LMFDB - Embedded newform 143.2.a.c.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [143,2,Mod(1,143)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(143, 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("143.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 143 = 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	143.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:	$1.14186074890$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.194616205.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 10x^{4} - 2x^{3} + 24x^{2} + 7x - 12 $ x^6 - 10x^4 - 2x^3 + 24x^2 + 7x - 12
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.70126$ of defining polynomial
Character	$\chi$	$=$	143.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.70126 q^{2} -2.43752 q^{3} +0.894288 q^{4} -4.04114 q^{5} +4.14685 q^{6} +4.09965 q^{7} +1.88110 q^{8} +2.94150 q^{9} +O(q^{10})$	\(q-1.70126 q^{2} -2.43752 q^{3} +0.894288 q^{4} -4.04114 q^{5} +4.14685 q^{6} +4.09965 q^{7} +1.88110 q^{8} +2.94150 q^{9} +6.87504 q^{10} -1.00000 q^{11} -2.17984 q^{12} +1.00000 q^{13} -6.97457 q^{14} +9.85036 q^{15} -4.98882 q^{16} +3.40252 q^{17} -5.00425 q^{18} -0.396376 q^{19} -3.61395 q^{20} -9.99296 q^{21} +1.70126 q^{22} +1.73007 q^{23} -4.58523 q^{24} +11.3308 q^{25} -1.70126 q^{26} +0.142600 q^{27} +3.66626 q^{28} +7.08646 q^{29} -16.7580 q^{30} -8.11941 q^{31} +4.72508 q^{32} +2.43752 q^{33} -5.78858 q^{34} -16.5673 q^{35} +2.63055 q^{36} +2.42720 q^{37} +0.674339 q^{38} -2.43752 q^{39} -7.60181 q^{40} +1.88822 q^{41} +17.0006 q^{42} +2.07827 q^{43} -0.894288 q^{44} -11.8870 q^{45} -2.94331 q^{46} +3.47252 q^{47} +12.1604 q^{48} +9.80709 q^{49} -19.2767 q^{50} -8.29371 q^{51} +0.894288 q^{52} +6.80709 q^{53} -0.242600 q^{54} +4.04114 q^{55} +7.71186 q^{56} +0.966174 q^{57} -12.0559 q^{58} +3.45580 q^{59} +8.80906 q^{60} +4.40670 q^{61} +13.8132 q^{62} +12.0591 q^{63} +1.93905 q^{64} -4.04114 q^{65} -4.14685 q^{66} -1.82972 q^{67} +3.04283 q^{68} -4.21709 q^{69} +28.1852 q^{70} -2.68563 q^{71} +5.53326 q^{72} +9.07614 q^{73} -4.12930 q^{74} -27.6191 q^{75} -0.354474 q^{76} -4.09965 q^{77} +4.14685 q^{78} +9.08646 q^{79} +20.1606 q^{80} -9.17208 q^{81} -3.21236 q^{82} -9.37689 q^{83} -8.93659 q^{84} -13.7501 q^{85} -3.53568 q^{86} -17.2734 q^{87} -1.88110 q^{88} -13.8034 q^{89} +20.2229 q^{90} +4.09965 q^{91} +1.54718 q^{92} +19.7912 q^{93} -5.90766 q^{94} +1.60181 q^{95} -11.5175 q^{96} +5.24437 q^{97} -16.6844 q^{98} -2.94150 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{3} + 8 q^{4} + q^{5} - 3 q^{6} + 4 q^{7} - 6 q^{8} + 13 q^{9}+O(q^{10}) $ 6 * q + 3 * q^3 + 8 * q^4 + q^5 - 3 * q^6 + 4 * q^7 - 6 * q^8 + 13 * q^9	\( 6 q + 3 q^{3} + 8 q^{4} + q^{5} - 3 q^{6} + 4 q^{7} - 6 q^{8} + 13 q^{9} + 6 q^{10} - 6 q^{11} - 6 q^{12} + 6 q^{13} - 12 q^{14} + 3 q^{15} + 8 q^{16} + 6 q^{18} - 10 q^{19} + 4 q^{20} - 12 q^{21} + 11 q^{23} - 38 q^{24} + 23 q^{25} + 9 q^{27} + 9 q^{28} + 2 q^{29} - 56 q^{30} - 9 q^{31} - 17 q^{32} - 3 q^{33} - 40 q^{34} - 24 q^{35} + 11 q^{36} + 15 q^{37} - 9 q^{38} + 3 q^{39} + 16 q^{40} - 4 q^{41} + 19 q^{42} - 2 q^{43} - 8 q^{44} - 26 q^{45} - 6 q^{46} + 6 q^{47} + 19 q^{48} + 20 q^{49} - 4 q^{50} + 6 q^{51} + 8 q^{52} + 2 q^{53} + 37 q^{54} - q^{55} - 39 q^{56} + 22 q^{57} + 18 q^{58} + 11 q^{59} - 24 q^{60} + 16 q^{61} + 16 q^{62} - 26 q^{63} + 36 q^{64} + q^{65} + 3 q^{66} + 9 q^{67} + 12 q^{68} - 3 q^{69} + 32 q^{70} - 15 q^{71} + 5 q^{72} + 32 q^{73} + 22 q^{74} + 4 q^{75} - 26 q^{76} - 4 q^{77} - 3 q^{78} + 14 q^{79} + 56 q^{80} - 2 q^{81} - 24 q^{82} - 26 q^{83} + 43 q^{84} - 12 q^{85} - 10 q^{86} - 38 q^{87} + 6 q^{88} - 23 q^{89} - 10 q^{90} + 4 q^{91} + 83 q^{92} + 23 q^{93} + 46 q^{94} - 52 q^{95} - 56 q^{96} + 27 q^{97} - 3 q^{98} - 13 q^{99}+O(q^{100}) \) 6 * q + 3 * q^3 + 8 * q^4 + q^5 - 3 * q^6 + 4 * q^7 - 6 * q^8 + 13 * q^9 + 6 * q^10 - 6 * q^11 - 6 * q^12 + 6 * q^13 - 12 * q^14 + 3 * q^15 + 8 * q^16 + 6 * q^18 - 10 * q^19 + 4 * q^20 - 12 * q^21 + 11 * q^23 - 38 * q^24 + 23 * q^25 + 9 * q^27 + 9 * q^28 + 2 * q^29 - 56 * q^30 - 9 * q^31 - 17 * q^32 - 3 * q^33 - 40 * q^34 - 24 * q^35 + 11 * q^36 + 15 * q^37 - 9 * q^38 + 3 * q^39 + 16 * q^40 - 4 * q^41 + 19 * q^42 - 2 * q^43 - 8 * q^44 - 26 * q^45 - 6 * q^46 + 6 * q^47 + 19 * q^48 + 20 * q^49 - 4 * q^50 + 6 * q^51 + 8 * q^52 + 2 * q^53 + 37 * q^54 - q^55 - 39 * q^56 + 22 * q^57 + 18 * q^58 + 11 * q^59 - 24 * q^60 + 16 * q^61 + 16 * q^62 - 26 * q^63 + 36 * q^64 + q^65 + 3 * q^66 + 9 * q^67 + 12 * q^68 - 3 * q^69 + 32 * q^70 - 15 * q^71 + 5 * q^72 + 32 * q^73 + 22 * q^74 + 4 * q^75 - 26 * q^76 - 4 * q^77 - 3 * q^78 + 14 * q^79 + 56 * q^80 - 2 * q^81 - 24 * q^82 - 26 * q^83 + 43 * q^84 - 12 * q^85 - 10 * q^86 - 38 * q^87 + 6 * q^88 - 23 * q^89 - 10 * q^90 + 4 * q^91 + 83 * q^92 + 23 * q^93 + 46 * q^94 - 52 * q^95 - 56 * q^96 + 27 * q^97 - 3 * q^98 - 13 * 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 $

$2$	−1.70126	−1.20297	−0.601486	−	0.798883i	$-0.705425\pi$
$2$	−1.70126	−1.20297	−0.601486	+	0.798883i	$0.705425\pi$
$3$	−2.43752	−1.40730	−0.703651	−	0.710546i	$-0.748448\pi$
$3$	−2.43752	−1.40730	−0.703651	+	0.710546i	$0.748448\pi$
$4$	0.894288	0.447144
$5$	−4.04114	−1.80725	−0.903627	−	0.428320i	$-0.859106\pi$
$5$	−4.04114	−1.80725	−0.903627	+	0.428320i	$0.859106\pi$
