LMFDB - Embedded newform 48.6.c.d.47.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,6,Mod(47,48)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(48, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("48.47");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	48.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.69842335102$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-14})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 14x^{2} + 196 $ x^4 - 14*x^2 + 196
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6}\cdot 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			47.1
Root			$3.24037 - 1.87083i$ of defining polynomial
Character	$\chi$	$=$	48.47
Dual form			48.6.c.d.47.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-12.9615 - 8.66025i) q^{3} +44.8999i q^{5} -38.1051i q^{7} +(93.0000 + 224.499i) q^{9} +O(q^{10})$	\(q+(-12.9615 - 8.66025i) q^{3} +44.8999i q^{5} -38.1051i q^{7} +(93.0000 + 224.499i) q^{9} +544.382 q^{11} +814.000 q^{13} +(388.844 - 581.969i) q^{15} +1975.60i q^{17} +38.1051i q^{19} +(-330.000 + 493.899i) q^{21} -1399.84 q^{23} +1109.00 q^{25} +(738.804 - 3715.25i) q^{27} -5432.89i q^{29} +10423.5i q^{31} +(-7056.00 - 4714.49i) q^{33} +1710.92 q^{35} -1594.00 q^{37} +(-10550.6 - 7049.45i) q^{39} -8890.18i q^{41} +9030.91i q^{43} +(-10080.0 + 4175.69i) q^{45} -16487.0 q^{47} +15355.0 q^{49} +(17109.2 - 25606.6i) q^{51} +19262.1i q^{53} +24442.7i q^{55} +(330.000 - 493.899i) q^{57} +45650.3 q^{59} +23870.0 q^{61} +(8554.58 - 3543.78i) q^{63} +36548.5i q^{65} -30390.6i q^{67} +(18144.0 + 12123.0i) q^{69} -32818.5 q^{71} +17578.0 q^{73} +(-14374.3 - 9604.22i) q^{75} -20743.7i q^{77} +7125.66i q^{79} +(-41751.0 + 41756.9i) q^{81} +16253.7 q^{83} -88704.0 q^{85} +(-47050.2 + 70418.3i) q^{87} -88452.8i q^{89} -31017.6i q^{91} +(90270.0 - 135104. i) q^{93} -1710.92 q^{95} -49070.0 q^{97} +(50627.5 + 122214. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 372 q^{9}+O(q^{10}) $ 4 * q + 372 * q^9	$ 4 q + 372 q^{9} + 3256 q^{13} - 1320 q^{21} + 4436 q^{25} - 28224 q^{33} - 6376 q^{37} - 40320 q^{45} + 61420 q^{49} + 1320 q^{57} + 95480 q^{61} + 72576 q^{69} + 70312 q^{73} - 167004 q^{81} - 354816 q^{85} + 361080 q^{93} - 196280 q^{97}+O(q^{100}) $ 4 * q + 372 * q^9 + 3256 * q^13 - 1320 * q^21 + 4436 * q^25 - 28224 * q^33 - 6376 * q^37 - 40320 * q^45 + 61420 * q^49 + 1320 * q^57 + 95480 * q^61 + 72576 * q^69 + 70312 * q^73 - 167004 * q^81 - 354816 * q^85 + 361080 * q^93 - 196280 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

$n$	$17$	$31$	$37$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−12.9615	−	8.66025i	−0.831479	−	0.555556i
$3$	−12.9615	−	8.66025i	−0.831479	−	0.555556i
$4$		0			0
$5$			44.8999i			0.803194i	0.915817	+	0.401597i	$0.131545\pi$
$5$			44.8999i			0.803194i	−0.915817	+	0.401597i	$0.868455\pi$
$6$		0			0
$7$		−	38.1051i		−	0.293926i	−0.989142	−	0.146963i	$-0.953050\pi$
$7$		−	38.1051i		−	0.293926i	0.989142	−	0.146963i	$-0.0469498\pi$
$8$		0			0
$9$	93.0000	+	224.499i	0.382716	+	0.923866i
$10$		0			0
$11$	544.382			1.35651			0.678254	−	0.734828i	$-0.262737\pi$
$11$	544.382			1.35651			0.678254	+	0.734828i	$0.262737\pi$
$12$		0			0
$13$	814.000			1.33588			0.667938	−	0.744217i	$-0.267177\pi$
$13$	814.000			1.33588			0.667938	+	0.744217i	$0.267177\pi$
$14$		0			0
$15$	388.844	−	581.969i	0.446219	−	0.667839i
$16$		0			0
$17$			1975.60i			1.65797i	0.559274	+	0.828983i	$0.311080\pi$
$17$			1975.60i			1.65797i	−0.559274	+	0.828983i	$0.688920\pi$
$18$		0			0
$19$			38.1051i			0.0242158i	0.999927	+	0.0121079i	$0.00385416\pi$
$19$			38.1051i			0.0242158i	−0.999927	+	0.0121079i	$0.996146\pi$
$20$		0			0
$21$	−330.000	+	493.899i	−0.163292	+	0.244394i
$22$		0			0
$23$	−1399.84			−0.551771			−0.275885	−	0.961191i	$-0.588971\pi$
$23$	−1399.84			−0.551771			−0.275885	+	0.961191i	$0.588971\pi$
$24$		0			0
$25$	1109.00			0.354880
$26$		0			0
$27$	738.804	−	3715.25i	0.195038	−	0.980796i
$28$		0			0
$29$		−	5432.89i		−	1.19960i	−0.800151	−	0.599799i	$-0.795247\pi$
$29$		−	5432.89i		−	1.19960i	0.800151	−	0.599799i	$-0.204753\pi$
$30$		0			0
$31$			10423.5i			1.94809i	0.226359	+	0.974044i	$0.427318\pi$
$31$			10423.5i			1.94809i	−0.226359	+	0.974044i	$0.572682\pi$
$32$		0			0
$33$	−7056.00	−	4714.49i	−1.12791	−	0.753615i
$34$		0			0
$35$	1710.92			0.236080
$36$		0			0
$37$	−1594.00			−0.191419			−0.0957093	−	0.995409i	$-0.530512\pi$
$37$	−1594.00			−0.191419			−0.0957093	+	0.995409i	$0.530512\pi$
$38$		0			0
$39$	−10550.6	−	7049.45i	−1.11075	−	0.742153i
$40$		0			0
$41$		−	8890.18i		−	0.825944i	−0.910744	−	0.412972i	$-0.864491\pi$
$41$		−	8890.18i		−	0.825944i	0.910744	−	0.412972i	$-0.135509\pi$
$42$		0			0
$43$			9030.91i			0.744836i	0.928065	+	0.372418i	$0.121471\pi$
$43$			9030.91i			0.744836i	−0.928065	+	0.372418i	$0.878529\pi$
$44$		0			0
$45$	−10080.0	+	4175.69i	−0.742043	+	0.307395i
$46$		0			0
$47$	−16487.0			−1.08867			−0.544336	−	0.838867i	$-0.683218\pi$
$47$	−16487.0			−1.08867			−0.544336	+	0.838867i	$0.683218\pi$
$48$		0			0
$49$	15355.0			0.913607
$50$		0			0
$51$	17109.2	−	25606.6i	0.921092	−	1.37856i
$52$		0			0
$53$			19262.1i			0.941918i	0.882155	+	0.470959i	$0.156092\pi$
$53$			19262.1i			0.941918i	−0.882155	+	0.470959i	$0.843908\pi$
$54$		0			0
$55$			24442.7i			1.08954i
$56$		0			0
$57$	330.000	−	493.899i	0.0134532	−	0.0201350i
$58$		0			0
$59$	45650.3			1.70732			0.853658	−	0.520834i	$-0.174379\pi$
$59$	45650.3			1.70732			0.853658	+	0.520834i	$0.174379\pi$
$60$		0			0
$61$	23870.0			0.821349			0.410675	−	0.911782i	$-0.365293\pi$
$61$	23870.0			0.821349			0.410675	+	0.911782i	$0.365293\pi$
$62$		0			0
$63$	8554.58	−	3543.78i	0.271548	−	0.112490i
$64$		0			0
$65$			36548.5i			1.07297i
$66$		0			0
$67$		−	30390.6i		−	0.827088i	−0.910484	−	0.413544i	$-0.864291\pi$
$67$		−	30390.6i		−	0.827088i	0.910484	−	0.413544i	$-0.135709\pi$
