LMFDB - Embedded newform 252.12.k.d.109.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,12,Mod(37,252)]

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, 2]))

N = Newforms(chi, 12, names="a")

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

chi := DirichletCharacter("252.37");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	252.k (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:	$193.622481501$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 581500324 x^{14} - 481772282104 x^{13} + \cdots + 79\!\cdots\!77 $ x^16 - 581500324x^14 - 481772282104x^13 + 132272376701859942x^12 + 189765040124256066208x^11 - 14668309022748191106194508x^10 - 25034330150368988089577197656x^9 + 804524023197576594568815873370179x^8 + 1124828921377792402289540847268007968x^7 - 19980431516277460534216470290766973558668x^6 + 592727132887361668148704829618109324342008x^5 + 215459975341822734071937522290785139860745873306x^4 - 372150170517680072482976606267991582419751904690704x^3 - 31534379943215460069637664338468383174583531082850128x^2 + 257934680050232001165280545701170549413209663811915341424x + 79978257504936591964642108900330900905737463001503418421877
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{42}\cdot 3^{15}\cdot 7^{9} $
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			109.2
Root			$-10168.9 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	252.109
Dual form			252.12.k.d.37.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4949.72 - 8573.16i) q^{5} +(29163.1 - 33568.4i) q^{7} +O(q^{10})$	$q+(-4949.72 - 8573.16i) q^{5} +(29163.1 - 33568.4i) q^{7} +(-25007.0 + 43313.5i) q^{11} +1.46252e6 q^{13} +(-3.16934e6 + 5.48946e6i) q^{17} +(-1.02494e7 - 1.77525e7i) q^{19} +(2.36024e7 + 4.08806e7i) q^{23} +(-2.45854e7 + 4.25831e7i) q^{25} +9.10208e7 q^{29} +(-4.83443e7 + 8.37349e7i) q^{31} +(-4.32137e8 - 8.38657e7i) q^{35} +(-7.14098e7 - 1.23685e8i) q^{37} -8.44357e8 q^{41} -1.55607e9 q^{43} +(4.22680e8 + 7.32103e8i) q^{47} +(-2.76354e8 - 1.95792e9i) q^{49} +(-1.26817e9 + 2.19654e9i) q^{53} +4.95111e8 q^{55} +(-2.80141e9 + 4.85219e9i) q^{59} +(-5.98273e8 - 1.03624e9i) q^{61} +(-7.23904e9 - 1.25384e10i) q^{65} +(-2.73114e9 + 4.73048e9i) q^{67} -1.81232e10 q^{71} +(9.87533e9 - 1.71046e10i) q^{73} +(7.24683e8 + 2.10260e9i) q^{77} +(-2.14642e10 - 3.71770e10i) q^{79} +5.21192e10 q^{83} +6.27494e10 q^{85} +(1.39910e10 + 2.42332e10i) q^{89} +(4.26515e10 - 4.90944e10i) q^{91} +(-1.01464e11 + 1.75740e11i) q^{95} +5.42003e10 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2156 q^{5} + 50512 q^{7}+O(q^{10}) $ 16 * q + 2156 * q^5 + 50512 * q^7	$ 16 q + 2156 q^{5} + 50512 q^{7} + 222796 q^{11} + 2703176 q^{13} - 5114600 q^{17} + 6910556 q^{19} + 51387712 q^{23} - 191456372 q^{25} - 118854616 q^{29} + 164659160 q^{31} - 55239344 q^{35} + 75658364 q^{37} + 1815568608 q^{41} + 10754408 q^{43} + 1034359464 q^{47} + 4123496848 q^{49} + 665159988 q^{53} - 1264543896 q^{55} - 1040514580 q^{59} - 14391208024 q^{61} + 20938150200 q^{65} - 33307097284 q^{67} - 65848902896 q^{71} + 17709749204 q^{73} - 8594484604 q^{77} - 26626784032 q^{79} + 210306955048 q^{83} - 25867402032 q^{85} + 55951560072 q^{89} + 66078280292 q^{91} - 106810047392 q^{95} - 156216030712 q^{97}+O(q^{100}) $ 16 * q + 2156 * q^5 + 50512 * q^7 + 222796 * q^11 + 2703176 * q^13 - 5114600 * q^17 + 6910556 * q^19 + 51387712 * q^23 - 191456372 * q^25 - 118854616 * q^29 + 164659160 * q^31 - 55239344 * q^35 + 75658364 * q^37 + 1815568608 * q^41 + 10754408 * q^43 + 1034359464 * q^47 + 4123496848 * q^49 + 665159988 * q^53 - 1264543896 * q^55 - 1040514580 * q^59 - 14391208024 * q^61 + 20938150200 * q^65 - 33307097284 * q^67 - 65848902896 * q^71 + 17709749204 * q^73 - 8594484604 * q^77 - 26626784032 * q^79 + 210306955048 * q^83 - 25867402032 * q^85 + 55951560072 * q^89 + 66078280292 * q^91 - 106810047392 * q^95 - 156216030712 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$73$	$127$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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
$5$	−4949.72	−	8573.16i	−0.708346	−	1.22689i	−0.965470	−	0.260513i	$-0.916108\pi$
$5$	−4949.72	−	8573.16i	−0.708346	−	1.22689i	0.257124	−	0.966378i	$-0.417225\pi$
$6$		0			0
$7$	29163.1	−	33568.4i	0.655835	−	0.754904i
$7$	29163.1	−	33568.4i	0.655835	−	0.754904i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−25007.0	+	43313.5i	−0.0468169	+	0.0810892i	−0.888484	−	0.458907i	$-0.848241\pi$
$11$	−25007.0	+	43313.5i	−0.0468169	+	0.0810892i	0.841667	+	0.539996i	$0.181574\pi$
$12$		0			0
$13$	1.46252e6			1.09248			0.546238	−	0.837630i	$-0.316059\pi$
$13$	1.46252e6			1.09248			0.546238	+	0.837630i	$0.316059\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−3.16934e6	+	5.48946e6i	−0.541378	+	0.937693i	0.457448	+	0.889237i	$0.348764\pi$
$17$	−3.16934e6	+	5.48946e6i	−0.541378	+	0.937693i	−0.998825	+	0.0484569i	$0.984570\pi$
$18$		0			0
$19$	−1.02494e7	−	1.77525e7i	−0.949632	−	1.64481i	−0.746201	−	0.665721i	$-0.768124\pi$
$19$	−1.02494e7	−	1.77525e7i	−0.949632	−	1.64481i	−0.203431	−	0.979089i	$-0.565209\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.36024e7	+	4.08806e7i	0.764634	+	1.32438i	0.940440	+	0.339960i	$0.110414\pi$
$23$	2.36024e7	+	4.08806e7i	0.764634	+	1.32438i	−0.175806	+	0.984425i	$0.556253\pi$
$24$		0			0
$25$	−2.45854e7	+	4.25831e7i	−0.503508	+	0.872102i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	9.10208e7			0.824046			0.412023	−	0.911173i	$-0.364822\pi$
$29$	9.10208e7			0.824046			0.412023	+	0.911173i	$0.364822\pi$
$30$		0			0
$31$	−4.83443e7	+	8.37349e7i	−0.303289	+	0.525312i	−0.976879	−	0.213794i	$-0.931418\pi$
$31$	−4.83443e7	+	8.37349e7i	−0.303289	+	0.525312i	0.673590	+	0.739105i	$0.264751\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−4.32137e8	−	8.38657e7i	−1.39074	−	0.269904i
$36$		0			0
$37$	−7.14098e7	−	1.23685e8i	−0.169297	−	0.293230i	0.768876	−	0.639398i	$-0.220816\pi$
$37$	−7.14098e7	−	1.23685e8i	−0.169297	−	0.293230i	−0.938173	+	0.346167i	$0.887483\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−8.44357e8			−1.13819			−0.569095	−	0.822272i	$-0.692706\pi$
$41$	−8.44357e8			−1.13819			−0.569095	+	0.822272i	$0.692706\pi$
$42$		0			0
$43$	−1.55607e9			−1.61418			−0.807089	−	0.590430i	$-0.798958\pi$
$43$	−1.55607e9			−1.61418			−0.807089	+	0.590430i	$0.798958\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	4.22680e8	+	7.32103e8i	0.268827	+	0.465623i	0.968559	−	0.248783i	$-0.0800306\pi$
