LMFDB - Embedded newform 45.9.d.a.44.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [45,9,Mod(44,45)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(45, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("45.44");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	45.d (of order $2$, degree $1$, 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:	$18.3320374528$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 1982 x^{14} + 1579736 x^{12} + 654647506 x^{10} + 151540734566 x^{8} + 19474609444738 x^{6} + \cdots + 29\!\cdots\!09 $ x^16 + 1982x^14 + 1579736x^12 + 654647506x^10 + 151540734566x^8 + 19474609444738x^6 + 1288318886608936x^4 + 36624709707917870*x^2 + 296773539014178009
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{15}\cdot 3^{42}\cdot 5^{10}\cdot 7^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			44.13
Root			$-6.77659i$ of defining polynomial
Character	$\chi$	$=$	45.44
Dual form			45.9.d.a.44.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+22.2774 q^{2} +240.281 q^{4} +(-622.133 - 59.7978i) q^{5} +2644.18i q^{7} -350.176 q^{8} +O(q^{10})$	\(q+22.2774 q^{2} +240.281 q^{4} +(-622.133 - 59.7978i) q^{5} +2644.18i q^{7} -350.176 q^{8} +(-13859.5 - 1332.14i) q^{10} +22455.9i q^{11} +11076.3i q^{13} +58905.4i q^{14} -69313.0 q^{16} +35513.3 q^{17} +3033.68 q^{19} +(-149487. - 14368.3i) q^{20} +500258. i q^{22} -352929. q^{23} +(383473. + 74404.4i) q^{25} +246750. i q^{26} +635347. i q^{28} -1.14240e6i q^{29} +317106. q^{31} -1.45447e6 q^{32} +791142. q^{34} +(158116. - 1.64503e6i) q^{35} +1.94595e6i q^{37} +67582.4 q^{38} +(217856. + 20939.8i) q^{40} +3.08883e6i q^{41} +255669. i q^{43} +5.39573e6i q^{44} -7.86233e6 q^{46} -5.90149e6 q^{47} -1.22689e6 q^{49} +(8.54278e6 + 1.65753e6i) q^{50} +2.66142e6i q^{52} +9.19732e6 q^{53} +(1.34281e6 - 1.39705e7i) q^{55} -925928. i q^{56} -2.54498e7i q^{58} -1.32577e7i q^{59} +2.48813e7 q^{61} +7.06429e6 q^{62} -1.46575e7 q^{64} +(662337. - 6.89091e6i) q^{65} +3.54713e7i q^{67} +8.53316e6 q^{68} +(3.52241e6 - 3.66470e7i) q^{70} -4.67255e7i q^{71} -4.36638e6i q^{73} +4.33507e7i q^{74} +728936. q^{76} -5.93774e7 q^{77} +1.73568e7 q^{79} +(4.31219e7 + 4.14477e6i) q^{80} +6.88110e7i q^{82} +5.54885e6 q^{83} +(-2.20940e7 - 2.12362e6i) q^{85} +5.69564e6i q^{86} -7.86351e6i q^{88} +9.75180e7i q^{89} -2.92876e7 q^{91} -8.48022e7 q^{92} -1.31470e8 q^{94} +(-1.88735e6 - 181408. i) q^{95} +1.26808e8i q^{97} -2.73319e7 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 1572 q^{4}+O(q^{10}) $ 16 * q + 1572 * q^4	$ 16 q + 1572 q^{4} + 16280 q^{10} - 12844 q^{16} + 263600 q^{19} + 1124860 q^{25} - 4312984 q^{31} + 2439352 q^{34} + 10217140 q^{40} - 5376344 q^{46} - 7338968 q^{49} + 5658120 q^{55} + 26097968 q^{61} - 123290756 q^{64} + 27888840 q^{70} + 222695760 q^{76} - 262645864 q^{79} + 202172900 q^{85} + 350561736 q^{91} - 789068384 q^{94}+O(q^{100}) $ 16 * q + 1572 * q^4 + 16280 * q^10 - 12844 * q^16 + 263600 * q^19 + 1124860 * q^25 - 4312984 * q^31 + 2439352 * q^34 + 10217140 * q^40 - 5376344 * q^46 - 7338968 * q^49 + 5658120 * q^55 + 26097968 * q^61 - 123290756 * q^64 + 27888840 * q^70 + 222695760 * q^76 - 262645864 * q^79 + 202172900 * q^85 + 350561736 * q^91 - 789068384 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$-1$	$-1$

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 $

$2$	22.2774			1.39234			0.696168	−	0.717879i	$-0.254887\pi$
$2$	22.2774			1.39234			0.696168	+	0.717879i	$0.254887\pi$
$3$		0			0
$3$		0			0
$4$	240.281			0.938598
$5$	−622.133	−	59.7978i	−0.995412	−	0.0956765i
$5$	−622.133	−	59.7978i	−0.995412	−	0.0956765i
$6$		0			0
$7$			2644.18i			1.10128i	0.834742	+	0.550642i	$0.185617\pi$
$7$			2644.18i			1.10128i	−0.834742	+	0.550642i	$0.814383\pi$
$8$	−350.176			−0.0854921
$9$		0			0
$10$	−13859.5	−	1332.14i	−1.38595	−	0.133214i
$11$			22455.9i			1.53377i	0.641786	+	0.766884i	$0.278194\pi$
$11$			22455.9i			1.53377i	−0.641786	+	0.766884i	$0.721806\pi$
$12$		0			0
$13$			11076.3i			0.387811i	0.981020	+	0.193905i	$0.0621155\pi$
$13$			11076.3i			0.387811i	−0.981020	+	0.193905i	$0.937885\pi$
$14$			58905.4i			1.53336i
$15$		0			0
$16$	−69313.0			−1.05763
$17$	35513.3			0.425201			0.212601	−	0.977139i	$-0.431807\pi$
$17$	35513.3			0.425201			0.212601	+	0.977139i	$0.431807\pi$
$18$		0			0
$19$	3033.68			0.0232785			0.0116393	−	0.999932i	$-0.496295\pi$
$19$	3033.68			0.0232785			0.0116393	+	0.999932i	$0.496295\pi$
$20$	−149487.	−	14368.3i	−0.934292	−	0.0898018i
$21$		0			0
$22$			500258.i			2.13552i
$23$	−352929.			−1.26118			−0.630589	−	0.776117i	$-0.717186\pi$
$23$	−352929.			−1.26118			−0.630589	+	0.776117i	$0.717186\pi$
$24$		0			0
$25$	383473.	+	74404.4i	0.981692	+	0.190475i
$26$			246750.i			0.539963i
$27$		0			0
$28$			635347.i			1.03366i
$29$		−	1.14240e6i		−	1.61521i	−0.589726	−	0.807603i	$-0.700764\pi$
$29$		−	1.14240e6i		−	1.61521i	0.589726	−	0.807603i	$-0.299236\pi$
$30$		0			0
$31$	317106.			0.343367			0.171683	−	0.985152i	$-0.445079\pi$
$31$	317106.			0.343367			0.171683	+	0.985152i	$0.445079\pi$
$32$	−1.45447e6			−1.38709
$33$		0			0
$34$	791142.			0.592023
$35$	158116.	−	1.64503e6i	0.105367	−	1.09623i
$36$		0			0
$37$			1.94595e6i			1.03831i	0.854681	+	0.519153i	$0.173753\pi$
$37$			1.94595e6i			1.03831i	−0.854681	+	0.519153i	$0.826247\pi$
$38$	67582.4			0.0324115
$39$		0			0
$40$	217856.	+	20939.8i	0.0850999	+	0.00817959i
$41$			3.08883e6i			1.09310i	0.837428	+	0.546548i	$0.184059\pi$
$41$			3.08883e6i			1.09310i	−0.837428	+	0.546548i	$0.815941\pi$
$42$		0			0
$43$			255669.i			0.0747833i	0.999301	+	0.0373916i	$0.0119049\pi$
$43$			255669.i			0.0747833i	−0.999301	+	0.0373916i	$0.988095\pi$
$44$			5.39573e6i			1.43959i
$45$		0			0
$46$	−7.86233e6			−1.75598
$47$	−5.90149e6			−1.20940			−0.604701	−	0.796453i	$-0.706707\pi$
$47$	−5.90149e6			−1.20940			−0.604701	+	0.796453i	$0.706707\pi$
$48$		0			0
$49$	−1.22689e6			−0.212824
$50$	8.54278e6	+	1.65753e6i	1.36684	+	0.265205i
$51$		0			0
$52$			2.66142e6i			0.363998i
$53$	9.19732e6			1.16562			0.582811	−	0.812608i	$-0.301953\pi$
$53$	9.19732e6			1.16562			0.582811	+	0.812608i	$0.301953\pi$
$54$		0			0
$55$	1.34281e6	−	1.39705e7i	0.146746	−	1.52673i
$56$		−	925928.i		−	0.0941510i
$57$		0			0
$58$		−	2.54498e7i		−	2.24891i
$59$		−	1.32577e7i		−	1.09411i	−0.837096	−	0.547056i	$-0.815749\pi$
$59$		−	1.32577e7i		−	1.09411i	0.837096	−	0.547056i	$-0.184251\pi$
$60$		0			0
