LMFDB - Embedded newform 648.4.i.a.217.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [648,4,Mod(217,648)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(648, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("648.217");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 648 = 2^{3} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	648.i (of order $3$, degree $2$, not 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:	$38.2332376837$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 72)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			217.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	648.217
Dual form			648.4.i.a.433.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-8.00000 - 13.8564i) q^{5} +(6.00000 - 10.3923i) q^{7} +O(q^{10})$	$q+(-8.00000 - 13.8564i) q^{5} +(6.00000 - 10.3923i) q^{7} +(-32.0000 + 55.4256i) q^{11} +(-29.0000 - 50.2295i) q^{13} +32.0000 q^{17} -136.000 q^{19} +(64.0000 + 110.851i) q^{23} +(-65.5000 + 113.449i) q^{25} +(72.0000 - 124.708i) q^{29} +(-10.0000 - 17.3205i) q^{31} -192.000 q^{35} -18.0000 q^{37} +(144.000 + 249.415i) q^{41} +(100.000 - 173.205i) q^{43} +(-192.000 + 332.554i) q^{47} +(99.5000 + 172.339i) q^{49} +496.000 q^{53} +1024.00 q^{55} +(64.0000 + 110.851i) q^{59} +(229.000 - 396.640i) q^{61} +(-464.000 + 803.672i) q^{65} +(248.000 + 429.549i) q^{67} +512.000 q^{71} -602.000 q^{73} +(384.000 + 665.108i) q^{77} +(-554.000 + 959.556i) q^{79} +(-352.000 + 609.682i) q^{83} +(-256.000 - 443.405i) q^{85} -960.000 q^{89} -696.000 q^{91} +(1088.00 + 1884.47i) q^{95} +(-103.000 + 178.401i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 16 q^{5} + 12 q^{7}+O(q^{10}) $ 2 * q - 16 * q^5 + 12 * q^7	$ 2 q - 16 q^{5} + 12 q^{7} - 64 q^{11} - 58 q^{13} + 64 q^{17} - 272 q^{19} + 128 q^{23} - 131 q^{25} + 144 q^{29} - 20 q^{31} - 384 q^{35} - 36 q^{37} + 288 q^{41} + 200 q^{43} - 384 q^{47} + 199 q^{49} + 992 q^{53} + 2048 q^{55} + 128 q^{59} + 458 q^{61} - 928 q^{65} + 496 q^{67} + 1024 q^{71} - 1204 q^{73} + 768 q^{77} - 1108 q^{79} - 704 q^{83} - 512 q^{85} - 1920 q^{89} - 1392 q^{91} + 2176 q^{95} - 206 q^{97}+O(q^{100}) $ 2 * q - 16 * q^5 + 12 * q^7 - 64 * q^11 - 58 * q^13 + 64 * q^17 - 272 * q^19 + 128 * q^23 - 131 * q^25 + 144 * q^29 - 20 * q^31 - 384 * q^35 - 36 * q^37 + 288 * q^41 + 200 * q^43 - 384 * q^47 + 199 * q^49 + 992 * q^53 + 2048 * q^55 + 128 * q^59 + 458 * q^61 - 928 * q^65 + 496 * q^67 + 1024 * q^71 - 1204 * q^73 + 768 * q^77 - 1108 * q^79 - 704 * q^83 - 512 * q^85 - 1920 * q^89 - 1392 * q^91 + 2176 * q^95 - 206 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/648\mathbb{Z}\right)^\times$.

$n$	$325$	$487$	$569$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−8.00000	−	13.8564i	−0.715542	−	1.23935i	−0.962750	−	0.270392i	$-0.912847\pi$
$5$	−8.00000	−	13.8564i	−0.715542	−	1.23935i	0.247208	−	0.968962i	$-0.420487\pi$
$6$		0			0
$7$	6.00000	−	10.3923i	0.323970	−	0.561132i	−0.657334	−	0.753600i	$-0.728316\pi$
$7$	6.00000	−	10.3923i	0.323970	−	0.561132i	0.981303	+	0.192468i	$0.0616491\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−32.0000	+	55.4256i	−0.877124	+	1.51922i	−0.0226410	+	0.999744i	$0.507207\pi$
$11$	−32.0000	+	55.4256i	−0.877124	+	1.51922i	−0.854483	+	0.519480i	$0.826126\pi$
$12$		0			0
$13$	−29.0000	−	50.2295i	−0.618704	−	1.07163i	−0.989722	−	0.143001i	$-0.954325\pi$
$13$	−29.0000	−	50.2295i	−0.618704	−	1.07163i	0.371018	−	0.928626i	$-0.379009\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	32.0000			0.456538			0.228269	−	0.973598i	$-0.426693\pi$
$17$	32.0000			0.456538			0.228269	+	0.973598i	$0.426693\pi$
$18$		0			0
$19$	−136.000			−1.64213			−0.821067	−	0.570832i	$-0.806621\pi$
$19$	−136.000			−1.64213			−0.821067	+	0.570832i	$0.806621\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	64.0000	+	110.851i	0.580214	+	1.00496i	0.995454	+	0.0952481i	$0.0303644\pi$
$23$	64.0000	+	110.851i	0.580214	+	1.00496i	−0.415240	+	0.909712i	$0.636302\pi$
$24$		0			0
$25$	−65.5000	+	113.449i	−0.524000	+	0.907595i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	72.0000	−	124.708i	0.461037	−	0.798539i	−0.537976	−	0.842960i	$-0.680811\pi$
$29$	72.0000	−	124.708i	0.461037	−	0.798539i	0.999013	+	0.0444210i	$0.0141443\pi$
$30$		0			0
$31$	−10.0000	−	17.3205i	−0.0579372	−	0.100350i	0.835602	−	0.549335i	$-0.185119\pi$
$31$	−10.0000	−	17.3205i	−0.0579372	−	0.100350i	−0.893539	+	0.448985i	$0.851786\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−192.000			−0.927255
$36$		0			0
$37$	−18.0000			−0.0799779			−0.0399889	−	0.999200i	$-0.512732\pi$
$37$	−18.0000			−0.0799779			−0.0399889	+	0.999200i	$0.512732\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	144.000	+	249.415i	0.548513	+	0.950052i	0.998377	+	0.0569549i	$0.0181391\pi$
$41$	144.000	+	249.415i	0.548513	+	0.950052i	−0.449864	+	0.893097i	$0.648528\pi$
$42$		0			0
$43$	100.000	−	173.205i	0.354648	−	0.614268i	−0.632410	−	0.774634i	$-0.717934\pi$
$43$	100.000	−	173.205i	0.354648	−	0.614268i	0.987058	+	0.160366i	$0.0512674\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−192.000	+	332.554i	−0.595874	+	1.03208i	0.397549	+	0.917581i	$0.369861\pi$
$47$	−192.000	+	332.554i	−0.595874	+	1.03208i	−0.993423	+	0.114503i	$0.963472\pi$
$48$		0			0
$49$	99.5000	+	172.339i	0.290087	+	0.502446i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	496.000			1.28549			0.642744	−	0.766081i	$-0.277796\pi$
$53$	496.000			1.28549			0.642744	+	0.766081i	$0.277796\pi$
$54$		0			0
$55$	1024.00			2.51048
$56$		0			0
$57$		0			0
$58$		0			0
$59$	64.0000	+	110.851i	0.141222	+	0.244603i	0.927957	−	0.372687i	$-0.121564\pi$
$59$	64.0000	+	110.851i	0.141222	+	0.244603i	−0.786735	+	0.617291i	$0.788230\pi$
$60$		0			0
$61$	229.000	−	396.640i	0.480663	−	0.832533i	−0.519091	−	0.854719i	$-0.673729\pi$
$61$	229.000	−	396.640i	0.480663	−	0.832533i	0.999754	+	0.0221863i	$0.00706269\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−464.000	+	803.672i	−0.885417	+	1.53359i
$66$		0			0
