LMFDB - Embedded newform 4026.2.a.w.1.2

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:	$6$
Coefficient field:	6.6.30998405.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 9x^{4} + 8x^{3} + 16x^{2} - 13x + 2 $ x^6 - x^5 - 9x^4 + 8x^3 + 16x^2 - 13x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$0.215842$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.40290 q^{5} +1.00000 q^{6} +2.64146 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.40290 q^{5} +1.00000 q^{6} +2.64146 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.40290 q^{10} +1.00000 q^{11} -1.00000 q^{12} -2.22074 q^{13} -2.64146 q^{14} +1.40290 q^{15} +1.00000 q^{16} -2.42561 q^{17} -1.00000 q^{18} +1.90697 q^{19} -1.40290 q^{20} -2.64146 q^{21} -1.00000 q^{22} -0.204870 q^{23} +1.00000 q^{24} -3.03186 q^{25} +2.22074 q^{26} -1.00000 q^{27} +2.64146 q^{28} +0.472061 q^{29} -1.40290 q^{30} +9.76569 q^{31} -1.00000 q^{32} -1.00000 q^{33} +2.42561 q^{34} -3.70571 q^{35} +1.00000 q^{36} -6.76367 q^{37} -1.90697 q^{38} +2.22074 q^{39} +1.40290 q^{40} -7.76093 q^{41} +2.64146 q^{42} -1.63963 q^{43} +1.00000 q^{44} -1.40290 q^{45} +0.204870 q^{46} +10.0230 q^{47} -1.00000 q^{48} -0.0227093 q^{49} +3.03186 q^{50} +2.42561 q^{51} -2.22074 q^{52} -9.17082 q^{53} +1.00000 q^{54} -1.40290 q^{55} -2.64146 q^{56} -1.90697 q^{57} -0.472061 q^{58} -10.6068 q^{59} +1.40290 q^{60} +1.00000 q^{61} -9.76569 q^{62} +2.64146 q^{63} +1.00000 q^{64} +3.11549 q^{65} +1.00000 q^{66} +6.95159 q^{67} -2.42561 q^{68} +0.204870 q^{69} +3.70571 q^{70} -7.05306 q^{71} -1.00000 q^{72} +13.5829 q^{73} +6.76367 q^{74} +3.03186 q^{75} +1.90697 q^{76} +2.64146 q^{77} -2.22074 q^{78} -11.7867 q^{79} -1.40290 q^{80} +1.00000 q^{81} +7.76093 q^{82} +11.9485 q^{83} -2.64146 q^{84} +3.40290 q^{85} +1.63963 q^{86} -0.472061 q^{87} -1.00000 q^{88} -17.0716 q^{89} +1.40290 q^{90} -5.86600 q^{91} -0.204870 q^{92} -9.76569 q^{93} -10.0230 q^{94} -2.67529 q^{95} +1.00000 q^{96} +3.02014 q^{97} +0.0227093 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} - 6 q^{3} + 6 q^{4} - q^{5} + 6 q^{6} + 5 q^{7} - 6 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q - 6 * q^2 - 6 * q^3 + 6 * q^4 - q^5 + 6 * q^6 + 5 * q^7 - 6 * q^8 + 6 * q^9	\( 6 q - 6 q^{2} - 6 q^{3} + 6 q^{4} - q^{5} + 6 q^{6} + 5 q^{7} - 6 q^{8} + 6 q^{9} + q^{10} + 6 q^{11} - 6 q^{12} + 2 q^{13} - 5 q^{14} + q^{15} + 6 q^{16} - 4 q^{17} - 6 q^{18} - 5 q^{19} - q^{20} - 5 q^{21} - 6 q^{22} - 6 q^{23} + 6 q^{24} - q^{25} - 2 q^{26} - 6 q^{27} + 5 q^{28} - 10 q^{29} - q^{30} - 15 q^{31} - 6 q^{32} - 6 q^{33} + 4 q^{34} - 21 q^{35} + 6 q^{36} - 3 q^{37} + 5 q^{38} - 2 q^{39} + q^{40} - 9 q^{41} + 5 q^{42} + 10 q^{43} + 6 q^{44} - q^{45} + 6 q^{46} - 14 q^{47} - 6 q^{48} + 3 q^{49} + q^{50} + 4 q^{51} + 2 q^{52} - 11 q^{53} + 6 q^{54} - q^{55} - 5 q^{56} + 5 q^{57} + 10 q^{58} - 20 q^{59} + q^{60} + 6 q^{61} + 15 q^{62} + 5 q^{63} + 6 q^{64} - 2 q^{65} + 6 q^{66} + 14 q^{67} - 4 q^{68} + 6 q^{69} + 21 q^{70} - 21 q^{71} - 6 q^{72} + 16 q^{73} + 3 q^{74} + q^{75} - 5 q^{76} + 5 q^{77} + 2 q^{78} - 6 q^{79} - q^{80} + 6 q^{81} + 9 q^{82} - 10 q^{83} - 5 q^{84} + 13 q^{85} - 10 q^{86} + 10 q^{87} - 6 q^{88} - 11 q^{89} + q^{90} - 21 q^{91} - 6 q^{92} + 15 q^{93} + 14 q^{94} + 9 q^{95} + 6 q^{96} + 2 q^{97} - 3 q^{98} + 6 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 - 6 * q^3 + 6 * q^4 - q^5 + 6 * q^6 + 5 * q^7 - 6 * q^8 + 6 * q^9 + q^10 + 6 * q^11 - 6 * q^12 + 2 * q^13 - 5 * q^14 + q^15 + 6 * q^16 - 4 * q^17 - 6 * q^18 - 5 * q^19 - q^20 - 5 * q^21 - 6 * q^22 - 6 * q^23 + 6 * q^24 - q^25 - 2 * q^26 - 6 * q^27 + 5 * q^28 - 10 * q^29 - q^30 - 15 * q^31 - 6 * q^32 - 6 * q^33 + 4 * q^34 - 21 * q^35 + 6 * q^36 - 3 * q^37 + 5 * q^38 - 2 * q^39 + q^40 - 9 * q^41 + 5 * q^42 + 10 * q^43 + 6 * q^44 - q^45 + 6 * q^46 - 14 * q^47 - 6 * q^48 + 3 * q^49 + q^50 + 4 * q^51 + 2 * q^52 - 11 * q^53 + 6 * q^54 - q^55 - 5 * q^56 + 5 * q^57 + 10 * q^58 - 20 * q^59 + q^60 + 6 * q^61 + 15 * q^62 + 5 * q^63 + 6 * q^64 - 2 * q^65 + 6 * q^66 + 14 * q^67 - 4 * q^68 + 6 * q^69 + 21 * q^70 - 21 * q^71 - 6 * q^72 + 16 * q^73 + 3 * q^74 + q^75 - 5 * q^76 + 5 * q^77 + 2 * q^78 - 6 * q^79 - q^80 + 6 * q^81 + 9 * q^82 - 10 * q^83 - 5 * q^84 + 13 * q^85 - 10 * q^86 + 10 * q^87 - 6 * q^88 - 11 * q^89 + q^90 - 21 * q^91 - 6 * q^92 + 15 * q^93 + 14 * q^94 + 9 * q^95 + 6 * q^96 + 2 * q^97 - 3 * 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
$5$	−1.40290	−0.627398	−0.313699	−	0.949522i	$-0.601568\pi$
$5$	−1.40290	−0.627398	−0.313699	+	0.949522i	$0.601568\pi$
$6$	1.00000	0.408248
$7$	2.64146	0.998377	0.499188	−	0.866494i	$-0.333632\pi$
$7$	2.64146	0.998377	0.499188	+	0.866494i	$0.333632\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	1.40290	0.443637
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.00000	−0.288675
$13$	−2.22074	−0.615924	−0.307962	−	0.951399i	$-0.599647\pi$
$13$	−2.22074	−0.615924	−0.307962	+	0.951399i	$0.599647\pi$
$14$	−2.64146	−0.705959
$15$	1.40290	0.362228
$16$	1.00000	0.250000
$17$	−2.42561	−0.588298	−0.294149	−	0.955760i	$-0.595036\pi$
$17$	−2.42561	−0.588298	−0.294149	+	0.955760i	$0.595036\pi$
$18$	−1.00000	−0.235702
$19$	1.90697	0.437488	0.218744	−	0.975782i	$-0.429804\pi$
$19$	1.90697	0.437488	0.218744	+	0.975782i	$0.429804\pi$
$20$	−1.40290	−0.313699
$21$	−2.64146	−0.576413
$22$	−1.00000	−0.213201
$23$	−0.204870	−0.0427183	−0.0213592	−	0.999772i	$-0.506799\pi$
$23$	−0.204870	−0.0427183	−0.0213592	+	0.999772i	$0.506799\pi$
$24$	1.00000	0.204124
$25$	−3.03186	−0.606372
$26$	2.22074	0.435524
$27$	−1.00000	−0.192450
$28$	2.64146	0.499188
$29$	0.472061	0.0876595	0.0438297	−	0.999039i	$-0.486044\pi$
$29$	0.472061	0.0876595	0.0438297	+	0.999039i	$0.486044\pi$
$30$	−1.40290	−0.256134
$31$	9.76569	1.75397	0.876985	−	0.480518i	$-0.159551\pi$
$31$	9.76569	1.75397	0.876985	+	0.480518i	$0.159551\pi$
$32$	−1.00000	−0.176777
$33$	−1.00000	−0.174078
$34$	2.42561	0.415989
$35$	−3.70571	−0.626379
$36$	1.00000	0.166667
$37$	−6.76367	−1.11194	−0.555970	−	0.831202i	$-0.687653\pi$
$37$	−6.76367	−1.11194	−0.555970	+	0.831202i	$0.687653\pi$