$47$	4.22680e8	+	7.32103e8i	0.268827	+	0.465623i	−0.699732	+	0.714405i	$0.746697\pi$
$48$		0			0
$49$	−2.76354e8	−	1.95792e9i	−0.139762	−	0.990185i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−1.26817e9	+	2.19654e9i	−0.416544	+	0.721476i	−0.995589	−	0.0938196i	$-0.970092\pi$
$53$	−1.26817e9	+	2.19654e9i	−0.416544	+	0.721476i	0.579045	+	0.815296i	$0.303426\pi$
$54$		0			0
$55$	4.95111e8			0.132650
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−2.80141e9	+	4.85219e9i	−0.510142	+	0.883592i	0.489789	+	0.871841i	$0.337074\pi$
$59$	−2.80141e9	+	4.85219e9i	−0.510142	+	0.883592i	−0.999931	+	0.0117512i	$0.996259\pi$
$60$		0			0
$61$	−5.98273e8	−	1.03624e9i	−0.0906955	−	0.157089i	0.817108	−	0.576484i	$-0.195576\pi$
$61$	−5.98273e8	−	1.03624e9i	−0.0906955	−	0.157089i	−0.907804	+	0.419395i	$0.862242\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−7.23904e9	−	1.25384e10i	−0.773851	−	1.34035i
$66$		0			0
$67$	−2.73114e9	+	4.73048e9i	−0.247134	+	0.428049i	−0.962730	−	0.270466i	$-0.912822\pi$
$67$	−2.73114e9	+	4.73048e9i	−0.247134	+	0.428049i	0.715595	+	0.698515i	$0.246156\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−1.81232e10			−1.19210			−0.596051	−	0.802947i	$-0.703264\pi$
$71$	−1.81232e10			−1.19210			−0.596051	+	0.802947i	$0.703264\pi$
$72$		0			0
$73$	9.87533e9	−	1.71046e10i	0.557540	−	0.965687i	−0.440161	−	0.897919i	$-0.645079\pi$
$73$	9.87533e9	−	1.71046e10i	0.557540	−	0.965687i	0.997701	−	0.0677684i	$-0.0215879\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	7.24683e8	+	2.10260e9i	0.0305105	+	0.0885234i
$78$		0			0
$79$	−2.14642e10	−	3.71770e10i	−0.784811	−	1.35933i	−0.929112	−	0.369799i	$-0.879427\pi$
$79$	−2.14642e10	−	3.71770e10i	−0.784811	−	1.35933i	0.144301	−	0.989534i	$-0.453907\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	5.21192e10			1.45234			0.726170	−	0.687515i	$-0.241299\pi$
$83$	5.21192e10			1.45234			0.726170	+	0.687515i	$0.241299\pi$
$84$		0			0
$85$	6.27494e10			1.53393
$86$		0			0
$87$		0			0
$88$		0			0
$89$	1.39910e10	+	2.42332e10i	0.265586	+	0.460008i	0.967717	−	0.252039i	$-0.0811013\pi$
$89$	1.39910e10	+	2.42332e10i	0.265586	+	0.460008i	−0.702131	+	0.712048i	$0.747768\pi$
$90$		0			0
$91$	4.26515e10	−	4.90944e10i	0.716484	−	0.824715i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−1.01464e11	+	1.75740e11i	−1.34534	+	2.33019i
$96$		0			0
$97$	5.42003e10			0.640851			0.320426	−	0.947274i	$-0.396174\pi$
$97$	5.42003e10			0.640851			0.320426	+	0.947274i	$0.396174\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−6.07024e10	+	1.05140e11i	−0.574696	+	0.995403i	0.421379	+	0.906885i	$0.361546\pi$
$101$	−6.07024e10	+	1.05140e11i	−0.574696	+	0.995403i	−0.996075	+	0.0885179i	$0.971787\pi$
$102$		0			0
$103$	8.26479e10	+	1.43150e11i	0.702469	+	1.21671i	0.967597	+	0.252499i	$0.0812525\pi$
$103$	8.26479e10	+	1.43150e11i	0.702469	+	1.21671i	−0.265128	+	0.964213i	$0.585414\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1.05098e11	−	1.82035e11i	−0.724410	−	1.25472i	−0.959216	−	0.282673i	$-0.908779\pi$
$107$	−1.05098e11	−	1.82035e11i	−0.724410	−	1.25472i	0.234806	−	0.972042i	$-0.424554\pi$
$108$		0			0
$109$	−4.57197e10	+	7.91888e10i	−0.284615	+	0.492967i	−0.972516	−	0.232837i	$-0.925199\pi$
$109$	−4.57197e10	+	7.91888e10i	−0.284615	+	0.492967i	0.687901	+	0.725805i	$0.258532\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	3.60006e9			0.0183814			0.00919068	−	0.999958i	$-0.497074\pi$
$113$	3.60006e9			0.0183814			0.00919068	+	0.999958i	$0.497074\pi$
$114$		0			0
$115$	2.33651e11	−	4.04695e11i	1.08325	−	1.87625i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	9.18449e10	+	2.66480e11i	0.352815	+	1.02366i
$120$		0			0
$121$	1.41405e11	+	2.44921e11i	0.495616	+	0.858433i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	3.39174e9			0.00994071
$126$		0			0
$127$	6.33083e11			1.70036			0.850179	−	0.526494i	$-0.176494\pi$
$127$	6.33083e11			1.70036			0.850179	+	0.526494i	$0.176494\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	4.80539e10	+	8.32318e10i	0.108827	+	0.188494i	0.915295	−	0.402783i	$-0.131957\pi$
$131$	4.80539e10	+	8.32318e10i	0.108827	+	0.188494i	−0.806468	+	0.591277i	$0.798624\pi$
$132$		0			0
$133$	−8.94831e11	−	1.73662e11i	−1.86448	−	0.361843i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	1.83227e10	−	3.17359e10i	0.0324360	−	0.0561808i	−0.849352	−	0.527827i	$-0.823007\pi$
$137$	1.83227e10	−	3.17359e10i	0.0324360	−	0.0561808i	0.881788	+	0.471647i	$0.156340\pi$
$138$		0			0
$139$	−7.27117e11			−1.18856			−0.594282	−	0.804257i	$-0.702564\pi$
$139$	−7.27117e11			−1.18856			−0.594282	+	0.804257i	$0.702564\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−3.65732e10	+	6.33466e10i	−0.0511463	+	0.0885880i
$144$		0			0
$145$	−4.50527e11	−	7.80336e11i	−0.583710	−	1.01102i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−5.76995e11	−	9.99385e11i	−0.643647	−	1.11483i	−0.984612	−	0.174754i	$-0.944087\pi$
$149$	−5.76995e11	−	9.99385e11i	−0.643647	−	1.11483i	0.340965	−	0.940076i	$-0.389246\pi$
$150$		0			0
$151$	−3.74264e11	+	6.48245e11i	−0.387976	+	0.671995i	−0.992177	−	0.124837i	$-0.960159\pi$
$151$	−3.74264e11	+	6.48245e11i	−0.387976	+	0.671995i	0.604201	+	0.796832i	$0.293492\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	9.57164e11			0.859334
$156$		0			0
$157$	−1.07175e12	+	1.85633e12i	−0.896697	+	1.55312i	−0.0650059	+	0.997885i	$0.520707\pi$
$157$	−1.07175e12	+	1.85633e12i	−0.896697	+	1.55312i	−0.831691	+	0.555239i	$0.812627\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	2.06062e12	+	3.99908e11i	1.50126	+	0.291352i
$162$		0			0
$163$	1.02063e10	+	1.76779e10i	0.00694765	+	0.0120337i	0.869478	−	0.493971i	$-0.164455\pi$
$163$	1.02063e10	+	1.76779e10i	0.00694765	+	0.0120337i	−0.862531	+	0.506005i	$0.831122\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	2.47826e11			0.147641			0.0738204	−	0.997272i	$-0.476481\pi$
$167$	2.47826e11			0.147641			0.0738204	+	0.997272i	$0.476481\pi$
$168$		0			0
$169$	3.46792e11			0.193505
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−9.53660e11	−	1.65179e12i	−0.467886	−	0.810402i	0.531441	−	0.847096i	$-0.321651\pi$
$173$	−9.53660e11	−	1.65179e12i	−0.467886	−	0.810402i	−0.999327	+	0.0366932i	$0.988318\pi$
$174$		0			0
$175$	7.12463e11	+	2.06715e12i	0.328136	+	0.952056i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−2.54501e11	+	4.40808e11i	−0.103514	+	0.179291i	−0.913130	−	0.407669i	$-0.866342\pi$
$179$	−2.54501e11	+	4.40808e11i	−0.103514	+	0.179291i	0.809616	+	0.586959i	$0.199675\pi$
