LMFDB - Embedded newform 252.9.z.c.145.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("252.73");

S:= CuspForms(chi, 9);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			145.2
Root			$-9.33129 + 16.1623i$ of defining polynomial
Character	$\chi$	$=$	252.145
Dual form			252.9.z.c.73.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-336.492 - 194.274i) q^{5} +(2329.92 + 579.874i) q^{7} +O(q^{10})$	$q+(-336.492 - 194.274i) q^{5} +(2329.92 + 579.874i) q^{7} +(1266.56 + 2193.75i) q^{11} -14249.8i q^{13} +(-97281.1 + 56165.3i) q^{17} +(110919. + 64039.0i) q^{19} +(-75905.1 + 131472. i) q^{23} +(-119828. - 207548. i) q^{25} +932928. q^{29} +(-471982. + 272499. i) q^{31} +(-671346. - 647766. i) q^{35} +(89738.6 - 155432. i) q^{37} -4.20802e6i q^{41} -6.11389e6 q^{43} +(4.84372e6 + 2.79652e6i) q^{47} +(5.09229e6 + 2.70213e6i) q^{49} +(-2.70086e6 - 4.67803e6i) q^{53} -984237. i q^{55} +(-4.27233e6 + 2.46663e6i) q^{59} +(9.35220e6 + 5.39950e6i) q^{61} +(-2.76837e6 + 4.79495e6i) q^{65} +(1.88549e6 + 3.26577e6i) q^{67} +2.11666e7 q^{71} +(-3.10113e7 + 1.79044e7i) q^{73} +(1.67889e6 + 5.84571e6i) q^{77} +(-2.85584e7 + 4.94645e7i) q^{79} +7.32501e7i q^{83} +4.36457e7 q^{85} +(-4.33379e6 - 2.50212e6i) q^{89} +(8.26312e6 - 3.32011e7i) q^{91} +(-2.48822e7 - 4.30972e7i) q^{95} -1.17807e8i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 837 q^{5} + 1526 q^{7}+O(q^{10}) $ 10 * q + 837 * q^5 + 1526 * q^7	$ 10 q + 837 q^{5} + 1526 q^{7} - 3705 q^{11} - 78003 q^{17} - 96741 q^{19} - 208533 q^{23} + 367978 q^{25} - 754764 q^{29} - 1053717 q^{31} + 1306389 q^{35} - 998075 q^{37} + 738292 q^{43} - 710883 q^{47} + 13288114 q^{49} - 10501461 q^{53} + 37089081 q^{59} - 8180481 q^{61} - 21459108 q^{65} + 48020189 q^{67} + 31918236 q^{71} - 133345593 q^{73} - 188477625 q^{77} + 53590181 q^{79} - 157179282 q^{85} + 241368273 q^{89} + 420709128 q^{91} - 347126775 q^{95}+O(q^{100}) $ 10 * q + 837 * q^5 + 1526 * q^7 - 3705 * q^11 - 78003 * q^17 - 96741 * q^19 - 208533 * q^23 + 367978 * q^25 - 754764 * q^29 - 1053717 * q^31 + 1306389 * q^35 - 998075 * q^37 + 738292 * q^43 - 710883 * q^47 + 13288114 * q^49 - 10501461 * q^53 + 37089081 * q^59 - 8180481 * q^61 - 21459108 * q^65 + 48020189 * q^67 + 31918236 * q^71 - 133345593 * q^73 - 188477625 * q^77 + 53590181 * q^79 - 157179282 * q^85 + 241368273 * q^89 + 420709128 * q^91 - 347126775 * q^95

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$	−336.492	−	194.274i	−0.538387	−	0.310838i	0.206038	−	0.978544i	$-0.433943\pi$
$5$	−336.492	−	194.274i	−0.538387	−	0.310838i	−0.744425	+	0.667706i	$0.767276\pi$
$6$		0			0
$7$	2329.92	+	579.874i	0.970397	+	0.241514i
$7$	2329.92	+	579.874i	0.970397	+	0.241514i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1266.56	+	2193.75i	0.0865078	+	0.149836i	0.906033	−	0.423208i	$-0.139096\pi$
$11$	1266.56	+	2193.75i	0.0865078	+	0.149836i	−0.819525	+	0.573044i	$0.805763\pi$
$12$		0			0
$13$		−	14249.8i		−	0.498927i	−0.968384	−	0.249463i	$-0.919746\pi$
$13$		−	14249.8i		−	0.498927i	0.968384	−	0.249463i	$-0.0802542\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−97281.1	+	56165.3i	−1.16475	+	0.672469i	−0.952438	−	0.304733i	$-0.901433\pi$
$17$	−97281.1	+	56165.3i	−1.16475	+	0.672469i	−0.212313	+	0.977202i	$0.568100\pi$
$18$		0			0
$19$	110919.	+	64039.0i	0.851120	+	0.491394i	0.861029	−	0.508557i	$-0.169821\pi$
$19$	110919.	+	64039.0i	0.851120	+	0.491394i	−0.00990873	+	0.999951i	$0.503154\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−75905.1	+	131472.i	−0.271244	+	0.469808i	−0.969181	−	0.246351i	$-0.920768\pi$
$23$	−75905.1	+	131472.i	−0.271244	+	0.469808i	0.697937	+	0.716159i	$0.254102\pi$
$24$		0			0
$25$	−119828.	−	207548.i	−0.306760	−	0.531324i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	932928.			1.31903			0.659517	−	0.751689i	$-0.270761\pi$
$29$	932928.			1.31903			0.659517	+	0.751689i	$0.270761\pi$
$30$		0			0
$31$	−471982.	+	272499.i	−0.511068	+	0.295065i	−0.733273	−	0.679935i	$-0.762008\pi$
$31$	−471982.	+	272499.i	−0.511068	+	0.295065i	0.222204	+	0.975000i	$0.428675\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−671346.	−	647766.i	−0.447378	−	0.431664i
$36$		0			0
$37$	89738.6	−	155432.i	0.0478820	−	0.0829341i	−0.841091	−	0.540894i	$-0.818086\pi$
$37$	89738.6	−	155432.i	0.0478820	−	0.0829341i	0.888973	+	0.457959i	$0.151420\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		−	4.20802e6i		−	1.48916i	−0.667531	−	0.744582i	$-0.732649\pi$
$41$		−	4.20802e6i		−	1.48916i	0.667531	−	0.744582i	$-0.267351\pi$
$42$		0			0
$43$	−6.11389e6			−1.78832			−0.894158	−	0.447752i	$-0.852225\pi$
$43$	−6.11389e6			−1.78832			−0.894158	+	0.447752i	$0.852225\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	4.84372e6	+	2.79652e6i	0.992631	+	0.573096i	0.906060	−	0.423150i	$-0.139076\pi$
$47$	4.84372e6	+	2.79652e6i	0.992631	+	0.573096i	0.0865714	+	0.996246i	$0.472409\pi$
$48$		0			0
$49$	5.09229e6	+	2.70213e6i	0.883342	+	0.468728i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−2.70086e6	−	4.67803e6i	−0.342294	−	0.592871i	0.642564	−	0.766232i	$-0.277871\pi$
$53$	−2.70086e6	−	4.67803e6i	−0.342294	−	0.592871i	−0.984858	+	0.173361i	$0.944537\pi$
$54$		0			0
$55$		−	984237.i		−	0.107560i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−4.27233e6	+	2.46663e6i	−0.352579	+	0.203562i	−0.665821	−	0.746112i	$-0.731918\pi$
$59$	−4.27233e6	+	2.46663e6i	−0.352579	+	0.203562i	0.313241	+	0.949674i	$0.398585\pi$
$60$		0			0
$61$	9.35220e6	+	5.39950e6i	0.675452	+	0.389972i	0.798139	−	0.602473i	$-0.205818\pi$
$61$	9.35220e6	+	5.39950e6i	0.675452	+	0.389972i	−0.122687	+	0.992445i	$0.539151\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−2.76837e6	+	4.79495e6i	−0.155085	+	0.268616i
$66$		0			0
$67$	1.88549e6	+	3.26577e6i	0.0935677	+	0.162064i	0.909010	−	0.416774i	$-0.136840\pi$
$67$	1.88549e6	+	3.26577e6i	0.0935677	+	0.162064i	−0.815442	+	0.578838i	$0.803506\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	2.11666e7			0.832949			0.416475	−	0.909147i	$-0.363265\pi$
$71$	2.11666e7			0.832949			0.416475	+	0.909147i	$0.363265\pi$
$72$		0			0
$73$	−3.10113e7	+	1.79044e7i	−1.09201	+	0.630475i	−0.934112	−	0.356980i	$-0.883806\pi$
