LMFDB - Embedded newform 3150.2.bp.b.1349.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [3150,2,Mod(899,3150)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("3150.899"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3150, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3150.bp (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,-4,0,-4,0,0,0,8,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$25.1528766367$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1349.1
Root			$0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	3150.1349
Dual form			3150.2.bp.b.899.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.09077 - 1.62132i) q^{7} +1.00000 q^{8} +(-2.59808 + 1.50000i) q^{11} +2.44949 q^{13} +(2.44949 - 1.00000i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(0.878680 - 0.507306i) q^{17} +(0.878680 + 0.507306i) q^{19} -3.00000i q^{22} +(-2.12132 + 3.67423i) q^{23} +(-1.22474 + 2.12132i) q^{26} +(-0.358719 + 2.62132i) q^{28} -1.24264i q^{29} +(4.86396 - 2.80821i) q^{31} +(-0.500000 - 0.866025i) q^{32} +1.01461i q^{34} +(-7.13834 - 4.12132i) q^{37} +(-0.878680 + 0.507306i) q^{38} +2.02922 q^{41} -8.24264i q^{43} +(2.59808 + 1.50000i) q^{44} +(-2.12132 - 3.67423i) q^{46} +(-0.878680 - 0.507306i) q^{47} +(1.74264 + 6.77962i) q^{49} +(-1.22474 - 2.12132i) q^{52} +(-0.621320 - 1.07616i) q^{53} +(-2.09077 - 1.62132i) q^{56} +(1.07616 + 0.621320i) q^{58} +(5.76500 + 9.98528i) q^{59} +(5.12132 + 2.95680i) q^{61} +5.61642i q^{62} +1.00000 q^{64} +(-8.66025 + 5.00000i) q^{67} +(-0.878680 - 0.507306i) q^{68} +10.2426i q^{71} +(-4.18154 - 7.24264i) q^{73} +(7.13834 - 4.12132i) q^{74} -1.01461i q^{76} +(7.86396 + 1.07616i) q^{77} +(-5.62132 + 9.73641i) q^{79} +(-1.01461 + 1.75736i) q^{82} +3.16693i q^{83} +(7.13834 + 4.12132i) q^{86} +(-2.59808 + 1.50000i) q^{88} +(-5.19615 + 9.00000i) q^{89} +(-5.12132 - 3.97141i) q^{91} +4.24264 q^{92} +(0.878680 - 0.507306i) q^{94} -3.76127 q^{97} +(-6.74264 - 1.88064i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} - 4 q^{4} + 8 q^{8} - 4 q^{16} + 24 q^{17} + 24 q^{19} - 12 q^{31} - 4 q^{32} - 24 q^{38} - 24 q^{47} - 20 q^{49} + 12 q^{53} + 24 q^{61} + 8 q^{64} - 24 q^{68} + 12 q^{77} - 28 q^{79} - 24 q^{91}+ \cdots - 20 q^{98}+O(q^{100}) $ 8 * q - 4 * q^2 - 4 * q^4 + 8 * q^8 - 4 * q^16 + 24 * q^17 + 24 * q^19 - 12 * q^31 - 4 * q^32 - 24 * q^38 - 24 * q^47 - 20 * q^49 + 12 * q^53 + 24 * q^61 + 8 * q^64 - 24 * q^68 + 12 * q^77 - 28 * q^79 - 24 * q^91 + 24 * q^94 - 20 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$2801$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−2.09077	−	1.62132i	−0.790237	−	0.612801i
$7$	−2.09077	−	1.62132i	−0.790237	−	0.612801i
$8$	1.00000			0.353553
$9$		0			0
$10$		0			0
$11$	−2.59808	+	1.50000i	−0.783349	+	0.452267i	−0.837616	−	0.546259i	$-0.816051\pi$
$11$	−2.59808	+	1.50000i	−0.783349	+	0.452267i	0.0542666	+	0.998526i	$0.482718\pi$
$12$		0			0
$13$	2.44949			0.679366			0.339683	−	0.940540i	$-0.389680\pi$
$13$	2.44949			0.679366			0.339683	+	0.940540i	$0.389680\pi$
$14$	2.44949	−	1.00000i	0.654654	−	0.267261i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.878680	−	0.507306i	0.213111	−	0.123040i	−0.389645	−	0.920965i	$-0.627402\pi$
$17$	0.878680	−	0.507306i	0.213111	−	0.123040i	0.602756	+	0.797925i	$0.294069\pi$
$18$		0			0
$19$	0.878680	+	0.507306i	0.201583	+	0.116384i	0.597394	−	0.801948i	$-0.296203\pi$
$19$	0.878680	+	0.507306i	0.201583	+	0.116384i	−0.395811	+	0.918332i	$0.629536\pi$
$20$		0			0
$21$		0			0
$22$		−	3.00000i		−	0.639602i
$23$	−2.12132	+	3.67423i	−0.442326	+	0.766131i	−0.997862	−	0.0653618i	$-0.979180\pi$
$23$	−2.12132	+	3.67423i	−0.442326	+	0.766131i	0.555536	+	0.831493i	$0.312513\pi$
$24$		0			0
$25$		0			0
$26$	−1.22474	+	2.12132i	−0.240192	+	0.416025i
$27$		0			0
$28$	−0.358719	+	2.62132i	−0.0677916	+	0.495383i
$29$		−	1.24264i		−	0.230753i	−0.993322	−	0.115376i	$-0.963193\pi$
$29$		−	1.24264i		−	0.230753i	0.993322	−	0.115376i	$-0.0368074\pi$
$30$		0			0
$31$	4.86396	−	2.80821i	0.873593	−	0.504369i	0.00505256	−	0.999987i	$-0.498392\pi$
$31$	4.86396	−	2.80821i	0.873593	−	0.504369i	0.868541	+	0.495618i	$0.165058\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$		0			0
$34$			1.01461i			0.174005i
$35$		0			0
$36$		0			0
$37$	−7.13834	−	4.12132i	−1.17354	−	0.677541i	−0.219025	−	0.975719i	$-0.570288\pi$
$37$	−7.13834	−	4.12132i	−1.17354	−	0.677541i	−0.954510	+	0.298178i	$0.903621\pi$
$38$	−0.878680	+	0.507306i	−0.142541	+	0.0822959i
$39$		0			0
$40$		0			0
$41$	2.02922			0.316912			0.158456	−	0.987366i	$-0.449348\pi$
$41$	2.02922			0.316912			0.158456	+	0.987366i	$0.449348\pi$
$42$		0			0
$43$		−	8.24264i		−	1.25699i	−0.777813	−	0.628495i	$-0.783671\pi$
$43$		−	8.24264i		−	1.25699i	0.777813	−	0.628495i	$-0.216329\pi$
$44$	2.59808	+	1.50000i	0.391675	+	0.226134i
$45$		0			0
$46$	−2.12132	−	3.67423i	−0.312772	−	0.541736i
$47$	−0.878680	−	0.507306i	−0.128169	−	0.0739982i	0.434545	−	0.900650i	$-0.356909\pi$
$47$	−0.878680	−	0.507306i	−0.128169	−	0.0739982i	−0.562713	+	0.826652i	$0.690243\pi$
$48$		0			0
$49$	1.74264	+	6.77962i	0.248949	+	0.968517i
$50$		0			0
$51$		0			0
$52$	−1.22474	−	2.12132i	−0.169842	−	0.294174i
$53$	−0.621320	−	1.07616i	−0.0853449	−	0.147822i	0.820193	−	0.572087i	$-0.193866\pi$
$53$	−0.621320	−	1.07616i	−0.0853449	−	0.147822i	−0.905538	+	0.424265i	$0.860533\pi$
$54$		0			0
$55$		0			0
$56$	−2.09077	−	1.62132i	−0.279391	−	0.216658i
$57$		0			0
$58$	1.07616	+	0.621320i	0.141307	+	0.0815834i
$59$	5.76500	+	9.98528i	0.750540	+	1.29997i	0.947561	+	0.319574i	$0.103540\pi$
$59$	5.76500	+	9.98528i	0.750540	+	1.29997i	−0.197022	+	0.980399i	$0.563127\pi$
$60$		0			0
$61$	5.12132	+	2.95680i	0.655718	+	0.378579i	0.790643	−	0.612277i	$-0.209746\pi$
$61$	5.12132	+	2.95680i	0.655718	+	0.378579i	−0.134926	+	0.990856i	$0.543080\pi$
$62$			5.61642i			0.713286i
$63$		0			0
$64$	1.00000			0.125000
$65$		0			0
$66$		0			0
$67$	−8.66025	+	5.00000i	−1.05802	+	0.610847i	−0.924883	−	0.380251i	$-0.875838\pi$
$67$	−8.66025	+	5.00000i	−1.05802	+	0.610847i	−0.133135	+	0.991098i	$0.542504\pi$
$68$	−0.878680	−	0.507306i	−0.106556	−	0.0615199i
$69$		0			0
$70$		0			0
$71$			10.2426i			1.21558i	0.794099	+	0.607789i	$0.207943\pi$
$71$			10.2426i			1.21558i	−0.794099	+	0.607789i	$0.792057\pi$
$72$		0			0
$73$	−4.18154	−	7.24264i	−0.489412	−	0.847687i	0.510513	−	0.859870i	$-0.329455\pi$
$73$	−4.18154	−	7.24264i	−0.489412	−	0.847687i	−0.999926	+	0.0121828i	$0.996122\pi$
$74$	7.13834	−	4.12132i	0.829815	−	0.479094i
$75$		0			0
$76$		−	1.01461i		−	0.116384i
$77$	7.86396	+	1.07616i	0.896182	+	0.122640i
$78$		0			0
$79$	−5.62132	+	9.73641i	−0.632448	+	1.09543i	0.354602	+	0.935017i	$0.384616\pi$
$79$	−5.62132	+	9.73641i	−0.632448	+	1.09543i	−0.987050	+	0.160415i	$0.948717\pi$
$80$		0			0
$81$		0			0
