LMFDB - Embedded newform 1890.2.i.g.991.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1890,2,Mod(991,1890)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1890, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1890.991");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1890.i (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$15.0917259820$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 7 x^{10} - 3 x^{9} - 2 x^{8} + 24 x^{7} - 21 x^{6} + 72 x^{5} - 18 x^{4} + \cdots + 729 $ x^12 - 3x^11 + 7x^10 - 3x^9 - 2x^8 + 24x^7 - 21x^6 + 72x^5 - 18x^4 - 81x^3 + 567x^2 - 729*x + 729
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	no (minimal twist has level 630)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			991.2
Root			$0.628063 + 1.61417i$ of defining polynomial
Character	$\chi$	$=$	1890.991
Dual form			1890.2.i.g.1171.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(-2.25729 - 1.38008i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(-2.25729 - 1.38008i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{10} +(0.480820 + 0.832805i) q^{11} +(-2.94219 - 5.09603i) q^{13} +(2.25729 + 1.38008i) q^{14} +1.00000 q^{16} +(-3.89714 + 6.75005i) q^{17} +(0.774437 + 1.34137i) q^{19} +(0.500000 - 0.866025i) q^{20} +(-0.480820 - 0.832805i) q^{22} +(-1.95495 + 3.38607i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(2.94219 + 5.09603i) q^{26} +(-2.25729 - 1.38008i) q^{28} +(0.543215 - 0.940877i) q^{29} +2.55756 q^{31} -1.00000 q^{32} +(3.89714 - 6.75005i) q^{34} +(-2.32383 + 1.26483i) q^{35} +(5.84787 + 10.1288i) q^{37} +(-0.774437 - 1.34137i) q^{38} +(-0.500000 + 0.866025i) q^{40} +(-1.15042 - 1.99258i) q^{41} +(-2.18820 + 3.79008i) q^{43} +(0.480820 + 0.832805i) q^{44} +(1.95495 - 3.38607i) q^{46} +3.55502 q^{47} +(3.19076 + 6.23049i) q^{49} +(0.500000 + 0.866025i) q^{50} +(-2.94219 - 5.09603i) q^{52} +(-0.274437 + 0.475340i) q^{53} +0.961641 q^{55} +(2.25729 + 1.38008i) q^{56} +(-0.543215 + 0.940877i) q^{58} +6.00868 q^{59} +14.6881 q^{61} -2.55756 q^{62} +1.00000 q^{64} -5.88439 q^{65} -0.821956 q^{67} +(-3.89714 + 6.75005i) q^{68} +(2.32383 - 1.26483i) q^{70} +3.96164 q^{71} +(0.368764 - 0.638718i) q^{73} +(-5.84787 - 10.1288i) q^{74} +(0.774437 + 1.34137i) q^{76} +(0.0639849 - 2.54346i) q^{77} -6.79796 q^{79} +(0.500000 - 0.866025i) q^{80} +(1.15042 + 1.99258i) q^{82} +(-6.12526 + 10.6093i) q^{83} +(3.89714 + 6.75005i) q^{85} +(2.18820 - 3.79008i) q^{86} +(-0.480820 - 0.832805i) q^{88} +(2.85680 + 4.94812i) q^{89} +(-0.391531 + 15.5637i) q^{91} +(-1.95495 + 3.38607i) q^{92} -3.55502 q^{94} +1.54887 q^{95} +(7.80249 - 13.5143i) q^{97} +(-3.19076 - 6.23049i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{2} + 12 q^{4} + 6 q^{5} + 4 q^{7} - 12 q^{8}+O(q^{10}) $ 12 * q - 12 * q^2 + 12 * q^4 + 6 * q^5 + 4 * q^7 - 12 * q^8	$ 12 q - 12 q^{2} + 12 q^{4} + 6 q^{5} + 4 q^{7} - 12 q^{8} - 6 q^{10} - 3 q^{11} - 2 q^{13} - 4 q^{14} + 12 q^{16} - q^{17} + 8 q^{19} + 6 q^{20} + 3 q^{22} - 11 q^{23} - 6 q^{25} + 2 q^{26} + 4 q^{28} - 13 q^{29} - 42 q^{31} - 12 q^{32} + q^{34} - 4 q^{35} + 18 q^{37} - 8 q^{38} - 6 q^{40} - 5 q^{41} - 11 q^{43} - 3 q^{44} + 11 q^{46} - 46 q^{47} + 6 q^{50} - 2 q^{52} - 2 q^{53} - 6 q^{55} - 4 q^{56} + 13 q^{58} + 2 q^{59} + 2 q^{61} + 42 q^{62} + 12 q^{64} - 4 q^{65} - 4 q^{67} - q^{68} + 4 q^{70} + 30 q^{71} + 22 q^{73} - 18 q^{74} + 8 q^{76} + 31 q^{77} - 54 q^{79} + 6 q^{80} + 5 q^{82} - 6 q^{83} + q^{85} + 11 q^{86} + 3 q^{88} + 18 q^{89} + 14 q^{91} - 11 q^{92} + 46 q^{94} + 16 q^{95} - 4 q^{97}+O(q^{100}) $ 12 * q - 12 * q^2 + 12 * q^4 + 6 * q^5 + 4 * q^7 - 12 * q^8 - 6 * q^10 - 3 * q^11 - 2 * q^13 - 4 * q^14 + 12 * q^16 - q^17 + 8 * q^19 + 6 * q^20 + 3 * q^22 - 11 * q^23 - 6 * q^25 + 2 * q^26 + 4 * q^28 - 13 * q^29 - 42 * q^31 - 12 * q^32 + q^34 - 4 * q^35 + 18 * q^37 - 8 * q^38 - 6 * q^40 - 5 * q^41 - 11 * q^43 - 3 * q^44 + 11 * q^46 - 46 * q^47 + 6 * q^50 - 2 * q^52 - 2 * q^53 - 6 * q^55 - 4 * q^56 + 13 * q^58 + 2 * q^59 + 2 * q^61 + 42 * q^62 + 12 * q^64 - 4 * q^65 - 4 * q^67 - q^68 + 4 * q^70 + 30 * q^71 + 22 * q^73 - 18 * q^74 + 8 * q^76 + 31 * q^77 - 54 * q^79 + 6 * q^80 + 5 * q^82 - 6 * q^83 + q^85 + 11 * q^86 + 3 * q^88 + 18 * q^89 + 14 * q^91 - 11 * q^92 + 46 * q^94 + 16 * q^95 - 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1890\mathbb{Z}\right)^\times$.

$n$	$757$	$1081$	$1541$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$		0			0
$3$		0			0
$4$	1.00000			0.500000
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$		0			0
$7$	−2.25729	−	1.38008i	−0.853177	−	0.521621i
$7$	−2.25729	−	1.38008i	−0.853177	−	0.521621i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−0.500000	+	0.866025i	−0.158114	+	0.273861i
$11$	0.480820	+	0.832805i	0.144973	+	0.251100i	0.929363	−	0.369168i	$-0.120357\pi$
$11$	0.480820	+	0.832805i	0.144973	+	0.251100i	−0.784390	+	0.620268i	$0.787024\pi$
$12$		0			0
$13$	−2.94219	−	5.09603i	−0.816018	−	1.41338i	−0.908595	−	0.417679i	$-0.862844\pi$
$13$	−2.94219	−	5.09603i	−0.816018	−	1.41338i	0.0925769	−	0.995706i	$-0.470490\pi$
$14$	2.25729	+	1.38008i	0.603287	+	0.368842i
$15$		0			0
$16$	1.00000			0.250000
$17$	−3.89714	+	6.75005i	−0.945195	+	1.63713i	−0.189836	+	0.981816i	$0.560796\pi$
$17$	−3.89714	+	6.75005i	−0.945195	+	1.63713i	−0.755360	+	0.655311i	$0.772538\pi$
$18$		0			0
$19$	0.774437	+	1.34137i	0.177668	+	0.307730i	0.941081	−	0.338180i	$-0.109811\pi$
$19$	0.774437	+	1.34137i	0.177668	+	0.307730i	−0.763413	+	0.645910i	$0.776478\pi$
$20$	0.500000	−	0.866025i	0.111803	−	0.193649i
$21$		0			0
$22$	−0.480820	−	0.832805i	−0.102511	−	0.177555i
$23$	−1.95495	+	3.38607i	−0.407634	+	0.706044i	−0.994624	−	0.103551i	$-0.966980\pi$
$23$	−1.95495	+	3.38607i	−0.407634	+	0.706044i	0.586990	+	0.809594i	$0.300313\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	2.94219	+	5.09603i	0.577012	+	0.999414i
$27$		0			0
$28$	−2.25729	−	1.38008i	−0.426589	−	0.260811i
$29$	0.543215	−	0.940877i	0.100873	−	0.174716i	−0.811172	−	0.584808i	$-0.801170\pi$
$29$	0.543215	−	0.940877i	0.100873	−	0.174716i	0.912044	+	0.410091i	$0.134503\pi$
$30$		0			0
$31$	2.55756			0.459351			0.229675	−	0.973267i	$-0.426234\pi$
$31$	2.55756			0.459351			0.229675	+	0.973267i	$0.426234\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$	3.89714	−	6.75005i	0.668354	−	1.15762i
$35$	−2.32383	+	1.26483i	−0.392799	+	0.213796i
$36$		0			0
$37$	5.84787	+	10.1288i	0.961384	+	1.66517i	0.719033	+	0.694976i	$0.244585\pi$
$37$	5.84787	+	10.1288i	0.961384	+	1.66517i	0.242351	+	0.970189i	$0.422081\pi$
$38$	−0.774437	−	1.34137i	−0.125630	−	0.217598i
$39$		0			0
$40$	−0.500000	+	0.866025i	−0.0790569	+	0.136931i
$41$	−1.15042	−	1.99258i	−0.179665	−	0.311188i	0.762101	−	0.647458i	$-0.224168\pi$
$41$	−1.15042	−	1.99258i	−0.179665	−	0.311188i	−0.941766	+	0.336270i	$0.890835\pi$
$42$		0			0
$43$	−2.18820	+	3.79008i	−0.333698	+	0.577982i	−0.983234	−	0.182349i	$-0.941630\pi$
$43$	−2.18820	+	3.79008i	−0.333698	+	0.577982i	0.649536	+	0.760331i	$0.274963\pi$
$44$	0.480820	+	0.832805i	0.0724864	+	0.125550i
$45$		0			0
$46$	1.95495	−	3.38607i	0.288241	−	0.499248i
$47$	3.55502			0.518553			0.259276	−	0.965803i	$-0.416516\pi$
$47$	3.55502			0.518553			0.259276	+	0.965803i	$0.416516\pi$
$48$		0			0
$49$	3.19076	+	6.23049i	0.455822	+	0.890071i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$		0			0
$52$	−2.94219	−	5.09603i	−0.408009	−	0.706692i
$53$	−0.274437	+	0.475340i	−0.0376969	+	0.0652929i	−0.884258	−	0.466998i	$-0.845335\pi$
