LMFDB - Embedded newform 585.2.h.d.64.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(64,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("585.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.h (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			64.1
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	585.64
Dual form			585.2.h.d.64.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000 q^{2} +2.00000 q^{4} +(2.00000 - 1.00000i) q^{5} +3.00000 q^{7} +O(q^{10})$	\(q+2.00000 q^{2} +2.00000 q^{4} +(2.00000 - 1.00000i) q^{5} +3.00000 q^{7} +(4.00000 - 2.00000i) q^{10} +5.00000i q^{11} +(-3.00000 - 2.00000i) q^{13} +6.00000 q^{14} -4.00000 q^{16} -3.00000i q^{17} -6.00000i q^{19} +(4.00000 - 2.00000i) q^{20} +10.0000i q^{22} +9.00000i q^{23} +(3.00000 - 4.00000i) q^{25} +(-6.00000 - 4.00000i) q^{26} +6.00000 q^{28} -8.00000 q^{32} -6.00000i q^{34} +(6.00000 - 3.00000i) q^{35} +3.00000 q^{37} -12.0000i q^{38} -5.00000i q^{41} +6.00000i q^{43} +10.0000i q^{44} +18.0000i q^{46} -8.00000 q^{47} +2.00000 q^{49} +(6.00000 - 8.00000i) q^{50} +(-6.00000 - 4.00000i) q^{52} +9.00000i q^{53} +(5.00000 + 10.0000i) q^{55} -4.00000i q^{59} -3.00000 q^{61} -8.00000 q^{64} +(-8.00000 - 1.00000i) q^{65} -12.0000 q^{67} -6.00000i q^{68} +(12.0000 - 6.00000i) q^{70} -5.00000i q^{71} -6.00000 q^{73} +6.00000 q^{74} -12.0000i q^{76} +15.0000i q^{77} +15.0000 q^{79} +(-8.00000 + 4.00000i) q^{80} -10.0000i q^{82} -4.00000 q^{83} +(-3.00000 - 6.00000i) q^{85} +12.0000i q^{86} +1.00000i q^{89} +(-9.00000 - 6.00000i) q^{91} +18.0000i q^{92} -16.0000 q^{94} +(-6.00000 - 12.0000i) q^{95} +3.00000 q^{97} +4.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 4 q^{2} + 4 q^{4} + 4 q^{5} + 6 q^{7}+O(q^{10}) $ 2 * q + 4 * q^2 + 4 * q^4 + 4 * q^5 + 6 * q^7	$ 2 q + 4 q^{2} + 4 q^{4} + 4 q^{5} + 6 q^{7} + 8 q^{10} - 6 q^{13} + 12 q^{14} - 8 q^{16} + 8 q^{20} + 6 q^{25} - 12 q^{26} + 12 q^{28} - 16 q^{32} + 12 q^{35} + 6 q^{37} - 16 q^{47} + 4 q^{49} + 12 q^{50} - 12 q^{52} + 10 q^{55} - 6 q^{61} - 16 q^{64} - 16 q^{65} - 24 q^{67} + 24 q^{70} - 12 q^{73} + 12 q^{74} + 30 q^{79} - 16 q^{80} - 8 q^{83} - 6 q^{85} - 18 q^{91} - 32 q^{94} - 12 q^{95} + 6 q^{97} + 8 q^{98}+O(q^{100}) $ 2 * q + 4 * q^2 + 4 * q^4 + 4 * q^5 + 6 * q^7 + 8 * q^10 - 6 * q^13 + 12 * q^14 - 8 * q^16 + 8 * q^20 + 6 * q^25 - 12 * q^26 + 12 * q^28 - 16 * q^32 + 12 * q^35 + 6 * q^37 - 16 * q^47 + 4 * q^49 + 12 * q^50 - 12 * q^52 + 10 * q^55 - 6 * q^61 - 16 * q^64 - 16 * q^65 - 24 * q^67 + 24 * q^70 - 12 * q^73 + 12 * q^74 + 30 * q^79 - 16 * q^80 - 8 * q^83 - 6 * q^85 - 18 * q^91 - 32 * q^94 - 12 * q^95 + 6 * q^97 + 8 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	2.00000			1.41421			0.707107	−	0.707107i	$-0.250000\pi$
$2$	2.00000			1.41421			0.707107	+	0.707107i	$0.250000\pi$
$3$		0			0
$3$		0			0
$4$	2.00000			1.00000
$5$	2.00000	−	1.00000i	0.894427	−	0.447214i
$5$	2.00000	−	1.00000i	0.894427	−	0.447214i
$6$		0			0
$7$	3.00000			1.13389			0.566947	−	0.823754i	$-0.308125\pi$
$7$	3.00000			1.13389			0.566947	+	0.823754i	$0.308125\pi$
$8$		0			0
$9$		0			0
$10$	4.00000	−	2.00000i	1.26491	−	0.632456i
$11$			5.00000i			1.50756i	0.657129	+	0.753778i	$0.271771\pi$
$11$			5.00000i			1.50756i	−0.657129	+	0.753778i	$0.728229\pi$
$12$		0			0
$13$	−3.00000	−	2.00000i	−0.832050	−	0.554700i
$13$	−3.00000	−	2.00000i	−0.832050	−	0.554700i
$14$	6.00000			1.60357
$15$		0			0
$16$	−4.00000			−1.00000
$17$		−	3.00000i		−	0.727607i	−0.931476	−	0.363803i	$-0.881478\pi$
$17$		−	3.00000i		−	0.727607i	0.931476	−	0.363803i	$-0.118522\pi$
$18$		0			0
$19$		−	6.00000i		−	1.37649i	−0.725476	−	0.688247i	$-0.758380\pi$
$19$		−	6.00000i		−	1.37649i	0.725476	−	0.688247i	$-0.241620\pi$
$20$	4.00000	−	2.00000i	0.894427	−	0.447214i
$21$		0			0
$22$			10.0000i			2.13201i
$23$			9.00000i			1.87663i	0.345782	+	0.938315i	$0.387614\pi$
$23$			9.00000i			1.87663i	−0.345782	+	0.938315i	$0.612386\pi$
$24$		0			0
$25$	3.00000	−	4.00000i	0.600000	−	0.800000i
$26$	−6.00000	−	4.00000i	−1.17670	−	0.784465i
$27$		0			0
$28$	6.00000			1.13389
$29$		0			0			−	1.00000i	$-0.5\pi$
$29$		0			0				1.00000i	$0.5\pi$
$30$		0			0
$31$		0			0		1.00000			$0$
$31$		0			0		−1.00000			$\pi$
$32$	−8.00000			−1.41421
$33$		0			0
$34$		−	6.00000i		−	1.02899i
$35$	6.00000	−	3.00000i	1.01419	−	0.507093i
$36$		0			0
$37$	3.00000			0.493197			0.246598	−	0.969118i	$-0.420687\pi$
$37$	3.00000			0.493197			0.246598	+	0.969118i	$0.420687\pi$
$38$		−	12.0000i		−	1.94666i
$39$		0			0
$40$		0			0
$41$		−	5.00000i		−	0.780869i	−0.920631	−	0.390434i	$-0.872325\pi$
$41$		−	5.00000i		−	0.780869i	0.920631	−	0.390434i	$-0.127675\pi$
$42$		0			0
$43$			6.00000i			0.914991i	0.889212	+	0.457496i	$0.151253\pi$
$43$			6.00000i			0.914991i	−0.889212	+	0.457496i	$0.848747\pi$
$44$			10.0000i			1.50756i
$45$		0			0
$46$			18.0000i			2.65396i
$47$	−8.00000			−1.16692			−0.583460	−	0.812142i	$-0.698301\pi$
$47$	−8.00000			−1.16692			−0.583460	+	0.812142i	$0.698301\pi$
$48$		0			0
$49$	2.00000			0.285714
$50$	6.00000	−	8.00000i	0.848528	−	1.13137i
$51$		0			0
$52$	−6.00000	−	4.00000i	−0.832050	−	0.554700i
$53$			9.00000i			1.23625i	0.786082	+	0.618123i	$0.212106\pi$
$53$			9.00000i			1.23625i	−0.786082	+	0.618123i	$0.787894\pi$
$54$		0			0
$55$	5.00000	+	10.0000i	0.674200	+	1.34840i
$56$		0			0
$57$		0			0
$58$		0			0
$59$		−	4.00000i		−	0.520756i	−0.965507	−	0.260378i	$-0.916153\pi$
$59$		−	4.00000i		−	0.520756i	0.965507	−	0.260378i	$-0.0838471\pi$
$60$		0			0
$61$	−3.00000			−0.384111			−0.192055	−	0.981384i	$-0.561515\pi$
$61$	−3.00000			−0.384111			−0.192055	+	0.981384i	$0.561515\pi$
$62$		0			0
$63$		0			0
$64$	−8.00000			−1.00000
$65$	−8.00000	−	1.00000i	−0.992278	−	0.124035i
$66$		0			0
$67$	−12.0000			−1.46603			−0.733017	−	0.680211i	$-0.761888\pi$
$67$	−12.0000			−1.46603			−0.733017	+	0.680211i	$0.761888\pi$
