LMFDB - Embedded newform 3584.2.m.v.897.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3584,2,Mod(897,3584)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3584, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("3584.897");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3584 = 2^{9} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3584.m (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:	$28.6183840844$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			897.1
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	3584.897
Dual form			3584.2.m.v.2689.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.00000i) q^{3} +1.00000i q^{7} +1.00000i q^{9} +O(q^{10})$	$q+(1.00000 - 1.00000i) q^{3} +1.00000i q^{7} +1.00000i q^{9} +(-2.00000 - 2.00000i) q^{11} +(2.00000 - 2.00000i) q^{13} -6.00000 q^{17} +(-3.00000 + 3.00000i) q^{19} +(1.00000 + 1.00000i) q^{21} -5.00000i q^{25} +(4.00000 + 4.00000i) q^{27} +(1.00000 - 1.00000i) q^{29} -10.0000 q^{31} -4.00000 q^{33} +(-3.00000 - 3.00000i) q^{37} -4.00000i q^{39} +10.0000i q^{41} +(6.00000 + 6.00000i) q^{43} -2.00000 q^{47} -1.00000 q^{49} +(-6.00000 + 6.00000i) q^{51} +(-9.00000 - 9.00000i) q^{53} +6.00000i q^{57} +(-1.00000 - 1.00000i) q^{59} -1.00000 q^{63} +(-8.00000 + 8.00000i) q^{67} -12.0000i q^{71} -2.00000i q^{73} +(-5.00000 - 5.00000i) q^{75} +(2.00000 - 2.00000i) q^{77} -4.00000 q^{79} +5.00000 q^{81} +(-5.00000 + 5.00000i) q^{83} -2.00000i q^{87} -2.00000i q^{89} +(2.00000 + 2.00000i) q^{91} +(-10.0000 + 10.0000i) q^{93} -2.00000 q^{97} +(2.00000 - 2.00000i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{3}+O(q^{10}) $ 2 * q + 2 * q^3	$ 2 q + 2 q^{3} - 4 q^{11} + 4 q^{13} - 12 q^{17} - 6 q^{19} + 2 q^{21} + 8 q^{27} + 2 q^{29} - 20 q^{31} - 8 q^{33} - 6 q^{37} + 12 q^{43} - 4 q^{47} - 2 q^{49} - 12 q^{51} - 18 q^{53} - 2 q^{59} - 2 q^{63} - 16 q^{67} - 10 q^{75} + 4 q^{77} - 8 q^{79} + 10 q^{81} - 10 q^{83} + 4 q^{91} - 20 q^{93} - 4 q^{97} + 4 q^{99}+O(q^{100}) $ 2 * q + 2 * q^3 - 4 * q^11 + 4 * q^13 - 12 * q^17 - 6 * q^19 + 2 * q^21 + 8 * q^27 + 2 * q^29 - 20 * q^31 - 8 * q^33 - 6 * q^37 + 12 * q^43 - 4 * q^47 - 2 * q^49 - 12 * q^51 - 18 * q^53 - 2 * q^59 - 2 * q^63 - 16 * q^67 - 10 * q^75 + 4 * q^77 - 8 * q^79 + 10 * q^81 - 10 * q^83 + 4 * q^91 - 20 * q^93 - 4 * q^97 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3584\mathbb{Z}\right)^\times$.

$n$	$1023$	$1025$	$1541$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$

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
$3$	1.00000	−	1.00000i	0.577350	−	0.577350i	−0.356822	−	0.934172i	$-0.616140\pi$
$3$	1.00000	−	1.00000i	0.577350	−	0.577350i	0.934172	+	0.356822i	$0.116140\pi$
$4$		0			0
$5$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$5$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$6$		0			0
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$		0			0
$9$			1.00000i			0.333333i
$10$		0			0
$11$	−2.00000	−	2.00000i	−0.603023	−	0.603023i	0.338091	−	0.941113i	$-0.390219\pi$
$11$	−2.00000	−	2.00000i	−0.603023	−	0.603023i	−0.941113	+	0.338091i	$0.890219\pi$
$12$		0			0
$13$	2.00000	−	2.00000i	0.554700	−	0.554700i	−0.373094	−	0.927794i	$-0.621703\pi$
$13$	2.00000	−	2.00000i	0.554700	−	0.554700i	0.927794	+	0.373094i	$0.121703\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−6.00000			−1.45521			−0.727607	−	0.685994i	$-0.759367\pi$
$17$	−6.00000			−1.45521			−0.727607	+	0.685994i	$0.759367\pi$
$18$		0			0
$19$	−3.00000	+	3.00000i	−0.688247	+	0.688247i	−0.961844	−	0.273597i	$-0.911786\pi$
$19$	−3.00000	+	3.00000i	−0.688247	+	0.688247i	0.273597	+	0.961844i	$0.411786\pi$
$20$		0			0
$21$	1.00000	+	1.00000i	0.218218	+	0.218218i
$22$		0			0
$23$		0			0		1.00000			$0$
$23$		0			0		−1.00000			$\pi$
$24$		0			0
$25$		−	5.00000i		−	1.00000i
$26$		0			0
$27$	4.00000	+	4.00000i	0.769800	+	0.769800i
$28$		0			0
$29$	1.00000	−	1.00000i	0.185695	−	0.185695i	−0.608137	−	0.793832i	$-0.708083\pi$
$29$	1.00000	−	1.00000i	0.185695	−	0.185695i	0.793832	+	0.608137i	$0.208083\pi$
$30$		0			0
$31$	−10.0000			−1.79605			−0.898027	−	0.439941i	$-0.854999\pi$
$31$	−10.0000			−1.79605			−0.898027	+	0.439941i	$0.854999\pi$
$32$		0			0
$33$	−4.00000			−0.696311
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−3.00000	−	3.00000i	−0.493197	−	0.493197i	0.416115	−	0.909312i	$-0.363391\pi$
$37$	−3.00000	−	3.00000i	−0.493197	−	0.493197i	−0.909312	+	0.416115i	$0.863391\pi$
$38$		0			0
$39$		−	4.00000i		−	0.640513i
$40$		0			0
$41$			10.0000i			1.56174i	0.624695	+	0.780869i	$0.285223\pi$
$41$			10.0000i			1.56174i	−0.624695	+	0.780869i	$0.714777\pi$
$42$		0			0
$43$	6.00000	+	6.00000i	0.914991	+	0.914991i	0.996660	−	0.0816682i	$-0.0260248\pi$
$43$	6.00000	+	6.00000i	0.914991	+	0.914991i	−0.0816682	+	0.996660i	$0.526025\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−2.00000			−0.291730			−0.145865	−	0.989305i	$-0.546597\pi$
$47$	−2.00000			−0.291730			−0.145865	+	0.989305i	$0.546597\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$		0			0
$51$	−6.00000	+	6.00000i	−0.840168	+	0.840168i
$52$		0			0
$53$	−9.00000	−	9.00000i	−1.23625	−	1.23625i	−0.961524	−	0.274721i	$-0.911414\pi$
$53$	−9.00000	−	9.00000i	−1.23625	−	1.23625i	−0.274721	−	0.961524i	$-0.588586\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$			6.00000i			0.794719i
$58$		0			0
$59$	−1.00000	−	1.00000i	−0.130189	−	0.130189i	0.639010	−	0.769199i	$-0.279344\pi$
$59$	−1.00000	−	1.00000i	−0.130189	−	0.130189i	−0.769199	+	0.639010i	$0.779344\pi$
$60$		0			0
$61$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$61$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$62$		0			0
$63$	−1.00000			−0.125988
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−8.00000	+	8.00000i	−0.977356	+	0.977356i	−0.999749	−	0.0223937i	$-0.992871\pi$