$68$		0			0
$69$	18144.0	+	12123.0i	0.458786	+	0.306539i
$70$		0			0
$71$	−32818.5			−0.772632			−0.386316	−	0.922367i	$-0.626253\pi$
$71$	−32818.5			−0.772632			−0.386316	+	0.922367i	$0.626253\pi$
$72$		0			0
$73$	17578.0			0.386067			0.193033	−	0.981192i	$-0.438167\pi$
$73$	17578.0			0.386067			0.193033	+	0.981192i	$0.438167\pi$
$74$		0			0
$75$	−14374.3	−	9604.22i	−0.295075	−	0.197156i
$76$		0			0
$77$		−	20743.7i		−	0.398713i
$78$		0			0
$79$			7125.66i			0.128457i	0.997935	+	0.0642284i	$0.0204586\pi$
$79$			7125.66i			0.128457i	−0.997935	+	0.0642284i	$0.979541\pi$
$80$		0			0
$81$	−41751.0	+	41756.9i	−0.707057	+	0.707157i
$82$		0			0
$83$	16253.7			0.258974			0.129487	−	0.991581i	$-0.458667\pi$
$83$	16253.7			0.258974			0.129487	+	0.991581i	$0.458667\pi$
$84$		0			0
$85$	−88704.0			−1.33167
$86$		0			0
$87$	−47050.2	+	70418.3i	−0.666443	+	0.997441i
$88$		0			0
$89$		−	88452.8i		−	1.18369i	−0.806053	−	0.591843i	$-0.798401\pi$
$89$		−	88452.8i		−	1.18369i	0.806053	−	0.591843i	$-0.201599\pi$
$90$		0			0
$91$		−	31017.6i		−	0.392649i
$92$		0			0
$93$	90270.0	−	135104.i	1.08227	−	1.61980i
$94$		0			0
$95$	−1710.92			−0.0194500
$96$		0			0
$97$	−49070.0			−0.529525			−0.264763	−	0.964314i	$-0.585294\pi$
$97$	−49070.0			−0.529525			−0.264763	+	0.964314i	$0.585294\pi$
$98$		0			0
$99$	50627.5	+	122214.i	0.519157	+	1.25323i
$100$		0			0
$101$		−	34079.0i		−	0.332417i	−0.986091	−	0.166209i	$-0.946847\pi$
$101$		−	34079.0i		−	0.332417i	0.986091	−	0.166209i	$-0.0531525\pi$
$102$		0			0
$103$		−	76858.0i		−	0.713832i	−0.934136	−	0.356916i	$-0.883828\pi$
$103$		−	76858.0i		−	0.713832i	0.934136	−	0.356916i	$-0.116172\pi$
$104$		0			0
$105$	−22176.0	−	14817.0i	−0.196295	−	0.131155i
$106$		0			0
$107$	−159971.			−1.35077			−0.675384	−	0.737466i	$-0.736022\pi$
$107$	−159971.			−1.35077			−0.675384	+	0.737466i	$0.736022\pi$
$108$		0			0
$109$	−140690.			−1.13422			−0.567110	−	0.823642i	$-0.691938\pi$
$109$	−140690.			−1.13422			−0.567110	+	0.823642i	$0.691938\pi$
$110$		0			0
$111$	20660.6	+	13804.4i	0.159161	+	0.106344i
$112$		0			0
$113$			32148.3i			0.236844i	0.992963	+	0.118422i	$0.0377835\pi$
$113$			32148.3i			0.236844i	−0.992963	+	0.118422i	$0.962216\pi$
$114$		0			0
$115$		−	62852.7i		−	0.443179i
$116$		0			0
$117$	75702.0	+	182743.i	0.511261	+	1.23417i
$118$		0			0
$119$	75280.3			0.487320
$120$		0			0
$121$	135301.			0.840113
$122$		0			0
$123$	−76991.2	+	115230.i	−0.458858	+	0.686756i
$124$		0			0
$125$			190106.i			1.08823i
$126$		0			0
$127$		−	277901.i		−	1.52890i	−0.644681	−	0.764452i	$-0.723010\pi$
$127$		−	277901.i		−	1.52890i	0.644681	−	0.764452i	$-0.276990\pi$
$128$		0			0
$129$	78210.0	−	117054.i	0.413798	−	0.619316i
$130$		0			0
$131$	149705.			0.762181			0.381091	−	0.924538i	$-0.375549\pi$
$131$	149705.			0.762181			0.381091	+	0.924538i	$0.375549\pi$
$132$		0			0
$133$	1452.00			0.00711766
$134$		0			0
$135$	166814.	+	33172.2i	0.787769	+	0.156654i
$136$		0			0
$137$			83424.0i			0.379743i	0.981809	+	0.189871i	$0.0608071\pi$
$137$			83424.0i			0.379743i	−0.981809	+	0.189871i	$0.939193\pi$
$138$		0			0
$139$			80668.5i			0.354134i	0.984199	+	0.177067i	$0.0566609\pi$
$139$			80668.5i			0.354134i	−0.984199	+	0.177067i	$0.943339\pi$
$140$		0			0
$141$	213696.	+	142782.i	0.905208	+	0.604818i
$142$		0			0
$143$	443127.			1.81213
$144$		0			0
$145$	243936.			0.963509
$146$		0			0
$147$	−199024.	−	132978.i	−0.759646	−	0.507560i
$148$		0			0
$149$		−	103225.i		−	0.380907i	−0.981696	−	0.190453i	$-0.939004\pi$
$149$		−	103225.i		−	0.380907i	0.981696	−	0.190453i	$-0.0609958\pi$
$150$		0			0
$151$			179513.i			0.640699i	0.947299	+	0.320349i	$0.103800\pi$
$151$			179513.i			0.640699i	−0.947299	+	0.320349i	$0.896200\pi$
$152$		0			0
$153$	−443520.	+	183730.i	−1.53174	+	0.634530i
$154$		0			0
$155$	−468013.			−1.56469
$156$		0			0
$157$	−324226.			−1.04978			−0.524890	−	0.851170i	$-0.675894\pi$
$157$	−324226.			−1.04978			−0.524890	+	0.851170i	$0.675894\pi$
$158$		0			0
$159$	166814.	−	249665.i	0.523288	−	0.783185i
$160$		0			0
$161$			53341.1i			0.162180i
$162$		0			0
$163$			204586.i			0.603126i	0.953446	+	0.301563i	$0.0975083\pi$
$163$			204586.i			0.603126i	−0.953446	+	0.301563i	$0.902492\pi$
$164$		0			0
$165$	211680.	−	316814.i	0.605299	−	0.905929i
$166$		0			0
$167$	−514986.			−1.42891			−0.714453	−	0.699683i	$-0.753325\pi$
$167$	−514986.			−1.42891			−0.714453	+	0.699683i	$0.753325\pi$
$168$		0			0
$169$	291303.			0.784564
$170$		0			0
$171$	−8554.58	+	3543.78i	−0.0223722	+	0.00926779i
$172$		0			0
$173$		−	355113.i		−	0.902094i	−0.892500	−	0.451047i	$-0.851051\pi$
$173$		−	355113.i		−	0.902094i	0.892500	−	0.451047i	$-0.148949\pi$
$174$		0			0
$175$		−	42258.6i		−	0.104309i
$176$		0			0
$177$	−591696.	−	395344.i	−1.41960	−	0.948509i
$178$		0			0
$179$	53582.8			0.124995			0.0624975	−	0.998045i	$-0.480093\pi$
$179$	53582.8			0.124995			0.0624975	+	0.998045i	$0.480093\pi$
$180$		0			0
$181$	−256202.			−0.581281			−0.290640	−	0.956832i	$-0.593868\pi$
$181$	−256202.			−0.581281			−0.290640	+	0.956832i	$0.593868\pi$
$182$		0			0
$183$	−309391.	−	206720.i	−0.682935	−	0.456305i
$184$		0			0
$185$		−	71570.4i		−	0.153746i
$186$		0			0
$187$			1.07548e6i			2.24904i
$188$		0			0
$189$	−141570.	−	28152.2i	−0.288281	−	0.0573269i
$190$		0			0
$191$	557447.			1.10566			0.552829	−	0.833295i	$-0.313548\pi$
$191$	557447.			1.10566			0.552829	+	0.833295i	$0.313548\pi$
$192$		0			0
$193$	203522.			0.393295			0.196647	−	0.980474i	$-0.436995\pi$
$193$	203522.			0.393295			0.196647	+	0.980474i	$0.436995\pi$
$194$		0			0
$195$	316519.	−	473723.i	0.596093	−	0.892150i
$196$		0			0
$197$		−	488466.i		−	0.896744i	−0.893847	−	0.448372i	$-0.852004\pi$
$197$		−	488466.i		−	0.896744i	0.893847	−	0.448372i	$-0.147996\pi$
$198$		0			0
$199$			504778.i			0.903583i	0.892124	+	0.451792i	$0.149215\pi$
$199$			504778.i			0.903583i	−0.892124	+	0.451792i	$0.850785\pi$