$68$		−	6.00000i		−	0.727607i
$69$		0			0
$70$	12.0000	−	6.00000i	1.43427	−	0.717137i
$71$		−	5.00000i		−	0.593391i	−0.954972	−	0.296695i	$-0.904115\pi$
$71$		−	5.00000i		−	0.593391i	0.954972	−	0.296695i	$-0.0958846\pi$
$72$		0			0
$73$	−6.00000			−0.702247			−0.351123	−	0.936329i	$-0.614200\pi$
$73$	−6.00000			−0.702247			−0.351123	+	0.936329i	$0.614200\pi$
$74$	6.00000			0.697486
$75$		0			0
$76$		−	12.0000i		−	1.37649i
$77$			15.0000i			1.70941i
$78$		0			0
$79$	15.0000			1.68763			0.843816	−	0.536633i	$-0.180304\pi$
$79$	15.0000			1.68763			0.843816	+	0.536633i	$0.180304\pi$
$80$	−8.00000	+	4.00000i	−0.894427	+	0.447214i
$81$		0			0
$82$		−	10.0000i		−	1.10432i
$83$	−4.00000			−0.439057			−0.219529	−	0.975606i	$-0.570452\pi$
$83$	−4.00000			−0.439057			−0.219529	+	0.975606i	$0.570452\pi$
$84$		0			0
$85$	−3.00000	−	6.00000i	−0.325396	−	0.650791i
$86$			12.0000i			1.29399i
$87$		0			0
$88$		0			0
$89$			1.00000i			0.106000i	0.998595	+	0.0529999i	$0.0168783\pi$
$89$			1.00000i			0.106000i	−0.998595	+	0.0529999i	$0.983122\pi$
$90$		0			0
$91$	−9.00000	−	6.00000i	−0.943456	−	0.628971i
$92$			18.0000i			1.87663i
$93$		0			0
$94$	−16.0000			−1.65027
$95$	−6.00000	−	12.0000i	−0.615587	−	1.23117i
$96$		0			0
$97$	3.00000			0.304604			0.152302	−	0.988334i	$-0.451331\pi$
$97$	3.00000			0.304604			0.152302	+	0.988334i	$0.451331\pi$
$98$	4.00000			0.404061
$99$		0			0
$100$	6.00000	−	8.00000i	0.600000	−	0.800000i
$101$	−12.0000			−1.19404			−0.597022	−	0.802225i	$-0.703650\pi$
$101$	−12.0000			−1.19404			−0.597022	+	0.802225i	$0.703650\pi$
$102$		0			0
$103$			6.00000i			0.591198i	0.955312	+	0.295599i	$0.0955191\pi$
$103$			6.00000i			0.591198i	−0.955312	+	0.295599i	$0.904481\pi$
$104$		0			0
$105$		0			0
$106$			18.0000i			1.74831i
$107$		−	3.00000i		−	0.290021i	−0.989430	−	0.145010i	$-0.953678\pi$
$107$		−	3.00000i		−	0.290021i	0.989430	−	0.145010i	$-0.0463216\pi$
$108$		0			0
$109$		−	6.00000i		−	0.574696i	−0.957826	−	0.287348i	$-0.907226\pi$
$109$		−	6.00000i		−	0.574696i	0.957826	−	0.287348i	$-0.0927736\pi$
$110$	10.0000	+	20.0000i	0.953463	+	1.90693i
$111$		0			0
$112$	−12.0000			−1.13389
$113$		−	6.00000i		−	0.564433i	−0.959351	−	0.282216i	$-0.908930\pi$
$113$		−	6.00000i		−	0.564433i	0.959351	−	0.282216i	$-0.0910696\pi$
$114$		0			0
$115$	9.00000	+	18.0000i	0.839254	+	1.67851i
$116$		0			0
$117$		0			0
$118$		−	8.00000i		−	0.736460i
$119$		−	9.00000i		−	0.825029i
$120$		0			0
$121$	−14.0000			−1.27273
$122$	−6.00000			−0.543214
$123$		0			0
$124$		0			0
$125$	2.00000	−	11.0000i	0.178885	−	0.983870i
$126$		0			0
$127$		−	2.00000i		−	0.177471i	−0.996055	−	0.0887357i	$-0.971717\pi$
$127$		−	2.00000i		−	0.177471i	0.996055	−	0.0887357i	$-0.0282826\pi$
$128$		0			0
$129$		0			0
$130$	−16.0000	−	2.00000i	−1.40329	−	0.175412i
$131$	18.0000			1.57267			0.786334	−	0.617802i	$-0.211977\pi$
$131$	18.0000			1.57267			0.786334	+	0.617802i	$0.211977\pi$
$132$		0			0
$133$		−	18.0000i		−	1.56080i
$134$	−24.0000			−2.07328
$135$		0			0
$136$		0			0
$137$	2.00000			0.170872			0.0854358	−	0.996344i	$-0.472772\pi$
$137$	2.00000			0.170872			0.0854358	+	0.996344i	$0.472772\pi$
$138$		0			0
$139$	5.00000			0.424094			0.212047	−	0.977259i	$-0.431987\pi$
$139$	5.00000			0.424094			0.212047	+	0.977259i	$0.431987\pi$
$140$	12.0000	−	6.00000i	1.01419	−	0.507093i
$141$		0			0
$142$		−	10.0000i		−	0.839181i
$143$	10.0000	−	15.0000i	0.836242	−	1.25436i
$144$		0			0
$145$		0			0
$146$	−12.0000			−0.993127
$147$		0			0
$148$	6.00000			0.493197
$149$			11.0000i			0.901155i	0.892737	+	0.450578i	$0.148782\pi$
$149$			11.0000i			0.901155i	−0.892737	+	0.450578i	$0.851218\pi$
$150$		0			0
$151$		0			0		1.00000			$0$
$151$		0			0		−1.00000			$\pi$
$152$		0			0
$153$		0			0
$154$			30.0000i			2.41747i
$155$		0			0
$156$		0			0
$157$			18.0000i			1.43656i	0.695756	+	0.718278i	$0.255069\pi$
$157$			18.0000i			1.43656i	−0.695756	+	0.718278i	$0.744931\pi$
$158$	30.0000			2.38667
$159$		0			0
$160$	−16.0000	+	8.00000i	−1.26491	+	0.632456i
$161$			27.0000i			2.12790i
$162$		0			0
$163$	9.00000			0.704934			0.352467	−	0.935824i	$-0.385343\pi$
$163$	9.00000			0.704934			0.352467	+	0.935824i	$0.385343\pi$
$164$		−	10.0000i		−	0.780869i
$165$		0			0
$166$	−8.00000			−0.620920
$167$	2.00000			0.154765			0.0773823	−	0.997001i	$-0.475344\pi$
$167$	2.00000			0.154765			0.0773823	+	0.997001i	$0.475344\pi$
$168$		0			0
$169$	5.00000	+	12.0000i	0.384615	+	0.923077i
$170$	−6.00000	−	12.0000i	−0.460179	−	0.920358i
$171$		0			0
$172$			12.0000i			0.914991i
$173$		−	6.00000i		−	0.456172i	−0.973641	−	0.228086i	$-0.926753\pi$
$173$		−	6.00000i		−	0.456172i	0.973641	−	0.228086i	$-0.0732467\pi$
$174$		0			0
$175$	9.00000	−	12.0000i	0.680336	−	0.907115i
$176$		−	20.0000i		−	1.50756i
$177$		0			0
$178$			2.00000i			0.149906i
$179$		0			0			−	1.00000i	$-0.5\pi$
$179$		0			0				1.00000i	$0.5\pi$
$180$		0			0
$181$	7.00000			0.520306			0.260153	−	0.965567i	$-0.416227\pi$
$181$	7.00000			0.520306			0.260153	+	0.965567i	$0.416227\pi$
$182$	−18.0000	−	12.0000i	−1.33425	−	0.889499i
$183$		0			0
$184$		0			0
$185$	6.00000	−	3.00000i	0.441129	−	0.220564i
$186$		0			0
$187$	15.0000			1.09691
$188$	−16.0000			−1.16692
$189$		0			0
$190$	−12.0000	−	24.0000i	−0.870572	−	1.74114i
$191$	18.0000			1.30243			0.651217	−	0.758891i	$-0.274259\pi$
$191$	18.0000			1.30243			0.651217	+	0.758891i	$0.274259\pi$
$192$		0			0
$193$	9.00000			0.647834			0.323917	−	0.946085i	$-0.395000\pi$
$193$	9.00000			0.647834			0.323917	+	0.946085i	$0.395000\pi$
$194$	6.00000			0.430775
$195$		0			0
$196$	4.00000			0.285714
$197$	−8.00000			−0.569976			−0.284988	−	0.958531i	$-0.591990\pi$
$197$	−8.00000			−0.569976			−0.284988	+	0.958531i	$0.591990\pi$
$198$		0			0
$199$		0			0			−	1.00000i	$-0.5\pi$
$199$		0			0				1.00000i	$0.5\pi$
$200$		0			0
$201$		0			0
$202$	−24.0000			−1.68863
