LMFDB - Embedded newform 4026.2.a.o.1.3

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:	$3$
Coefficient field:	3.3.1129.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 7x - 3 $ x^3 - 7*x - 3
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			1.3
Root			$2.83847$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.83847 q^{5} -1.00000 q^{6} -1.21844 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.83847 q^{5} -1.00000 q^{6} -1.21844 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.83847 q^{10} +1.00000 q^{11} -1.00000 q^{12} -4.62003 q^{13} -1.21844 q^{14} -1.83847 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} -1.62003 q^{19} +1.83847 q^{20} +1.21844 q^{21} +1.00000 q^{22} -3.62003 q^{23} -1.00000 q^{24} -1.62003 q^{25} -4.62003 q^{26} -1.00000 q^{27} -1.21844 q^{28} -8.89538 q^{29} -1.83847 q^{30} -6.21844 q^{31} +1.00000 q^{32} -1.00000 q^{33} +1.00000 q^{34} -2.24006 q^{35} +1.00000 q^{36} -8.05691 q^{37} -1.62003 q^{38} +4.62003 q^{39} +1.83847 q^{40} +5.11382 q^{41} +1.21844 q^{42} +2.83847 q^{43} +1.00000 q^{44} +1.83847 q^{45} -3.62003 q^{46} +7.95228 q^{47} -1.00000 q^{48} -5.51541 q^{49} -1.62003 q^{50} -1.00000 q^{51} -4.62003 q^{52} +4.40159 q^{53} -1.00000 q^{54} +1.83847 q^{55} -1.21844 q^{56} +1.62003 q^{57} -8.89538 q^{58} -7.57232 q^{59} -1.83847 q^{60} -1.00000 q^{61} -6.21844 q^{62} -1.21844 q^{63} +1.00000 q^{64} -8.49378 q^{65} -1.00000 q^{66} +6.21844 q^{67} +1.00000 q^{68} +3.62003 q^{69} -2.24006 q^{70} -6.21844 q^{71} +1.00000 q^{72} -2.89538 q^{73} -8.05691 q^{74} +1.62003 q^{75} -1.62003 q^{76} -1.21844 q^{77} +4.62003 q^{78} -4.62003 q^{79} +1.83847 q^{80} +1.00000 q^{81} +5.11382 q^{82} +6.13544 q^{83} +1.21844 q^{84} +1.83847 q^{85} +2.83847 q^{86} +8.89538 q^{87} +1.00000 q^{88} +7.62922 q^{89} +1.83847 q^{90} +5.62922 q^{91} -3.62003 q^{92} +6.21844 q^{93} +7.95228 q^{94} -2.97838 q^{95} -1.00000 q^{96} -13.1354 q^{97} -5.51541 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} - 3 q^{5} - 3 q^{6} - 2 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 - 3 * q^5 - 3 * q^6 - 2 * q^7 + 3 * q^8 + 3 * q^9	\( 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} - 3 q^{5} - 3 q^{6} - 2 q^{7} + 3 q^{8} + 3 q^{9} - 3 q^{10} + 3 q^{11} - 3 q^{12} - 7 q^{13} - 2 q^{14} + 3 q^{15} + 3 q^{16} + 3 q^{17} + 3 q^{18} + 2 q^{19} - 3 q^{20} + 2 q^{21} + 3 q^{22} - 4 q^{23} - 3 q^{24} + 2 q^{25} - 7 q^{26} - 3 q^{27} - 2 q^{28} - 8 q^{29} + 3 q^{30} - 17 q^{31} + 3 q^{32} - 3 q^{33} + 3 q^{34} + 7 q^{35} + 3 q^{36} - 14 q^{37} + 2 q^{38} + 7 q^{39} - 3 q^{40} - 5 q^{41} + 2 q^{42} + 3 q^{44} - 3 q^{45} - 4 q^{46} - 5 q^{47} - 3 q^{48} + 9 q^{49} + 2 q^{50} - 3 q^{51} - 7 q^{52} + 8 q^{53} - 3 q^{54} - 3 q^{55} - 2 q^{56} - 2 q^{57} - 8 q^{58} + 13 q^{59} + 3 q^{60} - 3 q^{61} - 17 q^{62} - 2 q^{63} + 3 q^{64} - 12 q^{65} - 3 q^{66} + 17 q^{67} + 3 q^{68} + 4 q^{69} + 7 q^{70} - 17 q^{71} + 3 q^{72} + 10 q^{73} - 14 q^{74} - 2 q^{75} + 2 q^{76} - 2 q^{77} + 7 q^{78} - 7 q^{79} - 3 q^{80} + 3 q^{81} - 5 q^{82} - 14 q^{83} + 2 q^{84} - 3 q^{85} + 8 q^{87} + 3 q^{88} - 23 q^{89} - 3 q^{90} - 29 q^{91} - 4 q^{92} + 17 q^{93} - 5 q^{94} - 21 q^{95} - 3 q^{96} - 7 q^{97} + 9 q^{98} + 3 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 - 3 * q^5 - 3 * q^6 - 2 * q^7 + 3 * q^8 + 3 * q^9 - 3 * q^10 + 3 * q^11 - 3 * q^12 - 7 * q^13 - 2 * q^14 + 3 * q^15 + 3 * q^16 + 3 * q^17 + 3 * q^18 + 2 * q^19 - 3 * q^20 + 2 * q^21 + 3 * q^22 - 4 * q^23 - 3 * q^24 + 2 * q^25 - 7 * q^26 - 3 * q^27 - 2 * q^28 - 8 * q^29 + 3 * q^30 - 17 * q^31 + 3 * q^32 - 3 * q^33 + 3 * q^34 + 7 * q^35 + 3 * q^36 - 14 * q^37 + 2 * q^38 + 7 * q^39 - 3 * q^40 - 5 * q^41 + 2 * q^42 + 3 * q^44 - 3 * q^45 - 4 * q^46 - 5 * q^47 - 3 * q^48 + 9 * q^49 + 2 * q^50 - 3 * q^51 - 7 * q^52 + 8 * q^53 - 3 * q^54 - 3 * q^55 - 2 * q^56 - 2 * q^57 - 8 * q^58 + 13 * q^59 + 3 * q^60 - 3 * q^61 - 17 * q^62 - 2 * q^63 + 3 * q^64 - 12 * q^65 - 3 * q^66 + 17 * q^67 + 3 * q^68 + 4 * q^69 + 7 * q^70 - 17 * q^71 + 3 * q^72 + 10 * q^73 - 14 * q^74 - 2 * q^75 + 2 * q^76 - 2 * q^77 + 7 * q^78 - 7 * q^79 - 3 * q^80 + 3 * q^81 - 5 * q^82 - 14 * q^83 + 2 * q^84 - 3 * q^85 + 8 * q^87 + 3 * q^88 - 23 * q^89 - 3 * q^90 - 29 * q^91 - 4 * q^92 + 17 * q^93 - 5 * q^94 - 21 * q^95 - 3 * q^96 - 7 * q^97 + 9 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	1.83847	0.822188	0.411094	−	0.911593i	$-0.365147\pi$
$5$	1.83847	0.822188	0.411094	+	0.911593i	$0.365147\pi$
$6$	−1.00000	−0.408248
$7$	−1.21844	−0.460526	−0.230263	−	0.973128i	$-0.573959\pi$
$7$	−1.21844	−0.460526	−0.230263	+	0.973128i	$0.573959\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	1.83847	0.581375
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.00000	−0.288675
$13$	−4.62003	−1.28137	−0.640683	−	0.767806i	$-0.721349\pi$
$13$	−4.62003	−1.28137	−0.640683	+	0.767806i	$0.721349\pi$
$14$	−1.21844	−0.325641
$15$	−1.83847	−0.474691
$16$	1.00000	0.250000
$17$	1.00000	0.242536	0.121268	−	0.992620i	$-0.461304\pi$
$17$	1.00000	0.242536	0.121268	+	0.992620i	$0.461304\pi$
$18$	1.00000	0.235702
$19$	−1.62003	−0.371661	−0.185830	−	0.982582i	$-0.559497\pi$
$19$	−1.62003	−0.371661	−0.185830	+	0.982582i	$0.559497\pi$
$20$	1.83847	0.411094
$21$	1.21844	0.265885
$22$	1.00000	0.213201
$23$	−3.62003	−0.754829	−0.377414	−	0.926045i	$-0.623187\pi$
$23$	−3.62003	−0.754829	−0.377414	+	0.926045i	$0.623187\pi$
$24$	−1.00000	−0.204124
$25$	−1.62003	−0.324006
$26$	−4.62003	−0.906063
$27$	−1.00000	−0.192450
$28$	−1.21844	−0.230263
$29$	−8.89538	−1.65183	−0.825915	−	0.563795i	$-0.809341\pi$
$29$	−8.89538	−1.65183	−0.825915	+	0.563795i	$0.809341\pi$
$30$	−1.83847	−0.335657
$31$	−6.21844	−1.11686	−0.558432	−	0.829550i	$-0.688597\pi$
$31$	−6.21844	−1.11686	−0.558432	+	0.829550i	$0.688597\pi$
$32$	1.00000	0.176777
$33$	−1.00000	−0.174078
$34$	1.00000	0.171499
$35$	−2.24006	−0.378640
$36$	1.00000	0.166667
$37$	−8.05691	−1.32455	−0.662274	−	0.749262i	$-0.730408\pi$
$37$	−8.05691	−1.32455	−0.662274	+	0.749262i	$0.730408\pi$
$38$	−1.62003	−0.262804
$39$	4.62003	0.739797
$40$	1.83847	0.290688
