LMFDB - Embedded newform 170.2.b.c.101.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [170,2,Mod(101,170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(170, 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("170.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 170 = 2 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	170.b (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:	$1.35745683436$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			101.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	170.101
Dual form			170.2.b.c.101.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{4} -1.00000i q^{5} -2.00000i q^{7} +1.00000 q^{8} +3.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{4} -1.00000i q^{5} -2.00000i q^{7} +1.00000 q^{8} +3.00000 q^{9} -1.00000i q^{10} +4.00000i q^{11} -2.00000 q^{13} -2.00000i q^{14} +1.00000 q^{16} +(-1.00000 + 4.00000i) q^{17} +3.00000 q^{18} -8.00000 q^{19} -1.00000i q^{20} +4.00000i q^{22} -6.00000i q^{23} -1.00000 q^{25} -2.00000 q^{26} -2.00000i q^{28} -6.00000i q^{29} +10.0000i q^{31} +1.00000 q^{32} +(-1.00000 + 4.00000i) q^{34} -2.00000 q^{35} +3.00000 q^{36} -2.00000i q^{37} -8.00000 q^{38} -1.00000i q^{40} +4.00000i q^{41} -8.00000 q^{43} +4.00000i q^{44} -3.00000i q^{45} -6.00000i q^{46} +3.00000 q^{49} -1.00000 q^{50} -2.00000 q^{52} +10.0000 q^{53} +4.00000 q^{55} -2.00000i q^{56} -6.00000i q^{58} +4.00000 q^{59} +10.0000i q^{61} +10.0000i q^{62} -6.00000i q^{63} +1.00000 q^{64} +2.00000i q^{65} -4.00000 q^{67} +(-1.00000 + 4.00000i) q^{68} -2.00000 q^{70} -10.0000i q^{71} +3.00000 q^{72} -12.0000i q^{73} -2.00000i q^{74} -8.00000 q^{76} +8.00000 q^{77} +6.00000i q^{79} -1.00000i q^{80} +9.00000 q^{81} +4.00000i q^{82} +(4.00000 + 1.00000i) q^{85} -8.00000 q^{86} +4.00000i q^{88} +2.00000 q^{89} -3.00000i q^{90} +4.00000i q^{91} -6.00000i q^{92} +8.00000i q^{95} -16.0000i q^{97} +3.00000 q^{98} +12.0000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 2 q^{4} + 2 q^{8} + 6 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 + 2 * q^4 + 2 * q^8 + 6 * q^9	$ 2 q + 2 q^{2} + 2 q^{4} + 2 q^{8} + 6 q^{9} - 4 q^{13} + 2 q^{16} - 2 q^{17} + 6 q^{18} - 16 q^{19} - 2 q^{25} - 4 q^{26} + 2 q^{32} - 2 q^{34} - 4 q^{35} + 6 q^{36} - 16 q^{38} - 16 q^{43} + 6 q^{49} - 2 q^{50} - 4 q^{52} + 20 q^{53} + 8 q^{55} + 8 q^{59} + 2 q^{64} - 8 q^{67} - 2 q^{68} - 4 q^{70} + 6 q^{72} - 16 q^{76} + 16 q^{77} + 18 q^{81} + 8 q^{85} - 16 q^{86} + 4 q^{89} + 6 q^{98}+O(q^{100}) $ 2 * q + 2 * q^2 + 2 * q^4 + 2 * q^8 + 6 * q^9 - 4 * q^13 + 2 * q^16 - 2 * q^17 + 6 * q^18 - 16 * q^19 - 2 * q^25 - 4 * q^26 + 2 * q^32 - 2 * q^34 - 4 * q^35 + 6 * q^36 - 16 * q^38 - 16 * q^43 + 6 * q^49 - 2 * q^50 - 4 * q^52 + 20 * q^53 + 8 * q^55 + 8 * q^59 + 2 * q^64 - 8 * q^67 - 2 * q^68 - 4 * q^70 + 6 * q^72 - 16 * q^76 + 16 * q^77 + 18 * q^81 + 8 * q^85 - 16 * q^86 + 4 * q^89 + 6 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/170\mathbb{Z}\right)^\times$.

$n$	$71$	$137$
$\chi(n)$	$-1$	$1$

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
$3$		0			0		1.00000			$0$
$3$		0			0		−1.00000			$\pi$
$4$	1.00000			0.500000
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$		0			0
$7$		−	2.00000i		−	0.755929i	−0.925820	−	0.377964i	$-0.876624\pi$
$7$		−	2.00000i		−	0.755929i	0.925820	−	0.377964i	$-0.123376\pi$
$8$	1.00000			0.353553
$9$	3.00000			1.00000
$10$		−	1.00000i		−	0.316228i
$11$			4.00000i			1.20605i	0.797724	+	0.603023i	$0.206037\pi$
$11$			4.00000i			1.20605i	−0.797724	+	0.603023i	$0.793963\pi$
$12$		0			0
$13$	−2.00000			−0.554700			−0.277350	−	0.960769i	$-0.589456\pi$
$13$	−2.00000			−0.554700			−0.277350	+	0.960769i	$0.589456\pi$
$14$		−	2.00000i		−	0.534522i
$15$		0			0
$16$	1.00000			0.250000
$17$	−1.00000	+	4.00000i	−0.242536	+	0.970143i
$17$	−1.00000	+	4.00000i	−0.242536	+	0.970143i
$18$	3.00000			0.707107
$19$	−8.00000			−1.83533			−0.917663	−	0.397360i	$-0.869927\pi$
$19$	−8.00000			−1.83533			−0.917663	+	0.397360i	$0.869927\pi$
$20$		−	1.00000i		−	0.223607i
$21$		0			0
$22$			4.00000i			0.852803i
$23$		−	6.00000i		−	1.25109i	−0.780189	−	0.625543i	$-0.784877\pi$
$23$		−	6.00000i		−	1.25109i	0.780189	−	0.625543i	$-0.215123\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$	−2.00000			−0.392232
$27$		0			0
$28$		−	2.00000i		−	0.377964i
$29$		−	6.00000i		−	1.11417i	−0.830455	−	0.557086i	$-0.811919\pi$
$29$		−	6.00000i		−	1.11417i	0.830455	−	0.557086i	$-0.188081\pi$
$30$		0			0
$31$			10.0000i			1.79605i	0.439941	+	0.898027i	$0.354999\pi$
$31$			10.0000i			1.79605i	−0.439941	+	0.898027i	$0.645001\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	−1.00000	+	4.00000i	−0.171499	+	0.685994i
$35$	−2.00000			−0.338062
$36$	3.00000			0.500000
$37$		−	2.00000i		−	0.328798i	−0.986394	−	0.164399i	$-0.947432\pi$
$37$		−	2.00000i		−	0.328798i	0.986394	−	0.164399i	$-0.0525685\pi$
$38$	−8.00000			−1.29777
$39$		0			0
$40$		−	1.00000i		−	0.158114i
$41$			4.00000i			0.624695i	0.949968	+	0.312348i	$0.101115\pi$
$41$			4.00000i			0.624695i	−0.949968	+	0.312348i	$0.898885\pi$
$42$		0			0
$43$	−8.00000			−1.21999			−0.609994	−	0.792406i	$-0.708828\pi$
$43$	−8.00000			−1.21999			−0.609994	+	0.792406i	$0.708828\pi$
$44$			4.00000i			0.603023i
$45$		−	3.00000i		−	0.447214i
$46$		−	6.00000i		−	0.884652i
$47$		0			0			−	1.00000i	$-0.5\pi$
$47$		0			0				1.00000i	$0.5\pi$
$48$		0			0
$49$	3.00000			0.428571
$50$	−1.00000			−0.141421
$51$		0			0
$52$	−2.00000			−0.277350
$53$	10.0000			1.37361			0.686803	−	0.726844i	$-0.259014\pi$
$53$	10.0000			1.37361			0.686803	+	0.726844i	$0.259014\pi$
$54$		0			0
$55$	4.00000			0.539360
$56$		−	2.00000i		−	0.267261i
$57$		0			0
$58$		−	6.00000i		−	0.787839i
$59$	4.00000			0.520756			0.260378	−	0.965507i	$-0.416153\pi$
$59$	4.00000			0.520756			0.260378	+	0.965507i	$0.416153\pi$
$60$		0			0
$61$			10.0000i			1.28037i	0.768221	+	0.640184i	$0.221142\pi$
