LMFDB - Embedded newform 5610.2.a.bv.1.2

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:	$2$
Coefficient field:	$\Q(\sqrt{41}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 10 $ x^2 - x - 10
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-2.70156$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +1.70156 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +1.70156 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -1.00000 q^{11} -1.00000 q^{12} -3.70156 q^{13} +1.70156 q^{14} -1.00000 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} +5.70156 q^{19} +1.00000 q^{20} -1.70156 q^{21} -1.00000 q^{22} +1.70156 q^{23} -1.00000 q^{24} +1.00000 q^{25} -3.70156 q^{26} -1.00000 q^{27} +1.70156 q^{28} -2.00000 q^{29} -1.00000 q^{30} +1.70156 q^{31} +1.00000 q^{32} +1.00000 q^{33} +1.00000 q^{34} +1.70156 q^{35} +1.00000 q^{36} -3.70156 q^{37} +5.70156 q^{38} +3.70156 q^{39} +1.00000 q^{40} +10.0000 q^{41} -1.70156 q^{42} +4.00000 q^{43} -1.00000 q^{44} +1.00000 q^{45} +1.70156 q^{46} -3.40312 q^{47} -1.00000 q^{48} -4.10469 q^{49} +1.00000 q^{50} -1.00000 q^{51} -3.70156 q^{52} -2.00000 q^{53} -1.00000 q^{54} -1.00000 q^{55} +1.70156 q^{56} -5.70156 q^{57} -2.00000 q^{58} +4.00000 q^{59} -1.00000 q^{60} +11.1047 q^{61} +1.70156 q^{62} +1.70156 q^{63} +1.00000 q^{64} -3.70156 q^{65} +1.00000 q^{66} -2.29844 q^{67} +1.00000 q^{68} -1.70156 q^{69} +1.70156 q^{70} +11.4031 q^{71} +1.00000 q^{72} -1.40312 q^{73} -3.70156 q^{74} -1.00000 q^{75} +5.70156 q^{76} -1.70156 q^{77} +3.70156 q^{78} -3.40312 q^{79} +1.00000 q^{80} +1.00000 q^{81} +10.0000 q^{82} -2.29844 q^{83} -1.70156 q^{84} +1.00000 q^{85} +4.00000 q^{86} +2.00000 q^{87} -1.00000 q^{88} +10.0000 q^{89} +1.00000 q^{90} -6.29844 q^{91} +1.70156 q^{92} -1.70156 q^{93} -3.40312 q^{94} +5.70156 q^{95} -1.00000 q^{96} +15.1047 q^{97} -4.10469 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} - 3 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 - 2 * q^6 - 3 * q^7 + 2 * q^8 + 2 * q^9	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} - 3 q^{7} + 2 q^{8} + 2 q^{9} + 2 q^{10} - 2 q^{11} - 2 q^{12} - q^{13} - 3 q^{14} - 2 q^{15} + 2 q^{16} + 2 q^{17} + 2 q^{18} + 5 q^{19} + 2 q^{20} + 3 q^{21} - 2 q^{22} - 3 q^{23} - 2 q^{24} + 2 q^{25} - q^{26} - 2 q^{27} - 3 q^{28} - 4 q^{29} - 2 q^{30} - 3 q^{31} + 2 q^{32} + 2 q^{33} + 2 q^{34} - 3 q^{35} + 2 q^{36} - q^{37} + 5 q^{38} + q^{39} + 2 q^{40} + 20 q^{41} + 3 q^{42} + 8 q^{43} - 2 q^{44} + 2 q^{45} - 3 q^{46} + 6 q^{47} - 2 q^{48} + 11 q^{49} + 2 q^{50} - 2 q^{51} - q^{52} - 4 q^{53} - 2 q^{54} - 2 q^{55} - 3 q^{56} - 5 q^{57} - 4 q^{58} + 8 q^{59} - 2 q^{60} + 3 q^{61} - 3 q^{62} - 3 q^{63} + 2 q^{64} - q^{65} + 2 q^{66} - 11 q^{67} + 2 q^{68} + 3 q^{69} - 3 q^{70} + 10 q^{71} + 2 q^{72} + 10 q^{73} - q^{74} - 2 q^{75} + 5 q^{76} + 3 q^{77} + q^{78} + 6 q^{79} + 2 q^{80} + 2 q^{81} + 20 q^{82} - 11 q^{83} + 3 q^{84} + 2 q^{85} + 8 q^{86} + 4 q^{87} - 2 q^{88} + 20 q^{89} + 2 q^{90} - 19 q^{91} - 3 q^{92} + 3 q^{93} + 6 q^{94} + 5 q^{95} - 2 q^{96} + 11 q^{97} + 11 q^{98} - 2 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 - 2 * q^6 - 3 * q^7 + 2 * q^8 + 2 * q^9 + 2 * q^10 - 2 * q^11 - 2 * q^12 - q^13 - 3 * q^14 - 2 * q^15 + 2 * q^16 + 2 * q^17 + 2 * q^18 + 5 * q^19 + 2 * q^20 + 3 * q^21 - 2 * q^22 - 3 * q^23 - 2 * q^24 + 2 * q^25 - q^26 - 2 * q^27 - 3 * q^28 - 4 * q^29 - 2 * q^30 - 3 * q^31 + 2 * q^32 + 2 * q^33 + 2 * q^34 - 3 * q^35 + 2 * q^36 - q^37 + 5 * q^38 + q^39 + 2 * q^40 + 20 * q^41 + 3 * q^42 + 8 * q^43 - 2 * q^44 + 2 * q^45 - 3 * q^46 + 6 * q^47 - 2 * q^48 + 11 * q^49 + 2 * q^50 - 2 * q^51 - q^52 - 4 * q^53 - 2 * q^54 - 2 * q^55 - 3 * q^56 - 5 * q^57 - 4 * q^58 + 8 * q^59 - 2 * q^60 + 3 * q^61 - 3 * q^62 - 3 * q^63 + 2 * q^64 - q^65 + 2 * q^66 - 11 * q^67 + 2 * q^68 + 3 * q^69 - 3 * q^70 + 10 * q^71 + 2 * q^72 + 10 * q^73 - q^74 - 2 * q^75 + 5 * q^76 + 3 * q^77 + q^78 + 6 * q^79 + 2 * q^80 + 2 * q^81 + 20 * q^82 - 11 * q^83 + 3 * q^84 + 2 * q^85 + 8 * q^86 + 4 * q^87 - 2 * q^88 + 20 * q^89 + 2 * q^90 - 19 * q^91 - 3 * q^92 + 3 * q^93 + 6 * q^94 + 5 * q^95 - 2 * q^96 + 11 * q^97 + 11 * q^98 - 2 * 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
$7$	1.70156	0.643130	0.321565	−	0.946888i	$-0.395791\pi$
$7$	1.70156	0.643130	0.321565	+	0.946888i	$0.395791\pi$
$8$	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
$13$	−3.70156	−1.02663	−0.513314	−	0.858201i	$-0.671582\pi$
$13$	−3.70156	−1.02663	−0.513314	+	0.858201i	$0.671582\pi$
$14$	1.70156	0.454762
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	1.00000	0.235702
$19$	5.70156	1.30803	0.654014	−	0.756482i	$-0.273084\pi$
$19$	5.70156	1.30803	0.654014	+	0.756482i	$0.273084\pi$
$20$	1.00000	0.223607
$21$	−1.70156	−0.371311
$22$	−1.00000	−0.213201
$23$	1.70156	0.354800	0.177400	−	0.984139i	$-0.443231\pi$
$23$	1.70156	0.354800	0.177400	+	0.984139i	$0.443231\pi$
$24$	−1.00000	−0.204124
$25$	1.00000	0.200000
$26$	−3.70156	−0.725936
$27$	−1.00000	−0.192450
$28$	1.70156	0.321565
$29$	−2.00000	−0.371391	−0.185695	−	0.982607i	$-0.559454\pi$
$29$	−2.00000	−0.371391	−0.185695	+	0.982607i	$0.559454\pi$
$30$	−1.00000	−0.182574
$31$	1.70156	0.305610	0.152805	−	0.988256i	$-0.451169\pi$
$31$	1.70156	0.305610	0.152805	+	0.988256i	$0.451169\pi$
$32$	1.00000	0.176777
$33$	1.00000	0.174078
$34$	1.00000	0.171499
$35$	1.70156	0.287616
$36$	1.00000	0.166667
$37$	−3.70156	−0.608533	−0.304267	−	0.952587i	$-0.598411\pi$
$37$	−3.70156	−0.608533	−0.304267	+	0.952587i	$0.598411\pi$
$38$	5.70156	0.924916
$39$	3.70156	0.592724
$40$	1.00000	0.158114
$41$	10.0000	1.56174	0.780869	−	0.624695i	$-0.214777\pi$
$41$	10.0000	1.56174	0.780869	+	0.624695i	$0.214777\pi$
$42$	−1.70156	−0.262557
$43$	4.00000	0.609994	0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000	0.609994	0.304997	+	0.952353i	$0.401344\pi$
$44$	−1.00000	−0.150756
$45$	1.00000	0.149071
$46$	1.70156	0.250882
$47$	−3.40312	−0.496397	−0.248198	−	0.968709i	$-0.579838\pi$
$47$	−3.40312	−0.496397	−0.248198	+	0.968709i	$0.579838\pi$
