LMFDB - Embedded newform 592.2.be.d.399.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [592,2,Mod(319,592)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("592.319"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(592, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 0, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 592 = 2^{4} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	592.be (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$4.72714379966$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 14x^{14} + 135x^{12} - 686x^{10} + 2521x^{8} - 4452x^{6} + 5592x^{4} - 2016x^{2} + 576 $ x^16 - 14x^14 + 135x^12 - 686x^10 + 2521x^8 - 4452x^6 + 5592x^4 - 2016*x^2 + 576
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			399.1
Root			$-2.22768 + 1.28615i$ of defining polynomial
Character	$\chi$	$=$	592.399
Dual form			592.2.be.d.319.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.28615 + 2.22768i) q^{3} +(-0.133975 - 0.500000i) q^{5} +(-0.256864 - 0.148300i) q^{7} +(-1.80837 - 3.13219i) q^{9} -4.15876 q^{11} +(-0.973243 - 3.63219i) q^{13} +(1.28615 + 0.344623i) q^{15} +(-3.07454 - 0.823821i) q^{17} +(-0.880988 + 0.236060i) q^{19} +(0.660731 - 0.381473i) q^{21} +(1.05009 + 1.05009i) q^{23} +(4.09808 - 2.36603i) q^{25} +1.58646 q^{27} +(-2.32382 - 2.32382i) q^{29} +(4.09452 - 4.09452i) q^{31} +(5.34880 - 9.26439i) q^{33} +(-0.0397369 + 0.148300i) q^{35} +(-4.04778 + 4.54042i) q^{37} +(9.34310 + 2.50348i) q^{39} +(-2.06087 - 1.18985i) q^{41} +(-5.44121 - 5.44121i) q^{43} +(-1.32382 + 1.32382i) q^{45} -5.23149i q^{47} +(-3.45601 - 5.98599i) q^{49} +(5.78953 - 5.78953i) q^{51} +(3.22396 + 5.58407i) q^{53} +(0.557168 + 2.07938i) q^{55} +(0.607218 - 2.26617i) q^{57} +(0.837547 - 3.12577i) q^{59} +(3.80659 - 1.01997i) q^{61} +1.07273i q^{63} +(-1.68571 + 0.973243i) q^{65} +(-0.0605407 + 0.104859i) q^{67} +(-3.68985 + 0.988691i) q^{69} +(-1.18587 - 0.684665i) q^{71} +3.46410i q^{73} +12.1723i q^{75} +(1.06823 + 0.616745i) q^{77} +(-10.4241 + 2.79313i) q^{79} +(3.38469 - 5.86246i) q^{81} +(-10.4366 + 6.02559i) q^{83} +1.64764i q^{85} +(8.16552 - 2.18794i) q^{87} +(-2.86010 + 10.6741i) q^{89} +(-0.288665 + 1.07731i) q^{91} +(3.85510 + 14.3874i) q^{93} +(0.236060 + 0.408868i) q^{95} +(9.25847 - 9.25847i) q^{97} +(7.52059 + 13.0260i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{5} - 4 q^{9} - 4 q^{13} + 12 q^{17} + 36 q^{21} + 24 q^{25} - 12 q^{29} + 8 q^{33} + 8 q^{37} - 36 q^{41} + 4 q^{45} + 20 q^{49} + 4 q^{53} + 12 q^{57} - 28 q^{61} - 20 q^{69} + 32 q^{81} + 20 q^{89}+ \cdots - 4 q^{97}+O(q^{100}) $ 16 * q - 16 * q^5 - 4 * q^9 - 4 * q^13 + 12 * q^17 + 36 * q^21 + 24 * q^25 - 12 * q^29 + 8 * q^33 + 8 * q^37 - 36 * q^41 + 4 * q^45 + 20 * q^49 + 4 * q^53 + 12 * q^57 - 28 * q^61 - 20 * q^69 + 32 * q^81 + 20 * q^89 - 60 * q^93 - 4 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/592\mathbb{Z}\right)^\times$.

$n$	$113$	$149$	$223$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.28615	+	2.22768i	−0.742560	+	1.28615i	0.208766	+	0.977966i	$0.433055\pi$
$3$	−1.28615	+	2.22768i	−0.742560	+	1.28615i	−0.951326	+	0.308186i	$0.900278\pi$
$4$		0			0
$5$	−0.133975	−	0.500000i	−0.0599153	−	0.223607i	0.929476	−	0.368883i	$-0.120260\pi$
$5$	−0.133975	−	0.500000i	−0.0599153	−	0.223607i	−0.989391	+	0.145276i	$0.953593\pi$
$6$		0			0
$7$	−0.256864	−	0.148300i	−0.0970853	−	0.0560522i	0.450671	−	0.892690i	$-0.351185\pi$
$7$	−0.256864	−	0.148300i	−0.0970853	−	0.0560522i	−0.547757	+	0.836638i	$0.684518\pi$
$8$		0			0
$9$	−1.80837	−	3.13219i	−0.602791	−	1.04406i
$10$		0			0
$11$	−4.15876			−1.25391			−0.626957	−	0.779054i	$-0.715700\pi$
$11$	−4.15876			−1.25391			−0.626957	+	0.779054i	$0.715700\pi$
$12$		0			0
$13$	−0.973243	−	3.63219i	−0.269929	−	1.00739i	−0.959164	−	0.282851i	$-0.908720\pi$
$13$	−0.973243	−	3.63219i	−0.269929	−	1.00739i	0.689235	−	0.724538i	$-0.257947\pi$
$14$		0			0
$15$	1.28615	+	0.344623i	0.332083	+	0.0889814i
$16$		0			0
$17$	−3.07454	−	0.823821i	−0.745686	−	0.199806i	−0.134082	−	0.990970i	$-0.542809\pi$
$17$	−3.07454	−	0.823821i	−0.745686	−	0.199806i	−0.611604	+	0.791164i	$0.709475\pi$
$18$		0			0
$19$	−0.880988	+	0.236060i	−0.202112	+	0.0541559i	−0.358455	−	0.933547i	$-0.616696\pi$
$19$	−0.880988	+	0.236060i	−0.202112	+	0.0541559i	0.156342	+	0.987703i	$0.450030\pi$
$20$		0			0
$21$	0.660731	−	0.381473i	0.144183	−	0.0832443i
$22$		0			0
$23$	1.05009	+	1.05009i	0.218959	+	0.218959i	0.808060	−	0.589101i	$-0.200518\pi$
$23$	1.05009	+	1.05009i	0.218959	+	0.218959i	−0.589101	+	0.808060i	$0.700518\pi$
$24$		0			0
$25$	4.09808	−	2.36603i	0.819615	−	0.473205i
$26$		0			0
$27$	1.58646			0.305314
$28$		0			0
$29$	−2.32382	−	2.32382i	−0.431523	−	0.431523i	0.457623	−	0.889146i	$-0.348701\pi$
$29$	−2.32382	−	2.32382i	−0.431523	−	0.431523i	−0.889146	+	0.457623i	$0.848701\pi$
$30$		0			0
$31$	4.09452	−	4.09452i	0.735397	−	0.735397i	−0.236287	−	0.971683i	$-0.575930\pi$
$31$	4.09452	−	4.09452i	0.735397	−	0.735397i	0.971683	+	0.236287i	$0.0759305\pi$
$32$		0			0
$33$	5.34880	−	9.26439i	0.931106	−	1.61272i
$34$		0			0
$35$	−0.0397369	+	0.148300i	−0.00671677	+	0.0250673i
$36$		0			0
$37$	−4.04778	+	4.54042i	−0.665452	+	0.746441i
$37$	−4.04778	+	4.54042i	−0.665452	+	0.746441i
$38$		0			0
$39$	9.34310	+	2.50348i	1.49609	+	0.400877i
$40$		0			0
$41$	−2.06087	−	1.18985i	−0.321854	−	0.185823i	0.330364	−	0.943853i	$-0.392828\pi$
$41$	−2.06087	−	1.18985i	−0.321854	−	0.185823i	−0.652219	+	0.758031i	$0.726162\pi$
$42$		0			0
$43$	−5.44121	−	5.44121i	−0.829776	−	0.829776i	0.157709	−	0.987486i	$-0.449589\pi$
$43$	−5.44121	−	5.44121i	−0.829776	−	0.829776i	−0.987486	+	0.157709i	$0.949589\pi$
$44$		0			0
$45$	−1.32382	+	1.32382i	−0.197344	+	0.197344i
$46$		0			0
$47$		−	5.23149i		−	0.763091i	−0.924350	−	0.381546i	$-0.875392\pi$
$47$		−	5.23149i		−	0.763091i	0.924350	−	0.381546i	$-0.124608\pi$
$48$		0			0
$49$	−3.45601	−	5.98599i	−0.493716	−	0.855142i
$50$		0			0
$51$	5.78953	−	5.78953i	0.810697	−	0.810697i
$52$		0			0
$53$	3.22396	+	5.58407i	0.442845	+	0.767031i	0.997899	−	0.0647836i	$-0.0206357\pi$
$53$	3.22396	+	5.58407i	0.442845	+	0.767031i	−0.555054	+	0.831814i	$0.687302\pi$
$54$		0			0
$55$	0.557168	+	2.07938i	0.0751285	+	0.280384i
$56$		0			0
$57$	0.607218	−	2.26617i	0.0804280	−	0.300161i
$58$		0			0
$59$	0.837547	−	3.12577i	0.109039	−	0.406940i	−0.889733	−	0.456482i	$-0.849109\pi$
$59$	0.837547	−	3.12577i	0.109039	−	0.406940i	0.998772	+	0.0495415i	$0.0157760\pi$
$60$		0			0
$61$	3.80659	−	1.01997i	0.487384	−	0.130594i	−0.00675473	−	0.999977i	$-0.502150\pi$
$61$	3.80659	−	1.01997i	0.487384	−	0.130594i	0.494139	+	0.869383i	$0.335483\pi$
$62$		0			0
$63$			1.07273i			0.135151i
$64$		0			0
$65$	−1.68571	+	0.973243i	−0.209086	+	0.120716i
$66$		0			0
