LMFDB - Embedded newform 900.3.y.a.89.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,3,Mod(89,900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(900, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 3]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("900.89");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	900.y (of order $10$, degree $4$, 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:	$24.5232237924$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			89.9
Character	$\chi$	$=$	900.89
Dual form			900.3.y.a.809.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.741250 - 4.94475i) q^{5} -10.0354i q^{7} +O(q^{10})$	$q+(-0.741250 - 4.94475i) q^{5} -10.0354i q^{7} +(-3.66357 - 5.04247i) q^{11} +(4.02230 - 5.53622i) q^{13} +(1.77489 + 5.46255i) q^{17} +(-5.92847 - 18.2459i) q^{19} +(-3.12015 + 2.26692i) q^{23} +(-23.9011 + 7.33059i) q^{25} +(14.8298 + 4.81848i) q^{29} +(5.61283 + 17.2745i) q^{31} +(-49.6224 + 7.43873i) q^{35} +(3.73385 - 5.13920i) q^{37} +(-19.8320 + 27.2964i) q^{41} -47.3822i q^{43} +(-21.5494 + 66.3224i) q^{47} -51.7089 q^{49} +(-8.03094 + 24.7167i) q^{53} +(-22.2181 + 21.8532i) q^{55} +(-12.0451 + 16.5787i) q^{59} +(-31.6445 + 22.9911i) q^{61} +(-30.3568 - 15.7856i) q^{65} +(89.1890 - 28.9793i) q^{67} +(-81.9408 - 26.6242i) q^{71} +(-20.2555 - 27.8793i) q^{73} +(-50.6031 + 36.7653i) q^{77} +(20.2131 - 62.2094i) q^{79} +(-0.704750 - 2.16900i) q^{83} +(25.6953 - 12.8255i) q^{85} +(-55.9085 - 76.9515i) q^{89} +(-55.5581 - 40.3653i) q^{91} +(-85.8272 + 42.8396i) q^{95} +(34.7583 + 11.2936i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q+O(q^{10}) $ 80 * q	$ 80 q + 60 q^{19} + 56 q^{25} - 120 q^{31} + 20 q^{37} - 680 q^{49} - 56 q^{55} - 80 q^{61} - 280 q^{67} - 360 q^{73} + 40 q^{79} + 192 q^{85} + 140 q^{91} - 40 q^{97}+O(q^{100}) $ 80 * q + 60 * q^19 + 56 * q^25 - 120 * q^31 + 20 * q^37 - 680 * q^49 - 56 * q^55 - 80 * q^61 - 280 * q^67 - 360 * q^73 + 40 * q^79 + 192 * q^85 + 140 * q^91 - 40 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{10}\right)$

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
$5$	−0.741250	−	4.94475i	−0.148250	−	0.988950i
$5$	−0.741250	−	4.94475i	−0.148250	−	0.988950i
$6$		0			0
$7$		−	10.0354i		−	1.43363i	−0.697266	−	0.716813i	$-0.745600\pi$
$7$		−	10.0354i		−	1.43363i	0.697266	−	0.716813i	$-0.254400\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−3.66357	−	5.04247i	−0.333052	−	0.458406i	0.609344	−	0.792906i	$-0.291433\pi$
$11$	−3.66357	−	5.04247i	−0.333052	−	0.458406i	−0.942396	+	0.334499i	$0.891433\pi$
$12$		0			0
$13$	4.02230	−	5.53622i	0.309408	−	0.425863i	−0.625789	−	0.779993i	$-0.715223\pi$
$13$	4.02230	−	5.53622i	0.309408	−	0.425863i	0.935196	+	0.354129i	$0.115223\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.77489	+	5.46255i	0.104405	+	0.321326i	0.989590	−	0.143913i	$-0.0459684\pi$
$17$	1.77489	+	5.46255i	0.104405	+	0.321326i	−0.885185	+	0.465239i	$0.845968\pi$
$18$		0			0
$19$	−5.92847	−	18.2459i	−0.312025	−	0.960313i	−0.976962	−	0.213414i	$-0.931542\pi$
$19$	−5.92847	−	18.2459i	−0.312025	−	0.960313i	0.664937	−	0.746899i	$-0.268458\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−3.12015	+	2.26692i	−0.135659	+	0.0985619i	−0.653545	−	0.756888i	$-0.726719\pi$
$23$	−3.12015	+	2.26692i	−0.135659	+	0.0985619i	0.517886	+	0.855449i	$0.326719\pi$
$24$		0			0
$25$	−23.9011	+	7.33059i	−0.956044	+	0.293224i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	14.8298	+	4.81848i	0.511371	+	0.166154i	0.553326	−	0.832965i	$-0.313359\pi$
$29$	14.8298	+	4.81848i	0.511371	+	0.166154i	−0.0419547	+	0.999120i	$0.513359\pi$
$30$		0			0
$31$	5.61283	+	17.2745i	0.181059	+	0.557242i	0.999858	−	0.0168378i	$-0.00535989\pi$
$31$	5.61283	+	17.2745i	0.181059	+	0.557242i	−0.818799	+	0.574080i	$0.805360\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−49.6224	+	7.43873i	−1.41778	+	0.212535i
$36$		0			0
$37$	3.73385	−	5.13920i	0.100915	−	0.138897i	−0.755573	−	0.655064i	$-0.772642\pi$
$37$	3.73385	−	5.13920i	0.100915	−	0.138897i	0.856488	+	0.516167i	$0.172642\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−19.8320	+	27.2964i	−0.483708	+	0.665767i	−0.979212	−	0.202839i	$-0.934983\pi$
$41$	−19.8320	+	27.2964i	−0.483708	+	0.665767i	0.495504	+	0.868606i	$0.334983\pi$
$42$		0			0
$43$		−	47.3822i		−	1.10191i	−0.834535	−	0.550955i	$-0.814263\pi$
$43$		−	47.3822i		−	1.10191i	0.834535	−	0.550955i	$-0.185737\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−21.5494	+	66.3224i	−0.458499	+	1.41111i	0.408479	+	0.912768i	$0.366059\pi$
$47$	−21.5494	+	66.3224i	−0.458499	+	1.41111i	−0.866978	+	0.498347i	$0.833941\pi$
$48$		0			0
$49$	−51.7089			−1.05528
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−8.03094	+	24.7167i	−0.151527	+	0.466352i	−0.997792	−	0.0664091i	$-0.978846\pi$
$53$	−8.03094	+	24.7167i	−0.151527	+	0.466352i	0.846265	+	0.532762i	$0.178846\pi$
$54$		0			0
$55$	−22.2181	+	21.8532i	−0.403966	+	0.397330i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−12.0451	+	16.5787i	−0.204154	+	0.280994i	−0.898801	−	0.438357i	$-0.855561\pi$
$59$	−12.0451	+	16.5787i	−0.204154	+	0.280994i	0.694647	+	0.719351i	$0.255561\pi$
$60$		0			0
$61$	−31.6445	+	22.9911i	−0.518763	+	0.376903i	−0.816138	−	0.577858i	$-0.803889\pi$
$61$	−31.6445	+	22.9911i	−0.518763	+	0.376903i	0.297375	+	0.954761i	$0.403889\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−30.3568	−	15.7856i	−0.467027	−	0.242855i
$66$		0			0
$67$	89.1890	−	28.9793i	1.33118	−	0.432526i	0.444859	−	0.895600i	$-0.353254\pi$
$67$	89.1890	−	28.9793i	1.33118	−	0.432526i	0.886320	+	0.463074i	$0.153254\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−81.9408	−	26.6242i	−1.15410	−	0.374988i	−0.331411	−	0.943487i	$-0.607525\pi$
$71$	−81.9408	−	26.6242i	−1.15410	−	0.374988i	−0.822685	+	0.568498i	$0.807525\pi$
$72$		0			0
$73$	−20.2555	−	27.8793i	−0.277472	−	0.381908i	0.647422	−	0.762132i	$-0.275847\pi$