$82$	−1.01461	+	1.75736i	−0.112045	+	0.194068i
$83$			3.16693i			0.347616i	0.984780	+	0.173808i	$0.0556071\pi$
$83$			3.16693i			0.347616i	−0.984780	+	0.173808i	$0.944393\pi$
$84$		0			0
$85$		0			0
$86$	7.13834	+	4.12132i	0.769747	+	0.444413i
$87$		0			0
$88$	−2.59808	+	1.50000i	−0.276956	+	0.159901i
$89$	−5.19615	+	9.00000i	−0.550791	+	0.953998i	0.447427	+	0.894321i	$0.352341\pi$
$89$	−5.19615	+	9.00000i	−0.550791	+	0.953998i	−0.998218	+	0.0596775i	$0.980993\pi$
$90$		0			0
$91$	−5.12132	−	3.97141i	−0.536860	−	0.416317i
$92$	4.24264			0.442326
$93$		0			0
$94$	0.878680	−	0.507306i	0.0906289	−	0.0523246i
$95$		0			0
$96$		0			0
$97$	−3.76127			−0.381900			−0.190950	−	0.981600i	$-0.561157\pi$
$97$	−3.76127			−0.381900			−0.190950	+	0.981600i	$0.561157\pi$
$98$	−6.74264	−	1.88064i	−0.681110	−	0.189973i
$99$		0			0
$100$		0			0
$101$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$101$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$102$		0			0
$103$	−7.64564	+	13.2426i	−0.753348	+	1.30484i	0.192844	+	0.981229i	$0.438229\pi$
$103$	−7.64564	+	13.2426i	−0.753348	+	1.30484i	−0.946192	+	0.323607i	$0.895105\pi$
$104$	2.44949			0.240192
$105$		0			0
$106$	1.24264			0.120696
$107$	−2.74264	+	4.75039i	−0.265141	+	0.459238i	−0.967601	−	0.252486i	$-0.918752\pi$
$107$	−2.74264	+	4.75039i	−0.265141	+	0.459238i	0.702459	+	0.711724i	$0.252085\pi$
$108$		0			0
$109$	0.757359	+	1.31178i	0.0725419	+	0.125646i	0.900015	−	0.435860i	$-0.143556\pi$
$109$	0.757359	+	1.31178i	0.0725419	+	0.125646i	−0.827473	+	0.561506i	$0.810222\pi$
$110$		0			0
$111$		0			0
$112$	2.44949	−	1.00000i	0.231455	−	0.0944911i
$113$	8.48528			0.798228			0.399114	−	0.916901i	$-0.369318\pi$
$113$	8.48528			0.798228			0.399114	+	0.916901i	$0.369318\pi$
$114$		0			0
$115$		0			0
$116$	−1.07616	+	0.621320i	−0.0999188	+	0.0576881i
$117$		0			0
$118$	−11.5300			−1.06142
$119$	−2.65962	−	0.363961i	−0.243807	−	0.0333643i
$120$		0			0
$121$	−1.00000	+	1.73205i	−0.0909091	+	0.157459i
$122$	−5.12132	+	2.95680i	−0.463663	+	0.267696i
$123$		0			0
$124$	−4.86396	−	2.80821i	−0.436797	−	0.252185i
$125$		0			0
$126$		0			0
$127$		−	5.24264i		−	0.465209i	−0.972571	−	0.232605i	$-0.925275\pi$
$127$		−	5.24264i		−	0.465209i	0.972571	−	0.232605i	$-0.0747248\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$		0			0
$130$		0			0
$131$	−2.59808	+	4.50000i	−0.226995	+	0.393167i	−0.956916	−	0.290365i	$-0.906223\pi$
$131$	−2.59808	+	4.50000i	−0.226995	+	0.393167i	0.729921	+	0.683531i	$0.239557\pi$
$132$		0			0
$133$	−1.01461	−	2.48528i	−0.0879780	−	0.215501i
$134$		−	10.0000i		−	0.863868i
$135$		0			0
$136$	0.878680	−	0.507306i	0.0753462	−	0.0435011i
$137$	7.24264	+	12.5446i	0.618781	+	1.07176i	0.989709	+	0.143098i	$0.0457063\pi$
$137$	7.24264	+	12.5446i	0.618781	+	1.07176i	−0.370928	+	0.928662i	$0.620960\pi$
$138$		0			0
$139$			20.1903i			1.71252i	0.516549	+	0.856258i	$0.327217\pi$
$139$			20.1903i			1.71252i	−0.516549	+	0.856258i	$0.672783\pi$
$140$		0			0
$141$		0			0
$142$	−8.87039	−	5.12132i	−0.744386	−	0.429772i
$143$	−6.36396	+	3.67423i	−0.532181	+	0.307255i
$144$		0			0
$145$		0			0
$146$	8.36308			0.692134
$147$		0			0
$148$			8.24264i			0.677541i
$149$	17.7408	+	10.2426i	1.45338	+	0.839110i	0.998671	−	0.0515300i	$-0.0164098\pi$
$149$	17.7408	+	10.2426i	1.45338	+	0.839110i	0.454709	+	0.890640i	$0.349743\pi$
$150$		0			0
$151$	1.62132	+	2.80821i	0.131941	+	0.228529i	0.924425	−	0.381364i	$-0.124546\pi$
$151$	1.62132	+	2.80821i	0.131941	+	0.228529i	−0.792484	+	0.609893i	$0.791212\pi$
$152$	0.878680	+	0.507306i	0.0712703	+	0.0411479i
$153$		0			0
$154$	−4.86396	+	6.27231i	−0.391949	+	0.505437i
$155$		0			0
$156$		0			0
$157$	−7.34847	−	12.7279i	−0.586472	−	1.01580i	−0.994690	−	0.102915i	$-0.967183\pi$
$157$	−7.34847	−	12.7279i	−0.586472	−	1.01580i	0.408219	−	0.912884i	$-0.366150\pi$
$158$	−5.62132	−	9.73641i	−0.447208	−	0.774587i
$159$		0			0
$160$		0			0
$161$	10.3923	−	4.24264i	0.819028	−	0.334367i
$162$		0			0
$163$	5.40629	+	3.12132i	0.423453	+	0.244481i	0.696554	−	0.717505i	$-0.254716\pi$
$163$	5.40629	+	3.12132i	0.423453	+	0.244481i	−0.273101	+	0.961985i	$0.588049\pi$
$164$	−1.01461	−	1.75736i	−0.0792279	−	0.137227i
$165$		0			0
$166$	−2.74264	−	1.58346i	−0.212870	−	0.122901i
$167$			23.0600i			1.78444i	0.451603	+	0.892219i	$0.350852\pi$
$167$			23.0600i			1.78444i	−0.451603	+	0.892219i	$0.649148\pi$
$168$		0			0
$169$	−7.00000			−0.538462
$170$		0			0
$171$		0			0
$172$	−7.13834	+	4.12132i	−0.544293	+	0.314248i
$173$	18.0000	+	10.3923i	1.36851	+	0.790112i	0.990738	−	0.135785i	$-0.0433555\pi$
$173$	18.0000	+	10.3923i	1.36851	+	0.790112i	0.377776	+	0.925897i	$0.376689\pi$
$174$		0			0
$175$		0			0
$176$		−	3.00000i		−	0.226134i
$177$		0			0
$178$	−5.19615	−	9.00000i	−0.389468	−	0.674579i
$179$	−8.23999	+	4.75736i	−0.615886	+	0.355582i	−0.775265	−	0.631636i	$-0.782384\pi$
$179$	−8.23999	+	4.75736i	−0.615886	+	0.355582i	0.159380	+	0.987217i	$0.449051\pi$
$180$		0			0
$181$			2.02922i			0.150831i	0.997152	+	0.0754155i	$0.0240283\pi$
$181$			2.02922i			0.150831i	−0.997152	+	0.0754155i	$0.975972\pi$
$182$	6.00000	−	2.44949i	0.444750	−	0.181568i
$183$		0			0
$184$	−2.12132	+	3.67423i	−0.156386	+	0.270868i
$185$		0			0
$186$		0			0
$187$	−1.52192	+	2.63604i	−0.111294	+	0.192766i
$188$			1.01461i			0.0739982i
$189$		0			0
$190$		0			0
$191$	−7.34847	−	4.24264i	−0.531717	−	0.306987i	0.209999	−	0.977702i	$-0.432654\pi$
$191$	−7.34847	−	4.24264i	−0.531717	−	0.306987i	−0.741715	+	0.670715i	$0.765987\pi$
$192$		0			0
$193$	6.48244	−	3.74264i	0.466617	−	0.269401i	−0.248206	−	0.968707i	$-0.579841\pi$
$193$	6.48244	−	3.74264i	0.466617	−	0.269401i	0.714822	+	0.699306i	$0.246508\pi$
$194$	1.88064	−	3.25736i	0.135022	−	0.233865i
$195$		0			0
$196$	5.00000	−	4.89898i	0.357143	−	0.349927i
$197$	−9.51472			−0.677896			−0.338948	−	0.940805i	$-0.610071\pi$
$197$	−9.51472			−0.677896			−0.338948	+	0.940805i	$0.610071\pi$
$198$		0			0
$199$	13.9706	−	8.06591i	0.990347	−	0.571777i	0.0849690	−	0.996384i	$-0.472921\pi$
$199$	13.9706	−	8.06591i	0.990347	−	0.571777i	0.905378	+	0.424607i	$0.139588\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−2.01472	+	2.59808i	−0.141406	+	0.182349i
$204$		0			0
$205$		0			0
$206$	−7.64564	−	13.2426i	−0.532697	−	0.922658i
$207$		0			0
$208$	−1.22474	+	2.12132i	−0.0849208	+	0.147087i
$209$	−3.04384			−0.210547
$210$		0			0
$211$	8.24264			0.567447			0.283723	−	0.958906i	$-0.408430\pi$
$211$	8.24264			0.567447			0.283723	+	0.958906i	$0.408430\pi$
$212$	−0.621320	+	1.07616i	−0.0426725	+	0.0739109i
$213$		0			0
$214$	−2.74264	−	4.75039i	−0.187483	−	0.324730i
$215$		0			0
$216$		0			0
$217$	−14.7224	−	2.01472i	−0.999424	−	0.136768i
$218$	−1.51472			−0.102590
$219$		0			0
$220$		0			0
$221$	2.15232	−	1.24264i	0.144780	−	0.0835891i
$222$		0			0
$223$	−12.5446			−0.840050			−0.420025	−	0.907513i	$-0.637979\pi$
