LMFDB - Embedded newform 6026.2.a.l.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6026,2,Mod(1,6026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6026, 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("6026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6026 = 2 \cdot 23 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6026.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:	$48.1178522580$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	6026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.09135 q^{3} +1.00000 q^{4} +2.51915 q^{5} +2.09135 q^{6} -0.00923183 q^{7} -1.00000 q^{8} +1.37373 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.09135 q^{3} +1.00000 q^{4} +2.51915 q^{5} +2.09135 q^{6} -0.00923183 q^{7} -1.00000 q^{8} +1.37373 q^{9} -2.51915 q^{10} +4.67342 q^{11} -2.09135 q^{12} -2.67438 q^{13} +0.00923183 q^{14} -5.26842 q^{15} +1.00000 q^{16} -3.35541 q^{17} -1.37373 q^{18} -4.27891 q^{19} +2.51915 q^{20} +0.0193070 q^{21} -4.67342 q^{22} -1.00000 q^{23} +2.09135 q^{24} +1.34611 q^{25} +2.67438 q^{26} +3.40109 q^{27} -0.00923183 q^{28} +10.1383 q^{29} +5.26842 q^{30} -1.35244 q^{31} -1.00000 q^{32} -9.77375 q^{33} +3.35541 q^{34} -0.0232564 q^{35} +1.37373 q^{36} -8.91903 q^{37} +4.27891 q^{38} +5.59306 q^{39} -2.51915 q^{40} -2.62592 q^{41} -0.0193070 q^{42} -9.13079 q^{43} +4.67342 q^{44} +3.46064 q^{45} +1.00000 q^{46} -3.08636 q^{47} -2.09135 q^{48} -6.99991 q^{49} -1.34611 q^{50} +7.01733 q^{51} -2.67438 q^{52} +9.56046 q^{53} -3.40109 q^{54} +11.7731 q^{55} +0.00923183 q^{56} +8.94869 q^{57} -10.1383 q^{58} +14.1547 q^{59} -5.26842 q^{60} +5.31805 q^{61} +1.35244 q^{62} -0.0126821 q^{63} +1.00000 q^{64} -6.73717 q^{65} +9.77375 q^{66} -6.26830 q^{67} -3.35541 q^{68} +2.09135 q^{69} +0.0232564 q^{70} +7.40926 q^{71} -1.37373 q^{72} +12.3909 q^{73} +8.91903 q^{74} -2.81519 q^{75} -4.27891 q^{76} -0.0431443 q^{77} -5.59306 q^{78} +15.3484 q^{79} +2.51915 q^{80} -11.2341 q^{81} +2.62592 q^{82} -5.37880 q^{83} +0.0193070 q^{84} -8.45278 q^{85} +9.13079 q^{86} -21.2027 q^{87} -4.67342 q^{88} +17.6458 q^{89} -3.46064 q^{90} +0.0246894 q^{91} -1.00000 q^{92} +2.82842 q^{93} +3.08636 q^{94} -10.7792 q^{95} +2.09135 q^{96} -8.65807 q^{97} +6.99991 q^{98} +6.42004 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 36 q^{2} + 4 q^{3} + 36 q^{4} + q^{5} - 4 q^{6} + 13 q^{7} - 36 q^{8} + 46 q^{9}+O(q^{10}) $ 36 * q - 36 * q^2 + 4 * q^3 + 36 * q^4 + q^5 - 4 * q^6 + 13 * q^7 - 36 * q^8 + 46 * q^9	\( 36 q - 36 q^{2} + 4 q^{3} + 36 q^{4} + q^{5} - 4 q^{6} + 13 q^{7} - 36 q^{8} + 46 q^{9} - q^{10} + 14 q^{11} + 4 q^{12} + 4 q^{13} - 13 q^{14} + 10 q^{15} + 36 q^{16} - 4 q^{17} - 46 q^{18} + 29 q^{19} + q^{20} + 24 q^{21} - 14 q^{22} - 36 q^{23} - 4 q^{24} + 49 q^{25} - 4 q^{26} + 19 q^{27} + 13 q^{28} - 13 q^{29} - 10 q^{30} + 21 q^{31} - 36 q^{32} - 5 q^{33} + 4 q^{34} + 30 q^{35} + 46 q^{36} + 13 q^{37} - 29 q^{38} + 30 q^{39} - q^{40} - 8 q^{41} - 24 q^{42} + 42 q^{43} + 14 q^{44} + 30 q^{45} + 36 q^{46} - 14 q^{47} + 4 q^{48} + 61 q^{49} - 49 q^{50} + 46 q^{51} + 4 q^{52} - 3 q^{53} - 19 q^{54} + 26 q^{55} - 13 q^{56} + 26 q^{57} + 13 q^{58} + 45 q^{59} + 10 q^{60} + 34 q^{61} - 21 q^{62} + 63 q^{63} + 36 q^{64} - 25 q^{65} + 5 q^{66} + 42 q^{67} - 4 q^{68} - 4 q^{69} - 30 q^{70} - 2 q^{71} - 46 q^{72} + 16 q^{73} - 13 q^{74} + 72 q^{75} + 29 q^{76} - 36 q^{77} - 30 q^{78} + 33 q^{79} + q^{80} + 96 q^{81} + 8 q^{82} + 8 q^{83} + 24 q^{84} + 18 q^{85} - 42 q^{86} + 11 q^{87} - 14 q^{88} + 21 q^{89} - 30 q^{90} + 60 q^{91} - 36 q^{92} - 27 q^{93} + 14 q^{94} - 44 q^{95} - 4 q^{96} + 20 q^{97} - 61 q^{98} + 76 q^{99}+O(q^{100}) \) 36 * q - 36 * q^2 + 4 * q^3 + 36 * q^4 + q^5 - 4 * q^6 + 13 * q^7 - 36 * q^8 + 46 * q^9 - q^10 + 14 * q^11 + 4 * q^12 + 4 * q^13 - 13 * q^14 + 10 * q^15 + 36 * q^16 - 4 * q^17 - 46 * q^18 + 29 * q^19 + q^20 + 24 * q^21 - 14 * q^22 - 36 * q^23 - 4 * q^24 + 49 * q^25 - 4 * q^26 + 19 * q^27 + 13 * q^28 - 13 * q^29 - 10 * q^30 + 21 * q^31 - 36 * q^32 - 5 * q^33 + 4 * q^34 + 30 * q^35 + 46 * q^36 + 13 * q^37 - 29 * q^38 + 30 * q^39 - q^40 - 8 * q^41 - 24 * q^42 + 42 * q^43 + 14 * q^44 + 30 * q^45 + 36 * q^46 - 14 * q^47 + 4 * q^48 + 61 * q^49 - 49 * q^50 + 46 * q^51 + 4 * q^52 - 3 * q^53 - 19 * q^54 + 26 * q^55 - 13 * q^56 + 26 * q^57 + 13 * q^58 + 45 * q^59 + 10 * q^60 + 34 * q^61 - 21 * q^62 + 63 * q^63 + 36 * q^64 - 25 * q^65 + 5 * q^66 + 42 * q^67 - 4 * q^68 - 4 * q^69 - 30 * q^70 - 2 * q^71 - 46 * q^72 + 16 * q^73 - 13 * q^74 + 72 * q^75 + 29 * q^76 - 36 * q^77 - 30 * q^78 + 33 * q^79 + q^80 + 96 * q^81 + 8 * q^82 + 8 * q^83 + 24 * q^84 + 18 * q^85 - 42 * q^86 + 11 * q^87 - 14 * q^88 + 21 * q^89 - 30 * q^90 + 60 * q^91 - 36 * q^92 - 27 * q^93 + 14 * q^94 - 44 * q^95 - 4 * q^96 + 20 * q^97 - 61 * q^98 + 76 * 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
$3$	−2.09135	−1.20744	−0.603720	−	0.797196i	$-0.706315\pi$
$3$	−2.09135	−1.20744	−0.603720	+	0.797196i	$0.706315\pi$
$4$	1.00000	0.500000
$5$	2.51915	1.12660	0.563299	−	0.826253i	$-0.309532\pi$
$5$	2.51915	1.12660	0.563299	+	0.826253i	$0.309532\pi$
$6$	2.09135	0.853789
$7$	−0.00923183	−0.00348930	−0.00174465	−	0.999998i	$-0.500555\pi$
$7$	−0.00923183	−0.00348930	−0.00174465	+	0.999998i	$0.500555\pi$
$8$	−1.00000	−0.353553
$9$	1.37373	0.457911
$10$	−2.51915	−0.796625
$11$	4.67342	1.40909	0.704545	−	0.709659i	$-0.251151\pi$
$11$	4.67342	1.40909	0.704545	+	0.709659i	$0.251151\pi$
$12$	−2.09135	−0.603720
$13$	−2.67438	−0.741740	−0.370870	−	0.928685i	$-0.620940\pi$
$13$	−2.67438	−0.741740	−0.370870	+	0.928685i	$0.620940\pi$
$14$	0.00923183	0.00246731
$15$	−5.26842	−1.36030
$16$	1.00000	0.250000
$17$	−3.35541	−0.813806	−0.406903	−	0.913471i	$-0.633391\pi$
$17$	−3.35541	−0.813806	−0.406903	+	0.913471i	$0.633391\pi$
$18$	−1.37373	−0.323792
$19$	−4.27891	−0.981650	−0.490825	−	0.871258i	$-0.663305\pi$
$19$	−4.27891	−0.981650	−0.490825	+	0.871258i	$0.663305\pi$
$20$	2.51915	0.563299
$21$	0.0193070	0.00421312
$22$	−4.67342	−0.996377
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	2.09135	0.426894
$25$	1.34611	0.269223
$26$	2.67438	0.524489
$27$	3.40109	0.654540
$28$	−0.00923183	−0.00174465
$29$	10.1383	1.88263	0.941317	−	0.337523i	$-0.109589\pi$