$61$			10.0000i			1.28037i	−0.768221	+	0.640184i	$0.778858\pi$
$62$			10.0000i			1.27000i
$63$		−	6.00000i		−	0.755929i
$64$	1.00000			0.125000
$65$			2.00000i			0.248069i
$66$		0			0
$67$	−4.00000			−0.488678			−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000			−0.488678			−0.244339	+	0.969690i	$0.578571\pi$
$68$	−1.00000	+	4.00000i	−0.121268	+	0.485071i
$69$		0			0
$70$	−2.00000			−0.239046
$71$		−	10.0000i		−	1.18678i	−0.804914	−	0.593391i	$-0.797789\pi$
$71$		−	10.0000i		−	1.18678i	0.804914	−	0.593391i	$-0.202211\pi$
$72$	3.00000			0.353553
$73$		−	12.0000i		−	1.40449i	−0.711934	−	0.702247i	$-0.752180\pi$
$73$		−	12.0000i		−	1.40449i	0.711934	−	0.702247i	$-0.247820\pi$
$74$		−	2.00000i		−	0.232495i
$75$		0			0
$76$	−8.00000			−0.917663
$77$	8.00000			0.911685
$78$		0			0
$79$			6.00000i			0.675053i	0.941316	+	0.337526i	$0.109590\pi$
$79$			6.00000i			0.675053i	−0.941316	+	0.337526i	$0.890410\pi$
$80$		−	1.00000i		−	0.111803i
$81$	9.00000			1.00000
$82$			4.00000i			0.441726i
$83$		0			0			−	1.00000i	$-0.5\pi$
$83$		0			0				1.00000i	$0.5\pi$
$84$		0			0
$85$	4.00000	+	1.00000i	0.433861	+	0.108465i
$86$	−8.00000			−0.862662
$87$		0			0
$88$			4.00000i			0.426401i
$89$	2.00000			0.212000			0.106000	−	0.994366i	$-0.466196\pi$
$89$	2.00000			0.212000			0.106000	+	0.994366i	$0.466196\pi$
$90$		−	3.00000i		−	0.316228i
$91$			4.00000i			0.419314i
$92$		−	6.00000i		−	0.625543i
$93$		0			0
$94$		0			0
$95$			8.00000i			0.820783i
$96$		0			0
$97$		−	16.0000i		−	1.62455i	−0.583272	−	0.812277i	$-0.698228\pi$
$97$		−	16.0000i		−	1.62455i	0.583272	−	0.812277i	$-0.301772\pi$
$98$	3.00000			0.303046
$99$			12.0000i			1.20605i
$100$	−1.00000			−0.100000
$101$	10.0000			0.995037			0.497519	−	0.867453i	$-0.334245\pi$
$101$	10.0000			0.995037			0.497519	+	0.867453i	$0.334245\pi$
$102$		0			0
$103$		0			0			−	1.00000i	$-0.5\pi$
$103$		0			0				1.00000i	$0.5\pi$
$104$	−2.00000			−0.196116
$105$		0			0
$106$	10.0000			0.971286
$107$		−	4.00000i		−	0.386695i	−0.981130	−	0.193347i	$-0.938066\pi$
$107$		−	4.00000i		−	0.386695i	0.981130	−	0.193347i	$-0.0619344\pi$
$108$		0			0
$109$		−	10.0000i		−	0.957826i	−0.877862	−	0.478913i	$-0.841031\pi$
$109$		−	10.0000i		−	0.957826i	0.877862	−	0.478913i	$-0.158969\pi$
$110$	4.00000			0.381385
$111$		0			0
$112$		−	2.00000i		−	0.188982i
$113$			4.00000i			0.376288i	0.982141	+	0.188144i	$0.0602472\pi$
$113$			4.00000i			0.376288i	−0.982141	+	0.188144i	$0.939753\pi$
$114$		0			0
$115$	−6.00000			−0.559503
$116$		−	6.00000i		−	0.557086i
$117$	−6.00000			−0.554700
$118$	4.00000			0.368230
$119$	8.00000	+	2.00000i	0.733359	+	0.183340i
$120$		0			0
$121$	−5.00000			−0.454545
$122$			10.0000i			0.905357i
$123$		0			0
$124$			10.0000i			0.898027i
$125$			1.00000i			0.0894427i
$126$		−	6.00000i		−	0.534522i
$127$		0			0			−	1.00000i	$-0.5\pi$
$127$		0			0				1.00000i	$0.5\pi$
$128$	1.00000			0.0883883
$129$		0			0
$130$			2.00000i			0.175412i
$131$		−	12.0000i		−	1.04844i	−0.851581	−	0.524222i	$-0.824356\pi$
$131$		−	12.0000i		−	1.04844i	0.851581	−	0.524222i	$-0.175644\pi$
$132$		0			0
$133$			16.0000i			1.38738i
$134$	−4.00000			−0.345547
$135$		0			0
$136$	−1.00000	+	4.00000i	−0.0857493	+	0.342997i
$137$	14.0000			1.19610			0.598050	−	0.801459i	$-0.295942\pi$
$137$	14.0000			1.19610			0.598050	+	0.801459i	$0.295942\pi$
$138$		0			0
$139$		−	4.00000i		−	0.339276i	−0.985506	−	0.169638i	$-0.945740\pi$
$139$		−	4.00000i		−	0.339276i	0.985506	−	0.169638i	$-0.0542598\pi$
$140$	−2.00000			−0.169031
$141$		0			0
$142$		−	10.0000i		−	0.839181i
$143$		−	8.00000i		−	0.668994i
$144$	3.00000			0.250000
$145$	−6.00000			−0.498273
$146$		−	12.0000i		−	0.993127i
$147$		0			0
$148$		−	2.00000i		−	0.164399i
$149$	−18.0000			−1.47462			−0.737309	−	0.675556i	$-0.763904\pi$
$149$	−18.0000			−1.47462			−0.737309	+	0.675556i	$0.763904\pi$
$150$		0			0
$151$	−8.00000			−0.651031			−0.325515	−	0.945537i	$-0.605538\pi$
$151$	−8.00000			−0.651031			−0.325515	+	0.945537i	$0.605538\pi$
$152$	−8.00000			−0.648886
$153$	−3.00000	+	12.0000i	−0.242536	+	0.970143i
$154$	8.00000			0.644658
$155$	10.0000			0.803219
$156$		0			0
$157$	−22.0000			−1.75579			−0.877896	−	0.478852i	$-0.841053\pi$
$157$	−22.0000			−1.75579			−0.877896	+	0.478852i	$0.841053\pi$
$158$			6.00000i			0.477334i
$159$		0			0
$160$		−	1.00000i		−	0.0790569i
$161$	−12.0000			−0.945732
$162$	9.00000			0.707107
$163$			16.0000i			1.25322i	0.779334	+	0.626608i	$0.215557\pi$
$163$			16.0000i			1.25322i	−0.779334	+	0.626608i	$0.784443\pi$
$164$			4.00000i			0.312348i
$165$		0			0
$166$		0			0
$167$		−	2.00000i		−	0.154765i	−0.997001	−	0.0773823i	$-0.975344\pi$
$167$		−	2.00000i		−	0.154765i	0.997001	−	0.0773823i	$-0.0246562\pi$
$168$		0			0
$169$	−9.00000			−0.692308
$170$	4.00000	+	1.00000i	0.306786	+	0.0766965i
$171$	−24.0000			−1.83533
$172$	−8.00000			−0.609994
$173$			2.00000i			0.152057i	0.997106	+	0.0760286i	$0.0242240\pi$
$173$			2.00000i			0.152057i	−0.997106	+	0.0760286i	$0.975776\pi$
$174$		0			0
$175$			2.00000i			0.151186i
$176$			4.00000i			0.301511i
$177$		0			0
$178$	2.00000			0.149906
$179$		0			0			−	1.00000i	$-0.5\pi$
$179$		0			0				1.00000i	$0.5\pi$
$180$		−	3.00000i		−	0.223607i
$181$			2.00000i			0.148659i	0.997234	+	0.0743294i	$0.0236816\pi$
$181$			2.00000i			0.148659i	−0.997234	+	0.0743294i	$0.976318\pi$
$182$			4.00000i			0.296500i
$183$		0			0
$184$		−	6.00000i		−	0.442326i
$185$	−2.00000			−0.147043
$186$		0			0
$187$	−16.0000	−	4.00000i	−1.17004	−	0.292509i
$188$		0			0
$189$		0			0
$190$			8.00000i			0.580381i
$191$	16.0000			1.15772			0.578860	−	0.815427i	$-0.303498\pi$
$191$	16.0000			1.15772			0.578860	+	0.815427i	$0.303498\pi$
$192$		0			0
$193$			16.0000i			1.15171i	0.817554	+	0.575853i	$0.195330\pi$
$193$			16.0000i			1.15171i	−0.817554	+	0.575853i	$0.804670\pi$
$194$		−	16.0000i		−	1.14873i
$195$		0			0
$196$	3.00000			0.214286
$197$			18.0000i			1.28245i	0.767354	+	0.641223i	$0.221573\pi$
