LMFDB - Embedded newform 880.2.cd.b.609.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [880,2,Mod(49,880)] 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("880.49"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(880, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 5, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 880 = 2^{4} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	880.cd (of order $10$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,0,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$7.02683537787$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 8 x^{14} + 10 x^{13} - 109 x^{12} + 280 x^{11} - 198 x^{10} - 1168 x^{9} + \cdots + 390625 $ x^16 - 4x^15 + 8x^14 + 10x^13 - 109x^12 + 280x^11 - 198x^10 - 1168x^9 + 4281x^8 - 5840x^7 - 4950x^6 + 35000x^5 - 68125x^4 + 31250x^3 + 125000x^2 - 312500*x + 390625
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 110)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			609.3
Root			$-2.23122 + 0.147217i$ of defining polynomial
Character	$\chi$	$=$	880.609
Dual form			880.2.cd.b.289.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.53884 + 0.500000i) q^{3} +(-1.43058 + 1.71856i) q^{5} +(3.59321 - 1.16751i) q^{7} +(-0.309017 - 0.224514i) q^{9} +(2.64861 - 1.99621i) q^{11} +(1.82151 - 2.50710i) q^{13} +(-3.06071 + 1.92930i) q^{15} +(1.93806 + 2.66751i) q^{17} +(0.400863 - 1.23373i) q^{19} +6.11314 q^{21} +0.556884i q^{23} +(-0.906896 - 4.91707i) q^{25} +(-3.21644 - 4.42705i) q^{27} +(2.95763 + 9.10264i) q^{29} +(4.32760 + 3.14419i) q^{31} +(5.07390 - 1.74755i) q^{33} +(-3.13394 + 7.84536i) q^{35} +(-7.52785 + 2.44595i) q^{37} +(4.05657 - 2.94727i) q^{39} +(1.94312 - 5.98030i) q^{41} +3.61803i q^{43} +(0.827913 - 0.209880i) q^{45} +(5.08740 + 1.65300i) q^{47} +(5.88499 - 4.27570i) q^{49} +(1.64861 + 5.07390i) q^{51} +(-6.47398 + 8.91067i) q^{53} +(-0.358428 + 7.40753i) q^{55} +(1.23373 - 1.69808i) q^{57} +(1.63693 + 5.03795i) q^{59} +(-1.98801 + 1.44437i) q^{61} +(-1.37249 - 0.445947i) q^{63} +(1.70278 + 6.71698i) q^{65} -9.21247i q^{67} +(-0.278442 + 0.856956i) q^{69} +(8.81173 - 6.40210i) q^{71} +(-3.22994 + 1.04947i) q^{73} +(1.06296 - 8.02003i) q^{75} +(7.18643 - 10.2651i) q^{77} +(-13.2383 - 9.61817i) q^{79} +(-2.38197 - 7.33094i) q^{81} +(-0.108199 - 0.148923i) q^{83} +(-7.35681 - 0.485408i) q^{85} +15.4863i q^{87} -6.09017 q^{89} +(3.61803 - 11.1352i) q^{91} +(5.08740 + 7.00220i) q^{93} +(1.54677 + 2.45385i) q^{95} +(7.26384 - 9.99782i) q^{97} +(-1.26664 + 0.0222142i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{5} + 4 q^{9} + 20 q^{11} - 2 q^{15} + 16 q^{19} - 16 q^{21} + 16 q^{29} + 4 q^{31} + 48 q^{35} + 8 q^{39} + 40 q^{41} - 4 q^{45} + 84 q^{49} + 4 q^{51} - 32 q^{55} + 20 q^{61} + 72 q^{65} + 56 q^{71}+ \cdots + 20 q^{99}+O(q^{100}) $ 16 * q - 6 * q^5 + 4 * q^9 + 20 * q^11 - 2 * q^15 + 16 * q^19 - 16 * q^21 + 16 * q^29 + 4 * q^31 + 48 * q^35 + 8 * q^39 + 40 * q^41 - 4 * q^45 + 84 * q^49 + 4 * q^51 - 32 * q^55 + 20 * q^61 + 72 * q^65 + 56 * q^71 - 32 * q^75 - 36 * q^79 - 56 * q^81 - 54 * q^85 - 8 * q^89 + 40 * q^91 + 50 * q^95 + 20 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/880\mathbb{Z}\right)^\times$.

$n$	$111$	$177$	$321$	$661$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{5}\right)$	$1$

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
$3$	1.53884	+	0.500000i	0.888451	+	0.288675i	0.717462	−	0.696598i	$-0.245304\pi$
$3$	1.53884	+	0.500000i	0.888451	+	0.288675i	0.170989	+	0.985273i	$0.445304\pi$
$4$		0			0
$5$	−1.43058	+	1.71856i	−0.639774	+	0.768563i
$5$	−1.43058	+	1.71856i	−0.639774	+	0.768563i
$6$		0			0
$7$	3.59321	−	1.16751i	1.35811	−	0.441276i	0.462696	−	0.886517i	$-0.346882\pi$
$7$	3.59321	−	1.16751i	1.35811	−	0.441276i	0.895411	+	0.445241i	$0.146882\pi$
$8$		0			0
$9$	−0.309017	−	0.224514i	−0.103006	−	0.0748380i
$10$		0			0
$11$	2.64861	−	1.99621i	0.798586	−	0.601881i
$11$	2.64861	−	1.99621i	0.798586	−	0.601881i
$12$		0			0
$13$	1.82151	−	2.50710i	0.505197	−	0.695344i	−0.477903	−	0.878412i	$-0.658603\pi$
$13$	1.82151	−	2.50710i	0.505197	−	0.695344i	0.983100	+	0.183069i	$0.0586031\pi$
$14$		0			0
$15$	−3.06071	+	1.92930i	−0.790273	+	0.498144i
$16$		0			0
$17$	1.93806	+	2.66751i	0.470048	+	0.646965i	0.976554	−	0.215271i	$-0.0690634\pi$
$17$	1.93806	+	2.66751i	0.470048	+	0.646965i	−0.506507	+	0.862236i	$0.669063\pi$
$18$		0			0
$19$	0.400863	−	1.23373i	0.0919642	−	0.283037i	−0.894486	−	0.447095i	$-0.852459\pi$
$19$	0.400863	−	1.23373i	0.0919642	−	0.283037i	0.986451	+	0.164058i	$0.0524586\pi$
$20$		0			0
$21$	6.11314			1.33400
$22$		0			0
$23$			0.556884i			0.116118i	0.998313	+	0.0580591i	$0.0184912\pi$
$23$			0.556884i			0.116118i	−0.998313	+	0.0580591i	$0.981509\pi$
$24$		0			0
$25$	−0.906896	−	4.91707i	−0.181379	−	0.983413i
$26$		0			0
$27$	−3.21644	−	4.42705i	−0.619004	−	0.851986i
$28$		0			0
$29$	2.95763	+	9.10264i	0.549217	+	1.69032i	0.710746	+	0.703449i	$0.248358\pi$
$29$	2.95763	+	9.10264i	0.549217	+	1.69032i	−0.161528	+	0.986868i	$0.551642\pi$
$30$		0			0
$31$	4.32760	+	3.14419i	0.777260	+	0.564712i	0.904155	−	0.427204i	$-0.140501\pi$
$31$	4.32760	+	3.14419i	0.777260	+	0.564712i	−0.126896	+	0.991916i	$0.540501\pi$
$32$		0			0
$33$	5.07390	−	1.74755i	0.883252	−	0.304210i
$34$		0			0
$35$	−3.13394	+	7.84536i	−0.529733	+	1.32611i
$36$		0			0
$37$	−7.52785	+	2.44595i	−1.23757	+	0.402111i	−0.853452	−	0.521172i	$-0.825495\pi$
$37$	−7.52785	+	2.44595i	−1.23757	+	0.402111i	−0.384120	+	0.923283i	$0.625495\pi$
$38$		0			0
$39$	4.05657	−	2.94727i	0.649571	−	0.471941i
$40$		0			0
$41$	1.94312	−	5.98030i	0.303464	−	0.933966i	−0.676782	−	0.736183i	$-0.736626\pi$
$41$	1.94312	−	5.98030i	0.303464	−	0.933966i	0.980246	−	0.197782i	$-0.0633739\pi$
$42$		0			0
$43$			3.61803i			0.551745i	0.961194	+	0.275873i	$0.0889668\pi$
$43$			3.61803i			0.551745i	−0.961194	+	0.275873i	$0.911033\pi$
$44$		0			0
$45$	0.827913	−	0.209880i	0.123418	−	0.0312870i
$46$		0			0
$47$	5.08740	+	1.65300i	0.742073	+	0.241114i	0.655567	−	0.755137i	$-0.272430\pi$
$47$	5.08740	+	1.65300i	0.742073	+	0.241114i	0.0865064	+	0.996251i	$0.472430\pi$
$48$		0			0
$49$	5.88499	−	4.27570i	0.840713	−	0.610814i
$50$		0			0
$51$	1.64861	+	5.07390i	0.230851	+	0.710488i
$52$		0			0
$53$	−6.47398	+	8.91067i	−0.889270	+	1.22397i	0.0844964	+	0.996424i	$0.473072\pi$
$53$	−6.47398	+	8.91067i	−0.889270	+	1.22397i	−0.973766	+	0.227551i	$0.926928\pi$
$54$		0			0
$55$	−0.358428	+	7.40753i	−0.0483304	+	0.998831i
$56$		0			0
$57$	1.23373	−	1.69808i	0.163411	−	0.224916i
$58$		0			0
$59$	1.63693	+	5.03795i	0.213110	+	0.655886i	0.999282	+	0.0378782i	$0.0120599\pi$
$59$	1.63693	+	5.03795i	0.213110	+	0.655886i	−0.786172	+	0.618008i	$0.787940\pi$
$60$		0			0
$61$	−1.98801	+	1.44437i	−0.254538	+	0.184933i	−0.707736	−	0.706477i	$-0.750283\pi$
$61$	−1.98801	+	1.44437i	−0.254538	+	0.184933i	0.453197	+	0.891410i	$0.350283\pi$
$62$		0			0
$63$	−1.37249	−	0.445947i	−0.172917	−	0.0561841i
$64$		0			0
