LMFDB - Embedded newform 1014.2.a.h.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1014,2,Mod(1,1014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1014, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1014.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1014 = 2 \cdot 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1014.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:	$8.09683076496$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{12})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 3 $ x^2 - 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 78)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.73205$ of defining polynomial
Character	$\chi$	$=$	1014.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.73205 q^{5} +1.00000 q^{6} +1.26795 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.73205 q^{5} +1.00000 q^{6} +1.26795 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.73205 q^{10} +1.26795 q^{11} -1.00000 q^{12} -1.26795 q^{14} -1.73205 q^{15} +1.00000 q^{16} +5.19615 q^{17} -1.00000 q^{18} +4.73205 q^{19} +1.73205 q^{20} -1.26795 q^{21} -1.26795 q^{22} -8.19615 q^{23} +1.00000 q^{24} -2.00000 q^{25} -1.00000 q^{27} +1.26795 q^{28} -3.00000 q^{29} +1.73205 q^{30} +9.46410 q^{31} -1.00000 q^{32} -1.26795 q^{33} -5.19615 q^{34} +2.19615 q^{35} +1.00000 q^{36} +3.00000 q^{37} -4.73205 q^{38} -1.73205 q^{40} +6.46410 q^{41} +1.26795 q^{42} -4.19615 q^{43} +1.26795 q^{44} +1.73205 q^{45} +8.19615 q^{46} -4.73205 q^{47} -1.00000 q^{48} -5.39230 q^{49} +2.00000 q^{50} -5.19615 q^{51} +3.00000 q^{53} +1.00000 q^{54} +2.19615 q^{55} -1.26795 q^{56} -4.73205 q^{57} +3.00000 q^{58} -13.8564 q^{59} -1.73205 q^{60} +15.1962 q^{61} -9.46410 q^{62} +1.26795 q^{63} +1.00000 q^{64} +1.26795 q^{66} +7.26795 q^{67} +5.19615 q^{68} +8.19615 q^{69} -2.19615 q^{70} -2.19615 q^{71} -1.00000 q^{72} +12.1244 q^{73} -3.00000 q^{74} +2.00000 q^{75} +4.73205 q^{76} +1.60770 q^{77} +8.39230 q^{79} +1.73205 q^{80} +1.00000 q^{81} -6.46410 q^{82} +5.66025 q^{83} -1.26795 q^{84} +9.00000 q^{85} +4.19615 q^{86} +3.00000 q^{87} -1.26795 q^{88} +9.46410 q^{89} -1.73205 q^{90} -8.19615 q^{92} -9.46410 q^{93} +4.73205 q^{94} +8.19615 q^{95} +1.00000 q^{96} +6.00000 q^{97} +5.39230 q^{98} +1.26795 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{6} + 6 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^6 + 6 * q^7 - 2 * q^8 + 2 * q^9	$ 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{6} + 6 q^{7} - 2 q^{8} + 2 q^{9} + 6 q^{11} - 2 q^{12} - 6 q^{14} + 2 q^{16} - 2 q^{18} + 6 q^{19} - 6 q^{21} - 6 q^{22} - 6 q^{23} + 2 q^{24} - 4 q^{25} - 2 q^{27} + 6 q^{28} - 6 q^{29} + 12 q^{31} - 2 q^{32} - 6 q^{33} - 6 q^{35} + 2 q^{36} + 6 q^{37} - 6 q^{38} + 6 q^{41} + 6 q^{42} + 2 q^{43} + 6 q^{44} + 6 q^{46} - 6 q^{47} - 2 q^{48} + 10 q^{49} + 4 q^{50} + 6 q^{53} + 2 q^{54} - 6 q^{55} - 6 q^{56} - 6 q^{57} + 6 q^{58} + 20 q^{61} - 12 q^{62} + 6 q^{63} + 2 q^{64} + 6 q^{66} + 18 q^{67} + 6 q^{69} + 6 q^{70} + 6 q^{71} - 2 q^{72} - 6 q^{74} + 4 q^{75} + 6 q^{76} + 24 q^{77} - 4 q^{79} + 2 q^{81} - 6 q^{82} - 6 q^{83} - 6 q^{84} + 18 q^{85} - 2 q^{86} + 6 q^{87} - 6 q^{88} + 12 q^{89} - 6 q^{92} - 12 q^{93} + 6 q^{94} + 6 q^{95} + 2 q^{96} + 12 q^{97} - 10 q^{98} + 6 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^6 + 6 * q^7 - 2 * q^8 + 2 * q^9 + 6 * q^11 - 2 * q^12 - 6 * q^14 + 2 * q^16 - 2 * q^18 + 6 * q^19 - 6 * q^21 - 6 * q^22 - 6 * q^23 + 2 * q^24 - 4 * q^25 - 2 * q^27 + 6 * q^28 - 6 * q^29 + 12 * q^31 - 2 * q^32 - 6 * q^33 - 6 * q^35 + 2 * q^36 + 6 * q^37 - 6 * q^38 + 6 * q^41 + 6 * q^42 + 2 * q^43 + 6 * q^44 + 6 * q^46 - 6 * q^47 - 2 * q^48 + 10 * q^49 + 4 * q^50 + 6 * q^53 + 2 * q^54 - 6 * q^55 - 6 * q^56 - 6 * q^57 + 6 * q^58 + 20 * q^61 - 12 * q^62 + 6 * q^63 + 2 * q^64 + 6 * q^66 + 18 * q^67 + 6 * q^69 + 6 * q^70 + 6 * q^71 - 2 * q^72 - 6 * q^74 + 4 * q^75 + 6 * q^76 + 24 * q^77 - 4 * q^79 + 2 * q^81 - 6 * q^82 - 6 * q^83 - 6 * q^84 + 18 * q^85 - 2 * q^86 + 6 * q^87 - 6 * q^88 + 12 * q^89 - 6 * q^92 - 12 * q^93 + 6 * q^94 + 6 * q^95 + 2 * q^96 + 12 * q^97 - 10 * q^98 + 6 * 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
$5$	1.73205	0.774597	0.387298	−	0.921954i	$-0.373408\pi$
$5$	1.73205	0.774597	0.387298	+	0.921954i	$0.373408\pi$
$6$	1.00000	0.408248
$7$	1.26795	0.479240	0.239620	−	0.970867i	$-0.422977\pi$
$7$	1.26795	0.479240	0.239620	+	0.970867i	$0.422977\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−1.73205	−0.547723
$11$	1.26795	0.382301	0.191151	−	0.981561i	$-0.438778\pi$
$11$	1.26795	0.382301	0.191151	+	0.981561i	$0.438778\pi$
$12$	−1.00000	−0.288675
$13$	0	0
$13$	0	0
$14$	−1.26795	−0.338874
$15$	−1.73205	−0.447214
$16$	1.00000	0.250000
$17$	5.19615	1.26025	0.630126	−	0.776493i	$-0.283003\pi$
$17$	5.19615	1.26025	0.630126	+	0.776493i	$0.283003\pi$
$18$	−1.00000	−0.235702
$19$	4.73205	1.08561	0.542803	−	0.839860i	$-0.317363\pi$
$19$	4.73205	1.08561	0.542803	+	0.839860i	$0.317363\pi$
$20$	1.73205	0.387298
$21$	−1.26795	−0.276689
$22$	−1.26795	−0.270328
$23$	−8.19615	−1.70902	−0.854508	−	0.519438i	$-0.826141\pi$
$23$	−8.19615	−1.70902	−0.854508	+	0.519438i	$0.826141\pi$
$24$	1.00000	0.204124
$25$	−2.00000	−0.400000
$26$	0	0
$27$	−1.00000	−0.192450
$28$	1.26795	0.239620
$29$	−3.00000	−0.557086	−0.278543	−	0.960424i	$-0.589851\pi$
$29$	−3.00000	−0.557086	−0.278543	+	0.960424i	$0.589851\pi$
$30$	1.73205	0.316228
$31$	9.46410	1.69980	0.849901	−	0.526942i	$-0.176661\pi$
$31$	9.46410	1.69980	0.849901	+	0.526942i	$0.176661\pi$
$32$	−1.00000	−0.176777
$33$	−1.26795	−0.220722
$34$	−5.19615	−0.891133
$35$	2.19615	0.371218
$36$	1.00000	0.166667
$37$	3.00000	0.493197	0.246598	−	0.969118i	$-0.420687\pi$
$37$	3.00000	0.493197	0.246598	+	0.969118i	$0.420687\pi$
$38$	−4.73205	−0.767640
$39$	0	0
$40$	−1.73205	−0.273861
$41$	6.46410	1.00952	0.504762	−	0.863259i	$-0.331580\pi$
$41$	6.46410	1.00952	0.504762	+	0.863259i	$0.331580\pi$
$42$	1.26795	0.195649
$43$	−4.19615	−0.639907	−0.319954	−	0.947433i	$-0.603667\pi$
$43$	−4.19615	−0.639907	−0.319954	+	0.947433i	$0.603667\pi$