$200$		0			0
$201$	−263190.	+	393907.i	−0.459493	+	0.687707i
$202$		0			0
$203$	−207021.			−0.352593
$204$		0			0
$205$	399168.			0.663393
$206$		0			0
$207$	−130185.	−	314263.i	−0.211172	−	0.509762i
$208$		0			0
$209$			20743.7i			0.0328490i
$210$		0			0
$211$		−	1.06294e6i		−	1.64363i	−0.569756	−	0.821814i	$-0.692962\pi$
$211$		−	1.06294e6i		−	1.64363i	0.569756	−	0.821814i	$-0.307038\pi$
$212$		0			0
$213$	425376.	+	284216.i	0.642427	+	0.429240i
$214$		0			0
$215$	−405487.			−0.598247
$216$		0			0
$217$	397188.			0.572594
$218$		0			0
$219$	−227837.	−	152230.i	−0.321006	−	0.214481i
$220$		0			0
$221$			1.60813e6i			2.21484i
$222$		0			0
$223$			531203.i			0.715316i	0.933853	+	0.357658i	$0.116425\pi$
$223$			531203.i			0.715316i	−0.933853	+	0.357658i	$0.883575\pi$
$224$		0			0
$225$	103137.	+	248970.i	0.135818	+	0.327862i
$226$		0			0
$227$	1.27207e6			1.63849			0.819247	−	0.573441i	$-0.194392\pi$
$227$	1.27207e6			1.63849			0.819247	+	0.573441i	$0.194392\pi$
$228$		0			0
$229$	−485594.			−0.611906			−0.305953	−	0.952047i	$-0.598975\pi$
$229$	−485594.			−0.611906			−0.305953	+	0.952047i	$0.598975\pi$
$230$		0			0
$231$	−179646.	+	268870.i	−0.221507	+	0.331522i
$232$		0			0
$233$			42475.3i			0.0512562i	0.999672	+	0.0256281i	$0.00815857\pi$
$233$			42475.3i			0.0512562i	−0.999672	+	0.0256281i	$0.991841\pi$
$234$		0			0
$235$		−	740265.i		−	0.874415i
$236$		0			0
$237$	61710.0	−	92359.1i	0.0713649	−	0.106809i
$238$		0			0
$239$	−229263.			−0.259620			−0.129810	−	0.991539i	$-0.541437\pi$
$239$	−229263.			−0.259620			−0.129810	+	0.991539i	$0.541437\pi$
$240$		0			0
$241$	1.33995e6			1.48610			0.743049	−	0.669237i	$-0.233379\pi$
$241$	1.33995e6			1.48610			0.743049	+	0.669237i	$0.233379\pi$
$242$		0			0
$243$	902780.	−	179657.i	0.980768	−	0.195177i
$244$		0			0
$245$			689438.i			0.733804i
$246$		0			0
$247$			31017.6i			0.0323493i
$248$		0			0
$249$	−210672.	−	140761.i	−0.215332	−	0.143875i
$250$		0			0
$251$	428273.			0.429078			0.214539	−	0.976715i	$-0.431175\pi$
$251$	428273.			0.429078			0.214539	+	0.976715i	$0.431175\pi$
$252$		0			0
$253$	−762048.			−0.748481
$254$		0			0
$255$	1.14974e6	+	768199.i	1.10725	+	0.739815i
$256$		0			0
$257$		−	1.24067e6i		−	1.17172i	−0.810411	−	0.585861i	$-0.800756\pi$
$257$		−	1.24067e6i		−	1.17172i	0.810411	−	0.585861i	$-0.199244\pi$
$258$		0			0
$259$			60739.6i			0.0562629i
$260$		0			0
$261$	1.21968e6	−	505258.i	1.10827	−	0.459105i
$262$		0			0
$263$	−1.86319e6			−1.66099			−0.830495	−	0.557026i	$-0.811942\pi$
$263$	−1.86319e6			−1.66099			−0.830495	+	0.557026i	$0.811942\pi$
$264$		0			0
$265$	−864864.			−0.756542
$266$		0			0
$267$	−766024.	+	1.14648e6i	−0.657603	+	0.984210i
$268$		0			0
$269$		−	1.14140e6i		−	0.961739i	−0.876792	−	0.480869i	$-0.840321\pi$
$269$		−	1.14140e6i		−	0.961739i	0.876792	−	0.480869i	$-0.159679\pi$
$270$		0			0
$271$		−	1.63902e6i		−	1.35569i	−0.735206	−	0.677844i	$-0.762914\pi$
$271$		−	1.63902e6i		−	1.35569i	0.735206	−	0.677844i	$-0.237086\pi$
$272$		0			0
$273$	−268620.	+	402034.i	−0.218138	+	0.326479i
$274$		0			0
$275$	603720.			0.481397
$276$		0			0
$277$	−1.11195e6			−0.870732			−0.435366	−	0.900254i	$-0.643381\pi$
$277$	−1.11195e6			−0.870732			−0.435366	+	0.900254i	$0.643381\pi$
$278$		0			0
$279$	−2.34007e6	+	969384.i	−1.79977	+	0.745565i
$280$		0			0
$281$			621325.i			0.469410i	0.972067	+	0.234705i	$0.0754125\pi$
$281$			621325.i			0.469410i	−0.972067	+	0.234705i	$0.924588\pi$
$282$		0			0
$283$		−	1.14875e6i		−	0.852631i	−0.904574	−	0.426316i	$-0.859811\pi$
$283$		−	1.14875e6i		−	0.852631i	0.904574	−	0.426316i	$-0.140189\pi$
$284$		0			0
$285$	22176.0	+	14817.0i	0.0161723	+	0.0108056i
$286$		0			0
$287$	−338761.			−0.242767
$288$		0			0
$289$	−2.48312e6			−1.74885
$290$		0			0
$291$	636020.	+	424959.i	0.440289	+	0.294181i
$292$		0			0
$293$		−	1.51182e6i		−	1.02880i	−0.857549	−	0.514402i	$-0.828014\pi$
$293$		−	1.51182e6i		−	1.02880i	0.857549	−	0.514402i	$-0.171986\pi$
$294$		0			0
$295$			2.04970e6i			1.37131i
$296$		0			0
$297$	402192.	−	2.02252e6i	0.264571	−	1.33046i
$298$		0			0
$299$	−1.13947e6			−0.737097
$300$		0			0
$301$	344124.			0.218927
$302$		0			0
$303$	−295133.	+	441715.i	−0.184676	+	0.276398i
$304$		0			0
$305$			1.07176e6i			0.659702i
$306$		0			0
$307$		−	1.09160e6i		−	0.661023i	−0.943802	−	0.330511i	$-0.892779\pi$
$307$		−	1.09160e6i		−	0.661023i	0.943802	−	0.330511i	$-0.107221\pi$
$308$		0			0
$309$	−665610.	+	996194.i	−0.396573	+	0.593537i
$310$		0			0
$311$	2.00628e6			1.17623			0.588113	−	0.808779i	$-0.299871\pi$
$311$	2.00628e6			1.17623			0.588113	+	0.808779i	$0.299871\pi$
$312$		0			0
$313$	1.56247e6			0.901471			0.450736	−	0.892657i	$-0.351162\pi$
$313$	1.56247e6			0.901471			0.450736	+	0.892657i	$0.351162\pi$
$314$		0			0
$315$	159115.	+	384100.i	0.0903515	+	0.218106i
$316$		0			0
$317$		−	2.81329e6i		−	1.57241i	−0.617964	−	0.786207i	$-0.712042\pi$
$317$		−	2.81329e6i		−	1.57241i	0.617964	−	0.786207i	$-0.287958\pi$
$318$		0			0
$319$		−	2.95757e6i		−	1.62726i
$320$		0			0
$321$	2.07346e6	+	1.38539e6i	1.12314	+	0.750427i
$322$		0			0
$323$	−75280.3			−0.0401490
$324$		0			0
$325$	902726.			0.474076
$326$		0			0
$327$	1.82355e6	+	1.21841e6i	0.943080	+	0.630122i
$328$		0			0
$329$			628239.i			0.319989i
$330$		0			0
$331$			2.43714e6i			1.22268i	0.791370	+	0.611338i	$0.209368\pi$
$331$			2.43714e6i			1.22268i	−0.791370	+	0.611338i	$0.790632\pi$
$332$		0			0
$333$	−148242.	−	357852.i	−0.0732589	−	0.176845i
$334$		0			0
$335$	1.36453e6			0.664312
$336$		0			0
$337$	−2.76525e6			−1.32635			−0.663176	−	0.748463i	$-0.730792\pi$
$337$	−2.76525e6			−1.32635			−0.663176	+	0.748463i	$0.730792\pi$
$338$		0			0
$339$	278413.	−	416690.i	0.131580	−	0.196931i
$340$		0			0
$341$			5.67436e6i			2.64260i
$342$		0			0
$343$		−	1.22554e6i		−	0.562459i
$344$		0			0
$345$	−544320.	+	814664.i	−0.246210	+	0.368494i