$65$	1.70278	+	6.71698i	0.211204	+	0.833139i
$66$		0			0
$67$		−	9.21247i		−	1.12548i	−0.826633	−	0.562741i	$-0.809747\pi$
$67$		−	9.21247i		−	1.12548i	0.826633	−	0.562741i	$-0.190253\pi$
$68$		0			0
$69$	−0.278442	+	0.856956i	−0.0335205	+	0.103165i
$70$		0			0
$71$	8.81173	−	6.40210i	1.04576	−	0.759789i	0.0743582	−	0.997232i	$-0.476309\pi$
$71$	8.81173	−	6.40210i	1.04576	−	0.759789i	0.971402	+	0.237443i	$0.0763092\pi$
$72$		0			0
$73$	−3.22994	+	1.04947i	−0.378036	+	0.122831i	−0.491871	−	0.870668i	$-0.663687\pi$
$73$	−3.22994	+	1.04947i	−0.378036	+	0.122831i	0.113834	+	0.993500i	$0.463687\pi$
$74$		0			0
$75$	1.06296	−	8.02003i	0.122741	−	0.926074i
$76$		0			0
$77$	7.18643	−	10.2651i	0.818969	−	1.16982i
$78$		0			0
$79$	−13.2383	−	9.61817i	−1.48942	−	1.08213i	−0.974365	−	0.224972i	$-0.927771\pi$
$79$	−13.2383	−	9.61817i	−1.48942	−	1.08213i	−0.515057	−	0.857156i	$-0.672229\pi$
$80$		0			0
$81$	−2.38197	−	7.33094i	−0.264663	−	0.814549i
$82$		0			0
$83$	−0.108199	−	0.148923i	−0.0118764	−	0.0163464i	0.803038	−	0.595928i	$-0.203216\pi$
$83$	−0.108199	−	0.148923i	−0.0118764	−	0.0163464i	−0.814914	+	0.579582i	$0.803216\pi$
$84$		0			0
$85$	−7.35681	−	0.485408i	−0.797958	−	0.0526499i
$86$		0			0
$87$			15.4863i			1.66031i
$88$		0			0
$89$	−6.09017			−0.645557			−0.322778	−	0.946475i	$-0.604617\pi$
$89$	−6.09017			−0.645557			−0.322778	+	0.946475i	$0.604617\pi$
$90$		0			0
$91$	3.61803	−	11.1352i	0.379273	−	1.16728i
$92$		0			0
$93$	5.08740	+	7.00220i	0.527539	+	0.726095i
$94$		0			0
$95$	1.54677	+	2.45385i	0.158695	+	0.251760i
$96$		0			0
$97$	7.26384	−	9.99782i	0.737531	−	1.01512i	−0.261226	−	0.965278i	$-0.584127\pi$
$97$	7.26384	−	9.99782i	0.737531	−	1.01512i	0.998757	−	0.0498467i	$-0.0158733\pi$
$98$		0			0
$99$	−1.26664	+	0.0222142i	−0.127302	+	0.00223261i
$100$		0			0
$101$	7.29264	+	5.29841i	0.725645	+	0.527212i	0.888183	−	0.459491i	$-0.151968\pi$
$101$	7.29264	+	5.29841i	0.725645	+	0.527212i	−0.162538	+	0.986702i	$0.551968\pi$
$102$		0			0
$103$	−10.8743	+	3.53329i	−1.07148	+	0.348145i	−0.791064	−	0.611733i	$-0.790473\pi$
$103$	−10.8743	+	3.53329i	−1.07148	+	0.348145i	−0.280416	+	0.959878i	$0.590473\pi$
$104$		0			0
$105$	−8.74532	+	10.5058i	−0.853456	+	1.02526i
$106$		0			0
$107$	−14.6031	−	4.74484i	−1.41174	−	0.458701i	−0.498770	−	0.866734i	$-0.666215\pi$
$107$	−14.6031	−	4.74484i	−1.41174	−	0.458701i	−0.912967	+	0.408033i	$0.866215\pi$
$108$		0			0
$109$	−2.42892			−0.232648			−0.116324	−	0.993211i	$-0.537111\pi$
$109$	−2.42892			−0.232648			−0.116324	+	0.993211i	$0.537111\pi$
$110$		0			0
$111$	−12.8071			−1.21560
$112$		0			0
$113$	−7.97113	−	2.58998i	−0.749860	−	0.243644i	−0.0909393	−	0.995856i	$-0.528987\pi$
$113$	−7.97113	−	2.58998i	−0.749860	−	0.243644i	−0.658921	+	0.752212i	$0.728987\pi$
$114$		0			0
$115$	−0.957038	−	0.796665i	−0.0892442	−	0.0742894i
$116$		0			0
$117$	−1.12576	+	0.365781i	−0.104076	+	0.0338164i
$118$		0			0
$119$	10.0782	+	7.32222i	0.923865	+	0.671227i
$120$		0			0
$121$	3.03026	−	10.5744i	0.275478	−	0.961307i
$122$		0			0
$123$	5.98030	−	8.23117i	0.539225	−	0.742180i
$124$		0			0
$125$	9.74766	+	5.47569i	0.871857	+	0.489761i
$126$		0			0
$127$	4.08713	+	5.62545i	0.362674	+	0.499178i	0.950891	−	0.309525i	$-0.100170\pi$
$127$	4.08713	+	5.62545i	0.362674	+	0.499178i	−0.588217	+	0.808703i	$0.700170\pi$
$128$		0			0
$129$	−1.80902	+	5.56758i	−0.159275	+	0.490198i
$130$		0			0
$131$	5.61741			0.490795			0.245398	−	0.969423i	$-0.421082\pi$
$131$	5.61741			0.490795			0.245398	+	0.969423i	$0.421082\pi$
$132$		0			0
$133$		−	4.90106i		−	0.424976i
$134$		0			0
$135$	12.2095	+	0.805594i	1.05083	+	0.0693345i
$136$		0			0
$137$	−4.51887	−	6.21969i	−0.386073	−	0.531384i	0.571108	−	0.820875i	$-0.306514\pi$
$137$	−4.51887	−	6.21969i	−0.386073	−	0.531384i	−0.957181	+	0.289491i	$0.906514\pi$
$138$		0			0
$139$	0.297218	+	0.914744i	0.0252097	+	0.0775876i	0.962870	−	0.269966i	$-0.0870125\pi$
$139$	0.297218	+	0.914744i	0.0252097	+	0.0775876i	−0.937660	+	0.347554i	$0.887012\pi$
$140$		0			0
$141$	7.00220	+	5.08740i	0.589692	+	0.428436i
$142$		0			0
$143$	−0.180227	−	10.2765i	−0.0150713	−	0.859360i
$144$		0			0
$145$	−19.8745	−	7.93917i	−1.65049	−	0.659312i
$146$		0			0
$147$	11.1939	−	3.63712i	0.923259	−	0.299985i
$148$		0			0
$149$	−7.11314	+	5.16800i	−0.582731	+	0.423379i	−0.839708	−	0.543039i	$-0.817274\pi$
$149$	−7.11314	+	5.16800i	−0.582731	+	0.423379i	0.256977	+	0.966418i	$0.417274\pi$
$150$		0			0
$151$	2.76194	−	8.50038i	0.224764	−	0.691751i	−0.773552	−	0.633733i	$-0.781522\pi$
$151$	2.76194	−	8.50038i	0.224764	−	0.691751i	0.998316	−	0.0580184i	$-0.0184782\pi$
$152$		0			0
$153$		−	1.25943i		−	0.101819i
$154$		0			0
$155$	−11.5944	+	2.93924i	−0.931288	+	0.236085i
$156$		0			0
$157$	16.7776	+	5.45137i	1.33900	+	0.435067i	0.888977	−	0.457952i	$-0.151417\pi$
$157$	16.7776	+	5.45137i	1.33900	+	0.435067i	0.450020	+	0.893018i	$0.351417\pi$
$158$		0			0
$159$	−14.4178	+	10.4751i	−1.14340	+	0.830731i
$160$		0			0
$161$	0.650165	+	2.00100i	0.0512402	+	0.157701i
$162$		0			0
$163$	−0.102445	+	0.141003i	−0.00802409	+	0.0110442i	−0.813010	−	0.582249i	$-0.802173\pi$
$163$	−0.102445	+	0.141003i	−0.00802409	+	0.0110442i	0.804986	+	0.593294i	$0.202173\pi$
$164$		0			0
$165$	−4.25533	+	11.2198i	−0.331277	+	0.873461i
$166$		0			0
$167$	3.22478	−	4.43854i	0.249541	−	0.343464i	−0.665809	−	0.746122i	$-0.731914\pi$
$167$	3.22478	−	4.43854i	0.249541	−	0.343464i	0.915351	+	0.402658i	$0.131914\pi$
$168$		0			0
$169$	1.04959	+	3.23031i	0.0807378	+	0.248485i
$170$		0			0
$171$	−0.400863	+	0.291244i	−0.0306547	+	0.0222720i
$172$		0			0
$173$	−22.8216	−	7.41518i	−1.73509	−	0.563766i	−0.740922	−	0.671591i	$-0.765611\pi$
$173$	−22.8216	−	7.41518i	−1.73509	−	0.563766i	−0.994170	+	0.107825i	$0.965611\pi$
$174$		0			0
$175$	−8.99937	−	16.6093i	−0.680289	−	1.25554i
$176$		0			0
$177$			8.57108i			0.644242i
$178$		0			0
$179$	−0.0658512	+	0.202669i	−0.00492195	+	0.0151482i	−0.953487	−	0.301433i	$-0.902535\pi$
$179$	−0.0658512	+	0.202669i	−0.00492195	+	0.0151482i	0.948565	+	0.316581i	$0.102535\pi$
$180$		0			0
$181$	−0.839906	+	0.610228i	−0.0624297	+	0.0453579i	−0.618562	−	0.785736i	$-0.712285\pi$
$181$	−0.839906	+	0.610228i	−0.0624297	+	0.0453579i	0.556133	+	0.831094i	$0.312285\pi$
$182$		0			0
$183$	−3.78141	+	1.22866i	−0.279530	+	0.0908249i
$184$		0			0
$185$	6.56567	−	16.4362i	0.482718	−	1.20841i
$186$		0			0
$187$	10.4581	+	3.19641i	0.764769	+	0.233744i
$188$		0			0
$189$	−16.7260	−	12.1521i	−1.21663	−	0.883937i
$190$		0			0
$191$	5.54206	+	17.0567i	0.401009	+	1.23418i	0.924182	+	0.381953i	$0.124748\pi$
$191$	5.54206	+	17.0567i	0.401009	+	1.23418i	−0.523172	+	0.852227i	$0.675252\pi$
$192$		0			0
$193$	5.30174	+	7.29722i	0.381628	+	0.525265i	0.956015	−	0.293318i	$-0.0947596\pi$
$193$	5.30174	+	7.29722i	0.381628	+	0.525265i	−0.574387	+	0.818584i	$0.694760\pi$
$194$		0			0
$195$	−0.738177	+	11.1878i	−0.0528620	+	0.801172i
$196$		0			0
$197$			3.68422i			0.262490i	0.991350	+	0.131245i	$0.0418974\pi$
