LMFDB - Embedded newform 45.5.d.a.44.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [45,5,Mod(44,45)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("45.44");

S:= CuspForms(chi, 5);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.65164833877$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 74x^{6} + 1729x^{4} - 2880x^{2} + 32400 $ x^8 - 74x^6 + 1729x^4 - 2880*x^2 + 32400
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2\cdot 3^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			44.5
Root			$-1.56128 - 1.41421i$ of defining polynomial
Character	$\chi$	$=$	45.44
Dual form			45.5.d.a.44.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.56128 q^{2} -13.5624 q^{4} +(-23.8583 - 7.46874i) q^{5} -82.9374i q^{7} -46.1553 q^{8} +(-37.2496 - 11.6608i) q^{10} +142.746i q^{11} -106.259i q^{13} -129.489i q^{14} +144.937 q^{16} -277.420 q^{17} -262.250 q^{19} +(323.575 + 101.294i) q^{20} +222.867i q^{22} +414.325 q^{23} +(513.436 + 356.383i) q^{25} -165.900i q^{26} +1124.83i q^{28} -1143.83i q^{29} -26.3726 q^{31} +964.772 q^{32} -433.132 q^{34} +(-619.437 + 1978.74i) q^{35} -1363.29i q^{37} -409.446 q^{38} +(1101.19 + 344.722i) q^{40} +678.999i q^{41} -2104.48i q^{43} -1935.98i q^{44} +646.879 q^{46} -2368.85 q^{47} -4477.60 q^{49} +(801.619 + 556.415i) q^{50} +1441.13i q^{52} -1644.51 q^{53} +(1066.13 - 3405.68i) q^{55} +3828.00i q^{56} -1785.85i q^{58} -5753.62i q^{59} +2163.24 q^{61} -41.1752 q^{62} -812.704 q^{64} +(-793.621 + 2535.16i) q^{65} +2280.85i q^{67} +3762.48 q^{68} +(-967.118 + 3089.38i) q^{70} +975.793i q^{71} +8648.81i q^{73} -2128.49i q^{74} +3556.73 q^{76} +11839.0 q^{77} +1708.36 q^{79} +(-3457.94 - 1082.49i) q^{80} +1060.11i q^{82} -1251.37 q^{83} +(6618.77 + 2071.98i) q^{85} -3285.69i q^{86} -6588.49i q^{88} +6067.49i q^{89} -8812.84 q^{91} -5619.23 q^{92} -3698.45 q^{94} +(6256.83 + 1958.67i) q^{95} +619.192i q^{97} -6990.81 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 36 q^{4} + 280 q^{10} + 148 q^{16} - 1520 q^{19} + 1940 q^{25} + 2968 q^{31} - 12424 q^{34} + 7220 q^{40} + 10088 q^{46} - 8944 q^{49} + 19800 q^{55} + 544 q^{61} - 29188 q^{64} + 1800 q^{70} + 3600 q^{76}+ \cdots + 40928 q^{94}+O(q^{100}) $ 8 * q + 36 * q^4 + 280 * q^10 + 148 * q^16 - 1520 * q^19 + 1940 * q^25 + 2968 * q^31 - 12424 * q^34 + 7220 * q^40 + 10088 * q^46 - 8944 * q^49 + 19800 * q^55 + 544 * q^61 - 29188 * q^64 + 1800 * q^70 + 3600 * q^76 - 12632 * q^79 - 3260 * q^85 - 24552 * q^91 + 40928 * q^94

Character values

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

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

Coefficient data

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

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

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

$2$	1.56128			0.390321			0.195161	−	0.980771i	$-0.437477\pi$
$2$	1.56128			0.390321			0.195161	+	0.980771i	$0.437477\pi$
$3$		0			0
$3$		0			0
$4$	−13.5624			−0.847649
$5$	−23.8583	−	7.46874i	−0.954332	−	0.298750i
$5$	−23.8583	−	7.46874i	−0.954332	−	0.298750i
$6$		0			0
$7$		−	82.9374i		−	1.69260i	−0.532707	−	0.846300i	$-0.678825\pi$
$7$		−	82.9374i		−	1.69260i	0.532707	−	0.846300i	$-0.321175\pi$
$8$	−46.1553			−0.721176
$9$		0			0
$10$	−37.2496	−	11.6608i	−0.372496	−	0.116608i
$11$			142.746i			1.17972i	0.807506	+	0.589860i	$0.200817\pi$
$11$			142.746i			1.17972i	−0.807506	+	0.589860i	$0.799183\pi$
$12$		0			0
$13$		−	106.259i		−	0.628751i	−0.949299	−	0.314376i	$-0.898205\pi$
$13$		−	106.259i		−	0.628751i	0.949299	−	0.314376i	$-0.101795\pi$
$14$		−	129.489i		−	0.660657i
$15$		0			0
$16$	144.937			0.566159
$17$	−277.420			−0.959931			−0.479966	−	0.877287i	$-0.659351\pi$
$17$	−277.420			−0.959931			−0.479966	+	0.877287i	$0.659351\pi$
$18$		0			0
$19$	−262.250			−0.726453			−0.363227	−	0.931701i	$-0.618325\pi$
$19$	−262.250			−0.726453			−0.363227	+	0.931701i	$0.618325\pi$
$20$	323.575	+	101.294i	0.808939	+	0.253235i
$21$		0			0
$22$			222.867i			0.460469i
$23$	414.325			0.783223			0.391611	−	0.920131i	$-0.371918\pi$
$23$	414.325			0.783223			0.391611	+	0.920131i	$0.371918\pi$
$24$		0			0
$25$	513.436	+	356.383i	0.821497	+	0.570212i
$26$		−	165.900i		−	0.245415i
$27$		0			0
$28$			1124.83i			1.43473i
$29$		−	1143.83i		−	1.36009i	−0.733172	−	0.680043i	$-0.761961\pi$
$29$		−	1143.83i		−	1.36009i	0.733172	−	0.680043i	$-0.238039\pi$
$30$		0			0
$31$	−26.3726			−0.0274429			−0.0137214	−	0.999906i	$-0.504368\pi$
$31$	−26.3726			−0.0274429			−0.0137214	+	0.999906i	$0.504368\pi$
$32$	964.772			0.942160
$33$		0			0
$34$	−433.132			−0.374681
$35$	−619.437	+	1978.74i	−0.505663	+	1.61530i
$36$		0			0
$37$		−	1363.29i		−	0.995830i	−0.867226	−	0.497915i	$-0.834099\pi$
$37$		−	1363.29i		−	0.995830i	0.867226	−	0.497915i	$-0.165901\pi$
$38$	−409.446			−0.283550
$39$		0			0
$40$	1101.19	+	344.722i	0.688241	+	0.215451i
$41$			678.999i			0.403926i	0.979393	+	0.201963i	$0.0647320\pi$
$41$			678.999i			0.403926i	−0.979393	+	0.201963i	$0.935268\pi$
$42$		0			0
$43$		−	2104.48i		−	1.13817i	−0.822278	−	0.569086i	$-0.807297\pi$
$43$		−	2104.48i		−	1.13817i	0.822278	−	0.569086i	$-0.192703\pi$
$44$		−	1935.98i		−	0.999989i
$45$		0			0
$46$	646.879			0.305708
$47$	−2368.85			−1.07236			−0.536181	−	0.844103i	$-0.680134\pi$
$47$	−2368.85			−1.07236			−0.536181	+	0.844103i	$0.680134\pi$
$48$		0			0
$49$	−4477.60			−1.86489
$50$	801.619	+	556.415i	0.320648	+	0.222566i
$51$		0			0
$52$			1441.13i			0.532961i
$53$	−1644.51			−0.585444			−0.292722	−	0.956198i	$-0.594561\pi$
$53$	−1644.51			−0.585444			−0.292722	+	0.956198i	$0.594561\pi$
$54$		0			0
$55$	1066.13	−	3405.68i	0.352441	−	1.12584i
$56$			3828.00i			1.22066i
$57$		0			0
$58$		−	1785.85i		−	0.530870i
$59$		−	5753.62i		−	1.65286i	−0.563036	−	0.826432i	$-0.690367\pi$
$59$		−	5753.62i		−	1.65286i	0.563036	−	0.826432i	$-0.309633\pi$
$60$		0			0
$61$	2163.24			0.581359			0.290680	−	0.956820i	$-0.406119\pi$
$61$	2163.24			0.581359			0.290680	+	0.956820i	$0.406119\pi$
$62$	−41.1752			−0.0107115
$63$		0			0
$64$	−812.704			−0.198414
