LMFDB - Embedded newform 5610.2.a.cf.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:	$4$
Coefficient field:	4.4.17428.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 6x^{2} + 4x + 6 $ x^4 - x^3 - 6x^2 + 4x + 6
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.787711$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -0.662077 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -0.662077 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -1.00000 q^{11} +1.00000 q^{12} +3.57542 q^{13} +0.662077 q^{14} -1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} +5.18360 q^{19} -1.00000 q^{20} -0.662077 q^{21} +1.00000 q^{22} +7.42110 q^{23} -1.00000 q^{24} +1.00000 q^{25} -3.57542 q^{26} +1.00000 q^{27} -0.662077 q^{28} +4.23750 q^{29} +1.00000 q^{30} +0.913344 q^{31} -1.00000 q^{32} -1.00000 q^{33} +1.00000 q^{34} +0.662077 q^{35} +1.00000 q^{36} +2.00000 q^{37} -5.18360 q^{38} +3.57542 q^{39} +1.00000 q^{40} -4.75902 q^{41} +0.662077 q^{42} -3.81292 q^{43} -1.00000 q^{44} -1.00000 q^{45} -7.42110 q^{46} +1.00000 q^{48} -6.56165 q^{49} -1.00000 q^{50} -1.00000 q^{51} +3.57542 q^{52} -11.6586 q^{53} -1.00000 q^{54} +1.00000 q^{55} +0.662077 q^{56} +5.18360 q^{57} -4.23750 q^{58} +1.57542 q^{59} -1.00000 q^{60} +5.15084 q^{61} -0.913344 q^{62} -0.662077 q^{63} +1.00000 q^{64} -3.57542 q^{65} +1.00000 q^{66} +5.71597 q^{67} -1.00000 q^{68} +7.42110 q^{69} -0.662077 q^{70} -12.2237 q^{71} -1.00000 q^{72} +5.74873 q^{73} -2.00000 q^{74} +1.00000 q^{75} +5.18360 q^{76} +0.662077 q^{77} -3.57542 q^{78} -10.7017 q^{79} -1.00000 q^{80} +1.00000 q^{81} +4.75902 q^{82} -9.51805 q^{83} -0.662077 q^{84} +1.00000 q^{85} +3.81292 q^{86} +4.23750 q^{87} +1.00000 q^{88} +0.675845 q^{89} +1.00000 q^{90} -2.36721 q^{91} +7.42110 q^{92} +0.913344 q^{93} -5.18360 q^{95} -1.00000 q^{96} +7.84568 q^{97} +6.56165 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} - 4 q^{5} - 4 q^{6} + 5 q^{7} - 4 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 - 4 * q^5 - 4 * q^6 + 5 * q^7 - 4 * q^8 + 4 * q^9	\( 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} - 4 q^{5} - 4 q^{6} + 5 q^{7} - 4 q^{8} + 4 q^{9} + 4 q^{10} - 4 q^{11} + 4 q^{12} + 6 q^{13} - 5 q^{14} - 4 q^{15} + 4 q^{16} - 4 q^{17} - 4 q^{18} + 8 q^{19} - 4 q^{20} + 5 q^{21} + 4 q^{22} + q^{23} - 4 q^{24} + 4 q^{25} - 6 q^{26} + 4 q^{27} + 5 q^{28} + q^{29} + 4 q^{30} + 3 q^{31} - 4 q^{32} - 4 q^{33} + 4 q^{34} - 5 q^{35} + 4 q^{36} + 8 q^{37} - 8 q^{38} + 6 q^{39} + 4 q^{40} + 2 q^{41} - 5 q^{42} + 9 q^{43} - 4 q^{44} - 4 q^{45} - q^{46} + 4 q^{48} + 5 q^{49} - 4 q^{50} - 4 q^{51} + 6 q^{52} - 2 q^{53} - 4 q^{54} + 4 q^{55} - 5 q^{56} + 8 q^{57} - q^{58} - 2 q^{59} - 4 q^{60} + 4 q^{61} - 3 q^{62} + 5 q^{63} + 4 q^{64} - 6 q^{65} + 4 q^{66} + 12 q^{67} - 4 q^{68} + q^{69} + 5 q^{70} - 10 q^{71} - 4 q^{72} + 16 q^{73} - 8 q^{74} + 4 q^{75} + 8 q^{76} - 5 q^{77} - 6 q^{78} + 12 q^{79} - 4 q^{80} + 4 q^{81} - 2 q^{82} + 4 q^{83} + 5 q^{84} + 4 q^{85} - 9 q^{86} + q^{87} + 4 q^{88} + 18 q^{89} + 4 q^{90} + 16 q^{91} + q^{92} + 3 q^{93} - 8 q^{95} - 4 q^{96} + 11 q^{97} - 5 q^{98} - 4 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 - 4 * q^5 - 4 * q^6 + 5 * q^7 - 4 * q^8 + 4 * q^9 + 4 * q^10 - 4 * q^11 + 4 * q^12 + 6 * q^13 - 5 * q^14 - 4 * q^15 + 4 * q^16 - 4 * q^17 - 4 * q^18 + 8 * q^19 - 4 * q^20 + 5 * q^21 + 4 * q^22 + q^23 - 4 * q^24 + 4 * q^25 - 6 * q^26 + 4 * q^27 + 5 * q^28 + q^29 + 4 * q^30 + 3 * q^31 - 4 * q^32 - 4 * q^33 + 4 * q^34 - 5 * q^35 + 4 * q^36 + 8 * q^37 - 8 * q^38 + 6 * q^39 + 4 * q^40 + 2 * q^41 - 5 * q^42 + 9 * q^43 - 4 * q^44 - 4 * q^45 - q^46 + 4 * q^48 + 5 * q^49 - 4 * q^50 - 4 * q^51 + 6 * q^52 - 2 * q^53 - 4 * q^54 + 4 * q^55 - 5 * q^56 + 8 * q^57 - q^58 - 2 * q^59 - 4 * q^60 + 4 * q^61 - 3 * q^62 + 5 * q^63 + 4 * q^64 - 6 * q^65 + 4 * q^66 + 12 * q^67 - 4 * q^68 + q^69 + 5 * q^70 - 10 * q^71 - 4 * q^72 + 16 * q^73 - 8 * q^74 + 4 * q^75 + 8 * q^76 - 5 * q^77 - 6 * q^78 + 12 * q^79 - 4 * q^80 + 4 * q^81 - 2 * q^82 + 4 * q^83 + 5 * q^84 + 4 * q^85 - 9 * q^86 + q^87 + 4 * q^88 + 18 * q^89 + 4 * q^90 + 16 * q^91 + q^92 + 3 * q^93 - 8 * q^95 - 4 * q^96 + 11 * q^97 - 5 * q^98 - 4 * 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
$7$	−0.662077	−0.250242	−0.125121	−	0.992142i	$-0.539932\pi$
$7$	−0.662077	−0.250242	−0.125121	+	0.992142i	$0.539932\pi$
$8$	−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
$13$	3.57542	0.991643	0.495822	−	0.868424i	$-0.334867\pi$
$13$	3.57542	0.991643	0.495822	+	0.868424i	$0.334867\pi$
$14$	0.662077	0.176948
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−1.00000	−0.235702
$19$	5.18360	1.18920	0.594600	−	0.804022i	$-0.297310\pi$
$19$	5.18360	1.18920	0.594600	+	0.804022i	$0.297310\pi$
$20$	−1.00000	−0.223607
$21$	−0.662077	−0.144477
$22$	1.00000	0.213201
$23$	7.42110	1.54741	0.773703	−	0.633548i	$-0.218402\pi$
$23$	7.42110	1.54741	0.773703	+	0.633548i	$0.218402\pi$
$24$	−1.00000	−0.204124
$25$	1.00000	0.200000
$26$	−3.57542	−0.701198
$27$	1.00000	0.192450
$28$	−0.662077	−0.125121
$29$	4.23750	0.786884	0.393442	−	0.919349i	$-0.371284\pi$
$29$	4.23750	0.786884	0.393442	+	0.919349i	$0.371284\pi$
$30$	1.00000	0.182574
$31$	0.913344	0.164041	0.0820207	−	0.996631i	$-0.473863\pi$
$31$	0.913344	0.164041	0.0820207	+	0.996631i	$0.473863\pi$
$32$	−1.00000	−0.176777
$33$	−1.00000	−0.174078
$34$	1.00000	0.171499
$35$	0.662077	0.111912
$36$	1.00000	0.166667
$37$	2.00000	0.328798	0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000	0.328798	0.164399	+	0.986394i	$0.447432\pi$
$38$	−5.18360	−0.840891
$39$	3.57542	0.572526
$40$	1.00000	0.158114
$41$	−4.75902	−0.743235	−0.371617	−	0.928386i	$-0.621197\pi$
$41$	−4.75902	−0.743235	−0.371617	+	0.928386i	$0.621197\pi$
$42$	0.662077	0.102161
$43$	−3.81292	−0.581465	−0.290732	−	0.956804i	$-0.593899\pi$
$43$	−3.81292	−0.581465	−0.290732	+	0.956804i	$0.593899\pi$
$44$	−1.00000	−0.150756
$45$	−1.00000	−0.149071
$46$	−7.42110	−1.09418
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	1.00000	0.144338