$197$			3.68422i			0.262490i	−0.991350	+	0.131245i	$0.958103\pi$
$198$		0			0
$199$	−4.23544			−0.300242			−0.150121	−	0.988668i	$-0.547966\pi$
$199$	−4.23544			−0.300242			−0.150121	+	0.988668i	$0.547966\pi$
$200$		0			0
$201$	4.60624	−	14.1765i	0.324899	−	0.999936i
$202$		0			0
$203$	21.2548	+	29.2547i	1.49179	+	2.05328i
$204$		0			0
$205$	7.49772	+	11.8946i	0.523663	+	0.830758i
$206$		0			0
$207$	0.125028	−	0.172087i	0.00869006	−	0.0119608i
$208$		0			0
$209$	−1.40106	−	4.06787i	−0.0969131	−	0.281380i
$210$		0			0
$211$	−11.0596	−	8.03527i	−0.761374	−	0.553171i	0.137958	−	0.990438i	$-0.455946\pi$
$211$	−11.0596	−	8.03527i	−0.761374	−	0.553171i	−0.899331	+	0.437268i	$0.855946\pi$
$212$		0			0
$213$	16.7609	−	5.44595i	1.14844	−	0.373150i
$214$		0			0
$215$	−6.21781	−	5.17588i	−0.424051	−	0.352992i
$216$		0			0
$217$	19.2208	+	6.24523i	1.30480	+	0.423954i
$218$		0			0
$219$	−5.49511			−0.371325
$220$		0			0
$221$	10.2179			0.687330
$222$		0			0
$223$	−22.7988	−	7.40777i	−1.52672	−	0.496061i	−0.579043	−	0.815297i	$-0.696574\pi$
$223$	−22.7988	−	7.40777i	−1.52672	−	0.496061i	−0.947675	+	0.319236i	$0.896574\pi$
$224$		0			0
$225$	−0.823704	+	1.72307i	−0.0549136	+	0.114871i
$226$		0			0
$227$	−19.6911	+	6.39803i	−1.30695	+	0.424652i	−0.877992	−	0.478675i	$-0.841117\pi$
$227$	−19.6911	+	6.39803i	−1.30695	+	0.424652i	−0.428953	+	0.903327i	$0.641117\pi$
$228$		0			0
$229$	−13.2199	−	9.60481i	−0.873594	−	0.634704i	0.0579546	−	0.998319i	$-0.481542\pi$
$229$	−13.2199	−	9.60481i	−0.873594	−	0.634704i	−0.931549	+	0.363616i	$0.881542\pi$
$230$		0			0
$231$	16.1913	−	12.2031i	1.06531	−	0.802907i
$232$		0			0
$233$	0.282302	−	0.388556i	0.0184942	−	0.0254551i	−0.799670	−	0.600440i	$-0.794992\pi$
$233$	0.282302	−	0.388556i	0.0184942	−	0.0254551i	0.818164	+	0.574985i	$0.194992\pi$
$234$		0			0
$235$	−10.1187	+	6.37826i	−0.660071	+	0.416072i
$236$		0			0
$237$	−15.5625	−	21.4200i	−1.01089	−	1.39138i
$238$		0			0
$239$	0.348754	−	1.07335i	0.0225590	−	0.0694295i	−0.939143	−	0.343526i	$-0.888379\pi$
$239$	0.348754	−	1.07335i	0.0225590	−	0.0694295i	0.961702	+	0.274096i	$0.0883787\pi$
$240$		0			0
$241$	−12.7220			−0.819497			−0.409748	−	0.912199i	$-0.634384\pi$
$241$	−12.7220			−0.819497			−0.409748	+	0.912199i	$0.634384\pi$
$242$		0			0
$243$			3.94427i			0.253025i
$244$		0			0
$245$	−1.07090	+	16.2304i	−0.0684171	+	1.03692i
$246$		0			0
$247$	−2.36290	−	3.25225i	−0.150348	−	0.206936i
$248$		0			0
$249$	−0.0920396	−	0.283269i	−0.00583277	−	0.0179514i
$250$		0			0
$251$	−2.29722	−	1.66903i	−0.144999	−	0.105348i	0.512921	−	0.858436i	$-0.328563\pi$
$251$	−2.29722	−	1.66903i	−0.144999	−	0.105348i	−0.657920	+	0.753088i	$0.728563\pi$
$252$		0			0
$253$	1.11166	+	1.47497i	0.0698894	+	0.0927304i
$254$		0			0
$255$	−11.0783	−	4.42537i	−0.693748	−	0.277127i
$256$		0			0
$257$	−29.3315	+	9.53038i	−1.82965	+	0.594489i	−0.830342	+	0.557254i	$0.811855\pi$
$257$	−29.3315	+	9.53038i	−1.82965	+	0.594489i	−0.999307	+	0.0372347i	$0.988145\pi$
$258$		0			0
$259$	−24.1935	+	17.5776i	−1.50331	+	1.09222i
$260$		0			0
$261$	1.12971	−	3.47690i	0.0699275	−	0.215215i
$262$		0			0
$263$		−	27.7069i		−	1.70848i	−0.519876	−	0.854242i	$-0.674022\pi$
$263$		−	27.7069i		−	1.70848i	0.519876	−	0.854242i	$-0.325978\pi$
$264$		0			0
$265$	−6.05199	−	23.8733i	−0.371771	−	1.46653i
$266$		0			0
$267$	−9.37181	−	3.04508i	−0.573545	−	0.186356i
$268$		0			0
$269$	10.3224	−	7.49966i	0.629367	−	0.457262i	−0.226814	−	0.973938i	$-0.572831\pi$
$269$	10.3224	−	7.49966i	0.629367	−	0.457262i	0.856181	+	0.516676i	$0.172831\pi$
$270$		0			0
$271$	−1.76218	−	5.42344i	−0.107045	−	0.329450i	0.883160	−	0.469072i	$-0.155411\pi$
$271$	−1.76218	−	5.42344i	−0.107045	−	0.329450i	−0.990205	+	0.139621i	$0.955411\pi$
$272$		0			0
$273$	11.1352	−	15.3262i	0.673931	−	0.927586i
$274$		0			0
$275$	−12.2175	−	11.2130i	−0.736745	−	0.676171i
$276$		0			0
$277$	−18.6489	+	25.6680i	−1.12050	+	1.54224i	−0.315548	+	0.948910i	$0.602188\pi$
$277$	−18.6489	+	25.6680i	−1.12050	+	1.54224i	−0.804957	+	0.593333i	$0.797812\pi$
$278$		0			0
$279$	−0.631388	−	1.94321i	−0.0378002	−	0.116337i
$280$		0			0
$281$	1.56805	−	1.13926i	0.0935423	−	0.0679624i	−0.540031	−	0.841645i	$-0.681588\pi$
$281$	1.56805	−	1.13926i	0.0935423	−	0.0679624i	0.633573	+	0.773683i	$0.281588\pi$
$282$		0			0
$283$	4.67528	+	1.51909i	0.277917	+	0.0903006i	0.444659	−	0.895700i	$-0.353325\pi$
$283$	4.67528	+	1.51909i	0.277917	+	0.0903006i	−0.166742	+	0.986000i	$0.553325\pi$
$284$		0			0
$285$	1.15331	+	4.54947i	0.0683162	+	0.269487i
$286$		0			0
$287$		−	23.7571i		−	1.40234i
$288$		0			0
$289$	1.89376	−	5.82841i	0.111398	−	0.342848i
$290$		0			0
$291$	16.1768	−	11.7531i	0.948301	−	0.688981i
$292$		0			0
$293$	−0.179488	+	0.0583193i	−0.0104858	+	0.00340705i	−0.314255	−	0.949339i	$-0.601755\pi$
$293$	−0.179488	+	0.0583193i	−0.0104858	+	0.00340705i	0.303769	+	0.952746i	$0.401755\pi$
$294$		0			0
$295$	−10.9998	−	4.39402i	−0.640432	−	0.255830i
$296$		0			0
$297$	−17.3564	−	5.30482i	−1.00712	−	0.307817i
$298$		0			0
$299$	1.39616	+	1.01437i	0.0807421	+	0.0586626i
$300$		0			0
$301$	4.22408	+	13.0004i	0.243472	+	0.749329i
$302$		0			0
$303$	8.57301	+	11.7997i	0.492507	+	0.677877i
$304$		0			0
$305$	0.361759	−	5.48280i	0.0207143	−	0.313944i
$306$		0			0
$307$			12.3820i			0.706676i	0.935496	+	0.353338i	$0.114953\pi$
$307$			12.3820i			0.706676i	−0.935496	+	0.353338i	$0.885047\pi$
$308$		0			0
$309$	−18.5005			−1.05246
$310$		0			0
$311$	6.52587	−	20.0846i	0.370048	−	1.13889i	−0.576711	−	0.816949i	$-0.695664\pi$
$311$	6.52587	−	20.0846i	0.370048	−	1.13889i	0.946759	−	0.321943i	$-0.104336\pi$
$312$		0			0
$313$	9.74502	+	13.4129i	0.550821	+	0.758140i	0.990123	−	0.140199i	$-0.0447742\pi$
$313$	9.74502	+	13.4129i	0.550821	+	0.758140i	−0.439302	+	0.898339i	$0.644774\pi$
$314$		0			0
$315$	2.72983	−	1.72074i	0.153809	−	0.0969525i
$316$		0			0
$317$	−11.5424	+	15.8867i	−0.648283	+	0.892285i	−0.999023	−	0.0441877i	$-0.985930\pi$
$317$	−11.5424	+	15.8867i	−0.648283	+	0.892285i	0.350740	+	0.936473i	$0.385930\pi$
$318$		0			0
$319$	26.0044	+	18.2053i	1.45597	+	1.01930i
$320$		0			0
$321$	−20.0995	−	14.6031i	−1.12184	−	0.815067i
$322$		0			0
$323$	4.06787	−	1.32173i	0.226342	−	0.0735431i
$324$		0			0
$325$	−13.9795	−	6.68283i	−0.775443	−	0.370696i
$326$		0			0
$327$	−3.73772	−	1.21446i	−0.206697	−	0.0671598i
$328$		0			0
$329$	20.2100			1.11421
$330$		0			0
$331$	23.4826			1.29072			0.645360	−	0.763879i	$-0.276707\pi$
$331$	23.4826			1.29072			0.645360	+	0.763879i	$0.276707\pi$
$332$		0			0
$333$	2.87538	+	0.934269i	0.157570	+	0.0511976i
$334$		0			0
$335$	15.8322	+	13.1792i	0.865004	+	0.720054i
$336$		0			0
$337$	−12.1974	+	3.96317i	−0.664434	+	0.215888i	−0.621768	−	0.783202i	$-0.713585\pi$
$337$	−12.1974	+	3.96317i	−0.664434	+	0.215888i	−0.0426660	+	0.999089i	$0.513585\pi$
$338$		0			0
$339$	−10.9713	−	7.97113i	−0.595880	−	0.432932i
$340$		0			0
$341$	17.7386	−	0.311096i	0.960598	−	0.0168468i
