LMFDB - Embedded newform 320.9.h.f.319.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [320,9,Mod(319,320)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(320, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("320.319");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 320 = 2^{6} \cdot 5 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	320.h (of order $2$, degree $1$, not 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:	$130.361155220$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 1394 x^{14} + 1332306 x^{12} - 657883370 x^{10} + 233333110300 x^{8} - 45644912663250 x^{6} + \cdots + 23\!\cdots\!00 $ x^16 - 1394x^14 + 1332306x^12 - 657883370x^10 + 233333110300x^8 - 45644912663250x^6 + 6418092533338125x^4 - 470478785036343750*x^2 + 23585385849201562500
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{99}\cdot 3^{9}\cdot 5^{10} $
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			319.11
Root			$-11.1856 + 6.45800i$ of defining polynomial
Character	$\chi$	$=$	320.319
Dual form			320.9.h.f.319.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+77.4652 q^{3} +(-586.915 - 214.840i) q^{5} +2766.32 q^{7} -560.136 q^{9} +O(q^{10})$	\(q+77.4652 q^{3} +(-586.915 - 214.840i) q^{5} +2766.32 q^{7} -560.136 q^{9} -18778.9i q^{11} +38629.0i q^{13} +(-45465.5 - 16642.6i) q^{15} -76484.1i q^{17} -33574.4i q^{19} +214293. q^{21} -222381. q^{23} +(298313. + 252185. i) q^{25} -551641. q^{27} -651811. q^{29} +1.03876e6i q^{31} -1.45471e6i q^{33} +(-1.62359e6 - 594315. i) q^{35} -2.60818e6i q^{37} +2.99241e6i q^{39} +4.22496e6 q^{41} -865193. q^{43} +(328752. + 120339. i) q^{45} +1.55589e6 q^{47} +1.88771e6 q^{49} -5.92486e6i q^{51} +1.13581e7i q^{53} +(-4.03445e6 + 1.10216e7i) q^{55} -2.60085e6i q^{57} -1.73206e7i q^{59} -6.27787e6 q^{61} -1.54951e6 q^{63} +(8.29905e6 - 2.26720e7i) q^{65} -3.69260e7 q^{67} -1.72268e7 q^{69} +2.42036e7i q^{71} +4.21399e7i q^{73} +(2.31089e7 + 1.95356e7i) q^{75} -5.19484e7i q^{77} -3.05498e7i q^{79} -3.90579e7 q^{81} -2.71605e7 q^{83} +(-1.64318e7 + 4.48897e7i) q^{85} -5.04927e7 q^{87} -3.34588e7 q^{89} +1.06860e8i q^{91} +8.04677e7i q^{93} +(-7.21313e6 + 1.97053e7i) q^{95} +1.14836e8i q^{97} +1.05187e7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 600 q^{5} + 42176 q^{9}+O(q^{10}) $ 16 * q - 600 * q^5 + 42176 * q^9	$ 16 q - 600 q^{5} + 42176 q^{9} - 619344 q^{21} + 1137040 q^{25} + 3497568 q^{29} - 2169168 q^{41} + 1930760 q^{45} + 26174912 q^{49} - 22772656 q^{61} + 12524160 q^{65} - 8461392 q^{69} - 224999456 q^{81} + 18124800 q^{85} - 94250976 q^{89}+O(q^{100}) $ 16 * q - 600 * q^5 + 42176 * q^9 - 619344 * q^21 + 1137040 * q^25 + 3497568 * q^29 - 2169168 * q^41 + 1930760 * q^45 + 26174912 * q^49 - 22772656 * q^61 + 12524160 * q^65 - 8461392 * q^69 - 224999456 * q^81 + 18124800 * q^85 - 94250976 * q^89

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/320\mathbb{Z}\right)^\times$.

$n$	$191$	$257$	$261$
$\chi(n)$	$-1$	$-1$	$1$

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
$3$	77.4652			0.956361			0.478181	−	0.878262i	$-0.341296\pi$
$3$	77.4652			0.956361			0.478181	+	0.878262i	$0.341296\pi$
$4$		0			0
$5$	−586.915	−	214.840i	−0.939064	−	0.343744i
$5$	−586.915	−	214.840i	−0.939064	−	0.343744i
$6$		0			0
$7$	2766.32			1.15215			0.576076	−	0.817396i	$-0.304583\pi$
$7$	2766.32			1.15215			0.576076	+	0.817396i	$0.304583\pi$
$8$		0			0
$9$	−560.136			−0.0853736
$10$		0			0
$11$		−	18778.9i		−	1.28262i	−0.767280	−	0.641312i	$-0.778390\pi$
$11$		−	18778.9i		−	1.28262i	0.767280	−	0.641312i	$-0.221610\pi$
$12$		0			0
$13$			38629.0i			1.35251i	0.736668	+	0.676255i	$0.236398\pi$
$13$			38629.0i			1.35251i	−0.736668	+	0.676255i	$0.763602\pi$
$14$		0			0
$15$	−45465.5	−	16642.6i	−0.898084	−	0.328743i
$16$		0			0
$17$		−	76484.1i		−	0.915747i	−0.889017	−	0.457874i	$-0.848611\pi$
$17$		−	76484.1i		−	0.915747i	0.889017	−	0.457874i	$-0.151389\pi$
$18$		0			0
$19$		−	33574.4i		−	0.257629i	−0.991669	−	0.128814i	$-0.958883\pi$
$19$		−	33574.4i		−	0.257629i	0.991669	−	0.128814i	$-0.0411172\pi$
$20$		0			0
$21$	214293.			1.10187
$22$		0			0
$23$	−222381.			−0.794670			−0.397335	−	0.917674i	$-0.630065\pi$
$23$	−222381.			−0.794670			−0.397335	+	0.917674i	$0.630065\pi$
$24$		0			0
$25$	298313.	+	252185.i	0.763681	+	0.645594i
$26$		0			0
$27$	−551641.			−1.03801
$28$		0			0
$29$	−651811.			−0.921573			−0.460786	−	0.887511i	$-0.652433\pi$
$29$	−651811.			−0.921573			−0.460786	+	0.887511i	$0.652433\pi$
$30$		0			0
$31$			1.03876e6i			1.12478i	0.826872	+	0.562390i	$0.190118\pi$
$31$			1.03876e6i			1.12478i	−0.826872	+	0.562390i	$0.809882\pi$
$32$		0			0
$33$		−	1.45471e6i		−	1.22665i
$34$		0			0
$35$	−1.62359e6	−	594315.i	−1.08194	−	0.396045i
$36$		0			0
$37$		−	2.60818e6i		−	1.39165i	−0.718210	−	0.695827i	$-0.755038\pi$
$37$		−	2.60818e6i		−	1.39165i	0.718210	−	0.695827i	$-0.244962\pi$
$38$		0			0
$39$			2.99241e6i			1.29349i
$40$		0			0
$41$	4.22496e6			1.49516			0.747580	−	0.664172i	$-0.231216\pi$
$41$	4.22496e6			1.49516			0.747580	+	0.664172i	$0.231216\pi$
$42$		0			0
$43$	−865193.			−0.253069			−0.126535	−	0.991962i	$-0.540385\pi$
$43$	−865193.			−0.253069			−0.126535	+	0.991962i	$0.540385\pi$
$44$		0			0
$45$	328752.	+	120339.i	0.0801712	+	0.0293466i
$46$		0			0
$47$	1.55589e6			0.318851			0.159425	−	0.987210i	$-0.449036\pi$
$47$	1.55589e6			0.318851			0.159425	+	0.987210i	$0.449036\pi$
$48$		0			0
$49$	1.88771e6			0.327454
$50$		0			0
$51$		−	5.92486e6i		−	0.875785i
$52$		0			0
$53$			1.13581e7i			1.43947i	0.694250	+	0.719734i	$0.255736\pi$
$53$			1.13581e7i			1.43947i	−0.694250	+	0.719734i	$0.744264\pi$
$54$		0			0
$55$	−4.03445e6	+	1.10216e7i	−0.440894	+	1.20447i
$56$		0			0
$57$		−	2.60085e6i		−	0.246386i
$58$		0			0
$59$		−	1.73206e7i		−	1.42940i	−0.699431	−	0.714700i	$-0.746563\pi$
$59$		−	1.73206e7i		−	1.42940i	0.699431	−	0.714700i	$-0.253437\pi$
$60$		0			0
