LMFDB - Embedded newform 252.9.z.d.145.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("252.73");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	252.z (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$102.659409735$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 148097 x^{10} + 46071824 x^{9} + 21578502553 x^{8} + 3561445462121 x^{7} + \cdots + 45\!\cdots\!96 $ x^12 - 3x^11 + 148097x^10 + 46071824x^9 + 21578502553x^8 + 3561445462121x^7 + 576413321817541x^6 + 47217566733462528x^5 + 5214056955297543333x^4 + 358752845334081085965x^3 + 30962072851910211245661x^2 + 1221542968331193193318500*x + 45396580558961892385326096
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{20}\cdot 3^{10}\cdot 7^{4} $
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			145.1
Root			$-41.5970 - 72.0480i$ of defining polynomial
Character	$\chi$	$=$	252.145
Dual form			252.9.z.d.73.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1011.88 - 584.207i) q^{5} +(-1829.74 - 1554.62i) q^{7} +O(q^{10})$	$q+(-1011.88 - 584.207i) q^{5} +(-1829.74 - 1554.62i) q^{7} +(13077.9 + 22651.7i) q^{11} -28593.8i q^{13} +(18015.1 - 10401.0i) q^{17} +(42991.6 + 24821.2i) q^{19} +(-170925. + 296051. i) q^{23} +(487282. + 843998. i) q^{25} +1.12659e6 q^{29} +(1.47519e6 - 851702. i) q^{31} +(943251. + 2.64203e6i) q^{35} +(320285. - 554750. i) q^{37} +1.34661e6i q^{41} -1.80008e6 q^{43} +(-7.88787e6 - 4.55406e6i) q^{47} +(931110. + 5.68911e6i) q^{49} +(1.82943e6 + 3.16867e6i) q^{53} -3.05609e7i q^{55} +(-9.97907e6 + 5.76142e6i) q^{59} +(-8.77419e6 - 5.06578e6i) q^{61} +(-1.67047e7 + 2.89334e7i) q^{65} +(-8.86768e6 - 1.53593e7i) q^{67} +3.79392e7 q^{71} +(2.94841e7 - 1.70227e7i) q^{73} +(1.12855e7 - 6.17779e7i) q^{77} +(-9.66395e6 + 1.67384e7i) q^{79} +960779. i q^{83} -2.43053e7 q^{85} +(-5.62273e7 - 3.24629e7i) q^{89} +(-4.44525e7 + 5.23193e7i) q^{91} +(-2.90015e7 - 5.02320e7i) q^{95} +2.66661e7i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 285 q^{5} + 198 q^{7}+O(q^{10}) $ 12 * q - 285 * q^5 + 198 * q^7	$ 12 q - 285 q^{5} + 198 q^{7} + 17919 q^{11} + 205782 q^{17} + 74313 q^{19} + 62832 q^{23} + 878679 q^{25} + 575454 q^{29} + 1442952 q^{31} + 3989514 q^{35} - 2058621 q^{37} + 7721322 q^{43} - 12088194 q^{47} - 16964694 q^{49} + 5506743 q^{53} - 7511901 q^{59} - 37215576 q^{61} - 5047122 q^{65} - 36824553 q^{67} + 30011556 q^{71} + 95080185 q^{73} + 38333727 q^{77} + 8514456 q^{79} + 20121540 q^{85} - 83038554 q^{89} - 198538635 q^{91} + 221605224 q^{95}+O(q^{100}) $ 12 * q - 285 * q^5 + 198 * q^7 + 17919 * q^11 + 205782 * q^17 + 74313 * q^19 + 62832 * q^23 + 878679 * q^25 + 575454 * q^29 + 1442952 * q^31 + 3989514 * q^35 - 2058621 * q^37 + 7721322 * q^43 - 12088194 * q^47 - 16964694 * q^49 + 5506743 * q^53 - 7511901 * q^59 - 37215576 * q^61 - 5047122 * q^65 - 36824553 * q^67 + 30011556 * q^71 + 95080185 * q^73 + 38333727 * q^77 + 8514456 * q^79 + 20121540 * q^85 - 83038554 * q^89 - 198538635 * q^91 + 221605224 * q^95

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$73$	$127$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−1011.88	−	584.207i	−1.61900	−	0.934731i	−0.987179	−	0.159617i	$-0.948974\pi$
$5$	−1011.88	−	584.207i	−1.61900	−	0.934731i	−0.631822	−	0.775114i	$-0.717693\pi$
$6$		0			0
$7$	−1829.74	−	1554.62i	−0.762075	−	0.647489i
$7$	−1829.74	−	1554.62i	−0.762075	−	0.647489i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	13077.9	+	22651.7i	0.893241	+	1.54714i	0.835967	+	0.548780i	$0.184907\pi$
$11$	13077.9	+	22651.7i	0.893241	+	1.54714i	0.0572739	+	0.998359i	$0.481759\pi$
$12$		0			0
$13$		−	28593.8i		−	1.00115i	−0.865694	−	0.500574i	$-0.833122\pi$
$13$		−	28593.8i		−	1.00115i	0.865694	−	0.500574i	$-0.166878\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	18015.1	−	10401.0i	0.215695	−	0.124532i	−0.388260	−	0.921550i	$-0.626924\pi$
$17$	18015.1	−	10401.0i	0.215695	−	0.124532i	0.603955	+	0.797018i	$0.293591\pi$
$18$		0			0
$19$	42991.6	+	24821.2i	0.329890	+	0.190462i	0.655792	−	0.754941i	$-0.272335\pi$
$19$	42991.6	+	24821.2i	0.329890	+	0.190462i	−0.325902	+	0.945404i	$0.605668\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−170925.	+	296051.i	−0.610794	+	1.05793i	0.380313	+	0.924858i	$0.375816\pi$
$23$	−170925.	+	296051.i	−0.610794	+	1.05793i	−0.991107	+	0.133068i	$0.957517\pi$
$24$		0			0
$25$	487282.	+	843998.i	1.24744	+	2.16063i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	1.12659e6			1.59284			0.796422	−	0.604741i	$-0.206723\pi$
$29$	1.12659e6			1.59284			0.796422	+	0.604741i	$0.206723\pi$
$30$		0			0
$31$	1.47519e6	−	851702.i	1.59735	−	0.922233i	0.605360	−	0.795951i	$-0.293029\pi$
$31$	1.47519e6	−	851702.i	1.59735	−	0.922233i	0.991994	−	0.126282i	$-0.0403044\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	943251.	+	2.64203e6i	0.628572	+	1.76062i
$36$		0			0
$37$	320285.	−	554750.i	0.170895	−	0.295999i	−0.767838	−	0.640644i	$-0.778667\pi$
$37$	320285.	−	554750.i	0.170895	−	0.295999i	0.938733	+	0.344645i	$0.112001\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$			1.34661e6i			0.476549i	0.971198	+	0.238275i	$0.0765818\pi$
$41$			1.34661e6i			0.476549i	−0.971198	+	0.238275i	$0.923418\pi$
$42$		0			0
$43$	−1.80008e6			−0.526524			−0.263262	−	0.964724i	$-0.584798\pi$
$43$	−1.80008e6			−0.526524			−0.263262	+	0.964724i	$0.584798\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−7.88787e6	−	4.55406e6i	−1.61647	−	0.933270i	−0.987823	−	0.155581i	$-0.950275\pi$
$47$	−7.88787e6	−	4.55406e6i	−1.61647	−	0.933270i	−0.628648	−	0.777690i	$-0.716392\pi$
$48$		0			0
$49$	931110.	+	5.68911e6i	0.161516	+	0.986870i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	1.82943e6	+	3.16867e6i	0.231853	+	0.401582i	0.958354	−	0.285584i	$-0.0921877\pi$
$53$	1.82943e6	+	3.16867e6i	0.231853	+	0.401582i	−0.726500	+	0.687166i	$0.758854\pi$
$54$		0			0
$55$		−	3.05609e7i		−	3.33976i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−9.97907e6	+	5.76142e6i	−0.823535	+	0.475468i	−0.851634	−	0.524137i	$-0.824388\pi$
$59$	−9.97907e6	+	5.76142e6i	−0.823535	+	0.475468i	0.0280988	+	0.999605i	$0.491055\pi$
$60$		0			0
$61$	−8.77419e6	−	5.06578e6i	−0.633706	−	0.365870i	0.148480	−	0.988915i	$-0.452562\pi$
$61$	−8.77419e6	−	5.06578e6i	−0.633706	−	0.365870i	−0.782186	+	0.623045i	$0.785895\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−1.67047e7	+	2.89334e7i	−0.935804	+	1.62086i