$48$	−1.00000	−0.144338
$49$	−4.10469	−0.586384
$50$	1.00000	0.141421
$51$	−1.00000	−0.140028
$52$	−3.70156	−0.513314
$53$	−2.00000	−0.274721	−0.137361	−	0.990521i	$-0.543862\pi$
$53$	−2.00000	−0.274721	−0.137361	+	0.990521i	$0.543862\pi$
$54$	−1.00000	−0.136083
$55$	−1.00000	−0.134840
$56$	1.70156	0.227381
$57$	−5.70156	−0.755190
$58$	−2.00000	−0.262613
$59$	4.00000	0.520756	0.260378	−	0.965507i	$-0.416153\pi$
$59$	4.00000	0.520756	0.260378	+	0.965507i	$0.416153\pi$
$60$	−1.00000	−0.129099
$61$	11.1047	1.42181	0.710905	−	0.703288i	$-0.248286\pi$
$61$	11.1047	1.42181	0.710905	+	0.703288i	$0.248286\pi$
$62$	1.70156	0.216099
$63$	1.70156	0.214377
$64$	1.00000	0.125000
$65$	−3.70156	−0.459122
$66$	1.00000	0.123091
$67$	−2.29844	−0.280799	−0.140399	−	0.990095i	$-0.544839\pi$
$67$	−2.29844	−0.280799	−0.140399	+	0.990095i	$0.544839\pi$
$68$	1.00000	0.121268
$69$	−1.70156	−0.204844
$70$	1.70156	0.203376
$71$	11.4031	1.35330	0.676651	−	0.736304i	$-0.263431\pi$
$71$	11.4031	1.35330	0.676651	+	0.736304i	$0.263431\pi$
$72$	1.00000	0.117851
$73$	−1.40312	−0.164223	−0.0821116	−	0.996623i	$-0.526166\pi$
$73$	−1.40312	−0.164223	−0.0821116	+	0.996623i	$0.526166\pi$
$74$	−3.70156	−0.430298
$75$	−1.00000	−0.115470
$76$	5.70156	0.654014
$77$	−1.70156	−0.193911
$78$	3.70156	0.419119
$79$	−3.40312	−0.382881	−0.191441	−	0.981504i	$-0.561316\pi$
$79$	−3.40312	−0.382881	−0.191441	+	0.981504i	$0.561316\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	10.0000	1.10432
$83$	−2.29844	−0.252286	−0.126143	−	0.992012i	$-0.540260\pi$
$83$	−2.29844	−0.252286	−0.126143	+	0.992012i	$0.540260\pi$
$84$	−1.70156	−0.185656
$85$	1.00000	0.108465
$86$	4.00000	0.431331
$87$	2.00000	0.214423
$88$	−1.00000	−0.106600
$89$	10.0000	1.06000	0.529999	−	0.847998i	$-0.322192\pi$
$89$	10.0000	1.06000	0.529999	+	0.847998i	$0.322192\pi$
$90$	1.00000	0.105409
$91$	−6.29844	−0.660256
$92$	1.70156	0.177400
$93$	−1.70156	−0.176444
$94$	−3.40312	−0.351005
$95$	5.70156	0.584968
$96$	−1.00000	−0.102062
$97$	15.1047	1.53365	0.766824	−	0.641857i	$-0.221836\pi$
$97$	15.1047	1.53365	0.766824	+	0.641857i	$0.221836\pi$
$98$	−4.10469	−0.414636
$99$	−1.00000	−0.100504
$100$	1.00000	0.100000
$101$	6.00000	0.597022	0.298511	−	0.954406i	$-0.403510\pi$
$101$	6.00000	0.597022	0.298511	+	0.954406i	$0.403510\pi$
$102$	−1.00000	−0.0990148
$103$	17.7016	1.74419	0.872093	−	0.489340i	$-0.162762\pi$
$103$	17.7016	1.74419	0.872093	+	0.489340i	$0.162762\pi$
$104$	−3.70156	−0.362968
$105$	−1.70156	−0.166055
$106$	−2.00000	−0.194257
$107$	7.40312	0.715687	0.357844	−	0.933782i	$-0.383512\pi$
$107$	7.40312	0.715687	0.357844	+	0.933782i	$0.383512\pi$
$108$	−1.00000	−0.0962250
$109$	−15.1047	−1.44677	−0.723383	−	0.690447i	$-0.757414\pi$
$109$	−15.1047	−1.44677	−0.723383	+	0.690447i	$0.757414\pi$
$110$	−1.00000	−0.0953463
$111$	3.70156	0.351337
$112$	1.70156	0.160783
$113$	−6.00000	−0.564433	−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000	−0.564433	−0.282216	+	0.959351i	$0.591070\pi$
$114$	−5.70156	−0.534000
$115$	1.70156	0.158671
$116$	−2.00000	−0.185695
$117$	−3.70156	−0.342210
$118$	4.00000	0.368230
$119$	1.70156	0.155982
$120$	−1.00000	−0.0912871
$121$	1.00000	0.0909091
$122$	11.1047	1.00537
$123$	−10.0000	−0.901670
$124$	1.70156	0.152805
$125$	1.00000	0.0894427
$126$	1.70156	0.151587
$127$	0	0		−	1.00000i	$-0.5\pi$
$127$	0	0			1.00000i	$0.5\pi$
$128$	1.00000	0.0883883
$129$	−4.00000	−0.352180
$130$	−3.70156	−0.324648
$131$	5.70156	0.498148	0.249074	−	0.968484i	$-0.419874\pi$
$131$	5.70156	0.498148	0.249074	+	0.968484i	$0.419874\pi$
$132$	1.00000	0.0870388
$133$	9.70156	0.841232
$134$	−2.29844	−0.198555
$135$	−1.00000	−0.0860663
$136$	1.00000	0.0857493
$137$	0.298438	0.0254973	0.0127486	−	0.999919i	$-0.495942\pi$
$137$	0.298438	0.0254973	0.0127486	+	0.999919i	$0.495942\pi$
$138$	−1.70156	−0.144847
$139$	−22.2094	−1.88377	−0.941887	−	0.335929i	$-0.890950\pi$
$139$	−22.2094	−1.88377	−0.941887	+	0.335929i	$0.890950\pi$
$140$	1.70156	0.143808
$141$	3.40312	0.286595
$142$	11.4031	0.956929
$143$	3.70156	0.309540
$144$	1.00000	0.0833333
$145$	−2.00000	−0.166091
$146$	−1.40312	−0.116123
$147$	4.10469	0.338549
$148$	−3.70156	−0.304267
$149$	−3.70156	−0.303244	−0.151622	−	0.988439i	$-0.548450\pi$
$149$	−3.70156	−0.303244	−0.151622	+	0.988439i	$0.548450\pi$
$150$	−1.00000	−0.0816497
$151$	−8.50781	−0.692356	−0.346178	−	0.938169i	$-0.612521\pi$
$151$	−8.50781	−0.692356	−0.346178	+	0.938169i	$0.612521\pi$
$152$	5.70156	0.462458
$153$	1.00000	0.0808452
$154$	−1.70156	−0.137116
$155$	1.70156	0.136673
$156$	3.70156	0.296362
$157$	17.4031	1.38892	0.694460	−	0.719531i	$-0.255643\pi$
$157$	17.4031	1.38892	0.694460	+	0.719531i	$0.255643\pi$
$158$	−3.40312	−0.270738
$159$	2.00000	0.158610
$160$	1.00000	0.0790569
$161$	2.89531	0.228183
$162$	1.00000	0.0785674
$163$	−10.8062	−0.846411	−0.423205	−	0.906034i	$-0.639095\pi$
$163$	−10.8062	−0.846411	−0.423205	+	0.906034i	$0.639095\pi$
$164$	10.0000	0.780869
$165$	1.00000	0.0778499
$166$	−2.29844	−0.178393
$167$	−22.8062	−1.76480	−0.882400	−	0.470500i	$-0.844074\pi$
$167$	−22.8062	−1.76480	−0.882400	+	0.470500i	$0.844074\pi$
$168$	−1.70156	−0.131278
$169$	0.701562	0.0539663
$170$	1.00000	0.0766965
$171$	5.70156	0.436009
$172$	4.00000	0.304997
$173$	−15.1047	−1.14839	−0.574194	−	0.818719i	$-0.694684\pi$
$173$	−15.1047	−1.14839	−0.574194	+	0.818719i	$0.694684\pi$
$174$	2.00000	0.151620
$175$	1.70156	0.128626
$176$	−1.00000	−0.0753778
$177$	−4.00000	−0.300658
$178$	10.0000	0.749532
$179$	2.29844	0.171793	0.0858967	−	0.996304i	$-0.472625\pi$
$179$	2.29844	0.171793	0.0858967	+	0.996304i	$0.472625\pi$
$180$	1.00000	0.0745356
$181$	2.59688	0.193024	0.0965121	−	0.995332i	$-0.469231\pi$
$181$	2.59688	0.193024	0.0965121	+	0.995332i	$0.469231\pi$
$182$	−6.29844	−0.466871
$183$	−11.1047	−0.820882
$184$	1.70156	0.125441
$185$	−3.70156	−0.272144
$186$	−1.70156	−0.124765
$187$	−1.00000	−0.0731272
$188$	−3.40312	−0.248198
$189$	−1.70156	−0.123770
$190$	5.70156	0.413635
