LMFDB - Embedded newform 465.2.i.b.211.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [465,2,Mod(211,465)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(465, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("465.211");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 465 = 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	465.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.71304369399$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{97})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 25x^{2} + 24x + 576 $ x^4 - x^3 + 25x^2 + 24x + 576
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			211.2
Root			$2.71221 - 4.69769i$ of defining polynomial
Character	$\chi$	$=$	465.211
Dual form			465.2.i.b.346.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{3} -2.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{3} -2.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{9} +(2.71221 - 4.69769i) q^{11} +(-1.00000 - 1.73205i) q^{12} +(2.21221 - 3.83167i) q^{13} +1.00000 q^{15} +4.00000 q^{16} +(2.00000 + 3.46410i) q^{17} +(4.21221 + 7.29577i) q^{19} +(-1.00000 + 1.73205i) q^{20} +2.00000 q^{23} +(-0.500000 - 0.866025i) q^{25} -1.00000 q^{27} +3.42443 q^{29} +(-4.71221 - 2.96564i) q^{31} +5.42443 q^{33} +(1.00000 - 1.73205i) q^{36} +(-4.21221 - 7.29577i) q^{37} +4.42443 q^{39} +(0.712214 - 1.23359i) q^{41} +(-3.21221 - 5.56372i) q^{43} +(-5.42443 + 9.39539i) q^{44} +(0.500000 + 0.866025i) q^{45} +8.84886 q^{47} +(2.00000 + 3.46410i) q^{48} +(3.50000 - 6.06218i) q^{49} +(-2.00000 + 3.46410i) q^{51} +(-4.42443 + 7.66334i) q^{52} +(-5.42443 + 9.39539i) q^{53} +(-2.71221 - 4.69769i) q^{55} +(-4.21221 + 7.29577i) q^{57} +(2.71221 + 4.69769i) q^{59} -2.00000 q^{60} +4.57557 q^{61} -8.00000 q^{64} +(-2.21221 - 3.83167i) q^{65} +(-3.42443 + 5.93128i) q^{67} +(-4.00000 - 6.92820i) q^{68} +(1.00000 + 1.73205i) q^{69} +(3.71221 - 6.42974i) q^{71} +(0.787786 - 1.36448i) q^{73} +(0.500000 - 0.866025i) q^{75} +(-8.42443 - 14.5915i) q^{76} +(-6.13664 - 10.6290i) q^{79} +(2.00000 - 3.46410i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-3.00000 + 5.19615i) q^{83} +4.00000 q^{85} +(1.71221 + 2.96564i) q^{87} -13.4244 q^{89} -4.00000 q^{92} +(0.212214 - 5.56372i) q^{93} +8.42443 q^{95} -12.4244 q^{97} +(2.71221 + 4.69769i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} - 8 q^{4} + 2 q^{5} - 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^3 - 8 * q^4 + 2 * q^5 - 2 * q^9	$ 4 q + 2 q^{3} - 8 q^{4} + 2 q^{5} - 2 q^{9} + q^{11} - 4 q^{12} - q^{13} + 4 q^{15} + 16 q^{16} + 8 q^{17} + 7 q^{19} - 4 q^{20} + 8 q^{23} - 2 q^{25} - 4 q^{27} - 6 q^{29} - 9 q^{31} + 2 q^{33} + 4 q^{36} - 7 q^{37} - 2 q^{39} - 7 q^{41} - 3 q^{43} - 2 q^{44} + 2 q^{45} - 4 q^{47} + 8 q^{48} + 14 q^{49} - 8 q^{51} + 2 q^{52} - 2 q^{53} - q^{55} - 7 q^{57} + q^{59} - 8 q^{60} + 38 q^{61} - 32 q^{64} + q^{65} + 6 q^{67} - 16 q^{68} + 4 q^{69} + 5 q^{71} + 13 q^{73} + 2 q^{75} - 14 q^{76} + 5 q^{79} + 8 q^{80} - 2 q^{81} - 12 q^{83} + 16 q^{85} - 3 q^{87} - 34 q^{89} - 16 q^{92} - 9 q^{93} + 14 q^{95} - 30 q^{97} + q^{99}+O(q^{100}) $ 4 * q + 2 * q^3 - 8 * q^4 + 2 * q^5 - 2 * q^9 + q^11 - 4 * q^12 - q^13 + 4 * q^15 + 16 * q^16 + 8 * q^17 + 7 * q^19 - 4 * q^20 + 8 * q^23 - 2 * q^25 - 4 * q^27 - 6 * q^29 - 9 * q^31 + 2 * q^33 + 4 * q^36 - 7 * q^37 - 2 * q^39 - 7 * q^41 - 3 * q^43 - 2 * q^44 + 2 * q^45 - 4 * q^47 + 8 * q^48 + 14 * q^49 - 8 * q^51 + 2 * q^52 - 2 * q^53 - q^55 - 7 * q^57 + q^59 - 8 * q^60 + 38 * q^61 - 32 * q^64 + q^65 + 6 * q^67 - 16 * q^68 + 4 * q^69 + 5 * q^71 + 13 * q^73 + 2 * q^75 - 14 * q^76 + 5 * q^79 + 8 * q^80 - 2 * q^81 - 12 * q^83 + 16 * q^85 - 3 * q^87 - 34 * q^89 - 16 * q^92 - 9 * q^93 + 14 * q^95 - 30 * q^97 + q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/465\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$406$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0			−	1.00000i	$-0.5\pi$
$2$		0			0				1.00000i	$0.5\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−2.00000			−1.00000
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$		0			0
$7$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$7$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	2.71221	−	4.69769i	0.817763	−	1.41641i	−0.0895631	−	0.995981i	$-0.528547\pi$
$11$	2.71221	−	4.69769i	0.817763	−	1.41641i	0.907327	−	0.420427i	$-0.138120\pi$
$12$	−1.00000	−	1.73205i	−0.288675	−	0.500000i
$13$	2.21221	−	3.83167i	0.613558	−	1.06271i	−0.377078	−	0.926182i	$-0.623071\pi$
$13$	2.21221	−	3.83167i	0.613558	−	1.06271i	0.990636	−	0.136532i	$-0.0435956\pi$
$14$		0			0
$15$	1.00000			0.258199
$16$	4.00000			1.00000
$17$	2.00000	+	3.46410i	0.485071	+	0.840168i	0.999853	−	0.0171533i	$-0.00546033\pi$
$17$	2.00000	+	3.46410i	0.485071	+	0.840168i	−0.514782	+	0.857321i	$0.672127\pi$
$18$		0			0
$19$	4.21221	+	7.29577i	0.966348	+	1.67376i	0.705948	+	0.708264i	$0.250521\pi$
$19$	4.21221	+	7.29577i	0.966348	+	1.67376i	0.260400	+	0.965501i	$0.416146\pi$
$20$	−1.00000	+	1.73205i	−0.223607	+	0.387298i
$21$		0			0
$22$		0			0
$23$	2.00000			0.417029			0.208514	−	0.978019i	$-0.433137\pi$
$23$	2.00000			0.417029			0.208514	+	0.978019i	$0.433137\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	3.42443			0.635900			0.317950	−	0.948107i	$-0.397006\pi$
$29$	3.42443			0.635900			0.317950	+	0.948107i	$0.397006\pi$
$30$		0			0
$31$	−4.71221	−	2.96564i	−0.846339	−	0.532645i
$31$	−4.71221	−	2.96564i	−0.846339	−	0.532645i
$32$		0			0
$33$	5.42443			0.944272
$34$		0			0
$35$		0			0
$36$	1.00000	−	1.73205i	0.166667	−	0.288675i
$37$	−4.21221	−	7.29577i	−0.692484	−	1.19942i	−0.971022	−	0.238992i	$-0.923183\pi$
$37$	−4.21221	−	7.29577i	−0.692484	−	1.19942i	0.278538	−	0.960425i	$-0.410150\pi$
$38$		0			0
$39$	4.42443			0.708476
$40$		0			0
$41$	0.712214	−	1.23359i	0.111229	−	0.192655i	−0.805037	−	0.593225i	$-0.797855\pi$
$41$	0.712214	−	1.23359i	0.111229	−	0.192655i	0.916266	+	0.400570i	$0.131188\pi$
$42$		0			0
$43$	−3.21221	−	5.56372i	−0.489858	−	0.848459i	0.510074	−	0.860131i	$-0.329618\pi$
$43$	−3.21221	−	5.56372i	−0.489858	−	0.848459i	−0.999932	+	0.0116715i	$0.996285\pi$
$44$	−5.42443	+	9.39539i	−0.817763	+	1.41641i
$45$	0.500000	+	0.866025i	0.0745356	+	0.129099i
$46$		0			0
$47$	8.84886			1.29074			0.645369	−	0.763871i	$-0.276704\pi$
$47$	8.84886			1.29074			0.645369	+	0.763871i	$0.276704\pi$
$48$	2.00000	+	3.46410i	0.288675	+	0.500000i
$49$	3.50000	−	6.06218i	0.500000	−	0.866025i
$50$		0			0
$51$	−2.00000	+	3.46410i	−0.280056	+	0.485071i
$52$	−4.42443	+	7.66334i	−0.613558	+	1.06271i
$53$	−5.42443	+	9.39539i	−0.745103	+	1.29056i	0.205044	+	0.978753i	$0.434266\pi$
$53$	−5.42443	+	9.39539i	−0.745103	+	1.29056i	−0.950147	+	0.311803i	$0.899067\pi$
$54$		0			0
$55$	−2.71221	−	4.69769i	−0.365715	−	0.633437i
$56$		0			0
$57$	−4.21221	+	7.29577i	−0.557921	+	0.966348i
$58$		0			0
$59$	2.71221	+	4.69769i	0.353100	+	0.611588i	0.986791	−	0.161999i	$-0.0517941\pi$
