LMFDB - Embedded newform 3900.2.bm.b.2257.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3900,2,Mod(2257,3900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3900, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("3900.2257");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3900 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3900.bm (of order $4$, degree $2$, 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:	$31.1416567883$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 780)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			2257.12
Character	$\chi$	$=$	3900.2257
Dual form			3900.2.bm.b.2293.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{3} -2.13466 q^{7} -1.00000i q^{9} +O(q^{10})$	$q+(0.707107 - 0.707107i) q^{3} -2.13466 q^{7} -1.00000i q^{9} +(1.89894 - 1.89894i) q^{11} +(-3.33364 + 1.37361i) q^{13} +(-1.22748 + 1.22748i) q^{17} +(-0.581270 + 0.581270i) q^{19} +(-1.50943 + 1.50943i) q^{21} +(4.10913 + 4.10913i) q^{23} +(-0.707107 - 0.707107i) q^{27} +1.81712i q^{29} +(4.74497 + 4.74497i) q^{31} -2.68551i q^{33} -6.00961 q^{37} +(-1.38595 + 3.32853i) q^{39} +(3.85523 + 3.85523i) q^{41} +(3.78653 + 3.78653i) q^{43} +2.75112 q^{47} -2.44322 q^{49} +1.73592i q^{51} +(7.79380 - 7.79380i) q^{53} +0.822039i q^{57} +(-0.434208 - 0.434208i) q^{59} +13.1423 q^{61} +2.13466i q^{63} -1.27294i q^{67} +5.81118 q^{69} +(-1.66190 - 1.66190i) q^{71} -0.637019i q^{73} +(-4.05360 + 4.05360i) q^{77} +0.837401i q^{79} -1.00000 q^{81} +5.22354 q^{83} +(1.28490 + 1.28490i) q^{87} +(3.92688 + 3.92688i) q^{89} +(7.11620 - 2.93220i) q^{91} +6.71041 q^{93} -6.15970i q^{97} +(-1.89894 - 1.89894i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q+O(q^{10}) $ 28 * q	$ 28 q + 8 q^{11} - 4 q^{17} + 16 q^{19} + 8 q^{21} - 8 q^{23} - 24 q^{37} - 8 q^{39} + 12 q^{41} + 16 q^{43} + 24 q^{47} + 36 q^{49} - 36 q^{53} - 16 q^{59} + 8 q^{61} + 8 q^{69} + 8 q^{71} - 48 q^{77} - 28 q^{81} + 24 q^{83} + 24 q^{87} + 36 q^{89} - 24 q^{91} - 8 q^{99}+O(q^{100}) $ 28 * q + 8 * q^11 - 4 * q^17 + 16 * q^19 + 8 * q^21 - 8 * q^23 - 24 * q^37 - 8 * q^39 + 12 * q^41 + 16 * q^43 + 24 * q^47 + 36 * q^49 - 36 * q^53 - 16 * q^59 + 8 * q^61 + 8 * q^69 + 8 * q^71 - 48 * q^77 - 28 * q^81 + 24 * q^83 + 24 * q^87 + 36 * q^89 - 24 * q^91 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3900\mathbb{Z}\right)^\times$.

$n$	$301$	$1301$	$1951$	$3277$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$	$e\left(\frac{1}{4}\right)$

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
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−2.13466			−0.806826			−0.403413	−	0.915018i	$-0.632176\pi$
$7$	−2.13466			−0.806826			−0.403413	+	0.915018i	$0.632176\pi$
$8$		0			0
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$	1.89894	−	1.89894i	0.572553	−	0.572553i	−0.360288	−	0.932841i	$-0.617322\pi$
$11$	1.89894	−	1.89894i	0.572553	−	0.572553i	0.932841	+	0.360288i	$0.117322\pi$
$12$		0			0
$13$	−3.33364	+	1.37361i	−0.924587	+	0.380972i
$13$	−3.33364	+	1.37361i	−0.924587	+	0.380972i
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.22748	+	1.22748i	−0.297708	+	0.297708i	−0.840115	−	0.542408i	$-0.817513\pi$
$17$	−1.22748	+	1.22748i	−0.297708	+	0.297708i	0.542408	+	0.840115i	$0.317513\pi$
$18$		0			0
$19$	−0.581270	+	0.581270i	−0.133352	+	0.133352i	−0.770632	−	0.637280i	$-0.780059\pi$
$19$	−0.581270	+	0.581270i	−0.133352	+	0.133352i	0.637280	+	0.770632i	$0.280059\pi$
$20$		0			0
$21$	−1.50943	+	1.50943i	−0.329385	+	0.329385i
$22$		0			0
$23$	4.10913	+	4.10913i	0.856812	+	0.856812i	0.990961	−	0.134149i	$-0.0428300\pi$
$23$	4.10913	+	4.10913i	0.856812	+	0.856812i	−0.134149	+	0.990961i	$0.542830\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$		0			0
$29$			1.81712i			0.337431i	0.985665	+	0.168715i	$0.0539619\pi$
$29$			1.81712i			0.337431i	−0.985665	+	0.168715i	$0.946038\pi$
$30$		0			0
$31$	4.74497	+	4.74497i	0.852223	+	0.852223i	0.990407	−	0.138184i	$-0.0441265\pi$
$31$	4.74497	+	4.74497i	0.852223	+	0.852223i	−0.138184	+	0.990407i	$0.544127\pi$
$32$		0			0
$33$		−	2.68551i		−	0.467487i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−6.00961			−0.987974			−0.493987	−	0.869469i	$-0.664461\pi$
$37$	−6.00961			−0.987974			−0.493987	+	0.869469i	$0.664461\pi$
$38$		0			0
$39$	−1.38595	+	3.32853i	−0.221930	+	0.532992i
$40$		0			0
$41$	3.85523	+	3.85523i	0.602086	+	0.602086i	0.940866	−	0.338780i	$-0.110014\pi$
$41$	3.85523	+	3.85523i	0.602086	+	0.602086i	−0.338780	+	0.940866i	$0.610014\pi$
$42$		0			0
$43$	3.78653	+	3.78653i	0.577440	+	0.577440i	0.934197	−	0.356757i	$-0.116118\pi$
$43$	3.78653	+	3.78653i	0.577440	+	0.577440i	−0.356757	+	0.934197i	$0.616118\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	2.75112			0.401292			0.200646	−	0.979664i	$-0.435696\pi$
$47$	2.75112			0.401292			0.200646	+	0.979664i	$0.435696\pi$
$48$		0			0
$49$	−2.44322			−0.349032
$50$		0			0
$51$			1.73592i			0.243077i
$52$		0			0
$53$	7.79380	−	7.79380i	1.07056	−	1.07056i	0.0732468	−	0.997314i	$-0.476664\pi$
$53$	7.79380	−	7.79380i	1.07056	−	1.07056i	0.997314	−	0.0732468i	$-0.0233361\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$			0.822039i			0.108882i
$58$		0			0
$59$	−0.434208	−	0.434208i	−0.0565290	−	0.0565290i	0.678277	−	0.734806i	$-0.262727\pi$
$59$	−0.434208	−	0.434208i	−0.0565290	−	0.0565290i	−0.734806	+	0.678277i	$0.762727\pi$
$60$		0			0
$61$	13.1423			1.68270			0.841352	−	0.540488i	$-0.181760\pi$
$61$	13.1423			1.68270			0.841352	+	0.540488i	$0.181760\pi$
$62$		0			0
$63$			2.13466i			0.268942i
$64$		0			0
$65$		0			0
$66$		0			0
$67$		−	1.27294i		−	0.155515i	−0.996972	−	0.0777573i	$-0.975224\pi$
$67$		−	1.27294i		−	0.155515i	0.996972	−	0.0777573i	$-0.0247759\pi$
$68$		0			0
$69$	5.81118			0.699584
$70$		0			0
$71$	−1.66190	−	1.66190i	−0.197231	−	0.197231i	0.601581	−	0.798812i	$-0.294538\pi$
$71$	−1.66190	−	1.66190i	−0.197231	−	0.197231i	−0.798812	+	0.601581i	$0.794538\pi$