$223$	−12.5446			−0.840050			−0.420025	+	0.907513i	$0.637979\pi$
$224$	−0.358719	+	2.62132i	−0.0239680	+	0.175144i
$225$		0			0
$226$	−4.24264	+	7.34847i	−0.282216	+	0.488813i
$227$	−13.5000	+	7.79423i	−0.896026	+	0.517321i	−0.875909	−	0.482476i	$-0.839737\pi$
$227$	−13.5000	+	7.79423i	−0.896026	+	0.517321i	−0.0201176	+	0.999798i	$0.506404\pi$
$228$		0			0
$229$	12.0000	+	6.92820i	0.792982	+	0.457829i	0.841011	−	0.541017i	$-0.181961\pi$
$229$	12.0000	+	6.92820i	0.792982	+	0.457829i	−0.0480291	+	0.998846i	$0.515294\pi$
$230$		0			0
$231$		0			0
$232$		−	1.24264i		−	0.0815834i
$233$	−3.36396	+	5.82655i	−0.220380	+	0.381710i	−0.954924	−	0.296852i	$-0.904063\pi$
$233$	−3.36396	+	5.82655i	−0.220380	+	0.381710i	0.734543	+	0.678562i	$0.237397\pi$
$234$		0			0
$235$		0			0
$236$	5.76500	−	9.98528i	0.375270	−	0.649986i
$237$		0			0
$238$	1.64501	−	2.12132i	0.106630	−	0.137505i
$239$		−	12.7279i		−	0.823301i	−0.911342	−	0.411650i	$-0.864952\pi$
$239$		−	12.7279i		−	0.823301i	0.911342	−	0.411650i	$-0.135048\pi$
$240$		0			0
$241$	14.7426	−	8.51167i	0.949657	−	0.548285i	0.0566826	−	0.998392i	$-0.481948\pi$
$241$	14.7426	−	8.51167i	0.949657	−	0.548285i	0.892974	+	0.450108i	$0.148614\pi$
$242$	−1.00000	−	1.73205i	−0.0642824	−	0.111340i
$243$		0			0
$244$		−	5.91359i		−	0.378579i
$245$		0			0
$246$		0			0
$247$	2.15232	+	1.24264i	0.136949	+	0.0790673i
$248$	4.86396	−	2.80821i	0.308862	−	0.178321i
$249$		0			0
$250$		0			0
$251$	−17.6177			−1.11202			−0.556009	−	0.831176i	$-0.687668\pi$
$251$	−17.6177			−1.11202			−0.556009	+	0.831176i	$0.687668\pi$
$252$		0			0
$253$		−	12.7279i		−	0.800198i
$254$	4.54026	+	2.62132i	0.284881	+	0.164476i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−21.7279	−	12.5446i	−1.35535	−	0.782512i	−0.366358	−	0.930474i	$-0.619395\pi$
$257$	−21.7279	−	12.5446i	−1.35535	−	0.782512i	−0.988993	+	0.147962i	$0.952729\pi$
$258$		0			0
$259$	8.24264	+	20.1903i	0.512173	+	1.25456i
$260$		0			0
$261$		0			0
$262$	−2.59808	−	4.50000i	−0.160510	−	0.278011i
$263$	13.6066	+	23.5673i	0.839019	+	1.45322i	0.890716	+	0.454561i	$0.150204\pi$
$263$	13.6066	+	23.5673i	0.839019	+	1.45322i	−0.0516967	+	0.998663i	$0.516463\pi$
$264$		0			0
$265$		0			0
$266$	2.65962	+	0.363961i	0.163072	+	0.0223159i
$267$		0			0
$268$	8.66025	+	5.00000i	0.529009	+	0.305424i
$269$	−5.25770	−	9.10660i	−0.320568	−	0.555239i	0.660038	−	0.751232i	$-0.270540\pi$
$269$	−5.25770	−	9.10660i	−0.320568	−	0.555239i	−0.980605	+	0.195993i	$0.937207\pi$
$270$		0			0
$271$	−9.62132	−	5.55487i	−0.584454	−	0.337434i	0.178448	−	0.983949i	$-0.442892\pi$
$271$	−9.62132	−	5.55487i	−0.584454	−	0.337434i	−0.762901	+	0.646515i	$0.776226\pi$
$272$			1.01461i			0.0615199i
$273$		0			0
$274$	−14.4853			−0.875088
$275$		0			0
$276$		0			0
$277$	−18.1610	+	10.4853i	−1.09119	+	0.630000i	−0.933893	−	0.357552i	$-0.883612\pi$
$277$	−18.1610	+	10.4853i	−1.09119	+	0.630000i	−0.157298	+	0.987551i	$0.550278\pi$
$278$	−17.4853	−	10.0951i	−1.04870	−	0.605466i
$279$		0			0
$280$		0			0
$281$		−	6.00000i		−	0.357930i	−0.983855	−	0.178965i	$-0.942725\pi$
$281$		−	6.00000i		−	0.357930i	0.983855	−	0.178965i	$-0.0572749\pi$
$282$		0			0
$283$	3.25397	+	5.63604i	0.193428	+	0.335028i	0.946384	−	0.323043i	$-0.104706\pi$
$283$	3.25397	+	5.63604i	0.193428	+	0.335028i	−0.752956	+	0.658071i	$0.771373\pi$
$284$	8.87039	−	5.12132i	0.526361	−	0.303894i
$285$		0			0
$286$		−	7.34847i		−	0.434524i
$287$	−4.24264	−	3.29002i	−0.250435	−	0.194204i
$288$		0			0
$289$	−7.98528	+	13.8309i	−0.469722	+	0.813583i
$290$		0			0
$291$		0			0
$292$	−4.18154	+	7.24264i	−0.244706	+	0.423843i
$293$		−	4.18154i		−	0.244288i	−0.992512	−	0.122144i	$-0.961023\pi$
$293$		−	4.18154i		−	0.244288i	0.992512	−	0.122144i	$-0.0389770\pi$
$294$		0			0
$295$		0			0
$296$	−7.13834	−	4.12132i	−0.414907	−	0.239547i
$297$		0			0
$298$	−17.7408	+	10.2426i	−1.02770	+	0.593340i
$299$	−5.19615	+	9.00000i	−0.300501	+	0.520483i
$300$		0			0
$301$	−13.3640	+	17.2335i	−0.770286	+	0.993321i
$302$	−3.24264			−0.186593
$303$		0			0
$304$	−0.878680	+	0.507306i	−0.0503957	+	0.0290960i
$305$		0			0
$306$		0			0
$307$	24.6690			1.40793			0.703966	−	0.710233i	$-0.251411\pi$
$307$	24.6690			1.40793			0.703966	+	0.710233i	$0.251411\pi$
$308$	−3.00000	−	7.34847i	−0.170941	−	0.418718i
$309$		0			0
$310$		0			0
$311$	−9.37769	−	16.2426i	−0.531760	−	0.921036i	−0.999313	−	0.0370703i	$-0.988197\pi$
$311$	−9.37769	−	16.2426i	−0.531760	−	0.921036i	0.467552	−	0.883965i	$-0.345136\pi$
$312$		0			0
$313$	−0.568852	+	0.985281i	−0.0321534	+	0.0556914i	−0.881654	−	0.471896i	$-0.843570\pi$
$313$	−0.568852	+	0.985281i	−0.0321534	+	0.0556914i	0.849501	+	0.527587i	$0.176903\pi$
$314$	14.6969			0.829396
$315$		0			0
$316$	11.2426			0.632448
$317$	3.62132	−	6.27231i	0.203394	−	0.352288i	−0.746226	−	0.665693i	$-0.768136\pi$
$317$	3.62132	−	6.27231i	0.203394	−	0.352288i	0.949620	+	0.313404i	$0.101470\pi$
$318$		0			0
$319$	1.86396	+	3.22848i	0.104362	+	0.180760i
$320$		0			0
$321$		0			0
$322$	−1.52192	+	11.1213i	−0.0848132	+	0.619767i
$323$	1.02944			0.0572794
$324$		0			0
$325$		0			0
$326$	−5.40629	+	3.12132i	−0.299426	+	0.172874i
$327$		0			0
$328$	2.02922			0.112045
$329$	1.01461	+	2.48528i	0.0559374	+	0.137018i
$330$		0			0
$331$	−8.72792	+	15.1172i	−0.479730	+	0.830917i	−0.999730	−	0.0232497i	$-0.992599\pi$
$331$	−8.72792	+	15.1172i	−0.479730	+	0.830917i	0.520000	+	0.854166i	$0.325932\pi$
$332$	2.74264	−	1.58346i	0.150522	−	0.0869039i
$333$		0			0
$334$	−19.9706	−	11.5300i	−1.09274	−	0.630894i
$335$		0			0
$336$		0			0
$337$		−	5.00000i		−	0.272367i	−0.990684	−	0.136184i	$-0.956516\pi$
$337$		−	5.00000i		−	0.272367i	0.990684	−	0.136184i	$-0.0434837\pi$
$338$	3.50000	−	6.06218i	0.190375	−	0.329739i
$339$		0			0
$340$		0			0
$341$	−8.42463	+	14.5919i	−0.456219	+	0.790195i
$342$		0			0
$343$	7.34847	−	17.0000i	0.396780	−	0.917914i
$344$		−	8.24264i		−	0.444413i
$345$		0			0
$346$	−18.0000	+	10.3923i	−0.967686	+	0.558694i
$347$	−7.24264	−	12.5446i	−0.388805	−	0.673431i	0.603484	−	0.797375i	$-0.293779\pi$
$347$	−7.24264	−	12.5446i	−0.388805	−	0.673431i	−0.992289	+	0.123945i	$0.960445\pi$
$348$		0			0
$349$		−	36.9164i		−	1.97609i	−0.154163	−	0.988045i	$-0.549268\pi$
$349$		−	36.9164i		−	1.97609i	0.154163	−	0.988045i	$-0.450732\pi$
$350$		0			0
$351$		0			0
$352$	2.59808	+	1.50000i	0.138478	+	0.0799503i
$353$	−16.2426	+	9.37769i	−0.864509	+	0.499124i	−0.865519	−	0.500875i	$-0.833012\pi$
$353$	−16.2426	+	9.37769i	−0.864509	+	0.499124i	0.00101095	+	0.999999i	$0.499678\pi$
$354$		0			0
$355$		0			0
$356$	10.3923			0.550791
$357$		0			0
$358$		−	9.51472i		−	0.502869i
$359$	15.5885	+	9.00000i	0.822727	+	0.475002i	0.851356	−	0.524588i	$-0.175781\pi$
$359$	15.5885	+	9.00000i	0.822727	+	0.475002i	−0.0286287	+	0.999590i	$0.509114\pi$
$360$		0			0
$361$	−8.98528	−	15.5630i	−0.472910	−	0.819103i
