LMFDB - Embedded newform 1620.4.i.t.1081.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1620,4,Mod(541,1620)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1620, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("1620.541");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1620 = 2^{2} \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1620.i (of order $3$, degree $2$, 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:	$95.5830942093$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 91x^{4} + 570x^{3} + 7860x^{2} + 21600x + 57600 $ x^6 - x^5 + 91x^4 + 570x^3 + 7860x^2 + 21600x + 57600
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1081.2
Root			$-3.48579 + 6.03757i$ of defining polynomial
Character	$\chi$	$=$	1620.1081
Dual form			1620.4.i.t.541.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.50000 + 4.33013i) q^{5} +(-0.606369 - 1.05026i) q^{7} +O(q^{10})$	$q+(-2.50000 + 4.33013i) q^{5} +(-0.606369 - 1.05026i) q^{7} +(-16.8084 - 29.1130i) q^{11} +(-38.7976 + 67.1995i) q^{13} +73.2335 q^{17} +39.2550 q^{19} +(-17.6064 + 30.4951i) q^{23} +(-12.5000 - 21.6506i) q^{25} +(7.89363 + 13.6722i) q^{29} +(-26.1702 + 45.3280i) q^{31} +6.06369 q^{35} -67.1061 q^{37} +(12.5208 - 21.6866i) q^{41} +(15.8717 + 27.4906i) q^{43} +(206.201 + 357.151i) q^{47} +(170.765 - 295.773i) q^{49} +54.7873 q^{53} +168.084 q^{55} +(-257.796 + 446.516i) q^{59} +(-431.445 - 747.284i) q^{61} +(-193.988 - 335.997i) q^{65} +(183.956 - 318.622i) q^{67} -930.929 q^{71} -797.654 q^{73} +(-20.3842 + 35.3064i) q^{77} +(42.7858 + 74.1073i) q^{79} +(-45.9783 - 79.6368i) q^{83} +(-183.084 + 317.110i) q^{85} +888.252 q^{89} +94.1028 q^{91} +(-98.1374 + 169.979i) q^{95} +(-166.554 - 288.479i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 15 q^{5} + 3 q^{7}+O(q^{10}) $ 6 * q - 15 * q^5 + 3 * q^7	$ 6 q - 15 q^{5} + 3 q^{7} + 24 q^{11} - 3 q^{13} - 60 q^{17} - 54 q^{19} - 99 q^{23} - 75 q^{25} + 54 q^{29} - 72 q^{31} - 30 q^{35} - 36 q^{37} - 411 q^{41} - 444 q^{43} + 75 q^{47} - 204 q^{49} + 342 q^{53} - 240 q^{55} - 297 q^{59} - 684 q^{61} - 15 q^{65} - 12 q^{67} + 1284 q^{71} - 132 q^{73} - 1044 q^{77} - 1122 q^{79} - 90 q^{83} + 150 q^{85} + 1512 q^{89} - 3306 q^{91} + 135 q^{95} - 1536 q^{97}+O(q^{100}) $ 6 * q - 15 * q^5 + 3 * q^7 + 24 * q^11 - 3 * q^13 - 60 * q^17 - 54 * q^19 - 99 * q^23 - 75 * q^25 + 54 * q^29 - 72 * q^31 - 30 * q^35 - 36 * q^37 - 411 * q^41 - 444 * q^43 + 75 * q^47 - 204 * q^49 + 342 * q^53 - 240 * q^55 - 297 * q^59 - 684 * q^61 - 15 * q^65 - 12 * q^67 + 1284 * q^71 - 132 * q^73 - 1044 * q^77 - 1122 * q^79 - 90 * q^83 + 150 * q^85 + 1512 * q^89 - 3306 * q^91 + 135 * q^95 - 1536 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times$.

$n$	$811$	$1297$	$1541$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−2.50000	+	4.33013i	−0.223607	+	0.387298i
$5$	−2.50000	+	4.33013i	−0.223607	+	0.387298i
$6$		0			0
$7$	−0.606369	−	1.05026i	−0.0327409	−	0.0567088i	0.849191	−	0.528086i	$-0.177090\pi$
$7$	−0.606369	−	1.05026i	−0.0327409	−	0.0567088i	−0.881932	+	0.471378i	$0.843757\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−16.8084	−	29.1130i	−0.460720	−	0.797990i	0.538277	−	0.842768i	$-0.319075\pi$
$11$	−16.8084	−	29.1130i	−0.460720	−	0.797990i	−0.998997	+	0.0447780i	$0.985742\pi$
$12$		0			0
$13$	−38.7976	+	67.1995i	−0.827733	+	1.43368i	0.0720795	+	0.997399i	$0.477036\pi$
$13$	−38.7976	+	67.1995i	−0.827733	+	1.43368i	−0.899813	+	0.436277i	$0.856297\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	73.2335			1.04481			0.522404	−	0.852698i	$-0.325035\pi$
$17$	73.2335			1.04481			0.522404	+	0.852698i	$0.325035\pi$
$18$		0			0
$19$	39.2550			0.473985			0.236992	−	0.971512i	$-0.423838\pi$
$19$	39.2550			0.473985			0.236992	+	0.971512i	$0.423838\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−17.6064	+	30.4951i	−0.159617	+	0.276464i	−0.934730	−	0.355358i	$-0.884359\pi$
$23$	−17.6064	+	30.4951i	−0.159617	+	0.276464i	0.775114	+	0.631822i	$0.217692\pi$
$24$		0			0
$25$	−12.5000	−	21.6506i	−0.100000	−	0.173205i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	7.89363	+	13.6722i	0.0505452	+	0.0875468i	0.890191	−	0.455587i	$-0.150571\pi$
$29$	7.89363	+	13.6722i	0.0505452	+	0.0875468i	−0.839646	+	0.543134i	$0.817237\pi$
$30$		0			0
$31$	−26.1702	+	45.3280i	−0.151623	+	0.262618i	−0.931824	−	0.362910i	$-0.881783\pi$
$31$	−26.1702	+	45.3280i	−0.151623	+	0.262618i	0.780202	+	0.625528i	$0.215116\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	6.06369			0.0292843
$36$		0			0
$37$	−67.1061			−0.298167			−0.149083	−	0.988825i	$-0.547632\pi$
$37$	−67.1061			−0.298167			−0.149083	+	0.988825i	$0.547632\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	12.5208	−	21.6866i	0.0476930	−	0.0826067i	−0.841193	−	0.540734i	$-0.818146\pi$
$41$	12.5208	−	21.6866i	0.0476930	−	0.0826067i	0.888886	+	0.458128i	$0.151480\pi$
$42$		0			0
$43$	15.8717	+	27.4906i	0.0562887	+	0.0974949i	0.892797	−	0.450460i	$-0.148740\pi$
$43$	15.8717	+	27.4906i	0.0562887	+	0.0974949i	−0.836508	+	0.547955i	$0.815407\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	206.201	+	357.151i	0.639947	+	1.10842i	0.985444	+	0.170001i	$0.0543770\pi$
$47$	206.201	+	357.151i	0.639947	+	1.10842i	−0.345497	+	0.938420i	$0.612290\pi$
$48$		0			0
$49$	170.765	−	295.773i	0.497856	−	0.862312i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	54.7873			0.141993			0.0709963	−	0.997477i	$-0.477382\pi$
$53$	54.7873			0.141993			0.0709963	+	0.997477i	$0.477382\pi$
$54$		0			0
$55$	168.084			0.412080
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−257.796	+	446.516i	−0.568851	+	0.985279i	0.427829	+	0.903860i	$0.359279\pi$
$59$	−257.796	+	446.516i	−0.568851	+	0.985279i	−0.996680	+	0.0814195i	$0.974055\pi$
$60$		0			0
$61$	−431.445	−	747.284i	−0.905588	−	1.56852i	−0.820126	−	0.572182i	$-0.806097\pi$
