LMFDB - Embedded newform 1734.2.b.b.577.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1734,2,Mod(577,1734)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1734, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1734.577");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1734 = 2 \cdot 3 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1734.b (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$13.8460597105$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 102)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			577.2
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	1734.577
Dual form			1734.2.b.b.577.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000i q^{3} +1.00000 q^{4} -2.00000i q^{5} -1.00000i q^{6} -1.00000 q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000i q^{3} +1.00000 q^{4} -2.00000i q^{5} -1.00000i q^{6} -1.00000 q^{8} -1.00000 q^{9} +2.00000i q^{10} +4.00000i q^{11} +1.00000i q^{12} -2.00000 q^{13} +2.00000 q^{15} +1.00000 q^{16} +1.00000 q^{18} -4.00000 q^{19} -2.00000i q^{20} -4.00000i q^{22} -1.00000i q^{24} +1.00000 q^{25} +2.00000 q^{26} -1.00000i q^{27} -10.0000i q^{29} -2.00000 q^{30} +8.00000i q^{31} -1.00000 q^{32} -4.00000 q^{33} -1.00000 q^{36} -2.00000i q^{37} +4.00000 q^{38} -2.00000i q^{39} +2.00000i q^{40} -10.0000i q^{41} -12.0000 q^{43} +4.00000i q^{44} +2.00000i q^{45} +1.00000i q^{48} +7.00000 q^{49} -1.00000 q^{50} -2.00000 q^{52} -6.00000 q^{53} +1.00000i q^{54} +8.00000 q^{55} -4.00000i q^{57} +10.0000i q^{58} -12.0000 q^{59} +2.00000 q^{60} +10.0000i q^{61} -8.00000i q^{62} +1.00000 q^{64} +4.00000i q^{65} +4.00000 q^{66} -12.0000 q^{67} +1.00000 q^{72} +10.0000i q^{73} +2.00000i q^{74} +1.00000i q^{75} -4.00000 q^{76} +2.00000i q^{78} +8.00000i q^{79} -2.00000i q^{80} +1.00000 q^{81} +10.0000i q^{82} -4.00000 q^{83} +12.0000 q^{86} +10.0000 q^{87} -4.00000i q^{88} -6.00000 q^{89} -2.00000i q^{90} -8.00000 q^{93} +8.00000i q^{95} -1.00000i q^{96} -14.0000i q^{97} -7.00000 q^{98} -4.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 2 q^{4} - 2 q^{8} - 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + 2 * q^4 - 2 * q^8 - 2 * q^9	$ 2 q - 2 q^{2} + 2 q^{4} - 2 q^{8} - 2 q^{9} - 4 q^{13} + 4 q^{15} + 2 q^{16} + 2 q^{18} - 8 q^{19} + 2 q^{25} + 4 q^{26} - 4 q^{30} - 2 q^{32} - 8 q^{33} - 2 q^{36} + 8 q^{38} - 24 q^{43} + 14 q^{49} - 2 q^{50} - 4 q^{52} - 12 q^{53} + 16 q^{55} - 24 q^{59} + 4 q^{60} + 2 q^{64} + 8 q^{66} - 24 q^{67} + 2 q^{72} - 8 q^{76} + 2 q^{81} - 8 q^{83} + 24 q^{86} + 20 q^{87} - 12 q^{89} - 16 q^{93} - 14 q^{98}+O(q^{100}) $ 2 * q - 2 * q^2 + 2 * q^4 - 2 * q^8 - 2 * q^9 - 4 * q^13 + 4 * q^15 + 2 * q^16 + 2 * q^18 - 8 * q^19 + 2 * q^25 + 4 * q^26 - 4 * q^30 - 2 * q^32 - 8 * q^33 - 2 * q^36 + 8 * q^38 - 24 * q^43 + 14 * q^49 - 2 * q^50 - 4 * q^52 - 12 * q^53 + 16 * q^55 - 24 * q^59 + 4 * q^60 + 2 * q^64 + 8 * q^66 - 24 * q^67 + 2 * q^72 - 8 * q^76 + 2 * q^81 - 8 * q^83 + 24 * q^86 + 20 * q^87 - 12 * q^89 - 16 * q^93 - 14 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1734\mathbb{Z}\right)^\times$.

$n$	$1157$	$1159$
$\chi(n)$	$1$	$-1$

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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.00000i	0.577350i
$3$	1.00000i	0.577350i
$4$	1.00000	0.500000
$5$	− 2.00000i	− 0.894427i	−0.894427	−	0.447214i	$-0.852416\pi$
$5$	− 2.00000i	− 0.894427i	0.894427	−	0.447214i	$-0.147584\pi$
$6$	− 1.00000i	− 0.408248i
$7$	0	0	1.00000			$0$
$7$	0	0	−1.00000			$\pi$
$8$	−1.00000	−0.353553
$9$	−1.00000	−0.333333
$10$	2.00000i	0.632456i
$11$	4.00000i	1.20605i	0.797724	+	0.603023i	$0.206037\pi$
$11$	4.00000i	1.20605i	−0.797724	+	0.603023i	$0.793963\pi$
$12$	1.00000i	0.288675i
$13$	−2.00000	−0.554700	−0.277350	−	0.960769i	$-0.589456\pi$
$13$	−2.00000	−0.554700	−0.277350	+	0.960769i	$0.589456\pi$
$14$	0	0
$15$	2.00000	0.516398
$16$	1.00000	0.250000
$17$	0	0
$17$	0	0
$18$	1.00000	0.235702
$19$	−4.00000	−0.917663	−0.458831	−	0.888523i	$-0.651732\pi$
$19$	−4.00000	−0.917663	−0.458831	+	0.888523i	$0.651732\pi$
$20$	− 2.00000i	− 0.447214i
$21$	0	0
$22$	− 4.00000i	− 0.852803i
$23$	0	0	1.00000			$0$
$23$	0	0	−1.00000			$\pi$
$24$	− 1.00000i	− 0.204124i
$25$	1.00000	0.200000
$26$	2.00000	0.392232
$27$	− 1.00000i	− 0.192450i
$28$	0	0
$29$	− 10.0000i	− 1.85695i	−0.371391	−	0.928477i	$-0.621119\pi$
$29$	− 10.0000i	− 1.85695i	0.371391	−	0.928477i	$-0.378881\pi$
$30$	−2.00000	−0.365148
$31$	8.00000i	1.43684i	0.695608	+	0.718421i	$0.255135\pi$
$31$	8.00000i	1.43684i	−0.695608	+	0.718421i	$0.744865\pi$
$32$	−1.00000	−0.176777
$33$	−4.00000	−0.696311
$34$	0	0
$35$	0	0
$36$	−1.00000	−0.166667
$37$	− 2.00000i	− 0.328798i	−0.986394	−	0.164399i	$-0.947432\pi$
$37$	− 2.00000i	− 0.328798i	0.986394	−	0.164399i	$-0.0525685\pi$
$38$	4.00000	0.648886
$39$	− 2.00000i	− 0.320256i
$40$	2.00000i	0.316228i
$41$	− 10.0000i	− 1.56174i	−0.624695	−	0.780869i	$-0.714777\pi$
$41$	− 10.0000i	− 1.56174i	0.624695	−	0.780869i	$-0.285223\pi$
$42$	0	0
$43$	−12.0000	−1.82998	−0.914991	−	0.403473i	$-0.867803\pi$
$43$	−12.0000	−1.82998	−0.914991	+	0.403473i	$0.867803\pi$
$44$	4.00000i	0.603023i
$45$	2.00000i	0.298142i
$46$	0	0
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	1.00000i	0.144338i
$49$	7.00000	1.00000
$50$	−1.00000	−0.141421
$51$	0	0
$52$	−2.00000	−0.277350
$53$	−6.00000	−0.824163	−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000	−0.824163	−0.412082	+	0.911147i	$0.635198\pi$
$54$	1.00000i	0.136083i
$55$	8.00000	1.07872
$56$	0	0
$57$	− 4.00000i	− 0.529813i
$58$	10.0000i	1.31306i
