LMFDB - Embedded newform 1183.2.c.j.337.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1183,2,Mod(337,1183)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1183, 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("1183.337");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1183 = 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1183.c (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:	$9.44630255912$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			337.1
Character	$\chi$	$=$	1183.337
Dual form			1183.2.c.j.337.24

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.62803i q^{2} -1.76762 q^{3} -4.90656 q^{4} +2.94291i q^{5} +4.64535i q^{6} +1.00000i q^{7} +7.63852i q^{8} +0.124466 q^{9} +O(q^{10})$	\(q-2.62803i q^{2} -1.76762 q^{3} -4.90656 q^{4} +2.94291i q^{5} +4.64535i q^{6} +1.00000i q^{7} +7.63852i q^{8} +0.124466 q^{9} +7.73406 q^{10} +4.28290i q^{11} +8.67291 q^{12} +2.62803 q^{14} -5.20193i q^{15} +10.2612 q^{16} -2.94049 q^{17} -0.327101i q^{18} -4.98782i q^{19} -14.4396i q^{20} -1.76762i q^{21} +11.2556 q^{22} -7.58085 q^{23} -13.5020i q^{24} -3.66072 q^{25} +5.08284 q^{27} -4.90656i q^{28} -1.82633 q^{29} -13.6709 q^{30} -6.57664i q^{31} -11.6897i q^{32} -7.57053i q^{33} +7.72771i q^{34} -2.94291 q^{35} -0.610701 q^{36} -8.31285i q^{37} -13.1082 q^{38} -22.4795 q^{40} +4.15934i q^{41} -4.64535 q^{42} +8.48158 q^{43} -21.0143i q^{44} +0.366293i q^{45} +19.9227i q^{46} +0.910136i q^{47} -18.1378 q^{48} -1.00000 q^{49} +9.62049i q^{50} +5.19766 q^{51} +4.47393 q^{53} -13.3579i q^{54} -12.6042 q^{55} -7.63852 q^{56} +8.81656i q^{57} +4.79965i q^{58} -9.42007i q^{59} +25.5236i q^{60} -1.75588 q^{61} -17.2836 q^{62} +0.124466i q^{63} -10.1985 q^{64} -19.8956 q^{66} -0.413638i q^{67} +14.4277 q^{68} +13.4000 q^{69} +7.73406i q^{70} +2.95901i q^{71} +0.950738i q^{72} -0.885074i q^{73} -21.8464 q^{74} +6.47075 q^{75} +24.4730i q^{76} -4.28290 q^{77} +10.0505 q^{79} +30.1977i q^{80} -9.35791 q^{81} +10.9309 q^{82} -6.04519i q^{83} +8.67291i q^{84} -8.65360i q^{85} -22.2899i q^{86} +3.22825 q^{87} -32.7151 q^{88} -3.82110i q^{89} +0.962630 q^{90} +37.1958 q^{92} +11.6250i q^{93} +2.39187 q^{94} +14.6787 q^{95} +20.6628i q^{96} +2.37500i q^{97} +2.62803i q^{98} +0.533077i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 16 q^{3} - 30 q^{4} + 52 q^{9}+O(q^{10}) $ 24 * q + 16 * q^3 - 30 * q^4 + 52 * q^9	$ 24 q + 16 q^{3} - 30 q^{4} + 52 q^{9} + 12 q^{10} - 26 q^{12} + 6 q^{14} + 26 q^{16} - 62 q^{17} - 8 q^{22} - 36 q^{23} - 64 q^{25} + 64 q^{27} + 30 q^{29} + 20 q^{30} - 8 q^{35} - 98 q^{36} - 90 q^{38} - 40 q^{40} + 4 q^{42} + 44 q^{43} + 22 q^{48} - 24 q^{49} - 36 q^{51} + 106 q^{53} - 52 q^{55} - 24 q^{56} + 44 q^{61} - 38 q^{62} - 4 q^{64} - 68 q^{66} + 68 q^{68} - 6 q^{69} - 80 q^{74} - 30 q^{75} - 24 q^{77} + 4 q^{79} + 72 q^{81} + 64 q^{82} + 54 q^{87} + 96 q^{88} + 52 q^{90} + 104 q^{92} - 88 q^{94} - 58 q^{95}+O(q^{100}) $ 24 * q + 16 * q^3 - 30 * q^4 + 52 * q^9 + 12 * q^10 - 26 * q^12 + 6 * q^14 + 26 * q^16 - 62 * q^17 - 8 * q^22 - 36 * q^23 - 64 * q^25 + 64 * q^27 + 30 * q^29 + 20 * q^30 - 8 * q^35 - 98 * q^36 - 90 * q^38 - 40 * q^40 + 4 * q^42 + 44 * q^43 + 22 * q^48 - 24 * q^49 - 36 * q^51 + 106 * q^53 - 52 * q^55 - 24 * q^56 + 44 * q^61 - 38 * q^62 - 4 * q^64 - 68 * q^66 + 68 * q^68 - 6 * q^69 - 80 * q^74 - 30 * q^75 - 24 * q^77 + 4 * q^79 + 72 * q^81 + 64 * q^82 + 54 * q^87 + 96 * q^88 + 52 * q^90 + 104 * q^92 - 88 * q^94 - 58 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times$.

$n$	$339$	$1016$
$\chi(n)$	$1$	$-1$

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 $

$2$	− 2.62803i	− 1.85830i	−0.369703	−	0.929150i	$-0.620541\pi$
$2$	− 2.62803i	− 1.85830i	0.369703	−	0.929150i	$-0.379459\pi$
$3$	−1.76762	−1.02053	−0.510267	−	0.860016i	$-0.670453\pi$
$3$	−1.76762	−1.02053	−0.510267	+	0.860016i	$0.670453\pi$
$4$	−4.90656	−2.45328
$5$	2.94291i	1.31611i	0.752970	+	0.658055i	$0.228620\pi$
$5$	2.94291i	1.31611i	−0.752970	+	0.658055i	$0.771380\pi$
$6$	4.64535i	1.89646i
$7$	1.00000i	0.377964i
$7$	1.00000i	0.377964i
$8$	7.63852i	2.70063i
$9$	0.124466	0.0414887
$10$	7.73406	2.44573
$11$	4.28290i	1.29134i	0.763615	+	0.645672i	$0.223423\pi$
$11$	4.28290i	1.29134i	−0.763615	+	0.645672i	$0.776577\pi$
$12$	8.67291	2.50365
$13$	0	0
$13$	0	0
$14$	2.62803	0.702371
$15$	− 5.20193i	− 1.34313i
$16$	10.2612	2.56529
$17$	−2.94049	−0.713174	−0.356587	−	0.934262i	$-0.616060\pi$
$17$	−2.94049	−0.713174	−0.356587	+	0.934262i	$0.616060\pi$
$18$	− 0.327101i	− 0.0770985i
$19$	− 4.98782i	− 1.14429i	−0.820154	−	0.572143i	$-0.806112\pi$
$19$	− 4.98782i	− 1.14429i	0.820154	−	0.572143i	$-0.193888\pi$
$20$	− 14.4396i	− 3.22878i
$21$	− 1.76762i	− 0.385725i
$22$	11.2556	2.39970
$23$	−7.58085	−1.58072	−0.790358	−	0.612646i	$-0.790105\pi$
$23$	−7.58085	−1.58072	−0.790358	+	0.612646i	$0.790105\pi$
$24$	− 13.5020i	− 2.75608i
$25$	−3.66072	−0.732144
$26$	0	0
$27$	5.08284	0.978193
$28$	− 4.90656i	− 0.927252i
$29$	−1.82633	−0.339141	−0.169570	−	0.985518i	$-0.554238\pi$
$29$	−1.82633	−0.339141	−0.169570	+	0.985518i	$0.554238\pi$
$30$	−13.6709	−2.49595
$31$	− 6.57664i	− 1.18120i	−0.806965	−	0.590600i	$-0.798891\pi$
$31$	− 6.57664i	− 1.18120i	0.806965	−	0.590600i	$-0.201109\pi$
$32$	− 11.6897i	− 2.06646i
$33$	− 7.57053i	− 1.31786i
$34$	7.72771i	1.32529i
$35$	−2.94291	−0.497443
$36$	−0.610701	−0.101783
$37$	− 8.31285i	− 1.36662i	−0.730126	−	0.683312i	$-0.760539\pi$
$37$	− 8.31285i	− 1.36662i	0.730126	−	0.683312i	$-0.239461\pi$
$38$	−13.1082	−2.12643
$39$	0	0
$40$	−22.4795	−3.55432
$41$	4.15934i	0.649579i	0.945786	+	0.324790i	$0.105293\pi$
$41$	4.15934i	0.649579i	−0.945786	+	0.324790i	$0.894707\pi$
$42$	−4.64535	−0.716793
$43$	8.48158	1.29343	0.646714	−	0.762733i	$-0.276143\pi$
$43$	8.48158	1.29343	0.646714	+	0.762733i	$0.276143\pi$
$44$	− 21.0143i	− 3.16803i
$45$	0.366293i	0.0546037i
$46$	19.9227i	2.93744i
$47$	0.910136i	0.132757i	0.997795	+	0.0663785i	$0.0211445\pi$
$47$	0.910136i	0.132757i	−0.997795	+	0.0663785i	$0.978856\pi$
