LMFDB - Embedded newform 912.2.bn.m.449.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,2,Mod(65,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))

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

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

chi := DirichletCharacter("912.65");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.bn (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.28235666434$
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:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 57)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			449.2
Root			$0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	912.449
Dual form			912.2.bn.m.65.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.158919 + 1.72474i) q^{3} +(-1.22474 + 0.707107i) q^{5} +3.73205 q^{7} +(-2.94949 - 0.548188i) q^{9} +O(q^{10})$	\(q+(-0.158919 + 1.72474i) q^{3} +(-1.22474 + 0.707107i) q^{5} +3.73205 q^{7} +(-2.94949 - 0.548188i) q^{9} +0.378937i q^{11} +(3.23205 + 1.86603i) q^{13} +(-1.02494 - 2.22474i) q^{15} +(4.24264 - 2.44949i) q^{17} +(1.73205 + 4.00000i) q^{19} +(-0.593092 + 6.43684i) q^{21} +(-0.328169 - 0.189469i) q^{23} +(-1.50000 + 2.59808i) q^{25} +(1.41421 - 5.00000i) q^{27} +(-3.86370 + 6.69213i) q^{29} +4.46410i q^{31} +(-0.653570 - 0.0602202i) q^{33} +(-4.57081 + 2.63896i) q^{35} -4.26795i q^{37} +(-3.73205 + 5.27792i) q^{39} +(-2.82843 - 4.89898i) q^{41} +(1.13397 + 1.96410i) q^{43} +(4.00000 - 1.41421i) q^{45} +(-9.14162 - 5.27792i) q^{47} +6.92820 q^{49} +(3.55051 + 7.70674i) q^{51} +(-3.01790 + 5.22715i) q^{53} +(-0.267949 - 0.464102i) q^{55} +(-7.17423 + 2.35167i) q^{57} +(4.19187 + 7.26054i) q^{59} +(1.76795 - 3.06218i) q^{61} +(-11.0076 - 2.04587i) q^{63} -5.27792 q^{65} +(-0.866025 - 0.500000i) q^{67} +(0.378937 - 0.535898i) q^{69} +(1.79315 + 3.10583i) q^{71} +(1.50000 + 2.59808i) q^{73} +(-4.24264 - 3.00000i) q^{75} +1.41421i q^{77} +(3.06218 - 1.76795i) q^{79} +(8.39898 + 3.23375i) q^{81} +7.72741i q^{83} +(-3.46410 + 6.00000i) q^{85} +(-10.9282 - 7.72741i) q^{87} +(-3.67423 + 6.36396i) q^{89} +(12.0622 + 6.96410i) q^{91} +(-7.69944 - 0.709429i) q^{93} +(-4.94975 - 3.67423i) q^{95} +(6.46410 - 3.73205i) q^{97} +(0.207729 - 1.11767i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 16 q^{7} - 4 q^{9}+O(q^{10}) $ 8 * q + 16 * q^7 - 4 * q^9	$ 8 q + 16 q^{7} - 4 q^{9} + 12 q^{13} - 12 q^{21} - 12 q^{25} + 24 q^{33} - 16 q^{39} + 16 q^{43} + 32 q^{45} + 48 q^{51} - 16 q^{55} - 28 q^{57} + 28 q^{61} - 8 q^{63} + 12 q^{73} - 24 q^{79} + 28 q^{81} - 32 q^{87} + 48 q^{91} - 4 q^{93} + 24 q^{97} + 32 q^{99}+O(q^{100}) $ 8 * q + 16 * q^7 - 4 * q^9 + 12 * q^13 - 12 * q^21 - 12 * q^25 + 24 * q^33 - 16 * q^39 + 16 * q^43 + 32 * q^45 + 48 * q^51 - 16 * q^55 - 28 * q^57 + 28 * q^61 - 8 * q^63 + 12 * q^73 - 24 * q^79 + 28 * q^81 - 32 * q^87 + 48 * q^91 - 4 * q^93 + 24 * q^97 + 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.158919	+	1.72474i	−0.0917517	+	0.995782i
$3$	−0.158919	+	1.72474i	−0.0917517	+	0.995782i
$4$		0			0
$5$	−1.22474	+	0.707107i	−0.547723	+	0.316228i	−0.748203	−	0.663470i	$-0.769083\pi$
$5$	−1.22474	+	0.707107i	−0.547723	+	0.316228i	0.200480	+	0.979698i	$0.435750\pi$
$6$		0			0
$7$	3.73205			1.41058			0.705291	−	0.708918i	$-0.250816\pi$
$7$	3.73205			1.41058			0.705291	+	0.708918i	$0.250816\pi$
$8$		0			0
$9$	−2.94949	−	0.548188i	−0.983163	−	0.182729i
$10$		0			0
$11$			0.378937i			0.114254i	0.998367	+	0.0571270i	$0.0181940\pi$
$11$			0.378937i			0.114254i	−0.998367	+	0.0571270i	$0.981806\pi$
$12$		0			0
$13$	3.23205	+	1.86603i	0.896410	+	0.517542i	0.876034	−	0.482250i	$-0.160180\pi$
$13$	3.23205	+	1.86603i	0.896410	+	0.517542i	0.0203760	+	0.999792i	$0.493514\pi$
$14$		0			0
$15$	−1.02494	−	2.22474i	−0.264639	−	0.574427i
$16$		0			0
$17$	4.24264	−	2.44949i	1.02899	−	0.594089i	0.112296	−	0.993675i	$-0.464180\pi$
$17$	4.24264	−	2.44949i	1.02899	−	0.594089i	0.916696	+	0.399586i	$0.130846\pi$
$18$		0			0
$19$	1.73205	+	4.00000i	0.397360	+	0.917663i
$19$	1.73205	+	4.00000i	0.397360	+	0.917663i
$20$		0			0
$21$	−0.593092	+	6.43684i	−0.129423	+	1.40463i
$22$		0			0
$23$	−0.328169	−	0.189469i	−0.0684280	−	0.0395070i	0.465396	−	0.885103i	$-0.345912\pi$
$23$	−0.328169	−	0.189469i	−0.0684280	−	0.0395070i	−0.533824	+	0.845596i	$0.679245\pi$
$24$		0			0
$25$	−1.50000	+	2.59808i	−0.300000	+	0.519615i
$26$		0			0
$27$	1.41421	−	5.00000i	0.272166	−	0.962250i
$28$		0			0
$29$	−3.86370	+	6.69213i	−0.717472	+	1.24270i	0.244527	+	0.969643i	$0.421367\pi$
$29$	−3.86370	+	6.69213i	−0.717472	+	1.24270i	−0.961998	+	0.273055i	$0.911966\pi$
$30$		0			0
$31$			4.46410i			0.801776i	0.916127	+	0.400888i	$0.131298\pi$
$31$			4.46410i			0.801776i	−0.916127	+	0.400888i	$0.868702\pi$
$32$		0			0
$33$	−0.653570	−	0.0602202i	−0.113772	−	0.0104830i
$34$		0			0
$35$	−4.57081	+	2.63896i	−0.772608	+	0.446065i
$36$		0			0
$37$		−	4.26795i		−	0.701647i	−0.936442	−	0.350823i	$-0.885902\pi$
$37$		−	4.26795i		−	0.701647i	0.936442	−	0.350823i	$-0.114098\pi$
$38$		0			0
$39$	−3.73205	+	5.27792i	−0.597606	+	0.845143i
$40$		0			0
$41$	−2.82843	−	4.89898i	−0.441726	−	0.765092i	0.556092	−	0.831121i	$-0.312300\pi$
$41$	−2.82843	−	4.89898i	−0.441726	−	0.765092i	−0.997818	+	0.0660290i	$0.978967\pi$
$42$		0			0
$43$	1.13397	+	1.96410i	0.172930	+	0.299523i	0.939443	−	0.342706i	$-0.111343\pi$
$43$	1.13397	+	1.96410i	0.172930	+	0.299523i	−0.766513	+	0.642228i	$0.778010\pi$
$44$		0			0
$45$	4.00000	−	1.41421i	0.596285	−	0.210819i
$46$		0			0
$47$	−9.14162	−	5.27792i	−1.33344	−	0.769863i	−0.347617	−	0.937637i	$-0.613009\pi$
$47$	−9.14162	−	5.27792i	−1.33344	−	0.769863i	−0.985826	+	0.167773i	$0.946342\pi$
$48$		0			0
$49$	6.92820			0.989743
$50$		0			0
$51$	3.55051	+	7.70674i	0.497171	+	1.07916i
$52$		0			0
$53$	−3.01790	+	5.22715i	−0.414540	+	0.718004i	−0.995380	−	0.0960135i	$-0.969391\pi$
$53$	−3.01790	+	5.22715i	−0.414540	+	0.718004i	0.580840	+	0.814018i	$0.302724\pi$
$54$		0			0
$55$	−0.267949	−	0.464102i	−0.0361303	−	0.0625794i
$56$		0			0
$57$	−7.17423	+	2.35167i	−0.950251	+	0.311486i
$58$		0			0
$59$	4.19187	+	7.26054i	0.545735	+	0.945241i	0.998560	+	0.0536419i	$0.0170829\pi$
$59$	4.19187	+	7.26054i	0.545735	+	0.945241i	−0.452825	+	0.891599i	$0.649584\pi$
$60$		0			0
$61$	1.76795	−	3.06218i	0.226363	−	0.392072i	−0.730365	−	0.683057i	$-0.760650\pi$
$61$	1.76795	−	3.06218i	0.226363	−	0.392072i	0.956727	+	0.290986i	$0.0939832\pi$
$62$		0			0
$63$	−11.0076	−	2.04587i	−1.38683	−	0.257755i
$64$		0			0
$65$	−5.27792			−0.654645
$66$		0			0
$67$	−0.866025	−	0.500000i	−0.105802	−	0.0610847i	0.446165	−	0.894951i	$-0.352789\pi$
$67$	−0.866025	−	0.500000i	−0.105802	−	0.0610847i	−0.551967	+	0.833866i	$0.686123\pi$