$346$		0			0
$347$	−1.73743e6			−0.774613			−0.387307	−	0.921951i	$-0.626594\pi$
$347$	−1.73743e6			−0.774613			−0.387307	+	0.921951i	$0.626594\pi$
$348$		0			0
$349$	3.70509e6			1.62830			0.814151	−	0.580654i	$-0.197203\pi$
$349$	3.70509e6			1.62830			0.814151	+	0.580654i	$0.197203\pi$
$350$		0			0
$351$	601387.	−	3.02421e6i	0.260547	−	1.31022i
$352$		0			0
$353$			2.34162e6i			1.00018i	0.865973	+	0.500091i	$0.166700\pi$
$353$			2.34162e6i			1.00018i	−0.865973	+	0.500091i	$0.833300\pi$
$354$		0			0
$355$		−	1.47355e6i		−	0.620573i
$356$		0			0
$357$	−975744.	−	651946.i	−0.405196	−	0.270733i
$358$		0			0
$359$	−843481.			−0.345414			−0.172707	−	0.984973i	$-0.555251\pi$
$359$	−843481.			−0.345414			−0.172707	+	0.984973i	$0.555251\pi$
$360$		0			0
$361$	2.47465e6			0.999414
$362$		0			0
$363$	−1.75370e6	−	1.17174e6i	−0.698536	−	0.466729i
$364$		0			0
$365$			789250.i			0.310086i
$366$		0			0
$367$			4.16399e6i			1.61378i	0.590701	+	0.806891i	$0.298851\pi$
$367$			4.16399e6i			1.61378i	−0.590701	+	0.806891i	$0.701149\pi$
$368$		0			0
$369$	1.99584e6	−	826787.i	0.763062	−	0.316102i
$370$		0			0
$371$	733983.			0.276854
$372$		0			0
$373$	−1.14011e6			−0.424300			−0.212150	−	0.977237i	$-0.568047\pi$
$373$	−1.14011e6			−0.424300			−0.212150	+	0.977237i	$0.568047\pi$
$374$		0			0
$375$	1.64637e6	−	2.46406e6i	0.604573	−	0.904842i
$376$		0			0
$377$		−	4.42237e6i		−	1.60251i
$378$		0			0
$379$			2.10182e6i			0.751618i	0.926697	+	0.375809i	$0.122635\pi$
$379$			2.10182e6i			0.751618i	−0.926697	+	0.375809i	$0.877365\pi$
$380$		0			0
$381$	−2.40669e6	+	3.60200e6i	−0.849391	+	1.27125i
$382$		0			0
$383$	3.45294e6			1.20280			0.601398	−	0.798950i	$-0.294611\pi$
$383$	3.45294e6			1.20280			0.601398	+	0.798950i	$0.294611\pi$
$384$		0			0
$385$	931392.			0.320244
$386$		0			0
$387$	−2.02743e6	+	839875.i	−0.688128	+	0.285061i
$388$		0			0
$389$		−	2.05457e6i		−	0.688411i	−0.938894	−	0.344205i	$-0.888148\pi$
$389$		−	2.05457e6i		−	0.688411i	0.938894	−	0.344205i	$-0.111852\pi$
$390$		0			0
$391$		−	2.76552e6i		−	0.914817i
$392$		0			0
$393$	−1.94040e6	−	1.29648e6i	−0.633738	−	0.423434i
$394$		0			0
$395$	−319941.			−0.103176
$396$		0			0
$397$	−50866.0			−0.0161976			−0.00809881	−	0.999967i	$-0.502578\pi$
$397$	−50866.0			−0.0161976			−0.00809881	+	0.999967i	$0.502578\pi$
$398$		0			0
$399$	−18820.1	−	12574.7i	−0.00591819	−	0.00395426i
$400$		0			0
$401$		−	2.59791e6i		−	0.806794i	−0.915025	−	0.403397i	$-0.867829\pi$
$401$		−	2.59791e6i		−	0.806794i	0.915025	−	0.403397i	$-0.132171\pi$
$402$		0			0
$403$			8.48471e6i			2.60240i
$404$		0			0
$405$	−1.87488e6	−	1.87462e6i	−0.567984	−	0.567904i
$406$		0			0
$407$	−867745.			−0.259661
$408$		0			0
$409$	−2.74861e6			−0.812467			−0.406233	−	0.913769i	$-0.633158\pi$
$409$	−2.74861e6			−0.812467			−0.406233	+	0.913769i	$0.633158\pi$
$410$		0			0
$411$	722473.	−	1.08130e6i	0.210968	−	0.315748i
$412$		0			0
$413$		−	1.73951e6i		−	0.501825i
$414$		0			0
$415$			729789.i			0.208007i
$416$		0			0
$417$	698610.	−	1.04558e6i	0.196741	−	0.294455i
$418$		0			0
$419$	−4.22277e6			−1.17507			−0.587534	−	0.809200i	$-0.699901\pi$
$419$	−4.22277e6			−1.17507			−0.587534	+	0.809200i	$0.699901\pi$
$420$		0			0
$421$	4.09284e6			1.12543			0.562716	−	0.826650i	$-0.309756\pi$
$421$	4.09284e6			1.12543			0.562716	+	0.826650i	$0.309756\pi$
$422$		0			0
$423$	−1.53329e6	−	3.70132e6i	−0.416652	−	1.00579i
$424$		0			0
$425$			2.19093e6i			0.588379i
$426$		0			0
$427$		−	909569.i		−	0.241416i
$428$		0			0
$429$	−5.74358e6	−	3.83759e6i	−1.50674	−	1.00674i
$430$		0			0
$431$	−1.36531e6			−0.354029			−0.177014	−	0.984208i	$-0.556644\pi$
$431$	−1.36531e6			−0.354029			−0.177014	+	0.984208i	$0.556644\pi$
$432$		0			0
$433$	−4.62384e6			−1.18518			−0.592588	−	0.805506i	$-0.701894\pi$
$433$	−4.62384e6			−1.18518			−0.592588	+	0.805506i	$0.701894\pi$
$434$		0			0
$435$	−3.16177e6	−	2.11255e6i	−0.801138	−	0.535283i
$436$		0			0
$437$		−	53341.1i		−	0.0133616i
$438$		0			0
$439$			4.07111e6i			1.00821i	0.863642	+	0.504106i	$0.168178\pi$
$439$			4.07111e6i			1.00821i	−0.863642	+	0.504106i	$0.831822\pi$
$440$		0			0
$441$	1.42802e6	+	3.44719e6i	0.349652	+	0.844051i
$442$		0			0
$443$	−1.58998e6			−0.384932			−0.192466	−	0.981304i	$-0.561648\pi$
$443$	−1.58998e6			−0.384932			−0.192466	+	0.981304i	$0.561648\pi$
$444$		0			0
$445$	3.97152e6			0.950729
$446$		0			0
$447$	−893953.	+	1.33795e6i	−0.211615	+	0.316716i
$448$		0			0
$449$		−	2.41274e6i		−	0.564800i	−0.959297	−	0.282400i	$-0.908869\pi$
$449$		−	2.41274e6i		−	0.564800i	0.959297	−	0.282400i	$-0.0911305\pi$
$450$		0			0
$451$		−	4.83965e6i		−	1.12040i
$452$		0			0
$453$	1.55463e6	−	2.32676e6i	0.355944	−	0.532728i
$454$		0			0
$455$	1.39269e6			0.315373
$456$		0			0
$457$	−1.52418e6			−0.341386			−0.170693	−	0.985324i	$-0.554601\pi$
$457$	−1.52418e6			−0.341386			−0.170693	+	0.985324i	$0.554601\pi$
$458$		0			0
$459$	7.33983e6	+	1.45958e6i	1.62613	+	0.323367i
$460$		0			0
$461$			3.39457e6i			0.743930i	0.928247	+	0.371965i	$0.121316\pi$
$461$			3.39457e6i			0.743930i	−0.928247	+	0.371965i	$0.878684\pi$
$462$		0			0
$463$			778927.i			0.168867i	0.996429	+	0.0844335i	$0.0269080\pi$
$463$			778927.i			0.168867i	−0.996429	+	0.0844335i	$0.973092\pi$
$464$		0			0
$465$	6.06614e6	+	4.05311e6i	1.30101	+	0.869273i
$466$		0			0
$467$	321108.			0.0681332			0.0340666	−	0.999420i	$-0.489154\pi$
$467$	321108.			0.0681332			0.0340666	+	0.999420i	$0.489154\pi$
$468$		0			0
$469$	−1.15804e6			−0.243103
$470$		0			0
$471$	4.20245e6	+	2.80788e6i	0.872871	+	0.583212i
$472$		0			0
$473$			4.91627e6i			1.01038i
$474$		0			0
$475$			42258.6i			0.00859371i
$476$		0			0
$477$	−4.32432e6	+	1.79137e6i	−0.870206	+	0.360487i
$478$		0			0
$479$	1.67670e6			0.333900			0.166950	−	0.985965i	$-0.446608\pi$
$479$	1.67670e6			0.333900			0.166950	+	0.985965i	$0.446608\pi$
$480$		0			0
$481$	−1.29752e6			−0.255711