$48$	−18.1378	−2.61797
$49$	−1.00000	−0.142857
$50$	9.62049i	1.36054i
$51$	5.19766	0.727818
$52$	0	0
$53$	4.47393	0.614542	0.307271	−	0.951622i	$-0.400584\pi$
$53$	4.47393	0.614542	0.307271	+	0.951622i	$0.400584\pi$
$54$	− 13.3579i	− 1.81778i
$55$	−12.6042	−1.69955
$56$	−7.63852	−1.02074
$57$	8.81656i	1.16778i
$58$	4.79965i	0.630225i
$59$	− 9.42007i	− 1.22639i	−0.789932	−	0.613194i	$-0.789884\pi$
$59$	− 9.42007i	− 1.22639i	0.789932	−	0.613194i	$-0.210116\pi$
$60$	25.5236i	3.29508i
$61$	−1.75588	−0.224817	−0.112409	−	0.993662i	$-0.535857\pi$
$61$	−1.75588	−0.224817	−0.112409	+	0.993662i	$0.535857\pi$
$62$	−17.2836	−2.19502
$63$	0.124466i	0.0156813i
$64$	−10.1985	−1.27481
$65$	0	0
$66$	−19.8956	−2.44898
$67$	− 0.413638i	− 0.0505340i	−0.999681	−	0.0252670i	$-0.991956\pi$
$67$	− 0.413638i	− 0.0505340i	0.999681	−	0.0252670i	$-0.00804358\pi$
$68$	14.4277	1.74961
$69$	13.4000	1.61317
$70$	7.73406i	0.924397i
$71$	2.95901i	0.351170i	0.984464	+	0.175585i	$0.0561817\pi$
$71$	2.95901i	0.351170i	−0.984464	+	0.175585i	$0.943818\pi$
$72$	0.950738i	0.112046i
$73$	− 0.885074i	− 0.103590i	−0.998658	−	0.0517951i	$-0.983506\pi$
$73$	− 0.885074i	− 0.103590i	0.998658	−	0.0517951i	$-0.0164943\pi$
$74$	−21.8464	−2.53960
$75$	6.47075	0.747177
$76$	24.4730i	2.80725i
$77$	−4.28290	−0.488082
$78$	0	0
$79$	10.0505	1.13077	0.565384	−	0.824828i	$-0.308728\pi$
$79$	10.0505	1.13077	0.565384	+	0.824828i	$0.308728\pi$
$80$	30.1977i	3.37621i
$81$	−9.35791	−1.03977
$82$	10.9309	1.20711
$83$	− 6.04519i	− 0.663546i	−0.943359	−	0.331773i	$-0.892353\pi$
$83$	− 6.04519i	− 0.663546i	0.943359	−	0.331773i	$-0.107647\pi$
$84$	8.67291i	0.946292i
$85$	− 8.65360i	− 0.938615i
$86$	− 22.2899i	− 2.40358i
$87$	3.22825	0.346104
$88$	−32.7151	−3.48744
$89$	− 3.82110i	− 0.405036i	−0.979279	−	0.202518i	$-0.935088\pi$
$89$	− 3.82110i	− 0.405036i	0.979279	−	0.202518i	$-0.0649124\pi$
$90$	0.962630	0.101470
$91$	0	0
$92$	37.1958	3.87793
$93$	11.6250i	1.20545i
$94$	2.39187	0.246702
$95$	14.6787	1.50600
$96$	20.6628i	2.10889i
$97$	2.37500i	0.241144i	0.992705	+	0.120572i	$0.0384729\pi$
$97$	2.37500i	0.241144i	−0.992705	+	0.120572i	$0.961527\pi$
$98$	2.62803i	0.265471i
$99$	0.533077i	0.0535762i
$100$	17.9615	1.79615
$101$	1.36229	0.135553	0.0677763	−	0.997701i	$-0.478410\pi$
$101$	1.36229	0.135553	0.0677763	+	0.997701i	$0.478410\pi$
$102$	− 13.6596i	− 1.35250i
$103$	−18.6811	−1.84071	−0.920354	−	0.391086i	$-0.872100\pi$
$103$	−18.6811	−1.84071	−0.920354	+	0.391086i	$0.872100\pi$
$104$	0	0
$105$	5.20193	0.507657
$106$	− 11.7576i	− 1.14200i
$107$	5.93855	0.574101	0.287051	−	0.957915i	$-0.407325\pi$
$107$	5.93855	0.574101	0.287051	+	0.957915i	$0.407325\pi$
$108$	−24.9392	−2.39978
$109$	− 1.63519i	− 0.156623i	−0.996929	−	0.0783115i	$-0.975047\pi$
$109$	− 1.63519i	− 0.156623i	0.996929	−	0.0783115i	$-0.0249529\pi$
$110$	33.1242i	3.15827i
$111$	14.6939i	1.39469i
$112$	10.2612i	0.969590i
$113$	0.870896	0.0819270	0.0409635	−	0.999161i	$-0.486957\pi$
$113$	0.870896	0.0819270	0.0409635	+	0.999161i	$0.486957\pi$
$114$	23.1702	2.17009
$115$	− 22.3097i	− 2.08039i
$116$	8.96098	0.832006
$117$	0	0
$118$	−24.7562	−2.27900
$119$	− 2.94049i	− 0.269554i
$120$	39.7351	3.62730
$121$	−7.34326	−0.667569
$122$	4.61451i	0.417778i
$123$	− 7.35211i	− 0.662917i
$124$	32.2686i	2.89781i
$125$	3.94138i	0.352528i
$126$	0.327101	0.0291405
$127$	5.72408	0.507930	0.253965	−	0.967213i	$-0.418265\pi$
$127$	5.72408	0.507930	0.253965	+	0.967213i	$0.418265\pi$
$128$	3.42255i	0.302514i
$129$	−14.9922	−1.31999
$130$	0	0
$131$	−4.27598	−0.373594	−0.186797	−	0.982398i	$-0.559811\pi$
$131$	−4.27598	−0.373594	−0.186797	+	0.982398i	$0.559811\pi$
$132$	37.1452i	3.23308i
$133$	4.98782	0.432499
$134$	−1.08705	−0.0939072
$135$	14.9583i	1.28741i
$136$	− 22.4610i	− 1.92602i
$137$	− 18.0596i	− 1.54294i	−0.636269	−	0.771468i	$-0.719523\pi$
$137$	− 18.0596i	− 1.54294i	0.636269	−	0.771468i	$-0.280477\pi$
$138$	− 35.2157i	− 2.99776i
$139$	−0.0934521	−0.00792650	−0.00396325	−	0.999992i	$-0.501262\pi$
$139$	−0.0934521	−0.00792650	−0.00396325	+	0.999992i	$0.501262\pi$
$140$	14.4396	1.22036
$141$	− 1.60877i	− 0.135483i
$142$	7.77638	0.652579
$143$	0	0
$144$	1.27717	0.106431
$145$	− 5.37472i	− 0.446346i
$146$	−2.32600	−0.192502
$147$	1.76762	0.145791
$148$	40.7875i	3.35271i
$149$	16.6989i	1.36802i	0.729470	+	0.684012i	$0.239767\pi$
$149$	16.6989i	1.36802i	−0.729470	+	0.684012i	$0.760233\pi$
$150$	− 17.0053i	− 1.38848i
$151$	− 16.4932i	− 1.34220i	−0.741368	−	0.671099i	$-0.765823\pi$
$151$	− 16.4932i	− 1.34220i	0.741368	−	0.671099i	$-0.234177\pi$
$152$	38.0996	3.09029
$153$	−0.365992	−0.0295887
$154$	11.2556i	0.907003i
$155$	19.3545	1.55459
$156$	0	0
$157$	−22.6447	−1.80724	−0.903622	−	0.428331i	$-0.859102\pi$
$157$	−22.6447	−1.80724	−0.903622	+	0.428331i	$0.859102\pi$
$158$	− 26.4130i	− 2.10131i
$159$	−7.90819	−0.627160
$160$	34.4016	2.71969
$161$	− 7.58085i	− 0.597454i
$162$	24.5929i	1.93220i
$163$	− 4.37249i	− 0.342480i	−0.985229	−	0.171240i	$-0.945223\pi$
$163$	− 4.37249i	− 0.342480i	0.985229	−	0.171240i	$-0.0547774\pi$
$164$	− 20.4080i	− 1.59360i
$165$	22.2794	1.73445
$166$	−15.8870	−1.23307
$167$	− 17.2083i	− 1.33162i	−0.746123	−	0.665808i	$-0.768087\pi$
$167$	− 17.2083i	− 1.33162i	0.746123	−	0.665808i	$-0.231913\pi$
$168$	13.5020	1.04170
$169$	0	0
$170$	−22.7419	−1.74423
$171$	− 0.620816i	− 0.0474750i
$172$	−41.6153	−3.17314
$173$	−22.4082	−1.70366	−0.851832	−	0.523815i	$-0.824508\pi$
$173$	−22.4082	−1.70366	−0.851832	+	0.523815i	$0.824508\pi$
$174$	− 8.48394i	− 0.643165i
$175$	− 3.66072i	− 0.276724i
$176$	43.9476i	3.31268i
$177$	16.6511i	1.25157i
$178$	−10.0420	−0.752678
$179$	2.75303	0.205771	0.102885	−	0.994693i	$-0.467192\pi$
$179$	2.75303	0.205771	0.102885	+	0.994693i	$0.467192\pi$
$180$	− 1.79724i	− 0.133958i
$181$	−6.26508	−0.465680	−0.232840	−	0.972515i	$-0.574802\pi$
$181$	−6.26508	−0.465680	−0.232840	+	0.972515i	$0.574802\pi$
$182$	0	0
$183$	3.10372	0.229434
$184$	− 57.9065i	− 4.26892i
$185$	24.4640	1.79863
