LMFDB - Embedded newform 5610.2.a.br.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:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
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			$-0.618034$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -1.23607 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -1.23607 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +1.00000 q^{11} -1.00000 q^{12} +0.763932 q^{13} +1.23607 q^{14} -1.00000 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} -0.763932 q^{19} +1.00000 q^{20} +1.23607 q^{21} -1.00000 q^{22} +7.23607 q^{23} +1.00000 q^{24} +1.00000 q^{25} -0.763932 q^{26} -1.00000 q^{27} -1.23607 q^{28} +2.00000 q^{29} +1.00000 q^{30} +6.47214 q^{31} -1.00000 q^{32} -1.00000 q^{33} -1.00000 q^{34} -1.23607 q^{35} +1.00000 q^{36} +4.47214 q^{37} +0.763932 q^{38} -0.763932 q^{39} -1.00000 q^{40} -8.94427 q^{41} -1.23607 q^{42} +2.76393 q^{43} +1.00000 q^{44} +1.00000 q^{45} -7.23607 q^{46} -8.94427 q^{47} -1.00000 q^{48} -5.47214 q^{49} -1.00000 q^{50} -1.00000 q^{51} +0.763932 q^{52} -7.70820 q^{53} +1.00000 q^{54} +1.00000 q^{55} +1.23607 q^{56} +0.763932 q^{57} -2.00000 q^{58} +13.2361 q^{59} -1.00000 q^{60} +2.94427 q^{61} -6.47214 q^{62} -1.23607 q^{63} +1.00000 q^{64} +0.763932 q^{65} +1.00000 q^{66} -8.47214 q^{67} +1.00000 q^{68} -7.23607 q^{69} +1.23607 q^{70} +5.23607 q^{71} -1.00000 q^{72} +1.70820 q^{73} -4.47214 q^{74} -1.00000 q^{75} -0.763932 q^{76} -1.23607 q^{77} +0.763932 q^{78} +4.76393 q^{79} +1.00000 q^{80} +1.00000 q^{81} +8.94427 q^{82} -4.94427 q^{83} +1.23607 q^{84} +1.00000 q^{85} -2.76393 q^{86} -2.00000 q^{87} -1.00000 q^{88} +14.0000 q^{89} -1.00000 q^{90} -0.944272 q^{91} +7.23607 q^{92} -6.47214 q^{93} +8.94427 q^{94} -0.763932 q^{95} +1.00000 q^{96} +4.94427 q^{97} +5.47214 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{6} + 2 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 + 2 * q^7 - 2 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} + 2 q^{9} - 2 q^{10} + 2 q^{11} - 2 q^{12} + 6 q^{13} - 2 q^{14} - 2 q^{15} + 2 q^{16} + 2 q^{17} - 2 q^{18} - 6 q^{19} + 2 q^{20} - 2 q^{21} - 2 q^{22} + 10 q^{23} + 2 q^{24} + 2 q^{25} - 6 q^{26} - 2 q^{27} + 2 q^{28} + 4 q^{29} + 2 q^{30} + 4 q^{31} - 2 q^{32} - 2 q^{33} - 2 q^{34} + 2 q^{35} + 2 q^{36} + 6 q^{38} - 6 q^{39} - 2 q^{40} + 2 q^{42} + 10 q^{43} + 2 q^{44} + 2 q^{45} - 10 q^{46} - 2 q^{48} - 2 q^{49} - 2 q^{50} - 2 q^{51} + 6 q^{52} - 2 q^{53} + 2 q^{54} + 2 q^{55} - 2 q^{56} + 6 q^{57} - 4 q^{58} + 22 q^{59} - 2 q^{60} - 12 q^{61} - 4 q^{62} + 2 q^{63} + 2 q^{64} + 6 q^{65} + 2 q^{66} - 8 q^{67} + 2 q^{68} - 10 q^{69} - 2 q^{70} + 6 q^{71} - 2 q^{72} - 10 q^{73} - 2 q^{75} - 6 q^{76} + 2 q^{77} + 6 q^{78} + 14 q^{79} + 2 q^{80} + 2 q^{81} + 8 q^{83} - 2 q^{84} + 2 q^{85} - 10 q^{86} - 4 q^{87} - 2 q^{88} + 28 q^{89} - 2 q^{90} + 16 q^{91} + 10 q^{92} - 4 q^{93} - 6 q^{95} + 2 q^{96} - 8 q^{97} + 2 q^{98} + 2 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 + 2 * q^9 - 2 * q^10 + 2 * q^11 - 2 * q^12 + 6 * q^13 - 2 * q^14 - 2 * q^15 + 2 * q^16 + 2 * q^17 - 2 * q^18 - 6 * q^19 + 2 * q^20 - 2 * q^21 - 2 * q^22 + 10 * q^23 + 2 * q^24 + 2 * q^25 - 6 * q^26 - 2 * q^27 + 2 * q^28 + 4 * q^29 + 2 * q^30 + 4 * q^31 - 2 * q^32 - 2 * q^33 - 2 * q^34 + 2 * q^35 + 2 * q^36 + 6 * q^38 - 6 * q^39 - 2 * q^40 + 2 * q^42 + 10 * q^43 + 2 * q^44 + 2 * q^45 - 10 * q^46 - 2 * q^48 - 2 * q^49 - 2 * q^50 - 2 * q^51 + 6 * q^52 - 2 * q^53 + 2 * q^54 + 2 * q^55 - 2 * q^56 + 6 * q^57 - 4 * q^58 + 22 * q^59 - 2 * q^60 - 12 * q^61 - 4 * q^62 + 2 * q^63 + 2 * q^64 + 6 * q^65 + 2 * q^66 - 8 * q^67 + 2 * q^68 - 10 * q^69 - 2 * q^70 + 6 * q^71 - 2 * q^72 - 10 * q^73 - 2 * q^75 - 6 * q^76 + 2 * q^77 + 6 * q^78 + 14 * q^79 + 2 * q^80 + 2 * q^81 + 8 * q^83 - 2 * q^84 + 2 * q^85 - 10 * q^86 - 4 * q^87 - 2 * q^88 + 28 * q^89 - 2 * q^90 + 16 * q^91 + 10 * q^92 - 4 * q^93 - 6 * q^95 + 2 * q^96 - 8 * q^97 + 2 * 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
$7$	−1.23607	−0.467190	−0.233595	−	0.972334i	$-0.575049\pi$
$7$	−1.23607	−0.467190	−0.233595	+	0.972334i	$0.575049\pi$
$8$	−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
$13$	0.763932	0.211877	0.105938	−	0.994373i	$-0.466215\pi$
$13$	0.763932	0.211877	0.105938	+	0.994373i	$0.466215\pi$
$14$	1.23607	0.330353
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.00000	−0.235702
$19$	−0.763932	−0.175258	−0.0876290	−	0.996153i	$-0.527929\pi$
$19$	−0.763932	−0.175258	−0.0876290	+	0.996153i	$0.527929\pi$
$20$	1.00000	0.223607
$21$	1.23607	0.269732
$22$	−1.00000	−0.213201
$23$	7.23607	1.50882	0.754412	−	0.656401i	$-0.227922\pi$
$23$	7.23607	1.50882	0.754412	+	0.656401i	$0.227922\pi$
$24$	1.00000	0.204124
$25$	1.00000	0.200000
$26$	−0.763932	−0.149819
$27$	−1.00000	−0.192450
$28$	−1.23607	−0.233595
$29$	2.00000	0.371391	0.185695	−	0.982607i	$-0.440546\pi$
$29$	2.00000	0.371391	0.185695	+	0.982607i	$0.440546\pi$
$30$	1.00000	0.182574
$31$	6.47214	1.16243	0.581215	−	0.813750i	$-0.302578\pi$
$31$	6.47214	1.16243	0.581215	+	0.813750i	$0.302578\pi$
$32$	−1.00000	−0.176777
$33$	−1.00000	−0.174078
$34$	−1.00000	−0.171499
$35$	−1.23607	−0.208934
$36$	1.00000	0.166667
$37$	4.47214	0.735215	0.367607	−	0.929981i	$-0.380177\pi$
$37$	4.47214	0.735215	0.367607	+	0.929981i	$0.380177\pi$
$38$	0.763932	0.123926
$39$	−0.763932	−0.122327
$40$	−1.00000	−0.158114
$41$	−8.94427	−1.39686	−0.698430	−	0.715678i	$-0.746118\pi$
$41$	−8.94427	−1.39686	−0.698430	+	0.715678i	$0.746118\pi$
$42$	−1.23607	−0.190729
$43$	2.76393	0.421496	0.210748	−	0.977540i	$-0.432410\pi$
$43$	2.76393	0.421496	0.210748	+	0.977540i	$0.432410\pi$
$44$	1.00000	0.150756
$45$	1.00000	0.149071
$46$	−7.23607	−1.06690
$47$	−8.94427	−1.30466	−0.652328	−	0.757937i	$-0.726208\pi$
$47$	−8.94427	−1.30466	−0.652328	+	0.757937i	$0.726208\pi$
$48$	−1.00000	−0.144338
$49$	−5.47214	−0.781734
$50$	−1.00000	−0.141421
$51$	−1.00000	−0.140028
$52$	0.763932	0.105938
