904i	0.966822	−	0.255452i	$-0.0822243\pi$
$114$	10.8294			1.01427
$115$	−1.87220	−	2.00362i	−0.174584	−	0.186838i
$116$		−	38.0908i		−	3.53664i
$117$		−	5.27466i		−	0.487643i
$118$		−	4.29160i		−	0.395073i
$119$	−4.63699	−	12.7270i	−0.425072	−	1.16668i
$120$	9.90691	−	9.25713i	0.904373	−	0.845056i
$121$	−1.84283	−	10.8445i	−0.167530	−	0.985867i
$122$	−18.5203			−1.67675
$123$	5.95804			0.537218
$124$		−	13.9071i		−	1.24890i
$125$	7.06239	+	8.66733i	0.631679	+	0.775230i
$126$	6.28758	−	2.29084i	0.560142	−	0.204084i
$127$	14.9817			1.32941			0.664707	−	0.747104i	$-0.268556\pi$
$127$	14.9817			1.32941			0.664707	+	0.747104i	$0.268556\pi$
$128$	13.6591			1.20730
$129$	7.87280			0.693162
$130$	−20.3674	−	21.7970i	−1.78634	−	1.91173i
$131$	−0.877747			−0.0766891			−0.0383446	−	0.999265i	$-0.512208\pi$
$131$	−0.877747			−0.0766891			−0.0383446	+	0.999265i	$0.512208\pi$
$132$	−9.40934	+	11.1432i	−0.818978	+	0.969888i
$133$	10.6436	−	3.87791i	0.922915	−	0.336257i
$134$		−	4.15913i		−	0.359294i
$135$	−1.63381	+	1.52665i	−0.140616	+	0.131393i
$136$		−	31.0441i		−	2.66201i
$137$		−	19.7845i		−	1.69030i	−0.534529	−	0.845150i	$-0.679511\pi$
$137$		−	19.7845i		−	1.69030i	0.534529	−	0.845150i	$-0.320489\pi$
$138$		−	3.10180i		−	0.264043i
$139$	−11.5988			−0.983800			−0.491900	−	0.870652i	$-0.663697\pi$
$139$	−11.5988			−0.983800			−0.491900	+	0.870652i	$0.663697\pi$
$140$	11.7795	−	23.1956i	0.995553	−	1.96038i
$141$	−6.85157			−0.577006
$142$	12.5213			1.05076
$143$	13.3663	+	11.2865i	1.11774	+	0.943827i
$144$	6.54214			0.545179
$145$	13.2241	+	14.1524i	1.09820	+	1.17529i
$146$		−	34.5371i		−	2.85831i
$147$	5.35935	−	4.50304i	0.442032	−	0.371404i
$148$			16.6664i			1.36997i
$149$		−	6.43246i		−	0.526967i	−0.964664	−	0.263484i	$-0.915128\pi$
$149$		−	6.43246i		−	0.526967i	0.964664	−	0.263484i	$-0.0848715\pi$
$150$	−0.856613	+	12.6175i	−0.0699421	+	1.03021i
$151$		−	20.2373i		−	1.64689i	−0.567396	−	0.823445i	$-0.692049\pi$
$151$		−	20.2373i		−	1.64689i	0.567396	−	0.823445i	$-0.307951\pi$
$152$	25.9622			2.10581
$153$			5.11968i			0.413902i
$154$	−7.64884	+	20.8349i	−0.616361	+	1.67892i
$155$	4.82819	+	5.16709i	0.387809	+	0.415031i
$156$		−	23.1947i		−	1.85706i
$157$	−19.2805			−1.53876			−0.769378	−	0.638794i	$-0.779434\pi$
$157$	−19.2805			−1.53876			−0.769378	+	0.638794i	$0.779434\pi$
$158$			5.10670i			0.406267i
$159$		−	12.4608i		−	0.988205i
$160$	7.22095	−	6.74734i	0.570866	−	0.533424i
$161$	−1.11072	−	3.04857i	−0.0875373	−	0.240261i
$162$	−2.52930			−0.198721
$163$		−	17.2041i		−	1.34753i	−0.738946	−	0.673765i	$-0.764676\pi$
$163$		−	17.2041i		−	1.34753i	0.738946	−	0.673765i	$-0.235324\pi$
$164$	26.1997			2.04585
$165$	−0.372642	−	7.40683i	−0.0290101	−	0.576621i
$166$			7.96427i			0.618147i
$167$		−	5.88119i		−	0.455100i	−0.973766	−	0.227550i	$-0.926928\pi$
$167$		−	5.88119i		−	0.455100i	0.973766	−	0.227550i	$-0.0730716\pi$
$168$	15.0737	−	5.49199i	1.16296	−	0.423716i
$169$	−14.8221			−1.14016
$170$	19.7689	+	21.1566i	1.51621	+	1.62264i
$171$	−4.28158			−0.327421
$172$	34.6197			2.63972
$173$		−	1.71236i		−	0.130188i	−0.997879	−	0.0650941i	$-0.979265\pi$
$173$		−	1.71236i		−	0.130188i	0.997879	−	0.0650941i	$-0.0207348\pi$
$174$			21.9093i			1.66094i
$175$	3.67628	+	12.7077i	0.277901	+	0.960610i
$176$	−13.9986	+	16.5781i	−1.05519	+	1.24962i
$177$			1.69675i			0.127536i
$178$			12.3480i			0.925523i
$179$	−7.42437			−0.554924			−0.277462	−	0.960737i	$-0.589493\pi$
$179$	−7.42437			−0.554924			−0.277462	+	0.960737i	$0.589493\pi$
$180$	−7.18448	+	6.71325i	−0.535499	+	0.500376i
$181$		−	7.98549i		−	0.593556i	−0.954946	−	0.296778i	$-0.904088\pi$
$181$		−	7.98549i		−	0.593556i	0.954946	−	0.296778i	$-0.0959122\pi$
$182$	−12.0834	−	33.1649i	−0.895680	−	2.45834i
$183$	7.32231			0.541281
$184$		−	7.43617i		−	0.548202i
$185$	−5.78613	−	6.19227i	−0.425405	−	0.455265i
$186$			7.99918i			0.586528i
$187$	−12.9735	−	10.9549i	−0.948719	−	0.801102i
$188$	−30.1289			−2.19738
$189$	−2.48590	+	0.905718i	−0.180822	+	0.0658813i
$190$	−17.6932	+	16.5327i	−1.28360	+	1.19941i
$191$	1.11911			0.0809760			0.0404880	−	0.999180i	$-0.487109\pi$
$191$	1.11911			0.0809760			0.0404880	+	0.999180i	$0.487109\pi$
$192$	−1.90553			−0.137520
$193$	−25.2805			−1.81973			−0.909865	−	0.414904i	$-0.863815\pi$
$193$	−25.2805			−1.81973			−0.909865	+	0.414904i	$0.863815\pi$
$194$	−39.6996			−2.85027
$195$	8.05257	+	8.61780i	0.576656	+	0.617134i
$196$	23.5671	−	19.8015i	1.68336	−	1.41440i
$197$	17.1708			1.22337			0.611683	−	0.791103i	$-0.290493\pi$
$197$	17.1708			1.22337			0.611683	+	0.791103i	$0.290493\pi$
$198$	5.41211	−	6.40938i	0.384622	−	0.455495i
$199$			23.6135i			1.67392i	0.547267	+	0.836958i	$0.315668\pi$
$199$			23.6135i			1.67392i	−0.547267	+	0.836958i	$0.684332\pi$
$200$	−2.05362	+	30.2488i	−0.145213	+	2.13891i
$201$			1.64438i			0.115986i
$202$	−8.02481			−0.564623
$203$	7.84549	+	21.5333i	0.550645	+	1.51134i
$204$			22.5131i			1.57624i
$205$	−9.73430	+	9.09584i	−0.679873	+	0.635281i
$206$	−20.4641			−1.42580
$207$			1.22635i			0.0852369i
$208$		−	34.5076i		−	2.39267i
$209$	9.16158	−	10.8498i	0.633720	−	0.750493i
$210$	−6.77541	+	13.3417i	−0.467548	+	0.920667i
$211$		−	6.53077i		−	0.449597i	−0.974405	−	0.224798i	$-0.927828\pi$
$211$		−	6.53077i		−	0.449597i	0.974405	−	0.224798i	$-0.0721724\pi$
$212$		−	54.7948i		−	3.76332i
$213$	−4.95049			−0.339202
$214$	29.2113			1.99685
$215$	−12.8627	+	12.0190i	−0.877227	+	0.819690i
$216$	−6.06368			−0.412581
$217$	2.86443	+	7.86190i	0.194450	+	0.533700i
$218$			31.0317i			2.10173i
$219$			13.6548i			0.922704i
$220$	−1.63865	−	32.5706i	−0.110477	−	2.19591i
$221$	27.0046			1.81653
$222$		−	9.58626i		−	0.643388i
$223$	18.7020			1.25238			0.626189	−	0.779671i	$-0.284614\pi$
$223$	18.7020			1.25238			0.626189	+	0.779671i	$0.284614\pi$
$224$	10.9869	−	4.00300i	0.734094	−	0.267462i
$225$	0.338675	−	4.98852i	0.0225784	−	0.332568i
$226$			13.7366i			0.913746i
$227$		−	20.9094i		−	1.38780i	−0.720070	−	0.693902i	$-0.755890\pi$
$227$		−	20.9094i		−	1.38780i	0.720070	−	0.693902i	$-0.244110\pi$
$228$	−18.8277			−1.24690
$229$			8.20518i			0.542214i	0.962549	+	0.271107i	$0.0873896\pi$
$229$			8.20518i			0.542214i	−0.962549	+	0.271107i	$0.912610\pi$
