LMFDB - Embedded newform 888.2.bo.c.625.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [888,2,Mod(49,888)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(888, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 0, 14]))

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

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

chi := DirichletCharacter("888.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 888 = 2^{3} \cdot 3 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	888.bo (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:	$7.09071569949$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			625.4
Character	$\chi$	$=$	888.625
Dual form			888.2.bo.c.601.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.173648 + 0.984808i) q^{3} +(2.85598 - 2.39645i) q^{5} +(-0.585166 + 0.491013i) q^{7} +(-0.939693 + 0.342020i) q^{9} +O(q^{10})$	\(q+(0.173648 + 0.984808i) q^{3} +(2.85598 - 2.39645i) q^{5} +(-0.585166 + 0.491013i) q^{7} +(-0.939693 + 0.342020i) q^{9} +(1.49968 - 2.59752i) q^{11} +(0.665439 + 0.242200i) q^{13} +(2.85598 + 2.39645i) q^{15} +(2.13726 - 0.777899i) q^{17} +(0.592912 + 3.36257i) q^{19} +(-0.585166 - 0.491013i) q^{21} +(-0.381940 - 0.661540i) q^{23} +(1.54540 - 8.76441i) q^{25} +(-0.500000 - 0.866025i) q^{27} +(4.38934 - 7.60256i) q^{29} -4.76785 q^{31} +(2.81847 + 1.02584i) q^{33} +(-0.494535 + 2.80465i) q^{35} +(5.04993 - 3.39091i) q^{37} +(-0.122968 + 0.697387i) q^{39} +(-4.61617 - 1.68015i) q^{41} +1.52668 q^{43} +(-1.86411 + 3.22873i) q^{45} +(5.60329 + 9.70517i) q^{47} +(-1.11421 + 6.31901i) q^{49} +(1.13721 + 1.96971i) q^{51} +(2.09133 + 1.75483i) q^{53} +(-1.94178 - 11.0124i) q^{55} +(-3.20853 + 1.16781i) q^{57} +(-2.71806 - 2.28073i) q^{59} +(0.305639 + 0.111243i) q^{61} +(0.381940 - 0.661540i) q^{63} +(2.48090 - 0.902974i) q^{65} +(3.97888 - 3.33868i) q^{67} +(0.585166 - 0.491013i) q^{69} +(1.46222 + 8.29267i) q^{71} -9.28253 q^{73} +8.89961 q^{75} +(0.397853 + 2.25634i) q^{77} +(6.79079 - 5.69815i) q^{79} +(0.766044 - 0.642788i) q^{81} +(-1.02771 + 0.374056i) q^{83} +(4.23977 - 7.34350i) q^{85} +(8.24927 + 3.00249i) q^{87} +(-0.125961 - 0.105694i) q^{89} +(-0.508315 + 0.185012i) q^{91} +(-0.827928 - 4.69541i) q^{93} +(9.75159 + 8.18256i) q^{95} +(-4.40886 - 7.63637i) q^{97} +(-0.520832 + 2.95379i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 3 q^{5} + 15 q^{7}+O(q^{10}) $ 24 * q + 3 * q^5 + 15 * q^7	$ 24 q + 3 q^{5} + 15 q^{7} + 12 q^{13} + 3 q^{15} + 3 q^{17} + 9 q^{19} + 15 q^{21} + 27 q^{25} - 12 q^{27} - 6 q^{29} - 30 q^{31} + 9 q^{33} + 15 q^{35} + 9 q^{37} + 3 q^{39} + 15 q^{41} - 54 q^{43} + 6 q^{45} - 12 q^{47} + 27 q^{49} + 18 q^{51} + 39 q^{53} - 6 q^{55} - 3 q^{59} + 12 q^{61} + 36 q^{65} + 48 q^{67} - 15 q^{69} + 33 q^{71} - 48 q^{73} + 60 q^{75} + 36 q^{77} + 18 q^{79} - 42 q^{83} + 15 q^{87} + 36 q^{89} - 36 q^{91} - 18 q^{93} + 27 q^{95} + 9 q^{97}+O(q^{100}) $ 24 * q + 3 * q^5 + 15 * q^7 + 12 * q^13 + 3 * q^15 + 3 * q^17 + 9 * q^19 + 15 * q^21 + 27 * q^25 - 12 * q^27 - 6 * q^29 - 30 * q^31 + 9 * q^33 + 15 * q^35 + 9 * q^37 + 3 * q^39 + 15 * q^41 - 54 * q^43 + 6 * q^45 - 12 * q^47 + 27 * q^49 + 18 * q^51 + 39 * q^53 - 6 * q^55 - 3 * q^59 + 12 * q^61 + 36 * q^65 + 48 * q^67 - 15 * q^69 + 33 * q^71 - 48 * q^73 + 60 * q^75 + 36 * q^77 + 18 * q^79 - 42 * q^83 + 15 * q^87 + 36 * q^89 - 36 * q^91 - 18 * q^93 + 27 * q^95 + 9 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/888\mathbb{Z}\right)^\times$.

$n$	$223$	$409$	$445$	$593$
$\chi(n)$	$1$	$e\left(\frac{5}{9}\right)$	$1$	$1$

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
$3$	0.173648	+	0.984808i	0.100256	+	0.568579i
$3$	0.173648	+	0.984808i	0.100256	+	0.568579i
$4$		0			0
$5$	2.85598	−	2.39645i	1.27723	−	1.07173i	0.283614	−	0.958938i	$-0.408466\pi$
$5$	2.85598	−	2.39645i	1.27723	−	1.07173i	0.993619	−	0.112788i	$-0.0359780\pi$
$6$		0			0
$7$	−0.585166	+	0.491013i	−0.221172	+	0.185585i	−0.746641	−	0.665228i	$-0.768334\pi$
$7$	−0.585166	+	0.491013i	−0.221172	+	0.185585i	0.525469	+	0.850813i	$0.323890\pi$
$8$		0			0
$9$	−0.939693	+	0.342020i	−0.313231	+	0.114007i
$10$		0			0
$11$	1.49968	−	2.59752i	0.452170	−	0.783181i	−0.546351	−	0.837556i	$-0.683984\pi$
$11$	1.49968	−	2.59752i	0.452170	−	0.783181i	0.998521	+	0.0543757i	$0.0173169\pi$
$12$		0			0
$13$	0.665439	+	0.242200i	0.184559	+	0.0671741i	0.432647	−	0.901564i	$-0.357580\pi$
$13$	0.665439	+	0.242200i	0.184559	+	0.0671741i	−0.248087	+	0.968738i	$0.579802\pi$
$14$		0			0
$15$	2.85598	+	2.39645i	0.737411	+	0.618761i
$16$		0			0
$17$	2.13726	−	0.777899i	0.518361	−	0.188668i	−0.0695728	−	0.997577i	$-0.522164\pi$
$17$	2.13726	−	0.777899i	0.518361	−	0.188668i	0.587934	+	0.808909i	$0.299941\pi$
$18$		0			0
$19$	0.592912	+	3.36257i	0.136023	+	0.771427i	0.974142	+	0.225938i	$0.0725448\pi$
$19$	0.592912	+	3.36257i	0.136023	+	0.771427i	−0.838118	+	0.545489i	$0.816344\pi$
$20$		0			0
$21$	−0.585166	−	0.491013i	−0.127694	−	0.107148i
$22$		0			0
$23$	−0.381940	−	0.661540i	−0.0796400	−	0.137941i	0.823455	−	0.567382i	$-0.192044\pi$
$23$	−0.381940	−	0.661540i	−0.0796400	−	0.137941i	−0.903095	+	0.429442i	$0.858710\pi$
$24$		0			0
$25$	1.54540	−	8.76441i	0.309080	−	1.75288i
$26$		0			0
$27$	−0.500000	−	0.866025i	−0.0962250	−	0.166667i
$28$		0			0
$29$	4.38934	−	7.60256i	0.815080	−	1.41176i	−0.0941897	−	0.995554i	$-0.530026\pi$
$29$	4.38934	−	7.60256i	0.815080	−	1.41176i	0.909270	−	0.416206i	$-0.136641\pi$
$30$		0			0
$31$	−4.76785			−0.856331			−0.428165	−	0.903700i	$-0.640840\pi$
$31$	−4.76785			−0.856331			−0.428165	+	0.903700i	$0.640840\pi$
$32$		0			0
$33$	2.81847	+	1.02584i	0.490633	+	0.178576i
$34$		0			0
$35$	−0.494535	+	2.80465i	−0.0835916	+	0.474072i
$36$		0			0
$37$	5.04993	−	3.39091i	0.830203	−	0.557461i
$37$	5.04993	−	3.39091i	0.830203	−	0.557461i
$38$		0			0
$39$	−0.122968	+	0.697387i	−0.0196907	+	0.111671i
$40$		0			0
$41$	−4.61617	−	1.68015i	−0.720925	−	0.262395i	−0.0446063	−	0.999005i	$-0.514203\pi$
$41$	−4.61617	−	1.68015i	−0.720925	−	0.262395i	−0.676318	+	0.736610i	$0.736426\pi$
$42$		0			0
$43$	1.52668			0.232816			0.116408	−	0.993201i	$-0.462862\pi$
$43$	1.52668			0.232816			0.116408	+	0.993201i	$0.462862\pi$
$44$		0			0
$45$	−1.86411	+	3.22873i	−0.277885	+	0.481311i
$46$		0			0
$47$	5.60329	+	9.70517i	0.817323	+	1.41565i	0.907648	+	0.419733i	$0.137876\pi$
$47$	5.60329	+	9.70517i	0.817323	+	1.41565i	−0.0903245	+	0.995912i	$0.528790\pi$
$48$		0			0
$49$	−1.11421	+	6.31901i	−0.159173	+	0.902715i
$50$		0			0
$51$	1.13721	+	1.96971i	0.159242	+	0.275814i
$52$		0			0
$53$	2.09133	+	1.75483i	0.287266	+	0.241045i	0.775021	−	0.631936i	$-0.217739\pi$
$53$	2.09133	+	1.75483i	0.287266	+	0.241045i	−0.487755	+	0.872981i	$0.662184\pi$
$54$		0			0
$55$	−1.94178	−	11.0124i	−0.261829	−	1.48491i
$56$		0			0
$57$	−3.20853	+	1.16781i	−0.424980	+	0.154680i
$58$		0			0
$59$	−2.71806	−	2.28073i	−0.353862	−	0.296925i	0.448477	−	0.893794i	$-0.351967\pi$
$59$	−2.71806	−	2.28073i	−0.353862	−	0.296925i	−0.802339	+	0.596869i	$0.796411\pi$