$44$	1.26795	0.191151
$45$	1.73205	0.258199
$46$	8.19615	1.20846
$47$	−4.73205	−0.690241	−0.345120	−	0.938558i	$-0.612162\pi$
$47$	−4.73205	−0.690241	−0.345120	+	0.938558i	$0.612162\pi$
$48$	−1.00000	−0.144338
$49$	−5.39230	−0.770329
$50$	2.00000	0.282843
$51$	−5.19615	−0.727607
$52$	0	0
$53$	3.00000	0.412082	0.206041	−	0.978543i	$-0.433942\pi$
$53$	3.00000	0.412082	0.206041	+	0.978543i	$0.433942\pi$
$54$	1.00000	0.136083
$55$	2.19615	0.296129
$56$	−1.26795	−0.169437
$57$	−4.73205	−0.626775
$58$	3.00000	0.393919
$59$	−13.8564	−1.80395	−0.901975	−	0.431788i	$-0.857883\pi$
$59$	−13.8564	−1.80395	−0.901975	+	0.431788i	$0.857883\pi$
$60$	−1.73205	−0.223607
$61$	15.1962	1.94567	0.972834	−	0.231504i	$-0.0743646\pi$
$61$	15.1962	1.94567	0.972834	+	0.231504i	$0.0743646\pi$
$62$	−9.46410	−1.20194
$63$	1.26795	0.159747
$64$	1.00000	0.125000
$65$	0	0
$66$	1.26795	0.156074
$67$	7.26795	0.887921	0.443961	−	0.896046i	$-0.353573\pi$
$67$	7.26795	0.887921	0.443961	+	0.896046i	$0.353573\pi$
$68$	5.19615	0.630126
$69$	8.19615	0.986701
$70$	−2.19615	−0.262490
$71$	−2.19615	−0.260635	−0.130318	−	0.991472i	$-0.541600\pi$
$71$	−2.19615	−0.260635	−0.130318	+	0.991472i	$0.541600\pi$
$72$	−1.00000	−0.117851
$73$	12.1244	1.41905	0.709524	−	0.704681i	$-0.248910\pi$
$73$	12.1244	1.41905	0.709524	+	0.704681i	$0.248910\pi$
$74$	−3.00000	−0.348743
$75$	2.00000	0.230940
$76$	4.73205	0.542803
$77$	1.60770	0.183214
$78$	0	0
$79$	8.39230	0.944208	0.472104	−	0.881543i	$-0.343495\pi$
$79$	8.39230	0.944208	0.472104	+	0.881543i	$0.343495\pi$
$80$	1.73205	0.193649
$81$	1.00000	0.111111
$82$	−6.46410	−0.713841
$83$	5.66025	0.621294	0.310647	−	0.950525i	$-0.399454\pi$
$83$	5.66025	0.621294	0.310647	+	0.950525i	$0.399454\pi$
$84$	−1.26795	−0.138345
$85$	9.00000	0.976187
$86$	4.19615	0.452483
$87$	3.00000	0.321634
$88$	−1.26795	−0.135164
$89$	9.46410	1.00319	0.501596	−	0.865102i	$-0.332746\pi$
$89$	9.46410	1.00319	0.501596	+	0.865102i	$0.332746\pi$
$90$	−1.73205	−0.182574
$91$	0	0
$92$	−8.19615	−0.854508
$93$	−9.46410	−0.981382
$94$	4.73205	0.488074
$95$	8.19615	0.840907
$96$	1.00000	0.102062
$97$	6.00000	0.609208	0.304604	−	0.952479i	$-0.401476\pi$
$97$	6.00000	0.609208	0.304604	+	0.952479i	$0.401476\pi$
$98$	5.39230	0.544705
$99$	1.26795	0.127434
$100$	−2.00000	−0.200000
$101$	19.3923	1.92961	0.964803	−	0.262973i	$-0.0847030\pi$
$101$	19.3923	1.92961	0.964803	+	0.262973i	$0.0847030\pi$
$102$	5.19615	0.514496
$103$	6.19615	0.610525	0.305263	−	0.952268i	$-0.401256\pi$
$103$	6.19615	0.610525	0.305263	+	0.952268i	$0.401256\pi$
$104$	0	0
$105$	−2.19615	−0.214323
$106$	−3.00000	−0.291386
$107$	−2.19615	−0.212310	−0.106155	−	0.994350i	$-0.533854\pi$
$107$	−2.19615	−0.212310	−0.106155	+	0.994350i	$0.533854\pi$
$108$	−1.00000	−0.0962250
$109$	−4.39230	−0.420707	−0.210353	−	0.977625i	$-0.567461\pi$
$109$	−4.39230	−0.420707	−0.210353	+	0.977625i	$0.567461\pi$
$110$	−2.19615	−0.209395
$111$	−3.00000	−0.284747
$112$	1.26795	0.119810
$113$	0.803848	0.0756196	0.0378098	−	0.999285i	$-0.487962\pi$
$113$	0.803848	0.0756196	0.0378098	+	0.999285i	$0.487962\pi$
$114$	4.73205	0.443197
$115$	−14.1962	−1.32380
$116$	−3.00000	−0.278543
$117$	0	0
$118$	13.8564	1.27559
$119$	6.58846	0.603963
$120$	1.73205	0.158114
$121$	−9.39230	−0.853846
$122$	−15.1962	−1.37579
$123$	−6.46410	−0.582848
$124$	9.46410	0.849901
$125$	−12.1244	−1.08444
$126$	−1.26795	−0.112958
$127$	−4.00000	−0.354943	−0.177471	−	0.984126i	$-0.556792\pi$
$127$	−4.00000	−0.354943	−0.177471	+	0.984126i	$0.556792\pi$
$128$	−1.00000	−0.0883883
$129$	4.19615	0.369451
$130$	0	0
$131$	−4.39230	−0.383757	−0.191879	−	0.981419i	$-0.561458\pi$
$131$	−4.39230	−0.383757	−0.191879	+	0.981419i	$0.561458\pi$
$132$	−1.26795	−0.110361
$133$	6.00000	0.520266
$134$	−7.26795	−0.627855
$135$	−1.73205	−0.149071
$136$	−5.19615	−0.445566
$137$	−9.00000	−0.768922	−0.384461	−	0.923141i	$-0.625613\pi$
$137$	−9.00000	−0.768922	−0.384461	+	0.923141i	$0.625613\pi$
$138$	−8.19615	−0.697703
$139$	−4.00000	−0.339276	−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000	−0.339276	−0.169638	+	0.985506i	$0.554260\pi$
$140$	2.19615	0.185609
$141$	4.73205	0.398511
$142$	2.19615	0.184297
$143$	0	0
$144$	1.00000	0.0833333
$145$	−5.19615	−0.431517
$146$	−12.1244	−1.00342
$147$	5.39230	0.444750
$148$	3.00000	0.246598
$149$	6.12436	0.501727	0.250863	−	0.968023i	$-0.419286\pi$
$149$	6.12436	0.501727	0.250863	+	0.968023i	$0.419286\pi$
$150$	−2.00000	−0.163299
$151$	10.7321	0.873362	0.436681	−	0.899616i	$-0.356154\pi$
$151$	10.7321	0.873362	0.436681	+	0.899616i	$0.356154\pi$
$152$	−4.73205	−0.383820
$153$	5.19615	0.420084
$154$	−1.60770	−0.129552
$155$	16.3923	1.31666
$156$	0	0
$157$	7.19615	0.574315	0.287158	−	0.957883i	$-0.407290\pi$
$157$	7.19615	0.574315	0.287158	+	0.957883i	$0.407290\pi$
$158$	−8.39230	−0.667656
$159$	−3.00000	−0.237915
$160$	−1.73205	−0.136931
$161$	−10.3923	−0.819028
$162$	−1.00000	−0.0785674
$163$	2.53590	0.198627	0.0993134	−	0.995056i	$-0.468335\pi$
$163$	2.53590	0.198627	0.0993134	+	0.995056i	$0.468335\pi$
$164$	6.46410	0.504762
$165$	−2.19615	−0.170970
$166$	−5.66025	−0.439321
$167$	−9.46410	−0.732354	−0.366177	−	0.930545i	$-0.619334\pi$
$167$	−9.46410	−0.732354	−0.366177	+	0.930545i	$0.619334\pi$
$168$	1.26795	0.0978244
$169$	0	0
$170$	−9.00000	−0.690268
$171$	4.73205	0.361869
$172$	−4.19615	−0.319954
$173$	−4.39230	−0.333941	−0.166970	−	0.985962i	$-0.553398\pi$
$173$	−4.39230	−0.333941	−0.166970	+	0.985962i	$0.553398\pi$
$174$	−3.00000	−0.227429
$175$	−2.53590	−0.191696
$176$	1.26795	0.0955753
$177$	13.8564	1.04151
$178$	−9.46410	−0.709364
$179$	2.19615	0.164148	0.0820741	−	0.996626i	$-0.473846\pi$
$179$	2.19615	0.164148	0.0820741	+	0.996626i	$0.473846\pi$
$180$	1.73205	0.129099
$181$	19.5885	1.45600	0.727999	−	0.685578i	$-0.240450\pi$
$181$	19.5885	1.45600	0.727999	+	0.685578i	$0.240450\pi$
$182$	0	0
$183$	−15.1962	−1.12333
$184$	8.19615	0.604228
$185$	5.19615	0.382029
$186$	9.46410	0.693942
$187$	6.58846	0.481796
$188$	−4.73205	−0.345120
$189$	−1.26795	−0.0922297
$190$	−8.19615	−0.594611