$73$	−20.2555	−	27.8793i	−0.277472	−	0.381908i	−0.924895	+	0.380223i	$0.875847\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−50.6031	+	36.7653i	−0.657183	+	0.477471i
$78$		0			0
$79$	20.2131	−	62.2094i	0.255862	−	0.787461i	−0.737797	−	0.675023i	$-0.764134\pi$
$79$	20.2131	−	62.2094i	0.255862	−	0.787461i	0.993659	−	0.112439i	$-0.0358661\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−0.704750	−	2.16900i	−0.00849096	−	0.0261325i	0.946721	−	0.322054i	$-0.104373\pi$
$83$	−0.704750	−	2.16900i	−0.00849096	−	0.0261325i	−0.955212	+	0.295922i	$0.904373\pi$
$84$		0			0
$85$	25.6953	−	12.8255i	0.302297	−	0.150888i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−55.9085	−	76.9515i	−0.628186	−	0.864623i	0.369731	−	0.929139i	$-0.379450\pi$
$89$	−55.9085	−	76.9515i	−0.628186	−	0.864623i	−0.997917	+	0.0645155i	$0.979450\pi$
$90$		0			0
$91$	−55.5581	−	40.3653i	−0.610529	−	0.443575i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−85.8272	+	42.8396i	−0.903444	+	0.450943i
$96$		0			0
$97$	34.7583	+	11.2936i	0.358333	+	0.116429i	0.482650	−	0.875813i	$-0.339674\pi$
$97$	34.7583	+	11.2936i	0.358333	+	0.116429i	−0.124318	+	0.992242i	$0.539674\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$			21.7607i			0.215453i	0.994181	+	0.107726i	$0.0343570\pi$
$101$			21.7607i			0.215453i	−0.994181	+	0.107726i	$0.965643\pi$
$102$		0			0
$103$	27.4314	+	8.91299i	0.266324	+	0.0865339i	0.439135	−	0.898421i	$-0.355285\pi$
$103$	27.4314	+	8.91299i	0.266324	+	0.0865339i	−0.172811	+	0.984955i	$0.555285\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−28.6093			−0.267377			−0.133689	−	0.991023i	$-0.542682\pi$
$107$	−28.6093			−0.267377			−0.133689	+	0.991023i	$0.542682\pi$
$108$		0			0
$109$	−173.374	−	125.963i	−1.59058	−	1.15563i	−0.903102	−	0.429425i	$-0.858716\pi$
$109$	−173.374	−	125.963i	−1.59058	−	1.15563i	−0.687482	−	0.726202i	$-0.741284\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−64.3112	−	46.7248i	−0.569126	−	0.413494i	0.265662	−	0.964066i	$-0.414410\pi$
$113$	−64.3112	−	46.7248i	−0.569126	−	0.413494i	−0.834788	+	0.550572i	$0.814410\pi$
$114$		0			0
$115$	13.5222	+	13.7480i	0.117584	+	0.119548i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	54.8187	−	17.8117i	0.460662	−	0.149678i
$120$		0			0
$121$	25.3863	−	78.1310i	0.209804	−	0.645711i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	53.9646	+	112.751i	0.431717	+	0.902009i
$126$		0			0
$127$	−35.4760	−	48.8285i	−0.279338	−	0.384476i	0.646176	−	0.763188i	$-0.276367\pi$
$127$	−35.4760	−	48.8285i	−0.279338	−	0.384476i	−0.925515	+	0.378712i	$0.876367\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	8.32302	−	2.70431i	0.0635345	−	0.0206436i	−0.277077	−	0.960848i	$-0.589366\pi$
$131$	8.32302	−	2.70431i	0.0635345	−	0.0206436i	0.340612	+	0.940204i	$0.389366\pi$
$132$		0			0
$133$	−183.105	+	59.4944i	−1.37673	+	0.447326i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	153.415	+	111.462i	1.11982	+	0.813593i	0.984181	−	0.177166i	$-0.0566929\pi$
$137$	153.415	+	111.462i	1.11982	+	0.813593i	0.135634	+	0.990759i	$0.456693\pi$
$138$		0			0
$139$	187.931	−	136.540i	1.35202	−	0.982303i	0.353117	−	0.935579i	$-0.385122\pi$
$139$	187.931	−	136.540i	1.35202	−	0.982303i	0.998908	−	0.0467238i	$-0.0148781\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−42.6522			−0.298267
$144$		0			0
$145$	12.8336	−	76.9011i	0.0885077	−	0.530353i
$146$		0			0
$147$		0			0
$148$		0			0
$149$			126.532i			0.849208i	0.905379	+	0.424604i	$0.139587\pi$
$149$			126.532i			0.849208i	−0.905379	+	0.424604i	$0.860413\pi$
$150$		0			0
$151$	−132.779			−0.879331			−0.439665	−	0.898162i	$-0.644903\pi$
$151$	−132.779			−0.879331			−0.439665	+	0.898162i	$0.644903\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	81.2576	−	40.5588i	0.524242	−	0.261669i
$156$		0			0
$157$		−	32.3212i		−	0.205868i	−0.994688	−	0.102934i	$-0.967177\pi$
$157$		−	32.3212i		−	0.205868i	0.994688	−	0.102934i	$-0.0328230\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	22.7494	+	31.3119i	0.141301	+	0.194484i
$162$		0			0
$163$	−100.199	+	137.912i	−0.614717	+	0.846085i	−0.996955	−	0.0779785i	$-0.975153\pi$
$163$	−100.199	+	137.912i	−0.614717	+	0.846085i	0.382238	+	0.924064i	$0.375153\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−72.1209	−	221.965i	−0.431861	−	1.32913i	−0.896269	−	0.443511i	$-0.853733\pi$
$167$	−72.1209	−	221.965i	−0.431861	−	1.32913i	0.464407	−	0.885622i	$-0.346267\pi$
$168$		0			0
$169$	37.7530	+	116.192i	0.223391	+	0.687526i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−212.306	+	154.249i	−1.22720	+	0.891615i	−0.996677	−	0.0814516i	$-0.974044\pi$
$173$	−212.306	+	154.249i	−1.22720	+	0.891615i	−0.230525	+	0.973066i	$0.574044\pi$
$174$		0			0
$175$	73.5653	+	239.857i	0.420373	+	1.37061i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	207.308	+	67.3583i	1.15814	+	0.376303i	0.824205	−	0.566292i	$-0.191622\pi$
$179$	207.308	+	67.3583i	1.15814	+	0.376303i	0.333938	+	0.942595i	$0.391622\pi$
$180$		0			0
$181$	−62.9015	−	193.591i	−0.347522	−	1.06956i	−0.960220	−	0.279245i	$-0.909916\pi$
$181$	−62.9015	−	193.591i	−0.347522	−	1.06956i	0.612698	−	0.790317i	$-0.290084\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−28.1798	−	14.6535i	−0.152323	−	0.0792081i
$186$		0			0
$187$	21.0423	−	28.9622i	0.112526	−	0.154878i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	191.644	−	263.775i	1.00337	−	1.38102i	0.0801358	−	0.996784i	$-0.474465\pi$
$191$	191.644	−	263.775i	1.00337	−	1.38102i	0.923235	−	0.384237i	$-0.125535\pi$
$192$		0			0
$193$			336.443i			1.74323i	0.490193	+	0.871614i	$0.336926\pi$
$193$			336.443i			1.74323i	−0.490193	+	0.871614i	$0.663074\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−62.9049	+	193.601i	−0.319314	+	0.982748i	0.654628	+	0.755951i	$0.272825\pi$
$197$	−62.9049	+	193.601i	−0.319314	+	0.982748i	−0.973942	+	0.226797i	$0.927175\pi$
$198$		0			0
$199$	173.745			0.873090			0.436545	−	0.899683i	$-0.356202\pi$
$199$	173.745			0.873090			0.436545	+	0.899683i	$0.356202\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	48.3553	−	148.822i	0.238203	−	0.733114i