$53$	−0.274437	+	0.475340i	−0.0376969	+	0.0652929i	0.846561	+	0.532291i	$0.178669\pi$
$54$		0			0
$55$	0.961641			0.129668
$56$	2.25729	+	1.38008i	0.301644	+	0.184421i
$57$		0			0
$58$	−0.543215	+	0.940877i	−0.0713277	+	0.123543i
$59$	6.00868			0.782264			0.391132	−	0.920335i	$-0.372084\pi$
$59$	6.00868			0.782264			0.391132	+	0.920335i	$0.372084\pi$
$60$		0			0
$61$	14.6881			1.88062			0.940312	−	0.340314i	$-0.110534\pi$
$61$	14.6881			1.88062			0.940312	+	0.340314i	$0.110534\pi$
$62$	−2.55756			−0.324810
$63$		0			0
$64$	1.00000			0.125000
$65$	−5.88439			−0.729869
$66$		0			0
$67$	−0.821956			−0.100418			−0.0502089	−	0.998739i	$-0.515989\pi$
$67$	−0.821956			−0.100418			−0.0502089	+	0.998739i	$0.515989\pi$
$68$	−3.89714	+	6.75005i	−0.472598	+	0.818563i
$69$		0			0
$70$	2.32383	−	1.26483i	0.277751	−	0.151177i
$71$	3.96164			0.470160			0.235080	−	0.971976i	$-0.424465\pi$
$71$	3.96164			0.470160			0.235080	+	0.971976i	$0.424465\pi$
$72$		0			0
$73$	0.368764	−	0.638718i	0.0431606	−	0.0747563i	−0.843638	−	0.536912i	$-0.819591\pi$
$73$	0.368764	−	0.638718i	0.0431606	−	0.0747563i	0.886799	+	0.462156i	$0.152924\pi$
$74$	−5.84787	−	10.1288i	−0.679801	−	1.17745i
$75$		0			0
$76$	0.774437	+	1.34137i	0.0888341	+	0.153865i
$77$	0.0639849	−	2.54346i	0.00729176	−	0.289854i
$78$		0			0
$79$	−6.79796			−0.764830			−0.382415	−	0.923991i	$-0.624908\pi$
$79$	−6.79796			−0.764830			−0.382415	+	0.923991i	$0.624908\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$		0			0
$82$	1.15042	+	1.99258i	0.127042	+	0.220043i
$83$	−6.12526	+	10.6093i	−0.672334	+	1.16452i	0.304906	+	0.952382i	$0.401375\pi$
$83$	−6.12526	+	10.6093i	−0.672334	+	1.16452i	−0.977240	+	0.212134i	$0.931959\pi$
$84$		0			0
$85$	3.89714	+	6.75005i	0.422704	+	0.732145i
$86$	2.18820	−	3.79008i	0.235960	−	0.408695i
$87$		0			0
$88$	−0.480820	−	0.832805i	−0.0512556	−	0.0887774i
$89$	2.85680	+	4.94812i	0.302820	+	0.524500i	0.976774	−	0.214274i	$-0.0687386\pi$
$89$	2.85680	+	4.94812i	0.302820	+	0.524500i	−0.673954	+	0.738774i	$0.735405\pi$
$90$		0			0
$91$	−0.391531	+	15.5637i	−0.0410436	+	1.63152i
$92$	−1.95495	+	3.38607i	−0.203817	+	0.353022i
$93$		0			0
$94$	−3.55502			−0.366672
$95$	1.54887			0.158911
$96$		0			0
$97$	7.80249	−	13.5143i	0.792223	−	1.37217i	−0.132365	−	0.991201i	$-0.542257\pi$
$97$	7.80249	−	13.5143i	0.792223	−	1.37217i	0.924588	−	0.380970i	$-0.124410\pi$
$98$	−3.19076	−	6.23049i	−0.322315	−	0.629375i
$99$		0			0
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	−4.80772	−	8.32722i	−0.478386	−	0.828590i	0.521307	−	0.853370i	$-0.325445\pi$
$101$	−4.80772	−	8.32722i	−0.478386	−	0.828590i	−0.999693	+	0.0247799i	$0.992111\pi$
$102$		0			0
$103$	−1.54448	+	2.67512i	−0.152183	+	0.263588i	−0.932030	−	0.362382i	$-0.881963\pi$
$103$	−1.54448	+	2.67512i	−0.152183	+	0.263588i	0.779847	+	0.625970i	$0.215297\pi$
$104$	2.94219	+	5.09603i	0.288506	+	0.499707i
$105$		0			0
$106$	0.274437	−	0.475340i	0.0266557	−	0.0461691i
$107$	1.73194	+	2.99980i	0.167433	+	0.290002i	0.937516	−	0.347941i	$-0.113119\pi$
$107$	1.73194	+	2.99980i	0.167433	+	0.290002i	−0.770084	+	0.637943i	$0.779786\pi$
$108$		0			0
$109$	−7.17178	+	12.4219i	−0.686932	+	1.18980i	0.285894	+	0.958261i	$0.407709\pi$
$109$	−7.17178	+	12.4219i	−0.686932	+	1.18980i	−0.972826	+	0.231539i	$0.925624\pi$
$110$	−0.961641			−0.0916889
$111$		0			0
$112$	−2.25729	−	1.38008i	−0.213294	−	0.130405i
$113$	−0.362337	−	0.627585i	−0.0340858	−	0.0590383i	0.848479	−	0.529229i	$-0.177519\pi$
$113$	−0.362337	−	0.627585i	−0.0340858	−	0.0590383i	−0.882565	+	0.470190i	$0.844185\pi$
$114$		0			0
$115$	1.95495	+	3.38607i	0.182300	+	0.315752i
$116$	0.543215	−	0.940877i	0.0504363	−	0.0873582i
$117$		0			0
$118$	−6.00868			−0.553144
$119$	18.1126	−	9.85847i	1.66038	−	0.903725i
$120$		0			0
$121$	5.03762	−	8.72542i	0.457966	−	0.793220i
$122$	−14.6881			−1.32980
$123$		0			0
$124$	2.55756			0.229675
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	13.1020			1.16262			0.581309	−	0.813683i	$-0.302541\pi$
$127$	13.1020			1.16262			0.581309	+	0.813683i	$0.302541\pi$
$128$	−1.00000			−0.0883883
$129$		0			0
$130$	5.88439			0.516095
$131$	−8.75462	+	15.1634i	−0.764895	+	1.32484i	0.175408	+	0.984496i	$0.443876\pi$
$131$	−8.75462	+	15.1634i	−0.764895	+	1.32484i	−0.940302	+	0.340340i	$0.889458\pi$
$132$		0			0
$133$	0.103058	−	4.09664i	0.00893625	−	0.355224i
$134$	0.821956			0.0710061
$135$		0			0
$136$	3.89714	−	6.75005i	0.334177	−	0.578812i
$137$	−4.34792	−	7.53082i	−0.371468	−	0.643401i	0.618324	−	0.785924i	$-0.287812\pi$
$137$	−4.34792	−	7.53082i	−0.371468	−	0.643401i	−0.989792	+	0.142522i	$0.954479\pi$
$138$		0			0
$139$	−6.56877	−	11.3774i	−0.557156	−	0.965022i	−0.997732	−	0.0673073i	$-0.978559\pi$
$139$	−6.56877	−	11.3774i	−0.557156	−	0.965022i	0.440576	−	0.897715i	$-0.354774\pi$
$140$	−2.32383	+	1.26483i	−0.196400	+	0.106898i
$141$		0			0
$142$	−3.96164			−0.332454
$143$	2.82933	−	4.90055i	0.236601	−	0.409805i
$144$		0			0
$145$	−0.543215	−	0.940877i	−0.0451116	−	0.0781355i
$146$	−0.368764	+	0.638718i	−0.0305191	+	0.0528607i
$147$		0			0
$148$	5.84787	+	10.1288i	0.480692	+	0.832583i
$149$	−8.49218	+	14.7089i	−0.695707	+	1.20500i	0.274235	+	0.961663i	$0.411575\pi$
$149$	−8.49218	+	14.7089i	−0.695707	+	1.20500i	−0.969942	+	0.243336i	$0.921758\pi$
$150$		0			0
$151$	7.91384	+	13.7072i	0.644019	+	1.11547i	0.984527	+	0.175232i	$0.0560675\pi$
$151$	7.91384	+	13.7072i	0.644019	+	1.11547i	−0.340508	+	0.940241i	$0.610599\pi$
$152$	−0.774437	−	1.34137i	−0.0628152	−	0.108799i
$153$		0			0
$154$	−0.0639849	+	2.54346i	−0.00515605	+	0.204958i
$155$	1.27878	−	2.21491i	0.102714	−	0.177906i
$156$		0			0
$157$	10.6557			0.850418			0.425209	−	0.905095i	$-0.360201\pi$
$157$	10.6557			0.850418			0.425209	+	0.905095i	$0.360201\pi$
$158$	6.79796			0.540816
$159$		0			0
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	9.08593	−	4.94537i	0.716072	−	0.389749i
$162$		0			0
$163$	3.88853	+	6.73513i	0.304573	+	0.527536i	0.977166	−	0.212476i	$-0.0681528\pi$
$163$	3.88853	+	6.73513i	0.304573	+	0.527536i	−0.672593	+	0.740013i	$0.734820\pi$
$164$	−1.15042	−	1.99258i	−0.0898324	−	0.155594i
$165$		0			0
$166$	6.12526	−	10.6093i	0.475412	−	0.823438i
$167$	7.14183	+	12.3700i	0.552651	+	0.957220i	0.998082	+	0.0619037i	$0.0197172\pi$
$167$	7.14183	+	12.3700i	0.552651	+	0.957220i	−0.445431	+	0.895316i	$0.646949\pi$
$168$		0			0
$169$	−10.8130	+	18.7287i	−0.831770	+	1.44067i
$170$	−3.89714	−	6.75005i	−0.298897	−	0.517705i
$171$		0			0
$172$	−2.18820	+	3.79008i	−0.166849	+	0.288991i
$173$	−1.96561			−0.149442			−0.0747211	−	0.997204i	$-0.523807\pi$
$173$	−1.96561			−0.149442			−0.0747211	+	0.997204i	$0.523807\pi$
$174$		0			0
$175$	−0.0665372	+	2.64491i	−0.00502974	+	0.199937i
$176$	0.480820	+	0.832805i	0.0362432	+	0.0627751i
$177$		0			0
$178$	−2.85680	−	4.94812i	−0.214126	−	0.370877i
$179$	−7.02161	+	12.1618i	−0.524819	+	0.909014i	0.474763	+	0.880114i	$0.342534\pi$
$179$	−7.02161	+	12.1618i	−0.524819	+	0.909014i	−0.999582	+	0.0289001i	$0.990800\pi$
$180$		0			0
$181$	−17.5794			−1.30667			−0.653334	−	0.757070i	$-0.726630\pi$
$181$	−17.5794			−1.30667			−0.653334	+	0.757070i	$0.726630\pi$
$182$	0.391531	−	15.5637i	0.0290222	−	1.15366i
$183$		0			0
$184$	1.95495	−	3.38607i	0.144121	−	0.249624i
$185$	11.6957			0.859888
$186$		0			0
$187$	−7.49530			−0.548111
$188$	3.55502			0.259276
$189$		0			0
$190$	−1.54887			−0.112367
$191$	19.3643			1.40115			0.700577	−	0.713577i	$-0.252926\pi$