$230$	4.73536	+	5.06775i	0.312241	+	0.334158i
$231$	3.02409	−	8.23741i	0.198971	−	0.541982i
$232$			52.5247i			3.44842i
$233$	−12.1849			−0.798261			−0.399131	−	0.916894i	$-0.630688\pi$
$233$	−12.1849			−0.798261			−0.399131	+	0.916894i	$0.630688\pi$
$234$			13.3412i			0.872143i
$235$	11.1942	−	10.4599i	0.730227	−	0.682332i
$236$			7.46125i			0.485686i
$237$		−	2.01901i		−	0.131149i
$238$	11.7283	+	32.1904i	0.760236	+	2.08659i
$239$		−	5.67839i		−	0.367304i	−0.982991	−	0.183652i	$-0.941208\pi$
$239$		−	5.67839i		−	0.367304i	0.982991	−	0.183652i	$-0.0587920\pi$
$240$	−10.6886	+	9.98757i	−0.689948	+	0.644695i
$241$	−18.7726			−1.20925			−0.604624	−	0.796511i	$-0.706677\pi$
$241$	−18.7726			−1.20925			−0.604624	+	0.796511i	$0.706677\pi$
$242$	4.66106	+	27.4291i	0.299625	+	1.76321i
$243$	1.00000			0.0641500
$244$	32.1989			2.06132
$245$	−1.88159	+	15.5390i	−0.120211	+	0.992748i
$246$	−15.0697			−0.960808
$247$			22.5839i			1.43698i
$248$			19.1770i			1.21774i
$249$		−	3.14880i		−	0.199547i
$250$	−17.8629	−	21.9223i	−1.12975	−	1.38649i
$251$			2.11549i			0.133528i	0.997769	+	0.0667642i	$0.0212675\pi$
$251$			2.11549i			0.133528i	−0.997769	+	0.0667642i	$0.978732\pi$
$252$	−10.9314	+	3.98278i	−0.688614	+	0.250892i
$253$	−3.10762	−	2.62409i	−0.195375	−	0.164975i
$254$	−37.8934			−2.37764
$255$	−7.81596	−	8.36459i	−0.489455	−	0.523811i
$256$	−30.7368			−1.92105
$257$	14.8176			0.924296			0.462148	−	0.886803i	$-0.347079\pi$
$257$	14.8176			0.924296			0.462148	+	0.886803i	$0.347079\pi$
$258$	−19.9127			−1.23971
$259$	−3.43274	−	9.42174i	−0.213300	−	0.585438i
$260$	35.4102	+	37.8957i	2.19604	+	2.35019i
$261$		−	8.66218i		−	0.536175i
$262$	2.22009			0.137157
$263$	−13.1506			−0.810903			−0.405452	−	0.914117i	$-0.632886\pi$
$263$	−13.1506			−0.810903			−0.405452	+	0.914117i	$0.632886\pi$
$264$	12.9748	−	15.3657i	0.798547	−	0.945692i
$265$	19.0233	+	20.3586i	1.16859	+	1.25062i
$266$	−26.9208	+	9.80840i	−1.65062	+	0.601392i
$267$		−	4.88199i		−	0.298773i
$268$			7.23095i			0.441700i
$269$			19.7999i			1.20722i	0.797280	+	0.603610i	$0.206271\pi$
$269$			19.7999i			1.20722i	−0.797280	+	0.603610i	$0.793729\pi$
$270$	4.13240	−	3.86136i	0.251490	−	0.234995i
$271$	11.6788			0.709435			0.354718	−	0.934973i	$-0.384577\pi$
$271$	11.6788			0.709435			0.354718	+	0.934973i	$0.384577\pi$
$272$			33.4937i			2.03085i
$273$	4.77736	+	13.1123i	0.289139	+	0.793590i
$274$			50.0409i			3.02308i
$275$	11.9165	+	11.5325i	0.718590	+	0.695434i
$276$			5.39270i			0.324602i
$277$	3.48113			0.209161			0.104580	−	0.994516i	$-0.466650\pi$
$277$	3.48113			0.209161			0.104580	+	0.994516i	$0.466650\pi$
$278$	29.3369			1.75951
$279$		−	3.16260i		−	0.189340i
$280$	−16.2432	+	31.9851i	−0.970717	+	1.91148i
$281$			22.0902i			1.31779i	0.752234	+	0.658896i	$0.228976\pi$
$281$			22.0902i			1.31779i	−0.752234	+	0.658896i	$0.771024\pi$
$282$	17.3297			1.03197
$283$		−	3.35901i		−	0.199672i	−0.995004	−	0.0998361i	$-0.968168\pi$
$283$		−	3.35901i		−	0.199672i	0.995004	−	0.0998361i	$-0.0318318\pi$
$284$	−21.7692			−1.29176
$285$	6.99530	−	6.53648i	0.414366	−	0.387188i
$286$	−33.8073	−	28.5471i	−1.99907	−	1.68802i
$287$	−14.8111	+	5.39630i	−0.874269	+	0.318534i
$288$	−4.41970			−0.260433
$289$	−9.21113			−0.541831
$290$	−33.4478	−	35.7956i	−1.96412	−	2.10199i
$291$	15.6959			0.920109
$292$			60.0451i			3.51388i
$293$		−	13.6906i		−	0.799812i	−0.916556	−	0.399906i	$-0.869043\pi$
$293$		−	13.6906i		−	0.799812i	0.916556	−	0.399906i	$-0.130957\pi$
$294$	−13.5554	+	11.3896i	−0.790568	+	0.664252i
$295$	−2.59035	−	2.77217i	−0.150816	−	0.161402i
$296$		−	22.9818i		−	1.33579i
$297$	−2.13976	+	2.53405i	−0.124162	+	0.147041i
$298$			16.2696i			0.942475i
$299$	6.46856			0.374087
$300$	1.48928	−	21.9364i	0.0859837	−	1.26650i
$301$	−19.5710	+	7.13054i	−1.12805	+	0.410997i
$302$			51.1863i			2.94544i
$303$	3.17273			0.182269
$304$	−28.0107			−1.60653
$305$	−11.9633	+	11.1786i	−0.685015	+	0.640085i
$306$		−	12.9492i		−	0.740258i
$307$			3.58318i			0.204503i	0.994759	+	0.102251i	$0.0326046\pi$
$307$			3.58318i			0.204503i	−0.994759	+	0.102251i	$0.967395\pi$
$308$	13.2981	−	36.2230i	0.757727	−	2.06399i
$309$	8.09081			0.460270
$310$	−12.2120	−	13.0691i	−0.693592	−	0.742277i
$311$			4.38304i			0.248540i	0.992248	+	0.124270i	$0.0396588\pi$
$311$			4.38304i			0.248540i	−0.992248	+	0.124270i	$0.960341\pi$
$312$			31.9839i			1.81073i
$313$	−15.3099			−0.865367			−0.432683	−	0.901546i	$-0.642433\pi$
$313$	−15.3099			−0.865367			−0.432683	+	0.901546i	$0.642433\pi$
$314$	48.7663			2.75204
$315$	2.67877	−	5.27487i	0.150931	−	0.297205i
$316$		−	8.87836i		−	0.499447i
$317$		−	22.3499i		−	1.25529i	−0.778499	−	0.627646i	$-0.784018\pi$
$317$		−	22.3499i		−	1.25529i	0.778499	−	0.627646i	$-0.215982\pi$
$318$			31.5171i			1.76739i
$319$	21.9504	+	18.5350i	1.22899	+	1.03776i
$320$	3.11328	−	2.90908i	0.174037	−	0.162623i
$321$	−11.5492			−0.644612
$322$	2.80936	+	7.71075i	0.156559	+	0.429703i
$323$		−	21.9203i		−	1.21968i
$324$	4.39737			0.244299
$325$	−26.3128	−	1.78640i	−1.45957	−	0.0990916i
$326$			43.5144i			2.41004i
$327$		−	12.2689i		−	0.678471i
$328$	−36.1276			−1.99482
$329$	17.0323	−	6.20559i	0.939020	−	0.342125i
$330$	0.942524	+	18.7341i	0.0518842	+	1.03128i
$331$	−17.0600			−0.937702			−0.468851	−	0.883277i	$-0.655332\pi$
$331$	−17.0600			−0.937702			−0.468851	+	0.883277i	$0.655332\pi$
$332$		−	13.8464i		−	0.759922i
$333$			3.79008i			0.207695i
$334$			14.8753i			0.813941i
$335$	−2.51039	−	2.68660i	−0.137157	−	0.146785i
$336$	−16.2631	+	5.92534i	−0.887224	+	0.323254i
$337$	−11.7119			−0.637989			−0.318994	−	0.947757i	$-0.603345\pi$
$337$	−11.7119			−0.637989			−0.318994	+	0.947757i	$0.603345\pi$
$338$	37.4895			2.03916
$339$		−	5.43099i		−	0.294971i
$340$	−34.3697	−	36.7822i	−1.86396	−	1.99480i
$341$	8.01419	+	6.76722i	0.433993	+	0.366465i
$342$	10.8294			0.585588
$343$	−9.24430	+	16.0481i	−0.499145	+	0.866518i
$344$	−47.7382			−2.57387
$345$	−1.87220	−	2.00362i	−0.100796	−	0.107871i
$346$			4.33107i			0.232840i
$347$	−22.2943			−1.19682			−0.598411	−	0.801189i	$-0.704201\pi$
$347$	−22.2943			−1.19682			−0.598411	+	0.801189i	$0.704201\pi$
$348$		−	38.0908i		−	2.04188i
