LMFDB - Embedded newform 4026.2.a.t.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4026,2,Mod(1,4026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4026, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("4026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4026 = 2 \cdot 3 \cdot 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4026.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:	$32.1477718538$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.2777.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 4x^{2} + x + 2 $ x^4 - x^3 - 4*x^2 + x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.50848$ of defining polynomial
Character	$\chi$	$=$	4026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.78400 q^{5} +1.00000 q^{6} +0.966641 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.78400 q^{5} +1.00000 q^{6} +0.966641 q^{7} +1.00000 q^{8} +1.00000 q^{9} -2.78400 q^{10} -1.00000 q^{11} +1.00000 q^{12} -0.856807 q^{13} +0.966641 q^{14} -2.78400 q^{15} +1.00000 q^{16} -2.44897 q^{17} +1.00000 q^{18} -6.19961 q^{19} -2.78400 q^{20} +0.966641 q^{21} -1.00000 q^{22} +3.52544 q^{23} +1.00000 q^{24} +2.75064 q^{25} -0.856807 q^{26} +1.00000 q^{27} +0.966641 q^{28} +0.0503213 q^{29} -2.78400 q^{30} -8.57409 q^{31} +1.00000 q^{32} -1.00000 q^{33} -2.44897 q^{34} -2.69113 q^{35} +1.00000 q^{36} -1.77790 q^{37} -6.19961 q^{38} -0.856807 q^{39} -2.78400 q^{40} -0.392555 q^{41} +0.966641 q^{42} +4.20570 q^{43} -1.00000 q^{44} -2.78400 q^{45} +3.52544 q^{46} -5.92409 q^{47} +1.00000 q^{48} -6.06561 q^{49} +2.75064 q^{50} -2.44897 q^{51} -0.856807 q^{52} -4.08257 q^{53} +1.00000 q^{54} +2.78400 q^{55} +0.966641 q^{56} -6.19961 q^{57} +0.0503213 q^{58} +12.7938 q^{59} -2.78400 q^{60} -1.00000 q^{61} -8.57409 q^{62} +0.966641 q^{63} +1.00000 q^{64} +2.38535 q^{65} -1.00000 q^{66} +4.74145 q^{67} -2.44897 q^{68} +3.52544 q^{69} -2.69113 q^{70} -9.26999 q^{71} +1.00000 q^{72} -11.4101 q^{73} -1.77790 q^{74} +2.75064 q^{75} -6.19961 q^{76} -0.966641 q^{77} -0.856807 q^{78} -13.0098 q^{79} -2.78400 q^{80} +1.00000 q^{81} -0.392555 q^{82} -5.02306 q^{83} +0.966641 q^{84} +6.81792 q^{85} +4.20570 q^{86} +0.0503213 q^{87} -1.00000 q^{88} +7.24993 q^{89} -2.78400 q^{90} -0.828225 q^{91} +3.52544 q^{92} -8.57409 q^{93} -5.92409 q^{94} +17.2597 q^{95} +1.00000 q^{96} -7.72038 q^{97} -6.06561 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} - 4 q^{5} + 4 q^{6} - 6 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 - 6 * q^7 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} - 4 q^{5} + 4 q^{6} - 6 q^{7} + 4 q^{8} + 4 q^{9} - 4 q^{10} - 4 q^{11} + 4 q^{12} - 5 q^{13} - 6 q^{14} - 4 q^{15} + 4 q^{16} - 10 q^{17} + 4 q^{18} - 8 q^{19} - 4 q^{20} - 6 q^{21} - 4 q^{22} - 7 q^{23} + 4 q^{24} - 6 q^{25} - 5 q^{26} + 4 q^{27} - 6 q^{28} - 4 q^{29} - 4 q^{30} - 9 q^{31} + 4 q^{32} - 4 q^{33} - 10 q^{34} - q^{35} + 4 q^{36} - 11 q^{37} - 8 q^{38} - 5 q^{39} - 4 q^{40} - 17 q^{41} - 6 q^{42} - 11 q^{43} - 4 q^{44} - 4 q^{45} - 7 q^{46} - 7 q^{47} + 4 q^{48} - 6 q^{49} - 6 q^{50} - 10 q^{51} - 5 q^{52} + 16 q^{53} + 4 q^{54} + 4 q^{55} - 6 q^{56} - 8 q^{57} - 4 q^{58} + 3 q^{59} - 4 q^{60} - 4 q^{61} - 9 q^{62} - 6 q^{63} + 4 q^{64} - 2 q^{65} - 4 q^{66} + 5 q^{67} - 10 q^{68} - 7 q^{69} - q^{70} - 10 q^{71} + 4 q^{72} - 9 q^{73} - 11 q^{74} - 6 q^{75} - 8 q^{76} + 6 q^{77} - 5 q^{78} - 11 q^{79} - 4 q^{80} + 4 q^{81} - 17 q^{82} + 5 q^{83} - 6 q^{84} - 8 q^{85} - 11 q^{86} - 4 q^{87} - 4 q^{88} + 8 q^{89} - 4 q^{90} - 3 q^{91} - 7 q^{92} - 9 q^{93} - 7 q^{94} + 7 q^{95} + 4 q^{96} - 12 q^{97} - 6 q^{98} - 4 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 - 4 * q^5 + 4 * q^6 - 6 * q^7 + 4 * q^8 + 4 * q^9 - 4 * q^10 - 4 * q^11 + 4 * q^12 - 5 * q^13 - 6 * q^14 - 4 * q^15 + 4 * q^16 - 10 * q^17 + 4 * q^18 - 8 * q^19 - 4 * q^20 - 6 * q^21 - 4 * q^22 - 7 * q^23 + 4 * q^24 - 6 * q^25 - 5 * q^26 + 4 * q^27 - 6 * q^28 - 4 * q^29 - 4 * q^30 - 9 * q^31 + 4 * q^32 - 4 * q^33 - 10 * q^34 - q^35 + 4 * q^36 - 11 * q^37 - 8 * q^38 - 5 * q^39 - 4 * q^40 - 17 * q^41 - 6 * q^42 - 11 * q^43 - 4 * q^44 - 4 * q^45 - 7 * q^46 - 7 * q^47 + 4 * q^48 - 6 * q^49 - 6 * q^50 - 10 * q^51 - 5 * q^52 + 16 * q^53 + 4 * q^54 + 4 * q^55 - 6 * q^56 - 8 * q^57 - 4 * q^58 + 3 * q^59 - 4 * q^60 - 4 * q^61 - 9 * q^62 - 6 * q^63 + 4 * q^64 - 2 * q^65 - 4 * q^66 + 5 * q^67 - 10 * q^68 - 7 * q^69 - q^70 - 10 * q^71 + 4 * q^72 - 9 * q^73 - 11 * q^74 - 6 * q^75 - 8 * q^76 + 6 * q^77 - 5 * q^78 - 11 * q^79 - 4 * q^80 + 4 * q^81 - 17 * q^82 + 5 * q^83 - 6 * q^84 - 8 * q^85 - 11 * q^86 - 4 * q^87 - 4 * q^88 + 8 * q^89 - 4 * q^90 - 3 * q^91 - 7 * q^92 - 9 * q^93 - 7 * q^94 + 7 * q^95 + 4 * q^96 - 12 * q^97 - 6 * 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
$5$	−2.78400	−1.24504	−0.622521	−	0.782603i	$-0.713891\pi$
$5$	−2.78400	−1.24504	−0.622521	+	0.782603i	$0.713891\pi$
$6$	1.00000	0.408248
$7$	0.966641	0.365356	0.182678	−	0.983173i	$-0.441523\pi$
$7$	0.966641	0.365356	0.182678	+	0.983173i	$0.441523\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−2.78400	−0.880377
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	1.00000	0.288675
$13$	−0.856807	−0.237636	−0.118818	−	0.992916i	$-0.537910\pi$
$13$	−0.856807	−0.237636	−0.118818	+	0.992916i	$0.537910\pi$
$14$	0.966641	0.258346
$15$	−2.78400	−0.718825
$16$	1.00000	0.250000
$17$	−2.44897	−0.593962	−0.296981	−	0.954883i	$-0.595980\pi$
$17$	−2.44897	−0.593962	−0.296981	+	0.954883i	$0.595980\pi$
$18$	1.00000	0.235702
$19$	−6.19961	−1.42229	−0.711144	−	0.703047i	$-0.751822\pi$
$19$	−6.19961	−1.42229	−0.711144	+	0.703047i	$0.751822\pi$
$20$	−2.78400	−0.622521
$21$	0.966641	0.210938
$22$	−1.00000	−0.213201
$23$	3.52544	0.735106	0.367553	−	0.930003i	$-0.380196\pi$
$23$	3.52544	0.735106	0.367553	+	0.930003i	$0.380196\pi$
$24$	1.00000	0.204124
$25$	2.75064	0.550128
$26$	−0.856807	−0.168034
$27$	1.00000	0.192450
$28$	0.966641	0.182678
$29$	0.0503213	0.00934444	0.00467222	−	0.999989i	$-0.498513\pi$
$29$	0.0503213	0.00934444	0.00467222	+	0.999989i	$0.498513\pi$
$30$	−2.78400	−0.508286
$31$	−8.57409	−1.53995	−0.769976	−	0.638073i	$-0.779732\pi$
$31$	−8.57409	−1.53995	−0.769976	+	0.638073i	$0.779732\pi$
