LMFDB - Embedded newform 1344.2.q.w.961.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1344,2,Mod(193,1344)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1344, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))

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

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

chi := DirichletCharacter("1344.193");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1344 = 2^{6} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1344.q (of order $3$, degree $2$, not 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:	$10.7318940317$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-19})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 4x^{2} - 5x + 25 $ x^4 - x^3 - 4x^2 - 5x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			961.2
Root			$2.13746 - 0.656712i$ of defining polynomial
Character	$\chi$	$=$	1344.961
Dual form			1344.2.q.w.193.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 - 0.866025i) q^{3} +(1.63746 - 2.83616i) q^{5} +(-1.50000 + 2.17945i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(1.63746 + 2.83616i) q^{11} -6.27492 q^{13} -3.27492 q^{15} +(2.00000 + 3.46410i) q^{17} +(-3.13746 + 5.43424i) q^{19} +(2.63746 + 0.209313i) q^{21} +(-2.00000 + 3.46410i) q^{23} +(-2.86254 - 4.95807i) q^{25} +1.00000 q^{27} -5.27492 q^{29} +(0.500000 + 0.866025i) q^{31} +(1.63746 - 2.83616i) q^{33} +(3.72508 + 7.82300i) q^{35} +(-1.13746 + 1.97014i) q^{37} +(3.13746 + 5.43424i) q^{39} -4.54983 q^{41} -0.274917 q^{43} +(1.63746 + 2.83616i) q^{45} +(3.00000 - 5.19615i) q^{47} +(-2.50000 - 6.53835i) q^{49} +(2.00000 - 3.46410i) q^{51} +(4.63746 + 8.03231i) q^{53} +10.7251 q^{55} +6.27492 q^{57} +(-0.637459 - 1.10411i) q^{59} +(5.00000 - 8.66025i) q^{61} +(-1.13746 - 2.38876i) q^{63} +(-10.2749 + 17.7967i) q^{65} +(-0.137459 - 0.238085i) q^{67} +4.00000 q^{69} +2.00000 q^{71} +(2.13746 + 3.70219i) q^{73} +(-2.86254 + 4.95807i) q^{75} +(-8.63746 - 0.685484i) q^{77} +(-5.77492 + 10.0025i) q^{79} +(-0.500000 - 0.866025i) q^{81} -7.27492 q^{83} +13.0997 q^{85} +(2.63746 + 4.56821i) q^{87} +(5.27492 - 9.13642i) q^{89} +(9.41238 - 13.6759i) q^{91} +(0.500000 - 0.866025i) q^{93} +(10.2749 + 17.7967i) q^{95} +8.72508 q^{97} -3.27492 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} - q^{5} - 6 q^{7} - 2 q^{9} - q^{11} - 10 q^{13} + 2 q^{15} + 8 q^{17} - 5 q^{19} + 3 q^{21} - 8 q^{23} - 19 q^{25} + 4 q^{27} - 6 q^{29} + 2 q^{31} - q^{33} + 30 q^{35} + 3 q^{37} + 5 q^{39}+ \cdots + 2 q^{99}+O(q^{100}) $ 4 * q - 2 * q^3 - q^5 - 6 * q^7 - 2 * q^9 - q^11 - 10 * q^13 + 2 * q^15 + 8 * q^17 - 5 * q^19 + 3 * q^21 - 8 * q^23 - 19 * q^25 + 4 * q^27 - 6 * q^29 + 2 * q^31 - q^33 + 30 * q^35 + 3 * q^37 + 5 * q^39 + 12 * q^41 + 14 * q^43 - q^45 + 12 * q^47 - 10 * q^49 + 8 * q^51 + 11 * q^53 + 58 * q^55 + 10 * q^57 + 5 * q^59 + 20 * q^61 + 3 * q^63 - 26 * q^65 + 7 * q^67 + 16 * q^69 + 8 * q^71 + q^73 - 19 * q^75 - 27 * q^77 - 8 * q^79 - 2 * q^81 - 14 * q^83 - 8 * q^85 + 3 * q^87 + 6 * q^89 + 15 * q^91 + 2 * q^93 + 26 * q^95 + 50 * q^97 + 2 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times$.

$n$	$127$	$449$	$577$	$1093$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$		0			0
$5$	1.63746	−	2.83616i	0.732294	−	1.26837i	−0.223607	−	0.974679i	$-0.571783\pi$
$5$	1.63746	−	2.83616i	0.732294	−	1.26837i	0.955901	−	0.293691i	$-0.0948835\pi$
$6$		0			0
$7$	−1.50000	+	2.17945i	−0.566947	+	0.823754i
$7$	−1.50000	+	2.17945i	−0.566947	+	0.823754i
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	1.63746	+	2.83616i	0.493712	+	0.855135i	0.999974	−	0.00724520i	$-0.00230624\pi$
$11$	1.63746	+	2.83616i	0.493712	+	0.855135i	−0.506261	+	0.862380i	$0.668973\pi$
$12$		0			0
$13$	−6.27492			−1.74035			−0.870174	−	0.492744i	$-0.835994\pi$
$13$	−6.27492			−1.74035			−0.870174	+	0.492744i	$0.835994\pi$
$14$		0			0
$15$	−3.27492			−0.845580
$16$		0			0
$17$	2.00000	+	3.46410i	0.485071	+	0.840168i	0.999853	−	0.0171533i	$-0.00546033\pi$
$17$	2.00000	+	3.46410i	0.485071	+	0.840168i	−0.514782	+	0.857321i	$0.672127\pi$
$18$		0			0
$19$	−3.13746	+	5.43424i	−0.719782	+	1.24670i	0.241303	+	0.970450i	$0.422425\pi$
$19$	−3.13746	+	5.43424i	−0.719782	+	1.24670i	−0.961086	+	0.276250i	$0.910908\pi$
$20$		0			0
$21$	2.63746	+	0.209313i	0.575541	+	0.0456759i
$22$		0			0
$23$	−2.00000	+	3.46410i	−0.417029	+	0.722315i	−0.995639	−	0.0932891i	$-0.970262\pi$
$23$	−2.00000	+	3.46410i	−0.417029	+	0.722315i	0.578610	+	0.815604i	$0.303595\pi$
$24$		0			0
$25$	−2.86254	−	4.95807i	−0.572508	−	0.991613i
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	−5.27492			−0.979528			−0.489764	−	0.871855i	$-0.662917\pi$
$29$	−5.27492			−0.979528			−0.489764	+	0.871855i	$0.662917\pi$
$30$		0			0
$31$	0.500000	+	0.866025i	0.0898027	+	0.155543i	0.907428	−	0.420208i	$-0.138043\pi$
$31$	0.500000	+	0.866025i	0.0898027	+	0.155543i	−0.817625	+	0.575751i	$0.804710\pi$
$32$		0			0
$33$	1.63746	−	2.83616i	0.285045	−	0.493712i
$34$		0			0
$35$	3.72508	+	7.82300i	0.629654	+	1.32233i
$36$		0			0
$37$	−1.13746	+	1.97014i	−0.186997	+	0.323888i	−0.944248	−	0.329236i	$-0.893209\pi$
$37$	−1.13746	+	1.97014i	−0.186997	+	0.323888i	0.757251	+	0.653124i	$0.226542\pi$
$38$		0			0
$39$	3.13746	+	5.43424i	0.502395	+	0.870174i
$40$		0			0
$41$	−4.54983			−0.710565			−0.355282	−	0.934759i	$-0.615615\pi$
$41$	−4.54983			−0.710565			−0.355282	+	0.934759i	$0.615615\pi$
$42$		0			0
$43$	−0.274917			−0.0419245			−0.0209622	−	0.999780i	$-0.506673\pi$
$43$	−0.274917			−0.0419245			−0.0209622	+	0.999780i	$0.506673\pi$
$44$		0			0
$45$	1.63746	+	2.83616i	0.244098	+	0.422790i
$46$		0			0
$47$	3.00000	−	5.19615i	0.437595	−	0.757937i	−0.559908	−	0.828554i	$-0.689164\pi$
$47$	3.00000	−	5.19615i	0.437595	−	0.757937i	0.997503	+	0.0706177i	$0.0224970\pi$
$48$		0			0
$49$	−2.50000	−	6.53835i	−0.357143	−	0.934050i
$50$		0			0
$51$	2.00000	−	3.46410i	0.280056	−	0.485071i
$52$		0			0
$53$	4.63746	+	8.03231i	0.637004	+	1.10332i	0.986087	+	0.166231i	$0.0531598\pi$
$53$	4.63746	+	8.03231i	0.637004	+	1.10332i	−0.349083	+	0.937092i	$0.613507\pi$
$54$		0			0
$55$	10.7251			1.44617
$56$		0			0
$57$	6.27492			0.831133
$58$		0			0
$59$	−0.637459	−	1.10411i	−0.0829900	−	0.143743i	0.821543	−	0.570147i	$-0.193114\pi$
$59$	−0.637459	−	1.10411i	−0.0829900	−	0.143743i	−0.904533	+	0.426404i	$0.859780\pi$
$60$		0			0
$61$	5.00000	−	8.66025i	0.640184	−	1.10883i	−0.345207	−	0.938527i	$-0.612191\pi$
$61$	5.00000	−	8.66025i	0.640184	−	1.10883i	0.985391	−	0.170305i	$-0.0544754\pi$
$62$		0			0
$63$	−1.13746	−	2.38876i	−0.143306	−	0.300956i
$64$		0			0
$65$	−10.2749	+	17.7967i	−1.27445	+	2.20741i
$66$		0			0
$67$	−0.137459	−	0.238085i	−0.0167932	−	0.0290867i	0.857507	−	0.514473i	$-0.172012\pi$