$60$		0			0
$61$	0.305639	+	0.111243i	0.0391330	+	0.0142433i	0.361513	−	0.932367i	$-0.382260\pi$
$61$	0.305639	+	0.111243i	0.0391330	+	0.0142433i	−0.322379	+	0.946611i	$0.604483\pi$
$62$		0			0
$63$	0.381940	−	0.661540i	0.0481199	−	0.0833462i
$64$		0			0
$65$	2.48090	−	0.902974i	0.307718	−	0.112000i
$66$		0			0
$67$	3.97888	−	3.33868i	0.486098	−	0.407884i	−0.366528	−	0.930407i	$-0.619453\pi$
$67$	3.97888	−	3.33868i	0.486098	−	0.407884i	0.852625	+	0.522523i	$0.175009\pi$
$68$		0			0
$69$	0.585166	−	0.491013i	0.0704457	−	0.0591110i
$70$		0			0
$71$	1.46222	+	8.29267i	0.173534	+	0.984159i	0.939823	+	0.341663i	$0.110990\pi$
$71$	1.46222	+	8.29267i	0.173534	+	0.984159i	−0.766289	+	0.642496i	$0.777899\pi$
$72$		0			0
$73$	−9.28253			−1.08644			−0.543219	−	0.839591i	$-0.682795\pi$
$73$	−9.28253			−1.08644			−0.543219	+	0.839591i	$0.682795\pi$
$74$		0			0
$75$	8.89961			1.02764
$76$		0			0
$77$	0.397853	+	2.25634i	0.0453396	+	0.257134i
$78$		0			0
$79$	6.79079	−	5.69815i	0.764023	−	0.641091i	−0.175148	−	0.984542i	$-0.556040\pi$
$79$	6.79079	−	5.69815i	0.764023	−	0.641091i	0.939171	+	0.343451i	$0.111596\pi$
$80$		0			0
$81$	0.766044	−	0.642788i	0.0851160	−	0.0714208i
$82$		0			0
$83$	−1.02771	+	0.374056i	−0.112806	+	0.0410580i	−0.397806	−	0.917469i	$-0.630228\pi$
$83$	−1.02771	+	0.374056i	−0.112806	+	0.0410580i	0.285001	+	0.958527i	$0.408006\pi$
$84$		0			0
$85$	4.23977	−	7.34350i	0.459868	−	0.796515i
$86$		0			0
$87$	8.24927	+	3.00249i	0.884414	+	0.321900i
$88$		0			0
$89$	−0.125961	−	0.105694i	−0.0133519	−	0.0112036i	0.636087	−	0.771617i	$-0.280552\pi$
$89$	−0.125961	−	0.105694i	−0.0133519	−	0.0112036i	−0.649439	+	0.760414i	$0.724996\pi$
$90$		0			0
$91$	−0.508315	+	0.185012i	−0.0532859	+	0.0193945i
$92$		0			0
$93$	−0.827928	−	4.69541i	−0.0858522	−	0.486892i
$94$		0			0
$95$	9.75159	+	8.18256i	1.00049	+	0.839513i
$96$		0			0
$97$	−4.40886	−	7.63637i	−0.447652	−	0.775355i	0.550581	−	0.834782i	$-0.314406\pi$
$97$	−4.40886	−	7.63637i	−0.447652	−	0.775355i	−0.998233	+	0.0594263i	$0.981073\pi$
$98$		0			0
$99$	−0.520832	+	2.95379i	−0.0523456	+	0.296867i
$100$		0			0
$101$	9.05085	+	15.6765i	0.900593	+	1.55987i	0.826726	+	0.562604i	$0.190201\pi$
$101$	9.05085	+	15.6765i	0.900593	+	1.55987i	0.0738664	+	0.997268i	$0.476466\pi$
$102$		0			0
$103$	−0.906253	+	1.56968i	−0.0892957	+	0.154665i	−0.907214	−	0.420670i	$-0.861795\pi$
$103$	−0.906253	+	1.56968i	−0.0892957	+	0.154665i	0.817918	+	0.575335i	$0.195128\pi$
$104$		0			0
$105$	−2.84791			−0.277928
$106$		0			0
$107$	4.19247	+	1.52594i	0.405302	+	0.147518i	0.536623	−	0.843822i	$-0.319700\pi$
$107$	4.19247	+	1.52594i	0.405302	+	0.147518i	−0.131321	+	0.991340i	$0.541922\pi$
$108$		0			0
$109$	−0.549855	+	3.11838i	−0.0526666	+	0.298687i	−0.999751	−	0.0222964i	$-0.992902\pi$
$109$	−0.549855	+	3.11838i	−0.0526666	+	0.298687i	0.947085	+	0.320983i	$0.104013\pi$
$110$		0			0
$111$	4.21630	+	4.38438i	0.400194	+	0.416147i
$112$		0			0
$113$	−2.35688	+	13.3666i	−0.221717	+	1.25742i	0.647146	+	0.762366i	$0.275963\pi$
$113$	−2.35688	+	13.3666i	−0.221717	+	1.25742i	−0.868863	+	0.495053i	$0.835149\pi$
$114$		0			0
$115$	−2.67616	−	0.974043i	−0.249553	−	0.0908300i
$116$		0			0
$117$	−0.708145			−0.0654680
$118$		0			0
$119$	−0.868694	+	1.50462i	−0.0796330	+	0.137928i
$120$		0			0
$121$	1.00194	+	1.73541i	0.0910854	+	0.157765i
$122$		0			0
$123$	0.853034	−	4.83779i	0.0769155	−	0.436209i
$124$		0			0
$125$	−7.26931	−	12.5908i	−0.650187	−	1.12616i
$126$		0			0
$127$	−9.79685	−	8.22053i	−0.869330	−	0.729454i	0.0946273	−	0.995513i	$-0.469834\pi$
$127$	−9.79685	−	8.22053i	−0.869330	−	0.729454i	−0.963957	+	0.266059i	$0.914279\pi$
$128$		0			0
$129$	0.265105	+	1.50348i	0.0233412	+	0.132374i
$130$		0			0
$131$	−17.3547	+	6.31660i	−1.51629	+	0.551884i	−0.960218	−	0.279252i	$-0.909913\pi$
$131$	−17.3547	+	6.31660i	−1.51629	+	0.551884i	−0.556070	+	0.831136i	$0.687691\pi$
$132$		0			0
$133$	−1.99802	−	1.67654i	−0.173250	−	0.145374i
$134$		0			0
$135$	−3.50338	−	1.27513i	−0.301523	−	0.109745i
$136$		0			0
$137$	8.18469	−	14.1763i	0.699266	−	1.21116i	−0.269456	−	0.963013i	$-0.586844\pi$
$137$	8.18469	−	14.1763i	0.699266	−	1.21116i	0.968721	−	0.248151i	$-0.0798229\pi$
$138$		0			0
$139$	2.87169	−	1.04521i	0.243574	−	0.0886537i	−0.217349	−	0.976094i	$-0.569741\pi$
$139$	2.87169	−	1.04521i	0.243574	−	0.0886537i	0.460922	+	0.887440i	$0.347519\pi$
$140$		0			0
$141$	−8.58473	+	7.20344i	−0.722965	+	0.606639i
$142$		0			0
$143$	1.62706	−	1.36527i	0.136062	−	0.114169i
$144$		0			0
$145$	−5.68331	−	32.2316i	−0.471973	−	2.67669i
$146$		0			0
$147$	−6.41649			−0.529223
$148$		0			0
$149$	−7.99238			−0.654761			−0.327380	−	0.944893i	$-0.606166\pi$
$149$	−7.99238			−0.654761			−0.327380	+	0.944893i	$0.606166\pi$
$150$		0			0
$151$	2.97374	+	16.8649i	0.242000	+	1.37245i	0.827359	+	0.561674i	$0.189842\pi$
$151$	2.97374	+	16.8649i	0.242000	+	1.37245i	−0.585359	+	0.810774i	$0.699046\pi$
$152$		0			0
$153$	−1.74231	+	1.46197i	−0.140857	+	0.118193i
$154$		0			0
$155$	−13.6169	+	11.4259i	−1.09373	+	0.917752i
$156$		0			0
$157$	−15.1814	+	5.52559i	−1.21161	+	0.440990i	−0.867262	−	0.497852i	$-0.834122\pi$
$157$	−15.1814	+	5.52559i	−1.21161	+	0.440990i	−0.344348	+	0.938842i	$0.611900\pi$
$158$		0			0
$159$	−1.36502	+	2.36428i	−0.108253	+	0.187500i
$160$		0			0
$161$	0.548323	+	0.199573i	0.0432139	+	0.0157286i
$162$		0			0
$163$	−8.23541	−	6.91033i	−0.645047	−	0.541259i	0.260516	−	0.965469i	$-0.416107\pi$
$163$	−8.23541	−	6.91033i	−0.645047	−	0.541259i	−0.905564	+	0.424210i	$0.860552\pi$
$164$		0			0
$165$	10.5079	−	3.82455i	0.818037	−	0.297741i
$166$		0			0
$167$	0.554040	+	3.14212i	0.0428729	+	0.243145i	0.998712	−	0.0507477i	$-0.0161604\pi$
$167$	0.554040	+	3.14212i	0.0428729	+	0.243145i	−0.955839	+	0.293892i	$0.905049\pi$
$168$		0			0
$169$	−9.57443	−	8.03390i	−0.736495	−	0.617992i
$170$		0			0
$171$	−1.70722	−	2.95700i	−0.130555	−	0.226127i
$172$		0			0
$173$	−2.22603	+	12.6245i	−0.169242	+	0.959820i	0.775340	+	0.631544i	$0.217579\pi$
$173$	−2.22603	+	12.6245i	−0.169242	+	0.959820i	−0.944582	+	0.328276i	$0.893532\pi$
$174$		0			0
$175$	3.39912	+	5.88745i	0.256949	+	0.445049i
$176$		0			0
$177$	1.77409	−	3.07281i	0.133349	−	0.230967i
$178$		0			0
$179$	−18.1558			−1.35703			−0.678515	−	0.734587i	$-0.737376\pi$
$179$	−18.1558			−1.35703			−0.678515	+	0.734587i	$0.737376\pi$
$180$		0			0
$181$	−7.05470	−	2.56770i	−0.524372	−	0.190856i	0.0662516	−	0.997803i	$-0.478896\pi$
$181$	−7.05470	−	2.56770i	−0.524372	−	0.190856i	−0.590624	+	0.806947i	$0.701118\pi$
$182$		0			0
$183$	−0.0564798	+	0.320313i	−0.00417511	+	0.0236782i
$184$		0			0
$185$	6.29635	−	21.7863i	0.462917	−	1.60176i
$186$		0			0
$187$	1.18459	−	6.71816i	0.0866260	−	0.491281i
$188$		0			0
$189$	0.717813	+	0.261262i	0.0522132	+	0.0190040i
$190$		0			0
$191$	−19.3334			−1.39892			−0.699458	−	0.714674i	$-0.746575\pi$
$191$	−19.3334			−1.39892			−0.699458	+	0.714674i	$0.746575\pi$
$192$		0			0