$61$	2.48813e7			1.79703			0.898513	−	0.438946i	$-0.144648\pi$
$61$	2.48813e7			1.79703			0.898513	+	0.438946i	$0.144648\pi$
$62$	7.06429e6			0.478082
$63$		0			0
$64$	−1.46575e7			−0.873657
$65$	662337.	−	6.89091e6i	0.0371044	−	0.386032i
$66$		0			0
$67$			3.54713e7i			1.76026i	0.474729	+	0.880132i	$0.342546\pi$
$67$			3.54713e7i			1.76026i	−0.474729	+	0.880132i	$0.657454\pi$
$68$	8.53316e6			0.399093
$69$		0			0
$70$	3.52241e6	−	3.66470e7i	0.146706	−	1.52632i
$71$		−	4.67255e7i		−	1.83874i	−0.393394	−	0.919370i	$-0.628699\pi$
$71$		−	4.67255e7i		−	1.83874i	0.393394	−	0.919370i	$-0.371301\pi$
$72$		0			0
$73$		−	4.36638e6i		−	0.153755i	−0.997041	−	0.0768777i	$-0.975505\pi$
$73$		−	4.36638e6i		−	0.153755i	0.997041	−	0.0768777i	$-0.0244951\pi$
$74$			4.33507e7i			1.44567i
$75$		0			0
$76$	728936.			0.0218492
$77$	−5.93774e7			−1.68911
$78$		0			0
$79$	1.73568e7			0.445617			0.222808	−	0.974862i	$-0.428478\pi$
$79$	1.73568e7			0.445617			0.222808	+	0.974862i	$0.428478\pi$
$80$	4.31219e7	+	4.14477e6i	1.05278	+	0.101191i
$81$		0			0
$82$			6.88110e7i			1.52196i
$83$	5.54885e6			0.116921			0.0584603	−	0.998290i	$-0.481381\pi$
$83$	5.54885e6			0.116921			0.0584603	+	0.998290i	$0.481381\pi$
$84$		0			0
$85$	−2.20940e7	−	2.12362e6i	−0.423251	−	0.0406818i
$86$			5.69564e6i			0.104123i
$87$		0			0
$88$		−	7.86351e6i		−	0.131125i
$89$			9.75180e7i			1.55426i	0.629338	+	0.777132i	$0.283326\pi$
$89$			9.75180e7i			1.55426i	−0.629338	+	0.777132i	$0.716674\pi$
$90$		0			0
$91$	−2.92876e7			−0.427089
$92$	−8.48022e7			−1.18374
$93$		0			0
$94$	−1.31470e8			−1.68389
$95$	−1.88735e6	−	181408.i	−0.0231717	−	0.00222721i
$96$		0			0
$97$			1.26808e8i			1.43238i	0.697905	+	0.716190i	$0.254116\pi$
$97$			1.26808e8i			1.43238i	−0.697905	+	0.716190i	$0.745884\pi$
$98$	−2.73319e7			−0.296323
$99$		0			0
$100$	9.21414e7	+	1.78780e7i	0.921414	+	0.178780i
$101$			7.63212e7i			0.733432i	0.930333	+	0.366716i	$0.119518\pi$
$101$			7.63212e7i			0.733432i	−0.930333	+	0.366716i	$0.880482\pi$
$102$		0			0
$103$			1.62029e8i			1.43960i	0.694180	+	0.719801i	$0.255767\pi$
$103$			1.62029e8i			1.43960i	−0.694180	+	0.719801i	$0.744233\pi$
$104$		−	3.87864e6i		−	0.0331548i
$105$		0			0
$106$	2.04892e8			1.62294
$107$	−1.38641e8			−1.05768			−0.528842	−	0.848720i	$-0.677374\pi$
$107$	−1.38641e8			−1.05768			−0.528842	+	0.848720i	$0.677374\pi$
$108$		0			0
$109$	−5.81922e7			−0.412248			−0.206124	−	0.978526i	$-0.566085\pi$
$109$	−5.81922e7			−0.412248			−0.206124	+	0.978526i	$0.566085\pi$
$110$	2.99144e7	−	3.11227e8i	0.204319	−	2.12572i
$111$		0			0
$112$		−	1.83276e8i		−	1.16475i
$113$	1.57487e7			0.0965899			0.0482949	−	0.998833i	$-0.484621\pi$
$113$	1.57487e7			0.0965899			0.0482949	+	0.998833i	$0.484621\pi$
$114$		0			0
$115$	2.19569e8	+	2.11044e7i	1.25539	+	0.120665i
$116$		−	2.74498e8i		−	1.51603i
$117$		0			0
$118$		−	2.95348e8i		−	1.52337i
$119$			9.39034e7i			0.468267i
$120$		0			0
$121$	−2.89908e8			−1.35244
$122$	5.54291e8			2.50206
$123$		0			0
$124$	7.61946e7			0.322283
$125$	−2.34122e8	−	6.92203e7i	−0.958964	−	0.283526i
$126$		0			0
$127$		−	8.56922e7i		−	0.329402i	−0.986344	−	0.164701i	$-0.947334\pi$
$127$		−	8.56922e7i		−	0.329402i	0.986344	−	0.164701i	$-0.0526660\pi$
$128$	4.58117e7			0.170662
$129$		0			0
$130$	1.47551e7	−	1.53511e8i	0.0516618	−	0.537486i
$131$			2.13424e8i			0.724699i	0.932042	+	0.362350i	$0.118025\pi$
$131$			2.13424e8i			0.724699i	−0.932042	+	0.362350i	$0.881975\pi$
$132$		0			0
$133$			8.02160e6i			0.0256362i
$134$			7.90207e8i			2.45088i
$135$		0			0
$136$	−1.24359e7			−0.0363514
$137$	4.29184e8			1.21832			0.609159	−	0.793048i	$-0.291507\pi$
$137$	4.29184e8			1.21832			0.609159	+	0.793048i	$0.291507\pi$
$138$		0			0
$139$	−5.52255e8			−1.47938			−0.739691	−	0.672947i	$-0.765028\pi$
$139$	−5.52255e8			−1.47938			−0.739691	+	0.672947i	$0.765028\pi$
$140$	3.79924e7	−	3.95270e8i	0.0988972	−	1.02892i
$141$		0			0
$142$		−	1.04092e9i		−	2.56014i
$143$	−2.48727e8			−0.594812
$144$		0			0
$145$	−6.83133e7	+	7.10727e8i	−0.154537	+	1.60780i
$146$		−	9.72715e7i		−	0.214079i
$147$		0			0
$148$			4.67576e8i			0.974553i
$149$			4.10444e8i			0.832738i	0.909196	+	0.416369i	$0.136698\pi$
$149$			4.10444e8i			0.832738i	−0.909196	+	0.416369i	$0.863302\pi$
$150$		0			0
$151$	8.42072e8			1.61973			0.809863	−	0.586619i	$-0.199541\pi$
$151$	8.42072e8			1.61973			0.809863	+	0.586619i	$0.199541\pi$
$152$	−1.06232e6			−0.00199013
$153$		0			0
$154$	−1.32277e9			−2.35181
$155$	−1.97282e8	−	1.89623e7i	−0.341791	−	0.0328521i
$156$		0			0
$157$		−	3.77763e8i		−	0.621757i	−0.950450	−	0.310878i	$-0.899377\pi$
$157$		−	3.77763e8i		−	0.621757i	0.950450	−	0.310878i	$-0.100623\pi$
$158$	3.86664e8			0.620448
$159$		0			0
$160$	9.04870e8	+	8.69739e7i	1.38072	+	0.132712i
$161$		−	9.33208e8i		−	1.38891i
$162$		0			0
$163$		−	1.59262e8i		−	0.225612i	−0.993617	−	0.112806i	$-0.964016\pi$
$163$		−	1.59262e8i		−	0.225612i	0.993617	−	0.112806i	$-0.0359839\pi$
$164$			7.42188e8i			1.02598i
$165$		0			0
$166$	1.23614e8			0.162793
$167$	−3.89514e7			−0.0500792			−0.0250396	−	0.999686i	$-0.507971\pi$
$167$	−3.89514e7			−0.0500792			−0.0250396	+	0.999686i	$0.507971\pi$
$168$		0			0
$169$	6.93047e8			0.849603
$170$	−4.92195e8	−	4.73086e7i	−0.589307	−	0.0566427i
$171$		0			0
$172$			6.14325e7i			0.0701914i
$173$	−9.12788e8			−1.01903			−0.509513	−	0.860463i	$-0.670175\pi$
$173$	−9.12788e8			−1.01903			−0.509513	+	0.860463i	$0.670175\pi$
$174$		0			0
$175$	−1.96739e8	+	1.01397e9i	−0.209767	+	1.08112i
$176$		−	1.55648e9i		−	1.62216i
$177$		0			0
$178$			2.17244e9i			2.16406i
$179$		−	1.70075e8i		−	0.165664i	−0.996564	−	0.0828321i	$-0.973603\pi$
$179$		−	1.70075e8i		−	0.165664i	0.996564	−	0.0828321i	$-0.0263965\pi$
$180$		0			0
$181$	7.47609e8			0.696563			0.348281	−	0.937390i	$-0.386765\pi$
$181$	7.47609e8			0.696563			0.348281	+	0.937390i	$0.386765\pi$
$182$	−6.52452e8			−0.594652
$183$		0			0
$184$	1.23587e8			0.107821
$185$	1.16364e8	−	1.21064e9i	0.0993416	−	1.03354i
$186$		0			0
$187$			7.97482e8i			0.652160i
$188$	−1.41802e9			−1.13514
$189$		0			0
$190$	−4.20452e7	−	4.04128e6i	−0.0322628	−	0.00310102i
$191$			1.90973e8i			0.143495i	0.997423	+	0.0717477i	$0.0228576\pi$
$191$			1.90973e8i			0.143495i	−0.997423	+	0.0717477i	$0.977142\pi$
$192$		0			0
$193$		−	1.57576e9i		−	1.13569i	−0.823134	−	0.567847i	$-0.807776\pi$
$193$		−	1.57576e9i		−	1.13569i	0.823134	−	0.567847i	$-0.192224\pi$
$194$			2.82494e9i			1.99435i
$195$		0			0