$29$	10.1383	1.88263	0.941317	+	0.337523i	$0.109589\pi$
$30$	5.26842	0.961877
$31$	−1.35244	−0.242906	−0.121453	−	0.992597i	$-0.538755\pi$
$31$	−1.35244	−0.242906	−0.121453	+	0.992597i	$0.538755\pi$
$32$	−1.00000	−0.176777
$33$	−9.77375	−1.70139
$34$	3.35541	0.575448
$35$	−0.0232564	−0.00393104
$36$	1.37373	0.228956
$37$	−8.91903	−1.46628	−0.733140	−	0.680078i	$-0.761946\pi$
$37$	−8.91903	−1.46628	−0.733140	+	0.680078i	$0.761946\pi$
$38$	4.27891	0.694131
$39$	5.59306	0.895607
$40$	−2.51915	−0.398313
$41$	−2.62592	−0.410100	−0.205050	−	0.978752i	$-0.565736\pi$
$41$	−2.62592	−0.410100	−0.205050	+	0.978752i	$0.565736\pi$
$42$	−0.0193070	−0.00297913
$43$	−9.13079	−1.39243	−0.696216	−	0.717832i	$-0.745135\pi$
$43$	−9.13079	−1.39243	−0.696216	+	0.717832i	$0.745135\pi$
$44$	4.67342	0.704545
$45$	3.46064	0.515882
$46$	1.00000	0.147442
$47$	−3.08636	−0.450192	−0.225096	−	0.974337i	$-0.572270\pi$
$47$	−3.08636	−0.450192	−0.225096	+	0.974337i	$0.572270\pi$
$48$	−2.09135	−0.301860
$49$	−6.99991	−0.999988
$50$	−1.34611	−0.190369
$51$	7.01733	0.982622
$52$	−2.67438	−0.370870
$53$	9.56046	1.31323	0.656615	−	0.754226i	$-0.271988\pi$
$53$	9.56046	1.31323	0.656615	+	0.754226i	$0.271988\pi$
$54$	−3.40109	−0.462829
$55$	11.7731	1.58748
$56$	0.00923183	0.00123366
$57$	8.94869	1.18528
$58$	−10.1383	−1.33122
$59$	14.1547	1.84279	0.921394	−	0.388629i	$-0.127051\pi$
$59$	14.1547	1.84279	0.921394	+	0.388629i	$0.127051\pi$
$60$	−5.26842	−0.680150
$61$	5.31805	0.680907	0.340454	−	0.940261i	$-0.389419\pi$
$61$	5.31805	0.680907	0.340454	+	0.940261i	$0.389419\pi$
$62$	1.35244	0.171760
$63$	−0.0126821	−0.00159779
$64$	1.00000	0.125000
$65$	−6.73717	−0.835643
$66$	9.77375	1.20307
$67$	−6.26830	−0.765794	−0.382897	−	0.923791i	$-0.625074\pi$
$67$	−6.26830	−0.765794	−0.382897	+	0.923791i	$0.625074\pi$
$68$	−3.35541	−0.406903
$69$	2.09135	0.251769
$70$	0.0232564	0.00277967
$71$	7.40926	0.879317	0.439659	−	0.898165i	$-0.355099\pi$
$71$	7.40926	0.879317	0.439659	+	0.898165i	$0.355099\pi$
$72$	−1.37373	−0.161896
$73$	12.3909	1.45024	0.725122	−	0.688621i	$-0.241783\pi$
$73$	12.3909	1.45024	0.725122	+	0.688621i	$0.241783\pi$
$74$	8.91903	1.03682
$75$	−2.81519	−0.325070
$76$	−4.27891	−0.490825
$77$	−0.0431443	−0.00491674
$78$	−5.59306	−0.633290
$79$	15.3484	1.72683	0.863416	−	0.504493i	$-0.168321\pi$
$79$	15.3484	1.72683	0.863416	+	0.504493i	$0.168321\pi$
$80$	2.51915	0.281649
$81$	−11.2341	−1.24823
$82$	2.62592	0.289984
$83$	−5.37880	−0.590400	−0.295200	−	0.955436i	$-0.595386\pi$
$83$	−5.37880	−0.590400	−0.295200	+	0.955436i	$0.595386\pi$
$84$	0.0193070	0.00210656
$85$	−8.45278	−0.916832
$86$	9.13079	0.984598
$87$	−21.2027	−2.27317
$88$	−4.67342	−0.498189
$89$	17.6458	1.87045	0.935227	−	0.354048i	$-0.115195\pi$
$89$	17.6458	1.87045	0.935227	+	0.354048i	$0.115195\pi$
$90$	−3.46064	−0.364784
$91$	0.0246894	0.00258816
$92$	−1.00000	−0.104257
$93$	2.82842	0.293294
$94$	3.08636	0.318334
$95$	−10.7792	−1.10592
$96$	2.09135	0.213447
$97$	−8.65807	−0.879093	−0.439547	−	0.898220i	$-0.644861\pi$
$97$	−8.65807	−0.879093	−0.439547	+	0.898220i	$0.644861\pi$
$98$	6.99991	0.707098
$99$	6.42004	0.645238
$100$	1.34611	0.134611
$101$	10.7151	1.06619	0.533096	−	0.846055i	$-0.321028\pi$
$101$	10.7151	1.06619	0.533096	+	0.846055i	$0.321028\pi$
$102$	−7.01733	−0.694819
$103$	0.614777	0.0605757	0.0302879	−	0.999541i	$-0.490358\pi$
$103$	0.614777	0.0605757	0.0302879	+	0.999541i	$0.490358\pi$
$104$	2.67438	0.262245
$105$	0.0486371	0.00474650
$106$	−9.56046	−0.928594
$107$	13.1791	1.27407	0.637035	−	0.770835i	$-0.280161\pi$
$107$	13.1791	1.27407	0.637035	+	0.770835i	$0.280161\pi$
$108$	3.40109	0.327270
$109$	−11.9283	−1.14252	−0.571261	−	0.820768i	$-0.693546\pi$
$109$	−11.9283	−1.14252	−0.571261	+	0.820768i	$0.693546\pi$
$110$	−11.7731	−1.12252
$111$	18.6528	1.77045
$112$	−0.00923183	−0.000872326 0
$113$	−5.10050	−0.479815	−0.239907	−	0.970796i	$-0.577117\pi$
$113$	−5.10050	−0.479815	−0.239907	+	0.970796i	$0.577117\pi$
$114$	−8.94869	−0.838122
$115$	−2.51915	−0.234912
$116$	10.1383	0.941317
$117$	−3.67389	−0.339651
$118$	−14.1547	−1.30305
$119$	0.0309766	0.00283962
$120$	5.26842	0.480938
$121$	10.8409	0.985536
$122$	−5.31805	−0.481474
$123$	5.49171	0.495171
$124$	−1.35244	−0.121453
$125$	−9.20469	−0.823292
$126$	0.0126821	0.00112981
$127$	20.4021	1.81039	0.905196	−	0.424994i	$-0.139724\pi$
$127$	20.4021	1.81039	0.905196	+	0.424994i	$0.139724\pi$
$128$	−1.00000	−0.0883883
$129$	19.0957	1.68128
$130$	6.73717	0.590889
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	−9.77375	−0.850696
$133$	0.0395022	0.00342528
$134$	6.26830	0.541498
$135$	8.56785	0.737403
$136$	3.35541	0.287724
$137$	−1.05643	−0.0902570	−0.0451285	−	0.998981i	$-0.514370\pi$
$137$	−1.05643	−0.0902570	−0.0451285	+	0.998981i	$0.514370\pi$
$138$	−2.09135	−0.178027
$139$	−4.61019	−0.391031	−0.195516	−	0.980701i	$-0.562638\pi$
$139$	−4.61019	−0.391031	−0.195516	+	0.980701i	$0.562638\pi$
$140$	−0.0232564	−0.00196552
$141$	6.45465	0.543580
$142$	−7.40926	−0.621771
$143$	−12.4985	−1.04518
$144$	1.37373	0.114478
$145$	25.5399	2.12097
$146$	−12.3909	−1.02548
$147$	14.6393	1.20743
$148$	−8.91903	−0.733140
$149$	−6.86799	−0.562648	−0.281324	−	0.959613i	$-0.590774\pi$
$149$	−6.86799	−0.562648	−0.281324	+	0.959613i	$0.590774\pi$
$150$	2.81519	0.229859
$151$	−3.32889	−0.270901	−0.135451	−	0.990784i	$-0.543248\pi$
$151$	−3.32889	−0.270901	−0.135451	+	0.990784i	$0.543248\pi$
$152$	4.27891	0.347066
$153$	−4.60944	−0.372651
$154$	0.0431443	0.00347666
$155$	−3.40700	−0.273657
$156$	5.59306	0.447803
$157$	15.5524	1.24121	0.620607	−	0.784122i	$-0.286886\pi$
$157$	15.5524	1.24121	0.620607	+	0.784122i	$0.286886\pi$
$158$	−15.3484	−1.22105
$159$	−19.9943	−1.58565
$160$	−2.51915	−0.199156
$161$	0.00923183	0.000727570 0
$162$	11.2341	0.882631
$163$	−5.18129	−0.405830	−0.202915	−	0.979196i	$-0.565041\pi$
$163$	−5.18129	−0.405830	−0.202915	+	0.979196i	$0.565041\pi$
$164$	−2.62592	−0.205050
$165$	−24.6215	−1.91678
$166$	5.37880	0.417476
$167$	18.3647	1.42110	0.710552	−	0.703645i	$-0.248445\pi$
$167$	18.3647	1.42110	0.710552	+	0.703645i	$0.248445\pi$
$168$	−0.0193070	−0.00148956
$169$	−5.84768	−0.449822
$170$	8.45278	0.648298
$171$	−5.87809	−0.449509
$172$	−9.13079	−0.696216
$173$	−14.7781	−1.12356	−0.561781	−	0.827286i	$-0.689884\pi$