$180$		0			0
$181$	−1.05292e12			−0.402869			−0.201434	−	0.979502i	$-0.564560\pi$
$181$	−1.05292e12			−0.402869			−0.201434	+	0.979502i	$0.564560\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−7.06917e11	+	1.22442e12i	−0.239841	+	0.415417i
$186$		0			0
$187$	−1.58512e11	−	2.74550e11i	−0.0506912	−	0.0877997i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	3.42442e12	+	5.93127e12i	0.974773	+	1.68836i	0.680681	+	0.732580i	$0.261684\pi$
$191$	3.42442e12	+	5.93127e12i	0.974773	+	1.68836i	0.294092	+	0.955777i	$0.404983\pi$
$192$		0			0
$193$	−1.13876e12	+	1.97240e12i	−0.306104	+	0.530187i	−0.977506	−	0.210906i	$-0.932359\pi$
$193$	−1.13876e12	+	1.97240e12i	−0.306104	+	0.530187i	0.671403	+	0.741093i	$0.265692\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−2.51939e12			−0.604966			−0.302483	−	0.953155i	$-0.597816\pi$
$197$	−2.51939e12			−0.604966			−0.302483	+	0.953155i	$0.597816\pi$
$198$		0			0
$199$	5.73459e11	−	9.93260e11i	0.130260	−	0.225617i	−0.793517	−	0.608548i	$-0.791752\pi$
$199$	5.73459e11	−	9.93260e11i	0.130260	−	0.225617i	0.923777	+	0.382932i	$0.125086\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	2.65445e12	−	3.05543e12i	0.540438	−	0.622076i
$204$		0			0
$205$	4.17933e12	+	7.23881e12i	0.806233	+	1.39644i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	1.02523e12			0.177835
$210$		0			0
$211$	−1.08695e12			−0.178919			−0.0894593	−	0.995990i	$-0.528514\pi$
$211$	−1.08695e12			−0.178919			−0.0894593	+	0.995990i	$0.528514\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	7.70209e12	+	1.33404e13i	1.14340	+	1.98042i
$216$		0			0
$217$	1.40098e12	+	4.06481e12i	0.197653	+	0.573472i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−4.63521e12	+	8.02843e12i	−0.591442	+	1.02441i
$222$		0			0
$223$	1.60167e13			1.94489			0.972447	−	0.233124i	$-0.0748949\pi$
$223$	1.60167e13			1.94489			0.972447	+	0.233124i	$0.0748949\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	5.82492e12	−	1.00891e13i	0.641428	−	1.11099i	−0.343686	−	0.939085i	$-0.611676\pi$
$227$	5.82492e12	−	1.00891e13i	0.641428	−	1.11099i	0.985114	−	0.171901i	$-0.0549910\pi$
$228$		0			0
$229$	4.67803e11	+	8.10258e11i	0.0490871	+	0.0850214i	0.889525	−	0.456887i	$-0.151035\pi$
$229$	4.67803e11	+	8.10258e11i	0.0490871	+	0.0850214i	−0.840438	+	0.541908i	$0.817702\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	6.06338e12	+	1.05021e13i	0.578438	+	1.00188i	0.995659	+	0.0930793i	$0.0296710\pi$
$233$	6.06338e12	+	1.05021e13i	0.578438	+	1.00188i	−0.417220	+	0.908805i	$0.636996\pi$
$234$		0			0
$235$	4.18429e12	−	7.24741e12i	0.380846	−	0.659644i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−2.98561e12			−0.247654			−0.123827	−	0.992304i	$-0.539517\pi$
$239$	−2.98561e12			−0.247654			−0.123827	+	0.992304i	$0.539517\pi$
$240$		0			0
$241$	−4.35089e12	+	7.53596e12i	−0.344734	+	0.597097i	−0.985305	−	0.170802i	$-0.945364\pi$
$241$	−4.35089e12	+	7.53596e12i	−0.344734	+	0.597097i	0.640571	+	0.767899i	$0.278698\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−1.54177e13	+	1.20604e13i	−1.11585	+	0.872866i
$246$		0			0
$247$	−1.49900e13	−	2.59634e13i	−1.03745	−	1.79692i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−1.10571e13			−0.700544			−0.350272	−	0.936648i	$-0.613911\pi$
$251$	−1.10571e13			−0.700544			−0.350272	+	0.936648i	$0.613911\pi$
$252$		0			0
$253$	−2.36091e12			−0.143191
$254$		0			0
$255$		0			0
$256$		0			0
$257$	1.27142e13	+	2.20217e13i	0.707387	+	1.22523i	0.965823	+	0.259202i	$0.0834596\pi$
$257$	1.27142e13	+	2.20217e13i	0.707387	+	1.22523i	−0.258436	+	0.966028i	$0.583207\pi$
$258$		0			0
$259$	−6.23446e12	−	1.20993e12i	−0.332392	−	0.0645079i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−1.68147e13	+	2.91239e13i	−0.824011	+	1.42723i	0.0786626	+	0.996901i	$0.474935\pi$
$263$	−1.68147e13	+	2.91239e13i	−0.824011	+	1.42723i	−0.902673	+	0.430327i	$0.858398\pi$
$264$		0			0
$265$	2.51084e13			1.18023
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−7.46102e12	+	1.29229e13i	−0.322969	+	0.559398i	−0.981099	−	0.193506i	$-0.938014\pi$
$269$	−7.46102e12	+	1.29229e13i	−0.322969	+	0.559398i	0.658130	+	0.752904i	$0.271348\pi$
$270$		0			0
$271$	1.07841e13	+	1.86786e13i	0.448179	+	0.776269i	0.998268	−	0.0588375i	$-0.0187394\pi$
$271$	1.07841e13	+	1.86786e13i	0.448179	+	0.776269i	−0.550089	+	0.835106i	$0.685406\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−1.22961e12	−	2.12975e12i	−0.0471454	−	0.0816582i
$276$		0			0
$277$	−1.45333e13	+	2.51724e13i	−0.535457	+	0.927439i	0.463684	+	0.886001i	$0.346527\pi$
$277$	−1.45333e13	+	2.51724e13i	−0.535457	+	0.927439i	−0.999141	+	0.0414380i	$0.986806\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−2.02171e13			−0.688390			−0.344195	−	0.938898i	$-0.611848\pi$
$281$	−2.02171e13			−0.688390			−0.344195	+	0.938898i	$0.611848\pi$
$282$		0			0
$283$	−2.44690e11	+	4.23815e11i	−0.00801291	+	0.0138788i	−0.870004	−	0.493045i	$-0.835884\pi$
$283$	−2.44690e11	+	4.23815e11i	−0.00801291	+	0.0138788i	0.861991	+	0.506923i	$0.169217\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−2.46241e13	+	2.83438e13i	−0.746465	+	0.859225i
$288$		0			0
$289$	−2.95353e12	−	5.11566e12i	−0.0861794	−	0.149267i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	6.82921e13			1.84756			0.923780	−	0.382924i	$-0.125083\pi$
$293$	6.82921e13			1.84756			0.923780	+	0.382924i	$0.125083\pi$
$294$		0			0
$295$	5.54649e13			1.44543
$296$		0			0
$297$		0			0
$298$		0			0
$299$	3.45189e13	+	5.97885e13i	0.835345	+	1.44686i
$300$		0			0
$301$	−4.53797e13	+	5.22347e13i	−1.05863	+	1.21855i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−5.92257e12	+	1.02582e13i	−0.128488	+	0.222547i
$306$		0			0
$307$	−2.82225e13			−0.590655			−0.295328	−	0.955396i	$-0.595429\pi$
$307$	−2.82225e13			−0.590655			−0.295328	+	0.955396i	$0.595429\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−3.53006e13	+	6.11425e13i	−0.688019	+	1.19168i	0.284459	+	0.958688i	$0.408186\pi$
$311$	−3.53006e13	+	6.11425e13i	−0.688019	+	1.19168i	−0.972478	+	0.232996i	$0.925147\pi$
$312$		0			0
$313$	1.75608e13	+	3.04162e13i	0.330408	+	0.572283i	0.982592	−	0.185778i	$-0.0594804\pi$
$313$	1.75608e13	+	3.04162e13i	0.330408	+	0.572283i	−0.652184	+	0.758061i	$0.726147\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−1.54610e13	−	2.67792e13i	−0.271275	−	0.469863i	0.697913	−	0.716182i	$-0.254112\pi$
$317$	−1.54610e13	−	2.67792e13i	−0.271275	−	0.469863i	−0.969189	+	0.246319i	$0.920779\pi$
$318$		0			0