$67$	−8.00000	+	8.00000i	−0.977356	+	0.977356i	0.0223937	+	0.999749i	$0.492871\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	12.0000i		−	1.42414i	−0.702109	−	0.712069i	$-0.747758\pi$
$71$		−	12.0000i		−	1.42414i	0.702109	−	0.712069i	$-0.252242\pi$
$72$		0			0
$73$		−	2.00000i		−	0.234082i	−0.993127	−	0.117041i	$-0.962659\pi$
$73$		−	2.00000i		−	0.234082i	0.993127	−	0.117041i	$-0.0373409\pi$
$74$		0			0
$75$	−5.00000	−	5.00000i	−0.577350	−	0.577350i
$76$		0			0
$77$	2.00000	−	2.00000i	0.227921	−	0.227921i
$78$		0			0
$79$	−4.00000			−0.450035			−0.225018	−	0.974355i	$-0.572244\pi$
$79$	−4.00000			−0.450035			−0.225018	+	0.974355i	$0.572244\pi$
$80$		0			0
$81$	5.00000			0.555556
$82$		0			0
$83$	−5.00000	+	5.00000i	−0.548821	+	0.548821i	−0.926100	−	0.377279i	$-0.876860\pi$
$83$	−5.00000	+	5.00000i	−0.548821	+	0.548821i	0.377279	+	0.926100i	$0.376860\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		−	2.00000i		−	0.214423i
$88$		0			0
$89$		−	2.00000i		−	0.212000i	−0.994366	−	0.106000i	$-0.966196\pi$
$89$		−	2.00000i		−	0.212000i	0.994366	−	0.106000i	$-0.0338043\pi$
$90$		0			0
$91$	2.00000	+	2.00000i	0.209657	+	0.209657i
$92$		0			0
$93$	−10.0000	+	10.0000i	−1.03695	+	1.03695i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−2.00000			−0.203069			−0.101535	−	0.994832i	$-0.532375\pi$
$97$	−2.00000			−0.203069			−0.101535	+	0.994832i	$0.532375\pi$
$98$		0			0
$99$	2.00000	−	2.00000i	0.201008	−	0.201008i
$100$		0			0
$101$	4.00000	+	4.00000i	0.398015	+	0.398015i	0.877532	−	0.479517i	$-0.159188\pi$
$101$	4.00000	+	4.00000i	0.398015	+	0.398015i	−0.479517	+	0.877532i	$0.659188\pi$
$102$		0			0
$103$			6.00000i			0.591198i	0.955312	+	0.295599i	$0.0955191\pi$
$103$			6.00000i			0.591198i	−0.955312	+	0.295599i	$0.904481\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$107$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$108$		0			0
$109$	3.00000	−	3.00000i	0.287348	−	0.287348i	−0.548683	−	0.836031i	$-0.684871\pi$
$109$	3.00000	−	3.00000i	0.287348	−	0.287348i	0.836031	+	0.548683i	$0.184871\pi$
$110$		0			0
$111$	−6.00000			−0.569495
$112$		0			0
$113$	−12.0000			−1.12887			−0.564433	−	0.825479i	$-0.690905\pi$
$113$	−12.0000			−1.12887			−0.564433	+	0.825479i	$0.690905\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	2.00000	+	2.00000i	0.184900	+	0.184900i
$118$		0			0
$119$		−	6.00000i		−	0.550019i
$120$		0			0
$121$		−	3.00000i		−	0.272727i
$122$		0			0
$123$	10.0000	+	10.0000i	0.901670	+	0.901670i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−12.0000			−1.06483			−0.532414	−	0.846484i	$-0.678715\pi$
$127$	−12.0000			−1.06483			−0.532414	+	0.846484i	$0.678715\pi$
$128$		0			0
$129$	12.0000			1.05654
$130$		0			0
$131$	−7.00000	+	7.00000i	−0.611593	+	0.611593i	−0.943361	−	0.331768i	$-0.892355\pi$
$131$	−7.00000	+	7.00000i	−0.611593	+	0.611593i	0.331768	+	0.943361i	$0.392355\pi$
$132$		0			0
$133$	−3.00000	−	3.00000i	−0.260133	−	0.260133i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		−	12.0000i		−	1.02523i	−0.858619	−	0.512615i	$-0.828677\pi$
$137$		−	12.0000i		−	1.02523i	0.858619	−	0.512615i	$-0.171323\pi$
$138$		0			0
$139$	−3.00000	−	3.00000i	−0.254457	−	0.254457i	0.568338	−	0.822795i	$-0.307586\pi$
$139$	−3.00000	−	3.00000i	−0.254457	−	0.254457i	−0.822795	+	0.568338i	$0.807586\pi$
$140$		0			0
$141$	−2.00000	+	2.00000i	−0.168430	+	0.168430i
$142$		0			0
$143$	−8.00000			−0.668994
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−1.00000	+	1.00000i	−0.0824786	+	0.0824786i
$148$		0			0
$149$	−5.00000	−	5.00000i	−0.409616	−	0.409616i	0.471989	−	0.881605i	$-0.343536\pi$
$149$	−5.00000	−	5.00000i	−0.409616	−	0.409616i	−0.881605	+	0.471989i	$0.843536\pi$
$150$		0			0
$151$			20.0000i			1.62758i	0.581161	+	0.813788i	$0.302599\pi$
$151$			20.0000i			1.62758i	−0.581161	+	0.813788i	$0.697401\pi$
$152$		0			0
$153$		−	6.00000i		−	0.485071i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	10.0000	−	10.0000i	0.798087	−	0.798087i	−0.184707	−	0.982794i	$-0.559134\pi$
$157$	10.0000	−	10.0000i	0.798087	−	0.798087i	0.982794	+	0.184707i	$0.0591335\pi$
$158$		0			0
$159$	−18.0000			−1.42749
$160$		0			0
$161$		0			0
$162$		0			0
$163$	2.00000	−	2.00000i	0.156652	−	0.156652i	−0.624429	−	0.781081i	$-0.714668\pi$
$163$	2.00000	−	2.00000i	0.156652	−	0.156652i	0.781081	+	0.624429i	$0.214668\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		−	22.0000i		−	1.70241i	−0.524832	−	0.851206i	$-0.675872\pi$
$167$		−	22.0000i		−	1.70241i	0.524832	−	0.851206i	$-0.324128\pi$
$168$		0			0
$169$			5.00000i			0.384615i
$170$		0			0
$171$	−3.00000	−	3.00000i	−0.229416	−	0.229416i
$172$		0			0
$173$	10.0000	−	10.0000i	0.760286	−	0.760286i	−0.216088	−	0.976374i	$-0.569330\pi$
$173$	10.0000	−	10.0000i	0.760286	−	0.760286i	0.976374	+	0.216088i	$0.0693298\pi$
$174$		0			0
$175$	5.00000			0.377964
$176$		0			0
$177$	−2.00000			−0.150329
$178$		0			0
$179$	−16.0000	+	16.0000i	−1.19590	+	1.19590i	−0.220512	+	0.975384i	$0.570773\pi$
$179$	−16.0000	+	16.0000i	−1.19590	+	1.19590i	−0.975384	+	0.220512i	$0.929227\pi$
$180$		0			0
$181$	6.00000	+	6.00000i	0.445976	+	0.445976i	0.894015	−	0.448038i	$-0.147877\pi$
$181$	6.00000	+	6.00000i	0.445976	+	0.445976i	−0.448038	+	0.894015i	$0.647877\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	12.0000	+	12.0000i	0.877527	+	0.877527i
$188$		0			0
$189$	−4.00000	+	4.00000i	−0.290957	+	0.290957i
$190$		0			0
$191$	−20.0000			−1.44715			−0.723575	−	0.690246i	$-0.757502\pi$
$191$	−20.0000			−1.44715			−0.723575	+	0.690246i	$0.757502\pi$
$192$		0			0
$193$	2.00000			0.143963			0.0719816	−	0.997406i	$-0.477068\pi$
$193$	2.00000			0.143963			0.0719816	+	0.997406i	$0.477068\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	13.0000	+	13.0000i	0.926212	+	0.926212i	0.997459	−	0.0712470i	$-0.0226979\pi$