$49$	−6.56165	−0.937379
$50$	−1.00000	−0.141421
$51$	−1.00000	−0.140028
$52$	3.57542	0.495822
$53$	−11.6586	−1.60143	−0.800716	−	0.599044i	$-0.795547\pi$
$53$	−11.6586	−1.60143	−0.800716	+	0.599044i	$0.795547\pi$
$54$	−1.00000	−0.136083
$55$	1.00000	0.134840
$56$	0.662077	0.0884738
$57$	5.18360	0.686585
$58$	−4.23750	−0.556411
$59$	1.57542	0.205102	0.102551	−	0.994728i	$-0.467299\pi$
$59$	1.57542	0.205102	0.102551	+	0.994728i	$0.467299\pi$
$60$	−1.00000	−0.129099
$61$	5.15084	0.659498	0.329749	−	0.944069i	$-0.393036\pi$
$61$	5.15084	0.659498	0.329749	+	0.944069i	$0.393036\pi$
$62$	−0.913344	−0.115995
$63$	−0.662077	−0.0834139
$64$	1.00000	0.125000
$65$	−3.57542	−0.443476
$66$	1.00000	0.123091
$67$	5.71597	0.698317	0.349159	−	0.937064i	$-0.386467\pi$
$67$	5.71597	0.698317	0.349159	+	0.937064i	$0.386467\pi$
$68$	−1.00000	−0.121268
$69$	7.42110	0.893396
$70$	−0.662077	−0.0791334
$71$	−12.2237	−1.45069	−0.725345	−	0.688386i	$-0.758320\pi$
$71$	−12.2237	−1.45069	−0.725345	+	0.688386i	$0.758320\pi$
$72$	−1.00000	−0.117851
$73$	5.74873	0.672838	0.336419	−	0.941712i	$-0.390784\pi$
$73$	5.74873	0.672838	0.336419	+	0.941712i	$0.390784\pi$
$74$	−2.00000	−0.232495
$75$	1.00000	0.115470
$76$	5.18360	0.594600
$77$	0.662077	0.0754507
$78$	−3.57542	−0.404837
$79$	−10.7017	−1.20403	−0.602015	−	0.798485i	$-0.705635\pi$
$79$	−10.7017	−1.20403	−0.602015	+	0.798485i	$0.705635\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	4.75902	0.525546
$83$	−9.51805	−1.04474	−0.522371	−	0.852718i	$-0.674952\pi$
$83$	−9.51805	−1.04474	−0.522371	+	0.852718i	$0.674952\pi$
$84$	−0.662077	−0.0722386
$85$	1.00000	0.108465
$86$	3.81292	0.411158
$87$	4.23750	0.454308
$88$	1.00000	0.106600
$89$	0.675845	0.0716394	0.0358197	−	0.999358i	$-0.488596\pi$
$89$	0.675845	0.0716394	0.0358197	+	0.999358i	$0.488596\pi$
$90$	1.00000	0.105409
$91$	−2.36721	−0.248151
$92$	7.42110	0.773703
$93$	0.913344	0.0947093
$94$	0	0
$95$	−5.18360	−0.531826
$96$	−1.00000	−0.102062
$97$	7.84568	0.796608	0.398304	−	0.917253i	$-0.369599\pi$
$97$	7.84568	0.796608	0.398304	+	0.917253i	$0.369599\pi$
$98$	6.56165	0.662827
$99$	−1.00000	−0.100504
$100$	1.00000	0.100000
$101$	5.80207	0.577328	0.288664	−	0.957430i	$-0.406789\pi$
$101$	5.80207	0.577328	0.288664	+	0.957430i	$0.406789\pi$
$102$	1.00000	0.0990148
$103$	−8.60470	−0.847847	−0.423923	−	0.905698i	$-0.639347\pi$
$103$	−8.60470	−0.847847	−0.423923	+	0.905698i	$0.639347\pi$
$104$	−3.57542	−0.350599
$105$	0.662077	0.0646121
$106$	11.6586	1.13238
$107$	−3.56165	−0.344318	−0.172159	−	0.985069i	$-0.555074\pi$
$107$	−3.56165	−0.344318	−0.172159	+	0.985069i	$0.555074\pi$
$108$	1.00000	0.0962250
$109$	13.6914	1.31139	0.655697	−	0.755024i	$-0.272375\pi$
$109$	13.6914	1.31139	0.655697	+	0.755024i	$0.272375\pi$
$110$	−1.00000	−0.0953463
$111$	2.00000	0.189832
$112$	−0.662077	−0.0625604
$113$	12.7017	1.19487	0.597435	−	0.801917i	$-0.296186\pi$
$113$	12.7017	1.19487	0.597435	+	0.801917i	$0.296186\pi$
$114$	−5.18360	−0.485489
$115$	−7.42110	−0.692021
$116$	4.23750	0.393442
$117$	3.57542	0.330548
$118$	−1.57542	−0.145029
$119$	0.662077	0.0606925
$120$	1.00000	0.0912871
$121$	1.00000	0.0909091
$122$	−5.15084	−0.466335
$123$	−4.75902	−0.429107
$124$	0.913344	0.0820207
$125$	−1.00000	−0.0894427
$126$	0.662077	0.0589825
$127$	21.4905	1.90697	0.953487	−	0.301433i	$-0.0974650\pi$
$127$	21.4905	1.90697	0.953487	+	0.301433i	$0.0974650\pi$
$128$	−1.00000	−0.0883883
$129$	−3.81292	−0.335709
$130$	3.57542	0.313585
$131$	−9.51805	−0.831596	−0.415798	−	0.909457i	$-0.636498\pi$
$131$	−9.51805	−0.831596	−0.415798	+	0.909457i	$0.636498\pi$
$132$	−1.00000	−0.0870388
$133$	−3.43195	−0.297587
$134$	−5.71597	−0.493785
$135$	−1.00000	−0.0860663
$136$	1.00000	0.0857493
$137$	21.2530	1.81577	0.907884	−	0.419222i	$-0.137697\pi$
$137$	21.2530	1.81577	0.907884	+	0.419222i	$0.137697\pi$
$138$	−7.42110	−0.631726
$139$	17.9289	1.52071	0.760353	−	0.649510i	$-0.225026\pi$
$139$	17.9289	1.52071	0.760353	+	0.649510i	$0.225026\pi$
$140$	0.662077	0.0559558
$141$	0	0
$142$	12.2237	1.02579
$143$	−3.57542	−0.298992
$144$	1.00000	0.0833333
$145$	−4.23750	−0.351905
$146$	−5.74873	−0.475769
$147$	−6.56165	−0.541196
$148$	2.00000	0.164399
$149$	7.90987	0.648002	0.324001	−	0.946057i	$-0.394972\pi$
$149$	7.90987	0.648002	0.324001	+	0.946057i	$0.394972\pi$
$150$	−1.00000	−0.0816497
$151$	20.6689	1.68201	0.841005	−	0.541027i	$-0.181964\pi$
$151$	20.6689	1.68201	0.841005	+	0.541027i	$0.181964\pi$
$152$	−5.18360	−0.420446
$153$	−1.00000	−0.0808452
$154$	−0.662077	−0.0533517
$155$	−0.913344	−0.0733615
$156$	3.57542	0.286263
$157$	−11.6012	−0.925879	−0.462939	−	0.886390i	$-0.653205\pi$
$157$	−11.6012	−0.925879	−0.462939	+	0.886390i	$0.653205\pi$
$158$	10.7017	0.851378
$159$	−11.6586	−0.924587
$160$	1.00000	0.0790569
$161$	−4.91334	−0.387226
$162$	−1.00000	−0.0785674
$163$	16.7986	1.31577	0.657884	−	0.753119i	$-0.271452\pi$
$163$	16.7986	1.31577	0.657884	+	0.753119i	$0.271452\pi$
$164$	−4.75902	−0.371617
$165$	1.00000	0.0778499
$166$	9.51805	0.738744
$167$	−10.5611	−0.817242	−0.408621	−	0.912704i	$-0.633990\pi$
$167$	−10.5611	−0.817242	−0.408621	+	0.912704i	$0.633990\pi$
$168$	0.662077	0.0510804
$169$	−0.216363	−0.0166433
$170$	−1.00000	−0.0766965
$171$	5.18360	0.396400
$172$	−3.81292	−0.290732
$173$	6.00000	0.456172	0.228086	−	0.973641i	$-0.426753\pi$
$173$	6.00000	0.456172	0.228086	+	0.973641i	$0.426753\pi$
$174$	−4.23750	−0.321244
$175$	−0.662077	−0.0500483
$176$	−1.00000	−0.0753778
$177$	1.57542	0.118416
$178$	−0.675845	−0.0506567
$179$	−1.57542	−0.117753	−0.0588763	−	0.998265i	$-0.518752\pi$
$179$	−1.57542	−0.117753	−0.0588763	+	0.998265i	$0.518752\pi$
$180$	−1.00000	−0.0745356
$181$	−21.9494	−1.63149	−0.815745	−	0.578412i	$-0.803672\pi$
$181$	−21.9494	−1.63149	−0.815745	+	0.578412i	$0.803672\pi$
$182$	2.36721	0.175469
$183$	5.15084	0.380761
$184$	−7.42110	−0.547091
$185$	−2.00000	−0.147043
$186$	−0.913344	−0.0669696
$187$	1.00000	0.0731272
$188$	0	0
