LMFDB - Embedded newform 882.2.f.s.589.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(295,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("882.295");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.f (of order $3$, degree $2$, 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:	$7.04280545828$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			589.4
Root			$-0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	882.589
Dual form			882.2.f.s.295.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 + 0.866025i) q^{2} +(1.22474 + 1.22474i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.258819 - 0.448288i) q^{5} +(-0.448288 + 1.67303i) q^{6} -1.00000 q^{8} +3.00000i q^{9} +0.517638 q^{10} +(0.732051 + 1.26795i) q^{11} +(-1.67303 + 0.448288i) q^{12} +(-1.22474 + 2.12132i) q^{13} +(0.866025 - 0.232051i) q^{15} +(-0.500000 - 0.866025i) q^{16} +3.48477 q^{17} +(-2.59808 + 1.50000i) q^{18} -0.517638 q^{19} +(0.258819 + 0.448288i) q^{20} +(-0.732051 + 1.26795i) q^{22} +(-3.96410 + 6.86603i) q^{23} +(-1.22474 - 1.22474i) q^{24} +(2.36603 + 4.09808i) q^{25} -2.44949 q^{26} +(-3.67423 + 3.67423i) q^{27} +(-1.36603 - 2.36603i) q^{29} +(0.633975 + 0.633975i) q^{30} +(3.67423 - 6.36396i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-0.656339 + 2.44949i) q^{33} +(1.74238 + 3.01790i) q^{34} +(-2.59808 - 1.50000i) q^{36} -8.00000 q^{37} +(-0.258819 - 0.448288i) q^{38} +(-4.09808 + 1.09808i) q^{39} +(-0.258819 + 0.448288i) q^{40} +(2.82843 - 4.89898i) q^{41} +(6.09808 + 10.5622i) q^{43} -1.46410 q^{44} +(1.34486 + 0.776457i) q^{45} -7.92820 q^{46} +(-2.31079 - 4.00240i) q^{47} +(0.448288 - 1.67303i) q^{48} +(-2.36603 + 4.09808i) q^{50} +(4.26795 + 4.26795i) q^{51} +(-1.22474 - 2.12132i) q^{52} +6.73205 q^{53} +(-5.01910 - 1.34486i) q^{54} +0.757875 q^{55} +(-0.633975 - 0.633975i) q^{57} +(1.36603 - 2.36603i) q^{58} +(7.39924 - 12.8159i) q^{59} +(-0.232051 + 0.866025i) q^{60} +(2.19067 + 3.79435i) q^{61} +7.34847 q^{62} +1.00000 q^{64} +(0.633975 + 1.09808i) q^{65} +(-2.44949 + 0.656339i) q^{66} +(1.90192 - 3.29423i) q^{67} +(-1.74238 + 3.01790i) q^{68} +(-13.2641 + 3.55412i) q^{69} -0.803848 q^{71} -3.00000i q^{72} -4.62158 q^{73} +(-4.00000 - 6.92820i) q^{74} +(-2.12132 + 7.91688i) q^{75} +(0.258819 - 0.448288i) q^{76} +(-3.00000 - 3.00000i) q^{78} +(-7.06218 - 12.2321i) q^{79} -0.517638 q^{80} -9.00000 q^{81} +5.65685 q^{82} +(-4.94975 - 8.57321i) q^{83} +(0.901924 - 1.56218i) q^{85} +(-6.09808 + 10.5622i) q^{86} +(1.22474 - 4.57081i) q^{87} +(-0.732051 - 1.26795i) q^{88} +16.1112 q^{89} +1.55291i q^{90} +(-3.96410 - 6.86603i) q^{92} +(12.2942 - 3.29423i) q^{93} +(2.31079 - 4.00240i) q^{94} +(-0.133975 + 0.232051i) q^{95} +(1.67303 - 0.448288i) q^{96} +(-0.517638 - 0.896575i) q^{97} +(-3.80385 + 2.19615i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} - 4 q^{4} - 8 q^{8} - 8 q^{11} - 4 q^{16} + 8 q^{22} - 4 q^{23} + 12 q^{25} - 4 q^{29} + 12 q^{30} + 4 q^{32} - 64 q^{37} - 12 q^{39} + 28 q^{43} + 16 q^{44} - 8 q^{46} - 12 q^{50} + 48 q^{51}+ \cdots - 72 q^{99}+O(q^{100}) $ 8 * q + 4 * q^2 - 4 * q^4 - 8 * q^8 - 8 * q^11 - 4 * q^16 + 8 * q^22 - 4 * q^23 + 12 * q^25 - 4 * q^29 + 12 * q^30 + 4 * q^32 - 64 * q^37 - 12 * q^39 + 28 * q^43 + 16 * q^44 - 8 * q^46 - 12 * q^50 + 48 * q^51 + 40 * q^53 - 12 * q^57 + 4 * q^58 + 12 * q^60 + 8 * q^64 + 12 * q^65 + 36 * q^67 - 48 * q^71 - 32 * q^74 - 24 * q^78 - 8 * q^79 - 72 * q^81 + 28 * q^85 - 28 * q^86 + 8 * q^88 - 4 * q^92 + 36 * q^93 - 8 * q^95 - 72 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	1.22474	+	1.22474i	0.707107	+	0.707107i
$3$	1.22474	+	1.22474i	0.707107	+	0.707107i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	0.258819	−	0.448288i	0.115747	−	0.200480i	−0.802331	−	0.596880i	$-0.796407\pi$
$5$	0.258819	−	0.448288i	0.115747	−	0.200480i	0.918078	+	0.396399i	$0.129740\pi$
$6$	−0.448288	+	1.67303i	−0.183013	+	0.683013i
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$			3.00000i			1.00000i
$10$	0.517638			0.163692
$11$	0.732051	+	1.26795i	0.220722	+	0.382301i	0.955027	−	0.296518i	$-0.0958254\pi$
$11$	0.732051	+	1.26795i	0.220722	+	0.382301i	−0.734306	+	0.678819i	$0.762492\pi$
$12$	−1.67303	+	0.448288i	−0.482963	+	0.129410i
$13$	−1.22474	+	2.12132i	−0.339683	+	0.588348i	−0.984373	−	0.176096i	$-0.943653\pi$
$13$	−1.22474	+	2.12132i	−0.339683	+	0.588348i	0.644690	+	0.764444i	$0.276986\pi$
$14$		0			0
$15$	0.866025	−	0.232051i	0.223607	−	0.0599153i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	3.48477			0.845180			0.422590	−	0.906321i	$-0.361121\pi$
$17$	3.48477			0.845180			0.422590	+	0.906321i	$0.361121\pi$
$18$	−2.59808	+	1.50000i	−0.612372	+	0.353553i
$19$	−0.517638			−0.118754			−0.0593772	−	0.998236i	$-0.518911\pi$
$19$	−0.517638			−0.118754			−0.0593772	+	0.998236i	$0.518911\pi$
$20$	0.258819	+	0.448288i	0.0578737	+	0.100240i
$21$		0			0
$22$	−0.732051	+	1.26795i	−0.156074	+	0.270328i
$23$	−3.96410	+	6.86603i	−0.826572	+	1.43167i	0.0741394	+	0.997248i	$0.476379\pi$
$23$	−3.96410	+	6.86603i	−0.826572	+	1.43167i	−0.900712	+	0.434417i	$0.856954\pi$
$24$	−1.22474	−	1.22474i	−0.250000	−	0.250000i
$25$	2.36603	+	4.09808i	0.473205	+	0.819615i
$26$	−2.44949			−0.480384
$27$	−3.67423	+	3.67423i	−0.707107	+	0.707107i
$28$		0			0
$29$	−1.36603	−	2.36603i	−0.253665	−	0.439360i	0.710867	−	0.703326i	$-0.248303\pi$
$29$	−1.36603	−	2.36603i	−0.253665	−	0.439360i	−0.964532	+	0.263966i	$0.914969\pi$
$30$	0.633975	+	0.633975i	0.115747	+	0.115747i
$31$	3.67423	−	6.36396i	0.659912	−	1.14300i	−0.320726	−	0.947172i	$-0.603927\pi$
$31$	3.67423	−	6.36396i	0.659912	−	1.14300i	0.980638	−	0.195829i	$-0.0627398\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−0.656339	+	2.44949i	−0.114254	+	0.426401i
$34$	1.74238	+	3.01790i	0.298816	+	0.517565i
$35$		0			0
$36$	−2.59808	−	1.50000i	−0.433013	−	0.250000i
$37$	−8.00000			−1.31519			−0.657596	−	0.753371i	$-0.728427\pi$
$37$	−8.00000			−1.31519			−0.657596	+	0.753371i	$0.728427\pi$
$38$	−0.258819	−	0.448288i	−0.0419860	−	0.0727219i
$39$	−4.09808	+	1.09808i	−0.656217	+	0.175833i
$40$	−0.258819	+	0.448288i	−0.0409229	+	0.0708805i
$41$	2.82843	−	4.89898i	0.441726	−	0.765092i	−0.556092	−	0.831121i	$-0.687700\pi$
$41$	2.82843	−	4.89898i	0.441726	−	0.765092i	0.997818	+	0.0660290i	$0.0210330\pi$
$42$		0			0
$43$	6.09808	+	10.5622i	0.929948	+	1.61072i	0.783404	+	0.621513i	$0.213482\pi$
$43$	6.09808	+	10.5622i	0.929948	+	1.61072i	0.146544	+	0.989204i	$0.453185\pi$
$44$	−1.46410			−0.220722
$45$	1.34486	+	0.776457i	0.200480	+	0.115747i
$46$	−7.92820			−1.16895
$47$	−2.31079	−	4.00240i	−0.337063	−	0.583811i	0.646816	−	0.762646i	$-0.276100\pi$
$47$	−2.31079	−	4.00240i	−0.337063	−	0.583811i	−0.983879	+	0.178836i	$0.942767\pi$
$48$	0.448288	−	1.67303i	0.0647048	−	0.241481i
$49$		0			0
$50$	−2.36603	+	4.09808i	−0.334607	+	0.579555i
$51$	4.26795	+	4.26795i	0.597632	+	0.597632i
$52$	−1.22474	−	2.12132i	−0.169842	−	0.294174i
$53$	6.73205			0.924718			0.462359	−	0.886693i	$-0.347003\pi$
$53$	6.73205			0.924718			0.462359	+	0.886693i	$0.347003\pi$
$54$	−5.01910	−	1.34486i	−0.683013	−	0.183013i
$55$	0.757875			0.102192
$56$		0			0
$57$	−0.633975	−	0.633975i	−0.0839720	−	0.0839720i
$58$	1.36603	−	2.36603i	0.179368	−	0.310674i
$59$	7.39924	−	12.8159i	0.963299	−	1.66848i	0.249180	−	0.968457i	$-0.419839\pi$
$59$	7.39924	−	12.8159i	0.963299	−	1.66848i	0.714118	−	0.700025i	$-0.246828\pi$
$60$	−0.232051	+	0.866025i	−0.0299576	+	0.111803i
$61$	2.19067	+	3.79435i	0.280487	+	0.485817i	0.971505	−	0.237020i	$-0.0761708\pi$
$61$	2.19067	+	3.79435i	0.280487	+	0.485817i	−0.691018	+	0.722838i	$0.742837\pi$
$62$	7.34847			0.933257
$63$		0			0
$64$	1.00000			0.125000
$65$	0.633975	+	1.09808i	0.0786349	+	0.136200i
$66$	−2.44949	+	0.656339i	−0.301511	+	0.0807897i
$67$	1.90192	−	3.29423i	0.232357	−	0.402454i	−0.726144	−	0.687542i	$-0.758690\pi$
$67$	1.90192	−	3.29423i	0.232357	−	0.402454i	0.958501	+	0.285088i	$0.0920229\pi$
$68$	−1.74238	+	3.01790i	−0.211295	+	0.365974i
$69$	−13.2641	+	3.55412i	−1.59682	+	0.427865i
$70$		0			0
$71$	−0.803848			−0.0953992			−0.0476996	−	0.998862i	$-0.515189\pi$
$71$	−0.803848			−0.0953992			−0.0476996	+	0.998862i	$0.515189\pi$
$72$		−	3.00000i		−	0.353553i