$41$	5.11382	0.798644	0.399322	−	0.916811i	$-0.369246\pi$
$41$	5.11382	0.798644	0.399322	+	0.916811i	$0.369246\pi$
$42$	1.21844	0.188009
$43$	2.83847	0.432863	0.216431	−	0.976298i	$-0.430558\pi$
$43$	2.83847	0.432863	0.216431	+	0.976298i	$0.430558\pi$
$44$	1.00000	0.150756
$45$	1.83847	0.274063
$46$	−3.62003	−0.533744
$47$	7.95228	1.15996	0.579980	−	0.814631i	$-0.303060\pi$
$47$	7.95228	1.15996	0.579980	+	0.814631i	$0.303060\pi$
$48$	−1.00000	−0.144338
$49$	−5.51541	−0.787915
$50$	−1.62003	−0.229107
$51$	−1.00000	−0.140028
$52$	−4.62003	−0.640683
$53$	4.40159	0.604605	0.302303	−	0.953212i	$-0.402245\pi$
$53$	4.40159	0.604605	0.302303	+	0.953212i	$0.402245\pi$
$54$	−1.00000	−0.136083
$55$	1.83847	0.247899
$56$	−1.21844	−0.162821
$57$	1.62003	0.214578
$58$	−8.89538	−1.16802
$59$	−7.57232	−0.985832	−0.492916	−	0.870077i	$-0.664069\pi$
$59$	−7.57232	−0.985832	−0.492916	+	0.870077i	$0.664069\pi$
$60$	−1.83847	−0.237345
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	−6.21844	−0.789742
$63$	−1.21844	−0.153509
$64$	1.00000	0.125000
$65$	−8.49378	−1.05352
$66$	−1.00000	−0.123091
$67$	6.21844	0.759703	0.379852	−	0.925047i	$-0.375975\pi$
$67$	6.21844	0.759703	0.379852	+	0.925047i	$0.375975\pi$
$68$	1.00000	0.121268
$69$	3.62003	0.435800
$70$	−2.24006	−0.267739
$71$	−6.21844	−0.737993	−0.368996	−	0.929431i	$-0.620299\pi$
$71$	−6.21844	−0.737993	−0.368996	+	0.929431i	$0.620299\pi$
$72$	1.00000	0.117851
$73$	−2.89538	−0.338878	−0.169439	−	0.985541i	$-0.554196\pi$
$73$	−2.89538	−0.338878	−0.169439	+	0.985541i	$0.554196\pi$
$74$	−8.05691	−0.936596
$75$	1.62003	0.187065
$76$	−1.62003	−0.185830
$77$	−1.21844	−0.138854
$78$	4.62003	0.523115
$79$	−4.62003	−0.519794	−0.259897	−	0.965636i	$-0.583689\pi$
$79$	−4.62003	−0.519794	−0.259897	+	0.965636i	$0.583689\pi$
$80$	1.83847	0.205547
$81$	1.00000	0.111111
$82$	5.11382	0.564726
$83$	6.13544	0.673452	0.336726	−	0.941603i	$-0.390680\pi$
$83$	6.13544	0.673452	0.336726	+	0.941603i	$0.390680\pi$
$84$	1.21844	0.132943
$85$	1.83847	0.199410
$86$	2.83847	0.306080
$87$	8.89538	0.953685
$88$	1.00000	0.106600
$89$	7.62922	0.808696	0.404348	−	0.914605i	$-0.367498\pi$
$89$	7.62922	0.808696	0.404348	+	0.914605i	$0.367498\pi$
$90$	1.83847	0.193792
$91$	5.62922	0.590103
$92$	−3.62003	−0.377414
$93$	6.21844	0.644822
$94$	7.95228	0.820216
$95$	−2.97838	−0.305575
$96$	−1.00000	−0.102062
$97$	−13.1354	−1.33370	−0.666851	−	0.745191i	$-0.732358\pi$
$97$	−13.1354	−1.33370	−0.666851	+	0.745191i	$0.732358\pi$
$98$	−5.51541	−0.557140
$99$	1.00000	0.100504
$100$	−1.62003	−0.162003
$101$	15.1923	1.51169	0.755847	−	0.654748i	$-0.227225\pi$
$101$	15.1923	1.51169	0.755847	+	0.654748i	$0.227225\pi$
$102$	−1.00000	−0.0990148
$103$	3.51541	0.346383	0.173192	−	0.984888i	$-0.444592\pi$
$103$	3.51541	0.346383	0.173192	+	0.984888i	$0.444592\pi$
$104$	−4.62003	−0.453031
$105$	2.24006	0.218608
$106$	4.40159	0.427520
$107$	1.49378	0.144410	0.0722048	−	0.997390i	$-0.476996\pi$
$107$	1.49378	0.144410	0.0722048	+	0.997390i	$0.476996\pi$
$108$	−1.00000	−0.0962250
$109$	−19.6076	−1.87807	−0.939034	−	0.343825i	$-0.888277\pi$
$109$	−19.6076	−1.87807	−0.939034	+	0.343825i	$0.888277\pi$
$110$	1.83847	0.175291
$111$	8.05691	0.764728
$112$	−1.21844	−0.115132
$113$	−8.51541	−0.801062	−0.400531	−	0.916283i	$-0.631174\pi$
$113$	−8.51541	−0.801062	−0.400531	+	0.916283i	$0.631174\pi$
$114$	1.62003	0.151730
$115$	−6.65532	−0.620611
$116$	−8.89538	−0.825915
$117$	−4.62003	−0.427122
$118$	−7.57232	−0.697088
$119$	−1.21844	−0.111694
$120$	−1.83847	−0.167829
$121$	1.00000	0.0909091
$122$	−1.00000	−0.0905357
$123$	−5.11382	−0.461097
$124$	−6.21844	−0.558432
$125$	−12.1707	−1.08858
$126$	−1.21844	−0.108547
$127$	−4.67694	−0.415011	−0.207506	−	0.978234i	$-0.566535\pi$
$127$	−4.67694	−0.415011	−0.207506	+	0.978234i	$0.566535\pi$
$128$	1.00000	0.0883883
$129$	−2.83847	−0.249913
$130$	−8.49378	−0.744954
$131$	0.952285	0.0832015	0.0416007	−	0.999134i	$-0.486754\pi$
$131$	0.952285	0.0832015	0.0416007	+	0.999134i	$0.486754\pi$
$132$	−1.00000	−0.0870388
$133$	1.97391	0.171160
$134$	6.21844	0.537191
$135$	−1.83847	−0.158230
$136$	1.00000	0.0857493
$137$	−3.32306	−0.283908	−0.141954	−	0.989873i	$-0.545339\pi$
$137$	−3.32306	−0.283908	−0.141954	+	0.989873i	$0.545339\pi$
$138$	3.62003	0.308157
$139$	3.86009	0.327409	0.163704	−	0.986509i	$-0.447656\pi$
$139$	3.86009	0.327409	0.163704	+	0.986509i	$0.447656\pi$
$140$	−2.24006	−0.189320
$141$	−7.95228	−0.669703
$142$	−6.21844	−0.521840
$143$	−4.62003	−0.386346
$144$	1.00000	0.0833333
$145$	−16.3539	−1.35812
$146$	−2.89538	−0.239623
$147$	5.51541	0.454903
$148$	−8.05691	−0.662274
$149$	10.0308	0.821756	0.410878	−	0.911690i	$-0.365222\pi$
$149$	10.0308	0.821756	0.410878	+	0.911690i	$0.365222\pi$
$150$	1.62003	0.132275
$151$	−5.35388	−0.435692	−0.217846	−	0.975983i	$-0.569903\pi$
$151$	−5.35388	−0.435692	−0.217846	+	0.975983i	$0.569903\pi$
$152$	−1.62003	−0.131402
$153$	1.00000	0.0808452
$154$	−1.21844	−0.0981846
$155$	−11.4324	−0.918273
$156$	4.62003	0.369899
$157$	−14.5723	−1.16300	−0.581499	−	0.813547i	$-0.697533\pi$
$157$	−14.5723	−1.16300	−0.581499	+	0.813547i	$0.697533\pi$
$158$	−4.62003	−0.367550
$159$	−4.40159	−0.349069
$160$	1.83847	0.145344
$161$	4.41078	0.347619
$162$	1.00000	0.0785674
$163$	9.21844	0.722044	0.361022	−	0.932557i	$-0.382428\pi$
$163$	9.21844	0.722044	0.361022	+	0.932557i	$0.382428\pi$
$164$	5.11382	0.399322
$165$	−1.83847	−0.143125
$166$	6.13544	0.476202
$167$	−2.72465	−0.210840	−0.105420	−	0.994428i	$-0.533619\pi$
$167$	−2.72465	−0.210840	−0.105420	+	0.994428i	$0.533619\pi$
$168$	1.21844	0.0940046
$169$	8.34468	0.641899
$170$	1.83847	0.141004
$171$	−1.62003	−0.123887
$172$	2.83847	0.216431
$173$	−10.8954	−0.828360	−0.414180	−	0.910195i	$-0.635932\pi$
$173$	−10.8954	−0.828360	−0.414180	+	0.910195i	$0.635932\pi$
$174$	8.89538	0.674357
$175$	1.97391	0.149213
$176$	1.00000	0.0753778
$177$	7.57232	0.569170
$178$	7.62922	0.571834
$179$	18.8260	1.40712	0.703562	−	0.710634i	$-0.251592\pi$
$179$	18.8260	1.40712	0.703562	+	0.710634i	$0.251592\pi$
$180$	1.83847	0.137031
