LMFDB - Embedded newform 1575.2.m.c.1457.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1575,2,Mod(1268,1575)] 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("1575.1268"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1575, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1575 = 3^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1575.m (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,0,0,0,0,-24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(8)] == traces)

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

Self dual:	no
Analytic conductor:	$12.5764383184$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 18x^{10} + 107x^{8} + 240x^{6} + 151x^{4} + 30x^{2} + 1 $ x^12 + 18x^10 + 107x^8 + 240x^6 + 151x^4 + 30*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 315)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1457.3
Root			$-0.203482i$ of defining polynomial
Character	$\chi$	$=$	1575.1457
Dual form			1575.2.m.c.1268.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.876184 + 0.876184i) q^{2} +0.464602i q^{4} +(0.707107 + 0.707107i) q^{7} +(-2.15945 - 2.15945i) q^{8} +4.66231i q^{11} +(-1.54889 + 1.54889i) q^{13} -1.23911 q^{14} +2.85494 q^{16} +(-2.32993 + 2.32993i) q^{17} -3.54791i q^{19} +(-4.08504 - 4.08504i) q^{22} +(-1.44259 - 1.44259i) q^{23} -2.71422i q^{26} +(-0.328523 + 0.328523i) q^{28} -7.58625 q^{29} +8.12691 q^{31} +(1.81744 - 1.81744i) q^{32} -4.08289i q^{34} +(6.00046 + 6.00046i) q^{37} +(3.10862 + 3.10862i) q^{38} -6.72475i q^{41} +(-5.46460 + 5.46460i) q^{43} -2.16612 q^{44} +2.52796 q^{46} +(-5.16658 + 5.16658i) q^{47} +1.00000i q^{49} +(-0.719616 - 0.719616i) q^{52} +(-6.86452 - 6.86452i) q^{53} -3.05392i q^{56} +(6.64695 - 6.64695i) q^{58} -6.40696 q^{59} -13.6036 q^{61} +(-7.12067 + 7.12067i) q^{62} +8.89470i q^{64} +(-2.77125 - 2.77125i) q^{67} +(-1.08249 - 1.08249i) q^{68} -0.576549i q^{71} +(4.94384 - 4.94384i) q^{73} -10.5150 q^{74} +1.64837 q^{76} +(-3.29675 + 3.29675i) q^{77} -2.50976i q^{79} +(5.89212 + 5.89212i) q^{82} +(3.99501 + 3.99501i) q^{83} -9.57600i q^{86} +(10.0680 - 10.0680i) q^{88} +6.86727 q^{89} -2.19046 q^{91} +(0.670232 - 0.670232i) q^{92} -9.05376i q^{94} +(-4.43407 - 4.43407i) q^{97} +(-0.876184 - 0.876184i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 24 q^{8} + 4 q^{13} - 4 q^{14} - 20 q^{16} - 8 q^{17} + 8 q^{22} - 8 q^{23} - 32 q^{29} - 48 q^{32} - 4 q^{37} - 24 q^{38} - 40 q^{43} - 64 q^{44} + 16 q^{46} - 24 q^{47} - 36 q^{52} + 40 q^{53}+ \cdots - 12 q^{97}+O(q^{100}) $ 12 * q - 24 * q^8 + 4 * q^13 - 4 * q^14 - 20 * q^16 - 8 * q^17 + 8 * q^22 - 8 * q^23 - 32 * q^29 - 48 * q^32 - 4 * q^37 - 24 * q^38 - 40 * q^43 - 64 * q^44 + 16 * q^46 - 24 * q^47 - 36 * q^52 + 40 * q^53 + 28 * q^58 - 80 * q^59 - 32 * q^61 - 16 * q^62 + 48 * q^67 - 32 * q^68 + 20 * q^73 - 64 * q^74 + 16 * q^76 - 20 * q^82 - 24 * q^83 - 56 * q^89 - 8 * q^92 - 12 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1575\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$1226$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−0.876184	+	0.876184i	−0.619556	+	0.619556i	−0.945417	−	0.325862i	$-0.894346\pi$
$2$	−0.876184	+	0.876184i	−0.619556	+	0.619556i	0.325862	+	0.945417i	$0.394346\pi$
$3$		0			0
$3$		0			0
$4$			0.464602i			0.232301i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$8$	−2.15945	−	2.15945i	−0.763479	−	0.763479i
$9$		0			0
$10$		0			0
$11$			4.66231i			1.40574i	0.711319	+	0.702870i	$0.248098\pi$
$11$			4.66231i			1.40574i	−0.711319	+	0.702870i	$0.751902\pi$
$12$		0			0
$13$	−1.54889	+	1.54889i	−0.429584	+	0.429584i	−0.888487	−	0.458903i	$-0.848243\pi$
$13$	−1.54889	+	1.54889i	−0.429584	+	0.429584i	0.458903	+	0.888487i	$0.348243\pi$
$14$	−1.23911			−0.331167
$15$		0			0
$16$	2.85494			0.713735
$17$	−2.32993	+	2.32993i	−0.565091	+	0.565091i	−0.930749	−	0.365658i	$-0.880844\pi$
$17$	−2.32993	+	2.32993i	−0.565091	+	0.565091i	0.365658	+	0.930749i	$0.380844\pi$
$18$		0			0
$19$		−	3.54791i		−	0.813946i	−0.913440	−	0.406973i	$-0.866584\pi$
$19$		−	3.54791i		−	0.813946i	0.913440	−	0.406973i	$-0.133416\pi$
$20$		0			0
$21$		0			0
$22$	−4.08504	−	4.08504i	−0.870934	−	0.870934i
$23$	−1.44259	−	1.44259i	−0.300802	−	0.300802i	0.540526	−	0.841327i	$-0.318225\pi$
$23$	−1.44259	−	1.44259i	−0.300802	−	0.300802i	−0.841327	+	0.540526i	$0.818225\pi$
$24$		0			0
$25$		0			0
$26$		−	2.71422i		−	0.532303i
$27$		0			0
$28$	−0.328523	+	0.328523i	−0.0620851	+	0.0620851i
$29$	−7.58625			−1.40873			−0.704366	−	0.709837i	$-0.748768\pi$
$29$	−7.58625			−1.40873			−0.704366	+	0.709837i	$0.748768\pi$
$30$		0			0
$31$	8.12691			1.45964			0.729818	−	0.683641i	$-0.239605\pi$
$31$	8.12691			1.45964			0.729818	+	0.683641i	$0.239605\pi$
$32$	1.81744	−	1.81744i	0.321280	−	0.321280i
$33$		0			0
$34$		−	4.08289i		−	0.700211i
$35$		0			0
$36$		0			0
$37$	6.00046	+	6.00046i	0.986470	+	0.986470i	0.999910	−	0.0134395i	$-0.00427804\pi$
$37$	6.00046	+	6.00046i	0.986470	+	0.986470i	−0.0134395	+	0.999910i	$0.504278\pi$
$38$	3.10862	+	3.10862i	0.504285	+	0.504285i
$39$		0			0
$40$		0			0
$41$		−	6.72475i		−	1.05023i	−0.851032	−	0.525114i	$-0.824023\pi$
$41$		−	6.72475i		−	1.05023i	0.851032	−	0.525114i	$-0.175977\pi$
$42$		0			0
$43$	−5.46460	+	5.46460i	−0.833344	+	0.833344i	−0.987973	−	0.154629i	$-0.950582\pi$
$43$	−5.46460	+	5.46460i	−0.833344	+	0.833344i	0.154629	+	0.987973i	$0.450582\pi$
$44$	−2.16612			−0.326555
$45$		0			0
$46$	2.52796			0.372727
$47$	−5.16658	+	5.16658i	−0.753623	+	0.753623i	−0.975154	−	0.221530i	$-0.928895\pi$
$47$	−5.16658	+	5.16658i	−0.753623	+	0.753623i	0.221530	+	0.975154i	$0.428895\pi$
$48$		0			0
$49$			1.00000i			0.142857i
$50$		0			0
$51$		0			0
$52$	−0.719616	−	0.719616i	−0.0997928	−	0.0997928i
$53$	−6.86452	−	6.86452i	−0.942915	−	0.942915i	0.0555419	−	0.998456i	$-0.482311\pi$
$53$	−6.86452	−	6.86452i	−0.942915	−	0.942915i	−0.998456	+	0.0555419i	$0.982311\pi$
$54$		0			0
$55$		0			0
$56$		−	3.05392i		−	0.408097i
$57$		0			0
$58$	6.64695	−	6.64695i	0.872788	−	0.872788i
$59$	−6.40696			−0.834116			−0.417058	−	0.908880i	$-0.636939\pi$
$59$	−6.40696			−0.834116			−0.417058	+	0.908880i	$0.636939\pi$
$60$		0			0
$61$	−13.6036			−1.74176			−0.870879	−	0.491498i	$-0.836450\pi$
$61$	−13.6036			−1.74176			−0.870879	+	0.491498i	$0.836450\pi$
$62$	−7.12067	+	7.12067i	−0.904326	+	0.904326i
