LMFDB - Embedded newform 220.2.m.b.201.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [220,2,Mod(81,220)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("220.81"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(220, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 220 = 2^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	220.m (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,5] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$1.75670884447$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.159390625.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 6x^{6} - 11x^{5} + 21x^{4} - 5x^{3} + 10x^{2} + 25x + 25 $ x^8 - x^7 + 6x^6 - 11x^5 + 21x^4 - 5x^3 + 10x^2 + 25x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			201.1
Root			$-0.628998 + 0.456994i$ of defining polynomial
Character	$\chi$	$=$	220.201
Dual form			220.2.m.b.81.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0492728 - 0.151646i) q^{3} +(-0.809017 - 0.587785i) q^{5} +(0.628998 - 1.93586i) q^{7} +(2.40648 - 1.74841i) q^{9} +(2.88699 - 1.63256i) q^{11} +(-0.528704 + 0.384126i) q^{13} +(-0.0492728 + 0.151646i) q^{15} +(3.47632 + 2.52570i) q^{17} +(-0.919194 - 2.82899i) q^{19} -0.324558 q^{21} -6.11210 q^{23} +(0.309017 + 0.951057i) q^{25} +(-0.770708 - 0.559952i) q^{27} +(-2.63577 + 8.11208i) q^{29} +(4.34733 - 3.15852i) q^{31} +(-0.389823 - 0.357361i) q^{33} +(-1.64674 + 1.19643i) q^{35} +(1.06768 - 3.28598i) q^{37} +(0.0843020 + 0.0612490i) q^{39} +(1.47374 + 4.53569i) q^{41} -10.1305 q^{43} -2.97458 q^{45} +(2.25733 + 6.94734i) q^{47} +(2.31122 + 1.67920i) q^{49} +(0.211724 - 0.651620i) q^{51} +(-8.99626 + 6.53617i) q^{53} +(-3.29522 - 0.376160i) q^{55} +(-0.383714 + 0.278785i) q^{57} +(1.70562 - 5.24935i) q^{59} +(7.77155 + 5.64636i) q^{61} +(-1.87100 - 5.75835i) q^{63} +0.653514 q^{65} -5.60966 q^{67} +(0.301160 + 0.926876i) q^{69} +(-0.0442449 - 0.0321458i) q^{71} +(-2.20562 + 6.78819i) q^{73} +(0.128998 - 0.0937225i) q^{75} +(-1.34450 - 6.61569i) q^{77} +(-2.37100 + 1.72263i) q^{79} +(2.71064 - 8.34250i) q^{81} +(9.98988 + 7.25807i) q^{83} +(-1.32784 - 4.08666i) q^{85} +1.36004 q^{87} +0.00487932 q^{89} +(0.411059 + 1.26511i) q^{91} +(-0.693182 - 0.503626i) q^{93} +(-0.919194 + 2.82899i) q^{95} +(14.7696 - 10.7307i) q^{97} +(4.09311 - 8.97639i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 5 q^{3} - 2 q^{5} - q^{7} + 3 q^{9} + 5 q^{11} + 4 q^{13} + 5 q^{15} + 9 q^{17} - 7 q^{19} - 28 q^{21} - 10 q^{23} - 2 q^{25} - 10 q^{27} - q^{29} + 22 q^{31} + q^{33} + 4 q^{35} + 4 q^{37} + 27 q^{39}+ \cdots + 60 q^{99}+O(q^{100}) $ 8 * q + 5 * q^3 - 2 * q^5 - q^7 + 3 * q^9 + 5 * q^11 + 4 * q^13 + 5 * q^15 + 9 * q^17 - 7 * q^19 - 28 * q^21 - 10 * q^23 - 2 * q^25 - 10 * q^27 - q^29 + 22 * q^31 + q^33 + 4 * q^35 + 4 * q^37 + 27 * q^39 + 24 * q^41 - 22 * q^43 + 8 * q^45 - 6 * q^47 - 27 * q^49 - 47 * q^51 - q^53 - 5 * q^55 - 25 * q^57 - 9 * q^59 + 22 * q^61 - 21 * q^63 - 26 * q^65 - 2 * q^67 + 11 * q^69 - 22 * q^71 + 5 * q^73 - 5 * q^75 + 16 * q^77 - 25 * q^79 - 28 * q^81 + 33 * q^83 + 4 * q^85 + 14 * q^87 + 8 * q^89 + 14 * q^91 + 31 * q^93 - 7 * q^95 + 20 * q^97 + 60 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$.

$n$	$101$	$111$	$177$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−0.0492728	−	0.151646i	−0.0284477	−	0.0875530i	0.935825	−	0.352466i	$-0.114657\pi$
$3$	−0.0492728	−	0.151646i	−0.0284477	−	0.0875530i	−0.964272	+	0.264913i	$0.914657\pi$
$4$		0			0
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$6$		0			0
$7$	0.628998	−	1.93586i	0.237739	−	0.731685i	−0.759007	−	0.651082i	$-0.774315\pi$
$7$	0.628998	−	1.93586i	0.237739	−	0.731685i	0.996746	−	0.0806031i	$-0.0256846\pi$
$8$		0			0
$9$	2.40648	−	1.74841i	0.802161	−	0.582804i
$10$		0			0
$11$	2.88699	−	1.63256i	0.870461	−	0.492237i
$11$	2.88699	−	1.63256i	0.870461	−	0.492237i
$12$		0			0
$13$	−0.528704	+	0.384126i	−0.146636	+	0.106537i	−0.658685	−	0.752419i	$-0.728887\pi$
$13$	−0.528704	+	0.384126i	−0.146636	+	0.106537i	0.512048	+	0.858957i	$0.328887\pi$
$14$		0			0
$15$	−0.0492728	+	0.151646i	−0.0127222	+	0.0391549i
$16$		0			0
$17$	3.47632	+	2.52570i	0.843132	+	0.612572i	0.923244	−	0.384214i	$-0.125528\pi$
$17$	3.47632	+	2.52570i	0.843132	+	0.612572i	−0.0801115	+	0.996786i	$0.525528\pi$
$18$		0			0
$19$	−0.919194	−	2.82899i	−0.210878	−	0.649015i	−0.999421	−	0.0340351i	$-0.989164\pi$
$19$	−0.919194	−	2.82899i	−0.210878	−	0.649015i	0.788543	−	0.614980i	$-0.210836\pi$
$20$		0			0
$21$	−0.324558			−0.0708243
$22$		0			0
$23$	−6.11210			−1.27446			−0.637230	−	0.770673i	$-0.719920\pi$
$23$	−6.11210			−1.27446			−0.637230	+	0.770673i	$0.719920\pi$
$24$		0			0
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$		0			0
$27$	−0.770708	−	0.559952i	−0.148323	−	0.107763i
$28$		0			0
$29$	−2.63577	+	8.11208i	−0.489451	+	1.50638i	0.335978	+	0.941870i	$0.390933\pi$
$29$	−2.63577	+	8.11208i	−0.489451	+	1.50638i	−0.825429	+	0.564505i	$0.809067\pi$
$30$		0			0
$31$	4.34733	−	3.15852i	0.780803	−	0.567286i	−0.124417	−	0.992230i	$-0.539706\pi$
$31$	4.34733	−	3.15852i	0.780803	−	0.567286i	0.905220	+	0.424944i	$0.139706\pi$
$32$		0			0
$33$	−0.389823	−	0.357361i	−0.0678594	−	0.0622085i
$34$		0			0
$35$	−1.64674	+	1.19643i	−0.278350	+	0.202233i
$36$		0			0
$37$	1.06768	−	3.28598i	0.175526	−	0.540212i	−0.824131	−	0.566399i	$-0.808336\pi$
$37$	1.06768	−	3.28598i	0.175526	−	0.540212i	0.999657	+	0.0261862i	$0.00833629\pi$
$38$		0			0
$39$	0.0843020	+	0.0612490i	0.0134991	+	0.00980769i
$40$		0			0
$41$	1.47374	+	4.53569i	0.230159	+	0.708356i	0.997727	+	0.0673885i	$0.0214667\pi$
$41$	1.47374	+	4.53569i	0.230159	+	0.708356i	−0.767568	+	0.640968i	$0.778533\pi$
$42$		0			0
$43$	−10.1305			−1.54489			−0.772446	−	0.635081i	$-0.780967\pi$
$43$	−10.1305			−1.54489			−0.772446	+	0.635081i	$0.780967\pi$
$44$		0			0
$45$	−2.97458			−0.443424
$46$		0			0
$47$	2.25733	+	6.94734i	0.329265	+	1.01337i	0.969478	+	0.245177i	$0.0788460\pi$
$47$	2.25733	+	6.94734i	0.329265	+	1.01337i	−0.640213	+	0.768197i	$0.721154\pi$
$48$		0			0
$49$	2.31122	+	1.67920i	0.330174	+	0.239885i
$50$		0			0
$51$	0.211724	−	0.651620i	0.0296473	−	0.0912450i
$52$		0			0
$53$	−8.99626	+	6.53617i	−1.23573	+	0.897812i	−0.997306	−	0.0733491i	$-0.976631\pi$
$53$	−8.99626	+	6.53617i	−1.23573	+	0.897812i	−0.238425	+	0.971161i	$0.576631\pi$
$54$		0			0
$55$	−3.29522	−	0.376160i	−0.444328	−	0.0507214i
$56$		0			0
$57$	−0.383714	+	0.278785i	−0.0508242	+	0.0369259i
$58$		0			0
$59$	1.70562	−	5.24935i	0.222052	−	0.683407i	−0.776525	−	0.630086i	$-0.783020\pi$
$59$	1.70562	−	5.24935i	0.222052	−	0.683407i	0.998577	−	0.0533204i	$-0.0169805\pi$
$60$		0			0
$61$	7.77155	+	5.64636i	0.995045	+	0.722942i	0.961020	−	0.276479i	$-0.0891675\pi$
$61$	7.77155	+	5.64636i	0.995045	+	0.722942i	0.0340247	+	0.999421i	$0.489168\pi$
$62$		0			0
$63$	−1.87100	−	5.75835i	−0.235724	−	0.725484i
$64$		0			0