$65$	−793.621	+	2535.16i	−0.187839	+	0.600037i
$66$		0			0
$67$			2280.85i			0.508097i	0.967191	+	0.254049i	$0.0817623\pi$
$67$			2280.85i			0.508097i	−0.967191	+	0.254049i	$0.918238\pi$
$68$	3762.48			0.813685
$69$		0			0
$70$	−967.118	+	3089.38i	−0.197371	+	0.630486i
$71$			975.793i			0.193571i	0.995305	+	0.0967856i	$0.0308561\pi$
$71$			975.793i			0.193571i	−0.995305	+	0.0967856i	$0.969144\pi$
$72$		0			0
$73$			8648.81i			1.62297i	0.584373	+	0.811485i	$0.301340\pi$
$73$			8648.81i			1.62297i	−0.584373	+	0.811485i	$0.698660\pi$
$74$		−	2128.49i		−	0.388694i
$75$		0			0
$76$	3556.73			0.615778
$77$	11839.0			1.99679
$78$		0			0
$79$	1708.36			0.273731			0.136866	−	0.990590i	$-0.456297\pi$
$79$	1708.36			0.273731			0.136866	+	0.990590i	$0.456297\pi$
$80$	−3457.94	−	1082.49i	−0.540304	−	0.169140i
$81$		0			0
$82$			1060.11i			0.157661i
$83$	−1251.37			−0.181647			−0.0908234	−	0.995867i	$-0.528950\pi$
$83$	−1251.37			−0.181647			−0.0908234	+	0.995867i	$0.528950\pi$
$84$		0			0
$85$	6618.77	+	2071.98i	0.916093	+	0.286779i
$86$		−	3285.69i		−	0.444253i
$87$		0			0
$88$		−	6588.49i		−	0.850786i
$89$			6067.49i			0.766001i	0.923748	+	0.383000i	$0.125109\pi$
$89$			6067.49i			0.766001i	−0.923748	+	0.383000i	$0.874891\pi$
$90$		0			0
$91$	−8812.84			−1.06422
$92$	−5619.23			−0.663898
$93$		0			0
$94$	−3698.45			−0.418566
$95$	6256.83	+	1958.67i	0.693277	+	0.217028i
$96$		0			0
$97$			619.192i			0.0658085i	0.999459	+	0.0329042i	$0.0104756\pi$
$97$			619.192i			0.0658085i	−0.999459	+	0.0329042i	$0.989524\pi$
$98$	−6990.81			−0.727906
$99$		0			0
$100$	−6963.42	−	4833.40i	−0.696342	−	0.483340i
$101$		−	13484.6i		−	1.32189i	−0.750435	−	0.660944i	$-0.770156\pi$
$101$		−	13484.6i		−	1.32189i	0.750435	−	0.660944i	$-0.229844\pi$
$102$		0			0
$103$		−	2373.71i		−	0.223744i	−0.993723	−	0.111872i	$-0.964315\pi$
$103$		−	2373.71i		−	0.223744i	0.993723	−	0.111872i	$-0.0356847\pi$
$104$			4904.42i			0.453441i
$105$		0			0
$106$	−2567.55			−0.228511
$107$	−21130.0			−1.84557			−0.922787	−	0.385311i	$-0.874094\pi$
$107$	−21130.0			−1.84557			−0.922787	+	0.385311i	$0.874094\pi$
$108$		0			0
$109$	18595.3			1.56513			0.782565	−	0.622569i	$-0.213911\pi$
$109$	18595.3			1.56513			0.782565	+	0.622569i	$0.213911\pi$
$110$	1664.54	−	5317.23i	0.137565	−	0.439441i
$111$		0			0
$112$		−	12020.7i		−	0.958280i
$113$	13972.2			1.09423			0.547113	−	0.837058i	$-0.315727\pi$
$113$	13972.2			1.09423			0.547113	+	0.837058i	$0.315727\pi$
$114$		0			0
$115$	−9885.08	−	3094.48i	−0.747454	−	0.233987i
$116$			15513.1i			1.15288i
$117$		0			0
$118$		−	8983.04i		−	0.645148i
$119$			23008.5i			1.62478i
$120$		0			0
$121$	−5735.45			−0.391739
$122$	3377.43			0.226917
$123$		0			0
$124$	357.676			0.0232620
$125$	−9587.97	−	12337.4i	−0.613630	−	0.789594i
$126$		0			0
$127$		−	6749.40i		−	0.418464i	−0.977866	−	0.209232i	$-0.932904\pi$
$127$		−	6749.40i		−	0.418464i	0.977866	−	0.209232i	$-0.0670964\pi$
$128$	−16705.2			−1.01961
$129$		0			0
$130$	−1239.07	+	3958.10i	−0.0733176	+	0.234207i
$131$		−	16379.3i		−	0.954451i	−0.878781	−	0.477226i	$-0.841642\pi$
$131$		−	16379.3i		−	0.954451i	0.878781	−	0.477226i	$-0.158358\pi$
$132$		0			0
$133$			21750.3i			1.22959i
$134$			3561.05i			0.198321i
$135$		0			0
$136$	12804.4			0.692280
$137$	23405.8			1.24705			0.623523	−	0.781805i	$-0.285701\pi$
$137$	23405.8			1.24705			0.623523	+	0.781805i	$0.285701\pi$
$138$		0			0
$139$	8086.69			0.418544			0.209272	−	0.977857i	$-0.432891\pi$
$139$	8086.69			0.418544			0.209272	+	0.977857i	$0.432891\pi$
$140$	8401.05	−	26836.5i	0.428625	−	1.36921i
$141$		0			0
$142$			1523.49i			0.0755549i
$143$	15168.1			0.741751
$144$		0			0
$145$	−8542.99	+	27289.9i	−0.406325	+	1.29797i
$146$			13503.2i			0.633479i
$147$		0			0
$148$			18489.5i			0.844115i
$149$			19374.0i			0.872663i	0.899786	+	0.436331i	$0.143722\pi$
$149$			19374.0i			0.872663i	−0.899786	+	0.436331i	$0.856278\pi$
$150$		0			0
$151$	−3225.62			−0.141468			−0.0707342	−	0.997495i	$-0.522534\pi$
$151$	−3225.62			−0.141468			−0.0707342	+	0.997495i	$0.522534\pi$
$152$	12104.2			0.523901
$153$		0			0
$154$	18484.0			0.779390
$155$	629.206	+	196.970i	0.0261896	+	0.00819855i
$156$		0			0
$157$			21942.0i			0.890177i	0.895487	+	0.445088i	$0.146828\pi$
$157$			21942.0i			0.890177i	−0.895487	+	0.445088i	$0.853172\pi$
$158$	2667.23			0.106843
$159$		0			0
$160$	−23017.8	−	7205.63i	−0.899133	−	0.281470i
$161$		−	34363.0i		−	1.32568i
$162$		0			0
$163$		−	36844.9i		−	1.38676i	−0.720571	−	0.693381i	$-0.756120\pi$
$163$		−	36844.9i		−	1.38676i	0.720571	−	0.693381i	$-0.243880\pi$
$164$		−	9208.85i		−	0.342387i
$165$		0			0
$166$	−1953.74			−0.0709006
$167$	−32169.9			−1.15350			−0.576750	−	0.816921i	$-0.695679\pi$
$167$	−32169.9			−1.15350			−0.576750	+	0.816921i	$0.695679\pi$
$168$		0			0
$169$	17270.0			0.604672
$170$	10333.8	+	3234.95i	0.357570	+	0.111936i
$171$		0			0
$172$			28541.8i			0.964772i
$173$	−9487.64			−0.317005			−0.158502	−	0.987359i	$-0.550667\pi$
$173$	−9487.64			−0.317005			−0.158502	+	0.987359i	$0.550667\pi$
$174$		0			0
$175$	29557.4	−	42583.0i	0.965141	−	1.39047i
$176$			20689.2i			0.667909i
$177$		0			0
$178$			9473.08i			0.298986i
$179$			22636.1i			0.706474i	0.935534	+	0.353237i	$0.114919\pi$
$179$			22636.1i			0.706474i	−0.935534	+	0.353237i	$0.885081\pi$
$180$		0			0
$181$	−48877.4			−1.49194			−0.745970	−	0.665980i	$-0.768014\pi$
$181$	−48877.4			−1.49194			−0.745970	+	0.665980i	$0.768014\pi$
$182$	−13759.3			−0.415389
$183$		0			0
$184$	−19123.3			−0.564842
$185$	−10182.1	+	32525.8i	−0.297504	+	0.950352i
$186$		0			0
$187$		−	39600.6i		−	1.13245i
$188$	32127.3			0.908988
$189$		0			0
$190$	9768.68	+	3058.05i	0.270601	+	0.0847104i
$191$		−	16675.9i		−	0.457113i	−0.973531	−	0.228556i	$-0.926600\pi$
$191$		−	16675.9i		−	0.457113i	0.973531	−	0.228556i	$-0.0734005\pi$
$192$		0			0
$193$		−	16981.6i		−	0.455894i	−0.973674	−	0.227947i	$-0.926799\pi$
$193$		−	16981.6i		−	0.455894i	0.973674	−	0.227947i	$-0.0732013\pi$
$194$			966.734i			0.0256864i
$195$		0			0
$196$	60727.0			1.58077
$197$	15439.8			0.397841			0.198920	−	0.980016i	$-0.436257\pi$