$59$	2.71221	+	4.69769i	0.353100	+	0.611588i	−0.633691	+	0.773587i	$0.718461\pi$
$60$	−2.00000			−0.258199
$61$	4.57557			0.585842			0.292921	−	0.956137i	$-0.405373\pi$
$61$	4.57557			0.585842			0.292921	+	0.956137i	$0.405373\pi$
$62$		0			0
$63$		0			0
$64$	−8.00000			−1.00000
$65$	−2.21221	−	3.83167i	−0.274391	−	0.475260i
$66$		0			0
$67$	−3.42443	+	5.93128i	−0.418361	+	0.724622i	−0.995775	−	0.0918296i	$-0.970728\pi$
$67$	−3.42443	+	5.93128i	−0.418361	+	0.724622i	0.577414	+	0.816451i	$0.304062\pi$
$68$	−4.00000	−	6.92820i	−0.485071	−	0.840168i
$69$	1.00000	+	1.73205i	0.120386	+	0.208514i
$70$		0			0
$71$	3.71221	−	6.42974i	0.440559	−	0.763070i	−0.557172	−	0.830397i	$-0.688114\pi$
$71$	3.71221	−	6.42974i	0.440559	−	0.763070i	0.997731	+	0.0673268i	$0.0214470\pi$
$72$		0			0
$73$	0.787786	−	1.36448i	0.0922033	−	0.159701i	−0.816235	−	0.577721i	$-0.803942\pi$
$73$	0.787786	−	1.36448i	0.0922033	−	0.159701i	0.908438	+	0.418020i	$0.137276\pi$
$74$		0			0
$75$	0.500000	−	0.866025i	0.0577350	−	0.100000i
$76$	−8.42443	−	14.5915i	−0.966348	−	1.67376i
$77$		0			0
$78$		0			0
$79$	−6.13664	−	10.6290i	−0.690426	−	1.19585i	−0.971698	−	0.236225i	$-0.924090\pi$
$79$	−6.13664	−	10.6290i	−0.690426	−	1.19585i	0.281272	−	0.959628i	$-0.409244\pi$
$80$	2.00000	−	3.46410i	0.223607	−	0.387298i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	−3.00000	+	5.19615i	−0.329293	+	0.570352i	−0.982372	−	0.186938i	$-0.940144\pi$
$83$	−3.00000	+	5.19615i	−0.329293	+	0.570352i	0.653079	+	0.757290i	$0.273477\pi$
$84$		0			0
$85$	4.00000			0.433861
$86$		0			0
$87$	1.71221	+	2.96564i	0.183569	+	0.317950i
$88$		0			0
$89$	−13.4244			−1.42299			−0.711493	−	0.702693i	$-0.751981\pi$
$89$	−13.4244			−1.42299			−0.711493	+	0.702693i	$0.751981\pi$
$90$		0			0
$91$		0			0
$92$	−4.00000			−0.417029
$93$	0.212214	−	5.56372i	0.0220056	−	0.576931i
$94$		0			0
$95$	8.42443			0.864328
$96$		0			0
$97$	−12.4244			−1.26151			−0.630755	−	0.775982i	$-0.717255\pi$
$97$	−12.4244			−1.26151			−0.630755	+	0.775982i	$0.717255\pi$
$98$		0			0
$99$	2.71221	+	4.69769i	0.272588	+	0.472136i
$100$	1.00000	+	1.73205i	0.100000	+	0.173205i
$101$	14.0000			1.39305			0.696526	−	0.717532i	$-0.254728\pi$
$101$	14.0000			1.39305			0.696526	+	0.717532i	$0.254728\pi$
$102$		0			0
$103$	−6.21221	+	10.7599i	−0.612108	+	1.06020i	0.378777	+	0.925488i	$0.376345\pi$
$103$	−6.21221	+	10.7599i	−0.612108	+	1.06020i	−0.990885	+	0.134714i	$0.956989\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	2.42443	+	4.19923i	0.234378	+	0.405955i	0.959092	−	0.283095i	$-0.0913612\pi$
$107$	2.42443	+	4.19923i	0.234378	+	0.405955i	−0.724713	+	0.689050i	$0.758028\pi$
$108$	2.00000			0.192450
$109$	−5.84886			−0.560219			−0.280109	−	0.959968i	$-0.590371\pi$
$109$	−5.84886			−0.560219			−0.280109	+	0.959968i	$0.590371\pi$
$110$		0			0
$111$	4.21221	−	7.29577i	0.399806	−	0.692484i
$112$		0			0
$113$	−8.42443	+	14.5915i	−0.792504	+	1.37266i	0.131909	+	0.991262i	$0.457889\pi$
$113$	−8.42443	+	14.5915i	−0.792504	+	1.37266i	−0.924412	+	0.381395i	$0.875444\pi$
$114$		0			0
$115$	1.00000	−	1.73205i	0.0932505	−	0.161515i
$116$	−6.84886			−0.635900
$117$	2.21221	+	3.83167i	0.204519	+	0.354238i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−9.21221	−	15.9560i	−0.837474	−	1.45055i
$122$		0			0
$123$	1.42443			0.128436
$124$	9.42443	+	5.93128i	0.846339	+	0.532645i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	3.21221	+	5.56372i	0.285038	+	0.493700i	0.972618	−	0.232408i	$-0.0746605\pi$
$127$	3.21221	+	5.56372i	0.285038	+	0.493700i	−0.687580	+	0.726108i	$0.741327\pi$
$128$		0			0
$129$	3.21221	−	5.56372i	0.282820	−	0.489858i
$130$		0			0
$131$	8.71221	+	15.0900i	0.761190	+	1.31842i	0.942238	+	0.334945i	$0.108718\pi$
$131$	8.71221	+	15.0900i	0.761190	+	1.31842i	−0.181048	+	0.983474i	$0.557949\pi$
$132$	−10.8489			−0.944272
$133$		0			0
$134$		0			0
$135$	−0.500000	+	0.866025i	−0.0430331	+	0.0745356i
$136$		0			0
$137$	−1.57557	+	2.72897i	−0.134610	+	0.233152i	−0.925448	−	0.378874i	$-0.876312\pi$
$137$	−1.57557	+	2.72897i	−0.134610	+	0.233152i	0.790838	+	0.612025i	$0.209645\pi$
$138$		0			0
$139$	9.42443			0.799370			0.399685	−	0.916653i	$-0.369120\pi$
$139$	9.42443			0.799370			0.399685	+	0.916653i	$0.369120\pi$
$140$		0			0
$141$	4.42443	+	7.66334i	0.372604	+	0.645369i
$142$		0			0
$143$	−12.0000	−	20.7846i	−1.00349	−	1.73810i
$144$	−2.00000	+	3.46410i	−0.166667	+	0.288675i
$145$	1.71221	−	2.96564i	0.142192	−	0.246283i
$146$		0			0
$147$	7.00000			0.577350
$148$	8.42443	+	14.5915i	0.692484	+	1.19942i
$149$	−7.13664	−	12.3610i	−0.584657	−	1.01265i	−0.994918	−	0.100687i	$-0.967896\pi$
$149$	−7.13664	−	12.3610i	−0.584657	−	1.01265i	0.410262	−	0.911968i	$-0.365437\pi$
$150$		0			0
$151$	−3.57557			−0.290976			−0.145488	−	0.989360i	$-0.546475\pi$
$151$	−3.57557			−0.290976			−0.145488	+	0.989360i	$0.546475\pi$
$152$		0			0
$153$	−4.00000			−0.323381
$154$		0			0
$155$	−4.92443	+	2.59808i	−0.395540	+	0.208683i
$156$	−8.84886			−0.708476
$157$	−22.4244			−1.78966			−0.894832	−	0.446403i	$-0.852705\pi$
$157$	−22.4244			−1.78966			−0.894832	+	0.446403i	$0.852705\pi$
$158$		0			0
$159$	−10.8489			−0.860370
$160$		0			0
$161$		0			0
$162$		0			0
$163$	16.4244			1.28646			0.643230	−	0.765673i	$-0.277594\pi$
$163$	16.4244			1.28646			0.643230	+	0.765673i	$0.277594\pi$
$164$	−1.42443	+	2.46718i	−0.111229	+	0.192655i
$165$	2.71221	−	4.69769i	0.211146	−	0.365715i
$166$		0			0
$167$	10.4244	+	18.0556i	0.806667	+	1.39719i	0.915160	+	0.403090i	$0.132064\pi$
$167$	10.4244	+	18.0556i	0.806667	+	1.39719i	−0.108494	+	0.994097i	$0.534603\pi$
$168$		0			0
$169$	−3.28779	−	5.69461i	−0.252907	−	0.438047i
$170$		0			0
$171$	−8.42443			−0.644232
$172$	6.42443	+	11.1274i	0.489858	+	0.848459i
$173$	−0.424429	+	0.735132i	−0.0322687	+	0.0558911i	−0.881709	−	0.471794i	$-0.843607\pi$
$173$	−0.424429	+	0.735132i	−0.0322687	+	0.0558911i	0.849440	+	0.527685i	$0.176940\pi$
$174$		0			0
$175$		0			0
$176$	10.8489	−	18.7908i	0.817763	−	1.41641i
$177$	−2.71221	+	4.69769i	−0.203863	+	0.353100i
$178$		0			0
$179$	−7.71221	−	13.3579i	−0.576438	−	0.998420i	−0.995884	−	0.0906395i	$-0.971109\pi$
$179$	−7.71221	−	13.3579i	−0.576438	−	0.998420i	0.419446	−	0.907780i	$-0.362224\pi$
$180$	−1.00000	−	1.73205i	−0.0745356	−	0.129099i
$181$	0.787786	−	1.36448i	0.0585556	−	0.101421i	−0.835262	−	0.549853i	$-0.814684\pi$
$181$	0.787786	−	1.36448i	0.0585556	−	0.101421i	0.893817	+	0.448431i	$0.148017\pi$
$182$		0			0
$183$	2.28779	+	3.96256i	0.169118	+	0.292921i
$184$		0			0
$185$	−8.42443			−0.619376
$186$		0			0
$187$	21.6977			1.58669
$188$	−17.6977			−1.29074
$189$		0			0
$190$		0			0
$191$	6.13664	−	10.6290i	0.444032	−	0.769086i	−0.553952	−	0.832548i	$-0.686881\pi$
$191$	6.13664	−	10.6290i	0.444032	−	0.769086i	0.997984	+	0.0634626i	$0.0202143\pi$
$192$	−4.00000	−	6.92820i	−0.288675	−	0.500000i
$193$	7.21221	+	12.4919i	0.519147	+	0.899188i	0.999752	+	0.0222515i	$0.00708345\pi$