$65$	0.653514			0.0810585
$66$		0			0
$67$	−5.60966			−0.685329			−0.342664	−	0.939458i	$-0.611329\pi$
$67$	−5.60966			−0.685329			−0.342664	+	0.939458i	$0.611329\pi$
$68$		0			0
$69$	0.301160	+	0.926876i	0.0362555	+	0.111583i
$70$		0			0
$71$	−0.0442449	−	0.0321458i	−0.00525091	−	0.00381501i	0.585157	−	0.810920i	$-0.301033\pi$
$71$	−0.0442449	−	0.0321458i	−0.00525091	−	0.00381501i	−0.590408	+	0.807105i	$0.701033\pi$
$72$		0			0
$73$	−2.20562	+	6.78819i	−0.258148	+	0.794497i	0.735045	+	0.678018i	$0.237161\pi$
$73$	−2.20562	+	6.78819i	−0.258148	+	0.794497i	−0.993193	+	0.116479i	$0.962839\pi$
$74$		0			0
$75$	0.128998	−	0.0937225i	0.0148954	−	0.0108221i
$76$		0			0
$77$	−1.34450	−	6.61569i	−0.153220	−	0.753927i
$78$		0			0
$79$	−2.37100	+	1.72263i	−0.266759	+	0.193811i	−0.713121	−	0.701041i	$-0.752719\pi$
$79$	−2.37100	+	1.72263i	−0.266759	+	0.193811i	0.446363	+	0.894852i	$0.352719\pi$
$80$		0			0
$81$	2.71064	−	8.34250i	0.301183	−	0.926945i
$82$		0			0
$83$	9.98988	+	7.25807i	1.09653	+	0.796677i	0.980490	−	0.196568i	$-0.0629796\pi$
$83$	9.98988	+	7.25807i	1.09653	+	0.796677i	0.116041	+	0.993244i	$0.462980\pi$
$84$		0			0
$85$	−1.32784	−	4.08666i	−0.144024	−	0.443261i
$86$		0			0
$87$	1.36004			0.145811
$88$		0			0
$89$	0.00487932			0.000517207			0.000258603	−	1.00000i	$-0.499918\pi$
$89$	0.00487932			0.000517207			0.000258603		1.00000i	$0.499918\pi$
$90$		0			0
$91$	0.411059	+	1.26511i	0.0430907	+	0.132620i
$92$		0			0
$93$	−0.693182	−	0.503626i	−0.0718797	−	0.0522236i
$94$		0			0
$95$	−0.919194	+	2.82899i	−0.0943074	+	0.290248i
$96$		0			0
$97$	14.7696	−	10.7307i	1.49962	−	1.08954i	0.529090	−	0.848566i	$-0.322533\pi$
$97$	14.7696	−	10.7307i	1.49962	−	1.08954i	0.970532	−	0.240973i	$-0.0774665\pi$
$98$		0			0
$99$	4.09311	−	8.97639i	0.411373	−	0.902161i
$100$		0			0
$101$	−2.14782	+	1.56048i	−0.213716	+	0.155274i	−0.689493	−	0.724292i	$-0.742167\pi$
$101$	−2.14782	+	1.56048i	−0.213716	+	0.155274i	0.475777	+	0.879566i	$0.342167\pi$
$102$		0			0
$103$	5.08650	−	15.6546i	0.501188	−	1.54250i	−0.305898	−	0.952064i	$-0.598957\pi$
$103$	5.08650	−	15.6546i	0.501188	−	1.54250i	0.807086	−	0.590433i	$-0.201043\pi$
$104$		0			0
$105$	0.262573	+	0.190770i	0.0256245	+	0.0186173i
$106$		0			0
$107$	3.80116	+	11.6988i	0.367472	+	1.13096i	0.948419	+	0.317021i	$0.102683\pi$
$107$	3.80116	+	11.6988i	0.367472	+	1.13096i	−0.580946	+	0.813942i	$0.697317\pi$
$108$		0			0
$109$	−8.73635			−0.836790			−0.418395	−	0.908265i	$-0.637407\pi$
$109$	−8.73635			−0.836790			−0.418395	+	0.908265i	$0.637407\pi$
$110$		0			0
$111$	−0.550915			−0.0522905
$112$		0			0
$113$	−0.510445	−	1.57099i	−0.0480186	−	0.147786i	0.924172	−	0.381976i	$-0.124756\pi$
$113$	−0.510445	−	1.57099i	−0.0480186	−	0.147786i	−0.972191	+	0.234190i	$0.924756\pi$
$114$		0			0
$115$	4.94479	+	3.59260i	0.461104	+	0.335012i
$116$		0			0
$117$	−0.600707	+	1.84878i	−0.0555353	+	0.170920i
$118$		0			0
$119$	7.07599	−	5.14101i	0.648655	−	0.471275i
$120$		0			0
$121$	5.66947	−	9.42641i	0.515406	−	0.856946i
$122$		0			0
$123$	0.615205	−	0.446973i	0.0554712	−	0.0403022i
$124$		0			0
$125$	0.309017	−	0.951057i	0.0276393	−	0.0850651i
$126$		0			0
$127$	2.22754	+	1.61841i	0.197663	+	0.143610i	0.682214	−	0.731152i	$-0.261017\pi$
$127$	2.22754	+	1.61841i	0.197663	+	0.143610i	−0.484552	+	0.874763i	$0.661017\pi$
$128$		0			0
$129$	0.499160	+	1.53626i	0.0439486	+	0.135260i
$130$		0			0
$131$	−2.85760			−0.249670			−0.124835	−	0.992178i	$-0.539840\pi$
$131$	−2.85760			−0.249670			−0.124835	+	0.992178i	$0.539840\pi$
$132$		0			0
$133$	−6.05469			−0.525008
$134$		0			0
$135$	0.294384	+	0.906022i	0.0253366	+	0.0779779i
$136$		0			0
$137$	−8.14080	−	5.91464i	−0.695516	−	0.505322i	0.182953	−	0.983122i	$-0.441434\pi$
$137$	−8.14080	−	5.91464i	−0.695516	−	0.505322i	−0.878469	+	0.477800i	$0.841434\pi$
$138$		0			0
$139$	0.118702	−	0.365326i	0.0100682	−	0.0309866i	−0.945896	−	0.324469i	$-0.894814\pi$
$139$	0.118702	−	0.365326i	0.0100682	−	0.0309866i	0.955964	+	0.293483i	$0.0948143\pi$
$140$		0			0
$141$	0.942313	−	0.684631i	0.0793571	−	0.0576563i
$142$		0			0
$143$	−0.899255	+	1.97211i	−0.0751995	+	0.164916i
$144$		0			0
$145$	6.90055	−	5.01354i	0.573059	−	0.416352i
$146$		0			0
$147$	0.140764	−	0.433226i	0.0116100	−	0.0357319i
$148$		0			0
$149$	6.72161	+	4.88353i	0.550656	+	0.400075i	0.828027	−	0.560688i	$-0.189463\pi$
$149$	6.72161	+	4.88353i	0.550656	+	0.400075i	−0.277372	+	0.960763i	$0.589463\pi$
$150$		0			0
$151$	1.65310	+	5.08772i	0.134527	+	0.414033i	0.995516	−	0.0945910i	$-0.0301543\pi$
$151$	1.65310	+	5.08772i	0.134527	+	0.414033i	−0.860989	+	0.508624i	$0.830154\pi$
$152$		0			0
$153$	12.7817			1.03334
$154$		0			0
$155$	−5.37359			−0.431617
$156$		0			0
$157$	−2.32242	−	7.14768i	−0.185349	−	0.570447i	0.814605	−	0.580016i	$-0.196954\pi$
$157$	−2.32242	−	7.14768i	−0.185349	−	0.570447i	−0.999954	+	0.00956968i	$0.996954\pi$
$158$		0			0
$159$	1.43446	+	1.04219i	0.113760	+	0.0826513i
$160$		0			0
$161$	−3.84450	+	11.8321i	−0.302989	+	0.932504i
$162$		0			0
$163$	2.45994	−	1.78725i	0.192678	−	0.139988i	−0.487264	−	0.873255i	$-0.662005\pi$
$163$	2.45994	−	1.78725i	0.192678	−	0.139988i	0.679942	+	0.733266i	$0.262005\pi$
$164$		0			0
$165$	0.105322	+	0.518243i	0.00819929	+	0.0403451i
$166$		0			0
$167$	−11.1539	+	8.10379i	−0.863115	+	0.627090i	−0.928731	−	0.370755i	$-0.879099\pi$
$167$	−11.1539	+	8.10379i	−0.863115	+	0.627090i	0.0656157	+	0.997845i	$0.479099\pi$
$168$		0			0
$169$	−3.88525	+	11.9576i	−0.298865	+	0.919812i
$170$		0			0
$171$	−7.15826	−	5.20078i	−0.547406	−	0.397714i
$172$		0			0
$173$	−4.26425	−	13.1240i	−0.324205	−	0.997801i	−0.971798	−	0.235814i	$-0.924224\pi$
$173$	−4.26425	−	13.1240i	−0.324205	−	0.997801i	0.647593	−	0.761986i	$-0.275776\pi$
$174$		0			0
$175$	2.03548			0.153868
$176$		0			0
$177$	−0.880084			−0.0661512
$178$		0			0
$179$	1.54508	+	4.75528i	0.115485	+	0.355427i	0.992048	−	0.125861i	$-0.0401693\pi$
$179$	1.54508	+	4.75528i	0.115485	+	0.355427i	−0.876563	+	0.481287i	$0.840169\pi$
$180$		0			0
$181$	−18.1760	−	13.2056i	−1.35101	−	0.981567i	−0.998960	−	0.0455868i	$-0.985484\pi$
$181$	−18.1760	−	13.2056i	−1.35101	−	0.981567i	−0.352051	−	0.935981i	$-0.614516\pi$
$182$		0			0
$183$	0.473323	−	1.45674i	0.0349890	−	0.107685i
$184$		0			0
$185$	−2.79522	+	2.03085i	−0.205509	+	0.149311i
$186$		0			0
$187$	14.1595	+	1.61635i	1.03544	+	0.118199i
$188$		0			0
$189$	−1.56876	+	1.13977i	−0.114111	+	0.0829062i
$190$		0			0
$191$	−2.22754	+	6.85567i	−0.161179	+	0.496059i	−0.998734	−	0.0502937i	$-0.983984\pi$
$191$	−2.22754	+	6.85567i	−0.161179	+	0.496059i	0.837555	+	0.546353i	$0.183984\pi$
$192$		0			0
$193$	17.1155	+	12.4352i	1.23200	+	0.895102i	0.997039	−	0.0769019i	$-0.0245028\pi$
$193$	17.1155	+	12.4352i	1.23200	+	0.895102i	0.234964	+	0.972004i	$0.424503\pi$
$194$		0			0
$195$	−0.0322005	−	0.0991029i	−0.00230593	−	0.00709691i
$196$		0			0