$68$		0			0
$69$	0.378937	−	0.535898i	0.0456187	−	0.0645146i
$70$		0			0
$71$	1.79315	+	3.10583i	0.212808	+	0.368594i	0.952592	−	0.304250i	$-0.0984058\pi$
$71$	1.79315	+	3.10583i	0.212808	+	0.368594i	−0.739784	+	0.672844i	$0.765072\pi$
$72$		0			0
$73$	1.50000	+	2.59808i	0.175562	+	0.304082i	0.940356	−	0.340193i	$-0.110493\pi$
$73$	1.50000	+	2.59808i	0.175562	+	0.304082i	−0.764794	+	0.644275i	$0.777159\pi$
$74$		0			0
$75$	−4.24264	−	3.00000i	−0.489898	−	0.346410i
$76$		0			0
$77$			1.41421i			0.161165i
$78$		0			0
$79$	3.06218	−	1.76795i	0.344522	−	0.198910i	−0.317748	−	0.948175i	$-0.602927\pi$
$79$	3.06218	−	1.76795i	0.344522	−	0.198910i	0.662270	+	0.749265i	$0.269593\pi$
$80$		0			0
$81$	8.39898	+	3.23375i	0.933220	+	0.359306i
$82$		0			0
$83$			7.72741i			0.848193i	0.905617	+	0.424097i	$0.139408\pi$
$83$			7.72741i			0.848193i	−0.905617	+	0.424097i	$0.860592\pi$
$84$		0			0
$85$	−3.46410	+	6.00000i	−0.375735	+	0.650791i
$86$		0			0
$87$	−10.9282	−	7.72741i	−1.17163	−	0.828465i
$88$		0			0
$89$	−3.67423	+	6.36396i	−0.389468	+	0.674579i	−0.992378	−	0.123231i	$-0.960674\pi$
$89$	−3.67423	+	6.36396i	−0.389468	+	0.674579i	0.602910	+	0.797809i	$0.294008\pi$
$90$		0			0
$91$	12.0622	+	6.96410i	1.26446	+	0.730036i
$92$		0			0
$93$	−7.69944	−	0.709429i	−0.798394	−	0.0735643i
$94$		0			0
$95$	−4.94975	−	3.67423i	−0.507833	−	0.376969i
$96$		0			0
$97$	6.46410	−	3.73205i	0.656330	−	0.378932i	−0.134547	−	0.990907i	$-0.542958\pi$
$97$	6.46410	−	3.73205i	0.656330	−	0.378932i	0.790877	+	0.611975i	$0.209625\pi$
$98$		0			0
$99$	0.207729	−	1.11767i	0.0208775	−	0.112330i
$100$		0			0
$101$	−6.69213	−	3.86370i	−0.665892	−	0.384453i	0.128626	−	0.991693i	$-0.458943\pi$
$101$	−6.69213	−	3.86370i	−0.665892	−	0.384453i	−0.794518	+	0.607240i	$0.792277\pi$
$102$		0			0
$103$		−	10.4641i		−	1.03106i	−0.856872	−	0.515529i	$-0.827595\pi$
$103$		−	10.4641i		−	1.03106i	0.856872	−	0.515529i	$-0.172405\pi$
$104$		0			0
$105$	−3.82514	−	8.30286i	−0.373296	−	0.810276i
$106$		0			0
$107$	4.89898			0.473602			0.236801	−	0.971558i	$-0.423901\pi$
$107$	4.89898			0.473602			0.236801	+	0.971558i	$0.423901\pi$
$108$		0			0
$109$	−12.4641	+	7.19615i	−1.19384	+	0.689266i	−0.959176	−	0.282809i	$-0.908734\pi$
$109$	−12.4641	+	7.19615i	−1.19384	+	0.689266i	−0.234668	+	0.972076i	$0.575400\pi$
$110$		0			0
$111$	7.36112	+	0.678257i	0.698687	+	0.0643773i
$112$		0			0
$113$	18.6622			1.75559			0.877795	−	0.479036i	$-0.159014\pi$
$113$	18.6622			1.75559			0.877795	+	0.479036i	$0.159014\pi$
$114$		0			0
$115$	0.535898			0.0499728
$116$		0			0
$117$	−8.50997	−	7.27559i	−0.786747	−	0.672629i
$118$		0			0
$119$	15.8338	−	9.14162i	1.45148	−	0.838011i
$120$		0			0
$121$	10.8564			0.986946
$122$		0			0
$123$	8.89898	−	4.09978i	0.802394	−	0.369664i
$124$		0			0
$125$		−	11.3137i		−	1.01193i
$126$		0			0
$127$	−6.80385	−	3.92820i	−0.603744	−	0.348572i	0.166769	−	0.985996i	$-0.446667\pi$
$127$	−6.80385	−	3.92820i	−0.603744	−	0.348572i	−0.770513	+	0.637424i	$0.780000\pi$
$128$		0			0
$129$	−3.56778	+	1.64368i	−0.314126	+	0.144718i
$130$		0			0
$131$	6.03579	−	3.48477i	0.527350	−	0.304465i	−0.212587	−	0.977142i	$-0.568189\pi$
$131$	6.03579	−	3.48477i	0.527350	−	0.304465i	0.739936	+	0.672677i	$0.234856\pi$
$132$		0			0
$133$	6.46410	+	14.9282i	0.560509	+	1.29444i
$134$		0			0
$135$	1.80348	+	7.12372i	0.155219	+	0.613113i
$136$		0			0
$137$	−0.656339	−	0.378937i	−0.0560748	−	0.0323748i	0.471700	−	0.881759i	$-0.343640\pi$
$137$	−0.656339	−	0.378937i	−0.0560748	−	0.0323748i	−0.527775	+	0.849384i	$0.676974\pi$
$138$		0			0
$139$	6.59808	−	11.4282i	0.559642	−	0.969328i	−0.437885	−	0.899031i	$-0.644272\pi$
$139$	6.59808	−	11.4282i	0.559642	−	0.969328i	0.997526	−	0.0702964i	$-0.0223945\pi$
$140$		0			0
$141$	10.5558	−	14.9282i	0.888962	−	1.25718i
$142$		0			0
$143$	−0.707107	+	1.22474i	−0.0591312	+	0.102418i
$144$		0			0
$145$		−	10.9282i		−	0.907538i
$146$		0			0
$147$	−1.10102	+	11.9494i	−0.0908106	+	0.985568i
$148$		0			0
$149$	14.6090	−	8.43451i	1.19682	−	0.690982i	0.236972	−	0.971516i	$-0.423845\pi$
$149$	14.6090	−	8.43451i	1.19682	−	0.690982i	0.959844	+	0.280534i	$0.0905116\pi$
$150$		0			0
$151$			2.00000i			0.162758i	0.996683	+	0.0813788i	$0.0259324\pi$
$151$			2.00000i			0.162758i	−0.996683	+	0.0813788i	$0.974068\pi$
$152$		0			0
$153$	−13.8564	+	4.89898i	−1.12022	+	0.396059i
$154$		0			0
$155$	−3.15660	−	5.46739i	−0.253544	−	0.439151i
$156$		0			0
$157$	−1.76795	−	3.06218i	−0.141098	−	0.244388i	0.786813	−	0.617192i	$-0.211730\pi$
$157$	−1.76795	−	3.06218i	−0.141098	−	0.244388i	−0.927910	+	0.372804i	$0.878397\pi$
$158$		0			0
$159$	−8.53590	−	6.03579i	−0.676941	−	0.478669i
$160$		0			0
$161$	−1.22474	−	0.707107i	−0.0965234	−	0.0557278i
$162$		0			0
$163$	−5.19615			−0.406994			−0.203497	−	0.979076i	$-0.565231\pi$
$163$	−5.19615			−0.406994			−0.203497	+	0.979076i	$0.565231\pi$
$164$		0			0
$165$	0.843039	−	0.388390i	0.0656305	−	0.0302361i
$166$		0			0
$167$	3.81294	−	6.60420i	0.295054	−	0.511048i	−0.679944	−	0.733264i	$-0.737996\pi$
$167$	3.81294	−	6.60420i	0.295054	−	0.511048i	0.974997	+	0.222216i	$0.0713291\pi$
$168$		0			0
$169$	0.464102	+	0.803848i	0.0357001	+	0.0618344i
$170$		0			0
$171$	−2.91591	−	12.7474i	−0.222985	−	0.974822i
$172$		0			0
$173$	5.93426	+	10.2784i	0.451173	+	0.781455i	0.998459	−	0.0554909i	$-0.0176724\pi$
$173$	5.93426	+	10.2784i	0.451173	+	0.781455i	−0.547286	+	0.836946i	$0.684339\pi$
$174$		0			0
$175$	−5.59808	+	9.69615i	−0.423175	+	0.732960i
$176$		0			0
$177$	−13.1887	+	6.07608i	−0.991326	+	0.456706i
$178$		0			0
$179$	−1.41421			−0.105703			−0.0528516	−	0.998602i	$-0.516831\pi$
$179$	−1.41421			−0.105703			−0.0528516	+	0.998602i	$0.516831\pi$
$180$		0			0
$181$	−3.00000	−	1.73205i	−0.222988	−	0.128742i	0.384345	−	0.923190i	$-0.374427\pi$
$181$	−3.00000	−	1.73205i	−0.222988	−	0.128742i	−0.607333	+	0.794447i	$0.707761\pi$
$182$		0			0
$183$	5.00052	+	3.53590i	0.369649	+	0.261381i
$184$		0			0
$185$	3.01790	+	5.22715i	0.221880	+	0.384308i
$186$		0			0
$187$	0.928203	+	1.60770i	0.0678769	+	0.117566i
$188$		0			0
$189$	5.27792	−	18.6603i	0.383912	−	1.35733i
$190$		0			0
$191$		−	1.69161i		−	0.122401i	−0.998125	−	0.0612005i	$-0.980507\pi$
$191$		−	1.69161i		−	0.122401i	0.998125	−	0.0612005i	$-0.0194929\pi$
$192$		0			0
$193$	11.4282	−	6.59808i	0.822620	−	0.474940i	−0.0286991	−	0.999588i	$-0.509136\pi$
$193$	11.4282	−	6.59808i	0.822620	−	0.474940i	0.851319	+	0.524648i	$0.175803\pi$
$194$		0			0
$195$	0.838759	−	9.10306i	0.0600648	−	0.651884i
$196$		0			0
$197$		−	9.14162i		−	0.651313i	−0.945488	−	0.325657i	$-0.894415\pi$
$197$		−	9.14162i		−	0.651313i	0.945488	−	0.325657i	$-0.105585\pi$
$198$		0			0