$349$	−18.3957			−0.984701			−0.492351	−	0.870397i	$-0.663862\pi$
$349$	−18.3957			−0.984701			−0.492351	+	0.870397i	$0.663862\pi$
$350$	−9.29842	−	32.1416i	−0.497022	−	1.71804i
$351$		−	5.27466i		−	0.281541i
$352$	9.45711	−	11.1997i	0.504066	−	0.596948i
$353$	−20.2639			−1.07854			−0.539270	−	0.842133i	$-0.681300\pi$
$353$	−20.2639			−1.07854			−0.539270	+	0.842133i	$0.681300\pi$
$354$		−	4.29160i		−	0.228096i
$355$	8.08817	−	7.55767i	0.429275	−	0.401120i
$356$		−	21.4679i		−	1.13780i
$357$	−4.63699	−	12.7270i	−0.245415	−	0.673584i
$358$	18.7785			0.992474
$359$		−	9.69378i		−	0.511618i	−0.966727	−	0.255809i	$-0.917658\pi$
$359$		−	9.69378i		−	0.511618i	0.966727	−	0.255809i	$-0.0823418\pi$
$360$	9.90691	−	9.25713i	0.522140	−	0.487893i
$361$	−0.668034			−0.0351597
$362$			20.1977i			1.06157i
$363$	−1.84283	−	10.8445i	−0.0967233	−	0.569191i
$364$	21.0078	+	57.6595i	1.10111	+	3.02218i
$365$	−20.8461	−	22.3093i	−1.09113	−	1.16772i
$366$	−18.5203			−0.968073
$367$	35.0965			1.83202			0.916012	−	0.401152i	$-0.131390\pi$
$367$	35.0965			1.83202			0.916012	+	0.401152i	$0.131390\pi$
$368$			8.02293i			0.418224i
$369$	5.95804			0.310163
$370$	14.6349	+	15.6621i	0.760831	+	0.814236i
$371$	11.2860	+	30.9762i	0.585938	+	1.60821i
$372$		−	13.9071i		−	0.721052i
$373$	−1.01774			−0.0526964			−0.0263482	−	0.999653i	$-0.508388\pi$
$373$	−1.01774			−0.0526964			−0.0263482	+	0.999653i	$0.508388\pi$
$374$	32.8140	+	27.7083i	1.69677	+	1.43276i
$375$	7.06239	+	8.66733i	0.364700	+	0.447579i
$376$	41.5457			2.14256
$377$	−45.6901			−2.35316
$378$	6.28758	−	2.29084i	0.323398	−	0.117828i
$379$	24.1247			1.23920			0.619601	−	0.784917i	$-0.287294\pi$
$379$	24.1247			1.23920			0.619601	+	0.784917i	$0.287294\pi$
$380$	30.7609	−	28.7434i	1.57800	−	1.47450i
$381$	14.9817			0.767538
$382$	−2.83057			−0.144825
$383$	−15.1817			−0.775749			−0.387875	−	0.921712i	$-0.626791\pi$
$383$	−15.1817			−0.775749			−0.387875	+	0.921712i	$0.626791\pi$
$384$	13.6591			0.697036
$385$	7.63485	+	18.0751i	0.389108	+	0.921192i
$386$	63.9421			3.25456
$387$	7.87280			0.400197
$388$	69.0207			3.50399
$389$	−1.96963			−0.0998644			−0.0499322	−	0.998753i	$-0.515901\pi$
$389$	−1.96963			−0.0998644			−0.0499322	+	0.998753i	$0.515901\pi$
$390$	−20.3674	−	21.7970i	−1.03134	−	1.10374i
$391$	−6.27850			−0.317517
$392$	−32.4974	+	27.3050i	−1.64137	+	1.37911i
$393$	−0.877747			−0.0442765
$394$	−43.4301			−2.18798
$395$	3.08233	+	3.29869i	0.155089	+	0.165975i
$396$	−9.40934	+	11.1432i	−0.472837	+	0.559965i
$397$	−2.33578			−0.117229			−0.0586146	−	0.998281i	$-0.518668\pi$
$397$	−2.33578			−0.117229			−0.0586146	+	0.998281i	$0.518668\pi$
$398$		−	59.7257i		−	2.99378i
$399$	10.6436	−	3.87791i	0.532845	−	0.194138i
$400$	2.21566	−	32.6356i	0.110783	−	1.63178i
$401$	30.6222			1.52920			0.764600	−	0.644505i	$-0.222936\pi$
$401$	30.6222			1.52920			0.764600	+	0.644505i	$0.222936\pi$
$402$		−	4.15913i		−	0.207439i
$403$	−16.6817			−0.830973
$404$	13.9517			0.694123
$405$	−1.63381	+	1.52665i	−0.0811847	+	0.0758599i
$406$	−19.8436	−	54.4641i	−0.984822	−	2.70301i
$407$	−9.60425	−	8.10987i	−0.476065	−	0.401992i
$408$		−	31.0441i		−	1.53691i
$409$	1.89620			0.0937609			0.0468804	−	0.998901i	$-0.485072\pi$
$409$	1.89620			0.0937609			0.0468804	+	0.998901i	$0.485072\pi$
$410$	24.6210	−	23.0061i	1.21594	−	1.13619i
$411$		−	19.7845i		−	0.975895i
$412$	35.5783			1.75282
$413$	−1.53678	−	4.21794i	−0.0756199	−	0.207551i
$414$		−	3.10180i		−	0.152445i
$415$	4.80712	+	5.14454i	0.235972	+	0.252536i
$416$			23.3124i			1.14299i
$417$	−11.5988			−0.567997
$418$	−23.1724	+	27.4423i	−1.13340	+	1.34225i
$419$			2.90534i			0.141935i	0.997479	+	0.0709677i	$0.0226087\pi$
$419$			2.90534i			0.141935i	−0.997479	+	0.0709677i	$0.977391\pi$
$420$	11.7795	−	23.1956i	0.574783	−	1.13183i
$421$	30.0571			1.46489			0.732446	−	0.680825i	$-0.238379\pi$
$421$	30.0571			1.46489			0.732446	+	0.680825i	$0.238379\pi$
$422$			16.5183i			0.804098i
$423$	−6.85157			−0.333135
$424$			75.5583i			3.66944i
$425$	25.5396	+	1.73391i	1.23885	+	0.0841070i
$426$	12.5213			0.606659
$427$	−18.2025	+	6.63195i	−0.880880	+	0.320942i
$428$	−50.7860			−2.45483
$429$	13.3663	+	11.2865i	0.645329	+	0.544919i
$430$	32.5336	−	30.3997i	1.56891	−	1.46601i
$431$			20.5074i			0.987807i	0.869517	+	0.493904i	$0.164430\pi$
$431$			20.5074i			0.987807i	−0.869517	+	0.493904i	$0.835570\pi$
$432$	6.54214			0.314759
$433$	−30.0295			−1.44313			−0.721563	−	0.692349i	$-0.756576\pi$
$433$	−30.0295			−1.44313			−0.721563	+	0.692349i	$0.756576\pi$
$434$	−7.24500	−	19.8851i	−0.347771	−	0.954516i
$435$	13.2241	+	14.1524i	0.634048	+	0.678554i
$436$		−	53.9509i		−	2.58378i
$437$		−	5.25070i		−	0.251175i
$438$		−	34.5371i		−	1.65024i
$439$	−25.5270			−1.21834			−0.609169	−	0.793041i	$-0.708497\pi$
$439$	−25.5270			−1.21834			−0.609169	+	0.793041i	$0.708497\pi$
$440$	2.25958	+	44.9127i	0.107721	+	2.14113i
$441$	5.35935	−	4.50304i	0.255207	−	0.214430i
$442$	−68.3028			−3.24883
$443$			14.5242i			0.690065i	0.938591	+	0.345032i	$0.112132\pi$
$443$			14.5242i			0.690065i	−0.938591	+	0.345032i	$0.887868\pi$
$444$			16.6664i			0.790952i
$445$	7.45309	+	7.97624i	0.353310	+	0.378110i
$446$	−47.3030			−2.23986
$447$		−	6.43246i		−	0.304245i
$448$	4.73695	−	1.72587i	0.223800	−	0.0815399i
$449$	4.91667			0.232032			0.116016	−	0.993247i	$-0.462988\pi$
$449$	4.91667			0.232032			0.116016	+	0.993247i	$0.462988\pi$
$450$	−0.856613	+	12.6175i	−0.0403811	+	0.594793i
$451$	−12.7488	+	15.0980i	−0.600317	+	0.710936i
$452$		−	23.8821i		−	1.12332i
$453$		−	20.2373i		−	0.950833i
$454$			52.8861i			2.48207i
$455$	−27.8231	−	14.1296i	−1.30437	−	0.662406i
$456$	25.9622			1.21579
$457$	30.2232			1.41378			0.706891	−	0.707323i	$-0.250097\pi$
$457$	30.2232			1.41378			0.706891	+	0.707323i	$0.250097\pi$
$458$		−	20.7534i		−	0.969742i
$459$			5.11968i			0.238966i
$460$	−8.23277	−	8.81065i	−0.383855	−	0.410799i
$461$	−21.0017			−0.978146			−0.489073	−	0.872243i	$-0.662665\pi$
$461$	−21.0017			−0.978146			−0.489073	+	0.872243i	$0.662665\pi$
$462$	−7.64884	+	20.8349i	−0.355856	+	0.969327i
$463$			15.0004i			0.697126i	0.937285	+	0.348563i	$0.113330\pi$
$463$			15.0004i			0.697126i	−0.937285	+	0.348563i	$0.886670\pi$
$464$		−	56.6692i		−	2.63080i