$193$	1.56615	−	2.71266i	0.112734	−	0.195261i	−0.804138	−	0.594443i	$-0.797372\pi$
$193$	1.56615	−	2.71266i	0.112734	−	0.195261i	0.916872	+	0.399182i	$0.130706\pi$
$194$		0			0
$195$	1.32006	+	2.28641i	0.0945314	+	0.163733i
$196$		0			0
$197$	−0.374905	+	2.12619i	−0.0267109	+	0.151485i	−0.995246	−	0.0973913i	$-0.968950\pi$
$197$	−0.374905	+	2.12619i	−0.0267109	+	0.151485i	0.968535	+	0.248876i	$0.0800613\pi$
$198$		0			0
$199$	−12.4258	−	21.5221i	−0.880840	−	1.52566i	−0.850409	−	0.526122i	$-0.823645\pi$
$199$	−12.4258	−	21.5221i	−0.880840	−	1.52566i	−0.0304309	−	0.999537i	$-0.509688\pi$
$200$		0			0
$201$	3.97888	+	3.33868i	0.280649	+	0.235492i
$202$		0			0
$203$	1.16446	+	6.60399i	0.0817291	+	0.463509i
$204$		0			0
$205$	−17.2101	+	6.26396i	−1.20200	+	0.437494i
$206$		0			0
$207$	0.585166	+	0.491013i	0.0406719	+	0.0341277i
$208$		0			0
$209$	9.62351	+	3.50267i	0.665672	+	0.242285i
$210$		0			0
$211$	−9.75574	+	16.8974i	−0.671613	+	1.16327i	0.305834	+	0.952085i	$0.401065\pi$
$211$	−9.75574	+	16.8974i	−0.671613	+	1.16327i	−0.977447	+	0.211182i	$0.932269\pi$
$212$		0			0
$213$	−7.91277	+	2.88001i	−0.542174	+	0.197335i
$214$		0			0
$215$	4.36016	−	3.65861i	0.297361	−	0.249515i
$216$		0			0
$217$	2.78998	−	2.34107i	0.189396	−	0.158922i
$218$		0			0
$219$	−1.61189	−	9.14151i	−0.108922	−	0.617726i
$220$		0			0
$221$	1.61062			0.108342
$222$		0			0
$223$	2.00165			0.134040			0.0670201	−	0.997752i	$-0.478651\pi$
$223$	2.00165			0.134040			0.0670201	+	0.997752i	$0.478651\pi$
$224$		0			0
$225$	1.54540	+	8.76441i	0.103027	+	0.584294i
$226$		0			0
$227$	−17.9784	+	15.0856i	−1.19327	+	1.00127i	−0.193470	+	0.981106i	$0.561974\pi$
$227$	−17.9784	+	15.0856i	−1.19327	+	1.00127i	−0.999797	+	0.0201630i	$0.993581\pi$
$228$		0			0
$229$	−20.5538	+	17.2467i	−1.35823	+	1.13969i	−0.381708	+	0.924283i	$0.624664\pi$
$229$	−20.5538	+	17.2467i	−1.35823	+	1.13969i	−0.976524	+	0.215409i	$0.930892\pi$
$230$		0			0
$231$	−2.15297	+	0.783618i	−0.141655	+	0.0515583i
$232$		0			0
$233$	1.76831	−	3.06281i	0.115846	−	0.200651i	−0.802272	−	0.596959i	$-0.796375\pi$
$233$	1.76831	−	3.06281i	0.115846	−	0.200651i	0.918118	+	0.396308i	$0.129709\pi$
$234$		0			0
$235$	39.2609	+	14.2898i	2.56110	+	0.932163i
$236$		0			0
$237$	6.79079	+	5.69815i	0.441109	+	0.370134i
$238$		0			0
$239$	22.6083	−	8.22874i	1.46241	−	0.532273i	0.516381	−	0.856359i	$-0.327279\pi$
$239$	22.6083	−	8.22874i	1.46241	−	0.532273i	0.946028	+	0.324086i	$0.105057\pi$
$240$		0			0
$241$	1.49091	+	8.45535i	0.0960377	+	0.544657i	0.994424	+	0.105451i	$0.0336288\pi$
$241$	1.49091	+	8.45535i	0.0960377	+	0.544657i	−0.898387	+	0.439205i	$0.855260\pi$
$242$		0			0
$243$	0.766044	+	0.642788i	0.0491418	+	0.0412348i
$244$		0			0
$245$	11.9610	+	20.7171i	0.764162	+	1.32357i
$246$		0			0
$247$	−0.419868	+	2.38119i	−0.0267155	+	0.151511i
$248$		0			0
$249$	−0.546833	−	0.947143i	−0.0346541	−	0.0600227i
$250$		0			0
$251$	8.96326	−	15.5248i	0.565756	−	0.979918i	−0.431223	−	0.902245i	$-0.641918\pi$
$251$	8.96326	−	15.5248i	0.565756	−	0.979918i	0.996979	−	0.0776725i	$-0.0247489\pi$
$252$		0			0
$253$	−2.29115			−0.144043
$254$		0			0
$255$	7.96817	+	2.90018i	0.498986	+	0.181616i
$256$		0			0
$257$	3.90197	−	22.1292i	0.243398	−	1.38038i	−0.580786	−	0.814057i	$-0.697255\pi$
$257$	3.90197	−	22.1292i	0.243398	−	1.38038i	0.824184	−	0.566323i	$-0.191634\pi$
$258$		0			0
$259$	−1.29007	+	4.46382i	−0.0801610	+	0.277368i
$260$		0			0
$261$	−1.52440	+	8.64532i	−0.0943582	+	0.535132i
$262$		0			0
$263$	−17.6717	−	6.43198i	−1.08969	−	0.396613i	−0.266181	−	0.963923i	$-0.585762\pi$
$263$	−17.6717	−	6.43198i	−1.08969	−	0.396613i	−0.823504	+	0.567310i	$0.807984\pi$
$264$		0			0
$265$	10.1782			0.625240
$266$		0			0
$267$	0.0822155	−	0.142401i	0.00503151	−	0.00871482i
$268$		0			0
$269$	7.11607	+	12.3254i	0.433875	+	0.751493i	0.997203	−	0.0747403i	$-0.0238128\pi$
$269$	7.11607	+	12.3254i	0.433875	+	0.751493i	−0.563329	+	0.826233i	$0.690479\pi$
$270$		0			0
$271$	−0.659909	+	3.74253i	−0.0400866	+	0.227343i	−0.998269	−	0.0588163i	$-0.981267\pi$
$271$	−0.659909	+	3.74253i	−0.0400866	+	0.227343i	0.958182	+	0.286159i	$0.0923785\pi$
$272$		0			0
$273$	−0.270469	−	0.468466i	−0.0163695	−	0.0283529i
$274$		0			0
$275$	−20.4481	−	17.1580i	−1.23307	−	1.03467i
$276$		0			0
$277$	4.64697	+	26.3543i	0.279209	+	1.58347i	0.725265	+	0.688470i	$0.241717\pi$
$277$	4.64697	+	26.3543i	0.279209	+	1.58347i	−0.446056	+	0.895005i	$0.647172\pi$
$278$		0			0
$279$	4.48031	−	1.63070i	0.268229	−	0.0976275i
$280$		0			0
$281$	10.2170	+	8.57305i	0.609493	+	0.511426i	0.894481	−	0.447106i	$-0.147545\pi$
$281$	10.2170	+	8.57305i	0.609493	+	0.511426i	−0.284988	+	0.958531i	$0.591990\pi$
$282$		0			0
$283$	27.5810	+	10.0387i	1.63952	+	0.596737i	0.986955	−	0.160995i	$-0.0514703\pi$
$283$	27.5810	+	10.0387i	1.63952	+	0.596737i	0.652566	+	0.757732i	$0.273693\pi$
$284$		0			0
$285$	−6.36490	+	11.0243i	−0.377024	+	0.653025i
$286$		0			0
$287$	3.52620	−	1.28343i	0.208145	−	0.0757586i
$288$		0			0
$289$	−9.06001	+	7.60225i	−0.532942	+	0.447191i
$290$		0			0
$291$	6.75476	−	5.66792i	0.395971	−	0.332259i
$292$		0			0
$293$	−3.88949	−	22.0584i	−0.227226	−	1.28866i	−0.858383	−	0.513009i	$-0.828531\pi$
$293$	−3.88949	−	22.0584i	−0.227226	−	1.28866i	0.631157	−	0.775655i	$-0.282580\pi$
$294$		0			0
$295$	−13.2284			−0.770187
$296$		0			0
$297$	−2.99935			−0.174040
$298$		0			0
$299$	−0.0939329	−	0.532720i	−0.00543228	−	0.0308080i
$300$		0			0
$301$	−0.893360	+	0.749618i	−0.0514924	+	0.0432073i
$302$		0			0
$303$	−13.8667	+	11.6355i	−0.796621	+	0.668444i
$304$		0			0
$305$	1.13949	−	0.414740i	0.0652469	−	0.0237479i
$306$		0			0
$307$	7.46672	−	12.9327i	0.426148	−	0.738110i	−0.570379	−	0.821382i	$-0.693204\pi$
$307$	7.46672	−	12.9327i	0.426148	−	0.738110i	0.996527	+	0.0832715i	$0.0265369\pi$
$308$		0			0
$309$	−1.70320	−	0.619913i	−0.0968916	−	0.0352656i
$310$		0			0
$311$	2.04270	+	1.71403i	0.115831	+	0.0971936i	0.698863	−	0.715255i	$-0.253690\pi$
$311$	2.04270	+	1.71403i	0.115831	+	0.0971936i	−0.583033	+	0.812449i	$0.698134\pi$
$312$		0			0
$313$	−1.16799	+	0.425112i	−0.0660185	+	0.0240288i	−0.374818	−	0.927098i	$-0.622295\pi$
$313$	−1.16799	+	0.425112i	−0.0660185	+	0.0240288i	0.308800	+	0.951127i	$0.400073\pi$
$314$		0			0
$315$	−0.494535	−	2.80465i	−0.0278639	−	0.158024i
$316$		0			0
$317$	24.4484	+	20.5146i	1.37316	+	1.15222i	0.971667	+	0.236353i	$0.0759520\pi$
$317$	24.4484	+	20.5146i	1.37316	+	1.15222i	0.401490	+	0.915863i	$0.368492\pi$
$318$		0			0
$319$	−13.1652	−	22.8028i	−0.737109	−	1.27671i
$320$		0			0
$321$	−0.774738	+	4.39376i	−0.0432416	+	0.245236i
$322$		0			0
$323$	3.88295	+	6.72546i	0.216053	+	0.374215i
$324$		0			0
$325$	3.15111	−	5.45788i	0.174792	−	0.302749i
$326$		0			0
$327$	−3.16649			−0.175107
$328$		0			0
$329$	−8.04422	−	2.92786i	−0.443492	−	0.161418i
$330$		0			0
$331$	4.28280	−	24.2890i	0.235404	−	1.33504i	−0.606358	−	0.795192i	$-0.707370\pi$
$331$	4.28280	−	24.2890i	0.235404	−	1.33504i	0.841761	−	0.539850i	$-0.181519\pi$
