LMFDB - Embedded newform 1152.2.w.a.1007.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1152,2,Mod(143,1152)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1152, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 1, 4]))

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

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

chi := DirichletCharacter("1152.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1152 = 2^{7} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1152.w (of order $8$, degree $4$, 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:	$9.19876631285$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 288)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			1007.2
Character	$\chi$	$=$	1152.1007
Dual form			1152.2.w.a.143.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.11994 - 2.70378i) q^{5} +(-1.57144 - 1.57144i) q^{7} +O(q^{10})$	$q+(-1.11994 - 2.70378i) q^{5} +(-1.57144 - 1.57144i) q^{7} +(1.00153 + 2.41791i) q^{11} +(-6.48559 - 2.68642i) q^{13} +0.520719 q^{17} +(-2.95774 + 7.14062i) q^{19} +(1.35340 + 1.35340i) q^{23} +(-2.52064 + 2.52064i) q^{25} +(5.31381 + 2.20105i) q^{29} +1.54505i q^{31} +(-2.48892 + 6.00877i) q^{35} +(-3.79897 + 1.57359i) q^{37} +(1.08917 - 1.08917i) q^{41} +(2.71012 - 1.12257i) q^{43} +11.1855i q^{47} -2.06113i q^{49} +(-3.70104 + 1.53302i) q^{53} +(5.41584 - 5.41584i) q^{55} +(-3.19376 + 1.32290i) q^{59} +(-3.78169 + 9.12981i) q^{61} +20.5443i q^{65} +(-10.9492 - 4.53532i) q^{67} +(6.83579 - 6.83579i) q^{71} +(2.94667 + 2.94667i) q^{73} +(2.22576 - 5.37346i) q^{77} -8.79533 q^{79} +(-13.9866 - 5.79342i) q^{83} +(-0.583176 - 1.40791i) q^{85} +(7.09089 + 7.09089i) q^{89} +(5.97019 + 14.4133i) q^{91} +22.6192 q^{95} -5.91713 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q - 8 q^{11} + 16 q^{29} + 24 q^{35} + 16 q^{53} + 32 q^{55} + 32 q^{59} + 32 q^{61} + 16 q^{67} + 16 q^{71} + 16 q^{77} + 32 q^{79} - 40 q^{83} + 48 q^{91} - 80 q^{95}+O(q^{100}) $ 32 * q - 8 * q^11 + 16 * q^29 + 24 * q^35 + 16 * q^53 + 32 * q^55 + 32 * q^59 + 32 * q^61 + 16 * q^67 + 16 * q^71 + 16 * q^77 + 32 * q^79 - 40 * q^83 + 48 * q^91 - 80 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times$.

$n$	$127$	$641$	$901$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{7}{8}\right)$

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
$5$	−1.11994	−	2.70378i	−0.500854	−	1.20917i	−0.949019	−	0.315218i	$-0.897922\pi$
$5$	−1.11994	−	2.70378i	−0.500854	−	1.20917i	0.448165	−	0.893951i	$-0.352078\pi$
$6$		0			0
$7$	−1.57144	−	1.57144i	−0.593950	−	0.593950i	0.344746	−	0.938696i	$-0.387965\pi$
$7$	−1.57144	−	1.57144i	−0.593950	−	0.593950i	−0.938696	+	0.344746i	$0.887965\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.00153	+	2.41791i	0.301973	+	0.729027i	0.999917	+	0.0128746i	$0.00409824\pi$
$11$	1.00153	+	2.41791i	0.301973	+	0.729027i	−0.697944	+	0.716152i	$0.745902\pi$
$12$		0			0
$13$	−6.48559	−	2.68642i	−1.79878	−	0.745079i	−0.986917	−	0.161230i	$-0.948454\pi$
$13$	−6.48559	−	2.68642i	−1.79878	−	0.745079i	−0.811863	−	0.583848i	$-0.801546\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.520719			0.126293			0.0631465	−	0.998004i	$-0.479886\pi$
$17$	0.520719			0.126293			0.0631465	+	0.998004i	$0.479886\pi$
$18$		0			0
$19$	−2.95774	+	7.14062i	−0.678552	+	1.63817i	0.0881038	+	0.996111i	$0.471919\pi$
$19$	−2.95774	+	7.14062i	−0.678552	+	1.63817i	−0.766656	+	0.642058i	$0.778081\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	1.35340	+	1.35340i	0.282204	+	0.282204i	0.833987	−	0.551784i	$-0.186053\pi$
$23$	1.35340	+	1.35340i	0.282204	+	0.282204i	−0.551784	+	0.833987i	$0.686053\pi$
$24$		0			0
$25$	−2.52064	+	2.52064i	−0.504128	+	0.504128i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	5.31381	+	2.20105i	0.986750	+	0.408725i	0.816922	−	0.576748i	$-0.195679\pi$
$29$	5.31381	+	2.20105i	0.986750	+	0.408725i	0.169828	+	0.985474i	$0.445679\pi$
$30$		0			0
$31$			1.54505i			0.277498i	0.990328	+	0.138749i	$0.0443082\pi$
$31$			1.54505i			0.277498i	−0.990328	+	0.138749i	$0.955692\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−2.48892	+	6.00877i	−0.420704	+	1.01567i
$36$		0			0
$37$	−3.79897	+	1.57359i	−0.624548	+	0.258696i	−0.672434	−	0.740157i	$-0.734751\pi$
$37$	−3.79897	+	1.57359i	−0.624548	+	0.258696i	0.0478869	+	0.998853i	$0.484751\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	1.08917	−	1.08917i	0.170100	−	0.170100i	−0.616923	−	0.787023i	$-0.711621\pi$
$41$	1.08917	−	1.08917i	0.170100	−	0.170100i	0.787023	+	0.616923i	$0.211621\pi$
$42$		0			0
$43$	2.71012	−	1.12257i	0.413290	−	0.171190i	−0.166343	−	0.986068i	$-0.553196\pi$
$43$	2.71012	−	1.12257i	0.413290	−	0.171190i	0.579633	+	0.814878i	$0.303196\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$			11.1855i			1.63157i	0.578358	+	0.815783i	$0.303694\pi$
$47$			11.1855i			1.63157i	−0.578358	+	0.815783i	$0.696306\pi$
$48$		0			0
$49$		−	2.06113i		−	0.294447i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−3.70104	+	1.53302i	−0.508377	+	0.210577i	−0.622103	−	0.782936i	$-0.713721\pi$
$53$	−3.70104	+	1.53302i	−0.508377	+	0.210577i	0.113726	+	0.993512i	$0.463721\pi$
$54$		0			0
$55$	5.41584	−	5.41584i	0.730272	−	0.730272i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−3.19376	+	1.32290i	−0.415792	+	0.172227i	−0.580765	−	0.814071i	$-0.697246\pi$
$59$	−3.19376	+	1.32290i	−0.415792	+	0.172227i	0.164973	+	0.986298i	$0.447246\pi$
$60$		0			0
$61$	−3.78169	+	9.12981i	−0.484196	+	1.16895i	0.473403	+	0.880846i	$0.343026\pi$
$61$	−3.78169	+	9.12981i	−0.484196	+	1.16895i	−0.957598	+	0.288106i	$0.906974\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$			20.5443i			2.54820i
$66$		0			0
$67$	−10.9492	−	4.53532i	−1.33766	−	0.554077i	−0.404830	−	0.914392i	$-0.632669\pi$
$67$	−10.9492	−	4.53532i	−1.33766	−	0.554077i	−0.932831	+	0.360314i	$0.882669\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	6.83579	−	6.83579i	0.811259	−	0.811259i	−0.173564	−	0.984823i	$-0.555528\pi$