$32$	1.00000	0.176777
$33$	−1.00000	−0.174078
$34$	−2.44897	−0.419995
$35$	−2.69113	−0.454883
$36$	1.00000	0.166667
$37$	−1.77790	−0.292286	−0.146143	−	0.989264i	$-0.546686\pi$
$37$	−1.77790	−0.292286	−0.146143	+	0.989264i	$0.546686\pi$
$38$	−6.19961	−1.00571
$39$	−0.856807	−0.137199
$40$	−2.78400	−0.440189
$41$	−0.392555	−0.0613068	−0.0306534	−	0.999530i	$-0.509759\pi$
$41$	−0.392555	−0.0613068	−0.0306534	+	0.999530i	$0.509759\pi$
$42$	0.966641	0.149156
$43$	4.20570	0.641363	0.320682	−	0.947187i	$-0.396088\pi$
$43$	4.20570	0.641363	0.320682	+	0.947187i	$0.396088\pi$
$44$	−1.00000	−0.150756
$45$	−2.78400	−0.415014
$46$	3.52544	0.519798
$47$	−5.92409	−0.864118	−0.432059	−	0.901845i	$-0.642213\pi$
$47$	−5.92409	−0.864118	−0.432059	+	0.901845i	$0.642213\pi$
$48$	1.00000	0.144338
$49$	−6.06561	−0.866515
$50$	2.75064	0.388999
$51$	−2.44897	−0.342924
$52$	−0.856807	−0.118818
$53$	−4.08257	−0.560784	−0.280392	−	0.959886i	$-0.590464\pi$
$53$	−4.08257	−0.560784	−0.280392	+	0.959886i	$0.590464\pi$
$54$	1.00000	0.136083
$55$	2.78400	0.375394
$56$	0.966641	0.129173
$57$	−6.19961	−0.821158
$58$	0.0503213	0.00660752
$59$	12.7938	1.66560	0.832802	−	0.553570i	$-0.186735\pi$
$59$	12.7938	1.66560	0.832802	+	0.553570i	$0.186735\pi$
$60$	−2.78400	−0.359412
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	−8.57409	−1.08891
$63$	0.966641	0.121785
$64$	1.00000	0.125000
$65$	2.38535	0.295866
$66$	−1.00000	−0.123091
$67$	4.74145	0.579260	0.289630	−	0.957139i	$-0.406468\pi$
$67$	4.74145	0.579260	0.289630	+	0.957139i	$0.406468\pi$
$68$	−2.44897	−0.296981
$69$	3.52544	0.424414
$70$	−2.69113	−0.321651
$71$	−9.26999	−1.10015	−0.550073	−	0.835117i	$-0.685400\pi$
$71$	−9.26999	−1.10015	−0.550073	+	0.835117i	$0.685400\pi$
$72$	1.00000	0.117851
$73$	−11.4101	−1.33545	−0.667725	−	0.744408i	$-0.732732\pi$
$73$	−11.4101	−1.33545	−0.667725	+	0.744408i	$0.732732\pi$
$74$	−1.77790	−0.206677
$75$	2.75064	0.317616
$76$	−6.19961	−0.711144
$77$	−0.966641	−0.110159
$78$	−0.856807	−0.0970143
$79$	−13.0098	−1.46371	−0.731856	−	0.681459i	$-0.761346\pi$
$79$	−13.0098	−1.46371	−0.731856	+	0.681459i	$0.761346\pi$
$80$	−2.78400	−0.311260
$81$	1.00000	0.111111
$82$	−0.392555	−0.0433504
$83$	−5.02306	−0.551352	−0.275676	−	0.961251i	$-0.588902\pi$
$83$	−5.02306	−0.551352	−0.275676	+	0.961251i	$0.588902\pi$
$84$	0.966641	0.105469
$85$	6.81792	0.739507
$86$	4.20570	0.453512
$87$	0.0503213	0.00539501
$88$	−1.00000	−0.106600
$89$	7.24993	0.768491	0.384245	−	0.923231i	$-0.374462\pi$
$89$	7.24993	0.768491	0.384245	+	0.923231i	$0.374462\pi$
$90$	−2.78400	−0.293459
$91$	−0.828225	−0.0868216
$92$	3.52544	0.367553
$93$	−8.57409	−0.889091
$94$	−5.92409	−0.611023
$95$	17.2597	1.77081
$96$	1.00000	0.102062
$97$	−7.72038	−0.783886	−0.391943	−	0.919990i	$-0.628197\pi$
$97$	−7.72038	−0.783886	−0.391943	+	0.919990i	$0.628197\pi$
$98$	−6.06561	−0.612719
$99$	−1.00000	−0.100504
$100$	2.75064	0.275064
$101$	6.40840	0.637660	0.318830	−	0.947812i	$-0.396710\pi$
$101$	6.40840	0.637660	0.318830	+	0.947812i	$0.396710\pi$
$102$	−2.44897	−0.242484
$103$	1.87986	0.185228	0.0926142	−	0.995702i	$-0.470478\pi$
$103$	1.87986	0.185228	0.0926142	+	0.995702i	$0.470478\pi$
$104$	−0.856807	−0.0840169
$105$	−2.69113	−0.262627
$106$	−4.08257	−0.396534
$107$	−16.6220	−1.60691	−0.803454	−	0.595367i	$-0.797007\pi$
$107$	−16.6220	−1.60691	−0.803454	+	0.595367i	$0.797007\pi$
$108$	1.00000	0.0962250
$109$	−12.9309	−1.23855	−0.619276	−	0.785174i	$-0.712574\pi$
$109$	−12.9309	−1.23855	−0.619276	+	0.785174i	$0.712574\pi$
$110$	2.78400	0.265444
$111$	−1.77790	−0.168751
$112$	0.966641	0.0913390
$113$	−5.08734	−0.478577	−0.239289	−	0.970949i	$-0.576914\pi$
$113$	−5.08734	−0.478577	−0.239289	+	0.970949i	$0.576914\pi$
$114$	−6.19961	−0.580646
$115$	−9.81482	−0.915237
$116$	0.0503213	0.00467222
$117$	−0.856807	−0.0792119
$118$	12.7938	1.17776
$119$	−2.36727	−0.217008
$120$	−2.78400	−0.254143
$121$	1.00000	0.0909091
$122$	−1.00000	−0.0905357
$123$	−0.392555	−0.0353955
$124$	−8.57409	−0.769976
$125$	6.26222	0.560110
$126$	0.966641	0.0861152
$127$	15.8046	1.40243	0.701217	−	0.712948i	$-0.252641\pi$
$127$	15.8046	1.40243	0.701217	+	0.712948i	$0.252641\pi$
$128$	1.00000	0.0883883
$129$	4.20570	0.370291
$130$	2.38535	0.209209
$131$	−9.37448	−0.819052	−0.409526	−	0.912298i	$-0.634306\pi$
$131$	−9.37448	−0.819052	−0.409526	+	0.912298i	$0.634306\pi$
$132$	−1.00000	−0.0870388
$133$	−5.99279	−0.519641
$134$	4.74145	0.409599
$135$	−2.78400	−0.239608
$136$	−2.44897	−0.209997
$137$	21.8427	1.86614	0.933072	−	0.359690i	$-0.117117\pi$
$137$	21.8427	1.86614	0.933072	+	0.359690i	$0.117117\pi$
$138$	3.52544	0.300106
$139$	−1.93018	−0.163716	−0.0818580	−	0.996644i	$-0.526085\pi$
$139$	−1.93018	−0.163716	−0.0818580	+	0.996644i	$0.526085\pi$
$140$	−2.69113	−0.227442
$141$	−5.92409	−0.498898
$142$	−9.26999	−0.777920
$143$	0.856807	0.0716498
$144$	1.00000	0.0833333
$145$	−0.140094	−0.0116342
$146$	−11.4101	−0.944305
$147$	−6.06561	−0.500283
$148$	−1.77790	−0.146143
$149$	18.6705	1.52955	0.764774	−	0.644298i	$-0.222851\pi$
$149$	18.6705	1.52955	0.764774	+	0.644298i	$0.222851\pi$
$150$	2.75064	0.224589
$151$	4.89794	0.398589	0.199294	−	0.979940i	$-0.436135\pi$
$151$	4.89794	0.398589	0.199294	+	0.979940i	$0.436135\pi$
$152$	−6.19961	−0.502855
$153$	−2.44897	−0.197987
$154$	−0.966641	−0.0778942
$155$	23.8702	1.91730
$156$	−0.856807	−0.0685995
$157$	−15.2836	−1.21976	−0.609882	−	0.792492i	$-0.708783\pi$
$157$	−15.2836	−1.21976	−0.609882	+	0.792492i	$0.708783\pi$
$158$	−13.0098	−1.03500
$159$	−4.08257	−0.323769
$160$	−2.78400	−0.220094
$161$	3.40784	0.268575
$162$	1.00000	0.0785674
$163$	0.802638	0.0628674	0.0314337	−	0.999506i	$-0.489993\pi$
$163$	0.802638	0.0628674	0.0314337	+	0.999506i	$0.489993\pi$
$164$	−0.392555	−0.0306534
$165$	2.78400	0.216734
$166$	−5.02306	−0.389865
$167$	18.7682	1.45232	0.726162	−	0.687523i	$-0.241302\pi$
$167$	18.7682	1.45232	0.726162	+	0.687523i	$0.241302\pi$
$168$	0.966641	0.0745780
$169$	−12.2659	−0.943529
$170$	6.81792	0.522911
$171$	−6.19961	−0.474096
$172$	4.20570	0.320682
$173$	−12.8476	−0.976786	−0.488393	−	0.872624i	$-0.662417\pi$
$173$	−12.8476	−0.976786	−0.488393	+	0.872624i	$0.662417\pi$