$319$	−2.27616e12	+	3.94242e12i	−0.0385793	+	0.0668212i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	1.29936e14			2.05644
$324$		0			0
$325$	−3.59565e13	+	6.22785e13i	−0.550071	+	0.952751i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	3.69022e13	+	7.16169e12i	0.527807	+	0.102433i
$330$		0			0
$331$	−1.86187e13	−	3.22486e13i	−0.257571	−	0.446125i	0.708020	−	0.706192i	$-0.249589\pi$
$331$	−1.86187e13	−	3.22486e13i	−0.257571	−	0.446125i	−0.965591	+	0.260067i	$0.916255\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	5.40736e13			0.700227
$336$		0			0
$337$	9.01286e13			1.12953			0.564766	−	0.825251i	$-0.308967\pi$
$337$	9.01286e13			1.12953			0.564766	+	0.825251i	$0.308967\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−2.41790e12	−	4.18792e12i	−0.0283981	−	0.0491869i
$342$		0			0
$343$	−7.37837e13	−	4.78222e13i	−0.839156	−	0.543891i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	4.20561e13	−	7.28433e13i	0.448763	−	0.777280i	−0.549543	−	0.835465i	$-0.685198\pi$
$347$	4.20561e13	−	7.28433e13i	0.448763	−	0.777280i	0.998306	+	0.0581855i	$0.0185315\pi$
$348$		0			0
$349$	1.62557e14			1.68061			0.840305	−	0.542114i	$-0.182376\pi$
$349$	1.62557e14			1.68061			0.840305	+	0.542114i	$0.182376\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	7.77383e13	−	1.34647e14i	0.754873	−	1.30748i	−0.190564	−	0.981675i	$-0.561032\pi$
$353$	7.77383e13	−	1.34647e14i	0.754873	−	1.30748i	0.945437	−	0.325804i	$-0.105635\pi$
$354$		0			0
$355$	8.97046e13	+	1.55373e14i	0.844421	+	1.46258i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	6.44669e13	+	1.11660e14i	0.570581	+	0.988275i	0.996506	+	0.0835170i	$0.0266153\pi$
$359$	6.44669e13	+	1.11660e14i	0.570581	+	0.988275i	−0.425925	+	0.904758i	$0.640051\pi$
$360$		0			0
$361$	−1.51857e14	+	2.63024e14i	−1.30360	+	2.25790i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−1.95520e14			−1.57972
$366$		0			0
$367$	8.09211e13	−	1.40159e14i	0.634452	−	1.09890i	−0.352179	−	0.935933i	$-0.614559\pi$
$367$	8.09211e13	−	1.40159e14i	0.634452	−	1.09890i	0.986631	−	0.162970i	$-0.0521074\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	3.67506e13	+	1.06629e14i	0.271461	+	0.787620i
$372$		0			0
$373$	7.49137e12	+	1.29754e13i	0.0537233	+	0.0930515i	0.891636	−	0.452752i	$-0.149558\pi$
$373$	7.49137e12	+	1.29754e13i	0.0537233	+	0.0930515i	−0.837913	+	0.545804i	$0.816224\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	1.33119e14			0.900251
$378$		0			0
$379$	−1.46414e14			−0.961758			−0.480879	−	0.876787i	$-0.659682\pi$
$379$	−1.46414e14			−0.961758			−0.480879	+	0.876787i	$0.659682\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−1.03039e14	−	1.78468e14i	−0.638861	−	1.10654i	−0.985683	−	0.168609i	$-0.946072\pi$
$383$	−1.03039e14	−	1.78468e14i	−0.638861	−	1.10654i	0.346822	−	0.937931i	$-0.387261\pi$
$384$		0			0
$385$	1.44390e13	−	1.66201e13i	0.0869966	−	0.100138i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−4.28674e13	+	7.42485e13i	−0.244008	+	0.422634i	−0.961852	−	0.273569i	$-0.911796\pi$
$389$	−4.28674e13	+	7.42485e13i	−0.244008	+	0.422634i	0.717844	+	0.696204i	$0.245129\pi$
$390$		0			0
$391$	−2.99217e14			−1.65582
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−2.12483e14	+	3.68032e14i	−1.11184	+	1.92576i
$396$		0			0
$397$	−5.18685e13	−	8.98388e13i	−0.263971	−	0.457210i	0.703323	−	0.710871i	$-0.251699\pi$
$397$	−5.18685e13	−	8.98388e13i	−0.263971	−	0.457210i	−0.967293	+	0.253660i	$0.918366\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−8.92898e13	−	1.54655e14i	−0.430039	−	0.744850i	0.566837	−	0.823830i	$-0.308167\pi$
$401$	−8.92898e13	−	1.54655e14i	−0.430039	−	0.744850i	−0.996876	+	0.0789803i	$0.974834\pi$
$402$		0			0
$403$	−7.07044e13	+	1.22464e14i	−0.331336	+	0.573891i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	7.14299e12			0.0317038
$408$		0			0
$409$	1.39715e14	−	2.41994e14i	0.603622	−	1.04550i	−0.388645	−	0.921388i	$-0.627057\pi$
$409$	1.39715e14	−	2.41994e14i	0.603622	−	1.04550i	0.992268	−	0.124117i	$-0.0396099\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	8.11826e13	+	2.35544e14i	0.332459	+	0.964599i
$414$		0			0
$415$	−2.57975e14	−	4.46827e14i	−1.02876	−	1.78186i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−1.47340e14			−0.557370			−0.278685	−	0.960383i	$-0.589898\pi$
$419$	−1.47340e14			−0.557370			−0.278685	+	0.960383i	$0.589898\pi$
$420$		0			0
$421$	1.13118e14			0.416852			0.208426	−	0.978038i	$-0.433166\pi$
$421$	1.13118e14			0.416852			0.208426	+	0.978038i	$0.433166\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−1.55839e14	−	2.69921e14i	−0.545176	−	0.944273i
$426$		0			0
$427$	−5.22325e13	−	1.01369e13i	−0.178069	−	0.0345581i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−2.21901e14	+	3.84344e14i	−0.718678	+	1.24479i	0.242845	+	0.970065i	$0.421919\pi$
$431$	−2.21901e14	+	3.84344e14i	−0.718678	+	1.24479i	−0.961524	+	0.274722i	$0.911414\pi$
$432$		0			0
$433$	3.99750e14			1.26213			0.631067	−	0.775729i	$-0.282617\pi$
$433$	3.99750e14			1.26213			0.631067	+	0.775729i	$0.282617\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	4.83823e14	−	8.38006e14i	1.45224	−	2.51536i
$438$		0			0
$439$	2.14931e14	+	3.72271e14i	0.629134	+	1.08969i	0.987726	+	0.156198i	$0.0499239\pi$
$439$	2.14931e14	+	3.72271e14i	0.629134	+	1.08969i	−0.358591	+	0.933495i	$0.616743\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	6.77263e13	+	1.17305e14i	0.188598	+	0.326661i	0.944783	−	0.327697i	$-0.106272\pi$
$443$	6.77263e13	+	1.17305e14i	0.188598	+	0.326661i	−0.756185	+	0.654358i	$0.772939\pi$
$444$		0			0
$445$	1.38503e14	−	2.39895e14i	0.376254	−	0.651690i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−9.79795e13			−0.253385			−0.126692	−	0.991942i	$-0.540436\pi$
$449$	−9.79795e13			−0.253385			−0.126692	+	0.991942i	$0.540436\pi$
$450$		0			0
$451$	2.11149e13	−	3.65720e13i	0.0532865	−	0.0922949i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−6.32007e14	−	1.22655e14i	−1.51935	−	0.294864i
$456$		0			0
$457$	−3.69842e14	−	6.40586e14i	−0.867916	−	1.50327i	−0.864123	−	0.503281i	$-0.832126\pi$
$457$	−3.69842e14	−	6.40586e14i	−0.867916	−	1.50327i	−0.00379321	−	0.999993i	$-0.501207\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−2.05197e14			−0.459003			−0.229501	−	0.973308i	$-0.573710\pi$
$461$	−2.05197e14			−0.459003			−0.229501	+	0.973308i	$0.573710\pi$
$462$		0			0
$463$	3.01270e14			0.658052			0.329026	−	0.944321i	$-0.393280\pi$
