LMFDB - Embedded newform 252.12.k.d.109.8

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			109.8
Root			$13166.9 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	252.109
Dual form			252.12.k.d.37.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(6718.22 + 11636.3i) q^{5} +(41445.4 - 16112.4i) q^{7} +O(q^{10})$	$q+(6718.22 + 11636.3i) q^{5} +(41445.4 - 16112.4i) q^{7} +(425643. - 737235. i) q^{11} +2.13303e6 q^{13} +(-1.28105e6 + 2.21884e6i) q^{17} +(8.87791e6 + 1.53770e7i) q^{19} +(1.81716e7 + 3.14742e7i) q^{23} +(-6.58548e7 + 1.14064e8i) q^{25} -571626. q^{29} +(1.07907e8 - 1.86901e8i) q^{31} +(4.65927e8 + 3.74024e8i) q^{35} +(-9.87524e7 - 1.71044e8i) q^{37} +2.72342e8 q^{41} +1.11575e9 q^{43} +(-3.98664e8 - 6.90506e8i) q^{47} +(1.45811e9 - 1.33557e9i) q^{49} +(6.76715e8 - 1.17210e9i) q^{53} +1.14382e10 q^{55} +(-3.81442e8 + 6.60677e8i) q^{59} +(-2.04039e9 - 3.53405e9i) q^{61} +(1.43301e10 + 2.48205e10i) q^{65} +(1.08784e9 - 1.88419e9i) q^{67} -1.82655e10 q^{71} +(1.03329e10 - 1.78972e10i) q^{73} +(5.76230e9 - 3.74131e10i) q^{77} +(-1.28553e10 - 2.22661e10i) q^{79} -1.36264e10 q^{83} -3.44255e10 q^{85} +(-5.18461e9 - 8.98001e9i) q^{89} +(8.84041e10 - 3.43682e10i) q^{91} +(-1.19287e11 + 2.06612e11i) q^{95} -1.14522e11 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	6718.22	+	11636.3i	0.961433	+	1.66525i	0.718908	+	0.695106i	$0.244642\pi$
$5$	6718.22	+	11636.3i	0.961433	+	1.66525i	0.242525	+	0.970145i	$0.422024\pi$
$6$		0			0
$7$	41445.4	−	16112.4i	0.932045	−	0.362344i
$7$	41445.4	−	16112.4i	0.932045	−	0.362344i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	425643.	−	737235.i	0.796866	−	1.38021i	−0.124781	−	0.992184i	$-0.539823\pi$
$11$	425643.	−	737235.i	0.796866	−	1.38021i	0.921647	−	0.388028i	$-0.126844\pi$
$12$		0			0
$13$	2.13303e6			1.59334			0.796669	−	0.604416i	$-0.206593\pi$
$13$	2.13303e6			1.59334			0.796669	+	0.604416i	$0.206593\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.28105e6	+	2.21884e6i	−0.218825	+	0.379016i	−0.954449	−	0.298374i	$-0.903556\pi$
$17$	−1.28105e6	+	2.21884e6i	−0.218825	+	0.379016i	0.735624	+	0.677390i	$0.236889\pi$
$18$		0			0
$19$	8.87791e6	+	1.53770e7i	0.822557	+	1.42471i	0.903772	+	0.428014i	$0.140787\pi$
$19$	8.87791e6	+	1.53770e7i	0.822557	+	1.42471i	−0.0812152	+	0.996697i	$0.525880\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	1.81716e7	+	3.14742e7i	0.588695	+	1.01965i	0.994404	+	0.105648i	$0.0336915\pi$
$23$	1.81716e7	+	3.14742e7i	0.588695	+	1.01965i	−0.405708	+	0.914003i	$0.632975\pi$
$24$		0			0
$25$	−6.58548e7	+	1.14064e8i	−1.34871	+	2.33603i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−571626.			−0.00517515			−0.00258757	−	0.999997i	$-0.500824\pi$
$29$	−571626.			−0.00517515			−0.00258757	+	0.999997i	$0.500824\pi$
$30$		0			0
$31$	1.07907e8	−	1.86901e8i	0.676956	−	1.17252i	−0.298936	−	0.954273i	$-0.596632\pi$
$31$	1.07907e8	−	1.86901e8i	0.676956	−	1.17252i	0.975893	−	0.218250i	$-0.0700348\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	4.65927e8	+	3.74024e8i	1.49949	+	1.20372i
$36$		0			0
$37$	−9.87524e7	−	1.71044e8i	−0.234120	−	0.405508i	0.724897	−	0.688858i	$-0.241887\pi$
$37$	−9.87524e7	−	1.71044e8i	−0.234120	−	0.405508i	−0.959017	+	0.283350i	$0.908554\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	2.72342e8			0.367116			0.183558	−	0.983009i	$-0.441238\pi$
$41$	2.72342e8			0.367116			0.183558	+	0.983009i	$0.441238\pi$
$42$		0			0
$43$	1.11575e9			1.15741			0.578707	−	0.815536i	$-0.303558\pi$
$43$	1.11575e9			1.15741			0.578707	+	0.815536i	$0.303558\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−3.98664e8	−	6.90506e8i	−0.253553	−	0.439167i	0.710949	−	0.703244i	$-0.248266\pi$
$47$	−3.98664e8	−	6.90506e8i	−0.253553	−	0.439167i	−0.964501	+	0.264077i	$0.914933\pi$
$48$		0			0
$49$	1.45811e9	−	1.33557e9i	0.737414	−	0.675441i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	6.76715e8	−	1.17210e9i	0.222274	−	0.384990i	−0.733224	−	0.679987i	$-0.761985\pi$
$53$	6.76715e8	−	1.17210e9i	0.222274	−	0.384990i	0.955498	+	0.294997i	$0.0953188\pi$
$54$		0			0
$55$	1.14382e10			3.06453
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−3.81442e8	+	6.60677e8i	−0.0694613	+	0.120310i	−0.898664	−	0.438637i	$-0.855461\pi$
$59$	−3.81442e8	+	6.60677e8i	−0.0694613	+	0.120310i	0.829203	+	0.558948i	$0.188795\pi$
$60$		0			0
$61$	−2.04039e9	−	3.53405e9i	−0.309313	−	0.535746i	0.668899	−	0.743353i	$-0.266766\pi$
$61$	−2.04039e9	−	3.53405e9i	−0.309313	−	0.535746i	−0.978212	+	0.207607i	$0.933432\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	1.43301e10	+	2.48205e10i	1.53189	+	2.65331i
$66$		0			0
$67$	1.08784e9	−	1.88419e9i	0.0984358	−	0.170496i	−0.812602	−	0.582820i	$-0.801949\pi$
$67$	1.08784e9	−	1.88419e9i	0.0984358	−	0.170496i	0.911037	+	0.412324i	$0.135283\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−1.82655e10			−1.20147			−0.600733	−	0.799450i	$-0.705124\pi$
$71$	−1.82655e10			−1.20147			−0.600733	+	0.799450i	$0.705124\pi$
$72$		0			0
$73$	1.03329e10	−	1.78972e10i	0.583375	−	1.01043i	−0.411701	−	0.911319i	$-0.635065\pi$
$73$	1.03329e10	−	1.78972e10i	0.583375	−	1.01043i	0.995076	−	0.0991158i	$-0.0316014\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	5.76230e9	−	3.74131e10i	0.242603	−	1.57516i
$78$		0			0
$79$	−1.28553e10	−	2.22661e10i	−0.470039	−	0.814132i	0.529374	−	0.848389i	$-0.322427\pi$
$79$	−1.28553e10	−	2.22661e10i	−0.470039	−	0.814132i	−0.999413	+	0.0342567i	$0.989094\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−1.36264e10			−0.379710			−0.189855	−	0.981812i	$-0.560802\pi$
$83$	−1.36264e10			−0.379710			−0.189855	+	0.981812i	$0.560802\pi$
$84$		0			0
$85$	−3.44255e10			−0.841542
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−5.18461e9	−	8.98001e9i	−0.0984173	−	0.170464i	0.812612	−	0.582804i	$-0.198045\pi$
$89$	−5.18461e9	−	8.98001e9i	−0.0984173	−	0.170464i	−0.911030	+	0.412341i	$0.864711\pi$
$90$		0			0