$6$	4.14685	1.69295
$7$	4.09965	1.54952	0.774760	−	0.632255i	$-0.217871\pi$
$7$	4.09965	1.54952	0.774760	+	0.632255i	$0.217871\pi$
$8$	1.88110	0.665071
$9$	2.94150	0.980499
$10$	6.87504	2.17408
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−2.17984	−0.629267
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−6.97457	−1.86403
$15$	9.85036	2.54335
$16$	−4.98882	−1.24721
$17$	3.40252	0.825233	0.412616	−	0.910905i	$-0.364615\pi$
$17$	3.40252	0.825233	0.412616	+	0.910905i	$0.364615\pi$
$18$	−5.00425	−1.17951
$19$	−0.396376	−0.0909349	−0.0454674	−	0.998966i	$-0.514478\pi$
$19$	−0.396376	−0.0909349	−0.0454674	+	0.998966i	$0.514478\pi$
$20$	−3.61395	−0.808103
$21$	−9.99296	−2.18064
$22$	1.70126	0.362710
$23$	1.73007	0.360745	0.180373	−	0.983598i	$-0.442270\pi$
$23$	1.73007	0.360745	0.180373	+	0.983598i	$0.442270\pi$
$24$	−4.58523	−0.935956
$25$	11.3308	2.26617
$26$	−1.70126	−0.333645
$27$	0.142600	0.0274435
$28$	3.66626	0.692859
$29$	7.08646	1.31592	0.657961	−	0.753052i	$-0.271419\pi$
$29$	7.08646	1.31592	0.657961	+	0.753052i	$0.271419\pi$
$30$	−16.7580	−3.05958
$31$	−8.11941	−1.45829	−0.729145	−	0.684360i	$-0.760082\pi$
$31$	−8.11941	−1.45829	−0.729145	+	0.684360i	$0.760082\pi$
$32$	4.72508	0.835285
$33$	2.43752	0.424318
$34$	−5.78858	−0.992733
$35$	−16.5673	−2.80038
$36$	2.63055	0.438424
$37$	2.42720	0.399029	0.199514	−	0.979895i	$-0.436064\pi$
$37$	2.42720	0.399029	0.199514	+	0.979895i	$0.436064\pi$
$38$	0.674339	0.109392
$39$	−2.43752	−0.390315
$40$	−7.60181	−1.20195
$41$	1.88822	0.294891	0.147445	−	0.989070i	$-0.452895\pi$
$41$	1.88822	0.294891	0.147445	+	0.989070i	$0.452895\pi$
$42$	17.0006	2.62325
$43$	2.07827	0.316933	0.158466	−	0.987364i	$-0.449345\pi$
$43$	2.07827	0.316933	0.158466	+	0.987364i	$0.449345\pi$
$44$	−0.894288	−0.134819
$45$	−11.8870	−1.77201
$46$	−2.94331	−0.433967
$47$	3.47252	0.506519	0.253259	−	0.967398i	$-0.418497\pi$
$47$	3.47252	0.506519	0.253259	+	0.967398i	$0.418497\pi$
$48$	12.1604	1.75520
$49$	9.80709	1.40101
$50$	−19.2767	−2.72614
$51$	−8.29371	−1.16135
$52$	0.894288	0.124015
$53$	6.80709	0.935026	0.467513	−	0.883986i	$-0.345150\pi$
$53$	6.80709	0.935026	0.467513	+	0.883986i	$0.345150\pi$
$54$	−0.242600	−0.0330137
$55$	4.04114	0.544908
$56$	7.71186	1.03054
$57$	0.966174	0.127973
$58$	−12.0559	−1.58302
$59$	3.45580	0.449907	0.224953	−	0.974370i	$-0.427777\pi$
$59$	3.45580	0.449907	0.224953	+	0.974370i	$0.427777\pi$
$60$	8.80906	1.13724
$61$	4.40670	0.564220	0.282110	−	0.959382i	$-0.408966\pi$
$61$	4.40670	0.564220	0.282110	+	0.959382i	$0.408966\pi$
$62$	13.8132	1.75428
$63$	12.0591	1.51930
$64$	1.93905	0.242381
$65$	−4.04114	−0.501242
$66$	−4.14685	−0.510443
$67$	−1.82972	−0.223536	−0.111768	−	0.993734i	$-0.535651\pi$
$67$	−1.82972	−0.223536	−0.111768	+	0.993734i	$0.535651\pi$
$68$	3.04283	0.368998
$69$	−4.21709	−0.507678
$70$	28.1852	3.36878
$71$	−2.68563	−0.318726	−0.159363	−	0.987220i	$-0.550944\pi$
$71$	−2.68563	−0.318726	−0.159363	+	0.987220i	$0.550944\pi$
$72$	5.53326	0.652101
$73$	9.07614	1.06228	0.531141	−	0.847283i	$-0.321763\pi$
$73$	9.07614	1.06228	0.531141	+	0.847283i	$0.321763\pi$
$74$	−4.12930	−0.480021
$75$	−27.6191	−3.18918
$76$	−0.354474	−0.0406610
$77$	−4.09965	−0.467198
$78$	4.14685	0.469539
$79$	9.08646	1.02231	0.511153	−	0.859490i	$-0.329218\pi$
$79$	9.08646	1.02231	0.511153	+	0.859490i	$0.329218\pi$
$80$	20.1606	2.25402
$81$	−9.17208	−1.01912
$82$	−3.21236	−0.354745
$83$	−9.37689	−1.02925	−0.514624	−	0.857416i	$-0.672068\pi$
$83$	−9.37689	−1.02925	−0.514624	+	0.857416i	$0.672068\pi$
$84$	−8.93659	−0.975061
$85$	−13.7501	−1.49141
$86$	−3.53568	−0.381262
$87$	−17.2734	−1.85190
$88$	−1.88110	−0.200526
$89$	−13.8034	−1.46315	−0.731576	−	0.681760i	$-0.761215\pi$
$89$	−13.8034	−1.46315	−0.731576	+	0.681760i	$0.761215\pi$
$90$	20.2229	2.13168
$91$	4.09965	0.429760
$92$	1.54718	0.161305
$93$	19.7912	2.05225
$94$	−5.90766	−0.609328
$95$	1.60181	0.164342
$96$	−11.5175	−1.17550
$97$	5.24437	0.532486	0.266243	−	0.963906i	$-0.414218\pi$
$97$	5.24437	0.532486	0.266243	+	0.963906i	$0.414218\pi$
$98$	−16.6844	−1.68538
$99$	−2.94150	−0.295632
$100$	10.1330	1.01330
$101$	9.69221	0.964411	0.482206	−	0.876058i	$-0.339836\pi$
$101$	9.69221	0.964411	0.482206	+	0.876058i	$0.339836\pi$
$102$	14.1098	1.39707
$103$	−16.8660	−1.66185	−0.830926	−	0.556383i	$-0.812189\pi$
$103$	−16.8660	−1.66185	−0.830926	+	0.556383i	$0.812189\pi$
$104$	1.88110	0.184457
$105$	40.3830	3.94098
$106$	−11.5806	−1.12481
$107$	7.89150	0.762901	0.381450	−	0.924389i	$-0.375425\pi$
$107$	7.89150	0.762901	0.381450	+	0.924389i	$0.375425\pi$
$108$	0.127526	0.0122712
$109$	4.28339	0.410274	0.205137	−	0.978733i	$-0.434236\pi$
$109$	4.28339	0.410274	0.205137	+	0.978733i	$0.434236\pi$
$110$	−6.87504	−0.655509
$111$	−5.91634	−0.561554
$112$	−20.4524	−1.93257
$113$	17.0473	1.60367	0.801837	−	0.597543i	$-0.203856\pi$
$113$	17.0473	1.60367	0.801837	+	0.597543i	$0.203856\pi$
$114$	−1.64371	−0.153948
$115$	−6.99147	−0.651958
$116$	6.33734	0.588407
$117$	2.94150	0.271942
$118$	−5.87921	−0.541225
$119$	13.9491	1.27871
$120$	18.5296	1.69151
$121$	1.00000	0.0909091
$122$	−7.49694	−0.678741
$123$	−4.60257	−0.415000
$124$	−7.26109	−0.652065
$125$	−25.5838	−2.28829
$126$	−20.5157	−1.82768
$127$	−11.8915	−1.05520	−0.527600	−	0.849493i	$-0.676908\pi$