$191$	−20.7846	−1.50392	−0.751961	−	0.659208i	$-0.770892\pi$
$191$	−20.7846	−1.50392	−0.751961	+	0.659208i	$0.770892\pi$
$192$	−1.00000	−0.0721688
$193$	−23.1962	−1.66970	−0.834848	−	0.550481i	$-0.814444\pi$
$193$	−23.1962	−1.66970	−0.834848	+	0.550481i	$0.814444\pi$
$194$	−6.00000	−0.430775
$195$	0	0
$196$	−5.39230	−0.385165
$197$	−6.92820	−0.493614	−0.246807	−	0.969065i	$-0.579381\pi$
$197$	−6.92820	−0.493614	−0.246807	+	0.969065i	$0.579381\pi$
$198$	−1.26795	−0.0901092
$199$	−22.5885	−1.60125	−0.800627	−	0.599164i	$-0.795500\pi$
$199$	−22.5885	−1.60125	−0.800627	+	0.599164i	$0.795500\pi$
$200$	2.00000	0.141421
$201$	−7.26795	−0.512642
$202$	−19.3923	−1.36444
$203$	−3.80385	−0.266978
$204$	−5.19615	−0.363803
$205$	11.1962	0.781973
$206$	−6.19615	−0.431706
$207$	−8.19615	−0.569672
$208$	0	0
$209$	6.00000	0.415029
$210$	2.19615	0.151549
$211$	−24.3923	−1.67924	−0.839618	−	0.543178i	$-0.817221\pi$
$211$	−24.3923	−1.67924	−0.839618	+	0.543178i	$0.817221\pi$
$212$	3.00000	0.206041
$213$	2.19615	0.150478
$214$	2.19615	0.150126
$215$	−7.26795	−0.495670
$216$	1.00000	0.0680414
$217$	12.0000	0.814613
$218$	4.39230	0.297484
$219$	−12.1244	−0.819288
$220$	2.19615	0.148065
$221$	0	0
$222$	3.00000	0.201347
$223$	−5.07180	−0.339633	−0.169816	−	0.985476i	$-0.554317\pi$
$223$	−5.07180	−0.339633	−0.169816	+	0.985476i	$0.554317\pi$
$224$	−1.26795	−0.0847184
$225$	−2.00000	−0.133333
$226$	−0.803848	−0.0534711
$227$	−20.1962	−1.34047	−0.670233	−	0.742151i	$-0.733806\pi$
$227$	−20.1962	−1.34047	−0.670233	+	0.742151i	$0.733806\pi$
$228$	−4.73205	−0.313388
$229$	−7.85641	−0.519166	−0.259583	−	0.965721i	$-0.583585\pi$
$229$	−7.85641	−0.519166	−0.259583	+	0.965721i	$0.583585\pi$
$230$	14.1962	0.936067
$231$	−1.60770	−0.105779
$232$	3.00000	0.196960
$233$	−18.0000	−1.17922	−0.589610	−	0.807688i	$-0.700718\pi$
$233$	−18.0000	−1.17922	−0.589610	+	0.807688i	$0.700718\pi$
$234$	0	0
$235$	−8.19615	−0.534658
$236$	−13.8564	−0.901975
$237$	−8.39230	−0.545139
$238$	−6.58846	−0.427066
$239$	6.58846	0.426172	0.213086	−	0.977033i	$-0.431649\pi$
$239$	6.58846	0.426172	0.213086	+	0.977033i	$0.431649\pi$
$240$	−1.73205	−0.111803
$241$	11.1962	0.721208	0.360604	−	0.932719i	$-0.382571\pi$
$241$	11.1962	0.721208	0.360604	+	0.932719i	$0.382571\pi$
$242$	9.39230	0.603760
$243$	−1.00000	−0.0641500
$244$	15.1962	0.972834
$245$	−9.33975	−0.596694
$246$	6.46410	0.412136
$247$	0	0
$248$	−9.46410	−0.600971
$249$	−5.66025	−0.358704
$250$	12.1244	0.766812
$251$	16.3923	1.03467	0.517337	−	0.855782i	$-0.326924\pi$
$251$	16.3923	1.03467	0.517337	+	0.855782i	$0.326924\pi$
$252$	1.26795	0.0798733
$253$	−10.3923	−0.653359
$254$	4.00000	0.250982
$255$	−9.00000	−0.563602
$256$	1.00000	0.0625000
$257$	23.1962	1.44694	0.723468	−	0.690358i	$-0.242547\pi$
$257$	23.1962	1.44694	0.723468	+	0.690358i	$0.242547\pi$
$258$	−4.19615	−0.261241
$259$	3.80385	0.236360
$260$	0	0
$261$	−3.00000	−0.185695
$262$	4.39230	0.271357
$263$	8.19615	0.505396	0.252698	−	0.967545i	$-0.418682\pi$
$263$	8.19615	0.505396	0.252698	+	0.967545i	$0.418682\pi$
$264$	1.26795	0.0780369
$265$	5.19615	0.319197
$266$	−6.00000	−0.367884
$267$	−9.46410	−0.579194
$268$	7.26795	0.443961
$269$	−7.60770	−0.463849	−0.231925	−	0.972734i	$-0.574502\pi$
$269$	−7.60770	−0.463849	−0.231925	+	0.972734i	$0.574502\pi$
$270$	1.73205	0.105409
$271$	0	0		−	1.00000i	$-0.5\pi$
$271$	0	0			1.00000i	$0.5\pi$
$272$	5.19615	0.315063
$273$	0	0
$274$	9.00000	0.543710
$275$	−2.53590	−0.152920
$276$	8.19615	0.493350
$277$	4.80385	0.288635	0.144318	−	0.989531i	$-0.453901\pi$
$277$	4.80385	0.288635	0.144318	+	0.989531i	$0.453901\pi$
$278$	4.00000	0.239904
$279$	9.46410	0.566601
$280$	−2.19615	−0.131245
$281$	17.5359	1.04610	0.523052	−	0.852301i	$-0.324793\pi$
$281$	17.5359	1.04610	0.523052	+	0.852301i	$0.324793\pi$
$282$	−4.73205	−0.281790
$283$	−19.8038	−1.17722	−0.588608	−	0.808418i	$-0.700324\pi$
$283$	−19.8038	−1.17722	−0.588608	+	0.808418i	$0.700324\pi$
$284$	−2.19615	−0.130318
$285$	−8.19615	−0.485498
$286$	0	0
$287$	8.19615	0.483804
$288$	−1.00000	−0.0589256
$289$	10.0000	0.588235
$290$	5.19615	0.305129
$291$	−6.00000	−0.351726
$292$	12.1244	0.709524
$293$	2.66025	0.155414	0.0777069	−	0.996976i	$-0.475240\pi$
$293$	2.66025	0.155414	0.0777069	+	0.996976i	$0.475240\pi$
$294$	−5.39230	−0.314486
$295$	−24.0000	−1.39733
$296$	−3.00000	−0.174371
$297$	−1.26795	−0.0735739
$298$	−6.12436	−0.354774
$299$	0	0
$300$	2.00000	0.115470
$301$	−5.32051	−0.306669
$302$	−10.7321	−0.617560
$303$	−19.3923	−1.11406
$304$	4.73205	0.271402
$305$	26.3205	1.50711
$306$	−5.19615	−0.297044
$307$	7.26795	0.414804	0.207402	−	0.978256i	$-0.433499\pi$
$307$	7.26795	0.414804	0.207402	+	0.978256i	$0.433499\pi$
$308$	1.60770	0.0916069
$309$	−6.19615	−0.352487
$310$	−16.3923	−0.931020
$311$	−8.19615	−0.464761	−0.232381	−	0.972625i	$-0.574651\pi$
$311$	−8.19615	−0.464761	−0.232381	+	0.972625i	$0.574651\pi$
$312$	0	0
$313$	−3.60770	−0.203919	−0.101959	−	0.994789i	$-0.532511\pi$
$313$	−3.60770	−0.203919	−0.101959	+	0.994789i	$0.532511\pi$
$314$	−7.19615	−0.406102
$315$	2.19615	0.123739
$316$	8.39230	0.472104
$317$	−18.1244	−1.01797	−0.508983	−	0.860777i	$-0.669978\pi$
$317$	−18.1244	−1.01797	−0.508983	+	0.860777i	$0.669978\pi$
$318$	3.00000	0.168232
$319$	−3.80385	−0.212975
$320$	1.73205	0.0968246
$321$	2.19615	0.122577
$322$	10.3923	0.579141
$323$	24.5885	1.36814
$324$	1.00000	0.0555556
$325$	0	0
$326$	−2.53590	−0.140450
$327$	4.39230	0.242895
$328$	−6.46410	−0.356920
$329$	−6.00000	−0.330791
$330$	2.19615	0.120894
$331$	12.0000	0.659580	0.329790	−	0.944054i	$-0.393022\pi$
$331$	12.0000	0.659580	0.329790	+	0.944054i	$0.393022\pi$
$332$	5.66025	0.310647
$333$	3.00000	0.164399
$334$	9.46410	0.517853
$335$	12.5885	0.687781
$336$	−1.26795	−0.0691723
$337$	−31.0000	−1.68868	−0.844339	−	0.535810i	$-0.820006\pi$
$337$	−31.0000	−1.68868	−0.844339	+	0.535810i	$0.820006\pi$
$338$	0	0
$339$	−0.803848	−0.0436590
$340$	9.00000	0.488094
$341$	12.0000	0.649836
$342$	−4.73205	−0.255880
$343$	−15.7128	−0.848412
$344$	4.19615	0.226241
$345$	14.1962	0.764295
$346$	4.39230	0.236132