$191$	19.3643			1.40115			0.700577	+	0.713577i	$0.252926\pi$
$192$		0			0
$193$	−15.9094			−1.14518			−0.572592	−	0.819841i	$-0.694062\pi$
$193$	−15.9094			−1.14518			−0.572592	+	0.819841i	$0.694062\pi$
$194$	−7.80249	+	13.5143i	−0.560186	+	0.970271i
$195$		0			0
$196$	3.19076	+	6.23049i	0.227911	+	0.445035i
$197$	−20.8910			−1.48842			−0.744211	−	0.667945i	$-0.767174\pi$
$197$	−20.8910			−1.48842			−0.744211	+	0.667945i	$0.767174\pi$
$198$		0			0
$199$	−6.51900	+	11.2912i	−0.462120	+	0.800415i	−0.999066	−	0.0432012i	$-0.986244\pi$
$199$	−6.51900	+	11.2912i	−0.462120	+	0.800415i	0.536947	+	0.843616i	$0.319578\pi$
$200$	0.500000	+	0.866025i	0.0353553	+	0.0612372i
$201$		0			0
$202$	4.80772	+	8.32722i	0.338270	+	0.585901i
$203$	−2.52468	+	1.37415i	−0.177198	+	0.0964468i
$204$		0			0
$205$	−2.30083			−0.160697
$206$	1.54448	−	2.67512i	0.107609	−	0.186385i
$207$		0			0
$208$	−2.94219	−	5.09603i	−0.204004	−	0.353346i
$209$	−0.744731	+	1.28991i	−0.0515141	+	0.0892250i
$210$		0			0
$211$	8.63625	+	14.9584i	0.594544	+	1.02978i	0.993611	+	0.112858i	$0.0360006\pi$
$211$	8.63625	+	14.9584i	0.594544	+	1.02978i	−0.399067	+	0.916922i	$0.630666\pi$
$212$	−0.274437	+	0.475340i	−0.0188484	+	0.0326465i
$213$		0			0
$214$	−1.73194	−	2.99980i	−0.118393	−	0.205062i
$215$	2.18820	+	3.79008i	0.149234	+	0.258481i
$216$		0			0
$217$	−5.77316	−	3.52963i	−0.391907	−	0.239607i
$218$	7.17178	−	12.4219i	0.485734	−	0.841316i
$219$		0			0
$220$	0.961641			0.0648338
$221$	45.8646			3.08519
$222$		0			0
$223$	−13.6681	+	23.6739i	−0.915287	+	1.58532i	−0.108806	+	0.994063i	$0.534703\pi$
$223$	−13.6681	+	23.6739i	−0.915287	+	1.58532i	−0.806481	+	0.591261i	$0.798630\pi$
$224$	2.25729	+	1.38008i	0.150822	+	0.0922105i
$225$		0			0
$226$	0.362337	+	0.627585i	0.0241023	+	0.0417464i
$227$	3.73097	+	6.46223i	0.247633	+	0.428914i	0.962869	−	0.269970i	$-0.0870138\pi$
$227$	3.73097	+	6.46223i	0.247633	+	0.428914i	−0.715235	+	0.698884i	$0.753681\pi$
$228$		0			0
$229$	4.73672	−	8.20425i	0.313012	−	0.542152i	−0.666001	−	0.745951i	$-0.731995\pi$
$229$	4.73672	−	8.20425i	0.313012	−	0.542152i	0.979013	+	0.203799i	$0.0653288\pi$
$230$	−1.95495	−	3.38607i	−0.128905	−	0.223271i
$231$		0			0
$232$	−0.543215	+	0.940877i	−0.0356638	+	0.0617716i
$233$	−7.21133	−	12.4904i	−0.472430	−	0.818272i	0.527072	−	0.849820i	$-0.323290\pi$
$233$	−7.21133	−	12.4904i	−0.472430	−	0.818272i	−0.999502	+	0.0315480i	$0.989956\pi$
$234$		0			0
$235$	1.77751	−	3.07874i	0.115952	−	0.200835i
$236$	6.00868			0.391132
$237$		0			0
$238$	−18.1126	+	9.85847i	−1.17407	+	0.639030i
$239$	4.82726	+	8.36106i	0.312249	+	0.540832i	0.978849	−	0.204584i	$-0.0655842\pi$
$239$	4.82726	+	8.36106i	0.312249	+	0.540832i	−0.666600	+	0.745416i	$0.732251\pi$
$240$		0			0
$241$	2.08005	+	3.60276i	0.133988	+	0.232074i	0.925210	−	0.379454i	$-0.123888\pi$
$241$	2.08005	+	3.60276i	0.133988	+	0.232074i	−0.791222	+	0.611529i	$0.790555\pi$
$242$	−5.03762	+	8.72542i	−0.323831	+	0.560891i
$243$		0			0
$244$	14.6881			0.940312
$245$	6.99115	+	0.351971i	0.446648	+	0.0224866i
$246$		0			0
$247$	4.55709	−	7.89311i	0.289961	−	0.502227i
$248$	−2.55756			−0.162405
$249$		0			0
$250$	1.00000			0.0632456
$251$	−22.3874			−1.41308			−0.706539	−	0.707674i	$-0.749745\pi$
$251$	−22.3874			−1.41308			−0.706539	+	0.707674i	$0.749745\pi$
$252$		0			0
$253$	−3.75991			−0.236384
$254$	−13.1020			−0.822095
$255$		0			0
$256$	1.00000			0.0625000
$257$	−7.74058	+	13.4071i	−0.482844	+	0.836311i	−0.999806	−	0.0196976i	$-0.993730\pi$
$257$	−7.74058	+	13.4071i	−0.482844	+	0.836311i	0.516962	+	0.856009i	$0.327063\pi$
$258$		0			0
$259$	0.778202	−	30.9342i	0.0483551	−	1.92216i
$260$	−5.88439			−0.364934
$261$		0			0
$262$	8.75462	−	15.1634i	0.540862	−	0.936801i
$263$	7.85472	+	13.6048i	0.484343	+	0.838906i	0.999838	−	0.0179863i	$-0.00572553\pi$
$263$	7.85472	+	13.6048i	0.484343	+	0.838906i	−0.515496	+	0.856892i	$0.672392\pi$
$264$		0			0
$265$	0.274437	+	0.475340i	0.0168586	+	0.0291999i
$266$	−0.103058	+	4.09664i	−0.00631888	+	0.251181i
$267$		0			0
$268$	−0.821956			−0.0502089
$269$	4.56038	−	7.89882i	0.278052	−	0.481599i	−0.692849	−	0.721083i	$-0.743645\pi$
$269$	4.56038	−	7.89882i	0.278052	−	0.481599i	0.970900	+	0.239483i	$0.0769781\pi$
$270$		0			0
$271$	13.3929	+	23.1972i	0.813561	+	1.40913i	0.910357	+	0.413825i	$0.135807\pi$
$271$	13.3929	+	23.1972i	0.813561	+	1.40913i	−0.0967955	+	0.995304i	$0.530859\pi$
$272$	−3.89714	+	6.75005i	−0.236299	+	0.409282i
$273$		0			0
$274$	4.34792	+	7.53082i	0.262668	+	0.454954i
$275$	0.480820	−	0.832805i	0.0289946	−	0.0502201i
$276$		0			0
$277$	−2.22622	−	3.85593i	−0.133761	−	0.231680i	0.791363	−	0.611347i	$-0.209372\pi$
$277$	−2.22622	−	3.85593i	−0.133761	−	0.231680i	−0.925123	+	0.379667i	$0.876039\pi$
$278$	6.56877	+	11.3774i	0.393969	+	0.682374i
$279$		0			0
$280$	2.32383	−	1.26483i	0.138876	−	0.0755883i
$281$	−10.7630	+	18.6420i	−0.642065	+	1.11209i	0.342906	+	0.939370i	$0.388589\pi$
$281$	−10.7630	+	18.6420i	−0.642065	+	1.11209i	−0.984971	+	0.172720i	$0.944745\pi$
$282$		0			0
$283$	−5.49623			−0.326717			−0.163358	−	0.986567i	$-0.552233\pi$
$283$	−5.49623			−0.326717			−0.163358	+	0.986567i	$0.552233\pi$
$284$	3.96164			0.235080
$285$		0			0
$286$	−2.82933	+	4.90055i	−0.167302	+	0.289776i
$287$	−0.153091	+	6.08550i	−0.00903667	+	0.359216i
$288$		0			0
$289$	−21.8754	−	37.8893i	−1.28679	−	2.22878i
$290$	0.543215	+	0.940877i	0.0318987	+	0.0552502i
$291$		0			0
$292$	0.368764	−	0.638718i	0.0215803	−	0.0373781i
$293$	−7.28966	−	12.6261i	−0.425866	−	0.737622i	0.570635	−	0.821204i	$-0.306697\pi$
$293$	−7.28966	−	12.6261i	−0.425866	−	0.737622i	−0.996501	+	0.0835819i	$0.973364\pi$
$294$		0			0
$295$	3.00434	−	5.20367i	0.174919	−	0.302969i
$296$	−5.84787	−	10.1288i	−0.339900	−	0.588725i
$297$		0			0
$298$	8.49218	−	14.7089i	0.491939	−	0.852063i
$299$	23.0073			1.33055
$300$		0			0
$301$	10.1700	−	5.53543i	0.586191	−	0.319057i
$302$	−7.91384	−	13.7072i	−0.455390	−	0.788759i
$303$		0			0
$304$	0.774437	+	1.34137i	0.0444170	+	0.0769326i
$305$	7.34407	−	12.7203i	0.420520	−	0.728362i
$306$		0			0
$307$	3.42914			0.195712			0.0978558	−	0.995201i	$-0.468802\pi$
$307$	3.42914			0.195712			0.0978558	+	0.995201i	$0.468802\pi$
$308$	0.0639849	−	2.54346i	0.00364588	−	0.144927i
$309$		0			0
$310$	−1.27878	+	2.21491i	−0.0726297	+	0.125798i
$311$	34.6413			1.96433			0.982164	−	0.188025i	$-0.0602087\pi$
$311$	34.6413			1.96433			0.982164	+	0.188025i	$0.0602087\pi$
$312$		0			0
$313$	30.5887			1.72897			0.864487	−	0.502655i	$-0.167644\pi$
$313$	30.5887			1.72897			0.864487	+	0.502655i	$0.167644\pi$
$314$	−10.6557			−0.601336
$315$		0			0
$316$	−6.79796			−0.382415
$317$	10.0424			0.564039			0.282020	−	0.959409i	$-0.408996\pi$
$317$	10.0424			0.564039			0.282020	+	0.959409i	$0.408996\pi$
$318$		0			0
$319$	1.04476			0.0584951
$320$	0.500000	−	0.866025i	0.0279508	−	0.0484123i
$321$		0			0
$322$	−9.08593	+	4.94537i	−0.506339	+	0.275594i
$323$	−12.0724			−0.671724
$324$		0			0
$325$	−2.94219	+	5.09603i	−0.163204	+	0.282677i
$326$	−3.88853	−	6.73513i	−0.215366	−	0.373024i
$327$		0			0
$328$	1.15042	+	1.99258i	0.0635211	+	0.110022i
$329$	−8.02472	−	4.90621i	−0.442417	−	0.270488i
$330$		0			0
$331$	−14.4680			−0.795234			−0.397617	−	0.917551i	$-0.630163\pi$
$331$	−14.4680			−0.795234			−0.397617	+	0.917551i	$0.630163\pi$
$332$	−6.12526	+	10.6093i	−0.336167	+	0.582258i
$333$		0			0
$334$	−7.14183	−	12.3700i	−0.390783	−	0.676857i
$335$	−0.410978	+	0.711834i	−0.0224541	+	0.0388917i