$67$	−0.137459	−	0.238085i	−0.0167932	−	0.0290867i	−0.874300	+	0.485386i	$0.838679\pi$
$68$		0			0
$69$	4.00000			0.481543
$70$		0			0
$71$	2.00000			0.237356			0.118678	−	0.992933i	$-0.462134\pi$
$71$	2.00000			0.237356			0.118678	+	0.992933i	$0.462134\pi$
$72$		0			0
$73$	2.13746	+	3.70219i	0.250171	+	0.433308i	0.963573	−	0.267447i	$-0.0861800\pi$
$73$	2.13746	+	3.70219i	0.250171	+	0.433308i	−0.713402	+	0.700755i	$0.752847\pi$
$74$		0			0
$75$	−2.86254	+	4.95807i	−0.330538	+	0.572508i
$76$		0			0
$77$	−8.63746	−	0.685484i	−0.984330	−	0.0781181i
$78$		0			0
$79$	−5.77492	+	10.0025i	−0.649729	+	1.12536i	0.333459	+	0.942765i	$0.391784\pi$
$79$	−5.77492	+	10.0025i	−0.649729	+	1.12536i	−0.983188	+	0.182599i	$0.941549\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	−7.27492			−0.798526			−0.399263	−	0.916836i	$-0.630734\pi$
$83$	−7.27492			−0.798526			−0.399263	+	0.916836i	$0.630734\pi$
$84$		0			0
$85$	13.0997			1.42086
$86$		0			0
$87$	2.63746	+	4.56821i	0.282765	+	0.489764i
$88$		0			0
$89$	5.27492	−	9.13642i	0.559140	−	0.968459i	−0.438428	−	0.898766i	$-0.644465\pi$
$89$	5.27492	−	9.13642i	0.559140	−	0.968459i	0.997568	−	0.0696929i	$-0.0222020\pi$
$90$		0			0
$91$	9.41238	−	13.6759i	0.986685	−	1.43362i
$92$		0			0
$93$	0.500000	−	0.866025i	0.0518476	−	0.0898027i
$94$		0			0
$95$	10.2749	+	17.7967i	1.05418	+	1.82590i
$96$		0			0
$97$	8.72508			0.885898			0.442949	−	0.896547i	$-0.353932\pi$
$97$	8.72508			0.885898			0.442949	+	0.896547i	$0.353932\pi$
$98$		0			0
$99$	−3.27492			−0.329142
$100$		0			0
$101$	−3.00000	−	5.19615i	−0.298511	−	0.517036i	0.677284	−	0.735721i	$-0.263157\pi$
$101$	−3.00000	−	5.19615i	−0.298511	−	0.517036i	−0.975796	+	0.218685i	$0.929823\pi$
$102$		0			0
$103$	−5.41238	+	9.37451i	−0.533297	+	0.923698i	0.465946	+	0.884813i	$0.345714\pi$
$103$	−5.41238	+	9.37451i	−0.533297	+	0.923698i	−0.999244	+	0.0388850i	$0.987619\pi$
$104$		0			0
$105$	4.91238	−	7.13752i	0.479399	−	0.696550i
$106$		0			0
$107$	−7.91238	+	13.7046i	−0.764918	+	1.32488i	0.175372	+	0.984502i	$0.443887\pi$
$107$	−7.91238	+	13.7046i	−0.764918	+	1.32488i	−0.940290	+	0.340375i	$0.889446\pi$
$108$		0			0
$109$	8.41238	+	14.5707i	0.805759	+	1.39562i	0.915777	+	0.401687i	$0.131576\pi$
$109$	8.41238	+	14.5707i	0.805759	+	1.39562i	−0.110018	+	0.993930i	$0.535091\pi$
$110$		0			0
$111$	2.27492			0.215926
$112$		0			0
$113$	−4.54983			−0.428012			−0.214006	−	0.976832i	$-0.568651\pi$
$113$	−4.54983			−0.428012			−0.214006	+	0.976832i	$0.568651\pi$
$114$		0			0
$115$	6.54983	+	11.3446i	0.610775	+	1.05789i
$116$		0			0
$117$	3.13746	−	5.43424i	0.290058	−	0.502395i
$118$		0			0
$119$	−10.5498	−	0.837253i	−0.967102	−	0.0767509i
$120$		0			0
$121$	0.137459	−	0.238085i	0.0124962	−	0.0216441i
$122$		0			0
$123$	2.27492	+	3.94027i	0.205122	+	0.355282i
$124$		0			0
$125$	−2.37459			−0.212389
$126$		0			0
$127$	−6.45017			−0.572360			−0.286180	−	0.958176i	$-0.592385\pi$
$127$	−6.45017			−0.572360			−0.286180	+	0.958176i	$0.592385\pi$
$128$		0			0
$129$	0.137459	+	0.238085i	0.0121026	+	0.0209622i
$130$		0			0
$131$	3.63746	−	6.30026i	0.317806	−	0.550457i	−0.662224	−	0.749306i	$-0.730387\pi$
$131$	3.63746	−	6.30026i	0.317806	−	0.550457i	0.980030	+	0.198850i	$0.0637205\pi$
$132$		0			0
$133$	−7.13746	−	14.9893i	−0.618896	−	1.29974i
$134$		0			0
$135$	1.63746	−	2.83616i	0.140930	−	0.244098i
$136$		0			0
$137$	−0.725083	−	1.25588i	−0.0619480	−	0.107297i	0.833388	−	0.552688i	$-0.186398\pi$
$137$	−0.725083	−	1.25588i	−0.0619480	−	0.107297i	−0.895336	+	0.445391i	$0.853065\pi$
$138$		0			0
$139$	−8.27492			−0.701869			−0.350935	−	0.936400i	$-0.614136\pi$
$139$	−8.27492			−0.701869			−0.350935	+	0.936400i	$0.614136\pi$
$140$		0			0
$141$	−6.00000			−0.505291
$142$		0			0
$143$	−10.2749	−	17.7967i	−0.859232	−	1.48823i
$144$		0			0
$145$	−8.63746	+	14.9605i	−0.717302	+	1.24240i
$146$		0			0
$147$	−4.41238	+	5.43424i	−0.363927	+	0.448208i
$148$		0			0
$149$	−7.27492	+	12.6005i	−0.595984	+	1.03228i	0.397423	+	0.917636i	$0.369905\pi$
$149$	−7.27492	+	12.6005i	−0.595984	+	1.03228i	−0.993407	+	0.114640i	$0.963429\pi$
$150$		0			0
$151$	−11.1873	−	19.3770i	−0.910409	−	1.57687i	−0.813487	−	0.581583i	$-0.802434\pi$
$151$	−11.1873	−	19.3770i	−0.910409	−	1.57687i	−0.0969217	−	0.995292i	$-0.530900\pi$
$152$		0			0
$153$	−4.00000			−0.323381
$154$		0			0
$155$	3.27492			0.263048
$156$		0			0
$157$	−0.274917	−	0.476171i	−0.0219408	−	0.0380026i	0.854847	−	0.518881i	$-0.173651\pi$
$157$	−0.274917	−	0.476171i	−0.0219408	−	0.0380026i	−0.876787	+	0.480878i	$0.840318\pi$
$158$		0			0
$159$	4.63746	−	8.03231i	0.367774	−	0.637004i
$160$		0			0
$161$	−4.54983	−	9.55505i	−0.358577	−	0.753044i
$162$		0			0
$163$	−6.00000	+	10.3923i	−0.469956	+	0.813988i	−0.999410	−	0.0343508i	$-0.989064\pi$
$163$	−6.00000	+	10.3923i	−0.469956	+	0.813988i	0.529454	+	0.848339i	$0.322397\pi$
$164$		0			0
$165$	−5.36254	−	9.28819i	−0.417473	−	0.723085i
$166$		0			0
$167$	−6.00000			−0.464294			−0.232147	−	0.972681i	$-0.574575\pi$
$167$	−6.00000			−0.464294			−0.232147	+	0.972681i	$0.574575\pi$
$168$		0			0
$169$	26.3746			2.02881
$170$		0			0
$171$	−3.13746	−	5.43424i	−0.239927	−	0.415567i
$172$		0			0
$173$	−11.2749	+	19.5287i	−0.857216	+	1.48474i	0.0173577	+	0.999849i	$0.494475\pi$
$173$	−11.2749	+	19.5287i	−0.857216	+	1.48474i	−0.874574	+	0.484892i	$0.838859\pi$
$174$		0			0
$175$	15.0997	+	1.19834i	1.14143	+	0.0905857i
$176$		0			0
$177$	−0.637459	+	1.10411i	−0.0479143	+	0.0829900i
$178$		0			0
$179$	−8.27492	−	14.3326i	−0.618496	−	1.07127i	−0.989760	−	0.142740i	$-0.954409\pi$
$179$	−8.27492	−	14.3326i	−0.618496	−	1.07127i	0.371264	−	0.928527i	$-0.378925\pi$
$180$		0			0
$181$	18.8248			1.39923			0.699616	−	0.714519i	$-0.253354\pi$
$181$	18.8248			1.39923			0.699616	+	0.714519i	$0.253354\pi$
$182$		0			0
$183$	−10.0000			−0.739221
$184$		0			0
$185$	3.72508	+	6.45203i	0.273874	+	0.474363i
$186$		0			0
$187$	−6.54983	+	11.3446i	−0.478971	+	0.829603i
$188$		0			0
$189$	−1.50000	+	2.17945i	−0.109109	+	0.158532i
$190$		0			0
$191$	−2.27492	+	3.94027i	−0.164607	+	0.285108i	−0.936516	−	0.350626i	$-0.885969\pi$
$191$	−2.27492	+	3.94027i	−0.164607	+	0.285108i	0.771909	+	0.635734i	$0.219302\pi$
$192$		0			0
$193$	−0.225083	−	0.389855i	−0.0162018	−	0.0280624i	0.857811	−	0.513966i	$-0.171824\pi$
$193$	−0.225083	−	0.389855i	−0.0162018	−	0.0280624i	−0.874013	+	0.485903i	$0.838491\pi$
$194$		0			0
$195$	20.5498			1.47160
$196$		0			0
$197$	1.45017			0.103320			0.0516600	−	0.998665i	$-0.483549\pi$
$197$	1.45017			0.103320			0.0516600	+	0.998665i	$0.483549\pi$
$198$		0			0
$199$	2.54983	+	4.41644i	0.180753	+	0.313073i	0.942137	−	0.335228i	$-0.108813\pi$
$199$	2.54983	+	4.41644i	0.180753	+	0.313073i	−0.761384	+	0.648301i	$0.775480\pi$