$67$	−0.0605407	+	0.104859i	−0.00739622	+	0.0128106i	−0.869700	−	0.493581i	$-0.835688\pi$
$67$	−0.0605407	+	0.104859i	−0.00739622	+	0.0128106i	0.862304	+	0.506392i	$0.169021\pi$
$68$		0			0
$69$	−3.68985	+	0.988691i	−0.444205	+	0.119024i
$70$		0			0
$71$	−1.18587	−	0.684665i	−0.140737	−	0.0812548i	0.427978	−	0.903789i	$-0.359226\pi$
$71$	−1.18587	−	0.684665i	−0.140737	−	0.0812548i	−0.568715	+	0.822534i	$0.692559\pi$
$72$		0			0
$73$			3.46410i			0.405442i	0.979236	+	0.202721i	$0.0649785\pi$
$73$			3.46410i			0.405442i	−0.979236	+	0.202721i	$0.935021\pi$
$74$		0			0
$75$			12.1723i			1.40553i
$76$		0			0
$77$	1.06823	+	0.616745i	0.121737	+	0.0702847i
$78$		0			0
$79$	−10.4241	+	2.79313i	−1.17280	+	0.314252i	−0.792069	−	0.610432i	$-0.790996\pi$
$79$	−10.4241	+	2.79313i	−1.17280	+	0.314252i	−0.380736	+	0.924684i	$0.624329\pi$
$80$		0			0
$81$	3.38469	−	5.86246i	0.376077	−	0.651385i
$82$		0			0
$83$	−10.4366	+	6.02559i	−1.14557	+	0.661395i	−0.947804	−	0.318854i	$-0.896702\pi$
$83$	−10.4366	+	6.02559i	−1.14557	+	0.661395i	−0.197766	+	0.980249i	$0.563369\pi$
$84$		0			0
$85$			1.64764i			0.178712i
$86$		0			0
$87$	8.16552	−	2.18794i	0.875435	−	0.234572i
$88$		0			0
$89$	−2.86010	+	10.6741i	−0.303171	+	1.13145i	0.631338	+	0.775508i	$0.282506\pi$
$89$	−2.86010	+	10.6741i	−0.303171	+	1.13145i	−0.934509	+	0.355940i	$0.884161\pi$
$90$		0			0
$91$	−0.288665	+	1.07731i	−0.0302603	+	0.112933i
$92$		0			0
$93$	3.85510	+	14.3874i	0.399756	+	1.49191i
$94$		0			0
$95$	0.236060	+	0.408868i	0.0242192	+	0.0419490i
$96$		0			0
$97$	9.25847	−	9.25847i	0.940055	−	0.940055i	−0.0582474	−	0.998302i	$-0.518551\pi$
$97$	9.25847	−	9.25847i	0.940055	−	0.940055i	0.998302	+	0.0582474i	$0.0185512\pi$
$98$		0			0
$99$	7.52059	+	13.0260i	0.755847	+	1.30917i
$100$		0			0
$101$			15.6096i			1.55322i	0.629985	+	0.776608i	$0.283061\pi$
$101$			15.6096i			1.55322i	−0.629985	+	0.776608i	$0.716939\pi$
$102$		0			0
$103$	−10.1932	+	10.1932i	−1.00436	+	1.00436i	−0.00437231	+	0.999990i	$0.501392\pi$
$103$	−10.1932	+	10.1932i	−1.00436	+	1.00436i	−0.999990	+	0.00437231i	$0.998608\pi$
$104$		0			0
$105$	−0.279258	−	0.279258i	−0.0272528	−	0.0272528i
$106$		0			0
$107$	−15.5794	−	8.99478i	−1.50612	−	0.869558i	−0.999975	−	0.00710869i	$-0.997737\pi$
$107$	−15.5794	−	8.99478i	−1.50612	−	0.869558i	−0.506144	−	0.862449i	$-0.668929\pi$
$108$		0			0
$109$	−2.86603	−	0.767949i	−0.274515	−	0.0735562i	0.118935	−	0.992902i	$-0.462052\pi$
$109$	−2.86603	−	0.767949i	−0.274515	−	0.0735562i	−0.393450	+	0.919346i	$0.628719\pi$
$110$		0			0
$111$	−4.90855	−	14.8568i	−0.465899	−	1.41015i
$112$		0			0
$113$	−3.13850	+	11.7130i	−0.295245	+	1.10187i	0.645777	+	0.763526i	$0.276533\pi$
$113$	−3.13850	+	11.7130i	−0.295245	+	1.10187i	−0.941022	+	0.338344i	$0.890133\pi$
$114$		0			0
$115$	0.384360	−	0.665732i	0.0358418	−	0.0620798i
$116$		0			0
$117$	−9.61675	+	9.61675i	−0.889068	+	0.889068i
$118$		0			0
$119$	0.667565	+	0.667565i	0.0611956	+	0.0611956i
$120$		0			0
$121$	6.29528			0.572298
$122$		0			0
$123$	5.30119	−	3.06065i	0.477992	−	0.275969i
$124$		0			0
$125$	−3.56218	−	3.56218i	−0.318611	−	0.318611i
$126$		0			0
$127$	−12.2554	+	7.07569i	−1.08750	+	0.627866i	−0.932908	−	0.360114i	$-0.882738\pi$
$127$	−12.2554	+	7.07569i	−1.08750	+	0.627866i	−0.154587	+	0.987979i	$0.549405\pi$
$128$		0			0
$129$	19.1195	−	5.12305i	1.68338	−	0.451060i
$130$		0			0
$131$	9.49511	+	2.54421i	0.829591	+	0.222288i	0.648535	−	0.761184i	$-0.275382\pi$
$131$	9.49511	+	2.54421i	0.829591	+	0.222288i	0.181056	+	0.983473i	$0.442048\pi$
$132$		0			0
$133$	0.261302	+	0.0700155i	0.0226577	+	0.00607112i
$134$		0			0
$135$	−0.212545	−	0.793228i	−0.0182929	−	0.0682702i
$136$		0			0
$137$	−13.3614			−1.14154			−0.570771	−	0.821109i	$-0.693356\pi$
$137$	−13.3614			−1.14154			−0.570771	+	0.821109i	$0.693356\pi$
$138$		0			0
$139$	−3.40897	−	5.90451i	−0.289145	−	0.500814i	0.684461	−	0.729050i	$-0.260038\pi$
$139$	−3.40897	−	5.90451i	−0.289145	−	0.500814i	−0.973606	+	0.228235i	$0.926704\pi$
$140$		0			0
$141$	11.6541	+	6.72849i	0.981451	+	0.566641i
$142$		0			0
$143$	4.04748	+	15.1054i	0.338468	+	1.26318i
$144$		0			0
$145$	−0.850577	+	1.47324i	−0.0706366	+	0.122346i
$146$		0			0
$147$	17.7798			1.46646
$148$		0			0
$149$	−20.4832			−1.67805			−0.839023	−	0.544096i	$-0.816873\pi$
$149$	−20.4832			−1.67805			−0.839023	+	0.544096i	$0.816873\pi$
$150$		0			0
$151$	5.38067	−	9.31959i	0.437872	−	0.758417i	−0.559653	−	0.828727i	$-0.689065\pi$
$151$	5.38067	−	9.31959i	0.437872	−	0.758417i	0.997525	+	0.0703099i	$0.0223988\pi$
$152$		0			0
$153$	2.97955	+	11.1198i	0.240882	+	0.898985i
$154$		0			0
$155$	−2.59582	−	1.49870i	−0.208501	−	0.120378i
$156$		0			0
$157$	7.84880	+	13.5945i	0.626402	+	1.08496i	0.988268	+	0.152730i	$0.0488065\pi$
$157$	7.84880	+	13.5945i	0.626402	+	1.08496i	−0.361866	+	0.932230i	$0.617860\pi$
$158$		0			0
$159$	−16.5860			−1.31536
$160$		0			0
$161$	−0.114001	−	0.425459i	−0.00898458	−	0.0335309i
$162$		0			0
$163$	6.34300	+	1.69960i	0.496822	+	0.133123i	0.498525	−	0.866875i	$-0.333875\pi$
$163$	6.34300	+	1.69960i	0.496822	+	0.133123i	−0.00170268	+	0.999999i	$0.500542\pi$
$164$		0			0
$165$	−5.34880	−	1.43321i	−0.416403	−	0.111575i
$166$		0			0
$167$	11.9053	−	3.19001i	0.921259	−	0.246851i	0.233135	−	0.972444i	$-0.425101\pi$
$167$	11.9053	−	3.19001i	0.921259	−	0.246851i	0.688123	+	0.725594i	$0.258435\pi$
$168$		0			0
$169$	−0.987296	+	0.570016i	−0.0759458	+	0.0438473i
$170$		0			0
$171$	2.33254	+	2.33254i	0.178374	+	0.178374i
$172$		0			0
$173$	0.642639	−	0.371028i	0.0488589	−	0.0282087i	−0.475372	−	0.879785i	$-0.657686\pi$
$173$	0.642639	−	0.371028i	0.0488589	−	0.0282087i	0.524230	+	0.851576i	$0.324353\pi$
$174$		0			0
$175$	−1.40353			−0.106097
$176$		0			0
$177$	5.88600	+	5.88600i	0.442419	+	0.442419i
$178$		0			0
$179$	16.8448	−	16.8448i	1.25904	−	1.25904i	0.307483	−	0.951554i	$-0.400513\pi$
$179$	16.8448	−	16.8448i	1.25904	−	1.25904i	0.951554	−	0.307483i	$-0.0994866\pi$
$180$		0			0
$181$	4.98908	−	8.64134i	0.370835	−	0.642305i	−0.618859	−	0.785502i	$-0.712405\pi$
$181$	4.98908	−	8.64134i	0.370835	−	0.642305i	0.989694	+	0.143197i	$0.0457381\pi$
$182$		0			0
$183$	−2.62368	+	9.79171i	−0.193948	+	0.723824i
$184$		0			0
$185$	2.81251	+	1.41559i	0.206780	+	0.104076i
$186$		0			0
$187$	12.7863	+	3.42607i	0.935025	+	0.250539i
$188$		0			0
$189$	−0.407503	−	0.235272i	−0.0296415	−	0.0171135i
$190$		0			0
$191$	−14.7128	−	14.7128i	−1.06458	−	1.06458i	−0.997765	−	0.0668134i	$-0.978717\pi$
$191$	−14.7128	−	14.7128i	−1.06458	−	1.06458i	−0.0668134	−	0.997765i	$-0.521283\pi$
$192$		0			0
$193$	7.47290	−	7.47290i	0.537911	−	0.537911i	−0.385004	−	0.922915i	$-0.625800\pi$
$193$	7.47290	−	7.47290i	0.537911	−	0.537911i	0.922915	+	0.385004i	$0.125800\pi$
$194$		0			0