$173$	−14.7781	−1.12356	−0.561781	+	0.827286i	$0.689884\pi$
$174$	21.2027	1.60737
$175$	−0.0124271	−0.000939400 0
$176$	4.67342	0.352273
$177$	−29.6025	−2.22506
$178$	−17.6458	−1.32261
$179$	−13.3102	−0.994850	−0.497425	−	0.867507i	$-0.665721\pi$
$179$	−13.3102	−0.994850	−0.497425	+	0.867507i	$0.665721\pi$
$180$	3.46064	0.257941
$181$	−16.5274	−1.22847	−0.614237	−	0.789121i	$-0.710536\pi$
$181$	−16.5274	−1.22847	−0.614237	+	0.789121i	$0.710536\pi$
$182$	−0.0246894	−0.00183010
$183$	−11.1219	−0.822154
$184$	1.00000	0.0737210
$185$	−22.4684	−1.65191
$186$	−2.82842	−0.207390
$187$	−15.6813	−1.14673
$188$	−3.08636	−0.225096
$189$	−0.0313983	−0.00228389
$190$	10.7792	0.782007
$191$	8.19574	0.593023	0.296511	−	0.955029i	$-0.404177\pi$
$191$	8.19574	0.593023	0.296511	+	0.955029i	$0.404177\pi$
$192$	−2.09135	−0.150930
$193$	−9.95911	−0.716872	−0.358436	−	0.933554i	$-0.616690\pi$
$193$	−9.95911	−0.716872	−0.358436	+	0.933554i	$0.616690\pi$
$194$	8.65807	0.621613
$195$	14.0898	1.00899
$196$	−6.99991	−0.499994
$197$	6.04857	0.430942	0.215471	−	0.976510i	$-0.430871\pi$
$197$	6.04857	0.430942	0.215471	+	0.976510i	$0.430871\pi$
$198$	−6.42004	−0.456252
$199$	20.8068	1.47496	0.737478	−	0.675372i	$-0.236017\pi$
$199$	20.8068	1.47496	0.737478	+	0.675372i	$0.236017\pi$
$200$	−1.34611	−0.0951846
$201$	13.1092	0.924651
$202$	−10.7151	−0.753912
$203$	−0.0935950	−0.00656908
$204$	7.01733	0.491311
$205$	−6.61509	−0.462018
$206$	−0.614777	−0.0428335
$207$	−1.37373	−0.0954811
$208$	−2.67438	−0.185435
$209$	−19.9972	−1.38323
$210$	−0.0486371	−0.00335628
$211$	−2.55267	−0.175733	−0.0878667	−	0.996132i	$-0.528005\pi$
$211$	−2.55267	−0.175733	−0.0878667	+	0.996132i	$0.528005\pi$
$212$	9.56046	0.656615
$213$	−15.4953	−1.06172
$214$	−13.1791	−0.900904
$215$	−23.0018	−1.56871
$216$	−3.40109	−0.231415
$217$	0.0124855	0.000847572 0
$218$	11.9283	0.807885
$219$	−25.9136	−1.75108
$220$	11.7731	0.793739
$221$	8.97365	0.603633
$222$	−18.6528	−1.25189
$223$	4.26682	0.285728	0.142864	−	0.989742i	$-0.454369\pi$
$223$	4.26682	0.285728	0.142864	+	0.989742i	$0.454369\pi$
$224$	0.00923183	0.000616828 0
$225$	1.84920	0.123280
$226$	5.10050	0.339280
$227$	−16.1348	−1.07090	−0.535451	−	0.844567i	$-0.679858\pi$
$227$	−16.1348	−1.07090	−0.535451	+	0.844567i	$0.679858\pi$
$228$	8.94869	0.592642
$229$	7.85142	0.518836	0.259418	−	0.965765i	$-0.416469\pi$
$229$	7.85142	0.518836	0.259418	+	0.965765i	$0.416469\pi$
$230$	2.51915	0.166108
$231$	0.0902296	0.00593667
$232$	−10.1383	−0.665612
$233$	15.1836	0.994710	0.497355	−	0.867547i	$-0.334305\pi$
$233$	15.1836	0.994710	0.497355	+	0.867547i	$0.334305\pi$
$234$	3.67389	0.240170
$235$	−7.77500	−0.507185
$236$	14.1547	0.921394
$237$	−32.0989	−2.08504
$238$	−0.0309766	−0.00200791
$239$	18.8303	1.21803	0.609017	−	0.793157i	$-0.291564\pi$
$239$	18.8303	1.21803	0.609017	+	0.793157i	$0.291564\pi$
$240$	−5.26842	−0.340075
$241$	−11.5506	−0.744040	−0.372020	−	0.928225i	$-0.621335\pi$
$241$	−11.5506	−0.744040	−0.372020	+	0.928225i	$0.621335\pi$
$242$	−10.8409	−0.696879
$243$	13.2911	0.852621
$244$	5.31805	0.340454
$245$	−17.6338	−1.12658
$246$	−5.49171	−0.350139
$247$	11.4434	0.728129
$248$	1.35244	0.0858801
$249$	11.2489	0.712872
$250$	9.20469	0.582155
$251$	−2.02763	−0.127983	−0.0639916	−	0.997950i	$-0.520383\pi$
$251$	−2.02763	−0.127983	−0.0639916	+	0.997950i	$0.520383\pi$
$252$	−0.0126821	−0.000798896 0
$253$	−4.67342	−0.293816
$254$	−20.4021	−1.28014
$255$	17.6777	1.10702
$256$	1.00000	0.0625000
$257$	0.852700	0.0531900	0.0265950	−	0.999646i	$-0.491534\pi$
$257$	0.852700	0.0531900	0.0265950	+	0.999646i	$0.491534\pi$
$258$	−19.0957	−1.18884
$259$	0.0823390	0.00511630
$260$	−6.73717	−0.417821
$261$	13.9273	0.862079
$262$	−1.00000	−0.0617802
$263$	29.0881	1.79365	0.896825	−	0.442386i	$-0.145868\pi$
$263$	29.0881	1.79365	0.896825	+	0.442386i	$0.145868\pi$
$264$	9.77375	0.601533
$265$	24.0842	1.47948
$266$	−0.0395022	−0.00242204
$267$	−36.9036	−2.25846
$268$	−6.26830	−0.382897
$269$	−4.27910	−0.260902	−0.130451	−	0.991455i	$-0.541642\pi$
$269$	−4.27910	−0.260902	−0.130451	+	0.991455i	$0.541642\pi$
$270$	−8.56785	−0.521423
$271$	9.40139	0.571094	0.285547	−	0.958365i	$-0.407825\pi$
$271$	9.40139	0.571094	0.285547	+	0.958365i	$0.407825\pi$
$272$	−3.35541	−0.203452
$273$	−0.0516342	−0.00312504
$274$	1.05643	0.0638213
$275$	6.29096	0.379359
$276$	2.09135	0.125884
$277$	−9.48666	−0.569998	−0.284999	−	0.958528i	$-0.591993\pi$
$277$	−9.48666	−0.569998	−0.284999	+	0.958528i	$0.591993\pi$
$278$	4.61019	0.276501
$279$	−1.85789	−0.111229
$280$	0.0232564	0.00138983
$281$	−19.7956	−1.18090	−0.590452	−	0.807073i	$-0.701050\pi$
$281$	−19.7956	−1.18090	−0.590452	+	0.807073i	$0.701050\pi$
$282$	−6.45465	−0.384369
$283$	23.0541	1.37043	0.685213	−	0.728343i	$-0.259709\pi$
$283$	23.0541	1.37043	0.685213	+	0.728343i	$0.259709\pi$
$284$	7.40926	0.439659
$285$	22.5431	1.33534
$286$	12.4985	0.739053
$287$	0.0242421	0.00143096
$288$	−1.37373	−0.0809480
$289$	−5.74123	−0.337719
$290$	−25.5399	−1.49975
$291$	18.1070	1.06145
$292$	12.3909	0.725122
$293$	12.2072	0.713151	0.356576	−	0.934266i	$-0.383944\pi$
$293$	12.2072	0.713151	0.356576	+	0.934266i	$0.383944\pi$
$294$	−14.6393	−0.853779
$295$	35.6579	2.07608
$296$	8.91903	0.518408
$297$	15.8947	0.922306
$298$	6.86799	0.397852
$299$	2.67438	0.154664
$300$	−2.81519	−0.162535
$301$	0.0842939	0.00485862
$302$	3.32889	0.191556
$303$	−22.4090	−1.28736
$304$	−4.27891	−0.245412
$305$	13.3970	0.767108
$306$	4.60944	0.263504
$307$	−12.3171	−0.702971	−0.351486	−	0.936193i	$-0.614323\pi$
$307$	−12.3171	−0.702971	−0.351486	+	0.936193i	$0.614323\pi$
$308$	−0.0431443	−0.00245837
$309$	−1.28571	−0.0731416
$310$	3.40700	0.193505
$311$	2.72285	0.154398	0.0771992	−	0.997016i	$-0.475402\pi$
$311$	2.72285	0.154398	0.0771992	+	0.997016i	$0.475402\pi$
$312$	−5.59306	−0.316645
$313$	24.4593	1.38252	0.691261	−	0.722605i	$-0.257056\pi$
$313$	24.4593	1.38252	0.691261	+	0.722605i	$0.257056\pi$
$314$	−15.5524	−0.877670
$315$	−0.0319480	−0.00180007
$316$	15.3484	0.863416
$317$	34.1037	1.91545	0.957726	−	0.287682i	$-0.0928845\pi$
$317$	34.1037	1.91545	0.957726	+	0.287682i	$0.0928845\pi$
$318$	19.9943	1.12122
$319$	47.3806	2.65280
$320$	2.51915	0.140825
$321$	−27.5620	−1.53836