$200$		0			0
$201$	−0.137459	+	0.238085i	−0.00969558	+	0.0167932i
$202$		0			0
$203$	7.91238	−	11.4964i	0.555340	−	0.806890i
$204$		0			0
$205$	−7.45017	+	12.9041i	−0.520342	+	0.901259i
$206$		0			0
$207$	−2.00000	−	3.46410i	−0.139010	−	0.240772i
$208$		0			0
$209$	−20.5498			−1.42146
$210$		0			0
$211$	27.6495			1.90347			0.951735	−	0.306921i	$-0.0992986\pi$
$211$	27.6495			1.90347			0.951735	+	0.306921i	$0.0992986\pi$
$212$		0			0
$213$	−1.00000	−	1.73205i	−0.0685189	−	0.118678i
$214$		0			0
$215$	−0.450166	+	0.779710i	−0.0307010	+	0.0531758i
$216$		0			0
$217$	−2.63746	−	0.209313i	−0.179042	−	0.0142091i
$218$		0			0
$219$	2.13746	−	3.70219i	0.144436	−	0.250171i
$220$		0			0
$221$	−12.5498	−	21.7370i	−0.844193	−	1.46219i
$222$		0			0
$223$	−1.27492			−0.0853748			−0.0426874	−	0.999088i	$-0.513592\pi$
$223$	−1.27492			−0.0853748			−0.0426874	+	0.999088i	$0.513592\pi$
$224$		0			0
$225$	5.72508			0.381672
$226$		0			0
$227$	−5.63746	−	9.76436i	−0.374171	−	0.648084i	0.616031	−	0.787722i	$-0.288739\pi$
$227$	−5.63746	−	9.76436i	−0.374171	−	0.648084i	−0.990203	+	0.139638i	$0.955406\pi$
$228$		0			0
$229$	9.13746	−	15.8265i	0.603820	−	1.04585i	−0.388416	−	0.921484i	$-0.626978\pi$
$229$	9.13746	−	15.8265i	0.603820	−	1.04585i	0.992237	−	0.124363i	$-0.0396889\pi$
$230$		0			0
$231$	3.72508	+	7.82300i	0.245092	+	0.514716i
$232$		0			0
$233$	0.274917	−	0.476171i	0.0180104	−	0.0311950i	−0.856880	−	0.515516i	$-0.827600\pi$
$233$	0.274917	−	0.476171i	0.0180104	−	0.0311950i	0.874890	+	0.484321i	$0.160933\pi$
$234$		0			0
$235$	−9.82475	−	17.0170i	−0.640896	−	1.11006i
$236$		0			0
$237$	11.5498			0.750242
$238$		0			0
$239$	15.4502			0.999388			0.499694	−	0.866202i	$-0.333446\pi$
$239$	15.4502			0.999388			0.499694	+	0.866202i	$0.333446\pi$
$240$		0			0
$241$	−4.91238	−	8.50848i	−0.316434	−	0.548080i	0.663307	−	0.748347i	$-0.269152\pi$
$241$	−4.91238	−	8.50848i	−0.316434	−	0.548080i	−0.979741	+	0.200267i	$0.935819\pi$
$242$		0			0
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$		0			0
$245$	−22.6375	−	3.61587i	−1.44625	−	0.231010i
$246$		0			0
$247$	19.6873	−	34.0994i	1.25267	−	2.16969i
$248$		0			0
$249$	3.63746	+	6.30026i	0.230515	+	0.399263i
$250$		0			0
$251$	18.3746			1.15979			0.579897	−	0.814690i	$-0.303093\pi$
$251$	18.3746			1.15979			0.579897	+	0.814690i	$0.303093\pi$
$252$		0			0
$253$	−13.0997			−0.823569
$254$		0			0
$255$	−6.54983	−	11.3446i	−0.410167	−	0.710429i
$256$		0			0
$257$	−5.54983	+	9.61260i	−0.346189	+	0.599617i	−0.985569	−	0.169274i	$-0.945858\pi$
$257$	−5.54983	+	9.61260i	−0.346189	+	0.599617i	0.639380	+	0.768891i	$0.279191\pi$
$258$		0			0
$259$	−2.58762	−	5.43424i	−0.160787	−	0.337667i
$260$		0			0
$261$	2.63746	−	4.56821i	0.163255	−	0.282765i
$262$		0			0
$263$	4.72508	+	8.18408i	0.291361	+	0.504652i	0.974132	−	0.225980i	$-0.0725586\pi$
$263$	4.72508	+	8.18408i	0.291361	+	0.504652i	−0.682771	+	0.730633i	$0.739225\pi$
$264$		0			0
$265$	30.3746			1.86590
$266$		0			0
$267$	−10.5498			−0.645639
$268$		0			0
$269$	10.3625	+	17.9484i	0.631815	+	1.09434i	0.987180	+	0.159609i	$0.0510232\pi$
$269$	10.3625	+	17.9484i	0.631815	+	1.09434i	−0.355365	+	0.934728i	$0.615643\pi$
$270$		0			0
$271$	−0.637459	+	1.10411i	−0.0387229	+	0.0670699i	−0.884737	−	0.466090i	$-0.845662\pi$
$271$	−0.637459	+	1.10411i	−0.0387229	+	0.0670699i	0.846014	+	0.533160i	$0.178996\pi$
$272$		0			0
$273$	−16.5498	−	1.31342i	−1.00164	−	0.0794920i
$274$		0			0
$275$	9.37459	−	16.2373i	0.565309	−	0.979144i
$276$		0			0
$277$	−13.4124	−	23.2309i	−0.805872	−	1.39581i	−0.915701	−	0.401860i	$-0.868364\pi$
$277$	−13.4124	−	23.2309i	−0.805872	−	1.39581i	0.109830	−	0.993950i	$-0.464970\pi$
$278$		0			0
$279$	−1.00000			−0.0598684
$280$		0			0
$281$	−26.5498			−1.58383			−0.791915	−	0.610631i	$-0.790916\pi$
$281$	−26.5498			−1.58383			−0.791915	+	0.610631i	$0.790916\pi$
$282$		0			0
$283$	−12.9622	−	22.4512i	−0.770523	−	1.33459i	−0.937276	−	0.348587i	$-0.886662\pi$
$283$	−12.9622	−	22.4512i	−0.770523	−	1.33459i	0.166753	−	0.985999i	$-0.446672\pi$
$284$		0			0
$285$	10.2749	−	17.7967i	0.608634	−	1.05418i
$286$		0			0
$287$	6.82475	−	9.91613i	0.402852	−	0.585331i
$288$		0			0
$289$	0.500000	−	0.866025i	0.0294118	−	0.0509427i
$290$		0			0
$291$	−4.36254	−	7.55614i	−0.255737	−	0.442949i
$292$		0			0
$293$	27.8248			1.62554			0.812770	−	0.582585i	$-0.197959\pi$
$293$	27.8248			1.62554			0.812770	+	0.582585i	$0.197959\pi$
$294$		0			0
$295$	−4.17525			−0.243092
$296$		0			0
$297$	1.63746	+	2.83616i	0.0950150	+	0.164571i
$298$		0			0
$299$	12.5498	−	21.7370i	0.725776	−	1.25708i
$300$		0			0
$301$	0.412376	−	0.599168i	0.0237689	−	0.0345355i
$302$		0			0
$303$	−3.00000	+	5.19615i	−0.172345	+	0.298511i
$304$		0			0
$305$	−16.3746	−	28.3616i	−0.937606	−	1.62398i
$306$		0			0
$307$	−11.3746			−0.649182			−0.324591	−	0.945854i	$-0.605227\pi$
$307$	−11.3746			−0.649182			−0.324591	+	0.945854i	$0.605227\pi$
$308$		0			0
$309$	10.8248			0.615799
$310$		0			0
$311$	2.27492	+	3.94027i	0.128999	+	0.223432i	0.923289	−	0.384106i	$-0.125490\pi$
$311$	2.27492	+	3.94027i	0.128999	+	0.223432i	−0.794290	+	0.607539i	$0.792157\pi$
$312$		0			0
$313$	9.77492	−	16.9307i	0.552511	−	0.956977i	−0.445582	−	0.895241i	$-0.647003\pi$
$313$	9.77492	−	16.9307i	0.552511	−	0.956977i	0.998093	−	0.0617357i	$-0.0196636\pi$
$314$		0			0
$315$	−8.63746	−	0.685484i	−0.486666	−	0.0386226i
$316$		0			0
$317$	−13.9124	+	24.0969i	−0.781397	+	1.35342i	0.149731	+	0.988727i	$0.452159\pi$
$317$	−13.9124	+	24.0969i	−0.781397	+	1.35342i	−0.931128	+	0.364692i	$0.881174\pi$
$318$		0			0
$319$	−8.63746	−	14.9605i	−0.483605	−	0.837628i
$320$		0			0
$321$	15.8248			0.883252
$322$		0			0
$323$	−25.0997			−1.39658
$324$		0			0
$325$	17.9622	+	31.1115i	0.996364	+	1.72575i
$326$		0			0
$327$	8.41238	−	14.5707i	0.465205	−	0.805759i
$328$		0			0
$329$	6.82475	+	14.3326i	0.376261	+	0.790181i
$330$		0			0
$331$	0.587624	−	1.01779i	0.0322987	−	0.0559431i	−0.849424	−	0.527711i	$-0.823051\pi$
$331$	0.587624	−	1.01779i	0.0322987	−	0.0559431i	0.881723	+	0.471768i	$0.156384\pi$
$332$		0			0
$333$	−1.13746	−	1.97014i	−0.0623323	−	0.107963i
$334$		0			0
$335$	−0.900331			−0.0491903
$336$		0			0
$337$	−24.0997			−1.31279			−0.656396	−	0.754416i	$-0.727920\pi$
$337$	−24.0997			−1.31279			−0.656396	+	0.754416i	$0.727920\pi$
$338$		0			0
$339$	2.27492	+	3.94027i	0.123557	+	0.214006i
$340$		0			0
$341$	−1.63746	+	2.83616i	−0.0886734	+	0.153587i
$342$		0			0
$343$	18.0000	+	4.35890i	0.971909	+	0.235358i
$344$		0			0
$345$	6.54983	−	11.3446i	0.352631	−	0.610775i
$346$		0			0
$347$	15.0997	+	26.1534i	0.810593	+	1.40399i	0.912450	+	0.409189i	$0.134188\pi$
$347$	15.0997	+	26.1534i	0.810593	+	1.40399i	−0.101857	+	0.994799i	$0.532478\pi$