$127$	−11.8915	−1.05520	−0.527600	+	0.849493i	$0.676908\pi$
$128$	−12.7490	−1.12686
$129$	−5.06582	−0.446020
$130$	6.87504	0.602981
$131$	−10.8912	−0.951568	−0.475784	−	0.879562i	$-0.657836\pi$
$131$	−10.8912	−0.951568	−0.475784	+	0.879562i	$0.657836\pi$
$132$	2.17984	0.189731
$133$	−1.62500	−0.140905
$134$	3.11283	0.268907
$135$	−0.576269	−0.0495973
$136$	6.40050	0.548838
$137$	−8.79918	−0.751764	−0.375882	−	0.926667i	$-0.622660\pi$
$137$	−8.79918	−0.751764	−0.375882	+	0.926667i	$0.622660\pi$
$138$	7.17436	0.610722
$139$	14.2550	1.20909	0.604546	−	0.796571i	$-0.293355\pi$
$139$	14.2550	1.20909	0.604546	+	0.796571i	$0.293355\pi$
$140$	−14.8159	−1.25217
$141$	−8.46432	−0.712825
$142$	4.56896	0.383419
$143$	−1.00000	−0.0836242
$144$	−14.6746	−1.22288
$145$	−28.6374	−2.37821
$146$	−15.4409	−1.27790
$147$	−23.9050	−1.97165
$148$	2.17061	0.178423
$149$	6.08751	0.498708	0.249354	−	0.968412i	$-0.419782\pi$
$149$	6.08751	0.498708	0.249354	+	0.968412i	$0.419782\pi$
$150$	46.9873	3.83650
$151$	−11.2279	−0.913713	−0.456856	−	0.889540i	$-0.651025\pi$
$151$	−11.2279	−0.913713	−0.456856	+	0.889540i	$0.651025\pi$
$152$	−0.745624	−0.0604781
$153$	10.0085	0.809140
$154$	6.97457	0.562026
$155$	32.8117	2.63550
$156$	−2.17984	−0.174527
$157$	2.66425	0.212631	0.106315	−	0.994332i	$-0.466095\pi$
$157$	2.66425	0.212631	0.106315	+	0.994332i	$0.466095\pi$
$158$	−15.4584	−1.22981
$159$	−16.5924	−1.31586
$160$	−19.0947	−1.50957
$161$	7.09269	0.558982
$162$	15.6041	1.22597
$163$	18.4973	1.44882	0.724408	−	0.689371i	$-0.242113\pi$
$163$	18.4973	1.44882	0.724408	+	0.689371i	$0.242113\pi$
$164$	1.68861	0.131859
$165$	−9.85036	−0.766850
$166$	15.9525	1.23816
$167$	12.2653	0.949117	0.474559	−	0.880224i	$-0.342608\pi$
$167$	12.2653	0.949117	0.474559	+	0.880224i	$0.342608\pi$
$168$	−18.7978	−1.45028
$169$	1.00000	0.0769231
$170$	23.3925	1.79412
$171$	−1.16594	−0.0891616
$172$	1.85857	0.141715
$173$	−1.21962	−0.0927258	−0.0463629	−	0.998925i	$-0.514763\pi$
$173$	−1.21962	−0.0927258	−0.0463629	+	0.998925i	$0.514763\pi$
$174$	29.3865	2.22779
$175$	46.4524	3.51147
$176$	4.98882	0.376047
$177$	−8.42357	−0.633154
$178$	23.4831	1.76013
$179$	4.17430	0.312002	0.156001	−	0.987757i	$-0.450140\pi$
$179$	4.17430	0.312002	0.156001	+	0.987757i	$0.450140\pi$
$180$	−10.6304	−0.792344
$181$	−22.8180	−1.69605	−0.848025	−	0.529957i	$-0.822208\pi$
$181$	−22.8180	−1.69605	−0.848025	+	0.529957i	$0.822208\pi$
$182$	−6.97457	−0.516989
$183$	−10.7414	−0.794028
$184$	3.25445	0.239921
$185$	−9.80865	−0.721146
$186$	−33.6700	−2.46881
$187$	−3.40252	−0.248817
$188$	3.10543	0.226487
$189$	0.584611	0.0425242
$190$	−2.72510	−0.197699
$191$	14.9720	1.08334	0.541668	−	0.840593i	$-0.317793\pi$
$191$	14.9720	1.08334	0.541668	+	0.840593i	$0.317793\pi$
$192$	−4.72648	−0.341104
$193$	18.5846	1.33775	0.668875	−	0.743375i	$-0.266776\pi$
$193$	18.5846	1.33775	0.668875	+	0.743375i	$0.266776\pi$
$194$	−8.92205	−0.640566
$195$	9.85036	0.705399
$196$	8.77036	0.626454
$197$	0.623951	0.0444547	0.0222273	−	0.999753i	$-0.492924\pi$
$197$	0.623951	0.0444547	0.0222273	+	0.999753i	$0.492924\pi$
$198$	5.00425	0.355637
$199$	11.8568	0.840503	0.420252	−	0.907408i	$-0.361942\pi$
$199$	11.8568	0.840503	0.420252	+	0.907408i	$0.361942\pi$
$200$	21.3145	1.50716
$201$	4.45997	0.314582
$202$	−16.4890	−1.16016
$203$	29.0520	2.03905
$204$	−7.41696	−0.519291
$205$	−7.63057	−0.532942
$206$	28.6934	1.99916
$207$	5.08901	0.353710
$208$	−4.98882	−0.345913
$209$	0.396376	0.0274179
$210$	−68.7020	−4.74089
$211$	−20.8282	−1.43387	−0.716936	−	0.697139i	$-0.754456\pi$
$211$	−20.8282	−1.43387	−0.716936	+	0.697139i	$0.754456\pi$
$212$	6.08750	0.418091
$213$	6.54628	0.448543
$214$	−13.4255	−0.917749
$215$	−8.39858	−0.572778
$216$	0.268246	0.0182518
$217$	−33.2867	−2.25965
$218$	−7.28716	−0.493549
$219$	−22.1233	−1.49495
$220$	3.61395	0.243652
$221$	3.40252	0.228878
$222$	10.0652	0.675534
$223$	−16.1934	−1.08439	−0.542196	−	0.840252i	$-0.682407\pi$
$223$	−16.1934	−1.08439	−0.542196	+	0.840252i	$0.682407\pi$
$224$	19.3712	1.29429
$225$	33.3296	2.22198
$226$	−29.0019	−1.92918
$227$	4.34277	0.288240	0.144120	−	0.989560i	$-0.453965\pi$
$227$	4.34277	0.288240	0.144120	+	0.989560i	$0.453965\pi$
$228$	0.864038	0.0572223
$229$	6.22428	0.411312	0.205656	−	0.978624i	$-0.434067\pi$
$229$	6.22428	0.411312	0.205656	+	0.978624i	$0.434067\pi$
$230$	11.8943	0.784288
$231$	9.99296	0.657489
$232$	13.3304	0.875182
$233$	2.48449	0.162764	0.0813822	−	0.996683i	$-0.474067\pi$
$233$	2.48449	0.162764	0.0813822	+	0.996683i	$0.474067\pi$
$234$	−5.00425	−0.327138
$235$	−14.0329	−0.915408
$236$	3.09048	0.201173
$237$	−22.1484	−1.43869
$238$	−23.7311	−1.53826
$239$	12.5609	0.812500	0.406250	−	0.913762i	$-0.366836\pi$
$239$	12.5609	0.812500	0.406250	+	0.913762i	$0.366836\pi$
$240$	−49.1417	−3.17209
$241$	7.29902	0.470171	0.235085	−	0.971975i	$-0.424463\pi$
$241$	7.29902	0.470171	0.235085	+	0.971975i	$0.424463\pi$
$242$	−1.70126	−0.109361
$243$	21.9293	1.40677
$244$	3.94086	0.252287
$245$	−39.6319	−2.53199
$246$	7.83018	0.499234
$247$	−0.396376	−0.0252208
$248$	−15.2735	−0.969866
$249$	22.8563	1.44846
$250$	43.5247	2.75275
$251$	14.2029	0.896479	0.448240	−	0.893913i	$-0.352051\pi$
$251$	14.2029	0.896479	0.448240	+	0.893913i	$0.352051\pi$
$252$	10.7843	0.679347
$253$	−1.73007	−0.108769
$254$	20.2305	1.26938