$197$	13.0000	+	13.0000i	0.926212	+	0.926212i	−0.0712470	+	0.997459i	$0.522698\pi$
$198$		0			0
$199$		−	22.0000i		−	1.55954i	−0.626067	−	0.779769i	$-0.715336\pi$
$199$		−	22.0000i		−	1.55954i	0.626067	−	0.779769i	$-0.284664\pi$
$200$		0			0
$201$			16.0000i			1.12855i
$202$		0			0
$203$	1.00000	+	1.00000i	0.0701862	+	0.0701862i
$204$		0			0
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	12.0000			0.830057
$210$		0			0
$211$	−20.0000	+	20.0000i	−1.37686	+	1.37686i	−0.526978	+	0.849879i	$0.676675\pi$
$211$	−20.0000	+	20.0000i	−1.37686	+	1.37686i	−0.849879	+	0.526978i	$0.823325\pi$
$212$		0			0
$213$	−12.0000	−	12.0000i	−0.822226	−	0.822226i
$214$		0			0
$215$		0			0
$216$		0			0
$217$		−	10.0000i		−	0.678844i
$218$		0			0
$219$	−2.00000	−	2.00000i	−0.135147	−	0.135147i
$220$		0			0
$221$	−12.0000	+	12.0000i	−0.807207	+	0.807207i
$222$		0			0
$223$	−16.0000			−1.07144			−0.535720	−	0.844396i	$-0.679960\pi$
$223$	−16.0000			−1.07144			−0.535720	+	0.844396i	$0.679960\pi$
$224$		0			0
$225$	5.00000			0.333333
$226$		0			0
$227$	1.00000	−	1.00000i	0.0663723	−	0.0663723i	−0.673141	−	0.739514i	$-0.735055\pi$
$227$	1.00000	−	1.00000i	0.0663723	−	0.0663723i	0.739514	+	0.673141i	$0.235055\pi$
$228$		0			0
$229$	18.0000	+	18.0000i	1.18947	+	1.18947i	0.977213	+	0.212260i	$0.0680825\pi$
$229$	18.0000	+	18.0000i	1.18947	+	1.18947i	0.212260	+	0.977213i	$0.431918\pi$
$230$		0			0
$231$		−	4.00000i		−	0.263181i
$232$		0			0
$233$		−	10.0000i		−	0.655122i	−0.944830	−	0.327561i	$-0.893773\pi$
$233$		−	10.0000i		−	0.655122i	0.944830	−	0.327561i	$-0.106227\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−4.00000	+	4.00000i	−0.259828	+	0.259828i
$238$		0			0
$239$		0			0			−	1.00000i	$-0.5\pi$
$239$		0			0				1.00000i	$0.5\pi$
$240$		0			0
$241$	2.00000			0.128831			0.0644157	−	0.997923i	$-0.479482\pi$
$241$	2.00000			0.128831			0.0644157	+	0.997923i	$0.479482\pi$
$242$		0			0
$243$	−7.00000	+	7.00000i	−0.449050	+	0.449050i
$244$		0			0
$245$		0			0
$246$		0			0
$247$			12.0000i			0.763542i
$248$		0			0
$249$			10.0000i			0.633724i
$250$		0			0
$251$	11.0000	+	11.0000i	0.694314	+	0.694314i	0.963178	−	0.268864i	$-0.0866483\pi$
$251$	11.0000	+	11.0000i	0.694314	+	0.694314i	−0.268864	+	0.963178i	$0.586648\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−6.00000			−0.374270			−0.187135	−	0.982334i	$-0.559920\pi$
$257$	−6.00000			−0.374270			−0.187135	+	0.982334i	$0.559920\pi$
$258$		0			0
$259$	3.00000	−	3.00000i	0.186411	−	0.186411i
$260$		0			0
$261$	1.00000	+	1.00000i	0.0618984	+	0.0618984i
$262$		0			0
$263$			12.0000i			0.739952i	0.929041	+	0.369976i	$0.120634\pi$
$263$			12.0000i			0.739952i	−0.929041	+	0.369976i	$0.879366\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−2.00000	−	2.00000i	−0.122398	−	0.122398i
$268$		0			0
$269$	−14.0000	+	14.0000i	−0.853595	+	0.853595i	−0.990574	−	0.136979i	$-0.956261\pi$
$269$	−14.0000	+	14.0000i	−0.853595	+	0.853595i	0.136979	+	0.990574i	$0.456261\pi$
$270$		0			0
$271$	24.0000			1.45790			0.728948	−	0.684569i	$-0.240010\pi$
$271$	24.0000			1.45790			0.728948	+	0.684569i	$0.240010\pi$
$272$		0			0
$273$	4.00000			0.242091
$274$		0			0
$275$	−10.0000	+	10.0000i	−0.603023	+	0.603023i
$276$		0			0
$277$	17.0000	+	17.0000i	1.02143	+	1.02143i	0.999765	+	0.0216657i	$0.00689696\pi$
$277$	17.0000	+	17.0000i	1.02143	+	1.02143i	0.0216657	+	0.999765i	$0.493103\pi$
$278$		0			0
$279$		−	10.0000i		−	0.598684i
$280$		0			0
$281$		−	10.0000i		−	0.596550i	−0.954480	−	0.298275i	$-0.903589\pi$
$281$		−	10.0000i		−	0.596550i	0.954480	−	0.298275i	$-0.0964112\pi$
$282$		0			0
$283$	15.0000	+	15.0000i	0.891657	+	0.891657i	0.994679	−	0.103022i	$-0.0328511\pi$
$283$	15.0000	+	15.0000i	0.891657	+	0.891657i	−0.103022	+	0.994679i	$0.532851\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−10.0000			−0.590281
$288$		0			0
$289$	19.0000			1.11765
$290$		0			0
$291$	−2.00000	+	2.00000i	−0.117242	+	0.117242i
$292$		0			0
$293$	−4.00000	−	4.00000i	−0.233682	−	0.233682i	0.580545	−	0.814228i	$-0.302839\pi$
$293$	−4.00000	−	4.00000i	−0.233682	−	0.233682i	−0.814228	+	0.580545i	$0.802839\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$		−	16.0000i		−	0.928414i
$298$		0			0
$299$		0			0
$300$		0			0
$301$	−6.00000	+	6.00000i	−0.345834	+	0.345834i
$302$		0			0
$303$	8.00000			0.459588
$304$		0			0
$305$		0			0
$306$		0			0
$307$	23.0000	−	23.0000i	1.31268	−	1.31268i	0.393246	−	0.919433i	$-0.371352\pi$
$307$	23.0000	−	23.0000i	1.31268	−	1.31268i	0.919433	−	0.393246i	$-0.128648\pi$
$308$		0			0
$309$	6.00000	+	6.00000i	0.341328	+	0.341328i
$310$		0			0
$311$			8.00000i			0.453638i	0.973937	+	0.226819i	$0.0728326\pi$
$311$			8.00000i			0.453638i	−0.973937	+	0.226819i	$0.927167\pi$
$312$		0			0
$313$			30.0000i			1.69570i	0.530236	+	0.847850i	$0.322103\pi$
$313$			30.0000i			1.69570i	−0.530236	+	0.847850i	$0.677897\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	17.0000	−	17.0000i	0.954815	−	0.954815i	−0.0442073	−	0.999022i	$-0.514076\pi$
$317$	17.0000	−	17.0000i	0.954815	−	0.954815i	0.999022	+	0.0442073i	$0.0140762\pi$
$318$		0			0
$319$	−4.00000			−0.223957
$320$		0			0
$321$		0			0
$322$		0			0
$323$	18.0000	−	18.0000i	1.00155	−	1.00155i
$324$		0			0
$325$	−10.0000	−	10.0000i	−0.554700	−	0.554700i
$326$		0			0
$327$		−	6.00000i		−	0.331801i
$328$		0			0
$329$		−	2.00000i		−	0.110264i
$330$		0			0
$331$	−6.00000	−	6.00000i	−0.329790	−	0.329790i	0.522717	−	0.852506i	$-0.324919\pi$
$331$	−6.00000	−	6.00000i	−0.329790	−	0.329790i	−0.852506	+	0.522717i	$0.824919\pi$
$332$		0			0
$333$	3.00000	−	3.00000i	0.164399	−	0.164399i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	16.0000			0.871576			0.435788	−	0.900049i	$-0.356470\pi$
$337$	16.0000			0.871576			0.435788	+	0.900049i	$0.356470\pi$
$338$		0			0
$339$	−12.0000	+	12.0000i	−0.651751	+	0.651751i