$199$	−6.40192	+	11.0885i	−0.453820	+	0.786040i	−0.998620	−	0.0525267i	$-0.983273\pi$
$199$	−6.40192	+	11.0885i	−0.453820	+	0.786040i	0.544799	+	0.838567i	$0.316606\pi$
$200$		0			0
$201$	1.00000	−	1.41421i	0.0705346	−	0.0997509i
$202$		0			0
$203$	−14.4195	+	24.9754i	−1.01205	+	1.75293i
$204$		0			0
$205$	6.92820	+	4.00000i	0.483887	+	0.279372i
$206$		0			0
$207$	0.864068	+	0.738735i	0.0600569	+	0.0513456i
$208$		0			0
$209$	−1.51575	+	0.656339i	−0.104847	+	0.0453999i
$210$		0			0
$211$	9.52628	−	5.50000i	0.655816	−	0.378636i	−0.134865	−	0.990864i	$-0.543060\pi$
$211$	9.52628	−	5.50000i	0.655816	−	0.378636i	0.790681	+	0.612228i	$0.209727\pi$
$212$		0			0
$213$	−5.64173	+	2.59915i	−0.386565	+	0.178091i
$214$		0			0
$215$	−2.77766	−	1.60368i	−0.189435	−	0.109370i
$216$		0			0
$217$			16.6603i			1.13097i
$218$		0			0
$219$	−4.71940	+	2.17423i	−0.318907	+	0.146921i
$220$		0			0
$221$	18.2832			1.22986
$222$		0			0
$223$	8.13397	−	4.69615i	0.544691	−	0.314478i	−0.202287	−	0.979326i	$-0.564837\pi$
$223$	8.13397	−	4.69615i	0.544691	−	0.314478i	0.746978	+	0.664849i	$0.231504\pi$
$224$		0			0
$225$	5.84847	−	6.84072i	0.389898	−	0.456048i
$226$		0			0
$227$	24.5964			1.63252			0.816261	−	0.577683i	$-0.196043\pi$
$227$	24.5964			1.63252			0.816261	+	0.577683i	$0.196043\pi$
$228$		0			0
$229$	9.39230			0.620661			0.310330	−	0.950629i	$-0.399560\pi$
$229$	9.39230			0.620661			0.310330	+	0.950629i	$0.399560\pi$
$230$		0			0
$231$	−2.43916	−	0.224745i	−0.160485	−	0.0147871i
$232$		0			0
$233$	3.10583	−	1.79315i	0.203470	−	0.117473i	−0.394803	−	0.918766i	$-0.629187\pi$
$233$	3.10583	−	1.79315i	0.203470	−	0.117473i	0.598273	+	0.801292i	$0.295854\pi$
$234$		0			0
$235$	14.9282			0.973809
$236$		0			0
$237$	2.56262	+	5.56244i	0.166460	+	0.361319i
$238$		0			0
$239$		−	29.9759i		−	1.93898i	−0.245133	−	0.969489i	$-0.578832\pi$
$239$		−	29.9759i		−	1.93898i	0.245133	−	0.969489i	$-0.421168\pi$
$240$		0			0
$241$	−24.8205	−	14.3301i	−1.59883	−	0.923085i	−0.991713	−	0.128472i	$-0.958993\pi$
$241$	−24.8205	−	14.3301i	−1.59883	−	0.923085i	−0.607116	−	0.794613i	$-0.707674\pi$
$242$		0			0
$243$	−6.91215	+	13.9722i	−0.443415	+	0.896317i
$244$		0			0
$245$	−8.48528	+	4.89898i	−0.542105	+	0.312984i
$246$		0			0
$247$	−1.86603	+	16.1603i	−0.118732	+	1.02825i
$248$		0			0
$249$	−13.3278	−	1.22803i	−0.844615	−	0.0778232i
$250$		0			0
$251$	−12.7279	−	7.34847i	−0.803379	−	0.463831i	0.0412721	−	0.999148i	$-0.486859\pi$
$251$	−12.7279	−	7.34847i	−0.803379	−	0.463831i	−0.844651	+	0.535317i	$0.820192\pi$
$252$		0			0
$253$	0.0717968	−	0.124356i	0.00451382	−	0.00781817i
$254$		0			0
$255$	−9.79796	−	6.92820i	−0.613572	−	0.433861i
$256$		0			0
$257$	−1.60368	+	2.77766i	−0.100035	+	0.173266i	−0.911699	−	0.410859i	$-0.865229\pi$
$257$	−1.60368	+	2.77766i	−0.100035	+	0.173266i	0.811664	+	0.584125i	$0.198562\pi$
$258$		0			0
$259$		−	15.9282i		−	0.989730i
$260$		0			0
$261$	15.0645	−	17.6203i	0.932469	−	1.09067i
$262$		0			0
$263$	−0.480473	+	0.277401i	−0.0296273	+	0.0171053i	−0.514740	−	0.857346i	$-0.672112\pi$
$263$	−0.480473	+	0.277401i	−0.0296273	+	0.0171053i	0.485113	+	0.874451i	$0.338778\pi$
$264$		0			0
$265$		−	8.53590i		−	0.524356i
$266$		0			0
$267$	−10.3923	−	7.34847i	−0.635999	−	0.449719i
$268$		0			0
$269$	−3.01790	−	5.22715i	−0.184004	−	0.318705i	0.759236	−	0.650815i	$-0.225573\pi$
$269$	−3.01790	−	5.22715i	−0.184004	−	0.318705i	−0.943241	+	0.332110i	$0.892239\pi$
$270$		0			0
$271$	−3.46410	−	6.00000i	−0.210429	−	0.364474i	0.741420	−	0.671042i	$-0.234153\pi$
$271$	−3.46410	−	6.00000i	−0.210429	−	0.364474i	−0.951849	+	0.306568i	$0.900819\pi$
$272$		0			0
$273$	−13.9282	+	19.6975i	−0.842973	+	1.19214i
$274$		0			0
$275$	−0.984508	−	0.568406i	−0.0593681	−	0.0342762i
$276$		0			0
$277$	−9.85641			−0.592214			−0.296107	−	0.955155i	$-0.595689\pi$
$277$	−9.85641			−0.592214			−0.296107	+	0.955155i	$0.595689\pi$
$278$		0			0
$279$	2.44717	−	13.1668i	0.146508	−	0.788277i
$280$		0			0
$281$	7.53794	−	13.0561i	0.449676	−	0.778861i	−0.548689	−	0.836027i	$-0.684873\pi$
$281$	7.53794	−	13.0561i	0.449676	−	0.778861i	0.998365	+	0.0571654i	$0.0182062\pi$
$282$		0			0
$283$	−10.9282	−	18.9282i	−0.649614	−	1.12516i	−0.983215	−	0.182450i	$-0.941597\pi$
$283$	−10.9282	−	18.9282i	−0.649614	−	1.12516i	0.333601	−	0.942714i	$-0.391736\pi$
$284$		0			0
$285$	7.12372	−	7.95315i	0.421973	−	0.471104i
$286$		0			0
$287$	−10.5558	−	18.2832i	−0.623091	−	1.07923i
$288$		0			0
$289$	3.50000	−	6.06218i	0.205882	−	0.356599i
$290$		0			0
$291$	5.40957	+	11.7420i	0.317115	+	0.688329i
$292$		0			0
$293$	−25.2528			−1.47528			−0.737641	−	0.675193i	$-0.764060\pi$
$293$	−25.2528			−1.47528			−0.737641	+	0.675193i	$0.764060\pi$
$294$		0			0
$295$	−10.2679	−	5.92820i	−0.597823	−	0.345153i
$296$		0			0
$297$	1.89469	+	0.535898i	0.109941	+	0.0310960i
$298$		0			0
$299$	−0.707107	−	1.22474i	−0.0408930	−	0.0708288i
$300$		0			0
$301$	4.23205	+	7.33013i	0.243931	+	0.422501i
$302$		0			0
$303$	7.72741	−	10.9282i	0.443928	−	0.627809i
$304$		0			0
$305$			5.00052i			0.286329i
$306$		0			0
$307$	12.0000	−	6.92820i	0.684876	−	0.395413i	−0.116814	−	0.993154i	$-0.537268\pi$
$307$	12.0000	−	6.92820i	0.684876	−	0.395413i	0.801690	+	0.597740i	$0.203935\pi$
$308$		0			0
$309$	18.0479	+	1.66294i	1.02671	+	0.0946014i
$310$		0			0
$311$			27.1475i			1.53939i	0.638411	+	0.769696i	$0.279592\pi$
$311$			27.1475i			1.53939i	−0.638411	+	0.769696i	$0.720408\pi$
$312$		0			0
$313$	12.3923	−	21.4641i	0.700454	−	1.21322i	−0.267853	−	0.963460i	$-0.586314\pi$
$313$	12.3923	−	21.4641i	0.700454	−	1.21322i	0.968307	−	0.249763i	$-0.0803527\pi$
$314$		0			0
$315$	14.9282	−	5.27792i	0.841109	−	0.297377i
$316$		0			0
$317$	6.88160	−	11.9193i	0.386509	−	0.669453i	−0.605468	−	0.795870i	$-0.707014\pi$
$317$	6.88160	−	11.9193i	0.386509	−	0.669453i	0.991977	+	0.126416i	$0.0403474\pi$
$318$		0			0
$319$	−2.53590	−	1.46410i	−0.141983	−	0.0819740i
$320$		0			0
$321$	−0.778539	+	8.44949i	−0.0434538	+	0.471605i
$322$		0			0
$323$	17.1464	+	12.7279i	0.954053	+	0.708201i
$324$		0			0
$325$	−9.69615	+	5.59808i	−0.537846	+	0.310525i
$326$		0			0
$327$	−10.4307	−	22.6410i	−0.576822	−	1.25205i
$328$		0			0
$329$	−34.1170	−	19.6975i	−1.88093	−	1.08596i
$330$		0			0
$331$			31.9282i			1.75493i	0.479638	+	0.877466i	$0.340768\pi$
$331$			31.9282i			1.75493i	−0.479638	+	0.877466i	$0.659232\pi$
$332$		0			0
$333$	−2.33964	+	12.5883i	−0.128211	+	0.689833i
$334$		0			0
$335$	1.41421			0.0772667
$336$		0			0
$337$	6.35641	−	3.66987i	0.346256	−	0.199911i	−0.316779	−	0.948499i	$-0.602601\pi$
$337$	6.35641	−	3.66987i	0.346256	−	0.199911i	0.663035	+	0.748589i	$0.269268\pi$
$338$		0			0
$339$	−2.96577	+	32.1875i	−0.161078	+	1.74818i
$340$		0			0