$59$	−12.0000	−1.56227	−0.781133	−	0.624364i	$-0.785358\pi$
$59$	−12.0000	−1.56227	−0.781133	+	0.624364i	$0.785358\pi$
$60$	2.00000	0.258199
$61$	10.0000i	1.28037i	0.768221	+	0.640184i	$0.221142\pi$
$61$	10.0000i	1.28037i	−0.768221	+	0.640184i	$0.778858\pi$
$62$	− 8.00000i	− 1.01600i
$63$	0	0
$64$	1.00000	0.125000
$65$	4.00000i	0.496139i
$66$	4.00000	0.492366
$67$	−12.0000	−1.46603	−0.733017	−	0.680211i	$-0.761888\pi$
$67$	−12.0000	−1.46603	−0.733017	+	0.680211i	$0.761888\pi$
$68$	0	0
$69$	0	0
$70$	0	0
$71$	0	0	1.00000			$0$
$71$	0	0	−1.00000			$\pi$
$72$	1.00000	0.117851
$73$	10.0000i	1.17041i	0.810885	+	0.585206i	$0.198986\pi$
$73$	10.0000i	1.17041i	−0.810885	+	0.585206i	$0.801014\pi$
$74$	2.00000i	0.232495i
$75$	1.00000i	0.115470i
$76$	−4.00000	−0.458831
$77$	0	0
$78$	2.00000i	0.226455i
$79$	8.00000i	0.900070i	0.893011	+	0.450035i	$0.148589\pi$
$79$	8.00000i	0.900070i	−0.893011	+	0.450035i	$0.851411\pi$
$80$	− 2.00000i	− 0.223607i
$81$	1.00000	0.111111
$82$	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
$85$	0	0
$86$	12.0000	1.29399
$87$	10.0000	1.07211
$88$	− 4.00000i	− 0.426401i
$89$	−6.00000	−0.635999	−0.317999	−	0.948091i	$-0.603011\pi$
$89$	−6.00000	−0.635999	−0.317999	+	0.948091i	$0.603011\pi$
$90$	− 2.00000i	− 0.210819i
$91$	0	0
$92$	0	0
$93$	−8.00000	−0.829561
$94$	0	0
$95$	8.00000i	0.820783i
$96$	− 1.00000i	− 0.102062i
$97$	− 14.0000i	− 1.42148i	−0.703452	−	0.710742i	$-0.748359\pi$
$97$	− 14.0000i	− 1.42148i	0.703452	−	0.710742i	$-0.251641\pi$
$98$	−7.00000	−0.707107
$99$	− 4.00000i	− 0.402015i
$100$	1.00000	0.100000
$101$	−10.0000	−0.995037	−0.497519	−	0.867453i	$-0.665755\pi$
$101$	−10.0000	−0.995037	−0.497519	+	0.867453i	$0.665755\pi$
$102$	0	0
$103$	−8.00000	−0.788263	−0.394132	−	0.919054i	$-0.628955\pi$
$103$	−8.00000	−0.788263	−0.394132	+	0.919054i	$0.628955\pi$
$104$	2.00000	0.196116
$105$	0	0
$106$	6.00000	0.582772
$107$	− 4.00000i	− 0.386695i	−0.981130	−	0.193347i	$-0.938066\pi$
$107$	− 4.00000i	− 0.386695i	0.981130	−	0.193347i	$-0.0619344\pi$
$108$	− 1.00000i	− 0.0962250i
$109$	10.0000i	0.957826i	0.877862	+	0.478913i	$0.158969\pi$
$109$	10.0000i	0.957826i	−0.877862	+	0.478913i	$0.841031\pi$
$110$	−8.00000	−0.762770
$111$	2.00000	0.189832
$112$	0	0
$113$	− 2.00000i	− 0.188144i	−0.995565	−	0.0940721i	$-0.970012\pi$
$113$	− 2.00000i	− 0.188144i	0.995565	−	0.0940721i	$-0.0299884\pi$
$114$	4.00000i	0.374634i
$115$	0	0
$116$	− 10.0000i	− 0.928477i
$117$	2.00000	0.184900
$118$	12.0000	1.10469
$119$	0	0
$120$	−2.00000	−0.182574
$121$	−5.00000	−0.454545
$122$	− 10.0000i	− 0.905357i
$123$	10.0000	0.901670
$124$	8.00000i	0.718421i
$125$	− 12.0000i	− 1.07331i
$126$	0	0
$127$	0	0		−	1.00000i	$-0.5\pi$
$127$	0	0			1.00000i	$0.5\pi$
$128$	−1.00000	−0.0883883
$129$	− 12.0000i	− 1.05654i
$130$	− 4.00000i	− 0.350823i
$131$	− 12.0000i	− 1.04844i	−0.851581	−	0.524222i	$-0.824356\pi$
$131$	− 12.0000i	− 1.04844i	0.851581	−	0.524222i	$-0.175644\pi$
$132$	−4.00000	−0.348155
$133$	0	0
$134$	12.0000	1.03664
$135$	−2.00000	−0.172133
$136$	0	0
$137$	10.0000	0.854358	0.427179	−	0.904167i	$-0.359507\pi$
$137$	10.0000	0.854358	0.427179	+	0.904167i	$0.359507\pi$
$138$	0	0
$139$	− 4.00000i	− 0.339276i	−0.985506	−	0.169638i	$-0.945740\pi$
$139$	− 4.00000i	− 0.339276i	0.985506	−	0.169638i	$-0.0542598\pi$
$140$	0	0
$141$	0	0
$142$	0	0
$143$	− 8.00000i	− 0.668994i
$144$	−1.00000	−0.0833333
$145$	−20.0000	−1.66091
$146$	− 10.0000i	− 0.827606i
$147$	7.00000i	0.577350i
$148$	− 2.00000i	− 0.164399i
$149$	−10.0000	−0.819232	−0.409616	−	0.912258i	$-0.634337\pi$
$149$	−10.0000	−0.819232	−0.409616	+	0.912258i	$0.634337\pi$
$150$	− 1.00000i	− 0.0816497i
$151$	−24.0000	−1.95309	−0.976546	−	0.215308i	$-0.930924\pi$
$151$	−24.0000	−1.95309	−0.976546	+	0.215308i	$0.930924\pi$
$152$	4.00000	0.324443
$153$	0	0
$154$	0	0
$155$	16.0000	1.28515
$156$	− 2.00000i	− 0.160128i
$157$	−2.00000	−0.159617	−0.0798087	−	0.996810i	$-0.525431\pi$
$157$	−2.00000	−0.159617	−0.0798087	+	0.996810i	$0.525431\pi$
$158$	− 8.00000i	− 0.636446i
$159$	− 6.00000i	− 0.475831i
$160$	2.00000i	0.158114i
$161$	0	0
$162$	−1.00000	−0.0785674
$163$	− 4.00000i	− 0.313304i	−0.987654	−	0.156652i	$-0.949930\pi$
$163$	− 4.00000i	− 0.313304i	0.987654	−	0.156652i	$-0.0500701\pi$
$164$	− 10.0000i	− 0.780869i
$165$	8.00000i	0.622799i
$166$	4.00000	0.310460
$167$	16.0000i	1.23812i	0.785345	+	0.619059i	$0.212486\pi$
$167$	16.0000i	1.23812i	−0.785345	+	0.619059i	$0.787514\pi$
$168$	0	0
$169$	−9.00000	−0.692308
$170$	0	0
$171$	4.00000	0.305888
$172$	−12.0000	−0.914991
$173$	6.00000i	0.456172i	0.973641	+	0.228086i	$0.0732467\pi$
$173$	6.00000i	0.456172i	−0.973641	+	0.228086i	$0.926753\pi$
$174$	−10.0000	−0.758098
$175$	0	0
$176$	4.00000i	0.301511i
$177$	− 12.0000i	− 0.901975i
$178$	6.00000	0.449719
$179$	12.0000	0.896922	0.448461	−	0.893802i	$-0.351972\pi$
$179$	12.0000	0.896922	0.448461	+	0.893802i	$0.351972\pi$
$180$	2.00000i	0.149071i
$181$	− 14.0000i	− 1.04061i	−0.853980	−	0.520306i	$-0.825818\pi$
$181$	− 14.0000i	− 1.04061i	0.853980	−	0.520306i	$-0.174182\pi$
$182$	0	0
$183$	−10.0000	−0.739221
$184$	0	0
$185$	−4.00000	−0.294086
$186$	8.00000	0.586588
$187$	0	0
$188$	0	0
$189$	0	0
$190$	− 8.00000i	− 0.580381i
$191$	−16.0000	−1.15772	−0.578860	−	0.815427i	$-0.696502\pi$
$191$	−16.0000	−1.15772	−0.578860	+	0.815427i	$0.696502\pi$
$192$	1.00000i	0.0721688i
$193$	− 18.0000i	− 1.29567i	−0.761781	−	0.647834i	$-0.775675\pi$
$193$	− 18.0000i	− 1.29567i	0.761781	−	0.647834i	$-0.224325\pi$
$194$	14.0000i	1.00514i
$195$	−4.00000	−0.286446
$196$	7.00000	0.500000