$347$	18.5885	0.997881	0.498940	−	0.866636i	$-0.333723\pi$
$347$	18.5885	0.997881	0.498940	+	0.866636i	$0.333723\pi$
$348$	3.00000	0.160817
$349$	9.46410	0.506602	0.253301	−	0.967388i	$-0.418484\pi$
$349$	9.46410	0.506602	0.253301	+	0.967388i	$0.418484\pi$
$350$	2.53590	0.135549
$351$	0	0
$352$	−1.26795	−0.0675819
$353$	−35.7846	−1.90462	−0.952311	−	0.305128i	$-0.901301\pi$
$353$	−35.7846	−1.90462	−0.952311	+	0.305128i	$0.901301\pi$
$354$	−13.8564	−0.736460
$355$	−3.80385	−0.201887
$356$	9.46410	0.501596
$357$	−6.58846	−0.348698
$358$	−2.19615	−0.116070
$359$	−16.0526	−0.847222	−0.423611	−	0.905844i	$-0.639238\pi$
$359$	−16.0526	−0.847222	−0.423611	+	0.905844i	$0.639238\pi$
$360$	−1.73205	−0.0912871
$361$	3.39230	0.178542
$362$	−19.5885	−1.02955
$363$	9.39230	0.492968
$364$	0	0
$365$	21.0000	1.09919
$366$	15.1962	0.794316
$367$	−13.8038	−0.720555	−0.360277	−	0.932845i	$-0.617318\pi$
$367$	−13.8038	−0.720555	−0.360277	+	0.932845i	$0.617318\pi$
$368$	−8.19615	−0.427254
$369$	6.46410	0.336508
$370$	−5.19615	−0.270135
$371$	3.80385	0.197486
$372$	−9.46410	−0.490691
$373$	−27.9808	−1.44879	−0.724394	−	0.689386i	$-0.757881\pi$
$373$	−27.9808	−1.44879	−0.724394	+	0.689386i	$0.757881\pi$
$374$	−6.58846	−0.340681
$375$	12.1244	0.626099
$376$	4.73205	0.244037
$377$	0	0
$378$	1.26795	0.0652163
$379$	30.2487	1.55377	0.776886	−	0.629641i	$-0.216798\pi$
$379$	30.2487	1.55377	0.776886	+	0.629641i	$0.216798\pi$
$380$	8.19615	0.420454
$381$	4.00000	0.204926
$382$	20.7846	1.06343
$383$	−23.3205	−1.19162	−0.595811	−	0.803125i	$-0.703169\pi$
$383$	−23.3205	−1.19162	−0.595811	+	0.803125i	$0.703169\pi$
$384$	1.00000	0.0510310
$385$	2.78461	0.141917
$386$	23.1962	1.18065
$387$	−4.19615	−0.213302
$388$	6.00000	0.304604
$389$	7.39230	0.374805	0.187402	−	0.982283i	$-0.439993\pi$
$389$	7.39230	0.374805	0.187402	+	0.982283i	$0.439993\pi$
$390$	0	0
$391$	−42.5885	−2.15379
$392$	5.39230	0.272353
$393$	4.39230	0.221562
$394$	6.92820	0.349038
$395$	14.5359	0.731380
$396$	1.26795	0.0637168
$397$	4.39230	0.220443	0.110222	−	0.993907i	$-0.464844\pi$
$397$	4.39230	0.220443	0.110222	+	0.993907i	$0.464844\pi$
$398$	22.5885	1.13226
$399$	−6.00000	−0.300376
$400$	−2.00000	−0.100000
$401$	21.0000	1.04869	0.524345	−	0.851506i	$-0.324310\pi$
$401$	21.0000	1.04869	0.524345	+	0.851506i	$0.324310\pi$
$402$	7.26795	0.362492
$403$	0	0
$404$	19.3923	0.964803
$405$	1.73205	0.0860663
$406$	3.80385	0.188782
$407$	3.80385	0.188550
$408$	5.19615	0.257248
$409$	−20.6603	−1.02158	−0.510792	−	0.859704i	$-0.670648\pi$
$409$	−20.6603	−1.02158	−0.510792	+	0.859704i	$0.670648\pi$
$410$	−11.1962	−0.552939
$411$	9.00000	0.443937
$412$	6.19615	0.305263
$413$	−17.5692	−0.864525
$414$	8.19615	0.402819
$415$	9.80385	0.481252
$416$	0	0
$417$	4.00000	0.195881
$418$	−6.00000	−0.293470
$419$	−4.39230	−0.214578	−0.107289	−	0.994228i	$-0.534217\pi$
$419$	−4.39230	−0.214578	−0.107289	+	0.994228i	$0.534217\pi$
$420$	−2.19615	−0.107161
$421$	−6.46410	−0.315041	−0.157521	−	0.987516i	$-0.550350\pi$
$421$	−6.46410	−0.315041	−0.157521	+	0.987516i	$0.550350\pi$
$422$	24.3923	1.18740
$423$	−4.73205	−0.230080
$424$	−3.00000	−0.145693
$425$	−10.3923	−0.504101
$426$	−2.19615	−0.106404
$427$	19.2679	0.932441
$428$	−2.19615	−0.106155
$429$	0	0
$430$	7.26795	0.350492
$431$	38.1962	1.83984	0.919922	−	0.392101i	$-0.128252\pi$
$431$	38.1962	1.83984	0.919922	+	0.392101i	$0.128252\pi$
$432$	−1.00000	−0.0481125
$433$	7.78461	0.374104	0.187052	−	0.982350i	$-0.440107\pi$
$433$	7.78461	0.374104	0.187052	+	0.982350i	$0.440107\pi$
$434$	−12.0000	−0.576018
$435$	5.19615	0.249136
$436$	−4.39230	−0.210353
$437$	−38.7846	−1.85532
$438$	12.1244	0.579324
$439$	−14.5885	−0.696269	−0.348135	−	0.937445i	$-0.613185\pi$
$439$	−14.5885	−0.696269	−0.348135	+	0.937445i	$0.613185\pi$
$440$	−2.19615	−0.104697
$441$	−5.39230	−0.256776
$442$	0	0
$443$	16.3923	0.778822	0.389411	−	0.921064i	$-0.372679\pi$
$443$	16.3923	0.778822	0.389411	+	0.921064i	$0.372679\pi$
$444$	−3.00000	−0.142374
$445$	16.3923	0.777070
$446$	5.07180	0.240157
$447$	−6.12436	−0.289672
$448$	1.26795	0.0599050
$449$	26.5359	1.25231	0.626153	−	0.779700i	$-0.284628\pi$
$449$	26.5359	1.25231	0.626153	+	0.779700i	$0.284628\pi$
$450$	2.00000	0.0942809
$451$	8.19615	0.385942
$452$	0.803848	0.0378098
$453$	−10.7321	−0.504236
$454$	20.1962	0.947852
$455$	0	0
$456$	4.73205	0.221599
$457$	−31.9808	−1.49600	−0.747998	−	0.663700i	$-0.768985\pi$
$457$	−31.9808	−1.49600	−0.747998	+	0.663700i	$0.768985\pi$
$458$	7.85641	0.367106
$459$	−5.19615	−0.242536
$460$	−14.1962	−0.661899
$461$	31.9808	1.48949	0.744746	−	0.667348i	$-0.232570\pi$
$461$	31.9808	1.48949	0.744746	+	0.667348i	$0.232570\pi$
$462$	1.60770	0.0747967
$463$	−15.8038	−0.734467	−0.367234	−	0.930129i	$-0.619695\pi$
$463$	−15.8038	−0.734467	−0.367234	+	0.930129i	$0.619695\pi$
$464$	−3.00000	−0.139272
$465$	−16.3923	−0.760175
$466$	18.0000	0.833834
$467$	5.41154	0.250416	0.125208	−	0.992130i	$-0.460040\pi$
$467$	5.41154	0.250416	0.125208	+	0.992130i	$0.460040\pi$
$468$	0	0
$469$	9.21539	0.425527
$470$	8.19615	0.378060
$471$	−7.19615	−0.331581
$472$	13.8564	0.637793
$473$	−5.32051	−0.244637
$474$	8.39230	0.385471
$475$	−9.46410	−0.434243
$476$	6.58846	0.301981
$477$	3.00000	0.137361
$478$	−6.58846	−0.301349
$479$	−0.679492	−0.0310468	−0.0155234	−	0.999880i	$-0.504941\pi$
$479$	−0.679492	−0.0310468	−0.0155234	+	0.999880i	$0.504941\pi$
$480$	1.73205	0.0790569
$481$	0	0
$482$	−11.1962	−0.509971
$483$	10.3923	0.472866
$484$	−9.39230	−0.426923
$485$	10.3923	0.471890
$486$	1.00000	0.0453609
$487$	−15.1244	−0.685350	−0.342675	−	0.939454i	$-0.611333\pi$
$487$	−15.1244	−0.685350	−0.342675	+	0.939454i	$0.611333\pi$
$488$	−15.1962	−0.687897
$489$	−2.53590	−0.114677
$490$	9.33975	0.421927
$491$	−30.5885	−1.38044	−0.690219	−	0.723601i	$-0.742486\pi$
$491$	−30.5885	−1.38044	−0.690219	+	0.723601i	$0.742486\pi$
$492$	−6.46410	−0.291424
$493$	−15.5885	−0.702069
$494$	0	0
$495$	2.19615	0.0987097
$496$	9.46410	0.424951
$497$	−2.78461	−0.124907
$498$	5.66025	0.253642
$499$	0	0		−	1.00000i	$-0.5\pi$
$499$	0	0			1.00000i	$0.5\pi$
