LMFDB - Embedded newform 342.7.d.a.37.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [342,7,Mod(37,342)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(342, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("342.37");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 342 = 2 \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	342.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:	$78.6784965980$
Analytic rank:	$0$
Dimension:	$10$
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} + 5050x^{8} + 7354489x^{6} + 2475755792x^{4} + 232626987584x^{2} + 2900002611200 $ x^10 + 5050x^8 + 7354489x^6 + 2475755792x^4 + 232626987584x^2 + 2900002611200
Coefficient ring:	$\Z[a_1, \ldots, a_{29}]$
Coefficient ring index:	$ 2^{11} $
Twist minimal:	no (minimal twist has level 38)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			37.7
Root			$-48.7374i$ of defining polynomial
Character	$\chi$	$=$	342.37
Dual form			342.7.d.a.37.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+5.65685i q^{2} -32.0000 q^{4} -39.9185 q^{5} -25.1565 q^{7} -181.019i q^{8} +O(q^{10})$	\(q+5.65685i q^{2} -32.0000 q^{4} -39.9185 q^{5} -25.1565 q^{7} -181.019i q^{8} -225.813i q^{10} +1368.34 q^{11} +157.072i q^{13} -142.306i q^{14} +1024.00 q^{16} +2735.86 q^{17} +(-3468.77 + 5917.22i) q^{19} +1277.39 q^{20} +7740.48i q^{22} -17315.8 q^{23} -14031.5 q^{25} -888.533 q^{26} +805.006 q^{28} -26064.3i q^{29} -26833.9i q^{31} +5792.62i q^{32} +15476.4i q^{34} +1004.21 q^{35} +85898.9i q^{37} +(-33472.9 - 19622.3i) q^{38} +7226.03i q^{40} -53613.3i q^{41} +111934. q^{43} -43786.8 q^{44} -97952.8i q^{46} -60698.5 q^{47} -117016. q^{49} -79374.2i q^{50} -5026.30i q^{52} +1359.96i q^{53} -54622.0 q^{55} +4553.80i q^{56} +147442. q^{58} -238887. i q^{59} +429630. q^{61} +151795. q^{62} -32768.0 q^{64} -6270.08i q^{65} +156985. i q^{67} -87547.6 q^{68} +5680.66i q^{70} -365008. i q^{71} -285370. q^{73} -485917. q^{74} +(111001. - 189351. i) q^{76} -34422.5 q^{77} -606939. i q^{79} -40876.6 q^{80} +303283. q^{82} +875034. q^{83} -109212. q^{85} +633195. i q^{86} -247695. i q^{88} -590538. i q^{89} -3951.37i q^{91} +554105. q^{92} -343363. i q^{94} +(138468. - 236207. i) q^{95} -1.00906e6i q^{97} -661943. i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 320 q^{4} + 112 q^{5} - 224 q^{7}+O(q^{10}) $ 10 * q - 320 * q^4 + 112 * q^5 - 224 * q^7	$ 10 q - 320 q^{4} + 112 q^{5} - 224 q^{7} - 3644 q^{11} + 10240 q^{16} + 10420 q^{17} - 17230 q^{19} - 3584 q^{20} - 37712 q^{23} - 52078 q^{25} + 7104 q^{26} + 7168 q^{28} + 161720 q^{35} - 25152 q^{38} + 6308 q^{43} + 116608 q^{44} - 322220 q^{47} - 235770 q^{49} - 377880 q^{55} + 445920 q^{58} + 426304 q^{61} - 59424 q^{62} - 327680 q^{64} - 333440 q^{68} - 786076 q^{73} + 293280 q^{74} + 551360 q^{76} - 2303716 q^{77} + 114688 q^{80} - 455136 q^{82} + 101500 q^{83} - 1261380 q^{85} + 1206784 q^{92} - 3106292 q^{95}+O(q^{100}) $ 10 * q - 320 * q^4 + 112 * q^5 - 224 * q^7 - 3644 * q^11 + 10240 * q^16 + 10420 * q^17 - 17230 * q^19 - 3584 * q^20 - 37712 * q^23 - 52078 * q^25 + 7104 * q^26 + 7168 * q^28 + 161720 * q^35 - 25152 * q^38 + 6308 * q^43 + 116608 * q^44 - 322220 * q^47 - 235770 * q^49 - 377880 * q^55 + 445920 * q^58 + 426304 * q^61 - 59424 * q^62 - 327680 * q^64 - 333440 * q^68 - 786076 * q^73 + 293280 * q^74 + 551360 * q^76 - 2303716 * q^77 + 114688 * q^80 - 455136 * q^82 + 101500 * q^83 - 1261380 * q^85 + 1206784 * q^92 - 3106292 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/342\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$1$	$-1$

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 $

$2$			5.65685i			0.707107i
$2$			5.65685i			0.707107i
$3$		0			0
$3$		0			0
$4$	−32.0000			−0.500000
$5$	−39.9185			−0.319348			−0.159674	−	0.987170i	$-0.551044\pi$
$5$	−39.9185			−0.319348			−0.159674	+	0.987170i	$0.551044\pi$
$6$		0			0
$7$	−25.1565			−0.0733424			−0.0366712	−	0.999327i	$-0.511675\pi$
$7$	−25.1565			−0.0733424			−0.0366712	+	0.999327i	$0.511675\pi$
$8$		−	181.019i		−	0.353553i
$9$		0			0
$10$		−	225.813i		−	0.225813i
$11$	1368.34			1.02805			0.514026	−	0.857775i	$-0.328154\pi$
$11$	1368.34			1.02805			0.514026	+	0.857775i	$0.328154\pi$
$12$		0			0
$13$			157.072i			0.0714938i	0.999361	+	0.0357469i	$0.0113810\pi$
$13$			157.072i			0.0714938i	−0.999361	+	0.0357469i	$0.988619\pi$
$14$		−	142.306i		−	0.0518609i
$15$		0			0
$16$	1024.00			0.250000
$17$	2735.86			0.556862			0.278431	−	0.960456i	$-0.410186\pi$
$17$	2735.86			0.556862			0.278431	+	0.960456i	$0.410186\pi$
$18$		0			0
$19$	−3468.77	+	5917.22i	−0.505726	+	0.862694i
$19$	−3468.77	+	5917.22i	−0.505726	+	0.862694i
$20$	1277.39			0.159674
$21$		0			0
$22$			7740.48i			0.726942i
$23$	−17315.8			−1.42317			−0.711587	−	0.702598i	$-0.752023\pi$
$23$	−17315.8			−1.42317			−0.711587	+	0.702598i	$0.752023\pi$
$24$		0			0
$25$	−14031.5			−0.898017
$26$	−888.533			−0.0505538
$27$		0			0
$28$	805.006			0.0366712
$29$		−	26064.3i		−	1.06869i	−0.845266	−	0.534345i	$-0.820558\pi$
$29$		−	26064.3i		−	1.06869i	0.845266	−	0.534345i	$-0.179442\pi$
$30$		0			0
$31$		−	26833.9i		−	0.900739i	−0.892842	−	0.450369i	$-0.851292\pi$
$31$		−	26833.9i		−	0.900739i	0.892842	−	0.450369i	$-0.148708\pi$
$32$			5792.62i			0.176777i
$33$		0			0
$34$			15476.4i			0.393761i
$35$	1004.21			0.0234218
$36$		0			0
$37$			85898.9i			1.69583i	0.530132	+	0.847915i	$0.322142\pi$
$37$			85898.9i			1.69583i	−0.530132	+	0.847915i	$0.677858\pi$
$38$	−33472.9	−	19622.3i	−0.610017	−	0.357602i
$39$		0			0
$40$			7226.03i			0.112907i
$41$		−	53613.3i		−	0.777895i	−0.921260	−	0.388948i	$-0.872839\pi$
$41$		−	53613.3i		−	0.777895i	0.921260	−	0.388948i	$-0.127161\pi$
$42$		0			0
$43$	111934.			1.40785			0.703926	−	0.710273i	$-0.251429\pi$
$43$	111934.			1.40785			0.703926	+	0.710273i	$0.251429\pi$
$44$	−43786.8			−0.514026
$45$		0			0
$46$		−	97952.8i		−	1.00634i
$47$	−60698.5			−0.584634			−0.292317	−	0.956321i	$-0.594426\pi$
$47$	−60698.5			−0.584634			−0.292317	+	0.956321i	$0.594426\pi$
$48$		0			0
$49$	−117016.			−0.994621
$50$		−	79374.2i		−	0.634994i
$51$		0			0
$52$		−	5026.30i		−	0.0357469i
