LMFDB - Embedded newform 380.2.u.b.101.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(61,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("380.61");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.u (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 3 x^{17} + 21 x^{16} - 30 x^{15} + 192 x^{14} - 207 x^{13} + 1178 x^{12} - 705 x^{11} + \cdots + 5329 $ x^18 - 3x^17 + 21x^16 - 30x^15 + 192x^14 - 207x^13 + 1178x^12 - 705x^11 + 4413x^10 - 2224x^9 + 11430x^8 - 4101x^7 + 19237x^6 - 7125x^5 + 21573x^4 - 5266x^3 + 13851x^2 - 3285*x + 5329
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			101.2
Root			$0.546970 - 0.947380i$ of defining polynomial
Character	$\chi$	$=$	380.101
Dual form			380.2.u.b.301.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.02797 + 0.374150i) q^{3} +(0.173648 + 0.984808i) q^{5} +(-1.81409 + 3.14209i) q^{7} +(-1.38140 - 1.15914i) q^{9} +O(q^{10})$	\(q+(1.02797 + 0.374150i) q^{3} +(0.173648 + 0.984808i) q^{5} +(-1.81409 + 3.14209i) q^{7} +(-1.38140 - 1.15914i) q^{9} +(2.71941 + 4.71016i) q^{11} +(1.31766 - 0.479589i) q^{13} +(-0.189961 + 1.07732i) q^{15} +(-2.12355 + 1.78187i) q^{17} +(1.94623 + 3.90028i) q^{19} +(-3.04044 + 2.55123i) q^{21} +(1.15141 - 6.52999i) q^{23} +(-0.939693 + 0.342020i) q^{25} +(-2.62726 - 4.55055i) q^{27} +(4.29734 + 3.60589i) q^{29} +(5.34951 - 9.26562i) q^{31} +(1.03316 + 5.85936i) q^{33} +(-3.40937 - 1.24091i) q^{35} -3.37063 q^{37} +1.53395 q^{39} +(-2.35936 - 0.858738i) q^{41} +(1.84304 + 10.4524i) q^{43} +(0.901647 - 1.56170i) q^{45} +(3.67626 + 3.08475i) q^{47} +(-3.08183 - 5.33789i) q^{49} +(-2.84963 + 1.03718i) q^{51} +(1.60632 - 9.10987i) q^{53} +(-4.16638 + 3.49601i) q^{55} +(0.541374 + 4.73754i) q^{57} +(1.79251 - 1.50409i) q^{59} +(-0.509501 + 2.88952i) q^{61} +(6.14810 - 2.23772i) q^{63} +(0.701112 + 1.21436i) q^{65} +(-1.64930 - 1.38393i) q^{67} +(3.62681 - 6.28182i) q^{69} +(-2.83920 - 16.1019i) q^{71} +(-12.1383 - 4.41799i) q^{73} -1.09394 q^{75} -19.7330 q^{77} +(10.7051 + 3.89632i) q^{79} +(-0.0587363 - 0.333110i) q^{81} +(5.51438 - 9.55118i) q^{83} +(-2.12355 - 1.78187i) q^{85} +(3.06838 + 5.31459i) q^{87} +(10.5328 - 3.83361i) q^{89} +(-0.883438 + 5.01023i) q^{91} +(8.96585 - 7.52325i) q^{93} +(-3.50307 + 2.59394i) q^{95} +(-7.22724 + 6.06437i) q^{97} +(1.70311 - 9.65879i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 3 q^{3} + 15 q^{9}+O(q^{10}) $ 18 * q + 3 * q^3 + 15 * q^9	$ 18 q + 3 q^{3} + 15 q^{9} + 9 q^{13} + 3 q^{15} + 12 q^{17} - 18 q^{19} - 9 q^{21} + 21 q^{23} + 18 q^{27} - 9 q^{29} + 6 q^{31} - 21 q^{33} - 6 q^{35} - 36 q^{37} - 12 q^{39} + 6 q^{41} - 12 q^{43} - 6 q^{45} + 21 q^{47} - 3 q^{49} - 9 q^{51} + 36 q^{53} - 3 q^{55} - 24 q^{57} - 6 q^{61} + 36 q^{63} + 15 q^{65} + 60 q^{67} + 27 q^{69} - 36 q^{71} - 60 q^{73} - 6 q^{75} - 36 q^{77} - 3 q^{79} + 3 q^{81} - 6 q^{83} + 12 q^{85} + 21 q^{87} + 6 q^{89} - 30 q^{91} - 48 q^{93} - 21 q^{95} - 57 q^{97} + 3 q^{99}+O(q^{100}) $ 18 * q + 3 * q^3 + 15 * q^9 + 9 * q^13 + 3 * q^15 + 12 * q^17 - 18 * q^19 - 9 * q^21 + 21 * q^23 + 18 * q^27 - 9 * q^29 + 6 * q^31 - 21 * q^33 - 6 * q^35 - 36 * q^37 - 12 * q^39 + 6 * q^41 - 12 * q^43 - 6 * q^45 + 21 * q^47 - 3 * q^49 - 9 * q^51 + 36 * q^53 - 3 * q^55 - 24 * q^57 - 6 * q^61 + 36 * q^63 + 15 * q^65 + 60 * q^67 + 27 * q^69 - 36 * q^71 - 60 * q^73 - 6 * q^75 - 36 * q^77 - 3 * q^79 + 3 * q^81 - 6 * q^83 + 12 * q^85 + 21 * q^87 + 6 * q^89 - 30 * q^91 - 48 * q^93 - 21 * q^95 - 57 * q^97 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$1$	$1$

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
$3$	1.02797	+	0.374150i	0.593498	+	0.216015i	0.621267	−	0.783599i	$-0.286618\pi$
$3$	1.02797	+	0.374150i	0.593498	+	0.216015i	−0.0277695	+	0.999614i	$0.508840\pi$
$4$		0			0
$5$	0.173648	+	0.984808i	0.0776578	+	0.440419i
$5$	0.173648	+	0.984808i	0.0776578	+	0.440419i
$6$		0			0
$7$	−1.81409	+	3.14209i	−0.685661	+	1.18760i	0.287568	+	0.957760i	$0.407153\pi$
$7$	−1.81409	+	3.14209i	−0.685661	+	1.18760i	−0.973229	+	0.229839i	$0.926180\pi$
$8$		0			0
$9$	−1.38140	−	1.15914i	−0.460468	−	0.386378i
$10$		0			0
$11$	2.71941	+	4.71016i	0.819933	+	1.42017i	0.905731	+	0.423853i	$0.139323\pi$
$11$	2.71941	+	4.71016i	0.819933	+	1.42017i	−0.0857978	+	0.996313i	$0.527344\pi$
$12$		0			0
$13$	1.31766	−	0.479589i	0.365453	−	0.133014i	−0.152765	−	0.988263i	$-0.548818\pi$
$13$	1.31766	−	0.479589i	0.365453	−	0.133014i	0.518218	+	0.855248i	$0.326596\pi$
$14$		0			0
$15$	−0.189961	+	1.07732i	−0.0490477	+	0.278163i
$16$		0			0
$17$	−2.12355	+	1.78187i	−0.515037	+	0.432168i	−0.862898	−	0.505379i	$-0.831353\pi$
$17$	−2.12355	+	1.78187i	−0.515037	+	0.432168i	0.347860	+	0.937546i	$0.386908\pi$
$18$		0			0
$19$	1.94623	+	3.90028i	0.446496	+	0.894786i
$19$	1.94623	+	3.90028i	0.446496	+	0.894786i
$20$		0			0
$21$	−3.04044	+	2.55123i	−0.663478	+	0.556724i
$22$		0			0
$23$	1.15141	−	6.52999i	0.240086	−	1.36160i	−0.591546	−	0.806271i	$-0.701482\pi$
$23$	1.15141	−	6.52999i	0.240086	−	1.36160i	0.831632	−	0.555327i	$-0.187407\pi$
$24$		0			0
$25$	−0.939693	+	0.342020i	−0.187939	+	0.0684040i
$26$		0			0
$27$	−2.62726	−	4.55055i	−0.505616	−	0.875753i
$28$		0			0
$29$	4.29734	+	3.60589i	0.797995	+	0.669597i	0.947710	−	0.319132i	$-0.103391\pi$
$29$	4.29734	+	3.60589i	0.797995	+	0.669597i	−0.149715	+	0.988729i	$0.547836\pi$
$30$		0			0
$31$	5.34951	−	9.26562i	0.960800	−	1.66416i	0.240302	−	0.970698i	$-0.422753\pi$
$31$	5.34951	−	9.26562i	0.960800	−	1.66416i	0.720498	−	0.693457i	$-0.243913\pi$
$32$		0			0
$33$	1.03316	+	5.85936i	0.179851	+	1.01998i
$34$		0			0
$35$	−3.40937	−	1.24091i	−0.576289	−	0.209752i
$36$		0			0
$37$	−3.37063			−0.554128			−0.277064	−	0.960851i	$-0.589361\pi$
$37$	−3.37063			−0.554128			−0.277064	+	0.960851i	$0.589361\pi$
$38$		0			0
$39$	1.53395			0.245629
$40$		0			0
$41$	−2.35936	−	0.858738i	−0.368471	−	0.134112i	0.151147	−	0.988511i	$-0.451703\pi$
$41$	−2.35936	−	0.858738i	−0.368471	−	0.134112i	−0.519618	+	0.854399i	$0.673926\pi$
$42$		0			0
$43$	1.84304	+	10.4524i	0.281061	+	1.59397i	0.719026	+	0.694983i	$0.244588\pi$
$43$	1.84304	+	10.4524i	0.281061	+	1.59397i	−0.437965	+	0.898992i	$0.644301\pi$
$44$		0			0
$45$	0.901647	−	1.56170i	0.134410	−	0.232804i
$46$		0			0
$47$	3.67626	+	3.08475i	0.536238	+	0.449957i	0.870249	−	0.492612i	$-0.163958\pi$
$47$	3.67626	+	3.08475i	0.536238	+	0.449957i	−0.334011	+	0.942569i	$0.608402\pi$
$48$		0			0
$49$	−3.08183	−	5.33789i	−0.440262	−	0.762556i
$50$		0			0
$51$	−2.84963	+	1.03718i	−0.399028	+	0.145234i
$52$		0			0
$53$	1.60632	−	9.10987i	0.220645	−	1.25134i	−0.650194	−	0.759768i	$-0.725312\pi$
$53$	1.60632	−	9.10987i	0.220645	−	1.25134i	0.870839	−	0.491569i	$-0.163577\pi$
$54$		0			0
$55$	−4.16638	+	3.49601i	−0.561794	+	0.471401i
$56$		0			0
$57$	0.541374	+	4.73754i	0.0717067	+	0.627503i
$58$		0			0
$59$	1.79251	−	1.50409i	0.233365	−	0.195816i	−0.518605	−	0.855014i	$-0.673548\pi$
$59$	1.79251	−	1.50409i	0.233365	−	0.195816i	0.751970	+	0.659198i	$0.229104\pi$
