LMFDB - Embedded newform 1155.2.k.a.769.14

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			769.14
Character	$\chi$	$=$	1155.769
Dual form			1155.2.k.a.769.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.63529 q^{2} -1.00000 q^{3} +0.674169 q^{4} +(1.84877 + 1.25780i) q^{5} +1.63529 q^{6} +(1.79271 + 1.94582i) q^{7} +2.16812 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.63529 q^{2} -1.00000 q^{3} +0.674169 q^{4} +(1.84877 + 1.25780i) q^{5} +1.63529 q^{6} +(1.79271 + 1.94582i) q^{7} +2.16812 q^{8} +1.00000 q^{9} +(-3.02327 - 2.05687i) q^{10} +(-3.27552 - 0.520547i) q^{11} -0.674169 q^{12} -4.17087i q^{13} +(-2.93159 - 3.18197i) q^{14} +(-1.84877 - 1.25780i) q^{15} -4.89383 q^{16} -7.58089i q^{17} -1.63529 q^{18} -5.73183 q^{19} +(1.24638 + 0.847970i) q^{20} +(-1.79271 - 1.94582i) q^{21} +(5.35642 + 0.851244i) q^{22} +2.17955i q^{23} -2.16812 q^{24} +(1.83588 + 4.65076i) q^{25} +6.82058i q^{26} -1.00000 q^{27} +(1.20859 + 1.31181i) q^{28} -5.39200i q^{29} +(3.02327 + 2.05687i) q^{30} +0.864081i q^{31} +3.66660 q^{32} +(3.27552 + 0.520547i) q^{33} +12.3969i q^{34} +(0.866846 + 5.85223i) q^{35} +0.674169 q^{36} -2.91371i q^{37} +9.37321 q^{38} +4.17087i q^{39} +(4.00834 + 2.72706i) q^{40} +3.36581 q^{41} +(2.93159 + 3.18197i) q^{42} +5.31325 q^{43} +(-2.20825 - 0.350936i) q^{44} +(1.84877 + 1.25780i) q^{45} -3.56419i q^{46} -10.7554 q^{47} +4.89383 q^{48} +(-0.572412 + 6.97656i) q^{49} +(-3.00219 - 7.60533i) q^{50} +7.58089i q^{51} -2.81187i q^{52} -11.1538i q^{53} +1.63529 q^{54} +(-5.40093 - 5.08232i) q^{55} +(3.88679 + 4.21876i) q^{56} +5.73183 q^{57} +8.81748i q^{58} -10.8770i q^{59} +(-1.24638 - 0.847970i) q^{60} -15.3838 q^{61} -1.41302i q^{62} +(1.79271 + 1.94582i) q^{63} +3.79172 q^{64} +(5.24612 - 7.71097i) q^{65} +(-5.35642 - 0.851244i) q^{66} +10.6944i q^{67} -5.11080i q^{68} -2.17955i q^{69} +(-1.41754 - 9.57008i) q^{70} -1.55383 q^{71} +2.16812 q^{72} -2.25681i q^{73} +4.76475i q^{74} +(-1.83588 - 4.65076i) q^{75} -3.86423 q^{76} +(-4.85916 - 7.30675i) q^{77} -6.82058i q^{78} -8.24756i q^{79} +(-9.04756 - 6.15546i) q^{80} +1.00000 q^{81} -5.50407 q^{82} -5.54564i q^{83} +(-1.20859 - 1.31181i) q^{84} +(9.53524 - 14.0153i) q^{85} -8.68870 q^{86} +5.39200i q^{87} +(-7.10171 - 1.12861i) q^{88} -1.62655i q^{89} +(-3.02327 - 2.05687i) q^{90} +(8.11575 - 7.47715i) q^{91} +1.46938i q^{92} -0.864081i q^{93} +17.5882 q^{94} +(-10.5968 - 7.20950i) q^{95} -3.66660 q^{96} -8.80400 q^{97} +(0.936058 - 11.4087i) q^{98} +(-3.27552 - 0.520547i) 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 $

$2$	−1.63529			−1.15632			−0.578162	−	0.815922i	$-0.696230\pi$
$2$	−1.63529			−1.15632			−0.578162	+	0.815922i	$0.696230\pi$
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	0.674169			0.337085
$5$	1.84877	+	1.25780i	0.826794	+	0.562505i
$5$	1.84877	+	1.25780i	0.826794	+	0.562505i
$6$	1.63529			0.667604
$7$	1.79271	+	1.94582i	0.677579	+	0.735450i
$7$	1.79271	+	1.94582i	0.677579	+	0.735450i
$8$	2.16812			0.766545
$9$	1.00000			0.333333
$10$	−3.02327	−	2.05687i	−0.956041	−	0.650438i
$11$	−3.27552	−	0.520547i	−0.987606	−	0.156951i
$11$	−3.27552	−	0.520547i	−0.987606	−	0.156951i
$12$	−0.674169			−0.194616
$13$		−	4.17087i		−	1.15679i	−0.815756	−	0.578396i	$-0.803679\pi$
$13$		−	4.17087i		−	1.15679i	0.815756	−	0.578396i	$-0.196321\pi$
$14$	−2.93159	−	3.18197i	−0.783501	−	0.850418i
$15$	−1.84877	−	1.25780i	−0.477350	−	0.324763i
$16$	−4.89383			−1.22346
$17$		−	7.58089i		−	1.83864i	−0.393516	−	0.919318i	$-0.628742\pi$
$17$		−	7.58089i		−	1.83864i	0.393516	−	0.919318i	$-0.371258\pi$
$18$	−1.63529			−0.385441
$19$	−5.73183			−1.31497			−0.657487	−	0.753466i	$-0.728380\pi$
$19$	−5.73183			−1.31497			−0.657487	+	0.753466i	$0.728380\pi$
$20$	1.24638	+	0.847970i	0.278699	+	0.189612i
$21$	−1.79271	−	1.94582i	−0.391200	−	0.424612i
$22$	5.35642	+	0.851244i	1.14199	+	0.181486i
$23$			2.17955i			0.454467i	0.973840	+	0.227233i	$0.0729681\pi$
$23$			2.17955i			0.454467i	−0.973840	+	0.227233i	$0.927032\pi$
$24$	−2.16812			−0.442565
$25$	1.83588	+	4.65076i	0.367176	+	0.930152i
$26$			6.82058i			1.33763i
$27$	−1.00000			−0.192450
$28$	1.20859	+	1.31181i	0.228402	+	0.247909i
$29$		−	5.39200i		−	1.00127i	−0.865659	−	0.500635i	$-0.833100\pi$
$29$		−	5.39200i		−	1.00127i	0.865659	−	0.500635i	$-0.166900\pi$
$30$	3.02327	+	2.05687i	0.551971	+	0.375531i
$31$			0.864081i			0.155194i	0.996985	+	0.0775968i	$0.0247247\pi$
$31$			0.864081i			0.155194i	−0.996985	+	0.0775968i	$0.975275\pi$
$32$	3.66660			0.648169
$33$	3.27552	+	0.520547i	0.570195	+	0.0906155i
$34$			12.3969i			2.12606i
$35$	0.866846	+	5.85223i	0.146524	+	0.989207i
$36$	0.674169			0.112362
$37$		−	2.91371i		−	0.479010i	−0.970895	−	0.239505i	$-0.923015\pi$
$37$		−	2.91371i		−	0.479010i	0.970895	−	0.239505i	$-0.0769852\pi$
$38$	9.37321			1.52053
$39$			4.17087i			0.667874i
$40$	4.00834	+	2.72706i	0.633774	+	0.431185i
$41$	3.36581			0.525651			0.262826	−	0.964843i	$-0.415346\pi$
$41$	3.36581			0.525651			0.262826	+	0.964843i	$0.415346\pi$
$42$	2.93159	+	3.18197i	0.452354	+	0.490989i
$43$	5.31325			0.810263			0.405132	−	0.914258i	$-0.367226\pi$
$43$	5.31325			0.810263			0.405132	+	0.914258i	$0.367226\pi$
$44$	−2.20825	−	0.350936i	−0.332907	−	0.0529057i
$45$	1.84877	+	1.25780i	0.275598	+	0.187502i
$46$		−	3.56419i		−	0.525511i
$47$	−10.7554			−1.56884			−0.784420	−	0.620229i	$-0.787039\pi$
$47$	−10.7554			−1.56884			−0.784420	+	0.620229i	$0.787039\pi$
$48$	4.89383			0.706364
$49$	−0.572412	+	6.97656i	−0.0817731	+	0.996651i
$50$	−3.00219	−	7.60533i	−0.424574	−	1.07556i
$51$			7.58089i			1.06154i
$52$		−	2.81187i		−	0.389937i
$53$		−	11.1538i		−	1.53209i	−0.642788	−	0.766044i	$-0.722223\pi$
$53$		−	11.1538i		−	1.53209i	0.642788	−	0.766044i	$-0.277777\pi$
$54$	1.63529			0.222535
$55$	−5.40093	−	5.08232i	−0.728261	−	0.685300i
$56$	3.88679	+	4.21876i	0.519395	+	0.563755i
$57$	5.73183			0.759200
$58$			8.81748i			1.15779i
$59$		−	10.8770i		−	1.41606i	−0.706180	−	0.708032i	$-0.749583\pi$
$59$		−	10.8770i		−	1.41606i	0.706180	−	0.708032i	$-0.250417\pi$
$60$	−1.24638	−	0.847970i	−0.160907	−	0.109472i
$61$	−15.3838			−1.96969			−0.984846	−	0.173430i	$-0.944515\pi$
$61$	−15.3838			−1.96969			−0.984846	+	0.173430i	$0.944515\pi$
$62$		−	1.41302i		−	0.179454i
$63$	1.79271	+	1.94582i	0.225860	+	0.245150i
$64$	3.79172			0.473965
$65$	5.24612	−	7.71097i	0.650701	−	0.956428i
$66$	−5.35642	−	0.851244i	−0.659330	−	0.104781i
$67$			10.6944i			1.30653i	0.757131	+	0.653263i	$0.226600\pi$
$67$			10.6944i			1.30653i	−0.757131	+	0.653263i	$0.773400\pi$
$68$		−	5.11080i		−	0.619776i
$69$		−	2.17955i		−	0.262387i
$70$	−1.41754	−	9.57008i	−0.169429	−	1.14384i
$71$	−1.55383			−0.184405			−0.0922027	−	0.995740i	$-0.529391\pi$
$71$	−1.55383			−0.184405			−0.0922027	+	0.995740i	$0.529391\pi$
$72$	2.16812			0.255515
$73$		−	2.25681i		−	0.264140i	−0.991240	−	0.132070i	$-0.957838\pi$
$73$		−	2.25681i		−	0.264140i	0.991240	−	0.132070i	$-0.0421623\pi$
$74$			4.76475i			0.553891i
$75$	−1.83588	−	4.65076i	−0.211989	−	0.537023i
$76$	−3.86423			−0.443257
$77$	−4.85916	−	7.30675i	−0.553752	−	0.832682i
$78$		−	6.82058i		−	0.772278i
$79$		−	8.24756i		−	0.927923i	−0.885855	−	0.463961i	$-0.846428\pi$
$79$		−	8.24756i		−	0.927923i	0.885855	−	0.463961i	$-0.153572\pi$