$73$	−3.10113e7	+	1.79044e7i	−1.09201	+	0.630475i	−0.157902	+	0.987455i	$0.550473\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	1.67889e6	+	5.84571e6i	0.0477595	+	0.166293i
$78$		0			0
$79$	−2.85584e7	+	4.94645e7i	−0.733204	+	1.26995i	0.222302	+	0.974978i	$0.428643\pi$
$79$	−2.85584e7	+	4.94645e7i	−0.733204	+	1.26995i	−0.955507	+	0.294969i	$0.904691\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$			7.32501e7i			1.54346i	0.635949	+	0.771731i	$0.280609\pi$
$83$			7.32501e7i			1.54346i	−0.635949	+	0.771731i	$0.719391\pi$
$84$		0			0
$85$	4.36457e7			0.836115
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−4.33379e6	−	2.50212e6i	−0.0690730	−	0.0398793i	0.465066	−	0.885276i	$-0.346031\pi$
$89$	−4.33379e6	−	2.50212e6i	−0.0690730	−	0.0398793i	−0.534139	+	0.845397i	$0.679364\pi$
$90$		0			0
$91$	8.26312e6	−	3.32011e7i	0.120498	−	0.484157i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−2.48822e7	−	4.30972e7i	−0.305488	−	0.529120i
$96$		0			0
$97$		−	1.17807e8i		−	1.33072i	−0.746525	−	0.665358i	$-0.768279\pi$
$97$		−	1.17807e8i		−	1.33072i	0.746525	−	0.665358i	$-0.231721\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	6.26734e7	−	3.61845e7i	0.602279	−	0.347726i	−0.167658	−	0.985845i	$-0.553621\pi$
$101$	6.26734e7	−	3.61845e7i	0.602279	−	0.347726i	0.769938	+	0.638119i	$0.220287\pi$
$102$		0			0
$103$	−4.48351e7	−	2.58856e7i	−0.398354	−	0.229990i	0.287419	−	0.957805i	$-0.407203\pi$
$103$	−4.48351e7	−	2.58856e7i	−0.398354	−	0.229990i	−0.685774	+	0.727815i	$0.740536\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1.18916e8	+	2.05969e8i	−0.907206	+	1.57133i	−0.0892782	+	0.996007i	$0.528456\pi$
$107$	−1.18916e8	+	2.05969e8i	−0.907206	+	1.57133i	−0.817928	+	0.575321i	$0.804877\pi$
$108$		0			0
$109$	1.00146e8	+	1.73457e8i	0.709456	+	1.22881i	0.965059	+	0.262032i	$0.0843927\pi$
$109$	1.00146e8	+	1.73457e8i	0.709456	+	1.22881i	−0.255603	+	0.966782i	$0.582274\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−1.04340e8			−0.639936			−0.319968	−	0.947428i	$-0.603672\pi$
$113$	−1.04340e8			−0.639936			−0.319968	+	0.947428i	$0.603672\pi$
$114$		0			0
$115$	5.10829e7	−	2.94927e7i	0.292068	−	0.168626i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−2.59227e8	+	7.44500e7i	−1.29268	+	0.371259i
$120$		0			0
$121$	1.03971e8	−	1.80083e8i	0.485033	−	0.840101i
$122$		0			0
$123$		0			0
$124$		0			0
$125$			2.44894e8i			1.00309i
$126$		0			0
$127$	−3.55208e8			−1.36542			−0.682712	−	0.730688i	$-0.739199\pi$
$127$	−3.55208e8			−1.36542			−0.682712	+	0.730688i	$0.739199\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	2.92194e8	+	1.68698e8i	0.992171	+	0.572830i	0.905923	−	0.423443i	$-0.139179\pi$
$131$	2.92194e8	+	1.68698e8i	0.992171	+	0.572830i	0.0862486	+	0.996274i	$0.472512\pi$
$132$		0			0
$133$	2.21298e8	+	2.13525e8i	0.707246	+	0.682405i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	2.42928e8	+	4.20763e8i	0.689596	+	1.19442i	0.971969	+	0.235110i	$0.0755452\pi$
$137$	2.42928e8	+	4.20763e8i	0.689596	+	1.19442i	−0.282373	+	0.959305i	$0.591121\pi$
$138$		0			0
$139$			4.38468e8i			1.17457i	0.809380	+	0.587285i	$0.199803\pi$
$139$			4.38468e8i			1.17457i	−0.809380	+	0.587285i	$0.800197\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	3.12606e7	−	1.80483e7i	0.0747571	−	0.0431610i
$144$		0			0
$145$	−3.13923e8	−	1.81243e8i	−0.710151	−	0.410006i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−2.21836e8	+	3.84231e8i	−0.450077	+	0.779557i	−0.998390	−	0.0567163i	$-0.981937\pi$
$149$	−2.21836e8	+	3.84231e8i	−0.450077	+	0.779557i	0.548313	+	0.836273i	$0.315270\pi$
$150$		0			0
$151$	4.87022e8	+	8.43546e8i	0.936786	+	1.62256i	0.771418	+	0.636329i	$0.219548\pi$
$151$	4.87022e8	+	8.43546e8i	0.936786	+	1.62256i	0.165368	+	0.986232i	$0.447119\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	2.11757e8			0.366870
$156$		0			0
$157$	−7.00295e8	+	4.04316e8i	−1.15261	+	0.665460i	−0.949522	−	0.313700i	$-0.898431\pi$
$157$	−7.00295e8	+	4.04316e8i	−1.15261	+	0.665460i	−0.203089	+	0.979160i	$0.565098\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−2.53090e8	+	2.62303e8i	−0.376679	+	0.390391i
$162$		0			0
$163$	−2.13690e8	+	3.70123e8i	−0.302715	+	0.524319i	−0.976750	−	0.214381i	$-0.931227\pi$
$163$	−2.13690e8	+	3.70123e8i	−0.302715	+	0.524319i	0.674035	+	0.738700i	$0.264560\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$			1.23279e9i			1.58497i	0.609889	+	0.792487i	$0.291214\pi$
$167$			1.23279e9i			1.58497i	−0.609889	+	0.792487i	$0.708786\pi$
$168$		0			0
$169$	6.12673e8			0.751072
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−9.22175e7	−	5.32418e7i	−0.102951	−	0.0594386i	0.447641	−	0.894214i	$-0.352264\pi$
$173$	−9.22175e7	−	5.32418e7i	−0.102951	−	0.0594386i	−0.550591	+	0.834775i	$0.685598\pi$
$174$		0			0
$175$	−1.58838e8	−	5.53057e8i	−0.169357	−	0.589682i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−3.11678e8	−	5.39842e8i	−0.303594	−	0.525841i	0.673353	−	0.739321i	$-0.264853\pi$
$179$	−3.11678e8	−	5.39842e8i	−0.303594	−	0.525841i	−0.976947	+	0.213480i	$0.931520\pi$
$180$		0			0
$181$			4.40025e7i			0.0409980i	0.999790	+	0.0204990i	$0.00652550\pi$
$181$			4.40025e7i			0.0409980i	−0.999790	+	0.0204990i	$0.993475\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−6.03926e7	+	3.48677e7i	−0.0515581	+	0.0297671i
$186$		0			0
$187$	−2.46425e8	−	1.42274e8i	−0.201520	−	0.116348i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−3.61563e7	+	6.26246e7i	−0.0271676	+	0.0470556i	−0.879290	−	0.476288i	$-0.841982\pi$
$191$	−3.61563e7	+	6.26246e7i	−0.0271676	+	0.0470556i	0.852122	+	0.523343i	$0.175315\pi$
$192$		0			0
$193$	2.43376e8	+	4.21540e8i	0.175408	+	0.303815i	0.940302	−	0.340340i	$-0.110542\pi$
$193$	2.43376e8	+	4.21540e8i	0.175408	+	0.303815i	−0.764895	+	0.644155i	$0.777209\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−1.82628e9			−1.21256			−0.606279	−	0.795252i	$-0.707339\pi$
$197$	−1.82628e9			−1.21256			−0.606279	+	0.795252i	$0.707339\pi$
$198$		0			0
$199$	4.68500e8	−	2.70489e8i	0.298743	−	0.172479i	−0.343135	−	0.939286i	$-0.611489\pi$
$199$	4.68500e8	−	2.70489e8i	0.298743	−	0.172479i	0.641878	+	0.766807i	$0.278156\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	2.17365e9	+	5.40981e8i	1.27999	+	0.318565i
$204$		0			0
$205$	−8.17508e8	+	1.41597e9i	−0.462889	+	0.801747i