$197$	15439.8			0.397841			0.198920	+	0.980016i	$0.436257\pi$
$198$		0			0
$199$	−33555.4			−0.847337			−0.423668	−	0.905817i	$-0.639258\pi$
$199$	−33555.4			−0.847337			−0.423668	+	0.905817i	$0.639258\pi$
$200$	−23697.8	−	16448.9i	−0.592445	−	0.411224i
$201$		0			0
$202$		−	21053.3i		−	0.515961i
$203$	−94866.5			−2.30208
$204$		0			0
$205$	5071.27	−	16199.8i	0.120673	−	0.385479i
$206$		−	3706.03i		−	0.0873322i
$207$		0			0
$208$		−	15400.8i		−	0.355973i
$209$		−	37435.1i		−	0.857011i
$210$		0			0
$211$	−45174.7			−1.01468			−0.507342	−	0.861745i	$-0.669372\pi$
$211$	−45174.7			−1.01468			−0.507342	+	0.861745i	$0.669372\pi$
$212$	22303.5			0.496251
$213$		0			0
$214$	−32989.9			−0.720366
$215$	−15717.8	+	50209.3i	−0.340029	+	1.08619i
$216$		0			0
$217$			2187.28i			0.0464498i
$218$	29032.6			0.610903
$219$		0			0
$220$	−14459.3	+	46189.1i	−0.298746	+	0.954321i
$221$			29478.4i			0.603558i
$222$		0			0
$223$			5287.44i			0.106325i	0.998586	+	0.0531625i	$0.0169301\pi$
$223$			5287.44i			0.106325i	−0.998586	+	0.0531625i	$0.983070\pi$
$224$		−	80015.6i		−	1.59470i
$225$		0			0
$226$	21814.5			0.427100
$227$	48260.3			0.936566			0.468283	−	0.883578i	$-0.344873\pi$
$227$	48260.3			0.936566			0.468283	+	0.883578i	$0.344873\pi$
$228$		0			0
$229$	20011.2			0.381594			0.190797	−	0.981629i	$-0.438893\pi$
$229$	20011.2			0.381594			0.190797	+	0.981629i	$0.438893\pi$
$230$	−15433.4	−	4831.37i	−0.291747	−	0.0913302i
$231$		0			0
$232$			52793.9i			0.980862i
$233$	49175.9			0.905817			0.452909	−	0.891557i	$-0.350386\pi$
$233$	49175.9			0.905817			0.452909	+	0.891557i	$0.350386\pi$
$234$		0			0
$235$	56516.7	+	17692.3i	1.02339	+	0.320368i
$236$			78032.9i			1.40105i
$237$		0			0
$238$			35922.8i			0.634185i
$239$		−	73316.8i		−	1.28353i	−0.766899	−	0.641767i	$-0.778201\pi$
$239$		−	73316.8i		−	1.28353i	0.766899	−	0.641767i	$-0.221799\pi$
$240$		0			0
$241$	103493.			1.78187			0.890936	−	0.454128i	$-0.150049\pi$
$241$	103493.			1.78187			0.890936	+	0.454128i	$0.150049\pi$
$242$	−8954.67			−0.152904
$243$		0			0
$244$	−29338.7			−0.492789
$245$	106828.	+	33442.1i	1.77972	+	0.557136i
$246$		0			0
$247$			27866.4i			0.456758i
$248$	1217.24			0.0197912
$249$		0			0
$250$	−14969.5	−	19262.2i	−0.239513	−	0.308195i
$251$			2650.77i			0.0420751i	0.999779	+	0.0210375i	$0.00669695\pi$
$251$			2650.77i			0.0420751i	−0.999779	+	0.0210375i	$0.993303\pi$
$252$		0			0
$253$			59143.2i			0.923983i
$254$		−	10537.7i		−	0.163335i
$255$		0			0
$256$	−13078.3			−0.199559
$257$	−92657.4			−1.40286			−0.701429	−	0.712739i	$-0.747454\pi$
$257$	−92657.4			−1.40286			−0.701429	+	0.712739i	$0.747454\pi$
$258$		0			0
$259$	−113068.			−1.68554
$260$	10763.4	−	34382.8i	0.159222	−	0.508621i
$261$		0			0
$262$		−	25572.8i		−	0.372542i
$263$	38269.8			0.553279			0.276640	−	0.960974i	$-0.410779\pi$
$263$	38269.8			0.553279			0.276640	+	0.960974i	$0.410779\pi$
$264$		0			0
$265$	39235.3	+	12282.4i	0.558708	+	0.174901i
$266$			33958.4i			0.479936i
$267$		0			0
$268$		−	30933.8i		−	0.430688i
$269$		−	8391.53i		−	0.115968i	−0.998318	−	0.0579838i	$-0.981533\pi$
$269$		−	8391.53i		−	0.115968i	0.998318	−	0.0579838i	$-0.0184672\pi$
$270$		0			0
$271$	−488.528			−0.00665198			−0.00332599	−	0.999994i	$-0.501059\pi$
$271$	−488.528			−0.00665198			−0.00332599	+	0.999994i	$0.501059\pi$
$272$	−40208.4			−0.543474
$273$		0			0
$274$	36543.1			0.486749
$275$	−50872.2	+	73291.0i	−0.672691	+	0.969137i
$276$		0			0
$277$			385.258i			0.00502102i	0.999997	+	0.00251051i	$0.000799121\pi$
$277$			385.258i			0.00502102i	−0.999997	+	0.00251051i	$0.999201\pi$
$278$	12625.6			0.163367
$279$		0			0
$280$	28590.3	−	91329.5i	0.364672	−	1.16492i
$281$		−	99259.3i		−	1.25707i	−0.777782	−	0.628534i	$-0.783655\pi$
$281$		−	99259.3i		−	1.25707i	0.777782	−	0.628534i	$-0.216345\pi$
$282$		0			0
$283$		−	44860.2i		−	0.560129i	−0.959981	−	0.280065i	$-0.909644\pi$
$283$		−	44860.2i		−	0.560129i	0.959981	−	0.280065i	$-0.0903559\pi$
$284$		−	13234.1i		−	0.164081i
$285$		0			0
$286$	23681.7			0.289521
$287$	56314.4			0.683684
$288$		0			0
$289$	−6559.05			−0.0785318
$290$	−13338.0	+	42607.3i	−0.158597	+	0.506626i
$291$		0			0
$292$		−	117299.i		−	1.37571i
$293$	−49598.8			−0.577744			−0.288872	−	0.957368i	$-0.593280\pi$
$293$	−49598.8			−0.577744			−0.288872	+	0.957368i	$0.593280\pi$
$294$		0			0
$295$	−42972.3	+	137272.i	−0.493792	+	1.57738i
$296$			62923.1i			0.718169i
$297$		0			0
$298$			30248.3i			0.340619i
$299$		−	44025.7i		−	0.492452i
$300$		0			0
$301$	−174540.			−1.92647
$302$	−5036.11			−0.0552181
$303$		0			0
$304$	−38009.6			−0.411288
$305$	−51611.1	−	16156.7i	−0.554809	−	0.173681i
$306$		0			0
$307$		−	80916.5i		−	0.858540i	−0.903176	−	0.429270i	$-0.858771\pi$
$307$		−	80916.5i		−	0.858540i	0.903176	−	0.429270i	$-0.141229\pi$
$308$	−160565.			−1.69258
$309$		0			0
$310$	982.369	+	307.526i	0.0102224	+	0.00320007i
$311$		−	39337.3i		−	0.406709i	−0.979105	−	0.203354i	$-0.934816\pi$
$311$		−	39337.3i		−	0.406709i	0.979105	−	0.203354i	$-0.0651843\pi$
$312$		0			0
$313$		−	106390.i		−	1.08595i	−0.839749	−	0.542975i	$-0.817298\pi$
$313$		−	106390.i		−	1.08595i	0.839749	−	0.542975i	$-0.182702\pi$
$314$			34257.6i			0.347455i
$315$		0			0
$316$	−23169.4			−0.232028
$317$	8729.59			0.0868711			0.0434355	−	0.999056i	$-0.486170\pi$
$317$	8729.59			0.0868711			0.0434355	+	0.999056i	$0.486170\pi$
$318$		0			0
$319$	163278.			1.60452
$320$	19389.7	+	6069.88i	0.189353	+	0.0592761i
$321$		0			0
$322$		−	53650.4i		−	0.517442i
$323$	72753.3			0.697345
$324$		0			0
$325$	37868.9	−	54557.2i	0.358522	−	0.516518i
$326$		−	57525.3i		−	0.541282i
$327$		0			0
$328$		−	31339.4i		−	0.291302i
$329$			196466.i			1.81508i
$330$		0			0
$331$	144483.			1.31875			0.659374	−	0.751815i	$-0.270821\pi$
$331$	144483.			1.31875			0.659374	+	0.751815i	$0.270821\pi$
$332$	16971.5			0.153973
$333$		0			0
$334$	−50226.4			−0.450235
$335$	17035.1	−	54417.2i	0.151794	−	0.484893i
$336$		0			0
$337$			202953.i			1.78705i	0.449017	+	0.893523i	$0.351774\pi$
$337$			202953.i			1.78705i	−0.449017	+	0.893523i	$0.648226\pi$