$61$	−431.445	−	747.284i	−0.905588	−	1.56852i	−0.0854613	−	0.996341i	$-0.527236\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−193.988	−	335.997i	−0.370173	−	0.641159i
$66$		0			0
$67$	183.956	−	318.622i	0.335431	−	0.580983i	−0.648137	−	0.761524i	$-0.724452\pi$
$67$	183.956	−	318.622i	0.335431	−	0.580983i	0.983567	+	0.180541i	$0.0577849\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−930.929			−1.55607			−0.778035	−	0.628221i	$-0.783783\pi$
$71$	−930.929			−1.55607			−0.778035	+	0.628221i	$0.783783\pi$
$72$		0			0
$73$	−797.654			−1.27888			−0.639441	−	0.768840i	$-0.720834\pi$
$73$	−797.654			−1.27888			−0.639441	+	0.768840i	$0.720834\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−20.3842	+	35.3064i	−0.0301687	+	0.0522537i
$78$		0			0
$79$	42.7858	+	74.1073i	0.0609340	+	0.105541i	0.894883	−	0.446301i	$-0.147259\pi$
$79$	42.7858	+	74.1073i	0.0609340	+	0.105541i	−0.833949	+	0.551841i	$0.813925\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−45.9783	−	79.6368i	−0.0608046	−	0.105317i	0.834021	−	0.551733i	$-0.186033\pi$
$83$	−45.9783	−	79.6368i	−0.0608046	−	0.105317i	−0.894825	+	0.446417i	$0.852700\pi$
$84$		0			0
$85$	−183.084	+	317.110i	−0.233626	+	0.404652i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	888.252			1.05792			0.528958	−	0.848648i	$-0.322583\pi$
$89$	888.252			1.05792			0.528958	+	0.848648i	$0.322583\pi$
$90$		0			0
$91$	94.1028			0.108403
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−98.1374	+	169.979i	−0.105986	+	0.183573i
$96$		0			0
$97$	−166.554	−	288.479i	−0.174340	−	0.301965i	0.765593	−	0.643325i	$-0.222446\pi$
$97$	−166.554	−	288.479i	−0.174340	−	0.301965i	−0.939933	+	0.341360i	$0.889112\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−770.912	−	1335.26i	−0.759492	−	1.31548i	−0.943110	−	0.332481i	$-0.892114\pi$
$101$	−770.912	−	1335.26i	−0.759492	−	1.31548i	0.183618	−	0.982998i	$-0.441219\pi$
$102$		0			0
$103$	−568.282	+	984.294i	−0.543636	+	0.941605i	0.455055	+	0.890463i	$0.349620\pi$
$103$	−568.282	+	984.294i	−0.543636	+	0.941605i	−0.998691	+	0.0511422i	$0.983714\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1437.65			1.29891			0.649454	−	0.760401i	$-0.274997\pi$
$107$	1437.65			1.29891			0.649454	+	0.760401i	$0.274997\pi$
$108$		0			0
$109$	−414.599			−0.364324			−0.182162	−	0.983269i	$-0.558310\pi$
$109$	−414.599			−0.364324			−0.182162	+	0.983269i	$0.558310\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−379.041	+	656.519i	−0.315550	+	0.546549i	−0.979554	−	0.201180i	$-0.935522\pi$
$113$	−379.041	+	656.519i	−0.315550	+	0.546549i	0.664004	+	0.747729i	$0.268856\pi$
$114$		0			0
$115$	−88.0318	−	152.476i	−0.0713827	−	0.123638i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−44.4065	−	76.9144i	−0.0342079	−	0.0592498i
$120$		0			0
$121$	100.457	−	173.997i	0.0754749	−	0.130726i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	125.000			0.0894427
$126$		0			0
$127$	−2154.40			−1.50529			−0.752646	−	0.658426i	$-0.771223\pi$
$127$	−2154.40			−1.50529			−0.752646	+	0.658426i	$0.771223\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	337.708	−	584.927i	0.225234	−	0.390117i	−0.731155	−	0.682211i	$-0.761019\pi$
$131$	337.708	−	584.927i	0.225234	−	0.390117i	0.956390	+	0.292094i	$0.0943519\pi$
$132$		0			0
$133$	−23.8030	−	41.2280i	−0.0155187	−	0.0268791i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	175.675	+	304.279i	0.109555	+	0.189754i	0.915590	−	0.402113i	$-0.131724\pi$
$137$	175.675	+	304.279i	0.109555	+	0.189754i	−0.806035	+	0.591867i	$0.798391\pi$
$138$		0			0
$139$	411.883	−	713.402i	0.251334	−	0.435324i	−0.712559	−	0.701612i	$-0.752464\pi$
$139$	411.883	−	713.402i	0.251334	−	0.435324i	0.963893	+	0.266288i	$0.0857973\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	2608.50			1.52541
$144$		0			0
$145$	−78.9363			−0.0452090
$146$		0			0
$147$		0			0
$148$		0			0
$149$	130.913	−	226.748i	0.0719787	−	0.124671i	−0.827790	−	0.561038i	$-0.810402\pi$
$149$	130.913	−	226.748i	0.0719787	−	0.124671i	0.899768	+	0.436368i	$0.143735\pi$
$150$		0			0
$151$	−1189.34	−	2059.99i	−0.640972	−	1.11020i	−0.985216	−	0.171316i	$-0.945198\pi$
$151$	−1189.34	−	2059.99i	−0.640972	−	1.11020i	0.344244	−	0.938880i	$-0.388135\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−130.851	−	226.640i	−0.0678077	−	0.117446i
$156$		0			0
$157$	952.389	−	1649.59i	0.484133	−	0.838543i	−0.515701	−	0.856769i	$-0.672468\pi$
$157$	952.389	−	1649.59i	0.484133	−	0.838543i	0.999834	+	0.0182255i	$0.00580167\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	42.7038			0.0209039
$162$		0			0
$163$	−777.966			−0.373834			−0.186917	−	0.982376i	$-0.559850\pi$
$163$	−777.966			−0.373834			−0.186917	+	0.982376i	$0.559850\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−809.103	+	1401.41i	−0.374912	+	0.649366i	−0.990314	−	0.138847i	$-0.955660\pi$
$167$	−809.103	+	1401.41i	−0.374912	+	0.649366i	0.615402	+	0.788213i	$0.288994\pi$
$168$		0			0
$169$	−1912.01	−	3311.71i	−0.870284	−	1.50738i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−1549.52	−	2683.84i	−0.680968	−	1.17947i	−0.974686	−	0.223579i	$-0.928226\pi$
$173$	−1549.52	−	2683.84i	−0.680968	−	1.17947i	0.293718	−	0.955892i	$-0.405107\pi$
$174$		0			0
$175$	−15.1592	+	26.2566i	−0.00654817	+	0.0113418i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−382.395			−0.159673			−0.0798367	−	0.996808i	$-0.525440\pi$
$179$	−382.395			−0.159673			−0.0798367	+	0.996808i	$0.525440\pi$
$180$		0			0
$181$	−1665.87			−0.684107			−0.342053	−	0.939681i	$-0.611122\pi$
$181$	−1665.87			−0.684107			−0.342053	+	0.939681i	$0.611122\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	167.765	−	290.578i	0.0666722	−	0.115480i
$186$		0			0
$187$	−1230.94	−	2132.04i	−0.481363	−	0.833746i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	183.743	+	318.252i	0.0696081	+	0.120565i	0.898729	−	0.438505i	$-0.144492\pi$
$191$	183.743	+	318.252i	0.0696081	+	0.120565i	−0.829121	+	0.559070i	$0.811158\pi$
$192$		0			0