$193$	7.21221	+	12.4919i	0.519147	+	0.899188i	−0.480606	+	0.876937i	$0.659583\pi$
$194$		0			0
$195$	2.21221	−	3.83167i	0.158420	−	0.274391i
$196$	−7.00000	+	12.1244i	−0.500000	+	0.866025i
$197$	0.575571	−	0.996918i	0.0410077	−	0.0710275i	−0.844793	−	0.535093i	$-0.820277\pi$
$197$	0.575571	−	0.996918i	0.0410077	−	0.0710275i	0.885801	+	0.464066i	$0.153610\pi$
$198$		0			0
$199$	−8.00000	+	13.8564i	−0.567105	+	0.982255i	0.429745	+	0.902950i	$0.358603\pi$
$199$	−8.00000	+	13.8564i	−0.567105	+	0.982255i	−0.996850	+	0.0793045i	$0.974730\pi$
$200$		0			0
$201$	−6.84886			−0.483081
$202$		0			0
$203$		0			0
$204$	4.00000	−	6.92820i	0.280056	−	0.485071i
$205$	−0.712214	−	1.23359i	−0.0497432	−	0.0861578i
$206$		0			0
$207$	−1.00000	+	1.73205i	−0.0695048	+	0.120386i
$208$	8.84886	−	15.3267i	0.613558	−	1.06271i
$209$	45.6977			3.16098
$210$		0			0
$211$	9.50000	+	16.4545i	0.654007	+	1.13277i	0.982142	+	0.188142i	$0.0602466\pi$
$211$	9.50000	+	16.4545i	0.654007	+	1.13277i	−0.328135	+	0.944631i	$0.606420\pi$
$212$	10.8489	−	18.7908i	0.745103	−	1.29056i
$213$	7.42443			0.508713
$214$		0			0
$215$	−6.42443			−0.438142
$216$		0			0
$217$		0			0
$218$		0			0
$219$	1.57557			0.106467
$220$	5.42443	+	9.39539i	0.365715	+	0.633437i
$221$	17.6977			1.19048
$222$		0			0
$223$	−4.21221	−	7.29577i	−0.282071	−	0.488561i	0.689824	−	0.723977i	$-0.257688\pi$
$223$	−4.21221	−	7.29577i	−0.282071	−	0.488561i	−0.971895	+	0.235416i	$0.924355\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$		0			0
$227$	−11.4244	+	19.7877i	−0.758266	+	1.31336i	0.185468	+	0.982650i	$0.440620\pi$
$227$	−11.4244	+	19.7877i	−0.758266	+	1.31336i	−0.943734	+	0.330705i	$0.892714\pi$
$228$	8.42443	−	14.5915i	0.557921	−	0.966348i
$229$	5.50000	+	9.52628i	0.363450	+	0.629514i	0.988526	−	0.151050i	$-0.0482653\pi$
$229$	5.50000	+	9.52628i	0.363450	+	0.629514i	−0.625076	+	0.780564i	$0.714932\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−22.8489			−1.49688			−0.748439	−	0.663203i	$-0.769196\pi$
$233$	−22.8489			−1.49688			−0.748439	+	0.663203i	$0.769196\pi$
$234$		0			0
$235$	4.42443	−	7.66334i	0.288618	−	0.499901i
$236$	−5.42443	−	9.39539i	−0.353100	−	0.611588i
$237$	6.13664	−	10.6290i	0.398618	−	0.690426i
$238$		0			0
$239$	5.13664	−	8.89693i	0.332262	−	0.575494i	−0.650693	−	0.759341i	$-0.725522\pi$
$239$	5.13664	−	8.89693i	0.332262	−	0.575494i	0.982955	+	0.183846i	$0.0588549\pi$
$240$	4.00000			0.258199
$241$	−7.21221	−	12.4919i	−0.464580	−	0.804675i	0.534603	−	0.845103i	$-0.320461\pi$
$241$	−7.21221	−	12.4919i	−0.464580	−	0.804675i	−0.999182	+	0.0404280i	$0.987128\pi$
$242$		0			0
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−9.15114			−0.585842
$245$	−3.50000	−	6.06218i	−0.223607	−	0.387298i
$246$		0			0
$247$	37.2733			2.37164
$248$		0			0
$249$	−6.00000			−0.380235
$250$		0			0
$251$	−2.42443	−	4.19923i	−0.153029	−	0.265053i	0.779311	−	0.626638i	$-0.215569\pi$
$251$	−2.42443	−	4.19923i	−0.153029	−	0.265053i	−0.932339	+	0.361584i	$0.882236\pi$
$252$		0			0
$253$	5.42443	−	9.39539i	0.341031	−	0.590683i
$254$		0			0
$255$	2.00000	+	3.46410i	0.125245	+	0.216930i
$256$	16.0000			1.00000
$257$	7.00000	−	12.1244i	0.436648	−	0.756297i	−0.560781	−	0.827964i	$-0.689499\pi$
$257$	7.00000	−	12.1244i	0.436648	−	0.756297i	0.997429	+	0.0716680i	$0.0228322\pi$
$258$		0			0
$259$		0			0
$260$	4.42443	+	7.66334i	0.274391	+	0.475260i
$261$	−1.71221	+	2.96564i	−0.105983	+	0.183569i
$262$		0			0
$263$	18.0000			1.10993			0.554964	−	0.831875i	$-0.312732\pi$
$263$	18.0000			1.10993			0.554964	+	0.831875i	$0.312732\pi$
$264$		0			0
$265$	5.42443	+	9.39539i	0.333220	+	0.577154i
$266$		0			0
$267$	−6.71221	−	11.6259i	−0.410781	−	0.711493i
$268$	6.84886	−	11.8626i	0.418361	−	0.724622i
$269$	−12.7122	+	22.0182i	−0.775077	+	1.34247i	0.159674	+	0.987170i	$0.448956\pi$
$269$	−12.7122	+	22.0182i	−0.775077	+	1.34247i	−0.934751	+	0.355304i	$0.884378\pi$
$270$		0			0
$271$	1.00000			0.0607457			0.0303728	−	0.999539i	$-0.490331\pi$
$271$	1.00000			0.0607457			0.0303728	+	0.999539i	$0.490331\pi$
$272$	8.00000	+	13.8564i	0.485071	+	0.840168i
$273$		0			0
$274$		0			0
$275$	−5.42443			−0.327105
$276$	−2.00000	−	3.46410i	−0.120386	−	0.208514i
$277$	−7.27329			−0.437009			−0.218505	−	0.975836i	$-0.570118\pi$
$277$	−7.27329			−0.437009			−0.218505	+	0.975836i	$0.570118\pi$
$278$		0			0
$279$	4.92443	−	2.59808i	0.294818	−	0.155543i
$280$		0			0
$281$	8.27329			0.493543			0.246771	−	0.969074i	$-0.420630\pi$
$281$	8.27329			0.493543			0.246771	+	0.969074i	$0.420630\pi$
$282$		0			0
$283$	1.27329			0.0756890			0.0378445	−	0.999284i	$-0.487951\pi$
$283$	1.27329			0.0756890			0.0378445	+	0.999284i	$0.487951\pi$
$284$	−7.42443	+	12.8595i	−0.440559	+	0.763070i
$285$	4.21221	+	7.29577i	0.249510	+	0.432164i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	0.500000	−	0.866025i	0.0294118	−	0.0509427i
$290$		0			0
$291$	−6.21221	−	10.7599i	−0.364166	−	0.630755i
$292$	−1.57557	+	2.72897i	−0.0922033	+	0.159701i
$293$	3.00000	+	5.19615i	0.175262	+	0.303562i	0.940252	−	0.340480i	$-0.110589\pi$
$293$	3.00000	+	5.19615i	0.175262	+	0.303562i	−0.764990	+	0.644042i	$0.777256\pi$
$294$		0			0
$295$	5.42443			0.315822
$296$		0			0
$297$	−2.71221	+	4.69769i	−0.157379	+	0.272588i
$298$		0			0
$299$	4.42443	−	7.66334i	0.255871	−	0.443182i
$300$	−1.00000	+	1.73205i	−0.0577350	+	0.100000i
$301$		0			0
$302$		0			0
$303$	7.00000	+	12.1244i	0.402139	+	0.696526i
$304$	16.8489	+	29.1831i	0.966348	+	1.67376i
$305$	2.28779	−	3.96256i	0.130998	−	0.226896i
$306$		0			0
$307$	−9.21221	−	15.9560i	−0.525769	−	0.910658i	−0.999549	−	0.0300154i	$-0.990444\pi$
$307$	−9.21221	−	15.9560i	−0.525769	−	0.910658i	0.473781	−	0.880643i	$-0.342889\pi$
$308$		0			0
$309$	−12.4244			−0.706801
$310$		0			0
$311$	0.575571			0.0326376			0.0163188	−	0.999867i	$-0.494805\pi$
$311$	0.575571			0.0326376			0.0163188	+	0.999867i	$0.494805\pi$
$312$		0			0
$313$	1.21221	+	2.09962i	0.0685184	+	0.118677i	0.898249	−	0.439486i	$-0.144839\pi$
$313$	1.21221	+	2.09962i	0.0685184	+	0.118677i	−0.829731	+	0.558164i	$0.811506\pi$
$314$		0			0
$315$		0			0
$316$	12.2733	+	21.2580i	0.690426	+	1.19585i
$317$	−9.84886	−	17.0587i	−0.553167	−	0.958113i	−0.998044	−	0.0625214i	$-0.980086\pi$
$317$	−9.84886	−	17.0587i	−0.553167	−	0.958113i	0.444877	−	0.895592i	$-0.353248\pi$
$318$		0			0
$319$	9.28779	−	16.0869i	0.520016	−	0.900694i
$320$	−4.00000	+	6.92820i	−0.223607	+	0.387298i
$321$	−2.42443	+	4.19923i	−0.135318	+	0.234378i
$322$		0			0
$323$	−16.8489	+	29.1831i	−0.937496	+	1.62379i
$324$	1.00000	+	1.73205i	0.0555556	+	0.0962250i
$325$	−4.42443			−0.245423
$326$		0			0
$327$	−2.92443	−	5.06526i	−0.161721	−	0.280109i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	7.50000	−	12.9904i	0.412237	−	0.714016i	−0.582897	−	0.812546i	$-0.698081\pi$
$331$	7.50000	−	12.9904i	0.412237	−	0.714016i	0.995134	+	0.0985303i	$0.0314141\pi$