$66$		0			0
$67$	−8.86768e6	−	1.53593e7i	−0.440059	−	0.762205i	0.557634	−	0.830087i	$-0.311709\pi$
$67$	−8.86768e6	−	1.53593e7i	−0.440059	−	0.762205i	−0.997693	+	0.0678821i	$0.978376\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	3.79392e7			1.49298			0.746491	−	0.665396i	$-0.231737\pi$
$71$	3.79392e7			1.49298			0.746491	+	0.665396i	$0.231737\pi$
$72$		0			0
$73$	2.94841e7	−	1.70227e7i	1.03824	−	0.599426i	0.118903	−	0.992906i	$-0.462062\pi$
$73$	2.94841e7	−	1.70227e7i	1.03824	−	0.599426i	0.919333	+	0.393480i	$0.128729\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	1.12855e7	−	6.17779e7i	0.321038	−	1.75740i
$78$		0			0
$79$	−9.66395e6	+	1.67384e7i	−0.248111	+	0.429741i	−0.963002	−	0.269495i	$-0.913143\pi$
$79$	−9.66395e6	+	1.67384e7i	−0.248111	+	0.429741i	0.714891	+	0.699236i	$0.246476\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$			960779.i			0.0202447i	0.999949	+	0.0101223i	$0.00322210\pi$
$83$			960779.i			0.0202447i	−0.999949	+	0.0101223i	$0.996778\pi$
$84$		0			0
$85$	−2.43053e7			−0.465614
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−5.62273e7	−	3.24629e7i	−0.896164	−	0.517400i	−0.0202100	−	0.999796i	$-0.506433\pi$
$89$	−5.62273e7	−	3.24629e7i	−0.896164	−	0.517400i	−0.875954	+	0.482395i	$0.839767\pi$
$90$		0			0
$91$	−4.44525e7	+	5.23193e7i	−0.648233	+	0.762950i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−2.90015e7	−	5.02320e7i	−0.356062	−	0.616717i
$96$		0			0
$97$			2.66661e7i			0.301213i	0.988594	+	0.150606i	$0.0481226\pi$
$97$			2.66661e7i			0.301213i	−0.988594	+	0.150606i	$0.951877\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−6.33466e6	+	3.65732e6i	−0.0608749	+	0.0351461i	−0.530129	−	0.847917i	$-0.677856\pi$
$101$	−6.33466e6	+	3.65732e6i	−0.0608749	+	0.0351461i	0.469254	+	0.883063i	$0.344523\pi$
$102$		0			0
$103$	2.35283e7	+	1.35841e7i	0.209046	+	0.120693i	0.600868	−	0.799348i	$-0.294822\pi$
$103$	2.35283e7	+	1.35841e7i	0.209046	+	0.120693i	−0.391822	+	0.920041i	$0.628155\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	6.81604e7	−	1.18057e8i	0.519992	−	0.900653i	−0.479737	−	0.877412i	$-0.659268\pi$
$107$	6.81604e7	−	1.18057e8i	0.519992	−	0.900653i	0.999730	−	0.0232412i	$-0.00739857\pi$
$108$		0			0
$109$	4.81540e7	+	8.34051e7i	0.341135	+	0.590863i	0.984644	−	0.174576i	$-0.0558554\pi$
$109$	4.81540e7	+	8.34051e7i	0.341135	+	0.590863i	−0.643509	+	0.765439i	$0.722522\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	8.83287e7			0.541737			0.270868	−	0.962616i	$-0.412689\pi$
$113$	8.83287e7			0.541737			0.270868	+	0.962616i	$0.412689\pi$
$114$		0			0
$115$	3.45910e8	−	1.99711e8i	1.97775	−	1.14185i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−4.91325e7	−	8.97544e6i	−0.245009	−	0.0447577i
$120$		0			0
$121$	−2.34885e8	+	4.06834e8i	−1.09576	+	1.89791i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		−	6.82283e8i		−	2.79463i
$126$		0			0
$127$	−3.88706e7			−0.149419			−0.0747097	−	0.997205i	$-0.523803\pi$
$127$	−3.88706e7			−0.149419			−0.0747097	+	0.997205i	$0.523803\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−3.31013e8	−	1.91111e8i	−1.12398	−	0.648933i	−0.181570	−	0.983378i	$-0.558118\pi$
$131$	−3.31013e8	−	1.91111e8i	−1.12398	−	0.648933i	−0.942415	+	0.334445i	$0.891451\pi$
$132$		0			0
$133$	−4.00760e7	−	1.12252e8i	−0.128079	−	0.358747i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	2.14124e7	+	3.70873e7i	0.0607831	+	0.105279i	0.894816	−	0.446436i	$-0.147307\pi$
$137$	2.14124e7	+	3.70873e7i	0.0607831	+	0.105279i	−0.834033	+	0.551715i	$0.813974\pi$
$138$		0			0
$139$		−	1.51148e8i		−	0.404896i	−0.979293	−	0.202448i	$-0.935110\pi$
$139$		−	1.51148e8i		−	0.404896i	0.979293	−	0.202448i	$-0.0648897\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	6.47697e8	−	3.73948e8i	1.54892	−	0.894267i
$144$		0			0
$145$	−1.13997e9	−	6.58161e8i	−2.57882	−	1.48888i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−1.30228e8	+	2.25561e8i	−0.264215	+	0.457634i	−0.967358	−	0.253415i	$-0.918446\pi$
$149$	−1.30228e8	+	2.25561e8i	−0.264215	+	0.457634i	0.703143	+	0.711049i	$0.251780\pi$
$150$		0			0
$151$	−2.43650e8	−	4.22014e8i	−0.468661	−	0.811744i	0.530698	−	0.847561i	$-0.321930\pi$
$151$	−2.43650e8	−	4.22014e8i	−0.468661	−	0.811744i	−0.999358	+	0.0358171i	$0.988597\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−1.99028e9			−3.44816
$156$		0			0
$157$	2.17705e8	−	1.25692e8i	0.358318	−	0.206875i	−0.310024	−	0.950729i	$-0.600337\pi$
$157$	2.17705e8	−	1.25692e8i	0.358318	−	0.206875i	0.668343	+	0.743853i	$0.267004\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	7.72996e8	−	2.75973e8i	1.15047	−	0.410736i
$162$		0			0
$163$	4.84569e8	−	8.39298e8i	0.686444	−	1.18896i	−0.286536	−	0.958069i	$-0.592504\pi$
$163$	4.84569e8	−	8.39298e8i	0.686444	−	1.18896i	0.972981	−	0.230887i	$-0.0741627\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		−	4.87973e8i		−	0.627378i	−0.949526	−	0.313689i	$-0.898435\pi$
$167$		−	4.87973e8i		−	0.627378i	0.949526	−	0.313689i	$-0.101565\pi$
$168$		0			0
$169$	−1.87509e6			−0.00229867
$170$		0			0
$171$		0			0
$172$		0			0
$173$	6.43728e7	+	3.71657e7i	0.0718651	+	0.0414914i	0.535502	−	0.844534i	$-0.320122\pi$
$173$	6.43728e7	+	3.71657e7i	0.0718651	+	0.0414914i	−0.463637	+	0.886025i	$0.653456\pi$
$174$		0			0
$175$	4.20496e8	−	2.30184e9i	0.448342	−	2.45427i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−2.17987e8	−	3.77565e8i	−0.212334	−	0.367773i	0.740111	−	0.672485i	$-0.234773\pi$
$179$	−2.17987e8	−	3.77565e8i	−0.212334	−	0.367773i	−0.952444	+	0.304712i	$0.901440\pi$
$180$		0			0
$181$			1.22472e9i			1.14110i	0.821264	+	0.570548i	$0.193269\pi$
$181$			1.22472e9i			1.14110i	−0.821264	+	0.570548i	$0.806731\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−6.48177e8	+	3.74225e8i	−0.553359	+	0.319482i
$186$		0			0
$187$	4.71200e8	+	2.72047e8i	0.385335	+	0.222473i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	3.18497e8	−	5.51652e8i	0.239316	−	0.414507i	−0.721202	−	0.692724i	$-0.756410\pi$
$191$	3.18497e8	−	5.51652e8i	0.239316	−	0.414507i	0.960518	+	0.278217i	$0.0897436\pi$
$192$		0			0
$193$	8.35413e8	+	1.44698e9i	0.602105	+	1.04288i	0.992502	+	0.122229i	$0.0390043\pi$