$193$	1031.44	−	1786.51i	0.384687	−	0.666298i	−0.607038	−	0.794672i	$-0.707643\pi$
$193$	1031.44	−	1786.51i	0.384687	−	0.666298i	0.991726	+	0.128375i	$0.0409760\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−1783.87			−0.645155			−0.322578	−	0.946543i	$-0.604549\pi$
$197$	−1783.87			−0.645155			−0.322578	+	0.946543i	$0.604549\pi$
$198$		0			0
$199$	−4475.65			−1.59432			−0.797162	−	0.603766i	$-0.793666\pi$
$199$	−4475.65			−1.59432			−0.797162	+	0.603766i	$0.793666\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	9.57291	−	16.5808i	0.00330979	−	0.00573272i
$204$		0			0
$205$	62.6038	+	108.433i	0.0213290	+	0.0369429i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−659.812	−	1142.83i	−0.218374	−	0.378235i
$210$		0			0
$211$	1709.72	−	2961.33i	0.557831	−	0.966191i	−0.439847	−	0.898073i	$-0.644967\pi$
$211$	1709.72	−	2961.33i	0.557831	−	0.966191i	0.997677	−	0.0681182i	$-0.0216995\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−158.717			−0.0503461
$216$		0			0
$217$	63.4751			0.0198570
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−2841.29	+	4921.25i	−0.864822	+	1.49792i
$222$		0			0
$223$	−2703.23	−	4682.13i	−0.811756	−	1.40600i	−0.911634	−	0.411003i	$-0.865178\pi$
$223$	−2703.23	−	4682.13i	−0.811756	−	1.40600i	0.0998776	−	0.995000i	$-0.468155\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−3078.92	−	5332.84i	−0.900242	−	1.55927i	−0.827180	−	0.561938i	$-0.810056\pi$
$227$	−3078.92	−	5332.84i	−0.900242	−	1.55927i	−0.0730625	−	0.997327i	$-0.523277\pi$
$228$		0			0
$229$	−1831.31	+	3171.91i	−0.528454	+	0.915310i	0.470995	+	0.882136i	$0.343895\pi$
$229$	−1831.31	+	3171.91i	−0.528454	+	0.915310i	−0.999450	+	0.0331741i	$0.989438\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	1548.60			0.435417			0.217709	−	0.976014i	$-0.430142\pi$
$233$	1548.60			0.435417			0.217709	+	0.976014i	$0.430142\pi$
$234$		0			0
$235$	−2062.01			−0.572386
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−1337.21	+	2316.12i	−0.361913	+	0.626851i	−0.988276	−	0.152681i	$-0.951209\pi$
$239$	−1337.21	+	2316.12i	−0.361913	+	0.626851i	0.626363	+	0.779531i	$0.284543\pi$
$240$		0			0
$241$	1174.28	+	2033.91i	0.313867	+	0.543634i	0.979196	−	0.202916i	$-0.0650419\pi$
$241$	1174.28	+	2033.91i	0.313867	+	0.543634i	−0.665329	+	0.746551i	$0.731709\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	853.823	+	1478.87i	0.222648	+	0.385638i
$246$		0			0
$247$	−1523.00	+	2637.91i	−0.392333	+	0.679540i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	6495.60			1.63346			0.816731	−	0.577019i	$-0.195784\pi$
$251$	6495.60			1.63346			0.816731	+	0.577019i	$0.195784\pi$
$252$		0			0
$253$	1183.74			0.294154
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−1231.64	+	2133.27i	−0.298941	+	0.517780i	−0.975894	−	0.218246i	$-0.929967\pi$
$257$	−1231.64	+	2133.27i	−0.298941	+	0.517780i	0.676953	+	0.736026i	$0.263300\pi$
$258$		0			0
$259$	40.6911	+	70.4790i	0.00976224	+	0.0169087i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	797.090	+	1380.60i	0.186885	+	0.323694i	0.944210	−	0.329344i	$-0.106828\pi$
$263$	797.090	+	1380.60i	0.186885	+	0.323694i	−0.757325	+	0.653038i	$0.773494\pi$
$264$		0			0
$265$	−136.968	+	237.236i	−0.0317505	+	0.0549935i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	2980.25			0.675497			0.337749	−	0.941236i	$-0.390335\pi$
$269$	2980.25			0.675497			0.337749	+	0.941236i	$0.390335\pi$
$270$		0			0
$271$	−7179.35			−1.60928			−0.804639	−	0.593764i	$-0.797641\pi$
$271$	−7179.35			−1.60928			−0.804639	+	0.593764i	$0.797641\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−420.209	+	727.824i	−0.0921439	+	0.159598i
$276$		0			0
$277$	−2187.92	−	3789.60i	−0.474583	−	0.822003i	0.524993	−	0.851107i	$-0.324068\pi$
$277$	−2187.92	−	3789.60i	−0.474583	−	0.822003i	−0.999576	+	0.0291040i	$0.990735\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	653.614	+	1132.09i	0.138759	+	0.240338i	0.927027	−	0.374994i	$-0.122355\pi$
$281$	653.614	+	1132.09i	0.138759	+	0.240338i	−0.788268	+	0.615332i	$0.789022\pi$
$282$		0			0
$283$	−192.222	+	332.938i	−0.0403760	+	0.0699332i	−0.885507	−	0.464626i	$-0.846189\pi$
$283$	−192.222	+	332.938i	−0.0403760	+	0.0699332i	0.845131	+	0.534559i	$0.179522\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−30.3688			−0.00624604
$288$		0			0
$289$	450.145			0.0916232
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−795.885	+	1378.51i	−0.158690	+	0.274859i	−0.934396	−	0.356235i	$-0.884060\pi$
$293$	−795.885	+	1378.51i	−0.158690	+	0.274859i	0.775707	+	0.631094i	$0.217394\pi$
$294$		0			0
$295$	−1288.98	−	2232.58i	−0.254398	−	0.440630i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−1366.17	−	2366.28i	−0.264240	−	0.457677i
$300$		0			0
$301$	19.2482	−	33.3389i	0.00368588	−	0.00638413i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	4314.45			0.809982
$306$		0			0
$307$	−3144.68			−0.584613			−0.292306	−	0.956325i	$-0.594423\pi$
$307$	−3144.68			−0.584613			−0.292306	+	0.956325i	$0.594423\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−1300.24	+	2252.08i	−0.237074	+	0.410623i	−0.959873	−	0.280434i	$-0.909522\pi$
$311$	−1300.24	+	2252.08i	−0.237074	+	0.410623i	0.722800	+	0.691058i	$0.242855\pi$
$312$		0			0
$313$	−3724.54	−	6451.09i	−0.672598	−	1.16497i	−0.977165	−	0.212483i	$-0.931845\pi$
$313$	−3724.54	−	6451.09i	−0.672598	−	1.16497i	0.304566	−	0.952491i	$-0.401489\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−1656.03	−	2868.33i	−0.293413	−	0.508206i	0.681202	−	0.732096i	$-0.261458\pi$
$317$	−1656.03	−	2868.33i	−0.293413	−	0.508206i	−0.974614	+	0.223890i	$0.928124\pi$
$318$		0			0
$319$	265.358	−	459.614i	0.0465743	−	0.0806691i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	2874.78			0.495223
$324$		0			0
$325$	1939.88			0.331093
$326$		0			0
$327$		0			0
$328$		0			0
$329$	250.068	−	433.130i	0.0419048	−	0.0725813i
$330$		0			0
$331$	−549.581	−	951.902i	−0.0912619	−	0.158070i	0.816780	−	0.576949i	$-0.195757\pi$