$181$	10.4677	0.778057	0.389029	−	0.921226i	$-0.372811\pi$
$181$	10.4677	0.778057	0.389029	+	0.921226i	$0.372811\pi$
$182$	5.62922	0.417266
$183$	1.00000	0.0739221
$184$	−3.62003	−0.266872
$185$	−14.8124	−1.08903
$186$	6.21844	0.455958
$187$	1.00000	0.0731272
$188$	7.95228	0.579980
$189$	1.21844	0.0886284
$190$	−2.97838	−0.216074
$191$	15.1707	1.09771	0.548857	−	0.835916i	$-0.315063\pi$
$191$	15.1707	1.09771	0.548857	+	0.835916i	$0.315063\pi$
$192$	−1.00000	−0.0721688
$193$	14.6553	1.05491	0.527456	−	0.849582i	$-0.323146\pi$
$193$	14.6553	1.05491	0.527456	+	0.849582i	$0.323146\pi$
$194$	−13.1354	−0.943070
$195$	8.49378	0.608253
$196$	−5.51541	−0.393958
$197$	−11.3323	−0.807390	−0.403695	−	0.914894i	$-0.632274\pi$
$197$	−11.3323	−0.807390	−0.403695	+	0.914894i	$0.632274\pi$
$198$	1.00000	0.0710669
$199$	−21.7908	−1.54471	−0.772353	−	0.635194i	$-0.780920\pi$
$199$	−21.7908	−1.54471	−0.772353	+	0.635194i	$0.780920\pi$
$200$	−1.62003	−0.114553
$201$	−6.21844	−0.438615
$202$	15.1923	1.06893
$203$	10.8385	0.760711
$204$	−1.00000	−0.0700140
$205$	9.40159	0.656636
$206$	3.51541	0.244930
$207$	−3.62003	−0.251610
$208$	−4.62003	−0.320341
$209$	−1.62003	−0.112060
$210$	2.24006	0.154579
$211$	0.689369	0.0474581	0.0237291	−	0.999718i	$-0.492446\pi$
$211$	0.689369	0.0474581	0.0237291	+	0.999718i	$0.492446\pi$
$212$	4.40159	0.302303
$213$	6.21844	0.426080
$214$	1.49378	0.102113
$215$	5.21844	0.355895
$216$	−1.00000	−0.0680414
$217$	7.57678	0.514346
$218$	−19.6076	−1.32799
$219$	2.89538	0.195651
$220$	1.83847	0.123950
$221$	−4.62003	−0.310777
$222$	8.05691	0.540744
$223$	15.1615	1.01529	0.507646	−	0.861566i	$-0.330516\pi$
$223$	15.1615	1.01529	0.507646	+	0.861566i	$0.330516\pi$
$224$	−1.21844	−0.0814103
$225$	−1.62003	−0.108002
$226$	−8.51541	−0.566436
$227$	−20.0216	−1.32888	−0.664441	−	0.747341i	$-0.731330\pi$
$227$	−20.0216	−1.32888	−0.664441	+	0.747341i	$0.731330\pi$
$228$	1.62003	0.107289
$229$	−9.50622	−0.628188	−0.314094	−	0.949392i	$-0.601701\pi$
$229$	−9.50622	−0.628188	−0.314094	+	0.949392i	$0.601701\pi$
$230$	−6.65532	−0.438838
$231$	1.21844	0.0801674
$232$	−8.89538	−0.584010
$233$	−20.5507	−1.34632	−0.673160	−	0.739497i	$-0.735064\pi$
$233$	−20.5507	−1.34632	−0.673160	+	0.739497i	$0.735064\pi$
$234$	−4.62003	−0.302021
$235$	14.6200	0.953706
$236$	−7.57232	−0.492916
$237$	4.62003	0.300103
$238$	−1.21844	−0.0789796
$239$	10.7122	0.692916	0.346458	−	0.938065i	$-0.387384\pi$
$239$	10.7122	0.692916	0.346458	+	0.938065i	$0.387384\pi$
$240$	−1.83847	−0.118673
$241$	15.2970	0.985364	0.492682	−	0.870209i	$-0.336017\pi$
$241$	15.2970	0.985364	0.492682	+	0.870209i	$0.336017\pi$
$242$	1.00000	0.0642824
$243$	−1.00000	−0.0641500
$244$	−1.00000	−0.0640184
$245$	−10.1399	−0.647815
$246$	−5.11382	−0.326045
$247$	7.48459	0.476233
$248$	−6.21844	−0.394871
$249$	−6.13544	−0.388818
$250$	−12.1707	−0.769744
$251$	5.26168	0.332115	0.166057	−	0.986116i	$-0.446896\pi$
$251$	5.26168	0.332115	0.166057	+	0.986116i	$0.446896\pi$
$252$	−1.21844	−0.0767544
$253$	−3.62003	−0.227589
$254$	−4.67694	−0.293457
$255$	−1.83847	−0.115129
$256$	1.00000	0.0625000
$257$	−13.2493	−0.826466	−0.413233	−	0.910625i	$-0.635600\pi$
$257$	−13.2493	−0.826466	−0.413233	+	0.910625i	$0.635600\pi$
$258$	−2.83847	−0.176715
$259$	9.81685	0.609989
$260$	−8.49378	−0.526762
$261$	−8.89538	−0.550610
$262$	0.952285	0.0588323
$263$	2.68613	0.165634	0.0828170	−	0.996565i	$-0.473608\pi$
$263$	2.68613	0.165634	0.0828170	+	0.996565i	$0.473608\pi$
$264$	−1.00000	−0.0615457
$265$	8.09219	0.497099
$266$	1.97391	0.121028
$267$	−7.62922	−0.466901
$268$	6.21844	0.379852
$269$	−21.0000	−1.28039	−0.640196	−	0.768211i	$-0.721147\pi$
$269$	−21.0000	−1.28039	−0.640196	+	0.768211i	$0.721147\pi$
$270$	−1.83847	−0.111886
$271$	−10.3800	−0.630538	−0.315269	−	0.949002i	$-0.602095\pi$
$271$	−10.3800	−0.630538	−0.315269	+	0.949002i	$0.602095\pi$
$272$	1.00000	0.0606339
$273$	−5.62922	−0.340696
$274$	−3.32306	−0.200753
$275$	−1.62003	−0.0976915
$276$	3.62003	0.217900
$277$	10.8477	0.651773	0.325886	−	0.945409i	$-0.394337\pi$
$277$	10.8477	0.651773	0.325886	+	0.945409i	$0.394337\pi$
$278$	3.86009	0.231513
$279$	−6.21844	−0.372288
$280$	−2.24006	−0.133869
$281$	8.13544	0.485320	0.242660	−	0.970111i	$-0.421980\pi$
$281$	8.13544	0.485320	0.242660	+	0.970111i	$0.421980\pi$
$282$	−7.95228	−0.473552
$283$	18.8385	1.11983	0.559915	−	0.828550i	$-0.310834\pi$
$283$	18.8385	1.11983	0.559915	+	0.828550i	$0.310834\pi$
$284$	−6.21844	−0.368996
$285$	2.97838	0.176424
$286$	−4.62003	−0.273188
$287$	−6.23087	−0.367797
$288$	1.00000	0.0589256
$289$	−16.0000	−0.941176
$290$	−16.3539	−0.960333
$291$	13.1354	0.770013
$292$	−2.89538	−0.169439
$293$	20.5154	1.19852	0.599261	−	0.800553i	$-0.295461\pi$
$293$	20.5154	1.19852	0.599261	+	0.800553i	$0.295461\pi$
$294$	5.51541	0.321665
$295$	−13.9215	−0.810539
$296$	−8.05691	−0.468298
$297$	−1.00000	−0.0580259
$298$	10.0308	0.581070
$299$	16.7247	0.967212
$300$	1.62003	0.0935325
$301$	−3.45850	−0.199345
$302$	−5.35388	−0.308081
$303$	−15.1923	−0.872777
$304$	−1.62003	−0.0929151
$305$	−1.83847	−0.105270
$306$	1.00000	0.0571662
$307$	6.37997	0.364124	0.182062	−	0.983287i	$-0.441723\pi$
$307$	6.37997	0.364124	0.182062	+	0.983287i	$0.441723\pi$
$308$	−1.21844	−0.0694270
$309$	−3.51541	−0.199985
$310$	−11.4324	−0.649317
$311$	−33.9615	−1.92578	−0.962889	−	0.269896i	$-0.913011\pi$
$311$	−33.9615	−1.92578	−0.962889	+	0.269896i	$0.913011\pi$
$312$	4.62003	0.261558
$313$	−18.7214	−1.05820	−0.529098	−	0.848560i	$-0.677470\pi$
$313$	−18.7214	−1.05820	−0.529098	+	0.848560i	$0.677470\pi$
$314$	−14.5723	−0.822363
$315$	−2.24006	−0.126213
$316$	−4.62003	−0.259897
$317$	−27.2232	−1.52901	−0.764503	−	0.644621i	$-0.777015\pi$
$317$	−27.2232	−1.52901	−0.764503	+	0.644621i	$0.777015\pi$
$318$	−4.40159	−0.246829
$319$	−8.89538	−0.498045
$320$	1.83847	0.102774
$321$	−1.49378	−0.0833749
$322$	4.41078	0.245803
$323$	−1.62003	−0.0901409
$324$	1.00000	0.0555556
$325$	7.48459	0.415170
$326$	9.21844	0.510562
$327$	19.6076	1.08430
$328$	5.11382	0.282363
$329$	−9.68937	−0.534192
$330$	−1.83847	−0.101204
$331$	−21.2493	−1.16796	−0.583982	−	0.811766i	$-0.698506\pi$