$465$	4.82819	+	5.16709i	0.223902	+	0.239618i
$466$	30.8194			1.42768
$467$	10.5444			0.487936			0.243968	−	0.969783i	$-0.421551\pi$
$467$	10.5444			0.487936			0.243968	+	0.969783i	$0.421551\pi$
$468$		−	23.1947i		−	1.07217i
$469$	−1.48934	−	4.08775i	−0.0687715	−	0.188755i
$470$	−28.3134	+	26.4564i	−1.30600	+	1.22034i
$471$	−19.2805			−0.888401
$472$		−	10.2886i		−	0.473569i
$473$	−16.8459	+	19.9501i	−0.774577	+	0.917306i
$474$			5.10670i			0.234559i
$475$	−1.45007	+	21.3588i	−0.0665336	+	0.980007i
$476$	−20.3906	−	55.9653i	−0.934600	−	2.56517i
$477$		−	12.4608i		−	0.570541i
$478$			14.3624i			0.656919i
$479$	29.2808			1.33787			0.668936	−	0.743320i	$-0.266750\pi$
$479$	29.2808			1.33787			0.668936	+	0.743320i	$0.266750\pi$
$480$	7.22095	−	6.74734i	0.329590	−	0.307972i
$481$	19.9914			0.911529
$482$	47.4815			2.16272
$483$	−1.11072	−	3.04857i	−0.0505397	−	0.138715i
$484$	−8.10359	−	47.6875i	−0.368345	−	2.16761i
$485$	−25.6441	+	23.9621i	−1.16444	+	1.08806i
$486$	−2.52930			−0.114732
$487$		−	8.75333i		−	0.396651i	−0.980136	−	0.198326i	$-0.936450\pi$
$487$		−	8.75333i		−	0.396651i	0.980136	−	0.198326i	$-0.0635504\pi$
$488$	−44.4002			−2.00990
$489$		−	17.2041i		−	0.777997i
$490$	4.75912	−	39.3028i	0.214995	−	1.77552i
$491$		−	8.44903i		−	0.381299i	−0.981658	−	0.190650i	$-0.938941\pi$
$491$		−	8.44903i		−	0.381299i	0.981658	−	0.190650i	$-0.0610595\pi$
$492$	26.1997			1.18117
$493$	44.3476			1.99731
$494$		−	57.1216i		−	2.57002i
$495$	−0.372642	−	7.40683i	−0.0167490	−	0.332912i
$496$		−	20.6902i		−	0.929017i
$497$	12.3064	−	4.48375i	0.552018	−	0.201124i
$498$			7.96427i			0.356887i
$499$	0.908981			0.0406916			0.0203458	−	0.999793i	$-0.493523\pi$
$499$	0.908981			0.0406916			0.0203458	+	0.999793i	$0.493523\pi$
$500$	31.0560	+	38.1135i	1.38887	+	1.70449i
$501$		−	5.88119i		−	0.262752i
$502$		−	5.35071i		−	0.238814i
$503$			17.3007i			0.771402i	0.922624	+	0.385701i	$0.126040\pi$
$503$			17.3007i			0.771402i	−0.922624	+	0.385701i	$0.873960\pi$
$504$	15.0737	−	5.49199i	0.671435	−	0.244633i
$505$	−5.18365	+	4.84366i	−0.230669	+	0.215540i
$506$	7.86012	+	6.63712i	0.349425	+	0.295056i
$507$	−14.8221			−0.658272
$508$	65.8803			2.92297
$509$		−	9.56749i		−	0.424072i	−0.977262	−	0.212036i	$-0.931991\pi$
$509$		−	9.56749i		−	0.424072i	0.977262	−	0.212036i	$-0.0680093\pi$
$510$	19.7689	+	21.1566i	0.875383	+	0.936829i
$511$	−12.3674	−	33.9443i	−0.547100	−	1.50161i
$512$	50.4247			2.22848
$513$	−4.28158			−0.189037
$514$	−37.4782			−1.65309
$515$	−13.2188	+	12.3518i	−0.582492	+	0.544287i
$516$	34.6197			1.52405
$517$	14.6607	−	17.3622i	0.644778	−	0.763589i
$518$	8.68245	+	23.8304i	0.381485	+	1.04705i
$519$		−	1.71236i		−	0.0751642i
$520$	−48.8282	−	52.2556i	−2.14126	−	2.29156i
$521$		−	0.937460i		−	0.0410709i	−0.999789	−	0.0205354i	$-0.993463\pi$
$521$		−	0.937460i		−	0.0410709i	0.999789	−	0.0205354i	$-0.00653709\pi$
$522$			21.9093i			0.958943i
$523$			10.0718i			0.440409i	0.975454	+	0.220205i	$0.0706725\pi$
$523$			10.0718i			0.440409i	−0.975454	+	0.220205i	$0.929328\pi$
$524$	−3.85978			−0.168615
$525$	3.67628	+	12.7077i	0.160446	+	0.554608i
$526$	33.2619			1.45029
$527$	16.1915			0.705313
$528$	−13.9986	+	16.5781i	−0.609213	+	0.721470i
$529$	21.4961			0.934612
$530$	−48.1156	−	51.4930i	−2.09001	−	2.23671i
$531$			1.69675i			0.0736327i
$532$	46.8038	−	17.0526i	2.02920	−	0.739324i
$533$		−	31.4266i		−	1.36124i
$534$			12.3480i			0.534351i
$535$	18.8692	−	17.6315i	0.815785	−	0.762278i
$536$		−	9.97099i		−	0.430681i
$537$	−7.42437			−0.320385
$538$		−	50.0799i		−	2.15910i
$539$	−0.0568077	+	23.2163i	−0.00244688	+	0.999997i
$540$	−7.18448	+	6.71325i	−0.309171	+	0.288892i
$541$			23.4799i			1.00948i	0.863272	+	0.504740i	$0.168411\pi$
$541$			23.4799i			1.00948i	−0.863272	+	0.504740i	$0.831589\pi$
$542$	−29.5392			−1.26882
$543$		−	7.98549i		−	0.342690i
$544$		−	22.6275i		−	0.970144i
$545$	18.7303	+	20.0450i	0.802318	+	0.858636i
$546$	−12.0834	−	33.1649i	−0.517121	−	1.41933i
$547$	−0.147356			−0.00630050			−0.00315025	−	0.999995i	$-0.501003\pi$
$547$	−0.147356			−0.00630050			−0.00315025	+	0.999995i	$0.501003\pi$
$548$		−	86.9996i		−	3.71644i
$549$	7.32231			0.312508
$550$	−30.1404	−	29.1691i	−1.28519	−	1.24377i
$551$			37.0878i			1.58000i
$552$		−	7.43617i		−	0.316504i
$553$	1.82866	+	5.01906i	0.0777625	+	0.213432i
$554$	−8.80483			−0.374081
$555$	−5.78613	−	6.19227i	−0.245607	−	0.262847i
$556$	−51.0044			−2.16307
$557$	−15.6424			−0.662790			−0.331395	−	0.943492i	$-0.607519\pi$
$557$	−15.6424			−0.662790			−0.331395	+	0.943492i	$0.607519\pi$
$558$			7.99918i			0.338632i
$559$		−	41.5264i		−	1.75638i
$560$	17.5249	−	34.5089i	0.740561	−	1.45827i
$561$	−12.9735	−	10.9549i	−0.547743	−	0.462516i
$562$		−	55.8728i		−	2.35685i
$563$			41.6902i			1.75703i	0.477714	+	0.878515i	$0.341466\pi$
$563$			41.6902i			1.75703i	−0.477714	+	0.878515i	$0.658534\pi$
$564$	−30.1289			−1.26866
$565$	8.29122	+	8.87320i	0.348814	+	0.373299i
$566$			8.49594i			0.357111i
$567$	−2.48590	+	0.905718i	−0.104398	+	0.0380366i
$568$	30.0182			1.25954
$569$		−	8.89030i		−	0.372701i	−0.982483	−	0.186350i	$-0.940334\pi$
$569$		−	8.89030i		−	0.372701i	0.982483	−	0.186350i	$-0.0596660\pi$
$570$	−17.6932	+	16.5327i	−0.741088	+	0.692481i
$571$		−	20.5378i		−	0.859478i	−0.902953	−	0.429739i	$-0.858606\pi$
$571$		−	20.5378i		−	0.859478i	0.902953	−	0.429739i	$-0.141394\pi$
$572$	58.7765	+	49.6311i	2.45757	+	2.07518i
$573$	1.11911			0.0467515
$574$	37.4616	−	13.6489i	1.56362	−	0.569693i
$575$	6.11765	+	0.415333i	0.255123	+	0.0173206i
$576$	−1.90553			−0.0793971
$577$	−20.0840			−0.836107			−0.418054	−	0.908422i	$-0.637288\pi$
$577$	−20.0840			−0.836107			−0.418054	+	0.908422i	$0.637288\pi$
$578$	23.2977			0.969059
$579$	−25.2805			−1.05062
$580$	58.1514	+	62.2332i	2.41460	+	2.58409i
$581$	2.85192	+	7.82758i	0.118318	+	0.324743i
$582$	−39.6996			−1.64560
$583$	31.5763	+	26.6632i	1.30776	+	1.10427i
$584$		−	82.7982i		−	3.42621i
$585$	8.05257	+	8.61780i	0.332933	+	0.356302i
$586$			34.6276i			1.43045i
$587$	−27.5953			−1.13898			−0.569490	−	0.821998i	$-0.692859\pi$
$587$	−27.5953			−1.13898			−0.569490	+	0.821998i	$0.692859\pi$
$588$	23.5671	−	19.8015i	0.971889	−	0.816602i