$195$		−	5.00695i		−	0.358555i
$196$		0			0
$197$	2.30029	+	3.98421i	0.163889	+	0.283863i	0.936260	−	0.351308i	$-0.114263\pi$
$197$	2.30029	+	3.98421i	0.163889	+	0.283863i	−0.772371	+	0.635171i	$0.780930\pi$
$198$		0			0
$199$	14.1514	−	14.1514i	1.00316	−	1.00316i	0.00316927	−	0.999995i	$-0.498991\pi$
$199$	14.1514	−	14.1514i	1.00316	−	1.00316i	0.999995	−	0.00316927i	$-0.00100881\pi$
$200$		0			0
$201$	−0.155729	−	0.269730i	−0.0109843	−	0.0190253i
$202$		0			0
$203$	0.252282	+	0.941528i	0.0177067	+	0.0660823i
$204$		0			0
$205$	−0.318818	+	1.18985i	−0.0222672	+	0.0831025i
$206$		0			0
$207$	1.39013	−	5.18805i	0.0966209	−	0.360594i
$208$		0			0
$209$	3.66382	−	0.981717i	0.253431	−	0.0679068i
$210$		0			0
$211$		−	23.7513i		−	1.63511i	−0.575851	−	0.817555i	$-0.695329\pi$
$211$		−	23.7513i		−	1.63511i	0.575851	−	0.817555i	$-0.304671\pi$
$212$		0			0
$213$	3.05043	−	1.76117i	0.209012	−	0.120673i
$214$		0			0
$215$	−1.99162	+	3.44959i	−0.135827	+	0.235260i
$216$		0			0
$217$	−1.65895	+	0.444514i	−0.112617	+	0.0301756i
$218$		0			0
$219$	−7.71691	−	4.45536i	−0.521460	−	0.301065i
$220$		0			0
$221$			11.9691i			0.805129i
$222$		0			0
$223$			14.7990i			0.991015i	0.868604	+	0.495508i	$0.165018\pi$
$223$			14.7990i			0.991015i	−0.868604	+	0.495508i	$0.834982\pi$
$224$		0			0
$225$	−14.8217	−	8.55731i	−0.988113	−	0.570487i
$226$		0			0
$227$	7.85181	−	2.10389i	0.521143	−	0.139640i	0.0113479	−	0.999936i	$-0.496388\pi$
$227$	7.85181	−	2.10389i	0.521143	−	0.139640i	0.509795	+	0.860296i	$0.329721\pi$
$228$		0			0
$229$	0.883255	−	1.52984i	0.0583671	−	0.101095i	−0.835365	−	0.549695i	$-0.814744\pi$
$229$	0.883255	−	1.52984i	0.0583671	−	0.101095i	0.893733	+	0.448600i	$0.148077\pi$
$230$		0			0
$231$	−2.74782	+	1.58646i	−0.180793	+	0.104381i
$232$		0			0
$233$		−	1.60386i		−	0.105072i	−0.998619	−	0.0525362i	$-0.983270\pi$
$233$		−	1.60386i		−	0.105072i	0.998619	−	0.0525362i	$-0.0167305\pi$
$234$		0			0
$235$	−2.61574	+	0.700887i	−0.170632	+	0.0457208i
$236$		0			0
$237$	7.18479	−	26.8140i	0.466702	−	1.74176i
$238$		0			0
$239$	−4.74131	+	17.6948i	−0.306690	+	1.14458i	0.624791	+	0.780792i	$0.285184\pi$
$239$	−4.74131	+	17.6948i	−0.306690	+	1.14458i	−0.931481	+	0.363791i	$0.881482\pi$
$240$		0			0
$241$	0.0702654	+	0.262234i	0.00452619	+	0.0168920i	0.968152	−	0.250363i	$-0.0805500\pi$
$241$	0.0702654	+	0.262234i	0.00452619	+	0.0168920i	−0.963626	+	0.267255i	$0.913883\pi$
$242$		0			0
$243$	11.0861	+	19.2018i	0.711177	+	1.23179i
$244$		0			0
$245$	−2.52998	+	2.52998i	−0.161634	+	0.161634i
$246$		0			0
$247$	1.71483	+	2.97017i	0.109112	+	0.188988i
$248$		0			0
$249$		−	30.9993i		−	1.96450i
$250$		0			0
$251$	−7.36587	+	7.36587i	−0.464930	+	0.464930i	−0.900267	−	0.435338i	$-0.856629\pi$
$251$	−7.36587	+	7.36587i	−0.464930	+	0.464930i	0.435338	+	0.900267i	$0.356629\pi$
$252$		0			0
$253$	−4.36708	−	4.36708i	−0.274556	−	0.274556i
$254$		0			0
$255$	−3.67042	−	2.11912i	−0.229850	−	0.132704i
$256$		0			0
$257$	−23.4198	−	6.27531i	−1.46089	−	0.391443i	−0.561090	−	0.827755i	$-0.689618\pi$
$257$	−23.4198	−	6.27531i	−1.46089	−	0.391443i	−0.899796	+	0.436312i	$0.856284\pi$
$258$		0			0
$259$	1.71307	−	0.565982i	0.106445	−	0.0351684i
$260$		0			0
$261$	−3.07632	+	11.4810i	−0.190420	+	0.710655i
$262$		0			0
$263$	−8.44589	+	14.6287i	−0.520796	+	0.902045i	0.478911	+	0.877863i	$0.341032\pi$
$263$	−8.44589	+	14.6287i	−0.520796	+	0.902045i	−0.999708	+	0.0241822i	$0.992302\pi$
$264$		0			0
$265$	2.36010	−	2.36010i	0.144980	−	0.144980i
$266$		0			0
$267$	−20.0999	−	20.0999i	−1.23009	−	1.23009i
$268$		0			0
$269$	−2.50355			−0.152644			−0.0763220	−	0.997083i	$-0.524318\pi$
$269$	−2.50355			−0.152644			−0.0763220	+	0.997083i	$0.524318\pi$
$270$		0			0
$271$	22.5697	−	13.0306i	1.37101	−	0.791554i	0.379956	−	0.925005i	$-0.375939\pi$
$271$	22.5697	−	13.0306i	1.37101	−	0.791554i	0.991055	+	0.133451i	$0.0426058\pi$
$272$		0			0
$273$	−2.02864	−	2.02864i	−0.122779	−	0.122779i
$274$		0			0
$275$	−17.0429	+	9.83973i	−1.02773	+	0.593358i
$276$		0			0
$277$	17.6416	−	4.72705i	1.05998	−	0.284021i	0.313610	−	0.949552i	$-0.398462\pi$
$277$	17.6416	−	4.72705i	1.05998	−	0.284021i	0.746370	+	0.665531i	$0.231795\pi$
$278$		0			0
$279$	−20.2292	−	5.42040i	−1.21109	−	0.324511i
$280$		0			0
$281$	−29.5227	−	7.91059i	−1.76118	−	0.471906i	−0.774224	−	0.632912i	$-0.781860\pi$
$281$	−29.5227	−	7.91059i	−1.76118	−	0.471906i	−0.986954	+	0.161005i	$0.948526\pi$
$282$		0			0
$283$	7.89701	+	29.4720i	0.469429	+	1.75193i	0.641773	+	0.766895i	$0.278199\pi$
$283$	7.89701	+	29.4720i	0.469429	+	1.75193i	−0.172344	+	0.985037i	$0.555134\pi$
$284$		0			0
$285$	−1.21444			−0.0719370
$286$		0			0
$287$	0.352909	+	0.611256i	0.0208316	+	0.0360813i
$288$		0			0
$289$	−5.94831	−	3.43426i	−0.349901	−	0.202015i
$290$		0			0
$291$	8.71711	+	32.5327i	0.511006	+	1.90710i
$292$		0			0
$293$	−2.12267	+	3.67657i	−0.124007	+	0.214787i	−0.921345	−	0.388747i	$-0.872908\pi$
$293$	−2.12267	+	3.67657i	−0.124007	+	0.214787i	0.797337	+	0.603534i	$0.206241\pi$
$294$		0			0
$295$	−1.67509			−0.0975277
$296$		0			0
$297$	−6.59769			−0.382837
$298$		0			0
$299$	2.79214	−	4.83613i	0.161474	−	0.279681i
$300$		0			0
$301$	0.590716	+	2.20458i	0.0340483	+	0.127070i
$302$		0			0
$303$	−34.7732	−	20.0763i	−1.99767	−	1.15336i
$304$		0			0
$305$	−1.01997	−	1.76665i	−0.0584035	−	0.101158i
$306$		0			0
$307$	−34.4112			−1.96395			−0.981976	−	0.189008i	$-0.939473\pi$
$307$	−34.4112			−1.96395			−0.981976	+	0.189008i	$0.939473\pi$
$308$		0			0
$309$	−9.59716	−	35.8171i	−0.545963	−	2.03756i
$310$		0			0
$311$	23.9565	+	6.41912i	1.35845	+	0.363995i	0.863246	−	0.504783i	$-0.168428\pi$
$311$	23.9565	+	6.41912i	1.35845	+	0.363995i	0.495201	+	0.868778i	$0.335094\pi$
$312$		0			0
$313$	10.0995	+	2.70616i	0.570858	+	0.152961i	0.532690	−	0.846310i	$-0.321181\pi$
$313$	10.0995	+	2.70616i	0.570858	+	0.152961i	0.0381681	+	0.999271i	$0.487848\pi$
$314$		0			0
$315$	0.536364	−	0.143718i	0.0302207	−	0.00809762i
$316$		0			0
$317$	22.7109	−	13.1121i	1.27557	−	0.736451i	0.299539	−	0.954084i	$-0.403167\pi$
$317$	22.7109	−	13.1121i	1.27557	−	0.736451i	0.976031	+	0.217633i	$0.0698337\pi$
$318$		0			0
$319$	9.66421	+	9.66421i	0.541092	+	0.541092i
$320$		0			0
$321$	40.0750	−	23.1373i	2.23677	−	1.29140i
$322$		0			0
$323$	2.90310			0.161533
$324$		0			0
$325$	−12.5823	−	12.5823i	−0.697940	−	0.697940i
$326$		0			0
$327$	5.39689	−	5.39689i	0.298449	−	0.298449i
$328$		0			0
$329$	−0.775831	+	1.34378i	−0.0427730	+	0.0740850i
$330$		0			0
$331$	2.78485	−	10.3932i	0.153069	−	0.571262i	−0.846194	−	0.532875i	$-0.821112\pi$
$331$	2.78485	−	10.3932i	0.153069	−	0.571262i	0.999263	−	0.0383865i	$-0.0122218\pi$
$332$		0			0
$333$	21.5414	+	4.46766i	1.18046	+	0.244826i
$334$		0			0
$335$	0.0605407	+	0.0162218i	0.00330769	+	0.000886293i