$186$	30.5508	2.24009
$187$	− 12.5938i	− 0.920953i
$188$	− 4.46563i	− 0.325690i
$189$	5.08284i	0.369722i
$190$	− 38.5761i	− 2.79861i
$191$	23.4239	1.69489	0.847445	−	0.530883i	$-0.178140\pi$
$191$	23.4239	1.69489	0.847445	+	0.530883i	$0.178140\pi$
$192$	18.0270	1.30098
$193$	16.4710i	1.18561i	0.805347	+	0.592803i	$0.201979\pi$
$193$	16.4710i	1.18561i	−0.805347	+	0.592803i	$0.798021\pi$
$194$	6.24157	0.448119
$195$	0	0
$196$	4.90656	0.350468
$197$	− 2.02734i	− 0.144442i	−0.997389	−	0.0722210i	$-0.976991\pi$
$197$	− 2.02734i	− 0.144442i	0.997389	−	0.0722210i	$-0.0230087\pi$
$198$	1.40094	0.0995607
$199$	27.1238	1.92276	0.961379	−	0.275229i	$-0.0887537\pi$
$199$	27.1238	1.92276	0.961379	+	0.275229i	$0.0887537\pi$
$200$	− 27.9625i	− 1.97725i
$201$	0.731154i	0.0515716i
$202$	− 3.58014i	− 0.251898i
$203$	− 1.82633i	− 0.128183i
$204$	−25.5026	−1.78554
$205$	−12.2406	−0.854917
$206$	49.0947i	3.42059i
$207$	−0.943559	−0.0655819
$208$	0	0
$209$	21.3624	1.47767
$210$	− 13.6709i	− 0.943379i
$211$	−3.11031	−0.214123	−0.107061	−	0.994252i	$-0.534144\pi$
$211$	−3.11031	−0.214123	−0.107061	+	0.994252i	$0.534144\pi$
$212$	−21.9516	−1.50764
$213$	− 5.23040i	− 0.358381i
$214$	− 15.6067i	− 1.06685i
$215$	24.9605i	1.70229i
$216$	38.8254i	2.64173i
$217$	6.57664	0.446451
$218$	−4.29734	−0.291052
$219$	1.56447i	0.105717i
$220$	61.8432	4.16947
$221$	0	0
$222$	38.6161	2.59174
$223$	15.7646i	1.05568i	0.849345	+	0.527838i	$0.176997\pi$
$223$	15.7646i	1.05568i	−0.849345	+	0.527838i	$0.823003\pi$
$224$	11.6897	0.781048
$225$	−0.455636	−0.0303757
$226$	− 2.28874i	− 0.152245i
$227$	− 4.65356i	− 0.308868i	−0.988003	−	0.154434i	$-0.950645\pi$
$227$	− 4.65356i	− 0.308868i	0.988003	−	0.154434i	$-0.0493554\pi$
$228$	− 43.2589i	− 2.86489i
$229$	− 16.5125i	− 1.09118i	−0.838053	−	0.545589i	$-0.816306\pi$
$229$	− 16.5125i	− 1.09118i	0.838053	−	0.545589i	$-0.183694\pi$
$230$	−58.6307	−3.86600
$231$	7.57053	0.498104
$232$	− 13.9504i	− 0.915892i
$233$	−17.2023	−1.12696	−0.563481	−	0.826129i	$-0.690538\pi$
$233$	−17.2023	−1.12696	−0.563481	+	0.826129i	$0.690538\pi$
$234$	0	0
$235$	−2.67845	−0.174723
$236$	46.2201i	3.00867i
$237$	−17.7654	−1.15399
$238$	−7.72771	−0.500913
$239$	− 4.42647i	− 0.286325i	−0.989699	−	0.143162i	$-0.954273\pi$
$239$	− 4.42647i	− 0.286325i	0.989699	−	0.143162i	$-0.0457271\pi$
$240$	− 53.3780i	− 3.44553i
$241$	− 18.5421i	− 1.19440i	−0.802091	−	0.597202i	$-0.796279\pi$
$241$	− 18.5421i	− 1.19440i	0.802091	−	0.597202i	$-0.203721\pi$
$242$	19.2983i	1.24054i
$243$	1.29267	0.0829247
$244$	8.61533	0.551540
$245$	− 2.94291i	− 0.188016i
$246$	−19.3216	−1.23190
$247$	0	0
$248$	50.2358	3.18998
$249$	10.6856i	0.677171i
$250$	10.3581	0.655102
$251$	−9.82212	−0.619967	−0.309983	−	0.950742i	$-0.600324\pi$
$251$	−9.82212	−0.619967	−0.309983	+	0.950742i	$0.600324\pi$
$252$	− 0.610701i	− 0.0384705i
$253$	− 32.4680i	− 2.04125i
$254$	− 15.0431i	− 0.943887i
$255$	15.2962i	0.957888i
$256$	−11.4023	−0.712645
$257$	−19.5729	−1.22092	−0.610462	−	0.792046i	$-0.709016\pi$
$257$	−19.5729	−1.22092	−0.610462	+	0.792046i	$0.709016\pi$
$258$	39.3999i	2.45293i
$259$	8.31285	0.516535
$260$	0	0
$261$	−0.227316	−0.0140705
$262$	11.2374i	0.694250i
$263$	−6.07215	−0.374425	−0.187212	−	0.982319i	$-0.559945\pi$
$263$	−6.07215	−0.374425	−0.187212	+	0.982319i	$0.559945\pi$
$264$	57.8277	3.55905
$265$	13.1664i	0.808804i
$266$	− 13.1082i	− 0.803713i
$267$	6.75424i	0.413353i
$268$	2.02954i	0.123974i
$269$	0.134388	0.00819378	0.00409689	−	0.999992i	$-0.498696\pi$
$269$	0.134388	0.00819378	0.00409689	+	0.999992i	$0.498696\pi$
$270$	39.3110	2.39239
$271$	− 14.9723i	− 0.909500i	−0.890619	−	0.454750i	$-0.849729\pi$
$271$	− 14.9723i	− 0.909500i	0.890619	−	0.454750i	$-0.150271\pi$
$272$	−30.1729	−1.82950
$273$	0	0
$274$	−47.4612	−2.86724
$275$	− 15.6785i	− 0.945450i
$276$	−65.7480	−3.95756
$277$	−15.5609	−0.934965	−0.467483	−	0.884002i	$-0.654839\pi$
$277$	−15.5609	−0.934965	−0.467483	+	0.884002i	$0.654839\pi$
$278$	0.245595i	0.0147298i
$279$	− 0.818570i	− 0.0490065i
$280$	− 22.4795i	− 1.34341i
$281$	22.3371i	1.33252i	0.745719	+	0.666261i	$0.232106\pi$
$281$	22.3371i	1.33252i	−0.745719	+	0.666261i	$0.767894\pi$
$282$	−4.22790	−0.251768
$283$	−3.08431	−0.183343	−0.0916715	−	0.995789i	$-0.529221\pi$
$283$	−3.08431	−0.183343	−0.0916715	+	0.995789i	$0.529221\pi$
$284$	− 14.5186i	− 0.861518i
$285$	−25.9463	−1.53693
$286$	0	0
$287$	−4.15934	−0.245518
$288$	− 1.45497i	− 0.0857348i
$289$	−8.35351	−0.491383
$290$	−14.1249	−0.829445
$291$	− 4.19808i	− 0.246096i
$292$	4.34267i	0.254135i
$293$	− 25.9733i	− 1.51737i	−0.651456	−	0.758687i	$-0.725841\pi$
$293$	− 25.9733i	− 1.51737i	0.651456	−	0.758687i	$-0.274159\pi$
$294$	− 4.64535i	− 0.270922i
$295$	27.7224	1.61406
$296$	63.4979	3.69074
$297$	21.7693i	1.26318i
$298$	43.8852	2.54220
$299$	0	0
$300$	−31.7491	−1.83303
$301$	8.48158i	0.488870i
$302$	−43.3447	−2.49421
$303$	−2.40800	−0.138336
$304$	− 51.1809i	− 2.93543i
$305$	− 5.16740i	− 0.295884i
$306$	0.961839i	0.0549847i
$307$	− 15.8008i	− 0.901800i	−0.892574	−	0.450900i	$-0.851103\pi$
$307$	− 15.8008i	− 0.901800i	0.892574	−	0.450900i	$-0.148897\pi$
$308$	21.0143	1.19740
$309$	33.0211	1.87850
$310$	− 50.8641i	− 2.88889i
$311$	−14.2953	−0.810613	−0.405307	−	0.914181i	$-0.632835\pi$
$311$	−14.2953	−0.810613	−0.405307	+	0.914181i	$0.632835\pi$
$312$	0	0
$313$	11.7613	0.664790	0.332395	−	0.943140i	$-0.392143\pi$
$313$	11.7613	0.664790	0.332395	+	0.943140i	$0.392143\pi$
$314$	59.5110i	3.35840i
$315$	−0.366293	−0.0206383
$316$	−49.3133	−2.77409
$317$	20.9307i	1.17559i	0.809011	+	0.587793i	$0.200003\pi$
$317$	20.9307i	1.17559i	−0.809011	+	0.587793i	$0.799997\pi$
$318$	20.7830i	1.16545i
$319$	− 7.82198i	− 0.437947i
$320$	− 30.0131i	− 1.67779i
$321$	−10.4971	−0.585889
$322$	−19.9227	−1.11025
$323$	14.6667i	0.816074i
$324$	45.9151	2.55084
$325$	0	0
$326$	−11.4911	−0.636431
$327$	2.89039i	0.159839i
$328$	−31.7712	−1.75427
$329$	−0.910136	−0.0501774
$330$	− 58.5509i	− 3.22312i
$331$	− 8.25635i	− 0.453810i	−0.973917	−	0.226905i	$-0.927139\pi$