$174$	0.0503213	0.00381485
$175$	2.65888	0.200992
$176$	−1.00000	−0.0753778
$177$	12.7938	0.961637
$178$	7.24993	0.543405
$179$	14.7357	1.10139	0.550697	−	0.834705i	$-0.314362\pi$
$179$	14.7357	1.10139	0.550697	+	0.834705i	$0.314362\pi$
$180$	−2.78400	−0.207507
$181$	−11.1346	−0.827626	−0.413813	−	0.910362i	$-0.635803\pi$
$181$	−11.1346	−0.827626	−0.413813	+	0.910362i	$0.635803\pi$
$182$	−0.828225	−0.0613921
$183$	−1.00000	−0.0739221
$184$	3.52544	0.259899
$185$	4.94968	0.363908
$186$	−8.57409	−0.628683
$187$	2.44897	0.179086
$188$	−5.92409	−0.432059
$189$	0.966641	0.0703128
$190$	17.2597	1.25215
$191$	−14.7451	−1.06692	−0.533459	−	0.845826i	$-0.679108\pi$
$191$	−14.7451	−1.06692	−0.533459	+	0.845826i	$0.679108\pi$
$192$	1.00000	0.0721688
$193$	8.06318	0.580400	0.290200	−	0.956966i	$-0.406278\pi$
$193$	8.06318	0.580400	0.290200	+	0.956966i	$0.406278\pi$
$194$	−7.72038	−0.554291
$195$	2.38535	0.170818
$196$	−6.06561	−0.433258
$197$	−10.1815	−0.725404	−0.362702	−	0.931905i	$-0.618146\pi$
$197$	−10.1815	−0.725404	−0.362702	+	0.931905i	$0.618146\pi$
$198$	−1.00000	−0.0710669
$199$	4.17544	0.295989	0.147995	−	0.988988i	$-0.452718\pi$
$199$	4.17544	0.295989	0.147995	+	0.988988i	$0.452718\pi$
$200$	2.75064	0.194499
$201$	4.74145	0.334436
$202$	6.40840	0.450894
$203$	0.0486427	0.00341405
$204$	−2.44897	−0.171462
$205$	1.09287	0.0763294
$206$	1.87986	0.130976
$207$	3.52544	0.245035
$208$	−0.856807	−0.0594089
$209$	6.19961	0.428836
$210$	−2.69113	−0.185705
$211$	−14.8651	−1.02336	−0.511679	−	0.859176i	$-0.670976\pi$
$211$	−14.8651	−1.02336	−0.511679	+	0.859176i	$0.670976\pi$
$212$	−4.08257	−0.280392
$213$	−9.26999	−0.635169
$214$	−16.6220	−1.13626
$215$	−11.7087	−0.798524
$216$	1.00000	0.0680414
$217$	−8.28806	−0.562630
$218$	−12.9309	−0.875788
$219$	−11.4101	−0.771022
$220$	2.78400	0.187697
$221$	2.09829	0.141147
$222$	−1.77790	−0.119325
$223$	−23.5510	−1.57709	−0.788547	−	0.614974i	$-0.789167\pi$
$223$	−23.5510	−1.57709	−0.788547	+	0.614974i	$0.789167\pi$
$224$	0.966641	0.0645864
$225$	2.75064	0.183376
$226$	−5.08734	−0.338405
$227$	−22.9194	−1.52122	−0.760608	−	0.649211i	$-0.775099\pi$
$227$	−22.9194	−1.52122	−0.760608	+	0.649211i	$0.775099\pi$
$228$	−6.19961	−0.410579
$229$	2.80294	0.185224	0.0926119	−	0.995702i	$-0.470478\pi$
$229$	2.80294	0.185224	0.0926119	+	0.995702i	$0.470478\pi$
$230$	−9.81482	−0.647170
$231$	−0.966641	−0.0636003
$232$	0.0503213	0.00330376
$233$	5.36671	0.351585	0.175792	−	0.984427i	$-0.443751\pi$
$233$	5.36671	0.351585	0.175792	+	0.984427i	$0.443751\pi$
$234$	−0.856807	−0.0560113
$235$	16.4927	1.07586
$236$	12.7938	0.832802
$237$	−13.0098	−0.845075
$238$	−2.36727	−0.153448
$239$	−18.3867	−1.18933	−0.594667	−	0.803972i	$-0.702716\pi$
$239$	−18.3867	−1.18933	−0.594667	+	0.803972i	$0.702716\pi$
$240$	−2.78400	−0.179706
$241$	18.3423	1.18153	0.590764	−	0.806844i	$-0.298826\pi$
$241$	18.3423	1.18153	0.590764	+	0.806844i	$0.298826\pi$
$242$	1.00000	0.0642824
$243$	1.00000	0.0641500
$244$	−1.00000	−0.0640184
$245$	16.8866	1.07885
$246$	−0.392555	−0.0250284
$247$	5.31187	0.337986
$248$	−8.57409	−0.544455
$249$	−5.02306	−0.318323
$250$	6.26222	0.396057
$251$	0.746974	0.0471486	0.0235743	−	0.999722i	$-0.492495\pi$
$251$	0.746974	0.0471486	0.0235743	+	0.999722i	$0.492495\pi$
$252$	0.966641	0.0608927
$253$	−3.52544	−0.221643
$254$	15.8046	0.991670
$255$	6.81792	0.426955
$256$	1.00000	0.0625000
$257$	−12.1093	−0.755357	−0.377678	−	0.925937i	$-0.623277\pi$
$257$	−12.1093	−0.755357	−0.377678	+	0.925937i	$0.623277\pi$
$258$	4.20570	0.261835
$259$	−1.71859	−0.106788
$260$	2.38535	0.147933
$261$	0.0503213	0.00311481
$262$	−9.37448	−0.579157
$263$	−3.12781	−0.192869	−0.0964344	−	0.995339i	$-0.530744\pi$
$263$	−3.12781	−0.192869	−0.0964344	+	0.995339i	$0.530744\pi$
$264$	−1.00000	−0.0615457
$265$	11.3659	0.698199
$266$	−5.99279	−0.367442
$267$	7.24993	0.443688
$268$	4.74145	0.289630
$269$	29.8466	1.81978	0.909890	−	0.414849i	$-0.136165\pi$
$269$	29.8466	1.81978	0.909890	+	0.414849i	$0.136165\pi$
$270$	−2.78400	−0.169429
$271$	12.1709	0.739331	0.369665	−	0.929165i	$-0.379472\pi$
$271$	12.1709	0.739331	0.369665	+	0.929165i	$0.379472\pi$
$272$	−2.44897	−0.148491
$273$	−0.828225	−0.0501265
$274$	21.8427	1.31956
$275$	−2.75064	−0.165870
$276$	3.52544	0.212207
$277$	−24.7695	−1.48825	−0.744127	−	0.668038i	$-0.767134\pi$
$277$	−24.7695	−1.48825	−0.744127	+	0.668038i	$0.767134\pi$
$278$	−1.93018	−0.115765
$279$	−8.57409	−0.513317
$280$	−2.69113	−0.160826
$281$	31.4461	1.87592	0.937958	−	0.346748i	$-0.112714\pi$
$281$	31.4461	1.87592	0.937958	+	0.346748i	$0.112714\pi$
$282$	−5.92409	−0.352774
$283$	−27.2525	−1.61999	−0.809996	−	0.586436i	$-0.800531\pi$
$283$	−27.2525	−1.61999	−0.809996	+	0.586436i	$0.800531\pi$
$284$	−9.26999	−0.550073
$285$	17.2597	1.02238
$286$	0.856807	0.0506641
$287$	−0.379460	−0.0223988
$288$	1.00000	0.0589256
$289$	−11.0026	−0.647209
$290$	−0.140094	−0.00822663
$291$	−7.72038	−0.452577
$292$	−11.4101	−0.667725
$293$	14.3648	0.839203	0.419602	−	0.907708i	$-0.362170\pi$
$293$	14.3648	0.839203	0.419602	+	0.907708i	$0.362170\pi$
$294$	−6.06561	−0.353753
$295$	−35.6178	−2.07375
$296$	−1.77790	−0.103339
$297$	−1.00000	−0.0580259
$298$	18.6705	1.08155
$299$	−3.02063	−0.174687
$300$	2.75064	0.158808
$301$	4.06540	0.234326
$302$	4.89794	0.281845
$303$	6.40840	0.368153
$304$	−6.19961	−0.355572
$305$	2.78400	0.159411
$306$	−2.44897	−0.139998
$307$	7.38602	0.421542	0.210771	−	0.977535i	$-0.432403\pi$
$307$	7.38602	0.421542	0.210771	+	0.977535i	$0.432403\pi$
$308$	−0.966641	−0.0550795
$309$	1.87986	0.106942
$310$	23.8702	1.35574
$311$	1.78201	0.101049	0.0505243	−	0.998723i	$-0.483911\pi$
$311$	1.78201	0.101049	0.0505243	+	0.998723i	$0.483911\pi$
$312$	−0.856807	−0.0485072
$313$	16.3987	0.926907	0.463454	−	0.886121i	$-0.346610\pi$
$313$	16.3987	0.926907	0.463454	+	0.886121i	$0.346610\pi$
$314$	−15.2836	−0.862503
$315$	−2.69113	−0.151628
$316$	−13.0098	−0.731856
$317$	27.3634	1.53688	0.768442	−	0.639920i	$-0.221033\pi$
$317$	27.3634	1.53688	0.768442	+	0.639920i	$0.221033\pi$
$318$	−4.08257	−0.228939
$319$	−0.0503213	−0.00281745
$320$	−2.78400	−0.155630
$321$	−16.6220	−0.927748
$322$	3.40784	0.189911