$255$	33.5161	2.09886
$256$	17.8113	1.11320
$257$	16.3651	1.02083	0.510413	−	0.859930i	$-0.329493\pi$
$257$	16.3651	1.02083	0.510413	+	0.859930i	$0.329493\pi$
$258$	8.61828	0.536551
$259$	9.95065	0.618303
$260$	−3.61395	−0.224127
$261$	20.8448	1.29026
$262$	18.5288	1.14471
$263$	−13.7931	−0.850517	−0.425258	−	0.905072i	$-0.639817\pi$
$263$	−13.7931	−0.850517	−0.425258	+	0.905072i	$0.639817\pi$
$264$	4.58523	0.282201
$265$	−27.5084	−1.68983
$266$	2.76455	0.169505
$267$	33.6459	2.05910
$268$	−1.63630	−0.0999527
$269$	−19.3937	−1.18245	−0.591226	−	0.806506i	$-0.701356\pi$
$269$	−19.3937	−1.18245	−0.591226	+	0.806506i	$0.701356\pi$
$270$	0.980383	0.0596642
$271$	−1.53363	−0.0931613	−0.0465807	−	0.998915i	$-0.514832\pi$
$271$	−1.53363	−0.0931613	−0.0465807	+	0.998915i	$0.514832\pi$
$272$	−16.9746	−1.02924
$273$	−9.99296	−0.604802
$274$	14.9697	0.904352
$275$	−11.3308	−0.683275
$276$	−3.77129	−0.227005
$277$	−2.29267	−0.137753	−0.0688765	−	0.997625i	$-0.521941\pi$
$277$	−2.29267	−0.137753	−0.0688765	+	0.997625i	$0.521941\pi$
$278$	−24.2514	−1.45450
$279$	−23.8832	−1.42985
$280$	−31.1647	−1.86245
$281$	−7.16268	−0.427290	−0.213645	−	0.976911i	$-0.568534\pi$
$281$	−7.16268	−0.427290	−0.213645	+	0.976911i	$0.568534\pi$
$282$	14.4000	0.857509
$283$	−14.6921	−0.873357	−0.436678	−	0.899618i	$-0.643845\pi$
$283$	−14.6921	−0.873357	−0.436678	+	0.899618i	$0.643845\pi$
$284$	−2.40173	−0.142516
$285$	−3.90445	−0.231279
$286$	1.70126	0.100598
$287$	7.74104	0.456939
$288$	13.8988	0.818996
$289$	−5.42285	−0.318991
$290$	48.7197	2.86092
$291$	−12.7833	−0.749368
$292$	8.11668	0.474993
$293$	−29.3925	−1.71713	−0.858563	−	0.512708i	$-0.828642\pi$
$293$	−29.3925	−1.71713	−0.858563	+	0.512708i	$0.828642\pi$
$294$	40.6686	2.37184
$295$	−13.9654	−0.813095
$296$	4.56581	0.265382
$297$	−0.142600	−0.00827451
$298$	−10.3564	−0.599933
$299$	1.73007	0.100053
$300$	−24.6995	−1.42602
$301$	8.52016	0.491094
$302$	19.1016	1.09917
$303$	−23.6250	−1.35722
$304$	1.97745	0.113415
$305$	−17.8081	−1.01969
$306$	−17.0271	−0.973374
$307$	16.9780	0.968984	0.484492	−	0.874796i	$-0.339005\pi$
$307$	16.9780	0.968984	0.484492	+	0.874796i	$0.339005\pi$
$308$	−3.66626	−0.208905
$309$	41.1111	2.33873
$310$	−55.8213	−3.17043
$311$	2.10668	0.119459	0.0597295	−	0.998215i	$-0.480976\pi$
$311$	2.10668	0.119459	0.0597295	+	0.998215i	$0.480976\pi$
$312$	−4.58523	−0.259587
$313$	26.9458	1.52307	0.761534	−	0.648125i	$-0.224446\pi$
$313$	26.9458	1.52307	0.761534	+	0.648125i	$0.224446\pi$
$314$	−4.53259	−0.255789
$315$	−48.7325	−2.74577
$316$	8.12591	0.457118
$317$	31.9377	1.79380	0.896900	−	0.442234i	$-0.145814\pi$
$317$	31.9377	1.79380	0.896900	+	0.442234i	$0.145814\pi$
$318$	28.2280	1.58295
$319$	−7.08646	−0.396766
$320$	−7.83599	−0.438045
$321$	−19.2357	−1.07363
$322$	−12.0665	−0.672440
$323$	−1.34868	−0.0750424
$324$	−8.20248	−0.455694
$325$	11.3308	0.628522
$326$	−31.4687	−1.74289
$327$	−10.4408	−0.577380
$328$	3.55194	0.196123
$329$	14.2361	0.784861
$330$	16.7580	0.922499
$331$	5.29162	0.290854	0.145427	−	0.989369i	$-0.453544\pi$
$331$	5.29162	0.290854	0.145427	+	0.989369i	$0.453544\pi$
$332$	−8.38564	−0.460222
$333$	7.13960	0.391247
$334$	−20.8665	−1.14176
$335$	7.39416	0.403986
$336$	49.8531	2.71971
$337$	−6.76654	−0.368597	−0.184299	−	0.982870i	$-0.559001\pi$
$337$	−6.76654	−0.368597	−0.184299	+	0.982870i	$0.559001\pi$
$338$	−1.70126	−0.0925364
$339$	−41.5531	−2.25685
$340$	−12.2965	−0.666873
$341$	8.11941	0.439691
$342$	1.98357	0.107259
$343$	11.5081	0.621378
$344$	3.90944	0.210783
$345$	17.0419	0.917502
$346$	2.07489	0.111547
$347$	−23.5754	−1.26560	−0.632798	−	0.774317i	$-0.718094\pi$
$347$	−23.5754	−1.26560	−0.632798	+	0.774317i	$0.718094\pi$
$348$	−15.4474	−0.828066
$349$	25.7778	1.37985	0.689927	−	0.723879i	$-0.257643\pi$
$349$	25.7778	1.37985	0.689927	+	0.723879i	$0.257643\pi$
$350$	−79.0277	−4.22421
$351$	0.142600	0.00761145
$352$	−4.72508	−0.251848
$353$	−7.74163	−0.412045	−0.206023	−	0.978547i	$-0.566052\pi$
$353$	−7.74163	−0.412045	−0.206023	+	0.978547i	$0.566052\pi$
$354$	14.3307	0.761668
$355$	10.8530	0.576018
$356$	−12.3442	−0.654240
$357$	−34.0013	−1.79954
$358$	−7.10157	−0.375330
$359$	−7.85807	−0.414733	−0.207367	−	0.978263i	$-0.566489\pi$
$359$	−7.85807	−0.414733	−0.207367	+	0.978263i	$0.566489\pi$
$360$	−22.3607	−1.17851
$361$	−18.8429	−0.991731
$362$	38.8194	2.04030
$363$	−2.43752	−0.127937
$364$	3.66626	0.192164
$365$	−36.6780	−1.91981
$366$	18.2739	0.955194
$367$	−3.89469	−0.203301	−0.101651	−	0.994820i	$-0.532412\pi$
$367$	−3.89469	−0.203301	−0.101651	+	0.994820i	$0.532412\pi$
$368$	−8.63103	−0.449924
$369$	5.55420	0.289140
$370$	16.6871	0.867520
$371$	27.9067	1.44884
$372$	17.6990	0.917653
$373$	9.93402	0.514364	0.257182	−	0.966363i	$-0.417206\pi$
$373$	9.93402	0.514364	0.257182	+	0.966363i	$0.417206\pi$
$374$	5.78858	0.299320
$375$	62.3610	3.22031
$376$	6.53217	0.336871
$377$	7.08646	0.364971
$378$	−0.994576	−0.0511555
$379$	−9.64280	−0.495317	−0.247659	−	0.968847i	$-0.579661\pi$
$379$	−9.64280	−0.495317	−0.247659	+	0.968847i	$0.579661\pi$
$380$	1.43248	0.0734847
$381$	28.9858	1.48499
$382$	−25.4713	−1.30322
$383$	−34.8472	−1.78061	−0.890305	−	0.455365i	$-0.849509\pi$
$383$	−34.8472	−1.78061	−0.890305	+	0.455365i	$0.849509\pi$
$384$	31.0759	1.58584
$385$	16.5673	0.844345