$71$	6.83579	−	6.83579i	0.811259	−	0.811259i	0.984823	+	0.173564i	$0.0555282\pi$
$72$		0			0
$73$	2.94667	+	2.94667i	0.344882	+	0.344882i	0.858199	−	0.513317i	$-0.171584\pi$
$73$	2.94667	+	2.94667i	0.344882	+	0.344882i	−0.513317	+	0.858199i	$0.671584\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	2.22576	−	5.37346i	0.253649	−	0.612362i
$78$		0			0
$79$	−8.79533			−0.989552			−0.494776	−	0.869021i	$-0.664750\pi$
$79$	−8.79533			−0.989552			−0.494776	+	0.869021i	$0.664750\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−13.9866	−	5.79342i	−1.53522	−	0.635911i	−0.554655	−	0.832081i	$-0.687150\pi$
$83$	−13.9866	−	5.79342i	−1.53522	−	0.635911i	−0.980570	+	0.196170i	$0.937150\pi$
$84$		0			0
$85$	−0.583176	−	1.40791i	−0.0632544	−	0.152710i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	7.09089	+	7.09089i	0.751633	+	0.751633i	0.974784	−	0.223151i	$-0.0716343\pi$
$89$	7.09089	+	7.09089i	0.751633	+	0.751633i	−0.223151	+	0.974784i	$0.571634\pi$
$90$		0			0
$91$	5.97019	+	14.4133i	0.625846	+	1.51092i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	22.6192			2.32068
$96$		0			0
$97$	−5.91713			−0.600793			−0.300397	−	0.953814i	$-0.597119\pi$
$97$	−5.91713			−0.600793			−0.300397	+	0.953814i	$0.597119\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−4.62448	−	11.1645i	−0.460153	−	1.11091i	−0.968334	−	0.249657i	$-0.919682\pi$
$101$	−4.62448	−	11.1645i	−0.460153	−	1.11091i	0.508182	−	0.861250i	$-0.330318\pi$
$102$		0			0
$103$	−12.0132	−	12.0132i	−1.18369	−	1.18369i	−0.978780	−	0.204913i	$-0.934309\pi$
$103$	−12.0132	−	12.0132i	−1.18369	−	1.18369i	−0.204913	−	0.978780i	$-0.565691\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−5.56773	−	13.4417i	−0.538253	−	1.29946i	−0.925941	−	0.377667i	$-0.876726\pi$
$107$	−5.56773	−	13.4417i	−0.538253	−	1.29946i	0.387688	−	0.921791i	$-0.373274\pi$
$108$		0			0
$109$	−5.97381	−	2.47443i	−0.572187	−	0.237008i	0.0777792	−	0.996971i	$-0.475217\pi$
$109$	−5.97381	−	2.47443i	−0.572187	−	0.237008i	−0.649966	+	0.759963i	$0.725217\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−10.0445			−0.944908			−0.472454	−	0.881355i	$-0.656632\pi$
$113$	−10.0445			−0.944908			−0.472454	+	0.881355i	$0.656632\pi$
$114$		0			0
$115$	2.14357	−	5.17504i	0.199889	−	0.482575i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−0.818281	−	0.818281i	−0.0750117	−	0.0750117i
$120$		0			0
$121$	2.93496	−	2.93496i	0.266815	−	0.266815i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−3.88069	−	1.60743i	−0.347099	−	0.143773i
$126$		0			0
$127$			12.2276i			1.08503i	0.840047	+	0.542513i	$0.182527\pi$
$127$			12.2276i			1.08503i	−0.840047	+	0.542513i	$0.817473\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−2.18881	+	5.28425i	−0.191237	+	0.461687i	−0.990194	−	0.139702i	$-0.955386\pi$
$131$	−2.18881	+	5.28425i	−0.191237	+	0.461687i	0.798957	+	0.601389i	$0.205386\pi$
$132$		0			0
$133$	15.8690	−	6.57316i	1.37602	−	0.569965i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−3.53314	+	3.53314i	−0.301856	+	0.301856i	−0.841740	−	0.539883i	$-0.818468\pi$
$137$	−3.53314	+	3.53314i	−0.301856	+	0.301856i	0.539883	+	0.841740i	$0.318468\pi$
$138$		0			0
$139$	−4.17495	+	1.72932i	−0.354115	+	0.146679i	−0.552648	−	0.833415i	$-0.686382\pi$
$139$	−4.17495	+	1.72932i	−0.354115	+	0.146679i	0.198533	+	0.980094i	$0.436382\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		−	18.3721i		−	1.53635i
$144$		0			0
$145$		−	16.8325i		−	1.39786i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	15.4396	−	6.39531i	1.26486	−	0.523924i	0.353465	−	0.935448i	$-0.385003\pi$
$149$	15.4396	−	6.39531i	1.26486	−	0.523924i	0.911399	+	0.411524i	$0.135003\pi$
$150$		0			0
$151$	−0.199339	+	0.199339i	−0.0162220	+	0.0162220i	−0.715171	−	0.698949i	$-0.753651\pi$
$151$	−0.199339	+	0.199339i	−0.0162220	+	0.0162220i	0.698949	+	0.715171i	$0.253651\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	4.17747	−	1.73036i	0.335542	−	0.138986i
$156$		0			0
$157$	−2.24745	+	5.42583i	−0.179366	+	0.433028i	−0.987834	−	0.155512i	$-0.950297\pi$
$157$	−2.24745	+	5.42583i	−0.179366	+	0.433028i	0.808468	+	0.588540i	$0.200297\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		−	4.25359i		−	0.335230i
$162$		0			0
$163$	−4.85740	−	2.01200i	−0.380461	−	0.157592i	0.184253	−	0.982879i	$-0.441013\pi$
$163$	−4.85740	−	2.01200i	−0.380461	−	0.157592i	−0.564714	+	0.825287i	$0.691013\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−14.1373	+	14.1373i	−1.09397	+	1.09397i	−0.0988739	+	0.995100i	$0.531524\pi$
$167$	−14.1373	+	14.1373i	−1.09397	+	1.09397i	−0.995100	+	0.0988739i	$0.968476\pi$
$168$		0			0
$169$	25.6537	+	25.6537i	1.97336	+	1.97336i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−3.98598	+	9.62302i	−0.303049	+	0.731625i	0.696847	+	0.717219i	$0.254585\pi$
$173$	−3.98598	+	9.62302i	−0.303049	+	0.731625i	−0.999896	+	0.0144051i	$0.995415\pi$
$174$		0			0
$175$	7.92208			0.598853
$176$		0			0
$177$		0			0
$178$		0			0
$179$	17.3296	+	7.17815i	1.29527	+	0.536520i	0.920553	−	0.390618i	$-0.127739\pi$
$179$	17.3296	+	7.17815i	1.29527	+	0.536520i	0.374721	+	0.927138i	$0.377739\pi$
$180$		0			0
$181$	−1.80823	−	4.36545i	−0.134404	−	0.324481i	0.842320	−	0.538977i	$-0.181189\pi$
$181$	−1.80823	−	4.36545i	−0.134404	−	0.324481i	−0.976725	+	0.214496i	$0.931189\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	8.50928	+	8.50928i	0.625614	+	0.625614i
$186$		0			0
$187$	0.521516	+	1.25905i	0.0381370	+	0.0920709i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	6.95000			0.502885			0.251442	−	0.967872i	$-0.419095\pi$
$191$	6.95000			0.502885			0.251442	+	0.967872i	$0.419095\pi$
$192$		0			0
$193$	10.4125			0.749511			0.374756	−	0.927124i	$-0.377727\pi$
$193$	10.4125			0.749511			0.374756	+	0.927124i	$0.377727\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−3.52349	−	8.50645i	−0.251038	−	0.606059i	0.747250	−	0.664543i	$-0.231374\pi$
$197$	−3.52349	−	8.50645i	−0.251038	−	0.606059i	−0.998288	+	0.0584832i	$0.981374\pi$