$204$		0			0
$205$	149.675	+	77.8309i	0.730120	+	0.379663i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−70.2853	+	96.7394i	−0.336293	+	0.462868i
$210$		0			0
$211$	−116.798	+	84.8588i	−0.553545	+	0.402174i	−0.829091	−	0.559114i	$-0.811142\pi$
$211$	−116.798	+	84.8588i	−0.553545	+	0.402174i	0.275546	+	0.961288i	$0.411142\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−234.293	+	35.1220i	−1.08973	+	0.163358i
$216$		0			0
$217$	173.356	−	56.3268i	0.798877	−	0.259571i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	37.3810	+	12.1458i	0.169145	+	0.0549585i
$222$		0			0
$223$	107.240	+	147.604i	0.480899	+	0.661900i	0.978677	−	0.205404i	$-0.0658508\pi$
$223$	107.240	+	147.604i	0.480899	+	0.661900i	−0.497779	+	0.867304i	$0.665851\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	273.262	−	198.536i	1.20380	−	0.874609i	0.209144	−	0.977885i	$-0.432932\pi$
$227$	273.262	−	198.536i	1.20380	−	0.874609i	0.994653	+	0.103276i	$0.0329324\pi$
$228$		0			0
$229$	−2.49872	+	7.69026i	−0.0109114	+	0.0335819i	−0.956364	−	0.292178i	$-0.905620\pi$
$229$	−2.49872	+	7.69026i	−0.0109114	+	0.0335819i	0.945453	+	0.325760i	$0.105620\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−111.396	−	342.841i	−0.478094	−	1.47142i	−0.841739	−	0.539885i	$-0.818468\pi$
$233$	−111.396	−	342.841i	−0.478094	−	1.47142i	0.363645	−	0.931538i	$-0.381532\pi$
$234$		0			0
$235$	343.921	+	57.3951i	1.46349	+	0.244235i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−104.950	−	144.451i	−0.439122	−	0.604399i	0.530895	−	0.847438i	$-0.321856\pi$
$239$	−104.950	−	144.451i	−0.439122	−	0.604399i	−0.970017	+	0.243038i	$0.921856\pi$
$240$		0			0
$241$	−144.962	−	105.321i	−0.601501	−	0.437016i	0.244910	−	0.969546i	$-0.421242\pi$
$241$	−144.962	−	105.321i	−0.601501	−	0.437016i	−0.846411	+	0.532529i	$0.821242\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	38.3292	+	255.687i	0.156446	+	1.04362i
$246$		0			0
$247$	−124.860	−	40.5694i	−0.505505	−	0.164249i
$248$		0			0
$249$		0			0
$250$		0			0
$251$		−	368.969i		−	1.46999i	−0.678070	−	0.734997i	$-0.737183\pi$
$251$		−	368.969i		−	1.46999i	0.678070	−	0.734997i	$-0.262817\pi$
$252$		0			0
$253$	22.8618	+	7.42824i	0.0903627	+	0.0293606i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−97.8088			−0.380579			−0.190289	−	0.981728i	$-0.560943\pi$
$257$	−97.8088			−0.380579			−0.190289	+	0.981728i	$0.560943\pi$
$258$		0			0
$259$	−51.5738	−	37.4706i	−0.199127	−	0.144674i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−120.646	−	87.6541i	−0.458728	−	0.333286i	0.334304	−	0.942465i	$-0.391499\pi$
$263$	−120.646	−	87.6541i	−0.458728	−	0.333286i	−0.793032	+	0.609180i	$0.791499\pi$
$264$		0			0
$265$	128.171	+	21.3897i	0.483663	+	0.0807159i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	468.849	−	152.338i	1.74293	−	0.566313i	0.747717	−	0.664017i	$-0.231150\pi$
$269$	468.849	−	152.338i	1.74293	−	0.566313i	0.995216	+	0.0977038i	$0.0311498\pi$
$270$		0			0
$271$	−9.48456	+	29.1905i	−0.0349984	+	0.107714i	−0.967030	−	0.254664i	$-0.918035\pi$
$271$	−9.48456	+	29.1905i	−0.0349984	+	0.107714i	0.932031	+	0.362378i	$0.118035\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	124.528	+	93.6644i	0.452828	+	0.340598i
$276$		0			0
$277$	315.614	+	434.405i	1.13940	+	1.56825i	0.768842	+	0.639439i	$0.220833\pi$
$277$	315.614	+	434.405i	1.13940	+	1.56825i	0.370557	+	0.928810i	$0.379167\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	503.832	−	163.705i	1.79300	−	0.582580i	0.793341	−	0.608778i	$-0.208340\pi$
$281$	503.832	−	163.705i	1.79300	−	0.582580i	0.999657	+	0.0261978i	$0.00833996\pi$
$282$		0			0
$283$	−40.7006	+	13.2244i	−0.143818	+	0.0467294i	−0.380042	−	0.924969i	$-0.624090\pi$
$283$	−40.7006	+	13.2244i	−0.143818	+	0.0467294i	0.236223	+	0.971699i	$0.424090\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	273.930	+	199.022i	0.954461	+	0.693456i
$288$		0			0
$289$	207.117	−	150.479i	0.716667	−	0.520689i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	201.301			0.687033			0.343516	−	0.939147i	$-0.388382\pi$
$293$	201.301			0.687033			0.343516	+	0.939147i	$0.388382\pi$
$294$		0			0
$295$	90.9058	+	47.2711i	0.308155	+	0.160241i
$296$		0			0
$297$		0			0
$298$		0			0
$299$			26.3921i			0.0882679i
$300$		0			0
$301$	−475.498			−1.57973
$302$		0			0
$303$		0			0
$304$		0			0
$305$	137.142	+	139.432i	0.449645	+	0.457154i
$306$		0			0
$307$		−	365.871i		−	1.19176i	−0.803073	−	0.595881i	$-0.796803\pi$
$307$		−	365.871i		−	1.19176i	0.803073	−	0.595881i	$-0.203197\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−134.867	−	185.628i	−0.433656	−	0.596876i	0.535132	−	0.844769i	$-0.320262\pi$
$311$	−134.867	−	185.628i	−0.433656	−	0.596876i	−0.968788	+	0.247893i	$0.920262\pi$
$312$		0			0
$313$	−325.451	+	447.945i	−1.03978	+	1.43114i	−0.142437	+	0.989804i	$0.545494\pi$
$313$	−325.451	+	447.945i	−1.03978	+	1.43114i	−0.897344	+	0.441332i	$0.854506\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	166.517	+	512.487i	0.525291	+	1.61668i	0.763740	+	0.645525i	$0.223361\pi$
$317$	166.517	+	512.487i	0.525291	+	1.61668i	−0.238448	+	0.971155i	$0.576639\pi$
$318$		0			0
$319$	−30.0328	−	92.4314i	−0.0941467	−	0.289754i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	89.1469	−	64.7690i	0.275997	−	0.200523i
$324$		0			0
$325$	−55.5536	+	161.808i	−0.170934	+	0.497870i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	665.570	+	216.257i	2.02301	+	0.657316i
$330$		0			0
$331$	19.4940	+	59.9964i	0.0588943	+	0.181258i	0.976176	−	0.216982i	$-0.0696212\pi$
$331$	19.4940	+	59.9964i	0.0588943	+	0.181258i	−0.917281	+	0.398240i	$0.869621\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−209.407	−	419.536i	−0.625094	−	1.25235i
$336$		0			0
$337$	52.6227	−	72.4289i	0.156150	−	0.214923i	−0.723773	−	0.690038i	$-0.757594\pi$
$337$	52.6227	−	72.4289i	0.156150	−	0.214923i	0.879923	+	0.475116i	$0.157594\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	66.5432	−	91.5888i	0.195141	−	0.268589i