$340$		0			0
$341$	20.0000	+	20.0000i	1.08306	+	1.08306i
$342$		0			0
$343$		−	1.00000i		−	0.0539949i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−22.0000	−	22.0000i	−1.18102	−	1.18102i	−0.979480	−	0.201542i	$-0.935405\pi$
$347$	−22.0000	−	22.0000i	−1.18102	−	1.18102i	−0.201542	−	0.979480i	$-0.564595\pi$
$348$		0			0
$349$	6.00000	−	6.00000i	0.321173	−	0.321173i	−0.528044	−	0.849217i	$-0.677074\pi$
$349$	6.00000	−	6.00000i	0.321173	−	0.321173i	0.849217	+	0.528044i	$0.177074\pi$
$350$		0			0
$351$	16.0000			0.854017
$352$		0			0
$353$	10.0000			0.532246			0.266123	−	0.963939i	$-0.414257\pi$
$353$	10.0000			0.532246			0.266123	+	0.963939i	$0.414257\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−6.00000	−	6.00000i	−0.317554	−	0.317554i
$358$		0			0
$359$		−	12.0000i		−	0.633336i	−0.948536	−	0.316668i	$-0.897436\pi$
$359$		−	12.0000i		−	0.633336i	0.948536	−	0.316668i	$-0.102564\pi$
$360$		0			0
$361$			1.00000i			0.0526316i
$362$		0			0
$363$	−3.00000	−	3.00000i	−0.157459	−	0.157459i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−8.00000			−0.417597			−0.208798	−	0.977959i	$-0.566955\pi$
$367$	−8.00000			−0.417597			−0.208798	+	0.977959i	$0.566955\pi$
$368$		0			0
$369$	−10.0000			−0.520579
$370$		0			0
$371$	9.00000	−	9.00000i	0.467257	−	0.467257i
$372$		0			0
$373$	−3.00000	−	3.00000i	−0.155334	−	0.155334i	0.625161	−	0.780496i	$-0.285033\pi$
$373$	−3.00000	−	3.00000i	−0.155334	−	0.155334i	−0.780496	+	0.625161i	$0.785033\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	4.00000i		−	0.206010i
$378$		0			0
$379$	2.00000	+	2.00000i	0.102733	+	0.102733i	0.756605	−	0.653872i	$-0.226857\pi$
$379$	2.00000	+	2.00000i	0.102733	+	0.102733i	−0.653872	+	0.756605i	$0.726857\pi$
$380$		0			0
$381$	−12.0000	+	12.0000i	−0.614779	+	0.614779i
$382$		0			0
$383$	−6.00000			−0.306586			−0.153293	−	0.988181i	$-0.548988\pi$
$383$	−6.00000			−0.306586			−0.153293	+	0.988181i	$0.548988\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−6.00000	+	6.00000i	−0.304997	+	0.304997i
$388$		0			0
$389$	−19.0000	−	19.0000i	−0.963338	−	0.963338i	0.0360131	−	0.999351i	$-0.488534\pi$
$389$	−19.0000	−	19.0000i	−0.963338	−	0.963338i	−0.999351	+	0.0360131i	$0.988534\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$			14.0000i			0.706207i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−10.0000	+	10.0000i	−0.501886	+	0.501886i	−0.912024	−	0.410138i	$-0.865481\pi$
$397$	−10.0000	+	10.0000i	−0.501886	+	0.501886i	0.410138	+	0.912024i	$0.365481\pi$
$398$		0			0
$399$	−6.00000			−0.300376
$400$		0			0
$401$	10.0000			0.499376			0.249688	−	0.968326i	$-0.419672\pi$
$401$	10.0000			0.499376			0.249688	+	0.968326i	$0.419672\pi$
$402$		0			0
$403$	−20.0000	+	20.0000i	−0.996271	+	0.996271i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			12.0000i			0.594818i
$408$		0			0
$409$		−	6.00000i		−	0.296681i	−0.988936	−	0.148340i	$-0.952607\pi$
$409$		−	6.00000i		−	0.296681i	0.988936	−	0.148340i	$-0.0473931\pi$
$410$		0			0
$411$	−12.0000	−	12.0000i	−0.591916	−	0.591916i
$412$		0			0
$413$	1.00000	−	1.00000i	0.0492068	−	0.0492068i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−6.00000			−0.293821
$418$		0			0
$419$	−3.00000	+	3.00000i	−0.146560	+	0.146560i	−0.776579	−	0.630020i	$-0.783047\pi$
$419$	−3.00000	+	3.00000i	−0.146560	+	0.146560i	0.630020	+	0.776579i	$0.283047\pi$
$420$		0			0
$421$	−17.0000	−	17.0000i	−0.828529	−	0.828529i	0.158784	−	0.987313i	$-0.449243\pi$
$421$	−17.0000	−	17.0000i	−0.828529	−	0.828529i	−0.987313	+	0.158784i	$0.949243\pi$
$422$		0			0
$423$		−	2.00000i		−	0.0972433i
$424$		0			0
$425$			30.0000i			1.45521i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−8.00000	+	8.00000i	−0.386244	+	0.386244i
$430$		0			0
$431$	16.0000			0.770693			0.385346	−	0.922772i	$-0.374082\pi$
$431$	16.0000			0.770693			0.385346	+	0.922772i	$0.374082\pi$
$432$		0			0
$433$	−26.0000			−1.24948			−0.624740	−	0.780833i	$-0.714795\pi$
$433$	−26.0000			−1.24948			−0.624740	+	0.780833i	$0.714795\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$			8.00000i			0.381819i	0.981608	+	0.190910i	$0.0611437\pi$
$439$			8.00000i			0.381819i	−0.981608	+	0.190910i	$0.938856\pi$
$440$		0			0
$441$		−	1.00000i		−	0.0476190i
$442$		0			0
$443$	20.0000	+	20.0000i	0.950229	+	0.950229i	0.998819	−	0.0485901i	$-0.0154728\pi$
$443$	20.0000	+	20.0000i	0.950229	+	0.950229i	−0.0485901	+	0.998819i	$0.515473\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−10.0000			−0.472984
$448$		0			0
$449$	−32.0000			−1.51017			−0.755087	−	0.655625i	$-0.772405\pi$
$449$	−32.0000			−1.51017			−0.755087	+	0.655625i	$0.772405\pi$
$450$		0			0
$451$	20.0000	−	20.0000i	0.941763	−	0.941763i
$452$		0			0
$453$	20.0000	+	20.0000i	0.939682	+	0.939682i
$454$		0			0
$455$		0			0
$456$		0			0
$457$		−	42.0000i		−	1.96468i	−0.187112	−	0.982339i	$-0.559913\pi$
$457$		−	42.0000i		−	1.96468i	0.187112	−	0.982339i	$-0.440087\pi$
$458$		0			0
$459$	−24.0000	−	24.0000i	−1.12022	−	1.12022i
$460$		0			0
$461$	14.0000	−	14.0000i	0.652045	−	0.652045i	−0.301440	−	0.953485i	$-0.597467\pi$
$461$	14.0000	−	14.0000i	0.652045	−	0.652045i	0.953485	+	0.301440i	$0.0974673\pi$
$462$		0			0
$463$	−40.0000			−1.85896			−0.929479	−	0.368875i	$-0.879743\pi$
$463$	−40.0000			−1.85896			−0.929479	+	0.368875i	$0.879743\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−5.00000	+	5.00000i	−0.231372	+	0.231372i	−0.813265	−	0.581893i	$-0.802312\pi$
$467$	−5.00000	+	5.00000i	−0.231372	+	0.231372i	0.581893	+	0.813265i	$0.302312\pi$
$468$		0			0
$469$	−8.00000	−	8.00000i	−0.369406	−	0.369406i
$470$		0			0
$471$		−	20.0000i		−	0.921551i
$472$		0			0
$473$		−	24.0000i		−	1.10352i
$474$		0			0
$475$	15.0000	+	15.0000i	0.688247	+	0.688247i
$476$		0			0
$477$	9.00000	−	9.00000i	0.412082	−	0.412082i
$478$		0			0