$80$	−9.04756	−	6.15546i	−1.01155	−	0.688202i
$81$	1.00000			0.111111
$82$	−5.50407			−0.607823
$83$		−	5.54564i		−	0.608713i	−0.952558	−	0.304357i	$-0.901559\pi$
$83$		−	5.54564i		−	0.608713i	0.952558	−	0.304357i	$-0.0984415\pi$
$84$	−1.20859	−	1.31181i	−0.131868	−	0.143130i
$85$	9.53524	−	14.0153i	1.03424	−	1.52017i
$86$	−8.68870			−0.936926
$87$			5.39200i			0.578083i
$88$	−7.10171	−	1.12861i	−0.757045	−	0.120310i
$89$		−	1.62655i		−	0.172414i	−0.996277	−	0.0862069i	$-0.972525\pi$
$89$		−	1.62655i		−	0.172414i	0.996277	−	0.0862069i	$-0.0274746\pi$
$90$	−3.02327	−	2.05687i	−0.318680	−	0.216813i
$91$	8.11575	−	7.47715i	0.850762	−	0.783818i
$92$			1.46938i			0.153194i
$93$		−	0.864081i		−	0.0896010i
$94$	17.5882			1.81409
$95$	−10.5968	−	7.20950i	−1.08721	−	0.739679i
$96$	−3.66660			−0.374221
$97$	−8.80400			−0.893911			−0.446955	−	0.894556i	$-0.647492\pi$
$97$	−8.80400			−0.893911			−0.446955	+	0.894556i	$0.647492\pi$
$98$	0.936058	−	11.4087i	0.0945562	−	1.15245i
$99$	−3.27552	−	0.520547i	−0.329202	−	0.0523169i
$100$	1.23769	+	3.13540i	0.123769	+	0.313540i
$101$	−0.825476			−0.0821379			−0.0410690	−	0.999156i	$-0.513076\pi$
$101$	−0.825476			−0.0821379			−0.0410690	+	0.999156i	$0.513076\pi$
$102$		−	12.3969i		−	1.22748i
$103$	11.5317			1.13625			0.568127	−	0.822941i	$-0.307668\pi$
$103$	11.5317			1.13625			0.568127	+	0.822941i	$0.307668\pi$
$104$		−	9.04293i		−	0.886733i
$105$	−0.866846	−	5.85223i	−0.0845955	−	0.571119i
$106$			18.2396i			1.77159i
$107$	9.69116			0.936880			0.468440	−	0.883495i	$-0.344816\pi$
$107$	9.69116			0.936880			0.468440	+	0.883495i	$0.344816\pi$
$108$	−0.674169			−0.0648720
$109$			10.2781i			0.984462i	0.870465	+	0.492231i	$0.163819\pi$
$109$			10.2781i			0.984462i	−0.870465	+	0.492231i	$0.836181\pi$
$110$	8.83208	+	8.31106i	0.842106	+	0.792428i
$111$			2.91371i			0.276557i
$112$	−8.77321	−	9.52251i	−0.828990	−	0.899792i
$113$		−	15.0285i		−	1.41376i	−0.707333	−	0.706881i	$-0.750102\pi$
$113$		−	15.0285i		−	1.41376i	0.707333	−	0.706881i	$-0.249898\pi$
$114$	−9.37321			−0.877881
$115$	−2.74143	+	4.02947i	−0.255640	+	0.375750i
$116$		−	3.63512i		−	0.337513i
$117$		−	4.17087i		−	0.385597i
$118$			17.7870i			1.63743i
$119$	14.7510	−	13.5903i	1.35222	−	1.24582i
$120$	−4.00834	−	2.72706i	−0.365910	−	0.248945i
$121$	10.4581	+	3.41012i	0.950733	+	0.310011i
$122$	25.1569			2.27760
$123$	−3.36581			−0.303485
$124$			0.582537i			0.0523134i
$125$	−2.45561	+	10.9073i	−0.219637	+	0.975582i
$126$	−2.93159	−	3.18197i	−0.261167	−	0.283473i
$127$	7.78569			0.690868			0.345434	−	0.938443i	$-0.387732\pi$
$127$	7.78569			0.690868			0.345434	+	0.938443i	$0.387732\pi$
$128$	−13.5338			−1.19623
$129$	−5.31325			−0.467806
$130$	−8.57892	+	12.6097i	−0.752421	+	1.10594i
$131$	−2.89541			−0.252973			−0.126486	−	0.991968i	$-0.540370\pi$
$131$	−2.89541			−0.252973			−0.126486	+	0.991968i	$0.540370\pi$
$132$	2.20825	+	0.350936i	0.192204	+	0.0305451i
$133$	−10.2755	−	11.1531i	−0.890998	−	0.967097i
$134$		−	17.4884i		−	1.51077i
$135$	−1.84877	−	1.25780i	−0.159117	−	0.108254i
$136$		−	16.4362i		−	1.40940i
$137$			9.16402i			0.782935i	0.920192	+	0.391468i	$0.128033\pi$
$137$			9.16402i			0.782935i	−0.920192	+	0.391468i	$0.871967\pi$
$138$			3.56419i			0.303404i
$139$	−7.30048			−0.619218			−0.309609	−	0.950864i	$-0.600198\pi$
$139$	−7.30048			−0.619218			−0.309609	+	0.950864i	$0.600198\pi$
$140$	0.584401	+	3.94539i	0.0493909	+	0.333447i
$141$	10.7554			0.905771
$142$	2.54096			0.213232
$143$	−2.17113	+	13.6618i	−0.181559	+	1.14245i
$144$	−4.89383			−0.407820
$145$	6.78206	−	9.96856i	0.563219	−	0.827844i
$146$			3.69054i			0.305431i
$147$	0.572412	−	6.97656i	0.0472117	−	0.575417i
$148$		−	1.96433i		−	0.161467i
$149$		−	16.9556i		−	1.38905i	−0.719467	−	0.694526i	$-0.755614\pi$
$149$		−	16.9556i		−	1.38905i	0.719467	−	0.694526i	$-0.244386\pi$
$150$	3.00219	+	7.60533i	0.245128	+	0.620973i
$151$			16.3343i			1.32927i	0.747170	+	0.664633i	$0.231412\pi$
$151$			16.3343i			1.32927i	−0.747170	+	0.664633i	$0.768588\pi$
$152$	−12.4273			−1.00799
$153$		−	7.58089i		−	0.612878i
$154$	7.94612	+	11.9486i	0.640317	+	0.962849i
$155$	−1.08684	+	1.59748i	−0.0872972	+	0.128313i
$156$			2.81187i			0.225130i
$157$	0.510450			0.0407384			0.0203692	−	0.999793i	$-0.493516\pi$
$157$	0.510450			0.0407384			0.0203692	+	0.999793i	$0.493516\pi$
$158$			13.4871i			1.07298i
$159$			11.1538i			0.884551i
$160$	6.77869	+	4.61185i	0.535902	+	0.364599i
$161$	−4.24100	+	3.90729i	−0.334238	+	0.307937i
$162$	−1.63529			−0.128480
$163$		−	24.3951i		−	1.91077i	−0.295362	−	0.955385i	$-0.595440\pi$
$163$		−	24.3951i		−	1.91077i	0.295362	−	0.955385i	$-0.404560\pi$
$164$	2.26912			0.177189
$165$	5.40093	+	5.08232i	0.420462	+	0.395658i
$166$			9.06873i			0.703870i
$167$		−	14.6558i		−	1.13410i	−0.823682	−	0.567052i	$-0.808084\pi$
$167$		−	14.6558i		−	1.13410i	0.823682	−	0.567052i	$-0.191916\pi$
$168$	−3.88679	−	4.21876i	−0.299873	−	0.325484i
$169$	−4.39617			−0.338167
$170$	−15.5929	+	22.9191i	−1.19592	+	1.75781i
$171$	−5.73183			−0.438324
$172$	3.58203			0.273127
$173$		−	17.0484i		−	1.29617i	−0.761569	−	0.648083i	$-0.775571\pi$
$173$		−	17.0484i		−	1.29617i	0.761569	−	0.648083i	$-0.224429\pi$
$174$		−	8.81748i		−	0.668452i
$175$	−5.75834	+	11.9097i	−0.435289	+	0.900291i
$176$	16.0299	+	2.54747i	1.20830	+	0.192023i
$177$			10.8770i			0.817565i
$178$			2.65988i			0.199366i
$179$	19.0830			1.42633			0.713166	−	0.700996i	$-0.247261\pi$
$179$	19.0830			1.42633			0.713166	+	0.700996i	$0.247261\pi$
$180$	1.24638	+	0.847970i	0.0928998	+	0.0632040i
$181$			7.90098i			0.587275i	0.955917	+	0.293638i	$0.0948659\pi$
$181$			7.90098i			0.587275i	−0.955917	+	0.293638i	$0.905134\pi$
$182$	−13.2716	+	12.2273i	−0.983757	+	0.906347i
$183$	15.3838			1.13720
$184$			4.72551i			0.348369i
$185$	3.66486	−	5.38676i	0.269446	−	0.396043i
$186$			1.41302i			0.103608i
$187$	−3.94620	+	24.8313i	−0.288575	+	1.81585i
$188$	−7.25098			−0.528832
$189$	−1.79271	−	1.94582i	−0.130400	−	0.141537i
$190$	17.3289	+	11.7896i	1.25717	+	0.855309i
$191$	0.577417			0.0417804			0.0208902	−	0.999782i	$-0.493350\pi$
$191$	0.577417			0.0417804			0.0208902	+	0.999782i	$0.493350\pi$
$192$	−3.79172			−0.273644
$193$	−14.2196			−1.02355			−0.511776	−	0.859119i	$-0.671012\pi$
$193$	−14.2196			−1.02355			−0.511776	+	0.859119i	$0.671012\pi$
$194$	14.3971			1.03365
$195$	−5.24612	+	7.71097i	−0.375683	+	0.552194i
$196$	−0.385902	+	4.70338i	−0.0275645	+	0.335956i
$197$	2.26374			0.161285			0.0806425	−	0.996743i	$-0.474303\pi$
$197$	2.26374			0.161285			0.0806425	+	0.996743i	$0.474303\pi$
$198$	5.35642	+	0.851244i	0.380664	+	0.0604953i
$199$			0.287141i			0.0203549i	0.999948	+	0.0101774i	$0.00323964\pi$
$199$			0.287141i			0.0203549i	−0.999948	+	0.0101774i	$0.996760\pi$
$200$	3.98040	+	10.0834i	0.281457	+	0.713003i
$201$		−	10.6944i		−	0.754323i
$202$	1.34989			0.0949780
$203$	10.4919	−	9.66627i	0.736384	−	0.678439i
$204$			5.11080i			0.357828i
$205$	6.22260	+	4.23351i	0.434605	+	0.295681i
$206$	−18.8577			−1.31388
$207$			2.17955i			0.151489i
$208$			20.4116i			1.41529i
$209$	18.7747	+	2.98369i	1.29868	+	0.206386i
$210$	1.41754	+	9.57008i	0.0978198	+	0.660398i
$211$		−	15.6678i		−	1.07861i	−0.842109	−	0.539307i	$-0.818686\pi$
$211$		−	15.6678i		−	1.07861i	0.842109	−	0.539307i	$-0.181314\pi$