$203$		0			0
$204$		0			0
$205$	−5.00000	−	10.0000i	−0.349215	−	0.698430i
$206$			12.0000i			0.836080i
$207$		0			0
$208$	12.0000	+	8.00000i	0.832050	+	0.554700i
$209$	30.0000			2.07514
$210$		0			0
$211$	12.0000			0.826114			0.413057	−	0.910705i	$-0.364461\pi$
$211$	12.0000			0.826114			0.413057	+	0.910705i	$0.364461\pi$
$212$			18.0000i			1.23625i
$213$		0			0
$214$		−	6.00000i		−	0.410152i
$215$	6.00000	+	12.0000i	0.409197	+	0.818393i
$216$		0			0
$217$		0			0
$218$		−	12.0000i		−	0.812743i
$219$		0			0
$220$	10.0000	+	20.0000i	0.674200	+	1.34840i
$221$	−6.00000	+	9.00000i	−0.403604	+	0.605406i
$222$		0			0
$223$	24.0000			1.60716			0.803579	−	0.595198i	$-0.202926\pi$
$223$	24.0000			1.60716			0.803579	+	0.595198i	$0.202926\pi$
$224$	−24.0000			−1.60357
$225$		0			0
$226$		−	12.0000i		−	0.798228i
$227$	2.00000			0.132745			0.0663723	−	0.997795i	$-0.478857\pi$
$227$	2.00000			0.132745			0.0663723	+	0.997795i	$0.478857\pi$
$228$		0			0
$229$		−	6.00000i		−	0.396491i	−0.980152	−	0.198246i	$-0.936476\pi$
$229$		−	6.00000i		−	0.396491i	0.980152	−	0.198246i	$-0.0635244\pi$
$230$	18.0000	+	36.0000i	1.18688	+	2.37377i
$231$		0			0
$232$		0			0
$233$			9.00000i			0.589610i	0.955557	+	0.294805i	$0.0952546\pi$
$233$			9.00000i			0.589610i	−0.955557	+	0.294805i	$0.904745\pi$
$234$		0			0
$235$	−16.0000	+	8.00000i	−1.04372	+	0.521862i
$236$		−	8.00000i		−	0.520756i
$237$		0			0
$238$		−	18.0000i		−	1.16677i
$239$		−	19.0000i		−	1.22901i	−0.788914	−	0.614504i	$-0.789356\pi$
$239$		−	19.0000i		−	1.22901i	0.788914	−	0.614504i	$-0.210644\pi$
$240$		0			0
$241$		0			0		1.00000			$0$
$241$		0			0		−1.00000			$\pi$
$242$	−28.0000			−1.79991
$243$		0			0
$244$	−6.00000			−0.384111
$245$	4.00000	−	2.00000i	0.255551	−	0.127775i
$246$		0			0
$247$	−12.0000	+	18.0000i	−0.763542	+	1.14531i
$248$		0			0
$249$		0			0
$250$	4.00000	−	22.0000i	0.252982	−	1.39140i
$251$	−12.0000			−0.757433			−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000			−0.757433			−0.378717	+	0.925513i	$0.623635\pi$
$252$		0			0
$253$	−45.0000			−2.82913
$254$		−	4.00000i		−	0.250982i
$255$		0			0
$256$	16.0000			1.00000
$257$		−	18.0000i		−	1.12281i	−0.827541	−	0.561405i	$-0.810261\pi$
$257$		−	18.0000i		−	1.12281i	0.827541	−	0.561405i	$-0.189739\pi$
$258$		0			0
$259$	9.00000			0.559233
$260$	−16.0000	−	2.00000i	−0.992278	−	0.124035i
$261$		0			0
$262$	36.0000			2.22409
$263$			24.0000i			1.47990i	0.672660	+	0.739952i	$0.265152\pi$
$263$			24.0000i			1.47990i	−0.672660	+	0.739952i	$0.734848\pi$
$264$		0			0
$265$	9.00000	+	18.0000i	0.552866	+	1.10573i
$266$		−	36.0000i		−	2.20730i
$267$		0			0
$268$	−24.0000			−1.46603
$269$	−30.0000			−1.82913			−0.914566	−	0.404436i	$-0.867468\pi$
$269$	−30.0000			−1.82913			−0.914566	+	0.404436i	$0.867468\pi$
$270$		0			0
$271$		−	30.0000i		−	1.82237i	−0.411997	−	0.911185i	$-0.635169\pi$
$271$		−	30.0000i		−	1.82237i	0.411997	−	0.911185i	$-0.364831\pi$
$272$			12.0000i			0.727607i
$273$		0			0
$274$	4.00000			0.241649
$275$	20.0000	+	15.0000i	1.20605	+	0.904534i
$276$		0			0
$277$		−	12.0000i		−	0.721010i	−0.932757	−	0.360505i	$-0.882604\pi$
$277$		−	12.0000i		−	0.721010i	0.932757	−	0.360505i	$-0.117396\pi$
$278$	10.0000			0.599760
$279$		0			0
$280$		0			0
$281$		−	10.0000i		−	0.596550i	−0.954480	−	0.298275i	$-0.903589\pi$
$281$		−	10.0000i		−	0.596550i	0.954480	−	0.298275i	$-0.0964112\pi$
$282$		0			0
$283$		−	4.00000i		−	0.237775i	−0.992908	−	0.118888i	$-0.962067\pi$
$283$		−	4.00000i		−	0.237775i	0.992908	−	0.118888i	$-0.0379328\pi$
$284$		−	10.0000i		−	0.593391i
$285$		0			0
$286$	20.0000	−	30.0000i	1.18262	−	1.77394i
$287$		−	15.0000i		−	0.885422i
$288$		0			0
$289$	8.00000			0.470588
$290$		0			0
$291$		0			0
$292$	−12.0000			−0.702247
$293$	−14.0000			−0.817889			−0.408944	−	0.912559i	$-0.634103\pi$
$293$	−14.0000			−0.817889			−0.408944	+	0.912559i	$0.634103\pi$
$294$		0			0
$295$	−4.00000	−	8.00000i	−0.232889	−	0.465778i
$296$		0			0
$297$		0			0
$298$			22.0000i			1.27443i
$299$	18.0000	−	27.0000i	1.04097	−	1.56145i
$300$		0			0
$301$			18.0000i			1.03750i
$302$		0			0
$303$		0			0
$304$			24.0000i			1.37649i
$305$	−6.00000	+	3.00000i	−0.343559	+	0.171780i
$306$		0			0
$307$	3.00000			0.171219			0.0856095	−	0.996329i	$-0.472716\pi$
$307$	3.00000			0.171219			0.0856095	+	0.996329i	$0.472716\pi$
$308$			30.0000i			1.70941i
$309$		0			0
$310$		0			0
$311$	18.0000			1.02069			0.510343	−	0.859971i	$-0.329518\pi$
$311$	18.0000			1.02069			0.510343	+	0.859971i	$0.329518\pi$
$312$		0			0
$313$			26.0000i			1.46961i	0.678280	+	0.734803i	$0.262726\pi$
$313$			26.0000i			1.46961i	−0.678280	+	0.734803i	$0.737274\pi$
$314$			36.0000i			2.03160i
$315$		0			0
$316$	30.0000			1.68763
$317$	22.0000			1.23564			0.617822	−	0.786318i	$-0.288015\pi$
$317$	22.0000			1.23564			0.617822	+	0.786318i	$0.288015\pi$
$318$		0			0
$319$		0			0
$320$	−16.0000	+	8.00000i	−0.894427	+	0.447214i
$321$		0			0
$322$			54.0000i			3.00930i
$323$	−18.0000			−1.00155
$324$		0			0
$325$	−17.0000	+	6.00000i	−0.942990	+	0.332820i
$326$	18.0000			0.996928
$327$		0			0
$328$		0			0
$329$	−24.0000			−1.32316
$330$		0			0
$331$		0			0		1.00000			$0$
$331$		0			0		−1.00000			$\pi$
$332$	−8.00000			−0.439057
$333$		0			0
$334$	4.00000			0.218870
$335$	−24.0000	+	12.0000i	−1.31126	+	0.655630i
$336$		0			0
$337$		−	22.0000i		−	1.19842i	−0.800593	−	0.599208i	$-0.795482\pi$
$337$		−	22.0000i		−	1.19842i	0.800593	−	0.599208i	$-0.204518\pi$
$338$	10.0000	+	24.0000i	0.543928	+	1.30543i
$339$		0			0
$340$	−6.00000	−	12.0000i	−0.325396	−	0.650791i
$341$		0			0
$342$		0			0
$343$	−15.0000			−0.809924
$344$		0			0
$345$		0			0
$346$		−	12.0000i		−	0.645124i
$347$		−	3.00000i		−	0.161048i	−0.996753	−	0.0805242i	$-0.974341\pi$
$347$		−	3.00000i		−	0.161048i	0.996753	−	0.0805242i	$-0.0256594\pi$
$348$		0			0
$349$		−	36.0000i		−	1.92704i	−0.267644	−	0.963518i	$-0.586245\pi$