$341$	−1.69161			−0.0916061
$342$		0			0
$343$	−0.267949			−0.0144679
$344$		0			0
$345$	−0.0851642	+	0.924288i	−0.00458509	+	0.0497620i
$346$		0			0
$347$	21.5414	−	12.4369i	1.15640	−	0.667649i	0.205963	−	0.978560i	$-0.433968\pi$
$347$	21.5414	−	12.4369i	1.15640	−	0.667649i	0.950439	+	0.310911i	$0.100634\pi$
$348$		0			0
$349$	−11.3923			−0.609816			−0.304908	−	0.952382i	$-0.598626\pi$
$349$	−11.3923			−0.609816			−0.304908	+	0.952382i	$0.598626\pi$
$350$		0			0
$351$	13.9009	−	13.5213i	0.741977	−	0.721713i
$352$		0			0
$353$			11.9700i			0.637101i	0.947906	+	0.318551i	$0.103196\pi$
$353$			11.9700i			0.637101i	−0.947906	+	0.318551i	$0.896804\pi$
$354$		0			0
$355$	−4.39230	−	2.53590i	−0.233119	−	0.134592i
$356$		0			0
$357$	13.2507	+	28.7620i	0.701301	+	1.52224i
$358$		0			0
$359$	−23.1822	+	13.3843i	−1.22351	+	0.706394i	−0.965665	−	0.259792i	$-0.916346\pi$
$359$	−23.1822	+	13.3843i	−1.22351	+	0.706394i	−0.257846	+	0.966186i	$0.583013\pi$
$360$		0			0
$361$	−13.0000	+	13.8564i	−0.684211	+	0.729285i
$362$		0			0
$363$	−1.72529	+	18.7245i	−0.0905540	+	0.982783i
$364$		0			0
$365$	−3.67423	−	2.12132i	−0.192318	−	0.111035i
$366$		0			0
$367$	−8.52628	+	14.7679i	−0.445068	+	0.770881i	−0.998057	−	0.0623080i	$-0.980154\pi$
$367$	−8.52628	+	14.7679i	−0.445068	+	0.770881i	0.552989	+	0.833189i	$0.313487\pi$
$368$		0			0
$369$	5.65685	+	16.0000i	0.294484	+	0.832927i
$370$		0			0
$371$	−11.2629	+	19.5080i	−0.584743	+	1.01280i
$372$		0			0
$373$		−	12.5359i		−	0.649084i	−0.945871	−	0.324542i	$-0.894790\pi$
$373$		−	12.5359i		−	0.649084i	0.945871	−	0.324542i	$-0.105210\pi$
$374$		0			0
$375$	19.5133	+	1.79796i	1.00766	+	0.0928462i
$376$		0			0
$377$	−24.9754	+	14.4195i	−1.28630	+	0.742644i
$378$		0			0
$379$			17.7846i			0.913534i	0.889586	+	0.456767i	$0.150993\pi$
$379$			17.7846i			0.913534i	−0.889586	+	0.456767i	$0.849007\pi$
$380$		0			0
$381$	7.85641	−	11.1106i	0.402496	−	0.569215i
$382$		0			0
$383$	13.3335	+	23.0943i	0.681310	+	1.18006i	0.974581	+	0.224034i	$0.0719226\pi$
$383$	13.3335	+	23.0943i	0.681310	+	1.18006i	−0.293272	+	0.956029i	$0.594744\pi$
$384$		0			0
$385$	−1.00000	−	1.73205i	−0.0509647	−	0.0882735i
$386$		0			0
$387$	−2.26795	−	6.41473i	−0.115286	−	0.326079i
$388$		0			0
$389$	−4.33057	−	2.50026i	−0.219569	−	0.126768i	0.386182	−	0.922423i	$-0.373794\pi$
$389$	−4.33057	−	2.50026i	−0.219569	−	0.126768i	−0.605751	+	0.795655i	$0.707127\pi$
$390$		0			0
$391$	−1.85641			−0.0938825
$392$		0			0
$393$	5.05113	+	10.9640i	0.254796	+	0.553060i
$394$		0			0
$395$	−2.50026	+	4.33057i	−0.125802	+	0.217895i
$396$		0			0
$397$	−4.16025	−	7.20577i	−0.208797	−	0.361647i	0.742539	−	0.669803i	$-0.233622\pi$
$397$	−4.16025	−	7.20577i	−0.208797	−	0.361647i	−0.951336	+	0.308156i	$0.900288\pi$
$398$		0			0
$399$	−26.7746	+	8.77656i	−1.34041	+	0.439377i
$400$		0			0
$401$	5.74479	+	9.95026i	0.286881	+	0.496892i	0.973064	−	0.230537i	$-0.0740482\pi$
$401$	5.74479	+	9.95026i	0.286881	+	0.496892i	−0.686183	+	0.727429i	$0.740715\pi$
$402$		0			0
$403$	−8.33013	+	14.4282i	−0.414953	+	0.718720i
$404$		0			0
$405$	−12.5732	+	1.97846i	−0.624768	+	0.0983103i
$406$		0			0
$407$	1.61729			0.0801659
$408$		0			0
$409$	24.4641	+	14.1244i	1.20967	+	0.698404i	0.962688	−	0.270615i	$-0.0872270\pi$
$409$	24.4641	+	14.1244i	1.20967	+	0.698404i	0.246984	+	0.969019i	$0.420560\pi$
$410$		0			0
$411$	0.757875	−	1.07180i	0.0373832	−	0.0528678i
$412$		0			0
$413$	15.6443	+	27.0967i	0.769805	+	1.33334i
$414$		0			0
$415$	−5.46410	−	9.46410i	−0.268222	−	0.464574i
$416$		0			0
$417$	18.6622	+	13.1962i	0.913891	+	0.646218i
$418$		0			0
$419$		−	32.0464i		−	1.56557i	−0.622292	−	0.782785i	$-0.713798\pi$
$419$		−	32.0464i		−	1.56557i	0.622292	−	0.782785i	$-0.286202\pi$
$420$		0			0
$421$	−30.7128	+	17.7321i	−1.49685	+	0.864207i	−0.999993	−	0.00362487i	$-0.998846\pi$
$421$	−30.7128	+	17.7321i	−1.49685	+	0.864207i	−0.496857	+	0.867832i	$0.665513\pi$
$422$		0			0
$423$	24.0698	+	20.5785i	1.17031	+	1.00056i
$424$		0			0
$425$			14.6969i			0.712906i
$426$		0			0
$427$	6.59808	−	11.4282i	0.319303	−	0.553050i
$428$		0			0
$429$	−2.00000	−	1.41421i	−0.0965609	−	0.0682789i
$430$		0			0
$431$	12.7279	−	22.0454i	0.613082	−	1.06189i	−0.377635	−	0.925954i	$-0.623263\pi$
$431$	12.7279	−	22.0454i	0.613082	−	1.06189i	0.990718	−	0.135935i	$-0.0434040\pi$
$432$		0			0
$433$	2.89230	+	1.66987i	0.138995	+	0.0802490i	0.567885	−	0.823108i	$-0.307762\pi$
$433$	2.89230	+	1.66987i	0.138995	+	0.0802490i	−0.428890	+	0.903357i	$0.641095\pi$
$434$		0			0
$435$	18.8484	+	1.73670i	0.903710	+	0.0832682i
$436$		0			0
$437$	0.189469	−	1.64085i	0.00906352	−	0.0784924i
$438$		0			0
$439$	−19.4545	+	11.2321i	−0.928512	+	0.536077i	−0.886341	−	0.463034i	$-0.846761\pi$
$439$	−19.4545	+	11.2321i	−0.928512	+	0.536077i	−0.0421712	+	0.999110i	$0.513427\pi$
$440$		0			0
$441$	−20.4347	−	3.79796i	−0.973079	−	0.180855i
$442$		0			0
$443$	−33.4607	−	19.3185i	−1.58976	−	0.917850i	−0.993345	−	0.115177i	$-0.963257\pi$
$443$	−33.4607	−	19.3185i	−1.58976	−	0.917850i	−0.596419	−	0.802674i	$-0.703410\pi$
$444$		0			0
$445$		−	10.3923i		−	0.492642i
$446$		0			0
$447$	12.2257	+	26.5372i	0.578258	+	1.25517i
$448$		0			0
$449$	34.4959			1.62796			0.813982	−	0.580890i	$-0.197296\pi$
$449$	34.4959			1.62796			0.813982	+	0.580890i	$0.197296\pi$
$450$		0			0
$451$	1.85641	−	1.07180i	0.0874148	−	0.0504689i
$452$		0			0
$453$	−3.44949	−	0.317837i	−0.162071	−	0.0149333i
$454$		0			0
$455$	−19.6975			−0.923431
$456$		0			0
$457$	−20.7128			−0.968905			−0.484452	−	0.874818i	$-0.660981\pi$
$457$	−20.7128			−0.968905			−0.484452	+	0.874818i	$0.660981\pi$
$458$		0			0
$459$	−6.24745	−	24.6773i	−0.291606	−	1.15184i
$460$		0			0
$461$	28.4737	−	16.4393i	1.32615	−	0.765656i	0.341452	−	0.939899i	$-0.389081\pi$
$461$	28.4737	−	16.4393i	1.32615	−	0.765656i	0.984703	+	0.174244i	$0.0557481\pi$
$462$		0			0
$463$	29.5885			1.37509			0.687546	−	0.726141i	$-0.258688\pi$
$463$	29.5885			1.37509			0.687546	+	0.726141i	$0.258688\pi$
$464$		0			0
$465$	9.93149	−	4.57545i	0.460562	−	0.212182i
$466$		0			0
$467$			22.6274i			1.04707i	0.852004	+	0.523536i	$0.175387\pi$
$467$			22.6274i			1.04707i	−0.852004	+	0.523536i	$0.824613\pi$
$468$		0			0
$469$	−3.23205	−	1.86603i	−0.149242	−	0.0861650i
$470$		0			0
$471$	5.56244	−	2.56262i	0.256304	−	0.118079i
$472$		0			0
$473$	−0.744272	+	0.429705i	−0.0342216	+	0.0197579i
$474$		0			0
$475$	−12.9904	−	1.50000i	−0.596040	−	0.0688247i
$476$		0			0
$477$	11.7667	−	13.7630i	0.538761	−	0.630167i
$478$		0			0
$479$	10.2784	+	5.93426i	0.469634	+	0.271143i	0.716086	−	0.698012i	$-0.245932\pi$
$479$	10.2784	+	5.93426i	0.469634	+	0.271143i	−0.246453	+	0.969155i	$0.579265\pi$
$480$		0			0