$500$	−12.1244	−0.542218
$501$	9.46410	0.422825
$502$	−16.3923	−0.731624
$503$	12.5885	0.561292	0.280646	−	0.959811i	$-0.409451\pi$
$503$	12.5885	0.561292	0.280646	+	0.959811i	$0.409451\pi$
$504$	−1.26795	−0.0564789
$505$	33.5885	1.49467
$506$	10.3923	0.461994
$507$	0	0
$508$	−4.00000	−0.177471
$509$	26.6603	1.18169	0.590847	−	0.806783i	$-0.298793\pi$
$509$	26.6603	1.18169	0.590847	+	0.806783i	$0.298793\pi$
$510$	9.00000	0.398527
$511$	15.3731	0.680064
$512$	−1.00000	−0.0441942
$513$	−4.73205	−0.208925
$514$	−23.1962	−1.02314
$515$	10.7321	0.472911
$516$	4.19615	0.184725
$517$	−6.00000	−0.263880
$518$	−3.80385	−0.167131
$519$	4.39230	0.192801
$520$	0	0
$521$	−29.1962	−1.27911	−0.639553	−	0.768747i	$-0.720881\pi$
$521$	−29.1962	−1.27911	−0.639553	+	0.768747i	$0.720881\pi$
$522$	3.00000	0.131306
$523$	32.5885	1.42499	0.712497	−	0.701675i	$-0.247564\pi$
$523$	32.5885	1.42499	0.712497	+	0.701675i	$0.247564\pi$
$524$	−4.39230	−0.191879
$525$	2.53590	0.110676
$526$	−8.19615	−0.357369
$527$	49.1769	2.14218
$528$	−1.26795	−0.0551804
$529$	44.1769	1.92074
$530$	−5.19615	−0.225706
$531$	−13.8564	−0.601317
$532$	6.00000	0.260133
$533$	0	0
$534$	9.46410	0.409552
$535$	−3.80385	−0.164455
$536$	−7.26795	−0.313928
$537$	−2.19615	−0.0947710
$538$	7.60770	0.327991
$539$	−6.83717	−0.294498
$540$	−1.73205	−0.0745356
$541$	−10.8564	−0.466753	−0.233377	−	0.972386i	$-0.574978\pi$
$541$	−10.8564	−0.466753	−0.233377	+	0.972386i	$0.574978\pi$
$542$	0	0
$543$	−19.5885	−0.840621
$544$	−5.19615	−0.222783
$545$	−7.60770	−0.325878
$546$	0	0
$547$	4.19615	0.179415	0.0897073	−	0.995968i	$-0.471407\pi$
$547$	4.19615	0.179415	0.0897073	+	0.995968i	$0.471407\pi$
$548$	−9.00000	−0.384461
$549$	15.1962	0.648556
$550$	2.53590	0.108131
$551$	−14.1962	−0.604776
$552$	−8.19615	−0.348851
$553$	10.6410	0.452502
$554$	−4.80385	−0.204096
$555$	−5.19615	−0.220564
$556$	−4.00000	−0.169638
$557$	25.7321	1.09030	0.545151	−	0.838338i	$-0.316472\pi$
$557$	25.7321	1.09030	0.545151	+	0.838338i	$0.316472\pi$
$558$	−9.46410	−0.400647
$559$	0	0
$560$	2.19615	0.0928044
$561$	−6.58846	−0.278165
$562$	−17.5359	−0.739707
$563$	−32.7846	−1.38171	−0.690853	−	0.722995i	$-0.742765\pi$
$563$	−32.7846	−1.38171	−0.690853	+	0.722995i	$0.742765\pi$
$564$	4.73205	0.199255
$565$	1.39230	0.0585747
$566$	19.8038	0.832418
$567$	1.26795	0.0532489
$568$	2.19615	0.0921485
$569$	8.78461	0.368270	0.184135	−	0.982901i	$-0.441052\pi$
$569$	8.78461	0.368270	0.184135	+	0.982901i	$0.441052\pi$
$570$	8.19615	0.343299
$571$	−24.1962	−1.01258	−0.506289	−	0.862364i	$-0.668983\pi$
$571$	−24.1962	−1.01258	−0.506289	+	0.862364i	$0.668983\pi$
$572$	0	0
$573$	20.7846	0.868290
$574$	−8.19615	−0.342101
$575$	16.3923	0.683606
$576$	1.00000	0.0416667
$577$	−19.7321	−0.821456	−0.410728	−	0.911758i	$-0.634725\pi$
$577$	−19.7321	−0.821456	−0.410728	+	0.911758i	$0.634725\pi$
$578$	−10.0000	−0.415945
$579$	23.1962	0.963999
$580$	−5.19615	−0.215758
$581$	7.17691	0.297749
$582$	6.00000	0.248708
$583$	3.80385	0.157539
$584$	−12.1244	−0.501709
$585$	0	0
$586$	−2.66025	−0.109894
$587$	0	0		−	1.00000i	$-0.5\pi$
$587$	0	0			1.00000i	$0.5\pi$
$588$	5.39230	0.222375
$589$	44.7846	1.84532
$590$	24.0000	0.988064
$591$	6.92820	0.284988
$592$	3.00000	0.123299
$593$	−19.1436	−0.786133	−0.393067	−	0.919510i	$-0.628586\pi$
$593$	−19.1436	−0.786133	−0.393067	+	0.919510i	$0.628586\pi$
$594$	1.26795	0.0520246
$595$	11.4115	0.467828
$596$	6.12436	0.250863
$597$	22.5885	0.924484
$598$	0	0
$599$	16.3923	0.669771	0.334886	−	0.942259i	$-0.391302\pi$
$599$	16.3923	0.669771	0.334886	+	0.942259i	$0.391302\pi$
$600$	−2.00000	−0.0816497
$601$	−19.7846	−0.807031	−0.403516	−	0.914973i	$-0.632212\pi$
$601$	−19.7846	−0.807031	−0.403516	+	0.914973i	$0.632212\pi$
$602$	5.32051	0.216848
$603$	7.26795	0.295974
$604$	10.7321	0.436681
$605$	−16.2679	−0.661386
$606$	19.3923	0.787759
$607$	−7.21539	−0.292864	−0.146432	−	0.989221i	$-0.546779\pi$
$607$	−7.21539	−0.292864	−0.146432	+	0.989221i	$0.546779\pi$
$608$	−4.73205	−0.191910
$609$	3.80385	0.154140
$610$	−26.3205	−1.06569
$611$	0	0
$612$	5.19615	0.210042
$613$	−13.1436	−0.530865	−0.265432	−	0.964129i	$-0.585515\pi$
$613$	−13.1436	−0.530865	−0.265432	+	0.964129i	$0.585515\pi$
$614$	−7.26795	−0.293311
$615$	−11.1962	−0.451472
$616$	−1.60770	−0.0647759
$617$	31.3923	1.26381	0.631903	−	0.775047i	$-0.282274\pi$
$617$	31.3923	1.26381	0.631903	+	0.775047i	$0.282274\pi$
$618$	6.19615	0.249246
$619$	−28.3923	−1.14118	−0.570592	−	0.821234i	$-0.693286\pi$
$619$	−28.3923	−1.14118	−0.570592	+	0.821234i	$0.693286\pi$
$620$	16.3923	0.658331
$621$	8.19615	0.328900
$622$	8.19615	0.328636
$623$	12.0000	0.480770
$624$	0	0
$625$	−11.0000	−0.440000
$626$	3.60770	0.144192
$627$	−6.00000	−0.239617
$628$	7.19615	0.287158
$629$	15.5885	0.621552
$630$	−2.19615	−0.0874968
$631$	−1.85641	−0.0739024	−0.0369512	−	0.999317i	$-0.511765\pi$
$631$	−1.85641	−0.0739024	−0.0369512	+	0.999317i	$0.511765\pi$
$632$	−8.39230	−0.333828
$633$	24.3923	0.969507
$634$	18.1244	0.719810
$635$	−6.92820	−0.274937
$636$	−3.00000	−0.118958
$637$	0	0
$638$	3.80385	0.150596
$639$	−2.19615	−0.0868784
$640$	−1.73205	−0.0684653
$641$	−41.1962	−1.62715	−0.813575	−	0.581460i	$-0.802482\pi$
$641$	−41.1962	−1.62715	−0.813575	+	0.581460i	$0.802482\pi$
$642$	−2.19615	−0.0866752
$643$	27.7128	1.09289	0.546443	−	0.837496i	$-0.315981\pi$
$643$	27.7128	1.09289	0.546443	+	0.837496i	$0.315981\pi$
$644$	−10.3923	−0.409514
$645$	7.26795	0.286175
$646$	−24.5885	−0.967420
$647$	−49.1769	−1.93334	−0.966672	−	0.256018i	$-0.917589\pi$
$647$	−49.1769	−1.93334	−0.966672	+	0.256018i	$0.917589\pi$
$648$	−1.00000	−0.0392837
$649$	−17.5692	−0.689652
$650$	0	0
$651$	−12.0000	−0.470317
$652$	2.53590	0.0993134
$653$	13.1769	0.515653	0.257826	−	0.966191i	$-0.416994\pi$
$653$	13.1769	0.515653	0.257826	+	0.966191i	$0.416994\pi$
$654$	−4.39230	−0.171753
$655$	−7.60770	−0.297257
$656$	6.46410	0.252381
$657$	12.1244	0.473016
$658$	6.00000	0.233904
$659$	−37.1769	−1.44821	−0.724103	−	0.689691i	$-0.757746\pi$
$659$	−37.1769	−1.44821	−0.724103	+	0.689691i	$0.757746\pi$