$331$	−549.581	−	951.902i	−0.0912619	−	0.158070i	−0.908042	+	0.418878i	$0.862423\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	919.782	+	1593.11i	0.150009	+	0.259823i
$336$		0			0
$337$	−454.308	+	786.885i	−0.0734355	+	0.127194i	−0.900405	−	0.435053i	$-0.856730\pi$
$337$	−454.308	+	786.885i	−0.0734355	+	0.127194i	0.826969	+	0.562247i	$0.190063\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	1759.51			0.279422
$342$		0			0
$343$	−830.155			−0.130683
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−435.939	+	755.068i	−0.0674421	+	0.116813i	−0.897775	−	0.440455i	$-0.854817\pi$
$347$	−435.939	+	755.068i	−0.0674421	+	0.116813i	0.830333	+	0.557268i	$0.188150\pi$
$348$		0			0
$349$	−5252.91	−	9098.31i	−0.805679	−	1.39548i	−0.915832	−	0.401562i	$-0.868468\pi$
$349$	−5252.91	−	9098.31i	−0.805679	−	1.39548i	0.110154	−	0.993915i	$-0.464866\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−431.811	−	747.919i	−0.0651076	−	0.112770i	0.831634	−	0.555324i	$-0.187406\pi$
$353$	−431.811	−	747.919i	−0.0651076	−	0.112770i	−0.896742	+	0.442554i	$0.854072\pi$
$354$		0			0
$355$	2327.32	−	4031.04i	0.347948	−	0.602663i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−8942.54			−1.31468			−0.657339	−	0.753595i	$-0.728318\pi$
$359$	−8942.54			−1.31468			−0.657339	+	0.753595i	$0.728318\pi$
$360$		0			0
$361$	−5318.05			−0.775339
$362$		0			0
$363$		0			0
$364$		0			0
$365$	1994.14	−	3453.94i	0.285967	−	0.495309i
$366$		0			0
$367$	−742.035	−	1285.24i	−0.105542	−	0.182804i	0.808418	−	0.588609i	$-0.200324\pi$
$367$	−742.035	−	1285.24i	−0.105542	−	0.182804i	−0.913960	+	0.405805i	$0.866991\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−33.2213	−	57.5410i	−0.00464896	−	0.00805224i
$372$		0			0
$373$	2055.42	−	3560.08i	0.285323	−	0.494194i	−0.687365	−	0.726313i	$-0.741233\pi$
$373$	2055.42	−	3560.08i	0.285323	−	0.494194i	0.972687	+	0.232119i	$0.0745659\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−1225.02			−0.167352
$378$		0			0
$379$	1154.58			0.156482			0.0782411	−	0.996934i	$-0.475070\pi$
$379$	1154.58			0.156482			0.0782411	+	0.996934i	$0.475070\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	6390.50	−	11068.7i	0.852583	−	1.47672i	−0.0262862	−	0.999654i	$-0.508368\pi$
$383$	6390.50	−	11068.7i	0.852583	−	1.47672i	0.878869	−	0.477063i	$-0.158299\pi$
$384$		0			0
$385$	−101.921	−	176.532i	−0.0134919	−	0.0233686i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−2910.92	−	5041.87i	−0.379408	−	0.657154i	0.611568	−	0.791192i	$-0.290539\pi$
$389$	−2910.92	−	5041.87i	−0.379408	−	0.657154i	−0.990976	+	0.134038i	$0.957206\pi$
$390$		0			0
$391$	−1289.38	+	2233.26i	−0.166769	+	0.288852i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−427.858			−0.0545010
$396$		0			0
$397$	3889.97			0.491768			0.245884	−	0.969299i	$-0.420922\pi$
$397$	3889.97			0.491768			0.245884	+	0.969299i	$0.420922\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−5691.37	+	9857.74i	−0.708762	+	1.22761i	0.256555	+	0.966530i	$0.417413\pi$
$401$	−5691.37	+	9857.74i	−0.708762	+	1.22761i	−0.965317	+	0.261082i	$0.915921\pi$
$402$		0			0
$403$	−2030.68	−	3517.24i	−0.251006	−	0.434755i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	1127.94	+	1953.66i	0.137371	+	0.237934i
$408$		0			0
$409$	6153.11	−	10657.5i	0.743892	−	1.28846i	−0.206819	−	0.978379i	$-0.566311\pi$
$409$	6153.11	−	10657.5i	0.743892	−	1.28846i	0.950711	−	0.310079i	$-0.100355\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	625.279			0.0744987
$414$		0			0
$415$	459.783			0.0543852
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−4152.99	+	7193.18i	−0.484216	+	0.838687i	−0.999836	−	0.0181304i	$-0.994229\pi$
$419$	−4152.99	+	7193.18i	−0.484216	+	0.838687i	0.515619	+	0.856818i	$0.327562\pi$
$420$		0			0
$421$	3093.44	+	5358.00i	0.358112	+	0.620268i	0.987645	−	0.156705i	$-0.0500873\pi$
$421$	3093.44	+	5358.00i	0.358112	+	0.620268i	−0.629533	+	0.776973i	$0.716754\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−915.419	−	1585.55i	−0.104481	−	0.180966i
$426$		0			0
$427$	−523.230	+	906.260i	−0.0592994	+	0.102710i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−15220.5			−1.70103			−0.850515	−	0.525951i	$-0.823710\pi$
$431$	−15220.5			−1.70103			−0.850515	+	0.525951i	$0.823710\pi$
$432$		0			0
$433$	−7462.98			−0.828287			−0.414143	−	0.910212i	$-0.635919\pi$
$433$	−7462.98			−0.828287			−0.414143	+	0.910212i	$0.635919\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−691.137	+	1197.09i	−0.0756558	+	0.131040i
$438$		0			0
$439$	7433.97	+	12876.0i	0.808210	+	1.39986i	0.914103	+	0.405483i	$0.132897\pi$
$439$	7433.97	+	12876.0i	0.808210	+	1.39986i	−0.105893	+	0.994378i	$0.533770\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	3963.86	+	6865.61i	0.425122	+	0.736332i	0.996432	−	0.0844020i	$-0.0268980\pi$
$443$	3963.86	+	6865.61i	0.425122	+	0.736332i	−0.571310	+	0.820734i	$0.693565\pi$
$444$		0			0
$445$	−2220.63	+	3846.24i	−0.236557	+	0.409729i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	17711.1			1.86155			0.930776	−	0.365591i	$-0.119133\pi$
$449$	17711.1			1.86155			0.930776	+	0.365591i	$0.119133\pi$
$450$		0			0
$451$	−841.814			−0.0878924
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−235.257	+	407.477i	−0.0242396	+	0.0419842i
$456$		0			0
$457$	5465.55	+	9466.61i	0.559448	+	0.968992i	0.997543	+	0.0700635i	$0.0223202\pi$
$457$	5465.55	+	9466.61i	0.559448	+	0.968992i	−0.438094	+	0.898929i	$0.644346\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−6768.03	−	11722.6i	−0.683771	−	1.18433i	−0.973821	−	0.227315i	$-0.927005\pi$
$461$	−6768.03	−	11722.6i	−0.683771	−	1.18433i	0.290050	−	0.957011i	$-0.406328\pi$
$462$		0			0
$463$	−8057.32	+	13955.7i	−0.808759	+	1.40081i	0.104964	+	0.994476i	$0.466527\pi$
$463$	−8057.32	+	13955.7i	−0.808759	+	1.40081i	−0.913724	+	0.406336i	$0.866806\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	3672.75			0.363929			0.181964	−	0.983305i	$-0.441754\pi$
