LMFDB - Embedded newform 252.9.z.c.73.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,9,Mod(73,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("252.73");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	252.z (of order $6$, 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:	$102.659409735$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 1442 x^{8} + 59551 x^{7} + 2229058 x^{6} + 41253567 x^{5} + 582209889 x^{4} + \cdots + 63214027776 $ x^10 - x^9 + 1442x^8 + 59551x^7 + 2229058x^6 + 41253567x^5 + 582209889x^4 + 4552713792x^3 + 25685059104x^2 + 45666643968x + 63214027776
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{9}\cdot 7^{6} $
Twist minimal:	no (minimal twist has level 28)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			73.5
Root			$-7.84041 - 13.5800i$ of defining polynomial
Character	$\chi$	$=$	252.73
Dual form			252.9.z.c.145.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(951.520 - 549.361i) q^{5} +(2332.69 + 568.626i) q^{7} +O(q^{10})$	$q+(951.520 - 549.361i) q^{5} +(2332.69 + 568.626i) q^{7} +(-8373.68 + 14503.6i) q^{11} -12172.5i q^{13} +(-92085.4 - 53165.5i) q^{17} +(-33869.3 + 19554.5i) q^{19} +(-217614. - 376919. i) q^{23} +(408281. - 707164. i) q^{25} -752691. q^{29} +(-611743. - 353190. i) q^{31} +(2.53199e6 - 740431. i) q^{35} +(-1.25781e6 - 2.17859e6i) q^{37} -3.11495e6i q^{41} +1.65406e6 q^{43} +(-5.50274e6 + 3.17701e6i) q^{47} +(5.11813e6 + 2.65286e6i) q^{49} +(-2.79222e6 + 4.83627e6i) q^{53} +1.84007e7i q^{55} +(-1.66779e6 - 962898. i) q^{59} +(1.54825e7 - 8.93885e6i) q^{61} +(-6.68711e6 - 1.15824e7i) q^{65} +(509223. - 882001. i) q^{67} -2.80284e6 q^{71} +(-1.40868e7 - 8.13300e6i) q^{73} +(-2.77804e7 + 2.90711e7i) q^{77} +(2.90749e7 + 5.03592e7i) q^{79} -6.45682e7i q^{83} -1.16828e8 q^{85} +(7.07065e7 - 4.08224e7i) q^{89} +(6.92162e6 - 2.83948e7i) q^{91} +(-2.14849e7 + 3.72129e7i) q^{95} -9.95327e7i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 837 q^{5} + 1526 q^{7}+O(q^{10}) $ 10 * q + 837 * q^5 + 1526 * q^7	$ 10 q + 837 q^{5} + 1526 q^{7} - 3705 q^{11} - 78003 q^{17} - 96741 q^{19} - 208533 q^{23} + 367978 q^{25} - 754764 q^{29} - 1053717 q^{31} + 1306389 q^{35} - 998075 q^{37} + 738292 q^{43} - 710883 q^{47} + 13288114 q^{49} - 10501461 q^{53} + 37089081 q^{59} - 8180481 q^{61} - 21459108 q^{65} + 48020189 q^{67} + 31918236 q^{71} - 133345593 q^{73} - 188477625 q^{77} + 53590181 q^{79} - 157179282 q^{85} + 241368273 q^{89} + 420709128 q^{91} - 347126775 q^{95}+O(q^{100}) $ 10 * q + 837 * q^5 + 1526 * q^7 - 3705 * q^11 - 78003 * q^17 - 96741 * q^19 - 208533 * q^23 + 367978 * q^25 - 754764 * q^29 - 1053717 * q^31 + 1306389 * q^35 - 998075 * q^37 + 738292 * q^43 - 710883 * q^47 + 13288114 * q^49 - 10501461 * q^53 + 37089081 * q^59 - 8180481 * q^61 - 21459108 * q^65 + 48020189 * q^67 + 31918236 * q^71 - 133345593 * q^73 - 188477625 * q^77 + 53590181 * q^79 - 157179282 * q^85 + 241368273 * q^89 + 420709128 * q^91 - 347126775 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	951.520	−	549.361i	1.52243	−	0.878977i	0.522784	−	0.852465i	$-0.324893\pi$
$5$	951.520	−	549.361i	1.52243	−	0.878977i	0.999649	−	0.0265117i	$-0.00843992\pi$
$6$		0			0
$7$	2332.69	+	568.626i	0.971551	+	0.236829i
$7$	2332.69	+	568.626i	0.971551	+	0.236829i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−8373.68	+	14503.6i	−0.571934	+	0.990618i	0.424434	+	0.905459i	$0.360473\pi$
$11$	−8373.68	+	14503.6i	−0.571934	+	0.990618i	−0.996367	+	0.0851591i	$0.972860\pi$
$12$		0			0
$13$		−	12172.5i		−	0.426194i	−0.977031	−	0.213097i	$-0.931645\pi$
$13$		−	12172.5i		−	0.426194i	0.977031	−	0.213097i	$-0.0683551\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−92085.4	−	53165.5i	−1.10254	−	0.636553i	−0.165655	−	0.986184i	$-0.552974\pi$
$17$	−92085.4	−	53165.5i	−1.10254	−	0.636553i	−0.936888	+	0.349631i	$0.886307\pi$
$18$		0			0
$19$	−33869.3	+	19554.5i	−0.259892	+	0.150048i	−0.624285	−	0.781197i	$-0.714610\pi$
$19$	−33869.3	+	19554.5i	−0.259892	+	0.150048i	0.364394	+	0.931245i	$0.381276\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−217614.	−	376919.i	−0.777635	−	1.34690i	−0.933301	−	0.359094i	$-0.883086\pi$
$23$	−217614.	−	376919.i	−0.777635	−	1.34690i	0.155666	−	0.987810i	$-0.450248\pi$
$24$		0			0
$25$	408281.	−	707164.i	1.04520	−	1.81034i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−752691.			−1.06420			−0.532102	−	0.846680i	$-0.678598\pi$
$29$	−752691.			−1.06420			−0.532102	+	0.846680i	$0.678598\pi$
$30$		0			0
$31$	−611743.	−	353190.i	−0.662403	−	0.382438i	0.130789	−	0.991410i	$-0.458249\pi$
$31$	−611743.	−	353190.i	−0.662403	−	0.382438i	−0.793192	+	0.608972i	$0.791582\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	2.53199e6	−	740431.i	1.68729	−	0.493415i
$36$		0			0
$37$	−1.25781e6	−	2.17859e6i	−0.671132	−	1.16244i	−0.977583	−	0.210549i	$-0.932475\pi$
$37$	−1.25781e6	−	2.17859e6i	−0.671132	−	1.16244i	0.306451	−	0.951886i	$-0.400858\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		−	3.11495e6i		−	1.10234i	−0.834392	−	0.551171i	$-0.814181\pi$
$41$		−	3.11495e6i		−	1.10234i	0.834392	−	0.551171i	$-0.185819\pi$
$42$		0			0
$43$	1.65406e6			0.483812			0.241906	−	0.970300i	$-0.422227\pi$
$43$	1.65406e6			0.483812			0.241906	+	0.970300i	$0.422227\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−5.50274e6	+	3.17701e6i	−1.12768	+	0.651069i	−0.943351	−	0.331795i	$-0.892346\pi$
$47$	−5.50274e6	+	3.17701e6i	−1.12768	+	0.651069i	−0.184333	+	0.982864i	$0.559012\pi$
$48$		0			0
$49$	5.11813e6	+	2.65286e6i	0.887824	+	0.460183i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−2.79222e6	+	4.83627e6i	−0.353872	+	0.612924i	−0.986924	−	0.161185i	$-0.948468\pi$
$53$	−2.79222e6	+	4.83627e6i	−0.353872	+	0.612924i	0.633052	+	0.774109i	$0.281802\pi$
$54$		0			0
$55$			1.84007e7i			2.01087i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−1.66779e6	−	962898.i	−0.137636	−	0.0794643i	0.429601	−	0.903019i	$-0.358654\pi$
$59$	−1.66779e6	−	962898.i	−0.137636	−	0.0794643i	−0.567237	+	0.823555i	$0.691988\pi$
$60$		0			0
$61$	1.54825e7	−	8.93885e6i	1.11821	−	0.645598i	0.177265	−	0.984163i	$-0.443275\pi$
$61$	1.54825e7	−	8.93885e6i	1.11821	−	0.645598i	0.940943	+	0.338565i	$0.109942\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−6.68711e6	−	1.15824e7i	−0.374615	−	0.648852i