$342$		0			0
$343$			27.1844i			0.0792549i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−5.72066	+	17.6064i	−0.0164861	+	0.0507389i	−0.958961	−	0.283538i	$-0.908492\pi$
$347$	−5.72066	+	17.6064i	−0.0164861	+	0.0507389i	0.942475	+	0.334276i	$0.108492\pi$
$348$		0			0
$349$	−417.200			−1.19541			−0.597707	−	0.801714i	$-0.703922\pi$
$349$	−417.200			−1.19541			−0.597707	+	0.801714i	$0.703922\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	3.01661	−	9.28418i	0.00854565	−	0.0263008i	−0.946693	−	0.322138i	$-0.895599\pi$
$353$	3.01661	−	9.28418i	0.00854565	−	0.0263008i	0.955238	+	0.295837i	$0.0955985\pi$
$354$		0			0
$355$	−70.9112	+	424.912i	−0.199750	+	1.19693i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	20.6471	−	28.4182i	0.0575127	−	0.0791595i	−0.779292	−	0.626661i	$-0.784421\pi$
$359$	20.6471	−	28.4182i	0.0575127	−	0.0791595i	0.836805	+	0.547502i	$0.184421\pi$
$360$		0			0
$361$	−5.71267	+	4.15050i	−0.0158246	+	0.0114972i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−122.842	+	120.824i	−0.336553	+	0.331024i
$366$		0			0
$367$	521.195	−	169.347i	1.42015	−	0.461435i	0.504500	−	0.863412i	$-0.331677\pi$
$367$	521.195	−	169.347i	1.42015	−	0.461435i	0.915650	+	0.401977i	$0.131677\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	248.041	+	80.5935i	0.668575	+	0.217233i
$372$		0			0
$373$	−51.9823	−	71.5475i	−0.139363	−	0.191816i	0.733631	−	0.679548i	$-0.237824\pi$
$373$	−51.9823	−	71.5475i	−0.139363	−	0.191816i	−0.872993	+	0.487732i	$0.837824\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	86.3259	−	62.7195i	0.228981	−	0.166365i
$378$		0			0
$379$	151.275	−	465.576i	0.399142	−	1.22843i	−0.526546	−	0.850147i	$-0.676513\pi$
$379$	151.275	−	465.576i	0.399142	−	1.22843i	0.925688	−	0.378287i	$-0.123487\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−114.841	−	353.445i	−0.299846	−	0.922832i	−0.981550	−	0.191204i	$-0.938761\pi$
$383$	−114.841	−	353.445i	−0.299846	−	0.922832i	0.681704	−	0.731628i	$-0.261239\pi$
$384$		0			0
$385$	219.305	+	222.967i	0.569623	+	0.579136i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−373.850	−	514.560i	−0.961053	−	1.32278i	−0.946439	−	0.322882i	$-0.895348\pi$
$389$	−373.850	−	514.560i	−0.961053	−	1.32278i	−0.0146136	−	0.999893i	$-0.504652\pi$
$390$		0			0
$391$	−17.9211	−	13.0204i	−0.0458340	−	0.0333003i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−322.593	−	53.8358i	−0.816691	−	0.136293i
$396$		0			0
$397$	602.095	+	195.633i	1.51661	+	0.492777i	0.944812	−	0.327614i	$-0.106245\pi$
$397$	602.095	+	195.633i	1.51661	+	0.492777i	0.571802	+	0.820392i	$0.306245\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$			108.143i			0.269684i	0.990867	+	0.134842i	$0.0430526\pi$
$401$			108.143i			0.269684i	−0.990867	+	0.134842i	$0.956947\pi$
$402$		0			0
$403$	118.212	+	38.4094i	0.293330	+	0.0953087i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−39.5934			−0.0972812
$408$		0			0
$409$	−402.449	−	292.397i	−0.983984	−	0.714906i	−0.0253883	−	0.999678i	$-0.508082\pi$
$409$	−402.449	−	292.397i	−0.983984	−	0.714906i	−0.958595	+	0.284772i	$0.908082\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	166.373	+	120.877i	0.402841	+	0.292681i
$414$		0			0
$415$	−10.2028	+	5.09258i	−0.0245850	+	0.0122713i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	760.537	−	247.114i	1.81513	−	0.589770i	0.815181	−	0.579206i	$-0.196637\pi$
$419$	760.537	−	247.114i	1.81513	−	0.589770i	0.999944	−	0.0105638i	$-0.00336261\pi$
$420$		0			0
$421$	−130.298	+	401.015i	−0.309496	+	0.952531i	0.668465	+	0.743744i	$0.266952\pi$
$421$	−130.298	+	401.015i	−0.309496	+	0.952531i	−0.977961	+	0.208787i	$0.933048\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−82.4655	−	117.550i	−0.194036	−	0.276588i
$426$		0			0
$427$	230.724	+	317.565i	0.540338	+	0.743711i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−630.199	+	204.764i	−1.46218	+	0.475091i	−0.928735	−	0.370744i	$-0.879103\pi$
$431$	−630.199	+	204.764i	−1.46218	+	0.475091i	−0.533445	+	0.845835i	$0.679103\pi$
$432$		0			0
$433$	−128.945	+	41.8967i	−0.297794	+	0.0967590i	−0.454103	−	0.890949i	$-0.650040\pi$
$433$	−128.945	+	41.8967i	−0.297794	+	0.0967590i	0.156310	+	0.987708i	$0.450040\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	59.8599	+	43.4907i	0.136979	+	0.0995211i
$438$		0			0
$439$	451.444	−	327.993i	1.02835	−	0.747137i	0.0603690	−	0.998176i	$-0.480772\pi$
$439$	451.444	−	327.993i	1.02835	−	0.747137i	0.967977	+	0.251039i	$0.0807723\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−633.459			−1.42993			−0.714965	−	0.699160i	$-0.753557\pi$
$443$	−633.459			−1.42993			−0.714965	+	0.699160i	$0.753557\pi$
$444$		0			0
$445$	−339.064	+	333.494i	−0.761941	+	0.749425i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			210.412i			0.468623i	0.972162	+	0.234311i	$0.0752836\pi$
$449$			210.412i			0.468623i	−0.972162	+	0.234311i	$0.924716\pi$
$450$		0			0
$451$	210.297			0.466292
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−158.414	+	304.642i	−0.348163	+	0.669542i
$456$		0			0
$457$		−	250.481i		−	0.548098i	−0.961716	−	0.274049i	$-0.911637\pi$
$457$		−	250.481i		−	0.548098i	0.961716	−	0.274049i	$-0.0883630\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−323.658	−	445.477i	−0.702078	−	0.966327i	−0.999931	−	0.0117153i	$-0.996271\pi$
$461$	−323.658	−	445.477i	−0.702078	−	0.966327i	0.297854	−	0.954611i	$-0.403729\pi$
$462$		0			0
$463$	−292.642	+	402.788i	−0.632057	+	0.869952i	−0.998161	−	0.0606221i	$-0.980692\pi$
$463$	−292.642	+	402.788i	−0.632057	+	0.869952i	0.366104	+	0.930574i	$0.380692\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	70.0902	+	215.716i	0.150086	+	0.461918i	0.997630	−	0.0688078i	$-0.0219195\pi$
$467$	70.0902	+	215.716i	0.150086	+	0.461918i	−0.847544	+	0.530726i	$0.821920\pi$
$468$		0			0
$469$	−290.818	−	895.045i	−0.620081	−	1.90841i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−238.923	+	173.588i	−0.505123	+	0.366993i
$474$		0			0