$342$		0			0
$343$	0.609033	−	0.838262i	0.0328847	−	0.0452619i
$344$		0			0
$345$	−1.07440	−	1.70446i	−0.0578436	−	0.0917651i
$346$		0			0
$347$	12.1634	+	16.7415i	0.652966	+	0.898730i	0.999223	−	0.0394093i	$-0.0125476\pi$
$347$	12.1634	+	16.7415i	0.652966	+	0.898730i	−0.346257	+	0.938140i	$0.612548\pi$
$348$		0			0
$349$	−6.71104	+	20.6544i	−0.359233	+	1.10561i	0.594280	+	0.804258i	$0.297437\pi$
$349$	−6.71104	+	20.6544i	−0.359233	+	1.10561i	−0.953514	+	0.301349i	$0.902563\pi$
$350$		0			0
$351$	−16.9578			−0.905143
$352$		0			0
$353$			0.260293i			0.0138540i	0.999976	+	0.00692701i	$0.00220495\pi$
$353$			0.260293i			0.0138540i	−0.999976	+	0.00692701i	$0.997795\pi$
$354$		0			0
$355$	−1.60348	+	24.3022i	−0.0851037	+	1.28983i
$356$		0			0
$357$	11.8476	+	16.3068i	0.627042	+	0.863049i
$358$		0			0
$359$	2.54070	+	7.81947i	0.134093	+	0.412696i	0.995448	−	0.0953081i	$-0.0303836\pi$
$359$	2.54070	+	7.81947i	0.134093	+	0.412696i	−0.861355	+	0.508004i	$0.830384\pi$
$360$		0			0
$361$	14.0099	+	10.1788i	0.737365	+	0.535727i
$362$		0			0
$363$	9.95028	−	14.7572i	0.522254	−	0.774550i
$364$		0			0
$365$	2.81710	−	7.05220i	0.147454	−	0.369129i
$366$		0			0
$367$	6.86029	−	2.22904i	0.358104	−	0.116355i	−0.124439	−	0.992227i	$-0.539713\pi$
$367$	6.86029	−	2.22904i	0.358104	−	0.116355i	0.482543	+	0.875872i	$0.339713\pi$
$368$		0			0
$369$	−1.94312	+	1.41176i	−0.101155	+	0.0734931i
$370$		0			0
$371$	−12.8591	+	39.5764i	−0.667613	+	2.05470i
$372$		0			0
$373$		−	29.9629i		−	1.55142i	−0.631090	−	0.775709i	$-0.717392\pi$
$373$		−	29.9629i		−	1.55142i	0.631090	−	0.775709i	$-0.282608\pi$
$374$		0			0
$375$	12.2623	+	13.3000i	0.633220	+	0.686812i
$376$		0			0
$377$	28.2086	+	9.16552i	1.45281	+	0.472048i
$378$		0			0
$379$	29.6962	−	21.5756i	1.52539	−	1.10826i	0.566661	−	0.823951i	$-0.308235\pi$
$379$	29.6962	−	21.5756i	1.52539	−	1.10826i	0.958732	−	0.284312i	$-0.0917651\pi$
$380$		0			0
$381$	3.47672	+	10.7002i	0.178118	+	0.548190i
$382$		0			0
$383$	−3.79013	+	5.21666i	−0.193666	+	0.266559i	−0.894796	−	0.446475i	$-0.852679\pi$
$383$	−3.79013	+	5.21666i	−0.193666	+	0.266559i	0.701130	+	0.713034i	$0.252679\pi$
$384$		0			0
$385$	7.36043	+	27.0353i	0.375122	+	1.37785i
$386$		0			0
$387$	0.812299	−	1.11803i	0.0412915	−	0.0568329i
$388$		0			0
$389$	8.83792	+	27.2003i	0.448100	+	1.37911i	0.879048	+	0.476734i	$0.158179\pi$
$389$	8.83792	+	27.2003i	0.448100	+	1.37911i	−0.430948	+	0.902377i	$0.641821\pi$
$390$		0			0
$391$	−1.48549	+	1.07927i	−0.0751245	+	0.0545811i
$392$		0			0
$393$	8.64430	+	2.80870i	0.436047	+	0.141680i
$394$		0			0
$395$	35.4678	−	8.99123i	1.78458	−	0.452398i
$396$		0			0
$397$		−	24.5049i		−	1.22987i	−0.788579	−	0.614934i	$-0.789183\pi$
$397$		−	24.5049i		−	1.22987i	0.788579	−	0.614934i	$-0.210817\pi$
$398$		0			0
$399$	2.45053	−	7.54195i	0.122680	−	0.377570i
$400$		0			0
$401$	24.8467	−	18.0522i	1.24079	−	0.901483i	0.243135	−	0.969992i	$-0.421824\pi$
$401$	24.8467	−	18.0522i	1.24079	−	0.901483i	0.997650	+	0.0685091i	$0.0218242\pi$
$402$		0			0
$403$	15.7656	−	5.12254i	0.785338	−	0.255172i
$404$		0			0
$405$	16.0062	+	6.39392i	0.795357	+	0.317717i
$406$		0			0
$407$	−15.0557	+	21.5056i	−0.746284	+	1.06599i
$408$		0			0
$409$	17.6836	+	12.8479i	0.874397	+	0.635287i	0.931763	−	0.363066i	$-0.118270\pi$
$409$	17.6836	+	12.8479i	0.874397	+	0.635287i	−0.0573660	+	0.998353i	$0.518270\pi$
$410$		0			0
$411$	−3.84398	−	11.8306i	−0.189609	−	0.583558i
$412$		0			0
$413$	11.7637	+	16.1913i	0.578853	+	0.796723i
$414$		0			0
$415$	0.410721	+	0.0270997i	0.0201615	+	0.00133027i
$416$		0			0
$417$			1.55626i			0.0762102i
$418$		0			0
$419$	4.17764			0.204091			0.102046	−	0.994780i	$-0.467461\pi$
$419$	4.17764			0.204091			0.102046	+	0.994780i	$0.467461\pi$
$420$		0			0
$421$	3.92266	−	12.0727i	0.191179	−	0.588388i	−0.808821	−	0.588055i	$-0.799894\pi$
$421$	3.92266	−	12.0727i	0.191179	−	0.588388i	1.00000		0.000333393i	$-0.000106122\pi$
$422$		0			0
$423$	−1.20097	−	1.65300i	−0.0583932	−	0.0803714i
$424$		0			0
$425$	11.3587	−	11.9487i	0.550977	−	0.579597i
$426$		0			0
$427$	−5.45702	+	7.51095i	−0.264084	+	0.363480i
$428$		0			0
$429$	4.86089	−	15.9039i	0.234686	−	0.767850i
$430$		0			0
$431$	−0.591217	−	0.429545i	−0.0284779	−	0.0206904i	0.573455	−	0.819237i	$-0.305603\pi$
$431$	−0.591217	−	0.429545i	−0.0284779	−	0.0206904i	−0.601933	+	0.798546i	$0.705603\pi$
$432$		0			0
$433$	−5.36947	+	1.74465i	−0.258040	+	0.0838424i	−0.435180	−	0.900343i	$-0.643315\pi$
$433$	−5.36947	+	1.74465i	−0.258040	+	0.0838424i	0.177140	+	0.984186i	$0.443315\pi$
$434$		0			0
$435$	−26.6142	−	22.1544i	−1.27605	−	1.06222i
$436$		0			0
$437$	0.687043	+	0.223234i	0.0328657	+	0.0106787i
$438$		0			0
$439$	13.7074			0.654220			0.327110	−	0.944986i	$-0.393925\pi$
$439$	13.7074			0.654220			0.327110	+	0.944986i	$0.393925\pi$
$440$		0			0
$441$	−2.77852			−0.132310
$442$		0			0
$443$	−13.3561	−	4.33967i	−0.634568	−	0.206184i	−0.0259707	−	0.999663i	$-0.508268\pi$
$443$	−13.3561	−	4.33967i	−0.634568	−	0.206184i	−0.608598	+	0.793479i	$0.708268\pi$
$444$		0			0
$445$	8.71246	−	10.4663i	0.413010	−	0.496151i
$446$		0			0
$447$	−13.5300	+	4.39616i	−0.639947	+	0.207931i
$448$		0			0
$449$	7.81141	+	5.67532i	0.368643	+	0.267835i	0.756648	−	0.653822i	$-0.226836\pi$
$449$	7.81141	+	5.67532i	0.368643	+	0.267835i	−0.388005	+	0.921657i	$0.626836\pi$
$450$		0			0
$451$	−6.79140	−	19.7183i	−0.319794	−	0.928501i
$452$		0			0
$453$	8.50038	−	11.6998i	0.399383	−	0.549703i
$454$		0			0
$455$	13.9606	+	22.1475i	0.654481	+	1.03829i
$456$		0			0
$457$	−0.604702	−	0.832300i	−0.0282867	−	0.0389334i	0.794639	−	0.607082i	$-0.207660\pi$
$457$	−0.604702	−	0.832300i	−0.0282867	−	0.0389334i	−0.822926	+	0.568148i	$0.807660\pi$
$458$		0			0
$459$	5.57554	−	17.1597i	0.260244	−	0.800948i
$460$		0			0
$461$	−8.05882			−0.375336			−0.187668	−	0.982232i	$-0.560093\pi$
$461$	−8.05882			−0.375336			−0.187668	+	0.982232i	$0.560093\pi$
$462$		0			0
$463$			7.46633i			0.346990i	0.984835	+	0.173495i	$0.0555060\pi$
$463$			7.46633i			0.346990i	−0.984835	+	0.173495i	$0.944494\pi$
$464$		0			0
$465$	−19.3116	−	1.27420i	−0.895555	−	0.0590894i
$466$		0			0
$467$	−6.57694	−	9.05238i	−0.304344	−	0.418894i	0.629263	−	0.777193i	$-0.283357\pi$
$467$	−6.57694	−	9.05238i	−0.304344	−	0.418894i	−0.933607	+	0.358299i	$0.883357\pi$
$468$		0			0
$469$	−10.7556	−	33.1024i	−0.496648	−	1.52853i
$470$		0			0
$471$	23.0924	+	16.7776i	1.06404	+	0.773071i
$472$		0			0
$473$	7.22237	+	9.58276i	0.332085	+	0.440616i
$474$		0			0
$475$	−6.42986	−	0.852205i	−0.295022	−	0.0391018i
$476$		0			0
$477$	4.00114	−	1.30005i	0.183200	−	0.0595252i
$478$		0			0
$479$	−21.6571	+	15.7348i	−0.989536	+	0.718940i	−0.959819	−	0.280618i	$-0.909461\pi$
$479$	−21.6571	+	15.7348i	−0.989536	+	0.718940i	−0.0297167	+	0.999558i	$0.509461\pi$
$480$		0			0
$481$	−7.57985	+	23.3284i	−0.345612	+	1.06368i
$482$		0			0
$483$			3.40431i			0.154901i
$484$		0			0
$485$	6.79036	+	26.7860i	0.308334	+	1.21629i
$486$		0			0