$197$	−20.5970			−1.46748			−0.733738	−	0.679432i	$-0.762226\pi$
$197$	−20.5970			−1.46748			−0.733738	+	0.679432i	$0.762226\pi$
$198$		0			0
$199$	−11.3763			−0.806445			−0.403223	−	0.915102i	$-0.632110\pi$
$199$	−11.3763			−0.806445			−0.403223	+	0.915102i	$0.632110\pi$
$200$		0			0
$201$	0.276404	+	0.850683i	0.0194960	+	0.0600026i
$202$		0			0
$203$	14.0459	+	10.2050i	0.985831	+	0.716248i
$204$		0			0
$205$	1.47374	−	4.53569i	0.102930	−	0.316786i
$206$		0			0
$207$	−14.7087	+	10.6865i	−1.02232	+	0.742761i
$208$		0			0
$209$	−7.27222	−	6.66663i	−0.503030	−	0.461141i
$210$		0			0
$211$	−22.7568	+	16.5338i	−1.56665	+	1.13823i	−0.636364	+	0.771389i	$0.719563\pi$
$211$	−22.7568	+	16.5338i	−1.56665	+	1.13823i	−0.930282	+	0.366846i	$0.880437\pi$
$212$		0			0
$213$	−0.00269472	+	0.00829349i	−0.000184639	+	0.000568261i
$214$		0			0
$215$	8.19577	+	5.95458i	0.558947	+	0.406099i
$216$		0			0
$217$	−3.37998	−	10.4025i	−0.229448	−	0.706168i
$218$		0			0
$219$	1.13808			0.0769043
$220$		0			0
$221$	−2.80813			−0.188895
$222$		0			0
$223$	6.06173	+	18.6561i	0.405923	+	1.24930i	0.920122	+	0.391633i	$0.128090\pi$
$223$	6.06173	+	18.6561i	0.405923	+	1.24930i	−0.514198	+	0.857671i	$0.671910\pi$
$224$		0			0
$225$	2.40648	+	1.74841i	0.160432	+	0.116561i
$226$		0			0
$227$	−4.98120	+	15.3306i	−0.330614	+	1.01753i	0.638228	+	0.769847i	$0.279668\pi$
$227$	−4.98120	+	15.3306i	−0.330614	+	1.01753i	−0.968842	+	0.247678i	$0.920332\pi$
$228$		0			0
$229$	−3.13012	+	2.27416i	−0.206844	+	0.150281i	−0.686385	−	0.727239i	$-0.740803\pi$
$229$	−3.13012	+	2.27416i	−0.206844	+	0.150281i	0.479541	+	0.877520i	$0.340803\pi$
$230$		0			0
$231$	−0.936997	+	0.529862i	−0.0616498	+	0.0348623i
$232$		0			0
$233$	23.0050	−	16.7141i	1.50711	−	1.09498i	0.539664	−	0.841881i	$-0.318551\pi$
$233$	23.0050	−	16.7141i	1.50711	−	1.09498i	0.967441	−	0.253095i	$-0.0814486\pi$
$234$		0			0
$235$	2.25733	−	6.94734i	0.147252	−	0.453195i
$236$		0			0
$237$	0.378057	+	0.274674i	0.0245574	+	0.0178420i
$238$		0			0
$239$	−0.517313	−	1.59212i	−0.0334622	−	0.102986i	0.932930	−	0.360057i	$-0.117243\pi$
$239$	−0.517313	−	1.59212i	−0.0334622	−	0.102986i	−0.966393	+	0.257071i	$0.917243\pi$
$240$		0			0
$241$	−21.4676			−1.38285			−0.691425	−	0.722448i	$-0.743017\pi$
$241$	−21.4676			−1.38285			−0.691425	+	0.722448i	$0.743017\pi$
$242$		0			0
$243$	−4.25661			−0.273062
$244$		0			0
$245$	−0.882806	−	2.71700i	−0.0564004	−	0.173583i
$246$		0			0
$247$	1.57267	+	1.14261i	0.100067	+	0.0727026i
$248$		0			0
$249$	0.608429	−	1.87255i	0.0385576	−	0.118668i
$250$		0			0
$251$	14.4964	−	10.5322i	0.915003	−	0.664789i	−0.0272722	−	0.999628i	$-0.508682\pi$
$251$	14.4964	−	10.5322i	0.915003	−	0.664789i	0.942275	+	0.334839i	$0.108682\pi$
$252$		0			0
$253$	−17.6456	+	9.97839i	−1.10937	+	0.627336i
$254$		0			0
$255$	−0.554301	+	0.402723i	−0.0347117	+	0.0252195i
$256$		0			0
$257$	−0.948139	+	2.91807i	−0.0591433	+	0.182024i	−0.976263	−	0.216587i	$-0.930508\pi$
$257$	−0.948139	+	2.91807i	−0.0591433	+	0.182024i	0.917120	+	0.398611i	$0.130508\pi$
$258$		0			0
$259$	−5.68962	−	4.13375i	−0.353536	−	0.256859i
$260$		0			0
$261$	7.84031	+	24.1300i	0.485303	+	1.49361i
$262$		0			0
$263$	20.4278			1.25963			0.629816	−	0.776744i	$-0.283130\pi$
$263$	20.4278			1.25963			0.629816	+	0.776744i	$0.283130\pi$
$264$		0			0
$265$	11.1200			0.683096
$266$		0			0
$267$	−0.000240418	0	0.000739930i	−1.47133e−5	0	4.52830e-5i
$268$		0			0
$269$	−6.56147	−	4.76718i	−0.400060	−	0.290660i	0.369506	−	0.929228i	$-0.379527\pi$
$269$	−6.56147	−	4.76718i	−0.400060	−	0.290660i	−0.769565	+	0.638568i	$0.779527\pi$
$270$		0			0
$271$	3.17624	−	9.77547i	0.192943	−	0.593818i	−0.807051	−	0.590481i	$-0.798938\pi$
$271$	3.17624	−	9.77547i	0.192943	−	0.593818i	0.999994	−	0.00333647i	$-0.00106203\pi$
$272$		0			0
$273$	0.171595	−	0.124671i	0.0103854	−	0.00754544i
$274$		0			0
$275$	2.44479	+	2.24120i	0.147426	+	0.135150i
$276$		0			0
$277$	13.5052	−	9.81209i	0.811447	−	0.589551i	−0.102802	−	0.994702i	$-0.532781\pi$
$277$	13.5052	−	9.81209i	0.811447	−	0.589551i	0.914250	+	0.405151i	$0.132781\pi$
$278$		0			0
$279$	4.93937	−	15.2018i	0.295713	−	0.910110i
$280$		0			0
$281$	−16.6701	−	12.1115i	−0.994455	−	0.722514i	−0.0335629	−	0.999437i	$-0.510685\pi$
$281$	−16.6701	−	12.1115i	−0.994455	−	0.722514i	−0.960892	+	0.276923i	$0.910685\pi$
$282$		0			0
$283$	−9.09747	−	27.9991i	−0.540788	−	1.66437i	−0.730799	−	0.682593i	$-0.760852\pi$
$283$	−9.09747	−	27.9991i	−0.540788	−	1.66437i	0.190011	−	0.981782i	$-0.439148\pi$
$284$		0			0
$285$	0.474297			0.0280949
$286$		0			0
$287$	9.70743			0.573011
$288$		0			0
$289$	0.452393	+	1.39232i	0.0266113	+	0.0819012i
$290$		0			0
$291$	−2.35501	−	1.71102i	−0.138053	−	0.100301i
$292$		0			0
$293$	2.25407	−	6.93732i	0.131684	−	0.405283i	−0.863375	−	0.504562i	$-0.831654\pi$
$293$	2.25407	−	6.93732i	0.131684	−	0.405283i	0.995060	+	0.0992797i	$0.0316539\pi$
$294$		0			0
$295$	−4.46536	+	3.24427i	−0.259983	+	0.188889i
$296$		0			0
$297$	−3.13919	−	0.358348i	−0.182154	−	0.0207935i
$298$		0			0
$299$	3.23149	−	2.34782i	0.186882	−	0.135778i
$300$		0			0
$301$	−6.37208	+	19.6113i	−0.367281	+	1.13037i
$302$		0			0
$303$	0.342470	+	0.248819i	0.0196744	+	0.0142943i
$304$		0			0
$305$	−2.96847	−	9.13600i	−0.169974	−	0.523126i
$306$		0			0
$307$	2.71978			0.155226			0.0776130	−	0.996984i	$-0.475270\pi$
$307$	2.71978			0.155226			0.0776130	+	0.996984i	$0.475270\pi$
$308$		0			0
$309$	−2.62459			−0.149308
$310$		0			0
$311$	−4.70857	−	14.4915i	−0.266999	−	0.821738i	−0.991226	−	0.132177i	$-0.957803\pi$
$311$	−4.70857	−	14.4915i	−0.266999	−	0.821738i	0.724227	−	0.689561i	$-0.242197\pi$
$312$		0			0
$313$	23.4305	+	17.0233i	1.32437	+	0.962213i	0.999867	+	0.0163292i	$0.00519799\pi$
$313$	23.4305	+	17.0233i	1.32437	+	0.962213i	0.324506	+	0.945884i	$0.394802\pi$
$314$		0			0
$315$	−1.87100	+	5.75835i	−0.105419	+	0.324446i
$316$		0			0
$317$	4.92286	−	3.57667i	0.276496	−	0.200886i	−0.440892	−	0.897560i	$-0.645338\pi$
$317$	4.92286	−	3.57667i	0.276496	−	0.200886i	0.717387	+	0.696674i	$0.245338\pi$
$318$		0			0
$319$	5.63403	+	27.7226i	0.315445	+	1.55217i
$320$		0			0
$321$	1.58678	−	1.15286i	0.0885654	−	0.0643465i
$322$		0			0
$323$	3.94975	−	12.1561i	0.219770	−	0.676383i
$324$		0			0
$325$	−0.528704	−	0.384126i	−0.0293272	−	0.0213075i
$326$		0			0
$327$	0.430465	+	1.32483i	0.0238047	+	0.0732635i
$328$		0			0
$329$	14.8689			0.819750
$330$		0			0
$331$	18.0542			0.992349			0.496175	−	0.868223i	$-0.334738\pi$
$331$	18.0542			0.992349			0.496175	+	0.868223i	$0.334738\pi$
$332$		0			0
$333$	−3.17590	−	9.77441i	−0.174038	−	0.535634i
$334$		0			0
$335$	4.53831	+	3.29727i	0.247954	+	0.180149i
$336$		0			0
$337$	3.23467	−	9.95528i	0.176204	−	0.542299i	−0.823483	−	0.567341i	$-0.807972\pi$
$337$	3.23467	−	9.95528i	0.176204	−	0.542299i	0.999686	+	0.0250425i	$0.00797210\pi$
$338$		0			0
$339$	−0.213083	+	0.154814i	−0.0115731	+	0.00840834i
$340$		0			0