$463$	3.01270e14			0.658052			0.329026	+	0.944321i	$0.393280\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	1.92054e14	+	3.32648e14i	0.400111	+	0.693013i	0.993739	−	0.111727i	$-0.0356381\pi$
$467$	1.92054e14	+	3.32648e14i	0.400111	+	0.693013i	−0.593628	+	0.804740i	$0.702305\pi$
$468$		0			0
$469$	7.91463e13	+	2.29636e14i	0.161057	+	0.467293i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	3.89126e13	−	6.73986e13i	0.0755707	−	0.130892i
$474$		0			0
$475$	1.00794e15			1.91259
$476$		0			0
$477$		0			0
$478$		0			0
$479$	3.73993e14	−	6.47776e14i	0.677671	−	1.17376i	−0.298010	−	0.954563i	$-0.596323\pi$
$479$	3.73993e14	−	6.47776e14i	0.677671	−	1.17376i	0.975681	−	0.219197i	$-0.0703438\pi$
$480$		0			0
$481$	−1.04438e14	−	1.80892e14i	−0.184953	−	0.320347i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−2.68276e14	−	4.64668e14i	−0.453945	−	0.786255i
$486$		0			0
$487$	6.99482e13	−	1.21154e14i	0.115709	−	0.200414i	−0.802354	−	0.596848i	$-0.796419\pi$
$487$	6.99482e13	−	1.21154e14i	0.115709	−	0.200414i	0.918063	+	0.396435i	$0.129753\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−2.86402e13			−0.0452926			−0.0226463	−	0.999744i	$-0.507209\pi$
$491$	−2.86402e13			−0.0452926			−0.0226463	+	0.999744i	$0.507209\pi$
$492$		0			0
$493$	−2.88476e14	+	4.99655e14i	−0.446120	+	0.772703i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−5.28528e14	+	6.08367e14i	−0.781822	+	0.899923i
$498$		0			0
$499$	−5.75867e14	−	9.97430e14i	−0.833238	−	1.44321i	−0.895457	−	0.445148i	$-0.853151\pi$
$499$	−5.75867e14	−	9.97430e14i	−0.833238	−	1.44321i	0.0622193	−	0.998063i	$-0.480182\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	9.85521e14			1.36472			0.682358	−	0.731019i	$-0.260955\pi$
$503$	9.85521e14			1.36472			0.682358	+	0.731019i	$0.260955\pi$
$504$		0			0
$505$	1.20184e15			1.62833
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−3.82938e14	−	6.63268e14i	−0.496799	−	0.860481i	0.503194	−	0.864173i	$-0.332158\pi$
$509$	−3.82938e14	−	6.63268e14i	−0.496799	−	0.860481i	−0.999993	+	0.00369203i	$0.998825\pi$
$510$		0			0
$511$	−2.86179e14	−	8.30322e14i	−0.363348	−	1.05422i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	8.18168e14	−	1.41711e15i	0.995183	−	1.72371i
$516$		0			0
$517$	−4.22799e13			−0.0503426
$518$		0			0
$519$		0			0
$520$		0			0
$521$	3.90199e14	−	6.75845e14i	0.445327	−	0.771329i	−0.552748	−	0.833349i	$-0.686421\pi$
$521$	3.90199e14	−	6.75845e14i	0.445327	−	0.771329i	0.998075	+	0.0620194i	$0.0197541\pi$
$522$		0			0
$523$	−1.32813e14	−	2.30039e14i	−0.148416	−	0.257064i	0.782226	−	0.622995i	$-0.214084\pi$
$523$	−1.32813e14	−	2.30039e14i	−0.148416	−	0.257064i	−0.930642	+	0.365930i	$0.880751\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−3.06440e14	−	5.30769e14i	−0.328388	−	0.568784i
$528$		0			0
$529$	−6.37744e14	+	1.10461e15i	−0.669330	+	1.15931i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−1.23489e15			−1.24345
$534$		0			0
$535$	−1.04041e15	+	1.80205e15i	−1.02627	+	1.77755i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	9.17151e13	+	3.69919e13i	0.0868365	+	0.0350242i
$540$		0			0
$541$	−2.32642e14	−	4.02947e14i	−0.215825	−	0.373820i	0.737702	−	0.675126i	$-0.235911\pi$
$541$	−2.32642e14	−	4.02947e14i	−0.215825	−	0.373820i	−0.953528	+	0.301306i	$0.902577\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	9.05198e14			0.806423
$546$		0			0
$547$	−4.31654e14			−0.376882			−0.188441	−	0.982084i	$-0.560343\pi$
$547$	−4.31654e14			−0.376882			−0.188441	+	0.982084i	$0.560343\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−9.32912e14	−	1.61585e15i	−0.782540	−	1.35540i
$552$		0			0
$553$	−1.87394e15	−	3.63679e14i	−1.54087	−	0.299040i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−1.93906e13	+	3.35855e13i	−0.0153246	+	0.0265429i	−0.873586	−	0.486670i	$-0.838211\pi$
$557$	−1.93906e13	+	3.35855e13i	−0.0153246	+	0.0265429i	0.858261	+	0.513213i	$0.171545\pi$
$558$		0			0
$559$	−2.27577e15			−1.76345
$560$		0			0
$561$		0			0
$562$		0			0
$563$	2.67759e14	−	4.63772e14i	0.199502	−	0.345548i	−0.748865	−	0.662723i	$-0.769401\pi$
$563$	2.67759e14	−	4.63772e14i	0.199502	−	0.345548i	0.948367	+	0.317175i	$0.102734\pi$
$564$		0			0
$565$	−1.78193e13	−	3.08639e13i	−0.0130204	−	0.0225519i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	4.33929e14	+	7.51587e14i	0.305001	+	0.528277i	0.977262	−	0.212038i	$-0.0680099\pi$
$569$	4.33929e14	+	7.51587e14i	0.305001	+	0.528277i	−0.672261	+	0.740314i	$0.734677\pi$
$570$		0			0
$571$	5.01450e14	−	8.68538e14i	0.345724	−	0.598811i	−0.639761	−	0.768574i	$-0.720967\pi$
$571$	5.01450e14	−	8.68538e14i	0.345724	−	0.598811i	0.985485	+	0.169762i	$0.0543000\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−2.32110e15			−1.54000
$576$		0			0
$577$	−1.70850e14	+	2.95920e14i	−0.111211	+	0.192623i	−0.916259	−	0.400587i	$-0.868806\pi$
$577$	−1.70850e14	+	2.95920e14i	−0.111211	+	0.192623i	0.805048	+	0.593210i	$0.202140\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	1.51996e15	−	1.74956e15i	0.952495	−	1.09638i
$582$		0			0
$583$	−6.34265e13	−	1.09858e14i	−0.0390026	−	0.0675545i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−1.31315e15			−0.777689			−0.388845	−	0.921303i	$-0.627126\pi$
$587$	−1.31315e15			−0.777689			−0.388845	+	0.921303i	$0.627126\pi$
$588$		0			0
$589$	1.98201e15			1.15205
$590$		0			0
$591$		0			0
$592$		0			0
$593$	1.42951e15	+	2.47598e15i	0.800543	+	1.38658i	0.919259	+	0.393654i	$0.128789\pi$
$593$	1.42951e15	+	2.47598e15i	0.800543	+	1.38658i	−0.118715	+	0.992928i	$0.537878\pi$
$594$		0			0
$595$	1.82997e15	−	2.10640e15i	1.00601	−	1.15797i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	1.07552e15	−	1.86285e15i	0.569862	−	0.987030i	−0.426717	−	0.904385i	$-0.640330\pi$
$599$	1.07552e15	−	1.86285e15i	0.569862	−	0.987030i	0.996579	−	0.0826451i	$-0.0263368\pi$
$600$		0			0
$601$	−3.46561e15			−1.80289			−0.901447	−	0.432889i	$-0.857494\pi$
$601$	−3.46561e15			−1.80289			−0.901447	+	0.432889i	$0.857494\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	1.39983e15	−	2.42458e15i	0.702136	−	1.21613i
$606$		0			0
$607$	8.39119e14	+	1.45340e15i	0.413319	+	0.715890i	0.995250	−	0.0973481i	$-0.0310360\pi$
$607$	8.39119e14	+	1.45340e15i	0.413319	+	0.715890i	−0.581931	+	0.813238i	$0.697703\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	6.18176e14	+	1.07071e15i	0.293688	+	0.508682i
$612$		0			0
$613$	2.51033e14	−	4.34802e14i	0.117138	−	0.202889i	−0.801494	−	0.598002i	$-0.795961\pi$