$332$		0			0
$333$	−3.58562	+	4.91359i	−0.196491	+	0.269263i
$334$		0			0
$335$	3.36263	−	19.0704i	0.183720	−	1.04193i
$336$		0			0
$337$	3.93026	+	1.43050i	0.214095	+	0.0779241i	0.446841	−	0.894613i	$-0.352549\pi$
$337$	3.93026	+	1.43050i	0.214095	+	0.0779241i	−0.232746	+	0.972537i	$0.574771\pi$
$338$		0			0
$339$	−13.5728			−0.737171
$340$		0			0
$341$	−7.15023	+	12.3846i	−0.387207	+	0.670662i
$342$		0			0
$343$	−5.12429	−	8.87554i	−0.276686	−	0.479234i
$344$		0			0
$345$	0.494535	−	2.80465i	0.0266249	−	0.150997i
$346$		0			0
$347$	−17.5188	−	30.3435i	−0.940460	−	1.62892i	−0.764596	−	0.644510i	$-0.777061\pi$
$347$	−17.5188	−	30.3435i	−0.940460	−	1.62892i	−0.175865	−	0.984414i	$-0.556272\pi$
$348$		0			0
$349$	−6.63920	−	5.57095i	−0.355388	−	0.298206i	0.447561	−	0.894253i	$-0.352293\pi$
$349$	−6.63920	−	5.57095i	−0.355388	−	0.298206i	−0.802949	+	0.596047i	$0.796737\pi$
$350$		0			0
$351$	−0.122968	−	0.697387i	−0.00656355	−	0.0372237i
$352$		0			0
$353$	32.4695	−	11.8179i	1.72818	−	0.629005i	0.729678	−	0.683791i	$-0.239670\pi$
$353$	32.4695	−	11.8179i	1.72818	−	0.629005i	0.998498	+	0.0547863i	$0.0174478\pi$
$354$		0			0
$355$	24.0491	+	20.1796i	1.27639	+	1.07102i
$356$		0			0
$357$	−1.63261	−	0.594221i	−0.0864069	−	0.0314495i
$358$		0			0
$359$	−9.99659	+	17.3146i	−0.527600	+	0.913829i	0.471883	+	0.881661i	$0.343575\pi$
$359$	−9.99659	+	17.3146i	−0.527600	+	0.913829i	−0.999482	+	0.0321681i	$0.989759\pi$
$360$		0			0
$361$	6.89881	−	2.51096i	0.363095	−	0.132156i
$362$		0			0
$363$	−1.53506	+	1.28807i	−0.0805698	+	0.0676061i
$364$		0			0
$365$	−26.5107	+	22.2451i	−1.38763	+	1.16436i
$366$		0			0
$367$	0.159093	+	0.902263i	0.00830461	+	0.0470978i	0.988678	−	0.150050i	$-0.0479434\pi$
$367$	0.159093	+	0.902263i	0.00830461	+	0.0470978i	−0.980374	+	0.197147i	$0.936832\pi$
$368$		0			0
$369$	4.91242			0.255731
$370$		0			0
$371$	−2.08542			−0.108270
$372$		0			0
$373$	2.93440	+	16.6418i	0.151937	+	0.861680i	0.961532	+	0.274691i	$0.0885756\pi$
$373$	2.93440	+	16.6418i	0.151937	+	0.861680i	−0.809595	+	0.586989i	$0.800313\pi$
$374$		0			0
$375$	11.1372	−	9.34524i	0.575124	−	0.482586i
$376$		0			0
$377$	4.76218	−	3.99594i	0.245265	−	0.205801i
$378$		0			0
$379$	−7.40320	+	2.69455i	−0.380277	+	0.138410i	−0.525084	−	0.851050i	$-0.675966\pi$
$379$	−7.40320	+	2.69455i	−0.380277	+	0.138410i	0.144807	+	0.989460i	$0.453744\pi$
$380$		0			0
$381$	6.39444	−	11.0755i	0.327597	−	0.567415i
$382$		0			0
$383$	2.20827	+	0.803745i	0.112837	+	0.0410694i	0.397822	−	0.917463i	$-0.369766\pi$
$383$	2.20827	+	0.803745i	0.112837	+	0.0410694i	−0.284984	+	0.958532i	$0.591988\pi$
$384$		0			0
$385$	6.54347	+	5.49062i	0.333486	+	0.279828i
$386$		0			0
$387$	−1.43461	+	0.522155i	−0.0729252	+	0.0265426i
$388$		0			0
$389$	1.24312	+	7.05007i	0.0630286	+	0.357453i	0.999968	+	0.00796177i	$0.00253434\pi$
$389$	1.24312	+	7.05007i	0.0630286	+	0.357453i	−0.936940	+	0.349491i	$0.886355\pi$
$390$		0			0
$391$	−1.33092	−	1.11677i	−0.0673073	−	0.0564775i
$392$		0			0
$393$	−9.23425	−	15.9942i	−0.465806	−	0.806800i
$394$		0			0
$395$	5.73902	−	32.5476i	0.288761	−	1.63765i
$396$		0			0
$397$	−7.58725	−	13.1415i	−0.380793	−	0.659553i	0.610383	−	0.792107i	$-0.291016\pi$
$397$	−7.58725	−	13.1415i	−0.380793	−	0.659553i	−0.991176	+	0.132554i	$0.957682\pi$
$398$		0			0
$399$	1.30411	−	2.25879i	0.0652873	−	0.113081i
$400$		0			0
$401$	−9.32332			−0.465584			−0.232792	−	0.972527i	$-0.574786\pi$
$401$	−9.32332			−0.465584			−0.232792	+	0.972527i	$0.574786\pi$
$402$		0			0
$403$	−3.17271	−	1.15477i	−0.158044	−	0.0575233i
$404$		0			0
$405$	0.647398	−	3.67158i	0.0321695	−	0.182442i
$406$		0			0
$407$	−1.23468	−	18.2025i	−0.0612006	−	0.902266i
$408$		0			0
$409$	−4.79905	+	27.2167i	−0.237298	+	1.34578i	0.600423	+	0.799682i	$0.294999\pi$
$409$	−4.79905	+	27.2167i	−0.237298	+	1.34578i	−0.837721	+	0.546099i	$0.816112\pi$
$410$		0			0
$411$	15.3822	+	5.59866i	0.758748	+	0.276162i
$412$		0			0
$413$	2.71038			0.133369
$414$		0			0
$415$	−2.03871	+	3.53116i	−0.100077	+	0.173338i
$416$		0			0
$417$	1.52800	+	2.64657i	0.0748263	+	0.129603i
$418$		0			0
$419$	0.840202	−	4.76502i	0.0410465	−	0.232787i	−0.957382	−	0.288824i	$-0.906736\pi$
$419$	0.840202	−	4.76502i	0.0410465	−	0.232787i	0.998429	+	0.0560378i	$0.0178467\pi$
$420$		0			0
$421$	13.4999	+	23.3825i	0.657944	+	1.13959i	0.981147	+	0.193263i	$0.0619072\pi$
$421$	13.4999	+	23.3825i	0.657944	+	1.13959i	−0.323203	+	0.946330i	$0.604760\pi$
$422$		0			0
$423$	−8.58473	−	7.20344i	−0.417404	−	0.350243i
$424$		0			0
$425$	−3.51490	−	19.9340i	−0.170498	−	0.966940i
$426$		0			0
$427$	−0.233471	+	0.0849767i	−0.0112985	+	0.00411231i
$428$		0			0
$429$	1.62706	+	1.36527i	0.0785552	+	0.0659157i
$430$		0			0
$431$	22.1316	+	8.05525i	1.06604	+	0.388008i	0.814695	−	0.579889i	$-0.196904\pi$
$431$	22.1316	+	8.05525i	1.06604	+	0.388008i	0.251347	+	0.967897i	$0.419126\pi$
$432$		0			0
$433$	11.4407	−	19.8159i	0.549806	−	0.952292i	−0.448482	−	0.893792i	$-0.648035\pi$
$433$	11.4407	−	19.8159i	0.549806	−	0.952292i	0.998287	−	0.0584996i	$-0.0186316\pi$
$434$		0			0
$435$	30.7551	−	11.1939i	1.47459	−	0.536708i
$436$		0			0
$437$	1.99802	−	1.67654i	0.0955782	−	0.0801996i
$438$		0			0
$439$	10.8385	−	9.09458i	0.517293	−	0.434061i	−0.346394	−	0.938089i	$-0.612594\pi$
$439$	10.8385	−	9.09458i	0.517293	−	0.434061i	0.863687	+	0.504029i	$0.168149\pi$
$440$		0			0
$441$	−1.11421	−	6.31901i	−0.0530577	−	0.300905i
$442$		0			0
$443$	−1.36923			−0.0650539			−0.0325270	−	0.999471i	$-0.510355\pi$
$443$	−1.36923			−0.0650539			−0.0325270	+	0.999471i	$0.510355\pi$
$444$		0			0
$445$	−0.613035			−0.0290606
$446$		0			0
$447$	−1.38786	−	7.87095i	−0.0656436	−	0.372283i
$448$		0			0
$449$	4.86123	−	4.07905i	0.229415	−	0.192502i	−0.520833	−	0.853659i	$-0.674378\pi$
$449$	4.86123	−	4.07905i	0.229415	−	0.192502i	0.750248	+	0.661156i	$0.229934\pi$
$450$		0			0
$451$	−11.2870	+	9.47090i	−0.531483	+	0.445967i
$452$		0			0
$453$	−16.0923	+	5.85713i	−0.756083	+	0.275192i
$454$		0			0
$455$	−1.00837	+	1.74654i	−0.0472730	+	0.0818792i
$456$		0			0
$457$	9.97593	+	3.63094i	0.466655	+	0.169848i	0.564636	−	0.825340i	$-0.309016\pi$
$457$	9.97593	+	3.63094i	0.466655	+	0.169848i	−0.0979818	+	0.995188i	$0.531239\pi$
$458$		0			0
$459$	−1.74231	−	1.46197i	−0.0813240	−	0.0682390i
$460$		0			0
$461$	39.4060	−	14.3426i	1.83532	−	0.668002i	0.844034	−	0.536290i	$-0.180175\pi$
$461$	39.4060	−	14.3426i	1.83532	−	0.668002i	0.991288	−	0.131712i	$-0.0420475\pi$
$462$		0			0
$463$	−2.56861	−	14.5673i	−0.119373	−	0.676999i	−0.984492	−	0.175431i	$-0.943868\pi$
$463$	−2.56861	−	14.5673i	−0.119373	−	0.676999i	0.865118	−	0.501568i	$-0.167243\pi$
$464$		0			0
$465$	−13.6169	−	11.4259i	−0.631468	−	0.529865i
$466$		0			0
$467$	4.96688	+	8.60288i	0.229840	+	0.398094i	0.957760	−	0.287567i	$-0.0928465\pi$
$467$	4.96688	+	8.60288i	0.229840	+	0.398094i	−0.727921	+	0.685661i	$0.759513\pi$
$468$		0			0
$469$	−0.688974	+	3.90736i	−0.0318138	+	0.180425i