$362$	−1.75736	−	1.01461i	−0.0923648	−	0.0533268i
$363$		0			0
$364$	−0.878680	+	6.42090i	−0.0460553	+	0.336546i
$365$		0			0
$366$		0			0
$367$	9.43924	+	16.3492i	0.492724	+	0.853424i	0.999965	−	0.00838099i	$-0.00266778\pi$
$367$	9.43924	+	16.3492i	0.492724	+	0.853424i	−0.507241	+	0.861804i	$0.669334\pi$
$368$	−2.12132	−	3.67423i	−0.110581	−	0.191533i
$369$		0			0
$370$		0			0
$371$	−0.445759	+	3.25736i	−0.0231427	+	0.169114i
$372$		0			0
$373$	18.5813	+	10.7279i	0.962104	+	0.555471i	0.896820	−	0.442396i	$-0.145871\pi$
$373$	18.5813	+	10.7279i	0.962104	+	0.555471i	0.0652837	+	0.997867i	$0.479205\pi$
$374$	−1.52192	−	2.63604i	−0.0786965	−	0.136306i
$375$		0			0
$376$	−0.878680	−	0.507306i	−0.0453144	−	0.0261623i
$377$		−	3.04384i		−	0.156766i
$378$		0			0
$379$	4.48528			0.230393			0.115197	−	0.993343i	$-0.463250\pi$
$379$	4.48528			0.230393			0.115197	+	0.993343i	$0.463250\pi$
$380$		0			0
$381$		0			0
$382$	7.34847	−	4.24264i	0.375980	−	0.217072i
$383$	10.7574	+	6.21076i	0.549675	+	0.317355i	0.748991	−	0.662580i	$-0.230539\pi$
$383$	10.7574	+	6.21076i	0.549675	+	0.317355i	−0.199316	+	0.979935i	$0.563872\pi$
$384$		0			0
$385$		0			0
$386$			7.48528i			0.380991i
$387$		0			0
$388$	1.88064	+	3.25736i	0.0954749	+	0.165367i
$389$	−16.8493	+	9.72792i	−0.854291	+	0.493225i	−0.862096	−	0.506744i	$-0.830849\pi$
$389$	−16.8493	+	9.72792i	−0.854291	+	0.493225i	0.00780525	+	0.999970i	$0.497515\pi$
$390$		0			0
$391$			4.30463i			0.217695i
$392$	1.74264	+	6.77962i	0.0880166	+	0.342422i
$393$		0			0
$394$	4.75736	−	8.23999i	0.239672	−	0.415125i
$395$		0			0
$396$		0			0
$397$	−6.92820	+	12.0000i	−0.347717	+	0.602263i	−0.985843	−	0.167668i	$-0.946376\pi$
$397$	−6.92820	+	12.0000i	−0.347717	+	0.602263i	0.638127	+	0.769931i	$0.279710\pi$
$398$			16.1318i			0.808615i
$399$		0			0
$400$		0			0
$401$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$401$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$402$		0			0
$403$	11.9142	−	6.87868i	0.593490	−	0.342651i
$404$		0			0
$405$		0			0
$406$	−1.24264	−	3.04384i	−0.0616712	−	0.151063i
$407$	24.7279			1.22572
$408$		0			0
$409$	3.98528	−	2.30090i	0.197059	−	0.113772i	−0.398224	−	0.917288i	$-0.630373\pi$
$409$	3.98528	−	2.30090i	0.197059	−	0.113772i	0.595283	+	0.803516i	$0.297040\pi$
$410$		0			0
$411$		0			0
$412$	15.2913			0.753348
$413$	4.13604	−	30.2238i	0.203521	−	1.48722i
$414$		0			0
$415$		0			0
$416$	−1.22474	−	2.12132i	−0.0600481	−	0.104006i
$417$		0			0
$418$	1.52192	−	2.63604i	0.0744394	−	0.128933i
$419$	−4.05845			−0.198268			−0.0991341	−	0.995074i	$-0.531607\pi$
$419$	−4.05845			−0.198268			−0.0991341	+	0.995074i	$0.531607\pi$
$420$		0			0
$421$	−5.75736			−0.280597			−0.140298	−	0.990109i	$-0.544806\pi$
$421$	−5.75736			−0.280597			−0.140298	+	0.990109i	$0.544806\pi$
$422$	−4.12132	+	7.13834i	−0.200623	+	0.347489i
$423$		0			0
$424$	−0.621320	−	1.07616i	−0.0301740	−	0.0522629i
$425$		0			0
$426$		0			0
$427$	−5.91359	−	14.4853i	−0.286179	−	0.700992i
$428$	5.48528			0.265141
$429$		0			0
$430$		0			0
$431$	−17.7408	+	10.2426i	−0.854543	+	0.493371i	−0.862181	−	0.506600i	$-0.830902\pi$
$431$	−17.7408	+	10.2426i	−0.854543	+	0.493371i	0.00763808	+	0.999971i	$0.497569\pi$
$432$		0			0
$433$	−3.46410			−0.166474			−0.0832370	−	0.996530i	$-0.526526\pi$
$433$	−3.46410			−0.166474			−0.0832370	+	0.996530i	$0.526526\pi$
$434$	9.10601	−	11.7426i	0.437103	−	0.563665i
$435$		0			0
$436$	0.757359	−	1.31178i	0.0362709	−	0.0628231i
$437$	−3.72792	+	2.15232i	−0.178331	+	0.102959i
$438$		0			0
$439$	−23.5919	−	13.6208i	−1.12598	−	0.650084i	−0.183059	−	0.983102i	$-0.558600\pi$
$439$	−23.5919	−	13.6208i	−1.12598	−	0.650084i	−0.942921	+	0.333018i	$0.891933\pi$
$440$		0			0
$441$		0			0
$442$			2.48528i			0.118213i
$443$	17.2279	−	29.8396i	0.818523	−	1.41772i	−0.0882469	−	0.996099i	$-0.528126\pi$
$443$	17.2279	−	29.8396i	0.818523	−	1.41772i	0.906770	−	0.421625i	$-0.138540\pi$
$444$		0			0
$445$		0			0
$446$	6.27231	−	10.8640i	0.297003	−	0.514423i
$447$		0			0
$448$	−2.09077	−	1.62132i	−0.0987796	−	0.0766002i
$449$		−	10.2426i		−	0.483380i	−0.970354	−	0.241690i	$-0.922298\pi$
$449$		−	10.2426i		−	0.483380i	0.970354	−	0.241690i	$-0.0777017\pi$
$450$		0			0
$451$	−5.27208	+	3.04384i	−0.248252	+	0.143329i
$452$	−4.24264	−	7.34847i	−0.199557	−	0.345643i
$453$		0			0
$454$		−	15.5885i		−	0.731603i
$455$		0			0
$456$		0			0
$457$	19.9186	+	11.5000i	0.931752	+	0.537947i	0.887365	−	0.461067i	$-0.152533\pi$
$457$	19.9186	+	11.5000i	0.931752	+	0.537947i	0.0443868	+	0.999014i	$0.485867\pi$
$458$	−12.0000	+	6.92820i	−0.560723	+	0.323734i
$459$		0			0
$460$		0			0
$461$	22.8138			1.06255			0.531273	−	0.847201i	$-0.321714\pi$
$461$	22.8138			1.06255			0.531273	+	0.847201i	$0.321714\pi$
$462$		0			0
$463$		−	21.4558i		−	0.997138i	−0.866850	−	0.498569i	$-0.833859\pi$
$463$		−	21.4558i		−	0.997138i	0.866850	−	0.498569i	$-0.166141\pi$
$464$	1.07616	+	0.621320i	0.0499594	+	0.0288441i
$465$		0			0
$466$	−3.36396	−	5.82655i	−0.155832	−	0.269910i
$467$	−16.4558	−	9.50079i	−0.761486	−	0.439644i	0.0683432	−	0.997662i	$-0.478229\pi$
$467$	−16.4558	−	9.50079i	−0.761486	−	0.439644i	−0.829829	+	0.558018i	$0.811562\pi$
$468$		0			0
$469$	26.2132	+	3.58719i	1.21041	+	0.165641i
$470$		0			0
$471$		0			0
$472$	5.76500	+	9.98528i	0.265356	+	0.459610i
$473$	12.3640	+	21.4150i	0.568496	+	0.984663i
$474$		0			0
$475$		0			0
$476$	1.01461	+	2.48528i	0.0465047	+	0.113913i
$477$		0			0
$478$	11.0227	+	6.36396i	0.504167	+	0.291081i
$479$	−18.2481	−	31.6066i	−0.833776	−	1.44414i	−0.895023	−	0.446020i	$-0.852841\pi$
$479$	−18.2481	−	31.6066i	−0.833776	−	1.44414i	0.0612470	−	0.998123i	$-0.480492\pi$
$480$		0			0
$481$	−17.4853	−	10.0951i	−0.797260	−	0.460298i
$482$			17.0233i			0.775392i
$483$		0			0
$484$	2.00000			0.0909091
$485$		0			0
$486$		0			0
$487$	24.4334	−	14.1066i	1.10718	−	0.639231i	0.169083	−	0.985602i	$-0.445919\pi$
$487$	24.4334	−	14.1066i	1.10718	−	0.639231i	0.938098	+	0.346371i	$0.112586\pi$
$488$	5.12132	+	2.95680i	0.231831	+	0.133848i
$489$		0			0
$490$		0			0
$491$		−	19.9706i		−	0.901259i	−0.892711	−	0.450629i	$-0.851200\pi$
$491$		−	19.9706i		−	0.901259i	0.892711	−	0.450629i	$-0.148800\pi$
$492$		0			0
$493$	−0.630399	−	1.09188i	−0.0283917	−	0.0491759i
$494$	−2.15232	+	1.24264i	−0.0968373	+	0.0559090i
$495$		0			0
$496$			5.61642i			0.252185i
$497$	16.6066	−	21.4150i	0.744908	−	0.960594i
$498$		0			0
$499$	−17.9706	+	31.1259i	−0.804473	+	1.39339i	0.112173	+	0.993689i	$0.464219\pi$
$499$	−17.9706	+	31.1259i	−0.804473	+	1.39339i	−0.916646	+	0.399699i	$0.869115\pi$
$500$		0			0
$501$		0			0
$502$	8.80884	−	15.2574i	0.393158	−	0.680969i
$503$		−	3.29002i		−	0.146695i	−0.997306	−	0.0733474i	$-0.976632\pi$
$503$		−	3.29002i		−	0.146695i	0.997306	−	0.0733474i	$-0.0233682\pi$
$504$		0			0
$505$		0			0