$386$	−31.6173	−1.60928
$387$	6.11322	0.310753
$388$	4.68998	0.238098
$389$	−14.5262	−0.736510	−0.368255	−	0.929725i	$-0.620045\pi$
$389$	−14.5262	−0.736510	−0.368255	+	0.929725i	$0.620045\pi$
$390$	−16.7580	−0.848576
$391$	5.88661	0.297699
$392$	18.4482	0.931773
$393$	26.5475	1.33914
$394$	−1.06150	−0.0534777
$395$	−36.7197	−1.84757
$396$	−2.63055	−0.132190
$397$	3.44615	0.172957	0.0864786	−	0.996254i	$-0.472439\pi$
$397$	3.44615	0.172957	0.0864786	+	0.996254i	$0.472439\pi$
$398$	−20.1714	−1.01110
$399$	3.96097	0.198296
$400$	−56.5276	−2.82638
$401$	−25.0358	−1.25023	−0.625115	−	0.780533i	$-0.714948\pi$
$401$	−25.0358	−1.25023	−0.625115	+	0.780533i	$0.714948\pi$
$402$	−7.58758	−0.378434
$403$	−8.11941	−0.404457
$404$	8.66763	0.431231
$405$	37.0657	1.84181
$406$	−49.4250	−2.45292
$407$	−2.42720	−0.120312
$408$	−15.6013	−0.772381
$409$	31.6483	1.56491	0.782455	−	0.622707i	$-0.213967\pi$
$409$	31.6483	1.56491	0.782455	+	0.622707i	$0.213967\pi$
$410$	12.9816	0.641115
$411$	21.4482	1.05796
$412$	−15.0830	−0.743087
$413$	14.1675	0.697139
$414$	−8.65773	−0.425504
$415$	37.8933	1.86011
$416$	4.72508	0.231666
$417$	−34.7468	−1.70156
$418$	−0.674339	−0.0329830
$419$	12.8660	0.628543	0.314271	−	0.949333i	$-0.398240\pi$
$419$	12.8660	0.628543	0.314271	+	0.949333i	$0.398240\pi$
$420$	36.1140	1.76218
$421$	22.0558	1.07494	0.537468	−	0.843284i	$-0.319381\pi$
$421$	22.0558	1.07494	0.537468	+	0.843284i	$0.319381\pi$
$422$	35.4342	1.72491
$423$	10.2144	0.496641
$424$	12.8048	0.621858
$425$	38.5534	1.87012
$426$	−11.1369	−0.539586
$427$	18.0659	0.874270
$428$	7.05728	0.341126
$429$	2.43752	0.117685
$430$	14.2882	0.689037
$431$	−8.67775	−0.417992	−0.208996	−	0.977916i	$-0.567020\pi$
$431$	−8.67775	−0.417992	−0.208996	+	0.977916i	$0.567020\pi$
$432$	−0.711408	−0.0342277
$433$	−12.0952	−0.581261	−0.290630	−	0.956835i	$-0.593865\pi$
$433$	−12.0952	−0.581261	−0.290630	+	0.956835i	$0.593865\pi$
$434$	56.6294	2.71830
$435$	69.8042	3.34686
$436$	3.83058	0.183452
$437$	−0.685760	−0.0328043
$438$	37.6374	1.79839
$439$	−36.2082	−1.72812	−0.864062	−	0.503386i	$-0.832087\pi$
$439$	−36.2082	−1.72812	−0.864062	+	0.503386i	$0.832087\pi$
$440$	7.60181	0.362402
$441$	28.8475	1.37369
$442$	−5.78858	−0.275334
$443$	6.22717	0.295862	0.147931	−	0.988998i	$-0.452739\pi$
$443$	6.22717	0.295862	0.147931	+	0.988998i	$0.452739\pi$
$444$	−5.29091	−0.251096
$445$	55.7813	2.64429
$446$	27.5492	1.30449
$447$	−14.8384	−0.701833
$448$	7.94942	0.375575
$449$	−33.6313	−1.58716	−0.793579	−	0.608467i	$-0.791785\pi$
$449$	−33.6313	−1.58716	−0.793579	+	0.608467i	$0.791785\pi$
$450$	−56.7024	−2.67298
$451$	−1.88822	−0.0889129
$452$	15.2452	0.717073
$453$	27.3682	1.28587
$454$	−7.38818	−0.346744
$455$	−16.5673	−0.776685
$456$	1.81747	0.0851110
$457$	36.9744	1.72959	0.864795	−	0.502126i	$-0.167448\pi$
$457$	36.9744	1.72959	0.864795	+	0.502126i	$0.167448\pi$
$458$	−10.5891	−0.494797
$459$	0.485201	0.0226472
$460$	−6.25239	−0.291519
$461$	−32.3747	−1.50784	−0.753919	−	0.656967i	$-0.771839\pi$
$461$	−32.3747	−1.50784	−0.753919	+	0.656967i	$0.771839\pi$
$462$	−17.0006	−0.790941
$463$	−22.9642	−1.06724	−0.533619	−	0.845725i	$-0.679168\pi$
$463$	−22.9642	−1.06724	−0.533619	+	0.845725i	$0.679168\pi$
$464$	−35.3531	−1.64123
$465$	−79.9791	−3.70894
$466$	−4.22677	−0.195801
$467$	40.8537	1.89048	0.945241	−	0.326374i	$-0.105827\pi$
$467$	40.8537	1.89048	0.945241	+	0.326374i	$0.105827\pi$
$468$	2.63055	0.121597
$469$	−7.50120	−0.346373
$470$	23.8737	1.10121
$471$	−6.49417	−0.299236
$472$	6.50072	0.299220
$473$	−2.07827	−0.0955589
$474$	37.6802	1.73071
$475$	−4.49127	−0.206074
$476$	12.4745	0.571770
$477$	20.0230	0.916792
$478$	−21.3694	−0.977416
$479$	−23.5490	−1.07598	−0.537991	−	0.842951i	$-0.680816\pi$
$479$	−23.5490	−1.07598	−0.537991	+	0.842951i	$0.680816\pi$
$480$	46.5438	2.12442
$481$	2.42720	0.110671
$482$	−12.4175	−0.565603
$483$	−17.2886	−0.786657
$484$	0.894288	0.0406495
$485$	−21.1933	−0.962337
$486$	−37.3075	−1.69230
$487$	−20.7103	−0.938473	−0.469236	−	0.883073i	$-0.655471\pi$
$487$	−20.7103	−0.938473	−0.469236	+	0.883073i	$0.655471\pi$
$488$	8.28946	0.375246
$489$	−45.0874	−2.03892
$490$	67.4241	3.04591
$491$	−12.3158	−0.555805	−0.277903	−	0.960609i	$-0.589639\pi$
$491$	−12.3158	−0.555805	−0.277903	+	0.960609i	$0.589639\pi$
$492$	−4.11603	−0.185565
$493$	24.1118	1.08594
$494$	0.674339	0.0303399
$495$	11.8870	0.534281
$496$	40.5063	1.81879
$497$	−11.0101	−0.493872
$498$	−38.8846	−1.74246
$499$	−5.19913	−0.232745	−0.116373	−	0.993206i	$-0.537127\pi$
$499$	−5.19913	−0.232745	−0.116373	+	0.993206i	$0.537127\pi$
$500$	−22.8793	−1.02319
$501$	−29.8969	−1.33569
$502$	−24.1628	−1.07844
$503$	21.3719	0.952926	0.476463	−	0.879195i	$-0.341919\pi$
$503$	21.3719	0.952926	0.476463	+	0.879195i	$0.341919\pi$
$504$	22.6844	1.01044
$505$	−39.1676	−1.74294
$506$	2.94331	0.130846
$507$	−2.43752	−0.108254
$508$	−10.6344	−0.471827
$509$	−37.8529	−1.67780	−0.838899	−	0.544287i	$-0.816800\pi$
$509$	−37.8529	−1.67780	−0.838899	+	0.544287i	$0.816800\pi$
$510$	−57.0196	−2.52487
$511$	37.2090	1.64603
$512$	−4.80361	−0.212292
$513$	−0.0565234	−0.00249557
$514$	−27.8413	−1.22802
$515$	68.1577	3.00339
$516$	−4.53030	−0.199435
$517$	−3.47252	−0.152721
$518$	−16.9286	−0.743802
$519$	2.97284	0.130493
$520$	−7.60181	−0.333361