$198$		0			0
$199$	5.74862	+	5.74862i	0.407509	+	0.407509i	0.880869	−	0.473360i	$-0.156959\pi$
$199$	5.74862	+	5.74862i	0.407509	+	0.407509i	−0.473360	+	0.880869i	$0.656959\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−4.89153	−	11.8092i	−0.343318	−	0.828843i
$204$		0			0
$205$	−4.16470	−	1.72507i	−0.290875	−	0.120484i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−20.2276			−1.39917
$210$		0			0
$211$	−3.53929	+	8.54461i	−0.243655	+	0.588235i	−0.997640	−	0.0686560i	$-0.978129\pi$
$211$	−3.53929	+	8.54461i	−0.243655	+	0.588235i	0.753985	+	0.656891i	$0.228129\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−6.07037	−	6.07037i	−0.413996	−	0.413996i
$216$		0			0
$217$	2.42795	−	2.42795i	0.164820	−	0.164820i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−3.37717	−	1.39887i	−0.227173	−	0.0940982i
$222$		0			0
$223$		−	11.5406i		−	0.772814i	−0.922328	−	0.386407i	$-0.873716\pi$
$223$		−	11.5406i		−	0.772814i	0.922328	−	0.386407i	$-0.126284\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−5.48691	+	13.2466i	−0.364179	+	0.879205i	0.630501	+	0.776188i	$0.282849\pi$
$227$	−5.48691	+	13.2466i	−0.364179	+	0.879205i	−0.994680	+	0.103017i	$0.967151\pi$
$228$		0			0
$229$	4.29256	−	1.77804i	0.283661	−	0.117496i	−0.236317	−	0.971676i	$-0.575940\pi$
$229$	4.29256	−	1.77804i	0.283661	−	0.117496i	0.519977	+	0.854180i	$0.325940\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	9.05679	−	9.05679i	0.593330	−	0.593330i	−0.345199	−	0.938529i	$-0.612189\pi$
$233$	9.05679	−	9.05679i	0.593330	−	0.593330i	0.938529	+	0.345199i	$0.112189\pi$
$234$		0			0
$235$	30.2430	−	12.5271i	1.97284	−	0.817177i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		−	8.04485i		−	0.520378i	−0.965558	−	0.260189i	$-0.916215\pi$
$239$		−	8.04485i		−	0.520378i	0.965558	−	0.260189i	$-0.0837849\pi$
$240$		0			0
$241$		−	19.0228i		−	1.22536i	−0.790329	−	0.612682i	$-0.790091\pi$
$241$		−	19.0228i		−	1.22536i	0.790329	−	0.612682i	$-0.209909\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−5.57284	+	2.30835i	−0.356036	+	0.147475i
$246$		0			0
$247$	38.3654	−	38.3654i	2.44113	−	2.44113i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−7.25290	+	3.00425i	−0.457799	+	0.189626i	−0.599651	−	0.800261i	$-0.704694\pi$
$251$	−7.25290	+	3.00425i	−0.457799	+	0.189626i	0.141853	+	0.989888i	$0.454694\pi$
$252$		0			0
$253$	−1.91693	+	4.62787i	−0.120516	+	0.290952i
$254$		0			0
$255$		0			0
$256$		0			0
$257$		−	23.0041i		−	1.43496i	−0.696581	−	0.717478i	$-0.745297\pi$
$257$		−	23.0041i		−	1.43496i	0.696581	−	0.717478i	$-0.254703\pi$
$258$		0			0
$259$	8.44268	+	3.49707i	0.524603	+	0.217298i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	1.44247	−	1.44247i	0.0889468	−	0.0889468i	−0.661233	−	0.750180i	$-0.729967\pi$
$263$	1.44247	−	1.44247i	0.0889468	−	0.0889468i	0.750180	+	0.661233i	$0.229967\pi$
$264$		0			0
$265$	8.28991	+	8.28991i	0.509245	+	0.509245i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−1.77582	+	4.28722i	−0.108274	+	0.261396i	−0.968725	−	0.248137i	$-0.920182\pi$
$269$	−1.77582	+	4.28722i	−0.108274	+	0.261396i	0.860451	+	0.509533i	$0.170182\pi$
$270$		0			0
$271$	−2.52337			−0.153284			−0.0766419	−	0.997059i	$-0.524420\pi$
$271$	−2.52337			−0.153284			−0.0766419	+	0.997059i	$0.524420\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−8.61916	−	3.57017i	−0.519755	−	0.215290i
$276$		0			0
$277$	−3.50691	−	8.46643i	−0.210710	−	0.508699i	0.782823	−	0.622245i	$-0.213779\pi$
$277$	−3.50691	−	8.46643i	−0.210710	−	0.508699i	−0.993533	+	0.113546i	$0.963779\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−5.34778	−	5.34778i	−0.319022	−	0.319022i	0.529369	−	0.848391i	$-0.322429\pi$
$281$	−5.34778	−	5.34778i	−0.319022	−	0.319022i	−0.848391	+	0.529369i	$0.822429\pi$
$282$		0			0
$283$	10.0243	+	24.2009i	0.595885	+	1.43859i	0.877741	+	0.479136i	$0.159050\pi$
$283$	10.0243	+	24.2009i	0.595885	+	1.43859i	−0.281856	+	0.959457i	$0.590950\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−3.42315			−0.202062
$288$		0			0
$289$	−16.7289			−0.984050
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−6.12975	−	14.7985i	−0.358104	−	0.864539i	−0.995567	−	0.0940580i	$-0.970016\pi$
$293$	−6.12975	−	14.7985i	−0.358104	−	0.864539i	0.637463	−	0.770481i	$-0.279984\pi$
$294$		0			0
$295$	7.15366	+	7.15366i	0.416502	+	0.416502i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−5.14180	−	12.4134i	−0.297358	−	0.717886i
$300$		0			0
$301$	−6.02286	−	2.49475i	−0.347152	−	0.143795i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	28.9203			1.65597
$306$		0			0
$307$	6.63881	−	16.0275i	0.378897	−	0.914738i	−0.613276	−	0.789869i	$-0.710149\pi$
$307$	6.63881	−	16.0275i	0.378897	−	0.914738i	0.992173	−	0.124870i	$-0.0398513\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−15.0561	−	15.0561i	−0.853754	−	0.853754i	0.136839	−	0.990593i	$-0.456306\pi$
$311$	−15.0561	−	15.0561i	−0.853754	−	0.853754i	−0.990593	+	0.136839i	$0.956306\pi$
$312$		0			0
$313$	4.19455	−	4.19455i	0.237090	−	0.237090i	−0.578554	−	0.815644i	$-0.696383\pi$
$313$	4.19455	−	4.19455i	0.237090	−	0.237090i	0.815644	+	0.578554i	$0.196383\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	13.3097	+	5.51307i	0.747549	+	0.309645i	0.723741	−	0.690072i	$-0.242421\pi$
$317$	13.3097	+	5.51307i	0.747549	+	0.309645i	0.0238078	+	0.999717i	$0.492421\pi$
$318$		0			0
$319$			15.0527i			0.842791i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−1.54015	+	3.71826i	−0.0856964	+	0.206889i
$324$		0			0
$325$	23.1193	−	9.57633i	1.28243	−	0.531199i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	17.5773	−	17.5773i	0.969069	−	0.969069i
$330$		0			0
$331$	−5.98959	+	2.48097i	−0.329218	+	0.136366i	−0.541169	−	0.840914i	$-0.682018\pi$
$331$	−5.98959	+	2.48097i	−0.329218	+	0.136366i	0.211951	+	0.977280i	$0.432018\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$			34.6836i			1.89497i
$336$		0			0