$348$		0			0
$349$	6.00000			0.321173			0.160586	−	0.987022i	$-0.448662\pi$
$349$	6.00000			0.321173			0.160586	+	0.987022i	$0.448662\pi$
$350$		0			0
$351$	−6.27492			−0.334930
$352$		0			0
$353$	10.2749	+	17.7967i	0.546879	+	0.947222i	0.998486	+	0.0550049i	$0.0175174\pi$
$353$	10.2749	+	17.7967i	0.546879	+	0.947222i	−0.451607	+	0.892217i	$0.649149\pi$
$354$		0			0
$355$	3.27492	−	5.67232i	0.173815	−	0.301056i
$356$		0			0
$357$	4.54983	+	9.55505i	0.240803	+	0.505707i
$358$		0			0
$359$	9.82475	−	17.0170i	0.518531	−	0.898121i	−0.481238	−	0.876590i	$-0.659813\pi$
$359$	9.82475	−	17.0170i	0.518531	−	0.898121i	0.999768	−	0.0215311i	$-0.00685409\pi$
$360$		0			0
$361$	−10.1873	−	17.6449i	−0.536173	−	0.928679i
$362$		0			0
$363$	−0.274917			−0.0144294
$364$		0			0
$365$	14.0000			0.732793
$366$		0			0
$367$	−11.0498	−	19.1389i	−0.576797	−	0.999041i	−0.995844	−	0.0910767i	$-0.970969\pi$
$367$	−11.0498	−	19.1389i	−0.576797	−	0.999041i	0.419047	−	0.907964i	$-0.362364\pi$
$368$		0			0
$369$	2.27492	−	3.94027i	0.118427	−	0.205122i
$370$		0			0
$371$	−24.4622	−	1.94136i	−1.27001	−	0.100791i
$372$		0			0
$373$	−3.13746	+	5.43424i	−0.162451	+	0.281374i	−0.935747	−	0.352671i	$-0.885273\pi$
$373$	−3.13746	+	5.43424i	−0.162451	+	0.281374i	0.773296	+	0.634045i	$0.218607\pi$
$374$		0			0
$375$	1.18729	+	2.05645i	0.0613115	+	0.106195i
$376$		0			0
$377$	33.0997			1.70472
$378$		0			0
$379$	−13.1752			−0.676767			−0.338384	−	0.941008i	$-0.609880\pi$
$379$	−13.1752			−0.676767			−0.338384	+	0.941008i	$0.609880\pi$
$380$		0			0
$381$	3.22508	+	5.58601i	0.165226	+	0.286180i
$382$		0			0
$383$	−5.27492	+	9.13642i	−0.269536	+	0.466849i	−0.968742	−	0.248070i	$-0.920204\pi$
$383$	−5.27492	+	9.13642i	−0.269536	+	0.466849i	0.699206	+	0.714920i	$0.253537\pi$
$384$		0			0
$385$	−16.0876	+	23.3748i	−0.819901	+	1.19129i
$386$		0			0
$387$	0.137459	−	0.238085i	0.00698741	−	0.0121026i
$388$		0			0
$389$	−1.00000	−	1.73205i	−0.0507020	−	0.0878185i	0.839561	−	0.543266i	$-0.182813\pi$
$389$	−1.00000	−	1.73205i	−0.0507020	−	0.0878185i	−0.890263	+	0.455448i	$0.849479\pi$
$390$		0			0
$391$	−16.0000			−0.809155
$392$		0			0
$393$	−7.27492			−0.366971
$394$		0			0
$395$	18.9124	+	32.7572i	0.951585	+	1.64819i
$396$		0			0
$397$	−1.68729	+	2.92248i	−0.0846828	+	0.146675i	−0.905256	−	0.424867i	$-0.860321\pi$
$397$	−1.68729	+	2.92248i	−0.0846828	+	0.146675i	0.820573	+	0.571541i	$0.193654\pi$
$398$		0			0
$399$	−9.41238	+	13.6759i	−0.471208	+	0.684650i
$400$		0			0
$401$	−12.0000	+	20.7846i	−0.599251	+	1.03793i	0.393680	+	0.919247i	$0.371202\pi$
$401$	−12.0000	+	20.7846i	−0.599251	+	1.03793i	−0.992932	+	0.118686i	$0.962132\pi$
$402$		0			0
$403$	−3.13746	−	5.43424i	−0.156288	−	0.270699i
$404$		0			0
$405$	−3.27492			−0.162732
$406$		0			0
$407$	−7.45017			−0.369291
$408$		0			0
$409$	−5.22508	−	9.05011i	−0.258364	−	0.447499i	0.707440	−	0.706773i	$-0.249850\pi$
$409$	−5.22508	−	9.05011i	−0.258364	−	0.447499i	−0.965804	+	0.259274i	$0.916517\pi$
$410$		0			0
$411$	−0.725083	+	1.25588i	−0.0357657	+	0.0619480i
$412$		0			0
$413$	3.36254	+	0.266857i	0.165460	+	0.0131312i
$414$		0			0
$415$	−11.9124	+	20.6328i	−0.584756	+	1.01283i
$416$		0			0
$417$	4.13746	+	7.16629i	0.202612	+	0.350935i
$418$		0			0
$419$	−28.5498			−1.39475			−0.697375	−	0.716706i	$-0.745649\pi$
$419$	−28.5498			−1.39475			−0.697375	+	0.716706i	$0.745649\pi$
$420$		0			0
$421$	−8.82475			−0.430092			−0.215046	−	0.976604i	$-0.568990\pi$
$421$	−8.82475			−0.430092			−0.215046	+	0.976604i	$0.568990\pi$
$422$		0			0
$423$	3.00000	+	5.19615i	0.145865	+	0.252646i
$424$		0			0
$425$	11.4502	−	19.8323i	0.555415	−	0.962006i
$426$		0			0
$427$	11.3746	+	23.8876i	0.550455	+	1.15600i
$428$		0			0
$429$	−10.2749	+	17.7967i	−0.496078	+	0.859232i
$430$		0			0
$431$	8.82475	+	15.2849i	0.425073	+	0.736249i	0.996427	−	0.0844552i	$-0.0269150\pi$
$431$	8.82475	+	15.2849i	0.425073	+	0.736249i	−0.571354	+	0.820704i	$0.693582\pi$
$432$		0			0
$433$	3.17525			0.152593			0.0762963	−	0.997085i	$-0.475690\pi$
$433$	3.17525			0.152593			0.0762963	+	0.997085i	$0.475690\pi$
$434$		0			0
$435$	17.2749			0.828269
$436$		0			0
$437$	−12.5498	−	21.7370i	−0.600340	−	1.03982i
$438$		0			0
$439$	−8.63746	+	14.9605i	−0.412243	+	0.714027i	−0.995135	−	0.0985236i	$-0.968588\pi$
$439$	−8.63746	+	14.9605i	−0.412243	+	0.714027i	0.582891	+	0.812550i	$0.301921\pi$
$440$		0			0
$441$	6.91238	+	1.10411i	0.329161	+	0.0525767i
$442$		0			0
$443$	−3.18729	+	5.52055i	−0.151433	+	0.262289i	−0.931754	−	0.363089i	$-0.881722\pi$
$443$	−3.18729	+	5.52055i	−0.151433	+	0.262289i	0.780322	+	0.625378i	$0.215055\pi$
$444$		0			0
$445$	−17.2749	−	29.9210i	−0.818910	−	1.41839i
$446$		0			0
$447$	14.5498			0.688184
$448$		0			0
$449$	20.5498			0.969807			0.484903	−	0.874568i	$-0.338855\pi$
$449$	20.5498			0.969807			0.484903	+	0.874568i	$0.338855\pi$
$450$		0			0
$451$	−7.45017	−	12.9041i	−0.350815	−	0.607629i
$452$		0			0
$453$	−11.1873	+	19.3770i	−0.525625	+	0.910409i
$454$		0			0
$455$	−23.3746	−	49.0887i	−1.09582	−	2.30131i
$456$		0			0
$457$	−18.3248	+	31.7394i	−0.857196	+	1.48471i	0.0173972	+	0.999849i	$0.494462\pi$
$457$	−18.3248	+	31.7394i	−0.857196	+	1.48471i	−0.874593	+	0.484858i	$0.838871\pi$
$458$		0			0
$459$	2.00000	+	3.46410i	0.0933520	+	0.161690i
$460$		0			0
$461$	3.64950			0.169974			0.0849872	−	0.996382i	$-0.472915\pi$
$461$	3.64950			0.169974			0.0849872	+	0.996382i	$0.472915\pi$
$462$		0			0
$463$	13.1752			0.612306			0.306153	−	0.951982i	$-0.400958\pi$
$463$	13.1752			0.612306			0.306153	+	0.951982i	$0.400958\pi$
$464$		0			0
$465$	−1.63746	−	2.83616i	−0.0759353	−	0.131524i
$466$		0			0
$467$	20.2749	−	35.1172i	0.938211	−	1.62503i	0.169406	−	0.985546i	$-0.445815\pi$
$467$	20.2749	−	35.1172i	0.938211	−	1.62503i	0.768805	−	0.639483i	$-0.220852\pi$
$468$		0			0
$469$	0.725083	+	0.0575438i	0.0334812	+	0.00265713i
$470$		0			0
$471$	−0.274917	+	0.476171i	−0.0126675	+	0.0219408i
$472$		0			0
$473$	−0.450166	−	0.779710i	−0.0206986	−	0.0358511i
$474$		0			0
$475$	35.9244			1.64833
$476$		0			0
$477$	−9.27492			−0.424669
$478$		0			0
$479$	2.72508	+	4.71998i	0.124512	+	0.215661i	0.921542	−	0.388278i	$-0.126930\pi$
$479$	2.72508	+	4.71998i	0.124512	+	0.215661i	−0.797030	+	0.603940i	$0.793597\pi$
$480$		0			0
$481$	7.13746	−	12.3624i	0.325440	−	0.563679i
$482$		0			0
$483$	−6.00000	+	8.71780i	−0.273009	+	0.396674i
$484$		0			0
$485$	14.2870	−	24.7457i	0.648738	−	1.12365i
$486$		0			0
$487$	−0.500000	−	0.866025i	−0.0226572	−	0.0392434i	0.854475	−	0.519493i	$-0.173879\pi$
$487$	−0.500000	−	0.866025i	−0.0226572	−	0.0392434i	−0.877132	+	0.480250i	$0.840546\pi$
$488$		0			0
$489$	12.0000			0.542659
$490$		0			0
$491$	−36.9244			−1.66638			−0.833188	−	0.552990i	$-0.813487\pi$