$61$	−6.27787e6			−0.453412			−0.226706	−	0.973963i	$-0.572796\pi$
$61$	−6.27787e6			−0.453412			−0.226706	+	0.973963i	$0.572796\pi$
$62$		0			0
$63$	−1.54951e6			−0.0983633
$64$		0			0
$65$	8.29905e6	−	2.26720e7i	0.464917	−	1.27009i
$66$		0			0
$67$	−3.69260e7			−1.83245			−0.916226	−	0.400661i	$-0.868781\pi$
$67$	−3.69260e7			−1.83245			−0.916226	+	0.400661i	$0.868781\pi$
$68$		0			0
$69$	−1.72268e7			−0.759992
$70$		0			0
$71$			2.42036e7i			0.952458i	0.879321	+	0.476229i	$0.157997\pi$
$71$			2.42036e7i			0.952458i	−0.879321	+	0.476229i	$0.842003\pi$
$72$		0			0
$73$			4.21399e7i			1.48389i	0.670461	+	0.741945i	$0.266096\pi$
$73$			4.21399e7i			1.48389i	−0.670461	+	0.741945i	$0.733904\pi$
$74$		0			0
$75$	2.31089e7	+	1.95356e7i	0.730354	+	0.617421i
$76$		0			0
$77$		−	5.19484e7i		−	1.47778i
$78$		0			0
$79$		−	3.05498e7i		−	0.784332i	−0.919894	−	0.392166i	$-0.871726\pi$
$79$		−	3.05498e7i		−	0.784332i	0.919894	−	0.392166i	$-0.128274\pi$
$80$		0			0
$81$	−3.90579e7			−0.907338
$82$		0			0
$83$	−2.71605e7			−0.572301			−0.286151	−	0.958185i	$-0.592376\pi$
$83$	−2.71605e7			−0.572301			−0.286151	+	0.958185i	$0.592376\pi$
$84$		0			0
$85$	−1.64318e7	+	4.48897e7i	−0.314782	+	0.859945i
$86$		0			0
$87$	−5.04927e7			−0.881356
$88$		0			0
$89$	−3.34588e7			−0.533274			−0.266637	−	0.963797i	$-0.585913\pi$
$89$	−3.34588e7			−0.533274			−0.266637	+	0.963797i	$0.585913\pi$
$90$		0			0
$91$			1.06860e8i			1.55830i
$92$		0			0
$93$			8.04677e7i			1.07570i
$94$		0			0
$95$	−7.21313e6	+	1.97053e7i	−0.0885583	+	0.241930i
$96$		0			0
$97$			1.14836e8i			1.29715i	0.761152	+	0.648574i	$0.224634\pi$
$97$			1.14836e8i			1.29715i	−0.761152	+	0.648574i	$0.775366\pi$
$98$		0			0
$99$			1.05187e7i			0.109502i
$100$		0			0
$101$	1.67657e6			0.0161115			0.00805577	−	0.999968i	$-0.497436\pi$
$101$	1.67657e6			0.0161115			0.00805577	+	0.999968i	$0.497436\pi$
$102$		0			0
$103$	−1.13496e8			−1.00840			−0.504201	−	0.863587i	$-0.668213\pi$
$103$	−1.13496e8			−1.00840			−0.504201	+	0.863587i	$0.668213\pi$
$104$		0			0
$105$	−1.25772e8	−	4.60387e7i	−1.03473	−	0.378762i
$106$		0			0
$107$	−9.58492e7			−0.731229			−0.365614	−	0.930766i	$-0.619141\pi$
$107$	−9.58492e7			−0.731229			−0.365614	+	0.930766i	$0.619141\pi$
$108$		0			0
$109$	8.28668e7			0.587049			0.293525	−	0.955952i	$-0.405172\pi$
$109$	8.28668e7			0.587049			0.293525	+	0.955952i	$0.405172\pi$
$110$		0			0
$111$		−	2.02043e8i		−	1.33092i
$112$		0			0
$113$		−	1.02658e8i		−	0.629622i	−0.949154	−	0.314811i	$-0.898059\pi$
$113$		−	1.02658e8i		−	0.629622i	0.949154	−	0.314811i	$-0.101941\pi$
$114$		0			0
$115$	1.30519e8	+	4.77763e7i	0.746246	+	0.273163i
$116$		0			0
$117$		−	2.16375e7i		−	0.115469i
$118$		0			0
$119$		−	2.11579e8i		−	1.05508i
$120$		0			0
$121$	−1.38288e8			−0.645125
$122$		0			0
$123$	3.27288e8			1.42991
$124$		0			0
$125$	−1.20905e8	−	2.12101e8i	−0.495226	−	0.868764i
$126$		0			0
$127$	1.03106e8			0.396340			0.198170	−	0.980168i	$-0.436500\pi$
$127$	1.03106e8			0.396340			0.198170	+	0.980168i	$0.436500\pi$
$128$		0			0
$129$	−6.70224e7			−0.242025
$130$		0			0
$131$			1.08809e8i			0.369470i	0.982788	+	0.184735i	$0.0591427\pi$
$131$			1.08809e8i			0.369470i	−0.982788	+	0.184735i	$0.940857\pi$
$132$		0			0
$133$		−	9.28776e7i		−	0.296828i
$134$		0			0
$135$	3.23766e8	+	1.18514e8i	0.974756	+	0.356809i
$136$		0			0
$137$			1.52729e8i			0.433549i	0.976222	+	0.216774i	$0.0695536\pi$
$137$			1.52729e8i			0.433549i	−0.976222	+	0.216774i	$0.930446\pi$
$138$		0			0
$139$		−	3.20534e8i		−	0.858648i	−0.903151	−	0.429324i	$-0.858752\pi$
$139$		−	3.20534e8i		−	0.858648i	0.903151	−	0.429324i	$-0.141248\pi$
$140$		0			0
$141$	1.20527e8			0.304936
$142$		0			0
$143$	7.25411e8			1.73476
$144$		0			0
$145$	3.82557e8	+	1.40035e8i	0.865415	+	0.316785i
$146$		0			0
$147$	1.46232e8			0.313164
$148$		0			0
$149$	−9.06879e8			−1.83994			−0.919972	−	0.391985i	$-0.871789\pi$
$149$	−9.06879e8			−1.83994			−0.919972	+	0.391985i	$0.871789\pi$
$150$		0			0
$151$			7.61728e7i			0.146518i	0.997313	+	0.0732592i	$0.0233400\pi$
$151$			7.61728e7i			0.146518i	−0.997313	+	0.0732592i	$0.976660\pi$
$152$		0			0
$153$			4.28415e7i			0.0781806i
$154$		0			0
$155$	2.23167e8	−	6.09663e8i	0.386636	−	1.05624i
$156$		0			0
$157$			9.20359e8i			1.51481i	0.652944	+	0.757406i	$0.273534\pi$
$157$			9.20359e8i			1.51481i	−0.652944	+	0.757406i	$0.726466\pi$
$158$		0			0
$159$			8.79858e8i			1.37665i
$160$		0			0
$161$	−6.15177e8			−0.915581
$162$		0			0
$163$	−3.80213e8			−0.538613			−0.269306	−	0.963055i	$-0.586794\pi$
$163$	−3.80213e8			−0.538613			−0.269306	+	0.963055i	$0.586794\pi$
$164$		0			0
$165$	−3.12530e8	+	8.53792e8i	−0.421654	+	1.15190i
$166$		0			0
$167$	−1.25104e9			−1.60844			−0.804219	−	0.594333i	$-0.797416\pi$
$167$	−1.25104e9			−1.60844			−0.804219	+	0.594333i	$0.797416\pi$
$168$		0			0
$169$	−6.76472e8			−0.829283
$170$		0			0
$171$			1.88063e7i			0.0219947i
$172$		0			0
$173$		−	6.69241e8i		−	0.747133i	−0.927603	−	0.373566i	$-0.878135\pi$
$173$		−	6.69241e8i		−	0.747133i	0.927603	−	0.373566i	$-0.121865\pi$
$174$		0			0
$175$	8.25228e8	+	6.97624e8i	0.879876	+	0.743823i
$176$		0			0
$177$		−	1.34174e9i		−	1.36702i
$178$		0			0
$179$		−	4.43467e8i		−	0.431966i	−0.976397	−	0.215983i	$-0.930704\pi$
$179$		−	4.43467e8i		−	0.431966i	0.976397	−	0.215983i	$-0.0692956\pi$
$180$		0			0
$181$	−1.71276e9			−1.59581			−0.797907	−	0.602781i	$-0.794059\pi$
$181$	−1.71276e9			−1.59581			−0.797907	+	0.602781i	$0.794059\pi$
$182$		0			0
$183$	−4.86317e8			−0.433625
$184$		0			0
$185$	−5.60341e8	+	1.53078e9i	−0.478372	+	1.30685i
$186$		0			0
$187$	−1.43629e9			−1.17456
$188$		0			0
$189$	−1.52601e9			−1.19594
$190$		0			0
$191$		−	2.30115e9i		−	1.72906i	−0.502578	−	0.864532i	$-0.667615\pi$
$191$		−	2.30115e9i		−	1.72906i	0.502578	−	0.864532i	$-0.332385\pi$
$192$		0			0
$193$			1.20124e9i			0.865765i	0.901450	+	0.432883i	$0.142504\pi$
$193$			1.20124e9i			0.865765i	−0.901450	+	0.432883i	$0.857496\pi$