$189$	−0.662077	−0.0481590
$190$	5.18360	0.376058
$191$	18.7125	1.35399	0.676994	−	0.735988i	$-0.263282\pi$
$191$	18.7125	1.35399	0.676994	+	0.735988i	$0.263282\pi$
$192$	1.00000	0.0721688
$193$	2.59789	0.187000	0.0935002	−	0.995619i	$-0.470194\pi$
$193$	2.59789	0.187000	0.0935002	+	0.995619i	$0.470194\pi$
$194$	−7.84568	−0.563287
$195$	−3.57542	−0.256041
$196$	−6.56165	−0.468690
$197$	4.95695	0.353168	0.176584	−	0.984286i	$-0.443495\pi$
$197$	4.95695	0.353168	0.176584	+	0.984286i	$0.443495\pi$
$198$	1.00000	0.0710669
$199$	17.5180	1.24182	0.620911	−	0.783881i	$-0.286763\pi$
$199$	17.5180	1.24182	0.620911	+	0.783881i	$0.286763\pi$
$200$	−1.00000	−0.0707107
$201$	5.71597	0.403174
$202$	−5.80207	−0.408233
$203$	−2.80555	−0.196911
$204$	−1.00000	−0.0700140
$205$	4.75902	0.332385
$206$	8.60470	0.599518
$207$	7.42110	0.515802
$208$	3.57542	0.247911
$209$	−5.18360	−0.358557
$210$	−0.662077	−0.0456877
$211$	6.23750	0.429407	0.214704	−	0.976679i	$-0.431121\pi$
$211$	6.23750	0.429407	0.214704	+	0.976679i	$0.431121\pi$
$212$	−11.6586	−0.800716
$213$	−12.2237	−0.837556
$214$	3.56165	0.243470
$215$	3.81292	0.260039
$216$	−1.00000	−0.0680414
$217$	−0.604704	−0.0410500
$218$	−13.6914	−0.927296
$219$	5.74873	0.388463
$220$	1.00000	0.0674200
$221$	−3.57542	−0.240509
$222$	−2.00000	−0.134231
$223$	24.2305	1.62260	0.811299	−	0.584632i	$-0.198761\pi$
$223$	24.2305	1.62260	0.811299	+	0.584632i	$0.198761\pi$
$224$	0.662077	0.0442369
$225$	1.00000	0.0666667
$226$	−12.7017	−0.844901
$227$	22.9719	1.52470	0.762350	−	0.647165i	$-0.224046\pi$
$227$	22.9719	1.52470	0.762350	+	0.647165i	$0.224046\pi$
$228$	5.18360	0.343292
$229$	−14.1939	−0.937959	−0.468979	−	0.883209i	$-0.655378\pi$
$229$	−14.1939	−0.937959	−0.468979	+	0.883209i	$0.655378\pi$
$230$	7.42110	0.489333
$231$	0.662077	0.0435615
$232$	−4.23750	−0.278205
$233$	−14.7986	−0.969488	−0.484744	−	0.874656i	$-0.661087\pi$
$233$	−14.7986	−0.969488	−0.484744	+	0.874656i	$0.661087\pi$
$234$	−3.57542	−0.233733
$235$	0	0
$236$	1.57542	0.102551
$237$	−10.7017	−0.695147
$238$	−0.662077	−0.0429161
$239$	17.3242	1.12061	0.560303	−	0.828288i	$-0.310685\pi$
$239$	17.3242	1.12061	0.560303	+	0.828288i	$0.310685\pi$
$240$	−1.00000	−0.0645497
$241$	−5.35558	−0.344983	−0.172492	−	0.985011i	$-0.555182\pi$
$241$	−5.35558	−0.344983	−0.172492	+	0.985011i	$0.555182\pi$
$242$	−1.00000	−0.0642824
$243$	1.00000	0.0641500
$244$	5.15084	0.329749
$245$	6.56165	0.419209
$246$	4.75902	0.303424
$247$	18.5336	1.17926
$248$	−0.913344	−0.0579974
$249$	−9.51805	−0.603182
$250$	1.00000	0.0632456
$251$	−0.532370	−0.0336029	−0.0168015	−	0.999859i	$-0.505348\pi$
$251$	−0.532370	−0.0336029	−0.0168015	+	0.999859i	$0.505348\pi$
$252$	−0.662077	−0.0417070
$253$	−7.42110	−0.466561
$254$	−21.4905	−1.34843
$255$	1.00000	0.0626224
$256$	1.00000	0.0625000
$257$	26.7331	1.66756	0.833782	−	0.552094i	$-0.186171\pi$
$257$	26.7331	1.66756	0.833782	+	0.552094i	$0.186171\pi$
$258$	3.81292	0.237382
$259$	−1.32415	−0.0822790
$260$	−3.57542	−0.221738
$261$	4.23750	0.262295
$262$	9.51805	0.588027
$263$	16.2305	1.00082	0.500409	−	0.865789i	$-0.333183\pi$
$263$	16.2305	1.00082	0.500409	+	0.865789i	$0.333183\pi$
$264$	1.00000	0.0615457
$265$	11.6586	0.716182
$266$	3.43195	0.210426
$267$	0.675845	0.0413611
$268$	5.71597	0.349159
$269$	13.0361	0.794825	0.397412	−	0.917640i	$-0.369908\pi$
$269$	13.0361	0.794825	0.397412	+	0.917640i	$0.369908\pi$
$270$	1.00000	0.0608581
$271$	−6.43139	−0.390679	−0.195340	−	0.980736i	$-0.562581\pi$
$271$	−6.43139	−0.390679	−0.195340	+	0.980736i	$0.562581\pi$
$272$	−1.00000	−0.0606339
$273$	−2.36721	−0.143270
$274$	−21.2530	−1.28394
$275$	−1.00000	−0.0603023
$276$	7.42110	0.446698
$277$	16.0206	0.962583	0.481292	−	0.876560i	$-0.340168\pi$
$277$	16.0206	0.962583	0.481292	+	0.876560i	$0.340168\pi$
$278$	−17.9289	−1.07530
$279$	0.913344	0.0546805
$280$	−0.662077	−0.0395667
$281$	15.9289	0.950236	0.475118	−	0.879922i	$-0.342405\pi$
$281$	15.9289	0.950236	0.475118	+	0.879922i	$0.342405\pi$
$282$	0	0
$283$	6.95695	0.413548	0.206774	−	0.978389i	$-0.433704\pi$
$283$	6.95695	0.413548	0.206774	+	0.978389i	$0.433704\pi$
$284$	−12.2237	−0.725345
$285$	−5.18360	−0.307050
$286$	3.57542	0.211419
$287$	3.15084	0.185988
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	4.23750	0.248834
$291$	7.84568	0.459922
$292$	5.74873	0.336419
$293$	26.7331	1.56176	0.780882	−	0.624679i	$-0.214770\pi$
$293$	26.7331	1.56176	0.780882	+	0.624679i	$0.214770\pi$
$294$	6.56165	0.382683
$295$	−1.57542	−0.0917246
$296$	−2.00000	−0.116248
$297$	−1.00000	−0.0580259
$298$	−7.90987	−0.458206
$299$	26.5336	1.53448
$300$	1.00000	0.0577350
$301$	2.52445	0.145507
$302$	−20.6689	−1.18936
$303$	5.80207	0.333320
$304$	5.18360	0.297300
$305$	−5.15084	−0.294936
$306$	1.00000	0.0571662
$307$	−14.7848	−0.843815	−0.421907	−	0.906639i	$-0.638639\pi$
$307$	−14.7848	−0.843815	−0.421907	+	0.906639i	$0.638639\pi$
$308$	0.662077	0.0377254
$309$	−8.60470	−0.489505
$310$	0.913344	0.0518744
$311$	−23.9151	−1.35610	−0.678050	−	0.735016i	$-0.737175\pi$
$311$	−23.9151	−1.35610	−0.678050	+	0.735016i	$0.737175\pi$
$312$	−3.57542	−0.202418
$313$	14.9690	0.846097	0.423049	−	0.906107i	$-0.360960\pi$
$313$	14.9690	0.846097	0.423049	+	0.906107i	$0.360960\pi$
$314$	11.6012	0.654695
$315$	0.662077	0.0373038
$316$	−10.7017	−0.602015
$317$	−30.3969	−1.70726	−0.853630	−	0.520880i	$-0.825604\pi$
$317$	−30.3969	−1.70726	−0.853630	+	0.520880i	$0.825604\pi$
$318$	11.6586	0.653782
$319$	−4.23750	−0.237254
$320$	−1.00000	−0.0559017
$321$	−3.56165	−0.198792
$322$	4.91334	0.273810
$323$	−5.18360	−0.288423
$324$	1.00000	0.0555556
$325$	3.57542	0.198329
$326$	−16.7986	−0.930388
$327$	13.6914	0.757134
$328$	4.75902	0.262773
$329$	0	0
$330$	−1.00000	−0.0550482
$331$	−17.3011	−0.950956	−0.475478	−	0.879728i	$-0.657725\pi$
$331$	−17.3011	−0.950956	−0.475478	+	0.879728i	$0.657725\pi$
$332$	−9.51805	−0.522371
$333$	2.00000	0.109599
$334$	10.5611	0.577878
$335$	−5.71597	−0.312297
$336$	−0.662077	−0.0361193