$336$		0			0
$337$	0.772692	+	1.33834i	0.0420912	+	0.0729041i	0.886304	−	0.463105i	$-0.153265\pi$
$337$	0.772692	+	1.33834i	0.0420912	+	0.0729041i	−0.844212	+	0.536009i	$0.819931\pi$
$338$	10.8130	−	18.7287i	0.588150	−	1.01871i
$339$		0			0
$340$	3.89714	+	6.75005i	0.211352	+	0.366073i
$341$	1.22973	+	2.12995i	0.0665934	+	0.115343i
$342$		0			0
$343$	1.39610	−	18.4676i	0.0753825	−	0.997155i
$344$	2.18820	−	3.79008i	0.117980	−	0.204348i
$345$		0			0
$346$	1.96561			0.105672
$347$	−13.1517			−0.706021			−0.353011	−	0.935619i	$-0.614842\pi$
$347$	−13.1517			−0.706021			−0.353011	+	0.935619i	$0.614842\pi$
$348$		0			0
$349$	0.752263	−	1.30296i	0.0402677	−	0.0697457i	−0.845189	−	0.534467i	$-0.820512\pi$
$349$	0.752263	−	1.30296i	0.0402677	−	0.0697457i	0.885457	+	0.464722i	$0.153846\pi$
$350$	0.0665372	−	2.64491i	0.00355656	−	0.141377i
$351$		0			0
$352$	−0.480820	−	0.832805i	−0.0256278	−	0.0443887i
$353$	−18.0095	−	31.1933i	−0.958547	−	1.66025i	−0.726033	−	0.687660i	$-0.758638\pi$
$353$	−18.0095	−	31.1933i	−0.958547	−	1.66025i	−0.232515	−	0.972593i	$-0.574695\pi$
$354$		0			0
$355$	1.98082	−	3.43088i	0.105131	−	0.182092i
$356$	2.85680	+	4.94812i	0.151410	+	0.262250i
$357$		0			0
$358$	7.02161	−	12.1618i	0.371103	−	0.642770i
$359$	−6.85269	−	11.8692i	−0.361671	−	0.626433i	0.626565	−	0.779369i	$-0.284460\pi$
$359$	−6.85269	−	11.8692i	−0.361671	−	0.626433i	−0.988236	+	0.152936i	$0.951127\pi$
$360$		0			0
$361$	8.30049	−	14.3769i	0.436868	−	0.756678i
$362$	17.5794			0.923953
$363$		0			0
$364$	−0.391531	+	15.5637i	−0.0205218	+	0.815760i
$365$	−0.368764	−	0.638718i	−0.0193020	−	0.0334320i
$366$		0			0
$367$	−16.0160	−	27.7406i	−0.836029	−	1.44805i	−0.893190	−	0.449680i	$-0.851538\pi$
$367$	−16.0160	−	27.7406i	−0.836029	−	1.44805i	0.0571604	−	0.998365i	$-0.481795\pi$
$368$	−1.95495	+	3.38607i	−0.101909	+	0.176511i
$369$		0			0
$370$	−11.6957			−0.608032
$371$	1.27549	−	0.694236i	0.0662203	−	0.0360429i
$372$		0			0
$373$	−3.86024	+	6.68613i	−0.199876	+	0.346195i	−0.948488	−	0.316813i	$-0.897387\pi$
$373$	−3.86024	+	6.68613i	−0.199876	+	0.346195i	0.748612	+	0.663008i	$0.230720\pi$
$374$	7.49530			0.387573
$375$		0			0
$376$	−3.55502			−0.183336
$377$	−6.39298			−0.329255
$378$		0			0
$379$	−2.47157			−0.126956			−0.0634780	−	0.997983i	$-0.520219\pi$
$379$	−2.47157			−0.126956			−0.0634780	+	0.997983i	$0.520219\pi$
$380$	1.54887			0.0794556
$381$		0			0
$382$	−19.3643			−0.990766
$383$	12.3131	−	21.3268i	0.629168	−	1.08975i	−0.358552	−	0.933510i	$-0.616729\pi$
$383$	12.3131	−	21.3268i	0.629168	−	1.08975i	0.987719	−	0.156240i	$-0.0499374\pi$
$384$		0			0
$385$	−2.17071	−	1.32714i	−0.110629	−	0.0676374i
$386$	15.9094			0.809767
$387$		0			0
$388$	7.80249	−	13.5143i	0.396112	−	0.686085i
$389$	−4.14338	−	7.17655i	−0.210078	−	0.363866i	0.741661	−	0.670775i	$-0.234038\pi$
$389$	−4.14338	−	7.17655i	−0.210078	−	0.363866i	−0.951739	+	0.306909i	$0.900705\pi$
$390$		0			0
$391$	−15.2374	−	26.3920i	−0.770588	−	1.33470i
$392$	−3.19076	−	6.23049i	−0.161158	−	0.314688i
$393$		0			0
$394$	20.8910			1.05247
$395$	−3.39898	+	5.88720i	−0.171021	+	0.296217i
$396$		0			0
$397$	9.42143	+	16.3184i	0.472848	+	0.818997i	0.999517	−	0.0310737i	$-0.00989266\pi$
$397$	9.42143	+	16.3184i	0.472848	+	0.818997i	−0.526669	+	0.850070i	$0.676559\pi$
$398$	6.51900	−	11.2912i	0.326768	−	0.565979i
$399$		0			0
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	−5.84903	+	10.1308i	−0.292087	+	0.505909i	−0.974303	−	0.225241i	$-0.927683\pi$
$401$	−5.84903	+	10.1308i	−0.292087	+	0.505909i	0.682216	+	0.731150i	$0.261016\pi$
$402$		0			0
$403$	−7.52483	−	13.0334i	−0.374838	−	0.649239i
$404$	−4.80772	−	8.32722i	−0.239193	−	0.414295i
$405$		0			0
$406$	2.52468	−	1.37415i	0.125298	−	0.0681982i
$407$	−5.62355	+	9.74027i	−0.278749	+	0.482807i
$408$		0			0
$409$	−18.0739			−0.893695			−0.446848	−	0.894610i	$-0.647453\pi$
$409$	−18.0739			−0.893695			−0.446848	+	0.894610i	$0.647453\pi$
$410$	2.30083			0.113630
$411$		0			0
$412$	−1.54448	+	2.67512i	−0.0760913	+	0.131794i
$413$	−13.5634	−	8.29246i	−0.667409	−	0.408045i
$414$		0			0
$415$	6.12526	+	10.6093i	0.300677	+	0.520788i
$416$	2.94219	+	5.09603i	0.144253	+	0.249853i
$417$		0			0
$418$	0.744731	−	1.28991i	0.0364260	−	0.0630916i
$419$	−9.88791	−	17.1264i	−0.483056	−	0.836677i	0.516755	−	0.856133i	$-0.327140\pi$
$419$	−9.88791	−	17.1264i	−0.483056	−	0.836677i	−0.999811	+	0.0194561i	$0.993807\pi$
$420$		0			0
$421$	−15.4734	+	26.8008i	−0.754129	+	1.30619i	0.191677	+	0.981458i	$0.438608\pi$
$421$	−15.4734	+	26.8008i	−0.754129	+	1.30619i	−0.945806	+	0.324732i	$0.894726\pi$
$422$	−8.63625	−	14.9584i	−0.420406	−	0.728164i
$423$		0			0
$424$	0.274437	−	0.475340i	0.0133279	−	0.0230845i
$425$	7.79428			0.378078
$426$		0			0
$427$	−33.1555	−	20.2708i	−1.60450	−	0.980973i
$428$	1.73194	+	2.99980i	0.0837163	+	0.145001i
$429$		0			0
$430$	−2.18820	−	3.79008i	−0.105525	−	0.182774i
$431$	−1.01707	+	1.76162i	−0.0489907	+	0.0848544i	−0.889481	−	0.456972i	$-0.848934\pi$
$431$	−1.01707	+	1.76162i	−0.0489907	+	0.0848544i	0.840490	+	0.541827i	$0.182267\pi$
$432$		0			0
$433$	−17.9368			−0.861989			−0.430994	−	0.902355i	$-0.641837\pi$
$433$	−17.9368			−0.861989			−0.430994	+	0.902355i	$0.641837\pi$
$434$	5.77316	+	3.52963i	0.277120	+	0.169428i
$435$		0			0
$436$	−7.17178	+	12.4219i	−0.343466	+	0.594900i
$437$	−6.05593			−0.289695
$438$		0			0
$439$	−34.2741			−1.63581			−0.817906	−	0.575352i	$-0.804865\pi$
$439$	−34.2741			−1.63581			−0.817906	+	0.575352i	$0.804865\pi$
$440$	−0.961641			−0.0458444
$441$		0			0
$442$	−45.8646			−2.18156
$443$	−13.9945			−0.664901			−0.332451	−	0.943121i	$-0.607875\pi$
$443$	−13.9945			−0.664901			−0.332451	+	0.943121i	$0.607875\pi$
$444$		0			0
$445$	5.71360			0.270850
$446$	13.6681	−	23.6739i	0.647206	−	1.12099i
$447$		0			0
$448$	−2.25729	−	1.38008i	−0.106647	−	0.0652027i
$449$	−24.3772			−1.15043			−0.575215	−	0.818002i	$-0.695082\pi$
$449$	−24.3772			−1.15043			−0.575215	+	0.818002i	$0.695082\pi$
$450$		0			0
$451$	1.10629	−	1.91614i	0.0520930	−	0.0902277i
$452$	−0.362337	−	0.627585i	−0.0170429	−	0.0295191i
$453$		0			0
$454$	−3.73097	−	6.46223i	−0.175103	−	0.303288i
$455$	13.2828	+	8.12093i	0.622707	+	0.380715i
$456$		0			0
$457$	−34.3746			−1.60798			−0.803989	−	0.594644i	$-0.797293\pi$
$457$	−34.3746			−1.60798			−0.803989	+	0.594644i	$0.797293\pi$
$458$	−4.73672	+	8.20425i	−0.221333	+	0.383359i
$459$		0			0
$460$	1.95495	+	3.38607i	0.0911498	+	0.157876i
$461$	14.6870	−	25.4386i	0.684042	−	1.18479i	−0.289695	−	0.957119i	$-0.593554\pi$
$461$	14.6870	−	25.4386i	0.684042	−	1.18479i	0.973737	−	0.227676i	$-0.0731127\pi$
$462$		0			0
$463$	10.5391	+	18.2542i	0.489792	+	0.848345i	0.999931	−	0.0117473i	$-0.00373938\pi$
$463$	10.5391	+	18.2542i	0.489792	+	0.848345i	−0.510139	+	0.860092i	$0.670406\pi$
$464$	0.543215	−	0.940877i	0.0252181	−	0.0436791i
$465$		0			0
$466$	7.21133	+	12.4904i	0.334058	+	0.578606i
$467$	20.8663	+	36.1415i	0.965578	+	1.67243i	0.708054	+	0.706158i	$0.249573\pi$
$467$	20.8663	+	36.1415i	0.965578	+	1.67243i	0.257524	+	0.966272i	$0.417093\pi$
$468$		0			0
$469$	1.85540	+	1.13436i	0.0856742	+	0.0523801i
$470$	−1.77751	+	3.07874i	−0.0819904	+	0.142012i
$471$		0			0
$472$	−6.00868			−0.276572
$473$	−4.20853			−0.193509
$474$		0			0
$475$	0.774437	−	1.34137i	0.0355336	−	0.0615460i
$476$	18.1126	−	9.85847i	0.830190	−	0.451862i
$477$		0			0
$478$	−4.82726	−	8.36106i	−0.220794	−	0.382426i