$63$		0			0
$64$			8.89470i			1.11184i
$65$		0			0
$66$		0			0
$67$	−2.77125	−	2.77125i	−0.338562	−	0.338562i	0.517264	−	0.855826i	$-0.326951\pi$
$67$	−2.77125	−	2.77125i	−0.338562	−	0.338562i	−0.855826	+	0.517264i	$0.826951\pi$
$68$	−1.08249	−	1.08249i	−0.131271	−	0.131271i
$69$		0			0
$70$		0			0
$71$		−	0.576549i		−	0.0684238i	−0.999415	−	0.0342119i	$-0.989108\pi$
$71$		−	0.576549i		−	0.0684238i	0.999415	−	0.0342119i	$-0.0108921\pi$
$72$		0			0
$73$	4.94384	−	4.94384i	0.578632	−	0.578632i	−0.355894	−	0.934526i	$-0.615824\pi$
$73$	4.94384	−	4.94384i	0.578632	−	0.578632i	0.934526	+	0.355894i	$0.115824\pi$
$74$	−10.5150			−1.22235
$75$		0			0
$76$	1.64837			0.189081
$77$	−3.29675	+	3.29675i	−0.375700	+	0.375700i
$78$		0			0
$79$		−	2.50976i		−	0.282370i	−0.989983	−	0.141185i	$-0.954909\pi$
$79$		−	2.50976i		−	0.282370i	0.989983	−	0.141185i	$-0.0450913\pi$
$80$		0			0
$81$		0			0
$82$	5.89212	+	5.89212i	0.650675	+	0.650675i
$83$	3.99501	+	3.99501i	0.438509	+	0.438509i	0.891510	−	0.453001i	$-0.149647\pi$
$83$	3.99501	+	3.99501i	0.438509	+	0.438509i	−0.453001	+	0.891510i	$0.649647\pi$
$84$		0			0
$85$		0			0
$86$		−	9.57600i		−	1.03261i
$87$		0			0
$88$	10.0680	−	10.0680i	1.07325	−	1.07325i
$89$	6.86727			0.727929			0.363964	−	0.931413i	$-0.381423\pi$
$89$	6.86727			0.727929			0.363964	+	0.931413i	$0.381423\pi$
$90$		0			0
$91$	−2.19046			−0.229622
$92$	0.670232	−	0.670232i	0.0698765	−	0.0698765i
$93$		0			0
$94$		−	9.05376i		−	0.933824i
$95$		0			0
$96$		0			0
$97$	−4.43407	−	4.43407i	−0.450212	−	0.450212i	0.445213	−	0.895425i	$-0.353128\pi$
$97$	−4.43407	−	4.43407i	−0.450212	−	0.450212i	−0.895425	+	0.445213i	$0.853128\pi$
$98$	−0.876184	−	0.876184i	−0.0885080	−	0.0885080i
$99$		0			0
$100$		0			0
$101$			2.63552i			0.262244i	0.991366	+	0.131122i	$0.0418579\pi$
$101$			2.63552i			0.262244i	−0.991366	+	0.131122i	$0.958142\pi$
$102$		0			0
$103$	−7.45961	+	7.45961i	−0.735017	+	0.735017i	−0.971609	−	0.236592i	$-0.923970\pi$
$103$	−7.45961	+	7.45961i	−0.735017	+	0.735017i	0.236592	+	0.971609i	$0.423970\pi$
$104$	6.68947			0.655957
$105$		0			0
$106$	12.0292			1.16838
$107$	−4.48615	+	4.48615i	−0.433692	+	0.433692i	−0.889882	−	0.456190i	$-0.849214\pi$
$107$	−4.48615	+	4.48615i	−0.433692	+	0.433692i	0.456190	+	0.889882i	$0.349214\pi$
$108$		0			0
$109$		−	7.54504i		−	0.722684i	−0.932433	−	0.361342i	$-0.882319\pi$
$109$		−	7.54504i		−	0.722684i	0.932433	−	0.361342i	$-0.117681\pi$
$110$		0			0
$111$		0			0
$112$	2.01875	+	2.01875i	0.190754	+	0.190754i
$113$	1.80305	+	1.80305i	0.169617	+	0.169617i	0.786811	−	0.617194i	$-0.211731\pi$
$113$	1.80305	+	1.80305i	0.169617	+	0.169617i	−0.617194	+	0.786811i	$0.711731\pi$
$114$		0			0
$115$		0			0
$116$		−	3.52459i		−	0.327250i
$117$		0			0
$118$	5.61368	−	5.61368i	0.516781	−	0.516781i
$119$	−3.29502			−0.302054
$120$		0			0
$121$	−10.7371			−0.976102
$122$	11.9192	−	11.9192i	1.07912	−	1.07912i
$123$		0			0
$124$			3.77578i			0.339075i
$125$		0			0
$126$		0			0
$127$	−14.3511	−	14.3511i	−1.27346	−	1.27346i	−0.944262	−	0.329195i	$-0.893223\pi$
$127$	−14.3511	−	14.3511i	−1.27346	−	1.27346i	−0.329195	−	0.944262i	$-0.606777\pi$
$128$	−4.15852	−	4.15852i	−0.367565	−	0.367565i
$129$		0			0
$130$		0			0
$131$		−	3.22579i		−	0.281839i	−0.990021	−	0.140919i	$-0.954994\pi$
$131$		−	3.22579i		−	0.281839i	0.990021	−	0.140919i	$-0.0450059\pi$
$132$		0			0
$133$	2.50875	−	2.50875i	0.217536	−	0.217536i
$134$	4.85626			0.419517
$135$		0			0
$136$	10.0627			0.862870
$137$	1.36108	−	1.36108i	0.116285	−	0.116285i	−0.646570	−	0.762855i	$-0.723797\pi$
$137$	1.36108	−	1.36108i	0.116285	−	0.116285i	0.762855	+	0.646570i	$0.223797\pi$
$138$		0			0
$139$		−	22.2867i		−	1.89033i	−0.326589	−	0.945166i	$-0.605899\pi$
$139$		−	22.2867i		−	1.89033i	0.326589	−	0.945166i	$-0.394101\pi$
$140$		0			0
$141$		0			0
$142$	0.505163	+	0.505163i	0.0423923	+	0.0423923i
$143$	−7.22139	−	7.22139i	−0.603883	−	0.603883i
$144$		0			0
$145$		0			0
$146$			8.66342i			0.716990i
$147$		0			0
$148$	−2.78783	+	2.78783i	−0.229158	+	0.229158i
$149$	−23.4052			−1.91743			−0.958713	−	0.284376i	$-0.908213\pi$
$149$	−23.4052			−1.91743			−0.958713	+	0.284376i	$0.908213\pi$
$150$		0			0
$151$	16.9889			1.38254			0.691269	−	0.722597i	$-0.257052\pi$
$151$	16.9889			1.38254			0.691269	+	0.722597i	$0.257052\pi$
$152$	−7.66152	+	7.66152i	−0.621431	+	0.621431i
$153$		0			0
$154$		−	5.77712i		−	0.465534i
$155$		0			0
$156$		0			0
$157$	−8.07929	−	8.07929i	−0.644798	−	0.644798i	0.306933	−	0.951731i	$-0.400697\pi$
$157$	−8.07929	−	8.07929i	−0.644798	−	0.644798i	−0.951731	+	0.306933i	$0.900697\pi$
$158$	2.19901	+	2.19901i	0.174944	+	0.174944i
$159$		0			0
$160$		0			0
$161$		−	2.04014i		−	0.160785i
$162$		0			0
$163$	−9.08622	+	9.08622i	−0.711688	+	0.711688i	−0.966888	−	0.255200i	$-0.917859\pi$
$163$	−9.08622	+	9.08622i	−0.711688	+	0.711688i	0.255200	+	0.966888i	$0.417859\pi$
$164$	3.12433			0.243969
$165$		0			0
$166$	−7.00073			−0.543362
$167$	13.5425	−	13.5425i	1.04795	−	1.04795i	0.0491596	−	0.998791i	$-0.484346\pi$
$167$	13.5425	−	13.5425i	1.04795	−	1.04795i	0.998791	−	0.0491596i	$-0.0156543\pi$
$168$		0			0
$169$			8.20190i			0.630915i
$170$		0			0
$171$		0			0
$172$	−2.53887	−	2.53887i	−0.193587	−	0.193587i
$173$	16.4883	+	16.4883i	1.25358	+	1.25358i	0.954102	+	0.299483i	$0.0968141\pi$
$173$	16.4883	+	16.4883i	1.25358	+	1.25358i	0.299483	+	0.954102i	$0.403186\pi$
$174$		0			0
$175$		0			0
$176$			13.3106i			1.00333i
$177$		0			0
$178$	−6.01699	+	6.01699i	−0.450993	+	0.450993i
$179$	7.15384			0.534703			0.267352	−	0.963599i	$-0.413852\pi$
$179$	7.15384			0.534703			0.267352	+	0.963599i	$0.413852\pi$
$180$		0			0
$181$	−4.86285			−0.361453			−0.180726	−	0.983533i	$-0.557845\pi$
$181$	−4.86285			−0.361453			−0.180726	+	0.983533i	$0.557845\pi$
$182$	1.91924	−	1.91924i	0.142264	−	0.142264i
$183$		0			0
$184$			6.23040i			0.459312i
$185$		0			0
$186$		0			0
$187$	−10.8628	−	10.8628i	−0.794370	−	0.794370i
$188$	−2.40040	−	2.40040i	−0.175067	−	0.175067i
$189$		0			0
$190$		0			0
$191$			0.990955i			0.0717030i	0.999357	+	0.0358515i	$0.0114143\pi$
$191$			0.990955i			0.0717030i	−0.999357	+	0.0358515i	$0.988586\pi$
$192$		0			0
$193$	−8.22384	+	8.22384i	−0.591965	+	0.591965i	−0.938162	−	0.346197i	$-0.887473\pi$
$193$	−8.22384	+	8.22384i	−0.591965	+	0.591965i	0.346197	+	0.938162i	$0.387473\pi$