$66$		0			0
$67$	509223.	−	882001.i	0.0252702	−	0.0437693i	−0.853114	−	0.521725i	$-0.825289\pi$
$67$	509223.	−	882001.i	0.0252702	−	0.0437693i	0.878384	+	0.477956i	$0.158622\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−2.80284e6			−0.110297			−0.0551486	−	0.998478i	$-0.517563\pi$
$71$	−2.80284e6			−0.110297			−0.0551486	+	0.998478i	$0.517563\pi$
$72$		0			0
$73$	−1.40868e7	−	8.13300e6i	−0.496044	−	0.286391i	0.231035	−	0.972946i	$-0.425789\pi$
$73$	−1.40868e7	−	8.13300e6i	−0.496044	−	0.286391i	−0.727078	+	0.686555i	$0.759122\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−2.77804e7	+	2.90711e7i	−0.790270	+	0.826986i
$78$		0			0
$79$	2.90749e7	+	5.03592e7i	0.746466	+	1.29292i	0.949507	+	0.313746i	$0.101584\pi$
$79$	2.90749e7	+	5.03592e7i	0.746466	+	1.29292i	−0.203041	+	0.979170i	$0.565083\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$		−	6.45682e7i		−	1.36053i	−0.732968	−	0.680263i	$-0.761866\pi$
$83$		−	6.45682e7i		−	1.36053i	0.732968	−	0.680263i	$-0.238134\pi$
$84$		0			0
$85$	−1.16828e8			−2.23806
$86$		0			0
$87$		0			0
$88$		0			0
$89$	7.07065e7	−	4.08224e7i	1.12694	−	0.650637i	0.183774	−	0.982969i	$-0.441169\pi$
$89$	7.07065e7	−	4.08224e7i	1.12694	−	0.650637i	0.943163	+	0.332331i	$0.107835\pi$
$90$		0			0
$91$	6.92162e6	−	2.83948e7i	0.100935	−	0.414070i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−2.14849e7	+	3.72129e7i	−0.263778	+	0.456877i
$96$		0			0
$97$		−	9.95327e7i		−	1.12429i	−0.827038	−	0.562146i	$-0.809976\pi$
$97$		−	9.95327e7i		−	1.12429i	0.827038	−	0.562146i	$-0.190024\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−7.72195e7	−	4.45827e7i	−0.742064	−	0.428431i	0.0807553	−	0.996734i	$-0.474267\pi$
$101$	−7.72195e7	−	4.45827e7i	−0.742064	−	0.428431i	−0.822819	+	0.568303i	$0.807600\pi$
$102$		0			0
$103$	1.19034e8	−	6.87243e7i	1.05760	−	0.610606i	0.132833	−	0.991138i	$-0.457592\pi$
$103$	1.19034e8	−	6.87243e7i	1.05760	−	0.610606i	0.924768	+	0.380532i	$0.124259\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	2.01907e7	+	3.49714e7i	0.154034	+	0.266795i	0.932707	−	0.360635i	$-0.117440\pi$
$107$	2.01907e7	+	3.49714e7i	0.154034	+	0.266795i	−0.778673	+	0.627430i	$0.784107\pi$
$108$		0			0
$109$	3.50017e7	−	6.06248e7i	0.247961	−	0.429481i	−0.714999	−	0.699126i	$-0.753573\pi$
$109$	3.50017e7	−	6.06248e7i	0.247961	−	0.429481i	0.962960	+	0.269644i	$0.0869062\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	7.09428e7			0.435105			0.217553	−	0.976049i	$-0.430193\pi$
$113$	7.09428e7			0.435105			0.217553	+	0.976049i	$0.430193\pi$
$114$		0			0
$115$	−4.14129e8	−	2.39097e8i	−2.36779	−	1.36705i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−1.84576e8	−	1.76381e8i	−0.920422	−	0.879558i
$120$		0			0
$121$	−3.30576e7	−	5.72574e7i	−0.154216	−	0.267110i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		−	4.67987e8i		−	1.91687i
$126$		0			0
$127$	3.25545e8			1.25140			0.625701	−	0.780063i	$-0.284813\pi$
$127$	3.25545e8			1.25140			0.625701	+	0.780063i	$0.284813\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	2.43722e7	−	1.40713e7i	0.0827580	−	0.0477803i	−0.458050	−	0.888926i	$-0.651452\pi$
$131$	2.43722e7	−	1.40713e7i	0.0827580	−	0.0477803i	0.540808	+	0.841146i	$0.318119\pi$
$132$		0			0
$133$	−9.01260e7	+	2.63556e7i	−0.288034	+	0.0842299i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−1.89204e8	+	3.27711e8i	−0.537092	+	0.930271i	0.461967	+	0.886897i	$0.347144\pi$
$137$	−1.89204e8	+	3.27711e8i	−0.537092	+	0.930271i	−0.999059	+	0.0433734i	$0.986189\pi$
$138$		0			0
$139$			3.66055e8i			0.980590i	0.871557	+	0.490295i	$0.163111\pi$
$139$			3.66055e8i			0.980590i	−0.871557	+	0.490295i	$0.836889\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	1.76546e8	+	1.01929e8i	0.422196	+	0.243755i
$144$		0			0
$145$	−7.16201e8	+	4.13499e8i	−1.62018	+	0.935410i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−3.03522e8	−	5.25716e8i	−0.615808	−	1.06661i	−0.990242	−	0.139358i	$-0.955496\pi$
$149$	−3.03522e8	−	5.25716e8i	−0.615808	−	1.06661i	0.374434	−	0.927254i	$-0.377837\pi$
$150$		0			0
$151$	1.16419e8	−	2.01644e8i	0.223932	−	0.387862i	−0.732066	−	0.681233i	$-0.761444\pi$
$151$	1.16419e8	−	2.01644e8i	0.223932	−	0.387862i	0.955999	+	0.293372i	$0.0947773\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−7.76114e8			−1.34462
$156$		0			0
$157$	−8.35185e8	−	4.82194e8i	−1.37462	−	0.793640i	−0.383118	−	0.923699i	$-0.625150\pi$
$157$	−8.35185e8	−	4.82194e8i	−1.37462	−	0.793640i	−0.991506	+	0.130060i	$0.958483\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−2.93302e8	−	1.00298e9i	−0.436527	−	1.49275i
$162$		0			0
$163$	3.96065e8	+	6.86005e8i	0.561069	+	0.971800i	0.997404	+	0.0720154i	$0.0229431\pi$
$163$	3.96065e8	+	6.86005e8i	0.561069	+	0.971800i	−0.436335	+	0.899784i	$0.643724\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$			2.87494e8i			0.369626i	0.982774	+	0.184813i	$0.0591679\pi$
$167$			2.87494e8i			0.369626i	−0.982774	+	0.184813i	$0.940832\pi$
$168$		0			0
$169$	6.67560e8			0.818359
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−3.55122e8	+	2.05030e8i	−0.396454	+	0.228893i	−0.684953	−	0.728587i	$-0.740177\pi$
$173$	−3.55122e8	+	2.05030e8i	−0.396454	+	0.228893i	0.288499	+	0.957480i	$0.406844\pi$
$174$		0			0
$175$	1.35451e9	−	1.41744e9i	1.44421	−	1.51130i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	4.85063e8	−	8.40154e8i	0.472483	−	0.818364i	−0.527021	−	0.849852i	$-0.676691\pi$
$179$	4.85063e8	−	8.40154e8i	0.472483	−	0.818364i	0.999504	+	0.0314879i	$0.0100246\pi$
$180$		0			0
$181$		−	2.97202e8i		−	0.276910i	−0.990369	−	0.138455i	$-0.955786\pi$
$181$		−	2.97202e8i		−	0.276910i	0.990369	−	0.138455i	$-0.0442136\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−2.39366e9	−	1.38198e9i	−2.04351	−	1.17982i
$186$		0			0
$187$	1.54219e9	−	8.90383e8i	1.26116	−	0.728132i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−4.42144e8	−	7.65816e8i	−0.332224	−	0.575428i	0.650724	−	0.759314i	$-0.274466\pi$
$191$	−4.42144e8	−	7.65816e8i	−0.332224	−	0.575428i	−0.982948	+	0.183886i	$0.941132\pi$
$192$		0			0
$193$	−1.15787e9	+	2.00549e9i	−0.834506	+	1.44541i	0.0599252	+	0.998203i	$0.480914\pi$
$193$	−1.15787e9	+	2.00549e9i	−0.834506	+	1.44541i	−0.894432	+	0.447205i	$0.852420\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	1.93628e9			1.28559			0.642797	−	0.766036i	$-0.277774\pi$