$479$	−9.11638	−	15.7900i	−0.416538	−	0.721465i	0.579051	−	0.815292i	$-0.303423\pi$
$479$	−9.11638	−	15.7900i	−0.416538	−	0.721465i	−0.995589	+	0.0938267i	$0.970090\pi$
$480$		0			0
$481$	34.4111	−	59.6018i	1.56901	−	2.71761i
$482$	−2.08005	−	3.60276i	−0.0947438	−	0.164101i
$483$		0			0
$484$	5.03762	−	8.72542i	0.228983	−	0.396610i
$485$	−7.80249	−	13.5143i	−0.354293	−	0.613653i
$486$		0			0
$487$	12.5910	−	21.8083i	0.570554	−	0.988228i	−0.425956	−	0.904744i	$-0.640062\pi$
$487$	12.5910	−	21.8083i	0.570554	−	0.988228i	0.996509	−	0.0834838i	$-0.0266047\pi$
$488$	−14.6881			−0.664901
$489$		0			0
$490$	−6.99115	−	0.351971i	−0.315828	−	0.0159004i
$491$	−18.6196	−	32.2501i	−0.840290	−	1.45542i	−0.889650	−	0.456644i	$-0.849051\pi$
$491$	−18.6196	−	32.2501i	−0.840290	−	1.45542i	0.0493598	−	0.998781i	$-0.484282\pi$
$492$		0			0
$493$	4.23397	+	7.33346i	0.190689	+	0.330282i
$494$	−4.55709	+	7.89311i	−0.205033	+	0.355128i
$495$		0			0
$496$	2.55756			0.114838
$497$	−8.94259	−	5.46738i	−0.401130	−	0.245246i
$498$		0			0
$499$	−3.69263	+	6.39582i	−0.165305	+	0.286316i	−0.936763	−	0.349963i	$-0.886194\pi$
$499$	−3.69263	+	6.39582i	−0.165305	+	0.286316i	0.771459	+	0.636279i	$0.219527\pi$
$500$	−1.00000			−0.0447214
$501$		0			0
$502$	22.3874			0.999197
$503$	18.0307			0.803947			0.401974	−	0.915651i	$-0.368324\pi$
$503$	18.0307			0.803947			0.401974	+	0.915651i	$0.368324\pi$
$504$		0			0
$505$	−9.61545			−0.427882
$506$	3.75991			0.167149
$507$		0			0
$508$	13.1020			0.581309
$509$	10.9524	−	18.9701i	0.485457	−	0.840836i	−0.514403	−	0.857548i	$-0.671987\pi$
$509$	10.9524	−	18.9701i	0.485457	−	0.840836i	0.999860	+	0.0167122i	$0.00531991\pi$
$510$		0			0
$511$	−1.71389	+	0.932851i	−0.0758181	+	0.0412669i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	7.74058	−	13.4071i	0.341423	−	0.591361i
$515$	1.54448	+	2.67512i	0.0680581	+	0.117880i
$516$		0			0
$517$	1.70933	+	2.96064i	0.0751761	+	0.130209i
$518$	−0.778202	+	30.9342i	−0.0341922	+	1.35917i
$519$		0			0
$520$	5.88439			0.258047
$521$	12.3028	−	21.3090i	0.538994	−	0.933565i	−0.459964	−	0.887937i	$-0.652138\pi$
$521$	12.3028	−	21.3090i	0.538994	−	0.933565i	0.998959	−	0.0456279i	$-0.0145289\pi$
$522$		0			0
$523$	−1.34318	−	2.32646i	−0.0587333	−	0.101729i	0.835164	−	0.550001i	$-0.185373\pi$
$523$	−1.34318	−	2.32646i	−0.0587333	−	0.101729i	−0.893897	+	0.448272i	$0.852039\pi$
$524$	−8.75462	+	15.1634i	−0.382447	+	0.662418i
$525$		0			0
$526$	−7.85472	−	13.6048i	−0.342482	−	0.593196i
$527$	−9.96715	+	17.2636i	−0.434176	+	0.752015i
$528$		0			0
$529$	3.85637	+	6.67943i	0.167668	+	0.290410i
$530$	−0.274437	−	0.475340i	−0.0119208	−	0.0206474i
$531$		0			0
$532$	0.103058	−	4.09664i	0.00446812	−	0.177612i
$533$	−6.76949	+	11.7251i	−0.293219	+	0.507871i
$534$		0			0
$535$	3.46387			0.149756
$536$	0.821956			0.0355031
$537$		0			0
$538$	−4.56038	+	7.89882i	−0.196612	+	0.340542i
$539$	−3.65461	+	5.65303i	−0.157415	+	0.243493i
$540$		0			0
$541$	13.7482	+	23.8125i	0.591080	+	1.02378i	0.994087	+	0.108584i	$0.0346315\pi$
$541$	13.7482	+	23.8125i	0.591080	+	1.02378i	−0.403007	+	0.915197i	$0.632035\pi$
$542$	−13.3929	−	23.1972i	−0.575275	−	0.996405i
$543$		0			0
$544$	3.89714	−	6.75005i	0.167089	−	0.289406i
$545$	7.17178	+	12.4219i	0.307205	+	0.532095i
$546$		0			0
$547$	0.0925609	−	0.160320i	0.00395762	−	0.00685480i	−0.864040	−	0.503423i	$-0.832074\pi$
$547$	0.0925609	−	0.160320i	0.00395762	−	0.00685480i	0.867997	+	0.496569i	$0.165407\pi$
$548$	−4.34792	−	7.53082i	−0.185734	−	0.321701i
$549$		0			0
$550$	−0.480820	+	0.832805i	−0.0205023	+	0.0355109i
$551$	1.68275			0.0716874
$552$		0			0
$553$	15.3450	+	9.38173i	0.652535	+	0.398952i
$554$	2.22622	+	3.85593i	0.0945831	+	0.163823i
$555$		0			0
$556$	−6.56877	−	11.3774i	−0.278578	−	0.482511i
$557$	12.0082	−	20.7988i	0.508804	−	0.881275i	−0.491144	−	0.871079i	$-0.663421\pi$
$557$	12.0082	−	20.7988i	0.508804	−	0.881275i	0.999948	−	0.0101964i	$-0.00324568\pi$
$558$		0			0
$559$	25.7525			1.08921
$560$	−2.32383	+	1.26483i	−0.0981998	+	0.0534490i
$561$		0			0
$562$	10.7630	−	18.6420i	0.454009	−	0.786366i
$563$	14.3498			0.604771			0.302385	−	0.953186i	$-0.402217\pi$
$563$	14.3498			0.604771			0.302385	+	0.953186i	$0.402217\pi$
$564$		0			0
$565$	−0.724673			−0.0304872
$566$	5.49623			0.231024
$567$		0			0
$568$	−3.96164			−0.166227
$569$	9.24379			0.387520			0.193760	−	0.981049i	$-0.437932\pi$
$569$	9.24379			0.387520			0.193760	+	0.981049i	$0.437932\pi$
$570$		0			0
$571$	41.3063			1.72861			0.864307	−	0.502965i	$-0.167757\pi$
$571$	41.3063			1.72861			0.864307	+	0.502965i	$0.167757\pi$
$572$	2.82933	−	4.90055i	0.118300	−	0.204902i
$573$		0			0
$574$	0.153091	−	6.08550i	0.00638989	−	0.254004i
$575$	3.90989			0.163054
$576$		0			0
$577$	−0.822047	+	1.42383i	−0.0342223	+	0.0592747i	−0.882629	−	0.470070i	$-0.844229\pi$
$577$	−0.822047	+	1.42383i	−0.0342223	+	0.0592747i	0.848407	+	0.529344i	$0.177562\pi$
$578$	21.8754	+	37.8893i	0.909897	+	1.57599i
$579$		0			0
$580$	−0.543215	−	0.940877i	−0.0225558	−	0.0390678i
$581$	28.4681	−	15.4949i	1.18106	−	0.642835i
$582$		0			0
$583$	−0.527821			−0.0218601
$584$	−0.368764	+	0.638718i	−0.0152596	+	0.0264303i
$585$		0			0
$586$	7.28966	+	12.6261i	0.301133	+	0.521578i
$587$	14.5885	−	25.2681i	0.602133	−	1.04292i	−0.390365	−	0.920660i	$-0.627651\pi$
$587$	14.5885	−	25.2681i	0.602133	−	1.04292i	0.992498	−	0.122264i	$-0.0390156\pi$
$588$		0			0
$589$	1.98067	+	3.43062i	0.0816120	+	0.141356i
$590$	−3.00434	+	5.20367i	−0.123687	+	0.214232i
$591$		0			0
$592$	5.84787	+	10.1288i	0.240346	+	0.416291i
$593$	15.0169	+	26.0101i	0.616672	+	1.06811i	0.990089	+	0.140444i	$0.0448529\pi$
$593$	15.0169	+	26.0101i	0.616672	+	1.06811i	−0.373417	+	0.927664i	$0.621814\pi$
$594$		0			0
$595$	0.518610	−	20.6152i	0.0212609	−	0.845141i
$596$	−8.49218	+	14.7089i	−0.347853	+	0.602500i
$597$		0			0
$598$	−23.0073			−0.940839
$599$	−37.8792			−1.54770			−0.773851	−	0.633368i	$-0.781672\pi$
$599$	−37.8792			−1.54770			−0.773851	+	0.633368i	$0.781672\pi$
$600$		0			0
$601$	−6.77702	+	11.7381i	−0.276441	+	0.478809i	−0.970498	−	0.241111i	$-0.922488\pi$
$601$	−6.77702	+	11.7381i	−0.276441	+	0.478809i	0.694057	+	0.719920i	$0.255822\pi$
$602$	−10.1700	+	5.53543i	−0.414500	+	0.225607i
$603$		0			0
$604$	7.91384	+	13.7072i	0.322009	+	0.557737i
$605$	−5.03762	−	8.72542i	−0.204809	−	0.354739i
$606$		0			0
$607$	−11.8784	+	20.5739i	−0.482127	+	0.835069i	−0.999790	−	0.0205159i	$-0.993469\pi$
$607$	−11.8784	+	20.5739i	−0.482127	+	0.835069i	0.517662	+	0.855585i	$0.326802\pi$
$608$	−0.774437	−	1.34137i	−0.0314076	−	0.0543995i
$609$		0			0
$610$	−7.34407	+	12.7203i	−0.297353	+	0.515030i
$611$	−10.4596	−	18.1165i	−0.423148	−	0.732914i
$612$		0			0
$613$	4.72021	−	8.17564i	0.190647	−	0.330211i	−0.754818	−	0.655935i	$-0.772275\pi$
$613$	4.72021	−	8.17564i	0.190647	−	0.330211i	0.945465	+	0.325724i	$0.105608\pi$
$614$	−3.42914			−0.138389
$615$		0			0
$616$	−0.0639849	+	2.54346i	−0.00257803	+	0.102479i
$617$	−8.40889	−	14.5646i	−0.338529	−	0.586350i	0.645627	−	0.763653i	$-0.276596\pi$
$617$	−8.40889	−	14.5646i	−0.338529	−	0.586350i	−0.984156	+	0.177303i	$0.943263\pi$
$618$		0			0
$619$	16.3229	+	28.2721i	0.656073	+	1.13635i	0.981624	+	0.190827i	$0.0611171\pi$
$619$	16.3229	+	28.2721i	0.656073	+	1.13635i	−0.325551	+	0.945525i	$0.605550\pi$
$620$	1.27878	−	2.21491i	0.0513570	−	0.0889529i
$621$		0			0
$622$	−34.6413			−1.38899
$623$	0.380167	−	15.1120i	0.0152311	−	0.605449i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−30.5887			−1.22257