$338$	26963.4			0.236016
$339$		0			0
$340$	−89766.4	−	28101.0i	−0.776526	−	0.243088i
$341$		−	3764.59i		−	0.0323749i
$342$		0			0
$343$			172228.i			1.46391i
$344$			97133.0i			0.820823i
$345$		0			0
$346$	−14812.9			−0.123734
$347$	67772.8			0.562855			0.281427	−	0.959582i	$-0.409192\pi$
$347$	67772.8			0.562855			0.281427	+	0.959582i	$0.409192\pi$
$348$		0			0
$349$	11678.9			0.0958849			0.0479424	−	0.998850i	$-0.484734\pi$
$349$	11678.9			0.0958849			0.0479424	+	0.998850i	$0.484734\pi$
$350$	46147.6	−	66484.2i	0.376715	−	0.542728i
$351$		0			0
$352$			137717.i			1.11149i
$353$	129628.			1.04028			0.520140	−	0.854081i	$-0.325880\pi$
$353$	129628.			1.04028			0.520140	+	0.854081i	$0.325880\pi$
$354$		0			0
$355$	7287.94	−	23280.7i	0.0578293	−	0.184731i
$356$		−	82289.7i		−	0.649300i
$357$		0			0
$358$			35341.5i			0.275752i
$359$		−	47869.9i		−	0.371427i	−0.982604	−	0.185714i	$-0.940540\pi$
$359$		−	47869.9i		−	0.371427i	0.982604	−	0.185714i	$-0.0594596\pi$
$360$		0			0
$361$	−61546.2			−0.472266
$362$	−76311.6			−0.582335
$363$		0			0
$364$	119523.			0.902089
$365$	64595.7	−	206346.i	0.484862	−	1.54885i
$366$		0			0
$367$			142380.i			1.05710i	0.848902	+	0.528550i	$0.177264\pi$
$367$			142380.i			1.05710i	−0.848902	+	0.528550i	$0.822736\pi$
$368$	60050.9			0.443429
$369$		0			0
$370$	−15897.1	+	50782.0i	−0.116122	+	0.370942i
$371$			136392.i			0.990922i
$372$		0			0
$373$		−	38609.9i		−	0.277512i	−0.990327	−	0.138756i	$-0.955690\pi$
$373$		−	38609.9i		−	0.277512i	0.990327	−	0.138756i	$-0.0443103\pi$
$374$		−	61827.9i		−	0.442019i
$375$		0			0
$376$	109335.			0.773363
$377$	−121543.			−0.855156
$378$		0			0
$379$	145465.			1.01270			0.506348	−	0.862329i	$-0.330995\pi$
$379$	145465.			1.01270			0.506348	+	0.862329i	$0.330995\pi$
$380$	−84857.5	−	26564.3i	−0.587656	−	0.183963i
$381$		0			0
$382$		−	26035.9i		−	0.178421i
$383$	−394.309			−0.00268806			−0.00134403	−	0.999999i	$-0.500428\pi$
$383$	−394.309			−0.00268806			−0.00134403	+	0.999999i	$0.500428\pi$
$384$		0			0
$385$	−282458.	−	88422.3i	−1.90560	−	0.596541i
$386$		−	26513.1i		−	0.177945i
$387$		0			0
$388$		−	8397.72i		−	0.0557825i
$389$			189831.i			1.25449i	0.778821	+	0.627247i	$0.215818\pi$
$389$			189831.i			1.25449i	−0.778821	+	0.627247i	$0.784182\pi$
$390$		0			0
$391$	−114942.			−0.751840
$392$	206665.			1.34492
$393$		0			0
$394$	24105.9			0.155286
$395$	−40758.4	−	12759.3i	−0.261230	−	0.0817770i
$396$		0			0
$397$		−	212776.i		−	1.35002i	−0.737808	−	0.675011i	$-0.764139\pi$
$397$		−	212776.i		−	1.35002i	0.737808	−	0.675011i	$-0.235861\pi$
$398$	−52389.5			−0.330733
$399$		0			0
$400$	74415.7	+	51652.9i	0.465098	+	0.322831i
$401$		−	46951.1i		−	0.291983i	−0.989286	−	0.145991i	$-0.953363\pi$
$401$		−	46951.1i		−	0.291983i	0.989286	−	0.145991i	$-0.0466372\pi$
$402$		0			0
$403$			2802.33i			0.0172548i
$404$			182883.i			1.12050i
$405$		0			0
$406$	−148114.			−0.898551
$407$	194605.			1.17480
$408$		0			0
$409$	33511.3			0.200330			0.100165	−	0.994971i	$-0.468063\pi$
$409$	33511.3			0.200330			0.100165	+	0.994971i	$0.468063\pi$
$410$	7917.69	−	25292.4i	0.0471011	−	0.150461i
$411$		0			0
$412$			32193.1i			0.189657i
$413$	−477190.			−2.79764
$414$		0			0
$415$	29855.4	+	9346.12i	0.173351	+	0.0542669i
$416$		−	102516.i		−	0.592385i
$417$		0			0
$418$		−	58446.8i		−	0.334509i
$419$			75612.8i			0.430692i	0.976538	+	0.215346i	$0.0690880\pi$
$419$			75612.8i			0.430692i	−0.976538	+	0.215346i	$0.930912\pi$
$420$		0			0
$421$	268477.			1.51476			0.757378	−	0.652977i	$-0.226480\pi$
$421$	268477.			1.51476			0.757378	+	0.652977i	$0.226480\pi$
$422$	−70530.6			−0.396052
$423$		0			0
$424$	75903.0			0.422209
$425$	−142437.	−	98867.7i	−0.788581	−	0.547365i
$426$		0			0
$427$		−	179413.i		−	0.984008i
$428$	286573.			1.56440
$429$		0			0
$430$	−24540.0	+	78391.0i	−0.132720	+	0.423964i
$431$		−	33271.4i		−	0.179109i	−0.995982	−	0.0895544i	$-0.971456\pi$
$431$		−	33271.4i		−	0.179109i	0.995982	−	0.0895544i	$-0.0285443\pi$
$432$		0			0
$433$		−	308075.i		−	1.64317i	−0.570089	−	0.821583i	$-0.693091\pi$
$433$		−	308075.i		−	1.64317i	0.570089	−	0.821583i	$-0.306909\pi$
$434$			3414.96i			0.0181303i
$435$		0			0
$436$	−252197.			−1.32668
$437$	−108656.			−0.568974
$438$		0			0
$439$	−265525.			−1.37777			−0.688886	−	0.724870i	$-0.741900\pi$
$439$	−265525.			−1.37777			−0.688886	+	0.724870i	$0.741900\pi$
$440$	−49207.7	+	157190.i	−0.254172	+	0.811932i
$441$		0			0
$442$			46024.1i			0.235581i
$443$	−40625.8			−0.207012			−0.103506	−	0.994629i	$-0.533006\pi$
$443$	−40625.8			−0.207012			−0.103506	+	0.994629i	$0.533006\pi$
$444$		0			0
$445$	45316.5	−	144760.i	0.228842	−	0.731019i
$446$			8255.19i			0.0415009i
$447$		0			0
$448$			67403.6i			0.335836i
$449$			215290.i			1.06790i	0.845516	+	0.533950i	$0.179293\pi$
$449$			215290.i			1.06790i	−0.845516	+	0.533950i	$0.820707\pi$
$450$		0			0
$451$	−96924.5			−0.476519
$452$	−189496.			−0.927521
$453$		0			0
$454$	75348.1			0.365562
$455$	210259.	+	65820.8i	1.01562	+	0.317937i
$456$		0			0
$457$		−	324639.i		−	1.55442i	−0.629241	−	0.777210i	$-0.716634\pi$
$457$		−	324639.i		−	1.55442i	0.629241	−	0.777210i	$-0.283366\pi$
$458$	31243.1			0.148944
$459$		0			0
$460$	134065.	+	41968.6i	0.633579	+	0.198339i
$461$			57912.7i			0.272503i	0.990674	+	0.136252i	$0.0435056\pi$
$461$			57912.7i			0.272503i	−0.990674	+	0.136252i	$0.956494\pi$
$462$		0			0
$463$			301265.i			1.40536i	0.711508	+	0.702678i	$0.248012\pi$
$463$			301265.i			1.40536i	−0.711508	+	0.702678i	$0.751988\pi$
$464$		−	165783.i		−	0.770025i
$465$		0			0
$466$	76777.6			0.353560
$467$	−294798.			−1.35173			−0.675866	−	0.737024i	$-0.736230\pi$
$467$	−294798.			−1.35173			−0.675866	+	0.737024i	$0.736230\pi$
$468$		0			0
$469$	189168.			0.860005
$470$	88238.6	+	27622.7i	0.399451	+	0.125046i
$471$		0			0
$472$			265560.i			1.19201i
$473$	300407.			1.34273
$474$		0			0
$475$	−134648.	−	93461.2i	−0.596779	−	0.414232i
$476$		−	312050.i		−	1.37724i
$477$		0			0
$478$		−	114468.i		−	0.500991i
$479$		−	428664.i		−	1.86830i	−0.356884	−	0.934149i	$-0.616161\pi$