$331$	−21.2493	−1.16796	−0.583982	+	0.811766i	$0.698506\pi$
$332$	6.13544	0.336726
$333$	−8.05691	−0.441516
$334$	−2.72465	−0.149086
$335$	11.4324	0.624619
$336$	1.21844	0.0664713
$337$	27.1014	1.47631	0.738153	−	0.674633i	$-0.235698\pi$
$337$	27.1014	1.47631	0.738153	+	0.674633i	$0.235698\pi$
$338$	8.34468	0.453891
$339$	8.51541	0.462493
$340$	1.83847	0.0997050
$341$	−6.21844	−0.336747
$342$	−1.62003	−0.0876012
$343$	15.2493	0.823382
$344$	2.83847	0.153040
$345$	6.65532	0.358310
$346$	−10.8954	−0.585739
$347$	19.0785	1.02419	0.512095	−	0.858929i	$-0.328870\pi$
$347$	19.0785	1.02419	0.512095	+	0.858929i	$0.328870\pi$
$348$	8.89538	0.476842
$349$	−17.1446	−0.917731	−0.458866	−	0.888506i	$-0.651744\pi$
$349$	−17.1446	−0.917731	−0.458866	+	0.888506i	$0.651744\pi$
$350$	1.97391	0.105510
$351$	4.62003	0.246599
$352$	1.00000	0.0533002
$353$	−2.02609	−0.107838	−0.0539190	−	0.998545i	$-0.517171\pi$
$353$	−2.02609	−0.107838	−0.0539190	+	0.998545i	$0.517171\pi$
$354$	7.57232	0.402464
$355$	−11.4324	−0.606769
$356$	7.62922	0.404348
$357$	1.21844	0.0644866
$358$	18.8260	0.994987
$359$	−17.4801	−0.922566	−0.461283	−	0.887253i	$-0.652611\pi$
$359$	−17.4801	−0.922566	−0.461283	+	0.887253i	$0.652611\pi$
$360$	1.83847	0.0968958
$361$	−16.3755	−0.861868
$362$	10.4677	0.550170
$363$	−1.00000	−0.0524864
$364$	5.62922	0.295051
$365$	−5.32306	−0.278622
$366$	1.00000	0.0522708
$367$	1.36631	0.0713207	0.0356603	−	0.999364i	$-0.488647\pi$
$367$	1.36631	0.0713207	0.0356603	+	0.999364i	$0.488647\pi$
$368$	−3.62003	−0.188707
$369$	5.11382	0.266215
$370$	−14.8124	−0.770059
$371$	−5.36307	−0.278437
$372$	6.21844	0.322411
$373$	7.34468	0.380293	0.190147	−	0.981756i	$-0.439104\pi$
$373$	7.34468	0.380293	0.190147	+	0.981756i	$0.439104\pi$
$374$	1.00000	0.0517088
$375$	12.1707	0.628493
$376$	7.95228	0.410108
$377$	41.0969	2.11660
$378$	1.21844	0.0626697
$379$	12.9046	0.662863	0.331432	−	0.943479i	$-0.392468\pi$
$379$	12.9046	0.662863	0.331432	+	0.943479i	$0.392468\pi$
$380$	−2.97838	−0.152788
$381$	4.67694	0.239607
$382$	15.1707	0.776202
$383$	3.64612	0.186308	0.0931541	−	0.995652i	$-0.470305\pi$
$383$	3.64612	0.186308	0.0931541	+	0.995652i	$0.470305\pi$
$384$	−1.00000	−0.0510310
$385$	−2.24006	−0.114164
$386$	14.6553	0.745936
$387$	2.83847	0.144288
$388$	−13.1354	−0.666851
$389$	25.2184	1.27863	0.639313	−	0.768947i	$-0.279219\pi$
$389$	25.2184	1.27863	0.639313	+	0.768947i	$0.279219\pi$
$390$	8.49378	0.430100
$391$	−3.62003	−0.183073
$392$	−5.51541	−0.278570
$393$	−0.952285	−0.0480364
$394$	−11.3323	−0.570911
$395$	−8.49378	−0.427369
$396$	1.00000	0.0502519
$397$	−34.9262	−1.75290	−0.876448	−	0.481497i	$-0.840093\pi$
$397$	−34.9262	−1.75290	−0.876448	+	0.481497i	$0.840093\pi$
$398$	−21.7908	−1.09227
$399$	−1.97391	−0.0988190
$400$	−1.62003	−0.0810015
$401$	1.56312	0.0780586	0.0390293	−	0.999238i	$-0.487573\pi$
$401$	1.56312	0.0780586	0.0390293	+	0.999238i	$0.487573\pi$
$402$	−6.21844	−0.310148
$403$	28.7294	1.43111
$404$	15.1923	0.755847
$405$	1.83847	0.0913543
$406$	10.8385	0.537904
$407$	−8.05691	−0.399366
$408$	−1.00000	−0.0495074
$409$	−11.2060	−0.554101	−0.277051	−	0.960855i	$-0.589357\pi$
$409$	−11.2060	−0.554101	−0.277051	+	0.960855i	$0.589357\pi$
$410$	9.40159	0.464312
$411$	3.32306	0.163915
$412$	3.51541	0.173192
$413$	9.22640	0.454001
$414$	−3.62003	−0.177915
$415$	11.2798	0.553704
$416$	−4.62003	−0.226516
$417$	−3.86009	−0.189030
$418$	−1.62003	−0.0792383
$419$	−8.18315	−0.399773	−0.199887	−	0.979819i	$-0.564057\pi$
$419$	−8.18315	−0.399773	−0.199887	+	0.979819i	$0.564057\pi$
$420$	2.24006	0.109304
$421$	22.6076	1.10183	0.550914	−	0.834562i	$-0.314279\pi$
$421$	22.6076	1.10183	0.550914	+	0.834562i	$0.314279\pi$
$422$	0.689369	0.0335580
$423$	7.95228	0.386653
$424$	4.40159	0.213760
$425$	−1.62003	−0.0785830
$426$	6.21844	0.301284
$427$	1.21844	0.0589644
$428$	1.49378	0.0722048
$429$	4.62003	0.223057
$430$	5.21844	0.251655
$431$	−19.1138	−0.920680	−0.460340	−	0.887743i	$-0.652273\pi$
$431$	−19.1138	−0.920680	−0.460340	+	0.887743i	$0.652273\pi$
$432$	−1.00000	−0.0481125
$433$	10.1446	0.487520	0.243760	−	0.969836i	$-0.421619\pi$
$433$	10.1446	0.487520	0.243760	+	0.969836i	$0.421619\pi$
$434$	7.57678	0.363697
$435$	16.3539	0.784108
$436$	−19.6076	−0.939034
$437$	5.86456	0.280540
$438$	2.89538	0.138346
$439$	−15.0569	−0.718627	−0.359313	−	0.933217i	$-0.616989\pi$
$439$	−15.0569	−0.718627	−0.359313	+	0.933217i	$0.616989\pi$
$440$	1.83847	0.0876456
$441$	−5.51541	−0.262638
$442$	−4.62003	−0.219752
$443$	32.8556	1.56102	0.780509	−	0.625145i	$-0.214960\pi$
$443$	32.8556	1.56102	0.780509	+	0.625145i	$0.214960\pi$
$444$	8.05691	0.382364
$445$	14.0261	0.664901
$446$	15.1615	0.717919
$447$	−10.0308	−0.474441
$448$	−1.21844	−0.0575658
$449$	8.14463	0.384369	0.192184	−	0.981359i	$-0.438443\pi$
$449$	8.14463	0.384369	0.192184	+	0.981359i	$0.438443\pi$
$450$	−1.62003	−0.0763690
$451$	5.11382	0.240800
$452$	−8.51541	−0.400531
$453$	5.35388	0.251547
$454$	−20.0216	−0.939661
$455$	10.3492	0.485176
$456$	1.62003	0.0758649
$457$	−12.3323	−0.576879	−0.288439	−	0.957498i	$-0.593136\pi$
$457$	−12.3323	−0.576879	−0.288439	+	0.957498i	$0.593136\pi$
$458$	−9.50622	−0.444196
$459$	−1.00000	−0.0466760
$460$	−6.65532	−0.310306
$461$	3.44931	0.160650	0.0803251	−	0.996769i	$-0.474404\pi$
$461$	3.44931	0.160650	0.0803251	+	0.996769i	$0.474404\pi$
$462$	1.21844	0.0566869
$463$	14.1832	0.659147	0.329574	−	0.944130i	$-0.393095\pi$
$463$	14.1832	0.659147	0.329574	+	0.944130i	$0.393095\pi$
$464$	−8.89538	−0.412958
$465$	11.4324	0.530165
$466$	−20.5507	−0.951992
$467$	−11.5246	−0.533295	−0.266647	−	0.963794i	$-0.585916\pi$
$467$	−11.5246	−0.533295	−0.266647	+	0.963794i	$0.585916\pi$
$468$	−4.62003	−0.213561
$469$	−7.57678	−0.349863
$470$	14.6200	0.674372
$471$	14.5723	0.671457
$472$	−7.57232	−0.348544
$473$	2.83847	0.130513
$474$	4.62003	0.212205
$475$	2.62450	0.120420
$476$	−1.21844	−0.0558470
$477$	4.40159	0.201535
$478$	10.7122	0.489966
$479$	10.0785	0.460500	0.230250	−	0.973132i	$-0.426046\pi$
$479$	10.0785	0.460500	0.230250	+	0.973132i	$0.426046\pi$