$197$	1.93628e9			1.28559			0.642797	+	0.766036i	$0.277774\pi$
$198$		0			0
$199$	−1.76811e9	−	1.02082e9i	−1.12745	−	0.650933i	−0.184157	−	0.982897i	$-0.558955\pi$
$199$	−1.76811e9	−	1.02082e9i	−1.12745	−	0.650933i	−0.943292	+	0.331964i	$0.892289\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−1.75580e9	−	4.28000e8i	−1.03393	−	0.252034i
$204$		0			0
$205$	−1.71123e9	−	2.96394e9i	−0.968933	−	1.67824i
$206$		0			0
$207$		0			0
$208$		0			0
$209$		−	6.54971e8i		−	0.343271i
$210$		0			0
$211$	−6.77399e8			−0.341755			−0.170877	−	0.985292i	$-0.554660\pi$
$211$	−6.77399e8			−0.341755			−0.170877	+	0.985292i	$0.554660\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	1.57387e9	−	9.08674e8i	0.736572	−	0.425260i
$216$		0			0
$217$	−1.22618e9	−	1.17174e9i	−0.552986	−	0.528435i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−6.47159e8	+	1.12091e9i	−0.271295	+	0.469897i
$222$		0			0
$223$		−	6.59852e8i		−	0.266826i	−0.991061	−	0.133413i	$-0.957406\pi$
$223$		−	6.59852e8i		−	0.266826i	0.991061	−	0.133413i	$-0.0425936\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−1.81748e9	−	1.04932e9i	−0.684488	−	0.395190i	0.117056	−	0.993125i	$-0.462654\pi$
$227$	−1.81748e9	−	1.04932e9i	−0.684488	−	0.395190i	−0.801544	+	0.597936i	$0.795988\pi$
$228$		0			0
$229$	1.72622e9	−	9.96636e8i	0.627705	−	0.362406i	−0.152158	−	0.988356i	$-0.548622\pi$
$229$	1.72622e9	−	9.96636e8i	0.627705	−	0.362406i	0.779863	+	0.625951i	$0.215289\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	8.79751e7	+	1.52377e8i	0.0298494	+	0.0517007i	0.880564	−	0.473927i	$-0.157164\pi$
$233$	8.79751e7	+	1.52377e8i	0.0298494	+	0.0517007i	−0.850715	+	0.525628i	$0.823831\pi$
$234$		0			0
$235$	−3.49065e9	+	6.04598e9i	−1.14455	+	1.98242i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−2.35853e8			−0.0722853			−0.0361426	−	0.999347i	$-0.511507\pi$
$239$	−2.35853e8			−0.0722853			−0.0361426	+	0.999347i	$0.511507\pi$
$240$		0			0
$241$	1.17101e9	+	6.76083e8i	0.347130	+	0.200416i	0.663421	−	0.748247i	$-0.269104\pi$
$241$	1.17101e9	+	6.76083e8i	0.347130	+	0.200416i	−0.316290	+	0.948662i	$0.602437\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	6.32738e9	−	2.87445e8i	1.75614	−	0.0797793i
$246$		0			0
$247$	2.38027e8	+	4.12275e8i	0.0639498	+	0.110764i
$248$		0			0
$249$		0			0
$250$		0			0
$251$		−	1.53179e9i		−	0.385925i	−0.981206	−	0.192963i	$-0.938190\pi$
$251$		−	1.53179e9i		−	0.385925i	0.981206	−	0.192963i	$-0.0618096\pi$
$252$		0			0
$253$	7.28893e9			1.77902
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−6.13579e9	+	3.54250e9i	−1.40649	+	0.812040i	−0.995048	−	0.0993948i	$-0.968309\pi$
$257$	−6.13579e9	+	3.54250e9i	−1.40649	+	0.812040i	−0.411446	+	0.911434i	$0.634976\pi$
$258$		0			0
$259$	−1.69528e9	−	5.79721e9i	−0.376741	−	1.28831i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−2.07747e9	+	3.59828e9i	−0.434222	+	0.752094i	−0.997232	−	0.0743560i	$-0.976310\pi$
$263$	−2.07747e9	+	3.59828e9i	−0.434222	+	0.752094i	0.563010	+	0.826450i	$0.309643\pi$
$264$		0			0
$265$			6.13574e9i			1.24418i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	2.19738e9	+	1.26866e9i	0.419659	+	0.242290i	0.694931	−	0.719076i	$-0.255435\pi$
$269$	2.19738e9	+	1.26866e9i	0.419659	+	0.242290i	−0.275272	+	0.961366i	$0.588768\pi$
$270$		0			0
$271$	1.49814e9	−	8.64950e8i	0.277763	−	0.160367i	−0.354647	−	0.935000i	$-0.615399\pi$
$271$	1.49814e9	−	8.64950e8i	0.277763	−	0.160367i	0.632410	+	0.774634i	$0.282066\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	6.83764e9	+	1.18431e10i	1.19557	+	2.07079i
$276$		0			0
$277$	−5.17823e9	+	8.96896e9i	−0.879554	+	1.52343i	−0.0277231	+	0.999616i	$0.508826\pi$
$277$	−5.17823e9	+	8.96896e9i	−0.879554	+	1.52343i	−0.851831	+	0.523817i	$0.824508\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	6.97916e9			1.11938			0.559690	−	0.828702i	$-0.310920\pi$
$281$	6.97916e9			1.11938			0.559690	+	0.828702i	$0.310920\pi$
$282$		0			0
$283$	−3.98236e9	−	2.29922e9i	−0.620861	−	0.358455i	0.156343	−	0.987703i	$-0.450030\pi$
$283$	−3.98236e9	−	2.29922e9i	−0.620861	−	0.358455i	−0.777204	+	0.629248i	$0.783363\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	1.77125e9	−	7.26624e9i	0.261066	−	1.07098i
$288$		0			0
$289$	2.16527e9	+	3.75036e9i	0.310400	+	0.537628i
$290$		0			0
$291$		0			0
$292$		0			0
$293$			1.25131e10i			1.69783i	0.528531	+	0.848914i	$0.322743\pi$
$293$			1.25131e10i			1.69783i	−0.528531	+	0.848914i	$0.677257\pi$
$294$		0			0
$295$	−2.11591e9			−0.279389
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−4.58806e9	+	2.64892e9i	−0.574043	+	0.331424i
$300$		0			0
$301$	3.85841e9	+	9.40541e8i	0.470049	+	0.114581i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	9.82130e9	−	1.70110e10i	1.13493	−	1.96576i
$306$		0			0
$307$		−	2.27861e9i		−	0.256517i	−0.991741	−	0.128258i	$-0.959061\pi$
$307$		−	2.27861e9i		−	0.256517i	0.991741	−	0.128258i	$-0.0409387\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−5.38801e9	−	3.11077e9i	−0.575953	−	0.332527i	0.183570	−	0.983007i	$-0.441234\pi$
$311$	−5.38801e9	−	3.11077e9i	−0.575953	−	0.332527i	−0.759523	+	0.650480i	$0.774568\pi$
$312$		0			0
$313$	9.86903e9	−	5.69789e9i	1.02825	−	0.593658i	0.111765	−	0.993735i	$-0.464350\pi$
$313$	9.86903e9	−	5.69789e9i	1.02825	−	0.593658i	0.916482	+	0.400076i	$0.131016\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	1.63164e9	+	2.82609e9i	0.161580	+	0.279865i	0.935436	−	0.353497i	$-0.115008\pi$
$317$	1.63164e9	+	2.82609e9i	0.161580	+	0.279865i	−0.773855	+	0.633362i	$0.781674\pi$
$318$		0			0
$319$	6.30279e9	−	1.09168e10i	0.608654	−	1.05422i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	4.15849e9			0.382055
$324$		0			0
$325$	−8.60798e9	−	4.96982e9i	−0.771557	−	0.445458i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−1.46427e10	+	4.28199e9i	−1.24980	+	0.365478i
$330$		0			0
$331$	5.31434e9	+	9.20472e9i	0.442729	+	0.766829i	0.997891	−	0.0649134i	$-0.0206771\pi$
$331$	5.31434e9	+	9.20472e9i	0.442729	+	0.766829i	−0.555162	+	0.831742i	$0.687344\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$		−	1.11899e9i		−	0.0888478i
$336$		0			0
$337$	−3.04095e8			−0.0235771			−0.0117885	−	0.999931i	$-0.503752\pi$
$337$	−3.04095e8			−0.0235771			−0.0117885	+	0.999931i	$0.503752\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	1.02451e10	−	5.91500e9i	0.757701	−	0.437459i