$521$	31.9468	1.39961	0.699807	−	0.714332i	$-0.253269\pi$
$521$	31.9468	1.39961	0.699807	+	0.714332i	$0.253269\pi$
$522$	−35.4625	−1.55215
$523$	−25.1609	−1.10021	−0.550106	−	0.835095i	$-0.685413\pi$
$523$	−25.1609	−1.10021	−0.550106	+	0.835095i	$0.685413\pi$
$524$	−9.73986	−0.425488
$525$	−113.229	−4.94170
$526$	23.4656	1.02315
$527$	−27.6265	−1.20343
$528$	−12.1604	−0.529212
$529$	−20.0068	−0.869863
$530$	46.7990	2.03282
$531$	10.1652	0.441133
$532$	−1.45322	−0.0630050
$533$	1.88822	0.0817879
$534$	−57.2405	−2.47704
$535$	−31.8907	−1.37876
$536$	−3.44189	−0.148667
$537$	−10.1749	−0.439081
$538$	32.9937	1.42246
$539$	−9.80709	−0.422421
$540$	−0.515350	−0.0221771
$541$	−2.80642	−0.120657	−0.0603286	−	0.998179i	$-0.519215\pi$
$541$	−2.80642	−0.120657	−0.0603286	+	0.998179i	$0.519215\pi$
$542$	2.60910	0.112071
$543$	55.6193	2.38685
$544$	16.0772	0.689304
$545$	−17.3098	−0.741470
$546$	17.0006	0.727560
$547$	−40.2758	−1.72207	−0.861034	−	0.508548i	$-0.830183\pi$
$547$	−40.2758	−1.72207	−0.861034	+	0.508548i	$0.830183\pi$
$548$	−7.86900	−0.336147
$549$	12.9623	0.553217
$550$	19.2767	0.821961
$551$	−2.80890	−0.119663
$552$	−7.93278	−0.337642
$553$	37.2513	1.58409
$554$	3.90042	0.165713
$555$	23.9088	1.01487
$556$	12.7481	0.540638
$557$	11.3325	0.480171	0.240086	−	0.970752i	$-0.422824\pi$
$557$	11.3325	0.480171	0.240086	+	0.970752i	$0.422824\pi$
$558$	40.6316	1.72007
$559$	2.07827	0.0879014
$560$	82.6511	3.49265
$561$	8.29371	0.350161
$562$	12.1856	0.514018
$563$	19.1734	0.808063	0.404031	−	0.914745i	$-0.367609\pi$
$563$	19.1734	0.808063	0.404031	+	0.914745i	$0.367609\pi$
$564$	−7.56954	−0.318735
$565$	−68.8905	−2.89825
$566$	24.9951	1.05062
$567$	−37.6023	−1.57915
$568$	−5.05195	−0.211975
$569$	10.5325	0.441547	0.220773	−	0.975325i	$-0.429142\pi$
$569$	10.5325	0.441547	0.220773	+	0.975325i	$0.429142\pi$
$570$	6.64248	0.278223
$571$	40.0798	1.67729	0.838643	−	0.544681i	$-0.183349\pi$
$571$	40.0798	1.67729	0.838643	+	0.544681i	$0.183349\pi$
$572$	−0.894288	−0.0373921
$573$	−36.4945	−1.52458
$574$	−13.1695	−0.549685
$575$	19.6032	0.817509
$576$	5.70372	0.237655
$577$	42.2857	1.76038	0.880189	−	0.474623i	$-0.157416\pi$
$577$	42.2857	1.76038	0.880189	+	0.474623i	$0.157416\pi$
$578$	9.22568	0.383738
$579$	−45.3003	−1.88262
$580$	−25.6101	−1.06340
$581$	−38.4419	−1.59484
$582$	21.7477	0.901469
$583$	−6.80709	−0.281921
$584$	17.0732	0.706493
$585$	−11.8870	−0.491467
$586$	50.0042	2.06566
$587$	38.7873	1.60092	0.800462	−	0.599383i	$-0.204587\pi$
$587$	38.7873	1.60092	0.800462	+	0.599383i	$0.204587\pi$
$588$	−21.3779	−0.881611
$589$	3.21834	0.132609
$590$	23.7587	0.978132
$591$	−1.52089	−0.0625611
$592$	−12.1089	−0.497671
$593$	25.3972	1.04294	0.521469	−	0.853270i	$-0.325384\pi$
$593$	25.3972	1.04294	0.521469	+	0.853270i	$0.325384\pi$
$594$	0.242600	0.00995402
$595$	−56.3704	−2.31096
$596$	5.44399	0.222994
$597$	−28.9011	−1.18284
$598$	−2.94331	−0.120361
$599$	−45.3898	−1.85458	−0.927289	−	0.374345i	$-0.877867\pi$
$599$	−45.3898	−1.85458	−0.927289	+	0.374345i	$0.877867\pi$
$600$	−51.9545	−2.12103
$601$	13.5602	0.553131	0.276566	−	0.960995i	$-0.410804\pi$
$601$	13.5602	0.553131	0.276566	+	0.960995i	$0.410804\pi$
$602$	−14.4950	−0.590773
$603$	−5.38211	−0.219177
$604$	−10.0410	−0.408561
$605$	−4.04114	−0.164296
$606$	40.1922	1.63270
$607$	15.7400	0.638866	0.319433	−	0.947609i	$-0.396508\pi$
$607$	15.7400	0.638866	0.319433	+	0.947609i	$0.396508\pi$
$608$	−1.87291	−0.0759565
$609$	−70.8147	−2.86956
$610$	30.2962	1.22666
$611$	3.47252	0.140483
$612$	8.95049	0.361802
$613$	−40.4979	−1.63570	−0.817848	−	0.575434i	$-0.804833\pi$
$613$	−40.4979	−1.63570	−0.817848	+	0.575434i	$0.804833\pi$
$614$	−28.8839	−1.16566
$615$	18.5997	0.750011
$616$	−7.71186	−0.310720
$617$	13.8502	0.557589	0.278794	−	0.960351i	$-0.410065\pi$
$617$	13.8502	0.557589	0.278794	+	0.960351i	$0.410065\pi$
$618$	−69.9407	−2.81343
$619$	−15.8763	−0.638121	−0.319060	−	0.947734i	$-0.603367\pi$
$619$	−15.8763	−0.638121	−0.319060	+	0.947734i	$0.603367\pi$
$620$	29.3431	1.17845
$621$	0.246709	0.00990010
$622$	−3.58402	−0.143706
$623$	−56.5888	−2.26718
$624$	12.1604	0.486804
$625$	46.7337	1.86935
$626$	−45.8419	−1.83221
$627$	−0.966174	−0.0385853
$628$	2.38261	0.0950765
$629$	8.25859	0.329292
$630$	82.9067	3.30308
$631$	27.3354	1.08821	0.544103	−	0.839019i	$-0.316870\pi$
$631$	27.3354	1.08821	0.544103	+	0.839019i	$0.316870\pi$
$632$	17.0926	0.679906
$633$	50.7691	2.01789
$634$	−54.3343	−2.15789
$635$	48.0553	1.90702
$636$	−14.8384	−0.588381
$637$	9.80709	0.388571
$638$	12.0559	0.477298
$639$	−7.89978	−0.312510
$640$	51.5205	2.03653
$641$	6.44245	0.254461	0.127231	−	0.991873i	$-0.459391\pi$
$641$	6.44245	0.254461	0.127231	+	0.991873i	$0.459391\pi$
$642$	32.7249	1.29155
$643$	7.20771	0.284244	0.142122	−	0.989849i	$-0.454607\pi$
$643$	7.20771	0.284244	0.142122	+	0.989849i	$0.454607\pi$
$644$	6.34291	0.249945
$645$	20.4717	0.806072
$646$	2.29445	0.0902740
$647$	−10.8445	−0.426343	−0.213171	−	0.977015i	$-0.568379\pi$
$647$	−10.8445	−0.426343	−0.213171	+	0.977015i	$0.568379\pi$
$648$	−17.2536	−0.677787
$649$	−3.45580	−0.135652
$650$	−19.2767	−0.756095
$651$	81.1370	3.18001
$652$	16.5419	0.647830
$653$	−25.7975	−1.00954	−0.504768	−	0.863255i	$-0.668422\pi$
$653$	−25.7975	−1.00954	−0.504768	+	0.863255i	$0.668422\pi$