$191$	16.0000	1.15772	0.578860	−	0.815427i	$-0.303498\pi$
$191$	16.0000	1.15772	0.578860	+	0.815427i	$0.303498\pi$
$192$	−1.00000	−0.0721688
$193$	13.4031	0.964778	0.482389	−	0.875957i	$-0.339769\pi$
$193$	13.4031	0.964778	0.482389	+	0.875957i	$0.339769\pi$
$194$	15.1047	1.08445
$195$	3.70156	0.265074
$196$	−4.10469	−0.293192
$197$	15.7016	1.11869	0.559345	−	0.828935i	$-0.311053\pi$
$197$	15.7016	1.11869	0.559345	+	0.828935i	$0.311053\pi$
$198$	−1.00000	−0.0710669
$199$	9.70156	0.687726	0.343863	−	0.939020i	$-0.388265\pi$
$199$	9.70156	0.687726	0.343863	+	0.939020i	$0.388265\pi$
$200$	1.00000	0.0707107
$201$	2.29844	0.162119
$202$	6.00000	0.422159
$203$	−3.40312	−0.238852
$204$	−1.00000	−0.0700140
$205$	10.0000	0.698430
$206$	17.7016	1.23333
$207$	1.70156	0.118267
$208$	−3.70156	−0.256657
$209$	−5.70156	−0.394385
$210$	−1.70156	−0.117419
$211$	15.4031	1.06039	0.530197	−	0.847874i	$-0.322118\pi$
$211$	15.4031	1.06039	0.530197	+	0.847874i	$0.322118\pi$
$212$	−2.00000	−0.137361
$213$	−11.4031	−0.781329
$214$	7.40312	0.506067
$215$	4.00000	0.272798
$216$	−1.00000	−0.0680414
$217$	2.89531	0.196547
$218$	−15.1047	−1.02302
$219$	1.40312	0.0948143
$220$	−1.00000	−0.0674200
$221$	−3.70156	−0.248994
$222$	3.70156	0.248433
$223$	−9.70156	−0.649665	−0.324832	−	0.945772i	$-0.605308\pi$
$223$	−9.70156	−0.649665	−0.324832	+	0.945772i	$0.605308\pi$
$224$	1.70156	0.113690
$225$	1.00000	0.0666667
$226$	−6.00000	−0.399114
$227$	−0.596876	−0.0396160	−0.0198080	−	0.999804i	$-0.506306\pi$
$227$	−0.596876	−0.0396160	−0.0198080	+	0.999804i	$0.506306\pi$
$228$	−5.70156	−0.377595
$229$	−7.10469	−0.469491	−0.234745	−	0.972057i	$-0.575426\pi$
$229$	−7.10469	−0.469491	−0.234745	+	0.972057i	$0.575426\pi$
$230$	1.70156	0.112198
$231$	1.70156	0.111955
$232$	−2.00000	−0.131306
$233$	0.806248	0.0528191	0.0264095	−	0.999651i	$-0.491593\pi$
$233$	0.806248	0.0528191	0.0264095	+	0.999651i	$0.491593\pi$
$234$	−3.70156	−0.241979
$235$	−3.40312	−0.221995
$236$	4.00000	0.260378
$237$	3.40312	0.221057
$238$	1.70156	0.110296
$239$	26.2094	1.69534	0.847672	−	0.530521i	$-0.178004\pi$
$239$	26.2094	1.69534	0.847672	+	0.530521i	$0.178004\pi$
$240$	−1.00000	−0.0645497
$241$	10.5078	0.676868	0.338434	−	0.940990i	$-0.390103\pi$
$241$	10.5078	0.676868	0.338434	+	0.940990i	$0.390103\pi$
$242$	1.00000	0.0642824
$243$	−1.00000	−0.0641500
$244$	11.1047	0.710905
$245$	−4.10469	−0.262239
$246$	−10.0000	−0.637577
$247$	−21.1047	−1.34286
$248$	1.70156	0.108049
$249$	2.29844	0.145658
$250$	1.00000	0.0632456
$251$	1.10469	0.0697272	0.0348636	−	0.999392i	$-0.488900\pi$
$251$	1.10469	0.0697272	0.0348636	+	0.999392i	$0.488900\pi$
$252$	1.70156	0.107188
$253$	−1.70156	−0.106976
$254$	0	0
$255$	−1.00000	−0.0626224
$256$	1.00000	0.0625000
$257$	2.00000	0.124757	0.0623783	−	0.998053i	$-0.480131\pi$
$257$	2.00000	0.124757	0.0623783	+	0.998053i	$0.480131\pi$
$258$	−4.00000	−0.249029
$259$	−6.29844	−0.391366
$260$	−3.70156	−0.229561
$261$	−2.00000	−0.123797
$262$	5.70156	0.352244
$263$	8.50781	0.524614	0.262307	−	0.964984i	$-0.415517\pi$
$263$	8.50781	0.524614	0.262307	+	0.964984i	$0.415517\pi$
$264$	1.00000	0.0615457
$265$	−2.00000	−0.122859
$266$	9.70156	0.594841
$267$	−10.0000	−0.611990
$268$	−2.29844	−0.140399
$269$	−2.50781	−0.152904	−0.0764520	−	0.997073i	$-0.524359\pi$
$269$	−2.50781	−0.152904	−0.0764520	+	0.997073i	$0.524359\pi$
$270$	−1.00000	−0.0608581
$271$	−6.80625	−0.413450	−0.206725	−	0.978399i	$-0.566281\pi$
$271$	−6.80625	−0.413450	−0.206725	+	0.978399i	$0.566281\pi$
$272$	1.00000	0.0606339
$273$	6.29844	0.381199
$274$	0.298438	0.0180293
$275$	−1.00000	−0.0603023
$276$	−1.70156	−0.102422
$277$	2.59688	0.156031	0.0780156	−	0.996952i	$-0.475142\pi$
$277$	2.59688	0.156031	0.0780156	+	0.996952i	$0.475142\pi$
$278$	−22.2094	−1.33203
$279$	1.70156	0.101870
$280$	1.70156	0.101688
$281$	−12.8062	−0.763957	−0.381978	−	0.924171i	$-0.624757\pi$
$281$	−12.8062	−0.763957	−0.381978	+	0.924171i	$0.624757\pi$
$282$	3.40312	0.202653
$283$	4.00000	0.237775	0.118888	−	0.992908i	$-0.462067\pi$
$283$	4.00000	0.237775	0.118888	+	0.992908i	$0.462067\pi$
$284$	11.4031	0.676651
$285$	−5.70156	−0.337731
$286$	3.70156	0.218878
$287$	17.0156	1.00440
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	−2.00000	−0.117444
$291$	−15.1047	−0.885452
$292$	−1.40312	−0.0821116
$293$	32.2094	1.88169	0.940846	−	0.338835i	$-0.110033\pi$
$293$	32.2094	1.88169	0.940846	+	0.338835i	$0.110033\pi$
$294$	4.10469	0.239390
$295$	4.00000	0.232889
$296$	−3.70156	−0.215149
$297$	1.00000	0.0580259
$298$	−3.70156	−0.214426
$299$	−6.29844	−0.364248
$300$	−1.00000	−0.0577350
$301$	6.80625	0.392306
$302$	−8.50781	−0.489569
$303$	−6.00000	−0.344691
$304$	5.70156	0.327007
$305$	11.1047	0.635852
$306$	1.00000	0.0571662
$307$	−26.8062	−1.52991	−0.764957	−	0.644082i	$-0.777240\pi$
$307$	−26.8062	−1.52991	−0.764957	+	0.644082i	$0.777240\pi$
$308$	−1.70156	−0.0969555
$309$	−17.7016	−1.00701
$310$	1.70156	0.0966422
$311$	−18.2094	−1.03256	−0.516279	−	0.856420i	$-0.672683\pi$
$311$	−18.2094	−1.03256	−0.516279	+	0.856420i	$0.672683\pi$
$312$	3.70156	0.209560
$313$	−12.2984	−0.695149	−0.347574	−	0.937652i	$-0.612995\pi$
$313$	−12.2984	−0.695149	−0.347574	+	0.937652i	$0.612995\pi$
$314$	17.4031	0.982115
$315$	1.70156	0.0958722
$316$	−3.40312	−0.191441
$317$	20.8062	1.16860	0.584298	−	0.811539i	$-0.301370\pi$
$317$	20.8062	1.16860	0.584298	+	0.811539i	$0.301370\pi$
$318$	2.00000	0.112154
$319$	2.00000	0.111979
$320$	1.00000	0.0559017
$321$	−7.40312	−0.413202
$322$	2.89531	0.161350
$323$	5.70156	0.317243
$324$	1.00000	0.0555556
$325$	−3.70156	−0.205326
$326$	−10.8062	−0.598503
$327$	15.1047	0.835291
$328$	10.0000	0.552158
$329$	−5.79063	−0.319248
$330$	1.00000	0.0550482
$331$	−4.00000	−0.219860	−0.109930	−	0.993939i	$-0.535063\pi$
$331$	−4.00000	−0.219860	−0.109930	+	0.993939i	$0.535063\pi$
$332$	−2.29844	−0.126143
$333$	−3.70156	−0.202844
$334$	−22.8062	−1.24790
$335$	−2.29844	−0.125577
$336$	−1.70156	−0.0928278
$337$	6.59688	0.359355	0.179677	−	0.983726i	$-0.442495\pi$