$627$		0			0
$628$	10.6557			0.425209
$629$	−91.1598			−3.63478
$630$		0			0
$631$	0.702170			0.0279530			0.0139765	−	0.999902i	$-0.495551\pi$
$631$	0.702170			0.0279530			0.0139765	+	0.999902i	$0.495551\pi$
$632$	6.79796			0.270408
$633$		0			0
$634$	−10.0424			−0.398836
$635$	6.55102	−	11.3467i	0.259969	−	0.450280i
$636$		0			0
$637$	22.3630	−	34.5915i	0.886053	−	1.37057i
$638$	−1.04476			−0.0413623
$639$		0			0
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	12.7260	+	22.0421i	0.502647	+	0.870610i	0.999995	+	0.00305935i	$0.000973824\pi$
$641$	12.7260	+	22.0421i	0.502647	+	0.870610i	−0.497348	+	0.867551i	$0.665693\pi$
$642$		0			0
$643$	3.50111	+	6.06410i	0.138070	+	0.239145i	0.926766	−	0.375639i	$-0.122577\pi$
$643$	3.50111	+	6.06410i	0.138070	+	0.239145i	−0.788696	+	0.614784i	$0.789243\pi$
$644$	9.08593	−	4.94537i	0.358036	−	0.194875i
$645$		0			0
$646$	12.0724			0.474981
$647$	18.5443	−	32.1197i	0.729052	−	1.26276i	−0.228232	−	0.973607i	$-0.573294\pi$
$647$	18.5443	−	32.1197i	0.729052	−	1.26276i	0.957284	−	0.289149i	$-0.0933723\pi$
$648$		0			0
$649$	2.88910	+	5.00406i	0.113407	+	0.196427i
$650$	2.94219	−	5.09603i	0.115402	−	0.199883i
$651$		0			0
$652$	3.88853	+	6.73513i	0.152287	+	0.263768i
$653$	−11.8804	+	20.5774i	−0.464916	+	0.805258i	−0.999198	−	0.0400487i	$-0.987249\pi$
$653$	−11.8804	+	20.5774i	−0.464916	+	0.805258i	0.534282	+	0.845306i	$0.320582\pi$
$654$		0			0
$655$	8.75462	+	15.1634i	0.342071	+	0.592485i
$656$	−1.15042	−	1.99258i	−0.0449162	−	0.0777971i
$657$		0			0
$658$	8.02472	+	4.90621i	0.312836	+	0.191264i
$659$	6.82703	−	11.8248i	0.265943	−	0.460627i	−0.701867	−	0.712308i	$-0.747650\pi$
$659$	6.82703	−	11.8248i	0.265943	−	0.460627i	0.967810	+	0.251681i	$0.0809833\pi$
$660$		0			0
$661$	−0.987650			−0.0384151			−0.0192076	−	0.999816i	$-0.506114\pi$
$661$	−0.987650			−0.0384151			−0.0192076	+	0.999816i	$0.506114\pi$
$662$	14.4680			0.562316
$663$		0			0
$664$	6.12526	−	10.6093i	0.237706	−	0.411719i
$665$	−3.49627	−	2.13757i	−0.135579	−	0.0828915i
$666$		0			0
$667$	2.12391	+	3.67873i	0.0822383	+	0.142441i
$668$	7.14183	+	12.3700i	0.276326	+	0.478610i
$669$		0			0
$670$	0.410978	−	0.711834i	0.0158775	−	0.0275006i
$671$	7.06236	+	12.2324i	0.272639	+	0.472225i
$672$		0			0
$673$	9.55432	−	16.5486i	0.368292	−	0.637901i	−0.621007	−	0.783805i	$-0.713276\pi$
$673$	9.55432	−	16.5486i	0.368292	−	0.637901i	0.989299	+	0.145905i	$0.0466093\pi$
$674$	−0.772692	−	1.33834i	−0.0297630	−	0.0515510i
$675$		0			0
$676$	−10.8130	+	18.7287i	−0.415885	+	0.720334i
$677$	−14.9499			−0.574571			−0.287285	−	0.957845i	$-0.592753\pi$
$677$	−14.9499			−0.574571			−0.287285	+	0.957845i	$0.592753\pi$
$678$		0			0
$679$	−36.2634	+	19.7377i	−1.39166	+	0.757464i
$680$	−3.89714	−	6.75005i	−0.149449	−	0.258852i
$681$		0			0
$682$	−1.22973	−	2.12995i	−0.0470886	−	0.0815599i
$683$	−12.5655	+	21.7641i	−0.480805	+	0.832779i	−0.999757	−	0.0220243i	$-0.992989\pi$
$683$	−12.5655	+	21.7641i	−0.480805	+	0.832779i	0.518952	+	0.854803i	$0.326322\pi$
$684$		0			0
$685$	−8.69584			−0.332251
$686$	−1.39610	+	18.4676i	−0.0533035	+	0.705095i
$687$		0			0
$688$	−2.18820	+	3.79008i	−0.0834245	+	0.144496i
$689$	3.22979			0.123045
$690$		0			0
$691$	−11.9676			−0.455271			−0.227635	−	0.973746i	$-0.573099\pi$
$691$	−11.9676			−0.455271			−0.227635	+	0.973746i	$0.573099\pi$
$692$	−1.96561			−0.0747211
$693$		0			0
$694$	13.1517			0.499233
$695$	−13.1375			−0.498335
$696$		0			0
$697$	17.9333			0.679273
$698$	−0.752263	+	1.30296i	−0.0284736	+	0.0493177i
$699$		0			0
$700$	−0.0665372	+	2.64491i	−0.00251487	+	0.0999684i
$701$	−0.886836			−0.0334953			−0.0167477	−	0.999860i	$-0.505331\pi$
$701$	−0.886836			−0.0334953			−0.0167477	+	0.999860i	$0.505331\pi$
$702$		0			0
$703$	−9.05762	+	15.6882i	−0.341614	+	0.591694i
$704$	0.480820	+	0.832805i	0.0181216	+	0.0313875i
$705$		0			0
$706$	18.0095	+	31.1933i	0.677795	+	1.17398i
$707$	−0.639785	+	25.4320i	−0.0240616	+	0.956470i
$708$		0			0
$709$	0.510807			0.0191838			0.00959189	−	0.999954i	$-0.496947\pi$
$709$	0.510807			0.0191838			0.00959189	+	0.999954i	$0.496947\pi$
$710$	−1.98082	+	3.43088i	−0.0743389	+	0.128759i
$711$		0			0
$712$	−2.85680	−	4.94812i	−0.107063	−	0.185439i
$713$	−4.99988	+	8.66005i	−0.187247	+	0.324322i
$714$		0			0
$715$	−2.82933	−	4.90055i	−0.105811	−	0.183270i
$716$	−7.02161	+	12.1618i	−0.262410	+	0.454507i
$717$		0			0
$718$	6.85269	+	11.8692i	0.255740	+	0.442955i
$719$	15.6774	+	27.1540i	0.584668	+	1.01268i	0.994917	+	0.100701i	$0.0321086\pi$
$719$	15.6774	+	27.1540i	0.584668	+	1.01268i	−0.410248	+	0.911974i	$0.634558\pi$
$720$		0			0
$721$	7.17824	−	3.90703i	0.267332	−	0.145506i
$722$	−8.30049	+	14.3769i	−0.308912	+	0.535052i
$723$		0			0
$724$	−17.5794			−0.653334
$725$	−1.08643			−0.0403490
$726$		0			0
$727$	−10.9429	+	18.9536i	−0.405848	+	0.702949i	−0.994420	−	0.105496i	$-0.966357\pi$
$727$	−10.9429	+	18.9536i	−0.405848	+	0.702949i	0.588572	+	0.808445i	$0.299690\pi$
$728$	0.391531	−	15.5637i	0.0145111	−	0.576829i
$729$		0			0
$730$	0.368764	+	0.638718i	0.0136486	+	0.0236400i
$731$	−17.0555	−	29.5410i	−0.630820	−	1.09261i
$732$		0			0
$733$	0.723740	−	1.25355i	0.0267320	−	0.0463011i	−0.852350	−	0.522972i	$-0.824823\pi$
$733$	0.723740	−	1.25355i	0.0267320	−	0.0463011i	0.879082	+	0.476671i	$0.158157\pi$
$734$	16.0160	+	27.7406i	0.591162	+	1.02392i
$735$		0			0
$736$	1.95495	−	3.38607i	0.0720603	−	0.124812i
$737$	−0.395213	−	0.684529i	−0.0145579	−	0.0252150i
$738$		0			0
$739$	−9.06843	+	15.7070i	−0.333588	+	0.577791i	−0.983212	−	0.182464i	$-0.941593\pi$
$739$	−9.06843	+	15.7070i	−0.333588	+	0.577791i	0.649625	+	0.760255i	$0.274926\pi$
$740$	11.6957			0.429944
$741$		0			0
$742$	−1.27549	+	0.694236i	−0.0468248	+	0.0254862i
$743$	−14.8404	−	25.7043i	−0.544440	−	0.942998i	−0.998642	−	0.0520988i	$-0.983409\pi$
$743$	−14.8404	−	25.7043i	−0.544440	−	0.942998i	0.454202	−	0.890899i	$-0.349924\pi$
$744$		0			0
$745$	8.49218	+	14.7089i	0.311129	+	0.538892i
$746$	3.86024	−	6.68613i	0.141333	−	0.244797i
$747$		0			0
$748$	−7.49530			−0.274055
$749$	0.230476	−	9.16165i	0.00842143	−	0.334759i
$750$		0			0
$751$	−6.22241	+	10.7775i	−0.227059	+	0.393277i	−0.956935	−	0.290302i	$-0.906244\pi$
$751$	−6.22241	+	10.7775i	−0.227059	+	0.393277i	0.729876	+	0.683579i	$0.239578\pi$
$752$	3.55502			0.129638
$753$		0			0
$754$	6.39298			0.232819
$755$	15.8277			0.576028
$756$		0			0
$757$	18.2077			0.661769			0.330885	−	0.943671i	$-0.392653\pi$
$757$	18.2077			0.661769			0.330885	+	0.943671i	$0.392653\pi$
$758$	2.47157			0.0897715
$759$		0			0
$760$	−1.54887			−0.0561836
$761$	5.52796	−	9.57471i	0.200388	−	0.347083i	−0.748265	−	0.663400i	$-0.769113\pi$
$761$	5.52796	−	9.57471i	0.200388	−	0.347083i	0.948654	+	0.316317i	$0.102446\pi$
$762$		0			0
$763$	33.3320	−	18.1422i	1.20670	−	0.656792i
$764$	19.3643			0.700577
$765$		0			0
$766$	−12.3131	+	21.3268i	−0.444889	+	0.770570i
$767$	−17.6787	−	30.6204i	−0.638341	−	1.10564i
$768$		0			0
$769$	−5.83441	−	10.1055i	−0.210394	−	0.364413i	0.741444	−	0.671015i	$-0.234141\pi$
$769$	−5.83441	−	10.1055i	−0.210394	−	0.364413i	−0.951838	+	0.306602i	$0.900808\pi$
$770$	2.17071	+	1.32714i	0.0782268	+	0.0478269i
$771$		0			0
$772$	−15.9094			−0.572592
$773$	16.6025	−	28.7563i	0.597149	−	1.03429i	−0.396091	−	0.918211i	$-0.629633\pi$
$773$	16.6025	−	28.7563i	0.597149	−	1.03429i	0.993240	−	0.116081i	$-0.0370333\pi$
$774$		0			0
$775$	−1.27878	−	2.21491i	−0.0459351	−	0.0795619i