$73$	−4.62158			−0.540915			−0.270457	−	0.962732i	$-0.587175\pi$
$73$	−4.62158			−0.540915			−0.270457	+	0.962732i	$0.587175\pi$
$74$	−4.00000	−	6.92820i	−0.464991	−	0.805387i
$75$	−2.12132	+	7.91688i	−0.244949	+	0.914162i
$76$	0.258819	−	0.448288i	0.0296886	−	0.0514221i
$77$		0			0
$78$	−3.00000	−	3.00000i	−0.339683	−	0.339683i
$79$	−7.06218	−	12.2321i	−0.794557	−	1.37621i	−0.923120	−	0.384512i	$-0.874370\pi$
$79$	−7.06218	−	12.2321i	−0.794557	−	1.37621i	0.128563	−	0.991701i	$-0.458964\pi$
$80$	−0.517638			−0.0578737
$81$	−9.00000			−1.00000
$82$	5.65685			0.624695
$83$	−4.94975	−	8.57321i	−0.543305	−	0.941033i	−0.998711	−	0.0507487i	$-0.983839\pi$
$83$	−4.94975	−	8.57321i	−0.543305	−	0.941033i	0.455406	−	0.890284i	$-0.349494\pi$
$84$		0			0
$85$	0.901924	−	1.56218i	0.0978274	−	0.169442i
$86$	−6.09808	+	10.5622i	−0.657572	+	1.13895i
$87$	1.22474	−	4.57081i	0.131306	−	0.490042i
$88$	−0.732051	−	1.26795i	−0.0780369	−	0.135164i
$89$	16.1112			1.70778			0.853889	−	0.520455i	$-0.174237\pi$
$89$	16.1112			1.70778			0.853889	+	0.520455i	$0.174237\pi$
$90$			1.55291i			0.163692i
$91$		0			0
$92$	−3.96410	−	6.86603i	−0.413286	−	0.715833i
$93$	12.2942	−	3.29423i	1.27485	−	0.341596i
$94$	2.31079	−	4.00240i	0.238340	−	0.412816i
$95$	−0.133975	+	0.232051i	−0.0137455	+	0.0238079i
$96$	1.67303	−	0.448288i	0.170753	−	0.0457532i
$97$	−0.517638	−	0.896575i	−0.0525582	−	0.0910334i	0.838549	−	0.544826i	$-0.183404\pi$
$97$	−0.517638	−	0.896575i	−0.0525582	−	0.0910334i	−0.891108	+	0.453792i	$0.850071\pi$
$98$		0			0
$99$	−3.80385	+	2.19615i	−0.382301	+	0.220722i
$100$	−4.73205			−0.473205
$101$	2.89778	+	5.01910i	0.288340	+	0.499419i	0.973414	−	0.229055i	$-0.0735635\pi$
$101$	2.89778	+	5.01910i	0.288340	+	0.499419i	−0.685074	+	0.728474i	$0.740230\pi$
$102$	−1.56218	+	5.83013i	−0.154679	+	0.577269i
$103$	−5.60609	+	9.71003i	−0.552384	+	0.956757i	0.445718	+	0.895174i	$0.352948\pi$
$103$	−5.60609	+	9.71003i	−0.552384	+	0.956757i	−0.998102	+	0.0615838i	$0.980385\pi$
$104$	1.22474	−	2.12132i	0.120096	−	0.208013i
$105$		0			0
$106$	3.36603	+	5.83013i	0.326937	+	0.566272i
$107$	3.07180			0.296962			0.148481	−	0.988915i	$-0.452562\pi$
$107$	3.07180			0.296962			0.148481	+	0.988915i	$0.452562\pi$
$108$	−1.34486	−	5.01910i	−0.129410	−	0.482963i
$109$	10.5885			1.01419			0.507095	−	0.861890i	$-0.330719\pi$
$109$	10.5885			1.01419			0.507095	+	0.861890i	$0.330719\pi$
$110$	0.378937	+	0.656339i	0.0361303	+	0.0625794i
$111$	−9.79796	−	9.79796i	−0.929981	−	0.929981i
$112$		0			0
$113$	7.33013	−	12.6962i	0.689560	−	1.19435i	−0.282420	−	0.959291i	$-0.591137\pi$
$113$	7.33013	−	12.6962i	0.689560	−	1.19435i	0.971980	−	0.235063i	$-0.0755295\pi$
$114$	0.232051	−	0.866025i	0.0217335	−	0.0811107i
$115$	2.05197	+	3.55412i	0.191347	+	0.331423i
$116$	2.73205			0.253665
$117$	−6.36396	−	3.67423i	−0.588348	−	0.339683i
$118$	14.7985			1.36231
$119$		0			0
$120$	−0.866025	+	0.232051i	−0.0790569	+	0.0211832i
$121$	4.42820	−	7.66987i	0.402564	−	0.697261i
$122$	−2.19067	+	3.79435i	−0.198334	+	0.343525i
$123$	9.46410	−	2.53590i	0.853349	−	0.228654i
$124$	3.67423	+	6.36396i	0.329956	+	0.571501i
$125$	5.03768			0.450584
$126$		0			0
$127$	−5.92820			−0.526043			−0.263021	−	0.964790i	$-0.584719\pi$
$127$	−5.92820			−0.526043			−0.263021	+	0.964790i	$0.584719\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−5.46739	+	20.4046i	−0.481376	+	1.79652i
$130$	−0.633975	+	1.09808i	−0.0556033	+	0.0963077i
$131$	6.24384	−	10.8147i	0.545527	−	0.944881i	−0.453046	−	0.891487i	$-0.649663\pi$
$131$	6.24384	−	10.8147i	0.545527	−	0.944881i	0.998574	−	0.0533937i	$-0.0170038\pi$
$132$	−1.79315	−	1.79315i	−0.156074	−	0.156074i
$133$		0			0
$134$	3.80385			0.328602
$135$	0.696152	+	2.59808i	0.0599153	+	0.223607i
$136$	−3.48477			−0.298816
$137$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$137$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$138$	−9.71003	−	9.71003i	−0.826572	−	0.826572i
$139$	−10.1075	+	17.5068i	−0.857311	+	1.48491i	0.0171736	+	0.999853i	$0.494533\pi$
$139$	−10.1075	+	17.5068i	−0.857311	+	1.48491i	−0.874485	+	0.485053i	$0.838800\pi$
$140$		0			0
$141$	2.07180	−	7.73205i	0.174477	−	0.651156i
$142$	−0.401924	−	0.696152i	−0.0337287	−	0.0584198i
$143$	−3.58630			−0.299902
$144$	2.59808	−	1.50000i	0.216506	−	0.125000i
$145$	−1.41421			−0.117444
$146$	−2.31079	−	4.00240i	−0.191242	−	0.331241i
$147$		0			0
$148$	4.00000	−	6.92820i	0.328798	−	0.569495i
$149$	1.19615	−	2.07180i	0.0979926	−	0.169728i	−0.812861	−	0.582458i	$-0.802091\pi$
$149$	1.19615	−	2.07180i	0.0979926	−	0.169728i	0.910854	+	0.412729i	$0.135425\pi$
$150$	−7.91688	+	2.12132i	−0.646410	+	0.173205i
$151$	8.69615	+	15.0622i	0.707683	+	1.22574i	0.965715	+	0.259606i	$0.0835928\pi$
$151$	8.69615	+	15.0622i	0.707683	+	1.22574i	−0.258032	+	0.966136i	$0.583074\pi$
$152$	0.517638			0.0419860
$153$			10.4543i			0.845180i
$154$		0			0
$155$	−1.90192	−	3.29423i	−0.152766	−	0.264599i
$156$	1.09808	−	4.09808i	0.0879165	−	0.328109i
$157$	−8.64256	+	14.9694i	−0.689752	+	1.19469i	0.282166	+	0.959366i	$0.408947\pi$
$157$	−8.64256	+	14.9694i	−0.689752	+	1.19469i	−0.971918	+	0.235320i	$0.924386\pi$
$158$	7.06218	−	12.2321i	0.561837	−	0.973130i
$159$	8.24504	+	8.24504i	0.653875	+	0.653875i
$160$	−0.258819	−	0.448288i	−0.0204614	−	0.0354403i
$161$		0			0
$162$	−4.50000	−	7.79423i	−0.353553	−	0.612372i
$163$	−7.07180			−0.553906			−0.276953	−	0.960883i	$-0.589325\pi$
$163$	−7.07180			−0.553906			−0.276953	+	0.960883i	$0.589325\pi$
$164$	2.82843	+	4.89898i	0.220863	+	0.382546i
$165$	0.928203	+	0.928203i	0.0722605	+	0.0722605i
$166$	4.94975	−	8.57321i	0.384175	−	0.665410i
$167$	6.64136	−	11.5032i	0.513924	−	0.890143i	−0.485945	−	0.873989i	$-0.661525\pi$
$167$	6.64136	−	11.5032i	0.513924	−	0.890143i	0.999870	−	0.0161534i	$-0.00514202\pi$
$168$		0			0
$169$	3.50000	+	6.06218i	0.269231	+	0.466321i
$170$	1.80385			0.138349
$171$		−	1.55291i		−	0.118754i
$172$	−12.1962			−0.929948
$173$	−9.71003	−	16.8183i	−0.738240	−	1.27867i	−0.953287	−	0.302065i	$-0.902324\pi$
$173$	−9.71003	−	16.8183i	−0.738240	−	1.27867i	0.215048	−	0.976604i	$-0.431009\pi$
$174$	4.57081	−	1.22474i	0.346512	−	0.0928477i
$175$		0			0
$176$	0.732051	−	1.26795i	0.0551804	−	0.0955753i
$177$	24.7583	−	6.63397i	1.86095	−	0.498640i
$178$	8.05558	+	13.9527i	0.603791	+	1.04580i
$179$	−8.19615			−0.612609			−0.306305	−	0.951934i	$-0.599093\pi$
$179$	−8.19615			−0.612609			−0.306305	+	0.951934i	$0.599093\pi$
$180$	−1.34486	+	0.776457i	−0.100240	+	0.0578737i
$181$	20.9730			1.55891			0.779454	−	0.626459i	$-0.215497\pi$
$181$	20.9730			1.55891			0.779454	+	0.626459i	$0.215497\pi$
$182$		0			0
$183$	−1.96410	+	7.33013i	−0.145191	+	0.541859i
$184$	3.96410	−	6.86603i	0.292237	−	0.506170i
$185$	−2.07055	+	3.58630i	−0.152230	+	0.263670i
$186$	9.00000	+	9.00000i	0.659912	+	0.659912i
$187$	2.55103	+	4.41851i	0.186549	+	0.323113i
$188$	4.62158			0.337063
$189$		0			0
$190$	−0.267949			−0.0194391
$191$	3.59808	+	6.23205i	0.260348	+	0.450935i	0.966334	−	0.257290i	$-0.0828295\pi$
$191$	3.59808	+	6.23205i	0.260348	+	0.450935i	−0.705987	+	0.708225i	$0.749496\pi$
$192$	1.22474	+	1.22474i	0.0883883	+	0.0883883i
$193$	11.8660	−	20.5526i	0.854135	−	1.47941i	−0.0233098	−	0.999728i	$-0.507420\pi$
$193$	11.8660	−	20.5526i	0.854135	−	1.47941i	0.877445	−	0.479677i	$-0.159246\pi$
$194$	0.517638	−	0.896575i	0.0371642	−	0.0643704i
$195$	−0.568406	+	2.12132i	−0.0407044	+	0.151911i
$196$		0			0
$197$	9.66025			0.688265			0.344132	−	0.938921i	$-0.388173\pi$
$197$	9.66025			0.688265			0.344132	+	0.938921i	$0.388173\pi$
$198$	−3.80385	−	2.19615i	−0.270328	−	0.156074i
$199$	−11.5911			−0.821672			−0.410836	−	0.911709i	$-0.634763\pi$
$199$	−11.5911			−0.821672			−0.410836	+	0.911709i	$0.634763\pi$
$200$	−2.36603	−	4.09808i	−0.167303	−	0.289778i
$201$	6.36396	−	1.70522i	0.448879	−	0.120277i
$202$	−2.89778	+	5.01910i	−0.203887	+	0.353142i
$203$		0			0
$204$	−5.83013	+	1.56218i	−0.408191	+	0.109374i
$205$	−1.46410	−	2.53590i	−0.102257	−	0.177115i
$206$	−11.2122			−0.781189
$207$	−20.5981	−	11.8923i	−1.43167	−	0.826572i
$208$	2.44949			0.169842
$209$	−0.378937	−	0.656339i	−0.0262116	−	0.0453999i
$210$		0			0
$211$	−0.633975	+	1.09808i	−0.0436446	+	0.0755947i	−0.887022	−	0.461726i	$-0.847230\pi$