$206$		0			0
$207$		0			0
$208$		0			0
$209$			3.24437e8i			0.170038i
$210$		0			0
$211$	−2.02990e9			−1.02410			−0.512052	−	0.858954i	$-0.671115\pi$
$211$	−2.02990e9			−1.02410			−0.512052	+	0.858954i	$0.671115\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	2.05727e9	+	1.18777e9i	0.962805	+	0.555876i
$216$		0			0
$217$	−1.25770e9	+	3.61212e8i	−0.567202	+	0.162901i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	8.00347e8	+	1.38624e9i	0.335513	+	0.581125i
$222$		0			0
$223$			1.36113e9i			0.550404i	0.961386	+	0.275202i	$0.0887448\pi$
$223$			1.36113e9i			0.550404i	−0.961386	+	0.275202i	$0.911255\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−1.84644e9	+	1.06604e9i	−0.695395	+	0.401487i	−0.805630	−	0.592419i	$-0.798173\pi$
$227$	−1.84644e9	+	1.06604e9i	−0.695395	+	0.401487i	0.110235	+	0.993906i	$0.464840\pi$
$228$		0			0
$229$	2.79560e9	+	1.61404e9i	1.01656	+	0.586911i	0.913106	−	0.407723i	$-0.133677\pi$
$229$	2.79560e9	+	1.61404e9i	1.01656	+	0.586911i	0.103454	+	0.994634i	$0.467011\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−2.09584e9	+	3.63010e9i	−0.711105	+	1.23167i	0.253337	+	0.967378i	$0.418472\pi$
$233$	−2.09584e9	+	3.63010e9i	−0.711105	+	1.23167i	−0.964443	+	0.264293i	$0.914862\pi$
$234$		0			0
$235$	−1.08658e9	−	1.88201e9i	−0.356280	−	0.617094i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−2.54547e8			−0.0780147			−0.0390074	−	0.999239i	$-0.512420\pi$
$239$	−2.54547e8			−0.0780147			−0.0390074	+	0.999239i	$0.512420\pi$
$240$		0			0
$241$	4.87324e9	−	2.81357e9i	1.44461	−	0.834044i	0.446455	−	0.894806i	$-0.352686\pi$
$241$	4.87324e9	−	2.81357e9i	1.44461	−	0.834044i	0.998152	+	0.0607615i	$0.0193529\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−1.18856e9	−	1.89854e9i	−0.329881	−	0.526933i
$246$		0			0
$247$	9.12546e8	−	1.58058e9i	0.245170	−	0.424646i
$248$		0			0
$249$		0			0
$250$		0			0
$251$		−	2.68042e9i		−	0.675317i	−0.941269	−	0.337659i	$-0.890365\pi$
$251$		−	2.68042e9i		−	0.675317i	0.941269	−	0.337659i	$-0.109635\pi$
$252$		0			0
$253$	−3.84554e8			−0.0938588
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−3.05037e9	−	1.76113e9i	−0.699230	−	0.403701i	0.107831	−	0.994169i	$-0.465610\pi$
$257$	−3.05037e9	−	1.76113e9i	−0.699230	−	0.403701i	−0.807061	+	0.590469i	$0.798943\pi$
$258$		0			0
$259$	2.99215e8	−	3.10107e8i	0.0664943	−	0.0689149i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	2.45771e9	+	4.25688e9i	0.513698	+	0.889751i	0.999874	+	0.0158897i	$0.00505805\pi$
$263$	2.45771e9	+	4.25688e9i	0.513698	+	0.889751i	−0.486176	+	0.873861i	$0.661609\pi$
$264$		0			0
$265$			2.09883e9i			0.425592i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−2.37772e9	+	1.37278e9i	−0.454099	+	0.262174i	−0.709560	−	0.704645i	$-0.751106\pi$
$269$	−2.37772e9	+	1.37278e9i	−0.454099	+	0.262174i	0.255461	+	0.966819i	$0.417773\pi$
$270$		0			0
$271$	−4.36365e9	−	2.51935e9i	−0.809045	−	0.467102i	0.0375790	−	0.999294i	$-0.488035\pi$
$271$	−4.36365e9	−	2.51935e9i	−0.809045	−	0.467102i	−0.846624	+	0.532191i	$0.821369\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	3.03539e8	−	5.25745e8i	0.0530742	−	0.0919273i
$276$		0			0
$277$	2.54553e9	+	4.40899e9i	0.432374	+	0.748893i	0.997077	−	0.0764008i	$-0.0243429\pi$
$277$	2.54553e9	+	4.40899e9i	0.432374	+	0.748893i	−0.564704	+	0.825294i	$0.691010\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	2.82407e9			0.452950			0.226475	−	0.974017i	$-0.427280\pi$
$281$	2.82407e9			0.452950			0.226475	+	0.974017i	$0.427280\pi$
$282$		0			0
$283$	5.16720e9	−	2.98328e9i	0.805582	−	0.465103i	−0.0398376	−	0.999206i	$-0.512684\pi$
$283$	5.16720e9	−	2.98328e9i	0.805582	−	0.465103i	0.845419	+	0.534103i	$0.179351\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	2.44012e9	−	9.80438e9i	0.359654	−	1.44508i
$288$		0			0
$289$	2.82120e9	−	4.88647e9i	0.404430	−	0.700492i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		−	1.15032e10i		−	1.56080i	−0.625278	−	0.780402i	$-0.715014\pi$
$293$		−	1.15032e10i		−	1.56080i	0.625278	−	0.780402i	$-0.284986\pi$
$294$		0			0
$295$	1.91681e9			0.253099
$296$		0			0
$297$		0			0
$298$		0			0
$299$	1.87345e9	+	1.08164e9i	0.234400	+	0.135331i
$300$		0			0
$301$	−1.42449e10	−	3.54529e9i	−1.73538	−	0.431903i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−2.09796e9	−	3.63377e9i	−0.242436	−	0.419912i
$306$		0			0
$307$			3.98746e8i			0.0448893i	0.999748	+	0.0224446i	$0.00714495\pi$
$307$			3.98746e8i			0.0448893i	−0.999748	+	0.0224446i	$0.992855\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	1.09596e10	−	6.32751e9i	1.17153	−	0.676380i	0.217486	−	0.976063i	$-0.430214\pi$
$311$	1.09596e10	−	6.32751e9i	1.17153	−	0.676380i	0.954039	+	0.299683i	$0.0968809\pi$
$312$		0			0
$313$	−1.04941e10	−	6.05876e9i	−1.09337	−	0.631257i	−0.158898	−	0.987295i	$-0.550794\pi$
$313$	−1.04941e10	−	6.05876e9i	−1.09337	−	0.631257i	−0.934471	+	0.356038i	$0.884127\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	6.00980e9	−	1.04093e10i	0.595145	−	1.03082i	−0.398381	−	0.917220i	$-0.630428\pi$
$317$	6.00980e9	−	1.04093e10i	0.595145	−	1.03082i	0.993526	−	0.113602i	$-0.0362388\pi$
$318$		0			0
$319$	1.18161e9	+	2.04661e9i	0.114107	+	0.197639i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−1.43871e10			−1.32179
$324$		0			0
$325$	−2.95753e9	+	1.70753e9i	−0.265092	+	0.153051i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	9.66388e9	+	9.32444e9i	0.824836	+	0.795865i
$330$		0			0
$331$	1.76799e9	−	3.06225e9i	0.147288	−	0.255111i	−0.782936	−	0.622102i	$-0.786279\pi$
$331$	1.76799e9	−	3.06225e9i	0.147288	−	0.255111i	0.930224	+	0.366991i	$0.119612\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$		−	1.46521e9i		−	0.116337i
$336$		0			0
$337$	1.23331e10			0.956206			0.478103	−	0.878304i	$-0.341325\pi$
$337$	1.23331e10			0.956206			0.478103	+	0.878304i	$0.341325\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−1.19559e9	−	6.90273e8i	−0.0884228	−	0.0510509i
$342$		0			0
$343$	1.02978e10	+	9.24864e9i	0.743989	+	0.668192i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−1.19704e10	−	2.07333e10i	−0.825638	−	1.43005i	−0.901431	−	0.432924i	$-0.857482\pi$
$347$	−1.19704e10	−	2.07333e10i	−0.825638	−	1.43005i	0.0757924	−	0.997124i	$-0.475851\pi$
$348$		0			0