$67$	248.000	+	429.549i	0.452209	+	0.783249i	0.998523	−	0.0543312i	$-0.0173027\pi$
$67$	248.000	+	429.549i	0.452209	+	0.783249i	−0.546314	+	0.837581i	$0.683969\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	512.000			0.855820			0.427910	−	0.903821i	$-0.359250\pi$
$71$	512.000			0.855820			0.427910	+	0.903821i	$0.359250\pi$
$72$		0			0
$73$	−602.000			−0.965189			−0.482594	−	0.875844i	$-0.660305\pi$
$73$	−602.000			−0.965189			−0.482594	+	0.875844i	$0.660305\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	384.000	+	665.108i	0.568323	+	0.984364i
$78$		0			0
$79$	−554.000	+	959.556i	−0.788986	+	1.36656i	0.137603	+	0.990487i	$0.456060\pi$
$79$	−554.000	+	959.556i	−0.788986	+	1.36656i	−0.926589	+	0.376076i	$0.877273\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−352.000	+	609.682i	−0.465506	+	0.806280i	−0.999224	−	0.0393820i	$-0.987461\pi$
$83$	−352.000	+	609.682i	−0.465506	+	0.806280i	0.533718	+	0.845663i	$0.320794\pi$
$84$		0			0
$85$	−256.000	−	443.405i	−0.326672	−	0.565812i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−960.000			−1.14337			−0.571684	−	0.820474i	$-0.693710\pi$
$89$	−960.000			−1.14337			−0.571684	+	0.820474i	$0.693710\pi$
$90$		0			0
$91$	−696.000			−0.801765
$92$		0			0
$93$		0			0
$94$		0			0
$95$	1088.00	+	1884.47i	1.17502	+	2.03519i
$96$		0			0
$97$	−103.000	+	178.401i	−0.107815	+	0.186741i	−0.914885	−	0.403715i	$-0.867719\pi$
$97$	−103.000	+	178.401i	−0.107815	+	0.186741i	0.807070	+	0.590456i	$0.201052\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−216.000	+	374.123i	−0.212800	+	0.368580i	−0.952590	−	0.304258i	$-0.901592\pi$
$101$	−216.000	+	374.123i	−0.212800	+	0.368580i	0.739790	+	0.672838i	$0.234925\pi$
$102$		0			0
$103$	34.0000	+	58.8897i	0.0325254	+	0.0563357i	0.881830	−	0.471568i	$-0.156312\pi$
$103$	34.0000	+	58.8897i	0.0325254	+	0.0563357i	−0.849304	+	0.527903i	$0.822978\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−384.000			−0.346941			−0.173470	−	0.984839i	$-0.555498\pi$
$107$	−384.000			−0.346941			−0.173470	+	0.984839i	$0.555498\pi$
$108$		0			0
$109$	−518.000			−0.455187			−0.227594	−	0.973756i	$-0.573086\pi$
$109$	−518.000			−0.455187			−0.227594	+	0.973756i	$0.573086\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	480.000	+	831.384i	0.399598	+	0.692124i	0.993676	−	0.112283i	$-0.0358163\pi$
$113$	480.000	+	831.384i	0.399598	+	0.692124i	−0.594078	+	0.804407i	$0.702483\pi$
$114$		0			0
$115$	1024.00	−	1773.62i	0.830335	−	1.43818i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	192.000	−	332.554i	0.147904	−	0.256178i
$120$		0			0
$121$	−1382.50	−	2394.56i	−1.03869	−	1.79907i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	96.0000			0.0686920
$126$		0			0
$127$	796.000			0.556170			0.278085	−	0.960556i	$-0.410300\pi$
$127$	796.000			0.556170			0.278085	+	0.960556i	$0.410300\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−256.000	−	443.405i	−0.170739	−	0.295729i	0.767939	−	0.640523i	$-0.221282\pi$
$131$	−256.000	−	443.405i	−0.170739	−	0.295729i	−0.938678	+	0.344794i	$0.887949\pi$
$132$		0			0
$133$	−816.000	+	1413.35i	−0.532001	+	0.921453i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−912.000	+	1579.63i	−0.568740	+	0.985087i	0.427951	+	0.903802i	$0.359236\pi$
$137$	−912.000	+	1579.63i	−0.568740	+	0.985087i	−0.996691	+	0.0812849i	$0.974098\pi$
$138$		0			0
$139$	1080.00	+	1870.61i	0.659024	+	1.14146i	0.980869	+	0.194671i	$0.0623640\pi$
$139$	1080.00	+	1870.61i	0.659024	+	1.14146i	−0.321844	+	0.946793i	$0.604303\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	3712.00			2.17072
$144$		0			0
$145$	−2304.00			−1.31956
$146$		0			0
$147$		0			0
$148$		0			0
$149$	344.000	+	595.825i	0.189138	+	0.327597i	0.944963	−	0.327177i	$-0.106097\pi$
$149$	344.000	+	595.825i	0.189138	+	0.327597i	−0.755825	+	0.654774i	$0.772764\pi$
$150$		0			0
$151$	422.000	−	730.925i	0.227430	−	0.393920i	−0.729616	−	0.683857i	$-0.760301\pi$
$151$	422.000	−	730.925i	0.227430	−	0.393920i	0.957046	+	0.289937i	$0.0936345\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−160.000	+	277.128i	−0.0829130	+	0.143609i
$156$		0			0
$157$	−59.0000	−	102.191i	−0.0299918	−	0.0519473i	0.850640	−	0.525749i	$-0.176215\pi$
$157$	−59.0000	−	102.191i	−0.0299918	−	0.0519473i	−0.880632	+	0.473801i	$0.842881\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	1536.00			0.751887
$162$		0			0
$163$	3576.00			1.71837			0.859184	−	0.511667i	$-0.170972\pi$
$163$	3576.00			1.71837			0.859184	+	0.511667i	$0.170972\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−192.000	−	332.554i	−0.0889665	−	0.154095i	0.818108	−	0.575065i	$-0.195023\pi$
$167$	−192.000	−	332.554i	−0.0889665	−	0.154095i	−0.907075	+	0.420970i	$0.861690\pi$
$168$		0			0
$169$	−583.500	+	1010.65i	−0.265589	+	0.460014i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−1224.00	+	2120.03i	−0.537913	+	0.931693i	0.461103	+	0.887347i	$0.347454\pi$
$173$	−1224.00	+	2120.03i	−0.537913	+	0.931693i	−0.999016	+	0.0443465i	$0.985879\pi$
$174$		0			0
$175$	786.000	+	1361.39i	0.339520	+	0.588066i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−4224.00			−1.76378			−0.881890	−	0.471455i	$-0.843729\pi$
$179$	−4224.00			−1.76378			−0.881890	+	0.471455i	$0.843729\pi$
$180$		0			0
$181$	−510.000			−0.209436			−0.104718	−	0.994502i	$-0.533394\pi$
$181$	−510.000			−0.209436			−0.104718	+	0.994502i	$0.533394\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	144.000	+	249.415i	0.0572275	+	0.0991210i
$186$		0			0
$187$	−1024.00	+	1773.62i	−0.400440	+	0.693583i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	192.000	−	332.554i	0.0727363	−	0.125983i	−0.827363	−	0.561667i	$-0.810160\pi$
$191$	192.000	−	332.554i	0.0727363	−	0.125983i	0.900100	+	0.435684i	$0.143494\pi$
$192$		0			0
$193$	1727.00	+	2991.25i	0.644105	+	1.11562i	0.984508	+	0.175342i	$0.0561032\pi$
$193$	1727.00	+	2991.25i	0.644105	+	1.11562i	−0.340403	+	0.940280i	$0.610563\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−3216.00			−1.16310			−0.581550	−	0.813511i	$-0.697553\pi$