$349$		−	36.0000i		−	1.92704i	0.267644	−	0.963518i	$-0.413755\pi$
$350$	18.0000	−	24.0000i	0.962140	−	1.28285i
$351$		0			0
$352$		−	40.0000i		−	2.13201i
$353$	16.0000			0.851594			0.425797	−	0.904819i	$-0.359994\pi$
$353$	16.0000			0.851594			0.425797	+	0.904819i	$0.359994\pi$
$354$		0			0
$355$	−5.00000	−	10.0000i	−0.265372	−	0.530745i
$356$			2.00000i			0.106000i
$357$		0			0
$358$		0			0
$359$			16.0000i			0.844448i	0.906492	+	0.422224i	$0.138750\pi$
$359$			16.0000i			0.844448i	−0.906492	+	0.422224i	$0.861250\pi$
$360$		0			0
$361$	−17.0000			−0.894737
$362$	14.0000			0.735824
$363$		0			0
$364$	−18.0000	−	12.0000i	−0.943456	−	0.628971i
$365$	−12.0000	+	6.00000i	−0.628109	+	0.314054i
$366$		0			0
$367$		−	12.0000i		−	0.626395i	−0.949688	−	0.313197i	$-0.898600\pi$
$367$		−	12.0000i		−	0.626395i	0.949688	−	0.313197i	$-0.101400\pi$
$368$		−	36.0000i		−	1.87663i
$369$		0			0
$370$	12.0000	−	6.00000i	0.623850	−	0.311925i
$371$			27.0000i			1.40177i
$372$		0			0
$373$		−	14.0000i		−	0.724893i	−0.932005	−	0.362446i	$-0.881942\pi$
$373$		−	14.0000i		−	0.724893i	0.932005	−	0.362446i	$-0.118058\pi$
$374$	30.0000			1.55126
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$			24.0000i			1.23280i	0.787434	+	0.616399i	$0.211409\pi$
$379$			24.0000i			1.23280i	−0.787434	+	0.616399i	$0.788591\pi$
$380$	−12.0000	−	24.0000i	−0.615587	−	1.23117i
$381$		0			0
$382$	36.0000			1.84192
$383$	−34.0000			−1.73732			−0.868659	−	0.495410i	$-0.835018\pi$
$383$	−34.0000			−1.73732			−0.868659	+	0.495410i	$0.835018\pi$
$384$		0			0
$385$	15.0000	+	30.0000i	0.764471	+	1.52894i
$386$	18.0000			0.916176
$387$		0			0
$388$	6.00000			0.304604
$389$	30.0000			1.52106			0.760530	−	0.649303i	$-0.224939\pi$
$389$	30.0000			1.52106			0.760530	+	0.649303i	$0.224939\pi$
$390$		0			0
$391$	27.0000			1.36545
$392$		0			0
$393$		0			0
$394$	−16.0000			−0.806068
$395$	30.0000	−	15.0000i	1.50946	−	0.754732i
$396$		0			0
$397$	3.00000			0.150566			0.0752828	−	0.997162i	$-0.476014\pi$
$397$	3.00000			0.150566			0.0752828	+	0.997162i	$0.476014\pi$
$398$		0			0
$399$		0			0
$400$	−12.0000	+	16.0000i	−0.600000	+	0.800000i
$401$			10.0000i			0.499376i	0.968326	+	0.249688i	$0.0803281\pi$
$401$			10.0000i			0.499376i	−0.968326	+	0.249688i	$0.919672\pi$
$402$		0			0
$403$		0			0
$404$	−24.0000			−1.19404
$405$		0			0
$406$		0			0
$407$			15.0000i			0.743522i
$408$		0			0
$409$		−	6.00000i		−	0.296681i	−0.988936	−	0.148340i	$-0.952607\pi$
$409$		−	6.00000i		−	0.296681i	0.988936	−	0.148340i	$-0.0473931\pi$
$410$	−10.0000	−	20.0000i	−0.493865	−	0.987730i
$411$		0			0
$412$			12.0000i			0.591198i
$413$		−	12.0000i		−	0.590481i
$414$		0			0
$415$	−8.00000	+	4.00000i	−0.392705	+	0.196352i
$416$	24.0000	+	16.0000i	1.17670	+	0.784465i
$417$		0			0
$418$	60.0000			2.93470
$419$		0			0			−	1.00000i	$-0.5\pi$
$419$		0			0				1.00000i	$0.5\pi$
$420$		0			0
$421$		0			0		1.00000			$0$
$421$		0			0		−1.00000			$\pi$
$422$	24.0000			1.16830
$423$		0			0
$424$		0			0
$425$	−12.0000	−	9.00000i	−0.582086	−	0.436564i
$426$		0			0
$427$	−9.00000			−0.435541
$428$		−	6.00000i		−	0.290021i
$429$		0			0
$430$	12.0000	+	24.0000i	0.578691	+	1.15738i
$431$		−	40.0000i		−	1.92673i	−0.268190	−	0.963366i	$-0.586425\pi$
$431$		−	40.0000i		−	1.92673i	0.268190	−	0.963366i	$-0.413575\pi$
$432$		0			0
$433$			16.0000i			0.768911i	0.923144	+	0.384455i	$0.125611\pi$
$433$			16.0000i			0.768911i	−0.923144	+	0.384455i	$0.874389\pi$
$434$		0			0
$435$		0			0
$436$		−	12.0000i		−	0.574696i
$437$	54.0000			2.58317
$438$		0			0
$439$	35.0000			1.67046			0.835229	−	0.549902i	$-0.185335\pi$
$439$	35.0000			1.67046			0.835229	+	0.549902i	$0.185335\pi$
$440$		0			0
$441$		0			0
$442$	−12.0000	+	18.0000i	−0.570782	+	0.856173i
$443$		−	21.0000i		−	0.997740i	−0.866677	−	0.498870i	$-0.833748\pi$
$443$		−	21.0000i		−	0.997740i	0.866677	−	0.498870i	$-0.166252\pi$
$444$		0			0
$445$	1.00000	+	2.00000i	0.0474045	+	0.0948091i
$446$	48.0000			2.27287
$447$		0			0
$448$	−24.0000			−1.13389
$449$			11.0000i			0.519122i	0.965727	+	0.259561i	$0.0835779\pi$
$449$			11.0000i			0.519122i	−0.965727	+	0.259561i	$0.916422\pi$
$450$		0			0
$451$	25.0000			1.17720
$452$		−	12.0000i		−	0.564433i
$453$		0			0
$454$	4.00000			0.187729
$455$	−24.0000	−	3.00000i	−1.12514	−	0.140642i
$456$		0			0
$457$	3.00000			0.140334			0.0701670	−	0.997535i	$-0.477647\pi$
$457$	3.00000			0.140334			0.0701670	+	0.997535i	$0.477647\pi$
$458$		−	12.0000i		−	0.560723i
$459$		0			0
$460$	18.0000	+	36.0000i	0.839254	+	1.67851i
$461$		−	25.0000i		−	1.16437i	−0.813058	−	0.582183i	$-0.802199\pi$
$461$		−	25.0000i		−	1.16437i	0.813058	−	0.582183i	$-0.197801\pi$
$462$		0			0
$463$	9.00000			0.418265			0.209133	−	0.977887i	$-0.432936\pi$
$463$	9.00000			0.418265			0.209133	+	0.977887i	$0.432936\pi$
$464$		0			0
$465$		0			0
$466$			18.0000i			0.833834i
$467$			27.0000i			1.24941i	0.780860	+	0.624705i	$0.214781\pi$
$467$			27.0000i			1.24941i	−0.780860	+	0.624705i	$0.785219\pi$
$468$		0			0
$469$	−36.0000			−1.66233
$470$	−32.0000	+	16.0000i	−1.47605	+	0.738025i
$471$		0			0
$472$		0			0
$473$	−30.0000			−1.37940
$474$		0			0
$475$	−24.0000	−	18.0000i	−1.10120	−	0.825897i
$476$		−	18.0000i		−	0.825029i
$477$		0			0
$478$		−	38.0000i		−	1.73808i
$479$			1.00000i			0.0456912i	0.999739	+	0.0228456i	$0.00727261\pi$
$479$			1.00000i			0.0456912i	−0.999739	+	0.0228456i	$0.992727\pi$
$480$		0			0
$481$	−9.00000	−	6.00000i	−0.410365	−	0.273576i
$482$		0			0
$483$		0			0
$484$	−28.0000			−1.27273
$485$	6.00000	−	3.00000i	0.272446	−	0.136223i
$486$		0			0
$487$	3.00000			0.135943			0.0679715	−	0.997687i	$-0.478347\pi$
$487$	3.00000			0.135943			0.0679715	+	0.997687i	$0.478347\pi$
$488$		0			0
$489$		0			0
$490$	8.00000	−	4.00000i	0.361403	−	0.180702i
$491$	−42.0000			−1.89543			−0.947717	−	0.319113i	$-0.896615\pi$