$194$	7.77013			0.557863
$195$		0			0
$196$	−0.464602			−0.0331859
$197$	1.80305	−	1.80305i	0.128462	−	0.128462i	−0.639952	−	0.768414i	$-0.721046\pi$
$197$	1.80305	−	1.80305i	0.128462	−	0.128462i	0.768414	+	0.639952i	$0.221046\pi$
$198$		0			0
$199$			16.0345i			1.13666i	0.822802	+	0.568328i	$0.192410\pi$
$199$			16.0345i			1.13666i	−0.822802	+	0.568328i	$0.807590\pi$
$200$		0			0
$201$		0			0
$202$	−2.30920	−	2.30920i	−0.162475	−	0.162475i
$203$	−5.36429	−	5.36429i	−0.376499	−	0.376499i
$204$		0			0
$205$		0			0
$206$		−	13.0720i		−	0.910769i
$207$		0			0
$208$	−4.42198	+	4.42198i	−0.306609	+	0.306609i
$209$	16.5415			1.14420
$210$		0			0
$211$	−22.1632			−1.52578			−0.762890	−	0.646528i	$-0.776220\pi$
$211$	−22.1632			−1.52578			−0.762890	+	0.646528i	$0.776220\pi$
$212$	3.18927	−	3.18927i	0.219040	−	0.219040i
$213$		0			0
$214$		−	7.86138i		−	0.537393i
$215$		0			0
$216$		0			0
$217$	5.74659	+	5.74659i	0.390104	+	0.390104i
$218$	6.61085	+	6.61085i	0.447743	+	0.447743i
$219$		0			0
$220$		0			0
$221$		−	7.21759i		−	0.485508i
$222$		0			0
$223$	13.4515	−	13.4515i	0.900781	−	0.900781i	−0.0947227	−	0.995504i	$-0.530196\pi$
$223$	13.4515	−	13.4515i	0.900781	−	0.900781i	0.995504	+	0.0947227i	$0.0301964\pi$
$224$	2.57024			0.171732
$225$		0			0
$226$	−3.15961			−0.210174
$227$	8.57603	−	8.57603i	0.569211	−	0.569211i	−0.362696	−	0.931907i	$-0.618144\pi$
$227$	8.57603	−	8.57603i	0.569211	−	0.569211i	0.931907	+	0.362696i	$0.118144\pi$
$228$		0			0
$229$			22.4314i			1.48231i	0.671335	+	0.741154i	$0.265721\pi$
$229$			22.4314i			1.48231i	−0.671335	+	0.741154i	$0.734279\pi$
$230$		0			0
$231$		0			0
$232$	16.3821	+	16.3821i	1.07554	+	1.07554i
$233$	−3.98861	−	3.98861i	−0.261303	−	0.261303i	0.564281	−	0.825583i	$-0.309154\pi$
$233$	−3.98861	−	3.98861i	−0.261303	−	0.261303i	−0.825583	+	0.564281i	$0.809154\pi$
$234$		0			0
$235$		0			0
$236$		−	2.97669i		−	0.193766i
$237$		0			0
$238$	2.88704	−	2.88704i	0.187139	−	0.187139i
$239$	−9.15757			−0.592354			−0.296177	−	0.955133i	$-0.595712\pi$
$239$	−9.15757			−0.592354			−0.296177	+	0.955133i	$0.595712\pi$
$240$		0			0
$241$	−13.5613			−0.873560			−0.436780	−	0.899568i	$-0.643881\pi$
$241$	−13.5613			−0.873560			−0.436780	+	0.899568i	$0.643881\pi$
$242$	9.40770	−	9.40770i	0.604750	−	0.604750i
$243$		0			0
$244$		−	6.32024i		−	0.404612i
$245$		0			0
$246$		0			0
$247$	5.49531	+	5.49531i	0.349658	+	0.349658i
$248$	−17.5496	−	17.5496i	−1.11440	−	1.11440i
$249$		0			0
$250$		0			0
$251$			23.8741i			1.50692i	0.657494	+	0.753460i	$0.271617\pi$
$251$			23.8741i			1.50692i	−0.657494	+	0.753460i	$0.728383\pi$
$252$		0			0
$253$	6.72582	−	6.72582i	0.422848	−	0.422848i
$254$	25.1485			1.57796
$255$		0			0
$256$	−10.5021			−0.656383
$257$	−12.0222	+	12.0222i	−0.749921	+	0.749921i	−0.974464	−	0.224543i	$-0.927911\pi$
$257$	−12.0222	+	12.0222i	−0.749921	+	0.749921i	0.224543	+	0.974464i	$0.427911\pi$
$258$		0			0
$259$			8.48594i			0.527291i
$260$		0			0
$261$		0			0
$262$	2.82639	+	2.82639i	0.174615	+	0.174615i
$263$	1.26198	+	1.26198i	0.0778167	+	0.0778167i	0.744944	−	0.667127i	$-0.232476\pi$
$263$	1.26198	+	1.26198i	0.0778167	+	0.0778167i	−0.667127	+	0.744944i	$0.732476\pi$
$264$		0			0
$265$		0			0
$266$			4.39626i			0.269552i
$267$		0			0
$268$	1.28753	−	1.28753i	0.0786484	−	0.0786484i
$269$	−3.41582			−0.208266			−0.104133	−	0.994563i	$-0.533207\pi$
$269$	−3.41582			−0.208266			−0.104133	+	0.994563i	$0.533207\pi$
$270$		0			0
$271$	8.21326			0.498920			0.249460	−	0.968385i	$-0.419747\pi$
$271$	8.21326			0.498920			0.249460	+	0.968385i	$0.419747\pi$
$272$	−6.65181	+	6.65181i	−0.403325	+	0.403325i
$273$		0			0
$274$			2.38511i			0.144090i
$275$		0			0
$276$		0			0
$277$	4.57498	+	4.57498i	0.274884	+	0.274884i	0.831063	−	0.556179i	$-0.187733\pi$
$277$	4.57498	+	4.57498i	0.274884	+	0.274884i	−0.556179	+	0.831063i	$0.687733\pi$
$278$	19.5273	+	19.5273i	1.17117	+	1.17117i
$279$		0			0
$280$		0			0
$281$			11.0476i			0.659042i	0.944148	+	0.329521i	$0.106887\pi$
$281$			11.0476i			0.659042i	−0.944148	+	0.329521i	$0.893113\pi$
$282$		0			0
$283$	4.42604	−	4.42604i	0.263101	−	0.263101i	−0.563212	−	0.826313i	$-0.690434\pi$
$283$	4.42604	−	4.42604i	0.263101	−	0.263101i	0.826313	+	0.563212i	$0.190434\pi$
$284$	0.267866			0.0158949
$285$		0			0
$286$	12.6545			0.748278
$287$	4.75511	−	4.75511i	0.280685	−	0.280685i
$288$		0			0
$289$			6.14286i			0.361345i
$290$		0			0
$291$		0			0
$292$	2.29692	+	2.29692i	0.134417	+	0.134417i
$293$	22.3120	+	22.3120i	1.30348	+	1.30348i	0.926029	+	0.377452i	$0.123200\pi$
$293$	22.3120	+	22.3120i	1.30348	+	1.30348i	0.377452	+	0.926029i	$0.376800\pi$
$294$		0			0
$295$		0			0
$296$		−	25.9154i		−	1.50630i
$297$		0			0
$298$	20.5072	−	20.5072i	1.18795	−	1.18795i
$299$	4.46883			0.258439
$300$		0			0
$301$	−7.72811			−0.445441
$302$	−14.8854	+	14.8854i	−0.856560	+	0.856560i
$303$		0			0
$304$		−	10.1291i		−	0.580942i
$305$		0			0
$306$		0			0
$307$	−4.65242	−	4.65242i	−0.265527	−	0.265527i	0.561768	−	0.827295i	$-0.310121\pi$
$307$	−4.65242	−	4.65242i	−0.265527	−	0.265527i	−0.827295	+	0.561768i	$0.810121\pi$
$308$	−1.53168	−	1.53168i	−0.0872754	−	0.0872754i
$309$		0			0
$310$		0			0
$311$			12.7033i			0.720337i	0.932887	+	0.360169i	$0.117281\pi$
$311$			12.7033i			0.720337i	−0.932887	+	0.360169i	$0.882719\pi$
$312$		0			0
$313$	−9.39195	+	9.39195i	−0.530864	+	0.530864i	−0.920830	−	0.389965i	$-0.872487\pi$
$313$	−9.39195	+	9.39195i	−0.530864	+	0.530864i	0.389965	+	0.920830i	$0.372487\pi$
$314$	14.1579			0.798977
$315$		0			0
$316$	1.16604			0.0655949
$317$	12.0566	−	12.0566i	0.677166	−	0.677166i	−0.282192	−	0.959358i	$-0.591061\pi$
$317$	12.0566	−	12.0566i	0.677166	−	0.677166i	0.959358	+	0.282192i	$0.0910615\pi$
$318$		0			0
$319$		−	35.3694i		−	1.98031i
$320$		0			0
$321$		0			0
$322$	1.78753	+	1.78753i	0.0996154	+	0.0996154i
$323$	8.26638	+	8.26638i	0.459954	+	0.459954i
$324$		0			0
$325$		0			0
$326$		−	15.9224i		−	0.881861i
$327$		0			0
$328$	−14.5217	+	14.5217i	−0.801828	+	0.801828i
$329$	−7.30665			−0.402829
$330$		0			0
$331$	−0.841491			−0.0462525			−0.0231263	−	0.999733i	$-0.507362\pi$
$331$	−0.841491			−0.0462525			−0.0231263	+	0.999733i	$0.507362\pi$
$332$	−1.85609	+	1.85609i	−0.101866	+	0.101866i
$333$		0			0
$334$			23.7315i			1.29853i
$335$		0			0