$91$	8.84041e10	−	3.43682e10i	1.48506	−	0.577336i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−1.19287e11	+	2.06612e11i	−1.58167	+	2.73953i
$96$		0			0
$97$	−1.14522e11			−1.35408			−0.677040	−	0.735947i	$-0.736737\pi$
$97$	−1.14522e11			−1.35408			−0.677040	+	0.735947i	$0.736737\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−1.25331e10	+	2.17079e10i	−0.118656	+	0.205518i	−0.919235	−	0.393708i	$-0.871192\pi$
$101$	−1.25331e10	+	2.17079e10i	−0.118656	+	0.205518i	0.800579	+	0.599227i	$0.204525\pi$
$102$		0			0
$103$	−3.90267e10	−	6.75962e10i	−0.331709	−	0.574536i	0.651138	−	0.758959i	$-0.274292\pi$
$103$	−3.90267e10	−	6.75962e10i	−0.331709	−	0.574536i	−0.982847	+	0.184423i	$0.940958\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1.14704e11	+	1.98672e11i	0.790617	+	1.36939i	0.925585	+	0.378539i	$0.123573\pi$
$107$	1.14704e11	+	1.98672e11i	0.790617	+	1.36939i	−0.134969	+	0.990850i	$0.543093\pi$
$108$		0			0
$109$	1.04619e11	−	1.81206e11i	0.651278	−	1.12805i	−0.331535	−	0.943443i	$-0.607567\pi$
$109$	1.04619e11	−	1.81206e11i	0.651278	−	1.12805i	0.982813	−	0.184603i	$-0.0591001\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	2.19133e11			1.11886			0.559432	−	0.828877i	$-0.311019\pi$
$113$	2.19133e11			1.11886			0.559432	+	0.828877i	$0.311019\pi$
$114$		0			0
$115$	−2.44162e11	+	4.22901e11i	−1.13198	+	1.96065i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−1.73427e10	+	1.12601e11i	−0.0666205	+	0.432549i
$120$		0			0
$121$	−2.19687e11	−	3.80510e11i	−0.769991	−	1.33366i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−1.11363e12			−3.26390
$126$		0			0
$127$	2.57513e11			0.691639			0.345819	−	0.938301i	$-0.387601\pi$
$127$	2.57513e11			0.691639			0.345819	+	0.938301i	$0.387601\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	2.19906e11	+	3.80889e11i	0.498018	+	0.862593i	0.999997	−	0.00228653i	$-0.000727827\pi$
$131$	2.19906e11	+	3.80889e11i	0.498018	+	0.862593i	−0.501979	+	0.864880i	$0.667394\pi$
$132$		0			0
$133$	6.15708e11	+	4.94261e11i	1.28289	+	1.02985i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	2.51907e11	−	4.36315e11i	0.445940	−	0.772391i	−0.552177	−	0.833727i	$-0.686203\pi$
$137$	2.51907e11	−	4.36315e11i	0.445940	−	0.772391i	0.998117	+	0.0613357i	$0.0195360\pi$
$138$		0			0
$139$	1.93201e11			0.315812			0.157906	−	0.987454i	$-0.449526\pi$
$139$	1.93201e11			0.315812			0.157906	+	0.987454i	$0.449526\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	9.07907e11	−	1.57254e12i	1.26968	−	2.19915i
$144$		0			0
$145$	−3.84031e9	−	6.65161e9i	−0.00497556	−	0.00861792i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−3.50276e10	−	6.06696e10i	−0.0390738	−	0.0676778i	0.845827	−	0.533457i	$-0.179107\pi$
$149$	−3.50276e10	−	6.06696e10i	−0.0390738	−	0.0676778i	−0.884901	+	0.465779i	$0.845774\pi$
$150$		0			0
$151$	5.29667e11	−	9.17410e11i	0.549073	−	0.951022i	−0.449266	−	0.893398i	$-0.648314\pi$
$151$	5.29667e11	−	9.17410e11i	0.549073	−	0.951022i	0.998338	−	0.0576234i	$-0.0183523\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	2.89977e12			2.60339
$156$		0			0
$157$	−2.29713e11	+	3.97875e11i	−0.192193	+	0.332888i	−0.945977	−	0.324234i	$-0.894893\pi$
$157$	−2.29713e11	+	3.97875e11i	−0.192193	+	0.332888i	0.753784	+	0.657123i	$0.228227\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	1.26025e12	+	1.01167e12i	0.918154	+	0.737049i
$162$		0			0
$163$	−1.42888e11	−	2.47489e11i	−0.0972665	−	0.168470i	0.813286	−	0.581864i	$-0.197677\pi$
$163$	−1.42888e11	−	2.47489e11i	−0.0972665	−	0.168470i	−0.910552	+	0.413394i	$0.864343\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−1.47522e12			−0.878850			−0.439425	−	0.898279i	$-0.644818\pi$
$167$	−1.47522e12			−0.878850			−0.439425	+	0.898279i	$0.644818\pi$
$168$		0			0
$169$	2.75764e12			1.53873
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−7.02485e11	−	1.21674e12i	−0.344654	−	0.596959i	0.640637	−	0.767844i	$-0.278670\pi$
$173$	−7.02485e11	−	1.21674e12i	−0.344654	−	0.596959i	−0.985291	+	0.170886i	$0.945337\pi$
$174$		0			0
$175$	−8.91535e11	+	5.78850e12i	−0.410610	+	2.66598i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−1.25836e12	+	2.17955e12i	−0.511816	+	0.886491i	0.488090	+	0.872793i	$0.337694\pi$
$179$	−1.25836e12	+	2.17955e12i	−0.511816	+	0.886491i	−0.999906	+	0.0136982i	$0.995640\pi$
$180$		0			0
$181$	−3.11043e12			−1.19011			−0.595056	−	0.803684i	$-0.702870\pi$
$181$	−3.11043e12			−1.19011			−0.595056	+	0.803684i	$0.702870\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	1.32688e12	−	2.29822e12i	0.450181	−	0.779737i
$186$		0			0
$187$	1.09054e12	+	1.88887e12i	0.348748	+	0.604049i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	5.63090e11	+	9.75301e11i	0.160286	+	0.277623i	0.934971	−	0.354724i	$-0.115425\pi$
$191$	5.63090e11	+	9.75301e11i	0.160286	+	0.277623i	−0.774686	+	0.632347i	$0.782092\pi$
$192$		0			0
$193$	−1.08140e12	+	1.87305e12i	−0.290685	+	0.503482i	−0.973972	−	0.226669i	$-0.927217\pi$
$193$	−1.08140e12	+	1.87305e12i	−0.290685	+	0.503482i	0.683287	+	0.730150i	$0.260550\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−6.02832e12			−1.44755			−0.723773	−	0.690038i	$-0.757594\pi$
$197$	−6.02832e12			−1.44755			−0.723773	+	0.690038i	$0.757594\pi$
$198$		0			0
$199$	−1.43126e12	+	2.47901e12i	−0.325106	+	0.563100i	−0.981534	−	0.191289i	$-0.938733\pi$
$199$	−1.43126e12	+	2.47901e12i	−0.325106	+	0.563100i	0.656428	+	0.754389i	$0.272067\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−2.36912e10	+	9.21026e9i	−0.00482347	+	0.00187518i
$204$		0			0
$205$	1.82965e12	+	3.16905e12i	0.352958	+	0.611341i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	1.51153e13			2.62187
$210$		0			0
$211$	−3.22306e12			−0.530535			−0.265268	−	0.964175i	$-0.585460\pi$
$211$	−3.22306e12			−0.530535			−0.265268	+	0.964175i	$0.585460\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	7.49582e12	+	1.29831e13i	1.11278	+	1.92738i
$216$		0			0