$332$	6.00000	−	10.3923i	0.329293	−	0.570352i
$333$	8.42443			0.461656
$334$		0			0
$335$	3.42443	+	5.93128i	0.187097	+	0.324061i
$336$		0			0
$337$	−24.8489			−1.35360			−0.676802	−	0.736165i	$-0.736635\pi$
$337$	−24.8489			−1.35360			−0.676802	+	0.736165i	$0.736635\pi$
$338$		0			0
$339$	−16.8489			−0.915104
$340$	−8.00000			−0.433861
$341$	−26.7122	+	14.0931i	−1.44655	+	0.763183i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	2.00000			0.107676
$346$		0			0
$347$	−12.8489	−	22.2549i	−0.689763	−	1.19470i	−0.971914	−	0.235334i	$-0.924381\pi$
$347$	−12.8489	−	22.2549i	−0.689763	−	1.19470i	0.282152	−	0.959370i	$-0.408952\pi$
$348$	−3.42443	−	5.93128i	−0.183569	−	0.317950i
$349$	−19.8489			−1.06248			−0.531242	−	0.847220i	$-0.678275\pi$
$349$	−19.8489			−1.06248			−0.531242	+	0.847220i	$0.678275\pi$
$350$		0			0
$351$	−2.21221	+	3.83167i	−0.118079	+	0.204519i
$352$		0			0
$353$	−9.00000	−	15.5885i	−0.479022	−	0.829690i	0.520689	−	0.853746i	$-0.325675\pi$
$353$	−9.00000	−	15.5885i	−0.479022	−	0.829690i	−0.999711	+	0.0240566i	$0.992342\pi$
$354$		0			0
$355$	−3.71221	−	6.42974i	−0.197024	−	0.341255i
$356$	26.8489			1.42299
$357$		0			0
$358$		0			0
$359$	0.287786	−	0.498459i	0.0151887	−	0.0263077i	−0.858331	−	0.513096i	$-0.828498\pi$
$359$	0.287786	−	0.498459i	0.0151887	−	0.0263077i	0.873520	+	0.486788i	$0.161832\pi$
$360$		0			0
$361$	−25.9855	+	45.0082i	−1.36766	+	2.36885i
$362$		0			0
$363$	9.21221	−	15.9560i	0.483516	−	0.837474i
$364$		0			0
$365$	−0.787786	−	1.36448i	−0.0412346	−	0.0714204i
$366$		0			0
$367$	−5.78779	+	10.0247i	−0.302120	+	0.523287i	−0.976616	−	0.214991i	$-0.931028\pi$
$367$	−5.78779	+	10.0247i	−0.302120	+	0.523287i	0.674496	+	0.738279i	$0.264361\pi$
$368$	8.00000			0.417029
$369$	0.712214	+	1.23359i	0.0370764	+	0.0642182i
$370$		0			0
$371$		0			0
$372$	−0.424429	+	11.1274i	−0.0220056	+	0.576931i
$373$	−24.1221			−1.24900			−0.624499	−	0.781026i	$-0.714697\pi$
$373$	−24.1221			−1.24900			−0.624499	+	0.781026i	$0.714697\pi$
$374$		0			0
$375$	−0.500000	−	0.866025i	−0.0258199	−	0.0447214i
$376$		0			0
$377$	7.57557	−	13.1213i	0.390162	−	0.675780i
$378$		0			0
$379$	−4.21221	−	7.29577i	−0.216367	−	0.374759i	0.737328	−	0.675535i	$-0.236087\pi$
$379$	−4.21221	−	7.29577i	−0.216367	−	0.374759i	−0.953695	+	0.300777i	$0.902754\pi$
$380$	−16.8489			−0.864328
$381$	−3.21221	+	5.56372i	−0.164567	+	0.285038i
$382$		0			0
$383$	17.4244	−	30.1800i	0.890347	−	1.54213i	0.0508866	−	0.998704i	$-0.483795\pi$
$383$	17.4244	−	30.1800i	0.890347	−	1.54213i	0.839460	−	0.543421i	$-0.182871\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	6.42443			0.326572
$388$	24.8489			1.26151
$389$	3.71221	+	6.42974i	0.188217	+	0.326001i	0.944656	−	0.328063i	$-0.106396\pi$
$389$	3.71221	+	6.42974i	0.188217	+	0.326001i	−0.756439	+	0.654064i	$0.773063\pi$
$390$		0			0
$391$	4.00000	+	6.92820i	0.202289	+	0.350374i
$392$		0			0
$393$	−8.71221	+	15.0900i	−0.439473	+	0.761190i
$394$		0			0
$395$	−12.2733			−0.617536
$396$	−5.42443	−	9.39539i	−0.272588	−	0.472136i
$397$	5.57557	+	9.65717i	0.279830	+	0.484680i	0.971342	−	0.237685i	$-0.0763886\pi$
$397$	5.57557	+	9.65717i	0.279830	+	0.484680i	−0.691512	+	0.722365i	$0.743055\pi$
$398$		0			0
$399$		0			0
$400$	−2.00000	−	3.46410i	−0.100000	−	0.173205i
$401$	−2.57557			−0.128618			−0.0643089	−	0.997930i	$-0.520484\pi$
$401$	−2.57557			−0.128618			−0.0643089	+	0.997930i	$0.520484\pi$
$402$		0			0
$403$	−21.7878	+	11.4950i	−1.08533	+	0.572607i
$404$	−28.0000			−1.39305
$405$	−1.00000			−0.0496904
$406$		0			0
$407$	−45.6977			−2.26515
$408$		0			0
$409$	−5.21221	−	9.02782i	−0.257727	−	0.446397i	0.707905	−	0.706307i	$-0.249640\pi$
$409$	−5.21221	−	9.02782i	−0.257727	−	0.446397i	−0.965633	+	0.259910i	$0.916307\pi$
$410$		0			0
$411$	−3.15114			−0.155434
$412$	12.4244	−	21.5197i	0.612108	−	1.06020i
$413$		0			0
$414$		0			0
$415$	3.00000	+	5.19615i	0.147264	+	0.255069i
$416$		0			0
$417$	4.71221	+	8.16179i	0.230758	+	0.399685i
$418$		0			0
$419$	34.2733			1.67436			0.837180	−	0.546928i	$-0.184203\pi$
$419$	34.2733			1.67436			0.837180	+	0.546928i	$0.184203\pi$
$420$		0			0
$421$	−15.1366	+	26.2174i	−0.737715	+	1.27776i	0.215807	+	0.976436i	$0.430762\pi$
$421$	−15.1366	+	26.2174i	−0.737715	+	1.27776i	−0.953522	+	0.301324i	$0.902572\pi$
$422$		0			0
$423$	−4.42443	+	7.66334i	−0.215123	+	0.372604i
$424$		0			0
$425$	2.00000	−	3.46410i	0.0970143	−	0.168034i
$426$		0			0
$427$		0			0
$428$	−4.84886	−	8.39847i	−0.234378	−	0.405955i
$429$	12.0000	−	20.7846i	0.579365	−	1.00349i
$430$		0			0
$431$	3.71221	+	6.42974i	0.178811	+	0.309710i	0.941474	−	0.337087i	$-0.109442\pi$
$431$	3.71221	+	6.42974i	0.178811	+	0.309710i	−0.762663	+	0.646797i	$0.776108\pi$
$432$	−4.00000			−0.192450
$433$	6.72671			0.323265			0.161633	−	0.986851i	$-0.448324\pi$
$433$	6.72671			0.323265			0.161633	+	0.986851i	$0.448324\pi$
$434$		0			0
$435$	3.42443			0.164189
$436$	11.6977			0.560219
$437$	8.42443	+	14.5915i	0.402995	+	0.698008i
$438$		0			0
$439$	12.9244	−	22.3858i	0.616849	−	1.06841i	−0.373208	−	0.927748i	$-0.621742\pi$
$439$	12.9244	−	22.3858i	0.616849	−	1.06841i	0.990057	−	0.140667i	$-0.0449246\pi$
$440$		0			0
$441$	3.50000	+	6.06218i	0.166667	+	0.288675i
$442$		0			0
$443$	−8.42443	+	14.5915i	−0.400257	+	0.693265i	−0.993757	−	0.111569i	$-0.964412\pi$
$443$	−8.42443	+	14.5915i	−0.400257	+	0.693265i	0.593500	+	0.804834i	$0.297746\pi$
$444$	−8.42443	+	14.5915i	−0.399806	+	0.692484i
$445$	−6.71221	+	11.6259i	−0.318189	+	0.551120i
$446$		0			0
$447$	7.13664	−	12.3610i	0.337552	−	0.584657i
$448$		0			0
$449$	21.1511			0.998184			0.499092	−	0.866549i	$-0.333667\pi$
$449$	21.1511			0.998184			0.499092	+	0.866549i	$0.333667\pi$
$450$		0			0
$451$	−3.86336	−	6.69153i	−0.181918	−	0.315092i
$452$	16.8489	−	29.1831i	0.792504	−	1.37266i
$453$	−1.78779	−	3.09654i	−0.0839975	−	0.145488i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	30.4244			1.42319			0.711597	−	0.702587i	$-0.247972\pi$
$457$	30.4244			1.42319			0.711597	+	0.702587i	$0.247972\pi$
$458$		0			0
$459$	−2.00000	−	3.46410i	−0.0933520	−	0.161690i
$460$	−2.00000	+	3.46410i	−0.0932505	+	0.161515i
$461$	−10.8489			−0.505282			−0.252641	−	0.967560i	$-0.581299\pi$
$461$	−10.8489			−0.505282			−0.252641	+	0.967560i	$0.581299\pi$
$462$		0			0
$463$	16.1221			0.749260			0.374630	−	0.927174i	$-0.377770\pi$
$463$	16.1221			0.749260			0.374630	+	0.927174i	$0.377770\pi$
$464$	13.6977			0.635900
$465$	−4.71221	−	2.96564i	−0.218524	−	0.137528i
$466$		0			0
$467$	−15.6977			−0.726404			−0.363202	−	0.931710i	$-0.618316\pi$
$467$	−15.6977			−0.726404			−0.363202	+	0.931710i	$0.618316\pi$
$468$	−4.42443	−	7.66334i	−0.204519	−	0.354238i
$469$		0			0
$470$		0			0
$471$	−11.2122	−	19.4201i	−0.516632	−	0.894832i
$472$		0			0
$473$	−34.8489			−1.60235
$474$		0			0
$475$	4.21221	−	7.29577i	0.193270	−	0.334753i
$476$		0			0
$477$	−5.42443	−	9.39539i	−0.248368	−	0.430185i
$478$		0			0
