LMFDB - Embedded newform 5610.2.a.cb.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5610,2,Mod(1,5610)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5610, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("5610.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5610 = 2 \cdot 3 \cdot 5 \cdot 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5610.a (trivial)

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:	yes
Analytic conductor:	$44.7960755339$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.2089.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 13x - 4 $ x^3 - 13*x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-3.44055$ of defining polynomial
Character	$\chi$	$=$	5610.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -2.44055 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -2.44055 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -1.00000 q^{11} +1.00000 q^{12} +4.00000 q^{13} +2.44055 q^{14} +1.00000 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} +1.00000 q^{20} -2.44055 q^{21} +1.00000 q^{22} +2.83740 q^{23} -1.00000 q^{24} +1.00000 q^{25} -4.00000 q^{26} +1.00000 q^{27} -2.44055 q^{28} +2.44055 q^{29} -1.00000 q^{30} +4.44055 q^{31} -1.00000 q^{32} -1.00000 q^{33} -1.00000 q^{34} -2.44055 q^{35} +1.00000 q^{36} -5.27795 q^{37} +4.00000 q^{39} -1.00000 q^{40} +7.27795 q^{41} +2.44055 q^{42} +10.4406 q^{43} -1.00000 q^{44} +1.00000 q^{45} -2.83740 q^{46} -7.27795 q^{47} +1.00000 q^{48} -1.04371 q^{49} -1.00000 q^{50} +1.00000 q^{51} +4.00000 q^{52} -14.1591 q^{53} -1.00000 q^{54} -1.00000 q^{55} +2.44055 q^{56} -2.44055 q^{58} -5.27795 q^{59} +1.00000 q^{60} +2.00000 q^{61} -4.44055 q^{62} -2.44055 q^{63} +1.00000 q^{64} +4.00000 q^{65} +1.00000 q^{66} +0.396844 q^{67} +1.00000 q^{68} +2.83740 q^{69} +2.44055 q^{70} +12.4843 q^{71} -1.00000 q^{72} +1.60316 q^{73} +5.27795 q^{74} +1.00000 q^{75} +2.44055 q^{77} -4.00000 q^{78} -14.5559 q^{79} +1.00000 q^{80} +1.00000 q^{81} -7.27795 q^{82} +14.5559 q^{83} -2.44055 q^{84} +1.00000 q^{85} -10.4406 q^{86} +2.44055 q^{87} +1.00000 q^{88} -1.11890 q^{89} -1.00000 q^{90} -9.76221 q^{91} +2.83740 q^{92} +4.44055 q^{93} +7.27795 q^{94} -1.00000 q^{96} +1.23424 q^{97} +1.04371 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} + 3 q^{5} - 3 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 + 3 * q^5 - 3 * q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9	\( 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} + 3 q^{5} - 3 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9} - 3 q^{10} - 3 q^{11} + 3 q^{12} + 12 q^{13} - 3 q^{14} + 3 q^{15} + 3 q^{16} + 3 q^{17} - 3 q^{18} + 3 q^{20} + 3 q^{21} + 3 q^{22} - q^{23} - 3 q^{24} + 3 q^{25} - 12 q^{26} + 3 q^{27} + 3 q^{28} - 3 q^{29} - 3 q^{30} + 3 q^{31} - 3 q^{32} - 3 q^{33} - 3 q^{34} + 3 q^{35} + 3 q^{36} + 4 q^{37} + 12 q^{39} - 3 q^{40} + 2 q^{41} - 3 q^{42} + 21 q^{43} - 3 q^{44} + 3 q^{45} + q^{46} - 2 q^{47} + 3 q^{48} + 8 q^{49} - 3 q^{50} + 3 q^{51} + 12 q^{52} - 2 q^{53} - 3 q^{54} - 3 q^{55} - 3 q^{56} + 3 q^{58} + 4 q^{59} + 3 q^{60} + 6 q^{61} - 3 q^{62} + 3 q^{63} + 3 q^{64} + 12 q^{65} + 3 q^{66} + 2 q^{67} + 3 q^{68} - q^{69} - 3 q^{70} + 16 q^{71} - 3 q^{72} + 4 q^{73} - 4 q^{74} + 3 q^{75} - 3 q^{77} - 12 q^{78} - 4 q^{79} + 3 q^{80} + 3 q^{81} - 2 q^{82} + 4 q^{83} + 3 q^{84} + 3 q^{85} - 21 q^{86} - 3 q^{87} + 3 q^{88} - 24 q^{89} - 3 q^{90} + 12 q^{91} - q^{92} + 3 q^{93} + 2 q^{94} - 3 q^{96} - 5 q^{97} - 8 q^{98} - 3 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 + 3 * q^5 - 3 * q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9 - 3 * q^10 - 3 * q^11 + 3 * q^12 + 12 * q^13 - 3 * q^14 + 3 * q^15 + 3 * q^16 + 3 * q^17 - 3 * q^18 + 3 * q^20 + 3 * q^21 + 3 * q^22 - q^23 - 3 * q^24 + 3 * q^25 - 12 * q^26 + 3 * q^27 + 3 * q^28 - 3 * q^29 - 3 * q^30 + 3 * q^31 - 3 * q^32 - 3 * q^33 - 3 * q^34 + 3 * q^35 + 3 * q^36 + 4 * q^37 + 12 * q^39 - 3 * q^40 + 2 * q^41 - 3 * q^42 + 21 * q^43 - 3 * q^44 + 3 * q^45 + q^46 - 2 * q^47 + 3 * q^48 + 8 * q^49 - 3 * q^50 + 3 * q^51 + 12 * q^52 - 2 * q^53 - 3 * q^54 - 3 * q^55 - 3 * q^56 + 3 * q^58 + 4 * q^59 + 3 * q^60 + 6 * q^61 - 3 * q^62 + 3 * q^63 + 3 * q^64 + 12 * q^65 + 3 * q^66 + 2 * q^67 + 3 * q^68 - q^69 - 3 * q^70 + 16 * q^71 - 3 * q^72 + 4 * q^73 - 4 * q^74 + 3 * q^75 - 3 * q^77 - 12 * q^78 - 4 * q^79 + 3 * q^80 + 3 * q^81 - 2 * q^82 + 4 * q^83 + 3 * q^84 + 3 * q^85 - 21 * q^86 - 3 * q^87 + 3 * q^88 - 24 * q^89 - 3 * q^90 + 12 * q^91 - q^92 + 3 * q^93 + 2 * q^94 - 3 * q^96 - 5 * q^97 - 8 * q^98 - 3 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.00000	−0.408248
$7$	−2.44055	−0.922442	−0.461221	−	0.887285i	$-0.652588\pi$
$7$	−2.44055	−0.922442	−0.461221	+	0.887285i	$0.652588\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−1.00000	−0.316228
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	1.00000	0.288675
$13$	4.00000	1.10940	0.554700	−	0.832050i	$-0.312833\pi$
$13$	4.00000	1.10940	0.554700	+	0.832050i	$0.312833\pi$
$14$	2.44055	0.652265
$15$	1.00000	0.258199
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.00000	−0.235702
$19$	0	0		−	1.00000i	$-0.5\pi$
$19$	0	0			1.00000i	$0.5\pi$
$20$	1.00000	0.223607
$21$	−2.44055	−0.532572
$22$	1.00000	0.213201
$23$	2.83740	0.591638	0.295819	−	0.955244i	$-0.404407\pi$
$23$	2.83740	0.591638	0.295819	+	0.955244i	$0.404407\pi$
$24$	−1.00000	−0.204124
$25$	1.00000	0.200000
$26$	−4.00000	−0.784465
$27$	1.00000	0.192450
$28$	−2.44055	−0.461221
$29$	2.44055	0.453199	0.226600	−	0.973988i	$-0.427239\pi$
$29$	2.44055	0.453199	0.226600	+	0.973988i	$0.427239\pi$
$30$	−1.00000	−0.182574
$31$	4.44055	0.797547	0.398773	−	0.917050i	$-0.369436\pi$
$31$	4.44055	0.797547	0.398773	+	0.917050i	$0.369436\pi$
$32$	−1.00000	−0.176777
$33$	−1.00000	−0.174078
$34$	−1.00000	−0.171499
$35$	−2.44055	−0.412529
$36$	1.00000	0.166667
$37$	−5.27795	−0.867689	−0.433845	−	0.900988i	$-0.642843\pi$
$37$	−5.27795	−0.867689	−0.433845	+	0.900988i	$0.642843\pi$
$38$	0	0