$60$		0			0
$61$	−0.509501	+	2.88952i	−0.0652349	+	0.369965i	0.934661	+	0.355540i	$0.115703\pi$
$61$	−0.509501	+	2.88952i	−0.0652349	+	0.369965i	−0.999896	+	0.0144254i	$0.995408\pi$
$62$		0			0
$63$	6.14810	−	2.23772i	0.774588	−	0.281927i
$64$		0			0
$65$	0.701112	+	1.21436i	0.0869623	+	0.150623i
$66$		0			0
$67$	−1.64930	−	1.38393i	−0.201494	−	0.169074i	0.536457	−	0.843927i	$-0.319762\pi$
$67$	−1.64930	−	1.38393i	−0.201494	−	0.169074i	−0.737951	+	0.674854i	$0.764207\pi$
$68$		0			0
$69$	3.62681	−	6.28182i	0.436617	−	0.756243i
$70$		0			0
$71$	−2.83920	−	16.1019i	−0.336951	−	1.91094i	−0.407053	−	0.913405i	$-0.633443\pi$
$71$	−2.83920	−	16.1019i	−0.336951	−	1.91094i	0.0701015	−	0.997540i	$-0.477668\pi$
$72$		0			0
$73$	−12.1383	−	4.41799i	−1.42068	−	0.517087i	−0.486438	−	0.873715i	$-0.661704\pi$
$73$	−12.1383	−	4.41799i	−1.42068	−	0.517087i	−0.934246	+	0.356628i	$0.883926\pi$
$74$		0			0
$75$	−1.09394			−0.126317
$76$		0			0
$77$	−19.7330			−2.24878
$78$		0			0
$79$	10.7051	+	3.89632i	1.20441	+	0.438371i	0.864763	−	0.502181i	$-0.167469\pi$
$79$	10.7051	+	3.89632i	1.20441	+	0.438371i	0.339651	+	0.940552i	$0.389691\pi$
$80$		0			0
$81$	−0.0587363	−	0.333110i	−0.00652625	−	0.0370122i
$82$		0			0
$83$	5.51438	−	9.55118i	0.605281	−	1.04838i	−0.386726	−	0.922195i	$-0.626394\pi$
$83$	5.51438	−	9.55118i	0.605281	−	1.04838i	0.992007	−	0.126183i	$-0.0402727\pi$
$84$		0			0
$85$	−2.12355	−	1.78187i	−0.230332	−	0.193271i
$86$		0			0
$87$	3.06838	+	5.31459i	0.328965	+	0.569784i
$88$		0			0
$89$	10.5328	−	3.83361i	1.11647	−	0.406362i	0.283108	−	0.959088i	$-0.408635\pi$
$89$	10.5328	−	3.83361i	1.11647	−	0.406362i	0.833363	+	0.552726i	$0.186412\pi$
$90$		0			0
$91$	−0.883438	+	5.01023i	−0.0926095	+	0.525215i
$92$		0			0
$93$	8.96585	−	7.52325i	0.929716	−	0.780124i
$94$		0			0
$95$	−3.50307	+	2.59394i	−0.359407	+	0.266133i
$96$		0			0
$97$	−7.22724	+	6.06437i	−0.733815	+	0.615744i	−0.931169	−	0.364589i	$-0.881210\pi$
$97$	−7.22724	+	6.06437i	−0.733815	+	0.615744i	0.197354	+	0.980332i	$0.436765\pi$
$98$		0			0
$99$	1.70311	−	9.65879i	0.171169	−	0.970745i
$100$		0			0
$101$	7.41652	−	2.69939i	0.737972	−	0.268600i	0.0544364	−	0.998517i	$-0.482664\pi$
$101$	7.41652	−	2.69939i	0.737972	−	0.268600i	0.683535	+	0.729918i	$0.260442\pi$
$102$		0			0
$103$	4.82309	+	8.35384i	0.475233	+	0.823129i	0.999598	−	0.0283656i	$-0.00903026\pi$
$103$	4.82309	+	8.35384i	0.475233	+	0.823129i	−0.524364	+	0.851494i	$0.675697\pi$
$104$		0			0
$105$	−3.04044	−	2.55123i	−0.296716	−	0.248975i
$106$		0			0
$107$	−0.380492	+	0.659031i	−0.0367835	+	0.0637109i	−0.883831	−	0.467806i	$-0.845045\pi$
$107$	−0.380492	+	0.659031i	−0.0367835	+	0.0637109i	0.847048	+	0.531517i	$0.178378\pi$
$108$		0			0
$109$	−2.75235	−	15.6093i	−0.263627	−	1.49510i	−0.772917	−	0.634507i	$-0.781203\pi$
$109$	−2.75235	−	15.6093i	−0.263627	−	1.49510i	0.509290	−	0.860595i	$-0.329908\pi$
$110$		0			0
$111$	−3.46490	−	1.26112i	−0.328874	−	0.119700i
$112$		0			0
$113$	−7.02323			−0.660690			−0.330345	−	0.943860i	$-0.607165\pi$
$113$	−7.02323			−0.660690			−0.330345	+	0.943860i	$0.607165\pi$
$114$		0			0
$115$	6.63073			0.618319
$116$		0			0
$117$	−2.37613	−	0.864840i	−0.219673	−	0.0799545i
$118$		0			0
$119$	−1.74650	−	9.90488i	−0.160101	−	0.907979i
$120$		0			0
$121$	−9.29039	+	16.0914i	−0.844581	+	1.46286i
$122$		0			0
$123$	−2.10405	−	1.76551i	−0.189716	−	0.159191i
$124$		0			0
$125$	−0.500000	−	0.866025i	−0.0447214	−	0.0774597i
$126$		0			0
$127$	−12.0843	+	4.39833i	−1.07231	+	0.390289i	−0.817040	−	0.576581i	$-0.804386\pi$
$127$	−12.0843	+	4.39833i	−1.07231	+	0.390289i	−0.255270	+	0.966870i	$0.582164\pi$
$128$		0			0
$129$	−2.01618	+	11.4343i	−0.177514	+	1.00673i
$130$		0			0
$131$	6.68167	−	5.60659i	0.583780	−	0.489850i	−0.302406	−	0.953179i	$-0.597790\pi$
$131$	6.68167	−	5.60659i	0.583780	−	0.489850i	0.886186	+	0.463329i	$0.153345\pi$
$132$		0			0
$133$	−15.7857	−	0.960215i	−1.36879	−	0.0832612i
$134$		0			0
$135$	4.02519	−	3.37754i	0.346434	−	0.290692i
$136$		0			0
$137$	1.56695	−	8.88664i	0.133874	−	0.759237i	−0.841763	−	0.539847i	$-0.818482\pi$
$137$	1.56695	−	8.88664i	0.133874	−	0.759237i	0.975637	−	0.219390i	$-0.0704068\pi$
$138$		0			0
$139$	−1.34030	+	0.487829i	−0.113683	+	0.0413771i	−0.398235	−	0.917283i	$-0.630377\pi$
$139$	−1.34030	+	0.487829i	−0.113683	+	0.0413771i	0.284552	+	0.958660i	$0.408155\pi$
$140$		0			0
$141$	2.62492	+	4.54650i	0.221058	+	0.382884i
$142$		0			0
$143$	5.84220	+	4.90219i	0.488549	+	0.409941i
$144$		0			0
$145$	−2.80489	+	4.85821i	−0.232933	+	0.403452i
$146$		0			0
$147$	−1.17086	−	6.64025i	−0.0965705	−	0.547679i
$148$		0			0
$149$	7.15124	+	2.60284i	0.585852	+	0.213233i	0.617904	−	0.786253i	$-0.287982\pi$
$149$	7.15124	+	2.60284i	0.585852	+	0.213233i	−0.0320520	+	0.999486i	$0.510204\pi$
$150$		0			0
$151$	−0.549782			−0.0447406			−0.0223703	−	0.999750i	$-0.507121\pi$
$151$	−0.549782			−0.0447406			−0.0223703	+	0.999750i	$0.507121\pi$
$152$		0			0
$153$	4.99892			0.404138
$154$		0			0
$155$	10.0538	+	3.65928i	0.807540	+	0.293920i
$156$		0			0
$157$	−1.14249	−	6.47938i	−0.0911806	−	0.517111i	−0.995851	−	0.0909989i	$-0.970994\pi$
$157$	−1.14249	−	6.47938i	−0.0911806	−	0.517111i	0.904670	−	0.426112i	$-0.140117\pi$
$158$		0			0
$159$	5.05970	−	8.76366i	0.401260	−	0.695003i
$160$		0			0
$161$	18.4291	+	15.4638i	1.45242	+	1.21872i
$162$		0			0
$163$	7.67500	+	13.2935i	0.601153	+	1.04123i	0.992647	+	0.121046i	$0.0386250\pi$
$163$	7.67500	+	13.2935i	0.601153	+	1.04123i	−0.391494	+	0.920181i	$0.628042\pi$
$164$		0			0
$165$	−5.59093	+	2.03493i	−0.435254	+	0.158419i
$166$		0			0
$167$	−0.778544	+	4.41534i	−0.0602456	+	0.341670i	−1.00000		0.000180770i	$-0.999942\pi$
$167$	−0.778544	+	4.41534i	−0.0602456	+	0.341670i	0.939754	+	0.341850i	$0.111054\pi$
$168$		0			0
$169$	−8.45236	+	7.09237i	−0.650181	+	0.545567i
$170$		0			0
$171$	1.83242	−	7.64380i	0.140129	−	0.584536i
$172$		0			0
$173$	−11.4578	+	9.61423i	−0.871120	+	0.730956i	−0.964334	−	0.264690i	$-0.914730\pi$
$173$	−11.4578	+	9.61423i	−0.871120	+	0.730956i	0.0932138	+	0.995646i	$0.470286\pi$
$174$		0			0
$175$	0.630026	−	3.57306i	0.0476255	−	0.270098i
$176$		0			0
$177$	2.40540	−	0.875492i	0.180801	−	0.0658060i
$178$		0			0
$179$	12.9951	+	22.5082i	0.971300	+	1.68234i	0.691642	+	0.722241i	$0.256888\pi$
$179$	12.9951	+	22.5082i	0.971300	+	1.68234i	0.279658	+	0.960100i	$0.409779\pi$
$180$		0			0
$181$	7.32648	+	6.14765i	0.544573	+	0.456951i	0.873098	−	0.487544i	$-0.162107\pi$
$181$	7.32648	+	6.14765i	0.544573	+	0.456951i	−0.328525	+	0.944495i	$0.606552\pi$
$182$		0			0
$183$	−1.60486	+	2.77971i	−0.118635	+	0.205482i
$184$		0			0
$185$	−0.585304	−	3.31942i	−0.0430324	−	0.244049i
$186$		0			0
$187$	−14.1677	−	5.15663i	−1.03605	−	0.377090i
$188$		0			0
$189$	19.0643			1.38673
$190$		0			0
$191$	−10.6025			−0.767172			−0.383586	−	0.923505i	$-0.625311\pi$
$191$	−10.6025			−0.767172			−0.383586	+	0.923505i	$0.625311\pi$
$192$		0			0