$53$			1359.96i			0.00913479i	0.999990	+	0.00456739i	$0.00145385\pi$
$53$			1359.96i			0.00913479i	−0.999990	+	0.00456739i	$0.998546\pi$
$54$		0			0
$55$	−54622.0			−0.328306
$56$			4553.80i			0.0259305i
$57$		0			0
$58$	147442.			0.755678
$59$		−	238887.i		−	1.16315i	−0.813492	−	0.581575i	$-0.802436\pi$
$59$		−	238887.i		−	1.16315i	0.813492	−	0.581575i	$-0.197564\pi$
$60$		0			0
$61$	429630.			1.89280			0.946401	−	0.322995i	$-0.104690\pi$
$61$	429630.			1.89280			0.946401	+	0.322995i	$0.104690\pi$
$62$	151795.			0.636918
$63$		0			0
$64$	−32768.0			−0.125000
$65$		−	6270.08i		−	0.0228314i
$66$		0			0
$67$			156985.i			0.521957i	0.965345	+	0.260979i	$0.0840452\pi$
$67$			156985.i			0.521957i	−0.965345	+	0.260979i	$0.915955\pi$
$68$	−87547.6			−0.278431
$69$		0			0
$70$			5680.66i			0.0165617i
$71$		−	365008.i		−	1.01983i	−0.860225	−	0.509915i	$-0.829677\pi$
$71$		−	365008.i		−	1.01983i	0.860225	−	0.509915i	$-0.170323\pi$
$72$		0			0
$73$	−285370.			−0.733566			−0.366783	−	0.930306i	$-0.619541\pi$
$73$	−285370.			−0.733566			−0.366783	+	0.930306i	$0.619541\pi$
$74$	−485917.			−1.19913
$75$		0			0
$76$	111001.	−	189351.i	0.252863	−	0.431347i
$77$	−34422.5			−0.0753998
$78$		0			0
$79$		−	606939.i		−	1.23102i	−0.788131	−	0.615508i	$-0.788951\pi$
$79$		−	606939.i		−	1.23102i	0.788131	−	0.615508i	$-0.211049\pi$
$80$	−40876.6			−0.0798371
$81$		0			0
$82$	303283.			0.550055
$83$	875034.			1.53035			0.765175	−	0.643822i	$-0.222652\pi$
$83$	875034.			1.53035			0.765175	+	0.643822i	$0.222652\pi$
$84$		0			0
$85$	−109212.			−0.177833
$86$			633195.i			0.995502i
$87$		0			0
$88$		−	247695.i		−	0.363471i
$89$		−	590538.i		−	0.837680i	−0.908060	−	0.418840i	$-0.862437\pi$
$89$		−	590538.i		−	0.837680i	0.908060	−	0.418840i	$-0.137563\pi$
$90$		0			0
$91$		−	3951.37i		−	0.00524353i
$92$	554105.			0.711587
$93$		0			0
$94$		−	343363.i		−	0.413399i
$95$	138468.	−	236207.i	0.161503	−	0.275500i
$96$		0			0
$97$		−	1.00906e6i		−	1.10561i	−0.833312	−	0.552803i	$-0.813558\pi$
$97$		−	1.00906e6i		−	1.10561i	0.833312	−	0.552803i	$-0.186442\pi$
$98$		−	661943.i		−	0.703303i
$99$		0			0
$100$	449008.			0.449008
$101$	534106.			0.518398			0.259199	−	0.965824i	$-0.416541\pi$
$101$	534106.			0.518398			0.259199	+	0.965824i	$0.416541\pi$
$102$		0			0
$103$			768218.i			0.703028i	0.936183	+	0.351514i	$0.114333\pi$
$103$			768218.i			0.703028i	−0.936183	+	0.351514i	$0.885667\pi$
$104$	28433.1			0.0252769
$105$		0			0
$106$	−7693.09			−0.00645927
$107$			1.46546e6i			1.19625i	0.801402	+	0.598126i	$0.204088\pi$
$107$			1.46546e6i			1.19625i	−0.801402	+	0.598126i	$0.795912\pi$
$108$		0			0
$109$		−	1.89935e6i		−	1.46665i	−0.679880	−	0.733323i	$-0.737968\pi$
$109$		−	1.89935e6i		−	1.46665i	0.679880	−	0.733323i	$-0.262032\pi$
$110$		−	308989.i		−	0.232148i
$111$		0			0
$112$	−25760.2			−0.0183356
$113$		−	1.16465e6i		−	0.807161i	−0.914944	−	0.403581i	$-0.867765\pi$
$113$		−	1.16465e6i		−	0.807161i	0.914944	−	0.403581i	$-0.132235\pi$
$114$		0			0
$115$	691220.			0.454488
$116$			834057.i			0.534345i
$117$		0			0
$118$	1.35135e6			0.822472
$119$	−68824.6			−0.0408416
$120$		0			0
$121$	100784.			0.0568900
$122$			2.43035e6i			1.33841i
$123$		0			0
$124$			858685.i			0.450369i
$125$	1.18384e6			0.606128
$126$		0			0
$127$		−	1.04931e6i		−	0.512264i	−0.966642	−	0.256132i	$-0.917552\pi$
$127$		−	1.04931e6i		−	0.512264i	0.966642	−	0.256132i	$-0.0824482\pi$
$128$		−	185364.i		−	0.0883883i
$129$		0			0
$130$	35468.9			0.0161443
$131$	−265738.			−0.118206			−0.0591030	−	0.998252i	$-0.518824\pi$
$131$	−265738.			−0.118206			−0.0591030	+	0.998252i	$0.518824\pi$
$132$		0			0
$133$	87262.0	−	148856.i	0.0370912	−	0.0632721i
$134$	−888043.			−0.369079
$135$		0			0
$136$		−	495244.i		−	0.196880i
$137$	213121.			0.0828827			0.0414414	−	0.999141i	$-0.486805\pi$
$137$	213121.			0.0828827			0.0414414	+	0.999141i	$0.486805\pi$
$138$		0			0
$139$	1.82687e6			0.680243			0.340122	−	0.940381i	$-0.389532\pi$
$139$	1.82687e6			0.680243			0.340122	+	0.940381i	$0.389532\pi$
$140$	−32134.7			−0.0117109
$141$		0			0
$142$	2.06480e6			0.721128
$143$			214927.i			0.0734993i
$144$		0			0
$145$			1.04045e6i			0.341284i
$146$		−	1.61430e6i		−	0.518710i
$147$		0			0
$148$		−	2.74876e6i		−	0.847915i
$149$	2.41401e6			0.729759			0.364880	−	0.931055i	$-0.381110\pi$
$149$	2.41401e6			0.729759			0.364880	+	0.931055i	$0.381110\pi$
$150$		0			0
$151$		−	366324.i		−	0.106398i	−0.998584	−	0.0531991i	$-0.983058\pi$
$151$		−	366324.i		−	0.106398i	0.998584	−	0.0531991i	$-0.0169418\pi$
$152$	1.07113e6	+	627915.i	0.305008	+	0.178801i
$153$		0			0
$154$		−	194723.i		−	0.0533157i
$155$			1.07117e6i			0.287649i
$156$		0			0
$157$	160372.			0.0414409			0.0207204	−	0.999785i	$-0.493404\pi$
$157$	160372.			0.0414409			0.0207204	+	0.999785i	$0.493404\pi$
$158$	3.43336e6			0.870460
$159$		0			0
$160$		−	231233.i		−	0.0564533i
$161$	435603.			0.104379
$162$		0			0
$163$	7.65828e6			1.76835			0.884176	−	0.467154i	$-0.154721\pi$
$163$	7.65828e6			1.76835			0.884176	+	0.467154i	$0.154721\pi$
$164$			1.71563e6i			0.388948i
$165$		0			0
$166$			4.94994e6i			1.08212i
$167$		−	1.10021e6i		−	0.236226i	−0.993000	−	0.118113i	$-0.962316\pi$
$167$		−	1.10021e6i		−	0.236226i	0.993000	−	0.118113i	$-0.0376845\pi$
$168$		0			0
$169$	4.80214e6			0.994889
$170$		−	617794.i		−	0.125747i
$171$		0			0
$172$	−3.58189e6			−0.703926
$173$		−	5.74022e6i		−	1.10864i	−0.832304	−	0.554320i	$-0.812978\pi$
$173$		−	5.74022e6i		−	1.10864i	0.832304	−	0.554320i	$-0.187022\pi$
$174$		0			0
$175$	352983.			0.0658627
$176$	1.40118e6			0.257013
$177$		0			0
$178$	3.34059e6			0.592329
$179$		−	5.04968e6i		−	0.880449i	−0.897888	−	0.440225i	$-0.854899\pi$
$179$		−	5.04968e6i		−	0.880449i	0.897888	−	0.440225i	$-0.145101\pi$
$180$		0			0
$181$		−	1.02257e6i		−	0.172447i	−0.996276	−	0.0862234i	$-0.972520\pi$
$181$		−	1.02257e6i		−	0.172447i	0.996276	−	0.0862234i	$-0.0274799\pi$
$182$	22352.3			0.00370774
$183$		0			0
$184$			3.13449e6i			0.503168i
$185$		−	3.42896e6i		−	0.541560i
$186$		0			0
$187$	3.74358e6			0.572483
$188$	1.94235e6			0.292317
$189$		0			0
$190$	1.33619e6	+	783295.i	0.194808	+	0.114200i