$613$	2.51033e14	−	4.34802e14i	0.117138	−	0.202889i	0.918632	+	0.395113i	$0.129295\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−3.06387e15			−1.37944			−0.689719	−	0.724077i	$-0.742266\pi$
$617$	−3.06387e15			−1.37944			−0.689719	+	0.724077i	$0.742266\pi$
$618$		0			0
$619$	6.07837e14	−	1.05280e15i	0.268837	−	0.465639i	−0.699725	−	0.714412i	$-0.746694\pi$
$619$	6.07837e14	−	1.05280e15i	0.268837	−	0.465639i	0.968562	+	0.248773i	$0.0800275\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	1.22149e15	+	2.37058e14i	0.521443	+	0.101197i
$624$		0			0
$625$	1.18367e15	+	2.05018e15i	0.496467	+	0.859906i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	9.05289e14			0.366614
$630$		0			0
$631$	2.29369e15			0.912794			0.456397	−	0.889776i	$-0.349140\pi$
$631$	2.29369e15			0.912794			0.456397	+	0.889776i	$0.349140\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−3.13358e15	−	5.42753e15i	−1.20444	−	2.08615i
$636$		0			0
$637$	−4.04173e14	−	2.86349e15i	−0.152686	−	1.08175i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−9.49382e13	+	1.64438e14i	−0.0346515	+	0.0600181i	−0.882831	−	0.469691i	$-0.844365\pi$
$641$	−9.49382e13	+	1.64438e14i	−0.0346515	+	0.0600181i	0.848180	+	0.529709i	$0.177699\pi$
$642$		0			0
$643$	1.75159e15			0.628452			0.314226	−	0.949348i	$-0.398255\pi$
$643$	1.75159e15			0.628452			0.314226	+	0.949348i	$0.398255\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−1.59994e15	+	2.77118e15i	−0.554793	+	0.960930i	0.443126	+	0.896459i	$0.353869\pi$
$647$	−1.59994e15	+	2.77118e15i	−0.554793	+	0.960930i	−0.997920	+	0.0644710i	$0.979464\pi$
$648$		0			0
$649$	−1.40110e14	−	2.42678e14i	−0.0477665	−	0.0827341i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	1.12815e15	+	1.95401e15i	0.371829	+	0.644026i	0.989847	−	0.142138i	$-0.0453976\pi$
$653$	1.12815e15	+	1.95401e15i	0.371829	+	0.644026i	−0.618018	+	0.786164i	$0.712064\pi$
$654$		0			0
$655$	4.75706e14	−	8.23948e14i	0.154174	−	0.267038i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−3.01218e15			−0.944084			−0.472042	−	0.881576i	$-0.656483\pi$
$659$	−3.01218e15			−0.944084			−0.472042	+	0.881576i	$0.656483\pi$
$660$		0			0
$661$	−1.47975e15	+	2.56300e15i	−0.456121	+	0.790024i	−0.998752	−	0.0499469i	$-0.984095\pi$
$661$	−1.47975e15	+	2.56300e15i	−0.456121	+	0.790024i	0.542631	+	0.839971i	$0.317428\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	2.94033e15	+	8.53111e15i	0.876753	+	2.54382i
$666$		0			0
$667$	2.14831e15	+	3.72098e15i	0.630094	+	1.09135i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	5.98442e13			0.0169843
$672$		0			0
$673$	4.01157e15			1.12004			0.560018	−	0.828481i	$-0.310794\pi$
$673$	4.01157e15			1.12004			0.560018	+	0.828481i	$0.310794\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	3.58231e15	+	6.20474e15i	0.968111	+	1.67682i	0.701015	+	0.713147i	$0.252731\pi$
$677$	3.58231e15	+	6.20474e15i	0.968111	+	1.67682i	0.267096	+	0.963670i	$0.413936\pi$
$678$		0			0
$679$	1.58065e15	−	1.81942e15i	0.420293	−	0.483782i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−7.37708e13	+	1.27775e14i	−0.0189920	+	0.0328951i	−0.875365	−	0.483462i	$-0.839379\pi$
$683$	−7.37708e13	+	1.27775e14i	−0.0189920	+	0.0328951i	0.856373	+	0.516357i	$0.172712\pi$
$684$		0			0
$685$	−3.62770e14			−0.0919037
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−1.85472e15	+	3.21248e15i	−0.455065	+	0.788196i
$690$		0			0
$691$	1.43011e15	+	2.47703e15i	0.345335	+	0.598138i	0.985415	−	0.170171i	$-0.0544319\pi$
$691$	1.43011e15	+	2.47703e15i	0.345335	+	0.598138i	−0.640079	+	0.768309i	$0.721099\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	3.59902e15	+	6.23369e15i	0.841915	+	1.45824i
$696$		0			0
$697$	2.67606e15	−	4.63507e15i	0.616191	−	1.06727i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−3.67571e14			−0.0820147			−0.0410073	−	0.999159i	$-0.513057\pi$
$701$	−3.67571e14			−0.0820147			−0.0410073	+	0.999159i	$0.513057\pi$
$702$		0			0
$703$	−1.46382e15	+	2.53541e15i	−0.321539	+	0.556922i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	1.75910e15	+	5.10388e15i	0.374528	+	1.08666i
$708$		0			0
$709$	−3.52656e15	−	6.10818e15i	−0.739259	−	1.28043i	−0.952829	−	0.303507i	$-0.901842\pi$
$709$	−3.52656e15	−	6.10818e15i	−0.739259	−	1.28043i	0.213570	−	0.976928i	$-0.431491\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−4.56418e15			−0.927620
$714$		0			0
$715$	7.24108e14			0.144917
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−3.63237e15	−	6.29146e15i	−0.704988	−	1.22108i	−0.966696	−	0.255928i	$-0.917619\pi$
$719$	−3.63237e15	−	6.29146e15i	−0.704988	−	1.22108i	0.261708	−	0.965147i	$-0.415714\pi$
$720$		0			0
$721$	7.21561e15	+	1.40035e15i	1.37921	+	0.267665i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−2.23778e15	+	3.87595e15i	−0.414914	+	0.718652i
$726$		0			0
$727$	−8.82541e15			−1.61174			−0.805871	−	0.592091i	$-0.798302\pi$
$727$	−8.82541e15			−1.61174			−0.805871	+	0.592091i	$0.798302\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	4.93171e15	−	8.54196e15i	0.873880	−	1.51360i
$732$		0			0
$733$	−3.25078e15	−	5.63051e15i	−0.567434	−	0.982825i	−0.996819	−	0.0797030i	$-0.974603\pi$
$733$	−3.25078e15	−	5.63051e15i	−0.567434	−	0.982825i	0.429384	−	0.903122i	$-0.358731\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−1.36596e14	−	2.36591e14i	−0.0231401	−	0.0400799i
$738$		0			0
$739$	−4.66487e15	+	8.07979e15i	−0.778565	+	1.34851i	0.154204	+	0.988039i	$0.450719\pi$
$739$	−4.66487e15	+	8.07979e15i	−0.778565	+	1.34851i	−0.932769	+	0.360475i	$0.882615\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−7.14846e15			−1.15817			−0.579087	−	0.815266i	$-0.696591\pi$
$743$	−7.14846e15			−1.15817			−0.579087	+	0.815266i	$0.696591\pi$
$744$		0			0
$745$	−5.71193e15	+	9.89335e15i	−0.911850	+	1.57937i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−9.17564e15	−	1.78073e15i	−1.42228	−	0.276025i
$750$		0			0
$751$	2.33373e15	+	4.04213e15i	0.356476	+	0.617434i	0.987369	−	0.158435i	$-0.0506448\pi$
$751$	2.33373e15	+	4.04213e15i	0.356476	+	0.617434i	−0.630893	+	0.775869i	$0.717312\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	7.41001e15			1.09929
$756$		0			0
$757$	4.72097e15			0.690246			0.345123	−	0.938557i	$-0.387837\pi$
$757$	4.72097e15			0.690246			0.345123	+	0.938557i	$0.387837\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−6.09532e14	−	1.05574e15i	−0.0865727	−	0.149948i	0.819488	−	0.573097i	$-0.194258\pi$
$761$	−6.09532e14	−	1.05574e15i	−0.0865727	−	0.149948i	−0.906060	+	0.423149i	$0.860925\pi$
$762$		0			0