$217$	1.46083e12	−	9.48480e12i	0.206097	−	1.33813i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−2.73251e12	+	4.73285e12i	−0.348662	+	0.603900i
$222$		0			0
$223$	−1.12361e13			−1.36440			−0.682198	−	0.731167i	$-0.738976\pi$
$223$	−1.12361e13			−1.36440			−0.682198	+	0.731167i	$0.738976\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−7.58401e12	+	1.31359e13i	−0.835135	+	1.44650i	0.0587856	+	0.998271i	$0.481277\pi$
$227$	−7.58401e12	+	1.31359e13i	−0.835135	+	1.44650i	−0.893921	+	0.448226i	$0.852056\pi$
$228$		0			0
$229$	−1.82140e12	−	3.15476e12i	−0.191122	−	0.331033i	0.754500	−	0.656300i	$-0.227879\pi$
$229$	−1.82140e12	−	3.15476e12i	−0.191122	−	0.331033i	−0.945622	+	0.325267i	$0.894546\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−6.03650e12	−	1.04555e13i	−0.575874	−	0.997443i	−0.995946	−	0.0899524i	$-0.971328\pi$
$233$	−6.03650e12	−	1.04555e13i	−0.575874	−	0.997443i	0.420072	−	0.907491i	$-0.362005\pi$
$234$		0			0
$235$	5.35662e12	−	9.27794e12i	0.487548	−	0.844458i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	1.62209e12			0.134551			0.0672756	−	0.997734i	$-0.478569\pi$
$239$	1.62209e12			0.134551			0.0672756	+	0.997734i	$0.478569\pi$
$240$		0			0
$241$	7.66226e12	−	1.32714e13i	0.607104	−	1.05154i	−0.384611	−	0.923079i	$-0.625664\pi$
$241$	7.66226e12	−	1.32714e13i	0.607104	−	1.05154i	0.991715	−	0.128456i	$-0.0410022\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	2.53369e13	+	7.99435e12i	1.83375	+	0.578588i
$246$		0			0
$247$	1.89368e13	+	3.27995e13i	1.31061	+	2.27005i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−1.41336e13			−0.895461			−0.447731	−	0.894169i	$-0.647768\pi$
$251$	−1.41336e13			−0.895461			−0.447731	+	0.894169i	$0.647768\pi$
$252$		0			0
$253$	3.09385e13			1.87645
$254$		0			0
$255$		0			0
$256$		0			0
$257$	7.51915e12	+	1.30235e13i	0.418347	+	0.724598i	0.995773	−	0.0918448i	$-0.0292764\pi$
$257$	7.51915e12	+	1.30235e13i	0.418347	+	0.724598i	−0.577427	+	0.816443i	$0.695943\pi$
$258$		0			0
$259$	−6.84876e12	−	5.49785e12i	−0.365143	−	0.293119i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	1.49881e13	−	2.59601e13i	0.734496	−	1.27218i	−0.220448	−	0.975399i	$-0.570752\pi$
$263$	1.49881e13	−	2.59601e13i	0.734496	−	1.27218i	0.954944	−	0.296786i	$-0.0959147\pi$
$264$		0			0
$265$	1.81853e13			0.854806
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−2.23799e13	+	3.87631e13i	−0.968769	+	1.67796i	−0.269642	+	0.962961i	$0.586905\pi$
$269$	−2.23799e13	+	3.87631e13i	−0.968769	+	1.67796i	−0.699127	+	0.714997i	$0.746428\pi$
$270$		0			0
$271$	5.30406e12	+	9.18689e12i	0.220433	+	0.381801i	0.954940	−	0.296800i	$-0.0959196\pi$
$271$	5.30406e12	+	9.18689e12i	0.220433	+	0.381801i	−0.734506	+	0.678602i	$0.762586\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	5.60612e13	+	9.71009e13i	2.14948	+	3.72300i
$276$		0			0
$277$	2.06423e13	−	3.57535e13i	0.760536	−	1.31729i	−0.182039	−	0.983291i	$-0.558270\pi$
$277$	2.06423e13	−	3.57535e13i	0.760536	−	1.31729i	0.942575	−	0.333996i	$-0.108397\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−5.69959e12			−0.194070			−0.0970350	−	0.995281i	$-0.530936\pi$
$281$	−5.69959e12			−0.194070			−0.0970350	+	0.995281i	$0.530936\pi$
$282$		0			0
$283$	−2.13160e11	+	3.69205e11i	−0.00698041	+	0.0120904i	−0.869495	−	0.493943i	$-0.835555\pi$
$283$	−2.13160e11	+	3.69205e11i	−0.00698041	+	0.0120904i	0.862514	+	0.506033i	$0.168889\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	1.12873e13	−	4.38808e12i	0.342169	−	0.133022i
$288$		0			0
$289$	1.38538e13	+	2.39954e13i	0.404231	+	0.700149i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	1.60966e13			0.435473			0.217737	−	0.976008i	$-0.430133\pi$
$293$	1.60966e13			0.435473			0.217737	+	0.976008i	$0.430133\pi$
$294$		0			0
$295$	−1.02504e13			−0.267129
$296$		0			0
$297$		0			0
$298$		0			0
$299$	3.87606e13	+	6.71353e13i	0.937991	+	1.62465i
$300$		0			0
$301$	4.62425e13	−	1.79773e13i	1.07876	−	0.419382i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	2.74155e13	−	4.74850e13i	0.594767	−	1.03017i
$306$		0			0
$307$	−5.67881e13			−1.18849			−0.594246	−	0.804283i	$-0.702550\pi$
$307$	−5.67881e13			−1.18849			−0.594246	+	0.804283i	$0.702550\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	2.92156e13	−	5.06029e13i	0.569420	−	0.986264i	−0.427203	−	0.904156i	$-0.640501\pi$
$311$	2.92156e13	−	5.06029e13i	0.569420	−	0.986264i	0.996623	−	0.0821088i	$-0.0261655\pi$
$312$		0			0
$313$	7.17860e12	+	1.24337e13i	0.135066	+	0.233941i	0.925623	−	0.378448i	$-0.123542\pi$
$313$	7.17860e12	+	1.24337e13i	0.135066	+	0.233941i	−0.790557	+	0.612389i	$0.790209\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	1.47676e13	+	2.55782e13i	0.259109	+	0.448790i	0.966004	−	0.258529i	$-0.0832377\pi$
$317$	1.47676e13	+	2.55782e13i	0.259109	+	0.448790i	−0.706894	+	0.707319i	$0.749904\pi$
$318$		0			0
$319$	−2.43308e11	+	4.21422e11i	−0.00412390	+	0.00714281i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−4.54921e13			−0.719983
$324$		0			0
$325$	−1.40470e14	+	2.43301e14i	−2.14895	+	3.72208i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−2.76485e13	−	2.21948e13i	−0.395452	−	0.317449i
$330$		0			0
$331$	5.55541e13	+	9.62225e13i	0.768532	+	1.33114i	0.938359	+	0.345663i	$0.112346\pi$
$331$	5.55541e13	+	9.62225e13i	0.768532	+	1.33114i	−0.169827	+	0.985474i	$0.554321\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	2.92334e13			0.378558
$336$		0			0
$337$	−8.99428e13			−1.12720			−0.563601	−	0.826047i	$-0.690585\pi$
$337$	−8.99428e13			−1.12720			−0.563601	+	0.826047i	$0.690585\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−9.18597e13	−	1.59106e14i	−1.07889	−	1.86869i
$342$		0			0
$343$	3.89127e13	−	7.88467e13i	0.442561	−	0.896738i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−5.22864e13	+	9.05626e13i	−0.557926	+	0.966355i	0.439744	+	0.898123i	$0.355069\pi$
$347$	−5.22864e13	+	9.05626e13i	−0.557926	+	0.966355i	−0.997669	+	0.0682322i	$0.978264\pi$
$348$		0			0
$349$	5.39858e13			0.558136			0.279068	−	0.960271i	$-0.409975\pi$