$475$	275.450	+	392.639i	0.579896	+	0.826608i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−8.28264	−	2.69119i	−0.0172915	−	0.00561836i	0.300358	−	0.953826i	$-0.402894\pi$
$479$	−8.28264	−	2.69119i	−0.0172915	−	0.00561836i	−0.317650	+	0.948208i	$0.602894\pi$
$480$		0			0
$481$	−13.4331	−	41.3428i	−0.0279274	−	0.0859518i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	30.0797	−	180.242i	0.0620199	−	0.371634i
$486$		0			0
$487$	366.213	−	504.049i	0.751977	−	1.03501i	−0.245862	−	0.969305i	$-0.579071\pi$
$487$	366.213	−	504.049i	0.751977	−	1.03501i	0.997839	−	0.0657026i	$-0.0209289\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	12.3374	−	16.9809i	0.0251270	−	0.0345844i	−0.796269	−	0.604943i	$-0.793196\pi$
$491$	12.3374	−	16.9809i	0.0251270	−	0.0345844i	0.821396	+	0.570359i	$0.193196\pi$
$492$		0			0
$493$			89.5605i			0.181664i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−267.184	+	822.307i	−0.537593	+	1.65454i
$498$		0			0
$499$	−216.108			−0.433082			−0.216541	−	0.976274i	$-0.569477\pi$
$499$	−216.108			−0.433082			−0.216541	+	0.976274i	$0.569477\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	57.5061	−	176.986i	0.114326	−	0.351860i	−0.877480	−	0.479614i	$-0.840777\pi$
$503$	57.5061	−	176.986i	0.114326	−	0.351860i	0.991806	+	0.127754i	$0.0407767\pi$
$504$		0			0
$505$	107.601	−	16.1301i	0.213072	−	0.0319409i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	210.486	−	289.709i	0.413528	−	0.569173i	−0.550546	−	0.834805i	$-0.685581\pi$
$509$	210.486	−	289.709i	0.413528	−	0.569173i	0.964075	+	0.265632i	$0.0855805\pi$
$510$		0			0
$511$	−279.779	+	203.272i	−0.547513	+	0.397792i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	23.7390	−	142.248i	0.0460952	−	0.276210i
$516$		0			0
$517$	413.376	−	134.314i	0.799568	−	0.259795i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−221.816	−	72.0723i	−0.425750	−	0.138335i	0.0883016	−	0.996094i	$-0.471856\pi$
$521$	−221.816	−	72.0723i	−0.425750	−	0.138335i	−0.514052	+	0.857759i	$0.671856\pi$
$522$		0			0
$523$	−141.451	−	194.690i	−0.270460	−	0.372256i	0.652085	−	0.758146i	$-0.273895\pi$
$523$	−141.451	−	194.690i	−0.270460	−	0.372256i	−0.922545	+	0.385890i	$0.873895\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−84.4006	+	61.3206i	−0.160153	+	0.116358i
$528$		0			0
$529$	−158.874	+	488.963i	−0.300328	+	0.924315i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	71.3488	+	219.589i	0.133863	+	0.411987i
$534$		0			0
$535$	21.2067	+	141.466i	0.0396387	+	0.264423i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	189.439	+	260.740i	0.351464	+	0.483748i
$540$		0			0
$541$	−691.247	−	502.220i	−1.27772	−	0.928318i	−0.278239	−	0.960512i	$-0.589751\pi$
$541$	−691.247	−	502.220i	−1.27772	−	0.928318i	−0.999482	+	0.0321933i	$0.989751\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−494.344	+	950.660i	−0.907053	+	1.74433i
$546$		0			0
$547$	155.602	+	50.5581i	0.284464	+	0.0924279i	0.447774	−	0.894147i	$-0.352217\pi$
$547$	155.602	+	50.5581i	0.284464	+	0.0924279i	−0.163310	+	0.986575i	$0.552217\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		−	299.149i		−	0.542920i
$552$		0			0
$553$	−624.295	−	202.846i	−1.12892	−	0.366810i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−238.780			−0.428689			−0.214344	−	0.976758i	$-0.568762\pi$
$557$	−238.780			−0.428689			−0.214344	+	0.976758i	$0.568762\pi$
$558$		0			0
$559$	−262.318	−	190.585i	−0.469263	−	0.340940i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	203.782	+	148.056i	0.361957	+	0.262977i	0.753868	−	0.657026i	$-0.228186\pi$
$563$	203.782	+	148.056i	0.361957	+	0.262977i	−0.391911	+	0.920003i	$0.628186\pi$
$564$		0			0
$565$	−183.372	+	352.638i	−0.324552	+	0.624137i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−897.385	+	291.578i	−1.57713	+	0.512440i	−0.961315	−	0.275453i	$-0.911172\pi$
$569$	−897.385	+	291.578i	−1.57713	+	0.512440i	−0.615812	+	0.787893i	$0.711172\pi$
$570$		0			0
$571$	50.8041	−	156.359i	0.0889739	−	0.273833i	−0.896663	−	0.442715i	$-0.854015\pi$
$571$	50.8041	−	156.359i	0.0889739	−	0.273833i	0.985636	+	0.168881i	$0.0540154\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	57.9571	−	77.0545i	0.100795	−	0.134008i
$576$		0			0
$577$	−359.248	−	494.463i	−0.622614	−	0.856954i	0.374926	−	0.927055i	$-0.377668\pi$
$577$	−359.248	−	494.463i	−0.622614	−	0.856954i	−0.997540	+	0.0701005i	$0.977668\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−21.7667	+	7.07244i	−0.0374642	+	0.0121729i
$582$		0			0
$583$	154.055	−	50.0555i	0.264245	−	0.0858585i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	370.877	+	269.458i	0.631818	+	0.459043i	0.857030	−	0.515267i	$-0.172307\pi$
$587$	370.877	+	269.458i	0.631818	+	0.459043i	−0.225212	+	0.974310i	$0.572307\pi$
$588$		0			0
$589$	281.914	−	204.823i	0.478632	−	0.347746i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	56.0856			0.0945795			0.0472897	−	0.998881i	$-0.484942\pi$
$593$	56.0856			0.0945795			0.0472897	+	0.998881i	$0.484942\pi$
$594$		0			0
$595$	−128.709	−	257.862i	−0.216317	−	0.433381i
$596$		0			0
$597$		0			0
$598$		0			0
$599$			293.225i			0.489524i	0.969583	+	0.244762i	$0.0787099\pi$
$599$			293.225i			0.489524i	−0.969583	+	0.244762i	$0.921290\pi$
$600$		0			0
$601$	−915.700			−1.52363			−0.761813	−	0.647797i	$-0.775691\pi$
$601$	−915.700			−1.52363			−0.761813	+	0.647797i	$0.775691\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−405.156	−	67.6143i	−0.669679	−	0.111759i
$606$		0			0
$607$		−	23.1336i		−	0.0381113i	−0.999818	−	0.0190557i	$-0.993934\pi$
$607$		−	23.1336i		−	0.0381113i	0.999818	−	0.0190557i	$-0.00606597\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	280.497	+	386.071i	0.459079	+	0.631868i
$612$		0			0
$613$	367.160	−	505.353i	0.598957	−	0.824393i	−0.396656	−	0.917967i	$-0.629829\pi$
$613$	367.160	−	505.353i	0.598957	−	0.824393i	0.995612	+	0.0935745i	$0.0298293\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−61.7064	−	189.913i	−0.100010	−	0.307800i	0.888517	−	0.458844i	$-0.151736\pi$