$589$			13.5409i			0.557945i
$590$	6.55177	+	7.01166i	0.269732	+	0.288665i
$591$	17.1708			0.706311
$592$			24.7952i			1.01908i
$593$		−	40.9519i		−	1.68169i	−0.541275	−	0.840846i	$-0.682058\pi$
$593$		−	40.9519i		−	1.68169i	0.541275	−	0.840846i	$-0.317942\pi$
$594$	5.41211	−	6.40938i	0.222062	−	0.262980i
$595$	27.0056	+	13.7144i	1.10712	+	0.562237i
$596$		−	28.2859i		−	1.15864i
$597$			23.6135i			0.966436i
$598$	−16.3610			−0.669049
$599$	−16.4285			−0.671251			−0.335625	−	0.941996i	$-0.608948\pi$
$599$	−16.4285			−0.671251			−0.335625	+	0.941996i	$0.608948\pi$
$600$	−2.05362	+	30.2488i	−0.0838387	+	1.23490i
$601$	2.68019			0.109327			0.0546636	−	0.998505i	$-0.482591\pi$
$601$	2.68019			0.109327			0.0546636	+	0.998505i	$0.482591\pi$
$602$	49.5009	−	18.0353i	2.01751	−	0.735064i
$603$			1.64438i			0.0669643i
$604$		−	88.9911i		−	3.62100i
$605$	19.5666	+	14.9046i	0.795497	+	0.605957i
$606$	−8.02481			−0.325985
$607$			26.9310i			1.09309i	0.837428	+	0.546547i	$0.184058\pi$
$607$			26.9310i			1.09309i	−0.837428	+	0.546547i	$0.815942\pi$
$608$	18.9233			0.767442
$609$	7.84549	+	21.5333i	0.317915	+	0.872572i
$610$	30.2587	−	28.2741i	1.22514	−	1.14478i
$611$			36.1397i			1.46206i
$612$			22.5131i			0.910040i
$613$	−17.3037			−0.698891			−0.349445	−	0.936957i	$-0.613630\pi$
$613$	−17.3037			−0.698891			−0.349445	+	0.936957i	$0.613630\pi$
$614$		−	9.06295i		−	0.365751i
$615$	−9.73430	+	9.09584i	−0.392525	+	0.366780i
$616$	−18.3371	+	49.9490i	−0.738824	+	2.01250i
$617$			32.5802i			1.31163i	0.754923	+	0.655814i	$0.227674\pi$
$617$			32.5802i			1.31163i	−0.754923	+	0.655814i	$0.772326\pi$
$618$	−20.4641			−0.823187
$619$		−	30.1512i		−	1.21188i	−0.795511	−	0.605940i	$-0.792797\pi$
$619$		−	30.1512i		−	1.21188i	0.795511	−	0.605940i	$-0.207203\pi$
$620$	21.2313	+	22.7216i	0.852671	+	0.912523i
$621$			1.22635i			0.0492116i
$622$		−	11.0860i		−	0.444510i
$623$	4.42170	+	12.1361i	0.177152	+	0.486223i
$624$		−	34.5076i		−	1.38141i
$625$	−24.7706	−	3.37898i	−0.990824	−	0.135159i
$626$	38.7234			1.54770
$627$	9.16158	−	10.8498i	0.365878	−	0.433297i
$628$	−84.7838			−3.38324
$629$	−19.4040			−0.773688
$630$	−6.77541	+	13.3417i	−0.269939	+	0.531547i
$631$	−46.9350			−1.86845			−0.934227	−	0.356680i	$-0.883909\pi$
$631$	−46.9350			−1.86845			−0.934227	+	0.356680i	$0.883909\pi$
$632$			12.2427i			0.486987i
$633$		−	6.53077i		−	0.259575i
$634$			56.5295i			2.24508i
$635$	−24.4773	+	22.8719i	−0.971353	+	0.907643i
$636$		−	54.7948i		−	2.17275i
$637$	−23.7520	−	28.2688i	−0.941089	−	1.12005i
$638$	−55.5192	−	46.8807i	−2.19803	−	1.85602i
$639$	−4.95049			−0.195838
$640$	−22.3163	+	20.8526i	−0.882130	+	0.824272i
$641$	27.4786			1.08534			0.542670	−	0.839946i	$-0.317413\pi$
$641$	27.4786			1.08534			0.542670	+	0.839946i	$0.317413\pi$
$642$	29.2113			1.15288
$643$	−4.30470			−0.169761			−0.0848805	−	0.996391i	$-0.527051\pi$
$643$	−4.30470			−0.169761			−0.0848805	+	0.996391i	$0.527051\pi$
$644$	−4.88426	−	13.4057i	−0.192467	−	0.528258i
$645$	−12.8627	+	12.0190i	−0.506467	+	0.473248i
$646$			55.4432i			2.18138i
$647$	−11.8230			−0.464808			−0.232404	−	0.972619i	$-0.574659\pi$
$647$	−11.8230			−0.464808			−0.232404	+	0.972619i	$0.574659\pi$
$648$	−6.06368			−0.238204
$649$	−4.29965	−	3.63064i	−0.168776	−	0.142515i
$650$	66.5529	+	4.51834i	2.61042	+	0.177224i
$651$	2.86443	+	7.86190i	0.112266	+	0.308132i
$652$		−	75.6529i		−	2.96280i
$653$		−	10.1480i		−	0.397121i	−0.980089	−	0.198561i	$-0.936373\pi$
$653$		−	10.1480i		−	0.397121i	0.980089	−	0.198561i	$-0.0636267\pi$
$654$			31.0317i			1.21344i
$655$	1.43407	−	1.34001i	0.0560338	−	0.0523586i
$656$	38.9783			1.52185
$657$			13.6548i			0.532723i
$658$	−43.0798	+	15.6958i	−1.67942	+	0.611886i
$659$		−	25.3086i		−	0.985882i	−0.870063	−	0.492941i	$-0.835922\pi$
$659$		−	25.3086i		−	0.985882i	0.870063	−	0.492941i	$-0.164078\pi$
$660$	−1.63865	−	32.5706i	−0.0637842	−	1.26781i
$661$		−	38.8425i		−	1.51080i	−0.655265	−	0.755399i	$-0.727443\pi$
$661$		−	38.8425i		−	1.51080i	0.655265	−	0.755399i	$-0.272557\pi$
$662$	43.1499			1.67707
$663$	27.0046			1.04877
$664$			19.0933i			0.740965i
$665$	−11.4694	+	22.5848i	−0.444763	+	0.875800i
$666$		−	9.58626i		−	0.371460i
$667$	10.6228			0.411317
$668$		−	25.8618i		−	1.00062i
$669$	18.7020			0.723061
$670$	6.34954	+	6.79523i	0.245304	+	0.262523i
$671$	−15.6680	+	18.5551i	−0.604857	+	0.716312i
$672$	10.9869	−	4.00300i	0.423829	−	0.154419i
$673$	−3.24113			−0.124936			−0.0624681	−	0.998047i	$-0.519897\pi$
$673$	−3.24113			−0.124936			−0.0624681	+	0.998047i	$0.519897\pi$
$674$	29.6230			1.14103
$675$	0.338675	−	4.98852i	0.0130356	−	0.192008i
$676$	−65.1782			−2.50685
$677$		−	14.4950i		−	0.557089i	−0.960423	−	0.278544i	$-0.910148\pi$
$677$		−	14.4950i		−	0.557089i	0.960423	−	0.278544i	$-0.0898520\pi$
$678$			13.7366i			0.527551i
$679$	−39.0183	+	14.2160i	−1.49739	+	0.545562i
$680$	47.3935	+	50.7202i	1.81746	+	1.94503i
$681$		−	20.9094i		−	0.801249i
$682$	−20.2703	−	17.1163i	−0.776191	−	0.655419i
$683$		−	17.8839i		−	0.684309i	−0.939644	−	0.342154i	$-0.888843\pi$
$683$		−	17.8839i		−	0.684309i	0.939644	−	0.342154i	$-0.111157\pi$
$684$	−18.8277			−0.719896
$685$	30.2040	+	32.3241i	1.15403	+	1.23504i
$686$	23.3816	−	40.5906i	0.892715	−	1.54976i
$687$			8.20518i			0.313047i
$688$	51.5050			1.96361
$689$	−65.7265			−2.50398
$690$	4.73536	+	5.06775i	0.180272	+	0.192926i
$691$			49.9283i			1.89936i	0.313219	+	0.949681i	$0.398593\pi$
$691$			49.9283i			1.89936i	−0.313219	+	0.949681i	$0.601407\pi$
$692$		−	7.52988i		−	0.286243i
$693$	3.02409	−	8.23741i	0.114876	−	0.312913i
$694$	56.3891			2.14050
$695$	18.9503	−	17.7074i	0.718825	−	0.671678i
$696$			52.5247i			1.99094i
$697$			30.5032i			1.15539i
$698$	46.5284			1.76113
$699$	−12.1849			−0.460876
$700$	16.1660	+	55.8804i	0.611016	+	2.11208i
$701$		−	6.73723i		−	0.254462i	−0.991873	−	0.127231i	$-0.959391\pi$
$701$		−	6.73723i		−	0.254462i	0.991873	−	0.127231i	$-0.0406089\pi$
$702$			13.3412i			0.503532i
$703$		−	16.2275i		−	0.612034i
$704$	4.07739	−	4.82871i	0.153672	−	0.181989i
$705$	11.1942	−	10.4599i	0.421597	−	0.393944i
$706$	51.2536			1.92896
$707$	−7.88708	+	2.87360i	−0.296624	+	0.108073i
$708$			7.46125i			0.280411i