$194$		0			0
$195$	6.42888e8	−	1.75629e9i	0.444628	−	1.21467i
$196$		0			0
$197$			1.12445e9i			0.746580i	0.927715	+	0.373290i	$0.121770\pi$
$197$			1.12445e9i			0.746580i	−0.927715	+	0.373290i	$0.878230\pi$
$198$		0			0
$199$			2.25000e9i			1.43473i	0.696697	+	0.717365i	$0.254652\pi$
$199$			2.25000e9i			1.43473i	−0.696697	+	0.717365i	$0.745348\pi$
$200$		0			0
$201$	−2.86048e9			−1.75249
$202$		0			0
$203$	−1.80312e9			−1.06179
$204$		0			0
$205$	−2.47969e9	−	9.07690e8i	−1.40405	−	0.513952i
$206$		0			0
$207$	1.24564e8			0.0678438
$208$		0			0
$209$	−6.30491e8			−0.330441
$210$		0			0
$211$			3.18331e9i			1.60601i	0.595969	+	0.803007i	$0.296768\pi$
$211$			3.18331e9i			1.60601i	−0.595969	+	0.803007i	$0.703232\pi$
$212$		0			0
$213$			1.87493e9i			0.910894i
$214$		0			0
$215$	5.07795e8	+	1.85878e8i	0.237648	+	0.0869909i
$216$		0			0
$217$			2.87354e9i			1.29592i
$218$		0			0
$219$			3.26437e9i			1.41913i
$220$		0			0
$221$	2.95451e9			1.23856
$222$		0			0
$223$	−3.56237e9			−1.44052			−0.720260	−	0.693704i	$-0.755978\pi$
$223$	−3.56237e9			−1.44052			−0.720260	+	0.693704i	$0.755978\pi$
$224$		0			0
$225$	−1.67096e8	−	1.41258e8i	−0.0651981	−	0.0551167i
$226$		0			0
$227$	3.62541e9			1.36538			0.682689	−	0.730709i	$-0.260810\pi$
$227$	3.62541e9			1.36538			0.682689	+	0.730709i	$0.260810\pi$
$228$		0			0
$229$	−6.49920e8			−0.236330			−0.118165	−	0.992994i	$-0.537701\pi$
$229$	−6.49920e8			−0.236330			−0.118165	+	0.992994i	$0.537701\pi$
$230$		0			0
$231$		−	4.02420e9i		−	1.41329i
$232$		0			0
$233$		−	1.18657e9i		−	0.402597i	−0.979530	−	0.201299i	$-0.935484\pi$
$233$		−	1.18657e9i		−	0.402597i	0.979530	−	0.201299i	$-0.0645162\pi$
$234$		0			0
$235$	−9.13175e8	−	3.34267e8i	−0.299421	−	0.109603i
$236$		0			0
$237$		−	2.36655e9i		−	0.750105i
$238$		0			0
$239$		−	1.67879e9i		−	0.514522i	−0.966342	−	0.257261i	$-0.917180\pi$
$239$		−	1.67879e9i		−	0.514522i	0.966342	−	0.257261i	$-0.0828201\pi$
$240$		0			0
$241$	−6.27098e9			−1.85895			−0.929474	−	0.368888i	$-0.879738\pi$
$241$	−6.27098e9			−1.85895			−0.929474	+	0.368888i	$0.879738\pi$
$242$		0			0
$243$	5.93683e8			0.170266
$244$		0			0
$245$	−1.10792e9	−	4.05555e8i	−0.307500	−	0.112560i
$246$		0			0
$247$	1.29695e9			0.348446
$248$		0			0
$249$	−2.10399e9			−0.547327
$250$		0			0
$251$			7.52982e9i			1.89710i	0.316632	+	0.948548i	$0.397448\pi$
$251$			7.52982e9i			1.89710i	−0.316632	+	0.948548i	$0.602552\pi$
$252$		0			0
$253$			4.17608e9i			1.01926i
$254$		0			0
$255$	−1.27290e9	+	3.47739e9i	−0.301046	+	0.822418i
$256$		0			0
$257$		−	1.46963e9i		−	0.336880i	−0.985712	−	0.168440i	$-0.946127\pi$
$257$		−	1.46963e9i		−	0.336880i	0.985712	−	0.168440i	$-0.0538729\pi$
$258$		0			0
$259$		−	7.21506e9i		−	1.60340i
$260$		0			0
$261$	3.65103e8			0.0786780
$262$		0			0
$263$	−3.91195e9			−0.817656			−0.408828	−	0.912611i	$-0.634062\pi$
$263$	−3.91195e9			−0.817656			−0.408828	+	0.912611i	$0.634062\pi$
$264$		0			0
$265$	2.44017e9	−	6.66623e9i	0.494808	−	1.35175i
$266$		0			0
$267$	−2.59190e9			−0.510003
$268$		0			0
$269$	−3.45528e9			−0.659894			−0.329947	−	0.943999i	$-0.607031\pi$
$269$	−3.45528e9			−0.659894			−0.329947	+	0.943999i	$0.607031\pi$
$270$		0			0
$271$		−	6.91923e9i		−	1.28286i	−0.767180	−	0.641432i	$-0.778341\pi$
$271$		−	6.91923e9i		−	1.28286i	0.767180	−	0.641432i	$-0.221659\pi$
$272$		0			0
$273$			8.27795e9i			1.49029i
$274$		0			0
$275$	4.73576e9	−	5.60199e9i	0.828055	−	0.979515i
$276$		0			0
$277$		−	4.71800e9i		−	0.801381i	−0.916213	−	0.400690i	$-0.868770\pi$
$277$		−	4.71800e9i		−	0.801381i	0.916213	−	0.400690i	$-0.131230\pi$
$278$		0			0
$279$		−	5.81846e8i		−	0.0960265i
$280$		0			0
$281$	−6.72838e8			−0.107916			−0.0539580	−	0.998543i	$-0.517184\pi$
$281$	−6.72838e8			−0.107916			−0.0539580	+	0.998543i	$0.517184\pi$
$282$		0			0
$283$	−9.27935e9			−1.44668			−0.723339	−	0.690493i	$-0.757394\pi$
$283$	−9.27935e9			−1.44668			−0.723339	+	0.690493i	$0.757394\pi$
$284$		0			0
$285$	−5.58767e8	+	1.52648e9i	−0.0846937	+	0.231372i
$286$		0			0
$287$	1.16876e10			1.72265
$288$		0			0
$289$	1.12593e9			0.161407
$290$		0			0
$291$			8.89577e9i			1.24054i
$292$		0			0
$293$		−	4.06323e9i		−	0.551316i	−0.961256	−	0.275658i	$-0.911104\pi$
$293$		−	4.06323e9i		−	0.551316i	0.961256	−	0.275658i	$-0.0888957\pi$
$294$		0			0
$295$	−3.72114e9	+	1.01657e10i	−0.491347	+	1.34230i
$296$		0			0
$297$			1.03592e10i			1.33138i
$298$		0			0
$299$		−	8.59038e9i		−	1.07480i
$300$		0			0
$301$	−2.39340e9			−0.291574
$302$		0			0
$303$	1.29876e8			0.0154085
$304$		0			0
$305$	3.68457e9	+	1.34874e9i	0.425783	+	0.155857i
$306$		0			0
$307$	8.05058e9			0.906304			0.453152	−	0.891433i	$-0.350300\pi$
$307$	8.05058e9			0.906304			0.453152	+	0.891433i	$0.350300\pi$
$308$		0			0
$309$	−8.79203e9			−0.964396
$310$		0			0
$311$			3.49045e9i			0.373113i	0.982444	+	0.186556i	$0.0597327\pi$
$311$			3.49045e9i			0.373113i	−0.982444	+	0.186556i	$0.940267\pi$
$312$		0			0
$313$		−	1.23084e10i		−	1.28241i	−0.767371	−	0.641203i	$-0.778436\pi$
$313$		−	1.23084e10i		−	1.28241i	0.767371	−	0.641203i	$-0.221564\pi$
$314$		0			0
$315$	9.09432e8	+	3.32897e8i	0.0923694	+	0.0338118i
$316$		0			0
$317$			1.41977e10i			1.40599i	0.711197	+	0.702993i	$0.248153\pi$
$317$			1.41977e10i			1.40599i	−0.711197	+	0.702993i	$0.751847\pi$
$318$		0			0
$319$			1.22403e10i			1.18203i
$320$		0			0
$321$	−7.42498e9			−0.699319
$322$		0			0
$323$	−2.56791e9			−0.235923
$324$		0			0
$325$	−9.74167e9	+	1.15235e10i	−0.873173	+	1.03289i
$326$		0			0
$327$	6.41929e9			0.561431
$328$		0			0
$329$	4.30408e9			0.367364
$330$		0			0
$331$		−	1.62596e10i		−	1.35456i	−0.735727	−	0.677278i	$-0.763159\pi$
$331$		−	1.62596e10i		−	1.35456i	0.735727	−	0.677278i	$-0.236841\pi$
$332$		0			0
$333$			1.46094e9i			0.118810i
$334$		0			0
$335$	2.16724e10	+	7.93317e9i	1.72079	+	0.629894i
$336$		0			0
$337$		−	3.64424e9i		−	0.282545i	−0.989971	−	0.141272i	$-0.954881\pi$