$337$			29.6988i			1.61779i	0.587950	+	0.808897i	$0.299935\pi$
$337$			29.6988i			1.61779i	−0.587950	+	0.808897i	$0.700065\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−3.73578	+	1.54741i	−0.202304	+	0.0837969i
$342$		0			0
$343$	−14.2391	+	14.2391i	−0.768837	+	0.768837i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	29.8947	−	12.3828i	1.60483	−	0.664744i	0.612745	−	0.790281i	$-0.290065\pi$
$347$	29.8947	−	12.3828i	1.60483	−	0.664744i	0.992089	+	0.125537i	$0.0400654\pi$
$348$		0			0
$349$	−8.37790	+	20.2260i	−0.448459	+	1.08268i	0.524441	+	0.851447i	$0.324274\pi$
$349$	−8.37790	+	20.2260i	−0.448459	+	1.08268i	−0.972899	+	0.231228i	$0.925726\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$		−	2.58104i		−	0.137375i	−0.997638	−	0.0686874i	$-0.978119\pi$
$353$		−	2.58104i		−	0.137375i	0.997638	−	0.0686874i	$-0.0218811\pi$
$354$		0			0
$355$	−26.1382	−	10.8268i	−1.38727	−	0.574627i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−11.3463	+	11.3463i	−0.598834	+	0.598834i	−0.940002	−	0.341168i	$-0.889177\pi$
$359$	−11.3463	+	11.3463i	−0.598834	+	0.598834i	0.341168	+	0.940002i	$0.389177\pi$
$360$		0			0
$361$	−28.8051	−	28.8051i	−1.51606	−	1.51606i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	4.66705	−	11.2673i	0.244285	−	0.589755i
$366$		0			0
$367$	−8.71339			−0.454835			−0.227418	−	0.973797i	$-0.573028\pi$
$367$	−8.71339			−0.454835			−0.227418	+	0.973797i	$0.573028\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	8.22503	+	3.40692i	0.427022	+	0.176878i
$372$		0			0
$373$	1.56395	+	3.77570i	0.0809781	+	0.195498i	0.959183	−	0.282786i	$-0.0912587\pi$
$373$	1.56395	+	3.77570i	0.0809781	+	0.195498i	−0.878205	+	0.478285i	$0.841259\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−28.5503	−	28.5503i	−1.47041	−	1.47041i
$378$		0			0
$379$	−8.85643	−	21.3813i	−0.454925	−	1.09828i	−0.970427	−	0.241397i	$-0.922395\pi$
$379$	−8.85643	−	21.3813i	−0.454925	−	1.09828i	0.515502	−	0.856888i	$-0.327605\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−3.90996			−0.199790			−0.0998949	−	0.994998i	$-0.531851\pi$
$383$	−3.90996			−0.199790			−0.0998949	+	0.994998i	$0.531851\pi$
$384$		0			0
$385$	−17.0214			−0.867490
$386$		0			0
$387$		0			0
$388$		0			0
$389$	3.92740	+	9.48159i	0.199127	+	0.480736i	0.991627	−	0.129137i	$-0.0412206\pi$
$389$	3.92740	+	9.48159i	0.199127	+	0.480736i	−0.792500	+	0.609872i	$0.791221\pi$
$390$		0			0
$391$	0.704742	+	0.704742i	0.0356403	+	0.0356403i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	9.85028	+	23.7807i	0.495621	+	1.19654i
$396$		0			0
$397$	15.8590	+	6.56903i	0.795942	+	0.329690i	0.743330	−	0.668925i	$-0.233245\pi$
$397$	15.8590	+	6.56903i	0.795942	+	0.329690i	0.0526124	+	0.998615i	$0.483245\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−18.8741			−0.942529			−0.471265	−	0.881992i	$-0.656202\pi$
$401$	−18.8741			−0.942529			−0.471265	+	0.881992i	$0.656202\pi$
$402$		0			0
$403$	4.15064	−	10.0205i	0.206758	−	0.499158i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−7.60957	−	7.60957i	−0.377193	−	0.377193i
$408$		0			0
$409$	−9.68899	+	9.68899i	−0.479089	+	0.479089i	−0.904840	−	0.425751i	$-0.860010\pi$
$409$	−9.68899	+	9.68899i	−0.479089	+	0.479089i	0.425751	+	0.904840i	$0.360010\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	7.09768	+	2.93995i	0.349254	+	0.144666i
$414$		0			0
$415$			44.3049i			2.17484i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	13.8806	−	33.5108i	0.678114	−	1.63711i	−0.0893350	−	0.996002i	$-0.528474\pi$
$419$	13.8806	−	33.5108i	0.678114	−	1.63711i	0.767449	−	0.641110i	$-0.221526\pi$
$420$		0			0
$421$	23.7882	−	9.85339i	1.15937	−	0.480225i	0.281702	−	0.959502i	$-0.409101\pi$
$421$	23.7882	−	9.85339i	1.15937	−	0.480225i	0.877664	+	0.479277i	$0.159101\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−1.31254	+	1.31254i	−0.0636678	+	0.0636678i
$426$		0			0
$427$	20.2897	−	8.40427i	0.981887	−	0.406711i
$428$		0			0
$429$		0			0
$430$		0			0
$431$		−	1.02776i		−	0.0495056i	−0.999694	−	0.0247528i	$-0.992120\pi$
$431$		−	1.02776i		−	0.0495056i	0.999694	−	0.0247528i	$-0.00787987\pi$
$432$		0			0
$433$		−	21.3662i		−	1.02680i	−0.858151	−	0.513398i	$-0.828386\pi$
$433$		−	21.3662i		−	1.02680i	0.858151	−	0.513398i	$-0.171614\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−13.6671	+	5.66111i	−0.653787	+	0.270807i
$438$		0			0
$439$	−13.4689	+	13.4689i	−0.642835	+	0.642835i	−0.951251	−	0.308417i	$-0.900201\pi$
$439$	−13.4689	+	13.4689i	−0.642835	+	0.642835i	0.308417	+	0.951251i	$0.400201\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−4.92612	+	2.04047i	−0.234047	+	0.0969454i	−0.496625	−	0.867965i	$-0.665427\pi$
$443$	−4.92612	+	2.04047i	−0.234047	+	0.0969454i	0.262578	+	0.964911i	$0.415427\pi$
$444$		0			0
$445$	11.2308	−	27.1136i	0.532393	−	1.28531i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			22.2980i			1.05231i	0.850390	+	0.526153i	$0.176366\pi$
$449$			22.2980i			1.05231i	−0.850390	+	0.526153i	$0.823634\pi$
$450$		0			0
$451$	3.72436	+	1.54268i	0.175373	+	0.0726419i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	32.2842	−	32.2842i	1.51351	−	1.51351i
$456$		0			0
$457$	−6.58505	−	6.58505i	−0.308035	−	0.308035i	0.536112	−	0.844147i	$-0.319893\pi$
$457$	−6.58505	−	6.58505i	−0.308035	−	0.308035i	−0.844147	+	0.536112i	$0.819893\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−14.3380	+	34.6150i	−0.667788	+	1.61218i	0.117515	+	0.993071i	$0.462507\pi$
$461$	−14.3380	+	34.6150i	−0.667788	+	1.61218i	−0.785303	+	0.619112i	$0.787493\pi$
$462$		0			0
$463$	14.4728			0.672607			0.336304	−	0.941754i	$-0.390823\pi$
$463$	14.4728			0.672607			0.336304	+	0.941754i	$0.390823\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	9.73511	+	4.03241i	0.450487	+	0.186598i	0.596380	−	0.802703i	$-0.296605\pi$
$467$	9.73511	+	4.03241i	0.450487	+	0.186598i	−0.145892	+	0.989300i	$0.546605\pi$
$468$		0			0
$469$	10.0791	+	24.3331i	0.465410	+	1.12360i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	5.42854	+	5.42854i	0.249605	+	0.249605i