$72$		0			0
$73$		−	0.637019i		−	0.0745575i	−0.999305	−	0.0372787i	$-0.988131\pi$
$73$		−	0.637019i		−	0.0745575i	0.999305	−	0.0372787i	$-0.0118689\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−4.05360	+	4.05360i	−0.461950	+	0.461950i
$78$		0			0
$79$			0.837401i			0.0942149i	0.998890	+	0.0471075i	$0.0150003\pi$
$79$			0.837401i			0.0942149i	−0.998890	+	0.0471075i	$0.985000\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	5.22354			0.573358			0.286679	−	0.958027i	$-0.407449\pi$
$83$	5.22354			0.573358			0.286679	+	0.958027i	$0.407449\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	1.28490	+	1.28490i	0.137756	+	0.137756i
$88$		0			0
$89$	3.92688	+	3.92688i	0.416248	+	0.416248i	0.883908	−	0.467660i	$-0.154903\pi$
$89$	3.92688	+	3.92688i	0.416248	+	0.416248i	−0.467660	+	0.883908i	$0.654903\pi$
$90$		0			0
$91$	7.11620	−	2.93220i	0.745981	−	0.307378i
$92$		0			0
$93$	6.71041			0.695837
$94$		0			0
$95$		0			0
$96$		0			0
$97$		−	6.15970i		−	0.625422i	−0.949848	−	0.312711i	$-0.898763\pi$
$97$		−	6.15970i		−	0.625422i	0.949848	−	0.312711i	$-0.101237\pi$
$98$		0			0
$99$	−1.89894	−	1.89894i	−0.190851	−	0.190851i
$100$		0			0
$101$			3.93730i			0.391776i	0.980626	+	0.195888i	$0.0627589\pi$
$101$			3.93730i			0.391776i	−0.980626	+	0.195888i	$0.937241\pi$
$102$		0			0
$103$	3.97517	+	3.97517i	0.391685	+	0.391685i	0.875288	−	0.483603i	$-0.160672\pi$
$103$	3.97517	+	3.97517i	0.391685	+	0.391685i	−0.483603	+	0.875288i	$0.660672\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	11.2103	+	11.2103i	1.08375	+	1.08375i	0.996157	+	0.0875884i	$0.0279160\pi$
$107$	11.2103	+	11.2103i	1.08375	+	1.08375i	0.0875884	+	0.996157i	$0.472084\pi$
$108$		0			0
$109$	8.33542	−	8.33542i	0.798388	−	0.798388i	−0.184453	−	0.982841i	$-0.559051\pi$
$109$	8.33542	−	8.33542i	0.798388	−	0.798388i	0.982841	+	0.184453i	$0.0590514\pi$
$110$		0			0
$111$	−4.24944	+	4.24944i	−0.403339	+	0.403339i
$112$		0			0
$113$	4.73416	−	4.73416i	0.445353	−	0.445353i	−0.448453	−	0.893806i	$-0.648025\pi$
$113$	4.73416	−	4.73416i	0.445353	−	0.445353i	0.893806	+	0.448453i	$0.148025\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	1.37361	+	3.33364i	0.126991	+	0.308196i
$118$		0			0
$119$	2.62025	−	2.62025i	0.240198	−	0.240198i
$120$		0			0
$121$			3.78804i			0.344367i
$122$		0			0
$123$	5.45212			0.491601
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−5.26184	+	5.26184i	−0.466913	+	0.466913i	−0.900913	−	0.434000i	$-0.857102\pi$
$127$	−5.26184	+	5.26184i	−0.466913	+	0.466913i	0.434000	+	0.900913i	$0.357102\pi$
$128$		0			0
$129$	5.35496			0.471478
$130$		0			0
$131$	−21.1234			−1.84556			−0.922779	−	0.385330i	$-0.874088\pi$
$131$	−21.1234			−1.84556			−0.922779	+	0.385330i	$0.874088\pi$
$132$		0			0
$133$	1.24081	−	1.24081i	0.107592	−	0.107592i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	13.1203			1.12094			0.560470	−	0.828175i	$-0.310621\pi$
$137$	13.1203			1.12094			0.560470	+	0.828175i	$0.310621\pi$
$138$		0			0
$139$		−	19.3191i		−	1.63862i	−0.573349	−	0.819311i	$-0.694356\pi$
$139$		−	19.3191i		−	1.63862i	0.573349	−	0.819311i	$-0.305644\pi$
$140$		0			0
$141$	1.94533	−	1.94533i	0.163827	−	0.163827i
$142$		0			0
$143$	−3.72199	+	8.93881i	−0.311248	+	0.747501i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−1.72762	+	1.72762i	−0.142492	+	0.142492i
$148$		0			0
$149$	3.41550	−	3.41550i	0.279808	−	0.279808i	−0.553224	−	0.833032i	$-0.686603\pi$
$149$	3.41550	−	3.41550i	0.279808	−	0.279808i	0.833032	+	0.553224i	$0.186603\pi$
$150$		0			0
$151$	−9.07740	+	9.07740i	−0.738709	+	0.738709i	−0.972328	−	0.233619i	$-0.924943\pi$
$151$	−9.07740	+	9.07740i	−0.738709	+	0.738709i	0.233619	+	0.972328i	$0.424943\pi$
$152$		0			0
$153$	1.22748	+	1.22748i	0.0992358	+	0.0992358i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	16.7071	+	16.7071i	1.33337	+	1.33337i	0.902335	+	0.431035i	$0.141851\pi$
$157$	16.7071	+	16.7071i	1.33337	+	1.33337i	0.431035	+	0.902335i	$0.358149\pi$
$158$		0			0
$159$		−	11.0221i		−	0.874109i
$160$		0			0
$161$	−8.77160	−	8.77160i	−0.691299	−	0.691299i
$162$		0			0
$163$		−	5.73933i		−	0.449539i	−0.974412	−	0.224769i	$-0.927837\pi$
$163$		−	5.73933i		−	0.449539i	0.974412	−	0.224769i	$-0.0721629\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−12.4964			−0.967002			−0.483501	−	0.875344i	$-0.660635\pi$
$167$	−12.4964			−0.967002			−0.483501	+	0.875344i	$0.660635\pi$
$168$		0			0
$169$	9.22638	−	9.15827i	0.709721	−	0.704483i
$170$		0			0
$171$	0.581270	+	0.581270i	0.0444508	+	0.0444508i
$172$		0			0
$173$	12.1397	+	12.1397i	0.922966	+	0.922966i	0.997238	−	0.0742720i	$-0.0236633\pi$
$173$	12.1397	+	12.1397i	0.922966	+	0.922966i	−0.0742720	+	0.997238i	$0.523663\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−0.614063			−0.0461558
$178$		0			0
$179$	−3.88220			−0.290169			−0.145085	−	0.989419i	$-0.546345\pi$
$179$	−3.88220			−0.290169			−0.145085	+	0.989419i	$0.546345\pi$
$180$		0			0
$181$			15.9058i			1.18227i	0.806572	+	0.591136i	$0.201320\pi$
$181$			15.9058i			1.18227i	−0.806572	+	0.591136i	$0.798680\pi$
$182$		0			0
$183$	9.29304	−	9.29304i	0.686961	−	0.686961i
$184$		0			0
$185$		0			0
$186$		0			0
$187$			4.66183i			0.340906i
$188$		0			0
$189$	1.50943	+	1.50943i	0.109795	+	0.109795i
$190$		0			0
$191$	−3.96501			−0.286898			−0.143449	−	0.989658i	$-0.545819\pi$
$191$	−3.96501			−0.286898			−0.143449	+	0.989658i	$0.545819\pi$
$192$		0			0
$193$			16.9136i			1.21747i	0.793374	+	0.608734i	$0.208322\pi$
$193$			16.9136i			1.21747i	−0.793374	+	0.608734i	$0.791678\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			23.1980i			1.65279i	0.563089	+	0.826396i	$0.309613\pi$
$197$			23.1980i			1.65279i	−0.563089	+	0.826396i	$0.690387\pi$
$198$		0			0
$199$	24.2812			1.72125			0.860625	−	0.509239i	$-0.170073\pi$
$199$	24.2812			1.72125			0.860625	+	0.509239i	$0.170073\pi$
$200$		0			0
$201$	−0.900106	−	0.900106i	−0.0634886	−	0.0634886i