$341$	7.39422	−	16.2159i	0.400420	−	0.878141i
$342$		0			0
$343$	16.2316	−	11.7929i	0.876424	−	0.636759i
$344$		0			0
$345$	0.301160	−	0.926876i	0.0162139	−	0.0499014i
$346$		0			0
$347$	−23.6624	−	17.1918i	−1.27027	−	0.922902i	−0.271052	−	0.962565i	$-0.587372\pi$
$347$	−23.6624	−	17.1918i	−1.27027	−	0.922902i	−0.999213	+	0.0396629i	$0.987372\pi$
$348$		0			0
$349$	8.23527	+	25.3455i	0.440824	+	1.35672i	0.886999	+	0.461770i	$0.152786\pi$
$349$	8.23527	+	25.3455i	0.440824	+	1.35672i	−0.446176	+	0.894945i	$0.647214\pi$
$350$		0			0
$351$	0.622569			0.0332303
$352$		0			0
$353$	0.908792			0.0483701			0.0241851	−	0.999707i	$-0.492301\pi$
$353$	0.908792			0.0483701			0.0241851	+	0.999707i	$0.492301\pi$
$354$		0			0
$355$	0.0169001	+	0.0520130i	0.000896962	+	0.00276057i
$356$		0			0
$357$	−1.12827	−	0.819735i	−0.0597143	−	0.0433850i
$358$		0			0
$359$	10.3305	−	31.7939i	0.545221	−	1.67802i	−0.175243	−	0.984525i	$-0.556071\pi$
$359$	10.3305	−	31.7939i	0.545221	−	1.67802i	0.720464	−	0.693493i	$-0.243929\pi$
$360$		0			0
$361$	8.21306	−	5.96714i	0.432266	−	0.314060i
$362$		0			0
$363$	−1.70883	−	0.395287i	−0.0896903	−	0.0207472i
$364$		0			0
$365$	5.77438	−	4.19533i	0.302245	−	0.219594i
$366$		0			0
$367$	−2.87918	+	8.86120i	−0.150292	+	0.462551i	−0.997653	−	0.0684653i	$-0.978190\pi$
$367$	−2.87918	+	8.86120i	−0.150292	+	0.462551i	0.847362	+	0.531016i	$0.178190\pi$
$368$		0			0
$369$	11.4768	+	8.33837i	0.597457	+	0.434078i
$370$		0			0
$371$	6.99445	+	21.5267i	0.363134	+	1.11761i
$372$		0			0
$373$	−0.730613			−0.0378297			−0.0189148	−	0.999821i	$-0.506021\pi$
$373$	−0.730613			−0.0378297			−0.0189148	+	0.999821i	$0.506021\pi$
$374$		0			0
$375$	−0.159450			−0.00823398
$376$		0			0
$377$	−1.72252	−	5.30136i	−0.0887141	−	0.273034i
$378$		0			0
$379$	−24.5280	−	17.8206i	−1.25992	−	0.915385i	−0.261165	−	0.965294i	$-0.584107\pi$
$379$	−24.5280	−	17.8206i	−1.25992	−	0.915385i	−0.998754	+	0.0499093i	$0.984107\pi$
$380$		0			0
$381$	0.135668	−	0.417542i	0.00695046	−	0.0213913i
$382$		0			0
$383$	−20.9497	+	15.2208i	−1.07048	+	0.777749i	−0.975998	−	0.217778i	$-0.930119\pi$
$383$	−20.9497	+	15.2208i	−1.07048	+	0.777749i	−0.0944808	+	0.995527i	$0.530119\pi$
$384$		0			0
$385$	−2.80088	+	6.14248i	−0.142746	+	0.313050i
$386$		0			0
$387$	−24.3789	+	17.7123i	−1.23925	+	0.900369i
$388$		0			0
$389$	1.72430	−	5.30686i	0.0874256	−	0.269068i	−0.897780	−	0.440444i	$-0.854821\pi$
$389$	1.72430	−	5.30686i	0.0874256	−	0.269068i	0.985206	+	0.171375i	$0.0548211\pi$
$390$		0			0
$391$	−21.2476	−	15.4373i	−1.07454	−	0.780698i
$392$		0			0
$393$	0.140802	+	0.433344i	0.00710252	+	0.0218593i
$394$		0			0
$395$	2.93072			0.147461
$396$		0			0
$397$	31.4006			1.57595			0.787974	−	0.615708i	$-0.211130\pi$
$397$	31.4006			1.57595			0.787974	+	0.615708i	$0.211130\pi$
$398$		0			0
$399$	0.298332	+	0.918171i	0.0149353	+	0.0459660i
$400$		0			0
$401$	−15.0194	−	10.9122i	−0.750034	−	0.544932i	0.145803	−	0.989314i	$-0.453423\pi$
$401$	−15.0194	−	10.9122i	−0.750034	−	0.544932i	−0.895837	+	0.444382i	$0.853423\pi$
$402$		0			0
$403$	−1.08518	+	3.33984i	−0.0540567	+	0.166369i
$404$		0			0
$405$	−7.09656	+	5.15595i	−0.352631	+	0.256201i
$406$		0			0
$407$	−2.28219	−	11.2297i	−0.113124	−	0.556634i
$408$		0			0
$409$	−5.05892	+	3.67552i	−0.250147	+	0.181743i	−0.705792	−	0.708419i	$-0.749409\pi$
$409$	−5.05892	+	3.67552i	−0.250147	+	0.181743i	0.455645	+	0.890162i	$0.349409\pi$
$410$		0			0
$411$	−0.495812	+	1.52595i	−0.0244566	+	0.0752697i
$412$		0			0
$413$	−9.08915	−	6.60366i	−0.447248	−	0.324945i
$414$		0			0
$415$	−3.81579	−	11.7438i	−0.187310	−	0.576481i
$416$		0			0
$417$	−0.0612491			−0.00299938
$418$		0			0
$419$	25.4340			1.24253			0.621266	−	0.783599i	$-0.286618\pi$
$419$	25.4340			1.24253			0.621266	+	0.783599i	$0.286618\pi$
$420$		0			0
$421$	6.09077	+	18.7455i	0.296846	+	0.913598i	0.982595	+	0.185760i	$0.0594747\pi$
$421$	6.09077	+	18.7455i	0.296846	+	0.913598i	−0.685749	+	0.727838i	$0.740525\pi$
$422$		0			0
$423$	17.5790	+	12.7719i	0.854722	+	0.620992i
$424$		0			0
$425$	−1.32784	+	4.08666i	−0.0644096	+	0.198232i
$426$		0			0
$427$	15.8188	−	11.4931i	0.765527	−	0.556188i
$428$		0			0
$429$	0.343372	+	0.0391970i	0.0165782	+	0.00189245i
$430$		0			0
$431$	−13.1828	+	9.57788i	−0.634994	+	0.461350i	−0.858127	−	0.513438i	$-0.828372\pi$
$431$	−13.1828	+	9.57788i	−0.634994	+	0.461350i	0.223133	+	0.974788i	$0.428372\pi$
$432$		0			0
$433$	−7.33287	+	22.5682i	−0.352395	+	1.08456i	0.605110	+	0.796142i	$0.293129\pi$
$433$	−7.33287	+	22.5682i	−0.352395	+	1.08456i	−0.957505	+	0.288418i	$0.906871\pi$
$434$		0			0
$435$	−1.10029	−	0.799410i	−0.0527551	−	0.0383288i
$436$		0			0
$437$	5.61821	+	17.2911i	0.268755	+	0.827144i
$438$		0			0
$439$	−14.3276			−0.683818			−0.341909	−	0.939733i	$-0.611073\pi$
$439$	−14.3276			−0.683818			−0.341909	+	0.939733i	$0.611073\pi$
$440$		0			0
$441$	8.49783			0.404658
$442$		0			0
$443$	−2.32348	−	7.15093i	−0.110392	−	0.339751i	0.880566	−	0.473923i	$-0.157162\pi$
$443$	−2.32348	−	7.15093i	−0.110392	−	0.339751i	−0.990958	+	0.134172i	$0.957162\pi$
$444$		0			0
$445$	−0.00394745	−	0.00286799i	−0.000187127	−	0.000135956i
$446$		0			0
$447$	0.409377	−	1.25993i	0.0193629	−	0.0595927i
$448$		0			0
$449$	−21.8022	+	15.8402i	−1.02891	+	0.747546i	−0.968090	−	0.250603i	$-0.919371\pi$
$449$	−21.8022	+	15.8402i	−1.02891	+	0.747546i	−0.0608183	+	0.998149i	$0.519371\pi$
$450$		0			0
$451$	11.6595	+	10.6885i	0.549023	+	0.503304i
$452$		0			0
$453$	0.690081	−	0.501373i	0.0324228	−	0.0235566i
$454$		0			0
$455$	0.411059	−	1.26511i	0.0192707	−	0.0593093i
$456$		0			0
$457$	−9.58406	−	6.96323i	−0.448323	−	0.325726i	0.340610	−	0.940205i	$-0.389366\pi$
$457$	−9.58406	−	6.96323i	−0.448323	−	0.325726i	−0.788933	+	0.614479i	$0.789366\pi$
$458$		0			0
$459$	−1.26496	−	3.89315i	−0.0590433	−	0.181717i
$460$		0			0
$461$	40.9558			1.90750			0.953751	−	0.300599i	$-0.0971866\pi$
$461$	40.9558			1.90750			0.953751	+	0.300599i	$0.0971866\pi$
$462$		0			0
$463$	−37.2115			−1.72937			−0.864684	−	0.502317i	$-0.832481\pi$
$463$	−37.2115			−1.72937			−0.864684	+	0.502317i	$0.832481\pi$
$464$		0			0
$465$	0.264772	+	0.814885i	0.0122785	+	0.0377894i
$466$		0			0
$467$	9.49602	+	6.89926i	0.439424	+	0.319260i	0.785406	−	0.618981i	$-0.212454\pi$
$467$	9.49602	+	6.89926i	0.439424	+	0.319260i	−0.345982	+	0.938241i	$0.612454\pi$
$468$		0			0
$469$	−3.52846	+	10.8595i	−0.162929	+	0.501445i
$470$		0			0
$471$	−0.969486	+	0.704373i	−0.0446715	+	0.0324558i
$472$		0			0
$473$	−29.2468	+	16.5387i	−1.34477	+	0.760452i
$474$		0			0
$475$	2.40648	−	1.74841i	0.110417	−	0.0802226i
$476$		0			0
$477$	−10.2214	+	31.4583i	−0.468007	+	1.44038i
$478$		0			0
$479$	−20.7572	−	15.0810i	−0.948421	−	0.689068i	0.00201220	−	0.999998i	$-0.499359\pi$
$479$	−20.7572	−	15.0810i	−0.948421	−	0.689068i	−0.950433	+	0.310930i	$0.899359\pi$
$480$		0			0
$481$	0.697744	+	2.14744i	0.0318144	+	0.0979147i