$776$	−7.80249	+	13.5143i	−0.280093	+	0.485136i
$777$		0			0
$778$	4.14338	+	7.17655i	0.148548	+	0.257292i
$779$	1.78185	−	3.08625i	0.0638414	−	0.110577i
$780$		0			0
$781$	1.90484	+	3.29928i	0.0681605	+	0.118057i
$782$	15.2374	+	26.3920i	0.544888	+	0.943774i
$783$		0			0
$784$	3.19076	+	6.23049i	0.113956	+	0.222518i
$785$	5.32785	−	9.22811i	0.190159	−	0.329365i
$786$		0			0
$787$	−16.7755			−0.597980			−0.298990	−	0.954256i	$-0.596650\pi$
$787$	−16.7755			−0.597980			−0.298990	+	0.954256i	$0.596650\pi$
$788$	−20.8910			−0.744211
$789$		0			0
$790$	3.39898	−	5.88720i	0.120930	−	0.209457i
$791$	−0.0482178	+	1.91670i	−0.00171443	+	0.0681500i
$792$		0			0
$793$	−43.2154	−	74.8512i	−1.53462	−	2.65804i
$794$	−9.42143	−	16.3184i	−0.334354	−	0.579118i
$795$		0			0
$796$	−6.51900	+	11.2912i	−0.231060	+	0.400208i
$797$	4.46594	+	7.73524i	0.158192	+	0.273996i	0.934217	−	0.356706i	$-0.116100\pi$
$797$	4.46594	+	7.73524i	0.158192	+	0.273996i	−0.776025	+	0.630702i	$0.782767\pi$
$798$		0			0
$799$	−13.8544	+	23.9965i	−0.490134	+	0.848936i
$800$	0.500000	+	0.866025i	0.0176777	+	0.0306186i
$801$		0			0
$802$	5.84903	−	10.1308i	0.206537	−	0.357732i
$803$	0.709237			0.0250284
$804$		0			0
$805$	0.260153	−	10.3413i	0.00916920	−	0.364484i
$806$	7.52483	+	13.0334i	0.265051	+	0.459081i
$807$		0			0
$808$	4.80772	+	8.32722i	0.169135	+	0.292951i
$809$	−13.9856	+	24.2237i	−0.491706	+	0.851660i	−0.999954	−	0.00955059i	$-0.996960\pi$
$809$	−13.9856	+	24.2237i	−0.491706	+	0.851660i	0.508248	+	0.861211i	$0.330293\pi$
$810$		0			0
$811$	52.5752			1.84617			0.923083	−	0.384600i	$-0.125661\pi$
$811$	52.5752			1.84617			0.923083	+	0.384600i	$0.125661\pi$
$812$	−2.52468	+	1.37415i	−0.0885990	+	0.0482234i
$813$		0			0
$814$	5.62355	−	9.74027i	0.197105	−	0.341396i
$815$	7.77706			0.272419
$816$		0			0
$817$	−6.77851			−0.237150
$818$	18.0739			0.631938
$819$		0			0
$820$	−2.30083			−0.0803485
$821$	−15.7961			−0.551289			−0.275644	−	0.961260i	$-0.588891\pi$
$821$	−15.7961			−0.551289			−0.275644	+	0.961260i	$0.588891\pi$
$822$		0			0
$823$	−15.5152			−0.540825			−0.270413	−	0.962745i	$-0.587160\pi$
$823$	−15.5152			−0.540825			−0.270413	+	0.962745i	$0.587160\pi$
$824$	1.54448	−	2.67512i	0.0538047	−	0.0931924i
$825$		0			0
$826$	13.5634	+	8.29246i	0.471930	+	0.288532i
$827$	37.0759			1.28925			0.644627	−	0.764497i	$-0.277013\pi$
$827$	37.0759			1.28925			0.644627	+	0.764497i	$0.277013\pi$
$828$		0			0
$829$	24.4304	−	42.3146i	0.848501	−	1.46965i	−0.0340444	−	0.999420i	$-0.510839\pi$
$829$	24.4304	−	42.3146i	0.848501	−	1.46965i	0.882546	−	0.470227i	$-0.155828\pi$
$830$	−6.12526	−	10.6093i	−0.212611	−	0.368253i
$831$		0			0
$832$	−2.94219	−	5.09603i	−0.102002	−	0.176673i
$833$	−54.4910	−	2.74336i	−1.88800	−	0.0950517i
$834$		0			0
$835$	14.2837			0.494306
$836$	−0.744731	+	1.28991i	−0.0257571	+	0.0446125i
$837$		0			0
$838$	9.88791	+	17.1264i	0.341572	+	0.591620i
$839$	−23.9417	+	41.4683i	−0.826561	+	1.43165i	0.0741600	+	0.997246i	$0.476372\pi$
$839$	−23.9417	+	41.4683i	−0.826561	+	1.43165i	−0.900721	+	0.434399i	$0.856961\pi$
$840$		0			0
$841$	13.9098	+	24.0925i	0.479649	+	0.830777i
$842$	15.4734	−	26.8008i	0.533250	−	0.923616i
$843$		0			0
$844$	8.63625	+	14.9584i	0.297272	+	0.514890i
$845$	10.8130	+	18.7287i	0.371979	+	0.644286i
$846$		0			0
$847$	−23.4132	+	12.7435i	−0.804486	+	0.437872i
$848$	−0.274437	+	0.475340i	−0.00942422	+	0.0163232i
$849$		0			0
$850$	−7.79428			−0.267342
$851$	−45.7291			−1.56757
$852$		0			0
$853$	6.59345	−	11.4202i	0.225756	−	0.391020i	−0.730790	−	0.682602i	$-0.760848\pi$
$853$	6.59345	−	11.4202i	0.225756	−	0.391020i	0.956546	+	0.291582i	$0.0941816\pi$
$854$	33.1555	+	20.2708i	1.13456	+	0.693653i
$855$		0			0
$856$	−1.73194	−	2.99980i	−0.0591964	−	0.102531i
$857$	21.2638	+	36.8300i	0.726359	+	1.25809i	0.958412	+	0.285387i	$0.0921222\pi$
$857$	21.2638	+	36.8300i	0.726359	+	1.25809i	−0.232054	+	0.972703i	$0.574544\pi$
$858$		0			0
$859$	18.4709	−	31.9925i	0.630217	−	1.09157i	−0.357290	−	0.933994i	$-0.616299\pi$
$859$	18.4709	−	31.9925i	0.630217	−	1.09157i	0.987507	−	0.157575i	$-0.0503675\pi$
$860$	2.18820	+	3.79008i	0.0746172	+	0.129241i
$861$		0			0
$862$	1.01707	−	1.76162i	0.0346417	−	0.0600011i
$863$	22.8978	+	39.6602i	0.779451	+	1.35005i	0.932259	+	0.361793i	$0.117835\pi$
$863$	22.8978	+	39.6602i	0.779451	+	1.35005i	−0.152807	+	0.988256i	$0.548831\pi$
$864$		0			0
$865$	−0.982803	+	1.70226i	−0.0334163	+	0.0578787i
$866$	17.9368			0.609518
$867$		0			0
$868$	−5.77316	−	3.52963i	−0.195954	−	0.119804i
$869$	−3.26860	−	5.66138i	−0.110880	−	0.192049i
$870$		0			0
$871$	2.41835	+	4.18871i	0.0819428	+	0.141929i
$872$	7.17178	−	12.4219i	0.242867	−	0.420658i
$873$		0			0
$874$	6.05593			0.204845
$875$	2.25729	+	1.38008i	0.0763105	+	0.0466552i
$876$		0			0
$877$	0.0372312	−	0.0644862i	0.00125721	−	0.00217755i	−0.865396	−	0.501088i	$-0.832933\pi$
$877$	0.0372312	−	0.0644862i	0.00125721	−	0.00217755i	0.866653	+	0.498911i	$0.166266\pi$
$878$	34.2741			1.15669
$879$		0			0
$880$	0.961641			0.0324169
$881$	44.0695			1.48474			0.742369	−	0.669991i	$-0.233702\pi$
$881$	44.0695			1.48474			0.742369	+	0.669991i	$0.233702\pi$
$882$		0			0
$883$	−0.388820			−0.0130848			−0.00654242	−	0.999979i	$-0.502083\pi$
$883$	−0.388820			−0.0130848			−0.00654242	+	0.999979i	$0.502083\pi$
$884$	45.8646			1.54259
$885$		0			0
$886$	13.9945			0.470156
$887$	−18.4983	+	32.0400i	−0.621111	+	1.07580i	0.368168	+	0.929759i	$0.379985\pi$
$887$	−18.4983	+	32.0400i	−0.621111	+	1.07580i	−0.989279	+	0.146037i	$0.953348\pi$
$888$		0			0
$889$	−29.5752	−	18.0819i	−0.991919	−	0.606446i
$890$	−5.71360			−0.191520
$891$		0			0
$892$	−13.6681	+	23.6739i	−0.457643	+	0.792662i
$893$	2.75314	+	4.76858i	0.0921303	+	0.159574i
$894$		0			0
$895$	7.02161	+	12.1618i	0.234706	+	0.406523i
$896$	2.25729	+	1.38008i	0.0754109	+	0.0461052i
$897$		0			0
$898$	24.3772			0.813477
$899$	1.38930	−	2.40634i	0.0463359	−	0.0802561i
$900$		0			0
$901$	−2.13904	−	3.70493i	−0.0712618	−	0.123429i
$902$	−1.10629	+	1.91614i	−0.0368353	+	0.0638006i
$903$		0			0
$904$	0.362337	+	0.627585i	0.0120511	+	0.0208732i
$905$	−8.78971	+	15.2242i	−0.292180	+	0.506070i
$906$		0			0
$907$	10.3447	+	17.9176i	0.343490	+	0.594943i	0.985078	−	0.172107i	$-0.0550574\pi$
$907$	10.3447	+	17.9176i	0.343490	+	0.594943i	−0.641588	+	0.767050i	$0.721724\pi$
$908$	3.73097	+	6.46223i	0.123817	+	0.214457i
$909$		0			0
$910$	−13.2828	−	8.12093i	−0.440320	−	0.269206i
$911$	−19.5423	+	33.8483i	−0.647466	+	1.12144i	0.336260	+	0.941769i	$0.390838\pi$
$911$	−19.5423	+	33.8483i	−0.647466	+	1.12144i	−0.983726	+	0.179675i	$0.942495\pi$
$912$		0			0
$913$	−11.7806			−0.389881
$914$	34.3746			1.13701
$915$		0			0
$916$	4.73672	−	8.20425i	0.156506	−	0.271076i
$917$	40.6885	−	22.1463i	1.34365	−	0.731335i
$918$		0			0
$919$	15.7521	+	27.2834i	0.519614	+	0.899997i	0.999740	+	0.0227981i	$0.00725750\pi$
$919$	15.7521	+	27.2834i	0.519614	+	0.899997i	−0.480126	+	0.877199i	$0.659409\pi$
$920$	−1.95495	−	3.38607i	−0.0644527	−	0.111635i
$921$		0			0
$922$	−14.6870	+	25.4386i	−0.483690	+	0.837776i
$923$	−11.6559	−	20.1886i	−0.383659	−	0.664517i
$924$		0			0
$925$	5.84787	−	10.1288i	0.192277	−	0.333033i
$926$	−10.5391	−	18.2542i	−0.346335	−	0.599870i
$927$		0			0
$928$	−0.543215	+	0.940877i	−0.0178319	+	0.0308858i
$929$	−25.0906			−0.823197			−0.411599	−	0.911365i	$-0.635029\pi$
$929$	−25.0906			−0.823197			−0.411599	+	0.911365i	$0.635029\pi$
$930$		0			0
$931$	−5.88633	+	9.10510i	−0.192917	+	0.298408i