$202$		0			0
$203$		−	3.87894i		−	0.272248i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	4.10913	−	4.10913i	0.285604	−	0.285604i
$208$		0			0
$209$			2.20760i			0.152703i
$210$		0			0
$211$	9.03724			0.622149			0.311075	−	0.950386i	$-0.399311\pi$
$211$	9.03724			0.622149			0.311075	+	0.950386i	$0.399311\pi$
$212$		0			0
$213$	−2.35028			−0.161039
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−10.1289	−	10.1289i	−0.687595	−	0.687595i
$218$		0			0
$219$	−0.450441	−	0.450441i	−0.0304380	−	0.0304380i
$220$		0			0
$221$	2.40590	−	5.77806i	0.161838	−	0.388675i
$222$		0			0
$223$	25.1082			1.68137			0.840684	−	0.541527i	$-0.182153\pi$
$223$	25.1082			1.68137			0.840684	+	0.541527i	$0.182153\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$			10.2921i			0.683110i	0.939862	+	0.341555i	$0.110954\pi$
$227$			10.2921i			0.683110i	−0.939862	+	0.341555i	$0.889046\pi$
$228$		0			0
$229$	−1.77751	−	1.77751i	−0.117461	−	0.117461i	0.645933	−	0.763394i	$-0.276468\pi$
$229$	−1.77751	−	1.77751i	−0.117461	−	0.117461i	−0.763394	+	0.645933i	$0.776468\pi$
$230$		0			0
$231$			5.73265i			0.377181i
$232$		0			0
$233$	−14.0627	−	14.0627i	−0.921280	−	0.921280i	0.0758398	−	0.997120i	$-0.475836\pi$
$233$	−14.0627	−	14.0627i	−0.921280	−	0.921280i	−0.997120	+	0.0758398i	$0.975836\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	0.592132	+	0.592132i	0.0384631	+	0.0384631i
$238$		0			0
$239$	−21.1880	+	21.1880i	−1.37054	+	1.37054i	−0.510901	+	0.859640i	$0.670688\pi$
$239$	−21.1880	+	21.1880i	−1.37054	+	1.37054i	−0.859640	+	0.510901i	$0.829312\pi$
$240$		0			0
$241$	1.79901	−	1.79901i	0.115885	−	0.115885i	−0.646786	−	0.762671i	$-0.723888\pi$
$241$	1.79901	−	1.79901i	0.115885	−	0.115885i	0.762671	+	0.646786i	$0.223888\pi$
$242$		0			0
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	1.13931	−	2.73619i	0.0724924	−	0.174099i
$248$		0			0
$249$	3.69360	−	3.69360i	0.234072	−	0.234072i
$250$		0			0
$251$		−	19.4291i		−	1.22635i	−0.789946	−	0.613177i	$-0.789891\pi$
$251$		−	19.4291i		−	1.22635i	0.789946	−	0.613177i	$-0.210109\pi$
$252$		0			0
$253$	15.6060			0.981140
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−7.19958	+	7.19958i	−0.449097	+	0.449097i	−0.895054	−	0.445957i	$-0.852863\pi$
$257$	−7.19958	+	7.19958i	−0.449097	+	0.449097i	0.445957	+	0.895054i	$0.352863\pi$
$258$		0			0
$259$	12.8285			0.797123
$260$		0			0
$261$	1.81712			0.112477
$262$		0			0
$263$	−9.21874	+	9.21874i	−0.568452	+	0.568452i	−0.931695	−	0.363243i	$-0.881670\pi$
$263$	−9.21874	+	9.21874i	−0.568452	+	0.568452i	0.363243	+	0.931695i	$0.381670\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	5.55344			0.339865
$268$		0			0
$269$		−	1.62017i		−	0.0987834i	−0.998779	−	0.0493917i	$-0.984272\pi$
$269$		−	1.62017i		−	0.0987834i	0.998779	−	0.0493917i	$-0.0157283\pi$
$270$		0			0
$271$	6.91766	−	6.91766i	0.420218	−	0.420218i	−0.465061	−	0.885279i	$-0.653968\pi$
$271$	6.91766	−	6.91766i	0.420218	−	0.420218i	0.885279	+	0.465061i	$0.153968\pi$
$272$		0			0
$273$	2.95854	−	7.10529i	0.179059	−	0.430032i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	7.18506	−	7.18506i	0.431709	−	0.431709i	−0.457501	−	0.889209i	$-0.651255\pi$
$277$	7.18506	−	7.18506i	0.431709	−	0.431709i	0.889209	+	0.457501i	$0.151255\pi$
$278$		0			0
$279$	4.74497	−	4.74497i	0.284074	−	0.284074i
$280$		0			0
$281$	10.6309	−	10.6309i	0.634185	−	0.634185i	−0.314930	−	0.949115i	$-0.601981\pi$
$281$	10.6309	−	10.6309i	0.634185	−	0.634185i	0.949115	+	0.314930i	$0.101981\pi$
$282$		0			0
$283$	−12.7919	−	12.7919i	−0.760399	−	0.760399i	0.215995	−	0.976394i	$-0.430700\pi$
$283$	−12.7919	−	12.7919i	−0.760399	−	0.760399i	−0.976394	+	0.215995i	$0.930700\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−8.22962	−	8.22962i	−0.485779	−	0.485779i
$288$		0			0
$289$			13.9866i			0.822740i
$290$		0			0
$291$	−4.35556	−	4.35556i	−0.255328	−	0.255328i
$292$		0			0
$293$		−	16.8122i		−	0.982178i	−0.871109	−	0.491089i	$-0.836599\pi$
$293$		−	16.8122i		−	0.982178i	0.871109	−	0.491089i	$-0.163401\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−2.68551			−0.155829
$298$		0			0
$299$	−19.3427	−	8.05402i	−1.11862	−	0.465776i
$300$		0			0
$301$	−8.08296	−	8.08296i	−0.465894	−	0.465894i
$302$		0			0
$303$	2.78409	+	2.78409i	0.159942	+	0.159942i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−14.6050			−0.833551			−0.416775	−	0.909009i	$-0.636840\pi$
$307$	−14.6050			−0.833551			−0.416775	+	0.909009i	$0.636840\pi$
$308$		0			0
$309$	5.62174			0.319809
$310$		0			0
$311$			27.4910i			1.55887i	0.626481	+	0.779436i	$0.284494\pi$
$311$			27.4910i			1.55887i	−0.626481	+	0.779436i	$0.715506\pi$
$312$		0			0
$313$	−4.82784	+	4.82784i	−0.272886	+	0.272886i	−0.830261	−	0.557375i	$-0.811809\pi$
$313$	−4.82784	+	4.82784i	−0.272886	+	0.272886i	0.557375	+	0.830261i	$0.311809\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$			27.3999i			1.53893i	0.638690	+	0.769464i	$0.279477\pi$
$317$			27.3999i			1.53893i	−0.638690	+	0.769464i	$0.720523\pi$
$318$		0			0
$319$	3.45061	+	3.45061i	0.193197	+	0.193197i
$320$		0			0
$321$	15.8538			0.884874
$322$		0			0
$323$		−	1.42699i		−	0.0794000i
$324$		0			0
$325$		0			0
$326$		0			0
$327$		−	11.7881i		−	0.651881i
$328$		0			0
$329$	−5.87271			−0.323773
$330$		0			0
$331$	−5.68185	−	5.68185i	−0.312303	−	0.312303i	0.533498	−	0.845801i	$-0.320877\pi$
$331$	−5.68185	−	5.68185i	−0.312303	−	0.312303i	−0.845801	+	0.533498i	$0.820877\pi$
$332$		0			0
$333$			6.00961i			0.329325i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	15.7975	−	15.7975i	0.860544	−	0.860544i	−0.130858	−	0.991401i	$-0.541773\pi$
$337$	15.7975	−	15.7975i	0.860544	−	0.860544i	0.991401	+	0.130858i	$0.0417731\pi$
$338$		0			0
$339$		−	6.69512i		−	0.363629i
$340$		0			0
$341$	18.0209			0.975885
$342$		0			0
$343$	20.1581			1.08843
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−17.2806	−	17.2806i	−0.927670	−	0.927670i	0.0698847	−	0.997555i	$-0.477737\pi$