$474$		0			0
$475$	−10.5435	−	25.4543i	−0.483770	−	1.16792i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−30.2779			−1.38343			−0.691717	−	0.722169i	$-0.743145\pi$
$479$	−30.2779			−1.38343			−0.691717	+	0.722169i	$0.743145\pi$
$480$		0			0
$481$	28.8659			1.31617
$482$		0			0
$483$		0			0
$484$		0			0
$485$	6.62685	+	15.9986i	0.300910	+	0.726461i
$486$		0			0
$487$	−11.6078	−	11.6078i	−0.526000	−	0.526000i	0.393377	−	0.919377i	$-0.371307\pi$
$487$	−11.6078	−	11.6078i	−0.526000	−	0.526000i	−0.919377	+	0.393377i	$0.871307\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	4.08448	+	9.86082i	0.184330	+	0.445012i	0.988850	−	0.148913i	$-0.0475774\pi$
$491$	4.08448	+	9.86082i	0.184330	+	0.445012i	−0.804520	+	0.593925i	$0.797577\pi$
$492$		0			0
$493$	2.76700	+	1.14613i	0.124620	+	0.0516191i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−21.4841			−0.963695
$498$		0			0
$499$	−10.5238	+	25.4066i	−0.471109	+	1.13736i	0.492565	+	0.870276i	$0.336059\pi$
$499$	−10.5238	+	25.4066i	−0.471109	+	1.13736i	−0.963674	+	0.267082i	$0.913941\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	16.9786	+	16.9786i	0.757040	+	0.757040i	0.975783	−	0.218742i	$-0.0701954\pi$
$503$	16.9786	+	16.9786i	0.757040	+	0.757040i	−0.218742	+	0.975783i	$0.570195\pi$
$504$		0			0
$505$	−25.0072	+	25.0072i	−1.11280	+	1.11280i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	25.0892	+	10.3923i	1.11206	+	0.460630i	0.861646	−	0.507509i	$-0.169434\pi$
$509$	25.0892	+	10.3923i	1.11206	+	0.460630i	0.250413	+	0.968139i	$0.419434\pi$
$510$		0			0
$511$		−	9.26105i		−	0.409685i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−19.0269	+	45.9351i	−0.838427	+	2.02414i
$516$		0			0
$517$	−27.0454	+	11.2026i	−1.18946	+	0.492688i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−3.51029	+	3.51029i	−0.153789	+	0.153789i	−0.779808	−	0.626019i	$-0.784683\pi$
$521$	−3.51029	+	3.51029i	−0.153789	+	0.153789i	0.626019	+	0.779808i	$0.284683\pi$
$522$		0			0
$523$	2.65762	−	1.10082i	0.116209	−	0.0481355i	−0.323821	−	0.946118i	$-0.604968\pi$
$523$	2.65762	−	1.10082i	0.116209	−	0.0481355i	0.440031	+	0.897983i	$0.354968\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$			0.804535i			0.0350461i
$528$		0			0
$529$		−	19.3366i		−	0.840722i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−9.98990	+	4.13795i	−0.432711	+	0.179235i
$534$		0			0
$535$	−30.1079	+	30.1079i	−1.30168	+	1.30168i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	4.98361	−	2.06428i	0.214659	−	0.0889148i
$540$		0			0
$541$	8.33435	−	20.1209i	0.358322	−	0.865066i	−0.637214	−	0.770687i	$-0.719913\pi$
$541$	8.33435	−	20.1209i	0.358322	−	0.865066i	0.995536	−	0.0943790i	$-0.0300866\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$			18.9231i			0.810577i
$546$		0			0
$547$	−15.3897	−	6.37463i	−0.658017	−	0.272560i	0.0285868	−	0.999591i	$-0.490899\pi$
$547$	−15.3897	−	6.37463i	−0.658017	−	0.272560i	−0.686604	+	0.727032i	$0.740899\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−31.4337	+	31.4337i	−1.33912	+	1.33912i
$552$		0			0
$553$	13.8214	+	13.8214i	0.587744	+	0.587744i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	3.13010	−	7.55673i	0.132627	−	0.320189i	−0.843590	−	0.536989i	$-0.819562\pi$
$557$	3.13010	−	7.55673i	0.132627	−	0.320189i	0.976216	+	0.216800i	$0.0695618\pi$
$558$		0			0
$559$	−20.5924			−0.870968
$560$		0			0
$561$		0			0
$562$		0			0
$563$	0.345832	+	0.143248i	0.0145751	+	0.00603719i	0.389959	−	0.920832i	$-0.372489\pi$
$563$	0.345832	+	0.143248i	0.0145751	+	0.00603719i	−0.375384	+	0.926869i	$0.622489\pi$
$564$		0			0
$565$	11.2493	+	27.1582i	0.473261	+	1.14255i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	31.8289	+	31.8289i	1.33434	+	1.33434i	0.901447	+	0.432890i	$0.142506\pi$
$569$	31.8289	+	31.8289i	1.33434	+	1.33434i	0.432890	+	0.901447i	$0.357494\pi$
$570$		0			0
$571$	−7.49818	−	18.1022i	−0.313789	−	0.757554i	−0.999558	−	0.0297343i	$-0.990534\pi$
$571$	−7.49818	−	18.1022i	−0.313789	−	0.757554i	0.685769	−	0.727819i	$-0.259466\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−6.82287			−0.284533
$576$		0			0
$577$	−19.6358			−0.817447			−0.408724	−	0.912658i	$-0.634026\pi$
$577$	−19.6358			−0.817447			−0.408724	+	0.912658i	$0.634026\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	12.8751	+	31.0831i	0.534147	+	1.28955i
$582$		0			0
$583$	−7.41340	−	7.41340i	−0.307032	−	0.307032i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	8.01640	+	19.3533i	0.330872	+	0.798796i	0.998523	+	0.0543221i	$0.0172998\pi$
$587$	8.01640	+	19.3533i	0.330872	+	0.798796i	−0.667651	+	0.744474i	$0.732700\pi$
$588$		0			0
$589$	−11.0326	−	4.56984i	−0.454589	−	0.188297i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	26.2206			1.07675			0.538376	−	0.842704i	$-0.319038\pi$
$593$	26.2206			1.07675			0.538376	+	0.842704i	$0.319038\pi$
$594$		0			0
$595$	−1.29603	+	3.12888i	−0.0531319	+	0.128272i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−13.4497	−	13.4497i	−0.549542	−	0.549542i	0.376767	−	0.926308i	$-0.377036\pi$
$599$	−13.4497	−	13.4497i	−0.549542	−	0.549542i	−0.926308	+	0.376767i	$0.877036\pi$
$600$		0			0
$601$	−10.7760	+	10.7760i	−0.439562	+	0.439562i	−0.891864	−	0.452303i	$-0.850603\pi$
$601$	−10.7760	+	10.7760i	−0.439562	+	0.439562i	0.452303	+	0.891864i	$0.350603\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−11.2225	−	4.64851i	−0.456259	−	0.188989i
$606$		0			0
$607$		−	5.71428i		−	0.231936i	−0.993253	−	0.115968i	$-0.963003\pi$
$607$		−	5.71428i		−	0.231936i	0.993253	−	0.115968i	$-0.0369969\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	30.0488	−	72.5443i	1.21565	−	2.93483i
$612$		0			0
$613$	−25.0980	+	10.3959i	−1.01370	+	0.419887i	−0.826802	−	0.562493i	$-0.809842\pi$
$613$	−25.0980	+	10.3959i	−1.01370	+	0.419887i	−0.186895	+	0.982380i	$0.559842\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	7.07388	−	7.07388i	0.284784	−	0.284784i	−0.550230	−	0.835013i	$-0.685460\pi$