$38$	−1.90697	−0.309351
$39$	2.22074	0.355604
$40$	1.40290	0.221819
$41$	−7.76093	−1.21205	−0.606027	−	0.795444i	$-0.707238\pi$
$41$	−7.76093	−1.21205	−0.606027	+	0.795444i	$0.707238\pi$
$42$	2.64146	0.407586
$43$	−1.63963	−0.250042	−0.125021	−	0.992154i	$-0.539900\pi$
$43$	−1.63963	−0.250042	−0.125021	+	0.992154i	$0.539900\pi$
$44$	1.00000	0.150756
$45$	−1.40290	−0.209133
$46$	0.204870	0.0302064
$47$	10.0230	1.46200	0.731000	−	0.682377i	$-0.239054\pi$
$47$	10.0230	1.46200	0.731000	+	0.682377i	$0.239054\pi$
$48$	−1.00000	−0.144338
$49$	−0.0227093	−0.00324419
$50$	3.03186	0.428770
$51$	2.42561	0.339654
$52$	−2.22074	−0.307962
$53$	−9.17082	−1.25971	−0.629855	−	0.776713i	$-0.716886\pi$
$53$	−9.17082	−1.25971	−0.629855	+	0.776713i	$0.716886\pi$
$54$	1.00000	0.136083
$55$	−1.40290	−0.189168
$56$	−2.64146	−0.352979
$57$	−1.90697	−0.252584
$58$	−0.472061	−0.0619846
$59$	−10.6068	−1.38088	−0.690441	−	0.723389i	$-0.742584\pi$
$59$	−10.6068	−1.38088	−0.690441	+	0.723389i	$0.742584\pi$
$60$	1.40290	0.181114
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	−9.76569	−1.24024
$63$	2.64146	0.332792
$64$	1.00000	0.125000
$65$	3.11549	0.386429
$66$	1.00000	0.123091
$67$	6.95159	0.849272	0.424636	−	0.905364i	$-0.360402\pi$
$67$	6.95159	0.849272	0.424636	+	0.905364i	$0.360402\pi$
$68$	−2.42561	−0.294149
$69$	0.204870	0.0246634
$70$	3.70571	0.442917
$71$	−7.05306	−0.837044	−0.418522	−	0.908207i	$-0.637452\pi$
$71$	−7.05306	−0.837044	−0.418522	+	0.908207i	$0.637452\pi$
$72$	−1.00000	−0.117851
$73$	13.5829	1.58976	0.794878	−	0.606769i	$-0.207535\pi$
$73$	13.5829	1.58976	0.794878	+	0.606769i	$0.207535\pi$
$74$	6.76367	0.786261
$75$	3.03186	0.350089
$76$	1.90697	0.218744
$77$	2.64146	0.301022
$78$	−2.22074	−0.251450
$79$	−11.7867	−1.32611	−0.663055	−	0.748571i	$-0.730740\pi$
$79$	−11.7867	−1.32611	−0.663055	+	0.748571i	$0.730740\pi$
$80$	−1.40290	−0.156849
$81$	1.00000	0.111111
$82$	7.76093	0.857052
$83$	11.9485	1.31152	0.655760	−	0.754970i	$-0.272349\pi$
$83$	11.9485	1.31152	0.655760	+	0.754970i	$0.272349\pi$
$84$	−2.64146	−0.288206
$85$	3.40290	0.369097
$86$	1.63963	0.176806
$87$	−0.472061	−0.0506102
$88$	−1.00000	−0.106600
$89$	−17.0716	−1.80958	−0.904792	−	0.425854i	$-0.859974\pi$
$89$	−17.0716	−1.80958	−0.904792	+	0.425854i	$0.859974\pi$
$90$	1.40290	0.147879
$91$	−5.86600	−0.614924
$92$	−0.204870	−0.0213592
$93$	−9.76569	−1.01266
$94$	−10.0230	−1.03379
$95$	−2.67529	−0.274479
$96$	1.00000	0.102062
$97$	3.02014	0.306649	0.153325	−	0.988176i	$-0.451002\pi$
$97$	3.02014	0.306649	0.153325	+	0.988176i	$0.451002\pi$
$98$	0.0227093	0.00229399
$99$	1.00000	0.100504
$100$	−3.03186	−0.303186
$101$	−6.26627	−0.623518	−0.311759	−	0.950161i	$-0.600918\pi$
$101$	−6.26627	−0.623518	−0.311759	+	0.950161i	$0.600918\pi$
$102$	−2.42561	−0.240172
$103$	8.42353	0.829995	0.414997	−	0.909823i	$-0.363782\pi$
$103$	8.42353	0.829995	0.414997	+	0.909823i	$0.363782\pi$
$104$	2.22074	0.217762
$105$	3.70571	0.361640
$106$	9.17082	0.890749
$107$	8.61317	0.832666	0.416333	−	0.909212i	$-0.363315\pi$
$107$	8.61317	0.832666	0.416333	+	0.909212i	$0.363315\pi$
$108$	−1.00000	−0.0962250
$109$	−0.270369	−0.0258967	−0.0129483	−	0.999916i	$-0.504122\pi$
$109$	−0.270369	−0.0258967	−0.0129483	+	0.999916i	$0.504122\pi$
$110$	1.40290	0.133762
$111$	6.76367	0.641979
$112$	2.64146	0.249594
$113$	−1.33006	−0.125121	−0.0625606	−	0.998041i	$-0.519927\pi$
$113$	−1.33006	−0.125121	−0.0625606	+	0.998041i	$0.519927\pi$
$114$	1.90697	0.178604
$115$	0.287413	0.0268014
$116$	0.472061	0.0438297
$117$	−2.22074	−0.205308
$118$	10.6068	0.976431
$119$	−6.40715	−0.587343
$120$	−1.40290	−0.128067
$121$	1.00000	0.0909091
$122$	−1.00000	−0.0905357
$123$	7.76093	0.699780
$124$	9.76569	0.876985
$125$	11.2679	1.00783
$126$	−2.64146	−0.235320
$127$	16.8165	1.49223	0.746113	−	0.665820i	$-0.231918\pi$
$127$	16.8165	1.49223	0.746113	+	0.665820i	$0.231918\pi$
$128$	−1.00000	−0.0883883
$129$	1.63963	0.144362
$130$	−3.11549	−0.273247
$131$	−8.83870	−0.772240	−0.386120	−	0.922448i	$-0.626185\pi$
$131$	−8.83870	−0.772240	−0.386120	+	0.922448i	$0.626185\pi$
$132$	−1.00000	−0.0870388
$133$	5.03717	0.436778
$134$	−6.95159	−0.600526
$135$	1.40290	0.120743
$136$	2.42561	0.207995
$137$	17.6367	1.50680	0.753401	−	0.657561i	$-0.228412\pi$
$137$	17.6367	1.50680	0.753401	+	0.657561i	$0.228412\pi$
$138$	−0.204870	−0.0174397
$139$	12.9773	1.10072	0.550360	−	0.834928i	$-0.314491\pi$
$139$	12.9773	1.10072	0.550360	+	0.834928i	$0.314491\pi$
$140$	−3.70571	−0.313190
$141$	−10.0230	−0.844086
$142$	7.05306	0.591880
$143$	−2.22074	−0.185708
$144$	1.00000	0.0833333
$145$	−0.662256	−0.0549974
$146$	−13.5829	−1.12413
$147$	0.0227093	0.00187303
$148$	−6.76367	−0.555970
$149$	2.01437	0.165023	0.0825116	−	0.996590i	$-0.473706\pi$
$149$	2.01437	0.165023	0.0825116	+	0.996590i	$0.473706\pi$
$150$	−3.03186	−0.247550
$151$	−15.4442	−1.25683	−0.628414	−	0.777879i	$-0.716296\pi$
$151$	−15.4442	−1.25683	−0.628414	+	0.777879i	$0.716296\pi$
$152$	−1.90697	−0.154675
$153$	−2.42561	−0.196099
$154$	−2.64146	−0.212855
$155$	−13.7003	−1.10044
$156$	2.22074	0.177802
$157$	−8.93090	−0.712763	−0.356382	−	0.934340i	$-0.615990\pi$
$157$	−8.93090	−0.712763	−0.356382	+	0.934340i	$0.615990\pi$
$158$	11.7867	0.937701
$159$	9.17082	0.727294
$160$	1.40290	0.110909
$161$	−0.541155	−0.0426490
$162$	−1.00000	−0.0785674
$163$	−10.0502	−0.787191	−0.393595	−	0.919284i	$-0.628769\pi$
$163$	−10.0502	−0.787191	−0.393595	+	0.919284i	$0.628769\pi$
$164$	−7.76093	−0.606027
$165$	1.40290	0.109216
$166$	−11.9485	−0.927384
$167$	−14.9634	−1.15790	−0.578950	−	0.815363i	$-0.696537\pi$
$167$	−14.9634	−1.15790	−0.578950	+	0.815363i	$0.696537\pi$
$168$	2.64146	0.203793
$169$	−8.06830	−0.620638
$170$	−3.40290	−0.260991
$171$	1.90697	0.145829
$172$	−1.63963	−0.125021
$173$	−19.1504	−1.45598	−0.727988	−	0.685589i	$-0.759545\pi$
$173$	−19.1504	−1.45598	−0.727988	+	0.685589i	$0.759545\pi$
$174$	0.472061	0.0357868
$175$	−8.00852	−0.605387
$176$	1.00000	0.0753778
$177$	10.6068	0.797253
$178$	17.0716	1.27957
$179$	−16.7367	−1.25096	−0.625480	−	0.780240i	$-0.715097\pi$
$179$	−16.7367	−1.25096	−0.625480	+	0.780240i	$0.715097\pi$
