LMFDB - Embedded newform 2394.2.e.c.1063.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2394,2,Mod(1063,2394)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2394, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("2394.1063");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2394 = 2 \cdot 3^{2} \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2394.e (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:	$19.1161862439$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 44x^{14} + 708x^{12} + 5378x^{10} + 20592x^{8} + 38856x^{6} + 33265x^{4} + 10216x^{2} + 900 $ x^16 + 44x^14 + 708x^12 + 5378x^10 + 20592x^8 + 38856x^6 + 33265x^4 + 10216*x^2 + 900
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 266)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1063.5
Root			$0.384810i$ of defining polynomial
Character	$\chi$	$=$	2394.1063
Dual form			2394.2.e.c.1063.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -1.00000 q^{4} +1.03210i q^{5} +(1.71160 - 2.01753i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q-1.00000i q^{2} -1.00000 q^{4} +1.03210i q^{5} +(1.71160 - 2.01753i) q^{7} +1.00000i q^{8} +1.03210 q^{10} -4.93476 q^{11} +4.53617 q^{13} +(-2.01753 - 1.71160i) q^{14} +1.00000 q^{16} +4.03506i q^{17} +(-3.25351 + 2.90080i) q^{19} -1.03210i q^{20} +4.93476i q^{22} +1.42320 q^{23} +3.93476 q^{25} -4.53617i q^{26} +(-1.71160 + 2.01753i) q^{28} +7.78723i q^{29} +2.76962 q^{31} -1.00000i q^{32} +4.03506 q^{34} +(2.08230 + 1.76655i) q^{35} -0.659104i q^{37} +(2.90080 + 3.25351i) q^{38} -1.03210 q^{40} +3.30062 q^{41} -5.50550 q^{43} +4.93476 q^{44} -1.42320i q^{46} -11.9269i q^{47} +(-1.14086 - 6.90640i) q^{49} -3.93476i q^{50} -4.53617 q^{52} +12.3580i q^{53} -5.09318i q^{55} +(2.01753 + 1.71160i) q^{56} +7.78723 q^{58} +5.06717 q^{59} -1.94484i q^{61} -2.76962i q^{62} -1.00000 q^{64} +4.68179i q^{65} +8.44633i q^{67} -4.03506i q^{68} +(1.76655 - 2.08230i) q^{70} +2.08837i q^{71} +13.8128i q^{73} -0.659104 q^{74} +(3.25351 - 2.90080i) q^{76} +(-8.44633 + 9.95604i) q^{77} +5.34090i q^{79} +1.03210i q^{80} -3.30062i q^{82} -4.33272i q^{83} -4.16460 q^{85} +5.50550i q^{86} -4.93476i q^{88} +16.0553 q^{89} +(7.76409 - 9.15186i) q^{91} -1.42320 q^{92} -11.9269 q^{94} +(-2.99393 - 3.35796i) q^{95} +13.2857 q^{97} +(-6.90640 + 1.14086i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{4} + 6 q^{7}+O(q^{10}) $ 16 * q - 16 * q^4 + 6 * q^7	$ 16 q - 16 q^{4} + 6 q^{7} + 12 q^{11} + 16 q^{16} - 20 q^{23} - 28 q^{25} - 6 q^{28} - 8 q^{35} - 4 q^{43} - 12 q^{44} + 10 q^{49} - 16 q^{58} - 16 q^{64} - 12 q^{74} + 4 q^{77} + 16 q^{85} + 20 q^{92} - 12 q^{95}+O(q^{100}) $ 16 * q - 16 * q^4 + 6 * q^7 + 12 * q^11 + 16 * q^16 - 20 * q^23 - 28 * q^25 - 6 * q^28 - 8 * q^35 - 4 * q^43 - 12 * q^44 + 10 * q^49 - 16 * q^58 - 16 * q^64 - 12 * q^74 + 4 * q^77 + 16 * q^85 + 20 * q^92 - 12 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2394\mathbb{Z}\right)^\times$.

$n$	$533$	$1009$	$1711$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$			1.03210i			0.461571i	0.973005	+	0.230785i	$0.0741295\pi$
$5$			1.03210i			0.461571i	−0.973005	+	0.230785i	$0.925871\pi$
$6$		0			0
$7$	1.71160	−	2.01753i	0.646923	−	0.762555i
$7$	1.71160	−	2.01753i	0.646923	−	0.762555i
$8$			1.00000i			0.353553i
$9$		0			0
$10$	1.03210			0.326380
$11$	−4.93476			−1.48789			−0.743944	−	0.668242i	$-0.767047\pi$
$11$	−4.93476			−1.48789			−0.743944	+	0.668242i	$0.767047\pi$
$12$		0			0
$13$	4.53617			1.25811			0.629053	−	0.777362i	$-0.283443\pi$
$13$	4.53617			1.25811			0.629053	+	0.777362i	$0.283443\pi$
$14$	−2.01753	−	1.71160i	−0.539208	−	0.457444i
$15$		0			0
$16$	1.00000			0.250000
$17$			4.03506i			0.978646i	0.872103	+	0.489323i	$0.162756\pi$
$17$			4.03506i			0.978646i	−0.872103	+	0.489323i	$0.837244\pi$
$18$		0			0
$19$	−3.25351	+	2.90080i	−0.746407	+	0.665490i
$19$	−3.25351	+	2.90080i	−0.746407	+	0.665490i
$20$		−	1.03210i		−	0.230785i
$21$		0			0
$22$			4.93476i			1.05210i
$23$	1.42320			0.296757			0.148378	−	0.988931i	$-0.452595\pi$
$23$	1.42320			0.296757			0.148378	+	0.988931i	$0.452595\pi$
$24$		0			0
$25$	3.93476			0.786953
$26$		−	4.53617i		−	0.889615i
$27$		0			0
$28$	−1.71160	+	2.01753i	−0.323462	+	0.381278i
$29$			7.78723i			1.44605i	0.690821	+	0.723026i	$0.257249\pi$
$29$			7.78723i			1.44605i	−0.690821	+	0.723026i	$0.742751\pi$
$30$		0			0
$31$	2.76962			0.497439			0.248719	−	0.968576i	$-0.419990\pi$
$31$	2.76962			0.497439			0.248719	+	0.968576i	$0.419990\pi$
$32$		−	1.00000i		−	0.176777i
$33$		0			0
$34$	4.03506			0.692008
$35$	2.08230	+	1.76655i	0.351973	+	0.298601i
$36$		0			0
$37$		−	0.659104i		−	0.108356i	−0.998531	−	0.0541780i	$-0.982746\pi$
$37$		−	0.659104i		−	0.108356i	0.998531	−	0.0541780i	$-0.0172539\pi$
$38$	2.90080	+	3.25351i	0.470573	+	0.527789i
$39$		0			0
$40$	−1.03210			−0.163190
$41$	3.30062			0.515470			0.257735	−	0.966216i	$-0.417024\pi$
$41$	3.30062			0.515470			0.257735	+	0.966216i	$0.417024\pi$
$42$		0			0
$43$	−5.50550			−0.839580			−0.419790	−	0.907621i	$-0.637896\pi$
$43$	−5.50550			−0.839580			−0.419790	+	0.907621i	$0.637896\pi$
$44$	4.93476			0.743944
$45$		0			0
$46$		−	1.42320i		−	0.209839i
$47$		−	11.9269i		−	1.73972i	−0.493302	−	0.869858i	$-0.664210\pi$
$47$		−	11.9269i		−	1.73972i	0.493302	−	0.869858i	$-0.335790\pi$
$48$		0			0
$49$	−1.14086	−	6.90640i	−0.162981	−	0.986629i
$50$		−	3.93476i		−	0.556460i
$51$		0			0
$52$	−4.53617			−0.629053
$53$			12.3580i			1.69750i	0.528797	+	0.848748i	$0.322643\pi$
$53$			12.3580i			1.69750i	−0.528797	+	0.848748i	$0.677357\pi$
$54$		0			0
$55$		−	5.09318i		−	0.686765i
$56$	2.01753	+	1.71160i	0.269604	+	0.228722i
$57$		0			0
$58$	7.78723			1.02251
$59$	5.06717			0.659689			0.329844	−	0.944035i	$-0.393004\pi$
$59$	5.06717			0.659689			0.329844	+	0.944035i	$0.393004\pi$
$60$		0			0
$61$		−	1.94484i		−	0.249011i	−0.992219	−	0.124505i	$-0.960266\pi$
$61$		−	1.94484i		−	0.249011i	0.992219	−	0.124505i	$-0.0397344\pi$
$62$		−	2.76962i		−	0.351742i
$63$		0			0
$64$	−1.00000			−0.125000
$65$			4.68179i			0.580705i
$66$		0			0