$193$	8.35413e8	+	1.44698e9i	0.602105	+	1.04288i	−0.390397	+	0.920646i	$0.627662\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	4.97108e8			0.330055			0.165027	−	0.986289i	$-0.447229\pi$
$197$	4.97108e8			0.330055			0.165027	+	0.986289i	$0.447229\pi$
$198$		0			0
$199$	1.42581e9	−	8.23189e8i	0.909176	−	0.524913i	0.0290099	−	0.999579i	$-0.490765\pi$
$199$	1.42581e9	−	8.23189e8i	0.909176	−	0.524913i	0.880166	+	0.474666i	$0.157431\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−2.06137e9	−	1.75142e9i	−1.21387	−	1.03135i
$204$		0			0
$205$	7.86701e8	−	1.36261e9i	0.445445	−	0.771533i
$206$		0			0
$207$		0			0
$208$		0			0
$209$			1.29844e9i			0.680515i
$210$		0			0
$211$	−3.49413e9			−1.76283			−0.881413	−	0.472347i	$-0.843407\pi$
$211$	−3.49413e9			−1.76283			−0.881413	+	0.472347i	$0.843407\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	1.82146e9	+	1.05162e9i	0.852442	+	0.492158i
$216$		0			0
$217$	−4.02329e9	−	7.34968e8i	−1.81444	−	0.331459i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−2.97404e8	−	5.15119e8i	−0.124675	−	0.215943i
$222$		0			0
$223$			2.69455e8i			0.108960i	0.998515	+	0.0544799i	$0.0173501\pi$
$223$			2.69455e8i			0.108960i	−0.998515	+	0.0544799i	$0.982650\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	1.25301e9	−	7.23427e8i	0.471902	−	0.272453i	−0.245134	−	0.969489i	$-0.578832\pi$
$227$	1.25301e9	−	7.23427e8i	0.471902	−	0.272453i	0.717036	+	0.697037i	$0.245499\pi$
$228$		0			0
$229$	1.59604e8	+	9.21477e7i	0.0580367	+	0.0335075i	0.528738	−	0.848785i	$-0.322666\pi$
$229$	1.59604e8	+	9.21477e7i	0.0580367	+	0.0335075i	−0.470701	+	0.882293i	$0.655999\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	2.09346e9	−	3.62598e9i	0.710299	−	1.23027i	−0.254446	−	0.967087i	$-0.581893\pi$
$233$	2.09346e9	−	3.62598e9i	0.710299	−	1.23027i	0.964745	−	0.263186i	$-0.0847734\pi$
$234$		0			0
$235$	5.32103e9	+	9.21629e9i	1.74471	+	3.02193i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−2.19326e9			−0.672201			−0.336101	−	0.941826i	$-0.609108\pi$
$239$	−2.19326e9			−0.672201			−0.336101	+	0.941826i	$0.609108\pi$
$240$		0			0
$241$	4.71562e9	−	2.72256e9i	1.39788	−	0.807067i	0.403711	−	0.914887i	$-0.367720\pi$
$241$	4.71562e9	−	2.72256e9i	1.39788	−	0.807067i	0.994171	+	0.107819i	$0.0343868\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	2.38145e9	−	6.30063e9i	0.660963	−	1.74872i
$246$		0			0
$247$	7.09734e8	−	1.22929e9i	0.190681	−	0.330269i
$248$		0			0
$249$		0			0
$250$		0			0
$251$			1.90950e9i			0.481089i	0.970638	+	0.240544i	$0.0773260\pi$
$251$			1.90950e9i			0.481089i	−0.970638	+	0.240544i	$0.922674\pi$
$252$		0			0
$253$	−8.94139e9			−2.18234
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−3.63082e9	−	2.09626e9i	−0.832286	−	0.480521i	0.0223487	−	0.999750i	$-0.492886\pi$
$257$	−3.63082e9	−	2.09626e9i	−0.832286	−	0.480521i	−0.854635	+	0.519230i	$0.826219\pi$
$258$		0			0
$259$	−1.44846e9	+	5.17127e8i	−0.321891	+	0.114921i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−2.08663e9	−	3.61415e9i	−0.436136	−	0.755410i	0.561251	−	0.827645i	$-0.310320\pi$
$263$	−2.08663e9	−	3.61415e9i	−0.436136	−	0.755410i	−0.997388	+	0.0722352i	$0.976987\pi$
$264$		0			0
$265$		−	4.27507e9i		−	0.866882i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	6.02865e9	−	3.48064e9i	1.15136	−	0.664737i	0.202141	−	0.979356i	$-0.435210\pi$
$269$	6.02865e9	−	3.48064e9i	1.15136	−	0.664737i	0.949218	+	0.314619i	$0.101877\pi$
$270$		0			0
$271$	−5.31995e9	−	3.07148e9i	−0.986349	−	0.569469i	−0.0821681	−	0.996618i	$-0.526184\pi$
$271$	−5.31995e9	−	3.07148e9i	−0.986349	−	0.569469i	−0.904181	+	0.427150i	$0.859518\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−1.27453e10	+	2.20755e10i	−2.22853	+	3.85993i
$276$		0			0
$277$	−2.03712e8	−	3.52839e8i	−0.0346016	−	0.0599318i	0.848206	−	0.529666i	$-0.177683\pi$
$277$	−2.03712e8	−	3.52839e8i	−0.0346016	−	0.0599318i	−0.882808	+	0.469735i	$0.844350\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	1.61123e9			0.258423			0.129212	−	0.991617i	$-0.458755\pi$
$281$	1.61123e9			0.258423			0.129212	+	0.991617i	$0.458755\pi$
$282$		0			0
$283$	−5.30872e9	+	3.06499e9i	−0.827645	+	0.477841i	−0.853046	−	0.521836i	$-0.825247\pi$
$283$	−5.30872e9	+	3.06499e9i	−0.827645	+	0.477841i	0.0254009	+	0.999677i	$0.491914\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	2.09347e9	−	2.46396e9i	0.308560	−	0.363166i
$288$		0			0
$289$	−3.27152e9	+	5.66643e9i	−0.468984	+	0.812304i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		−	8.04420e9i		−	1.09147i	−0.837957	−	0.545736i	$-0.816250\pi$
$293$		−	8.04420e9i		−	1.09147i	0.837957	−	0.545736i	$-0.183750\pi$
$294$		0			0
$295$	1.34634e10			1.77774
$296$		0			0
$297$		0			0
$298$		0			0
$299$	8.46522e9	+	4.88740e9i	1.05914	+	0.611495i
$300$		0			0
$301$	3.29368e9	+	2.79844e9i	0.401250	+	0.340918i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	5.91893e9	+	1.02519e10i	0.683981	+	1.18469i
$306$		0			0
$307$			5.92170e9i			0.666642i	0.942813	+	0.333321i	$0.108169\pi$
$307$			5.92170e9i			0.666642i	−0.942813	+	0.333321i	$0.891831\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−3.70737e8	+	2.14045e8i	−0.0396300	+	0.0228804i	−0.519684	−	0.854358i	$-0.673950\pi$
$311$	−3.70737e8	+	2.14045e8i	−0.0396300	+	0.0228804i	0.480054	+	0.877239i	$0.340617\pi$
$312$		0			0
$313$	−7.31975e9	−	4.22606e9i	−0.762639	−	0.440310i	0.0676034	−	0.997712i	$-0.478465\pi$
$313$	−7.31975e9	−	4.22606e9i	−0.762639	−	0.440310i	−0.830242	+	0.557402i	$0.811798\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−3.10216e9	+	5.37310e9i	−0.307204	+	0.532094i	−0.977750	−	0.209775i	$-0.932727\pi$
$317$	−3.10216e9	+	5.37310e9i	−0.307204	+	0.532094i	0.670545	+	0.741869i	$0.266060\pi$
$318$		0			0
$319$	1.47335e10	+	2.55191e10i	1.42279	+	2.46435i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	1.03266e9			0.0948743
$324$		0			0
$325$	2.41331e10	−	1.39333e10i	2.16312	−	1.24888i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	7.35292e9	+	2.05954e10i	0.627590	+	1.75787i
$330$		0			0
$331$	4.74528e8	−	8.21906e8i	0.0395321	−	0.0684716i	−0.845582	−	0.533845i	$-0.820747\pi$
$331$	4.74528e8	−	8.21906e8i	0.0395321	−	0.0684716i	0.885114	+	0.465373i	$0.154080\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$			2.07222e10i			1.64535i
$336$		0			0
$337$	1.18629e10			0.919752			0.459876	−	0.887983i	$-0.347894\pi$