$479$	0.863357	+	1.49538i	0.0394478	+	0.0683255i	0.885075	−	0.465448i	$-0.154107\pi$
$479$	0.863357	+	1.49538i	0.0394478	+	0.0683255i	−0.845627	+	0.533774i	$0.820773\pi$
$480$		0			0
$481$	−37.2733			−1.69952
$482$		0			0
$483$		0			0
$484$	18.4244	+	31.9120i	0.837474	+	1.45055i
$485$	−6.21221	+	10.7599i	−0.282082	+	0.488581i
$486$		0			0
$487$	−4.63664	+	8.03090i	−0.210106	+	0.363915i	−0.951748	−	0.306882i	$-0.900714\pi$
$487$	−4.63664	+	8.03090i	−0.210106	+	0.363915i	0.741641	+	0.670797i	$0.234048\pi$
$488$		0			0
$489$	8.21221	+	14.2240i	0.371369	+	0.643230i
$490$		0			0
$491$	−12.1366	+	21.0213i	−0.547719	+	0.948677i	0.450711	+	0.892670i	$0.351170\pi$
$491$	−12.1366	+	21.0213i	−0.547719	+	0.948677i	−0.998430	+	0.0560074i	$0.982163\pi$
$492$	−2.84886			−0.128436
$493$	6.84886	+	11.8626i	0.308457	+	0.534263i
$494$		0			0
$495$	5.42443			0.243810
$496$	−18.8489	−	11.8626i	−0.846339	−	0.532645i
$497$		0			0
$498$		0			0
$499$	1.86336	+	3.22743i	0.0834153	+	0.144480i	0.904715	−	0.426018i	$-0.140084\pi$
$499$	1.86336	+	3.22743i	0.0834153	+	0.144480i	−0.821300	+	0.570497i	$0.806751\pi$
$500$	2.00000			0.0894427
$501$	−10.4244	+	18.0556i	−0.465729	+	0.806667i
$502$		0			0
$503$	8.00000	+	13.8564i	0.356702	+	0.617827i	0.987408	−	0.158196i	$-0.0505677\pi$
$503$	8.00000	+	13.8564i	0.356702	+	0.617827i	−0.630705	+	0.776022i	$0.717234\pi$
$504$		0			0
$505$	7.00000	−	12.1244i	0.311496	−	0.539527i
$506$		0			0
$507$	3.28779	−	5.69461i	0.146016	−	0.252907i
$508$	−6.42443	−	11.1274i	−0.285038	−	0.493700i
$509$	5.13664	−	8.89693i	0.227678	−	0.394349i	−0.729442	−	0.684043i	$-0.760220\pi$
$509$	5.13664	−	8.89693i	0.227678	−	0.394349i	0.957119	+	0.289694i	$0.0935534\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−4.21221	−	7.29577i	−0.185974	−	0.322116i
$514$		0			0
$515$	6.21221	+	10.7599i	0.273743	+	0.474137i
$516$	−6.42443	+	11.1274i	−0.282820	+	0.489858i
$517$	24.0000	−	41.5692i	1.05552	−	1.82821i
$518$		0			0
$519$	−0.848858			−0.0372607
$520$		0			0
$521$	16.5611	+	28.6846i	0.725554	+	1.25670i	0.958746	+	0.284265i	$0.0917496\pi$
$521$	16.5611	+	28.6846i	0.725554	+	1.25670i	−0.233192	+	0.972431i	$0.574917\pi$
$522$		0			0
$523$	−16.0000			−0.699631			−0.349816	−	0.936819i	$-0.613756\pi$
$523$	−16.0000			−0.699631			−0.349816	+	0.936819i	$0.613756\pi$
$524$	−17.4244	−	30.1800i	−0.761190	−	1.31842i
$525$		0			0
$526$		0			0
$527$	0.848858	−	22.2549i	0.0369768	−	0.969438i
$528$	21.6977			0.944272
$529$	−19.0000			−0.826087
$530$		0			0
$531$	−5.42443			−0.235400
$532$		0			0
$533$	−3.15114	−	5.45794i	−0.136491	−	0.236410i
$534$		0			0
$535$	4.84886			0.209634
$536$		0			0
$537$	7.71221	−	13.3579i	0.332807	−	0.576438i
$538$		0			0
$539$	−18.9855	−	32.8839i	−0.817763	−	1.41641i
$540$	1.00000	−	1.73205i	0.0430331	−	0.0745356i
$541$	−7.07557	−	12.2552i	−0.304203	−	0.526894i	0.672881	−	0.739751i	$-0.265057\pi$
$541$	−7.07557	−	12.2552i	−0.304203	−	0.526894i	−0.977083	+	0.212857i	$0.931723\pi$
$542$		0			0
$543$	1.57557			0.0676142
$544$		0			0
$545$	−2.92443	+	5.06526i	−0.125269	+	0.216972i
$546$		0			0
$547$	4.63664	−	8.03090i	0.198249	−	0.343377i	−0.749712	−	0.661764i	$-0.769808\pi$
$547$	4.63664	−	8.03090i	0.198249	−	0.343377i	0.947961	+	0.318388i	$0.103141\pi$
$548$	3.15114	−	5.45794i	0.134610	−	0.233152i
$549$	−2.28779	+	3.96256i	−0.0976403	+	0.169118i
$550$		0			0
$551$	14.4244	+	24.9838i	0.614501	+	1.06435i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−4.21221	−	7.29577i	−0.178799	−	0.309688i
$556$	−18.8489			−0.799370
$557$	−20.8489			−0.883394			−0.441697	−	0.897164i	$-0.645623\pi$
$557$	−20.8489			−0.883394			−0.441697	+	0.897164i	$0.645623\pi$
$558$		0			0
$559$	−28.4244			−1.20223
$560$		0			0
$561$	10.8489	+	18.7908i	0.458039	+	0.793347i
$562$		0			0
$563$	−20.8489	+	36.1113i	−0.878675	+	1.52191i	−0.0258785	+	0.999665i	$0.508238\pi$
$563$	−20.8489	+	36.1113i	−0.878675	+	1.52191i	−0.852796	+	0.522244i	$0.825095\pi$
$564$	−8.84886	−	15.3267i	−0.372604	−	0.645369i
$565$	8.42443	+	14.5915i	0.354418	+	0.613871i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	3.71221	−	6.42974i	0.155624	−	0.269549i	−0.777662	−	0.628683i	$-0.783594\pi$
$569$	3.71221	−	6.42974i	0.155624	−	0.269549i	0.933286	+	0.359134i	$0.116928\pi$
$570$		0			0
$571$	−10.7733	+	18.6599i	−0.450848	+	0.780892i	−0.998439	−	0.0558545i	$-0.982212\pi$
$571$	−10.7733	+	18.6599i	−0.450848	+	0.780892i	0.547591	+	0.836746i	$0.315545\pi$
$572$	24.0000	+	41.5692i	1.00349	+	1.73810i
$573$	12.2733			0.512724
$574$		0			0
$575$	−1.00000	−	1.73205i	−0.0417029	−	0.0722315i
$576$	4.00000	−	6.92820i	0.166667	−	0.288675i
$577$	−4.42443	−	7.66334i	−0.184191	−	0.319029i	0.759112	−	0.650960i	$-0.225633\pi$
$577$	−4.42443	−	7.66334i	−0.184191	−	0.319029i	−0.943304	+	0.331931i	$0.892300\pi$
$578$		0			0
$579$	−7.21221	+	12.4919i	−0.299729	+	0.519147i
$580$	−3.42443	+	5.93128i	−0.142192	+	0.246283i
$581$		0			0
$582$		0			0
$583$	29.4244	+	50.9646i	1.21864	+	2.11074i
$584$		0			0
$585$	4.42443			0.182928
$586$		0			0
$587$	12.8489			0.530329			0.265165	−	0.964203i	$-0.414574\pi$
$587$	12.8489			0.530329			0.265165	+	0.964203i	$0.414574\pi$
$588$	−14.0000			−0.577350
$589$	1.78779	−	46.8712i	0.0736644	−	1.93129i
$590$		0			0
$591$	1.15114			0.0473517
$592$	−16.8489	−	29.1831i	−0.692484	−	1.19942i
$593$	−30.8489			−1.26681			−0.633405	−	0.773820i	$-0.718343\pi$
$593$	−30.8489			−1.26681			−0.633405	+	0.773820i	$0.718343\pi$
$594$		0			0
$595$		0			0
$596$	14.2733	+	24.7221i	0.584657	+	1.01265i
$597$	−16.0000			−0.654836
$598$		0			0
$599$	11.7122	−	20.2862i	0.478548	−	0.828870i	−0.521149	−	0.853465i	$-0.674497\pi$
$599$	11.7122	−	20.2862i	0.478548	−	0.828870i	0.999697	+	0.0245958i	$0.00782989\pi$
$600$		0			0
$601$	10.5611	+	18.2923i	0.430795	+	0.746159i	0.996942	−	0.0781454i	$-0.0248998\pi$
$601$	10.5611	+	18.2923i	0.430795	+	0.746159i	−0.566147	+	0.824304i	$0.691566\pi$
$602$		0			0
$603$	−3.42443	−	5.93128i	−0.139454	−	0.241541i
$604$	7.15114			0.290976
$605$	−18.4244			−0.749060
$606$		0			0
$607$	−17.2122	+	29.8124i	−0.698622	+	1.21005i	0.270322	+	0.962770i	$0.412870\pi$
$607$	−17.2122	+	29.8124i	−0.698622	+	1.21005i	−0.968944	+	0.247279i	$0.920464\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	19.5756	−	33.9059i	0.791943	−	1.37169i
$612$	8.00000			0.323381
$613$	−7.06107	−	12.2301i	−0.285194	−	0.493971i	0.687462	−	0.726220i	$-0.258725\pi$
$613$	−7.06107	−	12.2301i	−0.285194	−	0.493971i	−0.972656	+	0.232250i	$0.925391\pi$
$614$		0			0
$615$	0.712214	−	1.23359i	0.0287193	−	0.0497432i
$616$		0			0
$617$	5.42443	+	9.39539i	0.218379	+	0.378244i	0.954313	−	0.298810i	$-0.0965897\pi$
$617$	5.42443	+	9.39539i	0.218379	+	0.378244i	−0.735933	+	0.677054i	$0.763256\pi$
$618$		0			0
$619$	2.15114			0.0864617			0.0432309	−	0.999065i	$-0.486235\pi$
$619$	2.15114			0.0864617			0.0432309	+	0.999065i	$0.486235\pi$
$620$	9.84886	−	5.19615i	0.395540	−	0.208683i
$621$	−2.00000			−0.0802572