$67$			8.44633i			1.03188i	0.856624	+	0.515942i	$0.172558\pi$
$67$			8.44633i			1.03188i	−0.856624	+	0.515942i	$0.827442\pi$
$68$		−	4.03506i		−	0.489323i
$69$		0			0
$70$	1.76655	−	2.08230i	0.211143	−	0.248882i
$71$			2.08837i			0.247844i	0.992292	+	0.123922i	$0.0395473\pi$
$71$			2.08837i			0.247844i	−0.992292	+	0.123922i	$0.960453\pi$
$72$		0			0
$73$			13.8128i			1.61667i	0.588725	+	0.808334i	$0.299630\pi$
$73$			13.8128i			1.61667i	−0.588725	+	0.808334i	$0.700370\pi$
$74$	−0.659104			−0.0766193
$75$		0			0
$76$	3.25351	−	2.90080i	0.373203	−	0.332745i
$77$	−8.44633	+	9.95604i	−0.962549	+	1.13460i
$78$		0			0
$79$			5.34090i			0.600898i	0.953798	+	0.300449i	$0.0971365\pi$
$79$			5.34090i			0.600898i	−0.953798	+	0.300449i	$0.902864\pi$
$80$			1.03210i			0.115393i
$81$		0			0
$82$		−	3.30062i		−	0.364493i
$83$		−	4.33272i		−	0.475578i	−0.971317	−	0.237789i	$-0.923577\pi$
$83$		−	4.33272i		−	0.475578i	0.971317	−	0.237789i	$-0.0764227\pi$
$84$		0			0
$85$	−4.16460			−0.451714
$86$			5.50550i			0.593673i
$87$		0			0
$88$		−	4.93476i		−	0.526048i
$89$	16.0553			1.70186			0.850930	−	0.525280i	$-0.176039\pi$
$89$	16.0553			1.70186			0.850930	+	0.525280i	$0.176039\pi$
$90$		0			0
$91$	7.76409	−	9.15186i	0.813898	−	0.959375i
$92$	−1.42320			−0.148378
$93$		0			0
$94$	−11.9269			−1.23017
$95$	−2.99393	−	3.35796i	−0.307171	−	0.344519i
$96$		0			0
$97$	13.2857			1.34896			0.674479	−	0.738294i	$-0.264368\pi$
$97$	13.2857			1.34896			0.674479	+	0.738294i	$0.264368\pi$
$98$	−6.90640	+	1.14086i	−0.697652	+	0.115245i
$99$		0			0
$100$	−3.93476			−0.393476
$101$		−	2.26852i		−	0.225726i	−0.993611	−	0.112863i	$-0.963998\pi$
$101$		−	2.26852i		−	0.225726i	0.993611	−	0.112863i	$-0.0360021\pi$
$102$		0			0
$103$	15.6736			1.54436			0.772182	−	0.635402i	$-0.219166\pi$
$103$	15.6736			1.54436			0.772182	+	0.635402i	$0.219166\pi$
$104$			4.53617i			0.444808i
$105$		0			0
$106$	12.3580			1.20031
$107$			5.58780i			0.540193i	0.962833	+	0.270096i	$0.0870556\pi$
$107$			5.58780i			0.540193i	−0.962833	+	0.270096i	$0.912944\pi$
$108$		0			0
$109$			12.3580i			1.18368i	0.806056	+	0.591839i	$0.201598\pi$
$109$			12.3580i			1.18368i	−0.806056	+	0.591839i	$0.798402\pi$
$110$	−5.09318			−0.485616
$111$		0			0
$112$	1.71160	−	2.01753i	0.161731	−	0.190639i
$113$		−	20.0341i		−	1.88465i	−0.334696	−	0.942326i	$-0.608634\pi$
$113$		−	20.0341i		−	1.88465i	0.334696	−	0.942326i	$-0.391366\pi$
$114$		0			0
$115$			1.46888i			0.136974i
$116$		−	7.78723i		−	0.723026i
$117$		0			0
$118$		−	5.06717i		−	0.466470i
$119$	8.14086	+	6.90640i	0.746272	+	0.633109i
$120$		0			0
$121$	13.3519			1.21381
$122$	−1.94484			−0.176077
$123$		0			0
$124$	−2.76962			−0.248719
$125$			9.22160i			0.824805i
$126$		0			0
$127$			19.4861i			1.72911i	0.502538	+	0.864555i	$0.332400\pi$
$127$			19.4861i			1.72911i	−0.502538	+	0.864555i	$0.667600\pi$
$128$			1.00000i			0.0883883i
$129$		0			0
$130$	4.68179			0.410620
$131$			2.26852i			0.198201i	0.995077	+	0.0991006i	$0.0315966\pi$
$131$			2.26852i			0.198201i	−0.995077	+	0.0991006i	$0.968403\pi$
$132$		0			0
$133$	0.283760	+	11.5291i	0.0246051	+	0.999697i
$134$	8.44633			0.729652
$135$		0			0
$136$	−4.03506			−0.346004
$137$	11.9518			1.02111			0.510557	−	0.859844i	$-0.329439\pi$
$137$	11.9518			1.02111			0.510557	+	0.859844i	$0.329439\pi$
$138$		0			0
$139$		−	16.1747i		−	1.37192i	−0.727640	−	0.685959i	$-0.759383\pi$
$139$		−	16.1747i		−	1.37192i	0.727640	−	0.685959i	$-0.240617\pi$
$140$	−2.08230	−	1.76655i	−0.175986	−	0.149300i
$141$		0			0
$142$	2.08837			0.175252
$143$	−22.3849			−1.87192
$144$		0			0
$145$	−8.03722			−0.667455
$146$	13.8128			1.14316
$147$		0			0
$148$			0.659104i			0.0541780i
$149$	−1.83540			−0.150362			−0.0751809	−	0.997170i	$-0.523953\pi$
$149$	−1.83540			−0.150362			−0.0751809	+	0.997170i	$0.523953\pi$
$150$		0			0
$151$			3.14147i			0.255649i	0.991797	+	0.127824i	$0.0407994\pi$
$151$			3.14147i			0.255649i	−0.991797	+	0.127824i	$0.959201\pi$
$152$	−2.90080	−	3.25351i	−0.235286	−	0.263895i
$153$		0			0
$154$	9.95604	+	8.44633i	0.802280	+	0.680625i
$155$			2.85853i			0.229603i
$156$		0			0
$157$		−	6.72061i		−	0.536363i	−0.963368	−	0.268181i	$-0.913577\pi$
$157$		−	6.72061i		−	0.536363i	0.963368	−	0.268181i	$-0.0864227\pi$
$158$	5.34090			0.424899
$159$		0			0
$160$	1.03210			0.0815949
$161$	2.43594	−	2.87134i	0.191979	−	0.226293i
$162$		0			0
$163$	−3.06524			−0.240088			−0.120044	−	0.992769i	$-0.538304\pi$
$163$	−3.06524			−0.240088			−0.120044	+	0.992769i	$0.538304\pi$
$164$	−3.30062			−0.257735
$165$		0			0
$166$	−4.33272			−0.336285
$167$	−6.19262			−0.479199			−0.239600	−	0.970872i	$-0.577016\pi$
$167$	−6.19262			−0.479199			−0.239600	+	0.970872i	$0.577016\pi$
$168$		0			0
$169$	7.57680			0.582831
$170$			4.16460i			0.319410i
$171$		0			0
$172$	5.50550			0.419790
$173$	9.93002			0.754965			0.377483	−	0.926017i	$-0.376790\pi$
$173$	9.93002			0.754965			0.377483	+	0.926017i	$0.376790\pi$
$174$		0			0
$175$	6.73473	−	7.93851i	0.509098	−	0.600095i
$176$	−4.93476			−0.371972
$177$		0			0
$178$		−	16.0553i		−	1.20340i
$179$		−	1.31821i		−	0.0985276i	−0.998786	−	0.0492638i	$-0.984313\pi$
$179$		−	1.31821i		−	0.0985276i	0.998786	−	0.0492638i	$-0.0156875\pi$
$180$		0			0
$181$	9.27664			0.689527			0.344764	−	0.938689i	$-0.387959\pi$
$181$	9.27664			0.689527			0.344764	+	0.938689i	$0.387959\pi$
$182$	−9.15186	−	7.76409i	−0.678381	−	0.575513i
$183$		0			0
$184$			1.42320i			0.104919i
$185$	0.680264			0.0500140
$186$		0			0
$187$		−	19.9121i		−	1.45612i
$188$			11.9269i			0.869858i
$189$		0			0
$190$	−3.35796	+	2.99393i	−0.243612	+	0.217202i
$191$	20.1391			1.45722			0.728608	−	0.684931i	$-0.240168\pi$
$191$	20.1391			1.45722			0.728608	+	0.684931i	$0.240168\pi$
$192$		0			0
$193$		−	4.45967i		−	0.321014i	−0.987035	−	0.160507i	$-0.948687\pi$
$193$		−	4.45967i		−	0.321014i	0.987035	−	0.160507i	$-0.0513130\pi$
$194$		−	13.2857i		−	0.953857i
$195$		0			0
$196$	1.14086	+	6.90640i	0.0814904	+	0.493315i
$197$	−8.84639			−0.630279			−0.315140	−	0.949045i	$-0.602051\pi$
$197$	−8.84639			−0.630279			−0.315140	+	0.949045i	$0.602051\pi$