$193$	17.7019	+	6.44297i	1.27421	+	0.463775i	0.888514	−	0.458850i	$-0.151738\pi$
$193$	17.7019	+	6.44297i	1.27421	+	0.463775i	0.385698	+	0.922625i	$0.373961\pi$
$194$		0			0
$195$	0.266368	+	1.51065i	0.0190750	+	0.108180i
$196$		0			0
$197$	3.05611	−	5.29334i	0.217739	−	0.377135i	−0.736377	−	0.676571i	$-0.763465\pi$
$197$	3.05611	−	5.29334i	0.217739	−	0.377135i	0.954116	+	0.299436i	$0.0967985\pi$
$198$		0			0
$199$	5.17943	+	4.34605i	0.367160	+	0.308084i	0.807637	−	0.589680i	$-0.200746\pi$
$199$	5.17943	+	4.34605i	0.367160	+	0.308084i	−0.440477	+	0.897764i	$0.645191\pi$
$200$		0			0
$201$	−1.17763	−	2.03972i	−0.0830638	−	0.143871i
$202$		0			0
$203$	−19.1258	+	6.96122i	−1.34237	+	0.488582i
$204$		0			0
$205$	0.435993	−	2.47264i	0.0304511	−	0.172697i
$206$		0			0
$207$	−9.15971	+	7.68591i	−0.636644	+	0.534208i
$208$		0			0
$209$	−13.0783	+	19.7735i	−0.904647	+	1.36776i
$210$		0			0
$211$	−5.31397	+	4.45895i	−0.365829	+	0.306967i	−0.807109	−	0.590403i	$-0.798969\pi$
$211$	−5.31397	+	4.45895i	−0.365829	+	0.306967i	0.441280	+	0.897369i	$0.354525\pi$
$212$		0			0
$213$	3.10592	−	17.6145i	0.212814	−	1.20693i
$214$		0			0
$215$	−9.97356	+	3.63008i	−0.680191	+	0.247569i
$216$		0			0
$217$	19.4090	+	33.6173i	1.31757	+	2.28209i
$218$		0			0
$219$	−10.8248	−	9.08311i	−0.731474	−	0.613780i
$220$		0			0
$221$	−1.94356	+	3.36634i	−0.130738	+	0.226444i
$222$		0			0
$223$	3.76498	+	21.3522i	0.252122	+	1.42985i	0.803355	+	0.595501i	$0.203046\pi$
$223$	3.76498	+	21.3522i	0.252122	+	1.42985i	−0.551233	+	0.834351i	$0.685843\pi$
$224$		0			0
$225$	1.69454	+	0.616763i	0.112969	+	0.0411175i
$226$		0			0
$227$	23.7457			1.57605			0.788027	−	0.615640i	$-0.211103\pi$
$227$	23.7457			1.57605			0.788027	+	0.615640i	$0.211103\pi$
$228$		0			0
$229$	−14.4053			−0.951928			−0.475964	−	0.879465i	$-0.657901\pi$
$229$	−14.4053			−0.951928			−0.475964	+	0.879465i	$0.657901\pi$
$230$		0			0
$231$	−20.2849	−	7.38310i	−1.33465	−	0.485772i
$232$		0			0
$233$	−3.71518	−	21.0698i	−0.243389	−	1.38033i	−0.824204	−	0.566293i	$-0.808377\pi$
$233$	−3.71518	−	21.0698i	−0.243389	−	1.38033i	0.580814	−	0.814036i	$-0.302734\pi$
$234$		0			0
$235$	−2.39951	+	4.15607i	−0.156527	+	0.271112i
$236$		0			0
$237$	9.54665	+	8.01059i	0.620122	+	0.520344i
$238$		0			0
$239$	−8.14253	−	14.1033i	−0.526697	−	0.912265i	−0.999516	−	0.0311059i	$-0.990097\pi$
$239$	−8.14253	−	14.1033i	−0.526697	−	0.912265i	0.472820	−	0.881159i	$-0.343236\pi$
$240$		0			0
$241$	14.2617	−	5.19083i	0.918676	−	0.334371i	0.160964	−	0.986960i	$-0.448540\pi$
$241$	14.2617	−	5.19083i	0.918676	−	0.334371i	0.757711	+	0.652590i	$0.226317\pi$
$242$		0			0
$243$	−2.67306	+	15.1597i	−0.171477	+	0.972493i
$244$		0			0
$245$	4.72164	−	3.96193i	0.301655	−	0.253118i
$246$		0			0
$247$	4.43500	+	4.20585i	0.282192	+	0.267612i
$248$		0			0
$249$	9.24217	−	7.75510i	0.585699	−	0.491460i
$250$		0			0
$251$	0.706652	−	4.00762i	0.0446035	−	0.252959i	−0.954350	−	0.298689i	$-0.903451\pi$
$251$	0.706652	−	4.00762i	0.0446035	−	0.252959i	0.998954	+	0.0457307i	$0.0145616\pi$
$252$		0			0
$253$	33.8885	−	12.3344i	2.13055	−	0.775457i
$254$		0			0
$255$	−1.51626	−	2.62624i	−0.0949517	−	0.164461i
$256$		0			0
$257$	1.62041	+	1.35969i	0.101079	+	0.0848151i	0.691927	−	0.721968i	$-0.256762\pi$
$257$	1.62041	+	1.35969i	0.101079	+	0.0848151i	−0.590848	+	0.806783i	$0.701207\pi$
$258$		0			0
$259$	6.11462	−	10.5908i	0.379944	−	0.658083i
$260$		0			0
$261$	−1.75664	−	9.96238i	−0.108733	−	0.616656i
$262$		0			0
$263$	−13.6466	−	4.96697i	−0.841487	−	0.306276i	−0.114922	−	0.993374i	$-0.536662\pi$
$263$	−13.6466	−	4.96697i	−0.841487	−	0.306276i	−0.726564	+	0.687098i	$0.758884\pi$
$264$		0			0
$265$	9.25041			0.568248
$266$		0			0
$267$	12.2617			0.750403
$268$		0			0
$269$	−5.04169	−	1.83503i	−0.307397	−	0.111884i	0.183715	−	0.982979i	$-0.441188\pi$
$269$	−5.04169	−	1.83503i	−0.307397	−	0.111884i	−0.491113	+	0.871096i	$0.663410\pi$
$270$		0			0
$271$	1.13162	+	6.41774i	0.0687410	+	0.389850i	0.999695	+	0.0247122i	$0.00786694\pi$
$271$	1.13162	+	6.41774i	0.0687410	+	0.389850i	−0.930954	+	0.365138i	$0.881022\pi$
$272$		0			0
$273$	−2.78272	+	4.81982i	−0.168418	+	0.291709i
$274$		0			0
$275$	−4.16638	−	3.49601i	−0.251242	−	0.210817i
$276$		0			0
$277$	1.45749	+	2.52445i	0.0875724	+	0.151680i	0.906484	−	0.422239i	$-0.138756\pi$
$277$	1.45749	+	2.52445i	0.0875724	+	0.151680i	−0.818912	+	0.573919i	$0.805422\pi$
$278$		0			0
$279$	−18.1299	+	6.59876i	−1.08541	+	0.395057i
$280$		0			0
$281$	−0.417979	+	2.37048i	−0.0249345	+	0.141411i	−0.994734	−	0.102495i	$-0.967318\pi$
$281$	−0.417979	+	2.37048i	−0.0249345	+	0.141411i	0.969799	+	0.243905i	$0.0784286\pi$
$282$		0			0
$283$	0.821925	−	0.689677i	0.0488584	−	0.0409970i	−0.618031	−	0.786153i	$-0.712070\pi$
$283$	0.821925	−	0.689677i	0.0488584	−	0.0409970i	0.666890	+	0.745156i	$0.267625\pi$
$284$		0			0
$285$	−4.57156	+	1.35582i	−0.270796	+	0.0803116i
$286$		0			0
$287$	6.97833	−	5.85551i	0.411918	−	0.345640i
$288$		0			0
$289$	−1.61761	+	9.17393i	−0.0951536	+	0.539643i
$290$		0			0
$291$	−9.69835	+	3.52991i	−0.568527	+	0.206927i
$292$		0			0
$293$	−11.6287	−	20.1414i	−0.679354	−	1.17668i	−0.975176	−	0.221432i	$-0.928927\pi$
$293$	−11.6287	−	20.1414i	−0.679354	−	1.17668i	0.295822	−	0.955243i	$-0.404407\pi$
$294$		0			0
$295$	1.79251	+	1.50409i	0.104364	+	0.0875716i
$296$		0			0
$297$	14.2892	−	24.7496i	0.829143	−	1.43612i
$298$		0			0
$299$	−1.61454	−	9.15652i	−0.0933713	−	0.529535i
$300$		0			0
$301$	−36.1858	−	13.1706i	−2.08572	−	0.759139i
$302$		0			0
$303$	8.63393			0.496006
$304$		0			0
$305$	−2.93410			−0.168006
$306$		0			0
$307$	−25.6029	−	9.31870i	−1.46124	−	0.531846i	−0.515530	−	0.856871i	$-0.672405\pi$
$307$	−25.6029	−	9.31870i	−1.46124	−	0.531846i	−0.945705	+	0.325025i	$0.894627\pi$
$308$		0			0
$309$	1.83240	+	10.3920i	0.104241	+	0.591183i
$310$		0			0
$311$	6.75505	−	11.7001i	0.383044	−	0.663451i	−0.608452	−	0.793591i	$-0.708209\pi$
$311$	6.75505	−	11.7001i	0.383044	−	0.663451i	0.991496	+	0.130140i	$0.0415426\pi$
$312$		0			0
$313$	−17.7886	−	14.9264i	−1.00547	−	0.843692i	−0.0177397	−	0.999843i	$-0.505647\pi$
$313$	−17.7886	−	14.9264i	−1.00547	−	0.843692i	−0.987733	+	0.156151i	$0.950091\pi$
$314$		0			0
$315$	3.27134	+	5.66612i	0.184319	+	0.319250i
$316$		0			0
$317$	−4.96139	+	1.80580i	−0.278659	+	0.101424i	−0.477569	−	0.878594i	$-0.658482\pi$
$317$	−4.96139	+	1.80580i	−0.278659	+	0.101424i	0.198910	+	0.980018i	$0.436260\pi$
$318$		0			0
$319$	−5.29810	+	30.0470i	−0.296637	+	1.68231i
$320$		0			0
$321$	−0.637709	+	0.535102i	−0.0355935	+	0.0298665i
$322$		0			0
$323$	−11.0827	−	4.81452i	−0.616660	−	0.267887i
$324$		0			0
$325$	−1.07417	+	0.901333i	−0.0595840	+	0.0499969i
$326$		0			0
$327$	3.01090	−	17.0757i	0.166503	−	0.944287i
$328$		0			0
$329$	−16.3616	+	5.95515i	−0.902046	+	0.328318i
$330$		0			0
$331$	−9.73690	−	16.8648i	−0.535188	−	0.926973i	−0.999154	−	0.0411202i	$-0.986907\pi$
$331$	−9.73690	−	16.8648i	−0.535188	−	0.926973i	0.463966	−	0.885853i	$-0.346426\pi$