$331$	− 8.25635i	− 0.453810i	0.973917	−	0.226905i	$-0.0728607\pi$
$332$	29.6611i	1.62786i
$333$	− 1.03467i	− 0.0566995i
$334$	−45.2239	−2.47454
$335$	1.21730	0.0665082
$336$	− 18.1378i	− 0.989499i
$337$	13.4122	0.730611	0.365305	−	0.930888i	$-0.380965\pi$
$337$	13.4122	0.730611	0.365305	+	0.930888i	$0.380965\pi$
$338$	0	0
$339$	−1.53941	−0.0836092
$340$	42.4594i	2.30268i
$341$	28.1671	1.52533
$342$	−1.63152	−0.0882227
$343$	− 1.00000i	− 0.0539949i
$344$	64.7867i	3.49307i
$345$	39.4351i	2.12311i
$346$	58.8895i	3.16592i
$347$	−13.4937	−0.724379	−0.362190	−	0.932104i	$-0.617971\pi$
$347$	−13.4937	−0.724379	−0.362190	+	0.932104i	$0.617971\pi$
$348$	−15.8396	−0.849090
$349$	− 16.1192i	− 0.862843i	−0.902151	−	0.431421i	$-0.858012\pi$
$349$	− 16.1192i	− 0.862843i	0.902151	−	0.431421i	$-0.141988\pi$
$350$	−9.62049	−0.514237
$351$	0	0
$352$	50.0657	2.66851
$353$	− 37.4141i	− 1.99135i	−0.0929089	−	0.995675i	$-0.529617\pi$
$353$	− 37.4141i	− 1.99135i	0.0929089	−	0.995675i	$-0.470383\pi$
$354$	43.7595	2.32579
$355$	−8.70811	−0.462178
$356$	18.7484i	0.993665i
$357$	5.19766i	0.275089i
$358$	− 7.23505i	− 0.382384i
$359$	18.8373i	0.994192i	0.867695	+	0.497096i	$0.165600\pi$
$359$	18.8373i	0.994192i	−0.867695	+	0.497096i	$0.834400\pi$
$360$	−2.79794	−0.147464
$361$	−5.87839	−0.309389
$362$	16.4648i	0.865372i
$363$	12.9801	0.681277
$364$	0	0
$365$	2.60469	0.136336
$366$	− 8.15669i	− 0.426357i
$367$	32.9116	1.71797	0.858987	−	0.511997i	$-0.171094\pi$
$367$	32.9116	1.71797	0.858987	+	0.511997i	$0.171094\pi$
$368$	−77.7884	−4.05500
$369$	0.517697i	0.0269502i
$370$	− 64.2921i	− 3.34239i
$371$	4.47393i	0.232275i
$372$	− 57.0386i	− 2.95731i
$373$	−28.3543	−1.46813	−0.734065	−	0.679079i	$-0.762379\pi$
$373$	−28.3543	−1.46813	−0.734065	+	0.679079i	$0.762379\pi$
$374$	−33.0970	−1.71141
$375$	− 6.96685i	− 0.359766i
$376$	−6.95210	−0.358527
$377$	0	0
$378$	13.3579	0.687055
$379$	3.59222i	0.184520i	0.995735	+	0.0922600i	$0.0294091\pi$
$379$	3.59222i	0.184520i	−0.995735	+	0.0922600i	$0.970591\pi$
$380$	−72.0219	−3.69465
$381$	−10.1180	−0.518360
$382$	− 61.5587i	− 3.14961i
$383$	− 18.6107i	− 0.950962i	−0.879726	−	0.475481i	$-0.842274\pi$
$383$	− 18.6107i	− 0.950962i	0.879726	−	0.475481i	$-0.157726\pi$
$384$	− 6.04976i	− 0.308726i
$385$	− 12.6042i	− 0.642369i
$386$	43.2862	2.20321
$387$	1.05567	0.0536627
$388$	− 11.6531i	− 0.591594i
$389$	7.22028	0.366083	0.183041	−	0.983105i	$-0.441406\pi$
$389$	7.22028	0.366083	0.183041	+	0.983105i	$0.441406\pi$
$390$	0	0
$391$	22.2914	1.12732
$392$	− 7.63852i	− 0.385804i
$393$	7.55830	0.381266
$394$	−5.32791	−0.268416
$395$	29.5777i	1.48822i
$396$	− 2.61557i	− 0.131437i
$397$	− 3.49931i	− 0.175626i	−0.996137	−	0.0878128i	$-0.972012\pi$
$397$	− 3.49931i	− 0.175626i	0.996137	−	0.0878128i	$-0.0279877\pi$
$398$	− 71.2823i	− 3.57306i
$399$	−8.81656	−0.441380
$400$	−37.5633	−1.87816
$401$	37.0199i	1.84869i	0.381560	+	0.924344i	$0.375387\pi$
$401$	37.0199i	1.84869i	−0.381560	+	0.924344i	$0.624613\pi$
$402$	1.92150	0.0958355
$403$	0	0
$404$	−6.68414	−0.332548
$405$	− 27.5395i	− 1.36845i
$406$	−4.79965	−0.238203
$407$	35.6031	1.76478
$408$	39.7024i	1.96556i
$409$	35.4369i	1.75224i	0.482090	+	0.876122i	$0.339878\pi$
$409$	35.4369i	1.75224i	−0.482090	+	0.876122i	$0.660122\pi$
$410$	32.1686i	1.58869i
$411$	31.9224i	1.57462i
$412$	91.6601	4.51577
$413$	9.42007	0.463531
$414$	2.47970i	0.121871i
$415$	17.7904	0.873299
$416$	0	0
$417$	0.165187	0.00808926
$418$	− 56.1410i	− 2.74595i
$419$	13.3595	0.652657	0.326328	−	0.945256i	$-0.394189\pi$
$419$	13.3595	0.652657	0.326328	+	0.945256i	$0.394189\pi$
$420$	−25.5236	−1.24542
$421$	10.9549i	0.533911i	0.963709	+	0.266955i	$0.0860176\pi$
$421$	10.9549i	0.533911i	−0.963709	+	0.266955i	$0.913982\pi$
$422$	8.17401i	0.397904i
$423$	0.113281i	0.00550792i
$424$	34.1742i	1.65965i
$425$	10.7643	0.522146
$426$	−13.7457	−0.665979
$427$	− 1.75588i	− 0.0849730i
$428$	−29.1378	−1.40843
$429$	0	0
$430$	65.5970	3.16337
$431$	13.5976i	0.654971i	0.944856	+	0.327486i	$0.106201\pi$
$431$	13.5976i	0.654971i	−0.944856	+	0.327486i	$0.893799\pi$
$432$	52.1559	2.50935
$433$	17.8666	0.858613	0.429306	−	0.903159i	$-0.358758\pi$
$433$	17.8666	0.858613	0.429306	+	0.903159i	$0.358758\pi$
$434$	− 17.2836i	− 0.829640i
$435$	9.50044i	0.455511i
$436$	8.02316i	0.384240i
$437$	37.8119i	1.80879i
$438$	4.11148	0.196454
$439$	21.6009	1.03096	0.515478	−	0.856903i	$-0.327614\pi$
$439$	21.6009	1.03096	0.515478	+	0.856903i	$0.327614\pi$
$440$	− 96.2775i	− 4.58985i
$441$	−0.124466	−0.00592696
$442$	0	0
$443$	29.7875	1.41525	0.707623	−	0.706590i	$-0.249768\pi$
$443$	29.7875	1.41525	0.707623	+	0.706590i	$0.249768\pi$
$444$	− 72.0966i	− 3.42155i
$445$	11.2452	0.533071
$446$	41.4299	1.96176
$447$	− 29.5172i	− 1.39612i
$448$	− 10.1985i	− 0.481832i
$449$	17.6072i	0.830934i	0.909608	+	0.415467i	$0.136382\pi$
$449$	17.6072i	0.830934i	−0.909608	+	0.415467i	$0.863618\pi$
$450$	1.19743i	0.0564472i
$451$	−17.8140	−0.838830
$452$	−4.27310	−0.200990
$453$	29.1537i	1.36976i
$454$	−12.2297	−0.573969
$455$	0	0
$456$	−67.3455	−3.15374
$457$	− 18.0432i	− 0.844024i	−0.906590	−	0.422012i	$-0.861324\pi$
$457$	− 18.0432i	− 0.844024i	0.906590	−	0.422012i	$-0.138676\pi$
$458$	−43.3954	−2.02773
$459$	−14.9460	−0.697622
$460$	109.464i	5.10379i
$461$	− 15.1623i	− 0.706180i	−0.935589	−	0.353090i	$-0.885131\pi$
$461$	− 15.1623i	− 0.706180i	0.935589	−	0.353090i	$-0.114869\pi$
$462$	− 19.8956i	− 0.925627i
$463$	− 26.7145i	− 1.24153i	−0.783997	−	0.620765i	$-0.786822\pi$
$463$	− 26.7145i	− 1.24153i	0.783997	−	0.620765i	$-0.213178\pi$
$464$	−18.7403	−0.869995
$465$	−34.2113	−1.58651
$466$	45.2082i	2.09423i
$467$	29.4908	1.36467	0.682335	−	0.731039i	$-0.260964\pi$
$467$	29.4908	1.36467	0.682335	+	0.731039i	$0.260964\pi$
$468$	0	0
$469$	0.413638	0.0191000
$470$	7.03905i	0.324687i
$471$	40.0271	1.84435
$472$	71.9554	3.31202
$473$	36.3258i	1.67026i
$474$	46.6881i	2.14445i
$475$	18.2590i	0.837782i
$476$	14.4277i	0.661292i
$477$	0.556853	0.0254966