$337$	6.59688	0.359355	0.179677	+	0.983726i	$0.442495\pi$
$338$	0.701562	0.0381599
$339$	6.00000	0.325875
$340$	1.00000	0.0542326
$341$	−1.70156	−0.0921448
$342$	5.70156	0.308305
$343$	−18.8953	−1.02025
$344$	4.00000	0.215666
$345$	−1.70156	−0.0916090
$346$	−15.1047	−0.812033
$347$	−22.2094	−1.19226	−0.596131	−	0.802887i	$-0.703296\pi$
$347$	−22.2094	−1.19226	−0.596131	+	0.802887i	$0.703296\pi$
$348$	2.00000	0.107211
$349$	6.00000	0.321173	0.160586	−	0.987022i	$-0.448662\pi$
$349$	6.00000	0.321173	0.160586	+	0.987022i	$0.448662\pi$
$350$	1.70156	0.0909523
$351$	3.70156	0.197575
$352$	−1.00000	−0.0533002
$353$	−27.1047	−1.44264	−0.721318	−	0.692604i	$-0.756464\pi$
$353$	−27.1047	−1.44264	−0.721318	+	0.692604i	$0.756464\pi$
$354$	−4.00000	−0.212598
$355$	11.4031	0.605215
$356$	10.0000	0.529999
$357$	−1.70156	−0.0900562
$358$	2.29844	0.121476
$359$	20.5969	1.08706	0.543531	−	0.839389i	$-0.317087\pi$
$359$	20.5969	1.08706	0.543531	+	0.839389i	$0.317087\pi$
$360$	1.00000	0.0527046
$361$	13.5078	0.710937
$362$	2.59688	0.136489
$363$	−1.00000	−0.0524864
$364$	−6.29844	−0.330128
$365$	−1.40312	−0.0734429
$366$	−11.1047	−0.580451
$367$	8.00000	0.417597	0.208798	−	0.977959i	$-0.433045\pi$
$367$	8.00000	0.417597	0.208798	+	0.977959i	$0.433045\pi$
$368$	1.70156	0.0887001
$369$	10.0000	0.520579
$370$	−3.70156	−0.192435
$371$	−3.40312	−0.176681
$372$	−1.70156	−0.0882219
$373$	14.0000	0.724893	0.362446	−	0.932005i	$-0.381942\pi$
$373$	14.0000	0.724893	0.362446	+	0.932005i	$0.381942\pi$
$374$	−1.00000	−0.0517088
$375$	−1.00000	−0.0516398
$376$	−3.40312	−0.175503
$377$	7.40312	0.381280
$378$	−1.70156	−0.0875189
$379$	−2.29844	−0.118063	−0.0590314	−	0.998256i	$-0.518801\pi$
$379$	−2.29844	−0.118063	−0.0590314	+	0.998256i	$0.518801\pi$
$380$	5.70156	0.292484
$381$	0	0
$382$	16.0000	0.818631
$383$	12.5969	0.643670	0.321835	−	0.946796i	$-0.395700\pi$
$383$	12.5969	0.643670	0.321835	+	0.946796i	$0.395700\pi$
$384$	−1.00000	−0.0510310
$385$	−1.70156	−0.0867196
$386$	13.4031	0.682201
$387$	4.00000	0.203331
$388$	15.1047	0.766824
$389$	26.5969	1.34852	0.674258	−	0.738496i	$-0.264464\pi$
$389$	26.5969	1.34852	0.674258	+	0.738496i	$0.264464\pi$
$390$	3.70156	0.187436
$391$	1.70156	0.0860517
$392$	−4.10469	−0.207318
$393$	−5.70156	−0.287606
$394$	15.7016	0.791033
$395$	−3.40312	−0.171230
$396$	−1.00000	−0.0502519
$397$	−11.1938	−0.561798	−0.280899	−	0.959737i	$-0.590633\pi$
$397$	−11.1938	−0.561798	−0.280899	+	0.959737i	$0.590633\pi$
$398$	9.70156	0.486295
$399$	−9.70156	−0.485686
$400$	1.00000	0.0500000
$401$	26.5078	1.32374	0.661868	−	0.749620i	$-0.269764\pi$
$401$	26.5078	1.32374	0.661868	+	0.749620i	$0.269764\pi$
$402$	2.29844	0.114636
$403$	−6.29844	−0.313748
$404$	6.00000	0.298511
$405$	1.00000	0.0496904
$406$	−3.40312	−0.168894
$407$	3.70156	0.183480
$408$	−1.00000	−0.0495074
$409$	23.6125	1.16756	0.583781	−	0.811911i	$-0.301573\pi$
$409$	23.6125	1.16756	0.583781	+	0.811911i	$0.301573\pi$
$410$	10.0000	0.493865
$411$	−0.298438	−0.0147209
$412$	17.7016	0.872093
$413$	6.80625	0.334914
$414$	1.70156	0.0836272
$415$	−2.29844	−0.112826
$416$	−3.70156	−0.181484
$417$	22.2094	1.08760
$418$	−5.70156	−0.278873
$419$	−20.0000	−0.977064	−0.488532	−	0.872546i	$-0.662467\pi$
$419$	−20.0000	−0.977064	−0.488532	+	0.872546i	$0.662467\pi$
$420$	−1.70156	−0.0830277
$421$	22.5078	1.09696	0.548482	−	0.836163i	$-0.315206\pi$
$421$	22.5078	1.09696	0.548482	+	0.836163i	$0.315206\pi$
$422$	15.4031	0.749812
$423$	−3.40312	−0.165466
$424$	−2.00000	−0.0971286
$425$	1.00000	0.0485071
$426$	−11.4031	−0.552483
$427$	18.8953	0.914408
$428$	7.40312	0.357844
$429$	−3.70156	−0.178713
$430$	4.00000	0.192897
$431$	21.6125	1.04104	0.520519	−	0.853850i	$-0.325739\pi$
$431$	21.6125	1.04104	0.520519	+	0.853850i	$0.325739\pi$
$432$	−1.00000	−0.0481125
$433$	−14.0000	−0.672797	−0.336399	−	0.941720i	$-0.609209\pi$
$433$	−14.0000	−0.672797	−0.336399	+	0.941720i	$0.609209\pi$
$434$	2.89531	0.138980
$435$	2.00000	0.0958927
$436$	−15.1047	−0.723383
$437$	9.70156	0.464089
$438$	1.40312	0.0670439
$439$	−11.4031	−0.544241	−0.272121	−	0.962263i	$-0.587725\pi$
$439$	−11.4031	−0.544241	−0.272121	+	0.962263i	$0.587725\pi$
$440$	−1.00000	−0.0476731
$441$	−4.10469	−0.195461
$442$	−3.70156	−0.176065
$443$	37.0156	1.75867	0.879333	−	0.476208i	$-0.157989\pi$
$443$	37.0156	1.75867	0.879333	+	0.476208i	$0.157989\pi$
$444$	3.70156	0.175668
$445$	10.0000	0.474045
$446$	−9.70156	−0.459382
$447$	3.70156	0.175078
$448$	1.70156	0.0803913
$449$	7.10469	0.335291	0.167645	−	0.985847i	$-0.446384\pi$
$449$	7.10469	0.335291	0.167645	+	0.985847i	$0.446384\pi$
$450$	1.00000	0.0471405
$451$	−10.0000	−0.470882
$452$	−6.00000	−0.282216
$453$	8.50781	0.399732
$454$	−0.596876	−0.0280128
$455$	−6.29844	−0.295275
$456$	−5.70156	−0.267000
$457$	10.5078	0.491535	0.245767	−	0.969329i	$-0.420960\pi$
$457$	10.5078	0.491535	0.245767	+	0.969329i	$0.420960\pi$
$458$	−7.10469	−0.331980
$459$	−1.00000	−0.0466760
$460$	1.70156	0.0793357
$461$	30.0000	1.39724	0.698620	−	0.715493i	$-0.253798\pi$
$461$	30.0000	1.39724	0.698620	+	0.715493i	$0.253798\pi$
$462$	1.70156	0.0791638
$463$	−2.89531	−0.134557	−0.0672783	−	0.997734i	$-0.521432\pi$
$463$	−2.89531	−0.134557	−0.0672783	+	0.997734i	$0.521432\pi$
$464$	−2.00000	−0.0928477
$465$	−1.70156	−0.0789081
$466$	0.806248	0.0373487
$467$	−26.8062	−1.24045	−0.620223	−	0.784426i	$-0.712958\pi$
$467$	−26.8062	−1.24045	−0.620223	+	0.784426i	$0.712958\pi$
$468$	−3.70156	−0.171105
$469$	−3.91093	−0.180590
$470$	−3.40312	−0.156974
$471$	−17.4031	−0.801894
$472$	4.00000	0.184115
$473$	−4.00000	−0.183920
$474$	3.40312	0.156311
$475$	5.70156	0.261606
$476$	1.70156	0.0779910
$477$	−2.00000	−0.0915737
$478$	26.2094	1.19879
$479$	7.49219	0.342327	0.171163	−	0.985243i	$-0.445247\pi$
$479$	7.49219	0.342327	0.171163	+	0.985243i	$0.445247\pi$
$480$	−1.00000	−0.0456435
$481$	13.7016	0.624737
$482$	10.5078	0.478618
$483$	−2.89531	−0.131741
$484$	1.00000	0.0454545
$485$	15.1047	0.685868
$486$	−1.00000	−0.0453609