$53$	−7.70820	−1.05880	−0.529402	−	0.848371i	$-0.677584\pi$
$53$	−7.70820	−1.05880	−0.529402	+	0.848371i	$0.677584\pi$
$54$	1.00000	0.136083
$55$	1.00000	0.134840
$56$	1.23607	0.165177
$57$	0.763932	0.101185
$58$	−2.00000	−0.262613
$59$	13.2361	1.72319	0.861595	−	0.507597i	$-0.169466\pi$
$59$	13.2361	1.72319	0.861595	+	0.507597i	$0.169466\pi$
$60$	−1.00000	−0.129099
$61$	2.94427	0.376975	0.188488	−	0.982076i	$-0.439641\pi$
$61$	2.94427	0.376975	0.188488	+	0.982076i	$0.439641\pi$
$62$	−6.47214	−0.821962
$63$	−1.23607	−0.155730
$64$	1.00000	0.125000
$65$	0.763932	0.0947541
$66$	1.00000	0.123091
$67$	−8.47214	−1.03504	−0.517518	−	0.855672i	$-0.673144\pi$
$67$	−8.47214	−1.03504	−0.517518	+	0.855672i	$0.673144\pi$
$68$	1.00000	0.121268
$69$	−7.23607	−0.871120
$70$	1.23607	0.147738
$71$	5.23607	0.621407	0.310703	−	0.950507i	$-0.399435\pi$
$71$	5.23607	0.621407	0.310703	+	0.950507i	$0.399435\pi$
$72$	−1.00000	−0.117851
$73$	1.70820	0.199930	0.0999651	−	0.994991i	$-0.468127\pi$
$73$	1.70820	0.199930	0.0999651	+	0.994991i	$0.468127\pi$
$74$	−4.47214	−0.519875
$75$	−1.00000	−0.115470
$76$	−0.763932	−0.0876290
$77$	−1.23607	−0.140863
$78$	0.763932	0.0864983
$79$	4.76393	0.535984	0.267992	−	0.963421i	$-0.413640\pi$
$79$	4.76393	0.535984	0.267992	+	0.963421i	$0.413640\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	8.94427	0.987730
$83$	−4.94427	−0.542704	−0.271352	−	0.962480i	$-0.587471\pi$
$83$	−4.94427	−0.542704	−0.271352	+	0.962480i	$0.587471\pi$
$84$	1.23607	0.134866
$85$	1.00000	0.108465
$86$	−2.76393	−0.298042
$87$	−2.00000	−0.214423
$88$	−1.00000	−0.106600
$89$	14.0000	1.48400	0.741999	−	0.670402i	$-0.233878\pi$
$89$	14.0000	1.48400	0.741999	+	0.670402i	$0.233878\pi$
$90$	−1.00000	−0.105409
$91$	−0.944272	−0.0989866
$92$	7.23607	0.754412
$93$	−6.47214	−0.671129
$94$	8.94427	0.922531
$95$	−0.763932	−0.0783778
$96$	1.00000	0.102062
$97$	4.94427	0.502015	0.251007	−	0.967985i	$-0.419238\pi$
$97$	4.94427	0.502015	0.251007	+	0.967985i	$0.419238\pi$
$98$	5.47214	0.552769
$99$	1.00000	0.100504
$100$	1.00000	0.100000
$101$	−10.4721	−1.04202	−0.521008	−	0.853552i	$-0.674444\pi$
$101$	−10.4721	−1.04202	−0.521008	+	0.853552i	$0.674444\pi$
$102$	1.00000	0.0990148
$103$	−12.0000	−1.18240	−0.591198	−	0.806527i	$-0.701345\pi$
$103$	−12.0000	−1.18240	−0.591198	+	0.806527i	$0.701345\pi$
$104$	−0.763932	−0.0749097
$105$	1.23607	0.120628
$106$	7.70820	0.748687
$107$	4.94427	0.477981	0.238990	−	0.971022i	$-0.423184\pi$
$107$	4.94427	0.477981	0.238990	+	0.971022i	$0.423184\pi$
$108$	−1.00000	−0.0962250
$109$	10.0000	0.957826	0.478913	−	0.877862i	$-0.341031\pi$
$109$	10.0000	0.957826	0.478913	+	0.877862i	$0.341031\pi$
$110$	−1.00000	−0.0953463
$111$	−4.47214	−0.424476
$112$	−1.23607	−0.116797
$113$	19.1246	1.79909	0.899546	−	0.436826i	$-0.143897\pi$
$113$	19.1246	1.79909	0.899546	+	0.436826i	$0.143897\pi$
$114$	−0.763932	−0.0715488
$115$	7.23607	0.674767
$116$	2.00000	0.185695
$117$	0.763932	0.0706255
$118$	−13.2361	−1.21848
$119$	−1.23607	−0.113310
$120$	1.00000	0.0912871
$121$	1.00000	0.0909091
$122$	−2.94427	−0.266562
$123$	8.94427	0.806478
$124$	6.47214	0.581215
$125$	1.00000	0.0894427
$126$	1.23607	0.110118
$127$	−15.4164	−1.36798	−0.683992	−	0.729489i	$-0.739758\pi$
$127$	−15.4164	−1.36798	−0.683992	+	0.729489i	$0.739758\pi$
$128$	−1.00000	−0.0883883
$129$	−2.76393	−0.243351
$130$	−0.763932	−0.0670013
$131$	8.00000	0.698963	0.349482	−	0.936943i	$-0.386358\pi$
$131$	8.00000	0.698963	0.349482	+	0.936943i	$0.386358\pi$
$132$	−1.00000	−0.0870388
$133$	0.944272	0.0818788
$134$	8.47214	0.731881
$135$	−1.00000	−0.0860663
$136$	−1.00000	−0.0857493
$137$	−2.00000	−0.170872	−0.0854358	−	0.996344i	$-0.527228\pi$
$137$	−2.00000	−0.170872	−0.0854358	+	0.996344i	$0.527228\pi$
$138$	7.23607	0.615975
$139$	−17.8885	−1.51729	−0.758643	−	0.651506i	$-0.774137\pi$
$139$	−17.8885	−1.51729	−0.758643	+	0.651506i	$0.774137\pi$
$140$	−1.23607	−0.104467
$141$	8.94427	0.753244
$142$	−5.23607	−0.439401
$143$	0.763932	0.0638832
$144$	1.00000	0.0833333
$145$	2.00000	0.166091
$146$	−1.70820	−0.141372
$147$	5.47214	0.451334
$148$	4.47214	0.367607
$149$	0.944272	0.0773578	0.0386789	−	0.999252i	$-0.487685\pi$
$149$	0.944272	0.0773578	0.0386789	+	0.999252i	$0.487685\pi$
$150$	1.00000	0.0816497
$151$	12.9443	1.05339	0.526695	−	0.850054i	$-0.323431\pi$
$151$	12.9443	1.05339	0.526695	+	0.850054i	$0.323431\pi$
$152$	0.763932	0.0619631
$153$	1.00000	0.0808452
$154$	1.23607	0.0996052
$155$	6.47214	0.519854
$156$	−0.763932	−0.0611635
$157$	−12.0000	−0.957704	−0.478852	−	0.877896i	$-0.658947\pi$
$157$	−12.0000	−0.957704	−0.478852	+	0.877896i	$0.658947\pi$
$158$	−4.76393	−0.378998
$159$	7.70820	0.611300
$160$	−1.00000	−0.0790569
$161$	−8.94427	−0.704907
$162$	−1.00000	−0.0785674
$163$	2.47214	0.193633	0.0968163	−	0.995302i	$-0.469134\pi$
$163$	2.47214	0.193633	0.0968163	+	0.995302i	$0.469134\pi$
$164$	−8.94427	−0.698430
$165$	−1.00000	−0.0778499
$166$	4.94427	0.383750
$167$	−1.52786	−0.118230	−0.0591148	−	0.998251i	$-0.518828\pi$
$167$	−1.52786	−0.118230	−0.0591148	+	0.998251i	$0.518828\pi$
$168$	−1.23607	−0.0953647
$169$	−12.4164	−0.955108
$170$	−1.00000	−0.0766965
$171$	−0.763932	−0.0584193
$172$	2.76393	0.210748
$173$	−10.9443	−0.832078	−0.416039	−	0.909347i	$-0.636582\pi$
$173$	−10.9443	−0.832078	−0.416039	+	0.909347i	$0.636582\pi$
$174$	2.00000	0.151620
$175$	−1.23607	−0.0934380
$176$	1.00000	0.0753778
$177$	−13.2361	−0.994884
$178$	−14.0000	−1.04934
$179$	23.7082	1.77203	0.886017	−	0.463652i	$-0.153461\pi$
$179$	23.7082	1.77203	0.886017	+	0.463652i	$0.153461\pi$
$180$	1.00000	0.0745356
$181$	−11.8885	−0.883669	−0.441834	−	0.897097i	$-0.645672\pi$
$181$	−11.8885	−0.883669	−0.441834	+	0.897097i	$0.645672\pi$
$182$	0.944272	0.0699941
$183$	−2.94427	−0.217647
$184$	−7.23607	−0.533450
$185$	4.47214	0.328798
$186$	6.47214	0.474560
$187$	1.00000	0.0731272
$188$	−8.94427	−0.652328
$189$	1.23607	0.0899107
$190$	0.763932	0.0554215