$617$	7.07388	−	7.07388i	0.284784	−	0.284784i	0.835013	+	0.550230i	$0.185460\pi$
$618$		0			0
$619$	−32.9781	+	13.6600i	−1.32550	+	0.549041i	−0.929369	−	0.369151i	$-0.879648\pi$
$619$	−32.9781	+	13.6600i	−1.32550	+	0.549041i	−0.396134	+	0.918193i	$0.629648\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		−	22.2859i		−	0.892865i
$624$		0			0
$625$			30.1164i			1.20465i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−1.97820	+	0.819397i	−0.0788760	+	0.0326715i
$630$		0			0
$631$	2.15849	−	2.15849i	0.0859280	−	0.0859280i	−0.662836	−	0.748764i	$-0.730647\pi$
$631$	2.15849	−	2.15849i	0.0859280	−	0.0859280i	0.748764	+	0.662836i	$0.230647\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	33.0608	−	13.6943i	1.31198	−	0.543440i
$636$		0			0
$637$	−5.53705	+	13.3676i	−0.219386	+	0.529645i
$638$		0			0
$639$		0			0
$640$		0			0
$641$		−	38.0487i		−	1.50283i	−0.659827	−	0.751417i	$-0.729371\pi$
$641$		−	38.0487i		−	1.50283i	0.659827	−	0.751417i	$-0.270629\pi$
$642$		0			0
$643$	16.7464	+	6.93660i	0.660414	+	0.273553i	0.687613	−	0.726077i	$-0.258659\pi$
$643$	16.7464	+	6.93660i	0.660414	+	0.273553i	−0.0271985	+	0.999630i	$0.508659\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−1.77745	+	1.77745i	−0.0698786	+	0.0698786i	−0.741182	−	0.671304i	$-0.765735\pi$
$647$	−1.77745	+	1.77745i	−0.0698786	+	0.0698786i	0.671304	+	0.741182i	$0.265735\pi$
$648$		0			0
$649$	−6.39729	−	6.39729i	−0.251116	−	0.251116i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−8.13694	+	19.6443i	−0.318423	+	0.768742i	0.680915	+	0.732363i	$0.261582\pi$
$653$	−8.13694	+	19.6443i	−0.318423	+	0.768742i	−0.999338	+	0.0363791i	$0.988418\pi$
$654$		0			0
$655$	16.7388			0.654039
$656$		0			0
$657$		0			0
$658$		0			0
$659$	5.72478	+	2.37128i	0.223006	+	0.0923720i	0.491389	−	0.870940i	$-0.336489\pi$
$659$	5.72478	+	2.37128i	0.223006	+	0.0923720i	−0.268383	+	0.963312i	$0.586489\pi$
$660$		0			0
$661$	−14.6754	−	35.4296i	−0.570808	−	1.37805i	−0.900868	−	0.434092i	$-0.857069\pi$
$661$	−14.6754	−	35.4296i	−0.570808	−	1.37805i	0.330061	−	0.943960i	$-0.392931\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−35.5448	−	35.5448i	−1.37837	−	1.37837i
$666$		0			0
$667$	4.21281	+	10.1706i	0.163121	+	0.393808i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−25.8625			−0.998411
$672$		0			0
$673$	−32.6272			−1.25768			−0.628842	−	0.777533i	$-0.716471\pi$
$673$	−32.6272			−1.25768			−0.628842	+	0.777533i	$0.716471\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	11.1224	+	26.8518i	0.427468	+	1.03200i	0.980088	+	0.198565i	$0.0636281\pi$
$677$	11.1224	+	26.8518i	0.427468	+	1.03200i	−0.552620	+	0.833433i	$0.686372\pi$
$678$		0			0
$679$	9.29844	+	9.29844i	0.356841	+	0.356841i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	1.38525	+	3.34428i	0.0530050	+	0.127965i	0.948164	−	0.317782i	$-0.102938\pi$
$683$	1.38525	+	3.34428i	0.0530050	+	0.127965i	−0.895159	+	0.445747i	$0.852938\pi$
$684$		0			0
$685$	13.5098	+	5.59593i	0.516181	+	0.213809i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	28.1218			1.07135
$690$		0			0
$691$	13.4910	−	32.5702i	0.513223	−	1.23903i	−0.428775	−	0.903411i	$-0.641055\pi$
$691$	13.4910	−	32.5702i	0.513223	−	1.23903i	0.941998	−	0.335618i	$-0.108945\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	9.35143	+	9.35143i	0.354720	+	0.354720i
$696$		0			0
$697$	0.567153	−	0.567153i	0.0214825	−	0.0214825i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−3.25729	−	1.34921i	−0.123026	−	0.0509590i	0.320321	−	0.947309i	$-0.396209\pi$
$701$	−3.25729	−	1.34921i	−0.123026	−	0.0509590i	−0.443347	+	0.896350i	$0.646209\pi$
$702$		0			0
$703$		−	31.7813i		−	1.19865i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−10.2772	+	24.8115i	−0.386515	+	0.933131i
$708$		0			0
$709$	−27.0551	+	11.2066i	−1.01607	+	0.420872i	−0.827667	−	0.561219i	$-0.810332\pi$
$709$	−27.0551	+	11.2066i	−1.01607	+	0.420872i	−0.188407	+	0.982091i	$0.560332\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−2.09107	+	2.09107i	−0.0783110	+	0.0783110i
$714$		0			0
$715$	−49.6742	+	20.5757i	−1.85771	+	0.769488i
$716$		0			0
$717$		0			0
$718$		0			0
$719$		−	6.87831i		−	0.256518i	−0.991741	−	0.128259i	$-0.959061\pi$
$719$		−	6.87831i		−	0.256518i	0.991741	−	0.128259i	$-0.0409389\pi$
$720$		0			0
$721$			37.7561i			1.40611i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−18.9422	+	7.84614i	−0.703497	+	0.291398i
$726$		0			0
$727$	−8.61474	+	8.61474i	−0.319503	+	0.319503i	−0.848576	−	0.529073i	$-0.822540\pi$
$727$	−8.61474	+	8.61474i	−0.319503	+	0.319503i	0.529073	+	0.848576i	$0.322540\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	1.41121	−	0.584544i	0.0521956	−	0.0216201i
$732$		0			0
$733$	6.86842	−	16.5818i	0.253691	−	0.612464i	−0.744806	−	0.667282i	$-0.767458\pi$
$733$	6.86842	−	16.5818i	0.253691	−	0.612464i	0.998496	+	0.0548178i	$0.0174578\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	31.0165i		−	1.14251i
$738$		0			0
$739$	−8.65828	−	3.58638i	−0.318500	−	0.131927i	0.217706	−	0.976014i	$-0.430143\pi$
$739$	−8.65828	−	3.58638i	−0.318500	−	0.131927i	−0.536205	+	0.844088i	$0.680143\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−5.87413	+	5.87413i	−0.215501	+	0.215501i	−0.806599	−	0.591098i	$-0.798694\pi$
$743$	−5.87413	+	5.87413i	−0.215501	+	0.215501i	0.591098	+	0.806599i	$0.298694\pi$
$744$		0			0
$745$	−34.5830	−	34.5830i	−1.26702	−	1.26702i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−12.3735	+	29.8723i	−0.452118	+	1.09151i
$750$		0			0
$751$	−3.89687			−0.142199			−0.0710993	−	0.997469i	$-0.522651\pi$
$751$	−3.89687			−0.142199			−0.0710993	+	0.997469i	$0.522651\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	0.762219	+	0.315721i	0.0277400	+	0.0114903i
$756$		0			0
$757$	−4.04702	−	9.77036i	−0.147091	−	0.355110i	0.833112	−	0.553105i	$-0.186557\pi$
$757$	−4.04702	−	9.77036i	−0.147091	−	0.355110i	−0.980203	+	0.197995i	$0.936557\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−13.3848	−	13.3848i	−0.485198	−	0.485198i	0.421589	−	0.906787i	$-0.361472\pi$