$491$	−42.0000			−1.89543			−0.947717	+	0.319113i	$0.896615\pi$
$492$		0			0
$493$		0			0
$494$	−24.0000	+	36.0000i	−1.07981	+	1.61972i
$495$		0			0
$496$		0			0
$497$		−	15.0000i		−	0.672842i
$498$		0			0
$499$			24.0000i			1.07439i	0.843459	+	0.537194i	$0.180516\pi$
$499$			24.0000i			1.07439i	−0.843459	+	0.537194i	$0.819484\pi$
$500$	4.00000	−	22.0000i	0.178885	−	0.983870i
$501$		0			0
$502$	−24.0000			−1.07117
$503$			24.0000i			1.07011i	0.844818	+	0.535054i	$0.179709\pi$
$503$			24.0000i			1.07011i	−0.844818	+	0.535054i	$0.820291\pi$
$504$		0			0
$505$	−24.0000	+	12.0000i	−1.06799	+	0.533993i
$506$	−90.0000			−4.00099
$507$		0			0
$508$		−	4.00000i		−	0.177471i
$509$			31.0000i			1.37405i	0.726633	+	0.687025i	$0.241084\pi$
$509$			31.0000i			1.37405i	−0.726633	+	0.687025i	$0.758916\pi$
$510$		0			0
$511$	−18.0000			−0.796273
$512$	32.0000			1.41421
$513$		0			0
$514$		−	36.0000i		−	1.58789i
$515$	6.00000	+	12.0000i	0.264392	+	0.528783i
$516$		0			0
$517$		−	40.0000i		−	1.75920i
$518$	18.0000			0.790875
$519$		0			0
$520$		0			0
$521$	−12.0000			−0.525730			−0.262865	−	0.964833i	$-0.584667\pi$
$521$	−12.0000			−0.525730			−0.262865	+	0.964833i	$0.584667\pi$
$522$		0			0
$523$			36.0000i			1.57417i	0.616844	+	0.787085i	$0.288411\pi$
$523$			36.0000i			1.57417i	−0.616844	+	0.787085i	$0.711589\pi$
$524$	36.0000			1.57267
$525$		0			0
$526$			48.0000i			2.09290i
$527$		0			0
$528$		0			0
$529$	−58.0000			−2.52174
$530$	18.0000	+	36.0000i	0.781870	+	1.56374i
$531$		0			0
$532$		−	36.0000i		−	1.56080i
$533$	−10.0000	+	15.0000i	−0.433148	+	0.649722i
$534$		0			0
$535$	−3.00000	−	6.00000i	−0.129701	−	0.259403i
$536$		0			0
$537$		0			0
$538$	−60.0000			−2.58678
$539$			10.0000i			0.430730i
$540$		0			0
$541$			30.0000i			1.28980i	0.764267	+	0.644900i	$0.223101\pi$
$541$			30.0000i			1.28980i	−0.764267	+	0.644900i	$0.776899\pi$
$542$		−	60.0000i		−	2.57722i
$543$		0			0
$544$			24.0000i			1.02899i
$545$	−6.00000	−	12.0000i	−0.257012	−	0.514024i
$546$		0			0
$547$		−	42.0000i		−	1.79579i	−0.440209	−	0.897895i	$-0.645096\pi$
$547$		−	42.0000i		−	1.79579i	0.440209	−	0.897895i	$-0.354904\pi$
$548$	4.00000			0.170872
$549$		0			0
$550$	40.0000	+	30.0000i	1.70561	+	1.27920i
$551$		0			0
$552$		0			0
$553$	45.0000			1.91359
$554$		−	24.0000i		−	1.01966i
$555$		0			0
$556$	10.0000			0.424094
$557$	−28.0000			−1.18640			−0.593199	−	0.805056i	$-0.702135\pi$
$557$	−28.0000			−1.18640			−0.593199	+	0.805056i	$0.702135\pi$
$558$		0			0
$559$	12.0000	−	18.0000i	0.507546	−	0.761319i
$560$	−24.0000	+	12.0000i	−1.01419	+	0.507093i
$561$		0			0
$562$		−	20.0000i		−	0.843649i
$563$			9.00000i			0.379305i	0.981851	+	0.189652i	$0.0607361\pi$
$563$			9.00000i			0.379305i	−0.981851	+	0.189652i	$0.939264\pi$
$564$		0			0
$565$	−6.00000	−	12.0000i	−0.252422	−	0.504844i
$566$		−	8.00000i		−	0.336265i
$567$		0			0
$568$		0			0
$569$	30.0000			1.25767			0.628833	−	0.777541i	$-0.283533\pi$
$569$	30.0000			1.25767			0.628833	+	0.777541i	$0.283533\pi$
$570$		0			0
$571$	−33.0000			−1.38101			−0.690504	−	0.723329i	$-0.742611\pi$
$571$	−33.0000			−1.38101			−0.690504	+	0.723329i	$0.742611\pi$
$572$	20.0000	−	30.0000i	0.836242	−	1.25436i
$573$		0			0
$574$		−	30.0000i		−	1.25218i
$575$	36.0000	+	27.0000i	1.50130	+	1.12598i
$576$		0			0
$577$	3.00000			0.124892			0.0624458	−	0.998048i	$-0.480110\pi$
$577$	3.00000			0.124892			0.0624458	+	0.998048i	$0.480110\pi$
$578$	16.0000			0.665512
$579$		0			0
$580$		0			0
$581$	−12.0000			−0.497844
$582$		0			0
$583$	−45.0000			−1.86371
$584$		0			0
$585$		0			0
$586$	−28.0000			−1.15667
$587$	2.00000			0.0825488			0.0412744	−	0.999148i	$-0.486858\pi$
$587$	2.00000			0.0825488			0.0412744	+	0.999148i	$0.486858\pi$
$588$		0			0
$589$		0			0
$590$	−8.00000	−	16.0000i	−0.329355	−	0.658710i
$591$		0			0
$592$	−12.0000			−0.493197
$593$	−34.0000			−1.39621			−0.698106	−	0.715994i	$-0.745974\pi$
$593$	−34.0000			−1.39621			−0.698106	+	0.715994i	$0.745974\pi$
$594$		0			0
$595$	−9.00000	−	18.0000i	−0.368964	−	0.737928i
$596$			22.0000i			0.901155i
$597$		0			0
$598$	36.0000	−	54.0000i	1.47215	−	2.20822i
$599$	−30.0000			−1.22577			−0.612883	−	0.790173i	$-0.709990\pi$
$599$	−30.0000			−1.22577			−0.612883	+	0.790173i	$0.709990\pi$
$600$		0			0
$601$	−33.0000			−1.34610			−0.673049	−	0.739598i	$-0.735016\pi$
$601$	−33.0000			−1.34610			−0.673049	+	0.739598i	$0.735016\pi$
$602$			36.0000i			1.46725i
$603$		0			0
$604$		0			0
$605$	−28.0000	+	14.0000i	−1.13836	+	0.569181i
$606$		0			0
$607$			48.0000i			1.94826i	0.225989	+	0.974130i	$0.427439\pi$
$607$			48.0000i			1.94826i	−0.225989	+	0.974130i	$0.572561\pi$
$608$			48.0000i			1.94666i
$609$		0			0
$610$	−12.0000	+	6.00000i	−0.485866	+	0.242933i
$611$	24.0000	+	16.0000i	0.970936	+	0.647291i
$612$		0			0
$613$	9.00000			0.363507			0.181753	−	0.983344i	$-0.441823\pi$
$613$	9.00000			0.363507			0.181753	+	0.983344i	$0.441823\pi$
$614$	6.00000			0.242140
$615$		0			0
$616$		0			0
$617$	−8.00000			−0.322068			−0.161034	−	0.986949i	$-0.551483\pi$
$617$	−8.00000			−0.322068			−0.161034	+	0.986949i	$0.551483\pi$
$618$		0			0
$619$		−	6.00000i		−	0.241160i	−0.992704	−	0.120580i	$-0.961525\pi$
$619$		−	6.00000i		−	0.241160i	0.992704	−	0.120580i	$-0.0384755\pi$
$620$		0			0
$621$		0			0
$622$	36.0000			1.44347
$623$			3.00000i			0.120192i
$624$		0			0
$625$	−7.00000	−	24.0000i	−0.280000	−	0.960000i
$626$			52.0000i			2.07834i
$627$		0			0
$628$			36.0000i			1.43656i
$629$		−	9.00000i		−	0.358854i
$630$		0			0
$631$		−	30.0000i		−	1.19428i	−0.802137	−	0.597141i	$-0.796303\pi$
$631$		−	30.0000i		−	1.19428i	0.802137	−	0.597141i	$-0.203697\pi$
$632$		0			0
$633$		0			0
$634$	44.0000			1.74746
$635$	−2.00000	−	4.00000i	−0.0793676	−	0.158735i
$636$		0			0
$637$	−6.00000	−	4.00000i	−0.237729	−	0.158486i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−12.0000			−0.473972			−0.236986	−	0.971513i	$-0.576159\pi$