$349$		−	8.55802e9i		−	0.576861i	−0.957501	−	0.288431i	$-0.906867\pi$
$349$		−	8.55802e9i		−	0.576861i	0.957501	−	0.288431i	$-0.0931335\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−1.18970e9	+	6.86874e8i	−0.0766194	+	0.0442362i	−0.537820	−	0.843060i	$-0.680752\pi$
$353$	−1.18970e9	+	6.86874e8i	−0.0766194	+	0.0442362i	0.461201	+	0.887296i	$0.347419\pi$
$354$		0			0
$355$	−7.12240e9	−	4.11212e9i	−0.448449	−	0.258912i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	2.78141e9	−	4.81755e9i	0.167451	−	0.290034i	−0.770072	−	0.637957i	$-0.779780\pi$
$359$	2.78141e9	−	4.81755e9i	0.167451	−	0.290034i	0.937523	+	0.347923i	$0.113113\pi$
$360$		0			0
$361$	−2.89797e8	−	5.01944e8i	−0.0170634	−	0.0295547i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	1.39134e10			0.783902
$366$		0			0
$367$	−1.92997e9	+	1.11427e9i	−0.106387	+	0.0614224i	−0.552249	−	0.833679i	$-0.686230\pi$
$367$	−1.92997e9	+	1.11427e9i	−0.106387	+	0.0614224i	0.445863	+	0.895101i	$0.352897\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−3.58014e9	−	1.24656e10i	−0.188975	−	0.657989i
$372$		0			0
$373$	3.79200e9	−	6.56793e9i	0.195899	−	0.339307i	−0.751296	−	0.659966i	$-0.770571\pi$
$373$	3.79200e9	−	6.56793e9i	0.195899	−	0.339307i	0.947195	+	0.320658i	$0.103904\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	1.32941e10i		−	0.658102i
$378$		0			0
$379$	−2.55402e9			−0.123785			−0.0618925	−	0.998083i	$-0.519714\pi$
$379$	−2.55402e9			−0.123785			−0.0618925	+	0.998083i	$0.519714\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	2.27853e10	+	1.31551e10i	1.05891	+	0.611362i	0.925131	−	0.379649i	$-0.123955\pi$
$383$	2.27853e10	+	1.31551e10i	1.05891	+	0.611362i	0.133780	+	0.991011i	$0.457289\pi$
$384$		0			0
$385$	5.70734e8	−	2.29320e9i	0.0259771	−	0.104376i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−2.04442e10	−	3.54105e10i	−0.892838	−	1.54644i	−0.836458	−	0.548031i	$-0.815378\pi$
$389$	−2.04442e10	−	3.54105e10i	−0.892838	−	1.54644i	−0.0563796	−	0.998409i	$-0.517956\pi$
$390$		0			0
$391$		−	1.70529e10i		−	0.729612i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	1.92193e10	−	1.10963e10i	0.789495	−	0.455815i
$396$		0			0
$397$	1.13589e10	+	6.55804e9i	0.457270	+	0.264005i	0.710896	−	0.703297i	$-0.248290\pi$
$397$	1.13589e10	+	6.55804e9i	0.457270	+	0.264005i	−0.253626	+	0.967302i	$0.581623\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−2.18960e10	+	3.79251e10i	−0.846814	+	1.46673i	0.0372219	+	0.999307i	$0.488149\pi$
$401$	−2.18960e10	+	3.79251e10i	−0.846814	+	1.46673i	−0.884036	+	0.467418i	$0.845184\pi$
$402$		0			0
$403$	3.88307e9	+	6.72567e9i	0.147216	+	0.254986i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	4.54637e8			0.0165687
$408$		0			0
$409$	−1.37959e10	+	7.96507e9i	−0.493011	+	0.284640i	−0.725823	−	0.687882i	$-0.758541\pi$
$409$	−1.37959e10	+	7.96507e9i	−0.493011	+	0.284640i	0.232811	+	0.972522i	$0.425207\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−1.13845e10	+	3.26965e9i	−0.391305	+	0.112383i
$414$		0			0
$415$	1.42306e10	−	2.46481e10i	0.479766	−	0.830979i
$416$		0			0
$417$		0			0
$418$		0			0
$419$		−	4.47746e9i		−	0.145270i	−0.997359	−	0.0726350i	$-0.976859\pi$
$419$		−	4.47746e9i		−	0.145270i	0.997359	−	0.0726350i	$-0.0231408\pi$
$420$		0			0
$421$	−3.55257e10			−1.13087			−0.565437	−	0.824791i	$-0.691293\pi$
$421$	−3.55257e10			−1.13087			−0.565437	+	0.824791i	$0.691293\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	2.33140e10	+	1.34604e10i	0.714597	+	0.412573i
$426$		0			0
$427$	1.86589e10	+	1.80035e10i	0.561273	+	0.541559i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	1.21108e10	+	2.09764e10i	0.350964	+	0.607887i	0.986419	−	0.164251i	$-0.0525207\pi$
$431$	1.21108e10	+	2.09764e10i	0.350964	+	0.607887i	−0.635455	+	0.772138i	$0.719187\pi$
$432$		0			0
$433$			2.15952e10i			0.614334i	0.951656	+	0.307167i	$0.0993810\pi$
$433$			2.15952e10i			0.614334i	−0.951656	+	0.307167i	$0.900619\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−1.68386e10	+	9.72178e9i	−0.461722	+	0.266575i
$438$		0			0
$439$	−1.92303e10	−	1.11026e10i	−0.517759	−	0.298928i	0.218258	−	0.975891i	$-0.429962\pi$
$439$	−1.92303e10	−	1.11026e10i	−0.517759	−	0.298928i	−0.736017	+	0.676963i	$0.763296\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	1.49674e9	−	2.59242e9i	0.0388625	−	0.0673117i	−0.845940	−	0.533278i	$-0.820960\pi$
$443$	1.49674e9	−	2.59242e9i	0.0388625	−	0.0673117i	0.884802	+	0.465966i	$0.154293\pi$
$444$		0			0
$445$	9.72191e8	+	1.68388e9i	0.0247920	+	0.0429410i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−5.44497e10			−1.33971			−0.669853	−	0.742493i	$-0.733643\pi$
$449$	−5.44497e10			−1.33971			−0.669853	+	0.742493i	$0.733643\pi$
$450$		0			0
$451$	9.23134e9	−	5.32972e9i	0.223130	−	0.128824i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−9.23056e9	+	9.56658e9i	−0.215369	+	0.223209i
$456$		0			0
$457$	2.75303e10	−	4.76839e10i	0.631170	−	1.09322i	−0.356142	−	0.934432i	$-0.615908\pi$
$457$	2.75303e10	−	4.76839e10i	0.631170	−	1.09322i	0.987313	−	0.158787i	$-0.0507584\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$			5.88158e10i			1.30224i	0.758976	+	0.651119i	$0.225700\pi$
$461$			5.88158e10i			1.30224i	−0.758976	+	0.651119i	$0.774300\pi$
$462$		0			0
$463$	6.96889e10			1.51649			0.758245	−	0.651970i	$-0.226057\pi$
$463$	6.96889e10			1.51649			0.758245	+	0.651970i	$0.226057\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	2.09170e10	+	1.20764e10i	0.439777	+	0.253905i	0.703503	−	0.710692i	$-0.251618\pi$
$467$	2.09170e10	+	1.20764e10i	0.439777	+	0.253905i	−0.263726	+	0.964598i	$0.584952\pi$
$468$		0			0
$469$	2.49932e9	+	8.70235e9i	0.0516572	+	0.179864i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−7.74362e9	−	1.34123e10i	−0.154703	−	0.267954i
$474$		0			0
$475$		−	3.06947e10i		−	0.602960i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−3.34306e10	+	1.93011e10i	−0.635041	+	0.366641i	−0.782702	−	0.622397i	$-0.786159\pi$
$479$	−3.34306e10	+	1.93011e10i	−0.635041	+	0.366641i	0.147661	+	0.989038i	$0.452826\pi$
$480$		0			0
$481$	−2.21488e9	−	1.27876e9i	−0.0413780	−	0.0238896i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−2.28868e10	+	3.96412e10i	−0.413636	+	0.716439i
$486$		0			0