$191$	3.23276e6			0.463952			0.231976	−	0.972722i	$-0.425481\pi$
$191$	3.23276e6			0.463952			0.231976	+	0.972722i	$0.425481\pi$
$192$		0			0
$193$		−	338219.i		−	0.0470464i	−0.999723	−	0.0235232i	$-0.992512\pi$
$193$		−	338219.i		−	0.0470464i	0.999723	−	0.0235232i	$-0.00748836\pi$
$194$	5.70809e6			0.781782
$195$		0			0
$196$	3.74452e6			0.497310
$197$	−1.05750e7			−1.38319			−0.691593	−	0.722287i	$-0.743091\pi$
$197$	−1.05750e7			−1.38319			−0.691593	+	0.722287i	$0.743091\pi$
$198$		0			0
$199$	−6.64038e6			−0.842624			−0.421312	−	0.906916i	$-0.638430\pi$
$199$	−6.64038e6			−0.842624			−0.421312	+	0.906916i	$0.638430\pi$
$200$			2.53997e6i			0.317497i
$201$		0			0
$202$			3.02136e6i			0.366563i
$203$			655685.i			0.0783803i
$204$		0			0
$205$			2.14017e6i			0.248420i
$206$	−4.34570e6			−0.497116
$207$		0			0
$208$			160842.i			0.0178735i
$209$	−4.74645e6	+	8.09675e6i	−0.519912	+	0.886894i
$210$		0			0
$211$		−	5.89794e6i		−	0.627846i	−0.949448	−	0.313923i	$-0.898357\pi$
$211$		−	5.89794e6i		−	0.627846i	0.949448	−	0.313923i	$-0.101643\pi$
$212$		−	43518.7i		−	0.00456739i
$213$		0			0
$214$	−8.28990e6			−0.845878
$215$	−4.46825e6			−0.449595
$216$		0			0
$217$			675046.i			0.0660624i
$218$	1.07443e7			1.03708
$219$		0			0
$220$	1.74790e6			0.164153
$221$			429727.i			0.0398122i
$222$		0			0
$223$		−	1.43507e7i		−	1.29407i	−0.762460	−	0.647036i	$-0.776008\pi$
$223$		−	1.43507e7i		−	1.29407i	0.762460	−	0.647036i	$-0.223992\pi$
$224$		−	145722.i		−	0.0129652i
$225$		0			0
$226$	6.58826e6			0.570749
$227$		−	9.39539e6i		−	0.803225i	−0.915810	−	0.401613i	$-0.868450\pi$
$227$		−	9.39539e6i		−	0.803225i	0.915810	−	0.401613i	$-0.131550\pi$
$228$		0			0
$229$	1.31738e7			1.09699			0.548497	−	0.836152i	$-0.315200\pi$
$229$	1.31738e7			1.09699			0.548497	+	0.836152i	$0.315200\pi$
$230$			3.91013e6i			0.321372i
$231$		0			0
$232$	−4.71814e6			−0.377839
$233$	1.34530e7			1.06353			0.531767	−	0.846890i	$-0.321528\pi$
$233$	1.34530e7			1.06353			0.531767	+	0.846890i	$0.321528\pi$
$234$		0			0
$235$	2.42299e6			0.186702
$236$			7.64438e6i			0.581575i
$237$		0			0
$238$		−	389331.i		−	0.0288794i
$239$	−2.23712e7			−1.63869			−0.819344	−	0.573302i	$-0.805662\pi$
$239$	−2.23712e7			−1.63869			−0.819344	+	0.573302i	$0.805662\pi$
$240$		0			0
$241$		−	5.17298e6i		−	0.369564i	−0.982780	−	0.184782i	$-0.940842\pi$
$241$		−	5.17298e6i		−	0.369564i	0.982780	−	0.184782i	$-0.0591579\pi$
$242$			570121.i			0.0402273i
$243$		0			0
$244$	−1.37482e7			−0.946401
$245$	4.67111e6			0.317630
$246$		0			0
$247$	−929429.	−	544847.i	−0.0616773	−	0.0361563i
$248$	−4.85746e6			−0.318459
$249$		0			0
$250$			6.69683e6i			0.428597i
$251$	−1.08729e6			−0.0687582			−0.0343791	−	0.999409i	$-0.510945\pi$
$251$	−1.08729e6			−0.0687582			−0.0343791	+	0.999409i	$0.510945\pi$
$252$		0			0
$253$	−2.36938e7			−1.46310
$254$	5.93581e6			0.362226
$255$		0			0
$256$	1.04858e6			0.0625000
$257$		−	1.37915e7i		−	0.812480i	−0.913766	−	0.406240i	$-0.866840\pi$
$257$		−	1.37915e7i		−	0.812480i	0.913766	−	0.406240i	$-0.133160\pi$
$258$		0			0
$259$		−	2.16091e6i		−	0.124376i
$260$			200643.i			0.0114157i
$261$		0			0
$262$		−	1.50324e6i		−	0.0835843i
$263$	−1.18420e7			−0.650967			−0.325484	−	0.945548i	$-0.605527\pi$
$263$	−1.18420e7			−0.650967			−0.325484	+	0.945548i	$0.605527\pi$
$264$		0			0
$265$		−	54287.6i		−	0.00291718i
$266$	842058.	+	493629.i	0.0447401	+	0.0262274i
$267$		0			0
$268$		−	5.02353e6i		−	0.260979i
$269$			2.84915e7i			1.46372i	0.681453	+	0.731862i	$0.261348\pi$
$269$			2.84915e7i			1.46372i	−0.681453	+	0.731862i	$0.738652\pi$
$270$		0			0
$271$	242754.			0.0121971			0.00609857	−	0.999981i	$-0.498059\pi$
$271$	242754.			0.0121971			0.00609857	+	0.999981i	$0.498059\pi$
$272$	2.80152e6			0.139216
$273$		0			0
$274$			1.20559e6i			0.0586069i
$275$	−1.91998e7			−0.923207
$276$		0			0
$277$	−3.67776e7			−1.73039			−0.865195	−	0.501436i	$-0.832805\pi$
$277$	−3.67776e7			−1.73039			−0.865195	+	0.501436i	$0.832805\pi$
$278$			1.03344e7i			0.481005i
$279$		0			0
$280$		−	181781.i		−	0.00828085i
$281$		−	2.78086e7i		−	1.25331i	−0.779295	−	0.626657i	$-0.784423\pi$
$281$		−	2.78086e7i		−	1.25331i	0.779295	−	0.626657i	$-0.215577\pi$
$282$		0			0
$283$	−2.09382e7			−0.923803			−0.461901	−	0.886931i	$-0.652833\pi$
$283$	−2.09382e7			−0.923803			−0.461901	+	0.886931i	$0.652833\pi$
$284$			1.16803e7i			0.509915i
$285$		0			0
$286$	−1.21581e6			−0.0519719
$287$			1.34872e6i			0.0570527i
$288$		0			0
$289$	−1.66526e7			−0.689905
$290$	−5.88566e6			−0.241324
$291$		0			0
$292$	9.13183e6			0.366783
$293$		−	1.12853e7i		−	0.448651i	−0.974514	−	0.224325i	$-0.927982\pi$
$293$		−	1.12853e7i		−	0.448651i	0.974514	−	0.224325i	$-0.0720179\pi$
$294$		0			0
$295$			9.53601e6i			0.371450i
$296$	1.55494e7			0.599567
$297$		0			0
$298$			1.36557e7i			0.516018i
$299$		−	2.71982e6i		−	0.101748i
$300$		0			0
$301$	−2.81587e6			−0.103255
$302$	2.07224e6			0.0752350
$303$		0			0
$304$	−3.55202e6	+	6.05923e6i	−0.126431	+	0.215674i
$305$	−1.71502e7			−0.604463
$306$		0			0
$307$			762535.i			0.0263539i	0.999913	+	0.0131769i	$0.00419447\pi$
$307$			762535.i			0.0263539i	−0.999913	+	0.0131769i	$0.995806\pi$
$308$	1.10152e6			0.0376999
$309$		0			0
$310$	−6.05945e6			−0.203399
$311$	1.78594e7			0.593727			0.296864	−	0.954920i	$-0.404059\pi$
$311$	1.78594e7			0.593727			0.296864	+	0.954920i	$0.404059\pi$
$312$		0			0
$313$	−2.41177e7			−0.786506			−0.393253	−	0.919430i	$-0.628650\pi$
$313$	−2.41177e7			−0.786506			−0.393253	+	0.919430i	$0.628650\pi$
$314$			907200.i			0.0293031i
$315$		0			0
$316$			1.94220e7i			0.615508i
$317$		−	3.51314e7i		−	1.10285i	−0.834223	−	0.551427i	$-0.814084\pi$
$317$		−	3.51314e7i		−	1.10285i	0.834223	−	0.551427i	$-0.185916\pi$
$318$		0			0
$319$		−	3.56647e7i		−	1.09867i
$320$	1.30805e6			0.0399185
$321$		0			0
$322$			2.46414e6i			0.0738072i
$323$	−9.49009e6	+	1.61887e7i	−0.281620	+	0.480402i
$324$		0			0
$325$		−	2.20396e6i		−	0.0642027i
$326$			4.33218e7i			1.25041i
$327$		0			0
$328$	−9.70505e6			−0.275028
$329$	1.52696e6			0.0428785
$330$		0			0
$331$			2.71772e7i			0.749412i	0.927144	+	0.374706i	$0.122256\pi$
$331$			2.71772e7i			0.749412i	−0.927144	+	0.374706i	$0.877744\pi$