$617$	−61.7064	−	189.913i	−0.100010	−	0.307800i	−0.988527	+	0.151044i	$0.951736\pi$
$618$		0			0
$619$	−196.788	−	605.653i	−0.317914	−	0.978437i	−0.974539	−	0.224220i	$-0.928017\pi$
$619$	−196.788	−	605.653i	−0.317914	−	0.978437i	0.656625	−	0.754217i	$-0.271983\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−772.237	+	561.063i	−1.23955	+	0.900583i
$624$		0			0
$625$	517.525	−	350.418i	0.828040	−	0.560670i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	34.7003	+	11.2748i	0.0551674	+	0.0179250i
$630$		0			0
$631$	−374.206	−	1151.69i	−0.593037	−	1.82518i	−0.564265	−	0.825594i	$-0.690840\pi$
$631$	−374.206	−	1151.69i	−0.593037	−	1.82518i	−0.0287721	−	0.999586i	$-0.509160\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−215.148	+	211.614i	−0.338816	+	0.333250i
$636$		0			0
$637$	−207.989	+	286.272i	−0.326513	+	0.449406i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	173.069	−	238.210i	0.269999	−	0.371622i	−0.652390	−	0.757883i	$-0.726234\pi$
$641$	173.069	−	238.210i	0.269999	−	0.371622i	0.922389	+	0.386261i	$0.126234\pi$
$642$		0			0
$643$			1037.71i			1.61386i	0.590645	+	0.806932i	$0.298873\pi$
$643$			1037.71i			1.61386i	−0.590645	+	0.806932i	$0.701127\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	43.3231	−	133.335i	0.0669600	−	0.206082i	−0.911978	−	0.410239i	$-0.865445\pi$
$647$	43.3231	−	133.335i	0.0669600	−	0.206082i	0.978938	+	0.204157i	$0.0654454\pi$
$648$		0			0
$649$	127.725			0.196804
$650$		0			0
$651$		0			0
$652$		0			0
$653$	109.844	−	338.064i	0.168214	−	0.517710i	−0.831045	−	0.556206i	$-0.812257\pi$
$653$	109.844	−	338.064i	0.168214	−	0.517710i	0.999259	+	0.0384960i	$0.0122567\pi$
$654$		0			0
$655$	−19.5416	−	39.1507i	−0.0298345	−	0.0597720i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	145.144	−	199.773i	0.220248	−	0.303146i	−0.684567	−	0.728950i	$-0.740009\pi$
$659$	145.144	−	199.773i	0.220248	−	0.303146i	0.904815	+	0.425804i	$0.140009\pi$
$660$		0			0
$661$	−174.017	+	126.431i	−0.263264	+	0.191272i	−0.711585	−	0.702600i	$-0.752022\pi$
$661$	−174.017	+	126.431i	−0.263264	+	0.191272i	0.448321	+	0.893873i	$0.352022\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	429.912	+	861.308i	0.646484	+	1.29520i
$666$		0			0
$667$	−57.1942	+	18.5835i	−0.0857484	+	0.0278614i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	231.864	+	75.3371i	0.345549	+	0.112276i
$672$		0			0
$673$	−447.728	−	616.245i	−0.665272	−	0.915668i	0.334370	−	0.942442i	$-0.391477\pi$
$673$	−447.728	−	616.245i	−0.665272	−	0.915668i	−0.999642	+	0.0267740i	$0.991477\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−443.301	+	322.077i	−0.654802	+	0.475742i	−0.864904	−	0.501938i	$-0.832621\pi$
$677$	−443.301	+	322.077i	−0.654802	+	0.475742i	0.210101	+	0.977680i	$0.432621\pi$
$678$		0			0
$679$	113.336	−	348.812i	0.166916	−	0.513715i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−377.675	−	1162.36i	−0.552965	−	1.70185i	−0.701257	−	0.712908i	$-0.747378\pi$
$683$	−377.675	−	1162.36i	−0.552965	−	1.70185i	0.148292	−	0.988944i	$-0.452622\pi$
$684$		0			0
$685$	437.434	−	841.219i	0.638590	−	1.22806i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	104.534	+	143.879i	0.151719	+	0.208823i
$690$		0			0
$691$	1.73788	+	1.26264i	0.00251502	+	0.00182727i	0.589042	−	0.808102i	$-0.299505\pi$
$691$	1.73788	+	1.26264i	0.00251502	+	0.00182727i	−0.586527	+	0.809930i	$0.699505\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−814.461	−	828.063i	−1.17189	−	1.19146i
$696$		0			0
$697$	−184.308	−	59.8852i	−0.264430	−	0.0859185i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	500.163i		−	0.713499i	−0.934200	−	0.356750i	$-0.883885\pi$
$701$		−	500.163i		−	0.713499i	0.934200	−	0.356750i	$-0.116115\pi$
$702$		0			0
$703$	−115.906	−	37.6600i	−0.164873	−	0.0535704i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	218.377			0.308878
$708$		0			0
$709$	936.251	+	680.226i	1.32052	+	0.959416i	0.999926	+	0.0122009i	$0.00388377\pi$
$709$	936.251	+	680.226i	1.32052	+	0.959416i	0.320598	+	0.947215i	$0.396116\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−56.6728	−	41.1752i	−0.0794850	−	0.0577493i
$714$		0			0
$715$	31.6160	+	210.905i	0.0442181	+	0.294971i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−744.163	+	241.793i	−1.03500	+	0.336291i	−0.776764	−	0.629792i	$-0.783140\pi$
$719$	−744.163	+	241.793i	−1.03500	+	0.336291i	−0.258233	+	0.966083i	$0.583140\pi$
$720$		0			0
$721$	89.4453	−	275.284i	0.124057	−	0.381809i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−389.770	−	6.45603i	−0.537613	−	0.00890486i
$726$		0			0
$727$	−415.941	−	572.494i	−0.572134	−	0.787475i	0.420672	−	0.907213i	$-0.361794\pi$
$727$	−415.941	−	572.494i	−0.572134	−	0.787475i	−0.992805	+	0.119738i	$0.961794\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	258.827	−	84.0981i	0.354073	−	0.115045i
$732$		0			0
$733$	673.590	−	218.863i	0.918950	−	0.298585i	0.188914	−	0.981994i	$-0.439503\pi$
$733$	673.590	−	218.863i	0.918950	−	0.298585i	0.730036	+	0.683409i	$0.239503\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−472.877	−	343.565i	−0.641624	−	0.466167i
$738$		0			0
$739$	33.5475	−	24.3737i	0.0453958	−	0.0329820i	−0.564856	−	0.825190i	$-0.691068\pi$
$739$	33.5475	−	24.3737i	0.0453958	−	0.0329820i	0.610252	+	0.792208i	$0.291068\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−1127.87			−1.51799			−0.758995	−	0.651096i	$-0.774309\pi$
$743$	−1127.87			−1.51799			−0.758995	+	0.651096i	$0.774309\pi$
$744$		0			0
$745$	625.669	−	93.7918i	0.839824	−	0.125895i
$746$		0			0
$747$		0			0
$748$		0			0
$749$			287.106i			0.383319i
$750$		0			0
$751$	866.774			1.15416			0.577080	−	0.816688i	$-0.304192\pi$
$751$	866.774			1.15416			0.577080	+	0.816688i	$0.304192\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	98.4225	+	656.559i	0.130361	+	0.869614i
$756$		0			0
$757$			7.44545i			0.00983547i	0.999988	+	0.00491773i	$0.00156537\pi$