$337$	−4.89958	−0.266897	−0.133448	−	0.991056i	$-0.542605\pi$
$337$	−4.89958	−0.266897	−0.133448	+	0.991056i	$0.542605\pi$
$338$	0.216363	0.0117686
$339$	12.7017	0.689859
$340$	1.00000	0.0542326
$341$	−0.913344	−0.0494603
$342$	−5.18360	−0.280297
$343$	8.97886	0.484813
$344$	3.81292	0.205579
$345$	−7.42110	−0.399539
$346$	−6.00000	−0.322562
$347$	−33.9655	−1.82336	−0.911682	−	0.410896i	$-0.865216\pi$
$347$	−33.9655	−1.82336	−0.911682	+	0.410896i	$0.865216\pi$
$348$	4.23750	0.227154
$349$	−22.8474	−1.22299	−0.611497	−	0.791246i	$-0.709433\pi$
$349$	−22.8474	−1.22299	−0.611497	+	0.791246i	$0.709433\pi$
$350$	0.662077	0.0353895
$351$	3.57542	0.190842
$352$	1.00000	0.0533002
$353$	−25.3814	−1.35091	−0.675457	−	0.737399i	$-0.736054\pi$
$353$	−25.3814	−1.35091	−0.675457	+	0.737399i	$0.736054\pi$
$354$	−1.57542	−0.0837327
$355$	12.2237	0.648768
$356$	0.675845	0.0358197
$357$	0.662077	0.0350409
$358$	1.57542	0.0832636
$359$	−21.1439	−1.11593	−0.557966	−	0.829864i	$-0.688418\pi$
$359$	−21.1439	−1.11593	−0.557966	+	0.829864i	$0.688418\pi$
$360$	1.00000	0.0527046
$361$	7.86974	0.414197
$362$	21.9494	1.15364
$363$	1.00000	0.0524864
$364$	−2.36721	−0.124075
$365$	−5.74873	−0.300902
$366$	−5.15084	−0.269239
$367$	15.3212	0.799762	0.399881	−	0.916567i	$-0.369051\pi$
$367$	15.3212	0.799762	0.399881	+	0.916567i	$0.369051\pi$
$368$	7.42110	0.386852
$369$	−4.75902	−0.247745
$370$	2.00000	0.103975
$371$	7.71890	0.400745
$372$	0.913344	0.0473547
$373$	23.6546	1.22479	0.612394	−	0.790553i	$-0.290207\pi$
$373$	23.6546	1.22479	0.612394	+	0.790553i	$0.290207\pi$
$374$	−1.00000	−0.0517088
$375$	−1.00000	−0.0516398
$376$	0	0
$377$	15.1508	0.780308
$378$	0.662077	0.0340536
$379$	−25.5180	−1.31077	−0.655387	−	0.755293i	$-0.727494\pi$
$379$	−25.5180	−1.31077	−0.655387	+	0.755293i	$0.727494\pi$
$380$	−5.18360	−0.265913
$381$	21.4905	1.10099
$382$	−18.7125	−0.957415
$383$	−7.49747	−0.383103	−0.191551	−	0.981483i	$-0.561352\pi$
$383$	−7.49747	−0.383103	−0.191551	+	0.981483i	$0.561352\pi$
$384$	−1.00000	−0.0510310
$385$	−0.662077	−0.0337426
$386$	−2.59789	−0.132229
$387$	−3.81292	−0.193822
$388$	7.84568	0.398304
$389$	−25.5685	−1.29637	−0.648186	−	0.761482i	$-0.724472\pi$
$389$	−25.5685	−1.29637	−0.648186	+	0.761482i	$0.724472\pi$
$390$	3.57542	0.181048
$391$	−7.42110	−0.375301
$392$	6.56165	0.331414
$393$	−9.51805	−0.480122
$394$	−4.95695	−0.249727
$395$	10.7017	0.538458
$396$	−1.00000	−0.0502519
$397$	27.8647	1.39849	0.699244	−	0.714883i	$-0.253520\pi$
$397$	27.8647	1.39849	0.699244	+	0.714883i	$0.253520\pi$
$398$	−17.5180	−0.878100
$399$	−3.43195	−0.171812
$400$	1.00000	0.0500000
$401$	−20.9638	−1.04688	−0.523440	−	0.852062i	$-0.675352\pi$
$401$	−20.9638	−1.04688	−0.523440	+	0.852062i	$0.675352\pi$
$402$	−5.71597	−0.285087
$403$	3.26559	0.162671
$404$	5.80207	0.288664
$405$	−1.00000	−0.0496904
$406$	2.80555	0.139237
$407$	−2.00000	−0.0991363
$408$	1.00000	0.0495074
$409$	16.8422	0.832793	0.416397	−	0.909183i	$-0.363293\pi$
$409$	16.8422	0.832793	0.416397	+	0.909183i	$0.363293\pi$
$410$	−4.75902	−0.235031
$411$	21.2530	1.04833
$412$	−8.60470	−0.423923
$413$	−1.04305	−0.0513252
$414$	−7.42110	−0.364727
$415$	9.51805	0.467223
$416$	−3.57542	−0.175299
$417$	17.9289	0.877980
$418$	5.18360	0.253538
$419$	26.1228	1.27618	0.638090	−	0.769962i	$-0.279725\pi$
$419$	26.1228	1.27618	0.638090	+	0.769962i	$0.279725\pi$
$420$	0.662077	0.0323061
$421$	10.4750	0.510520	0.255260	−	0.966872i	$-0.417839\pi$
$421$	10.4750	0.510520	0.255260	+	0.966872i	$0.417839\pi$
$422$	−6.23750	−0.303637
$423$	0	0
$424$	11.6586	0.566192
$425$	−1.00000	−0.0485071
$426$	12.2237	0.592242
$427$	−3.41026	−0.165034
$428$	−3.56165	−0.172159
$429$	−3.57542	−0.172623
$430$	−3.81292	−0.183875
$431$	−21.6654	−1.04359	−0.521793	−	0.853072i	$-0.674737\pi$
$431$	−21.6654	−1.04359	−0.521793	+	0.853072i	$0.674737\pi$
$432$	1.00000	0.0481125
$433$	−29.1233	−1.39958	−0.699788	−	0.714350i	$-0.746722\pi$
$433$	−29.1233	−1.39958	−0.699788	+	0.714350i	$0.746722\pi$
$434$	0.604704	0.0290267
$435$	−4.23750	−0.203173
$436$	13.6914	0.655697
$437$	38.4680	1.84018
$438$	−5.74873	−0.274685
$439$	−3.57834	−0.170785	−0.0853925	−	0.996347i	$-0.527214\pi$
$439$	−3.57834	−0.170785	−0.0853925	+	0.996347i	$0.527214\pi$
$440$	−1.00000	−0.0476731
$441$	−6.56165	−0.312460
$442$	3.57542	0.170065
$443$	0.0763659	0.00362825	0.00181413	−	0.999998i	$-0.499423\pi$
$443$	0.0763659	0.00362825	0.00181413	+	0.999998i	$0.499423\pi$
$444$	2.00000	0.0949158
$445$	−0.675845	−0.0320381
$446$	−24.2305	−1.14735
$447$	7.90987	0.374124
$448$	−0.662077	−0.0312802
$449$	−29.5043	−1.39239	−0.696197	−	0.717851i	$-0.745126\pi$
$449$	−29.5043	−1.39239	−0.696197	+	0.717851i	$0.745126\pi$
$450$	−1.00000	−0.0471405
$451$	4.75902	0.224094
$452$	12.7017	0.597435
$453$	20.6689	0.971109
$454$	−22.9719	−1.07813
$455$	2.36721	0.110976
$456$	−5.18360	−0.242744
$457$	−4.30168	−0.201224	−0.100612	−	0.994926i	$-0.532080\pi$
$457$	−4.30168	−0.201224	−0.100612	+	0.994926i	$0.532080\pi$
$458$	14.1939	0.663237
$459$	−1.00000	−0.0466760
$460$	−7.42110	−0.346011
$461$	23.8168	1.10926	0.554630	−	0.832097i	$-0.312860\pi$
$461$	23.8168	1.10926	0.554630	+	0.832097i	$0.312860\pi$
$462$	−0.662077	−0.0308026
$463$	−24.8352	−1.15419	−0.577096	−	0.816676i	$-0.695814\pi$
$463$	−24.8352	−1.15419	−0.577096	+	0.816676i	$0.695814\pi$
$464$	4.23750	0.196721
$465$	−0.913344	−0.0423553
$466$	14.7986	0.685532
$467$	−2.88192	−0.133359	−0.0666796	−	0.997774i	$-0.521241\pi$
$467$	−2.88192	−0.133359	−0.0666796	+	0.997774i	$0.521241\pi$
$468$	3.57542	0.165274
$469$	−3.78442	−0.174748
$470$	0	0
$471$	−11.6012	−0.534556
$472$	−1.57542	−0.0725146
$473$	3.81292	0.175318
$474$	10.7017	0.491543
$475$	5.18360	0.237840
$476$	0.662077	0.0303463
$477$	−11.6586	−0.533811
$478$	−17.3242	−0.792388
$479$	−15.7379	−0.719082	−0.359541	−	0.933129i	$-0.617067\pi$
$479$	−15.7379	−0.719082	−0.359541	+	0.933129i	$0.617067\pi$
$480$	1.00000	0.0456435
$481$	7.15084	0.326050
$482$	5.35558	0.243940
$483$	−4.91334	−0.223565
$484$	1.00000	0.0454545