$491$	−36.9244			−1.66638			−0.833188	+	0.552990i	$0.813487\pi$
$492$		0			0
$493$	−10.5498	−	18.2728i	−0.475141	−	0.822968i
$494$		0			0
$495$	−5.36254	+	9.28819i	−0.241028	+	0.417473i
$496$		0			0
$497$	−3.00000	+	4.35890i	−0.134568	+	0.195523i
$498$		0			0
$499$	16.1375	−	27.9509i	0.722412	−	1.25125i	−0.237619	−	0.971359i	$-0.576367\pi$
$499$	16.1375	−	27.9509i	0.722412	−	1.25125i	0.960030	−	0.279896i	$-0.0902998\pi$
$500$		0			0
$501$	3.00000	+	5.19615i	0.134030	+	0.232147i
$502$		0			0
$503$	−37.6495			−1.67871			−0.839354	−	0.543585i	$-0.817067\pi$
$503$	−37.6495			−1.67871			−0.839354	+	0.543585i	$0.817067\pi$
$504$		0			0
$505$	−19.6495			−0.874391
$506$		0			0
$507$	−13.1873	−	22.8411i	−0.585668	−	1.01441i
$508$		0			0
$509$	−5.63746	+	9.76436i	−0.249876	+	0.432798i	−0.963491	−	0.267740i	$-0.913723\pi$
$509$	−5.63746	+	9.76436i	−0.249876	+	0.432798i	0.713615	+	0.700538i	$0.247057\pi$
$510$		0			0
$511$	−11.2749	−	0.894797i	−0.498773	−	0.0395835i
$512$		0			0
$513$	−3.13746	+	5.43424i	−0.138522	+	0.239927i
$514$		0			0
$515$	17.7251	+	30.7007i	0.781060	+	1.35284i
$516$		0			0
$517$	19.6495			0.864184
$518$		0			0
$519$	22.5498			0.989828
$520$		0			0
$521$	7.27492	+	12.6005i	0.318720	+	0.552039i	0.980221	−	0.197905i	$-0.0634137\pi$
$521$	7.27492	+	12.6005i	0.318720	+	0.552039i	−0.661501	+	0.749944i	$0.730080\pi$
$522$		0			0
$523$	−8.86254	+	15.3504i	−0.387532	+	0.671225i	−0.992117	−	0.125316i	$-0.960006\pi$
$523$	−8.86254	+	15.3504i	−0.387532	+	0.671225i	0.604585	+	0.796541i	$0.293339\pi$
$524$		0			0
$525$	−6.51204	−	13.6759i	−0.284209	−	0.596864i
$526$		0			0
$527$	−2.00000	+	3.46410i	−0.0871214	+	0.150899i
$528$		0			0
$529$	3.50000	+	6.06218i	0.152174	+	0.263573i
$530$		0			0
$531$	1.27492			0.0553267
$532$		0			0
$533$	28.5498			1.23663
$534$		0			0
$535$	25.9124	+	44.8816i	1.12029	+	1.94040i
$536$		0			0
$537$	−8.27492	+	14.3326i	−0.357089	+	0.618496i
$538$		0			0
$539$	14.4502	−	17.7967i	0.622413	−	0.766557i
$540$		0			0
$541$	−4.13746	+	7.16629i	−0.177883	+	0.308103i	−0.941155	−	0.337974i	$-0.890258\pi$
$541$	−4.13746	+	7.16629i	−0.177883	+	0.308103i	0.763272	+	0.646077i	$0.223592\pi$
$542$		0			0
$543$	−9.41238	−	16.3027i	−0.403924	−	0.699616i
$544$		0			0
$545$	55.0997			2.36021
$546$		0			0
$547$	28.0000			1.19719			0.598597	−	0.801050i	$-0.295725\pi$
$547$	28.0000			1.19719			0.598597	+	0.801050i	$0.295725\pi$
$548$		0			0
$549$	5.00000	+	8.66025i	0.213395	+	0.369611i
$550$		0			0
$551$	16.5498	−	28.6652i	0.705047	−	1.22118i
$552$		0			0
$553$	−13.1375	−	27.5898i	−0.558662	−	1.17324i
$554$		0			0
$555$	3.72508	−	6.45203i	0.158121	−	0.273874i
$556$		0			0
$557$	−14.9124	−	25.8290i	−0.631858	−	1.09441i	−0.987172	−	0.159663i	$-0.948959\pi$
$557$	−14.9124	−	25.8290i	−0.631858	−	1.09441i	0.355314	−	0.934747i	$-0.384374\pi$
$558$		0			0
$559$	1.72508			0.0729632
$560$		0			0
$561$	13.0997			0.553068
$562$		0			0
$563$	7.63746	+	13.2285i	0.321881	+	0.557513i	0.980876	−	0.194633i	$-0.0623517\pi$
$563$	7.63746	+	13.2285i	0.321881	+	0.557513i	−0.658996	+	0.752147i	$0.729018\pi$
$564$		0			0
$565$	−7.45017	+	12.9041i	−0.313431	+	0.542878i
$566$		0			0
$567$	2.63746	+	0.209313i	0.110763	+	0.00879034i
$568$		0			0
$569$	−5.72508	+	9.91613i	−0.240008	+	0.415706i	−0.960716	−	0.277532i	$-0.910483\pi$
$569$	−5.72508	+	9.91613i	−0.240008	+	0.415706i	0.720708	+	0.693238i	$0.243817\pi$
$570$		0			0
$571$	4.13746	+	7.16629i	0.173147	+	0.299900i	0.939519	−	0.342498i	$-0.111273\pi$
$571$	4.13746	+	7.16629i	0.173147	+	0.299900i	−0.766371	+	0.642398i	$0.777940\pi$
$572$		0			0
$573$	4.54983			0.190072
$574$		0			0
$575$	22.9003			0.955010
$576$		0			0
$577$	12.5000	+	21.6506i	0.520382	+	0.901328i	0.999719	+	0.0236970i	$0.00754370\pi$
$577$	12.5000	+	21.6506i	0.520382	+	0.901328i	−0.479337	+	0.877631i	$0.659123\pi$
$578$		0			0
$579$	−0.225083	+	0.389855i	−0.00935412	+	0.0162018i
$580$		0			0
$581$	10.9124	−	15.8553i	0.452722	−	0.657789i
$582$		0			0
$583$	−15.1873	+	26.3052i	−0.628993	+	1.08945i
$584$		0			0
$585$	−10.2749	−	17.7967i	−0.424816	−	0.735802i
$586$		0			0
$587$	−9.27492			−0.382817			−0.191408	−	0.981510i	$-0.561305\pi$
$587$	−9.27492			−0.382817			−0.191408	+	0.981510i	$0.561305\pi$
$588$		0			0
$589$	−6.27492			−0.258553
$590$		0			0
$591$	−0.725083	−	1.25588i	−0.0298259	−	0.0516600i
$592$		0			0
$593$	0.274917	−	0.476171i	0.0112895	−	0.0195540i	−0.860325	−	0.509745i	$-0.829740\pi$
$593$	0.274917	−	0.476171i	0.0112895	−	0.0195540i	0.871615	+	0.490191i	$0.163073\pi$
$594$		0			0
$595$	−19.6495	+	28.5501i	−0.805551	+	1.17044i
$596$		0			0
$597$	2.54983	−	4.41644i	0.104358	−	0.180753i
$598$		0			0
$599$	−11.2749	−	19.5287i	−0.460681	−	0.797922i	0.538314	−	0.842744i	$-0.319061\pi$
$599$	−11.2749	−	19.5287i	−0.460681	−	0.797922i	−0.998995	+	0.0448219i	$0.985728\pi$
$600$		0			0
$601$	4.09967			0.167229			0.0836145	−	0.996498i	$-0.473354\pi$
$601$	4.09967			0.167229			0.0836145	+	0.996498i	$0.473354\pi$
$602$		0			0
$603$	0.274917			0.0111955
$604$		0			0
$605$	−0.450166	−	0.779710i	−0.0183018	−	0.0316997i
$606$		0			0
$607$	3.50000	−	6.06218i	0.142061	−	0.246056i	−0.786212	−	0.617957i	$-0.787961\pi$
$607$	3.50000	−	6.06218i	0.142061	−	0.246056i	0.928272	+	0.371901i	$0.121294\pi$
$608$		0			0
$609$	−13.9124	−	1.10411i	−0.563758	−	0.0447408i
$610$		0			0
$611$	−18.8248	+	32.6054i	−0.761568	+	1.31907i
$612$		0			0
$613$	−4.27492	−	7.40437i	−0.172662	−	0.299060i	0.766688	−	0.642020i	$-0.221904\pi$
$613$	−4.27492	−	7.40437i	−0.172662	−	0.299060i	−0.939350	+	0.342961i	$0.888570\pi$
$614$		0			0
$615$	14.9003			0.600839
$616$		0			0
$617$	−6.00000			−0.241551			−0.120775	−	0.992680i	$-0.538538\pi$
$617$	−6.00000			−0.241551			−0.120775	+	0.992680i	$0.538538\pi$
$618$		0			0
$619$	14.4124	+	24.9630i	0.579282	+	1.00335i	0.995562	+	0.0941097i	$0.0300004\pi$
$619$	14.4124	+	24.9630i	0.579282	+	1.00335i	−0.416280	+	0.909237i	$0.636666\pi$
$620$		0			0
$621$	−2.00000	+	3.46410i	−0.0802572	+	0.139010i
$622$		0			0
$623$	12.0000	+	25.2011i	0.480770	+	1.00966i
$624$		0			0
$625$	10.4244	−	18.0556i	0.416977	−	0.722225i
$626$		0			0
$627$	10.2749	+	17.7967i	0.410341	+	0.710731i
$628$		0			0
$629$	−9.09967			−0.362828
$630$		0			0
$631$	19.8248			0.789211			0.394605	−	0.918851i	$-0.370881\pi$
$631$	19.8248			0.789211			0.394605	+	0.918851i	$0.370881\pi$
$632$		0			0
$633$	−13.8248	−	23.9452i	−0.549485	−	0.951735i
$634$		0			0
$635$	−10.5619	+	18.2937i	−0.419135	+	0.725964i
$636$		0			0
$637$	15.6873	+	41.0276i	0.621553	+	1.62557i
$638$		0			0
$639$	−1.00000	+	1.73205i	−0.0395594	+	0.0685189i
$640$		0			0
$641$	1.82475	+	3.16056i	0.0720734	+	0.124835i	0.899810	−	0.436282i	$-0.143705\pi$