$763$	1.32492e15	+	3.84413e15i	0.185483	+	0.538162i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−4.09711e15	+	7.09641e15i	−0.557318	+	0.965304i
$768$		0			0
$769$	4.52570e15			0.606864			0.303432	−	0.952853i	$-0.401867\pi$
$769$	4.52570e15			0.606864			0.303432	+	0.952853i	$0.401867\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	2.34216e15	−	4.05675e15i	0.305232	−	0.528677i	−0.672081	−	0.740478i	$-0.734599\pi$
$773$	2.34216e15	−	4.05675e15i	0.305232	−	0.528677i	0.977313	+	0.211800i	$0.0679327\pi$
$774$		0			0
$775$	−2.37713e15	−	4.11731e15i	−0.305417	−	0.528998i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	8.65418e15	+	1.49895e16i	1.08086	+	1.87211i
$780$		0			0
$781$	4.53207e14	−	7.84977e14i	0.0558105	−	0.0966666i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	2.12195e16			2.54069
$786$		0			0
$787$	−6.54085e15	+	1.13291e16i	−0.772277	+	1.33762i	0.164035	+	0.986455i	$0.447549\pi$
$787$	−6.54085e15	+	1.13291e16i	−0.772277	+	1.33762i	−0.936312	+	0.351169i	$0.885784\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	1.04989e14	−	1.20848e14i	0.0120551	−	0.0138762i
$792$		0			0
$793$	−8.74984e14	−	1.51552e15i	−0.0990827	−	0.171616i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	1.03303e16			1.13787			0.568933	−	0.822384i	$-0.307356\pi$
$797$	1.03303e16			1.13787			0.568933	+	0.822384i	$0.307356\pi$
$798$		0			0
$799$	−5.35847e15			−0.582148
$800$		0			0
$801$		0			0
$802$		0			0
$803$	4.93905e14	+	8.55469e14i	0.0522045	+	0.0904209i
$804$		0			0
$805$	−6.77100e15	−	1.96455e16i	−0.705953	−	2.04826i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	5.46347e15	−	9.46301e15i	0.554309	−	0.960091i	−0.443648	−	0.896201i	$-0.646316\pi$
$809$	5.46347e15	−	9.46301e15i	0.554309	−	0.960091i	0.997957	−	0.0638900i	$-0.0203507\pi$
$810$		0			0
$811$	−1.55193e16			−1.55330			−0.776652	−	0.629930i	$-0.783084\pi$
$811$	−1.55193e16			−1.55330			−0.776652	+	0.629930i	$0.783084\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	1.01037e14	−	1.75001e14i	0.00984268	−	0.0170480i
$816$		0			0
$817$	1.59488e16	+	2.76241e16i	1.53287	+	2.65502i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	7.25247e15	+	1.25617e16i	0.678577	+	1.17533i	0.975410	+	0.220400i	$0.0707362\pi$
$821$	7.25247e15	+	1.25617e16i	0.678577	+	1.17533i	−0.296833	+	0.954929i	$0.595931\pi$
$822$		0			0
$823$	1.41636e15	−	2.45320e15i	0.130760	−	0.226482i	−0.793210	−	0.608948i	$-0.791592\pi$
$823$	1.41636e15	−	2.45320e15i	0.130760	−	0.226482i	0.923970	+	0.382466i	$0.124925\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−1.88975e16			−1.69873			−0.849363	−	0.527809i	$-0.823014\pi$
$827$	−1.88975e16			−1.69873			−0.849363	+	0.527809i	$0.823014\pi$
$828$		0			0
$829$	1.55663e14	−	2.69617e14i	0.0138082	−	0.0239165i	−0.859039	−	0.511911i	$-0.828938\pi$
$829$	1.55663e14	−	2.69617e14i	0.0138082	−	0.0239165i	0.872847	+	0.487994i	$0.162271\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	1.16238e16	+	4.68828e15i	1.00415	+	0.405011i
$834$		0			0
$835$	−1.22667e15	−	2.12465e15i	−0.104581	−	0.181139i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−1.14467e16			−0.950583			−0.475292	−	0.879828i	$-0.657657\pi$
$839$	−1.14467e16			−0.950583			−0.475292	+	0.879828i	$0.657657\pi$
$840$		0			0
$841$	−3.91573e15			−0.320948
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−1.71652e15	−	2.97310e15i	−0.137068	−	0.237410i
$846$		0			0
$847$	1.23454e16	+	2.39590e15i	0.973077	+	0.188847i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	3.37089e15	−	5.83855e15i	0.258900	−	0.448428i
$852$		0			0
$853$	7.10747e15			0.538884			0.269442	−	0.963017i	$-0.413161\pi$
$853$	7.10747e15			0.538884			0.269442	+	0.963017i	$0.413161\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−7.28558e15	+	1.26190e16i	−0.538356	+	0.932460i	0.460637	+	0.887589i	$0.347621\pi$
$857$	−7.28558e15	+	1.26190e16i	−0.538356	+	0.932460i	−0.998993	+	0.0448714i	$0.985712\pi$
$858$		0			0
$859$	6.82398e15	+	1.18195e16i	0.497824	+	0.862256i	0.999997	−	0.00251138i	$-0.000799397\pi$
$859$	6.82398e15	+	1.18195e16i	0.497824	+	0.862256i	−0.502173	+	0.864767i	$0.667466\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−9.49537e15	−	1.64465e16i	−0.675231	−	1.16954i	−0.976401	−	0.215965i	$-0.930710\pi$
$863$	−9.49537e15	−	1.64465e16i	−0.675231	−	1.16954i	0.301170	−	0.953571i	$-0.402623\pi$
$864$		0			0
$865$	−9.44070e15	+	1.63518e16i	−0.662851	+	1.14809i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	2.14702e15			0.146970
$870$		0			0
$871$	−3.99434e15	+	6.91840e15i	−0.269989	+	0.467634i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	9.89136e13	−	1.13855e14i	0.00651946	−	0.00750429i
$876$		0			0
$877$	5.97907e15	+	1.03561e16i	0.389167	+	0.674057i	0.992338	−	0.123555i	$-0.0394296\pi$
$877$	5.97907e15	+	1.03561e16i	0.389167	+	0.674057i	−0.603171	+	0.797612i	$0.706096\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	1.04006e16			0.660221			0.330111	−	0.943942i	$-0.392914\pi$
$881$	1.04006e16			0.660221			0.330111	+	0.943942i	$0.392914\pi$
$882$		0			0
$883$	1.40425e16			0.880360			0.440180	−	0.897910i	$-0.354915\pi$
$883$	1.40425e16			0.880360			0.440180	+	0.897910i	$0.354915\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	1.17716e16	+	2.03890e16i	0.719873	+	1.24686i	0.961050	+	0.276375i	$0.0891333\pi$
$887$	1.17716e16	+	2.03890e16i	0.719873	+	1.24686i	−0.241177	+	0.970481i	$0.577533\pi$
$888$		0			0
$889$	1.84627e16	−	2.12516e16i	1.11515	−	1.28361i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	8.66446e15	−	1.50073e16i	0.510574	−	0.884340i
$894$		0			0
$895$	5.03882e15			0.293294
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−4.40034e15	+	7.62161e15i	−0.249924	+	0.432881i
$900$		0			0
$901$	−8.03855e15	−	1.39232e16i	−0.451016	−	0.781182i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	5.21166e15	+	9.02686e15i	0.285370	+	0.494276i
$906$		0			0
$907$	1.25037e16	−	2.16570e16i	0.676392	−	1.17154i	−0.299668	−	0.954043i	$-0.596876\pi$
$907$	1.25037e16	−	2.16570e16i	0.676392	−	1.17154i	0.976060	−	0.217501i	$-0.0697906\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−2.16094e16			−1.14102			−0.570508	−	0.821292i	$-0.693254\pi$
$911$	−2.16094e16			−1.14102			−0.570508	+	0.821292i	$0.693254\pi$
$912$		0			0
$913$	−1.30335e15	+	2.25746e15i	−0.0679940	+	0.117769i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	4.19536e15	+	8.14202e14i	0.213667	+	0.0414668i
$918$		0			0
$919$	−1.18711e16	−	2.05614e16i	−0.597388	−	1.03471i	−0.993205	−	0.116377i	$-0.962872\pi$