$342$		0			0
$343$	1.04305e10	+	9.09862e9i	0.753582	+	0.657354i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−8.60657e9	+	1.49070e10i	−0.593625	+	1.02819i	0.400115	+	0.916465i	$0.368970\pi$
$347$	−8.60657e9	+	1.49070e10i	−0.593625	+	1.02819i	−0.993739	+	0.111723i	$0.964363\pi$
$348$		0			0
$349$		−	1.62412e10i		−	1.09475i	−0.836886	−	0.547376i	$-0.815627\pi$
$349$		−	1.62412e10i		−	1.09475i	0.836886	−	0.547376i	$-0.184373\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	7.21336e9	+	4.16464e9i	0.464557	+	0.268212i	0.713958	−	0.700188i	$-0.246901\pi$
$353$	7.21336e9	+	4.16464e9i	0.464557	+	0.268212i	−0.249402	+	0.968400i	$0.580234\pi$
$354$		0			0
$355$	−2.66696e9	+	1.53977e9i	−0.167920	+	0.0969486i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	1.18335e10	+	2.04963e10i	0.712420	+	1.23395i	0.963946	+	0.266098i	$0.0857344\pi$
$359$	1.18335e10	+	2.04963e10i	0.712420	+	1.23395i	−0.251526	+	0.967851i	$0.580932\pi$
$360$		0			0
$361$	−7.72703e9	+	1.33836e10i	−0.454971	+	0.788033i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−1.78718e10			−1.00692
$366$		0			0
$367$	2.71073e10	+	1.56504e10i	1.49424	+	0.862702i	0.999978	−	0.00660862i	$-0.00210360\pi$
$367$	2.71073e10	+	1.56504e10i	1.49424	+	0.862702i	0.494266	+	0.869311i	$0.335437\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−9.26342e9	+	9.69380e9i	−0.488963	+	0.511680i
$372$		0			0
$373$	3.40622e9	+	5.89974e9i	0.175969	+	0.304788i	0.940496	−	0.339804i	$-0.110361\pi$
$373$	3.40622e9	+	5.89974e9i	0.175969	+	0.304788i	−0.764527	+	0.644592i	$0.777027\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			9.16215e9i			0.453557i
$378$		0			0
$379$	3.93276e9			0.190608			0.0953039	−	0.995448i	$-0.469618\pi$
$379$	3.93276e9			0.190608			0.0953039	+	0.995448i	$0.469618\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	2.38753e10	−	1.37844e10i	1.10957	−	0.640608i	0.170849	−	0.985297i	$-0.445349\pi$
$383$	2.38753e10	−	1.37844e10i	1.10957	−	0.640608i	0.938717	+	0.344689i	$0.112016\pi$
$384$		0			0
$385$	−1.04631e10	+	4.29232e10i	−0.476231	+	1.95366i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−6.53820e9	+	1.13245e10i	−0.285535	+	0.494562i	−0.972739	−	0.231903i	$-0.925505\pi$
$389$	−6.53820e9	+	1.13245e10i	−0.285535	+	0.494562i	0.687204	+	0.726465i	$0.258838\pi$
$390$		0			0
$391$			4.62783e10i			1.98002i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	5.53307e10	+	3.19452e10i	2.27289	+	1.31225i
$396$		0			0
$397$	2.20739e10	−	1.27443e10i	0.888620	−	0.513045i	0.0151293	−	0.999886i	$-0.495184\pi$
$397$	2.20739e10	−	1.27443e10i	0.888620	−	0.513045i	0.873491	+	0.486840i	$0.161851\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	3.61088e9	+	6.25423e9i	0.139648	+	0.241878i	0.927364	−	0.374162i	$-0.122069\pi$
$401$	3.61088e9	+	6.25423e9i	0.139648	+	0.241878i	−0.787715	+	0.616040i	$0.788736\pi$
$402$		0			0
$403$	−4.29921e9	+	7.44646e9i	−0.162993	+	0.282312i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	4.21300e10			1.53537
$408$		0			0
$409$	−3.57982e10	−	2.06681e10i	−1.27929	−	0.738596i	−0.302569	−	0.953127i	$-0.597844\pi$
$409$	−3.57982e10	−	2.06681e10i	−1.27929	−	0.738596i	−0.976717	+	0.214531i	$0.931178\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−3.34291e9	−	3.19449e9i	−0.114901	−	0.109800i
$414$		0			0
$415$	−3.54712e10	−	6.14380e10i	−1.19587	−	2.07131i
$416$		0			0
$417$		0			0
$418$		0			0
$419$		−	3.35673e10i		−	1.08908i	−0.838735	−	0.544540i	$-0.816704\pi$
$419$		−	3.35673e10i		−	1.08908i	0.838735	−	0.544540i	$-0.183296\pi$
$420$		0			0
$421$	−4.07727e10			−1.29790			−0.648950	−	0.760831i	$-0.724792\pi$
$421$	−4.07727e10			−1.29790			−0.648950	+	0.760831i	$0.724792\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−7.51936e10	+	4.34130e10i	−2.30476	+	1.33065i
$426$		0			0
$427$	4.11989e10	−	1.20478e10i	1.23929	−	0.362407i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	2.82732e10	−	4.89707e10i	0.819344	−	1.41915i	−0.0868218	−	0.996224i	$-0.527671\pi$
$431$	2.82732e10	−	4.89707e10i	0.819344	−	1.41915i	0.906166	−	0.422922i	$-0.138996\pi$
$432$		0			0
$433$			8.51213e9i			0.242151i	0.992643	+	0.121076i	$0.0386343\pi$
$433$			8.51213e9i			0.242151i	−0.992643	+	0.121076i	$0.961366\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	1.47409e10	+	8.51066e9i	0.404202	+	0.233366i
$438$		0			0
$439$	−1.55373e10	+	8.97044e9i	−0.418328	+	0.241522i	−0.694362	−	0.719626i	$-0.744313\pi$
$439$	−1.55373e10	+	8.97044e9i	−0.418328	+	0.241522i	0.276034	+	0.961148i	$0.410980\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−1.16407e10	−	2.01623e10i	−0.302249	−	0.523511i	0.674396	−	0.738370i	$-0.264404\pi$
$443$	−1.16407e10	−	2.01623e10i	−0.302249	−	0.523511i	−0.976645	+	0.214859i	$0.931071\pi$
$444$		0			0
$445$	4.48525e10	−	7.76867e10i	1.14379	−	1.98110i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−5.92327e10			−1.45739			−0.728695	−	0.684838i	$-0.759873\pi$
$449$	−5.92327e10			−1.45739			−0.728695	+	0.684838i	$0.759873\pi$
$450$		0			0
$451$	4.51782e10	+	2.60836e10i	1.09200	+	0.630466i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−9.01292e9	−	3.08207e10i	−0.210291	−	0.719113i
$456$		0			0
$457$	−3.43452e10	−	5.94876e10i	−0.787411	−	1.36384i	−0.927548	−	0.373703i	$-0.878088\pi$
$457$	−3.43452e10	−	5.94876e10i	−0.787411	−	1.36384i	0.140137	−	0.990132i	$-0.455246\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		−	2.73123e10i		−	0.604721i	−0.953194	−	0.302360i	$-0.902225\pi$
$461$		−	2.73123e10i		−	0.604721i	0.953194	−	0.302360i	$-0.0977746\pi$
$462$		0			0
$463$	−6.67622e10			−1.45280			−0.726401	−	0.687271i	$-0.758809\pi$
$463$	−6.67622e10			−1.45280			−0.726401	+	0.687271i	$0.758809\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	1.04633e10	−	6.04097e9i	0.219988	−	0.127010i	−0.385956	−	0.922517i	$-0.626129\pi$
$467$	1.04633e10	−	6.04097e9i	0.219988	−	0.127010i	0.605945	+	0.795507i	$0.292795\pi$
$468$		0			0
$469$	1.68939e9	−	1.76788e9i	0.0349172	−	0.0365394i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−1.38506e10	+	2.39899e10i	−0.276709	+	0.479273i
$474$		0			0
$475$			3.19349e10i			0.627323i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−3.50748e10	−	2.02504e10i	−0.666274	−	0.384673i	0.128390	−	0.991724i	$-0.459019\pi$