$197$	− 14.0000i	− 0.997459i	−0.866758	−	0.498729i	$-0.833800\pi$
$197$	− 14.0000i	− 0.997459i	0.866758	−	0.498729i	$-0.166200\pi$
$198$	4.00000i	0.284268i
$199$	0	0	1.00000			$0$
$199$	0	0	−1.00000			$\pi$
$200$	−1.00000	−0.0707107
$201$	− 12.0000i	− 0.846415i
$202$	10.0000	0.703598
$203$	0	0
$204$	0	0
$205$	−20.0000	−1.39686
$206$	8.00000	0.557386
$207$	0	0
$208$	−2.00000	−0.138675
$209$	− 16.0000i	− 1.10674i
$210$	0	0
$211$	28.0000i	1.92760i	0.266627	+	0.963800i	$0.414091\pi$
$211$	28.0000i	1.92760i	−0.266627	+	0.963800i	$0.585909\pi$
$212$	−6.00000	−0.412082
$213$	0	0
$214$	4.00000i	0.273434i
$215$	24.0000i	1.63679i
$216$	1.00000i	0.0680414i
$217$	0	0
$218$	− 10.0000i	− 0.677285i
$219$	−10.0000	−0.675737
$220$	8.00000	0.539360
$221$	0	0
$222$	−2.00000	−0.134231
$223$	−16.0000	−1.07144	−0.535720	−	0.844396i	$-0.679960\pi$
$223$	−16.0000	−1.07144	−0.535720	+	0.844396i	$0.679960\pi$
$224$	0	0
$225$	−1.00000	−0.0666667
$226$	2.00000i	0.133038i
$227$	− 4.00000i	− 0.265489i	−0.991150	−	0.132745i	$-0.957621\pi$
$227$	− 4.00000i	− 0.265489i	0.991150	−	0.132745i	$-0.0423790\pi$
$228$	− 4.00000i	− 0.264906i
$229$	26.0000	1.71813	0.859064	−	0.511868i	$-0.171046\pi$
$229$	26.0000	1.71813	0.859064	+	0.511868i	$0.171046\pi$
$230$	0	0
$231$	0	0
$232$	10.0000i	0.656532i
$233$	26.0000i	1.70332i	0.524097	+	0.851658i	$0.324403\pi$
$233$	26.0000i	1.70332i	−0.524097	+	0.851658i	$0.675597\pi$
$234$	−2.00000	−0.130744
$235$	0	0
$236$	−12.0000	−0.781133
$237$	−8.00000	−0.519656
$238$	0	0
$239$	0	0		−	1.00000i	$-0.5\pi$
$239$	0	0			1.00000i	$0.5\pi$
$240$	2.00000	0.129099
$241$	2.00000i	0.128831i	0.997923	+	0.0644157i	$0.0205183\pi$
$241$	2.00000i	0.128831i	−0.997923	+	0.0644157i	$0.979482\pi$
$242$	5.00000	0.321412
$243$	1.00000i	0.0641500i
$244$	10.0000i	0.640184i
$245$	− 14.0000i	− 0.894427i
$246$	−10.0000	−0.637577
$247$	8.00000	0.509028
$248$	− 8.00000i	− 0.508001i
$249$	− 4.00000i	− 0.253490i
$250$	12.0000i	0.758947i
$251$	28.0000	1.76734	0.883672	−	0.468106i	$-0.155064\pi$
$251$	28.0000	1.76734	0.883672	+	0.468106i	$0.155064\pi$
$252$	0	0
$253$	0	0
$254$	0	0
$255$	0	0
$256$	1.00000	0.0625000
$257$	−2.00000	−0.124757	−0.0623783	−	0.998053i	$-0.519869\pi$
$257$	−2.00000	−0.124757	−0.0623783	+	0.998053i	$0.519869\pi$
$258$	12.0000i	0.747087i
$259$	0	0
$260$	4.00000i	0.248069i
$261$	10.0000i	0.618984i
$262$	12.0000i	0.741362i
$263$	8.00000	0.493301	0.246651	−	0.969104i	$-0.420670\pi$
$263$	8.00000	0.493301	0.246651	+	0.969104i	$0.420670\pi$
$264$	4.00000	0.246183
$265$	12.0000i	0.737154i
$266$	0	0
$267$	− 6.00000i	− 0.367194i
$268$	−12.0000	−0.733017
$269$	6.00000i	0.365826i	0.983129	+	0.182913i	$0.0585527\pi$
$269$	6.00000i	0.365826i	−0.983129	+	0.182913i	$0.941447\pi$
$270$	2.00000	0.121716
$271$	16.0000	0.971931	0.485965	−	0.873978i	$-0.338468\pi$
$271$	16.0000	0.971931	0.485965	+	0.873978i	$0.338468\pi$
$272$	0	0
$273$	0	0
$274$	−10.0000	−0.604122
$275$	4.00000i	0.241209i
$276$	0	0
$277$	30.0000i	1.80253i	0.433273	+	0.901263i	$0.357359\pi$
$277$	30.0000i	1.80253i	−0.433273	+	0.901263i	$0.642641\pi$
$278$	4.00000i	0.239904i
$279$	− 8.00000i	− 0.478947i
$280$	0	0
$281$	6.00000	0.357930	0.178965	−	0.983855i	$-0.442725\pi$
$281$	6.00000	0.357930	0.178965	+	0.983855i	$0.442725\pi$
$282$	0	0
$283$	− 12.0000i	− 0.713326i	−0.934233	−	0.356663i	$-0.883914\pi$
$283$	− 12.0000i	− 0.713326i	0.934233	−	0.356663i	$-0.116086\pi$
$284$	0	0
$285$	−8.00000	−0.473879
$286$	8.00000i	0.473050i
$287$	0	0
$288$	1.00000	0.0589256
$289$	0	0
$290$	20.0000	1.17444
$291$	14.0000	0.820695
$292$	10.0000i	0.585206i
$293$	−26.0000	−1.51894	−0.759468	−	0.650545i	$-0.774541\pi$
$293$	−26.0000	−1.51894	−0.759468	+	0.650545i	$0.774541\pi$
$294$	− 7.00000i	− 0.408248i
$295$	24.0000i	1.39733i
$296$	2.00000i	0.116248i
$297$	4.00000	0.232104
$298$	10.0000	0.579284
$299$	0	0
$300$	1.00000i	0.0577350i
$301$	0	0
$302$	24.0000	1.38104
$303$	− 10.0000i	− 0.574485i
$304$	−4.00000	−0.229416
$305$	20.0000	1.14520
$306$	0	0
$307$	−12.0000	−0.684876	−0.342438	−	0.939540i	$-0.611253\pi$
$307$	−12.0000	−0.684876	−0.342438	+	0.939540i	$0.611253\pi$
$308$	0	0
$309$	− 8.00000i	− 0.455104i
$310$	−16.0000	−0.908739
$311$	0	0	1.00000			$0$
$311$	0	0	−1.00000			$\pi$
$312$	2.00000i	0.113228i
$313$	− 10.0000i	− 0.565233i	−0.959233	−	0.282617i	$-0.908798\pi$
$313$	− 10.0000i	− 0.565233i	0.959233	−	0.282617i	$-0.0912024\pi$
$314$	2.00000	0.112867
$315$	0	0
$316$	8.00000i	0.450035i
$317$	− 6.00000i	− 0.336994i	−0.985702	−	0.168497i	$-0.946109\pi$
$317$	− 6.00000i	− 0.336994i	0.985702	−	0.168497i	$-0.0538913\pi$
$318$	6.00000i	0.336463i
$319$	40.0000	2.23957
$320$	− 2.00000i	− 0.111803i
$321$	4.00000	0.223258
$322$	0	0
$323$	0	0
$324$	1.00000	0.0555556
$325$	−2.00000	−0.110940
$326$	4.00000i	0.221540i
$327$	−10.0000	−0.553001
$328$	10.0000i	0.552158i
$329$	0	0
$330$	− 8.00000i	− 0.440386i
$331$	20.0000	1.09930	0.549650	−	0.835395i	$-0.314761\pi$
$331$	20.0000	1.09930	0.549650	+	0.835395i	$0.314761\pi$
$332$	−4.00000	−0.219529
$333$	2.00000i	0.109599i
$334$	− 16.0000i	− 0.875481i
$335$	24.0000i	1.31126i
$336$	0	0
$337$	− 14.0000i	− 0.762629i	−0.924445	−	0.381314i	$-0.875472\pi$
$337$	− 14.0000i	− 0.762629i	0.924445	−	0.381314i	$-0.124528\pi$
$338$	9.00000	0.489535
$339$	2.00000	0.108625
$340$	0	0
$341$	−32.0000	−1.73290
$342$	−4.00000	−0.216295
$343$	0	0
$344$	12.0000	0.646997
$345$	0	0
$346$	− 6.00000i	− 0.322562i
$347$	− 28.0000i	− 1.50312i	−0.659665	−	0.751559i	$-0.729302\pi$
$347$	− 28.0000i	− 1.50312i	0.659665	−	0.751559i	$-0.270698\pi$
$348$	10.0000	0.536056
$349$	−14.0000	−0.749403	−0.374701	−	0.927146i	$-0.622255\pi$