$191$	21.8885	1.58380	0.791900	−	0.610651i	$-0.209092\pi$
$191$	21.8885	1.58380	0.791900	+	0.610651i	$0.209092\pi$
$192$	−1.00000	−0.0721688
$193$	−21.7082	−1.56259	−0.781295	−	0.624161i	$-0.785441\pi$
$193$	−21.7082	−1.56259	−0.781295	+	0.624161i	$0.785441\pi$
$194$	−4.94427	−0.354978
$195$	−0.763932	−0.0547063
$196$	−5.47214	−0.390867
$197$	7.52786	0.536338	0.268169	−	0.963372i	$-0.413581\pi$
$197$	7.52786	0.536338	0.268169	+	0.963372i	$0.413581\pi$
$198$	−1.00000	−0.0710669
$199$	14.4721	1.02590	0.512951	−	0.858418i	$-0.328552\pi$
$199$	14.4721	1.02590	0.512951	+	0.858418i	$0.328552\pi$
$200$	−1.00000	−0.0707107
$201$	8.47214	0.597578
$202$	10.4721	0.736817
$203$	−2.47214	−0.173510
$204$	−1.00000	−0.0700140
$205$	−8.94427	−0.624695
$206$	12.0000	0.836080
$207$	7.23607	0.502941
$208$	0.763932	0.0529692
$209$	−0.763932	−0.0528423
$210$	−1.23607	−0.0852968
$211$	19.4164	1.33668	0.668340	−	0.743856i	$-0.267005\pi$
$211$	19.4164	1.33668	0.668340	+	0.743856i	$0.267005\pi$
$212$	−7.70820	−0.529402
$213$	−5.23607	−0.358769
$214$	−4.94427	−0.337983
$215$	2.76393	0.188499
$216$	1.00000	0.0680414
$217$	−8.00000	−0.543075
$218$	−10.0000	−0.677285
$219$	−1.70820	−0.115430
$220$	1.00000	0.0674200
$221$	0.763932	0.0513876
$222$	4.47214	0.300150
$223$	−9.52786	−0.638033	−0.319016	−	0.947749i	$-0.603353\pi$
$223$	−9.52786	−0.638033	−0.319016	+	0.947749i	$0.603353\pi$
$224$	1.23607	0.0825883
$225$	1.00000	0.0666667
$226$	−19.1246	−1.27215
$227$	4.00000	0.265489	0.132745	−	0.991150i	$-0.457621\pi$
$227$	4.00000	0.265489	0.132745	+	0.991150i	$0.457621\pi$
$228$	0.763932	0.0505926
$229$	22.3607	1.47764	0.738818	−	0.673905i	$-0.235384\pi$
$229$	22.3607	1.47764	0.738818	+	0.673905i	$0.235384\pi$
$230$	−7.23607	−0.477132
$231$	1.23607	0.0813273
$232$	−2.00000	−0.131306
$233$	−7.52786	−0.493167	−0.246583	−	0.969122i	$-0.579308\pi$
$233$	−7.52786	−0.493167	−0.246583	+	0.969122i	$0.579308\pi$
$234$	−0.763932	−0.0499398
$235$	−8.94427	−0.583460
$236$	13.2361	0.861595
$237$	−4.76393	−0.309451
$238$	1.23607	0.0801224
$239$	10.4721	0.677386	0.338693	−	0.940897i	$-0.390015\pi$
$239$	10.4721	0.677386	0.338693	+	0.940897i	$0.390015\pi$
$240$	−1.00000	−0.0645497
$241$	−24.6525	−1.58801	−0.794003	−	0.607914i	$-0.792006\pi$
$241$	−24.6525	−1.58801	−0.794003	+	0.607914i	$0.792006\pi$
$242$	−1.00000	−0.0642824
$243$	−1.00000	−0.0641500
$244$	2.94427	0.188488
$245$	−5.47214	−0.349602
$246$	−8.94427	−0.570266
$247$	−0.583592	−0.0371331
$248$	−6.47214	−0.410981
$249$	4.94427	0.313331
$250$	−1.00000	−0.0632456
$251$	19.7082	1.24397	0.621985	−	0.783029i	$-0.286326\pi$
$251$	19.7082	1.24397	0.621985	+	0.783029i	$0.286326\pi$
$252$	−1.23607	−0.0778650
$253$	7.23607	0.454928
$254$	15.4164	0.967311
$255$	−1.00000	−0.0626224
$256$	1.00000	0.0625000
$257$	3.52786	0.220062	0.110031	−	0.993928i	$-0.464905\pi$
$257$	3.52786	0.220062	0.110031	+	0.993928i	$0.464905\pi$
$258$	2.76393	0.172075
$259$	−5.52786	−0.343485
$260$	0.763932	0.0473771
$261$	2.00000	0.123797
$262$	−8.00000	−0.494242
$263$	28.0000	1.72655	0.863277	−	0.504730i	$-0.168408\pi$
$263$	28.0000	1.72655	0.863277	+	0.504730i	$0.168408\pi$
$264$	1.00000	0.0615457
$265$	−7.70820	−0.473511
$266$	−0.944272	−0.0578970
$267$	−14.0000	−0.856786
$268$	−8.47214	−0.517518
$269$	4.47214	0.272671	0.136335	−	0.990663i	$-0.456467\pi$
$269$	4.47214	0.272671	0.136335	+	0.990663i	$0.456467\pi$
$270$	1.00000	0.0608581
$271$	24.3607	1.47981	0.739903	−	0.672714i	$-0.234871\pi$
$271$	24.3607	1.47981	0.739903	+	0.672714i	$0.234871\pi$
$272$	1.00000	0.0606339
$273$	0.944272	0.0571499
$274$	2.00000	0.120824
$275$	1.00000	0.0603023
$276$	−7.23607	−0.435560
$277$	1.05573	0.0634326	0.0317163	−	0.999497i	$-0.489903\pi$
$277$	1.05573	0.0634326	0.0317163	+	0.999497i	$0.489903\pi$
$278$	17.8885	1.07288
$279$	6.47214	0.387477
$280$	1.23607	0.0738692
$281$	9.41641	0.561736	0.280868	−	0.959746i	$-0.409378\pi$
$281$	9.41641	0.561736	0.280868	+	0.959746i	$0.409378\pi$
$282$	−8.94427	−0.532624
$283$	7.41641	0.440860	0.220430	−	0.975403i	$-0.429254\pi$
$283$	7.41641	0.440860	0.220430	+	0.975403i	$0.429254\pi$
$284$	5.23607	0.310703
$285$	0.763932	0.0452514
$286$	−0.763932	−0.0451722
$287$	11.0557	0.652599
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	−2.00000	−0.117444
$291$	−4.94427	−0.289838
$292$	1.70820	0.0999651
$293$	11.8885	0.694536	0.347268	−	0.937766i	$-0.387109\pi$
$293$	11.8885	0.694536	0.347268	+	0.937766i	$0.387109\pi$
$294$	−5.47214	−0.319141
$295$	13.2361	0.770634
$296$	−4.47214	−0.259938
$297$	−1.00000	−0.0580259
$298$	−0.944272	−0.0547002
$299$	5.52786	0.319685
$300$	−1.00000	−0.0577350
$301$	−3.41641	−0.196918
$302$	−12.9443	−0.744859
$303$	10.4721	0.601608
$304$	−0.763932	−0.0438145
$305$	2.94427	0.168589
$306$	−1.00000	−0.0571662
$307$	−0.652476	−0.0372388	−0.0186194	−	0.999827i	$-0.505927\pi$
$307$	−0.652476	−0.0372388	−0.0186194	+	0.999827i	$0.505927\pi$
$308$	−1.23607	−0.0704315
$309$	12.0000	0.682656
$310$	−6.47214	−0.367593
$311$	−1.81966	−0.103183	−0.0515917	−	0.998668i	$-0.516429\pi$
$311$	−1.81966	−0.103183	−0.0515917	+	0.998668i	$0.516429\pi$
$312$	0.763932	0.0432491
$313$	−9.88854	−0.558934	−0.279467	−	0.960155i	$-0.590158\pi$
$313$	−9.88854	−0.558934	−0.279467	+	0.960155i	$0.590158\pi$
$314$	12.0000	0.677199
$315$	−1.23607	−0.0696445
$316$	4.76393	0.267992
$317$	2.00000	0.112331	0.0561656	−	0.998421i	$-0.482113\pi$
$317$	2.00000	0.112331	0.0561656	+	0.998421i	$0.482113\pi$
$318$	−7.70820	−0.432255
$319$	2.00000	0.111979
$320$	1.00000	0.0559017
$321$	−4.94427	−0.275962
$322$	8.94427	0.498445
$323$	−0.763932	−0.0425063
$324$	1.00000	0.0555556
$325$	0.763932	0.0423753
$326$	−2.47214	−0.136919
$327$	−10.0000	−0.553001
$328$	8.94427	0.493865
$329$	11.0557	0.609522
$330$	1.00000	0.0550482
$331$	−25.8885	−1.42296	−0.711482	−	0.702705i	$-0.751975\pi$
$331$	−25.8885	−1.42296	−0.711482	+	0.702705i	$0.751975\pi$
$332$	−4.94427	−0.271352
$333$	4.47214	0.245072
$334$	1.52786	0.0836010
$335$	−8.47214	−0.462882