$337$	1.18629e10			0.919752			0.459876	+	0.887983i	$0.347894\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	3.85849e10	+	2.22770e10i	2.85364	+	1.64755i
$342$		0			0
$343$	7.14072e9	−	1.18571e10i	0.515900	−	0.856649i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	1.59847e9	+	2.76864e9i	0.110252	+	0.190963i	0.915872	−	0.401471i	$-0.131501\pi$
$347$	1.59847e9	+	2.76864e9i	0.110252	+	0.190963i	−0.805620	+	0.592433i	$0.798167\pi$
$348$		0			0
$349$			1.85896e10i			1.25305i	0.779401	+	0.626525i	$0.215523\pi$
$349$			1.85896e10i			1.25305i	−0.779401	+	0.626525i	$0.784477\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−2.29612e10	+	1.32566e10i	−1.47875	+	0.853758i	−0.999711	−	0.0240347i	$-0.992349\pi$
$353$	−2.29612e10	+	1.32566e10i	−1.47875	+	0.853758i	−0.479041	+	0.877793i	$0.659015\pi$
$354$		0			0
$355$	−3.83897e10	−	2.21643e10i	−2.41714	−	1.39554i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−4.13582e9	+	7.16345e9i	−0.248991	+	0.431265i	−0.963246	−	0.268620i	$-0.913432\pi$
$359$	−4.13582e9	+	7.16345e9i	−0.248991	+	0.431265i	0.714255	+	0.699886i	$0.246766\pi$
$360$		0			0
$361$	−7.25959e9	−	1.25740e10i	−0.427448	−	0.740362i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−3.97790e10			−2.24121
$366$		0			0
$367$	−9.87269e9	+	5.70000e9i	−0.544216	+	0.314203i	−0.746786	−	0.665065i	$-0.768404\pi$
$367$	−9.87269e9	+	5.70000e9i	−0.544216	+	0.314203i	0.202570	+	0.979268i	$0.435071\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	1.57869e9	−	8.64193e9i	0.0833301	−	0.456158i
$372$		0			0
$373$	1.55738e10	−	2.69746e10i	0.804562	−	1.39354i	−0.112025	−	0.993705i	$-0.535734\pi$
$373$	1.55738e10	−	2.69746e10i	0.804562	−	1.39354i	0.916587	−	0.399836i	$-0.130933\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	3.22135e10i		−	1.59467i
$378$		0			0
$379$	7.55220e9			0.366030			0.183015	−	0.983110i	$-0.441414\pi$
$379$	7.55220e9			0.366030			0.183015	+	0.983110i	$0.441414\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−6.02966e9	−	3.48123e9i	−0.280219	−	0.161785i	0.353303	−	0.935509i	$-0.385058\pi$
$383$	−6.02966e9	−	3.48123e9i	−0.280219	−	0.161785i	−0.633523	+	0.773724i	$0.718392\pi$
$384$		0			0
$385$	−4.75106e10	+	5.59185e10i	−2.16246	+	2.54515i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−8.85548e9	−	1.53381e10i	−0.386735	−	0.669845i	0.605273	−	0.796018i	$-0.293064\pi$
$389$	−8.85548e9	−	1.53381e10i	−0.386735	−	0.669845i	−0.992008	+	0.126173i	$0.959731\pi$
$390$		0			0
$391$			7.11117e9i			0.304252i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	1.95574e10	−	1.12915e10i	0.803384	−	0.463834i
$396$		0			0
$397$	2.62194e10	+	1.51378e10i	1.05551	+	0.609396i	0.924186	−	0.381944i	$-0.124745\pi$
$397$	2.62194e10	+	1.51378e10i	1.05551	+	0.609396i	0.131320	+	0.991340i	$0.458078\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	1.80548e9	−	3.12718e9i	0.0698257	−	0.120942i	−0.828999	−	0.559250i	$-0.811089\pi$
$401$	1.80548e9	−	3.12718e9i	0.0698257	−	0.120942i	0.898824	+	0.438309i	$0.144422\pi$
$402$		0			0
$403$	−2.43534e10	−	4.21813e10i	−0.923293	−	1.59919i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	1.67547e10			0.610602
$408$		0			0
$409$	−2.41617e10	+	1.39498e10i	−0.863446	+	0.498511i	−0.865165	−	0.501488i	$-0.832786\pi$
$409$	−2.41617e10	+	1.39498e10i	−0.863446	+	0.498511i	0.00171879	+	0.999999i	$0.499453\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	2.72160e10	+	4.97176e9i	0.935456	+	0.170887i
$414$		0			0
$415$	5.61293e8	−	9.72188e8i	0.0189233	−	0.0327762i
$416$		0			0
$417$		0			0
$418$		0			0
$419$			5.41022e8i			0.0175533i	0.999961	+	0.00877665i	$0.00279373\pi$
$419$			5.41022e8i			0.0175533i	−0.999961	+	0.00877665i	$0.997206\pi$
$420$		0			0
$421$	3.09569e10			0.985437			0.492718	−	0.870189i	$-0.336003\pi$
$421$	3.09569e10			0.985437			0.492718	+	0.870189i	$0.336003\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	1.75568e10	+	1.01364e10i	0.538134	+	0.310692i
$426$		0			0
$427$	8.17914e9	+	2.29096e10i	0.246035	+	0.689138i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−2.75045e10	−	4.76391e10i	−0.797066	−	1.38056i	−0.921519	−	0.388333i	$-0.873051\pi$
$431$	−2.75045e10	−	4.76391e10i	−0.797066	−	1.38056i	0.124453	−	0.992225i	$-0.460282\pi$
$432$		0			0
$433$		−	9.42119e9i		−	0.268012i	−0.990981	−	0.134006i	$-0.957216\pi$
$433$		−	9.42119e9i		−	0.268012i	0.990981	−	0.134006i	$-0.0427842\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−1.46967e10	+	8.48514e9i	−0.402990	+	0.232666i
$438$		0			0
$439$	2.49773e10	+	1.44206e10i	0.672492	+	0.388263i	0.797020	−	0.603953i	$-0.206408\pi$
$439$	2.49773e10	+	1.44206e10i	0.672492	+	0.388263i	−0.124529	+	0.992216i	$0.539742\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−1.66156e10	+	2.87791e10i	−0.431422	+	0.747245i	−0.996996	−	0.0774529i	$-0.975321\pi$
$443$	−1.66156e10	+	2.87791e10i	−0.431422	+	0.747245i	0.565574	+	0.824697i	$0.308655\pi$
$444$		0			0
$445$	3.79300e10	+	6.56967e10i	0.967260	+	1.67534i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	5.22184e9			0.128481			0.0642404	−	0.997934i	$-0.479538\pi$
$449$	5.22184e9			0.128481			0.0642404	+	0.997934i	$0.479538\pi$
$450$		0			0
$451$	−3.05030e10	+	1.76109e10i	−0.737287	+	0.425673i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	7.55457e10	−	2.69711e10i	1.76264	−	0.629294i
$456$		0			0
$457$	4.00779e10	−	6.94170e10i	0.918841	−	1.59148i	0.117664	−	0.993054i	$-0.462460\pi$
$457$	4.00779e10	−	6.94170e10i	0.918841	−	1.59148i	0.801178	−	0.598426i	$-0.204207\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		−	5.16689e9i		−	0.114400i	−0.998363	−	0.0571999i	$-0.981783\pi$
$461$		−	5.16689e9i		−	0.114400i	0.998363	−	0.0571999i	$-0.0182173\pi$
$462$		0			0
$463$	−1.17425e10			−0.255527			−0.127764	−	0.991805i	$-0.540780\pi$
$463$	−1.17425e10			−0.255527			−0.127764	+	0.991805i	$0.540780\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−6.41407e7	−	3.70316e7i	−0.00134855	−	0.000778584i	0.499326	−	0.866414i	$-0.333581\pi$
$467$	−6.41407e7	−	3.70316e7i	−0.00134855	−	0.000778584i	−0.500674	+	0.865636i	$0.666914\pi$
$468$		0			0
$469$	−7.65228e9	+	4.18894e10i	−0.158161	+	0.865790i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−2.35413e10	−	4.07748e10i	−0.470312	−	0.814605i
$474$		0			0