$336$		0			0
$337$	24.2316	+	13.9901i	1.31998	+	0.762091i	0.983725	−	0.179680i	$-0.0575062\pi$
$337$	24.2316	+	13.9901i	1.31998	+	0.762091i	0.336255	+	0.941771i	$0.390840\pi$
$338$		0			0
$339$	−22.0563	−	22.0563i	−1.19793	−	1.19793i
$340$		0			0
$341$	−17.0281	+	17.0281i	−0.922124	+	0.922124i
$342$		0			0
$343$			4.12632i			0.222800i
$344$		0			0
$345$	0.988691	+	1.71246i	0.0532293	+	0.0921959i
$346$		0			0
$347$	−1.52962	+	1.52962i	−0.0821143	+	0.0821143i	−0.746971	−	0.664857i	$-0.768493\pi$
$347$	−1.52962	+	1.52962i	−0.0821143	+	0.0821143i	0.664857	+	0.746971i	$0.268493\pi$
$348$		0			0
$349$	−15.9693	−	27.6597i	−0.854819	−	1.48059i	−0.876813	−	0.480832i	$-0.840335\pi$
$349$	−15.9693	−	27.6597i	−0.854819	−	1.48059i	0.0219936	−	0.999758i	$-0.492999\pi$
$350$		0			0
$351$	−1.54401	−	5.76232i	−0.0824130	−	0.307570i
$352$		0			0
$353$	−3.41689	+	12.7520i	−0.181863	+	0.678722i	0.813417	+	0.581680i	$0.197605\pi$
$353$	−3.41689	+	12.7520i	−0.181863	+	0.678722i	−0.995280	+	0.0970413i	$0.969062\pi$
$354$		0			0
$355$	−0.183455	+	0.684665i	−0.00973680	+	0.0363382i
$356$		0			0
$357$	−2.34571	+	0.628531i	−0.124148	+	0.0332654i
$358$		0			0
$359$		−	10.5767i		−	0.558214i	−0.960260	−	0.279107i	$-0.909962\pi$
$359$		−	10.5767i		−	0.558214i	0.960260	−	0.279107i	$-0.0900385\pi$
$360$		0			0
$361$	−15.7341	+	9.08407i	−0.828109	+	0.478109i
$362$		0			0
$363$	−8.09669	+	14.0239i	−0.424966	+	0.736063i
$364$		0			0
$365$	1.73205	−	0.464102i	0.0906597	−	0.0242922i
$366$		0			0
$367$	24.3917	+	14.0825i	1.27324	+	0.735103i	0.975596	−	0.219575i	$-0.0704671\pi$
$367$	24.3917	+	14.0825i	1.27324	+	0.735103i	0.297640	+	0.954678i	$0.403800\pi$
$368$		0			0
$369$			8.60674i			0.448049i
$370$		0			0
$371$		−	1.91246i		−	0.0992899i
$372$		0			0
$373$	6.02617	+	3.47921i	0.312023	+	0.180147i	0.647831	−	0.761784i	$-0.275676\pi$
$373$	6.02617	+	3.47921i	0.312023	+	0.180147i	−0.335808	+	0.941930i	$0.609009\pi$
$374$		0			0
$375$	12.5169	−	3.35389i	0.646370	−	0.173194i
$376$		0			0
$377$	−6.17892	+	10.7022i	−0.318231	+	0.551192i
$378$		0			0
$379$	1.08743	−	0.627828i	0.0558575	−	0.0322494i	−0.471811	−	0.881700i	$-0.656400\pi$
$379$	1.08743	−	0.627828i	0.0558575	−	0.0322494i	0.527669	+	0.849450i	$0.323066\pi$
$380$		0			0
$381$		−	36.4016i		−	1.86491i
$382$		0			0
$383$	29.3066	−	7.85269i	1.49750	−	0.401254i	0.585238	−	0.810862i	$-0.301001\pi$
$383$	29.3066	−	7.85269i	1.49750	−	0.401254i	0.912262	+	0.409608i	$0.134334\pi$
$384$		0			0
$385$	0.165256	−	0.616745i	0.00842225	−	0.0314323i
$386$		0			0
$387$	−7.20318	+	26.8826i	−0.366158	+	1.36652i
$388$		0			0
$389$	−0.663952	−	2.47790i	−0.0336637	−	0.125635i	0.947049	−	0.321089i	$-0.104049\pi$
$389$	−0.663952	−	2.47790i	−0.0336637	−	0.125635i	−0.980713	+	0.195454i	$0.937382\pi$
$390$		0			0
$391$	−2.36346	−	4.09364i	−0.119525	−	0.207024i
$392$		0			0
$393$	−17.8798	+	17.8798i	−0.901918	+	0.901918i
$394$		0			0
$395$	2.79313	+	4.83785i	0.140538	+	0.243419i
$396$		0			0
$397$		−	27.6714i		−	1.38879i	−0.719595	−	0.694394i	$-0.755672\pi$
$397$		−	27.6714i		−	1.38879i	0.719595	−	0.694394i	$-0.244328\pi$
$398$		0			0
$399$	−0.492046	+	0.492046i	−0.0246331	+	0.0246331i
$400$		0			0
$401$	−1.74389	−	1.74389i	−0.0870858	−	0.0870858i	0.662222	−	0.749308i	$-0.269614\pi$
$401$	−1.74389	−	1.74389i	−0.0870858	−	0.0870858i	−0.749308	+	0.662222i	$0.769614\pi$
$402$		0			0
$403$	−18.8570	−	10.8871i	−0.939336	−	0.542326i
$404$		0			0
$405$	−3.38469	−	0.906926i	−0.168187	−	0.0450655i
$406$		0			0
$407$	16.8338	−	18.8825i	0.834419	−	0.935972i
$408$		0			0
$409$	2.12805	−	7.94201i	0.105226	−	0.392707i	−0.893145	−	0.449769i	$-0.851506\pi$
$409$	2.12805	−	7.94201i	0.105226	−	0.392707i	0.998371	+	0.0570616i	$0.0181731\pi$
$410$		0			0
$411$	17.1848	−	29.7649i	0.847664	−	1.46820i
$412$		0			0
$413$	−0.678688	+	0.678688i	−0.0333960	+	0.0333960i
$414$		0			0
$415$	4.41104	+	4.41104i	0.216530	+	0.216530i
$416$		0			0
$417$	17.5378			0.858831
$418$		0			0
$419$	19.8643	−	11.4686i	0.970433	−	0.560280i	0.0710645	−	0.997472i	$-0.477360\pi$
$419$	19.8643	−	11.4686i	0.970433	−	0.560280i	0.899368	+	0.437192i	$0.144027\pi$
$420$		0			0
$421$	−4.36261	−	4.36261i	−0.212621	−	0.212621i	0.592759	−	0.805380i	$-0.298039\pi$
$421$	−4.36261	−	4.36261i	−0.212621	−	0.212621i	−0.805380	+	0.592759i	$0.798039\pi$
$422$		0			0
$423$	−16.3860	+	9.46048i	−0.796716	+	0.459984i
$424$		0			0
$425$	−14.5489	+	3.89836i	−0.705724	+	0.189098i
$426$		0			0
$427$	−1.12904	−	0.302525i	−0.0546379	−	0.0146402i
$428$		0			0
$429$	−38.8557	−	10.4114i	−1.87597	−	0.502665i
$430$		0			0
$431$	2.77321	+	10.3498i	0.133581	+	0.498530i	1.00000		0.000787611i	$-0.000250705\pi$
$431$	2.77321	+	10.3498i	0.133581	+	0.498530i	−0.866419	+	0.499318i	$0.833584\pi$
$432$		0			0
$433$	−6.55679			−0.315099			−0.157550	−	0.987511i	$-0.550359\pi$
$433$	−6.55679			−0.315099			−0.157550	+	0.987511i	$0.550359\pi$
$434$		0			0
$435$	−2.18794	−	3.78963i	−0.104904	−	0.181699i
$436$		0			0
$437$	−1.17300	−	0.677233i	−0.0561123	−	0.0323965i
$438$		0			0
$439$	5.37238	+	20.0500i	0.256410	+	0.956934i	0.967301	+	0.253632i	$0.0816252\pi$
$439$	5.37238	+	20.0500i	0.256410	+	0.956934i	−0.710891	+	0.703302i	$0.751708\pi$
$440$		0			0
$441$	−12.4995	+	21.6498i	−0.595215	+	1.03094i
$442$		0			0
$443$	8.86545			0.421210			0.210605	−	0.977571i	$-0.432457\pi$
$443$	8.86545			0.421210			0.210605	+	0.977571i	$0.432457\pi$
$444$		0			0
$445$	5.72021			0.271164
$446$		0			0
$447$	26.3444	−	45.6299i	1.24605	−	2.15822i
$448$		0			0
$449$	5.78614	+	21.5942i	0.273065	+	1.01909i	0.957127	+	0.289668i	$0.0935450\pi$
$449$	5.78614	+	21.5942i	0.273065	+	1.01909i	−0.684062	+	0.729424i	$0.739788\pi$
$450$		0			0
$451$	8.57068	+	4.94828i	0.403578	+	0.233006i
$452$		0			0
$453$	13.8407	+	23.9728i	0.650293	+	1.12634i
$454$		0			0
$455$	0.577329			0.0270656
$456$		0			0
$457$	3.18628	+	11.8914i	0.149048	+	0.556255i	0.999542	+	0.0302697i	$0.00963662\pi$
$457$	3.18628	+	11.8914i	0.149048	+	0.556255i	−0.850494	+	0.525985i	$0.823697\pi$
$458$		0			0
$459$	−4.87762	−	1.30696i	−0.227668	−	0.0610035i
$460$		0			0
$461$	41.1652	+	11.0302i	1.91725	+	0.513726i	0.990385	+	0.138336i	$0.0441753\pi$
$461$	41.1652	+	11.0302i	1.91725	+	0.513726i	0.926867	+	0.375390i	$0.122491\pi$
$462$		0			0
$463$	29.8430	−	7.99641i	1.38692	−	0.371625i	0.513292	−	0.858214i	$-0.328426\pi$
$463$	29.8430	−	7.99641i	1.38692	−	0.371625i	0.873631	+	0.486589i	$0.161759\pi$
$464$		0			0
$465$	6.67723	−	3.85510i	0.309649	−	0.178776i
$466$		0			0
$467$	−11.3491	−	11.3491i	−0.525174	−	0.525174i	0.393955	−	0.919130i	$-0.371106\pi$
$467$	−11.3491	−	11.3491i	−0.525174	−	0.525174i	−0.919130	+	0.393955i	$0.871106\pi$
$468$		0			0
$469$	0.0311014	−	0.0179564i	0.00143613	−	0.000829149i
$470$		0			0
$471$	−40.3790			−1.86056