$506$	11.0227	+	6.36396i	0.490019	+	0.282913i
$507$		0			0
$508$	−4.54026	+	2.62132i	−0.201441	+	0.116302i
$509$	−20.8462	+	36.1066i	−0.923990	+	1.60040i	−0.130812	+	0.991407i	$0.541758\pi$
$509$	−20.8462	+	36.1066i	−0.923990	+	1.60040i	−0.793178	+	0.608990i	$0.791575\pi$
$510$		0			0
$511$	−3.00000	+	21.9223i	−0.132712	+	0.969786i
$512$	1.00000			0.0441942
$513$		0			0
$514$	21.7279	−	12.5446i	0.958378	−	0.553320i
$515$		0			0
$516$		0			0
$517$	3.04384			0.133868
$518$	−21.6066	−	2.95680i	−0.949340	−	0.129914i
$519$		0			0
$520$		0			0
$521$	10.0081	+	17.3345i	0.438462	+	0.759439i	0.997571	−	0.0696551i	$-0.0221899\pi$
$521$	10.0081	+	17.3345i	0.438462	+	0.759439i	−0.559109	+	0.829094i	$0.688857\pi$
$522$		0			0
$523$	−13.7694	+	23.8492i	−0.602092	+	1.04285i	0.390411	+	0.920641i	$0.372333\pi$
$523$	−13.7694	+	23.8492i	−0.602092	+	1.04285i	−0.992504	+	0.122214i	$0.961001\pi$
$524$	5.19615			0.226995
$525$		0			0
$526$	−27.2132			−1.18655
$527$	2.84924	−	4.93503i	0.124115	−	0.214973i
$528$		0			0
$529$	2.50000	+	4.33013i	0.108696	+	0.188266i
$530$		0			0
$531$		0			0
$532$	−1.64501	+	2.12132i	−0.0713203	+	0.0919709i
$533$	4.97056			0.215299
$534$		0			0
$535$		0			0
$536$	−8.66025	+	5.00000i	−0.374066	+	0.215967i
$537$		0			0
$538$	10.5154			0.453351
$539$	−14.6969	−	15.0000i	−0.633042	−	0.646096i
$540$		0			0
$541$	5.36396	−	9.29065i	0.230615	−	0.399436i	−0.727374	−	0.686241i	$-0.759260\pi$
$541$	5.36396	−	9.29065i	0.230615	−	0.399436i	0.957989	+	0.286804i	$0.0925930\pi$
$542$	9.62132	−	5.55487i	0.413271	−	0.238602i
$543$		0			0
$544$	−0.878680	−	0.507306i	−0.0376731	−	0.0217506i
$545$		0			0
$546$		0			0
$547$			19.6985i			0.842246i	0.907003	+	0.421123i	$0.138364\pi$
$547$			19.6985i			0.842246i	−0.907003	+	0.421123i	$0.861636\pi$
$548$	7.24264	−	12.5446i	0.309390	−	0.535880i
$549$		0			0
$550$		0			0
$551$	0.630399	−	1.09188i	0.0268559	−	0.0465158i
$552$		0			0
$553$	27.5387	−	11.2426i	1.17107	−	0.478086i
$554$		−	20.9706i		−	0.890954i
$555$		0			0
$556$	17.4853	−	10.0951i	0.741541	−	0.428129i
$557$	−7.86396	−	13.6208i	−0.333207	−	0.577131i	0.649932	−	0.759992i	$-0.274797\pi$
$557$	−7.86396	−	13.6208i	−0.333207	−	0.577131i	−0.983139	+	0.182861i	$0.941464\pi$
$558$		0			0
$559$		−	20.1903i		−	0.853957i
$560$		0			0
$561$		0			0
$562$	5.19615	+	3.00000i	0.219186	+	0.126547i
$563$	−20.9558	+	12.0989i	−0.883184	+	0.509906i	−0.871707	−	0.490028i	$-0.836987\pi$
$563$	−20.9558	+	12.0989i	−0.883184	+	0.509906i	−0.0114768	+	0.999934i	$0.503653\pi$
$564$		0			0
$565$		0			0
$566$	−6.50794			−0.273549
$567$		0			0
$568$			10.2426i			0.429772i
$569$	1.52192	+	0.878680i	0.0638021	+	0.0368362i	0.531562	−	0.847020i	$-0.321605\pi$
$569$	1.52192	+	0.878680i	0.0638021	+	0.0368362i	−0.467760	+	0.883856i	$0.654939\pi$
$570$		0			0
$571$	8.36396	+	14.4868i	0.350021	+	0.606254i	0.986253	−	0.165244i	$-0.0528412\pi$
$571$	8.36396	+	14.4868i	0.350021	+	0.606254i	−0.636232	+	0.771498i	$0.719508\pi$
$572$	6.36396	+	3.67423i	0.266091	+	0.153627i
$573$		0			0
$574$	4.97056	−	2.02922i	0.207467	−	0.0846982i
$575$		0			0
$576$		0			0
$577$	10.2437	+	17.7426i	0.426452	+	0.738636i	0.996555	−	0.0829373i	$-0.0264301\pi$
$577$	10.2437	+	17.7426i	0.426452	+	0.738636i	−0.570103	+	0.821573i	$0.693097\pi$
$578$	−7.98528	−	13.8309i	−0.332144	−	0.575290i
$579$		0			0
$580$		0			0
$581$	5.13461	−	6.62132i	0.213019	−	0.274699i
$582$		0			0
$583$	3.22848	+	1.86396i	0.133710	+	0.0771974i
$584$	−4.18154	−	7.24264i	−0.173033	−	0.299703i
$585$		0			0
$586$	3.62132	+	2.09077i	0.149595	+	0.0863689i
$587$			5.19615i			0.214468i	0.994234	+	0.107234i	$0.0341994\pi$
$587$			5.19615i			0.214468i	−0.994234	+	0.107234i	$0.965801\pi$
$588$		0			0
$589$	5.69848			0.234802
$590$		0			0
$591$		0			0
$592$	7.13834	−	4.12132i	0.293384	−	0.169385i
$593$	−26.3345	−	15.2042i	−1.08143	−	0.624363i	−0.150148	−	0.988664i	$-0.547975\pi$
$593$	−26.3345	−	15.2042i	−1.08143	−	0.624363i	−0.931282	+	0.364300i	$0.881308\pi$
$594$		0			0
$595$		0			0
$596$		−	20.4853i		−	0.839110i
$597$		0			0
$598$	−5.19615	−	9.00000i	−0.212486	−	0.368037i
$599$	−37.6339	+	21.7279i	−1.53768	+	0.887779i	−0.538704	+	0.842495i	$0.681086\pi$
$599$	−37.6339	+	21.7279i	−1.53768	+	0.887779i	−0.998974	+	0.0452836i	$0.985581\pi$
$600$		0			0
$601$		−	6.03668i		−	0.246241i	−0.992392	−	0.123121i	$-0.960710\pi$
$601$		−	6.03668i		−	0.246241i	0.992392	−	0.123121i	$-0.0392902\pi$
$602$	−8.24264	−	20.1903i	−0.335945	−	0.822894i
$603$		0			0
$604$	1.62132	−	2.80821i	0.0659706	−	0.114264i
$605$		0			0
$606$		0			0
$607$	12.4831	−	21.6213i	0.506672	−	0.877582i	−0.493298	−	0.869860i	$-0.664209\pi$
$607$	12.4831	−	21.6213i	0.506672	−	0.877582i	0.999970	−	0.00772182i	$-0.00245796\pi$
$608$		−	1.01461i		−	0.0411479i
$609$		0			0
$610$		0			0
$611$	−2.15232	−	1.24264i	−0.0870734	−	0.0502719i
$612$		0			0
$613$	−4.51477	+	2.60660i	−0.182350	+	0.105280i	−0.588396	−	0.808573i	$-0.700240\pi$
$613$	−4.51477	+	2.60660i	−0.182350	+	0.105280i	0.406046	+	0.913852i	$0.366907\pi$
$614$	−12.3345	+	21.3640i	−0.497779	+	0.862179i
$615$		0			0
$616$	7.86396	+	1.07616i	0.316848	+	0.0433597i
$617$	41.6985			1.67872			0.839359	−	0.543578i	$-0.182931\pi$
$617$	41.6985			1.67872			0.839359	+	0.543578i	$0.182931\pi$
$618$		0			0
$619$	41.3345	−	23.8645i	1.66137	−	0.959195i	0.689315	−	0.724462i	$-0.257912\pi$
$619$	41.3345	−	23.8645i	1.66137	−	0.959195i	0.972060	−	0.234733i	$-0.0754217\pi$
$620$		0			0
$621$		0			0
$622$	18.7554			0.752022
$623$	25.4558	−	10.3923i	1.01987	−	0.416359i
$624$		0			0
$625$		0			0
$626$	−0.568852	−	0.985281i	−0.0227359	−	0.0393798i
$627$		0			0
$628$	−7.34847	+	12.7279i	−0.293236	+	0.507899i
$629$	−8.36308			−0.333458
$630$		0			0
$631$	33.2426			1.32337			0.661684	−	0.749783i	$-0.269842\pi$
$631$	33.2426			1.32337			0.661684	+	0.749783i	$0.269842\pi$
$632$	−5.62132	+	9.73641i	−0.223604	+	0.387294i
$633$		0			0
$634$	3.62132	+	6.27231i	0.143821	+	0.249105i
$635$		0			0
$636$		0			0
$637$	4.26858	+	16.6066i	0.169127	+	0.657978i
$638$	−3.72792			−0.147590
$639$		0			0
$640$		0			0
$641$	36.1119	−	20.8492i	1.42634	−	0.823496i	0.429507	−	0.903064i	$-0.358687\pi$
$641$	36.1119	−	20.8492i	1.42634	−	0.823496i	0.996829	+	0.0795681i	$0.0253541\pi$
$642$		0			0
$643$	2.62357			0.103463			0.0517317	−	0.998661i	$-0.483526\pi$
$643$	2.62357			0.103463			0.0517317	+	0.998661i	$0.483526\pi$
$644$	−8.87039	−	6.87868i	−0.349542	−	0.271058i
$645$		0			0
$646$	−0.514719	+	0.891519i	−0.0202513	+	0.0350763i
$647$	−10.0919	+	5.82655i	−0.396753	+	0.229065i	−0.685082	−	0.728466i	$-0.740234\pi$
$647$	−10.0919	+	5.82655i	−0.396753	+	0.229065i	0.288329	+	0.957531i	$0.406900\pi$
$648$		0			0
$649$	−29.9558	−	17.2950i	−1.17587	−	0.678889i
$650$		0			0
$651$		0			0
$652$		−	6.24264i		−	0.244481i
$653$	5.37868	−	9.31615i	0.210484	−	0.364569i	−0.741382	−	0.671083i	$-0.765829\pi$