$180$	−1.40290	−0.104566
$181$	5.52794	0.410888	0.205444	−	0.978669i	$-0.434136\pi$
$181$	5.52794	0.410888	0.205444	+	0.978669i	$0.434136\pi$
$182$	5.86600	0.434817
$183$	−1.00000	−0.0739221
$184$	0.204870	0.0151032
$185$	9.48879	0.697629
$186$	9.76569	0.716055
$187$	−2.42561	−0.177378
$188$	10.0230	0.731000
$189$	−2.64146	−0.192138
$190$	2.67529	0.194086
$191$	24.8007	1.79452	0.897259	−	0.441504i	$-0.145555\pi$
$191$	24.8007	1.79452	0.897259	+	0.441504i	$0.145555\pi$
$192$	−1.00000	−0.0721688
$193$	−7.11070	−0.511839	−0.255920	−	0.966698i	$-0.582378\pi$
$193$	−7.11070	−0.511839	−0.255920	+	0.966698i	$0.582378\pi$
$194$	−3.02014	−0.216834
$195$	−3.11549	−0.223105
$196$	−0.0227093	−0.00162209
$197$	−26.7828	−1.90819	−0.954097	−	0.299498i	$-0.903181\pi$
$197$	−26.7828	−1.90819	−0.954097	+	0.299498i	$0.903181\pi$
$198$	−1.00000	−0.0710669
$199$	−0.260455	−0.0184632	−0.00923160	−	0.999957i	$-0.502939\pi$
$199$	−0.260455	−0.0184632	−0.00923160	+	0.999957i	$0.502939\pi$
$200$	3.03186	0.214385
$201$	−6.95159	−0.490327
$202$	6.26627	0.440893
$203$	1.24693	0.0875172
$204$	2.42561	0.169827
$205$	10.8878	0.760440
$206$	−8.42353	−0.586895
$207$	−0.204870	−0.0142394
$208$	−2.22074	−0.153981
$209$	1.90697	0.131908
$210$	−3.70571	−0.255718
$211$	−15.3771	−1.05860	−0.529302	−	0.848433i	$-0.677546\pi$
$211$	−15.3771	−1.05860	−0.529302	+	0.848433i	$0.677546\pi$
$212$	−9.17082	−0.629855
$213$	7.05306	0.483268
$214$	−8.61317	−0.588784
$215$	2.30025	0.156876
$216$	1.00000	0.0680414
$217$	25.7957	1.75112
$218$	0.270369	0.0183117
$219$	−13.5829	−0.917846
$220$	−1.40290	−0.0945838
$221$	5.38667	0.362346
$222$	−6.76367	−0.453948
$223$	−2.25767	−0.151185	−0.0755924	−	0.997139i	$-0.524085\pi$
$223$	−2.25767	−0.151185	−0.0755924	+	0.997139i	$0.524085\pi$
$224$	−2.64146	−0.176490
$225$	−3.03186	−0.202124
$226$	1.33006	0.0884741
$227$	−18.0576	−1.19853	−0.599264	−	0.800552i	$-0.704540\pi$
$227$	−18.0576	−1.19853	−0.599264	+	0.800552i	$0.704540\pi$
$228$	−1.90697	−0.126292
$229$	2.29571	0.151705	0.0758523	−	0.997119i	$-0.475832\pi$
$229$	2.29571	0.151705	0.0758523	+	0.997119i	$0.475832\pi$
$230$	−0.287413	−0.0189514
$231$	−2.64146	−0.173795
$232$	−0.472061	−0.0309923
$233$	4.14358	0.271455	0.135728	−	0.990746i	$-0.456663\pi$
$233$	4.14358	0.271455	0.135728	+	0.990746i	$0.456663\pi$
$234$	2.22074	0.145175
$235$	−14.0613	−0.917256
$236$	−10.6068	−0.690441
$237$	11.7867	0.765630
$238$	6.40715	0.415314
$239$	−5.42149	−0.350687	−0.175343	−	0.984507i	$-0.556104\pi$
$239$	−5.42149	−0.350687	−0.175343	+	0.984507i	$0.556104\pi$
$240$	1.40290	0.0905571
$241$	−16.3458	−1.05293	−0.526463	−	0.850198i	$-0.676482\pi$
$241$	−16.3458	−1.05293	−0.526463	+	0.850198i	$0.676482\pi$
$242$	−1.00000	−0.0642824
$243$	−1.00000	−0.0641500
$244$	1.00000	0.0640184
$245$	0.0318590	0.00203540
$246$	−7.76093	−0.494819
$247$	−4.23488	−0.269459
$248$	−9.76569	−0.620122
$249$	−11.9485	−0.757206
$250$	−11.2679	−0.712647
$251$	11.3950	0.719247	0.359624	−	0.933097i	$-0.382905\pi$
$251$	11.3950	0.719247	0.359624	+	0.933097i	$0.382905\pi$
$252$	2.64146	0.166396
$253$	−0.204870	−0.0128801
$254$	−16.8165	−1.05516
$255$	−3.40290	−0.213098
$256$	1.00000	0.0625000
$257$	−0.941786	−0.0587470	−0.0293735	−	0.999569i	$-0.509351\pi$
$257$	−0.941786	−0.0587470	−0.0293735	+	0.999569i	$0.509351\pi$
$258$	−1.63963	−0.102079
$259$	−17.8659	−1.11014
$260$	3.11549	0.193215
$261$	0.472061	0.0292198
$262$	8.83870	0.546056
$263$	−15.9527	−0.983684	−0.491842	−	0.870684i	$-0.663676\pi$
$263$	−15.9527	−0.983684	−0.491842	+	0.870684i	$0.663676\pi$
$264$	1.00000	0.0615457
$265$	12.8658	0.790339
$266$	−5.03717	−0.308848
$267$	17.0716	1.04476
$268$	6.95159	0.424636
$269$	−31.4983	−1.92048	−0.960242	−	0.279169i	$-0.909941\pi$
$269$	−31.4983	−1.92048	−0.960242	+	0.279169i	$0.909941\pi$
$270$	−1.40290	−0.0853780
$271$	−30.1613	−1.83217	−0.916084	−	0.400987i	$-0.868667\pi$
$271$	−30.1613	−1.83217	−0.916084	+	0.400987i	$0.868667\pi$
$272$	−2.42561	−0.147074
$273$	5.86600	0.355026
$274$	−17.6367	−1.06547
$275$	−3.03186	−0.182828
$276$	0.204870	0.0123317
$277$	8.89171	0.534251	0.267125	−	0.963662i	$-0.413926\pi$
$277$	8.89171	0.534251	0.267125	+	0.963662i	$0.413926\pi$
$278$	−12.9773	−0.778326
$279$	9.76569	0.584657
$280$	3.70571	0.221459
$281$	−2.33522	−0.139308	−0.0696538	−	0.997571i	$-0.522189\pi$
$281$	−2.33522	−0.139308	−0.0696538	+	0.997571i	$0.522189\pi$
$282$	10.0230	0.596859
$283$	20.7019	1.23060	0.615299	−	0.788294i	$-0.289035\pi$
$283$	20.7019	1.23060	0.615299	+	0.788294i	$0.289035\pi$
$284$	−7.05306	−0.418522
$285$	2.67529	0.158471
$286$	2.22074	0.131315
$287$	−20.5002	−1.21009
$288$	−1.00000	−0.0589256
$289$	−11.1164	−0.653906
$290$	0.662256	0.0388890
$291$	−3.02014	−0.177044
$292$	13.5829	0.794878
$293$	−9.73347	−0.568636	−0.284318	−	0.958730i	$-0.591767\pi$
$293$	−9.73347	−0.568636	−0.284318	+	0.958730i	$0.591767\pi$
$294$	−0.0227093	−0.00132443
$295$	14.8803	0.866363
$296$	6.76367	0.393130
$297$	−1.00000	−0.0580259
$298$	−2.01437	−0.116689
$299$	0.454963	0.0263112
$300$	3.03186	0.175044
$301$	−4.33102	−0.249636
$302$	15.4442	0.888712
$303$	6.26627	0.359988
$304$	1.90697	0.109372
$305$	−1.40290	−0.0803301
$306$	2.42561	0.138663
$307$	−28.0902	−1.60319	−0.801596	−	0.597866i	$-0.796016\pi$
$307$	−28.0902	−1.60319	−0.801596	+	0.597866i	$0.796016\pi$
$308$	2.64146	0.150511
$309$	−8.42353	−0.479198
$310$	13.7003	0.778127
$311$	−21.6072	−1.22523	−0.612617	−	0.790380i	$-0.709883\pi$
$311$	−21.6072	−1.22523	−0.612617	+	0.790380i	$0.709883\pi$
$312$	−2.22074	−0.125725
$313$	17.7487	1.00321	0.501607	−	0.865095i	$-0.332742\pi$
$313$	17.7487	1.00321	0.501607	+	0.865095i	$0.332742\pi$
$314$	8.93090	0.504000
$315$	−3.70571	−0.208793
$316$	−11.7867	−0.663055
$317$	−12.4486	−0.699182	−0.349591	−	0.936902i	$-0.613679\pi$
$317$	−12.4486	−0.699182	−0.349591	+	0.936902i	$0.613679\pi$
$318$	−9.17082	−0.514274
$319$	0.472061	0.0264303
$320$	−1.40290	−0.0784247
$321$	−8.61317	−0.480740
$322$	0.541155	0.0301574
$323$	−4.62556	−0.257373
$324$	1.00000	0.0555556
$325$	6.73298	0.373479
$326$	10.0502	0.556628
$327$	0.270369	0.0149515
$328$	7.76093	0.428526