$337$		−	3.64424e9i		−	0.282545i	0.989971	−	0.141272i	$-0.0451194\pi$
$338$		0			0
$339$		−	7.95245e9i		−	0.602146i
$340$		0			0
$341$	1.95067e10			1.44267
$342$		0			0
$343$	−1.07253e10			−0.774875
$344$		0			0
$345$	1.01107e10	+	3.70101e9i	0.713680	+	0.261242i
$346$		0			0
$347$	2.11705e10			1.46020			0.730101	−	0.683340i	$-0.239473\pi$
$347$	2.11705e10			1.46020			0.730101	+	0.683340i	$0.239473\pi$
$348$		0			0
$349$	−3.13163e9			−0.211091			−0.105545	−	0.994415i	$-0.533659\pi$
$349$	−3.13163e9			−0.211091			−0.105545	+	0.994415i	$0.533659\pi$
$350$		0			0
$351$		−	2.13093e10i		−	1.40392i
$352$		0			0
$353$		−	6.38374e9i		−	0.411128i	−0.978644	−	0.205564i	$-0.934097\pi$
$353$		−	6.38374e9i		−	0.411128i	0.978644	−	0.205564i	$-0.0659028\pi$
$354$		0			0
$355$	5.19989e9	−	1.42054e10i	0.327401	−	0.894419i
$356$		0			0
$357$		−	1.63900e10i		−	1.00904i
$358$		0			0
$359$		−	1.14937e10i		−	0.691962i	−0.938242	−	0.345981i	$-0.887546\pi$
$359$		−	1.14937e10i		−	0.691962i	0.938242	−	0.345981i	$-0.112454\pi$
$360$		0			0
$361$	1.58563e10			0.933627
$362$		0			0
$363$	−1.07125e10			−0.616973
$364$		0			0
$365$	9.05332e9	−	2.47325e10i	0.510078	−	1.39347i
$366$		0			0
$367$	2.11024e10			1.16323			0.581617	−	0.813463i	$-0.302420\pi$
$367$	2.11024e10			1.16323			0.581617	+	0.813463i	$0.302420\pi$
$368$		0			0
$369$	−2.36655e9			−0.127647
$370$		0			0
$371$			3.14201e10i			1.65849i
$372$		0			0
$373$		−	2.32356e9i		−	0.120038i	−0.998197	−	0.0600191i	$-0.980884\pi$
$373$		−	2.32356e9i		−	0.120038i	0.998197	−	0.0600191i	$-0.0191162\pi$
$374$		0			0
$375$	−9.36591e9	−	1.64304e10i	−0.473615	−	0.830852i
$376$		0			0
$377$		−	2.51788e10i		−	1.24644i
$378$		0			0
$379$			7.87748e9i			0.381795i	0.981610	+	0.190898i	$0.0611399\pi$
$379$			7.87748e9i			0.381795i	−0.981610	+	0.190898i	$0.938860\pi$
$380$		0			0
$381$	7.98710e9			0.379044
$382$		0			0
$383$	−3.16820e10			−1.47237			−0.736186	−	0.676780i	$-0.763375\pi$
$383$	−3.16820e10			−1.47237			−0.736186	+	0.676780i	$0.763375\pi$
$384$		0			0
$385$	−1.11606e10	+	3.04893e10i	−0.507977	+	1.38773i
$386$		0			0
$387$	4.84626e8			0.0216054
$388$		0			0
$389$	3.57187e10			1.55990			0.779951	−	0.625840i	$-0.215244\pi$
$389$	3.57187e10			1.55990			0.779951	+	0.625840i	$0.215244\pi$
$390$		0			0
$391$			1.70086e10i			0.727717i
$392$		0			0
$393$			8.42891e9i			0.353347i
$394$		0			0
$395$	−6.56331e9	+	1.79301e10i	−0.269609	+	0.736538i
$396$		0			0
$397$			9.01725e9i			0.363004i	0.983391	+	0.181502i	$0.0580960\pi$
$397$			9.01725e9i			0.363004i	−0.983391	+	0.181502i	$0.941904\pi$
$398$		0			0
$399$		−	7.19478e9i		−	0.283874i
$400$		0			0
$401$	1.84446e10			0.713332			0.356666	−	0.934232i	$-0.383913\pi$
$401$	1.84446e10			0.713332			0.356666	+	0.934232i	$0.383913\pi$
$402$		0			0
$403$	−4.01262e10			−1.52128
$404$		0			0
$405$	2.29237e10	+	8.39119e9i	0.852048	+	0.311892i
$406$		0			0
$407$	−4.89788e10			−1.78497
$408$		0			0
$409$	4.11180e10			1.46939			0.734697	−	0.678395i	$-0.237324\pi$
$409$	4.11180e10			1.46939			0.734697	+	0.678395i	$0.237324\pi$
$410$		0			0
$411$			1.18312e10i			0.414629i
$412$		0			0
$413$		−	4.79141e10i		−	1.64689i
$414$		0			0
$415$	1.59409e10	+	5.83514e9i	0.537427	+	0.196725i
$416$		0			0
$417$		−	2.48302e10i		−	0.821177i
$418$		0			0
$419$			4.56118e10i			1.47986i	0.672683	+	0.739931i	$0.265142\pi$
$419$			4.56118e10i			1.47986i	−0.672683	+	0.739931i	$0.734858\pi$
$420$		0			0
$421$	1.43826e10			0.457834			0.228917	−	0.973446i	$-0.426482\pi$
$421$	1.43826e10			0.457834			0.228917	+	0.973446i	$0.426482\pi$
$422$		0			0
$423$	−8.71510e8			−0.0272214
$424$		0			0
$425$	1.92882e10	−	2.28162e10i	0.591201	−	0.699339i
$426$		0			0
$427$	−1.73666e10			−0.522399
$428$		0			0
$429$	5.61941e10			1.65906
$430$		0			0
$431$		−	1.99136e10i		−	0.577087i	−0.957467	−	0.288544i	$-0.906829\pi$
$431$		−	1.99136e10i		−	0.577087i	0.957467	−	0.288544i	$-0.0931710\pi$
$432$		0			0
$433$		−	1.13608e10i		−	0.323190i	−0.986857	−	0.161595i	$-0.948336\pi$
$433$		−	1.13608e10i		−	0.323190i	0.986857	−	0.161595i	$-0.0516638\pi$
$434$		0			0
$435$	2.96349e10	+	1.08478e10i	0.827650	+	0.302961i
$436$		0			0
$437$			7.46633e9i			0.204730i
$438$		0			0
$439$			3.17463e10i			0.854743i	0.904076	+	0.427372i	$0.140560\pi$
$439$			3.17463e10i			0.854743i	−0.904076	+	0.427372i	$0.859440\pi$
$440$		0			0
$441$	−1.05737e9			−0.0279559
$442$		0			0
$443$	2.49996e10			0.649111			0.324555	−	0.945867i	$-0.394785\pi$
$443$	2.49996e10			0.649111			0.324555	+	0.945867i	$0.394785\pi$
$444$		0			0
$445$	1.96375e10	+	7.18829e9i	0.500778	+	0.183310i
$446$		0			0
$447$	−7.02516e10			−1.75965
$448$		0			0
$449$	−2.89675e10			−0.712732			−0.356366	−	0.934347i	$-0.615984\pi$
$449$	−2.89675e10			−0.712732			−0.356366	+	0.934347i	$0.615984\pi$
$450$		0			0
$451$		−	7.93402e10i		−	1.91773i
$452$		0			0
$453$			5.90074e9i			0.140124i
$454$		0			0
$455$	2.29578e10	−	6.27178e10i	0.535655	−	1.46334i
$456$		0			0
$457$			1.50928e10i			0.346023i	0.984920	+	0.173012i	$0.0553499\pi$
$457$			1.50928e10i			0.346023i	−0.984920	+	0.173012i	$0.944650\pi$
$458$		0			0
$459$			4.21917e10i			0.950554i
$460$		0			0
$461$	3.37841e10			0.748012			0.374006	−	0.927426i	$-0.377984\pi$
$461$	3.37841e10			0.748012			0.374006	+	0.927426i	$0.377984\pi$
$462$		0			0
$463$	4.45040e9			0.0968445			0.0484223	−	0.998827i	$-0.484581\pi$
$463$	4.45040e9			0.0968445			0.0484223	+	0.998827i	$0.484581\pi$
$464$		0			0
$465$	1.72877e10	−	4.72277e10i	0.369764	−	1.01015i
$466$		0			0
$467$	−3.15089e10			−0.662470			−0.331235	−	0.943548i	$-0.607465\pi$
$467$	−3.15089e10			−0.662470			−0.331235	+	0.943548i	$0.607465\pi$
$468$		0			0
$469$	−1.02149e11			−2.11126
$470$		0			0
$471$			7.12958e10i			1.44871i
$472$		0			0
$473$			1.62474e10i			0.324593i
$474$		0			0
$475$	8.46698e9	−	1.00157e10i	0.166324	−	0.196746i
$476$		0			0
$477$		−	6.36208e9i		−	0.122893i
$478$		0			0
$479$		−	1.58978e9i		−	0.0301992i	−0.999886	−	0.0150996i	$-0.995193\pi$