$475$			4.83798e10i			0.950363i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−6.21346e10	+	3.58735e10i	−1.18030	+	0.681445i	−0.956084	−	0.293094i	$-0.905315\pi$
$479$	−6.21346e10	+	3.58735e10i	−1.18030	+	0.681445i	−0.224215	+	0.974540i	$0.571982\pi$
$480$		0			0
$481$	−1.58624e10	−	9.15816e9i	−0.296339	−	0.171091i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	1.55785e10	−	2.69828e10i	0.281553	−	0.487663i
$486$		0			0
$487$	−2.48075e10	−	4.29679e10i	−0.441029	−	0.763885i	0.556737	−	0.830689i	$-0.312053\pi$
$487$	−2.48075e10	−	4.29679e10i	−0.441029	−	0.763885i	−0.997766	+	0.0668039i	$0.978720\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	2.92296e10			0.502917			0.251458	−	0.967868i	$-0.419090\pi$
$491$	2.92296e10			0.502917			0.251458	+	0.967868i	$0.419090\pi$
$492$		0			0
$493$	2.02956e10	−	1.17177e10i	0.343569	−	0.198359i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−6.94189e10	−	5.89810e10i	−1.13776	−	0.966689i
$498$		0			0
$499$	3.45740e10	−	5.98840e10i	0.557632	−	0.965847i	−0.440061	−	0.897968i	$-0.645043\pi$
$499$	3.45740e10	−	5.98840e10i	0.557632	−	0.965847i	0.997694	−	0.0678795i	$-0.0216233\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		−	4.21850e10i		−	0.659001i	−0.944155	−	0.329501i	$-0.893120\pi$
$503$		−	4.21850e10i		−	0.659001i	0.944155	−	0.329501i	$-0.106880\pi$
$504$		0			0
$505$	8.54652e9			0.131409
$506$		0			0
$507$		0			0
$508$		0			0
$509$	3.01952e10	+	1.74332e10i	0.449849	+	0.259721i	0.707766	−	0.706446i	$-0.249703\pi$
$509$	3.01952e10	+	1.74332e10i	0.449849	+	0.259721i	−0.257917	+	0.966167i	$0.583036\pi$
$510$		0			0
$511$	−8.04120e10	−	1.46895e10i	−1.17934	−	0.215439i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−1.58718e10	−	2.74908e10i	−0.225630	−	0.390803i
$516$		0			0
$517$		−	2.38231e11i		−	3.33454i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−6.86868e10	+	3.96564e10i	−0.932229	+	0.538223i	−0.887516	−	0.460777i	$-0.847571\pi$
$521$	−6.86868e10	+	3.96564e10i	−0.932229	+	0.538223i	−0.0447131	+	0.999000i	$0.514237\pi$
$522$		0			0
$523$	1.49357e10	+	8.62310e9i	0.199626	+	0.115254i	0.596481	−	0.802627i	$-0.296565\pi$
$523$	1.49357e10	+	8.62310e9i	0.199626	+	0.115254i	−0.396855	+	0.917881i	$0.629898\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	1.77171e10	−	3.06869e10i	0.229694	−	0.397842i
$528$		0			0
$529$	−1.92753e10	−	3.33858e10i	−0.246138	−	0.426323i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	3.85048e10			0.477096
$534$		0			0
$535$	−1.37940e11	+	7.96395e10i	−1.68374	+	0.972106i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−1.16691e11	+	9.54930e10i	−1.38255	+	1.13140i
$540$		0			0
$541$	8.22880e10	−	1.42527e11i	0.960611	−	1.66383i	0.239641	−	0.970862i	$-0.422970\pi$
$541$	8.22880e10	−	1.42527e11i	0.960611	−	1.66383i	0.720970	−	0.692966i	$-0.243696\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		−	1.12527e11i		−	1.27548i
$546$		0			0
$547$	2.02743e10			0.226462			0.113231	−	0.993569i	$-0.463880\pi$
$547$	2.02743e10			0.226462			0.113231	+	0.993569i	$0.463880\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	4.84339e10	+	2.79633e10i	0.525464	+	0.303377i
$552$		0			0
$553$	4.37045e10	−	1.56033e10i	0.467332	−	0.166846i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−4.16250e10	−	7.20966e10i	−0.432448	−	0.749021i	0.564636	−	0.825340i	$-0.309017\pi$
$557$	−4.16250e10	−	7.20966e10i	−0.432448	−	0.749021i	−0.997083	+	0.0763188i	$0.975683\pi$
$558$		0			0
$559$			5.14711e10i			0.527128i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	1.59377e10	−	9.20165e9i	0.158633	−	0.0915867i	−0.418582	−	0.908179i	$-0.637473\pi$
$563$	1.59377e10	−	9.20165e9i	0.158633	−	0.0915867i	0.577215	+	0.816592i	$0.304139\pi$
$564$		0			0
$565$	−8.93777e10	−	5.16022e10i	−0.877072	−	0.506378i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	4.00051e10	−	6.92908e10i	0.381651	−	0.661038i	−0.609648	−	0.792672i	$-0.708689\pi$
$569$	4.00051e10	−	6.92908e10i	0.381651	−	0.661038i	0.991298	+	0.131634i	$0.0420225\pi$
$570$		0			0
$571$	−9.17409e10	−	1.58900e11i	−0.863015	−	1.49479i	−0.869004	−	0.494804i	$-0.835240\pi$
$571$	−9.17409e10	−	1.58900e11i	−0.863015	−	1.49479i	0.00598894	−	0.999982i	$-0.498094\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−3.33155e11			−3.04772
$576$		0			0
$577$	−2.30693e10	+	1.33190e10i	−0.208128	+	0.120163i	−0.600441	−	0.799669i	$-0.705008\pi$
$577$	−2.30693e10	+	1.33190e10i	−0.208128	+	0.120163i	0.392313	+	0.919832i	$0.371675\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	1.49365e9	−	1.75798e9i	0.0131082	−	0.0154280i
$582$		0			0
$583$	−4.78505e10	+	8.28794e10i	−0.414202	+	0.717419i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		−	9.04647e10i		−	0.761950i	−0.924585	−	0.380975i	$-0.875588\pi$
$587$		−	9.04647e10i		−	0.761950i	0.924585	−	0.380975i	$-0.124412\pi$
$588$		0			0
$589$	8.45612e10			0.702603
$590$		0			0
$591$		0			0
$592$		0			0
$593$	2.90780e10	+	1.67882e10i	0.235151	+	0.135764i	0.612946	−	0.790125i	$-0.289984\pi$
$593$	2.90780e10	+	1.67882e10i	0.235151	+	0.135764i	−0.377795	+	0.925889i	$0.623318\pi$
$594$		0			0
$595$	4.44725e10	+	3.77856e10i	0.354833	+	0.301480i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	7.46968e10	+	1.29379e11i	0.580223	+	1.00498i	0.995453	+	0.0952587i	$0.0303678\pi$
$599$	7.46968e10	+	1.29379e11i	0.580223	+	1.00498i	−0.415230	+	0.909717i	$0.636299\pi$
$600$		0			0
$601$			3.12742e10i			0.239711i	0.992791	+	0.119856i	$0.0382431\pi$
$601$			3.12742e10i			0.239711i	−0.992791	+	0.119856i	$0.961757\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	4.75350e11	−	2.74443e11i	3.54807	−	2.04848i
$606$		0			0
$607$	1.03866e11	+	5.99669e10i	0.765099	+	0.441730i	0.831124	−	0.556088i	$-0.187698\pi$
$607$	1.03866e11	+	5.99669e10i	0.765099	+	0.441730i	−0.0660244	+	0.997818i	$0.521032\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−1.30218e11	+	2.25544e11i	−0.934342	+	1.61833i
$612$		0			0
$613$	3.95362e10	+	6.84787e10i	0.279997	+	0.484968i	0.971384	−	0.237516i	$-0.0763333\pi$
$613$	3.95362e10	+	6.84787e10i	0.279997	+	0.484968i	−0.691387	+	0.722485i	$0.743000\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	7.35075e10			0.507214			0.253607	−	0.967307i	$-0.418383\pi$
$617$	7.35075e10			0.507214			0.253607	+	0.967307i	$0.418383\pi$
$618$		0			0