$641$	1.82475	+	3.16056i	0.0720734	+	0.124835i	−0.827736	+	0.561117i	$0.810372\pi$
$642$		0			0
$643$	−5.37459			−0.211953			−0.105976	−	0.994369i	$-0.533797\pi$
$643$	−5.37459			−0.211953			−0.105976	+	0.994369i	$0.533797\pi$
$644$		0			0
$645$	0.900331			0.0354505
$646$		0			0
$647$	17.0000	+	29.4449i	0.668339	+	1.15760i	0.978368	+	0.206870i	$0.0663277\pi$
$647$	17.0000	+	29.4449i	0.668339	+	1.15760i	−0.310029	+	0.950727i	$0.600339\pi$
$648$		0			0
$649$	2.08762	−	3.61587i	0.0819464	−	0.141935i
$650$		0			0
$651$	1.13746	+	2.38876i	0.0445805	+	0.0936230i
$652$		0			0
$653$	−3.46221	+	5.99672i	−0.135487	+	0.234670i	−0.925783	−	0.378055i	$-0.876593\pi$
$653$	−3.46221	+	5.99672i	−0.135487	+	0.234670i	0.790297	+	0.612725i	$0.209926\pi$
$654$		0			0
$655$	−11.9124	−	20.6328i	−0.465455	−	0.806192i
$656$		0			0
$657$	−4.27492			−0.166780
$658$		0			0
$659$	42.1993			1.64385			0.821926	−	0.569594i	$-0.192899\pi$
$659$	42.1993			1.64385			0.821926	+	0.569594i	$0.192899\pi$
$660$		0			0
$661$	3.58762	+	6.21395i	0.139542	+	0.241695i	0.927323	−	0.374261i	$-0.122104\pi$
$661$	3.58762	+	6.21395i	0.139542	+	0.241695i	−0.787781	+	0.615955i	$0.788770\pi$
$662$		0			0
$663$	−12.5498	+	21.7370i	−0.487395	+	0.844193i
$664$		0			0
$665$	−54.1993	−	4.30136i	−2.10176	−	0.166799i
$666$		0			0
$667$	10.5498	−	18.2728i	0.408491	−	0.707528i
$668$		0			0
$669$	0.637459	+	1.10411i	0.0246456	+	0.0426874i
$670$		0			0
$671$	32.7492			1.26427
$672$		0			0
$673$	41.5498			1.60163			0.800814	−	0.598913i	$-0.204400\pi$
$673$	41.5498			1.60163			0.800814	+	0.598913i	$0.204400\pi$
$674$		0			0
$675$	−2.86254	−	4.95807i	−0.110179	−	0.190836i
$676$		0			0
$677$	−6.63746	+	11.4964i	−0.255098	+	0.441843i	−0.964922	−	0.262536i	$-0.915441\pi$
$677$	−6.63746	+	11.4964i	−0.255098	+	0.441843i	0.709824	+	0.704379i	$0.248774\pi$
$678$		0			0
$679$	−13.0876	+	19.0159i	−0.502257	+	0.729762i
$680$		0			0
$681$	−5.63746	+	9.76436i	−0.216028	+	0.374171i
$682$		0			0
$683$	6.08762	+	10.5441i	0.232936	+	0.403458i	0.958671	−	0.284517i	$-0.0918332\pi$
$683$	6.08762	+	10.5441i	0.232936	+	0.403458i	−0.725735	+	0.687975i	$0.758500\pi$
$684$		0			0
$685$	−4.74917			−0.181457
$686$		0			0
$687$	−18.2749			−0.697232
$688$		0			0
$689$	−29.0997	−	50.4021i	−1.10861	−	1.92017i
$690$		0			0
$691$	−5.41238	+	9.37451i	−0.205896	+	0.356623i	−0.950418	−	0.310975i	$-0.899344\pi$
$691$	−5.41238	+	9.37451i	−0.205896	+	0.356623i	0.744522	+	0.667598i	$0.232678\pi$
$692$		0			0
$693$	4.91238	−	7.13752i	0.186606	−	0.271132i
$694$		0			0
$695$	−13.5498	+	23.4690i	−0.513975	+	0.890230i
$696$		0			0
$697$	−9.09967	−	15.7611i	−0.344675	−	0.596994i
$698$		0			0
$699$	−0.549834			−0.0207966
$700$		0			0
$701$	12.9244			0.488149			0.244074	−	0.969757i	$-0.421516\pi$
$701$	12.9244			0.488149			0.244074	+	0.969757i	$0.421516\pi$
$702$		0			0
$703$	−7.13746	−	12.3624i	−0.269194	−	0.466258i
$704$		0			0
$705$	−9.82475	+	17.0170i	−0.370022	+	0.640896i
$706$		0			0
$707$	15.8248	+	1.25588i	0.595151	+	0.0472322i
$708$		0			0
$709$	−14.0997	+	24.4213i	−0.529524	+	0.917163i	0.469883	+	0.882729i	$0.344296\pi$
$709$	−14.0997	+	24.4213i	−0.529524	+	0.917163i	−0.999407	+	0.0344340i	$0.989037\pi$
$710$		0			0
$711$	−5.77492	−	10.0025i	−0.216576	−	0.375121i
$712$		0			0
$713$	−4.00000			−0.149801
$714$		0			0
$715$	−67.2990			−2.51684
$716$		0			0
$717$	−7.72508	−	13.3802i	−0.288499	−	0.499694i
$718$		0			0
$719$	−14.0997	+	24.4213i	−0.525829	+	0.910762i	0.473718	+	0.880676i	$0.342911\pi$
$719$	−14.0997	+	24.4213i	−0.525829	+	0.910762i	−0.999547	+	0.0300860i	$0.990422\pi$
$720$		0			0
$721$	−12.3127	−	25.8578i	−0.458549	−	0.962993i
$722$		0			0
$723$	−4.91238	+	8.50848i	−0.182693	+	0.316434i
$724$		0			0
$725$	15.0997	+	26.1534i	0.560788	+	0.971313i
$726$		0			0
$727$	31.5498			1.17012			0.585059	−	0.810991i	$-0.301071\pi$
$727$	31.5498			1.17012			0.585059	+	0.810991i	$0.301071\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−0.549834	−	0.952341i	−0.0203364	−	0.0352236i
$732$		0			0
$733$	2.96221	−	5.13070i	0.109412	−	0.189507i	−0.806120	−	0.591752i	$-0.798437\pi$
$733$	2.96221	−	5.13070i	0.109412	−	0.189507i	0.915532	+	0.402245i	$0.131770\pi$
$734$		0			0
$735$	8.18729	+	21.4125i	0.301993	+	0.789814i
$736$		0			0
$737$	0.450166	−	0.779710i	0.0165821	−	0.0287210i
$738$		0			0
$739$	0.687293	+	1.19043i	0.0252825	+	0.0437905i	0.878390	−	0.477945i	$-0.158618\pi$
$739$	0.687293	+	1.19043i	0.0252825	+	0.0437905i	−0.853107	+	0.521735i	$0.825285\pi$
$740$		0			0
$741$	−39.3746			−1.44646
$742$		0			0
$743$	−44.1993			−1.62152			−0.810758	−	0.585381i	$-0.800945\pi$
$743$	−44.1993			−1.62152			−0.810758	+	0.585381i	$0.800945\pi$
$744$		0			0
$745$	23.8248	+	41.2657i	0.872871	+	1.51186i
$746$		0			0
$747$	3.63746	−	6.30026i	0.133088	−	0.230515i
$748$		0			0
$749$	−18.0000	−	37.8016i	−0.657706	−	1.38124i
$750$		0			0
$751$	5.22508	−	9.05011i	0.190666	−	0.330243i	−0.754805	−	0.655949i	$-0.772269\pi$
$751$	5.22508	−	9.05011i	0.190666	−	0.330243i	0.945471	+	0.325706i	$0.105602\pi$
$752$		0			0
$753$	−9.18729	−	15.9129i	−0.334804	−	0.579897i
$754$		0			0
$755$	−73.2749			−2.66675
$756$		0			0
$757$	22.0000			0.799604			0.399802	−	0.916602i	$-0.369079\pi$
$757$	22.0000			0.799604			0.399802	+	0.916602i	$0.369079\pi$
$758$		0			0
$759$	6.54983	+	11.3446i	0.237744	+	0.411785i
$760$		0			0
$761$	12.5498	−	21.7370i	0.454931	−	0.787964i	−0.543753	−	0.839245i	$-0.682997\pi$
$761$	12.5498	−	21.7370i	0.454931	−	0.787964i	0.998684	+	0.0512814i	$0.0163305\pi$
$762$		0			0
$763$	−44.3746	−	3.52165i	−1.60647	−	0.127492i
$764$		0			0
$765$	−6.54983	+	11.3446i	−0.236810	+	0.410167i
$766$		0			0
$767$	4.00000	+	6.92820i	0.144432	+	0.250163i
$768$		0			0
$769$	−32.6495			−1.17737			−0.588686	−	0.808362i	$-0.700354\pi$
$769$	−32.6495			−1.17737			−0.588686	+	0.808362i	$0.700354\pi$
$770$		0			0
$771$	11.0997			0.399745
$772$		0			0
$773$	1.54983	+	2.68439i	0.0557437	+	0.0965509i	0.892551	−	0.450947i	$-0.148914\pi$
$773$	1.54983	+	2.68439i	0.0557437	+	0.0965509i	−0.836807	+	0.547498i	$0.815580\pi$
$774$		0			0
$775$	2.86254	−	4.95807i	0.102826	−	0.178099i
$776$		0			0
$777$	−3.41238	+	4.95807i	−0.122418	+	0.177870i
$778$		0			0
$779$	14.2749	−	24.7249i	0.511452	−	0.885861i
$780$		0			0
$781$	3.27492	+	5.67232i	0.117186	+	0.202972i
$782$		0			0
$783$	−5.27492			−0.188510
$784$		0			0
$785$	−1.80066			−0.0642684
$786$		0			0
$787$	1.27492	+	2.20822i	0.0454459	+	0.0787146i	0.887854	−	0.460126i	$-0.152196\pi$
$787$	1.27492	+	2.20822i	0.0454459	+	0.0787146i	−0.842408	+	0.538841i	$0.818862\pi$
$788$		0			0
$789$	4.72508	−	8.18408i	0.168217	−	0.291361i
$790$		0			0
$791$	6.82475	−	9.91613i	0.242660	−	0.352577i
$792$		0			0
$793$	−31.3746	+	54.3424i	−1.11414	+	1.92975i
$794$		0			0