$919$	−1.18711e16	−	2.05614e16i	−0.597388	−	1.03471i	0.395817	−	0.918329i	$-0.370461\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−2.65054e16			−1.30234
$924$		0			0
$925$	7.02255e15			0.340969
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−7.80122e15	−	1.35121e16i	−0.369893	−	0.640674i	0.619655	−	0.784874i	$-0.287272\pi$
$929$	−7.80122e15	−	1.35121e16i	−0.369893	−	0.640674i	−0.989549	+	0.144200i	$0.953939\pi$
$930$		0			0
$931$	−3.19256e16	+	2.49736e16i	−1.49594	+	1.17019i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−1.56918e15	+	2.71789e15i	−0.0718138	+	0.124385i
$936$		0			0
$937$	8.89670e14			0.0402403			0.0201201	−	0.999798i	$-0.493595\pi$
$937$	8.89670e14			0.0402403			0.0201201	+	0.999798i	$0.493595\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−1.33102e16	+	2.30539e16i	−0.588086	+	1.01860i	0.406397	+	0.913697i	$0.366785\pi$
$941$	−1.33102e16	+	2.30539e16i	−0.588086	+	1.01860i	−0.994483	+	0.104899i	$0.966548\pi$
$942$		0			0
$943$	−1.99289e16	−	3.45178e16i	−0.870299	−	1.50740i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−1.01137e16	−	1.75174e16i	−0.431503	−	0.747385i	0.565500	−	0.824748i	$-0.308683\pi$
$947$	−1.01137e16	−	1.75174e16i	−0.431503	−	0.747385i	−0.997003	+	0.0773632i	$0.975350\pi$
$948$		0			0
$949$	1.44428e16	−	2.50157e16i	0.609099	−	1.05499i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−1.14065e16			−0.470046			−0.235023	−	0.971990i	$-0.575516\pi$
$953$	−1.14065e16			−0.470046			−0.235023	+	0.971990i	$0.575516\pi$
$954$		0			0
$955$	3.38998e16	−	5.87162e16i	1.38095	−	2.39188i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−5.30978e14	−	1.54058e15i	−0.0211385	−	0.0613314i
$960$		0			0
$961$	8.02989e15	+	1.39082e16i	0.316032	+	0.547383i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	2.25462e16			0.867309
$966$		0			0
$967$	−1.90477e16			−0.724429			−0.362215	−	0.932095i	$-0.617979\pi$
$967$	−1.90477e16			−0.724429			−0.362215	+	0.932095i	$0.617979\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−1.73660e16	−	3.00788e16i	−0.645646	−	1.11829i	−0.984152	−	0.177328i	$-0.943255\pi$
$971$	−1.73660e16	−	3.00788e16i	−0.645646	−	1.11829i	0.338506	−	0.940964i	$-0.390079\pi$
$972$		0			0
$973$	−2.12050e16	+	2.44082e16i	−0.779502	+	0.897253i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	8.05853e15	−	1.39578e16i	0.289625	−	0.501645i	−0.684095	−	0.729393i	$-0.739803\pi$
$977$	8.05853e15	−	1.39578e16i	0.289625	−	0.501645i	0.973720	+	0.227748i	$0.0731361\pi$
$978$		0			0
$979$	−1.39950e15			−0.0497356
$980$		0			0
$981$		0			0
$982$		0			0
$983$	7.46353e15	−	1.29272e16i	0.259358	−	0.449222i	−0.706712	−	0.707501i	$-0.749822\pi$
$983$	7.46353e15	−	1.29272e16i	0.259358	−	0.449222i	0.966070	+	0.258280i	$0.0831556\pi$
$984$		0			0
$985$	1.24703e16	+	2.15991e16i	0.428525	+	0.742227i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−3.67269e16	−	6.36129e16i	−1.23426	−	2.13779i
$990$		0			0
$991$	−1.12354e16	+	1.94603e16i	−0.373408	+	0.646762i	−0.990087	−	0.140452i	$-0.955144\pi$
$991$	−1.12354e16	+	1.94603e16i	−0.373408	+	0.646762i	0.616679	+	0.787215i	$0.288478\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−1.13538e16			−0.369076
$996$		0			0
$997$	1.44345e16	−	2.50012e16i	0.464064	−	0.803782i	−0.535095	−	0.844792i	$-0.679724\pi$
$997$	1.44345e16	−	2.50012e16i	0.464064	−	0.803782i	0.999159	+	0.0410101i	$0.0130576\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.12.k.d.109.2		16
3.2	odd	2		84.12.i.b.25.7	✓	16
7.2	even	3	inner	252.12.k.d.37.2		16
21.2	odd	6		84.12.i.b.37.7	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.12.i.b.25.7	✓	16	3.2	odd	2
84.12.i.b.37.7	yes	16	21.2	odd	6
252.12.k.d.37.2		16	7.2	even	3	inner
252.12.k.d.109.2		16	1.1	even	1	trivial

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:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	252.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-4949.72 - 8573.16i) q^{5} +(29163.1 - 33568.4i) q^{7} +O(q^{10})\)	\(q+(-4949.72 - 8573.16i) q^{5} +(29163.1 - 33568.4i) q^{7} +(-25007.0 + 43313.5i) q^{11} +1.46252e6 q^{13} +(-3.16934e6 + 5.48946e6i) q^{17} +(-1.02494e7 - 1.77525e7i) q^{19} +(2.36024e7 + 4.08806e7i) q^{23} +(-2.45854e7 + 4.25831e7i) q^{25} +9.10208e7 q^{29} +(-4.83443e7 + 8.37349e7i) q^{31} +(-4.32137e8 - 8.38657e7i) q^{35} +(-7.14098e7 - 1.23685e8i) q^{37} -8.44357e8 q^{41} -1.55607e9 q^{43} +(4.22680e8 + 7.32103e8i) q^{47} +(-2.76354e8 - 1.95792e9i) q^{49} +(-1.26817e9 + 2.19654e9i) q^{53} +4.95111e8 q^{55} +(-2.80141e9 + 4.85219e9i) q^{59} +(-5.98273e8 - 1.03624e9i) q^{61} +(-7.23904e9 - 1.25384e10i) q^{65} +(-2.73114e9 + 4.73048e9i) q^{67} -1.81232e10 q^{71} +(9.87533e9 - 1.71046e10i) q^{73} +(7.24683e8 + 2.10260e9i) q^{77} +(-2.14642e10 - 3.71770e10i) q^{79} +5.21192e10 q^{83} +6.27494e10 q^{85} +(1.39910e10 + 2.42332e10i) q^{89} +(4.26515e10 - 4.90944e10i) q^{91} +(-1.01464e11 + 1.75740e11i) q^{95} +5.42003e10 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2156 q^{5} + 50512 q^{7}+O(q^{10}) \) 16 * q + 2156 * q^5 + 50512 * q^7	\( 16 q + 2156 q^{5} + 50512 q^{7} + 222796 q^{11} + 2703176 q^{13} - 5114600 q^{17} + 6910556 q^{19} + 51387712 q^{23} - 191456372 q^{25} - 118854616 q^{29} + 164659160 q^{31} - 55239344 q^{35} + 75658364 q^{37} + 1815568608 q^{41} + 10754408 q^{43} + 1034359464 q^{47} + 4123496848 q^{49} + 665159988 q^{53} - 1264543896 q^{55} - 1040514580 q^{59} - 14391208024 q^{61} + 20938150200 q^{65} - 33307097284 q^{67} - 65848902896 q^{71} + 17709749204 q^{73} - 8594484604 q^{77} - 26626784032 q^{79} + 210306955048 q^{83} - 25867402032 q^{85} + 55951560072 q^{89} + 66078280292 q^{91} - 106810047392 q^{95} - 156216030712 q^{97}+O(q^{100}) \) 16 * q + 2156 * q^5 + 50512 * q^7 + 222796 * q^11 + 2703176 * q^13 - 5114600 * q^17 + 6910556 * q^19 + 51387712 * q^23 - 191456372 * q^25 - 118854616 * q^29 + 164659160 * q^31 - 55239344 * q^35 + 75658364 * q^37 + 1815568608 * q^41 + 10754408 * q^43 + 1034359464 * q^47 + 4123496848 * q^49 + 665159988 * q^53 - 1264543896 * q^55 - 1040514580 * q^59 - 14391208024 * q^61 + 20938150200 * q^65 - 33307097284 * q^67 - 65848902896 * q^71 + 17709749204 * q^73 - 8594484604 * q^77 - 26626784032 * q^79 + 210306955048 * q^83 - 25867402032 * q^85 + 55951560072 * q^89 + 66078280292 * q^91 - 106810047392 * q^95 - 156216030712 * q^97

Introduction

L-functions

Modular forms

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Database

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