$198$		0			0
$199$			15.4058i			1.09209i	0.837756	+	0.546044i	$0.183867\pi$
$199$			15.4058i			1.09209i	−0.837756	+	0.546044i	$0.816133\pi$
$200$			3.93476i			0.278230i
$201$		0			0
$202$	−2.26852			−0.159612
$203$	15.7110	+	13.3286i	1.10269	+	0.935484i
$204$		0			0
$205$			3.40658i			0.237926i
$206$		−	15.6736i		−	1.09203i
$207$		0			0
$208$	4.53617			0.314527
$209$	16.0553	−	14.3148i	1.11057	−	0.990174i
$210$		0			0
$211$		−	16.2696i		−	1.12004i	−0.828478	−	0.560022i	$-0.810793\pi$
$211$		−	16.2696i		−	1.12004i	0.828478	−	0.560022i	$-0.189207\pi$
$212$		−	12.3580i		−	0.848748i
$213$		0			0
$214$	5.58780			0.381974
$215$		−	5.68224i		−	0.387526i
$216$		0			0
$217$	4.74048	−	5.58780i	0.321805	−	0.379324i
$218$	12.3580			0.836987
$219$		0			0
$220$			5.09318i			0.343382i
$221$			18.3037i			1.23124i
$222$		0			0
$223$	−21.3229			−1.42789			−0.713944	−	0.700203i	$-0.753093\pi$
$223$	−21.3229			−1.42789			−0.713944	+	0.700203i	$0.753093\pi$
$224$	−2.01753	−	1.71160i	−0.134802	−	0.114361i
$225$		0			0
$226$	−20.0341			−1.33265
$227$	−9.24135			−0.613370			−0.306685	−	0.951811i	$-0.599220\pi$
$227$	−9.24135			−0.613370			−0.306685	+	0.951811i	$0.599220\pi$
$228$		0			0
$229$		−	2.50099i		−	0.165270i	−0.996580	−	0.0826350i	$-0.973666\pi$
$229$		−	2.50099i		−	0.165270i	0.996580	−	0.0826350i	$-0.0263336\pi$
$230$	1.46888			0.0968554
$231$		0			0
$232$	−7.78723			−0.511256
$233$	−15.0994			−0.989192			−0.494596	−	0.869123i	$-0.664684\pi$
$233$	−15.0994			−0.989192			−0.494596	+	0.869123i	$0.664684\pi$
$234$		0			0
$235$	12.3098			0.803002
$236$	−5.06717			−0.329844
$237$		0			0
$238$	6.90640	−	8.14086i	0.447676	−	0.527694i
$239$	11.2927			0.730465			0.365233	−	0.930916i	$-0.380989\pi$
$239$	11.2927			0.730465			0.365233	+	0.930916i	$0.380989\pi$
$240$		0			0
$241$	−11.4288			−0.736194			−0.368097	−	0.929787i	$-0.619991\pi$
$241$	−11.4288			−0.736194			−0.368097	+	0.929787i	$0.619991\pi$
$242$		−	13.3519i		−	0.858292i
$243$		0			0
$244$			1.94484i			0.124505i
$245$	7.12812	−	1.17749i	0.455399	−	0.0752271i
$246$		0			0
$247$	−14.7585	+	13.1585i	−0.939059	+	0.837257i
$248$			2.76962i			0.175871i
$249$		0			0
$250$	9.22160			0.583225
$251$			7.86581i			0.496486i	0.968698	+	0.248243i	$0.0798531\pi$
$251$			7.86581i			0.496486i	−0.968698	+	0.248243i	$0.920147\pi$
$252$		0			0
$253$	−7.02313			−0.441541
$254$	19.4861			1.22267
$255$		0			0
$256$	1.00000			0.0625000
$257$	−13.4350			−0.838049			−0.419025	−	0.907975i	$-0.637628\pi$
$257$	−13.4350			−0.838049			−0.419025	+	0.907975i	$0.637628\pi$
$258$		0			0
$259$	−1.32976	−	1.12812i	−0.0826275	−	0.0700981i
$260$		−	4.68179i		−	0.290352i
$261$		0			0
$262$	2.26852			0.140149
$263$	0.517191			0.0318913			0.0159457	−	0.999873i	$-0.494924\pi$
$263$	0.517191			0.0318913			0.0159457	+	0.999873i	$0.494924\pi$
$264$		0			0
$265$	−12.7547			−0.783514
$266$	11.5291	−	0.283760i	0.706893	−	0.0173984i
$267$		0			0
$268$		−	8.44633i		−	0.515942i
$269$	20.3551			1.24107			0.620537	−	0.784177i	$-0.286915\pi$
$269$	20.3551			1.24107			0.620537	+	0.784177i	$0.286915\pi$
$270$		0			0
$271$		−	2.61195i		−	0.158665i	−0.996848	−	0.0793323i	$-0.974721\pi$
$271$		−	2.61195i		−	0.158665i	0.996848	−	0.0793323i	$-0.0252788\pi$
$272$			4.03506i			0.244662i
$273$		0			0
$274$		−	11.9518i		−	0.722036i
$275$	−19.4171			−1.17090
$276$		0			0
$277$	−10.5513			−0.633967			−0.316984	−	0.948431i	$-0.602670\pi$
$277$	−10.5513			−0.633967			−0.316984	+	0.948431i	$0.602670\pi$
$278$	−16.1747			−0.970093
$279$		0			0
$280$	−1.76655	+	2.08230i	−0.105571	+	0.124441i
$281$		0			0		1.00000			$0$
$281$		0			0		−1.00000			$\pi$
$282$		0			0
$283$			26.1223i			1.55281i	0.630234	+	0.776405i	$0.282959\pi$
$283$			26.1223i			1.55281i	−0.630234	+	0.776405i	$0.717041\pi$
$284$		−	2.08837i		−	0.123922i
$285$		0			0
$286$			22.3849i			1.32365i
$287$	5.64933	−	6.65910i	0.333470	−	0.393075i
$288$		0			0
$289$	0.718270			0.0422512
$290$			8.03722i			0.471962i
$291$		0			0
$292$		−	13.8128i		−	0.808334i
$293$	−5.70826			−0.333480			−0.166740	−	0.986001i	$-0.553324\pi$
$293$	−5.70826			−0.333480			−0.166740	+	0.986001i	$0.553324\pi$
$294$		0			0
$295$			5.22984i			0.304493i
$296$	0.659104			0.0383097
$297$		0			0
$298$			1.83540i			0.106322i
$299$	6.45585			0.373352
$300$		0			0
$301$	−9.42320	+	11.1075i	−0.543144	+	0.640226i
$302$	3.14147			0.180771
$303$		0			0
$304$	−3.25351	+	2.90080i	−0.186602	+	0.166373i
$305$	2.00727			0.114936
$306$		0			0
$307$	−10.4610			−0.597042			−0.298521	−	0.954403i	$-0.596493\pi$
$307$	−10.4610			−0.597042			−0.298521	+	0.954403i	$0.596493\pi$
$308$	8.44633	−	9.95604i	0.481274	−	0.567298i
$309$		0			0
$310$	2.85853			0.162354
$311$			10.3647i			0.587726i	0.955848	+	0.293863i	$0.0949409\pi$
$311$			10.3647i			0.587726i	−0.955848	+	0.293863i	$0.905059\pi$
$312$		0			0
$313$		−	19.8187i		−	1.12022i	−0.828418	−	0.560110i	$-0.810759\pi$
$313$		−	19.8187i		−	1.12022i	0.828418	−	0.560110i	$-0.189241\pi$
$314$	−6.72061			−0.379266
$315$		0			0
$316$		−	5.34090i		−	0.300449i
$317$		−	13.0739i		−	0.734302i	−0.930161	−	0.367151i	$-0.880333\pi$
$317$		−	13.0739i		−	0.734302i	0.930161	−	0.367151i	$-0.119667\pi$
$318$		0			0
$319$		−	38.4281i		−	2.15156i
$320$		−	1.03210i		−	0.0576963i
$321$		0			0
$322$	−2.87134	−	2.43594i	−0.160014	−	0.135750i
$323$	−11.7049	−	13.1281i	−0.651279	−	0.730468i
$324$		0			0
$325$	17.8487			0.990070
$326$			3.06524i			0.169768i
$327$		0			0
$328$			3.30062i			0.182246i
$329$	−24.0629	−	20.4140i	−1.32663	−	1.12546i
$330$		0			0
$331$		−	6.41220i		−	0.352447i	−0.984350	−	0.176223i	$-0.943612\pi$
$331$		−	6.41220i		−	0.352447i	0.984350	−	0.176223i	$-0.0563881\pi$
$332$			4.33272i			0.237789i
$333$		0			0
$334$			6.19262i			0.338845i
$335$	−8.71748			−0.476287
$336$		0			0
$337$		−	8.85853i		−	0.482555i	−0.970456	−	0.241278i	$-0.922434\pi$
$337$		−	8.85853i		−	0.482555i	0.970456	−	0.241278i	$-0.0775664\pi$
$338$		−	7.57680i		−	0.412124i
$339$		0			0
$340$	4.16460			0.225857
$341$	−13.6674			−0.740132
$342$		0			0
$343$	−15.8866	−	9.51926i	−0.857795	−	0.513992i