$332$	−2.80011e7			−0.765175
$333$		0			0
$334$	6.22375e6			0.167037
$335$		−	6.26663e6i		−	0.166686i
$336$		0			0
$337$			6.30310e7i			1.64689i	0.567397	+	0.823444i	$0.307951\pi$
$337$			6.30310e7i			1.64689i	−0.567397	+	0.823444i	$0.692049\pi$
$338$			2.71650e7i			0.703492i
$339$		0			0
$340$	3.49477e6			0.0889165
$341$		−	3.67178e7i		−	0.926006i
$342$		0			0
$343$	5.90334e6			0.146290
$344$		−	2.02622e7i		−	0.497751i
$345$		0			0
$346$	3.24716e7			0.783927
$347$	−3.67501e6			−0.0879571			−0.0439785	−	0.999032i	$-0.514003\pi$
$347$	−3.67501e6			−0.0879571			−0.0439785	+	0.999032i	$0.514003\pi$
$348$		0			0
$349$	−4.34206e7			−1.02146			−0.510728	−	0.859742i	$-0.670624\pi$
$349$	−4.34206e7			−1.02146			−0.510728	+	0.859742i	$0.670624\pi$
$350$			1.99677e6i			0.0465720i
$351$		0			0
$352$			7.92625e6i			0.181736i
$353$	1.09059e7			0.247934			0.123967	−	0.992286i	$-0.460438\pi$
$353$	1.09059e7			0.247934			0.123967	+	0.992286i	$0.460438\pi$
$354$		0			0
$355$			1.45706e7i			0.325681i
$356$			1.88972e7i			0.418840i
$357$		0			0
$358$	2.85653e7			0.622572
$359$	−8.16663e7			−1.76506			−0.882530	−	0.470256i	$-0.844161\pi$
$359$	−8.16663e7			−1.76506			−0.882530	+	0.470256i	$0.844161\pi$
$360$		0			0
$361$	−2.29811e7	−	4.10510e7i	−0.488483	−	0.872574i
$362$	5.78450e6			0.121938
$363$		0			0
$364$			126444.i			0.00262177i
$365$	1.13915e7			0.234263
$366$		0			0
$367$	5.31200e7			1.07463			0.537316	−	0.843381i	$-0.319438\pi$
$367$	5.31200e7			1.07463			0.537316	+	0.843381i	$0.319438\pi$
$368$	−1.77313e7			−0.355794
$369$		0			0
$370$	1.93971e7			0.382941
$371$		−	34211.8i		−	0.000669967i
$372$		0			0
$373$			2.35968e7i			0.454703i	0.973813	+	0.227351i	$0.0730066\pi$
$373$			2.35968e7i			0.454703i	−0.973813	+	0.227351i	$0.926993\pi$
$374$			2.11769e7i			0.404807i
$375$		0			0
$376$			1.09876e7i			0.206699i
$377$	4.09397e6			0.0764048
$378$		0			0
$379$			6.20101e7i			1.13906i	0.821972	+	0.569528i	$0.192874\pi$
$379$			6.20101e7i			1.13906i	−0.821972	+	0.569528i	$0.807126\pi$
$380$	−4.43099e6	+	7.55861e6i	−0.0807513	+	0.137750i
$381$		0			0
$382$			1.82872e7i			0.328064i
$383$		−	6.21448e7i		−	1.10614i	−0.833136	−	0.553068i	$-0.813457\pi$
$383$		−	6.21448e7i		−	1.10614i	0.833136	−	0.553068i	$-0.186543\pi$
$384$		0			0
$385$	1.37410e6			0.0240788
$386$	1.91326e6			0.0332668
$387$		0			0
$388$			3.22898e7i			0.552803i
$389$	4.71506e7			0.801011			0.400506	−	0.916294i	$-0.368835\pi$
$389$	4.71506e7			0.801011			0.400506	+	0.916294i	$0.368835\pi$
$390$		0			0
$391$	−4.73736e7			−0.792512
$392$			2.11822e7i			0.351652i
$393$		0			0
$394$		−	5.98211e7i		−	0.978061i
$395$			2.42281e7i			0.393123i
$396$		0			0
$397$	5.12175e7			0.818553			0.409277	−	0.912410i	$-0.365781\pi$
$397$	5.12175e7			0.818553			0.409277	+	0.912410i	$0.365781\pi$
$398$		−	3.75637e7i		−	0.595825i
$399$		0			0
$400$	−1.43683e7			−0.224504
$401$			6.30653e7i			0.978041i	0.872272	+	0.489021i	$0.162646\pi$
$401$			6.30653e7i			0.978041i	−0.872272	+	0.489021i	$0.837354\pi$
$402$		0			0
$403$	4.21485e6			0.0643973
$404$	−1.70914e7			−0.259199
$405$		0			0
$406$	−3.70911e6			−0.0554233
$407$			1.17539e8i			1.74340i
$408$		0			0
$409$			6.35675e7i			0.929107i	0.885545	+	0.464553i	$0.153785\pi$
$409$			6.35675e7i			0.929107i	−0.885545	+	0.464553i	$0.846215\pi$
$410$	−1.21066e7			−0.175659
$411$		0			0
$412$		−	2.45830e7i		−	0.351514i
$413$			6.00954e6i			0.0853083i
$414$		0			0
$415$	−3.49301e7			−0.488715
$416$	−909858.			−0.0126384
$417$		0			0
$418$	−4.58021e7	−	2.68500e7i	−0.627129	−	0.367633i
$419$	−3.77509e7			−0.513198			−0.256599	−	0.966518i	$-0.582602\pi$
$419$	−3.77509e7			−0.513198			−0.256599	+	0.966518i	$0.582602\pi$
$420$		0			0
$421$		−	6.28689e7i		−	0.842537i	−0.906936	−	0.421269i	$-0.861585\pi$
$421$		−	6.28689e7i		−	0.842537i	0.906936	−	0.421269i	$-0.138415\pi$
$422$	3.33638e7			0.443954
$423$		0			0
$424$	246179.			0.00322964
$425$	−3.83883e7			−0.500071
$426$		0			0
$427$	−1.08080e7			−0.138823
$428$		−	4.68947e7i		−	0.598126i
$429$		0			0
$430$		−	2.52762e7i		−	0.317912i
$431$		−	7.64637e7i		−	0.955045i	−0.878620	−	0.477522i	$-0.841535\pi$
$431$		−	7.64637e7i		−	0.955045i	0.878620	−	0.477522i	$-0.158465\pi$
$432$		0			0
$433$			3.83030e7i			0.471812i	0.971776	+	0.235906i	$0.0758058\pi$
$433$			3.83030e7i			0.471812i	−0.971776	+	0.235906i	$0.924194\pi$
$434$	−3.81864e6			−0.0467131
$435$		0			0
$436$			6.07792e7i			0.733323i
$437$	6.00645e7	−	1.02461e8i	0.719736	−	1.22776i
$438$		0			0
$439$		−	5.64059e7i		−	0.666701i	−0.942803	−	0.333350i	$-0.891821\pi$
$439$		−	5.64059e7i		−	0.666701i	0.942803	−	0.333350i	$-0.108179\pi$
$440$			9.88764e6i			0.116074i
$441$		0			0
$442$	−2.43091e6			−0.0281515
$443$	1.05839e8			1.21740			0.608701	−	0.793400i	$-0.291691\pi$
$443$	1.05839e8			1.21740			0.608701	+	0.793400i	$0.291691\pi$
$444$		0			0
$445$			2.35734e7i			0.267512i
$446$	8.11798e7			0.915047
$447$		0			0
$448$	824327.			0.00916780
$449$			8.94076e7i			0.987724i	0.869540	+	0.493862i	$0.164415\pi$
$449$			8.94076e7i			0.987724i	−0.869540	+	0.493862i	$0.835585\pi$
$450$		0			0
$451$		−	7.33611e7i		−	0.799717i
$452$			3.72688e7i			0.403581i
$453$		0			0
$454$	5.31484e7			0.567966
$455$			157733.i			0.00167451i
$456$		0			0
$457$	−3.60536e7			−0.377747			−0.188873	−	0.982001i	$-0.560484\pi$
$457$	−3.60536e7			−0.377747			−0.188873	+	0.982001i	$0.560484\pi$
$458$			7.45223e7i			0.775693i
$459$		0			0
$460$	−2.21190e7			−0.227244
$461$	−4.22650e7			−0.431398			−0.215699	−	0.976460i	$-0.569203\pi$
$461$	−4.22650e7			−0.431398			−0.215699	+	0.976460i	$0.569203\pi$
$462$		0			0
$463$	1.05402e8			1.06195			0.530977	−	0.847386i	$-0.321825\pi$
$463$	1.05402e8			1.06195			0.530977	+	0.847386i	$0.321825\pi$
$464$		−	2.66898e7i		−	0.267173i
$465$		0			0
$466$			7.61017e7i			0.752033i
$467$	1.16729e8			1.14611			0.573055	−	0.819517i	$-0.305758\pi$
$467$	1.16729e8			1.14611			0.573055	+	0.819517i	$0.305758\pi$
$468$		0			0
$469$		−	3.94919e6i		−	0.0382816i
$470$			1.37065e7i			0.132018i
$471$		0			0
$472$	−4.32431e7			−0.411236
$473$	1.53164e8			1.44734
$474$		0			0
$475$	4.86721e7	−	8.30275e7i	0.454150	−	0.774714i