$482$		0			0
$483$	461947.	−	691379.i	0.0900999	−	0.134849i
$484$		0			0
$485$		−	2.20324e6i		−	0.425311i
$486$		0			0
$487$		−	5.00131e6i		−	0.955568i	−0.878477	−	0.477784i	$-0.841440\pi$
$487$		−	5.00131e6i		−	0.955568i	0.878477	−	0.477784i	$-0.158560\pi$
$488$		0			0
$489$	1.77177e6	−	2.65174e6i	0.335070	−	0.501486i
$490$		0			0
$491$	8.25773e6			1.54581			0.772907	−	0.634520i	$-0.218802\pi$
$491$	8.25773e6			1.54581			0.772907	+	0.634520i	$0.218802\pi$
$492$		0			0
$493$	1.07332e7			1.98889
$494$		0			0
$495$	−5.48737e6	+	2.27317e6i	−1.00659	+	0.416984i
$496$		0			0
$497$			1.25055e6i			0.227097i
$498$		0			0
$499$		−	4.53752e6i		−	0.815769i	−0.913034	−	0.407884i	$-0.866267\pi$
$499$		−	4.53752e6i		−	0.815769i	0.913034	−	0.407884i	$-0.133733\pi$
$500$		0			0
$501$	6.67498e6	+	4.45991e6i	1.18811	+	0.793837i
$502$		0			0
$503$	3.72466e6			0.656398			0.328199	−	0.944609i	$-0.393558\pi$
$503$	3.72466e6			0.656398			0.328199	+	0.944609i	$0.393558\pi$
$504$		0			0
$505$	1.53014e6			0.266995
$506$		0			0
$507$	−3.77572e6	−	2.52276e6i	−0.652349	−	0.435869i
$508$		0			0
$509$			5.12573e6i			0.876922i	0.898750	+	0.438461i	$0.144476\pi$
$509$			5.12573e6i			0.876922i	−0.898750	+	0.438461i	$0.855524\pi$
$510$		0			0
$511$		−	669812.i		−	0.113475i
$512$		0			0
$513$	141570.	+	28152.2i	0.0237508	+	0.00472302i
$514$		0			0
$515$	3.45092e6			0.573345
$516$		0			0
$517$	−8.97523e6			−1.47679
$518$		0			0
$519$	−3.07537e6	+	4.60279e6i	−0.501163	+	0.750072i
$520$		0			0
$521$			6.38665e6i			1.03081i	0.856947	+	0.515405i	$0.172359\pi$
$521$			6.38665e6i			1.03081i	−0.856947	+	0.515405i	$0.827641\pi$
$522$		0			0
$523$		−	6.82367e6i		−	1.09085i	−0.838160	−	0.545424i	$-0.816369\pi$
$523$		−	6.82367e6i		−	1.09085i	0.838160	−	0.545424i	$-0.183631\pi$
$524$		0			0
$525$	−365970.	+	547734.i	−0.0579492	+	0.0867304i
$526$		0			0
$527$	−2.05926e7			−3.22986
$528$		0			0
$529$	−4.47679e6			−0.695549
$530$		0			0
$531$	4.24548e6	+	1.02485e7i	0.653417	+	1.57733i
$532$		0			0
$533$		−	7.23660e6i		−	1.10336i
$534$		0			0
$535$		−	7.18266e6i		−	1.08493i
$536$		0			0
$537$	−694512.	−	464040.i	−0.103931	−	0.0694416i
$538$		0			0
$539$	8.35899e6			1.23932
$540$		0			0
$541$	−7.13616e6			−1.04827			−0.524133	−	0.851636i	$-0.675611\pi$
$541$	−7.13616e6			−1.04827			−0.524133	+	0.851636i	$0.675611\pi$
$542$		0			0
$543$	3.32076e6	+	2.21877e6i	0.483323	+	0.322934i
$544$		0			0
$545$		−	6.31697e6i		−	0.910998i
$546$		0			0
$547$			3.27738e6i			0.468337i	0.972196	+	0.234169i	$0.0752368\pi$
$547$			3.27738e6i			0.468337i	−0.972196	+	0.234169i	$0.924763\pi$
$548$		0			0
$549$	2.21991e6	+	5.35880e6i	0.314344	+	0.758817i
$550$		0			0
$551$	207021.			0.0290493
$552$		0			0
$553$	271524.			0.0377568
$554$		0			0
$555$	−619818.	+	927659.i	−0.0854145	+	0.127837i
$556$		0			0
$557$		−	1.13745e6i		−	0.155344i	−0.996979	−	0.0776719i	$-0.975251\pi$
$557$		−	1.13745e6i		−	0.155344i	0.996979	−	0.0776719i	$-0.0247487\pi$
$558$		0			0
$559$			7.35116e6i			0.995008i
$560$		0			0
$561$	9.31392e6	−	1.39398e7i	1.24947	−	1.87003i
$562$		0			0
$563$	−5.43815e6			−0.723069			−0.361535	−	0.932359i	$-0.617747\pi$
$563$	−5.43815e6			−0.723069			−0.361535	+	0.932359i	$0.617747\pi$
$564$		0			0
$565$	−1.44346e6			−0.190231
$566$		0			0
$567$	1.59115e6	+	1.59093e6i	0.207852	+	0.207822i
$568$		0			0
$569$		−	1.35081e7i		−	1.74910i	−0.484935	−	0.874550i	$-0.661157\pi$
$569$		−	1.35081e7i		−	1.74910i	0.484935	−	0.874550i	$-0.338843\pi$
$570$		0			0
$571$		−	1.10323e7i		−	1.41604i	−0.706191	−	0.708021i	$-0.749588\pi$
$571$		−	1.10323e7i		−	1.41604i	0.706191	−	0.708021i	$-0.250412\pi$
$572$		0			0
$573$	−7.22534e6	−	4.82764e6i	−0.919331	−	0.614254i
$574$		0			0
$575$	−1.55242e6			−0.195812
$576$		0			0
$577$	−3.75240e6			−0.469212			−0.234606	−	0.972091i	$-0.575380\pi$
$577$	−3.75240e6			−0.469212			−0.234606	+	0.972091i	$0.575380\pi$
$578$		0			0
$579$	−2.63795e6	−	1.76255e6i	−0.327016	−	0.218497i
$580$		0			0
$581$		−	619349.i		−	0.0761194i
$582$		0			0
$583$			1.04859e7i			1.27772i
$584$		0			0
$585$	−8.20512e6	+	3.39901e6i	−0.991278	+	0.410642i
$586$		0			0
$587$	140528.			0.0168333			0.00841664	−	0.999965i	$-0.497321\pi$
$587$	140528.			0.0168333			0.00841664	+	0.999965i	$0.497321\pi$
$588$		0			0
$589$	−397188.			−0.0471746
$590$		0			0
$591$	−4.23024e6	+	6.33124e6i	−0.498191	+	0.745625i
$592$		0			0
$593$			6.25671e6i			0.730650i	0.930880	+	0.365325i	$0.119042\pi$
$593$			6.25671e6i			0.730650i	−0.930880	+	0.365325i	$0.880958\pi$
$594$		0			0
$595$			3.38008e6i			0.391412i
$596$		0			0
$597$	4.37151e6	−	6.54268e6i	0.501991	−	0.751311i
$598$		0			0
$599$	5.32546e6			0.606443			0.303221	−	0.952920i	$-0.401938\pi$
$599$	5.32546e6			0.606443			0.303221	+	0.952920i	$0.401938\pi$
$600$		0			0
$601$	296186.			0.0334486			0.0167243	−	0.999860i	$-0.494676\pi$
$601$	296186.			0.0334486			0.0167243	+	0.999860i	$0.494676\pi$
$602$		0			0
$603$	6.82266e6	−	2.82632e6i	0.764119	−	0.316540i
$604$		0			0
$605$			6.07500e6i			0.674773i
$606$		0			0
$607$		−	4.96818e6i		−	0.547301i	−0.961829	−	0.273650i	$-0.911769\pi$
$607$		−	4.96818e6i		−	0.547301i	0.961829	−	0.273650i	$-0.0882311\pi$
$608$		0			0
$609$	2.68330e6	+	1.79285e6i	0.293174	+	0.195885i
$610$		0			0
$611$	−1.34204e7			−1.45433
$612$		0			0
$613$	−769978.			−0.0827613			−0.0413806	−	0.999143i	$-0.513176\pi$
$613$	−769978.			−0.0827613			−0.0413806	+	0.999143i	$0.513176\pi$
$614$		0			0
$615$	−5.17381e6	−	3.45690e6i	−0.551598	−	0.368552i
$616$		0			0
$617$			1.44120e6i			0.152409i	0.997092	+	0.0762044i	$0.0242802\pi$
$617$			1.44120e6i			0.152409i	−0.997092	+	0.0762044i	$0.975720\pi$
$618$		0			0
$619$		−	5.11377e6i		−	0.536431i	−0.963359	−	0.268216i	$-0.913566\pi$
$619$		−	5.11377e6i		−	0.536431i	0.963359	−	0.268216i	$-0.0864340\pi$
$620$		0			0
$621$	−1.03421e6	+	5.20075e6i	−0.107617	+	0.541174i
$622$		0			0