$211$	−0.633975	+	1.09808i	−0.0436446	+	0.0755947i	0.843378	+	0.537321i	$0.180564\pi$
$212$	−3.36603	+	5.83013i	−0.231180	+	0.400415i
$213$	−0.984508	−	0.984508i	−0.0674574	−	0.0674574i
$214$	1.53590	+	2.66025i	0.104992	+	0.181851i
$215$	6.31319			0.430556
$216$	3.67423	−	3.67423i	0.250000	−	0.250000i
$217$		0			0
$218$	5.29423	+	9.16987i	0.358570	+	0.621062i
$219$	−5.66025	−	5.66025i	−0.382485	−	0.382485i
$220$	−0.378937	+	0.656339i	−0.0255480	+	0.0442504i
$221$	−4.26795	+	7.39230i	−0.287093	+	0.497260i
$222$	3.58630	−	13.3843i	0.240697	−	0.898293i
$223$	1.88108	+	3.25813i	0.125967	+	0.218181i	0.922110	−	0.386927i	$-0.126463\pi$
$223$	1.88108	+	3.25813i	0.125967	+	0.218181i	−0.796144	+	0.605108i	$0.793130\pi$
$224$		0			0
$225$	−12.2942	+	7.09808i	−0.819615	+	0.473205i
$226$	14.6603			0.975186
$227$	1.67303	+	2.89778i	0.111043	+	0.192332i	0.916191	−	0.400742i	$-0.131248\pi$
$227$	1.67303	+	2.89778i	0.111043	+	0.192332i	−0.805148	+	0.593074i	$0.797914\pi$
$228$	0.866025	−	0.232051i	0.0573539	−	0.0153679i
$229$	6.90018	−	11.9515i	0.455977	−	0.789775i	−0.542767	−	0.839883i	$-0.682623\pi$
$229$	6.90018	−	11.9515i	0.455977	−	0.789775i	0.998744	+	0.0501083i	$0.0159567\pi$
$230$	−2.05197	+	3.55412i	−0.135303	+	0.234351i
$231$		0			0
$232$	1.36603	+	2.36603i	0.0896840	+	0.155337i
$233$	1.39230			0.0912129			0.0456065	−	0.998959i	$-0.485478\pi$
$233$	1.39230			0.0912129			0.0456065	+	0.998959i	$0.485478\pi$
$234$		−	7.34847i		−	0.480384i
$235$	−2.39230			−0.156057
$236$	7.39924	+	12.8159i	0.481649	+	0.834241i
$237$	6.33178	−	23.6305i	0.411293	−	1.53497i
$238$		0			0
$239$	6.23205	−	10.7942i	0.403118	−	0.698221i	−0.590983	−	0.806684i	$-0.701260\pi$
$239$	6.23205	−	10.7942i	0.403118	−	0.698221i	0.994100	+	0.108464i	$0.0345931\pi$
$240$	−0.633975	−	0.633975i	−0.0409229	−	0.0409229i
$241$	6.36396	+	11.0227i	0.409939	+	0.710035i	0.994882	−	0.101039i	$-0.0322167\pi$
$241$	6.36396	+	11.0227i	0.409939	+	0.710035i	−0.584944	+	0.811074i	$0.698883\pi$
$242$	8.85641			0.569311
$243$	−11.0227	−	11.0227i	−0.707107	−	0.707107i
$244$	−4.38134			−0.280487
$245$		0			0
$246$	6.92820	+	6.92820i	0.441726	+	0.441726i
$247$	0.633975	−	1.09808i	0.0403388	−	0.0698689i
$248$	−3.67423	+	6.36396i	−0.233314	+	0.404112i
$249$	4.43782	−	16.5622i	0.281236	−	1.04959i
$250$	2.51884	+	4.36276i	0.159305	+	0.275925i
$251$	0.517638			0.0326730			0.0163365	−	0.999867i	$-0.494800\pi$
$251$	0.517638			0.0326730			0.0163365	+	0.999867i	$0.494800\pi$
$252$		0			0
$253$	−11.6077			−0.729770
$254$	−2.96410	−	5.13397i	−0.185984	−	0.322134i
$255$	3.01790	−	0.808643i	0.188988	−	0.0506392i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	1.88108	−	3.25813i	0.117339	−	0.203237i	−0.801373	−	0.598164i	$-0.795897\pi$
$257$	1.88108	−	3.25813i	0.117339	−	0.203237i	0.918712	+	0.394928i	$0.129230\pi$
$258$	−20.4046	+	5.46739i	−1.27033	+	0.340385i
$259$		0			0
$260$	−1.26795			−0.0786349
$261$	7.09808	−	4.09808i	0.439360	−	0.253665i
$262$	12.4877			0.771492
$263$	−1.33013	−	2.30385i	−0.0820191	−	0.142061i	0.822098	−	0.569346i	$-0.192804\pi$
$263$	−1.33013	−	2.30385i	−0.0820191	−	0.142061i	−0.904117	+	0.427285i	$0.859470\pi$
$264$	0.656339	−	2.44949i	0.0403949	−	0.150756i
$265$	1.74238	−	3.01790i	0.107034	−	0.185388i
$266$		0			0
$267$	19.7321	+	19.7321i	1.20758	+	1.20758i
$268$	1.90192	+	3.29423i	0.116178	+	0.201227i
$269$	−26.9072			−1.64056			−0.820281	−	0.571961i	$-0.806183\pi$
$269$	−26.9072			−1.64056			−0.820281	+	0.571961i	$0.806183\pi$
$270$	−1.90192	+	1.90192i	−0.115747	+	0.115747i
$271$	−14.7985			−0.898943			−0.449472	−	0.893295i	$-0.648388\pi$
$271$	−14.7985			−0.898943			−0.449472	+	0.893295i	$0.648388\pi$
$272$	−1.74238	−	3.01790i	−0.105647	−	0.182987i
$273$		0			0
$274$		0			0
$275$	−3.46410	+	6.00000i	−0.208893	+	0.361814i
$276$	3.55412	−	13.2641i	0.213933	−	0.798408i
$277$	8.09808	+	14.0263i	0.486566	+	0.842757i	0.999881	−	0.0154431i	$-0.00491589\pi$
$277$	8.09808	+	14.0263i	0.486566	+	0.842757i	−0.513315	+	0.858201i	$0.671583\pi$
$278$	−20.2151			−1.21242
$279$	19.0919	+	11.0227i	1.14300	+	0.659912i
$280$		0			0
$281$	8.69615	+	15.0622i	0.518769	+	0.898534i	0.999762	+	0.0218099i	$0.00694284\pi$
$281$	8.69615	+	15.0622i	0.518769	+	0.898534i	−0.480993	+	0.876724i	$0.659724\pi$
$282$	7.73205	−	2.07180i	0.460437	−	0.123374i
$283$	4.88040	−	8.45310i	0.290109	−	0.502484i	−0.683726	−	0.729739i	$-0.739642\pi$
$283$	4.88040	−	8.45310i	0.290109	−	0.502484i	0.973835	+	0.227255i	$0.0729749\pi$
$284$	0.401924	−	0.696152i	0.0238498	−	0.0413090i
$285$	−0.448288	+	0.120118i	−0.0265543	+	0.00711520i
$286$	−1.79315	−	3.10583i	−0.106031	−	0.183651i
$287$		0			0
$288$	2.59808	+	1.50000i	0.153093	+	0.0883883i
$289$	−4.85641			−0.285671
$290$	−0.707107	−	1.22474i	−0.0415227	−	0.0719195i
$291$	0.464102	−	1.73205i	0.0272061	−	0.101535i
$292$	2.31079	−	4.00240i	0.135229	−	0.234223i
$293$	−1.48356	+	2.56961i	−0.0866707	+	0.150118i	−0.906102	−	0.423059i	$-0.860956\pi$
$293$	−1.48356	+	2.56961i	−0.0866707	+	0.150118i	0.819431	+	0.573178i	$0.194289\pi$
$294$		0			0
$295$	−3.83013	−	6.63397i	−0.222999	−	0.386245i
$296$	8.00000			0.464991
$297$	−7.34847	−	1.96902i	−0.426401	−	0.114254i
$298$	2.39230			0.138582
$299$	−9.71003	−	16.8183i	−0.561545	−	0.972625i
$300$	−5.79555	−	5.79555i	−0.334607	−	0.334607i
$301$		0			0
$302$	−8.69615	+	15.0622i	−0.500407	+	0.866731i
$303$	−2.59808	+	9.69615i	−0.149256	+	0.557029i
$304$	0.258819	+	0.448288i	0.0148443	+	0.0257111i
$305$	2.26795			0.129862
$306$	−9.05369	+	5.22715i	−0.517565	+	0.298816i
$307$	11.9329			0.681046			0.340523	−	0.940236i	$-0.389396\pi$
$307$	11.9329			0.681046			0.340523	+	0.940236i	$0.389396\pi$
$308$		0			0
$309$	−18.7583	+	5.02628i	−1.06712	+	0.285935i
$310$	1.90192	−	3.29423i	0.108022	−	0.187100i
$311$	9.09085	−	15.7458i	0.515495	−	0.892863i	−0.484343	−	0.874878i	$-0.660941\pi$
$311$	9.09085	−	15.7458i	0.515495	−	0.892863i	0.999838	−	0.0179854i	$-0.00572524\pi$
$312$	4.09808	−	1.09808i	0.232008	−	0.0621663i
$313$	−3.34607	−	5.79555i	−0.189131	−	0.327584i	0.755830	−	0.654768i	$-0.227234\pi$
$313$	−3.34607	−	5.79555i	−0.189131	−	0.327584i	−0.944961	+	0.327184i	$0.893900\pi$
$314$	−17.2851			−0.975456
$315$		0			0
$316$	14.1244			0.794557
$317$	−16.2942	−	28.2224i	−0.915175	−	1.58513i	−0.806645	−	0.591037i	$-0.798719\pi$
$317$	−16.2942	−	28.2224i	−0.915175	−	1.58513i	−0.108530	−	0.994093i	$-0.534614\pi$
$318$	−3.01790	+	11.2629i	−0.169235	+	0.631594i
$319$	2.00000	−	3.46410i	0.111979	−	0.193952i
$320$	0.258819	−	0.448288i	0.0144684	−	0.0250600i
$321$	3.76217	+	3.76217i	0.209984	+	0.209984i
$322$		0			0
$323$	−1.80385			−0.100369
$324$	4.50000	−	7.79423i	0.250000	−	0.433013i
$325$	−11.5911			−0.642959
$326$	−3.53590	−	6.12436i	−0.195835	−	0.339197i
$327$	12.9682	+	12.9682i	0.717141	+	0.717141i
$328$	−2.82843	+	4.89898i	−0.156174	+	0.270501i
$329$		0			0
$330$	−0.339746	+	1.26795i	−0.0187024	+	0.0697983i
$331$	6.02628	+	10.4378i	0.331234	+	0.573715i	0.982754	−	0.184917i	$-0.0592016\pi$
$331$	6.02628	+	10.4378i	0.331234	+	0.573715i	−0.651520	+	0.758632i	$0.725868\pi$
$332$	9.89949			0.543305
$333$		−	24.0000i		−	1.31519i
$334$	13.2827			0.726798
$335$	−0.984508	−	1.70522i	−0.0537894	−	0.0931660i
$336$		0			0
$337$	10.6603	−	18.4641i	0.580701	−	1.00580i	−0.414695	−	0.909960i	$-0.636112\pi$
$337$	10.6603	−	18.4641i	0.580701	−	1.00580i	0.995396	−	0.0958434i	$-0.0305548\pi$
$338$	−3.50000	+	6.06218i	−0.190375	+	0.329739i
$339$	24.5271	−	6.57201i	1.33213	−	0.356943i
$340$	0.901924	+	1.56218i	0.0489137	+	0.0847210i
$341$	10.7589			0.582627
$342$	1.34486	−	0.776457i	0.0727219	−	0.0419860i
$343$		0			0
$344$	−6.09808	−	10.5622i	−0.328786	−	0.569474i
$345$	−1.83975	+	6.86603i	−0.0990486	+	0.369654i
$346$	9.71003	−	16.8183i	0.522014	−	0.904155i
$347$	−10.8564	+	18.8038i	−0.582802	+	1.00944i	0.412343	+	0.911029i	$0.364711\pi$
$347$	−10.8564	+	18.8038i	−0.582802	+	1.00944i	−0.995145	+	0.0984148i	$0.968623\pi$
$348$	3.34607	+	3.34607i	0.179368	+	0.179368i
$349$	−17.2987	−	29.9623i	−0.925980	−	1.60384i	−0.789978	−	0.613136i	$-0.789908\pi$
$349$	−17.2987	−	29.9623i	−0.925980	−	1.60384i	−0.136002	−	0.990709i	$-0.543425\pi$
$350$		0			0
$351$	−3.29423	−	12.2942i	−0.175833	−	0.656217i