$480$	−1.83847	−0.0839143
$481$	37.2232	1.69723
$482$	15.2970	0.696758
$483$	−4.41078	−0.200698
$484$	1.00000	0.0454545
$485$	−24.1491	−1.09655
$486$	−1.00000	−0.0453609
$487$	21.1046	0.956342	0.478171	−	0.878267i	$-0.341300\pi$
$487$	21.1046	0.956342	0.478171	+	0.878267i	$0.341300\pi$
$488$	−1.00000	−0.0452679
$489$	−9.21844	−0.416872
$490$	−10.1399	−0.458074
$491$	−18.1923	−0.821009	−0.410505	−	0.911859i	$-0.634647\pi$
$491$	−18.1923	−0.821009	−0.410505	+	0.911859i	$0.634647\pi$
$492$	−5.11382	−0.230549
$493$	−8.89538	−0.400628
$494$	7.48459	0.336748
$495$	1.83847	0.0826330
$496$	−6.21844	−0.279216
$497$	7.57678	0.339865
$498$	−6.13544	−0.274936
$499$	23.3800	1.04663	0.523316	−	0.852139i	$-0.324695\pi$
$499$	23.3800	1.04663	0.523316	+	0.852139i	$0.324695\pi$
$500$	−12.1707	−0.544291
$501$	2.72465	0.121729
$502$	5.26168	0.234840
$503$	−21.2060	−0.945529	−0.472765	−	0.881189i	$-0.656744\pi$
$503$	−21.2060	−0.945529	−0.472765	+	0.881189i	$0.656744\pi$
$504$	−1.21844	−0.0542736
$505$	27.9307	1.24290
$506$	−3.62003	−0.160930
$507$	−8.34468	−0.370600
$508$	−4.67694	−0.207506
$509$	−25.6633	−1.13750	−0.568752	−	0.822509i	$-0.692574\pi$
$509$	−25.6633	−1.13750	−0.568752	+	0.822509i	$0.692574\pi$
$510$	−1.83847	−0.0814088
$511$	3.52784	0.156062
$512$	1.00000	0.0441942
$513$	1.62003	0.0715261
$514$	−13.2493	−0.584400
$515$	6.46297	0.284792
$516$	−2.83847	−0.124957
$517$	7.95228	0.349741
$518$	9.81685	0.431327
$519$	10.8954	0.478254
$520$	−8.49378	−0.372477
$521$	−19.6553	−0.861115	−0.430557	−	0.902563i	$-0.641683\pi$
$521$	−19.6553	−0.861115	−0.430557	+	0.902563i	$0.641683\pi$
$522$	−8.89538	−0.389340
$523$	44.1675	1.93131	0.965655	−	0.259829i	$-0.0836662\pi$
$523$	44.1675	1.93131	0.965655	+	0.259829i	$0.0836662\pi$
$524$	0.952285	0.0416007
$525$	−1.97391	−0.0861484
$526$	2.68613	0.117121
$527$	−6.21844	−0.270879
$528$	−1.00000	−0.0435194
$529$	−9.89538	−0.430234
$530$	8.09219	0.351502
$531$	−7.57232	−0.328611
$532$	1.97391	0.0855798
$533$	−23.6260	−1.02335
$534$	−7.62922	−0.330149
$535$	2.74628	0.118732
$536$	6.21844	0.268596
$537$	−18.8260	−0.812404
$538$	−21.0000	−0.905374
$539$	−5.51541	−0.237565
$540$	−1.83847	−0.0791151
$541$	35.5030	1.52639	0.763196	−	0.646167i	$-0.223629\pi$
$541$	35.5030	1.52639	0.763196	+	0.646167i	$0.223629\pi$
$542$	−10.3800	−0.445858
$543$	−10.4677	−0.449212
$544$	1.00000	0.0428746
$545$	−36.0480	−1.54413
$546$	−5.62922	−0.240909
$547$	11.8601	0.507101	0.253550	−	0.967322i	$-0.418402\pi$
$547$	11.8601	0.507101	0.253550	+	0.967322i	$0.418402\pi$
$548$	−3.32306	−0.141954
$549$	−1.00000	−0.0426790
$550$	−1.62003	−0.0690783
$551$	14.4108	0.613920
$552$	3.62003	0.154079
$553$	5.62922	0.239379
$554$	10.8477	0.460873
$555$	14.8124	0.628750
$556$	3.86009	0.163704
$557$	−2.42768	−0.102864	−0.0514321	−	0.998676i	$-0.516379\pi$
$557$	−2.42768	−0.102864	−0.0514321	+	0.998676i	$0.516379\pi$
$558$	−6.21844	−0.263247
$559$	−13.1138	−0.554655
$560$	−2.24006	−0.0946599
$561$	−1.00000	−0.0422200
$562$	8.13544	0.343173
$563$	12.1695	0.512883	0.256441	−	0.966560i	$-0.417450\pi$
$563$	12.1695	0.512883	0.256441	+	0.966560i	$0.417450\pi$
$564$	−7.95228	−0.334852
$565$	−15.6553	−0.658624
$566$	18.8385	0.791840
$567$	−1.21844	−0.0511696
$568$	−6.21844	−0.260920
$569$	27.9386	1.17125	0.585624	−	0.810583i	$-0.300850\pi$
$569$	27.9386	1.17125	0.585624	+	0.810583i	$0.300850\pi$
$570$	2.97838	0.124750
$571$	28.7555	1.20338	0.601689	−	0.798730i	$-0.294494\pi$
$571$	28.7555	1.20338	0.601689	+	0.798730i	$0.294494\pi$
$572$	−4.62003	−0.193173
$573$	−15.1707	−0.633766
$574$	−6.23087	−0.260071
$575$	5.86456	0.244569
$576$	1.00000	0.0416667
$577$	33.2448	1.38400	0.691999	−	0.721898i	$-0.256730\pi$
$577$	33.2448	1.38400	0.691999	+	0.721898i	$0.256730\pi$
$578$	−16.0000	−0.665512
$579$	−14.6553	−0.609054
$580$	−16.3539	−0.679058
$581$	−7.47565	−0.310142
$582$	13.1354	0.544481
$583$	4.40159	0.182295
$584$	−2.89538	−0.119812
$585$	−8.49378	−0.351175
$586$	20.5154	0.847484
$587$	41.2925	1.70432	0.852162	−	0.523278i	$-0.175291\pi$
$587$	41.2925	1.70432	0.852162	+	0.523278i	$0.175291\pi$
$588$	5.51541	0.227452
$589$	10.0741	0.415094
$590$	−13.9215	−0.573138
$591$	11.3323	0.466147
$592$	−8.05691	−0.331137
$593$	−2.17396	−0.0892739	−0.0446370	−	0.999003i	$-0.514213\pi$
$593$	−2.17396	−0.0892739	−0.0446370	+	0.999003i	$0.514213\pi$
$594$	−1.00000	−0.0410305
$595$	−2.24006	−0.0918336
$596$	10.0308	0.410878
$597$	21.7908	0.891836
$598$	16.7247	0.683922
$599$	0.829277	0.0338833	0.0169417	−	0.999856i	$-0.494607\pi$
$599$	0.829277	0.0338833	0.0169417	+	0.999856i	$0.494607\pi$
$600$	1.62003	0.0661375
$601$	−21.2276	−0.865893	−0.432947	−	0.901420i	$-0.642526\pi$
$601$	−21.2276	−0.865893	−0.432947	+	0.901420i	$0.642526\pi$
$602$	−3.45850	−0.140958
$603$	6.21844	0.253234
$604$	−5.35388	−0.217846
$605$	1.83847	0.0747444
$606$	−15.1923	−0.617147
$607$	31.6476	1.28454	0.642268	−	0.766480i	$-0.277993\pi$
$607$	31.6476	1.28454	0.642268	+	0.766480i	$0.277993\pi$
$608$	−1.62003	−0.0657009
$609$	−10.8385	−0.439197
$610$	−1.83847	−0.0744374
$611$	−36.7398	−1.48633
$612$	1.00000	0.0404226
$613$	3.36754	0.136014	0.0680068	−	0.997685i	$-0.478336\pi$
$613$	3.36754	0.136014	0.0680068	+	0.997685i	$0.478336\pi$
$614$	6.37997	0.257475
$615$	−9.40159	−0.379109
$616$	−1.21844	−0.0490923
$617$	22.2925	0.897462	0.448731	−	0.893667i	$-0.351876\pi$
$617$	22.2925	0.897462	0.448731	+	0.893667i	$0.351876\pi$
$618$	−3.51541	−0.141410
$619$	−38.2937	−1.53915	−0.769577	−	0.638553i	$-0.779533\pi$
$619$	−38.2937	−1.53915	−0.769577	+	0.638553i	$0.779533\pi$
$620$	−11.4324	−0.459137
$621$	3.62003	0.145267
$622$	−33.9615	−1.36173
$623$	−9.29574	−0.372426
$624$	4.62003	0.184949
$625$	−14.2753	−0.571014
$626$	−18.7214	−0.748258
$627$	1.62003	0.0646978
$628$	−14.5723	−0.581499
$629$	−8.05691	−0.321250
$630$	−2.24006	−0.0892462
$631$	30.1230	1.19918	0.599589	−	0.800308i	$-0.295331\pi$
$631$	30.1230	1.19918	0.599589	+	0.800308i	$0.295331\pi$
$632$	−4.62003	−0.183775
$633$	−0.689369	−0.0274000
$634$	−27.2232	−1.08117
$635$	−8.59841	−0.341217
$636$	−4.40159	−0.174534