$344$		−	5.50550i		−	0.296836i
$345$		0			0
$346$		−	9.93002i		−	0.533841i
$347$	−26.0220			−1.39693			−0.698467	−	0.715643i	$-0.746134\pi$
$347$	−26.0220			−1.39693			−0.698467	+	0.715643i	$0.746134\pi$
$348$		0			0
$349$			34.0225i			1.82119i	0.413305	+	0.910593i	$0.364374\pi$
$349$			34.0225i			1.82119i	−0.413305	+	0.910593i	$0.635626\pi$
$350$	−7.93851	−	6.73473i	−0.424331	−	0.359987i
$351$		0			0
$352$			4.93476i			0.263024i
$353$			3.43974i			0.183079i	0.995801	+	0.0915395i	$0.0291788\pi$
$353$			3.43974i			0.183079i	−0.995801	+	0.0915395i	$0.970821\pi$
$354$		0			0
$355$	−2.15541			−0.114398
$356$	−16.0553			−0.850930
$357$		0			0
$358$	−1.31821			−0.0696695
$359$	7.71827			0.407355			0.203677	−	0.979038i	$-0.434711\pi$
$359$	7.71827			0.407355			0.203677	+	0.979038i	$0.434711\pi$
$360$		0			0
$361$	2.17067	−	18.8756i	0.114246	−	0.993453i
$362$		−	9.27664i		−	0.487570i
$363$		0			0
$364$	−7.76409	+	9.15186i	−0.406949	+	0.479688i
$365$	−14.2562			−0.746206
$366$		0			0
$367$			19.8792i			1.03768i	0.854870	+	0.518842i	$0.173637\pi$
$367$			19.8792i			1.03768i	−0.854870	+	0.518842i	$0.826363\pi$
$368$	1.42320			0.0741892
$369$		0			0
$370$		−	0.680264i		−	0.0353652i
$371$	24.9326	+	21.1519i	1.29443	+	1.09815i
$372$		0			0
$373$			7.78723i			0.403207i	0.979467	+	0.201604i	$0.0646153\pi$
$373$			7.78723i			0.403207i	−0.979467	+	0.201604i	$0.935385\pi$
$374$	−19.9121			−1.02963
$375$		0			0
$376$	11.9269			0.615083
$377$			35.3242i			1.81929i
$378$		0			0
$379$			3.55367i			0.182540i	0.995826	+	0.0912699i	$0.0290926\pi$
$379$			3.55367i			0.182540i	−0.995826	+	0.0912699i	$0.970907\pi$
$380$	2.99393	+	3.35796i	0.153585	+	0.172260i
$381$		0			0
$382$		−	20.1391i		−	1.03041i
$383$	−35.6437			−1.82131			−0.910654	−	0.413169i	$-0.864422\pi$
$383$	−35.6437			−1.82131			−0.910654	+	0.413169i	$0.864422\pi$
$384$		0			0
$385$	−10.2757	−	8.71748i	−0.523696	−	0.444284i
$386$	−4.45967			−0.226991
$387$		0			0
$388$	−13.2857			−0.674479
$389$	−15.8695			−0.804617			−0.402308	−	0.915504i	$-0.631792\pi$
$389$	−15.8695			−0.804617			−0.402308	+	0.915504i	$0.631792\pi$
$390$		0			0
$391$			5.74268i			0.290420i
$392$	6.90640	−	1.14086i	0.348826	−	0.0576224i
$393$		0			0
$394$			8.84639i			0.445675i
$395$	−5.51235			−0.277357
$396$		0			0
$397$		−	13.1915i		−	0.662061i	−0.943620	−	0.331030i	$-0.892604\pi$
$397$		−	13.1915i		−	0.662061i	0.943620	−	0.331030i	$-0.107396\pi$
$398$	15.4058			0.772223
$399$		0			0
$400$	3.93476			0.196738
$401$		−	17.1756i		−	0.857708i	−0.903374	−	0.428854i	$-0.858917\pi$
$401$		−	17.1756i		−	0.857708i	0.903374	−	0.428854i	$-0.141083\pi$
$402$		0			0
$403$	12.5635			0.625831
$404$			2.26852i			0.112863i
$405$		0			0
$406$	13.3286	−	15.7110i	0.661487	−	0.779722i
$407$			3.25252i			0.161222i
$408$		0			0
$409$	−17.2274			−0.851840			−0.425920	−	0.904761i	$-0.640050\pi$
$409$	−17.2274			−0.851840			−0.425920	+	0.904761i	$0.640050\pi$
$410$	3.40658			0.168239
$411$		0			0
$412$	−15.6736			−0.772182
$413$	8.67295	−	10.2232i	0.426768	−	0.503049i
$414$		0			0
$415$	4.47182			0.219513
$416$		−	4.53617i		−	0.222404i
$417$		0			0
$418$	−14.3148	−	16.0553i	−0.700159	−	0.785291i
$419$		−	8.15659i		−	0.398475i	−0.979951	−	0.199238i	$-0.936153\pi$
$419$		−	8.15659i		−	0.398475i	0.979951	−	0.199238i	$-0.0638466\pi$
$420$		0			0
$421$			13.1281i			0.639826i	0.947447	+	0.319913i	$0.103654\pi$
$421$			13.1281i			0.639826i	−0.947447	+	0.319913i	$0.896346\pi$
$422$	−16.2696			−0.791991
$423$		0			0
$424$	−12.3580			−0.600156
$425$			15.8770i			0.770148i
$426$		0			0
$427$	−3.92377	−	3.32878i	−0.189885	−	0.161091i
$428$		−	5.58780i		−	0.270096i
$429$		0			0
$430$	−5.68224			−0.274022
$431$		−	35.6628i		−	1.71782i	−0.512128	−	0.858909i	$-0.671143\pi$
$431$		−	35.6628i		−	1.71782i	0.512128	−	0.858909i	$-0.328857\pi$
$432$		0			0
$433$	33.0502			1.58829			0.794147	−	0.607726i	$-0.207918\pi$
$433$	33.0502			1.58829			0.794147	+	0.607726i	$0.207918\pi$
$434$	−5.58780	−	4.74048i	−0.268223	−	0.227550i
$435$		0			0
$436$		−	12.3580i		−	0.591839i
$437$	−4.63038	+	4.12841i	−0.221501	+	0.197489i
$438$		0			0
$439$	26.0281			1.24225			0.621126	−	0.783710i	$-0.286675\pi$
$439$	26.0281			1.24225			0.621126	+	0.783710i	$0.286675\pi$
$440$	5.09318			0.242808
$441$		0			0
$442$	18.3037			0.870619
$443$	3.81271			0.181147			0.0905737	−	0.995890i	$-0.471130\pi$
$443$	3.81271			0.181147			0.0905737	+	0.995890i	$0.471130\pi$
$444$		0			0
$445$			16.5707i			0.785528i
$446$			21.3229i			1.00967i
$447$		0			0
$448$	−1.71160	+	2.01753i	−0.0808654	+	0.0953194i
$449$			23.1756i			1.09372i	0.837223	+	0.546862i	$0.184178\pi$
$449$			23.1756i			1.09372i	−0.837223	+	0.546862i	$0.815822\pi$
$450$		0			0
$451$	−16.2878			−0.766962
$452$			20.0341i			0.942326i
$453$		0			0
$454$			9.24135i			0.433718i
$455$	9.44566	+	8.01334i	0.442819	+	0.375671i
$456$		0			0
$457$	−22.6993			−1.06183			−0.530914	−	0.847426i	$-0.678151\pi$
$457$	−22.6993			−1.06183			−0.530914	+	0.847426i	$0.678151\pi$
$458$	−2.50099			−0.116863
$459$		0			0
$460$		−	1.46888i		−	0.0684871i
$461$		−	30.1658i		−	1.40496i	−0.711703	−	0.702480i	$-0.752076\pi$
$461$		−	30.1658i		−	1.40496i	0.711703	−	0.702480i	$-0.247924\pi$
$462$		0			0
$463$	−16.4330			−0.763706			−0.381853	−	0.924223i	$-0.624714\pi$
$463$	−16.4330			−0.763706			−0.381853	+	0.924223i	$0.624714\pi$
$464$			7.78723i			0.361513i
$465$		0			0
$466$			15.0994i			0.699465i
$467$			0.799632i			0.0370026i	0.999829	+	0.0185013i	$0.00588948\pi$
$467$			0.799632i			0.0370026i	−0.999829	+	0.0185013i	$0.994111\pi$
$468$		0			0
$469$	17.0407	+	14.4567i	0.786868	+	0.667549i
$470$		−	12.3098i		−	0.567808i
$471$		0			0
$472$			5.06717i			0.233235i
$473$	27.1683			1.24920
$474$		0			0
$475$	−12.8018	+	11.4140i	−0.587387	+	0.523709i
$476$	−8.14086	−	6.90640i	−0.373136	−	0.316555i
$477$		0			0
$478$		−	11.2927i		−	0.516517i
$479$			0.879830i			0.0402004i	0.999798	+	0.0201002i	$0.00639853\pi$
$479$			0.879830i			0.0402004i	−0.999798	+	0.0201002i	$0.993601\pi$
$480$		0			0
$481$		−	2.98981i		−	0.136323i