$623$	−3.37050e6			−0.347916
$624$		0			0
$625$	−5.07012e6			−0.519180
$626$		0			0
$627$	179646.	−	268870.i	0.0182494	−	0.0273132i
$628$		0			0
$629$		−	3.14910e6i		−	0.317365i
$630$		0			0
$631$		−	7.41169e6i		−	0.741044i	−0.928824	−	0.370522i	$-0.879179\pi$
$631$		−	7.41169e6i		−	0.741044i	0.928824	−	0.370522i	$-0.120821\pi$
$632$		0			0
$633$	−9.20535e6	+	1.37773e7i	−0.913127	+	1.36664i
$634$		0			0
$635$	1.24777e7			1.22801
$636$		0			0
$637$	1.24990e7			1.22047
$638$		0			0
$639$	−3.05212e6	−	7.36773e6i	−0.295699	−	0.713808i
$640$		0			0
$641$			8.88766e6i			0.854363i	0.904166	+	0.427182i	$0.140493\pi$
$641$			8.88766e6i			0.854363i	−0.904166	+	0.427182i	$0.859507\pi$
$642$		0			0
$643$			1.66294e7i			1.58616i	0.609115	+	0.793082i	$0.291525\pi$
$643$			1.66294e7i			1.58616i	−0.609115	+	0.793082i	$0.708475\pi$
$644$		0			0
$645$	5.25571e6	+	3.51162e6i	0.497430	+	0.332360i
$646$		0			0
$647$	1.58519e7			1.48875			0.744375	−	0.667762i	$-0.232747\pi$
$647$	1.58519e7			1.48875			0.744375	+	0.667762i	$0.232747\pi$
$648$		0			0
$649$	2.48512e7			2.31599
$650$		0			0
$651$	−5.14814e6	−	3.43975e6i	−0.476100	−	0.318108i
$652$		0			0
$653$		−	8.40512e6i		−	0.771367i	−0.922631	−	0.385684i	$-0.873966\pi$
$653$		−	8.40512e6i		−	0.771367i	0.922631	−	0.385684i	$-0.126034\pi$
$654$		0			0
$655$			6.72174e6i			0.612179i
$656$		0			0
$657$	1.63475e6	+	3.94625e6i	0.147754	+	0.356674i
$658$		0			0
$659$	−1.34564e6			−0.120702			−0.0603509	−	0.998177i	$-0.519222\pi$
$659$	−1.34564e6			−0.120702			−0.0603509	+	0.998177i	$0.519222\pi$
$660$		0			0
$661$	−1.30657e6			−0.116313			−0.0581566	−	0.998307i	$-0.518522\pi$
$661$	−1.30657e6			−0.116313			−0.0581566	+	0.998307i	$0.518522\pi$
$662$		0			0
$663$	1.39269e7	−	2.08438e7i	1.23046	−	1.84159i
$664$		0			0
$665$			65194.6i			0.00571686i
$666$		0			0
$667$			7.60517e6i			0.661903i
$668$		0			0
$669$	4.60035e6	−	6.88517e6i	0.397398	−	0.594771i
$670$		0			0
$671$	1.29944e7			1.11417
$672$		0			0
$673$	2.11752e6			0.180215			0.0901074	−	0.995932i	$-0.471279\pi$
$673$	2.11752e6			0.180215			0.0901074	+	0.995932i	$0.471279\pi$
$674$		0			0
$675$	819334.	−	4.12021e6i	0.0692152	−	0.348065i
$676$		0			0
$677$			2.13735e7i			1.79227i	0.443782	+	0.896135i	$0.353636\pi$
$677$			2.13735e7i			1.79227i	−0.443782	+	0.896135i	$0.646364\pi$
$678$		0			0
$679$			1.86982e6i			0.155641i
$680$		0			0
$681$	−1.64879e7	−	1.10164e7i	−1.36237	−	0.910275i
$682$		0			0
$683$	−6.12702e6			−0.502571			−0.251286	−	0.967913i	$-0.580853\pi$
$683$	−6.12702e6			−0.502571			−0.251286	+	0.967913i	$0.580853\pi$
$684$		0			0
$685$	−3.74573e6			−0.305007
$686$		0			0
$687$	6.29402e6	+	4.20537e6i	0.508787	+	0.339948i
$688$		0			0
$689$			1.56793e7i			1.25828i
$690$		0			0
$691$			1.60101e6i			0.127555i	0.997964	+	0.0637776i	$0.0203148\pi$
$691$			1.60101e6i			0.127555i	−0.997964	+	0.0637776i	$0.979685\pi$
$692$		0			0
$693$	4.65696e6	−	1.92917e6i	0.368357	−	0.152594i
$694$		0			0
$695$	−3.62201e6			−0.284438
$696$		0			0
$697$	1.75634e7			1.36939
$698$		0			0
$699$	367847.	−	550543.i	0.0284757	−	0.0426185i
$700$		0			0
$701$		−	9.20775e6i		−	0.707715i	−0.935299	−	0.353858i	$-0.884870\pi$
$701$		−	9.20775e6i		−	0.707715i	0.935299	−	0.353858i	$-0.115130\pi$
$702$		0			0
$703$		−	60739.6i		−	0.00463536i
$704$		0			0
$705$	−6.41088e6	+	9.59493e6i	−0.485786	+	0.727058i
$706$		0			0
$707$	−1.29858e6			−0.0977061
$708$		0			0
$709$	−2.23300e7			−1.66830			−0.834148	−	0.551540i	$-0.814040\pi$
$709$	−2.23300e7			−1.66830			−0.834148	+	0.551540i	$0.814040\pi$
$710$		0			0
$711$	−1.59971e6	+	662686.i	−0.118677	+	0.0491625i
$712$		0			0
$713$		−	1.45912e7i		−	1.07490i
$714$		0			0
$715$			1.98964e7i			1.45549i
$716$		0			0
$717$	2.97158e6	+	1.98547e6i	0.215869	+	0.144233i
$718$		0			0
$719$	−1.94705e7			−1.40461			−0.702305	−	0.711877i	$-0.747846\pi$
$719$	−1.94705e7			−1.40461			−0.702305	+	0.711877i	$0.747846\pi$
$720$		0			0
$721$	−2.92868e6			−0.209814
$722$		0			0
$723$	−1.73678e7	−	1.16043e7i	−1.23566	−	0.825610i
$724$		0			0
$725$		−	6.02507e6i		−	0.425713i
$726$		0			0
$727$		−	1.67551e7i		−	1.17574i	−0.808957	−	0.587868i	$-0.799967\pi$
$727$		−	1.67551e7i		−	1.17574i	0.808957	−	0.587868i	$-0.200033\pi$
$728$		0			0
$729$	−1.32572e7	−	5.48968e6i	−0.923920	−	0.382586i
$730$		0			0
$731$	−1.78414e7			−1.23491
$732$		0			0
$733$	1.64496e7			1.13082			0.565412	−	0.824808i	$-0.308717\pi$
$733$	1.64496e7			1.13082			0.565412	+	0.824808i	$0.308717\pi$
$734$		0			0
$735$	5.97071e6	−	8.93614e6i	0.407669	−	0.610143i
$736$		0			0
$737$		−	1.65441e7i		−	1.12195i
$738$		0			0
$739$			2.44852e6i			0.164927i	0.996594	+	0.0824637i	$0.0262788\pi$
$739$			2.44852e6i			0.164927i	−0.996594	+	0.0824637i	$0.973721\pi$
$740$		0			0
$741$	268620.	−	402034.i	0.0179719	−	0.0268978i
$742$		0			0
$743$	374691.			0.0249001			0.0124500	−	0.999922i	$-0.496037\pi$
$743$	374691.			0.0249001			0.0124500	+	0.999922i	$0.496037\pi$
$744$		0			0
$745$	4.63478e6			0.305942
$746$		0			0
$747$	1.51159e6	+	3.64895e6i	0.0991137	+	0.239258i
$748$		0			0
$749$			6.09570e6i			0.397026i
$750$		0			0
$751$			1.80458e7i			1.16755i	0.811914	+	0.583777i	$0.198426\pi$
$751$			1.80458e7i			1.16755i	−0.811914	+	0.583777i	$0.801574\pi$
$752$		0			0
$753$	−5.55106e6	−	3.70896e6i	−0.356770	−	0.238377i
$754$		0			0
$755$	−8.06012e6			−0.514605
$756$		0			0
$757$	−2.11408e7			−1.34086			−0.670428	−	0.741975i	$-0.733889\pi$
$757$	−2.11408e7			−1.34086			−0.670428	+	0.741975i	$0.733889\pi$
$758$		0			0
$759$	9.87727e6	+	6.59953e6i	0.622347	+	0.415823i
$760$		0			0
$761$		−	2.09206e7i		−	1.30952i	−0.755837	−	0.654759i	$-0.772770\pi$
$761$		−	2.09206e7i		−	1.30952i	0.755837	−	0.654759i	$-0.227230\pi$
$762$		0			0
$763$			5.36101e6i			0.333377i
$764$		0			0
$765$	−8.24947e6	−	1.99140e7i	−0.509651	−	1.23028i
$766$		0			0
$767$	3.71594e7			2.28076
$768$		0			0