$487$	17.4787	+	5.67918i	0.792037	+	0.257348i	0.676971	−	0.736009i	$-0.263292\pi$
$487$	17.4787	+	5.67918i	0.792037	+	0.257348i	0.115066	+	0.993358i	$0.463292\pi$
$488$		0			0
$489$	−0.228148	+	0.165759i	−0.0103172	+	0.00749589i
$490$		0			0
$491$	8.02923	+	24.7114i	0.362354	+	1.11521i	0.951622	+	0.307273i	$0.0994164\pi$
$491$	8.02923	+	24.7114i	0.362354	+	1.11521i	−0.589268	+	0.807938i	$0.700584\pi$
$492$		0			0
$493$	−18.5493	+	25.5309i	−0.835418	+	1.14985i
$494$		0			0
$495$	1.77385	−	2.20858i	0.0797288	−	0.0992683i
$496$		0			0
$497$	24.1879	−	33.2918i	1.08498	−	1.49334i
$498$		0			0
$499$	5.24736	+	16.1497i	0.234904	+	0.722960i	0.997134	+	0.0756541i	$0.0241045\pi$
$499$	5.24736	+	16.1497i	0.234904	+	0.722960i	−0.762230	+	0.647306i	$0.775896\pi$
$500$		0			0
$501$	7.18170	−	5.21781i	0.320855	−	0.233115i
$502$		0			0
$503$	12.7362	+	4.13825i	0.567880	+	0.184515i	0.578864	−	0.815424i	$-0.303496\pi$
$503$	12.7362	+	4.13825i	0.567880	+	0.184515i	−0.0109840	+	0.999940i	$0.503496\pi$
$504$		0			0
$505$	−19.5383	+	4.95305i	−0.869444	+	0.220408i
$506$		0			0
$507$			5.49573i			0.244074i
$508$		0			0
$509$	6.18963	−	19.0497i	0.274351	−	0.844365i	−0.715040	−	0.699084i	$-0.753591\pi$
$509$	6.18963	−	19.0497i	0.274351	−	0.844365i	0.989390	−	0.145281i	$-0.0464086\pi$
$510$		0			0
$511$	−10.3806	+	7.54195i	−0.459211	+	0.333636i
$512$		0			0
$513$	−6.75113	+	2.19357i	−0.298070	+	0.0968487i
$514$		0			0
$515$	9.48442	−	23.7428i	0.417933	−	1.04623i
$516$		0			0
$517$	16.7743	−	5.77739i	0.737731	−	0.254090i
$518$		0			0
$519$	−31.4112	−	22.8216i	−1.37880	−	1.00176i
$520$		0			0
$521$	0.718847	+	2.21238i	0.0314933	+	0.0969263i	0.965568	−	0.260152i	$-0.0837728\pi$
$521$	0.718847	+	2.21238i	0.0314933	+	0.0969263i	−0.934074	+	0.357079i	$0.883773\pi$
$522$		0			0
$523$	−11.2376	−	15.4672i	−0.491386	−	0.676335i	0.489257	−	0.872140i	$-0.337268\pi$
$523$	−11.2376	−	15.4672i	−0.491386	−	0.676335i	−0.980643	+	0.195805i	$0.937268\pi$
$524$		0			0
$525$	−5.54398	−	30.0587i	−0.241959	−	1.31187i
$526$		0			0
$527$			17.6375i			0.768302i
$528$		0			0
$529$	22.6899			0.986517
$530$		0			0
$531$	0.625252	−	1.92433i	0.0271336	−	0.0835087i
$532$		0			0
$533$	−11.4538	−	15.7648i	−0.496118	−	0.682848i
$534$		0			0
$535$	29.0452	−	18.3085i	1.25573	−	0.791544i
$536$		0			0
$537$	−0.202669	+	0.278950i	−0.00874581	+	0.0120376i
$538$		0			0
$539$	7.05184	−	23.0723i	0.303744	−	0.993796i
$540$		0			0
$541$	−24.1108	−	17.5175i	−1.03660	−	0.753136i	−0.0669831	−	0.997754i	$-0.521337\pi$
$541$	−24.1108	−	17.5175i	−1.03660	−	0.753136i	−0.969619	+	0.244618i	$0.921337\pi$
$542$		0			0
$543$	−1.59760	+	0.519091i	−0.0685594	+	0.0222763i
$544$		0			0
$545$	3.47476	−	4.17425i	0.148842	−	0.178805i
$546$		0			0
$547$	18.0221	+	5.85573i	0.770569	+	0.250373i	0.667808	−	0.744333i	$-0.267233\pi$
$547$	18.0221	+	5.85573i	0.770569	+	0.250373i	0.102760	+	0.994706i	$0.467233\pi$
$548$		0			0
$549$	0.938610			0.0400589
$550$		0			0
$551$	12.4158			0.528930
$552$		0			0
$553$	−58.7972	−	19.1044i	−2.50031	−	0.812400i
$554$		0			0
$555$	18.3216	−	22.0098i	0.777709	−	0.934266i
$556$		0			0
$557$	6.35647	−	2.06534i	0.269332	−	0.0875114i	−0.171237	−	0.985230i	$-0.554776\pi$
$557$	6.35647	−	2.06534i	0.269332	−	0.0875114i	0.440570	+	0.897718i	$0.354776\pi$
$558$		0			0
$559$	9.07077	+	6.59030i	0.383652	+	0.278740i
$560$		0			0
$561$	14.4951	+	10.1478i	0.611984	+	0.428440i
$562$		0			0
$563$	−5.59814	+	7.70518i	−0.235933	+	0.324735i	−0.910523	−	0.413459i	$-0.864321\pi$
$563$	−5.59814	+	7.70518i	−0.235933	+	0.324735i	0.674589	+	0.738193i	$0.264321\pi$
$564$		0			0
$565$	15.8543	−	9.99370i	0.666997	−	0.420438i
$566$		0			0
$567$	−17.1178	−	23.5607i	−0.718881	−	0.989455i
$568$		0			0
$569$	−8.67150	+	26.6881i	−0.363528	+	1.11883i	0.587369	+	0.809319i	$0.300164\pi$
$569$	−8.67150	+	26.6881i	−0.363528	+	1.11883i	−0.950897	+	0.309506i	$0.899836\pi$
$570$		0			0
$571$	1.61429			0.0675561			0.0337781	−	0.999429i	$-0.489246\pi$
$571$	1.61429			0.0675561			0.0337781	+	0.999429i	$0.489246\pi$
$572$		0			0
$573$			29.0186i			1.21227i
$574$		0			0
$575$	2.73823	−	0.505035i	0.114192	−	0.0210614i
$576$		0			0
$577$	−1.92182	−	2.64516i	−0.0800066	−	0.110120i	0.767138	−	0.641482i	$-0.221680\pi$
$577$	−1.92182	−	2.64516i	−0.0800066	−	0.110120i	−0.847145	+	0.531363i	$0.821680\pi$
$578$		0			0
$579$	4.50993	+	13.8801i	0.187426	+	0.576839i
$580$		0			0
$581$	−0.562651	−	0.408790i	−0.0233427	−	0.0169595i
$582$		0			0
$583$	0.640558	+	36.5243i	0.0265292	+	1.51268i
$584$		0			0
$585$	0.981867	−	2.45796i	0.0405952	−	0.101624i
$586$		0			0
$587$	3.33276	−	1.08288i	0.137558	−	0.0446952i	−0.239429	−	0.970914i	$-0.576960\pi$
$587$	3.33276	−	1.08288i	0.137558	−	0.0446952i	0.376987	+	0.926219i	$0.376960\pi$
$588$		0			0
$589$	5.61384	−	4.07869i	0.231314	−	0.168060i
$590$		0			0
$591$	−1.84211	+	5.66943i	−0.0757742	+	0.233209i
$592$		0			0
$593$			27.6283i			1.13456i	0.823526	+	0.567278i	$0.192004\pi$
$593$			27.6283i			1.13456i	−0.823526	+	0.567278i	$0.807996\pi$
$594$		0			0
$595$	−27.0013	+	6.84494i	−1.10695	+	0.280615i
$596$		0			0
$597$	−6.51767	−	2.11772i	−0.266751	−	0.0866725i
$598$		0			0
$599$	6.43434	−	4.67482i	0.262900	−	0.191008i	−0.448524	−	0.893771i	$-0.648050\pi$
$599$	6.43434	−	4.67482i	0.262900	−	0.191008i	0.711425	+	0.702762i	$0.248050\pi$
$600$		0			0
$601$	2.01909	+	6.21412i	0.0823604	+	0.253479i	0.983754	−	0.179521i	$-0.0574548\pi$
$601$	2.01909	+	6.21412i	0.0823604	+	0.253479i	−0.901394	+	0.433000i	$0.857455\pi$
$602$		0			0
$603$	−2.06833	+	2.84681i	−0.0842288	+	0.115931i
$604$		0			0
$605$	13.8377	+	20.3352i	0.562582	+	0.826742i
$606$		0			0
$607$	4.92460	−	6.77813i	0.199883	−	0.275116i	−0.697295	−	0.716784i	$-0.745613\pi$
$607$	4.92460	−	6.77813i	0.199883	−	0.275116i	0.897178	+	0.441668i	$0.145613\pi$
$608$		0			0
$609$	18.0804	+	55.6457i	0.732654	+	2.25488i
$610$		0			0
$611$	13.4110	−	9.74365i	0.542550	−	0.394186i
$612$		0			0
$613$	17.0358	+	5.53528i	0.688071	+	0.223568i	0.632125	−	0.774866i	$-0.282183\pi$
$613$	17.0358	+	5.53528i	0.688071	+	0.223568i	0.0559453	+	0.998434i	$0.482183\pi$
$614$		0			0
$615$	5.59048	+	22.0528i	0.225430	+	0.889256i
$616$		0			0
$617$			21.3999i			0.861529i	0.902464	+	0.430765i	$0.141756\pi$
$617$			21.3999i			0.861529i	−0.902464	+	0.430765i	$0.858244\pi$
$618$		0			0
$619$	−1.82954	+	5.63076i	−0.0735356	+	0.226319i	−0.981068	−	0.193662i	$-0.937963\pi$
$619$	−1.82954	+	5.63076i	−0.0735356	+	0.226319i	0.907533	+	0.419981i	$0.137963\pi$
$620$		0			0
$621$	2.46535	−	1.79118i	0.0989312	−	0.0718777i
$622$		0			0
$623$	−21.8833	+	7.11031i	−0.876735	+	0.284868i
$624$		0			0
$625$	−23.3551	+	8.91853i	−0.934203	+	0.356741i
$626$		0			0
$627$	−0.122069	−	6.96034i	−0.00487497	−	0.277969i
$628$		0			0
$629$	−21.1140	−	15.3402i	−0.841870	−	0.611654i
$630$		0			0
$631$	−5.62521	−	17.3126i	−0.223936	−	0.689204i	−0.998398	−	0.0565834i	$-0.981979\pi$
$631$	−5.62521	−	17.3126i	−0.223936	−	0.689204i	0.774462	−	0.632620i	$-0.218021\pi$