$349$	5.39858e13			0.558136			0.279068	+	0.960271i	$0.409975\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−1.09068e13	+	1.88911e13i	−0.105910	+	0.183441i	−0.914110	−	0.405467i	$-0.867109\pi$
$353$	−1.09068e13	+	1.88911e13i	−0.105910	+	0.183441i	0.808200	+	0.588909i	$0.200442\pi$
$354$		0			0
$355$	−1.22712e14	−	2.12543e14i	−1.15513	−	2.00074i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	6.99484e13	+	1.21154e14i	0.619096	+	1.07231i	0.989651	+	0.143495i	$0.0458343\pi$
$359$	6.99484e13	+	1.21154e14i	0.619096	+	1.07231i	−0.370555	+	0.928811i	$0.620832\pi$
$360$		0			0
$361$	−9.93895e13	+	1.72148e14i	−0.853200	+	1.47779i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	2.77675e14			2.24350
$366$		0			0
$367$	−1.60223e13	+	2.77514e13i	−0.125621	+	0.217581i	−0.921975	−	0.387249i	$-0.873426\pi$
$367$	−1.60223e13	+	2.77514e13i	−0.125621	+	0.217581i	0.796355	+	0.604830i	$0.206759\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	9.16129e12	−	5.94818e13i	0.0676706	−	0.439367i
$372$		0			0
$373$	9.32722e13	+	1.61552e14i	0.668888	+	1.15855i	0.978215	+	0.207593i	$0.0665629\pi$
$373$	9.32722e13	+	1.61552e14i	0.668888	+	1.15855i	−0.309327	+	0.950956i	$0.600104\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−1.21929e12			−0.00824576
$378$		0			0
$379$	2.85750e13			0.187703			0.0938515	−	0.995586i	$-0.470082\pi$
$379$	2.85750e13			0.187703			0.0938515	+	0.995586i	$0.470082\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	1.81568e13	+	3.14486e13i	0.112576	+	0.194988i	0.916808	−	0.399328i	$-0.130756\pi$
$383$	1.81568e13	+	3.14486e13i	0.112576	+	0.194988i	−0.804232	+	0.594315i	$0.797423\pi$
$384$		0			0
$385$	4.74062e14	−	1.84297e14i	2.85628	−	1.11041i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−8.04933e13	+	1.39419e14i	−0.458181	+	0.793593i	−0.998865	−	0.0476332i	$-0.984832\pi$
$389$	−8.04933e13	+	1.39419e14i	−0.458181	+	0.793593i	0.540684	+	0.841226i	$0.318165\pi$
$390$		0			0
$391$	−9.31149e13			−0.515285
$392$		0			0
$393$		0			0
$394$		0			0
$395$	1.72730e14	−	2.99177e14i	0.903823	−	1.56547i
$396$		0			0
$397$	1.79387e14	+	3.10707e14i	0.912940	+	1.58126i	0.809889	+	0.586583i	$0.199527\pi$
$397$	1.79387e14	+	3.10707e14i	0.912940	+	1.58126i	0.103052	+	0.994676i	$0.467139\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	8.22260e13	+	1.42420e14i	0.396018	+	0.685923i	0.993231	−	0.116160i	$-0.0370585\pi$
$401$	8.22260e13	+	1.42420e14i	0.396018	+	0.685923i	−0.597213	+	0.802083i	$0.703725\pi$
$402$		0			0
$403$	2.30169e14	−	3.98664e14i	1.07862	−	1.86823i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−1.68133e14			−0.746249
$408$		0			0
$409$	3.13369e13	−	5.42771e13i	0.135387	−	0.234498i	−0.790358	−	0.612645i	$-0.790105\pi$
$409$	3.13369e13	−	5.42771e13i	0.135387	−	0.234498i	0.925745	+	0.378148i	$0.123439\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−5.16392e12	+	3.35280e13i	−0.0211473	+	0.137304i
$414$		0			0
$415$	−9.15452e13	−	1.58561e14i	−0.365066	−	0.632312i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−8.23062e13			−0.311355			−0.155677	−	0.987808i	$-0.549756\pi$
$419$	−8.23062e13			−0.311355			−0.155677	+	0.987808i	$0.549756\pi$
$420$		0			0
$421$	−6.99072e13			−0.257614			−0.128807	−	0.991670i	$-0.541115\pi$
$421$	−6.99072e13			−0.257614			−0.128807	+	0.991670i	$0.541115\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−1.68726e14	−	2.92243e14i	−0.590261	−	1.02236i
$426$		0			0
$427$	−1.41506e14	−	1.13595e14i	−0.482417	−	0.387261i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	1.23307e14	−	2.13574e14i	0.399358	−	0.691708i	−0.594289	−	0.804252i	$-0.702566\pi$
$431$	1.23307e14	−	2.13574e14i	0.399358	−	0.691708i	0.993647	+	0.112544i	$0.0358998\pi$
$432$		0			0
$433$	−4.21634e14			−1.33123			−0.665614	−	0.746296i	$-0.731830\pi$
$433$	−4.21634e14			−1.33123			−0.665614	+	0.746296i	$0.731830\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−3.22652e14	+	5.58850e14i	−0.968471	+	1.67744i
$438$		0			0
$439$	−4.27459e13	−	7.40380e13i	−0.125124	−	0.216720i	0.796658	−	0.604431i	$-0.206599\pi$
$439$	−4.27459e13	−	7.40380e13i	−0.125124	−	0.216720i	−0.921781	+	0.387710i	$0.873266\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	2.86748e14	+	4.96662e14i	0.798509	+	1.38306i	0.920587	+	0.390537i	$0.127711\pi$
$443$	2.86748e14	+	4.96662e14i	0.798509	+	1.38306i	−0.122078	+	0.992520i	$0.538956\pi$
$444$		0			0
$445$	6.96627e13	−	1.20659e14i	0.189243	−	0.327779i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−6.33244e14			−1.63763			−0.818815	−	0.574057i	$-0.805369\pi$
$449$	−6.33244e14			−1.63763			−0.818815	+	0.574057i	$0.805369\pi$
$450$		0			0
$451$	1.15920e14	−	2.00780e14i	0.292543	−	0.506699i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	9.93836e14	+	7.97803e14i	2.38920	+	1.91793i
$456$		0			0
$457$	1.99228e13	+	3.45073e13i	0.0467532	+	0.0809788i	0.888455	−	0.458964i	$-0.151779\pi$
$457$	1.99228e13	+	3.45073e13i	0.0467532	+	0.0809788i	−0.841702	+	0.539943i	$0.818446\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−8.47695e14			−1.89620			−0.948101	−	0.317970i	$-0.896999\pi$
$461$	−8.47695e14			−1.89620			−0.948101	+	0.317970i	$0.896999\pi$
$462$		0			0
$463$	7.99938e14			1.74727			0.873636	−	0.486579i	$-0.161756\pi$
$463$	7.99938e14			1.74727			0.873636	+	0.486579i	$0.161756\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−4.29125e14	−	7.43267e14i	−0.894008	−	1.54847i	−0.835028	−	0.550207i	$-0.814549\pi$
$467$	−4.29125e14	−	7.43267e14i	−0.894008	−	1.54847i	−0.0589797	−	0.998259i	$-0.518785\pi$
$468$		0			0
$469$	1.47270e13	−	9.56187e13i	0.0299685	−	0.194577i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	4.74909e14	−	8.22566e14i	0.922304	−	1.59748i
$474$		0			0
$475$	−2.33861e15			−4.43755
$476$		0			0
$477$		0			0
$478$		0			0
$479$	6.28415e13	−	1.08845e14i	0.113868	−	0.197225i	−0.803459	−	0.595360i	$-0.797009\pi$
$479$	6.28415e13	−	1.08845e14i	0.113868	−	0.197225i	0.917327	+	0.398135i	$0.130343\pi$