$196$	−2.94798e8			−0.199756
$197$	−3.35396e7			−0.0222686			−0.0111343	−	0.999938i	$-0.503544\pi$
$197$	−3.35396e7			−0.0222686			−0.0111343	+	0.999938i	$0.503544\pi$
$198$		0			0
$199$	−1.16032e9			−0.739890			−0.369945	−	0.929054i	$-0.620623\pi$
$199$	−1.16032e9			−0.739890			−0.369945	+	0.929054i	$0.620623\pi$
$200$	−1.34283e8	−	2.60546e7i	−0.0839269	−	0.0162841i
$201$		0			0
$202$			1.70024e9i			1.02118i
$203$	3.02072e9			1.77880
$204$		0			0
$205$	1.84705e8	−	1.92166e9i	0.104584	−	1.08808i
$206$			3.60957e9i			2.00441i
$207$		0			0
$208$		−	7.67729e8i		−	0.410161i
$209$			6.81240e7i			0.0357039i
$210$		0			0
$211$	−1.65320e9			−0.834059			−0.417029	−	0.908893i	$-0.636929\pi$
$211$	−1.65320e9			−0.834059			−0.417029	+	0.908893i	$0.636929\pi$
$212$	2.20994e9			1.09405
$213$		0			0
$214$	−3.08855e9			−1.47265
$215$	1.52885e7	−	1.59060e8i	0.00715501	−	0.0744402i
$216$		0			0
$217$			8.38486e8i			0.378144i
$218$	−1.29637e9			−0.573988
$219$		0			0
$220$	3.22653e8	−	3.35686e9i	0.137735	−	1.43299i
$221$			3.93354e8i			0.164898i
$222$		0			0
$223$		−	3.62653e9i		−	1.46647i	−0.679977	−	0.733233i	$-0.738010\pi$
$223$		−	3.62653e9i		−	1.46647i	0.679977	−	0.733233i	$-0.261990\pi$
$224$		−	3.84587e9i		−	1.52757i
$225$		0			0
$226$	3.50840e8			0.134486
$227$	−3.32488e9			−1.25220			−0.626099	−	0.779744i	$-0.715349\pi$
$227$	−3.32488e9			−1.25220			−0.626099	+	0.779744i	$0.715349\pi$
$228$		0			0
$229$	4.14773e9			1.50823			0.754117	−	0.656740i	$-0.228065\pi$
$229$	4.14773e9			1.50823			0.754117	+	0.656740i	$0.228065\pi$
$230$	4.89141e9	+	4.70150e8i	1.74793	+	0.168006i
$231$		0			0
$232$			4.00042e8i			0.138087i
$233$	4.25813e9			1.44476			0.722380	−	0.691496i	$-0.243048\pi$
$233$	4.25813e9			1.44476			0.722380	+	0.691496i	$0.243048\pi$
$234$		0			0
$235$	3.67151e9	+	3.52897e8i	1.20385	+	0.115711i
$236$		−	3.18559e9i		−	1.02693i
$237$		0			0
$238$			2.09192e9i			0.651985i
$239$		−	3.02690e9i		−	0.927698i	−0.885914	−	0.463849i	$-0.846468\pi$
$239$		−	3.02690e9i		−	0.927698i	0.885914	−	0.463849i	$-0.153532\pi$
$240$		0			0
$241$	−3.38816e9			−1.00438			−0.502188	−	0.864758i	$-0.667471\pi$
$241$	−3.38816e9			−1.00438			−0.502188	+	0.864758i	$0.667471\pi$
$242$	−6.45840e9			−1.88306
$243$		0			0
$244$	5.97852e9			1.68669
$245$	7.63288e8	+	7.33653e7i	0.211848	+	0.0203623i
$246$		0			0
$247$			3.36018e7i			0.00902766i
$248$	−1.11043e8			−0.0293551
$249$		0			0
$250$	−5.21563e9	−	1.54205e9i	−1.33520	−	0.394764i
$251$			2.21606e9i			0.558324i	0.960244	+	0.279162i	$0.0900566\pi$
$251$			2.21606e9i			0.558324i	−0.960244	+	0.279162i	$0.909943\pi$
$252$		0			0
$253$		−	7.92534e9i		−	1.93435i
$254$		−	1.90900e9i		−	0.458639i
$255$		0			0
$256$	4.77289e9			1.11128
$257$	3.68531e9			0.844777			0.422388	−	0.906415i	$-0.361192\pi$
$257$	3.68531e9			0.844777			0.422388	+	0.906415i	$0.361192\pi$
$258$		0			0
$259$	−5.14545e9			−1.14347
$260$	1.59147e8	−	1.65575e9i	0.0348261	−	0.362329i
$261$		0			0
$262$			4.75452e9i			1.00902i
$263$	2.54121e9			0.531151			0.265575	−	0.964090i	$-0.414438\pi$
$263$	2.54121e9			0.531151			0.265575	+	0.964090i	$0.414438\pi$
$264$		0			0
$265$	−5.72196e9	−	5.49980e8i	−1.16028	−	0.111523i
$266$			1.78700e8i			0.0356942i
$267$		0			0
$268$			8.52308e9i			1.65218i
$269$			4.48964e9i			0.857437i	0.903438	+	0.428718i	$0.141035\pi$
$269$			4.48964e9i			0.857437i	−0.903438	+	0.428718i	$0.858965\pi$
$270$		0			0
$271$	−1.36070e8			−0.0252281			−0.0126141	−	0.999920i	$-0.504015\pi$
$271$	−1.36070e8			−0.0252281			−0.0126141	+	0.999920i	$0.504015\pi$
$272$	−2.46153e9			−0.449707
$273$		0			0
$274$	9.56108e9			1.69631
$275$	−1.67082e9	+	8.61124e9i	−0.292145	+	1.50569i
$276$		0			0
$277$			5.79752e9i			0.984743i	0.870385	+	0.492372i	$0.163870\pi$
$277$			5.79752e9i			0.984743i	−0.870385	+	0.492372i	$0.836130\pi$
$278$	−1.23028e10			−2.05980
$279$		0			0
$280$	−5.53685e7	+	5.76050e8i	−0.00900804	+	0.0937191i
$281$			4.33689e9i			0.695589i	0.937571	+	0.347794i	$0.113069\pi$
$281$			4.33689e9i			0.695589i	−0.937571	+	0.347794i	$0.886931\pi$
$282$		0			0
$283$			2.93677e9i			0.457850i	0.973444	+	0.228925i	$0.0735211\pi$
$283$			2.93677e9i			0.457850i	−0.973444	+	0.228925i	$0.926479\pi$
$284$		−	1.12272e10i		−	1.72584i
$285$		0			0
$286$	−5.54099e9			−0.828178
$287$	−8.16742e9			−1.20381
$288$		0			0
$289$	−5.71457e9			−0.819204
$290$	−1.52184e9	+	1.58331e10i	−0.215168	+	2.23859i
$291$		0			0
$292$		−	1.04916e9i		−	0.144314i
$293$	9.39536e9			1.27480			0.637401	−	0.770532i	$-0.280009\pi$
$293$	9.39536e9			1.27480			0.637401	+	0.770532i	$0.280009\pi$
$294$		0			0
$295$	−7.92785e8	+	8.24808e9i	−0.104681	+	1.08909i
$296$		−	6.81426e8i		−	0.0887670i
$297$		0			0
$298$			9.14360e9i			1.15945i
$299$		−	3.90914e9i		−	0.489098i
$300$		0			0
$301$	−6.76035e8			−0.0823575
$302$	1.87592e10			2.25520
$303$		0			0
$304$	−2.10273e8			−0.0246201
$305$	−1.54795e10	−	1.48785e9i	−1.78878	−	0.171933i
$306$		0			0
$307$		−	3.64974e9i		−	0.410874i	−0.978670	−	0.205437i	$-0.934138\pi$
$307$		−	3.64974e9i		−	0.410874i	0.978670	−	0.205437i	$-0.0658616\pi$
$308$	−1.42673e10			−1.58540
$309$		0			0
$310$	−4.39493e9	−	4.22429e8i	−0.475888	−	0.0457412i
$311$		−	1.33369e9i		−	0.142566i	−0.997456	−	0.0712828i	$-0.977291\pi$
$311$		−	1.33369e9i		−	0.142566i	0.997456	−	0.0712828i	$-0.0227093\pi$
$312$		0			0
$313$		−	1.07379e10i		−	1.11878i	−0.828906	−	0.559389i	$-0.811036\pi$
$313$		−	1.07379e10i		−	1.11878i	0.828906	−	0.559389i	$-0.188964\pi$
$314$		−	8.41556e9i		−	0.865694i
$315$		0			0
$316$	4.17051e9			0.418255
$317$	1.03929e10			1.02920			0.514602	−	0.857429i	$-0.327940\pi$
$317$	1.03929e10			1.02920			0.514602	+	0.857429i	$0.327940\pi$
$318$		0			0
$319$	2.56537e10			2.47735
$320$	9.11894e9	+	8.76489e8i	0.869649	+	0.0835885i
$321$		0			0
$322$		−	2.07894e10i		−	1.93383i
$323$	1.07736e8			0.00989806
$324$		0			0
$325$	−8.24123e8	+	4.24745e9i	−0.0738684	+	0.380711i
$326$		−	3.54794e9i		−	0.314128i
$327$		0			0
$328$		−	1.08163e9i		−	0.0934512i
$329$		−	1.56046e10i		−	1.33189i
$330$		0			0
$331$	6.63188e9			0.552491			0.276245	−	0.961087i	$-0.410910\pi$
$331$	6.63188e9			0.552491			0.276245	+	0.961087i	$0.410910\pi$
$332$	1.33328e9			0.109741
$333$		0			0
$334$	−8.67735e8			−0.0697270
$335$	2.12111e9	−	2.20679e10i	0.168416	−	1.75219i
$336$		0			0
$337$		−	1.60918e10i		−	1.24763i	−0.781574	−	0.623813i	$-0.785583\pi$
$337$		−	1.60918e10i		−	1.24763i	0.781574	−	0.623813i	$-0.214417\pi$
$338$	1.54393e10			1.18293