$39$	4.00000	0.640513
$40$	−1.00000	−0.158114
$41$	7.27795	1.13662	0.568312	−	0.822813i	$-0.307597\pi$
$41$	7.27795	1.13662	0.568312	+	0.822813i	$0.307597\pi$
$42$	2.44055	0.376585
$43$	10.4406	1.59217	0.796085	−	0.605185i	$-0.206901\pi$
$43$	10.4406	1.59217	0.796085	+	0.605185i	$0.206901\pi$
$44$	−1.00000	−0.150756
$45$	1.00000	0.149071
$46$	−2.83740	−0.418351
$47$	−7.27795	−1.06160	−0.530799	−	0.847498i	$-0.678108\pi$
$47$	−7.27795	−1.06160	−0.530799	+	0.847498i	$0.678108\pi$
$48$	1.00000	0.144338
$49$	−1.04371	−0.149101
$50$	−1.00000	−0.141421
$51$	1.00000	0.140028
$52$	4.00000	0.554700
$53$	−14.1591	−1.94490	−0.972448	−	0.233122i	$-0.925106\pi$
$53$	−14.1591	−1.94490	−0.972448	+	0.233122i	$0.925106\pi$
$54$	−1.00000	−0.136083
$55$	−1.00000	−0.134840
$56$	2.44055	0.326132
$57$	0	0
$58$	−2.44055	−0.320460
$59$	−5.27795	−0.687130	−0.343565	−	0.939129i	$-0.611635\pi$
$59$	−5.27795	−0.687130	−0.343565	+	0.939129i	$0.611635\pi$
$60$	1.00000	0.129099
$61$	2.00000	0.256074	0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000	0.256074	0.128037	+	0.991769i	$0.459132\pi$
$62$	−4.44055	−0.563951
$63$	−2.44055	−0.307481
$64$	1.00000	0.125000
$65$	4.00000	0.496139
$66$	1.00000	0.123091
$67$	0.396844	0.0484822	0.0242411	−	0.999706i	$-0.492283\pi$
$67$	0.396844	0.0484822	0.0242411	+	0.999706i	$0.492283\pi$
$68$	1.00000	0.121268
$69$	2.83740	0.341582
$70$	2.44055	0.291702
$71$	12.4843	1.48161	0.740804	−	0.671721i	$-0.234444\pi$
$71$	12.4843	1.48161	0.740804	+	0.671721i	$0.234444\pi$
$72$	−1.00000	−0.117851
$73$	1.60316	0.187635	0.0938176	−	0.995589i	$-0.470093\pi$
$73$	1.60316	0.187635	0.0938176	+	0.995589i	$0.470093\pi$
$74$	5.27795	0.613549
$75$	1.00000	0.115470
$76$	0	0
$77$	2.44055	0.278127
$78$	−4.00000	−0.452911
$79$	−14.5559	−1.63767	−0.818833	−	0.574032i	$-0.805379\pi$
$79$	−14.5559	−1.63767	−0.818833	+	0.574032i	$0.805379\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	−7.27795	−0.803715
$83$	14.5559	1.59772	0.798859	−	0.601519i	$-0.205438\pi$
$83$	14.5559	1.59772	0.798859	+	0.601519i	$0.205438\pi$
$84$	−2.44055	−0.266286
$85$	1.00000	0.108465
$86$	−10.4406	−1.12583
$87$	2.44055	0.261655
$88$	1.00000	0.106600
$89$	−1.11890	−0.118603	−0.0593014	−	0.998240i	$-0.518887\pi$
$89$	−1.11890	−0.118603	−0.0593014	+	0.998240i	$0.518887\pi$
$90$	−1.00000	−0.105409
$91$	−9.76221	−1.02336
$92$	2.83740	0.295819
$93$	4.44055	0.460464
$94$	7.27795	0.750663
$95$	0	0
$96$	−1.00000	−0.102062
$97$	1.23424	0.125318	0.0626590	−	0.998035i	$-0.480042\pi$
$97$	1.23424	0.125318	0.0626590	+	0.998035i	$0.480042\pi$
$98$	1.04371	0.105430
$99$	−1.00000	−0.100504
$100$	1.00000	0.100000
$101$	−2.39684	−0.238495	−0.119247	−	0.992865i	$-0.538048\pi$
$101$	−2.39684	−0.238495	−0.119247	+	0.992865i	$0.538048\pi$
$102$	−1.00000	−0.0990148
$103$	15.7185	1.54879	0.774395	−	0.632703i	$-0.218054\pi$
$103$	15.7185	1.54879	0.774395	+	0.632703i	$0.218054\pi$
$104$	−4.00000	−0.392232
$105$	−2.44055	−0.238173
$106$	14.1591	1.37525
$107$	−7.71850	−0.746175	−0.373088	−	0.927796i	$-0.621701\pi$
$107$	−7.71850	−0.746175	−0.373088	+	0.927796i	$0.621701\pi$
$108$	1.00000	0.0962250
$109$	−10.8811	−1.04222	−0.521110	−	0.853489i	$-0.674482\pi$
$109$	−10.8811	−1.04222	−0.521110	+	0.853489i	$0.674482\pi$
$110$	1.00000	0.0953463
$111$	−5.27795	−0.500961
$112$	−2.44055	−0.230610
$113$	2.00000	0.188144	0.0940721	−	0.995565i	$-0.470012\pi$
$113$	2.00000	0.188144	0.0940721	+	0.995565i	$0.470012\pi$
$114$	0	0
$115$	2.83740	0.264589
$116$	2.44055	0.226600
$117$	4.00000	0.369800
$118$	5.27795	0.485874
$119$	−2.44055	−0.223725
$120$	−1.00000	−0.0912871
$121$	1.00000	0.0909091
$122$	−2.00000	−0.181071
$123$	7.27795	0.656230
$124$	4.44055	0.398773
$125$	1.00000	0.0894427
$126$	2.44055	0.217422
$127$	−4.15905	−0.369056	−0.184528	−	0.982827i	$-0.559076\pi$
$127$	−4.15905	−0.369056	−0.184528	+	0.982827i	$0.559076\pi$
$128$	−1.00000	−0.0883883
$129$	10.4406	0.919239
$130$	−4.00000	−0.350823
$131$	17.7622	1.55189	0.775946	−	0.630800i	$-0.217273\pi$
$131$	17.7622	1.55189	0.775946	+	0.630800i	$0.217273\pi$
$132$	−1.00000	−0.0870388
$133$	0	0
$134$	−0.396844	−0.0342821
$135$	1.00000	0.0860663
$136$	−1.00000	−0.0857493
$137$	−18.5996	−1.58907	−0.794536	−	0.607218i	$-0.792286\pi$
$137$	−18.5996	−1.58907	−0.794536	+	0.607218i	$0.792286\pi$
$138$	−2.83740	−0.241535
$139$	18.9248	1.60518	0.802591	−	0.596530i	$-0.203454\pi$
$139$	18.9248	1.60518	0.802591	+	0.596530i	$0.203454\pi$
$140$	−2.44055	−0.206264
$141$	−7.27795	−0.612914
$142$	−12.4843	−1.04766
$143$	−4.00000	−0.334497
$144$	1.00000	0.0833333
$145$	2.44055	0.202677
$146$	−1.60316	−0.132678
$147$	−1.04371	−0.0860836
$148$	−5.27795	−0.433845
$149$	11.2779	0.923925	0.461963	−	0.886899i	$-0.347145\pi$
$149$	11.2779	0.923925	0.461963	+	0.886899i	$0.347145\pi$
$150$	−1.00000	−0.0816497
$151$	15.2779	1.24330	0.621651	−	0.783294i	$-0.286462\pi$
$151$	15.2779	1.24330	0.621651	+	0.783294i	$0.286462\pi$
$152$	0	0
$153$	1.00000	0.0808452
$154$	−2.44055	−0.196665
$155$	4.44055	0.356674
$156$	4.00000	0.320256
$157$	8.15905	0.651163	0.325582	−	0.945514i	$-0.394440\pi$
$157$	8.15905	0.651163	0.325582	+	0.945514i	$0.394440\pi$
$158$	14.5559	1.15800
$159$	−14.1591	−1.12289
$160$	−1.00000	−0.0790569
$161$	−6.92481	−0.545752
$162$	−1.00000	−0.0785674
$163$	6.04371	0.473380	0.236690	−	0.971585i	$-0.423937\pi$
$163$	6.04371	0.473380	0.236690	+	0.971585i	$0.423937\pi$
$164$	7.27795	0.568312
$165$	−1.00000	−0.0778499
$166$	−14.5559	−1.12976
$167$	16.1591	1.25042	0.625212	−	0.780455i	$-0.285012\pi$
$167$	16.1591	1.25042	0.625212	+	0.780455i	$0.285012\pi$
$168$	2.44055	0.188293
$169$	3.00000	0.230769
$170$	−1.00000	−0.0766965
$171$	0	0
$172$	10.4406	0.796085
$173$	−8.48426	−0.645046	−0.322523	−	0.946562i	$-0.604531\pi$
$173$	−8.48426	−0.645046	−0.322523	+	0.946562i	$0.604531\pi$
$174$	−2.44055	−0.185018
$175$	−2.44055	−0.184488
$176$	−1.00000	−0.0753778
$177$	−5.27795	−0.396715
$178$	1.11890	0.0838649
$179$	−1.27795	−0.0955183	−0.0477591	−	0.998859i	$-0.515208\pi$