$619$	2.19835e11	−	1.26922e11i	1.49739	−	0.864517i	0.497393	−	0.867526i	$-0.334291\pi$
$619$	2.19835e11	−	1.26922e11i	1.49739	−	0.864517i	0.999995	+	0.00300805i	$0.000957493\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	5.24140e10	+	1.46811e11i	0.347933	+	0.974554i
$624$		0			0
$625$	−2.08250e11	+	3.60699e11i	−1.36478	+	2.36388i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		−	1.33251e10i		−	0.0851273i
$630$		0			0
$631$	6.11257e9			0.0385573			0.0192786	−	0.999814i	$-0.493863\pi$
$631$	6.11257e9			0.0385573			0.0192786	+	0.999814i	$0.493863\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	3.93322e10	+	2.27085e10i	0.241910	+	0.139667i
$636$		0			0
$637$	1.62673e11	−	2.66240e10i	0.988004	−	0.161702i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−9.48169e10	−	1.64228e11i	−0.561634	−	0.972779i	−0.997354	−	0.0726969i	$-0.976839\pi$
$641$	−9.48169e10	−	1.64228e11i	−0.561634	−	0.972779i	0.435720	−	0.900082i	$-0.356494\pi$
$642$		0			0
$643$			1.50630e11i			0.881188i	0.897706	+	0.440594i	$0.145232\pi$
$643$			1.50630e11i			0.881188i	−0.897706	+	0.440594i	$0.854768\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−1.86275e11	+	1.07546e11i	−1.06301	+	0.613729i	−0.926264	−	0.376876i	$-0.876998\pi$
$647$	−1.86275e11	+	1.07546e11i	−1.06301	+	0.613729i	−0.136747	+	0.990606i	$0.543665\pi$
$648$		0			0
$649$	−2.61011e11	−	1.50695e11i	−1.47123	−	0.849415i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	1.66655e11	−	2.88654e11i	0.916567	−	1.58754i	0.111977	−	0.993711i	$-0.464282\pi$
$653$	1.66655e11	−	2.88654e11i	0.916567	−	1.58754i	0.804590	−	0.593831i	$-0.202385\pi$
$654$		0			0
$655$	2.23296e11	+	3.86761e11i	1.21316	+	2.10125i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	6.54805e10			0.347193			0.173596	−	0.984817i	$-0.444461\pi$
$659$	6.54805e10			0.347193			0.173596	+	0.984817i	$0.444461\pi$
$660$		0			0
$661$	1.46661e11	−	8.46750e10i	0.768263	−	0.443557i	−0.0639915	−	0.997950i	$-0.520383\pi$
$661$	1.46661e11	−	8.46750e10i	0.768263	−	0.443557i	0.832255	+	0.554394i	$0.187050\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−2.50265e10	+	1.36998e11i	−0.127972	+	0.700531i
$666$		0			0
$667$	−1.92562e11	+	3.33528e11i	−0.972899	+	1.68511i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		−	2.65000e11i		−	1.30724i
$672$		0			0
$673$	−1.23724e11			−0.603105			−0.301552	−	0.953450i	$-0.597505\pi$
$673$	−1.23724e11			−0.603105			−0.301552	+	0.953450i	$0.597505\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−2.80203e11	−	1.61775e11i	−1.33389	−	0.770119i	−0.347993	−	0.937497i	$-0.613137\pi$
$677$	−2.80203e11	−	1.61775e11i	−1.33389	−	0.770119i	−0.985893	+	0.167378i	$0.946470\pi$
$678$		0			0
$679$	4.14557e10	−	4.87921e10i	0.195032	−	0.229547i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	9.35871e10	+	1.62098e11i	0.430064	+	0.744893i	0.996878	−	0.0789529i	$-0.0251577\pi$
$683$	9.35871e10	+	1.62098e11i	0.430064	+	0.744893i	−0.566814	+	0.823846i	$0.691824\pi$
$684$		0			0
$685$		−	5.00370e10i		−	0.227263i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	9.06045e10	−	5.23105e10i	0.402043	−	0.232120i
$690$		0			0
$691$	1.13839e11	+	6.57249e10i	0.499319	+	0.288282i	0.728432	−	0.685118i	$-0.240249\pi$
$691$	1.13839e11	+	6.57249e10i	0.499319	+	0.288282i	−0.229113	+	0.973400i	$0.573583\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−8.83017e10	+	1.52943e11i	−0.378469	+	0.655527i
$696$		0			0
$697$	1.40061e10	+	2.42593e10i	0.0593454	+	0.102789i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	1.13631e10			0.0470569			0.0235285	−	0.999723i	$-0.492510\pi$
$701$	1.13631e10			0.0470569			0.0235285	+	0.999723i	$0.492510\pi$
$702$		0			0
$703$	2.75391e10	−	1.58997e10i	0.112753	−	0.0650981i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	1.72765e10	+	3.15605e9i	0.0691479	+	0.0126318i
$708$		0			0
$709$	1.67229e11	−	2.89649e11i	0.661801	−	1.14627i	−0.318341	−	0.947976i	$-0.603126\pi$
$709$	1.67229e11	−	2.89649e11i	0.661801	−	1.14627i	0.980142	−	0.198296i	$-0.0635408\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$			5.82309e11i			2.25318i
$714$		0			0
$715$	−8.73852e11			−3.34359
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−2.41998e11	−	1.39717e11i	−0.905515	−	0.522800i	−0.0265298	−	0.999648i	$-0.508446\pi$
$719$	−2.41998e11	−	1.39717e11i	−0.905515	−	0.522800i	−0.878985	+	0.476849i	$0.841779\pi$
$720$		0			0
$721$	−2.19326e10	−	6.14329e10i	−0.0811614	−	0.227332i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	5.48967e11	+	9.50839e11i	1.98698	+	3.44156i
$726$		0			0
$727$		−	4.98526e11i		−	1.78464i	−0.451407	−	0.892318i	$-0.649078\pi$
$727$		−	4.98526e11i		−	1.78464i	0.451407	−	0.892318i	$-0.350922\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−3.24286e10	+	1.87226e10i	−0.113569	+	0.0655688i
$732$		0			0
$733$	2.34185e11	+	1.35207e11i	0.811229	+	0.468363i	0.847383	−	0.530983i	$-0.178177\pi$
$733$	2.34185e11	+	1.35207e11i	0.811229	+	0.468363i	−0.0361535	+	0.999346i	$0.511511\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	2.31942e11	−	4.01735e11i	0.786157	−	1.36166i
$738$		0			0
$739$	−2.38418e11	−	4.12953e11i	−0.799396	−	1.38459i	−0.920010	−	0.391894i	$-0.871820\pi$
$739$	−2.38418e11	−	4.12953e11i	−0.799396	−	1.38459i	0.120615	−	0.992699i	$-0.461513\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−4.19326e11			−1.37593			−0.687966	−	0.725743i	$-0.741496\pi$
$743$	−4.19326e11			−1.37593			−0.687966	+	0.725743i	$0.741496\pi$
$744$		0			0
$745$	2.63548e11	−	1.52160e11i	0.855529	−	0.493940i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−3.08250e11	+	1.10051e11i	−0.979436	+	0.349676i
$750$		0			0
$751$	1.18803e10	−	2.05772e10i	0.0373479	−	0.0646885i	−0.846747	−	0.531995i	$-0.821442\pi$
$751$	1.18803e10	−	2.05772e10i	0.0373479	−	0.0646885i	0.884095	+	0.467307i	$0.154776\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$			5.69368e11i			1.75229i
$756$		0			0
$757$	−4.90289e11			−1.49303			−0.746516	−	0.665368i	$-0.768275\pi$
$757$	−4.90289e11			−1.49303			−0.746516	+	0.665368i	$0.768275\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	2.40688e11	+	1.38961e11i	0.717656	+	0.414339i	0.813889	−	0.581020i	$-0.197346\pi$
$761$	2.40688e11	+	1.38961e11i	0.717656	+	0.414339i	−0.0962332	+	0.995359i	$0.530679\pi$
$762$		0			0