$479$	14.0000			0.639676			0.319838	−	0.947472i	$-0.396371\pi$
$479$	14.0000			0.639676			0.319838	+	0.947472i	$0.396371\pi$
$480$		0			0
$481$	−12.0000			−0.547153
$482$		0			0
$483$		0			0
$484$		0			0
$485$		0			0
$486$		0			0
$487$			8.00000i			0.362515i	0.983436	+	0.181257i	$0.0580167\pi$
$487$			8.00000i			0.362515i	−0.983436	+	0.181257i	$0.941983\pi$
$488$		0			0
$489$		−	4.00000i		−	0.180886i
$490$		0			0
$491$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$491$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$492$		0			0
$493$	−6.00000	+	6.00000i	−0.270226	+	0.270226i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	12.0000			0.538274
$498$		0			0
$499$	12.0000	−	12.0000i	0.537194	−	0.537194i	−0.385510	−	0.922704i	$-0.625974\pi$
$499$	12.0000	−	12.0000i	0.537194	−	0.537194i	0.922704	+	0.385510i	$0.125974\pi$
$500$		0			0
$501$	−22.0000	−	22.0000i	−0.982888	−	0.982888i
$502$		0			0
$503$			16.0000i			0.713405i	0.934218	+	0.356702i	$0.116099\pi$
$503$			16.0000i			0.713405i	−0.934218	+	0.356702i	$0.883901\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	5.00000	+	5.00000i	0.222058	+	0.222058i
$508$		0			0
$509$	26.0000	−	26.0000i	1.15243	−	1.15243i	0.166366	−	0.986064i	$-0.446797\pi$
$509$	26.0000	−	26.0000i	1.15243	−	1.15243i	0.986064	−	0.166366i	$-0.0532032\pi$
$510$		0			0
$511$	2.00000			0.0884748
$512$		0			0
$513$	−24.0000			−1.05963
$514$		0			0
$515$		0			0
$516$		0			0
$517$	4.00000	+	4.00000i	0.175920	+	0.175920i
$518$		0			0
$519$		−	20.0000i		−	0.877903i
$520$		0			0
$521$		−	30.0000i		−	1.31432i	−0.753749	−	0.657162i	$-0.771757\pi$
$521$		−	30.0000i		−	1.31432i	0.753749	−	0.657162i	$-0.228243\pi$
$522$		0			0
$523$	−11.0000	−	11.0000i	−0.480996	−	0.480996i	0.424453	−	0.905450i	$-0.360466\pi$
$523$	−11.0000	−	11.0000i	−0.480996	−	0.480996i	−0.905450	+	0.424453i	$0.860466\pi$
$524$		0			0
$525$	5.00000	−	5.00000i	0.218218	−	0.218218i
$526$		0			0
$527$	60.0000			2.61364
$528$		0			0
$529$	23.0000			1.00000
$530$		0			0
$531$	1.00000	−	1.00000i	0.0433963	−	0.0433963i
$532$		0			0
$533$	20.0000	+	20.0000i	0.866296	+	0.866296i
$534$		0			0
$535$		0			0
$536$		0			0
$537$			32.0000i			1.38090i
$538$		0			0
$539$	2.00000	+	2.00000i	0.0861461	+	0.0861461i
$540$		0			0
$541$	1.00000	−	1.00000i	0.0429934	−	0.0429934i	−0.685283	−	0.728277i	$-0.740322\pi$
$541$	1.00000	−	1.00000i	0.0429934	−	0.0429934i	0.728277	+	0.685283i	$0.240322\pi$
$542$		0			0
$543$	12.0000			0.514969
$544$		0			0
$545$		0			0
$546$		0			0
$547$	22.0000	−	22.0000i	0.940652	−	0.940652i	−0.0576829	−	0.998335i	$-0.518371\pi$
$547$	22.0000	−	22.0000i	0.940652	−	0.940652i	0.998335	+	0.0576829i	$0.0183712\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$			6.00000i			0.255609i
$552$		0			0
$553$		−	4.00000i		−	0.170097i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−1.00000	+	1.00000i	−0.0423714	+	0.0423714i	−0.727975	−	0.685604i	$-0.759538\pi$
$557$	−1.00000	+	1.00000i	−0.0423714	+	0.0423714i	0.685604	+	0.727975i	$0.259538\pi$
$558$		0			0
$559$	24.0000			1.01509
$560$		0			0
$561$	24.0000			1.01328
$562$		0			0
$563$	15.0000	−	15.0000i	0.632175	−	0.632175i	−0.316438	−	0.948613i	$-0.602487\pi$
$563$	15.0000	−	15.0000i	0.632175	−	0.632175i	0.948613	+	0.316438i	$0.102487\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$			5.00000i			0.209980i
$568$		0			0
$569$		−	18.0000i		−	0.754599i	−0.926091	−	0.377300i	$-0.876853\pi$
$569$		−	18.0000i		−	0.754599i	0.926091	−	0.377300i	$-0.123147\pi$
$570$		0			0
$571$	6.00000	+	6.00000i	0.251092	+	0.251092i	0.821418	−	0.570326i	$-0.193183\pi$
$571$	6.00000	+	6.00000i	0.251092	+	0.251092i	−0.570326	+	0.821418i	$0.693183\pi$
$572$		0			0
$573$	−20.0000	+	20.0000i	−0.835512	+	0.835512i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	2.00000			0.0832611			0.0416305	−	0.999133i	$-0.486745\pi$
$577$	2.00000			0.0832611			0.0416305	+	0.999133i	$0.486745\pi$
$578$		0			0
$579$	2.00000	−	2.00000i	0.0831172	−	0.0831172i
$580$		0			0
$581$	−5.00000	−	5.00000i	−0.207435	−	0.207435i
$582$		0			0
$583$			36.0000i			1.49097i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−21.0000	−	21.0000i	−0.866763	−	0.866763i	0.125350	−	0.992113i	$-0.459995\pi$
$587$	−21.0000	−	21.0000i	−0.866763	−	0.866763i	−0.992113	+	0.125350i	$0.959995\pi$
$588$		0			0
$589$	30.0000	−	30.0000i	1.23613	−	1.23613i
$590$		0			0
$591$	26.0000			1.06950
$592$		0			0
$593$	−6.00000			−0.246390			−0.123195	−	0.992382i	$-0.539314\pi$
$593$	−6.00000			−0.246390			−0.123195	+	0.992382i	$0.539314\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−22.0000	−	22.0000i	−0.900400	−	0.900400i
$598$		0			0
$599$			40.0000i			1.63436i	0.576386	+	0.817178i	$0.304463\pi$
$599$			40.0000i			1.63436i	−0.576386	+	0.817178i	$0.695537\pi$
$600$		0			0
$601$			30.0000i			1.22373i	0.790964	+	0.611863i	$0.209580\pi$
$601$			30.0000i			1.22373i	−0.790964	+	0.611863i	$0.790420\pi$
$602$		0			0
$603$	−8.00000	−	8.00000i	−0.325785	−	0.325785i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	8.00000			0.324710			0.162355	−	0.986732i	$-0.448091\pi$
$607$	8.00000			0.324710			0.162355	+	0.986732i	$0.448091\pi$
$608$		0			0
$609$	2.00000			0.0810441
$610$		0			0
$611$	−4.00000	+	4.00000i	−0.161823	+	0.161823i
$612$		0			0
$613$	−19.0000	−	19.0000i	−0.767403	−	0.767403i	0.210246	−	0.977649i	$-0.432574\pi$
$613$	−19.0000	−	19.0000i	−0.767403	−	0.767403i	−0.977649	+	0.210246i	$0.932574\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$			40.0000i			1.61034i	0.593045	+	0.805170i	$0.297926\pi$
$617$			40.0000i			1.61034i	−0.593045	+	0.805170i	$0.702074\pi$
$618$		0			0
$619$	27.0000	+	27.0000i	1.08522	+	1.08522i	0.996013	+	0.0892087i	$0.0284338\pi$
$619$	27.0000	+	27.0000i	1.08522	+	1.08522i	0.0892087	+	0.996013i	$0.471566\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	2.00000			0.0801283