$476$	2.20239e6			0.0204208
$477$		0			0
$478$		−	1.26551e8i		−	1.15873i
$479$	2.50394e7			0.227833			0.113916	−	0.993490i	$-0.463660\pi$
$479$	2.50394e7			0.227833			0.113916	+	0.993490i	$0.463660\pi$
$480$		0			0
$481$	−1.34923e7			−0.121241
$482$	2.92628e7			0.261321
$483$		0			0
$484$	−3.22509e6			−0.0284450
$485$			4.02801e7i			0.353074i
$486$		0			0
$487$		−	7.51465e7i		−	0.650612i	−0.945609	−	0.325306i	$-0.894533\pi$
$487$		−	7.51465e7i		−	0.650612i	0.945609	−	0.325306i	$-0.105467\pi$
$488$		−	7.77713e7i		−	0.669206i
$489$		0			0
$490$			2.64238e7i			0.224599i
$491$	−1.74282e8			−1.47234			−0.736170	−	0.676797i	$-0.763367\pi$
$491$	−1.74282e8			−1.47234			−0.736170	+	0.676797i	$0.763367\pi$
$492$		0			0
$493$		−	7.13083e7i		−	0.595113i
$494$	3.08212e6	−	5.25765e6i	0.0255663	−	0.0436124i
$495$		0			0
$496$		−	2.74779e7i		−	0.225185i
$497$			9.18231e6i			0.0747967i
$498$		0			0
$499$	1.36562e8			1.09908			0.549538	−	0.835469i	$-0.314804\pi$
$499$	1.36562e8			1.09908			0.549538	+	0.835469i	$0.314804\pi$
$500$	−3.78830e7			−0.303064
$501$		0			0
$502$		−	6.15064e6i		−	0.0486194i
$503$	−1.51696e8			−1.19198			−0.595991	−	0.802991i	$-0.703241\pi$
$503$	−1.51696e8			−1.19198			−0.595991	+	0.802991i	$0.703241\pi$
$504$		0			0
$505$	−2.13207e7			−0.165549
$506$		−	1.34032e8i		−	1.03457i
$507$		0			0
$508$			3.35780e7i			0.256132i
$509$			2.19152e8i			1.66185i	0.556386	+	0.830924i	$0.312188\pi$
$509$			2.19152e8i			1.66185i	−0.556386	+	0.830924i	$0.687812\pi$
$510$		0			0
$511$	7.17889e6			0.0538015
$512$			5.93164e6i			0.0441942i
$513$		0			0
$514$	7.80166e7			0.574510
$515$		−	3.06661e7i		−	0.224511i
$516$		0			0
$517$	−8.30560e7			−0.601034
$518$	1.22240e7			0.0879473
$519$		0			0
$520$	−1.13501e6			−0.00807213
$521$		−	1.55803e8i		−	1.10170i	−0.834605	−	0.550849i	$-0.814304\pi$
$521$		−	1.55803e8i		−	1.10170i	0.834605	−	0.550849i	$-0.185696\pi$
$522$		0			0
$523$		−	3.83749e7i		−	0.268251i	−0.990964	−	0.134126i	$-0.957177\pi$
$523$		−	3.83749e7i		−	0.268251i	0.990964	−	0.134126i	$-0.0428226\pi$
$524$	8.50362e6			0.0591030
$525$		0			0
$526$		−	6.69886e7i		−	0.460303i
$527$		−	7.34139e7i		−	0.501587i
$528$		0			0
$529$	1.51800e8			1.02543
$530$	307097.			0.00206276
$531$		0			0
$532$	−2.79238e6	+	4.76340e6i	−0.0185456	+	0.0316360i
$533$	8.42115e6			0.0556147
$534$		0			0
$535$		−	5.84990e7i		−	0.382021i
$536$	2.84174e7			0.184540
$537$		0			0
$538$	−1.61172e8			−1.03501
$539$	−1.60117e8			−1.02252
$540$		0			0
$541$	2.36964e8			1.49655			0.748274	−	0.663390i	$-0.230883\pi$
$541$	2.36964e8			1.49655			0.748274	+	0.663390i	$0.230883\pi$
$542$			1.37322e6i			0.00862468i
$543$		0			0
$544$			1.58478e7i			0.0984402i
$545$			7.58193e7i			0.468371i
$546$		0			0
$547$		−	1.85456e8i		−	1.13313i	−0.824018	−	0.566563i	$-0.808273\pi$
$547$		−	1.85456e8i		−	1.13313i	0.824018	−	0.566563i	$-0.191727\pi$
$548$	−6.81986e6			−0.0414414
$549$		0			0
$550$		−	1.08611e8i		−	0.652806i
$551$	1.54228e8	+	9.04111e7i	0.921953	+	0.540464i
$552$		0			0
$553$			1.52684e7i			0.0902857i
$554$		−	2.08045e8i		−	1.22357i
$555$		0			0
$556$	−5.84600e7			−0.340122
$557$	4.79023e7			0.277198			0.138599	−	0.990349i	$-0.455740\pi$
$557$	4.79023e7			0.277198			0.138599	+	0.990349i	$0.455740\pi$
$558$		0			0
$559$			1.75817e7i			0.100653i
$560$	1.02831e6			0.00585544
$561$		0			0
$562$	1.57309e8			0.886227
$563$			6.64627e7i			0.372437i	0.982508	+	0.186219i	$0.0596233\pi$
$563$			6.64627e7i			0.372437i	−0.982508	+	0.186219i	$0.940377\pi$
$564$		0			0
$565$			4.64911e7i			0.257766i
$566$		−	1.18444e8i		−	0.653227i
$567$		0			0
$568$	−6.60735e7			−0.360564
$569$		−	2.63899e8i		−	1.43252i	−0.697834	−	0.716259i	$-0.745853\pi$
$569$		−	2.63899e8i		−	1.43252i	0.697834	−	0.716259i	$-0.254147\pi$
$570$		0			0
$571$	2.72456e8			1.46348			0.731742	−	0.681581i	$-0.238707\pi$
$571$	2.72456e8			1.46348			0.731742	+	0.681581i	$0.238707\pi$
$572$		−	6.87767e6i		−	0.0367497i
$573$		0			0
$574$	−7.62952e6			−0.0403424
$575$	2.42966e8			1.27803
$576$		0			0
$577$	1.43860e8			0.748879			0.374439	−	0.927251i	$-0.377835\pi$
$577$	1.43860e8			0.748879			0.374439	+	0.927251i	$0.377835\pi$
$578$		−	9.42014e7i		−	0.487836i
$579$		0			0
$580$		−	3.32943e7i		−	0.170642i
$581$	−2.20128e7			−0.112240
$582$		0			0
$583$			1.86088e6i			0.00939103i
$584$			5.16574e7i			0.259355i
$585$		0			0
$586$	6.38391e7			0.317244
$587$	−2.03952e8			−1.00836			−0.504179	−	0.863599i	$-0.668205\pi$
$587$	−2.03952e8			−1.00836			−0.504179	+	0.863599i	$0.668205\pi$
$588$		0			0
$589$	1.58782e8	+	9.30807e7i	0.777062	+	0.455527i
$590$	−5.39438e7			−0.262655
$591$		0			0
$592$			8.79605e7i			0.423958i
$593$	1.29678e7			0.0621872			0.0310936	−	0.999516i	$-0.490101\pi$
$593$	1.29678e7			0.0621872			0.0310936	+	0.999516i	$0.490101\pi$
$594$		0			0
$595$	2.74738e6			0.0130427
$596$	−7.72482e7			−0.364880
$597$		0			0
$598$	1.53856e7			0.0719469
$599$		−	3.81320e8i		−	1.77423i	−0.461549	−	0.887114i	$-0.652706\pi$
$599$		−	3.81320e8i		−	1.77423i	0.461549	−	0.887114i	$-0.347294\pi$
$600$		0			0
$601$			1.47262e8i			0.678370i	0.940720	+	0.339185i	$0.110151\pi$
$601$			1.47262e8i			0.678370i	−0.940720	+	0.339185i	$0.889849\pi$
$602$		−	1.59289e7i		−	0.0730125i
$603$		0			0
$604$			1.17224e7i			0.0531991i
$605$	−4.02315e6			−0.0181677
$606$		0			0
$607$			9.07363e7i			0.405709i	0.979209	+	0.202855i	$0.0650219\pi$
$607$			9.07363e7i			0.405709i	−0.979209	+	0.202855i	$0.934978\pi$
$608$	−3.42762e7	−	2.00933e7i	−0.152504	−	0.0894005i
$609$		0			0
$610$		−	9.70161e7i		−	0.427420i
$611$		−	9.53403e6i		−	0.0417977i
$612$		0			0
$613$	−1.02413e8			−0.444603			−0.222302	−	0.974978i	$-0.571357\pi$
$613$	−1.02413e8			−0.444603			−0.222302	+	0.974978i	$0.571357\pi$
$614$	−4.31355e6			−0.0186350
$615$		0			0
$616$			6.23114e6i			0.0266579i
$617$	2.66718e8			1.13552			0.567762	−	0.823193i	$-0.307809\pi$
$617$	2.66718e8			1.13552			0.567762	+	0.823193i	$0.307809\pi$
$618$		0			0
$619$	−4.23626e8			−1.78612			−0.893061	−	0.449936i	$-0.851447\pi$
$619$	−4.23626e8			−1.78612			−0.893061	+	0.449936i	$0.851447\pi$
$620$		−	3.42774e7i		−	0.143825i
$621$		0			0
$622$			1.01028e8i			0.419828i