$349$	−14.0000	−0.749403	−0.374701	+	0.927146i	$0.622255\pi$
$350$	0	0
$351$	2.00000i	0.106752i
$352$	− 4.00000i	− 0.213201i
$353$	−30.0000	−1.59674	−0.798369	−	0.602168i	$-0.794304\pi$
$353$	−30.0000	−1.59674	−0.798369	+	0.602168i	$0.794304\pi$
$354$	12.0000i	0.637793i
$355$	0	0
$356$	−6.00000	−0.317999
$357$	0	0
$358$	−12.0000	−0.634220
$359$	24.0000	1.26667	0.633336	−	0.773877i	$-0.281685\pi$
$359$	24.0000	1.26667	0.633336	+	0.773877i	$0.281685\pi$
$360$	− 2.00000i	− 0.105409i
$361$	−3.00000	−0.157895
$362$	14.0000i	0.735824i
$363$	− 5.00000i	− 0.262432i
$364$	0	0
$365$	20.0000	1.04685
$366$	10.0000	0.522708
$367$	− 24.0000i	− 1.25279i	−0.779506	−	0.626395i	$-0.784530\pi$
$367$	− 24.0000i	− 1.25279i	0.779506	−	0.626395i	$-0.215470\pi$
$368$	0	0
$369$	10.0000i	0.520579i
$370$	4.00000	0.207950
$371$	0	0
$372$	−8.00000	−0.414781
$373$	6.00000	0.310668	0.155334	−	0.987862i	$-0.450355\pi$
$373$	6.00000	0.310668	0.155334	+	0.987862i	$0.450355\pi$
$374$	0	0
$375$	12.0000	0.619677
$376$	0	0
$377$	20.0000i	1.03005i
$378$	0	0
$379$	− 4.00000i	− 0.205466i	−0.994709	−	0.102733i	$-0.967241\pi$
$379$	− 4.00000i	− 0.205466i	0.994709	−	0.102733i	$-0.0327588\pi$
$380$	8.00000i	0.410391i
$381$	0	0
$382$	16.0000	0.818631
$383$	16.0000	0.817562	0.408781	−	0.912633i	$-0.365954\pi$
$383$	16.0000	0.817562	0.408781	+	0.912633i	$0.365954\pi$
$384$	− 1.00000i	− 0.0510310i
$385$	0	0
$386$	18.0000i	0.916176i
$387$	12.0000	0.609994
$388$	− 14.0000i	− 0.710742i
$389$	26.0000	1.31825	0.659126	−	0.752032i	$-0.270926\pi$
$389$	26.0000	1.31825	0.659126	+	0.752032i	$0.270926\pi$
$390$	4.00000	0.202548
$391$	0	0
$392$	−7.00000	−0.353553
$393$	12.0000	0.605320
$394$	14.0000i	0.705310i
$395$	16.0000	0.805047
$396$	− 4.00000i	− 0.201008i
$397$	26.0000i	1.30490i	0.757831	+	0.652451i	$0.226259\pi$
$397$	26.0000i	1.30490i	−0.757831	+	0.652451i	$0.773741\pi$
$398$	0	0
$399$	0	0
$400$	1.00000	0.0500000
$401$	14.0000i	0.699127i	0.936913	+	0.349563i	$0.113670\pi$
$401$	14.0000i	0.699127i	−0.936913	+	0.349563i	$0.886330\pi$
$402$	12.0000i	0.598506i
$403$	− 16.0000i	− 0.797017i
$404$	−10.0000	−0.497519
$405$	− 2.00000i	− 0.0993808i
$406$	0	0
$407$	8.00000	0.396545
$408$	0	0
$409$	26.0000	1.28562	0.642809	−	0.766027i	$-0.277769\pi$
$409$	26.0000	1.28562	0.642809	+	0.766027i	$0.277769\pi$
$410$	20.0000	0.987730
$411$	10.0000i	0.493264i
$412$	−8.00000	−0.394132
$413$	0	0
$414$	0	0
$415$	8.00000i	0.392705i
$416$	2.00000	0.0980581
$417$	4.00000	0.195881
$418$	16.0000i	0.782586i
$419$	− 4.00000i	− 0.195413i	−0.995215	−	0.0977064i	$-0.968849\pi$
$419$	− 4.00000i	− 0.195413i	0.995215	−	0.0977064i	$-0.0311506\pi$
$420$	0	0
$421$	22.0000	1.07221	0.536107	−	0.844150i	$-0.319894\pi$
$421$	22.0000	1.07221	0.536107	+	0.844150i	$0.319894\pi$
$422$	− 28.0000i	− 1.36302i
$423$	0	0
$424$	6.00000	0.291386
$425$	0	0
$426$	0	0
$427$	0	0
$428$	− 4.00000i	− 0.193347i
$429$	8.00000	0.386244
$430$	− 24.0000i	− 1.15738i
$431$	8.00000i	0.385346i	0.981263	+	0.192673i	$0.0617157\pi$
$431$	8.00000i	0.385346i	−0.981263	+	0.192673i	$0.938284\pi$
$432$	− 1.00000i	− 0.0481125i
$433$	14.0000	0.672797	0.336399	−	0.941720i	$-0.390791\pi$
$433$	14.0000	0.672797	0.336399	+	0.941720i	$0.390791\pi$
$434$	0	0
$435$	− 20.0000i	− 0.958927i
$436$	10.0000i	0.478913i
$437$	0	0
$438$	10.0000	0.477818
$439$	16.0000i	0.763638i	0.924237	+	0.381819i	$0.124702\pi$
$439$	16.0000i	0.763638i	−0.924237	+	0.381819i	$0.875298\pi$
$440$	−8.00000	−0.381385
$441$	−7.00000	−0.333333
$442$	0	0
$443$	−4.00000	−0.190046	−0.0950229	−	0.995475i	$-0.530292\pi$
$443$	−4.00000	−0.190046	−0.0950229	+	0.995475i	$0.530292\pi$
$444$	2.00000	0.0949158
$445$	12.0000i	0.568855i
$446$	16.0000	0.757622
$447$	− 10.0000i	− 0.472984i
$448$	0	0
$449$	− 2.00000i	− 0.0943858i	−0.998886	−	0.0471929i	$-0.984972\pi$
$449$	− 2.00000i	− 0.0943858i	0.998886	−	0.0471929i	$-0.0150276\pi$
$450$	1.00000	0.0471405
$451$	40.0000	1.88353
$452$	− 2.00000i	− 0.0940721i
$453$	− 24.0000i	− 1.12762i
$454$	4.00000i	0.187729i
$455$	0	0
$456$	4.00000i	0.187317i
$457$	−10.0000	−0.467780	−0.233890	−	0.972263i	$-0.575146\pi$
$457$	−10.0000	−0.467780	−0.233890	+	0.972263i	$0.575146\pi$
$458$	−26.0000	−1.21490
$459$	0	0
$460$	0	0
$461$	−30.0000	−1.39724	−0.698620	−	0.715493i	$-0.746202\pi$
$461$	−30.0000	−1.39724	−0.698620	+	0.715493i	$0.746202\pi$
$462$	0	0
$463$	32.0000	1.48717	0.743583	−	0.668644i	$-0.233125\pi$
$463$	32.0000	1.48717	0.743583	+	0.668644i	$0.233125\pi$
$464$	− 10.0000i	− 0.464238i
$465$	16.0000i	0.741982i
$466$	− 26.0000i	− 1.20443i
$467$	12.0000	0.555294	0.277647	−	0.960683i	$-0.410445\pi$
$467$	12.0000	0.555294	0.277647	+	0.960683i	$0.410445\pi$
$468$	2.00000	0.0924500
$469$	0	0
$470$	0	0
$471$	− 2.00000i	− 0.0921551i
$472$	12.0000	0.552345
$473$	− 48.0000i	− 2.20704i
$474$	8.00000	0.367452
$475$	−4.00000	−0.183533
$476$	0	0
$477$	6.00000	0.274721
$478$	0	0
$479$	24.0000i	1.09659i	0.836286	+	0.548294i	$0.184723\pi$
$479$	24.0000i	1.09659i	−0.836286	+	0.548294i	$0.815277\pi$
$480$	−2.00000	−0.0912871
$481$	4.00000i	0.182384i
$482$	− 2.00000i	− 0.0910975i
$483$	0	0
$484$	−5.00000	−0.227273
$485$	−28.0000	−1.27141
$486$	− 1.00000i	− 0.0453609i
$487$	16.0000i	0.725029i	0.931978	+	0.362515i	$0.118082\pi$
$487$	16.0000i	0.725029i	−0.931978	+	0.362515i	$0.881918\pi$
$488$	− 10.0000i	− 0.452679i
$489$	4.00000	0.180886
$490$	14.0000i	0.632456i
$491$	−12.0000	−0.541552	−0.270776	−	0.962642i	$-0.587280\pi$
$491$	−12.0000	−0.541552	−0.270776	+	0.962642i	$0.587280\pi$
$492$	10.0000	0.450835
$493$	0	0
$494$	−8.00000	−0.359937