$179$	−1.27795	−0.0955183	−0.0477591	+	0.998859i	$0.515208\pi$
$180$	1.00000	0.0745356
$181$	17.8775	1.32883	0.664414	−	0.747365i	$-0.268681\pi$
$181$	17.8775	1.32883	0.664414	+	0.747365i	$0.268681\pi$
$182$	9.76221	0.723623
$183$	2.00000	0.147844
$184$	−2.83740	−0.209176
$185$	−5.27795	−0.388042
$186$	−4.44055	−0.325597
$187$	−1.00000	−0.0731272
$188$	−7.27795	−0.530799
$189$	−2.44055	−0.177524
$190$	0	0
$191$	−14.1153	−1.02135	−0.510675	−	0.859774i	$-0.670605\pi$
$191$	−14.1153	−1.02135	−0.510675	+	0.859774i	$0.670605\pi$
$192$	1.00000	0.0721688
$193$	23.3654	1.68188	0.840938	−	0.541132i	$-0.182004\pi$
$193$	23.3654	1.68188	0.840938	+	0.541132i	$0.182004\pi$
$194$	−1.23424	−0.0886133
$195$	4.00000	0.286446
$196$	−1.04371	−0.0745505
$197$	10.1591	0.723802	0.361901	−	0.932216i	$-0.382128\pi$
$197$	10.1591	0.723802	0.361901	+	0.932216i	$0.382128\pi$
$198$	1.00000	0.0710669
$199$	17.0402	1.20794	0.603972	−	0.797005i	$-0.293584\pi$
$199$	17.0402	1.20794	0.603972	+	0.797005i	$0.293584\pi$
$200$	−1.00000	−0.0707107
$201$	0.396844	0.0279912
$202$	2.39684	0.168641
$203$	−5.95629	−0.418050
$204$	1.00000	0.0700140
$205$	7.27795	0.508314
$206$	−15.7185	−1.09516
$207$	2.83740	0.197213
$208$	4.00000	0.277350
$209$	0	0
$210$	2.44055	0.168414
$211$	24.5996	1.69351	0.846753	−	0.531986i	$-0.178554\pi$
$211$	24.5996	1.69351	0.846753	+	0.531986i	$0.178554\pi$
$212$	−14.1591	−0.972448
$213$	12.4843	0.855407
$214$	7.71850	0.527626
$215$	10.4406	0.712040
$216$	−1.00000	−0.0680414
$217$	−10.8374	−0.735690
$218$	10.8811	0.736961
$219$	1.60316	0.108331
$220$	−1.00000	−0.0674200
$221$	4.00000	0.269069
$222$	5.27795	0.354233
$223$	9.16260	0.613573	0.306787	−	0.951778i	$-0.400746\pi$
$223$	9.16260	0.613573	0.306787	+	0.951778i	$0.400746\pi$
$224$	2.44055	0.163066
$225$	1.00000	0.0666667
$226$	−2.00000	−0.133038
$227$	26.3618	1.74969	0.874847	−	0.484399i	$-0.160962\pi$
$227$	26.3618	1.74969	0.874847	+	0.484399i	$0.160962\pi$
$228$	0	0
$229$	5.11890	0.338266	0.169133	−	0.985593i	$-0.445903\pi$
$229$	5.11890	0.338266	0.169133	+	0.985593i	$0.445903\pi$
$230$	−2.83740	−0.187092
$231$	2.44055	0.160577
$232$	−2.44055	−0.160230
$233$	−17.7185	−1.16078	−0.580389	−	0.814340i	$-0.697099\pi$
$233$	−17.7185	−1.16078	−0.580389	+	0.814340i	$0.697099\pi$
$234$	−4.00000	−0.261488
$235$	−7.27795	−0.474761
$236$	−5.27795	−0.343565
$237$	−14.5559	−0.945507
$238$	2.44055	0.158197
$239$	−7.43700	−0.481059	−0.240530	−	0.970642i	$-0.577321\pi$
$239$	−7.43700	−0.481059	−0.240530	+	0.970642i	$0.577321\pi$
$240$	1.00000	0.0645497
$241$	17.7185	1.14135	0.570674	−	0.821176i	$-0.306682\pi$
$241$	17.7185	1.14135	0.570674	+	0.821176i	$0.306682\pi$
$242$	−1.00000	−0.0642824
$243$	1.00000	0.0641500
$244$	2.00000	0.128037
$245$	−1.04371	−0.0666800
$246$	−7.27795	−0.464025
$247$	0	0
$248$	−4.44055	−0.281975
$249$	14.5559	0.922442
$250$	−1.00000	−0.0632456
$251$	14.9527	0.943809	0.471904	−	0.881650i	$-0.343567\pi$
$251$	14.9527	0.943809	0.471904	+	0.881650i	$0.343567\pi$
$252$	−2.44055	−0.153740
$253$	−2.83740	−0.178386
$254$	4.15905	0.260962
$255$	1.00000	0.0626224
$256$	1.00000	0.0625000
$257$	2.59960	0.162159	0.0810794	−	0.996708i	$-0.474163\pi$
$257$	2.59960	0.162159	0.0810794	+	0.996708i	$0.474163\pi$
$258$	−10.4406	−0.650000
$259$	12.8811	0.800393
$260$	4.00000	0.248069
$261$	2.44055	0.151066
$262$	−17.7622	−1.09735
$263$	6.04371	0.372671	0.186335	−	0.982486i	$-0.440339\pi$
$263$	6.04371	0.372671	0.186335	+	0.982486i	$0.440339\pi$
$264$	1.00000	0.0615457
$265$	−14.1591	−0.869784
$266$	0	0
$267$	−1.11890	−0.0684754
$268$	0.396844	0.0242411
$269$	−10.0000	−0.609711	−0.304855	−	0.952399i	$-0.598608\pi$
$269$	−10.0000	−0.609711	−0.304855	+	0.952399i	$0.598608\pi$
$270$	−1.00000	−0.0608581
$271$	15.6469	0.950479	0.475240	−	0.879856i	$-0.342361\pi$
$271$	15.6469	0.950479	0.475240	+	0.879856i	$0.342361\pi$
$272$	1.00000	0.0606339
$273$	−9.76221	−0.590836
$274$	18.5996	1.12364
$275$	−1.00000	−0.0603023
$276$	2.83740	0.170791
$277$	−2.00000	−0.120168	−0.0600842	−	0.998193i	$-0.519137\pi$
$277$	−2.00000	−0.120168	−0.0600842	+	0.998193i	$0.519137\pi$
$278$	−18.9248	−1.13503
$279$	4.44055	0.265849
$280$	2.44055	0.145851
$281$	−0.0437076	−0.00260738	−0.00130369	−	0.999999i	$-0.500415\pi$
$281$	−0.0437076	−0.00260738	−0.00130369	+	0.999999i	$0.500415\pi$
$282$	7.27795	0.433395
$283$	−8.08742	−0.480747	−0.240373	−	0.970680i	$-0.577270\pi$
$283$	−8.08742	−0.480747	−0.240373	+	0.970680i	$0.577270\pi$
$284$	12.4843	0.740804
$285$	0	0
$286$	4.00000	0.236525
$287$	−17.7622	−1.04847
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	−2.44055	−0.143314
$291$	1.23424	0.0723524
$292$	1.60316	0.0938176
$293$	−20.9248	−1.22244	−0.611220	−	0.791461i	$-0.709321\pi$
$293$	−20.9248	−1.22244	−0.611220	+	0.791461i	$0.709321\pi$
$294$	1.04371	0.0608703
$295$	−5.27795	−0.307294
$296$	5.27795	0.306774
$297$	−1.00000	−0.0580259
$298$	−11.2779	−0.653314
$299$	11.3496	0.656363
$300$	1.00000	0.0577350
$301$	−25.4807	−1.46868
$302$	−15.2779	−0.879147
$303$	−2.39684	−0.137695
$304$	0	0
$305$	2.00000	0.114520
$306$	−1.00000	−0.0571662
$307$	−22.9527	−1.30998	−0.654991	−	0.755637i	$-0.727328\pi$
$307$	−22.9527	−1.30998	−0.654991	+	0.755637i	$0.727328\pi$
$308$	2.44055	0.139063
$309$	15.7185	0.894194
$310$	−4.44055	−0.252206
$311$	6.15905	0.349248	0.174624	−	0.984635i	$-0.444129\pi$
$311$	6.15905	0.349248	0.174624	+	0.984635i	$0.444129\pi$
$312$	−4.00000	−0.226455
$313$	−31.7901	−1.79688	−0.898442	−	0.439092i	$-0.855300\pi$
$313$	−31.7901	−1.79688	−0.898442	+	0.439092i	$0.855300\pi$
$314$	−8.15905	−0.460442
$315$	−2.44055	−0.137510
$316$	−14.5559	−0.818833
$317$	−17.7185	−0.995170	−0.497585	−	0.867415i	$-0.665780\pi$
$317$	−17.7185	−0.995170	−0.497585	+	0.867415i	$0.665780\pi$
$318$	14.1591	0.794000
$319$	−2.44055	−0.136645
$320$	1.00000	0.0559017
$321$	−7.71850	−0.430805
$322$	6.92481	0.385905
$323$	0	0
$324$	1.00000	0.0555556
$325$	4.00000	0.221880
$326$	−6.04371	−0.334730
$327$	−10.8811	−0.601726
$328$	−7.27795	−0.401857