$336$	1.23607	0.0674330
$337$	4.76393	0.259508	0.129754	−	0.991546i	$-0.458581\pi$
$337$	4.76393	0.259508	0.129754	+	0.991546i	$0.458581\pi$
$338$	12.4164	0.675364
$339$	−19.1246	−1.03871
$340$	1.00000	0.0542326
$341$	6.47214	0.350486
$342$	0.763932	0.0413087
$343$	15.4164	0.832408
$344$	−2.76393	−0.149021
$345$	−7.23607	−0.389577
$346$	10.9443	0.588368
$347$	−21.8885	−1.17504	−0.587519	−	0.809210i	$-0.699895\pi$
$347$	−21.8885	−1.17504	−0.587519	+	0.809210i	$0.699895\pi$
$348$	−2.00000	−0.107211
$349$	−12.6525	−0.677272	−0.338636	−	0.940918i	$-0.609965\pi$
$349$	−12.6525	−0.677272	−0.338636	+	0.940918i	$0.609965\pi$
$350$	1.23607	0.0660706
$351$	−0.763932	−0.0407757
$352$	−1.00000	−0.0533002
$353$	−28.4721	−1.51542	−0.757709	−	0.652592i	$-0.773682\pi$
$353$	−28.4721	−1.51542	−0.757709	+	0.652592i	$0.773682\pi$
$354$	13.2361	0.703489
$355$	5.23607	0.277902
$356$	14.0000	0.741999
$357$	1.23607	0.0654197
$358$	−23.7082	−1.25302
$359$	−1.52786	−0.0806376	−0.0403188	−	0.999187i	$-0.512837\pi$
$359$	−1.52786	−0.0806376	−0.0403188	+	0.999187i	$0.512837\pi$
$360$	−1.00000	−0.0527046
$361$	−18.4164	−0.969285
$362$	11.8885	0.624848
$363$	−1.00000	−0.0524864
$364$	−0.944272	−0.0494933
$365$	1.70820	0.0894115
$366$	2.94427	0.153900
$367$	24.4721	1.27744	0.638718	−	0.769441i	$-0.279465\pi$
$367$	24.4721	1.27744	0.638718	+	0.769441i	$0.279465\pi$
$368$	7.23607	0.377206
$369$	−8.94427	−0.465620
$370$	−4.47214	−0.232495
$371$	9.52786	0.494662
$372$	−6.47214	−0.335565
$373$	6.65248	0.344452	0.172226	−	0.985057i	$-0.444904\pi$
$373$	6.65248	0.344452	0.172226	+	0.985057i	$0.444904\pi$
$374$	−1.00000	−0.0517088
$375$	−1.00000	−0.0516398
$376$	8.94427	0.461266
$377$	1.52786	0.0786890
$378$	−1.23607	−0.0635765
$379$	0	0		−	1.00000i	$-0.5\pi$
$379$	0	0			1.00000i	$0.5\pi$
$380$	−0.763932	−0.0391889
$381$	15.4164	0.789807
$382$	−21.8885	−1.11992
$383$	−13.8885	−0.709671	−0.354836	−	0.934929i	$-0.615463\pi$
$383$	−13.8885	−0.709671	−0.354836	+	0.934929i	$0.615463\pi$
$384$	1.00000	0.0510310
$385$	−1.23607	−0.0629959
$386$	21.7082	1.10492
$387$	2.76393	0.140499
$388$	4.94427	0.251007
$389$	33.7082	1.70907	0.854537	−	0.519391i	$-0.173841\pi$
$389$	33.7082	1.70907	0.854537	+	0.519391i	$0.173841\pi$
$390$	0.763932	0.0386832
$391$	7.23607	0.365944
$392$	5.47214	0.276385
$393$	−8.00000	−0.403547
$394$	−7.52786	−0.379248
$395$	4.76393	0.239699
$396$	1.00000	0.0502519
$397$	34.3607	1.72451	0.862257	−	0.506472i	$-0.169051\pi$
$397$	34.3607	1.72451	0.862257	+	0.506472i	$0.169051\pi$
$398$	−14.4721	−0.725423
$399$	−0.944272	−0.0472727
$400$	1.00000	0.0500000
$401$	−13.1246	−0.655412	−0.327706	−	0.944780i	$-0.606276\pi$
$401$	−13.1246	−0.655412	−0.327706	+	0.944780i	$0.606276\pi$
$402$	−8.47214	−0.422552
$403$	4.94427	0.246292
$404$	−10.4721	−0.521008
$405$	1.00000	0.0496904
$406$	2.47214	0.122690
$407$	4.47214	0.221676
$408$	1.00000	0.0495074
$409$	6.00000	0.296681	0.148340	−	0.988936i	$-0.452607\pi$
$409$	6.00000	0.296681	0.148340	+	0.988936i	$0.452607\pi$
$410$	8.94427	0.441726
$411$	2.00000	0.0986527
$412$	−12.0000	−0.591198
$413$	−16.3607	−0.805056
$414$	−7.23607	−0.355633
$415$	−4.94427	−0.242705
$416$	−0.763932	−0.0374548
$417$	17.8885	0.876006
$418$	0.763932	0.0373651
$419$	−1.52786	−0.0746410	−0.0373205	−	0.999303i	$-0.511882\pi$
$419$	−1.52786	−0.0746410	−0.0373205	+	0.999303i	$0.511882\pi$
$420$	1.23607	0.0603139
$421$	−3.88854	−0.189516	−0.0947580	−	0.995500i	$-0.530208\pi$
$421$	−3.88854	−0.189516	−0.0947580	+	0.995500i	$0.530208\pi$
$422$	−19.4164	−0.945176
$423$	−8.94427	−0.434885
$424$	7.70820	0.374343
$425$	1.00000	0.0485071
$426$	5.23607	0.253688
$427$	−3.63932	−0.176119
$428$	4.94427	0.238990
$429$	−0.763932	−0.0368830
$430$	−2.76393	−0.133289
$431$	17.4164	0.838919	0.419459	−	0.907774i	$-0.362220\pi$
$431$	17.4164	0.838919	0.419459	+	0.907774i	$0.362220\pi$
$432$	−1.00000	−0.0481125
$433$	32.8328	1.57784	0.788922	−	0.614493i	$-0.210639\pi$
$433$	32.8328	1.57784	0.788922	+	0.614493i	$0.210639\pi$
$434$	8.00000	0.384012
$435$	−2.00000	−0.0958927
$436$	10.0000	0.478913
$437$	−5.52786	−0.264434
$438$	1.70820	0.0816211
$439$	−29.1246	−1.39004	−0.695021	−	0.718989i	$-0.744605\pi$
$439$	−29.1246	−1.39004	−0.695021	+	0.718989i	$0.744605\pi$
$440$	−1.00000	−0.0476731
$441$	−5.47214	−0.260578
$442$	−0.763932	−0.0363365
$443$	−5.70820	−0.271205	−0.135602	−	0.990763i	$-0.543297\pi$
$443$	−5.70820	−0.271205	−0.135602	+	0.990763i	$0.543297\pi$
$444$	−4.47214	−0.212238
$445$	14.0000	0.663664
$446$	9.52786	0.451157
$447$	−0.944272	−0.0446625
$448$	−1.23607	−0.0583987
$449$	−14.6525	−0.691493	−0.345747	−	0.938328i	$-0.612374\pi$
$449$	−14.6525	−0.691493	−0.345747	+	0.938328i	$0.612374\pi$
$450$	−1.00000	−0.0471405
$451$	−8.94427	−0.421169
$452$	19.1246	0.899546
$453$	−12.9443	−0.608175
$454$	−4.00000	−0.187729
$455$	−0.944272	−0.0442681
$456$	−0.763932	−0.0357744
$457$	36.8328	1.72297	0.861483	−	0.507786i	$-0.169536\pi$
$457$	36.8328	1.72297	0.861483	+	0.507786i	$0.169536\pi$
$458$	−22.3607	−1.04485
$459$	−1.00000	−0.0466760
$460$	7.23607	0.337383
$461$	−12.9443	−0.602875	−0.301437	−	0.953486i	$-0.597466\pi$
$461$	−12.9443	−0.602875	−0.301437	+	0.953486i	$0.597466\pi$
$462$	−1.23607	−0.0575071
$463$	17.5279	0.814589	0.407294	−	0.913297i	$-0.366472\pi$
$463$	17.5279	0.814589	0.407294	+	0.913297i	$0.366472\pi$
$464$	2.00000	0.0928477
$465$	−6.47214	−0.300138
$466$	7.52786	0.348722
$467$	34.0689	1.57652	0.788260	−	0.615342i	$-0.210982\pi$
$467$	34.0689	1.57652	0.788260	+	0.615342i	$0.210982\pi$
$468$	0.763932	0.0353128
$469$	10.4721	0.483558
$470$	8.94427	0.412568
$471$	12.0000	0.552931
$472$	−13.2361	−0.609239
$473$	2.76393	0.127086
$474$	4.76393	0.218815
$475$	−0.763932	−0.0350516
$476$	−1.23607	−0.0566551
$477$	−7.70820	−0.352934
$478$	−10.4721	−0.478984
$479$	38.9443	1.77941	0.889705	−	0.456537i	$-0.150910\pi$
$479$	38.9443	1.77941	0.889705	+	0.456537i	$0.150910\pi$
$480$	1.00000	0.0456435
$481$	3.41641	0.155775