$339$		0			0
$340$	−5.30876e9	−	5.10265e8i	−0.397262	−	0.0381839i
$341$			7.12091e9i			0.526645i
$342$		0			0
$343$			1.19991e10i			0.866903i
$344$		−	8.95291e7i		−	0.00639338i
$345$		0			0
$346$	−2.03345e10			−1.41883
$347$	−7.03461e9			−0.485201			−0.242601	−	0.970126i	$-0.578000\pi$
$347$	−7.03461e9			−0.485201			−0.242601	+	0.970126i	$0.578000\pi$
$348$		0			0
$349$	7.52532e9			0.507252			0.253626	−	0.967302i	$-0.418377\pi$
$349$	7.52532e9			0.507252			0.253626	+	0.967302i	$0.418377\pi$
$350$	−4.38282e9	+	2.25886e10i	−0.292066	+	1.50528i
$351$		0			0
$352$		−	3.26613e10i		−	2.12747i
$353$	−7.21191e9			−0.464464			−0.232232	−	0.972660i	$-0.574603\pi$
$353$	−7.21191e9			−0.464464			−0.232232	+	0.972660i	$0.574603\pi$
$354$		0			0
$355$	−2.79408e9	+	2.90694e10i	−0.175924	+	1.83030i
$356$			2.34317e10i			1.45883i
$357$		0			0
$358$		−	3.78882e9i		−	0.230660i
$359$		−	3.85025e9i		−	0.231799i	−0.993261	−	0.115899i	$-0.963025\pi$
$359$		−	3.85025e9i		−	0.231799i	0.993261	−	0.115899i	$-0.0369750\pi$
$360$		0			0
$361$	−1.69744e10			−0.999458
$362$	1.66548e10			0.969849
$363$		0			0
$364$	−7.03727e9			−0.400865
$365$	−2.61100e8	+	2.71647e9i	−0.0147108	+	0.153050i
$366$		0			0
$367$			1.32948e10i			0.732857i	0.930446	+	0.366428i	$0.119420\pi$
$367$			1.32948e10i			0.732857i	−0.930446	+	0.366428i	$0.880580\pi$
$368$	2.44626e10			1.33386
$369$		0			0
$370$	2.59228e9	−	2.69699e10i	0.138317	−	1.43904i
$371$			2.43194e10i			1.28368i
$372$		0			0
$373$		−	2.34647e10i		−	1.21221i	−0.795383	−	0.606107i	$-0.792730\pi$
$373$		−	2.34647e10i		−	1.21221i	0.795383	−	0.606107i	$-0.207270\pi$
$374$			1.77658e10i			0.908026i
$375$		0			0
$376$	2.06656e9			0.103394
$377$	1.26536e10			0.626394
$378$		0			0
$379$	−2.18561e10			−1.05929			−0.529646	−	0.848219i	$-0.677675\pi$
$379$	−2.18561e10			−1.05929			−0.529646	+	0.848219i	$0.677675\pi$
$380$	−4.53495e8	−	4.35888e7i	−0.0217489	−	0.00209045i
$381$		0			0
$382$			4.25437e9i			0.199794i
$383$	−2.96898e10			−1.37979			−0.689894	−	0.723911i	$-0.742343\pi$
$383$	−2.96898e10			−1.37979			−0.689894	+	0.723911i	$0.742343\pi$
$384$		0			0
$385$	3.69407e10	+	3.55064e9i	1.68136	+	0.161608i
$386$		−	3.51038e10i		−	1.58127i
$387$		0			0
$388$			3.04695e10i			1.34443i
$389$		−	1.55829e10i		−	0.680533i	−0.940329	−	0.340266i	$-0.889483\pi$
$389$		−	1.55829e10i		−	0.680533i	0.940329	−	0.340266i	$-0.110517\pi$
$390$		0			0
$391$	−1.25337e10			−0.536254
$392$	4.29627e8			0.0181948
$393$		0			0
$394$	−7.47174e8			−0.0310054
$395$	−1.07982e10	−	1.03790e9i	−0.443572	−	0.0426351i
$396$		0			0
$397$			3.23824e10i			1.30361i	0.758388	+	0.651803i	$0.225987\pi$
$397$			3.23824e10i			1.30361i	−0.758388	+	0.651803i	$0.774013\pi$
$398$	−2.58490e10			−1.03017
$399$		0			0
$400$	−2.65797e10	−	5.15719e9i	−1.03827	−	0.201453i
$401$		−	1.02122e10i		−	0.394951i	−0.980308	−	0.197475i	$-0.936726\pi$
$401$		−	1.02122e10i		−	0.394951i	0.980308	−	0.197475i	$-0.0632743\pi$
$402$		0			0
$403$			3.51235e9i			0.133161i
$404$			1.83385e10i			0.688398i
$405$		0			0
$406$	6.72938e10			2.47669
$407$	−4.36981e10			−1.59252
$408$		0			0
$409$	2.75586e9			0.0984836			0.0492418	−	0.998787i	$-0.484320\pi$
$409$	2.75586e9			0.0984836			0.0492418	+	0.998787i	$0.484320\pi$
$410$	4.11475e9	−	4.28096e10i	0.145616	−	1.51498i
$411$		0			0
$412$			3.89324e10i			1.35121i
$413$	3.50559e10			1.20493
$414$		0			0
$415$	−3.45212e9	−	3.31809e8i	−0.116384	−	0.0111866i
$416$		−	1.61100e10i		−	0.537927i
$417$		0			0
$418$			1.51762e9i			0.0497117i
$419$			3.02983e10i			0.983019i	0.870872	+	0.491510i	$0.163555\pi$
$419$			3.02983e10i			0.983019i	−0.870872	+	0.491510i	$0.836445\pi$
$420$		0			0
$421$	2.76263e10			0.879417			0.439709	−	0.898141i	$-0.355082\pi$
$421$	2.76263e10			0.879417			0.439709	+	0.898141i	$0.355082\pi$
$422$	−3.68290e10			−1.16129
$423$		0			0
$424$	−3.22068e9			−0.0996515
$425$	1.36184e10	+	2.64234e9i	0.417417	+	0.0809904i
$426$		0			0
$427$			6.57908e10i			1.97903i
$428$	−3.33128e10			−0.992740
$429$		0			0
$430$	3.40587e8	−	3.54344e9i	0.00996217	−	0.103646i
$431$		−	2.12776e10i		−	0.616614i	−0.951287	−	0.308307i	$-0.900238\pi$
$431$		−	2.12776e10i		−	0.616614i	0.951287	−	0.308307i	$-0.0997624\pi$
$432$		0			0
$433$		−	9.56994e9i		−	0.272244i	−0.990692	−	0.136122i	$-0.956536\pi$
$433$		−	9.56994e9i		−	0.272244i	0.990692	−	0.136122i	$-0.0434638\pi$
$434$			1.86793e10i			0.526503i
$435$		0			0
$436$	−1.39825e10			−0.386935
$437$	−1.07067e9			−0.0293583
$438$		0			0
$439$	2.49688e10			0.672264			0.336132	−	0.941815i	$-0.390881\pi$
$439$	2.49688e10			0.672264			0.336132	+	0.941815i	$0.390881\pi$
$440$	−4.70221e8	+	4.89215e9i	−0.0125456	+	0.130524i
$441$		0			0
$442$			8.76290e9i			0.229593i
$443$	4.80091e9			0.124655			0.0623273	−	0.998056i	$-0.480148\pi$
$443$	4.80091e9			0.124655			0.0623273	+	0.998056i	$0.480148\pi$
$444$		0			0
$445$	5.83136e9	−	6.06691e10i	0.148707	−	1.54713i
$446$		−	8.07896e10i		−	2.04181i
$447$		0			0
$448$		−	3.87572e10i		−	0.962144i
$449$			2.77325e10i			0.682345i	0.940001	+	0.341172i	$0.110824\pi$
$449$			2.77325e10i			0.682345i	−0.940001	+	0.341172i	$0.889176\pi$
$450$		0			0
$451$	−6.93625e10			−1.67656
$452$	3.78412e9			0.0906591
$453$		0			0
$454$	−7.40696e10			−1.74348
$455$	1.82208e10	+	1.75134e9i	0.425130	+	0.0408624i
$456$		0			0
$457$		−	5.03683e10i		−	1.15476i	−0.816475	−	0.577381i	$-0.804075\pi$
$457$		−	5.03683e10i		−	1.15476i	0.816475	−	0.577381i	$-0.195925\pi$
$458$	9.24006e10			2.09997
$459$		0			0
$460$	5.27582e10	+	5.07099e9i	1.17831	+	0.113256i
$461$			5.32820e10i			1.17971i	0.807508	+	0.589857i	$0.200816\pi$
$461$			5.32820e10i			1.17971i	−0.807508	+	0.589857i	$0.799184\pi$
$462$		0			0
$463$			3.43748e10i			0.748025i	0.927424	+	0.374013i	$0.122018\pi$
$463$			3.43748e10i			0.748025i	−0.927424	+	0.374013i	$0.877982\pi$
$464$			7.91834e10i			1.70829i
$465$		0			0
$466$	9.48600e10			2.01159
$467$	−5.12262e10			−1.07702			−0.538511	−	0.842618i	$-0.681013\pi$
$467$	−5.12262e10			−1.07702			−0.538511	+	0.842618i	$0.681013\pi$
$468$		0			0
$469$	−9.37925e10			−1.93855
$470$	8.17917e10	+	7.86161e9i	1.67617	+	0.161109i
$471$		0			0
$472$			4.64254e9i			0.0935379i
$473$	−5.74128e9			−0.114700
$474$		0			0
$475$	1.16334e9	+	2.25719e8i	0.0228523	+	0.00443398i
$476$			2.25632e10i			0.439515i
$477$		0			0
$478$		−	6.74314e10i		−	1.29167i
$479$			4.70739e10i			0.894208i	0.894482	+	0.447104i	$0.147545\pi$