$197$			18.0000i			1.28245i	−0.767354	+	0.641223i	$0.778427\pi$
$198$			12.0000i			0.852803i
$199$		−	2.00000i		−	0.141776i	−0.997484	−	0.0708881i	$-0.977417\pi$
$199$		−	2.00000i		−	0.141776i	0.997484	−	0.0708881i	$-0.0225833\pi$
$200$	−1.00000			−0.0707107
$201$		0			0
$202$	10.0000			0.703598
$203$	−12.0000			−0.842235
$204$		0			0
$205$	4.00000			0.279372
$206$		0			0
$207$		−	18.0000i		−	1.25109i
$208$	−2.00000			−0.138675
$209$		−	32.0000i		−	2.21349i
$210$		0			0
$211$		−	20.0000i		−	1.37686i	−0.725304	−	0.688428i	$-0.758301\pi$
$211$		−	20.0000i		−	1.37686i	0.725304	−	0.688428i	$-0.241699\pi$
$212$	10.0000			0.686803
$213$		0			0
$214$		−	4.00000i		−	0.273434i
$215$			8.00000i			0.545595i
$216$		0			0
$217$	20.0000			1.35769
$218$		−	10.0000i		−	0.677285i
$219$		0			0
$220$	4.00000			0.269680
$221$	2.00000	−	8.00000i	0.134535	−	0.538138i
$222$		0			0
$223$	8.00000			0.535720			0.267860	−	0.963458i	$-0.413684\pi$
$223$	8.00000			0.535720			0.267860	+	0.963458i	$0.413684\pi$
$224$		−	2.00000i		−	0.133631i
$225$	−3.00000			−0.200000
$226$			4.00000i			0.266076i
$227$			24.0000i			1.59294i	0.604681	+	0.796468i	$0.293301\pi$
$227$			24.0000i			1.59294i	−0.604681	+	0.796468i	$0.706699\pi$
$228$		0			0
$229$	2.00000			0.132164			0.0660819	−	0.997814i	$-0.478950\pi$
$229$	2.00000			0.132164			0.0660819	+	0.997814i	$0.478950\pi$
$230$	−6.00000			−0.395628
$231$		0			0
$232$		−	6.00000i		−	0.393919i
$233$			12.0000i			0.786146i	0.919507	+	0.393073i	$0.128588\pi$
$233$			12.0000i			0.786146i	−0.919507	+	0.393073i	$0.871412\pi$
$234$	−6.00000			−0.392232
$235$		0			0
$236$	4.00000			0.260378
$237$		0			0
$238$	8.00000	+	2.00000i	0.518563	+	0.129641i
$239$	16.0000			1.03495			0.517477	−	0.855697i	$-0.326871\pi$
$239$	16.0000			1.03495			0.517477	+	0.855697i	$0.326871\pi$
$240$		0			0
$241$			4.00000i			0.257663i	0.991667	+	0.128831i	$0.0411226\pi$
$241$			4.00000i			0.257663i	−0.991667	+	0.128831i	$0.958877\pi$
$242$	−5.00000			−0.321412
$243$		0			0
$244$			10.0000i			0.640184i
$245$		−	3.00000i		−	0.191663i
$246$		0			0
$247$	16.0000			1.01806
$248$			10.0000i			0.635001i
$249$		0			0
$250$			1.00000i			0.0632456i
$251$	16.0000			1.00991			0.504956	−	0.863145i	$-0.331509\pi$
$251$	16.0000			1.00991			0.504956	+	0.863145i	$0.331509\pi$
$252$		−	6.00000i		−	0.377964i
$253$	24.0000			1.50887
$254$		0			0
$255$		0			0
$256$	1.00000			0.0625000
$257$	−18.0000			−1.12281			−0.561405	−	0.827541i	$-0.689739\pi$
$257$	−18.0000			−1.12281			−0.561405	+	0.827541i	$0.689739\pi$
$258$		0			0
$259$	−4.00000			−0.248548
$260$			2.00000i			0.124035i
$261$		−	18.0000i		−	1.11417i
$262$		−	12.0000i		−	0.741362i
$263$	24.0000			1.47990			0.739952	−	0.672660i	$-0.234848\pi$
$263$	24.0000			1.47990			0.739952	+	0.672660i	$0.234848\pi$
$264$		0			0
$265$		−	10.0000i		−	0.614295i
$266$			16.0000i			0.981023i
$267$		0			0
$268$	−4.00000			−0.244339
$269$			2.00000i			0.121942i	0.998140	+	0.0609711i	$0.0194197\pi$
$269$			2.00000i			0.121942i	−0.998140	+	0.0609711i	$0.980580\pi$
$270$		0			0
$271$	24.0000			1.45790			0.728948	−	0.684569i	$-0.240010\pi$
$271$	24.0000			1.45790			0.728948	+	0.684569i	$0.240010\pi$
$272$	−1.00000	+	4.00000i	−0.0606339	+	0.242536i
$273$		0			0
$274$	14.0000			0.845771
$275$		−	4.00000i		−	0.241209i
$276$		0			0
$277$		−	22.0000i		−	1.32185i	−0.750451	−	0.660926i	$-0.770164\pi$
$277$		−	22.0000i		−	1.32185i	0.750451	−	0.660926i	$-0.229836\pi$
$278$		−	4.00000i		−	0.239904i
$279$			30.0000i			1.79605i
$280$	−2.00000			−0.119523
$281$	−18.0000			−1.07379			−0.536895	−	0.843649i	$-0.680403\pi$
$281$	−18.0000			−1.07379			−0.536895	+	0.843649i	$0.680403\pi$
$282$		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
$286$		−	8.00000i		−	0.473050i
$287$	8.00000			0.472225
$288$	3.00000			0.176777
$289$	−15.0000	−	8.00000i	−0.882353	−	0.470588i
$290$	−6.00000			−0.352332
$291$		0			0
$292$		−	12.0000i		−	0.702247i
$293$	−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
$295$		−	4.00000i		−	0.232889i
$296$		−	2.00000i		−	0.116248i
$297$		0			0
$298$	−18.0000			−1.04271
$299$			12.0000i			0.693978i
$300$		0			0
$301$			16.0000i			0.922225i
$302$	−8.00000			−0.460348
$303$		0			0
$304$	−8.00000			−0.458831
$305$	10.0000			0.572598
$306$	−3.00000	+	12.0000i	−0.171499	+	0.685994i
$307$	16.0000			0.913168			0.456584	−	0.889680i	$-0.349073\pi$
$307$	16.0000			0.913168			0.456584	+	0.889680i	$0.349073\pi$
$308$	8.00000			0.455842
$309$		0			0
$310$	10.0000			0.567962
$311$		−	14.0000i		−	0.793867i	−0.917847	−	0.396934i	$-0.870074\pi$
$311$		−	14.0000i		−	0.793867i	0.917847	−	0.396934i	$-0.129926\pi$
$312$		0			0
$313$			16.0000i			0.904373i	0.891923	+	0.452187i	$0.149356\pi$
$313$			16.0000i			0.904373i	−0.891923	+	0.452187i	$0.850644\pi$
$314$	−22.0000			−1.24153
$315$	−6.00000			−0.338062
$316$			6.00000i			0.337526i
$317$			2.00000i			0.112331i	0.998421	+	0.0561656i	$0.0178875\pi$
$317$			2.00000i			0.112331i	−0.998421	+	0.0561656i	$0.982113\pi$
$318$		0			0
$319$	24.0000			1.34374
$320$		−	1.00000i		−	0.0559017i
$321$		0			0
$322$	−12.0000			−0.668734
$323$	8.00000	−	32.0000i	0.445132	−	1.78053i
$324$	9.00000			0.500000
$325$	2.00000			0.110940
$326$			16.0000i			0.886158i
$327$		0			0
$328$			4.00000i			0.220863i
$329$		0			0
$330$		0			0
$331$	−28.0000			−1.53902			−0.769510	−	0.638635i	$-0.779499\pi$
$331$	−28.0000			−1.53902			−0.769510	+	0.638635i	$0.779499\pi$
$332$		0			0
$333$		−	6.00000i		−	0.328798i
$334$		−	2.00000i		−	0.109435i
$335$			4.00000i			0.218543i
$336$		0			0
$337$			28.0000i			1.52526i	0.646837	+	0.762629i	$0.276092\pi$
$337$			28.0000i			1.52526i	−0.646837	+	0.762629i	$0.723908\pi$
$338$	−9.00000			−0.489535
$339$		0			0
$340$	4.00000	+	1.00000i	0.216930	+	0.0542326i
$341$	−40.0000			−2.16612
$342$	−24.0000			−1.29777
$343$		−	20.0000i		−	1.07990i
$344$	−8.00000			−0.431331
$345$		0			0
$346$			2.00000i			0.107521i