$329$	17.7622	0.979262
$330$	1.00000	0.0550482
$331$	1.95629	0.107528	0.0537638	−	0.998554i	$-0.482878\pi$
$331$	1.95629	0.107528	0.0537638	+	0.998554i	$0.482878\pi$
$332$	14.5559	0.798859
$333$	−5.27795	−0.289230
$334$	−16.1591	−0.884184
$335$	0.396844	0.0216819
$336$	−2.44055	−0.133143
$337$	−19.3654	−1.05490	−0.527449	−	0.849587i	$-0.676852\pi$
$337$	−19.3654	−1.05490	−0.527449	+	0.849587i	$0.676852\pi$
$338$	−3.00000	−0.163178
$339$	2.00000	0.108625
$340$	1.00000	0.0542326
$341$	−4.44055	−0.240469
$342$	0	0
$343$	19.6311	1.05998
$344$	−10.4406	−0.562917
$345$	2.83740	0.152760
$346$	8.48426	0.456117
$347$	−16.9685	−0.910918	−0.455459	−	0.890257i	$-0.650525\pi$
$347$	−16.9685	−0.910918	−0.455459	+	0.890257i	$0.650525\pi$
$348$	2.44055	0.130827
$349$	16.4843	0.882382	0.441191	−	0.897413i	$-0.354556\pi$
$349$	16.4843	0.882382	0.441191	+	0.897413i	$0.354556\pi$
$350$	2.44055	0.130453
$351$	4.00000	0.213504
$352$	1.00000	0.0533002
$353$	3.16260	0.168328	0.0841642	−	0.996452i	$-0.473178\pi$
$353$	3.16260	0.168328	0.0841642	+	0.996452i	$0.473178\pi$
$354$	5.27795	0.280520
$355$	12.4843	0.662596
$356$	−1.11890	−0.0593014
$357$	−2.44055	−0.129168
$358$	1.27795	0.0675416
$359$	1.67479	0.0883921	0.0441961	−	0.999023i	$-0.485927\pi$
$359$	1.67479	0.0883921	0.0441961	+	0.999023i	$0.485927\pi$
$360$	−1.00000	−0.0527046
$361$	−19.0000	−1.00000
$362$	−17.8775	−0.939623
$363$	1.00000	0.0524864
$364$	−9.76221	−0.511679
$365$	1.60316	0.0839130
$366$	−2.00000	−0.104542
$367$	−35.1118	−1.83282	−0.916410	−	0.400240i	$-0.868927\pi$
$367$	−35.1118	−1.83282	−0.916410	+	0.400240i	$0.868927\pi$
$368$	2.83740	0.147909
$369$	7.27795	0.378875
$370$	5.27795	0.274387
$371$	34.5559	1.79405
$372$	4.44055	0.230232
$373$	−18.6433	−0.965314	−0.482657	−	0.875809i	$-0.660328\pi$
$373$	−18.6433	−0.965314	−0.482657	+	0.875809i	$0.660328\pi$
$374$	1.00000	0.0517088
$375$	1.00000	0.0516398
$376$	7.27795	0.375331
$377$	9.76221	0.502779
$378$	2.44055	0.125528
$379$	38.0803	1.95605	0.978027	−	0.208478i	$-0.0668510\pi$
$379$	38.0803	1.95605	0.978027	+	0.208478i	$0.0668510\pi$
$380$	0	0
$381$	−4.15905	−0.213075
$382$	14.1153	0.722204
$383$	33.0402	1.68827	0.844137	−	0.536128i	$-0.180114\pi$
$383$	33.0402	1.68827	0.844137	+	0.536128i	$0.180114\pi$
$384$	−1.00000	−0.0510310
$385$	2.44055	0.124382
$386$	−23.3654	−1.18927
$387$	10.4406	0.530723
$388$	1.23424	0.0626590
$389$	−4.08742	−0.207240	−0.103620	−	0.994617i	$-0.533043\pi$
$389$	−4.08742	−0.207240	−0.103620	+	0.994617i	$0.533043\pi$
$390$	−4.00000	−0.202548
$391$	2.83740	0.143493
$392$	1.04371	0.0527152
$393$	17.7622	0.895985
$394$	−10.1591	−0.511806
$395$	−14.5559	−0.732387
$396$	−1.00000	−0.0502519
$397$	−24.4843	−1.22883	−0.614415	−	0.788983i	$-0.710608\pi$
$397$	−24.4843	−1.22883	−0.614415	+	0.788983i	$0.710608\pi$
$398$	−17.0402	−0.854146
$399$	0	0
$400$	1.00000	0.0500000
$401$	−34.9964	−1.74764	−0.873820	−	0.486250i	$-0.838364\pi$
$401$	−34.9964	−1.74764	−0.873820	+	0.486250i	$0.838364\pi$
$402$	−0.396844	−0.0197928
$403$	17.7622	0.884799
$404$	−2.39684	−0.119247
$405$	1.00000	0.0496904
$406$	5.95629	0.295606
$407$	5.27795	0.261618
$408$	−1.00000	−0.0495074
$409$	27.6748	1.36843	0.684215	−	0.729280i	$-0.260145\pi$
$409$	27.6748	1.36843	0.684215	+	0.729280i	$0.260145\pi$
$410$	−7.27795	−0.359432
$411$	−18.5996	−0.917451
$412$	15.7185	0.774395
$413$	12.8811	0.633838
$414$	−2.83740	−0.139450
$415$	14.5559	0.714521
$416$	−4.00000	−0.196116
$417$	18.9248	0.926752
$418$	0	0
$419$	−17.3933	−0.849718	−0.424859	−	0.905260i	$-0.639676\pi$
$419$	−17.3933	−0.849718	−0.424859	+	0.905260i	$0.639676\pi$
$420$	−2.44055	−0.119087
$421$	32.6433	1.59094	0.795469	−	0.605995i	$-0.207225\pi$
$421$	32.6433	1.59094	0.795469	+	0.605995i	$0.207225\pi$
$422$	−24.5996	−1.19749
$423$	−7.27795	−0.353866
$424$	14.1591	0.687624
$425$	1.00000	0.0485071
$426$	−12.4843	−0.604864
$427$	−4.88110	−0.236213
$428$	−7.71850	−0.373088
$429$	−4.00000	−0.193122
$430$	−10.4406	−0.503488
$431$	−34.0366	−1.63949	−0.819743	−	0.572732i	$-0.805884\pi$
$431$	−34.0366	−1.63949	−0.819743	+	0.572732i	$0.805884\pi$
$432$	1.00000	0.0481125
$433$	19.6748	0.945510	0.472755	−	0.881194i	$-0.343260\pi$
$433$	19.6748	0.945510	0.472755	+	0.881194i	$0.343260\pi$
$434$	10.8374	0.520212
$435$	2.44055	0.117015
$436$	−10.8811	−0.521110
$437$	0	0
$438$	−1.60316	−0.0766018
$439$	21.6748	1.03448	0.517241	−	0.855840i	$-0.326959\pi$
$439$	21.6748	1.03448	0.517241	+	0.855840i	$0.326959\pi$
$440$	1.00000	0.0476731
$441$	−1.04371	−0.0497004
$442$	−4.00000	−0.190261
$443$	−2.74998	−0.130656	−0.0653278	−	0.997864i	$-0.520809\pi$
$443$	−2.74998	−0.130656	−0.0653278	+	0.997864i	$0.520809\pi$
$444$	−5.27795	−0.250480
$445$	−1.11890	−0.0530408
$446$	−9.16260	−0.433862
$447$	11.2779	0.533429
$448$	−2.44055	−0.115305
$449$	−34.4334	−1.62501	−0.812507	−	0.582951i	$-0.801898\pi$
$449$	−34.4334	−1.62501	−0.812507	+	0.582951i	$0.801898\pi$
$450$	−1.00000	−0.0471405
$451$	−7.27795	−0.342705
$452$	2.00000	0.0940721
$453$	15.2779	0.717821
$454$	−26.3618	−1.23722
$455$	−9.76221	−0.457659
$456$	0	0
$457$	26.9685	1.26153	0.630767	−	0.775972i	$-0.282740\pi$
$457$	26.9685	1.26153	0.630767	+	0.775972i	$0.282740\pi$
$458$	−5.11890	−0.239190
$459$	1.00000	0.0466760
$460$	2.83740	0.132294
$461$	27.3654	1.27453	0.637266	−	0.770644i	$-0.280065\pi$
$461$	27.3654	1.27453	0.637266	+	0.770644i	$0.280065\pi$
$462$	−2.44055	−0.113545
$463$	28.3181	1.31605	0.658027	−	0.752994i	$-0.271391\pi$
$463$	28.3181	1.31605	0.658027	+	0.752994i	$0.271391\pi$
$464$	2.44055	0.113300
$465$	4.44055	0.205926
$466$	17.7185	0.820794
$467$	11.3496	0.525196	0.262598	−	0.964905i	$-0.415421\pi$
$467$	11.3496	0.525196	0.262598	+	0.964905i	$0.415421\pi$
$468$	4.00000	0.184900
$469$	−0.968518	−0.0447220
$470$	7.27795	0.335707
$471$	8.15905	0.375949
$472$	5.27795	0.242937
$473$	−10.4406	−0.480057
$474$	14.5559	0.668574
$475$	0	0
$476$	−2.44055	−0.111863
$477$	−14.1591	−0.648298
$478$	7.43700	0.340160
$479$	−14.5996	−0.667073	−0.333536	−	0.942737i	$-0.608242\pi$