$479$		−	1.58978e9i		−	0.0301992i	0.999886	−	0.0150996i	$-0.00480653\pi$
$480$		0			0
$481$	1.00752e11			1.88223
$482$		0			0
$483$	−4.76548e10			−0.875626
$484$		0			0
$485$	2.46713e10	−	6.73987e10i	0.445886	−	1.21810i
$486$		0			0
$487$	9.45450e10			1.68083			0.840413	−	0.541947i	$-0.182313\pi$
$487$	9.45450e10			1.68083			0.840413	+	0.541947i	$0.182313\pi$
$488$		0			0
$489$	−2.94533e10			−0.515108
$490$		0			0
$491$		−	9.07795e10i		−	1.56193i	−0.624574	−	0.780966i	$-0.714727\pi$
$491$		−	9.07795e10i		−	1.56193i	0.624574	−	0.780966i	$-0.285273\pi$
$492$		0			0
$493$			4.98532e10i			0.843928i
$494$		0			0
$495$	2.25984e9	−	6.17360e9i	0.0376407	−	0.102830i
$496$		0			0
$497$			6.69547e10i			1.09738i
$498$		0			0
$499$		−	7.75766e10i		−	1.25121i	−0.780142	−	0.625603i	$-0.784853\pi$
$499$		−	7.75766e10i		−	1.25121i	0.780142	−	0.625603i	$-0.215147\pi$
$500$		0			0
$501$	−9.69119e10			−1.53825
$502$		0			0
$503$	6.36077e10			0.993659			0.496830	−	0.867848i	$-0.334497\pi$
$503$	6.36077e10			0.993659			0.496830	+	0.867848i	$0.334497\pi$
$504$		0			0
$505$	−9.84006e8	−	3.60195e8i	−0.0151298	−	0.00553824i
$506$		0			0
$507$	−5.24031e10			−0.793094
$508$		0			0
$509$	1.93388e10			0.288110			0.144055	−	0.989570i	$-0.453986\pi$
$509$	1.93388e10			0.288110			0.144055	+	0.989570i	$0.453986\pi$
$510$		0			0
$511$			1.16572e11i			1.70967i
$512$		0			0
$513$			1.85210e10i			0.267421i
$514$		0			0
$515$	6.66127e10	+	2.43836e10i	0.946953	+	0.346631i
$516$		0			0
$517$		−	2.92179e10i		−	0.408966i
$518$		0			0
$519$		−	5.18429e10i		−	0.714529i
$520$		0			0
$521$	1.07366e11			1.45720			0.728598	−	0.684942i	$-0.240172\pi$
$521$	1.07366e11			1.45720			0.728598	+	0.684942i	$0.240172\pi$
$522$		0			0
$523$	1.40757e11			1.88132			0.940661	−	0.339347i	$-0.110206\pi$
$523$	1.40757e11			1.88132			0.940661	+	0.339347i	$0.110206\pi$
$524$		0			0
$525$	6.39265e10	+	5.40416e10i	0.841479	+	0.711363i
$526$		0			0
$527$	7.94485e10			1.03001
$528$		0			0
$529$	−2.88576e10			−0.368499
$530$		0			0
$531$			9.70187e9i			0.122033i
$532$		0			0
$533$			1.63206e11i			2.02222i
$534$		0			0
$535$	5.62553e10	+	2.05922e10i	0.686670	+	0.251355i
$536$		0			0
$537$		−	3.43533e10i		−	0.413116i
$538$		0			0
$539$		−	3.54491e10i		−	0.420001i
$540$		0			0
$541$	−1.50605e10			−0.175812			−0.0879062	−	0.996129i	$-0.528018\pi$
$541$	−1.50605e10			−0.175812			−0.0879062	+	0.996129i	$0.528018\pi$
$542$		0			0
$543$	−1.32679e11			−1.52617
$544$		0			0
$545$	−4.86357e10	−	1.78031e10i	−0.551276	−	0.201794i
$546$		0			0
$547$	4.59183e10			0.512905			0.256453	−	0.966557i	$-0.417446\pi$
$547$	4.59183e10			0.512905			0.256453	+	0.966557i	$0.417446\pi$
$548$		0			0
$549$	3.51646e9			0.0387094
$550$		0			0
$551$			2.18842e10i			0.237424i
$552$		0			0
$553$		−	8.45104e10i		−	0.903670i
$554$		0			0
$555$	−4.34070e10	+	1.18582e11i	−0.457496	+	1.24982i
$556$		0			0
$557$		−	1.70367e11i		−	1.76996i	−0.465627	−	0.884981i	$-0.654171\pi$
$557$		−	1.70367e11i		−	1.76996i	0.465627	−	0.884981i	$-0.345829\pi$
$558$		0			0
$559$		−	3.34216e10i		−	0.342279i
$560$		0			0
$561$	−1.11262e11			−1.12330
$562$		0			0
$563$	−5.69946e10			−0.567283			−0.283642	−	0.958930i	$-0.591543\pi$
$563$	−5.69946e10			−0.567283			−0.283642	+	0.958930i	$0.591543\pi$
$564$		0			0
$565$	−2.20551e10	+	6.02517e10i	−0.216429	+	0.591256i
$566$		0			0
$567$	−1.08047e11			−1.04539
$568$		0			0
$569$	−9.84498e9			−0.0939217			−0.0469608	−	0.998897i	$-0.514954\pi$
$569$	−9.84498e9			−0.0939217			−0.0469608	+	0.998897i	$0.514954\pi$
$570$		0			0
$571$		−	1.60223e11i		−	1.50723i	−0.657314	−	0.753617i	$-0.728307\pi$
$571$		−	1.60223e11i		−	1.50723i	0.657314	−	0.753617i	$-0.271693\pi$
$572$		0			0
$573$		−	1.78259e11i		−	1.65361i
$574$		0			0
$575$	−6.63392e10	−	5.60813e10i	−0.606874	−	0.513034i
$576$		0			0
$577$			8.28831e9i			0.0747761i	0.999301	+	0.0373880i	$0.0119038\pi$
$577$			8.28831e9i			0.0747761i	−0.999301	+	0.0373880i	$0.988096\pi$
$578$		0			0
$579$			9.30543e10i			0.827984i
$580$		0			0
$581$	−7.51344e10			−0.659378
$582$		0			0
$583$	2.13293e11			1.84630
$584$		0			0
$585$	−4.64860e9	+	1.26994e10i	−0.0396916	+	0.108432i
$586$		0			0
$587$	3.23397e10			0.272385			0.136193	−	0.990682i	$-0.456513\pi$
$587$	3.23397e10			0.272385			0.136193	+	0.990682i	$0.456513\pi$
$588$		0			0
$589$	3.48757e10			0.289776
$590$		0			0
$591$			8.71060e10i			0.714000i
$592$		0			0
$593$		−	4.22957e10i		−	0.342041i	−0.985268	−	0.171020i	$-0.945294\pi$
$593$		−	4.22957e10i		−	0.342041i	0.985268	−	0.171020i	$-0.0547064\pi$
$594$		0			0
$595$	−4.54557e10	+	1.24179e11i	−0.362677	+	0.990787i
$596$		0			0
$597$			1.74297e11i			1.37212i
$598$		0			0
$599$		−	2.31039e11i		−	1.79464i	−0.441381	−	0.897320i	$-0.645511\pi$
$599$		−	2.31039e11i		−	1.79464i	0.441381	−	0.897320i	$-0.354489\pi$
$600$		0			0
$601$	6.77311e10			0.519147			0.259573	−	0.965723i	$-0.416418\pi$
$601$	6.77311e10			0.519147			0.259573	+	0.965723i	$0.416418\pi$
$602$		0			0
$603$	2.06836e10			0.156443
$604$		0			0
$605$	8.11634e10	+	2.97098e10i	0.605814	+	0.221758i
$606$		0			0
$607$	5.53753e9			0.0407907			0.0203954	−	0.999792i	$-0.493508\pi$
$607$	5.53753e9			0.0407907			0.0203954	+	0.999792i	$0.493508\pi$
$608$		0			0
$609$	−1.39679e11			−1.01546
$610$		0			0
$611$			6.01025e10i			0.431249i
$612$		0			0
$613$		−	1.98304e11i		−	1.40439i	−0.711983	−	0.702197i	$-0.752203\pi$
$613$		−	1.98304e11i		−	1.40439i	0.711983	−	0.702197i	$-0.247797\pi$
$614$		0			0
$615$	−1.92090e11	−	7.03144e10i	−1.34278	−	0.491523i
$616$		0			0
$617$			5.63115e10i			0.388559i	0.980946	+	0.194279i	$0.0622368\pi$
$617$			5.63115e10i			0.388559i	−0.980946	+	0.194279i	$0.937763\pi$
$618$		0			0
$619$			2.07195e10i			0.141129i	0.997507	+	0.0705646i	$0.0224801\pi$
$619$			2.07195e10i			0.141129i	−0.997507	+	0.0705646i	$0.977520\pi$
$620$		0			0
$621$	1.22675e11			0.824875
$622$		0			0
$623$	−9.25577e10			−0.614413
$624$		0			0