$495$	−8.00000	−0.359573
$496$	8.00000i	0.359211i
$497$	0	0
$498$	4.00000i	0.179244i
$499$	− 4.00000i	− 0.179065i	−0.995984	−	0.0895323i	$-0.971463\pi$
$499$	− 4.00000i	− 0.179065i	0.995984	−	0.0895323i	$-0.0285372\pi$
$500$	− 12.0000i	− 0.536656i
$501$	−16.0000	−0.714827
$502$	−28.0000	−1.24970
$503$	0	0	1.00000			$0$
$503$	0	0	−1.00000			$\pi$
$504$	0	0
$505$	20.0000i	0.889988i
$506$	0	0
$507$	− 9.00000i	− 0.399704i
$508$	0	0
$509$	30.0000	1.32973	0.664863	−	0.746965i	$-0.268490\pi$
$509$	30.0000	1.32973	0.664863	+	0.746965i	$0.268490\pi$
$510$	0	0
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	4.00000i	0.176604i
$514$	2.00000	0.0882162
$515$	16.0000i	0.705044i
$516$	− 12.0000i	− 0.528271i
$517$	0	0
$518$	0	0
$519$	−6.00000	−0.263371
$520$	− 4.00000i	− 0.175412i
$521$	22.0000i	0.963837i	0.876216	+	0.481919i	$0.160060\pi$
$521$	22.0000i	0.963837i	−0.876216	+	0.481919i	$0.839940\pi$
$522$	− 10.0000i	− 0.437688i
$523$	−4.00000	−0.174908	−0.0874539	−	0.996169i	$-0.527873\pi$
$523$	−4.00000	−0.174908	−0.0874539	+	0.996169i	$0.527873\pi$
$524$	− 12.0000i	− 0.524222i
$525$	0	0
$526$	−8.00000	−0.348817
$527$	0	0
$528$	−4.00000	−0.174078
$529$	23.0000	1.00000
$530$	− 12.0000i	− 0.521247i
$531$	12.0000	0.520756
$532$	0	0
$533$	20.0000i	0.866296i
$534$	6.00000i	0.259645i
$535$	−8.00000	−0.345870
$536$	12.0000	0.518321
$537$	12.0000i	0.517838i
$538$	− 6.00000i	− 0.258678i
$539$	28.0000i	1.20605i
$540$	−2.00000	−0.0860663
$541$	− 10.0000i	− 0.429934i	−0.976621	−	0.214967i	$-0.931036\pi$
$541$	− 10.0000i	− 0.429934i	0.976621	−	0.214967i	$-0.0689643\pi$
$542$	−16.0000	−0.687259
$543$	14.0000	0.600798
$544$	0	0
$545$	20.0000	0.856706
$546$	0	0
$547$	− 12.0000i	− 0.513083i	−0.966533	−	0.256541i	$-0.917417\pi$
$547$	− 12.0000i	− 0.513083i	0.966533	−	0.256541i	$-0.0825830\pi$
$548$	10.0000	0.427179
$549$	− 10.0000i	− 0.426790i
$550$	− 4.00000i	− 0.170561i
$551$	40.0000i	1.70406i
$552$	0	0
$553$	0	0
$554$	− 30.0000i	− 1.27458i
$555$	− 4.00000i	− 0.169791i
$556$	− 4.00000i	− 0.169638i
$557$	−34.0000	−1.44063	−0.720313	−	0.693649i	$-0.756002\pi$
$557$	−34.0000	−1.44063	−0.720313	+	0.693649i	$0.756002\pi$
$558$	8.00000i	0.338667i
$559$	24.0000	1.01509
$560$	0	0
$561$	0	0
$562$	−6.00000	−0.253095
$563$	−36.0000	−1.51722	−0.758610	−	0.651546i	$-0.774121\pi$
$563$	−36.0000	−1.51722	−0.758610	+	0.651546i	$0.774121\pi$
$564$	0	0
$565$	−4.00000	−0.168281
$566$	12.0000i	0.504398i
$567$	0	0
$568$	0	0
$569$	6.00000	0.251533	0.125767	−	0.992060i	$-0.459861\pi$
$569$	6.00000	0.251533	0.125767	+	0.992060i	$0.459861\pi$
$570$	8.00000	0.335083
$571$	− 28.0000i	− 1.17176i	−0.810397	−	0.585882i	$-0.800748\pi$
$571$	− 28.0000i	− 1.17176i	0.810397	−	0.585882i	$-0.199252\pi$
$572$	− 8.00000i	− 0.334497i
$573$	− 16.0000i	− 0.668410i
$574$	0	0
$575$	0	0
$576$	−1.00000	−0.0416667
$577$	2.00000	0.0832611	0.0416305	−	0.999133i	$-0.486745\pi$
$577$	2.00000	0.0832611	0.0416305	+	0.999133i	$0.486745\pi$
$578$	0	0
$579$	18.0000	0.748054
$580$	−20.0000	−0.830455
$581$	0	0
$582$	−14.0000	−0.580319
$583$	− 24.0000i	− 0.993978i
$584$	− 10.0000i	− 0.413803i
$585$	− 4.00000i	− 0.165380i
$586$	26.0000	1.07405
$587$	20.0000	0.825488	0.412744	−	0.910847i	$-0.364570\pi$
$587$	20.0000	0.825488	0.412744	+	0.910847i	$0.364570\pi$
$588$	7.00000i	0.288675i
$589$	− 32.0000i	− 1.31854i
$590$	− 24.0000i	− 0.988064i
$591$	14.0000	0.575883
$592$	− 2.00000i	− 0.0821995i
$593$	14.0000	0.574911	0.287456	−	0.957794i	$-0.407191\pi$
$593$	14.0000	0.574911	0.287456	+	0.957794i	$0.407191\pi$
$594$	−4.00000	−0.164122
$595$	0	0
$596$	−10.0000	−0.409616
$597$	0	0
$598$	0	0
$599$	−8.00000	−0.326871	−0.163436	−	0.986554i	$-0.552258\pi$
$599$	−8.00000	−0.326871	−0.163436	+	0.986554i	$0.552258\pi$
$600$	− 1.00000i	− 0.0408248i
$601$	6.00000i	0.244745i	0.992484	+	0.122373i	$0.0390503\pi$
$601$	6.00000i	0.244745i	−0.992484	+	0.122373i	$0.960950\pi$
$602$	0	0
$603$	12.0000	0.488678
$604$	−24.0000	−0.976546
$605$	10.0000i	0.406558i
$606$	10.0000i	0.406222i
$607$	− 24.0000i	− 0.974130i	−0.873366	−	0.487065i	$-0.838067\pi$
$607$	− 24.0000i	− 0.974130i	0.873366	−	0.487065i	$-0.161933\pi$
$608$	4.00000	0.162221
$609$	0	0
$610$	−20.0000	−0.809776
$611$	0	0
$612$	0	0
$613$	38.0000	1.53481	0.767403	−	0.641165i	$-0.221549\pi$
$613$	38.0000	1.53481	0.767403	+	0.641165i	$0.221549\pi$
$614$	12.0000	0.484281
$615$	− 20.0000i	− 0.806478i
$616$	0	0
$617$	− 6.00000i	− 0.241551i	−0.992680	−	0.120775i	$-0.961462\pi$
$617$	− 6.00000i	− 0.241551i	0.992680	−	0.120775i	$-0.0385381\pi$
$618$	8.00000i	0.321807i
$619$	20.0000i	0.803868i	0.915669	+	0.401934i	$0.131662\pi$
$619$	20.0000i	0.803868i	−0.915669	+	0.401934i	$0.868338\pi$
$620$	16.0000	0.642575
$621$	0	0
$622$	0	0
$623$	0	0
$624$	− 2.00000i	− 0.0800641i
$625$	−19.0000	−0.760000
$626$	10.0000i	0.399680i
$627$	16.0000	0.638978
$628$	−2.00000	−0.0798087
$629$	0	0
$630$	0	0
$631$	24.0000	0.955425	0.477712	−	0.878516i	$-0.341466\pi$
$631$	24.0000	0.955425	0.477712	+	0.878516i	$0.341466\pi$
$632$	− 8.00000i	− 0.318223i
$633$	−28.0000	−1.11290
$634$	6.00000i	0.238290i
$635$	0	0
$636$	− 6.00000i	− 0.237915i
$637$	−14.0000	−0.554700
$638$	−40.0000	−1.58362
$639$	0	0
$640$	2.00000i	0.0790569i
$641$	2.00000i	0.0789953i	0.999220	+	0.0394976i	$0.0125758\pi$
$641$	2.00000i	0.0789953i	−0.999220	+	0.0394976i	$0.987424\pi$
$642$	−4.00000	−0.157867
$643$	− 28.0000i	− 1.10421i	−0.833774	−	0.552106i	$-0.813824\pi$
$643$	− 28.0000i	− 1.10421i	0.833774	−	0.552106i	$-0.186176\pi$
$644$	0	0
$645$	−24.0000	−0.944999
$646$	0	0
$647$	−40.0000	−1.57256	−0.786281	−	0.617869i	$-0.787996\pi$