$482$		0			0
$483$	1.98373			0.0902628
$484$		0			0
$485$	−18.2562			−0.828970
$486$		0			0
$487$	−2.56893	−	7.90636i	−0.116409	−	0.358272i	0.875829	−	0.482622i	$-0.160315\pi$
$487$	−2.56893	−	7.90636i	−0.116409	−	0.358272i	−0.992238	+	0.124350i	$0.960315\pi$
$488$		0			0
$489$	−0.392239	−	0.284978i	−0.0177376	−	0.0128871i
$490$		0			0
$491$	7.45825	−	22.9541i	0.336586	−	1.03591i	−0.629349	−	0.777123i	$-0.716678\pi$
$491$	7.45825	−	22.9541i	0.336586	−	1.03591i	0.965935	−	0.258783i	$-0.0833215\pi$
$492$		0			0
$493$	−29.6515	+	21.5430i	−1.33543	+	0.970250i
$494$		0			0
$495$	−8.58758	+	4.85619i	−0.385983	+	0.218269i
$496$		0			0
$497$	−0.0900597	+	0.0654322i	−0.00403973	+	0.00293504i
$498$		0			0
$499$	−9.92681	+	30.5516i	−0.444385	+	1.36768i	0.438772	+	0.898599i	$0.355414\pi$
$499$	−9.92681	+	30.5516i	−0.444385	+	1.36768i	−0.883157	+	0.469078i	$0.844586\pi$
$500$		0			0
$501$	1.77849	+	1.29215i	0.0794572	+	0.0577290i
$502$		0			0
$503$	−11.7697	−	36.2233i	−0.524783	−	1.61512i	−0.764745	−	0.644333i	$-0.777135\pi$
$503$	−11.7697	−	36.2233i	−0.524783	−	1.61512i	0.239962	−	0.970782i	$-0.422865\pi$
$504$		0			0
$505$	2.65485			0.118139
$506$		0			0
$507$	2.00476			0.0890343
$508$		0			0
$509$	−12.9730	−	39.9268i	−0.575019	−	1.76973i	−0.636115	−	0.771594i	$-0.719460\pi$
$509$	−12.9730	−	39.9268i	−0.575019	−	1.76973i	0.0610967	−	0.998132i	$-0.480540\pi$
$510$		0			0
$511$	11.7536	+	8.53951i	0.519950	+	0.377766i
$512$		0			0
$513$	−0.875668	+	2.69503i	−0.0386617	+	0.118988i
$514$		0			0
$515$	−13.3166	+	9.67510i	−0.586801	+	0.426336i
$516$		0			0
$517$	17.8589	+	16.3717i	0.785432	+	0.720027i
$518$		0			0
$519$	−1.78010	+	1.29332i	−0.0781376	+	0.0567703i
$520$		0			0
$521$	−8.98355	+	27.6485i	−0.393577	+	1.21130i	0.536488	+	0.843908i	$0.319751\pi$
$521$	−8.98355	+	27.6485i	−0.393577	+	1.21130i	−0.930065	+	0.367396i	$0.880249\pi$
$522$		0			0
$523$	−10.1709	−	7.38957i	−0.444741	−	0.323123i	0.342775	−	0.939418i	$-0.388633\pi$
$523$	−10.1709	−	7.38957i	−0.444741	−	0.323123i	−0.787516	+	0.616294i	$0.788633\pi$
$524$		0			0
$525$	−0.100294	−	0.308673i	−0.00437718	−	0.0134716i
$526$		0			0
$527$	23.0902			1.00582
$528$		0			0
$529$	14.3577			0.624250
$530$		0			0
$531$	−5.07348	−	15.6146i	−0.220170	−	0.677615i
$532$		0			0
$533$	−2.52145	−	1.83194i	−0.109216	−	0.0793501i
$534$		0			0
$535$	3.80116	−	11.6988i	0.164338	−	0.505782i
$536$		0			0
$537$	0.644990	−	0.468613i	0.0278334	−	0.0202221i
$538$		0			0
$539$	9.41386	+	1.07462i	0.405484	+	0.0462873i
$540$		0			0
$541$	16.1438	−	11.7292i	0.694076	−	0.504276i	−0.183921	−	0.982941i	$-0.558879\pi$
$541$	16.1438	−	11.7292i	0.694076	−	0.504276i	0.877998	+	0.478665i	$0.158879\pi$
$542$		0			0
$543$	−1.10700	+	3.40700i	−0.0475060	+	0.146208i
$544$		0			0
$545$	7.06785	+	5.13510i	0.302754	+	0.219963i
$546$		0			0
$547$	8.01221	+	24.6590i	0.342577	+	1.05434i	0.962868	+	0.269972i	$0.0870146\pi$
$547$	8.01221	+	24.6590i	0.342577	+	1.05434i	−0.620291	+	0.784372i	$0.712985\pi$
$548$		0			0
$549$	28.5743			1.21952
$550$		0			0
$551$	25.3718			1.08087
$552$		0			0
$553$	1.84342	+	5.67345i	0.0783901	+	0.241260i
$554$		0			0
$555$	0.445699	+	0.323819i	0.0189189	+	0.0137454i
$556$		0			0
$557$	2.39837	−	7.38143i	0.101622	−	0.312761i	−0.887301	−	0.461192i	$-0.847422\pi$
$557$	2.39837	−	7.38143i	0.101622	−	0.312761i	0.988923	+	0.148430i	$0.0474221\pi$
$558$		0			0
$559$	5.35605	−	3.89140i	0.226537	−	0.164589i
$560$		0			0
$561$	−0.452565	−	2.22687i	−0.0191073	−	0.0940187i
$562$		0			0
$563$	−7.68369	+	5.58253i	−0.323829	+	0.235275i	−0.737808	−	0.675011i	$-0.764139\pi$
$563$	−7.68369	+	5.58253i	−0.323829	+	0.235275i	0.413979	+	0.910287i	$0.364139\pi$
$564$		0			0
$565$	−0.510445	+	1.57099i	−0.0214746	+	0.0660919i
$566$		0			0
$567$	−14.4449	−	10.4948i	−0.606629	−	0.440742i
$568$		0			0
$569$	3.69665	+	11.3771i	0.154972	+	0.476954i	0.998158	−	0.0606674i	$-0.0193229\pi$
$569$	3.69665	+	11.3771i	0.154972	+	0.476954i	−0.843186	+	0.537622i	$0.819323\pi$
$570$		0			0
$571$	−18.0419			−0.755028			−0.377514	−	0.926004i	$-0.623221\pi$
$571$	−18.0419			−0.755028			−0.377514	+	0.926004i	$0.623221\pi$
$572$		0			0
$573$	1.14939			0.0480166
$574$		0			0
$575$	−1.88874	−	5.81295i	−0.0787660	−	0.242417i
$576$		0			0
$577$	−32.5505	−	23.6493i	−1.35509	−	0.984533i	−0.998740	−	0.0501822i	$-0.984020\pi$
$577$	−32.5505	−	23.6493i	−1.35509	−	0.984533i	−0.356354	−	0.934351i	$-0.615980\pi$
$578$		0			0
$579$	1.04241	−	3.20822i	0.0433212	−	0.133329i
$580$		0			0
$581$	20.3342	−	14.7737i	0.843605	−	0.612915i
$582$		0			0
$583$	−15.3014	+	33.5569i	−0.633721	+	1.38978i
$584$		0			0
$585$	1.57267	−	1.14261i	0.0650219	−	0.0472412i
$586$		0			0
$587$	9.73384	−	29.9577i	0.401759	−	1.23649i	−0.521813	−	0.853060i	$-0.674744\pi$
$587$	9.73384	−	29.9577i	0.401759	−	1.23649i	0.923572	−	0.383426i	$-0.125256\pi$
$588$		0			0
$589$	−12.9314	−	9.39525i	−0.532831	−	0.387124i
$590$		0			0
$591$	1.01487	+	3.12346i	0.0417463	+	0.128482i
$592$		0			0
$593$	15.9481			0.654909			0.327454	−	0.944867i	$-0.393809\pi$
$593$	15.9481			0.654909			0.327454	+	0.944867i	$0.393809\pi$
$594$		0			0
$595$	−8.74640			−0.358568
$596$		0			0
$597$	0.560543	+	1.72517i	0.0229415	+	0.0706067i
$598$		0			0
$599$	35.3013	+	25.6479i	1.44237	+	1.04794i	0.987540	+	0.157367i	$0.0503007\pi$
$599$	35.3013	+	25.6479i	1.44237	+	1.04794i	0.454832	+	0.890577i	$0.349699\pi$
$600$		0			0
$601$	0.147257	−	0.453211i	0.00600675	−	0.0184869i	−0.948008	−	0.318246i	$-0.896906\pi$
$601$	0.147257	−	0.453211i	0.00600675	−	0.0184869i	0.954015	+	0.299759i	$0.0969063\pi$
$602$		0			0
$603$	−13.4995	+	9.80799i	−0.549744	+	0.399412i
$604$		0			0
$605$	−10.1274	+	4.29369i	−0.411737	+	0.174563i
$606$		0			0
$607$	26.4257	−	19.1994i	1.07259	−	0.779280i	0.0962116	−	0.995361i	$-0.469327\pi$
$607$	26.4257	−	19.1994i	1.07259	−	0.779280i	0.976375	+	0.216081i	$0.0693275\pi$
$608$		0			0
$609$	0.855461	−	2.63284i	0.0346650	−	0.106688i
$610$		0			0
$611$	−3.86211	−	2.80599i	−0.156244	−	0.113518i
$612$		0			0
$613$	−15.0751	−	46.3965i	−0.608879	−	1.87394i	−0.467534	−	0.883975i	$-0.654858\pi$
$613$	−15.0751	−	46.3965i	−0.608879	−	1.87394i	−0.141344	−	0.989960i	$-0.545142\pi$
$614$		0			0
$615$	−0.760436			−0.0306637
$616$		0			0
$617$	−7.77343			−0.312947			−0.156473	−	0.987682i	$-0.550013\pi$
$617$	−7.77343			−0.312947			−0.156473	+	0.987682i	$0.550013\pi$
$618$		0			0
$619$	12.6221	+	38.8470i	0.507327	+	1.56139i	0.796823	+	0.604212i	$0.206512\pi$
$619$	12.6221	+	38.8470i	0.507327	+	1.56139i	−0.289497	+	0.957179i	$0.593488\pi$
$620$		0			0
$621$	4.71064	+	3.42248i	0.189032	+	0.137340i
$622$		0			0
$623$	0.00306908	−	0.00944566i	0.000122960	−	0.000378432i
$624$		0			0
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$		0			0
$627$	−0.652647	+	1.43129i	−0.0260642	+	0.0571601i
$628$		0			0
$629$	12.0110	−	8.72650i	0.478910	−	0.347949i
$630$		0			0