$932$	−7.21133	−	12.4904i	−0.236215	−	0.409136i
$933$		0			0
$934$	−20.8663	−	36.1415i	−0.682767	−	1.18259i
$935$	−3.74765	+	6.49112i	−0.122561	+	0.212282i
$936$		0			0
$937$	38.4082			1.25474			0.627370	−	0.778721i	$-0.284131\pi$
$937$	38.4082			1.25474			0.627370	+	0.778721i	$0.284131\pi$
$938$	−1.85540	−	1.13436i	−0.0605808	−	0.0370383i
$939$		0			0
$940$	1.77751	−	3.07874i	0.0579760	−	0.100417i
$941$	1.64141			0.0535085			0.0267543	−	0.999642i	$-0.491483\pi$
$941$	1.64141			0.0535085			0.0267543	+	0.999642i	$0.491483\pi$
$942$		0			0
$943$	8.99600			0.292950
$944$	6.00868			0.195566
$945$		0			0
$946$	4.20853			0.136831
$947$	43.7932			1.42309			0.711544	−	0.702641i	$-0.247996\pi$
$947$	43.7932			1.42309			0.711544	+	0.702641i	$0.247996\pi$
$948$		0			0
$949$	−4.33990			−0.140879
$950$	−0.774437	+	1.34137i	−0.0251261	+	0.0435196i
$951$		0			0
$952$	−18.1126	+	9.85847i	−0.587033	+	0.319515i
$953$	18.7035			0.605866			0.302933	−	0.953012i	$-0.402034\pi$
$953$	18.7035			0.605866			0.302933	+	0.953012i	$0.402034\pi$
$954$		0			0
$955$	9.68217	−	16.7700i	0.313308	−	0.542665i
$956$	4.82726	+	8.36106i	0.156125	+	0.270416i
$957$		0			0
$958$	9.11638	+	15.7900i	0.294537	+	0.510153i
$959$	−0.578597	+	22.9998i	−0.0186839	+	0.742701i
$960$		0			0
$961$	−24.4589			−0.788997
$962$	−34.4111	+	59.6018i	−1.10946	+	1.92164i
$963$		0			0
$964$	2.08005	+	3.60276i	0.0669940	+	0.116037i
$965$	−7.95470	+	13.7779i	−0.256071	+	0.443528i
$966$		0			0
$967$	−18.5396	−	32.1115i	−0.596193	−	1.03264i	−0.993377	−	0.114897i	$-0.963346\pi$
$967$	−18.5396	−	32.1115i	−0.596193	−	1.03264i	0.397185	−	0.917739i	$-0.369987\pi$
$968$	−5.03762	+	8.72542i	−0.161915	+	0.280446i
$969$		0			0
$970$	7.80249	+	13.5143i	0.250523	+	0.433918i
$971$	−8.50573	−	14.7324i	−0.272962	−	0.472784i	0.696657	−	0.717404i	$-0.254670\pi$
$971$	−8.50573	−	14.7324i	−0.272962	−	0.472784i	−0.969619	+	0.244620i	$0.921337\pi$
$972$		0			0
$973$	−0.874136	+	34.7477i	−0.0280235	+	1.11396i
$974$	−12.5910	+	21.8083i	−0.403442	+	0.698783i
$975$		0			0
$976$	14.6881			0.470156
$977$	−7.72418			−0.247118			−0.123559	−	0.992337i	$-0.539431\pi$
$977$	−7.72418			−0.247118			−0.123559	+	0.992337i	$0.539431\pi$
$978$		0			0
$979$	−2.74721	+	4.75832i	−0.0878014	+	0.152076i
$980$	6.99115	+	0.351971i	0.223324	+	0.0112433i
$981$		0			0
$982$	18.6196	+	32.2501i	0.594175	+	1.02914i
$983$	30.7645	+	53.2856i	0.981234	+	1.69955i	0.657603	+	0.753364i	$0.271570\pi$
$983$	30.7645	+	53.2856i	0.981234	+	1.69955i	0.323631	+	0.946183i	$0.395096\pi$
$984$		0			0
$985$	−10.4455	+	18.0921i	−0.332821	+	0.576463i
$986$	−4.23397	−	7.33346i	−0.134837	−	0.233545i
$987$		0			0
$988$	4.55709	−	7.89311i	0.144980	−	0.251113i
$989$	−8.55565	−	14.8188i	−0.272054	−	0.471211i
$990$		0			0
$991$	−7.41984	+	12.8515i	−0.235699	+	0.408243i	−0.959476	−	0.281792i	$-0.909071\pi$
$991$	−7.41984	+	12.8515i	−0.235699	+	0.408243i	0.723777	+	0.690034i	$0.242405\pi$
$992$	−2.55756			−0.0812025
$993$		0			0
$994$	8.94259	+	5.46738i	0.283642	+	0.173415i
$995$	6.51900	+	11.2912i	0.206666	+	0.357956i
$996$		0			0
$997$	−27.8834	−	48.2954i	−0.883075	−	1.52953i	−0.847904	−	0.530149i	$-0.822136\pi$
$997$	−27.8834	−	48.2954i	−0.883075	−	1.52953i	−0.0351706	−	0.999381i	$-0.511197\pi$
$998$	3.69263	−	6.39582i	0.116888	−	0.202456i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1890.2.i.g.991.2		12
3.2	odd	2		630.2.i.g.151.3	yes	12
7.2	even	3		1890.2.l.g.1801.5		12
9.4	even	3		1890.2.l.g.361.5		12
9.5	odd	6		630.2.l.g.571.6	yes	12
21.2	odd	6		630.2.l.g.331.6	yes	12
63.23	odd	6		630.2.i.g.121.3	✓	12
63.58	even	3	inner	1890.2.i.g.1171.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.i.g.121.3	✓	12	63.23	odd	6
630.2.i.g.151.3	yes	12	3.2	odd	2
630.2.l.g.331.6	yes	12	21.2	odd	6
630.2.l.g.571.6	yes	12	9.5	odd	6
1890.2.i.g.991.2		12	1.1	even	1	trivial
1890.2.i.g.1171.2		12	63.58	even	3	inner
1890.2.l.g.361.5		12	9.4	even	3
1890.2.l.g.1801.5		12	7.2	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1890.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(-2.25729 - 1.38008i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(-2.25729 - 1.38008i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{10} +(0.480820 + 0.832805i) q^{11} +(-2.94219 - 5.09603i) q^{13} +(2.25729 + 1.38008i) q^{14} +1.00000 q^{16} +(-3.89714 + 6.75005i) q^{17} +(0.774437 + 1.34137i) q^{19} +(0.500000 - 0.866025i) q^{20} +(-0.480820 - 0.832805i) q^{22} +(-1.95495 + 3.38607i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(2.94219 + 5.09603i) q^{26} +(-2.25729 - 1.38008i) q^{28} +(0.543215 - 0.940877i) q^{29} +2.55756 q^{31} -1.00000 q^{32} +(3.89714 - 6.75005i) q^{34} +(-2.32383 + 1.26483i) q^{35} +(5.84787 + 10.1288i) q^{37} +(-0.774437 - 1.34137i) q^{38} +(-0.500000 + 0.866025i) q^{40} +(-1.15042 - 1.99258i) q^{41} +(-2.18820 + 3.79008i) q^{43} +(0.480820 + 0.832805i) q^{44} +(1.95495 - 3.38607i) q^{46} +3.55502 q^{47} +(3.19076 + 6.23049i) q^{49} +(0.500000 + 0.866025i) q^{50} +(-2.94219 - 5.09603i) q^{52} +(-0.274437 + 0.475340i) q^{53} +0.961641 q^{55} +(2.25729 + 1.38008i) q^{56} +(-0.543215 + 0.940877i) q^{58} +6.00868 q^{59} +14.6881 q^{61} -2.55756 q^{62} +1.00000 q^{64} -5.88439 q^{65} -0.821956 q^{67} +(-3.89714 + 6.75005i) q^{68} +(2.32383 - 1.26483i) q^{70} +3.96164 q^{71} +(0.368764 - 0.638718i) q^{73} +(-5.84787 - 10.1288i) q^{74} +(0.774437 + 1.34137i) q^{76} +(0.0639849 - 2.54346i) q^{77} -6.79796 q^{79} +(0.500000 - 0.866025i) q^{80} +(1.15042 + 1.99258i) q^{82} +(-6.12526 + 10.6093i) q^{83} +(3.89714 + 6.75005i) q^{85} +(2.18820 - 3.79008i) q^{86} +(-0.480820 - 0.832805i) q^{88} +(2.85680 + 4.94812i) q^{89} +(-0.391531 + 15.5637i) q^{91} +(-1.95495 + 3.38607i) q^{92} -3.55502 q^{94} +1.54887 q^{95} +(7.80249 - 13.5143i) q^{97} +(-3.19076 - 6.23049i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{2} + 12 q^{4} + 6 q^{5} + 4 q^{7} - 12 q^{8}+O(q^{10}) \) 12 * q - 12 * q^2 + 12 * q^4 + 6 * q^5 + 4 * q^7 - 12 * q^8	\( 12 q - 12 q^{2} + 12 q^{4} + 6 q^{5} + 4 q^{7} - 12 q^{8} - 6 q^{10} - 3 q^{11} - 2 q^{13} - 4 q^{14} + 12 q^{16} - q^{17} + 8 q^{19} + 6 q^{20} + 3 q^{22} - 11 q^{23} - 6 q^{25} + 2 q^{26} + 4 q^{28} - 13 q^{29} - 42 q^{31} - 12 q^{32} + q^{34} - 4 q^{35} + 18 q^{37} - 8 q^{38} - 6 q^{40} - 5 q^{41} - 11 q^{43} - 3 q^{44} + 11 q^{46} - 46 q^{47} + 6 q^{50} - 2 q^{52} - 2 q^{53} - 6 q^{55} - 4 q^{56} + 13 q^{58} + 2 q^{59} + 2 q^{61} + 42 q^{62} + 12 q^{64} - 4 q^{65} - 4 q^{67} - q^{68} + 4 q^{70} + 30 q^{71} + 22 q^{73} - 18 q^{74} + 8 q^{76} + 31 q^{77} - 54 q^{79} + 6 q^{80} + 5 q^{82} - 6 q^{83} + q^{85} + 11 q^{86} + 3 q^{88} + 18 q^{89} + 14 q^{91} - 11 q^{92} + 46 q^{94} + 16 q^{95} - 4 q^{97}+O(q^{100}) \) 12 * q - 12 * q^2 + 12 * q^4 + 6 * q^5 + 4 * q^7 - 12 * q^8 - 6 * q^10 - 3 * q^11 - 2 * q^13 - 4 * q^14 + 12 * q^16 - q^17 + 8 * q^19 + 6 * q^20 + 3 * q^22 - 11 * q^23 - 6 * q^25 + 2 * q^26 + 4 * q^28 - 13 * q^29 - 42 * q^31 - 12 * q^32 + q^34 - 4 * q^35 + 18 * q^37 - 8 * q^38 - 6 * q^40 - 5 * q^41 - 11 * q^43 - 3 * q^44 + 11 * q^46 - 46 * q^47 + 6 * q^50 - 2 * q^52 - 2 * q^53 - 6 * q^55 - 4 * q^56 + 13 * q^58 + 2 * q^59 + 2 * q^61 + 42 * q^62 + 12 * q^64 - 4 * q^65 - 4 * q^67 - q^68 + 4 * q^70 + 30 * q^71 + 22 * q^73 - 18 * q^74 + 8 * q^76 + 31 * q^77 - 54 * q^79 + 6 * q^80 + 5 * q^82 - 6 * q^83 + q^85 + 11 * q^86 + 3 * q^88 + 18 * q^89 + 14 * q^91 - 11 * q^92 + 46 * q^94 + 16 * q^95 - 4 * q^97

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