$653$	5.37868	−	9.31615i	0.210484	−	0.364569i	0.951866	+	0.306514i	$0.0991627\pi$
$654$		0			0
$655$		0			0
$656$	−1.01461	+	1.75736i	−0.0396139	+	0.0686134i
$657$		0			0
$658$	−2.65962	−	0.363961i	−0.103683	−	0.0141887i
$659$			6.00000i			0.233727i	0.993148	+	0.116863i	$0.0372840\pi$
$659$			6.00000i			0.233727i	−0.993148	+	0.116863i	$0.962716\pi$
$660$		0			0
$661$	35.1213	−	20.2773i	1.36606	−	0.788696i	0.375639	−	0.926766i	$-0.377423\pi$
$661$	35.1213	−	20.2773i	1.36606	−	0.788696i	0.990422	+	0.138071i	$0.0440901\pi$
$662$	−8.72792	−	15.1172i	−0.339220	−	0.587547i
$663$		0			0
$664$			3.16693i			0.122901i
$665$		0			0
$666$		0			0
$667$	4.56575	+	2.63604i	0.176787	+	0.102068i
$668$	19.9706	−	11.5300i	0.772684	−	0.446109i
$669$		0			0
$670$		0			0
$671$	−17.7408			−0.684875
$672$		0			0
$673$			15.9706i			0.615620i	0.951448	+	0.307810i	$0.0995961\pi$
$673$			15.9706i			0.615620i	−0.951448	+	0.307810i	$0.900404\pi$
$674$	4.33013	+	2.50000i	0.166790	+	0.0962964i
$675$		0			0
$676$	3.50000	+	6.06218i	0.134615	+	0.233161i
$677$	−10.8640	−	6.27231i	−0.417536	−	0.241064i	0.276487	−	0.961018i	$-0.410830\pi$
$677$	−10.8640	−	6.27231i	−0.417536	−	0.241064i	−0.694023	+	0.719953i	$0.744163\pi$
$678$		0			0
$679$	7.86396	+	6.09823i	0.301791	+	0.234029i
$680$		0			0
$681$		0			0
$682$	−8.42463	−	14.5919i	−0.322596	−	0.558752i
$683$	−12.9853	−	22.4912i	−0.496868	−	0.860601i	0.503125	−	0.864213i	$-0.332183\pi$
$683$	−12.9853	−	22.4912i	−0.496868	−	0.860601i	−0.999993	+	0.00361277i	$0.998850\pi$
$684$		0			0
$685$		0			0
$686$	11.0482	+	14.8640i	0.421822	+	0.567509i
$687$		0			0
$688$	7.13834	+	4.12132i	0.272147	+	0.157124i
$689$	−1.52192	−	2.63604i	−0.0579805	−	0.100425i
$690$		0			0
$691$	−0.727922	−	0.420266i	−0.0276915	−	0.0159877i	0.486090	−	0.873909i	$-0.338423\pi$
$691$	−0.727922	−	0.420266i	−0.0276915	−	0.0159877i	−0.513782	+	0.857921i	$0.671756\pi$
$692$		−	20.7846i		−	0.790112i
$693$		0			0
$694$	14.4853			0.549854
$695$		0			0
$696$		0			0
$697$	1.78304	−	1.02944i	0.0675374	−	0.0389927i
$698$	31.9706	+	18.4582i	1.21010	+	0.698654i
$699$		0			0
$700$		0			0
$701$			38.6985i			1.46162i	0.682580	+	0.730811i	$0.260858\pi$
$701$			38.6985i			1.46162i	−0.682580	+	0.730811i	$0.739142\pi$
$702$		0			0
$703$	−4.18154	−	7.24264i	−0.157710	−	0.273161i
$704$	−2.59808	+	1.50000i	−0.0979187	+	0.0565334i
$705$		0			0
$706$		−	18.7554i		−	0.705868i
$707$		0			0
$708$		0			0
$709$	−3.48528	+	6.03668i	−0.130892	+	0.226712i	−0.924021	−	0.382342i	$-0.875118\pi$
$709$	−3.48528	+	6.03668i	−0.130892	+	0.226712i	0.793128	+	0.609055i	$0.208451\pi$
$710$		0			0
$711$		0			0
$712$	−5.19615	+	9.00000i	−0.194734	+	0.337289i
$713$			23.8284i			0.892382i
$714$		0			0
$715$		0			0
$716$	8.23999	+	4.75736i	0.307943	+	0.177791i
$717$		0			0
$718$	−15.5885	+	9.00000i	−0.581756	+	0.335877i
$719$	−11.5300	+	19.9706i	−0.429997	+	0.744776i	−0.996872	−	0.0790270i	$-0.974819\pi$
$719$	−11.5300	+	19.9706i	−0.429997	+	0.744776i	0.566876	+	0.823803i	$0.308152\pi$
$720$		0			0
$721$	37.4558	−	15.2913i	1.39493	−	0.569477i
$722$	17.9706			0.668795
$723$		0			0
$724$	1.75736	−	1.01461i	0.0653117	−	0.0377078i
$725$		0			0
$726$		0			0
$727$	26.4010			0.979160			0.489580	−	0.871958i	$-0.337150\pi$
$727$	26.4010			0.979160			0.489580	+	0.871958i	$0.337150\pi$
$728$	−5.12132	−	3.97141i	−0.189809	−	0.147190i
$729$		0			0
$730$		0			0
$731$	−4.18154	−	7.24264i	−0.154660	−	0.267879i
$732$		0			0
$733$	−19.6830	+	34.0919i	−0.727007	+	1.25921i	0.231136	+	0.972921i	$0.425756\pi$
$733$	−19.6830	+	34.0919i	−0.727007	+	1.25921i	−0.958143	+	0.286291i	$0.907578\pi$
$734$	−18.8785			−0.696817
$735$		0			0
$736$	4.24264			0.156386
$737$	15.0000	−	25.9808i	0.552532	−	0.957014i
$738$		0			0
$739$	−17.7279	−	30.7057i	−0.652132	−	1.12953i	−0.982605	−	0.185710i	$-0.940541\pi$
$739$	−17.7279	−	30.7057i	−0.652132	−	1.12953i	0.330472	−	0.943816i	$-0.392792\pi$
$740$		0			0
$741$		0			0
$742$	−2.59808	−	2.01472i	−0.0953784	−	0.0739626i
$743$	−21.5147			−0.789298			−0.394649	−	0.918832i	$-0.629134\pi$
$743$	−21.5147			−0.789298			−0.394649	+	0.918832i	$0.629134\pi$
$744$		0			0
$745$		0			0
$746$	−18.5813	+	10.7279i	−0.680310	+	0.392777i
$747$		0			0
$748$	3.04384			0.111294
$749$	13.4361	−	5.48528i	0.490946	−	0.200428i
$750$		0			0
$751$	−13.3787	+	23.1726i	−0.488195	+	0.845578i	−0.999908	−	0.0135781i	$-0.995678\pi$
$751$	−13.3787	+	23.1726i	−0.488195	+	0.845578i	0.511713	+	0.859157i	$0.329011\pi$
$752$	0.878680	−	0.507306i	0.0320422	−	0.0184995i
$753$		0			0
$754$	2.63604	+	1.52192i	0.0959989	+	0.0554250i
$755$		0			0
$756$		0			0
$757$		−	42.2426i		−	1.53533i	−0.640848	−	0.767667i	$-0.721417\pi$
$757$		−	42.2426i		−	1.53533i	0.640848	−	0.767667i	$-0.278583\pi$
$758$	−2.24264	+	3.88437i	−0.0814564	+	0.141087i
$759$		0			0
$760$		0			0
$761$	−2.53653	+	4.39340i	−0.0919491	+	0.159261i	−0.908331	−	0.418252i	$-0.862643\pi$
$761$	−2.53653	+	4.39340i	−0.0919491	+	0.159261i	0.816382	+	0.577512i	$0.195976\pi$
$762$		0			0
$763$	0.543359	−	3.97056i	0.0196709	−	0.143744i
$764$			8.48528i			0.306987i
$765$		0			0
$766$	−10.7574	+	6.21076i	−0.388679	+	0.224404i
$767$	14.1213	+	24.4588i	0.509891	+	0.883158i
$768$		0			0
$769$		−	49.0408i		−	1.76846i	−0.467056	−	0.884228i	$-0.654685\pi$
$769$		−	49.0408i		−	1.76846i	0.467056	−	0.884228i	$-0.345315\pi$
$770$		0			0
$771$		0			0
$772$	−6.48244	−	3.74264i	−0.233308	−	0.134701i
$773$	−19.9706	+	11.5300i	−0.718291	+	0.414706i	−0.814123	−	0.580692i	$-0.802782\pi$
$773$	−19.9706	+	11.5300i	−0.718291	+	0.414706i	0.0958322	+	0.995398i	$0.469449\pi$
$774$		0			0
$775$		0			0
$776$	−3.76127			−0.135022
$777$		0			0
$778$		−	19.4558i		−	0.697526i
$779$	1.78304	+	1.02944i	0.0638840	+	0.0368834i
$780$		0			0
$781$	−15.3640	−	26.6112i	−0.549766	−	0.952222i
$782$	−3.72792	−	2.15232i	−0.133310	−	0.0769667i
$783$		0			0
$784$	−6.74264	−	1.88064i	−0.240809	−	0.0671656i
$785$		0			0
$786$		0			0
$787$	18.5453	+	32.1213i	0.661067	+	1.14500i	0.980336	+	0.197337i	$0.0632294\pi$
$787$	18.5453	+	32.1213i	0.661067	+	1.14500i	−0.319269	+	0.947664i	$0.603437\pi$
$788$	4.75736	+	8.23999i	0.169474	+	0.293537i
$789$		0			0
$790$		0			0
$791$	−17.7408	−	13.7574i	−0.630789	−	0.489155i
$792$		0			0
$793$	12.5446	+	7.24264i	0.445473	+	0.257194i
$794$	−6.92820	−	12.0000i	−0.245873	−	0.425864i
$795$		0			0
$796$	−13.9706	−	8.06591i	−0.495173	−	0.285889i
$797$		−	37.6339i		−	1.33306i	−0.745478	−	0.666530i	$-0.767779\pi$
$797$		−	37.6339i		−	1.33306i	0.745478	−	0.666530i	$-0.232221\pi$
$798$		0			0
$799$	−1.02944			−0.0364189
$800$		0			0
$801$		0			0
$802$		0			0
$803$	21.7279	+	12.5446i	0.766762	+	0.442690i
$804$		0			0
$805$		0			0
$806$			13.7574i			0.484582i
$807$		0			0
$808$		0			0
$809$	35.4815	−	20.4853i	1.24746	−	0.720224i	0.276862	−	0.960910i	$-0.410706\pi$
$809$	35.4815	−	20.4853i	1.24746	−	0.720224i	0.970603	+	0.240686i	$0.0773723\pi$