$472$		0			0
$473$	22.6287	+	22.6287i	1.04047	+	1.04047i
$474$		0			0
$475$	−3.05183	+	3.05183i	−0.140028	+	0.140028i
$476$		0			0
$477$	11.6603	−	20.1962i	0.533886	−	0.924718i
$478$		0			0
$479$	−3.75547	+	14.0156i	−0.171592	+	0.640389i	0.825515	+	0.564379i	$0.190885\pi$
$479$	−3.75547	+	14.0156i	−0.171592	+	0.640389i	−0.997107	+	0.0760092i	$0.975782\pi$
$480$		0			0
$481$	20.4312	+	10.2834i	0.931581	+	0.468883i
$482$		0			0
$483$	1.09441	+	0.293246i	0.0497974	+	0.0133432i
$484$		0			0
$485$	−5.86963	−	3.38883i	−0.266526	−	0.153879i
$486$		0			0
$487$	−2.12282	−	2.12282i	−0.0961942	−	0.0961942i	0.657372	−	0.753566i	$-0.271668\pi$
$487$	−2.12282	−	2.12282i	−0.0961942	−	0.0961942i	−0.753566	+	0.657372i	$0.771668\pi$
$488$		0			0
$489$	−11.9442	+	11.9442i	−0.540137	+	0.540137i
$490$		0			0
$491$		−	5.86263i		−	0.264577i	−0.991211	−	0.132288i	$-0.957767\pi$
$491$		−	5.86263i		−	0.264577i	0.991211	−	0.132288i	$-0.0422325\pi$
$492$		0			0
$493$	5.23027	+	9.05909i	0.235559	+	0.408001i
$494$		0			0
$495$	5.50545	−	5.50545i	0.247452	−	0.247452i
$496$		0			0
$497$	0.203072	+	0.351731i	0.00910902	+	0.0157773i
$498$		0			0
$499$	−6.82612	−	25.4754i	−0.305579	−	1.14044i	−0.932446	−	0.361310i	$-0.882330\pi$
$499$	−6.82612	−	25.4754i	−0.305579	−	1.14044i	0.626867	−	0.779126i	$-0.284337\pi$
$500$		0			0
$501$	−8.20568	+	30.6240i	−0.366603	+	1.36818i
$502$		0			0
$503$	−1.01864	+	3.80162i	−0.0454189	+	0.169506i	−0.984910	−	0.173068i	$-0.944632\pi$
$503$	−1.01864	+	3.80162i	−0.0454189	+	0.169506i	0.939491	+	0.342574i	$0.111299\pi$
$504$		0			0
$505$	7.80481	−	2.09129i	0.347309	−	0.0930613i
$506$		0			0
$507$		−	2.93251i		−	0.130237i
$508$		0			0
$509$	14.7791	−	8.53272i	0.655072	−	0.378206i	−0.135324	−	0.990801i	$-0.543208\pi$
$509$	14.7791	−	8.53272i	0.655072	−	0.378206i	0.790397	+	0.612595i	$0.209874\pi$
$510$		0			0
$511$	0.513727	−	0.889802i	0.0227260	−	0.0393625i
$512$		0			0
$513$	−1.39765	+	0.374499i	−0.0617077	+	0.0165345i
$514$		0			0
$515$	6.46221	+	3.73096i	0.284759	+	0.164406i
$516$		0			0
$517$			21.7565i			0.956850i
$518$		0			0
$519$			1.90879i			0.0837867i
$520$		0			0
$521$	−35.2639	−	20.3596i	−1.54494	−	0.891971i	−0.998516	−	0.0544629i	$-0.982655\pi$
$521$	−35.2639	−	20.3596i	−1.54494	−	0.891971i	−0.546424	−	0.837509i	$-0.684011\pi$
$522$		0			0
$523$	8.32393	−	2.23039i	0.363980	−	0.0975282i	−0.0721936	−	0.997391i	$-0.523000\pi$
$523$	8.32393	−	2.23039i	0.363980	−	0.0975282i	0.436174	+	0.899862i	$0.356333\pi$
$524$		0			0
$525$	1.80515	−	3.12661i	0.0787833	−	0.136457i
$526$		0			0
$527$	−15.9619	+	9.21561i	−0.695311	+	0.401438i
$528$		0			0
$529$		−	20.7946i		−	0.904114i
$530$		0			0
$531$	−11.3051	+	3.02919i	−0.490600	+	0.131456i
$532$		0			0
$533$	−2.31602	+	8.64350i	−0.100318	+	0.374392i
$534$		0			0
$535$	−2.41014	+	8.99478i	−0.104200	+	0.388878i
$536$		0			0
$537$	15.8598	+	59.1896i	0.684402	+	2.55422i
$538$		0			0
$539$	14.3727	+	24.8943i	0.619077	+	1.07227i
$540$		0			0
$541$	−17.0279	+	17.0279i	−0.732085	+	0.732085i	−0.971032	−	0.238948i	$-0.923198\pi$
$541$	−17.0279	+	17.0279i	−0.732085	+	0.732085i	0.238948	+	0.971032i	$0.423198\pi$
$542$		0			0
$543$	12.8334	+	22.2281i	0.550735	+	0.953901i
$544$		0			0
$545$			1.53590i			0.0657907i
$546$		0			0
$547$	−28.0196	+	28.0196i	−1.19803	+	1.19803i	−0.223277	+	0.974755i	$0.571676\pi$
$547$	−28.0196	+	28.0196i	−1.19803	+	1.19803i	−0.974755	+	0.223277i	$0.928324\pi$
$548$		0			0
$549$	−10.0785	−	10.0785i	−0.430139	−	0.430139i
$550$		0			0
$551$	2.59582	+	1.49870i	0.110586	+	0.0638466i
$552$		0			0
$553$	3.09180	+	0.828445i	0.131477	+	0.0352291i
$554$		0			0
$555$	−6.77080	+	4.44471i	−0.287404	+	0.188668i
$556$		0			0
$557$	0.681281	−	2.54258i	0.0288668	−	0.107732i	−0.949989	−	0.312282i	$-0.898906\pi$
$557$	0.681281	−	2.54258i	0.0288668	−	0.107732i	0.978856	+	0.204550i	$0.0655731\pi$
$558$		0			0
$559$	−14.4679	+	25.0591i	−0.611927	+	1.05989i
$560$		0			0
$561$	−24.0773	+	24.0773i	−1.01654	+	1.01654i
$562$		0			0
$563$	−26.9635	−	26.9635i	−1.13637	−	1.13637i	−0.989095	−	0.147280i	$-0.952948\pi$
$563$	−26.9635	−	26.9635i	−1.13637	−	1.13637i	−0.147280	−	0.989095i	$-0.547052\pi$
$564$		0			0
$565$	6.27700			0.264075
$566$		0			0
$567$	−1.73881	+	1.00390i	−0.0730232	+	0.0421599i
$568$		0			0
$569$	−13.5552	−	13.5552i	−0.568264	−	0.568264i	0.363378	−	0.931642i	$-0.381623\pi$
$569$	−13.5552	−	13.5552i	−0.568264	−	0.568264i	−0.931642	+	0.363378i	$0.881623\pi$
$570$		0			0
$571$	−12.0499	+	6.95700i	−0.504272	+	0.291142i	−0.730476	−	0.682938i	$-0.760702\pi$
$571$	−12.0499	+	6.95700i	−0.504272	+	0.291142i	0.226204	+	0.974080i	$0.427368\pi$
$572$		0			0
$573$	51.6982	−	13.8525i	2.15972	−	0.578696i
$574$		0			0
$575$	6.78790	+	1.81881i	0.283075	+	0.0758497i
$576$		0			0
$577$	−27.3782	−	7.33596i	−1.13977	−	0.305400i	−0.360910	−	0.932601i	$-0.617534\pi$
$577$	−27.3782	−	7.33596i	−1.13977	−	0.305400i	−0.778858	+	0.627201i	$0.784201\pi$
$578$		0			0
$579$	7.03595	+	26.2585i	0.292404	+	1.09127i
$580$		0			0
$581$	3.57439			0.148291
$582$		0			0
$583$	−13.4077	−	23.2228i	−0.555290	−	0.961790i
$584$		0			0
$585$	6.09677	+	3.51997i	0.252071	+	0.145533i
$586$		0			0
$587$	6.20176	+	23.1453i	0.255974	+	0.955308i	0.967546	+	0.252695i	$0.0813168\pi$
$587$	6.20176	+	23.1453i	0.255974	+	0.955308i	−0.711572	+	0.702613i	$0.752017\pi$
$588$		0			0
$589$	−2.64067	+	4.57377i	−0.108807	+	0.188459i
$590$		0			0
$591$	−11.8341			−0.486788
$592$		0			0
$593$	−30.2397			−1.24179			−0.620897	−	0.783892i	$-0.713231\pi$
$593$	−30.2397			−1.24179			−0.620897	+	0.783892i	$0.713231\pi$
$594$		0			0
$595$	0.244346	−	0.423219i	0.0100172	−	0.0173503i
$596$		0			0
$597$	13.3239	+	49.7255i	0.545312	+	2.03513i
$598$		0			0
$599$	−27.9974	−	16.1643i	−1.14394	−	0.660456i	−0.196540	−	0.980496i	$-0.562971\pi$
$599$	−27.9974	−	16.1643i	−1.14394	−	0.660456i	−0.947404	+	0.320039i	$0.896304\pi$
$600$		0			0
$601$	4.56535	+	7.90743i	0.186225	+	0.322551i	0.943989	−	0.329978i	$-0.107041\pi$
$601$	4.56535	+	7.90743i	0.186225	+	0.322551i	−0.757764	+	0.652529i	$0.773708\pi$
$602$		0			0
$603$	0.437920			0.0178335
$604$		0			0
$605$	−0.843408	−	3.14764i	−0.0342894	−	0.127970i
$606$		0			0
$607$	5.63295	+	1.50934i	0.228634	+	0.0612624i	0.371317	−	0.928506i	$-0.378906\pi$
$607$	5.63295	+	1.50934i	0.228634	+	0.0612624i	−0.142683	+	0.989768i	$0.545573\pi$
$608$		0			0
$609$	−2.42190	−	0.648945i	−0.0981402	−	0.0262966i
$610$		0			0
$611$	−19.0018	+	5.09151i	−0.768730	+	0.205980i
$612$		0			0
$613$	13.7965	−	7.96541i	0.557235	−	0.321720i	−0.194800	−	0.980843i	$-0.562406\pi$
$613$	13.7965	−	7.96541i	0.557235	−	0.321720i	0.752035	+	0.659123i	$0.229072\pi$
$614$		0			0
$615$	−2.24055	−	2.24055i	−0.0903476	−	0.0903476i
$616$		0			0
$617$	−27.2288	+	15.7205i	−1.09619	+	0.632885i	−0.935217	−	0.354074i	$-0.884796\pi$