$212$		−	7.51953i		−	0.516443i
$213$	1.55383			0.106467
$214$	−15.8478			−1.08334
$215$	9.82296	+	6.68301i	0.669920	+	0.455777i
$216$	−2.16812			−0.147522
$217$	−1.68134	+	1.54904i	−0.114137	+	0.105156i
$218$		−	16.8076i		−	1.13836i
$219$			2.25681i			0.152501i
$220$	−3.64114	−	3.42634i	−0.245486	−	0.231004i
$221$	−31.6189			−2.12692
$222$		−	4.76475i		−	0.319789i
$223$	21.1236			1.41454			0.707269	−	0.706945i	$-0.249927\pi$
$223$	21.1236			1.41454			0.707269	+	0.706945i	$0.249927\pi$
$224$	6.57314	+	7.13453i	0.439186	+	0.476696i
$225$	1.83588	+	4.65076i	0.122392	+	0.310051i
$226$			24.5759i			1.63477i
$227$			7.65754i			0.508249i	0.967172	+	0.254124i	$0.0817873\pi$
$227$			7.65754i			0.508249i	−0.967172	+	0.254124i	$0.918213\pi$
$228$	3.86423			0.255915
$229$		−	19.9463i		−	1.31809i	−0.752103	−	0.659045i	$-0.770961\pi$
$229$		−	19.9463i		−	1.31809i	0.752103	−	0.659045i	$-0.229039\pi$
$230$	4.48304	−	6.58935i	0.295603	−	0.434489i
$231$	4.85916	+	7.30675i	0.319709	+	0.480749i
$232$		−	11.6905i		−	0.767518i
$233$	5.69495			0.373088			0.186544	−	0.982447i	$-0.440271\pi$
$233$	5.69495			0.373088			0.186544	+	0.982447i	$0.440271\pi$
$234$			6.82058i			0.445875i
$235$	−19.8843	−	13.5282i	−1.29711	−	0.882481i
$236$		−	7.33293i		−	0.477333i
$237$			8.24756i			0.535736i
$238$	−24.1222	+	22.2241i	−1.56361	+	1.44057i
$239$			9.91495i			0.641345i	0.947190	+	0.320672i	$0.103909\pi$
$239$			9.91495i			0.641345i	−0.947190	+	0.320672i	$0.896091\pi$
$240$	9.04756	+	6.15546i	0.584017	+	0.397334i
$241$	−2.07373			−0.133581			−0.0667903	−	0.997767i	$-0.521276\pi$
$241$	−2.07373			−0.133581			−0.0667903	+	0.997767i	$0.521276\pi$
$242$	−17.1020	−	5.57653i	−1.09936	−	0.358473i
$243$	−1.00000			−0.0641500
$244$	−10.3713			−0.663953
$245$	−9.83337	+	12.1780i	−0.628231	+	0.778027i
$246$	5.50407			0.350927
$247$			23.9067i			1.52115i
$248$			1.87343i			0.118963i
$249$			5.54564i			0.351441i
$250$	4.01563	−	17.8366i	0.253971	−	1.12809i
$251$		−	9.03128i		−	0.570049i	−0.958520	−	0.285025i	$-0.907998\pi$
$251$		−	9.03128i		−	0.570049i	0.958520	−	0.285025i	$-0.0920018\pi$
$252$	1.20859	+	1.31181i	0.0761338	+	0.0826363i
$253$	1.13456	−	7.13915i	0.0713289	−	0.448835i
$254$	−12.7319			−0.798868
$255$	−9.53524	+	14.0153i	−0.597120	+	0.877672i
$256$	14.5482			0.909260
$257$	−15.2678			−0.952376			−0.476188	−	0.879343i	$-0.657982\pi$
$257$	−15.2678			−0.952376			−0.476188	+	0.879343i	$0.657982\pi$
$258$	8.68870			0.540935
$259$	5.66954	−	5.22342i	0.352288	−	0.324567i
$260$	3.53677	−	5.19850i	0.219341	−	0.322397i
$261$		−	5.39200i		−	0.333757i
$262$	4.73483			0.292518
$263$	−6.40729			−0.395090			−0.197545	−	0.980294i	$-0.563297\pi$
$263$	−6.40729			−0.395090			−0.197545	+	0.980294i	$0.563297\pi$
$264$	7.10171	+	1.12861i	0.437080	+	0.0694609i
$265$	14.0292	−	20.6207i	0.861807	−	1.26672i
$266$	16.8034	+	18.2385i	1.03028	+	1.11828i
$267$			1.62655i			0.0995432i
$268$			7.20982i			0.440410i
$269$			13.5541i			0.826410i	0.910638	+	0.413205i	$0.135591\pi$
$269$			13.5541i			0.826410i	−0.910638	+	0.413205i	$0.864409\pi$
$270$	3.02327	+	2.05687i	0.183990	+	0.125177i
$271$	−13.5515			−0.823195			−0.411598	−	0.911366i	$-0.635029\pi$
$271$	−13.5515			−0.823195			−0.411598	+	0.911366i	$0.635029\pi$
$272$			37.0996i			2.24949i
$273$	−8.11575	+	7.47715i	−0.491188	+	0.452537i
$274$		−	14.9858i		−	0.905327i
$275$	−3.59252	−	16.1893i	−0.216637	−	0.976252i
$276$		−	1.46938i		−	0.0884465i
$277$	10.5948			0.636580			0.318290	−	0.947993i	$-0.396891\pi$
$277$	10.5948			0.636580			0.318290	+	0.947993i	$0.396891\pi$
$278$	11.9384			0.716017
$279$			0.864081i			0.0517312i
$280$	1.87942	+	12.6883i	0.112317	+	0.758272i
$281$			11.4974i			0.685880i	0.939357	+	0.342940i	$0.111423\pi$
$281$			11.4974i			0.685880i	−0.939357	+	0.342940i	$0.888577\pi$
$282$	−17.5882			−1.04736
$283$		−	21.6818i		−	1.28885i	−0.764668	−	0.644424i	$-0.777097\pi$
$283$		−	21.6818i		−	1.28885i	0.764668	−	0.644424i	$-0.222903\pi$
$284$	−1.04754			−0.0621602
$285$	10.5968	+	7.20950i	0.627702	+	0.427054i
$286$	3.55043	−	22.3409i	0.209941	−	1.32105i
$287$	6.03390	+	6.54925i	0.356170	+	0.386590i
$288$	3.66660			0.216056
$289$	−40.4698			−2.38058
$290$	−11.0906	+	16.3015i	−0.651264	+	0.957255i
$291$	8.80400			0.516100
$292$		−	1.52147i		−	0.0890375i
$293$			7.13847i			0.417034i	0.978019	+	0.208517i	$0.0668636\pi$
$293$			7.13847i			0.417034i	−0.978019	+	0.208517i	$0.933136\pi$
$294$	−0.936058	+	11.4087i	−0.0545920	+	0.665368i
$295$	13.6811	−	20.1090i	0.796543	−	1.17079i
$296$		−	6.31725i		−	0.367183i
$297$	3.27552	+	0.520547i	0.190065	+	0.0302052i
$298$			27.7272i			1.60619i
$299$	9.09061			0.525724
$300$	−1.23769	−	3.13540i	−0.0714582	−	0.181022i
$301$	9.52509	+	10.3386i	0.549017	+	0.595908i
$302$		−	26.7113i		−	1.53706i
$303$	0.825476			0.0474223
$304$	28.0507			1.60882
$305$	−28.4410	−	19.3497i	−1.62853	−	1.10796i
$306$			12.3969i			0.708686i
$307$		−	15.4378i		−	0.881081i	−0.897733	−	0.440540i	$-0.854787\pi$
$307$		−	15.4378i		−	0.881081i	0.897733	−	0.440540i	$-0.145213\pi$
$308$	−3.27589	−	4.92599i	−0.186661	−	0.280684i
$309$	−11.5317			−0.656016
$310$	1.77730	−	2.61235i	0.100944	−	0.148371i
$311$			30.4383i			1.72600i	0.505208	+	0.862998i	$0.331416\pi$
$311$			30.4383i			1.72600i	−0.505208	+	0.862998i	$0.668584\pi$
$312$			9.04293i			0.511955i
$313$	31.1303			1.75959			0.879795	−	0.475354i	$-0.157680\pi$
$313$	31.1303			1.75959			0.879795	+	0.475354i	$0.157680\pi$
$314$	−0.834734			−0.0471068
$315$	0.866846	+	5.85223i	0.0488412	+	0.329736i
$316$		−	5.56025i		−	0.312789i
$317$			28.5646i			1.60435i	0.597089	+	0.802175i	$0.296324\pi$
$317$			28.5646i			1.60435i	−0.597089	+	0.802175i	$0.703676\pi$
$318$		−	18.2396i		−	1.02283i
$319$	−2.80679	+	17.6616i	−0.157150	+	0.988860i
$320$	7.01000	+	4.76922i	0.391871	+	0.266608i
$321$	−9.69116			−0.540908
$322$	6.93526	−	6.38954i	0.386487	−	0.356075i
$323$			43.4524i			2.41776i
$324$	0.674169			0.0374538
$325$	19.3977	−	7.65721i	1.07599	−	0.424746i
$326$			39.8930i			2.20947i
$327$		−	10.2781i		−	0.568380i
$328$	7.29746			0.402935
$329$	−19.2813	−	20.9281i	−1.06301	−	1.15380i
$330$	−8.83208	−	8.31106i	−0.486190	−	0.457509i
$331$	−26.6099			−1.46261			−0.731306	−	0.682050i	$-0.761089\pi$
$331$	−26.6099			−1.46261			−0.731306	+	0.682050i	$0.761089\pi$
$332$		−	3.73870i		−	0.205188i
$333$		−	2.91371i		−	0.159670i
$334$			23.9665i			1.31139i
$335$	−13.4514	+	19.7714i	−0.734927	+	1.08023i
$336$	8.77321	+	9.52251i	0.478618	+	0.519495i
$337$	−19.0036			−1.03519			−0.517597	−	0.855625i	$-0.673173\pi$
$337$	−19.0036			−1.03519			−0.517597	+	0.855625i	$0.673173\pi$
$338$	7.18900			0.391030
$339$			15.0285i			0.816236i
$340$	6.42837	−	9.44868i	0.348627	−	0.512427i
$341$	0.449794	−	2.83032i	0.0243577	−	0.153270i
$342$	9.37321			0.506845
$343$	−14.6013	+	11.3931i	−0.788395	+	0.615170i
$344$	11.5197			0.621103
$345$	2.74143	−	4.02947i	0.147594	−	0.216940i
$346$			27.8791i			1.49879i
$347$	−7.26940			−0.390242			−0.195121	−	0.980779i	$-0.562510\pi$
$347$	−7.26940			−0.390242			−0.195121	+	0.980779i	$0.562510\pi$
$348$			3.63512i			0.194863i
$349$	−0.888707			−0.0475714			−0.0237857	−	0.999717i	$-0.507572\pi$
$349$	−0.888707			−0.0475714			−0.0237857	+	0.999717i	$0.507572\pi$
$350$	9.41654	−	19.4758i	0.503335	−	1.04103i
$351$			4.17087i			0.222625i