$485$	−7.84568	−0.356254
$486$	−1.00000	−0.0453609
$487$	38.9254	1.76388	0.881939	−	0.471364i	$-0.156238\pi$
$487$	38.9254	1.76388	0.881939	+	0.471364i	$0.156238\pi$
$488$	−5.15084	−0.233168
$489$	16.7986	0.759659
$490$	−6.56165	−0.296425
$491$	27.4004	1.23656	0.618281	−	0.785957i	$-0.287829\pi$
$491$	27.4004	1.23656	0.618281	+	0.785957i	$0.287829\pi$
$492$	−4.75902	−0.214553
$493$	−4.23750	−0.190847
$494$	−18.5336	−0.833864
$495$	1.00000	0.0449467
$496$	0.913344	0.0410103
$497$	8.09306	0.363023
$498$	9.51805	0.426514
$499$	−11.4975	−0.514697	−0.257349	−	0.966319i	$-0.582849\pi$
$499$	−11.4975	−0.514697	−0.257349	+	0.966319i	$0.582849\pi$
$500$	−1.00000	−0.0447214
$501$	−10.5611	−0.471835
$502$	0.532370	0.0237609
$503$	−6.14578	−0.274027	−0.137013	−	0.990569i	$-0.543750\pi$
$503$	−6.14578	−0.274027	−0.137013	+	0.990569i	$0.543750\pi$
$504$	0.662077	0.0294913
$505$	−5.80207	−0.258189
$506$	7.42110	0.329908
$507$	−0.216363	−0.00960903
$508$	21.4905	0.953487
$509$	−25.5685	−1.13330	−0.566651	−	0.823958i	$-0.691761\pi$
$509$	−25.5685	−1.13330	−0.566651	+	0.823958i	$0.691761\pi$
$510$	−1.00000	−0.0442807
$511$	−3.80611	−0.168372
$512$	−1.00000	−0.0441942
$513$	5.18360	0.228862
$514$	−26.7331	−1.17915
$515$	8.60470	0.379169
$516$	−3.81292	−0.167854
$517$	0	0
$518$	1.32415	0.0581800
$519$	6.00000	0.263371
$520$	3.57542	0.156793
$521$	16.1159	0.706052	0.353026	−	0.935613i	$-0.385153\pi$
$521$	16.1159	0.706052	0.353026	+	0.935613i	$0.385153\pi$
$522$	−4.23750	−0.185470
$523$	1.42402	0.0622682	0.0311341	−	0.999515i	$-0.490088\pi$
$523$	1.42402	0.0622682	0.0311341	+	0.999515i	$0.490088\pi$
$524$	−9.51805	−0.415798
$525$	−0.662077	−0.0288954
$526$	−16.2305	−0.707685
$527$	−0.913344	−0.0397859
$528$	−1.00000	−0.0435194
$529$	32.0727	1.39447
$530$	−11.6586	−0.506417
$531$	1.57542	0.0683675
$532$	−3.43195	−0.148794
$533$	−17.0155	−0.737024
$534$	−0.675845	−0.0292467
$535$	3.56165	0.153984
$536$	−5.71597	−0.246892
$537$	−1.57542	−0.0679844
$538$	−13.0361	−0.562026
$539$	6.56165	0.282630
$540$	−1.00000	−0.0430331
$541$	27.7119	1.19143	0.595715	−	0.803196i	$-0.296869\pi$
$541$	27.7119	1.19143	0.595715	+	0.803196i	$0.296869\pi$
$542$	6.43139	0.276252
$543$	−21.9494	−0.941941
$544$	1.00000	0.0428746
$545$	−13.6914	−0.586473
$546$	2.36721	0.101307
$547$	14.6758	0.627494	0.313747	−	0.949507i	$-0.398416\pi$
$547$	14.6758	0.627494	0.313747	+	0.949507i	$0.398416\pi$
$548$	21.2530	0.907884
$549$	5.15084	0.219833
$550$	1.00000	0.0426401
$551$	21.9655	0.935762
$552$	−7.42110	−0.315863
$553$	7.08532	0.301299
$554$	−16.0206	−0.680649
$555$	−2.00000	−0.0848953
$556$	17.9289	0.760353
$557$	−27.2461	−1.15445	−0.577226	−	0.816584i	$-0.695865\pi$
$557$	−27.2461	−1.15445	−0.577226	+	0.816584i	$0.695865\pi$
$558$	−0.913344	−0.0386649
$559$	−13.6328	−0.576606
$560$	0.662077	0.0279779
$561$	1.00000	0.0422200
$562$	−15.9289	−0.671918
$563$	−18.0803	−0.761992	−0.380996	−	0.924577i	$-0.624419\pi$
$563$	−18.0803	−0.761992	−0.380996	+	0.924577i	$0.624419\pi$
$564$	0	0
$565$	−12.7017	−0.534362
$566$	−6.95695	−0.292422
$567$	−0.662077	−0.0278046
$568$	12.2237	0.512896
$569$	−23.2369	−0.974143	−0.487072	−	0.873362i	$-0.661935\pi$
$569$	−23.2369	−0.974143	−0.487072	+	0.873362i	$0.661935\pi$
$570$	5.18360	0.217117
$571$	−16.4475	−0.688305	−0.344152	−	0.938914i	$-0.611834\pi$
$571$	−16.4475	−0.688305	−0.344152	+	0.938914i	$0.611834\pi$
$572$	−3.57542	−0.149496
$573$	18.7125	0.781726
$574$	−3.15084	−0.131514
$575$	7.42110	0.309481
$576$	1.00000	0.0416667
$577$	25.3827	1.05670	0.528348	−	0.849028i	$-0.322812\pi$
$577$	25.3827	1.05670	0.528348	+	0.849028i	$0.322812\pi$
$578$	−1.00000	−0.0415945
$579$	2.59789	0.107965
$580$	−4.23750	−0.175953
$581$	6.30168	0.261438
$582$	−7.84568	−0.325214
$583$	11.6586	0.482850
$584$	−5.74873	−0.237884
$585$	−3.57542	−0.147825
$586$	−26.7331	−1.10433
$587$	−31.0469	−1.28144	−0.640722	−	0.767773i	$-0.721365\pi$
$587$	−31.0469	−1.28144	−0.640722	+	0.767773i	$0.721365\pi$
$588$	−6.56165	−0.270598
$589$	4.73441	0.195078
$590$	1.57542	0.0648591
$591$	4.95695	0.203902
$592$	2.00000	0.0821995
$593$	9.81973	0.403248	0.201624	−	0.979463i	$-0.435378\pi$
$593$	9.81973	0.403248	0.201624	+	0.979463i	$0.435378\pi$
$594$	1.00000	0.0410305
$595$	−0.662077	−0.0271425
$596$	7.90987	0.324001
$597$	17.5180	0.716966
$598$	−26.5336	−1.08504
$599$	−3.84860	−0.157250	−0.0786248	−	0.996904i	$-0.525053\pi$
$599$	−3.84860	−0.157250	−0.0786248	+	0.996904i	$0.525053\pi$
$600$	−1.00000	−0.0408248
$601$	20.7017	0.844438	0.422219	−	0.906494i	$-0.361251\pi$
$601$	20.7017	0.844438	0.422219	+	0.906494i	$0.361251\pi$
$602$	−2.52445	−0.102889
$603$	5.71597	0.232772
$604$	20.6689	0.841005
$605$	−1.00000	−0.0406558
$606$	−5.80207	−0.235693
$607$	19.4676	0.790167	0.395083	−	0.918645i	$-0.370716\pi$
$607$	19.4676	0.790167	0.395083	+	0.918645i	$0.370716\pi$
$608$	−5.18360	−0.210223
$609$	−2.80555	−0.113687
$610$	5.15084	0.208552
$611$	0	0
$612$	−1.00000	−0.0404226
$613$	25.9151	1.04670	0.523350	−	0.852118i	$-0.324682\pi$
$613$	25.9151	1.04670	0.523350	+	0.852118i	$0.324682\pi$
$614$	14.7848	0.596667
$615$	4.75902	0.191902
$616$	−0.662077	−0.0266759
$617$	−0.480222	−0.0193330	−0.00966651	−	0.999953i	$-0.503077\pi$
$617$	−0.480222	−0.0193330	−0.00966651	+	0.999953i	$0.503077\pi$
$618$	8.60470	0.346132
$619$	10.6208	0.426885	0.213442	−	0.976956i	$-0.431532\pi$
$619$	10.6208	0.426885	0.213442	+	0.976956i	$0.431532\pi$
$620$	−0.913344	−0.0366808
$621$	7.42110	0.297799
$622$	23.9151	0.958908
$623$	−0.447462	−0.0179272
$624$	3.57542	0.143131
$625$	1.00000	0.0400000
$626$	−14.9690	−0.598281
$627$	−5.18360	−0.207013
$628$	−11.6012	−0.462939
$629$	−2.00000	−0.0797452
$630$	−0.662077	−0.0263778
$631$	−21.3102	−0.848347	−0.424174	−	0.905581i	$-0.639435\pi$
$631$	−21.3102	−0.848347	−0.424174	+	0.905581i	$0.639435\pi$
$632$	10.7017	0.425689
$633$	6.23750	0.247918
$634$	30.3969	1.20722
$635$	−21.4905	−0.852825
$636$	−11.6586	−0.462294
$637$	−23.4607	−0.929546
$638$	4.23750	0.167764