$623$			1.48558e7i			0.0614375i
$624$		0			0
$625$	1.71985e8			0.704451
$626$		−	1.36430e8i		−	0.556144i
$627$		0			0
$628$	−5.13190e6			−0.0207204
$629$			2.35008e8i			0.944344i
$630$		0			0
$631$	−1.14563e8			−0.455991			−0.227996	−	0.973662i	$-0.573217\pi$
$631$	−1.14563e8			−0.455991			−0.227996	+	0.973662i	$0.573217\pi$
$632$	−1.09868e8			−0.435230
$633$		0			0
$634$	1.98733e8			0.779835
$635$			4.18871e7i			0.163591i
$636$		0			0
$637$		−	1.83800e7i		−	0.0711093i
$638$	2.01750e8			0.776876
$639$		0			0
$640$			7.39945e6i			0.0282267i
$641$			3.79080e8i			1.43932i	0.694328	+	0.719658i	$0.255702\pi$
$641$			3.79080e8i			1.43932i	−0.694328	+	0.719658i	$0.744298\pi$
$642$		0			0
$643$	1.05304e8			0.396107			0.198054	−	0.980191i	$-0.436538\pi$
$643$	1.05304e8			0.396107			0.198054	+	0.980191i	$0.436538\pi$
$644$	−1.39393e7			−0.0521895
$645$		0			0
$646$	−9.15771e7	−	5.36841e7i	−0.339695	−	0.199135i
$647$	−4.50756e8			−1.66429			−0.832144	−	0.554560i	$-0.812887\pi$
$647$	−4.50756e8			−1.66429			−0.832144	+	0.554560i	$0.812887\pi$
$648$		0			0
$649$		−	3.26878e8i		−	1.19578i
$650$	1.24675e7			0.0453981
$651$		0			0
$652$	−2.45065e8			−0.884176
$653$	3.55740e8			1.27759			0.638797	−	0.769376i	$-0.279432\pi$
$653$	3.55740e8			1.27759			0.638797	+	0.769376i	$0.279432\pi$
$654$		0			0
$655$	1.06079e7			0.0377489
$656$		−	5.49000e7i		−	0.194474i
$657$		0			0
$658$			8.63778e6i			0.0303197i
$659$		−	1.16578e6i		−	0.00407344i	−0.999998	−	0.00203672i	$-0.999352\pi$
$659$		−	1.16578e6i		−	0.00407344i	0.999998	−	0.00203672i	$-0.000648309\pi$
$660$		0			0
$661$			5.43258e8i			1.88106i	0.339715	+	0.940528i	$0.389669\pi$
$661$			5.43258e8i			1.88106i	−0.339715	+	0.940528i	$0.610331\pi$
$662$	−1.53737e8			−0.529914
$663$		0			0
$664$		−	1.58398e8i		−	0.541060i
$665$	−3.48337e6	+	5.94212e6i	−0.0118450	+	0.0202058i
$666$		0			0
$667$			4.51323e8i			1.52093i
$668$			3.52068e7i			0.118113i
$669$		0			0
$670$	3.54494e7			0.117865
$671$	5.87878e8			1.94590
$672$		0			0
$673$			1.90275e8i			0.624217i	0.950046	+	0.312109i	$0.101035\pi$
$673$			1.90275e8i			0.624217i	−0.950046	+	0.312109i	$0.898965\pi$
$674$	−3.56557e8			−1.16453
$675$		0			0
$676$	−1.53668e8			−0.497444
$677$			4.81730e7i			0.155252i	0.996983	+	0.0776261i	$0.0247340\pi$
$677$			4.81730e7i			0.155252i	−0.996983	+	0.0776261i	$0.975266\pi$
$678$		0			0
$679$			2.53843e7i			0.0810879i
$680$			1.97694e7i			0.0628734i
$681$		0			0
$682$	2.07707e8			0.654785
$683$			1.89512e8i			0.594806i	0.954752	+	0.297403i	$0.0961205\pi$
$683$			1.89512e8i			0.594806i	−0.954752	+	0.297403i	$0.903879\pi$
$684$		0			0
$685$	−8.50747e6			−0.0264684
$686$			3.33943e7i			0.103443i
$687$		0			0
$688$	1.14621e8			0.351963
$689$	−213612.			−0.000653081
$690$		0			0
$691$	6.88902e7			0.208796			0.104398	−	0.994536i	$-0.466708\pi$
$691$	6.88902e7			0.208796			0.104398	+	0.994536i	$0.466708\pi$
$692$			1.83687e8i			0.554320i
$693$		0			0
$694$		−	2.07890e7i		−	0.0621950i
$695$	−7.29261e7			−0.217234
$696$		0			0
$697$		−	1.46679e8i		−	0.433180i
$698$		−	2.45624e8i		−	0.722279i
$699$		0			0
$700$	−1.12955e7			−0.0329314
$701$	−3.42895e8			−0.995420			−0.497710	−	0.867343i	$-0.665826\pi$
$701$	−3.42895e8			−0.995420			−0.497710	+	0.867343i	$0.665826\pi$
$702$		0			0
$703$	−5.08283e8	−	2.97964e8i	−1.46298	−	0.857625i
$704$	−4.48377e7			−0.128506
$705$		0			0
$706$			6.16930e7i			0.175316i
$707$	−1.34362e7			−0.0380206
$708$		0			0
$709$	−1.95474e8			−0.548468			−0.274234	−	0.961663i	$-0.588424\pi$
$709$	−1.95474e8			−0.548468			−0.274234	+	0.961663i	$0.588424\pi$
$710$	−8.24237e7			−0.230291
$711$		0			0
$712$	−1.06899e8			−0.296164
$713$			4.64650e8i			1.28191i
$714$		0			0
$715$		−	8.57958e6i		−	0.0234719i
$716$			1.61590e8i			0.440225i
$717$		0			0
$718$		−	4.61974e8i		−	1.24809i
$719$	2.31962e8			0.624066			0.312033	−	0.950071i	$-0.398990\pi$
$719$	2.31962e8			0.624066			0.312033	+	0.950071i	$0.398990\pi$
$720$		0			0
$721$		−	1.93256e7i		−	0.0515618i
$722$	2.32219e8	−	1.30001e8i	0.617003	−	0.345409i
$723$		0			0
$724$			3.27221e7i			0.0862234i
$725$			3.65721e8i			0.959702i
$726$		0			0
$727$	−3.54964e8			−0.923806			−0.461903	−	0.886930i	$-0.652833\pi$
$727$	−3.54964e8			−0.923806			−0.461903	+	0.886930i	$0.652833\pi$
$728$	−715275.			−0.00185387
$729$		0			0
$730$			6.44403e7i			0.165649i
$731$	3.06236e8			0.783980
$732$		0			0
$733$	−4.30151e8			−1.09222			−0.546108	−	0.837715i	$-0.683891\pi$
$733$	−4.30151e8			−1.09222			−0.546108	+	0.837715i	$0.683891\pi$
$734$			3.00492e8i			0.759879i
$735$		0			0
$736$		−	1.00304e8i		−	0.251584i
$737$			2.14809e8i			0.536599i
$738$		0			0
$739$	2.90982e8			0.720995			0.360497	−	0.932760i	$-0.382607\pi$
$739$	2.90982e8			0.720995			0.360497	+	0.932760i	$0.382607\pi$
$740$			1.09727e8i			0.270780i
$741$		0			0
$742$	193531.			0.000473739
$743$		−	3.06553e8i		−	0.747375i	−0.927555	−	0.373688i	$-0.878093\pi$
$743$		−	3.06553e8i		−	0.747375i	0.927555	−	0.373688i	$-0.121907\pi$
$744$		0			0
$745$	−9.63636e7			−0.233047
$746$	−1.33484e8			−0.321523
$747$		0			0
$748$	−1.19795e8			−0.286241
$749$		−	3.68658e7i		−	0.0877361i
$750$		0			0
$751$			4.56545e8i			1.07786i	0.842349	+	0.538932i	$0.181172\pi$
$751$			4.56545e8i			1.07786i	−0.842349	+	0.538932i	$0.818828\pi$
$752$	−6.21553e7			−0.146159
$753$		0			0
$754$			2.31590e7i			0.0540263i
$755$			1.46231e7i			0.0339781i
$756$		0			0
$757$	−2.12640e7			−0.0490182			−0.0245091	−	0.999700i	$-0.507802\pi$
$757$	−2.12640e7			−0.0490182			−0.0245091	+	0.999700i	$0.507802\pi$
$758$	−3.50782e8			−0.805434
$759$		0			0
$760$	−4.27580e7	−	2.50654e7i	−0.0974039	−	0.0570998i
$761$	−2.83195e8			−0.642586			−0.321293	−	0.946980i	$-0.604117\pi$
$761$	−2.83195e8			−0.642586			−0.321293	+	0.946980i	$0.604117\pi$
$762$		0			0
$763$			4.77809e7i			0.107567i
$764$	−1.03448e8			−0.231976
$765$		0			0
$766$	3.51544e8			0.782157
$767$	3.75224e7			0.0831581
$768$		0			0
$769$	1.63966e8			0.360557			0.180278	−	0.983616i	$-0.442300\pi$
$769$	1.63966e8			0.360557			0.180278	+	0.983616i	$0.442300\pi$
$770$			7.77306e6i			0.0170263i
$771$		0			0
$772$			1.08230e7i			0.0235232i