$479$	−14.5996	−0.667073	−0.333536	+	0.942737i	$0.608242\pi$
$480$	−1.00000	−0.0456435
$481$	−21.1118	−0.962615
$482$	−17.7185	−0.807056
$483$	−6.92481	−0.315090
$484$	1.00000	0.0454545
$485$	1.23424	0.0560439
$486$	−1.00000	−0.0453609
$487$	27.1118	1.22855	0.614276	−	0.789091i	$-0.289448\pi$
$487$	27.1118	1.22855	0.614276	+	0.789091i	$0.289448\pi$
$488$	−2.00000	−0.0905357
$489$	6.04371	0.273306
$490$	1.04371	0.0471499
$491$	−10.9527	−0.494290	−0.247145	−	0.968978i	$-0.579492\pi$
$491$	−10.9527	−0.494290	−0.247145	+	0.968978i	$0.579492\pi$
$492$	7.27795	0.328115
$493$	2.44055	0.109917
$494$	0	0
$495$	−1.00000	−0.0449467
$496$	4.44055	0.199387
$497$	−30.4685	−1.36670
$498$	−14.5559	−0.652265
$499$	−23.5244	−1.05310	−0.526549	−	0.850145i	$-0.676514\pi$
$499$	−23.5244	−1.05310	−0.526549	+	0.850145i	$0.676514\pi$
$500$	1.00000	0.0447214
$501$	16.1591	0.721933
$502$	−14.9527	−0.667373
$503$	−35.5960	−1.58715	−0.793575	−	0.608473i	$-0.791782\pi$
$503$	−35.5960	−1.58715	−0.793575	+	0.608473i	$0.791782\pi$
$504$	2.44055	0.108711
$505$	−2.39684	−0.106658
$506$	2.83740	0.126138
$507$	3.00000	0.133235
$508$	−4.15905	−0.184528
$509$	−4.08742	−0.181171	−0.0905857	−	0.995889i	$-0.528874\pi$
$509$	−4.08742	−0.181171	−0.0905857	+	0.995889i	$0.528874\pi$
$510$	−1.00000	−0.0442807
$511$	−3.91258	−0.173083
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	−2.59960	−0.114664
$515$	15.7185	0.692640
$516$	10.4406	0.459620
$517$	7.27795	0.320084
$518$	−12.8811	−0.565963
$519$	−8.48426	−0.372418
$520$	−4.00000	−0.175412
$521$	−14.3968	−0.630737	−0.315369	−	0.948969i	$-0.602128\pi$
$521$	−14.3968	−0.630737	−0.315369	+	0.948969i	$0.602128\pi$
$522$	−2.44055	−0.106820
$523$	−19.3217	−0.844877	−0.422438	−	0.906392i	$-0.638826\pi$
$523$	−19.3217	−0.844877	−0.422438	+	0.906392i	$0.638826\pi$
$524$	17.7622	0.775946
$525$	−2.44055	−0.106514
$526$	−6.04371	−0.263518
$527$	4.44055	0.193433
$528$	−1.00000	−0.0435194
$529$	−14.9492	−0.649965
$530$	14.1591	0.615030
$531$	−5.27795	−0.229043
$532$	0	0
$533$	29.1118	1.26097
$534$	1.11890	0.0484194
$535$	−7.71850	−0.333700
$536$	−0.396844	−0.0171411
$537$	−1.27795	−0.0551475
$538$	10.0000	0.431131
$539$	1.04371	0.0449557
$540$	1.00000	0.0430331
$541$	9.11890	0.392052	0.196026	−	0.980599i	$-0.437196\pi$
$541$	9.11890	0.392052	0.196026	+	0.980599i	$0.437196\pi$
$542$	−15.6469	−0.672090
$543$	17.8775	0.767199
$544$	−1.00000	−0.0428746
$545$	−10.8811	−0.466095
$546$	9.76221	0.417784
$547$	14.3252	0.612502	0.306251	−	0.951951i	$-0.400925\pi$
$547$	14.3252	0.612502	0.306251	+	0.951951i	$0.400925\pi$
$548$	−18.5996	−0.794536
$549$	2.00000	0.0853579
$550$	1.00000	0.0426401
$551$	0	0
$552$	−2.83740	−0.120768
$553$	35.5244	1.51065
$554$	2.00000	0.0849719
$555$	−5.27795	−0.224036
$556$	18.9248	0.802591
$557$	4.92481	0.208671	0.104335	−	0.994542i	$-0.466728\pi$
$557$	4.92481	0.208671	0.104335	+	0.994542i	$0.466728\pi$
$558$	−4.44055	−0.187984
$559$	41.7622	1.76635
$560$	−2.44055	−0.103132
$561$	−1.00000	−0.0422200
$562$	0.0437076	0.00184369
$563$	−40.3181	−1.69921	−0.849603	−	0.527423i	$-0.823158\pi$
$563$	−40.3181	−1.69921	−0.849603	+	0.527423i	$0.823158\pi$
$564$	−7.27795	−0.306457
$565$	2.00000	0.0841406
$566$	8.08742	0.339939
$567$	−2.44055	−0.102494
$568$	−12.4843	−0.523828
$569$	38.9685	1.63365	0.816823	−	0.576889i	$-0.195733\pi$
$569$	38.9685	1.63365	0.816823	+	0.576889i	$0.195733\pi$
$570$	0	0
$571$	−12.0000	−0.502184	−0.251092	−	0.967963i	$-0.580790\pi$
$571$	−12.0000	−0.502184	−0.251092	+	0.967963i	$0.580790\pi$
$572$	−4.00000	−0.167248
$573$	−14.1153	−0.589677
$574$	17.7622	0.741380
$575$	2.83740	0.118328
$576$	1.00000	0.0416667
$577$	−18.0000	−0.749350	−0.374675	−	0.927156i	$-0.622246\pi$
$577$	−18.0000	−0.749350	−0.374675	+	0.927156i	$0.622246\pi$
$578$	−1.00000	−0.0415945
$579$	23.3654	0.971031
$580$	2.44055	0.101338
$581$	−35.5244	−1.47380
$582$	−1.23424	−0.0511609
$583$	14.1591	0.586408
$584$	−1.60316	−0.0663391
$585$	4.00000	0.165380
$586$	20.9248	0.864396
$587$	14.2744	0.589167	0.294584	−	0.955626i	$-0.404819\pi$
$587$	14.2744	0.589167	0.294584	+	0.955626i	$0.404819\pi$
$588$	−1.04371	−0.0430418
$589$	0	0
$590$	5.27795	0.217290
$591$	10.1591	0.417888
$592$	−5.27795	−0.216922
$593$	44.8740	1.84275	0.921377	−	0.388670i	$-0.127065\pi$
$593$	44.8740	1.84275	0.921377	+	0.388670i	$0.127065\pi$
$594$	1.00000	0.0410305
$595$	−2.44055	−0.100053
$596$	11.2779	0.461963
$597$	17.0402	0.697407
$598$	−11.3496	−0.464119
$599$	19.0839	0.779745	0.389873	−	0.920869i	$-0.372519\pi$
$599$	19.0839	0.779745	0.389873	+	0.920869i	$0.372519\pi$
$600$	−1.00000	−0.0408248
$601$	30.9685	1.26323	0.631616	−	0.775281i	$-0.282392\pi$
$601$	30.9685	1.26323	0.631616	+	0.775281i	$0.282392\pi$
$602$	25.4807	1.03852
$603$	0.396844	0.0161607
$604$	15.2779	0.621651
$605$	1.00000	0.0406558
$606$	2.39684	0.0973651
$607$	−17.3654	−0.704838	−0.352419	−	0.935842i	$-0.614641\pi$
$607$	−17.3654	−0.704838	−0.352419	+	0.935842i	$0.614641\pi$
$608$	0	0
$609$	−5.95629	−0.241361
$610$	−2.00000	−0.0809776
$611$	−29.1118	−1.17774
$612$	1.00000	0.0404226
$613$	−10.6433	−0.429879	−0.214940	−	0.976627i	$-0.568955\pi$
$613$	−10.6433	−0.429879	−0.214940	+	0.976627i	$0.568955\pi$
$614$	22.9527	0.926297
$615$	7.27795	0.293475
$616$	−2.44055	−0.0983326
$617$	43.1118	1.73562	0.867808	−	0.496900i	$-0.165529\pi$
$617$	43.1118	1.73562	0.867808	+	0.496900i	$0.165529\pi$
$618$	−15.7185	−0.632291
$619$	35.4370	1.42433	0.712167	−	0.702010i	$-0.247714\pi$
$619$	35.4370	1.42433	0.712167	+	0.702010i	$0.247714\pi$
$620$	4.44055	0.178337
$621$	2.83740	0.113861
$622$	−6.15905	−0.246955
$623$	2.73073	0.109404
$624$	4.00000	0.160128
$625$	1.00000	0.0400000
$626$	31.7901	1.27059
$627$	0	0
$628$	8.15905	0.325582
$629$	−5.27795	−0.210446
$630$	2.44055	0.0972339
$631$	21.9929	0.875523	0.437762	−	0.899091i	$-0.355771\pi$
$631$	21.9929	0.875523	0.437762	+	0.899091i	$0.355771\pi$
$632$	14.5559	0.579002
$633$	24.5996	0.977746
$634$	17.7185	0.703691
$635$	−4.15905	−0.165047
$636$	−14.1591	−0.561443