$479$	−3.50748e10	−	2.02504e10i	−0.666274	−	0.384673i	−0.794663	+	0.607051i	$0.792353\pi$
$480$		0			0
$481$	−2.65190e10	+	1.53107e10i	−0.495423	+	0.286033i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−5.46793e10	−	9.47074e10i	−0.988226	−	1.71166i
$486$		0			0
$487$	4.41202e10	−	7.64184e10i	0.784370	−	1.35857i	−0.145004	−	0.989431i	$-0.546319\pi$
$487$	4.41202e10	−	7.64184e10i	0.784370	−	1.35857i	0.929374	−	0.369138i	$-0.120347\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	2.36572e10			0.407040			0.203520	−	0.979071i	$-0.434762\pi$
$491$	2.36572e10			0.407040			0.203520	+	0.979071i	$0.434762\pi$
$492$		0			0
$493$	6.93119e10	+	4.00172e10i	1.17333	+	0.677422i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−6.53816e9	−	1.59377e9i	−0.107159	−	0.0261216i
$498$		0			0
$499$	1.22878e10	+	2.12831e10i	0.198186	+	0.343268i	0.947940	−	0.318448i	$-0.103162\pi$
$499$	1.22878e10	+	2.12831e10i	0.198186	+	0.343268i	−0.749754	+	0.661716i	$0.769828\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$			6.06519e10i			0.947485i	0.880663	+	0.473743i	$0.157097\pi$
$503$			6.06519e10i			0.947485i	−0.880663	+	0.473743i	$0.842903\pi$
$504$		0			0
$505$	−9.79679e10			−1.50632
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−1.13327e10	+	6.54296e9i	−0.168835	+	0.0974772i	−0.582037	−	0.813163i	$-0.697744\pi$
$509$	−1.13327e10	+	6.54296e9i	−0.168835	+	0.0974772i	0.413201	+	0.910640i	$0.364411\pi$
$510$		0			0
$511$	−2.82355e10	−	2.69819e10i	−0.414106	−	0.395721i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	7.55088e10	−	1.30785e11i	1.07342	−	1.85921i
$516$		0			0
$517$		−	1.06413e11i		−	1.48947i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−3.34178e10	−	1.92938e10i	−0.453552	−	0.261859i	0.255777	−	0.966736i	$-0.417669\pi$
$521$	−3.34178e10	−	1.92938e10i	−0.453552	−	0.261859i	−0.709329	+	0.704877i	$0.751002\pi$
$522$		0			0
$523$	−1.72278e10	+	9.94646e9i	−0.230262	+	0.132942i	−0.610693	−	0.791867i	$-0.709109\pi$
$523$	−1.72278e10	+	9.94646e9i	−0.230262	+	0.132942i	0.380431	+	0.924809i	$0.375776\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	3.75551e10	+	6.50473e10i	0.486885	+	0.843309i
$528$		0			0
$529$	−5.55564e10	+	9.62266e10i	−0.709434	+	1.22877i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−3.79169e10			−0.469812
$534$		0			0
$535$	3.84238e10	+	2.21840e10i	0.469013	+	0.270785i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−8.13338e10	+	5.20173e10i	−0.963642	+	0.616300i
$540$		0			0
$541$	3.36734e10	+	5.83241e10i	0.393096	+	0.680862i	0.992856	−	0.119318i	$-0.0380707\pi$
$541$	3.36734e10	+	5.83241e10i	0.393096	+	0.680862i	−0.599760	+	0.800180i	$0.704737\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		−	7.69143e10i		−	0.871808i
$546$		0			0
$547$	8.19574e10			0.915459			0.457730	−	0.889091i	$-0.348663\pi$
$547$	8.19574e10			0.915459			0.457730	+	0.889091i	$0.348663\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	2.54931e10	−	1.47185e10i	0.276577	−	0.159682i
$552$		0			0
$553$	3.91873e10	+	1.34005e11i	0.419030	+	1.43292i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−6.06558e8	+	1.05059e9i	−0.00630161	+	0.0109147i	−0.869159	−	0.494533i	$-0.835339\pi$
$557$	−6.06558e8	+	1.05059e9i	−0.00630161	+	0.0109147i	0.862857	+	0.505447i	$0.168673\pi$
$558$		0			0
$559$		−	2.01341e10i		−	0.206198i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−2.65134e10	−	1.53075e10i	−0.263895	−	0.152360i	0.362215	−	0.932095i	$-0.382021\pi$
$563$	−2.65134e10	−	1.53075e10i	−0.263895	−	0.152360i	−0.626110	+	0.779735i	$0.715354\pi$
$564$		0			0
$565$	6.75035e10	−	3.89732e10i	0.662419	−	0.382448i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	1.55965e10	+	2.70139e10i	0.148791	+	0.257714i	0.930781	−	0.365577i	$-0.119128\pi$
$569$	1.55965e10	+	2.70139e10i	0.148791	+	0.257714i	−0.781990	+	0.623291i	$0.785795\pi$
$570$		0			0
$571$	−9.85497e9	+	1.70693e10i	−0.0927066	+	0.160573i	−0.908649	−	0.417560i	$-0.862885\pi$
$571$	−9.85497e9	+	1.70693e10i	−0.0927066	+	0.160573i	0.815943	+	0.578133i	$0.196219\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−3.55391e11			−3.25114
$576$		0			0
$577$	−3.34009e9	−	1.92840e9i	−0.0301339	−	0.0173978i	0.484857	−	0.874593i	$-0.338872\pi$
$577$	−3.34009e9	−	1.92840e9i	−0.0301339	−	0.0173978i	−0.514991	+	0.857195i	$0.672205\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	3.67152e10	−	1.50618e11i	0.322212	−	1.32182i
$582$		0			0
$583$	−4.67623e10	−	8.09947e10i	−0.404782	−	0.701104i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		−	3.81949e10i		−	0.321701i	−0.986979	−	0.160851i	$-0.948576\pi$
$587$		−	3.81949e10i		−	0.321701i	0.986979	−	0.160851i	$-0.0514238\pi$
$588$		0			0
$589$	2.76257e10			0.229537
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−1.00185e11	+	5.78419e10i	−0.810186	+	0.467761i	−0.847020	−	0.531561i	$-0.821606\pi$
$593$	−1.00185e11	+	5.78419e10i	−0.810186	+	0.467761i	0.0368348	+	0.999321i	$0.488272\pi$
$594$		0			0
$595$	−2.72525e11	−	6.64316e10i	−2.17439	−	0.530038i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	6.59567e10	−	1.14240e11i	0.512332	−	0.887385i	−0.487566	−	0.873086i	$-0.662115\pi$
$599$	6.59567e10	−	1.14240e11i	0.512332	−	0.887385i	0.999898	−	0.0142987i	$-0.00455158\pi$
$600$		0			0
$601$		−	5.94719e10i		−	0.455842i	−0.973680	−	0.227921i	$-0.926807\pi$
$601$		−	5.94719e10i		−	0.455842i	0.973680	−	0.227921i	$-0.0731927\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−6.29100e10	−	3.63211e10i	−0.469567	−	0.271105i
$606$		0			0
$607$	5.36055e10	−	3.09492e10i	0.394871	−	0.227979i	−0.289398	−	0.957209i	$-0.593455\pi$
$607$	5.36055e10	−	3.09492e10i	0.394871	−	0.227979i	0.684268	+	0.729230i	$0.260122\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	3.86722e10	+	6.69823e10i	0.277482	+	0.480612i
$612$		0			0
$613$	−7.56037e9	+	1.30949e10i	−0.0535428	+	0.0927389i	−0.891555	−	0.452913i	$-0.850385\pi$
$613$	−7.56037e9	+	1.30949e10i	−0.0535428	+	0.0927389i	0.838012	+	0.545652i	$0.183718\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	8.79329e10			0.606752			0.303376	−	0.952871i	$-0.401886\pi$
$617$	8.79329e10			0.606752			0.303376	+	0.952871i	$0.401886\pi$
$618$		0			0
$619$	−5.53923e10	−	3.19807e10i	−0.377300	−	0.217834i	0.299343	−	0.954146i	$-0.403233\pi$
$619$	−5.53923e10	−	3.19807e10i	−0.377300	−	0.217834i	−0.676643	+	0.736311i	$0.736566\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	1.88149e11	−	5.50207e10i	1.24897	−	0.365236i