$467$	3672.75			0.363929			0.181964	+	0.983305i	$0.441754\pi$
$468$		0			0
$469$	−446.182			−0.0439291
$470$		0			0
$471$		0			0
$472$		0			0
$473$	533.555	−	924.145i	0.0518666	−	0.0898356i
$474$		0			0
$475$	−490.687	−	849.895i	−0.0473985	−	0.0820965i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	2604.05	+	4510.36i	0.248397	+	0.430237i	0.963081	−	0.269211i	$-0.0867628\pi$
$479$	2604.05	+	4510.36i	0.248397	+	0.430237i	−0.714684	+	0.699447i	$0.753429\pi$
$480$		0			0
$481$	2603.56	−	4509.50i	0.246803	−	0.427475i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	1665.54			0.155934
$486$		0			0
$487$	−16705.3			−1.55439			−0.777197	−	0.629257i	$-0.783359\pi$
$487$	−16705.3			−1.55439			−0.777197	+	0.629257i	$0.783359\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	5988.77	−	10372.9i	0.550447	−	0.953402i	−0.447795	−	0.894136i	$-0.647791\pi$
$491$	5988.77	−	10372.9i	0.550447	−	0.953402i	0.998242	−	0.0592661i	$-0.0188760\pi$
$492$		0			0
$493$	578.078	+	1001.26i	0.0528100	+	0.0914696i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	564.487	+	977.720i	0.0509471	+	0.0882429i
$498$		0			0
$499$	−2864.72	+	4961.84i	−0.256999	+	0.445135i	−0.965436	−	0.260638i	$-0.916067\pi$
$499$	−2864.72	+	4961.84i	−0.256999	+	0.445135i	0.708438	+	0.705773i	$0.249400\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	13436.4			1.19105			0.595524	−	0.803337i	$-0.296944\pi$
$503$	13436.4			1.19105			0.595524	+	0.803337i	$0.296944\pi$
$504$		0			0
$505$	7709.12			0.679310
$506$		0			0
$507$		0			0
$508$		0			0
$509$	676.942	−	1172.50i	0.0589488	−	0.102102i	−0.835045	−	0.550182i	$-0.814558\pi$
$509$	676.942	−	1172.50i	0.0589488	−	0.102102i	0.893994	+	0.448079i	$0.147892\pi$
$510$		0			0
$511$	483.673	+	837.746i	0.0418717	+	0.0725239i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−2841.41	−	4921.47i	−0.243121	−	0.421099i
$516$		0			0
$517$	6931.81	−	12006.2i	0.589672	−	1.02134i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−13883.9			−1.16749			−0.583747	−	0.811935i	$-0.698414\pi$
$521$	−13883.9			−1.16749			−0.583747	+	0.811935i	$0.698414\pi$
$522$		0			0
$523$	21068.5			1.76149			0.880745	−	0.473591i	$-0.157042\pi$
$523$	21068.5			1.76149			0.880745	+	0.473591i	$0.157042\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1916.53	+	3319.53i	−0.158416	+	0.274385i
$528$		0			0
$529$	5463.53	+	9463.11i	0.449045	+	0.777769i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	971.552	+	1682.78i	0.0789542	+	0.136753i
$534$		0			0
$535$	−3594.13	+	6225.22i	−0.290445	+	0.503065i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−11481.1			−0.917488
$540$		0			0
$541$	9944.84			0.790318			0.395159	−	0.918613i	$-0.370690\pi$
$541$	9944.84			0.790318			0.395159	+	0.918613i	$0.370690\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	1036.50	−	1795.26i	0.0814654	−	0.141102i
$546$		0			0
$547$	312.355	+	541.015i	0.0244156	+	0.0422891i	0.877975	−	0.478706i	$-0.158894\pi$
$547$	312.355	+	541.015i	0.0244156	+	0.0422891i	−0.853559	+	0.520996i	$0.825561\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	309.864	+	536.701i	0.0239576	+	0.0414958i
$552$		0			0
$553$	51.8880	−	89.8727i	0.00399006	−	0.00691099i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−3677.40			−0.279742			−0.139871	−	0.990170i	$-0.544669\pi$
$557$	−3677.40			−0.279742			−0.139871	+	0.990170i	$0.544669\pi$
$558$		0			0
$559$	−2463.14			−0.186368
$560$		0			0
$561$		0			0
$562$		0			0
$563$	7853.02	−	13601.8i	0.587861	−	1.01820i	−0.406652	−	0.913583i	$-0.633304\pi$
$563$	7853.02	−	13601.8i	0.587861	−	1.01820i	0.994512	−	0.104621i	$-0.0333630\pi$
$564$		0			0
$565$	−1895.21	−	3282.59i	−0.141118	−	0.244424i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	2893.22	+	5011.21i	0.213164	+	0.369210i	0.952703	−	0.303903i	$-0.0982899\pi$
$569$	2893.22	+	5011.21i	0.213164	+	0.369210i	−0.739539	+	0.673113i	$0.764957\pi$
$570$		0			0
$571$	−3382.19	+	5858.12i	−0.247881	+	0.429343i	−0.962938	−	0.269724i	$-0.913068\pi$
$571$	−3382.19	+	5858.12i	−0.247881	+	0.429343i	0.715057	+	0.699067i	$0.246401\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	880.318			0.0638466
$576$		0			0
$577$	9208.77			0.664413			0.332207	−	0.943207i	$-0.392207\pi$
$577$	9208.77			0.664413			0.332207	+	0.943207i	$0.392207\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−55.7597	+	96.5786i	−0.00398159	+	0.00689631i
$582$		0			0
$583$	−920.885	−	1595.02i	−0.0654188	−	0.113309i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	9458.83	+	16383.2i	0.665090	+	1.15197i	0.979261	+	0.202603i	$0.0649402\pi$
$587$	9458.83	+	16383.2i	0.665090	+	1.15197i	−0.314171	+	0.949366i	$0.601726\pi$
$588$		0			0
$589$	−1027.31	+	1779.35i	−0.0718667	+	0.124477i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	16715.2			1.15752			0.578762	−	0.815497i	$-0.303536\pi$
$593$	16715.2			1.15752			0.578762	+	0.815497i	$0.303536\pi$
$594$		0			0
$595$	444.065			0.0305965
$596$		0			0
$597$		0			0
$598$		0			0
$599$	10521.1	−	18223.1i	0.717664	−	1.24303i	−0.244259	−	0.969710i	$-0.578545\pi$
$599$	10521.1	−	18223.1i	0.717664	−	1.24303i	0.961923	−	0.273320i	$-0.0881219\pi$
$600$		0			0
$601$	−731.468	−	1266.94i	−0.0496459	−	0.0859893i	0.840135	−	0.542378i	$-0.182476\pi$
$601$	−731.468	−	1266.94i	−0.0496459	−	0.0859893i	−0.889780	+	0.456389i	$0.849143\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	502.286	+	869.984i	0.0337534	+	0.0584626i
$606$		0			0
$607$	4750.62	−	8228.32i	0.317664	−	0.550210i	−0.662336	−	0.749207i	$-0.730435\pi$
$607$	4750.62	−	8228.32i	0.317664	−	0.550210i	0.980000	+	0.198997i	$0.0637684\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−32000.4			−2.11882
$612$		0			0
$613$	20347.2			1.34064			0.670322	−	0.742070i	$-0.266156\pi$
$613$	20347.2			1.34064			0.670322	+	0.742070i	$0.266156\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−196.273	+	339.955i	−0.0128066	+	0.0221817i	−0.872358	−	0.488868i	$-0.837410\pi$