$481$	7.96410	−	13.7942i	0.363132	−	0.628963i
$482$		0			0
$483$	1.41421	−	2.00000i	0.0643489	−	0.0910032i
$484$		0			0
$485$	−5.27792	+	9.14162i	−0.239658	+	0.415100i
$486$		0			0
$487$		−	24.9282i		−	1.12960i	−0.825226	−	0.564802i	$-0.808952\pi$
$487$		−	24.9282i		−	1.12960i	0.825226	−	0.564802i	$-0.191048\pi$
$488$		0			0
$489$	0.825765	−	8.96204i	0.0373424	−	0.405277i
$490$		0			0
$491$	−8.66115	+	5.00052i	−0.390872	+	0.225670i	−0.682538	−	0.730850i	$-0.739124\pi$
$491$	−8.66115	+	5.00052i	−0.390872	+	0.225670i	0.291666	+	0.956520i	$0.405790\pi$
$492$		0			0
$493$			37.8564i			1.70497i
$494$		0			0
$495$	0.535898	+	1.51575i	0.0240868	+	0.0681279i
$496$		0			0
$497$	6.69213	+	11.5911i	0.300183	+	0.519932i
$498$		0			0
$499$	−8.06218	−	13.9641i	−0.360913	−	0.625119i	0.627199	−	0.778859i	$-0.284201\pi$
$499$	−8.06218	−	13.9641i	−0.360913	−	0.625119i	−0.988111	+	0.153740i	$0.950868\pi$
$500$		0			0
$501$	10.7846	+	7.62587i	0.481821	+	0.340699i
$502$		0			0
$503$	15.8338	+	9.14162i	0.705992	+	0.407605i	0.809575	−	0.587016i	$-0.199697\pi$
$503$	15.8338	+	9.14162i	0.705992	+	0.407605i	−0.103583	+	0.994621i	$0.533031\pi$
$504$		0			0
$505$	10.9282			0.486299
$506$		0			0
$507$	−1.46019	+	0.672711i	−0.0648492	+	0.0298761i
$508$		0			0
$509$	−6.79367	+	11.7670i	−0.301124	+	0.521562i	−0.976391	−	0.216011i	$-0.930695\pi$
$509$	−6.79367	+	11.7670i	−0.301124	+	0.521562i	0.675267	+	0.737574i	$0.264028\pi$
$510$		0			0
$511$	5.59808	+	9.69615i	0.247644	+	0.428933i
$512$		0			0
$513$	22.4495	−	3.00340i	0.991169	−	0.132603i
$514$		0			0
$515$	7.39924	+	12.8159i	0.326049	+	0.564734i
$516$		0			0
$517$	2.00000	−	3.46410i	0.0879599	−	0.152351i
$518$		0			0
$519$	−18.6707	+	8.60164i	−0.819554	+	0.377570i
$520$		0			0
$521$	−4.52004			−0.198027			−0.0990133	−	0.995086i	$-0.531569\pi$
$521$	−4.52004			−0.198027			−0.0990133	+	0.995086i	$0.531569\pi$
$522$		0			0
$523$	14.5981	+	8.42820i	0.638329	+	0.368540i	0.783971	−	0.620798i	$-0.213191\pi$
$523$	14.5981	+	8.42820i	0.638329	+	0.368540i	−0.145641	+	0.989337i	$0.546525\pi$
$524$		0			0
$525$	−15.8338	−	11.1962i	−0.691042	−	0.488640i
$526$		0			0
$527$	10.9348	+	18.9396i	0.476326	+	0.825021i
$528$		0			0
$529$	−11.4282	−	19.7942i	−0.496878	−	0.860619i
$530$		0			0
$531$	−8.38375	−	23.7128i	−0.363824	−	1.02905i
$532$		0			0
$533$		−	21.1117i		−	0.914448i
$534$		0			0
$535$	−6.00000	+	3.46410i	−0.259403	+	0.149766i
$536$		0			0
$537$	0.224745	−	2.43916i	0.00969846	−	0.105257i
$538$		0			0
$539$			2.62536i			0.113082i
$540$		0			0
$541$	8.76795	−	15.1865i	0.376964	−	0.652920i	−0.613655	−	0.789574i	$-0.710302\pi$
$541$	8.76795	−	15.1865i	0.376964	−	0.652920i	0.990619	+	0.136654i	$0.0436349\pi$
$542$		0			0
$543$	3.46410	−	4.89898i	0.148659	−	0.210235i
$544$		0			0
$545$	10.1769	−	17.6269i	0.435930	−	0.755054i
$546$		0			0
$547$	11.1340	+	6.42820i	0.476054	+	0.274850i	0.718771	−	0.695247i	$-0.244705\pi$
$547$	11.1340	+	6.42820i	0.476054	+	0.274850i	−0.242716	+	0.970097i	$0.578038\pi$
$548$		0			0
$549$	−6.89320	+	8.06269i	−0.294195	+	0.344107i
$550$		0			0
$551$	−33.4607	−	3.86370i	−1.42547	−	0.164599i
$552$		0			0
$553$	11.4282	−	6.59808i	0.485977	−	0.280579i
$554$		0			0
$555$	−9.49510	+	4.37441i	−0.403044	+	0.185683i
$556$		0			0
$557$	−2.92996	−	1.69161i	−0.124147	−	0.0716760i	0.436641	−	0.899636i	$-0.356168\pi$
$557$	−2.92996	−	1.69161i	−0.124147	−	0.0716760i	−0.560787	+	0.827960i	$0.689501\pi$
$558$		0			0
$559$			8.46410i			0.357993i
$560$		0			0
$561$	−2.92037	+	1.34542i	−0.123298	+	0.0568037i
$562$		0			0
$563$	−3.38323			−0.142586			−0.0712931	−	0.997455i	$-0.522713\pi$
$563$	−3.38323			−0.142586			−0.0712931	+	0.997455i	$0.522713\pi$
$564$		0			0
$565$	−22.8564	+	13.1962i	−0.961576	+	0.555166i
$566$		0			0
$567$	31.3454	+	12.0685i	1.31638	+	0.506830i
$568$		0			0
$569$	−13.9391			−0.584356			−0.292178	−	0.956364i	$-0.594380\pi$
$569$	−13.9391			−0.584356			−0.292178	+	0.956364i	$0.594380\pi$
$570$		0			0
$571$	−25.1962			−1.05443			−0.527213	−	0.849733i	$-0.676763\pi$
$571$	−25.1962			−1.05443			−0.527213	+	0.849733i	$0.676763\pi$
$572$		0			0
$573$	2.91760	+	0.268829i	0.121885	+	0.0112305i
$574$		0			0
$575$	0.984508	−	0.568406i	0.0410568	−	0.0237042i
$576$		0			0
$577$	42.9282			1.78712			0.893562	−	0.448939i	$-0.148198\pi$
$577$	42.9282			1.78712			0.893562	+	0.448939i	$0.148198\pi$
$578$		0			0
$579$	9.56384	+	20.7593i	0.397460	+	0.862727i
$580$		0			0
$581$			28.8391i			1.19645i
$582$		0			0
$583$	−1.98076	−	1.14359i	−0.0820348	−	0.0473628i
$584$		0			0
$585$	15.5672	+	2.89329i	0.643623	+	0.119623i
$586$		0			0
$587$	−9.29392	+	5.36585i	−0.383601	+	0.221472i	−0.679384	−	0.733783i	$-0.737753\pi$
$587$	−9.29392	+	5.36585i	−0.383601	+	0.221472i	0.295783	+	0.955255i	$0.404420\pi$
$588$		0			0
$589$	−17.8564	+	7.73205i	−0.735760	+	0.318594i
$590$		0			0
$591$	15.7670	+	1.45277i	0.648566	+	0.0597591i
$592$		0			0
$593$	−21.7816	−	12.5756i	−0.894463	−	0.516419i	−0.0190636	−	0.999818i	$-0.506069\pi$
$593$	−21.7816	−	12.5756i	−0.894463	−	0.516419i	−0.875400	+	0.483400i	$0.839402\pi$
$594$		0			0
$595$	−12.9282	+	22.3923i	−0.530005	+	0.917995i
$596$		0			0
$597$	−18.1074	−	12.8038i	−0.741086	−	0.524027i
$598$		0			0
$599$	8.43451	−	14.6090i	0.344625	−	0.596908i	−0.640661	−	0.767824i	$-0.721339\pi$
$599$	8.43451	−	14.6090i	0.344625	−	0.596908i	0.985286	+	0.170916i	$0.0546728\pi$
$600$		0			0
$601$			44.3731i			1.81002i	0.425395	+	0.905008i	$0.360135\pi$
$601$			44.3731i			1.81002i	−0.425395	+	0.905008i	$0.639865\pi$
$602$		0			0
$603$	2.28024	+	1.94949i	0.0928585	+	0.0793894i
$604$		0			0
$605$	−13.2963	+	7.67664i	−0.540573	+	0.312100i
$606$		0			0
$607$			13.2487i			0.537749i	0.963175	+	0.268874i	$0.0866516\pi$
$607$			13.2487i			0.537749i	−0.963175	+	0.268874i	$0.913348\pi$
$608$		0			0
$609$	−40.7846	−	28.8391i	−1.65268	−	1.16862i
$610$		0			0
$611$	−19.6975	−	34.1170i	−0.796874	−	1.38023i
$612$		0			0
$613$	−11.3205	−	19.6077i	−0.457231	−	0.791947i	0.541582	−	0.840648i	$-0.317825\pi$
$613$	−11.3205	−	19.6077i	−0.457231	−	0.791947i	−0.998813	+	0.0487003i	$0.984492\pi$
$614$		0			0
$615$	−8.00000	+	11.3137i	−0.322591	+	0.456213i
$616$		0			0
$617$	22.4379	+	12.9546i	0.903318	+	0.521531i	0.878275	−	0.478156i	$-0.158695\pi$
$617$	22.4379	+	12.9546i	0.903318	+	0.521531i	0.0250427	+	0.999686i	$0.492028\pi$
$618$		0			0
$619$	−2.80385			−0.112696			−0.0563481	−	0.998411i	$-0.517946\pi$
$619$	−2.80385			−0.112696			−0.0563481	+	0.998411i	$0.517946\pi$
$620$		0			0
$621$	−1.41145	+	1.37290i	−0.0566393	+	0.0550925i
$622$		0			0
$623$	−13.7124	+	23.7506i	−0.549377	+	0.951549i
$624$		0			0
$625$	0.500000	+	0.866025i	0.0200000	+	0.0346410i
$626$		0			0
$627$	−0.891136	−	2.71859i	−0.0355885	−	0.108570i