$631$	2.54159	−	7.82221i	0.101179	−	0.311397i	−0.887636	−	0.460546i	$-0.847654\pi$
$631$	2.54159	−	7.82221i	0.101179	−	0.311397i	0.988815	+	0.149149i	$0.0476535\pi$
$632$		0			0
$633$	3.62859	+	2.63632i	0.144223	+	0.104784i
$634$		0			0
$635$	−0.850846	−	2.61863i	−0.0337648	−	0.103917i
$636$		0			0
$637$	−1.86697			−0.0739721
$638$		0			0
$639$	−0.162679			−0.00643547
$640$		0			0
$641$	−10.3204	−	31.7630i	−0.407632	−	1.25456i	−0.918678	−	0.395008i	$-0.870742\pi$
$641$	−10.3204	−	31.7630i	−0.407632	−	1.25456i	0.511046	−	0.859553i	$-0.329258\pi$
$642$		0			0
$643$	−1.47304	−	1.07023i	−0.0580912	−	0.0422057i	0.558361	−	0.829598i	$-0.311431\pi$
$643$	−1.47304	−	1.07023i	−0.0580912	−	0.0422057i	−0.616452	+	0.787393i	$0.711431\pi$
$644$		0			0
$645$	0.499160	−	1.53626i	0.0196544	−	0.0604900i
$646$		0			0
$647$	−10.7974	+	7.84479i	−0.424491	+	0.308410i	−0.779442	−	0.626474i	$-0.784497\pi$
$647$	−10.7974	+	7.84479i	−0.424491	+	0.308410i	0.354952	+	0.934885i	$0.384497\pi$
$648$		0			0
$649$	−3.64579	−	17.9394i	−0.143110	−	0.704181i
$650$		0			0
$651$	−1.41096	+	1.02512i	−0.0552998	+	0.0401777i
$652$		0			0
$653$	6.98228	−	21.4893i	0.273238	−	0.840940i	−0.716442	−	0.697646i	$-0.754231\pi$
$653$	6.98228	−	21.4893i	0.273238	−	0.840940i	0.989680	−	0.143293i	$-0.0457693\pi$
$654$		0			0
$655$	2.31185	+	1.67965i	0.0903313	+	0.0656295i
$656$		0			0
$657$	6.56077	+	20.1920i	0.255960	+	0.787764i
$658$		0			0
$659$	−16.9078			−0.658636			−0.329318	−	0.944219i	$-0.606819\pi$
$659$	−16.9078			−0.658636			−0.329318	+	0.944219i	$0.606819\pi$
$660$		0			0
$661$	49.7772			1.93611			0.968055	−	0.250740i	$-0.0806738\pi$
$661$	49.7772			1.93611			0.968055	+	0.250740i	$0.0806738\pi$
$662$		0			0
$663$	0.138365	+	0.425843i	0.00537364	+	0.0165384i
$664$		0			0
$665$	4.89835	+	3.55886i	0.189950	+	0.138007i
$666$		0			0
$667$	16.1101	−	49.5818i	0.623786	−	1.91982i
$668$		0			0
$669$	2.53045	−	1.83848i	0.0978327	−	0.0710796i
$670$		0			0
$671$	31.6545	+	3.61346i	1.22201	+	0.139496i
$672$		0			0
$673$	20.9313	−	15.2075i	0.806843	−	0.586206i	−0.106071	−	0.994359i	$-0.533827\pi$
$673$	20.9313	−	15.2075i	0.806843	−	0.586206i	0.912914	+	0.408153i	$0.133827\pi$
$674$		0			0
$675$	0.294384	−	0.906022i	0.0113309	−	0.0348728i
$676$		0			0
$677$	23.4068	+	17.0060i	0.899597	+	0.653595i	0.938362	−	0.345653i	$-0.112343\pi$
$677$	23.4068	+	17.0060i	0.899597	+	0.653595i	−0.0387658	+	0.999248i	$0.512343\pi$
$678$		0			0
$679$	−11.4831	−	35.3413i	−0.440681	−	1.35628i
$680$		0			0
$681$	2.57026			0.0984926
$682$		0			0
$683$	11.9698			0.458011			0.229005	−	0.973425i	$-0.426453\pi$
$683$	11.9698			0.458011			0.229005	+	0.973425i	$0.426453\pi$
$684$		0			0
$685$	3.10951	+	9.57009i	0.118808	+	0.365654i
$686$		0			0
$687$	0.499098	+	0.362616i	0.0190418	+	0.0138347i
$688$		0			0
$689$	2.24565	−	6.91140i	0.0855524	−	0.263303i
$690$		0			0
$691$	23.7872	−	17.2824i	0.904909	−	0.657455i	−0.0348130	−	0.999394i	$-0.511084\pi$
$691$	23.7872	−	17.2824i	0.904909	−	0.657455i	0.939722	+	0.341939i	$0.111084\pi$
$692$		0			0
$693$	−14.8025	−	13.5698i	−0.562299	−	0.515474i
$694$		0			0
$695$	−0.310765	+	0.225784i	−0.0117880	+	0.00856448i
$696$		0			0
$697$	−6.33260	+	19.4897i	−0.239864	+	0.738227i
$698$		0			0
$699$	−3.66815	−	2.66506i	−0.138742	−	0.100802i
$700$		0			0
$701$	8.42772	+	25.9379i	0.318311	+	0.979659i	0.974370	+	0.224950i	$0.0722219\pi$
$701$	8.42772	+	25.9379i	0.318311	+	0.979659i	−0.656060	+	0.754709i	$0.727778\pi$
$702$		0			0
$703$	−10.2774			−0.387620
$704$		0			0
$705$	−1.16476			−0.0438675
$706$		0			0
$707$	1.66990	+	5.13941i	0.0628029	+	0.193287i
$708$		0			0
$709$	6.16553	+	4.47952i	0.231552	+	0.168232i	0.697511	−	0.716574i	$-0.254291\pi$
$709$	6.16553	+	4.47952i	0.231552	+	0.168232i	−0.465960	+	0.884806i	$0.654291\pi$
$710$		0			0
$711$	−2.69390	+	8.29098i	−0.101029	+	0.310936i
$712$		0			0
$713$	−26.5713	+	19.3052i	−0.995102	+	0.722984i
$714$		0			0
$715$	1.88669	−	1.06690i	0.0705583	−	0.0398999i
$716$		0			0
$717$	−0.215950	+	0.156897i	−0.00806481	+	0.00585943i
$718$		0			0
$719$	−6.58192	+	20.2571i	−0.245464	+	0.755461i	0.750096	+	0.661329i	$0.230007\pi$
$719$	−6.58192	+	20.2571i	−0.245464	+	0.755461i	−0.995560	+	0.0941314i	$0.969993\pi$
$720$		0			0
$721$	−27.1057	−	19.6935i	−1.00947	−	0.733423i
$722$		0			0
$723$	1.05777	+	3.25548i	0.0393389	+	0.121073i
$724$		0			0
$725$	−8.52954			−0.316779
$726$		0			0
$727$	6.19488			0.229755			0.114878	−	0.993380i	$-0.463352\pi$
$727$	6.19488			0.229755			0.114878	+	0.993380i	$0.463352\pi$
$728$		0			0
$729$	−7.92220	−	24.3820i	−0.293415	−	0.903037i
$730$		0			0
$731$	−35.2170	−	25.5866i	−1.30255	−	0.946356i
$732$		0			0
$733$	−3.15230	+	9.70179i	−0.116433	+	0.358344i	−0.992243	−	0.124312i	$-0.960328\pi$
$733$	−3.15230	+	9.70179i	−0.116433	+	0.358344i	0.875810	+	0.482656i	$0.160328\pi$
$734$		0			0
$735$	−0.368524	+	0.267748i	−0.0135932	+	0.00987605i
$736$		0			0
$737$	−16.1950	+	9.15813i	−0.596552	+	0.337344i
$738$		0			0
$739$	3.50898	−	2.54942i	0.129080	−	0.0937819i	−0.521372	−	0.853329i	$-0.674580\pi$
$739$	3.50898	−	2.54942i	0.129080	−	0.0937819i	0.650452	+	0.759548i	$0.274580\pi$
$740$		0			0
$741$	0.0957828	−	0.294789i	0.00351867	−	0.0108294i
$742$		0			0
$743$	6.08102	+	4.41812i	0.223091	+	0.162085i	0.693717	−	0.720248i	$-0.255972\pi$
$743$	6.08102	+	4.41812i	0.223091	+	0.162085i	−0.470626	+	0.882333i	$0.655972\pi$
$744$		0			0
$745$	−2.56743	−	7.90172i	−0.0940632	−	0.289497i
$746$		0			0
$747$	36.7306			1.34390
$748$		0			0
$749$	25.0381			0.914871
$750$		0			0
$751$	12.5726	+	38.6946i	0.458782	+	1.41199i	0.866637	+	0.498939i	$0.166277\pi$
$751$	12.5726	+	38.6946i	0.458782	+	1.41199i	−0.407855	+	0.913047i	$0.633723\pi$
$752$		0			0
$753$	−2.31145	−	1.67937i	−0.0842339	−	0.0611995i
$754$		0			0
$755$	1.65310	−	5.08772i	0.0601625	−	0.185161i
$756$		0			0
$757$	21.1944	−	15.3986i	0.770323	−	0.559672i	−0.131736	−	0.991285i	$-0.542055\pi$
$757$	21.1944	−	15.3986i	0.770323	−	0.559672i	0.902059	+	0.431613i	$0.142055\pi$
$758$		0			0
$759$	2.38263	+	2.18422i	0.0864841	+	0.0792823i
$760$		0			0
$761$	−28.4182	+	20.6470i	−1.03016	+	0.748453i	−0.968340	−	0.249634i	$-0.919690\pi$
$761$	−28.4182	+	20.6470i	−1.03016	+	0.748453i	−0.0618172	+	0.998087i	$0.519690\pi$
$762$		0			0
$763$	−5.49514	+	16.9123i	−0.198938	+	0.612267i
$764$		0			0
$765$	−10.3406	−	7.51288i	−0.373865	−	0.271629i
$766$		0			0
$767$	1.11464	+	3.43052i	0.0402475	+	0.123869i
$768$		0			0
$769$	−29.6963			−1.07088			−0.535439	−	0.844574i	$-0.679854\pi$
$769$	−29.6963			−1.07088			−0.535439	+	0.844574i	$0.679854\pi$
$770$		0			0
$771$	0.489232			0.0176193
$772$		0			0
$773$	−4.78158	−	14.7162i	−0.171981	−	0.529305i	0.827501	−	0.561464i	$-0.189762\pi$
$773$	−4.78158	−	14.7162i	−0.171981	−	0.529305i	−0.999483	+	0.0321592i	$0.989762\pi$
$774$		0			0
$775$	4.34733	+	3.15852i	0.156161	+	0.113457i
$776$		0			0
$777$	−0.346524	+	1.06649i	−0.0124315	+	0.0382602i