$329$	26.4752	1.45963
$330$	−1.40290	−0.0772274
$331$	−0.976434	−0.0536697	−0.0268348	−	0.999640i	$-0.508543\pi$
$331$	−0.976434	−0.0536697	−0.0268348	+	0.999640i	$0.508543\pi$
$332$	11.9485	0.655760
$333$	−6.76367	−0.370647
$334$	14.9634	0.818759
$335$	−9.75242	−0.532831
$336$	−2.64146	−0.144103
$337$	17.4423	0.950145	0.475072	−	0.879947i	$-0.342422\pi$
$337$	17.4423	0.950145	0.475072	+	0.879947i	$0.342422\pi$
$338$	8.06830	0.438857
$339$	1.33006	0.0722388
$340$	3.40290	0.184548
$341$	9.76569	0.528842
$342$	−1.90697	−0.103117
$343$	−18.5502	−1.00162
$344$	1.63963	0.0884031
$345$	−0.287413	−0.0154738
$346$	19.1504	1.02953
$347$	21.7867	1.16957	0.584785	−	0.811188i	$-0.301179\pi$
$347$	21.7867	1.16957	0.584785	+	0.811188i	$0.301179\pi$
$348$	−0.472061	−0.0253051
$349$	−19.7730	−1.05842	−0.529211	−	0.848490i	$-0.677512\pi$
$349$	−19.7730	−1.05842	−0.529211	+	0.848490i	$0.677512\pi$
$350$	8.00852	0.428074
$351$	2.22074	0.118535
$352$	−1.00000	−0.0533002
$353$	21.3484	1.13626	0.568131	−	0.822938i	$-0.307667\pi$
$353$	21.3484	1.13626	0.568131	+	0.822938i	$0.307667\pi$
$354$	−10.6068	−0.563743
$355$	9.89477	0.525160
$356$	−17.0716	−0.904792
$357$	6.40715	0.339102
$358$	16.7367	0.884563
$359$	29.6515	1.56495	0.782474	−	0.622683i	$-0.213957\pi$
$359$	29.6515	1.56495	0.782474	+	0.622683i	$0.213957\pi$
$360$	1.40290	0.0739396
$361$	−15.3635	−0.808604
$362$	−5.52794	−0.290542
$363$	−1.00000	−0.0524864
$364$	−5.86600	−0.307462
$365$	−19.0555	−0.997410
$366$	1.00000	0.0522708
$367$	−14.4904	−0.756390	−0.378195	−	0.925726i	$-0.623455\pi$
$367$	−14.4904	−0.756390	−0.378195	+	0.925726i	$0.623455\pi$
$368$	−0.204870	−0.0106796
$369$	−7.76093	−0.404018
$370$	−9.48879	−0.493299
$371$	−24.2243	−1.25766
$372$	−9.76569	−0.506328
$373$	1.73036	0.0895946	0.0447973	−	0.998996i	$-0.485736\pi$
$373$	1.73036	0.0895946	0.0447973	+	0.998996i	$0.485736\pi$
$374$	2.42561	0.125426
$375$	−11.2679	−0.581873
$376$	−10.0230	−0.516895
$377$	−1.04833	−0.0539915
$378$	2.64146	0.135862
$379$	−6.62732	−0.340422	−0.170211	−	0.985408i	$-0.554445\pi$
$379$	−6.62732	−0.340422	−0.170211	+	0.985408i	$0.554445\pi$
$380$	−2.67529	−0.137239
$381$	−16.8165	−0.861537
$382$	−24.8007	−1.26892
$383$	−4.86064	−0.248367	−0.124184	−	0.992259i	$-0.539631\pi$
$383$	−4.86064	−0.248367	−0.124184	+	0.992259i	$0.539631\pi$
$384$	1.00000	0.0510310
$385$	−3.70571	−0.188861
$386$	7.11070	0.361925
$387$	−1.63963	−0.0833472
$388$	3.02014	0.153325
$389$	−31.9781	−1.62136	−0.810678	−	0.585493i	$-0.800901\pi$
$389$	−31.9781	−1.62136	−0.810678	+	0.585493i	$0.800901\pi$
$390$	3.11549	0.157759
$391$	0.496935	0.0251311
$392$	0.0227093	0.00114699
$393$	8.83870	0.445853
$394$	26.7828	1.34930
$395$	16.5356	0.831999
$396$	1.00000	0.0502519
$397$	−31.1227	−1.56200	−0.781002	−	0.624529i	$-0.785291\pi$
$397$	−31.1227	−1.56200	−0.781002	+	0.624529i	$0.785291\pi$
$398$	0.260455	0.0130554
$399$	−5.03717	−0.252174
$400$	−3.03186	−0.151593
$401$	33.2402	1.65994	0.829969	−	0.557810i	$-0.188358\pi$
$401$	33.2402	1.65994	0.829969	+	0.557810i	$0.188358\pi$
$402$	6.95159	0.346714
$403$	−21.6871	−1.08031
$404$	−6.26627	−0.311759
$405$	−1.40290	−0.0697109
$406$	−1.24693	−0.0618840
$407$	−6.76367	−0.335263
$408$	−2.42561	−0.120086
$409$	−29.5147	−1.45941	−0.729705	−	0.683762i	$-0.760343\pi$
$409$	−29.5147	−1.45941	−0.729705	+	0.683762i	$0.760343\pi$
$410$	−10.8878	−0.537712
$411$	−17.6367	−0.869953
$412$	8.42353	0.414997
$413$	−28.0173	−1.37864
$414$	0.204870	0.0100688
$415$	−16.7626	−0.822844
$416$	2.22074	0.108881
$417$	−12.9773	−0.635501
$418$	−1.90697	−0.0932727
$419$	4.82984	0.235953	0.117976	−	0.993016i	$-0.462359\pi$
$419$	4.82984	0.235953	0.117976	+	0.993016i	$0.462359\pi$
$420$	3.70571	0.180820
$421$	−6.50405	−0.316988	−0.158494	−	0.987360i	$-0.550664\pi$
$421$	−6.50405	−0.316988	−0.158494	+	0.987360i	$0.550664\pi$
$422$	15.3771	0.748546
$423$	10.0230	0.487333
$424$	9.17082	0.445375
$425$	7.35412	0.356727
$426$	−7.05306	−0.341722
$427$	2.64146	0.127829
$428$	8.61317	0.416333
$429$	2.22074	0.107219
$430$	−2.30025	−0.110928
$431$	33.0122	1.59014	0.795070	−	0.606517i	$-0.207434\pi$
$431$	33.0122	1.59014	0.795070	+	0.606517i	$0.207434\pi$
$432$	−1.00000	−0.0481125
$433$	23.4933	1.12902	0.564509	−	0.825427i	$-0.309066\pi$
$433$	23.4933	1.12902	0.564509	+	0.825427i	$0.309066\pi$
$434$	−25.7957	−1.23823
$435$	0.662256	0.0317527
$436$	−0.270369	−0.0129483
$437$	−0.390680	−0.0186887
$438$	13.5829	0.649015
$439$	21.8941	1.04495	0.522473	−	0.852656i	$-0.325009\pi$
$439$	21.8941	1.04495	0.522473	+	0.852656i	$0.325009\pi$
$440$	1.40290	0.0668808
$441$	−0.0227093	−0.00108140
$442$	−5.38667	−0.256218
$443$	−31.7620	−1.50906	−0.754530	−	0.656265i	$-0.772135\pi$
$443$	−31.7620	−1.50906	−0.754530	+	0.656265i	$0.772135\pi$
$444$	6.76367	0.320990
$445$	23.9498	1.13533
$446$	2.25767	0.106904
$447$	−2.01437	−0.0952762
$448$	2.64146	0.124797
$449$	−33.8087	−1.59553	−0.797765	−	0.602968i	$-0.793985\pi$
$449$	−33.8087	−1.59553	−0.797765	+	0.602968i	$0.793985\pi$
$450$	3.03186	0.142923
$451$	−7.76093	−0.365448
$452$	−1.33006	−0.0625606
$453$	15.4442	0.725631
$454$	18.0576	0.847487
$455$	8.22943	0.385802
$456$	1.90697	0.0893018
$457$	−14.3858	−0.672937	−0.336469	−	0.941695i	$-0.609233\pi$
$457$	−14.3858	−0.672937	−0.336469	+	0.941695i	$0.609233\pi$
$458$	−2.29571	−0.107271
$459$	2.42561	0.113218
$460$	0.287413	0.0134007
$461$	−1.24112	−0.0578046	−0.0289023	−	0.999582i	$-0.509201\pi$
$461$	−1.24112	−0.0578046	−0.0289023	+	0.999582i	$0.509201\pi$
$462$	2.64146	0.122892
$463$	−18.1466	−0.843343	−0.421672	−	0.906749i	$-0.638557\pi$
$463$	−18.1466	−0.843343	−0.421672	+	0.906749i	$0.638557\pi$
$464$	0.472061	0.0219149
$465$	13.7003	0.635338
$466$	−4.14358	−0.191948
$467$	−10.7033	−0.495290	−0.247645	−	0.968851i	$-0.579657\pi$
$467$	−10.7033	−0.495290	−0.247645	+	0.968851i	$0.579657\pi$
$468$	−2.22074	−0.102654
$469$	18.3623	0.847893
$470$	14.0613	0.648598
$471$	8.93090	0.411514
$472$	10.6068	0.488216
$473$	−1.63963	−0.0753904
$474$	−11.7867	−0.541382
$475$	−5.78165	−0.265280
$476$	−6.40715	−0.293671
$477$	−9.17082	−0.419903
$478$	5.42149	0.247973