$347$			24.0000i			1.28839i	0.764862	+	0.644194i	$0.222807\pi$
$347$			24.0000i			1.28839i	−0.764862	+	0.644194i	$0.777193\pi$
$348$		0			0
$349$	30.0000			1.60586			0.802932	−	0.596071i	$-0.203272\pi$
$349$	30.0000			1.60586			0.802932	+	0.596071i	$0.203272\pi$
$350$			2.00000i			0.106904i
$351$		0			0
$352$			4.00000i			0.213201i
$353$	−34.0000			−1.80964			−0.904819	−	0.425797i	$-0.859994\pi$
$353$	−34.0000			−1.80964			−0.904819	+	0.425797i	$0.859994\pi$
$354$		0			0
$355$	−10.0000			−0.530745
$356$	2.00000			0.106000
$357$		0			0
$358$		0			0
$359$	−16.0000			−0.844448			−0.422224	−	0.906492i	$-0.638750\pi$
$359$	−16.0000			−0.844448			−0.422224	+	0.906492i	$0.638750\pi$
$360$		−	3.00000i		−	0.158114i
$361$	45.0000			2.36842
$362$			2.00000i			0.105118i
$363$		0			0
$364$			4.00000i			0.209657i
$365$	−12.0000			−0.628109
$366$		0			0
$367$		−	14.0000i		−	0.730794i	−0.930852	−	0.365397i	$-0.880933\pi$
$367$		−	14.0000i		−	0.730794i	0.930852	−	0.365397i	$-0.119067\pi$
$368$		−	6.00000i		−	0.312772i
$369$			12.0000i			0.624695i
$370$	−2.00000			−0.103975
$371$		−	20.0000i		−	1.03835i
$372$		0			0
$373$	−26.0000			−1.34623			−0.673114	−	0.739538i	$-0.735044\pi$
$373$	−26.0000			−1.34623			−0.673114	+	0.739538i	$0.735044\pi$
$374$	−16.0000	−	4.00000i	−0.827340	−	0.206835i
$375$		0			0
$376$		0			0
$377$			12.0000i			0.618031i
$378$		0			0
$379$			16.0000i			0.821865i	0.911666	+	0.410932i	$0.134797\pi$
$379$			16.0000i			0.821865i	−0.911666	+	0.410932i	$0.865203\pi$
$380$			8.00000i			0.410391i
$381$		0			0
$382$	16.0000			0.818631
$383$	−16.0000			−0.817562			−0.408781	−	0.912633i	$-0.634046\pi$
$383$	−16.0000			−0.817562			−0.408781	+	0.912633i	$0.634046\pi$
$384$		0			0
$385$		−	8.00000i		−	0.407718i
$386$			16.0000i			0.814379i
$387$	−24.0000			−1.21999
$388$		−	16.0000i		−	0.812277i
$389$	−6.00000			−0.304212			−0.152106	−	0.988364i	$-0.548606\pi$
$389$	−6.00000			−0.304212			−0.152106	+	0.988364i	$0.548606\pi$
$390$		0			0
$391$	24.0000	+	6.00000i	1.21373	+	0.303433i
$392$	3.00000			0.151523
$393$		0			0
$394$			18.0000i			0.906827i
$395$	6.00000			0.301893
$396$			12.0000i			0.603023i
$397$		−	14.0000i		−	0.702640i	−0.936255	−	0.351320i	$-0.885733\pi$
$397$		−	14.0000i		−	0.702640i	0.936255	−	0.351320i	$-0.114267\pi$
$398$		−	2.00000i		−	0.100251i
$399$		0			0
$400$	−1.00000			−0.0500000
$401$			12.0000i			0.599251i	0.954057	+	0.299626i	$0.0968618\pi$
$401$			12.0000i			0.599251i	−0.954057	+	0.299626i	$0.903138\pi$
$402$		0			0
$403$		−	20.0000i		−	0.996271i
$404$	10.0000			0.497519
$405$		−	9.00000i		−	0.447214i
$406$	−12.0000			−0.595550
$407$	8.00000			0.396545
$408$		0			0
$409$	−10.0000			−0.494468			−0.247234	−	0.968956i	$-0.579522\pi$
$409$	−10.0000			−0.494468			−0.247234	+	0.968956i	$0.579522\pi$
$410$	4.00000			0.197546
$411$		0			0
$412$		0			0
$413$		−	8.00000i		−	0.393654i
$414$		−	18.0000i		−	0.884652i
$415$		0			0
$416$	−2.00000			−0.0980581
$417$		0			0
$418$		−	32.0000i		−	1.56517i
$419$			16.0000i			0.781651i	0.920465	+	0.390826i	$0.127810\pi$
$419$			16.0000i			0.781651i	−0.920465	+	0.390826i	$0.872190\pi$
$420$		0			0
$421$	−6.00000			−0.292422			−0.146211	−	0.989253i	$-0.546708\pi$
$421$	−6.00000			−0.292422			−0.146211	+	0.989253i	$0.546708\pi$
$422$		−	20.0000i		−	0.973585i
$423$		0			0
$424$	10.0000			0.485643
$425$	1.00000	−	4.00000i	0.0485071	−	0.194029i
$426$		0			0
$427$	20.0000			0.967868
$428$		−	4.00000i		−	0.193347i
$429$		0			0
$430$			8.00000i			0.385794i
$431$			22.0000i			1.05970i	0.848091	+	0.529851i	$0.177752\pi$
$431$			22.0000i			1.05970i	−0.848091	+	0.529851i	$0.822248\pi$
$432$		0			0
$433$	34.0000			1.63394			0.816968	−	0.576683i	$-0.195653\pi$
$433$	34.0000			1.63394			0.816968	+	0.576683i	$0.195653\pi$
$434$	20.0000			0.960031
$435$		0			0
$436$		−	10.0000i		−	0.478913i
$437$			48.0000i			2.29615i
$438$		0			0
$439$		−	10.0000i		−	0.477274i	−0.971109	−	0.238637i	$-0.923299\pi$
$439$		−	10.0000i		−	0.477274i	0.971109	−	0.238637i	$-0.0767006\pi$
$440$	4.00000			0.190693
$441$	9.00000			0.428571
$442$	2.00000	−	8.00000i	0.0951303	−	0.380521i
$443$	12.0000			0.570137			0.285069	−	0.958507i	$-0.407984\pi$
$443$	12.0000			0.570137			0.285069	+	0.958507i	$0.407984\pi$
$444$		0			0
$445$		−	2.00000i		−	0.0948091i
$446$	8.00000			0.378811
$447$		0			0
$448$		−	2.00000i		−	0.0944911i
$449$		−	12.0000i		−	0.566315i	−0.959073	−	0.283158i	$-0.908618\pi$
$449$		−	12.0000i		−	0.566315i	0.959073	−	0.283158i	$-0.0913819\pi$
$450$	−3.00000			−0.141421
$451$	−16.0000			−0.753411
$452$			4.00000i			0.188144i
$453$		0			0
$454$			24.0000i			1.12638i
$455$	4.00000			0.187523
$456$		0			0
$457$	−6.00000			−0.280668			−0.140334	−	0.990104i	$-0.544818\pi$
$457$	−6.00000			−0.280668			−0.140334	+	0.990104i	$0.544818\pi$
$458$	2.00000			0.0934539
$459$		0			0
$460$	−6.00000			−0.279751
$461$	6.00000			0.279448			0.139724	−	0.990190i	$-0.455378\pi$
$461$	6.00000			0.279448			0.139724	+	0.990190i	$0.455378\pi$
$462$		0			0
$463$	−24.0000			−1.11537			−0.557687	−	0.830051i	$-0.688311\pi$
$463$	−24.0000			−1.11537			−0.557687	+	0.830051i	$0.688311\pi$
$464$		−	6.00000i		−	0.278543i
$465$		0			0
$466$			12.0000i			0.555889i
$467$	−4.00000			−0.185098			−0.0925490	−	0.995708i	$-0.529501\pi$
$467$	−4.00000			−0.185098			−0.0925490	+	0.995708i	$0.529501\pi$
$468$	−6.00000			−0.277350
$469$			8.00000i			0.369406i
$470$		0			0
$471$		0			0
$472$	4.00000			0.184115
$473$		−	32.0000i		−	1.47136i
$474$		0			0
$475$	8.00000			0.367065
$476$	8.00000	+	2.00000i	0.366679	+	0.0916698i
$477$	30.0000			1.37361
$478$	16.0000			0.731823
$479$		−	18.0000i		−	0.822441i	−0.911536	−	0.411220i	$-0.865103\pi$
$479$		−	18.0000i		−	0.822441i	0.911536	−	0.411220i	$-0.134897\pi$
$480$		0			0
$481$			4.00000i			0.182384i
$482$			4.00000i			0.182195i
$483$		0			0
$484$	−5.00000			−0.227273
$485$	−16.0000			−0.726523
$486$		0			0
$487$			2.00000i			0.0906287i	0.998973	+	0.0453143i	$0.0144289\pi$