$778$		0			0
$779$	11.4768	−	8.33837i	0.411198	−	0.298753i
$780$		0			0
$781$	−0.180215	−	0.0205721i	−0.00644860	−	0.000736128i
$782$		0			0
$783$	6.57379	−	4.77614i	0.234928	−	0.170685i
$784$		0			0
$785$	−2.32242	+	7.14768i	−0.0828907	+	0.255111i
$786$		0			0
$787$	−18.8179	−	13.6720i	−0.670784	−	0.487353i	0.199503	−	0.979897i	$-0.436067\pi$
$787$	−18.8179	−	13.6720i	−0.670784	−	0.487353i	−0.870288	+	0.492544i	$0.836067\pi$
$788$		0			0
$789$	−1.00654	−	3.09780i	−0.0358336	−	0.110285i
$790$		0			0
$791$	−3.36228			−0.119549
$792$		0			0
$793$	−6.27776			−0.222930
$794$		0			0
$795$	−0.547914	−	1.68630i	−0.0194325	−	0.0598071i
$796$		0			0
$797$	1.49693	+	1.08758i	0.0530240	+	0.0385242i	0.613982	−	0.789320i	$-0.289567\pi$
$797$	1.49693	+	1.08758i	0.0530240	+	0.0385242i	−0.560958	+	0.827845i	$0.689567\pi$
$798$		0			0
$799$	−9.69968	+	29.8525i	−0.343150	+	1.05611i
$800$		0			0
$801$	0.0117420	−	0.00853106i	0.000414883	−	0.000301430i
$802$		0			0
$803$	4.71455	+	23.1983i	0.166373	+	0.818649i
$804$		0			0
$805$	10.0650	−	7.31267i	0.354745	−	0.257738i
$806$		0			0
$807$	−0.399623	+	1.22991i	−0.0140674	+	0.0432950i
$808$		0			0
$809$	−27.4388	−	19.9354i	−0.964696	−	0.700893i	−0.0104597	−	0.999945i	$-0.503329\pi$
$809$	−27.4388	−	19.9354i	−0.964696	−	0.700893i	−0.954237	+	0.299052i	$0.903329\pi$
$810$		0			0
$811$	17.3581	+	53.4228i	0.609526	+	1.87593i	0.462024	+	0.886868i	$0.347124\pi$
$811$	17.3581	+	53.4228i	0.609526	+	1.87593i	0.147503	+	0.989062i	$0.452876\pi$
$812$		0			0
$813$	−1.63892			−0.0574793
$814$		0			0
$815$	−3.04066			−0.106510
$816$		0			0
$817$	9.31193	+	28.6592i	0.325783	+	1.00266i
$818$		0			0
$819$	3.20114	+	2.32576i	0.111857	+	0.0812688i
$820$		0			0
$821$	3.61846	−	11.1365i	0.126285	−	0.388666i	−0.867848	−	0.496830i	$-0.834497\pi$
$821$	3.61846	−	11.1365i	0.126285	−	0.388666i	0.994133	+	0.108164i	$0.0344972\pi$
$822$		0			0
$823$	−11.7102	+	8.50793i	−0.408191	+	0.296568i	−0.772869	−	0.634566i	$-0.781179\pi$
$823$	−11.7102	+	8.50793i	−0.408191	+	0.296568i	0.364678	+	0.931134i	$0.381179\pi$
$824$		0			0
$825$	0.219408	−	0.481174i	0.00763882	−	0.0167523i
$826$		0			0
$827$	−37.6707	+	27.3693i	−1.30994	+	0.951725i	−0.309938	+	0.950757i	$0.600308\pi$
$827$	−37.6707	+	27.3693i	−1.30994	+	0.951725i	−1.00000		0.000968458i	$0.999692\pi$
$828$		0			0
$829$	2.05309	−	6.31876i	0.0713068	−	0.219460i	−0.909052	−	0.416683i	$-0.863192\pi$
$829$	2.05309	−	6.31876i	0.0713068	−	0.219460i	0.980359	+	0.197223i	$0.0631925\pi$
$830$		0			0
$831$	−2.15340	−	1.56454i	−0.0747008	−	0.0542733i
$832$		0			0
$833$	3.79339	+	11.6749i	0.131433	+	0.404510i
$834$		0			0
$835$	13.7870			0.477118
$836$		0			0
$837$	−5.11914			−0.176943
$838$		0			0
$839$	0.276899	+	0.852208i	0.00955962	+	0.0294215i	0.955723	−	0.294269i	$-0.0950763\pi$
$839$	0.276899	+	0.852208i	0.00955962	+	0.0294215i	−0.946163	+	0.323691i	$0.895076\pi$
$840$		0			0
$841$	−35.3970	−	25.7174i	−1.22059	−	0.886808i
$842$		0			0
$843$	−1.01529	+	3.12473i	−0.0349683	+	0.107621i
$844$		0			0
$845$	10.1717	−	7.39018i	0.349917	−	0.254230i
$846$		0			0
$847$	−14.6821	−	16.9045i	−0.504483	−	0.580844i
$848$		0			0
$849$	−3.79770	+	2.75919i	−0.130337	+	0.0946952i
$850$		0			0
$851$	−6.52577	+	20.0843i	−0.223700	+	0.688479i
$852$		0			0
$853$	25.2255	+	18.3274i	0.863706	+	0.627519i	0.928891	−	0.370354i	$-0.120764\pi$
$853$	25.2255	+	18.3274i	0.863706	+	0.627519i	−0.0651850	+	0.997873i	$0.520764\pi$
$854$		0			0
$855$	2.73421	+	8.41504i	0.0935081	+	0.287788i
$856$		0			0
$857$	−45.0004			−1.53718			−0.768592	−	0.639740i	$-0.779042\pi$
$857$	−45.0004			−1.53718			−0.768592	+	0.639740i	$0.779042\pi$
$858$		0			0
$859$	−31.3959			−1.07122			−0.535608	−	0.844467i	$-0.679917\pi$
$859$	−31.3959			−1.07122			−0.535608	+	0.844467i	$0.679917\pi$
$860$		0			0
$861$	−0.478312	−	1.47209i	−0.0163008	−	0.0501688i
$862$		0			0
$863$	35.3252	+	25.6652i	1.20248	+	0.873654i	0.994527	−	0.104484i	$-0.0333191\pi$
$863$	35.3252	+	25.6652i	1.20248	+	0.873654i	0.207956	+	0.978138i	$0.433319\pi$
$864$		0			0
$865$	−4.26425	+	13.1240i	−0.144989	+	0.446230i
$866$		0			0
$867$	0.188850	−	0.137207i	0.00641367	−	0.00465980i
$868$		0			0
$869$	−4.03276	+	8.84405i	−0.136802	+	0.300014i
$870$		0			0
$871$	2.96585	−	2.15482i	0.100494	−	0.0730131i
$872$		0			0
$873$	16.7810	−	51.6465i	0.567950	−	1.74797i
$874$		0			0
$875$	−1.64674	−	1.19643i	−0.0556699	−	0.0404466i
$876$		0			0
$877$	−8.05620	−	24.7944i	−0.272038	−	0.837248i	−0.989988	−	0.141153i	$-0.954919\pi$
$877$	−8.05620	−	24.7944i	−0.272038	−	0.837248i	0.717949	−	0.696095i	$-0.245081\pi$
$878$		0			0
$879$	−1.16308			−0.0392298
$880$		0			0
$881$	−25.3513			−0.854106			−0.427053	−	0.904227i	$-0.640448\pi$
$881$	−25.3513			−0.854106			−0.427053	+	0.904227i	$0.640448\pi$
$882$		0			0
$883$	−1.08110	−	3.32728i	−0.0363819	−	0.111972i	0.931216	−	0.364467i	$-0.118749\pi$
$883$	−1.08110	−	3.32728i	−0.0363819	−	0.111972i	−0.967598	+	0.252495i	$0.918749\pi$
$884$		0			0
$885$	0.712003	+	0.517300i	0.0239337	+	0.0173889i
$886$		0			0
$887$	−11.4323	+	35.1849i	−0.383858	+	1.18139i	0.553447	+	0.832885i	$0.313312\pi$
$887$	−11.4323	+	35.1849i	−0.383858	+	1.18139i	−0.937305	+	0.348510i	$0.886688\pi$
$888$		0			0
$889$	4.53412	−	3.29423i	0.152070	−	0.110485i
$890$		0			0
$891$	−5.79406	−	28.5101i	−0.194108	−	0.955123i
$892$		0			0
$893$	17.5790	−	12.7719i	0.588260	−	0.427396i
$894$		0			0
$895$	1.54508	−	4.75528i	0.0516465	−	0.158952i
$896$		0			0
$897$	−0.515262	−	0.374360i	−0.0172041	−	0.0124995i
$898$		0			0
$899$	14.1636	+	43.5910i	0.472382	+	1.45384i
$900$		0			0
$901$	−47.7823			−1.59186
$902$		0			0
$903$	3.28794			0.109416
$904$		0			0
$905$	6.94262	+	21.3672i	0.230780	+	0.710269i
$906$		0			0
$907$	2.69877	+	1.96077i	0.0896111	+	0.0651063i	0.631689	−	0.775222i	$-0.282362\pi$
$907$	2.69877	+	1.96077i	0.0896111	+	0.0651063i	−0.542078	+	0.840328i	$0.682362\pi$
$908$		0			0
$909$	−2.44032	+	7.51054i	−0.0809404	+	0.249109i
$910$		0			0
$911$	−22.5772	+	16.4033i	−0.748017	+	0.543466i	−0.895212	−	0.445641i	$-0.852976\pi$
$911$	−22.5772	+	16.4033i	−0.748017	+	0.543466i	0.147194	+	0.989108i	$0.452976\pi$
$912$		0			0
$913$	40.6900	+	4.64489i	1.34664	+	0.153723i
$914$		0			0
$915$	−1.23918	+	0.900314i	−0.0409659	+	0.0297635i
$916$		0			0
$917$	−1.79742	+	5.53190i	−0.0593562	+	0.182679i
$918$		0			0
$919$	39.9573	+	29.0307i	1.31807	+	0.957635i	0.999954	+	0.00958329i	$0.00305050\pi$
$919$	39.9573	+	29.0307i	1.31807	+	0.957635i	0.318117	+	0.948051i	$0.396949\pi$
$920$		0			0
$921$	−0.134011	−	0.412444i	−0.00441582	−	0.0135905i
$922$		0			0
$923$	0.0357405			0.00117641
$924$		0			0
$925$	3.45509			0.113603
$926$		0			0
$927$	−15.1302	−	46.5659i	−0.496940	−	1.52943i
$928$		0			0
$929$	−16.9604	−	12.3224i	−0.556451	−	0.404286i	0.273707	−	0.961813i	$-0.411750\pi$
$929$	−16.9604	−	12.3224i	−0.556451	−	0.404286i	−0.830159	+	0.557527i	$0.811750\pi$