$479$	12.1296	0.554214	0.277107	−	0.960839i	$-0.410624\pi$
$479$	12.1296	0.554214	0.277107	+	0.960839i	$0.410624\pi$
$480$	−1.40290	−0.0640335
$481$	15.0204	0.684871
$482$	16.3458	0.744531
$483$	0.541155	0.0246234
$484$	1.00000	0.0454545
$485$	−4.23697	−0.192391
$486$	1.00000	0.0453609
$487$	8.75526	0.396739	0.198369	−	0.980127i	$-0.436435\pi$
$487$	8.75526	0.396739	0.198369	+	0.980127i	$0.436435\pi$
$488$	−1.00000	−0.0452679
$489$	10.0502	0.454485
$490$	−0.0318590	−0.00143924
$491$	27.0828	1.22223	0.611114	−	0.791542i	$-0.290722\pi$
$491$	27.0828	1.22223	0.611114	+	0.791542i	$0.290722\pi$
$492$	7.76093	0.349890
$493$	−1.14504	−0.0515699
$494$	4.23488	0.190536
$495$	−1.40290	−0.0630559
$496$	9.76569	0.438493
$497$	−18.6303	−0.835685
$498$	11.9485	0.535425
$499$	−15.6902	−0.702390	−0.351195	−	0.936302i	$-0.614225\pi$
$499$	−15.6902	−0.702390	−0.351195	+	0.936302i	$0.614225\pi$
$500$	11.2679	0.503917
$501$	14.9634	0.668514
$502$	−11.3950	−0.508585
$503$	−13.2252	−0.589684	−0.294842	−	0.955546i	$-0.595267\pi$
$503$	−13.2252	−0.589684	−0.294842	+	0.955546i	$0.595267\pi$
$504$	−2.64146	−0.117660
$505$	8.79098	0.391194
$506$	0.204870	0.00910757
$507$	8.06830	0.358326
$508$	16.8165	0.746113
$509$	4.07223	0.180498	0.0902492	−	0.995919i	$-0.471234\pi$
$509$	4.07223	0.180498	0.0902492	+	0.995919i	$0.471234\pi$
$510$	3.40290	0.150683
$511$	35.8786	1.58717
$512$	−1.00000	−0.0441942
$513$	−1.90697	−0.0841946
$514$	0.941786	0.0415404
$515$	−11.8174	−0.520737
$516$	1.63963	0.0721808
$517$	10.0230	0.440810
$518$	17.8659	0.784985
$519$	19.1504	0.840609
$520$	−3.11549	−0.136623
$521$	−20.4104	−0.894196	−0.447098	−	0.894485i	$-0.647543\pi$
$521$	−20.4104	−0.894196	−0.447098	+	0.894485i	$0.647543\pi$
$522$	−0.472061	−0.0206615
$523$	−11.8863	−0.519750	−0.259875	−	0.965642i	$-0.583681\pi$
$523$	−11.8863	−0.519750	−0.259875	+	0.965642i	$0.583681\pi$
$524$	−8.83870	−0.386120
$525$	8.00852	0.349521
$526$	15.9527	0.695570
$527$	−23.6878	−1.03186
$528$	−1.00000	−0.0435194
$529$	−22.9580	−0.998175
$530$	−12.8658	−0.558854
$531$	−10.6068	−0.460294
$532$	5.03717	0.218389
$533$	17.2350	0.746533
$534$	−17.0716	−0.738759
$535$	−12.0835	−0.522413
$536$	−6.95159	−0.300263
$537$	16.7367	0.722243
$538$	31.4983	1.35799
$539$	−0.0227093	−0.000978160 0
$540$	1.40290	0.0603714
$541$	−11.3744	−0.489022	−0.244511	−	0.969647i	$-0.578627\pi$
$541$	−11.3744	−0.489022	−0.244511	+	0.969647i	$0.578627\pi$
$542$	30.1613	1.29554
$543$	−5.52794	−0.237226
$544$	2.42561	0.103997
$545$	0.379302	0.0162475
$546$	−5.86600	−0.251042
$547$	45.7026	1.95410	0.977051	−	0.213007i	$-0.0683257\pi$
$547$	45.7026	1.95410	0.977051	+	0.213007i	$0.0683257\pi$
$548$	17.6367	0.753401
$549$	1.00000	0.0426790
$550$	3.03186	0.129279
$551$	0.900203	0.0383499
$552$	−0.204870	−0.00871984
$553$	−31.1341	−1.32396
$554$	−8.89171	−0.377772
$555$	−9.48879	−0.402777
$556$	12.9773	0.550360
$557$	44.5611	1.88811	0.944056	−	0.329784i	$-0.106976\pi$
$557$	44.5611	1.88811	0.944056	+	0.329784i	$0.106976\pi$
$558$	−9.76569	−0.413415
$559$	3.64121	0.154007
$560$	−3.70571	−0.156595
$561$	2.42561	0.102409
$562$	2.33522	0.0985054
$563$	−41.5519	−1.75120	−0.875601	−	0.483034i	$-0.839535\pi$
$563$	−41.5519	−1.75120	−0.875601	+	0.483034i	$0.839535\pi$
$564$	−10.0230	−0.422043
$565$	1.86594	0.0785008
$566$	−20.7019	−0.870165
$567$	2.64146	0.110931
$568$	7.05306	0.295940
$569$	13.9534	0.584955	0.292477	−	0.956272i	$-0.405520\pi$
$569$	13.9534	0.584955	0.292477	+	0.956272i	$0.405520\pi$
$570$	−2.67529	−0.112056
$571$	30.2505	1.26594	0.632972	−	0.774175i	$-0.281835\pi$
$571$	30.2505	1.26594	0.632972	+	0.774175i	$0.281835\pi$
$572$	−2.22074	−0.0928540
$573$	−24.8007	−1.03607
$574$	20.5002	0.855660
$575$	0.621136	0.0259032
$576$	1.00000	0.0416667
$577$	−22.6783	−0.944108	−0.472054	−	0.881570i	$-0.656487\pi$
$577$	−22.6783	−0.944108	−0.472054	+	0.881570i	$0.656487\pi$
$578$	11.1164	0.462381
$579$	7.11070	0.295511
$580$	−0.662256	−0.0274987
$581$	31.5615	1.30939
$582$	3.02014	0.125189
$583$	−9.17082	−0.379817
$584$	−13.5829	−0.562064
$585$	3.11549	0.128810
$586$	9.73347	0.402086
$587$	−37.4818	−1.54704	−0.773519	−	0.633773i	$-0.781505\pi$
$587$	−37.4818	−1.54704	−0.773519	+	0.633773i	$0.781505\pi$
$588$	0.0227093	0.000936516 0
$589$	18.6228	0.767341
$590$	−14.8803	−0.612611
$591$	26.7828	1.10170
$592$	−6.76367	−0.277985
$593$	29.6644	1.21817	0.609085	−	0.793105i	$-0.291537\pi$
$593$	29.6644	1.21817	0.609085	+	0.793105i	$0.291537\pi$
$594$	1.00000	0.0410305
$595$	8.98862	0.368498
$596$	2.01437	0.0825116
$597$	0.260455	0.0106597
$598$	−0.454963	−0.0186048
$599$	3.48715	0.142481	0.0712405	−	0.997459i	$-0.477304\pi$
$599$	3.48715	0.142481	0.0712405	+	0.997459i	$0.477304\pi$
$600$	−3.03186	−0.123775
$601$	12.6710	0.516862	0.258431	−	0.966030i	$-0.416795\pi$
$601$	12.6710	0.516862	0.258431	+	0.966030i	$0.416795\pi$
$602$	4.33102	0.176519
$603$	6.95159	0.283091
$604$	−15.4442	−0.628414
$605$	−1.40290	−0.0570362
$606$	−6.26627	−0.254550
$607$	−19.2100	−0.779712	−0.389856	−	0.920876i	$-0.627475\pi$
$607$	−19.2100	−0.779712	−0.389856	+	0.920876i	$0.627475\pi$
$608$	−1.90697	−0.0773377
$609$	−1.24693	−0.0505281
$610$	1.40290	0.0568019
$611$	−22.2584	−0.900480
$612$	−2.42561	−0.0980496
$613$	−35.6456	−1.43971	−0.719856	−	0.694123i	$-0.755792\pi$
$613$	−35.6456	−1.43971	−0.719856	+	0.694123i	$0.755792\pi$
$614$	28.0902	1.13363
$615$	−10.8878	−0.439040
$616$	−2.64146	−0.106427
$617$	−37.3566	−1.50392	−0.751961	−	0.659208i	$-0.770892\pi$
$617$	−37.3566	−1.50392	−0.751961	+	0.659208i	$0.770892\pi$
$618$	8.42353	0.338844
$619$	−16.5413	−0.664853	−0.332426	−	0.943129i	$-0.607867\pi$
$619$	−16.5413	−0.664853	−0.332426	+	0.943129i	$0.607867\pi$
$620$	−13.7003	−0.550219
$621$	0.204870	0.00822114
$622$	21.6072	0.866372
$623$	−45.0938	−1.80665
$624$	2.22074	0.0889009
$625$	−0.648536	−0.0259414
$626$	−17.7487	−0.709380
$627$	−1.90697	−0.0761569
$628$	−8.93090	−0.356382
$629$	16.4061	0.654152
$630$	3.70571	0.147639
$631$	32.9320	1.31100	0.655500	−	0.755195i	$-0.272458\pi$
$631$	32.9320	1.31100	0.655500	+	0.755195i	$0.272458\pi$
$632$	11.7867	0.468851
$633$	15.3771	0.611185