$479$		−	428664.i		−	1.86830i	0.356884	−	0.934149i	$-0.383839\pi$
$480$		0			0
$481$	−144862.			−0.626130
$482$	161582.			0.695502
$483$		0			0
$484$	77786.5			0.332057
$485$	4624.58	−	14772.9i	0.0196602	−	0.0628031i
$486$		0			0
$487$			457302.i			1.92817i	0.265596	+	0.964085i	$0.414431\pi$
$487$			457302.i			1.92817i	−0.265596	+	0.964085i	$0.585569\pi$
$488$	−99844.9			−0.419263
$489$		0			0
$490$	166789.	+	52212.6i	0.694664	+	0.217462i
$491$			154537.i			0.641018i	0.947245	+	0.320509i	$0.103854\pi$
$491$			154537.i			0.641018i	−0.947245	+	0.320509i	$0.896146\pi$
$492$		0			0
$493$			317322.i			1.30559i
$494$			43507.3i			0.178282i
$495$		0			0
$496$	−3822.36			−0.0155370
$497$	80929.7			0.327639
$498$		0			0
$499$	−362181.			−1.45454			−0.727269	−	0.686353i	$-0.759211\pi$
$499$	−362181.			−1.45454			−0.727269	+	0.686353i	$0.759211\pi$
$500$	130036.	+	167325.i	0.520143	+	0.669299i
$501$		0			0
$502$			4138.61i			0.0164228i
$503$	193565.			0.765050			0.382525	−	0.923945i	$-0.375055\pi$
$503$	193565.			0.765050			0.382525	+	0.923945i	$0.375055\pi$
$504$		0			0
$505$	−100713.	+	321719.i	−0.394913	+	1.26152i
$506$			92339.4i			0.360650i
$507$		0			0
$508$			91538.1i			0.354711i
$509$		−	331435.i		−	1.27927i	−0.768677	−	0.639637i	$-0.779085\pi$
$509$		−	331435.i		−	1.27927i	0.768677	−	0.639637i	$-0.220915\pi$
$510$		0			0
$511$	717309.			2.74704
$512$	246864.			0.941713
$513$		0			0
$514$	−144665.			−0.547565
$515$	−17728.6	+	56632.5i	−0.0668436	+	0.213526i
$516$		0			0
$517$		−	338144.i		−	1.26509i
$518$	−176531.			−0.657902
$519$		0			0
$520$	36629.8	−	117011.i	0.135465	−	0.432733i
$521$			503767.i			1.85590i	0.372707	+	0.927949i	$0.378430\pi$
$521$			503767.i			1.85590i	−0.372707	+	0.927949i	$0.621570\pi$
$522$		0			0
$523$		−	171122.i		−	0.625608i	−0.949818	−	0.312804i	$-0.898732\pi$
$523$		−	171122.i		−	0.625608i	0.949818	−	0.312804i	$-0.101268\pi$
$524$			222143.i			0.809040i
$525$		0			0
$526$	59750.0			0.215957
$527$	7316.30			0.0263433
$528$		0			0
$529$	−108176.			−0.386562
$530$	61257.4	+	19176.4i	0.218075	+	0.0682676i
$531$		0			0
$532$		−	294986.i		−	1.04226i
$533$	72149.8			0.253969
$534$		0			0
$535$	504125.	+	157814.i	1.76129	+	0.551364i
$536$		−	105273.i		−	0.366428i
$537$		0			0
$538$		−	13101.6i		−	0.0452646i
$539$		−	639161.i		−	2.20005i
$540$		0			0
$541$	−170873.			−0.583819			−0.291910	−	0.956446i	$-0.594291\pi$
$541$	−170873.			−0.583819			−0.291910	+	0.956446i	$0.594291\pi$
$542$	−762.732			−0.00259641
$543$		0			0
$544$	−267647.			−0.904409
$545$	−443652.	−	138884.i	−1.49365	−	0.467582i
$546$		0			0
$547$			187183.i			0.625594i	0.949820	+	0.312797i	$0.101266\pi$
$547$			187183.i			0.625594i	−0.949820	+	0.312797i	$0.898734\pi$
$548$	−317439.			−1.05706
$549$		0			0
$550$	−79426.0	+	114428.i	−0.262565	+	0.378274i
$551$			299970.i			0.988039i
$552$		0			0
$553$		−	141686.i		−	0.463317i
$554$			601.497i			0.00195981i
$555$		0			0
$556$	−109675.			−0.354779
$557$	292929.			0.944175			0.472088	−	0.881552i	$-0.343501\pi$
$557$	292929.			0.944175			0.472088	+	0.881552i	$0.343501\pi$
$558$		0			0
$559$	−223620.			−0.715628
$560$	−89779.2	+	286793.i	−0.286286	+	0.914517i
$561$		0			0
$562$		−	154972.i		−	0.490660i
$563$	16709.7			0.0527171			0.0263586	−	0.999653i	$-0.491609\pi$
$563$	16709.7			0.0527171			0.0263586	+	0.999653i	$0.491609\pi$
$564$		0			0
$565$	−333352.	−	104355.i	−1.04426	−	0.326900i
$566$		−	70039.5i		−	0.218630i
$567$		0			0
$568$		−	45038.0i		−	0.139599i
$569$		−	47426.8i		−	0.146487i	−0.997314	−	0.0732435i	$-0.976665\pi$
$569$		−	47426.8i		−	0.146487i	0.997314	−	0.0732435i	$-0.0233350\pi$
$570$		0			0
$571$	124644.			0.382296			0.191148	−	0.981561i	$-0.438779\pi$
$571$	124644.			0.382296			0.191148	+	0.981561i	$0.438779\pi$
$572$	−205715.			−0.628745
$573$		0			0
$574$	87922.7			0.266856
$575$	212729.	+	147658.i	0.643415	+	0.446603i
$576$		0			0
$577$			209682.i			0.629810i	0.949123	+	0.314905i	$0.101973\pi$
$577$			209682.i			0.629810i	−0.949123	+	0.314905i	$0.898027\pi$
$578$	−10240.5			−0.0306526
$579$		0			0
$580$	115863.	−	370116.i	0.344421	−	1.10023i
$581$			103785.i			0.307455i
$582$		0			0
$583$		−	234748.i		−	0.690660i
$584$		−	399188.i		−	1.17045i
$585$		0			0
$586$	−77437.8			−0.225506
$587$	−417823.			−1.21260			−0.606299	−	0.795237i	$-0.707346\pi$
$587$	−417823.			−1.21260			−0.606299	+	0.795237i	$0.707346\pi$
$588$		0			0
$589$	6916.21			0.0199360
$590$	−67091.9	+	214320.i	−0.192738	+	0.615685i
$591$		0			0
$592$		−	197591.i		−	0.563798i
$593$	−25723.9			−0.0731522			−0.0365761	−	0.999331i	$-0.511645\pi$
$593$	−25723.9			−0.0731522			−0.0365761	+	0.999331i	$0.511645\pi$
$594$		0			0
$595$	171844.	−	548943.i	0.485402	−	1.55058i
$596$		−	262758.i		−	0.739712i
$597$		0			0
$598$		−	68736.7i		−	0.192215i
$599$			57586.1i			0.160496i	0.996775	+	0.0802479i	$0.0255712\pi$
$599$			57586.1i			0.160496i	−0.996775	+	0.0802479i	$0.974429\pi$
$600$		0			0
$601$	174151.			0.482146			0.241073	−	0.970507i	$-0.422501\pi$
$601$	174151.			0.482146			0.241073	+	0.970507i	$0.422501\pi$
$602$	−272507.			−0.751942
$603$		0			0
$604$	43747.1			0.119916
$605$	136838.	+	42836.6i	0.373849	+	0.117032i
$606$		0			0
$607$			250149.i			0.678923i	0.940620	+	0.339462i	$0.110245\pi$
$607$			250149.i			0.678923i	−0.940620	+	0.339462i	$0.889755\pi$
$608$	−253011.			−0.684435
$609$		0			0
$610$	−80579.7	−	25225.1i	−0.216554	−	0.0677913i
$611$			251712.i			0.674250i
$612$		0			0
$613$			274395.i			0.730222i	0.930964	+	0.365111i	$0.118969\pi$
$613$			274395.i			0.730222i	−0.930964	+	0.365111i	$0.881031\pi$
$614$		−	126334.i		−	0.335106i
$615$		0			0
$616$	−546432.			−1.44004
$617$	58332.7			0.153229			0.0766147	−	0.997061i	$-0.475589\pi$
$617$	58332.7			0.153229			0.0766147	+	0.997061i	$0.475589\pi$
$618$		0			0
$619$	−464866.			−1.21324			−0.606620	−	0.794992i	$-0.707475\pi$
$619$	−464866.			−1.21324			−0.606620	+	0.794992i	$0.707475\pi$
$620$	−8533.53	−	2671.39i	−0.0221996	−	0.00694950i
$621$		0			0
$622$		−	61416.6i		−	0.158747i
$623$	503222.			1.29653