$480$		0			0
$481$	−2.10642e14	−	3.64842e14i	−0.373032	−	0.646111i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−7.69383e14	−	1.33261e15i	−1.30186	−	2.25488i
$486$		0			0
$487$	4.87117e14	−	8.43711e14i	0.805794	−	1.39568i	−0.109960	−	0.993936i	$-0.535072\pi$
$487$	4.87117e14	−	8.43711e14i	0.805794	−	1.39568i	0.915754	−	0.401739i	$-0.131594\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−1.14406e15			−1.80926			−0.904628	−	0.426201i	$-0.859852\pi$
$491$	−1.14406e15			−1.80926			−0.904628	+	0.426201i	$0.859852\pi$
$492$		0			0
$493$	7.32281e11	−	1.26835e12i	0.00113245	−	0.00196146i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−7.57021e14	+	2.94301e14i	−1.11982	+	0.435343i
$498$		0			0
$499$	6.44591e14	+	1.11646e15i	0.932677	+	1.61544i	0.778725	+	0.627366i	$0.215867\pi$
$499$	6.44591e14	+	1.11646e15i	0.932677	+	1.61544i	0.153952	+	0.988078i	$0.450800\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−1.01920e15			−1.41135			−0.705677	−	0.708534i	$-0.749357\pi$
$503$	−1.01920e15			−1.41135			−0.705677	+	0.708534i	$0.749357\pi$
$504$		0			0
$505$	−3.36800e14			−0.456320
$506$		0			0
$507$		0			0
$508$		0			0
$509$	1.28883e14	+	2.23232e14i	0.167205	+	0.289607i	0.937436	−	0.348158i	$-0.113193\pi$
$509$	1.28883e14	+	2.23232e14i	0.167205	+	0.289607i	−0.770231	+	0.637765i	$0.779859\pi$
$510$		0			0
$511$	1.39886e14	−	9.08242e14i	0.177607	−	1.15315i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	5.24379e14	−	9.08252e14i	0.637831	−	1.10476i
$516$		0			0
$517$	−6.78753e14			−0.808191
$518$		0			0
$519$		0			0
$520$		0			0
$521$	1.50755e14	−	2.61115e14i	0.172053	−	0.298005i	−0.767084	−	0.641546i	$-0.778293\pi$
$521$	1.50755e14	−	2.61115e14i	0.172053	−	0.298005i	0.939138	+	0.343541i	$0.111627\pi$
$522$		0			0
$523$	−1.19275e14	−	2.06590e14i	−0.133287	−	0.230860i	0.791655	−	0.610969i	$-0.209220\pi$
$523$	−1.19275e14	−	2.06590e14i	−0.133287	−	0.230860i	−0.924942	+	0.380109i	$0.875887\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	2.76468e14	+	4.78857e14i	0.296270	+	0.513154i
$528$		0			0
$529$	−1.84011e14	+	3.18716e14i	−0.193124	+	0.334501i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	5.80913e14			0.584940
$534$		0			0
$535$	−1.54121e15	+	2.66945e15i	−1.52025	+	2.63315i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−3.63993e14	−	1.64344e15i	−0.344632	−	1.55602i
$540$		0			0
$541$	−7.15031e14	−	1.23847e15i	−0.663346	−	1.14895i	−0.979731	−	0.200318i	$-0.935803\pi$
$541$	−7.15031e14	−	1.23847e15i	−0.663346	−	1.14895i	0.316385	−	0.948631i	$-0.397531\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	2.81142e15			2.50464
$546$		0			0
$547$	9.19792e14			0.803081			0.401540	−	0.915841i	$-0.368475\pi$
$547$	9.19792e14			0.803081			0.401540	+	0.915841i	$0.368475\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−5.07484e12	−	8.78989e12i	−0.00425686	−	0.00737309i
$552$		0			0
$553$	−8.91553e14	−	7.15696e14i	−0.733093	−	0.588491i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	5.08145e14	−	8.80133e14i	0.401591	−	0.695576i	−0.592327	−	0.805698i	$-0.701791\pi$
$557$	5.08145e14	−	8.80133e14i	0.401591	−	0.695576i	0.993918	+	0.110121i	$0.0351239\pi$
$558$		0			0
$559$	2.37992e15			1.84415
$560$		0			0
$561$		0			0
$562$		0			0
$563$	6.05790e14	−	1.04926e15i	0.451363	−	0.781784i	−0.547108	−	0.837062i	$-0.684271\pi$
$563$	6.05790e14	−	1.04926e15i	0.451363	−	0.781784i	0.998471	+	0.0552782i	$0.0176046\pi$
$564$		0			0
$565$	1.47219e15	+	2.54990e15i	1.07571	+	1.86319i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	7.24341e14	+	1.25460e15i	0.509126	+	0.881833i	0.999944	+	0.0105706i	$0.00336477\pi$
$569$	7.24341e14	+	1.25460e15i	0.509126	+	0.881833i	−0.490818	+	0.871262i	$0.663302\pi$
$570$		0			0
$571$	−2.13063e14	+	3.69036e14i	−0.146896	+	0.254431i	−0.930079	−	0.367360i	$-0.880262\pi$
$571$	−2.13063e14	+	3.69036e14i	−0.146896	+	0.254431i	0.783183	+	0.621792i	$0.213595\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−4.78676e15			−3.17591
$576$		0			0
$577$	2.04431e14	−	3.54086e14i	0.133070	−	0.230484i	−0.791788	−	0.610795i	$-0.790850\pi$
$577$	2.04431e14	−	3.54086e14i	0.133070	−	0.230484i	0.924859	+	0.380311i	$0.124183\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−5.64751e14	+	2.19554e14i	−0.353907	+	0.137586i
$582$		0			0
$583$	−5.76077e14	−	9.97795e14i	−0.354245	−	0.613570i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	7.59585e14			0.449849			0.224925	−	0.974376i	$-0.427786\pi$
$587$	7.59585e14			0.449849			0.224925	+	0.974376i	$0.427786\pi$
$588$		0			0
$589$	3.83196e15			2.22734
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−1.64766e15	−	2.85384e15i	−0.922715	−	1.59819i	−0.795196	−	0.606353i	$-0.792632\pi$
$593$	−1.64766e15	−	2.85384e15i	−0.922715	−	1.59819i	−0.127519	−	0.991836i	$-0.540701\pi$
$594$		0			0
$595$	−1.42678e15	+	5.54676e14i	−0.784354	+	0.304927i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−1.26409e15	+	2.18947e15i	−0.669777	+	1.16009i	0.308189	+	0.951325i	$0.400277\pi$
$599$	−1.26409e15	+	2.18947e15i	−0.669777	+	1.16009i	−0.977966	+	0.208763i	$0.933056\pi$
$600$		0			0
$601$	1.40595e15			0.731410			0.365705	−	0.930731i	$-0.380828\pi$
$601$	1.40595e15			0.731410			0.365705	+	0.930731i	$0.380828\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	2.95182e15	−	5.11270e15i	1.48059	−	2.56446i
$606$		0			0
$607$	−1.31451e15	−	2.27680e15i	−0.647480	−	1.12147i	−0.983723	−	0.179694i	$-0.942489\pi$
$607$	−1.31451e15	−	2.27680e15i	−0.647480	−	1.12147i	0.336242	−	0.941776i	$-0.390844\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−8.50361e14	−	1.47287e15i	−0.403995	−	0.699741i
$612$		0			0
$613$	−2.36386e14	+	4.09433e14i	−0.110304	+	0.191051i	−0.915893	−	0.401423i	$-0.868516\pi$
$613$	−2.36386e14	+	4.09433e14i	−0.110304	+	0.191051i	0.805589	+	0.592475i	$0.201849\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−6.41641e14			−0.288884			−0.144442	−	0.989513i	$-0.546139\pi$