$654$	17.7626	0.694572
$655$	44.0128	1.71972
$656$	−9.42000	−0.367789
$657$	26.6974	1.04157
$658$	−24.2193	−0.944166
$659$	−17.8193	−0.694143	−0.347071	−	0.937839i	$-0.612824\pi$
$659$	−17.8193	−0.694143	−0.347071	+	0.937839i	$0.612824\pi$
$660$	−8.80906	−0.342892
$661$	−29.3578	−1.14188	−0.570942	−	0.820990i	$-0.693422\pi$
$661$	−29.3578	−1.14188	−0.570942	+	0.820990i	$0.693422\pi$
$662$	−9.00242	−0.349889
$663$	−8.29371	−0.322101
$664$	−17.6389	−0.684522
$665$	6.56686	0.254652
$666$	−12.1463	−0.470660
$667$	12.2601	0.474713
$668$	10.9687	0.424392
$669$	39.4718	1.52607
$670$	−12.5794	−0.485984
$671$	−4.40670	−0.170119
$672$	−47.2176	−1.82146
$673$	44.4945	1.71514	0.857569	−	0.514370i	$-0.171974\pi$
$673$	44.4945	1.71514	0.857569	+	0.514370i	$0.171974\pi$
$674$	11.5117	0.443412
$675$	1.61578	0.0621915
$676$	0.894288	0.0343957
$677$	−37.9617	−1.45898	−0.729492	−	0.683989i	$-0.760244\pi$
$677$	−37.9617	−1.45898	−0.729492	+	0.683989i	$0.760244\pi$
$678$	70.6926	2.71493
$679$	21.5001	0.825097
$680$	−25.8653	−0.991890
$681$	−10.5856	−0.405640
$682$	−13.8132	−0.528936
$683$	−41.5368	−1.58936	−0.794681	−	0.607028i	$-0.792362\pi$
$683$	−41.5368	−1.58936	−0.794681	+	0.607028i	$0.792362\pi$
$684$	−1.04269	−0.0398681
$685$	35.5587	1.35863
$686$	−19.5782	−0.747500
$687$	−15.1718	−0.578840
$688$	−10.3681	−0.395281
$689$	6.80709	0.259329
$690$	−28.9926	−1.10373
$691$	−20.7049	−0.787652	−0.393826	−	0.919185i	$-0.628849\pi$
$691$	−20.7049	−0.787652	−0.393826	+	0.919185i	$0.628849\pi$
$692$	−1.09069	−0.0414618
$693$	−12.0591	−0.458087
$694$	40.1080	1.52248
$695$	−57.6064	−2.18513
$696$	−32.4930	−1.23165
$697$	6.42471	0.243353
$698$	−43.8547	−1.65993
$699$	−6.05599	−0.229059
$700$	41.5418	1.57013
$701$	−27.7358	−1.04757	−0.523783	−	0.851852i	$-0.675480\pi$
$701$	−27.7358	−1.04757	−0.523783	+	0.851852i	$0.675480\pi$
$702$	−0.242600	−0.00915636
$703$	−0.962083	−0.0362856
$704$	−1.93905	−0.0730808
$705$	34.2055	1.28826
$706$	13.1705	0.495680
$707$	39.7346	1.49437
$708$	−7.53310	−0.283111
$709$	−19.8829	−0.746718	−0.373359	−	0.927687i	$-0.621794\pi$
$709$	−19.8829	−0.746718	−0.373359	+	0.927687i	$0.621794\pi$
$710$	−18.4638	−0.692935
$711$	26.7278	1.00237
$712$	−25.9655	−0.973100
$713$	−14.0472	−0.526071
$714$	57.8450	2.16480
$715$	4.04114	0.151130
$716$	3.73302	0.139510
$717$	−30.6175	−1.14343
$718$	13.3686	0.498913
$719$	35.3506	1.31835	0.659177	−	0.751988i	$-0.270905\pi$
$719$	35.3506	1.31835	0.659177	+	0.751988i	$0.270905\pi$
$720$	59.3022	2.21006
$721$	−69.1444	−2.57507
$722$	32.0567	1.19303
$723$	−17.7915	−0.661673
$724$	−20.4059	−0.758378
$725$	80.2955	2.98210
$726$	4.14685	0.153904
$727$	−10.0544	−0.372897	−0.186449	−	0.982465i	$-0.559698\pi$
$727$	−10.0544	−0.372897	−0.186449	+	0.982465i	$0.559698\pi$
$728$	7.71186	0.285821
$729$	−25.9369	−0.960626
$730$	62.3988	2.30948
$731$	7.07135	0.261543
$732$	−9.60591	−0.355045
$733$	−12.6585	−0.467554	−0.233777	−	0.972290i	$-0.575109\pi$
$733$	−12.6585	−0.467554	−0.233777	+	0.972290i	$0.575109\pi$
$734$	6.62589	0.244566
$735$	96.6034	3.56327
$736$	8.17474	0.301325
$737$	1.82972	0.0673986
$738$	−9.44914	−0.347828
$739$	19.6098	0.721357	0.360679	−	0.932690i	$-0.382545\pi$
$739$	19.6098	0.721357	0.360679	+	0.932690i	$0.382545\pi$
$740$	−8.77176	−0.322456
$741$	0.966174	0.0354933
$742$	−47.4765	−1.74292
$743$	17.5525	0.643940	0.321970	−	0.946750i	$-0.395655\pi$
$743$	17.5525	0.643940	0.321970	+	0.946750i	$0.395655\pi$
$744$	37.2293	1.36489
$745$	−24.6005	−0.901293
$746$	−16.9004	−0.618766
$747$	−27.5821	−1.00918
$748$	−3.04283	−0.111257
$749$	32.3524	1.18213
$750$	−106.092	−3.87394
$751$	15.6289	0.570305	0.285152	−	0.958482i	$-0.407956\pi$
$751$	15.6289	0.570305	0.285152	+	0.958482i	$0.407956\pi$
$752$	−17.3238	−0.631733
$753$	−34.6198	−1.26162
$754$	−12.0559	−0.439051
$755$	45.3735	1.65131
$756$	0.522811	0.0190144
$757$	2.19987	0.0799555	0.0399778	−	0.999201i	$-0.487271\pi$
$757$	2.19987	0.0799555	0.0399778	+	0.999201i	$0.487271\pi$
$758$	16.4049	0.595853
$759$	4.21709	0.153071
$760$	3.01318	0.109299
$761$	17.6200	0.638723	0.319362	−	0.947633i	$-0.396532\pi$
$761$	17.6200	0.638723	0.319362	+	0.947633i	$0.396532\pi$
$762$	−49.3123	−1.78640
$763$	17.5604	0.635728
$764$	13.3893	0.484407
$765$	−40.4458	−1.46232
$766$	59.2842	2.14203
$767$	3.45580	0.124782
$768$	−43.4153	−1.56661
$769$	−19.7861	−0.713506	−0.356753	−	0.934199i	$-0.616116\pi$
$769$	−19.7861	−0.713506	−0.356753	+	0.934199i	$0.616116\pi$
$770$	−28.1852	−1.01572
$771$	−39.8902	−1.43661
$772$	16.6200	0.598167
$773$	16.2817	0.585610	0.292805	−	0.956172i	$-0.405411\pi$
$773$	16.2817	0.585610	0.292805	+	0.956172i	$0.405411\pi$
$774$	−10.4002	−0.373827
$775$	−91.9997	−3.30473
$776$	9.86522	0.354141
$777$	−24.2549	−0.870139
$778$	24.7129	0.886001
$779$	−0.748445	−0.0268158
$780$	8.80906	0.315415
$781$	2.68563	0.0960994
$782$	−10.0147	−0.358124
$783$	1.01053	0.0361135
$784$	−48.9259	−1.74735
$785$	−10.7666	−0.384278
$786$	−45.1642	−1.61095
$787$	39.3508	1.40271	0.701353	−	0.712814i	$-0.252580\pi$
$787$	39.3508	1.40271	0.701353	+	0.712814i	$0.252580\pi$
$788$	0.557992	0.0198776
$789$	33.6209	1.19693
$790$	62.4698	2.22257
$791$	69.8878	2.48493
$792$	−5.53326	−0.196616
$793$	4.40670	0.156486
$794$	−5.86280	−0.208063
$795$	67.0523	2.37810
$796$	10.6034	0.375826