$757$			7.44545i			0.00983547i	−0.999988	+	0.00491773i	$0.998435\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−185.364	−	255.131i	−0.243579	−	0.335258i	0.669671	−	0.742658i	$-0.266435\pi$
$761$	−185.364	−	255.131i	−0.243579	−	0.335258i	−0.913250	+	0.407401i	$0.866435\pi$
$762$		0			0
$763$	−1264.09	+	1739.87i	−1.65674	+	2.28030i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	43.3342	+	133.369i	0.0564982	+	0.173884i
$768$		0			0
$769$	164.786	+	507.160i	0.214287	+	0.659506i	0.999203	+	0.0399053i	$0.0127056\pi$
$769$	164.786	+	507.160i	0.214287	+	0.659506i	−0.784917	+	0.619601i	$0.787294\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−587.182	+	426.613i	−0.759615	+	0.551892i	−0.898792	−	0.438375i	$-0.855554\pi$
$773$	−587.182	+	426.613i	−0.759615	+	0.551892i	0.139177	+	0.990267i	$0.455554\pi$
$774$		0			0
$775$	−260.785	−	371.734i	−0.336497	−	0.479657i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	615.623	+	200.028i	0.790273	+	0.256775i
$780$		0			0
$781$	165.944	+	510.723i	0.212476	+	0.653935i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−159.820	+	23.9581i	−0.203593	+	0.0305199i
$786$		0			0
$787$	52.8297	−	72.7139i	0.0671280	−	0.0923938i	−0.774133	−	0.633023i	$-0.781814\pi$
$787$	52.8297	−	72.7139i	0.0671280	−	0.0923938i	0.841261	+	0.540629i	$0.181814\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−468.901	+	645.387i	−0.592796	+	0.815913i
$792$		0			0
$793$			267.668i			0.337539i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	211.060	−	649.575i	0.264818	−	0.815025i	−0.726918	−	0.686724i	$-0.759048\pi$
$797$	211.060	−	649.575i	0.264818	−	0.815025i	0.991735	−	0.128300i	$-0.0409521\pi$
$798$		0			0
$799$	−400.537			−0.501298
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−66.3731	+	204.275i	−0.0826564	+	0.254390i
$804$		0			0
$805$	137.967	−	135.700i	0.171387	−	0.168572i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−42.7022	+	58.7745i	−0.0527839	+	0.0726508i	−0.834593	−	0.550867i	$-0.814297\pi$
$809$	−42.7022	+	58.7745i	−0.0527839	+	0.0726508i	0.781809	+	0.623518i	$0.214297\pi$
$810$		0			0
$811$	48.8437	−	35.4870i	0.0602265	−	0.0437571i	−0.557265	−	0.830335i	$-0.688149\pi$
$811$	48.8437	−	35.4870i	0.0602265	−	0.0437571i	0.617491	+	0.786578i	$0.288149\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	756.212	+	393.231i	0.927868	+	0.482492i
$816$		0			0
$817$	−864.532	+	280.904i	−1.05818	+	0.343823i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−327.083	−	106.276i	−0.398396	−	0.129447i	0.102965	−	0.994685i	$-0.467167\pi$
$821$	−327.083	−	106.276i	−0.398396	−	0.129447i	−0.501361	+	0.865238i	$0.667167\pi$
$822$		0			0
$823$	319.745	+	440.092i	0.388512	+	0.534741i	0.957814	−	0.287387i	$-0.0927867\pi$
$823$	319.745	+	440.092i	0.388512	+	0.534741i	−0.569303	+	0.822128i	$0.692787\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−569.480	+	413.751i	−0.688609	+	0.500304i	−0.876203	−	0.481943i	$-0.839931\pi$
$827$	−569.480	+	413.751i	−0.688609	+	0.500304i	0.187593	+	0.982247i	$0.439931\pi$
$828$		0			0
$829$	6.27152	−	19.3018i	0.00756517	−	0.0232832i	−0.947203	−	0.320635i	$-0.896104\pi$
$829$	6.27152	−	19.3018i	0.00756517	−	0.0232832i	0.954768	+	0.297352i	$0.0961036\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−91.7775	−	282.462i	−0.110177	−	0.339090i
$834$		0			0
$835$	−1044.10	+	521.151i	−1.25042	+	0.624133i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	200.734	+	276.287i	0.239254	+	0.329305i	0.911712	−	0.410831i	$-0.134761\pi$
$839$	200.734	+	276.287i	0.239254	+	0.329305i	−0.672458	+	0.740136i	$0.734761\pi$
$840$		0			0
$841$	−483.679	−	351.414i	−0.575124	−	0.417852i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	546.555	−	272.806i	0.646811	−	0.322848i
$846$		0			0
$847$	−784.074	−	254.761i	−0.925707	−	0.300781i
$848$		0			0
$849$		0			0
$850$		0			0
$851$			24.4994i			0.0287890i
$852$		0			0
$853$	849.859	+	276.136i	0.996318	+	0.323723i	0.761393	−	0.648290i	$-0.224516\pi$
$853$	849.859	+	276.136i	0.996318	+	0.323723i	0.234925	+	0.972014i	$0.424516\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	1205.27			1.40639			0.703193	−	0.710999i	$-0.251757\pi$
$857$	1205.27			1.40639			0.703193	+	0.710999i	$0.251757\pi$
$858$		0			0
$859$	699.676	+	508.345i	0.814524	+	0.591787i	0.915139	−	0.403139i	$-0.132081\pi$
$859$	699.676	+	508.345i	0.814524	+	0.591787i	−0.100614	+	0.994925i	$0.532081\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	708.525	+	514.773i	0.821002	+	0.596493i	0.916999	−	0.398889i	$-0.130604\pi$
$863$	708.525	+	514.773i	0.821002	+	0.596493i	−0.0959973	+	0.995382i	$0.530604\pi$
$864$		0			0
$865$	920.096	+	935.463i	1.06370	+	1.08146i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−387.741	+	125.985i	−0.446192	+	0.144977i
$870$		0			0
$871$	198.309	−	610.334i	0.227680	−	0.700727i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	1131.50	−	541.556i	1.29314	−	0.618921i
$876$		0			0
$877$	299.525	+	412.261i	0.341534	+	0.470081i	0.944889	−	0.327392i	$-0.106170\pi$
$877$	299.525	+	412.261i	0.341534	+	0.470081i	−0.603355	+	0.797473i	$0.706170\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	1372.72	−	446.023i	1.55814	−	0.506269i	0.601827	−	0.798627i	$-0.294440\pi$
$881$	1372.72	−	446.023i	1.55814	−	0.506269i	0.956309	+	0.292357i	$0.0944397\pi$
$882$		0			0
$883$	273.856	−	88.9812i	0.310143	−	0.100771i	−0.149810	−	0.988715i	$-0.547866\pi$
$883$	273.856	−	88.9812i	0.310143	−	0.100771i	0.459953	+	0.887943i	$0.347866\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−649.326	−	471.763i	−0.732048	−	0.531864i	0.158163	−	0.987413i	$-0.449443\pi$
$887$	−649.326	−	471.763i	−0.732048	−	0.531864i	−0.890211	+	0.455549i	$0.849443\pi$
$888$		0			0
$889$	−490.012	+	356.015i	−0.551195	+	0.400466i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	1337.87			1.49817
$894$		0			0
$895$	179.403	−	1075.01i	0.200450	−	1.20113i
$896$		0			0
$897$		0			0
$898$		0			0
$899$			283.222i			0.315041i
$900$		0			0
$901$	−149.270			−0.165671
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−910.632	+	454.531i	−1.00622	+	0.502244i