$795$	−15.1873	−	26.3052i	−0.538638	−	0.932948i
$796$		0			0
$797$	31.4743			1.11488			0.557438	−	0.830219i	$-0.311785\pi$
$797$	31.4743			1.11488			0.557438	+	0.830219i	$0.311785\pi$
$798$		0			0
$799$	24.0000			0.849059
$800$		0			0
$801$	5.27492	+	9.13642i	0.186380	+	0.322820i
$802$		0			0
$803$	−7.00000	+	12.1244i	−0.247025	+	0.427859i
$804$		0			0
$805$	−34.5498	−	2.74194i	−1.21772	−	0.0966405i
$806$		0			0
$807$	10.3625	−	17.9484i	0.364779	−	0.631815i
$808$		0			0
$809$	14.8248	+	25.6772i	0.521211	+	0.902763i	0.999696	+	0.0246675i	$0.00785270\pi$
$809$	14.8248	+	25.6772i	0.521211	+	0.902763i	−0.478485	+	0.878096i	$0.658814\pi$
$810$		0			0
$811$	42.5498			1.49413			0.747063	−	0.664753i	$-0.231463\pi$
$811$	42.5498			1.49413			0.747063	+	0.664753i	$0.231463\pi$
$812$		0			0
$813$	1.27492			0.0447133
$814$		0			0
$815$	19.6495	+	34.0339i	0.688292	+	1.19216i
$816$		0			0
$817$	0.862541	−	1.49397i	0.0301765	−	0.0522672i
$818$		0			0
$819$	7.13746	+	14.9893i	0.249403	+	0.523768i
$820$		0			0
$821$	6.36254	−	11.0202i	0.222054	−	0.384609i	−0.733377	−	0.679822i	$-0.762057\pi$
$821$	6.36254	−	11.0202i	0.222054	−	0.384609i	0.955432	+	0.295213i	$0.0953905\pi$
$822$		0			0
$823$	17.0997	+	29.6175i	0.596057	+	1.03240i	0.993397	+	0.114729i	$0.0366001\pi$
$823$	17.0997	+	29.6175i	0.596057	+	1.03240i	−0.397340	+	0.917672i	$0.630067\pi$
$824$		0			0
$825$	−18.7492			−0.652762
$826$		0			0
$827$	44.0241			1.53087			0.765434	−	0.643515i	$-0.222524\pi$
$827$	44.0241			1.53087			0.765434	+	0.643515i	$0.222524\pi$
$828$		0			0
$829$	15.1375	+	26.2188i	0.525746	+	0.910618i	0.999550	+	0.0299882i	$0.00954697\pi$
$829$	15.1375	+	26.2188i	0.525746	+	0.910618i	−0.473805	+	0.880630i	$0.657120\pi$
$830$		0			0
$831$	−13.4124	+	23.2309i	−0.465270	+	0.805872i
$832$		0			0
$833$	17.6495	−	21.7370i	0.611519	−	0.753141i
$834$		0			0
$835$	−9.82475	+	17.0170i	−0.340000	+	0.588896i
$836$		0			0
$837$	0.500000	+	0.866025i	0.0172825	+	0.0299342i
$838$		0			0
$839$	−30.1993			−1.04260			−0.521298	−	0.853374i	$-0.674552\pi$
$839$	−30.1993			−1.04260			−0.521298	+	0.853374i	$0.674552\pi$
$840$		0			0
$841$	−1.17525			−0.0405258
$842$		0			0
$843$	13.2749	+	22.9928i	0.457212	+	0.791915i
$844$		0			0
$845$	43.1873	−	74.8026i	1.48569	−	2.57329i
$846$		0			0
$847$	0.312707	+	0.656712i	0.0107447	+	0.0225649i
$848$		0			0
$849$	−12.9622	+	22.4512i	−0.444862	+	0.770523i
$850$		0			0
$851$	−4.54983	−	7.88054i	−0.155966	−	0.270142i
$852$		0			0
$853$	−13.3746			−0.457937			−0.228969	−	0.973434i	$-0.573535\pi$
$853$	−13.3746			−0.457937			−0.228969	+	0.973434i	$0.573535\pi$
$854$		0			0
$855$	−20.5498			−0.702790
$856$		0			0
$857$	6.72508	+	11.6482i	0.229724	+	0.397894i	0.957726	−	0.287681i	$-0.0928842\pi$
$857$	6.72508	+	11.6482i	0.229724	+	0.397894i	−0.728002	+	0.685575i	$0.759551\pi$
$858$		0			0
$859$	−27.8248	+	48.1939i	−0.949368	+	1.64435i	−0.202609	+	0.979260i	$0.564942\pi$
$859$	−27.8248	+	48.1939i	−0.949368	+	1.64435i	−0.746759	+	0.665094i	$0.768391\pi$
$860$		0			0
$861$	−12.0000	−	0.952341i	−0.408959	−	0.0324557i
$862$		0			0
$863$	−9.54983	+	16.5408i	−0.325080	+	0.563055i	−0.981529	−	0.191316i	$-0.938725\pi$
$863$	−9.54983	+	16.5408i	−0.325080	+	0.563055i	0.656448	+	0.754371i	$0.272058\pi$
$864$		0			0
$865$	36.9244	+	63.9550i	1.25547	+	2.17453i
$866$		0			0
$867$	−1.00000			−0.0339618
$868$		0			0
$869$	−37.8248			−1.28312
$870$		0			0
$871$	0.862541	+	1.49397i	0.0292261	+	0.0506211i
$872$		0			0
$873$	−4.36254	+	7.55614i	−0.147650	+	0.255737i
$874$		0			0
$875$	3.56188	−	5.17529i	0.120413	−	0.174957i
$876$		0			0
$877$	23.3746	−	40.4860i	0.789304	−	1.36711i	−0.137090	−	0.990559i	$-0.543775\pi$
$877$	23.3746	−	40.4860i	0.789304	−	1.36711i	0.926394	−	0.376556i	$-0.122892\pi$
$878$		0			0
$879$	−13.9124	−	24.0969i	−0.469253	−	0.812770i
$880$		0			0
$881$	9.45017			0.318384			0.159192	−	0.987248i	$-0.449111\pi$
$881$	9.45017			0.318384			0.159192	+	0.987248i	$0.449111\pi$
$882$		0			0
$883$	−7.37459			−0.248175			−0.124087	−	0.992271i	$-0.539600\pi$
$883$	−7.37459			−0.248175			−0.124087	+	0.992271i	$0.539600\pi$
$884$		0			0
$885$	2.08762	+	3.61587i	0.0701747	+	0.121546i
$886$		0			0
$887$	−16.8248	+	29.1413i	−0.564920	+	0.978470i	0.432137	+	0.901808i	$0.357760\pi$
$887$	−16.8248	+	29.1413i	−0.564920	+	0.978470i	−0.997057	+	0.0766621i	$0.975574\pi$
$888$		0			0
$889$	9.67525	−	14.0578i	0.324497	−	0.471484i
$890$		0			0
$891$	1.63746	−	2.83616i	0.0548569	−	0.0950150i
$892$		0			0
$893$	18.8248	+	32.6054i	0.629946	+	1.09110i
$894$		0			0
$895$	−54.1993			−1.81168
$896$		0			0
$897$	−25.0997			−0.838054
$898$		0			0
$899$	−2.63746	−	4.56821i	−0.0879642	−	0.152358i
$900$		0			0
$901$	−18.5498	+	32.1293i	−0.617985	+	1.07038i
$902$		0			0
$903$	−0.725083	−	0.0575438i	−0.0241292	−	0.00191494i
$904$		0			0
$905$	30.8248	−	53.3900i	1.02465	−	1.77474i
$906$		0			0
$907$	−14.8625	−	25.7427i	−0.493503	−	0.854772i	0.506469	−	0.862258i	$-0.330950\pi$
$907$	−14.8625	−	25.7427i	−0.493503	−	0.854772i	−0.999972	+	0.00748639i	$0.997617\pi$
$908$		0			0
$909$	6.00000			0.199007
$910$		0			0
$911$	53.8488			1.78409			0.892046	−	0.451945i	$-0.149270\pi$
$911$	53.8488			1.78409			0.892046	+	0.451945i	$0.149270\pi$
$912$		0			0
$913$	−11.9124	−	20.6328i	−0.394242	−	0.682847i
$914$		0			0
$915$	−16.3746	+	28.3616i	−0.541327	+	0.937606i
$916$		0			0
$917$	8.27492	+	17.3781i	0.273262	+	0.573874i
$918$		0			0
$919$	1.41238	−	2.44631i	0.0465900	−	0.0806962i	−0.841790	−	0.539805i	$-0.818498\pi$
$919$	1.41238	−	2.44631i	0.0465900	−	0.0806962i	0.888380	+	0.459109i	$0.151831\pi$
$920$		0			0
$921$	5.68729	+	9.85068i	0.187403	+	0.324591i
$922$		0			0
$923$	−12.5498			−0.413083
$924$		0			0
$925$	13.0241			0.428229
$926$		0			0
$927$	−5.41238	−	9.37451i	−0.177766	−	0.307899i
$928$		0			0
$929$	20.0997	−	34.8136i	0.659449	−	1.14220i	−0.321310	−	0.946974i	$-0.604123\pi$
$929$	20.0997	−	34.8136i	0.659449	−	1.14220i	0.980759	−	0.195225i	$-0.0625436\pi$
$930$		0			0
$931$	43.3746	+	6.92820i	1.42154	+	0.227063i
$932$		0			0
$933$	2.27492	−	3.94027i	0.0744774	−	0.128999i
$934$		0			0
$935$	21.4502	+	37.1528i	0.701495	+	1.21503i
$936$		0			0
$937$	−6.09967			−0.199267			−0.0996337	−	0.995024i	$-0.531767\pi$
$937$	−6.09967			−0.199267			−0.0996337	+	0.995024i	$0.531767\pi$
$938$		0			0
$939$	−19.5498			−0.637985
$940$		0			0
$941$	25.9124	+	44.8816i	0.844719	+	1.46310i	0.885865	+	0.463944i	$0.153566\pi$
$941$	25.9124	+	44.8816i	0.844719	+	1.46310i	−0.0411454	+	0.999153i	$0.513101\pi$
$942$		0			0
$943$	9.09967	−	15.7611i	0.296326	−	0.513252i
$944$		0			0
$945$	3.72508	+	7.82300i	0.121177	+	0.254482i
$946$		0			0
$947$	−9.72508	+	16.8443i	−0.316023	+	0.547367i	−0.979654	−	0.200692i	$-0.935681\pi$