$632$		0			0
$633$	−13.0013	−	17.8948i	−0.516757	−	0.711254i
$634$		0			0
$635$	−15.5146	−	1.02367i	−0.615679	−	0.0406230i
$636$		0			0
$637$		−	22.5425i		−	0.893166i
$638$		0			0
$639$	−4.16033			−0.164580
$640$		0			0
$641$	5.44931	−	16.7712i	0.215235	−	0.662424i	−0.783902	−	0.620884i	$-0.786774\pi$
$641$	5.44931	−	16.7712i	0.215235	−	0.662424i	0.999137	−	0.0415398i	$-0.0132263\pi$
$642$		0			0
$643$	−25.8329	−	35.5559i	−1.01875	−	1.40219i	−0.913077	−	0.407788i	$-0.866300\pi$
$643$	−25.8329	−	35.5559i	−1.01875	−	1.40219i	−0.105673	−	0.994401i	$-0.533700\pi$
$644$		0			0
$645$	−6.98028	−	11.0738i	−0.274848	−	0.436029i
$646$		0			0
$647$	0.291613	−	0.401371i	0.0114645	−	0.0157795i	−0.803246	−	0.595647i	$-0.796896\pi$
$647$	0.291613	−	0.401371i	0.0114645	−	0.0157795i	0.814711	+	0.579868i	$0.196896\pi$
$648$		0			0
$649$	14.3924	+	10.0759i	0.564952	+	0.395514i
$650$		0			0
$651$	26.4552	+	19.2208i	1.03686	+	0.753324i
$652$		0			0
$653$	−17.2685	+	5.61086i	−0.675767	+	0.219570i	−0.626741	−	0.779228i	$-0.715612\pi$
$653$	−17.2685	+	5.61086i	−0.675767	+	0.219570i	−0.0490258	+	0.998798i	$0.515612\pi$
$654$		0			0
$655$	−8.03613	+	9.65385i	−0.313998	+	0.377207i
$656$		0			0
$657$	1.23373	+	0.400863i	0.0481323	+	0.0156391i
$658$		0			0
$659$	−14.4974			−0.564739			−0.282370	−	0.959306i	$-0.591120\pi$
$659$	−14.4974			−0.564739			−0.282370	+	0.959306i	$0.591120\pi$
$660$		0			0
$661$	−11.6178			−0.451880			−0.225940	−	0.974141i	$-0.572545\pi$
$661$	−11.6178			−0.451880			−0.225940	+	0.974141i	$0.572545\pi$
$662$		0			0
$663$	15.7237	+	5.10895i	0.610659	+	0.198415i
$664$		0			0
$665$	8.42276	+	7.01134i	0.326621	+	0.271888i
$666$		0			0
$667$	−5.06911	+	1.64705i	−0.196277	+	0.0637742i
$668$		0			0
$669$	−31.3798	−	22.7988i	−1.21321	−	0.881451i
$670$		0			0
$671$	−2.38218	+	7.79406i	−0.0919630	+	0.300886i
$672$		0			0
$673$	20.9418	−	28.8239i	0.807246	−	1.11108i	−0.184497	−	0.982833i	$-0.559066\pi$
$673$	20.9418	−	28.8239i	0.807246	−	1.11108i	0.991743	−	0.128245i	$-0.0409344\pi$
$674$		0			0
$675$	−18.8511	+	19.8303i	−0.725580	+	0.763270i
$676$		0			0
$677$	14.4064	+	19.8288i	0.553684	+	0.762081i	0.990506	−	0.137467i	$-0.0438961\pi$
$677$	14.4064	+	19.8288i	0.553684	+	0.762081i	−0.436822	+	0.899548i	$0.643896\pi$
$678$		0			0
$679$	14.4280	−	44.4049i	0.553696	−	1.70410i
$680$		0			0
$681$	−33.5005			−1.28374
$682$		0			0
$683$			25.5212i			0.976540i	0.872693	+	0.488270i	$0.162372\pi$
$683$			25.5212i			0.976540i	−0.872693	+	0.488270i	$0.837628\pi$
$684$		0			0
$685$	17.1535	+	1.13180i	0.655401	+	0.0432439i
$686$		0			0
$687$	−15.5409	−	21.3902i	−0.592922	−	0.816088i
$688$		0			0
$689$	10.5475	+	32.4618i	0.401827	+	1.23670i
$690$		0			0
$691$	−36.7992	−	26.7362i	−1.39991	−	1.01709i	−0.994695	−	0.102872i	$-0.967197\pi$
$691$	−36.7992	−	26.7362i	−1.39991	−	1.01709i	−0.405215	−	0.914222i	$-0.632803\pi$
$692$		0			0
$693$	−4.52538	+	1.55863i	−0.171905	+	0.0592076i
$694$		0			0
$695$	−1.99724	−	0.797825i	−0.0757595	−	0.0302632i
$696$		0			0
$697$	19.7183	−	6.40688i	0.746886	−	0.242678i
$698$		0			0
$699$	0.628696	−	0.456775i	0.0237795	−	0.0172768i
$700$		0			0
$701$	−9.00678	+	27.7200i	−0.340182	+	1.04697i	0.623932	+	0.781479i	$0.285534\pi$
$701$	−9.00678	+	27.7200i	−0.340182	+	1.04697i	−0.964113	+	0.265492i	$0.914466\pi$
$702$		0			0
$703$			10.2678i			0.387258i
$704$		0			0
$705$	−18.7602	+	4.75579i	−0.706550	+	0.179113i
$706$		0			0
$707$	32.3899	+	10.5241i	1.21815	+	0.395800i
$708$		0			0
$709$	25.0122	−	18.1724i	0.939353	−	0.682480i	−0.00891175	−	0.999960i	$-0.502837\pi$
$709$	25.0122	−	18.1724i	0.939353	−	0.682480i	0.948265	+	0.317480i	$0.102837\pi$
$710$		0			0
$711$	1.93144	+	5.94435i	0.0724346	+	0.222931i
$712$		0			0
$713$	−1.75095	+	2.40997i	−0.0655734	+	0.0902541i
$714$		0			0
$715$	17.9185	+	14.3915i	0.670115	+	0.538213i
$716$		0			0
$717$	1.07335	−	1.47734i	0.0400851	−	0.0551725i
$718$		0			0
$719$	−5.42235	−	16.6883i	−0.202220	−	0.622368i	−0.999816	−	0.0191765i	$-0.993896\pi$
$719$	−5.42235	−	16.6883i	−0.202220	−	0.622368i	0.797597	−	0.603191i	$-0.206104\pi$
$720$		0			0
$721$	−34.9487	+	25.3917i	−1.30156	+	0.945636i
$722$		0			0
$723$	−19.5772	−	6.36101i	−0.728083	−	0.236568i
$724$		0			0
$725$	42.0760	−	22.7980i	1.56266	−	0.846696i
$726$		0			0
$727$		−	16.7731i		−	0.622080i	−0.950397	−	0.311040i	$-0.899323\pi$
$727$		−	16.7731i		−	0.622080i	0.950397	−	0.311040i	$-0.100677\pi$
$728$		0			0
$729$	−9.11803	+	28.0624i	−0.337705	+	1.03935i
$730$		0			0
$731$	−9.65113	+	7.01195i	−0.356960	+	0.259346i
$732$		0			0
$733$	8.79812	−	2.85868i	0.324966	−	0.105588i	−0.141991	−	0.989868i	$-0.545350\pi$
$733$	8.79812	−	2.85868i	0.324966	−	0.105588i	0.466957	+	0.884280i	$0.345350\pi$
$734$		0			0
$735$	−9.76315	+	24.4406i	−0.360119	+	0.901505i
$736$		0			0
$737$	−18.3901	−	24.4002i	−0.677407	−	0.898794i
$738$		0			0
$739$	−6.06468	−	4.40625i	−0.223093	−	0.162087i	0.470625	−	0.882333i	$-0.344029\pi$
$739$	−6.06468	−	4.40625i	−0.223093	−	0.162087i	−0.693718	+	0.720247i	$0.744029\pi$
$740$		0			0
$741$	−2.01000	−	6.18615i	−0.0738393	−	0.227254i
$742$		0			0
$743$	−3.82251	−	5.26124i	−0.140234	−	0.193016i	0.733123	−	0.680096i	$-0.238062\pi$
$743$	−3.82251	−	5.26124i	−0.140234	−	0.193016i	−0.873357	+	0.487080i	$0.838062\pi$
$744$		0			0
$745$	1.29438	−	19.6176i	0.0474225	−	0.718732i
$746$		0			0
$747$			0.0703120i			0.00257258i
$748$		0			0
$749$	−58.0118			−2.11970
$750$		0			0
$751$	−6.27064	+	19.2991i	−0.228819	+	0.704232i	0.769062	+	0.639174i	$0.220723\pi$
$751$	−6.27064	+	19.2991i	−0.228819	+	0.704232i	−0.997881	+	0.0650587i	$0.979277\pi$
$752$		0			0
$753$	−2.70054	−	3.71698i	−0.0984132	−	0.135454i
$754$		0			0
$755$	10.6572	+	16.9070i	0.387857	+	0.615310i
$756$		0			0
$757$	−10.8452	+	14.9271i	−0.394174	+	0.542534i	−0.959270	−	0.282492i	$-0.908839\pi$
$757$	−10.8452	+	14.9271i	−0.394174	+	0.542534i	0.565096	+	0.825025i	$0.308839\pi$
$758$		0			0
$759$	0.973183	+	2.82557i	0.0353243	+	0.102562i
$760$		0			0
$761$	11.0383	+	8.01981i	0.400139	+	0.290718i	0.769598	−	0.638529i	$-0.220457\pi$
$761$	11.0383	+	8.01981i	0.400139	+	0.290718i	−0.369459	+	0.929247i	$0.620457\pi$
$762$		0			0
$763$	−8.72763	+	2.83578i	−0.315961	+	0.102662i
$764$		0			0
$765$	2.16440	+	1.80171i	0.0782540	+	0.0651408i
$766$		0			0
$767$	15.6123	+	5.07275i	0.563729	+	0.183167i
$768$		0			0
$769$	6.77400			0.244277			0.122138	−	0.992513i	$-0.461025\pi$
$769$	6.77400			0.244277			0.122138	+	0.992513i	$0.461025\pi$
$770$		0			0
$771$	−49.9017			−1.79717
$772$		0			0
$773$	17.8559	+	5.80173i	0.642231	+	0.208674i	0.611986	−	0.790869i	$-0.290371\pi$
$773$	17.8559	+	5.80173i	0.642231	+	0.208674i	0.0302456	+	0.999542i	$0.490371\pi$
$774$		0			0
$775$	11.5355	−	24.1305i	0.414367	−	0.866795i
$776$		0			0
$777$	−46.0188	+	14.9524i	−1.65092	+	0.536415i
$778$		0			0
$779$	−6.59914	−	4.79455i	−0.236439	−	0.171783i
$780$		0			0
$781$	10.5589	−	34.5467i	0.377826	−	1.23618i
$782$		0			0
$783$	30.7848	−	42.3717i	1.10016	−	1.51424i