$930$		0			0
$931$	2.62597	−	8.08191i	0.0860628	−	0.264874i
$932$		0			0
$933$	−1.96558	+	1.42807i	−0.0643501	+	0.0467531i
$934$		0			0
$935$	−10.5052	−	9.63039i	−0.343557	−	0.314948i
$936$		0			0
$937$	−4.56205	+	3.31452i	−0.149036	+	0.108281i	−0.659804	−	0.751437i	$-0.729361\pi$
$937$	−4.56205	+	3.31452i	−0.149036	+	0.108281i	0.510769	+	0.859718i	$0.329361\pi$
$938$		0			0
$939$	1.42703	−	4.39194i	0.0465693	−	0.143325i
$940$		0			0
$941$	8.84980	+	6.42976i	0.288495	+	0.209604i	0.722614	−	0.691251i	$-0.242940\pi$
$941$	8.84980	+	6.42976i	0.288495	+	0.209604i	−0.434119	+	0.900856i	$0.642940\pi$
$942$		0			0
$943$	−9.00762	−	27.7226i	−0.293328	−	0.902772i
$944$		0			0
$945$	1.93910			0.0630788
$946$		0			0
$947$	−20.5884			−0.669032			−0.334516	−	0.942390i	$-0.608573\pi$
$947$	−20.5884			−0.669032			−0.334516	+	0.942390i	$0.608573\pi$
$948$		0			0
$949$	−1.44140	−	4.43618i	−0.0467899	−	0.144004i
$950$		0			0
$951$	−0.784952	−	0.570301i	−0.0254538	−	0.0184933i
$952$		0			0
$953$	−0.454983	+	1.40029i	−0.0147384	+	0.0453600i	−0.958155	−	0.286249i	$-0.907592\pi$
$953$	−0.454983	+	1.40029i	−0.0147384	+	0.0453600i	0.943417	+	0.331609i	$0.107592\pi$
$954$		0			0
$955$	5.83178	−	4.23704i	0.188712	−	0.137107i
$956$		0			0
$957$	3.92642	−	2.22035i	0.126923	−	0.0717737i
$958$		0			0
$959$	−16.5704	+	12.0391i	−0.535087	+	0.388764i
$960$		0			0
$961$	−0.656515	+	2.02055i	−0.0211779	+	0.0651789i
$962$		0			0
$963$	29.6017	+	21.5069i	0.953901	+	0.693050i
$964$		0			0
$965$	−6.53755	−	20.1205i	−0.210451	−	0.647702i
$966$		0			0
$967$	5.72960			0.184252			0.0921258	−	0.995747i	$-0.470634\pi$
$967$	5.72960			0.184252			0.0921258	+	0.995747i	$0.470634\pi$
$968$		0			0
$969$	−2.03804			−0.0654713
$970$		0			0
$971$	4.37523	+	13.4656i	0.140408	+	0.432131i	0.996392	−	0.0848714i	$-0.0270479\pi$
$971$	4.37523	+	13.4656i	0.140408	+	0.432131i	−0.855984	+	0.517002i	$0.827048\pi$
$972$		0			0
$973$	−0.632556	−	0.459579i	−0.0202788	−	0.0147334i
$974$		0			0
$975$	−0.0322005	+	0.0991029i	−0.00103124	+	0.00317383i
$976$		0			0
$977$	−0.372572	+	0.270689i	−0.0119196	+	0.00866012i	−0.593729	−	0.804665i	$-0.702345\pi$
$977$	−0.372572	+	0.270689i	−0.0119196	+	0.00866012i	0.581809	+	0.813325i	$0.302345\pi$
$978$		0			0
$979$	0.0140866	−	0.00796580i	0.000450208	−	0.000254588i
$980$		0			0
$981$	−21.0239	+	15.2747i	−0.671240	+	0.487685i
$982$		0			0
$983$	4.06585	−	12.5134i	0.129680	−	0.399115i	−0.865044	−	0.501696i	$-0.832710\pi$
$983$	4.06585	−	12.5134i	0.129680	−	0.399115i	0.994725	+	0.102580i	$0.0327098\pi$
$984$		0			0
$985$	16.6633	+	12.1066i	0.530938	+	0.385749i
$986$		0			0
$987$	−0.732634	−	2.25481i	−0.0233200	−	0.0717715i
$988$		0			0
$989$	61.9188			1.96890
$990$		0			0
$991$	−37.4029			−1.18814			−0.594072	−	0.804412i	$-0.702480\pi$
$991$	−37.4029			−1.18814			−0.594072	+	0.804412i	$0.702480\pi$
$992$		0			0
$993$	−0.889582	−	2.73785i	−0.0282300	−	0.0868831i
$994$		0			0
$995$	9.20363	+	6.68683i	0.291775	+	0.211987i
$996$		0			0
$997$	−2.51288	+	7.73384i	−0.0795836	+	0.244933i	−0.982930	−	0.183978i	$-0.941103\pi$
$997$	−2.51288	+	7.73384i	−0.0795836	+	0.244933i	0.903347	+	0.428911i	$0.141103\pi$
$998$		0			0
$999$	−2.66286	+	1.93468i	−0.0842493	+	0.0612107i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	220.2.m.b.201.1	yes	8
3.2	odd	2		1980.2.z.d.1081.2		8
4.3	odd	2		880.2.bo.c.641.2		8
5.2	odd	4		1100.2.cb.b.949.2		16
5.3	odd	4		1100.2.cb.b.949.3		16
5.4	even	2		1100.2.n.b.201.2		8
11.2	odd	10		2420.2.a.l.1.2		4
11.4	even	5	inner	220.2.m.b.81.1	✓	8
11.9	even	5		2420.2.a.k.1.2		4
33.26	odd	10		1980.2.z.d.1621.2		8
44.15	odd	10		880.2.bo.c.81.2		8
44.31	odd	10		9680.2.a.cp.1.3		4
44.35	even	10		9680.2.a.co.1.3		4
55.4	even	10		1100.2.n.b.301.2		8
55.37	odd	20		1100.2.cb.b.1049.3		16
55.48	odd	20		1100.2.cb.b.1049.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.2.m.b.81.1	✓	8	11.4	even	5	inner
220.2.m.b.201.1	yes	8	1.1	even	1	trivial
880.2.bo.c.81.2		8	44.15	odd	10
880.2.bo.c.641.2		8	4.3	odd	2
1100.2.n.b.201.2		8	5.4	even	2
1100.2.n.b.301.2		8	55.4	even	10
1100.2.cb.b.949.2		16	5.2	odd	4
1100.2.cb.b.949.3		16	5.3	odd	4
1100.2.cb.b.1049.2		16	55.48	odd	20
1100.2.cb.b.1049.3		16	55.37	odd	20
1980.2.z.d.1081.2		8	3.2	odd	2
1980.2.z.d.1621.2		8	33.26	odd	10
2420.2.a.k.1.2		4	11.9	even	5
2420.2.a.l.1.2		4	11.2	odd	10
9680.2.a.co.1.3		4	44.35	even	10
9680.2.a.cp.1.3		4	44.31	odd	10

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	220.m (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0492728 - 0.151646i) q^{3} +(-0.809017 - 0.587785i) q^{5} +(0.628998 - 1.93586i) q^{7} +(2.40648 - 1.74841i) q^{9} +(2.88699 - 1.63256i) q^{11} +(-0.528704 + 0.384126i) q^{13} +(-0.0492728 + 0.151646i) q^{15} +(3.47632 + 2.52570i) q^{17} +(-0.919194 - 2.82899i) q^{19} -0.324558 q^{21} -6.11210 q^{23} +(0.309017 + 0.951057i) q^{25} +(-0.770708 - 0.559952i) q^{27} +(-2.63577 + 8.11208i) q^{29} +(4.34733 - 3.15852i) q^{31} +(-0.389823 - 0.357361i) q^{33} +(-1.64674 + 1.19643i) q^{35} +(1.06768 - 3.28598i) q^{37} +(0.0843020 + 0.0612490i) q^{39} +(1.47374 + 4.53569i) q^{41} -10.1305 q^{43} -2.97458 q^{45} +(2.25733 + 6.94734i) q^{47} +(2.31122 + 1.67920i) q^{49} +(0.211724 - 0.651620i) q^{51} +(-8.99626 + 6.53617i) q^{53} +(-3.29522 - 0.376160i) q^{55} +(-0.383714 + 0.278785i) q^{57} +(1.70562 - 5.24935i) q^{59} +(7.77155 + 5.64636i) q^{61} +(-1.87100 - 5.75835i) q^{63} +0.653514 q^{65} -5.60966 q^{67} +(0.301160 + 0.926876i) q^{69} +(-0.0442449 - 0.0321458i) q^{71} +(-2.20562 + 6.78819i) q^{73} +(0.128998 - 0.0937225i) q^{75} +(-1.34450 - 6.61569i) q^{77} +(-2.37100 + 1.72263i) q^{79} +(2.71064 - 8.34250i) q^{81} +(9.98988 + 7.25807i) q^{83} +(-1.32784 - 4.08666i) q^{85} +1.36004 q^{87} +0.00487932 q^{89} +(0.411059 + 1.26511i) q^{91} +(-0.693182 - 0.503626i) q^{93} +(-0.919194 + 2.82899i) q^{95} +(14.7696 - 10.7307i) q^{97} +(4.09311 - 8.97639i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 5 q^{3} - 2 q^{5} - q^{7} + 3 q^{9} + 5 q^{11} + 4 q^{13} + 5 q^{15} + 9 q^{17} - 7 q^{19} - 28 q^{21} - 10 q^{23} - 2 q^{25} - 10 q^{27} - q^{29} + 22 q^{31} + q^{33} + 4 q^{35} + 4 q^{37} + 27 q^{39}+ \cdots + 60 q^{99}+O(q^{100}) \) 8 * q + 5 * q^3 - 2 * q^5 - q^7 + 3 * q^9 + 5 * q^11 + 4 * q^13 + 5 * q^15 + 9 * q^17 - 7 * q^19 - 28 * q^21 - 10 * q^23 - 2 * q^25 - 10 * q^27 - q^29 + 22 * q^31 + q^33 + 4 * q^35 + 4 * q^37 + 27 * q^39 + 24 * q^41 - 22 * q^43 + 8 * q^45 - 6 * q^47 - 27 * q^49 - 47 * q^51 - q^53 - 5 * q^55 - 25 * q^57 - 9 * q^59 + 22 * q^61 - 21 * q^63 - 26 * q^65 - 2 * q^67 + 11 * q^69 - 22 * q^71 + 5 * q^73 - 5 * q^75 + 16 * q^77 - 25 * q^79 - 28 * q^81 + 33 * q^83 + 4 * q^85 + 14 * q^87 + 8 * q^89 + 14 * q^91 + 31 * q^93 - 7 * q^95 + 20 * q^97 + 60 * q^99

Introduction

L-functions

Modular forms

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Database

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