$322$	−0.00923183	−0.000514470 0
$323$	14.3575	0.798873
$324$	−11.2341	−0.624114
$325$	−3.60002	−0.199693
$326$	5.18129	0.286965
$327$	24.9462	1.37953
$328$	2.62592	0.144992
$329$	0.0284928	0.00157086
$330$	24.6215	1.35537
$331$	12.3823	0.680592	0.340296	−	0.940318i	$-0.389473\pi$
$331$	12.3823	0.680592	0.340296	+	0.940318i	$0.389473\pi$
$332$	−5.37880	−0.295200
$333$	−12.2524	−0.671426
$334$	−18.3647	−1.00487
$335$	−15.7908	−0.862742
$336$	0.0193070	0.00105328
$337$	−17.7782	−0.968443	−0.484221	−	0.874946i	$-0.660897\pi$
$337$	−17.7782	−0.968443	−0.484221	+	0.874946i	$0.660897\pi$
$338$	5.84768	0.318072
$339$	10.6669	0.579347
$340$	−8.45278	−0.458416
$341$	−6.32053	−0.342276
$342$	5.87809	0.317851
$343$	0.129245	0.00697857
$344$	9.13079	0.492299
$345$	5.26842	0.283642
$346$	14.7781	0.794478
$347$	−5.06440	−0.271871	−0.135936	−	0.990718i	$-0.543404\pi$
$347$	−5.06440	−0.271871	−0.135936	+	0.990718i	$0.543404\pi$
$348$	−21.2027	−1.13658
$349$	2.26890	0.121452	0.0607258	−	0.998154i	$-0.480658\pi$
$349$	2.26890	0.121452	0.0607258	+	0.998154i	$0.480658\pi$
$350$	0.0124271	0.000664256 0
$351$	−9.09581	−0.485498
$352$	−4.67342	−0.249094
$353$	−3.34304	−0.177932	−0.0889659	−	0.996035i	$-0.528356\pi$
$353$	−3.34304	−0.177932	−0.0889659	+	0.996035i	$0.528356\pi$
$354$	29.6025	1.57335
$355$	18.6650	0.990637
$356$	17.6458	0.935227
$357$	−0.0647828	−0.00342867
$358$	13.3102	0.703465
$359$	7.87218	0.415478	0.207739	−	0.978184i	$-0.433390\pi$
$359$	7.87218	0.415478	0.207739	+	0.978184i	$0.433390\pi$
$360$	−3.46064	−0.182392
$361$	−0.690903	−0.0363633
$362$	16.5274	0.868663
$363$	−22.6721	−1.18998
$364$	0.0246894	0.00129408
$365$	31.2145	1.63384
$366$	11.1219	0.581351
$367$	−13.3995	−0.699449	−0.349724	−	0.936853i	$-0.613725\pi$
$367$	−13.3995	−0.699449	−0.349724	+	0.936853i	$0.613725\pi$
$368$	−1.00000	−0.0521286
$369$	−3.60732	−0.187789
$370$	22.4684	1.16808
$371$	−0.0882606	−0.00458226
$372$	2.82842	0.146647
$373$	−30.2931	−1.56852	−0.784260	−	0.620433i	$-0.786957\pi$
$373$	−30.2931	−1.56852	−0.784260	+	0.620433i	$0.786957\pi$
$374$	15.6813	0.810858
$375$	19.2502	0.994076
$376$	3.08636	0.159167
$377$	−27.1137	−1.39643
$378$	0.0313983	0.00161495
$379$	5.21721	0.267990	0.133995	−	0.990982i	$-0.457219\pi$
$379$	5.21721	0.267990	0.133995	+	0.990982i	$0.457219\pi$
$380$	−10.7792	−0.552962
$381$	−42.6679	−2.18594
$382$	−8.19574	−0.419330
$383$	19.7303	1.00817	0.504086	−	0.863653i	$-0.331829\pi$
$383$	19.7303	1.00817	0.504086	+	0.863653i	$0.331829\pi$
$384$	2.09135	0.106724
$385$	−0.108687	−0.00553919
$386$	9.95911	0.506905
$387$	−12.5433	−0.637610
$388$	−8.65807	−0.439547
$389$	23.1265	1.17256	0.586280	−	0.810109i	$-0.300592\pi$
$389$	23.1265	1.17256	0.586280	+	0.810109i	$0.300592\pi$
$390$	−14.0898	−0.713463
$391$	3.35541	0.169690
$392$	6.99991	0.353549
$393$	−2.09135	−0.105495
$394$	−6.04857	−0.304722
$395$	38.6649	1.94544
$396$	6.42004	0.322619
$397$	34.5463	1.73383	0.866914	−	0.498458i	$-0.166100\pi$
$397$	34.5463	1.73383	0.866914	+	0.498458i	$0.166100\pi$
$398$	−20.8068	−1.04295
$399$	−0.0826128	−0.00413581
$400$	1.34611	0.0673057
$401$	17.2245	0.860153	0.430076	−	0.902793i	$-0.358487\pi$
$401$	17.2245	0.860153	0.430076	+	0.902793i	$0.358487\pi$
$402$	−13.1092	−0.653827
$403$	3.61695	0.180173
$404$	10.7151	0.533096
$405$	−28.3003	−1.40625
$406$	0.0935950	0.00464504
$407$	−41.6824	−2.06612
$408$	−7.01733	−0.347409
$409$	−22.5670	−1.11587	−0.557933	−	0.829886i	$-0.688405\pi$
$409$	−22.5670	−1.11587	−0.557933	+	0.829886i	$0.688405\pi$
$410$	6.61509	0.326696
$411$	2.20936	0.108980
$412$	0.614777	0.0302879
$413$	−0.130674	−0.00643005
$414$	1.37373	0.0675153
$415$	−13.5500	−0.665143
$416$	2.67438	0.131122
$417$	9.64151	0.472147
$418$	19.9972	0.978094
$419$	30.2151	1.47610	0.738051	−	0.674745i	$-0.235746\pi$
$419$	30.2151	1.47610	0.738051	+	0.674745i	$0.235746\pi$
$420$	0.0486371	0.00237325
$421$	0.852279	0.0415375	0.0207688	−	0.999784i	$-0.493389\pi$
$421$	0.852279	0.0415375	0.0207688	+	0.999784i	$0.493389\pi$
$422$	2.55267	0.124262
$423$	−4.23984	−0.206148
$424$	−9.56046	−0.464297
$425$	−4.51676	−0.219095
$426$	15.4953	0.750751
$427$	−0.0490954	−0.00237589
$428$	13.1791	0.637035
$429$	26.1387	1.26199
$430$	23.0018	1.10925
$431$	22.0042	1.05991	0.529954	−	0.848027i	$-0.322209\pi$
$431$	22.0042	1.05991	0.529954	+	0.848027i	$0.322209\pi$
$432$	3.40109	0.163635
$433$	10.8909	0.523384	0.261692	−	0.965151i	$-0.415720\pi$
$433$	10.8909	0.523384	0.261692	+	0.965151i	$0.415720\pi$
$434$	−0.0124855	−0.000599324 0
$435$	−53.4128	−2.56095
$436$	−11.9283	−0.571261
$437$	4.27891	0.204688
$438$	25.9136	1.23820
$439$	−23.0418	−1.09972	−0.549862	−	0.835255i	$-0.685320\pi$
$439$	−23.0418	−1.09972	−0.549862	+	0.835255i	$0.685320\pi$
$440$	−11.7731	−0.561258
$441$	−9.61602	−0.457906
$442$	−8.97365	−0.426833
$443$	7.68732	0.365235	0.182618	−	0.983184i	$-0.441543\pi$
$443$	7.68732	0.365235	0.182618	+	0.983184i	$0.441543\pi$
$444$	18.6528	0.885223
$445$	44.4525	2.10725
$446$	−4.26682	−0.202040
$447$	14.3634	0.679363
$448$	−0.00923183	−0.000436163 0
$449$	−28.7734	−1.35790	−0.678950	−	0.734184i	$-0.737565\pi$
$449$	−28.7734	−1.35790	−0.678950	+	0.734184i	$0.737565\pi$
$450$	−1.84920	−0.0871722
$451$	−12.2720	−0.577868
$452$	−5.10050	−0.239907
$453$	6.96187	0.327097
$454$	16.1348	0.757241
$455$	0.0621964	0.00291581
$456$	−8.94869	−0.419061
$457$	35.8890	1.67882	0.839408	−	0.543503i	$-0.182902\pi$
$457$	35.8890	1.67882	0.839408	+	0.543503i	$0.182902\pi$
$458$	−7.85142	−0.366873
$459$	−11.4120	−0.532668
$460$	−2.51915	−0.117456
$461$	−9.28404	−0.432401	−0.216200	−	0.976349i	$-0.569366\pi$
$461$	−9.28404	−0.432401	−0.216200	+	0.976349i	$0.569366\pi$
$462$	−0.0902296	−0.00419786
$463$	11.2372	0.522235	0.261118	−	0.965307i	$-0.415909\pi$
$463$	11.2372	0.522235	0.261118	+	0.965307i	$0.415909\pi$
$464$	10.1383	0.470659
$465$	7.12522	0.330424
$466$	−15.1836	−0.703366
$467$	1.79804	0.0832034	0.0416017	−	0.999134i	$-0.486754\pi$
$467$	1.79804	0.0832034	0.0416017	+	0.999134i	$0.486754\pi$
$468$	−3.67389	−0.169826
$469$	0.0578678	0.00267209
$470$	7.77500	0.358634
$471$	−32.5254	−1.49869
$472$	−14.1547	−0.651524
$473$	−42.6721	−1.96206
$474$	32.0989	1.47435
$475$	−5.75990	−0.264283
$476$	0.0309766	0.00141981
$477$	13.1335	0.601343