$470$		0			0
$471$	−8.07787	−	13.9913i	−0.372208	−	0.644684i
$472$		0			0
$473$	2.28952	−	3.96557i	0.105272	−	0.182337i
$474$		0			0
$475$	30.3872			1.39426
$476$		0			0
$477$	−2.56539	−	0.933727i	−0.117461	−	0.0427524i
$478$		0			0
$479$	−4.59002	+	26.0313i	−0.209723	+	1.18940i	0.680108	+	0.733112i	$0.261933\pi$
$479$	−4.59002	+	26.0313i	−0.209723	+	1.18940i	−0.889832	+	0.456289i	$0.849178\pi$
$480$		0			0
$481$	4.18169	−	1.03335i	0.190669	−	0.0471166i
$482$		0			0
$483$	−0.101326	+	0.574648i	−0.00461049	+	0.0261474i
$484$		0			0
$485$	−30.8918	−	11.2437i	−1.40272	−	0.510550i
$486$		0			0
$487$	−17.1652			−0.777831			−0.388916	−	0.921273i	$-0.627150\pi$
$487$	−17.1652			−0.777831			−0.388916	+	0.921273i	$0.627150\pi$
$488$		0			0
$489$	5.37528	−	9.31027i	0.243079	−	0.421025i
$490$		0			0
$491$	−6.60661	−	11.4430i	−0.298152	−	0.516414i	0.677561	−	0.735466i	$-0.263037\pi$
$491$	−6.60661	−	11.4430i	−0.298152	−	0.516414i	−0.975713	+	0.219052i	$0.929704\pi$
$492$		0			0
$493$	3.46714	−	19.6631i	0.156152	−	0.885582i
$494$		0			0
$495$	5.59112	+	9.68411i	0.251302	+	0.435268i
$496$		0			0
$497$	−4.92745	−	4.13462i	−0.221026	−	0.185463i
$498$		0			0
$499$	−0.823590	−	4.67081i	−0.0368689	−	0.209094i	0.960808	−	0.277214i	$-0.0894111\pi$
$499$	−0.823590	−	4.67081i	−0.0368689	−	0.209094i	−0.997677	+	0.0681198i	$0.978300\pi$
$500$		0			0
$501$	−2.99818	+	1.09125i	−0.133949	+	0.0487533i
$502$		0			0
$503$	22.8884	+	19.2056i	1.02054	+	0.856337i	0.989696	−	0.143187i	$-0.0457351\pi$
$503$	22.8884	+	19.2056i	1.02054	+	0.856337i	0.0308470	+	0.999524i	$0.490180\pi$
$504$		0			0
$505$	63.4171	+	23.0819i	2.82202	+	1.02713i
$506$		0			0
$507$	6.24927	−	10.8240i	0.277540	−	0.480713i
$508$		0			0
$509$	−20.4994	+	7.46116i	−0.908618	+	0.330710i	−0.753701	−	0.657217i	$-0.771733\pi$
$509$	−20.4994	+	7.46116i	−0.908618	+	0.330710i	−0.154917	+	0.987927i	$0.549511\pi$
$510$		0			0
$511$	5.43182	−	4.55784i	0.240290	−	0.201627i
$512$		0			0
$513$	2.61562	−	2.19476i	0.115482	−	0.0969012i
$514$		0			0
$515$	1.17341	+	6.65476i	0.0517068	+	0.293244i
$516$		0			0
$517$	33.6125			1.47827
$518$		0			0
$519$	−12.8192			−0.562701
$520$		0			0
$521$	6.24343	+	35.4083i	0.273530	+	1.55126i	0.743594	+	0.668632i	$0.233120\pi$
$521$	6.24343	+	35.4083i	0.273530	+	1.55126i	−0.470064	+	0.882632i	$0.655769\pi$
$522$		0			0
$523$	−4.06882	+	3.41415i	−0.177917	+	0.149290i	−0.727397	−	0.686216i	$-0.759270\pi$
$523$	−4.06882	+	3.41415i	−0.177917	+	0.149290i	0.549480	+	0.835507i	$0.314826\pi$
$524$		0			0
$525$	−5.20775	+	4.36982i	−0.227285	+	0.190715i
$526$		0			0
$527$	−10.1901	+	3.70890i	−0.443889	+	0.161562i
$528$		0			0
$529$	11.2082	−	19.4132i	0.487315	−	0.844054i
$530$		0			0
$531$	3.33420	+	1.21355i	0.144692	+	0.0526636i
$532$		0			0
$533$	−2.66485	−	2.23607i	−0.115427	−	0.0968550i
$534$		0			0
$535$	15.6305	−	5.68902i	0.675764	−	0.245958i
$536$		0			0
$537$	−3.15272	−	17.8800i	−0.136050	−	0.771579i
$538$		0			0
$539$	14.7428	+	12.3706i	0.635016	+	0.532842i
$540$		0			0
$541$	9.97603	+	17.2790i	0.428903	+	0.742882i	0.996776	−	0.0802343i	$-0.0255669\pi$
$541$	9.97603	+	17.2790i	0.428903	+	0.742882i	−0.567873	+	0.823116i	$0.692234\pi$
$542$		0			0
$543$	1.30366	−	7.39340i	0.0559453	−	0.317281i
$544$		0			0
$545$	5.90268	+	10.2237i	0.252843	+	0.437937i
$546$		0			0
$547$	4.42616	−	7.66634i	0.189249	−	0.327789i	−0.755751	−	0.654859i	$-0.772728\pi$
$547$	4.42616	−	7.66634i	0.189249	−	0.327789i	0.945000	+	0.327070i	$0.106061\pi$
$548$		0			0
$549$	−0.325254			−0.0138815
$550$		0			0
$551$	28.1667	+	10.2518i	1.19994	+	0.436743i
$552$		0			0
$553$	−1.17588	+	6.66872i	−0.0500033	+	0.283583i
$554$		0			0
$555$	22.5486	+	2.41755i	0.957136	+	0.102619i
$556$		0			0
$557$	1.39239	−	7.89661i	0.0589973	−	0.334590i	−0.940995	−	0.338419i	$-0.890108\pi$
$557$	1.39239	−	7.89661i	0.0589973	−	0.334590i	0.999993	+	0.00382916i	$0.00121886\pi$
$558$		0			0
$559$	1.01591	+	0.369761i	0.0429684	+	0.0156392i
$560$		0			0
$561$	6.82180			0.288017
$562$		0			0
$563$	−14.6161	+	25.3158i	−0.615994	+	1.06693i	0.374215	+	0.927342i	$0.377912\pi$
$563$	−14.6161	+	25.3158i	−0.615994	+	1.06693i	−0.990209	+	0.139591i	$0.955421\pi$
$564$		0			0
$565$	25.3011	+	43.8228i	1.06443	+	1.84364i
$566$		0			0
$567$	−0.132646	+	0.752275i	−0.00557063	+	0.0315926i
$568$		0			0
$569$	−2.72444	−	4.71888i	−0.114215	−	0.197826i	0.803251	−	0.595641i	$-0.203102\pi$
$569$	−2.72444	−	4.71888i	−0.114215	−	0.197826i	−0.917466	+	0.397815i	$0.869768\pi$
$570$		0			0
$571$	−14.6585	−	12.2999i	−0.613438	−	0.514736i	0.282295	−	0.959328i	$-0.408904\pi$
$571$	−14.6585	−	12.2999i	−0.613438	−	0.514736i	−0.895733	+	0.444592i	$0.853349\pi$
$572$		0			0
$573$	−3.35721	−	19.0397i	−0.140249	−	0.795394i
$574$		0			0
$575$	−6.38825	+	2.32513i	−0.266409	+	0.0969648i
$576$		0			0
$577$	−16.8685	−	14.1544i	−0.702245	−	0.589253i	0.220166	−	0.975462i	$-0.429340\pi$
$577$	−16.8685	−	14.1544i	−0.702245	−	0.589253i	−0.922411	+	0.386209i	$0.873784\pi$
$578$		0			0
$579$	2.94341	+	1.07131i	0.122324	+	0.0445222i
$580$		0			0
$581$	0.417715	−	0.723504i	0.0173297	−	0.0300160i
$582$		0			0
$583$	7.69452	−	2.80058i	0.318675	−	0.115988i
$584$		0			0
$585$	−2.02245	+	1.69704i	−0.0836180	+	0.0701638i
$586$		0			0
$587$	−13.2897	+	11.1514i	−0.548523	+	0.460266i	−0.874441	−	0.485133i	$-0.838771\pi$
$587$	−13.2897	+	11.1514i	−0.548523	+	0.460266i	0.325917	+	0.945398i	$0.394327\pi$
$588$		0			0
$589$	−2.82692	−	16.0322i	−0.116481	−	0.660597i
$590$		0			0
$591$	−2.15899			−0.0888091
$592$		0			0
$593$	−43.2482			−1.77599			−0.887995	−	0.459853i	$-0.847902\pi$
$593$	−43.2482			−1.77599			−0.887995	+	0.459853i	$0.847902\pi$
$594$		0			0
$595$	1.12478	+	6.37895i	0.0461115	+	0.261512i
$596$		0			0
$597$	19.0374	−	15.9743i	0.779149	−	0.653783i
$598$		0			0
$599$	34.5475	−	28.9888i	1.41157	−	1.18445i	0.455895	−	0.890034i	$-0.349319\pi$
$599$	34.5475	−	28.9888i	1.41157	−	1.18445i	0.955677	−	0.294416i	$-0.0951251\pi$
$600$		0			0
$601$	−23.1578	+	8.42877i	−0.944628	+	0.343817i	−0.767992	−	0.640460i	$-0.778744\pi$
$601$	−23.1578	+	8.42877i	−0.944628	+	0.343817i	−0.176636	+	0.984276i	$0.556522\pi$
$602$		0			0
$603$	−2.59703	+	4.49819i	−0.105759	+	0.183180i
$604$		0			0
$605$	7.02035	+	2.55520i	0.285418	+	0.103884i
$606$		0			0
$607$	22.4319	+	18.8226i	0.910484	+	0.763987i	0.972211	−	0.234106i	$-0.0752164\pi$
$607$	22.4319	+	18.8226i	0.910484	+	0.763987i	−0.0617272	+	0.998093i	$0.519661\pi$
$608$		0			0
$609$	−6.30145	+	2.29354i	−0.255348	+	0.0929390i
$610$		0			0
$611$	1.37805	+	7.81531i	0.0557500	+	0.316174i
$612$		0			0
$613$	31.1127	+	26.1066i	1.25663	+	1.05444i	0.996033	+	0.0889891i	$0.0283636\pi$
$613$	31.1127	+	26.1066i	1.25663	+	1.05444i	0.260596	+	0.965448i	$0.416081\pi$
$614$		0			0
$615$	−9.15730	−	15.8609i	−0.369258	−	0.639573i
$616$		0			0
$617$	1.69647	−	9.62117i	0.0682974	−	0.387334i	−0.931429	−	0.363924i	$-0.881437\pi$
$617$	1.69647	−	9.62117i	0.0682974	−	0.387334i	0.999726	−	0.0234095i	$-0.00745216\pi$