$625$	2.53931e10	+	1.50460e11i	0.166416	+	0.986056i
$626$		0			0
$627$	−4.88412e10			−0.316021
$628$		0			0
$629$	−1.99485e11			−1.27440
$630$		0			0
$631$		−	1.23968e11i		−	0.781972i	−0.920397	−	0.390986i	$-0.872134\pi$
$631$		−	1.23968e11i		−	0.781972i	0.920397	−	0.390986i	$-0.127866\pi$
$632$		0			0
$633$			2.46596e11i			1.53593i
$634$		0			0
$635$	−6.05142e10	−	2.21512e10i	−0.372188	−	0.136239i
$636$		0			0
$637$			7.29204e10i			0.442885i
$638$		0			0
$639$		−	1.35573e10i		−	0.0813148i
$640$		0			0
$641$	−2.28203e11			−1.35173			−0.675864	−	0.737026i	$-0.736229\pi$
$641$	−2.28203e11			−1.35173			−0.675864	+	0.737026i	$0.736229\pi$
$642$		0			0
$643$	1.01445e11			0.593454			0.296727	−	0.954962i	$-0.404105\pi$
$643$	1.01445e11			0.593454			0.296727	+	0.954962i	$0.404105\pi$
$644$		0			0
$645$	3.93364e10	+	1.43991e10i	0.227277	+	0.0831947i
$646$		0			0
$647$	−4.69107e10			−0.267704			−0.133852	−	0.991001i	$-0.542735\pi$
$647$	−4.69107e10			−0.267704			−0.133852	+	0.991001i	$0.542735\pi$
$648$		0			0
$649$	−3.25261e11			−1.83338
$650$		0			0
$651$			2.22599e11i			1.23937i
$652$		0			0
$653$			1.35671e11i			0.746164i	0.927798	+	0.373082i	$0.121699\pi$
$653$			1.35671e11i			0.746164i	−0.927798	+	0.373082i	$0.878301\pi$
$654$		0			0
$655$	2.33765e10	−	6.38616e10i	0.127003	−	0.346956i
$656$		0			0
$657$		−	2.36041e10i		−	0.126685i
$658$		0			0
$659$			1.08963e11i			0.577747i	0.957367	+	0.288873i	$0.0932806\pi$
$659$			1.08963e11i			0.577747i	−0.957367	+	0.288873i	$0.906719\pi$
$660$		0			0
$661$	−2.92896e11			−1.53429			−0.767145	−	0.641474i	$-0.778323\pi$
$661$	−2.92896e11			−1.53429			−0.767145	+	0.641474i	$0.778323\pi$
$662$		0			0
$663$	2.28872e11			1.18451
$664$		0			0
$665$	−1.99538e10	+	5.45112e10i	−0.102033	+	0.278740i
$666$		0			0
$667$	1.44951e11			0.732346
$668$		0			0
$669$	−2.75960e11			−1.37766
$670$		0			0
$671$			1.17891e11i			0.581557i
$672$		0			0
$673$		−	5.87465e10i		−	0.286366i	−0.989696	−	0.143183i	$-0.954266\pi$
$673$		−	5.87465e10i		−	0.286366i	0.989696	−	0.143183i	$-0.0457338\pi$
$674$		0			0
$675$	−1.64561e11	−	1.39116e11i	−0.792707	−	0.670133i
$676$		0			0
$677$			3.37409e11i			1.60621i	0.595837	+	0.803105i	$0.296820\pi$
$677$			3.37409e11i			1.60621i	−0.595837	+	0.803105i	$0.703180\pi$
$678$		0			0
$679$			3.17672e11i			1.49451i
$680$		0			0
$681$	2.80843e11			1.30580
$682$		0			0
$683$	2.03880e11			0.936898			0.468449	−	0.883490i	$-0.344813\pi$
$683$	2.03880e11			0.936898			0.468449	+	0.883490i	$0.344813\pi$
$684$		0			0
$685$	3.28122e10	−	8.96387e10i	0.149030	−	0.407130i
$686$		0			0
$687$	−5.03462e10			−0.226016
$688$		0			0
$689$	−4.38752e11			−1.94690
$690$		0			0
$691$		−	2.14740e11i		−	0.941889i	−0.882163	−	0.470945i	$-0.843913\pi$
$691$		−	2.14740e11i		−	0.941889i	0.882163	−	0.470945i	$-0.156087\pi$
$692$		0			0
$693$			2.90982e10i			0.126163i
$694$		0			0
$695$	−6.88635e10	+	1.88126e11i	−0.295155	+	0.806325i
$696$		0			0
$697$		−	3.23143e11i		−	1.36919i
$698$		0			0
$699$		−	9.19182e10i		−	0.385028i
$700$		0			0
$701$	6.87506e10			0.284711			0.142356	−	0.989816i	$-0.454532\pi$
$701$	6.87506e10			0.284711			0.142356	+	0.989816i	$0.454532\pi$
$702$		0			0
$703$	−8.75683e10			−0.358530
$704$		0			0
$705$	−7.07393e10	−	2.58941e10i	−0.286355	−	0.104820i
$706$		0			0
$707$	4.63793e9			0.0185629
$708$		0			0
$709$	−4.61613e11			−1.82681			−0.913405	−	0.407052i	$-0.866557\pi$
$709$	−4.61613e11			−1.82681			−0.913405	+	0.407052i	$0.866557\pi$
$710$		0			0
$711$			1.71120e10i			0.0669612i
$712$		0			0
$713$		−	2.31000e11i		−	0.893830i
$714$		0			0
$715$	−4.25754e11	−	1.55847e11i	−1.62905	−	0.596313i
$716$		0			0
$717$		−	1.30048e11i		−	0.492069i
$718$		0			0
$719$			1.60395e11i			0.600173i	0.953912	+	0.300087i	$0.0970156\pi$
$719$			1.60395e11i			0.600173i	−0.953912	+	0.300087i	$0.902984\pi$
$720$		0			0
$721$	−3.13967e11			−1.16183
$722$		0			0
$723$	−4.85783e11			−1.77782
$724$		0			0
$725$	−1.94444e11	−	1.64377e11i	−0.703787	−	0.594962i
$726$		0			0
$727$	−1.50548e11			−0.538936			−0.269468	−	0.963009i	$-0.586848\pi$
$727$	−1.50548e11			−0.538936			−0.269468	+	0.963009i	$0.586848\pi$
$728$		0			0
$729$	3.02249e11			1.07017
$730$		0			0
$731$			6.61735e10i			0.231747i
$732$		0			0
$733$			4.60328e11i			1.59460i	0.603584	+	0.797300i	$0.293739\pi$
$733$			4.60328e11i			1.59460i	−0.603584	+	0.797300i	$0.706261\pi$
$734$		0			0
$735$	−8.58256e10	−	3.14164e10i	−0.294081	−	0.107648i
$736$		0			0
$737$			6.93429e11i			2.35035i
$738$		0			0
$739$		−	8.28300e10i		−	0.277722i	−0.990312	−	0.138861i	$-0.955656\pi$
$739$		−	8.28300e10i		−	0.277722i	0.990312	−	0.138861i	$-0.0443441\pi$
$740$		0			0
$741$	1.00468e11			0.333240
$742$		0			0
$743$	−6.13495e10			−0.201306			−0.100653	−	0.994922i	$-0.532093\pi$
$743$	−6.13495e10			−0.201306			−0.100653	+	0.994922i	$0.532093\pi$
$744$		0			0
$745$	5.32261e11	+	1.94834e11i	1.72782	+	0.632469i
$746$		0			0
$747$	1.52135e10			0.0488594
$748$		0			0
$749$	−2.65149e11			−0.842487
$750$		0			0
$751$		−	3.54621e11i		−	1.11482i	−0.830238	−	0.557409i	$-0.811795\pi$
$751$		−	3.54621e11i		−	1.11482i	0.830238	−	0.557409i	$-0.188205\pi$
$752$		0			0
$753$			5.83299e11i			1.81431i
$754$		0			0
$755$	1.63649e10	−	4.47069e10i	0.0503647	−	0.137590i
$756$		0			0
$757$		−	8.91287e10i		−	0.271415i	−0.990749	−	0.135708i	$-0.956669\pi$
$757$		−	8.91287e10i		−	0.271415i	0.990749	−	0.135708i	$-0.0433307\pi$
$758$		0			0
$759$			3.23501e11i			0.974784i
$760$		0			0
$761$	1.57826e9			0.00470586			0.00235293	−	0.999997i	$-0.499251\pi$
$761$	1.57826e9			0.00470586			0.00235293	+	0.999997i	$0.499251\pi$
$762$		0			0
$763$	2.29236e11			0.676370
$764$		0			0
$765$	9.20406e9	−	2.51443e10i	0.0268741	−	0.0734166i
$766$		0			0
$767$	6.69076e11			1.93328
$768$		0			0
$769$	−3.83818e11			−1.09754			−0.548769	−	0.835974i	$-0.684903\pi$
$769$	−3.83818e11			−1.09754			−0.548769	+	0.835974i	$0.684903\pi$
$770$		0			0
$771$		−	1.13845e11i		−	0.322179i
$772$		0			0