$323$	15.1826	0.844785
$324$	1.00000	0.0555556
$325$	−2.35677	−0.130730
$326$	0.802638	0.0444540
$327$	−12.9309	−0.715078
$328$	−0.392555	−0.0216752
$329$	−5.72647	−0.315710
$330$	2.78400	0.153254
$331$	18.2047	1.00062	0.500310	−	0.865846i	$-0.333219\pi$
$331$	18.2047	1.00062	0.500310	+	0.865846i	$0.333219\pi$
$332$	−5.02306	−0.275676
$333$	−1.77790	−0.0974285
$334$	18.7682	1.02695
$335$	−13.2002	−0.721202
$336$	0.966641	0.0527346
$337$	−3.17813	−0.173124	−0.0865618	−	0.996246i	$-0.527588\pi$
$337$	−3.17813	−0.173124	−0.0865618	+	0.996246i	$0.527588\pi$
$338$	−12.2659	−0.667176
$339$	−5.08734	−0.276307
$340$	6.81792	0.369754
$341$	8.57409	0.464313
$342$	−6.19961	−0.335236
$343$	−12.6298	−0.681942
$344$	4.20570	0.226756
$345$	−9.81482	−0.528412
$346$	−12.8476	−0.690692
$347$	31.7170	1.70266	0.851329	−	0.524633i	$-0.175797\pi$
$347$	31.7170	1.70266	0.851329	+	0.524633i	$0.175797\pi$
$348$	0.0503213	0.00269751
$349$	−15.7361	−0.842334	−0.421167	−	0.906983i	$-0.638379\pi$
$349$	−15.7361	−0.842334	−0.421167	+	0.906983i	$0.638379\pi$
$350$	2.65888	0.142123
$351$	−0.856807	−0.0457330
$352$	−1.00000	−0.0533002
$353$	−15.7075	−0.836028	−0.418014	−	0.908441i	$-0.637274\pi$
$353$	−15.7075	−0.836028	−0.418014	+	0.908441i	$0.637274\pi$
$354$	12.7938	0.679980
$355$	25.8076	1.36973
$356$	7.24993	0.384245
$357$	−2.36727	−0.125289
$358$	14.7357	0.778804
$359$	3.42581	0.180807	0.0904037	−	0.995905i	$-0.471184\pi$
$359$	3.42581	0.180807	0.0904037	+	0.995905i	$0.471184\pi$
$360$	−2.78400	−0.146730
$361$	19.4351	1.02290
$362$	−11.1346	−0.585220
$363$	1.00000	0.0524864
$364$	−0.828225	−0.0434108
$365$	31.7656	1.66269
$366$	−1.00000	−0.0522708
$367$	−2.05783	−0.107418	−0.0537090	−	0.998557i	$-0.517104\pi$
$367$	−2.05783	−0.107418	−0.0537090	+	0.998557i	$0.517104\pi$
$368$	3.52544	0.183776
$369$	−0.392555	−0.0204356
$370$	4.94968	0.257322
$371$	−3.94638	−0.204886
$372$	−8.57409	−0.444546
$373$	22.5977	1.17006	0.585032	−	0.811010i	$-0.301082\pi$
$373$	22.5977	1.17006	0.585032	+	0.811010i	$0.301082\pi$
$374$	2.44897	0.126633
$375$	6.26222	0.323379
$376$	−5.92409	−0.305512
$377$	−0.0431157	−0.00222057
$378$	0.966641	0.0497187
$379$	31.8950	1.63833	0.819167	−	0.573555i	$-0.194436\pi$
$379$	31.8950	1.63833	0.819167	+	0.573555i	$0.194436\pi$
$380$	17.2597	0.885403
$381$	15.8046	0.809695
$382$	−14.7451	−0.754425
$383$	−24.9303	−1.27388	−0.636940	−	0.770914i	$-0.719800\pi$
$383$	−24.9303	−1.27388	−0.636940	+	0.770914i	$0.719800\pi$
$384$	1.00000	0.0510310
$385$	2.69113	0.137152
$386$	8.06318	0.410405
$387$	4.20570	0.213788
$388$	−7.72038	−0.391943
$389$	19.4665	0.986991	0.493495	−	0.869748i	$-0.335719\pi$
$389$	19.4665	0.986991	0.493495	+	0.869748i	$0.335719\pi$
$390$	2.38535	0.120787
$391$	−8.63370	−0.436625
$392$	−6.06561	−0.306359
$393$	−9.37448	−0.472880
$394$	−10.1815	−0.512938
$395$	36.2191	1.82238
$396$	−1.00000	−0.0502519
$397$	6.94146	0.348382	0.174191	−	0.984712i	$-0.444269\pi$
$397$	6.94146	0.348382	0.174191	+	0.984712i	$0.444269\pi$
$398$	4.17544	0.209296
$399$	−5.99279	−0.300015
$400$	2.75064	0.137532
$401$	−9.15228	−0.457043	−0.228522	−	0.973539i	$-0.573389\pi$
$401$	−9.15228	−0.457043	−0.228522	+	0.973539i	$0.573389\pi$
$402$	4.74145	0.236482
$403$	7.34634	0.365947
$404$	6.40840	0.318830
$405$	−2.78400	−0.138338
$406$	0.0486427	0.00241410
$407$	1.77790	0.0881274
$408$	−2.44897	−0.121242
$409$	35.2187	1.74145	0.870726	−	0.491769i	$-0.163650\pi$
$409$	35.2187	1.74145	0.870726	+	0.491769i	$0.163650\pi$
$410$	1.09287	0.0539731
$411$	21.8427	1.07742
$412$	1.87986	0.0926142
$413$	12.3670	0.608539
$414$	3.52544	0.173266
$415$	13.9842	0.686456
$416$	−0.856807	−0.0420084
$417$	−1.93018	−0.0945215
$418$	6.19961	0.303233
$419$	−20.4599	−0.999529	−0.499765	−	0.866161i	$-0.666580\pi$
$419$	−20.4599	−0.999529	−0.499765	+	0.866161i	$0.666580\pi$
$420$	−2.69113	−0.131313
$421$	32.2600	1.57226	0.786128	−	0.618064i	$-0.212083\pi$
$421$	32.2600	1.57226	0.786128	+	0.618064i	$0.212083\pi$
$422$	−14.8651	−0.723624
$423$	−5.92409	−0.288039
$424$	−4.08257	−0.198267
$425$	−6.73623	−0.326755
$426$	−9.26999	−0.449132
$427$	−0.966641	−0.0467790
$428$	−16.6220	−0.803454
$429$	0.856807	0.0413671
$430$	−11.7087	−0.564641
$431$	3.56531	0.171735	0.0858674	−	0.996307i	$-0.472634\pi$
$431$	3.56531	0.171735	0.0858674	+	0.996307i	$0.472634\pi$
$432$	1.00000	0.0481125
$433$	−34.5927	−1.66242	−0.831211	−	0.555958i	$-0.812352\pi$
$433$	−34.5927	−1.66242	−0.831211	+	0.555958i	$0.812352\pi$
$434$	−8.28806	−0.397840
$435$	−0.140094	−0.00671702
$436$	−12.9309	−0.619276
$437$	−21.8564	−1.04553
$438$	−11.4101	−0.545195
$439$	16.3540	0.780533	0.390266	−	0.920702i	$-0.372383\pi$
$439$	16.3540	0.780533	0.390266	+	0.920702i	$0.372383\pi$
$440$	2.78400	0.132722
$441$	−6.06561	−0.288838
$442$	2.09829	0.0998057
$443$	6.31355	0.299966	0.149983	−	0.988689i	$-0.452078\pi$
$443$	6.31355	0.299966	0.149983	+	0.988689i	$0.452078\pi$
$444$	−1.77790	−0.0843756
$445$	−20.1838	−0.956803
$446$	−23.5510	−1.11517
$447$	18.6705	0.883085
$448$	0.966641	0.0456695
$449$	14.8367	0.700189	0.350095	−	0.936714i	$-0.386149\pi$
$449$	14.8367	0.700189	0.350095	+	0.936714i	$0.386149\pi$
$450$	2.75064	0.129666
$451$	0.392555	0.0184847
$452$	−5.08734	−0.239289
$453$	4.89794	0.230125
$454$	−22.9194	−1.07566
$455$	2.30578	0.108096
$456$	−6.19961	−0.290323
$457$	−3.50595	−0.164001	−0.0820007	−	0.996632i	$-0.526131\pi$
$457$	−3.50595	−0.164001	−0.0820007	+	0.996632i	$0.526131\pi$
$458$	2.80294	0.130973
$459$	−2.44897	−0.114308
$460$	−9.81482	−0.457619
$461$	−25.1011	−1.16908	−0.584538	−	0.811367i	$-0.698724\pi$
$461$	−25.1011	−1.16908	−0.584538	+	0.811367i	$0.698724\pi$
$462$	−0.966641	−0.0449722
$463$	5.11115	0.237535	0.118768	−	0.992922i	$-0.462106\pi$
$463$	5.11115	0.237535	0.118768	+	0.992922i	$0.462106\pi$
$464$	0.0503213	0.00233611
$465$	23.8702	1.10696
$466$	5.36671	0.248608
$467$	4.60388	0.213042	0.106521	−	0.994310i	$-0.466029\pi$
$467$	4.60388	0.213042	0.106521	+	0.994310i	$0.466029\pi$
$468$	−0.856807	−0.0396059
$469$	4.58328	0.211636
$470$	16.4927	0.760749
$471$	−15.2836	−0.704231
$472$	12.7938	0.588880
$473$	−4.20570	−0.193378
$474$	−13.0098	−0.597558
$475$	−17.0529	−0.782439
$476$	−2.36727	−0.108504