$332$		0			0
$333$	4.65620	+	3.90702i	0.255158	+	0.214103i
$334$		0			0
$335$	1.07650	−	1.86456i	0.0588157	−	0.101872i
$336$		0			0
$337$	−1.33374	−	7.56400i	−0.0726533	−	0.412037i	−0.999344	−	0.0362127i	$-0.988471\pi$
$337$	−1.33374	−	7.56400i	−0.0726533	−	0.412037i	0.926691	−	0.375825i	$-0.122640\pi$
$338$		0			0
$339$	−7.21965	−	2.62774i	−0.392118	−	0.142719i
$340$		0			0
$341$	58.1901			3.15117
$342$		0			0
$343$	−3.03436			−0.163840
$344$		0			0
$345$	6.81618	+	2.48089i	0.366971	+	0.133566i
$346$		0			0
$347$	0.443233	+	2.51370i	0.0237940	+	0.134942i	0.994391	−	0.105769i	$-0.0337304\pi$
$347$	0.443233	+	2.51370i	0.0237940	+	0.134942i	−0.970597	+	0.240711i	$0.922619\pi$
$348$		0			0
$349$	−0.851409	+	1.47468i	−0.0455749	+	0.0789380i	−0.887913	−	0.460011i	$-0.847845\pi$
$349$	−0.851409	+	1.47468i	−0.0455749	+	0.0789380i	0.842338	+	0.538949i	$0.181179\pi$
$350$		0			0
$351$	−5.64423	−	4.73607i	−0.301267	−	0.252793i
$352$		0			0
$353$	11.8829	+	20.5818i	0.632465	+	1.09546i	0.987046	+	0.160436i	$0.0512900\pi$
$353$	11.8829	+	20.5818i	0.632465	+	1.09546i	−0.354582	+	0.935025i	$0.615377\pi$
$354$		0			0
$355$	15.3643	−	5.59213i	0.815450	−	0.296800i
$356$		0			0
$357$	1.91056	−	10.8353i	0.101118	−	0.573468i
$358$		0			0
$359$	−5.04166	+	4.23046i	−0.266089	+	0.223275i	−0.766063	−	0.642765i	$-0.777787\pi$
$359$	−5.04166	+	4.23046i	−0.266089	+	0.223275i	0.499975	+	0.866040i	$0.333343\pi$
$360$		0			0
$361$	−11.4244	+	15.1817i	−0.601283	+	0.799036i
$362$		0			0
$363$	−15.5708	+	13.0655i	−0.817256	+	0.685759i
$364$		0			0
$365$	2.24307	−	12.7211i	0.117408	−	0.665853i
$366$		0			0
$367$	27.6541	−	10.0653i	1.44353	−	0.525404i	0.502757	−	0.864428i	$-0.332319\pi$
$367$	27.6541	−	10.0653i	1.44353	−	0.525404i	0.940778	+	0.339024i	$0.110097\pi$
$368$		0			0
$369$	2.26384	+	3.92109i	0.117851	+	0.204124i
$370$		0			0
$371$	25.7101	+	21.5733i	1.33480	+	1.12003i
$372$		0			0
$373$	13.0673	−	22.6332i	0.676598	−	1.17190i	−0.299401	−	0.954127i	$-0.596787\pi$
$373$	13.0673	−	22.6332i	0.676598	−	1.17190i	0.975999	−	0.217775i	$-0.0698799\pi$
$374$		0			0
$375$	−0.189961	−	1.07732i	−0.00980953	−	0.0556326i
$376$		0			0
$377$	7.39177	+	2.69039i	0.380696	+	0.138562i
$378$		0			0
$379$	−16.3067			−0.837620			−0.418810	−	0.908074i	$-0.637553\pi$
$379$	−16.3067			−0.837620			−0.418810	+	0.908074i	$0.637553\pi$
$380$		0			0
$381$	−14.0679			−0.720722
$382$		0			0
$383$	−4.64354	−	1.69011i	−0.237274	−	0.0863606i	0.220647	−	0.975354i	$-0.429183\pi$
$383$	−4.64354	−	1.69011i	−0.237274	−	0.0863606i	−0.457920	+	0.888993i	$0.651405\pi$
$384$		0			0
$385$	−3.42660	−	19.4332i	−0.174636	−	0.990408i
$386$		0			0
$387$	9.56975	−	16.5753i	0.486458	−	0.842570i
$388$		0			0
$389$	−13.1979	−	11.0743i	−0.669159	−	0.561491i	0.243657	−	0.969861i	$-0.421653\pi$
$389$	−13.1979	−	11.0743i	−0.669159	−	0.561491i	−0.912816	+	0.408370i	$0.866097\pi$
$390$		0			0
$391$	9.19053	+	15.9185i	0.464785	+	0.805031i
$392$		0			0
$393$	8.96625	−	3.26345i	0.452287	−	0.164619i
$394$		0			0
$395$	−1.97822	+	11.2190i	−0.0995348	+	0.564490i
$396$		0			0
$397$	11.1837	−	9.38426i	0.561295	−	0.470983i	−0.317449	−	0.948275i	$-0.602826\pi$
$397$	11.1837	−	9.38426i	0.561295	−	0.470983i	0.878744	+	0.477293i	$0.158382\pi$
$398$		0			0
$399$	−15.8679	−	6.89328i	−0.794389	−	0.345096i
$400$		0			0
$401$	−0.893471	+	0.749711i	−0.0446178	+	0.0374388i	−0.664824	−	0.747000i	$-0.731493\pi$
$401$	−0.893471	+	0.749711i	−0.0446178	+	0.0374388i	0.620206	+	0.784439i	$0.287049\pi$
$402$		0			0
$403$	2.60514	−	14.7745i	0.129771	−	0.735971i
$404$		0			0
$405$	0.317850	−	0.115688i	0.0157941	−	0.00574858i
$406$		0			0
$407$	−9.16613	−	15.8762i	−0.454348	−	0.786954i
$408$		0			0
$409$	−10.7111	−	8.98771i	−0.529631	−	0.444413i	0.338343	−	0.941023i	$-0.390134\pi$
$409$	−10.7111	−	8.98771i	−0.529631	−	0.444413i	−0.867974	+	0.496609i	$0.834578\pi$
$410$		0			0
$411$	4.93571	−	8.54891i	0.243461	−	0.421686i
$412$		0			0
$413$	1.47423	+	8.36078i	0.0725422	+	0.411407i
$414$		0			0
$415$	10.3636	+	3.77206i	0.508731	+	0.185163i
$416$		0			0
$417$	−1.56031			−0.0764085
$418$		0			0
$419$	−8.57709			−0.419018			−0.209509	−	0.977807i	$-0.567187\pi$
$419$	−8.57709			−0.419018			−0.209509	+	0.977807i	$0.567187\pi$
$420$		0			0
$421$	−4.02175	−	1.46380i	−0.196008	−	0.0713411i	0.242151	−	0.970239i	$-0.422147\pi$
$421$	−4.02175	−	1.46380i	−0.196008	−	0.0713411i	−0.438159	+	0.898898i	$0.644369\pi$
$422$		0			0
$423$	−1.50276	−	8.52257i	−0.0730666	−	0.414381i
$424$		0			0
$425$	1.38605	−	2.40071i	0.0672334	−	0.116452i
$426$		0			0
$427$	−8.15487	−	6.84275i	−0.394642	−	0.331144i
$428$		0			0
$429$	4.17144	+	7.22515i	0.201399	+	0.348833i
$430$		0			0
$431$	2.04618	−	0.744750i	0.0985612	−	0.0358733i	−0.292269	−	0.956336i	$-0.594410\pi$
$431$	2.04618	−	0.744750i	0.0985612	−	0.0358733i	0.390830	+	0.920463i	$0.372188\pi$
$432$		0			0
$433$	0.796344	−	4.51629i	0.0382699	−	0.217039i	−0.959675	−	0.281110i	$-0.909297\pi$
$433$	0.796344	−	4.51629i	0.0382699	−	0.217039i	0.997945	+	0.0640711i	$0.0204084\pi$
$434$		0			0
$435$	−4.70103	+	3.94463i	−0.225397	+	0.189131i
$436$		0			0
$437$	27.7097	−	8.21804i	1.32554	−	0.393122i
$438$		0			0
$439$	−25.3814	+	21.2975i	−1.21139	+	1.01648i	−0.212160	+	0.977235i	$0.568050\pi$
$439$	−25.3814	+	21.2975i	−1.21139	+	1.01648i	−0.999230	+	0.0392414i	$0.987506\pi$
$440$		0			0
$441$	−1.93008	+	10.9460i	−0.0919087	+	0.521240i
$442$		0			0
$443$	−20.8133	+	7.57541i	−0.988868	+	0.359919i	−0.785282	−	0.619138i	$-0.787482\pi$
$443$	−20.8133	+	7.57541i	−0.988868	+	0.359919i	−0.203586	+	0.979057i	$0.565260\pi$
$444$		0			0
$445$	5.60437	+	9.70705i	0.265673	+	0.460158i
$446$		0			0
$447$	6.37739	+	5.35127i	0.301640	+	0.253106i
$448$		0			0
$449$	2.53652	−	4.39338i	0.119706	−	0.207336i	−0.799945	−	0.600073i	$-0.795138\pi$
$449$	2.53652	−	4.39338i	0.119706	−	0.207336i	0.919651	+	0.392736i	$0.128472\pi$
$450$		0			0
$451$	−2.37129	−	13.4482i	−0.111660	−	0.633253i
$452$		0			0
$453$	−0.565158	−	0.205701i	−0.0265535	−	0.00966467i
$454$		0			0
$455$	−5.08752			−0.238507
$456$		0			0
$457$	−15.0185			−0.702536			−0.351268	−	0.936275i	$-0.614249\pi$
$457$	−15.0185			−0.702536			−0.351268	+	0.936275i	$0.614249\pi$
$458$		0			0
$459$	13.6876	+	4.98189i	0.638883	+	0.232535i
$460$		0			0
$461$	1.02997	+	5.84127i	0.0479707	+	0.272055i	0.999353	−	0.0359561i	$-0.0114476\pi$
$461$	1.02997	+	5.84127i	0.0479707	+	0.272055i	−0.951383	+	0.308011i	$0.900337\pi$
$462$		0			0
$463$	0.383739	−	0.664655i	0.0178339	−	0.0308891i	−0.856971	−	0.515365i	$-0.827656\pi$
$463$	0.383739	−	0.664655i	0.0178339	−	0.0308891i	0.874805	+	0.484476i	$0.160990\pi$
$464$		0			0
$465$	8.96585	+	7.52325i	0.415782	+	0.348882i
$466$		0			0
$467$	−7.70383	−	13.3434i	−0.356491	−	0.617460i	0.630881	−	0.775880i	$-0.282694\pi$
$467$	−7.70383	−	13.3434i	−0.356491	−	0.617460i	−0.987372	+	0.158419i	$0.949360\pi$
$468$		0			0
$469$	7.34041	−	2.67169i	0.338949	−	0.123367i
$470$		0			0
$471$	1.24982	−	7.08806i	0.0575885	−	0.326600i