$617$	−6.41641e14			−0.288884			−0.144442	+	0.989513i	$0.546139\pi$
$618$		0			0
$619$	−1.06581e15	+	1.84603e15i	−0.471390	+	0.816471i	−0.999464	−	0.0327268i	$-0.989581\pi$
$619$	−1.06581e15	+	1.84603e15i	−0.471390	+	0.816471i	0.528074	+	0.849198i	$0.322914\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−3.59568e14	−	2.88643e14i	−0.153496	−	0.123219i
$624$		0			0
$625$	−4.26605e15	−	7.38902e15i	−1.78931	−	3.09918i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	5.06027e14			0.204925
$630$		0			0
$631$	−2.49076e15			−0.991219			−0.495609	−	0.868545i	$-0.665055\pi$
$631$	−2.49076e15			−0.991219			−0.495609	+	0.868545i	$0.665055\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	1.73003e15	+	2.99650e15i	0.664964	+	1.15175i
$636$		0			0
$637$	3.11018e15	−	2.84880e15i	1.17495	−	1.07621i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−1.64178e15	+	2.84365e15i	−0.599233	+	1.03790i	0.393701	+	0.919239i	$0.371195\pi$
$641$	−1.64178e15	+	2.84365e15i	−0.599233	+	1.03790i	−0.992934	+	0.118664i	$0.962139\pi$
$642$		0			0
$643$	1.94429e15			0.697592			0.348796	−	0.937199i	$-0.386591\pi$
$643$	1.94429e15			0.697592			0.348796	+	0.937199i	$0.386591\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	3.24795e14	−	5.62562e14i	0.112625	−	0.195073i	−0.804203	−	0.594355i	$-0.797407\pi$
$647$	3.24795e14	−	5.62562e14i	0.112625	−	0.195073i	0.916828	+	0.399282i	$0.130741\pi$
$648$		0			0
$649$	3.24716e14	+	5.62425e14i	0.110703	+	0.191743i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	1.92474e15	+	3.33375e15i	0.634380	+	1.09878i	0.986646	+	0.162879i	$0.0520779\pi$
$653$	1.92474e15	+	3.33375e15i	0.634380	+	1.09878i	−0.352266	+	0.935900i	$0.614589\pi$
$654$		0			0
$655$	−2.95476e15	+	5.11779e15i	−0.957623	+	1.65865i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−1.40489e15			−0.440324			−0.220162	−	0.975463i	$-0.570659\pi$
$659$	−1.40489e15			−0.440324			−0.220162	+	0.975463i	$0.570659\pi$
$660$		0			0
$661$	−1.55113e15	+	2.68663e15i	−0.478123	+	0.828134i	−0.999685	−	0.0250796i	$-0.992016\pi$
$661$	−1.55113e15	+	2.68663e15i	−0.478123	+	0.828134i	0.521562	+	0.853213i	$0.325349\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−1.61490e15	+	1.04851e16i	−0.481533	+	3.12647i
$666$		0			0
$667$	−1.03874e13	−	1.79915e13i	−0.00304659	−	0.00527684i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−3.47390e15			−0.985924
$672$		0			0
$673$	−4.65798e15			−1.30051			−0.650256	−	0.759715i	$-0.725338\pi$
$673$	−4.65798e15			−1.30051			−0.650256	+	0.759715i	$0.725338\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	1.70181e15	+	2.94763e15i	0.459912	+	0.796590i	0.998956	−	0.0456873i	$-0.0145478\pi$
$677$	1.70181e15	+	2.94763e15i	0.459912	+	0.796590i	−0.539044	+	0.842277i	$0.681214\pi$
$678$		0			0
$679$	−4.74640e15	+	1.84522e15i	−1.26206	+	0.490642i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−8.52660e14	+	1.47685e15i	−0.219514	+	0.380209i	−0.954659	−	0.297700i	$-0.903780\pi$
$683$	−8.52660e14	+	1.47685e15i	−0.219514	+	0.380209i	0.735146	+	0.677909i	$0.237114\pi$
$684$		0			0
$685$	6.76946e15			1.71497
$686$		0			0
$687$		0			0
$688$		0			0
$689$	1.44345e15	−	2.50013e15i	0.354157	−	0.613419i
$690$		0			0
$691$	2.28018e15	+	3.94939e15i	0.550606	+	0.953677i	0.998231	+	0.0594557i	$0.0189365\pi$
$691$	2.28018e15	+	3.94939e15i	0.550606	+	0.953677i	−0.447625	+	0.894221i	$0.647730\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	1.29797e15	+	2.24814e15i	0.303632	+	0.525905i
$696$		0			0
$697$	−3.48884e14	+	6.04284e14i	−0.0803341	+	0.139143i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	2.93440e15			0.654741			0.327371	−	0.944896i	$-0.393837\pi$
$701$	2.93440e15			0.654741			0.327371	+	0.944896i	$0.393837\pi$
$702$		0			0
$703$	1.75343e15	−	3.03703e15i	0.385154	−	0.667106i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−1.69671e14	+	1.10163e15i	−0.0361245	+	0.234547i
$708$		0			0
$709$	−1.47790e15	−	2.55980e15i	−0.309807	−	0.536601i	0.668513	−	0.743700i	$-0.266931\pi$
$709$	−1.47790e15	−	2.55980e15i	−0.309807	−	0.536601i	−0.978320	+	0.207099i	$0.933598\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	7.84339e15			1.59408
$714$		0			0
$715$	2.43981e16			4.88284
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−1.47695e15	−	2.55816e15i	−0.286654	−	0.496499i	0.686355	−	0.727266i	$-0.259210\pi$
$719$	−1.47695e15	−	2.55816e15i	−0.286654	−	0.496499i	−0.973009	+	0.230768i	$0.925876\pi$
$720$		0			0
$721$	−2.70661e15	−	2.17273e15i	−0.517347	−	0.415301i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	3.76443e13	−	6.52019e13i	0.00697976	−	0.0120893i
$726$		0			0
$727$	−5.57462e15			−1.01807			−0.509033	−	0.860747i	$-0.669997\pi$
$727$	−5.57462e15			−1.01807			−0.509033	+	0.860747i	$0.669997\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−1.42932e15	+	2.47566e15i	−0.253271	+	0.438678i
$732$		0			0
$733$	−4.84328e15	−	8.38880e15i	−0.845410	−	1.46429i	−0.885264	−	0.465088i	$-0.846023\pi$
$733$	−4.84328e15	−	8.38880e15i	−0.845410	−	1.46429i	0.0398541	−	0.999206i	$-0.487311\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−9.26061e14	−	1.60399e15i	−0.156880	−	0.271725i
$738$		0			0
$739$	−9.18308e14	+	1.59056e15i	−0.153265	+	0.265463i	−0.932426	−	0.361361i	$-0.882312\pi$
$739$	−9.18308e14	+	1.59056e15i	−0.153265	+	0.265463i	0.779161	+	0.626824i	$0.215646\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−5.66724e13			−0.00918191			−0.00459095	−	0.999989i	$-0.501461\pi$
$743$	−5.66724e13			−0.00918191			−0.00459095	+	0.999989i	$0.501461\pi$
$744$		0			0
$745$	4.70646e14	−	8.15182e14i	0.0751337	−	0.130135i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	7.95502e15	+	6.38590e15i	1.23308	+	0.989856i
$750$		0			0
$751$	8.39714e14	+	1.45443e15i	0.128266	+	0.222163i	0.923005	−	0.384788i	$-0.125726\pi$
$751$	8.39714e14	+	1.45443e15i	0.128266	+	0.222163i	−0.794739	+	0.606952i	$0.792392\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	1.42337e16			2.11159