$773$			2.80416e8i			0.607106i	0.952815	+	0.303553i	$0.0981730\pi$
$773$			2.80416e8i			0.607106i	−0.952815	+	0.303553i	$0.901827\pi$
$774$		0			0
$775$			3.76520e8i			0.808878i
$776$	−1.82659e8			−0.390891
$777$		0			0
$778$			2.66724e8i			0.566400i
$779$	3.17242e8	+	1.85972e8i	0.671086	+	0.393402i
$780$		0			0
$781$		−	4.99454e8i		−	1.04844i
$782$		−	2.67985e8i		−	0.560391i
$783$		0			0
$784$	−1.19825e8			−0.248655
$785$	−6.40181e6			−0.0132341
$786$		0			0
$787$			1.78603e8i			0.366407i	0.983075	+	0.183203i	$0.0586467\pi$
$787$			1.78603e8i			0.366407i	−0.983075	+	0.183203i	$0.941353\pi$
$788$	3.38399e8			0.691593
$789$		0			0
$790$	−1.37055e8			−0.277980
$791$			2.92985e7i			0.0591992i
$792$		0			0
$793$			6.74828e7i			0.135324i
$794$			2.89730e8i			0.578805i
$795$		0			0
$796$	2.12492e8			0.421312
$797$			5.39911e8i			1.06647i	0.845968	+	0.533233i	$0.179023\pi$
$797$			5.39911e8i			1.06647i	−0.845968	+	0.533233i	$0.820977\pi$
$798$		0			0
$799$	−1.66063e8			−0.325561
$800$		−	8.12792e7i		−	0.158748i
$801$		0			0
$802$	−3.56751e8			−0.691580
$803$	−3.90482e8			−0.754144
$804$		0			0
$805$	−1.73886e7			−0.0333333
$806$			2.38428e7i			0.0455357i
$807$		0			0
$808$		−	9.66835e7i		−	0.183281i
$809$	4.24059e8			0.800904			0.400452	−	0.916318i	$-0.368853\pi$
$809$	4.24059e8			0.800904			0.400452	+	0.916318i	$0.368853\pi$
$810$		0			0
$811$		−	1.50159e8i		−	0.281507i	−0.990045	−	0.140754i	$-0.955047\pi$
$811$		−	1.50159e8i		−	0.281507i	0.990045	−	0.140754i	$-0.0449525\pi$
$812$		−	2.09819e7i		−	0.0391902i
$813$		0			0
$814$	−6.64899e8			−1.23277
$815$	−3.05707e8			−0.564720
$816$		0			0
$817$	−3.88274e8	+	6.62339e8i	−0.711987	+	1.21455i
$818$	−3.59592e8			−0.656978
$819$		0			0
$820$		−	6.84853e7i		−	0.124210i
$821$	1.77116e8			0.320057			0.160029	−	0.987112i	$-0.448841\pi$
$821$	1.77116e8			0.320057			0.160029	+	0.987112i	$0.448841\pi$
$822$		0			0
$823$	−5.42120e8			−0.972514			−0.486257	−	0.873816i	$-0.661638\pi$
$823$	−5.42120e8			−0.972514			−0.486257	+	0.873816i	$0.661638\pi$
$824$	1.39062e8			0.248558
$825$		0			0
$826$	−3.39951e7			−0.0603221
$827$			2.17728e8i			0.384945i	0.981302	+	0.192472i	$0.0616506\pi$
$827$			2.17728e8i			0.384945i	−0.981302	+	0.192472i	$0.938349\pi$
$828$		0			0
$829$		−	2.27590e8i		−	0.399474i	−0.979850	−	0.199737i	$-0.935991\pi$
$829$		−	2.27590e8i		−	0.399474i	0.979850	−	0.199737i	$-0.0640088\pi$
$830$		−	1.97594e8i		−	0.345573i
$831$		0			0
$832$		−	5.14693e6i		−	0.00893673i
$833$	−3.20140e8			−0.553867
$834$		0			0
$835$			4.39189e7i			0.0754383i
$836$	1.51886e8	−	2.59096e8i	0.259956	−	0.443447i
$837$		0			0
$838$		−	2.13551e8i		−	0.362886i
$839$		−	3.59559e8i		−	0.608814i	−0.952542	−	0.304407i	$-0.901542\pi$
$839$		−	3.59559e8i		−	0.608814i	0.952542	−	0.304407i	$-0.0984582\pi$
$840$		0			0
$841$	−8.45237e7			−0.142099
$842$	3.55640e8			0.595764
$843$		0			0
$844$			1.88734e8i			0.313923i
$845$	−1.91694e8			−0.317716
$846$		0			0
$847$	−2.53537e6			−0.00417245
$848$			1.39260e6i			0.00228370i
$849$		0			0
$850$		−	2.17157e8i		−	0.353604i
$851$		−	1.48741e9i		−	2.41346i
$852$		0			0
$853$	8.96407e8			1.44430			0.722151	−	0.691736i	$-0.243154\pi$
$853$	8.96407e8			1.44430			0.722151	+	0.691736i	$0.243154\pi$
$854$		−	6.11391e7i		−	0.0981624i
$855$		0			0
$856$	2.65277e8			0.422939
$857$		−	2.39428e7i		−	0.0380394i	−0.999819	−	0.0190197i	$-0.993945\pi$
$857$		−	2.39428e7i		−	0.0380394i	0.999819	−	0.0190197i	$-0.00605452\pi$
$858$		0			0
$859$	−5.73924e8			−0.905471			−0.452736	−	0.891645i	$-0.649552\pi$
$859$	−5.73924e8			−0.905471			−0.452736	+	0.891645i	$0.649552\pi$
$860$	1.42984e8			0.224798
$861$		0			0
$862$	4.32544e8			0.675319
$863$			9.59089e8i			1.49220i	0.665835	+	0.746099i	$0.268076\pi$
$863$			9.59089e8i			1.49220i	−0.665835	+	0.746099i	$0.731924\pi$
$864$		0			0
$865$			2.29141e8i			0.354042i
$866$	−2.16675e8			−0.333622
$867$		0			0
$868$		−	2.16015e7i		−	0.0330312i
$869$		−	8.30497e8i		−	1.26555i
$870$		0			0
$871$	−2.46580e7			−0.0373167
$872$	−3.43819e8			−0.518538
$873$		0			0
$874$	5.79608e8	+	3.39776e8i	0.868161	+	0.508930i
$875$	−2.97813e7			−0.0444549
$876$		0			0
$877$			2.35518e8i			0.349160i	0.984643	+	0.174580i	$0.0558568\pi$
$877$			2.35518e8i			0.349160i	−0.984643	+	0.174580i	$0.944143\pi$
$878$	3.19080e8			0.471429
$879$		0			0
$880$	−5.59329e7			−0.0820766
$881$	−6.93176e8			−1.01372			−0.506858	−	0.862030i	$-0.669193\pi$
$881$	−6.93176e8			−1.01372			−0.506858	+	0.862030i	$0.669193\pi$
$882$		0			0
$883$	−9.08954e8			−1.32026			−0.660130	−	0.751151i	$-0.729499\pi$
$883$	−9.08954e8			−1.32026			−0.660130	+	0.751151i	$0.729499\pi$
$884$		−	1.37513e7i		−	0.0199061i
$885$		0			0
$886$			5.98715e8i			0.860833i
$887$		−	1.21284e9i		−	1.73794i	−0.494868	−	0.868968i	$-0.664783\pi$
$887$		−	1.21284e9i		−	1.73794i	0.494868	−	0.868968i	$-0.335217\pi$
$888$		0			0
$889$			2.63970e7i			0.0375707i
$890$	−1.33351e8			−0.189159
$891$		0			0
$892$			4.59222e8i			0.647036i
$893$	2.10549e8	−	3.59166e8i	0.295665	−	0.504361i
$894$		0			0
$895$			2.01576e8i			0.281170i
$896$			4.66310e6i			0.00648262i
$897$		0			0
$898$	−5.05766e8			−0.698426
$899$	−6.99407e8			−0.962611
$900$		0			0
$901$			3.72066e6i			0.00508682i
$902$	4.14993e8			0.565485
$903$		0			0
$904$	−2.10824e8			−0.285375
$905$			4.08193e7i			0.0550706i
$906$		0			0
$907$		−	6.70720e8i		−	0.898916i	−0.893301	−	0.449458i	$-0.851617\pi$
$907$		−	6.70720e8i		−	0.898916i	0.893301	−	0.449458i	$-0.148383\pi$
$908$			3.00653e8i			0.401613i
$909$		0			0
$910$	−892272.			−0.00118406
$911$		−	4.11499e8i		−	0.544269i	−0.962259	−	0.272134i	$-0.912270\pi$
$911$		−	4.11499e8i		−	0.544269i	0.962259	−	0.272134i	$-0.0877296\pi$
$912$		0			0
$913$	1.19734e9			1.57328
$914$		−	2.03950e8i		−	0.267107i
$915$		0			0
$916$	−4.21562e8			−0.548497
$917$	6.68502e6			0.00866952
$918$		0			0
$919$	9.76999e8			1.25877			0.629387	−	0.777092i	$-0.283306\pi$
$919$	9.76999e8			1.25877			0.629387	+	0.777092i	$0.283306\pi$
$920$		−	1.25124e8i		−	0.160686i
$921$		0			0
$922$		−	2.39087e8i		−	0.305044i
$923$	5.73325e7			0.0729115
$924$		0			0
$925$		−	1.20529e9i		−	1.52288i
$926$			5.96243e8i			0.750914i
$927$		0			0