$472$		0			0
$473$	−44.2204	+	37.1053i	−2.03326	+	1.70611i
$474$		0			0
$475$	−3.16283	−	2.99941i	−0.145121	−	0.137623i
$476$		0			0
$477$	−12.7785	+	10.7225i	−0.585089	+	0.490948i
$478$		0			0
$479$	2.05385	−	11.6479i	0.0938427	−	0.532208i	−0.901253	−	0.433293i	$-0.857352\pi$
$479$	2.05385	−	11.6479i	0.0938427	−	0.532208i	0.995096	−	0.0989155i	$-0.0315373\pi$
$480$		0			0
$481$	−4.44135	+	1.61652i	−0.202508	+	0.0737069i
$482$		0			0
$483$	13.1587	+	22.7916i	0.598742	+	1.03705i
$484$		0			0
$485$	−7.22724	−	6.06437i	−0.328172	−	0.275369i
$486$		0			0
$487$	12.0770	−	20.9180i	0.547262	−	0.947886i	−0.451199	−	0.892424i	$-0.649003\pi$
$487$	12.0770	−	20.9180i	0.547262	−	0.947886i	0.998461	−	0.0554623i	$-0.0176632\pi$
$488$		0			0
$489$	2.91590	+	16.5369i	0.131862	+	0.747824i
$490$		0			0
$491$	−31.1082	−	11.3225i	−1.40390	−	0.510976i	−0.474563	−	0.880221i	$-0.657394\pi$
$491$	−31.1082	−	11.3225i	−1.40390	−	0.510976i	−0.929332	+	0.369245i	$0.879616\pi$
$492$		0			0
$493$	−15.5509			−0.700376
$494$		0			0
$495$	9.80779			0.440828
$496$		0			0
$497$	55.7443	+	20.2892i	2.50047	+	0.910097i
$498$		0			0
$499$	−0.397816	−	2.25613i	−0.0178087	−	0.100998i	0.974608	−	0.223919i	$-0.0718850\pi$
$499$	−0.397816	−	2.25613i	−0.0178087	−	0.100998i	−0.992416	+	0.122921i	$0.960774\pi$
$500$		0			0
$501$	−2.45232	+	4.24754i	−0.109561	+	0.189766i
$502$		0			0
$503$	17.8176	+	14.9507i	0.794448	+	0.666621i	0.946842	−	0.321699i	$-0.104254\pi$
$503$	17.8176	+	14.9507i	0.794448	+	0.666621i	−0.152394	+	0.988320i	$0.548698\pi$
$504$		0			0
$505$	3.94625	+	6.83510i	0.175606	+	0.304158i
$506$		0			0
$507$	−11.3424	+	4.12828i	−0.503732	+	0.183343i
$508$		0			0
$509$	1.69142	−	9.59254i	0.0749710	−	0.425182i	−0.924102	−	0.382145i	$-0.875186\pi$
$509$	1.69142	−	9.59254i	0.0749710	−	0.425182i	0.999073	−	0.0430371i	$-0.0137034\pi$
$510$		0			0
$511$	35.9018	−	30.1252i	1.58820	−	1.33266i
$512$		0			0
$513$	12.6352	−	19.1035i	0.557856	−	0.843438i
$514$		0			0
$515$	−7.38941	+	6.20045i	−0.325616	+	0.273224i
$516$		0			0
$517$	−4.53239	+	25.7045i	−0.199334	+	1.13048i
$518$		0			0
$519$	−15.3754	+	5.59619i	−0.674905	+	0.245645i
$520$		0			0
$521$	13.1193	+	22.7232i	0.574765	+	0.995523i	0.996067	+	0.0886021i	$0.0282399\pi$
$521$	13.1193	+	22.7232i	0.574765	+	0.995523i	−0.421302	+	0.906920i	$0.638427\pi$
$522$		0			0
$523$	−8.90505	−	7.47222i	−0.389391	−	0.326737i	0.426985	−	0.904259i	$-0.359576\pi$
$523$	−8.90505	−	7.47222i	−0.389391	−	0.326737i	−0.816376	+	0.577521i	$0.804020\pi$
$524$		0			0
$525$	1.98451	−	3.43726i	0.0866109	−	0.150014i
$526$		0			0
$527$	5.15019	+	29.2082i	0.224346	+	1.27233i
$528$		0			0
$529$	−19.7021	−	7.17099i	−0.856615	−	0.311782i
$530$		0			0
$531$	−4.21962			−0.183116
$532$		0			0
$533$	−3.52068			−0.152498
$534$		0			0
$535$	−0.715090	−	0.260272i	−0.0309161	−	0.0112525i
$536$		0			0
$537$	4.93712	+	27.9998i	0.213052	+	1.20828i
$538$		0			0
$539$	16.7615	−	29.0318i	0.721971	−	1.25049i
$540$		0			0
$541$	−22.8419	−	19.1666i	−0.982051	−	0.824039i	0.00234659	−	0.999997i	$-0.499253\pi$
$541$	−22.8419	−	19.1666i	−0.982051	−	0.824039i	−0.984398	+	0.175959i	$0.943698\pi$
$542$		0			0
$543$	5.23125	+	9.06079i	0.224494	+	0.388836i
$544$		0			0
$545$	14.8942	−	5.42106i	0.637999	−	0.232213i
$546$		0			0
$547$	−2.79368	+	15.8437i	−0.119449	+	0.677429i	0.865002	+	0.501769i	$0.167317\pi$
$547$	−2.79368	+	15.8437i	−0.119449	+	0.677429i	−0.984451	+	0.175660i	$0.943794\pi$
$548$		0			0
$549$	4.05317	−	3.40101i	0.172985	−	0.145152i
$550$		0			0
$551$	−5.70039	+	23.7787i	−0.242845	+	1.01301i
$552$		0			0
$553$	−31.6625	+	26.5680i	−1.34643	+	1.12979i
$554$		0			0
$555$	0.640288	−	3.63125i	0.0271787	−	0.154138i
$556$		0			0
$557$	−13.3701	+	4.86630i	−0.566508	+	0.206192i	−0.609366	−	0.792889i	$-0.708576\pi$
$557$	−13.3701	+	4.86630i	−0.566508	+	0.206192i	0.0428582	+	0.999081i	$0.486354\pi$
$558$		0			0
$559$	7.44135	+	12.8888i	0.314736	+	0.545138i
$560$		0			0
$561$	−12.6346	−	10.6017i	−0.533434	−	0.447604i
$562$		0			0
$563$	2.10390	−	3.64407i	0.0886690	−	0.153579i	−0.818280	−	0.574820i	$-0.805072\pi$
$563$	2.10390	−	3.64407i	0.0886690	−	0.153579i	0.906949	+	0.421241i	$0.138405\pi$
$564$		0			0
$565$	−1.21957	−	6.91653i	−0.0513077	−	0.290981i
$566$		0			0
$567$	1.15322	+	0.419736i	0.0484305	+	0.0176273i
$568$		0			0
$569$	0.192878			0.00808588			0.00404294	−	0.999992i	$-0.498713\pi$
$569$	0.192878			0.00808588			0.00404294	+	0.999992i	$0.498713\pi$
$570$		0			0
$571$	−11.7824			−0.493079			−0.246540	−	0.969133i	$-0.579294\pi$
$571$	−11.7824			−0.493079			−0.246540	+	0.969133i	$0.579294\pi$
$572$		0			0
$573$	−10.8991	−	3.96693i	−0.455315	−	0.165721i
$574$		0			0
$575$	1.15141	+	6.52999i	0.0480173	+	0.272320i
$576$		0			0
$577$	16.7487	−	29.0096i	0.697258	−	1.20769i	−0.272156	−	0.962253i	$-0.587737\pi$
$577$	16.7487	−	29.0096i	0.697258	−	1.20769i	0.969414	−	0.245432i	$-0.0789299\pi$
$578$		0			0
$579$	15.7864	+	13.2463i	0.656059	+	0.550499i
$580$		0			0
$581$	20.0071	+	34.6534i	0.830036	+	1.43766i
$582$		0			0
$583$	47.2772	−	17.2075i	1.95802	−	0.712661i
$584$		0			0
$585$	0.439091	−	2.49021i	0.0181542	−	0.102957i
$586$		0			0
$587$	10.1030	−	8.47746i	0.416997	−	0.349902i	−0.410022	−	0.912076i	$-0.634479\pi$
$587$	10.1030	−	8.47746i	0.416997	−	0.349902i	0.827019	+	0.562173i	$0.190035\pi$
$588$		0			0
$589$	46.5499	+	2.83155i	1.91806	+	0.116672i
$590$		0			0
$591$	5.12209	−	4.29794i	0.210694	−	0.176794i
$592$		0			0
$593$	6.73080	−	38.1723i	0.276401	−	1.56755i	−0.458075	−	0.888913i	$-0.651461\pi$
$593$	6.73080	−	38.1723i	0.276401	−	1.56755i	0.734476	−	0.678634i	$-0.237428\pi$
$594$		0			0
$595$	9.45113	−	3.43993i	0.387458	−	0.141023i
$596$		0			0
$597$	3.69821	+	6.40549i	0.151358	+	0.262159i
$598$		0			0
$599$	19.3433	+	16.2310i	0.790347	+	0.663180i	0.945831	−	0.324658i	$-0.105249\pi$
$599$	19.3433	+	16.2310i	0.790347	+	0.663180i	−0.155484	+	0.987838i	$0.549694\pi$
$600$		0			0
$601$	−13.1344	+	22.7495i	−0.535765	+	0.927972i	0.463361	+	0.886170i	$0.346643\pi$
$601$	−13.1344	+	22.7495i	−0.535765	+	0.927972i	−0.999126	+	0.0418023i	$0.986690\pi$
$602$		0			0
$603$	0.674191	+	3.82353i	0.0274552	+	0.155706i
$604$		0			0
$605$	−17.4602	−	6.35500i	−0.709859	−	0.258367i
$606$		0			0
$607$	36.0403			1.46283			0.731415	−	0.681933i	$-0.238860\pi$
$607$	36.0403			1.46283			0.731415	+	0.681933i	$0.238860\pi$
$608$		0			0
$609$	−22.2652			−0.902233
$610$		0			0
$611$	6.32348	+	2.30156i	0.255820	+	0.0931110i
$612$		0			0
$613$	1.14364	+	6.48591i	0.0461912	+	0.261964i	0.999154	−	0.0411237i	$-0.0130938\pi$
$613$	1.14364	+	6.48591i	0.0461912	+	0.261964i	−0.952963	+	0.303087i	$0.901983\pi$
$614$		0			0
$615$	1.37332	−	2.37867i	0.0553777	−	0.0959171i
$616$		0			0
$617$	−3.23564	−	2.71502i	−0.130262	−	0.109303i	0.575329	−	0.817922i	$-0.304874\pi$
$617$	−3.23564	−	2.71502i	−0.130262	−	0.109303i	−0.705591	+	0.708619i	$0.749318\pi$
$618$		0			0
$619$	8.09543	+	14.0217i	0.325383	+	0.563579i	0.981590	−	0.191001i	$-0.0611735\pi$