$810$		0			0
$811$			31.1769i			1.09477i	0.836881	+	0.547385i	$0.184377\pi$
$811$			31.1769i			1.09477i	−0.836881	+	0.547385i	$0.815623\pi$
$812$	3.25736	+	0.445759i	0.114311	+	0.0156431i
$813$		0			0
$814$	−12.3640	+	21.4150i	−0.433357	+	0.750596i
$815$		0			0
$816$		0			0
$817$	4.18154	−	7.24264i	0.146294	−	0.253388i
$818$			4.60181i			0.160898i
$819$		0			0
$820$		0			0
$821$	42.6454	+	24.6213i	1.48833	+	0.859290i	0.999911	−	0.0133172i	$-0.00423912\pi$
$821$	42.6454	+	24.6213i	1.48833	+	0.859290i	0.488423	+	0.872607i	$0.337572\pi$
$822$		0			0
$823$	32.8580	−	18.9706i	1.14536	−	0.661272i	0.197606	−	0.980282i	$-0.436683\pi$
$823$	32.8580	−	18.9706i	1.14536	−	0.661272i	0.947752	+	0.319009i	$0.103350\pi$
$824$	−7.64564	+	13.2426i	−0.266349	+	0.461329i
$825$		0			0
$826$	24.1066	+	18.6938i	0.838776	+	0.650442i
$827$	4.02944			0.140117			0.0700586	−	0.997543i	$-0.477681\pi$
$827$	4.02944			0.140117			0.0700586	+	0.997543i	$0.477681\pi$
$828$		0			0
$829$	35.3345	−	20.4004i	1.22722	−	0.708535i	0.260772	−	0.965401i	$-0.416023\pi$
$829$	35.3345	−	20.4004i	1.22722	−	0.708535i	0.966447	+	0.256865i	$0.0826897\pi$
$830$		0			0
$831$		0			0
$832$	2.44949			0.0849208
$833$	4.97056	+	5.07306i	0.172220	+	0.175771i
$834$		0			0
$835$		0			0
$836$	1.52192	+	2.63604i	0.0526366	+	0.0911693i
$837$		0			0
$838$	2.02922	−	3.51472i	0.0700984	−	0.121414i
$839$	24.0746			0.831149			0.415574	−	0.909559i	$-0.363581\pi$
$839$	24.0746			0.831149			0.415574	+	0.909559i	$0.363581\pi$
$840$		0			0
$841$	27.4558			0.946753
$842$	2.87868	−	4.98602i	0.0992059	−	0.171830i
$843$		0			0
$844$	−4.12132	−	7.13834i	−0.141862	−	0.245712i
$845$		0			0
$846$		0			0
$847$	4.89898	−	2.00000i	0.168331	−	0.0687208i
$848$	1.24264			0.0426725
$849$		0			0
$850$		0			0
$851$	30.2854	−	17.4853i	1.03817	−	0.599388i
$852$		0			0
$853$	−2.27541			−0.0779085			−0.0389543	−	0.999241i	$-0.512403\pi$
$853$	−2.27541			−0.0779085			−0.0389543	+	0.999241i	$0.512403\pi$
$854$	15.5014	+	2.12132i	0.530448	+	0.0725901i
$855$		0			0
$856$	−2.74264	+	4.75039i	−0.0937415	+	0.162365i
$857$	17.3345	−	10.0081i	0.592136	−	0.341870i	−0.173806	−	0.984780i	$-0.555606\pi$
$857$	17.3345	−	10.0081i	0.592136	−	0.341870i	0.765942	+	0.642910i	$0.222273\pi$
$858$		0			0
$859$	−3.87868	−	2.23936i	−0.132339	−	0.0764059i	0.432369	−	0.901697i	$-0.357678\pi$
$859$	−3.87868	−	2.23936i	−0.132339	−	0.0764059i	−0.564708	+	0.825291i	$0.691011\pi$
$860$		0			0
$861$		0			0
$862$		−	20.4853i		−	0.697731i
$863$	25.2426	−	43.7215i	0.859269	−	1.48830i	−0.0133573	−	0.999911i	$-0.504252\pi$
$863$	25.2426	−	43.7215i	0.859269	−	1.48830i	0.872627	−	0.488388i	$-0.162415\pi$
$864$		0			0
$865$		0			0
$866$	1.73205	−	3.00000i	0.0588575	−	0.101944i
$867$		0			0
$868$	5.61642	+	13.7574i	0.190634	+	0.466955i
$869$		−	33.7279i		−	1.14414i
$870$		0			0
$871$	−21.2132	+	12.2474i	−0.718782	+	0.414989i
$872$	0.757359	+	1.31178i	0.0256474	+	0.0444226i
$873$		0			0
$874$		−	4.30463i		−	0.145606i
$875$		0			0
$876$		0			0
$877$	10.8126	+	6.24264i	0.365115	+	0.210799i	0.671322	−	0.741166i	$-0.265727\pi$
$877$	10.8126	+	6.24264i	0.365115	+	0.210799i	−0.306207	+	0.951965i	$0.599060\pi$
$878$	23.5919	−	13.6208i	0.796187	−	0.459679i
$879$		0			0
$880$		0			0
$881$	−39.7862			−1.34043			−0.670215	−	0.742167i	$-0.733798\pi$
$881$	−39.7862			−1.34043			−0.670215	+	0.742167i	$0.733798\pi$
$882$		0			0
$883$			9.45584i			0.318214i	0.987261	+	0.159107i	$0.0508616\pi$
$883$			9.45584i			0.318214i	−0.987261	+	0.159107i	$0.949138\pi$
$884$	−2.15232	−	1.24264i	−0.0723902	−	0.0417945i
$885$		0			0
$886$	17.2279	+	29.8396i	0.578783	+	1.00248i
$887$	38.8492	+	22.4296i	1.30443	+	0.753113i	0.981161	−	0.193194i	$-0.0618847\pi$
$887$	38.8492	+	22.4296i	1.30443	+	0.753113i	0.323269	+	0.946307i	$0.395218\pi$
$888$		0			0
$889$	−8.50000	+	10.9612i	−0.285081	+	0.367625i
$890$		0			0
$891$		0			0
$892$	6.27231	+	10.8640i	0.210012	+	0.363752i
$893$	−0.514719	−	0.891519i	−0.0172244	−	0.0298335i
$894$		0			0
$895$		0			0
$896$	2.44949	−	1.00000i	0.0818317	−	0.0334077i
$897$		0			0
$898$	8.87039	+	5.12132i	0.296009	+	0.170901i
$899$	−3.48960	−	6.04416i	−0.116385	−	0.201584i
$900$		0			0
$901$	−1.09188	−	0.630399i	−0.0363759	−	0.0210016i
$902$		−	6.08767i		−	0.202697i
$903$		0			0
$904$	8.48528			0.282216
$905$		0			0
$906$		0			0
$907$	23.9876	−	13.8492i	0.796495	−	0.459857i	−0.0457492	−	0.998953i	$-0.514567\pi$
$907$	23.9876	−	13.8492i	0.796495	−	0.459857i	0.842244	+	0.539096i	$0.181234\pi$
$908$	13.5000	+	7.79423i	0.448013	+	0.258661i
$909$		0			0
$910$		0			0
$911$		−	18.7279i		−	0.620484i	−0.950658	−	0.310242i	$-0.899590\pi$
$911$		−	18.7279i		−	0.620484i	0.950658	−	0.310242i	$-0.100410\pi$
$912$		0			0
$913$	−4.75039	−	8.22792i	−0.157215	−	0.272304i
$914$	−19.9186	+	11.5000i	−0.658848	+	0.380386i
$915$		0			0
$916$		−	13.8564i		−	0.457829i
$917$	12.7279	−	5.19615i	0.420313	−	0.171592i
$918$		0			0
$919$	9.75736	−	16.9002i	0.321866	−	0.557488i	−0.659007	−	0.752136i	$-0.729023\pi$
$919$	9.75736	−	16.9002i	0.321866	−	0.557488i	0.980873	+	0.194649i	$0.0623567\pi$
$920$		0			0
$921$		0			0
$922$	−11.4069	+	19.7574i	−0.375667	+	0.650674i
$923$			25.0892i			0.825823i
$924$		0			0
$925$		0			0
$926$	18.5813	+	10.7279i	0.610620	+	0.352541i
$927$		0			0
$928$	−1.07616	+	0.621320i	−0.0353266	+	0.0203958i
$929$	−1.64501	+	2.84924i	−0.0539711	+	0.0934806i	−0.891749	−	0.452531i	$-0.850521\pi$
$929$	−1.64501	+	2.84924i	−0.0539711	+	0.0934806i	0.837778	+	0.546012i	$0.183855\pi$
$930$		0			0
$931$	−1.90812	+	6.84116i	−0.0625360	+	0.224210i
$932$	6.72792			0.220380
$933$		0			0
$934$	16.4558	−	9.50079i	0.538452	−	0.310875i
$935$		0			0
$936$		0			0
$937$	−4.00746			−0.130918			−0.0654590	−	0.997855i	$-0.520851\pi$
$937$	−4.00746			−0.130918			−0.0654590	+	0.997855i	$0.520851\pi$
$938$	−16.2132	+	20.9077i	−0.529380	+	0.682661i
$939$		0			0
$940$		0			0
$941$	26.0423	+	45.1066i	0.848955	+	1.47043i	0.882142	+	0.470984i	$0.156101\pi$
$941$	26.0423	+	45.1066i	0.848955	+	1.47043i	−0.0331867	+	0.999449i	$0.510566\pi$
$942$		0			0
$943$	−4.30463	+	7.45584i	−0.140178	+	0.242796i
$944$	−11.5300			−0.375270
$945$		0			0
$946$	−24.7279			−0.803974
$947$	−11.4853	+	19.8931i	−0.373221	+	0.646439i	−0.990059	−	0.140652i	$-0.955080\pi$
$947$	−11.4853	+	19.8931i	−0.373221	+	0.646439i	0.616838	+	0.787090i	$0.288414\pi$
$948$		0			0
$949$	−10.2426	−	17.7408i	−0.332490	−	0.575890i
$950$		0			0
$951$		0			0
$952$	−2.65962	−	0.363961i	−0.0861989	−	0.0117960i
$953$	−41.6985			−1.35075			−0.675373	−	0.737476i	$-0.736017\pi$
$953$	−41.6985			−1.35075			−0.675373	+	0.737476i	$0.736017\pi$
$954$		0			0
$955$		0			0
$956$	−11.0227	+	6.36396i	−0.356500	+	0.205825i
$957$		0			0
$958$	36.4962			1.17914
$959$	5.19615	−	37.9706i	0.167793	−	1.22613i
$960$		0			0