$482$	24.6525	1.12289
$483$	8.94427	0.406978
$484$	1.00000	0.0454545
$485$	4.94427	0.224508
$486$	1.00000	0.0453609
$487$	2.58359	0.117074	0.0585369	−	0.998285i	$-0.481356\pi$
$487$	2.58359	0.117074	0.0585369	+	0.998285i	$0.481356\pi$
$488$	−2.94427	−0.133281
$489$	−2.47214	−0.111794
$490$	5.47214	0.247206
$491$	−4.47214	−0.201825	−0.100912	−	0.994895i	$-0.532176\pi$
$491$	−4.47214	−0.201825	−0.100912	+	0.994895i	$0.532176\pi$
$492$	8.94427	0.403239
$493$	2.00000	0.0900755
$494$	0.583592	0.0262571
$495$	1.00000	0.0449467
$496$	6.47214	0.290607
$497$	−6.47214	−0.290315
$498$	−4.94427	−0.221558
$499$	36.0000	1.61158	0.805791	−	0.592200i	$-0.201741\pi$
$499$	36.0000	1.61158	0.805791	+	0.592200i	$0.201741\pi$
$500$	1.00000	0.0447214
$501$	1.52786	0.0682599
$502$	−19.7082	−0.879620
$503$	21.8885	0.975962	0.487981	−	0.872854i	$-0.337734\pi$
$503$	21.8885	0.975962	0.487981	+	0.872854i	$0.337734\pi$
$504$	1.23607	0.0550588
$505$	−10.4721	−0.466004
$506$	−7.23607	−0.321682
$507$	12.4164	0.551432
$508$	−15.4164	−0.683992
$509$	2.87539	0.127449	0.0637247	−	0.997968i	$-0.479702\pi$
$509$	2.87539	0.127449	0.0637247	+	0.997968i	$0.479702\pi$
$510$	1.00000	0.0442807
$511$	−2.11146	−0.0934053
$512$	−1.00000	−0.0441942
$513$	0.763932	0.0337284
$514$	−3.52786	−0.155607
$515$	−12.0000	−0.528783
$516$	−2.76393	−0.121675
$517$	−8.94427	−0.393369
$518$	5.52786	0.242880
$519$	10.9443	0.480400
$520$	−0.763932	−0.0335006
$521$	40.5410	1.77613	0.888067	−	0.459714i	$-0.152048\pi$
$521$	40.5410	1.77613	0.888067	+	0.459714i	$0.152048\pi$
$522$	−2.00000	−0.0875376
$523$	23.1246	1.01117	0.505584	−	0.862777i	$-0.331277\pi$
$523$	23.1246	1.01117	0.505584	+	0.862777i	$0.331277\pi$
$524$	8.00000	0.349482
$525$	1.23607	0.0539464
$526$	−28.0000	−1.22086
$527$	6.47214	0.281931
$528$	−1.00000	−0.0435194
$529$	29.3607	1.27655
$530$	7.70820	0.334823
$531$	13.2361	0.574396
$532$	0.944272	0.0409394
$533$	−6.83282	−0.295962
$534$	14.0000	0.605839
$535$	4.94427	0.213760
$536$	8.47214	0.365941
$537$	−23.7082	−1.02308
$538$	−4.47214	−0.192807
$539$	−5.47214	−0.235702
$540$	−1.00000	−0.0430331
$541$	−37.7771	−1.62416	−0.812082	−	0.583543i	$-0.801666\pi$
$541$	−37.7771	−1.62416	−0.812082	+	0.583543i	$0.801666\pi$
$542$	−24.3607	−1.04638
$543$	11.8885	0.510186
$544$	−1.00000	−0.0428746
$545$	10.0000	0.428353
$546$	−0.944272	−0.0404111
$547$	−15.4164	−0.659158	−0.329579	−	0.944128i	$-0.606907\pi$
$547$	−15.4164	−0.659158	−0.329579	+	0.944128i	$0.606907\pi$
$548$	−2.00000	−0.0854358
$549$	2.94427	0.125658
$550$	−1.00000	−0.0426401
$551$	−1.52786	−0.0650892
$552$	7.23607	0.307988
$553$	−5.88854	−0.250406
$554$	−1.05573	−0.0448536
$555$	−4.47214	−0.189832
$556$	−17.8885	−0.758643
$557$	20.8328	0.882715	0.441357	−	0.897331i	$-0.354497\pi$
$557$	20.8328	0.882715	0.441357	+	0.897331i	$0.354497\pi$
$558$	−6.47214	−0.273987
$559$	2.11146	0.0893051
$560$	−1.23607	−0.0522334
$561$	−1.00000	−0.0422200
$562$	−9.41641	−0.397207
$563$	30.8328	1.29945	0.649724	−	0.760170i	$-0.274884\pi$
$563$	30.8328	1.29945	0.649724	+	0.760170i	$0.274884\pi$
$564$	8.94427	0.376622
$565$	19.1246	0.804578
$566$	−7.41641	−0.311735
$567$	−1.23607	−0.0519100
$568$	−5.23607	−0.219701
$569$	−3.52786	−0.147896	−0.0739479	−	0.997262i	$-0.523560\pi$
$569$	−3.52786	−0.147896	−0.0739479	+	0.997262i	$0.523560\pi$
$570$	−0.763932	−0.0319976
$571$	−20.9443	−0.876491	−0.438245	−	0.898855i	$-0.644400\pi$
$571$	−20.9443	−0.876491	−0.438245	+	0.898855i	$0.644400\pi$
$572$	0.763932	0.0319416
$573$	−21.8885	−0.914407
$574$	−11.0557	−0.461457
$575$	7.23607	0.301765
$576$	1.00000	0.0416667
$577$	−42.9443	−1.78779	−0.893897	−	0.448273i	$-0.852039\pi$
$577$	−42.9443	−1.78779	−0.893897	+	0.448273i	$0.852039\pi$
$578$	−1.00000	−0.0415945
$579$	21.7082	0.902162
$580$	2.00000	0.0830455
$581$	6.11146	0.253546
$582$	4.94427	0.204947
$583$	−7.70820	−0.319241
$584$	−1.70820	−0.0706860
$585$	0.763932	0.0315847
$586$	−11.8885	−0.491111
$587$	13.3475	0.550911	0.275456	−	0.961314i	$-0.411171\pi$
$587$	13.3475	0.550911	0.275456	+	0.961314i	$0.411171\pi$
$588$	5.47214	0.225667
$589$	−4.94427	−0.203725
$590$	−13.2361	−0.544920
$591$	−7.52786	−0.309655
$592$	4.47214	0.183804
$593$	39.3050	1.61406	0.807030	−	0.590510i	$-0.201073\pi$
$593$	39.3050	1.61406	0.807030	+	0.590510i	$0.201073\pi$
$594$	1.00000	0.0410305
$595$	−1.23607	−0.0506738
$596$	0.944272	0.0386789
$597$	−14.4721	−0.592305
$598$	−5.52786	−0.226051
$599$	2.11146	0.0862718	0.0431359	−	0.999069i	$-0.486265\pi$
$599$	2.11146	0.0862718	0.0431359	+	0.999069i	$0.486265\pi$
$600$	1.00000	0.0408248
$601$	−6.18034	−0.252101	−0.126051	−	0.992024i	$-0.540230\pi$
$601$	−6.18034	−0.252101	−0.126051	+	0.992024i	$0.540230\pi$
$602$	3.41641	0.139242
$603$	−8.47214	−0.345012
$604$	12.9443	0.526695
$605$	1.00000	0.0406558
$606$	−10.4721	−0.425401
$607$	−9.23607	−0.374880	−0.187440	−	0.982276i	$-0.560019\pi$
$607$	−9.23607	−0.374880	−0.187440	+	0.982276i	$0.560019\pi$
$608$	0.763932	0.0309815
$609$	2.47214	0.100176
$610$	−2.94427	−0.119210
$611$	−6.83282	−0.276426
$612$	1.00000	0.0404226
$613$	−26.0689	−1.05291	−0.526456	−	0.850202i	$-0.676480\pi$
$613$	−26.0689	−1.05291	−0.526456	+	0.850202i	$0.676480\pi$
$614$	0.652476	0.0263318
$615$	8.94427	0.360668
$616$	1.23607	0.0498026
$617$	−6.18034	−0.248811	−0.124406	−	0.992231i	$-0.539702\pi$
$617$	−6.18034	−0.248811	−0.124406	+	0.992231i	$0.539702\pi$
$618$	−12.0000	−0.482711
$619$	42.8328	1.72160	0.860798	−	0.508947i	$-0.169965\pi$
$619$	42.8328	1.72160	0.860798	+	0.508947i	$0.169965\pi$
$620$	6.47214	0.259927
$621$	−7.23607	−0.290373
$622$	1.81966	0.0729617
$623$	−17.3050	−0.693308
$624$	−0.763932	−0.0305818
$625$	1.00000	0.0400000
$626$	9.88854	0.395226
$627$	0.763932	0.0305085
$628$	−12.0000	−0.478852
$629$	4.47214	0.178316
$630$	1.23607	0.0492461
$631$	28.0000	1.11466	0.557331	−	0.830290i	$-0.311825\pi$
$631$	28.0000	1.11466	0.557331	+	0.830290i	$0.311825\pi$
$632$	−4.76393	−0.189499
$633$	−19.4164	−0.771733