$352$	−12.0100	−	1.90864i	−0.640136	−	0.101731i
$353$	−12.9562			−0.689589			−0.344794	−	0.938678i	$-0.612051\pi$
$353$	−12.9562			−0.689589			−0.344794	+	0.938678i	$0.612051\pi$
$354$		−	17.7870i		−	0.945370i
$355$	−2.87267	−	1.95440i	−0.152465	−	0.103729i
$356$		−	1.09657i		−	0.0581181i
$357$	−14.7510	+	13.5903i	−0.780707	+	0.719275i
$358$	−31.2062			−1.64930
$359$			8.33660i			0.439989i	0.975501	+	0.219994i	$0.0706039\pi$
$359$			8.33660i			0.439989i	−0.975501	+	0.219994i	$0.929396\pi$
$360$	4.00834	+	2.72706i	0.211258	+	0.143728i
$361$	13.8539			0.729154
$362$		−	12.9204i		−	0.679081i
$363$	−10.4581	−	3.41012i	−0.548906	−	0.178985i
$364$	5.47139	−	5.04086i	0.286779	−	0.264213i
$365$	2.83862	−	4.17232i	0.148580	−	0.218389i
$366$	−25.1569			−1.31497
$367$	22.9597			1.19849			0.599243	−	0.800567i	$-0.295468\pi$
$367$	22.9597			1.19849			0.599243	+	0.800567i	$0.295468\pi$
$368$		−	10.6663i		−	0.556022i
$369$	3.36581			0.175217
$370$	−5.99310	+	8.80892i	−0.311567	+	0.457954i
$371$	21.7032	−	19.9954i	1.12677	−	1.03811i
$372$		−	0.582537i		−	0.0302031i
$373$	35.0778			1.81626			0.908129	−	0.418691i	$-0.137511\pi$
$373$	35.0778			1.81626			0.908129	+	0.418691i	$0.137511\pi$
$374$	6.45318	−	40.6064i	0.333686	−	2.09971i
$375$	2.45561	−	10.9073i	0.126807	−	0.563252i
$376$	−23.3190			−1.20259
$377$	−22.4893			−1.15826
$378$	2.93159	+	3.18197i	0.150785	+	0.163663i
$379$	−5.09918			−0.261928			−0.130964	−	0.991387i	$-0.541807\pi$
$379$	−5.09918			−0.261928			−0.130964	+	0.991387i	$0.541807\pi$
$380$	−7.14406	−	4.86042i	−0.366482	−	0.249335i
$381$	−7.78569			−0.398873
$382$	−0.944243			−0.0483117
$383$	2.21160			0.113008			0.0565038	−	0.998402i	$-0.482005\pi$
$383$	2.21160			0.113008			0.0565038	+	0.998402i	$0.482005\pi$
$384$	13.5338			0.690642
$385$	0.206986	−	19.6203i	0.0105490	−	0.999944i
$386$	23.2532			1.18356
$387$	5.31325			0.270088
$388$	−5.93539			−0.301324
$389$	33.7532			1.71135			0.855677	−	0.517510i	$-0.173141\pi$
$389$	33.7532			1.71135			0.855677	+	0.517510i	$0.173141\pi$
$390$	8.57892	−	12.6097i	0.434411	−	0.638515i
$391$	16.5229			0.835599
$392$	−1.24105	+	15.1260i	−0.0626827	+	0.763978i
$393$	2.89541			0.146054
$394$	−3.70187			−0.186498
$395$	10.3738	−	15.2478i	0.521961	−	0.767201i
$396$	−2.20825	−	0.350936i	−0.110969	−	0.0176352i
$397$	7.81103			0.392024			0.196012	−	0.980601i	$-0.437201\pi$
$397$	7.81103			0.392024			0.196012	+	0.980601i	$0.437201\pi$
$398$		−	0.469559i		−	0.0235368i
$399$	10.2755	+	11.1531i	0.514418	+	0.558354i
$400$	−8.98448	−	22.7600i	−0.449224	−	1.13800i
$401$	−14.3745			−0.717827			−0.358914	−	0.933371i	$-0.616853\pi$
$401$	−14.3745			−0.717827			−0.358914	+	0.933371i	$0.616853\pi$
$402$			17.4884i			0.872241i
$403$	3.60397			0.179527
$404$	−0.556510			−0.0276874
$405$	1.84877	+	1.25780i	0.0918660	+	0.0625006i
$406$	−17.1572	+	15.8071i	−0.851498	+	0.784496i
$407$	−1.51672	+	9.54390i	−0.0751810	+	0.473074i
$408$			16.4362i			0.813715i
$409$	11.9091			0.588866			0.294433	−	0.955672i	$-0.404869\pi$
$409$	11.9091			0.588866			0.294433	+	0.955672i	$0.404869\pi$
$410$	−10.1757	−	6.92302i	−0.502544	−	0.341903i
$411$		−	9.16402i		−	0.452028i
$412$	7.77433			0.383014
$413$	21.1646	−	19.4992i	1.04144	−	0.959495i
$414$		−	3.56419i		−	0.175170i
$415$	6.97531	−	10.2526i	0.342404	−	0.503280i
$416$		−	15.2929i		−	0.749797i
$417$	7.30048			0.357506
$418$	−30.7021	−	4.87919i	−1.50169	−	0.238649i
$419$		−	2.62704i		−	0.128339i	−0.997939	−	0.0641696i	$-0.979560\pi$
$419$		−	2.62704i		−	0.128339i	0.997939	−	0.0641696i	$-0.0204399\pi$
$420$	−0.584401	−	3.94539i	−0.0285158	−	0.192515i
$421$	−13.4735			−0.656656			−0.328328	−	0.944564i	$-0.606485\pi$
$421$	−13.4735			−0.656656			−0.328328	+	0.944564i	$0.606485\pi$
$422$			25.6214i			1.24723i
$423$	−10.7554			−0.522947
$424$		−	24.1827i		−	1.17441i
$425$	35.2569	−	13.9176i	1.71021	−	0.675102i
$426$	−2.54096			−0.123110
$427$	−27.5786	−	29.9340i	−1.33462	−	1.44861i
$428$	6.53348			0.315808
$429$	2.17113	−	13.6618i	0.104823	−	0.659597i
$430$	−16.0634	−	10.9286i	−0.774645	−	0.527026i
$431$		−	17.8620i		−	0.860382i	−0.902738	−	0.430191i	$-0.858446\pi$
$431$		−	17.8620i		−	0.860382i	0.902738	−	0.430191i	$-0.141554\pi$
$432$	4.89383			0.235455
$433$	−0.555819			−0.0267109			−0.0133555	−	0.999911i	$-0.504251\pi$
$433$	−0.555819			−0.0267109			−0.0133555	+	0.999911i	$0.504251\pi$
$434$	2.74948	−	2.53313i	0.131979	−	0.121594i
$435$	−6.78206	+	9.96856i	−0.325175	+	0.477956i
$436$			6.92917i			0.331847i
$437$		−	12.4928i		−	0.597612i
$438$		−	3.69054i		−	0.176341i
$439$	−19.6767			−0.939117			−0.469558	−	0.882901i	$-0.655587\pi$
$439$	−19.6767			−0.939117			−0.469558	+	0.882901i	$0.655587\pi$
$440$	−11.7098	−	11.0191i	−0.558245	−	0.525313i
$441$	−0.572412	+	6.97656i	−0.0272577	+	0.332217i
$442$	51.7060			2.45941
$443$			40.6848i			1.93299i	0.256677	+	0.966497i	$0.417372\pi$
$443$			40.6848i			1.93299i	−0.256677	+	0.966497i	$0.582628\pi$
$444$			1.96433i			0.0932230i
$445$	2.04587	−	3.00711i	0.0969837	−	0.142551i
$446$	−34.5431			−1.63566
$447$			16.9556i			0.801970i
$448$	6.79744	+	7.37799i	0.321149	+	0.348577i
$449$	15.5339			0.733088			0.366544	−	0.930401i	$-0.380541\pi$
$449$	15.5339			0.733088			0.366544	+	0.930401i	$0.380541\pi$
$450$	−3.00219	−	7.60533i	−0.141525	−	0.358519i
$451$	−11.0248	−	1.75206i	−0.519136	−	0.0825013i
$452$		−	10.1317i		−	0.476557i
$453$		−	16.3343i		−	0.767453i
$454$		−	12.5223i		−	0.587700i
$455$	24.4089	−	3.61550i	1.14431	−	0.169497i
$456$	12.4273			0.581961
$457$	−28.8051			−1.34745			−0.673724	−	0.738983i	$-0.735306\pi$
$457$	−28.8051			−1.34745			−0.673724	+	0.738983i	$0.735306\pi$
$458$			32.6180i			1.52414i
$459$			7.58089i			0.353846i
$460$	−1.84819	+	2.71655i	−0.0861723	+	0.126660i
$461$	−19.9251			−0.928005			−0.464003	−	0.885834i	$-0.653587\pi$
$461$	−19.9251			−0.928005			−0.464003	+	0.885834i	$0.653587\pi$
$462$	−7.94612	−	11.9486i	−0.369687	−	0.555901i
$463$			8.87783i			0.412588i	0.978490	+	0.206294i	$0.0661403\pi$
$463$			8.87783i			0.412588i	−0.978490	+	0.206294i	$0.933860\pi$
$464$			26.3876i			1.22501i
$465$	1.08684	−	1.59748i	0.0504011	−	0.0740816i
$466$	−9.31288			−0.431411
$467$	31.9600			1.47893			0.739465	−	0.673195i	$-0.235078\pi$
$467$	31.9600			1.47893			0.739465	+	0.673195i	$0.235078\pi$
$468$		−	2.81187i		−	0.129979i
$469$	−20.8093	+	19.1719i	−0.960884	+	0.885274i
$470$	32.5165	+	22.1225i	1.49988	+	1.02043i
$471$	−0.510450			−0.0235203
$472$		−	23.5826i		−	1.08548i
$473$	−17.4037	−	2.76579i	−0.800221	−	0.127171i
$474$		−	13.4871i		−	0.619485i
$475$	−10.5230	−	26.6574i	−0.482826	−	1.22312i
$476$	9.94469	−	9.16216i	0.455814	−	0.419947i
$477$		−	11.1538i		−	0.510696i
$478$		−	16.2138i		−	0.741602i
$479$	−9.36547			−0.427919			−0.213960	−	0.976842i	$-0.568636\pi$
$479$	−9.36547			−0.427919			−0.213960	+	0.976842i	$0.568636\pi$
$480$	−6.77869	−	4.61185i	−0.309403	−	0.210501i
$481$	−12.1527			−0.554115
$482$	3.39115			0.154462
$483$	4.24100	−	3.90729i	0.192972	−	0.177788i
$484$	7.05050	+	2.29900i	0.320477	+	0.104500i
$485$	−16.2765	−	11.0737i	−0.739080	−	0.502830i
$486$	1.63529			0.0741782
$487$		−	15.8582i		−	0.718602i	−0.933222	−	0.359301i	$-0.883015\pi$
$487$		−	15.8582i		−	0.718602i	0.933222	−	0.359301i	$-0.116985\pi$
$488$	−33.3538			−1.50986
$489$			24.3951i			1.10318i