$634$	12.4486	0.494396
$635$	−23.5920	−0.936219
$636$	9.17082	0.363647
$637$	0.0504316	0.00199817
$638$	−0.472061	−0.0186891
$639$	−7.05306	−0.279015
$640$	1.40290	0.0554547
$641$	30.3581	1.19907	0.599537	−	0.800347i	$-0.295352\pi$
$641$	30.3581	1.19907	0.599537	+	0.800347i	$0.295352\pi$
$642$	8.61317	0.339935
$643$	−18.0158	−0.710473	−0.355237	−	0.934776i	$-0.615600\pi$
$643$	−18.0158	−0.710473	−0.355237	+	0.934776i	$0.615600\pi$
$644$	−0.541155	−0.0213245
$645$	−2.30025	−0.0905722
$646$	4.62556	0.181990
$647$	11.6729	0.458907	0.229454	−	0.973320i	$-0.426306\pi$
$647$	11.6729	0.458907	0.229454	+	0.973320i	$0.426306\pi$
$648$	−1.00000	−0.0392837
$649$	−10.6068	−0.416352
$650$	−6.73298	−0.264089
$651$	−25.7957	−1.01101
$652$	−10.0502	−0.393595
$653$	36.4917	1.42803	0.714015	−	0.700130i	$-0.246875\pi$
$653$	36.4917	1.42803	0.714015	+	0.700130i	$0.246875\pi$
$654$	−0.270369	−0.0105723
$655$	12.3998	0.484502
$656$	−7.76093	−0.303014
$657$	13.5829	0.529919
$658$	−26.4752	−1.03211
$659$	5.48686	0.213738	0.106869	−	0.994273i	$-0.465918\pi$
$659$	5.48686	0.213738	0.106869	+	0.994273i	$0.465918\pi$
$660$	1.40290	0.0546080
$661$	35.2662	1.37170	0.685849	−	0.727744i	$-0.259431\pi$
$661$	35.2662	1.37170	0.685849	+	0.727744i	$0.259431\pi$
$662$	0.976434	0.0379502
$663$	−5.38667	−0.209201
$664$	−11.9485	−0.463692
$665$	−7.06666	−0.274033
$666$	6.76367	0.262087
$667$	−0.0967110	−0.00374466
$668$	−14.9634	−0.578950
$669$	2.25767	0.0872866
$670$	9.75242	0.376769
$671$	1.00000	0.0386046
$672$	2.64146	0.101896
$673$	−41.5066	−1.59996	−0.799980	−	0.600027i	$-0.795157\pi$
$673$	−41.5066	−1.59996	−0.799980	+	0.600027i	$0.795157\pi$
$674$	−17.4423	−0.671854
$675$	3.03186	0.116696
$676$	−8.06830	−0.310319
$677$	26.8982	1.03378	0.516890	−	0.856052i	$-0.327089\pi$
$677$	26.8982	1.03378	0.516890	+	0.856052i	$0.327089\pi$
$678$	−1.33006	−0.0510805
$679$	7.97758	0.306151
$680$	−3.40290	−0.130495
$681$	18.0576	0.691970
$682$	−9.76569	−0.373948
$683$	−5.04293	−0.192962	−0.0964811	−	0.995335i	$-0.530759\pi$
$683$	−5.04293	−0.192962	−0.0964811	+	0.995335i	$0.530759\pi$
$684$	1.90697	0.0729146
$685$	−24.7426	−0.945365
$686$	18.5502	0.708249
$687$	−2.29571	−0.0875867
$688$	−1.63963	−0.0625104
$689$	20.3661	0.775885
$690$	0.287413	0.0109416
$691$	−39.2907	−1.49469	−0.747344	−	0.664437i	$-0.768671\pi$
$691$	−39.2907	−1.49469	−0.747344	+	0.664437i	$0.768671\pi$
$692$	−19.1504	−0.727988
$693$	2.64146	0.100341
$694$	−21.7867	−0.827011
$695$	−18.2059	−0.690589
$696$	0.472061	0.0178934
$697$	18.8250	0.713049
$698$	19.7730	0.748418
$699$	−4.14358	−0.156725
$700$	−8.00852	−0.302694
$701$	30.7614	1.16184	0.580920	−	0.813960i	$-0.302693\pi$
$701$	30.7614	1.16184	0.580920	+	0.813960i	$0.302693\pi$
$702$	−2.22074	−0.0838166
$703$	−12.8981	−0.486461
$704$	1.00000	0.0376889
$705$	14.0613	0.529578
$706$	−21.3484	−0.803459
$707$	−16.5521	−0.622505
$708$	10.6068	0.398626
$709$	−12.5072	−0.469716	−0.234858	−	0.972030i	$-0.575463\pi$
$709$	−12.5072	−0.469716	−0.234858	+	0.972030i	$0.575463\pi$
$710$	−9.89477	−0.371344
$711$	−11.7867	−0.442037
$712$	17.0716	0.639784
$713$	−2.00070	−0.0749266
$714$	−6.40715	−0.239782
$715$	3.11549	0.116513
$716$	−16.7367	−0.625480
$717$	5.42149	0.202469
$718$	−29.6515	−1.10659
$719$	−45.6483	−1.70240	−0.851198	−	0.524845i	$-0.824123\pi$
$719$	−45.6483	−1.70240	−0.851198	+	0.524845i	$0.824123\pi$
$720$	−1.40290	−0.0522832
$721$	22.2504	0.828647
$722$	15.3635	0.571770
$723$	16.3458	0.607907
$724$	5.52794	0.205444
$725$	−1.43122	−0.0531542
$726$	1.00000	0.0371135
$727$	16.8878	0.626333	0.313166	−	0.949698i	$-0.398610\pi$
$727$	16.8878	0.626333	0.313166	+	0.949698i	$0.398610\pi$
$728$	5.86600	0.217408
$729$	1.00000	0.0370370
$730$	19.0555	0.705275
$731$	3.97712	0.147099
$732$	−1.00000	−0.0369611
$733$	46.9017	1.73235	0.866176	−	0.499738i	$-0.166570\pi$
$733$	46.9017	1.73235	0.866176	+	0.499738i	$0.166570\pi$
$734$	14.4904	0.534849
$735$	−0.0318590	−0.00117514
$736$	0.204870	0.00755160
$737$	6.95159	0.256065
$738$	7.76093	0.285684
$739$	8.48511	0.312130	0.156065	−	0.987747i	$-0.450119\pi$
$739$	8.48511	0.312130	0.156065	+	0.987747i	$0.450119\pi$
$740$	9.48879	0.348815
$741$	4.23488	0.155572
$742$	24.2243	0.889303
$743$	−4.60862	−0.169074	−0.0845370	−	0.996420i	$-0.526941\pi$
$743$	−4.60862	−0.169074	−0.0845370	+	0.996420i	$0.526941\pi$
$744$	9.76569	0.358028
$745$	−2.82596	−0.103535
$746$	−1.73036	−0.0633530
$747$	11.9485	0.437173
$748$	−2.42561	−0.0886892
$749$	22.7513	0.831315
$750$	11.2679	0.411447
$751$	−1.59252	−0.0581117	−0.0290559	−	0.999578i	$-0.509250\pi$
$751$	−1.59252	−0.0581117	−0.0290559	+	0.999578i	$0.509250\pi$
$752$	10.0230	0.365500
$753$	−11.3950	−0.415258
$754$	1.04833	0.0381778
$755$	21.6667	0.788532
$756$	−2.64146	−0.0960688
$757$	47.1004	1.71189	0.855947	−	0.517064i	$-0.172975\pi$
$757$	47.1004	1.71189	0.855947	+	0.517064i	$0.172975\pi$
$758$	6.62732	0.240715
$759$	0.204870	0.00743630
$760$	2.67529	0.0970430
$761$	−9.97039	−0.361426	−0.180713	−	0.983536i	$-0.557841\pi$
$761$	−9.97039	−0.361426	−0.180713	+	0.983536i	$0.557841\pi$
$762$	16.8165	0.609199
$763$	−0.714169	−0.0258546
$764$	24.8007	0.897259
$765$	3.40290	0.123032
$766$	4.86064	0.175622
$767$	23.5549	0.850518
$768$	−1.00000	−0.0360844
$769$	−24.1099	−0.869427	−0.434713	−	0.900569i	$-0.643150\pi$
$769$	−24.1099	−0.869427	−0.434713	+	0.900569i	$0.643150\pi$
$770$	3.70571	0.133545
$771$	0.941786	0.0339176
$772$	−7.11070	−0.255920
$773$	46.8756	1.68600	0.843000	−	0.537914i	$-0.180788\pi$
$773$	46.8756	1.68600	0.843000	+	0.537914i	$0.180788\pi$
$774$	1.63963	0.0589354
$775$	−29.6082	−1.06356
$776$	−3.02014	−0.108417
$777$	17.8659	0.640937
$778$	31.9781	1.14647
$779$	−14.7998	−0.530259
$780$	−3.11549	−0.111552
$781$	−7.05306	−0.252378
$782$	−0.496935	−0.0177704
$783$	−0.472061	−0.0168701
$784$	−0.0227093	−0.000811047 0
$785$	12.5292	0.447186
$786$	−8.83870	−0.315266
$787$	32.5751	1.16118	0.580589	−	0.814197i	$-0.302822\pi$
$787$	32.5751	1.16118	0.580589	+	0.814197i	$0.302822\pi$
$788$	−26.7828	−0.954097
$789$	15.9527	0.567930
$790$	−16.5356	−0.588312
$791$	−3.51329	−0.124918
$792$	−1.00000	−0.0355335