$487$	−6.80625	−0.308421	−0.154210	−	0.988038i	$-0.549283\pi$
$487$	−6.80625	−0.308421	−0.154210	+	0.988038i	$0.549283\pi$
$488$	11.1047	0.502686
$489$	10.8062	0.488675
$490$	−4.10469	−0.185431
$491$	−14.2094	−0.641260	−0.320630	−	0.947205i	$-0.603895\pi$
$491$	−14.2094	−0.641260	−0.320630	+	0.947205i	$0.603895\pi$
$492$	−10.0000	−0.450835
$493$	−2.00000	−0.0900755
$494$	−21.1047	−0.949545
$495$	−1.00000	−0.0449467
$496$	1.70156	0.0764024
$497$	19.4031	0.870349
$498$	2.29844	0.102995
$499$	−33.6125	−1.50470	−0.752351	−	0.658762i	$-0.771080\pi$
$499$	−33.6125	−1.50470	−0.752351	+	0.658762i	$0.771080\pi$
$500$	1.00000	0.0447214
$501$	22.8062	1.01891
$502$	1.10469	0.0493046
$503$	6.80625	0.303476	0.151738	−	0.988421i	$-0.451513\pi$
$503$	6.80625	0.303476	0.151738	+	0.988421i	$0.451513\pi$
$504$	1.70156	0.0757936
$505$	6.00000	0.266996
$506$	−1.70156	−0.0756437
$507$	−0.701562	−0.0311575
$508$	0	0
$509$	12.8062	0.567627	0.283813	−	0.958880i	$-0.408400\pi$
$509$	12.8062	0.567627	0.283813	+	0.958880i	$0.408400\pi$
$510$	−1.00000	−0.0442807
$511$	−2.38750	−0.105617
$512$	1.00000	0.0441942
$513$	−5.70156	−0.251730
$514$	2.00000	0.0882162
$515$	17.7016	0.780024
$516$	−4.00000	−0.176090
$517$	3.40312	0.149669
$518$	−6.29844	−0.276737
$519$	15.1047	0.663022
$520$	−3.70156	−0.162324
$521$	−40.7172	−1.78385	−0.891926	−	0.452181i	$-0.850646\pi$
$521$	−40.7172	−1.78385	−0.891926	+	0.452181i	$0.850646\pi$
$522$	−2.00000	−0.0875376
$523$	−28.0000	−1.22435	−0.612177	−	0.790721i	$-0.709706\pi$
$523$	−28.0000	−1.22435	−0.612177	+	0.790721i	$0.709706\pi$
$524$	5.70156	0.249074
$525$	−1.70156	−0.0742623
$526$	8.50781	0.370958
$527$	1.70156	0.0741212
$528$	1.00000	0.0435194
$529$	−20.1047	−0.874117
$530$	−2.00000	−0.0868744
$531$	4.00000	0.173585
$532$	9.70156	0.420616
$533$	−37.0156	−1.60332
$534$	−10.0000	−0.432742
$535$	7.40312	0.320065
$536$	−2.29844	−0.0992774
$537$	−2.29844	−0.0991849
$538$	−2.50781	−0.108119
$539$	4.10469	0.176801
$540$	−1.00000	−0.0430331
$541$	14.0000	0.601907	0.300954	−	0.953639i	$-0.402695\pi$
$541$	14.0000	0.601907	0.300954	+	0.953639i	$0.402695\pi$
$542$	−6.80625	−0.292353
$543$	−2.59688	−0.111443
$544$	1.00000	0.0428746
$545$	−15.1047	−0.647014
$546$	6.29844	0.269548
$547$	9.10469	0.389288	0.194644	−	0.980874i	$-0.437645\pi$
$547$	9.10469	0.389288	0.194644	+	0.980874i	$0.437645\pi$
$548$	0.298438	0.0127486
$549$	11.1047	0.473936
$550$	−1.00000	−0.0426401
$551$	−11.4031	−0.485789
$552$	−1.70156	−0.0724233
$553$	−5.79063	−0.246243
$554$	2.59688	0.110331
$555$	3.70156	0.157123
$556$	−22.2094	−0.941887
$557$	−44.2094	−1.87321	−0.936606	−	0.350385i	$-0.886051\pi$
$557$	−44.2094	−1.87321	−0.936606	+	0.350385i	$0.886051\pi$
$558$	1.70156	0.0720329
$559$	−14.8062	−0.626238
$560$	1.70156	0.0719041
$561$	1.00000	0.0422200
$562$	−12.8062	−0.540199
$563$	−42.1203	−1.77516	−0.887580	−	0.460654i	$-0.847615\pi$
$563$	−42.1203	−1.77516	−0.887580	+	0.460654i	$0.847615\pi$
$564$	3.40312	0.143297
$565$	−6.00000	−0.252422
$566$	4.00000	0.168133
$567$	1.70156	0.0714589
$568$	11.4031	0.478464
$569$	−3.10469	−0.130155	−0.0650776	−	0.997880i	$-0.520729\pi$
$569$	−3.10469	−0.130155	−0.0650776	+	0.997880i	$0.520729\pi$
$570$	−5.70156	−0.238812
$571$	−22.2094	−0.929433	−0.464717	−	0.885459i	$-0.653844\pi$
$571$	−22.2094	−0.929433	−0.464717	+	0.885459i	$0.653844\pi$
$572$	3.70156	0.154770
$573$	−16.0000	−0.668410
$574$	17.0156	0.710218
$575$	1.70156	0.0709600
$576$	1.00000	0.0416667
$577$	2.00000	0.0832611	0.0416305	−	0.999133i	$-0.486745\pi$
$577$	2.00000	0.0832611	0.0416305	+	0.999133i	$0.486745\pi$
$578$	1.00000	0.0415945
$579$	−13.4031	−0.557015
$580$	−2.00000	−0.0830455
$581$	−3.91093	−0.162253
$582$	−15.1047	−0.626109
$583$	2.00000	0.0828315
$584$	−1.40312	−0.0580617
$585$	−3.70156	−0.153041
$586$	32.2094	1.33056
$587$	16.5969	0.685026	0.342513	−	0.939513i	$-0.388722\pi$
$587$	16.5969	0.685026	0.342513	+	0.939513i	$0.388722\pi$
$588$	4.10469	0.169274
$589$	9.70156	0.399746
$590$	4.00000	0.164677
$591$	−15.7016	−0.645876
$592$	−3.70156	−0.152133
$593$	−14.0000	−0.574911	−0.287456	−	0.957794i	$-0.592809\pi$
$593$	−14.0000	−0.574911	−0.287456	+	0.957794i	$0.592809\pi$
$594$	1.00000	0.0410305
$595$	1.70156	0.0697572
$596$	−3.70156	−0.151622
$597$	−9.70156	−0.397059
$598$	−6.29844	−0.257562
$599$	−34.7172	−1.41851	−0.709253	−	0.704954i	$-0.750968\pi$
$599$	−34.7172	−1.41851	−0.709253	+	0.704954i	$0.750968\pi$
$600$	−1.00000	−0.0408248
$601$	−11.1047	−0.452970	−0.226485	−	0.974015i	$-0.572723\pi$
$601$	−11.1047	−0.452970	−0.226485	+	0.974015i	$0.572723\pi$
$602$	6.80625	0.277402
$603$	−2.29844	−0.0935996
$604$	−8.50781	−0.346178
$605$	1.00000	0.0406558
$606$	−6.00000	−0.243733
$607$	9.70156	0.393774	0.196887	−	0.980426i	$-0.436917\pi$
$607$	9.70156	0.393774	0.196887	+	0.980426i	$0.436917\pi$
$608$	5.70156	0.231229
$609$	3.40312	0.137902
$610$	11.1047	0.449616
$611$	12.5969	0.509615
$612$	1.00000	0.0404226
$613$	4.80625	0.194123	0.0970613	−	0.995278i	$-0.469056\pi$
$613$	4.80625	0.194123	0.0970613	+	0.995278i	$0.469056\pi$
$614$	−26.8062	−1.08181
$615$	−10.0000	−0.403239
$616$	−1.70156	−0.0685579
$617$	34.0000	1.36879	0.684394	−	0.729112i	$-0.260067\pi$
$617$	34.0000	1.36879	0.684394	+	0.729112i	$0.260067\pi$
$618$	−17.7016	−0.712061
$619$	7.91093	0.317967	0.158984	−	0.987281i	$-0.449178\pi$
$619$	7.91093	0.317967	0.158984	+	0.987281i	$0.449178\pi$
$620$	1.70156	0.0683364
$621$	−1.70156	−0.0682813
$622$	−18.2094	−0.730129
$623$	17.0156	0.681716
$624$	3.70156	0.148181
$625$	1.00000	0.0400000
$626$	−12.2984	−0.491544
$627$	5.70156	0.227698
$628$	17.4031	0.694460
$629$	−3.70156	−0.147591
$630$	1.70156	0.0677919
$631$	11.4031	0.453951	0.226976	−	0.973900i	$-0.427116\pi$
$631$	11.4031	0.453951	0.226976	+	0.973900i	$0.427116\pi$
$632$	−3.40312	−0.135369
$633$	−15.4031	−0.612219
$634$	20.8062	0.826322
$635$	0	0
$636$	2.00000	0.0793052
$637$	15.1938	0.601998
$638$	2.00000	0.0791808
$639$	11.4031	0.451101
$640$	1.00000	0.0395285
$641$	−6.00000	−0.236986	−0.118493	−	0.992955i	$-0.537806\pi$