$634$	−2.00000	−0.0794301
$635$	−15.4164	−0.611781
$636$	7.70820	0.305650
$637$	−4.18034	−0.165631
$638$	−2.00000	−0.0791808
$639$	5.23607	0.207136
$640$	−1.00000	−0.0395285
$641$	−14.2918	−0.564492	−0.282246	−	0.959342i	$-0.591079\pi$
$641$	−14.2918	−0.564492	−0.282246	+	0.959342i	$0.591079\pi$
$642$	4.94427	0.195135
$643$	4.94427	0.194983	0.0974915	−	0.995236i	$-0.468918\pi$
$643$	4.94427	0.194983	0.0974915	+	0.995236i	$0.468918\pi$
$644$	−8.94427	−0.352454
$645$	−2.76393	−0.108830
$646$	0.763932	0.0300565
$647$	21.5279	0.846348	0.423174	−	0.906049i	$-0.360916\pi$
$647$	21.5279	0.846348	0.423174	+	0.906049i	$0.360916\pi$
$648$	−1.00000	−0.0392837
$649$	13.2361	0.519561
$650$	−0.763932	−0.0299639
$651$	8.00000	0.313545
$652$	2.47214	0.0968163
$653$	28.8328	1.12832	0.564158	−	0.825667i	$-0.309201\pi$
$653$	28.8328	1.12832	0.564158	+	0.825667i	$0.309201\pi$
$654$	10.0000	0.391031
$655$	8.00000	0.312586
$656$	−8.94427	−0.349215
$657$	1.70820	0.0666434
$658$	−11.0557	−0.430997
$659$	40.4721	1.57657	0.788285	−	0.615310i	$-0.210969\pi$
$659$	40.4721	1.57657	0.788285	+	0.615310i	$0.210969\pi$
$660$	−1.00000	−0.0389249
$661$	24.4721	0.951856	0.475928	−	0.879484i	$-0.342112\pi$
$661$	24.4721	0.951856	0.475928	+	0.879484i	$0.342112\pi$
$662$	25.8885	1.00619
$663$	−0.763932	−0.0296687
$664$	4.94427	0.191875
$665$	0.944272	0.0366173
$666$	−4.47214	−0.173292
$667$	14.4721	0.560363
$668$	−1.52786	−0.0591148
$669$	9.52786	0.368369
$670$	8.47214	0.327307
$671$	2.94427	0.113662
$672$	−1.23607	−0.0476824
$673$	18.2918	0.705097	0.352548	−	0.935794i	$-0.385315\pi$
$673$	18.2918	0.705097	0.352548	+	0.935794i	$0.385315\pi$
$674$	−4.76393	−0.183500
$675$	−1.00000	−0.0384900
$676$	−12.4164	−0.477554
$677$	10.5836	0.406760	0.203380	−	0.979100i	$-0.434807\pi$
$677$	10.5836	0.406760	0.203380	+	0.979100i	$0.434807\pi$
$678$	19.1246	0.734476
$679$	−6.11146	−0.234536
$680$	−1.00000	−0.0383482
$681$	−4.00000	−0.153280
$682$	−6.47214	−0.247831
$683$	−0.944272	−0.0361316	−0.0180658	−	0.999837i	$-0.505751\pi$
$683$	−0.944272	−0.0361316	−0.0180658	+	0.999837i	$0.505751\pi$
$684$	−0.763932	−0.0292097
$685$	−2.00000	−0.0764161
$686$	−15.4164	−0.588601
$687$	−22.3607	−0.853113
$688$	2.76393	0.105374
$689$	−5.88854	−0.224336
$690$	7.23607	0.275472
$691$	−41.8885	−1.59352	−0.796758	−	0.604299i	$-0.793453\pi$
$691$	−41.8885	−1.59352	−0.796758	+	0.604299i	$0.793453\pi$
$692$	−10.9443	−0.416039
$693$	−1.23607	−0.0469543
$694$	21.8885	0.830878
$695$	−17.8885	−0.678551
$696$	2.00000	0.0758098
$697$	−8.94427	−0.338788
$698$	12.6525	0.478903
$699$	7.52786	0.284730
$700$	−1.23607	−0.0467190
$701$	−16.0000	−0.604312	−0.302156	−	0.953259i	$-0.597706\pi$
$701$	−16.0000	−0.604312	−0.302156	+	0.953259i	$0.597706\pi$
$702$	0.763932	0.0288328
$703$	−3.41641	−0.128852
$704$	1.00000	0.0376889
$705$	8.94427	0.336861
$706$	28.4721	1.07156
$707$	12.9443	0.486819
$708$	−13.2361	−0.497442
$709$	40.2492	1.51159	0.755796	−	0.654808i	$-0.227250\pi$
$709$	40.2492	1.51159	0.755796	+	0.654808i	$0.227250\pi$
$710$	−5.23607	−0.196506
$711$	4.76393	0.178661
$712$	−14.0000	−0.524672
$713$	46.8328	1.75390
$714$	−1.23607	−0.0462587
$715$	0.763932	0.0285694
$716$	23.7082	0.886017
$717$	−10.4721	−0.391089
$718$	1.52786	0.0570194
$719$	35.7082	1.33169	0.665846	−	0.746090i	$-0.268071\pi$
$719$	35.7082	1.33169	0.665846	+	0.746090i	$0.268071\pi$
$720$	1.00000	0.0372678
$721$	14.8328	0.552403
$722$	18.4164	0.685388
$723$	24.6525	0.916835
$724$	−11.8885	−0.441834
$725$	2.00000	0.0742781
$726$	1.00000	0.0371135
$727$	−32.9443	−1.22184	−0.610918	−	0.791694i	$-0.709199\pi$
$727$	−32.9443	−1.22184	−0.610918	+	0.791694i	$0.709199\pi$
$728$	0.944272	0.0349970
$729$	1.00000	0.0370370
$730$	−1.70820	−0.0632235
$731$	2.76393	0.102228
$732$	−2.94427	−0.108823
$733$	−50.0689	−1.84934	−0.924668	−	0.380774i	$-0.875658\pi$
$733$	−50.0689	−1.84934	−0.924668	+	0.380774i	$0.875658\pi$
$734$	−24.4721	−0.903283
$735$	5.47214	0.201843
$736$	−7.23607	−0.266725
$737$	−8.47214	−0.312075
$738$	8.94427	0.329243
$739$	3.23607	0.119041	0.0595203	−	0.998227i	$-0.481043\pi$
$739$	3.23607	0.119041	0.0595203	+	0.998227i	$0.481043\pi$
$740$	4.47214	0.164399
$741$	0.583592	0.0214388
$742$	−9.52786	−0.349779
$743$	14.8328	0.544163	0.272082	−	0.962274i	$-0.412288\pi$
$743$	14.8328	0.544163	0.272082	+	0.962274i	$0.412288\pi$
$744$	6.47214	0.237280
$745$	0.944272	0.0345954
$746$	−6.65248	−0.243564
$747$	−4.94427	−0.180901
$748$	1.00000	0.0365636
$749$	−6.11146	−0.223308
$750$	1.00000	0.0365148
$751$	16.9443	0.618305	0.309153	−	0.951012i	$-0.399955\pi$
$751$	16.9443	0.618305	0.309153	+	0.951012i	$0.399955\pi$
$752$	−8.94427	−0.326164
$753$	−19.7082	−0.718207
$754$	−1.52786	−0.0556415
$755$	12.9443	0.471090
$756$	1.23607	0.0449554
$757$	9.30495	0.338194	0.169097	−	0.985599i	$-0.445915\pi$
$757$	9.30495	0.338194	0.169097	+	0.985599i	$0.445915\pi$
$758$	0	0
$759$	−7.23607	−0.262653
$760$	0.763932	0.0277107
$761$	13.4164	0.486344	0.243172	−	0.969983i	$-0.421812\pi$
$761$	13.4164	0.486344	0.243172	+	0.969983i	$0.421812\pi$
$762$	−15.4164	−0.558478
$763$	−12.3607	−0.447487
$764$	21.8885	0.791900
$765$	1.00000	0.0361551
$766$	13.8885	0.501813
$767$	10.1115	0.365104
$768$	−1.00000	−0.0360844
$769$	17.4164	0.628052	0.314026	−	0.949414i	$-0.398322\pi$
$769$	17.4164	0.628052	0.314026	+	0.949414i	$0.398322\pi$
$770$	1.23607	0.0445448
$771$	−3.52786	−0.127053
$772$	−21.7082	−0.781295
$773$	−29.0132	−1.04353	−0.521765	−	0.853089i	$-0.674726\pi$
$773$	−29.0132	−1.04353	−0.521765	+	0.853089i	$0.674726\pi$
$774$	−2.76393	−0.0993475
$775$	6.47214	0.232486
$776$	−4.94427	−0.177489
$777$	5.52786	0.198311
$778$	−33.7082	−1.20850
$779$	6.83282	0.244811
$780$	−0.763932	−0.0273532
$781$	5.23607	0.187361
$782$	−7.23607	−0.258761
$783$	−2.00000	−0.0714742
$784$	−5.47214	−0.195433
$785$	−12.0000	−0.428298
$786$	8.00000	0.285351
$787$	35.7771	1.27532	0.637658	−	0.770320i	$-0.279903\pi$
$787$	35.7771	1.27532	0.637658	+	0.770320i	$0.279903\pi$