$336$		0			0
$337$	16.1936	+	16.1936i	0.882124	+	0.882124i	0.993750	−	0.111626i	$-0.0356059\pi$
$337$	16.1936	+	16.1936i	0.882124	+	0.882124i	−0.111626	+	0.993750i	$0.535606\pi$
$338$	−7.18638	−	7.18638i	−0.390887	−	0.390887i
$339$		0			0
$340$		0			0
$341$			37.8902i			2.05187i
$342$		0			0
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$	23.6010			1.27248
$345$		0			0
$346$	−28.8936			−1.55333
$347$	6.72445	−	6.72445i	0.360988	−	0.360988i	−0.503189	−	0.864176i	$-0.667840\pi$
$347$	6.72445	−	6.72445i	0.360988	−	0.360988i	0.864176	+	0.503189i	$0.167840\pi$
$348$		0			0
$349$			25.9697i			1.39013i	0.718949	+	0.695063i	$0.244624\pi$
$349$			25.9697i			1.39013i	−0.718949	+	0.695063i	$0.755376\pi$
$350$		0			0
$351$		0			0
$352$	8.47345	+	8.47345i	0.451637	+	0.451637i
$353$	20.5943	+	20.5943i	1.09612	+	1.09612i	0.994860	+	0.101264i	$0.0322885\pi$
$353$	20.5943	+	20.5943i	1.09612	+	1.09612i	0.101264	+	0.994860i	$0.467711\pi$
$354$		0			0
$355$		0			0
$356$			3.19055i			0.169099i
$357$		0			0
$358$	−6.26808	+	6.26808i	−0.331278	+	0.331278i
$359$	−29.4326			−1.55339			−0.776697	−	0.629874i	$-0.783107\pi$
$359$	−29.4326			−1.55339			−0.776697	+	0.629874i	$0.783107\pi$
$360$		0			0
$361$	6.41233			0.337491
$362$	4.26075	−	4.26075i	0.223940	−	0.223940i
$363$		0			0
$364$		−	1.01769i		−	0.0533415i
$365$		0			0
$366$		0			0
$367$	13.4205	+	13.4205i	0.700544	+	0.700544i	0.964527	−	0.263983i	$-0.0850363\pi$
$367$	13.4205	+	13.4205i	0.700544	+	0.700544i	−0.263983	+	0.964527i	$0.585036\pi$
$368$	−4.11852	−	4.11852i	−0.214693	−	0.214693i
$369$		0			0
$370$		0			0
$371$		−	9.70790i		−	0.504009i
$372$		0			0
$373$	−1.38704	+	1.38704i	−0.0718184	+	0.0718184i	−0.742104	−	0.670285i	$-0.766172\pi$
$373$	−1.38704	+	1.38704i	−0.0718184	+	0.0718184i	0.670285	+	0.742104i	$0.266172\pi$
$374$	19.0357			0.984313
$375$		0			0
$376$	22.3139			1.15075
$377$	11.7502	−	11.7502i	0.605168	−	0.605168i
$378$		0			0
$379$			25.3851i			1.30394i	0.758243	+	0.651972i	$0.226058\pi$
$379$			25.3851i			1.30394i	−0.758243	+	0.651972i	$0.773942\pi$
$380$		0			0
$381$		0			0
$382$	−0.868259	−	0.868259i	−0.0444240	−	0.0444240i
$383$	−3.12729	−	3.12729i	−0.159797	−	0.159797i	0.622680	−	0.782477i	$-0.286044\pi$
$383$	−3.12729	−	3.12729i	−0.159797	−	0.159797i	−0.782477	+	0.622680i	$0.786044\pi$
$384$		0			0
$385$		0			0
$386$		−	14.4112i		−	0.733511i
$387$		0			0
$388$	2.06008	−	2.06008i	0.104585	−	0.104585i
$389$	10.5100			0.532876			0.266438	−	0.963852i	$-0.414153\pi$
$389$	10.5100			0.532876			0.266438	+	0.963852i	$0.414153\pi$
$390$		0			0
$391$	6.72228			0.339960
$392$	2.15945	−	2.15945i	0.109068	−	0.109068i
$393$		0			0
$394$			3.15961i			0.159179i
$395$		0			0
$396$		0			0
$397$	3.72909	+	3.72909i	0.187158	+	0.187158i	0.794466	−	0.607308i	$-0.207751\pi$
$397$	3.72909	+	3.72909i	0.187158	+	0.187158i	−0.607308	+	0.794466i	$0.707751\pi$
$398$	−14.0492	−	14.0492i	−0.704222	−	0.704222i
$399$		0			0
$400$		0			0
$401$			17.8421i			0.890994i	0.895283	+	0.445497i	$0.146973\pi$
$401$			17.8421i			0.890994i	−0.895283	+	0.445497i	$0.853027\pi$
$402$		0			0
$403$	−12.5877	+	12.5877i	−0.627036	+	0.627036i
$404$	−1.22447			−0.0609195
$405$		0			0
$406$	9.40021			0.466525
$407$	−27.9760	+	27.9760i	−1.38672	+	1.38672i
$408$		0			0
$409$		−	14.9681i		−	0.740127i	−0.929006	−	0.370064i	$-0.879336\pi$
$409$		−	14.9681i		−	0.740127i	0.929006	−	0.370064i	$-0.120664\pi$
$410$		0			0
$411$		0			0
$412$	−3.46575	−	3.46575i	−0.170745	−	0.170745i
$413$	−4.53041	−	4.53041i	−0.222927	−	0.222927i
$414$		0			0
$415$		0			0
$416$			5.63001i			0.276034i
$417$		0			0
$418$	−14.4934	+	14.4934i	−0.708894	+	0.708894i
$419$	6.71408			0.328004			0.164002	−	0.986460i	$-0.447560\pi$
$419$	6.71408			0.328004			0.164002	+	0.986460i	$0.447560\pi$
$420$		0			0
$421$	−30.1593			−1.46987			−0.734937	−	0.678136i	$-0.762788\pi$
$421$	−30.1593			−1.46987			−0.734937	+	0.678136i	$0.762788\pi$
$422$	19.4191	−	19.4191i	0.945307	−	0.945307i
$423$		0			0
$424$			29.6471i			1.43979i
$425$		0			0
$426$		0			0
$427$	−9.61917	−	9.61917i	−0.465504	−	0.465504i
$428$	−2.08427	−	2.08427i	−0.100747	−	0.100747i
$429$		0			0
$430$		0			0
$431$			14.5595i			0.701304i	0.936506	+	0.350652i	$0.114040\pi$
$431$			14.5595i			0.701304i	−0.936506	+	0.350652i	$0.885960\pi$
$432$		0			0
$433$	−14.3159	+	14.3159i	−0.687976	+	0.687976i	−0.961784	−	0.273808i	$-0.911717\pi$
$433$	−14.3159	+	14.3159i	−0.687976	+	0.687976i	0.273808	+	0.961784i	$0.411717\pi$
$434$	−10.0702			−0.483383
$435$		0			0
$436$	3.50544			0.167880
$437$	−5.11819	+	5.11819i	−0.244836	+	0.244836i
$438$		0			0
$439$			23.7496i			1.13351i	0.823887	+	0.566754i	$0.191801\pi$
$439$			23.7496i			1.13351i	−0.823887	+	0.566754i	$0.808199\pi$
$440$		0			0
$441$		0			0
$442$	6.32394	+	6.32394i	0.300799	+	0.300799i
$443$	−28.0781	−	28.0781i	−1.33403	−	1.33403i	−0.901730	−	0.432299i	$-0.857702\pi$
$443$	−28.0781	−	28.0781i	−1.33403	−	1.33403i	−0.432299	−	0.901730i	$-0.642298\pi$
$444$		0			0
$445$		0			0
$446$			23.5720i			1.11617i
$447$		0			0
$448$	−6.28950	+	6.28950i	−0.297151	+	0.297151i
$449$	23.1170			1.09096			0.545479	−	0.838125i	$-0.316348\pi$
$449$	23.1170			1.09096			0.545479	+	0.838125i	$0.316348\pi$
$450$		0			0
$451$	31.3528			1.47635
$452$	−0.837701	+	0.837701i	−0.0394021	+	0.0394021i
$453$		0			0
$454$			15.0284i			0.705316i
$455$		0			0
$456$		0			0
$457$	2.41339	+	2.41339i	0.112893	+	0.112893i	0.761297	−	0.648403i	$-0.224563\pi$
$457$	2.41339	+	2.41339i	0.112893	+	0.112893i	−0.648403	+	0.761297i	$0.724563\pi$
$458$	−19.6540	−	19.6540i	−0.918373	−	0.918373i
$459$		0			0
$460$		0			0
$461$			12.9836i			0.604705i	0.953196	+	0.302353i	$0.0977720\pi$
$461$			12.9836i			0.604705i	−0.953196	+	0.302353i	$0.902228\pi$
$462$		0			0
$463$	−21.5619	+	21.5619i	−1.00207	+	1.00207i	−0.00206902	+	0.999998i	$0.500659\pi$
$463$	−21.5619	+	21.5619i	−1.00207	+	1.00207i	−0.999998	+	0.00206902i	$0.999341\pi$
$464$	−21.6583			−1.00546
$465$		0			0
$466$	6.98952			0.323783
$467$	−4.14681	+	4.14681i	−0.191891	+	0.191891i	−0.796513	−	0.604622i	$-0.793324\pi$
$467$	−4.14681	+	4.14681i	−0.191891	+	0.191891i	0.604622	+	0.796513i	$0.293324\pi$
$468$		0			0
$469$		−	3.91914i		−	0.180969i
$470$		0			0
$471$		0			0
$472$	13.8355	+	13.8355i	0.636830	+	0.636830i
$473$	−25.4777	−	25.4777i	−1.17146	−	1.17146i
$474$		0			0