$773$		−	9.96655e10i		−	0.279143i	−0.990212	−	0.139572i	$-0.955427\pi$
$773$		−	9.96655e10i		−	0.279143i	0.990212	−	0.139572i	$-0.0445725\pi$
$774$		0			0
$775$	−2.61960e11	+	3.09875e11i	−0.726152	+	0.858973i
$776$		0			0
$777$		−	5.58916e11i		−	1.53343i
$778$		0			0
$779$		−	1.41851e11i		−	0.385196i
$780$		0			0
$781$	4.54516e11			1.22165
$782$		0			0
$783$	3.59565e11			0.956601
$784$		0			0
$785$	1.97730e11	−	5.40172e11i	0.520707	−	1.42250i
$786$		0			0
$787$	−3.42072e11			−0.891699			−0.445850	−	0.895108i	$-0.647098\pi$
$787$	−3.42072e11			−0.891699			−0.445850	+	0.895108i	$0.647098\pi$
$788$		0			0
$789$	−3.03040e11			−0.781974
$790$		0			0
$791$		−	2.83985e11i		−	0.725421i
$792$		0			0
$793$		−	2.42508e11i		−	0.613244i
$794$		0			0
$795$	1.89028e11	−	5.16401e11i	0.473215	−	1.29276i
$796$		0			0
$797$			1.59158e11i			0.394453i	0.980358	+	0.197227i	$0.0631935\pi$
$797$			1.59158e11i			0.394453i	−0.980358	+	0.197227i	$0.936807\pi$
$798$		0			0
$799$		−	1.19001e11i		−	0.291987i
$800$		0			0
$801$	1.87415e10			0.0455275
$802$		0			0
$803$	7.91340e11			1.90327
$804$		0			0
$805$	3.61056e11	+	1.32164e11i	0.859789	+	0.314725i
$806$		0			0
$807$	−2.67664e11			−0.631097
$808$		0			0
$809$	2.05240e11			0.479147			0.239574	−	0.970878i	$-0.422992\pi$
$809$	2.05240e11			0.479147			0.239574	+	0.970878i	$0.422992\pi$
$810$		0			0
$811$			7.69411e11i			1.77859i	0.457337	+	0.889294i	$0.348803\pi$
$811$			7.69411e11i			1.77859i	−0.457337	+	0.889294i	$0.651197\pi$
$812$		0			0
$813$		−	5.36000e11i		−	1.22688i
$814$		0			0
$815$	2.23153e11	+	8.16849e10i	0.505791	+	0.185145i
$816$		0			0
$817$			2.90484e10i			0.0651979i
$818$		0			0
$819$		−	5.98562e10i		−	0.133037i
$820$		0			0
$821$	4.68809e10			0.103187			0.0515933	−	0.998668i	$-0.483570\pi$
$821$	4.68809e10			0.103187			0.0515933	+	0.998668i	$0.483570\pi$
$822$		0			0
$823$	3.89198e11			0.848342			0.424171	−	0.905582i	$-0.360566\pi$
$823$	3.89198e11			0.848342			0.424171	+	0.905582i	$0.360566\pi$
$824$		0			0
$825$	3.66857e11	−	4.33959e11i	0.791919	−	0.936770i
$826$		0			0
$827$	1.45057e11			0.310112			0.155056	−	0.987906i	$-0.450444\pi$
$827$	1.45057e11			0.310112			0.155056	+	0.987906i	$0.450444\pi$
$828$		0			0
$829$	4.47485e11			0.947459			0.473730	−	0.880670i	$-0.342907\pi$
$829$	4.47485e11			0.947459			0.473730	+	0.880670i	$0.342907\pi$
$830$		0			0
$831$		−	3.65481e11i		−	0.766409i
$832$		0			0
$833$		−	1.44380e11i		−	0.299865i
$834$		0			0
$835$	7.34252e11	+	2.68772e11i	1.51043	+	0.552890i
$836$		0			0
$837$		−	5.73021e11i		−	1.16753i
$838$		0			0
$839$			9.70318e9i			0.0195824i	0.999952	+	0.00979121i	$0.00311669\pi$
$839$			9.70318e9i			0.0195824i	−0.999952	+	0.00979121i	$0.996883\pi$
$840$		0			0
$841$	−7.53890e10			−0.150704
$842$		0			0
$843$	−5.21216e10			−0.103207
$844$		0			0
$845$	3.97031e11	+	1.45333e11i	0.778750	+	0.285061i
$846$		0			0
$847$	−3.82549e11			−0.743282
$848$		0			0
$849$	−7.18827e11			−1.38355
$850$		0			0
$851$			5.80011e11i			1.10591i
$852$		0			0
$853$			4.23212e11i			0.799395i	0.916647	+	0.399697i	$0.130885\pi$
$853$			4.23212e11i			0.799395i	−0.916647	+	0.399697i	$0.869115\pi$
$854$		0			0
$855$	4.04033e9	−	1.10377e10i	0.00756053	−	0.0206544i
$856$		0			0
$857$			6.71291e11i			1.24448i	0.782827	+	0.622239i	$0.213777\pi$
$857$			6.71291e11i			1.24448i	−0.782827	+	0.622239i	$0.786223\pi$
$858$		0			0
$859$			3.79497e11i			0.697005i	0.937308	+	0.348502i	$0.113310\pi$
$859$			3.79497e11i			0.697005i	−0.937308	+	0.348502i	$0.886690\pi$
$860$		0			0
$861$	9.05382e11			1.64748
$862$		0			0
$863$	3.15242e11			0.568330			0.284165	−	0.958775i	$-0.408284\pi$
$863$	3.15242e11			0.568330			0.284165	+	0.958775i	$0.408284\pi$
$864$		0			0
$865$	−1.43779e11	+	3.92787e11i	−0.256822	+	0.701605i
$866$		0			0
$867$	8.72208e10			0.154363
$868$		0			0
$869$	−5.73692e11			−1.00600
$870$		0			0
$871$		−	1.42642e12i		−	2.47841i
$872$		0			0
$873$		−	6.43235e10i		−	0.110742i
$874$		0			0
$875$	−3.34461e11	−	5.86738e11i	−0.570575	−	1.00095i
$876$		0			0
$877$		−	1.04593e12i		−	1.76809i	−0.467405	−	0.884043i	$-0.654811\pi$
$877$		−	1.04593e12i		−	1.76809i	0.467405	−	0.884043i	$-0.345189\pi$
$878$		0			0
$879$		−	3.14759e11i		−	0.527257i
$880$		0			0
$881$	6.83612e10			0.113476			0.0567382	−	0.998389i	$-0.481930\pi$
$881$	6.83612e10			0.113476			0.0567382	+	0.998389i	$0.481930\pi$
$882$		0			0
$883$	7.76186e11			1.27680			0.638400	−	0.769705i	$-0.279597\pi$
$883$	7.76186e11			1.27680			0.638400	+	0.769705i	$0.279597\pi$
$884$		0			0
$885$	−2.88259e11	+	7.87488e11i	−0.469905	+	1.28372i
$886$		0			0
$887$	−2.37333e11			−0.383409			−0.191705	−	0.981453i	$-0.561402\pi$
$887$	−2.37333e11			−0.383409			−0.191705	+	0.981453i	$0.561402\pi$
$888$		0			0
$889$	2.85223e11			0.456644
$890$		0			0
$891$			7.33465e11i			1.16377i
$892$		0			0
$893$		−	5.22381e10i		−	0.0821451i
$894$		0			0
$895$	−9.52744e10	+	2.60278e11i	−0.148486	+	0.405644i
$896$		0			0
$897$		−	6.65456e11i		−	1.02790i
$898$		0			0
$899$		−	6.77074e11i		−	1.03657i
$900$		0			0
$901$	8.68714e11			1.31819
$902$		0			0
$903$	−1.85405e11			−0.278850
$904$		0			0
$905$	1.00524e12	+	3.67969e11i	1.49857	+	0.548551i
$906$		0			0
$907$	−9.84438e11			−1.45465			−0.727326	−	0.686292i	$-0.759237\pi$
$907$	−9.84438e11			−1.45465			−0.727326	+	0.686292i	$0.759237\pi$
$908$		0			0
$909$	−9.39109e8			−0.00137550
$910$		0			0
$911$			6.01816e11i			0.873756i	0.899521	+	0.436878i	$0.143916\pi$
$911$			6.01816e11i			0.873756i	−0.899521	+	0.436878i	$0.856084\pi$
$912$		0			0
$913$			5.10043e11i			0.734047i
$914$		0			0
$915$	2.85426e11	+	1.04480e11i	0.407202	+	0.149056i
$916$		0			0
$917$			3.01000e11i			0.425686i
$918$		0			0
$919$		−	6.81576e11i		−	0.955548i	−0.878483	−	0.477774i	$-0.841444\pi$
$919$		−	6.81576e11i		−	0.955548i	0.878483	−	0.477774i	$-0.158556\pi$
$920$		0			0
$921$	6.23640e11			0.866753
$922$		0			0
$923$	−9.34960e11			−1.28821
$924$		0			0