$793$	−2.22074	−0.0788609
$794$	31.1227	1.10450
$795$	−12.8658	−0.456303
$796$	−0.260455	−0.00923160
$797$	−32.9894	−1.16855	−0.584273	−	0.811557i	$-0.698620\pi$
$797$	−32.9894	−1.16855	−0.584273	+	0.811557i	$0.698620\pi$
$798$	5.03717	0.178314
$799$	−24.3119	−0.860092
$800$	3.03186	0.107192
$801$	−17.0716	−0.603195
$802$	−33.2402	−1.17375
$803$	13.5829	0.479329
$804$	−6.95159	−0.245164
$805$	0.759188	0.0267579
$806$	21.6871	0.763896
$807$	31.4983	1.10879
$808$	6.26627	0.220447
$809$	20.2167	0.710781	0.355390	−	0.934718i	$-0.384348\pi$
$809$	20.2167	0.710781	0.355390	+	0.934718i	$0.384348\pi$
$810$	1.40290	0.0492930
$811$	27.5565	0.967641	0.483821	−	0.875167i	$-0.339249\pi$
$811$	27.5565	0.967641	0.483821	+	0.875167i	$0.339249\pi$
$812$	1.24693	0.0437586
$813$	30.1613	1.05780
$814$	6.76367	0.237067
$815$	14.0994	0.493882
$816$	2.42561	0.0849135
$817$	−3.12672	−0.109390
$818$	29.5147	1.03196
$819$	−5.86600	−0.204975
$820$	10.8878	0.380220
$821$	−44.7464	−1.56166	−0.780830	−	0.624744i	$-0.785203\pi$
$821$	−44.7464	−1.56166	−0.780830	+	0.624744i	$0.785203\pi$
$822$	17.6367	0.615150
$823$	−10.7699	−0.375416	−0.187708	−	0.982225i	$-0.560106\pi$
$823$	−10.7699	−0.375416	−0.187708	+	0.982225i	$0.560106\pi$
$824$	−8.42353	−0.293447
$825$	3.03186	0.105556
$826$	28.0173	0.974846
$827$	−25.6957	−0.893526	−0.446763	−	0.894652i	$-0.647423\pi$
$827$	−25.6957	−0.893526	−0.446763	+	0.894652i	$0.647423\pi$
$828$	−0.204870	−0.00711972
$829$	−49.0904	−1.70498	−0.852490	−	0.522744i	$-0.824908\pi$
$829$	−49.0904	−1.70498	−0.852490	+	0.522744i	$0.824908\pi$
$830$	16.7626	0.581839
$831$	−8.89171	−0.308450
$832$	−2.22074	−0.0769904
$833$	0.0550840	0.00190855
$834$	12.9773	0.449367
$835$	20.9922	0.726464
$836$	1.90697	0.0659538
$837$	−9.76569	−0.337552
$838$	−4.82984	−0.166844
$839$	−19.7433	−0.681615	−0.340808	−	0.940133i	$-0.610700\pi$
$839$	−19.7433	−0.681615	−0.340808	+	0.940133i	$0.610700\pi$
$840$	−3.70571	−0.127859
$841$	−28.7772	−0.992316
$842$	6.50405	0.224144
$843$	2.33522	0.0804293
$844$	−15.3771	−0.529302
$845$	11.3190	0.389387
$846$	−10.0230	−0.344597
$847$	2.64146	0.0907615
$848$	−9.17082	−0.314927
$849$	−20.7019	−0.710486
$850$	−7.35412	−0.252244
$851$	1.38567	0.0475002
$852$	7.05306	0.241634
$853$	39.3259	1.34649	0.673246	−	0.739418i	$-0.264899\pi$
$853$	39.3259	1.34649	0.673246	+	0.739418i	$0.264899\pi$
$854$	−2.64146	−0.0903888
$855$	−2.67529	−0.0914930
$856$	−8.61317	−0.294392
$857$	4.11788	0.140664	0.0703320	−	0.997524i	$-0.477594\pi$
$857$	4.11788	0.140664	0.0703320	+	0.997524i	$0.477594\pi$
$858$	−2.22074	−0.0758149
$859$	−6.03347	−0.205859	−0.102930	−	0.994689i	$-0.532822\pi$
$859$	−6.03347	−0.205859	−0.102930	+	0.994689i	$0.532822\pi$
$860$	2.30025	0.0784378
$861$	20.5002	0.698644
$862$	−33.0122	−1.12440
$863$	23.0371	0.784193	0.392097	−	0.919924i	$-0.371750\pi$
$863$	23.0371	0.784193	0.392097	+	0.919924i	$0.371750\pi$
$864$	1.00000	0.0340207
$865$	26.8662	0.913477
$866$	−23.4933	−0.798336
$867$	11.1164	0.377533
$868$	25.7957	0.875561
$869$	−11.7867	−0.399837
$870$	−0.662256	−0.0224526
$871$	−15.4377	−0.523087
$872$	0.270369	0.00915586
$873$	3.02014	0.102216
$874$	0.390680	0.0132149
$875$	29.7637	1.00620
$876$	−13.5829	−0.458923
$877$	−30.2921	−1.02289	−0.511446	−	0.859316i	$-0.670890\pi$
$877$	−30.2921	−1.02289	−0.511446	+	0.859316i	$0.670890\pi$
$878$	−21.8941	−0.738889
$879$	9.73347	0.328302
$880$	−1.40290	−0.0472919
$881$	−34.6308	−1.16674	−0.583370	−	0.812207i	$-0.698266\pi$
$881$	−34.6308	−1.16674	−0.583370	+	0.812207i	$0.698266\pi$
$882$	0.0227093	0.000764662 0
$883$	−28.4064	−0.955951	−0.477975	−	0.878373i	$-0.658629\pi$
$883$	−28.4064	−0.955951	−0.477975	+	0.878373i	$0.658629\pi$
$884$	5.38667	0.181173
$885$	−14.8803	−0.500195
$886$	31.7620	1.06707
$887$	−17.6978	−0.594235	−0.297118	−	0.954841i	$-0.596025\pi$
$887$	−17.6978	−0.594235	−0.297118	+	0.954841i	$0.596025\pi$
$888$	−6.76367	−0.226974
$889$	44.4201	1.48980
$890$	−23.9498	−0.802799
$891$	1.00000	0.0335013
$892$	−2.25767	−0.0755924
$893$	19.1135	0.639607
$894$	2.01437	0.0673705
$895$	23.4800	0.784850
$896$	−2.64146	−0.0882449
$897$	−0.454963	−0.0151908
$898$	33.8087	1.12821
$899$	4.61000	0.153752
$900$	−3.03186	−0.101062
$901$	22.2449	0.741084
$902$	7.76093	0.258411
$903$	4.33102	0.144127
$904$	1.33006	0.0442371
$905$	−7.75517	−0.257790
$906$	−15.4442	−0.513098
$907$	49.8878	1.65650	0.828249	−	0.560360i	$-0.189337\pi$
$907$	49.8878	1.65650	0.828249	+	0.560360i	$0.189337\pi$
$908$	−18.0576	−0.599264
$909$	−6.26627	−0.207839
$910$	−8.22943	−0.272803
$911$	49.2332	1.63117	0.815584	−	0.578638i	$-0.196416\pi$
$911$	49.2332	1.63117	0.815584	+	0.578638i	$0.196416\pi$
$912$	−1.90697	−0.0631459
$913$	11.9485	0.395438
$914$	14.3858	0.475839
$915$	1.40290	0.0463786
$916$	2.29571	0.0758523
$917$	−23.3470	−0.770987
$918$	−2.42561	−0.0800572
$919$	44.7060	1.47472	0.737358	−	0.675503i	$-0.236073\pi$
$919$	44.7060	1.47472	0.737358	+	0.675503i	$0.236073\pi$
$920$	−0.287413	−0.00947572
$921$	28.0902	0.925604
$922$	1.24112	0.0408740
$923$	15.6630	0.515555
$924$	−2.64146	−0.0868975
$925$	20.5065	0.674250
$926$	18.1466	0.596334
$927$	8.42353	0.276665
$928$	−0.472061	−0.0154962
$929$	7.24383	0.237662	0.118831	−	0.992914i	$-0.462085\pi$
$929$	7.24383	0.237662	0.118831	+	0.992914i	$0.462085\pi$
$930$	−13.7003	−0.449252
$931$	−0.0433059	−0.00141929
$932$	4.14358	0.135728
$933$	21.6072	0.707390
$934$	10.7033	0.350223
$935$	3.40290	0.111287
$936$	2.22074	0.0725873
$937$	0.341181	0.0111459	0.00557294	−	0.999984i	$-0.498226\pi$
$937$	0.341181	0.0111459	0.00557294	+	0.999984i	$0.498226\pi$
$938$	−18.3623	−0.599551
$939$	−17.7487	−0.579206
$940$	−14.0613	−0.458628
$941$	−16.4129	−0.535047	−0.267523	−	0.963551i	$-0.586205\pi$
$941$	−16.4129	−0.535047	−0.267523	+	0.963551i	$0.586205\pi$
$942$	−8.93090	−0.290984
$943$	1.58998	0.0517769
$944$	−10.6068	−0.345221
$945$	3.70571	0.120547
$946$	1.63963	0.0533091
$947$	−22.2932	−0.724431	−0.362215	−	0.932094i	$-0.617980\pi$
$947$	−22.2932	−0.724431	−0.362215	+	0.932094i	$0.617980\pi$
$948$	11.7867	0.382815
$949$	−30.1641	−0.979168
$950$	5.78165	0.187581
$951$	12.4486	0.403673