$475$		0			0
$476$		−	1.53087i		−	0.0701674i
$477$		0			0
$478$	8.02372	−	8.02372i	0.366996	−	0.366996i
$479$	−11.3977			−0.520774			−0.260387	−	0.965504i	$-0.583850\pi$
$479$	−11.3977			−0.520774			−0.260387	+	0.965504i	$0.583850\pi$
$480$		0			0
$481$	−18.5881			−0.847544
$482$	11.8822	−	11.8822i	0.541219	−	0.541219i
$483$		0			0
$484$		−	4.98849i		−	0.226750i
$485$		0			0
$486$		0			0
$487$	11.0942	+	11.0942i	0.502727	+	0.502727i	0.912284	−	0.409558i	$-0.134317\pi$
$487$	11.0942	+	11.0942i	0.502727	+	0.502727i	−0.409558	+	0.912284i	$0.634317\pi$
$488$	29.3762	+	29.3762i	1.32980	+	1.32980i
$489$		0			0
$490$		0			0
$491$		−	28.4593i		−	1.28435i	−0.766559	−	0.642174i	$-0.778033\pi$
$491$		−	28.4593i		−	1.28435i	0.766559	−	0.642174i	$-0.221967\pi$
$492$		0			0
$493$	17.6754	−	17.6754i	0.796061	−	0.796061i
$494$	−9.62981			−0.433266
$495$		0			0
$496$	23.2019			1.04179
$497$	0.407682	−	0.407682i	0.0182870	−	0.0182870i
$498$		0			0
$499$		−	13.0081i		−	0.582323i	−0.956674	−	0.291161i	$-0.905958\pi$
$499$		−	13.0081i		−	0.582323i	0.956674	−	0.291161i	$-0.0940417\pi$
$500$		0			0
$501$		0			0
$502$	−20.9181	−	20.9181i	−0.933621	−	0.933621i
$503$	19.6010	+	19.6010i	0.873966	+	0.873966i	0.992902	−	0.118936i	$-0.0379482\pi$
$503$	19.6010	+	19.6010i	0.873966	+	0.873966i	−0.118936	+	0.992902i	$0.537948\pi$
$504$		0			0
$505$		0			0
$506$			11.7861i			0.523957i
$507$		0			0
$508$	6.66756	−	6.66756i	0.295825	−	0.295825i
$509$	42.4087			1.87973			0.939866	−	0.341545i	$-0.110950\pi$
$509$	42.4087			1.87973			0.939866	+	0.341545i	$0.110950\pi$
$510$		0			0
$511$	6.99164			0.309292
$512$	17.5189	−	17.5189i	0.774231	−	0.774231i
$513$		0			0
$514$		−	21.0672i		−	0.929236i
$515$		0			0
$516$		0			0
$517$	−24.0882	−	24.0882i	−1.05940	−	1.05940i
$518$	−7.43525	−	7.43525i	−0.326686	−	0.326686i
$519$		0			0
$520$		0			0
$521$		−	13.9987i		−	0.613296i	−0.951823	−	0.306648i	$-0.900793\pi$
$521$		−	13.9987i		−	0.613296i	0.951823	−	0.306648i	$-0.0992074\pi$
$522$		0			0
$523$	−15.7665	+	15.7665i	−0.689421	+	0.689421i	−0.962104	−	0.272683i	$-0.912089\pi$
$523$	−15.7665	+	15.7665i	−0.689421	+	0.689421i	0.272683	+	0.962104i	$0.412089\pi$
$524$	1.49871			0.0654715
$525$		0			0
$526$	−2.21145			−0.0964236
$527$	−18.9351	+	18.9351i	−0.824827	+	0.824827i
$528$		0			0
$529$		−	18.8378i		−	0.819037i
$530$		0			0
$531$		0			0
$532$	1.16557	+	1.16557i	0.0505339	+	0.0505339i
$533$	10.4159	+	10.4159i	0.451161	+	0.451161i
$534$		0			0
$535$		0			0
$536$			11.9687i			0.516971i
$537$		0			0
$538$	2.99289	−	2.99289i	0.129033	−	0.129033i
$539$	−4.66231			−0.200820
$540$		0			0
$541$	40.1080			1.72438			0.862189	−	0.506587i	$-0.169093\pi$
$541$	40.1080			1.72438			0.862189	+	0.506587i	$0.169093\pi$
$542$	−7.19633	+	7.19633i	−0.309109	+	0.309109i
$543$		0			0
$544$			8.46900i			0.363105i
$545$		0			0
$546$		0			0
$547$	8.55083	+	8.55083i	0.365607	+	0.365607i	0.865872	−	0.500265i	$-0.166764\pi$
$547$	8.55083	+	8.55083i	0.365607	+	0.365607i	−0.500265	+	0.865872i	$0.666764\pi$
$548$	0.632361	+	0.632361i	0.0270131	+	0.0270131i
$549$		0			0
$550$		0			0
$551$			26.9153i			1.14663i
$552$		0			0
$553$	1.77467	−	1.77467i	0.0754667	−	0.0754667i
$554$	−8.01704			−0.340612
$555$		0			0
$556$	10.3544			0.439126
$557$	15.5128	−	15.5128i	0.657300	−	0.657300i	−0.297441	−	0.954740i	$-0.596133\pi$
$557$	15.5128	−	15.5128i	0.657300	−	0.657300i	0.954740	+	0.297441i	$0.0961330\pi$
$558$		0			0
$559$		−	16.9281i		−	0.715982i
$560$		0			0
$561$		0			0
$562$	−9.67970	−	9.67970i	−0.408313	−	0.408313i
$563$	15.5187	+	15.5187i	0.654036	+	0.654036i	0.953962	−	0.299926i	$-0.0969620\pi$
$563$	15.5187	+	15.5187i	0.654036	+	0.654036i	−0.299926	+	0.953962i	$0.596962\pi$
$564$		0			0
$565$		0			0
$566$			7.75605i			0.326011i
$567$		0			0
$568$	−1.24503	+	1.24503i	−0.0522401	+	0.0522401i
$569$	31.6235			1.32573			0.662863	−	0.748741i	$-0.269341\pi$
$569$	31.6235			1.32573			0.662863	+	0.748741i	$0.269341\pi$
$570$		0			0
$571$	−25.0465			−1.04816			−0.524082	−	0.851668i	$-0.675592\pi$
$571$	−25.0465			−1.04816			−0.524082	+	0.851668i	$0.675592\pi$
$572$	3.35507	−	3.35507i	0.140283	−	0.140283i
$573$		0			0
$574$			8.33271i			0.347801i
$575$		0			0
$576$		0			0
$577$	20.1909	+	20.1909i	0.840557	+	0.840557i	0.988931	−	0.148375i	$-0.0474042\pi$
$577$	20.1909	+	20.1909i	0.840557	+	0.840557i	−0.148375	+	0.988931i	$0.547404\pi$
$578$	−5.38228	−	5.38228i	−0.223873	−	0.223873i
$579$		0			0
$580$		0			0
$581$			5.64980i			0.234393i
$582$		0			0
$583$	32.0045	−	32.0045i	1.32549	−	1.32549i
$584$	−21.3519			−0.883548
$585$		0			0
$586$	−39.0989			−1.61516
$587$	−15.4569	+	15.4569i	−0.637976	+	0.637976i	−0.950056	−	0.312080i	$-0.898974\pi$
$587$	−15.4569	+	15.4569i	−0.637976	+	0.637976i	0.312080	+	0.950056i	$0.398974\pi$
$588$		0			0
$589$		−	28.8336i		−	1.18807i
$590$		0			0
$591$		0			0
$592$	17.1310	+	17.1310i	0.704079	+	0.704079i
$593$	2.50889	+	2.50889i	0.103028	+	0.103028i	0.756742	−	0.653714i	$-0.226790\pi$
$593$	2.50889	+	2.50889i	0.103028	+	0.103028i	−0.653714	+	0.756742i	$0.726790\pi$
$594$		0			0
$595$		0			0
$596$		−	10.8741i		−	0.445420i
$597$		0			0
$598$	−3.91552	+	3.91552i	−0.160117	+	0.160117i
$599$	−23.0111			−0.940207			−0.470104	−	0.882611i	$-0.655783\pi$
$599$	−23.0111			−0.940207			−0.470104	+	0.882611i	$0.655783\pi$
$600$		0			0
$601$	11.4097			0.465411			0.232706	−	0.972547i	$-0.425242\pi$
$601$	11.4097			0.465411			0.232706	+	0.972547i	$0.425242\pi$
$602$	6.77125	−	6.77125i	0.275976	−	0.275976i
$603$		0			0
$604$			7.89308i			0.321165i
$605$		0			0
$606$		0			0
$607$	−26.7473	−	26.7473i	−1.08564	−	1.08564i	−0.995972	−	0.0896663i	$-0.971420\pi$
$607$	−26.7473	−	26.7473i	−1.08564	−	1.08564i	−0.0896663	−	0.995972i	$-0.528580\pi$
$608$	−6.44810	−	6.44810i	−0.261505	−	0.261505i
$609$		0			0
$610$		0			0
$611$		−	16.0049i		−	0.647489i
$612$		0			0
$613$	9.33197	−	9.33197i	0.376915	−	0.376915i	−0.493073	−	0.869988i	$-0.664126\pi$
$613$	9.33197	−	9.33197i	0.376915	−	0.376915i	0.869988	+	0.493073i	$0.164126\pi$
$614$	8.15275			0.329018
$615$		0			0
$616$	14.2383			0.573678
$617$	−3.34333	+	3.34333i	−0.134597	+	0.134597i	−0.771196	−	0.636598i	$-0.780341\pi$
$617$	−3.34333	+	3.34333i	−0.134597	+	0.134597i	0.636598	+	0.771196i	$0.280341\pi$
$618$		0			0
$619$		−	15.3147i		−	0.615549i	−0.951459	−	0.307774i	$-0.900416\pi$