$487$	1.59488e10	+	2.76241e10i	0.283539	+	0.491103i	0.972254	−	0.233929i	$-0.0751582\pi$
$487$	1.59488e10	+	2.76241e10i	0.283539	+	0.491103i	−0.688715	+	0.725032i	$0.741825\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	3.85743e10			0.663701			0.331851	−	0.943332i	$-0.392327\pi$
$491$	3.85743e10			0.663701			0.331851	+	0.943332i	$0.392327\pi$
$492$		0			0
$493$	−9.07563e10	+	5.23982e10i	−1.53635	+	0.887010i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	4.93167e10	+	1.22740e10i	0.808292	+	0.201169i
$498$		0			0
$499$	−5.26168e10	+	9.11349e10i	−0.848637	+	1.46988i	0.0337882	+	0.999429i	$0.489243\pi$
$499$	−5.26168e10	+	9.11349e10i	−0.848637	+	1.46988i	−0.882425	+	0.470453i	$0.844091\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$			2.20726e10i			0.344812i	0.985026	+	0.172406i	$0.0551540\pi$
$503$			2.20726e10i			0.344812i	−0.985026	+	0.172406i	$0.944846\pi$
$504$		0			0
$505$	−2.81188e10			−0.432346
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−3.30492e10	−	1.90809e10i	−0.492367	−	0.284268i	0.233189	−	0.972432i	$-0.425084\pi$
$509$	−3.30492e10	−	1.90809e10i	−0.492367	−	0.284268i	−0.725556	+	0.688163i	$0.758417\pi$
$510$		0			0
$511$	−8.26362e10	+	2.37332e10i	−1.21196	+	0.348075i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	1.00578e10	+	1.74206e10i	0.142979	+	0.247647i
$516$		0			0
$517$			1.41679e10i			0.198309i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	5.10553e10	−	2.94768e10i	0.692931	−	0.400064i	−0.111778	−	0.993733i	$-0.535655\pi$
$521$	5.10553e10	−	2.94768e10i	0.692931	−	0.400064i	0.804709	+	0.593669i	$0.202321\pi$
$522$		0			0
$523$	2.68858e9	+	1.55225e9i	0.0359349	+	0.0207470i	0.517860	−	0.855465i	$-0.326729\pi$
$523$	2.68858e9	+	1.55225e9i	0.0359349	+	0.0207470i	−0.481925	+	0.876213i	$0.660062\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	3.06100e10	−	5.30180e10i	0.396845	−	0.687355i
$528$		0			0
$529$	2.76323e10	+	4.78606e10i	0.352854	+	0.611160i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−5.99637e10			−0.742984
$534$		0			0
$535$	8.00287e10	−	4.62046e10i	0.976856	−	0.563988i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	5.21914e8	+	1.45936e10i	0.00618364	+	0.172905i
$540$		0			0
$541$	1.38564e10	−	2.39999e10i	0.161756	−	0.280169i	−0.773743	−	0.633500i	$-0.781618\pi$
$541$	1.38564e10	−	2.39999e10i	0.161756	−	0.280169i	0.935498	+	0.353331i	$0.114951\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		−	7.78225e10i		−	0.882103i
$546$		0			0
$547$	6.63111e10			0.740691			0.370346	−	0.928894i	$-0.379239\pi$
$547$	6.63111e10			0.740691			0.370346	+	0.928894i	$0.379239\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	1.03479e11	+	5.97438e10i	1.12266	+	0.648166i
$552$		0			0
$553$	−9.52221e10	+	9.86884e10i	−1.01821	+	1.05527i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	8.94739e10	+	1.54973e11i	0.929556	+	1.61004i	0.784065	+	0.620678i	$0.213143\pi$
$557$	8.94739e10	+	1.54973e11i	0.929556	+	1.61004i	0.145490	+	0.989360i	$0.453524\pi$
$558$		0			0
$559$			8.71220e10i			0.892238i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−1.50601e11	+	8.69493e10i	−1.49897	+	0.865431i	−0.999999	−	0.00118726i	$-0.999622\pi$
$563$	−1.50601e11	+	8.69493e10i	−1.49897	+	0.865431i	−0.498971	+	0.866618i	$0.666289\pi$
$564$		0			0
$565$	3.51095e10	+	2.02705e10i	0.344533	+	0.198916i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−8.33787e10	+	1.44416e11i	−0.795438	+	1.37774i	0.127123	+	0.991887i	$0.459426\pi$
$569$	−8.33787e10	+	1.44416e11i	−0.795438	+	1.37774i	−0.922561	+	0.385852i	$0.873908\pi$
$570$		0			0
$571$	−2.56910e10	−	4.44981e10i	−0.241678	−	0.418598i	0.719515	−	0.694477i	$-0.244364\pi$
$571$	−2.56910e10	−	4.44981e10i	−0.241678	−	0.418598i	−0.961192	+	0.275879i	$0.911031\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	3.63823e10			0.332827
$576$		0			0
$577$	6.16751e9	−	3.56082e9i	0.0556425	−	0.0321252i	−0.471921	−	0.881641i	$-0.656439\pi$
$577$	6.16751e9	−	3.56082e9i	0.0556425	−	0.0321252i	0.527563	+	0.849516i	$0.323106\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−4.24759e10	+	1.70667e11i	−0.372767	+	1.49777i
$582$		0			0
$583$	6.84162e9	−	1.18500e10i	0.0592222	−	0.102576i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		−	1.65778e11i		−	1.39629i	−0.715958	−	0.698143i	$-0.754010\pi$
$587$		−	1.65778e11i		−	1.39629i	0.715958	−	0.698143i	$-0.245990\pi$
$588$		0			0
$589$	−6.98022e10			−0.579974
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−3.34687e10	−	1.93231e10i	−0.270657	−	0.156264i	0.358529	−	0.933519i	$-0.383278\pi$
$593$	−3.34687e10	−	1.93231e10i	−0.270657	−	0.156264i	−0.629186	+	0.777255i	$0.716612\pi$
$594$		0			0
$595$	1.01691e11	+	2.53090e10i	0.811364	+	0.201933i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	8.58924e9	+	1.48770e10i	0.0667186	+	0.115560i	0.897455	−	0.441106i	$-0.145414\pi$
$599$	8.58924e9	+	1.48770e10i	0.0667186	+	0.115560i	−0.830736	+	0.556666i	$0.812080\pi$
$600$		0			0
$601$			1.06427e11i			0.815746i	0.913039	+	0.407873i	$0.133729\pi$
$601$			1.06427e11i			0.815746i	−0.913039	+	0.407873i	$0.866271\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−6.99708e10	+	4.03977e10i	−0.522270	+	0.301533i
$606$		0			0
$607$	9.18674e10	+	5.30397e10i	0.676716	+	0.390702i	0.798617	−	0.601840i	$-0.205566\pi$
$607$	9.18674e10	+	5.30397e10i	0.676716	+	0.390702i	−0.121900	+	0.992542i	$0.538899\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	3.98500e10	−	6.90223e10i	0.285933	−	0.495250i
$612$		0			0
$613$	−1.13332e11	−	1.96297e11i	−0.802623	−	1.39018i	−0.917884	−	0.396848i	$-0.870104\pi$
$613$	−1.13332e11	−	1.96297e11i	−0.802623	−	1.39018i	0.115262	−	0.993335i	$-0.463229\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−1.29345e11			−0.892501			−0.446251	−	0.894908i	$-0.647241\pi$
$617$	−1.29345e11			−0.892501			−0.446251	+	0.894908i	$0.647241\pi$
$618$		0			0
$619$	1.18633e11	−	6.84929e10i	0.808060	−	0.466534i	−0.0382214	−	0.999269i	$-0.512169\pi$
$619$	1.18633e11	−	6.84929e10i	0.808060	−	0.466534i	0.846282	+	0.532735i	$0.178836\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−8.64650e9	−	8.34280e9i	−0.0573969	−	0.0553809i
$624$		0			0
$625$	7.68586e8	−	1.33123e9i	0.00503700	−	0.00872435i
$626$		0			0
$627$		0			0
$628$		0			0