$637$	25.4814	1.00961
$638$	−8.89538	−0.352171
$639$	−6.21844	−0.245998
$640$	1.83847	0.0726719
$641$	−33.4861	−1.32262	−0.661310	−	0.750112i	$-0.729999\pi$
$641$	−33.4861	−1.32262	−0.661310	+	0.750112i	$0.729999\pi$
$642$	−1.49378	−0.0589550
$643$	9.83847	0.387991	0.193996	−	0.981002i	$-0.437855\pi$
$643$	9.83847	0.387991	0.193996	+	0.981002i	$0.437855\pi$
$644$	4.41078	0.173809
$645$	−5.21844	−0.205476
$646$	−1.62003	−0.0637393
$647$	12.3062	0.483805	0.241903	−	0.970301i	$-0.422229\pi$
$647$	12.3062	0.483805	0.241903	+	0.970301i	$0.422229\pi$
$648$	1.00000	0.0392837
$649$	−7.57232	−0.297239
$650$	7.48459	0.293570
$651$	−7.57678	−0.296958
$652$	9.21844	0.361022
$653$	6.56312	0.256835	0.128417	−	0.991720i	$-0.459010\pi$
$653$	6.56312	0.256835	0.128417	+	0.991720i	$0.459010\pi$
$654$	19.6076	0.766718
$655$	1.75075	0.0684073
$656$	5.11382	0.199661
$657$	−2.89538	−0.112959
$658$	−9.68937	−0.377731
$659$	−6.27088	−0.244279	−0.122139	−	0.992513i	$-0.538975\pi$
$659$	−6.27088	−0.244279	−0.122139	+	0.992513i	$0.538975\pi$
$660$	−1.83847	−0.0715623
$661$	−29.5678	−1.15006	−0.575028	−	0.818134i	$-0.695009\pi$
$661$	−29.5678	−1.15006	−0.575028	+	0.818134i	$0.695009\pi$
$662$	−21.2493	−0.825876
$663$	4.62003	0.179427
$664$	6.13544	0.238101
$665$	3.62897	0.140725
$666$	−8.05691	−0.312199
$667$	32.2015	1.24685
$668$	−2.72465	−0.105420
$669$	−15.1615	−0.586179
$670$	11.4324	0.441672
$671$	−1.00000	−0.0386046
$672$	1.21844	0.0470023
$673$	20.0661	0.773491	0.386746	−	0.922186i	$-0.373599\pi$
$673$	20.0661	0.773491	0.386746	+	0.922186i	$0.373599\pi$
$674$	27.1014	1.04391
$675$	1.62003	0.0623550
$676$	8.34468	0.320949
$677$	−17.5154	−0.673172	−0.336586	−	0.941653i	$-0.609272\pi$
$677$	−17.5154	−0.673172	−0.336586	+	0.941653i	$0.609272\pi$
$678$	8.51541	0.327032
$679$	16.0047	0.614205
$680$	1.83847	0.0705021
$681$	20.0216	0.767230
$682$	−6.21844	−0.238116
$683$	31.9478	1.22245	0.611225	−	0.791457i	$-0.290677\pi$
$683$	31.9478	1.22245	0.611225	+	0.791457i	$0.290677\pi$
$684$	−1.62003	−0.0619434
$685$	−6.10935	−0.233426
$686$	15.2493	0.582219
$687$	9.50622	0.362685
$688$	2.83847	0.108216
$689$	−20.3355	−0.774721
$690$	6.65532	0.253364
$691$	−39.7999	−1.51406	−0.757031	−	0.653379i	$-0.773351\pi$
$691$	−39.7999	−1.51406	−0.757031	+	0.653379i	$0.773351\pi$
$692$	−10.8954	−0.414180
$693$	−1.21844	−0.0462846
$694$	19.0785	0.724211
$695$	7.09666	0.269192
$696$	8.89538	0.337178
$697$	5.11382	0.193700
$698$	−17.1446	−0.648934
$699$	20.5507	0.777299
$700$	1.97391	0.0746067
$701$	−13.2537	−0.500586	−0.250293	−	0.968170i	$-0.580527\pi$
$701$	−13.2537	−0.500586	−0.250293	+	0.968170i	$0.580527\pi$
$702$	4.62003	0.174372
$703$	13.0524	0.492282
$704$	1.00000	0.0376889
$705$	−14.6200	−0.550622
$706$	−2.02609	−0.0762530
$707$	−18.5109	−0.696176
$708$	7.57232	0.284585
$709$	40.5939	1.52454	0.762269	−	0.647261i	$-0.224085\pi$
$709$	40.5939	1.52454	0.762269	+	0.647261i	$0.224085\pi$
$710$	−11.4324	−0.429051
$711$	−4.62003	−0.173265
$712$	7.62922	0.285917
$713$	22.5109	0.843041
$714$	1.21844	0.0455989
$715$	−8.49378	−0.317650
$716$	18.8260	0.703562
$717$	−10.7122	−0.400055
$718$	−17.4801	−0.652352
$719$	7.42322	0.276839	0.138420	−	0.990374i	$-0.455798\pi$
$719$	7.42322	0.276839	0.138420	+	0.990374i	$0.455798\pi$
$720$	1.83847	0.0685157
$721$	−4.28331	−0.159519
$722$	−16.3755	−0.609433
$723$	−15.2970	−0.568900
$724$	10.4677	0.389029
$725$	14.4108	0.535203
$726$	−1.00000	−0.0371135
$727$	−40.5599	−1.50428	−0.752141	−	0.659002i	$-0.770979\pi$
$727$	−40.5599	−1.50428	−0.752141	+	0.659002i	$0.770979\pi$
$728$	5.62922	0.208633
$729$	1.00000	0.0370370
$730$	−5.32306	−0.197015
$731$	2.83847	0.104985
$732$	1.00000	0.0369611
$733$	−18.6031	−0.687122	−0.343561	−	0.939130i	$-0.611633\pi$
$733$	−18.6031	−0.687122	−0.343561	+	0.939130i	$0.611633\pi$
$734$	1.36631	0.0504313
$735$	10.1399	0.374016
$736$	−3.62003	−0.133436
$737$	6.21844	0.229059
$738$	5.11382	0.188242
$739$	20.6906	0.761116	0.380558	−	0.924757i	$-0.375732\pi$
$739$	20.6906	0.761116	0.380558	+	0.924757i	$0.375732\pi$
$740$	−14.8124	−0.544514
$741$	−7.48459	−0.274953
$742$	−5.36307	−0.196884
$743$	21.4677	0.787573	0.393787	−	0.919202i	$-0.371165\pi$
$743$	21.4677	0.787573	0.393787	+	0.919202i	$0.371165\pi$
$744$	6.21844	0.227979
$745$	18.4413	0.675639
$746$	7.34468	0.268908
$747$	6.13544	0.224484
$748$	1.00000	0.0365636
$749$	−1.82008	−0.0665044
$750$	12.1707	0.444412
$751$	43.6909	1.59430	0.797151	−	0.603780i	$-0.206339\pi$
$751$	43.6909	1.59430	0.797151	+	0.603780i	$0.206339\pi$
$752$	7.95228	0.289990
$753$	−5.26168	−0.191746
$754$	41.0969	1.49666
$755$	−9.84294	−0.358221
$756$	1.21844	0.0443142
$757$	−45.3506	−1.64830	−0.824148	−	0.566374i	$-0.808346\pi$
$757$	−45.3506	−1.64830	−0.824148	+	0.566374i	$0.808346\pi$
$758$	12.9046	0.468715
$759$	3.62003	0.131399
$760$	−2.97838	−0.108037
$761$	38.5862	1.39875	0.699375	−	0.714755i	$-0.253462\pi$
$761$	38.5862	1.39875	0.699375	+	0.714755i	$0.253462\pi$
$762$	4.67694	0.169428
$763$	23.8907	0.864900
$764$	15.1707	0.548857
$765$	1.83847	0.0664700
$766$	3.64612	0.131740
$767$	34.9843	1.26321
$768$	−1.00000	−0.0360844
$769$	29.7955	1.07445	0.537226	−	0.843438i	$-0.319472\pi$
$769$	29.7955	1.07445	0.537226	+	0.843438i	$0.319472\pi$
$770$	−2.24006	−0.0807262
$771$	13.2493	0.477160
$772$	14.6553	0.527456
$773$	7.49378	0.269533	0.134766	−	0.990877i	$-0.456972\pi$
$773$	7.49378	0.269533	0.134766	+	0.990877i	$0.456972\pi$
$774$	2.83847	0.102027
$775$	10.0741	0.361871
$776$	−13.1354	−0.471535
$777$	−9.81685	−0.352177
$778$	25.2184	0.904125
$779$	−8.28454	−0.296824
$780$	8.49378	0.304126
$781$	−6.21844	−0.222513
$782$	−3.62003	−0.129452
$783$	8.89538	0.317895
$784$	−5.51541	−0.196979
$785$	−26.7908	−0.956203
$786$	−0.952285	−0.0339669
$787$	11.6814	0.416397	0.208199	−	0.978087i	$-0.433240\pi$
$787$	11.6814	0.416397	0.208199	+	0.978087i	$0.433240\pi$
$788$	−11.3323	−0.403695
$789$	−2.68613	−0.0956288
$790$	−8.49378	−0.302195
$791$	10.3755	0.368910
$792$	1.00000	0.0355335
$793$	4.62003	0.164062
$794$	−34.9262	−1.23948
$795$	−8.09219	−0.287000
$796$	−21.7908	−0.772353