$647$	−40.0000	−1.57256	−0.786281	+	0.617869i	$0.787996\pi$
$648$	−1.00000	−0.0392837
$649$	− 48.0000i	− 1.88416i
$650$	2.00000	0.0784465
$651$	0	0
$652$	− 4.00000i	− 0.156652i
$653$	− 6.00000i	− 0.234798i	−0.993085	−	0.117399i	$-0.962544\pi$
$653$	− 6.00000i	− 0.234798i	0.993085	−	0.117399i	$-0.0374557\pi$
$654$	10.0000	0.391031
$655$	−24.0000	−0.937758
$656$	− 10.0000i	− 0.390434i
$657$	− 10.0000i	− 0.390137i
$658$	0	0
$659$	36.0000	1.40236	0.701180	−	0.712984i	$-0.252657\pi$
$659$	36.0000	1.40236	0.701180	+	0.712984i	$0.252657\pi$
$660$	8.00000i	0.311400i
$661$	−6.00000	−0.233373	−0.116686	−	0.993169i	$-0.537227\pi$
$661$	−6.00000	−0.233373	−0.116686	+	0.993169i	$0.537227\pi$
$662$	−20.0000	−0.777322
$663$	0	0
$664$	4.00000	0.155230
$665$	0	0
$666$	− 2.00000i	− 0.0774984i
$667$	0	0
$668$	16.0000i	0.619059i
$669$	− 16.0000i	− 0.618596i
$670$	− 24.0000i	− 0.927201i
$671$	−40.0000	−1.54418
$672$	0	0
$673$	46.0000i	1.77317i	0.462566	+	0.886585i	$0.346929\pi$
$673$	46.0000i	1.77317i	−0.462566	+	0.886585i	$0.653071\pi$
$674$	14.0000i	0.539260i
$675$	− 1.00000i	− 0.0384900i
$676$	−9.00000	−0.346154
$677$	46.0000i	1.76792i	0.467559	+	0.883962i	$0.345134\pi$
$677$	46.0000i	1.76792i	−0.467559	+	0.883962i	$0.654866\pi$
$678$	−2.00000	−0.0768095
$679$	0	0
$680$	0	0
$681$	4.00000	0.153280
$682$	32.0000	1.22534
$683$	− 20.0000i	− 0.765279i	−0.923898	−	0.382639i	$-0.875015\pi$
$683$	− 20.0000i	− 0.765279i	0.923898	−	0.382639i	$-0.124985\pi$
$684$	4.00000	0.152944
$685$	− 20.0000i	− 0.764161i
$686$	0	0
$687$	26.0000i	0.991962i
$688$	−12.0000	−0.457496
$689$	12.0000	0.457164
$690$	0	0
$691$	28.0000i	1.06517i	0.846376	+	0.532585i	$0.178779\pi$
$691$	28.0000i	1.06517i	−0.846376	+	0.532585i	$0.821221\pi$
$692$	6.00000i	0.228086i
$693$	0	0
$694$	28.0000i	1.06287i
$695$	−8.00000	−0.303457
$696$	−10.0000	−0.379049
$697$	0	0
$698$	14.0000	0.529908
$699$	−26.0000	−0.983410
$700$	0	0
$701$	46.0000	1.73740	0.868698	−	0.495342i	$-0.164957\pi$
$701$	46.0000	1.73740	0.868698	+	0.495342i	$0.164957\pi$
$702$	− 2.00000i	− 0.0754851i
$703$	8.00000i	0.301726i
$704$	4.00000i	0.150756i
$705$	0	0
$706$	30.0000	1.12906
$707$	0	0
$708$	− 12.0000i	− 0.450988i
$709$	46.0000i	1.72757i	0.503864	+	0.863783i	$0.331911\pi$
$709$	46.0000i	1.72757i	−0.503864	+	0.863783i	$0.668089\pi$
$710$	0	0
$711$	− 8.00000i	− 0.300023i
$712$	6.00000	0.224860
$713$	0	0
$714$	0	0
$715$	−16.0000	−0.598366
$716$	12.0000	0.448461
$717$	0	0
$718$	−24.0000	−0.895672
$719$	40.0000i	1.49175i	0.666087	+	0.745874i	$0.267968\pi$
$719$	40.0000i	1.49175i	−0.666087	+	0.745874i	$0.732032\pi$
$720$	2.00000i	0.0745356i
$721$	0	0
$722$	3.00000	0.111648
$723$	−2.00000	−0.0743808
$724$	− 14.0000i	− 0.520306i
$725$	− 10.0000i	− 0.371391i
$726$	5.00000i	0.185567i
$727$	−8.00000	−0.296704	−0.148352	−	0.988935i	$-0.547397\pi$
$727$	−8.00000	−0.296704	−0.148352	+	0.988935i	$0.547397\pi$
$728$	0	0
$729$	−1.00000	−0.0370370
$730$	−20.0000	−0.740233
$731$	0	0
$732$	−10.0000	−0.369611
$733$	−46.0000	−1.69905	−0.849524	−	0.527549i	$-0.823111\pi$
$733$	−46.0000	−1.69905	−0.849524	+	0.527549i	$0.823111\pi$
$734$	24.0000i	0.885856i
$735$	14.0000	0.516398
$736$	0	0
$737$	− 48.0000i	− 1.76810i
$738$	− 10.0000i	− 0.368105i
$739$	−52.0000	−1.91285	−0.956425	−	0.291977i	$-0.905687\pi$
$739$	−52.0000	−1.91285	−0.956425	+	0.291977i	$0.905687\pi$
$740$	−4.00000	−0.147043
$741$	8.00000i	0.293887i
$742$	0	0
$743$	− 16.0000i	− 0.586983i	−0.955962	−	0.293492i	$-0.905183\pi$
$743$	− 16.0000i	− 0.586983i	0.955962	−	0.293492i	$-0.0948173\pi$
$744$	8.00000	0.293294
$745$	20.0000i	0.732743i
$746$	−6.00000	−0.219676
$747$	4.00000	0.146352
$748$	0	0
$749$	0	0
$750$	−12.0000	−0.438178
$751$	8.00000i	0.291924i	0.989290	+	0.145962i	$0.0466277\pi$
$751$	8.00000i	0.291924i	−0.989290	+	0.145962i	$0.953372\pi$
$752$	0	0
$753$	28.0000i	1.02038i
$754$	− 20.0000i	− 0.728357i
$755$	48.0000i	1.74690i
$756$	0	0
$757$	10.0000	0.363456	0.181728	−	0.983349i	$-0.441831\pi$
$757$	10.0000	0.363456	0.181728	+	0.983349i	$0.441831\pi$
$758$	4.00000i	0.145287i
$759$	0	0
$760$	− 8.00000i	− 0.290191i
$761$	−6.00000	−0.217500	−0.108750	−	0.994069i	$-0.534685\pi$
$761$	−6.00000	−0.217500	−0.108750	+	0.994069i	$0.534685\pi$
$762$	0	0
$763$	0	0
$764$	−16.0000	−0.578860
$765$	0	0
$766$	−16.0000	−0.578103
$767$	24.0000	0.866590
$768$	1.00000i	0.0360844i
$769$	−30.0000	−1.08183	−0.540914	−	0.841078i	$-0.681921\pi$
$769$	−30.0000	−1.08183	−0.540914	+	0.841078i	$0.681921\pi$
$770$	0	0
$771$	− 2.00000i	− 0.0720282i
$772$	− 18.0000i	− 0.647834i
$773$	−38.0000	−1.36677	−0.683383	−	0.730061i	$-0.739492\pi$
$773$	−38.0000	−1.36677	−0.683383	+	0.730061i	$0.739492\pi$
$774$	−12.0000	−0.431331
$775$	8.00000i	0.287368i
$776$	14.0000i	0.502571i
$777$	0	0
$778$	−26.0000	−0.932145
$779$	40.0000i	1.43315i
$780$	−4.00000	−0.143223
$781$	0	0
$782$	0	0
$783$	−10.0000	−0.357371
$784$	7.00000	0.250000
$785$	4.00000i	0.142766i
$786$	−12.0000	−0.428026
$787$	4.00000i	0.142585i	0.997455	+	0.0712923i	$0.0227123\pi$
$787$	4.00000i	0.142585i	−0.997455	+	0.0712923i	$0.977288\pi$
$788$	− 14.0000i	− 0.498729i
$789$	8.00000i	0.284808i
$790$	−16.0000	−0.569254
$791$	0	0
$792$	4.00000i	0.142134i
$793$	− 20.0000i	− 0.710221i
$794$	− 26.0000i	− 0.922705i
$795$	−12.0000	−0.425596
$796$	0	0
$797$	−14.0000	−0.495905	−0.247953	−	0.968772i	$-0.579758\pi$
$797$	−14.0000	−0.495905	−0.247953	+	0.968772i	$0.579758\pi$
$798$	0	0
$799$	0	0
$800$	−1.00000	−0.0353553
$801$	6.00000	0.212000
$802$	− 14.0000i	− 0.494357i
$803$	−40.0000	−1.41157
$804$	− 12.0000i	− 0.423207i
$805$	0	0