$347$	−17.2806	−	17.2806i	−0.927670	−	0.927670i	−0.997555	+	0.0698847i	$0.977737\pi$
$348$		0			0
$349$	−19.0865	−	19.0865i	−1.02168	−	1.02168i	−0.999760	−	0.0219165i	$-0.993023\pi$
$349$	−19.0865	−	19.0865i	−1.02168	−	1.02168i	−0.0219165	−	0.999760i	$-0.506977\pi$
$350$		0			0
$351$	3.32853	+	1.38595i	0.177664	+	0.0739766i
$352$		0			0
$353$	−33.0078			−1.75683			−0.878414	−	0.477901i	$-0.841398\pi$
$353$	−33.0078			−1.75683			−0.878414	+	0.477901i	$0.841398\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		−	3.70560i		−	0.196121i
$358$		0			0
$359$	−15.0109	−	15.0109i	−0.792247	−	0.792247i	0.189612	−	0.981859i	$-0.439277\pi$
$359$	−15.0109	−	15.0109i	−0.792247	−	0.792247i	−0.981859	+	0.189612i	$0.939277\pi$
$360$		0			0
$361$			18.3243i			0.964434i
$362$		0			0
$363$	2.67855	+	2.67855i	0.140587	+	0.140587i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	2.95951	+	2.95951i	0.154485	+	0.154485i	0.780118	−	0.625633i	$-0.215159\pi$
$367$	2.95951	+	2.95951i	0.154485	+	0.154485i	−0.625633	+	0.780118i	$0.715159\pi$
$368$		0			0
$369$	3.85523	−	3.85523i	0.200695	−	0.200695i
$370$		0			0
$371$	−16.6371	+	16.6371i	−0.863756	+	0.863756i
$372$		0			0
$373$	−3.69960	+	3.69960i	−0.191558	+	0.191558i	−0.796369	−	0.604811i	$-0.793249\pi$
$373$	−3.69960	+	3.69960i	−0.191558	+	0.191558i	0.604811	+	0.796369i	$0.293249\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−2.49602	−	6.05764i	−0.128552	−	0.311984i
$378$		0			0
$379$	−6.73427	+	6.73427i	−0.345916	+	0.345916i	−0.858586	−	0.512670i	$-0.828657\pi$
$379$	−6.73427	+	6.73427i	−0.345916	+	0.345916i	0.512670	+	0.858586i	$0.328657\pi$
$380$		0			0
$381$			7.44137i			0.381233i
$382$		0			0
$383$	16.7639			0.856597			0.428299	−	0.903637i	$-0.359113\pi$
$383$	16.7639			0.856597			0.428299	+	0.903637i	$0.359113\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	3.78653	−	3.78653i	0.192480	−	0.192480i
$388$		0			0
$389$	20.1793			1.02313			0.511566	−	0.859244i	$-0.329066\pi$
$389$	20.1793			1.02313			0.511566	+	0.859244i	$0.329066\pi$
$390$		0			0
$391$	−10.0877			−0.510159
$392$		0			0
$393$	−14.9365	+	14.9365i	−0.753446	+	0.753446i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	26.6617			1.33811			0.669055	−	0.743213i	$-0.266699\pi$
$397$	26.6617			1.33811			0.669055	+	0.743213i	$0.266699\pi$
$398$		0			0
$399$		−	1.75478i		−	0.0878487i
$400$		0			0
$401$	21.5935	−	21.5935i	1.07833	−	1.07833i	0.0816678	−	0.996660i	$-0.473975\pi$
$401$	21.5935	−	21.5935i	1.07833	−	1.07833i	0.996660	−	0.0816678i	$-0.0260246\pi$
$402$		0			0
$403$	−22.3358	−	9.30030i	−1.11263	−	0.463281i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−11.4119	+	11.4119i	−0.565667	+	0.565667i
$408$		0			0
$409$	−2.53012	+	2.53012i	−0.125107	+	0.125107i	−0.766888	−	0.641781i	$-0.778196\pi$
$409$	−2.53012	+	2.53012i	−0.125107	+	0.125107i	0.641781	+	0.766888i	$0.278196\pi$
$410$		0			0
$411$	9.27742	−	9.27742i	0.457622	−	0.457622i
$412$		0			0
$413$	0.926887	+	0.926887i	0.0456091	+	0.0456091i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−13.6606	−	13.6606i	−0.668965	−	0.668965i
$418$		0			0
$419$			20.4939i			1.00119i	0.865681	+	0.500596i	$0.166886\pi$
$419$			20.4939i			1.00119i	−0.865681	+	0.500596i	$0.833114\pi$
$420$		0			0
$421$	−22.7083	−	22.7083i	−1.10674	−	1.10674i	−0.993577	−	0.113160i	$-0.963903\pi$
$421$	−22.7083	−	22.7083i	−1.10674	−	1.10674i	−0.113160	−	0.993577i	$-0.536097\pi$
$422$		0			0
$423$		−	2.75112i		−	0.133764i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−28.0544			−1.35765
$428$		0			0
$429$	3.68885	+	8.95254i	0.178099	+	0.432233i
$430$		0			0
$431$	−7.07318	−	7.07318i	−0.340703	−	0.340703i	0.515929	−	0.856632i	$-0.327447\pi$
$431$	−7.07318	−	7.07318i	−0.340703	−	0.340703i	−0.856632	+	0.515929i	$0.827447\pi$
$432$		0			0
$433$	27.4138	+	27.4138i	1.31742	+	1.31742i	0.915809	+	0.401614i	$0.131551\pi$
$433$	27.4138	+	27.4138i	1.31742	+	1.31742i	0.401614	+	0.915809i	$0.368449\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−4.77702			−0.228516
$438$		0			0
$439$	37.5366			1.79152			0.895762	−	0.444533i	$-0.146630\pi$
$439$	37.5366			1.79152			0.895762	+	0.444533i	$0.146630\pi$
$440$		0			0
$441$			2.44322i			0.116344i
$442$		0			0
$443$	−6.57913	+	6.57913i	−0.312584	+	0.312584i	−0.845910	−	0.533326i	$-0.820942\pi$
$443$	−6.57913	+	6.57913i	−0.312584	+	0.312584i	0.533326	+	0.845910i	$0.320942\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		−	4.83024i		−	0.228463i
$448$		0			0
$449$	12.5481	+	12.5481i	0.592183	+	0.592183i	0.938221	−	0.346038i	$-0.112473\pi$
$449$	12.5481	+	12.5481i	0.592183	+	0.592183i	−0.346038	+	0.938221i	$0.612473\pi$
$450$		0			0
$451$	14.6417			0.689452
$452$		0			0
$453$			12.8374i			0.603153i
$454$		0			0
$455$		0			0
$456$		0			0
$457$		−	21.0694i		−	0.985583i	−0.870147	−	0.492791i	$-0.835977\pi$
$457$		−	21.0694i		−	0.985583i	0.870147	−	0.492791i	$-0.164023\pi$
$458$		0			0
$459$	1.73592			0.0810257
$460$		0			0
$461$	−11.1853	−	11.1853i	−0.520949	−	0.520949i	0.396909	−	0.917858i	$-0.370083\pi$
$461$	−11.1853	−	11.1853i	−0.520949	−	0.520949i	−0.917858	+	0.396909i	$0.870083\pi$
$462$		0			0
$463$		−	38.6791i		−	1.79757i	−0.438389	−	0.898786i	$-0.644451\pi$
$463$		−	38.6791i		−	1.79757i	0.438389	−	0.898786i	$-0.355549\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	13.3530	−	13.3530i	0.617904	−	0.617904i	−0.327090	−	0.944993i	$-0.606068\pi$
$467$	13.3530	−	13.3530i	0.617904	−	0.617904i	0.944993	+	0.327090i	$0.106068\pi$
$468$		0			0
$469$			2.71730i			0.125473i
$470$		0			0
$471$	23.6274			1.08869
$472$		0			0
$473$	14.3808			0.661230
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−7.79380	−	7.79380i	−0.356854	−	0.356854i
$478$		0			0
$479$	1.95863	+	1.95863i	0.0894919	+	0.0894919i	0.750436	−	0.660944i	$-0.229844\pi$
$479$	1.95863	+	1.95863i	0.0894919	+	0.0894919i	−0.660944	+	0.750436i	$0.729844\pi$
$480$		0			0
$481$	20.0339	−	8.25488i	0.913467	−	0.376390i