$906$		0			0
$907$			1132.02i			1.24809i	0.781388	+	0.624046i	$0.214512\pi$
$907$			1132.02i			1.24809i	−0.781388	+	0.624046i	$0.785488\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	748.271	+	1029.91i	0.821373	+	1.13052i	0.989468	+	0.144752i	$0.0462386\pi$
$911$	748.271	+	1029.91i	0.821373	+	1.13052i	−0.168095	+	0.985771i	$0.553761\pi$
$912$		0			0
$913$	−8.35520	+	11.5000i	−0.00915137	+	0.0125958i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−27.1388	−	83.5246i	−0.0295952	−	0.0910847i
$918$		0			0
$919$	−304.488	−	937.116i	−0.331325	−	1.01971i	−0.968504	−	0.248997i	$-0.919899\pi$
$919$	−304.488	−	937.116i	−0.331325	−	1.01971i	0.637179	−	0.770716i	$-0.280101\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−476.988	+	346.552i	−0.516780	+	0.375463i
$924$		0			0
$925$	−51.5696	+	150.204i	−0.0557510	+	0.162382i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−517.685	−	168.206i	−0.557250	−	0.181061i	0.0168335	−	0.999858i	$-0.494641\pi$
$929$	−517.685	−	168.206i	−0.557250	−	0.181061i	−0.574083	+	0.818797i	$0.694641\pi$
$930$		0			0
$931$	306.554	+	943.477i	0.329274	+	1.01340i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−158.809	−	82.5806i	−0.169849	−	0.0883215i
$936$		0			0
$937$	381.468	−	525.045i	0.407116	−	0.560347i	−0.555396	−	0.831586i	$-0.687433\pi$
$937$	381.468	−	525.045i	0.407116	−	0.560347i	0.962512	+	0.271239i	$0.0874333\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	57.3184	−	78.8920i	0.0609122	−	0.0838384i	−0.777474	−	0.628915i	$-0.783499\pi$
$941$	57.3184	−	78.8920i	0.0609122	−	0.0838384i	0.838386	+	0.545076i	$0.183499\pi$
$942$		0			0
$943$		−	130.127i		−	0.137992i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	172.773	−	531.739i	0.182442	−	0.561499i	−0.817453	−	0.575995i	$-0.804615\pi$
$947$	172.773	−	531.739i	0.182442	−	0.561499i	0.999895	+	0.0144967i	$0.00461462\pi$
$948$		0			0
$949$	−235.820			−0.248493
$950$		0			0
$951$		0			0
$952$		0			0
$953$	413.337	−	1272.12i	0.433722	−	1.33486i	−0.460669	−	0.887572i	$-0.652391\pi$
$953$	413.337	−	1272.12i	0.433722	−	1.33486i	0.894391	−	0.447286i	$-0.147609\pi$
$954$		0			0
$955$	−1446.36	−	752.107i	−1.51451	−	0.787547i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	1118.57	−	1539.57i	1.16639	−	1.60540i
$960$		0			0
$961$	510.561	−	370.944i	0.531281	−	0.385998i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	1663.63	−	249.389i	1.72397	−	0.258434i
$966$		0			0
$967$	−14.7971	+	4.80787i	−0.0153021	+	0.00497195i	−0.316658	−	0.948540i	$-0.602561\pi$
$967$	−14.7971	+	4.80787i	−0.0153021	+	0.00497195i	0.301356	+	0.953512i	$0.402561\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−101.838	−	33.0891i	−0.104879	−	0.0340774i	0.256107	−	0.966648i	$-0.417560\pi$
$971$	−101.838	−	33.0891i	−0.104879	−	0.0340774i	−0.360987	+	0.932571i	$0.617560\pi$
$972$		0			0
$973$	−1370.23	−	1885.96i	−1.40826	−	1.93830i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	147.231	−	106.970i	0.150697	−	0.109488i	−0.509882	−	0.860245i	$-0.670311\pi$
$977$	147.231	−	106.970i	0.150697	−	0.109488i	0.660579	+	0.750756i	$0.270311\pi$
$978$		0			0
$979$	−183.201	+	563.834i	−0.187130	+	0.575928i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−212.527	−	654.092i	−0.216203	−	0.665404i	−0.999066	−	0.0432100i	$-0.986242\pi$
$983$	−212.527	−	654.092i	−0.216203	−	0.665404i	0.782863	−	0.622194i	$-0.213758\pi$
$984$		0			0
$985$	1003.94	+	167.542i	1.01923	+	0.170093i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	107.412	+	147.839i	0.108606	+	0.149484i
$990$		0			0
$991$	894.399	+	649.819i	0.902522	+	0.655720i	0.939112	−	0.343610i	$-0.111650\pi$
$991$	894.399	+	649.819i	0.902522	+	0.655720i	−0.0365908	+	0.999330i	$0.511650\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−128.788	−	859.125i	−0.129436	−	0.863442i
$996$		0			0
$997$	1322.82	+	429.810i	1.32680	+	0.431103i	0.884824	−	0.465925i	$-0.154278\pi$
$997$	1322.82	+	429.810i	1.32680	+	0.431103i	0.441974	+	0.897028i	$0.354278\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.3.y.a.89.9	✓	80
3.2	odd	2	inner	900.3.y.a.89.12	yes	80
25.9	even	10	inner	900.3.y.a.809.12	yes	80
75.59	odd	10	inner	900.3.y.a.809.9	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
900.3.y.a.89.9	✓	80	1.1	even	1	trivial
900.3.y.a.89.12	yes	80	3.2	odd	2	inner
900.3.y.a.809.9	yes	80	75.59	odd	10	inner
900.3.y.a.809.12	yes	80	25.9	even	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	900.y (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.741250 - 4.94475i) q^{5} -10.0354i q^{7} +O(q^{10})\)	\(q+(-0.741250 - 4.94475i) q^{5} -10.0354i q^{7} +(-3.66357 - 5.04247i) q^{11} +(4.02230 - 5.53622i) q^{13} +(1.77489 + 5.46255i) q^{17} +(-5.92847 - 18.2459i) q^{19} +(-3.12015 + 2.26692i) q^{23} +(-23.9011 + 7.33059i) q^{25} +(14.8298 + 4.81848i) q^{29} +(5.61283 + 17.2745i) q^{31} +(-49.6224 + 7.43873i) q^{35} +(3.73385 - 5.13920i) q^{37} +(-19.8320 + 27.2964i) q^{41} -47.3822i q^{43} +(-21.5494 + 66.3224i) q^{47} -51.7089 q^{49} +(-8.03094 + 24.7167i) q^{53} +(-22.2181 + 21.8532i) q^{55} +(-12.0451 + 16.5787i) q^{59} +(-31.6445 + 22.9911i) q^{61} +(-30.3568 - 15.7856i) q^{65} +(89.1890 - 28.9793i) q^{67} +(-81.9408 - 26.6242i) q^{71} +(-20.2555 - 27.8793i) q^{73} +(-50.6031 + 36.7653i) q^{77} +(20.2131 - 62.2094i) q^{79} +(-0.704750 - 2.16900i) q^{83} +(25.6953 - 12.8255i) q^{85} +(-55.9085 - 76.9515i) q^{89} +(-55.5581 - 40.3653i) q^{91} +(-85.8272 + 42.8396i) q^{95} +(34.7583 + 11.2936i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q+O(q^{10}) \) 80 * q	\( 80 q + 60 q^{19} + 56 q^{25} - 120 q^{31} + 20 q^{37} - 680 q^{49} - 56 q^{55} - 80 q^{61} - 280 q^{67} - 360 q^{73} + 40 q^{79} + 192 q^{85} + 140 q^{91} - 40 q^{97}+O(q^{100}) \) 80 * q + 60 * q^19 + 56 * q^25 - 120 * q^31 + 20 * q^37 - 680 * q^49 - 56 * q^55 - 80 * q^61 - 280 * q^67 - 360 * q^73 + 40 * q^79 + 192 * q^85 + 140 * q^91 - 40 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more