$478$	−11.6329	−0.532077
$479$	− 33.4865i	− 1.53004i	−0.644007	−	0.765019i	$-0.722729\pi$
$479$	− 33.4865i	− 1.53004i	0.644007	−	0.765019i	$-0.277271\pi$
$480$	−60.8089	−2.77553
$481$	0	0
$482$	−48.7293	−2.21956
$483$	13.4000i	0.609722i
$484$	36.0301	1.63773
$485$	−6.98940	−0.317372
$486$	− 3.39717i	− 0.154099i
$487$	− 11.4592i	− 0.519265i	−0.965707	−	0.259633i	$-0.916399\pi$
$487$	− 11.4592i	− 0.519265i	0.965707	−	0.259633i	$-0.0836015\pi$
$488$	− 13.4123i	− 0.607148i
$489$	7.72889i	0.349513i
$490$	−7.73406	−0.349389
$491$	33.5043	1.51203	0.756013	−	0.654557i	$-0.227145\pi$
$491$	33.5043	1.51203	0.756013	+	0.654557i	$0.227145\pi$
$492$	36.0735i	1.62632i
$493$	5.37030	0.241866
$494$	0	0
$495$	−1.56880	−0.0705122
$496$	− 67.4841i	− 3.03012i
$497$	−2.95901	−0.132730
$498$	28.0820	1.25839
$499$	− 26.3516i	− 1.17966i	−0.807527	−	0.589831i	$-0.799194\pi$
$499$	− 26.3516i	− 1.17966i	0.807527	−	0.589831i	$-0.200806\pi$
$500$	− 19.3386i	− 0.864849i
$501$	30.4176i	1.35896i
$502$	25.8129i	1.15208i
$503$	−28.4677	−1.26931	−0.634657	−	0.772794i	$-0.718858\pi$
$503$	−28.4677	−1.26931	−0.634657	+	0.772794i	$0.718858\pi$
$504$	−0.950738	−0.0423492
$505$	4.00909i	0.178402i
$506$	−85.3270	−3.79325
$507$	0	0
$508$	−28.0855	−1.24609
$509$	29.8491i	1.32304i	0.749929	+	0.661519i	$0.230088\pi$
$509$	29.8491i	1.32304i	−0.749929	+	0.661519i	$0.769912\pi$
$510$	40.1990	1.78004
$511$	0.885074	0.0391534
$512$	36.8108i	1.62682i
$513$	− 25.3523i	− 1.11933i
$514$	51.4382i	2.26884i
$515$	− 54.9769i	− 2.42257i
$516$	73.5599	3.23829
$517$	−3.89803	−0.171435
$518$	− 21.8464i	− 0.959877i
$519$	39.6091	1.73865
$520$	0	0
$521$	10.9955	0.481724	0.240862	−	0.970559i	$-0.422570\pi$
$521$	10.9955	0.481724	0.240862	+	0.970559i	$0.422570\pi$
$522$	0.597394i	0.0261472i
$523$	4.19652	0.183501	0.0917505	−	0.995782i	$-0.470754\pi$
$523$	4.19652	0.183501	0.0917505	+	0.995782i	$0.470754\pi$
$524$	20.9804	0.916531
$525$	6.47075i	0.282407i
$526$	15.9578i	0.695793i
$527$	19.3385i	0.842400i
$528$	− 77.6825i	− 3.38070i
$529$	34.4692	1.49866
$530$	34.6017	1.50300
$531$	− 1.17248i	− 0.0508813i
$532$	−24.4730	−1.06104
$533$	0	0
$534$	17.7504	0.768133
$535$	17.4766i	0.755580i
$536$	3.15959	0.136473
$537$	−4.86630	−0.209996
$538$	− 0.353176i	− 0.0152265i
$539$	− 4.28290i	− 0.184478i
$540$	− 73.3939i	− 3.15837i
$541$	7.98767i	0.343417i	0.985148	+	0.171708i	$0.0549287\pi$
$541$	7.98767i	0.343417i	−0.985148	+	0.171708i	$0.945071\pi$
$542$	−39.3476	−1.69012
$543$	11.0743	0.475242
$544$	34.3733i	1.47374i
$545$	4.81222	0.206133
$546$	0	0
$547$	−20.5549	−0.878865	−0.439433	−	0.898276i	$-0.644820\pi$
$547$	−20.5549	−0.878865	−0.439433	+	0.898276i	$0.644820\pi$
$548$	88.6104i	3.78525i
$549$	−0.218548	−0.00932740
$550$	−41.2036	−1.75693
$551$	9.10940i	0.388074i
$552$	102.356i	4.35658i
$553$	10.0505i	0.427390i
$554$	40.8946i	1.73745i
$555$	−43.2429	−1.83556
$556$	0.458528	0.0194459
$557$	− 8.79065i	− 0.372472i	−0.982505	−	0.186236i	$-0.940371\pi$
$557$	− 8.79065i	− 0.372472i	0.982505	−	0.186236i	$-0.0596289\pi$
$558$	−2.15123	−0.0910687
$559$	0	0
$560$	−30.1977	−1.27609
$561$	22.2611i	0.939863i
$562$	58.7027	2.47623
$563$	−30.9567	−1.30467	−0.652335	−	0.757931i	$-0.726210\pi$
$563$	−30.9567	−1.30467	−0.652335	+	0.757931i	$0.726210\pi$
$564$	7.89353i	0.332377i
$565$	2.56297i	0.107825i
$566$	8.10566i	0.340706i
$567$	− 9.35791i	− 0.392995i
$568$	−22.6025	−0.948379
$569$	−23.4540	−0.983242	−0.491621	−	0.870809i	$-0.663595\pi$
$569$	−23.4540	−0.983242	−0.491621	+	0.870809i	$0.663595\pi$
$570$	68.1878i	2.85607i
$571$	−16.6808	−0.698071	−0.349036	−	0.937109i	$-0.613491\pi$
$571$	−16.6808	−0.698071	−0.349036	+	0.937109i	$0.613491\pi$
$572$	0	0
$573$	−41.4044	−1.72969
$574$	10.9309i	0.456246i
$575$	27.7514	1.15731
$576$	−1.26936	−0.0528901
$577$	− 16.8209i	− 0.700263i	−0.936701	−	0.350132i	$-0.886137\pi$
$577$	− 16.8209i	− 0.700263i	0.936701	−	0.350132i	$-0.113863\pi$
$578$	21.9533i	0.913137i
$579$	− 29.1143i	− 1.20995i
$580$	26.3714i	1.09501i
$581$	6.04519	0.250797
$582$	−11.0327	−0.457320
$583$	19.1614i	0.793584i
$584$	6.76066	0.279758
$585$	0	0
$586$	−68.2585	−2.81973
$587$	− 25.0653i	− 1.03455i	−0.855818	−	0.517277i	$-0.826946\pi$
$587$	− 25.0653i	− 1.03455i	0.855818	−	0.517277i	$-0.173054\pi$
$588$	−8.67291	−0.357665
$589$	−32.8031	−1.35163
$590$	− 72.8554i	− 2.99941i
$591$	3.58356i	0.147408i
$592$	− 85.2996i	− 3.50579i
$593$	− 9.99617i	− 0.410493i	−0.978710	−	0.205247i	$-0.934200\pi$
$593$	− 9.99617i	− 0.410493i	0.978710	−	0.205247i	$-0.0657997\pi$
$594$	57.2105	2.34737
$595$	8.65360	0.354763
$596$	− 81.9339i	− 3.35615i
$597$	−47.9445	−1.96224
$598$	0	0
$599$	−5.51511	−0.225341	−0.112671	−	0.993632i	$-0.535941\pi$
$599$	−5.51511	−0.225341	−0.112671	+	0.993632i	$0.535941\pi$
$600$	49.4269i	2.01785i
$601$	−13.1290	−0.535544	−0.267772	−	0.963482i	$-0.586287\pi$
$601$	−13.1290	−0.535544	−0.267772	+	0.963482i	$0.586287\pi$
$602$	22.2899	0.908467
$603$	− 0.0514840i	− 0.00209659i
$604$	80.9248i	3.29278i
$605$	− 21.6106i	− 0.878594i
$606$	6.32831i	0.257070i
$607$	−12.8493	−0.521537	−0.260768	−	0.965401i	$-0.583976\pi$
$607$	−12.8493	−0.521537	−0.260768	+	0.965401i	$0.583976\pi$
$608$	−58.3060	−2.36462
$609$	3.22825i	0.130815i
$610$	−13.5801	−0.549842
$611$	0	0
$612$	1.79576	0.0725893
$613$	23.9497i	0.967321i	0.875256	+	0.483660i	$0.160693\pi$
$613$	23.9497i	0.967321i	−0.875256	+	0.483660i	$0.839307\pi$
$614$	−41.5251	−1.67581
$615$	21.6366	0.872472
$616$	− 32.7151i	− 1.31813i
$617$	− 33.6198i	− 1.35348i	−0.736221	−	0.676742i	$-0.763391\pi$
$617$	− 33.6198i	− 1.35348i	0.736221	−	0.676742i	$-0.236609\pi$
$618$	− 86.7805i	− 3.49082i
$619$	39.1125i	1.57206i	0.618187	+	0.786031i	$0.287868\pi$
$619$	39.1125i	1.57206i	−0.618187	+	0.786031i	$0.712132\pi$
$620$	−94.9637	−3.81384
$621$	−38.5322	−1.54624
$622$	37.5686i	1.50636i
$623$	3.82110	0.153089
$624$	0	0
$625$	−29.9027	−1.19611
$626$	− 30.9092i	− 1.23538i
$627$	−37.7605	−1.50801
$628$	111.107	4.43367
$629$	24.4439i	0.974640i
$630$	0.962630i	0.0383521i