$660$	−2.19615	−0.0854851
$661$	9.00000	0.350059	0.175030	−	0.984563i	$-0.443998\pi$
$661$	9.00000	0.350059	0.175030	+	0.984563i	$0.443998\pi$
$662$	−12.0000	−0.466393
$663$	0	0
$664$	−5.66025	−0.219660
$665$	10.3923	0.402996
$666$	−3.00000	−0.116248
$667$	24.5885	0.952069
$668$	−9.46410	−0.366177
$669$	5.07180	0.196087
$670$	−12.5885	−0.486335
$671$	19.2679	0.743831
$672$	1.26795	0.0489122
$673$	1.00000	0.0385472	0.0192736	−	0.999814i	$-0.493865\pi$
$673$	1.00000	0.0385472	0.0192736	+	0.999814i	$0.493865\pi$
$674$	31.0000	1.19408
$675$	2.00000	0.0769800
$676$	0	0
$677$	−16.3923	−0.630007	−0.315004	−	0.949090i	$-0.602006\pi$
$677$	−16.3923	−0.630007	−0.315004	+	0.949090i	$0.602006\pi$
$678$	0.803848	0.0308716
$679$	7.60770	0.291957
$680$	−9.00000	−0.345134
$681$	20.1962	0.773918
$682$	−12.0000	−0.459504
$683$	−27.7128	−1.06040	−0.530201	−	0.847872i	$-0.677883\pi$
$683$	−27.7128	−1.06040	−0.530201	+	0.847872i	$0.677883\pi$
$684$	4.73205	0.180934
$685$	−15.5885	−0.595604
$686$	15.7128	0.599918
$687$	7.85641	0.299741
$688$	−4.19615	−0.159977
$689$	0	0
$690$	−14.1962	−0.540438
$691$	25.5167	0.970700	0.485350	−	0.874320i	$-0.338692\pi$
$691$	25.5167	0.970700	0.485350	+	0.874320i	$0.338692\pi$
$692$	−4.39230	−0.166970
$693$	1.60770	0.0610713
$694$	−18.5885	−0.705608
$695$	−6.92820	−0.262802
$696$	−3.00000	−0.113715
$697$	33.5885	1.27225
$698$	−9.46410	−0.358222
$699$	18.0000	0.680823
$700$	−2.53590	−0.0958479
$701$	−16.3923	−0.619129	−0.309564	−	0.950878i	$-0.600183\pi$
$701$	−16.3923	−0.619129	−0.309564	+	0.950878i	$0.600183\pi$
$702$	0	0
$703$	14.1962	0.535418
$704$	1.26795	0.0477876
$705$	8.19615	0.308685
$706$	35.7846	1.34677
$707$	24.5885	0.924744
$708$	13.8564	0.520756
$709$	−45.2487	−1.69935	−0.849676	−	0.527306i	$-0.823202\pi$
$709$	−45.2487	−1.69935	−0.849676	+	0.527306i	$0.823202\pi$
$710$	3.80385	0.142756
$711$	8.39230	0.314736
$712$	−9.46410	−0.354682
$713$	−77.5692	−2.90499
$714$	6.58846	0.246567
$715$	0	0
$716$	2.19615	0.0820741
$717$	−6.58846	−0.246050
$718$	16.0526	0.599076
$719$	31.6077	1.17877	0.589384	−	0.807853i	$-0.299370\pi$
$719$	31.6077	1.17877	0.589384	+	0.807853i	$0.299370\pi$
$720$	1.73205	0.0645497
$721$	7.85641	0.292588
$722$	−3.39230	−0.126249
$723$	−11.1962	−0.416389
$724$	19.5885	0.727999
$725$	6.00000	0.222834
$726$	−9.39230	−0.348581
$727$	−13.8038	−0.511956	−0.255978	−	0.966683i	$-0.582398\pi$
$727$	−13.8038	−0.511956	−0.255978	+	0.966683i	$0.582398\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−21.0000	−0.777245
$731$	−21.8038	−0.806444
$732$	−15.1962	−0.561666
$733$	20.3205	0.750555	0.375278	−	0.926912i	$-0.377547\pi$
$733$	20.3205	0.750555	0.375278	+	0.926912i	$0.377547\pi$
$734$	13.8038	0.509509
$735$	9.33975	0.344502
$736$	8.19615	0.302114
$737$	9.21539	0.339453
$738$	−6.46410	−0.237947
$739$	−5.07180	−0.186569	−0.0932845	−	0.995639i	$-0.529737\pi$
$739$	−5.07180	−0.186569	−0.0932845	+	0.995639i	$0.529737\pi$
$740$	5.19615	0.191014
$741$	0	0
$742$	−3.80385	−0.139644
$743$	−16.3923	−0.601375	−0.300688	−	0.953723i	$-0.597216\pi$
$743$	−16.3923	−0.601375	−0.300688	+	0.953723i	$0.597216\pi$
$744$	9.46410	0.346971
$745$	10.6077	0.388636
$746$	27.9808	1.02445
$747$	5.66025	0.207098
$748$	6.58846	0.240898
$749$	−2.78461	−0.101747
$750$	−12.1244	−0.442719
$751$	26.9808	0.984542	0.492271	−	0.870442i	$-0.336167\pi$
$751$	26.9808	0.984542	0.492271	+	0.870442i	$0.336167\pi$
$752$	−4.73205	−0.172560
$753$	−16.3923	−0.597369
$754$	0	0
$755$	18.5885	0.676503
$756$	−1.26795	−0.0461149
$757$	−22.7846	−0.828121	−0.414060	−	0.910249i	$-0.635890\pi$
$757$	−22.7846	−0.828121	−0.414060	+	0.910249i	$0.635890\pi$
$758$	−30.2487	−1.09868
$759$	10.3923	0.377217
$760$	−8.19615	−0.297306
$761$	16.3923	0.594221	0.297110	−	0.954843i	$-0.403977\pi$
$761$	16.3923	0.594221	0.297110	+	0.954843i	$0.403977\pi$
$762$	−4.00000	−0.144905
$763$	−5.56922	−0.201619
$764$	−20.7846	−0.751961
$765$	9.00000	0.325396
$766$	23.3205	0.842604
$767$	0	0
$768$	−1.00000	−0.0360844
$769$	−21.7128	−0.782984	−0.391492	−	0.920181i	$-0.628041\pi$
$769$	−21.7128	−0.782984	−0.391492	+	0.920181i	$0.628041\pi$
$770$	−2.78461	−0.100350
$771$	−23.1962	−0.835389
$772$	−23.1962	−0.834848
$773$	−9.21539	−0.331455	−0.165727	−	0.986172i	$-0.552997\pi$
$773$	−9.21539	−0.331455	−0.165727	+	0.986172i	$0.552997\pi$
$774$	4.19615	0.150828
$775$	−18.9282	−0.679921
$776$	−6.00000	−0.215387
$777$	−3.80385	−0.136462
$778$	−7.39230	−0.265027
$779$	30.5885	1.09595
$780$	0	0
$781$	−2.78461	−0.0996412
$782$	42.5885	1.52296
$783$	3.00000	0.107211
$784$	−5.39230	−0.192582
$785$	12.4641	0.444863
$786$	−4.39230	−0.156668
$787$	−21.4641	−0.765113	−0.382556	−	0.923932i	$-0.624956\pi$
$787$	−21.4641	−0.765113	−0.382556	+	0.923932i	$0.624956\pi$
$788$	−6.92820	−0.246807
$789$	−8.19615	−0.291791
$790$	−14.5359	−0.517164
$791$	1.01924	0.0362399
$792$	−1.26795	−0.0450546
$793$	0	0
$794$	−4.39230	−0.155877
$795$	−5.19615	−0.184289
$796$	−22.5885	−0.800627
$797$	6.00000	0.212531	0.106265	−	0.994338i	$-0.466111\pi$
$797$	6.00000	0.212531	0.106265	+	0.994338i	$0.466111\pi$
$798$	6.00000	0.212398
$799$	−24.5885	−0.869877
$800$	2.00000	0.0707107
$801$	9.46410	0.334398
$802$	−21.0000	−0.741536
$803$	15.3731	0.542504
$804$	−7.26795	−0.256321
$805$	−18.0000	−0.634417
$806$	0	0
$807$	7.60770	0.267804
$808$	−19.3923	−0.682219
$809$	−36.8038	−1.29395	−0.646977	−	0.762509i	$-0.723967\pi$
$809$	−36.8038	−1.29395	−0.646977	+	0.762509i	$0.723967\pi$
$810$	−1.73205	−0.0608581
$811$	−16.3923	−0.575612	−0.287806	−	0.957689i	$-0.592926\pi$
$811$	−16.3923	−0.575612	−0.287806	+	0.957689i	$0.592926\pi$
$812$	−3.80385	−0.133489
$813$	0	0
$814$	−3.80385	−0.133325
$815$	4.39230	0.153856
$816$	−5.19615	−0.181902
$817$	−19.8564	−0.694688
$818$	20.6603	0.722369
$819$	0	0
$820$	11.1962	0.390987
$821$	28.6410	0.999578	0.499789	−	0.866147i	$-0.333411\pi$
$821$	28.6410	0.999578	0.499789	+	0.866147i	$0.333411\pi$
$822$	−9.00000	−0.313911
$823$	−32.0000	−1.11545	−0.557725	−	0.830026i	$-0.688326\pi$
$823$	−32.0000	−1.11545	−0.557725	+	0.830026i	$0.688326\pi$
$824$	−6.19615	−0.215853