$619$		−	15.3147i		−	0.615549i	0.951459	−	0.307774i	$-0.0995842\pi$
$620$		0			0
$621$		0			0
$622$	−11.1304	−	11.1304i	−0.446289	−	0.446289i
$623$	4.85589	+	4.85589i	0.194547	+	0.194547i
$624$		0			0
$625$		0			0
$626$		−	16.4582i		−	0.657800i
$627$		0			0
$628$	3.75366	−	3.75366i	0.149787	−	0.149787i
$629$	−27.9613			−1.11489
$630$		0			0
$631$	−25.4390			−1.01271			−0.506355	−	0.862325i	$-0.669007\pi$
$631$	−25.4390			−1.01271			−0.506355	+	0.862325i	$0.669007\pi$
$632$	−5.41970	+	5.41970i	−0.215584	+	0.215584i
$633$		0			0
$634$			21.1276i			0.839085i
$635$		0			0
$636$		0			0
$637$	−1.54889	−	1.54889i	−0.0613691	−	0.0613691i
$638$	30.9902	+	30.9902i	1.22691	+	1.22691i
$639$		0			0
$640$		0			0
$641$		−	19.2081i		−	0.758674i	−0.925259	−	0.379337i	$-0.876152\pi$
$641$		−	19.2081i		−	0.758674i	0.925259	−	0.379337i	$-0.123848\pi$
$642$		0			0
$643$	2.50256	−	2.50256i	0.0986915	−	0.0986915i	−0.656037	−	0.754729i	$-0.727769\pi$
$643$	2.50256	−	2.50256i	0.0986915	−	0.0986915i	0.754729	+	0.656037i	$0.227769\pi$
$644$	0.947851			0.0373506
$645$		0			0
$646$	−14.4857			−0.569934
$647$	−10.7695	+	10.7695i	−0.423393	+	0.423393i	−0.886370	−	0.462977i	$-0.846781\pi$
$647$	−10.7695	+	10.7695i	−0.423393	+	0.423393i	0.462977	+	0.886370i	$0.346781\pi$
$648$		0			0
$649$		−	29.8712i		−	1.17255i
$650$		0			0
$651$		0			0
$652$	−4.22148	−	4.22148i	−0.165326	−	0.165326i
$653$	26.4630	+	26.4630i	1.03558	+	1.03558i	0.999343	+	0.0362330i	$0.0115358\pi$
$653$	26.4630	+	26.4630i	1.03558	+	1.03558i	0.0362330	+	0.999343i	$0.488464\pi$
$654$		0			0
$655$		0			0
$656$		−	19.1988i		−	0.749585i
$657$		0			0
$658$	6.40197	−	6.40197i	0.249575	−	0.249575i
$659$	8.78898			0.342370			0.171185	−	0.985239i	$-0.445240\pi$
$659$	8.78898			0.342370			0.171185	+	0.985239i	$0.445240\pi$
$660$		0			0
$661$	−7.11790			−0.276854			−0.138427	−	0.990373i	$-0.544205\pi$
$661$	−7.11790			−0.276854			−0.138427	+	0.990373i	$0.544205\pi$
$662$	0.737301	−	0.737301i	0.0286560	−	0.0286560i
$663$		0			0
$664$		−	17.2540i		−	0.669586i
$665$		0			0
$666$		0			0
$667$	10.9439	+	10.9439i	0.423749	+	0.423749i
$668$	6.29188	+	6.29188i	0.243440	+	0.243440i
$669$		0			0
$670$		0			0
$671$		−	63.4240i		−	2.44846i
$672$		0			0
$673$	−0.822154	+	0.822154i	−0.0316917	+	0.0316917i	−0.722775	−	0.691083i	$-0.757134\pi$
$673$	−0.822154	+	0.822154i	−0.0316917	+	0.0316917i	0.691083	+	0.722775i	$0.257134\pi$
$674$	−28.3772			−1.09305
$675$		0			0
$676$	−3.81062			−0.146562
$677$	−19.7788	+	19.7788i	−0.760162	+	0.760162i	−0.976352	−	0.216189i	$-0.930637\pi$
$677$	−19.7788	+	19.7788i	−0.760162	+	0.760162i	0.216189	+	0.976352i	$0.430637\pi$
$678$		0			0
$679$		−	6.27073i		−	0.240648i
$680$		0			0
$681$		0			0
$682$	−33.1988	−	33.1988i	−1.27125	−	1.27125i
$683$	−22.2292	−	22.2292i	−0.850576	−	0.850576i	0.139628	−	0.990204i	$-0.455409\pi$
$683$	−22.2292	−	22.2292i	−0.850576	−	0.850576i	−0.990204	+	0.139628i	$0.955409\pi$
$684$		0			0
$685$		0			0
$686$		−	1.23911i		−	0.0473095i
$687$		0			0
$688$	−15.6011	+	15.6011i	−0.594787	+	0.594787i
$689$	21.2647			0.810122
$690$		0			0
$691$	10.5768			0.402361			0.201180	−	0.979554i	$-0.435522\pi$
$691$	10.5768			0.402361			0.201180	+	0.979554i	$0.435522\pi$
$692$	−7.66051	+	7.66051i	−0.291209	+	0.291209i
$693$		0			0
$694$			11.7837i			0.447304i
$695$		0			0
$696$		0			0
$697$	15.6682	+	15.6682i	0.593475	+	0.593475i
$698$	−22.7542	−	22.7542i	−0.861261	−	0.861261i
$699$		0			0
$700$		0			0
$701$			20.2841i			0.766121i	0.923723	+	0.383061i	$0.125130\pi$
$701$			20.2841i			0.766121i	−0.923723	+	0.383061i	$0.874870\pi$
$702$		0			0
$703$	21.2891	−	21.2891i	0.802934	−	0.802934i
$704$	−41.4698			−1.56295
$705$		0			0
$706$	−36.0888			−1.35822
$707$	−1.86359	+	1.86359i	−0.0700876	+	0.0700876i
$708$		0			0
$709$			10.7396i			0.403333i	0.979454	+	0.201666i	$0.0646356\pi$
$709$			10.7396i			0.403333i	−0.979454	+	0.201666i	$0.935364\pi$
$710$		0			0
$711$		0			0
$712$	−14.8295	−	14.8295i	−0.555759	−	0.555759i
$713$	−11.7238	−	11.7238i	−0.439061	−	0.439061i
$714$		0			0
$715$		0			0
$716$			3.32369i			0.124212i
$717$		0			0
$718$	25.7884	−	25.7884i	0.962415	−	0.962415i
$719$	−24.5967			−0.917302			−0.458651	−	0.888616i	$-0.651667\pi$
$719$	−24.5967			−0.917302			−0.458651	+	0.888616i	$0.651667\pi$
$720$		0			0
$721$	−10.5495			−0.392883
$722$	−5.61838	+	5.61838i	−0.209095	+	0.209095i
$723$		0			0
$724$		−	2.25929i		−	0.0839658i
$725$		0			0
$726$		0			0
$727$	22.1032	+	22.1032i	0.819763	+	0.819763i	0.986073	−	0.166310i	$-0.0531854\pi$
$727$	22.1032	+	22.1032i	0.819763	+	0.819763i	−0.166310	+	0.986073i	$0.553185\pi$
$728$	4.73017	+	4.73017i	0.175312	+	0.175312i
$729$		0			0
$730$		0			0
$731$		−	25.4643i		−	0.941830i
$732$		0			0
$733$	−3.38234	+	3.38234i	−0.124930	+	0.124930i	−0.766807	−	0.641878i	$-0.778156\pi$
$733$	−3.38234	+	3.38234i	−0.124930	+	0.124930i	0.641878	+	0.766807i	$0.278156\pi$
$734$	−23.5177			−0.868053
$735$		0			0
$736$	−5.24365			−0.193283
$737$	12.9204	−	12.9204i	0.475930	−	0.475930i
$738$		0			0
$739$		−	18.0189i		−	0.662838i	−0.943484	−	0.331419i	$-0.892473\pi$
$739$		−	18.0189i		−	0.662838i	0.943484	−	0.331419i	$-0.107527\pi$
$740$		0			0
$741$		0			0
$742$	8.50591	+	8.50591i	0.312262	+	0.312262i
$743$	−13.7680	−	13.7680i	−0.505099	−	0.505099i	0.407919	−	0.913018i	$-0.366255\pi$
$743$	−13.7680	−	13.7680i	−0.505099	−	0.505099i	−0.913018	+	0.407919i	$0.866255\pi$
$744$		0			0
$745$		0			0
$746$		−	2.43061i		−	0.0889910i
$747$		0			0
$748$	5.04690	−	5.04690i	0.184533	−	0.184533i
$749$	−6.34437			−0.231818
$750$		0			0
$751$	−12.7248			−0.464336			−0.232168	−	0.972676i	$-0.574582\pi$
$751$	−12.7248			−0.464336			−0.232168	+	0.972676i	$0.574582\pi$
$752$	−14.7503	+	14.7503i	−0.537888	+	0.537888i
$753$		0			0
$754$			20.5908i			0.749871i
$755$		0			0
$756$		0			0
$757$	−31.2644	−	31.2644i	−1.13633	−	1.13633i	−0.989103	−	0.147222i	$-0.952967\pi$
$757$	−31.2644	−	31.2644i	−1.13633	−	1.13633i	−0.147222	−	0.989103i	$-0.547033\pi$
$758$	−22.2420	−	22.2420i	−0.807866	−	0.807866i
$759$		0			0
$760$		0			0
$761$		−	35.1072i		−	1.27264i	−0.771427	−	0.636318i	$-0.780457\pi$
$761$		−	35.1072i		−	1.27264i	0.771427	−	0.636318i	$-0.219543\pi$
$762$		0			0
$763$	5.33515	−	5.33515i	0.193145	−	0.193145i
$764$	−0.460400			−0.0166567
$765$		0			0
$766$	5.48017			0.198006