$629$			2.01608e10i			0.128797i
$630$		0			0
$631$	−1.67031e11			−1.05361			−0.526804	−	0.849987i	$-0.676610\pi$
$631$	−1.67031e11			−1.05361			−0.526804	+	0.849987i	$0.676610\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	1.19524e11	+	6.90074e10i	0.735126	+	0.424425i
$636$		0			0
$637$	3.85049e10	−	7.25644e10i	0.233861	−	0.440723i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−2.13973e10	−	3.70612e10i	−0.126744	−	0.219526i	0.795670	−	0.605731i	$-0.207119\pi$
$641$	−2.13973e10	−	3.70612e10i	−0.126744	−	0.219526i	−0.922413	+	0.386205i	$0.873786\pi$
$642$		0			0
$643$		−	1.40089e11i		−	0.819520i	−0.912193	−	0.409760i	$-0.865612\pi$
$643$		−	1.40089e11i		−	0.819520i	0.912193	−	0.409760i	$-0.134388\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	2.13225e11	−	1.23106e11i	1.21681	−	0.702523i	0.252573	−	0.967578i	$-0.418723\pi$
$647$	2.13225e11	−	1.23106e11i	1.21681	−	0.702523i	0.964233	+	0.265054i	$0.0853899\pi$
$648$		0			0
$649$	−1.08223e10	−	6.24828e9i	−0.0610017	−	0.0352194i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	8.06302e10	−	1.39656e11i	0.443450	−	0.768078i	−0.554493	−	0.832189i	$-0.687088\pi$
$653$	8.06302e10	−	1.39656e11i	0.443450	−	0.768078i	0.997943	+	0.0641102i	$0.0204209\pi$
$654$		0			0
$655$	−6.55473e10	−	1.13531e11i	−0.356115	−	0.616808i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	4.42560e10			0.234655			0.117328	−	0.993093i	$-0.462567\pi$
$659$	4.42560e10			0.234655			0.117328	+	0.993093i	$0.462567\pi$
$660$		0			0
$661$	−7.86298e9	+	4.53970e9i	−0.0411890	+	0.0237805i	−0.520453	−	0.853890i	$-0.674237\pi$
$661$	−7.86298e9	+	4.53970e9i	−0.0411890	+	0.0237805i	0.479264	+	0.877671i	$0.340904\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−3.29826e10	−	1.14842e11i	−0.168655	−	0.587236i
$666$		0			0
$667$	−7.08140e10	+	1.22653e11i	−0.357780	+	0.619693i
$668$		0			0
$669$		0			0
$670$		0			0
$671$			2.73552e10i			0.134943i
$672$		0			0
$673$	8.65408e10			0.421852			0.210926	−	0.977502i	$-0.432352\pi$
$673$	8.65408e10			0.421852			0.210926	+	0.977502i	$0.432352\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−2.82894e11	−	1.63329e11i	−1.34669	−	0.777514i	−0.358913	−	0.933371i	$-0.616853\pi$
$677$	−2.82894e11	−	1.63329e11i	−1.34669	−	0.777514i	−0.987780	+	0.155857i	$0.950186\pi$
$678$		0			0
$679$	6.83134e10	−	2.74482e11i	0.321386	−	1.29132i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	5.51338e10	+	9.54946e10i	0.253358	+	0.438830i	0.964448	−	0.264271i	$-0.0851315\pi$
$683$	5.51338e10	+	9.54946e10i	0.253358	+	0.438830i	−0.711090	+	0.703101i	$0.751798\pi$
$684$		0			0
$685$		−	1.88778e11i		−	0.857410i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−6.66613e10	+	3.84869e10i	−0.295799	+	0.170780i
$690$		0			0
$691$	3.05011e10	+	1.76098e10i	0.133784	+	0.0772400i	0.565398	−	0.824818i	$-0.308723\pi$
$691$	3.05011e10	+	1.76098e10i	0.133784	+	0.0772400i	−0.431614	+	0.902058i	$0.642056\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	8.51828e10	−	1.47541e11i	0.365101	−	0.632373i
$696$		0			0
$697$	2.36345e11	+	4.09361e11i	1.00142	+	1.73451i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−4.47112e11			−1.85159			−0.925794	−	0.378029i	$-0.876602\pi$
$701$	−4.47112e11			−1.85159			−0.925794	+	0.378029i	$0.876602\pi$
$702$		0			0
$703$	1.99074e10	−	1.14935e10i	0.0815067	−	0.0470579i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	1.67007e11	−	4.79645e10i	0.668431	−	0.191974i
$708$		0			0
$709$	−7.80091e10	+	1.35116e11i	−0.308717	+	0.534713i	−0.978082	−	0.208221i	$-0.933233\pi$
$709$	−7.80091e10	+	1.35116e11i	−0.308717	+	0.534713i	0.669365	+	0.742933i	$0.266566\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		−	8.27363e10i		−	0.320139i
$714$		0			0
$715$	−1.40252e10			−0.0536643
$716$		0			0
$717$		0			0
$718$		0			0
$719$	1.75088e11	+	1.01087e11i	0.655150	+	0.378251i	0.790426	−	0.612557i	$-0.209859\pi$
$719$	1.75088e11	+	1.01087e11i	0.655150	+	0.378251i	−0.135277	+	0.990808i	$0.543192\pi$
$720$		0			0
$721$	−8.94520e10	−	8.63101e10i	−0.331016	−	0.319390i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−1.11791e11	−	1.93628e11i	−0.404627	−	0.700834i
$726$		0			0
$727$		−	4.20114e11i		−	1.50394i	−0.659200	−	0.751968i	$-0.729105\pi$
$727$		−	4.20114e11i		−	1.50394i	0.659200	−	0.751968i	$-0.270895\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	5.94767e11	−	3.43389e11i	2.08294	−	1.20259i
$732$		0			0
$733$	2.10010e11	+	1.21249e11i	0.727484	+	0.420013i	0.817501	−	0.575927i	$-0.195359\pi$
$733$	2.10010e11	+	1.21249e11i	0.727484	+	0.420013i	−0.0900168	+	0.995940i	$0.528692\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−4.77619e9	+	8.27260e9i	−0.0161887	+	0.0280396i
$738$		0			0
$739$	3.83974e10	+	6.65063e10i	0.128743	+	0.222990i	0.923190	−	0.384344i	$-0.125572\pi$
$739$	3.83974e10	+	6.65063e10i	0.128743	+	0.222990i	−0.794447	+	0.607334i	$0.792239\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−1.24474e11			−0.408435			−0.204218	−	0.978925i	$-0.565465\pi$
$743$	−1.24474e11			−0.408435			−0.204218	+	0.978925i	$0.565465\pi$
$744$		0			0
$745$	1.49292e11	−	8.61938e10i	0.484631	−	0.279802i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−3.96502e11	+	4.10936e11i	−1.25985	+	1.30571i
$750$		0			0
$751$	7.19661e10	−	1.24649e11i	0.226240	−	0.391858i	−0.730451	−	0.682965i	$-0.760690\pi$
$751$	7.19661e10	−	1.24649e11i	0.226240	−	0.391858i	0.956691	+	0.291107i	$0.0940235\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		−	3.78462e11i		−	1.16475i
$756$		0			0
$757$	−5.76514e11			−1.75560			−0.877802	−	0.479025i	$-0.840990\pi$
$757$	−5.76514e11			−1.75560			−0.877802	+	0.479025i	$0.840990\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	7.79898e10	+	4.50274e10i	0.232541	+	0.134257i	0.611744	−	0.791056i	$-0.290468\pi$
$761$	7.79898e10	+	4.50274e10i	0.232541	+	0.134257i	−0.379203	+	0.925314i	$0.623802\pi$
$762$		0			0
$763$	1.32748e11	+	4.62214e11i	0.391679	+	1.36378i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	3.51491e10	+	6.08801e10i	0.101562	+	0.175911i
$768$		0			0
$769$		−	1.18223e11i		−	0.338063i	−0.985611	−	0.169031i	$-0.945936\pi$
$769$		−	1.18223e11i		−	0.338063i	0.985611	−	0.169031i	$-0.0540640\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	4.57013e11	−	2.63856e11i	1.28000	−	0.739009i	0.303153	−	0.952942i	$-0.401961\pi$