$624$		0			0
$625$	136608.	+	365959.i	0.349716	+	0.936856i
$626$		−	166104.i		−	0.423869i
$627$		0			0
$628$		−	297585.i		−	0.754558i
$629$			378205.i			0.955929i
$630$		0			0
$631$	150594.			0.378224			0.189112	−	0.981956i	$-0.439439\pi$
$631$	150594.			0.378224			0.189112	+	0.981956i	$0.439439\pi$
$632$	−78849.6			−0.197408
$633$		0			0
$634$	13629.4			0.0339076
$635$	−50409.5	+	161029.i	−0.125016	+	0.399353i
$636$		0			0
$637$			475786.i			1.17255i
$638$	254923.			0.626278
$639$		0			0
$640$	398558.	+	124767.i	0.973042	+	0.304607i
$641$		−	740861.i		−	1.80310i	−0.432672	−	0.901552i	$-0.642429\pi$
$641$		−	740861.i		−	1.80310i	0.432672	−	0.901552i	$-0.357571\pi$
$642$		0			0
$643$			28233.2i			0.0682870i	0.999417	+	0.0341435i	$0.0108703\pi$
$643$			28233.2i			0.0682870i	−0.999417	+	0.0341435i	$0.989130\pi$
$644$			466044.i			1.12371i
$645$		0			0
$646$	113589.			0.272188
$647$	759101.			1.81339			0.906694	−	0.421788i	$-0.138598\pi$
$647$	759101.			1.81339			0.906694	+	0.421788i	$0.138598\pi$
$648$		0			0
$649$	821307.			1.94992
$650$	59124.1	−	85179.3i	0.139939	−	0.201608i
$651$		0			0
$652$			499705.i			1.17549i
$653$	−480373.			−1.12655			−0.563277	−	0.826268i	$-0.690459\pi$
$653$	−480373.			−1.12655			−0.563277	+	0.826268i	$0.690459\pi$
$654$		0			0
$655$	−122333.	+	390783.i	−0.285142	+	0.910863i
$656$			98411.9i			0.228686i
$657$		0			0
$658$			306739.i			0.708464i
$659$		−	257235.i		−	0.592323i	−0.955138	−	0.296162i	$-0.904293\pi$
$659$		−	257235.i		−	0.592323i	0.955138	−	0.296162i	$-0.0957067\pi$
$660$		0			0
$661$	175393.			0.401430			0.200715	−	0.979650i	$-0.435674\pi$
$661$	175393.			0.401430			0.200715	+	0.979650i	$0.435674\pi$
$662$	225580.			0.514735
$663$		0			0
$664$	57757.1			0.130999
$665$	162447.	−	518925.i	0.367341	−	1.17344i
$666$		0			0
$667$		−	473918.i		−	1.06525i
$668$	436301.			0.977763
$669$		0			0
$670$	26596.6	−	84960.6i	0.0592483	−	0.189264i
$671$			308794.i			0.685841i
$672$		0			0
$673$			462605.i			1.02136i	0.859770	+	0.510681i	$0.170607\pi$
$673$			462605.i			1.02136i	−0.859770	+	0.510681i	$0.829393\pi$
$674$			316867.i			0.697522i
$675$		0			0
$676$	−234223.			−0.512550
$677$	671725.			1.46560			0.732798	−	0.680446i	$-0.238214\pi$
$677$	671725.			1.46560			0.732798	+	0.680446i	$0.238214\pi$
$678$		0			0
$679$	51354.1			0.111387
$680$	−305491.	−	95632.8i	−0.660665	−	0.206818i
$681$		0			0
$682$		−	5877.59i		−	0.0126366i
$683$	−475276.			−1.01884			−0.509418	−	0.860519i	$-0.670139\pi$
$683$	−475276.			−1.01884			−0.509418	+	0.860519i	$0.670139\pi$
$684$		0			0
$685$	−558423.	−	174812.i	−1.19010	−	0.372555i
$686$			268897.i			0.571397i
$687$		0			0
$688$		−	305017.i		−	0.644387i
$689$			174744.i			0.368099i
$690$		0			0
$691$	−115300.			−0.241475			−0.120737	−	0.992684i	$-0.538526\pi$
$691$	−115300.			−0.241475			−0.120737	+	0.992684i	$0.538526\pi$
$692$	128675.			0.268709
$693$		0			0
$694$	105813.			0.219694
$695$	−192935.	−	60397.4i	−0.399430	−	0.125040i
$696$		0			0
$697$		−	188368.i		−	0.387741i
$698$	18234.0			0.0374259
$699$		0			0
$700$	−400870.	+	577528.i	−0.818101	+	1.17863i
$701$		−	514039.i		−	1.04607i	−0.852312	−	0.523034i	$-0.824800\pi$
$701$		−	514039.i		−	1.04607i	0.852312	−	0.523034i	$-0.175200\pi$
$702$		0			0
$703$			357523.i			0.723424i
$704$		−	116010.i		−	0.234073i
$705$		0			0
$706$	202387.			0.406044
$707$	−1.11838e6			−2.23743
$708$		0			0
$709$	43609.5			0.0867539			0.0433769	−	0.999059i	$-0.486188\pi$
$709$	43609.5			0.0867539			0.0433769	+	0.999059i	$0.486188\pi$
$710$	11378.5	−	36347.9i	0.0225720	−	0.0721045i
$711$		0			0
$712$		−	280047.i		−	0.552422i
$713$	−10926.8			−0.0214939
$714$		0			0
$715$	−361884.	−	113286.i	−0.707876	−	0.221598i
$716$		−	307000.i		−	0.598843i
$717$		0			0
$718$		−	74738.5i		−	0.144976i
$719$		−	36282.5i		−	0.0701842i	−0.999384	−	0.0350921i	$-0.988828\pi$
$719$		−	36282.5i		−	0.0701842i	0.999384	−	0.0350921i	$-0.0111725\pi$
$720$		0			0
$721$	−196869.			−0.378710
$722$	−96091.0			−0.184335
$723$		0			0
$724$	662895.			1.26464
$725$	407642.	−	587285.i	0.775538	−	1.11731i
$726$		0			0
$727$		−	565757.i		−	1.07044i	−0.844714	−	0.535218i	$-0.820229\pi$
$727$		−	565757.i		−	1.07044i	0.844714	−	0.535218i	$-0.179771\pi$
$728$	406759.			0.767493
$729$		0			0
$730$	100852.	−	322164.i	0.189252	−	0.604549i
$731$			583826.i			1.09257i
$732$		0			0
$733$		−	394264.i		−	0.733802i	−0.930260	−	0.366901i	$-0.880419\pi$
$733$		−	394264.i		−	0.733802i	0.930260	−	0.366901i	$-0.119581\pi$
$734$			222295.i			0.412609i
$735$		0			0
$736$	399729.			0.737921
$737$	−325582.			−0.599413
$738$		0			0
$739$	−252058.			−0.461542			−0.230771	−	0.973008i	$-0.574125\pi$
$739$	−252058.			−0.461542			−0.230771	+	0.973008i	$0.574125\pi$
$740$	138093.	−	441128.i	0.252179	−	0.805566i
$741$		0			0
$742$			212946.i			0.386778i
$743$	−291552.			−0.528127			−0.264064	−	0.964505i	$-0.585063\pi$
$743$	−291552.			−0.528127			−0.264064	+	0.964505i	$0.585063\pi$
$744$		0			0
$745$	144699.	−	462230.i	0.260708	−	0.832810i
$746$		−	60281.1i		−	0.108319i
$747$		0			0
$748$			537080.i			0.959921i
$749$			1.75246e6i			3.12382i
$750$		0			0
$751$	−694419.			−1.23124			−0.615618	−	0.788044i	$-0.711094\pi$
$751$	−694419.			−1.23124			−0.615618	+	0.788044i	$0.711094\pi$
$752$	−343333.			−0.607128
$753$		0			0
$754$	−189762.			−0.333786
$755$	76957.8	+	24091.3i	0.135008	+	0.0422636i
$756$		0			0
$757$			254690.i			0.444447i	0.974996	+	0.222223i	$0.0713314\pi$
$757$			254690.i			0.444447i	−0.974996	+	0.222223i	$0.928669\pi$
$758$	227111.			0.395276
$759$		0			0
$760$	−288786.	−	90403.2i	−0.499975	−	0.156515i
$761$			379005.i			0.654448i	0.944947	+	0.327224i	$0.106113\pi$
$761$			379005.i			0.654448i	−0.944947	+	0.327224i	$0.893887\pi$
$762$		0			0
$763$		−	1.54225e6i		−	2.64914i
$764$			226165.i			0.387471i
$765$		0			0
$766$	−615.629			−0.00104921
$767$	−611374.			−1.03924
$768$		0			0
$769$	729722.			1.23397			0.616985	−	0.786975i	$-0.288354\pi$
$769$	729722.			1.23397			0.616985	+	0.786975i	$0.288354\pi$
$770$	−440997.	−	138052.i	−0.743797	−	0.232842i
$771$		0			0