$479$			4.70739e10i			0.894208i	−0.894482	+	0.447104i	$0.852455\pi$
$480$		0			0
$481$	−2.15539e10			−0.402667
$482$	−7.54794e10			−1.39843
$483$		0			0
$484$	−6.96595e10			−1.26940
$485$	7.58282e9	−	7.88912e10i	0.137045	−	1.42581i
$486$		0			0
$487$			5.31750e9i			0.0945348i	0.998882	+	0.0472674i	$0.0150513\pi$
$487$			5.31750e9i			0.0945348i	−0.998882	+	0.0472674i	$0.984949\pi$
$488$	−8.71284e9			−0.153632
$489$		0			0
$490$	1.70041e10	+	1.63439e9i	0.294963	+	0.0283511i
$491$			8.86772e10i			1.52576i	0.646540	+	0.762880i	$0.276215\pi$
$491$			8.86772e10i			1.52576i	−0.646540	+	0.762880i	$0.723785\pi$
$492$		0			0
$493$		−	4.05705e10i		−	0.686788i
$494$			7.48561e8i			0.0125695i
$495$		0			0
$496$	−2.19796e10			−0.363155
$497$	1.23551e11			2.02497
$498$		0			0
$499$	6.19202e10			0.998688			0.499344	−	0.866404i	$-0.333574\pi$
$499$	6.19202e10			0.998688			0.499344	+	0.866404i	$0.333574\pi$
$500$	−5.62551e10	−	1.66323e10i	−0.900082	−	0.266117i
$501$		0			0
$502$			4.93679e10i			0.777374i
$503$	5.89096e10			0.920268			0.460134	−	0.887850i	$-0.347801\pi$
$503$	5.89096e10			0.920268			0.460134	+	0.887850i	$0.347801\pi$
$504$		0			0
$505$	4.56384e9	−	4.74819e10i	0.0701722	−	0.730067i
$506$		−	1.76556e11i		−	2.69327i
$507$		0			0
$508$		−	2.05902e10i		−	0.309176i
$509$		−	8.77959e10i		−	1.30799i	−0.756501	−	0.653993i	$-0.773093\pi$
$509$		−	8.77959e10i		−	1.30799i	0.756501	−	0.653993i	$-0.226907\pi$
$510$		0			0
$511$	1.15455e10			0.169328
$512$	9.45997e10			1.37661
$513$		0			0
$514$	8.20991e10			1.17621
$515$	9.68896e9	−	1.00803e11i	0.137736	−	1.43300i
$516$		0			0
$517$		−	1.32523e11i		−	1.85494i
$518$	−1.14627e11			−1.59209
$519$		0			0
$520$	−2.31934e8	+	2.41303e9i	−0.00317213	+	0.0330027i
$521$			6.67388e10i			0.905790i	0.891564	+	0.452895i	$0.149609\pi$
$521$			6.67388e10i			0.905790i	−0.891564	+	0.452895i	$0.850391\pi$
$522$		0			0
$523$			4.80448e10i			0.642155i	0.947053	+	0.321078i	$0.104045\pi$
$523$			4.80448e10i			0.642155i	−0.947053	+	0.321078i	$0.895955\pi$
$524$			5.12817e10i			0.680201i
$525$		0			0
$526$	5.66115e10			0.739540
$527$	1.12615e10			0.146000
$528$		0			0
$529$	4.62479e10			0.590568
$530$	−1.27470e11	−	1.22521e10i	−1.61549	−	0.155277i
$531$		0			0
$532$			1.92744e9i			0.0240621i
$533$	−3.42127e10			−0.423915
$534$		0			0
$535$	8.62530e10	+	8.29042e9i	1.05283	+	0.101196i
$536$		−	1.24212e10i		−	0.150489i
$537$		0			0
$538$			1.00017e11i			1.19384i
$539$		−	2.75509e10i		−	0.326423i
$540$		0			0
$541$	−7.05776e10			−0.823906			−0.411953	−	0.911205i	$-0.635153\pi$
$541$	−7.05776e10			−0.823906			−0.411953	+	0.911205i	$0.635153\pi$
$542$	−3.03128e9			−0.0351260
$543$		0			0
$544$	−5.16528e10			−0.589791
$545$	3.62033e10	+	3.47977e9i	0.410357	+	0.0394425i
$546$		0			0
$547$		−	3.29854e10i		−	0.368445i	−0.982885	−	0.184222i	$-0.941023\pi$
$547$		−	3.29854e10i		−	0.368445i	0.982885	−	0.184222i	$-0.0589767\pi$
$548$	1.03125e11			1.14351
$549$		0			0
$550$	−3.72214e10	+	1.91836e11i	−0.406764	+	2.09642i
$551$		−	3.46569e9i		−	0.0375996i
$552$		0			0
$553$			4.58945e10i			0.490750i
$554$			1.29153e11i			1.37109i
$555$		0			0
$556$	−1.32696e11			−1.38855
$557$	−1.44778e10			−0.150412			−0.0752060	−	0.997168i	$-0.523961\pi$
$557$	−1.44778e10			−0.150412			−0.0752060	+	0.997168i	$0.523961\pi$
$558$		0			0
$559$	−2.83186e9			−0.0290018
$560$	−1.09595e10	+	1.14022e11i	−0.111439	+	1.15941i
$561$		0			0
$562$			9.66144e10i			0.968493i
$563$	−1.90253e11			−1.89364			−0.946820	−	0.321765i	$-0.895724\pi$
$563$	−1.90253e11			−1.89364			−0.946820	+	0.321765i	$0.895724\pi$
$564$		0			0
$565$	−9.79780e9	−	9.41740e8i	−0.0961468	−	0.00924139i
$566$			6.54234e10i			0.637481i
$567$		0			0
$568$			1.63621e10i			0.157198i
$569$		−	1.91216e10i		−	0.182422i	−0.995832	−	0.0912108i	$-0.970926\pi$
$569$		−	1.91216e10i		−	0.182422i	0.995832	−	0.0912108i	$-0.0290737\pi$
$570$		0			0
$571$	7.67341e10			0.721845			0.360923	−	0.932596i	$-0.382462\pi$
$571$	7.67341e10			0.721845			0.360923	+	0.932596i	$0.382462\pi$
$572$	−5.97645e10			−0.558289
$573$		0			0
$574$	−1.81949e11			−1.67611
$575$	−1.35339e11	−	2.62595e10i	−1.23809	−	0.240223i
$576$		0			0
$577$		−	1.10167e11i		−	0.993910i	−0.867776	−	0.496955i	$-0.834451\pi$
$577$		−	1.10167e11i		−	0.993910i	0.867776	−	0.496955i	$-0.165549\pi$
$578$	−1.27305e11			−1.14061
$579$		0			0
$580$	−1.64144e10	+	1.70774e11i	−0.145048	+	1.50907i
$581$			1.46722e10i			0.128763i
$582$		0			0
$583$			2.06534e11i			1.78779i
$584$			1.52900e9i			0.0131449i
$585$		0			0
$586$	2.09304e11			1.77495
$587$	1.70283e11			1.43423			0.717116	−	0.696954i	$-0.245462\pi$
$587$	1.70283e11			1.43423			0.717116	+	0.696954i	$0.245462\pi$
$588$		0			0
$589$	9.61999e8			0.00799307
$590$	−1.76612e10	+	1.83745e11i	−0.145751	+	1.51638i
$591$		0			0
$592$		−	1.34880e11i		−	1.09815i
$593$	2.23071e11			1.80395			0.901976	−	0.431785i	$-0.142116\pi$
$593$	2.23071e11			1.80395			0.901976	+	0.431785i	$0.142116\pi$
$594$		0			0
$595$	5.61522e9	−	5.84204e10i	0.0448022	−	0.466119i
$596$			9.86218e10i			0.781606i
$597$		0			0
$598$		−	8.70853e10i		−	0.680989i
$599$		−	2.26036e11i		−	1.75578i	−0.478862	−	0.877890i	$-0.658951\pi$
$599$		−	2.26036e11i		−	1.75578i	0.478862	−	0.877890i	$-0.341049\pi$
$600$		0			0
$601$	−7.83332e10			−0.600410			−0.300205	−	0.953875i	$-0.597055\pi$
$601$	−7.83332e10			−0.600410			−0.300205	+	0.953875i	$0.597055\pi$
$602$	−1.50603e10			−0.114669
$603$		0			0
$604$	2.02334e11			1.52027
$605$	1.80362e11	+	1.73359e10i	1.34624	+	0.129397i
$606$		0			0
$607$		−	1.42070e11i		−	1.04652i	−0.852173	−	0.523260i	$-0.824716\pi$
$607$		−	1.42070e11i		−	1.04652i	0.852173	−	0.523260i	$-0.175284\pi$
$608$	−4.41238e9			−0.0322893
$609$		0			0
$610$	−3.44843e11	−	3.31454e10i	−2.49059	−	0.239389i
$611$		−	6.53665e10i		−	0.469019i
$612$		0			0
$613$		−	5.77570e10i		−	0.409037i	−0.978863	−	0.204518i	$-0.934437\pi$
$613$		−	5.77570e10i		−	0.409037i	0.978863	−	0.204518i	$-0.0655629\pi$
$614$		−	8.13066e10i		−	0.572074i
$615$		0			0
$616$	2.07925e10			0.144406
$617$	−4.44327e10			−0.306593			−0.153296	−	0.988180i	$-0.548989\pi$
$617$	−4.44327e10			−0.306593			−0.153296	+	0.988180i	$0.548989\pi$
$618$		0			0
$619$	2.00759e10			0.136745			0.0683727	−	0.997660i	$-0.478219\pi$
$619$	2.00759e10			0.136745			0.0683727	+	0.997660i	$0.478219\pi$
$620$	−4.74032e10	−	4.55628e9i	−0.320805	−	0.0308349i
$621$		0			0
$622$		−	2.97112e10i		−	0.198499i
$623$	−2.57855e11			−1.71168
$624$		0			0