$637$	−4.17483	−0.165413
$638$	2.44055	0.0966224
$639$	12.4843	0.493870
$640$	−1.00000	−0.0395285
$641$	−8.52797	−0.336834	−0.168417	−	0.985716i	$-0.553866\pi$
$641$	−8.52797	−0.336834	−0.168417	+	0.985716i	$0.553866\pi$
$642$	7.71850	0.304625
$643$	−28.5996	−1.12786	−0.563929	−	0.825823i	$-0.690711\pi$
$643$	−28.5996	−1.12786	−0.563929	+	0.825823i	$0.690711\pi$
$644$	−6.92481	−0.272876
$645$	10.4406	0.411096
$646$	0	0
$647$	−14.5717	−0.572872	−0.286436	−	0.958099i	$-0.592471\pi$
$647$	−14.5717	−0.572872	−0.286436	+	0.958099i	$0.592471\pi$
$648$	−1.00000	−0.0392837
$649$	5.27795	0.207178
$650$	−4.00000	−0.156893
$651$	−10.8374	−0.424751
$652$	6.04371	0.236690
$653$	5.63108	0.220361	0.110181	−	0.993912i	$-0.464857\pi$
$653$	5.63108	0.220361	0.110181	+	0.993912i	$0.464857\pi$
$654$	10.8811	0.425485
$655$	17.7622	0.694027
$656$	7.27795	0.284156
$657$	1.60316	0.0625451
$658$	−17.7622	−0.692443
$659$	−4.20276	−0.163716	−0.0818581	−	0.996644i	$-0.526085\pi$
$659$	−4.20276	−0.163716	−0.0818581	+	0.996644i	$0.526085\pi$
$660$	−1.00000	−0.0389249
$661$	34.8811	1.35672	0.678359	−	0.734731i	$-0.262692\pi$
$661$	34.8811	1.35672	0.678359	+	0.734731i	$0.262692\pi$
$662$	−1.95629	−0.0760335
$663$	4.00000	0.155347
$664$	−14.5559	−0.564878
$665$	0	0
$666$	5.27795	0.204516
$667$	6.92481	0.268130
$668$	16.1591	0.625212
$669$	9.16260	0.354247
$670$	−0.396844	−0.0153314
$671$	−2.00000	−0.0772091
$672$	2.44055	0.0941463
$673$	9.51574	0.366805	0.183402	−	0.983038i	$-0.441289\pi$
$673$	9.51574	0.366805	0.183402	+	0.983038i	$0.441289\pi$
$674$	19.3654	0.745926
$675$	1.00000	0.0384900
$676$	3.00000	0.115385
$677$	−29.2779	−1.12524	−0.562621	−	0.826715i	$-0.690207\pi$
$677$	−29.2779	−1.12524	−0.562621	+	0.826715i	$0.690207\pi$
$678$	−2.00000	−0.0768095
$679$	−3.01223	−0.115599
$680$	−1.00000	−0.0383482
$681$	26.3618	1.01019
$682$	4.44055	0.170038
$683$	−5.76221	−0.220485	−0.110242	−	0.993905i	$-0.535163\pi$
$683$	−5.76221	−0.220485	−0.110242	+	0.993905i	$0.535163\pi$
$684$	0	0
$685$	−18.5996	−0.710654
$686$	−19.6311	−0.749518
$687$	5.11890	0.195298
$688$	10.4406	0.398042
$689$	−56.6362	−2.15767
$690$	−2.83740	−0.108018
$691$	0.968518	0.0368442	0.0184221	−	0.999830i	$-0.494136\pi$
$691$	0.968518	0.0368442	0.0184221	+	0.999830i	$0.494136\pi$
$692$	−8.48426	−0.322523
$693$	2.44055	0.0927089
$694$	16.9685	0.644116
$695$	18.9248	0.717859
$696$	−2.44055	−0.0925089
$697$	7.27795	0.275672
$698$	−16.4843	−0.623938
$699$	−17.7185	−0.670175
$700$	−2.44055	−0.0922442
$701$	20.9527	0.791374	0.395687	−	0.918385i	$-0.370507\pi$
$701$	20.9527	0.791374	0.395687	+	0.918385i	$0.370507\pi$
$702$	−4.00000	−0.150970
$703$	0	0
$704$	−1.00000	−0.0376889
$705$	−7.27795	−0.274103
$706$	−3.16260	−0.119026
$707$	5.84962	0.219998
$708$	−5.27795	−0.198357
$709$	−26.2465	−0.985707	−0.492853	−	0.870112i	$-0.664046\pi$
$709$	−26.2465	−0.985707	−0.492853	+	0.870112i	$0.664046\pi$
$710$	−12.4843	−0.468526
$711$	−14.5559	−0.545889
$712$	1.11890	0.0419324
$713$	12.5996	0.471859
$714$	2.44055	0.0913354
$715$	−4.00000	−0.149592
$716$	−1.27795	−0.0477591
$717$	−7.43700	−0.277740
$718$	−1.67479	−0.0625027
$719$	25.5960	0.954572	0.477286	−	0.878748i	$-0.341621\pi$
$719$	25.5960	0.954572	0.477286	+	0.878748i	$0.341621\pi$
$720$	1.00000	0.0372678
$721$	−38.3618	−1.42867
$722$	19.0000	0.707107
$723$	17.7185	0.658958
$724$	17.8775	0.664414
$725$	2.44055	0.0906398
$726$	−1.00000	−0.0371135
$727$	44.6870	1.65735	0.828675	−	0.559730i	$-0.189095\pi$
$727$	44.6870	1.65735	0.828675	+	0.559730i	$0.189095\pi$
$728$	9.76221	0.361811
$729$	1.00000	0.0370370
$730$	−1.60316	−0.0593355
$731$	10.4406	0.386158
$732$	2.00000	0.0739221
$733$	−44.9685	−1.66095	−0.830475	−	0.557056i	$-0.811931\pi$
$733$	−44.9685	−1.66095	−0.830475	+	0.557056i	$0.811931\pi$
$734$	35.1118	1.29600
$735$	−1.04371	−0.0384977
$736$	−2.83740	−0.104588
$737$	−0.396844	−0.0146179
$738$	−7.27795	−0.267905
$739$	4.56300	0.167853	0.0839264	−	0.996472i	$-0.473254\pi$
$739$	4.56300	0.167853	0.0839264	+	0.996472i	$0.473254\pi$
$740$	−5.27795	−0.194021
$741$	0	0
$742$	−34.5559	−1.26859
$743$	−44.5646	−1.63492	−0.817458	−	0.575989i	$-0.804617\pi$
$743$	−44.5646	−1.63492	−0.817458	+	0.575989i	$0.804617\pi$
$744$	−4.44055	−0.162799
$745$	11.2779	0.413192
$746$	18.6433	0.682580
$747$	14.5559	0.532572
$748$	−1.00000	−0.0365636
$749$	18.8374	0.688303
$750$	−1.00000	−0.0365148
$751$	−13.2342	−0.482924	−0.241462	−	0.970410i	$-0.577627\pi$
$751$	−13.2342	−0.482924	−0.241462	+	0.970410i	$0.577627\pi$
$752$	−7.27795	−0.265399
$753$	14.9527	0.544908
$754$	−9.76221	−0.355519
$755$	15.2779	0.556021
$756$	−2.44055	−0.0887620
$757$	−9.79724	−0.356087	−0.178043	−	0.984023i	$-0.556977\pi$
$757$	−9.79724	−0.356087	−0.178043	+	0.984023i	$0.556977\pi$
$758$	−38.0803	−1.38314
$759$	−2.83740	−0.102991
$760$	0	0
$761$	−14.3689	−0.520873	−0.260436	−	0.965491i	$-0.583866\pi$
$761$	−14.3689	−0.520873	−0.260436	+	0.965491i	$0.583866\pi$
$762$	4.15905	0.150667
$763$	26.5559	0.961388
$764$	−14.1153	−0.510675
$765$	1.00000	0.0361551
$766$	−33.0402	−1.19379
$767$	−21.1118	−0.762303
$768$	1.00000	0.0360844
$769$	−5.34958	−0.192911	−0.0964554	−	0.995337i	$-0.530751\pi$
$769$	−5.34958	−0.192911	−0.0964554	+	0.995337i	$0.530751\pi$
$770$	−2.44055	−0.0879514
$771$	2.59960	0.0936224
$772$	23.3654	0.840938
$773$	−20.7149	−0.745065	−0.372532	−	0.928019i	$-0.621510\pi$
$773$	−20.7149	−0.745065	−0.372532	+	0.928019i	$0.621510\pi$
$774$	−10.4406	−0.375278
$775$	4.44055	0.159509
$776$	−1.23424	−0.0443066
$777$	12.8811	0.462107
$778$	4.08742	0.146541
$779$	0	0
$780$	4.00000	0.143223
$781$	−12.4843	−0.446722
$782$	−2.83740	−0.101465
$783$	2.44055	0.0872182
$784$	−1.04371	−0.0372753
$785$	8.15905	0.291209
$786$	−17.7622	−0.633557
$787$	41.9055	1.49377	0.746884	−	0.664954i	$-0.231549\pi$
$787$	41.9055	1.49377	0.746884	+	0.664954i	$0.231549\pi$
$788$	10.1591	0.361901
$789$	6.04371	0.215162
$790$	14.5559	0.517875
$791$	−4.88110	−0.173552
$792$	1.00000	0.0355335
$793$	8.00000	0.284088