$641$	−6.00000	−0.236986	−0.118493	+	0.992955i	$0.537806\pi$
$642$	−7.40312	−0.292178
$643$	−36.0000	−1.41970	−0.709851	−	0.704352i	$-0.751238\pi$
$643$	−36.0000	−1.41970	−0.709851	+	0.704352i	$0.751238\pi$
$644$	2.89531	0.114091
$645$	−4.00000	−0.157500
$646$	5.70156	0.224325
$647$	2.20937	0.0868594	0.0434297	−	0.999056i	$-0.486172\pi$
$647$	2.20937	0.0868594	0.0434297	+	0.999056i	$0.486172\pi$
$648$	1.00000	0.0392837
$649$	−4.00000	−0.157014
$650$	−3.70156	−0.145187
$651$	−2.89531	−0.113476
$652$	−10.8062	−0.423205
$653$	8.20937	0.321258	0.160629	−	0.987015i	$-0.448648\pi$
$653$	8.20937	0.321258	0.160629	+	0.987015i	$0.448648\pi$
$654$	15.1047	0.590640
$655$	5.70156	0.222778
$656$	10.0000	0.390434
$657$	−1.40312	−0.0547411
$658$	−5.79063	−0.225742
$659$	16.5969	0.646522	0.323261	−	0.946310i	$-0.395221\pi$
$659$	16.5969	0.646522	0.323261	+	0.946310i	$0.395221\pi$
$660$	1.00000	0.0389249
$661$	−35.7016	−1.38863	−0.694315	−	0.719671i	$-0.744292\pi$
$661$	−35.7016	−1.38863	−0.694315	+	0.719671i	$0.744292\pi$
$662$	−4.00000	−0.155464
$663$	3.70156	0.143757
$664$	−2.29844	−0.0891967
$665$	9.70156	0.376210
$666$	−3.70156	−0.143433
$667$	−3.40312	−0.131769
$668$	−22.8062	−0.882400
$669$	9.70156	0.375084
$670$	−2.29844	−0.0887964
$671$	−11.1047	−0.428692
$672$	−1.70156	−0.0656392
$673$	−18.5969	−0.716857	−0.358428	−	0.933557i	$-0.616687\pi$
$673$	−18.5969	−0.716857	−0.358428	+	0.933557i	$0.616687\pi$
$674$	6.59688	0.254102
$675$	−1.00000	−0.0384900
$676$	0.701562	0.0269832
$677$	−0.806248	−0.0309866	−0.0154933	−	0.999880i	$-0.504932\pi$
$677$	−0.806248	−0.0309866	−0.0154933	+	0.999880i	$0.504932\pi$
$678$	6.00000	0.230429
$679$	25.7016	0.986335
$680$	1.00000	0.0383482
$681$	0.596876	0.0228723
$682$	−1.70156	−0.0651562
$683$	−38.7172	−1.48147	−0.740736	−	0.671796i	$-0.765523\pi$
$683$	−38.7172	−1.48147	−0.740736	+	0.671796i	$0.765523\pi$
$684$	5.70156	0.218005
$685$	0.298438	0.0114027
$686$	−18.8953	−0.721426
$687$	7.10469	0.271061
$688$	4.00000	0.152499
$689$	7.40312	0.282037
$690$	−1.70156	−0.0647774
$691$	−6.89531	−0.262310	−0.131155	−	0.991362i	$-0.541869\pi$
$691$	−6.89531	−0.262310	−0.131155	+	0.991362i	$0.541869\pi$
$692$	−15.1047	−0.574194
$693$	−1.70156	−0.0646370
$694$	−22.2094	−0.843056
$695$	−22.2094	−0.842450
$696$	2.00000	0.0758098
$697$	10.0000	0.378777
$698$	6.00000	0.227103
$699$	−0.806248	−0.0304951
$700$	1.70156	0.0643130
$701$	−18.0000	−0.679851	−0.339925	−	0.940452i	$-0.610402\pi$
$701$	−18.0000	−0.679851	−0.339925	+	0.940452i	$0.610402\pi$
$702$	3.70156	0.139706
$703$	−21.1047	−0.795978
$704$	−1.00000	−0.0376889
$705$	3.40312	0.128169
$706$	−27.1047	−1.02010
$707$	10.2094	0.383963
$708$	−4.00000	−0.150329
$709$	−26.0000	−0.976450	−0.488225	−	0.872718i	$-0.662356\pi$
$709$	−26.0000	−0.976450	−0.488225	+	0.872718i	$0.662356\pi$
$710$	11.4031	0.427952
$711$	−3.40312	−0.127627
$712$	10.0000	0.374766
$713$	2.89531	0.108430
$714$	−1.70156	−0.0636794
$715$	3.70156	0.138431
$716$	2.29844	0.0858967
$717$	−26.2094	−0.978807
$718$	20.5969	0.768669
$719$	−28.5969	−1.06648	−0.533242	−	0.845963i	$-0.679026\pi$
$719$	−28.5969	−1.06648	−0.533242	+	0.845963i	$0.679026\pi$
$720$	1.00000	0.0372678
$721$	30.1203	1.12174
$722$	13.5078	0.502709
$723$	−10.5078	−0.390790
$724$	2.59688	0.0965121
$725$	−2.00000	−0.0742781
$726$	−1.00000	−0.0371135
$727$	−40.0000	−1.48352	−0.741759	−	0.670667i	$-0.766008\pi$
$727$	−40.0000	−1.48352	−0.741759	+	0.670667i	$0.766008\pi$
$728$	−6.29844	−0.233436
$729$	1.00000	0.0370370
$730$	−1.40312	−0.0519320
$731$	4.00000	0.147945
$732$	−11.1047	−0.410441
$733$	−0.298438	−0.0110231	−0.00551153	−	0.999985i	$-0.501754\pi$
$733$	−0.298438	−0.0110231	−0.00551153	+	0.999985i	$0.501754\pi$
$734$	8.00000	0.295285
$735$	4.10469	0.151404
$736$	1.70156	0.0627204
$737$	2.29844	0.0846640
$738$	10.0000	0.368105
$739$	−29.7016	−1.09259	−0.546295	−	0.837593i	$-0.683962\pi$
$739$	−29.7016	−1.09259	−0.546295	+	0.837593i	$0.683962\pi$
$740$	−3.70156	−0.136072
$741$	21.1047	0.775300
$742$	−3.40312	−0.124933
$743$	−38.8062	−1.42366	−0.711832	−	0.702350i	$-0.752134\pi$
$743$	−38.8062	−1.42366	−0.711832	+	0.702350i	$0.752134\pi$
$744$	−1.70156	−0.0623823
$745$	−3.70156	−0.135615
$746$	14.0000	0.512576
$747$	−2.29844	−0.0840954
$748$	−1.00000	−0.0365636
$749$	12.5969	0.460280
$750$	−1.00000	−0.0365148
$751$	37.6125	1.37250	0.686250	−	0.727366i	$-0.259256\pi$
$751$	37.6125	1.37250	0.686250	+	0.727366i	$0.259256\pi$
$752$	−3.40312	−0.124099
$753$	−1.10469	−0.0402570
$754$	7.40312	0.269606
$755$	−8.50781	−0.309631
$756$	−1.70156	−0.0618852
$757$	6.00000	0.218074	0.109037	−	0.994038i	$-0.465223\pi$
$757$	6.00000	0.218074	0.109037	+	0.994038i	$0.465223\pi$
$758$	−2.29844	−0.0834830
$759$	1.70156	0.0617628
$760$	5.70156	0.206817
$761$	−3.10469	−0.112545	−0.0562724	−	0.998415i	$-0.517922\pi$
$761$	−3.10469	−0.112545	−0.0562724	+	0.998415i	$0.517922\pi$
$762$	0	0
$763$	−25.7016	−0.930459
$764$	16.0000	0.578860
$765$	1.00000	0.0361551
$766$	12.5969	0.455144
$767$	−14.8062	−0.534623
$768$	−1.00000	−0.0360844
$769$	7.79063	0.280937	0.140469	−	0.990085i	$-0.455139\pi$
$769$	7.79063	0.280937	0.140469	+	0.990085i	$0.455139\pi$
$770$	−1.70156	−0.0613200
$771$	−2.00000	−0.0720282
$772$	13.4031	0.482389
$773$	21.3141	0.766613	0.383307	−	0.923621i	$-0.374785\pi$
$773$	21.3141	0.766613	0.383307	+	0.923621i	$0.374785\pi$
$774$	4.00000	0.143777
$775$	1.70156	0.0611219
$776$	15.1047	0.542227
$777$	6.29844	0.225955
$778$	26.5969	0.953544
$779$	57.0156	2.04280
$780$	3.70156	0.132537
$781$	−11.4031	−0.408036
$782$	1.70156	0.0608477
$783$	2.00000	0.0714742
$784$	−4.10469	−0.146596
$785$	17.4031	0.621144
$786$	−5.70156	−0.203368
$787$	−53.5234	−1.90790	−0.953952	−	0.299959i	$-0.903027\pi$
$787$	−53.5234	−1.90790	−0.953952	+	0.299959i	$0.903027\pi$
$788$	15.7016	0.559345
$789$	−8.50781	−0.302886
$790$	−3.40312	−0.121078
$791$	−10.2094	−0.363004
$792$	−1.00000	−0.0355335
$793$	−41.1047	−1.45967
$794$	−11.1938	−0.397251
$795$	2.00000	0.0709327