$709$	−10.5335			−0.395592			−0.197796	−	0.980243i	$-0.563378\pi$
$709$	−10.5335			−0.395592			−0.197796	+	0.980243i	$0.563378\pi$
$710$	−20.4574	+	19.1156i	−0.767754	+	0.717397i
$711$		−	2.01901i		−	0.0757190i
$712$			29.6028i			1.10941i
$713$	3.87844			0.145249
$714$	11.7283	+	32.1904i	0.438922	+	1.20470i
$715$	−39.0685	+	1.96556i	−1.46108	+	0.0735078i
$716$	−32.6477			−1.22010
$717$		−	5.67839i		−	0.212063i
$718$			24.5185i			0.915022i
$719$		−	53.0463i		−	1.97830i	−0.146926	−	0.989148i	$-0.546938\pi$
$719$		−	53.0463i		−	1.97830i	0.146926	−	0.989148i	$-0.453062\pi$
$720$	−10.6886	+	9.98757i	−0.398342	+	0.372215i
$721$	−20.1129	+	7.32799i	−0.749043	+	0.272909i
$722$	1.68966			0.0628827
$723$	−18.7726			−0.698160
$724$		−	35.1152i		−	1.30504i
$725$	−43.2114	−	2.93367i	−1.60483	−	0.108954i
$726$	4.66106	+	27.4291i	0.172988	+	1.01799i
$727$	−38.0980			−1.41298			−0.706488	−	0.707725i	$-0.749722\pi$
$727$	−38.0980			−1.41298			−0.706488	+	0.707725i	$0.749722\pi$
$728$	−28.9684	−	79.5086i	−1.07364	−	2.94678i
$729$	1.00000			0.0370370
$730$	52.7260	+	56.4270i	1.95148	+	2.08846i
$731$			40.3062i			1.49078i
$732$	32.1989			1.19011
$733$		−	23.1051i		−	0.853408i	−0.904391	−	0.426704i	$-0.859675\pi$
$733$		−	23.1051i		−	0.853408i	0.904391	−	0.426704i	$-0.140325\pi$
$734$	−88.7697			−3.27655
$735$	−1.88159	+	15.5390i	−0.0694036	+	0.573164i
$736$		−	5.42008i		−	0.199787i
$737$	−4.16694	−	3.51858i	−0.153491	−	0.129609i
$738$	−15.0697			−0.554723
$739$			49.3616i			1.81579i	0.419193	+	0.907897i	$0.362313\pi$
$739$			49.3616i			1.81579i	−0.419193	+	0.907897i	$0.637687\pi$
$740$	−25.4438	−	27.2297i	−0.935331	−	1.00098i
$741$			22.5839i			0.829641i
$742$	−28.5456	−	78.3483i	−1.04794	−	2.87626i
$743$	23.1357			0.848767			0.424384	−	0.905483i	$-0.360491\pi$
$743$	23.1357			0.848767			0.424384	+	0.905483i	$0.360491\pi$
$744$			19.1770i			0.703063i
$745$	9.82012	+	10.5094i	0.359781	+	0.385035i
$746$	2.57416			0.0942468
$747$		−	3.14880i		−	0.115209i
$748$	−57.0495	−	48.1728i	−2.08593	−	1.76137i
$749$	28.7100	−	10.4603i	1.04904	−	0.382211i
$750$	−17.8629	−	21.9223i	−0.652262	−	0.800489i
$751$	19.0911			0.696643			0.348322	−	0.937375i	$-0.386752\pi$
$751$	19.0911			0.696643			0.348322	+	0.937375i	$0.386752\pi$
$752$	−44.8239			−1.63456
$753$			2.11549i			0.0770927i
$754$	115.564			4.20859
$755$	30.8953	+	33.0640i	1.12440	+	1.20332i
$756$	−10.9314	+	3.98278i	−0.397571	+	0.144852i
$757$		−	50.0487i		−	1.81905i	−0.415650	−	0.909525i	$-0.636446\pi$
$757$		−	50.0487i		−	1.81905i	0.415650	−	0.909525i	$-0.363554\pi$
$758$	−61.0187			−2.21630
$759$	−3.10762	−	2.62409i	−0.112800	−	0.0952484i
$760$	−42.4173	+	39.6352i	−1.53864	+	1.43772i
$761$	2.79970			0.101489			0.0507444	−	0.998712i	$-0.483841\pi$
$761$	2.79970			0.101489			0.0507444	+	0.998712i	$0.483841\pi$
$762$	−37.8934			−1.37273
$763$	11.1122	+	30.4992i	0.402287	+	1.10414i
$764$	4.92115			0.178041
$765$	−7.81596	−	8.36459i	−0.282587	−	0.302422i
$766$	38.3991			1.38742
$767$	8.94979			0.323158
$768$	−30.7368			−1.10912
$769$	−17.6150			−0.635212			−0.317606	−	0.948223i	$-0.602879\pi$
$769$	−17.6150			−0.635212			−0.317606	+	0.948223i	$0.602879\pi$
$770$	−19.3108	−	45.7174i	−0.695915	−	1.64754i
$771$	14.8176			0.533642
$772$	−111.168			−4.00102
$773$	19.1967			0.690457			0.345228	−	0.938519i	$-0.387801\pi$
$773$	19.1967			0.690457			0.345228	+	0.938519i	$0.387801\pi$
$774$	−19.9127			−0.715747
$775$	−15.7767	−	1.07110i	−0.566716	−	0.0384749i
$776$	−95.1749			−3.41658
$777$	−3.43274	−	9.42174i	−0.123149	−	0.338003i
$778$	4.98180			0.178606
$779$	−25.5098			−0.913985
$780$	35.4102	+	37.8957i	1.26789	+	1.35688i
$781$	10.5929	−	12.5448i	0.379043	−	0.448888i
$782$	15.8802			0.567876
$783$		−	8.66218i		−	0.309561i
$784$	35.0616	−	29.4595i	1.25220	−	1.05213i
$785$	31.5008	−	29.4347i	1.12431	−	1.05057i
$786$	2.22009			0.0791879
$787$		−	49.9063i		−	1.77897i	−0.456966	−	0.889484i	$-0.651064\pi$
$787$		−	49.9063i		−	1.77897i	0.456966	−	0.889484i	$-0.348936\pi$
$788$	75.5063			2.68980
$789$	−13.1506			−0.468175
$790$	−7.79615	−	8.34338i	−0.277374	−	0.296844i
$791$	4.91894	+	13.5009i	0.174897	+	0.480035i
$792$	12.9748	−	15.3657i	0.461041	−	0.545996i
$793$		−	38.6227i		−	1.37153i
$794$	5.90788			0.209663
$795$	19.0233	+	20.3586i	0.674686	+	0.722044i
$796$			103.837i			3.68042i
$797$	50.0048			1.77126			0.885631	−	0.464390i	$-0.153726\pi$
$797$	50.0048			1.77126			0.885631	+	0.464390i	$0.153726\pi$
$798$	−26.9208	+	9.80840i	−0.952986	+	0.347214i
$799$		−	35.0778i		−	1.24096i
$800$	−1.49684	+	22.0477i	−0.0529214	+	0.779505i
$801$		−	4.88199i		−	0.172496i
$802$	−77.4529			−2.73496
$803$	−34.6019	−	29.2180i	−1.22107	−	1.03108i
$804$			7.23095i			0.255016i
$805$	6.46881	+	3.28509i	0.227996	+	0.115784i
$806$	42.1930			1.48618
$807$			19.7999i			0.696988i
$808$	−19.2385			−0.676806
$809$		−	3.95612i		−	0.139090i	−0.997579	−	0.0695449i	$-0.977845\pi$
$809$		−	3.95612i		−	0.139090i	0.997579	−	0.0695449i	$-0.0221547\pi$
$810$	4.13240	−	3.86136i	0.145198	−	0.135674i
$811$	15.5581			0.546318			0.273159	−	0.961969i	$-0.411932\pi$
$811$	15.5581			0.546318			0.273159	+	0.961969i	$0.411932\pi$
$812$	34.4995	+	94.6898i	1.21070	+	3.32296i
$813$	11.6788			0.409593
$814$	24.2921	+	20.5123i	0.851437	+	0.718957i
$815$	26.2647	+	28.1083i	0.920011	+	0.984590i
$816$			33.4937i			1.17251i
$817$	−33.7081			−1.17930
$818$	−4.79606			−0.167690
$819$	4.77736	+	13.1123i	0.166934	+	0.458180i
$820$	−42.8054	+	39.9978i	−1.49483	+	1.39678i
$821$		−	12.6375i		−	0.441052i	−0.975381	−	0.220526i	$-0.929223\pi$
$821$		−	12.6375i		−	0.441052i	0.975381	−	0.220526i	$-0.0707774\pi$
$822$			50.0409i			1.74538i
$823$		−	51.2750i		−	1.78733i	−0.448730	−	0.893667i	$-0.648124\pi$
$823$		−	51.2750i		−	1.78733i	0.448730	−	0.893667i	$-0.351876\pi$
$824$	−49.0601			−1.70909
$825$	11.9165	+	11.5325i	0.414878	+	0.401509i
$826$	3.88698	+	10.6685i	0.135245	+	0.371203i
$827$	40.9493			1.42395			0.711974	−	0.702206i	$-0.247802\pi$
$827$	40.9493			1.42395			0.711974	+	0.702206i	$0.247802\pi$
$828$			5.39270i			0.187409i
$829$		−	5.57913i		−	0.193771i	−0.995296	−	0.0968856i	$-0.969112\pi$
$829$		−	5.57913i		−	0.193771i	0.995296	−	0.0968856i	$-0.0308881\pi$
$830$	−12.1587	−	13.0121i	−0.422033	−	0.451657i