$624$		0			0
$625$	−25.0000			−1.00000
$626$		0			0
$627$	12.0000	−	12.0000i	0.479234	−	0.479234i
$628$		0			0
$629$	18.0000	+	18.0000i	0.717707	+	0.717707i
$630$		0			0
$631$			20.0000i			0.796187i	0.917345	+	0.398094i	$0.130328\pi$
$631$			20.0000i			0.796187i	−0.917345	+	0.398094i	$0.869672\pi$
$632$		0			0
$633$			40.0000i			1.58986i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−2.00000	+	2.00000i	−0.0792429	+	0.0792429i
$638$		0			0
$639$	12.0000			0.474713
$640$		0			0
$641$	2.00000			0.0789953			0.0394976	−	0.999220i	$-0.487424\pi$
$641$	2.00000			0.0789953			0.0394976	+	0.999220i	$0.487424\pi$
$642$		0			0
$643$	17.0000	−	17.0000i	0.670415	−	0.670415i	−0.287397	−	0.957812i	$-0.592790\pi$
$643$	17.0000	−	17.0000i	0.670415	−	0.670415i	0.957812	+	0.287397i	$0.0927899\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	38.0000i		−	1.49393i	−0.664861	−	0.746967i	$-0.731509\pi$
$647$		−	38.0000i		−	1.49393i	0.664861	−	0.746967i	$-0.268491\pi$
$648$		0			0
$649$			4.00000i			0.157014i
$650$		0			0
$651$	−10.0000	−	10.0000i	−0.391931	−	0.391931i
$652$		0			0
$653$	−19.0000	+	19.0000i	−0.743527	+	0.743527i	−0.973255	−	0.229728i	$-0.926216\pi$
$653$	−19.0000	+	19.0000i	−0.743527	+	0.743527i	0.229728	+	0.973255i	$0.426216\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	2.00000			0.0780274
$658$		0			0
$659$	14.0000	−	14.0000i	0.545363	−	0.545363i	−0.379733	−	0.925096i	$-0.623984\pi$
$659$	14.0000	−	14.0000i	0.545363	−	0.545363i	0.925096	+	0.379733i	$0.123984\pi$
$660$		0			0
$661$	−28.0000	−	28.0000i	−1.08907	−	1.08907i	−0.995624	−	0.0934498i	$-0.970211\pi$
$661$	−28.0000	−	28.0000i	−1.08907	−	1.08907i	−0.0934498	−	0.995624i	$-0.529789\pi$
$662$		0			0
$663$			24.0000i			0.932083i
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$	−16.0000	+	16.0000i	−0.618596	+	0.618596i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−36.0000			−1.38770			−0.693849	−	0.720121i	$-0.744086\pi$
$673$	−36.0000			−1.38770			−0.693849	+	0.720121i	$0.744086\pi$
$674$		0			0
$675$	20.0000	−	20.0000i	0.769800	−	0.769800i
$676$		0			0
$677$	−2.00000	−	2.00000i	−0.0768662	−	0.0768662i	0.667628	−	0.744495i	$-0.267310\pi$
$677$	−2.00000	−	2.00000i	−0.0768662	−	0.0768662i	−0.744495	+	0.667628i	$0.767310\pi$
$678$		0			0
$679$		−	2.00000i		−	0.0767530i
$680$		0			0
$681$		−	2.00000i		−	0.0766402i
$682$		0			0
$683$	16.0000	+	16.0000i	0.612223	+	0.612223i	0.943525	−	0.331302i	$-0.107488\pi$
$683$	16.0000	+	16.0000i	0.612223	+	0.612223i	−0.331302	+	0.943525i	$0.607488\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	36.0000			1.37349
$688$		0			0
$689$	−36.0000			−1.37149
$690$		0			0
$691$	15.0000	−	15.0000i	0.570627	−	0.570627i	−0.361677	−	0.932304i	$-0.617796\pi$
$691$	15.0000	−	15.0000i	0.570627	−	0.570627i	0.932304	+	0.361677i	$0.117796\pi$
$692$		0			0
$693$	2.00000	+	2.00000i	0.0759737	+	0.0759737i
$694$		0			0
$695$		0			0
$696$		0			0
$697$		−	60.0000i		−	2.27266i
$698$		0			0
$699$	−10.0000	−	10.0000i	−0.378235	−	0.378235i
$700$		0			0
$701$	−21.0000	+	21.0000i	−0.793159	+	0.793159i	−0.982006	−	0.188847i	$-0.939525\pi$
$701$	−21.0000	+	21.0000i	−0.793159	+	0.793159i	0.188847	+	0.982006i	$0.439525\pi$
$702$		0			0
$703$	18.0000			0.678883
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−4.00000	+	4.00000i	−0.150435	+	0.150435i
$708$		0			0
$709$	−27.0000	−	27.0000i	−1.01401	−	1.01401i	−0.999901	−	0.0141058i	$-0.995510\pi$
$709$	−27.0000	−	27.0000i	−1.01401	−	1.01401i	−0.0141058	−	0.999901i	$-0.504490\pi$
$710$		0			0
$711$		−	4.00000i		−	0.150012i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$	26.0000			0.969636			0.484818	−	0.874615i	$-0.338886\pi$
$719$	26.0000			0.969636			0.484818	+	0.874615i	$0.338886\pi$
$720$		0			0
$721$	−6.00000			−0.223452
$722$		0			0
$723$	2.00000	−	2.00000i	0.0743808	−	0.0743808i
$724$		0			0
$725$	−5.00000	−	5.00000i	−0.185695	−	0.185695i
$726$		0			0
$727$		−	30.0000i		−	1.11264i	−0.830969	−	0.556319i	$-0.812213\pi$
$727$		−	30.0000i		−	1.11264i	0.830969	−	0.556319i	$-0.187787\pi$
$728$		0			0
$729$			29.0000i			1.07407i
$730$		0			0
$731$	−36.0000	−	36.0000i	−1.33151	−	1.33151i
$732$		0			0
$733$	24.0000	−	24.0000i	0.886460	−	0.886460i	−0.107721	−	0.994181i	$-0.534355\pi$
$733$	24.0000	−	24.0000i	0.886460	−	0.886460i	0.994181	+	0.107721i	$0.0343553\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	32.0000			1.17874
$738$		0			0
$739$	22.0000	−	22.0000i	0.809283	−	0.809283i	−0.175242	−	0.984525i	$-0.556071\pi$
$739$	22.0000	−	22.0000i	0.809283	−	0.809283i	0.984525	+	0.175242i	$0.0560709\pi$
$740$		0			0
$741$	12.0000	+	12.0000i	0.440831	+	0.440831i
$742$		0			0
$743$		−	44.0000i		−	1.61420i	−0.590412	−	0.807102i	$-0.701035\pi$
$743$		−	44.0000i		−	1.61420i	0.590412	−	0.807102i	$-0.298965\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−5.00000	−	5.00000i	−0.182940	−	0.182940i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−32.0000			−1.16770			−0.583848	−	0.811863i	$-0.698454\pi$
$751$	−32.0000			−1.16770			−0.583848	+	0.811863i	$0.698454\pi$
$752$		0			0
$753$	22.0000			0.801725
$754$		0			0
$755$		0			0
$756$		0			0
$757$	37.0000	+	37.0000i	1.34479	+	1.34479i	0.891224	+	0.453564i	$0.149848\pi$
$757$	37.0000	+	37.0000i	1.34479	+	1.34479i	0.453564	+	0.891224i	$0.350152\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$			42.0000i			1.52250i	0.648459	+	0.761249i	$0.275414\pi$
$761$			42.0000i			1.52250i	−0.648459	+	0.761249i	$0.724586\pi$
$762$		0			0
$763$	3.00000	+	3.00000i	0.108607	+	0.108607i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−4.00000			−0.144432
$768$		0			0
$769$	−38.0000			−1.37032			−0.685158	−	0.728395i	$-0.740267\pi$
$769$	−38.0000			−1.37032			−0.685158	+	0.728395i	$0.740267\pi$
$770$		0			0
$771$	−6.00000	+	6.00000i	−0.216085	+	0.216085i