$796$	9.70156	0.343863
$797$	−49.3141	−1.74679	−0.873397	−	0.487009i	$-0.838088\pi$
$797$	−49.3141	−1.74679	−0.873397	+	0.487009i	$0.838088\pi$
$798$	−9.70156	−0.343432
$799$	−3.40312	−0.120394
$800$	1.00000	0.0353553
$801$	10.0000	0.353333
$802$	26.5078	0.936023
$803$	1.40312	0.0495152
$804$	2.29844	0.0810597
$805$	2.89531	0.102046
$806$	−6.29844	−0.221853
$807$	2.50781	0.0882791
$808$	6.00000	0.211079
$809$	0.806248	0.0283462	0.0141731	−	0.999900i	$-0.495488\pi$
$809$	0.806248	0.0283462	0.0141731	+	0.999900i	$0.495488\pi$
$810$	1.00000	0.0351364
$811$	−38.2094	−1.34171	−0.670856	−	0.741587i	$-0.734073\pi$
$811$	−38.2094	−1.34171	−0.670856	+	0.741587i	$0.734073\pi$
$812$	−3.40312	−0.119426
$813$	6.80625	0.238706
$814$	3.70156	0.129740
$815$	−10.8062	−0.378526
$816$	−1.00000	−0.0350070
$817$	22.8062	0.797890
$818$	23.6125	0.825592
$819$	−6.29844	−0.220085
$820$	10.0000	0.349215
$821$	15.1938	0.530266	0.265133	−	0.964212i	$-0.414584\pi$
$821$	15.1938	0.530266	0.265133	+	0.964212i	$0.414584\pi$
$822$	−0.298438	−0.0104092
$823$	−39.8219	−1.38810	−0.694052	−	0.719925i	$-0.744176\pi$
$823$	−39.8219	−1.38810	−0.694052	+	0.719925i	$0.744176\pi$
$824$	17.7016	0.616663
$825$	1.00000	0.0348155
$826$	6.80625	0.236820
$827$	−45.0156	−1.56535	−0.782673	−	0.622433i	$-0.786144\pi$
$827$	−45.0156	−1.56535	−0.782673	+	0.622433i	$0.786144\pi$
$828$	1.70156	0.0591334
$829$	−17.4922	−0.607529	−0.303764	−	0.952747i	$-0.598244\pi$
$829$	−17.4922	−0.607529	−0.303764	+	0.952747i	$0.598244\pi$
$830$	−2.29844	−0.0797799
$831$	−2.59688	−0.0900846
$832$	−3.70156	−0.128329
$833$	−4.10469	−0.142219
$834$	22.2094	0.769048
$835$	−22.8062	−0.789243
$836$	−5.70156	−0.197193
$837$	−1.70156	−0.0588146
$838$	−20.0000	−0.690889
$839$	−30.8062	−1.06355	−0.531775	−	0.846886i	$-0.678475\pi$
$839$	−30.8062	−1.06355	−0.531775	+	0.846886i	$0.678475\pi$
$840$	−1.70156	−0.0587095
$841$	−25.0000	−0.862069
$842$	22.5078	0.775670
$843$	12.8062	0.441071
$844$	15.4031	0.530197
$845$	0.701562	0.0241345
$846$	−3.40312	−0.117002
$847$	1.70156	0.0584664
$848$	−2.00000	−0.0686803
$849$	−4.00000	−0.137280
$850$	1.00000	0.0342997
$851$	−6.29844	−0.215908
$852$	−11.4031	−0.390665
$853$	−29.4031	−1.00674	−0.503372	−	0.864070i	$-0.667907\pi$
$853$	−29.4031	−1.00674	−0.503372	+	0.864070i	$0.667907\pi$
$854$	18.8953	0.646584
$855$	5.70156	0.194989
$856$	7.40312	0.253034
$857$	10.5078	0.358940	0.179470	−	0.983763i	$-0.442562\pi$
$857$	10.5078	0.358940	0.179470	+	0.983763i	$0.442562\pi$
$858$	−3.70156	−0.126369
$859$	−20.0000	−0.682391	−0.341196	−	0.939992i	$-0.610832\pi$
$859$	−20.0000	−0.682391	−0.341196	+	0.939992i	$0.610832\pi$
$860$	4.00000	0.136399
$861$	−17.0156	−0.579891
$862$	21.6125	0.736125
$863$	−2.38750	−0.0812715	−0.0406358	−	0.999174i	$-0.512938\pi$
$863$	−2.38750	−0.0812715	−0.0406358	+	0.999174i	$0.512938\pi$
$864$	−1.00000	−0.0340207
$865$	−15.1047	−0.513575
$866$	−14.0000	−0.475739
$867$	−1.00000	−0.0339618
$868$	2.89531	0.0982733
$869$	3.40312	0.115443
$870$	2.00000	0.0678064
$871$	8.50781	0.288276
$872$	−15.1047	−0.511509
$873$	15.1047	0.511216
$874$	9.70156	0.328160
$875$	1.70156	0.0575233
$876$	1.40312	0.0474072
$877$	−19.0156	−0.642112	−0.321056	−	0.947060i	$-0.604038\pi$
$877$	−19.0156	−0.642112	−0.321056	+	0.947060i	$0.604038\pi$
$878$	−11.4031	−0.384837
$879$	−32.2094	−1.08640
$880$	−1.00000	−0.0337100
$881$	32.8062	1.10527	0.552635	−	0.833423i	$-0.313622\pi$
$881$	32.8062	1.10527	0.552635	+	0.833423i	$0.313622\pi$
$882$	−4.10469	−0.138212
$883$	−25.6125	−0.861929	−0.430965	−	0.902369i	$-0.641827\pi$
$883$	−25.6125	−0.861929	−0.430965	+	0.902369i	$0.641827\pi$
$884$	−3.70156	−0.124497
$885$	−4.00000	−0.134459
$886$	37.0156	1.24356
$887$	25.1938	0.845923	0.422962	−	0.906148i	$-0.360990\pi$
$887$	25.1938	0.845923	0.422962	+	0.906148i	$0.360990\pi$
$888$	3.70156	0.124216
$889$	0	0
$890$	10.0000	0.335201
$891$	−1.00000	−0.0335013
$892$	−9.70156	−0.324832
$893$	−19.4031	−0.649301
$894$	3.70156	0.123799
$895$	2.29844	0.0768283
$896$	1.70156	0.0568452
$897$	6.29844	0.210299
$898$	7.10469	0.237086
$899$	−3.40312	−0.113501
$900$	1.00000	0.0333333
$901$	−2.00000	−0.0666297
$902$	−10.0000	−0.332964
$903$	−6.80625	−0.226498
$904$	−6.00000	−0.199557
$905$	2.59688	0.0863231
$906$	8.50781	0.282653
$907$	33.6125	1.11608	0.558042	−	0.829812i	$-0.311553\pi$
$907$	33.6125	1.11608	0.558042	+	0.829812i	$0.311553\pi$
$908$	−0.596876	−0.0198080
$909$	6.00000	0.199007
$910$	−6.29844	−0.208791
$911$	36.4187	1.20661	0.603303	−	0.797512i	$-0.293851\pi$
$911$	36.4187	1.20661	0.603303	+	0.797512i	$0.293851\pi$
$912$	−5.70156	−0.188798
$913$	2.29844	0.0760672
$914$	10.5078	0.347567
$915$	−11.1047	−0.367110
$916$	−7.10469	−0.234745
$917$	9.70156	0.320374
$918$	−1.00000	−0.0330049
$919$	27.9109	0.920697	0.460348	−	0.887738i	$-0.347724\pi$
$919$	27.9109	0.920697	0.460348	+	0.887738i	$0.347724\pi$
$920$	1.70156	0.0560988
$921$	26.8062	0.883296
$922$	30.0000	0.987997
$923$	−42.2094	−1.38934
$924$	1.70156	0.0559773
$925$	−3.70156	−0.121707
$926$	−2.89531	−0.0951459
$927$	17.7016	0.581396
$928$	−2.00000	−0.0656532
$929$	0.298438	0.00979143	0.00489571	−	0.999988i	$-0.498442\pi$
$929$	0.298438	0.00979143	0.00489571	+	0.999988i	$0.498442\pi$
$930$	−1.70156	−0.0557964
$931$	−23.4031	−0.767006
$932$	0.806248	0.0264095
$933$	18.2094	0.596148
$934$	−26.8062	−0.877127
$935$	−1.00000	−0.0327035
$936$	−3.70156	−0.120989
$937$	−3.10469	−0.101426	−0.0507128	−	0.998713i	$-0.516149\pi$
$937$	−3.10469	−0.101426	−0.0507128	+	0.998713i	$0.516149\pi$
$938$	−3.91093	−0.127697
$939$	12.2984	0.401344
$940$	−3.40312	−0.110998
$941$	−12.2094	−0.398014	−0.199007	−	0.979998i	$-0.563772\pi$
$941$	−12.2094	−0.398014	−0.199007	+	0.979998i	$0.563772\pi$
$942$	−17.4031	−0.567024
$943$	17.0156	0.554105
$944$	4.00000	0.130189
$945$	−1.70156	−0.0553518
$946$	−4.00000	−0.130051
$947$	−17.6125	−0.572329	−0.286165	−	0.958180i	$-0.592380\pi$
$947$	−17.6125	−0.572329	−0.286165	+	0.958180i	$0.592380\pi$
$948$	3.40312	0.110528
$949$	5.19375	0.168596