$797$	1.39835	0.0495322	0.0247661	−	0.999693i	$-0.492116\pi$
$797$	1.39835	0.0495322	0.0247661	+	0.999693i	$0.492116\pi$
$798$	−1.97391	−0.0698756
$799$	7.95228	0.281332
$800$	−1.62003	−0.0572767
$801$	7.62922	0.269565
$802$	1.56312	0.0551958
$803$	−2.89538	−0.102176
$804$	−6.21844	−0.219307
$805$	8.10909	0.285808
$806$	28.7294	1.01195
$807$	21.0000	0.739235
$808$	15.1923	0.534465
$809$	−34.3231	−1.20673	−0.603367	−	0.797463i	$-0.706175\pi$
$809$	−34.3231	−1.20673	−0.603367	+	0.797463i	$0.706175\pi$
$810$	1.83847	0.0645972
$811$	−11.4461	−0.401926	−0.200963	−	0.979599i	$-0.564407\pi$
$811$	−11.4461	−0.401926	−0.200963	+	0.979599i	$0.564407\pi$
$812$	10.8385	0.380356
$813$	10.3800	0.364041
$814$	−8.05691	−0.282394
$815$	16.9478	0.593656
$816$	−1.00000	−0.0350070
$817$	−4.59841	−0.160878
$818$	−11.2060	−0.391809
$819$	5.62922	0.196701
$820$	9.40159	0.328318
$821$	27.6123	0.963677	0.481838	−	0.876260i	$-0.339969\pi$
$821$	27.6123	0.963677	0.481838	+	0.876260i	$0.339969\pi$
$822$	3.32306	0.115905
$823$	−7.09692	−0.247383	−0.123691	−	0.992321i	$-0.539473\pi$
$823$	−7.09692	−0.247383	−0.123691	+	0.992321i	$0.539473\pi$
$824$	3.51541	0.122465
$825$	1.62003	0.0564022
$826$	9.22640	0.321028
$827$	−14.6384	−0.509028	−0.254514	−	0.967069i	$-0.581915\pi$
$827$	−14.6384	−0.509028	−0.254514	+	0.967069i	$0.581915\pi$
$828$	−3.62003	−0.125805
$829$	−20.2368	−0.702854	−0.351427	−	0.936215i	$-0.614303\pi$
$829$	−20.2368	−0.702854	−0.351427	+	0.936215i	$0.614303\pi$
$830$	11.2798	0.391528
$831$	−10.8477	−0.376301
$832$	−4.62003	−0.160171
$833$	−5.51541	−0.191098
$834$	−3.86009	−0.133664
$835$	−5.00919	−0.173350
$836$	−1.62003	−0.0560299
$837$	6.21844	0.214941
$838$	−8.18315	−0.282682
$839$	−10.9876	−0.379333	−0.189667	−	0.981849i	$-0.560741\pi$
$839$	−10.9876	−0.379333	−0.189667	+	0.981849i	$0.560741\pi$
$840$	2.24006	0.0772895
$841$	50.1277	1.72854
$842$	22.6076	0.779109
$843$	−8.13544	−0.280199
$844$	0.689369	0.0237291
$845$	15.3414	0.527762
$846$	7.95228	0.273405
$847$	−1.21844	−0.0418660
$848$	4.40159	0.151151
$849$	−18.8385	−0.646535
$850$	−1.62003	−0.0555666
$851$	29.1663	0.999806
$852$	6.21844	0.213040
$853$	8.53703	0.292302	0.146151	−	0.989262i	$-0.453311\pi$
$853$	8.53703	0.292302	0.146151	+	0.989262i	$0.453311\pi$
$854$	1.21844	0.0416941
$855$	−2.97838	−0.101858
$856$	1.49378	0.0510565
$857$	−7.72465	−0.263869	−0.131935	−	0.991258i	$-0.542119\pi$
$857$	−7.72465	−0.263869	−0.131935	+	0.991258i	$0.542119\pi$
$858$	4.62003	0.157725
$859$	−20.6906	−0.705954	−0.352977	−	0.935632i	$-0.614831\pi$
$859$	−20.6906	−0.705954	−0.352977	+	0.935632i	$0.614831\pi$
$860$	5.21844	0.177947
$861$	6.23087	0.212347
$862$	−19.1138	−0.651019
$863$	39.3767	1.34040	0.670200	−	0.742181i	$-0.266208\pi$
$863$	39.3767	1.34040	0.670200	+	0.742181i	$0.266208\pi$
$864$	−1.00000	−0.0340207
$865$	−20.0308	−0.681068
$866$	10.1446	0.344729
$867$	16.0000	0.543388
$868$	7.57678	0.257173
$869$	−4.62003	−0.156724
$870$	16.3539	0.554448
$871$	−28.7294	−0.973458
$872$	−19.6076	−0.663997
$873$	−13.1354	−0.444567
$874$	5.86456	0.198372
$875$	14.8293	0.501321
$876$	2.89538	0.0978257
$877$	13.5154	0.456383	0.228191	−	0.973616i	$-0.426719\pi$
$877$	13.5154	0.456383	0.228191	+	0.973616i	$0.426719\pi$
$878$	−15.0569	−0.508146
$879$	−20.5154	−0.691968
$880$	1.83847	0.0619748
$881$	4.50298	0.151709	0.0758546	−	0.997119i	$-0.475832\pi$
$881$	4.50298	0.151709	0.0758546	+	0.997119i	$0.475832\pi$
$882$	−5.51541	−0.185713
$883$	52.3462	1.76159	0.880794	−	0.473499i	$-0.157009\pi$
$883$	52.3462	1.76159	0.880794	+	0.473499i	$0.157009\pi$
$884$	−4.62003	−0.155388
$885$	13.9215	0.467965
$886$	32.8556	1.10381
$887$	12.3675	0.415261	0.207631	−	0.978207i	$-0.433425\pi$
$887$	12.3675	0.415261	0.207631	+	0.978207i	$0.433425\pi$
$888$	8.05691	0.270372
$889$	5.69856	0.191124
$890$	14.0261	0.470156
$891$	1.00000	0.0335013
$892$	15.1615	0.507646
$893$	−12.8829	−0.431111
$894$	−10.0308	−0.335481
$895$	34.6111	1.15692
$896$	−1.21844	−0.0407052
$897$	−16.7247	−0.558420
$898$	8.14463	0.271790
$899$	55.3154	1.84487
$900$	−1.62003	−0.0540010
$901$	4.40159	0.146638
$902$	5.11382	0.170271
$903$	3.45850	0.115092
$904$	−8.51541	−0.283218
$905$	19.2445	0.639710
$906$	5.35388	0.177871
$907$	−46.5862	−1.54687	−0.773435	−	0.633875i	$-0.781463\pi$
$907$	−46.5862	−1.54687	−0.773435	+	0.633875i	$0.781463\pi$
$908$	−20.0216	−0.664441
$909$	15.1923	0.503898
$910$	10.3492	0.343071
$911$	−55.0139	−1.82269	−0.911346	−	0.411641i	$-0.864956\pi$
$911$	−55.0139	−1.82269	−0.911346	+	0.411641i	$0.864956\pi$
$912$	1.62003	0.0536446
$913$	6.13544	0.203053
$914$	−12.3323	−0.407915
$915$	1.83847	0.0607779
$916$	−9.50622	−0.314094
$917$	−1.16030	−0.0383165
$918$	−1.00000	−0.0330049
$919$	40.2676	1.32831	0.664153	−	0.747596i	$-0.268792\pi$
$919$	40.2676	1.32831	0.664153	+	0.747596i	$0.268792\pi$
$920$	−6.65532	−0.219419
$921$	−6.37997	−0.210227
$922$	3.44931	0.113597
$923$	28.7294	0.945639
$924$	1.21844	0.0400837
$925$	13.0524	0.429162
$926$	14.1832	0.466087
$927$	3.51541	0.115461
$928$	−8.89538	−0.292005
$929$	17.6461	0.578951	0.289475	−	0.957185i	$-0.406519\pi$
$929$	17.6461	0.578951	0.289475	+	0.957185i	$0.406519\pi$
$930$	11.4324	0.374883
$931$	8.93513	0.292837
$932$	−20.5507	−0.673160
$933$	33.9615	1.11185
$934$	−11.5246	−0.377096
$935$	1.83847	0.0601244
$936$	−4.62003	−0.151010
$937$	27.2662	0.890746	0.445373	−	0.895345i	$-0.353071\pi$
$937$	27.2662	0.890746	0.445373	+	0.895345i	$0.353071\pi$
$938$	−7.57678	−0.247391
$939$	18.7214	0.610950
$940$	14.6200	0.476853
$941$	25.8738	0.843460	0.421730	−	0.906721i	$-0.361423\pi$
$941$	25.8738	0.843460	0.421730	+	0.906721i	$0.361423\pi$
$942$	14.5723	0.474792
$943$	−18.5122	−0.602839
$944$	−7.57232	−0.246458
$945$	2.24006	0.0728692
$946$	2.83847	0.0922866
$947$	−45.3278	−1.47296	−0.736478	−	0.676462i	$-0.763512\pi$
$947$	−45.3278	−1.47296	−0.736478	+	0.676462i	$0.763512\pi$
$948$	4.62003	0.150052
$949$	13.3767	0.434227
$950$	2.62450	0.0851500
$951$	27.2232	0.882772
$952$	−1.21844	−0.0394898
$953$	−21.4153	−0.693708	−0.346854	−	0.937919i	$-0.612750\pi$
$953$	−21.4153	−0.693708	−0.346854	+	0.937919i	$0.612750\pi$