$482$		0			0
$483$	−12.4049			−0.564443
$484$		0			0
$485$		0			0
$486$		0			0
$487$			17.7479i			0.804234i	0.915588	+	0.402117i	$0.131725\pi$
$487$			17.7479i			0.804234i	−0.915588	+	0.402117i	$0.868275\pi$
$488$		0			0
$489$	−4.05832	−	4.05832i	−0.183524	−	0.183524i
$490$		0			0
$491$			24.6538i			1.11261i	0.830978	+	0.556306i	$0.187782\pi$
$491$			24.6538i			1.11261i	−0.830978	+	0.556306i	$0.812218\pi$
$492$		0			0
$493$	−2.23048	−	2.23048i	−0.100456	−	0.100456i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	3.54759	+	3.54759i	0.159131	+	0.159131i
$498$		0			0
$499$	−0.763548	+	0.763548i	−0.0341811	+	0.0341811i	−0.723991	−	0.689810i	$-0.757694\pi$
$499$	−0.763548	+	0.763548i	−0.0341811	+	0.0341811i	0.689810	+	0.723991i	$0.257694\pi$
$500$		0			0
$501$	−8.83631	+	8.83631i	−0.394777	+	0.394777i
$502$		0			0
$503$	−17.2923	+	17.2923i	−0.771026	+	0.771026i	−0.978286	−	0.207260i	$-0.933546\pi$
$503$	−17.2923	+	17.2923i	−0.771026	+	0.771026i	0.207260	+	0.978286i	$0.433546\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	0.0481545	−	12.9999i	0.00213862	−	0.577346i
$508$		0			0
$509$	−22.2401	+	22.2401i	−0.985776	+	0.985776i	−0.999900	−	0.0141241i	$-0.995504\pi$
$509$	−22.2401	+	22.2401i	−0.985776	+	0.985776i	0.0141241	+	0.999900i	$0.495504\pi$
$510$		0			0
$511$			1.35982i			0.0601549i
$512$		0			0
$513$	0.822039			0.0362939
$514$		0			0
$515$		0			0
$516$		0			0
$517$	5.22421	−	5.22421i	0.229761	−	0.229761i
$518$		0			0
$519$	17.1682			0.753599
$520$		0			0
$521$	3.21481			0.140843			0.0704217	−	0.997517i	$-0.477565\pi$
$521$	3.21481			0.140843			0.0704217	+	0.997517i	$0.477565\pi$
$522$		0			0
$523$	−7.33192	+	7.33192i	−0.320603	+	0.320603i	−0.848998	−	0.528396i	$-0.822794\pi$
$523$	−7.33192	+	7.33192i	−0.320603	+	0.320603i	0.528396	+	0.848998i	$0.322794\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−11.6487			−0.507426
$528$		0			0
$529$			10.7699i			0.468255i
$530$		0			0
$531$	−0.434208	+	0.434208i	−0.0188430	+	0.0188430i
$532$		0			0
$533$	−18.1476	−	7.55638i	−0.786059	−	0.327303i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−2.74513	+	2.74513i	−0.118461	+	0.118461i
$538$		0			0
$539$	−4.63954	+	4.63954i	−0.199839	+	0.199839i
$540$		0			0
$541$	−0.865604	+	0.865604i	−0.0372152	+	0.0372152i	−0.725470	−	0.688254i	$-0.758377\pi$
$541$	−0.865604	+	0.865604i	−0.0372152	+	0.0372152i	0.688254	+	0.725470i	$0.258377\pi$
$542$		0			0
$543$	11.2471	+	11.2471i	0.482661	+	0.482661i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−14.4611	−	14.4611i	−0.618311	−	0.618311i	0.326787	−	0.945098i	$-0.394034\pi$
$547$	−14.4611	−	14.4611i	−0.618311	−	0.618311i	−0.945098	+	0.326787i	$0.894034\pi$
$548$		0			0
$549$		−	13.1423i		−	0.560901i
$550$		0			0
$551$	−1.05624	−	1.05624i	−0.0449972	−	0.0449972i
$552$		0			0
$553$		−	1.78757i		−	0.0760151i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	20.5392			0.870272			0.435136	−	0.900365i	$-0.356700\pi$
$557$	20.5392			0.870272			0.435136	+	0.900365i	$0.356700\pi$
$558$		0			0
$559$	−17.8242	−	7.42172i	−0.753882	−	0.313905i
$560$		0			0
$561$	3.29641	+	3.29641i	0.139174	+	0.139174i
$562$		0			0
$563$	−3.91042	−	3.91042i	−0.164804	−	0.164804i	0.619887	−	0.784691i	$-0.287179\pi$
$563$	−3.91042	−	3.91042i	−0.164804	−	0.164804i	−0.784691	+	0.619887i	$0.787179\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	2.13466			0.0896473
$568$		0			0
$569$	−29.0908			−1.21955			−0.609775	−	0.792574i	$-0.708740\pi$
$569$	−29.0908			−1.21955			−0.609775	+	0.792574i	$0.708740\pi$
$570$		0			0
$571$			27.8608i			1.16594i	0.812494	+	0.582969i	$0.198109\pi$
$571$			27.8608i			1.16594i	−0.812494	+	0.582969i	$0.801891\pi$
$572$		0			0
$573$	−2.80368	+	2.80368i	−0.117126	+	0.117126i
$574$		0			0
$575$		0			0
$576$		0			0
$577$		−	11.1273i		−	0.463235i	−0.972807	−	0.231618i	$-0.925598\pi$
$577$		−	11.1273i		−	0.463235i	0.972807	−	0.231618i	$-0.0744018\pi$
$578$		0			0
$579$	11.9597	+	11.9597i	0.497029	+	0.497029i
$580$		0			0
$581$	−11.1505			−0.462600
$582$		0			0
$583$		−	29.5999i		−	1.22590i
$584$		0			0
$585$		0			0
$586$		0			0
$587$			27.0251i			1.11545i	0.830027	+	0.557723i	$0.188325\pi$
$587$			27.0251i			1.11545i	−0.830027	+	0.557723i	$0.811675\pi$
$588$		0			0
$589$	−5.51622			−0.227292
$590$		0			0
$591$	16.4035	+	16.4035i	0.674750	+	0.674750i
$592$		0			0
$593$			23.2668i			0.955454i	0.878508	+	0.477727i	$0.158539\pi$
$593$			23.2668i			0.955454i	−0.878508	+	0.477727i	$0.841461\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	17.1694	−	17.1694i	0.702698	−	0.702698i
$598$		0			0
$599$			35.1115i			1.43462i	0.696756	+	0.717308i	$0.254626\pi$
$599$			35.1115i			1.43462i	−0.696756	+	0.717308i	$0.745374\pi$
$600$		0			0
$601$	−11.3510			−0.463015			−0.231508	−	0.972833i	$-0.574366\pi$
$601$	−11.3510			−0.463015			−0.231508	+	0.972833i	$0.574366\pi$
$602$		0			0
$603$	−1.27294			−0.0518382
$604$		0			0
$605$		0			0
$606$		0			0
$607$	25.0768	+	25.0768i	1.01784	+	1.01784i	0.999838	+	0.0179998i	$0.00572983\pi$
$607$	25.0768	+	25.0768i	1.01784	+	1.01784i	0.0179998	+	0.999838i	$0.494270\pi$
$608$		0			0
$609$	−2.74282	−	2.74282i	−0.111145	−	0.111145i
$610$		0			0
$611$	−9.17125	+	3.77897i	−0.371029	+	0.152881i
$612$		0			0
$613$	32.7471			1.32264			0.661322	−	0.750103i	$-0.269996\pi$
$613$	32.7471			1.32264			0.661322	+	0.750103i	$0.269996\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	3.04921i		−	0.122757i	−0.998115	−	0.0613784i	$-0.980450\pi$
$617$		−	3.04921i		−	0.122757i	0.998115	−	0.0613784i	$-0.0195496\pi$
$618$		0			0
$619$	2.15135	+	2.15135i	0.0864701	+	0.0864701i	0.749019	−	0.662549i	$-0.230525\pi$
$619$	2.15135	+	2.15135i	0.0864701	+	0.0864701i	−0.662549	+	0.749019i	$0.730525\pi$
$620$		0			0
$621$		−	5.81118i		−	0.233195i
$622$		0			0
$623$	−8.38255	−	8.38255i	−0.335840	−	0.335840i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	1.56101	+	1.56101i	0.0623406	+	0.0623406i