$625$	1.41516e11	+	5.70642e10i	0.927438	+	0.373976i
$626$		−	2.39213e11i		−	1.55771i
$627$		0			0
$628$		−	9.07692e10i		−	0.583580i
$629$			6.91071e10i			0.441489i
$630$		0			0
$631$	−1.22887e11			−0.775153			−0.387577	−	0.921837i	$-0.626688\pi$
$631$	−1.22887e11			−0.775153			−0.387577	+	0.921837i	$0.626688\pi$
$632$	−6.07793e9			−0.0380967
$633$		0			0
$634$	2.31527e11			1.43300
$635$	−5.12421e9	+	5.33120e10i	−0.0315161	+	0.327891i
$636$		0			0
$637$		−	1.35894e10i		−	0.0825355i
$638$	5.71497e11			3.44930
$639$		0			0
$640$	−2.85010e10	−	2.73944e9i	−0.169879	−	0.0163283i
$641$		−	2.11826e10i		−	0.125472i	−0.998030	−	0.0627362i	$-0.980017\pi$
$641$		−	2.11826e10i		−	0.125472i	0.998030	−	0.0627362i	$-0.0199827\pi$
$642$		0			0
$643$			8.09819e10i			0.473744i	0.971541	+	0.236872i	$0.0761223\pi$
$643$			8.09819e10i			0.473744i	−0.971541	+	0.236872i	$0.923878\pi$
$644$		−	2.24232e11i		−	1.30363i
$645$		0			0
$646$	2.40007e9			0.0137814
$647$	6.55894e10			0.374297			0.187149	−	0.982332i	$-0.440075\pi$
$647$	6.55894e10			0.374297			0.187149	+	0.982332i	$0.440075\pi$
$648$		0			0
$649$	2.97715e11			1.67811
$650$	−1.83593e10	+	9.46221e10i	−0.102850	+	0.530077i
$651$		0			0
$652$		−	3.82677e10i		−	0.211759i
$653$	−2.79107e11			−1.53504			−0.767518	−	0.641028i	$-0.778508\pi$
$653$	−2.79107e11			−1.53504			−0.767518	+	0.641028i	$0.778508\pi$
$654$		0			0
$655$	1.27623e10	−	1.32778e11i	0.0693367	−	0.721375i
$656$		−	2.14096e11i		−	1.15609i
$657$		0			0
$658$		−	3.47630e11i		−	1.85444i
$659$		−	4.32498e10i		−	0.229320i	−0.993405	−	0.114660i	$-0.963422\pi$
$659$		−	4.32498e10i		−	0.229320i	0.993405	−	0.114660i	$-0.0365779\pi$
$660$		0			0
$661$	−1.31191e11			−0.687226			−0.343613	−	0.939111i	$-0.611651\pi$
$661$	−1.31191e11			−0.687226			−0.343613	+	0.939111i	$0.611651\pi$
$662$	1.47741e11			0.769252
$663$		0			0
$664$	−1.94307e9			−0.00999579
$665$	4.79674e8	−	4.99050e9i	0.00245279	−	0.0255186i
$666$		0			0
$667$			4.03188e11i			2.03706i
$668$	−9.35929e9			−0.0470042
$669$		0			0
$670$	4.72527e10	−	4.91614e11i	0.234492	−	2.43964i
$671$			5.58733e11i			2.75622i
$672$		0			0
$673$		−	3.54815e10i		−	0.172958i	−0.996254	−	0.0864792i	$-0.972438\pi$
$673$		−	3.54815e10i		−	0.172958i	0.996254	−	0.0864792i	$-0.0275616\pi$
$674$		−	3.58482e11i		−	1.73711i
$675$		0			0
$676$	1.66526e11			0.797435
$677$	5.19019e10			0.247075			0.123537	−	0.992340i	$-0.460576\pi$
$677$	5.19019e10			0.247075			0.123537	+	0.992340i	$0.460576\pi$
$678$		0			0
$679$	−3.35302e11			−1.57746
$680$	7.73677e9	+	7.43639e8i	0.0361846	+	0.00347797i
$681$		0			0
$682$			1.58635e11i			0.733266i
$683$	4.75602e10			0.218555			0.109278	−	0.994011i	$-0.465146\pi$
$683$	4.75602e10			0.218555			0.109278	+	0.994011i	$0.465146\pi$
$684$		0			0
$685$	−2.67009e11	−	2.56643e10i	−1.21273	−	0.116565i
$686$			2.67307e11i			1.20702i
$687$		0			0
$688$		−	1.77212e10i		−	0.0790932i
$689$			1.01872e11i			0.452041i
$690$		0			0
$691$	−1.97123e11			−0.864618			−0.432309	−	0.901726i	$-0.642301\pi$
$691$	−1.97123e11			−0.864618			−0.432309	+	0.901726i	$0.642301\pi$
$692$	−2.19326e11			−0.956457
$693$		0			0
$694$	−1.56713e11			−0.675563
$695$	3.43576e11	+	3.30236e10i	1.47260	+	0.141542i
$696$		0			0
$697$			1.09694e11i			0.464786i
$698$	1.67644e11			0.706265
$699$		0			0
$700$	−4.72726e10	+	2.43639e11i	−0.196887	+	1.01474i
$701$			4.52903e11i			1.87557i	0.347220	+	0.937784i	$0.387126\pi$
$701$			4.52903e11i			1.87557i	−0.347220	+	0.937784i	$0.612874\pi$
$702$		0			0
$703$			5.90340e9i			0.0241702i
$704$		−	3.29148e11i		−	1.33999i
$705$		0			0
$706$	−1.60662e11			−0.646689
$707$	−2.01807e11			−0.807716
$708$		0			0
$709$	3.64885e11			1.44401			0.722007	−	0.691886i	$-0.243220\pi$
$709$	3.64885e11			1.44401			0.722007	+	0.691886i	$0.243220\pi$
$710$	−6.22448e10	+	6.47591e11i	−0.244946	+	2.54840i
$711$		0			0
$712$		−	3.41484e10i		−	0.132877i
$713$	−1.11916e11			−0.433046
$714$		0			0
$715$	1.54742e11	+	1.48734e10i	0.592083	+	0.0569095i
$716$		−	4.08658e10i		−	0.155492i
$717$		0			0
$718$		−	8.57735e10i		−	0.322742i
$719$		−	1.83828e10i		−	0.0687853i	−0.999408	−	0.0343927i	$-0.989050\pi$
$719$		−	1.83828e10i		−	0.0687853i	0.999408	−	0.0343927i	$-0.0109497\pi$
$720$		0			0
$721$	−4.28433e11			−1.58541
$722$	−3.78144e11			−1.39158
$723$		0			0
$724$	1.79636e11			0.653792
$725$	8.49999e10	−	4.38082e11i	0.307657	−	1.58564i
$726$		0			0
$727$			4.01714e11i			1.43807i	0.694975	+	0.719034i	$0.255416\pi$
$727$			4.01714e11i			1.43807i	−0.694975	+	0.719034i	$0.744584\pi$
$728$	1.02558e10			0.0365128
$729$		0			0
$730$	−5.81662e9	+	6.05158e10i	−0.0204823	+	0.213097i
$731$			9.07964e9i			0.0317980i
$732$		0			0
$733$			4.34842e11i			1.50632i	0.657840	+	0.753158i	$0.271470\pi$
$733$			4.34842e11i			1.50632i	−0.657840	+	0.753158i	$0.728530\pi$
$734$			2.96174e11i			1.02038i
$735$		0			0
$736$	5.13323e11			1.74936
$737$	−7.96540e11			−2.69984
$738$		0			0
$739$	1.89228e11			0.634466			0.317233	−	0.948348i	$-0.397246\pi$
$739$	1.89228e11			0.634466			0.317233	+	0.948348i	$0.397246\pi$
$740$	2.79600e10	−	2.90894e11i	0.0932418	−	0.970082i
$741$		0			0
$742$			5.41772e11i			1.78731i
$743$	1.56871e11			0.514739			0.257369	−	0.966313i	$-0.417144\pi$
$743$	1.56871e11			0.514739			0.257369	+	0.966313i	$0.417144\pi$
$744$		0			0
$745$	2.45436e10	−	2.55350e11i	0.0796735	−	0.828918i
$746$		−	5.22731e11i		−	1.68781i
$747$		0			0
$748$			1.91620e11i			0.612116i
$749$		−	3.66591e11i		−	1.16481i
$750$		0			0
$751$	1.09763e11			0.345061			0.172530	−	0.985004i	$-0.444806\pi$
$751$	1.09763e11			0.345061			0.172530	+	0.985004i	$0.444806\pi$
$752$	4.09050e11			1.27910
$753$		0			0
$754$	2.81888e11			0.872151
$755$	−5.23881e11	−	5.03541e10i	−1.61230	−	0.154970i
$756$		0			0
$757$			7.49572e10i			0.228260i	0.993466	+	0.114130i	$0.0364081\pi$
$757$			7.49572e10i			0.228260i	−0.993466	+	0.114130i	$0.963592\pi$
$758$	−4.86897e11			−1.47489
$759$		0			0
$760$	6.60905e8	+	6.35245e7i	0.00198100	+	0.000190409i
$761$		−	3.28200e11i		−	0.978589i	−0.872119	−	0.489295i	$-0.837254\pi$
$761$		−	3.28200e11i		−	0.978589i	0.872119	−	0.489295i	$-0.162746\pi$
$762$		0			0
$763$		−	1.53871e11i		−	0.454002i
$764$			4.58871e10i			0.134684i
$765$		0			0
$766$	−6.61411e11			−1.92113
$767$	1.46846e11			0.424308
$768$		0			0
$769$	−2.35427e11			−0.673210			−0.336605	−	0.941646i	$-0.609279\pi$
$769$	−2.35427e11			−0.673210			−0.336605	+	0.941646i	$0.609279\pi$
$770$	8.22941e11	+	7.90990e10i	2.34102	+	0.225013i