$772$			230311.i			0.386438i
$773$	312829.			0.523537			0.261769	−	0.965131i	$-0.415694\pi$
$773$	312829.			0.523537			0.261769	+	0.965131i	$0.415694\pi$
$774$		0			0
$775$	−13540.6	−	9398.74i	−0.0225443	−	0.0156483i
$776$		−	28579.0i		−	0.0474595i
$777$		0			0
$778$			296380.i			0.489655i
$779$		−	178067.i		−	0.293433i
$780$		0			0
$781$	−139291.			−0.228360
$782$	−179457.			−0.293459
$783$		0			0
$784$	−648969.			−1.05583
$785$	163879.	−	523498.i	0.265940	−	0.849524i
$786$		0			0
$787$		−	1.03100e6i		−	1.66460i	−0.554323	−	0.832302i	$-0.687023\pi$
$787$		−	1.03100e6i		−	1.66460i	0.554323	−	0.832302i	$-0.312977\pi$
$788$	−209401.			−0.337229
$789$		0			0
$790$	−63635.5	−	19920.8i	−0.101964	−	0.0319193i
$791$		−	1.15882e6i		−	1.85209i
$792$		0			0
$793$		−	229863.i		−	0.365530i
$794$		−	332203.i		−	0.526942i
$795$		0			0
$796$	455091.			0.718245
$797$	−125784.			−0.198020			−0.0990098	−	0.995086i	$-0.531568\pi$
$797$	−125784.			−0.198020			−0.0990098	+	0.995086i	$0.531568\pi$
$798$		0			0
$799$	657167.			1.02939
$800$	495349.	+	343828.i	0.773982	+	0.537231i
$801$		0			0
$802$		−	73304.1i		−	0.113967i
$803$	−1.23458e6			−1.91465
$804$		0			0
$805$	−256648.	+	819842.i	−0.396047	+	1.26514i
$806$			4375.23i			0.00673490i
$807$		0			0
$808$			622385.i			0.953314i
$809$			567816.i			0.867582i	0.901014	+	0.433791i	$0.142824\pi$
$809$			567816.i			0.867582i	−0.901014	+	0.433791i	$0.857176\pi$
$810$		0			0
$811$	−170998.			−0.259985			−0.129993	−	0.991515i	$-0.541495\pi$
$811$	−170998.			−0.259985			−0.129993	+	0.991515i	$0.541495\pi$
$812$	1.28662e6			1.95136
$813$		0			0
$814$	303833.			0.458550
$815$	−275185.	+	879056.i	−0.414295	+	1.32343i
$816$		0			0
$817$			551899.i			0.826829i
$818$	52320.7			0.0781929
$819$		0			0
$820$	−68778.5	+	219707.i	−0.102288	+	0.326751i
$821$		−	443785.i		−	0.658394i	−0.944261	−	0.329197i	$-0.893222\pi$
$821$		−	443785.i		−	0.658394i	0.944261	−	0.329197i	$-0.106778\pi$
$822$		0			0
$823$			583186.i			0.861008i	0.902589	+	0.430504i	$0.141664\pi$
$823$			583186.i			0.861008i	−0.902589	+	0.430504i	$0.858336\pi$
$824$			109559.i			0.161359i
$825$		0			0
$826$	−745029.			−1.09198
$827$	1.16796e6			1.70773			0.853863	−	0.520498i	$-0.174254\pi$
$827$	1.16796e6			1.70773			0.853863	+	0.520498i	$0.174254\pi$
$828$		0			0
$829$	199102.			0.289713			0.144856	−	0.989453i	$-0.453728\pi$
$829$	199102.			0.289713			0.144856	+	0.989453i	$0.453728\pi$
$830$	46612.8	+	14591.9i	0.0676627	+	0.0211815i
$831$		0			0
$832$			86357.2i			0.124753i
$833$	1.24218e6			1.79017
$834$		0			0
$835$	767520.	+	240269.i	1.10082	+	0.344607i
$836$			507710.i			0.726445i
$837$		0			0
$838$			118053.i			0.168108i
$839$		−	804194.i		−	1.14245i	−0.820794	−	0.571225i	$-0.806468\pi$
$839$		−	804194.i		−	1.14245i	0.820794	−	0.571225i	$-0.193532\pi$
$840$		0			0
$841$	−601073.			−0.849836
$842$	419168.			0.591241
$843$		0			0
$844$	612678.			0.860096
$845$	−412033.	−	128985.i	−0.577057	−	0.180645i
$846$		0			0
$847$			475683.i			0.663057i
$848$	−238350.			−0.331455
$849$		0			0
$850$	−222385.	−	154361.i	−0.307800	−	0.213648i
$851$		−	564846.i		−	0.779957i
$852$		0			0
$853$			767685.i			1.05508i	0.849530	+	0.527540i	$0.176885\pi$
$853$			767685.i			1.05508i	−0.849530	+	0.527540i	$0.823115\pi$
$854$		−	280115.i		−	0.384079i
$855$		0			0
$856$	975260.			1.33098
$857$	−391943.			−0.533656			−0.266828	−	0.963744i	$-0.585976\pi$
$857$	−391943.			−0.533656			−0.266828	+	0.963744i	$0.585976\pi$
$858$		0			0
$859$	−822992.			−1.11534			−0.557672	−	0.830061i	$-0.688305\pi$
$859$	−822992.			−1.11534			−0.557672	+	0.830061i	$0.688305\pi$
$860$	213171.	−	680959.i	0.288225	−	0.920712i
$861$		0			0
$862$		−	51946.2i		−	0.0699099i
$863$	486383.			0.653066			0.326533	−	0.945186i	$-0.394120\pi$
$863$	486383.			0.653066			0.326533	+	0.945186i	$0.394120\pi$
$864$		0			0
$865$	226359.	+	70860.7i	0.302528	+	0.0947050i
$866$		−	480993.i		−	0.641362i
$867$		0			0
$868$		−	29664.7i		−	0.0393732i
$869$			243861.i			0.322926i
$870$		0			0
$871$	242361.			0.319467
$872$	−858272.			−1.12873
$873$		0			0
$874$	−169644.			−0.222083
$875$	−1.02323e6	+	795201.i	−1.33647	+	1.03863i
$876$		0			0
$877$			784033.i			1.01938i	0.860359	+	0.509689i	$0.170240\pi$
$877$			784033.i			1.01938i	−0.860359	+	0.509689i	$0.829760\pi$
$878$	−414561.			−0.537773
$879$		0			0
$880$	154522.	−	493608.i	0.199538	−	0.637407i
$881$			95885.0i			0.123537i	0.998090	+	0.0617687i	$0.0196741\pi$
$881$			95885.0i			0.123537i	−0.998090	+	0.0617687i	$0.980326\pi$
$882$		0			0
$883$		−	917120.i		−	1.17626i	−0.808765	−	0.588132i	$-0.799863\pi$
$883$		−	917120.i		−	1.17626i	0.808765	−	0.588132i	$-0.200137\pi$
$884$		−	399797.i		−	0.511606i
$885$		0			0
$886$	−63428.5			−0.0808010
$887$	1.08304e6			1.37657			0.688286	−	0.725439i	$-0.258363\pi$
$887$	1.08304e6			1.37657			0.688286	+	0.725439i	$0.258363\pi$
$888$		0			0
$889$	−559778.			−0.708292
$890$	70751.9	−	226011.i	0.0893220	−	0.285332i
$891$		0			0
$892$		−	71710.3i		−	0.0901263i
$893$	621230.			0.779021
$894$		0			0
$895$	169063.	−	540060.i	0.211059	−	0.674211i
$896$			1.38549e6i			1.72578i
$897$		0			0
$898$			336128.i			0.416824i
$899$			30165.9i			0.0373247i
$900$		0			0
$901$	456221.			0.561986
$902$	−151327.			−0.185995
$903$		0			0
$904$	−644890.			−0.789131
$905$	1.16613e6	+	365053.i	1.42380	+	0.445716i
$906$		0			0
$907$		−	114196.i		−	0.138815i	−0.997588	−	0.0694074i	$-0.977889\pi$
$907$		−	114196.i		−	0.138815i	0.997588	−	0.0694074i	$-0.0221108\pi$
$908$	−654526.			−0.793880
$909$		0			0
$910$	328275.	+	102765.i	0.396419	+	0.124097i
$911$			1.03714e6i			1.24968i	0.780751	+	0.624842i	$0.214837\pi$
$911$			1.03714e6i			1.24968i	−0.780751	+	0.624842i	$0.785163\pi$
$912$		0			0
$913$		−	178628.i		−	0.214292i
$914$		−	506854.i		−	0.606723i
$915$		0			0
$916$	−271400.			−0.323458
$917$	−1.35846e6			−1.61550
$918$		0			0
$919$	−513316.			−0.607790			−0.303895	−	0.952705i	$-0.598287\pi$
$919$	−513316.			−0.607790			−0.303895	+	0.952705i	$0.598287\pi$
$920$	456249.	+	142827.i	0.539046	+	0.168746i
$921$		0			0