$639$	−12.2237	−0.483563
$640$	1.00000	0.0395285
$641$	−0.488765	−0.0193051	−0.00965253	−	0.999953i	$-0.503073\pi$
$641$	−0.488765	−0.0193051	−0.00965253	+	0.999953i	$0.503073\pi$
$642$	3.56165	0.140567
$643$	−10.9994	−0.433776	−0.216888	−	0.976197i	$-0.569591\pi$
$643$	−10.9994	−0.433776	−0.216888	+	0.976197i	$0.569591\pi$
$644$	−4.91334	−0.193613
$645$	3.81292	0.150134
$646$	5.18360	0.203946
$647$	34.9430	1.37375	0.686876	−	0.726774i	$-0.258981\pi$
$647$	34.9430	1.37375	0.686876	+	0.726774i	$0.258981\pi$
$648$	−1.00000	−0.0392837
$649$	−1.57542	−0.0618407
$650$	−3.57542	−0.140240
$651$	−0.604704	−0.0237002
$652$	16.7986	0.657884
$653$	−11.1348	−0.435737	−0.217869	−	0.975978i	$-0.569910\pi$
$653$	−11.1348	−0.435737	−0.217869	+	0.975978i	$0.569910\pi$
$654$	−13.6914	−0.535375
$655$	9.51805	0.371901
$656$	−4.75902	−0.185809
$657$	5.74873	0.224279
$658$	0	0
$659$	−20.8438	−0.811959	−0.405979	−	0.913882i	$-0.633070\pi$
$659$	−20.8438	−0.811959	−0.405979	+	0.913882i	$0.633070\pi$
$660$	1.00000	0.0389249
$661$	−41.3963	−1.61013	−0.805066	−	0.593186i	$-0.797870\pi$
$661$	−41.3963	−1.61013	−0.805066	+	0.593186i	$0.797870\pi$
$662$	17.3011	0.672428
$663$	−3.57542	−0.138858
$664$	9.51805	0.369372
$665$	3.43195	0.133085
$666$	−2.00000	−0.0774984
$667$	31.4469	1.21763
$668$	−10.5611	−0.408621
$669$	24.2305	0.936807
$670$	5.71597	0.220827
$671$	−5.15084	−0.198846
$672$	0.662077	0.0255402
$673$	−10.9581	−0.422405	−0.211203	−	0.977442i	$-0.567738\pi$
$673$	−10.9581	−0.422405	−0.211203	+	0.977442i	$0.567738\pi$
$674$	4.89958	0.188725
$675$	1.00000	0.0384900
$676$	−0.216363	−0.00832166
$677$	23.1714	0.890550	0.445275	−	0.895394i	$-0.353106\pi$
$677$	23.1714	0.890550	0.445275	+	0.895394i	$0.353106\pi$
$678$	−12.7017	−0.487804
$679$	−5.19445	−0.199345
$680$	−1.00000	−0.0383482
$681$	22.9719	0.880286
$682$	0.913344	0.0349737
$683$	45.9000	1.75631	0.878157	−	0.478372i	$-0.158773\pi$
$683$	45.9000	1.75631	0.878157	+	0.478372i	$0.158773\pi$
$684$	5.18360	0.198200
$685$	−21.2530	−0.812036
$686$	−8.97886	−0.342815
$687$	−14.1939	−0.541531
$688$	−3.81292	−0.145366
$689$	−41.6844	−1.58805
$690$	7.42110	0.282517
$691$	51.6395	1.96446	0.982229	−	0.187687i	$-0.0600990\pi$
$691$	51.6395	1.96446	0.982229	+	0.187687i	$0.0600990\pi$
$692$	6.00000	0.228086
$693$	0.662077	0.0251502
$694$	33.9655	1.28931
$695$	−17.9289	−0.680080
$696$	−4.23750	−0.160622
$697$	4.75902	0.180261
$698$	22.8474	0.864788
$699$	−14.7986	−0.559734
$700$	−0.662077	−0.0250242
$701$	24.5651	0.927812	0.463906	−	0.885884i	$-0.346448\pi$
$701$	24.5651	0.927812	0.463906	+	0.885884i	$0.346448\pi$
$702$	−3.57542	−0.134946
$703$	10.3672	0.391007
$704$	−1.00000	−0.0376889
$705$	0	0
$706$	25.3814	0.955241
$707$	−3.84142	−0.144472
$708$	1.57542	0.0592080
$709$	−0.703381	−0.0264160	−0.0132080	−	0.999913i	$-0.504204\pi$
$709$	−0.703381	−0.0264160	−0.0132080	+	0.999913i	$0.504204\pi$
$710$	−12.2237	−0.458748
$711$	−10.7017	−0.401343
$712$	−0.675845	−0.0253284
$713$	6.77802	0.253839
$714$	−0.662077	−0.0247776
$715$	3.57542	0.133713
$716$	−1.57542	−0.0588763
$717$	17.3242	0.646982
$718$	21.1439	0.789083
$719$	−28.5048	−1.06305	−0.531525	−	0.847042i	$-0.678381\pi$
$719$	−28.5048	−1.06305	−0.531525	+	0.847042i	$0.678381\pi$
$720$	−1.00000	−0.0372678
$721$	5.69698	0.212167
$722$	−7.86974	−0.292881
$723$	−5.35558	−0.199176
$724$	−21.9494	−0.815745
$725$	4.23750	0.157377
$726$	−1.00000	−0.0371135
$727$	44.4624	1.64902	0.824510	−	0.565847i	$-0.191451\pi$
$727$	44.4624	1.64902	0.824510	+	0.565847i	$0.191451\pi$
$728$	2.36721	0.0877345
$729$	1.00000	0.0370370
$730$	5.74873	0.212770
$731$	3.81292	0.141026
$732$	5.15084	0.190381
$733$	−32.1892	−1.18894	−0.594468	−	0.804119i	$-0.702637\pi$
$733$	−32.1892	−1.18894	−0.594468	+	0.804119i	$0.702637\pi$
$734$	−15.3212	−0.565517
$735$	6.56165	0.242030
$736$	−7.42110	−0.273545
$737$	−5.71597	−0.210551
$738$	4.75902	0.175182
$739$	20.4733	0.753121	0.376561	−	0.926392i	$-0.377107\pi$
$739$	20.4733	0.753121	0.376561	+	0.926392i	$0.377107\pi$
$740$	−2.00000	−0.0735215
$741$	18.5336	0.680847
$742$	−7.71890	−0.283370
$743$	29.7499	1.09142	0.545709	−	0.837974i	$-0.316260\pi$
$743$	29.7499	1.09142	0.545709	+	0.837974i	$0.316260\pi$
$744$	−0.913344	−0.0334848
$745$	−7.90987	−0.289795
$746$	−23.6546	−0.866055
$747$	−9.51805	−0.348247
$748$	1.00000	0.0365636
$749$	2.35809	0.0861627
$750$	1.00000	0.0365148
$751$	28.8858	1.05406	0.527029	−	0.849847i	$-0.323306\pi$
$751$	28.8858	1.05406	0.527029	+	0.849847i	$0.323306\pi$
$752$	0	0
$753$	−0.532370	−0.0194007
$754$	−15.1508	−0.551761
$755$	−20.6689	−0.752218
$756$	−0.662077	−0.0240795
$757$	−40.9620	−1.48879	−0.744395	−	0.667739i	$-0.767262\pi$
$757$	−40.9620	−1.48879	−0.744395	+	0.667739i	$0.767262\pi$
$758$	25.5180	0.926857
$759$	−7.42110	−0.269369
$760$	5.18360	0.188029
$761$	36.1824	1.31161	0.655806	−	0.754929i	$-0.272329\pi$
$761$	36.1824	1.31161	0.655806	+	0.754929i	$0.272329\pi$
$762$	−21.4905	−0.778519
$763$	−9.06474	−0.328166
$764$	18.7125	0.676994
$765$	1.00000	0.0361551
$766$	7.49747	0.270895
$767$	5.63279	0.203388
$768$	1.00000	0.0360844
$769$	−2.34662	−0.0846215	−0.0423107	−	0.999105i	$-0.513472\pi$
$769$	−2.34662	−0.0846215	−0.0423107	+	0.999105i	$0.513472\pi$
$770$	0.662077	0.0238596
$771$	26.7331	0.962768
$772$	2.59789	0.0935002
$773$	−12.9448	−0.465591	−0.232795	−	0.972526i	$-0.574787\pi$
$773$	−12.9448	−0.465591	−0.232795	+	0.972526i	$0.574787\pi$
$774$	3.81292	0.137053
$775$	0.913344	0.0328083
$776$	−7.84568	−0.281644
$777$	−1.32415	−0.0475038
$778$	25.5685	0.916674
$779$	−24.6689	−0.883855
$780$	−3.57542	−0.128021
$781$	12.2237	0.437399
$782$	7.42110	0.265378
$783$	4.23750	0.151436
$784$	−6.56165	−0.234345
$785$	11.6012	0.414066
$786$	9.51805	0.339498
$787$	0.281104	0.0100203	0.00501014	−	0.999987i	$-0.498405\pi$
$787$	0.281104	0.0100203	0.00501014	+	0.999987i	$0.498405\pi$
$788$	4.95695	0.176584
$789$	16.2305	0.577823
$790$	−10.7017	−0.380748
$791$	−8.40948	−0.299007
$792$	1.00000	0.0355335
$793$	18.4164	0.653987