$487$			2.00000i			0.0906287i	−0.998973	+	0.0453143i	$0.985571\pi$
$488$			10.0000i			0.452679i
$489$		0			0
$490$		−	3.00000i		−	0.135526i
$491$		0			0			−	1.00000i	$-0.5\pi$
$491$		0			0				1.00000i	$0.5\pi$
$492$		0			0
$493$	24.0000	+	6.00000i	1.08091	+	0.270226i
$494$	16.0000			0.719874
$495$	12.0000			0.539360
$496$			10.0000i			0.449013i
$497$	−20.0000			−0.897123
$498$		0			0
$499$			20.0000i			0.895323i	0.894203	+	0.447661i	$0.147743\pi$
$499$			20.0000i			0.895323i	−0.894203	+	0.447661i	$0.852257\pi$
$500$			1.00000i			0.0447214i
$501$		0			0
$502$	16.0000			0.714115
$503$		−	30.0000i		−	1.33763i	−0.743427	−	0.668817i	$-0.766801\pi$
$503$		−	30.0000i		−	1.33763i	0.743427	−	0.668817i	$-0.233199\pi$
$504$		−	6.00000i		−	0.267261i
$505$		−	10.0000i		−	0.444994i
$506$	24.0000			1.06693
$507$		0			0
$508$		0			0
$509$	−18.0000			−0.797836			−0.398918	−	0.916987i	$-0.630614\pi$
$509$	−18.0000			−0.797836			−0.398918	+	0.916987i	$0.630614\pi$
$510$		0			0
$511$	−24.0000			−1.06170
$512$	1.00000			0.0441942
$513$		0			0
$514$	−18.0000			−0.793946
$515$		0			0
$516$		0			0
$517$		0			0
$518$	−4.00000			−0.175750
$519$		0			0
$520$			2.00000i			0.0877058i
$521$		−	36.0000i		−	1.57719i	−0.614914	−	0.788594i	$-0.710809\pi$
$521$		−	36.0000i		−	1.57719i	0.614914	−	0.788594i	$-0.289191\pi$
$522$		−	18.0000i		−	0.787839i
$523$	−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
$526$	24.0000			1.04645
$527$	−40.0000	−	10.0000i	−1.74243	−	0.435607i
$528$		0			0
$529$	−13.0000			−0.565217
$530$		−	10.0000i		−	0.434372i
$531$	12.0000			0.520756
$532$			16.0000i			0.693688i
$533$		−	8.00000i		−	0.346518i
$534$		0			0
$535$	−4.00000			−0.172935
$536$	−4.00000			−0.172774
$537$		0			0
$538$			2.00000i			0.0862261i
$539$			12.0000i			0.516877i
$540$		0			0
$541$			22.0000i			0.945854i	0.881102	+	0.472927i	$0.156803\pi$
$541$			22.0000i			0.945854i	−0.881102	+	0.472927i	$0.843197\pi$
$542$	24.0000			1.03089
$543$		0			0
$544$	−1.00000	+	4.00000i	−0.0428746	+	0.171499i
$545$	−10.0000			−0.428353
$546$		0			0
$547$			36.0000i			1.53925i	0.638497	+	0.769624i	$0.279557\pi$
$547$			36.0000i			1.53925i	−0.638497	+	0.769624i	$0.720443\pi$
$548$	14.0000			0.598050
$549$			30.0000i			1.28037i
$550$		−	4.00000i		−	0.170561i
$551$			48.0000i			2.04487i
$552$		0			0
$553$	12.0000			0.510292
$554$		−	22.0000i		−	0.934690i
$555$		0			0
$556$		−	4.00000i		−	0.169638i
$557$	30.0000			1.27114			0.635570	−	0.772043i	$-0.280765\pi$
$557$	30.0000			1.27114			0.635570	+	0.772043i	$0.280765\pi$
$558$			30.0000i			1.27000i
$559$	16.0000			0.676728
$560$	−2.00000			−0.0845154
$561$		0			0
$562$	−18.0000			−0.759284
$563$	−24.0000			−1.01148			−0.505740	−	0.862686i	$-0.668780\pi$
$563$	−24.0000			−1.01148			−0.505740	+	0.862686i	$0.668780\pi$
$564$		0			0
$565$	4.00000			0.168281
$566$		−	4.00000i		−	0.168133i
$567$		−	18.0000i		−	0.755929i
$568$		−	10.0000i		−	0.419591i
$569$	42.0000			1.76073			0.880366	−	0.474295i	$-0.157297\pi$
$569$	42.0000			1.76073			0.880366	+	0.474295i	$0.157297\pi$
$570$		0			0
$571$		−	32.0000i		−	1.33916i	−0.742741	−	0.669579i	$-0.766474\pi$
$571$		−	32.0000i		−	1.33916i	0.742741	−	0.669579i	$-0.233526\pi$
$572$		−	8.00000i		−	0.334497i
$573$		0			0
$574$	8.00000			0.333914
$575$			6.00000i			0.250217i
$576$	3.00000			0.125000
$577$	−34.0000			−1.41544			−0.707719	−	0.706494i	$-0.750276\pi$
$577$	−34.0000			−1.41544			−0.707719	+	0.706494i	$0.750276\pi$
$578$	−15.0000	−	8.00000i	−0.623918	−	0.332756i
$579$		0			0
$580$	−6.00000			−0.249136
$581$		0			0
$582$		0			0
$583$			40.0000i			1.65663i
$584$		−	12.0000i		−	0.496564i
$585$			6.00000i			0.248069i
$586$	−14.0000			−0.578335
$587$	44.0000			1.81607			0.908037	−	0.418890i	$-0.137581\pi$
$587$	44.0000			1.81607			0.908037	+	0.418890i	$0.137581\pi$
$588$		0			0
$589$		−	80.0000i		−	3.29634i
$590$		−	4.00000i		−	0.164677i
$591$		0			0
$592$		−	2.00000i		−	0.0821995i
$593$	−14.0000			−0.574911			−0.287456	−	0.957794i	$-0.592809\pi$
$593$	−14.0000			−0.574911			−0.287456	+	0.957794i	$0.592809\pi$
$594$		0			0
$595$	2.00000	−	8.00000i	0.0819920	−	0.327968i
$596$	−18.0000			−0.737309
$597$		0			0
$598$			12.0000i			0.490716i
$599$	−16.0000			−0.653742			−0.326871	−	0.945069i	$-0.605994\pi$
$599$	−16.0000			−0.653742			−0.326871	+	0.945069i	$0.605994\pi$
$600$		0			0
$601$		−	16.0000i		−	0.652654i	−0.945257	−	0.326327i	$-0.894189\pi$
$601$		−	16.0000i		−	0.652654i	0.945257	−	0.326327i	$-0.105811\pi$
$602$			16.0000i			0.652111i
$603$	−12.0000			−0.488678
$604$	−8.00000			−0.325515
$605$			5.00000i			0.203279i
$606$		0			0
$607$		−	18.0000i		−	0.730597i	−0.930890	−	0.365299i	$-0.880967\pi$
$607$		−	18.0000i		−	0.730597i	0.930890	−	0.365299i	$-0.119033\pi$
$608$	−8.00000			−0.324443
$609$		0			0
$610$	10.0000			0.404888
$611$		0			0
$612$	−3.00000	+	12.0000i	−0.121268	+	0.485071i
$613$	2.00000			0.0807792			0.0403896	−	0.999184i	$-0.487140\pi$
$613$	2.00000			0.0807792			0.0403896	+	0.999184i	$0.487140\pi$
$614$	16.0000			0.645707
$615$		0			0
$616$	8.00000			0.322329
$617$			20.0000i			0.805170i	0.915383	+	0.402585i	$0.131888\pi$
$617$			20.0000i			0.805170i	−0.915383	+	0.402585i	$0.868112\pi$
$618$		0			0
$619$			16.0000i			0.643094i	0.946894	+	0.321547i	$0.104203\pi$
$619$			16.0000i			0.643094i	−0.946894	+	0.321547i	$0.895797\pi$
$620$	10.0000			0.401610
$621$		0			0
$622$		−	14.0000i		−	0.561349i
$623$		−	4.00000i		−	0.160257i
$624$		0			0
$625$	1.00000			0.0400000
$626$			16.0000i			0.639489i
$627$		0			0
$628$	−22.0000			−0.877896
$629$	8.00000	+	2.00000i	0.318981	+	0.0797452i
$630$	−6.00000			−0.239046
$631$	8.00000			0.318475			0.159237	−	0.987240i	$-0.449096\pi$
$631$	8.00000			0.318475			0.159237	+	0.987240i	$0.449096\pi$
$632$			6.00000i			0.238667i
$633$		0			0
$634$			2.00000i			0.0794301i
$635$		0			0
$636$		0			0
$637$	−6.00000			−0.237729
$638$	24.0000			0.950169