$641$	−12.0000			−0.473972			−0.236986	+	0.971513i	$0.576159\pi$
$642$		0			0
$643$	−21.0000			−0.828159			−0.414080	−	0.910241i	$-0.635896\pi$
$643$	−21.0000			−0.828159			−0.414080	+	0.910241i	$0.635896\pi$
$644$			54.0000i			2.12790i
$645$		0			0
$646$	−36.0000			−1.41640
$647$		−	3.00000i		−	0.117942i	−0.998260	−	0.0589711i	$-0.981218\pi$
$647$		−	3.00000i		−	0.117942i	0.998260	−	0.0589711i	$-0.0187820\pi$
$648$		0			0
$649$	20.0000			0.785069
$650$	−34.0000	+	12.0000i	−1.33359	+	0.470679i
$651$		0			0
$652$	18.0000			0.704934
$653$		−	6.00000i		−	0.234798i	−0.993085	−	0.117399i	$-0.962544\pi$
$653$		−	6.00000i		−	0.234798i	0.993085	−	0.117399i	$-0.0374557\pi$
$654$		0			0
$655$	36.0000	−	18.0000i	1.40664	−	0.703318i
$656$			20.0000i			0.780869i
$657$		0			0
$658$	−48.0000			−1.87123
$659$	−30.0000			−1.16863			−0.584317	−	0.811525i	$-0.698638\pi$
$659$	−30.0000			−1.16863			−0.584317	+	0.811525i	$0.698638\pi$
$660$		0			0
$661$			30.0000i			1.16686i	0.812162	+	0.583432i	$0.198291\pi$
$661$			30.0000i			1.16686i	−0.812162	+	0.583432i	$0.801709\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−18.0000	−	36.0000i	−0.698010	−	1.39602i
$666$		0			0
$667$		0			0
$668$	4.00000			0.154765
$669$		0			0
$670$	−48.0000	+	24.0000i	−1.85440	+	0.927201i
$671$		−	15.0000i		−	0.579069i
$672$		0			0
$673$			36.0000i			1.38770i	0.720121	+	0.693849i	$0.244086\pi$
$673$			36.0000i			1.38770i	−0.720121	+	0.693849i	$0.755914\pi$
$674$		−	44.0000i		−	1.69482i
$675$		0			0
$676$	10.0000	+	24.0000i	0.384615	+	0.923077i
$677$			27.0000i			1.03769i	0.854867	+	0.518847i	$0.173639\pi$
$677$			27.0000i			1.03769i	−0.854867	+	0.518847i	$0.826361\pi$
$678$		0			0
$679$	9.00000			0.345388
$680$		0			0
$681$		0			0
$682$		0			0
$683$	16.0000			0.612223			0.306111	−	0.951996i	$-0.400972\pi$
$683$	16.0000			0.612223			0.306111	+	0.951996i	$0.400972\pi$
$684$		0			0
$685$	4.00000	−	2.00000i	0.152832	−	0.0764161i
$686$	−30.0000			−1.14541
$687$		0			0
$688$		−	24.0000i		−	0.914991i
$689$	18.0000	−	27.0000i	0.685745	−	1.02862i
$690$		0			0
$691$			30.0000i			1.14125i	0.821209	+	0.570627i	$0.193300\pi$
$691$			30.0000i			1.14125i	−0.821209	+	0.570627i	$0.806700\pi$
$692$		−	12.0000i		−	0.456172i
$693$		0			0
$694$		−	6.00000i		−	0.227757i
$695$	10.0000	−	5.00000i	0.379322	−	0.189661i
$696$		0			0
$697$	−15.0000			−0.568166
$698$		−	72.0000i		−	2.72524i
$699$		0			0
$700$	18.0000	−	24.0000i	0.680336	−	0.907115i
$701$	−12.0000			−0.453234			−0.226617	−	0.973984i	$-0.572767\pi$
$701$	−12.0000			−0.453234			−0.226617	+	0.973984i	$0.572767\pi$
$702$		0			0
$703$		−	18.0000i		−	0.678883i
$704$		−	40.0000i		−	1.50756i
$705$		0			0
$706$	32.0000			1.20434
$707$	−36.0000			−1.35392
$708$		0			0
$709$			24.0000i			0.901339i	0.892691	+	0.450669i	$0.148815\pi$
$709$			24.0000i			0.901339i	−0.892691	+	0.450669i	$0.851185\pi$
$710$	−10.0000	−	20.0000i	−0.375293	−	0.750587i
$711$		0			0
$712$		0			0
$713$		0			0
$714$		0			0
$715$	5.00000	−	40.0000i	0.186989	−	1.49592i
$716$		0			0
$717$		0			0
$718$			32.0000i			1.19423i
$719$		0			0			−	1.00000i	$-0.5\pi$
$719$		0			0				1.00000i	$0.5\pi$
$720$		0			0
$721$			18.0000i			0.670355i
$722$	−34.0000			−1.26535
$723$		0			0
$724$	14.0000			0.520306
$725$		0			0
$726$		0			0
$727$			28.0000i			1.03846i	0.854634	+	0.519231i	$0.173782\pi$
$727$			28.0000i			1.03846i	−0.854634	+	0.519231i	$0.826218\pi$
$728$		0			0
$729$		0			0
$730$	−24.0000	+	12.0000i	−0.888280	+	0.444140i
$731$	18.0000			0.665754
$732$		0			0
$733$	−21.0000			−0.775653			−0.387826	−	0.921732i	$-0.626774\pi$
$733$	−21.0000			−0.775653			−0.387826	+	0.921732i	$0.626774\pi$
$734$		−	24.0000i		−	0.885856i
$735$		0			0
$736$		−	72.0000i		−	2.65396i
$737$		−	60.0000i		−	2.21013i
$738$		0			0
$739$		−	36.0000i		−	1.32428i	−0.749380	−	0.662141i	$-0.769648\pi$
$739$		−	36.0000i		−	1.32428i	0.749380	−	0.662141i	$-0.230352\pi$
$740$	12.0000	−	6.00000i	0.441129	−	0.220564i
$741$		0			0
$742$			54.0000i			1.98240i
$743$	26.0000			0.953847			0.476924	−	0.878945i	$-0.341752\pi$
$743$	26.0000			0.953847			0.476924	+	0.878945i	$0.341752\pi$
$744$		0			0
$745$	11.0000	+	22.0000i	0.403009	+	0.806018i
$746$		−	28.0000i		−	1.02515i
$747$		0			0
$748$	30.0000			1.09691
$749$		−	9.00000i		−	0.328853i
$750$		0			0
$751$	−23.0000			−0.839282			−0.419641	−	0.907690i	$-0.637844\pi$
$751$	−23.0000			−0.839282			−0.419641	+	0.907690i	$0.637844\pi$
$752$	32.0000			1.16692
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$			38.0000i			1.38113i	0.723269	+	0.690567i	$0.242639\pi$
$757$			38.0000i			1.38113i	−0.723269	+	0.690567i	$0.757361\pi$
$758$			48.0000i			1.74344i
$759$		0			0
$760$		0			0
$761$		−	10.0000i		−	0.362500i	−0.983437	−	0.181250i	$-0.941986\pi$
$761$		−	10.0000i		−	0.362500i	0.983437	−	0.181250i	$-0.0580143\pi$
$762$		0			0
$763$		−	18.0000i		−	0.651644i
$764$	36.0000			1.30243
$765$		0			0
$766$	−68.0000			−2.45694
$767$	−8.00000	+	12.0000i	−0.288863	+	0.433295i
$768$		0			0
$769$		−	6.00000i		−	0.216366i	−0.994131	−	0.108183i	$-0.965497\pi$
$769$		−	6.00000i		−	0.216366i	0.994131	−	0.108183i	$-0.0345032\pi$
$770$	30.0000	+	60.0000i	1.08112	+	2.16225i
$771$		0			0
$772$	18.0000			0.647834
$773$	−4.00000			−0.143870			−0.0719350	−	0.997409i	$-0.522917\pi$
$773$	−4.00000			−0.143870			−0.0719350	+	0.997409i	$0.522917\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$	60.0000			2.15110
$779$	−30.0000			−1.07486
$780$		0			0
$781$	25.0000			0.894570
$782$	54.0000			1.93104
$783$		0			0
$784$	−8.00000			−0.285714
$785$	18.0000	+	36.0000i	0.642448	+	1.28490i
$786$		0			0
$787$	48.0000			1.71102			0.855508	−	0.517790i	$-0.173245\pi$
$787$	48.0000			1.71102			0.855508	+	0.517790i	$0.173245\pi$
$788$	−16.0000			−0.569976
$789$		0			0
$790$	60.0000	−	30.0000i	2.13470	−	1.06735i