$352$	1.46410			0.0780369
$353$	0.0507680	+	0.0879327i	0.00270211	+	0.00468019i	0.867373	−	0.497658i	$-0.165807\pi$
$353$	0.0507680	+	0.0879327i	0.00270211	+	0.00468019i	−0.864671	+	0.502338i	$0.832473\pi$
$354$	18.1244	+	18.1244i	0.963299	+	0.963299i
$355$	−0.208051	+	0.360355i	−0.0110422	+	0.0191257i
$356$	−8.05558	+	13.9527i	−0.426945	+	0.739490i
$357$		0			0
$358$	−4.09808	−	7.09808i	−0.216590	−	0.375145i
$359$	−13.9282			−0.735102			−0.367551	−	0.930003i	$-0.619804\pi$
$359$	−13.9282			−0.735102			−0.367551	+	0.930003i	$0.619804\pi$
$360$	−1.34486	−	0.776457i	−0.0708805	−	0.0409229i
$361$	−18.7321			−0.985897
$362$	10.4865	+	18.1631i	0.551157	+	0.954632i
$363$	14.8171	−	3.97022i	0.777694	−	0.208382i
$364$		0			0
$365$	−1.19615	+	2.07180i	−0.0626095	+	0.108443i
$366$	−7.33013	+	1.96410i	−0.383152	+	0.102665i
$367$	−0.138701	−	0.240237i	−0.00724012	−	0.0125403i	0.862383	−	0.506257i	$-0.168971\pi$
$367$	−0.138701	−	0.240237i	−0.00724012	−	0.0125403i	−0.869623	+	0.493717i	$0.835638\pi$
$368$	7.92820			0.413286
$369$	14.6969	+	8.48528i	0.765092	+	0.441726i
$370$	−4.14110			−0.215286
$371$		0			0
$372$	−3.29423	+	12.2942i	−0.170798	+	0.637426i
$373$	−9.56218	+	16.5622i	−0.495111	+	0.857557i	−0.999984	−	0.00563639i	$-0.998206\pi$
$373$	−9.56218	+	16.5622i	−0.495111	+	0.857557i	0.504873	+	0.863193i	$0.331539\pi$
$374$	−2.55103	+	4.41851i	−0.131910	+	0.228476i
$375$	6.16987	+	6.16987i	0.318611	+	0.318611i
$376$	2.31079	+	4.00240i	0.119170	+	0.206408i
$377$	6.69213			0.344662
$378$		0			0
$379$	−27.5167			−1.41344			−0.706718	−	0.707495i	$-0.749825\pi$
$379$	−27.5167			−1.41344			−0.706718	+	0.707495i	$0.749825\pi$
$380$	−0.133975	−	0.232051i	−0.00687275	−	0.0119040i
$381$	−7.26054	−	7.26054i	−0.371969	−	0.371969i
$382$	−3.59808	+	6.23205i	−0.184094	+	0.318859i
$383$	−17.1093	+	29.6341i	−0.874243	+	1.51423i	−0.0166751	+	0.999861i	$0.505308\pi$
$383$	−17.1093	+	29.6341i	−0.874243	+	1.51423i	−0.857567	+	0.514372i	$0.828025\pi$
$384$	−0.448288	+	1.67303i	−0.0228766	+	0.0853766i
$385$		0			0
$386$	23.7321			1.20793
$387$	−31.6865	+	18.2942i	−1.61072	+	0.929948i
$388$	1.03528			0.0525582
$389$	2.43782	+	4.22243i	0.123602	+	0.214086i	0.921186	−	0.389123i	$-0.127222\pi$
$389$	2.43782	+	4.22243i	0.123602	+	0.214086i	−0.797583	+	0.603209i	$0.793889\pi$
$390$	−2.12132	+	0.568406i	−0.107417	+	0.0287824i
$391$	−13.8140	+	23.9265i	−0.698602	+	1.21001i
$392$		0			0
$393$	20.8923	−	5.59808i	1.05388	−	0.282386i
$394$	4.83013	+	8.36603i	0.243338	+	0.421474i
$395$	−7.31130			−0.367872
$396$		−	4.39230i		−	0.220722i
$397$	−26.3896			−1.32446			−0.662228	−	0.749303i	$-0.730389\pi$
$397$	−26.3896			−1.32446			−0.662228	+	0.749303i	$0.730389\pi$
$398$	−5.79555	−	10.0382i	−0.290505	−	0.503169i
$399$		0			0
$400$	2.36603	−	4.09808i	0.118301	−	0.204904i
$401$	12.5263	−	21.6962i	0.625533	−	1.08345i	−0.362905	−	0.931826i	$-0.618215\pi$
$401$	12.5263	−	21.6962i	0.625533	−	1.08345i	0.988438	−	0.151628i	$-0.0484516\pi$
$402$	4.65874	+	4.65874i	0.232357	+	0.232357i
$403$	9.00000	+	15.5885i	0.448322	+	0.776516i
$404$	−5.79555			−0.288340
$405$	−2.32937	+	4.03459i	−0.115747	+	0.200480i
$406$		0			0
$407$	−5.85641	−	10.1436i	−0.290291	−	0.502799i
$408$	−4.26795	−	4.26795i	−0.211295	−	0.211295i
$409$	8.90138	−	15.4176i	0.440145	−	0.762354i	−0.557555	−	0.830140i	$-0.688260\pi$
$409$	8.90138	−	15.4176i	0.440145	−	0.762354i	0.997700	+	0.0677865i	$0.0215937\pi$
$410$	1.46410	−	2.53590i	0.0723068	−	0.125239i
$411$		0			0
$412$	−5.60609	−	9.71003i	−0.276192	−	0.478379i
$413$		0			0
$414$		−	23.7846i		−	1.16895i
$415$	−5.12436			−0.251545
$416$	1.22474	+	2.12132i	0.0600481	+	0.104006i
$417$	−33.8205	+	9.06218i	−1.65620	+	0.443777i
$418$	0.378937	−	0.656339i	0.0185344	−	0.0321026i
$419$	−11.3323	+	19.6281i	−0.553619	+	0.958896i	0.444391	+	0.895833i	$0.353420\pi$
$419$	−11.3323	+	19.6281i	−0.553619	+	0.958896i	−0.998010	+	0.0630626i	$0.979913\pi$
$420$		0			0
$421$	−14.0263	−	24.2942i	−0.683599	−	1.18403i	−0.973875	−	0.227085i	$-0.927080\pi$
$421$	−14.0263	−	24.2942i	−0.683599	−	1.18403i	0.290276	−	0.956943i	$-0.406253\pi$
$422$	−1.26795			−0.0617228
$423$	12.0072	−	6.93237i	0.583811	−	0.337063i
$424$	−6.73205			−0.326937
$425$	8.24504	+	14.2808i	0.399943	+	0.692722i
$426$	0.360355	−	1.34486i	0.0174593	−	0.0651588i
$427$		0			0
$428$	−1.53590	+	2.66025i	−0.0742405	+	0.128588i
$429$	−4.39230	−	4.39230i	−0.212062	−	0.212062i
$430$	3.15660	+	5.46739i	0.152225	+	0.263661i
$431$	−26.7846			−1.29017			−0.645085	−	0.764111i	$-0.723178\pi$
$431$	−26.7846			−1.29017			−0.645085	+	0.764111i	$0.723178\pi$
$432$	5.01910	+	1.34486i	0.241481	+	0.0647048i
$433$	20.2523			0.973261			0.486631	−	0.873608i	$-0.338226\pi$
$433$	20.2523			0.973261			0.486631	+	0.873608i	$0.338226\pi$
$434$		0			0
$435$	−1.73205	−	1.73205i	−0.0830455	−	0.0830455i
$436$	−5.29423	+	9.16987i	−0.253548	+	0.439157i
$437$	2.05197	−	3.55412i	0.0981590	−	0.170016i
$438$	2.07180	−	7.73205i	0.0989943	−	0.369452i
$439$	9.14162	+	15.8338i	0.436306	+	0.755704i	0.997401	−	0.0720474i	$-0.0229533\pi$
$439$	9.14162	+	15.8338i	0.436306	+	0.755704i	−0.561095	+	0.827751i	$0.689620\pi$
$440$	−0.757875			−0.0361303
$441$		0			0
$442$	−8.53590			−0.406011
$443$	18.4904	+	32.0263i	0.878505	+	1.52161i	0.852982	+	0.521940i	$0.174792\pi$
$443$	18.4904	+	32.0263i	0.878505	+	1.52161i	0.0255224	+	0.999674i	$0.491875\pi$
$444$	13.3843	−	3.58630i	0.635189	−	0.170198i
$445$	4.16987	−	7.22243i	0.197671	−	0.342376i
$446$	−1.88108	+	3.25813i	−0.0890719	+	0.154277i
$447$	4.00240	−	1.07244i	0.189307	−	0.0507247i
$448$		0			0
$449$	−23.7846			−1.12247			−0.561233	−	0.827658i	$-0.689673\pi$
$449$	−23.7846			−1.12247			−0.561233	+	0.827658i	$0.689673\pi$
$450$	−12.2942	−	7.09808i	−0.579555	−	0.334607i
$451$	8.28221			0.389994
$452$	7.33013	+	12.6962i	0.344780	+	0.597177i
$453$	−7.79676	+	29.0979i	−0.366324	+	1.36714i
$454$	−1.67303	+	2.89778i	−0.0785193	+	0.135999i
$455$		0			0
$456$	0.633975	+	0.633975i	0.0296886	+	0.0296886i
$457$	11.1340	+	19.2846i	0.520825	+	0.902096i	0.999707	+	0.0242164i	$0.00770906\pi$
$457$	11.1340	+	19.2846i	0.520825	+	0.902096i	−0.478881	+	0.877880i	$0.658958\pi$
$458$	13.8004			0.644849
$459$	−12.8038	+	12.8038i	−0.597632	+	0.597632i
$460$	−4.10394			−0.191347
$461$	19.4894	+	33.7566i	0.907712	+	1.57220i	0.817235	+	0.576305i	$0.195506\pi$
$461$	19.4894	+	33.7566i	0.907712	+	1.57220i	0.0904771	+	0.995899i	$0.471161\pi$
$462$		0			0
$463$	−3.33013	+	5.76795i	−0.154764	+	0.268059i	−0.932973	−	0.359946i	$-0.882795\pi$
$463$	−3.33013	+	5.76795i	−0.154764	+	0.268059i	0.778209	+	0.628005i	$0.216128\pi$
$464$	−1.36603	+	2.36603i	−0.0634161	+	0.109840i
$465$	1.70522	−	6.36396i	0.0790776	−	0.295122i
$466$	0.696152	+	1.20577i	0.0322486	+	0.0558563i
$467$	−24.5964			−1.13819			−0.569094	−	0.822273i	$-0.692706\pi$
$467$	−24.5964			−1.13819			−0.569094	+	0.822273i	$0.692706\pi$
$468$	6.36396	−	3.67423i	0.294174	−	0.169842i
$469$		0			0
$470$	−1.19615	−	2.07180i	−0.0551744	−	0.0955649i
$471$	−28.9186	+	7.74871i	−1.33250	+	0.357042i
$472$	−7.39924	+	12.8159i	−0.340577	+	0.589898i
$473$	−8.92820	+	15.4641i	−0.410519	+	0.711040i
$474$	23.6305	−	6.33178i	1.08539	−	0.290828i
$475$	−1.22474	−	2.12132i	−0.0561951	−	0.0973329i
$476$		0			0
$477$			20.1962i			0.924718i
$478$	12.4641			0.570095
$479$	−6.64136	−	11.5032i	−0.303452	−	0.525594i	0.673464	−	0.739220i	$-0.264806\pi$
$479$	−6.64136	−	11.5032i	−0.303452	−	0.525594i	−0.976915	+	0.213627i	$0.931472\pi$
$480$	0.232051	−	0.866025i	0.0105916	−	0.0395285i
$481$	9.79796	−	16.9706i	0.446748	−	0.773791i
$482$	−6.36396	+	11.0227i	−0.289870	+	0.502070i
$483$		0			0
$484$	4.42820	+	7.66987i	0.201282	+	0.348631i
$485$	−0.535898			−0.0243339
$486$	4.03459	−	15.0573i	0.183013	−	0.683013i
$487$	−32.3205			−1.46458			−0.732291	−	0.680992i	$-0.761549\pi$
$487$	−32.3205			−1.46458			−0.732291	+	0.680992i	$0.761549\pi$
$488$	−2.19067	−	3.79435i	−0.0991670	−	0.171762i
$489$	−8.66115	−	8.66115i	−0.391671	−	0.391671i
$490$		0			0
$491$	2.53590	−	4.39230i	0.114443	−	0.198222i	−0.803114	−	0.595826i	$-0.796825\pi$
$491$	2.53590	−	4.39230i	0.114443	−	0.198222i	0.917557	+	0.397604i	$0.130158\pi$
$492$	−2.53590	+	9.46410i	−0.114327	+	0.426675i
$493$	−4.76028	−	8.24504i	−0.214392	−	0.371338i