$773$	4.57013e11	−	2.63856e11i	1.28000	−	0.739009i	0.976848	+	0.213933i	$0.0686274\pi$
$774$		0			0
$775$	1.13113e11	+	6.53061e10i	0.313550	+	0.181028i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	2.69478e11	−	4.66749e11i	0.731767	−	1.26746i
$780$		0			0
$781$	2.68088e10	+	4.64343e10i	0.0720566	+	0.124806i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	3.14191e11			0.827400
$786$		0			0
$787$	−2.48825e11	+	1.43659e11i	−0.648628	+	0.374485i	−0.787930	−	0.615764i	$-0.788847\pi$
$787$	−2.48825e11	+	1.43659e11i	−0.648628	+	0.374485i	0.139303	+	0.990250i	$0.455514\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−2.43104e11	−	6.05040e10i	−0.620992	−	0.154553i
$792$		0			0
$793$	7.69420e10	−	1.33267e11i	0.194568	−	0.337001i
$794$		0			0
$795$		0			0
$796$		0			0
$797$		−	2.35974e11i		−	0.584831i	−0.956291	−	0.292415i	$-0.905541\pi$
$797$		−	2.35974e11i		−	0.584831i	0.956291	−	0.292415i	$-0.0944590\pi$
$798$		0			0
$799$	−6.28271e11			−1.54156
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−7.85554e10	−	4.53540e10i	−0.188936	−	0.109082i
$804$		0			0
$805$	1.36121e11	−	3.90941e10i	0.324148	−	0.0930954i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−2.09106e10	−	3.62182e10i	−0.0488172	−	0.0845538i	0.840584	−	0.541681i	$-0.182212\pi$
$809$	−2.09106e10	−	3.62182e10i	−0.0488172	−	0.0845538i	−0.889401	+	0.457127i	$0.848878\pi$
$810$		0			0
$811$			1.99731e8i			0.000461703i	1.00000		0.000230851i	$7.34823e-5\pi$
$811$			1.99731e8i			0.000461703i	−1.00000		0.000230851i	$0.999927\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	1.43810e11	−	8.30288e10i	0.325956	−	0.188191i
$816$		0			0
$817$	−6.78146e11	−	3.91528e11i	−1.52207	−	0.878768i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	2.18116e11	−	3.77789e11i	0.480082	−	0.831527i	−0.519656	−	0.854375i	$-0.673940\pi$
$821$	2.18116e11	−	3.77789e11i	0.480082	−	0.831527i	0.999739	+	0.0228481i	$0.00727340\pi$
$822$		0			0
$823$	−5.75405e10	−	9.96630e10i	−0.125422	−	0.217237i	0.796476	−	0.604670i	$-0.206695\pi$
$823$	−5.75405e10	−	9.96630e10i	−0.125422	−	0.217237i	−0.921898	+	0.387433i	$0.873362\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	9.19446e10			0.196564			0.0982821	−	0.995159i	$-0.468665\pi$
$827$	9.19446e10			0.196564			0.0982821	+	0.995159i	$0.468665\pi$
$828$		0			0
$829$	2.31678e11	−	1.33759e11i	0.490531	−	0.283208i	−0.234264	−	0.972173i	$-0.575268\pi$
$829$	2.31678e11	−	1.33759e11i	0.490531	−	0.283208i	0.724795	+	0.688965i	$0.241935\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−6.47150e11	+	2.31442e10i	−1.34408	+	0.0480686i
$834$		0			0
$835$	2.39498e11	−	4.14822e11i	0.492669	−	0.853328i
$836$		0			0
$837$		0			0
$838$		0			0
$839$		−	5.55981e11i		−	1.12205i	−0.827799	−	0.561024i	$-0.810407\pi$
$839$		−	5.55981e11i		−	1.12205i	0.827799	−	0.561024i	$-0.189593\pi$
$840$		0			0
$841$	3.70108e11			0.739852
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−2.06159e11	−	1.19026e11i	−0.404367	−	0.233462i
$846$		0			0
$847$	3.46670e11	−	3.59290e11i	0.673571	−	0.698090i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	1.36232e10	+	2.35961e10i	0.0259754	+	0.0449907i
$852$		0			0
$853$		−	1.58042e11i		−	0.298523i	−0.988798	−	0.149261i	$-0.952310\pi$
$853$		−	1.58042e11i		−	0.298523i	0.988798	−	0.149261i	$-0.0476896\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−3.46613e11	+	2.00117e11i	−0.642572	+	0.370989i	−0.785605	−	0.618729i	$-0.787648\pi$
$857$	−3.46613e11	+	2.00117e11i	−0.642572	+	0.370989i	0.143032	+	0.989718i	$0.454315\pi$
$858$		0			0
$859$	7.13409e11	+	4.11887e11i	1.31028	+	0.756493i	0.982143	−	0.188135i	$-0.0602444\pi$
$859$	7.13409e11	+	4.11887e11i	1.31028	+	0.756493i	0.328141	+	0.944629i	$0.393578\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−2.50858e11	+	4.34499e11i	−0.452256	+	0.783331i	−0.998526	−	0.0542787i	$-0.982714\pi$
$863$	−2.50858e11	+	4.34499e11i	−0.452256	+	0.783331i	0.546270	+	0.837609i	$0.316047\pi$
$864$		0			0
$865$	2.06870e10	+	3.58309e10i	0.0369515	+	0.0640019i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−1.44684e11			−0.253712
$870$		0			0
$871$	4.65367e10	−	2.68680e10i	0.0808581	−	0.0466834i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−1.42008e11	+	5.70584e11i	−0.242259	+	0.973392i
$876$		0			0
$877$	−1.82819e11	+	3.16652e11i	−0.309046	+	0.535284i	−0.978154	−	0.207882i	$-0.933343\pi$
$877$	−1.82819e11	+	3.16652e11i	−0.309046	+	0.535284i	0.669108	+	0.743165i	$0.266676\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			1.85597e11i			0.308082i	0.988064	+	0.154041i	$0.0492288\pi$
$881$			1.85597e11i			0.308082i	−0.988064	+	0.154041i	$0.950771\pi$
$882$		0			0
$883$	4.09560e11			0.673713			0.336856	−	0.941556i	$-0.390636\pi$
$883$	4.09560e11			0.673713			0.336856	+	0.941556i	$0.390636\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	7.06127e11	+	4.07683e11i	1.14074	+	0.658609i	0.946615	−	0.322367i	$-0.104478\pi$
$887$	7.06127e11	+	4.07683e11i	1.14074	+	0.658609i	0.194129	+	0.980976i	$0.437812\pi$
$888$		0			0
$889$	−8.27607e11	−	2.05976e11i	−1.32500	−	0.329768i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	3.58173e11	+	6.20374e11i	0.563232	+	0.975546i
$894$		0			0
$895$			2.42203e11i			0.377474i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−4.40325e11	+	2.54222e11i	−0.674117	+	0.389201i
$900$		0			0
$901$	5.25486e11	+	3.03390e11i	0.797374	+	0.460364i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	8.54853e9	−	1.48065e10i	0.0127437	−	0.0220728i
$906$		0			0
$907$	−2.67691e11	−	4.63654e11i	−0.395553	−	0.685117i	0.597619	−	0.801780i	$-0.296114\pi$
$907$	−2.67691e11	−	4.63654e11i	−0.395553	−	0.685117i	−0.993172	+	0.116663i	$0.962780\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−1.14219e12			−1.65831			−0.829153	−	0.559021i	$-0.811177\pi$
$911$	−1.14219e12			−1.65831			−0.829153	+	0.559021i	$0.811177\pi$
$912$		0			0
$913$	−1.60692e11	+	9.27757e10i	−0.231266	+	0.133521i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	5.82967e11	+	5.62491e11i	0.824454	+	0.795496i
$918$		0			0
$919$	−4.97479e11	+	8.61659e11i	−0.697449	+	1.20802i	0.271899	+	0.962326i	$0.412348\pi$