$831$	3.48113			0.120759
$832$			10.0510i			0.348457i
$833$	23.0541	+	27.4382i	0.798778	+	0.950676i
$834$	29.3369			1.01586
$835$	8.97853	+	9.60875i	0.310715	+	0.332525i
$836$	40.2869	−	47.7104i	1.39335	−	1.65010i
$837$		−	3.16260i		−	0.109316i
$838$		−	7.34850i		−	0.253850i
$839$		−	21.3749i		−	0.737942i	−0.929441	−	0.368971i	$-0.879710\pi$
$839$		−	21.3749i		−	0.737942i	0.929441	−	0.368971i	$-0.120290\pi$
$840$	−16.2432	+	31.9851i	−0.560443	+	1.10359i
$841$	−46.0333			−1.58736
$842$	−76.0234			−2.61994
$843$			22.0902i			0.760827i
$844$		−	28.7182i		−	0.988523i
$845$	24.2165	−	22.6281i	0.833072	−	0.778432i
$846$	17.3297			0.595807
$847$	14.4032	+	25.2893i	0.494899	+	0.868951i
$848$		−	81.5203i		−	2.79942i
$849$		−	3.35901i		−	0.115281i
$850$	−64.5974	−	4.38558i	−2.21567	−	0.150424i
$851$	−4.64795			−0.159330
$852$	−21.7692			−0.745799
$853$			24.9537i			0.854398i	0.904158	+	0.427199i	$0.140500\pi$
$853$			24.9537i			0.854398i	−0.904158	+	0.427199i	$0.859500\pi$
$854$	46.0396	−	16.7742i	1.57544	−	0.574001i
$855$	6.99530	−	6.53648i	0.239234	−	0.223543i
$856$	70.0305			2.39359
$857$		−	26.2752i		−	0.897543i	−0.893647	−	0.448771i	$-0.851862\pi$
$857$		−	26.2752i		−	0.897543i	0.893647	−	0.448771i	$-0.148138\pi$
$858$	−33.8073	−	28.5471i	−1.15416	−	0.974581i
$859$			4.31760i			0.147315i	0.997284	+	0.0736573i	$0.0234671\pi$
$859$			4.31760i			0.147315i	−0.997284	+	0.0736573i	$0.976533\pi$
$860$	−56.5620	+	52.8521i	−1.92875	+	1.80224i
$861$	−14.8111	+	5.39630i	−0.504759	+	0.183905i
$862$		−	51.8695i		−	1.76668i
$863$			34.2800i			1.16690i	0.812147	+	0.583452i	$0.198298\pi$
$863$			34.2800i			1.16690i	−0.812147	+	0.583452i	$0.801702\pi$
$864$	−4.41970			−0.150361
$865$	2.61417	+	2.79767i	0.0888846	+	0.0951237i
$866$	75.9537			2.58101
$867$	−9.21113			−0.312826
$868$	12.5959	+	34.5717i	0.427534	+	1.17344i
$869$	5.11629	+	4.32021i	0.173558	+	0.146553i
$870$	−33.4478	−	35.7956i	−1.13399	−	1.21358i
$871$	8.67354			0.293892
$872$			74.3947i			2.51932i
$873$	15.6959			0.531225
$874$			13.2806i			0.449224i
$875$	−25.4065	−	15.1495i	−0.858897	−	0.512148i
$876$			60.0451i			2.02874i
$877$	16.9574			0.572610			0.286305	−	0.958139i	$-0.407573\pi$
$877$	16.9574			0.572610			0.286305	+	0.958139i	$0.407573\pi$
$878$	64.5655			2.17898
$879$		−	13.6906i		−	0.461772i
$880$	−2.43788	−	48.4566i	−0.0821808	−	1.63347i
$881$			24.9230i			0.839678i	0.907599	+	0.419839i	$0.137914\pi$
$881$			24.9230i			0.839678i	−0.907599	+	0.419839i	$0.862086\pi$
$882$	−13.5554	+	11.3896i	−0.456435	+	0.383506i
$883$			50.6335i			1.70395i	0.523579	+	0.851977i	$0.324597\pi$
$883$			50.6335i			1.70395i	−0.523579	+	0.851977i	$0.675403\pi$
$884$	118.749			3.99397
$885$	−2.59035	−	2.77217i	−0.0870735	−	0.0931855i
$886$		−	36.7361i		−	1.23417i
$887$		−	49.0775i		−	1.64786i	−0.566691	−	0.823930i	$-0.691777\pi$
$887$		−	49.0775i		−	1.64786i	0.566691	−	0.823930i	$-0.308223\pi$
$888$		−	22.9818i		−	0.771220i
$889$	−37.2430	+	13.5692i	−1.24909	+	0.455097i
$890$	−18.8511	−	20.1743i	−0.631891	−	0.676245i
$891$	−2.13976	+	2.53405i	−0.0716848	+	0.0848939i
$892$	82.2396			2.75359
$893$	29.3356			0.981677
$894$			16.2696i			0.544138i
$895$	12.1300	−	11.3344i	0.405462	−	0.378868i
$896$	−33.9550	+	12.3713i	−1.13436	+	0.413295i
$897$	6.46856			0.215979
$898$	−12.4357			−0.414986
$899$	−27.3950			−0.913675
$900$	1.48928	−	21.9364i	0.0496427	−	0.731212i
$901$	63.7953			2.12533
$902$	32.2455	−	38.1873i	1.07366	−	1.27150i
$903$	−19.5710	+	7.13054i	−0.651281	+	0.237290i
$904$			32.9318i			1.09529i
$905$	12.1910	+	13.0468i	0.405244	+	0.433689i
$906$			51.1863i			1.70055i
$907$		−	14.0049i		−	0.465025i	−0.972593	−	0.232512i	$-0.925305\pi$
$907$		−	14.0049i		−	0.465025i	0.972593	−	0.232512i	$-0.0746946\pi$
$908$		−	91.9463i		−	3.05135i
$909$	3.17273			0.105233
$910$	70.3732	+	35.7380i	2.33285	+	1.18470i
$911$	−14.3142			−0.474252			−0.237126	−	0.971479i	$-0.576205\pi$
$911$	−14.3142			−0.474252			−0.237126	+	0.971479i	$0.576205\pi$
$912$	−28.0107			−0.927528
$913$	7.97922	+	6.73769i	0.264074	+	0.222985i
$914$	−76.4436			−2.52853
$915$	−11.9633	+	11.1786i	−0.395493	+	0.369553i
$916$			36.0812i			1.19216i
$917$	2.18199	−	0.794991i	0.0720556	−	0.0262529i
$918$		−	12.9492i		−	0.427388i
$919$		−	0.700370i		−	0.0231031i	−0.999933	−	0.0115515i	$-0.996323\pi$
$919$		−	0.700370i		−	0.0231031i	0.999933	−	0.0115515i	$-0.00367705\pi$
$920$	11.3524	+	12.1493i	0.374279	+	0.400550i
$921$			3.58318i			0.118070i
$922$	53.1196			1.74940
$923$			26.1122i			0.859493i
$924$	13.2981	−	36.2230i	0.437474	−	1.19165i
$925$	18.9069	+	1.28361i	0.621654	+	0.0422047i
$926$		−	37.9405i		−	1.24680i
$927$	8.09081			0.265737
$928$			38.2842i			1.25674i
$929$		−	10.7090i		−	0.351351i	−0.984448	−	0.175675i	$-0.943789\pi$
$929$		−	10.7090i		−	0.351351i	0.984448	−	0.175675i	$-0.0562109\pi$
$930$	−12.2120	−	13.0691i	−0.400446	−	0.428554i
$931$	−22.9465	+	19.2801i	−0.752041	+	0.631881i
$932$	−53.5817			−1.75513
$933$			4.38304i			0.143494i
$934$	−26.6699			−0.872667
$935$	37.9206	−	1.90781i	1.24014	−	0.0623920i
$936$			31.9839i			1.04543i
$937$		−	52.3296i		−	1.70953i	−0.519013	−	0.854767i	$-0.673700\pi$
$937$		−	52.3296i		−	1.70953i	0.519013	−	0.854767i	$-0.326300\pi$
$938$	3.76700	+	10.3392i	0.122997	+	0.337586i
$939$	−15.3099			−0.499620
$940$	49.2249	−	45.9963i	1.60554	−	1.50023i
$941$	18.6624			0.608375			0.304188	−	0.952612i	$-0.401615\pi$
$941$	18.6624			0.608375			0.304188	+	0.952612i	$0.401615\pi$
$942$	48.7663			1.58889
$943$			7.30661i			0.237936i
$944$			11.1004i			0.361287i
$945$	2.67877	−	5.27487i	0.0871403	−	0.171591i
$946$	42.6085	−	50.4598i	1.38532	−	1.64059i
$947$		−	9.59885i		−	0.311921i	−0.987763	−	0.155960i	$-0.950153\pi$
$947$		−	9.59885i		−	0.311921i	0.987763	−	0.155960i	$-0.0498472\pi$
$948$		−	8.87836i		−	0.288356i
$949$	72.0243			2.33801
$950$	3.66766	−	54.0228i	0.118995	−	1.75273i
$951$		−	22.3499i		−	0.724744i
$952$	28.1172	+	77.1724i	0.911284	+	2.50117i
$953$	−14.5092			−0.469999			−0.235000	−	0.971995i	$-0.575509\pi$
$953$	−14.5092			−0.469999			−0.235000	+	0.971995i	$0.575509\pi$
$954$			31.5171i			1.02040i
$955$	−1.82841	+	1.70849i	−0.0591661	+	0.0552855i
$956$		−	24.9700i		−	0.807587i