$478$	−18.8303	−0.861280
$479$	0.460452	0.0210386	0.0105193	−	0.999945i	$-0.496652\pi$
$479$	0.460452	0.0210386	0.0105193	+	0.999945i	$0.496652\pi$
$480$	5.26842	0.240469
$481$	23.8529	1.08760
$482$	11.5506	0.526116
$483$	−0.0193070	−0.000878497 0
$484$	10.8409	0.492768
$485$	−21.8110	−0.990385
$486$	−13.2911	−0.602894
$487$	8.59122	0.389306	0.194653	−	0.980872i	$-0.437642\pi$
$487$	8.59122	0.389306	0.194653	+	0.980872i	$0.437642\pi$
$488$	−5.31805	−0.240737
$489$	10.8359	0.490015
$490$	17.6338	0.796615
$491$	−8.76682	−0.395641	−0.197821	−	0.980238i	$-0.563386\pi$
$491$	−8.76682	−0.395641	−0.197821	+	0.980238i	$0.563386\pi$
$492$	5.49171	0.247586
$493$	−34.0181	−1.53210
$494$	−11.4434	−0.514865
$495$	16.1730	0.726924
$496$	−1.35244	−0.0607264
$497$	−0.0684010	−0.00306821
$498$	−11.2489	−0.504077
$499$	26.1038	1.16856	0.584282	−	0.811551i	$-0.301376\pi$
$499$	26.1038	1.16856	0.584282	+	0.811551i	$0.301376\pi$
$500$	−9.20469	−0.411646
$501$	−38.4070	−1.71590
$502$	2.02763	0.0904977
$503$	7.21853	0.321858	0.160929	−	0.986966i	$-0.448551\pi$
$503$	7.21853	0.321858	0.160929	+	0.986966i	$0.448551\pi$
$504$	0.0126821	0.000564905 0
$505$	26.9929	1.20117
$506$	4.67342	0.207759
$507$	12.2295	0.543133
$508$	20.4021	0.905196
$509$	10.9947	0.487334	0.243667	−	0.969859i	$-0.421650\pi$
$509$	10.9947	0.487334	0.243667	+	0.969859i	$0.421650\pi$
$510$	−17.6777	−0.782781
$511$	−0.114391	−0.00506034
$512$	−1.00000	−0.0441942
$513$	−14.5530	−0.642529
$514$	−0.852700	−0.0376110
$515$	1.54871	0.0682445
$516$	19.0957	0.840639
$517$	−14.4239	−0.634361
$518$	−0.0823390	−0.00361777
$519$	30.9062	1.35663
$520$	6.73717	0.295444
$521$	−18.1108	−0.793447	−0.396723	−	0.917938i	$-0.629853\pi$
$521$	−18.1108	−0.793447	−0.396723	+	0.917938i	$0.629853\pi$
$522$	−13.9273	−0.609582
$523$	1.57305	0.0687846	0.0343923	−	0.999408i	$-0.489050\pi$
$523$	1.57305	0.0687846	0.0343923	+	0.999408i	$0.489050\pi$
$524$	1.00000	0.0436852
$525$	0.0259894	0.00113427
$526$	−29.0881	−1.26830
$527$	4.53799	0.197678
$528$	−9.77375	−0.425348
$529$	1.00000	0.0434783
$530$	−24.0842	−1.04615
$531$	19.4448	0.843834
$532$	0.0395022	0.00171264
$533$	7.02272	0.304188
$534$	36.9036	1.59697
$535$	33.2001	1.43537
$536$	6.26830	0.270749
$537$	27.8362	1.20122
$538$	4.27910	0.184485
$539$	−32.7136	−1.40907
$540$	8.56785	0.368701
$541$	−7.49441	−0.322210	−0.161105	−	0.986937i	$-0.551506\pi$
$541$	−7.49441	−0.322210	−0.161105	+	0.986937i	$0.551506\pi$
$542$	−9.40139	−0.403824
$543$	34.5646	1.48331
$544$	3.35541	0.143862
$545$	−30.0491	−1.28716
$546$	0.0516342	0.00220974
$547$	1.78777	0.0764397	0.0382199	−	0.999269i	$-0.487831\pi$
$547$	1.78777	0.0764397	0.0382199	+	0.999269i	$0.487831\pi$
$548$	−1.05643	−0.0451285
$549$	7.30559	0.311795
$550$	−6.29096	−0.268247
$551$	−43.3809	−1.84809
$552$	−2.09135	−0.0890137
$553$	−0.141694	−0.00602544
$554$	9.48666	0.403050
$555$	46.9892	1.99458
$556$	−4.61019	−0.195516
$557$	23.1527	0.981012	0.490506	−	0.871438i	$-0.336812\pi$
$557$	23.1527	0.981012	0.490506	+	0.871438i	$0.336812\pi$
$558$	1.85789	0.0786509
$559$	24.4192	1.03282
$560$	−0.0232564	−0.000982761 0
$561$	32.7949	1.38460
$562$	19.7956	0.835025
$563$	14.7912	0.623376	0.311688	−	0.950185i	$-0.399106\pi$
$563$	14.7912	0.623376	0.311688	+	0.950185i	$0.399106\pi$
$564$	6.45465	0.271790
$565$	−12.8489	−0.540558
$566$	−23.0541	−0.969038
$567$	0.103711	0.00435545
$568$	−7.40926	−0.310886
$569$	23.4925	0.984857	0.492429	−	0.870353i	$-0.336109\pi$
$569$	23.4925	0.984857	0.492429	+	0.870353i	$0.336109\pi$
$570$	−22.5431	−0.944226
$571$	33.4587	1.40020	0.700101	−	0.714044i	$-0.253138\pi$
$571$	33.4587	1.40020	0.700101	+	0.714044i	$0.253138\pi$
$572$	−12.4985	−0.522589
$573$	−17.1401	−0.716039
$574$	−0.0242421	−0.00101184
$575$	−1.34611	−0.0561368
$576$	1.37373	0.0572389
$577$	−31.0622	−1.29314	−0.646568	−	0.762856i	$-0.723796\pi$
$577$	−31.0622	−1.29314	−0.646568	+	0.762856i	$0.723796\pi$
$578$	5.74123	0.238804
$579$	20.8280	0.865580
$580$	25.5399	1.06049
$581$	0.0496561	0.00206008
$582$	−18.1070	−0.750560
$583$	44.6801	1.85046
$584$	−12.3909	−0.512738
$585$	−9.25507	−0.382650
$586$	−12.2072	−0.504274
$587$	−9.68841	−0.399883	−0.199942	−	0.979808i	$-0.564075\pi$
$587$	−9.68841	−0.399883	−0.199942	+	0.979808i	$0.564075\pi$
$588$	14.6393	0.603713
$589$	5.78698	0.238448
$590$	−35.6579	−1.46801
$591$	−12.6497	−0.520337
$592$	−8.91903	−0.366570
$593$	8.43613	0.346430	0.173215	−	0.984884i	$-0.444584\pi$
$593$	8.43613	0.346430	0.173215	+	0.984884i	$0.444584\pi$
$594$	−15.8947	−0.652168
$595$	0.0780346	0.00319911
$596$	−6.86799	−0.281324
$597$	−43.5142	−1.78092
$598$	−2.67438	−0.109364
$599$	2.77280	0.113294	0.0566468	−	0.998394i	$-0.481959\pi$
$599$	2.77280	0.113294	0.0566468	+	0.998394i	$0.481959\pi$
$600$	2.81519	0.114930
$601$	28.1724	1.14918	0.574588	−	0.818443i	$-0.305162\pi$
$601$	28.1724	1.14918	0.574588	+	0.818443i	$0.305162\pi$
$602$	−0.0842939	−0.00343556
$603$	−8.61097	−0.350666
$604$	−3.32889	−0.135451
$605$	27.3098	1.11030
$606$	22.4090	0.910304
$607$	−20.5942	−0.835892	−0.417946	−	0.908472i	$-0.637250\pi$
$607$	−20.5942	−0.835892	−0.417946	+	0.908472i	$0.637250\pi$
$608$	4.27891	0.173533
$609$	0.195740	0.00793177
$610$	−13.3970	−0.542428
$611$	8.25411	0.333925
$612$	−4.60944	−0.186326
$613$	40.0024	1.61568	0.807841	−	0.589401i	$-0.200636\pi$
$613$	40.0024	1.61568	0.807841	+	0.589401i	$0.200636\pi$
$614$	12.3171	0.497076
$615$	13.8344	0.557859
$616$	0.0431443	0.00173833
$617$	30.1979	1.21572	0.607861	−	0.794043i	$-0.292028\pi$
$617$	30.1979	1.21572	0.607861	+	0.794043i	$0.292028\pi$
$618$	1.28571	0.0517189
$619$	28.9794	1.16478	0.582390	−	0.812909i	$-0.302118\pi$
$619$	28.9794	1.16478	0.582390	+	0.812909i	$0.302118\pi$
$620$	−3.40700	−0.136828
$621$	−3.40109	−0.136481
$622$	−2.72285	−0.109176
$623$	−0.162903	−0.00652658
$624$	5.59306	0.223902
$625$	−29.9185	−1.19674
$626$	−24.4593	−0.977591
$627$	41.8210	1.67017
$628$	15.5524	0.620607
$629$	29.9270	1.19327
$630$	0.0319480	0.00127284
$631$	−3.76436	−0.149857	−0.0749285	−	0.997189i	$-0.523873\pi$
$631$	−3.76436	−0.149857	−0.0749285	+	0.997189i	$0.523873\pi$
$632$	−15.3484	−0.610527
$633$	5.33853	0.212187
$634$	−34.1037	−1.35443
$635$	51.3959	2.03958
$636$	−19.9943	−0.792824
$637$	18.7204	0.741731
$638$	−47.3806	−1.87581