$482$			11.4288i			0.520568i
$483$		0			0
$484$	−13.3519			−0.606904
$485$			13.7122i			0.622639i
$486$		0			0
$487$			23.2324i			1.05276i	0.850249	+	0.526380i	$0.176451\pi$
$487$			23.2324i			1.05276i	−0.850249	+	0.526380i	$0.823549\pi$
$488$	1.94484			0.0880387
$489$		0			0
$490$	−1.17749	−	7.12812i	−0.0531936	−	0.322016i
$491$	26.0220			1.17436			0.587178	−	0.809458i	$-0.300239\pi$
$491$	26.0220			1.17436			0.587178	+	0.809458i	$0.300239\pi$
$492$		0			0
$493$	−31.4219			−1.41517
$494$	13.1585	+	14.7585i	0.592030	+	0.664015i
$495$		0			0
$496$	2.76962			0.124360
$497$	4.21335	+	3.57445i	0.188995	+	0.160336i
$498$		0			0
$499$	38.5628			1.72631			0.863153	−	0.504942i	$-0.168486\pi$
$499$	38.5628			1.72631			0.863153	+	0.504942i	$0.168486\pi$
$500$		−	9.22160i		−	0.412402i
$501$		0			0
$502$	7.86581			0.351068
$503$		−	9.39989i		−	0.419120i	−0.977796	−	0.209560i	$-0.932797\pi$
$503$		−	9.39989i		−	0.419120i	0.977796	−	0.209560i	$-0.0672032\pi$
$504$		0			0
$505$	2.34134			0.104188
$506$			7.02313i			0.312216i
$507$		0			0
$508$		−	19.4861i		−	0.864555i
$509$	2.45522			0.108826			0.0544128	−	0.998519i	$-0.482671\pi$
$509$	2.45522			0.108826			0.0544128	+	0.998519i	$0.482671\pi$
$510$		0			0
$511$	27.8678	+	23.6420i	1.23280	+	1.04586i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$			13.4350i			0.592590i
$515$			16.1767i			0.712832i
$516$		0			0
$517$			58.8564i			2.58850i
$518$	−1.12812	+	1.32976i	−0.0495668	+	0.0584265i
$519$		0			0
$520$	−4.68179			−0.205310
$521$	−19.8600			−0.870084			−0.435042	−	0.900410i	$-0.643267\pi$
$521$	−19.8600			−0.870084			−0.435042	+	0.900410i	$0.643267\pi$
$522$		0			0
$523$	16.3781			0.716165			0.358083	−	0.933690i	$-0.383431\pi$
$523$	16.3781			0.716165			0.358083	+	0.933690i	$0.383431\pi$
$524$		−	2.26852i		−	0.0991006i
$525$		0			0
$526$		−	0.517191i		−	0.0225506i
$527$			11.1756i			0.486816i
$528$		0			0
$529$	−20.9745			−0.911935
$530$			12.7547i			0.554028i
$531$		0			0
$532$	−0.283760	−	11.5291i	−0.0123025	−	0.499849i
$533$	14.9722			0.648516
$534$		0			0
$535$	−5.76718			−0.249337
$536$	−8.44633			−0.364826
$537$		0			0
$538$		−	20.3551i		−	0.877572i
$539$	5.62990	+	34.0815i	0.242497	+	1.46799i
$540$		0			0
$541$	12.4597			0.535683			0.267842	−	0.963463i	$-0.413690\pi$
$541$	12.4597			0.535683			0.267842	+	0.963463i	$0.413690\pi$
$542$	−2.61195			−0.112193
$543$		0			0
$544$	4.03506			0.173002
$545$	−12.7547			−0.546351
$546$		0			0
$547$		−	25.4318i		−	1.08739i	−0.839284	−	0.543693i	$-0.817025\pi$
$547$		−	25.4318i		−	1.08739i	0.839284	−	0.543693i	$-0.182975\pi$
$548$	−11.9518			−0.510557
$549$		0			0
$550$			19.4171i			0.827949i
$551$	−22.5892	−	25.3358i	−0.962333	−	1.07934i
$552$		0			0
$553$	10.7754	+	9.14147i	0.458218	+	0.388735i
$554$			10.5513i			0.448283i
$555$		0			0
$556$			16.1747i			0.685959i
$557$	−35.1026			−1.48735			−0.743673	−	0.668543i	$-0.766918\pi$
$557$	−35.1026			−1.48735			−0.743673	+	0.668543i	$0.766918\pi$
$558$		0			0
$559$	−24.9738			−1.05628
$560$	2.08230	+	1.76655i	0.0879932	+	0.0746502i
$561$		0			0
$562$		0			0
$563$	17.5586			0.740008			0.370004	−	0.929030i	$-0.379356\pi$
$563$	17.5586			0.740008			0.370004	+	0.929030i	$0.379356\pi$
$564$		0			0
$565$	20.6773			0.869900
$566$	26.1223			1.09800
$567$		0			0
$568$	−2.08837			−0.0876261
$569$			36.4330i			1.52735i	0.645601	+	0.763675i	$0.276607\pi$
$569$			36.4330i			1.52735i	−0.645601	+	0.763675i	$0.723393\pi$
$570$		0			0
$571$	−35.6727			−1.49285			−0.746427	−	0.665467i	$-0.768232\pi$
$571$	−35.6727			−1.49285			−0.746427	+	0.665467i	$0.768232\pi$
$572$	22.3849			0.935960
$573$		0			0
$574$	−6.65910	−	5.64933i	−0.277946	−	0.235799i
$575$	5.59994			0.233534
$576$		0			0
$577$			37.3758i			1.55598i	0.628279	+	0.777988i	$0.283760\pi$
$577$			37.3758i			1.55598i	−0.628279	+	0.777988i	$0.716240\pi$
$578$		−	0.718270i		−	0.0298761i
$579$		0			0
$580$	8.03722			0.333727
$581$	−8.74140	−	7.41588i	−0.362655	−	0.307663i
$582$		0			0
$583$		−	60.9836i		−	2.52568i
$584$	−13.8128			−0.571578
$585$		0			0
$586$			5.70826i			0.235806i
$587$			12.6416i			0.521774i	0.965369	+	0.260887i	$0.0840150\pi$
$587$			12.6416i			0.521774i	−0.965369	+	0.260887i	$0.915985\pi$
$588$		0			0
$589$	−9.01099	+	8.03413i	−0.371291	+	0.331040i
$590$	5.22984			0.215309
$591$		0			0
$592$		−	0.659104i		−	0.0270890i
$593$		−	12.0118i		−	0.493267i	−0.969109	−	0.246634i	$-0.920676\pi$
$593$		−	12.0118i		−	0.493267i	0.969109	−	0.246634i	$-0.0793244\pi$
$594$		0			0
$595$	−7.12812	+	8.40221i	−0.292225	+	0.344457i
$596$	1.83540			0.0751809
$597$		0			0
$598$		−	6.45585i		−	0.263999i
$599$		−	21.9116i		−	0.895285i	−0.894213	−	0.447642i	$-0.852264\pi$
$599$		−	21.9116i		−	0.895285i	0.894213	−	0.447642i	$-0.147736\pi$
$600$		0			0
$601$	−18.6711			−0.761611			−0.380806	−	0.924655i	$-0.624353\pi$
$601$	−18.6711			−0.761611			−0.380806	+	0.924655i	$0.624353\pi$
$602$	11.1075	+	9.42320i	0.452708	+	0.384061i
$603$		0			0
$604$		−	3.14147i		−	0.127824i
$605$			13.7805i			0.560258i
$606$		0			0
$607$	−24.7459			−1.00441			−0.502203	−	0.864750i	$-0.667477\pi$
$607$	−24.7459			−1.00441			−0.502203	+	0.864750i	$0.667477\pi$
$608$	2.90080	+	3.25351i	0.117643	+	0.131947i
$609$		0			0
$610$		−	2.00727i		−	0.0812721i
$611$		−	54.1024i		−	2.18875i
$612$		0			0
$613$	−16.0463			−0.648103			−0.324051	−	0.946039i	$-0.605045\pi$
$613$	−16.0463			−0.648103			−0.324051	+	0.946039i	$0.605045\pi$
$614$			10.4610i			0.422172i
$615$		0			0
$616$	−9.95604	−	8.44633i	−0.401140	−	0.340312i
$617$	45.3970			1.82761			0.913807	−	0.406148i	$-0.133128\pi$
$617$	45.3970			1.82761			0.913807	+	0.406148i	$0.133128\pi$
$618$		0			0
$619$		−	43.5616i		−	1.75089i	−0.483321	−	0.875443i	$-0.660569\pi$
$619$		−	43.5616i		−	1.75089i	0.483321	−	0.875443i	$-0.339431\pi$
$620$		−	2.85853i		−	0.114801i
$621$		0			0
$622$	10.3647			0.415585
$623$	27.4802	−	32.3921i	1.10097	−	1.29776i
$624$		0			0
$625$	10.1562			0.406247
$626$	−19.8187			−0.792116
$627$		0			0
$628$			6.72061i			0.268181i
$629$	2.65953			0.106042
$630$		0			0
$631$	−37.9037			−1.50892			−0.754460	−	0.656346i	$-0.772101\pi$