$950$	5.70156	0.184983
$951$	−20.8062	−0.674689
$952$	1.70156	0.0551479
$953$	13.4031	0.434170	0.217085	−	0.976153i	$-0.430345\pi$
$953$	13.4031	0.434170	0.217085	+	0.976153i	$0.430345\pi$
$954$	−2.00000	−0.0647524
$955$	16.0000	0.517748
$956$	26.2094	0.847672
$957$	−2.00000	−0.0646508
$958$	7.49219	0.242062
$959$	0.507811	0.0163981
$960$	−1.00000	−0.0322749
$961$	−28.1047	−0.906603
$962$	13.7016	0.441756
$963$	7.40312	0.238562
$964$	10.5078	0.338434
$965$	13.4031	0.431462
$966$	−2.89531	−0.0931552
$967$	13.7906	0.443477	0.221738	−	0.975106i	$-0.428827\pi$
$967$	13.7906	0.443477	0.221738	+	0.975106i	$0.428827\pi$
$968$	1.00000	0.0321412
$969$	−5.70156	−0.183161
$970$	15.1047	0.484982
$971$	50.1203	1.60844	0.804219	−	0.594334i	$-0.202584\pi$
$971$	50.1203	1.60844	0.804219	+	0.594334i	$0.202584\pi$
$972$	−1.00000	−0.0320750
$973$	−37.7906	−1.21151
$974$	−6.80625	−0.218086
$975$	3.70156	0.118545
$976$	11.1047	0.355452
$977$	41.3141	1.32175	0.660877	−	0.750494i	$-0.270185\pi$
$977$	41.3141	1.32175	0.660877	+	0.750494i	$0.270185\pi$
$978$	10.8062	0.345546
$979$	−10.0000	−0.319601
$980$	−4.10469	−0.131119
$981$	−15.1047	−0.482256
$982$	−14.2094	−0.453439
$983$	−30.8062	−0.982567	−0.491283	−	0.871000i	$-0.663472\pi$
$983$	−30.8062	−0.982567	−0.491283	+	0.871000i	$0.663472\pi$
$984$	−10.0000	−0.318788
$985$	15.7016	0.500293
$986$	−2.00000	−0.0636930
$987$	5.79063	0.184318
$988$	−21.1047	−0.671430
$989$	6.80625	0.216426
$990$	−1.00000	−0.0317821
$991$	−40.5078	−1.28677	−0.643387	−	0.765542i	$-0.722471\pi$
$991$	−40.5078	−1.28677	−0.643387	+	0.765542i	$0.722471\pi$
$992$	1.70156	0.0540247
$993$	4.00000	0.126936
$994$	19.4031	0.615430
$995$	9.70156	0.307560
$996$	2.29844	0.0728288
$997$	−10.0000	−0.316703	−0.158352	−	0.987383i	$-0.550618\pi$
$997$	−10.0000	−0.316703	−0.158352	+	0.987383i	$0.550618\pi$
$998$	−33.6125	−1.06398
$999$	3.70156	0.117112

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5610.2.a.bv.1.2	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5610.2.a.bv.1.2	✓	2	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +1.70156 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +1.70156 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -1.00000 q^{11} -1.00000 q^{12} -3.70156 q^{13} +1.70156 q^{14} -1.00000 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} +5.70156 q^{19} +1.00000 q^{20} -1.70156 q^{21} -1.00000 q^{22} +1.70156 q^{23} -1.00000 q^{24} +1.00000 q^{25} -3.70156 q^{26} -1.00000 q^{27} +1.70156 q^{28} -2.00000 q^{29} -1.00000 q^{30} +1.70156 q^{31} +1.00000 q^{32} +1.00000 q^{33} +1.00000 q^{34} +1.70156 q^{35} +1.00000 q^{36} -3.70156 q^{37} +5.70156 q^{38} +3.70156 q^{39} +1.00000 q^{40} +10.0000 q^{41} -1.70156 q^{42} +4.00000 q^{43} -1.00000 q^{44} +1.00000 q^{45} +1.70156 q^{46} -3.40312 q^{47} -1.00000 q^{48} -4.10469 q^{49} +1.00000 q^{50} -1.00000 q^{51} -3.70156 q^{52} -2.00000 q^{53} -1.00000 q^{54} -1.00000 q^{55} +1.70156 q^{56} -5.70156 q^{57} -2.00000 q^{58} +4.00000 q^{59} -1.00000 q^{60} +11.1047 q^{61} +1.70156 q^{62} +1.70156 q^{63} +1.00000 q^{64} -3.70156 q^{65} +1.00000 q^{66} -2.29844 q^{67} +1.00000 q^{68} -1.70156 q^{69} +1.70156 q^{70} +11.4031 q^{71} +1.00000 q^{72} -1.40312 q^{73} -3.70156 q^{74} -1.00000 q^{75} +5.70156 q^{76} -1.70156 q^{77} +3.70156 q^{78} -3.40312 q^{79} +1.00000 q^{80} +1.00000 q^{81} +10.0000 q^{82} -2.29844 q^{83} -1.70156 q^{84} +1.00000 q^{85} +4.00000 q^{86} +2.00000 q^{87} -1.00000 q^{88} +10.0000 q^{89} +1.00000 q^{90} -6.29844 q^{91} +1.70156 q^{92} -1.70156 q^{93} -3.40312 q^{94} +5.70156 q^{95} -1.00000 q^{96} +15.1047 q^{97} -4.10469 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} - 3 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 - 2 * q^6 - 3 * q^7 + 2 * q^8 + 2 * q^9	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} - 3 q^{7} + 2 q^{8} + 2 q^{9} + 2 q^{10} - 2 q^{11} - 2 q^{12} - q^{13} - 3 q^{14} - 2 q^{15} + 2 q^{16} + 2 q^{17} + 2 q^{18} + 5 q^{19} + 2 q^{20} + 3 q^{21} - 2 q^{22} - 3 q^{23} - 2 q^{24} + 2 q^{25} - q^{26} - 2 q^{27} - 3 q^{28} - 4 q^{29} - 2 q^{30} - 3 q^{31} + 2 q^{32} + 2 q^{33} + 2 q^{34} - 3 q^{35} + 2 q^{36} - q^{37} + 5 q^{38} + q^{39} + 2 q^{40} + 20 q^{41} + 3 q^{42} + 8 q^{43} - 2 q^{44} + 2 q^{45} - 3 q^{46} + 6 q^{47} - 2 q^{48} + 11 q^{49} + 2 q^{50} - 2 q^{51} - q^{52} - 4 q^{53} - 2 q^{54} - 2 q^{55} - 3 q^{56} - 5 q^{57} - 4 q^{58} + 8 q^{59} - 2 q^{60} + 3 q^{61} - 3 q^{62} - 3 q^{63} + 2 q^{64} - q^{65} + 2 q^{66} - 11 q^{67} + 2 q^{68} + 3 q^{69} - 3 q^{70} + 10 q^{71} + 2 q^{72} + 10 q^{73} - q^{74} - 2 q^{75} + 5 q^{76} + 3 q^{77} + q^{78} + 6 q^{79} + 2 q^{80} + 2 q^{81} + 20 q^{82} - 11 q^{83} + 3 q^{84} + 2 q^{85} + 8 q^{86} + 4 q^{87} - 2 q^{88} + 20 q^{89} + 2 q^{90} - 19 q^{91} - 3 q^{92} + 3 q^{93} + 6 q^{94} + 5 q^{95} - 2 q^{96} + 11 q^{97} + 11 q^{98} - 2 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 - 2 * q^6 - 3 * q^7 + 2 * q^8 + 2 * q^9 + 2 * q^10 - 2 * q^11 - 2 * q^12 - q^13 - 3 * q^14 - 2 * q^15 + 2 * q^16 + 2 * q^17 + 2 * q^18 + 5 * q^19 + 2 * q^20 + 3 * q^21 - 2 * q^22 - 3 * q^23 - 2 * q^24 + 2 * q^25 - q^26 - 2 * q^27 - 3 * q^28 - 4 * q^29 - 2 * q^30 - 3 * q^31 + 2 * q^32 + 2 * q^33 + 2 * q^34 - 3 * q^35 + 2 * q^36 - q^37 + 5 * q^38 + q^39 + 2 * q^40 + 20 * q^41 + 3 * q^42 + 8 * q^43 - 2 * q^44 + 2 * q^45 - 3 * q^46 + 6 * q^47 - 2 * q^48 + 11 * q^49 + 2 * q^50 - 2 * q^51 - q^52 - 4 * q^53 - 2 * q^54 - 2 * q^55 - 3 * q^56 - 5 * q^57 - 4 * q^58 + 8 * q^59 - 2 * q^60 + 3 * q^61 - 3 * q^62 - 3 * q^63 + 2 * q^64 - q^65 + 2 * q^66 - 11 * q^67 + 2 * q^68 + 3 * q^69 - 3 * q^70 + 10 * q^71 + 2 * q^72 + 10 * q^73 - q^74 - 2 * q^75 + 5 * q^76 + 3 * q^77 + q^78 + 6 * q^79 + 2 * q^80 + 2 * q^81 + 20 * q^82 - 11 * q^83 + 3 * q^84 + 2 * q^85 + 8 * q^86 + 4 * q^87 - 2 * q^88 + 20 * q^89 + 2 * q^90 - 19 * q^91 - 3 * q^92 + 3 * q^93 + 6 * q^94 + 5 * q^95 - 2 * q^96 + 11 * q^97 + 11 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

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