$771$		0			0
$772$		−	3.78626e11i		−	1.06596i
$773$	2.82657e11			0.791666			0.395833	−	0.918323i	$-0.370456\pi$
$773$	2.82657e11			0.791666			0.395833	+	0.918323i	$0.370456\pi$
$774$		0			0
$775$	1.21602e11	+	2.35941e10i	0.337080	+	0.0654028i
$776$		−	4.44049e10i		−	0.122457i
$777$		0			0
$778$		−	3.47145e11i		−	0.947530i
$779$			9.37052e9i			0.0254457i
$780$		0			0
$781$	1.04926e12			2.82020
$782$	−2.79217e11			−0.746646
$783$		0			0
$784$	8.50393e10			0.225090
$785$	−2.25894e10	+	2.35019e11i	−0.0594875	+	0.618904i
$786$		0			0
$787$		−	4.22808e11i		−	1.10216i	−0.834452	−	0.551080i	$-0.814216\pi$
$787$		−	4.22808e11i		−	1.10216i	0.834452	−	0.551080i	$-0.185784\pi$
$788$	−8.05894e9			−0.0209013
$789$		0			0
$790$	−2.40556e11	−	2.31217e10i	−0.617601	−	0.0593623i
$791$			4.16425e10i			0.106373i
$792$		0			0
$793$			2.75592e11i			0.696906i
$794$			7.21394e11i			1.81506i
$795$		0			0
$796$	−2.78804e11			−0.694459
$797$	2.99331e11			0.741855			0.370927	−	0.928662i	$-0.379040\pi$
$797$	2.99331e11			0.741855			0.370927	+	0.928662i	$0.379040\pi$
$798$		0			0
$799$	−2.09581e11			−0.514239
$800$	−5.57749e11	−	1.08219e11i	−1.36169	−	0.264206i
$801$		0			0
$802$		−	2.27502e11i		−	0.549904i
$803$	9.80510e10			0.235825
$804$		0			0
$805$	−5.58038e10	+	5.80579e11i	−0.132886	+	1.38254i
$806$			7.82460e10i			0.185405i
$807$		0			0
$808$		−	2.67258e10i		−	0.0627026i
$809$		−	2.38530e11i		−	0.556864i	−0.960456	−	0.278432i	$-0.910185\pi$
$809$		−	2.38530e11i		−	0.556864i	0.960456	−	0.278432i	$-0.0898147\pi$
$810$		0			0
$811$	1.52223e11			0.351883			0.175941	−	0.984401i	$-0.443703\pi$
$811$	1.52223e11			0.351883			0.175941	+	0.984401i	$0.443703\pi$
$812$	7.25823e11			1.66958
$813$		0			0
$814$	−9.73479e11			−2.21732
$815$	−9.52354e9	+	9.90823e10i	−0.0215858	+	0.224577i
$816$		0			0
$817$			7.75618e8i			0.00174084i
$818$	6.13933e10			0.137122
$819$		0			0
$820$	4.43812e10	−	4.61739e11i	0.0981621	−	1.02127i
$821$			1.26619e11i			0.278693i	0.990244	+	0.139346i	$0.0445001\pi$
$821$			1.26619e11i			0.278693i	−0.990244	+	0.139346i	$0.955500\pi$
$822$		0			0
$823$		−	7.97934e11i		−	1.73927i	−0.493694	−	0.869636i	$-0.664354\pi$
$823$		−	7.97934e11i		−	1.73927i	0.493694	−	0.869636i	$-0.335646\pi$
$824$		−	5.67385e10i		−	0.123075i
$825$		0			0
$826$	7.80953e11			1.67766
$827$	4.23420e11			0.905211			0.452605	−	0.891711i	$-0.350495\pi$
$827$	4.23420e11			0.905211			0.452605	+	0.891711i	$0.350495\pi$
$828$		0			0
$829$	−5.03970e11			−1.06705			−0.533527	−	0.845783i	$-0.679134\pi$
$829$	−5.03970e11			−1.06705			−0.533527	+	0.845783i	$0.679134\pi$
$830$	−7.69042e10	−	7.39184e9i	−0.162046	−	0.0155754i
$831$		0			0
$832$		−	1.62351e11i		−	0.338814i
$833$	−4.35708e10			−0.0904932
$834$		0			0
$835$	2.42330e10	+	2.32921e9i	0.0498495	+	0.00479140i
$836$			1.63689e10i			0.0335116i
$837$		0			0
$838$			6.74966e11i			1.36869i
$839$			4.10460e11i			0.828367i	0.910193	+	0.414184i	$0.135933\pi$
$839$			4.10460e11i			0.828367i	−0.910193	+	0.414184i	$0.864067\pi$
$840$		0			0
$841$	−8.04842e11			−1.60889
$842$	6.15442e11			1.22444
$843$		0			0
$844$	−3.97234e11			−0.782846
$845$	−4.31167e11	−	4.14427e10i	−0.845705	−	0.0812871i
$846$		0			0
$847$		−	7.66570e11i		−	1.48942i
$848$	−6.37494e11			−1.23280
$849$		0			0
$850$	3.03382e11	+	5.88644e10i	0.581184	+	0.112766i
$851$		−	6.86784e11i		−	1.30949i
$852$		0			0
$853$		−	1.32498e11i		−	0.250273i	−0.992140	−	0.125137i	$-0.960063\pi$
$853$		−	1.32498e11i		−	0.250273i	0.992140	−	0.125137i	$-0.0399369\pi$
$854$			1.46565e12i			2.75548i
$855$		0			0
$856$	4.85487e10			0.0904237
$857$	4.11482e11			0.762830			0.381415	−	0.924404i	$-0.375437\pi$
$857$	4.11482e11			0.762830			0.381415	+	0.924404i	$0.375437\pi$
$858$		0			0
$859$	5.76431e11			1.05870			0.529352	−	0.848402i	$-0.322435\pi$
$859$	5.76431e11			1.05870			0.529352	+	0.848402i	$0.322435\pi$
$860$	3.67353e9	−	3.82191e10i	0.00671567	−	0.0698694i
$861$		0			0
$862$		−	4.74009e11i		−	0.858534i
$863$	3.26350e11			0.588356			0.294178	−	0.955751i	$-0.404954\pi$
$863$	3.26350e11			0.588356			0.294178	+	0.955751i	$0.404954\pi$
$864$		0			0
$865$	5.67875e11	+	5.45828e10i	1.01435	+	0.0974970i
$866$		−	2.13193e11i		−	0.379054i
$867$		0			0
$868$			2.01472e11i			0.354925i
$869$			3.89763e11i			0.683472i
$870$		0			0
$871$	−3.92890e11			−0.682650
$872$	2.03775e10			0.0352440
$873$		0			0
$874$	−2.38518e10			−0.0408767
$875$	1.83031e11	−	6.19061e11i	0.312243	−	1.05609i
$876$		0			0
$877$		−	3.76864e11i		−	0.637069i	−0.947911	−	0.318534i	$-0.896809\pi$
$877$		−	3.76864e11i		−	0.637069i	0.947911	−	0.318534i	$-0.103191\pi$
$878$	5.56239e11			0.936017
$879$		0			0
$880$	−9.30744e10	+	9.68340e11i	−0.155203	+	1.61472i
$881$		−	3.14014e11i		−	0.521250i	−0.965440	−	0.260625i	$-0.916071\pi$
$881$		−	3.14014e11i		−	0.521250i	0.965440	−	0.260625i	$-0.0839286\pi$
$882$		0			0
$883$		−	2.57879e11i		−	0.424203i	−0.977248	−	0.212101i	$-0.931969\pi$
$883$		−	2.57879e11i		−	0.424203i	0.977248	−	0.212101i	$-0.0680307\pi$
$884$			9.45156e10i			0.154773i
$885$		0			0
$886$	1.06952e11			0.173561
$887$	1.12112e11			0.181117			0.0905583	−	0.995891i	$-0.471135\pi$
$887$	1.12112e11			0.181117			0.0905583	+	0.995891i	$0.471135\pi$
$888$		0			0
$889$	2.26586e11			0.362765
$890$	1.29907e11	−	1.35155e12i	0.207049	−	2.15413i
$891$		0			0
$892$		−	8.71387e11i		−	1.37642i
$893$	−1.79032e10			−0.0281531
$894$		0			0
$895$	−1.01701e10	+	1.05809e11i	−0.0158502	+	0.164904i
$896$			1.21134e11i			0.187947i
$897$		0			0
$898$			6.17807e11i			0.950053i
$899$		−	3.62264e11i		−	0.554608i
$900$		0			0
$901$	3.26627e11			0.495624
$902$	−1.54521e12			−2.33433
$903$		0			0
$904$	−5.51482e9			−0.00825767
$905$	−4.65112e11	−	4.47054e10i	−0.693367	−	0.0666447i
$906$		0			0
$907$		−	5.92285e10i		−	0.0875189i	−0.999042	−	0.0437594i	$-0.986066\pi$
$907$		−	5.92285e10i		−	0.0875189i	0.999042	−	0.0437594i	$-0.0139335\pi$
$908$	−7.98906e11			−1.17531
$909$		0			0
$910$	4.05912e11	+	3.90152e10i	0.591924	+	0.0568942i
$911$		−	4.67364e11i		−	0.678549i	−0.940687	−	0.339275i	$-0.889818\pi$
$911$		−	4.67364e11i		−	0.678549i	0.940687	−	0.339275i	$-0.110182\pi$
$912$		0			0
$913$			1.24604e11i			0.179329i
$914$		−	1.12207e12i		−	1.60782i
$915$		0			0
$916$	9.96622e11			1.41563
$917$	−5.64331e11			−0.798099
$918$		0			0
$919$	1.65426e11			0.231922			0.115961	−	0.993254i	$-0.463005\pi$
$919$	1.65426e11			0.231922			0.115961	+	0.993254i	$0.463005\pi$
$920$	−7.68876e10	−	7.39025e9i	−0.107326	−	0.0103159i