$957$	21.9504	+	18.5350i	0.709556	+	0.599152i
$958$	−74.0599			−2.39277
$959$	17.9191	+	49.1821i	0.578639	+	1.58817i
$960$	3.11328	−	2.90908i	0.100481	−	0.0938902i
$961$	20.9979			0.677353
$962$	−50.5643			−1.63026
$963$	−11.5492			−0.372167
$964$	−82.5500			−2.65876
$965$	41.3036	−	38.5945i	1.32961	−	1.24240i
$966$	2.80936	+	7.71075i	0.0903895	+	0.248089i
$967$	−28.9914			−0.932302			−0.466151	−	0.884705i	$-0.654360\pi$
$967$	−28.9914			−0.932302			−0.466151	+	0.884705i	$0.654360\pi$
$968$	11.1743	+	65.7578i	0.359156	+	2.11354i
$969$		−	21.9203i		−	0.704183i
$970$	64.8617	−	60.6075i	2.08258	−	1.94599i
$971$		−	19.0976i		−	0.612870i	−0.951892	−	0.306435i	$-0.900864\pi$
$971$		−	19.0976i		−	0.612870i	0.951892	−	0.306435i	$-0.0991362\pi$
$972$	4.39737			0.141046
$973$	28.8335	−	10.5053i	0.924359	−	0.336783i
$974$			22.1398i			0.709406i
$975$	−26.3128	−	1.78640i	−0.842682	−	0.0572105i
$976$	47.9036			1.53336
$977$		−	26.7156i		−	0.854708i	−0.904084	−	0.427354i	$-0.859446\pi$
$977$		−	26.7156i		−	0.854708i	0.904084	−	0.427354i	$-0.140554\pi$
$978$			43.5144i			1.39144i
$979$	12.3712	+	10.4463i	0.395385	+	0.333865i
$980$	−8.27407	+	68.3307i	−0.264305	+	2.18274i
$981$		−	12.2689i		−	0.391716i
$982$			21.3702i			0.681949i
$983$	−53.8774			−1.71842			−0.859211	−	0.511621i	$-0.829045\pi$
$983$	−53.8774			−1.71842			−0.859211	+	0.511621i	$0.829045\pi$
$984$	−36.1276			−1.15171
$985$	−28.0538	+	26.2138i	−0.893868	+	0.835240i
$986$	−112.168			−3.57217
$987$	17.0323	−	6.20559i	0.542143	−	0.197526i
$988$			99.3099i			3.15947i
$989$			9.65478i			0.307004i
$990$	0.942524	+	18.7341i	0.0299554	+	0.595409i
$991$	−53.8681			−1.71118			−0.855588	−	0.517657i	$-0.826804\pi$
$991$	−53.8681			−1.71118			−0.855588	+	0.517657i	$0.826804\pi$
$992$			13.9777i			0.443794i
$993$	−17.0600			−0.541383
$994$	−31.1266	+	11.3408i	−0.987277	+	0.359707i
$995$	−36.0496	−	38.5800i	−1.14285	−	1.22307i
$996$		−	13.8464i		−	0.438741i
$997$			52.7933i			1.67198i	0.548745	+	0.835990i	$0.315106\pi$
$997$			52.7933i			1.67198i	−0.548745	+	0.835990i	$0.684894\pi$
$998$	−2.29909			−0.0727763
$999$			3.79008i			0.119913i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.k.b.769.4	yes	48
5.4	even	2		1155.2.k.a.769.45	yes	48
7.6	odd	2		1155.2.k.a.769.3	✓	48
11.10	odd	2	inner	1155.2.k.b.769.45	yes	48
35.34	odd	2	inner	1155.2.k.b.769.46	yes	48
55.54	odd	2		1155.2.k.a.769.4	yes	48
77.76	even	2		1155.2.k.a.769.46	yes	48
385.384	even	2	inner	1155.2.k.b.769.3	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.k.a.769.3	✓	48	7.6	odd	2
1155.2.k.a.769.4	yes	48	55.54	odd	2
1155.2.k.a.769.45	yes	48	5.4	even	2
1155.2.k.a.769.46	yes	48	77.76	even	2
1155.2.k.b.769.3	yes	48	385.384	even	2	inner
1155.2.k.b.769.4	yes	48	1.1	even	1	trivial
1155.2.k.b.769.45	yes	48	11.10	odd	2	inner
1155.2.k.b.769.46	yes	48	35.34	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1155.k (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.52930 q^{2} +1.00000 q^{3} +4.39737 q^{4} +(-1.63381 + 1.52665i) q^{5} -2.52930 q^{6} +(-2.48590 + 0.905718i) q^{7} -6.06368 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.52930 q^{2} +1.00000 q^{3} +4.39737 q^{4} +(-1.63381 + 1.52665i) q^{5} -2.52930 q^{6} +(-2.48590 + 0.905718i) q^{7} -6.06368 q^{8} +1.00000 q^{9} +(4.13240 - 3.86136i) q^{10} +(-2.13976 + 2.53405i) q^{11} +4.39737 q^{12} -5.27466i q^{13} +(6.28758 - 2.29084i) q^{14} +(-1.63381 + 1.52665i) q^{15} +6.54214 q^{16} +5.11968i q^{17} -2.52930 q^{18} -4.28158 q^{19} +(-7.18448 + 6.71325i) q^{20} +(-2.48590 + 0.905718i) q^{21} +(5.41211 - 6.40938i) q^{22} +1.22635i q^{23} -6.06368 q^{24} +(0.338675 - 4.98852i) q^{25} +13.3412i q^{26} +1.00000 q^{27} +(-10.9314 + 3.98278i) q^{28} -8.66218i q^{29} +(4.13240 - 3.86136i) q^{30} -3.16260i q^{31} -4.41970 q^{32} +(-2.13976 + 2.53405i) q^{33} -12.9492i q^{34} +(2.67877 - 5.27487i) q^{35} +4.39737 q^{36} +3.79008i q^{37} +10.8294 q^{38} -5.27466i q^{39} +(9.90691 - 9.25713i) q^{40} +5.95804 q^{41} +(6.28758 - 2.29084i) q^{42} +7.87280 q^{43} +(-9.40934 + 11.1432i) q^{44} +(-1.63381 + 1.52665i) q^{45} -3.10180i q^{46} -6.85157 q^{47} +6.54214 q^{48} +(5.35935 - 4.50304i) q^{49} +(-0.856613 + 12.6175i) q^{50} +5.11968i q^{51} -23.1947i q^{52} -12.4608i q^{53} -2.52930 q^{54} +(-0.372642 - 7.40683i) q^{55} +(15.0737 - 5.49199i) q^{56} -4.28158 q^{57} +21.9093i q^{58} +1.69675i q^{59} +(-7.18448 + 6.71325i) q^{60} +7.32231 q^{61} +7.99918i q^{62} +(-2.48590 + 0.905718i) q^{63} -1.90553 q^{64} +(8.05257 + 8.61780i) q^{65} +(5.41211 - 6.40938i) q^{66} +1.64438i q^{67} +22.5131i q^{68} +1.22635i q^{69} +(-6.77541 + 13.3417i) q^{70} -4.95049 q^{71} -6.06368 q^{72} +13.6548i q^{73} -9.58626i q^{74} +(0.338675 - 4.98852i) q^{75} -18.8277 q^{76} +(3.02409 - 8.23741i) q^{77} +13.3412i q^{78} -2.01901i q^{79} +(-10.6886 + 9.98757i) q^{80} +1.00000 q^{81} -15.0697 q^{82} -3.14880i q^{83} +(-10.9314 + 3.98278i) q^{84} +(-7.81596 - 8.36459i) q^{85} -19.9127 q^{86} -8.66218i q^{87} +(12.9748 - 15.3657i) q^{88} -4.88199i q^{89} +(4.13240 - 3.86136i) q^{90} +(4.77736 + 13.1123i) q^{91} +5.39270i q^{92} -3.16260i q^{93} +17.3297 q^{94} +(6.99530 - 6.53648i) q^{95} -4.41970 q^{96} +15.6959 q^{97} +(-13.5554 + 11.3896i) q^{98} +(-2.13976 + 2.53405i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 48 q^{3} + 48 q^{4} - 4 q^{5} + 48 q^{9}+O(q^{10}) \) 48 * q + 48 * q^3 + 48 * q^4 - 4 * q^5 + 48 * q^9	\( 48 q + 48 q^{3} + 48 q^{4} - 4 q^{5} + 48 q^{9} + 48 q^{12} - 4 q^{15} + 40 q^{16} - 18 q^{20} + 20 q^{25} + 48 q^{27} + 48 q^{36} - 20 q^{38} - 16 q^{44} - 4 q^{45} + 8 q^{47} + 40 q^{48} + 24 q^{49} - 8 q^{55} - 8 q^{56} - 18 q^{60} - 4 q^{64} - 14 q^{70} - 32 q^{71} + 20 q^{75} - 32 q^{77} - 46 q^{80} + 48 q^{81} - 32 q^{82} - 16 q^{86} + 68 q^{97}+O(q^{100}) \) 48 * q + 48 * q^3 + 48 * q^4 - 4 * q^5 + 48 * q^9 + 48 * q^12 - 4 * q^15 + 40 * q^16 - 18 * q^20 + 20 * q^25 + 48 * q^27 + 48 * q^36 - 20 * q^38 - 16 * q^44 - 4 * q^45 + 8 * q^47 + 40 * q^48 + 24 * q^49 - 8 * q^55 - 8 * q^56 - 18 * q^60 - 4 * q^64 - 14 * q^70 - 32 * q^71 + 20 * q^75 - 32 * q^77 - 46 * q^80 + 48 * q^81 - 32 * q^82 - 16 * q^86 + 68 * q^97

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