$784$		0			0
$785$	−33.3702	+	21.0347i	−1.19103	+	0.750760i
$786$		0			0
$787$	−16.1285	−	22.1990i	−0.574921	−	0.791310i	0.418206	−	0.908352i	$-0.362659\pi$
$787$	−16.1285	−	22.1990i	−0.574921	−	0.791310i	−0.993127	+	0.117042i	$0.962659\pi$
$788$		0			0
$789$	13.8535	−	42.6366i	0.493197	−	1.51790i
$790$		0			0
$791$	−31.6658			−1.12590
$792$		0			0
$793$			7.61507i			0.270419i
$794$		0			0
$795$	2.62361	−	39.7633i	0.0930500	−	1.41026i
$796$		0			0
$797$	−31.6667	−	43.5855i	−1.12169	−	1.54388i	−0.802960	−	0.596032i	$-0.796743\pi$
$797$	−31.6667	−	43.5855i	−1.12169	−	1.54388i	−0.318732	−	0.947845i	$-0.603257\pi$
$798$		0			0
$799$	5.45029	+	16.7743i	0.192817	+	0.593431i
$800$		0			0
$801$	1.88197	+	1.36733i	0.0664960	+	0.0483122i
$802$		0			0
$803$	−6.45988	+	9.22729i	−0.227964	+	0.325624i
$804$		0			0
$805$	−4.36895	−	1.74524i	−0.153985	−	0.0615117i
$806$		0			0
$807$	19.6344	−	6.37959i	0.691162	−	0.224572i
$808$		0			0
$809$	26.1612	−	19.0073i	0.919781	−	0.668260i	−0.0236888	−	0.999719i	$-0.507541\pi$
$809$	26.1612	−	19.0073i	0.919781	−	0.668260i	0.943469	+	0.331460i	$0.107541\pi$
$810$		0			0
$811$	−14.1920	+	43.6785i	−0.498349	+	1.53376i	0.313322	+	0.949647i	$0.398558\pi$
$811$	−14.1920	+	43.6785i	−0.498349	+	1.53376i	−0.811671	+	0.584114i	$0.801442\pi$
$812$		0			0
$813$		−	9.22691i		−	0.323602i
$814$		0			0
$815$	−0.0957671	−	0.377773i	−0.00335458	−	0.0132328i
$816$		0			0
$817$	4.46367	+	1.45033i	0.156164	+	0.0507408i
$818$		0			0
$819$	−3.61803	+	2.62866i	−0.126424	+	0.0918527i
$820$		0			0
$821$	8.78690	+	27.0433i	0.306665	+	0.943818i	0.979051	+	0.203617i	$0.0652697\pi$
$821$	8.78690	+	27.0433i	0.306665	+	0.943818i	−0.672386	+	0.740201i	$0.734730\pi$
$822$		0			0
$823$	6.09146	−	8.38417i	0.212335	−	0.292254i	−0.689543	−	0.724245i	$-0.742189\pi$
$823$	6.09146	−	8.38417i	0.212335	−	0.292254i	0.901878	+	0.431991i	$0.142189\pi$
$824$		0			0
$825$	−13.1943	−	23.3638i	−0.459367	−	0.813425i
$826$		0			0
$827$	11.5254	−	15.8634i	0.400779	−	0.551625i	−0.560161	−	0.828384i	$-0.689261\pi$
$827$	11.5254	−	15.8634i	0.400779	−	0.551625i	0.960939	+	0.276760i	$0.0892605\pi$
$828$		0			0
$829$	−15.4118	−	47.4327i	−0.535275	−	1.64741i	−0.743054	−	0.669231i	$-0.766624\pi$
$829$	−15.4118	−	47.4327i	−0.535275	−	1.64741i	0.207780	−	0.978176i	$-0.433376\pi$
$830$		0			0
$831$	−41.5317	+	30.1746i	−1.44072	+	1.04674i
$832$		0			0
$833$	22.8109	+	7.41171i	0.790350	+	0.256800i
$834$		0			0
$835$	3.01458	+	11.8917i	0.104324	+	0.411528i
$836$		0			0
$837$		−	29.2716i		−	1.01177i
$838$		0			0
$839$	−3.25249	+	10.0101i	−0.112289	+	0.345589i	−0.991372	−	0.131080i	$-0.958156\pi$
$839$	−3.25249	+	10.0101i	−0.112289	+	0.345589i	0.879083	+	0.476668i	$0.158156\pi$
$840$		0			0
$841$	−50.6490	+	36.7986i	−1.74652	+	1.26892i
$842$		0			0
$843$	2.98262	−	0.969111i	0.102727	−	0.0333779i
$844$		0			0
$845$	−7.05300	−	2.81742i	−0.242631	−	0.0969223i
$846$		0			0
$847$	−1.45728	−	41.5338i	−0.0500726	−	1.42712i
$848$		0			0
$849$	6.43497	+	4.67528i	0.220848	+	0.160455i
$850$		0			0
$851$	−1.36211	−	4.19214i	−0.0466925	−	0.143705i
$852$		0			0
$853$	9.24016	+	12.7180i	0.316377	+	0.435456i	0.937357	−	0.348371i	$-0.113265\pi$
$853$	9.24016	+	12.7180i	0.316377	+	0.435456i	−0.620980	+	0.783827i	$0.713265\pi$
$854$		0			0
$855$	0.0729453	−	1.10555i	0.00249468	−	0.0378091i
$856$		0			0
$857$			37.8967i			1.29453i	0.762267	+	0.647263i	$0.224086\pi$
$857$			37.8967i			1.29453i	−0.762267	+	0.647263i	$0.775914\pi$
$858$		0			0
$859$	20.5913			0.702567			0.351283	−	0.936269i	$-0.385745\pi$
$859$	20.5913			0.702567			0.351283	+	0.936269i	$0.385745\pi$
$860$		0			0
$861$	11.8785	−	36.5584i	0.404820	−	1.24591i
$862$		0			0
$863$	−5.05094	−	6.95203i	−0.171936	−	0.236650i	0.714349	−	0.699789i	$-0.246723\pi$
$863$	−5.05094	−	6.95203i	−0.171936	−	0.236650i	−0.886285	+	0.463140i	$0.846723\pi$
$864$		0			0
$865$	45.3915	−	28.6122i	1.54336	−	0.972846i
$866$		0			0
$867$	5.82841	−	8.02212i	0.197943	−	0.272445i
$868$		0			0
$869$	−54.2629	+	0.951654i	−1.84074	+	0.0322826i
$870$		0			0
$871$	−23.0966	−	16.7806i	−0.782597	−	0.568590i
$872$		0			0
$873$	−4.48930	+	1.45866i	−0.151940	+	0.0493682i
$874$		0			0
$875$	41.4183	+	8.29488i	1.40019	+	0.280418i
$876$		0			0
$877$	42.9395	+	13.9519i	1.44996	+	0.471122i	0.924989	−	0.379995i	$-0.124074\pi$
$877$	42.9395	+	13.9519i	1.44996	+	0.471122i	0.524976	+	0.851117i	$0.324074\pi$
$878$		0			0
$879$	−0.305364			−0.0102997
$880$		0			0
$881$	−38.4847			−1.29658			−0.648291	−	0.761393i	$-0.724516\pi$
$881$	−38.4847			−1.29658			−0.648291	+	0.761393i	$0.724516\pi$
$882$		0			0
$883$	37.3951	+	12.1504i	1.25845	+	0.408894i	0.860940	−	0.508706i	$-0.169876\pi$
$883$	37.3951	+	12.1504i	1.25845	+	0.408894i	0.397505	+	0.917600i	$0.369876\pi$
$884$		0			0
$885$	−14.7299	−	12.2616i	−0.495141	−	0.412169i
$886$		0			0
$887$	7.46016	−	2.42395i	0.250488	−	0.0813883i	−0.181082	−	0.983468i	$-0.557960\pi$
$887$	7.46016	−	2.42395i	0.250488	−	0.0813883i	0.431570	+	0.902080i	$0.357960\pi$
$888$		0			0
$889$	21.2537	+	15.4417i	0.712825	+	0.517897i
$890$		0			0
$891$	−20.9430	−	14.6619i	−0.701617	−	0.491191i
$892$		0			0
$893$	4.07869	−	5.61384i	0.136488	−	0.187860i
$894$		0			0
$895$	−0.254094	−	0.403103i	−0.00849341	−	0.0134742i
$896$		0			0
$897$	1.64129	+	2.25904i	0.0548010	+	0.0754271i
$898$		0			0
$899$	−15.8210	+	48.6919i	−0.527658	+	1.62397i
$900$		0			0
$901$	−36.3162			−1.20987
$902$		0			0
$903$			22.1175i			0.736026i
$904$		0			0
$905$	0.152838	−	2.31641i	0.00508052	−	0.0770000i
$906$		0			0
$907$	26.0762	+	35.8908i	0.865845	+	1.19173i	0.980144	+	0.198287i	$0.0635379\pi$
$907$	26.0762	+	35.8908i	0.865845	+	1.19173i	−0.114299	+	0.993446i	$0.536462\pi$
$908$		0			0
$909$	−1.06398	−	3.27460i	−0.0352900	−	0.108612i
$910$		0			0
$911$	11.2063	+	8.14186i	0.371282	+	0.269752i	0.757742	−	0.652554i	$-0.226302\pi$
$911$	11.2063	+	8.14186i	0.371282	+	0.269752i	−0.386460	+	0.922306i	$0.626302\pi$
$912$		0			0
$913$	−0.583860	−	0.178451i	−0.0193229	−	0.00590587i
$914$		0			0
$915$	3.29809	−	8.25627i	0.109031	−	0.272944i
$916$		0			0
$917$	20.1845	−	6.55835i	0.666552	−	0.216576i
$918$		0			0
$919$	12.3286	−	8.95726i	0.406684	−	0.295473i	−0.365574	−	0.930782i	$-0.619127\pi$
$919$	12.3286	−	8.95726i	0.406684	−	0.295473i	0.772258	+	0.635309i	$0.219127\pi$
$920$		0			0
$921$	−6.19098	+	19.0539i	−0.204000	+	0.627847i
$922$		0			0
$923$		−	33.7534i		−	1.11101i
$924$		0			0
$925$	18.8539	+	34.7967i	0.619911	+	1.14411i
$926$		0			0
$927$	4.15363	+	1.34960i	0.136423	+	0.0443265i
$928$		0			0
$929$	30.6793	−	22.2898i	1.00656	−	0.731306i	0.0430721	−	0.999072i	$-0.486285\pi$
$929$	30.6793	−	22.2898i	1.00656	−	0.731306i	0.963484	+	0.267766i	$0.0862855\pi$
$930$		0			0
$931$	−2.91597	−	8.97444i	−0.0955672	−	0.294126i
$932$		0			0
$933$	20.0846	−	27.6440i	0.657540	−	0.905025i
$934$		0			0
$935$	−20.4543	+	13.4001i	−0.668927	+	0.438230i
$936$		0			0
$937$	3.21963	−	4.43144i	0.105181	−	0.144769i	−0.753182	−	0.657812i	$-0.771482\pi$