$825$	2.53590	0.0882886
$826$	17.5692	0.611311
$827$	44.1051	1.53369	0.766843	−	0.641835i	$-0.221827\pi$
$827$	44.1051	1.53369	0.766843	+	0.641835i	$0.221827\pi$
$828$	−8.19615	−0.284836
$829$	39.9808	1.38859	0.694295	−	0.719691i	$-0.255716\pi$
$829$	39.9808	1.38859	0.694295	+	0.719691i	$0.255716\pi$
$830$	−9.80385	−0.340297
$831$	−4.80385	−0.166644
$832$	0	0
$833$	−28.0192	−0.970809
$834$	−4.00000	−0.138509
$835$	−16.3923	−0.567279
$836$	6.00000	0.207514
$837$	−9.46410	−0.327127
$838$	4.39230	0.151730
$839$	−12.0000	−0.414286	−0.207143	−	0.978311i	$-0.566417\pi$
$839$	−12.0000	−0.414286	−0.207143	+	0.978311i	$0.566417\pi$
$840$	2.19615	0.0757745
$841$	−20.0000	−0.689655
$842$	6.46410	0.222768
$843$	−17.5359	−0.603968
$844$	−24.3923	−0.839618
$845$	0	0
$846$	4.73205	0.162691
$847$	−11.9090	−0.409197
$848$	3.00000	0.103020
$849$	19.8038	0.679666
$850$	10.3923	0.356453
$851$	−24.5885	−0.842881
$852$	2.19615	0.0752389
$853$	9.00000	0.308154	0.154077	−	0.988059i	$-0.450760\pi$
$853$	9.00000	0.308154	0.154077	+	0.988059i	$0.450760\pi$
$854$	−19.2679	−0.659336
$855$	8.19615	0.280302
$856$	2.19615	0.0750629
$857$	18.3731	0.627612	0.313806	−	0.949487i	$-0.398396\pi$
$857$	18.3731	0.627612	0.313806	+	0.949487i	$0.398396\pi$
$858$	0	0
$859$	−20.5885	−0.702469	−0.351235	−	0.936288i	$-0.614238\pi$
$859$	−20.5885	−0.702469	−0.351235	+	0.936288i	$0.614238\pi$
$860$	−7.26795	−0.247835
$861$	−8.19615	−0.279324
$862$	−38.1962	−1.30097
$863$	49.5167	1.68557	0.842783	−	0.538253i	$-0.180915\pi$
$863$	49.5167	1.68557	0.842783	+	0.538253i	$0.180915\pi$
$864$	1.00000	0.0340207
$865$	−7.60770	−0.258669
$866$	−7.78461	−0.264532
$867$	−10.0000	−0.339618
$868$	12.0000	0.407307
$869$	10.6410	0.360972
$870$	−5.19615	−0.176166
$871$	0	0
$872$	4.39230	0.148742
$873$	6.00000	0.203069
$874$	38.7846	1.31191
$875$	−15.3731	−0.519705
$876$	−12.1244	−0.409644
$877$	22.6077	0.763408	0.381704	−	0.924285i	$-0.375337\pi$
$877$	22.6077	0.763408	0.381704	+	0.924285i	$0.375337\pi$
$878$	14.5885	0.492337
$879$	−2.66025	−0.0897281
$880$	2.19615	0.0740323
$881$	−13.9808	−0.471024	−0.235512	−	0.971871i	$-0.575677\pi$
$881$	−13.9808	−0.471024	−0.235512	+	0.971871i	$0.575677\pi$
$882$	5.39230	0.181568
$883$	16.7846	0.564847	0.282424	−	0.959290i	$-0.408862\pi$
$883$	16.7846	0.564847	0.282424	+	0.959290i	$0.408862\pi$
$884$	0	0
$885$	24.0000	0.806751
$886$	−16.3923	−0.550710
$887$	48.0000	1.61168	0.805841	−	0.592132i	$-0.201714\pi$
$887$	48.0000	1.61168	0.805841	+	0.592132i	$0.201714\pi$
$888$	3.00000	0.100673
$889$	−5.07180	−0.170103
$890$	−16.3923	−0.549471
$891$	1.26795	0.0424779
$892$	−5.07180	−0.169816
$893$	−22.3923	−0.749330
$894$	6.12436	0.204829
$895$	3.80385	0.127149
$896$	−1.26795	−0.0423592
$897$	0	0
$898$	−26.5359	−0.885514
$899$	−28.3923	−0.946936
$900$	−2.00000	−0.0666667
$901$	15.5885	0.519327
$902$	−8.19615	−0.272902
$903$	5.32051	0.177055
$904$	−0.803848	−0.0267356
$905$	33.9282	1.12781
$906$	10.7321	0.356549
$907$	21.1769	0.703168	0.351584	−	0.936156i	$-0.385643\pi$
$907$	21.1769	0.703168	0.351584	+	0.936156i	$0.385643\pi$
$908$	−20.1962	−0.670233
$909$	19.3923	0.643202
$910$	0	0
$911$	−25.1769	−0.834148	−0.417074	−	0.908872i	$-0.636944\pi$
$911$	−25.1769	−0.834148	−0.417074	+	0.908872i	$0.636944\pi$
$912$	−4.73205	−0.156694
$913$	7.17691	0.237521
$914$	31.9808	1.05783
$915$	−26.3205	−0.870129
$916$	−7.85641	−0.259583
$917$	−5.56922	−0.183912
$918$	5.19615	0.171499
$919$	11.6077	0.382903	0.191451	−	0.981502i	$-0.438681\pi$
$919$	11.6077	0.382903	0.191451	+	0.981502i	$0.438681\pi$
$920$	14.1962	0.468033
$921$	−7.26795	−0.239487
$922$	−31.9808	−1.05323
$923$	0	0
$924$	−1.60770	−0.0528893
$925$	−6.00000	−0.197279
$926$	15.8038	0.519347
$927$	6.19615	0.203508
$928$	3.00000	0.0984798
$929$	−55.3923	−1.81736	−0.908681	−	0.417491i	$-0.862910\pi$
$929$	−55.3923	−1.81736	−0.908681	+	0.417491i	$0.862910\pi$
$930$	16.3923	0.537525
$931$	−25.5167	−0.836275
$932$	−18.0000	−0.589610
$933$	8.19615	0.268330
$934$	−5.41154	−0.177071
$935$	11.4115	0.373197
$936$	0	0
$937$	−15.3923	−0.502845	−0.251422	−	0.967877i	$-0.580898\pi$
$937$	−15.3923	−0.502845	−0.251422	+	0.967877i	$0.580898\pi$
$938$	−9.21539	−0.300893
$939$	3.60770	0.117733
$940$	−8.19615	−0.267329
$941$	−38.7846	−1.26434	−0.632171	−	0.774829i	$-0.717836\pi$
$941$	−38.7846	−1.26434	−0.632171	+	0.774829i	$0.717836\pi$
$942$	7.19615	0.234463
$943$	−52.9808	−1.72529
$944$	−13.8564	−0.450988
$945$	−2.19615	−0.0714408
$946$	5.32051	0.172985
$947$	−29.0718	−0.944706	−0.472353	−	0.881409i	$-0.656595\pi$
$947$	−29.0718	−0.944706	−0.472353	+	0.881409i	$0.656595\pi$
$948$	−8.39230	−0.272569
$949$	0	0
$950$	9.46410	0.307056
$951$	18.1244	0.587722
$952$	−6.58846	−0.213533
$953$	−24.0000	−0.777436	−0.388718	−	0.921357i	$-0.627082\pi$
$953$	−24.0000	−0.777436	−0.388718	+	0.921357i	$0.627082\pi$
$954$	−3.00000	−0.0971286
$955$	−36.0000	−1.16493
$956$	6.58846	0.213086
$957$	3.80385	0.122961
$958$	0.679492	0.0219534
$959$	−11.4115	−0.368498
$960$	−1.73205	−0.0559017
$961$	58.5692	1.88933
$962$	0	0
$963$	−2.19615	−0.0707700
$964$	11.1962	0.360604
$965$	−40.1769	−1.29334
$966$	−10.3923	−0.334367
$967$	−39.1244	−1.25815	−0.629077	−	0.777343i	$-0.716567\pi$
$967$	−39.1244	−1.25815	−0.629077	+	0.777343i	$0.716567\pi$
$968$	9.39230	0.301880
$969$	−24.5885	−0.789895
$970$	−10.3923	−0.333677
$971$	49.1769	1.57816	0.789081	−	0.614289i	$-0.210557\pi$
$971$	49.1769	1.57816	0.789081	+	0.614289i	$0.210557\pi$
$972$	−1.00000	−0.0320750
$973$	−5.07180	−0.162594
$974$	15.1244	0.484616
$975$	0	0
$976$	15.1962	0.486417
$977$	10.8564	0.347327	0.173664	−	0.984805i	$-0.444439\pi$
$977$	10.8564	0.347327	0.173664	+	0.984805i	$0.444439\pi$
$978$	2.53590	0.0810891
$979$	12.0000	0.383522
$980$	−9.33975	−0.298347
$981$	−4.39230	−0.140236
$982$	30.5885	0.976117
$983$	20.7846	0.662926	0.331463	−	0.943468i	$-0.392458\pi$
$983$	20.7846	0.662926	0.331463	+	0.943468i	$0.392458\pi$
$984$	6.46410	0.206068
$985$	−12.0000	−0.382352
$986$	15.5885	0.496438
$987$	6.00000	0.190982
$988$	0	0
$989$	34.3923	1.09361
$990$	−2.19615	−0.0697983