$806$	16.0000i	0.563576i
$807$	−6.00000	−0.211210
$808$	10.0000	0.351799
$809$	22.0000i	0.773479i	0.922189	+	0.386739i	$0.126399\pi$
$809$	22.0000i	0.773479i	−0.922189	+	0.386739i	$0.873601\pi$
$810$	2.00000i	0.0702728i
$811$	− 20.0000i	− 0.702295i	−0.936320	−	0.351147i	$-0.885792\pi$
$811$	− 20.0000i	− 0.702295i	0.936320	−	0.351147i	$-0.114208\pi$
$812$	0	0
$813$	16.0000i	0.561144i
$814$	−8.00000	−0.280400
$815$	−8.00000	−0.280228
$816$	0	0
$817$	48.0000	1.67931
$818$	−26.0000	−0.909069
$819$	0	0
$820$	−20.0000	−0.698430
$821$	− 34.0000i	− 1.18661i	−0.804978	−	0.593304i	$-0.797823\pi$
$821$	− 34.0000i	− 1.18661i	0.804978	−	0.593304i	$-0.202177\pi$
$822$	− 10.0000i	− 0.348790i
$823$	− 32.0000i	− 1.11545i	−0.830026	−	0.557725i	$-0.811674\pi$
$823$	− 32.0000i	− 1.11545i	0.830026	−	0.557725i	$-0.188326\pi$
$824$	8.00000	0.278693
$825$	−4.00000	−0.139262
$826$	0	0
$827$	20.0000i	0.695468i	0.937593	+	0.347734i	$0.113049\pi$
$827$	20.0000i	0.695468i	−0.937593	+	0.347734i	$0.886951\pi$
$828$	0	0
$829$	−34.0000	−1.18087	−0.590434	−	0.807086i	$-0.701044\pi$
$829$	−34.0000	−1.18087	−0.590434	+	0.807086i	$0.701044\pi$
$830$	− 8.00000i	− 0.277684i
$831$	−30.0000	−1.04069
$832$	−2.00000	−0.0693375
$833$	0	0
$834$	−4.00000	−0.138509
$835$	32.0000	1.10741
$836$	− 16.0000i	− 0.553372i
$837$	8.00000	0.276520
$838$	4.00000i	0.138178i
$839$	0	0	1.00000			$0$
$839$	0	0	−1.00000			$\pi$
$840$	0	0
$841$	−71.0000	−2.44828
$842$	−22.0000	−0.758170
$843$	6.00000i	0.206651i
$844$	28.0000i	0.963800i
$845$	18.0000i	0.619219i
$846$	0	0
$847$	0	0
$848$	−6.00000	−0.206041
$849$	12.0000	0.411839
$850$	0	0
$851$	0	0
$852$	0	0
$853$	− 2.00000i	− 0.0684787i	−0.999414	−	0.0342393i	$-0.989099\pi$
$853$	− 2.00000i	− 0.0684787i	0.999414	−	0.0342393i	$-0.0109009\pi$
$854$	0	0
$855$	− 8.00000i	− 0.273594i
$856$	4.00000i	0.136717i
$857$	6.00000i	0.204956i	0.994735	+	0.102478i	$0.0326771\pi$
$857$	6.00000i	0.204956i	−0.994735	+	0.102478i	$0.967323\pi$
$858$	−8.00000	−0.273115
$859$	36.0000	1.22830	0.614152	−	0.789188i	$-0.289498\pi$
$859$	36.0000	1.22830	0.614152	+	0.789188i	$0.289498\pi$
$860$	24.0000i	0.818393i
$861$	0	0
$862$	− 8.00000i	− 0.272481i
$863$	−32.0000	−1.08929	−0.544646	−	0.838666i	$-0.683336\pi$
$863$	−32.0000	−1.08929	−0.544646	+	0.838666i	$0.683336\pi$
$864$	1.00000i	0.0340207i
$865$	12.0000	0.408012
$866$	−14.0000	−0.475739
$867$	0	0
$868$	0	0
$869$	−32.0000	−1.08553
$870$	20.0000i	0.678064i
$871$	24.0000	0.813209
$872$	− 10.0000i	− 0.338643i
$873$	14.0000i	0.473828i
$874$	0	0
$875$	0	0
$876$	−10.0000	−0.337869
$877$	− 22.0000i	− 0.742887i	−0.928456	−	0.371444i	$-0.878863\pi$
$877$	− 22.0000i	− 0.742887i	0.928456	−	0.371444i	$-0.121137\pi$
$878$	− 16.0000i	− 0.539974i
$879$	− 26.0000i	− 0.876958i
$880$	8.00000	0.269680
$881$	2.00000i	0.0673817i	0.999432	+	0.0336909i	$0.0107262\pi$
$881$	2.00000i	0.0673817i	−0.999432	+	0.0336909i	$0.989274\pi$
$882$	7.00000	0.235702
$883$	36.0000	1.21150	0.605748	−	0.795656i	$-0.292874\pi$
$883$	36.0000	1.21150	0.605748	+	0.795656i	$0.292874\pi$
$884$	0	0
$885$	−24.0000	−0.806751
$886$	4.00000	0.134383
$887$	− 48.0000i	− 1.61168i	−0.592132	−	0.805841i	$-0.701714\pi$
$887$	− 48.0000i	− 1.61168i	0.592132	−	0.805841i	$-0.298286\pi$
$888$	−2.00000	−0.0671156
$889$	0	0
$890$	− 12.0000i	− 0.402241i
$891$	4.00000i	0.134005i
$892$	−16.0000	−0.535720
$893$	0	0
$894$	10.0000i	0.334450i
$895$	− 24.0000i	− 0.802232i
$896$	0	0
$897$	0	0
$898$	2.00000i	0.0667409i
$899$	80.0000	2.66815
$900$	−1.00000	−0.0333333
$901$	0	0
$902$	−40.0000	−1.33185
$903$	0	0
$904$	2.00000i	0.0665190i
$905$	−28.0000	−0.930751
$906$	24.0000i	0.797347i
$907$	− 28.0000i	− 0.929725i	−0.885383	−	0.464862i	$-0.846104\pi$
$907$	− 28.0000i	− 0.929725i	0.885383	−	0.464862i	$-0.153896\pi$
$908$	− 4.00000i	− 0.132745i
$909$	10.0000	0.331679
$910$	0	0
$911$	− 8.00000i	− 0.265052i	−0.991180	−	0.132526i	$-0.957691\pi$
$911$	− 8.00000i	− 0.265052i	0.991180	−	0.132526i	$-0.0423088\pi$
$912$	− 4.00000i	− 0.132453i
$913$	− 16.0000i	− 0.529523i
$914$	10.0000	0.330771
$915$	20.0000i	0.661180i
$916$	26.0000	0.859064
$917$	0	0
$918$	0	0
$919$	24.0000	0.791687	0.395843	−	0.918318i	$-0.370452\pi$
$919$	24.0000	0.791687	0.395843	+	0.918318i	$0.370452\pi$
$920$	0	0
$921$	− 12.0000i	− 0.395413i
$922$	30.0000	0.987997
$923$	0	0
$924$	0	0
$925$	− 2.00000i	− 0.0657596i
$926$	−32.0000	−1.05159
$927$	8.00000	0.262754
$928$	10.0000i	0.328266i
$929$	− 2.00000i	− 0.0656179i	−0.999462	−	0.0328089i	$-0.989555\pi$
$929$	− 2.00000i	− 0.0656179i	0.999462	−	0.0328089i	$-0.0104453\pi$
$930$	− 16.0000i	− 0.524661i
$931$	−28.0000	−0.917663
$932$	26.0000i	0.851658i
$933$	0	0
$934$	−12.0000	−0.392652
$935$	0	0
$936$	−2.00000	−0.0653720
$937$	22.0000	0.718709	0.359354	−	0.933201i	$-0.382997\pi$
$937$	22.0000	0.718709	0.359354	+	0.933201i	$0.382997\pi$
$938$	0	0
$939$	10.0000	0.326338
$940$	0	0
$941$	10.0000i	0.325991i	0.986627	+	0.162995i	$0.0521156\pi$
$941$	10.0000i	0.325991i	−0.986627	+	0.162995i	$0.947884\pi$
$942$	2.00000i	0.0651635i
$943$	0	0
$944$	−12.0000	−0.390567
$945$	0	0
$946$	48.0000i	1.56061i
$947$	− 28.0000i	− 0.909878i	−0.890523	−	0.454939i	$-0.849661\pi$
$947$	− 28.0000i	− 0.909878i	0.890523	−	0.454939i	$-0.150339\pi$
$948$	−8.00000	−0.259828
$949$	− 20.0000i	− 0.649227i
$950$	4.00000	0.129777
$951$	6.00000	0.194563
$952$	0	0
$953$	−6.00000	−0.194359	−0.0971795	−	0.995267i	$-0.530982\pi$
$953$	−6.00000	−0.194359	−0.0971795	+	0.995267i	$0.530982\pi$
$954$	−6.00000	−0.194257
$955$	32.0000i	1.03550i
$956$	0	0
$957$	40.0000i	1.29302i
$958$	− 24.0000i	− 0.775405i
$959$	0	0