$631$	−37.9037			−1.50892			−0.754460	+	0.656346i	$0.772101\pi$
$632$	−5.34090			−0.212449
$633$		0			0
$634$	−13.0739			−0.519230
$635$	−20.1116			−0.798106
$636$		0			0
$637$	−5.17515	−	31.3286i	−0.205047	−	1.24128i
$638$	−38.4281			−1.52138
$639$		0			0
$640$	−1.03210			−0.0407975
$641$		−	3.14147i		−	0.124080i	−0.998074	−	0.0620402i	$-0.980239\pi$
$641$		−	3.14147i		−	0.124080i	0.998074	−	0.0620402i	$-0.0197607\pi$
$642$		0			0
$643$		−	45.8645i		−	1.80872i	−0.426771	−	0.904360i	$-0.640349\pi$
$643$		−	45.8645i		−	1.80872i	0.426771	−	0.904360i	$-0.359651\pi$
$644$	−2.43594	+	2.87134i	−0.0959894	+	0.113147i
$645$		0			0
$646$	−13.1281	+	11.7049i	−0.516519	+	0.460524i
$647$			34.9613i			1.37447i	0.726435	+	0.687235i	$0.241176\pi$
$647$			34.9613i			1.37447i	−0.726435	+	0.687235i	$0.758824\pi$
$648$		0			0
$649$	−25.0053			−0.981542
$650$		−	17.8487i		−	0.700085i
$651$		0			0
$652$	3.06524			0.120044
$653$	−30.6196			−1.19824			−0.599118	−	0.800661i	$-0.704482\pi$
$653$	−30.6196			−1.19824			−0.599118	+	0.800661i	$0.704482\pi$
$654$		0			0
$655$	−2.34134			−0.0914839
$656$	3.30062			0.128868
$657$		0			0
$658$	−20.4140	+	24.0629i	−0.795823	+	0.938069i
$659$			46.5941i			1.81505i	0.420000	+	0.907524i	$0.362030\pi$
$659$			46.5941i			1.81505i	−0.420000	+	0.907524i	$0.637970\pi$
$660$		0			0
$661$	−18.7391			−0.728867			−0.364434	−	0.931229i	$-0.618737\pi$
$661$	−18.7391			−0.728867			−0.364434	+	0.931229i	$0.618737\pi$
$662$	−6.41220			−0.249217
$663$		0			0
$664$	4.33272			0.168142
$665$	−11.8992	+	0.292869i	−0.461431	+	0.0113570i
$666$		0			0
$667$			11.0827i			0.429126i
$668$	6.19262			0.239600
$669$		0			0
$670$			8.71748i			0.336786i
$671$			9.59731i			0.370500i
$672$		0			0
$673$			22.5733i			0.870137i	0.900397	+	0.435068i	$0.143276\pi$
$673$			22.5733i			0.870137i	−0.900397	+	0.435068i	$0.856724\pi$
$674$	−8.85853			−0.341218
$675$		0			0
$676$	−7.57680			−0.291416
$677$	39.9351			1.53483			0.767416	−	0.641150i	$-0.221542\pi$
$677$	39.9351			1.53483			0.767416	+	0.641150i	$0.221542\pi$
$678$		0			0
$679$	22.7398	−	26.8043i	0.872672	−	1.02865i
$680$		−	4.16460i		−	0.159705i
$681$		0			0
$682$			13.6674i			0.523353i
$683$		−	19.6011i		−	0.750017i	−0.927021	−	0.375008i	$-0.877640\pi$
$683$		−	19.6011i		−	0.750017i	0.927021	−	0.375008i	$-0.122360\pi$
$684$		0			0
$685$			12.3355i			0.471316i
$686$	−9.51926	+	15.8866i	−0.363447	+	0.606553i
$687$		0			0
$688$	−5.50550			−0.209895
$689$			56.0578i			2.13563i
$690$		0			0
$691$		−	20.3551i		−	0.774345i	−0.922007	−	0.387173i	$-0.873452\pi$
$691$		−	20.3551i		−	0.774345i	0.922007	−	0.387173i	$-0.126548\pi$
$692$	−9.93002			−0.377483
$693$		0			0
$694$			26.0220i			0.987781i
$695$	16.6939			0.633237
$696$		0			0
$697$			13.3182i			0.504463i
$698$	34.0225			1.28777
$699$		0			0
$700$	−6.73473	+	7.93851i	−0.254549	+	0.300047i
$701$	−46.0804			−1.74043			−0.870216	−	0.492670i	$-0.836021\pi$
$701$	−46.0804			−1.74043			−0.870216	+	0.492670i	$0.836021\pi$
$702$		0			0
$703$	1.91193	+	2.14440i	0.0721099	+	0.0808777i
$704$	4.93476			0.185986
$705$		0			0
$706$	3.43974			0.129456
$707$	−4.57680	−	3.88279i	−0.172128	−	0.146027i
$708$		0			0
$709$	−20.4330			−0.767377			−0.383688	−	0.923463i	$-0.625346\pi$
$709$	−20.4330			−0.767377			−0.383688	+	0.923463i	$0.625346\pi$
$710$			2.15541i			0.0808913i
$711$		0			0
$712$			16.0553i			0.601698i
$713$	3.94171			0.147618
$714$		0			0
$715$		−	23.1035i		−	0.864023i
$716$			1.31821i			0.0492638i
$717$		0			0
$718$		−	7.71827i		−	0.288043i
$719$		−	27.1236i		−	1.01154i	−0.862668	−	0.505771i	$-0.831208\pi$
$719$		−	27.1236i		−	1.01154i	0.862668	−	0.505771i	$-0.168792\pi$
$720$		0			0
$721$	26.8269	−	31.6219i	0.999084	−	1.17766i
$722$	−18.8756	−	2.17067i	−0.702477	−	0.0807840i
$723$		0			0
$724$	−9.27664			−0.344764
$725$			30.6409i			1.13797i
$726$		0			0
$727$		−	21.1506i		−	0.784434i	−0.919873	−	0.392217i	$-0.871708\pi$
$727$		−	21.1506i		−	0.784434i	0.919873	−	0.392217i	$-0.128292\pi$
$728$	9.15186	+	7.76409i	0.339190	+	0.287756i
$729$		0			0
$730$			14.2562i			0.527647i
$731$		−	22.2150i		−	0.821652i
$732$		0			0
$733$		−	17.5810i		−	0.649368i	−0.945823	−	0.324684i	$-0.894742\pi$
$733$		−	17.5810i		−	0.649368i	0.945823	−	0.324684i	$-0.105258\pi$
$734$	19.8792			0.733754
$735$		0			0
$736$		−	1.42320i		−	0.0524597i
$737$		−	41.6806i		−	1.53533i
$738$		0			0
$739$	−0.637120			−0.0234368			−0.0117184	−	0.999931i	$-0.503730\pi$
$739$	−0.637120			−0.0234368			−0.0117184	+	0.999931i	$0.503730\pi$
$740$	−0.680264			−0.0250070
$741$		0			0
$742$	21.1519	−	24.9326i	0.776509	−	0.915303i
$743$		−	5.84594i		−	0.214467i	−0.994234	−	0.107233i	$-0.965801\pi$
$743$		−	5.84594i		−	0.214467i	0.994234	−	0.107233i	$-0.0341992\pi$
$744$		0			0
$745$		−	1.89432i		−	0.0694026i
$746$	7.78723			0.285111
$747$		0			0
$748$			19.9121i			0.728058i
$749$	11.2736	+	9.56406i	0.411927	+	0.349463i
$750$		0			0
$751$			10.7386i			0.391857i	0.980618	+	0.195929i	$0.0627721\pi$
$751$			10.7386i			0.391857i	−0.980618	+	0.195929i	$0.937228\pi$
$752$		−	11.9269i		−	0.434929i
$753$		0			0
$754$	35.3242			1.28643
$755$	−3.24232			−0.118000
$756$		0			0
$757$	15.2219			0.553248			0.276624	−	0.960978i	$-0.410784\pi$
$757$	15.2219			0.553248			0.276624	+	0.960978i	$0.410784\pi$
$758$	3.55367			0.129075
$759$		0			0
$760$	3.35796	−	2.99393i	0.121806	−	0.108601i
$761$			2.27540i			0.0824833i	0.999149	+	0.0412417i	$0.0131314\pi$
$761$			2.27540i			0.0824833i	−0.999149	+	0.0412417i	$0.986869\pi$
$762$		0			0
$763$	24.9326	+	21.1519i	0.902620	+	0.765749i
$764$	−20.1391			−0.728608
$765$		0			0
$766$			35.6437i			1.28786i
$767$	22.9855			0.829959
$768$		0			0
$769$			11.3920i			0.410807i	0.978677	+	0.205403i	$0.0658506\pi$
$769$			11.3920i			0.410807i	−0.978677	+	0.205403i	$0.934149\pi$
$770$	−8.71748	+	10.2757i	−0.314156	+	0.370309i
$771$		0			0
$772$			4.45967i			0.160507i
$773$	−10.6187			−0.381928			−0.190964	−	0.981597i	$-0.561161\pi$
$773$	−10.6187			−0.381928			−0.190964	+	0.981597i	$0.561161\pi$
$774$		0			0
$775$	10.8978			0.391461