$639$		−	30.0000i		−	1.18678i
$640$		−	1.00000i		−	0.0395285i
$641$			44.0000i			1.73790i	0.494904	+	0.868948i	$0.335203\pi$
$641$			44.0000i			1.73790i	−0.494904	+	0.868948i	$0.664797\pi$
$642$		0			0
$643$			24.0000i			0.946468i	0.880937	+	0.473234i	$0.156913\pi$
$643$			24.0000i			0.946468i	−0.880937	+	0.473234i	$0.843087\pi$
$644$	−12.0000			−0.472866
$645$		0			0
$646$	8.00000	−	32.0000i	0.314756	−	1.25902i
$647$	32.0000			1.25805			0.629025	−	0.777385i	$-0.283454\pi$
$647$	32.0000			1.25805			0.629025	+	0.777385i	$0.283454\pi$
$648$	9.00000			0.353553
$649$			16.0000i			0.628055i
$650$	2.00000			0.0784465
$651$		0			0
$652$			16.0000i			0.626608i
$653$			38.0000i			1.48705i	0.668705	+	0.743527i	$0.266849\pi$
$653$			38.0000i			1.48705i	−0.668705	+	0.743527i	$0.733151\pi$
$654$		0			0
$655$	−12.0000			−0.468879
$656$			4.00000i			0.156174i
$657$		−	36.0000i		−	1.40449i
$658$		0			0
$659$	−20.0000			−0.779089			−0.389545	−	0.921008i	$-0.627368\pi$
$659$	−20.0000			−0.779089			−0.389545	+	0.921008i	$0.627368\pi$
$660$		0			0
$661$	−18.0000			−0.700119			−0.350059	−	0.936727i	$-0.613839\pi$
$661$	−18.0000			−0.700119			−0.350059	+	0.936727i	$0.613839\pi$
$662$	−28.0000			−1.08825
$663$		0			0
$664$		0			0
$665$	16.0000			0.620453
$666$		−	6.00000i		−	0.232495i
$667$	−36.0000			−1.39393
$668$		−	2.00000i		−	0.0773823i
$669$		0			0
$670$			4.00000i			0.154533i
$671$	−40.0000			−1.54418
$672$		0			0
$673$			24.0000i			0.925132i	0.886585	+	0.462566i	$0.153071\pi$
$673$			24.0000i			0.925132i	−0.886585	+	0.462566i	$0.846929\pi$
$674$			28.0000i			1.07852i
$675$		0			0
$676$	−9.00000			−0.346154
$677$		−	42.0000i		−	1.61419i	−0.590421	−	0.807096i	$-0.701038\pi$
$677$		−	42.0000i		−	1.61419i	0.590421	−	0.807096i	$-0.298962\pi$
$678$		0			0
$679$	−32.0000			−1.22805
$680$	4.00000	+	1.00000i	0.153393	+	0.0383482i
$681$		0			0
$682$	−40.0000			−1.53168
$683$		−	8.00000i		−	0.306111i	−0.988218	−	0.153056i	$-0.951089\pi$
$683$		−	8.00000i		−	0.306111i	0.988218	−	0.153056i	$-0.0489114\pi$
$684$	−24.0000			−0.917663
$685$		−	14.0000i		−	0.534913i
$686$		−	20.0000i		−	0.763604i
$687$		0			0
$688$	−8.00000			−0.304997
$689$	−20.0000			−0.761939
$690$		0			0
$691$		−	12.0000i		−	0.456502i	−0.973602	−	0.228251i	$-0.926699\pi$
$691$		−	12.0000i		−	0.456502i	0.973602	−	0.228251i	$-0.0733006\pi$
$692$			2.00000i			0.0760286i
$693$	24.0000			0.911685
$694$			24.0000i			0.911028i
$695$	−4.00000			−0.151729
$696$		0			0
$697$	−16.0000	−	4.00000i	−0.606043	−	0.151511i
$698$	30.0000			1.13552
$699$		0			0
$700$			2.00000i			0.0755929i
$701$	42.0000			1.58632			0.793159	−	0.609015i	$-0.208435\pi$
$701$	42.0000			1.58632			0.793159	+	0.609015i	$0.208435\pi$
$702$		0			0
$703$			16.0000i			0.603451i
$704$			4.00000i			0.150756i
$705$		0			0
$706$	−34.0000			−1.27961
$707$		−	20.0000i		−	0.752177i
$708$		0			0
$709$		−	22.0000i		−	0.826227i	−0.910679	−	0.413114i	$-0.864441\pi$
$709$		−	22.0000i		−	0.826227i	0.910679	−	0.413114i	$-0.135559\pi$
$710$	−10.0000			−0.375293
$711$			18.0000i			0.675053i
$712$	2.00000			0.0749532
$713$	60.0000			2.24702
$714$		0			0
$715$	−8.00000			−0.299183
$716$		0			0
$717$		0			0
$718$	−16.0000			−0.597115
$719$			6.00000i			0.223762i	0.993722	+	0.111881i	$0.0356876\pi$
$719$			6.00000i			0.223762i	−0.993722	+	0.111881i	$0.964312\pi$
$720$		−	3.00000i		−	0.111803i
$721$		0			0
$722$	45.0000			1.67473
$723$		0			0
$724$			2.00000i			0.0743294i
$725$			6.00000i			0.222834i
$726$		0			0
$727$	−32.0000			−1.18681			−0.593407	−	0.804902i	$-0.702218\pi$
$727$	−32.0000			−1.18681			−0.593407	+	0.804902i	$0.702218\pi$
$728$			4.00000i			0.148250i
$729$	27.0000			1.00000
$730$	−12.0000			−0.444140
$731$	8.00000	−	32.0000i	0.295891	−	1.18356i
$732$		0			0
$733$	−6.00000			−0.221615			−0.110808	−	0.993842i	$-0.535344\pi$
$733$	−6.00000			−0.221615			−0.110808	+	0.993842i	$0.535344\pi$
$734$		−	14.0000i		−	0.516749i
$735$		0			0
$736$		−	6.00000i		−	0.221163i
$737$		−	16.0000i		−	0.589368i
$738$			12.0000i			0.441726i
$739$	24.0000			0.882854			0.441427	−	0.897297i	$-0.354472\pi$
$739$	24.0000			0.882854			0.441427	+	0.897297i	$0.354472\pi$
$740$	−2.00000			−0.0735215
$741$		0			0
$742$		−	20.0000i		−	0.734223i
$743$			38.0000i			1.39408i	0.717030	+	0.697042i	$0.245501\pi$
$743$			38.0000i			1.39408i	−0.717030	+	0.697042i	$0.754499\pi$
$744$		0			0
$745$			18.0000i			0.659469i
$746$	−26.0000			−0.951928
$747$		0			0
$748$	−16.0000	−	4.00000i	−0.585018	−	0.146254i
$749$	−8.00000			−0.292314
$750$		0			0
$751$			6.00000i			0.218943i	0.993990	+	0.109472i	$0.0349159\pi$
$751$			6.00000i			0.218943i	−0.993990	+	0.109472i	$0.965084\pi$
$752$		0			0
$753$		0			0
$754$			12.0000i			0.437014i
$755$			8.00000i			0.291150i
$756$		0			0
$757$	22.0000			0.799604			0.399802	−	0.916602i	$-0.369079\pi$
$757$	22.0000			0.799604			0.399802	+	0.916602i	$0.369079\pi$
$758$			16.0000i			0.581146i
$759$		0			0
$760$			8.00000i			0.290191i
$761$	6.00000			0.217500			0.108750	−	0.994069i	$-0.465315\pi$
$761$	6.00000			0.217500			0.108750	+	0.994069i	$0.465315\pi$
$762$		0			0
$763$	−20.0000			−0.724049
$764$	16.0000			0.578860
$765$	12.0000	+	3.00000i	0.433861	+	0.108465i
$766$	−16.0000			−0.578103
$767$	−8.00000			−0.288863
$768$		0			0
$769$	−2.00000			−0.0721218			−0.0360609	−	0.999350i	$-0.511481\pi$
$769$	−2.00000			−0.0721218			−0.0360609	+	0.999350i	$0.511481\pi$
$770$		−	8.00000i		−	0.288300i
$771$		0			0
$772$			16.0000i			0.575853i
$773$	−42.0000			−1.51064			−0.755318	−	0.655359i	$-0.772517\pi$
$773$	−42.0000			−1.51064			−0.755318	+	0.655359i	$0.772517\pi$
$774$	−24.0000			−0.862662
$775$		−	10.0000i		−	0.359211i
$776$		−	16.0000i		−	0.574367i
$777$		0			0
$778$	−6.00000			−0.215110
$779$		−	32.0000i		−	1.14652i
$780$		0			0
$781$	40.0000			1.43131
$782$	24.0000	+	6.00000i	0.858238	+	0.214560i
$783$		0			0
$784$	3.00000			0.107143
$785$			22.0000i			0.785214i
$786$		0			0