$617$	−196.273	+	339.955i	−0.0128066	+	0.0221817i	0.859551	+	0.511050i	$0.170743\pi$
$618$		0			0
$619$	−7235.06	−	12531.5i	−0.469793	−	0.813705i	0.529611	−	0.848241i	$-0.322338\pi$
$619$	−7235.06	−	12531.5i	−0.469793	−	0.813705i	−0.999403	+	0.0345359i	$0.989005\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−538.608	−	932.897i	−0.0346371	−	0.0599932i
$624$		0			0
$625$	−312.500	+	541.266i	−0.0200000	+	0.0346410i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−4914.42			−0.311527
$630$		0			0
$631$	10534.0			0.664585			0.332293	−	0.943176i	$-0.392178\pi$
$631$	10534.0			0.664585			0.332293	+	0.943176i	$0.392178\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	5386.00	−	9328.82i	0.336593	−	0.582997i
$636$		0			0
$637$	13250.5	+	22950.6i	0.824184	+	1.42753i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	1366.89	+	2367.53i	0.0842262	+	0.145884i	0.905061	−	0.425281i	$-0.139825\pi$
$641$	1366.89	+	2367.53i	0.0842262	+	0.145884i	−0.820835	+	0.571165i	$0.806491\pi$
$642$		0			0
$643$	−11246.3	+	19479.1i	−0.689751	+	1.19468i	0.282168	+	0.959365i	$0.408947\pi$
$643$	−11246.3	+	19479.1i	−0.689751	+	1.19468i	−0.971918	+	0.235318i	$0.924387\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−18181.3			−1.10476			−0.552381	−	0.833592i	$-0.686281\pi$
$647$	−18181.3			−1.10476			−0.552381	+	0.833592i	$0.686281\pi$
$648$		0			0
$649$	17332.6			1.04832
$650$		0			0
$651$		0			0
$652$		0			0
$653$	3739.98	−	6477.83i	0.224130	−	0.388204i	−0.731928	−	0.681382i	$-0.761379\pi$
$653$	3739.98	−	6477.83i	0.224130	−	0.388204i	0.956058	+	0.293178i	$0.0947128\pi$
$654$		0			0
$655$	1688.54	+	2924.64i	0.100728	+	0.174466i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	10819.6	+	18740.1i	0.639561	+	1.10775i	0.985529	+	0.169506i	$0.0542173\pi$
$659$	10819.6	+	18740.1i	0.639561	+	1.10775i	−0.345968	+	0.938246i	$0.612449\pi$
$660$		0			0
$661$	14782.5	−	25604.0i	0.869852	−	1.50663i	0.00770503	−	0.999970i	$-0.497547\pi$
$661$	14782.5	−	25604.0i	0.869852	−	1.50663i	0.862147	−	0.506658i	$-0.169119\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	238.030			0.0138803
$666$		0			0
$667$	−555.913			−0.0322714
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−14503.8	+	25121.3i	−0.834444	+	1.44530i
$672$		0			0
$673$	12248.5	+	21215.1i	0.701555	+	1.21513i	0.967920	+	0.251257i	$0.0808440\pi$
$673$	12248.5	+	21215.1i	0.701555	+	1.21513i	−0.266365	+	0.963872i	$0.585823\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	13001.4	+	22519.0i	0.738085	+	1.27840i	0.953357	+	0.301846i	$0.0976028\pi$
$677$	13001.4	+	22519.0i	0.738085	+	1.27840i	−0.215272	+	0.976554i	$0.569064\pi$
$678$		0			0
$679$	−201.986	+	349.850i	−0.0114161	+	0.0197732i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	16344.5			0.915675			0.457838	−	0.889036i	$-0.348624\pi$
$683$	16344.5			0.915675			0.457838	+	0.889036i	$0.348624\pi$
$684$		0			0
$685$	−1756.75			−0.0979885
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−2125.62	+	3681.68i	−0.117532	+	0.203571i
$690$		0			0
$691$	9359.01	+	16210.3i	0.515244	+	0.892429i	0.999843	+	0.0176926i	$0.00563204\pi$
$691$	9359.01	+	16210.3i	0.515244	+	0.892429i	−0.484599	+	0.874736i	$0.661035\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	2059.42	+	3567.01i	0.112400	+	0.194683i
$696$		0			0
$697$	916.939	−	1588.18i	0.0498300	−	0.0863082i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−21470.7			−1.15683			−0.578415	−	0.815743i	$-0.696329\pi$
$701$	−21470.7			−1.15683			−0.578415	+	0.815743i	$0.696329\pi$
$702$		0			0
$703$	−2634.25			−0.141327
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−934.915	+	1619.32i	−0.0497328	+	0.0861398i
$708$		0			0
$709$	9144.70	+	15839.1i	0.484396	+	0.838998i	0.999839	−	0.0179256i	$-0.00570621\pi$
$709$	9144.70	+	15839.1i	0.484396	+	0.838998i	−0.515444	+	0.856923i	$0.672373\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−921.523	−	1596.12i	−0.0484030	−	0.0838364i
$714$		0			0
$715$	−6521.25	+	11295.1i	−0.341092	+	0.590789i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−12985.9			−0.673566			−0.336783	−	0.941582i	$-0.609339\pi$
$719$	−12985.9			−0.673566			−0.336783	+	0.941582i	$0.609339\pi$
$720$		0			0
$721$	1378.36			0.0711965
$722$		0			0
$723$		0			0
$724$		0			0
$725$	197.341	−	341.804i	0.0101090	−	0.0175094i
$726$		0			0
$727$	4766.94	+	8256.58i	0.243186	+	0.421210i	0.961620	−	0.274385i	$-0.0884743\pi$
$727$	4766.94	+	8256.58i	0.243186	+	0.421210i	−0.718434	+	0.695595i	$0.755141\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	1162.34	+	2013.23i	0.0588108	+	0.101863i
$732$		0			0
$733$	−12206.8	+	21142.7i	−0.615099	+	1.06538i	0.375268	+	0.926916i	$0.377551\pi$
$733$	−12206.8	+	21142.7i	−0.615099	+	1.06538i	−0.990367	+	0.138466i	$0.955783\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−12368.0			−0.618158
$738$		0			0
$739$	−22293.3			−1.10970			−0.554852	−	0.831949i	$-0.687225\pi$
$739$	−22293.3			−1.10970			−0.554852	+	0.831949i	$0.687225\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	5703.64	−	9879.00i	0.281624	−	0.487786i	−0.690161	−	0.723656i	$-0.742460\pi$
$743$	5703.64	−	9879.00i	0.281624	−	0.487786i	0.971785	+	0.235869i	$0.0757937\pi$
$744$		0			0
$745$	654.566	+	1133.74i	0.0321898	+	0.0557544i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−871.749	−	1509.91i	−0.0425274	−	0.0736596i
$750$		0			0
$751$	885.790	−	1534.23i	0.0430399	−	0.0745473i	−0.843703	−	0.536810i	$-0.819629\pi$
$751$	885.790	−	1534.23i	0.0430399	−	0.0745473i	0.886743	+	0.462263i	$0.152962\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	11893.4			0.573303
$756$		0			0
$757$	24629.9			1.18255			0.591275	−	0.806470i	$-0.298625\pi$
$757$	24629.9			1.18255			0.591275	+	0.806470i	$0.298625\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	1098.84	−	1903.25i	0.0523429	−	0.0906606i	−0.838667	−	0.544645i	$-0.816664\pi$