$794$	24.4843	0.868914
$795$	−14.1591	−0.502170
$796$	17.0402	0.603972
$797$	31.9213	1.13071	0.565354	−	0.824848i	$-0.308739\pi$
$797$	31.9213	1.13071	0.565354	+	0.824848i	$0.308739\pi$
$798$	0	0
$799$	−7.27795	−0.257475
$800$	−1.00000	−0.0353553
$801$	−1.11890	−0.0395343
$802$	34.9964	1.23577
$803$	−1.60316	−0.0565741
$804$	0.396844	0.0139956
$805$	−6.92481	−0.244068
$806$	−17.7622	−0.625647
$807$	−10.0000	−0.352017
$808$	2.39684	0.0843207
$809$	37.1276	1.30534	0.652668	−	0.757644i	$-0.273650\pi$
$809$	37.1276	1.30534	0.652668	+	0.757644i	$0.273650\pi$
$810$	−1.00000	−0.0351364
$811$	5.76221	0.202338	0.101169	−	0.994869i	$-0.467742\pi$
$811$	5.76221	0.202338	0.101169	+	0.994869i	$0.467742\pi$
$812$	−5.95629	−0.209025
$813$	15.6469	0.548759
$814$	−5.27795	−0.184992
$815$	6.04371	0.211702
$816$	1.00000	0.0350070
$817$	0	0
$818$	−27.6748	−0.967626
$819$	−9.76221	−0.341119
$820$	7.27795	0.254157
$821$	8.76576	0.305927	0.152964	−	0.988232i	$-0.451118\pi$
$821$	8.76576	0.305927	0.152964	+	0.988232i	$0.451118\pi$
$822$	18.5996	0.648736
$823$	13.5244	0.471431	0.235716	−	0.971822i	$-0.424257\pi$
$823$	13.5244	0.471431	0.235716	+	0.971822i	$0.424257\pi$
$824$	−15.7185	−0.547580
$825$	−1.00000	−0.0348155
$826$	−12.8811	−0.448191
$827$	−46.8374	−1.62870	−0.814348	−	0.580377i	$-0.802905\pi$
$827$	−46.8374	−1.62870	−0.814348	+	0.580377i	$0.802905\pi$
$828$	2.83740	0.0986063
$829$	−6.31810	−0.219437	−0.109718	−	0.993963i	$-0.534995\pi$
$829$	−6.31810	−0.219437	−0.109718	+	0.993963i	$0.534995\pi$
$830$	−14.5559	−0.505242
$831$	−2.00000	−0.0693792
$832$	4.00000	0.138675
$833$	−1.04371	−0.0361623
$834$	−18.9248	−0.655313
$835$	16.1591	0.559207
$836$	0	0
$837$	4.44055	0.153488
$838$	17.3933	0.600841
$839$	−36.8024	−1.27056	−0.635279	−	0.772282i	$-0.719115\pi$
$839$	−36.8024	−1.27056	−0.635279	+	0.772282i	$0.719115\pi$
$840$	2.44055	0.0842070
$841$	−23.0437	−0.794611
$842$	−32.6433	−1.12496
$843$	−0.0437076	−0.00150537
$844$	24.5996	0.846753
$845$	3.00000	0.103203
$846$	7.27795	0.250221
$847$	−2.44055	−0.0838583
$848$	−14.1591	−0.486224
$849$	−8.08742	−0.277559
$850$	−1.00000	−0.0342997
$851$	−14.9756	−0.513358
$852$	12.4843	0.427704
$853$	0.837396	0.0286719	0.0143359	−	0.999897i	$-0.495437\pi$
$853$	0.837396	0.0286719	0.0143359	+	0.999897i	$0.495437\pi$
$854$	4.88110	0.167028
$855$	0	0
$856$	7.71850	0.263813
$857$	−47.7114	−1.62979	−0.814895	−	0.579609i	$-0.803205\pi$
$857$	−47.7114	−1.62979	−0.814895	+	0.579609i	$0.803205\pi$
$858$	4.00000	0.136558
$859$	2.51929	0.0859572	0.0429786	−	0.999076i	$-0.486315\pi$
$859$	2.51929	0.0859572	0.0429786	+	0.999076i	$0.486315\pi$
$860$	10.4406	0.356020
$861$	−17.7622	−0.605334
$862$	34.0366	1.15929
$863$	17.0402	0.580054	0.290027	−	0.957019i	$-0.406336\pi$
$863$	17.0402	0.580054	0.290027	+	0.957019i	$0.406336\pi$
$864$	−1.00000	−0.0340207
$865$	−8.48426	−0.288473
$866$	−19.6748	−0.668577
$867$	1.00000	0.0339618
$868$	−10.8374	−0.367845
$869$	14.5559	0.493775
$870$	−2.44055	−0.0827425
$871$	1.58738	0.0537862
$872$	10.8811	0.368481
$873$	1.23424	0.0417727
$874$	0	0
$875$	−2.44055	−0.0825057
$876$	1.60316	0.0541656
$877$	52.5051	1.77297	0.886485	−	0.462757i	$-0.153140\pi$
$877$	52.5051	1.77297	0.886485	+	0.462757i	$0.153140\pi$
$878$	−21.6748	−0.731489
$879$	−20.9248	−0.705776
$880$	−1.00000	−0.0337100
$881$	13.0036	0.438101	0.219050	−	0.975714i	$-0.429704\pi$
$881$	13.0036	0.438101	0.219050	+	0.975714i	$0.429704\pi$
$882$	1.04371	0.0351435
$883$	−21.5086	−0.723823	−0.361912	−	0.932212i	$-0.617876\pi$
$883$	−21.5086	−0.723823	−0.361912	+	0.932212i	$0.617876\pi$
$884$	4.00000	0.134535
$885$	−5.27795	−0.177416
$886$	2.74998	0.0923874
$887$	−30.6275	−1.02837	−0.514186	−	0.857679i	$-0.671906\pi$
$887$	−30.6275	−1.02837	−0.514186	+	0.857679i	$0.671906\pi$
$888$	5.27795	0.177116
$889$	10.1504	0.340433
$890$	1.11890	0.0375055
$891$	−1.00000	−0.0335013
$892$	9.16260	0.306787
$893$	0	0
$894$	−11.2779	−0.377191
$895$	−1.27795	−0.0427171
$896$	2.44055	0.0815331
$897$	11.3496	0.378952
$898$	34.4334	1.14906
$899$	10.8374	0.361447
$900$	1.00000	0.0333333
$901$	−14.1591	−0.471706
$902$	7.27795	0.242329
$903$	−25.4807	−0.847945
$904$	−2.00000	−0.0665190
$905$	17.8775	0.594270
$906$	−15.2779	−0.507576
$907$	−30.0437	−0.997585	−0.498792	−	0.866721i	$-0.666223\pi$
$907$	−30.0437	−0.997585	−0.498792	+	0.866721i	$0.666223\pi$
$908$	26.3618	0.874847
$909$	−2.39684	−0.0794983
$910$	9.76221	0.323614
$911$	−49.3654	−1.63555	−0.817774	−	0.575540i	$-0.804792\pi$
$911$	−49.3654	−1.63555	−0.817774	+	0.575540i	$0.804792\pi$
$912$	0	0
$913$	−14.5559	−0.481730
$914$	−26.9685	−0.892039
$915$	2.00000	0.0661180
$916$	5.11890	0.169133
$917$	−43.3496	−1.43153
$918$	−1.00000	−0.0330049
$919$	9.79724	0.323181	0.161591	−	0.986858i	$-0.448338\pi$
$919$	9.79724	0.323181	0.161591	+	0.986858i	$0.448338\pi$
$920$	−2.83740	−0.0935462
$921$	−22.9527	−0.756318
$922$	−27.3654	−0.901230
$923$	49.9370	1.64370
$924$	2.44055	0.0802883
$925$	−5.27795	−0.173538
$926$	−28.3181	−0.930591
$927$	15.7185	0.516263
$928$	−2.44055	−0.0801150
$929$	−13.9721	−0.458409	−0.229204	−	0.973378i	$-0.573612\pi$
$929$	−13.9721	−0.458409	−0.229204	+	0.973378i	$0.573612\pi$
$930$	−4.44055	−0.145611
$931$	0	0
$932$	−17.7185	−0.580389
$933$	6.15905	0.201638
$934$	−11.3496	−0.371370
$935$	−1.00000	−0.0327035
$936$	−4.00000	−0.130744
$937$	25.5244	0.833846	0.416923	−	0.908942i	$-0.363108\pi$
$937$	25.5244	0.833846	0.416923	+	0.908942i	$0.363108\pi$
$938$	0.968518	0.0316232
$939$	−31.7901	−1.03743
$940$	−7.27795	−0.237380
$941$	17.4528	0.568944	0.284472	−	0.958684i	$-0.408182\pi$
$941$	17.4528	0.568944	0.284472	+	0.958684i	$0.408182\pi$
$942$	−8.15905	−0.265836
$943$	20.6504	0.672470
$944$	−5.27795	−0.171783
$945$	−2.44055	−0.0793912
$946$	10.4406	0.339452
$947$	−54.7866	−1.78032	−0.890162	−	0.455644i	$-0.849409\pi$
$947$	−54.7866	−1.78032	−0.890162	+	0.455644i	$0.849409\pi$
$948$	−14.5559	−0.472753
$949$	6.41262	0.208163
$950$	0	0
$951$	−17.7185	−0.574562
$952$	2.44055	0.0790987