$490$	16.0804	−	19.9146i	0.726438	−	0.899651i
$491$		−	26.6209i		−	1.20139i	−0.799480	−	0.600693i	$-0.794892\pi$
$491$		−	26.6209i		−	1.20139i	0.799480	−	0.600693i	$-0.205108\pi$
$492$	−2.26912			−0.102300
$493$	−40.8762			−1.84097
$494$		−	39.0944i		−	1.75894i
$495$	−5.40093	−	5.08232i	−0.242754	−	0.228433i
$496$		−	4.22867i		−	0.189873i
$497$	−2.78556	−	3.02347i	−0.124949	−	0.135621i
$498$		−	9.06873i		−	0.406379i
$499$	−12.2258			−0.547301			−0.273651	−	0.961829i	$-0.588231\pi$
$499$	−12.2258			−0.547301			−0.273651	+	0.961829i	$0.588231\pi$
$500$	−1.65550	+	7.35339i	−0.0740361	+	0.328854i
$501$			14.6558i			0.654775i
$502$			14.7687i			0.659161i
$503$		−	0.335068i		−	0.0149400i	−0.999972	−	0.00746998i	$-0.997622\pi$
$503$		−	0.335068i		−	0.0149400i	0.999972	−	0.00746998i	$-0.00237779\pi$
$504$	3.88679	+	4.21876i	0.173132	+	0.187918i
$505$	−1.52611	−	1.03828i	−0.0679111	−	0.0462030i
$506$	−1.85533	+	11.6746i	−0.0824793	+	0.518998i
$507$	4.39617			0.195241
$508$	5.24887			0.232881
$509$		−	21.9958i		−	0.974948i	−0.873138	−	0.487474i	$-0.837918\pi$
$509$		−	21.9958i		−	0.974948i	0.873138	−	0.487474i	$-0.162082\pi$
$510$	15.5929	−	22.9191i	0.690464	−	1.01487i
$511$	4.39134	−	4.04580i	0.194262	−	0.178976i
$512$	3.27707			0.144827
$513$	5.73183			0.253067
$514$	24.9672			1.10126
$515$	21.3195	+	14.5046i	0.939447	+	0.639149i
$516$	−3.58203			−0.157690
$517$	35.2296	+	5.59870i	1.54940	+	0.246231i
$518$	−9.27134	+	8.54180i	−0.407359	+	0.375305i
$519$			17.0484i			0.748342i
$520$	11.3742	−	16.7183i	0.498792	−	0.733145i
$521$			6.25907i			0.274215i	0.990556	+	0.137107i	$0.0437806\pi$
$521$			6.25907i			0.274215i	−0.990556	+	0.137107i	$0.956219\pi$
$522$			8.81748i			0.385931i
$523$			36.1671i			1.58148i	0.612155	+	0.790738i	$0.290303\pi$
$523$			36.1671i			1.58148i	−0.612155	+	0.790738i	$0.709697\pi$
$524$	−1.95199			−0.0852732
$525$	5.75834	−	11.9097i	0.251314	−	0.519783i
$526$	10.4778			0.456852
$527$	6.55050			0.285344
$528$	−16.0299	−	2.54747i	−0.697610	−	0.110864i
$529$	18.2496			0.793460
$530$	−22.9418	+	33.7208i	−0.996528	+	1.46474i
$531$		−	10.8770i		−	0.472021i
$532$	−6.92742	−	7.51908i	−0.300342	−	0.325993i
$533$		−	14.0384i		−	0.608069i
$534$		−	2.65988i		−	0.115104i
$535$	17.9167	+	12.1895i	0.774606	+	0.527000i
$536$			23.1866i			1.00151i
$537$	−19.0830			−0.823493
$538$		−	22.1649i		−	0.955598i
$539$	5.50657	−	22.5539i	0.237185	−	0.971465i
$540$	−1.24638	−	0.847970i	−0.0536357	−	0.0364908i
$541$		−	0.696188i		−	0.0299315i	−0.999888	−	0.0149657i	$-0.995236\pi$
$541$		−	0.696188i		−	0.0299315i	0.999888	−	0.0149657i	$-0.00476392\pi$
$542$	22.1606			0.951880
$543$		−	7.90098i		−	0.339064i
$544$		−	27.7961i		−	1.19175i
$545$	−12.9278	+	19.0018i	−0.553765	+	0.813947i
$546$	13.2716	−	12.2273i	0.567972	−	0.523280i
$547$	−27.6211			−1.18099			−0.590496	−	0.807041i	$-0.701068\pi$
$547$	−27.6211			−1.18099			−0.590496	+	0.807041i	$0.701068\pi$
$548$			6.17810i			0.263915i
$549$	−15.3838			−0.656564
$550$	5.87481	+	26.4742i	0.250503	+	1.12886i
$551$			30.9061i			1.31664i
$552$		−	4.72551i		−	0.201131i
$553$	16.0482	−	14.7854i	0.682441	−	0.628741i
$554$	−17.3256			−0.736093
$555$	−3.66486	+	5.38676i	−0.155565	+	0.228655i
$556$	−4.92176			−0.208729
$557$	36.7731			1.55813			0.779063	−	0.626946i	$-0.215695\pi$
$557$	36.7731			1.55813			0.779063	+	0.626946i	$0.215695\pi$
$558$		−	1.41302i		−	0.0598180i
$559$		−	22.1609i		−	0.937305i
$560$	−4.24220	−	28.6398i	−0.179266	−	1.21025i
$561$	3.94620	−	24.8313i	0.166609	−	1.04838i
$562$		−	18.8016i		−	0.793099i
$563$		−	3.23737i		−	0.136439i	−0.997670	−	0.0682195i	$-0.978268\pi$
$563$		−	3.23737i		−	0.136439i	0.997670	−	0.0682195i	$-0.0217318\pi$
$564$	7.25098			0.305321
$565$	18.9028	−	27.7842i	0.795248	−	1.16889i
$566$			35.4560i			1.49033i
$567$	1.79271	+	1.94582i	0.0752866	+	0.0817167i
$568$	−3.36888			−0.141355
$569$			9.36538i			0.392617i	0.980542	+	0.196309i	$0.0628954\pi$
$569$			9.36538i			0.392617i	−0.980542	+	0.196309i	$0.937105\pi$
$570$	−17.3289	−	11.7896i	−0.725827	−	0.493813i
$571$			12.0341i			0.503611i	0.967778	+	0.251805i	$0.0810243\pi$
$571$			12.0341i			0.503611i	−0.967778	+	0.251805i	$0.918976\pi$
$572$	−1.46371	+	9.21035i	−0.0612008	+	0.385104i
$573$	−0.577417			−0.0241219
$574$	−9.86718	−	10.7099i	−0.411848	−	0.447023i
$575$	−10.1365	+	4.00138i	−0.422723	+	0.166869i
$576$	3.79172			0.157988
$577$	−2.09996			−0.0874223			−0.0437111	−	0.999044i	$-0.513918\pi$
$577$	−2.09996			−0.0874223			−0.0437111	+	0.999044i	$0.513918\pi$
$578$	66.1799			2.75272
$579$	14.2196			0.590948
$580$	4.57226	−	6.72049i	0.189853	−	0.279053i
$581$	10.7908	−	9.94171i	0.447678	−	0.412451i
$582$	−14.3971			−0.596778
$583$	−5.80605	+	36.5344i	−0.240462	+	1.51310i
$584$		−	4.89303i		−	0.202475i
$585$	5.24612	−	7.71097i	0.216900	−	0.318809i
$586$		−	11.6735i		−	0.482226i
$587$	−41.4514			−1.71088			−0.855441	−	0.517901i	$-0.826714\pi$
$587$	−41.4514			−1.71088			−0.855441	+	0.517901i	$0.826714\pi$
$588$	0.385902	−	4.70338i	0.0159143	−	0.193964i
$589$		−	4.95277i		−	0.204075i
$590$	−22.3725	+	32.8841i	−0.921062	+	1.35382i
$591$	−2.26374			−0.0931179
$592$			14.2592i			0.586049i
$593$		−	35.3731i		−	1.45260i	−0.687377	−	0.726300i	$-0.741238\pi$
$593$		−	35.3731i		−	1.45260i	0.687377	−	0.726300i	$-0.258762\pi$
$594$	−5.35642	−	0.851244i	−0.219777	−	0.0349270i
$595$	44.3651	−	6.57146i	1.81879	−	0.269404i
$596$		−	11.4309i		−	0.468228i
$597$		−	0.287141i		−	0.0117519i
$598$	−14.8658			−0.607907
$599$	−29.7933			−1.21732			−0.608662	−	0.793430i	$-0.708293\pi$
$599$	−29.7933			−1.21732			−0.608662	+	0.793430i	$0.708293\pi$
$600$	−3.98040	−	10.0834i	−0.162499	−	0.411652i
$601$	39.9860			1.63106			0.815531	−	0.578713i	$-0.196445\pi$
$601$	39.9860			1.63106			0.815531	+	0.578713i	$0.196445\pi$
$602$	−15.5763	−	16.9066i	−0.634842	−	0.689062i
$603$			10.6944i			0.435508i
$604$			11.0121i			0.448075i
$605$	15.0453	+	19.4587i	0.611677	+	0.791107i
$606$	−1.34989			−0.0548356
$607$			0.361266i			0.0146634i	0.999973	+	0.00733168i	$0.00233377\pi$
$607$			0.361266i			0.0146634i	−0.999973	+	0.00733168i	$0.997666\pi$
$608$	−21.0163			−0.852325
$609$	−10.4919	+	9.66627i	−0.425151	+	0.391697i
$610$	46.5093	+	31.6424i	1.88311	+	1.28116i
$611$			44.8595i			1.81482i
$612$		−	5.11080i		−	0.206592i
$613$	−26.4191			−1.06706			−0.533528	−	0.845782i	$-0.679134\pi$
$613$	−26.4191			−1.06706			−0.533528	+	0.845782i	$0.679134\pi$
$614$			25.2452i			1.01881i
$615$	−6.22260	−	4.23351i	−0.250919	−	0.170712i
$616$	−10.5352	−	15.8419i	−0.424476	−	0.638288i
$617$		−	23.7919i		−	0.957825i	−0.877863	−	0.478912i	$-0.841031\pi$
$617$		−	23.7919i		−	0.957825i	0.877863	−	0.478912i	$-0.158969\pi$
$618$	18.8577			0.758567
$619$			20.1966i			0.811770i	0.913924	+	0.405885i	$0.133037\pi$
$619$			20.1966i			0.811770i	−0.913924	+	0.405885i	$0.866963\pi$
$620$	−0.732715	+	1.07698i	−0.0294265	+	0.0432524i
$621$		−	2.17955i		−	0.0874622i
$622$		−	49.7753i		−	1.99581i
$623$	3.16497	−	2.91592i	0.126802	−	0.116824i
$624$		−	20.4116i		−	0.817116i
$625$	−18.2591	+	17.0765i	−0.730364	+	0.683058i
$626$	−50.9070			−2.03465
$627$	−18.7747	−	2.98369i	−0.749791	−	0.119157i
$628$	0.344130			0.0137323
$629$	−22.0885			−0.880725
$630$	−1.41754	−	9.57008i	−0.0564763	−	0.381281i
$631$	−21.8127			−0.868351			−0.434175	−	0.900828i	$-0.642960\pi$