$761$	1098.84	−	1903.25i	0.0523429	−	0.0906606i	0.891010	+	0.453984i	$0.149998\pi$
$762$		0			0
$763$	251.400	+	435.437i	0.0119283	+	0.0206604i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−20003.8	−	34647.6i	−0.941714	−	1.63110i
$768$		0			0
$769$	−5486.58	+	9503.03i	−0.257284	+	0.445628i	−0.965513	−	0.260354i	$-0.916161\pi$
$769$	−5486.58	+	9503.03i	−0.257284	+	0.445628i	0.708230	+	0.705982i	$0.249494\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	31206.3			1.45202			0.726011	−	0.687683i	$-0.241372\pi$
$773$	31206.3			1.45202			0.726011	+	0.687683i	$0.241372\pi$
$774$		0			0
$775$	1308.51			0.0606490
$776$		0			0
$777$		0			0
$778$		0			0
$779$	491.502	−	851.306i	0.0226058	−	0.0391543i
$780$		0			0
$781$	15647.4	+	27102.1i	0.716912	+	1.24173i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	4761.94	+	8247.93i	0.216511	+	0.375008i
$786$		0			0
$787$	−6272.26	+	10863.9i	−0.284094	+	0.492065i	−0.972389	−	0.233366i	$-0.925026\pi$
$787$	−6272.26	+	10863.9i	−0.284094	+	0.492065i	0.688295	+	0.725431i	$0.258359\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	919.356			0.0413256
$792$		0			0
$793$	66956.2			2.99834
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−6236.70	+	10802.3i	−0.277184	+	0.480096i	−0.970684	−	0.240360i	$-0.922734\pi$
$797$	−6236.70	+	10802.3i	−0.277184	+	0.480096i	0.693500	+	0.720457i	$0.256068\pi$
$798$		0			0
$799$	15100.8	+	26155.4i	0.668621	+	1.15809i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	13407.3	+	23222.1i	0.589206	+	1.02053i
$804$		0			0
$805$	−106.760	+	184.913i	−0.00467426	+	0.00809606i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−24513.6			−1.06533			−0.532666	−	0.846326i	$-0.678810\pi$
$809$	−24513.6			−1.06533			−0.532666	+	0.846326i	$0.678810\pi$
$810$		0			0
$811$	−35753.3			−1.54805			−0.774026	−	0.633154i	$-0.781760\pi$
$811$	−35753.3			−1.54805			−0.774026	+	0.633154i	$0.781760\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	1944.91	−	3368.69i	0.0835919	−	0.144785i
$816$		0			0
$817$	623.043	+	1079.14i	0.0266800	+	0.0462111i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	9279.71	+	16072.9i	0.394475	+	0.683251i	0.993034	−	0.117828i	$-0.0375931\pi$
$821$	9279.71	+	16072.9i	0.394475	+	0.683251i	−0.598559	+	0.801079i	$0.704260\pi$
$822$		0			0
$823$	2063.53	−	3574.13i	0.0873997	−	0.151381i	−0.819012	−	0.573777i	$-0.805478\pi$
$823$	2063.53	−	3574.13i	0.0873997	−	0.151381i	0.906411	+	0.422396i	$0.138811\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−44400.0			−1.86692			−0.933458	−	0.358687i	$-0.883225\pi$
$827$	−44400.0			−1.86692			−0.933458	+	0.358687i	$0.883225\pi$
$828$		0			0
$829$	23025.7			0.964673			0.482337	−	0.875986i	$-0.339788\pi$
$829$	23025.7			0.964673			0.482337	+	0.875986i	$0.339788\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	12505.7	−	21660.5i	0.520164	−	0.900950i
$834$		0			0
$835$	−4045.51	−	7007.03i	−0.167666	−	0.290405i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−127.236	−	220.379i	−0.00523560	−	0.00906832i	0.863396	−	0.504527i	$-0.168333\pi$
$839$	−127.236	−	220.379i	−0.00523560	−	0.00906832i	−0.868631	+	0.495459i	$0.835000\pi$
$840$		0			0
$841$	12069.9	−	20905.6i	0.494890	−	0.857175i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	19120.1			0.778406
$846$		0			0
$847$	−243.656			−0.00988445
$848$		0			0
$849$		0			0
$850$		0			0
$851$	1181.50	−	2046.41i	0.0475924	−	0.0824324i
$852$		0			0
$853$	−19330.2	−	33480.9i	−0.775913	−	1.34392i	−0.934280	−	0.356540i	$-0.883956\pi$
$853$	−19330.2	−	33480.9i	−0.775913	−	1.34392i	0.158368	−	0.987380i	$-0.449377\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−13862.4	−	24010.4i	−0.552544	−	0.957034i	−0.998090	−	0.0617749i	$-0.980324\pi$
$857$	−13862.4	−	24010.4i	−0.552544	−	0.957034i	0.445546	−	0.895259i	$-0.353009\pi$
$858$		0			0
$859$	−9605.50	+	16637.2i	−0.381531	+	0.660832i	−0.991281	−	0.131762i	$-0.957937\pi$
$859$	−9605.50	+	16637.2i	−0.381531	+	0.660832i	0.609750	+	0.792594i	$0.291270\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−11208.8			−0.442122			−0.221061	−	0.975260i	$-0.570952\pi$
$863$	−11208.8			−0.442122			−0.221061	+	0.975260i	$0.570952\pi$
$864$		0			0
$865$	15495.2			0.609076
$866$		0			0
$867$		0			0
$868$		0			0
$869$	1438.32	−	2491.24i	0.0561469	−	0.0972494i
$870$		0			0
$871$	14274.1	+	24723.5i	0.555294	+	0.961797i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−75.7961	−	131.283i	−0.00292843	−	0.00507219i
$876$		0			0
$877$	−4316.73	+	7476.79i	−0.166209	+	0.287883i	−0.937084	−	0.349104i	$-0.886486\pi$
$877$	−4316.73	+	7476.79i	−0.166209	+	0.287883i	0.770875	+	0.636987i	$0.219819\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−8788.05			−0.336069			−0.168035	−	0.985781i	$-0.553742\pi$
$881$	−8788.05			−0.336069			−0.168035	+	0.985781i	$0.553742\pi$
$882$		0			0
$883$	−6897.27			−0.262867			−0.131434	−	0.991325i	$-0.541958\pi$
$883$	−6897.27			−0.262867			−0.131434	+	0.991325i	$0.541958\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	22934.5	−	39723.7i	0.868167	−	1.50371i	0.00429939	−	0.999991i	$-0.498631\pi$
$887$	22934.5	−	39723.7i	0.868167	−	1.50371i	0.863868	−	0.503719i	$-0.168035\pi$
$888$		0			0
$889$	1306.36	+	2262.68i	0.0492845	+	0.0853633i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	8094.41	+	14019.9i	0.303325	+	0.525374i
$894$		0			0
$895$	955.987	−	1655.82i	0.0357041	−	0.0618412i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−826.310			−0.0306552
$900$		0			0
$901$	4012.26			0.148355
$902$		0			0
$903$		0			0
$904$		0			0
$905$	4164.68	−	7213.44i	0.152971	−	0.264953i
$906$		0			0
$907$	−3597.27	−	6230.65i	−0.131693	−	0.228098i	0.792637	−	0.609694i	$-0.208708\pi$
$907$	−3597.27	−	6230.65i	−0.131693	−	0.228098i	−0.924329	+	0.381596i	$0.875375\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	15896.6	+	27533.6i	0.578130	+	1.00135i	0.995694	+	0.0927029i	$0.0295507\pi$
$911$	15896.6	+	27533.6i	0.578130	+	1.00135i	−0.417564	+	0.908648i	$0.637116\pi$