$628$		0			0
$629$	−10.4543	−	18.1074i	−0.416840	−	0.721988i
$630$		0			0
$631$	24.5263	−	42.4808i	0.976376	−	1.69113i	0.301058	−	0.953606i	$-0.402660\pi$
$631$	24.5263	−	42.4808i	0.976376	−	1.69113i	0.675318	−	0.737526i	$-0.264006\pi$
$632$		0			0
$633$	7.97219	+	17.3045i	0.316866	+	0.687790i
$634$		0			0
$635$	11.1106			0.440912
$636$		0			0
$637$	22.3923	+	12.9282i	0.887215	+	0.512234i
$638$		0			0
$639$	−3.58630	−	10.1436i	−0.141872	−	0.401274i
$640$		0			0
$641$	−6.41473	−	11.1106i	−0.253367	−	0.438844i	0.711084	−	0.703107i	$-0.248205\pi$
$641$	−6.41473	−	11.1106i	−0.253367	−	0.438844i	−0.964451	+	0.264263i	$0.914871\pi$
$642$		0			0
$643$	−21.7942	−	37.7487i	−0.859480	−	1.48866i	−0.872425	−	0.488748i	$-0.837454\pi$
$643$	−21.7942	−	37.7487i	−0.859480	−	1.48866i	0.0129447	−	0.999916i	$-0.495879\pi$
$644$		0			0
$645$	3.20736	−	4.53590i	0.126290	−	0.178601i
$646$		0			0
$647$			20.5569i			0.808174i	0.914721	+	0.404087i	$0.132411\pi$
$647$			20.5569i			0.808174i	−0.914721	+	0.404087i	$0.867589\pi$
$648$		0			0
$649$	−2.75129	+	1.58846i	−0.107998	+	0.0623524i
$650$		0			0
$651$	−28.7347	−	2.64762i	−1.12620	−	0.103769i
$652$		0			0
$653$			47.1223i			1.84404i	0.387144	+	0.922019i	$0.373462\pi$
$653$			47.1223i			1.84404i	−0.387144	+	0.922019i	$0.626538\pi$
$654$		0			0
$655$	−4.92820	+	8.53590i	−0.192561	+	0.333525i
$656$		0			0
$657$	−3.00000	−	8.48528i	−0.117041	−	0.331042i
$658$		0			0
$659$	16.5409	−	28.6496i	0.644340	−	1.11603i	−0.340113	−	0.940385i	$-0.610465\pi$
$659$	16.5409	−	28.6496i	0.644340	−	1.11603i	0.984453	−	0.175646i	$-0.0562013\pi$
$660$		0			0
$661$	5.32051	+	3.07180i	0.206944	+	0.119479i	0.599890	−	0.800082i	$-0.295211\pi$
$661$	5.32051	+	3.07180i	0.206944	+	0.119479i	−0.392946	+	0.919561i	$0.628544\pi$
$662$		0			0
$663$	−2.90555	+	31.5339i	−0.112842	+	1.22468i
$664$		0			0
$665$	−18.4727	−	13.7124i	−0.716341	−	0.531745i
$666$		0			0
$667$	2.53590	−	1.46410i	0.0981904	−	0.0566902i
$668$		0			0
$669$	6.80702	+	14.7753i	0.263175	+	0.571248i
$670$		0			0
$671$	1.16037	+	0.669942i	0.0447957	+	0.0258628i
$672$		0			0
$673$		−	21.9808i		−	0.847296i	−0.905827	−	0.423648i	$-0.860749\pi$
$673$		−	21.9808i		−	0.847296i	0.905827	−	0.423648i	$-0.139251\pi$
$674$		0			0
$675$	10.8691	+	11.1742i	0.418350	+	0.430096i
$676$		0			0
$677$	−18.8380			−0.724005			−0.362002	−	0.932177i	$-0.617907\pi$
$677$	−18.8380			−0.724005			−0.362002	+	0.932177i	$0.617907\pi$
$678$		0			0
$679$	24.1244	−	13.9282i	0.925808	−	0.534515i
$680$		0			0
$681$	−3.90883	+	42.4226i	−0.149787	+	1.62564i
$682$		0			0
$683$	16.3142			0.624246			0.312123	−	0.950042i	$-0.398960\pi$
$683$	16.3142			0.624246			0.312123	+	0.950042i	$0.398960\pi$
$684$		0			0
$685$	1.07180			0.0409512
$686$		0			0
$687$	−1.49261	+	16.1993i	−0.0569467	+	0.618043i
$688$		0			0
$689$	−19.5080	+	11.2629i	−0.743195	+	0.429084i
$690$		0			0
$691$	−9.85641			−0.374955			−0.187478	−	0.982269i	$-0.560031\pi$
$691$	−9.85641			−0.374955			−0.187478	+	0.982269i	$0.560031\pi$
$692$		0			0
$693$	0.775255	−	4.17121i	0.0294495	−	0.158451i
$694$		0			0
$695$			18.6622i			0.707897i
$696$		0			0
$697$	−24.0000	−	13.8564i	−0.909065	−	0.524849i
$698$		0			0
$699$	2.59915	+	5.64173i	0.0983090	+	0.213390i
$700$		0			0
$701$	17.2344	−	9.95026i	0.650933	−	0.375816i	−0.137881	−	0.990449i	$-0.544029\pi$
$701$	17.2344	−	9.95026i	0.650933	−	0.375816i	0.788814	+	0.614633i	$0.210696\pi$
$702$		0			0
$703$	17.0718	−	7.39230i	0.643875	−	0.278806i
$704$		0			0
$705$	−2.37237	+	25.7473i	−0.0893486	+	0.969701i
$706$		0			0
$707$	−24.9754	−	14.4195i	−0.939295	−	0.542303i
$708$		0			0
$709$	−21.1603	+	36.6506i	−0.794690	+	1.37644i	0.128346	+	0.991729i	$0.459033\pi$
$709$	−21.1603	+	36.6506i	−0.794690	+	1.37644i	−0.923036	+	0.384714i	$0.874300\pi$
$710$		0			0
$711$	−10.0010	+	3.53590i	−0.375068	+	0.132607i
$712$		0			0
$713$	0.845807	−	1.46498i	0.0316757	−	0.0548640i
$714$		0			0
$715$		−	2.00000i		−	0.0747958i
$716$		0			0
$717$	51.7008	+	4.76373i	1.93080	+	0.177905i
$718$		0			0
$719$	5.22715	−	3.01790i	0.194940	−	0.112549i	−0.399353	−	0.916797i	$-0.630765\pi$
$719$	5.22715	−	3.01790i	0.194940	−	0.112549i	0.594293	+	0.804249i	$0.297432\pi$
$720$		0			0
$721$		−	39.0526i		−	1.45439i
$722$		0			0
$723$	28.6603	−	40.5317i	1.06589	−	1.50739i
$724$		0			0
$725$	−11.5911	−	20.0764i	−0.430483	−	0.745618i
$726$		0			0
$727$	−6.79423	−	11.7679i	−0.251984	−	0.436449i	0.712088	−	0.702090i	$-0.247750\pi$
$727$	−6.79423	−	11.7679i	−0.251984	−	0.436449i	−0.964072	+	0.265641i	$0.914416\pi$
$728$		0			0
$729$	−23.0000	−	14.1421i	−0.851852	−	0.523783i
$730$		0			0
$731$	9.62209	+	5.55532i	0.355886	+	0.205471i
$732$		0			0
$733$	−35.7128			−1.31908			−0.659541	−	0.751668i	$-0.729249\pi$
$733$	−35.7128			−1.31908			−0.659541	+	0.751668i	$0.729249\pi$
$734$		0			0
$735$	−7.10102	−	15.4135i	−0.261925	−	0.568535i
$736$		0			0
$737$	0.189469	−	0.328169i	0.00697917	−	0.0120883i
$738$		0			0
$739$	−17.4019	−	30.1410i	−0.640140	−	1.10876i	−0.985401	−	0.170249i	$-0.945543\pi$
$739$	−17.4019	−	30.1410i	−0.640140	−	1.10876i	0.345261	−	0.938507i	$-0.387790\pi$
$740$		0			0
$741$	−27.5758	−	5.78658i	−1.01302	−	0.212575i
$742$		0			0
$743$	−3.53553	−	6.12372i	−0.129706	−	0.224658i	0.793857	−	0.608105i	$-0.208070\pi$
$743$	−3.53553	−	6.12372i	−0.129706	−	0.224658i	−0.923563	+	0.383447i	$0.874737\pi$
$744$		0			0
$745$	−11.9282	+	20.6603i	−0.437016	+	0.756933i
$746$		0			0
$747$	4.23607	−	22.7919i	0.154990	−	0.833912i
$748$		0			0
$749$	18.2832			0.668055
$750$		0			0
$751$	7.45448	+	4.30385i	0.272018	+	0.157050i	0.629804	−	0.776754i	$-0.283135\pi$
$751$	7.45448	+	4.30385i	0.272018	+	0.157050i	−0.357786	+	0.933803i	$0.616468\pi$
$752$		0			0
$753$	14.6969	−	20.7846i	0.535586	−	0.757433i
$754$		0			0
$755$	−1.41421	−	2.44949i	−0.0514685	−	0.0891461i
$756$		0			0
$757$	−2.30385	−	3.99038i	−0.0837348	−	0.145033i	0.821117	−	0.570760i	$-0.193352\pi$
$757$	−2.30385	−	3.99038i	−0.0837348	−	0.145033i	−0.904851	+	0.425728i	$0.860018\pi$
$758$		0			0
$759$	0.203072	+	0.143594i	0.00737104	+	0.00521212i
$760$		0			0
$761$		−	46.2629i		−	1.67703i	−0.544879	−	0.838514i	$-0.683425\pi$
$761$		−	46.2629i		−	1.67703i	0.544879	−	0.838514i	$-0.316575\pi$
$762$		0			0
$763$	−46.5167	+	26.8564i	−1.68402	+	0.972267i
$764$		0			0
$765$	13.5065	−	15.7980i	0.488327	−	0.571176i
$766$		0			0
$767$			31.2886i			1.12976i
$768$		0			0
$769$	0.428203	−	0.741670i	0.0154414	−	0.0267453i	−0.858201	−	0.513313i	$-0.828418\pi$
$769$	0.428203	−	0.741670i	0.0154414	−	0.0267453i	0.873643	+	0.486568i	$0.161751\pi$
$770$		0			0
$771$	−4.53590	−	3.20736i	−0.163356	−	0.115510i
$772$		0			0