$925$	6.57745e11	−	7.78054e11i	0.898443	−	1.06278i
$926$		0			0
$927$	6.35734e10			0.0860908
$928$		0			0
$929$	−6.14720e11			−0.825306			−0.412653	−	0.910888i	$-0.635398\pi$
$929$	−6.14720e11			−0.825306			−0.412653	+	0.910888i	$0.635398\pi$
$930$		0			0
$931$		−	6.33788e10i		−	0.0843616i
$932$		0			0
$933$			2.70389e11i			0.356830i
$934$		0			0
$935$	8.42979e11	+	3.08572e11i	1.10299	+	0.403747i
$936$		0			0
$937$			6.96324e11i			0.903344i	0.892184	+	0.451672i	$0.149172\pi$
$937$			6.96324e11i			0.903344i	−0.892184	+	0.451672i	$0.850828\pi$
$938$		0			0
$939$		−	9.53476e11i		−	1.22644i
$940$		0			0
$941$	6.95595e11			0.887152			0.443576	−	0.896237i	$-0.353710\pi$
$941$	6.95595e11			0.887152			0.443576	+	0.896237i	$0.353710\pi$
$942$		0			0
$943$	−9.39553e11			−1.18816
$944$		0			0
$945$	8.95639e11	+	3.27848e11i	1.12307	+	0.411098i
$946$		0			0
$947$	−6.10922e11			−0.759601			−0.379800	−	0.925068i	$-0.624007\pi$
$947$	−6.10922e11			−0.759601			−0.379800	+	0.925068i	$0.624007\pi$
$948$		0			0
$949$	−1.62782e12			−2.00698
$950$		0			0
$951$			1.09983e12i			1.34463i
$952$		0			0
$953$		−	1.33023e12i		−	1.61271i	−0.591431	−	0.806356i	$-0.701437\pi$
$953$		−	1.33023e12i		−	1.61271i	0.591431	−	0.806356i	$-0.298563\pi$
$954$		0			0
$955$	−4.94378e11	+	1.35058e12i	−0.594355	+	1.62370i
$956$		0			0
$957$			9.48197e11i			1.13045i
$958$		0			0
$959$			4.22496e11i			0.499514i
$960$		0			0
$961$	−2.26128e11			−0.265131
$962$		0			0
$963$	5.36886e10			0.0624276
$964$		0			0
$965$	2.58074e11	−	7.05025e11i	0.297601	−	0.813009i
$966$		0			0
$967$	−7.24211e11			−0.828246			−0.414123	−	0.910221i	$-0.635912\pi$
$967$	−7.24211e11			−0.828246			−0.414123	+	0.910221i	$0.635912\pi$
$968$		0			0
$969$	−1.98924e11			−0.225627
$970$		0			0
$971$		−	2.63532e11i		−	0.296453i	−0.988953	−	0.148226i	$-0.952644\pi$
$971$		−	2.63532e11i		−	0.296453i	0.988953	−	0.148226i	$-0.0473564\pi$
$972$		0			0
$973$		−	8.86699e11i		−	0.989293i
$974$		0			0
$975$	−7.54641e11	+	8.92673e11i	−0.835068	+	0.987812i
$976$		0			0
$977$		−	1.12946e12i		−	1.23963i	−0.784748	−	0.619815i	$-0.787208\pi$
$977$		−	1.12946e12i		−	1.23963i	0.784748	−	0.619815i	$-0.212792\pi$
$978$		0			0
$979$			6.28320e11i			0.683991i
$980$		0			0
$981$	−4.64167e10			−0.0501185
$982$		0			0
$983$	−1.31157e12			−1.40468			−0.702339	−	0.711843i	$-0.747861\pi$
$983$	−1.31157e12			−1.40468			−0.702339	+	0.711843i	$0.747861\pi$
$984$		0			0
$985$	2.41577e11	−	6.59958e11i	0.256632	−	0.701086i
$986$		0			0
$987$	3.33417e11			0.351333
$988$		0			0
$989$	1.92403e11			0.201106
$990$		0			0
$991$		−	4.89727e11i		−	0.507761i	−0.967236	−	0.253881i	$-0.918293\pi$
$991$		−	4.89727e11i		−	0.507761i	0.967236	−	0.253881i	$-0.0817071\pi$
$992$		0			0
$993$		−	1.25955e12i		−	1.29545i
$994$		0			0
$995$	4.83389e11	−	1.32056e12i	0.493179	−	1.34730i
$996$		0			0
$997$			9.63334e11i			0.974981i	0.873128	+	0.487490i	$0.162088\pi$
$997$			9.63334e11i			0.974981i	−0.873128	+	0.487490i	$0.837912\pi$
$998$		0			0
$999$			1.43878e12i			1.44455i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	320.9.h.f.319.11		16
4.3	odd	2	inner	320.9.h.f.319.5		16
5.4	even	2	inner	320.9.h.f.319.6		16
8.3	odd	2		80.9.h.d.79.12	yes	16
8.5	even	2		80.9.h.d.79.6	yes	16
20.19	odd	2	inner	320.9.h.f.319.12		16
40.3	even	4		400.9.b.m.351.11		16
40.13	odd	4		400.9.b.m.351.6		16
40.19	odd	2		80.9.h.d.79.5	✓	16
40.27	even	4		400.9.b.m.351.5		16
40.29	even	2		80.9.h.d.79.11	yes	16
40.37	odd	4		400.9.b.m.351.12		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.9.h.d.79.5	✓	16	40.19	odd	2
80.9.h.d.79.6	yes	16	8.5	even	2
80.9.h.d.79.11	yes	16	40.29	even	2
80.9.h.d.79.12	yes	16	8.3	odd	2
320.9.h.f.319.5		16	4.3	odd	2	inner
320.9.h.f.319.6		16	5.4	even	2	inner
320.9.h.f.319.11		16	1.1	even	1	trivial
320.9.h.f.319.12		16	20.19	odd	2	inner
400.9.b.m.351.5		16	40.27	even	4
400.9.b.m.351.6		16	40.13	odd	4
400.9.b.m.351.11		16	40.3	even	4
400.9.b.m.351.12		16	40.37	odd	4

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:	\( N \)	\(=\)	\( 320 = 2^{6} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	320.h (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+77.4652 q^{3} +(-586.915 - 214.840i) q^{5} +2766.32 q^{7} -560.136 q^{9} +O(q^{10})\)	\(q+77.4652 q^{3} +(-586.915 - 214.840i) q^{5} +2766.32 q^{7} -560.136 q^{9} -18778.9i q^{11} +38629.0i q^{13} +(-45465.5 - 16642.6i) q^{15} -76484.1i q^{17} -33574.4i q^{19} +214293. q^{21} -222381. q^{23} +(298313. + 252185. i) q^{25} -551641. q^{27} -651811. q^{29} +1.03876e6i q^{31} -1.45471e6i q^{33} +(-1.62359e6 - 594315. i) q^{35} -2.60818e6i q^{37} +2.99241e6i q^{39} +4.22496e6 q^{41} -865193. q^{43} +(328752. + 120339. i) q^{45} +1.55589e6 q^{47} +1.88771e6 q^{49} -5.92486e6i q^{51} +1.13581e7i q^{53} +(-4.03445e6 + 1.10216e7i) q^{55} -2.60085e6i q^{57} -1.73206e7i q^{59} -6.27787e6 q^{61} -1.54951e6 q^{63} +(8.29905e6 - 2.26720e7i) q^{65} -3.69260e7 q^{67} -1.72268e7 q^{69} +2.42036e7i q^{71} +4.21399e7i q^{73} +(2.31089e7 + 1.95356e7i) q^{75} -5.19484e7i q^{77} -3.05498e7i q^{79} -3.90579e7 q^{81} -2.71605e7 q^{83} +(-1.64318e7 + 4.48897e7i) q^{85} -5.04927e7 q^{87} -3.34588e7 q^{89} +1.06860e8i q^{91} +8.04677e7i q^{93} +(-7.21313e6 + 1.97053e7i) q^{95} +1.14836e8i q^{97} +1.05187e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 600 q^{5} + 42176 q^{9}+O(q^{10}) \) 16 * q - 600 * q^5 + 42176 * q^9	\( 16 q - 600 q^{5} + 42176 q^{9} - 619344 q^{21} + 1137040 q^{25} + 3497568 q^{29} - 2169168 q^{41} + 1930760 q^{45} + 26174912 q^{49} - 22772656 q^{61} + 12524160 q^{65} - 8461392 q^{69} - 224999456 q^{81} + 18124800 q^{85} - 94250976 q^{89}+O(q^{100}) \) 16 * q - 600 * q^5 + 42176 * q^9 - 619344 * q^21 + 1137040 * q^25 + 3497568 * q^29 - 2169168 * q^41 + 1930760 * q^45 + 26174912 * q^49 - 22772656 * q^61 + 12524160 * q^65 - 8461392 * q^69 - 224999456 * q^81 + 18124800 * q^85 - 94250976 * q^89

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more