$961$	0.272078	−	0.471253i	0.00877671	−	0.0152017i
$962$	17.4853	−	10.0951i	0.563748	−	0.325480i
$963$		0			0
$964$	−14.7426	−	8.51167i	−0.474828	−	0.274142i
$965$		0			0
$966$		0			0
$967$			22.2721i			0.716222i	0.933679	+	0.358111i	$0.116579\pi$
$967$			22.2721i			0.716222i	−0.933679	+	0.358111i	$0.883421\pi$
$968$	−1.00000	+	1.73205i	−0.0321412	+	0.0556702i
$969$		0			0
$970$		0			0
$971$	−25.6581	+	44.4411i	−0.823407	+	1.42618i	0.0797229	+	0.996817i	$0.474596\pi$
$971$	−25.6581	+	44.4411i	−0.823407	+	1.42618i	−0.903130	+	0.429367i	$0.858737\pi$
$972$		0			0
$973$	32.7349	−	42.2132i	1.04943	−	1.35329i
$974$			28.2132i			0.904009i
$975$		0			0
$976$	−5.12132	+	2.95680i	−0.163929	+	0.0946447i
$977$	−15.8787	−	27.5027i	−0.508004	−	0.879889i	−0.999957	−	0.00926698i	$-0.997050\pi$
$977$	−15.8787	−	27.5027i	−0.508004	−	0.879889i	0.491953	−	0.870622i	$-0.336283\pi$
$978$		0			0
$979$		−	31.1769i		−	0.996419i
$980$		0			0
$981$		0			0
$982$	17.2950	+	9.98528i	0.551906	+	0.318643i
$983$	−7.02944	+	4.05845i	−0.224204	+	0.129444i	−0.607895	−	0.794017i	$-0.707986\pi$
$983$	−7.02944	+	4.05845i	−0.224204	+	0.129444i	0.383691	+	0.923461i	$0.374653\pi$
$984$		0			0
$985$		0			0
$986$	1.26080			0.0401520
$987$		0			0
$988$		−	2.48528i		−	0.0790673i
$989$	30.2854	+	17.4853i	0.963020	+	0.556000i
$990$		0			0
$991$	−4.89340	−	8.47561i	−0.155444	−	0.269237i	0.777777	−	0.628541i	$-0.216347\pi$
$991$	−4.89340	−	8.47561i	−0.155444	−	0.269237i	−0.933221	+	0.359304i	$0.883014\pi$
$992$	−4.86396	−	2.80821i	−0.154431	−	0.0891607i
$993$		0			0
$994$	10.2426	+	25.0892i	0.324877	+	0.795782i
$995$		0			0
$996$		0			0
$997$	−4.77589	−	8.27208i	−0.151254	−	0.261979i	0.780435	−	0.625237i	$-0.214998\pi$
$997$	−4.77589	−	8.27208i	−0.151254	−	0.261979i	−0.931689	+	0.363258i	$0.881664\pi$
$998$	−17.9706	−	31.1259i	−0.568848	−	0.985274i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3150.2.bp.b.1349.1		8
3.2	odd	2		3150.2.bp.e.1349.1		8
5.2	odd	4		3150.2.bf.a.1601.2		8
5.3	odd	4		126.2.k.a.89.4	yes	8
5.4	even	2		3150.2.bp.e.1349.4		8
7.3	odd	6	inner	3150.2.bp.b.899.4		8
15.2	even	4		3150.2.bf.a.1601.4		8
15.8	even	4		126.2.k.a.89.1	yes	8
15.14	odd	2	inner	3150.2.bp.b.1349.4		8
20.3	even	4		1008.2.bt.c.593.4		8
21.17	even	6		3150.2.bp.e.899.4		8
35.3	even	12		126.2.k.a.17.1	✓	8
35.13	even	4		882.2.k.a.215.3		8
35.17	even	12		3150.2.bf.a.1151.4		8
35.18	odd	12		882.2.k.a.521.2		8
35.23	odd	12		882.2.d.a.881.1		8
35.24	odd	6		3150.2.bp.e.899.1		8
35.33	even	12		882.2.d.a.881.4		8
45.13	odd	12		1134.2.t.e.593.1		8
45.23	even	12		1134.2.t.e.593.4		8
45.38	even	12		1134.2.l.f.215.3		8
45.43	odd	12		1134.2.l.f.215.2		8
60.23	odd	4		1008.2.bt.c.593.1		8
105.17	odd	12		3150.2.bf.a.1151.2		8
105.23	even	12		882.2.d.a.881.8		8
105.38	odd	12		126.2.k.a.17.4	yes	8
105.53	even	12		882.2.k.a.521.3		8
105.59	even	6	inner	3150.2.bp.b.899.1		8
105.68	odd	12		882.2.d.a.881.5		8
105.83	odd	4		882.2.k.a.215.2		8
140.3	odd	12		1008.2.bt.c.17.1		8
140.23	even	12		7056.2.k.f.881.2		8
140.103	odd	12		7056.2.k.f.881.8		8
315.38	odd	12		1134.2.t.e.1025.1		8
315.178	even	12		1134.2.t.e.1025.4		8
315.248	odd	12		1134.2.l.f.269.4		8
315.283	even	12		1134.2.l.f.269.1		8
420.23	odd	12		7056.2.k.f.881.7		8
420.143	even	12		1008.2.bt.c.17.4		8
420.383	even	12		7056.2.k.f.881.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.k.a.17.1	✓	8	35.3	even	12
126.2.k.a.17.4	yes	8	105.38	odd	12
126.2.k.a.89.1	yes	8	15.8	even	4
126.2.k.a.89.4	yes	8	5.3	odd	4
882.2.d.a.881.1		8	35.23	odd	12
882.2.d.a.881.4		8	35.33	even	12
882.2.d.a.881.5		8	105.68	odd	12
882.2.d.a.881.8		8	105.23	even	12
882.2.k.a.215.2		8	105.83	odd	4
882.2.k.a.215.3		8	35.13	even	4
882.2.k.a.521.2		8	35.18	odd	12
882.2.k.a.521.3		8	105.53	even	12
1008.2.bt.c.17.1		8	140.3	odd	12
1008.2.bt.c.17.4		8	420.143	even	12
1008.2.bt.c.593.1		8	60.23	odd	4
1008.2.bt.c.593.4		8	20.3	even	4
1134.2.l.f.215.2		8	45.43	odd	12
1134.2.l.f.215.3		8	45.38	even	12
1134.2.l.f.269.1		8	315.283	even	12
1134.2.l.f.269.4		8	315.248	odd	12
1134.2.t.e.593.1		8	45.13	odd	12
1134.2.t.e.593.4		8	45.23	even	12
1134.2.t.e.1025.1		8	315.38	odd	12
1134.2.t.e.1025.4		8	315.178	even	12
3150.2.bf.a.1151.2		8	105.17	odd	12
3150.2.bf.a.1151.4		8	35.17	even	12
3150.2.bf.a.1601.2		8	5.2	odd	4
3150.2.bf.a.1601.4		8	15.2	even	4
3150.2.bp.b.899.1		8	105.59	even	6	inner
3150.2.bp.b.899.4		8	7.3	odd	6	inner
3150.2.bp.b.1349.1		8	1.1	even	1	trivial
3150.2.bp.b.1349.4		8	15.14	odd	2	inner
3150.2.bp.e.899.1		8	35.24	odd	6
3150.2.bp.e.899.4		8	21.17	even	6
3150.2.bp.e.1349.1		8	3.2	odd	2
3150.2.bp.e.1349.4		8	5.4	even	2
7056.2.k.f.881.1		8	420.383	even	12
7056.2.k.f.881.2		8	140.23	even	12
7056.2.k.f.881.7		8	420.23	odd	12
7056.2.k.f.881.8		8	140.103	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3150.bp (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.09077 - 1.62132i) q^{7} +1.00000 q^{8} +(-2.59808 + 1.50000i) q^{11} +2.44949 q^{13} +(2.44949 - 1.00000i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(0.878680 - 0.507306i) q^{17} +(0.878680 + 0.507306i) q^{19} -3.00000i q^{22} +(-2.12132 + 3.67423i) q^{23} +(-1.22474 + 2.12132i) q^{26} +(-0.358719 + 2.62132i) q^{28} -1.24264i q^{29} +(4.86396 - 2.80821i) q^{31} +(-0.500000 - 0.866025i) q^{32} +1.01461i q^{34} +(-7.13834 - 4.12132i) q^{37} +(-0.878680 + 0.507306i) q^{38} +2.02922 q^{41} -8.24264i q^{43} +(2.59808 + 1.50000i) q^{44} +(-2.12132 - 3.67423i) q^{46} +(-0.878680 - 0.507306i) q^{47} +(1.74264 + 6.77962i) q^{49} +(-1.22474 - 2.12132i) q^{52} +(-0.621320 - 1.07616i) q^{53} +(-2.09077 - 1.62132i) q^{56} +(1.07616 + 0.621320i) q^{58} +(5.76500 + 9.98528i) q^{59} +(5.12132 + 2.95680i) q^{61} +5.61642i q^{62} +1.00000 q^{64} +(-8.66025 + 5.00000i) q^{67} +(-0.878680 - 0.507306i) q^{68} +10.2426i q^{71} +(-4.18154 - 7.24264i) q^{73} +(7.13834 - 4.12132i) q^{74} -1.01461i q^{76} +(7.86396 + 1.07616i) q^{77} +(-5.62132 + 9.73641i) q^{79} +(-1.01461 + 1.75736i) q^{82} +3.16693i q^{83} +(7.13834 + 4.12132i) q^{86} +(-2.59808 + 1.50000i) q^{88} +(-5.19615 + 9.00000i) q^{89} +(-5.12132 - 3.97141i) q^{91} +4.24264 q^{92} +(0.878680 - 0.507306i) q^{94} -3.76127 q^{97} +(-6.74264 - 1.88064i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} - 4 q^{4} + 8 q^{8} - 4 q^{16} + 24 q^{17} + 24 q^{19} - 12 q^{31} - 4 q^{32} - 24 q^{38} - 24 q^{47} - 20 q^{49} + 12 q^{53} + 24 q^{61} + 8 q^{64} - 24 q^{68} + 12 q^{77} - 28 q^{79} - 24 q^{91}+ \cdots - 20 q^{98}+O(q^{100}) \) 8 * q - 4 * q^2 - 4 * q^4 + 8 * q^8 - 4 * q^16 + 24 * q^17 + 24 * q^19 - 12 * q^31 - 4 * q^32 - 24 * q^38 - 24 * q^47 - 20 * q^49 + 12 * q^53 + 24 * q^61 + 8 * q^64 - 24 * q^68 + 12 * q^77 - 28 * q^79 - 24 * q^91 + 24 * q^94 - 20 * q^98

Introduction

L-functions

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Database

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