$628$		0			0
$629$	7.37667	−	7.37667i	0.294127	−	0.294127i
$630$		0			0
$631$	−26.1168	+	26.1168i	−1.03969	+	1.03969i	−0.0405145	+	0.999179i	$0.512900\pi$
$631$	−26.1168	+	26.1168i	−1.03969	+	1.03969i	−0.999179	+	0.0405145i	$0.987100\pi$
$632$		0			0
$633$	6.39029	−	6.39029i	0.253991	−	0.253991i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	8.14483	−	3.35604i	0.322710	−	0.132971i
$638$		0			0
$639$	−1.66190	+	1.66190i	−0.0657437	+	0.0657437i
$640$		0			0
$641$		−	14.0903i		−	0.556534i	−0.960504	−	0.278267i	$-0.910240\pi$
$641$		−	14.0903i		−	0.556534i	0.960504	−	0.278267i	$-0.0897599\pi$
$642$		0			0
$643$	9.89537			0.390235			0.195118	−	0.980780i	$-0.437491\pi$
$643$	9.89537			0.390235			0.195118	+	0.980780i	$0.437491\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−7.48001	+	7.48001i	−0.294069	+	0.294069i	−0.838685	−	0.544616i	$-0.816675\pi$
$647$	−7.48001	+	7.48001i	−0.294069	+	0.294069i	0.544616	+	0.838685i	$0.316675\pi$
$648$		0			0
$649$	−1.64907			−0.0647317
$650$		0			0
$651$	−14.3244			−0.561419
$652$		0			0
$653$	−10.0579	+	10.0579i	−0.393595	+	0.393595i	−0.875967	−	0.482372i	$-0.839775\pi$
$653$	−10.0579	+	10.0579i	−0.393595	+	0.393595i	0.482372	+	0.875967i	$0.339775\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−0.637019			−0.0248525
$658$		0			0
$659$		−	36.4548i		−	1.42008i	−0.704164	−	0.710038i	$-0.748678\pi$
$659$		−	36.4548i		−	1.42008i	0.704164	−	0.710038i	$-0.251322\pi$
$660$		0			0
$661$	−6.58265	+	6.58265i	−0.256035	+	0.256035i	−0.823439	−	0.567404i	$-0.807948\pi$
$661$	−6.58265	+	6.58265i	−0.256035	+	0.256035i	0.567404	+	0.823439i	$0.307948\pi$
$662$		0			0
$663$	−2.38448	−	5.78693i	−0.0926055	−	0.224746i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−7.46678	+	7.46678i	−0.289115	+	0.289115i
$668$		0			0
$669$	17.7542	−	17.7542i	0.686415	−	0.686415i
$670$		0			0
$671$	24.9565	−	24.9565i	0.963437	−	0.963437i
$672$		0			0
$673$	−10.3834	−	10.3834i	−0.400252	−	0.400252i	0.478070	−	0.878322i	$-0.341337\pi$
$673$	−10.3834	−	10.3834i	−0.400252	−	0.400252i	−0.878322	+	0.478070i	$0.841337\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	22.0470	+	22.0470i	0.847334	+	0.847334i	0.989800	−	0.142466i	$-0.0455031\pi$
$677$	22.0470	+	22.0470i	0.847334	+	0.847334i	−0.142466	+	0.989800i	$0.545503\pi$
$678$		0			0
$679$			13.1489i			0.504607i
$680$		0			0
$681$	7.27761	+	7.27761i	0.278879	+	0.278879i
$682$		0			0
$683$		−	44.6066i		−	1.70682i	−0.521237	−	0.853412i	$-0.674529\pi$
$683$		−	44.6066i		−	1.70682i	0.521237	−	0.853412i	$-0.325471\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−2.51377			−0.0959064
$688$		0			0
$689$	−15.2761	+	36.6874i	−0.581973	+	1.39768i
$690$		0			0
$691$	−33.1306	−	33.1306i	−1.26035	−	1.26035i	−0.950924	−	0.309424i	$-0.899864\pi$
$691$	−33.1306	−	33.1306i	−1.26035	−	1.26035i	−0.309424	−	0.950924i	$-0.600136\pi$
$692$		0			0
$693$	4.05360	+	4.05360i	0.153983	+	0.153983i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−9.46444			−0.358491
$698$		0			0
$699$	−19.8877			−0.752222
$700$		0			0
$701$			5.40260i			0.204053i	0.994782	+	0.102027i	$0.0325327\pi$
$701$			5.40260i			0.204053i	−0.994782	+	0.102027i	$0.967467\pi$
$702$		0			0
$703$	3.49320	−	3.49320i	0.131749	−	0.131749i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		−	8.40480i		−	0.316095i
$708$		0			0
$709$	−34.9371	−	34.9371i	−1.31209	−	1.31209i	−0.919873	−	0.392216i	$-0.871708\pi$
$709$	−34.9371	−	34.9371i	−1.31209	−	1.31209i	−0.392216	−	0.919873i	$-0.628292\pi$
$710$		0			0
$711$	0.837401			0.0314050
$712$		0			0
$713$			38.9954i			1.46039i
$714$		0			0
$715$		0			0
$716$		0			0
$717$			29.9644i			1.11904i
$718$		0			0
$719$	−23.4590			−0.874872			−0.437436	−	0.899249i	$-0.644113\pi$
$719$	−23.4590			−0.874872			−0.437436	+	0.899249i	$0.644113\pi$
$720$		0			0
$721$	−8.48564	−	8.48564i	−0.316022	−	0.316022i
$722$		0			0
$723$		−	2.54419i		−	0.0946194i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	8.12835	−	8.12835i	0.301464	−	0.301464i	−0.540123	−	0.841586i	$-0.681622\pi$
$727$	8.12835	−	8.12835i	0.301464	−	0.301464i	0.841586	+	0.540123i	$0.181622\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	−9.29577			−0.343817
$732$		0			0
$733$	15.4133			0.569303			0.284652	−	0.958631i	$-0.408122\pi$
$733$	15.4133			0.569303			0.284652	+	0.958631i	$0.408122\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−2.41724	−	2.41724i	−0.0890403	−	0.0890403i
$738$		0			0
$739$	6.33555	+	6.33555i	0.233057	+	0.233057i	0.813967	−	0.580910i	$-0.197303\pi$
$739$	6.33555	+	6.33555i	0.233057	+	0.233057i	−0.580910	+	0.813967i	$0.697303\pi$
$740$		0			0
$741$	−1.12916	−	2.74039i	−0.0414809	−	0.100671i
$742$		0			0
$743$	−44.7202			−1.64063			−0.820313	−	0.571915i	$-0.806201\pi$
$743$	−44.7202			−1.64063			−0.820313	+	0.571915i	$0.806201\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$		−	5.22354i		−	0.191119i
$748$		0			0
$749$	−23.9303	−	23.9303i	−0.874394	−	0.874394i
$750$		0			0
$751$		−	4.64023i		−	0.169324i	−0.996410	−	0.0846621i	$-0.973019\pi$
$751$		−	4.64023i		−	0.169324i	0.996410	−	0.0846621i	$-0.0269811\pi$
$752$		0			0
$753$	−13.7384	−	13.7384i	−0.500657	−	0.500657i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	20.4954	+	20.4954i	0.744918	+	0.744918i	0.973520	−	0.228602i	$-0.0734155\pi$
$757$	20.4954	+	20.4954i	0.744918	+	0.744918i	−0.228602	+	0.973520i	$0.573416\pi$
$758$		0			0
$759$	11.0351	−	11.0351i	0.400549	−	0.400549i
$760$		0			0
$761$	17.6249	−	17.6249i	0.638902	−	0.638902i	−0.311383	−	0.950285i	$-0.600792\pi$
$761$	17.6249	−	17.6249i	0.638902	−	0.638902i	0.950285	+	0.311383i	$0.100792\pi$
$762$		0			0
$763$	−17.7933	+	17.7933i	−0.644160	+	0.644160i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	2.04393	+	0.851061i	0.0738020	+	0.0307300i
$768$		0			0
$769$	−35.6848	+	35.6848i	−1.28683	+	1.28683i	−0.350123	+	0.936704i	$0.613860\pi$
$769$	−35.6848	+	35.6848i	−1.28683	+	1.28683i	−0.936704	+	0.350123i	$0.886140\pi$