$639$	10.1783	0.402649
$640$	−2.51915	−0.0995781
$641$	21.8544	0.863196	0.431598	−	0.902066i	$-0.357950\pi$
$641$	21.8544	0.863196	0.431598	+	0.902066i	$0.357950\pi$
$642$	27.5620	1.08779
$643$	3.88052	0.153033	0.0765164	−	0.997068i	$-0.475620\pi$
$643$	3.88052	0.153033	0.0765164	+	0.997068i	$0.475620\pi$
$644$	0.00923183	0.000363785 0
$645$	48.1048	1.89412
$646$	−14.3575	−0.564888
$647$	−47.0477	−1.84964	−0.924818	−	0.380410i	$-0.875783\pi$
$647$	−47.0477	−1.84964	−0.924818	+	0.380410i	$0.875783\pi$
$648$	11.2341	0.441315
$649$	66.1510	2.59666
$650$	3.60002	0.141205
$651$	−0.0261115	−0.00102339
$652$	−5.18129	−0.202915
$653$	13.7284	0.537235	0.268618	−	0.963247i	$-0.413433\pi$
$653$	13.7284	0.537235	0.268618	+	0.963247i	$0.413433\pi$
$654$	−24.9462	−0.975473
$655$	2.51915	0.0984313
$656$	−2.62592	−0.102525
$657$	17.0218	0.664083
$658$	−0.0284928	−0.00111076
$659$	24.5474	0.956230	0.478115	−	0.878297i	$-0.341320\pi$
$659$	24.5474	0.956230	0.478115	+	0.878297i	$0.341320\pi$
$660$	−24.6215	−0.958392
$661$	6.57169	0.255609	0.127805	−	0.991799i	$-0.459207\pi$
$661$	6.57169	0.255609	0.127805	+	0.991799i	$0.459207\pi$
$662$	−12.3823	−0.481251
$663$	−18.7670	−0.728850
$664$	5.37880	0.208738
$665$	0.0995119	0.00385891
$666$	12.2524	0.474770
$667$	−10.1383	−0.392556
$668$	18.3647	0.710552
$669$	−8.92341	−0.344999
$670$	15.7908	0.610051
$671$	24.8535	0.959460
$672$	−0.0193070	−0.000744782 0
$673$	19.9614	0.769455	0.384727	−	0.923030i	$-0.374295\pi$
$673$	19.9614	0.769455	0.384727	+	0.923030i	$0.374295\pi$
$674$	17.7782	0.684792
$675$	4.57825	0.176217
$676$	−5.84768	−0.224911
$677$	−12.1312	−0.466240	−0.233120	−	0.972448i	$-0.574894\pi$
$677$	−12.1312	−0.466240	−0.233120	+	0.972448i	$0.574894\pi$
$678$	−10.6669	−0.409660
$679$	0.0799298	0.00306742
$680$	8.45278	0.324149
$681$	33.7434	1.29305
$682$	6.32053	0.242026
$683$	−14.4421	−0.552613	−0.276307	−	0.961070i	$-0.589111\pi$
$683$	−14.4421	−0.552613	−0.276307	+	0.961070i	$0.589111\pi$
$684$	−5.87809	−0.224754
$685$	−2.66131	−0.101683
$686$	−0.129245	−0.00493459
$687$	−16.4200	−0.626464
$688$	−9.13079	−0.348108
$689$	−25.5683	−0.974076
$690$	−5.26842	−0.200565
$691$	−13.1216	−0.499169	−0.249584	−	0.968353i	$-0.580294\pi$
$691$	−13.1216	−0.499169	−0.249584	+	0.968353i	$0.580294\pi$
$692$	−14.7781	−0.561781
$693$	−0.0592687	−0.00225143
$694$	5.06440	0.192242
$695$	−11.6138	−0.440535
$696$	21.2027	0.803686
$697$	8.81104	0.333742
$698$	−2.26890	−0.0858793
$699$	−31.7542	−1.20105
$700$	−0.0124271	−0.000469700 0
$701$	8.98330	0.339294	0.169647	−	0.985505i	$-0.445737\pi$
$701$	8.98330	0.339294	0.169647	+	0.985505i	$0.445737\pi$
$702$	9.09581	0.343299
$703$	38.1638	1.43937
$704$	4.67342	0.176136
$705$	16.2602	0.612396
$706$	3.34304	0.125817
$707$	−0.0989200	−0.00372027
$708$	−29.6025	−1.11253
$709$	−1.22863	−0.0461421	−0.0230710	−	0.999734i	$-0.507344\pi$
$709$	−1.22863	−0.0461421	−0.0230710	+	0.999734i	$0.507344\pi$
$710$	−18.6650	−0.700486
$711$	21.0846	0.790735
$712$	−17.6458	−0.661305
$713$	1.35244	0.0506493
$714$	0.0647828	0.00242443
$715$	−31.4856	−1.17750
$716$	−13.3102	−0.497425
$717$	−39.3808	−1.47070
$718$	−7.87218	−0.293787
$719$	40.2160	1.49980	0.749902	−	0.661549i	$-0.230101\pi$
$719$	40.2160	1.49980	0.749902	+	0.661549i	$0.230101\pi$
$720$	3.46064	0.128970
$721$	−0.00567551	−0.000211367 0
$722$	0.690903	0.0257127
$723$	24.1563	0.898384
$724$	−16.5274	−0.614237
$725$	13.6473	0.506848
$726$	22.6721	0.841439
$727$	−5.34907	−0.198386	−0.0991930	−	0.995068i	$-0.531626\pi$
$727$	−5.34907	−0.198386	−0.0991930	+	0.995068i	$0.531626\pi$
$728$	−0.0246894	−0.000915052 0
$729$	5.90597	0.218739
$730$	−31.2145	−1.15530
$731$	30.6375	1.13317
$732$	−11.1219	−0.411077
$733$	−36.4603	−1.34669	−0.673347	−	0.739327i	$-0.735144\pi$
$733$	−36.4603	−1.34669	−0.673347	+	0.739327i	$0.735144\pi$
$734$	13.3995	0.494585
$735$	36.8785	1.36028
$736$	1.00000	0.0368605
$737$	−29.2944	−1.07907
$738$	3.60732	0.132787
$739$	10.0568	0.369944	0.184972	−	0.982744i	$-0.440780\pi$
$739$	10.0568	0.369944	0.184972	+	0.982744i	$0.440780\pi$
$740$	−22.4684	−0.825954
$741$	−23.9322	−0.879172
$742$	0.0882606	0.00324015
$743$	24.8870	0.913016	0.456508	−	0.889719i	$-0.349100\pi$
$743$	24.8870	0.913016	0.456508	+	0.889719i	$0.349100\pi$
$744$	−2.82842	−0.103695
$745$	−17.3015	−0.633878
$746$	30.2931	1.10911
$747$	−7.38903	−0.270351
$748$	−15.6813	−0.573363
$749$	−0.121667	−0.00444562
$750$	−19.2502	−0.702918
$751$	−45.3959	−1.65652	−0.828260	−	0.560343i	$-0.810669\pi$
$751$	−45.3959	−1.65652	−0.828260	+	0.560343i	$0.810669\pi$
$752$	−3.08636	−0.112548
$753$	4.24049	0.154532
$754$	27.1137	0.987422
$755$	−8.38597	−0.305197
$756$	−0.0313983	−0.00114194
$757$	−6.58004	−0.239156	−0.119578	−	0.992825i	$-0.538154\pi$
$757$	−6.58004	−0.239156	−0.119578	+	0.992825i	$0.538154\pi$
$758$	−5.21721	−0.189497
$759$	9.77375	0.354765
$760$	10.7792	0.391003
$761$	6.28003	0.227651	0.113825	−	0.993501i	$-0.463690\pi$
$761$	6.28003	0.227651	0.113825	+	0.993501i	$0.463690\pi$
$762$	42.6679	1.54569
$763$	0.110120	0.00398661
$764$	8.19574	0.296511
$765$	−11.6119	−0.419828
$766$	−19.7303	−0.712885
$767$	−37.8551	−1.36687
$768$	−2.09135	−0.0754650
$769$	−44.6833	−1.61132	−0.805661	−	0.592377i	$-0.798190\pi$
$769$	−44.6833	−1.61132	−0.805661	+	0.592377i	$0.798190\pi$
$770$	0.108687	0.00391680
$771$	−1.78329	−0.0642237
$772$	−9.95911	−0.358436
$773$	−27.7041	−0.996445	−0.498223	−	0.867049i	$-0.666014\pi$
$773$	−27.7041	−0.996445	−0.498223	+	0.867049i	$0.666014\pi$
$774$	12.5433	0.450859
$775$	−1.82054	−0.0653957
$776$	8.65807	0.310806
$777$	−0.172199	−0.00617762
$778$	−23.1265	−0.829125
$779$	11.2361	0.402575
$780$	14.0898	0.504494
$781$	34.6266	1.23904
$782$	−3.35541	−0.119989
$783$	34.4812	1.23226
$784$	−6.99991	−0.249997
$785$	39.1787	1.39835
$786$	2.09135	0.0745959
$787$	34.9683	1.24649	0.623243	−	0.782028i	$-0.285815\pi$
$787$	34.9683	1.24649	0.623243	+	0.782028i	$0.285815\pi$
$788$	6.04857	0.215471
$789$	−60.8333	−2.16572
$790$	−38.6649	−1.37564
$791$	0.0470869	0.00167422
$792$	−6.42004	−0.228126
$793$	−14.2225	−0.505056
$794$	−34.5463	−1.22600
$795$	−50.3685	−1.78639
$796$	20.8068	0.737478
$797$	6.85672	0.242877	0.121439	−	0.992599i	$-0.461249\pi$
$797$	6.85672	0.242877	0.121439	+	0.992599i	$0.461249\pi$