$197$	−3216.00			−1.16310			−0.581550	+	0.813511i	$0.697553\pi$
$198$		0			0
$199$	1708.00			0.608427			0.304213	−	0.952604i	$-0.401606\pi$
$199$	1708.00			0.608427			0.304213	+	0.952604i	$0.401606\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−864.000	−	1496.49i	−0.298724	−	0.517405i
$204$		0			0
$205$	2304.00	−	3990.65i	0.784968	−	1.35960i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	4352.00	−	7537.89i	1.44035	−	2.49477i
$210$		0			0
$211$	−1160.00	−	2009.18i	−0.378472	−	0.655534i	0.612368	−	0.790573i	$-0.290217\pi$
$211$	−1160.00	−	2009.18i	−0.378472	−	0.655534i	−0.990840	+	0.135039i	$0.956884\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−3200.00			−1.01506
$216$		0			0
$217$	−240.000			−0.0750795
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−928.000	−	1607.34i	−0.282462	−	0.489238i
$222$		0			0
$223$	58.0000	−	100.459i	0.0174169	−	0.0301669i	−0.857186	−	0.515008i	$-0.827789\pi$
$223$	58.0000	−	100.459i	0.0174169	−	0.0301669i	0.874602	+	0.484841i	$0.161122\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−672.000	+	1163.94i	−0.196485	+	0.340323i	−0.947386	−	0.320092i	$-0.896286\pi$
$227$	−672.000	+	1163.94i	−0.196485	+	0.340323i	0.750901	+	0.660415i	$0.229620\pi$
$228$		0			0
$229$	−2297.00	−	3978.52i	−0.662839	−	1.14807i	−0.979866	−	0.199654i	$-0.936018\pi$
$229$	−2297.00	−	3978.52i	−0.662839	−	1.14807i	0.317028	−	0.948416i	$-0.397315\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	5056.00			1.42159			0.710793	−	0.703401i	$-0.248336\pi$
$233$	5056.00			1.42159			0.710793	+	0.703401i	$0.248336\pi$
$234$		0			0
$235$	6144.00			1.70549
$236$		0			0
$237$		0			0
$238$		0			0
$239$	1856.00	+	3214.69i	0.502321	+	0.870045i	0.999996	+	0.00268185i	$0.000853660\pi$
$239$	1856.00	+	3214.69i	0.502321	+	0.870045i	−0.497676	+	0.867363i	$0.665813\pi$
$240$		0			0
$241$	489.000	−	846.973i	0.130702	−	0.226383i	−0.793245	−	0.608902i	$-0.791610\pi$
$241$	489.000	−	846.973i	0.130702	−	0.226383i	0.923948	+	0.382519i	$0.124943\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	1592.00	−	2757.42i	0.415139	−	0.719043i
$246$		0			0
$247$	3944.00	+	6831.21i	1.01599	+	1.75975i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	1856.00			0.466732			0.233366	−	0.972389i	$-0.425026\pi$
$251$	1856.00			0.466732			0.233366	+	0.972389i	$0.425026\pi$
$252$		0			0
$253$	−8192.00			−2.03568
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−3904.00	−	6761.93i	−0.947567	−	1.64123i	−0.750527	−	0.660840i	$-0.770200\pi$
$257$	−3904.00	−	6761.93i	−0.947567	−	1.64123i	−0.197040	−	0.980395i	$-0.563133\pi$
$258$		0			0
$259$	−108.000	+	187.061i	−0.0259104	+	0.0448781i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−512.000	+	886.810i	−0.120043	+	0.207920i	−0.919784	−	0.392424i	$-0.871637\pi$
$263$	−512.000	+	886.810i	−0.120043	+	0.207920i	0.799741	+	0.600345i	$0.204970\pi$
$264$		0			0
$265$	−3968.00	−	6872.78i	−0.919820	−	1.59317i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	1328.00			0.301002			0.150501	−	0.988610i	$-0.451911\pi$
$269$	1328.00			0.301002			0.150501	+	0.988610i	$0.451911\pi$
$270$		0			0
$271$	−5812.00			−1.30278			−0.651391	−	0.758742i	$-0.725814\pi$
$271$	−5812.00			−1.30278			−0.651391	+	0.758742i	$0.725814\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−4192.00	−	7260.76i	−0.919226	−	1.59215i
$276$		0			0
$277$	−4193.00	+	7262.49i	−0.909505	+	1.57531i	−0.0947524	+	0.995501i	$0.530206\pi$
$277$	−4193.00	+	7262.49i	−0.909505	+	1.57531i	−0.814753	+	0.579808i	$0.803127\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	320.000	−	554.256i	0.0679345	−	0.117666i	−0.830057	−	0.557678i	$-0.811692\pi$
$281$	320.000	−	554.256i	0.0679345	−	0.117666i	0.897992	+	0.440012i	$0.145026\pi$
$282$		0			0
$283$	−2416.00	−	4184.63i	−0.507478	−	0.878978i	−0.999963	−	0.00865656i	$-0.997244\pi$
$283$	−2416.00	−	4184.63i	−0.507478	−	0.878978i	0.492484	−	0.870321i	$-0.336089\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	3456.00			0.710806
$288$		0			0
$289$	−3889.00			−0.791573
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−3192.00	−	5528.71i	−0.636446	−	1.10236i	−0.986207	−	0.165518i	$-0.947071\pi$
$293$	−3192.00	−	5528.71i	−0.636446	−	1.10236i	0.349761	−	0.936839i	$-0.386263\pi$
$294$		0			0
$295$	1024.00	−	1773.62i	0.202100	−	0.350048i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	3712.00	−	6429.37i	0.717962	−	1.24355i
$300$		0			0
$301$	−1200.00	−	2078.46i	−0.229790	−	0.398008i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−7328.00			−1.37574
$306$		0			0
$307$	−3312.00			−0.615719			−0.307860	−	0.951432i	$-0.599613\pi$
$307$	−3312.00			−0.615719			−0.307860	+	0.951432i	$0.599613\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−4992.00	−	8646.40i	−0.910194	−	1.57650i	−0.813789	−	0.581160i	$-0.802599\pi$
$311$	−4992.00	−	8646.40i	−0.910194	−	1.57650i	−0.0964048	−	0.995342i	$-0.530734\pi$
$312$		0			0
$313$	−1293.00	+	2239.54i	−0.233497	+	0.404429i	−0.958835	−	0.283964i	$-0.908350\pi$
$313$	−1293.00	+	2239.54i	−0.233497	+	0.404429i	0.725338	+	0.688393i	$0.241684\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	1416.00	−	2452.58i	0.250885	−	0.434545i	−0.712885	−	0.701281i	$-0.752612\pi$
$317$	1416.00	−	2452.58i	0.250885	−	0.434545i	0.963770	+	0.266736i	$0.0859451\pi$
$318$		0			0
$319$	4608.00	+	7981.29i	0.808773	+	1.40084i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−4352.00			−0.749696
$324$		0			0
$325$	7598.00			1.29680
$326$		0			0
$327$		0			0
$328$		0			0
$329$	2304.00	+	3990.65i	0.386090	+	0.668728i
$330$		0			0
$331$	2960.00	−	5126.87i	0.491530	−	0.851354i	−0.508423	−	0.861108i	$-0.669771\pi$
$331$	2960.00	−	5126.87i	0.491530	−	0.851354i	0.999952	+	0.00975326i	$0.00310461\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	3968.00	−	6872.78i	0.647149	−	1.12090i
$336$		0			0
$337$	2337.00	+	4047.80i	0.377758	+	0.654296i	0.990736	−	0.135804i	$-0.0433617\pi$