$912$		0			0
$913$	−1545.64	+	2677.13i	−0.0560277	+	0.0970428i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−819.103			−0.0294974
$918$		0			0
$919$	35807.1			1.28528			0.642638	−	0.766170i	$-0.277840\pi$
$919$	35807.1			1.28528			0.642638	+	0.766170i	$0.277840\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	36117.8	−	62558.0i	1.28801	−	2.23090i
$924$		0			0
$925$	838.826	+	1452.89i	0.0298167	+	0.0516440i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−18828.0	−	32611.0i	−0.664936	−	1.15170i	−0.979303	−	0.202402i	$-0.935125\pi$
$929$	−18828.0	−	32611.0i	−0.664936	−	1.15170i	0.314366	−	0.949302i	$-0.398208\pi$
$930$		0			0
$931$	6703.36	−	11610.6i	0.235976	−	0.408723i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	12309.4			0.430545
$936$		0			0
$937$	3282.72			0.114452			0.0572261	−	0.998361i	$-0.481774\pi$
$937$	3282.72			0.114452			0.0572261	+	0.998361i	$0.481774\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−19866.5	+	34409.8i	−0.688235	+	1.19206i	0.284174	+	0.958773i	$0.408281\pi$
$941$	−19866.5	+	34409.8i	−0.688235	+	1.19206i	−0.972408	+	0.233285i	$0.925053\pi$
$942$		0			0
$943$	440.890	+	763.644i	0.0152252	+	0.0263708i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	23677.3	+	41010.2i	0.812468	+	1.40724i	0.911132	+	0.412116i	$0.135210\pi$
$947$	23677.3	+	41010.2i	0.812468	+	1.40724i	−0.0986631	+	0.995121i	$0.531457\pi$
$948$		0			0
$949$	30947.1	−	53602.0i	1.05857	−	1.83350i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	48567.4			1.65084			0.825421	−	0.564517i	$-0.190938\pi$
$953$	48567.4			1.65084			0.825421	+	0.564517i	$0.190938\pi$
$954$		0			0
$955$	−1837.43			−0.0622594
$956$		0			0
$957$		0			0
$958$		0			0
$959$	213.048	−	369.011i	0.00717382	−	0.0124254i
$960$		0			0
$961$	13525.7	+	23427.3i	0.454021	+	0.786388i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	5157.20	+	8932.53i	0.172037	+	0.297977i
$966$		0			0
$967$	4107.35	−	7114.14i	0.136591	−	0.236583i	−0.789613	−	0.613605i	$-0.789719\pi$
$967$	4107.35	−	7114.14i	0.136591	−	0.236583i	0.926204	+	0.377023i	$0.123052\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−33867.2			−1.11931			−0.559655	−	0.828726i	$-0.689066\pi$
$971$	−33867.2			−1.11931			−0.559655	+	0.828726i	$0.689066\pi$
$972$		0			0
$973$	−999.013			−0.0329156
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−20096.6	+	34808.4i	−0.658084	+	1.13984i	0.323027	+	0.946390i	$0.395300\pi$
$977$	−20096.6	+	34808.4i	−0.658084	+	1.13984i	−0.981111	+	0.193446i	$0.938034\pi$
$978$		0			0
$979$	−14930.1	−	25859.6i	−0.487403	−	0.844206i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−6856.44	−	11875.7i	−0.222468	−	0.385327i	0.733088	−	0.680133i	$-0.238078\pi$
$983$	−6856.44	−	11875.7i	−0.222468	−	0.385327i	−0.955557	+	0.294807i	$0.904745\pi$
$984$		0			0
$985$	4459.68	−	7724.39i	0.144261	−	0.249868i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−1117.77			−0.0359384
$990$		0			0
$991$	−43284.5			−1.38746			−0.693732	−	0.720233i	$-0.744035\pi$
$991$	−43284.5			−1.38746			−0.693732	+	0.720233i	$0.744035\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	11189.1	−	19380.1i	0.356502	−	0.617479i
$996$		0			0
$997$	4694.35	+	8130.85i	0.149119	+	0.258281i	0.930902	−	0.365269i	$-0.119023\pi$
$997$	4694.35	+	8130.85i	0.149119	+	0.258281i	−0.781783	+	0.623550i	$0.785690\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1620.4.i.t.1081.2		6
3.2	odd	2		1620.4.i.v.1081.2		6
9.2	odd	6		1620.4.i.v.541.2		6
9.4	even	3		1620.4.a.e.1.2	yes	3
9.5	odd	6		1620.4.a.c.1.2	✓	3
9.7	even	3	inner	1620.4.i.t.541.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1620.4.a.c.1.2	✓	3	9.5	odd	6
1620.4.a.e.1.2	yes	3	9.4	even	3
1620.4.i.t.541.2		6	9.7	even	3	inner
1620.4.i.t.1081.2		6	1.1	even	1	trivial
1620.4.i.v.541.2		6	9.2	odd	6
1620.4.i.v.1081.2		6	3.2	odd	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:	\( N \)	\(=\)	\( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1620.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.50000 + 4.33013i) q^{5} +(-0.606369 - 1.05026i) q^{7} +O(q^{10})\)	\(q+(-2.50000 + 4.33013i) q^{5} +(-0.606369 - 1.05026i) q^{7} +(-16.8084 - 29.1130i) q^{11} +(-38.7976 + 67.1995i) q^{13} +73.2335 q^{17} +39.2550 q^{19} +(-17.6064 + 30.4951i) q^{23} +(-12.5000 - 21.6506i) q^{25} +(7.89363 + 13.6722i) q^{29} +(-26.1702 + 45.3280i) q^{31} +6.06369 q^{35} -67.1061 q^{37} +(12.5208 - 21.6866i) q^{41} +(15.8717 + 27.4906i) q^{43} +(206.201 + 357.151i) q^{47} +(170.765 - 295.773i) q^{49} +54.7873 q^{53} +168.084 q^{55} +(-257.796 + 446.516i) q^{59} +(-431.445 - 747.284i) q^{61} +(-193.988 - 335.997i) q^{65} +(183.956 - 318.622i) q^{67} -930.929 q^{71} -797.654 q^{73} +(-20.3842 + 35.3064i) q^{77} +(42.7858 + 74.1073i) q^{79} +(-45.9783 - 79.6368i) q^{83} +(-183.084 + 317.110i) q^{85} +888.252 q^{89} +94.1028 q^{91} +(-98.1374 + 169.979i) q^{95} +(-166.554 - 288.479i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 15 q^{5} + 3 q^{7}+O(q^{10}) \) 6 * q - 15 * q^5 + 3 * q^7	\( 6 q - 15 q^{5} + 3 q^{7} + 24 q^{11} - 3 q^{13} - 60 q^{17} - 54 q^{19} - 99 q^{23} - 75 q^{25} + 54 q^{29} - 72 q^{31} - 30 q^{35} - 36 q^{37} - 411 q^{41} - 444 q^{43} + 75 q^{47} - 204 q^{49} + 342 q^{53} - 240 q^{55} - 297 q^{59} - 684 q^{61} - 15 q^{65} - 12 q^{67} + 1284 q^{71} - 132 q^{73} - 1044 q^{77} - 1122 q^{79} - 90 q^{83} + 150 q^{85} + 1512 q^{89} - 3306 q^{91} + 135 q^{95} - 1536 q^{97}+O(q^{100}) \) 6 * q - 15 * q^5 + 3 * q^7 + 24 * q^11 - 3 * q^13 - 60 * q^17 - 54 * q^19 - 99 * q^23 - 75 * q^25 + 54 * q^29 - 72 * q^31 - 30 * q^35 - 36 * q^37 - 411 * q^41 - 444 * q^43 + 75 * q^47 - 204 * q^49 + 342 * q^53 - 240 * q^55 - 297 * q^59 - 684 * q^61 - 15 * q^65 - 12 * q^67 + 1284 * q^71 - 132 * q^73 - 1044 * q^77 - 1122 * q^79 - 90 * q^83 + 150 * q^85 + 1512 * q^89 - 3306 * q^91 + 135 * q^95 - 1536 * q^97

Introduction

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