$788$	7.52786	0.268169
$789$	−28.0000	−0.996826
$790$	−4.76393	−0.169493
$791$	−23.6393	−0.840517
$792$	−1.00000	−0.0355335
$793$	2.24922	0.0798723
$794$	−34.3607	−1.21941
$795$	7.70820	0.273382
$796$	14.4721	0.512951
$797$	51.1246	1.81093	0.905463	−	0.424425i	$-0.139524\pi$
$797$	51.1246	1.81093	0.905463	+	0.424425i	$0.139524\pi$
$798$	0.944272	0.0334269
$799$	−8.94427	−0.316426
$800$	−1.00000	−0.0353553
$801$	14.0000	0.494666
$802$	13.1246	0.463446
$803$	1.70820	0.0602812
$804$	8.47214	0.298789
$805$	−8.94427	−0.315244
$806$	−4.94427	−0.174155
$807$	−4.47214	−0.157427
$808$	10.4721	0.368408
$809$	5.52786	0.194349	0.0971747	−	0.995267i	$-0.469019\pi$
$809$	5.52786	0.194349	0.0971747	+	0.995267i	$0.469019\pi$
$810$	−1.00000	−0.0351364
$811$	−54.4721	−1.91278	−0.956388	−	0.292100i	$-0.905646\pi$
$811$	−54.4721	−1.91278	−0.956388	+	0.292100i	$0.905646\pi$
$812$	−2.47214	−0.0867550
$813$	−24.3607	−0.854366
$814$	−4.47214	−0.156748
$815$	2.47214	0.0865951
$816$	−1.00000	−0.0350070
$817$	−2.11146	−0.0738705
$818$	−6.00000	−0.209785
$819$	−0.944272	−0.0329955
$820$	−8.94427	−0.312348
$821$	50.7214	1.77019	0.885094	−	0.465413i	$-0.154094\pi$
$821$	50.7214	1.77019	0.885094	+	0.465413i	$0.154094\pi$
$822$	−2.00000	−0.0697580
$823$	−20.8328	−0.726186	−0.363093	−	0.931753i	$-0.618279\pi$
$823$	−20.8328	−0.726186	−0.363093	+	0.931753i	$0.618279\pi$
$824$	12.0000	0.418040
$825$	−1.00000	−0.0348155
$826$	16.3607	0.569261
$827$	−8.00000	−0.278187	−0.139094	−	0.990279i	$-0.544419\pi$
$827$	−8.00000	−0.278187	−0.139094	+	0.990279i	$0.544419\pi$
$828$	7.23607	0.251471
$829$	−28.8328	−1.00141	−0.500703	−	0.865619i	$-0.666925\pi$
$829$	−28.8328	−1.00141	−0.500703	+	0.865619i	$0.666925\pi$
$830$	4.94427	0.171618
$831$	−1.05573	−0.0366228
$832$	0.763932	0.0264846
$833$	−5.47214	−0.189598
$834$	−17.8885	−0.619430
$835$	−1.52786	−0.0528739
$836$	−0.763932	−0.0264211
$837$	−6.47214	−0.223710
$838$	1.52786	0.0527792
$839$	−34.5410	−1.19249	−0.596244	−	0.802803i	$-0.703341\pi$
$839$	−34.5410	−1.19249	−0.596244	+	0.802803i	$0.703341\pi$
$840$	−1.23607	−0.0426484
$841$	−25.0000	−0.862069
$842$	3.88854	0.134008
$843$	−9.41641	−0.324318
$844$	19.4164	0.668340
$845$	−12.4164	−0.427137
$846$	8.94427	0.307510
$847$	−1.23607	−0.0424718
$848$	−7.70820	−0.264701
$849$	−7.41641	−0.254530
$850$	−1.00000	−0.0342997
$851$	32.3607	1.10931
$852$	−5.23607	−0.179385
$853$	6.36068	0.217786	0.108893	−	0.994054i	$-0.465269\pi$
$853$	6.36068	0.217786	0.108893	+	0.994054i	$0.465269\pi$
$854$	3.63932	0.124535
$855$	−0.763932	−0.0261259
$856$	−4.94427	−0.168992
$857$	−39.8885	−1.36257	−0.681283	−	0.732020i	$-0.738578\pi$
$857$	−39.8885	−1.36257	−0.681283	+	0.732020i	$0.738578\pi$
$858$	0.763932	0.0260802
$859$	−38.8328	−1.32496	−0.662479	−	0.749080i	$-0.730496\pi$
$859$	−38.8328	−1.32496	−0.662479	+	0.749080i	$0.730496\pi$
$860$	2.76393	0.0942493
$861$	−11.0557	−0.376778
$862$	−17.4164	−0.593205
$863$	39.4164	1.34175	0.670875	−	0.741570i	$-0.265919\pi$
$863$	39.4164	1.34175	0.670875	+	0.741570i	$0.265919\pi$
$864$	1.00000	0.0340207
$865$	−10.9443	−0.372116
$866$	−32.8328	−1.11570
$867$	−1.00000	−0.0339618
$868$	−8.00000	−0.271538
$869$	4.76393	0.161605
$870$	2.00000	0.0678064
$871$	−6.47214	−0.219300
$872$	−10.0000	−0.338643
$873$	4.94427	0.167338
$874$	5.52786	0.186983
$875$	−1.23607	−0.0417867
$876$	−1.70820	−0.0577149
$877$	27.3050	0.922023	0.461011	−	0.887394i	$-0.347487\pi$
$877$	27.3050	0.922023	0.461011	+	0.887394i	$0.347487\pi$
$878$	29.1246	0.982908
$879$	−11.8885	−0.400991
$880$	1.00000	0.0337100
$881$	−14.6525	−0.493654	−0.246827	−	0.969060i	$-0.579388\pi$
$881$	−14.6525	−0.493654	−0.246827	+	0.969060i	$0.579388\pi$
$882$	5.47214	0.184256
$883$	14.9443	0.502915	0.251457	−	0.967868i	$-0.419090\pi$
$883$	14.9443	0.502915	0.251457	+	0.967868i	$0.419090\pi$
$884$	0.763932	0.0256938
$885$	−13.2361	−0.444926
$886$	5.70820	0.191771
$887$	−31.4164	−1.05486	−0.527430	−	0.849599i	$-0.676844\pi$
$887$	−31.4164	−1.05486	−0.527430	+	0.849599i	$0.676844\pi$
$888$	4.47214	0.150075
$889$	19.0557	0.639109
$890$	−14.0000	−0.469281
$891$	1.00000	0.0335013
$892$	−9.52786	−0.319016
$893$	6.83282	0.228651
$894$	0.944272	0.0315812
$895$	23.7082	0.792478
$896$	1.23607	0.0412941
$897$	−5.52786	−0.184570
$898$	14.6525	0.488959
$899$	12.9443	0.431716
$900$	1.00000	0.0333333
$901$	−7.70820	−0.256798
$902$	8.94427	0.297812
$903$	3.41641	0.113691
$904$	−19.1246	−0.636075
$905$	−11.8885	−0.395189
$906$	12.9443	0.430045
$907$	14.8328	0.492516	0.246258	−	0.969204i	$-0.420799\pi$
$907$	14.8328	0.492516	0.246258	+	0.969204i	$0.420799\pi$
$908$	4.00000	0.132745
$909$	−10.4721	−0.347339
$910$	0.944272	0.0313023
$911$	−29.8197	−0.987969	−0.493985	−	0.869471i	$-0.664460\pi$
$911$	−29.8197	−0.987969	−0.493985	+	0.869471i	$0.664460\pi$
$912$	0.763932	0.0252963
$913$	−4.94427	−0.163632
$914$	−36.8328	−1.21832
$915$	−2.94427	−0.0973346
$916$	22.3607	0.738818
$917$	−9.88854	−0.326548
$918$	1.00000	0.0330049
$919$	−35.7771	−1.18018	−0.590089	−	0.807338i	$-0.700907\pi$
$919$	−35.7771	−1.18018	−0.590089	+	0.807338i	$0.700907\pi$
$920$	−7.23607	−0.238566
$921$	0.652476	0.0214998
$922$	12.9443	0.426297
$923$	4.00000	0.131662
$924$	1.23607	0.0406637
$925$	4.47214	0.147043
$926$	−17.5279	−0.576001
$927$	−12.0000	−0.394132
$928$	−2.00000	−0.0656532
$929$	−26.6525	−0.874439	−0.437220	−	0.899355i	$-0.644037\pi$
$929$	−26.6525	−0.874439	−0.437220	+	0.899355i	$0.644037\pi$
$930$	6.47214	0.212230
$931$	4.18034	0.137005
$932$	−7.52786	−0.246583
$933$	1.81966	0.0595730
$934$	−34.0689	−1.11477
$935$	1.00000	0.0327035
$936$	−0.763932	−0.0249699
$937$	31.5279	1.02997	0.514985	−	0.857199i	$-0.327797\pi$
$937$	31.5279	1.02997	0.514985	+	0.857199i	$0.327797\pi$
$938$	−10.4721	−0.341927
$939$	9.88854	0.322700
$940$	−8.94427	−0.291730
$941$	−47.8885	−1.56112	−0.780561	−	0.625080i	$-0.785066\pi$
$941$	−47.8885	−1.56112	−0.780561	+	0.625080i	$0.785066\pi$