$756$		0			0
$757$	5.82897e15			0.852245			0.426122	−	0.904666i	$-0.359879\pi$
$757$	5.82897e15			0.852245			0.426122	+	0.904666i	$0.359879\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−3.73179e15	−	6.46364e15i	−0.530031	−	0.918041i	−0.999386	−	0.0350311i	$-0.988847\pi$
$761$	−3.73179e15	−	6.46364e15i	−0.530031	−	0.918041i	0.469355	−	0.883009i	$-0.344486\pi$
$762$		0			0
$763$	1.41632e15	−	9.19582e15i	0.198279	−	1.28738i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−8.13627e14	+	1.40924e15i	−0.110675	+	0.191695i
$768$		0			0
$769$	4.93564e15			0.661833			0.330917	−	0.943660i	$-0.392642\pi$
$769$	4.93564e15			0.661833			0.330917	+	0.943660i	$0.392642\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−3.32146e15	+	5.75293e15i	−0.432854	+	0.749725i	−0.997118	−	0.0758695i	$-0.975827\pi$
$773$	−3.32146e15	+	5.75293e15i	−0.432854	+	0.749725i	0.564264	+	0.825595i	$0.309160\pi$
$774$		0			0
$775$	1.42124e16	+	2.46166e16i	1.82603	+	3.16278i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	2.41783e15	+	4.18780e15i	0.301974	+	0.523034i
$780$		0			0
$781$	−7.77458e15	+	1.34660e16i	−0.957407	+	1.65828i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−6.17305e15			−0.739123
$786$		0			0
$787$	3.38350e15	−	5.86039e15i	0.399489	−	0.691935i	−0.594174	−	0.804337i	$-0.702521\pi$
$787$	3.38350e15	−	5.86039e15i	0.399489	−	0.691935i	0.993663	+	0.112401i	$0.0358542\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	9.08206e15	−	3.53076e15i	1.04283	−	0.405413i
$792$		0			0
$793$	−4.35220e15	−	7.53822e15i	−0.492840	−	0.853624i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	1.32772e16			1.46246			0.731232	−	0.682129i	$-0.238946\pi$
$797$	1.32772e16			1.46246			0.731232	+	0.682129i	$0.238946\pi$
$798$		0			0
$799$	2.04283e15			0.221935
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−8.79627e15	−	1.52356e16i	−0.929743	−	1.61036i
$804$		0			0
$805$	−3.30543e15	+	2.14613e16i	−0.344628	+	2.23758i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	3.65847e15	−	6.33665e15i	0.371178	−	0.642900i	−0.618569	−	0.785731i	$-0.712287\pi$
$809$	3.65847e15	−	6.33665e15i	0.371178	−	0.642900i	0.989747	+	0.142831i	$0.0456206\pi$
$810$		0			0
$811$	−8.29518e15			−0.830254			−0.415127	−	0.909763i	$-0.636263\pi$
$811$	−8.29518e15			−0.830254			−0.415127	+	0.909763i	$0.636263\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	1.91990e15	−	3.32537e15i	0.187030	−	0.323946i
$816$		0			0
$817$	9.90549e15	+	1.71568e16i	0.952039	+	1.64898i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	5.14344e14	+	8.90870e14i	0.0481245	+	0.0833541i	0.889084	−	0.457744i	$-0.151342\pi$
$821$	5.14344e14	+	8.90870e14i	0.0481245	+	0.0833541i	−0.840960	+	0.541098i	$0.818009\pi$
$822$		0			0
$823$	−5.29428e15	+	9.16996e15i	−0.488774	+	0.846581i	−0.999917	−	0.0129147i	$-0.995889\pi$
$823$	−5.29428e15	+	9.16996e15i	−0.488774	+	0.846581i	0.511143	+	0.859496i	$0.329222\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	5.40430e15			0.485802			0.242901	−	0.970051i	$-0.421901\pi$
$827$	5.40430e15			0.485802			0.242901	+	0.970051i	$0.421901\pi$
$828$		0			0
$829$	−6.56988e15	+	1.13794e16i	−0.582784	+	1.00941i	0.412364	+	0.911019i	$0.364703\pi$
$829$	−6.56988e15	+	1.13794e16i	−0.582784	+	1.00941i	−0.995148	+	0.0983919i	$0.968630\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	1.09550e15	+	4.94624e15i	0.0946382	+	0.427295i
$834$		0			0
$835$	−9.91082e15	−	1.71660e16i	−0.844956	−	1.46351i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−1.43166e16			−1.18891			−0.594455	−	0.804129i	$-0.702632\pi$
$839$	−1.43166e16			−1.18891			−0.594455	+	0.804129i	$0.702632\pi$
$840$		0			0
$841$	−1.22002e16			−0.999973
$842$		0			0
$843$		0			0
$844$		0			0
$845$	1.85264e16	+	3.20887e16i	1.47938	+	2.56236i
$846$		0			0
$847$	−1.52359e16	−	1.22307e16i	−1.20091	−	0.964033i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	3.58898e15	−	6.21630e15i	0.275651	−	0.477441i
$852$		0			0
$853$	1.17265e16			0.889098			0.444549	−	0.895755i	$-0.353364\pi$
$853$	1.17265e16			0.889098			0.444549	+	0.895755i	$0.353364\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	4.25484e15	−	7.36960e15i	0.314404	−	0.544564i	−0.664906	−	0.746927i	$-0.731529\pi$
$857$	4.25484e15	−	7.36960e15i	0.314404	−	0.544564i	0.979311	+	0.202362i	$0.0648619\pi$
$858$		0			0
$859$	−5.63364e15	−	9.75774e15i	−0.410985	−	0.711848i	0.584012	−	0.811745i	$-0.301482\pi$
$859$	−5.63364e15	−	9.75774e15i	−0.410985	−	0.711848i	−0.994998	+	0.0998972i	$0.968149\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	2.68765e15	+	4.65514e15i	0.191123	+	0.331035i	0.945623	−	0.325266i	$-0.105454\pi$
$863$	2.68765e15	+	4.65514e15i	0.191123	+	0.331035i	−0.754500	+	0.656300i	$0.772120\pi$
$864$		0			0
$865$	9.43890e15	−	1.63486e16i	0.662724	−	1.14787i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−2.18871e16			−1.49823
$870$		0			0
$871$	2.32039e15	−	4.01903e15i	0.156842	−	0.271657i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−4.61549e16	+	1.79433e16i	−3.04210	+	1.18265i
$876$		0			0
$877$	9.70359e15	+	1.68071e16i	0.631589	+	1.09394i	0.987227	+	0.159321i	$0.0509304\pi$
$877$	9.70359e15	+	1.68071e16i	0.631589	+	1.09394i	−0.355638	+	0.934624i	$0.615736\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	2.05160e16			1.30234			0.651171	−	0.758931i	$-0.274278\pi$
$881$	2.05160e16			1.30234			0.651171	+	0.758931i	$0.274278\pi$
$882$		0			0
$883$	−1.29505e16			−0.811903			−0.405951	−	0.913895i	$-0.633060\pi$
$883$	−1.29505e16			−0.811903			−0.405951	+	0.913895i	$0.633060\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	3.64435e15	+	6.31220e15i	0.222864	+	0.386012i	0.955676	−	0.294419i	$-0.0951261\pi$
$887$	3.64435e15	+	6.31220e15i	0.222864	+	0.386012i	−0.732812	+	0.680431i	$0.761793\pi$
$888$		0			0
$889$	1.06727e16	−	4.14916e15i	0.644638	−	0.250611i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	7.07860e15	−	1.22605e16i	0.417123	−	0.722479i