$494$	1.26795			0.0570477
$495$			2.27362i			0.102192i
$496$	−7.34847			−0.329956
$497$		0			0
$498$	16.5622	−	4.43782i	0.742169	−	0.198864i
$499$	−3.66025	+	6.33975i	−0.163855	+	0.283806i	−0.936248	−	0.351339i	$-0.885726\pi$
$499$	−3.66025	+	6.33975i	−0.163855	+	0.283806i	0.772393	+	0.635145i	$0.219060\pi$
$500$	−2.51884	+	4.36276i	−0.112646	+	0.195109i
$501$	22.2224	−	5.95448i	0.992825	−	0.266027i
$502$	0.258819	+	0.448288i	0.0115517	+	0.0200081i
$503$	−28.9406			−1.29040			−0.645199	−	0.764015i	$-0.723226\pi$
$503$	−28.9406			−1.29040			−0.645199	+	0.764015i	$0.723226\pi$
$504$		0			0
$505$	3.00000			0.133498
$506$	−5.80385	−	10.0526i	−0.258012	−	0.446891i
$507$	−3.13801	+	11.7112i	−0.139364	+	0.520114i
$508$	2.96410	−	5.13397i	0.131511	−	0.227783i
$509$	−3.81294	+	6.60420i	−0.169005	+	0.292726i	−0.938070	−	0.346445i	$-0.887389\pi$
$509$	−3.81294	+	6.60420i	−0.169005	+	0.292726i	0.769065	+	0.639171i	$0.220722\pi$
$510$	2.20925	+	2.20925i	0.0978274	+	0.0978274i
$511$		0			0
$512$	−1.00000			−0.0441942
$513$	1.90192	−	1.90192i	0.0839720	−	0.0839720i
$514$	3.76217			0.165942
$515$	2.90192	+	5.02628i	0.127874	+	0.221484i
$516$	−14.9372	−	14.9372i	−0.657572	−	0.657572i
$517$	3.38323	−	5.85993i	0.148794	−	0.257719i
$518$		0			0
$519$	8.70577	−	32.4904i	0.382141	−	1.42617i
$520$	−0.633975	−	1.09808i	−0.0278016	−	0.0481538i
$521$	32.5269			1.42503			0.712515	−	0.701657i	$-0.247556\pi$
$521$	32.5269			1.42503			0.712515	+	0.701657i	$0.247556\pi$
$522$	7.09808	+	4.09808i	0.310674	+	0.179368i
$523$	−39.2562			−1.71655			−0.858277	−	0.513187i	$-0.828465\pi$
$523$	−39.2562			−1.71655			−0.858277	+	0.513187i	$0.828465\pi$
$524$	6.24384	+	10.8147i	0.272764	+	0.472440i
$525$		0			0
$526$	1.33013	−	2.30385i	0.0579963	−	0.100453i
$527$	12.8038	−	22.1769i	0.557744	−	0.966042i
$528$	2.44949	−	0.656339i	0.106600	−	0.0285635i
$529$	−19.9282	−	34.5167i	−0.866444	−	1.50072i
$530$	3.48477			0.151369
$531$	38.4476	+	22.1977i	1.66848	+	0.963299i
$532$		0			0
$533$	6.92820	+	12.0000i	0.300094	+	0.519778i
$534$	−7.22243	+	26.9545i	−0.312545	+	1.16643i
$535$	0.795040	−	1.37705i	0.0343726	−	0.0595350i
$536$	−1.90192	+	3.29423i	−0.0821506	+	0.142289i
$537$	−10.0382	−	10.0382i	−0.433180	−	0.433180i
$538$	−13.4536	−	23.3023i	−0.580026	−	1.00464i
$539$		0			0
$540$	−2.59808	−	0.696152i	−0.111803	−	0.0299576i
$541$	20.7321			0.891340			0.445670	−	0.895197i	$-0.352965\pi$
$541$	20.7321			0.891340			0.445670	+	0.895197i	$0.352965\pi$
$542$	−7.39924	−	12.8159i	−0.317824	−	0.550488i
$543$	25.6865	+	25.6865i	1.10231	+	1.10231i
$544$	1.74238	−	3.01790i	0.0747041	−	0.129391i
$545$	2.74049	−	4.74668i	0.117390	−	0.203325i
$546$		0			0
$547$	5.73205	+	9.92820i	0.245085	+	0.424499i	0.962155	−	0.272501i	$-0.0878509\pi$
$547$	5.73205	+	9.92820i	0.245085	+	0.424499i	−0.717071	+	0.697000i	$0.754518\pi$
$548$		0			0
$549$	−11.3831	+	6.57201i	−0.485817	+	0.280487i
$550$	−6.92820			−0.295420
$551$	0.707107	+	1.22474i	0.0301238	+	0.0521759i
$552$	13.2641	−	3.55412i	0.564559	−	0.151273i
$553$		0			0
$554$	−8.09808	+	14.0263i	−0.344054	+	0.595920i
$555$	−6.92820	+	1.85641i	−0.294086	+	0.0788001i
$556$	−10.1075	−	17.5068i	−0.428655	−	0.742453i
$557$	2.87564			0.121845			0.0609225	−	0.998143i	$-0.480596\pi$
$557$	2.87564			0.121845			0.0609225	+	0.998143i	$0.480596\pi$
$558$			22.0454i			0.933257i
$559$	−29.8744			−1.26355
$560$		0			0
$561$	−2.28719	+	8.53590i	−0.0965651	+	0.360386i
$562$	−8.69615	+	15.0622i	−0.366825	+	0.635360i
$563$	−0.637756	+	1.10463i	−0.0268782	+	0.0465545i	−0.879152	−	0.476542i	$-0.841890\pi$
$563$	−0.637756	+	1.10463i	−0.0268782	+	0.0465545i	0.852273	+	0.523097i	$0.175223\pi$
$564$	5.66025	+	5.66025i	0.238340	+	0.238340i
$565$	−3.79435	−	6.57201i	−0.159630	−	0.276487i
$566$	9.76079			0.410277
$567$		0			0
$568$	0.803848			0.0337287
$569$	−13.4641	−	23.3205i	−0.564445	−	0.977647i	−0.997101	−	0.0760878i	$-0.975757\pi$
$569$	−13.4641	−	23.3205i	−0.564445	−	0.977647i	0.432657	−	0.901559i	$-0.357576\pi$
$570$	−0.328169	−	0.328169i	−0.0137455	−	0.0137455i
$571$	−2.00000	+	3.46410i	−0.0836974	+	0.144968i	−0.904835	−	0.425762i	$-0.860006\pi$
$571$	−2.00000	+	3.46410i	−0.0836974	+	0.144968i	0.821138	+	0.570730i	$0.193340\pi$
$572$	1.79315	−	3.10583i	0.0749754	−	0.129861i
$573$	−3.22595	+	12.0394i	−0.134766	+	0.502953i
$574$		0			0
$575$	−37.5167			−1.56455
$576$			3.00000i			0.125000i
$577$	−26.2880			−1.09439			−0.547193	−	0.837007i	$-0.684304\pi$
$577$	−26.2880			−1.09439			−0.547193	+	0.837007i	$0.684304\pi$
$578$	−2.42820	−	4.20577i	−0.101000	−	0.174937i
$579$	39.7045	−	10.6388i	1.65006	−	0.442133i
$580$	0.707107	−	1.22474i	0.0293610	−	0.0508548i
$581$		0			0
$582$	1.73205	−	0.464102i	0.0717958	−	0.0192376i
$583$	4.92820	+	8.53590i	0.204105	+	0.353521i
$584$	4.62158			0.191242
$585$	−3.29423	+	1.90192i	−0.136200	+	0.0786349i
$586$	−2.96713			−0.122571
$587$	1.76097	+	3.05008i	0.0726828	+	0.125890i	0.900076	−	0.435732i	$-0.143511\pi$
$587$	1.76097	+	3.05008i	0.0726828	+	0.125890i	−0.827393	+	0.561623i	$0.810177\pi$
$588$		0			0
$589$	−1.90192	+	3.29423i	−0.0783674	+	0.135736i
$590$	3.83013	−	6.63397i	0.157684	−	0.273116i
$591$	11.8313	+	11.8313i	0.486677	+	0.486677i
$592$	4.00000	+	6.92820i	0.164399	+	0.284747i
$593$	6.79367			0.278982			0.139491	−	0.990223i	$-0.455453\pi$
$593$	6.79367			0.278982			0.139491	+	0.990223i	$0.455453\pi$
$594$	−1.96902	−	7.34847i	−0.0807897	−	0.301511i
$595$		0			0
$596$	1.19615	+	2.07180i	0.0489963	+	0.0848641i
$597$	−14.1962	−	14.1962i	−0.581010	−	0.581010i
$598$	9.71003	−	16.8183i	0.397073	−	0.687750i
$599$	6.19615	−	10.7321i	0.253168	−	0.438500i	−0.711228	−	0.702961i	$-0.751861\pi$
$599$	6.19615	−	10.7321i	0.253168	−	0.438500i	0.964396	+	0.264461i	$0.0851941\pi$
$600$	2.12132	−	7.91688i	0.0866025	−	0.323205i
$601$	−20.9730	−	36.3262i	−0.855505	−	1.48178i	−0.876176	−	0.481992i	$-0.839913\pi$
$601$	−20.9730	−	36.3262i	−0.855505	−	1.48178i	0.0206704	−	0.999786i	$-0.493420\pi$
$602$		0			0
$603$	9.88269	+	5.70577i	0.402454	+	0.232357i
$604$	−17.3923			−0.707683
$605$	−2.29221	−	3.97022i	−0.0931915	−	0.161412i
$606$	−9.69615	+	2.59808i	−0.393879	+	0.105540i
$607$	−10.6945	+	18.5235i	−0.434078	+	0.751845i	−0.997220	−	0.0745153i	$-0.976259\pi$
$607$	−10.6945	+	18.5235i	−0.434078	+	0.751845i	0.563142	+	0.826360i	$0.309592\pi$
$608$	−0.258819	+	0.448288i	−0.0104965	+	0.0181805i
$609$		0			0
$610$	1.13397	+	1.96410i	0.0459133	+	0.0795241i
$611$	11.3205			0.457979
$612$	−9.05369	−	5.22715i	−0.365974	−	0.211295i
$613$	20.4449			0.825760			0.412880	−	0.910785i	$-0.364523\pi$
$613$	20.4449			0.825760			0.412880	+	0.910785i	$0.364523\pi$
$614$	5.96644	+	10.3342i	0.240786	+	0.417054i
$615$	1.31268	−	4.89898i	0.0529323	−	0.197546i
$616$		0			0
$617$	−21.1962	+	36.7128i	−0.853325	+	1.47800i	0.0248653	+	0.999691i	$0.492084\pi$
$617$	−21.1962	+	36.7128i	−0.853325	+	1.47800i	−0.878190	+	0.478311i	$0.841249\pi$
$618$	−13.7321	−	13.7321i	−0.552384	−	0.552384i
$619$	−3.74358	−	6.48408i	−0.150467	−	0.260617i	0.780932	−	0.624616i	$-0.214745\pi$
$619$	−3.74358	−	6.48408i	−0.150467	−	0.260617i	−0.931399	+	0.363999i	$0.881411\pi$
$620$	3.80385			0.152766
$621$	−10.6623	−	39.7924i	−0.427865	−	1.59682i
$622$	18.1817			0.729020
$623$		0			0
$624$	3.00000	+	3.00000i	0.120096	+	0.120096i
$625$	−10.5263	+	18.2321i	−0.421051	+	0.729282i
$626$	3.34607	−	5.79555i	0.133736	−	0.231637i
$627$	0.339746	−	1.26795i	0.0135681	−	0.0506370i
$628$	−8.64256	−	14.9694i	−0.344876	−	0.597343i
$629$	−27.8781			−1.11157
$630$		0			0
$631$	−3.87564			−0.154287			−0.0771435	−	0.997020i	$-0.524580\pi$
$631$	−3.87564			−0.154287			−0.0771435	+	0.997020i	$0.524580\pi$
$632$	7.06218	+	12.2321i	0.280918	+	0.486565i
$633$	−2.12132	+	0.568406i	−0.0843149	+	0.0225921i
$634$	16.2942	−	28.2224i	0.647126	−	1.12086i
$635$	−1.53433	+	2.65754i	−0.0608881	+	0.105461i
$636$	−11.2629	+	3.01790i	−0.446605	+	0.119667i
$637$		0			0
$638$	4.00000			0.158362
$639$		−	2.41154i		−	0.0953992i
$640$	0.517638			0.0204614
$641$	1.52628	+	2.64359i	0.0602844	+	0.104416i	0.894593	−	0.446883i	$-0.147466\pi$
$641$	1.52628	+	2.64359i	0.0602844	+	0.104416i	−0.834308	+	0.551298i	$0.814133\pi$
$642$	−1.37705	+	5.13922i	−0.0543478	+	0.202829i