$631$	−21.8127			−0.868351			−0.434175	+	0.900828i	$0.642960\pi$
$632$		−	17.8817i		−	0.711294i
$633$			15.6678i			0.622739i
$634$		−	46.7114i		−	1.85515i
$635$	14.3939	+	9.79284i	0.571206	+	0.388617i
$636$			7.51953i			0.298169i
$637$	29.0983	+	2.38746i	1.15292	+	0.0945944i
$638$	4.58991	−	28.8818i	0.181716	−	1.14344i
$639$	−1.55383			−0.0614685
$640$	−25.0208	−	17.0228i	−0.989032	−	0.672884i
$641$	16.3512			0.645834			0.322917	−	0.946427i	$-0.395337\pi$
$641$	16.3512			0.645834			0.322917	+	0.946427i	$0.395337\pi$
$642$	15.8478			0.625465
$643$	−18.3877			−0.725141			−0.362571	−	0.931956i	$-0.618101\pi$
$643$	−18.3877			−0.725141			−0.362571	+	0.931956i	$0.618101\pi$
$644$	−2.85915	+	2.63417i	−0.112666	+	0.103801i
$645$	−9.82296	−	6.68301i	−0.386779	−	0.263143i
$646$		−	71.0572i		−	2.79571i
$647$	−2.00293			−0.0787434			−0.0393717	−	0.999225i	$-0.512536\pi$
$647$	−2.00293			−0.0787434			−0.0393717	+	0.999225i	$0.512536\pi$
$648$	2.16812			0.0851716
$649$	−5.66198	+	35.6278i	−0.222252	+	1.39851i
$650$	−31.7209	+	12.5218i	−1.24419	+	0.491144i
$651$	1.68134	−	1.54904i	0.0658971	−	0.0607118i
$652$		−	16.4464i		−	0.644091i
$653$		−	4.94844i		−	0.193647i	−0.995302	−	0.0968236i	$-0.969132\pi$
$653$		−	4.94844i		−	0.193647i	0.995302	−	0.0968236i	$-0.0308683\pi$
$654$			16.8076i			0.657231i
$655$	−5.35293	−	3.64184i	−0.209156	−	0.142299i
$656$	−16.4717			−0.643112
$657$		−	2.25681i		−	0.0880466i
$658$	31.5305	+	34.2235i	1.22919	+	1.33417i
$659$			4.46793i			0.174046i	0.996206	+	0.0870228i	$0.0277353\pi$
$659$			4.46793i			0.174046i	−0.996206	+	0.0870228i	$0.972265\pi$
$660$	3.64114	+	3.42634i	0.141731	+	0.133370i
$661$		−	0.732284i		−	0.0284826i	−0.999899	−	0.0142413i	$-0.995467\pi$
$661$		−	0.732284i		−	0.0284826i	0.999899	−	0.0142413i	$-0.00453329\pi$
$662$	43.5149			1.69125
$663$	31.6189			1.22798
$664$		−	12.0236i		−	0.466606i
$665$	−4.96862	−	33.5440i	−0.192675	−	1.30078i
$666$			4.76475i			0.184630i
$667$	11.7521			0.455044
$668$		−	9.88052i		−	0.382289i
$669$	−21.1236			−0.816684
$670$	21.9969	−	32.3319i	0.849814	−	1.24909i
$671$	50.3899	+	8.00798i	1.94528	+	0.309145i
$672$	−6.57314	−	7.13453i	−0.253564	−	0.275221i
$673$	27.7263			1.06877			0.534386	−	0.845241i	$-0.320543\pi$
$673$	27.7263			1.06877			0.534386	+	0.845241i	$0.320543\pi$
$674$	31.0764			1.19702
$675$	−1.83588	−	4.65076i	−0.0706630	−	0.179008i
$676$	−2.96376			−0.113991
$677$			20.7844i			0.798809i	0.916775	+	0.399405i	$0.130783\pi$
$677$			20.7844i			0.798809i	−0.916775	+	0.399405i	$0.869217\pi$
$678$		−	24.5759i		−	0.943833i
$679$	−15.7830	−	17.1310i	−0.605695	−	0.657427i
$680$	20.6735	−	30.3868i	0.792793	−	1.16528i
$681$		−	7.65754i		−	0.293438i
$682$	−0.735544	+	4.62838i	−0.0281654	+	0.177230i
$683$			20.6169i			0.788882i	0.918921	+	0.394441i	$0.129062\pi$
$683$			20.6169i			0.788882i	−0.918921	+	0.394441i	$0.870938\pi$
$684$	−3.86423			−0.147752
$685$	−11.5265	+	16.9421i	−0.440405	+	0.647326i
$686$	23.8773	−	18.6310i	0.911639	−	0.711336i
$687$			19.9463i			0.761000i
$688$	−26.0022			−0.991323
$689$	−46.5209			−1.77231
$690$	−4.48304	+	6.58935i	−0.170666	+	0.250852i
$691$			2.23979i			0.0852056i	0.999092	+	0.0426028i	$0.0135650\pi$
$691$			2.23979i			0.0852056i	−0.999092	+	0.0426028i	$0.986435\pi$
$692$		−	11.4935i		−	0.436918i
$693$	−4.85916	−	7.30675i	−0.184584	−	0.277561i
$694$	11.8876			0.451246
$695$	−13.4969	−	9.18254i	−0.511966	−	0.348314i
$696$			11.6905i			0.443127i
$697$		−	25.5158i		−	0.966480i
$698$	1.45329			0.0550080
$699$	−5.69495			−0.215403
$700$	−3.88209	+	8.02917i	−0.146729	+	0.303474i
$701$			12.8382i			0.484891i	0.970165	+	0.242446i	$0.0779496\pi$
$701$			12.8382i			0.484891i	−0.970165	+	0.242446i	$0.922050\pi$
$702$		−	6.82058i		−	0.257426i
$703$			16.7009i			0.629886i
$704$	−12.4199	−	1.97377i	−0.468091	−	0.0743891i
$705$	19.8843	+	13.5282i	0.748885	+	0.509501i
$706$	21.1871			0.797388
$707$	−1.47984	−	1.60623i	−0.0556549	−	0.0604083i
$708$			7.33293i			0.275589i
$709$	5.22136			0.196092			0.0980462	−	0.995182i	$-0.468741\pi$
$709$	5.22136			0.196092			0.0980462	+	0.995182i	$0.468741\pi$
$710$	4.69764	+	3.19602i	0.176299	+	0.119944i
$711$		−	8.24756i		−	0.309308i
$712$		−	3.52655i		−	0.132163i
$713$	−1.88331			−0.0705304
$714$	24.1222	−	22.2241i	0.902750	−	0.831715i
$715$	−21.1977	+	22.5266i	−0.792749	+	0.842446i
$716$	12.8652			0.480794
$717$		−	9.91495i		−	0.370281i
$718$		−	13.6327i		−	0.508769i
$719$		−	13.5036i		−	0.503599i	−0.967779	−	0.251800i	$-0.918978\pi$
$719$		−	13.5036i		−	0.503599i	0.967779	−	0.251800i	$-0.0810224\pi$
$720$	−9.04756	−	6.15546i	−0.337183	−	0.229401i
$721$	20.6730	+	22.4386i	0.769902	+	0.835658i
$722$	−22.6552			−0.843138
$723$	2.07373			0.0771228
$724$			5.32660i			0.197962i
$725$	25.0769	−	9.89906i	0.931333	−	0.367642i
$726$	17.1020	+	5.57653i	0.634713	+	0.206965i
$727$	1.97850			0.0733786			0.0366893	−	0.999327i	$-0.488319\pi$
$727$	1.97850			0.0733786			0.0366893	+	0.999327i	$0.488319\pi$
$728$	17.5959	−	16.2113i	0.652147	−	0.600831i
$729$	1.00000			0.0370370
$730$	−4.64196	+	6.82295i	−0.171807	+	0.252529i
$731$		−	40.2791i		−	1.48978i
$732$	10.3713			0.383333
$733$		−	3.81876i		−	0.141049i	−0.997510	−	0.0705245i	$-0.977533\pi$
$733$		−	3.81876i		−	0.141049i	0.997510	−	0.0705245i	$-0.0224673\pi$
$734$	−37.5457			−1.38584
$735$	9.83337	−	12.1780i	0.362709	−	0.449194i
$736$			7.99153i			0.294572i
$737$	5.56692	−	35.0296i	0.205060	−	1.29033i
$738$	−5.50407			−0.202608
$739$			12.4867i			0.459332i	0.973270	+	0.229666i	$0.0737633\pi$
$739$			12.4867i			0.459332i	−0.973270	+	0.229666i	$0.926237\pi$
$740$	2.47074	−	3.63159i	0.0908261	−	0.133500i
$741$		−	23.9067i		−	0.878236i
$742$	−35.4910	+	32.6983i	−1.30292	+	1.20039i
$743$	−37.0586			−1.35955			−0.679775	−	0.733421i	$-0.737922\pi$
$743$	−37.0586			−1.35955			−0.679775	+	0.733421i	$0.737922\pi$
$744$		−	1.87343i		−	0.0686832i
$745$	21.3267	−	31.3469i	0.781350	−	1.14846i
$746$	−57.3623			−2.10018
$747$		−	5.54564i		−	0.202904i
$748$	−2.66041	+	16.7405i	−0.0972742	+	0.612094i
$749$	17.3734	+	18.8572i	0.634810	+	0.689028i
$750$	−4.01563	+	17.8366i	−0.146630	+	0.651302i
$751$	3.95633			0.144369			0.0721843	−	0.997391i	$-0.477003\pi$
$751$	3.95633			0.144369			0.0721843	+	0.997391i	$0.477003\pi$
$752$	52.6353			1.91941
$753$			9.03128i			0.329118i
$754$	36.7766			1.33932
$755$	−20.5453	+	30.1983i	−0.747720	+	1.09903i
$756$	−1.20859	−	1.31181i	−0.0439559	−	0.0477101i
$757$			20.8523i			0.757888i	0.925420	+	0.378944i	$0.123713\pi$
$757$			20.8523i			0.757888i	−0.925420	+	0.378944i	$0.876287\pi$
$758$	8.33864			0.302873
$759$	−1.13456	+	7.13915i	−0.0411818	+	0.259135i
$760$	−22.9752	−	15.6310i	−0.833396	−	0.566997i
$761$	−37.0384			−1.34264			−0.671320	−	0.741167i	$-0.734273\pi$
$761$	−37.0384			−1.34264			−0.671320	+	0.741167i	$0.734273\pi$
$762$	12.7319			0.461226
$763$	−19.9993	+	18.4256i	−0.724023	+	0.667051i
$764$	0.389276			0.0140835
$765$	9.53524	−	14.0153i	0.344747	−	0.506724i
$766$	−3.61661			−0.130673
$767$	−45.3665			−1.63809
$768$	−14.5482			−0.524962
$769$	20.7036			0.746590			0.373295	−	0.927713i	$-0.378228\pi$
$769$	20.7036			0.746590			0.373295	+	0.927713i	$0.378228\pi$
$770$	−0.338481	+	32.0849i	−0.0121980	+	1.15626i
$771$	15.2678			0.549855
$772$	−9.58645			−0.345024