$954$	4.40159	0.142507
$955$	27.8909	0.902529
$956$	10.7122	0.346458
$957$	8.89538	0.287547
$958$	10.0785	0.325623
$959$	4.04895	0.130747
$960$	−1.83847	−0.0593363
$961$	7.66898	0.247386
$962$	37.2232	1.20012
$963$	1.49378	0.0481365
$964$	15.2970	0.492682
$965$	26.9433	0.867337
$966$	−4.41078	−0.141915
$967$	18.9386	0.609025	0.304513	−	0.952508i	$-0.401506\pi$
$967$	18.9386	0.609025	0.304513	+	0.952508i	$0.401506\pi$
$968$	1.00000	0.0321412
$969$	1.62003	0.0520429
$970$	−24.1491	−0.775381
$971$	−28.1230	−0.902510	−0.451255	−	0.892395i	$-0.649024\pi$
$971$	−28.1230	−0.902510	−0.451255	+	0.892395i	$0.649024\pi$
$972$	−1.00000	−0.0320750
$973$	−4.70329	−0.150780
$974$	21.1046	0.676236
$975$	−7.48459	−0.239699
$976$	−1.00000	−0.0320092
$977$	−60.1526	−1.92445	−0.962226	−	0.272252i	$-0.912232\pi$
$977$	−60.1526	−1.92445	−0.962226	+	0.272252i	$0.912232\pi$
$978$	−9.21844	−0.294773
$979$	7.62922	0.243831
$980$	−10.1399	−0.323907
$981$	−19.6076	−0.626022
$982$	−18.1923	−0.580541
$983$	11.7985	0.376312	0.188156	−	0.982139i	$-0.439749\pi$
$983$	11.7985	0.376312	0.188156	+	0.982139i	$0.439749\pi$
$984$	−5.11382	−0.163022
$985$	−20.8340	−0.663826
$986$	−8.89538	−0.283287
$987$	9.68937	0.308416
$988$	7.48459	0.238117
$989$	−10.2753	−0.326737
$990$	1.83847	0.0584304
$991$	−22.2264	−0.706045	−0.353022	−	0.935615i	$-0.614846\pi$
$991$	−22.2264	−0.706045	−0.353022	+	0.935615i	$0.614846\pi$
$992$	−6.21844	−0.197436
$993$	21.2493	0.674325
$994$	7.57678	0.240321
$995$	−40.0616	−1.27004
$996$	−6.13544	−0.194409
$997$	16.5166	0.523087	0.261544	−	0.965192i	$-0.415768\pi$
$997$	16.5166	0.523087	0.261544	+	0.965192i	$0.415768\pi$
$998$	23.3800	0.740080
$999$	8.05691	0.254909

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4026.2.a.o.1.3	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4026.2.a.o.1.3	✓	3	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 4026 = 2 \cdot 3 \cdot 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4026.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.83847 q^{5} -1.00000 q^{6} -1.21844 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.83847 q^{5} -1.00000 q^{6} -1.21844 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.83847 q^{10} +1.00000 q^{11} -1.00000 q^{12} -4.62003 q^{13} -1.21844 q^{14} -1.83847 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} -1.62003 q^{19} +1.83847 q^{20} +1.21844 q^{21} +1.00000 q^{22} -3.62003 q^{23} -1.00000 q^{24} -1.62003 q^{25} -4.62003 q^{26} -1.00000 q^{27} -1.21844 q^{28} -8.89538 q^{29} -1.83847 q^{30} -6.21844 q^{31} +1.00000 q^{32} -1.00000 q^{33} +1.00000 q^{34} -2.24006 q^{35} +1.00000 q^{36} -8.05691 q^{37} -1.62003 q^{38} +4.62003 q^{39} +1.83847 q^{40} +5.11382 q^{41} +1.21844 q^{42} +2.83847 q^{43} +1.00000 q^{44} +1.83847 q^{45} -3.62003 q^{46} +7.95228 q^{47} -1.00000 q^{48} -5.51541 q^{49} -1.62003 q^{50} -1.00000 q^{51} -4.62003 q^{52} +4.40159 q^{53} -1.00000 q^{54} +1.83847 q^{55} -1.21844 q^{56} +1.62003 q^{57} -8.89538 q^{58} -7.57232 q^{59} -1.83847 q^{60} -1.00000 q^{61} -6.21844 q^{62} -1.21844 q^{63} +1.00000 q^{64} -8.49378 q^{65} -1.00000 q^{66} +6.21844 q^{67} +1.00000 q^{68} +3.62003 q^{69} -2.24006 q^{70} -6.21844 q^{71} +1.00000 q^{72} -2.89538 q^{73} -8.05691 q^{74} +1.62003 q^{75} -1.62003 q^{76} -1.21844 q^{77} +4.62003 q^{78} -4.62003 q^{79} +1.83847 q^{80} +1.00000 q^{81} +5.11382 q^{82} +6.13544 q^{83} +1.21844 q^{84} +1.83847 q^{85} +2.83847 q^{86} +8.89538 q^{87} +1.00000 q^{88} +7.62922 q^{89} +1.83847 q^{90} +5.62922 q^{91} -3.62003 q^{92} +6.21844 q^{93} +7.95228 q^{94} -2.97838 q^{95} -1.00000 q^{96} -13.1354 q^{97} -5.51541 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} - 3 q^{5} - 3 q^{6} - 2 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 - 3 * q^5 - 3 * q^6 - 2 * q^7 + 3 * q^8 + 3 * q^9	\( 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} - 3 q^{5} - 3 q^{6} - 2 q^{7} + 3 q^{8} + 3 q^{9} - 3 q^{10} + 3 q^{11} - 3 q^{12} - 7 q^{13} - 2 q^{14} + 3 q^{15} + 3 q^{16} + 3 q^{17} + 3 q^{18} + 2 q^{19} - 3 q^{20} + 2 q^{21} + 3 q^{22} - 4 q^{23} - 3 q^{24} + 2 q^{25} - 7 q^{26} - 3 q^{27} - 2 q^{28} - 8 q^{29} + 3 q^{30} - 17 q^{31} + 3 q^{32} - 3 q^{33} + 3 q^{34} + 7 q^{35} + 3 q^{36} - 14 q^{37} + 2 q^{38} + 7 q^{39} - 3 q^{40} - 5 q^{41} + 2 q^{42} + 3 q^{44} - 3 q^{45} - 4 q^{46} - 5 q^{47} - 3 q^{48} + 9 q^{49} + 2 q^{50} - 3 q^{51} - 7 q^{52} + 8 q^{53} - 3 q^{54} - 3 q^{55} - 2 q^{56} - 2 q^{57} - 8 q^{58} + 13 q^{59} + 3 q^{60} - 3 q^{61} - 17 q^{62} - 2 q^{63} + 3 q^{64} - 12 q^{65} - 3 q^{66} + 17 q^{67} + 3 q^{68} + 4 q^{69} + 7 q^{70} - 17 q^{71} + 3 q^{72} + 10 q^{73} - 14 q^{74} - 2 q^{75} + 2 q^{76} - 2 q^{77} + 7 q^{78} - 7 q^{79} - 3 q^{80} + 3 q^{81} - 5 q^{82} - 14 q^{83} + 2 q^{84} - 3 q^{85} + 8 q^{87} + 3 q^{88} - 23 q^{89} - 3 q^{90} - 29 q^{91} - 4 q^{92} + 17 q^{93} - 5 q^{94} - 21 q^{95} - 3 q^{96} - 7 q^{97} + 9 q^{98} + 3 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 - 3 * q^5 - 3 * q^6 - 2 * q^7 + 3 * q^8 + 3 * q^9 - 3 * q^10 + 3 * q^11 - 3 * q^12 - 7 * q^13 - 2 * q^14 + 3 * q^15 + 3 * q^16 + 3 * q^17 + 3 * q^18 + 2 * q^19 - 3 * q^20 + 2 * q^21 + 3 * q^22 - 4 * q^23 - 3 * q^24 + 2 * q^25 - 7 * q^26 - 3 * q^27 - 2 * q^28 - 8 * q^29 + 3 * q^30 - 17 * q^31 + 3 * q^32 - 3 * q^33 + 3 * q^34 + 7 * q^35 + 3 * q^36 - 14 * q^37 + 2 * q^38 + 7 * q^39 - 3 * q^40 - 5 * q^41 + 2 * q^42 + 3 * q^44 - 3 * q^45 - 4 * q^46 - 5 * q^47 - 3 * q^48 + 9 * q^49 + 2 * q^50 - 3 * q^51 - 7 * q^52 + 8 * q^53 - 3 * q^54 - 3 * q^55 - 2 * q^56 - 2 * q^57 - 8 * q^58 + 13 * q^59 + 3 * q^60 - 3 * q^61 - 17 * q^62 - 2 * q^63 + 3 * q^64 - 12 * q^65 - 3 * q^66 + 17 * q^67 + 3 * q^68 + 4 * q^69 + 7 * q^70 - 17 * q^71 + 3 * q^72 + 10 * q^73 - 14 * q^74 - 2 * q^75 + 2 * q^76 - 2 * q^77 + 7 * q^78 - 7 * q^79 - 3 * q^80 + 3 * q^81 - 5 * q^82 - 14 * q^83 + 2 * q^84 - 3 * q^85 + 8 * q^87 + 3 * q^88 - 23 * q^89 - 3 * q^90 - 29 * q^91 - 4 * q^92 + 17 * q^93 - 5 * q^94 - 21 * q^95 - 3 * q^96 - 7 * q^97 + 9 * q^98 + 3 * q^99

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