$769$	−1.04790e7			−0.639003			−0.319502	−	0.947586i	$-0.603515\pi$
$769$	−1.04790e7			−0.639003			−0.319502	+	0.947586i	$0.603515\pi$
$770$		0			0
$771$	−1.07445e7	+	1.60810e7i	−0.650957	+	0.974263i
$772$		0			0
$773$			1.30483e7i			0.785427i	0.919661	+	0.392713i	$0.128464\pi$
$773$			1.30483e7i			0.785427i	−0.919661	+	0.392713i	$0.871536\pi$
$774$		0			0
$775$			1.15596e7i			0.691337i
$776$		0			0
$777$	526020.	−	787275.i	0.0312572	−	0.0467815i
$778$		0			0
$779$	338761.			0.0200009
$780$		0			0
$781$	−1.78658e7			−1.04808
$782$		0			0
$783$	−2.01845e7	−	4.01384e6i	−1.17656	−	0.233968i
$784$		0			0
$785$		−	1.45577e7i		−	0.843177i
$786$		0			0
$787$		−	1.41787e7i		−	0.816019i	−0.912978	−	0.408010i	$-0.866223\pi$
$787$		−	1.41787e7i		−	0.816019i	0.912978	−	0.408010i	$-0.133777\pi$
$788$		0			0
$789$	2.41497e7	+	1.61357e7i	1.38108	+	0.922772i
$790$		0			0
$791$	1.22502e6			0.0696146
$792$		0			0
$793$	1.94302e7			1.09722
$794$		0			0
$795$	1.12099e7	+	7.48994e6i	0.629049	+	0.420301i
$796$		0			0
$797$		−	7.24258e6i		−	0.403875i	−0.979398	−	0.201938i	$-0.935276\pi$
$797$		−	7.24258e6i		−	0.403875i	0.979398	−	0.201938i	$-0.0647238\pi$
$798$		0			0
$799$		−	3.25716e7i		−	1.80498i
$800$		0			0
$801$	1.98576e7	−	8.22611e6i	1.09357	−	0.453016i
$802$		0			0
$803$	9.56915e6			0.523702
$804$		0			0
$805$	−2.39501e6			−0.130262
$806$		0			0
$807$	−9.88481e6	+	1.47942e7i	−0.534299	+	0.799666i
$808$		0			0
$809$			3.44297e7i			1.84953i	0.380537	+	0.924766i	$0.375739\pi$
$809$			3.44297e7i			1.84953i	−0.380537	+	0.924766i	$0.624261\pi$
$810$		0			0
$811$		−	1.11847e7i		−	0.597136i	−0.954388	−	0.298568i	$-0.903491\pi$
$811$		−	1.11847e7i		−	0.597136i	0.954388	−	0.298568i	$-0.0965090\pi$
$812$		0			0
$813$	−1.41943e7	+	2.12441e7i	−0.753160	+	1.12723i
$814$		0			0
$815$	−9.18591e6			−0.484427
$816$		0			0
$817$	−344124.			−0.0180368
$818$		0			0
$819$	6.96343e6	−	2.88463e6i	0.362755	−	0.150273i
$820$		0			0
$821$		−	2.61613e7i		−	1.35457i	−0.735720	−	0.677286i	$-0.763156\pi$
$821$		−	2.61613e7i		−	1.35457i	0.735720	−	0.677286i	$-0.236844\pi$
$822$		0			0
$823$			5.00520e6i			0.257586i	0.991672	+	0.128793i	$0.0411102\pi$
$823$			5.00520e6i			0.257586i	−0.991672	+	0.128793i	$0.958890\pi$
$824$		0			0
$825$	−7.82510e6	−	5.22837e6i	−0.400272	−	0.267443i
$826$		0			0
$827$	3.10788e6			0.158016			0.0790078	−	0.996874i	$-0.474825\pi$
$827$	3.10788e6			0.158016			0.0790078	+	0.996874i	$0.474825\pi$
$828$		0			0
$829$	9.08573e6			0.459170			0.229585	−	0.973289i	$-0.426263\pi$
$829$	9.08573e6			0.459170			0.229585	+	0.973289i	$0.426263\pi$
$830$		0			0
$831$	1.44125e7	+	9.62973e6i	0.723995	+	0.483740i
$832$		0			0
$833$			3.03353e7i			1.51473i
$834$		0			0
$835$		−	2.31228e7i		−	1.14769i
$836$		0			0
$837$	3.87258e7	+	7.70091e6i	1.91068	+	0.379952i
$838$		0			0
$839$	−3.36414e7			−1.64994			−0.824972	−	0.565173i	$-0.808809\pi$
$839$	−3.36414e7			−1.64994			−0.824972	+	0.565173i	$0.808809\pi$
$840$		0			0
$841$	−9.00511e6			−0.439035
$842$		0			0
$843$	5.38083e6	−	8.05329e6i	0.260784	−	0.390305i
$844$		0			0
$845$			1.30795e7i			0.630157i
$846$		0			0
$847$		−	5.15566e6i		−	0.246931i
$848$		0			0
$849$	−9.94851e6	+	1.48896e7i	−0.473684	+	0.708945i
$850$		0			0
$851$	2.23134e6			0.105619
$852$		0			0
$853$	−7.95236e6			−0.374217			−0.187109	−	0.982339i	$-0.559912\pi$
$853$	−7.95236e6			−0.374217			−0.187109	+	0.982339i	$0.559912\pi$
$854$		0			0
$855$	−159115.	−	384100.i	−0.00744383	−	0.0179692i
$856$		0			0
$857$			4.01609e7i			1.86789i	0.357417	+	0.933945i	$0.383657\pi$
$857$			4.01609e7i			1.86789i	−0.357417	+	0.933945i	$0.616343\pi$
$858$		0			0
$859$		−	1.27508e7i		−	0.589594i	−0.955560	−	0.294797i	$-0.904748\pi$
$859$		−	1.27508e7i		−	0.589594i	0.955560	−	0.294797i	$-0.0952520\pi$
$860$		0			0
$861$	4.39085e6	+	2.93376e6i	0.201855	+	0.134870i
$862$		0			0
$863$	2.08452e7			0.952749			0.476375	−	0.879242i	$-0.341951\pi$
$863$	2.08452e7			0.952749			0.476375	+	0.879242i	$0.341951\pi$
$864$		0			0
$865$	1.59445e7			0.724556
$866$		0			0
$867$	3.21849e7	+	2.15044e7i	1.45413	+	0.971584i
$868$		0			0
$869$			3.87908e6i			0.174253i
$870$		0			0
$871$		−	2.47379e7i		−	1.10489i
$872$		0			0
$873$	−4.56351e6	−	1.10162e7i	−0.202658	−	0.489210i
$874$		0			0
$875$	7.24402e6			0.319860
$876$		0			0
$877$	1.27745e7			0.560850			0.280425	−	0.959876i	$-0.409525\pi$
$877$	1.27745e7			0.560850			0.280425	+	0.959876i	$0.409525\pi$
$878$		0			0
$879$	−1.30928e7	+	1.95955e7i	−0.571557	+	0.855429i
$880$		0			0
$881$		−	2.52368e7i		−	1.09545i	−0.836657	−	0.547727i	$-0.815493\pi$
$881$		−	2.52368e7i		−	1.09545i	0.836657	−	0.547727i	$-0.184507\pi$
$882$		0			0
$883$			1.30381e7i			0.562746i	0.959599	+	0.281373i	$0.0907897\pi$
$883$			1.30381e7i			0.562746i	−0.959599	+	0.281373i	$0.909210\pi$
$884$		0			0
$885$	1.77509e7	−	2.65671e7i	0.761836	−	1.14021i
$886$		0			0
$887$	1.04315e7			0.445180			0.222590	−	0.974912i	$-0.428549\pi$
$887$	1.04315e7			0.445180			0.222590	+	0.974912i	$0.428549\pi$
$888$		0			0
$889$	−1.05894e7			−0.449385
$890$		0			0
$891$	−2.27285e7	+	2.27317e7i	−0.959128	+	0.959263i
$892$		0			0
$893$		−	628239.i		−	0.0263631i
$894$		0			0
$895$			2.40586e6i			0.100395i
$896$		0			0
$897$	1.47692e7	+	9.86810e6i	0.612881	+	0.409499i
$898$		0			0
$899$	5.66296e7			2.33692
$900$		0			0
$901$	−3.80540e7			−1.56167
$902$		0			0
$903$	−4.46036e6	−	2.98020e6i	−0.182033	−	0.121626i
$904$		0			0
$905$		−	1.15034e7i		−	0.466881i
$906$		0			0
$907$		−	4.08000e7i		−	1.64681i	−0.567458	−	0.823403i	$-0.692073\pi$
$907$		−	4.08000e7i		−	1.64681i	0.567458	−	0.823403i	$-0.307927\pi$
$908$		0			0
$909$	7.65072e6	−	3.16935e6i	0.307109	−	0.127221i
$910$		0			0
$911$	−3.81425e7			−1.52270			−0.761349	−	0.648343i	$-0.775462\pi$
$911$	−3.81425e7			−1.52270			−0.761349	+	0.648343i	$0.775462\pi$
$912$		0			0
$913$	8.84822e6			0.351301
$914$		0			0
$915$	9.28172e6	−	1.38916e7i	0.366501	−	0.548529i