$337$	2337.00	+	4047.80i	0.377758	+	0.654296i	−0.612978	+	0.790100i	$0.710028\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	1280.00			0.203272
$342$		0			0
$343$	6504.00			1.02386
$344$		0			0
$345$		0			0
$346$		0			0
$347$	4512.00	+	7815.01i	0.698031	+	1.20903i	0.969148	+	0.246479i	$0.0792737\pi$
$347$	4512.00	+	7815.01i	0.698031	+	1.20903i	−0.271117	+	0.962546i	$0.587393\pi$
$348$		0			0
$349$	2181.00	−	3777.60i	0.334516	−	0.579400i	−0.648875	−	0.760895i	$-0.724760\pi$
$349$	2181.00	−	3777.60i	0.334516	−	0.579400i	0.983392	+	0.181495i	$0.0580937\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−4384.00	+	7593.31i	−0.661011	+	1.14490i	0.319340	+	0.947640i	$0.396539\pi$
$353$	−4384.00	+	7593.31i	−0.661011	+	1.14490i	−0.980350	+	0.197264i	$0.936794\pi$
$354$		0			0
$355$	−4096.00	−	7094.48i	−0.612375	−	1.06066i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−6144.00			−0.903253			−0.451627	−	0.892207i	$-0.649156\pi$
$359$	−6144.00			−0.903253			−0.451627	+	0.892207i	$0.649156\pi$
$360$		0			0
$361$	11637.0			1.69660
$362$		0			0
$363$		0			0
$364$		0			0
$365$	4816.00	+	8341.56i	0.690633	+	1.19621i
$366$		0			0
$367$	−2282.00	+	3952.54i	−0.324576	+	0.562182i	−0.981426	−	0.191839i	$-0.938555\pi$
$367$	−2282.00	+	3952.54i	−0.324576	+	0.562182i	0.656850	+	0.754021i	$0.271888\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	2976.00	−	5154.58i	0.416459	−	0.721328i
$372$		0			0
$373$	4385.00	+	7595.04i	0.608704	+	1.05431i	0.991454	+	0.130455i	$0.0416437\pi$
$373$	4385.00	+	7595.04i	0.608704	+	1.05431i	−0.382750	+	0.923852i	$0.625023\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−8352.00			−1.14098
$378$		0			0
$379$	−1096.00			−0.148543			−0.0742714	−	0.997238i	$-0.523663\pi$
$379$	−1096.00			−0.148543			−0.0742714	+	0.997238i	$0.523663\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−5184.00	−	8978.95i	−0.691619	−	1.19792i	−0.971307	−	0.237828i	$-0.923564\pi$
$383$	−5184.00	−	8978.95i	−0.691619	−	1.19792i	0.279688	−	0.960091i	$-0.409769\pi$
$384$		0			0
$385$	6144.00	−	10641.7i	0.813317	−	1.40871i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	1624.00	−	2812.85i	0.211671	−	0.366625i	−0.740567	−	0.671983i	$-0.765443\pi$
$389$	1624.00	−	2812.85i	0.211671	−	0.366625i	0.952238	+	0.305358i	$0.0987761\pi$
$390$		0			0
$391$	2048.00	+	3547.24i	0.264890	+	0.458802i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	17728.0			2.25821
$396$		0			0
$397$	−6106.00			−0.771918			−0.385959	−	0.922516i	$-0.626129\pi$
$397$	−6106.00			−0.771918			−0.385959	+	0.922516i	$0.626129\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−3504.00	−	6069.11i	−0.436363	−	0.755802i	0.561043	−	0.827787i	$-0.310400\pi$
$401$	−3504.00	−	6069.11i	−0.436363	−	0.755802i	−0.997406	+	0.0719843i	$0.977067\pi$
$402$		0			0
$403$	−580.000	+	1004.59i	−0.0716920	+	0.124174i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	576.000	−	997.661i	0.0701505	−	0.121504i
$408$		0			0
$409$	−795.000	−	1376.98i	−0.0961130	−	0.166473i	0.813960	−	0.580922i	$-0.197308\pi$
$409$	−795.000	−	1376.98i	−0.0961130	−	0.166473i	−0.910073	+	0.414449i	$0.863974\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	1536.00			0.183006
$414$		0			0
$415$	11264.0			1.33236
$416$		0			0
$417$		0			0
$418$		0			0
$419$	96.0000	+	166.277i	0.0111931	+	0.0193870i	0.871568	−	0.490275i	$-0.163104\pi$
$419$	96.0000	+	166.277i	0.0111931	+	0.0193870i	−0.860375	+	0.509662i	$0.829770\pi$
$420$		0			0
$421$	−4537.00	+	7858.31i	−0.525225	+	0.909717i	0.474343	+	0.880340i	$0.342686\pi$
$421$	−4537.00	+	7858.31i	−0.525225	+	0.909717i	−0.999568	+	0.0293768i	$0.990648\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−2096.00	+	3630.38i	−0.239226	+	0.414351i
$426$		0			0
$427$	−2748.00	−	4759.68i	−0.311440	−	0.539431i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−5248.00			−0.586513			−0.293257	−	0.956034i	$-0.594739\pi$
$431$	−5248.00			−0.586513			−0.293257	+	0.956034i	$0.594739\pi$
$432$		0			0
$433$	−8222.00			−0.912527			−0.456263	−	0.889845i	$-0.650813\pi$
$433$	−8222.00			−0.912527			−0.456263	+	0.889845i	$0.650813\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−8704.00	−	15075.8i	−0.952789	−	1.65028i
$438$		0			0
$439$	−8118.00	+	14060.8i	−0.882576	+	1.52867i	−0.0341097	+	0.999418i	$0.510860\pi$
$439$	−8118.00	+	14060.8i	−0.882576	+	1.52867i	−0.848467	+	0.529249i	$0.822474\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−7264.00	+	12581.6i	−0.779059	+	1.34937i	0.153426	+	0.988160i	$0.450969\pi$
$443$	−7264.00	+	12581.6i	−0.779059	+	1.34937i	−0.932485	+	0.361209i	$0.882364\pi$
$444$		0			0
$445$	7680.00	+	13302.2i	0.818128	+	1.41704i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	6304.00			0.662593			0.331296	−	0.943527i	$-0.392514\pi$
$449$	6304.00			0.662593			0.331296	+	0.943527i	$0.392514\pi$
$450$		0			0
$451$	−18432.0			−1.92445
$452$		0			0
$453$		0			0
$454$		0			0
$455$	5568.00	+	9644.06i	0.573696	+	0.993671i
$456$		0			0
$457$	−979.000	+	1695.68i	−0.100209	+	0.173568i	−0.911771	−	0.410699i	$-0.865285\pi$
$457$	−979.000	+	1695.68i	−0.100209	+	0.173568i	0.811561	+	0.584267i	$0.198618\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−2024.00	+	3505.67i	−0.204484	+	0.354177i	−0.949968	−	0.312347i	$-0.898885\pi$
$461$	−2024.00	+	3505.67i	−0.204484	+	0.354177i	0.745484	+	0.666523i	$0.232218\pi$
$462$		0			0
$463$	−8494.00	−	14712.0i	−0.852591	−	1.47673i	−0.878862	−	0.477076i	$-0.841697\pi$
$463$	−8494.00	−	14712.0i	−0.852591	−	1.47673i	0.0262709	−	0.999655i	$-0.491637\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	6720.00			0.665877			0.332938	−	0.942949i	$-0.391960\pi$
$467$	6720.00			0.665877			0.332938	+	0.942949i	$0.391960\pi$
$468$		0			0
$469$	5952.00			0.586008
$470$		0			0
$471$		0			0
$472$		0			0
$473$	6400.00	+	11085.1i	0.622140	+	1.07758i
$474$		0			0
$475$	8908.00	−	15429.1i	0.860478	−	1.49039i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−4864.00	+	8424.70i	−0.463970	+	0.803620i	−0.999154	−	0.0411152i	$-0.986909\pi$
$479$	−4864.00	+	8424.70i	−0.463970	+	0.803620i	0.535184	+	0.844736i	$0.320242\pi$