$919$	−4.97479e11	+	8.61659e11i	−0.697449	+	1.20802i	−0.969348	+	0.245692i	$0.920985\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		−	3.01621e11i		−	0.415581i
$924$		0			0
$925$	−4.30128e10			−0.0587531
$926$		0			0
$927$		0			0
$928$		0			0
$929$	1.06967e12	+	6.17574e11i	1.43611	+	0.829136i	0.997576	−	0.0695806i	$-0.0221661\pi$
$929$	1.06967e12	+	6.17574e11i	1.43611	+	0.829136i	0.438530	+	0.898717i	$0.355499\pi$
$930$		0			0
$931$	3.91789e11	+	6.25822e11i	0.521500	+	0.833013i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	5.52800e10	+	9.57477e10i	0.0723305	+	0.125280i
$936$		0			0
$937$		−	1.13852e12i		−	1.47701i	−0.674247	−	0.738506i	$-0.735532\pi$
$937$		−	1.13852e12i		−	1.47701i	0.674247	−	0.738506i	$-0.264468\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	6.65227e10	−	3.84069e10i	0.0848421	−	0.0489836i	−0.456979	−	0.889478i	$-0.651068\pi$
$941$	6.65227e10	−	3.84069e10i	0.0848421	−	0.0489836i	0.541821	+	0.840494i	$0.317735\pi$
$942$		0			0
$943$	5.53235e11	+	3.19411e11i	0.699621	+	0.403927i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−2.44480e11	+	4.23452e11i	−0.303979	+	0.526507i	−0.977033	−	0.213086i	$-0.931649\pi$
$947$	−2.44480e11	+	4.23452e11i	−0.303979	+	0.526507i	0.673054	+	0.739593i	$0.264982\pi$
$948$		0			0
$949$	2.55135e11	+	4.41906e11i	0.314561	+	0.544835i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−1.61651e12			−1.95978			−0.979888	−	0.199547i	$-0.936053\pi$
$953$	−1.61651e12			−1.95978			−0.979888	+	0.199547i	$0.936053\pi$
$954$		0			0
$955$	2.43326e10	−	1.40484e10i	0.0292533	−	0.0168894i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	3.22013e11	+	1.12121e12i	0.380715	+	1.32560i
$960$		0			0
$961$	−2.77934e11	+	4.81396e11i	−0.325873	+	0.564428i
$962$		0			0
$963$		0			0
$964$		0			0
$965$		−	1.89126e11i		−	0.218093i
$966$		0			0
$967$	−9.69849e11			−1.10917			−0.554585	−	0.832127i	$-0.687123\pi$
$967$	−9.69849e11			−1.10917			−0.554585	+	0.832127i	$0.687123\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−1.82528e11	−	1.05383e11i	−0.205330	−	0.118548i	0.393809	−	0.919192i	$-0.371157\pi$
$971$	−1.82528e11	−	1.05383e11i	−0.205330	−	0.118548i	−0.599139	+	0.800645i	$0.704490\pi$
$972$		0			0
$973$	−2.54257e11	+	1.02160e12i	−0.283675	+	1.13980i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	8.51788e11	+	1.47534e12i	0.934874	+	1.61925i	0.774858	+	0.632135i	$0.217821\pi$
$977$	8.51788e11	+	1.47534e12i	0.934874	+	1.61925i	0.160016	+	0.987114i	$0.448845\pi$
$978$		0			0
$979$		−	1.26763e10i		−	0.0137995i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	5.56165e11	−	3.21102e11i	0.595648	−	0.343897i	−0.171680	−	0.985153i	$-0.554919\pi$
$983$	5.56165e11	−	3.21102e11i	0.595648	−	0.343897i	0.767327	+	0.641256i	$0.221586\pi$
$984$		0			0
$985$	6.14528e11	+	3.54798e11i	0.652825	+	0.376909i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	4.64076e11	−	8.03803e11i	0.485069	−	0.840165i
$990$		0			0
$991$	−2.16995e11	−	3.75846e11i	−0.224986	−	0.389687i	0.731330	−	0.682024i	$-0.238900\pi$
$991$	−2.16995e11	−	3.75846e11i	−0.224986	−	0.389687i	−0.956315	+	0.292338i	$0.905567\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−2.10195e11			−0.214452
$996$		0			0
$997$	−3.10449e11	+	1.79238e11i	−0.314203	+	0.181405i	−0.648806	−	0.760954i	$-0.724731\pi$
$997$	−3.10449e11	+	1.79238e11i	−0.314203	+	0.181405i	0.334603	+	0.942359i	$0.391398\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.9.z.c.145.2		10
3.2	odd	2		28.9.h.a.5.5	✓	10
7.3	odd	6	inner	252.9.z.c.73.2		10
12.11	even	2		112.9.s.b.33.1		10
21.2	odd	6		196.9.b.a.97.9		10
21.5	even	6		196.9.b.a.97.2		10
21.11	odd	6		196.9.h.a.129.1		10
21.17	even	6		28.9.h.a.17.5	yes	10
21.20	even	2		196.9.h.a.117.1		10
84.59	odd	6		112.9.s.b.17.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
28.9.h.a.5.5	✓	10	3.2	odd	2
28.9.h.a.17.5	yes	10	21.17	even	6
112.9.s.b.17.1		10	84.59	odd	6
112.9.s.b.33.1		10	12.11	even	2
196.9.b.a.97.2		10	21.5	even	6
196.9.b.a.97.9		10	21.2	odd	6
196.9.h.a.117.1		10	21.20	even	2
196.9.h.a.129.1		10	21.11	odd	6
252.9.z.c.73.2		10	7.3	odd	6	inner
252.9.z.c.145.2		10	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)

\(f(q)\)	\(=\)	\(q+(-336.492 - 194.274i) q^{5} +(2329.92 + 579.874i) q^{7} +O(q^{10})\)	\(q+(-336.492 - 194.274i) q^{5} +(2329.92 + 579.874i) q^{7} +(1266.56 + 2193.75i) q^{11} -14249.8i q^{13} +(-97281.1 + 56165.3i) q^{17} +(110919. + 64039.0i) q^{19} +(-75905.1 + 131472. i) q^{23} +(-119828. - 207548. i) q^{25} +932928. q^{29} +(-471982. + 272499. i) q^{31} +(-671346. - 647766. i) q^{35} +(89738.6 - 155432. i) q^{37} -4.20802e6i q^{41} -6.11389e6 q^{43} +(4.84372e6 + 2.79652e6i) q^{47} +(5.09229e6 + 2.70213e6i) q^{49} +(-2.70086e6 - 4.67803e6i) q^{53} -984237. i q^{55} +(-4.27233e6 + 2.46663e6i) q^{59} +(9.35220e6 + 5.39950e6i) q^{61} +(-2.76837e6 + 4.79495e6i) q^{65} +(1.88549e6 + 3.26577e6i) q^{67} +2.11666e7 q^{71} +(-3.10113e7 + 1.79044e7i) q^{73} +(1.67889e6 + 5.84571e6i) q^{77} +(-2.85584e7 + 4.94645e7i) q^{79} +7.32501e7i q^{83} +4.36457e7 q^{85} +(-4.33379e6 - 2.50212e6i) q^{89} +(8.26312e6 - 3.32011e7i) q^{91} +(-2.48822e7 - 4.30972e7i) q^{95} -1.17807e8i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 837 q^{5} + 1526 q^{7}+O(q^{10}) \) 10 * q + 837 * q^5 + 1526 * q^7	\( 10 q + 837 q^{5} + 1526 q^{7} - 3705 q^{11} - 78003 q^{17} - 96741 q^{19} - 208533 q^{23} + 367978 q^{25} - 754764 q^{29} - 1053717 q^{31} + 1306389 q^{35} - 998075 q^{37} + 738292 q^{43} - 710883 q^{47} + 13288114 q^{49} - 10501461 q^{53} + 37089081 q^{59} - 8180481 q^{61} - 21459108 q^{65} + 48020189 q^{67} + 31918236 q^{71} - 133345593 q^{73} - 188477625 q^{77} + 53590181 q^{79} - 157179282 q^{85} + 241368273 q^{89} + 420709128 q^{91} - 347126775 q^{95}+O(q^{100}) \) 10 * q + 837 * q^5 + 1526 * q^7 - 3705 * q^11 - 78003 * q^17 - 96741 * q^19 - 208533 * q^23 + 367978 * q^25 - 754764 * q^29 - 1053717 * q^31 + 1306389 * q^35 - 998075 * q^37 + 738292 * q^43 - 710883 * q^47 + 13288114 * q^49 - 10501461 * q^53 + 37089081 * q^59 - 8180481 * q^61 - 21459108 * q^65 + 48020189 * q^67 + 31918236 * q^71 - 133345593 * q^73 - 188477625 * q^77 + 53590181 * q^79 - 157179282 * q^85 + 241368273 * q^89 + 420709128 * q^91 - 347126775 * q^95

Introduction

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