$619$	8.09543	+	14.0217i	0.325383	+	0.563579i	−0.656207	+	0.754581i	$0.727840\pi$
$620$		0			0
$621$	−32.7401	+	11.9164i	−1.31382	+	0.478190i
$622$		0			0
$623$	−7.06180	+	40.0495i	−0.282925	+	1.60455i
$624$		0			0
$625$	0.766044	−	0.642788i	0.0306418	−	0.0257115i
$626$		0			0
$627$	−20.8424	+	15.4333i	−0.832364	+	0.616346i
$628$		0			0
$629$	7.15772	−	6.00604i	0.285397	−	0.239476i
$630$		0			0
$631$	−5.49646	+	31.1720i	−0.218811	+	1.24094i	0.655359	+	0.755317i	$0.272517\pi$
$631$	−5.49646	+	31.1720i	−0.218811	+	1.24094i	−0.874170	+	0.485620i	$0.838594\pi$
$632$		0			0
$633$	−7.13090	+	2.59544i	−0.283428	+	0.103159i
$634$		0			0
$635$	−6.42993	−	11.1370i	−0.255164	−	0.441957i
$636$		0			0
$637$	−6.62081	−	5.55552i	−0.262326	−	0.220118i
$638$		0			0
$639$	−14.7422	+	25.5342i	−0.583192	+	1.01012i
$640$		0			0
$641$	−7.47565	−	42.3965i	−0.295270	−	1.67456i	−0.666102	−	0.745861i	$-0.732038\pi$
$641$	−7.47565	−	42.3965i	−0.295270	−	1.67456i	0.370832	−	0.928700i	$-0.379073\pi$
$642$		0			0
$643$	22.8293	+	8.30920i	0.900301	+	0.327683i	0.750373	−	0.661014i	$-0.229874\pi$
$643$	22.8293	+	8.30920i	0.900301	+	0.327683i	0.149928	+	0.988697i	$0.452096\pi$
$644$		0			0
$645$	−11.6107			−0.457170
$646$		0			0
$647$	−28.7229			−1.12921			−0.564606	−	0.825360i	$-0.690972\pi$
$647$	−28.7229			−1.12921			−0.564606	+	0.825360i	$0.690972\pi$
$648$		0			0
$649$	11.9591	+	4.35275i	0.469435	+	0.170860i
$650$		0			0
$651$	7.37389	+	41.8194i	0.289005	+	1.63903i
$652$		0			0
$653$	−19.1944	+	33.2458i	−0.751137	+	1.30101i	0.196135	+	0.980577i	$0.437161\pi$
$653$	−19.1944	+	33.2458i	−0.751137	+	1.30101i	−0.947272	+	0.320430i	$0.896173\pi$
$654$		0			0
$655$	6.68167	+	5.60659i	0.261074	+	0.219067i
$656$		0			0
$657$	11.6469	+	20.1730i	0.454388	+	0.787024i
$658$		0			0
$659$	−30.2296	+	11.0027i	−1.17758	+	0.428603i	−0.855346	−	0.518058i	$-0.826655\pi$
$659$	−30.2296	+	11.0027i	−1.17758	+	0.428603i	−0.322232	+	0.946661i	$0.604433\pi$
$660$		0			0
$661$	3.47112	−	19.6857i	0.135011	−	0.765685i	−0.839841	−	0.542832i	$-0.817352\pi$
$661$	3.47112	−	19.6857i	0.135011	−	0.765685i	0.974852	−	0.222853i	$-0.0715369\pi$
$662$		0			0
$663$	−3.25743	+	2.73331i	−0.126508	+	0.106153i
$664$		0			0
$665$	−1.79553	−	15.7126i	−0.0696276	−	0.609308i
$666$		0			0
$667$	28.4945	−	23.9097i	1.10331	−	0.925787i
$668$		0			0
$669$	−4.11866	+	23.3581i	−0.159237	+	0.903076i
$670$		0			0
$671$	−14.9956	+	5.45797i	−0.578900	+	0.210702i
$672$		0			0
$673$	2.59611	+	4.49660i	0.100073	+	0.173331i	0.911714	−	0.410824i	$-0.134759\pi$
$673$	2.59611	+	4.49660i	0.100073	+	0.173331i	−0.811642	+	0.584156i	$0.801426\pi$
$674$		0			0
$675$	4.02519	+	3.37754i	0.154930	+	0.130002i
$676$		0			0
$677$	−2.39094	+	4.14124i	−0.0918915	+	0.159161i	−0.908307	−	0.418304i	$-0.862625\pi$
$677$	−2.39094	+	4.14124i	−0.0918915	+	0.159161i	0.816416	+	0.577465i	$0.195958\pi$
$678$		0			0
$679$	−5.94398	−	33.7100i	−0.228109	−	1.29367i
$680$		0			0
$681$	24.4098	+	8.88443i	0.935384	+	0.340452i
$682$		0			0
$683$	−2.33827			−0.0894714			−0.0447357	−	0.998999i	$-0.514245\pi$
$683$	−2.33827			−0.0894714			−0.0447357	+	0.998999i	$0.514245\pi$
$684$		0			0
$685$	9.02373			0.344779
$686$		0			0
$687$	−14.8082	−	5.38974i	−0.564967	−	0.205631i
$688$		0			0
$689$	−2.25242	−	12.7741i	−0.0858102	−	0.486654i
$690$		0			0
$691$	17.5669	−	30.4267i	0.668275	−	1.15749i	−0.310111	−	0.950700i	$-0.600366\pi$
$691$	17.5669	−	30.4267i	0.668275	−	1.15749i	0.978386	−	0.206786i	$-0.0663003\pi$
$692$		0			0
$693$	27.2592	+	22.8732i	1.03549	+	0.868882i
$694$		0			0
$695$	−0.713158	−	1.23523i	−0.0270516	−	0.0468548i
$696$		0			0
$697$	6.54040	−	2.38051i	0.247735	−	0.0901683i
$698$		0			0
$699$	4.06418	−	23.0491i	0.153722	−	0.871798i
$700$		0			0
$701$	3.92698	−	3.29513i	0.148320	−	0.124455i	−0.565608	−	0.824674i	$-0.691359\pi$
$701$	3.92698	−	3.29513i	0.148320	−	0.124455i	0.713928	+	0.700219i	$0.246914\pi$
$702$		0			0
$703$	−6.56002	−	13.1464i	−0.247416	−	0.495826i
$704$		0			0
$705$	−4.02161	+	3.37453i	−0.151463	+	0.127092i
$706$		0			0
$707$	−4.97248	+	28.2003i	−0.187009	+	1.06058i
$708$		0			0
$709$	14.4095	−	5.24461i	0.541158	−	0.196966i	−0.0569555	−	0.998377i	$-0.518139\pi$
$709$	14.4095	−	5.24461i	0.541158	−	0.196966i	0.598114	+	0.801411i	$0.295917\pi$
$710$		0			0
$711$	−10.2716	−	17.7910i	−0.385217	−	0.667215i
$712$		0			0
$713$	−54.3450	−	45.6008i	−2.03523	−	1.70776i
$714$		0			0
$715$	−3.81322	+	6.60470i	−0.142607	+	0.247002i
$716$		0			0
$717$	−3.09352	−	17.5442i	−0.115530	−	0.655202i
$718$		0			0
$719$	−1.47862	−	0.538174i	−0.0551432	−	0.0200705i	0.314301	−	0.949323i	$-0.398230\pi$
$719$	−1.47862	−	0.538174i	−0.0551432	−	0.0200705i	−0.369445	+	0.929253i	$0.620452\pi$
$720$		0			0
$721$	−34.9981			−1.30340
$722$		0			0
$723$	16.6027			0.617461
$724$		0			0
$725$	−5.27146	−	1.91866i	−0.195777	−	0.0712571i
$726$		0			0
$727$	−7.85960	−	44.5740i	−0.291496	−	1.65316i	−0.681111	−	0.732180i	$-0.738503\pi$
$727$	−7.85960	−	44.5740i	−0.291496	−	1.65316i	0.389615	−	0.920978i	$-0.372608\pi$
$728$		0			0
$729$	−8.92718	+	15.4623i	−0.330636	+	0.572679i
$730$		0			0
$731$	−22.5386	−	18.9122i	−0.833621	−	0.699491i
$732$		0			0
$733$	−18.5796	−	32.1808i	−0.686253	−	1.18863i	−0.973041	−	0.230631i	$-0.925921\pi$
$733$	−18.5796	−	32.1808i	−0.686253	−	1.18863i	0.286788	−	0.957994i	$-0.407412\pi$
$734$		0			0
$735$	6.33605	−	2.30614i	0.233709	−	0.0850631i
$736$		0			0
$737$	2.03339	−	11.5319i	0.0749009	−	0.424784i
$738$		0			0
$739$	20.3874	−	17.1071i	0.749964	−	0.629295i	−0.185529	−	0.982639i	$-0.559400\pi$
$739$	20.3874	−	17.1071i	0.749964	−	0.629295i	0.935493	+	0.353344i	$0.114956\pi$
$740$		0			0
$741$	2.98542	+	5.98284i	0.109672	+	0.219785i
$742$		0			0
$743$	−24.0072	+	20.1445i	−0.880740	+	0.739028i	−0.966331	−	0.257302i	$-0.917166\pi$
$743$	−24.0072	+	20.1445i	−0.880740	+	0.739028i	0.0855914	+	0.996330i	$0.472722\pi$
$744$		0			0
$745$	−1.32150	+	7.49457i	−0.0484158	+	0.274580i
$746$		0			0
$747$	−18.6887	+	6.80212i	−0.683783	+	0.248877i
$748$		0			0
$749$	−1.38049	−	2.39108i	−0.0504420	−	0.0873682i
$750$		0			0
$751$	15.2232	+	12.7737i	0.555501	+	0.466121i	0.876799	−	0.480858i	$-0.159675\pi$
$751$	15.2232	+	12.7737i	0.555501	+	0.466121i	−0.321298	+	0.946978i	$0.604119\pi$
$752$		0			0
$753$	2.22587	−	3.85531i	0.0811150	−	0.140495i
$754$		0			0
$755$	−0.0954687	−	0.541430i	−0.00347446	−	0.0197046i
$756$		0			0
$757$	−43.5045	−	15.8344i	−1.58120	−	0.575509i	−0.605735	−	0.795667i	$-0.707121\pi$
$757$	−43.5045	−	15.8344i	−1.58120	−	0.575509i	−0.975464	+	0.220157i	$0.929343\pi$
$758$		0			0
$759$	39.4512			1.43199
$760$		0			0
$761$	38.1331			1.38232			0.691161	−	0.722701i	$-0.257099\pi$
$761$	38.1331			1.38232			0.691161	+	0.722701i	$0.257099\pi$
$762$		0			0
$763$	54.0390	+	19.6686i	1.95634	+	0.712050i
$764$		0			0
$765$	0.868053	+	4.92297i	0.0313845	+	0.177990i
$766$		0			0
$767$	1.64057	−	2.84155i	0.0592375	−	0.102602i
$768$		0			0