$770$		0			0
$771$			10.1817i			0.366687i
$772$		0			0
$773$	−10.4900			−0.377301			−0.188650	−	0.982044i	$-0.560411\pi$
$773$	−10.4900			−0.377301			−0.188650	+	0.982044i	$0.560411\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	9.07111	−	9.07111i	0.325424	−	0.325424i
$778$		0			0
$779$	−4.48186			−0.160579
$780$		0			0
$781$	−6.31170			−0.225850
$782$		0			0
$783$	1.28490	−	1.28490i	0.0459185	−	0.0459185i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−16.0980			−0.573832			−0.286916	−	0.957956i	$-0.592630\pi$
$787$	−16.0980			−0.573832			−0.286916	+	0.957956i	$0.592630\pi$
$788$		0			0
$789$			13.0373i			0.464139i
$790$		0			0
$791$	−10.1058	+	10.1058i	−0.359322	+	0.359322i
$792$		0			0
$793$	−43.8119	+	18.0525i	−1.55581	+	0.641062i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	17.8833	−	17.8833i	0.633460	−	0.633460i	−0.315474	−	0.948934i	$-0.602164\pi$
$797$	17.8833	−	17.8833i	0.633460	−	0.633460i	0.948934	+	0.315474i	$0.102164\pi$
$798$		0			0
$799$	−3.37694	+	3.37694i	−0.119468	+	0.119468i
$800$		0			0
$801$	3.92688	−	3.92688i	0.138749	−	0.138749i
$802$		0			0
$803$	−1.20966	−	1.20966i	−0.0426881	−	0.0426881i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−1.14563	−	1.14563i	−0.0403282	−	0.0403282i
$808$		0			0
$809$			20.4265i			0.718157i	0.933307	+	0.359079i	$0.116909\pi$
$809$			20.4265i			0.718157i	−0.933307	+	0.359079i	$0.883091\pi$
$810$		0			0
$811$	4.25247	+	4.25247i	0.149325	+	0.149325i	0.777816	−	0.628492i	$-0.216327\pi$
$811$	4.25247	+	4.25247i	0.149325	+	0.149325i	−0.628492	+	0.777816i	$0.716327\pi$
$812$		0			0
$813$		−	9.78305i		−	0.343106i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−4.40199			−0.154006
$818$		0			0
$819$	−2.93220	−	7.11620i	−0.102459	−	0.248660i
$820$		0			0
$821$	−26.9521	−	26.9521i	−0.940636	−	0.940636i	0.0576979	−	0.998334i	$-0.481624\pi$
$821$	−26.9521	−	26.9521i	−0.940636	−	0.940636i	−0.998334	+	0.0576979i	$0.981624\pi$
$822$		0			0
$823$	−25.9491	−	25.9491i	−0.904528	−	0.904528i	0.0912955	−	0.995824i	$-0.470899\pi$
$823$	−25.9491	−	25.9491i	−0.904528	−	0.904528i	−0.995824	+	0.0912955i	$0.970899\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−45.6260			−1.58657			−0.793287	−	0.608848i	$-0.791632\pi$
$827$	−45.6260			−1.58657			−0.793287	+	0.608848i	$0.791632\pi$
$828$		0			0
$829$	42.7307			1.48410			0.742049	−	0.670346i	$-0.233854\pi$
$829$	42.7307			1.48410			0.742049	+	0.670346i	$0.233854\pi$
$830$		0			0
$831$		−	10.1612i		−	0.352489i
$832$		0			0
$833$	2.99900	−	2.99900i	0.103909	−	0.103909i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		−	6.71041i		−	0.231946i
$838$		0			0
$839$	−3.57427	−	3.57427i	−0.123398	−	0.123398i	0.642711	−	0.766109i	$-0.277810\pi$
$839$	−3.57427	−	3.57427i	−0.123398	−	0.123398i	−0.766109	+	0.642711i	$0.777810\pi$
$840$		0			0
$841$	25.6981			0.886140
$842$		0			0
$843$		−	15.0343i		−	0.517810i
$844$		0			0
$845$		0			0
$846$		0			0
$847$		−	8.08617i		−	0.277844i
$848$		0			0
$849$	−18.0905			−0.620863
$850$		0			0
$851$	−24.6943	−	24.6943i	−0.846508	−	0.846508i
$852$		0			0
$853$		−	10.6644i		−	0.365141i	−0.983193	−	0.182571i	$-0.941558\pi$
$853$		−	10.6644i		−	0.365141i	0.983193	−	0.182571i	$-0.0584418\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	17.7615	−	17.7615i	0.606720	−	0.606720i	−0.335367	−	0.942087i	$-0.608860\pi$
$857$	17.7615	−	17.7615i	0.606720	−	0.606720i	0.942087	+	0.335367i	$0.108860\pi$
$858$		0			0
$859$			0.529028i			0.0180502i	0.999959	+	0.00902510i	$0.00287282\pi$
$859$			0.529028i			0.0180502i	−0.999959	+	0.00902510i	$0.997127\pi$
$860$		0			0
$861$	−11.6384			−0.396637
$862$		0			0
$863$	−16.5919			−0.564795			−0.282397	−	0.959298i	$-0.591130\pi$
$863$	−16.5919			−0.564795			−0.282397	+	0.959298i	$0.591130\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	9.89001	+	9.89001i	0.335882	+	0.335882i
$868$		0			0
$869$	1.59018	+	1.59018i	0.0539430	+	0.0539430i
$870$		0			0
$871$	1.74853	+	4.24353i	0.0592466	+	0.143787i
$872$		0			0
$873$	−6.15970			−0.208474
$874$		0			0
$875$		0			0
$876$		0			0
$877$			31.7095i			1.07075i	0.844613	+	0.535377i	$0.179830\pi$
$877$			31.7095i			1.07075i	−0.844613	+	0.535377i	$0.820170\pi$
$878$		0			0
$879$	−11.8880	−	11.8880i	−0.400973	−	0.400973i
$880$		0			0
$881$		−	45.8764i		−	1.54561i	−0.634641	−	0.772807i	$-0.718852\pi$
$881$		−	45.8764i		−	1.54561i	0.634641	−	0.772807i	$-0.281148\pi$
$882$		0			0
$883$	−7.59797	−	7.59797i	−0.255692	−	0.255692i	0.567607	−	0.823299i	$-0.307869\pi$
$883$	−7.59797	−	7.59797i	−0.255692	−	0.255692i	−0.823299	+	0.567607i	$0.807869\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	2.01004	+	2.01004i	0.0674905	+	0.0674905i	0.740046	−	0.672556i	$-0.234804\pi$
$887$	2.01004	+	2.01004i	0.0674905	+	0.0674905i	−0.672556	+	0.740046i	$0.734804\pi$
$888$		0			0
$889$	11.2323	−	11.2323i	0.376718	−	0.376718i
$890$		0			0
$891$	−1.89894	+	1.89894i	−0.0636170	+	0.0636170i
$892$		0			0
$893$	−1.59914	+	1.59914i	−0.0535132	+	0.0535132i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−19.3724	+	7.98232i	−0.646826	+	0.266522i
$898$		0			0
$899$	−8.62219	+	8.62219i	−0.287566	+	0.287566i
$900$		0			0
$901$			19.1335i			0.637428i
$902$		0			0
$903$	−11.4310			−0.380401
$904$		0			0
$905$		0			0
$906$		0			0
$907$	24.3483	−	24.3483i	0.808472	−	0.808472i	−0.175931	−	0.984403i	$-0.556293\pi$
$907$	24.3483	−	24.3483i	0.808472	−	0.808472i	0.984403	+	0.175931i	$0.0562934\pi$
$908$		0			0
$909$	3.93730			0.130592
$910$		0			0
$911$	−41.9116			−1.38859			−0.694297	−	0.719689i	$-0.744284\pi$
$911$	−41.9116			−1.38859			−0.694297	+	0.719689i	$0.744284\pi$
$912$		0			0
$913$	9.91920	−	9.91920i	0.328278	−	0.328278i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	45.0912			1.48904
$918$		0			0
$919$		−	31.6303i		−	1.04339i	−0.853133	−	0.521693i	$-0.825301\pi$
$919$		−	31.6303i		−	1.04339i	0.853133	−	0.521693i	$-0.174699\pi$
$920$		0			0