$794$	−27.8647	−0.988880
$795$	11.6586	0.413488
$796$	17.5180	0.620911
$797$	−9.79393	−0.346919	−0.173459	−	0.984841i	$-0.555495\pi$
$797$	−9.79393	−0.346919	−0.173459	+	0.984841i	$0.555495\pi$
$798$	3.43195	0.121490
$799$	0	0
$800$	−1.00000	−0.0353553
$801$	0.675845	0.0238798
$802$	20.9638	0.740256
$803$	−5.74873	−0.202868
$804$	5.71597	0.201587
$805$	4.91334	0.173173
$806$	−3.26559	−0.115025
$807$	13.0361	0.458892
$808$	−5.80207	−0.204116
$809$	−11.2134	−0.394244	−0.197122	−	0.980379i	$-0.563159\pi$
$809$	−11.2134	−0.394244	−0.197122	+	0.980379i	$0.563159\pi$
$810$	1.00000	0.0351364
$811$	27.4319	0.963266	0.481633	−	0.876373i	$-0.340044\pi$
$811$	27.4319	0.963266	0.481633	+	0.876373i	$0.340044\pi$
$812$	−2.80555	−0.0984556
$813$	−6.43139	−0.225559
$814$	2.00000	0.0701000
$815$	−16.7986	−0.588429
$816$	−1.00000	−0.0350070
$817$	−19.7647	−0.691478
$818$	−16.8422	−0.588874
$819$	−2.36721	−0.0827169
$820$	4.75902	0.166192
$821$	−3.50309	−0.122259	−0.0611293	−	0.998130i	$-0.519470\pi$
$821$	−3.50309	−0.122259	−0.0611293	+	0.998130i	$0.519470\pi$
$822$	−21.2530	−0.741284
$823$	−28.5582	−0.995475	−0.497738	−	0.867328i	$-0.665836\pi$
$823$	−28.5582	−0.995475	−0.497738	+	0.867328i	$0.665836\pi$
$824$	8.60470	0.299759
$825$	−1.00000	−0.0348155
$826$	1.04305	0.0362924
$827$	51.1658	1.77921	0.889605	−	0.456731i	$-0.150980\pi$
$827$	51.1658	1.77921	0.889605	+	0.456731i	$0.150980\pi$
$828$	7.42110	0.257901
$829$	−46.3819	−1.61091	−0.805456	−	0.592656i	$-0.798079\pi$
$829$	−46.3819	−1.61091	−0.805456	+	0.592656i	$0.798079\pi$
$830$	−9.51805	−0.330376
$831$	16.0206	0.555748
$832$	3.57542	0.123955
$833$	6.56165	0.227348
$834$	−17.9289	−0.620826
$835$	10.5611	0.365482
$836$	−5.18360	−0.179279
$837$	0.913344	0.0315698
$838$	−26.1228	−0.902396
$839$	36.2753	1.25236	0.626182	−	0.779677i	$-0.284617\pi$
$839$	36.2753	1.25236	0.626182	+	0.779677i	$0.284617\pi$
$840$	−0.662077	−0.0228438
$841$	−11.0436	−0.380814
$842$	−10.4750	−0.360992
$843$	15.9289	0.548619
$844$	6.23750	0.214704
$845$	0.216363	0.00744312
$846$	0	0
$847$	−0.662077	−0.0227492
$848$	−11.6586	−0.400358
$849$	6.95695	0.238762
$850$	1.00000	0.0342997
$851$	14.8422	0.508784
$852$	−12.2237	−0.418778
$853$	−2.67023	−0.0914268	−0.0457134	−	0.998955i	$-0.514556\pi$
$853$	−2.67023	−0.0914268	−0.0457134	+	0.998955i	$0.514556\pi$
$854$	3.41026	0.116697
$855$	−5.18360	−0.177275
$856$	3.56165	0.121735
$857$	−18.9925	−0.648771	−0.324386	−	0.945925i	$-0.605158\pi$
$857$	−18.9925	−0.648771	−0.324386	+	0.945925i	$0.605158\pi$
$858$	3.57542	0.122063
$859$	−56.3694	−1.92330	−0.961649	−	0.274283i	$-0.911559\pi$
$859$	−56.3694	−1.92330	−0.961649	+	0.274283i	$0.911559\pi$
$860$	3.81292	0.130019
$861$	3.15084	0.107380
$862$	21.6654	0.737927
$863$	−26.9294	−0.916688	−0.458344	−	0.888775i	$-0.651557\pi$
$863$	−26.9294	−0.916688	−0.458344	+	0.888775i	$0.651557\pi$
$864$	−1.00000	−0.0340207
$865$	−6.00000	−0.204006
$866$	29.1233	0.989650
$867$	1.00000	0.0339618
$868$	−0.604704	−0.0205250
$869$	10.7017	0.363029
$870$	4.23750	0.143665
$871$	20.4370	0.692482
$872$	−13.6914	−0.463648
$873$	7.84568	0.265536
$874$	−38.4680	−1.30120
$875$	0.662077	0.0223823
$876$	5.74873	0.194232
$877$	35.5330	1.19986	0.599932	−	0.800051i	$-0.295194\pi$
$877$	35.5330	1.19986	0.599932	+	0.800051i	$0.295194\pi$
$878$	3.57834	0.120763
$879$	26.7331	0.901684
$880$	1.00000	0.0337100
$881$	−12.6276	−0.425434	−0.212717	−	0.977114i	$-0.568231\pi$
$881$	−12.6276	−0.425434	−0.212717	+	0.977114i	$0.568231\pi$
$882$	6.56165	0.220942
$883$	40.8117	1.37342	0.686712	−	0.726929i	$-0.259053\pi$
$883$	40.8117	1.37342	0.686712	+	0.726929i	$0.259053\pi$
$884$	−3.57542	−0.120254
$885$	−1.57542	−0.0529572
$886$	−0.0763659	−0.00256556
$887$	−28.5541	−0.958754	−0.479377	−	0.877609i	$-0.659137\pi$
$887$	−28.5541	−0.958754	−0.479377	+	0.877609i	$0.659137\pi$
$888$	−2.00000	−0.0671156
$889$	−14.2284	−0.477205
$890$	0.675845	0.0226544
$891$	−1.00000	−0.0335013
$892$	24.2305	0.811299
$893$	0	0
$894$	−7.90987	−0.264546
$895$	1.57542	0.0526605
$896$	0.662077	0.0221185
$897$	26.5336	0.885930
$898$	29.5043	0.984571
$899$	3.87029	0.129081
$900$	1.00000	0.0333333
$901$	11.6586	0.388404
$902$	−4.75902	−0.158458
$903$	2.52445	0.0840084
$904$	−12.7017	−0.422451
$905$	21.9494	0.729624
$906$	−20.6689	−0.686678
$907$	−10.9994	−0.365231	−0.182615	−	0.983184i	$-0.558456\pi$
$907$	−10.9994	−0.365231	−0.182615	+	0.983184i	$0.558456\pi$
$908$	22.9719	0.762350
$909$	5.80207	0.192443
$910$	−2.36721	−0.0784721
$911$	−36.8709	−1.22159	−0.610794	−	0.791789i	$-0.709150\pi$
$911$	−36.8709	−1.22159	−0.610794	+	0.791789i	$0.709150\pi$
$912$	5.18360	0.171646
$913$	9.51805	0.315001
$914$	4.30168	0.142287
$915$	−5.15084	−0.170282
$916$	−14.1939	−0.468979
$917$	6.30168	0.208100
$918$	1.00000	0.0330049
$919$	−27.5753	−0.909625	−0.454812	−	0.890587i	$-0.650294\pi$
$919$	−27.5753	−0.909625	−0.454812	+	0.890587i	$0.650294\pi$
$920$	7.42110	0.244666
$921$	−14.7848	−0.487177
$922$	−23.8168	−0.784365
$923$	−43.7050	−1.43857
$924$	0.662077	0.0217807
$925$	2.00000	0.0657596
$926$	24.8352	0.816137
$927$	−8.60470	−0.282616
$928$	−4.23750	−0.139103
$929$	17.6570	0.579308	0.289654	−	0.957131i	$-0.406460\pi$
$929$	17.6570	0.579308	0.289654	+	0.957131i	$0.406460\pi$
$930$	0.913344	0.0299497
$931$	−34.0130	−1.11473
$932$	−14.7986	−0.484744
$933$	−23.9151	−0.782945
$934$	2.88192	0.0942992
$935$	−1.00000	−0.0327035
$936$	−3.57542	−0.116866
$937$	30.0412	0.981402	0.490701	−	0.871328i	$-0.336741\pi$
$937$	30.0412	0.981402	0.490701	+	0.871328i	$0.336741\pi$
$938$	3.78442	0.123566
$939$	14.9690	0.488494
$940$	0	0
$941$	4.58279	0.149395	0.0746973	−	0.997206i	$-0.476201\pi$
$941$	4.58279	0.149395	0.0746973	+	0.997206i	$0.476201\pi$
$942$	11.6012	0.377988
$943$	−35.3172	−1.15009
$944$	1.57542	0.0512756
$945$	0.662077	0.0215374
$946$	−3.81292	−0.123969
$947$	39.9725	1.29893	0.649465	−	0.760391i	$-0.274993\pi$
$947$	39.9725	1.29893	0.649465	+	0.760391i	$0.274993\pi$
$948$	−10.7017	−0.347573
$949$	20.5541	0.667216