$773$	−9.70891			−0.349205			−0.174603	−	0.984639i	$-0.555864\pi$
$773$	−9.70891			−0.349205			−0.174603	+	0.984639i	$0.555864\pi$
$774$	−8.68870			−0.312309
$775$	−4.01863	+	1.58635i	−0.144354	+	0.0569833i
$776$	−19.0881			−0.685223
$777$	−5.66954	+	5.22342i	−0.203394	+	0.187389i
$778$	−55.1962			−1.97888
$779$	−19.2923			−0.691217
$780$	−3.53677	+	5.19850i	−0.126637	+	0.186136i
$781$	5.08959	+	0.808840i	0.182120	+	0.0289426i
$782$	−27.0197			−0.966223
$783$			5.39200i			0.192694i
$784$	2.80129	−	34.1421i	0.100046	−	1.21936i
$785$	0.943704	+	0.642045i	0.0336822	+	0.0229156i
$786$	−4.73483			−0.168886
$787$		−	7.13561i		−	0.254357i	−0.991880	−	0.127178i	$-0.959408\pi$
$787$		−	7.13561i		−	0.254357i	0.991880	−	0.127178i	$-0.0405921\pi$
$788$	1.52614			0.0543667
$789$	6.40729			0.228106
$790$	−16.9641	+	24.9346i	−0.603556	+	0.887132i
$791$	29.2427	−	26.9417i	1.03975	−	0.957935i
$792$	−7.10171	−	1.12861i	−0.252348	−	0.0401032i
$793$			64.1638i			2.27852i
$794$	−12.7733			−0.453307
$795$	−14.0292	+	20.6207i	−0.497565	+	0.731341i
$796$			0.193582i			0.00686132i
$797$	18.5441			0.656866			0.328433	−	0.944527i	$-0.393480\pi$
$797$	18.5441			0.656866			0.328433	+	0.944527i	$0.393480\pi$
$798$	−16.8034	−	18.2385i	−0.594834	−	0.645638i
$799$			81.5357i			2.88453i
$800$	6.73143	+	17.0525i	0.237992	+	0.602896i
$801$		−	1.62655i		−	0.0574713i
$802$	23.5064			0.830041
$803$	−1.17478	+	7.39223i	−0.0414569	+	0.260866i
$804$		−	7.20982i		−	0.254271i
$805$	−12.7552	+	1.88933i	−0.449562	+	0.0665902i
$806$	−5.89353			−0.207591
$807$		−	13.5541i		−	0.477128i
$808$	−1.78973			−0.0629624
$809$			25.3382i			0.890845i	0.895320	+	0.445422i	$0.146947\pi$
$809$			25.3382i			0.890845i	−0.895320	+	0.445422i	$0.853053\pi$
$810$	−3.02327	−	2.05687i	−0.106227	−	0.0722709i
$811$	14.9314			0.524311			0.262155	−	0.965026i	$-0.415567\pi$
$811$	14.9314			0.524311			0.262155	+	0.965026i	$0.415567\pi$
$812$	7.07329	−	6.51671i	0.248224	−	0.228692i
$813$	13.5515			0.475272
$814$	2.48027	−	15.6070i	0.0869336	−	0.547026i
$815$	30.6841	−	45.1008i	1.07482	−	1.57981i
$816$		−	37.0996i		−	1.29875i
$817$	−30.4547			−1.06547
$818$	−19.4748			−0.680920
$819$	8.11575	−	7.47715i	0.283587	−	0.261273i
$820$	4.19508	+	2.85411i	0.146499	+	0.0996697i
$821$		−	31.8707i		−	1.11230i	−0.831083	−	0.556148i	$-0.812279\pi$
$821$		−	31.8707i		−	1.11230i	0.831083	−	0.556148i	$-0.187721\pi$
$822$			14.9858i			0.522691i
$823$			5.84104i			0.203606i	0.994805	+	0.101803i	$0.0324611\pi$
$823$			5.84104i			0.203606i	−0.994805	+	0.101803i	$0.967539\pi$
$824$	25.0021			0.870989
$825$	3.59252	+	16.1893i	0.125076	+	0.563639i
$826$	−34.6103	+	31.8869i	−1.20425	+	1.10949i
$827$	−12.8645			−0.447341			−0.223671	−	0.974665i	$-0.571804\pi$
$827$	−12.8645			−0.447341			−0.223671	+	0.974665i	$0.571804\pi$
$828$			1.46938i			0.0510646i
$829$		−	4.31992i		−	0.150037i	−0.997182	−	0.0750185i	$-0.976098\pi$
$829$		−	4.31992i		−	0.150037i	0.997182	−	0.0750185i	$-0.0239016\pi$
$830$	−11.4066	+	16.7660i	−0.395930	+	0.581955i
$831$	−10.5948			−0.367530
$832$		−	15.8148i		−	0.548279i
$833$	52.8885	+	4.33939i	1.83248	+	0.150351i
$834$	−11.9384			−0.413393
$835$	18.4341	−	27.0952i	0.637939	−	0.937669i
$836$	12.6574	+	2.01151i	0.437764	+	0.0695695i
$837$		−	0.864081i		−	0.0298670i
$838$			4.29597i			0.148402i
$839$			46.0836i			1.59098i	0.605965	+	0.795491i	$0.292787\pi$
$839$			46.0836i			1.59098i	−0.605965	+	0.795491i	$0.707213\pi$
$840$	−1.87942	−	12.6883i	−0.0648462	−	0.437788i
$841$	−0.0736920			−0.00254110
$842$	22.0330			0.759307
$843$		−	11.4974i		−	0.395993i
$844$		−	10.5627i		−	0.363584i
$845$	−8.12749	−	5.52950i	−0.279594	−	0.190221i
$846$	17.5882			0.604696
$847$	12.1128	+	26.4628i	0.416199	+	0.909273i
$848$			54.5847i			1.87445i
$849$			21.6818i			0.744117i
$850$	−57.6552	+	22.7593i	−1.97756	+	0.780637i
$851$	6.35056			0.217694
$852$	1.04754			0.0358882
$853$			32.2381i			1.10381i	0.833907	+	0.551906i	$0.186099\pi$
$853$			32.2381i			1.10381i	−0.833907	+	0.551906i	$0.813901\pi$
$854$	45.0990	+	48.9508i	1.54326	+	1.67506i
$855$	−10.5968	−	7.20950i	−0.362404	−	0.246560i
$856$	21.0116			0.718160
$857$			29.0750i			0.993182i	0.867985	+	0.496591i	$0.165415\pi$
$857$			29.0750i			0.993182i	−0.867985	+	0.496591i	$0.834585\pi$
$858$	−3.55043	+	22.3409i	−0.121210	+	0.762707i
$859$			27.8898i			0.951588i	0.879557	+	0.475794i	$0.157839\pi$
$859$			27.8898i			0.951588i	−0.879557	+	0.475794i	$0.842161\pi$
$860$	6.62234	+	4.50548i	0.225820	+	0.153635i
$861$	−6.03390	−	6.54925i	−0.205635	−	0.223198i
$862$			29.2095i			0.994880i
$863$		−	53.7247i		−	1.82881i	−0.404799	−	0.914406i	$-0.632658\pi$
$863$		−	53.7247i		−	1.82881i	0.404799	−	0.914406i	$-0.367342\pi$
$864$	−3.66660			−0.124740
$865$	21.4435	−	31.5185i	0.729100	−	1.07166i
$866$	0.908924			0.0308865
$867$	40.4698			1.37443
$868$	−1.13351	+	1.04432i	−0.0384739	+	0.0354464i
$869$	−4.29324	+	27.0150i	−0.145638	+	0.916423i
$870$	11.0906	−	16.3015i	0.376007	−	0.552672i
$871$	44.6048			1.51138
$872$			22.2841i			0.754634i
$873$	−8.80400			−0.297970
$874$			20.4293i			0.691033i
$875$	−25.6259	+	14.7755i	−0.866313	+	0.499502i
$876$			1.52147i			0.0514058i
$877$	31.4715			1.06272			0.531358	−	0.847147i	$-0.321682\pi$
$877$	31.4715			1.06272			0.531358	+	0.847147i	$0.321682\pi$
$878$	32.1770			1.08592
$879$		−	7.13847i		−	0.240774i
$880$	26.4313	+	24.8720i	0.890997	+	0.838436i
$881$			31.4582i			1.05985i	0.848044	+	0.529926i	$0.177780\pi$
$881$			31.4582i			1.05985i	−0.848044	+	0.529926i	$0.822220\pi$
$882$	0.936058	−	11.4087i	0.0315187	−	0.384150i
$883$		−	33.5011i		−	1.12740i	−0.825980	−	0.563700i	$-0.809377\pi$
$883$		−	33.5011i		−	1.12740i	0.825980	−	0.563700i	$-0.190623\pi$
$884$	−21.3165			−0.716951
$885$	−13.6811	+	20.1090i	−0.459885	+	0.675958i
$886$		−	66.5314i		−	2.23517i
$887$		−	48.3621i		−	1.62384i	−0.583768	−	0.811920i	$-0.698422\pi$
$887$		−	48.3621i		−	1.62384i	0.583768	−	0.811920i	$-0.301578\pi$
$888$			6.31725i			0.211993i
$889$	13.9575	+	15.1495i	0.468118	+	0.508099i
$890$	−3.34559	+	4.91749i	−0.112145	+	0.164835i
$891$	−3.27552	−	0.520547i	−0.109734	−	0.0174390i
$892$	14.2408			0.476819
$893$	61.6484			2.06298
$894$		−	27.7272i		−	0.927337i
$895$	35.2800	+	24.0026i	1.17928	+	0.802319i
$896$	−24.2620	−	26.3342i	−0.810538	−	0.879764i
$897$	−9.09061			−0.303527
$898$	−25.4024			−0.847687
$899$	4.65913			0.155391
$900$	1.23769	+	3.13540i	0.0412564	+	0.104513i
$901$	−84.5554			−2.81695
$902$	18.0287	+	2.86512i	0.600290	+	0.0953982i
$903$	−9.52509	−	10.3386i	−0.316975	−	0.344048i
$904$		−	32.5835i		−	1.08371i
$905$	−9.93786	+	14.6071i	−0.330346	+	0.485556i
$906$			26.7113i			0.887424i
$907$			36.1121i			1.19908i	0.800344	+	0.599541i	$0.204650\pi$
$907$			36.1121i			1.19908i	−0.800344	+	0.599541i	$0.795350\pi$
$908$			5.16248i			0.171323i
$909$	−0.825476			−0.0273793
$910$	−39.9156	+	5.91239i	−1.32319	+	0.195994i
$911$	−24.7742			−0.820804			−0.410402	−	0.911905i	$-0.634612\pi$
$911$	−24.7742			−0.820804			−0.410402	+	0.911905i	$0.634612\pi$
$912$	−28.0507			−0.928850
$913$	−2.88677	+	18.1649i	−0.0955380	+	0.601169i
$914$	47.1047			1.55809
$915$	28.4410	+	19.3497i	0.940232	+	0.639682i
$916$		−	13.4472i		−	0.444308i
$917$	−5.19061	−	5.63393i	−0.171409	−	0.186049i
$918$		−	12.3969i		−	0.409160i