$947$	−9.72508	+	16.8443i	−0.316023	+	0.547367i	0.663632	+	0.748060i	$0.269014\pi$
$948$		0			0
$949$	−13.4124	−	23.2309i	−0.435384	−	0.754107i
$950$		0			0
$951$	27.8248			0.902279
$952$		0			0
$953$	55.6495			1.80266			0.901332	−	0.433129i	$-0.142590\pi$
$953$	55.6495			1.80266			0.901332	+	0.433129i	$0.142590\pi$
$954$		0			0
$955$	7.45017	+	12.9041i	0.241082	+	0.417566i
$956$		0			0
$957$	−8.63746	+	14.9605i	−0.279209	+	0.483605i
$958$		0			0
$959$	3.82475	+	0.303539i	0.123508	+	0.00980179i
$960$		0			0
$961$	15.0000	−	25.9808i	0.483871	−	0.838089i
$962$		0			0
$963$	−7.91238	−	13.7046i	−0.254973	−	0.441626i
$964$		0			0
$965$	−1.47425			−0.0474579
$966$		0			0
$967$	−53.5498			−1.72205			−0.861023	−	0.508566i	$-0.830176\pi$
$967$	−53.5498			−1.72205			−0.861023	+	0.508566i	$0.830176\pi$
$968$		0			0
$969$	12.5498	+	21.7370i	0.403159	+	0.698291i
$970$		0			0
$971$	28.2870	−	48.9945i	0.907772	−	1.57231i	0.0906191	−	0.995886i	$-0.471115\pi$
$971$	28.2870	−	48.9945i	0.907772	−	1.57231i	0.817153	−	0.576421i	$-0.195551\pi$
$972$		0			0
$973$	12.4124	−	18.0348i	0.397923	−	0.578168i
$974$		0			0
$975$	17.9622	−	31.1115i	0.575251	−	0.996364i
$976$		0			0
$977$	−4.45017	−	7.70791i	−0.142373	−	0.246598i	0.786017	−	0.618205i	$-0.212140\pi$
$977$	−4.45017	−	7.70791i	−0.142373	−	0.246598i	−0.928390	+	0.371608i	$0.878807\pi$
$978$		0			0
$979$	34.5498			1.10422
$980$		0			0
$981$	−16.8248			−0.537173
$982$		0			0
$983$	−19.6495	−	34.0339i	−0.626722	−	1.08551i	−0.988205	−	0.153135i	$-0.951063\pi$
$983$	−19.6495	−	34.0339i	−0.626722	−	1.08551i	0.361483	−	0.932379i	$-0.382270\pi$
$984$		0			0
$985$	2.37459	−	4.11290i	0.0756606	−	0.131048i
$986$		0			0
$987$	9.00000	−	13.0767i	0.286473	−	0.416236i
$988$		0			0
$989$	0.549834	−	0.952341i	0.0174837	−	0.0302827i
$990$		0			0
$991$	7.04983	+	12.2107i	0.223945	+	0.387885i	0.956003	−	0.293358i	$-0.0947729\pi$
$991$	7.04983	+	12.2107i	0.223945	+	0.387885i	−0.732057	+	0.681243i	$0.761440\pi$
$992$		0			0
$993$	−1.17525			−0.0372954
$994$		0			0
$995$	16.7010			0.529457
$996$		0			0
$997$	−22.4124	−	38.8194i	−0.709807	−	1.22942i	−0.964928	−	0.262513i	$-0.915449\pi$
$997$	−22.4124	−	38.8194i	−0.709807	−	1.22942i	0.255121	−	0.966909i	$-0.417885\pi$
$998$		0			0
$999$	−1.13746	+	1.97014i	−0.0359876	+	0.0623323i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1344.2.q.w.961.2		4
4.3	odd	2		1344.2.q.x.961.2		4
7.2	even	3		9408.2.a.ec.1.1		2
7.4	even	3	inner	1344.2.q.w.193.2		4
7.5	odd	6		9408.2.a.dj.1.2		2
8.3	odd	2		336.2.q.g.289.1		4
8.5	even	2		168.2.q.c.121.1	yes	4
24.5	odd	2		504.2.s.i.289.2		4
24.11	even	2		1008.2.s.r.289.2		4
28.11	odd	6		1344.2.q.x.193.2		4
28.19	even	6		9408.2.a.dw.1.2		2
28.23	odd	6		9408.2.a.dp.1.1		2
56.3	even	6		2352.2.q.bf.1537.2		4
56.5	odd	6		1176.2.a.n.1.1		2
56.11	odd	6		336.2.q.g.193.1		4
56.13	odd	2		1176.2.q.l.961.2		4
56.19	even	6		2352.2.a.ba.1.1		2
56.27	even	2		2352.2.q.bf.961.2		4
56.37	even	6		1176.2.a.k.1.2		2
56.45	odd	6		1176.2.q.l.361.2		4
56.51	odd	6		2352.2.a.bf.1.2		2
56.53	even	6		168.2.q.c.25.1	✓	4
168.5	even	6		3528.2.a.bd.1.2		2
168.11	even	6		1008.2.s.r.865.2		4
168.53	odd	6		504.2.s.i.361.2		4
168.101	even	6		3528.2.s.bk.361.1		4
168.107	even	6		7056.2.a.cu.1.1		2
168.125	even	2		3528.2.s.bk.3313.1		4
168.131	odd	6		7056.2.a.ch.1.2		2
168.149	odd	6		3528.2.a.bk.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.q.c.25.1	✓	4	56.53	even	6
168.2.q.c.121.1	yes	4	8.5	even	2
336.2.q.g.193.1		4	56.11	odd	6
336.2.q.g.289.1		4	8.3	odd	2
504.2.s.i.289.2		4	24.5	odd	2
504.2.s.i.361.2		4	168.53	odd	6
1008.2.s.r.289.2		4	24.11	even	2
1008.2.s.r.865.2		4	168.11	even	6
1176.2.a.k.1.2		2	56.37	even	6
1176.2.a.n.1.1		2	56.5	odd	6
1176.2.q.l.361.2		4	56.45	odd	6
1176.2.q.l.961.2		4	56.13	odd	2
1344.2.q.w.193.2		4	7.4	even	3	inner
1344.2.q.w.961.2		4	1.1	even	1	trivial
1344.2.q.x.193.2		4	28.11	odd	6
1344.2.q.x.961.2		4	4.3	odd	2
2352.2.a.ba.1.1		2	56.19	even	6
2352.2.a.bf.1.2		2	56.51	odd	6
2352.2.q.bf.961.2		4	56.27	even	2
2352.2.q.bf.1537.2		4	56.3	even	6
3528.2.a.bd.1.2		2	168.5	even	6
3528.2.a.bk.1.1		2	168.149	odd	6
3528.2.s.bk.361.1		4	168.101	even	6
3528.2.s.bk.3313.1		4	168.125	even	2
7056.2.a.ch.1.2		2	168.131	odd	6
7056.2.a.cu.1.1		2	168.107	even	6
9408.2.a.dj.1.2		2	7.5	odd	6
9408.2.a.dp.1.1		2	28.23	odd	6
9408.2.a.dw.1.2		2	28.19	even	6
9408.2.a.ec.1.1		2	7.2	even	3

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:	\( N \)	\(=\)	\( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1344.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{3} +(1.63746 - 2.83616i) q^{5} +(-1.50000 + 2.17945i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(1.63746 + 2.83616i) q^{11} -6.27492 q^{13} -3.27492 q^{15} +(2.00000 + 3.46410i) q^{17} +(-3.13746 + 5.43424i) q^{19} +(2.63746 + 0.209313i) q^{21} +(-2.00000 + 3.46410i) q^{23} +(-2.86254 - 4.95807i) q^{25} +1.00000 q^{27} -5.27492 q^{29} +(0.500000 + 0.866025i) q^{31} +(1.63746 - 2.83616i) q^{33} +(3.72508 + 7.82300i) q^{35} +(-1.13746 + 1.97014i) q^{37} +(3.13746 + 5.43424i) q^{39} -4.54983 q^{41} -0.274917 q^{43} +(1.63746 + 2.83616i) q^{45} +(3.00000 - 5.19615i) q^{47} +(-2.50000 - 6.53835i) q^{49} +(2.00000 - 3.46410i) q^{51} +(4.63746 + 8.03231i) q^{53} +10.7251 q^{55} +6.27492 q^{57} +(-0.637459 - 1.10411i) q^{59} +(5.00000 - 8.66025i) q^{61} +(-1.13746 - 2.38876i) q^{63} +(-10.2749 + 17.7967i) q^{65} +(-0.137459 - 0.238085i) q^{67} +4.00000 q^{69} +2.00000 q^{71} +(2.13746 + 3.70219i) q^{73} +(-2.86254 + 4.95807i) q^{75} +(-8.63746 - 0.685484i) q^{77} +(-5.77492 + 10.0025i) q^{79} +(-0.500000 - 0.866025i) q^{81} -7.27492 q^{83} +13.0997 q^{85} +(2.63746 + 4.56821i) q^{87} +(5.27492 - 9.13642i) q^{89} +(9.41238 - 13.6759i) q^{91} +(0.500000 - 0.866025i) q^{93} +(10.2749 + 17.7967i) q^{95} +8.72508 q^{97} -3.27492 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} - q^{5} - 6 q^{7} - 2 q^{9} - q^{11} - 10 q^{13} + 2 q^{15} + 8 q^{17} - 5 q^{19} + 3 q^{21} - 8 q^{23} - 19 q^{25} + 4 q^{27} - 6 q^{29} + 2 q^{31} - q^{33} + 30 q^{35} + 3 q^{37} + 5 q^{39}+ \cdots + 2 q^{99}+O(q^{100}) \) 4 * q - 2 * q^3 - q^5 - 6 * q^7 - 2 * q^9 - q^11 - 10 * q^13 + 2 * q^15 + 8 * q^17 - 5 * q^19 + 3 * q^21 - 8 * q^23 - 19 * q^25 + 4 * q^27 - 6 * q^29 + 2 * q^31 - q^33 + 30 * q^35 + 3 * q^37 + 5 * q^39 + 12 * q^41 + 14 * q^43 - q^45 + 12 * q^47 - 10 * q^49 + 8 * q^51 + 11 * q^53 + 58 * q^55 + 10 * q^57 + 5 * q^59 + 20 * q^61 + 3 * q^63 - 26 * q^65 + 7 * q^67 + 16 * q^69 + 8 * q^71 + q^73 - 19 * q^75 - 27 * q^77 - 8 * q^79 - 2 * q^81 - 14 * q^83 - 8 * q^85 + 3 * q^87 + 6 * q^89 + 15 * q^91 + 2 * q^93 + 26 * q^95 + 50 * q^97 + 2 * q^99

Introduction

L-functions

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