$950$	−5.18360	−0.168178
$951$	−30.3969	−0.985687
$952$	−0.662077	−0.0214581
$953$	38.1664	1.23633	0.618165	−	0.786049i	$-0.287876\pi$
$953$	38.1664	1.23633	0.618165	+	0.786049i	$0.287876\pi$
$954$	11.6586	0.377461
$955$	−18.7125	−0.605522
$956$	17.3242	0.560303
$957$	−4.23750	−0.136979
$958$	15.7379	0.508468
$959$	−14.0711	−0.454381
$960$	−1.00000	−0.0322749
$961$	−30.1658	−0.973090
$962$	−7.15084	−0.230552
$963$	−3.56165	−0.114773
$964$	−5.35558	−0.172492
$965$	−2.59789	−0.0836291
$966$	4.91334	0.158084
$967$	−10.6758	−0.343312	−0.171656	−	0.985157i	$-0.554912\pi$
$967$	−10.6758	−0.343312	−0.171656	+	0.985157i	$0.554912\pi$
$968$	−1.00000	−0.0321412
$969$	−5.18360	−0.166521
$970$	7.84568	0.251910
$971$	−18.5037	−0.593813	−0.296906	−	0.954907i	$-0.595955\pi$
$971$	−18.5037	−0.593813	−0.296906	+	0.954907i	$0.595955\pi$
$972$	1.00000	0.0320750
$973$	−11.8703	−0.380544
$974$	−38.9254	−1.24725
$975$	3.57542	0.114505
$976$	5.15084	0.164874
$977$	15.1222	0.483802	0.241901	−	0.970301i	$-0.422229\pi$
$977$	15.1222	0.483802	0.241901	+	0.970301i	$0.422229\pi$
$978$	−16.7986	−0.537160
$979$	−0.675845	−0.0216001
$980$	6.56165	0.209604
$981$	13.6914	0.437131
$982$	−27.4004	−0.874381
$983$	40.9252	1.30531	0.652656	−	0.757654i	$-0.273655\pi$
$983$	40.9252	1.30531	0.652656	+	0.757654i	$0.273655\pi$
$984$	4.75902	0.151712
$985$	−4.95695	−0.157942
$986$	4.23750	0.134949
$987$	0	0
$988$	18.5336	0.589631
$989$	−28.2961	−0.899763
$990$	−1.00000	−0.0317821
$991$	−18.8928	−0.600148	−0.300074	−	0.953916i	$-0.597011\pi$
$991$	−18.8928	−0.600148	−0.300074	+	0.953916i	$0.597011\pi$
$992$	−0.913344	−0.0289987
$993$	−17.3011	−0.549035
$994$	−8.09306	−0.256696
$995$	−17.5180	−0.555359
$996$	−9.51805	−0.301591
$997$	−45.2011	−1.43153	−0.715767	−	0.698339i	$-0.753923\pi$
$997$	−45.2011	−1.43153	−0.715767	+	0.698339i	$0.753923\pi$
$998$	11.4975	0.363946
$999$	2.00000	0.0632772

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5610.2.a.cf.1.2	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5610.2.a.cf.1.2	✓	4	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -0.662077 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -0.662077 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -1.00000 q^{11} +1.00000 q^{12} +3.57542 q^{13} +0.662077 q^{14} -1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} +5.18360 q^{19} -1.00000 q^{20} -0.662077 q^{21} +1.00000 q^{22} +7.42110 q^{23} -1.00000 q^{24} +1.00000 q^{25} -3.57542 q^{26} +1.00000 q^{27} -0.662077 q^{28} +4.23750 q^{29} +1.00000 q^{30} +0.913344 q^{31} -1.00000 q^{32} -1.00000 q^{33} +1.00000 q^{34} +0.662077 q^{35} +1.00000 q^{36} +2.00000 q^{37} -5.18360 q^{38} +3.57542 q^{39} +1.00000 q^{40} -4.75902 q^{41} +0.662077 q^{42} -3.81292 q^{43} -1.00000 q^{44} -1.00000 q^{45} -7.42110 q^{46} +1.00000 q^{48} -6.56165 q^{49} -1.00000 q^{50} -1.00000 q^{51} +3.57542 q^{52} -11.6586 q^{53} -1.00000 q^{54} +1.00000 q^{55} +0.662077 q^{56} +5.18360 q^{57} -4.23750 q^{58} +1.57542 q^{59} -1.00000 q^{60} +5.15084 q^{61} -0.913344 q^{62} -0.662077 q^{63} +1.00000 q^{64} -3.57542 q^{65} +1.00000 q^{66} +5.71597 q^{67} -1.00000 q^{68} +7.42110 q^{69} -0.662077 q^{70} -12.2237 q^{71} -1.00000 q^{72} +5.74873 q^{73} -2.00000 q^{74} +1.00000 q^{75} +5.18360 q^{76} +0.662077 q^{77} -3.57542 q^{78} -10.7017 q^{79} -1.00000 q^{80} +1.00000 q^{81} +4.75902 q^{82} -9.51805 q^{83} -0.662077 q^{84} +1.00000 q^{85} +3.81292 q^{86} +4.23750 q^{87} +1.00000 q^{88} +0.675845 q^{89} +1.00000 q^{90} -2.36721 q^{91} +7.42110 q^{92} +0.913344 q^{93} -5.18360 q^{95} -1.00000 q^{96} +7.84568 q^{97} +6.56165 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} - 4 q^{5} - 4 q^{6} + 5 q^{7} - 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 - 4 * q^5 - 4 * q^6 + 5 * q^7 - 4 * q^8 + 4 * q^9	\( 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} - 4 q^{5} - 4 q^{6} + 5 q^{7} - 4 q^{8} + 4 q^{9} + 4 q^{10} - 4 q^{11} + 4 q^{12} + 6 q^{13} - 5 q^{14} - 4 q^{15} + 4 q^{16} - 4 q^{17} - 4 q^{18} + 8 q^{19} - 4 q^{20} + 5 q^{21} + 4 q^{22} + q^{23} - 4 q^{24} + 4 q^{25} - 6 q^{26} + 4 q^{27} + 5 q^{28} + q^{29} + 4 q^{30} + 3 q^{31} - 4 q^{32} - 4 q^{33} + 4 q^{34} - 5 q^{35} + 4 q^{36} + 8 q^{37} - 8 q^{38} + 6 q^{39} + 4 q^{40} + 2 q^{41} - 5 q^{42} + 9 q^{43} - 4 q^{44} - 4 q^{45} - q^{46} + 4 q^{48} + 5 q^{49} - 4 q^{50} - 4 q^{51} + 6 q^{52} - 2 q^{53} - 4 q^{54} + 4 q^{55} - 5 q^{56} + 8 q^{57} - q^{58} - 2 q^{59} - 4 q^{60} + 4 q^{61} - 3 q^{62} + 5 q^{63} + 4 q^{64} - 6 q^{65} + 4 q^{66} + 12 q^{67} - 4 q^{68} + q^{69} + 5 q^{70} - 10 q^{71} - 4 q^{72} + 16 q^{73} - 8 q^{74} + 4 q^{75} + 8 q^{76} - 5 q^{77} - 6 q^{78} + 12 q^{79} - 4 q^{80} + 4 q^{81} - 2 q^{82} + 4 q^{83} + 5 q^{84} + 4 q^{85} - 9 q^{86} + q^{87} + 4 q^{88} + 18 q^{89} + 4 q^{90} + 16 q^{91} + q^{92} + 3 q^{93} - 8 q^{95} - 4 q^{96} + 11 q^{97} - 5 q^{98} - 4 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 - 4 * q^5 - 4 * q^6 + 5 * q^7 - 4 * q^8 + 4 * q^9 + 4 * q^10 - 4 * q^11 + 4 * q^12 + 6 * q^13 - 5 * q^14 - 4 * q^15 + 4 * q^16 - 4 * q^17 - 4 * q^18 + 8 * q^19 - 4 * q^20 + 5 * q^21 + 4 * q^22 + q^23 - 4 * q^24 + 4 * q^25 - 6 * q^26 + 4 * q^27 + 5 * q^28 + q^29 + 4 * q^30 + 3 * q^31 - 4 * q^32 - 4 * q^33 + 4 * q^34 - 5 * q^35 + 4 * q^36 + 8 * q^37 - 8 * q^38 + 6 * q^39 + 4 * q^40 + 2 * q^41 - 5 * q^42 + 9 * q^43 - 4 * q^44 - 4 * q^45 - q^46 + 4 * q^48 + 5 * q^49 - 4 * q^50 - 4 * q^51 + 6 * q^52 - 2 * q^53 - 4 * q^54 + 4 * q^55 - 5 * q^56 + 8 * q^57 - q^58 - 2 * q^59 - 4 * q^60 + 4 * q^61 - 3 * q^62 + 5 * q^63 + 4 * q^64 - 6 * q^65 + 4 * q^66 + 12 * q^67 - 4 * q^68 + q^69 + 5 * q^70 - 10 * q^71 - 4 * q^72 + 16 * q^73 - 8 * q^74 + 4 * q^75 + 8 * q^76 - 5 * q^77 - 6 * q^78 + 12 * q^79 - 4 * q^80 + 4 * q^81 - 2 * q^82 + 4 * q^83 + 5 * q^84 + 4 * q^85 - 9 * q^86 + q^87 + 4 * q^88 + 18 * q^89 + 4 * q^90 + 16 * q^91 + q^92 + 3 * q^93 - 8 * q^95 - 4 * q^96 + 11 * q^97 - 5 * q^98 - 4 * q^99

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