$631$	− 22.4517i	− 0.893788i	−0.894587	−	0.446894i	$-0.852530\pi$
$631$	− 22.4517i	− 0.893788i	0.894587	−	0.446894i	$-0.147470\pi$
$632$	76.7709i	3.05378i
$633$	5.49784	0.218520
$634$	55.0066	2.18459
$635$	16.8455i	0.668492i
$636$	38.8020	1.53860
$637$	0	0
$638$	−20.5564	−0.813837
$639$	0.368297i	0.0145696i
$640$	−10.0723	−0.398141
$641$	30.5785	1.20778	0.603888	−	0.797069i	$-0.293617\pi$
$641$	30.5785	1.20778	0.603888	+	0.797069i	$0.293617\pi$
$642$	27.5866i	1.08876i
$643$	43.9241i	1.73220i	0.499874	+	0.866098i	$0.333380\pi$
$643$	43.9241i	1.73220i	−0.499874	+	0.866098i	$0.666620\pi$
$644$	37.1958i	1.46572i
$645$	− 44.1206i	− 1.73725i
$646$	38.5444	1.51651
$647$	−5.07899	−0.199676	−0.0998379	−	0.995004i	$-0.531832\pi$
$647$	−5.07899	−0.199676	−0.0998379	+	0.995004i	$0.531832\pi$
$648$	− 71.4806i	− 2.80802i
$649$	40.3452	1.58369
$650$	0	0
$651$	−11.6250	−0.455619
$652$	21.4539i	0.840199i
$653$	−13.6294	−0.533360	−0.266680	−	0.963785i	$-0.585927\pi$
$653$	−13.6294	−0.533360	−0.266680	+	0.963785i	$0.585927\pi$
$654$	7.59604	0.297029
$655$	− 12.5838i	− 0.491691i
$656$	42.6797i	1.66636i
$657$	− 0.110162i	− 0.00429782i
$658$	2.39187i	0.0932447i
$659$	−41.6783	−1.62356	−0.811778	−	0.583967i	$-0.801500\pi$
$659$	−41.6783	−1.62356	−0.811778	+	0.583967i	$0.801500\pi$
$660$	−109.315	−4.25508
$661$	− 21.5457i	− 0.838029i	−0.907979	−	0.419015i	$-0.862376\pi$
$661$	− 21.5457i	− 0.838029i	0.907979	−	0.419015i	$-0.137624\pi$
$662$	−21.6980	−0.843315
$663$	0	0
$664$	46.1763	1.79199
$665$	14.6787i	0.569216i
$666$	−2.71914	−0.105365
$667$	13.8451	0.536085
$668$	84.4334i	3.26683i
$669$	− 27.8658i	− 1.07735i
$670$	− 3.19910i	− 0.123592i
$671$	− 7.52027i	− 0.290317i
$672$	−20.6628	−0.797086
$673$	−30.4598	−1.17414	−0.587070	−	0.809536i	$-0.699719\pi$
$673$	−30.4598	−1.17414	−0.587070	+	0.809536i	$0.699719\pi$
$674$	− 35.2478i	− 1.35769i
$675$	−18.6069	−0.716178
$676$	0	0
$677$	−32.1171	−1.23436	−0.617179	−	0.786822i	$-0.711725\pi$
$677$	−32.1171	−1.23436	−0.617179	+	0.786822i	$0.711725\pi$
$678$	4.04562i	0.155371i
$679$	−2.37500	−0.0911440
$680$	66.1007	2.53485
$681$	8.22571i	0.315210i
$682$	− 74.0241i	− 2.83453i
$683$	30.4004i	1.16324i	0.813460	+	0.581620i	$0.197581\pi$
$683$	30.4004i	1.16324i	−0.813460	+	0.581620i	$0.802419\pi$
$684$	3.04607i	0.116469i
$685$	53.1478	2.03067
$686$	−2.62803	−0.100339
$687$	29.1878i	1.11358i
$688$	87.0309	3.31802
$689$	0	0
$690$	103.637	3.94538
$691$	10.0657i	0.382917i	0.981501	+	0.191458i	$0.0613217\pi$
$691$	10.0657i	0.382917i	−0.981501	+	0.191458i	$0.938678\pi$
$692$	109.947	4.17956
$693$	−0.533077	−0.0202499
$694$	35.4619i	1.34611i
$695$	− 0.275021i	− 0.0104321i
$696$	24.6590i	0.934698i
$697$	− 12.2305i	− 0.463263i
$698$	−42.3619	−1.60342
$699$	30.4071	1.15010
$700$	17.9615i	0.678882i
$701$	10.9013	0.411738	0.205869	−	0.978580i	$-0.433998\pi$
$701$	10.9013	0.411738	0.205869	+	0.978580i	$0.433998\pi$
$702$	0	0
$703$	−41.4630	−1.56381
$704$	− 43.6790i	− 1.64621i
$705$	4.73447	0.178310
$706$	−98.3254	−3.70052
$707$	1.36229i	0.0512341i
$708$	− 81.6994i	− 3.07045i
$709$	− 21.2250i	− 0.797122i	−0.917142	−	0.398561i	$-0.869510\pi$
$709$	− 21.2250i	− 0.797122i	0.917142	−	0.398561i	$-0.130490\pi$
$710$	22.8852i	0.858866i
$711$	1.25095	0.0469142
$712$	29.1876	1.09385
$713$	49.8565i	1.86714i
$714$	13.6596	0.511198
$715$	0	0
$716$	−13.5079	−0.504813
$717$	7.82430i	0.292204i
$718$	49.5049	1.84751
$719$	−17.3439	−0.646819	−0.323409	−	0.946259i	$-0.604829\pi$
$719$	−17.3439	−0.646819	−0.323409	+	0.946259i	$0.604829\pi$
$720$	3.75860i	0.140075i
$721$	− 18.6811i	− 0.695722i
$722$	15.4486i	0.574937i
$723$	32.7754i	1.21893i
$724$	30.7400	1.14244
$725$	6.68567	0.248300
$726$	− 34.1120i	− 1.26602i
$727$	−44.4135	−1.64720	−0.823602	−	0.567168i	$-0.808039\pi$
$727$	−44.4135	−1.64720	−0.823602	+	0.567168i	$0.808039\pi$
$728$	0	0
$729$	25.7888	0.955140
$730$	− 6.84522i	− 0.253353i
$731$	−24.9400	−0.922439
$732$	−15.2286	−0.562865
$733$	− 16.4500i	− 0.607594i	−0.952737	−	0.303797i	$-0.901746\pi$
$733$	− 16.4500i	− 0.607594i	0.952737	−	0.303797i	$-0.0982545\pi$
$734$	− 86.4929i	− 3.19251i
$735$	5.20193i	0.191876i
$736$	88.6175i	3.26648i
$737$	1.77157	0.0652567
$738$	1.36052	0.0500816
$739$	− 16.2732i	− 0.598621i	−0.954156	−	0.299310i	$-0.903243\pi$
$739$	− 16.2732i	− 0.598621i	0.954156	−	0.299310i	$-0.0967566\pi$
$740$	−120.034	−4.41253
$741$	0	0
$742$	11.7576	0.431636
$743$	1.61345i	0.0591918i	0.999562	+	0.0295959i	$0.00942204\pi$
$743$	1.61345i	0.0591918i	−0.999562	+	0.0295959i	$0.990578\pi$
$744$	−88.7976	−3.25548
$745$	−49.1433	−1.80047
$746$	74.5160i	2.72823i
$747$	− 0.752422i	− 0.0275297i
$748$	61.7924i	2.25935i
$749$	5.93855i	0.216990i
$750$	−18.3091	−0.668554
$751$	3.02262	0.110297	0.0551485	−	0.998478i	$-0.482437\pi$
$751$	3.02262	0.110297	0.0551485	+	0.998478i	$0.482437\pi$
$752$	9.33907i	0.340561i
$753$	17.3617	0.632697
$754$	0	0
$755$	48.5380	1.76648
$756$	− 24.9392i	− 0.907031i
$757$	−30.4752	−1.10764	−0.553821	−	0.832636i	$-0.686831\pi$
$757$	−30.4752	−1.10764	−0.553821	+	0.832636i	$0.686831\pi$
$758$	9.44047	0.342893
$759$	57.3910i	2.08316i
$760$	112.124i	4.06715i
$761$	24.4562i	0.886538i	0.896389	+	0.443269i	$0.146181\pi$
$761$	24.4562i	0.886538i	−0.896389	+	0.443269i	$0.853819\pi$
$762$	26.5904i	0.963268i
$763$	1.63519	0.0591979
$764$	−114.930	−4.15804
$765$	− 1.07708i	− 0.0389420i
$766$	−48.9095	−1.76717
$767$	0	0
$768$	20.1549	0.727279
$769$	34.3811i	1.23982i	0.784675	+	0.619908i	$0.212830\pi$
$769$	34.3811i	1.23982i	−0.784675	+	0.619908i	$0.787170\pi$
$770$	−33.1242	−1.19371
$771$	34.5974	1.24599
$772$	− 80.8157i	− 2.90862i
$773$	0.930605i	0.0334715i	0.999860	+	0.0167358i	$0.00532741\pi$
$773$	0.930605i	0.0334715i	−0.999860	+	0.0167358i	$0.994673\pi$
$774$	− 2.77433i	− 0.0997214i
$775$	24.0752i	0.864808i
$776$	−18.1415	−0.651241
$777$	−14.6939	−0.527142
$778$	− 18.9751i	− 0.680291i
$779$	20.7460	0.743304
$780$	0	0
$781$	−12.6732	−0.453481
$782$	− 58.5825i	− 2.09491i
$783$	−9.28293	−0.331745
$784$	−10.2612	−0.366471