$773$	−9.04008	+	15.6579i	−0.325149	+	0.563175i	−0.981543	−	0.191244i	$-0.938748\pi$
$773$	−9.04008	+	15.6579i	−0.325149	+	0.563175i	0.656393	+	0.754419i	$0.272081\pi$
$774$		0			0
$775$	−11.5981	−	6.69615i	−0.416615	−	0.240533i
$776$		0			0
$777$	27.4721	+	2.53129i	0.985556	+	0.0908095i
$778$		0			0
$779$	14.6969	−	19.7990i	0.526572	−	0.709372i
$780$		0			0
$781$	−1.17691	+	0.679492i	−0.0421133	+	0.0243141i
$782$		0			0
$783$	27.9966	+	28.7826i	1.00052	+	1.02861i
$784$		0			0
$785$	4.33057	+	2.50026i	0.154565	+	0.0892380i
$786$		0			0
$787$		−	24.0718i		−	0.858067i	−0.903289	−	0.429033i	$-0.858854\pi$
$787$		−	24.0718i		−	0.858067i	0.903289	−	0.429033i	$-0.141146\pi$
$788$		0			0
$789$	−0.402091	−	0.872778i	−0.0143148	−	0.0310717i
$790$		0			0
$791$	69.6482			2.47640
$792$		0			0
$793$	11.4282	−	6.59808i	0.405827	−	0.234305i
$794$		0			0
$795$	14.7222	+	1.35651i	0.522144	+	0.0481106i
$796$		0			0
$797$	14.4939			0.513399			0.256700	−	0.966491i	$-0.417365\pi$
$797$	14.4939			0.513399			0.256700	+	0.966491i	$0.417365\pi$
$798$		0			0
$799$	−51.7128			−1.82947
$800$		0			0
$801$	14.3258	−	16.7563i	0.506176	−	0.592054i
$802$		0			0
$803$	−0.984508	+	0.568406i	−0.0347425	+	0.0200586i
$804$		0			0
$805$	2.00000			0.0704907
$806$		0			0
$807$	9.49510	−	4.37441i	0.334243	−	0.153986i
$808$		0			0
$809$		−	51.1619i		−	1.79876i	−0.437172	−	0.899378i	$-0.644020\pi$
$809$		−	51.1619i		−	1.79876i	0.437172	−	0.899378i	$-0.355980\pi$
$810$		0			0
$811$	−18.8038	−	10.8564i	−0.660292	−	0.381220i	0.132096	−	0.991237i	$-0.457829\pi$
$811$	−18.8038	−	10.8564i	−0.660292	−	0.381220i	−0.792388	+	0.610017i	$0.791163\pi$
$812$		0			0
$813$	10.8990	−	5.02118i	0.382244	−	0.176100i
$814$		0			0
$815$	6.36396	−	3.67423i	0.222920	−	0.128703i
$816$		0			0
$817$	−5.89230	+	7.93782i	−0.206146	+	0.277709i
$818$		0			0
$819$	−31.7596	−	27.1529i	−1.10977	−	0.948799i
$820$		0			0
$821$	29.8744	+	17.2480i	1.04262	+	0.601958i	0.920575	−	0.390566i	$-0.127721\pi$
$821$	29.8744	+	17.2480i	1.04262	+	0.601958i	0.122047	+	0.992524i	$0.461054\pi$
$822$		0			0
$823$	−4.00000	+	6.92820i	−0.139431	+	0.241502i	−0.927281	−	0.374365i	$-0.877861\pi$
$823$	−4.00000	+	6.92820i	−0.139431	+	0.241502i	0.787850	+	0.615867i	$0.211194\pi$
$824$		0			0
$825$	1.13681	−	1.60770i	0.0395787	−	0.0559728i
$826$		0			0
$827$	12.2474	−	21.2132i	0.425886	−	0.737655i	−0.570617	−	0.821216i	$-0.693296\pi$
$827$	12.2474	−	21.2132i	0.425886	−	0.737655i	0.996503	+	0.0835608i	$0.0266293\pi$
$828$		0			0
$829$		−	38.6603i		−	1.34273i	−0.741129	−	0.671363i	$-0.765709\pi$
$829$		−	38.6603i		−	1.34273i	0.741129	−	0.671363i	$-0.234291\pi$
$830$		0			0
$831$	1.56637	−	16.9998i	0.0543367	−	0.589716i
$832$		0			0
$833$	29.3939	−	16.9706i	1.01844	−	0.587995i
$834$		0			0
$835$			10.7846i			0.373217i
$836$		0			0
$837$	22.3205	+	6.31319i	0.771510	+	0.218216i
$838$		0			0
$839$	−2.87920	−	4.98691i	−0.0994009	−	0.172167i	0.812036	−	0.583607i	$-0.198359\pi$
$839$	−2.87920	−	4.98691i	−0.0994009	−	0.172167i	−0.911437	+	0.411440i	$0.865026\pi$
$840$		0			0
$841$	−15.3564	−	26.5981i	−0.529531	−	0.917175i
$842$		0			0
$843$	21.3205	+	15.0759i	0.734317	+	0.519241i
$844$		0			0
$845$	−1.13681	−	0.656339i	−0.0391075	−	0.0225787i
$846$		0			0
$847$	40.5167			1.39217
$848$		0			0
$849$	34.3830	−	15.8403i	1.18002	−	0.543638i
$850$		0			0
$851$	−0.808643	+	1.40061i	−0.0277199	+	0.0480123i
$852$		0			0
$853$	−9.83975	−	17.0429i	−0.336906	−	0.583539i	0.646943	−	0.762539i	$-0.276047\pi$
$853$	−9.83975	−	17.0429i	−0.336906	−	0.583539i	−0.983849	+	0.178999i	$0.942714\pi$
$854$		0			0
$855$	12.5851	+	13.5505i	0.430400	+	0.463418i
$856$		0			0
$857$	1.51575	+	2.62536i	0.0517770	+	0.0896804i	0.890752	−	0.454489i	$-0.150178\pi$
$857$	1.51575	+	2.62536i	0.0517770	+	0.0896804i	−0.838975	+	0.544170i	$0.816845\pi$
$858$		0			0
$859$	−2.33013	+	4.03590i	−0.0795029	+	0.137703i	−0.903036	−	0.429566i	$-0.858667\pi$
$859$	−2.33013	+	4.03590i	−0.0795029	+	0.137703i	0.823533	+	0.567269i	$0.192000\pi$
$860$		0			0
$861$	33.2114	−	15.3006i	1.13184	−	0.521442i
$862$		0			0
$863$	−18.2832			−0.622369			−0.311184	−	0.950350i	$-0.600726\pi$
$863$	−18.2832			−0.622369			−0.311184	+	0.950350i	$0.600726\pi$
$864$		0			0
$865$	−14.5359	−	8.39230i	−0.494235	−	0.285347i
$866$		0			0
$867$	9.89949	+	7.00000i	0.336204	+	0.237732i
$868$		0			0
$869$	0.669942	+	1.16037i	0.0227262	+	0.0393630i
$870$		0			0
$871$	−1.86603	−	3.23205i	−0.0632279	−	0.109514i
$872$		0			0
$873$	−21.1117	+	7.46410i	−0.714522	+	0.252622i
$874$		0			0
$875$		−	42.2233i		−	1.42741i
$876$		0			0
$877$	−3.23205	+	1.86603i	−0.109139	+	0.0630112i	−0.553576	−	0.832799i	$-0.686737\pi$
$877$	−3.23205	+	1.86603i	−0.109139	+	0.0630112i	0.444437	+	0.895810i	$0.353404\pi$
$878$		0			0
$879$	4.01314	−	43.5546i	0.135360	−	1.46906i
$880$		0			0
$881$			39.8482i			1.34252i	0.741222	+	0.671260i	$0.234246\pi$
$881$			39.8482i			1.34252i	−0.741222	+	0.671260i	$0.765754\pi$
$882$		0			0
$883$	−11.1340	+	19.2846i	−0.374688	+	0.648979i	−0.990280	−	0.139086i	$-0.955584\pi$
$883$	−11.1340	+	19.2846i	−0.374688	+	0.648979i	0.615592	+	0.788065i	$0.288917\pi$
$884$		0			0
$885$	11.8564	−	16.7675i	0.398549	−	0.563633i
$886$		0			0
$887$	5.98502	−	10.3664i	0.200957	−	0.348068i	−0.747880	−	0.663834i	$-0.768928\pi$
$887$	5.98502	−	10.3664i	0.200957	−	0.348068i	0.948837	+	0.315766i	$0.102261\pi$
$888$		0			0
$889$	−25.3923	−	14.6603i	−0.851631	−	0.491689i
$890$		0			0
$891$	−1.22539	+	3.18269i	−0.0410521	+	0.106624i
$892$		0			0
$893$	5.27792	−	45.7081i	0.176619	−	1.52956i
$894$		0			0
$895$	1.73205	−	1.00000i	0.0578961	−	0.0334263i
$896$		0			0
$897$	2.22474	−	1.02494i	0.0742821	−	0.0342219i
$898$		0			0
$899$	−29.8744	−	17.2480i	−0.996365	−	0.575252i
$900$		0			0
$901$			29.5692i			0.985094i
$902$		0			0
$903$	−13.3152	+	6.13431i	−0.443100	+	0.204137i
$904$		0			0
$905$	4.89898			0.162848
$906$		0			0
$907$	−35.4449	+	20.4641i	−1.17693	+	0.679499i	−0.955302	−	0.295632i	$-0.904470\pi$
$907$	−35.4449	+	20.4641i	−1.17693	+	0.679499i	−0.221626	+	0.975132i	$0.571136\pi$
$908$		0			0
$909$	17.6203	+	15.0645i	0.584430	+	0.499658i
$910$		0			0
$911$	40.9107			1.35543			0.677715	−	0.735324i	$-0.262970\pi$
$911$	40.9107			1.35543			0.677715	+	0.735324i	$0.262970\pi$
$912$		0			0
$913$	−2.92820			−0.0969094
$914$		0			0
$915$	−8.62461	−	0.794675i	−0.285121	−	0.0262711i
$916$		0			0
$917$	22.5259	−	13.0053i	0.743870	−	0.429474i
$918$		0			0
$919$	31.9808			1.05495			0.527474	−	0.849571i	$-0.323139\pi$
$919$	31.9808			1.05495			0.527474	+	0.849571i	$0.323139\pi$
$920$		0			0
$921$	10.0424	+	21.7980i	0.330907	+	0.718267i
$922$		0			0
$923$			13.3843i			0.440548i
$924$		0			0
$925$	11.0885	+	6.40192i	0.364586	+	0.210494i
$926$		0			0