$763$	4.15540e10	−	2.27471e11i	0.122607	−	0.671163i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	1.64741e11	+	2.85340e11i	0.476014	+	0.824481i
$768$		0			0
$769$			1.97929e11i			0.565984i	0.959122	+	0.282992i	$0.0913270\pi$
$769$			1.97929e11i			0.565984i	−0.959122	+	0.282992i	$0.908673\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	4.68415e11	−	2.70439e11i	1.31194	−	0.757447i	0.329520	−	0.944149i	$-0.393113\pi$
$773$	4.68415e11	−	2.70439e11i	1.31194	−	0.757447i	0.982417	+	0.186702i	$0.0597799\pi$
$774$		0			0
$775$	1.43767e12	+	8.30038e11i	3.98522	+	2.30087i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−3.34246e10	+	5.78931e10i	−0.0907646	+	0.157209i
$780$		0			0
$781$	4.96166e11	+	8.59385e11i	1.33359	+	2.30985i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−2.93720e11			−0.773490
$786$		0			0
$787$	3.58532e11	−	2.06999e11i	0.934607	−	0.539596i	0.0463413	−	0.998926i	$-0.485244\pi$
$787$	3.58532e11	−	2.06999e11i	0.934607	−	0.539596i	0.888266	+	0.459330i	$0.151910\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−1.61619e11	−	1.37318e11i	−0.412844	−	0.350768i
$792$		0			0
$793$	−1.44850e11	+	2.50888e11i	−0.366291	+	0.634434i
$794$		0			0
$795$		0			0
$796$		0			0
$797$		−	2.99422e11i		−	0.742080i	−0.928617	−	0.371040i	$-0.879001\pi$
$797$		−	2.99422e11i		−	0.742080i	0.928617	−	0.371040i	$-0.120999\pi$
$798$		0			0
$799$	−1.89467e11			−0.464887
$800$		0			0
$801$		0			0
$802$		0			0
$803$	7.71182e11	+	4.45242e11i	1.85479	+	1.07086i
$804$		0			0
$805$	−9.43401e11	−	1.72339e11i	−2.24653	−	0.410393i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	1.92320e11	+	3.33107e11i	0.448982	+	0.777660i	0.998320	−	0.0579400i	$-0.0184532\pi$
$809$	1.92320e11	+	3.33107e11i	0.448982	+	0.777660i	−0.549338	+	0.835601i	$0.685120\pi$
$810$		0			0
$811$		−	3.67004e11i		−	0.848374i	−0.905575	−	0.424187i	$-0.860560\pi$
$811$		−	3.67004e11i		−	0.848374i	0.905575	−	0.424187i	$-0.139440\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−9.80647e11	+	5.66177e11i	−2.22271	+	1.28328i
$816$		0			0
$817$	−7.73884e10	−	4.46802e10i	−0.173695	−	0.100283i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−1.74573e11	+	3.02370e11i	−0.384242	+	0.665527i	−0.991664	−	0.128853i	$-0.958870\pi$
$821$	−1.74573e11	+	3.02370e11i	−0.384242	+	0.665527i	0.607422	+	0.794380i	$0.292204\pi$
$822$		0			0
$823$	−3.55497e11	−	6.15739e11i	−0.774885	−	1.34214i	−0.934859	−	0.355018i	$-0.884475\pi$
$823$	−3.55497e11	−	6.15739e11i	−0.774885	−	1.34214i	0.159975	−	0.987121i	$-0.448859\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	4.40466e11			0.941651			0.470825	−	0.882226i	$-0.343956\pi$
$827$	4.40466e11			0.941651			0.470825	+	0.882226i	$0.343956\pi$
$828$		0			0
$829$	−8.98343e10	+	5.18659e10i	−0.190206	+	0.109815i	−0.592079	−	0.805880i	$-0.701693\pi$
$829$	−8.98343e10	+	5.18659e10i	−0.190206	+	0.109815i	0.401873	+	0.915695i	$0.368359\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	7.59464e10	+	9.28052e10i	0.157735	+	0.192749i
$834$		0			0
$835$	−2.85077e11	+	4.93768e11i	−0.586430	+	1.01573i
$836$		0			0
$837$		0			0
$838$		0			0
$839$		−	6.98433e11i		−	1.40954i	−0.709437	−	0.704769i	$-0.751051\pi$
$839$		−	6.98433e11i		−	1.40954i	0.709437	−	0.704769i	$-0.248949\pi$
$840$		0			0
$841$	7.68956e11			1.53715
$842$		0			0
$843$		0			0
$844$		0			0
$845$	1.89736e9	+	1.09544e9i	0.00372155	+	0.00214864i
$846$		0			0
$847$	1.06225e12	−	3.79243e11i	2.06392	−	0.736857i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	1.09489e11	+	1.89641e11i	0.208763	+	0.361589i
$852$		0			0
$853$			5.88287e11i			1.11120i	0.831449	+	0.555601i	$0.187512\pi$
$853$			5.88287e11i			1.11120i	−0.831449	+	0.555601i	$0.812488\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	4.73418e11	−	2.73328e11i	0.877650	−	0.506711i	0.00776698	−	0.999970i	$-0.497528\pi$
$857$	4.73418e11	−	2.73328e11i	0.877650	−	0.506711i	0.869883	+	0.493259i	$0.164194\pi$
$858$		0			0
$859$	−1.67471e11	−	9.66896e10i	−0.307587	−	0.177585i	0.338259	−	0.941053i	$-0.390162\pi$
$859$	−1.67471e11	−	9.66896e10i	−0.307587	−	0.177585i	−0.645846	+	0.763468i	$0.723495\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	2.49869e11	−	4.32786e11i	0.450474	−	0.780244i	−0.547941	−	0.836517i	$-0.684588\pi$
$863$	2.49869e11	−	4.32786e11i	0.450474	−	0.780244i	0.998415	+	0.0562729i	$0.0179217\pi$
$864$		0			0
$865$	−4.34249e10	−	7.52141e10i	−0.0775665	−	0.134349i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−5.05538e11			−0.886492
$870$		0			0
$871$	−4.39180e11	+	2.53561e11i	−0.763080	+	0.440565i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−1.06069e12	+	1.24840e12i	−1.80949	+	2.12972i
$876$		0			0
$877$	1.06031e10	−	1.83651e10i	0.0179239	−	0.0310452i	−0.856924	−	0.515442i	$-0.827628\pi$
$877$	1.06031e10	−	1.83651e10i	0.0179239	−	0.0310452i	0.874848	+	0.484397i	$0.160961\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	8.92261e11i		−	1.48111i	−0.671994	−	0.740557i	$-0.734562\pi$
$881$		−	8.92261e11i		−	1.48111i	0.671994	−	0.740557i	$-0.265438\pi$
$882$		0			0
$883$	−6.55925e11			−1.07898			−0.539488	−	0.841994i	$-0.681382\pi$
$883$	−6.55925e11			−1.07898			−0.539488	+	0.841994i	$0.681382\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−7.06329e11	−	4.07799e11i	−1.14107	−	0.658797i	−0.194375	−	0.980927i	$-0.562268\pi$
$887$	−7.06329e11	−	4.07799e11i	−1.14107	−	0.658797i	−0.946696	+	0.322130i	$0.895601\pi$
$888$		0			0
$889$	7.11232e10	+	6.04291e10i	0.113869	+	0.0967473i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−2.26075e11	−	3.91573e11i	−0.355506	−	0.615754i
$894$		0			0
$895$			5.09399e11i			0.793900i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	1.66193e12	−	9.59518e11i	2.54434	−	1.46897i
$900$		0			0
$901$	6.59148e10	+	3.80559e10i	0.100019	+	0.0577461i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	7.15489e11	−	1.23926e12i	1.06662	−	1.84744i
$906$		0			0
$907$	7.36544e10	+	1.27573e11i	0.108835	+	0.188508i	0.915299	−	0.402776i	$-0.131955\pi$
$907$	7.36544e10	+	1.27573e11i	0.108835	+	0.188508i	−0.806463	+	0.591284i	$0.798621\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−5.13012e11			−0.744824			−0.372412	−	0.928067i	$-0.621469\pi$
$911$	−5.13012e11			−0.744824			−0.372412	+	0.928067i	$0.621469\pi$
$912$		0			0