$776$			13.2857i			0.476928i
$777$		0			0
$778$			15.8695i			0.568950i
$779$	−10.7386	+	9.57445i	−0.384750	+	0.343040i
$780$		0			0
$781$		−	10.3056i		−	0.368764i
$782$	5.74268			0.205358
$783$		0			0
$784$	−1.14086	−	6.90640i	−0.0407452	−	0.246657i
$785$	6.93636			0.247569
$786$		0			0
$787$	−37.9413			−1.35246			−0.676230	−	0.736691i	$-0.736387\pi$
$787$	−37.9413			−1.35246			−0.676230	+	0.736691i	$0.736387\pi$
$788$	8.84639			0.315140
$789$		0			0
$790$			5.51235i			0.196121i
$791$	−40.4195	−	34.2904i	−1.43715	−	1.21923i
$792$		0			0
$793$		−	8.82211i		−	0.313282i
$794$	−13.1915			−0.468148
$795$		0			0
$796$		−	15.4058i		−	0.546044i
$797$	−9.24135			−0.327345			−0.163673	−	0.986515i	$-0.552334\pi$
$797$	−9.24135			−0.327345			−0.163673	+	0.986515i	$0.552334\pi$
$798$		0			0
$799$	48.1258			1.70257
$800$		−	3.93476i		−	0.139115i
$801$		0			0
$802$	−17.1756			−0.606491
$803$		−	68.1629i		−	2.40542i
$804$		0			0
$805$	2.96352	+	2.51414i	0.104450	+	0.0886118i
$806$		−	12.5635i		−	0.442529i
$807$		0			0
$808$	2.26852			0.0798062
$809$	−43.9860			−1.54646			−0.773232	−	0.634123i	$-0.781361\pi$
$809$	−43.9860			−1.54646			−0.773232	+	0.634123i	$0.781361\pi$
$810$		0			0
$811$	6.27843			0.220465			0.110233	−	0.993906i	$-0.464840\pi$
$811$	6.27843			0.220465			0.110233	+	0.993906i	$0.464840\pi$
$812$	−15.7110	−	13.3286i	−0.551347	−	0.467742i
$813$		0			0
$814$	3.25252			0.114001
$815$		−	3.16364i		−	0.110817i
$816$		0			0
$817$	17.9122	−	15.9704i	0.626668	−	0.558732i
$818$			17.2274i			0.602342i
$819$		0			0
$820$		−	3.40658i		−	0.118963i
$821$	−17.4099			−0.607608			−0.303804	−	0.952735i	$-0.598257\pi$
$821$	−17.4099			−0.607608			−0.303804	+	0.952735i	$0.598257\pi$
$822$		0			0
$823$	26.7877			0.933760			0.466880	−	0.884321i	$-0.345378\pi$
$823$	26.7877			0.933760			0.466880	+	0.884321i	$0.345378\pi$
$824$			15.6736i			0.546015i
$825$		0			0
$826$	−10.2232	−	8.67295i	−0.355709	−	0.301771i
$827$		−	24.8452i		−	0.863952i	−0.901885	−	0.431976i	$-0.857817\pi$
$827$		−	24.8452i		−	0.863952i	0.901885	−	0.431976i	$-0.142183\pi$
$828$		0			0
$829$	−27.3297			−0.949200			−0.474600	−	0.880202i	$-0.657407\pi$
$829$	−27.3297			−0.949200			−0.474600	+	0.880202i	$0.657407\pi$
$830$		−	4.47182i		−	0.155219i
$831$		0			0
$832$	−4.53617			−0.157263
$833$	27.8678	−	4.60346i	0.965561	−	0.159500i
$834$		0			0
$835$		−	6.39142i		−	0.221184i
$836$	−16.0553	+	14.3148i	−0.555284	+	0.495087i
$837$		0			0
$838$	−8.15659			−0.281765
$839$	13.5496			0.467783			0.233892	−	0.972263i	$-0.424854\pi$
$839$	13.5496			0.467783			0.233892	+	0.972263i	$0.424854\pi$
$840$		0			0
$841$	−31.6409			−1.09107
$842$	13.1281			0.452425
$843$		0			0
$844$			16.2696i			0.560022i
$845$			7.82004i			0.269018i
$846$		0			0
$847$	22.8531	−	26.9379i	0.785241	−	0.925596i
$848$			12.3580i			0.424374i
$849$		0			0
$850$	15.8770			0.544577
$851$		−	0.938035i		−	0.0321554i
$852$		0			0
$853$		−	41.2649i		−	1.41288i	−0.707772	−	0.706441i	$-0.750299\pi$
$853$		−	41.2649i		−	1.41288i	0.707772	−	0.706441i	$-0.249701\pi$
$854$	−3.32878	+	3.92377i	−0.113909	+	0.134269i
$855$		0			0
$856$	−5.58780			−0.190987
$857$	−3.82387			−0.130621			−0.0653104	−	0.997865i	$-0.520804\pi$
$857$	−3.82387			−0.130621			−0.0653104	+	0.997865i	$0.520804\pi$
$858$		0			0
$859$			29.2988i			0.999663i	0.866123	+	0.499831i	$0.166605\pi$
$859$			29.2988i			0.999663i	−0.866123	+	0.499831i	$0.833395\pi$
$860$			5.68224i			0.193763i
$861$		0			0
$862$	−35.6628			−1.21468
$863$		−	2.70448i		−	0.0920615i	−0.998940	−	0.0460308i	$-0.985343\pi$
$863$		−	2.70448i		−	0.0920615i	0.998940	−	0.0460308i	$-0.0146572\pi$
$864$		0			0
$865$			10.2488i			0.348470i
$866$		−	33.0502i		−	1.12309i
$867$		0			0
$868$	−4.74048	+	5.58780i	−0.160902	+	0.189662i
$869$		−	26.3561i		−	0.894068i
$870$		0			0
$871$			38.3140i			1.29822i
$872$	−12.3580			−0.418493
$873$		0			0
$874$	4.12841	+	4.63038i	0.139646	+	0.156625i
$875$	18.6049	+	15.7837i	0.628959	+	0.533585i
$876$		0			0
$877$			5.92497i			0.200072i	0.994984	+	0.100036i	$0.0318958\pi$
$877$			5.92497i			0.200072i	−0.994984	+	0.100036i	$0.968104\pi$
$878$		−	26.0281i		−	0.878406i
$879$		0			0
$880$		−	5.09318i		−	0.171691i
$881$			5.41060i			0.182288i	0.995838	+	0.0911438i	$0.0290523\pi$
$881$			5.41060i			0.182288i	−0.995838	+	0.0911438i	$0.970948\pi$
$882$		0			0
$883$	6.86181			0.230918			0.115459	−	0.993312i	$-0.463166\pi$
$883$	6.86181			0.230918			0.115459	+	0.993312i	$0.463166\pi$
$884$		−	18.3037i		−	0.615621i
$885$		0			0
$886$		−	3.81271i		−	0.128091i
$887$	11.4333			0.383894			0.191947	−	0.981405i	$-0.438520\pi$
$887$	11.4333			0.383894			0.191947	+	0.981405i	$0.438520\pi$
$888$		0			0
$889$	39.3138	+	33.3523i	1.31854	+	1.11860i
$890$	16.5707			0.555452
$891$		0			0
$892$	21.3229			0.713944
$893$	34.5976	+	38.8043i	1.15776	+	1.29854i
$894$		0			0
$895$	1.36053			0.0454774
$896$	2.01753	+	1.71160i	0.0674010	+	0.0571805i
$897$		0			0
$898$	23.1756			0.773380
$899$			21.5677i			0.719322i
$900$		0			0
$901$	−49.8651			−1.66125
$902$			16.2878i			0.542324i
$903$		0			0
$904$	20.0341			0.666325
$905$			9.57445i			0.318266i
$906$		0			0
$907$		−	41.7014i		−	1.38467i	−0.721575	−	0.692337i	$-0.756581\pi$
$907$		−	41.7014i		−	1.38467i	0.721575	−	0.692337i	$-0.243419\pi$
$908$	9.24135			0.306685
$909$		0			0
$910$	8.01334	−	9.44566i	0.265640	−	0.313121i
$911$		−	15.5176i		−	0.514122i	−0.966395	−	0.257061i	$-0.917246\pi$
$911$		−	15.5176i		−	0.514122i	0.966395	−	0.257061i	$-0.0827542\pi$
$912$		0			0
$913$			21.3810i			0.707607i
$914$			22.6993i			0.750826i
$915$		0			0
$916$			2.50099i			0.0826350i
$917$	4.57680	+	3.88279i	0.151139	+	0.128221i
$918$		0			0
$919$	−38.9013			−1.28324			−0.641618	−	0.767025i	$-0.721736\pi$
$919$	−38.9013			−1.28324			−0.641618	+	0.767025i	$0.721736\pi$
$920$	−1.46888			−0.0484277
$921$		0			0
$922$	−30.1658			−0.993457
$923$			9.47320i			0.311814i
$924$		0			0
$925$		−	2.59342i		−	0.0852711i
$926$			16.4330i			0.540021i
$927$		0			0
$928$	7.78723			0.255628
$929$			0.910593i			0.0298756i	0.999888	+	0.0149378i	$0.00475503\pi$