$927$	−5.73630	+	30.8638i	−0.188405	+	1.01370i
$928$		0			0
$929$	17.7148	−	10.2277i	0.581205	−	0.335559i	−0.180407	−	0.983592i	$-0.557742\pi$
$929$	17.7148	−	10.2277i	0.581205	−	0.335559i	0.761612	+	0.648033i	$0.224408\pi$
$930$		0			0
$931$	12.0000	+	27.7128i	0.393284	+	0.908251i
$932$		0			0
$933$	−46.8224	−	4.31424i	−1.53290	−	0.141242i
$934$		0			0
$935$	−2.27362	−	1.31268i	−0.0743555	−	0.0429291i
$936$		0			0
$937$	−2.89230	+	5.00962i	−0.0944875	+	0.163657i	−0.909395	−	0.415934i	$-0.863455\pi$
$937$	−2.89230	+	5.00962i	−0.0944875	+	0.163657i	0.814907	+	0.579592i	$0.196788\pi$
$938$		0			0
$939$	35.0507	+	24.7846i	1.14384	+	0.808815i
$940$		0			0
$941$	−6.96953	+	12.0716i	−0.227200	+	0.393522i	−0.956977	−	0.290163i	$-0.906291\pi$
$941$	−6.96953	+	12.0716i	−0.227200	+	0.393522i	0.729777	+	0.683685i	$0.239624\pi$
$942$		0			0
$943$			2.14359i			0.0698050i
$944$		0			0
$945$	6.73069	+	26.5861i	0.218949	+	0.864846i
$946$		0			0
$947$	−38.3596	+	22.1469i	−1.24652	+	0.719679i	−0.970414	−	0.241448i	$-0.922378\pi$
$947$	−38.3596	+	22.1469i	−1.24652	+	0.719679i	−0.276107	+	0.961127i	$0.589044\pi$
$948$		0			0
$949$			11.1962i			0.363442i
$950$		0			0
$951$	19.4641	+	13.7632i	0.631167	+	0.446302i
$952$		0			0
$953$	21.3011	+	36.8947i	0.690011	+	1.19513i	0.971834	+	0.235668i	$0.0757279\pi$
$953$	21.3011	+	36.8947i	0.690011	+	1.19513i	−0.281822	+	0.959467i	$0.590939\pi$
$954$		0			0
$955$	1.19615	+	2.07180i	0.0387066	+	0.0670418i
$956$		0			0
$957$	2.92820	−	4.14110i	0.0946554	−	0.133863i
$958$		0			0
$959$	−2.44949	−	1.41421i	−0.0790981	−	0.0456673i
$960$		0			0
$961$	11.0718			0.357155
$962$		0			0
$963$	−14.4495	−	2.68556i	−0.465628	−	0.0865410i
$964$		0			0
$965$	−9.33109	+	16.1619i	−0.300378	+	0.520271i
$966$		0			0
$967$	−4.40192	−	7.62436i	−0.141556	−	0.245183i	0.786527	−	0.617556i	$-0.211877\pi$
$967$	−4.40192	−	7.62436i	−0.141556	−	0.245183i	−0.928083	+	0.372374i	$0.878544\pi$
$968$		0			0
$969$	−24.6773	+	27.5505i	−0.792749	+	0.885050i
$970$		0			0
$971$	7.17260	+	12.4233i	0.230180	+	0.398683i	0.957861	−	0.287232i	$-0.0927352\pi$
$971$	7.17260	+	12.4233i	0.230180	+	0.398683i	−0.727681	+	0.685916i	$0.759402\pi$
$972$		0			0
$973$	24.6244	−	42.6506i	0.789421	−	1.36732i
$974$		0			0
$975$	−8.11435	−	17.6130i	−0.259867	−	0.564068i
$976$		0			0
$977$	20.3538			0.651176			0.325588	−	0.945512i	$-0.394438\pi$
$977$	20.3538			0.651176			0.325588	+	0.945512i	$0.394438\pi$
$978$		0			0
$979$	−2.41154	−	1.39230i	−0.0770732	−	0.0444983i
$980$		0			0
$981$	40.7076	−	14.3923i	1.29969	−	0.459511i
$982$		0			0
$983$	−16.2635	−	28.1691i	−0.518724	−	0.898456i	−0.999763	−	0.0217569i	$-0.993074\pi$
$983$	−16.2635	−	28.1691i	−0.518724	−	0.898456i	0.481040	−	0.876699i	$-0.340259\pi$
$984$		0			0
$985$	6.46410	+	11.1962i	0.205963	+	0.356739i
$986$		0			0
$987$	39.3949	−	55.7128i	1.25395	−	1.77336i
$988$		0			0
$989$		−	0.859411i		−	0.0273277i
$990$		0			0
$991$	3.61731	−	2.08846i	0.114908	−	0.0663420i	−0.441445	−	0.897289i	$-0.645534\pi$
$991$	3.61731	−	2.08846i	0.114908	−	0.0663420i	0.556352	+	0.830946i	$0.312200\pi$
$992$		0			0
$993$	−55.0680	−	5.07399i	−1.74753	−	0.161018i
$994$		0			0
$995$		−	18.1074i		−	0.574042i
$996$		0			0
$997$	−25.0885	+	43.4545i	−0.794559	+	1.37622i	0.128559	+	0.991702i	$0.458965\pi$
$997$	−25.0885	+	43.4545i	−0.794559	+	1.37622i	−0.923119	+	0.384515i	$0.874369\pi$
$998$		0			0
$999$	−21.3397	−	6.03579i	−0.675160	−	0.190964i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.bn.m.449.2		8
3.2	odd	2	inner	912.2.bn.m.449.1		8
4.3	odd	2		57.2.f.a.50.4	yes	8
12.11	even	2		57.2.f.a.50.1	yes	8
19.8	odd	6	inner	912.2.bn.m.65.1		8
57.8	even	6	inner	912.2.bn.m.65.2		8
76.7	odd	6		1083.2.d.b.1082.2		8
76.27	even	6		57.2.f.a.8.1	✓	8
76.31	even	6		1083.2.d.b.1082.7		8
228.83	even	6		1083.2.d.b.1082.8		8
228.107	odd	6		1083.2.d.b.1082.1		8
228.179	odd	6		57.2.f.a.8.4	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
57.2.f.a.8.1	✓	8	76.27	even	6
57.2.f.a.8.4	yes	8	228.179	odd	6
57.2.f.a.50.1	yes	8	12.11	even	2
57.2.f.a.50.4	yes	8	4.3	odd	2
912.2.bn.m.65.1		8	19.8	odd	6	inner
912.2.bn.m.65.2		8	57.8	even	6	inner
912.2.bn.m.449.1		8	3.2	odd	2	inner
912.2.bn.m.449.2		8	1.1	even	1	trivial
1083.2.d.b.1082.1		8	228.107	odd	6
1083.2.d.b.1082.2		8	76.7	odd	6
1083.2.d.b.1082.7		8	76.31	even	6
1083.2.d.b.1082.8		8	228.83	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.bn (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.158919 + 1.72474i) q^{3} +(-1.22474 + 0.707107i) q^{5} +3.73205 q^{7} +(-2.94949 - 0.548188i) q^{9} +O(q^{10})\)	\(q+(-0.158919 + 1.72474i) q^{3} +(-1.22474 + 0.707107i) q^{5} +3.73205 q^{7} +(-2.94949 - 0.548188i) q^{9} +0.378937i q^{11} +(3.23205 + 1.86603i) q^{13} +(-1.02494 - 2.22474i) q^{15} +(4.24264 - 2.44949i) q^{17} +(1.73205 + 4.00000i) q^{19} +(-0.593092 + 6.43684i) q^{21} +(-0.328169 - 0.189469i) q^{23} +(-1.50000 + 2.59808i) q^{25} +(1.41421 - 5.00000i) q^{27} +(-3.86370 + 6.69213i) q^{29} +4.46410i q^{31} +(-0.653570 - 0.0602202i) q^{33} +(-4.57081 + 2.63896i) q^{35} -4.26795i q^{37} +(-3.73205 + 5.27792i) q^{39} +(-2.82843 - 4.89898i) q^{41} +(1.13397 + 1.96410i) q^{43} +(4.00000 - 1.41421i) q^{45} +(-9.14162 - 5.27792i) q^{47} +6.92820 q^{49} +(3.55051 + 7.70674i) q^{51} +(-3.01790 + 5.22715i) q^{53} +(-0.267949 - 0.464102i) q^{55} +(-7.17423 + 2.35167i) q^{57} +(4.19187 + 7.26054i) q^{59} +(1.76795 - 3.06218i) q^{61} +(-11.0076 - 2.04587i) q^{63} -5.27792 q^{65} +(-0.866025 - 0.500000i) q^{67} +(0.378937 - 0.535898i) q^{69} +(1.79315 + 3.10583i) q^{71} +(1.50000 + 2.59808i) q^{73} +(-4.24264 - 3.00000i) q^{75} +1.41421i q^{77} +(3.06218 - 1.76795i) q^{79} +(8.39898 + 3.23375i) q^{81} +7.72741i q^{83} +(-3.46410 + 6.00000i) q^{85} +(-10.9282 - 7.72741i) q^{87} +(-3.67423 + 6.36396i) q^{89} +(12.0622 + 6.96410i) q^{91} +(-7.69944 - 0.709429i) q^{93} +(-4.94975 - 3.67423i) q^{95} +(6.46410 - 3.73205i) q^{97} +(0.207729 - 1.11767i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 16 q^{7} - 4 q^{9}+O(q^{10}) \) 8 * q + 16 * q^7 - 4 * q^9	\( 8 q + 16 q^{7} - 4 q^{9} + 12 q^{13} - 12 q^{21} - 12 q^{25} + 24 q^{33} - 16 q^{39} + 16 q^{43} + 32 q^{45} + 48 q^{51} - 16 q^{55} - 28 q^{57} + 28 q^{61} - 8 q^{63} + 12 q^{73} - 24 q^{79} + 28 q^{81} - 32 q^{87} + 48 q^{91} - 4 q^{93} + 24 q^{97} + 32 q^{99}+O(q^{100}) \) 8 * q + 16 * q^7 - 4 * q^9 + 12 * q^13 - 12 * q^21 - 12 * q^25 + 24 * q^33 - 16 * q^39 + 16 * q^43 + 32 * q^45 + 48 * q^51 - 16 * q^55 - 28 * q^57 + 28 * q^61 - 8 * q^63 + 12 * q^73 - 24 * q^79 + 28 * q^81 - 32 * q^87 + 48 * q^91 - 4 * q^93 + 24 * q^97 + 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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