$913$	−2.17632e10	+	1.25650e10i	−0.0313213	+	0.0180834i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	3.08565e11	+	8.64284e11i	0.436384	+	1.22230i
$918$		0			0
$919$	−4.96143e11	+	8.59345e11i	−0.695577	+	1.20477i	0.274409	+	0.961613i	$0.411518\pi$
$919$	−4.96143e11	+	8.59345e11i	−0.695577	+	1.20477i	−0.969986	+	0.243161i	$0.921816\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		−	1.08483e12i		−	1.49470i
$924$		0			0
$925$	6.24277e11			0.852727
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−1.54446e11	−	8.91694e10i	−0.207355	−	0.119716i	0.392727	−	0.919655i	$-0.371532\pi$
$929$	−1.54446e11	−	8.91694e10i	−0.207355	−	0.119716i	−0.600081	+	0.799939i	$0.704865\pi$
$930$		0			0
$931$	−1.01181e11	+	2.67695e11i	−0.134679	+	0.356322i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−3.17864e11	−	5.50556e11i	−0.415905	−	0.720369i
$936$		0			0
$937$		−	1.01978e12i		−	1.32296i	−0.749961	−	0.661482i	$-0.769928\pi$
$937$		−	1.01978e12i		−	1.32296i	0.749961	−	0.661482i	$-0.230072\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−8.89803e11	+	5.13728e11i	−1.13484	+	0.655201i	−0.945148	−	0.326642i	$-0.894083\pi$
$941$	−8.89803e11	+	5.13728e11i	−1.13484	+	0.655201i	−0.189694	+	0.981843i	$0.560750\pi$
$942$		0			0
$943$	−3.98666e11	−	2.30170e11i	−0.504153	−	0.291073i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−6.89538e10	+	1.19431e11i	−0.0857350	+	0.148497i	−0.905704	−	0.423910i	$-0.860657\pi$
$947$	−6.89538e10	+	1.19431e11i	−0.0857350	+	0.148497i	0.819969	+	0.572408i	$0.193990\pi$
$948$		0			0
$949$	−4.86742e11	−	8.43063e11i	−0.600115	−	1.03943i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−3.56628e11			−0.432359			−0.216179	−	0.976354i	$-0.569360\pi$
$953$	−3.56628e11			−0.432359			−0.216179	+	0.976354i	$0.569360\pi$
$954$		0			0
$955$	−6.44558e11	+	3.72136e11i	−0.774905	+	0.447392i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	1.84776e10	−	1.01148e11i	0.0218460	−	0.119587i
$960$		0			0
$961$	1.02435e12	−	1.77422e12i	1.20103	−	2.08024i
$962$		0			0
$963$		0			0
$964$		0			0
$965$		−	1.95221e12i		−	2.25122i
$966$		0			0
$967$	−1.50903e12			−1.72581			−0.862903	−	0.505370i	$-0.831356\pi$
$967$	−1.50903e12			−1.72581			−0.862903	+	0.505370i	$0.831356\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	1.39050e12	+	8.02804e11i	1.56420	+	0.903094i	0.996824	+	0.0796379i	$0.0253764\pi$
$971$	1.39050e12	+	8.02804e11i	1.56420	+	0.903094i	0.567380	+	0.823456i	$0.307957\pi$
$972$		0			0
$973$	−2.34978e11	+	2.76562e11i	−0.262166	+	0.308561i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	3.81046e11	+	6.59991e11i	0.418215	+	0.724369i	0.995760	−	0.0919895i	$-0.0293226\pi$
$977$	3.81046e11	+	6.59991e11i	0.418215	+	0.724369i	−0.577545	+	0.816359i	$0.695989\pi$
$978$		0			0
$979$		−	1.69819e12i		−	1.84865i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	1.46472e12	−	8.45658e11i	1.56870	−	0.905692i	0.572384	−	0.819986i	$-0.306019\pi$
$983$	1.46472e12	−	8.45658e11i	1.56870	−	0.905692i	0.996320	−	0.0857061i	$-0.0273146\pi$
$984$		0			0
$985$	−5.03011e11	−	2.90414e11i	−0.534359	−	0.308512i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	3.07679e11	−	5.32915e11i	0.321597	−	0.557023i
$990$		0			0
$991$	8.67808e10	+	1.50309e11i	0.0899764	+	0.155844i	0.907501	−	0.420050i	$-0.137987\pi$
$991$	8.67808e10	+	1.50309e11i	0.0899764	+	0.155844i	−0.817524	+	0.575894i	$0.804654\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−1.92365e12			−1.96261
$996$		0			0
$997$	−7.36634e11	+	4.25296e11i	−0.745541	+	0.430438i	−0.824080	−	0.566473i	$-0.808308\pi$
$997$	−7.36634e11	+	4.25296e11i	−0.745541	+	0.430438i	0.0785396	+	0.996911i	$0.474974\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.9.z.d.145.1		12
3.2	odd	2		84.9.m.b.61.6	✓	12
7.3	odd	6	inner	252.9.z.d.73.1		12
21.17	even	6		84.9.m.b.73.6	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.9.m.b.61.6	✓	12	3.2	odd	2
84.9.m.b.73.6	yes	12	21.17	even	6
252.9.z.d.73.1		12	7.3	odd	6	inner
252.9.z.d.145.1		12	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:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	252.z (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1011.88 - 584.207i) q^{5} +(-1829.74 - 1554.62i) q^{7} +O(q^{10})\)	\(q+(-1011.88 - 584.207i) q^{5} +(-1829.74 - 1554.62i) q^{7} +(13077.9 + 22651.7i) q^{11} -28593.8i q^{13} +(18015.1 - 10401.0i) q^{17} +(42991.6 + 24821.2i) q^{19} +(-170925. + 296051. i) q^{23} +(487282. + 843998. i) q^{25} +1.12659e6 q^{29} +(1.47519e6 - 851702. i) q^{31} +(943251. + 2.64203e6i) q^{35} +(320285. - 554750. i) q^{37} +1.34661e6i q^{41} -1.80008e6 q^{43} +(-7.88787e6 - 4.55406e6i) q^{47} +(931110. + 5.68911e6i) q^{49} +(1.82943e6 + 3.16867e6i) q^{53} -3.05609e7i q^{55} +(-9.97907e6 + 5.76142e6i) q^{59} +(-8.77419e6 - 5.06578e6i) q^{61} +(-1.67047e7 + 2.89334e7i) q^{65} +(-8.86768e6 - 1.53593e7i) q^{67} +3.79392e7 q^{71} +(2.94841e7 - 1.70227e7i) q^{73} +(1.12855e7 - 6.17779e7i) q^{77} +(-9.66395e6 + 1.67384e7i) q^{79} +960779. i q^{83} -2.43053e7 q^{85} +(-5.62273e7 - 3.24629e7i) q^{89} +(-4.44525e7 + 5.23193e7i) q^{91} +(-2.90015e7 - 5.02320e7i) q^{95} +2.66661e7i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 285 q^{5} + 198 q^{7}+O(q^{10}) \) 12 * q - 285 * q^5 + 198 * q^7	\( 12 q - 285 q^{5} + 198 q^{7} + 17919 q^{11} + 205782 q^{17} + 74313 q^{19} + 62832 q^{23} + 878679 q^{25} + 575454 q^{29} + 1442952 q^{31} + 3989514 q^{35} - 2058621 q^{37} + 7721322 q^{43} - 12088194 q^{47} - 16964694 q^{49} + 5506743 q^{53} - 7511901 q^{59} - 37215576 q^{61} - 5047122 q^{65} - 36824553 q^{67} + 30011556 q^{71} + 95080185 q^{73} + 38333727 q^{77} + 8514456 q^{79} + 20121540 q^{85} - 83038554 q^{89} - 198538635 q^{91} + 221605224 q^{95}+O(q^{100}) \) 12 * q - 285 * q^5 + 198 * q^7 + 17919 * q^11 + 205782 * q^17 + 74313 * q^19 + 62832 * q^23 + 878679 * q^25 + 575454 * q^29 + 1442952 * q^31 + 3989514 * q^35 - 2058621 * q^37 + 7721322 * q^43 - 12088194 * q^47 - 16964694 * q^49 + 5506743 * q^53 - 7511901 * q^59 - 37215576 * q^61 - 5047122 * q^65 - 36824553 * q^67 + 30011556 * q^71 + 95080185 * q^73 + 38333727 * q^77 + 8514456 * q^79 + 20121540 * q^85 - 83038554 * q^89 - 198538635 * q^91 + 221605224 * q^95

Introduction

L-functions

Modular forms

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Database

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