$785$	− 66.6413i	− 2.37853i
$786$	− 19.8635i	− 0.708506i
$787$	35.7268i	1.27352i	0.771061	+	0.636762i	$0.219726\pi$
$787$	35.7268i	1.27352i	−0.771061	+	0.636762i	$0.780274\pi$
$788$	9.94725i	0.354356i
$789$	10.7332	0.382113
$790$	77.7311	2.76555
$791$	0.870896i	0.0309655i
$792$	−4.07192	−0.144689
$793$	0	0
$794$	−9.19631	−0.326365
$795$	− 23.2731i	− 0.825412i
$796$	−133.085	−4.71706
$797$	−14.1123	−0.499884	−0.249942	−	0.968261i	$-0.580412\pi$
$797$	−14.1123	−0.499884	−0.249942	+	0.968261i	$0.580412\pi$
$798$	23.1702i	0.820216i
$799$	− 2.67625i	− 0.0946788i
$800$	42.7926i	1.51295i
$801$	− 0.475598i	− 0.0168044i
$802$	97.2896	3.43542
$803$	3.79069	0.133770
$804$	− 3.58745i	− 0.126519i
$805$	22.3097	0.786315
$806$	0	0
$807$	−0.237546	−0.00836203
$808$	10.4059i	0.366077i
$809$	−26.6217	−0.935970	−0.467985	−	0.883736i	$-0.655020\pi$
$809$	−26.6217	−0.935970	−0.467985	+	0.883736i	$0.655020\pi$
$810$	−72.3746	−2.54299
$811$	− 54.9687i	− 1.93021i	−0.261861	−	0.965106i	$-0.584336\pi$
$811$	− 54.9687i	− 1.93021i	0.261861	−	0.965106i	$-0.415664\pi$
$812$	8.96098i	0.314469i
$813$	26.4652i	0.928176i
$814$	− 93.5662i	− 3.27949i
$815$	12.8679	0.450741
$816$	53.3341	1.86707
$817$	− 42.3046i	− 1.48005i
$818$	93.1294	3.25619
$819$	0	0
$820$	60.0590	2.09735
$821$	− 24.9388i	− 0.870370i	−0.900341	−	0.435185i	$-0.856683\pi$
$821$	− 24.9388i	− 0.870370i	0.900341	−	0.435185i	$-0.143317\pi$
$822$	83.8932	2.92611
$823$	2.81664	0.0981820	0.0490910	−	0.998794i	$-0.484368\pi$
$823$	2.81664	0.0981820	0.0490910	+	0.998794i	$0.484368\pi$
$824$	− 142.696i	− 4.97106i
$825$	27.7136i	0.964863i
$826$	− 24.7562i	− 0.861380i
$827$	− 27.5297i	− 0.957302i	−0.878005	−	0.478651i	$-0.841126\pi$
$827$	− 27.5297i	− 0.957302i	0.878005	−	0.478651i	$-0.158874\pi$
$828$	4.62963	0.160891
$829$	−22.5946	−0.784744	−0.392372	−	0.919807i	$-0.628345\pi$
$829$	−22.5946	−0.784744	−0.392372	+	0.919807i	$0.628345\pi$
$830$	− 46.7539i	− 1.62285i
$831$	27.5057	0.954164
$832$	0	0
$833$	2.94049	0.101882
$834$	− 0.434118i	− 0.0150323i
$835$	50.6424	1.75255
$836$	−104.816	−3.62512
$837$	− 33.4280i	− 1.15544i
$838$	− 35.1093i	− 1.21283i
$839$	− 35.2752i	− 1.21784i	−0.793233	−	0.608918i	$-0.791604\pi$
$839$	− 35.2752i	− 1.21784i	0.793233	−	0.608918i	$-0.208396\pi$
$840$	39.7351i	1.37099i
$841$	−25.6645	−0.884984
$842$	28.7899	0.992166
$843$	− 39.4835i	− 1.35988i
$844$	15.2609	0.525303
$845$	0	0
$846$	0.297707	0.0102354
$847$	− 7.34326i	− 0.252317i
$848$	45.9078	1.57648
$849$	5.45187	0.187108
$850$	− 28.2890i	− 0.970304i
$851$	63.0184i	2.16024i
$852$	25.6632i	0.879208i
$853$	− 48.7120i	− 1.66787i	−0.551864	−	0.833934i	$-0.686083\pi$
$853$	− 48.7120i	− 1.66787i	0.551864	−	0.833934i	$-0.313917\pi$
$854$	−4.61451	−0.157905
$855$	1.82700	0.0624822
$856$	45.3617i	1.55043i
$857$	7.16347	0.244700	0.122350	−	0.992487i	$-0.460957\pi$
$857$	7.16347	0.244700	0.122350	+	0.992487i	$0.460957\pi$
$858$	0	0
$859$	−36.8202	−1.25629	−0.628144	−	0.778097i	$-0.716185\pi$
$859$	−36.8202	−1.25629	−0.628144	+	0.778097i	$0.716185\pi$
$860$	− 122.470i	− 4.17620i
$861$	7.35211	0.250559
$862$	35.7348	1.21713
$863$	− 11.2697i	− 0.383624i	−0.981432	−	0.191812i	$-0.938564\pi$
$863$	− 11.2697i	− 0.383624i	0.981432	−	0.191812i	$-0.0614364\pi$
$864$	− 59.4167i	− 2.02140i
$865$	− 65.9453i	− 2.24221i
$866$	− 46.9539i	− 1.59556i
$867$	14.7658	0.501473
$868$	−32.2686	−1.09527
$869$	43.0453i	1.46021i
$870$	24.9675	0.846476
$871$	0	0
$872$	12.4905	0.422980
$873$	0.295607i	0.0100048i
$874$	99.3710	3.36127
$875$	−3.94138	−0.133243
$876$	− 7.67617i	− 0.259354i
$877$	− 24.5926i	− 0.830432i	−0.909723	−	0.415216i	$-0.863706\pi$
$877$	− 24.5926i	− 0.830432i	0.909723	−	0.415216i	$-0.136294\pi$
$878$	− 56.7679i	− 1.91582i
$879$	45.9107i	1.54853i
$880$	−129.334	−4.35984
$881$	25.1057	0.845832	0.422916	−	0.906169i	$-0.361007\pi$
$881$	25.1057	0.845832	0.422916	+	0.906169i	$0.361007\pi$
$882$	0.327101i	0.0110141i
$883$	−55.6948	−1.87428	−0.937140	−	0.348953i	$-0.886537\pi$
$883$	−55.6948	−1.87428	−0.937140	+	0.348953i	$0.886537\pi$
$884$	0	0
$885$	−49.0026	−1.64720
$886$	− 78.2825i	− 2.62995i
$887$	28.0635	0.942281	0.471141	−	0.882058i	$-0.343842\pi$
$887$	28.0635	0.942281	0.471141	+	0.882058i	$0.343842\pi$
$888$	−112.240	−3.76652
$889$	5.72408i	0.191980i
$890$	− 29.5526i	− 0.990606i
$891$	− 40.0790i	− 1.34270i
$892$	− 77.3499i	− 2.58987i
$893$	4.53960	0.151912
$894$	−77.5722	−2.59440
$895$	8.10191i	0.270817i
$896$	−3.42255	−0.114340
$897$	0	0
$898$	46.2722	1.54412
$899$	12.0111i	0.400593i
$900$	2.23560	0.0745201
$901$	−13.1556	−0.438275
$902$	46.8159i	1.55880i
$903$	− 14.9922i	− 0.498908i
$904$	6.65236i	0.221254i
$905$	− 18.4376i	− 0.612885i
$906$	76.6168	2.54542
$907$	34.1285	1.13322	0.566609	−	0.823987i	$-0.308255\pi$
$907$	34.1285	1.13322	0.566609	+	0.823987i	$0.308255\pi$
$908$	22.8330i	0.757739i
$909$	0.169559	0.00562391
$910$	0	0
$911$	32.8842	1.08950	0.544751	−	0.838598i	$-0.316624\pi$
$911$	32.8842	1.08950	0.544751	+	0.838598i	$0.316624\pi$
$912$	90.4682i	2.99570i
$913$	25.8910	0.856866
$914$	−47.4180	−1.56845
$915$	9.13398i	0.301960i
$916$	81.0195i	2.67696i
$917$	− 4.27598i	− 0.141205i
$918$	39.2787i	1.29639i
$919$	−8.57983	−0.283022	−0.141511	−	0.989937i	$-0.545196\pi$
$919$	−8.57983	−0.283022	−0.141511	+	0.989937i	$0.545196\pi$
$920$	170.414	5.61837
$921$	27.9298i	0.920317i
$922$	−39.8471	−1.31229
$923$	0	0
$924$	−37.1452	−1.22199
$925$	30.4310i	1.00057i
$926$	−70.2067	−2.30713
$927$	−2.32517	−0.0763687
$928$	21.3491i	0.700820i
$929$	31.4204i	1.03087i	0.856929	+	0.515435i	$0.172370\pi$
$929$	31.4204i	1.03087i	−0.856929	+	0.515435i	$0.827630\pi$
$930$	89.9083i	2.94821i
$931$	4.98782i	0.163469i
$932$	84.4041	2.76475
$933$	25.2686	0.827258
$934$	− 77.5028i	− 2.53597i
$935$	37.0625	1.21207
$936$	0	0
$937$	5.52675	0.180551	0.0902755	−	0.995917i	$-0.471225\pi$
$937$	5.52675	0.180551	0.0902755	+	0.995917i	$0.471225\pi$
$938$	− 1.08705i	− 0.0354936i
$939$	−20.7895	−0.678441
$940$	13.1420	0.428644
$941$	− 49.6039i	− 1.61704i	−0.588468	−	0.808521i	$-0.700269\pi$