$942$	−12.0000	−0.390981
$943$	−64.7214	−2.10762
$944$	13.2361	0.430797
$945$	1.23607	0.0402093
$946$	−2.76393	−0.0898632
$947$	4.00000	0.129983	0.0649913	−	0.997886i	$-0.479298\pi$
$947$	4.00000	0.129983	0.0649913	+	0.997886i	$0.479298\pi$
$948$	−4.76393	−0.154725
$949$	1.30495	0.0423605
$950$	0.763932	0.0247852
$951$	−2.00000	−0.0648544
$952$	1.23607	0.0400612
$953$	−26.3607	−0.853906	−0.426953	−	0.904274i	$-0.640413\pi$
$953$	−26.3607	−0.853906	−0.426953	+	0.904274i	$0.640413\pi$
$954$	7.70820	0.249562
$955$	21.8885	0.708297
$956$	10.4721	0.338693
$957$	−2.00000	−0.0646508
$958$	−38.9443	−1.25823
$959$	2.47214	0.0798294
$960$	−1.00000	−0.0322749
$961$	10.8885	0.351243
$962$	−3.41641	−0.110149
$963$	4.94427	0.159327
$964$	−24.6525	−0.794003
$965$	−21.7082	−0.698812
$966$	−8.94427	−0.287777
$967$	53.6656	1.72577	0.862885	−	0.505400i	$-0.168655\pi$
$967$	53.6656	1.72577	0.862885	+	0.505400i	$0.168655\pi$
$968$	−1.00000	−0.0321412
$969$	0.763932	0.0245410
$970$	−4.94427	−0.158751
$971$	−9.81966	−0.315128	−0.157564	−	0.987509i	$-0.550364\pi$
$971$	−9.81966	−0.315128	−0.157564	+	0.987509i	$0.550364\pi$
$972$	−1.00000	−0.0320750
$973$	22.1115	0.708861
$974$	−2.58359	−0.0827836
$975$	−0.763932	−0.0244654
$976$	2.94427	0.0942438
$977$	−24.2492	−0.775801	−0.387901	−	0.921701i	$-0.626800\pi$
$977$	−24.2492	−0.775801	−0.387901	+	0.921701i	$0.626800\pi$
$978$	2.47214	0.0790502
$979$	14.0000	0.447442
$980$	−5.47214	−0.174801
$981$	10.0000	0.319275
$982$	4.47214	0.142712
$983$	−11.5967	−0.369879	−0.184939	−	0.982750i	$-0.559209\pi$
$983$	−11.5967	−0.369879	−0.184939	+	0.982750i	$0.559209\pi$
$984$	−8.94427	−0.285133
$985$	7.52786	0.239858
$986$	−2.00000	−0.0636930
$987$	−11.0557	−0.351908
$988$	−0.583592	−0.0185665
$989$	20.0000	0.635963
$990$	−1.00000	−0.0317821
$991$	−22.1115	−0.702394	−0.351197	−	0.936302i	$-0.614225\pi$
$991$	−22.1115	−0.702394	−0.351197	+	0.936302i	$0.614225\pi$
$992$	−6.47214	−0.205491
$993$	25.8885	0.821548
$994$	6.47214	0.205284
$995$	14.4721	0.458798
$996$	4.94427	0.156665
$997$	−49.4164	−1.56503	−0.782517	−	0.622630i	$-0.786064\pi$
$997$	−49.4164	−1.56503	−0.782517	+	0.622630i	$0.786064\pi$
$998$	−36.0000	−1.13956
$999$	−4.47214	−0.141492

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5610.2.a.br.1.1	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -1.23607 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -1.23607 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +1.00000 q^{11} -1.00000 q^{12} +0.763932 q^{13} +1.23607 q^{14} -1.00000 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} -0.763932 q^{19} +1.00000 q^{20} +1.23607 q^{21} -1.00000 q^{22} +7.23607 q^{23} +1.00000 q^{24} +1.00000 q^{25} -0.763932 q^{26} -1.00000 q^{27} -1.23607 q^{28} +2.00000 q^{29} +1.00000 q^{30} +6.47214 q^{31} -1.00000 q^{32} -1.00000 q^{33} -1.00000 q^{34} -1.23607 q^{35} +1.00000 q^{36} +4.47214 q^{37} +0.763932 q^{38} -0.763932 q^{39} -1.00000 q^{40} -8.94427 q^{41} -1.23607 q^{42} +2.76393 q^{43} +1.00000 q^{44} +1.00000 q^{45} -7.23607 q^{46} -8.94427 q^{47} -1.00000 q^{48} -5.47214 q^{49} -1.00000 q^{50} -1.00000 q^{51} +0.763932 q^{52} -7.70820 q^{53} +1.00000 q^{54} +1.00000 q^{55} +1.23607 q^{56} +0.763932 q^{57} -2.00000 q^{58} +13.2361 q^{59} -1.00000 q^{60} +2.94427 q^{61} -6.47214 q^{62} -1.23607 q^{63} +1.00000 q^{64} +0.763932 q^{65} +1.00000 q^{66} -8.47214 q^{67} +1.00000 q^{68} -7.23607 q^{69} +1.23607 q^{70} +5.23607 q^{71} -1.00000 q^{72} +1.70820 q^{73} -4.47214 q^{74} -1.00000 q^{75} -0.763932 q^{76} -1.23607 q^{77} +0.763932 q^{78} +4.76393 q^{79} +1.00000 q^{80} +1.00000 q^{81} +8.94427 q^{82} -4.94427 q^{83} +1.23607 q^{84} +1.00000 q^{85} -2.76393 q^{86} -2.00000 q^{87} -1.00000 q^{88} +14.0000 q^{89} -1.00000 q^{90} -0.944272 q^{91} +7.23607 q^{92} -6.47214 q^{93} +8.94427 q^{94} -0.763932 q^{95} +1.00000 q^{96} +4.94427 q^{97} +5.47214 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} + 2 q^{9} - 2 q^{10} + 2 q^{11} - 2 q^{12} + 6 q^{13} - 2 q^{14} - 2 q^{15} + 2 q^{16} + 2 q^{17} - 2 q^{18} - 6 q^{19} + 2 q^{20} - 2 q^{21} - 2 q^{22} + 10 q^{23} + 2 q^{24} + 2 q^{25} - 6 q^{26} - 2 q^{27} + 2 q^{28} + 4 q^{29} + 2 q^{30} + 4 q^{31} - 2 q^{32} - 2 q^{33} - 2 q^{34} + 2 q^{35} + 2 q^{36} + 6 q^{38} - 6 q^{39} - 2 q^{40} + 2 q^{42} + 10 q^{43} + 2 q^{44} + 2 q^{45} - 10 q^{46} - 2 q^{48} - 2 q^{49} - 2 q^{50} - 2 q^{51} + 6 q^{52} - 2 q^{53} + 2 q^{54} + 2 q^{55} - 2 q^{56} + 6 q^{57} - 4 q^{58} + 22 q^{59} - 2 q^{60} - 12 q^{61} - 4 q^{62} + 2 q^{63} + 2 q^{64} + 6 q^{65} + 2 q^{66} - 8 q^{67} + 2 q^{68} - 10 q^{69} - 2 q^{70} + 6 q^{71} - 2 q^{72} - 10 q^{73} - 2 q^{75} - 6 q^{76} + 2 q^{77} + 6 q^{78} + 14 q^{79} + 2 q^{80} + 2 q^{81} + 8 q^{83} - 2 q^{84} + 2 q^{85} - 10 q^{86} - 4 q^{87} - 2 q^{88} + 28 q^{89} - 2 q^{90} + 16 q^{91} + 10 q^{92} - 4 q^{93} - 6 q^{95} + 2 q^{96} - 8 q^{97} + 2 q^{98} + 2 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 + 2 * q^9 - 2 * q^10 + 2 * q^11 - 2 * q^12 + 6 * q^13 - 2 * q^14 - 2 * q^15 + 2 * q^16 + 2 * q^17 - 2 * q^18 - 6 * q^19 + 2 * q^20 - 2 * q^21 - 2 * q^22 + 10 * q^23 + 2 * q^24 + 2 * q^25 - 6 * q^26 - 2 * q^27 + 2 * q^28 + 4 * q^29 + 2 * q^30 + 4 * q^31 - 2 * q^32 - 2 * q^33 - 2 * q^34 + 2 * q^35 + 2 * q^36 + 6 * q^38 - 6 * q^39 - 2 * q^40 + 2 * q^42 + 10 * q^43 + 2 * q^44 + 2 * q^45 - 10 * q^46 - 2 * q^48 - 2 * q^49 - 2 * q^50 - 2 * q^51 + 6 * q^52 - 2 * q^53 + 2 * q^54 + 2 * q^55 - 2 * q^56 + 6 * q^57 - 4 * q^58 + 22 * q^59 - 2 * q^60 - 12 * q^61 - 4 * q^62 + 2 * q^63 + 2 * q^64 + 6 * q^65 + 2 * q^66 - 8 * q^67 + 2 * q^68 - 10 * q^69 - 2 * q^70 + 6 * q^71 - 2 * q^72 - 10 * q^73 - 2 * q^75 - 6 * q^76 + 2 * q^77 + 6 * q^78 + 14 * q^79 + 2 * q^80 + 2 * q^81 + 8 * q^83 - 2 * q^84 + 2 * q^85 - 10 * q^86 - 4 * q^87 - 2 * q^88 + 28 * q^89 - 2 * q^90 + 16 * q^91 + 10 * q^92 - 4 * q^93 - 6 * q^95 + 2 * q^96 - 8 * q^97 + 2 * q^98 + 2 * q^99

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