$480$		0			0
$481$	522.000	+	904.131i	0.0494826	+	0.0857065i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	3296.00			0.308585
$486$		0			0
$487$	−8444.00			−0.785696			−0.392848	−	0.919603i	$-0.628510\pi$
$487$	−8444.00			−0.785696			−0.392848	+	0.919603i	$0.628510\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	7680.00	+	13302.2i	0.705893	+	1.22264i	0.966368	+	0.257162i	$0.0827875\pi$
$491$	7680.00	+	13302.2i	0.705893	+	1.22264i	−0.260475	+	0.965481i	$0.583879\pi$
$492$		0			0
$493$	2304.00	−	3990.65i	0.210481	−	0.364563i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	3072.00	−	5320.86i	0.277260	−	0.480228i
$498$		0			0
$499$	−3312.00	−	5736.55i	−0.297125	−	0.514636i	0.678352	−	0.734737i	$-0.262695\pi$
$499$	−3312.00	−	5736.55i	−0.297125	−	0.514636i	−0.975477	+	0.220101i	$0.929361\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−6912.00			−0.612705			−0.306353	−	0.951918i	$-0.599109\pi$
$503$	−6912.00			−0.612705			−0.306353	+	0.951918i	$0.599109\pi$
$504$		0			0
$505$	6912.00			0.609069
$506$		0			0
$507$		0			0
$508$		0			0
$509$	9960.00	+	17251.2i	0.867327	+	1.50225i	0.864718	+	0.502257i	$0.167497\pi$
$509$	9960.00	+	17251.2i	0.867327	+	1.50225i	0.00260828	+	0.999997i	$0.499170\pi$
$510$		0			0
$511$	−3612.00	+	6256.17i	−0.312692	+	0.541598i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	544.000	−	942.236i	0.0465466	−	0.0806211i
$516$		0			0
$517$	−12288.0	−	21283.4i	−1.04531	−	1.81053i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	3680.00			0.309451			0.154725	−	0.987958i	$-0.450551\pi$
$521$	3680.00			0.309451			0.154725	+	0.987958i	$0.450551\pi$
$522$		0			0
$523$	−11720.0			−0.979885			−0.489942	−	0.871755i	$-0.662982\pi$
$523$	−11720.0			−0.979885			−0.489942	+	0.871755i	$0.662982\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−320.000	−	554.256i	−0.0264505	−	0.0458136i
$528$		0			0
$529$	−2108.50	+	3652.03i	−0.173297	+	0.300159i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	8352.00	−	14466.1i	0.678734	−	1.17560i
$534$		0			0
$535$	3072.00	+	5320.86i	0.248251	+	0.429983i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−12736.0			−1.01777
$540$		0			0
$541$	11754.0			0.934092			0.467046	−	0.884233i	$-0.345318\pi$
$541$	11754.0			0.934092			0.467046	+	0.884233i	$0.345318\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	4144.00	+	7177.62i	0.325705	+	0.564138i
$546$		0			0
$547$	9452.00	−	16371.3i	0.738827	−	1.27969i	−0.214197	−	0.976791i	$-0.568713\pi$
$547$	9452.00	−	16371.3i	0.738827	−	1.27969i	0.953024	−	0.302895i	$-0.0979532\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−9792.00	+	16960.2i	−0.757084	+	1.31131i
$552$		0			0
$553$	6648.00	+	11514.7i	0.511215	+	0.885450i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	3088.00			0.234906			0.117453	−	0.993078i	$-0.462527\pi$
$557$	3088.00			0.234906			0.117453	+	0.993078i	$0.462527\pi$
$558$		0			0
$559$	−11600.0			−0.877688
$560$		0			0
$561$		0			0
$562$		0			0
$563$	10720.0	+	18567.6i	0.802476	+	1.38993i	0.917982	+	0.396623i	$0.129818\pi$
$563$	10720.0	+	18567.6i	0.802476	+	1.38993i	−0.115505	+	0.993307i	$0.536849\pi$
$564$		0			0
$565$	7680.00	−	13302.2i	0.571858	−	0.990488i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−11312.0	+	19593.0i	−0.833434	+	1.44355i	0.0618659	+	0.998084i	$0.480295\pi$
$569$	−11312.0	+	19593.0i	−0.833434	+	1.44355i	−0.895299	+	0.445465i	$0.853038\pi$
$570$		0			0
$571$	3000.00	+	5196.15i	0.219871	+	0.380827i	0.954768	−	0.297351i	$-0.0961032\pi$
$571$	3000.00	+	5196.15i	0.219871	+	0.380827i	−0.734898	+	0.678178i	$0.762770\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−16768.0			−1.21613
$576$		0			0
$577$	19922.0			1.43737			0.718686	−	0.695335i	$-0.244744\pi$
$577$	19922.0			1.43737			0.718686	+	0.695335i	$0.244744\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	4224.00	+	7316.18i	0.301620	+	0.522421i
$582$		0			0
$583$	−15872.0	+	27491.1i	−1.12753	+	1.95294i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	1792.00	−	3103.84i	0.126003	−	0.218244i	−0.796122	−	0.605137i	$-0.793118\pi$
$587$	1792.00	−	3103.84i	0.126003	−	0.218244i	0.922125	+	0.386893i	$0.126452\pi$
$588$		0			0
$589$	1360.00	+	2355.59i	0.0951406	+	0.164788i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	1984.00			0.137391			0.0686957	−	0.997638i	$-0.478116\pi$
$593$	1984.00			0.137391			0.0686957	+	0.997638i	$0.478116\pi$
$594$		0			0
$595$	−6144.00			−0.423327
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−7488.00	−	12969.6i	−0.510770	−	0.884680i	−0.999922	−	0.0124814i	$-0.996027\pi$
$599$	−7488.00	−	12969.6i	−0.510770	−	0.884680i	0.489152	−	0.872199i	$-0.337306\pi$
$600$		0			0
$601$	−12869.0	+	22289.8i	−0.873440	+	1.51284i	−0.0150248	+	0.999887i	$0.504783\pi$
$601$	−12869.0	+	22289.8i	−0.873440	+	1.51284i	−0.858415	+	0.512955i	$0.828551\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−22120.0	+	38313.0i	−1.48646	+	2.57462i
$606$		0			0
$607$	4274.00	+	7402.79i	0.285793	+	0.495008i	0.972801	−	0.231642i	$-0.0744097\pi$
$607$	4274.00	+	7402.79i	0.285793	+	0.495008i	−0.687008	+	0.726650i	$0.741076\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	22272.0			1.47468
$612$		0			0
$613$	8558.00			0.563873			0.281937	−	0.959433i	$-0.409023\pi$
$613$	8558.00			0.563873			0.281937	+	0.959433i	$0.409023\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	5184.00	+	8978.95i	0.338250	+	0.585865i	0.984104	−	0.177596i	$-0.0568319\pi$
$617$	5184.00	+	8978.95i	0.338250	+	0.585865i	−0.645854	+	0.763461i	$0.723499\pi$
$618$		0			0
$619$	6544.00	−	11334.5i	0.424920	−	0.735983i	−0.571493	−	0.820607i	$-0.693636\pi$
$619$	6544.00	−	11334.5i	0.424920	−	0.735983i	0.996413	+	0.0846238i	$0.0269688\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−5760.00	+	9976.61i	−0.370417	+	0.641580i
$624$		0			0
$625$	7419.50	+	12851.0i	0.474848	+	0.822461i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−576.000			−0.0365129
$630$		0			0