$769$	−14.2867	−	11.9880i	−0.515193	−	0.432298i	0.347759	−	0.937584i	$-0.386943\pi$
$769$	−14.2867	−	11.9880i	−0.515193	−	0.432298i	−0.862952	+	0.505286i	$0.831387\pi$
$770$		0			0
$771$	1.15701	+	2.00399i	0.0416686	+	0.0721721i
$772$		0			0
$773$	36.8574	−	13.4150i	1.32567	−	0.482504i	0.420398	−	0.907340i	$-0.361891\pi$
$773$	36.8574	−	13.4150i	1.32567	−	0.482504i	0.905270	+	0.424836i	$0.139668\pi$
$774$		0			0
$775$	−1.85787	+	10.5365i	−0.0667365	+	0.378481i
$776$		0			0
$777$	10.2482	−	8.59926i	0.367652	−	0.308497i
$778$		0			0
$779$	−1.24255	−	10.8735i	−0.0445188	−	0.389583i
$780$		0			0
$781$	68.1216	−	57.1608i	2.43758	−	2.04537i
$782$		0			0
$783$	5.11857	−	29.0288i	0.182923	−	1.03741i
$784$		0			0
$785$	6.18255	−	2.25027i	0.220665	−	0.0803154i
$786$		0			0
$787$	12.0053	+	20.7938i	0.427942	+	0.741218i	0.996690	−	0.0812940i	$-0.0259053\pi$
$787$	12.0053	+	20.7938i	0.427942	+	0.741218i	−0.568748	+	0.822512i	$0.692572\pi$
$788$		0			0
$789$	−12.1699	−	10.2118i	−0.433260	−	0.363548i
$790$		0			0
$791$	12.7408	−	22.0676i	0.453009	−	0.784635i
$792$		0			0
$793$	0.714434	+	4.05176i	0.0253703	+	0.143882i
$794$		0			0
$795$	9.50912	+	3.46104i	0.337254	+	0.122750i
$796$		0			0
$797$	−40.9652			−1.45106			−0.725531	−	0.688189i	$-0.758406\pi$
$797$	−40.9652			−1.45106			−0.725531	+	0.688189i	$0.758406\pi$
$798$		0			0
$799$	−13.3034			−0.470639
$800$		0			0
$801$	−18.9937	−	6.91313i	−0.671108	−	0.244264i
$802$		0			0
$803$	−12.1997	−	69.1878i	−0.430517	−	2.44158i
$804$		0			0
$805$	−12.0287	+	20.8344i	−0.423957	+	0.734315i
$806$		0			0
$807$	−4.49612	−	3.77270i	−0.158271	−	0.132805i
$808$		0			0
$809$	4.09979	+	7.10104i	0.144141	+	0.249659i	0.929052	−	0.369949i	$-0.120625\pi$
$809$	4.09979	+	7.10104i	0.144141	+	0.249659i	−0.784911	+	0.619608i	$0.787291\pi$
$810$		0			0
$811$	−2.52242	+	0.918087i	−0.0885743	+	0.0322384i	−0.385927	−	0.922529i	$-0.626118\pi$
$811$	−2.52242	+	0.918087i	−0.0885743	+	0.0322384i	0.297353	+	0.954768i	$0.403896\pi$
$812$		0			0
$813$	−1.23793	+	7.02062i	−0.0434159	+	0.246224i
$814$		0			0
$815$	−11.7588	+	9.86680i	−0.411892	+	0.345619i
$816$		0			0
$817$	−37.1803	+	27.5311i	−1.30077	+	0.963192i
$818$		0			0
$819$	7.02792	−	5.89712i	0.245575	−	0.206062i
$820$		0			0
$821$	−6.56808	+	37.2495i	−0.229228	+	1.30001i	0.625208	+	0.780458i	$0.285014\pi$
$821$	−6.56808	+	37.2495i	−0.229228	+	1.30001i	−0.854436	+	0.519557i	$0.826097\pi$
$822$		0			0
$823$	−20.1960	+	7.35073i	−0.703987	+	0.256230i	−0.669112	−	0.743161i	$-0.733326\pi$
$823$	−20.1960	+	7.35073i	−0.703987	+	0.256230i	−0.0348749	+	0.999392i	$0.511103\pi$
$824$		0			0
$825$	−2.97487	−	5.15263i	−0.103572	−	0.179392i
$826$		0			0
$827$	22.0020	+	18.4619i	0.765085	+	0.641983i	0.939445	−	0.342699i	$-0.111341\pi$
$827$	22.0020	+	18.4619i	0.765085	+	0.641983i	−0.174360	+	0.984682i	$0.555786\pi$
$828$		0			0
$829$	27.6642	−	47.9158i	0.960818	−	1.66419i	0.240365	−	0.970683i	$-0.422733\pi$
$829$	27.6642	−	47.9158i	0.960818	−	1.66419i	0.720453	−	0.693504i	$-0.243934\pi$
$830$		0			0
$831$	0.553734	+	3.14038i	0.0192088	+	0.108939i
$832$		0			0
$833$	16.0559	+	5.84387i	0.556304	+	0.202478i
$834$		0			0
$835$	−4.48346			−0.155156
$836$		0			0
$837$	−56.2182			−1.94319
$838$		0			0
$839$	−34.9725	−	12.7289i	−1.20738	−	0.439452i	−0.341588	−	0.939850i	$-0.610965\pi$
$839$	−34.9725	−	12.7289i	−1.20738	−	0.439452i	−0.865796	+	0.500398i	$0.833187\pi$
$840$		0			0
$841$	0.428834	+	2.43204i	0.0147874	+	0.0838634i
$842$		0			0
$843$	−1.31658	+	2.28039i	−0.0453455	+	0.0785407i
$844$		0			0
$845$	−8.45236	−	7.09237i	−0.290770	−	0.243985i
$846$		0			0
$847$	−33.7072	−	58.3825i	−1.15819	−	2.00605i
$848$		0			0
$849$	1.10295	−	0.401443i	0.0378533	−	0.0137775i
$850$		0			0
$851$	−3.88099	+	22.0102i	−0.133039	+	0.754500i
$852$		0			0
$853$	−4.42194	+	3.71045i	−0.151404	+	0.127043i	−0.715343	−	0.698773i	$-0.753730\pi$
$853$	−4.42194	+	3.71045i	−0.151404	+	0.127043i	0.563939	+	0.825816i	$0.309285\pi$
$854$		0			0
$855$	7.84587	+	0.477251i	0.268323	+	0.0163216i
$856$		0			0
$857$	−1.64015	+	1.37625i	−0.0560263	+	0.0470116i	−0.670371	−	0.742026i	$-0.733865\pi$
$857$	−1.64015	+	1.37625i	−0.0560263	+	0.0470116i	0.614345	+	0.789038i	$0.289421\pi$
$858$		0			0
$859$	5.87056	−	33.2936i	0.200301	−	1.13596i	−0.704364	−	0.709839i	$-0.748768\pi$
$859$	5.87056	−	33.2936i	0.200301	−	1.13596i	0.904665	−	0.426123i	$-0.140121\pi$
$860$		0			0
$861$	9.36434	−	3.40834i	0.319136	−	0.116156i
$862$		0			0
$863$	−9.75915	−	16.9033i	−0.332205	−	0.575396i	0.650739	−	0.759302i	$-0.274459\pi$
$863$	−9.75915	−	16.9033i	−0.332205	−	0.575396i	−0.982944	+	0.183905i	$0.941126\pi$
$864$		0			0
$865$	−11.4578	−	9.61423i	−0.389577	−	0.326894i
$866$		0			0
$867$	−5.09527	+	8.82527i	−0.173045	+	0.299722i
$868$		0			0
$869$	10.7592	+	61.0182i	0.364980	+	2.06990i
$870$		0			0
$871$	−2.83694	−	1.03256i	−0.0961259	−	0.0349870i
$872$		0			0
$873$	17.0132			0.575808
$874$		0			0
$875$	3.62818			0.122655
$876$		0			0
$877$	−22.8968	−	8.33374i	−0.773169	−	0.281410i	−0.0748475	−	0.997195i	$-0.523847\pi$
$877$	−22.8968	−	8.33374i	−0.773169	−	0.281410i	−0.698321	+	0.715785i	$0.746069\pi$
$878$		0			0
$879$	−4.41798	−	25.0556i	−0.149015	−	0.845105i
$880$		0			0
$881$	−13.1878	+	22.8419i	−0.444308	+	0.769563i	−0.998004	−	0.0631555i	$-0.979884\pi$
$881$	−13.1878	+	22.8419i	−0.444308	+	0.769563i	0.553696	+	0.832719i	$0.313217\pi$
$882$		0			0
$883$	12.8920	+	10.8176i	0.433849	+	0.364042i	0.833402	−	0.552668i	$-0.186390\pi$
$883$	12.8920	+	10.8176i	0.433849	+	0.364042i	−0.399553	+	0.916710i	$0.630835\pi$
$884$		0			0
$885$	1.27988	+	2.21682i	0.0430228	+	0.0745177i
$886$		0			0
$887$	−21.7494	+	7.91613i	−0.730273	+	0.265798i	−0.680281	−	0.732952i	$-0.738142\pi$
$887$	−21.7494	+	7.91613i	−0.730273	+	0.265798i	−0.0499928	+	0.998750i	$0.515920\pi$
$888$		0			0
$889$	8.10205	−	45.9490i	0.271734	−	1.54108i
$890$		0			0
$891$	1.40927	−	1.18252i	0.0472124	−	0.0396159i
$892$		0			0
$893$	−4.87654	+	20.3421i	−0.163187	+	0.680722i
$894$		0			0
$895$	−19.9097	+	16.7062i	−0.665506	+	0.558426i
$896$		0			0
$897$	1.76621	−	10.0167i	0.0589721	−	0.334447i
$898$		0			0
$899$	56.3995	−	20.5277i	1.88103	−	0.684638i
$900$		0			0
$901$	12.8215	+	22.2076i	0.427147	+	0.739841i
$902$		0			0
$903$	−32.2701	−	27.0778i	−1.07388	−	0.901094i
$904$		0			0
$905$	−4.78202	+	8.28271i	−0.158960	+	0.275326i
$906$		0			0
$907$	9.99460	+	56.6822i	0.331865	+	1.88210i	0.456224	+	0.889865i	$0.349201\pi$
$907$	9.99460	+	56.6822i	0.331865	+	1.88210i	−0.124359	+	0.992237i	$0.539687\pi$
$908$		0			0
$909$	−13.3742	−	4.86780i	−0.443593	−	0.161455i
$910$		0			0
$911$	49.4081			1.63696			0.818482	−	0.574533i	$-0.194816\pi$
$911$	49.4081			1.63696			0.818482	+	0.574533i	$0.194816\pi$
$912$		0			0
$913$	59.9834			1.98516
$914$		0			0
$915$	−3.01616	−	1.09779i	−0.0997111	−	0.0362919i
$916$		0			0
$917$	5.49528	+	31.1653i	0.181470	+	1.02917i
$918$		0			0
$919$	−7.31500	+	12.6700i	−0.241300	+	0.417943i	−0.961085	−	0.276254i	$-0.910907\pi$