$772$		0			0
$773$	12.0000	+	12.0000i	0.431610	+	0.431610i	0.889176	−	0.457566i	$-0.151279\pi$
$773$	12.0000	+	12.0000i	0.431610	+	0.431610i	−0.457566	+	0.889176i	$0.651279\pi$
$774$		0			0
$775$			50.0000i			1.79605i
$776$		0			0
$777$		−	6.00000i		−	0.215249i
$778$		0			0
$779$	−30.0000	−	30.0000i	−1.07486	−	1.07486i
$780$		0			0
$781$	−24.0000	+	24.0000i	−0.858788	+	0.858788i
$782$		0			0
$783$	8.00000			0.285897
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−13.0000	+	13.0000i	−0.463400	+	0.463400i	−0.899768	−	0.436368i	$-0.856265\pi$
$787$	−13.0000	+	13.0000i	−0.463400	+	0.463400i	0.436368	+	0.899768i	$0.356265\pi$
$788$		0			0
$789$	12.0000	+	12.0000i	0.427211	+	0.427211i
$790$		0			0
$791$		−	12.0000i		−	0.426671i
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$	22.0000	−	22.0000i	0.779280	−	0.779280i	−0.200428	−	0.979708i	$-0.564233\pi$
$797$	22.0000	−	22.0000i	0.779280	−	0.779280i	0.979708	+	0.200428i	$0.0642334\pi$
$798$		0			0
$799$	12.0000			0.424529
$800$		0			0
$801$	2.00000			0.0706665
$802$		0			0
$803$	−4.00000	+	4.00000i	−0.141157	+	0.141157i
$804$		0			0
$805$		0			0
$806$		0			0
$807$			28.0000i			0.985647i
$808$		0			0
$809$		−	22.0000i		−	0.773479i	−0.922189	−	0.386739i	$-0.873601\pi$
$809$		−	22.0000i		−	0.773479i	0.922189	−	0.386739i	$-0.126399\pi$
$810$		0			0
$811$	7.00000	+	7.00000i	0.245803	+	0.245803i	0.819246	−	0.573443i	$-0.194392\pi$
$811$	7.00000	+	7.00000i	0.245803	+	0.245803i	−0.573443	+	0.819246i	$0.694392\pi$
$812$		0			0
$813$	24.0000	−	24.0000i	0.841717	−	0.841717i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−36.0000			−1.25948
$818$		0			0
$819$	−2.00000	+	2.00000i	−0.0698857	+	0.0698857i
$820$		0			0
$821$	−31.0000	−	31.0000i	−1.08191	−	1.08191i	−0.996332	−	0.0855758i	$-0.972727\pi$
$821$	−31.0000	−	31.0000i	−1.08191	−	1.08191i	−0.0855758	−	0.996332i	$-0.527273\pi$
$822$		0			0
$823$			8.00000i			0.278862i	0.990232	+	0.139431i	$0.0445274\pi$
$823$			8.00000i			0.278862i	−0.990232	+	0.139431i	$0.955473\pi$
$824$		0			0
$825$			20.0000i			0.696311i
$826$		0			0
$827$	−20.0000	−	20.0000i	−0.695468	−	0.695468i	0.267961	−	0.963430i	$-0.413650\pi$
$827$	−20.0000	−	20.0000i	−0.695468	−	0.695468i	−0.963430	+	0.267961i	$0.913650\pi$
$828$		0			0
$829$	32.0000	−	32.0000i	1.11141	−	1.11141i	0.118445	−	0.992961i	$-0.462209\pi$
$829$	32.0000	−	32.0000i	1.11141	−	1.11141i	0.992961	−	0.118445i	$-0.0377910\pi$
$830$		0			0
$831$	34.0000			1.17945
$832$		0			0
$833$	6.00000			0.207888
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−40.0000	−	40.0000i	−1.38260	−	1.38260i
$838$		0			0
$839$			30.0000i			1.03572i	0.855467	+	0.517858i	$0.173270\pi$
$839$			30.0000i			1.03572i	−0.855467	+	0.517858i	$0.826730\pi$
$840$		0			0
$841$			27.0000i			0.931034i
$842$		0			0
$843$	−10.0000	−	10.0000i	−0.344418	−	0.344418i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	3.00000			0.103081
$848$		0			0
$849$	30.0000			1.02960
$850$		0			0
$851$		0			0
$852$		0			0
$853$	10.0000	+	10.0000i	0.342393	+	0.342393i	0.857266	−	0.514873i	$-0.172161\pi$
$853$	10.0000	+	10.0000i	0.342393	+	0.342393i	−0.514873	+	0.857266i	$0.672161\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		−	22.0000i		−	0.751506i	−0.926720	−	0.375753i	$-0.877384\pi$
$857$		−	22.0000i		−	0.751506i	0.926720	−	0.375753i	$-0.122616\pi$
$858$		0			0
$859$	33.0000	+	33.0000i	1.12595	+	1.12595i	0.990830	+	0.135116i	$0.0431406\pi$
$859$	33.0000	+	33.0000i	1.12595	+	1.12595i	0.135116	+	0.990830i	$0.456859\pi$
$860$		0			0
$861$	−10.0000	+	10.0000i	−0.340799	+	0.340799i
$862$		0			0
$863$	−4.00000			−0.136162			−0.0680808	−	0.997680i	$-0.521688\pi$
$863$	−4.00000			−0.136162			−0.0680808	+	0.997680i	$0.521688\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	19.0000	−	19.0000i	0.645274	−	0.645274i
$868$		0			0
$869$	8.00000	+	8.00000i	0.271381	+	0.271381i
$870$		0			0
$871$			32.0000i			1.08428i
$872$		0			0
$873$		−	2.00000i		−	0.0676897i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−1.00000	+	1.00000i	−0.0337676	+	0.0337676i	−0.723789	−	0.690021i	$-0.757601\pi$
$877$	−1.00000	+	1.00000i	−0.0337676	+	0.0337676i	0.690021	+	0.723789i	$0.257601\pi$
$878$		0			0
$879$	−8.00000			−0.269833
$880$		0			0
$881$	26.0000			0.875962			0.437981	−	0.898984i	$-0.355694\pi$
$881$	26.0000			0.875962			0.437981	+	0.898984i	$0.355694\pi$
$882$		0			0
$883$	28.0000	−	28.0000i	0.942275	−	0.942275i	−0.0561475	−	0.998422i	$-0.517882\pi$
$883$	28.0000	−	28.0000i	0.942275	−	0.942275i	0.998422	+	0.0561475i	$0.0178817\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$		−	38.0000i		−	1.27592i	−0.770072	−	0.637958i	$-0.779780\pi$
$887$		−	38.0000i		−	1.27592i	0.770072	−	0.637958i	$-0.220220\pi$
$888$		0			0
$889$		−	12.0000i		−	0.402467i
$890$		0			0
$891$	−10.0000	−	10.0000i	−0.335013	−	0.335013i
$892$		0			0
$893$	6.00000	−	6.00000i	0.200782	−	0.200782i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−10.0000	+	10.0000i	−0.333519	+	0.333519i
$900$		0			0
$901$	54.0000	+	54.0000i	1.79900	+	1.79900i
$902$		0			0
$903$			12.0000i			0.399335i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	16.0000	+	16.0000i	0.531271	+	0.531271i	0.920951	−	0.389679i	$-0.127414\pi$
$907$	16.0000	+	16.0000i	0.531271	+	0.531271i	−0.389679	+	0.920951i	$0.627414\pi$
$908$		0			0
$909$	−4.00000	+	4.00000i	−0.132672	+	0.132672i
$910$		0			0
$911$	−12.0000			−0.397578			−0.198789	−	0.980042i	$-0.563701\pi$
$911$	−12.0000			−0.397578			−0.198789	+	0.980042i	$0.563701\pi$
$912$		0			0
$913$	20.0000			0.661903
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−7.00000	−	7.00000i	−0.231160	−	0.231160i
$918$		0			0
$919$			32.0000i			1.05558i	0.849374	+	0.527791i	$0.176980\pi$
$919$			32.0000i			1.05558i	−0.849374	+	0.527791i	$0.823020\pi$
$920$		0			0
$921$		−	46.0000i		−	1.51575i