$624$		0			0
$625$	−9.76086e10	−	1.69063e11i	−0.639688	−	1.10797i
$626$		0			0
$627$		0			0
$628$		0			0
$629$			2.67489e11i			1.70885i
$630$		0			0
$631$	1.11045e11			0.700454			0.350227	−	0.936665i	$-0.386104\pi$
$631$	1.11045e11			0.700454			0.350227	+	0.936665i	$0.386104\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	3.09763e11	−	1.78842e11i	1.90517	−	1.09995i
$636$		0			0
$637$	3.22921e10	−	6.23006e10i	0.196127	−	0.378385i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−5.52383e10	+	9.56756e10i	−0.327196	+	0.566721i	−0.981954	−	0.189118i	$-0.939437\pi$
$641$	−5.52383e10	+	9.56756e10i	−0.327196	+	0.566721i	0.654758	+	0.755838i	$0.272770\pi$
$642$		0			0
$643$		−	1.07943e11i		−	0.631469i	−0.948848	−	0.315734i	$-0.897749\pi$
$643$		−	1.07943e11i		−	0.631469i	0.948848	−	0.315734i	$-0.102251\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	1.24745e11	+	7.20218e10i	0.711881	+	0.411005i	0.811757	−	0.583995i	$-0.198511\pi$
$647$	1.24745e11	+	7.20218e10i	0.711881	+	0.411005i	−0.0998760	+	0.995000i	$0.531845\pi$
$648$		0			0
$649$	2.79310e10	−	1.61260e10i	0.157438	−	0.0908966i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−1.54870e11	−	2.68242e11i	−0.851754	−	1.47528i	−0.879624	−	0.475669i	$-0.842206\pi$
$653$	−1.54870e11	−	2.68242e11i	−0.851754	−	1.47528i	0.0278708	−	0.999612i	$-0.491127\pi$
$654$		0			0
$655$	1.54604e10	−	2.67783e10i	0.0839956	−	0.145485i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	1.36428e11			0.723374			0.361687	−	0.932300i	$-0.382201\pi$
$659$	1.36428e11			0.723374			0.361687	+	0.932300i	$0.382201\pi$
$660$		0			0
$661$	−1.59491e11	−	9.20825e10i	−0.835472	−	0.482360i	0.0202508	−	0.999795i	$-0.493554\pi$
$661$	−1.59491e11	−	9.20825e10i	−0.835472	−	0.482360i	−0.855722	+	0.517435i	$0.826887\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−7.12780e10	+	7.45895e10i	−0.364476	+	0.381409i
$666$		0			0
$667$	1.63796e11	+	2.83704e11i	0.827562	+	1.43338i
$668$		0			0
$669$		0			0
$670$		0			0
$671$			2.99404e11i			1.47696i
$672$		0			0
$673$	−2.79758e11			−1.36371			−0.681855	−	0.731488i	$-0.738826\pi$
$673$	−2.79758e11			−1.36371			−0.681855	+	0.731488i	$0.738826\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	2.08685e11	−	1.20484e11i	0.993427	−	0.573555i	0.0871301	−	0.996197i	$-0.472230\pi$
$677$	2.08685e11	−	1.20484e11i	0.993427	−	0.573555i	0.906297	+	0.422642i	$0.138897\pi$
$678$		0			0
$679$	5.65969e10	−	2.32179e11i	0.266265	−	1.09231i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−4.47119e10	+	7.74434e10i	−0.205466	+	0.355878i	−0.950281	−	0.311393i	$-0.899204\pi$
$683$	−4.47119e10	+	7.74434e10i	−0.205466	+	0.355878i	0.744815	+	0.667271i	$0.232538\pi$
$684$		0			0
$685$			4.15765e11i			1.88837i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	5.88696e10	+	3.39884e10i	0.261225	+	0.150818i
$690$		0			0
$691$	7.31870e10	−	4.22545e10i	0.321012	−	0.185337i	−0.330831	−	0.943690i	$-0.607329\pi$
$691$	7.31870e10	−	4.22545e10i	0.321012	−	0.185337i	0.651844	+	0.758353i	$0.273996\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	2.01096e11	+	3.48309e11i	0.861916	+	1.49288i
$696$		0			0
$697$	−1.65608e11	+	2.86842e11i	−0.701699	+	1.21538i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−3.62284e10			−0.150029			−0.0750147	−	0.997182i	$-0.523900\pi$
$701$	−3.62284e10			−0.150029			−0.0750147	+	0.997182i	$0.523900\pi$
$702$		0			0
$703$	8.52024e10	+	4.91916e10i	0.348843	+	0.201405i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−1.54779e11	−	1.47907e11i	−0.619488	−	0.591985i
$708$		0			0
$709$	2.38422e11	+	4.12960e11i	0.943544	+	1.63427i	0.758641	+	0.651509i	$0.225864\pi$
$709$	2.38422e11	+	4.12960e11i	0.943544	+	1.63427i	0.184903	+	0.982757i	$0.440803\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$			3.07437e11i			1.18959i
$714$		0			0
$715$	2.23983e11			0.857019
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−3.84901e10	+	2.22223e10i	−0.144024	+	0.0831520i	−0.570280	−	0.821450i	$-0.693165\pi$
$719$	−3.84901e10	+	2.22223e10i	−0.144024	+	0.0831520i	0.426257	+	0.904602i	$0.359832\pi$
$720$		0			0
$721$	3.16748e11	−	9.26269e10i	1.17212	−	0.342765i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−3.07310e11	+	5.32276e11i	−1.11231	+	1.92657i
$726$		0			0
$727$			2.67401e11i			0.957249i	0.878020	+	0.478624i	$0.158864\pi$
$727$			2.67401e11i			0.957249i	−0.878020	+	0.478624i	$0.841136\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−1.52315e11	−	8.79389e10i	−0.533424	−	0.307972i
$732$		0			0
$733$	2.03305e11	−	1.17378e11i	0.704257	−	0.406603i	−0.104674	−	0.994507i	$-0.533380\pi$
$733$	2.03305e11	−	1.17378e11i	0.704257	−	0.406603i	0.808931	+	0.587903i	$0.200047\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	8.52815e9	+	1.47712e10i	0.0289058	+	0.0500663i
$738$		0			0
$739$	4.82037e10	−	8.34913e10i	0.161623	−	0.279939i	−0.773828	−	0.633396i	$-0.781660\pi$
$739$	4.82037e10	−	8.34913e10i	0.161623	−	0.279939i	0.935451	+	0.353457i	$0.114994\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	5.45547e11			1.79010			0.895049	−	0.445967i	$-0.147140\pi$
$743$	5.45547e11			1.79010			0.895049	+	0.445967i	$0.147140\pi$
$744$		0			0
$745$	−5.77615e11	−	3.33486e11i	−1.87505	−	1.08256i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	2.72132e10	+	9.30585e10i	0.0864673	+	0.295685i
$750$		0			0
$751$	2.58934e11	+	4.48487e11i	0.814009	+	1.40990i	0.910037	+	0.414526i	$0.136053\pi$
$751$	2.58934e11	+	4.48487e11i	0.814009	+	1.40990i	−0.0960283	+	0.995379i	$0.530614\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		−	2.55824e11i		−	0.787324i
$756$		0			0
$757$	7.93020e10			0.241491			0.120745	−	0.992684i	$-0.461472\pi$
$757$	7.93020e10			0.241491			0.120745	+	0.992684i	$0.461472\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	2.52930e11	−	1.46029e11i	0.754158	−	0.435413i	−0.0730362	−	0.997329i	$-0.523269\pi$
$761$	2.52930e11	−	1.46029e11i	0.754158	−	0.435413i	0.827194	+	0.561916i	$0.189936\pi$
$762$		0			0
$763$	1.16121e11	−	1.21516e11i	0.342620	−	0.358539i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−1.17209e10	+	2.03012e10i	−0.0338672	+	0.0586598i
$768$		0			0
$769$			3.74868e11i			1.07195i	0.844235	+	0.535973i	$0.180055\pi$