$767$	9.92366	−	9.92366i	0.358323	−	0.358323i
$768$		0			0
$769$			25.2815i			0.911673i	0.890063	+	0.455837i	$0.150660\pi$
$769$			25.2815i			0.911673i	−0.890063	+	0.455837i	$0.849340\pi$
$770$		0			0
$771$		0			0
$772$	−3.82081	−	3.82081i	−0.137514	−	0.137514i
$773$	−15.4411	−	15.4411i	−0.555376	−	0.555376i	0.372611	−	0.927988i	$-0.378463\pi$
$773$	−15.4411	−	15.4411i	−0.555376	−	0.555376i	−0.927988	+	0.372611i	$0.878463\pi$
$774$		0			0
$775$		0			0
$776$			19.1503i			0.687455i
$777$		0			0
$778$	−9.20867	+	9.20867i	−0.330147	+	0.330147i
$779$	−23.8588			−0.854830
$780$		0			0
$781$	2.68805			0.0961859
$782$	−5.88996	+	5.88996i	−0.210624	+	0.210624i
$783$		0			0
$784$			2.85494i			0.101962i
$785$		0			0
$786$		0			0
$787$	−17.7487	−	17.7487i	−0.632673	−	0.632673i	0.316065	−	0.948738i	$-0.397638\pi$
$787$	−17.7487	−	17.7487i	−0.632673	−	0.632673i	−0.948738	+	0.316065i	$0.897638\pi$
$788$	0.837701	+	0.837701i	0.0298419	+	0.0298419i
$789$		0			0
$790$		0			0
$791$			2.54990i			0.0906639i
$792$		0			0
$793$	21.0704	−	21.0704i	0.748231	−	0.748231i
$794$	−6.53474			−0.231909
$795$		0			0
$796$	−7.44966			−0.264046
$797$	17.3136	−	17.3136i	0.613280	−	0.613280i	−0.330520	−	0.943799i	$-0.607224\pi$
$797$	17.3136	−	17.3136i	0.613280	−	0.613280i	0.943799	+	0.330520i	$0.107224\pi$
$798$		0			0
$799$		−	24.0755i		−	0.851731i
$800$		0			0
$801$		0			0
$802$	−15.6330	−	15.6330i	−0.552021	−	0.552021i
$803$	23.0497	+	23.0497i	0.813406	+	0.813406i
$804$		0			0
$805$		0			0
$806$		−	22.0582i		−	0.776968i
$807$		0			0
$808$	5.69126	−	5.69126i	0.200218	−	0.200218i
$809$	23.6436			0.831265			0.415632	−	0.909533i	$-0.363560\pi$
$809$	23.6436			0.831265			0.415632	+	0.909533i	$0.363560\pi$
$810$		0			0
$811$	−13.9945			−0.491412			−0.245706	−	0.969344i	$-0.579020\pi$
$811$	−13.9945			−0.491412			−0.245706	+	0.969344i	$0.579020\pi$
$812$	2.49226	−	2.49226i	0.0874612	−	0.0874612i
$813$		0			0
$814$		−	49.0243i		−	1.71830i
$815$		0			0
$816$		0			0
$817$	19.3879	+	19.3879i	0.678297	+	0.678297i
$818$	13.1149	+	13.1149i	0.458550	+	0.458550i
$819$		0			0
$820$		0			0
$821$			32.7797i			1.14402i	0.820247	+	0.572010i	$0.193836\pi$
$821$			32.7797i			1.14402i	−0.820247	+	0.572010i	$0.806164\pi$
$822$		0			0
$823$	15.2743	−	15.2743i	0.532430	−	0.532430i	−0.388865	−	0.921295i	$-0.627133\pi$
$823$	15.2743	−	15.2743i	0.532430	−	0.532430i	0.921295	+	0.388865i	$0.127133\pi$
$824$	32.2173			1.12234
$825$		0			0
$826$	7.93894			0.276231
$827$	−19.3251	+	19.3251i	−0.672000	+	0.672000i	−0.958177	−	0.286177i	$-0.907615\pi$
$827$	−19.3251	+	19.3251i	−0.672000	+	0.672000i	0.286177	+	0.958177i	$0.407615\pi$
$828$		0			0
$829$			46.8148i			1.62595i	0.582302	+	0.812973i	$0.302152\pi$
$829$			46.8148i			1.62595i	−0.582302	+	0.812973i	$0.697848\pi$
$830$		0			0
$831$		0			0
$832$	−13.7769	−	13.7769i	−0.477628	−	0.477628i
$833$	−2.32993	−	2.32993i	−0.0807272	−	0.0807272i
$834$		0			0
$835$		0			0
$836$			7.68519i			0.265798i
$837$		0			0
$838$	−5.88277	+	5.88277i	−0.203217	+	0.203217i
$839$	31.1400			1.07507			0.537535	−	0.843241i	$-0.319355\pi$
$839$	31.1400			1.07507			0.537535	+	0.843241i	$0.319355\pi$
$840$		0			0
$841$	28.5512			0.984524
$842$	26.4251	−	26.4251i	0.910669	−	0.910669i
$843$		0			0
$844$		−	10.2971i		−	0.354440i
$845$		0			0
$846$		0			0
$847$	−7.59229	−	7.59229i	−0.260874	−	0.260874i
$848$	−19.5978	−	19.5978i	−0.672991	−	0.672991i
$849$		0			0
$850$		0			0
$851$		−	17.3125i		−	0.593464i
$852$		0			0
$853$	−34.5421	+	34.5421i	−1.18270	+	1.18270i	−0.203657	+	0.979042i	$0.565283\pi$
$853$	−34.5421	+	34.5421i	−1.18270	+	1.18270i	−0.979042	+	0.203657i	$0.934717\pi$
$854$	16.8563			0.576812
$855$		0			0
$856$	19.3752			0.662230
$857$	29.4941	−	29.4941i	1.00750	−	1.00750i	0.00752899	−	0.999972i	$-0.497603\pi$
$857$	29.4941	−	29.4941i	1.00750	−	1.00750i	0.999972	−	0.00752899i	$-0.00239658\pi$
$858$		0			0
$859$		−	43.7748i		−	1.49358i	−0.665061	−	0.746789i	$-0.731594\pi$
$859$		−	43.7748i		−	1.49358i	0.665061	−	0.746789i	$-0.268406\pi$
$860$		0			0
$861$		0			0
$862$	−12.7568	−	12.7568i	−0.434497	−	0.434497i
$863$	−9.59074	−	9.59074i	−0.326472	−	0.326472i	0.524771	−	0.851243i	$-0.324151\pi$
$863$	−9.59074	−	9.59074i	−0.326472	−	0.326472i	−0.851243	+	0.524771i	$0.824151\pi$
$864$		0			0
$865$		0			0
$866$		−	25.0867i		−	0.852479i
$867$		0			0
$868$	−2.66988	+	2.66988i	−0.0906216	+	0.0906216i
$869$	11.7013			0.396939
$870$		0			0
$871$	8.58471			0.290882
$872$	−16.2931	+	16.2931i	−0.551754	+	0.551754i
$873$		0			0
$874$		−	8.96896i		−	0.303380i
$875$		0			0
$876$		0			0
$877$	−38.7983	−	38.7983i	−1.31013	−	1.31013i	−0.921319	−	0.388809i	$-0.872887\pi$
$877$	−38.7983	−	38.7983i	−1.31013	−	1.31013i	−0.388809	−	0.921319i	$-0.627113\pi$
$878$	−20.8091	−	20.8091i	−0.702272	−	0.702272i
$879$		0			0
$880$		0			0
$881$		−	14.2447i		−	0.479918i	−0.970783	−	0.239959i	$-0.922866\pi$
$881$		−	14.2447i		−	0.479918i	0.970783	−	0.239959i	$-0.0771339\pi$
$882$		0			0
$883$	34.0748	−	34.0748i	1.14671	−	1.14671i	0.159511	−	0.987196i	$-0.449008\pi$
$883$	34.0748	−	34.0748i	1.14671	−	1.14671i	0.987196	−	0.159511i	$-0.0509916\pi$
$884$	3.35331			0.112784
$885$		0			0
$886$	49.2031			1.65301
$887$	−0.895283	+	0.895283i	−0.0300607	+	0.0300607i	−0.721977	−	0.691917i	$-0.756767\pi$
$887$	−0.895283	+	0.895283i	−0.0300607	+	0.0300607i	0.691917	+	0.721977i	$0.256767\pi$
$888$		0			0
$889$		−	20.2956i		−	0.680691i
$890$		0			0
$891$		0			0
$892$	6.24961	+	6.24961i	0.209252	+	0.209252i
$893$	18.3306	+	18.3306i	0.613409	+	0.613409i
$894$		0			0
$895$		0			0
$896$		−	5.88104i		−	0.196472i
$897$		0			0
$898$	−20.2547	+	20.2547i	−0.675909	+	0.675909i
$899$	−61.6528			−2.05624
$900$		0			0
$901$	31.9877			1.06566
$902$	−27.4709	+	27.4709i	−0.914680	+	0.914680i
$903$		0			0
$904$		−	7.78718i		−	0.258998i
$905$		0			0
$906$		0			0
$907$	−16.4485	−	16.4485i	−0.546164	−	0.546164i	0.379165	−	0.925329i	$-0.376211\pi$
$907$	−16.4485	−	16.4485i	−0.546164	−	0.546164i	−0.925329	+	0.379165i	$0.876211\pi$
$908$	3.98444	+	3.98444i	0.132228	+	0.132228i
$909$		0			0
$910$		0			0
$911$			19.8928i			0.659078i	0.944142	+	0.329539i	$0.106893\pi$
$911$			19.8928i			0.659078i	−0.944142	+	0.329539i	$0.893107\pi$
$912$		0			0
$913$	−18.6260	+	18.6260i	−0.616430	+	0.616430i
$914$	−4.22914			−0.139888
$915$		0			0
$916$	−10.4217			−0.344342