$791$		−	18.0000i		−	0.640006i
$792$		0			0
$793$	9.00000	+	6.00000i	0.319599	+	0.213066i
$794$	6.00000			0.212932
$795$		0			0
$796$		0			0
$797$		−	33.0000i		−	1.16892i	−0.811423	−	0.584460i	$-0.801306\pi$
$797$		−	33.0000i		−	1.16892i	0.811423	−	0.584460i	$-0.198694\pi$
$798$		0			0
$799$			24.0000i			0.849059i
$800$	−24.0000	+	32.0000i	−0.848528	+	1.13137i
$801$		0			0
$802$			20.0000i			0.706225i
$803$		−	30.0000i		−	1.05868i
$804$		0			0
$805$	27.0000	+	54.0000i	0.951625	+	1.90325i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	30.0000			1.05474			0.527372	−	0.849635i	$-0.323177\pi$
$809$	30.0000			1.05474			0.527372	+	0.849635i	$0.323177\pi$
$810$		0			0
$811$			30.0000i			1.05344i	0.850038	+	0.526721i	$0.176579\pi$
$811$			30.0000i			1.05344i	−0.850038	+	0.526721i	$0.823421\pi$
$812$		0			0
$813$		0			0
$814$			30.0000i			1.05150i
$815$	18.0000	−	9.00000i	0.630512	−	0.315256i
$816$		0			0
$817$	36.0000			1.25948
$818$		−	12.0000i		−	0.419570i
$819$		0			0
$820$	−10.0000	−	20.0000i	−0.349215	−	0.698430i
$821$			35.0000i			1.22151i	0.791820	+	0.610754i	$0.209134\pi$
$821$			35.0000i			1.22151i	−0.791820	+	0.610754i	$0.790866\pi$
$822$		0			0
$823$		−	24.0000i		−	0.836587i	−0.908312	−	0.418294i	$-0.862628\pi$
$823$		−	24.0000i		−	0.836587i	0.908312	−	0.418294i	$-0.137372\pi$
$824$		0			0
$825$		0			0
$826$		−	24.0000i		−	0.835067i
$827$	−8.00000			−0.278187			−0.139094	−	0.990279i	$-0.544419\pi$
$827$	−8.00000			−0.278187			−0.139094	+	0.990279i	$0.544419\pi$
$828$		0			0
$829$	−30.0000			−1.04194			−0.520972	−	0.853574i	$-0.674430\pi$
$829$	−30.0000			−1.04194			−0.520972	+	0.853574i	$0.674430\pi$
$830$	−16.0000	+	8.00000i	−0.555368	+	0.277684i
$831$		0			0
$832$	24.0000	+	16.0000i	0.832050	+	0.554700i
$833$		−	6.00000i		−	0.207888i
$834$		0			0
$835$	4.00000	−	2.00000i	0.138426	−	0.0692129i
$836$	60.0000			2.07514
$837$		0			0
$838$		0			0
$839$		−	29.0000i		−	1.00119i	−0.865681	−	0.500596i	$-0.833114\pi$
$839$		−	29.0000i		−	1.00119i	0.865681	−	0.500596i	$-0.166886\pi$
$840$		0			0
$841$	−29.0000			−1.00000
$842$		0			0
$843$		0			0
$844$	24.0000			0.826114
$845$	22.0000	+	19.0000i	0.756823	+	0.653620i
$846$		0			0
$847$	−42.0000			−1.44314
$848$		−	36.0000i		−	1.23625i
$849$		0			0
$850$	−24.0000	−	18.0000i	−0.823193	−	0.617395i
$851$			27.0000i			0.925548i
$852$		0			0
$853$	−21.0000			−0.719026			−0.359513	−	0.933140i	$-0.617057\pi$
$853$	−21.0000			−0.719026			−0.359513	+	0.933140i	$0.617057\pi$
$854$	−18.0000			−0.615947
$855$		0			0
$856$		0			0
$857$		−	33.0000i		−	1.12726i	−0.826028	−	0.563629i	$-0.809405\pi$
$857$		−	33.0000i		−	1.12726i	0.826028	−	0.563629i	$-0.190595\pi$
$858$		0			0
$859$	−15.0000			−0.511793			−0.255897	−	0.966704i	$-0.582371\pi$
$859$	−15.0000			−0.511793			−0.255897	+	0.966704i	$0.582371\pi$
$860$	12.0000	+	24.0000i	0.409197	+	0.818393i
$861$		0			0
$862$		−	80.0000i		−	2.72481i
$863$	16.0000			0.544646			0.272323	−	0.962206i	$-0.412208\pi$
$863$	16.0000			0.544646			0.272323	+	0.962206i	$0.412208\pi$
$864$		0			0
$865$	−6.00000	−	12.0000i	−0.204006	−	0.408012i
$866$			32.0000i			1.08740i
$867$		0			0
$868$		0			0
$869$			75.0000i			2.54420i
$870$		0			0
$871$	36.0000	+	24.0000i	1.21981	+	0.813209i
$872$		0			0
$873$		0			0
$874$	108.000			3.65315
$875$	6.00000	−	33.0000i	0.202837	−	1.11560i
$876$		0			0
$877$	18.0000			0.607817			0.303908	−	0.952701i	$-0.401708\pi$
$877$	18.0000			0.607817			0.303908	+	0.952701i	$0.401708\pi$
$878$	70.0000			2.36239
$879$		0			0
$880$	−20.0000	−	40.0000i	−0.674200	−	1.34840i
$881$	−12.0000			−0.404290			−0.202145	−	0.979356i	$-0.564791\pi$
$881$	−12.0000			−0.404290			−0.202145	+	0.979356i	$0.564791\pi$
$882$		0			0
$883$		−	34.0000i		−	1.14419i	−0.820187	−	0.572096i	$-0.806131\pi$
$883$		−	34.0000i		−	1.14419i	0.820187	−	0.572096i	$-0.193869\pi$
$884$	−12.0000	+	18.0000i	−0.403604	+	0.605406i
$885$		0			0
$886$		−	42.0000i		−	1.41102i
$887$			27.0000i			0.906571i	0.891365	+	0.453286i	$0.149748\pi$
$887$			27.0000i			0.906571i	−0.891365	+	0.453286i	$0.850252\pi$
$888$		0			0
$889$		−	6.00000i		−	0.201234i
$890$	2.00000	+	4.00000i	0.0670402	+	0.134080i
$891$		0			0
$892$	48.0000			1.60716
$893$			48.0000i			1.60626i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$			22.0000i			0.734150i
$899$		0			0
$900$		0			0
$901$	27.0000			0.899500
$902$	50.0000			1.66482
$903$		0			0
$904$		0			0
$905$	14.0000	−	7.00000i	0.465376	−	0.232688i
$906$		0			0
$907$			28.0000i			0.929725i	0.885383	+	0.464862i	$0.153896\pi$
$907$			28.0000i			0.929725i	−0.885383	+	0.464862i	$0.846104\pi$
$908$	4.00000			0.132745
$909$		0			0
$910$	−48.0000	−	6.00000i	−1.59118	−	0.198898i
$911$	−12.0000			−0.397578			−0.198789	−	0.980042i	$-0.563701\pi$
$911$	−12.0000			−0.397578			−0.198789	+	0.980042i	$0.563701\pi$
$912$		0			0
$913$		−	20.0000i		−	0.661903i
$914$	6.00000			0.198462
$915$		0			0
$916$		−	12.0000i		−	0.396491i
$917$	54.0000			1.78324
$918$		0			0
$919$	15.0000			0.494804			0.247402	−	0.968913i	$-0.420423\pi$
$919$	15.0000			0.494804			0.247402	+	0.968913i	$0.420423\pi$
$920$		0			0
$921$		0			0
$922$		−	50.0000i		−	1.64666i
$923$	−10.0000	+	15.0000i	−0.329154	+	0.493731i
$924$		0			0
$925$	9.00000	−	12.0000i	0.295918	−	0.394558i
$926$	18.0000			0.591517
$927$		0			0
$928$		0			0
$929$		−	29.0000i		−	0.951459i	−0.879592	−	0.475730i	$-0.842184\pi$
$929$		−	29.0000i		−	0.951459i	0.879592	−	0.475730i	$-0.157816\pi$
$930$		0			0
$931$		−	12.0000i		−	0.393284i
$932$			18.0000i			0.589610i
$933$		0			0
$934$			54.0000i			1.76693i
$935$	30.0000	−	15.0000i	0.981105	−	0.490552i
$936$		0			0
$937$		−	2.00000i		−	0.0653372i	−0.999466	−	0.0326686i	$-0.989599\pi$
$937$		−	2.00000i		−	0.0653372i	0.999466	−	0.0326686i	$-0.0104006\pi$
$938$	−72.0000			−2.35088
$939$		0			0
$940$	−32.0000	+	16.0000i	−1.04372	+	0.521862i