$769$			3.74868e11i			1.07195i	−0.844235	+	0.535973i	$0.819945\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	7.87493e10	+	4.54659e10i	0.220561	+	0.127341i	0.606210	−	0.795305i	$-0.292689\pi$
$773$	7.87493e10	+	4.54659e10i	0.220561	+	0.127341i	−0.385649	+	0.922646i	$0.626022\pi$
$774$		0			0
$775$	−4.99526e11	+	2.88402e11i	−1.38469	+	0.799449i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	6.09113e10	+	1.05501e11i	0.165405	+	0.286489i
$780$		0			0
$781$	2.34701e10	−	4.06513e10i	0.0630826	−	0.109262i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−1.05959e12			−2.79036
$786$		0			0
$787$	5.02936e11	+	2.90370e11i	1.31103	+	0.756925i	0.982267	−	0.187487i	$-0.0600342\pi$
$787$	5.02936e11	+	2.90370e11i	1.31103	+	0.756925i	0.328765	+	0.944412i	$0.393367\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	1.65488e11	+	4.03399e10i	0.422727	+	0.103046i
$792$		0			0
$793$	−1.08808e11	−	1.88462e11i	−0.275150	−	0.476574i
$794$		0			0
$795$		0			0
$796$		0			0
$797$			1.24466e11i			0.308473i	0.988034	+	0.154237i	$0.0492918\pi$
$797$			1.24466e11i			0.308473i	−0.988034	+	0.154237i	$0.950708\pi$
$798$		0			0
$799$	6.75629e11			1.65776
$800$		0			0
$801$		0			0
$802$		0			0
$803$	2.35916e11	−	1.36206e11i	0.567408	−	0.327593i
$804$		0			0
$805$	−8.30079e11	−	7.93226e11i	−1.97668	−	1.88892i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	1.43040e11	−	2.47752e11i	0.333936	−	0.578393i	−0.649344	−	0.760495i	$-0.724957\pi$
$809$	1.43040e11	−	2.47752e11i	0.333936	−	0.578393i	0.983280	+	0.182101i	$0.0582899\pi$
$810$		0			0
$811$		−	1.88700e11i		−	0.436203i	−0.975926	−	0.218101i	$-0.930014\pi$
$811$		−	1.88700e11i		−	0.436203i	0.975926	−	0.218101i	$-0.0699864\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	7.53728e11	+	4.35165e11i	1.70838	+	0.986333i
$816$		0			0
$817$	−5.60218e10	+	3.23442e10i	−0.125739	+	0.0725953i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−1.55431e7	−	2.69215e7i	−3.42110e−5	−	5.92552e-5i	0.866008	−	0.500030i	$-0.166678\pi$
$821$	−1.55431e7	−	2.69215e7i	−3.42110e−5	−	5.92552e-5i	−0.866043	+	0.499970i	$0.833344\pi$
$822$		0			0
$823$	4.17131e11	−	7.22493e11i	0.909229	−	1.57483i	0.0940919	−	0.995564i	$-0.470005\pi$
$823$	4.17131e11	−	7.22493e11i	0.909229	−	1.57483i	0.815137	−	0.579268i	$-0.196661\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	4.64694e11			0.993447			0.496723	−	0.867909i	$-0.334536\pi$
$827$	4.64694e11			0.993447			0.496723	+	0.867909i	$0.334536\pi$
$828$		0			0
$829$	−1.04849e11	−	6.05349e10i	−0.221997	−	0.128170i	0.384877	−	0.922968i	$-0.374244\pi$
$829$	−1.04849e11	−	6.05349e10i	−0.221997	−	0.128170i	−0.606875	+	0.794797i	$0.707577\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−3.30264e11	−	5.16398e11i	−0.685933	−	1.07252i
$834$		0			0
$835$	1.57938e11	+	2.73556e11i	0.324893	+	0.562731i
$836$		0			0
$837$		0			0
$838$		0			0
$839$			3.96352e11i			0.799895i	0.916538	+	0.399947i	$0.130972\pi$
$839$			3.96352e11i			0.799895i	−0.916538	+	0.399947i	$0.869028\pi$
$840$		0			0
$841$	6.62974e10			0.132529
$842$		0			0
$843$		0			0
$844$		0			0
$845$	6.35197e11	−	3.66731e11i	1.24590	−	0.719318i
$846$		0			0
$847$	−4.45552e10	−	1.52362e11i	−0.0865695	−	0.296034i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−5.47435e11	+	9.48185e11i	−1.04379	+	1.80790i
$852$		0			0
$853$			8.52086e11i			1.60949i	0.593624	+	0.804743i	$0.297697\pi$
$853$			8.52086e11i			1.60949i	−0.593624	+	0.804743i	$0.702303\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	5.09148e10	+	2.93957e10i	0.0943889	+	0.0544955i	0.546451	−	0.837491i	$-0.315978\pi$
$857$	5.09148e10	+	2.93957e10i	0.0943889	+	0.0544955i	−0.452063	+	0.891986i	$0.649312\pi$
$858$		0			0
$859$	−8.19057e10	+	4.72883e10i	−0.150432	+	0.0868522i	−0.573327	−	0.819327i	$-0.694347\pi$
$859$	−8.19057e10	+	4.72883e10i	−0.150432	+	0.0868522i	0.422894	+	0.906179i	$0.361014\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−6.19265e10	−	1.07260e11i	−0.111643	−	0.193372i	0.804790	−	0.593560i	$-0.202278\pi$
$863$	−6.19265e10	−	1.07260e11i	−0.111643	−	0.193372i	−0.916433	+	0.400188i	$0.868945\pi$
$864$		0			0
$865$	−2.25270e11	+	3.90180e11i	−0.402383	+	0.696947i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−9.73856e11			−1.70772
$870$		0			0
$871$	−1.07362e10	−	6.19854e9i	−0.0186542	−	0.0107700i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	2.66110e11	−	1.09167e12i	0.453971	−	1.86234i
$876$		0			0
$877$	−4.14086e11	−	7.17218e11i	−0.699991	−	1.21242i	−0.968469	−	0.249134i	$-0.919854\pi$
$877$	−4.14086e11	−	7.17218e11i	−0.699991	−	1.21242i	0.268478	−	0.963286i	$-0.413479\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			6.49040e11i			1.07738i	0.842505	+	0.538689i	$0.181080\pi$
$881$			6.49040e11i			1.07738i	−0.842505	+	0.538689i	$0.818920\pi$
$882$		0			0
$883$	−3.91705e11			−0.644341			−0.322171	−	0.946682i	$-0.604413\pi$
$883$	−3.91705e11			−0.644341			−0.322171	+	0.946682i	$0.604413\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−4.35609e11	+	2.51499e11i	−0.703723	+	0.406295i	−0.808733	−	0.588176i	$-0.799846\pi$
$887$	−4.35609e11	+	2.51499e11i	−0.703723	+	0.406295i	0.105009	+	0.994471i	$0.466513\pi$
$888$		0			0
$889$	7.59398e11	+	1.85114e11i	1.21580	+	0.296368i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	1.24249e11	−	2.15206e11i	0.195384	−	0.338414i
$894$		0			0
$895$		−	1.06590e12i		−	1.66121i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	4.60453e11	+	2.65843e11i	0.704931	+	0.406992i
$900$		0			0
$901$	5.14245e11	−	2.96900e11i	0.780317	−	0.450516i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−1.63271e11	−	2.82794e11i	−0.243397	−	0.421576i
$906$		0			0
$907$	−2.50039e11	+	4.33081e11i	−0.369470	+	0.639941i	−0.989483	−	0.144651i	$-0.953794\pi$
$907$	−2.50039e11	+	4.33081e11i	−0.369470	+	0.639941i	0.620013	+	0.784592i	$0.287127\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−1.21913e12			−1.77002			−0.885008	−	0.465576i	$-0.845847\pi$
$911$	−1.21913e12			−1.77002			−0.885008	+	0.465576i	$0.845847\pi$
$912$		0			0
$913$	9.36475e11	+	5.40674e11i	1.34776	+	0.778130i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	6.48543e10	−	1.89654e10i	0.0917194	−	0.0268216i
$918$		0			0
$919$	1.75579e11	+	3.04112e11i	0.246156	+	0.426355i	0.962456	−	0.271438i	$-0.0874990\pi$