$928$	1.50980e8			0.188920
$929$	−7.27336e8			−0.907168			−0.453584	−	0.891213i	$-0.649855\pi$
$929$	−7.27336e8			−0.907168			−0.453584	+	0.891213i	$0.649855\pi$
$930$		0			0
$931$	4.05903e8	−	6.92410e8i	0.503005	−	0.858054i
$932$	−4.30496e8			−0.531767
$933$		0			0
$934$			6.60317e8i			0.810423i
$935$	−1.49438e8			−0.182821
$936$		0			0
$937$	−7.48977e8			−0.910437			−0.455218	−	0.890380i	$-0.650439\pi$
$937$	−7.48977e8			−0.910437			−0.455218	+	0.890380i	$0.650439\pi$
$938$	2.23400e7			0.0270692
$939$		0			0
$940$	−7.75358e7			−0.0933510
$941$		−	7.23039e7i		−	0.0867746i	−0.999058	−	0.0433873i	$-0.986185\pi$
$941$		−	7.23039e7i		−	0.0867746i	0.999058	−	0.0433873i	$-0.0138149\pi$
$942$		0			0
$943$			9.28356e8i			1.10708i
$944$		−	2.44620e8i		−	0.290788i
$945$		0			0
$946$			8.66424e8i			1.02343i
$947$	−1.18089e9			−1.39046			−0.695231	−	0.718786i	$-0.744698\pi$
$947$	−1.18089e9			−1.39046			−0.695231	+	0.718786i	$0.744698\pi$
$948$		0			0
$949$		−	4.48236e7i		−	0.0524455i
$950$	4.69675e8	+	2.75331e8i	0.547805	+	0.321133i
$951$		0			0
$952$			1.24586e7i			0.0144397i
$953$			5.02689e8i			0.580792i	0.956907	+	0.290396i	$0.0937870\pi$
$953$			5.02689e8i			0.580792i	−0.956907	+	0.290396i	$0.906213\pi$
$954$		0			0
$955$	−1.29047e8			−0.148162
$956$	7.15880e8			0.819344
$957$		0			0
$958$			1.41644e8i			0.161102i
$959$	−5.36136e6			−0.00607882
$960$		0			0
$961$	1.67445e8			0.188670
$962$		−	7.63240e7i		−	0.0857306i
$963$		0			0
$964$			1.65535e8i			0.184782i
$965$			1.35012e7i			0.0150242i
$966$		0			0
$967$	−7.99455e8			−0.884127			−0.442063	−	0.896984i	$-0.645753\pi$
$967$	−7.99455e8			−0.884127			−0.442063	+	0.896984i	$0.645753\pi$
$968$		−	1.82439e7i		−	0.0201136i
$969$		0			0
$970$	−2.27859e8			−0.249661
$971$		−	1.39572e9i		−	1.52455i	−0.647255	−	0.762274i	$-0.724083\pi$
$971$		−	1.39572e9i		−	1.52455i	0.647255	−	0.762274i	$-0.275917\pi$
$972$		0			0
$973$	−4.59577e7			−0.0498907
$974$	4.25093e8			0.460052
$975$		0			0
$976$	4.39941e8			0.473200
$977$			1.42354e9i			1.52646i	0.646129	+	0.763228i	$0.276387\pi$
$977$			1.42354e9i			1.52646i	−0.646129	+	0.763228i	$0.723613\pi$
$978$		0			0
$979$		−	8.08055e8i		−	0.861178i
$980$	−1.49476e8			−0.158815
$981$		0			0
$982$		−	9.85887e8i		−	1.04110i
$983$		−	3.32507e8i		−	0.350058i	−0.984563	−	0.175029i	$-0.943998\pi$
$983$		−	3.32507e8i		−	0.350058i	0.984563	−	0.175029i	$-0.0560019\pi$
$984$		0			0
$985$	4.22138e8			0.441718
$986$	4.03381e8			0.420808
$987$		0			0
$988$	2.97417e7	+	1.74351e7i	0.0308387	+	0.0180781i
$989$	−1.93823e9			−2.00362
$990$		0			0
$991$		−	8.50991e8i		−	0.874388i	−0.899367	−	0.437194i	$-0.855972\pi$
$991$		−	8.50991e8i		−	0.874388i	0.899367	−	0.437194i	$-0.144028\pi$
$992$	1.55439e8			0.159230
$993$		0			0
$994$	−5.19430e7			−0.0528893
$995$	2.65074e8			0.269091
$996$		0			0
$997$	1.54040e9			1.55435			0.777174	−	0.629286i	$-0.216653\pi$
$997$	1.54040e9			1.55435			0.777174	+	0.629286i	$0.216653\pi$
$998$			7.72510e8i			0.777164i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	342.7.d.a.37.7		10
3.2	odd	2		38.7.b.a.37.5	✓	10
12.11	even	2		304.7.e.e.113.1		10
19.18	odd	2	inner	342.7.d.a.37.2		10
57.56	even	2		38.7.b.a.37.6	yes	10
228.227	odd	2		304.7.e.e.113.10		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.7.b.a.37.5	✓	10	3.2	odd	2
38.7.b.a.37.6	yes	10	57.56	even	2
304.7.e.e.113.1		10	12.11	even	2
304.7.e.e.113.10		10	228.227	odd	2
342.7.d.a.37.2		10	19.18	odd	2	inner
342.7.d.a.37.7		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:	\( N \)	\(=\)	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	342.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+5.65685i q^{2} -32.0000 q^{4} -39.9185 q^{5} -25.1565 q^{7} -181.019i q^{8} +O(q^{10})\)	\(q+5.65685i q^{2} -32.0000 q^{4} -39.9185 q^{5} -25.1565 q^{7} -181.019i q^{8} -225.813i q^{10} +1368.34 q^{11} +157.072i q^{13} -142.306i q^{14} +1024.00 q^{16} +2735.86 q^{17} +(-3468.77 + 5917.22i) q^{19} +1277.39 q^{20} +7740.48i q^{22} -17315.8 q^{23} -14031.5 q^{25} -888.533 q^{26} +805.006 q^{28} -26064.3i q^{29} -26833.9i q^{31} +5792.62i q^{32} +15476.4i q^{34} +1004.21 q^{35} +85898.9i q^{37} +(-33472.9 - 19622.3i) q^{38} +7226.03i q^{40} -53613.3i q^{41} +111934. q^{43} -43786.8 q^{44} -97952.8i q^{46} -60698.5 q^{47} -117016. q^{49} -79374.2i q^{50} -5026.30i q^{52} +1359.96i q^{53} -54622.0 q^{55} +4553.80i q^{56} +147442. q^{58} -238887. i q^{59} +429630. q^{61} +151795. q^{62} -32768.0 q^{64} -6270.08i q^{65} +156985. i q^{67} -87547.6 q^{68} +5680.66i q^{70} -365008. i q^{71} -285370. q^{73} -485917. q^{74} +(111001. - 189351. i) q^{76} -34422.5 q^{77} -606939. i q^{79} -40876.6 q^{80} +303283. q^{82} +875034. q^{83} -109212. q^{85} +633195. i q^{86} -247695. i q^{88} -590538. i q^{89} -3951.37i q^{91} +554105. q^{92} -343363. i q^{94} +(138468. - 236207. i) q^{95} -1.00906e6i q^{97} -661943. i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 320 q^{4} + 112 q^{5} - 224 q^{7}+O(q^{10}) \) 10 * q - 320 * q^4 + 112 * q^5 - 224 * q^7	\( 10 q - 320 q^{4} + 112 q^{5} - 224 q^{7} - 3644 q^{11} + 10240 q^{16} + 10420 q^{17} - 17230 q^{19} - 3584 q^{20} - 37712 q^{23} - 52078 q^{25} + 7104 q^{26} + 7168 q^{28} + 161720 q^{35} - 25152 q^{38} + 6308 q^{43} + 116608 q^{44} - 322220 q^{47} - 235770 q^{49} - 377880 q^{55} + 445920 q^{58} + 426304 q^{61} - 59424 q^{62} - 327680 q^{64} - 333440 q^{68} - 786076 q^{73} + 293280 q^{74} + 551360 q^{76} - 2303716 q^{77} + 114688 q^{80} - 455136 q^{82} + 101500 q^{83} - 1261380 q^{85} + 1206784 q^{92} - 3106292 q^{95}+O(q^{100}) \) 10 * q - 320 * q^4 + 112 * q^5 - 224 * q^7 - 3644 * q^11 + 10240 * q^16 + 10420 * q^17 - 17230 * q^19 - 3584 * q^20 - 37712 * q^23 - 52078 * q^25 + 7104 * q^26 + 7168 * q^28 + 161720 * q^35 - 25152 * q^38 + 6308 * q^43 + 116608 * q^44 - 322220 * q^47 - 235770 * q^49 - 377880 * q^55 + 445920 * q^58 + 426304 * q^61 - 59424 * q^62 - 327680 * q^64 - 333440 * q^68 - 786076 * q^73 + 293280 * q^74 + 551360 * q^76 - 2303716 * q^77 + 114688 * q^80 - 455136 * q^82 + 101500 * q^83 - 1261380 * q^85 + 1206784 * q^92 - 3106292 * q^95

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