$941$	− 49.6039i	− 1.61704i	0.588468	−	0.808521i	$-0.299731\pi$
$942$	− 105.193i	− 3.42736i
$943$	− 31.5313i	− 1.02680i
$944$	− 96.6610i	− 3.14605i
$945$	−14.9583	−0.486595
$946$	95.4653	3.10384
$947$	16.3021i	0.529748i	0.964283	+	0.264874i	$0.0853303\pi$
$947$	16.3021i	0.529748i	−0.964283	+	0.264874i	$0.914670\pi$
$948$	87.1670	2.83105
$949$	0	0
$950$	47.9853	1.55685
$951$	− 36.9975i	− 1.19972i
$952$	22.4610	0.727965
$953$	−49.6685	−1.60892	−0.804461	−	0.594006i	$-0.797546\pi$
$953$	−49.6685	−1.60892	−0.804461	+	0.594006i	$0.797546\pi$
$954$	− 1.46343i	− 0.0473802i
$955$	68.9343i	2.23066i
$956$	21.7187i	0.702434i
$957$	13.8263i	0.446940i
$958$	−88.0037	−2.84327
$959$	18.0596	0.583175
$960$	53.0517i	1.71224i
$961$	−12.2522	−0.395232
$962$	0	0
$963$	0.739149	0.0238187
$964$	90.9780i	2.93020i
$965$	−48.4726	−1.56039
$966$	35.2157	1.13305
$967$	− 0.978584i	− 0.0314691i	−0.999876	−	0.0157346i	$-0.994991\pi$
$967$	− 0.978584i	− 0.0314691i	0.999876	−	0.0157346i	$-0.00500867\pi$
$968$	− 56.0917i	− 1.80285i
$969$	− 25.9250i	− 0.832831i
$970$	18.3684i	0.589773i
$971$	−8.33615	−0.267520	−0.133760	−	0.991014i	$-0.542705\pi$
$971$	−8.33615	−0.267520	−0.133760	+	0.991014i	$0.542705\pi$
$972$	−6.34254	−0.203437
$973$	− 0.0934521i	− 0.00299594i
$974$	−30.1151	−0.964951
$975$	0	0
$976$	−18.0174	−0.576723
$977$	− 46.0001i	− 1.47167i	−0.677159	−	0.735837i	$-0.736789\pi$
$977$	− 46.0001i	− 1.47167i	0.677159	−	0.735837i	$-0.263211\pi$
$978$	20.3118	0.649499
$979$	16.3654	0.523040
$980$	14.4396i	0.461255i
$981$	− 0.203526i	− 0.00649809i
$982$	− 88.0503i	− 2.80980i
$983$	21.5565i	0.687546i	0.939053	+	0.343773i	$0.111705\pi$
$983$	21.5565i	0.687546i	−0.939053	+	0.343773i	$0.888295\pi$
$984$	56.1593	1.79029
$985$	5.96628	0.190101
$986$	− 14.1133i	− 0.449460i
$987$	1.60877	0.0512078
$988$	0	0
$989$	−64.2975	−2.04454
$990$	4.12285i	0.131033i
$991$	−20.8493	−0.662299	−0.331150	−	0.943578i	$-0.607437\pi$
$991$	−20.8493	−0.662299	−0.331150	+	0.943578i	$0.607437\pi$
$992$	−76.8787	−2.44090
$993$	14.5941i	0.463128i
$994$	7.77638i	0.246652i
$995$	79.8230i	2.53056i
$996$	− 52.4294i	− 1.66129i
$997$	2.72406	0.0862718	0.0431359	−	0.999069i	$-0.486265\pi$
$997$	2.72406	0.0862718	0.0431359	+	0.999069i	$0.486265\pi$
$998$	−69.2530	−2.19216
$999$	− 42.2529i	− 1.33682i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.c.j.337.1		24
13.5	odd	4		1183.2.a.q.1.1	✓	12
13.8	odd	4		1183.2.a.r.1.12	yes	12
13.12	even	2	inner	1183.2.c.j.337.24		24
91.34	even	4		8281.2.a.cq.1.12		12
91.83	even	4		8281.2.a.cn.1.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1183.2.a.q.1.1	✓	12	13.5	odd	4
1183.2.a.r.1.12	yes	12	13.8	odd	4
1183.2.c.j.337.1		24	1.1	even	1	trivial
1183.2.c.j.337.24		24	13.12	even	2	inner
8281.2.a.cn.1.1		12	91.83	even	4
8281.2.a.cq.1.12		12	91.34	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:	\( N \)	\(=\)	\( 1183 = 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1183.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-2.62803i q^{2} -1.76762 q^{3} -4.90656 q^{4} +2.94291i q^{5} +4.64535i q^{6} +1.00000i q^{7} +7.63852i q^{8} +0.124466 q^{9} +O(q^{10})\)	\(q-2.62803i q^{2} -1.76762 q^{3} -4.90656 q^{4} +2.94291i q^{5} +4.64535i q^{6} +1.00000i q^{7} +7.63852i q^{8} +0.124466 q^{9} +7.73406 q^{10} +4.28290i q^{11} +8.67291 q^{12} +2.62803 q^{14} -5.20193i q^{15} +10.2612 q^{16} -2.94049 q^{17} -0.327101i q^{18} -4.98782i q^{19} -14.4396i q^{20} -1.76762i q^{21} +11.2556 q^{22} -7.58085 q^{23} -13.5020i q^{24} -3.66072 q^{25} +5.08284 q^{27} -4.90656i q^{28} -1.82633 q^{29} -13.6709 q^{30} -6.57664i q^{31} -11.6897i q^{32} -7.57053i q^{33} +7.72771i q^{34} -2.94291 q^{35} -0.610701 q^{36} -8.31285i q^{37} -13.1082 q^{38} -22.4795 q^{40} +4.15934i q^{41} -4.64535 q^{42} +8.48158 q^{43} -21.0143i q^{44} +0.366293i q^{45} +19.9227i q^{46} +0.910136i q^{47} -18.1378 q^{48} -1.00000 q^{49} +9.62049i q^{50} +5.19766 q^{51} +4.47393 q^{53} -13.3579i q^{54} -12.6042 q^{55} -7.63852 q^{56} +8.81656i q^{57} +4.79965i q^{58} -9.42007i q^{59} +25.5236i q^{60} -1.75588 q^{61} -17.2836 q^{62} +0.124466i q^{63} -10.1985 q^{64} -19.8956 q^{66} -0.413638i q^{67} +14.4277 q^{68} +13.4000 q^{69} +7.73406i q^{70} +2.95901i q^{71} +0.950738i q^{72} -0.885074i q^{73} -21.8464 q^{74} +6.47075 q^{75} +24.4730i q^{76} -4.28290 q^{77} +10.0505 q^{79} +30.1977i q^{80} -9.35791 q^{81} +10.9309 q^{82} -6.04519i q^{83} +8.67291i q^{84} -8.65360i q^{85} -22.2899i q^{86} +3.22825 q^{87} -32.7151 q^{88} -3.82110i q^{89} +0.962630 q^{90} +37.1958 q^{92} +11.6250i q^{93} +2.39187 q^{94} +14.6787 q^{95} +20.6628i q^{96} +2.37500i q^{97} +2.62803i q^{98} +0.533077i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 16 q^{3} - 30 q^{4} + 52 q^{9}+O(q^{10}) \) 24 * q + 16 * q^3 - 30 * q^4 + 52 * q^9	\( 24 q + 16 q^{3} - 30 q^{4} + 52 q^{9} + 12 q^{10} - 26 q^{12} + 6 q^{14} + 26 q^{16} - 62 q^{17} - 8 q^{22} - 36 q^{23} - 64 q^{25} + 64 q^{27} + 30 q^{29} + 20 q^{30} - 8 q^{35} - 98 q^{36} - 90 q^{38} - 40 q^{40} + 4 q^{42} + 44 q^{43} + 22 q^{48} - 24 q^{49} - 36 q^{51} + 106 q^{53} - 52 q^{55} - 24 q^{56} + 44 q^{61} - 38 q^{62} - 4 q^{64} - 68 q^{66} + 68 q^{68} - 6 q^{69} - 80 q^{74} - 30 q^{75} - 24 q^{77} + 4 q^{79} + 72 q^{81} + 64 q^{82} + 54 q^{87} + 96 q^{88} + 52 q^{90} + 104 q^{92} - 88 q^{94} - 58 q^{95}+O(q^{100}) \) 24 * q + 16 * q^3 - 30 * q^4 + 52 * q^9 + 12 * q^10 - 26 * q^12 + 6 * q^14 + 26 * q^16 - 62 * q^17 - 8 * q^22 - 36 * q^23 - 64 * q^25 + 64 * q^27 + 30 * q^29 + 20 * q^30 - 8 * q^35 - 98 * q^36 - 90 * q^38 - 40 * q^40 + 4 * q^42 + 44 * q^43 + 22 * q^48 - 24 * q^49 - 36 * q^51 + 106 * q^53 - 52 * q^55 - 24 * q^56 + 44 * q^61 - 38 * q^62 - 4 * q^64 - 68 * q^66 + 68 * q^68 - 6 * q^69 - 80 * q^74 - 30 * q^75 - 24 * q^77 + 4 * q^79 + 72 * q^81 + 64 * q^82 + 54 * q^87 + 96 * q^88 + 52 * q^90 + 104 * q^92 - 88 * q^94 - 58 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

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