$477$	−4.08257	−0.186928
$478$	−18.3867	−0.840986
$479$	−8.24993	−0.376949	−0.188474	−	0.982078i	$-0.560354\pi$
$479$	−8.24993	−0.376949	−0.188474	+	0.982078i	$0.560354\pi$
$480$	−2.78400	−0.127071
$481$	1.52332	0.0694575
$482$	18.3423	0.835467
$483$	3.40784	0.155062
$484$	1.00000	0.0454545
$485$	21.4935	0.975970
$486$	1.00000	0.0453609
$487$	−0.668070	−0.0302732	−0.0151366	−	0.999885i	$-0.504818\pi$
$487$	−0.668070	−0.0302732	−0.0151366	+	0.999885i	$0.504818\pi$
$488$	−1.00000	−0.0452679
$489$	0.802638	0.0362965
$490$	16.8866	0.762860
$491$	33.9709	1.53308	0.766542	−	0.642194i	$-0.221976\pi$
$491$	33.9709	1.53308	0.766542	+	0.642194i	$0.221976\pi$
$492$	−0.392555	−0.0176977
$493$	−0.123235	−0.00555024
$494$	5.31187	0.238992
$495$	2.78400	0.125131
$496$	−8.57409	−0.384988
$497$	−8.96075	−0.401945
$498$	−5.02306	−0.225088
$499$	−29.6851	−1.32889	−0.664443	−	0.747339i	$-0.731331\pi$
$499$	−29.6851	−1.32889	−0.664443	+	0.747339i	$0.731331\pi$
$500$	6.26222	0.280055
$501$	18.7682	0.838500
$502$	0.746974	0.0333391
$503$	−7.17010	−0.319699	−0.159849	−	0.987141i	$-0.551101\pi$
$503$	−7.17010	−0.319699	−0.159849	+	0.987141i	$0.551101\pi$
$504$	0.966641	0.0430576
$505$	−17.8410	−0.793913
$506$	−3.52544	−0.156725
$507$	−12.2659	−0.544747
$508$	15.8046	0.701217
$509$	−5.36219	−0.237675	−0.118837	−	0.992914i	$-0.537917\pi$
$509$	−5.36219	−0.237675	−0.118837	+	0.992914i	$0.537917\pi$
$510$	6.81792	0.301903
$511$	−11.0295	−0.487914
$512$	1.00000	0.0441942
$513$	−6.19961	−0.273719
$514$	−12.1093	−0.534118
$515$	−5.23353	−0.230617
$516$	4.20570	0.185146
$517$	5.92409	0.260541
$518$	−1.71859	−0.0755107
$519$	−12.8476	−0.563948
$520$	2.38535	0.104604
$521$	−0.720377	−0.0315603	−0.0157801	−	0.999875i	$-0.505023\pi$
$521$	−0.720377	−0.0315603	−0.0157801	+	0.999875i	$0.505023\pi$
$522$	0.0503213	0.00220251
$523$	−0.524878	−0.0229513	−0.0114757	−	0.999934i	$-0.503653\pi$
$523$	−0.524878	−0.0229513	−0.0114757	+	0.999934i	$0.503653\pi$
$524$	−9.37448	−0.409526
$525$	2.65888	0.116043
$526$	−3.12781	−0.136379
$527$	20.9977	0.914673
$528$	−1.00000	−0.0435194
$529$	−10.5712	−0.459619
$530$	11.3659	0.493701
$531$	12.7938	0.555202
$532$	−5.99279	−0.259821
$533$	0.336344	0.0145687
$534$	7.24993	0.313735
$535$	46.2755	2.00067
$536$	4.74145	0.204799
$537$	14.7357	0.635891
$538$	29.8466	1.28678
$539$	6.06561	0.261264
$540$	−2.78400	−0.119804
$541$	18.3219	0.787719	0.393860	−	0.919171i	$-0.371140\pi$
$541$	18.3219	0.787719	0.393860	+	0.919171i	$0.371140\pi$
$542$	12.1709	0.522786
$543$	−11.1346	−0.477830
$544$	−2.44897	−0.104999
$545$	35.9995	1.54205
$546$	−0.828225	−0.0354448
$547$	35.1687	1.50370	0.751852	−	0.659331i	$-0.229161\pi$
$547$	35.1687	1.50370	0.751852	+	0.659331i	$0.229161\pi$
$548$	21.8427	0.933072
$549$	−1.00000	−0.0426790
$550$	−2.75064	−0.117288
$551$	−0.311973	−0.0132905
$552$	3.52544	0.150053
$553$	−12.5758	−0.534776
$554$	−24.7695	−1.05235
$555$	4.94968	0.210102
$556$	−1.93018	−0.0818580
$557$	−21.3603	−0.905066	−0.452533	−	0.891748i	$-0.649480\pi$
$557$	−21.3603	−0.905066	−0.452533	+	0.891748i	$0.649480\pi$
$558$	−8.57409	−0.362970
$559$	−3.60347	−0.152411
$560$	−2.69113	−0.113721
$561$	2.44897	0.103396
$562$	31.4461	1.32647
$563$	−28.8330	−1.21517	−0.607583	−	0.794256i	$-0.707861\pi$
$563$	−28.8330	−1.21517	−0.607583	+	0.794256i	$0.707861\pi$
$564$	−5.92409	−0.249449
$565$	14.1631	0.595848
$566$	−27.2525	−1.14551
$567$	0.966641	0.0405951
$568$	−9.26999	−0.388960
$569$	−42.6459	−1.78781	−0.893905	−	0.448257i	$-0.852045\pi$
$569$	−42.6459	−1.78781	−0.893905	+	0.448257i	$0.852045\pi$
$570$	17.2597	0.722929
$571$	8.96542	0.375191	0.187596	−	0.982246i	$-0.439931\pi$
$571$	8.96542	0.375191	0.187596	+	0.982246i	$0.439931\pi$
$572$	0.856807	0.0358249
$573$	−14.7451	−0.615986
$574$	−0.379460	−0.0158383
$575$	9.69722	0.404402
$576$	1.00000	0.0416667
$577$	−4.98136	−0.207377	−0.103688	−	0.994610i	$-0.533064\pi$
$577$	−4.98136	−0.207377	−0.103688	+	0.994610i	$0.533064\pi$
$578$	−11.0026	−0.457646
$579$	8.06318	0.335094
$580$	−0.140094	−0.00581711
$581$	−4.85549	−0.201440
$582$	−7.72038	−0.320020
$583$	4.08257	0.169083
$584$	−11.4101	−0.472153
$585$	2.38535	0.0986220
$586$	14.3648	0.593406
$587$	24.3072	1.00327	0.501633	−	0.865081i	$-0.332733\pi$
$587$	24.3072	1.00327	0.501633	+	0.865081i	$0.332733\pi$
$588$	−6.06561	−0.250141
$589$	53.1560	2.19025
$590$	−35.6178	−1.46636
$591$	−10.1815	−0.418812
$592$	−1.77790	−0.0730714
$593$	41.1338	1.68916	0.844582	−	0.535426i	$-0.179849\pi$
$593$	41.1338	1.68916	0.844582	+	0.535426i	$0.179849\pi$
$594$	−1.00000	−0.0410305
$595$	6.59048	0.270183
$596$	18.6705	0.764774
$597$	4.17544	0.170889
$598$	−3.02063	−0.123523
$599$	18.5287	0.757061	0.378530	−	0.925589i	$-0.376430\pi$
$599$	18.5287	0.757061	0.378530	+	0.925589i	$0.376430\pi$
$600$	2.75064	0.112294
$601$	−8.66265	−0.353357	−0.176678	−	0.984269i	$-0.556535\pi$
$601$	−8.66265	−0.353357	−0.176678	+	0.984269i	$0.556535\pi$
$602$	4.06540	0.165693
$603$	4.74145	0.193087
$604$	4.89794	0.199294
$605$	−2.78400	−0.113186
$606$	6.40840	0.260324
$607$	8.65392	0.351252	0.175626	−	0.984457i	$-0.443805\pi$
$607$	8.65392	0.351252	0.175626	+	0.984457i	$0.443805\pi$
$608$	−6.19961	−0.251427
$609$	0.0486427	0.00197110
$610$	2.78400	0.112721
$611$	5.07581	0.205345
$612$	−2.44897	−0.0989937
$613$	15.7238	0.635076	0.317538	−	0.948245i	$-0.397144\pi$
$613$	15.7238	0.635076	0.317538	+	0.948245i	$0.397144\pi$
$614$	7.38602	0.298075
$615$	1.09287	0.0440688
$616$	−0.966641	−0.0389471
$617$	24.7429	0.996110	0.498055	−	0.867145i	$-0.334048\pi$
$617$	24.7429	0.996110	0.498055	+	0.867145i	$0.334048\pi$
$618$	1.87986	0.0756192
$619$	29.8769	1.20085	0.600427	−	0.799680i	$-0.294997\pi$
$619$	29.8769	1.20085	0.600427	+	0.799680i	$0.294997\pi$
$620$	23.8702	0.958651
$621$	3.52544	0.141471
$622$	1.78201	0.0714521
$623$	7.00808	0.280773
$624$	−0.856807	−0.0342997
$625$	−31.1872	−1.24749
$626$	16.3987	0.655423
$627$	6.19961	0.247588
$628$	−15.2836	−0.609882
$629$	4.35403	0.173607
$630$	−2.69113	−0.107217
$631$	−12.0290	−0.478869	−0.239434	−	0.970913i	$-0.576962\pi$
$631$	−12.0290	−0.478869	−0.239434	+	0.970913i	$0.576962\pi$
$632$	−13.0098	−0.517500
$633$	−14.8651	−0.590836