$921$		0			0
$922$			1.18698e12i			1.64256i
$923$	5.17544e11			0.713083
$924$		0			0
$925$	−1.44788e11	+	7.46222e11i	−0.197772	+	1.01930i
$926$			7.65780e11i			1.04150i
$927$		0			0
$928$			1.66159e12i			2.24043i
$929$			4.15075e11i			0.557267i	0.960398	+	0.278633i	$0.0898815\pi$
$929$			4.15075e11i			0.557267i	−0.960398	+	0.278633i	$0.910119\pi$
$930$		0			0
$931$	−3.72199e9			−0.00495423
$932$	1.02315e12			1.35605
$933$		0			0
$934$	−1.14118e12			−1.49958
$935$	4.76877e10	−	4.96140e11i	0.0623964	−	0.649169i
$936$		0			0
$937$			8.22206e11i			1.06665i	0.845910	+	0.533325i	$0.179058\pi$
$937$			8.22206e11i			1.06665i	−0.845910	+	0.533325i	$0.820942\pi$
$938$	−2.08945e12			−2.69911
$939$		0			0
$940$	8.82195e11	+	8.47944e10i	1.12993	+	0.108606i
$941$			1.31518e12i			1.67737i	0.544619	+	0.838684i	$0.316674\pi$
$941$			1.31518e12i			1.67737i	−0.544619	+	0.838684i	$0.683326\pi$
$942$		0			0
$943$		−	1.09014e12i		−	1.37859i
$944$			9.18934e11i			1.15717i
$945$		0			0
$946$	−1.27901e11			−0.159701
$947$	3.76228e11			0.467791			0.233895	−	0.972262i	$-0.424853\pi$
$947$	3.76228e11			0.467791			0.233895	+	0.972262i	$0.424853\pi$
$948$		0			0
$949$	4.83632e10			0.0596280
$950$	2.59161e10	+	5.02843e9i	0.0318181	+	0.00617359i
$951$		0			0
$952$		−	3.28827e10i		−	0.0400331i
$953$	4.73339e11			0.573854			0.286927	−	0.957953i	$-0.407366\pi$
$953$	4.73339e11			0.573854			0.286927	+	0.957953i	$0.407366\pi$
$954$		0			0
$955$	1.14198e10	−	1.18810e11i	0.0137291	−	0.142837i
$956$		−	7.27307e11i		−	0.870736i
$957$		0			0
$958$			1.04868e12i			1.24504i
$959$			1.13484e12i			1.34171i
$960$		0			0
$961$	−7.52335e11			−0.882099
$962$	−4.80164e11			−0.560647
$963$		0			0
$964$	−8.14112e11			−0.942705
$965$	−9.42272e10	+	9.80333e11i	−0.108659	+	1.13048i
$966$		0			0
$967$		−	4.76879e11i		−	0.545384i	−0.962101	−	0.272692i	$-0.912086\pi$
$967$		−	4.76879e11i		−	0.545384i	0.962101	−	0.272692i	$-0.0879140\pi$
$968$	1.01519e11			0.115623
$969$		0			0
$970$	1.68925e11	−	1.75749e12i	0.190813	−	1.98520i
$971$			8.83200e11i			0.993533i	0.867884	+	0.496766i	$0.165479\pi$
$971$			8.83200e11i			0.993533i	−0.867884	+	0.496766i	$0.834521\pi$
$972$		0			0
$973$		−	1.46026e12i		−	1.62922i
$974$			1.18460e11i			0.131624i
$975$		0			0
$976$	−1.72460e12			−1.90059
$977$	−7.00113e11			−0.768405			−0.384203	−	0.923249i	$-0.625524\pi$
$977$	−7.00113e11			−0.768405			−0.384203	+	0.923249i	$0.625524\pi$
$978$		0			0
$979$	−2.18985e12			−2.38388
$980$	1.83404e11	+	1.76283e10i	0.198840	+	0.0191120i
$981$		0			0
$982$			1.97550e12i			2.12437i
$983$	1.59079e12			1.70372			0.851860	−	0.523770i	$-0.175475\pi$
$983$	1.59079e12			1.70372			0.851860	+	0.523770i	$0.175475\pi$
$984$		0			0
$985$	2.08661e10	+	2.00560e9i	0.0221665	+	0.00213058i
$986$		−	9.03804e11i		−	0.956239i
$987$		0			0
$988$			8.07389e9i			0.00847335i
$989$		−	9.02331e10i		−	0.0943149i
$990$		0			0
$991$	5.78061e11			0.599348			0.299674	−	0.954042i	$-0.403122\pi$
$991$	5.78061e11			0.599348			0.299674	+	0.954042i	$0.403122\pi$
$992$	−4.61220e11			−0.476279
$993$		0			0
$994$	2.75238e12			2.81944
$995$	7.21876e11	+	6.93849e10i	0.736496	+	0.0707901i
$996$		0			0
$997$			1.39941e12i			1.41633i	0.706046	+	0.708166i	$0.250477\pi$
$997$			1.39941e12i			1.41633i	−0.706046	+	0.708166i	$0.749523\pi$
$998$	1.37942e12			1.39051
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.9.d.a.44.13	yes	16
3.2	odd	2	inner	45.9.d.a.44.4	yes	16
5.2	odd	4		225.9.c.e.26.13		16
5.3	odd	4		225.9.c.e.26.4		16
5.4	even	2	inner	45.9.d.a.44.3	✓	16
15.2	even	4		225.9.c.e.26.3		16
15.8	even	4		225.9.c.e.26.14		16
15.14	odd	2	inner	45.9.d.a.44.14	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.9.d.a.44.3	✓	16	5.4	even	2	inner
45.9.d.a.44.4	yes	16	3.2	odd	2	inner
45.9.d.a.44.13	yes	16	1.1	even	1	trivial
45.9.d.a.44.14	yes	16	15.14	odd	2	inner
225.9.c.e.26.3		16	15.2	even	4
225.9.c.e.26.4		16	5.3	odd	4
225.9.c.e.26.13		16	5.2	odd	4
225.9.c.e.26.14		16	15.8	even	4

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:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	45.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+22.2774 q^{2} +240.281 q^{4} +(-622.133 - 59.7978i) q^{5} +2644.18i q^{7} -350.176 q^{8} +O(q^{10})\)	\(q+22.2774 q^{2} +240.281 q^{4} +(-622.133 - 59.7978i) q^{5} +2644.18i q^{7} -350.176 q^{8} +(-13859.5 - 1332.14i) q^{10} +22455.9i q^{11} +11076.3i q^{13} +58905.4i q^{14} -69313.0 q^{16} +35513.3 q^{17} +3033.68 q^{19} +(-149487. - 14368.3i) q^{20} +500258. i q^{22} -352929. q^{23} +(383473. + 74404.4i) q^{25} +246750. i q^{26} +635347. i q^{28} -1.14240e6i q^{29} +317106. q^{31} -1.45447e6 q^{32} +791142. q^{34} +(158116. - 1.64503e6i) q^{35} +1.94595e6i q^{37} +67582.4 q^{38} +(217856. + 20939.8i) q^{40} +3.08883e6i q^{41} +255669. i q^{43} +5.39573e6i q^{44} -7.86233e6 q^{46} -5.90149e6 q^{47} -1.22689e6 q^{49} +(8.54278e6 + 1.65753e6i) q^{50} +2.66142e6i q^{52} +9.19732e6 q^{53} +(1.34281e6 - 1.39705e7i) q^{55} -925928. i q^{56} -2.54498e7i q^{58} -1.32577e7i q^{59} +2.48813e7 q^{61} +7.06429e6 q^{62} -1.46575e7 q^{64} +(662337. - 6.89091e6i) q^{65} +3.54713e7i q^{67} +8.53316e6 q^{68} +(3.52241e6 - 3.66470e7i) q^{70} -4.67255e7i q^{71} -4.36638e6i q^{73} +4.33507e7i q^{74} +728936. q^{76} -5.93774e7 q^{77} +1.73568e7 q^{79} +(4.31219e7 + 4.14477e6i) q^{80} +6.88110e7i q^{82} +5.54885e6 q^{83} +(-2.20940e7 - 2.12362e6i) q^{85} +5.69564e6i q^{86} -7.86351e6i q^{88} +9.75180e7i q^{89} -2.92876e7 q^{91} -8.48022e7 q^{92} -1.31470e8 q^{94} +(-1.88735e6 - 181408. i) q^{95} +1.26808e8i q^{97} -2.73319e7 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 1572 q^{4}+O(q^{10}) \) 16 * q + 1572 * q^4	\( 16 q + 1572 q^{4} + 16280 q^{10} - 12844 q^{16} + 263600 q^{19} + 1124860 q^{25} - 4312984 q^{31} + 2439352 q^{34} + 10217140 q^{40} - 5376344 q^{46} - 7338968 q^{49} + 5658120 q^{55} + 26097968 q^{61} - 123290756 q^{64} + 27888840 q^{70} + 222695760 q^{76} - 262645864 q^{79} + 202172900 q^{85} + 350561736 q^{91} - 789068384 q^{94}+O(q^{100}) \) 16 * q + 1572 * q^4 + 16280 * q^10 - 12844 * q^16 + 263600 * q^19 + 1124860 * q^25 - 4312984 * q^31 + 2439352 * q^34 + 10217140 * q^40 - 5376344 * q^46 - 7338968 * q^49 + 5658120 * q^55 + 26097968 * q^61 - 123290756 * q^64 + 27888840 * q^70 + 222695760 * q^76 - 262645864 * q^79 + 202172900 * q^85 + 350561736 * q^91 - 789068384 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more