$960$	2.00000	0.0645497
$961$	−33.0000	−1.06452
$962$	− 4.00000i	− 0.128965i
$963$	4.00000i	0.128898i
$964$	2.00000i	0.0644157i
$965$	−36.0000	−1.15888
$966$	0	0
$967$	8.00000	0.257263	0.128631	−	0.991692i	$-0.458942\pi$
$967$	8.00000	0.257263	0.128631	+	0.991692i	$0.458942\pi$
$968$	5.00000	0.160706
$969$	0	0
$970$	28.0000	0.899026
$971$	4.00000	0.128366	0.0641831	−	0.997938i	$-0.479556\pi$
$971$	4.00000	0.128366	0.0641831	+	0.997938i	$0.479556\pi$
$972$	1.00000i	0.0320750i
$973$	0	0
$974$	− 16.0000i	− 0.512673i
$975$	− 2.00000i	− 0.0640513i
$976$	10.0000i	0.320092i
$977$	46.0000	1.47167	0.735835	−	0.677161i	$-0.236790\pi$
$977$	46.0000	1.47167	0.735835	+	0.677161i	$0.236790\pi$
$978$	−4.00000	−0.127906
$979$	− 24.0000i	− 0.767043i
$980$	− 14.0000i	− 0.447214i
$981$	− 10.0000i	− 0.319275i
$982$	12.0000	0.382935
$983$	48.0000i	1.53096i	0.643458	+	0.765481i	$0.277499\pi$
$983$	48.0000i	1.53096i	−0.643458	+	0.765481i	$0.722501\pi$
$984$	−10.0000	−0.318788
$985$	−28.0000	−0.892154
$986$	0	0
$987$	0	0
$988$	8.00000	0.254514
$989$	0	0
$990$	8.00000	0.254257
$991$	− 40.0000i	− 1.27064i	−0.772248	−	0.635321i	$-0.780868\pi$
$991$	− 40.0000i	− 1.27064i	0.772248	−	0.635321i	$-0.219132\pi$
$992$	− 8.00000i	− 0.254000i
$993$	20.0000i	0.634681i
$994$	0	0
$995$	0	0
$996$	− 4.00000i	− 0.126745i
$997$	2.00000i	0.0633406i	0.999498	+	0.0316703i	$0.0100827\pi$
$997$	2.00000i	0.0633406i	−0.999498	+	0.0316703i	$0.989917\pi$
$998$	4.00000i	0.126618i
$999$	−2.00000	−0.0632772

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1734.2.b.b.577.2		2
17.2	even	8		1734.2.f.e.829.2		4
17.4	even	4		102.2.a.c.1.1	✓	1
17.8	even	8		1734.2.f.e.1483.2		4
17.9	even	8		1734.2.f.e.1483.1		4
17.13	even	4		1734.2.a.j.1.1		1
17.15	even	8		1734.2.f.e.829.1		4
17.16	even	2	inner	1734.2.b.b.577.1		2
51.38	odd	4		306.2.a.b.1.1		1
51.47	odd	4		5202.2.a.c.1.1		1
68.55	odd	4		816.2.a.b.1.1		1
85.4	even	4		2550.2.a.c.1.1		1
85.38	odd	4		2550.2.d.m.2449.1		2
85.72	odd	4		2550.2.d.m.2449.2		2
119.55	odd	4		4998.2.a.be.1.1		1
136.21	even	4		3264.2.a.m.1.1		1
136.123	odd	4		3264.2.a.bc.1.1		1
204.191	even	4		2448.2.a.p.1.1		1
255.89	odd	4		7650.2.a.ca.1.1		1
408.293	odd	4		9792.2.a.k.1.1		1
408.395	even	4		9792.2.a.l.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
102.2.a.c.1.1	✓	1	17.4	even	4
306.2.a.b.1.1		1	51.38	odd	4
816.2.a.b.1.1		1	68.55	odd	4
1734.2.a.j.1.1		1	17.13	even	4
1734.2.b.b.577.1		2	17.16	even	2	inner
1734.2.b.b.577.2		2	1.1	even	1	trivial
1734.2.f.e.829.1		4	17.15	even	8
1734.2.f.e.829.2		4	17.2	even	8
1734.2.f.e.1483.1		4	17.9	even	8
1734.2.f.e.1483.2		4	17.8	even	8
2448.2.a.p.1.1		1	204.191	even	4
2550.2.a.c.1.1		1	85.4	even	4
2550.2.d.m.2449.1		2	85.38	odd	4
2550.2.d.m.2449.2		2	85.72	odd	4
3264.2.a.m.1.1		1	136.21	even	4
3264.2.a.bc.1.1		1	136.123	odd	4
4998.2.a.be.1.1		1	119.55	odd	4
5202.2.a.c.1.1		1	51.47	odd	4
7650.2.a.ca.1.1		1	255.89	odd	4
9792.2.a.k.1.1		1	408.293	odd	4
9792.2.a.l.1.1		1	408.395	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1734 = 2 \cdot 3 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1734.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000i q^{3} +1.00000 q^{4} -2.00000i q^{5} -1.00000i q^{6} -1.00000 q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000i q^{3} +1.00000 q^{4} -2.00000i q^{5} -1.00000i q^{6} -1.00000 q^{8} -1.00000 q^{9} +2.00000i q^{10} +4.00000i q^{11} +1.00000i q^{12} -2.00000 q^{13} +2.00000 q^{15} +1.00000 q^{16} +1.00000 q^{18} -4.00000 q^{19} -2.00000i q^{20} -4.00000i q^{22} -1.00000i q^{24} +1.00000 q^{25} +2.00000 q^{26} -1.00000i q^{27} -10.0000i q^{29} -2.00000 q^{30} +8.00000i q^{31} -1.00000 q^{32} -4.00000 q^{33} -1.00000 q^{36} -2.00000i q^{37} +4.00000 q^{38} -2.00000i q^{39} +2.00000i q^{40} -10.0000i q^{41} -12.0000 q^{43} +4.00000i q^{44} +2.00000i q^{45} +1.00000i q^{48} +7.00000 q^{49} -1.00000 q^{50} -2.00000 q^{52} -6.00000 q^{53} +1.00000i q^{54} +8.00000 q^{55} -4.00000i q^{57} +10.0000i q^{58} -12.0000 q^{59} +2.00000 q^{60} +10.0000i q^{61} -8.00000i q^{62} +1.00000 q^{64} +4.00000i q^{65} +4.00000 q^{66} -12.0000 q^{67} +1.00000 q^{72} +10.0000i q^{73} +2.00000i q^{74} +1.00000i q^{75} -4.00000 q^{76} +2.00000i q^{78} +8.00000i q^{79} -2.00000i q^{80} +1.00000 q^{81} +10.0000i q^{82} -4.00000 q^{83} +12.0000 q^{86} +10.0000 q^{87} -4.00000i q^{88} -6.00000 q^{89} -2.00000i q^{90} -8.00000 q^{93} +8.00000i q^{95} -1.00000i q^{96} -14.0000i q^{97} -7.00000 q^{98} -4.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{4} - 2 q^{8} - 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + 2 * q^4 - 2 * q^8 - 2 * q^9	\( 2 q - 2 q^{2} + 2 q^{4} - 2 q^{8} - 2 q^{9} - 4 q^{13} + 4 q^{15} + 2 q^{16} + 2 q^{18} - 8 q^{19} + 2 q^{25} + 4 q^{26} - 4 q^{30} - 2 q^{32} - 8 q^{33} - 2 q^{36} + 8 q^{38} - 24 q^{43} + 14 q^{49} - 2 q^{50} - 4 q^{52} - 12 q^{53} + 16 q^{55} - 24 q^{59} + 4 q^{60} + 2 q^{64} + 8 q^{66} - 24 q^{67} + 2 q^{72} - 8 q^{76} + 2 q^{81} - 8 q^{83} + 24 q^{86} + 20 q^{87} - 12 q^{89} - 16 q^{93} - 14 q^{98}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^4 - 2 * q^8 - 2 * q^9 - 4 * q^13 + 4 * q^15 + 2 * q^16 + 2 * q^18 - 8 * q^19 + 2 * q^25 + 4 * q^26 - 4 * q^30 - 2 * q^32 - 8 * q^33 - 2 * q^36 + 8 * q^38 - 24 * q^43 + 14 * q^49 - 2 * q^50 - 4 * q^52 - 12 * q^53 + 16 * q^55 - 24 * q^59 + 4 * q^60 + 2 * q^64 + 8 * q^66 - 24 * q^67 + 2 * q^72 - 8 * q^76 + 2 * q^81 - 8 * q^83 + 24 * q^86 + 20 * q^87 - 12 * q^89 - 16 * q^93 - 14 * q^98

Introduction

L-functions

Modular forms

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