$919$			25.4495i			0.839501i	0.907639	+	0.419751i	$0.137882\pi$
$919$			25.4495i			0.839501i	−0.907639	+	0.419751i	$0.862118\pi$
$920$	−5.94375	+	8.73637i	−0.195960	+	0.288030i
$921$			15.4378i			0.508692i
$922$	32.5833			1.07307
$923$			6.48082i			0.213319i
$924$	3.27589	+	4.92599i	0.107769	+	0.162053i
$925$	13.5509	−	5.34921i	0.445552	−	0.175881i
$926$		−	14.5178i		−	0.477085i
$927$	11.5317			0.378751
$928$		−	19.7703i		−	0.648992i
$929$		−	40.7403i		−	1.33665i	−0.743871	−	0.668324i	$-0.767012\pi$
$929$		−	40.7403i		−	1.33665i	0.743871	−	0.668324i	$-0.232988\pi$
$930$	−1.77730	+	2.61235i	−0.0582799	+	0.0856623i
$931$	3.28097	−	39.9885i	0.107529	−	1.31057i
$932$	3.83936			0.125762
$933$		−	30.4383i		−	0.996504i
$934$	−52.2637			−1.71012
$935$	−38.5285	+	40.9438i	−1.26002	+	1.33901i
$936$		−	9.04293i		−	0.295578i
$937$		−	7.83618i		−	0.255997i	−0.991774	−	0.127998i	$-0.959145\pi$
$937$		−	7.83618i		−	0.255997i	0.991774	−	0.127998i	$-0.0408552\pi$
$938$	34.0292	−	31.3515i	1.11109	−	1.02366i
$939$	−31.1303			−1.01590
$940$	−13.4054	−	9.12028i	−0.437235	−	0.297471i
$941$	4.89025			0.159418			0.0797089	−	0.996818i	$-0.474601\pi$
$941$	4.89025			0.159418			0.0797089	+	0.996818i	$0.474601\pi$
$942$	0.834734			0.0271971
$943$			7.33594i			0.238891i
$944$			53.2302i			1.73250i
$945$	−0.866846	−	5.85223i	−0.0281985	−	0.190373i
$946$	28.4600	+	4.52287i	0.925315	+	0.147051i
$947$		−	16.5945i		−	0.539248i	−0.962966	−	0.269624i	$-0.913101\pi$
$947$		−	16.5945i		−	0.539248i	0.962966	−	0.269624i	$-0.0868995\pi$
$948$			5.56025i			0.180589i
$949$	−9.41287			−0.305555
$950$	17.2081	+	43.5925i	0.558303	+	1.41433i
$951$		−	28.5646i		−	0.926272i
$952$	31.9819	−	29.4653i	1.03654	−	0.954977i
$953$	−38.7567			−1.25545			−0.627726	−	0.778434i	$-0.716014\pi$
$953$	−38.7567			−1.25545			−0.627726	+	0.778434i	$0.716014\pi$
$954$			18.2396i			0.590530i
$955$	1.06751	+	0.726275i	0.0345438	+	0.0235017i
$956$			6.68436i			0.216188i
$957$	2.80679	−	17.6616i	0.0907306	−	0.570919i
$958$	15.3153			0.494813
$959$	−17.8315	+	16.4284i	−0.575810	+	0.530501i
$960$	−7.01000	−	4.76922i	−0.226247	−	0.153926i
$961$	30.2534			0.975915
$962$	19.8732			0.640737
$963$	9.69116			0.312293
$964$	−1.39804			−0.0450280
$965$	−26.2888	−	17.8855i	−0.846267	−	0.575754i
$966$	−6.93526	+	6.38954i	−0.223138	+	0.205580i
$967$	−9.16393			−0.294692			−0.147346	−	0.989085i	$-0.547073\pi$
$967$	−9.16393			−0.294692			−0.147346	+	0.989085i	$0.547073\pi$
$968$	22.6743	+	7.39354i	0.728779	+	0.237637i
$969$		−	43.4524i		−	1.39589i
$970$	26.6169	+	18.1087i	0.854616	+	0.581434i
$971$			23.3469i			0.749237i	0.927179	+	0.374619i	$0.122226\pi$
$971$			23.3469i			0.749237i	−0.927179	+	0.374619i	$0.877774\pi$
$972$	−0.674169			−0.0216240
$973$	−13.0876	−	14.2054i	−0.419570	−	0.455404i
$974$			25.9327i			0.830936i
$975$	−19.3977	+	7.65721i	−0.621224	+	0.245227i
$976$	75.2857			2.40984
$977$		−	29.9628i		−	0.958596i	−0.877652	−	0.479298i	$-0.840891\pi$
$977$		−	29.9628i		−	0.958596i	0.877652	−	0.479298i	$-0.159109\pi$
$978$		−	39.8930i		−	1.27564i
$979$	−0.846694	+	5.32779i	−0.0270605	+	0.170277i
$980$	−6.62936	+	8.21007i	−0.211767	+	0.262261i
$981$			10.2781i			0.328154i
$982$			43.5329i			1.38919i
$983$	−24.6226			−0.785338			−0.392669	−	0.919680i	$-0.628448\pi$
$983$	−24.6226			−0.785338			−0.392669	+	0.919680i	$0.628448\pi$
$984$	−7.29746			−0.232635
$985$	4.18513	+	2.84733i	0.133349	+	0.0907236i
$986$	66.8443			2.12876
$987$	19.2813	+	20.9281i	0.613731	+	0.666149i
$988$			16.1172i			0.512756i
$989$			11.5805i			0.368238i
$990$	8.83208	+	8.31106i	0.280702	+	0.264143i
$991$	12.5327			0.398115			0.199058	−	0.979988i	$-0.436212\pi$
$991$	12.5327			0.398115			0.199058	+	0.979988i	$0.436212\pi$
$992$			3.16824i			0.100592i
$993$	26.6099			0.844439
$994$	4.55519	+	4.94424i	0.144482	+	0.156822i
$995$	−0.361166	+	0.530857i	−0.0114497	+	0.0168293i
$996$			3.73870i			0.118465i
$997$		−	17.7248i		−	0.561349i	−0.959803	−	0.280675i	$-0.909442\pi$
$997$		−	17.7248i		−	0.561349i	0.959803	−	0.280675i	$-0.0905582\pi$
$998$	19.9927			0.632857
$999$			2.91371i			0.0921856i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.k.a.769.14	yes	48
5.4	even	2		1155.2.k.b.769.35	yes	48
7.6	odd	2		1155.2.k.b.769.13	yes	48
11.10	odd	2	inner	1155.2.k.a.769.35	yes	48
35.34	odd	2	inner	1155.2.k.a.769.36	yes	48
55.54	odd	2		1155.2.k.b.769.14	yes	48
77.76	even	2		1155.2.k.b.769.36	yes	48
385.384	even	2	inner	1155.2.k.a.769.13	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.k.a.769.13	✓	48	385.384	even	2	inner
1155.2.k.a.769.14	yes	48	1.1	even	1	trivial
1155.2.k.a.769.35	yes	48	11.10	odd	2	inner
1155.2.k.a.769.36	yes	48	35.34	odd	2	inner
1155.2.k.b.769.13	yes	48	7.6	odd	2
1155.2.k.b.769.14	yes	48	55.54	odd	2
1155.2.k.b.769.35	yes	48	5.4	even	2
1155.2.k.b.769.36	yes	48	77.76	even	2

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)

\(f(q)\)	\(=\)	\(q-1.63529 q^{2} -1.00000 q^{3} +0.674169 q^{4} +(1.84877 + 1.25780i) q^{5} +1.63529 q^{6} +(1.79271 + 1.94582i) q^{7} +2.16812 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.63529 q^{2} -1.00000 q^{3} +0.674169 q^{4} +(1.84877 + 1.25780i) q^{5} +1.63529 q^{6} +(1.79271 + 1.94582i) q^{7} +2.16812 q^{8} +1.00000 q^{9} +(-3.02327 - 2.05687i) q^{10} +(-3.27552 - 0.520547i) q^{11} -0.674169 q^{12} -4.17087i q^{13} +(-2.93159 - 3.18197i) q^{14} +(-1.84877 - 1.25780i) q^{15} -4.89383 q^{16} -7.58089i q^{17} -1.63529 q^{18} -5.73183 q^{19} +(1.24638 + 0.847970i) q^{20} +(-1.79271 - 1.94582i) q^{21} +(5.35642 + 0.851244i) q^{22} +2.17955i q^{23} -2.16812 q^{24} +(1.83588 + 4.65076i) q^{25} +6.82058i q^{26} -1.00000 q^{27} +(1.20859 + 1.31181i) q^{28} -5.39200i q^{29} +(3.02327 + 2.05687i) q^{30} +0.864081i q^{31} +3.66660 q^{32} +(3.27552 + 0.520547i) q^{33} +12.3969i q^{34} +(0.866846 + 5.85223i) q^{35} +0.674169 q^{36} -2.91371i q^{37} +9.37321 q^{38} +4.17087i q^{39} +(4.00834 + 2.72706i) q^{40} +3.36581 q^{41} +(2.93159 + 3.18197i) q^{42} +5.31325 q^{43} +(-2.20825 - 0.350936i) q^{44} +(1.84877 + 1.25780i) q^{45} -3.56419i q^{46} -10.7554 q^{47} +4.89383 q^{48} +(-0.572412 + 6.97656i) q^{49} +(-3.00219 - 7.60533i) q^{50} +7.58089i q^{51} -2.81187i q^{52} -11.1538i q^{53} +1.63529 q^{54} +(-5.40093 - 5.08232i) q^{55} +(3.88679 + 4.21876i) q^{56} +5.73183 q^{57} +8.81748i q^{58} -10.8770i q^{59} +(-1.24638 - 0.847970i) q^{60} -15.3838 q^{61} -1.41302i q^{62} +(1.79271 + 1.94582i) q^{63} +3.79172 q^{64} +(5.24612 - 7.71097i) q^{65} +(-5.35642 - 0.851244i) q^{66} +10.6944i q^{67} -5.11080i q^{68} -2.17955i q^{69} +(-1.41754 - 9.57008i) q^{70} -1.55383 q^{71} +2.16812 q^{72} -2.25681i q^{73} +4.76475i q^{74} +(-1.83588 - 4.65076i) q^{75} -3.86423 q^{76} +(-4.85916 - 7.30675i) q^{77} -6.82058i q^{78} -8.24756i q^{79} +(-9.04756 - 6.15546i) q^{80} +1.00000 q^{81} -5.50407 q^{82} -5.54564i q^{83} +(-1.20859 - 1.31181i) q^{84} +(9.53524 - 14.0153i) q^{85} -8.68870 q^{86} +5.39200i q^{87} +(-7.10171 - 1.12861i) q^{88} -1.62655i q^{89} +(-3.02327 - 2.05687i) q^{90} +(8.11575 - 7.47715i) q^{91} +1.46938i q^{92} -0.864081i q^{93} +17.5882 q^{94} +(-10.5968 - 7.20950i) q^{95} -3.66660 q^{96} -8.80400 q^{97} +(0.936058 - 11.4087i) q^{98} +(-3.27552 - 0.520547i) 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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