$922$			90418.2i			0.106364i
$923$	103687.			0.121708
$924$		0			0
$925$	485854.	−	699963.i	0.567835	−	0.818072i
$926$			470360.i			0.548540i
$927$		0			0
$928$		−	1.10354e6i		−	1.28142i
$929$		−	517344.i		−	0.599444i	−0.954027	−	0.299722i	$-0.903106\pi$
$929$		−	517344.i		−	0.599444i	0.954027	−	0.299722i	$-0.0968938\pi$
$930$		0			0
$931$	1.17425e6			1.35476
$932$	−666943.			−0.767816
$933$		0			0
$934$	−460264.			−0.527610
$935$	−295767.	+	944804.i	−0.338319	+	1.08073i
$936$		0			0
$937$			514142.i			0.585604i	0.956173	+	0.292802i	$0.0945877\pi$
$937$			514142.i			0.585604i	−0.956173	+	0.292802i	$0.905412\pi$
$938$	295344.			0.335678
$939$		0			0
$940$	−766502.	−	239950.i	−0.867476	−	0.271560i
$941$		−	1.53216e6i		−	1.73032i	−0.501497	−	0.865160i	$-0.667217\pi$
$941$		−	1.53216e6i		−	1.73032i	0.501497	−	0.865160i	$-0.332783\pi$
$942$		0			0
$943$			281326.i			0.316364i
$944$		−	833911.i		−	0.935784i
$945$		0			0
$946$	469020.			0.524094
$947$	22247.6			0.0248075			0.0124037	−	0.999923i	$-0.496052\pi$
$947$	22247.6			0.0248075			0.0124037	+	0.999923i	$0.496052\pi$
$948$		0			0
$949$	919014.			1.02044
$950$	−210224.	−	145919.i	−0.232936	−	0.161684i
$951$		0			0
$952$		−	1.06196e6i		−	1.17175i
$953$	−1.22370e6			−1.34737			−0.673686	−	0.739018i	$-0.735290\pi$
$953$	−1.22370e6			−1.34737			−0.673686	+	0.739018i	$0.735290\pi$
$954$		0			0
$955$	−124548.	+	397859.i	−0.136562	+	0.436237i
$956$			994351.i			1.08799i
$957$		0			0
$958$		−	669266.i		−	0.729236i
$959$		−	1.94122e6i		−	2.11075i
$960$		0			0
$961$	−922825.			−0.999247
$962$	−226171.			−0.244392
$963$		0			0
$964$	−1.40361e6			−1.51040
$965$	−126831.	+	405152.i	−0.136198	+	0.435074i
$966$		0			0
$967$		−	184358.i		−	0.197156i	−0.995129	−	0.0985780i	$-0.968571\pi$
$967$		−	184358.i		−	0.197156i	0.995129	−	0.0985780i	$-0.0314294\pi$
$968$	264721.			0.282513
$969$		0			0
$970$	7220.29	−	23064.6i	0.00767381	−	0.0245134i
$971$			1.64182e6i			1.74135i	0.491858	+	0.870675i	$0.336318\pi$
$971$			1.64182e6i			1.74135i	−0.491858	+	0.870675i	$0.663682\pi$
$972$		0			0
$973$		−	670689.i		−	0.708427i
$974$			713978.i			0.752605i
$975$		0			0
$976$	313533.			0.329142
$977$	1.32358e6			1.38664			0.693318	−	0.720632i	$-0.256148\pi$
$977$	1.32358e6			1.38664			0.693318	+	0.720632i	$0.256148\pi$
$978$		0			0
$979$	−866111.			−0.903666
$980$	−1.44884e6	−	453554.i	−1.50858	−	0.472256i
$981$		0			0
$982$			241277.i			0.250203i
$983$	−1.21359e6			−1.25593			−0.627967	−	0.778240i	$-0.716113\pi$
$983$	−1.21359e6			−1.25593			−0.627967	+	0.778240i	$0.716113\pi$
$984$		0			0
$985$	−368367.	−	115316.i	−0.379672	−	0.118855i
$986$			495430.i			0.509599i
$987$		0			0
$988$		−	377935.i		−	0.387171i
$989$		−	871939.i		−	0.891443i
$990$		0			0
$991$	−1.11765e6			−1.13804			−0.569021	−	0.822323i	$-0.692678\pi$
$991$	−1.11765e6			−1.13804			−0.569021	+	0.822323i	$0.692678\pi$
$992$	−25443.6			−0.0258556
$993$		0			0
$994$	126354.			0.127884
$995$	800574.	+	250616.i	0.808640	+	0.253141i
$996$		0			0
$997$		−	533846.i		−	0.537063i	−0.963271	−	0.268532i	$-0.913462\pi$
$997$		−	533846.i		−	0.537063i	0.963271	−	0.268532i	$-0.0865384\pi$
$998$	−565468.			−0.567737
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.5.d.a.44.5	yes	8
3.2	odd	2	inner	45.5.d.a.44.4	yes	8
4.3	odd	2		720.5.c.c.449.1		8
5.2	odd	4		225.5.c.e.26.6		8
5.3	odd	4		225.5.c.e.26.3		8
5.4	even	2	inner	45.5.d.a.44.3	✓	8
12.11	even	2		720.5.c.c.449.8		8
15.2	even	4		225.5.c.e.26.4		8
15.8	even	4		225.5.c.e.26.5		8
15.14	odd	2	inner	45.5.d.a.44.6	yes	8
20.19	odd	2		720.5.c.c.449.7		8
60.59	even	2		720.5.c.c.449.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.5.d.a.44.3	✓	8	5.4	even	2	inner
45.5.d.a.44.4	yes	8	3.2	odd	2	inner
45.5.d.a.44.5	yes	8	1.1	even	1	trivial
45.5.d.a.44.6	yes	8	15.14	odd	2	inner
225.5.c.e.26.3		8	5.3	odd	4
225.5.c.e.26.4		8	15.2	even	4
225.5.c.e.26.5		8	15.8	even	4
225.5.c.e.26.6		8	5.2	odd	4
720.5.c.c.449.1		8	4.3	odd	2
720.5.c.c.449.2		8	60.59	even	2
720.5.c.c.449.7		8	20.19	odd	2
720.5.c.c.449.8		8	12.11	even	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:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	45.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.56128 q^{2} -13.5624 q^{4} +(-23.8583 - 7.46874i) q^{5} -82.9374i q^{7} -46.1553 q^{8} +(-37.2496 - 11.6608i) q^{10} +142.746i q^{11} -106.259i q^{13} -129.489i q^{14} +144.937 q^{16} -277.420 q^{17} -262.250 q^{19} +(323.575 + 101.294i) q^{20} +222.867i q^{22} +414.325 q^{23} +(513.436 + 356.383i) q^{25} -165.900i q^{26} +1124.83i q^{28} -1143.83i q^{29} -26.3726 q^{31} +964.772 q^{32} -433.132 q^{34} +(-619.437 + 1978.74i) q^{35} -1363.29i q^{37} -409.446 q^{38} +(1101.19 + 344.722i) q^{40} +678.999i q^{41} -2104.48i q^{43} -1935.98i q^{44} +646.879 q^{46} -2368.85 q^{47} -4477.60 q^{49} +(801.619 + 556.415i) q^{50} +1441.13i q^{52} -1644.51 q^{53} +(1066.13 - 3405.68i) q^{55} +3828.00i q^{56} -1785.85i q^{58} -5753.62i q^{59} +2163.24 q^{61} -41.1752 q^{62} -812.704 q^{64} +(-793.621 + 2535.16i) q^{65} +2280.85i q^{67} +3762.48 q^{68} +(-967.118 + 3089.38i) q^{70} +975.793i q^{71} +8648.81i q^{73} -2128.49i q^{74} +3556.73 q^{76} +11839.0 q^{77} +1708.36 q^{79} +(-3457.94 - 1082.49i) q^{80} +1060.11i q^{82} -1251.37 q^{83} +(6618.77 + 2071.98i) q^{85} -3285.69i q^{86} -6588.49i q^{88} +6067.49i q^{89} -8812.84 q^{91} -5619.23 q^{92} -3698.45 q^{94} +(6256.83 + 1958.67i) q^{95} +619.192i q^{97} -6990.81 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 36 q^{4} + 280 q^{10} + 148 q^{16} - 1520 q^{19} + 1940 q^{25} + 2968 q^{31} - 12424 q^{34} + 7220 q^{40} + 10088 q^{46} - 8944 q^{49} + 19800 q^{55} + 544 q^{61} - 29188 q^{64} + 1800 q^{70} + 3600 q^{76}+ \cdots + 40928 q^{94}+O(q^{100}) \) 8 * q + 36 * q^4 + 280 * q^10 + 148 * q^16 - 1520 * q^19 + 1940 * q^25 + 2968 * q^31 - 12424 * q^34 + 7220 * q^40 + 10088 * q^46 - 8944 * q^49 + 19800 * q^55 + 544 * q^61 - 29188 * q^64 + 1800 * q^70 + 3600 * q^76 - 12632 * q^79 - 3260 * q^85 - 24552 * q^91 + 40928 * q^94

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