$941$		−	35.0000i		−	1.14097i	−0.821309	−	0.570484i	$-0.806756\pi$
$941$		−	35.0000i		−	1.14097i	0.821309	−	0.570484i	$-0.193244\pi$
$942$		0			0
$943$	45.0000			1.46540
$944$			16.0000i			0.520756i
$945$		0			0
$946$	−60.0000			−1.95077
$947$	22.0000			0.714904			0.357452	−	0.933932i	$-0.383646\pi$
$947$	22.0000			0.714904			0.357452	+	0.933932i	$0.383646\pi$
$948$		0			0
$949$	18.0000	+	12.0000i	0.584305	+	0.389536i
$950$	−48.0000	−	36.0000i	−1.55733	−	1.16799i
$951$		0			0
$952$		0			0
$953$			39.0000i			1.26333i	0.775240	+	0.631667i	$0.217629\pi$
$953$			39.0000i			1.26333i	−0.775240	+	0.631667i	$0.782371\pi$
$954$		0			0
$955$	36.0000	−	18.0000i	1.16493	−	0.582466i
$956$		−	38.0000i		−	1.22901i
$957$		0			0
$958$			2.00000i			0.0646171i
$959$	6.00000			0.193750
$960$		0			0
$961$	31.0000			1.00000
$962$	−18.0000	−	12.0000i	−0.580343	−	0.386896i
$963$		0			0
$964$		0			0
$965$	18.0000	−	9.00000i	0.579441	−	0.289720i
$966$		0			0
$967$	−12.0000			−0.385894			−0.192947	−	0.981209i	$-0.561805\pi$
$967$	−12.0000			−0.385894			−0.192947	+	0.981209i	$0.561805\pi$
$968$		0			0
$969$		0			0
$970$	12.0000	−	6.00000i	0.385297	−	0.192648i
$971$	−12.0000			−0.385098			−0.192549	−	0.981287i	$-0.561675\pi$
$971$	−12.0000			−0.385098			−0.192549	+	0.981287i	$0.561675\pi$
$972$		0			0
$973$	15.0000			0.480878
$974$	6.00000			0.192252
$975$		0			0
$976$	12.0000			0.384111
$977$	−38.0000			−1.21573			−0.607864	−	0.794041i	$-0.707973\pi$
$977$	−38.0000			−1.21573			−0.607864	+	0.794041i	$0.707973\pi$
$978$		0			0
$979$	−5.00000			−0.159801
$980$	8.00000	−	4.00000i	0.255551	−	0.127775i
$981$		0			0
$982$	−84.0000			−2.68055
$983$	16.0000			0.510321			0.255160	−	0.966899i	$-0.417872\pi$
$983$	16.0000			0.510321			0.255160	+	0.966899i	$0.417872\pi$
$984$		0			0
$985$	−16.0000	+	8.00000i	−0.509802	+	0.254901i
$986$		0			0
$987$		0			0
$988$	−24.0000	+	36.0000i	−0.763542	+	1.14531i
$989$	−54.0000			−1.71710
$990$		0			0
$991$	47.0000			1.49300			0.746502	−	0.665383i	$-0.231732\pi$
$991$	47.0000			1.49300			0.746502	+	0.665383i	$0.231732\pi$
$992$		0			0
$993$		0			0
$994$		−	30.0000i		−	0.951542i
$995$		0			0
$996$		0			0
$997$		−	42.0000i		−	1.33015i	−0.746775	−	0.665077i	$-0.768399\pi$
$997$		−	42.0000i		−	1.33015i	0.746775	−	0.665077i	$-0.231601\pi$
$998$			48.0000i			1.51941i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.h.d.64.1		2
3.2	odd	2		195.2.h.a.64.1	✓	2
5.4	even	2		585.2.h.a.64.1		2
12.11	even	2		3120.2.r.a.2209.2		2
13.12	even	2		585.2.h.a.64.2		2
15.2	even	4		975.2.b.a.376.1		2
15.8	even	4		975.2.b.c.376.2		2
15.14	odd	2		195.2.h.b.64.2	yes	2
39.38	odd	2		195.2.h.b.64.1	yes	2
60.59	even	2		3120.2.r.f.2209.1		2
65.64	even	2	inner	585.2.h.d.64.2		2
156.155	even	2		3120.2.r.f.2209.2		2
195.38	even	4		975.2.b.c.376.1		2
195.77	even	4		975.2.b.a.376.2		2
195.194	odd	2		195.2.h.a.64.2	yes	2
780.779	even	2		3120.2.r.a.2209.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.h.a.64.1	✓	2	3.2	odd	2
195.2.h.a.64.2	yes	2	195.194	odd	2
195.2.h.b.64.1	yes	2	39.38	odd	2
195.2.h.b.64.2	yes	2	15.14	odd	2
585.2.h.a.64.1		2	5.4	even	2
585.2.h.a.64.2		2	13.12	even	2
585.2.h.d.64.1		2	1.1	even	1	trivial
585.2.h.d.64.2		2	65.64	even	2	inner
975.2.b.a.376.1		2	15.2	even	4
975.2.b.a.376.2		2	195.77	even	4
975.2.b.c.376.1		2	195.38	even	4
975.2.b.c.376.2		2	15.8	even	4
3120.2.r.a.2209.1		2	780.779	even	2
3120.2.r.a.2209.2		2	12.11	even	2
3120.2.r.f.2209.1		2	60.59	even	2
3120.2.r.f.2209.2		2	156.155	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} +2.00000 q^{4} +(2.00000 - 1.00000i) q^{5} +3.00000 q^{7} +O(q^{10})\)	\(q+2.00000 q^{2} +2.00000 q^{4} +(2.00000 - 1.00000i) q^{5} +3.00000 q^{7} +(4.00000 - 2.00000i) q^{10} +5.00000i q^{11} +(-3.00000 - 2.00000i) q^{13} +6.00000 q^{14} -4.00000 q^{16} -3.00000i q^{17} -6.00000i q^{19} +(4.00000 - 2.00000i) q^{20} +10.0000i q^{22} +9.00000i q^{23} +(3.00000 - 4.00000i) q^{25} +(-6.00000 - 4.00000i) q^{26} +6.00000 q^{28} -8.00000 q^{32} -6.00000i q^{34} +(6.00000 - 3.00000i) q^{35} +3.00000 q^{37} -12.0000i q^{38} -5.00000i q^{41} +6.00000i q^{43} +10.0000i q^{44} +18.0000i q^{46} -8.00000 q^{47} +2.00000 q^{49} +(6.00000 - 8.00000i) q^{50} +(-6.00000 - 4.00000i) q^{52} +9.00000i q^{53} +(5.00000 + 10.0000i) q^{55} -4.00000i q^{59} -3.00000 q^{61} -8.00000 q^{64} +(-8.00000 - 1.00000i) q^{65} -12.0000 q^{67} -6.00000i q^{68} +(12.0000 - 6.00000i) q^{70} -5.00000i q^{71} -6.00000 q^{73} +6.00000 q^{74} -12.0000i q^{76} +15.0000i q^{77} +15.0000 q^{79} +(-8.00000 + 4.00000i) q^{80} -10.0000i q^{82} -4.00000 q^{83} +(-3.00000 - 6.00000i) q^{85} +12.0000i q^{86} +1.00000i q^{89} +(-9.00000 - 6.00000i) q^{91} +18.0000i q^{92} -16.0000 q^{94} +(-6.00000 - 12.0000i) q^{95} +3.00000 q^{97} +4.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 4 q^{2} + 4 q^{4} + 4 q^{5} + 6 q^{7}+O(q^{10}) \) 2 * q + 4 * q^2 + 4 * q^4 + 4 * q^5 + 6 * q^7	\( 2 q + 4 q^{2} + 4 q^{4} + 4 q^{5} + 6 q^{7} + 8 q^{10} - 6 q^{13} + 12 q^{14} - 8 q^{16} + 8 q^{20} + 6 q^{25} - 12 q^{26} + 12 q^{28} - 16 q^{32} + 12 q^{35} + 6 q^{37} - 16 q^{47} + 4 q^{49} + 12 q^{50} - 12 q^{52} + 10 q^{55} - 6 q^{61} - 16 q^{64} - 16 q^{65} - 24 q^{67} + 24 q^{70} - 12 q^{73} + 12 q^{74} + 30 q^{79} - 16 q^{80} - 8 q^{83} - 6 q^{85} - 18 q^{91} - 32 q^{94} - 12 q^{95} + 6 q^{97} + 8 q^{98}+O(q^{100}) \) 2 * q + 4 * q^2 + 4 * q^4 + 4 * q^5 + 6 * q^7 + 8 * q^10 - 6 * q^13 + 12 * q^14 - 8 * q^16 + 8 * q^20 + 6 * q^25 - 12 * q^26 + 12 * q^28 - 16 * q^32 + 12 * q^35 + 6 * q^37 - 16 * q^47 + 4 * q^49 + 12 * q^50 - 12 * q^52 + 10 * q^55 - 6 * q^61 - 16 * q^64 - 16 * q^65 - 24 * q^67 + 24 * q^70 - 12 * q^73 + 12 * q^74 + 30 * q^79 - 16 * q^80 - 8 * q^83 - 6 * q^85 - 18 * q^91 - 32 * q^94 - 12 * q^95 + 6 * q^97 + 8 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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