$617$	−27.2288	+	15.7205i	−1.09619	+	0.632885i	−0.160972	+	0.986959i	$0.551463\pi$
$618$		0			0
$619$	39.5031			1.58776			0.793881	−	0.608073i	$-0.208057\pi$
$619$	39.5031			1.58776			0.793881	+	0.608073i	$0.208057\pi$
$620$		0			0
$621$	1.66592	+	1.66592i	0.0668513	+	0.0668513i
$622$		0			0
$623$	2.31762	−	2.31762i	0.0928536	−	0.0928536i
$624$		0			0
$625$	10.5263	−	18.2321i	0.421051	−	0.729282i
$626$		0			0
$627$	−2.52527	+	9.42445i	−0.100850	+	0.376376i
$628$		0			0
$629$	16.1856	−	10.6251i	0.645361	−	0.423649i
$630$		0			0
$631$	−10.5720	−	2.83276i	−0.420864	−	0.112770i	0.0421703	−	0.999110i	$-0.486573\pi$
$631$	−10.5720	−	2.83276i	−0.420864	−	0.112770i	−0.463035	+	0.886340i	$0.653239\pi$
$632$		0			0
$633$	52.9104	+	30.5478i	2.10300	+	1.21417i
$634$		0			0
$635$	5.17976	+	5.17976i	0.205553	+	0.205553i
$636$		0			0
$637$	−18.3787	+	18.3787i	−0.728192	+	0.728192i
$638$		0			0
$639$			4.95252i			0.195919i
$640$		0			0
$641$	9.98316	+	17.2913i	0.394311	+	0.682967i	0.993013	−	0.118005i	$-0.0376500\pi$
$641$	9.98316	+	17.2913i	0.394311	+	0.682967i	−0.598702	+	0.800972i	$0.704317\pi$
$642$		0			0
$643$	7.33949	−	7.33949i	0.289441	−	0.289441i	−0.547418	−	0.836859i	$-0.684389\pi$
$643$	7.33949	−	7.33949i	0.289441	−	0.289441i	0.836859	+	0.547418i	$0.184389\pi$
$644$		0			0
$645$	−5.12305	−	8.87339i	−0.201720	−	0.349389i
$646$		0			0
$647$	4.21236	+	15.7207i	0.165605	+	0.618046i	0.997962	+	0.0638065i	$0.0203240\pi$
$647$	4.21236	+	15.7207i	0.165605	+	0.618046i	−0.832357	+	0.554239i	$0.813009\pi$
$648$		0			0
$649$	−3.48316	+	12.9993i	−0.136726	+	0.510268i
$650$		0			0
$651$	1.14343	−	4.26732i	0.0448144	−	0.167250i
$652$		0			0
$653$	13.0872	−	3.50669i	0.512140	−	0.137227i	0.00651143	−	0.999979i	$-0.497927\pi$
$653$	13.0872	−	3.50669i	0.512140	−	0.137227i	0.505628	+	0.862751i	$0.331261\pi$
$654$		0			0
$655$		−	5.08841i		−	0.198821i
$656$		0			0
$657$	10.8502	−	6.26439i	0.423308	−	0.244397i
$658$		0			0
$659$	1.66039	−	2.87588i	0.0646797	−	0.112029i	−0.831872	−	0.554967i	$-0.812731\pi$
$659$	1.66039	−	2.87588i	0.0646797	−	0.112029i	0.896552	+	0.442939i	$0.146064\pi$
$660$		0			0
$661$	8.81827	−	2.36285i	0.342991	−	0.0919042i	−0.0832116	−	0.996532i	$-0.526518\pi$
$661$	8.81827	−	2.36285i	0.342991	−	0.0919042i	0.426203	+	0.904628i	$0.359851\pi$
$662$		0			0
$663$	−26.6633	−	15.3941i	−1.03552	−	0.597857i
$664$		0			0
$665$		−	0.140031i		−	0.00543017i
$666$		0			0
$667$		−	4.88045i		−	0.188972i
$668$		0			0
$669$	−32.9675	−	19.0338i	−1.27460	−	0.735888i
$670$		0			0
$671$	−15.8307	+	4.24182i	−0.611137	+	0.163754i
$672$		0			0
$673$	−2.14668	+	3.71816i	−0.0827484	+	0.143324i	−0.904430	−	0.426623i	$-0.859703\pi$
$673$	−2.14668	+	3.71816i	−0.0827484	+	0.143324i	0.821681	+	0.569947i	$0.193036\pi$
$674$		0			0
$675$	6.50142	−	3.75360i	0.250240	−	0.144476i
$676$		0			0
$677$		−	33.2544i		−	1.27807i	−0.769178	−	0.639035i	$-0.779334\pi$
$677$		−	33.2544i		−	1.27807i	0.769178	−	0.639035i	$-0.220666\pi$
$678$		0			0
$679$	−3.75120	+	1.00513i	−0.143958	+	0.0385734i
$680$		0			0
$681$	−5.41184	+	20.1973i	−0.207382	+	0.773960i
$682$		0			0
$683$	12.4399	−	46.4263i	0.475999	−	1.77645i	−0.141560	−	0.989930i	$-0.545212\pi$
$683$	12.4399	−	46.4263i	0.475999	−	1.77645i	0.617559	−	0.786524i	$-0.288122\pi$
$684$		0			0
$685$	1.79009	+	6.68070i	0.0683958	+	0.255257i
$686$		0			0
$687$	2.27200	+	3.93522i	0.0866822	+	0.150138i
$688$		0			0
$689$	17.1447	−	17.1447i	0.653162	−	0.653162i
$690$		0			0
$691$	−0.893506	−	1.54760i	−0.0339906	−	0.0588734i	0.848530	−	0.529148i	$-0.177488\pi$
$691$	−0.893506	−	1.54760i	−0.0339906	−	0.0588734i	−0.882520	+	0.470274i	$0.844155\pi$
$692$		0			0
$693$		−	4.46122i		−	0.169468i
$694$		0			0
$695$	−2.49554	+	2.49554i	−0.0946613	+	0.0946613i
$696$		0			0
$697$	5.35602	+	5.35602i	0.202874	+	0.202874i
$698$		0			0
$699$	3.57289	+	2.06281i	0.135139	+	0.0780226i
$700$		0			0
$701$	42.8692	+	11.4868i	1.61915	+	0.433849i	0.950751	−	0.309957i	$-0.100314\pi$
$701$	42.8692	+	11.4868i	1.61915	+	0.433849i	0.668396	+	0.743806i	$0.266981\pi$
$702$		0			0
$703$	2.49424	−	4.95558i	0.0940719	−	0.186903i
$704$		0			0
$705$	1.80289	−	6.72849i	0.0679009	−	0.253410i
$706$		0			0
$707$	2.31491	−	4.00954i	0.0870612	−	0.150794i
$708$		0			0
$709$	−25.7523	+	25.7523i	−0.967146	+	0.967146i	−0.999477	−	0.0323308i	$-0.989707\pi$
$709$	−25.7523	+	25.7523i	−0.967146	+	0.967146i	0.0323308	+	0.999477i	$0.489707\pi$
$710$		0			0
$711$	27.5993	+	27.5993i	1.03506	+	1.03506i
$712$		0			0
$713$	8.59923			0.322044
$714$		0			0
$715$	7.01045	−	4.04748i	0.262176	−	0.151367i
$716$		0			0
$717$	−33.3204	−	33.3204i	−1.24437	−	1.24437i
$718$		0			0
$719$	17.8103	−	10.2828i	0.664213	−	0.383484i	−0.129667	−	0.991558i	$-0.541391\pi$
$719$	17.8103	−	10.2828i	0.664213	−	0.383484i	0.793880	+	0.608074i	$0.208058\pi$
$720$		0			0
$721$	4.12990	−	1.10660i	0.153806	−	0.0412121i
$722$		0			0
$723$	−0.674546	−	0.180744i	−0.0250866	−	0.00672194i
$724$		0			0
$725$	−15.0214	−	4.02498i	−0.557881	−	0.149484i
$726$		0			0
$727$	−10.5396	−	39.3344i	−0.390893	−	1.45883i	−0.828664	−	0.559746i	$-0.810899\pi$
$727$	−10.5396	−	39.3344i	−0.390893	−	1.45883i	0.437771	−	0.899087i	$-0.355768\pi$
$728$		0			0
$729$	−36.7257			−1.36021
$730$		0			0
$731$	12.2466	+	21.2118i	0.452958	+	0.784547i
$732$		0			0
$733$	−5.51097	−	3.18176i	−0.203552	−	0.117521i	0.394759	−	0.918785i	$-0.370828\pi$
$733$	−5.51097	−	3.18176i	−0.203552	−	0.117521i	−0.598311	+	0.801264i	$0.704161\pi$
$734$		0			0
$735$	−2.38205	−	8.88992i	−0.0878631	−	0.327910i
$736$		0			0
$737$	0.251774	−	0.436085i	0.00927422	−	0.0160634i
$738$		0			0
$739$	23.0713			0.848690			0.424345	−	0.905501i	$-0.360504\pi$
$739$	23.0713			0.848690			0.424345	+	0.905501i	$0.360504\pi$
$740$		0			0
$741$	−8.82213			−0.324089
$742$		0			0
$743$	−14.2247	+	24.6380i	−0.521855	+	0.903880i	0.477822	+	0.878457i	$0.341427\pi$
$743$	−14.2247	+	24.6380i	−0.521855	+	0.903880i	−0.999677	+	0.0254229i	$0.991907\pi$
$744$		0			0
$745$	2.74422	+	10.2416i	0.100541	+	0.375222i
$746$		0			0
$747$	37.7467	+	21.7930i	1.38108	+	0.797366i
$748$		0			0
$749$	2.66786	+	4.62086i	0.0974813	+	0.168843i
$750$		0			0
$751$	−10.7992			−0.394068			−0.197034	−	0.980397i	$-0.563131\pi$
$751$	−10.7992			−0.394068			−0.197034	+	0.980397i	$0.563131\pi$
$752$		0			0
$753$	−6.93518	−	25.8824i	−0.252732	−	0.943208i
$754$		0			0
$755$	−5.38067	−	1.44175i	−0.195823	−	0.0524705i
$756$		0			0
$757$	−41.0579	−	11.0014i	−1.49228	−	0.399854i	−0.581771	−	0.813353i	$-0.697640\pi$
$757$	−41.0579	−	11.0014i	−1.49228	−	0.399854i	−0.910505	+	0.413498i	$0.864307\pi$
$758$		0			0
$759$	15.3452	−	4.11173i	0.556995	−	0.149246i
$760$		0			0
$761$	9.19288	−	5.30751i	0.333242	−	0.192397i	−0.324038	−	0.946044i	$-0.605041\pi$