$919$	−7.31500	+	12.6700i	−0.241300	+	0.417943i	0.719785	+	0.694197i	$0.244240\pi$
$920$		0			0
$921$	−22.8324	−	19.1587i	−0.752353	−	0.631299i
$922$		0			0
$923$	−11.4634	−	19.8552i	−0.377322	−	0.653542i
$924$		0			0
$925$	3.16736	−	1.15282i	0.104142	−	0.0379046i
$926$		0			0
$927$	3.02059	−	17.1306i	0.0992093	−	0.562644i
$928$		0			0
$929$	−32.5929	+	27.3487i	−1.06934	+	0.897281i	−0.994992	−	0.0999517i	$-0.968131\pi$
$929$	−32.5929	+	27.3487i	−1.06934	+	0.897281i	−0.0743454	+	0.997233i	$0.523687\pi$
$930$		0			0
$931$	14.8213	−	22.4088i	0.485749	−	0.734418i
$932$		0			0
$933$	11.3216	−	9.49991i	0.370651	−	0.311013i
$934$		0			0
$935$	2.61809	−	14.8479i	0.0856206	−	0.485579i
$936$		0			0
$937$	27.8225	−	10.1266i	0.908921	−	0.330820i	0.155099	−	0.987899i	$-0.450430\pi$
$937$	27.8225	−	10.1266i	0.908921	−	0.330820i	0.753822	+	0.657079i	$0.228208\pi$
$938$		0			0
$939$	−12.7014	−	21.9995i	−0.414495	−	0.717927i
$940$		0			0
$941$	0.307053	+	0.257648i	0.0100096	+	0.00839908i	0.647779	−	0.761829i	$-0.275698\pi$
$941$	0.307053	+	0.257648i	0.0100096	+	0.00839908i	−0.637769	+	0.770228i	$0.720143\pi$
$942$		0			0
$943$	−8.32416	+	14.4179i	−0.271072	+	0.469510i
$944$		0			0
$945$	3.31048	+	18.7747i	0.107690	+	0.610741i
$946$		0			0
$947$	47.1594	+	17.1646i	1.53247	+	0.557775i	0.964226	−	0.265083i	$-0.0853994\pi$
$947$	47.1594	+	17.1646i	1.53247	+	0.557775i	0.568248	+	0.822858i	$0.307622\pi$
$948$		0			0
$949$	−18.1130			−0.587974
$950$		0			0
$951$	−5.77579			−0.187293
$952$		0			0
$953$	11.2443	+	4.09260i	0.364239	+	0.132572i	0.517655	−	0.855590i	$-0.326805\pi$
$953$	11.2443	+	4.09260i	0.364239	+	0.132572i	−0.153416	+	0.988162i	$0.549027\pi$
$954$		0			0
$955$	−1.84111	−	10.4415i	−0.0595769	−	0.337877i
$956$		0			0
$957$	−16.6884	+	28.9051i	−0.539458	+	0.934369i
$958$		0			0
$959$	25.0801	+	21.0447i	0.809878	+	0.679568i
$960$		0			0
$961$	−41.7345	−	72.2863i	−1.34627	−	2.33182i
$962$		0			0
$963$	1.28952	−	0.469346i	0.0415541	−	0.0151245i
$964$		0			0
$965$	−3.27118	+	18.5518i	−0.105303	+	0.597203i
$966$		0			0
$967$	−30.4106	+	25.5176i	−0.977940	+	0.820589i	−0.983777	−	0.179394i	$-0.942586\pi$
$967$	−30.4106	+	25.5176i	−0.977940	+	0.820589i	0.00583706	+	0.999983i	$0.498142\pi$
$968$		0			0
$969$	−9.59134	−	9.09577i	−0.308118	−	0.292198i
$970$		0			0
$971$	35.7267	−	29.9783i	1.14652	−	0.962048i	0.146892	−	0.989153i	$-0.453073\pi$
$971$	35.7267	−	29.9783i	1.14652	−	0.962048i	0.999633	+	0.0271043i	$0.00862861\pi$
$972$		0			0
$973$	0.898617	−	5.09631i	0.0288083	−	0.163380i
$974$		0			0
$975$	−1.44144	+	0.524642i	−0.0461631	+	0.0168020i
$976$		0			0
$977$	5.52776	+	9.57437i	0.176849	+	0.306311i	0.940800	−	0.338963i	$-0.110076\pi$
$977$	5.52776	+	9.57437i	0.176849	+	0.306311i	−0.763951	+	0.645275i	$0.776743\pi$
$978$		0			0
$979$	46.6998	+	39.1858i	1.49253	+	1.25238i
$980$		0			0
$981$	−14.2912	+	24.7531i	−0.456284	+	0.790306i
$982$		0			0
$983$	−3.88991	−	22.0608i	−0.124069	−	0.703630i	−0.981856	−	0.189626i	$-0.939273\pi$
$983$	−3.88991	−	22.0608i	−0.124069	−	0.703630i	0.857788	−	0.514004i	$-0.171839\pi$
$984$		0			0
$985$	5.74361	+	2.09050i	0.183007	+	0.0666090i
$986$		0			0
$987$	−19.0474			−0.606284
$988$		0			0
$989$	70.3762			2.23783
$990$		0			0
$991$	−18.7269	−	6.81605i	−0.594881	−	0.216519i	0.0269940	−	0.999636i	$-0.491406\pi$
$991$	−18.7269	−	6.81605i	−0.594881	−	0.216519i	−0.621875	+	0.783117i	$0.713629\pi$
$992$		0			0
$993$	−3.69926	−	20.9795i	−0.117392	−	0.665765i
$994$		0			0
$995$	−3.38063	+	5.85542i	−0.107173	+	0.185629i
$996$		0			0
$997$	−14.7562	−	12.3819i	−0.467334	−	0.392140i	0.378487	−	0.925607i	$-0.376445\pi$
$997$	−14.7562	−	12.3819i	−0.467334	−	0.392140i	−0.845821	+	0.533467i	$0.820889\pi$
$998$		0			0
$999$	8.85552	+	15.3382i	0.280176	+	0.485280i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.u.b.101.2	✓	18
19.4	even	9		7220.2.a.w.1.4		9
19.15	odd	18		7220.2.a.y.1.6		9
19.16	even	9	inner	380.2.u.b.301.2	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.u.b.101.2	✓	18	1.1	even	1	trivial
380.2.u.b.301.2	yes	18	19.16	even	9	inner
7220.2.a.w.1.4		9	19.4	even	9
7220.2.a.y.1.6		9	19.15	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.02797 + 0.374150i) q^{3} +(0.173648 + 0.984808i) q^{5} +(-1.81409 + 3.14209i) q^{7} +(-1.38140 - 1.15914i) q^{9} +O(q^{10})\)	\(q+(1.02797 + 0.374150i) q^{3} +(0.173648 + 0.984808i) q^{5} +(-1.81409 + 3.14209i) q^{7} +(-1.38140 - 1.15914i) q^{9} +(2.71941 + 4.71016i) q^{11} +(1.31766 - 0.479589i) q^{13} +(-0.189961 + 1.07732i) q^{15} +(-2.12355 + 1.78187i) q^{17} +(1.94623 + 3.90028i) q^{19} +(-3.04044 + 2.55123i) q^{21} +(1.15141 - 6.52999i) q^{23} +(-0.939693 + 0.342020i) q^{25} +(-2.62726 - 4.55055i) q^{27} +(4.29734 + 3.60589i) q^{29} +(5.34951 - 9.26562i) q^{31} +(1.03316 + 5.85936i) q^{33} +(-3.40937 - 1.24091i) q^{35} -3.37063 q^{37} +1.53395 q^{39} +(-2.35936 - 0.858738i) q^{41} +(1.84304 + 10.4524i) q^{43} +(0.901647 - 1.56170i) q^{45} +(3.67626 + 3.08475i) q^{47} +(-3.08183 - 5.33789i) q^{49} +(-2.84963 + 1.03718i) q^{51} +(1.60632 - 9.10987i) q^{53} +(-4.16638 + 3.49601i) q^{55} +(0.541374 + 4.73754i) q^{57} +(1.79251 - 1.50409i) q^{59} +(-0.509501 + 2.88952i) q^{61} +(6.14810 - 2.23772i) q^{63} +(0.701112 + 1.21436i) q^{65} +(-1.64930 - 1.38393i) q^{67} +(3.62681 - 6.28182i) q^{69} +(-2.83920 - 16.1019i) q^{71} +(-12.1383 - 4.41799i) q^{73} -1.09394 q^{75} -19.7330 q^{77} +(10.7051 + 3.89632i) q^{79} +(-0.0587363 - 0.333110i) q^{81} +(5.51438 - 9.55118i) q^{83} +(-2.12355 - 1.78187i) q^{85} +(3.06838 + 5.31459i) q^{87} +(10.5328 - 3.83361i) q^{89} +(-0.883438 + 5.01023i) q^{91} +(8.96585 - 7.52325i) q^{93} +(-3.50307 + 2.59394i) q^{95} +(-7.22724 + 6.06437i) q^{97} +(1.70311 - 9.65879i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 3 q^{3} + 15 q^{9}+O(q^{10}) \) 18 * q + 3 * q^3 + 15 * q^9	\( 18 q + 3 q^{3} + 15 q^{9} + 9 q^{13} + 3 q^{15} + 12 q^{17} - 18 q^{19} - 9 q^{21} + 21 q^{23} + 18 q^{27} - 9 q^{29} + 6 q^{31} - 21 q^{33} - 6 q^{35} - 36 q^{37} - 12 q^{39} + 6 q^{41} - 12 q^{43} - 6 q^{45} + 21 q^{47} - 3 q^{49} - 9 q^{51} + 36 q^{53} - 3 q^{55} - 24 q^{57} - 6 q^{61} + 36 q^{63} + 15 q^{65} + 60 q^{67} + 27 q^{69} - 36 q^{71} - 60 q^{73} - 6 q^{75} - 36 q^{77} - 3 q^{79} + 3 q^{81} - 6 q^{83} + 12 q^{85} + 21 q^{87} + 6 q^{89} - 30 q^{91} - 48 q^{93} - 21 q^{95} - 57 q^{97} + 3 q^{99}+O(q^{100}) \) 18 * q + 3 * q^3 + 15 * q^9 + 9 * q^13 + 3 * q^15 + 12 * q^17 - 18 * q^19 - 9 * q^21 + 21 * q^23 + 18 * q^27 - 9 * q^29 + 6 * q^31 - 21 * q^33 - 6 * q^35 - 36 * q^37 - 12 * q^39 + 6 * q^41 - 12 * q^43 - 6 * q^45 + 21 * q^47 - 3 * q^49 - 9 * q^51 + 36 * q^53 - 3 * q^55 - 24 * q^57 - 6 * q^61 + 36 * q^63 + 15 * q^65 + 60 * q^67 + 27 * q^69 - 36 * q^71 - 60 * q^73 - 6 * q^75 - 36 * q^77 - 3 * q^79 + 3 * q^81 - 6 * q^83 + 12 * q^85 + 21 * q^87 + 6 * q^89 - 30 * q^91 - 48 * q^93 - 21 * q^95 - 57 * q^97 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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