$919$	1.75579e11	+	3.04112e11i	0.246156	+	0.426355i	−0.716300	+	0.697793i	$0.754166\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$			3.41176e10i			0.0470080i
$924$		0			0
$925$	−2.05416e12			−2.80587
$926$		0			0
$927$		0			0
$928$		0			0
$929$	8.75423e11	−	5.05426e11i	1.17532	−	0.678570i	0.220390	−	0.975412i	$-0.429267\pi$
$929$	8.75423e11	−	5.05426e11i	1.17532	−	0.678570i	0.954927	+	0.296842i	$0.0959335\pi$
$930$		0			0
$931$	−2.25223e11	+	1.02316e10i	−0.299788	+	0.0136190i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	9.78282e11	−	1.69443e12i	1.28002	−	2.21706i
$936$		0			0
$937$		−	4.93644e11i		−	0.640406i	−0.947349	−	0.320203i	$-0.896249\pi$
$937$		−	4.93644e11i		−	0.640406i	0.947349	−	0.320203i	$-0.103751\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−4.43259e11	−	2.55916e11i	−0.565326	−	0.326391i	0.189954	−	0.981793i	$-0.439166\pi$
$941$	−4.43259e11	−	2.55916e11i	−0.565326	−	0.326391i	−0.755281	+	0.655402i	$0.772499\pi$
$942$		0			0
$943$	−1.17409e12	+	6.77858e11i	−1.48475	+	0.857220i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−1.79118e11	−	3.10242e11i	−0.222710	−	0.385745i	0.732920	−	0.680315i	$-0.238157\pi$
$947$	−1.79118e11	−	3.10242e11i	−0.222710	−	0.385745i	−0.955630	+	0.294570i	$0.904824\pi$
$948$		0			0
$949$	−9.89992e10	+	1.71472e11i	−0.122058	+	0.211411i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	5.04177e11			0.611240			0.305620	−	0.952154i	$-0.401136\pi$
$953$	5.04177e11			0.611240			0.305620	+	0.952154i	$0.401136\pi$
$954$		0			0
$955$	−8.41419e11	−	4.85793e11i	−1.01158	−	0.584034i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−6.27701e11	+	6.56864e11i	−0.742127	+	0.776607i
$960$		0			0
$961$	−1.76959e11	−	3.06503e11i	−0.207482	−	0.359369i
$962$		0			0
$963$		0			0
$964$		0			0
$965$			2.54435e12i			2.93405i
$966$		0			0
$967$	−2.60109e11			−0.297475			−0.148737	−	0.988877i	$-0.547521\pi$
$967$	−2.60109e11			−0.297475			−0.148737	+	0.988877i	$0.547521\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	5.07503e11	−	2.93007e11i	0.570902	−	0.329610i	−0.186607	−	0.982435i	$-0.559749\pi$
$971$	5.07503e11	−	2.93007e11i	0.570902	−	0.329610i	0.757510	+	0.652824i	$0.226416\pi$
$972$		0			0
$973$	−2.08149e11	+	8.53895e11i	−0.232232	+	0.952694i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	2.83365e11	−	4.90803e11i	0.311006	−	0.538678i	−0.667575	−	0.744543i	$-0.732668\pi$
$977$	2.83365e11	−	4.90803e11i	0.311006	−	0.538678i	0.978580	+	0.205865i	$0.0660009\pi$
$978$		0			0
$979$			1.36734e12i			1.48848i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−5.92810e11	−	3.42259e11i	−0.634894	−	0.366556i	0.147751	−	0.989025i	$-0.452797\pi$
$983$	−5.92810e11	−	3.42259e11i	−0.634894	−	0.366556i	−0.782645	+	0.622468i	$0.786130\pi$
$984$		0			0
$985$	1.84241e12	−	1.06372e12i	1.95723	−	1.13001i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−3.59947e11	−	6.23446e11i	−0.376230	−	0.651649i
$990$		0			0
$991$	9.56595e11	−	1.65687e12i	0.991822	−	1.71789i	0.385381	−	0.922758i	$-0.374070\pi$
$991$	9.56595e11	−	1.65687e12i	0.991822	−	1.71789i	0.606441	−	0.795128i	$-0.292596\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−2.24319e12			−2.28862
$996$		0			0
$997$	1.28100e12	+	7.39588e11i	1.29649	+	0.748530i	0.979796	−	0.199998i	$-0.0640935\pi$
$997$	1.28100e12	+	7.39588e11i	1.29649	+	0.748530i	0.316695	+	0.948527i	$0.397427\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.9.z.c.73.5		10
3.2	odd	2		28.9.h.a.17.1	yes	10
7.5	odd	6	inner	252.9.z.c.145.5		10
12.11	even	2		112.9.s.b.17.5		10
21.2	odd	6		196.9.h.a.117.5		10
21.5	even	6		28.9.h.a.5.1	✓	10
21.11	odd	6		196.9.b.a.97.10		10
21.17	even	6		196.9.b.a.97.1		10
21.20	even	2		196.9.h.a.129.5		10
84.47	odd	6		112.9.s.b.33.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
28.9.h.a.5.1	✓	10	21.5	even	6
28.9.h.a.17.1	yes	10	3.2	odd	2
112.9.s.b.17.5		10	12.11	even	2
112.9.s.b.33.5		10	84.47	odd	6
196.9.b.a.97.1		10	21.17	even	6
196.9.b.a.97.10		10	21.11	odd	6
196.9.h.a.117.5		10	21.2	odd	6
196.9.h.a.129.5		10	21.20	even	2
252.9.z.c.73.5		10	1.1	even	1	trivial
252.9.z.c.145.5		10	7.5	odd	6	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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	252.z (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(951.520 - 549.361i) q^{5} +(2332.69 + 568.626i) q^{7} +O(q^{10})\)	\(q+(951.520 - 549.361i) q^{5} +(2332.69 + 568.626i) q^{7} +(-8373.68 + 14503.6i) q^{11} -12172.5i q^{13} +(-92085.4 - 53165.5i) q^{17} +(-33869.3 + 19554.5i) q^{19} +(-217614. - 376919. i) q^{23} +(408281. - 707164. i) q^{25} -752691. q^{29} +(-611743. - 353190. i) q^{31} +(2.53199e6 - 740431. i) q^{35} +(-1.25781e6 - 2.17859e6i) q^{37} -3.11495e6i q^{41} +1.65406e6 q^{43} +(-5.50274e6 + 3.17701e6i) q^{47} +(5.11813e6 + 2.65286e6i) q^{49} +(-2.79222e6 + 4.83627e6i) q^{53} +1.84007e7i q^{55} +(-1.66779e6 - 962898. i) q^{59} +(1.54825e7 - 8.93885e6i) q^{61} +(-6.68711e6 - 1.15824e7i) q^{65} +(509223. - 882001. i) q^{67} -2.80284e6 q^{71} +(-1.40868e7 - 8.13300e6i) q^{73} +(-2.77804e7 + 2.90711e7i) q^{77} +(2.90749e7 + 5.03592e7i) q^{79} -6.45682e7i q^{83} -1.16828e8 q^{85} +(7.07065e7 - 4.08224e7i) q^{89} +(6.92162e6 - 2.83948e7i) q^{91} +(-2.14849e7 + 3.72129e7i) q^{95} -9.95327e7i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 837 q^{5} + 1526 q^{7}+O(q^{10}) \) 10 * q + 837 * q^5 + 1526 * q^7	\( 10 q + 837 q^{5} + 1526 q^{7} - 3705 q^{11} - 78003 q^{17} - 96741 q^{19} - 208533 q^{23} + 367978 q^{25} - 754764 q^{29} - 1053717 q^{31} + 1306389 q^{35} - 998075 q^{37} + 738292 q^{43} - 710883 q^{47} + 13288114 q^{49} - 10501461 q^{53} + 37089081 q^{59} - 8180481 q^{61} - 21459108 q^{65} + 48020189 q^{67} + 31918236 q^{71} - 133345593 q^{73} - 188477625 q^{77} + 53590181 q^{79} - 157179282 q^{85} + 241368273 q^{89} + 420709128 q^{91} - 347126775 q^{95}+O(q^{100}) \) 10 * q + 837 * q^5 + 1526 * q^7 - 3705 * q^11 - 78003 * q^17 - 96741 * q^19 - 208533 * q^23 + 367978 * q^25 - 754764 * q^29 - 1053717 * q^31 + 1306389 * q^35 - 998075 * q^37 + 738292 * q^43 - 710883 * q^47 + 13288114 * q^49 - 10501461 * q^53 + 37089081 * q^59 - 8180481 * q^61 - 21459108 * q^65 + 48020189 * q^67 + 31918236 * q^71 - 133345593 * q^73 - 188477625 * q^77 + 53590181 * q^79 - 157179282 * q^85 + 241368273 * q^89 + 420709128 * q^91 - 347126775 * q^95

Introduction

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