$798$	0.0826128	0.00292446
$799$	10.3560	0.366369
$800$	−1.34611	−0.0475923
$801$	24.2407	0.856502
$802$	−17.2245	−0.608220
$803$	57.9079	2.04352
$804$	13.1092	0.462325
$805$	0.0232564	0.000819679 0
$806$	−3.61695	−0.127401
$807$	8.94909	0.315023
$808$	−10.7151	−0.376956
$809$	−21.1625	−0.744034	−0.372017	−	0.928226i	$-0.621334\pi$
$809$	−21.1625	−0.744034	−0.372017	+	0.928226i	$0.621334\pi$
$810$	28.3003	0.994370
$811$	31.3539	1.10098	0.550492	−	0.834840i	$-0.314440\pi$
$811$	31.3539	1.10098	0.550492	+	0.834840i	$0.314440\pi$
$812$	−0.0935950	−0.00328454
$813$	−19.6616	−0.689562
$814$	41.6824	1.46097
$815$	−13.0524	−0.457207
$816$	7.01733	0.245656
$817$	39.0699	1.36688
$818$	22.5670	0.789036
$819$	0.0339167	0.00118515
$820$	−6.61509	−0.231009
$821$	−23.0494	−0.804431	−0.402216	−	0.915545i	$-0.631760\pi$
$821$	−23.0494	−0.804431	−0.402216	+	0.915545i	$0.631760\pi$
$822$	−2.20936	−0.0770604
$823$	23.8235	0.830436	0.415218	−	0.909722i	$-0.363705\pi$
$823$	23.8235	0.830436	0.415218	+	0.909722i	$0.363705\pi$
$824$	−0.614777	−0.0214168
$825$	−13.1566	−0.458054
$826$	0.130674	0.00454673
$827$	4.10790	0.142846	0.0714229	−	0.997446i	$-0.477246\pi$
$827$	4.10790	0.142846	0.0714229	+	0.997446i	$0.477246\pi$
$828$	−1.37373	−0.0477405
$829$	−47.1594	−1.63791	−0.818957	−	0.573855i	$-0.805447\pi$
$829$	−47.1594	−1.63791	−0.818957	+	0.573855i	$0.805447\pi$
$830$	13.5500	0.470327
$831$	19.8399	0.688239
$832$	−2.67438	−0.0927175
$833$	23.4876	0.813796
$834$	−9.64151	−0.333858
$835$	46.2635	1.60101
$836$	−19.9972	−0.691617
$837$	−4.59977	−0.158991
$838$	−30.2151	−1.04376
$839$	−0.305418	−0.0105442	−0.00527210	−	0.999986i	$-0.501678\pi$
$839$	−0.305418	−0.0105442	−0.00527210	+	0.999986i	$0.501678\pi$
$840$	−0.0486371	−0.00167814
$841$	73.7851	2.54431
$842$	−0.852279	−0.0293715
$843$	41.3994	1.42587
$844$	−2.55267	−0.0878667
$845$	−14.7312	−0.506768
$846$	4.23984	0.145769
$847$	−0.100081	−0.00343883
$848$	9.56046	0.328308
$849$	−48.2142	−1.65471
$850$	4.51676	0.154924
$851$	8.91903	0.305741
$852$	−15.4953	−0.530861
$853$	56.1545	1.92269	0.961347	−	0.275341i	$-0.0887907\pi$
$853$	56.1545	1.92269	0.961347	+	0.275341i	$0.0887907\pi$
$854$	0.0490954	0.00168001
$855$	−14.8078	−0.506415
$856$	−13.1791	−0.450452
$857$	−30.1610	−1.03028	−0.515140	−	0.857106i	$-0.672260\pi$
$857$	−30.1610	−1.03028	−0.515140	+	0.857106i	$0.672260\pi$
$858$	−26.1387	−0.892362
$859$	1.36238	0.0464837	0.0232418	−	0.999730i	$-0.492601\pi$
$859$	1.36238	0.0464837	0.0232418	+	0.999730i	$0.492601\pi$
$860$	−23.0018	−0.784356
$861$	−0.0506986	−0.00172780
$862$	−22.0042	−0.749468
$863$	−7.49322	−0.255072	−0.127536	−	0.991834i	$-0.540707\pi$
$863$	−7.49322	−0.255072	−0.127536	+	0.991834i	$0.540707\pi$
$864$	−3.40109	−0.115707
$865$	−37.2284	−1.26580
$866$	−10.8909	−0.370088
$867$	12.0069	0.407776
$868$	0.0124855	0.000423786 0
$869$	71.7296	2.43326
$870$	53.4128	1.81086
$871$	16.7638	0.568020
$872$	11.9283	0.403943
$873$	−11.8939	−0.402547
$874$	−4.27891	−0.144736
$875$	0.0849761	0.00287272
$876$	−25.9136	−0.875541
$877$	22.0890	0.745892	0.372946	−	0.927853i	$-0.378348\pi$
$877$	22.0890	0.745892	0.372946	+	0.927853i	$0.378348\pi$
$878$	23.0418	0.777623
$879$	−25.5295	−0.861087
$880$	11.7731	0.396870
$881$	−13.2862	−0.447622	−0.223811	−	0.974633i	$-0.571850\pi$
$881$	−13.2862	−0.447622	−0.223811	+	0.974633i	$0.571850\pi$
$882$	9.61602	0.323788
$883$	18.5737	0.625053	0.312527	−	0.949909i	$-0.398825\pi$
$883$	18.5737	0.625053	0.312527	+	0.949909i	$0.398825\pi$
$884$	8.97365	0.301816
$885$	−74.5730	−2.50674
$886$	−7.68732	−0.258260
$887$	−36.5046	−1.22570	−0.612852	−	0.790198i	$-0.709978\pi$
$887$	−36.5046	−1.22570	−0.612852	+	0.790198i	$0.709978\pi$
$888$	−18.6528	−0.625947
$889$	−0.188349	−0.00631701
$890$	−44.4525	−1.49005
$891$	−52.5015	−1.75887
$892$	4.26682	0.142864
$893$	13.2063	0.441931
$894$	−14.3634	−0.480382
$895$	−33.5303	−1.12080
$896$	0.00923183	0.000308414 0
$897$	−5.59306	−0.186747
$898$	28.7734	0.960180
$899$	−13.7115	−0.457303
$900$	1.84920	0.0616401
$901$	−32.0793	−1.06872
$902$	12.2720	0.408614
$903$	−0.176288	−0.00586649
$904$	5.10050	0.169640
$905$	−41.6351	−1.38400
$906$	−6.96187	−0.231293
$907$	−47.4615	−1.57593	−0.787966	−	0.615719i	$-0.788866\pi$
$907$	−47.4615	−1.57593	−0.787966	+	0.615719i	$0.788866\pi$
$908$	−16.1348	−0.535451
$909$	14.7197	0.488222
$910$	−0.0621964	−0.00206179
$911$	32.5504	1.07844	0.539221	−	0.842164i	$-0.318719\pi$
$911$	32.5504	1.07844	0.539221	+	0.842164i	$0.318719\pi$
$912$	8.94869	0.296321
$913$	−25.1374	−0.831927
$914$	−35.8890	−1.18710
$915$	−28.0177	−0.926237
$916$	7.85142	0.259418
$917$	−0.00923183	−0.000304862 0
$918$	11.4120	0.376653
$919$	−15.9451	−0.525980	−0.262990	−	0.964799i	$-0.584709\pi$
$919$	−15.9451	−0.525980	−0.262990	+	0.964799i	$0.584709\pi$
$920$	2.51915	0.0830539
$921$	25.7592	0.848796
$922$	9.28404	0.305754
$923$	−19.8152	−0.652225
$924$	0.0902296	0.00296834
$925$	−12.0060	−0.394756
$926$	−11.2372	−0.369276
$927$	0.844539	0.0277383
$928$	−10.1383	−0.332806
$929$	17.2957	0.567453	0.283726	−	0.958905i	$-0.408429\pi$
$929$	17.2957	0.567453	0.283726	+	0.958905i	$0.408429\pi$
$930$	−7.12522	−0.233645
$931$	29.9520	0.981638
$932$	15.1836	0.497355
$933$	−5.69442	−0.186427
$934$	−1.79804	−0.0588337
$935$	−39.5034	−1.29190
$936$	3.67389	0.120085
$937$	−45.0137	−1.47053	−0.735266	−	0.677778i	$-0.762943\pi$
$937$	−45.0137	−1.47053	−0.735266	+	0.677778i	$0.762943\pi$
$938$	−0.0578678	−0.00188945
$939$	−51.1529	−1.66931
$940$	−7.77500	−0.253593
$941$	−56.9144	−1.85536	−0.927679	−	0.373379i	$-0.878199\pi$
$941$	−56.9144	−1.85536	−0.927679	+	0.373379i	$0.878199\pi$
$942$	32.5254	1.05973
$943$	2.62592	0.0855117
$944$	14.1547	0.460697
$945$	−0.0790969	−0.00257302
$946$	42.6721	1.38739
$947$	12.4673	0.405132	0.202566	−	0.979269i	$-0.435072\pi$
$947$	12.4673	0.405132	0.202566	+	0.979269i	$0.435072\pi$
$948$	−32.0989	−1.04252
$949$	−33.1380	−1.07570
$950$	5.75990	0.186876
$951$	−71.3226	−2.31279
$952$	−0.0309766	−0.00100396
$953$	38.4092	1.24420	0.622098	−	0.782940i	$-0.286281\pi$
$953$	38.4092	1.24420	0.622098	+	0.782940i	$0.286281\pi$
$954$	−13.1335	−0.425214
$955$	20.6463	0.668098
$956$	18.8303	0.609017
$957$	−99.0892	−3.20310
$958$	−0.460452	−0.0148765