$634$	27.3634	1.08674
$635$	−44.0000	−1.74609
$636$	−4.08257	−0.161884
$637$	5.19706	0.205915
$638$	−0.0503213	−0.00199224
$639$	−9.26999	−0.366715
$640$	−2.78400	−0.110047
$641$	−30.5407	−1.20629	−0.603143	−	0.797633i	$-0.706085\pi$
$641$	−30.5407	−1.20629	−0.603143	+	0.797633i	$0.706085\pi$
$642$	−16.6220	−0.656017
$643$	17.6531	0.696171	0.348085	−	0.937463i	$-0.386832\pi$
$643$	17.6531	0.696171	0.348085	+	0.937463i	$0.386832\pi$
$644$	3.40784	0.134288
$645$	−11.7087	−0.461028
$646$	15.1826	0.597353
$647$	13.9982	0.550327	0.275163	−	0.961397i	$-0.411268\pi$
$647$	13.9982	0.550327	0.275163	+	0.961397i	$0.411268\pi$
$648$	1.00000	0.0392837
$649$	−12.7938	−0.502199
$650$	−2.35677	−0.0924400
$651$	−8.28806	−0.324835
$652$	0.802638	0.0314337
$653$	10.0796	0.394444	0.197222	−	0.980359i	$-0.436808\pi$
$653$	10.0796	0.394444	0.197222	+	0.980359i	$0.436808\pi$
$654$	−12.9309	−0.505636
$655$	26.0985	1.01975
$656$	−0.392555	−0.0153267
$657$	−11.4101	−0.445150
$658$	−5.72647	−0.223241
$659$	−16.0965	−0.627032	−0.313516	−	0.949583i	$-0.601507\pi$
$659$	−16.0965	−0.627032	−0.313516	+	0.949583i	$0.601507\pi$
$660$	2.78400	0.108367
$661$	46.6073	1.81281	0.906407	−	0.422406i	$-0.138814\pi$
$661$	46.6073	1.81281	0.906407	+	0.422406i	$0.138814\pi$
$662$	18.2047	0.707545
$663$	2.09829	0.0814910
$664$	−5.02306	−0.194932
$665$	16.6839	0.646975
$666$	−1.77790	−0.0688924
$667$	0.177405	0.00686915
$668$	18.7682	0.726162
$669$	−23.5510	−0.910536
$670$	−13.2002	−0.509967
$671$	1.00000	0.0386046
$672$	0.966641	0.0372890
$673$	2.17433	0.0838141	0.0419071	−	0.999122i	$-0.486657\pi$
$673$	2.17433	0.0838141	0.0419071	+	0.999122i	$0.486657\pi$
$674$	−3.17813	−0.122417
$675$	2.75064	0.105872
$676$	−12.2659	−0.471765
$677$	−7.36820	−0.283183	−0.141592	−	0.989925i	$-0.545222\pi$
$677$	−7.36820	−0.283183	−0.141592	+	0.989925i	$0.545222\pi$
$678$	−5.08734	−0.195378
$679$	−7.46283	−0.286397
$680$	6.81792	0.261455
$681$	−22.9194	−0.878275
$682$	8.57409	0.328319
$683$	49.2385	1.88406	0.942030	−	0.335530i	$-0.108915\pi$
$683$	49.2385	1.88406	0.942030	+	0.335530i	$0.108915\pi$
$684$	−6.19961	−0.237048
$685$	−60.8099	−2.32343
$686$	−12.6298	−0.482206
$687$	2.80294	0.106939
$688$	4.20570	0.160341
$689$	3.49797	0.133262
$690$	−9.81482	−0.373644
$691$	−14.3216	−0.544820	−0.272410	−	0.962181i	$-0.587821\pi$
$691$	−14.3216	−0.544820	−0.272410	+	0.962181i	$0.587821\pi$
$692$	−12.8476	−0.488393
$693$	−0.966641	−0.0367197
$694$	31.7170	1.20396
$695$	5.37363	0.203833
$696$	0.0503213	0.00190743
$697$	0.961354	0.0364139
$698$	−15.7361	−0.595620
$699$	5.36671	0.202988
$700$	2.65888	0.100496
$701$	24.3237	0.918695	0.459347	−	0.888257i	$-0.348083\pi$
$701$	24.3237	0.918695	0.459347	+	0.888257i	$0.348083\pi$
$702$	−0.856807	−0.0323381
$703$	11.0223	0.415714
$704$	−1.00000	−0.0376889
$705$	16.4927	0.621149
$706$	−15.7075	−0.591161
$707$	6.19463	0.232973
$708$	12.7938	0.480819
$709$	−20.5203	−0.770657	−0.385329	−	0.922779i	$-0.625912\pi$
$709$	−20.5203	−0.770657	−0.385329	+	0.922779i	$0.625912\pi$
$710$	25.8076	0.968543
$711$	−13.0098	−0.487904
$712$	7.24993	0.271703
$713$	−30.2275	−1.13203
$714$	−2.36727	−0.0885930
$715$	−2.38535	−0.0892070
$716$	14.7357	0.550697
$717$	−18.3867	−0.686663
$718$	3.42581	0.127850
$719$	−39.4395	−1.47085	−0.735423	−	0.677608i	$-0.763017\pi$
$719$	−39.4395	−1.47085	−0.735423	+	0.677608i	$0.763017\pi$
$720$	−2.78400	−0.103753
$721$	1.81715	0.0676743
$722$	19.4351	0.723300
$723$	18.3423	0.682156
$724$	−11.1346	−0.413813
$725$	0.138416	0.00514063
$726$	1.00000	0.0371135
$727$	−2.17823	−0.0807861	−0.0403930	−	0.999184i	$-0.512861\pi$
$727$	−2.17823	−0.0807861	−0.0403930	+	0.999184i	$0.512861\pi$
$728$	−0.828225	−0.0306961
$729$	1.00000	0.0370370
$730$	31.7656	1.17570
$731$	−10.2996	−0.380945
$732$	−1.00000	−0.0369611
$733$	43.5144	1.60724	0.803621	−	0.595142i	$-0.202904\pi$
$733$	43.5144	1.60724	0.803621	+	0.595142i	$0.202904\pi$
$734$	−2.05783	−0.0759560
$735$	16.8866	0.622873
$736$	3.52544	0.129950
$737$	−4.74145	−0.174653
$738$	−0.392555	−0.0144501
$739$	−3.98869	−0.146726	−0.0733631	−	0.997305i	$-0.523373\pi$
$739$	−3.98869	−0.146726	−0.0733631	+	0.997305i	$0.523373\pi$
$740$	4.94968	0.181954
$741$	5.31187	0.195136
$742$	−3.94638	−0.144876
$743$	−22.4658	−0.824190	−0.412095	−	0.911141i	$-0.635203\pi$
$743$	−22.4658	−0.824190	−0.412095	+	0.911141i	$0.635203\pi$
$744$	−8.57409	−0.314341
$745$	−51.9787	−1.90435
$746$	22.5977	0.827361
$747$	−5.02306	−0.183784
$748$	2.44897	0.0895432
$749$	−16.0675	−0.587093
$750$	6.26222	0.228664
$751$	−19.5751	−0.714305	−0.357153	−	0.934046i	$-0.616252\pi$
$751$	−19.5751	−0.714305	−0.357153	+	0.934046i	$0.616252\pi$
$752$	−5.92409	−0.216029
$753$	0.746974	0.0272212
$754$	−0.0431157	−0.00157018
$755$	−13.6358	−0.496259
$756$	0.966641	0.0351564
$757$	−48.1255	−1.74915	−0.874576	−	0.484889i	$-0.838860\pi$
$757$	−48.1255	−1.74915	−0.874576	+	0.484889i	$0.838860\pi$
$758$	31.8950	1.15848
$759$	−3.52544	−0.127965
$760$	17.2597	0.626075
$761$	−50.1715	−1.81871	−0.909357	−	0.416017i	$-0.863426\pi$
$761$	−50.1715	−1.81871	−0.909357	+	0.416017i	$0.863426\pi$
$762$	15.8046	0.572541
$763$	−12.4995	−0.452512
$764$	−14.7451	−0.533459
$765$	6.81792	0.246502
$766$	−24.9303	−0.900769
$767$	−10.9618	−0.395807
$768$	1.00000	0.0360844
$769$	−21.1015	−0.760940	−0.380470	−	0.924793i	$-0.624238\pi$
$769$	−21.1015	−0.760940	−0.380470	+	0.924793i	$0.624238\pi$
$770$	2.69113	0.0969814
$771$	−12.1093	−0.436105
$772$	8.06318	0.290200
$773$	−30.1871	−1.08576	−0.542878	−	0.839812i	$-0.682665\pi$
$773$	−30.1871	−1.08576	−0.542878	+	0.839812i	$0.682665\pi$
$774$	4.20570	0.151171
$775$	−23.5842	−0.847170
$776$	−7.72038	−0.277145
$777$	−1.71859	−0.0616542
$778$	19.4665	0.697908
$779$	2.43369	0.0871958
$780$	2.38535	0.0854092
$781$	9.26999	0.331706
$782$	−8.63370	−0.308741
$783$	0.0503213	0.00179834
$784$	−6.06561	−0.216629
$785$	42.5495	1.51866
$786$	−9.37448	−0.334377
$787$	−32.0671	−1.14307	−0.571535	−	0.820578i	$-0.693652\pi$
$787$	−32.0671	−1.14307	−0.571535	+	0.820578i	$0.693652\pi$
$788$	−10.1815	−0.362702
$789$	−3.12781	−0.111353
$790$	36.2191	1.28862
$791$	−4.91764	−0.174851
$792$	−1.00000	−0.0355335
$793$	0.856807	0.0304261
$794$	6.94146	0.246343