$761$	9.19288	−	5.30751i	0.333242	−	0.192397i	0.657279	+	0.753647i	$0.271707\pi$
$762$		0			0
$763$	0.622291	+	0.622291i	0.0225284	+	0.0225284i
$764$		0			0
$765$	5.16073	−	2.97955i	0.186587	−	0.107726i
$766$		0			0
$767$	−12.1685			−0.439380
$768$		0			0
$769$	10.2432	+	10.2432i	0.369380	+	0.369380i	0.867251	−	0.497871i	$-0.165885\pi$
$769$	10.2432	+	10.2432i	0.369380	+	0.369380i	−0.497871	+	0.867251i	$0.665885\pi$
$770$		0			0
$771$	44.1008	−	44.1008i	1.58825	−	1.58825i
$772$		0			0
$773$	13.6617	−	23.6627i	0.491377	−	0.851090i	−0.508574	−	0.861018i	$-0.669827\pi$
$773$	13.6617	−	23.6627i	0.491377	−	0.851090i	0.999951	+	0.00992855i	$0.00316041\pi$
$774$		0			0
$775$	7.09191	−	26.4674i	0.254749	−	0.950736i
$776$		0			0
$777$	−0.942447	+	4.54412i	−0.0338101	+	0.163019i
$778$		0			0
$779$	2.09648	+	0.561750i	0.0751142	+	0.0201268i
$780$		0			0
$781$	4.93177	+	2.84736i	0.176472	+	0.101886i
$782$		0			0
$783$	−3.68664	−	3.68664i	−0.131750	−	0.131750i
$784$		0			0
$785$	5.74572	−	5.74572i	0.205073	−	0.205073i
$786$		0			0
$787$			2.90029i			0.103384i	0.998663	+	0.0516921i	$0.0164614\pi$
$787$			2.90029i			0.103384i	−0.998663	+	0.0516921i	$0.983539\pi$
$788$		0			0
$789$	−21.7254	−	37.6295i	−0.773445	−	1.33965i
$790$		0			0
$791$	2.54321	−	2.54321i	0.0904263	−	0.0904263i
$792$		0			0
$793$	−7.40948	−	12.8336i	−0.263118	−	0.455734i
$794$		0			0
$795$	2.22211	+	8.29301i	0.0788100	+	0.294123i
$796$		0			0
$797$	10.3694	−	38.6991i	0.367302	−	1.37079i	−0.496970	−	0.867768i	$-0.665554\pi$
$797$	10.3694	−	38.6991i	0.367302	−	1.37079i	0.864273	−	0.503024i	$-0.167779\pi$
$798$		0			0
$799$	−4.30981	+	16.0844i	−0.152470	+	0.569026i
$800$		0			0
$801$	38.6053	−	10.3443i	1.36405	−	0.365497i
$802$		0			0
$803$		−	14.4064i		−	0.508390i
$804$		0			0
$805$	−0.197456	+	0.114001i	−0.00695942	+	0.00401802i
$806$		0			0
$807$	3.21994	−	5.57710i	0.113347	−	0.196323i
$808$		0			0
$809$	−21.1055	+	5.65519i	−0.742029	+	0.198826i	−0.609980	−	0.792417i	$-0.708822\pi$
$809$	−21.1055	+	5.65519i	−0.742029	+	0.198826i	−0.132049	+	0.991243i	$0.542156\pi$
$810$		0			0
$811$	−2.77274	−	1.60084i	−0.0973642	−	0.0562133i	0.450527	−	0.892763i	$-0.351236\pi$
$811$	−2.77274	−	1.60084i	−0.0973642	−	0.0562133i	−0.547892	+	0.836549i	$0.684569\pi$
$812$		0			0
$813$			67.0374i			2.35111i
$814$		0			0
$815$		−	3.39920i		−	0.119069i
$816$		0			0
$817$	6.07809	+	3.50919i	0.212645	+	0.122771i
$818$		0			0
$819$	3.89636	−	1.04403i	0.136150	−	0.0364812i
$820$		0			0
$821$	10.5454	−	18.2652i	0.368038	−	0.637460i	−0.621221	−	0.783636i	$-0.713363\pi$
$821$	10.5454	−	18.2652i	0.368038	−	0.637460i	0.989259	+	0.146175i	$0.0466963\pi$
$822$		0			0
$823$	13.8815	−	8.01450i	0.483880	−	0.279368i	−0.238152	−	0.971228i	$-0.576542\pi$
$823$	13.8815	−	8.01450i	0.483880	−	0.279368i	0.722032	+	0.691860i	$0.243208\pi$
$824$		0			0
$825$		−	50.6216i		−	1.76242i
$826$		0			0
$827$	−31.9156	+	8.55175i	−1.10981	+	0.297373i	−0.766754	−	0.641941i	$-0.778129\pi$
$827$	−31.9156	+	8.55175i	−1.10981	+	0.297373i	−0.343058	+	0.939314i	$0.611463\pi$
$828$		0			0
$829$	7.48085	−	27.9189i	0.259821	−	0.969664i	−0.705524	−	0.708686i	$-0.749288\pi$
$829$	7.48085	−	27.9189i	0.259821	−	0.969664i	0.965345	−	0.260978i	$-0.0840451\pi$
$830$		0			0
$831$	−12.1594	+	45.3795i	−0.421805	+	1.57420i
$832$		0			0
$833$	5.69427	+	21.2513i	0.197295	+	0.736314i
$834$		0			0
$835$	−3.19001	−	5.52526i	−0.110395	−	0.191210i
$836$		0			0
$837$	6.49577	−	6.49577i	0.224527	−	0.224527i
$838$		0			0
$839$	−14.2369	−	24.6591i	−0.491514	−	0.851327i	0.508438	−	0.861098i	$-0.330223\pi$
$839$	−14.2369	−	24.6591i	−0.491514	−	0.851327i	−0.999952	+	0.00977112i	$0.996890\pi$
$840$		0			0
$841$		−	18.1997i		−	0.627576i
$842$		0			0
$843$	55.5930	−	55.5930i	1.91472	−	1.91472i
$844$		0			0
$845$	0.417280	+	0.417280i	0.0143549	+	0.0143549i
$846$		0			0
$847$	−1.61703	−	0.933592i	−0.0555618	−	0.0320786i
$848$		0			0
$849$	−75.8111	−	20.3135i	−2.60183	−	0.697158i
$850$		0			0
$851$	−9.01841	+	0.517317i	−0.309147	+	0.0177334i
$852$		0			0
$853$	−4.99961	+	18.6588i	−0.171184	+	0.638866i	0.825987	+	0.563690i	$0.190619\pi$
$853$	−4.99961	+	18.6588i	−0.171184	+	0.638866i	−0.997170	+	0.0751761i	$0.976048\pi$
$854$		0			0
$855$	0.853769	−	1.47877i	0.0291983	−	0.0505729i
$856$		0			0
$857$	9.55942	−	9.55942i	0.326544	−	0.326544i	−0.524727	−	0.851271i	$-0.675833\pi$
$857$	9.55942	−	9.55942i	0.326544	−	0.326544i	0.851271	+	0.524727i	$0.175833\pi$
$858$		0			0
$859$	17.1237	+	17.1237i	0.584254	+	0.584254i	0.936069	−	0.351815i	$-0.114435\pi$
$859$	17.1237	+	17.1237i	0.584254	+	0.584254i	−0.351815	+	0.936069i	$0.614435\pi$
$860$		0			0
$861$	−1.81558			−0.0618748
$862$		0			0
$863$	−2.25254	+	1.30050i	−0.0766773	+	0.0442696i	−0.537848	−	0.843042i	$-0.680763\pi$
$863$	−2.25254	+	1.30050i	−0.0766773	+	0.0442696i	0.461171	+	0.887311i	$0.347429\pi$
$864$		0			0
$865$	−0.271611	−	0.271611i	−0.00923506	−	0.00923506i
$866$		0			0
$867$	15.3009	−	8.83396i	0.519645	−	0.300017i
$868$		0			0
$869$	43.3514	−	11.6160i	1.47060	−	0.394045i
$870$		0			0
$871$	0.439791	+	0.117842i	0.0149017	+	0.00399291i
$872$		0			0
$873$	−45.7421	−	12.2565i	−1.54813	−	0.414821i
$874$		0			0
$875$	0.386722	+	1.44327i	0.0130736	+	0.0487913i
$876$		0			0
$877$	−26.8250			−0.905816			−0.452908	−	0.891557i	$-0.649613\pi$
$877$	−26.8250			−0.905816			−0.452908	+	0.891557i	$0.649613\pi$
$878$		0			0
$879$	−5.46014	−	9.45724i	−0.184166	−	0.318985i
$880$		0			0
$881$	8.84197	+	5.10491i	0.297894	+	0.171989i	0.641496	−	0.767126i	$-0.278314\pi$
$881$	8.84197	+	5.10491i	0.297894	+	0.171989i	−0.343603	+	0.939115i	$0.611647\pi$
$882$		0			0
$883$	−8.91107	−	33.2566i	−0.299881	−	1.11917i	−0.937263	−	0.348624i	$-0.886649\pi$
$883$	−8.91107	−	33.2566i	−0.299881	−	1.11917i	0.637381	−	0.770549i	$-0.280018\pi$
$884$		0			0
$885$	2.15442	−	3.73157i	0.0724202	−	0.125435i
$886$		0			0
$887$	−24.5451			−0.824144			−0.412072	−	0.911151i	$-0.635195\pi$
$887$	−24.5451			−0.824144			−0.412072	+	0.911151i	$0.635195\pi$
$888$		0			0
$889$	4.19731			0.140773
$890$		0			0
$891$	−14.0761	+	24.3806i	−0.471568	+	0.816780i
$892$		0			0
$893$	1.23495	+	4.60888i	0.0413259	+	0.154230i
$894$		0			0
$895$	−10.6791	−	6.16561i	−0.356965	−	0.206094i
$896$		0			0
$897$	7.18224	+	12.4400i	0.239808	+	0.415359i
$898$		0			0
$899$	−19.0298			−0.634681
$900$		0			0
$901$	−5.31194	−	19.8244i	−0.176966	−	0.660447i
$902$		0			0
$903$	−5.67085	−	1.51950i	−0.188714	−	0.0505658i
$904$		0			0
$905$	−4.98908	−	1.33682i	−0.165843	−	0.0444374i
$906$		0			0
$907$	−46.9660	+	12.5845i	−1.55948	+	0.417861i	−0.932499	−	0.361174i	$-0.882376\pi$
$907$	−46.9660	+	12.5845i	−1.55948	+	0.417861i	−0.626981	+	0.779035i	$0.715710\pi$
$908$		0			0
$909$	48.8923	−	28.2280i	1.62166	−	0.936264i
$910$		0			0