$916$		0			0
$917$		−	5.70453e6i		−	0.224025i
$918$		0			0
$919$			3.53807e7i			1.38190i	0.722901	+	0.690952i	$0.242808\pi$
$919$			3.53807e7i			1.38190i	−0.722901	+	0.690952i	$0.757192\pi$
$920$		0			0
$921$	−9.45351e6	+	1.41487e7i	−0.367235	+	0.549627i
$922$		0			0
$923$	−2.67142e7			−1.03214
$924$		0			0
$925$	−1.76775e6			−0.0679306
$926$		0			0
$927$	1.72546e7	−	7.14780e6i	0.659485	−	0.273195i
$928$		0			0
$929$		−	2.87489e7i		−	1.09290i	−0.837491	−	0.546451i	$-0.815978\pi$
$929$		−	2.87489e7i		−	1.09290i	0.837491	−	0.546451i	$-0.184022\pi$
$930$		0			0
$931$			585104.i			0.0221238i
$932$		0			0
$933$	−2.60044e7	−	1.73749e7i	−0.978008	−	0.653459i
$934$		0			0
$935$	−4.82889e7			−1.80642
$936$		0			0
$937$	4.29526e6			0.159823			0.0799117	−	0.996802i	$-0.474536\pi$
$937$	4.29526e6			0.159823			0.0799117	+	0.996802i	$0.474536\pi$
$938$		0			0
$939$	−2.02520e7	−	1.35314e7i	−0.749555	−	0.500817i
$940$		0			0
$941$		−	1.68316e7i		−	0.619656i	−0.950793	−	0.309828i	$-0.899729\pi$
$941$		−	1.68316e7i		−	0.619656i	0.950793	−	0.309828i	$-0.100271\pi$
$942$		0			0
$943$			1.24448e7i			0.455732i
$944$		0			0
$945$	1.26403e6	−	6.35648e6i	0.0460446	−	0.231546i
$946$		0			0
$947$	1.60541e7			0.581715			0.290857	−	0.956766i	$-0.406059\pi$
$947$	1.60541e7			0.581715			0.290857	+	0.956766i	$0.406059\pi$
$948$		0			0
$949$	1.43085e7			0.515737
$950$		0			0
$951$	−2.43638e7	+	3.64644e7i	−0.873563	+	1.30743i
$952$		0			0
$953$		−	1.68904e7i		−	0.602430i	−0.953556	−	0.301215i	$-0.902608\pi$
$953$		−	1.68904e7i		−	0.602430i	0.953556	−	0.301215i	$-0.0973921\pi$
$954$		0			0
$955$			2.50293e7i			0.888057i
$956$		0			0
$957$	−2.56133e7	+	3.83344e7i	−0.904035	+	1.35304i
$958$		0			0
$959$	3.17888e6			0.111616
$960$		0			0
$961$	−8.00198e7			−2.79505
$962$		0			0
$963$	−1.48773e7	−	3.59133e7i	−0.516961	−	1.24793i
$964$		0			0
$965$			9.13812e6i			0.315892i
$966$		0			0
$967$			4.23491e7i			1.45639i	0.685370	+	0.728195i	$0.259641\pi$
$967$			4.23491e7i			1.45639i	−0.685370	+	0.728195i	$0.740359\pi$
$968$		0			0
$969$	975744.	+	651946.i	0.0333831	+	0.0223050i
$970$		0			0
$971$	−7.19152e6			−0.244778			−0.122389	−	0.992482i	$-0.539056\pi$
$971$	−7.19152e6			−0.244778			−0.122389	+	0.992482i	$0.539056\pi$
$972$		0			0
$973$	3.07388e6			0.104089
$974$		0			0
$975$	−1.17007e7	−	7.81784e6i	−0.394184	−	0.263375i
$976$		0			0
$977$			7.26570e6i			0.243524i	0.992559	+	0.121762i	$0.0388544\pi$
$977$			7.26570e6i			0.243524i	−0.992559	+	0.121762i	$0.961146\pi$
$978$		0			0
$979$		−	4.81521e7i		−	1.60568i
$980$		0			0
$981$	−1.30842e7	−	3.15848e7i	−0.434084	−	1.04787i
$982$		0			0
$983$	2.69900e7			0.890880			0.445440	−	0.895312i	$-0.353047\pi$
$983$	2.69900e7			0.890880			0.445440	+	0.895312i	$0.353047\pi$
$984$		0			0
$985$	2.19321e7			0.720259
$986$		0			0
$987$	5.44071e6	−	8.14291e6i	0.177772	−	0.266064i
$988$		0			0
$989$		−	1.26418e7i		−	0.410979i
$990$		0			0
$991$		−	3.49060e7i		−	1.12906i	−0.825413	−	0.564529i	$-0.809058\pi$
$991$		−	3.49060e7i		−	1.12906i	0.825413	−	0.564529i	$-0.190942\pi$
$992$		0			0
$993$	2.11063e7	−	3.15890e7i	0.679264	−	1.01663i
$994$		0			0
$995$	−2.26645e7			−0.725752
$996$		0			0
$997$	3.41372e7			1.08765			0.543825	−	0.839198i	$-0.316975\pi$
$997$	3.41372e7			1.08765			0.543825	+	0.839198i	$0.316975\pi$
$998$		0			0
$999$	−1.17765e6	+	5.92211e6i	−0.0373340	+	0.187742i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.6.c.d.47.1	✓	4
3.2	odd	2	inner	48.6.c.d.47.3	yes	4
4.3	odd	2	inner	48.6.c.d.47.4	yes	4
8.3	odd	2		192.6.c.d.191.1		4
8.5	even	2		192.6.c.d.191.4		4
12.11	even	2	inner	48.6.c.d.47.2	yes	4
24.5	odd	2		192.6.c.d.191.2		4
24.11	even	2		192.6.c.d.191.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.6.c.d.47.1	✓	4	1.1	even	1	trivial
48.6.c.d.47.2	yes	4	12.11	even	2	inner
48.6.c.d.47.3	yes	4	3.2	odd	2	inner
48.6.c.d.47.4	yes	4	4.3	odd	2	inner
192.6.c.d.191.1		4	8.3	odd	2
192.6.c.d.191.2		4	24.5	odd	2
192.6.c.d.191.3		4	24.11	even	2
192.6.c.d.191.4		4	8.5	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	48.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-12.9615 - 8.66025i) q^{3} +44.8999i q^{5} -38.1051i q^{7} +(93.0000 + 224.499i) q^{9} +O(q^{10})\)	\(q+(-12.9615 - 8.66025i) q^{3} +44.8999i q^{5} -38.1051i q^{7} +(93.0000 + 224.499i) q^{9} +544.382 q^{11} +814.000 q^{13} +(388.844 - 581.969i) q^{15} +1975.60i q^{17} +38.1051i q^{19} +(-330.000 + 493.899i) q^{21} -1399.84 q^{23} +1109.00 q^{25} +(738.804 - 3715.25i) q^{27} -5432.89i q^{29} +10423.5i q^{31} +(-7056.00 - 4714.49i) q^{33} +1710.92 q^{35} -1594.00 q^{37} +(-10550.6 - 7049.45i) q^{39} -8890.18i q^{41} +9030.91i q^{43} +(-10080.0 + 4175.69i) q^{45} -16487.0 q^{47} +15355.0 q^{49} +(17109.2 - 25606.6i) q^{51} +19262.1i q^{53} +24442.7i q^{55} +(330.000 - 493.899i) q^{57} +45650.3 q^{59} +23870.0 q^{61} +(8554.58 - 3543.78i) q^{63} +36548.5i q^{65} -30390.6i q^{67} +(18144.0 + 12123.0i) q^{69} -32818.5 q^{71} +17578.0 q^{73} +(-14374.3 - 9604.22i) q^{75} -20743.7i q^{77} +7125.66i q^{79} +(-41751.0 + 41756.9i) q^{81} +16253.7 q^{83} -88704.0 q^{85} +(-47050.2 + 70418.3i) q^{87} -88452.8i q^{89} -31017.6i q^{91} +(90270.0 - 135104. i) q^{93} -1710.92 q^{95} -49070.0 q^{97} +(50627.5 + 122214. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 372 q^{9}+O(q^{10}) \) 4 * q + 372 * q^9	\( 4 q + 372 q^{9} + 3256 q^{13} - 1320 q^{21} + 4436 q^{25} - 28224 q^{33} - 6376 q^{37} - 40320 q^{45} + 61420 q^{49} + 1320 q^{57} + 95480 q^{61} + 72576 q^{69} + 70312 q^{73} - 167004 q^{81} - 354816 q^{85} + 361080 q^{93} - 196280 q^{97}+O(q^{100}) \) 4 * q + 372 * q^9 + 3256 * q^13 - 1320 * q^21 + 4436 * q^25 - 28224 * q^33 - 6376 * q^37 - 40320 * q^45 + 61420 * q^49 + 1320 * q^57 + 95480 * q^61 + 72576 * q^69 + 70312 * q^73 - 167004 * q^81 - 354816 * q^85 + 361080 * q^93 - 196280 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more