$622$		0			0
$623$		0			0
$624$	17.6977			0.708476
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	22.8489	+	39.5754i	0.912495	+	1.58049i
$628$	44.8489			1.78966
$629$	16.8489	−	29.1831i	0.671808	−	1.16361i
$630$		0			0
$631$	4.13664	−	7.16488i	0.164677	−	0.285229i	−0.771863	−	0.635788i	$-0.780675\pi$
$631$	4.13664	−	7.16488i	0.164677	−	0.285229i	0.936541	+	0.350559i	$0.114008\pi$
$632$		0			0
$633$	−9.50000	+	16.4545i	−0.377591	+	0.654007i
$634$		0			0
$635$	6.42443			0.254946
$636$	21.6977			0.860370
$637$	−15.4855	−	26.8217i	−0.613558	−	1.06271i
$638$		0			0
$639$	3.71221	+	6.42974i	0.146853	+	0.254357i
$640$		0			0
$641$	−23.8489	+	41.3074i	−0.941973	+	1.63155i	−0.180272	+	0.983617i	$0.557698\pi$
$641$	−23.8489	+	41.3074i	−0.941973	+	1.63155i	−0.761701	+	0.647929i	$0.775635\pi$
$642$		0			0
$643$	−15.2733			−0.602320			−0.301160	−	0.953574i	$-0.597374\pi$
$643$	−15.2733			−0.602320			−0.301160	+	0.953574i	$0.597374\pi$
$644$		0			0
$645$	−3.21221	−	5.56372i	−0.126481	−	0.219071i
$646$		0			0
$647$	14.5466			0.571885			0.285942	−	0.958247i	$-0.407693\pi$
$647$	14.5466			0.571885			0.285942	+	0.958247i	$0.407693\pi$
$648$		0			0
$649$	29.4244			1.15501
$650$		0			0
$651$		0			0
$652$	−32.8489			−1.28646
$653$	47.3954			1.85473			0.927363	−	0.374162i	$-0.122070\pi$
$653$	47.3954			1.85473			0.927363	+	0.374162i	$0.122070\pi$
$654$		0			0
$655$	17.4244			0.680829
$656$	2.84886	−	4.93437i	0.111229	−	0.192655i
$657$	0.787786	+	1.36448i	0.0307344	+	0.0532336i
$658$		0			0
$659$	−6.30228			−0.245502			−0.122751	−	0.992437i	$-0.539172\pi$
$659$	−6.30228			−0.245502			−0.122751	+	0.992437i	$0.539172\pi$
$660$	−5.42443	+	9.39539i	−0.211146	+	0.365715i
$661$	16.0611	−	27.8186i	0.624703	−	1.08202i	−0.363895	−	0.931440i	$-0.618553\pi$
$661$	16.0611	−	27.8186i	0.624703	−	1.08202i	0.988598	−	0.150578i	$-0.0481134\pi$
$662$		0			0
$663$	8.84886	+	15.3267i	0.343661	+	0.595239i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	6.84886			0.265189
$668$	−20.8489	−	36.1113i	−0.806667	−	1.39719i
$669$	4.21221	−	7.29577i	0.162854	−	0.282071i
$670$		0			0
$671$	12.4099	−	21.4946i	0.479080	−	0.829791i
$672$		0			0
$673$	−16.6977	+	28.9213i	−0.643650	+	1.11483i	0.340962	+	0.940077i	$0.389247\pi$
$673$	−16.6977	+	28.9213i	−0.643650	+	1.11483i	−0.984612	+	0.174757i	$0.944086\pi$
$674$		0			0
$675$	0.500000	+	0.866025i	0.0192450	+	0.0333333i
$676$	6.57557	+	11.3892i	0.252907	+	0.438047i
$677$	12.0000	−	20.7846i	0.461197	−	0.798817i	−0.537823	−	0.843057i	$-0.680753\pi$
$677$	12.0000	−	20.7846i	0.461197	−	0.798817i	0.999021	+	0.0442400i	$0.0140866\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−22.8489			−0.875570
$682$		0			0
$683$	11.6977			0.447601			0.223800	−	0.974635i	$-0.428154\pi$
$683$	11.6977			0.447601			0.223800	+	0.974635i	$0.428154\pi$
$684$	16.8489			0.644232
$685$	1.57557	+	2.72897i	0.0601995	+	0.104269i
$686$		0			0
$687$	−5.50000	+	9.52628i	−0.209838	+	0.363450i
$688$	−12.8489	−	22.2549i	−0.489858	−	0.848459i
$689$	24.0000	+	41.5692i	0.914327	+	1.58366i
$690$		0			0
$691$	16.7122	−	28.9464i	0.635763	−	1.10117i	−0.350590	−	0.936529i	$-0.614019\pi$
$691$	16.7122	−	28.9464i	0.635763	−	1.10117i	0.986353	−	0.164644i	$-0.0526476\pi$
$692$	0.848858	−	1.47026i	0.0322687	−	0.0558911i
$693$		0			0
$694$		0			0
$695$	4.71221	−	8.16179i	0.178744	−	0.309595i
$696$		0			0
$697$	5.69772			0.215816
$698$		0			0
$699$	−11.4244	−	19.7877i	−0.432112	−	0.748439i
$700$		0			0
$701$	7.56107	+	13.0962i	0.285578	+	0.494635i	0.972749	−	0.231860i	$-0.0744812\pi$
$701$	7.56107	+	13.0962i	0.285578	+	0.494635i	−0.687171	+	0.726495i	$0.741148\pi$
$702$		0			0
$703$	35.4855	−	61.4627i	1.33836	−	2.31811i
$704$	−21.6977	+	37.5815i	−0.817763	+	1.41641i
$705$	8.84886			0.333267
$706$		0			0
$707$		0			0
$708$	5.42443	−	9.39539i	0.203863	−	0.353100i
$709$	−47.2733			−1.77539			−0.887693	−	0.460436i	$-0.847693\pi$
$709$	−47.2733			−1.77539			−0.887693	+	0.460436i	$0.847693\pi$
$710$		0			0
$711$	12.2733			0.460284
$712$		0			0
$713$	−9.42443	−	5.93128i	−0.352948	−	0.222128i
$714$		0			0
$715$	−24.0000			−0.897549
$716$	15.4244	+	26.7159i	0.576438	+	0.998420i
$717$	10.2733			0.383663
$718$		0			0
$719$	16.4244	+	28.4479i	0.612528	+	1.06093i	0.990813	+	0.135240i	$0.0431806\pi$
$719$	16.4244	+	28.4479i	0.612528	+	1.06093i	−0.378285	+	0.925689i	$0.623486\pi$
$720$	2.00000	+	3.46410i	0.0745356	+	0.129099i
$721$		0			0
$722$		0			0
$723$	7.21221	−	12.4919i	0.268225	−	0.464580i
$724$	−1.57557	+	2.72897i	−0.0585556	+	0.101421i
$725$	−1.71221	−	2.96564i	−0.0635900	−	0.110141i
$726$		0			0
$727$	10.7878	+	18.6850i	0.400097	+	0.692988i	0.993737	−	0.111742i	$-0.0356432\pi$
$727$	10.7878	+	18.6850i	0.400097	+	0.692988i	−0.593640	+	0.804730i	$0.702310\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	12.8489	−	22.2549i	0.475232	−	0.823126i
$732$	−4.57557	−	7.92512i	−0.169118	−	0.292921i
$733$	10.2122	−	17.6881i	0.377197	−	0.653324i	−0.613456	−	0.789729i	$-0.710221\pi$
$733$	10.2122	−	17.6881i	0.377197	−	0.653324i	0.990653	+	0.136405i	$0.0435547\pi$
$734$		0			0
$735$	3.50000	−	6.06218i	0.129099	−	0.223607i
$736$		0			0
$737$	18.5756	+	32.1738i	0.684240	+	1.18514i
$738$		0			0
$739$	16.9244	−	29.3140i	0.622575	−	1.07833i	−0.366429	−	0.930446i	$-0.619420\pi$
$739$	16.9244	−	29.3140i	0.622575	−	1.07833i	0.989004	−	0.147886i	$-0.0472468\pi$
$740$	16.8489			0.619376
$741$	18.6366	+	32.2796i	0.684634	+	1.18582i
$742$		0			0
$743$	47.6977			1.74986			0.874930	−	0.484250i	$-0.160907\pi$
$743$	47.6977			1.74986			0.874930	+	0.484250i	$0.160907\pi$
$744$		0			0
$745$	−14.2733			−0.522933
$746$		0			0
$747$	−3.00000	−	5.19615i	−0.109764	−	0.190117i
$748$	−43.3954			−1.58669
$749$		0			0
$750$		0			0
$751$	0.938928	+	1.62627i	0.0342620	+	0.0593435i	0.882648	−	0.470035i	$-0.155759\pi$
$751$	0.938928	+	1.62627i	0.0342620	+	0.0593435i	−0.848386	+	0.529378i	$0.822425\pi$
$752$	35.3954			1.29074
$753$	2.42443	−	4.19923i	0.0883511	−	0.153029i
$754$		0			0
$755$	−1.78779	+	3.09654i	−0.0650642	+	0.112694i
$756$		0			0
$757$	0.151142	−	0.261786i	0.00549336	−	0.00951477i	−0.863266	−	0.504750i	$-0.831585\pi$
$757$	0.151142	−	0.261786i	0.00549336	−	0.00951477i	0.868759	+	0.495235i	$0.164918\pi$
$758$		0			0
$759$	10.8489			0.393789
$760$		0			0
$761$	−19.8489	−	34.3792i	−0.719521	−	1.24625i	−0.961190	−	0.275887i	$-0.911028\pi$
$761$	−19.8489	−	34.3792i	−0.719521	−	1.24625i	0.241669	−	0.970359i	$-0.422305\pi$
$762$		0			0
$763$		0			0
$764$	−12.2733	+	21.2580i	−0.444032	+	0.769086i
$765$	−2.00000	+	3.46410i	−0.0723102	+	0.125245i
$766$		0			0
$767$	24.0000			0.866590
$768$	8.00000	+	13.8564i	0.288675	+	0.500000i
$769$	−9.98550	−	17.2954i	−0.360086	−	0.623688i	0.627888	−	0.778303i	$-0.283919\pi$
$769$	−9.98550	−	17.2954i	−0.360086	−	0.623688i	−0.987975	+	0.154616i	$0.950586\pi$
$770$		0			0
$771$	14.0000			0.504198
$772$	−14.4244	−	24.9838i	−0.519147	−	0.899188i