$643$	−0.845807	+	1.46498i	−0.0333554	+	0.0577732i	−0.882221	−	0.470835i	$-0.843953\pi$
$643$	−0.845807	+	1.46498i	−0.0333554	+	0.0577732i	0.848866	+	0.528608i	$0.177286\pi$
$644$		0			0
$645$	7.73205	+	7.73205i	0.304449	+	0.304449i
$646$	−0.901924	−	1.56218i	−0.0354857	−	0.0614631i
$647$	15.8338			0.622489			0.311244	−	0.950330i	$-0.399254\pi$
$647$	15.8338			0.622489			0.311244	+	0.950330i	$0.399254\pi$
$648$	9.00000			0.353553
$649$	21.6665			0.850483
$650$	−5.79555	−	10.0382i	−0.227320	−	0.393730i
$651$		0			0
$652$	3.53590	−	6.12436i	0.138476	−	0.239848i
$653$	20.6603	−	35.7846i	0.808498	−	1.40036i	−0.105406	−	0.994429i	$-0.533614\pi$
$653$	20.6603	−	35.7846i	0.808498	−	1.40036i	0.913904	−	0.405931i	$-0.133053\pi$
$654$	−4.74668	+	17.7148i	−0.185610	+	0.692705i
$655$	−3.23205	−	5.59808i	−0.126287	−	0.218735i
$656$	−5.65685			−0.220863
$657$		−	13.8647i		−	0.540915i
$658$		0			0
$659$	19.5622	+	33.8827i	0.762034	+	1.31988i	0.941800	+	0.336173i	$0.109133\pi$
$659$	19.5622	+	33.8827i	0.762034	+	1.31988i	−0.179766	+	0.983709i	$0.557534\pi$
$660$	−1.26795	+	0.339746i	−0.0493549	+	0.0132246i
$661$	10.7267	−	18.5792i	0.417221	−	0.722648i	−0.578438	−	0.815727i	$-0.696337\pi$
$661$	10.7267	−	18.5792i	0.417221	−	0.722648i	0.995659	+	0.0930785i	$0.0296708\pi$
$662$	−6.02628	+	10.4378i	−0.234218	+	0.405677i
$663$	−14.2808	+	3.82654i	−0.554622	+	0.148610i
$664$	4.94975	+	8.57321i	0.192087	+	0.332705i
$665$		0			0
$666$	20.7846	−	12.0000i	0.805387	−	0.464991i
$667$	21.6603			0.838688
$668$	6.64136	+	11.5032i	0.256962	+	0.445071i
$669$	−1.68653	+	6.29423i	−0.0652052	+	0.243349i
$670$	0.984508	−	1.70522i	0.0380349	−	0.0658783i
$671$	−3.20736	+	5.55532i	−0.123819	+	0.214461i
$672$		0			0
$673$	20.0885	+	34.7942i	0.774353	+	1.34122i	0.935157	+	0.354233i	$0.115258\pi$
$673$	20.0885	+	34.7942i	0.774353	+	1.34122i	−0.160804	+	0.986986i	$0.551409\pi$
$674$	21.3205			0.821235
$675$	−23.7506	−	6.36396i	−0.914162	−	0.244949i
$676$	−7.00000			−0.269231
$677$	0.568406	+	0.984508i	0.0218456	+	0.0378377i	0.876742	−	0.480962i	$-0.159712\pi$
$677$	0.568406	+	0.984508i	0.0218456	+	0.0378377i	−0.854896	+	0.518800i	$0.826379\pi$
$678$	17.9551	+	17.9551i	0.689560	+	0.689560i
$679$		0			0
$680$	−0.901924	+	1.56218i	−0.0345872	+	0.0599068i
$681$	−1.50000	+	5.59808i	−0.0574801	+	0.214519i
$682$	5.37945	+	9.31749i	0.205990	+	0.356785i
$683$	−13.6077			−0.520684			−0.260342	−	0.965516i	$-0.583835\pi$
$683$	−13.6077			−0.520684			−0.260342	+	0.965516i	$0.583835\pi$
$684$	1.34486	+	0.776457i	0.0514221	+	0.0296886i
$685$		0			0
$686$		0			0
$687$	23.0885	−	6.18653i	0.880880	−	0.236031i
$688$	6.09808	−	10.5622i	0.232487	−	0.402679i
$689$	−8.24504	+	14.2808i	−0.314111	+	0.544057i
$690$	−6.86603	+	1.83975i	−0.261385	+	0.0700379i
$691$	−18.4913	−	32.0279i	−0.703442	−	1.21840i	−0.967251	−	0.253822i	$-0.918312\pi$
$691$	−18.4913	−	32.0279i	−0.703442	−	1.21840i	0.263809	−	0.964575i	$-0.415021\pi$
$692$	19.4201			0.738240
$693$		0			0
$694$	−21.7128			−0.824207
$695$	5.23205	+	9.06218i	0.198463	+	0.343748i
$696$	−1.22474	+	4.57081i	−0.0464238	+	0.173256i
$697$	9.85641	−	17.0718i	0.373338	−	0.646640i
$698$	17.2987	−	29.9623i	0.654767	−	1.13409i
$699$	1.70522	+	1.70522i	0.0644973	+	0.0644973i
$700$		0			0
$701$	20.5359			0.775630			0.387815	−	0.921737i	$-0.373230\pi$
$701$	20.5359			0.775630			0.387815	+	0.921737i	$0.373230\pi$
$702$	9.00000	−	9.00000i	0.339683	−	0.339683i
$703$	4.14110			0.156185
$704$	0.732051	+	1.26795i	0.0275902	+	0.0477876i
$705$	−2.92996	−	2.92996i	−0.110349	−	0.110349i
$706$	−0.0507680	+	0.0879327i	−0.00191068	+	0.00330939i
$707$		0			0
$708$	−6.63397	+	24.7583i	−0.249320	+	0.930475i
$709$	11.2679	+	19.5167i	0.423177	+	0.732964i	0.996248	−	0.0865418i	$-0.0275816\pi$
$709$	11.2679	+	19.5167i	0.423177	+	0.732964i	−0.573072	+	0.819505i	$0.694248\pi$
$710$	−0.416102			−0.0156160
$711$	36.6962	−	21.1865i	1.37621	−	0.794557i
$712$	−16.1112			−0.603791
$713$	29.1301	+	50.4548i	1.09093	+	1.88955i
$714$		0			0
$715$	−0.928203	+	1.60770i	−0.0347128	+	0.0601244i
$716$	4.09808	−	7.09808i	0.153152	−	0.265268i
$717$	20.8528	−	5.58750i	0.778764	−	0.208669i
$718$	−6.96410	−	12.0622i	−0.259898	−	0.450156i
$719$	34.0155			1.26856			0.634281	−	0.773102i	$-0.281296\pi$
$719$	34.0155			1.26856			0.634281	+	0.773102i	$0.281296\pi$
$720$		−	1.55291i		−	0.0578737i
$721$		0			0
$722$	−9.36603	−	16.2224i	−0.348567	−	0.603736i
$723$	−5.70577	+	21.2942i	−0.212200	+	0.791941i
$724$	−10.4865	+	18.1631i	−0.389727	+	0.675027i
$725$	6.46410	−	11.1962i	0.240071	−	0.415815i
$726$	10.8468	+	10.8468i	0.402564	+	0.402564i
$727$	−14.8864	−	25.7840i	−0.552106	−	0.956276i	−0.998122	−	0.0612512i	$-0.980491\pi$
$727$	−14.8864	−	25.7840i	−0.552106	−	0.956276i	0.446016	−	0.895025i	$-0.352842\pi$
$728$		0			0
$729$		−	27.0000i		−	1.00000i
$730$	−2.39230			−0.0885432
$731$	21.2504	+	36.8067i	0.785973	+	1.36135i
$732$	−5.36603	−	5.36603i	−0.198334	−	0.198334i
$733$	15.0573	−	26.0800i	0.556154	−	0.963287i	−0.441659	−	0.897183i	$-0.645610\pi$
$733$	15.0573	−	26.0800i	0.556154	−	0.963287i	0.997813	−	0.0661037i	$-0.0210568\pi$
$734$	0.138701	−	0.240237i	0.00511954	−	0.00886730i
$735$		0			0
$736$	3.96410	+	6.86603i	0.146119	+	0.253085i
$737$	5.56922			0.205145
$738$			16.9706i			0.624695i
$739$	−16.1436			−0.593852			−0.296926	−	0.954901i	$-0.595961\pi$
$739$	−16.1436			−0.593852			−0.296926	+	0.954901i	$0.595961\pi$
$740$	−2.07055	−	3.58630i	−0.0761150	−	0.131835i
$741$	2.12132	−	0.568406i	0.0779287	−	0.0208809i
$742$		0			0
$743$	14.1244	−	24.4641i	0.518172	−	0.897501i	−0.481605	−	0.876389i	$-0.659946\pi$
$743$	14.1244	−	24.4641i	0.518172	−	0.897501i	0.999777	−	0.0211123i	$-0.00672076\pi$
$744$	−12.2942	+	3.29423i	−0.450728	+	0.120772i
$745$	−0.619174	−	1.07244i	−0.0226848	−	0.0392912i
$746$	−19.1244			−0.700192
$747$	25.7196	−	14.8492i	0.941033	−	0.543305i
$748$	−5.10205			−0.186549
$749$		0			0
$750$	−2.25833	+	8.42820i	−0.0824626	+	0.307754i
$751$	25.0885	−	43.4545i	0.915491	−	1.58568i	0.109310	−	0.994008i	$-0.465136\pi$
$751$	25.0885	−	43.4545i	0.915491	−	1.58568i	0.806181	−	0.591669i	$-0.201531\pi$
$752$	−2.31079	+	4.00240i	−0.0842658	+	0.145953i
$753$	0.633975	+	0.633975i	0.0231033	+	0.0231033i
$754$	3.34607	+	5.79555i	0.121857	+	0.211062i
$755$	9.00292			0.327650
$756$		0			0
$757$	20.2487			0.735952			0.367976	−	0.929835i	$-0.380051\pi$
$757$	20.2487			0.735952			0.367976	+	0.929835i	$0.380051\pi$
$758$	−13.7583	−	23.8301i	−0.499725	−	0.865549i
$759$	−14.2165	−	14.2165i	−0.516025	−	0.516025i
$760$	0.133975	−	0.232051i	0.00485977	−	0.00841737i
$761$	−19.8869	+	34.4452i	−0.720900	+	1.24864i	0.239739	+	0.970837i	$0.422938\pi$
$761$	−19.8869	+	34.4452i	−0.720900	+	1.24864i	−0.960639	+	0.277799i	$0.910395\pi$
$762$	2.65754	−	9.91808i	0.0962725	−	0.359294i
$763$		0			0
$764$	−7.19615			−0.260348
$765$	4.68653	+	2.70577i	0.169442	+	0.0978274i
$766$	−34.2185			−1.23637
$767$	18.1244	+	31.3923i	0.654433	+	1.13351i
$768$	−1.67303	+	0.448288i	−0.0603704	+	0.0161762i
$769$	14.9372	−	25.8719i	0.538648	−	0.932966i	−0.460329	−	0.887748i	$-0.652268\pi$
$769$	14.9372	−	25.8719i	0.538648	−	0.932966i	0.998977	−	0.0452178i	$-0.0143982\pi$
$770$		0			0
$771$	6.29423	−	1.68653i	0.226681	−	0.0607390i
$772$	11.8660	+	20.5526i	0.427068	+	0.739703i
$773$	−13.5230			−0.486387			−0.243194	−	0.969978i	$-0.578195\pi$
$773$	−13.5230			−0.486387			−0.243194	+	0.969978i	$0.578195\pi$
$774$	−31.6865	−	18.2942i	−1.13895	−	0.657572i
$775$	34.7733			1.24909
$776$	0.517638	+	0.896575i	0.0185821	+	0.0321852i
$777$		0			0
$778$	−2.43782	+	4.22243i	−0.0874002	+	0.151382i
$779$	−1.46410	+	2.53590i	−0.0524569	+	0.0908580i
$780$	−1.55291	−	1.55291i	−0.0556033	−	0.0556033i
$781$	−0.588457	−	1.01924i	−0.0210567	−	0.0364712i
$782$	−27.6279			−0.987973
$783$	13.7124	+	3.67423i	0.490042	+	0.131306i
$784$		0			0
$785$	4.47372	+	7.74871i	0.159674	+	0.276563i
$786$	15.2942	+	15.2942i	0.545527	+	0.545527i
$787$	−18.0938	+	31.3393i	−0.644973	+	1.11713i	0.339334	+	0.940666i	$0.389798\pi$
$787$	−18.0938	+	31.3393i	−0.644973	+	1.11713i	−0.984308	+	0.176461i	$0.943535\pi$
$788$	−4.83013	+	8.36603i	−0.172066	+	0.298027i
$789$	1.19256	−	4.45069i	0.0424562	−	0.158449i
$790$	−3.65565	−	6.33178i	−0.130062	−	0.225274i