$795$	11.3659	0.403105
$796$	4.17544	0.147995
$797$	−41.5158	−1.47057	−0.735283	−	0.677761i	$-0.762951\pi$
$797$	−41.5158	−1.47057	−0.735283	+	0.677761i	$0.762951\pi$
$798$	−5.99279	−0.212143
$799$	14.5079	0.513253
$800$	2.75064	0.0972497
$801$	7.24993	0.256164
$802$	−9.15228	−0.323178
$803$	11.4101	0.402653
$804$	4.74145	0.167218
$805$	−9.48741	−0.334387
$806$	7.34634	0.258764
$807$	29.8466	1.05065
$808$	6.40840	0.225447
$809$	−10.4577	−0.367674	−0.183837	−	0.982957i	$-0.558852\pi$
$809$	−10.4577	−0.367674	−0.183837	+	0.982957i	$0.558852\pi$
$810$	−2.78400	−0.0978197
$811$	21.0692	0.739838	0.369919	−	0.929064i	$-0.379385\pi$
$811$	21.0692	0.739838	0.369919	+	0.929064i	$0.379385\pi$
$812$	0.0486427	0.00170702
$813$	12.1709	0.426853
$814$	1.77790	0.0623155
$815$	−2.23454	−0.0782726
$816$	−2.44897	−0.0857311
$817$	−26.0737	−0.912203
$818$	35.2187	1.23139
$819$	−0.828225	−0.0289405
$820$	1.09287	0.0381647
$821$	12.4570	0.434754	0.217377	−	0.976088i	$-0.430250\pi$
$821$	12.4570	0.434754	0.217377	+	0.976088i	$0.430250\pi$
$822$	21.8427	0.761850
$823$	−22.8650	−0.797023	−0.398512	−	0.917163i	$-0.630473\pi$
$823$	−22.8650	−0.797023	−0.398512	+	0.917163i	$0.630473\pi$
$824$	1.87986	0.0654881
$825$	−2.75064	−0.0957649
$826$	12.3670	0.430302
$827$	3.20560	0.111470	0.0557348	−	0.998446i	$-0.482250\pi$
$827$	3.20560	0.111470	0.0557348	+	0.998446i	$0.482250\pi$
$828$	3.52544	0.122518
$829$	−18.1844	−0.631571	−0.315786	−	0.948831i	$-0.602268\pi$
$829$	−18.1844	−0.631571	−0.315786	+	0.948831i	$0.602268\pi$
$830$	13.9842	0.485398
$831$	−24.7695	−0.859244
$832$	−0.856807	−0.0297045
$833$	14.8545	0.514677
$834$	−1.93018	−0.0668368
$835$	−52.2505	−1.80820
$836$	6.19961	0.214418
$837$	−8.57409	−0.296364
$838$	−20.4599	−0.706774
$839$	−8.93134	−0.308344	−0.154172	−	0.988044i	$-0.549271\pi$
$839$	−8.93134	−0.308344	−0.154172	+	0.988044i	$0.549271\pi$
$840$	−2.69113	−0.0928527
$841$	−28.9975	−0.999913
$842$	32.2600	1.11175
$843$	31.4461	1.08306
$844$	−14.8651	−0.511679
$845$	34.1482	1.17473
$846$	−5.92409	−0.203674
$847$	0.966641	0.0332142
$848$	−4.08257	−0.140196
$849$	−27.2525	−0.935303
$850$	−6.73623	−0.231051
$851$	−6.26790	−0.214861
$852$	−9.26999	−0.317585
$853$	−22.3466	−0.765132	−0.382566	−	0.923928i	$-0.624960\pi$
$853$	−22.3466	−0.765132	−0.382566	+	0.923928i	$0.624960\pi$
$854$	−0.966641	−0.0330778
$855$	17.2597	0.590269
$856$	−16.6220	−0.568128
$857$	−35.9447	−1.22785	−0.613924	−	0.789365i	$-0.710410\pi$
$857$	−35.9447	−1.22785	−0.613924	+	0.789365i	$0.710410\pi$
$858$	0.856807	0.0292509
$859$	4.78410	0.163231	0.0816157	−	0.996664i	$-0.473992\pi$
$859$	4.78410	0.163231	0.0816157	+	0.996664i	$0.473992\pi$
$860$	−11.7087	−0.399262
$861$	−0.379460	−0.0129319
$862$	3.56531	0.121435
$863$	−15.8769	−0.540456	−0.270228	−	0.962796i	$-0.587099\pi$
$863$	−15.8769	−0.540456	−0.270228	+	0.962796i	$0.587099\pi$
$864$	1.00000	0.0340207
$865$	35.7677	1.21614
$866$	−34.5927	−1.17551
$867$	−11.0026	−0.373666
$868$	−8.28806	−0.281315
$869$	13.0098	0.441326
$870$	−0.140094	−0.00474965
$871$	−4.06251	−0.137653
$872$	−12.9309	−0.437894
$873$	−7.72038	−0.261295
$874$	−21.8564	−0.739303
$875$	6.05332	0.204639
$876$	−11.4101	−0.385511
$877$	4.68537	0.158214	0.0791069	−	0.996866i	$-0.474793\pi$
$877$	4.68537	0.158214	0.0791069	+	0.996866i	$0.474793\pi$
$878$	16.3540	0.551920
$879$	14.3648	0.484514
$880$	2.78400	0.0938485
$881$	28.2987	0.953408	0.476704	−	0.879064i	$-0.341831\pi$
$881$	28.2987	0.953408	0.476704	+	0.879064i	$0.341831\pi$
$882$	−6.06561	−0.204240
$883$	18.0982	0.609053	0.304527	−	0.952504i	$-0.401502\pi$
$883$	18.0982	0.609053	0.304527	+	0.952504i	$0.401502\pi$
$884$	2.09829	0.0705733
$885$	−35.6178	−1.19728
$886$	6.31355	0.212108
$887$	−3.24928	−0.109100	−0.0545501	−	0.998511i	$-0.517372\pi$
$887$	−3.24928	−0.109100	−0.0545501	+	0.998511i	$0.517372\pi$
$888$	−1.77790	−0.0596625
$889$	15.2774	0.512387
$890$	−20.1838	−0.676562
$891$	−1.00000	−0.0335013
$892$	−23.5510	−0.788547
$893$	36.7270	1.22902
$894$	18.6705	0.624436
$895$	−41.0240	−1.37128
$896$	0.966641	0.0322932
$897$	−3.02063	−0.100856
$898$	14.8367	0.495109
$899$	−0.431460	−0.0143900
$900$	2.75064	0.0916879
$901$	9.99808	0.333084
$902$	0.392555	0.0130706
$903$	4.06540	0.135288
$904$	−5.08734	−0.169203
$905$	30.9986	1.03043
$906$	4.89794	0.162723
$907$	−16.2749	−0.540398	−0.270199	−	0.962804i	$-0.587089\pi$
$907$	−16.2749	−0.540398	−0.270199	+	0.962804i	$0.587089\pi$
$908$	−22.9194	−0.760608
$909$	6.40840	0.212553
$910$	2.30578	0.0764357
$911$	−3.97087	−0.131561	−0.0657804	−	0.997834i	$-0.520954\pi$
$911$	−3.97087	−0.131561	−0.0657804	+	0.997834i	$0.520954\pi$
$912$	−6.19961	−0.205289
$913$	5.02306	0.166239
$914$	−3.50595	−0.115966
$915$	2.78400	0.0920361
$916$	2.80294	0.0926119
$917$	−9.06176	−0.299246
$918$	−2.44897	−0.0808280
$919$	−51.2682	−1.69118	−0.845591	−	0.533831i	$-0.820752\pi$
$919$	−51.2682	−1.69118	−0.845591	+	0.533831i	$0.820752\pi$
$920$	−9.81482	−0.323585
$921$	7.38602	0.243378
$922$	−25.1011	−0.826661
$923$	7.94260	0.261434
$924$	−0.966641	−0.0318002
$925$	−4.89037	−0.160794
$926$	5.11115	0.167963
$927$	1.87986	0.0617428
$928$	0.0503213	0.00165188
$929$	53.1859	1.74497	0.872487	−	0.488638i	$-0.162506\pi$
$929$	53.1859	1.74497	0.872487	+	0.488638i	$0.162506\pi$
$930$	23.8702	0.782736
$931$	37.6044	1.23243
$932$	5.36671	0.175792
$933$	1.78201	0.0583404
$934$	4.60388	0.150644
$935$	−6.81792	−0.222970
$936$	−0.856807	−0.0280056
$937$	9.21912	0.301176	0.150588	−	0.988597i	$-0.451883\pi$
$937$	9.21912	0.301176	0.150588	+	0.988597i	$0.451883\pi$
$938$	4.58328	0.149649
$939$	16.3987	0.535150
$940$	16.4927	0.537931
$941$	−6.08779	−0.198456	−0.0992281	−	0.995065i	$-0.531637\pi$
$941$	−6.08779	−0.198456	−0.0992281	+	0.995065i	$0.531637\pi$
$942$	−15.2836	−0.497966
$943$	−1.38393	−0.0450670
$944$	12.7938	0.416401
$945$	−2.69113	−0.0875423
$946$	−4.20570	−0.136739
$947$	10.8528	0.352670	0.176335	−	0.984330i	$-0.443576\pi$
$947$	10.8528	0.352670	0.176335	+	0.984330i	$0.443576\pi$
$948$	−13.0098	−0.422537
$949$	9.77624	0.317350
$950$	−17.0529	−0.553268
$951$	27.3634	0.887320
$952$	−2.36727	−0.0767238
$953$	−31.3757	−1.01636	−0.508180	−	0.861251i	$-0.669681\pi$