$787$			44.0000i			1.56843i	0.620489	+	0.784215i	$0.286934\pi$
$787$			44.0000i			1.56843i	−0.620489	+	0.784215i	$0.713066\pi$
$788$			18.0000i			0.641223i
$789$		0			0
$790$	6.00000			0.213470
$791$	8.00000			0.284447
$792$			12.0000i			0.426401i
$793$		−	20.0000i		−	0.710221i
$794$		−	14.0000i		−	0.496841i
$795$		0			0
$796$		−	2.00000i		−	0.0708881i
$797$	−6.00000			−0.212531			−0.106265	−	0.994338i	$-0.533889\pi$
$797$	−6.00000			−0.212531			−0.106265	+	0.994338i	$0.533889\pi$
$798$		0			0
$799$		0			0
$800$	−1.00000			−0.0353553
$801$	6.00000			0.212000
$802$			12.0000i			0.423735i
$803$	48.0000			1.69388
$804$		0			0
$805$			12.0000i			0.422944i
$806$		−	20.0000i		−	0.704470i
$807$		0			0
$808$	10.0000			0.351799
$809$		−	4.00000i		−	0.140633i	−0.997525	−	0.0703163i	$-0.977599\pi$
$809$		−	4.00000i		−	0.140633i	0.997525	−	0.0703163i	$-0.0224008\pi$
$810$		−	9.00000i		−	0.316228i
$811$		−	56.0000i		−	1.96643i	−0.182462	−	0.983213i	$-0.558407\pi$
$811$		−	56.0000i		−	1.96643i	0.182462	−	0.983213i	$-0.441593\pi$
$812$	−12.0000			−0.421117
$813$		0			0
$814$	8.00000			0.280400
$815$	16.0000			0.560456
$816$		0			0
$817$	64.0000			2.23908
$818$	−10.0000			−0.349642
$819$			12.0000i			0.419314i
$820$	4.00000			0.139686
$821$		−	18.0000i		−	0.628204i	−0.949389	−	0.314102i	$-0.898297\pi$
$821$		−	18.0000i		−	0.628204i	0.949389	−	0.314102i	$-0.101703\pi$
$822$		0			0
$823$		−	22.0000i		−	0.766872i	−0.923567	−	0.383436i	$-0.874741\pi$
$823$		−	22.0000i		−	0.766872i	0.923567	−	0.383436i	$-0.125259\pi$
$824$		0			0
$825$		0			0
$826$		−	8.00000i		−	0.278356i
$827$			20.0000i			0.695468i	0.937593	+	0.347734i	$0.113049\pi$
$827$			20.0000i			0.695468i	−0.937593	+	0.347734i	$0.886951\pi$
$828$		−	18.0000i		−	0.625543i
$829$	6.00000			0.208389			0.104194	−	0.994557i	$-0.466774\pi$
$829$	6.00000			0.208389			0.104194	+	0.994557i	$0.466774\pi$
$830$		0			0
$831$		0			0
$832$	−2.00000			−0.0693375
$833$	−3.00000	+	12.0000i	−0.103944	+	0.415775i
$834$		0			0
$835$	−2.00000			−0.0692129
$836$		−	32.0000i		−	1.10674i
$837$		0			0
$838$			16.0000i			0.552711i
$839$		−	14.0000i		−	0.483334i	−0.970359	−	0.241667i	$-0.922306\pi$
$839$		−	14.0000i		−	0.483334i	0.970359	−	0.241667i	$-0.0776941\pi$
$840$		0			0
$841$	−7.00000			−0.241379
$842$	−6.00000			−0.206774
$843$		0			0
$844$		−	20.0000i		−	0.688428i
$845$			9.00000i			0.309609i
$846$		0			0
$847$			10.0000i			0.343604i
$848$	10.0000			0.343401
$849$		0			0
$850$	1.00000	−	4.00000i	0.0342997	−	0.137199i
$851$	−12.0000			−0.411355
$852$		0			0
$853$			50.0000i			1.71197i	0.517003	+	0.855984i	$0.327048\pi$
$853$			50.0000i			1.71197i	−0.517003	+	0.855984i	$0.672952\pi$
$854$	20.0000			0.684386
$855$			24.0000i			0.820783i
$856$		−	4.00000i		−	0.136717i
$857$		−	32.0000i		−	1.09310i	−0.837427	−	0.546550i	$-0.815941\pi$
$857$		−	32.0000i		−	1.09310i	0.837427	−	0.546550i	$-0.184059\pi$
$858$		0			0
$859$	12.0000			0.409435			0.204717	−	0.978821i	$-0.434372\pi$
$859$	12.0000			0.409435			0.204717	+	0.978821i	$0.434372\pi$
$860$			8.00000i			0.272798i
$861$		0			0
$862$			22.0000i			0.749323i
$863$	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
$865$	2.00000			0.0680020
$866$	34.0000			1.15537
$867$		0			0
$868$	20.0000			0.678844
$869$	−24.0000			−0.814144
$870$		0			0
$871$	8.00000			0.271070
$872$		−	10.0000i		−	0.338643i
$873$		−	48.0000i		−	1.62455i
$874$			48.0000i			1.62362i
$875$	2.00000			0.0676123
$876$		0			0
$877$		−	34.0000i		−	1.14810i	−0.818821	−	0.574049i	$-0.805372\pi$
$877$		−	34.0000i		−	1.14810i	0.818821	−	0.574049i	$-0.194628\pi$
$878$		−	10.0000i		−	0.337484i
$879$		0			0
$880$	4.00000			0.134840
$881$		−	24.0000i		−	0.808581i	−0.914631	−	0.404290i	$-0.867519\pi$
$881$		−	24.0000i		−	0.808581i	0.914631	−	0.404290i	$-0.132481\pi$
$882$	9.00000			0.303046
$883$	−4.00000			−0.134611			−0.0673054	−	0.997732i	$-0.521440\pi$
$883$	−4.00000			−0.134611			−0.0673054	+	0.997732i	$0.521440\pi$
$884$	2.00000	−	8.00000i	0.0672673	−	0.269069i
$885$		0			0
$886$	12.0000			0.403148
$887$		−	54.0000i		−	1.81314i	−0.422053	−	0.906571i	$-0.638690\pi$
$887$		−	54.0000i		−	1.81314i	0.422053	−	0.906571i	$-0.361310\pi$
$888$		0			0
$889$		0			0
$890$		−	2.00000i		−	0.0670402i
$891$			36.0000i			1.20605i
$892$	8.00000			0.267860
$893$		0			0
$894$		0			0
$895$		0			0
$896$		−	2.00000i		−	0.0668153i
$897$		0			0
$898$		−	12.0000i		−	0.400445i
$899$	60.0000			2.00111
$900$	−3.00000			−0.100000
$901$	−10.0000	+	40.0000i	−0.333148	+	1.33259i
$902$	−16.0000			−0.532742
$903$		0			0
$904$			4.00000i			0.133038i
$905$	2.00000			0.0664822
$906$		0			0
$907$		−	12.0000i		−	0.398453i	−0.979953	−	0.199227i	$-0.936157\pi$
$907$		−	12.0000i		−	0.398453i	0.979953	−	0.199227i	$-0.0638430\pi$
$908$			24.0000i			0.796468i
$909$	30.0000			0.995037
$910$	4.00000			0.132599
$911$		−	6.00000i		−	0.198789i	−0.995048	−	0.0993944i	$-0.968309\pi$
$911$		−	6.00000i		−	0.198789i	0.995048	−	0.0993944i	$-0.0316906\pi$
$912$		0			0
$913$		0			0
$914$	−6.00000			−0.198462
$915$		0			0
$916$	2.00000			0.0660819
$917$	−24.0000			−0.792550
$918$		0			0
$919$	−40.0000			−1.31948			−0.659739	−	0.751495i	$-0.729333\pi$
$919$	−40.0000			−1.31948			−0.659739	+	0.751495i	$0.729333\pi$
$920$	−6.00000			−0.197814
$921$		0			0
$922$	6.00000			0.197599
$923$			20.0000i			0.658308i
$924$		0			0
$925$			2.00000i			0.0657596i
$926$	−24.0000			−0.788689
$927$		0			0
$928$		−	6.00000i		−	0.196960i
$929$			36.0000i			1.18112i	0.806993	+	0.590561i	$0.201093\pi$
$929$			36.0000i			1.18112i	−0.806993	+	0.590561i	$0.798907\pi$
$930$		0			0
$931$	−24.0000			−0.786568
$932$			12.0000i			0.393073i
$933$		0			0
$934$	−4.00000			−0.130884
$935$	−4.00000	+	16.0000i	−0.130814	+	0.523256i
$936$	−6.00000			−0.196116
$937$	38.0000			1.24141			0.620703	−	0.784046i	$-0.286847\pi$
$937$	38.0000			1.24141			0.620703	+	0.784046i	$0.286847\pi$
$938$			8.00000i			0.261209i
$939$		0			0
$940$		0			0