$631$	−4412.00			−0.278350			−0.139175	−	0.990268i	$-0.544445\pi$
$631$	−4412.00			−0.278350			−0.139175	+	0.990268i	$0.544445\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−6368.00	−	11029.7i	−0.397963	−	0.689292i
$636$		0			0
$637$	5771.00	−	9995.67i	0.358957	−	0.621731i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	15088.0	−	26133.2i	0.929704	−	1.61029i	0.145888	−	0.989301i	$-0.453396\pi$
$641$	15088.0	−	26133.2i	0.929704	−	1.61029i	0.783816	−	0.620993i	$-0.213271\pi$
$642$		0			0
$643$	−10644.0	−	18435.9i	−0.652812	−	1.13070i	−0.982437	−	0.186592i	$-0.940256\pi$
$643$	−10644.0	−	18435.9i	−0.652812	−	1.13070i	0.329625	−	0.944112i	$-0.393078\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	17024.0			1.03444			0.517220	−	0.855853i	$-0.326967\pi$
$647$	17024.0			1.03444			0.517220	+	0.855853i	$0.326967\pi$
$648$		0			0
$649$	−8192.00			−0.495476
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−1128.00	−	1953.75i	−0.0675989	−	0.117085i	0.830245	−	0.557399i	$-0.188200\pi$
$653$	−1128.00	−	1953.75i	−0.0675989	−	0.117085i	−0.897844	+	0.440314i	$0.854867\pi$
$654$		0			0
$655$	−4096.00	+	7094.48i	−0.244342	+	0.423213i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−11904.0	+	20618.3i	−0.703663	+	1.21878i	0.263509	+	0.964657i	$0.415120\pi$
$659$	−11904.0	+	20618.3i	−0.703663	+	1.21878i	−0.967172	+	0.254123i	$0.918213\pi$
$660$		0			0
$661$	13121.0	+	22726.2i	0.772084	+	1.33729i	0.936419	+	0.350885i	$0.114119\pi$
$661$	13121.0	+	22726.2i	0.772084	+	1.33729i	−0.164334	+	0.986405i	$0.552548\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	26112.0			1.52268
$666$		0			0
$667$	18432.0			1.07000
$668$		0			0
$669$		0			0
$670$		0			0
$671$	14656.0	+	25384.9i	0.843202	+	1.46047i
$672$		0			0
$673$	12295.0	−	21295.6i	0.704216	−	1.21974i	−0.262758	−	0.964862i	$-0.584632\pi$
$673$	12295.0	−	21295.6i	0.704216	−	1.21974i	0.966974	−	0.254876i	$-0.0820347\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	1432.00	−	2480.30i	0.0812943	−	0.140806i	−0.822512	−	0.568748i	$-0.807428\pi$
$677$	1432.00	−	2480.30i	0.0812943	−	0.140806i	0.903806	+	0.427942i	$0.140761\pi$
$678$		0			0
$679$	1236.00	+	2140.81i	0.0698576	+	0.120997i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−7616.00			−0.426674			−0.213337	−	0.976979i	$-0.568433\pi$
$683$	−7616.00			−0.426674			−0.213337	+	0.976979i	$0.568433\pi$
$684$		0			0
$685$	29184.0			1.62783
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−14384.0	−	24913.8i	−0.795336	−	1.37756i
$690$		0			0
$691$	−1084.00	+	1877.54i	−0.0596777	+	0.103365i	−0.894321	−	0.447426i	$-0.852341\pi$
$691$	−1084.00	+	1877.54i	−0.0596777	+	0.103365i	0.834643	+	0.550791i	$0.185674\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	17280.0	−	29929.8i	0.943119	−	1.63353i
$696$		0			0
$697$	4608.00	+	7981.29i	0.250417	+	0.433734i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−18000.0			−0.969830			−0.484915	−	0.874561i	$-0.661149\pi$
$701$	−18000.0			−0.969830			−0.484915	+	0.874561i	$0.661149\pi$
$702$		0			0
$703$	2448.00			0.131334
$704$		0			0
$705$		0			0
$706$		0			0
$707$	2592.00	+	4489.48i	0.137881	+	0.238818i
$708$		0			0
$709$	−1753.00	+	3036.29i	−0.0928566	+	0.160832i	−0.908712	−	0.417424i	$-0.862933\pi$
$709$	−1753.00	+	3036.29i	−0.0928566	+	0.160832i	0.815855	+	0.578256i	$0.196266\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	1280.00	−	2217.03i	0.0672319	−	0.116449i
$714$		0			0
$715$	−29696.0	−	51435.0i	−1.55324	−	2.69029i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	15616.0			0.809984			0.404992	−	0.914320i	$-0.367274\pi$
$719$	15616.0			0.809984			0.404992	+	0.914320i	$0.367274\pi$
$720$		0			0
$721$	816.000			0.0421490
$722$		0			0
$723$		0			0
$724$		0			0
$725$	9432.00	+	16336.7i	0.483166	+	0.836869i
$726$		0			0
$727$	7518.00	−	13021.6i	0.383531	−	0.664296i	−0.608033	−	0.793912i	$-0.708041\pi$
$727$	7518.00	−	13021.6i	0.383531	−	0.664296i	0.991564	+	0.129616i	$0.0413745\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	3200.00	−	5542.56i	0.161910	−	0.280437i
$732$		0			0
$733$	9563.00	+	16563.6i	0.481879	+	0.834639i	0.999784	−	0.0207992i	$-0.00662106\pi$
$733$	9563.00	+	16563.6i	0.481879	+	0.834639i	−0.517904	+	0.855438i	$0.673288\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−31744.0			−1.58657
$738$		0			0
$739$	−17392.0			−0.865731			−0.432865	−	0.901459i	$-0.642497\pi$
$739$	−17392.0			−0.865731			−0.432865	+	0.901459i	$0.642497\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	16192.0	+	28045.4i	0.799498	+	1.38477i	0.919944	+	0.392051i	$0.128234\pi$
$743$	16192.0	+	28045.4i	0.799498	+	1.38477i	−0.120446	+	0.992720i	$0.538432\pi$
$744$		0			0
$745$	5504.00	−	9533.21i	0.270672	−	0.468818i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−2304.00	+	3990.65i	−0.112398	+	0.194680i
$750$		0			0
$751$	13854.0	+	23995.8i	0.673155	+	1.16594i	0.977004	+	0.213219i	$0.0683948\pi$
$751$	13854.0	+	23995.8i	0.673155	+	1.16594i	−0.303849	+	0.952720i	$0.598272\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−13504.0			−0.650942
$756$		0			0
$757$	−37246.0			−1.78828			−0.894141	−	0.447786i	$-0.852213\pi$
$757$	−37246.0			−1.78828			−0.894141	+	0.447786i	$0.852213\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	2096.00	+	3630.38i	0.0998422	+	0.172932i	0.911619	−	0.411036i	$-0.134833\pi$
$761$	2096.00	+	3630.38i	0.0998422	+	0.172932i	−0.811777	+	0.583968i	$0.801500\pi$
$762$		0			0
$763$	−3108.00	+	5383.21i	−0.147467	+	0.255420i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	3712.00	−	6429.37i	0.174749	−	0.302674i
$768$		0			0
$769$	−13441.0	−	23280.5i	−0.630292	−	1.09170i	−0.987492	−	0.157670i	$-0.949602\pi$
$769$	−13441.0	−	23280.5i	−0.630292	−	1.09170i	0.357199	−	0.934028i	$-0.383732\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−17232.0			−0.801801			−0.400900	−	0.916122i	$-0.631303\pi$
$773$	−17232.0			−0.801801			−0.400900	+	0.916122i	$0.631303\pi$
$774$		0			0
$775$	2620.00			0.121436
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−19584.0	−	33920.5i	−0.900731	−	1.56011i