$953$	10.3181	0.334236	0.167118	−	0.985937i	$-0.446554\pi$
$953$	10.3181	0.334236	0.167118	+	0.985937i	$0.446554\pi$
$954$	14.1591	0.458416
$955$	−14.1153	−0.456762
$956$	−7.43700	−0.240530
$957$	−2.44055	−0.0788918
$958$	14.5996	0.471692
$959$	45.3933	1.46583
$960$	1.00000	0.0322749
$961$	−11.2815	−0.363919
$962$	21.1118	0.680671
$963$	−7.71850	−0.248725
$964$	17.7185	0.570674
$965$	23.3654	0.752158
$966$	6.92481	0.222802
$967$	−55.0330	−1.76974	−0.884872	−	0.465835i	$-0.845754\pi$
$967$	−55.0330	−1.76974	−0.884872	+	0.465835i	$0.845754\pi$
$968$	−1.00000	−0.0321412
$969$	0	0
$970$	−1.23424	−0.0396291
$971$	28.7149	0.921506	0.460753	−	0.887528i	$-0.347579\pi$
$971$	28.7149	0.921506	0.460753	+	0.887528i	$0.347579\pi$
$972$	1.00000	0.0320750
$973$	−46.1870	−1.48069
$974$	−27.1118	−0.868718
$975$	4.00000	0.128103
$976$	2.00000	0.0640184
$977$	16.0803	0.514455	0.257227	−	0.966351i	$-0.417191\pi$
$977$	16.0803	0.514455	0.257227	+	0.966351i	$0.417191\pi$
$978$	−6.04371	−0.193256
$979$	1.11890	0.0357601
$980$	−1.04371	−0.0333400
$981$	−10.8811	−0.347407
$982$	10.9527	0.349516
$983$	−34.9248	−1.11393	−0.556964	−	0.830536i	$-0.688034\pi$
$983$	−34.9248	−1.11393	−0.556964	+	0.830536i	$0.688034\pi$
$984$	−7.27795	−0.232012
$985$	10.1591	0.323694
$986$	−2.44055	−0.0777230
$987$	17.7622	0.565377
$988$	0	0
$989$	29.6240	0.941988
$990$	1.00000	0.0317821
$991$	61.9579	1.96816	0.984078	−	0.177737i	$-0.0568775\pi$
$991$	61.9579	1.96816	0.984078	+	0.177737i	$0.0568775\pi$
$992$	−4.44055	−0.140988
$993$	1.95629	0.0620811
$994$	30.4685	0.966401
$995$	17.0402	0.540209
$996$	14.5559	0.461221
$997$	−28.0437	−0.888153	−0.444077	−	0.895989i	$-0.646468\pi$
$997$	−28.0437	−0.888153	−0.444077	+	0.895989i	$0.646468\pi$
$998$	23.5244	0.744652
$999$	−5.27795	−0.166987

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5610.2.a.cb.1.1	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5610.2.a.cb.1.1	✓	3	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 5610 = 2 \cdot 3 \cdot 5 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5610.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -2.44055 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -2.44055 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -1.00000 q^{11} +1.00000 q^{12} +4.00000 q^{13} +2.44055 q^{14} +1.00000 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} +1.00000 q^{20} -2.44055 q^{21} +1.00000 q^{22} +2.83740 q^{23} -1.00000 q^{24} +1.00000 q^{25} -4.00000 q^{26} +1.00000 q^{27} -2.44055 q^{28} +2.44055 q^{29} -1.00000 q^{30} +4.44055 q^{31} -1.00000 q^{32} -1.00000 q^{33} -1.00000 q^{34} -2.44055 q^{35} +1.00000 q^{36} -5.27795 q^{37} +4.00000 q^{39} -1.00000 q^{40} +7.27795 q^{41} +2.44055 q^{42} +10.4406 q^{43} -1.00000 q^{44} +1.00000 q^{45} -2.83740 q^{46} -7.27795 q^{47} +1.00000 q^{48} -1.04371 q^{49} -1.00000 q^{50} +1.00000 q^{51} +4.00000 q^{52} -14.1591 q^{53} -1.00000 q^{54} -1.00000 q^{55} +2.44055 q^{56} -2.44055 q^{58} -5.27795 q^{59} +1.00000 q^{60} +2.00000 q^{61} -4.44055 q^{62} -2.44055 q^{63} +1.00000 q^{64} +4.00000 q^{65} +1.00000 q^{66} +0.396844 q^{67} +1.00000 q^{68} +2.83740 q^{69} +2.44055 q^{70} +12.4843 q^{71} -1.00000 q^{72} +1.60316 q^{73} +5.27795 q^{74} +1.00000 q^{75} +2.44055 q^{77} -4.00000 q^{78} -14.5559 q^{79} +1.00000 q^{80} +1.00000 q^{81} -7.27795 q^{82} +14.5559 q^{83} -2.44055 q^{84} +1.00000 q^{85} -10.4406 q^{86} +2.44055 q^{87} +1.00000 q^{88} -1.11890 q^{89} -1.00000 q^{90} -9.76221 q^{91} +2.83740 q^{92} +4.44055 q^{93} +7.27795 q^{94} -1.00000 q^{96} +1.23424 q^{97} +1.04371 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} + 3 q^{5} - 3 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 + 3 * q^5 - 3 * q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9	\( 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} + 3 q^{5} - 3 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9} - 3 q^{10} - 3 q^{11} + 3 q^{12} + 12 q^{13} - 3 q^{14} + 3 q^{15} + 3 q^{16} + 3 q^{17} - 3 q^{18} + 3 q^{20} + 3 q^{21} + 3 q^{22} - q^{23} - 3 q^{24} + 3 q^{25} - 12 q^{26} + 3 q^{27} + 3 q^{28} - 3 q^{29} - 3 q^{30} + 3 q^{31} - 3 q^{32} - 3 q^{33} - 3 q^{34} + 3 q^{35} + 3 q^{36} + 4 q^{37} + 12 q^{39} - 3 q^{40} + 2 q^{41} - 3 q^{42} + 21 q^{43} - 3 q^{44} + 3 q^{45} + q^{46} - 2 q^{47} + 3 q^{48} + 8 q^{49} - 3 q^{50} + 3 q^{51} + 12 q^{52} - 2 q^{53} - 3 q^{54} - 3 q^{55} - 3 q^{56} + 3 q^{58} + 4 q^{59} + 3 q^{60} + 6 q^{61} - 3 q^{62} + 3 q^{63} + 3 q^{64} + 12 q^{65} + 3 q^{66} + 2 q^{67} + 3 q^{68} - q^{69} - 3 q^{70} + 16 q^{71} - 3 q^{72} + 4 q^{73} - 4 q^{74} + 3 q^{75} - 3 q^{77} - 12 q^{78} - 4 q^{79} + 3 q^{80} + 3 q^{81} - 2 q^{82} + 4 q^{83} + 3 q^{84} + 3 q^{85} - 21 q^{86} - 3 q^{87} + 3 q^{88} - 24 q^{89} - 3 q^{90} + 12 q^{91} - q^{92} + 3 q^{93} + 2 q^{94} - 3 q^{96} - 5 q^{97} - 8 q^{98} - 3 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 + 3 * q^5 - 3 * q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9 - 3 * q^10 - 3 * q^11 + 3 * q^12 + 12 * q^13 - 3 * q^14 + 3 * q^15 + 3 * q^16 + 3 * q^17 - 3 * q^18 + 3 * q^20 + 3 * q^21 + 3 * q^22 - q^23 - 3 * q^24 + 3 * q^25 - 12 * q^26 + 3 * q^27 + 3 * q^28 - 3 * q^29 - 3 * q^30 + 3 * q^31 - 3 * q^32 - 3 * q^33 - 3 * q^34 + 3 * q^35 + 3 * q^36 + 4 * q^37 + 12 * q^39 - 3 * q^40 + 2 * q^41 - 3 * q^42 + 21 * q^43 - 3 * q^44 + 3 * q^45 + q^46 - 2 * q^47 + 3 * q^48 + 8 * q^49 - 3 * q^50 + 3 * q^51 + 12 * q^52 - 2 * q^53 - 3 * q^54 - 3 * q^55 - 3 * q^56 + 3 * q^58 + 4 * q^59 + 3 * q^60 + 6 * q^61 - 3 * q^62 + 3 * q^63 + 3 * q^64 + 12 * q^65 + 3 * q^66 + 2 * q^67 + 3 * q^68 - q^69 - 3 * q^70 + 16 * q^71 - 3 * q^72 + 4 * q^73 - 4 * q^74 + 3 * q^75 - 3 * q^77 - 12 * q^78 - 4 * q^79 + 3 * q^80 + 3 * q^81 - 2 * q^82 + 4 * q^83 + 3 * q^84 + 3 * q^85 - 21 * q^86 - 3 * q^87 + 3 * q^88 - 24 * q^89 - 3 * q^90 + 12 * q^91 - q^92 + 3 * q^93 + 2 * q^94 - 3 * q^96 - 5 * q^97 - 8 * q^98 - 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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