$773$	−30.5466			−1.09868			−0.549342	−	0.835598i	$-0.685122\pi$
$773$	−30.5466			−1.09868			−0.549342	+	0.835598i	$0.685122\pi$
$774$		0			0
$775$	−0.212214	+	5.56372i	−0.00762297	+	0.199855i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	12.0000			0.429945
$780$	−4.42443	+	7.66334i	−0.158420	+	0.274391i
$781$	−20.1366	−	34.8777i	−0.720546	−	1.24802i
$782$		0			0
$783$	−3.42443			−0.122379
$784$	14.0000	−	24.2487i	0.500000	−	0.866025i
$785$	−11.2122	+	19.4201i	−0.400181	+	0.693134i
$786$		0			0
$787$	19.6366	+	34.0117i	0.699971	+	1.21238i	0.968476	+	0.249107i	$0.0801370\pi$
$787$	19.6366	+	34.0117i	0.699971	+	1.21238i	−0.268505	+	0.963278i	$0.586530\pi$
$788$	−1.15114	+	1.99384i	−0.0410077	+	0.0710275i
$789$	9.00000	+	15.5885i	0.320408	+	0.554964i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	10.1221	−	17.5321i	0.359448	−	0.622582i
$794$		0			0
$795$	−5.42443	+	9.39539i	−0.192385	+	0.333220i
$796$	16.0000	−	27.7128i	0.567105	−	0.982255i
$797$	17.6977	−	30.6533i	0.626885	−	1.08580i	−0.361288	−	0.932454i	$-0.617663\pi$
$797$	17.6977	−	30.6533i	0.626885	−	1.08580i	0.988173	−	0.153343i	$-0.0490039\pi$
$798$		0			0
$799$	17.6977	+	30.6533i	0.626100	+	1.08444i
$800$		0			0
$801$	6.71221	−	11.6259i	0.237164	−	0.410781i
$802$		0			0
$803$	−4.27329	−	7.40155i	−0.150801	−	0.261195i
$804$	13.6977			0.483081
$805$		0			0
$806$		0			0
$807$	−25.4244			−0.894982
$808$		0			0
$809$	6.27329	+	10.8657i	0.220557	+	0.382016i	0.954977	−	0.296679i	$-0.0958792\pi$
$809$	6.27329	+	10.8657i	0.220557	+	0.382016i	−0.734420	+	0.678695i	$0.762546\pi$
$810$		0			0
$811$	−26.7733	+	46.3727i	−0.940137	+	1.62837i	−0.174931	+	0.984581i	$0.555970\pi$
$811$	−26.7733	+	46.3727i	−0.940137	+	1.62837i	−0.765207	+	0.643785i	$0.777363\pi$
$812$		0			0
$813$	0.500000	+	0.866025i	0.0175358	+	0.0303728i
$814$		0			0
$815$	8.21221	−	14.2240i	0.287661	−	0.498244i
$816$	−8.00000	+	13.8564i	−0.280056	+	0.485071i
$817$	27.0611	−	46.8712i	0.946747	−	1.63981i
$818$		0			0
$819$		0			0
$820$	1.42443	+	2.46718i	0.0497432	+	0.0861578i
$821$	15.4244			0.538316			0.269158	−	0.963096i	$-0.413255\pi$
$821$	15.4244			0.538316			0.269158	+	0.963096i	$0.413255\pi$
$822$		0			0
$823$	−18.5756	−	32.1738i	−0.647504	−	1.12151i	−0.983717	−	0.179724i	$-0.942480\pi$
$823$	−18.5756	−	32.1738i	−0.647504	−	1.12151i	0.336213	−	0.941786i	$-0.390854\pi$
$824$		0			0
$825$	−2.71221	−	4.69769i	−0.0944272	−	0.163553i
$826$		0			0
$827$	−0.424429	+	0.735132i	−0.0147588	+	0.0255631i	−0.873310	−	0.487164i	$-0.838031\pi$
$827$	−0.424429	+	0.735132i	−0.0147588	+	0.0255631i	0.858552	+	0.512727i	$0.171365\pi$
$828$	2.00000	−	3.46410i	0.0695048	−	0.120386i
$829$	2.15114			0.0747123			0.0373561	−	0.999302i	$-0.488106\pi$
$829$	2.15114			0.0747123			0.0373561	+	0.999302i	$0.488106\pi$
$830$		0			0
$831$	−3.63664	−	6.29885i	−0.126154	−	0.218505i
$832$	−17.6977	+	30.6533i	−0.613558	+	1.06271i
$833$	28.0000			0.970143
$834$		0			0
$835$	20.8489			0.721504
$836$	−91.3954			−3.16098
$837$	4.71221	+	2.96564i	0.162878	+	0.102508i
$838$		0			0
$839$	−27.1221			−0.936360			−0.468180	−	0.883633i	$-0.655090\pi$
$839$	−27.1221			−0.936360			−0.468180	+	0.883633i	$0.655090\pi$
$840$		0			0
$841$	−17.2733			−0.595631
$842$		0			0
$843$	4.13664	+	7.16488i	0.142474	+	0.246771i
$844$	−19.0000	−	32.9090i	−0.654007	−	1.13277i
$845$	−6.57557			−0.226207
$846$		0			0
$847$		0			0
$848$	−21.6977	+	37.5815i	−0.745103	+	1.29056i
$849$	0.636643	+	1.10270i	0.0218495	+	0.0378445i
$850$		0			0
$851$	−8.42443	−	14.5915i	−0.288786	−	0.500192i
$852$	−14.8489			−0.508713
$853$	11.2733			0.385990			0.192995	−	0.981200i	$-0.438180\pi$
$853$	11.2733			0.385990			0.192995	+	0.981200i	$0.438180\pi$
$854$		0			0
$855$	−4.21221	+	7.29577i	−0.144055	+	0.249510i
$856$		0			0
$857$	−4.27329	+	7.40155i	−0.145973	+	0.252832i	−0.929735	−	0.368228i	$-0.879964\pi$
$857$	−4.27329	+	7.40155i	−0.145973	+	0.252832i	0.783763	+	0.621060i	$0.213298\pi$
$858$		0			0
$859$	−3.07557	+	5.32705i	−0.104937	+	0.181756i	−0.913713	−	0.406361i	$-0.866797\pi$
$859$	−3.07557	+	5.32705i	−0.104937	+	0.181756i	0.808775	+	0.588118i	$0.200131\pi$
$860$	12.8489			0.438142
$861$		0			0
$862$		0			0
$863$	−7.42443	+	12.8595i	−0.252730	+	0.437742i	−0.964277	−	0.264897i	$-0.914662\pi$
$863$	−7.42443	+	12.8595i	−0.252730	+	0.437742i	0.711546	+	0.702639i	$0.247995\pi$
$864$		0			0
$865$	0.424429	+	0.735132i	0.0144310	+	0.0249953i
$866$		0			0
$867$	1.00000			0.0339618
$868$		0			0
$869$	−66.5756			−2.25842
$870$		0			0
$871$	15.1511	+	26.2425i	0.513377	+	0.889195i
$872$		0			0
$873$	6.21221	−	10.7599i	0.210252	−	0.364166i
$874$		0			0
$875$		0			0
$876$	−3.15114			−0.106467
$877$	0.363357	−	0.629352i	0.0122697	−	0.0212517i	−0.859825	−	0.510588i	$-0.829428\pi$
$877$	0.363357	−	0.629352i	0.0122697	−	0.0212517i	0.872095	+	0.489337i	$0.162761\pi$
$878$		0			0
$879$	−3.00000	+	5.19615i	−0.101187	+	0.175262i
$880$	−10.8489	−	18.7908i	−0.365715	−	0.633437i
$881$	14.6977	−	25.4572i	0.495179	−	0.857675i	−0.504806	−	0.863233i	$-0.668436\pi$
$881$	14.6977	−	25.4572i	0.495179	−	0.857675i	0.999985	+	0.00555833i	$0.00176928\pi$
$882$		0			0
$883$	−50.9710			−1.71531			−0.857655	−	0.514225i	$-0.828080\pi$
$883$	−50.9710			−1.71531			−0.857655	+	0.514225i	$0.828080\pi$
$884$	−35.3954			−1.19048
$885$	2.71221	+	4.69769i	0.0911701	+	0.157911i
$886$		0			0
$887$	−4.57557	−	7.92512i	−0.153633	−	0.266100i	0.778928	−	0.627114i	$-0.215764\pi$
$887$	−4.57557	−	7.92512i	−0.153633	−	0.266100i	−0.932560	+	0.361014i	$0.882431\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−5.42443			−0.181725
$892$	8.42443	+	14.5915i	0.282071	+	0.488561i
$893$	37.2733	+	64.5592i	1.24730	+	2.16039i
$894$		0			0
$895$	−15.4244			−0.515582
$896$		0			0
$897$	8.84886			0.295455
$898$		0			0
$899$	−16.1366	−	10.1556i	−0.538187	−	0.338709i
$900$	−2.00000			−0.0666667
$901$	−43.3954			−1.44571
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−0.787786	−	1.36448i	−0.0261869	−	0.0453570i
$906$		0			0
$907$	−58.2443			−1.93397			−0.966985	−	0.254834i	$-0.917979\pi$
$907$	−58.2443			−1.93397			−0.966985	+	0.254834i	$0.917979\pi$
$908$	22.8489	−	39.5754i	0.758266	−	1.31336i
$909$	−7.00000	+	12.1244i	−0.232175	+	0.402139i
$910$		0			0
$911$	−12.7122	−	22.0182i	−0.421174	−	0.729496i	0.574880	−	0.818238i	$-0.305049\pi$
$911$	−12.7122	−	22.0182i	−0.421174	−	0.729496i	−0.996055	+	0.0887420i	$0.971715\pi$
$912$	−16.8489	+	29.1831i	−0.557921	+	0.966348i
$913$	16.2733	+	28.1862i	0.538567	+	0.932826i
$914$		0			0
$915$	4.57557			0.151264
$916$	−11.0000	−	19.0526i	−0.363450	−	0.629514i
$917$		0			0
$918$		0			0
$919$	−3.50000	+	6.06218i	−0.115454	+	0.199973i	−0.917961	−	0.396670i	$-0.870166\pi$
$919$	−3.50000	+	6.06218i	−0.115454	+	0.199973i	0.802507	+	0.596643i	$0.203499\pi$
$920$		0			0
$921$	9.21221	−	15.9560i	0.303553	−	0.525769i
$922$		0			0
$923$	−16.4244	−	28.4479i	−0.540617	−	0.936376i
$924$		0			0
$925$	−4.21221	+	7.29577i	−0.138497	+	0.239883i