$952$	6.40715	0.207657
$953$	−25.7282	−0.833417	−0.416708	−	0.909040i	$-0.636816\pi$
$953$	−25.7282	−0.833417	−0.416708	+	0.909040i	$0.636816\pi$
$954$	9.17082	0.296916
$955$	−34.7931	−1.12588
$956$	−5.42149	−0.175343
$957$	−0.472061	−0.0152596
$958$	−12.1296	−0.391888
$959$	46.5865	1.50436
$960$	1.40290	0.0452785
$961$	64.3688	2.07641
$962$	−15.0204	−0.484277
$963$	8.61317	0.277555
$964$	−16.3458	−0.526463
$965$	9.97563	0.321127
$966$	−0.541155	−0.0174114
$967$	54.0660	1.73865	0.869323	−	0.494245i	$-0.164555\pi$
$967$	54.0660	1.73865	0.869323	+	0.494245i	$0.164555\pi$
$968$	−1.00000	−0.0321412
$969$	4.62556	0.148594
$970$	4.23697	0.136041
$971$	−45.7026	−1.46667	−0.733333	−	0.679870i	$-0.762036\pi$
$971$	−45.7026	−1.46667	−0.733333	+	0.679870i	$0.762036\pi$
$972$	−1.00000	−0.0320750
$973$	34.2789	1.09893
$974$	−8.75526	−0.280537
$975$	−6.73298	−0.215628
$976$	1.00000	0.0320092
$977$	45.6848	1.46159	0.730793	−	0.682599i	$-0.239150\pi$
$977$	45.6848	1.46159	0.730793	+	0.682599i	$0.239150\pi$
$978$	−10.0502	−0.321369
$979$	−17.0716	−0.545610
$980$	0.0318590	0.00101770
$981$	−0.270369	−0.00863223
$982$	−27.0828	−0.864246
$983$	10.5994	0.338067	0.169034	−	0.985610i	$-0.445935\pi$
$983$	10.5994	0.338067	0.169034	+	0.985610i	$0.445935\pi$
$984$	−7.76093	−0.247409
$985$	37.5737	1.19720
$986$	1.14504	0.0364654
$987$	−26.4752	−0.842716
$988$	−4.23488	−0.134730
$989$	0.335911	0.0106814
$990$	1.40290	0.0445872
$991$	57.0151	1.81115	0.905573	−	0.424191i	$-0.139441\pi$
$991$	57.0151	1.81115	0.905573	+	0.424191i	$0.139441\pi$
$992$	−9.76569	−0.310061
$993$	0.976434	0.0309862
$994$	18.6303	0.590919
$995$	0.365394	0.0115838
$996$	−11.9485	−0.378603
$997$	−23.7030	−0.750681	−0.375340	−	0.926887i	$-0.622474\pi$
$997$	−23.7030	−0.750681	−0.375340	+	0.926887i	$0.622474\pi$
$998$	15.6902	0.496665
$999$	6.76367	0.213993

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4026.2.a.w.1.2	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4026.2.a.w.1.2	✓	6	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.40290 q^{5} +1.00000 q^{6} +2.64146 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.40290 q^{5} +1.00000 q^{6} +2.64146 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.40290 q^{10} +1.00000 q^{11} -1.00000 q^{12} -2.22074 q^{13} -2.64146 q^{14} +1.40290 q^{15} +1.00000 q^{16} -2.42561 q^{17} -1.00000 q^{18} +1.90697 q^{19} -1.40290 q^{20} -2.64146 q^{21} -1.00000 q^{22} -0.204870 q^{23} +1.00000 q^{24} -3.03186 q^{25} +2.22074 q^{26} -1.00000 q^{27} +2.64146 q^{28} +0.472061 q^{29} -1.40290 q^{30} +9.76569 q^{31} -1.00000 q^{32} -1.00000 q^{33} +2.42561 q^{34} -3.70571 q^{35} +1.00000 q^{36} -6.76367 q^{37} -1.90697 q^{38} +2.22074 q^{39} +1.40290 q^{40} -7.76093 q^{41} +2.64146 q^{42} -1.63963 q^{43} +1.00000 q^{44} -1.40290 q^{45} +0.204870 q^{46} +10.0230 q^{47} -1.00000 q^{48} -0.0227093 q^{49} +3.03186 q^{50} +2.42561 q^{51} -2.22074 q^{52} -9.17082 q^{53} +1.00000 q^{54} -1.40290 q^{55} -2.64146 q^{56} -1.90697 q^{57} -0.472061 q^{58} -10.6068 q^{59} +1.40290 q^{60} +1.00000 q^{61} -9.76569 q^{62} +2.64146 q^{63} +1.00000 q^{64} +3.11549 q^{65} +1.00000 q^{66} +6.95159 q^{67} -2.42561 q^{68} +0.204870 q^{69} +3.70571 q^{70} -7.05306 q^{71} -1.00000 q^{72} +13.5829 q^{73} +6.76367 q^{74} +3.03186 q^{75} +1.90697 q^{76} +2.64146 q^{77} -2.22074 q^{78} -11.7867 q^{79} -1.40290 q^{80} +1.00000 q^{81} +7.76093 q^{82} +11.9485 q^{83} -2.64146 q^{84} +3.40290 q^{85} +1.63963 q^{86} -0.472061 q^{87} -1.00000 q^{88} -17.0716 q^{89} +1.40290 q^{90} -5.86600 q^{91} -0.204870 q^{92} -9.76569 q^{93} -10.0230 q^{94} -2.67529 q^{95} +1.00000 q^{96} +3.02014 q^{97} +0.0227093 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} - 6 q^{3} + 6 q^{4} - q^{5} + 6 q^{6} + 5 q^{7} - 6 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 - 6 * q^3 + 6 * q^4 - q^5 + 6 * q^6 + 5 * q^7 - 6 * q^8 + 6 * q^9	\( 6 q - 6 q^{2} - 6 q^{3} + 6 q^{4} - q^{5} + 6 q^{6} + 5 q^{7} - 6 q^{8} + 6 q^{9} + q^{10} + 6 q^{11} - 6 q^{12} + 2 q^{13} - 5 q^{14} + q^{15} + 6 q^{16} - 4 q^{17} - 6 q^{18} - 5 q^{19} - q^{20} - 5 q^{21} - 6 q^{22} - 6 q^{23} + 6 q^{24} - q^{25} - 2 q^{26} - 6 q^{27} + 5 q^{28} - 10 q^{29} - q^{30} - 15 q^{31} - 6 q^{32} - 6 q^{33} + 4 q^{34} - 21 q^{35} + 6 q^{36} - 3 q^{37} + 5 q^{38} - 2 q^{39} + q^{40} - 9 q^{41} + 5 q^{42} + 10 q^{43} + 6 q^{44} - q^{45} + 6 q^{46} - 14 q^{47} - 6 q^{48} + 3 q^{49} + q^{50} + 4 q^{51} + 2 q^{52} - 11 q^{53} + 6 q^{54} - q^{55} - 5 q^{56} + 5 q^{57} + 10 q^{58} - 20 q^{59} + q^{60} + 6 q^{61} + 15 q^{62} + 5 q^{63} + 6 q^{64} - 2 q^{65} + 6 q^{66} + 14 q^{67} - 4 q^{68} + 6 q^{69} + 21 q^{70} - 21 q^{71} - 6 q^{72} + 16 q^{73} + 3 q^{74} + q^{75} - 5 q^{76} + 5 q^{77} + 2 q^{78} - 6 q^{79} - q^{80} + 6 q^{81} + 9 q^{82} - 10 q^{83} - 5 q^{84} + 13 q^{85} - 10 q^{86} + 10 q^{87} - 6 q^{88} - 11 q^{89} + q^{90} - 21 q^{91} - 6 q^{92} + 15 q^{93} + 14 q^{94} + 9 q^{95} + 6 q^{96} + 2 q^{97} - 3 q^{98} + 6 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 - 6 * q^3 + 6 * q^4 - q^5 + 6 * q^6 + 5 * q^7 - 6 * q^8 + 6 * q^9 + q^10 + 6 * q^11 - 6 * q^12 + 2 * q^13 - 5 * q^14 + q^15 + 6 * q^16 - 4 * q^17 - 6 * q^18 - 5 * q^19 - q^20 - 5 * q^21 - 6 * q^22 - 6 * q^23 + 6 * q^24 - q^25 - 2 * q^26 - 6 * q^27 + 5 * q^28 - 10 * q^29 - q^30 - 15 * q^31 - 6 * q^32 - 6 * q^33 + 4 * q^34 - 21 * q^35 + 6 * q^36 - 3 * q^37 + 5 * q^38 - 2 * q^39 + q^40 - 9 * q^41 + 5 * q^42 + 10 * q^43 + 6 * q^44 - q^45 + 6 * q^46 - 14 * q^47 - 6 * q^48 + 3 * q^49 + q^50 + 4 * q^51 + 2 * q^52 - 11 * q^53 + 6 * q^54 - q^55 - 5 * q^56 + 5 * q^57 + 10 * q^58 - 20 * q^59 + q^60 + 6 * q^61 + 15 * q^62 + 5 * q^63 + 6 * q^64 - 2 * q^65 + 6 * q^66 + 14 * q^67 - 4 * q^68 + 6 * q^69 + 21 * q^70 - 21 * q^71 - 6 * q^72 + 16 * q^73 + 3 * q^74 + q^75 - 5 * q^76 + 5 * q^77 + 2 * q^78 - 6 * q^79 - q^80 + 6 * q^81 + 9 * q^82 - 10 * q^83 - 5 * q^84 + 13 * q^85 - 10 * q^86 + 10 * q^87 - 6 * q^88 - 11 * q^89 + q^90 - 21 * q^91 - 6 * q^92 + 15 * q^93 + 14 * q^94 + 9 * q^95 + 6 * q^96 + 2 * q^97 - 3 * q^98 + 6 * q^99

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