$761$	−13.3848	−	13.3848i	−0.485198	−	0.485198i	−0.906787	+	0.421589i	$0.861472\pi$
$762$		0			0
$763$	5.49908	+	13.2759i	0.199080	+	0.480621i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	24.2673			0.876241
$768$		0			0
$769$	5.94152			0.214257			0.107128	−	0.994245i	$-0.465834\pi$
$769$	5.94152			0.214257			0.107128	+	0.994245i	$0.465834\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	3.97648	+	9.60006i	0.143024	+	0.345290i	0.979117	−	0.203297i	$-0.0651658\pi$
$773$	3.97648	+	9.60006i	0.143024	+	0.345290i	−0.836093	+	0.548588i	$0.815166\pi$
$774$		0			0
$775$	−3.89450	−	3.89450i	−0.139895	−	0.139895i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	4.55587	+	10.9988i	0.163231	+	0.394075i
$780$		0			0
$781$	23.3746	+	9.68206i	0.836408	+	0.346451i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	17.1873			0.613440
$786$		0			0
$787$	−6.79001	+	16.3925i	−0.242038	+	0.584331i	−0.997485	−	0.0708787i	$-0.977420\pi$
$787$	−6.79001	+	16.3925i	−0.242038	+	0.584331i	0.755447	+	0.655210i	$0.227420\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	15.7844	+	15.7844i	0.561228	+	0.561228i
$792$		0			0
$793$	49.0530	−	49.0530i	1.74192	−	1.74192i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−8.96338	−	3.71275i	−0.317499	−	0.131512i	0.218242	−	0.975895i	$-0.429968\pi$
$797$	−8.96338	−	3.71275i	−0.317499	−	0.131512i	−0.535741	+	0.844382i	$0.679968\pi$
$798$		0			0
$799$			5.82448i			0.206055i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−4.17360	+	10.0760i	−0.147283	+	0.355573i
$804$		0			0
$805$	−11.5008	+	4.76378i	−0.405349	+	0.167901i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−23.4525	+	23.4525i	−0.824546	+	0.824546i	−0.986756	−	0.162210i	$-0.948138\pi$
$809$	−23.4525	+	23.4525i	−0.824546	+	0.824546i	0.162210	+	0.986756i	$0.448138\pi$
$810$		0			0
$811$	−17.8512	+	7.39420i	−0.626840	+	0.259645i	−0.673410	−	0.739270i	$-0.735171\pi$
$811$	−17.8512	+	7.39420i	−0.626840	+	0.259645i	0.0465700	+	0.998915i	$0.485171\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$			15.3867i			0.538972i
$816$		0			0
$817$			22.6722i			0.793201i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	44.1323	−	18.2802i	1.54023	−	0.637984i	0.558712	−	0.829362i	$-0.311296\pi$
$821$	44.1323	−	18.2802i	1.54023	−	0.637984i	0.981516	+	0.191378i	$0.0612956\pi$
$822$		0			0
$823$	24.6647	−	24.6647i	0.859758	−	0.859758i	−0.131551	−	0.991309i	$-0.541996\pi$
$823$	24.6647	−	24.6647i	0.859758	−	0.859758i	0.991309	+	0.131551i	$0.0419958\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−48.5767	+	20.1211i	−1.68918	+	0.699680i	−0.999697	−	0.0246236i	$-0.992161\pi$
$827$	−48.5767	+	20.1211i	−1.68918	+	0.699680i	−0.689481	+	0.724304i	$0.742161\pi$
$828$		0			0
$829$	−7.29929	+	17.6220i	−0.253515	+	0.612039i	−0.998483	−	0.0550611i	$-0.982465\pi$
$829$	−7.29929	+	17.6220i	−0.253515	+	0.612039i	0.744968	+	0.667100i	$0.232465\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		−	1.07327i		−	0.0371865i
$834$		0			0
$835$	54.0570	+	22.3912i	1.87072	+	0.774878i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	5.24139	−	5.24139i	0.180953	−	0.180953i	−0.610818	−	0.791771i	$-0.709159\pi$
$839$	5.24139	−	5.24139i	0.180953	−	0.180953i	0.791771	+	0.610818i	$0.209159\pi$
$840$		0			0
$841$	2.88586	+	2.88586i	0.0995125	+	0.0995125i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	40.6313	−	98.0926i	1.39776	−	3.37449i
$846$		0			0
$847$	−9.22425			−0.316949
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−7.27123	−	3.01184i	−0.249255	−	0.103245i
$852$		0			0
$853$	−4.60778	−	11.1242i	−0.157767	−	0.380884i	0.825155	−	0.564907i	$-0.191088\pi$
$853$	−4.60778	−	11.1242i	−0.157767	−	0.380884i	−0.982922	+	0.184023i	$0.941088\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	26.4017	+	26.4017i	0.901866	+	0.901866i	0.995598	−	0.0937316i	$-0.0298795\pi$
$857$	26.4017	+	26.4017i	0.901866	+	0.901866i	−0.0937316	+	0.995598i	$0.529880\pi$
$858$		0			0
$859$	3.63668	+	8.77971i	0.124082	+	0.299560i	0.973698	−	0.227841i	$-0.0731666\pi$
$859$	3.63668	+	8.77971i	0.124082	+	0.299560i	−0.849617	+	0.527401i	$0.823167\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−15.7981			−0.537773			−0.268887	−	0.963172i	$-0.586656\pi$
$863$	−15.7981			−0.537773			−0.268887	+	0.963172i	$0.586656\pi$
$864$		0			0
$865$	30.4826			1.03644
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−8.80879	−	21.2663i	−0.298818	−	0.721410i
$870$		0			0
$871$	58.8285	+	58.8285i	1.99333	+	1.99333i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	3.57229	+	8.62427i	0.120765	+	0.291554i
$876$		0			0
$877$	4.17572	+	1.72964i	0.141004	+	0.0584058i	0.452070	−	0.891983i	$-0.350686\pi$
$877$	4.17572	+	1.72964i	0.141004	+	0.0584058i	−0.311066	+	0.950388i	$0.600686\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−23.9005			−0.805228			−0.402614	−	0.915370i	$-0.631898\pi$
$881$	−23.9005			−0.805228			−0.402614	+	0.915370i	$0.631898\pi$
$882$		0			0
$883$	15.1690	−	36.6212i	0.510477	−	1.23240i	−0.433129	−	0.901332i	$-0.642591\pi$
$883$	15.1690	−	36.6212i	0.510477	−	1.23240i	0.943606	−	0.331069i	$-0.107409\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	26.0807	+	26.0807i	0.875704	+	0.875704i	0.993087	−	0.117383i	$-0.0374505\pi$
$887$	26.0807	+	26.0807i	0.875704	+	0.875704i	−0.117383	+	0.993087i	$0.537451\pi$
$888$		0			0
$889$	19.2150	−	19.2150i	0.644451	−	0.644451i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−79.8710	−	33.0837i	−2.67278	−	1.10710i
$894$		0			0
$895$		−	54.8946i		−	1.83492i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−3.40073	+	8.21008i	−0.113421	+	0.273822i
$900$		0			0
$901$	−1.92720	+	0.798273i	−0.0642044	+	0.0265943i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−9.77811	+	9.77811i	−0.325035	+	0.325035i
$906$		0			0
$907$	38.9974	−	16.1532i	1.29489	−	0.536359i	0.374448	−	0.927248i	$-0.377832\pi$