$926$		0			0
$927$	−6.21221	−	10.7599i	−0.204036	−	0.353401i
$928$		0			0
$929$	4.57557			0.150120			0.0750598	−	0.997179i	$-0.476085\pi$
$929$	4.57557			0.150120			0.0750598	+	0.997179i	$0.476085\pi$
$930$		0			0
$931$	58.9710			1.93270
$932$	45.6977			1.49688
$933$	0.287786	+	0.498459i	0.00942168	+	0.0163188i
$934$		0			0
$935$	10.8489	−	18.7908i	0.354796	−	0.614524i
$936$		0			0
$937$	3.21221	+	5.56372i	0.104938	+	0.181759i	0.913713	−	0.406360i	$-0.133202\pi$
$937$	3.21221	+	5.56372i	0.104938	+	0.181759i	−0.808775	+	0.588119i	$0.799869\pi$
$938$		0			0
$939$	−1.21221	+	2.09962i	−0.0395591	+	0.0685184i
$940$	−8.84886	+	15.3267i	−0.288618	+	0.499901i
$941$	4.57557	−	7.92512i	0.149159	−	0.258352i	−0.781758	−	0.623582i	$-0.785677\pi$
$941$	4.57557	−	7.92512i	0.149159	−	0.258352i	0.930917	+	0.365231i	$0.119010\pi$
$942$		0			0
$943$	1.42443	−	2.46718i	0.0463858	−	0.0803425i
$944$	10.8489	+	18.7908i	0.353100	+	0.611588i
$945$		0			0
$946$		0			0
$947$	12.6977	+	21.9931i	0.412620	+	0.714679i	0.995175	−	0.0981119i	$-0.0312803\pi$
$947$	12.6977	+	21.9931i	0.412620	+	0.714679i	−0.582555	+	0.812791i	$0.697947\pi$
$948$	−12.2733	+	21.2580i	−0.398618	+	0.690426i
$949$	−3.48550	−	6.03707i	−0.113144	−	0.195971i
$950$		0			0
$951$	9.84886	−	17.0587i	0.319371	−	0.553167i
$952$		0			0
$953$	23.6977			0.767644			0.383822	−	0.923407i	$-0.374608\pi$
$953$	23.6977			0.767644			0.383822	+	0.923407i	$0.374608\pi$
$954$		0			0
$955$	−6.13664	−	10.6290i	−0.198577	−	0.343946i
$956$	−10.2733	+	17.7939i	−0.332262	+	0.575494i
$957$	18.5756			0.600463
$958$		0			0
$959$		0			0
$960$	−8.00000			−0.258199
$961$	13.4099	+	27.9495i	0.432578	+	0.901596i
$962$		0			0
$963$	−4.84886			−0.156252
$964$	14.4244	+	24.9838i	0.464580	+	0.804675i
$965$	14.4244			0.464339
$966$		0			0
$967$	27.6977	+	47.9739i	0.890698	+	1.54274i	0.839040	+	0.544070i	$0.183118\pi$
$967$	27.6977	+	47.9739i	0.890698	+	1.54274i	0.0516588	+	0.998665i	$0.483549\pi$
$968$		0			0
$969$	−33.6977			−1.08253
$970$		0			0
$971$	−1.27329	+	2.20540i	−0.0408617	+	0.0707746i	−0.885733	−	0.464195i	$-0.846344\pi$
$971$	−1.27329	+	2.20540i	−0.0408617	+	0.0707746i	0.844871	+	0.534970i	$0.179677\pi$
$972$	−1.00000	+	1.73205i	−0.0320750	+	0.0555556i
$973$		0			0
$974$		0			0
$975$	−2.21221	−	3.83167i	−0.0708476	−	0.122712i
$976$	18.3023			0.585842
$977$	−37.6977			−1.20606			−0.603028	−	0.797720i	$-0.706039\pi$
$977$	−37.6977			−1.20606			−0.603028	+	0.797720i	$0.706039\pi$
$978$		0			0
$979$	−36.4099	+	63.0638i	−1.16367	+	2.01553i
$980$	7.00000	+	12.1244i	0.223607	+	0.387298i
$981$	2.92443	−	5.06526i	0.0933698	−	0.161721i
$982$		0			0
$983$	16.6977	−	28.9213i	0.532574	−	0.922446i	−0.466702	−	0.884415i	$-0.654558\pi$
$983$	16.6977	−	28.9213i	0.532574	−	0.922446i	0.999277	−	0.0380314i	$-0.0121087\pi$
$984$		0			0
$985$	−0.575571	−	0.996918i	−0.0183392	−	0.0317645i
$986$		0			0
$987$		0			0
$988$	−74.5466			−2.37164
$989$	−6.42443	−	11.1274i	−0.204285	−	0.353832i
$990$		0			0
$991$	58.0931			1.84539			0.922695	−	0.385531i	$-0.125982\pi$
$991$	58.0931			1.84539			0.922695	+	0.385531i	$0.125982\pi$
$992$		0			0
$993$	15.0000			0.476011
$994$		0			0
$995$	8.00000	+	13.8564i	0.253617	+	0.439278i
$996$	12.0000			0.380235
$997$	24.1221	−	41.7808i	0.763956	−	1.32321i	−0.176841	−	0.984239i	$-0.556588\pi$
$997$	24.1221	−	41.7808i	0.763956	−	1.32321i	0.940797	−	0.338971i	$-0.110079\pi$
$998$		0			0
$999$	4.21221	+	7.29577i	0.133269	+	0.230828i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	465.2.i.b.211.2	✓	4
31.5	even	3	inner	465.2.i.b.346.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
465.2.i.b.211.2	✓	4	1.1	even	1	trivial
465.2.i.b.346.2	yes	4	31.5	even	3	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 465 = 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	465.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{3} -2.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{3} -2.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{9} +(2.71221 - 4.69769i) q^{11} +(-1.00000 - 1.73205i) q^{12} +(2.21221 - 3.83167i) q^{13} +1.00000 q^{15} +4.00000 q^{16} +(2.00000 + 3.46410i) q^{17} +(4.21221 + 7.29577i) q^{19} +(-1.00000 + 1.73205i) q^{20} +2.00000 q^{23} +(-0.500000 - 0.866025i) q^{25} -1.00000 q^{27} +3.42443 q^{29} +(-4.71221 - 2.96564i) q^{31} +5.42443 q^{33} +(1.00000 - 1.73205i) q^{36} +(-4.21221 - 7.29577i) q^{37} +4.42443 q^{39} +(0.712214 - 1.23359i) q^{41} +(-3.21221 - 5.56372i) q^{43} +(-5.42443 + 9.39539i) q^{44} +(0.500000 + 0.866025i) q^{45} +8.84886 q^{47} +(2.00000 + 3.46410i) q^{48} +(3.50000 - 6.06218i) q^{49} +(-2.00000 + 3.46410i) q^{51} +(-4.42443 + 7.66334i) q^{52} +(-5.42443 + 9.39539i) q^{53} +(-2.71221 - 4.69769i) q^{55} +(-4.21221 + 7.29577i) q^{57} +(2.71221 + 4.69769i) q^{59} -2.00000 q^{60} +4.57557 q^{61} -8.00000 q^{64} +(-2.21221 - 3.83167i) q^{65} +(-3.42443 + 5.93128i) q^{67} +(-4.00000 - 6.92820i) q^{68} +(1.00000 + 1.73205i) q^{69} +(3.71221 - 6.42974i) q^{71} +(0.787786 - 1.36448i) q^{73} +(0.500000 - 0.866025i) q^{75} +(-8.42443 - 14.5915i) q^{76} +(-6.13664 - 10.6290i) q^{79} +(2.00000 - 3.46410i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-3.00000 + 5.19615i) q^{83} +4.00000 q^{85} +(1.71221 + 2.96564i) q^{87} -13.4244 q^{89} -4.00000 q^{92} +(0.212214 - 5.56372i) q^{93} +8.42443 q^{95} -12.4244 q^{97} +(2.71221 + 4.69769i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} - 8 q^{4} + 2 q^{5} - 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^3 - 8 * q^4 + 2 * q^5 - 2 * q^9	\( 4 q + 2 q^{3} - 8 q^{4} + 2 q^{5} - 2 q^{9} + q^{11} - 4 q^{12} - q^{13} + 4 q^{15} + 16 q^{16} + 8 q^{17} + 7 q^{19} - 4 q^{20} + 8 q^{23} - 2 q^{25} - 4 q^{27} - 6 q^{29} - 9 q^{31} + 2 q^{33} + 4 q^{36} - 7 q^{37} - 2 q^{39} - 7 q^{41} - 3 q^{43} - 2 q^{44} + 2 q^{45} - 4 q^{47} + 8 q^{48} + 14 q^{49} - 8 q^{51} + 2 q^{52} - 2 q^{53} - q^{55} - 7 q^{57} + q^{59} - 8 q^{60} + 38 q^{61} - 32 q^{64} + q^{65} + 6 q^{67} - 16 q^{68} + 4 q^{69} + 5 q^{71} + 13 q^{73} + 2 q^{75} - 14 q^{76} + 5 q^{79} + 8 q^{80} - 2 q^{81} - 12 q^{83} + 16 q^{85} - 3 q^{87} - 34 q^{89} - 16 q^{92} - 9 q^{93} + 14 q^{95} - 30 q^{97} + q^{99}+O(q^{100}) \) 4 * q + 2 * q^3 - 8 * q^4 + 2 * q^5 - 2 * q^9 + q^11 - 4 * q^12 - q^13 + 4 * q^15 + 16 * q^16 + 8 * q^17 + 7 * q^19 - 4 * q^20 + 8 * q^23 - 2 * q^25 - 4 * q^27 - 6 * q^29 - 9 * q^31 + 2 * q^33 + 4 * q^36 - 7 * q^37 - 2 * q^39 - 7 * q^41 - 3 * q^43 - 2 * q^44 + 2 * q^45 - 4 * q^47 + 8 * q^48 + 14 * q^49 - 8 * q^51 + 2 * q^52 - 2 * q^53 - q^55 - 7 * q^57 + q^59 - 8 * q^60 + 38 * q^61 - 32 * q^64 + q^65 + 6 * q^67 - 16 * q^68 + 4 * q^69 + 5 * q^71 + 13 * q^73 + 2 * q^75 - 14 * q^76 + 5 * q^79 + 8 * q^80 - 2 * q^81 - 12 * q^83 + 16 * q^85 - 3 * q^87 - 34 * q^89 - 16 * q^92 - 9 * q^93 + 14 * q^95 - 30 * q^97 + q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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