$791$		0			0
$792$	3.80385	−	2.19615i	0.135164	−	0.0780369i
$793$	−10.7321			−0.381106
$794$	−13.1948	−	22.8541i	−0.468266	−	0.811060i
$795$	5.83013	−	1.56218i	0.206773	−	0.0554047i
$796$	5.79555	−	10.0382i	0.205418	−	0.355794i
$797$	12.2796	−	21.2690i	0.434967	−	0.753385i	−0.562326	−	0.826916i	$-0.690093\pi$
$797$	12.2796	−	21.2690i	0.434967	−	0.753385i	0.997293	+	0.0735308i	$0.0234267\pi$
$798$		0			0
$799$	−8.05256	−	13.9474i	−0.284879	−	0.493425i
$800$	4.73205			0.167303
$801$			48.3335i			1.70778i
$802$	25.0526			0.884637
$803$	−3.38323	−	5.85993i	−0.119392	−	0.206792i
$804$	−1.70522	+	6.36396i	−0.0601384	+	0.224440i
$805$		0			0
$806$	−9.00000	+	15.5885i	−0.317011	+	0.549080i
$807$	−32.9545	−	32.9545i	−1.16005	−	1.16005i
$808$	−2.89778	−	5.01910i	−0.101943	−	0.176571i
$809$	33.3205			1.17149			0.585743	−	0.810497i	$-0.300803\pi$
$809$	33.3205			1.17149			0.585743	+	0.810497i	$0.300803\pi$
$810$	−4.65874			−0.163692
$811$	−7.82894			−0.274911			−0.137456	−	0.990508i	$-0.543892\pi$
$811$	−7.82894			−0.274911			−0.137456	+	0.990508i	$0.543892\pi$
$812$		0			0
$813$	−18.1244	−	18.1244i	−0.635649	−	0.635649i
$814$	5.85641	−	10.1436i	0.205267	−	0.355533i
$815$	−1.83032	+	3.17020i	−0.0641132	+	0.111047i
$816$	1.56218	−	5.83013i	0.0546872	−	0.204095i
$817$	−3.15660	−	5.46739i	−0.110435	−	0.191280i
$818$	17.8028			0.622459
$819$		0			0
$820$	2.92820			0.102257
$821$	3.33975	+	5.78461i	0.116558	+	0.201884i	0.918401	−	0.395650i	$-0.129481\pi$
$821$	3.33975	+	5.78461i	0.116558	+	0.201884i	−0.801844	+	0.597534i	$0.796147\pi$
$822$		0			0
$823$	3.66025	−	6.33975i	0.127588	−	0.220990i	−0.795153	−	0.606408i	$-0.792610\pi$
$823$	3.66025	−	6.33975i	0.127588	−	0.220990i	0.922742	+	0.385419i	$0.125943\pi$
$824$	5.60609	−	9.71003i	0.195297	−	0.338265i
$825$	−11.5911	+	3.10583i	−0.403551	+	0.108131i
$826$		0			0
$827$	−52.7321			−1.83367			−0.916837	−	0.399263i	$-0.869266\pi$
$827$	−52.7321			−1.83367			−0.916837	+	0.399263i	$0.869266\pi$
$828$	20.5981	−	11.8923i	0.715833	−	0.413286i
$829$	1.89469			0.0658052			0.0329026	−	0.999459i	$-0.489525\pi$
$829$	1.89469			0.0658052			0.0329026	+	0.999459i	$0.489525\pi$
$830$	−2.56218	−	4.43782i	−0.0889345	−	0.154039i
$831$	−7.26054	+	27.0967i	−0.251865	+	0.939974i
$832$	−1.22474	+	2.12132i	−0.0424604	+	0.0735436i
$833$		0			0
$834$	−24.7583	−	24.7583i	−0.857311	−	0.857311i
$835$	−3.43782	−	5.95448i	−0.118971	−	0.206063i
$836$	0.757875			0.0262116
$837$	9.88269	+	36.8827i	0.341596	+	1.27485i
$838$	−22.6646			−0.782935
$839$	−22.4751	−	38.9280i	−0.775927	−	1.34395i	−0.934272	−	0.356561i	$-0.883949\pi$
$839$	−22.4751	−	38.9280i	−0.775927	−	1.34395i	0.158345	−	0.987384i	$-0.449384\pi$
$840$		0			0
$841$	10.7679	−	18.6506i	0.371309	−	0.643125i
$842$	14.0263	−	24.2942i	0.483378	−	0.837234i
$843$	−7.79676	+	29.0979i	−0.268535	+	1.00218i
$844$	−0.633975	−	1.09808i	−0.0218223	−	0.0377973i
$845$	3.62347			0.124651
$846$	12.0072	+	6.93237i	0.412816	+	0.238340i
$847$		0			0
$848$	−3.36603	−	5.83013i	−0.115590	−	0.200207i
$849$	16.3301	−	4.37564i	0.560449	−	0.150172i
$850$	−8.24504	+	14.2808i	−0.282803	+	0.489829i
$851$	31.7128	−	54.9282i	1.08710	−	1.88291i
$852$	1.34486	−	0.360355i	0.0460743	−	0.0123456i
$853$	11.7992	+	20.4367i	0.403996	+	0.699741i	0.994204	−	0.107510i	$-0.0342878\pi$
$853$	11.7992	+	20.4367i	0.403996	+	0.699741i	−0.590208	+	0.807251i	$0.700954\pi$
$854$		0			0
$855$	−0.696152	−	0.401924i	−0.0238079	−	0.0137455i
$856$	−3.07180			−0.104992
$857$	2.72689	+	4.72311i	0.0931488	+	0.161339i	0.908835	−	0.417157i	$-0.136973\pi$
$857$	2.72689	+	4.72311i	0.0931488	+	0.161339i	−0.815686	+	0.578495i	$0.803640\pi$
$858$	1.60770	−	6.00000i	0.0548858	−	0.204837i
$859$	4.84821	−	8.39735i	0.165419	−	0.286514i	−0.771385	−	0.636369i	$-0.780436\pi$
$859$	4.84821	−	8.39735i	0.165419	−	0.286514i	0.936804	+	0.349855i	$0.113769\pi$
$860$	−3.15660	+	5.46739i	−0.107639	+	0.186436i
$861$		0			0
$862$	−13.3923	−	23.1962i	−0.456144	−	0.790064i
$863$	21.1962			0.721525			0.360763	−	0.932658i	$-0.382516\pi$
$863$	21.1962			0.721525			0.360763	+	0.932658i	$0.382516\pi$
$864$	1.34486	+	5.01910i	0.0457532	+	0.170753i
$865$	−10.0526			−0.341797
$866$	10.1261	+	17.5390i	0.344100	+	0.595998i
$867$	−5.94786	−	5.94786i	−0.202000	−	0.202000i
$868$		0			0
$869$	10.3397	−	17.9090i	0.350752	−	0.607520i
$870$	0.633975	−	2.36603i	0.0214938	−	0.0802158i
$871$	4.65874	+	8.06918i	0.157855	+	0.273414i
$872$	−10.5885			−0.358570
$873$	2.68973	−	1.55291i	0.0910334	−	0.0525582i
$874$	4.10394			0.138818
$875$		0			0
$876$	7.73205	−	2.07180i	0.261242	−	0.0699995i
$877$	−12.0263	+	20.8301i	−0.406099	+	0.703383i	−0.994449	−	0.105223i	$-0.966444\pi$
$877$	−12.0263	+	20.8301i	−0.406099	+	0.703383i	0.588350	+	0.808606i	$0.299778\pi$
$878$	−9.14162	+	15.8338i	−0.308515	+	0.534363i
$879$	−4.96410	+	1.33013i	−0.167435	+	0.0448641i
$880$	−0.378937	−	0.656339i	−0.0127740	−	0.0221252i
$881$	−0.480473			−0.0161876			−0.00809378	−	0.999967i	$-0.502576\pi$
$881$	−0.480473			−0.0161876			−0.00809378	+	0.999967i	$0.502576\pi$
$882$		0			0
$883$	38.2487			1.28717			0.643586	−	0.765374i	$-0.277446\pi$
$883$	38.2487			1.28717			0.643586	+	0.765374i	$0.277446\pi$
$884$	−4.26795	−	7.39230i	−0.143547	−	0.248630i
$885$	3.43400	−	12.8159i	0.115433	−	0.430800i
$886$	−18.4904	+	32.0263i	−0.621197	+	1.07594i
$887$	13.4858	−	23.3581i	0.452809	−	0.784288i	−0.545751	−	0.837948i	$-0.683755\pi$
$887$	13.4858	−	23.3581i	0.452809	−	0.784288i	0.998559	+	0.0536600i	$0.0170887\pi$
$888$	9.79796	+	9.79796i	0.328798	+	0.328798i
$889$		0			0
$890$	8.33975			0.279549
$891$	−6.58846	−	11.4115i	−0.220722	−	0.382301i
$892$	−3.76217			−0.125967
$893$	1.19615	+	2.07180i	0.0400277	+	0.0693300i
$894$	2.92996	+	2.92996i	0.0979926	+	0.0979926i
$895$	−2.12132	+	3.67423i	−0.0709079	+	0.122816i
$896$		0			0
$897$	8.70577	−	32.4904i	0.290677	−	1.08482i
$898$	−11.8923	−	20.5981i	−0.396851	−	0.687367i
$899$	−20.0764			−0.669585
$900$		−	14.1962i		−	0.473205i
$901$	23.4596			0.781553
$902$	4.14110	+	7.17260i	0.137884	+	0.238822i
$903$		0			0
$904$	−7.33013	+	12.6962i	−0.243796	+	0.422268i
$905$	5.42820	−	9.40192i	0.180440	−	0.312531i
$906$	−29.0979	+	7.79676i	−0.966713	+	0.259030i
$907$	2.56218	+	4.43782i	0.0850757	+	0.147355i	0.905423	−	0.424510i	$-0.139553\pi$
$907$	2.56218	+	4.43782i	0.0850757	+	0.147355i	−0.820348	+	0.571865i	$0.806220\pi$
$908$	−3.34607			−0.111043
$909$	−15.0573	+	8.69333i	−0.499419	+	0.288340i
$910$		0			0
$911$	−13.8923	−	24.0622i	−0.460273	−	0.797216i	0.538702	−	0.842497i	$-0.318915\pi$
$911$	−13.8923	−	24.0622i	−0.460273	−	0.797216i	−0.998974	+	0.0452811i	$0.985582\pi$
$912$	−0.232051	+	0.866025i	−0.00768397	+	0.0286770i
$913$	7.24693	−	12.5521i	0.239838	−	0.415412i
$914$	−11.1340	+	19.2846i	−0.368279	+	0.637878i
$915$	2.77766	+	2.77766i	0.0918266	+	0.0918266i
$916$	6.90018	+	11.9515i	0.227988	+	0.394888i
$917$		0			0
$918$	−17.4904	−	4.68653i	−0.577269	−	0.154679i
$919$	16.3731			0.540098			0.270049	−	0.962847i	$-0.412960\pi$
$919$	16.3731			0.540098			0.270049	+	0.962847i	$0.412960\pi$
$920$	−2.05197	−	3.55412i	−0.0676514	−	0.117176i
$921$	14.6147	+	14.6147i	0.481572	+	0.481572i
$922$	−19.4894	+	33.7566i	−0.641849	+	1.11172i
$923$	0.984508	−	1.70522i	0.0324055	−	0.0561279i
$924$		0			0
$925$	−18.9282	−	32.7846i	−0.622355	−	1.07795i
$926$	−6.66025			−0.218870
$927$	−29.1301	−	16.8183i	−0.956757	−	0.552384i
$928$	−2.73205			−0.0896840
$929$	2.01978	+	3.49837i	0.0662670	+	0.114778i	0.897255	−	0.441512i	$-0.145558\pi$
$929$	2.01978	+	3.49837i	0.0662670	+	0.114778i	−0.830988	+	0.556290i	$0.812224\pi$
$930$	6.36396	−	1.70522i	0.208683	−	0.0559163i
$931$		0			0
$932$	−0.696152	+	1.20577i	−0.0228032	+	0.0394964i
$933$	30.4186	−	8.15064i	0.995860	−	0.266840i
$934$	−12.2982	−	21.3011i	−0.402410	−	0.696994i
$935$	2.64102			0.0863705
$936$	6.36396	+	3.67423i	0.208013	+	0.120096i
$937$	−31.7690			−1.03785			−0.518925	−	0.854820i	$-0.673667\pi$
$937$	−31.7690			−1.03785			−0.518925	+	0.854820i	$0.673667\pi$
$938$		0			0
$939$	3.00000	−	11.1962i	0.0979013	−	0.365373i
$940$	1.19615	−	2.07180i	0.0390142	−	0.0675746i
$941$	−29.1994	+	50.5749i	−0.951874	+	1.64869i	−0.210510	+	0.977592i	$0.567512\pi$
$941$	−29.1994	+	50.5749i	−0.951874	+	1.64869i	−0.741364	+	0.671103i	$0.765821\pi$