$618$		0			0
$619$	−1.80947	−	3.13409i	−0.0727287	−	0.125970i	0.827368	−	0.561661i	$-0.189837\pi$
$619$	−1.80947	−	3.13409i	−0.0727287	−	0.125970i	−0.900096	+	0.435691i	$0.856504\pi$
$620$		0			0
$621$	−0.381940	+	0.661540i	−0.0153267	+	0.0265467i
$622$		0			0
$623$	0.125606			0.00503228
$624$		0			0
$625$	−9.11977	−	3.31932i	−0.364791	−	0.132773i
$626$		0			0
$627$	−1.77835	+	10.0855i	−0.0710206	+	0.402778i
$628$		0			0
$629$	8.15522	−	11.1756i	0.325170	−	0.445599i
$630$		0			0
$631$	−6.58826	+	37.3639i	−0.262274	+	1.48743i	0.514411	+	0.857544i	$0.328010\pi$
$631$	−6.58826	+	37.3639i	−0.262274	+	1.48743i	−0.776686	+	0.629888i	$0.783101\pi$
$632$		0			0
$633$	−18.3348	−	6.67332i	−0.728742	−	0.265241i
$634$		0			0
$635$	−47.6797			−1.89211
$636$		0			0
$637$	−2.27190	+	3.93505i	−0.0900160	+	0.155912i
$638$		0			0
$639$	−4.21030	−	7.29245i	−0.166557	−	0.288485i
$640$		0			0
$641$	−1.14617	+	6.50026i	−0.0452710	+	0.256745i	−0.999041	−	0.0437941i	$-0.986055\pi$
$641$	−1.14617	+	6.50026i	−0.0452710	+	0.256745i	0.953770	+	0.300539i	$0.0971665\pi$
$642$		0			0
$643$	−10.7396	−	18.6015i	−0.423527	−	0.733571i	0.572754	−	0.819727i	$-0.305875\pi$
$643$	−10.7396	−	18.6015i	−0.423527	−	0.733571i	−0.996282	+	0.0861564i	$0.972542\pi$
$644$		0			0
$645$	4.36016	+	3.65861i	0.171681	+	0.144058i
$646$		0			0
$647$	−7.49876	−	42.5276i	−0.294807	−	1.67193i	−0.667988	−	0.744172i	$-0.732844\pi$
$647$	−7.49876	−	42.5276i	−0.294807	−	1.67193i	0.373181	−	0.927759i	$-0.378267\pi$
$648$		0			0
$649$	−10.0004	+	3.63986i	−0.392552	+	0.142877i
$650$		0			0
$651$	2.78998	+	2.34107i	0.109348	+	0.0917539i
$652$		0			0
$653$	19.5234	+	7.10595i	0.764011	+	0.278077i	0.694489	−	0.719503i	$-0.255630\pi$
$653$	19.5234	+	7.10595i	0.764011	+	0.278077i	0.0695219	+	0.997580i	$0.477853\pi$
$654$		0			0
$655$	−34.4273	+	59.6298i	−1.34519	+	2.32993i
$656$		0			0
$657$	8.72272	−	3.17481i	0.340306	−	0.123861i
$658$		0			0
$659$	37.2188	−	31.2303i	1.44984	−	1.21656i	0.517139	−	0.855902i	$-0.326997\pi$
$659$	37.2188	−	31.2303i	1.44984	−	1.21656i	0.932699	−	0.360657i	$-0.117447\pi$
$660$		0			0
$661$	−26.0974	+	21.8983i	−1.01507	+	0.851745i	−0.989000	−	0.147915i	$-0.952744\pi$
$661$	−26.0974	+	21.8983i	−1.01507	+	0.851745i	−0.0260702	+	0.999660i	$0.508299\pi$
$662$		0			0
$663$	0.279682	+	1.58615i	0.0108619	+	0.0616011i
$664$		0			0
$665$	−9.72404			−0.377082
$666$		0			0
$667$	−6.70586			−0.259652
$668$		0			0
$669$	0.347582	+	1.97124i	0.0134383	+	0.0762125i
$670$		0			0
$671$	0.747316	−	0.627073i	0.0288498	−	0.0242079i
$672$		0			0
$673$	−5.84930	+	4.90815i	−0.225474	+	0.189195i	−0.748526	−	0.663106i	$-0.769238\pi$
$673$	−5.84930	+	4.90815i	−0.225474	+	0.189195i	0.523052	+	0.852301i	$0.324794\pi$
$674$		0			0
$675$	−8.36290	+	3.04385i	−0.321888	+	0.117158i
$676$		0			0
$677$	6.86008	−	11.8820i	0.263654	−	0.456663i	−0.703556	−	0.710640i	$-0.748406\pi$
$677$	6.86008	−	11.8820i	0.263654	−	0.456663i	0.967210	+	0.253977i	$0.0817389\pi$
$678$		0			0
$679$	6.32947	+	2.30374i	0.242903	+	0.0884093i
$680$		0			0
$681$	−17.9784	−	15.0856i	−0.688933	−	0.578083i
$682$		0			0
$683$	−14.3115	+	5.20895i	−0.547614	+	0.199315i	−0.600986	−	0.799260i	$-0.705225\pi$
$683$	−14.3115	+	5.20895i	−0.547614	+	0.199315i	0.0533723	+	0.998575i	$0.483003\pi$
$684$		0			0
$685$	−10.5975	−	60.1015i	−0.404910	−	2.29636i
$686$		0			0
$687$	−20.5538	−	17.2467i	−0.784176	−	0.658001i
$688$		0			0
$689$	0.966630	+	1.67425i	0.0368257	+	0.0637840i
$690$		0			0
$691$	−8.03276	+	45.5560i	−0.305581	+	1.73303i	0.315179	+	0.949032i	$0.397935\pi$
$691$	−8.03276	+	45.5560i	−0.305581	+	1.73303i	−0.620759	+	0.784001i	$0.713176\pi$
$692$		0			0
$693$	−1.14557	−	1.98419i	−0.0435167	−	0.0753732i
$694$		0			0
$695$	5.69670	−	9.86698i	0.216088	−	0.374276i
$696$		0			0
$697$	−11.1729			−0.423205
$698$		0			0
$699$	3.32334	+	1.20960i	0.125700	+	0.0457512i
$700$		0			0
$701$	−0.928540	+	5.26601i	−0.0350705	+	0.198895i	−0.997309	−	0.0733133i	$-0.976643\pi$
$701$	−0.928540	+	5.26601i	−0.0350705	+	0.198895i	0.962238	+	0.272208i	$0.0877538\pi$
$702$		0			0
$703$	14.3963	+	14.9702i	0.542968	+	0.564613i
$704$		0			0
$705$	−7.25512	+	41.1458i	−0.273243	+	1.54964i
$706$		0			0
$707$	−12.9936	−	4.72929i	−0.488675	−	0.177863i
$708$		0			0
$709$	−13.7566			−0.516641			−0.258321	−	0.966059i	$-0.583169\pi$
$709$	−13.7566			−0.516641			−0.258321	+	0.966059i	$0.583169\pi$
$710$		0			0
$711$	−4.43237	+	7.67709i	−0.166227	+	0.287913i
$712$		0			0
$713$	1.82103	+	3.15412i	0.0681982	+	0.118123i
$714$		0			0
$715$	1.37506	−	7.79835i	0.0514243	−	0.291642i
$716$		0			0
$717$	12.0296	+	20.8359i	0.449254	+	0.778131i
$718$		0			0
$719$	−16.4312	−	13.7874i	−0.612780	−	0.514183i	0.282745	−	0.959195i	$-0.408755\pi$
$719$	−16.4312	−	13.7874i	−0.612780	−	0.514183i	−0.895525	+	0.445012i	$0.853199\pi$
$720$		0			0
$721$	−0.240422	−	1.36350i	−0.00895380	−	0.0507795i
$722$		0			0
$723$	−8.06800	+	2.93651i	−0.300052	+	0.109210i
$724$		0			0
$725$	−59.8487	−	50.2190i	−2.22272	−	1.86509i
$726$		0			0
$727$	−37.2519	−	13.5586i	−1.38160	−	0.502860i	−0.458934	−	0.888470i	$-0.651769\pi$
$727$	−37.2519	−	13.5586i	−1.38160	−	0.502860i	−0.922662	+	0.385610i	$0.873991\pi$
$728$		0			0
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$		0			0
$731$	3.26291	−	1.18760i	0.120683	−	0.0439250i
$732$		0			0
$733$	−10.2938	+	8.63754i	−0.380211	+	0.319035i	−0.812785	−	0.582564i	$-0.802050\pi$
$733$	−10.2938	+	8.63754i	−0.380211	+	0.319035i	0.432574	+	0.901598i	$0.357605\pi$
$734$		0			0
$735$	−18.3254	+	15.3768i	−0.675941	+	0.567182i
$736$		0			0
$737$	−2.70523	−	15.3421i	−0.0996486	−	0.565135i
$738$		0			0
$739$	9.69479			0.356629			0.178314	−	0.983974i	$-0.442936\pi$
$739$	9.69479			0.356629			0.178314	+	0.983974i	$0.442936\pi$
$740$		0			0
$741$	−2.41792			−0.0888246
$742$		0			0
$743$	−4.07447	−	23.1075i	−0.149478	−	0.847730i	−0.963662	−	0.267124i	$-0.913927\pi$
$743$	−4.07447	−	23.1075i	−0.149478	−	0.847730i	0.814184	−	0.580606i	$-0.197184\pi$
$744$		0			0
$745$	−22.8261	+	19.1534i	−0.836283	+	0.701724i
$746$		0			0
$747$	0.837797	−	0.702995i	0.0306534	−	0.0257212i
$748$		0			0
$749$	−3.20255	+	1.16563i	−0.117019	+	0.0425913i
$750$		0			0
$751$	9.75762	−	16.9007i	0.356061	−	0.616715i	−0.631238	−	0.775589i	$-0.717453\pi$
$751$	9.75762	−	16.9007i	0.356061	−	0.616715i	0.987299	+	0.158874i	$0.0507864\pi$
$752$		0			0
$753$	16.8454	+	6.13123i	0.613881	+	0.223434i
$754$		0			0
$755$	48.9089	+	41.0395i	1.77998	+	1.49358i
$756$		0			0
$757$	−4.83714	+	1.76058i	−0.175809	+	0.0639892i	−0.428425	−	0.903577i	$-0.640931\pi$
$757$	−4.83714	+	1.76058i	−0.175809	+	0.0639892i	0.252616	+	0.967567i	$0.418709\pi$
$758$		0			0
$759$	−0.397853	−	2.25634i	−0.0144412	−	0.0818999i
$760$		0			0
$761$	−34.1514	−	28.6564i	−1.23799	−	1.03880i	−0.997679	−	0.0680989i	$-0.978307\pi$
$761$	−34.1514	−	28.6564i	−1.23799	−	1.03880i	−0.240309	−	0.970696i	$-0.577249\pi$
$762$		0			0
$763$	−1.20941	−	2.09476i	−0.0437836	−	0.0758353i
$764$		0			0