$959$	0.00975279	0.000314934 0
$960$	−5.26842	−0.170037
$961$	−29.1709	−0.940997
$962$	−23.8529	−0.769049
$963$	18.1046	0.583411
$964$	−11.5506	−0.372020
$965$	−25.0885	−0.807627
$966$	0.0193070	0.000621191 0
$967$	25.0761	0.806393	0.403197	−	0.915113i	$-0.367899\pi$
$967$	25.0761	0.806393	0.403197	+	0.915113i	$0.367899\pi$
$968$	−10.8409	−0.348439
$969$	−30.0265	−0.964591
$970$	21.8110	0.700308
$971$	1.31638	0.0422445	0.0211223	−	0.999777i	$-0.493276\pi$
$971$	1.31638	0.0422445	0.0211223	+	0.999777i	$0.493276\pi$
$972$	13.2911	0.426311
$973$	0.0425605	0.00136443
$974$	−8.59122	−0.275281
$975$	7.52890	0.241118
$976$	5.31805	0.170227
$977$	−43.9290	−1.40541	−0.702706	−	0.711481i	$-0.748025\pi$
$977$	−43.9290	−1.40541	−0.702706	+	0.711481i	$0.748025\pi$
$978$	−10.8359	−0.346493
$979$	82.4664	2.63564
$980$	−17.6338	−0.563292
$981$	−16.3863	−0.523174
$982$	8.76682	0.279761
$983$	−25.5134	−0.813752	−0.406876	−	0.913483i	$-0.633382\pi$
$983$	−25.5134	−0.813752	−0.406876	+	0.913483i	$0.633382\pi$
$984$	−5.49171	−0.175069
$985$	15.2372	0.485499
$986$	34.0181	1.08336
$987$	−0.0595882	−0.00189671
$988$	11.4434	0.364065
$989$	9.13079	0.290342
$990$	−16.1730	−0.514013
$991$	46.4486	1.47549	0.737744	−	0.675080i	$-0.235891\pi$
$991$	46.4486	1.47549	0.737744	+	0.675080i	$0.235891\pi$
$992$	1.35244	0.0429401
$993$	−25.8957	−0.821774
$994$	0.0684010	0.00216955
$995$	52.4154	1.66168
$996$	11.2489	0.356436
$997$	−32.6582	−1.03429	−0.517147	−	0.855896i	$-0.673006\pi$
$997$	−32.6582	−1.03429	−0.517147	+	0.855896i	$0.673006\pi$
$998$	−26.1038	−0.826300
$999$	−30.3344	−0.959739

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.l.1.8	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.l.1.8	✓	36	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:	\( N \)	\(=\)	\( 6026 = 2 \cdot 23 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6026.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.09135 q^{3} +1.00000 q^{4} +2.51915 q^{5} +2.09135 q^{6} -0.00923183 q^{7} -1.00000 q^{8} +1.37373 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.09135 q^{3} +1.00000 q^{4} +2.51915 q^{5} +2.09135 q^{6} -0.00923183 q^{7} -1.00000 q^{8} +1.37373 q^{9} -2.51915 q^{10} +4.67342 q^{11} -2.09135 q^{12} -2.67438 q^{13} +0.00923183 q^{14} -5.26842 q^{15} +1.00000 q^{16} -3.35541 q^{17} -1.37373 q^{18} -4.27891 q^{19} +2.51915 q^{20} +0.0193070 q^{21} -4.67342 q^{22} -1.00000 q^{23} +2.09135 q^{24} +1.34611 q^{25} +2.67438 q^{26} +3.40109 q^{27} -0.00923183 q^{28} +10.1383 q^{29} +5.26842 q^{30} -1.35244 q^{31} -1.00000 q^{32} -9.77375 q^{33} +3.35541 q^{34} -0.0232564 q^{35} +1.37373 q^{36} -8.91903 q^{37} +4.27891 q^{38} +5.59306 q^{39} -2.51915 q^{40} -2.62592 q^{41} -0.0193070 q^{42} -9.13079 q^{43} +4.67342 q^{44} +3.46064 q^{45} +1.00000 q^{46} -3.08636 q^{47} -2.09135 q^{48} -6.99991 q^{49} -1.34611 q^{50} +7.01733 q^{51} -2.67438 q^{52} +9.56046 q^{53} -3.40109 q^{54} +11.7731 q^{55} +0.00923183 q^{56} +8.94869 q^{57} -10.1383 q^{58} +14.1547 q^{59} -5.26842 q^{60} +5.31805 q^{61} +1.35244 q^{62} -0.0126821 q^{63} +1.00000 q^{64} -6.73717 q^{65} +9.77375 q^{66} -6.26830 q^{67} -3.35541 q^{68} +2.09135 q^{69} +0.0232564 q^{70} +7.40926 q^{71} -1.37373 q^{72} +12.3909 q^{73} +8.91903 q^{74} -2.81519 q^{75} -4.27891 q^{76} -0.0431443 q^{77} -5.59306 q^{78} +15.3484 q^{79} +2.51915 q^{80} -11.2341 q^{81} +2.62592 q^{82} -5.37880 q^{83} +0.0193070 q^{84} -8.45278 q^{85} +9.13079 q^{86} -21.2027 q^{87} -4.67342 q^{88} +17.6458 q^{89} -3.46064 q^{90} +0.0246894 q^{91} -1.00000 q^{92} +2.82842 q^{93} +3.08636 q^{94} -10.7792 q^{95} +2.09135 q^{96} -8.65807 q^{97} +6.99991 q^{98} +6.42004 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 36 q^{2} + 4 q^{3} + 36 q^{4} + q^{5} - 4 q^{6} + 13 q^{7} - 36 q^{8} + 46 q^{9}+O(q^{10}) \) 36 * q - 36 * q^2 + 4 * q^3 + 36 * q^4 + q^5 - 4 * q^6 + 13 * q^7 - 36 * q^8 + 46 * q^9	\( 36 q - 36 q^{2} + 4 q^{3} + 36 q^{4} + q^{5} - 4 q^{6} + 13 q^{7} - 36 q^{8} + 46 q^{9} - q^{10} + 14 q^{11} + 4 q^{12} + 4 q^{13} - 13 q^{14} + 10 q^{15} + 36 q^{16} - 4 q^{17} - 46 q^{18} + 29 q^{19} + q^{20} + 24 q^{21} - 14 q^{22} - 36 q^{23} - 4 q^{24} + 49 q^{25} - 4 q^{26} + 19 q^{27} + 13 q^{28} - 13 q^{29} - 10 q^{30} + 21 q^{31} - 36 q^{32} - 5 q^{33} + 4 q^{34} + 30 q^{35} + 46 q^{36} + 13 q^{37} - 29 q^{38} + 30 q^{39} - q^{40} - 8 q^{41} - 24 q^{42} + 42 q^{43} + 14 q^{44} + 30 q^{45} + 36 q^{46} - 14 q^{47} + 4 q^{48} + 61 q^{49} - 49 q^{50} + 46 q^{51} + 4 q^{52} - 3 q^{53} - 19 q^{54} + 26 q^{55} - 13 q^{56} + 26 q^{57} + 13 q^{58} + 45 q^{59} + 10 q^{60} + 34 q^{61} - 21 q^{62} + 63 q^{63} + 36 q^{64} - 25 q^{65} + 5 q^{66} + 42 q^{67} - 4 q^{68} - 4 q^{69} - 30 q^{70} - 2 q^{71} - 46 q^{72} + 16 q^{73} - 13 q^{74} + 72 q^{75} + 29 q^{76} - 36 q^{77} - 30 q^{78} + 33 q^{79} + q^{80} + 96 q^{81} + 8 q^{82} + 8 q^{83} + 24 q^{84} + 18 q^{85} - 42 q^{86} + 11 q^{87} - 14 q^{88} + 21 q^{89} - 30 q^{90} + 60 q^{91} - 36 q^{92} - 27 q^{93} + 14 q^{94} - 44 q^{95} - 4 q^{96} + 20 q^{97} - 61 q^{98} + 76 q^{99}+O(q^{100}) \) 36 * q - 36 * q^2 + 4 * q^3 + 36 * q^4 + q^5 - 4 * q^6 + 13 * q^7 - 36 * q^8 + 46 * q^9 - q^10 + 14 * q^11 + 4 * q^12 + 4 * q^13 - 13 * q^14 + 10 * q^15 + 36 * q^16 - 4 * q^17 - 46 * q^18 + 29 * q^19 + q^20 + 24 * q^21 - 14 * q^22 - 36 * q^23 - 4 * q^24 + 49 * q^25 - 4 * q^26 + 19 * q^27 + 13 * q^28 - 13 * q^29 - 10 * q^30 + 21 * q^31 - 36 * q^32 - 5 * q^33 + 4 * q^34 + 30 * q^35 + 46 * q^36 + 13 * q^37 - 29 * q^38 + 30 * q^39 - q^40 - 8 * q^41 - 24 * q^42 + 42 * q^43 + 14 * q^44 + 30 * q^45 + 36 * q^46 - 14 * q^47 + 4 * q^48 + 61 * q^49 - 49 * q^50 + 46 * q^51 + 4 * q^52 - 3 * q^53 - 19 * q^54 + 26 * q^55 - 13 * q^56 + 26 * q^57 + 13 * q^58 + 45 * q^59 + 10 * q^60 + 34 * q^61 - 21 * q^62 + 63 * q^63 + 36 * q^64 - 25 * q^65 + 5 * q^66 + 42 * q^67 - 4 * q^68 - 4 * q^69 - 30 * q^70 - 2 * q^71 - 46 * q^72 + 16 * q^73 - 13 * q^74 + 72 * q^75 + 29 * q^76 - 36 * q^77 - 30 * q^78 + 33 * q^79 + q^80 + 96 * q^81 + 8 * q^82 + 8 * q^83 + 24 * q^84 + 18 * q^85 - 42 * q^86 + 11 * q^87 - 14 * q^88 + 21 * q^89 - 30 * q^90 + 60 * q^91 - 36 * q^92 - 27 * q^93 + 14 * q^94 - 44 * q^95 - 4 * q^96 + 20 * q^97 - 61 * q^98 + 76 * q^99

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