$953$	−31.3757	−1.01636	−0.508180	+	0.861251i	$0.669681\pi$
$954$	−4.08257	−0.132178
$955$	41.0503	1.32836
$956$	−18.3867	−0.594667
$957$	−0.0503213	−0.00162666
$958$	−8.24993	−0.266543
$959$	21.1140	0.681807
$960$	−2.78400	−0.0898531
$961$	42.5150	1.37145
$962$	1.52332	0.0491139
$963$	−16.6220	−0.535636
$964$	18.3423	0.590764
$965$	−22.4479	−0.722622
$966$	3.40784	0.109645
$967$	−31.1880	−1.00294	−0.501469	−	0.865176i	$-0.667207\pi$
$967$	−31.1880	−1.00294	−0.501469	+	0.865176i	$0.667207\pi$
$968$	1.00000	0.0321412
$969$	15.1826	0.487737
$970$	21.4935	0.690115
$971$	44.3322	1.42269	0.711344	−	0.702844i	$-0.248087\pi$
$971$	44.3322	1.42269	0.711344	+	0.702844i	$0.248087\pi$
$972$	1.00000	0.0320750
$973$	−1.86580	−0.0598146
$974$	−0.668070	−0.0214064
$975$	−2.35677	−0.0754769
$976$	−1.00000	−0.0320092
$977$	57.1864	1.82956	0.914778	−	0.403957i	$-0.132365\pi$
$977$	57.1864	1.82956	0.914778	+	0.403957i	$0.132365\pi$
$978$	0.802638	0.0256655
$979$	−7.24993	−0.231709
$980$	16.8866	0.539423
$981$	−12.9309	−0.412850
$982$	33.9709	1.08405
$983$	48.7740	1.55565	0.777824	−	0.628482i	$-0.216323\pi$
$983$	48.7740	1.55565	0.777824	+	0.628482i	$0.216323\pi$
$984$	−0.392555	−0.0125142
$985$	28.3454	0.903158
$986$	−0.123235	−0.00392462
$987$	−5.72647	−0.182276
$988$	5.31187	0.168993
$989$	14.8270	0.471470
$990$	2.78400	0.0884812
$991$	−19.6676	−0.624763	−0.312381	−	0.949957i	$-0.601127\pi$
$991$	−19.6676	−0.624763	−0.312381	+	0.949957i	$0.601127\pi$
$992$	−8.57409	−0.272228
$993$	18.2047	0.577708
$994$	−8.96075	−0.284218
$995$	−11.6244	−0.368518
$996$	−5.02306	−0.159162
$997$	−8.79564	−0.278561	−0.139280	−	0.990253i	$-0.544479\pi$
$997$	−8.79564	−0.278561	−0.139280	+	0.990253i	$0.544479\pi$
$998$	−29.6851	−0.939664
$999$	−1.77790	−0.0562504

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4026.2.a.t.1.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4026.2.a.t.1.1	✓	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:	\( N \)	\(=\)	\( 4026 = 2 \cdot 3 \cdot 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4026.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.78400 q^{5} +1.00000 q^{6} +0.966641 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.78400 q^{5} +1.00000 q^{6} +0.966641 q^{7} +1.00000 q^{8} +1.00000 q^{9} -2.78400 q^{10} -1.00000 q^{11} +1.00000 q^{12} -0.856807 q^{13} +0.966641 q^{14} -2.78400 q^{15} +1.00000 q^{16} -2.44897 q^{17} +1.00000 q^{18} -6.19961 q^{19} -2.78400 q^{20} +0.966641 q^{21} -1.00000 q^{22} +3.52544 q^{23} +1.00000 q^{24} +2.75064 q^{25} -0.856807 q^{26} +1.00000 q^{27} +0.966641 q^{28} +0.0503213 q^{29} -2.78400 q^{30} -8.57409 q^{31} +1.00000 q^{32} -1.00000 q^{33} -2.44897 q^{34} -2.69113 q^{35} +1.00000 q^{36} -1.77790 q^{37} -6.19961 q^{38} -0.856807 q^{39} -2.78400 q^{40} -0.392555 q^{41} +0.966641 q^{42} +4.20570 q^{43} -1.00000 q^{44} -2.78400 q^{45} +3.52544 q^{46} -5.92409 q^{47} +1.00000 q^{48} -6.06561 q^{49} +2.75064 q^{50} -2.44897 q^{51} -0.856807 q^{52} -4.08257 q^{53} +1.00000 q^{54} +2.78400 q^{55} +0.966641 q^{56} -6.19961 q^{57} +0.0503213 q^{58} +12.7938 q^{59} -2.78400 q^{60} -1.00000 q^{61} -8.57409 q^{62} +0.966641 q^{63} +1.00000 q^{64} +2.38535 q^{65} -1.00000 q^{66} +4.74145 q^{67} -2.44897 q^{68} +3.52544 q^{69} -2.69113 q^{70} -9.26999 q^{71} +1.00000 q^{72} -11.4101 q^{73} -1.77790 q^{74} +2.75064 q^{75} -6.19961 q^{76} -0.966641 q^{77} -0.856807 q^{78} -13.0098 q^{79} -2.78400 q^{80} +1.00000 q^{81} -0.392555 q^{82} -5.02306 q^{83} +0.966641 q^{84} +6.81792 q^{85} +4.20570 q^{86} +0.0503213 q^{87} -1.00000 q^{88} +7.24993 q^{89} -2.78400 q^{90} -0.828225 q^{91} +3.52544 q^{92} -8.57409 q^{93} -5.92409 q^{94} +17.2597 q^{95} +1.00000 q^{96} -7.72038 q^{97} -6.06561 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} - 4 q^{5} + 4 q^{6} - 6 q^{7} + 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 - 4 * q^5 + 4 * q^6 - 6 * q^7 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} - 4 q^{5} + 4 q^{6} - 6 q^{7} + 4 q^{8} + 4 q^{9} - 4 q^{10} - 4 q^{11} + 4 q^{12} - 5 q^{13} - 6 q^{14} - 4 q^{15} + 4 q^{16} - 10 q^{17} + 4 q^{18} - 8 q^{19} - 4 q^{20} - 6 q^{21} - 4 q^{22} - 7 q^{23} + 4 q^{24} - 6 q^{25} - 5 q^{26} + 4 q^{27} - 6 q^{28} - 4 q^{29} - 4 q^{30} - 9 q^{31} + 4 q^{32} - 4 q^{33} - 10 q^{34} - q^{35} + 4 q^{36} - 11 q^{37} - 8 q^{38} - 5 q^{39} - 4 q^{40} - 17 q^{41} - 6 q^{42} - 11 q^{43} - 4 q^{44} - 4 q^{45} - 7 q^{46} - 7 q^{47} + 4 q^{48} - 6 q^{49} - 6 q^{50} - 10 q^{51} - 5 q^{52} + 16 q^{53} + 4 q^{54} + 4 q^{55} - 6 q^{56} - 8 q^{57} - 4 q^{58} + 3 q^{59} - 4 q^{60} - 4 q^{61} - 9 q^{62} - 6 q^{63} + 4 q^{64} - 2 q^{65} - 4 q^{66} + 5 q^{67} - 10 q^{68} - 7 q^{69} - q^{70} - 10 q^{71} + 4 q^{72} - 9 q^{73} - 11 q^{74} - 6 q^{75} - 8 q^{76} + 6 q^{77} - 5 q^{78} - 11 q^{79} - 4 q^{80} + 4 q^{81} - 17 q^{82} + 5 q^{83} - 6 q^{84} - 8 q^{85} - 11 q^{86} - 4 q^{87} - 4 q^{88} + 8 q^{89} - 4 q^{90} - 3 q^{91} - 7 q^{92} - 9 q^{93} - 7 q^{94} + 7 q^{95} + 4 q^{96} - 12 q^{97} - 6 q^{98} - 4 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 - 4 * q^5 + 4 * q^6 - 6 * q^7 + 4 * q^8 + 4 * q^9 - 4 * q^10 - 4 * q^11 + 4 * q^12 - 5 * q^13 - 6 * q^14 - 4 * q^15 + 4 * q^16 - 10 * q^17 + 4 * q^18 - 8 * q^19 - 4 * q^20 - 6 * q^21 - 4 * q^22 - 7 * q^23 + 4 * q^24 - 6 * q^25 - 5 * q^26 + 4 * q^27 - 6 * q^28 - 4 * q^29 - 4 * q^30 - 9 * q^31 + 4 * q^32 - 4 * q^33 - 10 * q^34 - q^35 + 4 * q^36 - 11 * q^37 - 8 * q^38 - 5 * q^39 - 4 * q^40 - 17 * q^41 - 6 * q^42 - 11 * q^43 - 4 * q^44 - 4 * q^45 - 7 * q^46 - 7 * q^47 + 4 * q^48 - 6 * q^49 - 6 * q^50 - 10 * q^51 - 5 * q^52 + 16 * q^53 + 4 * q^54 + 4 * q^55 - 6 * q^56 - 8 * q^57 - 4 * q^58 + 3 * q^59 - 4 * q^60 - 4 * q^61 - 9 * q^62 - 6 * q^63 + 4 * q^64 - 2 * q^65 - 4 * q^66 + 5 * q^67 - 10 * q^68 - 7 * q^69 - q^70 - 10 * q^71 + 4 * q^72 - 9 * q^73 - 11 * q^74 - 6 * q^75 - 8 * q^76 + 6 * q^77 - 5 * q^78 - 11 * q^79 - 4 * q^80 + 4 * q^81 - 17 * q^82 + 5 * q^83 - 6 * q^84 - 8 * q^85 - 11 * q^86 - 4 * q^87 - 4 * q^88 + 8 * q^89 - 4 * q^90 - 3 * q^91 - 7 * q^92 - 9 * q^93 - 7 * q^94 + 7 * q^95 + 4 * q^96 - 12 * q^97 - 6 * q^98 - 4 * q^99

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