$929$			0.910593i			0.0298756i	−0.999888	+	0.0149378i	$0.995245\pi$
$930$		0			0
$931$	23.7459	+	19.1606i	0.778242	+	0.627965i
$932$	15.0994			0.494596
$933$		0			0
$934$	0.799632			0.0261648
$935$	20.5513			0.672100
$936$		0			0
$937$		−	28.7792i		−	0.940177i	−0.882619	−	0.470088i	$-0.844222\pi$
$937$		−	28.7792i		−	0.940177i	0.882619	−	0.470088i	$-0.155778\pi$
$938$	14.4567	−	17.0407i	0.472029	−	0.556400i
$939$		0			0
$940$	−12.3098			−0.401501
$941$	60.0859			1.95875			0.979373	−	0.202062i	$-0.0647643\pi$
$941$	60.0859			1.95875			0.979373	+	0.202062i	$0.0647643\pi$
$942$		0			0
$943$	4.69743			0.152969
$944$	5.06717			0.164922
$945$		0			0
$946$		−	27.1683i		−	0.883318i
$947$	−1.85411			−0.0602506			−0.0301253	−	0.999546i	$-0.509591\pi$
$947$	−1.85411			−0.0602506			−0.0301253	+	0.999546i	$0.509591\pi$
$948$		0			0
$949$			62.6572i			2.03394i
$950$	11.4140	+	12.8018i	0.370318	+	0.415345i
$951$		0			0
$952$	−6.90640	+	8.14086i	−0.223838	+	0.263847i
$953$			57.7489i			1.87067i	0.353763	+	0.935335i	$0.384902\pi$
$953$			57.7489i			1.87067i	−0.353763	+	0.935335i	$0.615098\pi$
$954$		0			0
$955$			20.7856i			0.672608i
$956$	−11.2927			−0.365233
$957$		0			0
$958$	0.879830			0.0284260
$959$	20.4567	−	24.1132i	0.660582	−	0.778655i
$960$		0			0
$961$	−23.3292			−0.752555
$962$	−2.98981			−0.0963953
$963$		0			0
$964$	11.4288			0.368097
$965$	4.60284			0.148171
$966$		0			0
$967$	43.3402			1.39373			0.696863	−	0.717204i	$-0.254578\pi$
$967$	43.3402			1.39373			0.696863	+	0.717204i	$0.254578\pi$
$968$			13.3519i			0.429146i
$969$		0			0
$970$	13.7122			0.440272
$971$	−23.2863			−0.747293			−0.373646	−	0.927571i	$-0.621893\pi$
$971$	−23.2863			−0.747293			−0.373646	+	0.927571i	$0.621893\pi$
$972$		0			0
$973$	−32.6329	−	27.6845i	−1.04616	−	0.887526i
$974$	23.2324			0.744414
$975$		0			0
$976$		−	1.94484i		−	0.0622527i
$977$		−	20.5392i		−	0.657106i	−0.944485	−	0.328553i	$-0.893439\pi$
$977$		−	20.5392i		−	0.657106i	0.944485	−	0.328553i	$-0.106561\pi$
$978$		0			0
$979$	−79.2291			−2.53217
$980$	−7.12812	+	1.17749i	−0.227699	+	0.0376135i
$981$		0			0
$982$		−	26.0220i		−	0.830395i
$983$	−0.951906			−0.0303611			−0.0151805	−	0.999885i	$-0.504832\pi$
$983$	−0.951906			−0.0303611			−0.0151805	+	0.999885i	$0.504832\pi$
$984$		0			0
$985$		−	9.13039i		−	0.290918i
$986$			31.4219i			1.00068i
$987$		0			0
$988$	14.7585	−	13.1585i	0.469529	−	0.418629i
$989$	−7.83540			−0.249151
$990$		0			0
$991$		−	42.9810i		−	1.36534i	−0.730728	−	0.682669i	$-0.760819\pi$
$991$		−	42.9810i		−	1.36534i	0.730728	−	0.682669i	$-0.239181\pi$
$992$		−	2.76962i		−	0.0879355i
$993$		0			0
$994$	3.57445	−	4.21335i	0.113375	−	0.133639i
$995$	−15.9004			−0.504076
$996$		0			0
$997$			15.5168i			0.491421i	0.969343	+	0.245711i	$0.0790213\pi$
$997$			15.5168i			0.491421i	−0.969343	+	0.245711i	$0.920979\pi$
$998$		−	38.5628i		−	1.22068i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2394.2.e.c.1063.5		16
3.2	odd	2		266.2.d.a.265.11	yes	16
7.6	odd	2	inner	2394.2.e.c.1063.4		16
12.11	even	2		2128.2.m.f.1329.11		16
19.18	odd	2	inner	2394.2.e.c.1063.13		16
21.20	even	2		266.2.d.a.265.14	yes	16
57.56	even	2		266.2.d.a.265.6	yes	16
84.83	odd	2		2128.2.m.f.1329.6		16
133.132	even	2	inner	2394.2.e.c.1063.12		16
228.227	odd	2		2128.2.m.f.1329.5		16
399.398	odd	2		266.2.d.a.265.3	✓	16
1596.1595	even	2		2128.2.m.f.1329.12		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
266.2.d.a.265.3	✓	16	399.398	odd	2
266.2.d.a.265.6	yes	16	57.56	even	2
266.2.d.a.265.11	yes	16	3.2	odd	2
266.2.d.a.265.14	yes	16	21.20	even	2
2128.2.m.f.1329.5		16	228.227	odd	2
2128.2.m.f.1329.6		16	84.83	odd	2
2128.2.m.f.1329.11		16	12.11	even	2
2128.2.m.f.1329.12		16	1596.1595	even	2
2394.2.e.c.1063.4		16	7.6	odd	2	inner
2394.2.e.c.1063.5		16	1.1	even	1	trivial
2394.2.e.c.1063.12		16	133.132	even	2	inner
2394.2.e.c.1063.13		16	19.18	odd	2	inner

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:	\( N \)	\(=\)	\( 2394 = 2 \cdot 3^{2} \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2394.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000 q^{4} +1.03210i q^{5} +(1.71160 - 2.01753i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q-1.00000i q^{2} -1.00000 q^{4} +1.03210i q^{5} +(1.71160 - 2.01753i) q^{7} +1.00000i q^{8} +1.03210 q^{10} -4.93476 q^{11} +4.53617 q^{13} +(-2.01753 - 1.71160i) q^{14} +1.00000 q^{16} +4.03506i q^{17} +(-3.25351 + 2.90080i) q^{19} -1.03210i q^{20} +4.93476i q^{22} +1.42320 q^{23} +3.93476 q^{25} -4.53617i q^{26} +(-1.71160 + 2.01753i) q^{28} +7.78723i q^{29} +2.76962 q^{31} -1.00000i q^{32} +4.03506 q^{34} +(2.08230 + 1.76655i) q^{35} -0.659104i q^{37} +(2.90080 + 3.25351i) q^{38} -1.03210 q^{40} +3.30062 q^{41} -5.50550 q^{43} +4.93476 q^{44} -1.42320i q^{46} -11.9269i q^{47} +(-1.14086 - 6.90640i) q^{49} -3.93476i q^{50} -4.53617 q^{52} +12.3580i q^{53} -5.09318i q^{55} +(2.01753 + 1.71160i) q^{56} +7.78723 q^{58} +5.06717 q^{59} -1.94484i q^{61} -2.76962i q^{62} -1.00000 q^{64} +4.68179i q^{65} +8.44633i q^{67} -4.03506i q^{68} +(1.76655 - 2.08230i) q^{70} +2.08837i q^{71} +13.8128i q^{73} -0.659104 q^{74} +(3.25351 - 2.90080i) q^{76} +(-8.44633 + 9.95604i) q^{77} +5.34090i q^{79} +1.03210i q^{80} -3.30062i q^{82} -4.33272i q^{83} -4.16460 q^{85} +5.50550i q^{86} -4.93476i q^{88} +16.0553 q^{89} +(7.76409 - 9.15186i) q^{91} -1.42320 q^{92} -11.9269 q^{94} +(-2.99393 - 3.35796i) q^{95} +13.2857 q^{97} +(-6.90640 + 1.14086i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{4} + 6 q^{7}+O(q^{10}) \) 16 * q - 16 * q^4 + 6 * q^7	\( 16 q - 16 q^{4} + 6 q^{7} + 12 q^{11} + 16 q^{16} - 20 q^{23} - 28 q^{25} - 6 q^{28} - 8 q^{35} - 4 q^{43} - 12 q^{44} + 10 q^{49} - 16 q^{58} - 16 q^{64} - 12 q^{74} + 4 q^{77} + 16 q^{85} + 20 q^{92} - 12 q^{95}+O(q^{100}) \) 16 * q - 16 * q^4 + 6 * q^7 + 12 * q^11 + 16 * q^16 - 20 * q^23 - 28 * q^25 - 6 * q^28 - 8 * q^35 - 4 * q^43 - 12 * q^44 + 10 * q^49 - 16 * q^58 - 16 * q^64 - 12 * q^74 + 4 * q^77 + 16 * q^85 + 20 * q^92 - 12 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more