$911$	25.0804	+	25.0804i	0.830951	+	0.830951i	0.987647	−	0.156696i	$-0.0500843\pi$
$911$	25.0804	+	25.0804i	0.830951	+	0.830951i	−0.156696	+	0.987647i	$0.550084\pi$
$912$		0			0
$913$	43.4035	−	25.0590i	1.43644	−	0.829332i
$914$		0			0
$915$	5.24736			0.173472
$916$		0			0
$917$	−2.06164	−	2.06164i	−0.0680814	−	0.0680814i
$918$		0			0
$919$	−40.2335	+	40.2335i	−1.32718	+	1.32718i	−0.419361	+	0.907820i	$0.637746\pi$
$919$	−40.2335	+	40.2335i	−1.32718	+	1.32718i	−0.907820	+	0.419361i	$0.862254\pi$
$920$		0			0
$921$	44.2580	−	76.6572i	1.45835	−	2.52594i
$922$		0			0
$923$	−1.33269	+	4.97367i	−0.0438661	+	0.163710i
$924$		0			0
$925$	−5.84537	+	28.1842i	−0.192195	+	0.926690i
$926$		0			0
$927$	50.3600	+	13.4939i	1.65404	+	0.443199i
$928$		0			0
$929$	−4.20850	−	2.42978i	−0.138076	−	0.0797185i	0.429370	−	0.903128i	$-0.358735\pi$
$929$	−4.20850	−	2.42978i	−0.138076	−	0.0797185i	−0.567447	+	0.823410i	$0.692069\pi$
$930$		0			0
$931$	4.45776	+	4.45776i	0.146097	+	0.146097i
$932$		0			0
$933$	−45.1114	+	45.1114i	−1.47688	+	1.47688i
$934$		0			0
$935$		−	6.85214i		−	0.224089i
$936$		0			0
$937$	−19.0638	−	33.0194i	−0.622786	−	1.07870i	−0.988965	−	0.148152i	$-0.952668\pi$
$937$	−19.0638	−	33.0194i	−0.622786	−	1.07870i	0.366179	−	0.930544i	$-0.380666\pi$
$938$		0			0
$939$	−19.0180	+	19.0180i	−0.620628	+	0.620628i
$940$		0			0
$941$	13.5124	+	23.4041i	0.440490	+	0.762952i	0.997726	−	0.0674027i	$-0.0214712\pi$
$941$	13.5124	+	23.4041i	0.440490	+	0.762952i	−0.557235	+	0.830355i	$0.688138\pi$
$942$		0			0
$943$	−0.914659	−	3.41355i	−0.0297854	−	0.111161i
$944$		0			0
$945$	−0.0630409	+	0.235272i	−0.00205072	+	0.00765340i
$946$		0			0
$947$	3.97061	−	14.8185i	0.129027	−	0.481537i	−0.870924	−	0.491418i	$-0.836479\pi$
$947$	3.97061	−	14.8185i	0.129027	−	0.481537i	0.999951	+	0.00988126i	$0.00314535\pi$
$948$		0			0
$949$	12.5823	−	3.37141i	0.408438	−	0.109441i
$950$		0			0
$951$			67.4567i			2.18743i
$952$		0			0
$953$	6.95313	−	4.01439i	0.225234	−	0.130039i	−0.383137	−	0.923691i	$-0.625156\pi$
$953$	6.95313	−	4.01439i	0.225234	−	0.130039i	0.608371	+	0.793652i	$0.291823\pi$
$954$		0			0
$955$	−5.38525	+	9.32752i	−0.174263	+	0.301832i
$956$		0			0
$957$	−33.9584	+	9.09913i	−1.09772	+	0.294133i
$958$		0			0
$959$	3.43206	+	1.98150i	0.110827	+	0.0639860i
$960$		0			0
$961$		−	2.53011i		−	0.0816165i
$962$		0			0
$963$			65.0636i			2.09665i
$964$		0			0
$965$	−4.73763	−	2.73527i	−0.152510	−	0.0880515i
$966$		0			0
$967$	−53.7080	+	14.3910i	−1.72713	+	0.462784i	−0.979520	−	0.201349i	$-0.935467\pi$
$967$	−53.7080	+	14.3910i	−1.72713	+	0.462784i	−0.747614	+	0.664133i	$0.768801\pi$
$968$		0			0
$969$	−3.73383	+	6.46719i	−0.119948	+	0.207756i
$970$		0			0
$971$	−6.25891	+	3.61358i	−0.200858	+	0.115965i	−0.597056	−	0.802200i	$-0.703663\pi$
$971$	−6.25891	+	3.61358i	−0.200858	+	0.115965i	0.396198	+	0.918165i	$0.370329\pi$
$972$		0			0
$973$			2.02221i			0.0648290i
$974$		0			0
$975$	44.2120	−	11.8466i	1.41592	−	0.379394i
$976$		0			0
$977$	1.91222	−	7.13651i	0.0611774	−	0.228317i	−0.928567	−	0.371164i	$-0.878959\pi$
$977$	1.91222	−	7.13651i	0.0611774	−	0.228317i	0.989745	+	0.142846i	$0.0456255\pi$
$978$		0			0
$979$	11.8945	−	44.3908i	0.380150	−	1.41874i
$980$		0			0
$981$	2.77748	+	10.3657i	0.0886780	+	0.330951i
$982$		0			0
$983$	−16.5421	−	28.6517i	−0.527610	−	0.913847i	−0.999482	−	0.0321798i	$-0.989755\pi$
$983$	−16.5421	−	28.6517i	−0.527610	−	0.913847i	0.471872	−	0.881667i	$-0.343578\pi$
$984$		0			0
$985$	1.68393	−	1.68393i	0.0536543	−	0.0536543i
$986$		0			0
$987$	−1.99567	−	3.45661i	−0.0635230	−	0.110025i
$988$		0			0
$989$		−	11.4275i		−	0.363374i
$990$		0			0
$991$	−19.2544	+	19.2544i	−0.611635	+	0.611635i	−0.943372	−	0.331737i	$-0.892365\pi$
$991$	−19.2544	+	19.2544i	−0.611635	+	0.611635i	0.331737	+	0.943372i	$0.392365\pi$
$992$		0			0
$993$	19.5710	+	19.5710i	0.621066	+	0.621066i
$994$		0			0
$995$	−8.97161	−	5.17976i	−0.284419	−	0.164209i
$996$		0			0
$997$	−28.3214	−	7.58868i	−0.896946	−	0.240336i	−0.219242	−	0.975671i	$-0.570358\pi$
$997$	−28.3214	−	7.58868i	−0.896946	−	0.240336i	−0.677704	+	0.735334i	$0.737025\pi$
$998$		0			0
$999$	−6.42163	+	7.20318i	−0.203171	+	0.227899i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	592.2.be.d.399.1	yes	16
4.3	odd	2	inner	592.2.be.d.399.4	yes	16
37.23	odd	12	inner	592.2.be.d.319.4	yes	16
148.23	even	12	inner	592.2.be.d.319.1	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
592.2.be.d.319.1	✓	16	148.23	even	12	inner
592.2.be.d.319.4	yes	16	37.23	odd	12	inner
592.2.be.d.399.1	yes	16	1.1	even	1	trivial
592.2.be.d.399.4	yes	16	4.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 592 = 2^{4} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	592.be (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.28615 + 2.22768i) q^{3} +(-0.133975 - 0.500000i) q^{5} +(-0.256864 - 0.148300i) q^{7} +(-1.80837 - 3.13219i) q^{9} -4.15876 q^{11} +(-0.973243 - 3.63219i) q^{13} +(1.28615 + 0.344623i) q^{15} +(-3.07454 - 0.823821i) q^{17} +(-0.880988 + 0.236060i) q^{19} +(0.660731 - 0.381473i) q^{21} +(1.05009 + 1.05009i) q^{23} +(4.09808 - 2.36603i) q^{25} +1.58646 q^{27} +(-2.32382 - 2.32382i) q^{29} +(4.09452 - 4.09452i) q^{31} +(5.34880 - 9.26439i) q^{33} +(-0.0397369 + 0.148300i) q^{35} +(-4.04778 + 4.54042i) q^{37} +(9.34310 + 2.50348i) q^{39} +(-2.06087 - 1.18985i) q^{41} +(-5.44121 - 5.44121i) q^{43} +(-1.32382 + 1.32382i) q^{45} -5.23149i q^{47} +(-3.45601 - 5.98599i) q^{49} +(5.78953 - 5.78953i) q^{51} +(3.22396 + 5.58407i) q^{53} +(0.557168 + 2.07938i) q^{55} +(0.607218 - 2.26617i) q^{57} +(0.837547 - 3.12577i) q^{59} +(3.80659 - 1.01997i) q^{61} +1.07273i q^{63} +(-1.68571 + 0.973243i) q^{65} +(-0.0605407 + 0.104859i) q^{67} +(-3.68985 + 0.988691i) q^{69} +(-1.18587 - 0.684665i) q^{71} +3.46410i q^{73} +12.1723i q^{75} +(1.06823 + 0.616745i) q^{77} +(-10.4241 + 2.79313i) q^{79} +(3.38469 - 5.86246i) q^{81} +(-10.4366 + 6.02559i) q^{83} +1.64764i q^{85} +(8.16552 - 2.18794i) q^{87} +(-2.86010 + 10.6741i) q^{89} +(-0.288665 + 1.07731i) q^{91} +(3.85510 + 14.3874i) q^{93} +(0.236060 + 0.408868i) q^{95} +(9.25847 - 9.25847i) q^{97} +(7.52059 + 13.0260i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{5} - 4 q^{9} - 4 q^{13} + 12 q^{17} + 36 q^{21} + 24 q^{25} - 12 q^{29} + 8 q^{33} + 8 q^{37} - 36 q^{41} + 4 q^{45} + 20 q^{49} + 4 q^{53} + 12 q^{57} - 28 q^{61} - 20 q^{69} + 32 q^{81} + 20 q^{89}+ \cdots - 4 q^{97}+O(q^{100}) \) 16 * q - 16 * q^5 - 4 * q^9 - 4 * q^13 + 12 * q^17 + 36 * q^21 + 24 * q^25 - 12 * q^29 + 8 * q^33 + 8 * q^37 - 36 * q^41 + 4 * q^45 + 20 * q^49 + 4 * q^53 + 12 * q^57 - 28 * q^61 - 20 * q^69 + 32 * q^81 + 20 * q^89 - 60 * q^93 - 4 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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