$937$	3.21963	−	4.43144i	0.105181	−	0.144769i	0.858363	+	0.513043i	$0.171482\pi$
$938$		0			0
$939$	8.28961	+	25.5128i	0.270521	+	0.832579i
$940$		0			0
$941$	−37.5713	+	27.2971i	−1.22479	+	0.889861i	−0.996489	−	0.0837293i	$-0.973317\pi$
$941$	−37.5713	+	27.2971i	−1.22479	+	0.889861i	−0.228301	+	0.973591i	$0.573317\pi$
$942$		0			0
$943$	3.33033	+	1.08209i	0.108450	+	0.0352377i
$944$		0			0
$945$	44.8119	−	11.3600i	1.45773	−	0.369541i
$946$		0			0
$947$		−	22.7220i		−	0.738366i	−0.929357	−	0.369183i	$-0.879638\pi$
$947$		−	22.7220i		−	0.738366i	0.929357	−	0.369183i	$-0.120362\pi$
$948$		0			0
$949$	−3.25225	+	10.0094i	−0.105573	+	0.324919i
$950$		0			0
$951$	−25.7052	+	18.6759i	−0.833548	+	0.605608i
$952$		0			0
$953$	34.2554	−	11.1302i	1.10964	−	0.360544i	0.303835	−	0.952725i	$-0.401733\pi$
$953$	34.2554	−	11.1302i	1.10964	−	0.360544i	0.805805	+	0.592181i	$0.201733\pi$
$954$		0			0
$955$	−37.2413	−	14.8766i	−1.20510	−	0.481395i
$956$		0			0
$957$	30.9140	+	41.0172i	0.999309	+	1.32590i
$958$		0			0
$959$	−23.4988	−	17.0729i	−0.758815	−	0.551311i
$960$		0			0
$961$	−0.737310	−	2.26921i	−0.0237842	−	0.0732002i
$962$		0			0
$963$	3.44733	+	4.74484i	0.111089	+	0.152900i
$964$		0			0
$965$	−20.1253	−	1.32788i	−0.647855	−	0.0427460i
$966$		0			0
$967$		−	23.8349i		−	0.766479i	−0.923649	−	0.383240i	$-0.874808\pi$
$967$		−	23.8349i		−	0.766479i	0.923649	−	0.383240i	$-0.125192\pi$
$968$		0			0
$969$	6.92067			0.222324
$970$		0			0
$971$	10.9297	−	33.6381i	0.350750	−	1.07950i	−0.607682	−	0.794180i	$-0.707901\pi$
$971$	10.9297	−	33.6381i	0.350750	−	1.07950i	0.958433	−	0.285319i	$-0.0920994\pi$
$972$		0			0
$973$	2.13594	+	2.93987i	0.0684750	+	0.0942478i
$974$		0			0
$975$	−18.1708	−	17.2736i	−0.581932	−	0.553196i
$976$		0			0
$977$	6.63066	−	9.12632i	0.212134	−	0.291977i	−0.689669	−	0.724124i	$-0.742244\pi$
$977$	6.63066	−	9.12632i	0.212134	−	0.291977i	0.901803	+	0.432148i	$0.142244\pi$
$978$		0			0
$979$	−16.1305	+	12.1573i	−0.515532	+	0.388548i
$980$		0			0
$981$	0.750578	+	0.545327i	0.0239641	+	0.0174109i
$982$		0			0
$983$	−8.14486	+	2.64643i	−0.259781	+	0.0844079i	−0.436012	−	0.899941i	$-0.643609\pi$
$983$	−8.14486	+	2.64643i	−0.259781	+	0.0844079i	0.176231	+	0.984349i	$0.443609\pi$
$984$		0			0
$985$	−6.33155	−	5.27056i	−0.201740	−	0.167934i
$986$		0			0
$987$	31.1000	+	10.1050i	0.989923	+	0.321645i
$988$		0			0
$989$	−2.01482			−0.0640677
$990$		0			0
$991$	15.9978			0.508185			0.254093	−	0.967180i	$-0.418223\pi$
$991$	15.9978			0.508185			0.254093	+	0.967180i	$0.418223\pi$
$992$		0			0
$993$	36.1360	+	11.7413i	1.14674	+	0.372599i
$994$		0			0
$995$	6.05913	−	7.27886i	0.192087	−	0.230755i
$996$		0			0
$997$	−27.0137	+	8.77729i	−0.855533	+	0.277979i	−0.703762	−	0.710436i	$-0.748498\pi$
$997$	−27.0137	+	8.77729i	−0.855533	+	0.277979i	−0.151771	+	0.988416i	$0.548498\pi$
$998$		0			0
$999$	35.0412	+	25.4589i	1.10866	+	0.805485i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	880.2.cd.b.609.3		16
4.3	odd	2		110.2.j.b.59.1	✓	16
5.4	even	2	inner	880.2.cd.b.609.1		16
11.3	even	5	inner	880.2.cd.b.289.1		16
12.11	even	2		990.2.ba.h.829.4		16
20.3	even	4		550.2.h.n.301.2		8
20.7	even	4		550.2.h.j.301.1		8
20.19	odd	2		110.2.j.b.59.3	yes	16
44.3	odd	10		110.2.j.b.69.3	yes	16
44.27	odd	10		1210.2.b.k.969.2		8
44.39	even	10		1210.2.b.l.969.6		8
55.14	even	10	inner	880.2.cd.b.289.3		16
60.59	even	2		990.2.ba.h.829.2		16
132.47	even	10		990.2.ba.h.289.2		16
220.3	even	20		550.2.h.n.201.2		8
220.27	even	20		6050.2.a.di.1.1		4
220.39	even	10		1210.2.b.l.969.4		8
220.47	even	20		550.2.h.j.201.1		8
220.83	odd	20		6050.2.a.dl.1.3		4
220.127	odd	20		6050.2.a.da.1.2		4
220.159	odd	10		1210.2.b.k.969.8		8
220.179	odd	10		110.2.j.b.69.1	yes	16
220.203	even	20		6050.2.a.dd.1.4		4
660.179	even	10		990.2.ba.h.289.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.2.j.b.59.1	✓	16	4.3	odd	2
110.2.j.b.59.3	yes	16	20.19	odd	2
110.2.j.b.69.1	yes	16	220.179	odd	10
110.2.j.b.69.3	yes	16	44.3	odd	10
550.2.h.j.201.1		8	220.47	even	20
550.2.h.j.301.1		8	20.7	even	4
550.2.h.n.201.2		8	220.3	even	20
550.2.h.n.301.2		8	20.3	even	4
880.2.cd.b.289.1		16	11.3	even	5	inner
880.2.cd.b.289.3		16	55.14	even	10	inner
880.2.cd.b.609.1		16	5.4	even	2	inner
880.2.cd.b.609.3		16	1.1	even	1	trivial
990.2.ba.h.289.2		16	132.47	even	10
990.2.ba.h.289.4		16	660.179	even	10
990.2.ba.h.829.2		16	60.59	even	2
990.2.ba.h.829.4		16	12.11	even	2
1210.2.b.k.969.2		8	44.27	odd	10
1210.2.b.k.969.8		8	220.159	odd	10
1210.2.b.l.969.4		8	220.39	even	10
1210.2.b.l.969.6		8	44.39	even	10
6050.2.a.da.1.2		4	220.127	odd	20
6050.2.a.dd.1.4		4	220.203	even	20
6050.2.a.di.1.1		4	220.27	even	20
6050.2.a.dl.1.3		4	220.83	odd	20

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:	\( N \)	\(=\)	\( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	880.cd (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.53884 + 0.500000i) q^{3} +(-1.43058 + 1.71856i) q^{5} +(3.59321 - 1.16751i) q^{7} +(-0.309017 - 0.224514i) q^{9} +(2.64861 - 1.99621i) q^{11} +(1.82151 - 2.50710i) q^{13} +(-3.06071 + 1.92930i) q^{15} +(1.93806 + 2.66751i) q^{17} +(0.400863 - 1.23373i) q^{19} +6.11314 q^{21} +0.556884i q^{23} +(-0.906896 - 4.91707i) q^{25} +(-3.21644 - 4.42705i) q^{27} +(2.95763 + 9.10264i) q^{29} +(4.32760 + 3.14419i) q^{31} +(5.07390 - 1.74755i) q^{33} +(-3.13394 + 7.84536i) q^{35} +(-7.52785 + 2.44595i) q^{37} +(4.05657 - 2.94727i) q^{39} +(1.94312 - 5.98030i) q^{41} +3.61803i q^{43} +(0.827913 - 0.209880i) q^{45} +(5.08740 + 1.65300i) q^{47} +(5.88499 - 4.27570i) q^{49} +(1.64861 + 5.07390i) q^{51} +(-6.47398 + 8.91067i) q^{53} +(-0.358428 + 7.40753i) q^{55} +(1.23373 - 1.69808i) q^{57} +(1.63693 + 5.03795i) q^{59} +(-1.98801 + 1.44437i) q^{61} +(-1.37249 - 0.445947i) q^{63} +(1.70278 + 6.71698i) q^{65} -9.21247i q^{67} +(-0.278442 + 0.856956i) q^{69} +(8.81173 - 6.40210i) q^{71} +(-3.22994 + 1.04947i) q^{73} +(1.06296 - 8.02003i) q^{75} +(7.18643 - 10.2651i) q^{77} +(-13.2383 - 9.61817i) q^{79} +(-2.38197 - 7.33094i) q^{81} +(-0.108199 - 0.148923i) q^{83} +(-7.35681 - 0.485408i) q^{85} +15.4863i q^{87} -6.09017 q^{89} +(3.61803 - 11.1352i) q^{91} +(5.08740 + 7.00220i) q^{93} +(1.54677 + 2.45385i) q^{95} +(7.26384 - 9.99782i) q^{97} +(-1.26664 + 0.0222142i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{5} + 4 q^{9} + 20 q^{11} - 2 q^{15} + 16 q^{19} - 16 q^{21} + 16 q^{29} + 4 q^{31} + 48 q^{35} + 8 q^{39} + 40 q^{41} - 4 q^{45} + 84 q^{49} + 4 q^{51} - 32 q^{55} + 20 q^{61} + 72 q^{65} + 56 q^{71}+ \cdots + 20 q^{99}+O(q^{100}) \) 16 * q - 6 * q^5 + 4 * q^9 + 20 * q^11 - 2 * q^15 + 16 * q^19 - 16 * q^21 + 16 * q^29 + 4 * q^31 + 48 * q^35 + 8 * q^39 + 40 * q^41 - 4 * q^45 + 84 * q^49 + 4 * q^51 - 32 * q^55 + 20 * q^61 + 72 * q^65 + 56 * q^71 - 32 * q^75 - 36 * q^79 - 56 * q^81 - 54 * q^85 - 8 * q^89 + 40 * q^91 + 50 * q^95 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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