$921$	−10.3273	+	10.3273i	−0.340296	+	0.340296i
$922$		0			0
$923$	7.82299	+	3.25737i	0.257497	+	0.107218i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	3.97517	−	3.97517i	0.130562	−	0.130562i
$928$		0			0
$929$	−19.6715	+	19.6715i	−0.645400	+	0.645400i	−0.951878	−	0.306477i	$-0.900850\pi$
$929$	−19.6715	+	19.6715i	−0.645400	+	0.645400i	0.306477	+	0.951878i	$0.400850\pi$
$930$		0			0
$931$	1.42017	−	1.42017i	0.0465442	−	0.0465442i
$932$		0			0
$933$	19.4391	+	19.4391i	0.636407	+	0.636407i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−9.54342	−	9.54342i	−0.311770	−	0.311770i	0.533825	−	0.845595i	$-0.320754\pi$
$937$	−9.54342	−	9.54342i	−0.311770	−	0.311770i	−0.845595	+	0.533825i	$0.820754\pi$
$938$		0			0
$939$			6.82759i			0.222810i
$940$		0			0
$941$	10.4194	+	10.4194i	0.339662	+	0.339662i	0.856240	−	0.516578i	$-0.172794\pi$
$941$	10.4194	+	10.4194i	0.339662	+	0.339662i	−0.516578	+	0.856240i	$0.672794\pi$
$942$		0			0
$943$			31.6833i			1.03175i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	3.83373			0.124580			0.0622898	−	0.998058i	$-0.480160\pi$
$947$	3.83373			0.124580			0.0622898	+	0.998058i	$0.480160\pi$
$948$		0			0
$949$	0.875018	+	2.12360i	0.0284043	+	0.0689349i
$950$		0			0
$951$	19.3746	+	19.3746i	0.628265	+	0.628265i
$952$		0			0
$953$	−27.0921	−	27.0921i	−0.877598	−	0.877598i	0.115687	−	0.993286i	$-0.463093\pi$
$953$	−27.0921	−	27.0921i	−0.877598	−	0.877598i	−0.993286	+	0.115687i	$0.963093\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	4.87990			0.157745
$958$		0			0
$959$	−28.0073			−0.904403
$960$		0			0
$961$			14.0296i			0.452566i
$962$		0			0
$963$	11.2103	−	11.2103i	0.361248	−	0.361248i
$964$		0			0
$965$		0			0
$966$		0			0
$967$		−	60.6472i		−	1.95028i	−0.221586	−	0.975141i	$-0.571123\pi$
$967$		−	60.6472i		−	1.95028i	0.221586	−	0.975141i	$-0.428877\pi$
$968$		0			0
$969$	−1.00904	−	1.00904i	−0.0324149	−	0.0324149i
$970$		0			0
$971$	−21.1997			−0.680331			−0.340165	−	0.940366i	$-0.610483\pi$
$971$	−21.1997			−0.680331			−0.340165	+	0.940366i	$0.610483\pi$
$972$		0			0
$973$			41.2397i			1.32208i
$974$		0			0
$975$		0			0
$976$		0			0
$977$		−	24.6849i		−	0.789739i	−0.918737	−	0.394869i	$-0.870790\pi$
$977$		−	24.6849i		−	0.789739i	0.918737	−	0.394869i	$-0.129210\pi$
$978$		0			0
$979$	14.9138			0.476648
$980$		0			0
$981$	−8.33542	−	8.33542i	−0.266129	−	0.266129i
$982$		0			0
$983$		−	35.5810i		−	1.13486i	−0.823423	−	0.567428i	$-0.807938\pi$
$983$		−	35.5810i		−	1.13486i	0.823423	−	0.567428i	$-0.192062\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−4.15263	+	4.15263i	−0.132180	+	0.132180i
$988$		0			0
$989$			31.1187i			0.989516i
$990$		0			0
$991$	−5.07037			−0.161065			−0.0805327	−	0.996752i	$-0.525662\pi$
$991$	−5.07037			−0.161065			−0.0805327	+	0.996752i	$0.525662\pi$
$992$		0			0
$993$	−8.03535			−0.254994
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−21.7495	−	21.7495i	−0.688814	−	0.688814i	0.273156	−	0.961970i	$-0.411933\pi$
$997$	−21.7495	−	21.7495i	−0.688814	−	0.688814i	−0.961970	+	0.273156i	$0.911933\pi$
$998$		0			0
$999$	4.24944	+	4.24944i	0.134446	+	0.134446i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3900.2.bm.b.2257.12		28
5.2	odd	4		780.2.r.a.73.6	✓	28
5.3	odd	4		3900.2.r.b.3193.12		28
5.4	even	2		780.2.bm.a.697.6	yes	28
13.5	odd	4		3900.2.r.b.1357.12		28
15.2	even	4		2340.2.u.i.73.5		28
15.14	odd	2		2340.2.bp.i.1477.3		28
65.18	even	4	inner	3900.2.bm.b.2293.12		28
65.44	odd	4		780.2.r.a.577.6	yes	28
65.57	even	4		780.2.bm.a.733.6	yes	28
195.44	even	4		2340.2.u.i.577.5		28
195.122	odd	4		2340.2.bp.i.1513.3		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
780.2.r.a.73.6	✓	28	5.2	odd	4
780.2.r.a.577.6	yes	28	65.44	odd	4
780.2.bm.a.697.6	yes	28	5.4	even	2
780.2.bm.a.733.6	yes	28	65.57	even	4
2340.2.u.i.73.5		28	15.2	even	4
2340.2.u.i.577.5		28	195.44	even	4
2340.2.bp.i.1477.3		28	15.14	odd	2
2340.2.bp.i.1513.3		28	195.122	odd	4
3900.2.r.b.1357.12		28	13.5	odd	4
3900.2.r.b.3193.12		28	5.3	odd	4
3900.2.bm.b.2257.12		28	1.1	even	1	trivial
3900.2.bm.b.2293.12		28	65.18	even	4	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:	\( N \)	\(=\)	\( 3900 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3900.bm (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{3} -2.13466 q^{7} -1.00000i q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{3} -2.13466 q^{7} -1.00000i q^{9} +(1.89894 - 1.89894i) q^{11} +(-3.33364 + 1.37361i) q^{13} +(-1.22748 + 1.22748i) q^{17} +(-0.581270 + 0.581270i) q^{19} +(-1.50943 + 1.50943i) q^{21} +(4.10913 + 4.10913i) q^{23} +(-0.707107 - 0.707107i) q^{27} +1.81712i q^{29} +(4.74497 + 4.74497i) q^{31} -2.68551i q^{33} -6.00961 q^{37} +(-1.38595 + 3.32853i) q^{39} +(3.85523 + 3.85523i) q^{41} +(3.78653 + 3.78653i) q^{43} +2.75112 q^{47} -2.44322 q^{49} +1.73592i q^{51} +(7.79380 - 7.79380i) q^{53} +0.822039i q^{57} +(-0.434208 - 0.434208i) q^{59} +13.1423 q^{61} +2.13466i q^{63} -1.27294i q^{67} +5.81118 q^{69} +(-1.66190 - 1.66190i) q^{71} -0.637019i q^{73} +(-4.05360 + 4.05360i) q^{77} +0.837401i q^{79} -1.00000 q^{81} +5.22354 q^{83} +(1.28490 + 1.28490i) q^{87} +(3.92688 + 3.92688i) q^{89} +(7.11620 - 2.93220i) q^{91} +6.71041 q^{93} -6.15970i q^{97} +(-1.89894 - 1.89894i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q+O(q^{10}) \) 28 * q	\( 28 q + 8 q^{11} - 4 q^{17} + 16 q^{19} + 8 q^{21} - 8 q^{23} - 24 q^{37} - 8 q^{39} + 12 q^{41} + 16 q^{43} + 24 q^{47} + 36 q^{49} - 36 q^{53} - 16 q^{59} + 8 q^{61} + 8 q^{69} + 8 q^{71} - 48 q^{77} - 28 q^{81} + 24 q^{83} + 24 q^{87} + 36 q^{89} - 24 q^{91} - 8 q^{99}+O(q^{100}) \) 28 * q + 8 * q^11 - 4 * q^17 + 16 * q^19 + 8 * q^21 - 8 * q^23 - 24 * q^37 - 8 * q^39 + 12 * q^41 + 16 * q^43 + 24 * q^47 + 36 * q^49 - 36 * q^53 - 16 * q^59 + 8 * q^61 + 8 * q^69 + 8 * q^71 - 48 * q^77 - 28 * q^81 + 24 * q^83 + 24 * q^87 + 36 * q^89 - 24 * q^91 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more