$922$		0			0
$923$	−24.0000	−	24.0000i	−0.789970	−	0.789970i
$924$		0			0
$925$	−15.0000	+	15.0000i	−0.493197	+	0.493197i
$926$		0			0
$927$	−6.00000			−0.197066
$928$		0			0
$929$	6.00000			0.196854			0.0984268	−	0.995144i	$-0.468619\pi$
$929$	6.00000			0.196854			0.0984268	+	0.995144i	$0.468619\pi$
$930$		0			0
$931$	3.00000	−	3.00000i	0.0983210	−	0.0983210i
$932$		0			0
$933$	8.00000	+	8.00000i	0.261908	+	0.261908i
$934$		0			0
$935$		0			0
$936$		0			0
$937$			30.0000i			0.980057i	0.871706	+	0.490029i	$0.163014\pi$
$937$			30.0000i			0.980057i	−0.871706	+	0.490029i	$0.836986\pi$
$938$		0			0
$939$	30.0000	+	30.0000i	0.979013	+	0.979013i
$940$		0			0
$941$	−28.0000	+	28.0000i	−0.912774	+	0.912774i	−0.996490	−	0.0837158i	$-0.973321\pi$
$941$	−28.0000	+	28.0000i	−0.912774	+	0.912774i	0.0837158	+	0.996490i	$0.473321\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$	38.0000	−	38.0000i	1.23483	−	1.23483i	0.272749	−	0.962085i	$-0.412067\pi$
$947$	38.0000	−	38.0000i	1.23483	−	1.23483i	0.962085	−	0.272749i	$-0.0879328\pi$
$948$		0			0
$949$	−4.00000	−	4.00000i	−0.129845	−	0.129845i
$950$		0			0
$951$		−	34.0000i		−	1.10253i
$952$		0			0
$953$		−	16.0000i		−	0.518291i	−0.965838	−	0.259145i	$-0.916559\pi$
$953$		−	16.0000i		−	0.518291i	0.965838	−	0.259145i	$-0.0834409\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−4.00000	+	4.00000i	−0.129302	+	0.129302i
$958$		0			0
$959$	12.0000			0.387500
$960$		0			0
$961$	69.0000			2.22581
$962$		0			0
$963$		0			0
$964$		0			0
$965$		0			0
$966$		0			0
$967$			24.0000i			0.771788i	0.922543	+	0.385894i	$0.126107\pi$
$967$			24.0000i			0.771788i	−0.922543	+	0.385894i	$0.873893\pi$
$968$		0			0
$969$		−	36.0000i		−	1.15649i
$970$		0			0
$971$	−15.0000	−	15.0000i	−0.481373	−	0.481373i	0.424197	−	0.905570i	$-0.360556\pi$
$971$	−15.0000	−	15.0000i	−0.481373	−	0.481373i	−0.905570	+	0.424197i	$0.860556\pi$
$972$		0			0
$973$	3.00000	−	3.00000i	0.0961756	−	0.0961756i
$974$		0			0
$975$	−20.0000			−0.640513
$976$		0			0
$977$	−20.0000			−0.639857			−0.319928	−	0.947442i	$-0.603659\pi$
$977$	−20.0000			−0.639857			−0.319928	+	0.947442i	$0.603659\pi$
$978$		0			0
$979$	−4.00000	+	4.00000i	−0.127841	+	0.127841i
$980$		0			0
$981$	3.00000	+	3.00000i	0.0957826	+	0.0957826i
$982$		0			0
$983$		−	6.00000i		−	0.191370i	−0.995412	−	0.0956851i	$-0.969496\pi$
$983$		−	6.00000i		−	0.191370i	0.995412	−	0.0956851i	$-0.0305042\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−2.00000	−	2.00000i	−0.0636607	−	0.0636607i
$988$		0			0
$989$		0			0
$990$		0			0
$991$	48.0000			1.52477			0.762385	−	0.647124i	$-0.224028\pi$
$991$	48.0000			1.52477			0.762385	+	0.647124i	$0.224028\pi$
$992$		0			0
$993$	−12.0000			−0.380808
$994$		0			0
$995$		0			0
$996$		0			0
$997$	20.0000	+	20.0000i	0.633406	+	0.633406i	0.948921	−	0.315514i	$-0.102177\pi$
$997$	20.0000	+	20.0000i	0.633406	+	0.633406i	−0.315514	+	0.948921i	$0.602177\pi$
$998$		0			0
$999$		−	24.0000i		−	0.759326i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3584.2.m.v.897.1	yes	2
4.3	odd	2		3584.2.m.h.897.1	yes	2
8.3	odd	2		3584.2.m.u.897.1	yes	2
8.5	even	2		3584.2.m.g.897.1	✓	2
16.3	odd	4		3584.2.m.h.2689.1	yes	2
16.5	even	4		3584.2.m.g.2689.1	yes	2
16.11	odd	4		3584.2.m.u.2689.1	yes	2
16.13	even	4	inner	3584.2.m.v.2689.1	yes	2
32.3	odd	8		7168.2.a.e.1.1		2
32.13	even	8		7168.2.a.n.1.1		2
32.19	odd	8		7168.2.a.e.1.2		2
32.29	even	8		7168.2.a.n.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3584.2.m.g.897.1	✓	2	8.5	even	2
3584.2.m.g.2689.1	yes	2	16.5	even	4
3584.2.m.h.897.1	yes	2	4.3	odd	2
3584.2.m.h.2689.1	yes	2	16.3	odd	4
3584.2.m.u.897.1	yes	2	8.3	odd	2
3584.2.m.u.2689.1	yes	2	16.11	odd	4
3584.2.m.v.897.1	yes	2	1.1	even	1	trivial
3584.2.m.v.2689.1	yes	2	16.13	even	4	inner
7168.2.a.e.1.1		2	32.3	odd	8
7168.2.a.e.1.2		2	32.19	odd	8
7168.2.a.n.1.1		2	32.13	even	8
7168.2.a.n.1.2		2	32.29	even	8

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:	\( N \)	\(=\)	\( 3584 = 2^{9} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3584.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.00000i) q^{3} +1.00000i q^{7} +1.00000i q^{9} +O(q^{10})\)	\(q+(1.00000 - 1.00000i) q^{3} +1.00000i q^{7} +1.00000i q^{9} +(-2.00000 - 2.00000i) q^{11} +(2.00000 - 2.00000i) q^{13} -6.00000 q^{17} +(-3.00000 + 3.00000i) q^{19} +(1.00000 + 1.00000i) q^{21} -5.00000i q^{25} +(4.00000 + 4.00000i) q^{27} +(1.00000 - 1.00000i) q^{29} -10.0000 q^{31} -4.00000 q^{33} +(-3.00000 - 3.00000i) q^{37} -4.00000i q^{39} +10.0000i q^{41} +(6.00000 + 6.00000i) q^{43} -2.00000 q^{47} -1.00000 q^{49} +(-6.00000 + 6.00000i) q^{51} +(-9.00000 - 9.00000i) q^{53} +6.00000i q^{57} +(-1.00000 - 1.00000i) q^{59} -1.00000 q^{63} +(-8.00000 + 8.00000i) q^{67} -12.0000i q^{71} -2.00000i q^{73} +(-5.00000 - 5.00000i) q^{75} +(2.00000 - 2.00000i) q^{77} -4.00000 q^{79} +5.00000 q^{81} +(-5.00000 + 5.00000i) q^{83} -2.00000i q^{87} -2.00000i q^{89} +(2.00000 + 2.00000i) q^{91} +(-10.0000 + 10.0000i) q^{93} -2.00000 q^{97} +(2.00000 - 2.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{3}+O(q^{10}) \) 2 * q + 2 * q^3	\( 2 q + 2 q^{3} - 4 q^{11} + 4 q^{13} - 12 q^{17} - 6 q^{19} + 2 q^{21} + 8 q^{27} + 2 q^{29} - 20 q^{31} - 8 q^{33} - 6 q^{37} + 12 q^{43} - 4 q^{47} - 2 q^{49} - 12 q^{51} - 18 q^{53} - 2 q^{59} - 2 q^{63} - 16 q^{67} - 10 q^{75} + 4 q^{77} - 8 q^{79} + 10 q^{81} - 10 q^{83} + 4 q^{91} - 20 q^{93} - 4 q^{97} + 4 q^{99}+O(q^{100}) \) 2 * q + 2 * q^3 - 4 * q^11 + 4 * q^13 - 12 * q^17 - 6 * q^19 + 2 * q^21 + 8 * q^27 + 2 * q^29 - 20 * q^31 - 8 * q^33 - 6 * q^37 + 12 * q^43 - 4 * q^47 - 2 * q^49 - 12 * q^51 - 18 * q^53 - 2 * q^59 - 2 * q^63 - 16 * q^67 - 10 * q^75 + 4 * q^77 - 8 * q^79 + 10 * q^81 - 10 * q^83 + 4 * q^91 - 20 * q^93 - 4 * q^97 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more