$894$		0			0
$895$	−3.38158e16			−1.96831
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−6.16825e13	+	1.06837e14i	−0.00350335	+	0.00606798i
$900$		0			0
$901$	1.73381e15	+	3.00305e15i	0.0972781	+	0.168491i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−2.08965e16	−	3.61939e16i	−1.14421	−	1.98184i
$906$		0			0
$907$	6.98204e15	−	1.20933e16i	0.377696	−	0.654189i	−0.613031	−	0.790059i	$-0.710050\pi$
$907$	6.98204e15	−	1.20933e16i	0.377696	−	0.654189i	0.990727	+	0.135871i	$0.0433831\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	1.74544e16			0.921623			0.460812	−	0.887498i	$-0.347558\pi$
$911$	1.74544e16			0.921623			0.460812	+	0.887498i	$0.347558\pi$
$912$		0			0
$913$	−5.79998e15	+	1.00459e16i	−0.302578	+	0.524080i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	1.52511e16	+	1.22429e16i	0.776731	+	0.623522i
$918$		0			0
$919$	−9.96055e15	−	1.72522e16i	−0.501242	−	0.868177i	−0.999999	−	0.00143523i	$-0.999543\pi$
$919$	−9.96055e15	−	1.72522e16i	−0.501242	−	0.868177i	0.498757	−	0.866742i	$-0.333790\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−3.89608e16			−1.91434
$924$		0			0
$925$	2.60133e16			1.26304
$926$		0			0
$927$		0			0
$928$		0			0
$929$	3.73858e15	+	6.47541e15i	0.177264	+	0.307030i	0.940942	−	0.338567i	$-0.109942\pi$
$929$	3.73858e15	+	6.47541e15i	0.177264	+	0.307030i	−0.763679	+	0.645597i	$0.776609\pi$
$930$		0			0
$931$	3.34820e16	+	1.05643e16i	1.56887	+	0.495013i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−1.46529e16	+	2.53796e16i	−0.670596	+	1.16151i
$936$		0			0
$937$	2.31704e16			1.04801			0.524006	−	0.851715i	$-0.324437\pi$
$937$	2.31704e16			1.04801			0.524006	+	0.851715i	$0.324437\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	6.48966e15	−	1.12404e16i	0.286734	−	0.496638i	−0.686294	−	0.727324i	$-0.740764\pi$
$941$	6.48966e15	−	1.12404e16i	0.286734	−	0.496638i	0.973028	+	0.230686i	$0.0740971\pi$
$942$		0			0
$943$	4.94890e15	+	8.57174e15i	0.216120	+	0.374330i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	1.37270e16	+	2.37759e16i	0.585667	+	1.01440i	0.994792	+	0.101926i	$0.0325006\pi$
$947$	1.37270e16	+	2.37759e16i	0.585667	+	1.01440i	−0.409125	+	0.912478i	$0.634166\pi$
$948$		0			0
$949$	2.20404e16	−	3.81751e16i	0.929513	−	1.60996i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	4.34657e15			0.179117			0.0895583	−	0.995982i	$-0.471454\pi$
$953$	4.34657e15			0.179117			0.0895583	+	0.995982i	$0.471454\pi$
$954$		0			0
$955$	−7.56592e15	+	1.31046e16i	−0.308208	+	0.533831i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	3.41028e15	−	2.21421e16i	0.135765	−	0.881487i
$960$		0			0
$961$	−1.05836e16	−	1.83314e16i	−0.416540	−	0.721469i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−2.90604e16			−1.11790
$966$		0			0
$967$	−4.78536e15			−0.181999			−0.0909995	−	0.995851i	$-0.529006\pi$
$967$	−4.78536e15			−0.181999			−0.0909995	+	0.995851i	$0.529006\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−3.79192e15	−	6.56779e15i	−0.140978	−	0.244182i	0.786887	−	0.617097i	$-0.211692\pi$
$971$	−3.79192e15	−	6.56779e15i	−0.140978	−	0.244182i	−0.927865	+	0.372915i	$0.878358\pi$
$972$		0			0
$973$	8.00729e15	−	3.11293e15i	0.294350	−	0.114432i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	1.61885e16	−	2.80392e16i	0.581816	−	1.00773i	−0.413448	−	0.910528i	$-0.635676\pi$
$977$	1.61885e16	−	2.80392e16i	0.581816	−	1.00773i	0.995264	−	0.0972072i	$-0.0309909\pi$
$978$		0			0
$979$	−8.82717e15			−0.313701
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−4.83330e15	+	8.37152e15i	−0.167957	+	0.290911i	−0.937702	−	0.347442i	$-0.887050\pi$
$983$	−4.83330e15	+	8.37152e15i	−0.167957	+	0.290911i	0.769744	+	0.638353i	$0.220384\pi$
$984$		0			0
$985$	−4.04996e16	−	7.01473e16i	−1.39172	−	2.41053i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	2.02749e16	+	3.51172e16i	0.681364	+	1.18016i
$990$		0			0
$991$	2.36964e16	−	4.10434e16i	0.787549	−	1.36407i	−0.139916	−	0.990163i	$-0.544683\pi$
$991$	2.36964e16	−	4.10434e16i	0.787549	−	1.36407i	0.927465	−	0.373911i	$-0.121984\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−3.84619e16			−1.25027
$996$		0			0
$997$	−4.37128e15	+	7.57128e15i	−0.140535	+	0.243414i	−0.927698	−	0.373331i	$-0.878216\pi$
$997$	−4.37128e15	+	7.57128e15i	−0.140535	+	0.243414i	0.787163	+	0.616745i	$0.211549\pi$
$998$		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.109.8		16
3.2	odd	2		84.12.i.b.25.1	✓	16
7.2	even	3	inner	252.12.k.d.37.8		16
21.2	odd	6		84.12.i.b.37.1	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.12.i.b.25.1	✓	16	3.2	odd	2
84.12.i.b.37.1	yes	16	21.2	odd	6
252.12.k.d.37.8		16	7.2	even	3	inner
252.12.k.d.109.8		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)

\(f(q)\)	\(=\)	\(q+(6718.22 + 11636.3i) q^{5} +(41445.4 - 16112.4i) q^{7} +O(q^{10})\)	\(q+(6718.22 + 11636.3i) q^{5} +(41445.4 - 16112.4i) q^{7} +(425643. - 737235. i) q^{11} +2.13303e6 q^{13} +(-1.28105e6 + 2.21884e6i) q^{17} +(8.87791e6 + 1.53770e7i) q^{19} +(1.81716e7 + 3.14742e7i) q^{23} +(-6.58548e7 + 1.14064e8i) q^{25} -571626. q^{29} +(1.07907e8 - 1.86901e8i) q^{31} +(4.65927e8 + 3.74024e8i) q^{35} +(-9.87524e7 - 1.71044e8i) q^{37} +2.72342e8 q^{41} +1.11575e9 q^{43} +(-3.98664e8 - 6.90506e8i) q^{47} +(1.45811e9 - 1.33557e9i) q^{49} +(6.76715e8 - 1.17210e9i) q^{53} +1.14382e10 q^{55} +(-3.81442e8 + 6.60677e8i) q^{59} +(-2.04039e9 - 3.53405e9i) q^{61} +(1.43301e10 + 2.48205e10i) q^{65} +(1.08784e9 - 1.88419e9i) q^{67} -1.82655e10 q^{71} +(1.03329e10 - 1.78972e10i) q^{73} +(5.76230e9 - 3.74131e10i) q^{77} +(-1.28553e10 - 2.22661e10i) q^{79} -1.36264e10 q^{83} -3.44255e10 q^{85} +(-5.18461e9 - 8.98001e9i) q^{89} +(8.84041e10 - 3.43682e10i) q^{91} +(-1.19287e11 + 2.06612e11i) q^{95} -1.14522e11 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2156 q^{5} + 50512 q^{7}+O(q^{10}) \) 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

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more