$765$	−1.47246	+	8.35072i	−0.0532368	+	0.301921i
$766$		0			0
$767$	−1.25631	−	2.17600i	−0.0453628	−	0.0785707i
$768$		0			0
$769$	1.08877	−	1.88581i	0.0392622	−	0.0680042i	−0.845727	−	0.533617i	$-0.820833\pi$
$769$	1.08877	−	1.88581i	0.0392622	−	0.0680042i	0.884989	+	0.465612i	$0.154166\pi$
$770$		0			0
$771$	22.4705			0.809257
$772$		0			0
$773$	−8.52475	−	3.10275i	−0.306614	−	0.111598i	0.184131	−	0.982902i	$-0.441053\pi$
$773$	−8.52475	−	3.10275i	−0.306614	−	0.111598i	−0.490745	+	0.871303i	$0.663275\pi$
$774$		0			0
$775$	−7.36824	+	41.7874i	−0.264675	+	1.50105i
$776$		0			0
$777$	−4.62002	−	0.495335i	−0.165742	−	0.0177700i
$778$		0			0
$779$	2.91264	−	16.5184i	0.104356	−	0.591833i
$780$		0			0
$781$	23.7332	+	8.63818i	0.849241	+	0.309098i
$782$		0			0
$783$	−8.77869			−0.313725
$784$		0			0
$785$	−30.1160	+	52.1625i	−1.07489	+	1.86176i
$786$		0			0
$787$	−11.5744	−	20.0475i	−0.412584	−	0.714616i	0.582588	−	0.812768i	$-0.302040\pi$
$787$	−11.5744	−	20.0475i	−0.412584	−	0.714616i	−0.995171	+	0.0981518i	$0.968707\pi$
$788$		0			0
$789$	3.26560	−	18.5202i	0.116259	−	0.659335i
$790$		0			0
$791$	−5.18398	−	8.97891i	−0.184321	−	0.319253i
$792$		0			0
$793$	0.176441	+	0.148051i	0.00626559	+	0.00525746i
$794$		0			0
$795$	1.76742	+	10.0235i	0.0626839	+	0.355498i
$796$		0			0
$797$	33.2727	−	12.1103i	1.17858	−	0.428968i	0.322879	−	0.946440i	$-0.395349\pi$
$797$	33.2727	−	12.1103i	1.17858	−	0.428968i	0.855700	+	0.517472i	$0.173127\pi$
$798$		0			0
$799$	19.5253	+	16.3837i	0.690756	+	0.579613i
$800$		0			0
$801$	0.154515	+	0.0562387i	0.00545950	+	0.00198710i
$802$		0			0
$803$	−13.9208	+	24.1115i	−0.491254	+	0.850877i
$804$		0			0
$805$	2.04427	−	0.744052i	0.0720510	−	0.0262244i
$806$		0			0
$807$	−10.9025	+	9.14824i	−0.383785	+	0.322033i
$808$		0			0
$809$	4.77841	−	4.00957i	0.168000	−	0.140969i	−0.554911	−	0.831909i	$-0.687248\pi$
$809$	4.77841	−	4.00957i	0.168000	−	0.140969i	0.722912	+	0.690941i	$0.242803\pi$
$810$		0			0
$811$	1.74244	+	9.88186i	0.0611853	+	0.346999i	0.999997	+	0.00256748i	$0.000817255\pi$
$811$	1.74244	+	9.88186i	0.0611853	+	0.346999i	−0.938811	+	0.344432i	$0.888072\pi$
$812$		0			0
$813$	−3.80027			−0.133281
$814$		0			0
$815$	−40.0805			−1.40396
$816$		0			0
$817$	0.905186	+	5.13356i	0.0316684	+	0.179601i
$818$		0			0
$819$	0.414382	−	0.347708i	0.0144797	−	0.0121499i
$820$		0			0
$821$	8.98243	−	7.53716i	0.313489	−	0.263049i	−0.472443	−	0.881361i	$-0.656628\pi$
$821$	8.98243	−	7.53716i	0.313489	−	0.263049i	0.785932	+	0.618313i	$0.212183\pi$
$822$		0			0
$823$	44.1166	−	16.0571i	1.53781	−	0.559716i	0.572290	−	0.820052i	$-0.306055\pi$
$823$	44.1166	−	16.0571i	1.53781	−	0.559716i	0.965518	+	0.260335i	$0.0838331\pi$
$824$		0			0
$825$	13.3465	−	23.1169i	0.464667	−	0.804827i
$826$		0			0
$827$	26.6774	+	9.70977i	0.927663	+	0.337642i	0.761283	−	0.648420i	$-0.224570\pi$
$827$	26.6774	+	9.70977i	0.927663	+	0.337642i	0.166380	+	0.986062i	$0.446792\pi$
$828$		0			0
$829$	15.9001	+	13.3418i	0.552234	+	0.463380i	0.875697	−	0.482861i	$-0.160403\pi$
$829$	15.9001	+	13.3418i	0.552234	+	0.463380i	−0.323463	+	0.946241i	$0.604847\pi$
$830$		0			0
$831$	−25.1470	+	9.15274i	−0.872338	+	0.317505i
$832$		0			0
$833$	2.53419	+	14.3721i	0.0878044	+	0.497964i
$834$		0			0
$835$	9.11227	+	7.64610i	0.315343	+	0.264604i
$836$		0			0
$837$	2.38392	+	4.12908i	0.0824005	+	0.142722i
$838$		0			0
$839$	2.35129	−	13.3348i	0.0811755	−	0.460369i	−0.916941	−	0.399023i	$-0.869349\pi$
$839$	2.35129	−	13.3348i	0.0811755	−	0.460369i	0.998117	−	0.0613463i	$-0.0195394\pi$
$840$		0			0
$841$	−24.0327	−	41.6258i	−0.828712	−	1.43537i
$842$		0			0
$843$	−6.66865	+	11.5504i	−0.229681	+	0.397818i
$844$		0			0
$845$	−46.5973			−1.60299
$846$		0			0
$847$	−1.43841	−	0.523538i	−0.0494243	−	0.0179890i
$848$		0			0
$849$	−5.09677	+	28.9052i	−0.174921	+	0.992024i
$850$		0			0
$851$	−4.17199	−	2.04560i	−0.143014	−	0.0701224i
$852$		0			0
$853$	1.65996	−	9.41412i	0.0568361	−	0.322333i	−0.943113	−	0.332474i	$-0.892117\pi$
$853$	1.65996	−	9.41412i	0.0568361	−	0.322333i	0.999949	+	0.0101404i	$0.00322784\pi$
$854$		0			0
$855$	−11.9621	−	4.35385i	−0.409095	−	0.148898i
$856$		0			0
$857$	23.1848			0.791977			0.395988	−	0.918255i	$-0.370402\pi$
$857$	23.1848			0.791977			0.395988	+	0.918255i	$0.370402\pi$
$858$		0			0
$859$	5.41234	−	9.37444i	0.184667	−	0.319852i	−0.758798	−	0.651327i	$-0.774213\pi$
$859$	5.41234	−	9.37444i	0.184667	−	0.319852i	0.943464	+	0.331475i	$0.107546\pi$
$860$		0			0
$861$	1.87625	+	3.24976i	0.0639425	+	0.110752i
$862$		0			0
$863$	6.71512	−	38.0833i	0.228585	−	1.29637i	−0.627126	−	0.778918i	$-0.715769\pi$
$863$	6.71512	−	38.0833i	0.228585	−	1.29637i	0.855711	−	0.517453i	$-0.173120\pi$
$864$		0			0
$865$	23.8964	+	41.3898i	0.812503	+	1.40730i
$866$		0			0
$867$	−9.06001	−	7.60225i	−0.307694	−	0.258186i
$868$		0			0
$869$	−4.61704	−	26.1846i	−0.156622	−	0.888250i
$870$		0			0
$871$	3.45633	−	1.25800i	0.117113	−	0.0426257i
$872$		0			0
$873$	6.75476	+	5.66792i	0.228614	+	0.191830i
$874$		0			0
$875$	10.4360	+	3.79839i	0.352801	+	0.128409i
$876$		0			0
$877$	9.74892	−	16.8856i	0.329198	−	0.570187i	−0.653155	−	0.757224i	$-0.726555\pi$
$877$	9.74892	−	16.8856i	0.329198	−	0.570187i	0.982353	+	0.187037i	$0.0598885\pi$
$878$		0			0
$879$	21.0479	−	7.66079i	0.709927	−	0.258392i
$880$		0			0
$881$	27.4241	−	23.0116i	0.923943	−	0.775280i	−0.0507770	−	0.998710i	$-0.516170\pi$
$881$	27.4241	−	23.0116i	0.923943	−	0.775280i	0.974720	+	0.223430i	$0.0717253\pi$
$882$		0			0
$883$	−2.06569	+	1.73332i	−0.0695160	+	0.0583309i	−0.676884	−	0.736090i	$-0.736670\pi$
$883$	−2.06569	+	1.73332i	−0.0695160	+	0.0583309i	0.607368	+	0.794421i	$0.292226\pi$
$884$		0			0
$885$	−2.29709	−	13.0274i	−0.0772157	−	0.437912i
$886$		0			0
$887$	43.6571			1.46586			0.732931	−	0.680303i	$-0.238152\pi$
$887$	43.6571			1.46586			0.732931	+	0.680303i	$0.238152\pi$
$888$		0			0
$889$	9.76917			0.327647
$890$		0			0
$891$	−0.520832	−	2.95379i	−0.0174485	−	0.0989556i
$892$		0			0
$893$	−29.3121	+	24.5958i	−0.980892	+	0.823066i
$894$		0			0
$895$	−51.8527	+	43.5096i	−1.73324	+	1.45436i
$896$		0			0
$897$	0.508315	−	0.185012i	0.0169722	−	0.00617736i
$898$		0			0
$899$	−20.9277	+	36.2479i	−0.697979	+	1.20893i
$900$		0			0
$901$	5.83479	+	2.12369i	0.194385	+	0.0707504i
$902$		0			0
$903$	−0.893360	−	0.749618i	−0.0297292	−	0.0249457i
$904$		0			0
$905$	−26.3015	+	9.57296i	−0.874291	+	0.318216i
$906$		0			0
$907$	−6.72048	−	38.1138i	−0.223150	−	1.26555i	−0.866190	−	0.499714i	$-0.833438\pi$
$907$	−6.72048	−	38.1138i	−0.223150	−	1.26555i	0.643040	−	0.765832i	$-0.277673\pi$
$908$		0			0
$909$	−13.8667	−	11.6355i	−0.459929	−	0.385927i
$910$		0			0
$911$	23.3908	+	40.5140i	0.774971	+	1.34229i	0.934811	+	0.355146i	$0.115569\pi$
$911$	23.3908	+	40.5140i	0.774971	+	1.34229i	−0.159840	+	0.987143i	$0.551098\pi$
$912$		0			0
$913$	−0.569617	+	3.23046i	−0.0188516	+	0.106913i
$914$		0			0
$915$	0.606309	+	1.05016i	0.0200440	+	0.0347172i
$916$		0			0