$942$	−21.1699	−	21.1699i	−0.689752	−	0.689752i
$943$	22.4243	+	38.8401i	0.730237	+	1.26481i
$944$	−14.7985			−0.481649
$945$		0			0
$946$	−17.8564			−0.580562
$947$	17.8301	+	30.8827i	0.579401	+	1.00355i	0.995548	+	0.0942550i	$0.0300469\pi$
$947$	17.8301	+	30.8827i	0.579401	+	1.00355i	−0.416147	+	0.909297i	$0.636620\pi$
$948$	17.2987	+	17.2987i	0.561837	+	0.561837i
$949$	5.66025	−	9.80385i	0.183740	−	0.318246i
$950$	1.22474	−	2.12132i	0.0397360	−	0.0688247i
$951$	14.6090	−	54.5216i	0.473729	−	1.76798i
$952$		0			0
$953$	23.7128			0.768133			0.384067	−	0.923305i	$-0.374523\pi$
$953$	23.7128			0.768133			0.384067	+	0.923305i	$0.374523\pi$
$954$	−17.4904	+	10.0981i	−0.566272	+	0.326937i
$955$	3.72500			0.120538
$956$	6.23205	+	10.7942i	0.201559	+	0.349110i
$957$	6.69213	−	1.79315i	0.216326	−	0.0579643i
$958$	6.64136	−	11.5032i	0.214573	−	0.371651i
$959$		0			0
$960$	0.866025	−	0.232051i	0.0279508	−	0.00748941i
$961$	−11.5000	−	19.9186i	−0.370968	−	0.642535i
$962$	19.5959			0.631798
$963$			9.21539i			0.296962i
$964$	−12.7279			−0.409939
$965$	−6.14231	−	10.6388i	−0.197728	−	0.342475i
$966$		0			0
$967$	0.232051	−	0.401924i	0.00746225	−	0.0129250i	−0.862270	−	0.506449i	$-0.830958\pi$
$967$	0.232051	−	0.401924i	0.00746225	−	0.0129250i	0.869732	+	0.493524i	$0.164291\pi$
$968$	−4.42820	+	7.66987i	−0.142328	+	0.246519i
$969$	−2.20925	−	2.20925i	−0.0709714	−	0.0709714i
$970$	−0.267949	−	0.464102i	−0.00860333	−	0.0149014i
$971$	−28.5988			−0.917780			−0.458890	−	0.888493i	$-0.651753\pi$
$971$	−28.5988			−0.917780			−0.458890	+	0.888493i	$0.651753\pi$
$972$	15.0573	−	4.03459i	0.482963	−	0.129410i
$973$		0			0
$974$	−16.1603	−	27.9904i	−0.517808	−	0.896870i
$975$	−14.1962	−	14.1962i	−0.454641	−	0.454641i
$976$	2.19067	−	3.79435i	0.0701217	−	0.121454i
$977$	8.07180	−	13.9808i	0.258240	−	0.447284i	−0.707531	−	0.706683i	$-0.750191\pi$
$977$	8.07180	−	13.9808i	0.258240	−	0.447284i	0.965770	+	0.259398i	$0.0835242\pi$
$978$	3.17020	−	11.8313i	0.101372	−	0.378325i
$979$	11.7942	+	20.4281i	0.376944	+	0.652886i
$980$		0			0
$981$			31.7654i			1.01419i
$982$	5.07180			0.161848
$983$	−11.8177	−	20.4689i	−0.376927	−	0.652858i	0.613686	−	0.789550i	$-0.289686\pi$
$983$	−11.8177	−	20.4689i	−0.376927	−	0.652858i	−0.990614	+	0.136693i	$0.956353\pi$
$984$	−9.46410	+	2.53590i	−0.301705	+	0.0808415i
$985$	2.50026	−	4.33057i	0.0796648	−	0.137984i
$986$	4.76028	−	8.24504i	0.151598	−	0.262576i
$987$		0			0
$988$	0.633975	+	1.09808i	0.0201694	+	0.0349345i
$989$	−96.6936			−3.07468
$990$	−1.96902	+	1.13681i	−0.0625794	+	0.0361303i
$991$	14.6795			0.466309			0.233155	−	0.972440i	$-0.425095\pi$
$991$	14.6795			0.466309			0.233155	+	0.972440i	$0.425095\pi$
$992$	−3.67423	−	6.36396i	−0.116657	−	0.202056i
$993$	−5.40301	+	20.1643i	−0.171459	+	0.639895i
$994$		0			0
$995$	−3.00000	+	5.19615i	−0.0951064	+	0.164729i
$996$	12.1244	+	12.1244i	0.384175	+	0.384175i
$997$	21.9389	+	37.9993i	0.694812	+	1.20345i	0.970244	+	0.242129i	$0.0778456\pi$
$997$	21.9389	+	37.9993i	0.694812	+	1.20345i	−0.275432	+	0.961320i	$0.588821\pi$
$998$	−7.32051			−0.231727
$999$	29.3939	−	29.3939i	0.929981	−	0.929981i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.f.s.589.4	yes	8
3.2	odd	2		2646.2.f.q.1765.2		8
7.2	even	3		882.2.h.t.67.1		8
7.3	odd	6		882.2.e.q.373.2		8
7.4	even	3		882.2.e.q.373.3		8
7.5	odd	6		882.2.h.t.67.4		8
7.6	odd	2	inner	882.2.f.s.589.1	yes	8
9.2	odd	6		2646.2.f.q.883.2		8
9.4	even	3		7938.2.a.cj.1.2		4
9.5	odd	6		7938.2.a.co.1.3		4
9.7	even	3	inner	882.2.f.s.295.3	yes	8
21.2	odd	6		2646.2.h.q.361.3		8
21.5	even	6		2646.2.h.q.361.2		8
21.11	odd	6		2646.2.e.t.1549.2		8
21.17	even	6		2646.2.e.t.1549.3		8
21.20	even	2		2646.2.f.q.1765.3		8
63.2	odd	6		2646.2.e.t.2125.2		8
63.11	odd	6		2646.2.h.q.667.3		8
63.13	odd	6		7938.2.a.cj.1.3		4
63.16	even	3		882.2.e.q.655.3		8
63.20	even	6		2646.2.f.q.883.3		8
63.25	even	3		882.2.h.t.79.1		8
63.34	odd	6	inner	882.2.f.s.295.2	✓	8
63.38	even	6		2646.2.h.q.667.2		8
63.41	even	6		7938.2.a.co.1.2		4
63.47	even	6		2646.2.e.t.2125.3		8
63.52	odd	6		882.2.h.t.79.4		8
63.61	odd	6		882.2.e.q.655.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.e.q.373.2		8	7.3	odd	6
882.2.e.q.373.3		8	7.4	even	3
882.2.e.q.655.2		8	63.61	odd	6
882.2.e.q.655.3		8	63.16	even	3
882.2.f.s.295.2	✓	8	63.34	odd	6	inner
882.2.f.s.295.3	yes	8	9.7	even	3	inner
882.2.f.s.589.1	yes	8	7.6	odd	2	inner
882.2.f.s.589.4	yes	8	1.1	even	1	trivial
882.2.h.t.67.1		8	7.2	even	3
882.2.h.t.67.4		8	7.5	odd	6
882.2.h.t.79.1		8	63.25	even	3
882.2.h.t.79.4		8	63.52	odd	6
2646.2.e.t.1549.2		8	21.11	odd	6
2646.2.e.t.1549.3		8	21.17	even	6
2646.2.e.t.2125.2		8	63.2	odd	6
2646.2.e.t.2125.3		8	63.47	even	6
2646.2.f.q.883.2		8	9.2	odd	6
2646.2.f.q.883.3		8	63.20	even	6
2646.2.f.q.1765.2		8	3.2	odd	2
2646.2.f.q.1765.3		8	21.20	even	2
2646.2.h.q.361.2		8	21.5	even	6
2646.2.h.q.361.3		8	21.2	odd	6
2646.2.h.q.667.2		8	63.38	even	6
2646.2.h.q.667.3		8	63.11	odd	6
7938.2.a.cj.1.2		4	9.4	even	3
7938.2.a.cj.1.3		4	63.13	odd	6
7938.2.a.co.1.2		4	63.41	even	6
7938.2.a.co.1.3		4	9.5	odd	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:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(1.22474 + 1.22474i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.258819 - 0.448288i) q^{5} +(-0.448288 + 1.67303i) q^{6} -1.00000 q^{8} +3.00000i q^{9} +0.517638 q^{10} +(0.732051 + 1.26795i) q^{11} +(-1.67303 + 0.448288i) q^{12} +(-1.22474 + 2.12132i) q^{13} +(0.866025 - 0.232051i) q^{15} +(-0.500000 - 0.866025i) q^{16} +3.48477 q^{17} +(-2.59808 + 1.50000i) q^{18} -0.517638 q^{19} +(0.258819 + 0.448288i) q^{20} +(-0.732051 + 1.26795i) q^{22} +(-3.96410 + 6.86603i) q^{23} +(-1.22474 - 1.22474i) q^{24} +(2.36603 + 4.09808i) q^{25} -2.44949 q^{26} +(-3.67423 + 3.67423i) q^{27} +(-1.36603 - 2.36603i) q^{29} +(0.633975 + 0.633975i) q^{30} +(3.67423 - 6.36396i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-0.656339 + 2.44949i) q^{33} +(1.74238 + 3.01790i) q^{34} +(-2.59808 - 1.50000i) q^{36} -8.00000 q^{37} +(-0.258819 - 0.448288i) q^{38} +(-4.09808 + 1.09808i) q^{39} +(-0.258819 + 0.448288i) q^{40} +(2.82843 - 4.89898i) q^{41} +(6.09808 + 10.5622i) q^{43} -1.46410 q^{44} +(1.34486 + 0.776457i) q^{45} -7.92820 q^{46} +(-2.31079 - 4.00240i) q^{47} +(0.448288 - 1.67303i) q^{48} +(-2.36603 + 4.09808i) q^{50} +(4.26795 + 4.26795i) q^{51} +(-1.22474 - 2.12132i) q^{52} +6.73205 q^{53} +(-5.01910 - 1.34486i) q^{54} +0.757875 q^{55} +(-0.633975 - 0.633975i) q^{57} +(1.36603 - 2.36603i) q^{58} +(7.39924 - 12.8159i) q^{59} +(-0.232051 + 0.866025i) q^{60} +(2.19067 + 3.79435i) q^{61} +7.34847 q^{62} +1.00000 q^{64} +(0.633975 + 1.09808i) q^{65} +(-2.44949 + 0.656339i) q^{66} +(1.90192 - 3.29423i) q^{67} +(-1.74238 + 3.01790i) q^{68} +(-13.2641 + 3.55412i) q^{69} -0.803848 q^{71} -3.00000i q^{72} -4.62158 q^{73} +(-4.00000 - 6.92820i) q^{74} +(-2.12132 + 7.91688i) q^{75} +(0.258819 - 0.448288i) q^{76} +(-3.00000 - 3.00000i) q^{78} +(-7.06218 - 12.2321i) q^{79} -0.517638 q^{80} -9.00000 q^{81} +5.65685 q^{82} +(-4.94975 - 8.57321i) q^{83} +(0.901924 - 1.56218i) q^{85} +(-6.09808 + 10.5622i) q^{86} +(1.22474 - 4.57081i) q^{87} +(-0.732051 - 1.26795i) q^{88} +16.1112 q^{89} +1.55291i q^{90} +(-3.96410 - 6.86603i) q^{92} +(12.2942 - 3.29423i) q^{93} +(2.31079 - 4.00240i) q^{94} +(-0.133975 + 0.232051i) q^{95} +(1.67303 - 0.448288i) q^{96} +(-0.517638 - 0.896575i) q^{97} +(-3.80385 + 2.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} - 4 q^{4} - 8 q^{8} - 8 q^{11} - 4 q^{16} + 8 q^{22} - 4 q^{23} + 12 q^{25} - 4 q^{29} + 12 q^{30} + 4 q^{32} - 64 q^{37} - 12 q^{39} + 28 q^{43} + 16 q^{44} - 8 q^{46} - 12 q^{50} + 48 q^{51}+ \cdots - 72 q^{99}+O(q^{100}) \) 8 * q + 4 * q^2 - 4 * q^4 - 8 * q^8 - 8 * q^11 - 4 * q^16 + 8 * q^22 - 4 * q^23 + 12 * q^25 - 4 * q^29 + 12 * q^30 + 4 * q^32 - 64 * q^37 - 12 * q^39 + 28 * q^43 + 16 * q^44 - 8 * q^46 - 12 * q^50 + 48 * q^51 + 40 * q^53 - 12 * q^57 + 4 * q^58 + 12 * q^60 + 8 * q^64 + 12 * q^65 + 36 * q^67 - 48 * q^71 - 32 * q^74 - 24 * q^78 - 8 * q^79 - 72 * q^81 + 28 * q^85 - 28 * q^86 + 8 * q^88 - 4 * q^92 + 36 * q^93 - 8 * q^95 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more