$941$			10.0000i			0.325991i	0.986627	+	0.162995i	$0.0521156\pi$
$941$			10.0000i			0.325991i	−0.986627	+	0.162995i	$0.947884\pi$
$942$		0			0
$943$	24.0000			0.781548
$944$	4.00000			0.130189
$945$		0			0
$946$		−	32.0000i		−	1.04041i
$947$		−	20.0000i		−	0.649913i	−0.945729	−	0.324956i	$-0.894650\pi$
$947$		−	20.0000i		−	0.649913i	0.945729	−	0.324956i	$-0.105350\pi$
$948$		0			0
$949$			24.0000i			0.779073i
$950$	8.00000			0.259554
$951$		0			0
$952$	8.00000	+	2.00000i	0.259281	+	0.0648204i
$953$	−22.0000			−0.712650			−0.356325	−	0.934362i	$-0.615970\pi$
$953$	−22.0000			−0.712650			−0.356325	+	0.934362i	$0.615970\pi$
$954$	30.0000			0.971286
$955$		−	16.0000i		−	0.517748i
$956$	16.0000			0.517477
$957$		0			0
$958$		−	18.0000i		−	0.581554i
$959$		−	28.0000i		−	0.904167i
$960$		0			0
$961$	−69.0000			−2.22581
$962$			4.00000i			0.128965i
$963$		−	12.0000i		−	0.386695i
$964$			4.00000i			0.128831i
$965$	16.0000			0.515058
$966$		0			0
$967$	−40.0000			−1.28631			−0.643157	−	0.765735i	$-0.722376\pi$
$967$	−40.0000			−1.28631			−0.643157	+	0.765735i	$0.722376\pi$
$968$	−5.00000			−0.160706
$969$		0			0
$970$	−16.0000			−0.513729
$971$	28.0000			0.898563			0.449281	−	0.893390i	$-0.351680\pi$
$971$	28.0000			0.898563			0.449281	+	0.893390i	$0.351680\pi$
$972$		0			0
$973$	−8.00000			−0.256468
$974$			2.00000i			0.0640841i
$975$		0			0
$976$			10.0000i			0.320092i
$977$	−22.0000			−0.703842			−0.351921	−	0.936030i	$-0.614471\pi$
$977$	−22.0000			−0.703842			−0.351921	+	0.936030i	$0.614471\pi$
$978$		0			0
$979$			8.00000i			0.255681i
$980$		−	3.00000i		−	0.0958315i
$981$		−	30.0000i		−	0.957826i
$982$		0			0
$983$		−	22.0000i		−	0.701691i	−0.936433	−	0.350846i	$-0.885894\pi$
$983$		−	22.0000i		−	0.701691i	0.936433	−	0.350846i	$-0.114106\pi$
$984$		0			0
$985$	18.0000			0.573528
$986$	24.0000	+	6.00000i	0.764316	+	0.191079i
$987$		0			0
$988$	16.0000			0.509028
$989$			48.0000i			1.52631i
$990$	12.0000			0.381385
$991$			62.0000i			1.96949i	0.173990	+	0.984747i	$0.444334\pi$
$991$			62.0000i			1.96949i	−0.173990	+	0.984747i	$0.555666\pi$
$992$			10.0000i			0.317500i
$993$		0			0
$994$	−20.0000			−0.634361
$995$	−2.00000			−0.0634043
$996$		0			0
$997$			18.0000i			0.570066i	0.958518	+	0.285033i	$0.0920045\pi$
$997$			18.0000i			0.570066i	−0.958518	+	0.285033i	$0.907995\pi$
$998$			20.0000i			0.633089i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	170.2.b.c.101.1	✓	2
3.2	odd	2		1530.2.c.a.271.2		2
4.3	odd	2		1360.2.c.d.1121.1		2
5.2	odd	4		850.2.d.e.849.2		2
5.3	odd	4		850.2.d.d.849.1		2
5.4	even	2		850.2.b.e.101.2		2
17.4	even	4		2890.2.a.f.1.1		1
17.13	even	4		2890.2.a.g.1.1		1
17.16	even	2	inner	170.2.b.c.101.2	yes	2
51.50	odd	2		1530.2.c.a.271.1		2
68.67	odd	2		1360.2.c.d.1121.2		2
85.33	odd	4		850.2.d.e.849.1		2
85.67	odd	4		850.2.d.d.849.2		2
85.84	even	2		850.2.b.e.101.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.2.b.c.101.1	✓	2	1.1	even	1	trivial
170.2.b.c.101.2	yes	2	17.16	even	2	inner
850.2.b.e.101.1		2	85.84	even	2
850.2.b.e.101.2		2	5.4	even	2
850.2.d.d.849.1		2	5.3	odd	4
850.2.d.d.849.2		2	85.67	odd	4
850.2.d.e.849.1		2	85.33	odd	4
850.2.d.e.849.2		2	5.2	odd	4
1360.2.c.d.1121.1		2	4.3	odd	2
1360.2.c.d.1121.2		2	68.67	odd	2
1530.2.c.a.271.1		2	51.50	odd	2
1530.2.c.a.271.2		2	3.2	odd	2
2890.2.a.f.1.1		1	17.4	even	4
2890.2.a.g.1.1		1	17.13	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:	\( N \)	\(=\)	\( 170 = 2 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	170.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{4} -1.00000i q^{5} -2.00000i q^{7} +1.00000 q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{4} -1.00000i q^{5} -2.00000i q^{7} +1.00000 q^{8} +3.00000 q^{9} -1.00000i q^{10} +4.00000i q^{11} -2.00000 q^{13} -2.00000i q^{14} +1.00000 q^{16} +(-1.00000 + 4.00000i) q^{17} +3.00000 q^{18} -8.00000 q^{19} -1.00000i q^{20} +4.00000i q^{22} -6.00000i q^{23} -1.00000 q^{25} -2.00000 q^{26} -2.00000i q^{28} -6.00000i q^{29} +10.0000i q^{31} +1.00000 q^{32} +(-1.00000 + 4.00000i) q^{34} -2.00000 q^{35} +3.00000 q^{36} -2.00000i q^{37} -8.00000 q^{38} -1.00000i q^{40} +4.00000i q^{41} -8.00000 q^{43} +4.00000i q^{44} -3.00000i q^{45} -6.00000i q^{46} +3.00000 q^{49} -1.00000 q^{50} -2.00000 q^{52} +10.0000 q^{53} +4.00000 q^{55} -2.00000i q^{56} -6.00000i q^{58} +4.00000 q^{59} +10.0000i q^{61} +10.0000i q^{62} -6.00000i q^{63} +1.00000 q^{64} +2.00000i q^{65} -4.00000 q^{67} +(-1.00000 + 4.00000i) q^{68} -2.00000 q^{70} -10.0000i q^{71} +3.00000 q^{72} -12.0000i q^{73} -2.00000i q^{74} -8.00000 q^{76} +8.00000 q^{77} +6.00000i q^{79} -1.00000i q^{80} +9.00000 q^{81} +4.00000i q^{82} +(4.00000 + 1.00000i) q^{85} -8.00000 q^{86} +4.00000i q^{88} +2.00000 q^{89} -3.00000i q^{90} +4.00000i q^{91} -6.00000i q^{92} +8.00000i q^{95} -16.0000i q^{97} +3.00000 q^{98} +12.0000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 2 q^{4} + 2 q^{8} + 6 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 + 2 * q^4 + 2 * q^8 + 6 * q^9	\( 2 q + 2 q^{2} + 2 q^{4} + 2 q^{8} + 6 q^{9} - 4 q^{13} + 2 q^{16} - 2 q^{17} + 6 q^{18} - 16 q^{19} - 2 q^{25} - 4 q^{26} + 2 q^{32} - 2 q^{34} - 4 q^{35} + 6 q^{36} - 16 q^{38} - 16 q^{43} + 6 q^{49} - 2 q^{50} - 4 q^{52} + 20 q^{53} + 8 q^{55} + 8 q^{59} + 2 q^{64} - 8 q^{67} - 2 q^{68} - 4 q^{70} + 6 q^{72} - 16 q^{76} + 16 q^{77} + 18 q^{81} + 8 q^{85} - 16 q^{86} + 4 q^{89} + 6 q^{98}+O(q^{100}) \) 2 * q + 2 * q^2 + 2 * q^4 + 2 * q^8 + 6 * q^9 - 4 * q^13 + 2 * q^16 - 2 * q^17 + 6 * q^18 - 16 * q^19 - 2 * q^25 - 4 * q^26 + 2 * q^32 - 2 * q^34 - 4 * q^35 + 6 * q^36 - 16 * q^38 - 16 * q^43 + 6 * q^49 - 2 * q^50 - 4 * q^52 + 20 * q^53 + 8 * q^55 + 8 * q^59 + 2 * q^64 - 8 * q^67 - 2 * q^68 - 4 * q^70 + 6 * q^72 - 16 * q^76 + 16 * q^77 + 18 * q^81 + 8 * q^85 - 16 * q^86 + 4 * q^89 + 6 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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