$907$	38.9974	−	16.1532i	1.29489	−	0.536359i	0.920438	+	0.390888i	$0.127832\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$			21.6843i			0.718433i	0.933254	+	0.359217i	$0.116956\pi$
$911$			21.6843i			0.718433i	−0.933254	+	0.359217i	$0.883044\pi$
$912$		0			0
$913$		−	39.6205i		−	1.31125i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	11.7435	−	4.86431i	0.387804	−	0.160634i
$918$		0			0
$919$	−31.7214	+	31.7214i	−1.04639	+	1.04639i	−0.0475231	+	0.998870i	$0.515133\pi$
$919$	−31.7214	+	31.7214i	−1.04639	+	1.04639i	−0.998870	+	0.0475231i	$0.984867\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−62.6980	+	25.9703i	−2.06373	+	0.854824i
$924$		0			0
$925$	5.60940	−	13.5423i	0.184436	−	0.445267i
$926$		0			0
$927$		0			0
$928$		0			0
$929$			0.364065i			0.0119446i	0.999982	+	0.00597230i	$0.00190105\pi$
$929$			0.364065i			0.0119446i	−0.999982	+	0.00597230i	$0.998099\pi$
$930$		0			0
$931$	14.7177	+	6.09628i	0.482354	+	0.199797i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	2.82013	−	2.82013i	0.0922282	−	0.0922282i
$936$		0			0
$937$	1.47325	+	1.47325i	0.0481290	+	0.0481290i	0.730762	−	0.682633i	$-0.239165\pi$
$937$	1.47325	+	1.47325i	0.0481290	+	0.0481290i	−0.682633	+	0.730762i	$0.739165\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	0.412404	−	0.995632i	0.0134440	−	0.0324567i	−0.917015	−	0.398853i	$-0.869408\pi$
$941$	0.412404	−	0.995632i	0.0134440	−	0.0324567i	0.930459	+	0.366396i	$0.119408\pi$
$942$		0			0
$943$	2.94817			0.0960057
$944$		0			0
$945$		0			0
$946$		0			0
$947$	49.6561	+	20.5682i	1.61361	+	0.668377i	0.993255	−	0.115948i	$-0.0369905\pi$
$947$	49.6561	+	20.5682i	1.61361	+	0.668377i	0.620350	+	0.784325i	$0.286990\pi$
$948$		0			0
$949$	−11.1949	−	27.0269i	−0.363402	−	0.877330i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	14.7097	+	14.7097i	0.476493	+	0.476493i	0.904008	−	0.427515i	$-0.140611\pi$
$953$	14.7097	+	14.7097i	0.476493	+	0.476493i	−0.427515	+	0.904008i	$0.640611\pi$
$954$		0			0
$955$	−7.78361	−	18.7913i	−0.251872	−	0.608072i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	11.1043			0.358575
$960$		0			0
$961$	28.6128			0.922995
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−11.6615	−	28.1533i	−0.375396	−	0.906285i
$966$		0			0
$967$	6.95466	+	6.95466i	0.223647	+	0.223647i	0.810032	−	0.586385i	$-0.199450\pi$
$967$	6.95466	+	6.95466i	0.223647	+	0.223647i	−0.586385	+	0.810032i	$0.699450\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−19.3256	−	46.6562i	−0.620189	−	1.49727i	−0.851482	−	0.524384i	$-0.824296\pi$
$971$	−19.3256	−	46.6562i	−0.620189	−	1.49727i	0.231293	−	0.972884i	$-0.425704\pi$
$972$		0			0
$973$	9.27824	+	3.84317i	0.297447	+	0.123206i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	22.2374			0.711439			0.355720	−	0.934593i	$-0.384236\pi$
$977$	22.2374			0.711439			0.355720	+	0.934593i	$0.384236\pi$
$978$		0			0
$979$	−10.0434	+	24.2469i	−0.320988	+	0.774933i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−37.7122	−	37.7122i	−1.20283	−	1.20283i	−0.973301	−	0.229531i	$-0.926281\pi$
$983$	−37.7122	−	37.7122i	−1.20283	−	1.20283i	−0.229531	−	0.973301i	$-0.573719\pi$
$984$		0			0
$985$	−19.0535	+	19.0535i	−0.607095	+	0.607095i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	5.18717	+	2.14860i	0.164942	+	0.0683214i
$990$		0			0
$991$		−	39.0360i		−	1.24002i	−0.784594	−	0.620010i	$-0.787129\pi$
$991$		−	39.0360i		−	1.24002i	0.784594	−	0.620010i	$-0.212871\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	9.10490	−	21.9812i	0.288645	−	0.696850i
$996$		0			0
$997$	16.9640	−	7.02670i	0.537254	−	0.222538i	−0.0975229	−	0.995233i	$-0.531092\pi$
$997$	16.9640	−	7.02670i	0.537254	−	0.222538i	0.634777	+	0.772695i	$0.281092\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1152.2.w.a.1007.2		32
3.2	odd	2		1152.2.w.b.1007.7		32
4.3	odd	2		288.2.w.b.179.1	yes	32
12.11	even	2		288.2.w.a.179.8	✓	32
32.5	even	8		288.2.w.a.251.8	yes	32
32.27	odd	8		1152.2.w.b.143.7		32
96.5	odd	8		288.2.w.b.251.1	yes	32
96.59	even	8	inner	1152.2.w.a.143.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.w.a.179.8	✓	32	12.11	even	2
288.2.w.a.251.8	yes	32	32.5	even	8
288.2.w.b.179.1	yes	32	4.3	odd	2
288.2.w.b.251.1	yes	32	96.5	odd	8
1152.2.w.a.143.2		32	96.59	even	8	inner
1152.2.w.a.1007.2		32	1.1	even	1	trivial
1152.2.w.b.143.7		32	32.27	odd	8
1152.2.w.b.1007.7		32	3.2	odd	2

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:	\( N \)	\(=\)	\( 1152 = 2^{7} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1152.w (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.11994 - 2.70378i) q^{5} +(-1.57144 - 1.57144i) q^{7} +O(q^{10})\)	\(q+(-1.11994 - 2.70378i) q^{5} +(-1.57144 - 1.57144i) q^{7} +(1.00153 + 2.41791i) q^{11} +(-6.48559 - 2.68642i) q^{13} +0.520719 q^{17} +(-2.95774 + 7.14062i) q^{19} +(1.35340 + 1.35340i) q^{23} +(-2.52064 + 2.52064i) q^{25} +(5.31381 + 2.20105i) q^{29} +1.54505i q^{31} +(-2.48892 + 6.00877i) q^{35} +(-3.79897 + 1.57359i) q^{37} +(1.08917 - 1.08917i) q^{41} +(2.71012 - 1.12257i) q^{43} +11.1855i q^{47} -2.06113i q^{49} +(-3.70104 + 1.53302i) q^{53} +(5.41584 - 5.41584i) q^{55} +(-3.19376 + 1.32290i) q^{59} +(-3.78169 + 9.12981i) q^{61} +20.5443i q^{65} +(-10.9492 - 4.53532i) q^{67} +(6.83579 - 6.83579i) q^{71} +(2.94667 + 2.94667i) q^{73} +(2.22576 - 5.37346i) q^{77} -8.79533 q^{79} +(-13.9866 - 5.79342i) q^{83} +(-0.583176 - 1.40791i) q^{85} +(7.09089 + 7.09089i) q^{89} +(5.97019 + 14.4133i) q^{91} +22.6192 q^{95} -5.91713 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q - 8 q^{11} + 16 q^{29} + 24 q^{35} + 16 q^{53} + 32 q^{55} + 32 q^{59} + 32 q^{61} + 16 q^{67} + 16 q^{71} + 16 q^{77} + 32 q^{79} - 40 q^{83} + 48 q^{91} - 80 q^{95}+O(q^{100}) \) 32 * q - 8 * q^11 + 16 * q^29 + 24 * q^35 + 16 * q^53 + 32 * q^55 + 32 * q^59 + 32 * q^61 + 16 * q^67 + 16 * q^71 + 16 * q^77 + 32 * q^79 - 40 * q^83 + 48 * q^91 - 80 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more