$917$	7.05386	−	12.2176i	0.232939	−	0.403462i
$918$		0			0
$919$	12.8141			0.422699			0.211350	−	0.977411i	$-0.432214\pi$
$919$	12.8141			0.422699			0.211350	+	0.977411i	$0.432214\pi$
$920$		0			0
$921$	14.0328	+	5.10754i	0.462398	+	0.168299i
$922$		0			0
$923$	−1.03546	+	5.87241i	−0.0340827	+	0.193293i
$924$		0			0
$925$	−21.9151	−	49.4999i	−0.720565	−	1.62755i
$926$		0			0
$927$	0.314738	−	1.78497i	0.0103374	−	0.0586261i
$928$		0			0
$929$	−25.7372	−	9.36759i	−0.844412	−	0.307341i	−0.116652	−	0.993173i	$-0.537216\pi$
$929$	−25.7372	−	9.36759i	−0.844412	−	0.307341i	−0.727760	+	0.685832i	$0.759438\pi$
$930$		0			0
$931$	−21.9087			−0.718030
$932$		0			0
$933$	−1.33328	+	2.30930i	−0.0436495	+	0.0756032i
$934$		0			0
$935$	−12.7166	−	22.0258i	−0.415877	−	0.720320i
$936$		0			0
$937$	−7.01203	+	39.7672i	−0.229073	+	1.29914i	0.625671	+	0.780087i	$0.284825\pi$
$937$	−7.01203	+	39.7672i	−0.229073	+	1.29914i	−0.854744	+	0.519050i	$0.826286\pi$
$938$		0			0
$939$	−0.621472	−	1.07642i	−0.0202810	−	0.0351277i
$940$		0			0
$941$	43.4106	+	36.4258i	1.41514	+	1.18745i	0.953882	+	0.300183i	$0.0970477\pi$
$941$	43.4106	+	36.4258i	1.41514	+	1.18745i	0.461262	+	0.887264i	$0.347397\pi$
$942$		0			0
$943$	0.651615	+	3.69550i	0.0212195	+	0.120342i
$944$		0			0
$945$	2.67616	−	0.974043i	0.0870556	−	0.0316856i
$946$		0			0
$947$	−31.3693	−	26.3219i	−1.01936	−	0.855348i	−0.0298170	−	0.999555i	$-0.509492\pi$
$947$	−31.3693	−	26.3219i	−1.01936	−	0.855348i	−0.989548	+	0.144207i	$0.953937\pi$
$948$		0			0
$949$	−6.17695	−	2.24823i	−0.200512	−	0.0729805i
$950$		0			0
$951$	−15.9575	+	27.6393i	−0.517459	+	0.896265i
$952$		0			0
$953$	17.5298	−	6.38031i	0.567845	−	0.206679i	−0.0421126	−	0.999113i	$-0.513409\pi$
$953$	17.5298	−	6.38031i	0.567845	−	0.206679i	0.609957	+	0.792434i	$0.291187\pi$
$954$		0			0
$955$	−55.2158	+	46.3316i	−1.78674	+	1.49925i
$956$		0			0
$957$	20.1702	−	16.9248i	0.652011	−	0.547102i
$958$		0			0
$959$	2.17134	+	12.3143i	0.0701162	+	0.397649i
$960$		0			0
$961$	−8.26762			−0.266697
$962$		0			0
$963$	−4.46154			−0.143771
$964$		0			0
$965$	−2.02785	−	11.5005i	−0.0652788	−	0.370215i
$966$		0			0
$967$	6.72543	−	5.64331i	0.216275	−	0.181477i	−0.528213	−	0.849112i	$-0.677138\pi$
$967$	6.72543	−	5.64331i	0.216275	−	0.181477i	0.744489	+	0.667635i	$0.232693\pi$
$968$		0			0
$969$	−5.94902	+	4.99182i	−0.191110	+	0.160360i
$970$		0			0
$971$	27.0784	−	9.85575i	0.868989	−	0.316286i	0.131231	−	0.991352i	$-0.458107\pi$
$971$	27.0784	−	9.85575i	0.868989	−	0.316286i	0.737758	+	0.675066i	$0.235885\pi$
$972$		0			0
$973$	−1.16721	+	2.02166i	−0.0374189	+	0.0648115i
$974$		0			0
$975$	5.92215	+	2.15549i	0.189660	+	0.0690308i
$976$		0			0
$977$	19.2400	+	16.1443i	0.615543	+	0.516502i	0.896399	−	0.443248i	$-0.146174\pi$
$977$	19.2400	+	16.1443i	0.615543	+	0.516502i	−0.280856	+	0.959750i	$0.590618\pi$
$978$		0			0
$979$	−0.463444	+	0.168680i	−0.0148117	+	0.00539103i
$980$		0			0
$981$	−0.549855	−	3.11838i	−0.0175555	−	0.0995623i
$982$		0			0
$983$	43.9027	+	36.8387i	1.40028	+	1.17497i	0.960976	+	0.276633i	$0.0892187\pi$
$983$	43.9027	+	36.8387i	1.40028	+	1.17497i	0.439302	+	0.898339i	$0.355226\pi$
$984$		0			0
$985$	4.02460	+	6.97081i	0.128234	+	0.222109i
$986$		0			0
$987$	1.48651	−	8.43042i	0.0473162	−	0.268343i
$988$		0			0
$989$	−0.583099	−	1.00996i	−0.0185415	−	0.0321148i
$990$		0			0
$991$	−20.3498	+	35.2469i	−0.646433	+	1.11966i	0.337535	+	0.941313i	$0.390407\pi$
$991$	−20.3498	+	35.2469i	−0.646433	+	1.11966i	−0.983968	+	0.178342i	$0.942927\pi$
$992$		0			0
$993$	24.6637			0.782677
$994$		0			0
$995$	−87.0644	−	31.6889i	−2.76013	−	1.00460i
$996$		0			0
$997$	7.17373	−	40.6843i	0.227194	−	1.28848i	−0.631251	−	0.775579i	$-0.717458\pi$
$997$	7.17373	−	40.6843i	0.227194	−	1.28848i	0.858445	−	0.512905i	$-0.171431\pi$
$998$		0			0
$999$	−5.46157	−	2.67791i	−0.172797	−	0.0847254i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	888.2.bo.c.625.4	yes	24
37.9	even	9	inner	888.2.bo.c.601.4	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
888.2.bo.c.601.4	✓	24	37.9	even	9	inner
888.2.bo.c.625.4	yes	24	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 888 = 2^{3} \cdot 3 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	888.bo (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.173648 + 0.984808i) q^{3} +(2.85598 - 2.39645i) q^{5} +(-0.585166 + 0.491013i) q^{7} +(-0.939693 + 0.342020i) q^{9} +O(q^{10})\)	\(q+(0.173648 + 0.984808i) q^{3} +(2.85598 - 2.39645i) q^{5} +(-0.585166 + 0.491013i) q^{7} +(-0.939693 + 0.342020i) q^{9} +(1.49968 - 2.59752i) q^{11} +(0.665439 + 0.242200i) q^{13} +(2.85598 + 2.39645i) q^{15} +(2.13726 - 0.777899i) q^{17} +(0.592912 + 3.36257i) q^{19} +(-0.585166 - 0.491013i) q^{21} +(-0.381940 - 0.661540i) q^{23} +(1.54540 - 8.76441i) q^{25} +(-0.500000 - 0.866025i) q^{27} +(4.38934 - 7.60256i) q^{29} -4.76785 q^{31} +(2.81847 + 1.02584i) q^{33} +(-0.494535 + 2.80465i) q^{35} +(5.04993 - 3.39091i) q^{37} +(-0.122968 + 0.697387i) q^{39} +(-4.61617 - 1.68015i) q^{41} +1.52668 q^{43} +(-1.86411 + 3.22873i) q^{45} +(5.60329 + 9.70517i) q^{47} +(-1.11421 + 6.31901i) q^{49} +(1.13721 + 1.96971i) q^{51} +(2.09133 + 1.75483i) q^{53} +(-1.94178 - 11.0124i) q^{55} +(-3.20853 + 1.16781i) q^{57} +(-2.71806 - 2.28073i) q^{59} +(0.305639 + 0.111243i) q^{61} +(0.381940 - 0.661540i) q^{63} +(2.48090 - 0.902974i) q^{65} +(3.97888 - 3.33868i) q^{67} +(0.585166 - 0.491013i) q^{69} +(1.46222 + 8.29267i) q^{71} -9.28253 q^{73} +8.89961 q^{75} +(0.397853 + 2.25634i) q^{77} +(6.79079 - 5.69815i) q^{79} +(0.766044 - 0.642788i) q^{81} +(-1.02771 + 0.374056i) q^{83} +(4.23977 - 7.34350i) q^{85} +(8.24927 + 3.00249i) q^{87} +(-0.125961 - 0.105694i) q^{89} +(-0.508315 + 0.185012i) q^{91} +(-0.827928 - 4.69541i) q^{93} +(9.75159 + 8.18256i) q^{95} +(-4.40886 - 7.63637i) q^{97} +(-0.520832 + 2.95379i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{5} + 15 q^{7}+O(q^{10}) \) 24 * q + 3 * q^5 + 15 * q^7	\( 24 q + 3 q^{5} + 15 q^{7} + 12 q^{13} + 3 q^{15} + 3 q^{17} + 9 q^{19} + 15 q^{21} + 27 q^{25} - 12 q^{27} - 6 q^{29} - 30 q^{31} + 9 q^{33} + 15 q^{35} + 9 q^{37} + 3 q^{39} + 15 q^{41} - 54 q^{43} + 6 q^{45} - 12 q^{47} + 27 q^{49} + 18 q^{51} + 39 q^{53} - 6 q^{55} - 3 q^{59} + 12 q^{61} + 36 q^{65} + 48 q^{67} - 15 q^{69} + 33 q^{71} - 48 q^{73} + 60 q^{75} + 36 q^{77} + 18 q^{79} - 42 q^{83} + 15 q^{87} + 36 q^{89} - 36 q^{91} - 18 q^{93} + 27 q^{95} + 9 q^{97}+O(q^{100}) \) 24 * q + 3 * q^5 + 15 * q^7 + 12 * q^13 + 3 * q^15 + 3 * q^17 + 9 * q^19 + 15 * q^21 + 27 * q^25 - 12 * q^27 - 6 * q^29 - 30 * q^31 + 9 * q^33 + 15 * q^35 + 9 * q^37 + 3 * q^39 + 15 * q^41 - 54 * q^43 + 6 * q^45 - 12 * q^47 + 27 * q^49 + 18 * q^51 + 39 * q^53 - 6 * q^55 - 3 * q^59 + 12 * q^61 + 36 * q^65 + 48 * q^67 - 15 * q^69 + 33 * q^71 - 48 * q^73 + 60 * q^75 + 36 * q^77 + 18 * q^79 - 42 * q^83 + 15 * q^87 + 36 * q^89 - 36 * q^91 - 18 * q^93 + 27 * q^95 + 9 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more