$991$	−43.3731	−1.37779	−0.688895	−	0.724861i	$-0.741904\pi$
$991$	−43.3731	−1.37779	−0.688895	+	0.724861i	$0.741904\pi$
$992$	−9.46410	−0.300486
$993$	−12.0000	−0.380808
$994$	2.78461	0.0883225
$995$	−39.1244	−1.24033
$996$	−5.66025	−0.179352
$997$	2.80385	0.0887987	0.0443994	−	0.999014i	$-0.485863\pi$
$997$	2.80385	0.0887987	0.0443994	+	0.999014i	$0.485863\pi$
$998$	0	0
$999$	−3.00000	−0.0949158

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1014.2.a.h.1.2		2
3.2	odd	2		3042.2.a.v.1.1		2
4.3	odd	2		8112.2.a.bq.1.2		2
13.2	odd	12		78.2.i.b.43.1	✓	4
13.3	even	3		1014.2.e.j.529.2		4
13.4	even	6		1014.2.e.h.991.1		4
13.5	odd	4		1014.2.b.d.337.3		4
13.6	odd	12		1014.2.i.f.361.2		4
13.7	odd	12		78.2.i.b.49.1	yes	4
13.8	odd	4		1014.2.b.d.337.2		4
13.9	even	3		1014.2.e.j.991.2		4
13.10	even	6		1014.2.e.h.529.1		4
13.11	odd	12		1014.2.i.f.823.2		4
13.12	even	2		1014.2.a.j.1.1		2
39.2	even	12		234.2.l.a.199.2		4
39.5	even	4		3042.2.b.l.1351.2		4
39.8	even	4		3042.2.b.l.1351.3		4
39.20	even	12		234.2.l.a.127.2		4
39.38	odd	2		3042.2.a.s.1.2		2
52.7	even	12		624.2.bv.d.49.1		4
52.15	even	12		624.2.bv.d.433.1		4
52.51	odd	2		8112.2.a.bx.1.1		2
65.2	even	12		1950.2.y.h.199.1		4
65.7	even	12		1950.2.y.a.49.2		4
65.28	even	12		1950.2.y.a.199.2		4
65.33	even	12		1950.2.y.h.49.1		4
65.54	odd	12		1950.2.bc.c.901.2		4
65.59	odd	12		1950.2.bc.c.751.2		4
156.59	odd	12		1872.2.by.k.1297.1		4
156.119	odd	12		1872.2.by.k.433.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.2.i.b.43.1	✓	4	13.2	odd	12
78.2.i.b.49.1	yes	4	13.7	odd	12
234.2.l.a.127.2		4	39.20	even	12
234.2.l.a.199.2		4	39.2	even	12
624.2.bv.d.49.1		4	52.7	even	12
624.2.bv.d.433.1		4	52.15	even	12
1014.2.a.h.1.2		2	1.1	even	1	trivial
1014.2.a.j.1.1		2	13.12	even	2
1014.2.b.d.337.2		4	13.8	odd	4
1014.2.b.d.337.3		4	13.5	odd	4
1014.2.e.h.529.1		4	13.10	even	6
1014.2.e.h.991.1		4	13.4	even	6
1014.2.e.j.529.2		4	13.3	even	3
1014.2.e.j.991.2		4	13.9	even	3
1014.2.i.f.361.2		4	13.6	odd	12
1014.2.i.f.823.2		4	13.11	odd	12
1872.2.by.k.433.1		4	156.119	odd	12
1872.2.by.k.1297.1		4	156.59	odd	12
1950.2.y.a.49.2		4	65.7	even	12
1950.2.y.a.199.2		4	65.28	even	12
1950.2.y.h.49.1		4	65.33	even	12
1950.2.y.h.199.1		4	65.2	even	12
1950.2.bc.c.751.2		4	65.59	odd	12
1950.2.bc.c.901.2		4	65.54	odd	12
3042.2.a.s.1.2		2	39.38	odd	2
3042.2.a.v.1.1		2	3.2	odd	2
3042.2.b.l.1351.2		4	39.5	even	4
3042.2.b.l.1351.3		4	39.8	even	4
8112.2.a.bq.1.2		2	4.3	odd	2
8112.2.a.bx.1.1		2	52.51	odd	2

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:	\( N \)	\(=\)	\( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1014.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.73205 q^{5} +1.00000 q^{6} +1.26795 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.73205 q^{5} +1.00000 q^{6} +1.26795 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.73205 q^{10} +1.26795 q^{11} -1.00000 q^{12} -1.26795 q^{14} -1.73205 q^{15} +1.00000 q^{16} +5.19615 q^{17} -1.00000 q^{18} +4.73205 q^{19} +1.73205 q^{20} -1.26795 q^{21} -1.26795 q^{22} -8.19615 q^{23} +1.00000 q^{24} -2.00000 q^{25} -1.00000 q^{27} +1.26795 q^{28} -3.00000 q^{29} +1.73205 q^{30} +9.46410 q^{31} -1.00000 q^{32} -1.26795 q^{33} -5.19615 q^{34} +2.19615 q^{35} +1.00000 q^{36} +3.00000 q^{37} -4.73205 q^{38} -1.73205 q^{40} +6.46410 q^{41} +1.26795 q^{42} -4.19615 q^{43} +1.26795 q^{44} +1.73205 q^{45} +8.19615 q^{46} -4.73205 q^{47} -1.00000 q^{48} -5.39230 q^{49} +2.00000 q^{50} -5.19615 q^{51} +3.00000 q^{53} +1.00000 q^{54} +2.19615 q^{55} -1.26795 q^{56} -4.73205 q^{57} +3.00000 q^{58} -13.8564 q^{59} -1.73205 q^{60} +15.1962 q^{61} -9.46410 q^{62} +1.26795 q^{63} +1.00000 q^{64} +1.26795 q^{66} +7.26795 q^{67} +5.19615 q^{68} +8.19615 q^{69} -2.19615 q^{70} -2.19615 q^{71} -1.00000 q^{72} +12.1244 q^{73} -3.00000 q^{74} +2.00000 q^{75} +4.73205 q^{76} +1.60770 q^{77} +8.39230 q^{79} +1.73205 q^{80} +1.00000 q^{81} -6.46410 q^{82} +5.66025 q^{83} -1.26795 q^{84} +9.00000 q^{85} +4.19615 q^{86} +3.00000 q^{87} -1.26795 q^{88} +9.46410 q^{89} -1.73205 q^{90} -8.19615 q^{92} -9.46410 q^{93} +4.73205 q^{94} +8.19615 q^{95} +1.00000 q^{96} +6.00000 q^{97} +5.39230 q^{98} +1.26795 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{6} + 6 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^6 + 6 * q^7 - 2 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{6} + 6 q^{7} - 2 q^{8} + 2 q^{9} + 6 q^{11} - 2 q^{12} - 6 q^{14} + 2 q^{16} - 2 q^{18} + 6 q^{19} - 6 q^{21} - 6 q^{22} - 6 q^{23} + 2 q^{24} - 4 q^{25} - 2 q^{27} + 6 q^{28} - 6 q^{29} + 12 q^{31} - 2 q^{32} - 6 q^{33} - 6 q^{35} + 2 q^{36} + 6 q^{37} - 6 q^{38} + 6 q^{41} + 6 q^{42} + 2 q^{43} + 6 q^{44} + 6 q^{46} - 6 q^{47} - 2 q^{48} + 10 q^{49} + 4 q^{50} + 6 q^{53} + 2 q^{54} - 6 q^{55} - 6 q^{56} - 6 q^{57} + 6 q^{58} + 20 q^{61} - 12 q^{62} + 6 q^{63} + 2 q^{64} + 6 q^{66} + 18 q^{67} + 6 q^{69} + 6 q^{70} + 6 q^{71} - 2 q^{72} - 6 q^{74} + 4 q^{75} + 6 q^{76} + 24 q^{77} - 4 q^{79} + 2 q^{81} - 6 q^{82} - 6 q^{83} - 6 q^{84} + 18 q^{85} - 2 q^{86} + 6 q^{87} - 6 q^{88} + 12 q^{89} - 6 q^{92} - 12 q^{93} + 6 q^{94} + 6 q^{95} + 2 q^{96} + 12 q^{97} - 10 q^{98} + 6 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^6 + 6 * q^7 - 2 * q^8 + 2 * q^9 + 6 * q^11 - 2 * q^12 - 6 * q^14 + 2 * q^16 - 2 * q^18 + 6 * q^19 - 6 * q^21 - 6 * q^22 - 6 * q^23 + 2 * q^24 - 4 * q^25 - 2 * q^27 + 6 * q^28 - 6 * q^29 + 12 * q^31 - 2 * q^32 - 6 * q^33 - 6 * q^35 + 2 * q^36 + 6 * q^37 - 6 * q^38 + 6 * q^41 + 6 * q^42 + 2 * q^43 + 6 * q^44 + 6 * q^46 - 6 * q^47 - 2 * q^48 + 10 * q^49 + 4 * q^50 + 6 * q^53 + 2 * q^54 - 6 * q^55 - 6 * q^56 - 6 * q^57 + 6 * q^58 + 20 * q^61 - 12 * q^62 + 6 * q^63 + 2 * q^64 + 6 * q^66 + 18 * q^67 + 6 * q^69 + 6 * q^70 + 6 * q^71 - 2 * q^72 - 6 * q^74 + 4 * q^75 + 6 * q^76 + 24 * q^77 - 4 * q^79 + 2 * q^81 - 6 * q^82 - 6 * q^83 - 6 * q^84 + 18 * q^85 - 2 * q^86 + 6 * q^87 - 6 * q^88 + 12 * q^89 - 6 * q^92 - 12 * q^93 + 6 * q^94 + 6 * q^95 + 2 * q^96 + 12 * q^97 - 10 * q^98 + 6 * q^99

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