$780$		0			0
$781$	−16384.0	+	28377.9i	−0.750660	+	1.30018i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−944.000	+	1635.06i	−0.0429208	+	0.0743410i
$786$		0			0
$787$	−15908.0	−	27553.5i	−0.720532	−	1.24800i	−0.960787	−	0.277289i	$-0.910564\pi$
$787$	−15908.0	−	27553.5i	−0.720532	−	1.24800i	0.240254	−	0.970710i	$-0.422769\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	11520.0			0.517831
$792$		0			0
$793$	−26564.0			−1.18955
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−4136.00	−	7163.76i	−0.183820	−	0.318386i	0.759358	−	0.650673i	$-0.225513\pi$
$797$	−4136.00	−	7163.76i	−0.183820	−	0.318386i	−0.943178	+	0.332287i	$0.892180\pi$
$798$		0			0
$799$	−6144.00	+	10641.7i	−0.272039	+	0.471185i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	19264.0	−	33366.2i	0.846590	−	1.46634i
$804$		0			0
$805$	−12288.0	−	21283.4i	−0.538006	−	0.931854i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−9184.00			−0.399125			−0.199563	−	0.979885i	$-0.563952\pi$
$809$	−9184.00			−0.399125			−0.199563	+	0.979885i	$0.563952\pi$
$810$		0			0
$811$	−19832.0			−0.858688			−0.429344	−	0.903141i	$-0.641255\pi$
$811$	−19832.0			−0.858688			−0.429344	+	0.903141i	$0.641255\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−28608.0	−	49550.5i	−1.22956	−	2.12967i
$816$		0			0
$817$	−13600.0	+	23555.9i	−0.582379	+	1.00871i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−7608.00	+	13177.4i	−0.323412	+	0.560166i	−0.981190	−	0.193046i	$-0.938163\pi$
$821$	−7608.00	+	13177.4i	−0.323412	+	0.560166i	0.657778	+	0.753212i	$0.271497\pi$
$822$		0			0
$823$	19886.0	+	34443.6i	0.842263	+	1.45884i	0.887977	+	0.459888i	$0.152110\pi$
$823$	19886.0	+	34443.6i	0.842263	+	1.45884i	−0.0457142	+	0.998955i	$0.514556\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−18304.0			−0.769640			−0.384820	−	0.922992i	$-0.625737\pi$
$827$	−18304.0			−0.769640			−0.384820	+	0.922992i	$0.625737\pi$
$828$		0			0
$829$	4906.00			0.205540			0.102770	−	0.994705i	$-0.467229\pi$
$829$	4906.00			0.205540			0.102770	+	0.994705i	$0.467229\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	3184.00	+	5514.85i	0.132436	+	0.229386i
$834$		0			0
$835$	−3072.00	+	5320.86i	−0.127318	+	0.220522i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−7680.00	+	13302.2i	−0.316023	+	0.547367i	−0.979654	−	0.200692i	$-0.935681\pi$
$839$	−7680.00	+	13302.2i	−0.316023	+	0.547367i	0.663632	+	0.748060i	$0.269014\pi$
$840$		0			0
$841$	1826.50	+	3163.59i	0.0748903	+	0.129714i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	18672.0			0.760161
$846$		0			0
$847$	−33180.0			−1.34602
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−1152.00	−	1995.32i	−0.0464043	−	0.0803746i
$852$		0			0
$853$	12401.0	−	21479.2i	0.497775	−	0.862172i	−0.502222	−	0.864739i	$-0.667484\pi$
$853$	12401.0	−	21479.2i	0.497775	−	0.862172i	0.999997	+	0.00256720i	$0.000817166\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−7536.00	+	13052.7i	−0.300379	+	0.520272i	−0.976222	−	0.216774i	$-0.930447\pi$
$857$	−7536.00	+	13052.7i	−0.300379	+	0.520272i	0.675843	+	0.737046i	$0.263780\pi$
$858$		0			0
$859$	−900.000	−	1558.85i	−0.0357481	−	0.0619175i	0.847598	−	0.530639i	$-0.178048\pi$
$859$	−900.000	−	1558.85i	−0.0357481	−	0.0619175i	−0.883346	+	0.468722i	$0.844715\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	7552.00			0.297883			0.148942	−	0.988846i	$-0.452413\pi$
$863$	7552.00			0.297883			0.148942	+	0.988846i	$0.452413\pi$
$864$		0			0
$865$	39168.0			1.53960
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−35456.0	−	61411.6i	−1.38408	−	2.39729i
$870$		0			0
$871$	14384.0	−	24913.8i	0.559567	−	0.969199i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	576.000	−	997.661i	0.0222541	−	0.0385453i
$876$		0			0
$877$	−10419.0	−	18046.2i	−0.401168	−	0.694844i	0.592699	−	0.805424i	$-0.298062\pi$
$877$	−10419.0	−	18046.2i	−0.401168	−	0.694844i	−0.993867	+	0.110580i	$0.964729\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	47744.0			1.82581			0.912904	−	0.408175i	$-0.133835\pi$
$881$	47744.0			1.82581			0.912904	+	0.408175i	$0.133835\pi$
$882$		0			0
$883$	28280.0			1.07780			0.538900	−	0.842370i	$-0.318840\pi$
$883$	28280.0			1.07780			0.538900	+	0.842370i	$0.318840\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−3712.00	−	6429.37i	−0.140515	−	0.243379i	0.787176	−	0.616729i	$-0.211542\pi$
$887$	−3712.00	−	6429.37i	−0.140515	−	0.243379i	−0.927691	+	0.373350i	$0.878209\pi$
$888$		0			0
$889$	4776.00	−	8272.27i	0.180182	−	0.312085i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	26112.0	−	45227.3i	0.978505	−	1.69482i
$894$		0			0
$895$	33792.0	+	58529.5i	1.26206	+	2.18595i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−2880.00			−0.106845
$900$		0			0
$901$	15872.0			0.586873
$902$		0			0
$903$		0			0
$904$		0			0
$905$	4080.00	+	7066.77i	0.149861	+	0.259566i
$906$		0			0
$907$	2956.00	−	5119.94i	0.108217	−	0.187436i	−0.806831	−	0.590782i	$-0.798819\pi$
$907$	2956.00	−	5119.94i	0.108217	−	0.187436i	0.915048	+	0.403345i	$0.132153\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	13120.0	−	22724.5i	0.477151	−	0.826451i	−0.522506	−	0.852636i	$-0.675003\pi$
$911$	13120.0	−	22724.5i	0.477151	−	0.826451i	0.999657	+	0.0261852i	$0.00833597\pi$
$912$		0			0
$913$	−22528.0	−	39019.6i	−0.816613	−	1.41442i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−6144.00			−0.221257
$918$		0			0
$919$	35620.0			1.27856			0.639279	−	0.768975i	$-0.279233\pi$
$919$	35620.0			1.27856			0.639279	+	0.768975i	$0.279233\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−14848.0	−	25717.5i	−0.529499	−	0.917120i
$924$		0			0
$925$	1179.00	−	2042.09i	0.0419084	−	0.0725875i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	1616.00	−	2798.99i	0.0570713	−	0.0988504i	−0.836078	−	0.548610i	$-0.815157\pi$
$929$	1616.00	−	2798.99i	0.0570713	−	0.0988504i	0.893150	+	0.449760i	$0.148490\pi$
$930$		0			0