$917$	2.28098	−	2.28098i	0.0753246	−	0.0753246i
$918$		0			0
$919$		−	39.3303i		−	1.29739i	−0.761050	−	0.648693i	$-0.775316\pi$
$919$		−	39.3303i		−	1.29739i	0.761050	−	0.648693i	$-0.224684\pi$
$920$		0			0
$921$		0			0
$922$	−11.3760	−	11.3760i	−0.374649	−	0.374649i
$923$	0.893009	+	0.893009i	0.0293937	+	0.0293937i
$924$		0			0
$925$		0			0
$926$		−	37.7844i		−	1.24167i
$927$		0			0
$928$	−13.7875	+	13.7875i	−0.452598	+	0.452598i
$929$	−26.3786			−0.865455			−0.432728	−	0.901525i	$-0.642449\pi$
$929$	−26.3786			−0.865455			−0.432728	+	0.901525i	$0.642449\pi$
$930$		0			0
$931$	3.54791			0.116278
$932$	1.85312	−	1.85312i	0.0607008	−	0.0607008i
$933$		0			0
$934$		−	7.26673i		−	0.237775i
$935$		0			0
$936$		0			0
$937$	37.2937	+	37.2937i	1.21833	+	1.21833i	0.968215	+	0.250118i	$0.0804694\pi$
$937$	37.2937	+	37.2937i	1.21833	+	1.21833i	0.250118	+	0.968215i	$0.419531\pi$
$938$	3.43389	+	3.43389i	0.112121	+	0.112121i
$939$		0			0
$940$		0			0
$941$			48.3991i			1.57776i	0.614544	+	0.788882i	$0.289340\pi$
$941$			48.3991i			1.57776i	−0.614544	+	0.788882i	$0.710660\pi$
$942$		0			0
$943$	−9.70107	+	9.70107i	−0.315910	+	0.315910i
$944$	−18.2915			−0.595338
$945$		0			0
$946$	44.6463			1.45158
$947$	−27.4439	+	27.4439i	−0.891806	+	0.891806i	−0.994693	−	0.102887i	$-0.967192\pi$
$947$	−27.4439	+	27.4439i	−0.891806	+	0.891806i	0.102887	+	0.994693i	$0.467192\pi$
$948$		0			0
$949$			15.3149i			0.497142i
$950$		0			0
$951$		0			0
$952$	7.11541	+	7.11541i	0.230612	+	0.230612i
$953$	7.74667	+	7.74667i	0.250939	+	0.250939i	0.821356	−	0.570416i	$-0.193218\pi$
$953$	7.74667	+	7.74667i	0.250939	+	0.250939i	−0.570416	+	0.821356i	$0.693218\pi$
$954$		0			0
$955$		0			0
$956$		−	4.25463i		−	0.137604i
$957$		0			0
$958$	9.98648	−	9.98648i	0.322648	−	0.322648i
$959$	1.92486			0.0621569
$960$		0			0
$961$	35.0467			1.13054
$962$	16.2866	−	16.2866i	0.525101	−	0.525101i
$963$		0			0
$964$		−	6.30061i		−	0.202929i
$965$		0			0
$966$		0			0
$967$	−12.8257	−	12.8257i	−0.412448	−	0.412448i	0.470143	−	0.882590i	$-0.344203\pi$
$967$	−12.8257	−	12.8257i	−0.412448	−	0.412448i	−0.882590	+	0.470143i	$0.844203\pi$
$968$	23.1862	+	23.1862i	0.745234	+	0.745234i
$969$		0			0
$970$		0			0
$971$			30.4338i			0.976666i	0.872657	+	0.488333i	$0.162395\pi$
$971$			30.4338i			0.976666i	−0.872657	+	0.488333i	$0.837605\pi$
$972$		0			0
$973$	15.7591	−	15.7591i	0.505213	−	0.505213i
$974$	−19.4412			−0.622935
$975$		0			0
$976$	−38.8374			−1.24315
$977$	−4.71670	+	4.71670i	−0.150901	+	0.150901i	−0.778520	−	0.627620i	$-0.784029\pi$
$977$	−4.71670	+	4.71670i	−0.150901	+	0.150901i	0.627620	+	0.778520i	$0.284029\pi$
$978$		0			0
$979$			32.0173i			1.02328i
$980$		0			0
$981$		0			0
$982$	24.9356	+	24.9356i	0.795726	+	0.795726i
$983$	−28.6631	−	28.6631i	−0.914211	−	0.914211i	0.0823888	−	0.996600i	$-0.473745\pi$
$983$	−28.6631	−	28.6631i	−0.914211	−	0.914211i	−0.996600	+	0.0823888i	$0.973745\pi$
$984$		0			0
$985$		0			0
$986$			30.9739i			0.986409i
$987$		0			0
$988$	−2.55313	+	2.55313i	−0.0812260	+	0.0812260i
$989$	15.7664			0.501342
$990$		0			0
$991$	40.6787			1.29220			0.646101	−	0.763252i	$-0.276398\pi$
$991$	40.6787			1.29220			0.646101	+	0.763252i	$0.276398\pi$
$992$	14.7701	−	14.7701i	0.468953	−	0.468953i
$993$		0			0
$994$			0.714408i			0.0226597i
$995$		0			0
$996$		0			0
$997$	24.6947	+	24.6947i	0.782090	+	0.782090i	0.980183	−	0.198094i	$-0.0634750\pi$
$997$	24.6947	+	24.6947i	0.782090	+	0.782090i	−0.198094	+	0.980183i	$0.563475\pi$
$998$	11.3975	+	11.3975i	0.360782	+	0.360782i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1575.2.m.c.1457.3		12
3.2	odd	2		1575.2.m.d.1457.4		12
5.2	odd	4		315.2.m.b.8.3	yes	12
5.3	odd	4		1575.2.m.d.1268.4		12
5.4	even	2		315.2.m.a.197.4	yes	12
15.2	even	4		315.2.m.a.8.4	✓	12
15.8	even	4	inner	1575.2.m.c.1268.3		12
15.14	odd	2		315.2.m.b.197.3	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.m.a.8.4	✓	12	15.2	even	4
315.2.m.a.197.4	yes	12	5.4	even	2
315.2.m.b.8.3	yes	12	5.2	odd	4
315.2.m.b.197.3	yes	12	15.14	odd	2
1575.2.m.c.1268.3		12	15.8	even	4	inner
1575.2.m.c.1457.3		12	1.1	even	1	trivial
1575.2.m.d.1268.4		12	5.3	odd	4
1575.2.m.d.1457.4		12	3.2	odd	2

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:	\( N \)	\(=\)	\( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1575.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.876184 + 0.876184i) q^{2} +0.464602i q^{4} +(0.707107 + 0.707107i) q^{7} +(-2.15945 - 2.15945i) q^{8} +4.66231i q^{11} +(-1.54889 + 1.54889i) q^{13} -1.23911 q^{14} +2.85494 q^{16} +(-2.32993 + 2.32993i) q^{17} -3.54791i q^{19} +(-4.08504 - 4.08504i) q^{22} +(-1.44259 - 1.44259i) q^{23} -2.71422i q^{26} +(-0.328523 + 0.328523i) q^{28} -7.58625 q^{29} +8.12691 q^{31} +(1.81744 - 1.81744i) q^{32} -4.08289i q^{34} +(6.00046 + 6.00046i) q^{37} +(3.10862 + 3.10862i) q^{38} -6.72475i q^{41} +(-5.46460 + 5.46460i) q^{43} -2.16612 q^{44} +2.52796 q^{46} +(-5.16658 + 5.16658i) q^{47} +1.00000i q^{49} +(-0.719616 - 0.719616i) q^{52} +(-6.86452 - 6.86452i) q^{53} -3.05392i q^{56} +(6.64695 - 6.64695i) q^{58} -6.40696 q^{59} -13.6036 q^{61} +(-7.12067 + 7.12067i) q^{62} +8.89470i q^{64} +(-2.77125 - 2.77125i) q^{67} +(-1.08249 - 1.08249i) q^{68} -0.576549i q^{71} +(4.94384 - 4.94384i) q^{73} -10.5150 q^{74} +1.64837 q^{76} +(-3.29675 + 3.29675i) q^{77} -2.50976i q^{79} +(5.89212 + 5.89212i) q^{82} +(3.99501 + 3.99501i) q^{83} -9.57600i q^{86} +(10.0680 - 10.0680i) q^{88} +6.86727 q^{89} -2.19046 q^{91} +(0.670232 - 0.670232i) q^{92} -9.05376i q^{94} +(-4.43407 - 4.43407i) q^{97} +(-0.876184 - 0.876184i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 24 q^{8} + 4 q^{13} - 4 q^{14} - 20 q^{16} - 8 q^{17} + 8 q^{22} - 8 q^{23} - 32 q^{29} - 48 q^{32} - 4 q^{37} - 24 q^{38} - 40 q^{43} - 64 q^{44} + 16 q^{46} - 24 q^{47} - 36 q^{52} + 40 q^{53}+ \cdots - 12 q^{97}+O(q^{100}) \) 12 * q - 24 * q^8 + 4 * q^13 - 4 * q^14 - 20 * q^16 - 8 * q^17 + 8 * q^22 - 8 * q^23 - 32 * q^29 - 48 * q^32 - 4 * q^37 - 24 * q^38 - 40 * q^43 - 64 * q^44 + 16 * q^46 - 24 * q^47 - 36 * q^52 + 40 * q^53 + 28 * q^58 - 80 * q^59 - 32 * q^61 - 16 * q^62 + 48 * q^67 - 32 * q^68 + 20 * q^73 - 64 * q^74 + 16 * q^76 - 20 * q^82 - 24 * q^83 - 56 * q^89 - 8 * q^92 - 12 * q^97

Introduction

L-functions

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