$931$	−13532.0	−	23438.1i	−0.476362	−	0.825084i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	32768.0			1.14613
$936$		0			0
$937$	−11478.0			−0.400181			−0.200091	−	0.979777i	$-0.564124\pi$
$937$	−11478.0			−0.400181			−0.200091	+	0.979777i	$0.564124\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	19992.0	+	34627.2i	0.692583	+	1.19959i	0.970989	+	0.239125i	$0.0768607\pi$
$941$	19992.0	+	34627.2i	0.692583	+	1.19959i	−0.278406	+	0.960464i	$0.589806\pi$
$942$		0			0
$943$	−18432.0	+	31925.2i	−0.636510	+	1.10247i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−12096.0	+	20950.9i	−0.415066	+	0.718915i	−0.995435	−	0.0954383i	$-0.969575\pi$
$947$	−12096.0	+	20950.9i	−0.415066	+	0.718915i	0.580370	+	0.814353i	$0.302908\pi$
$948$		0			0
$949$	17458.0	+	30238.1i	0.597166	+	1.03432i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−39456.0			−1.34114			−0.670569	−	0.741847i	$-0.733950\pi$
$953$	−39456.0			−1.34114			−0.670569	+	0.741847i	$0.733950\pi$
$954$		0			0
$955$	−6144.00			−0.208183
$956$		0			0
$957$		0			0
$958$		0			0
$959$	10944.0	+	18955.6i	0.368509	+	0.638276i
$960$		0			0
$961$	14695.5	−	25453.4i	0.493287	−	0.854397i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	27632.0	−	47860.0i	0.921767	−	1.59655i
$966$		0			0
$967$	20834.0	+	36085.5i	0.692840	+	1.20003i	0.970903	+	0.239471i	$0.0769741\pi$
$967$	20834.0	+	36085.5i	0.692840	+	1.20003i	−0.278063	+	0.960563i	$0.589693\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−51648.0			−1.70697			−0.853483	−	0.521121i	$-0.825514\pi$
$971$	−51648.0			−1.70697			−0.853483	+	0.521121i	$0.825514\pi$
$972$		0			0
$973$	25920.0			0.854015
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−27888.0	−	48303.4i	−0.913220	−	1.58174i	−0.809486	−	0.587139i	$-0.800254\pi$
$977$	−27888.0	−	48303.4i	−0.913220	−	1.58174i	−0.103734	−	0.994605i	$-0.533079\pi$
$978$		0			0
$979$	30720.0	−	53208.6i	1.00288	−	1.73703i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	18048.0	−	31260.1i	0.585597	−	1.01428i	−0.409204	−	0.912443i	$-0.634193\pi$
$983$	18048.0	−	31260.1i	0.585597	−	1.01428i	0.994801	−	0.101841i	$-0.0324732\pi$
$984$		0			0
$985$	25728.0	+	44562.2i	0.832246	+	1.44149i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	25600.0			0.823087
$990$		0			0
$991$	42532.0			1.36334			0.681672	−	0.731658i	$-0.261253\pi$
$991$	42532.0			1.36334			0.681672	+	0.731658i	$0.261253\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−13664.0	−	23666.7i	−0.435355	−	0.754056i
$996$		0			0
$997$	−14903.0	+	25812.8i	−0.473403	+	0.819958i	−0.999536	−	0.0304440i	$-0.990308\pi$
$997$	−14903.0	+	25812.8i	−0.473403	+	0.819958i	0.526134	+	0.850402i	$0.323641\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	648.4.i.a.217.1		2
3.2	odd	2		648.4.i.l.217.1		2
9.2	odd	6		72.4.a.a.1.1	✓	1
9.4	even	3	inner	648.4.i.a.433.1		2
9.5	odd	6		648.4.i.l.433.1		2
9.7	even	3		72.4.a.d.1.1	yes	1
36.7	odd	6		144.4.a.f.1.1		1
36.11	even	6		144.4.a.a.1.1		1
45.2	even	12		1800.4.f.b.649.1		2
45.7	odd	12		1800.4.f.x.649.1		2
45.29	odd	6		1800.4.a.z.1.1		1
45.34	even	6		1800.4.a.ba.1.1		1
45.38	even	12		1800.4.f.b.649.2		2
45.43	odd	12		1800.4.f.x.649.2		2
72.11	even	6		576.4.a.x.1.1		1
72.29	odd	6		576.4.a.w.1.1		1
72.43	odd	6		576.4.a.d.1.1		1
72.61	even	6		576.4.a.c.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.4.a.a.1.1	✓	1	9.2	odd	6
72.4.a.d.1.1	yes	1	9.7	even	3
144.4.a.a.1.1		1	36.11	even	6
144.4.a.f.1.1		1	36.7	odd	6
576.4.a.c.1.1		1	72.61	even	6
576.4.a.d.1.1		1	72.43	odd	6
576.4.a.w.1.1		1	72.29	odd	6
576.4.a.x.1.1		1	72.11	even	6
648.4.i.a.217.1		2	1.1	even	1	trivial
648.4.i.a.433.1		2	9.4	even	3	inner
648.4.i.l.217.1		2	3.2	odd	2
648.4.i.l.433.1		2	9.5	odd	6
1800.4.a.z.1.1		1	45.29	odd	6
1800.4.a.ba.1.1		1	45.34	even	6
1800.4.f.b.649.1		2	45.2	even	12
1800.4.f.b.649.2		2	45.38	even	12
1800.4.f.x.649.1		2	45.7	odd	12
1800.4.f.x.649.2		2	45.43	odd	12

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:	\( N \)	\(=\)	\( 648 = 2^{3} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	648.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-8.00000 - 13.8564i) q^{5} +(6.00000 - 10.3923i) q^{7} +O(q^{10})\)	\(q+(-8.00000 - 13.8564i) q^{5} +(6.00000 - 10.3923i) q^{7} +(-32.0000 + 55.4256i) q^{11} +(-29.0000 - 50.2295i) q^{13} +32.0000 q^{17} -136.000 q^{19} +(64.0000 + 110.851i) q^{23} +(-65.5000 + 113.449i) q^{25} +(72.0000 - 124.708i) q^{29} +(-10.0000 - 17.3205i) q^{31} -192.000 q^{35} -18.0000 q^{37} +(144.000 + 249.415i) q^{41} +(100.000 - 173.205i) q^{43} +(-192.000 + 332.554i) q^{47} +(99.5000 + 172.339i) q^{49} +496.000 q^{53} +1024.00 q^{55} +(64.0000 + 110.851i) q^{59} +(229.000 - 396.640i) q^{61} +(-464.000 + 803.672i) q^{65} +(248.000 + 429.549i) q^{67} +512.000 q^{71} -602.000 q^{73} +(384.000 + 665.108i) q^{77} +(-554.000 + 959.556i) q^{79} +(-352.000 + 609.682i) q^{83} +(-256.000 - 443.405i) q^{85} -960.000 q^{89} -696.000 q^{91} +(1088.00 + 1884.47i) q^{95} +(-103.000 + 178.401i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 16 q^{5} + 12 q^{7}+O(q^{10}) \) 2 * q - 16 * q^5 + 12 * q^7	\( 2 q - 16 q^{5} + 12 q^{7} - 64 q^{11} - 58 q^{13} + 64 q^{17} - 272 q^{19} + 128 q^{23} - 131 q^{25} + 144 q^{29} - 20 q^{31} - 384 q^{35} - 36 q^{37} + 288 q^{41} + 200 q^{43} - 384 q^{47} + 199 q^{49} + 992 q^{53} + 2048 q^{55} + 128 q^{59} + 458 q^{61} - 928 q^{65} + 496 q^{67} + 1024 q^{71} - 1204 q^{73} + 768 q^{77} - 1108 q^{79} - 704 q^{83} - 512 q^{85} - 1920 q^{89} - 1392 q^{91} + 2176 q^{95} - 206 q^{97}+O(q^{100}) \) 2 * q - 16 * q^5 + 12 * q^7 - 64 * q^11 - 58 * q^13 + 64 * q^17 - 272 * q^19 + 128 * q^23 - 131 * q^25 + 144 * q^29 - 20 * q^31 - 384 * q^35 - 36 * q^37 + 288 * q^41 + 200 * q^43 - 384 * q^47 + 199 * q^49 + 992 * q^53 + 2048 * q^55 + 128 * q^59 + 458 * q^61 - 928 * q^65 + 496 * q^67 + 1024 * q^71 - 1204 * q^73 + 768 * q^77 - 1108 * q^79 - 704 * q^83 - 512 * q^85 - 1920 * q^89 - 1392 * q^91 + 2176 * q^95 - 206 * q^97

Introduction

L-functions

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