$797$	−8.45475	−0.299483	−0.149741	−	0.988725i	$-0.547844\pi$
$797$	−8.45475	−0.299483	−0.149741	+	0.988725i	$0.547844\pi$
$798$	−6.73864	−0.238545
$799$	11.8153	0.417996
$800$	53.5391	1.89289
$801$	−40.6025	−1.43462
$802$	42.5925	1.50399
$803$	−9.07614	−0.320290
$804$	3.98850	0.140664
$805$	−28.6626	−1.01022
$806$	13.8132	0.486550
$807$	47.2724	1.66407
$808$	18.2321	0.641402
$809$	41.3280	1.45302	0.726508	−	0.687158i	$-0.241142\pi$
$809$	41.3280	1.45302	0.726508	+	0.687158i	$0.241142\pi$
$810$	−63.0584	−2.21565
$811$	−43.7144	−1.53502	−0.767510	−	0.641037i	$-0.778504\pi$
$811$	−43.7144	−1.53502	−0.767510	+	0.641037i	$0.778504\pi$
$812$	25.9808	0.911749
$813$	3.73825	0.131106
$814$	4.12930	0.144732
$815$	−74.7501	−2.61838
$816$	41.3759	1.44845
$817$	−0.823776	−0.0288203
$818$	−53.8421	−1.88254
$819$	12.0591	0.421379
$820$	−6.82393	−0.238302
$821$	−1.33444	−0.0465724	−0.0232862	−	0.999729i	$-0.507413\pi$
$821$	−1.33444	−0.0465724	−0.0232862	+	0.999729i	$0.507413\pi$
$822$	−36.4889	−1.27270
$823$	14.2469	0.496617	0.248309	−	0.968681i	$-0.420125\pi$
$823$	14.2469	0.496617	0.248309	+	0.968681i	$0.420125\pi$
$824$	−31.7266	−1.10525
$825$	27.6191	0.961574
$826$	−24.1027	−0.838640
$827$	0.959058	0.0333497	0.0166749	−	0.999861i	$-0.494692\pi$
$827$	0.959058	0.0333497	0.0166749	+	0.999861i	$0.494692\pi$
$828$	4.55104	0.158160
$829$	4.39778	0.152741	0.0763706	−	0.997079i	$-0.475667\pi$
$829$	4.39778	0.152741	0.0763706	+	0.997079i	$0.475667\pi$
$830$	−64.4665	−2.23766
$831$	5.58842	0.193860
$832$	1.93905	0.0672245
$833$	33.3688	1.15616
$834$	59.1133	2.04693
$835$	−49.5658	−1.71530
$836$	0.354474	0.0122597
$837$	−1.15783	−0.0400205
$838$	−21.8883	−0.756120
$839$	−26.9417	−0.930129	−0.465065	−	0.885277i	$-0.653969\pi$
$839$	−26.9417	−0.930129	−0.465065	+	0.885277i	$0.653969\pi$
$840$	75.9646	2.62103
$841$	21.2179	0.731653
$842$	−37.5227	−1.29312
$843$	17.4592	0.601326
$844$	−18.6264	−0.641147
$845$	−4.04114	−0.139020
$846$	−17.3774	−0.597446
$847$	4.09965	0.140865
$848$	−33.9594	−1.16617
$849$	35.8124	1.22908
$850$	−65.5894	−2.24970
$851$	4.19923	0.143948
$852$	5.85426	0.200564
$853$	7.53259	0.257911	0.128955	−	0.991650i	$-0.458838\pi$
$853$	7.53259	0.257911	0.128955	+	0.991650i	$0.458838\pi$
$854$	−30.7348	−1.05172
$855$	4.71173	0.161138
$856$	14.8447	0.507383
$857$	−35.5761	−1.21526	−0.607628	−	0.794222i	$-0.707879\pi$
$857$	−35.5761	−1.21526	−0.607628	+	0.794222i	$0.707879\pi$
$858$	−4.14685	−0.141571
$859$	47.9461	1.63590	0.817949	−	0.575290i	$-0.195111\pi$
$859$	47.9461	1.63590	0.817949	+	0.575290i	$0.195111\pi$
$860$	−7.51075	−0.256114
$861$	−18.8689	−0.643051
$862$	14.7631	0.502834
$863$	29.5686	1.00653	0.503264	−	0.864133i	$-0.332132\pi$
$863$	29.5686	1.00653	0.503264	+	0.864133i	$0.332132\pi$
$864$	0.673799	0.0229231
$865$	4.92865	0.167579
$866$	20.5772	0.699241
$867$	13.2183	0.448917
$868$	−29.7679	−1.01039
$869$	−9.08646	−0.308237
$870$	−118.755	−4.02618
$871$	−1.82972	−0.0619977
$872$	8.05750	0.272861
$873$	15.4263	0.522102
$874$	1.16666	0.0394627
$875$	−104.885	−3.54574
$876$	−19.7846	−0.668459
$877$	40.2347	1.35863	0.679314	−	0.733848i	$-0.262277\pi$
$877$	40.2347	1.35863	0.679314	+	0.733848i	$0.262277\pi$
$878$	61.5996	2.07889
$879$	71.6447	2.41652
$880$	−20.1606	−0.679612
$881$	21.9870	0.740761	0.370380	−	0.928880i	$-0.379227\pi$
$881$	21.9870	0.740761	0.370380	+	0.928880i	$0.379227\pi$
$882$	−49.0772	−1.65251
$883$	−1.77397	−0.0596988	−0.0298494	−	0.999554i	$-0.509503\pi$
$883$	−1.77397	−0.0596988	−0.0298494	+	0.999554i	$0.509503\pi$
$884$	3.04283	0.102342
$885$	34.0409	1.14427
$886$	−10.5940	−0.355914
$887$	38.1865	1.28218	0.641088	−	0.767467i	$-0.278483\pi$
$887$	38.1865	1.28218	0.641088	+	0.767467i	$0.278483\pi$
$888$	−11.1293	−0.373473
$889$	−48.7509	−1.63505
$890$	−94.8986	−3.18101
$891$	9.17208	0.307276
$892$	−14.4816	−0.484879
$893$	−1.37642	−0.0460602
$894$	25.2440	0.844287
$895$	−16.8689	−0.563866
$896$	−52.2664	−1.74610
$897$	−4.21709	−0.140804
$898$	57.2156	1.90931
$899$	−57.5379	−1.91900
$900$	29.8063	0.993543
$901$	23.1613	0.771614
$902$	3.21236	0.106960
$903$	−20.7681	−0.691118
$904$	32.0677	1.06656
$905$	92.2108	3.06519
$906$	−46.5604	−1.54687
$907$	−2.76903	−0.0919442	−0.0459721	−	0.998943i	$-0.514639\pi$
$907$	−2.76903	−0.0919442	−0.0459721	+	0.998943i	$0.514639\pi$
$908$	3.88368	0.128885
$909$	28.5096	0.945605
$910$	28.1852	0.934331
$911$	10.0971	0.334532	0.167266	−	0.985912i	$-0.446506\pi$
$911$	10.0971	0.334532	0.167266	+	0.985912i	$0.446506\pi$
$912$	−4.82007	−0.159609
$913$	9.37689	0.310330
$914$	−62.9031	−2.08065
$915$	43.4076	1.43501
$916$	5.56630	0.183916
$917$	−44.6500	−1.47447
$918$	−0.825453	−0.0272440
$919$	3.01599	0.0994884	0.0497442	−	0.998762i	$-0.484159\pi$
$919$	3.01599	0.0994884	0.0497442	+	0.998762i	$0.484159\pi$
$920$	−13.1517	−0.433599
$921$	−41.3841	−1.36365
$922$	55.0777	1.81389
$923$	−2.68563	−0.0883986
$924$	8.93659	0.293992
$925$	27.5022	0.904266
$926$	39.0681	1.28386
$927$	−49.6112	−1.62944
$928$	33.4841	1.09917
$929$	55.3486	1.81593	0.907964	−	0.419048i	$-0.137636\pi$
$929$	55.3486	1.81593	0.907964	+	0.419048i	$0.137636\pi$
$930$	136.065	4.46176
$931$	−3.88729	−0.127401
$932$	2.22185	0.0727791
$933$	−5.13508	−0.168115
$934$	−69.5027	−2.27420
$935$	13.7501	0.449676
$936$	5.53326	0.180860
$937$	−26.9462	−0.880295	−0.440148	−	0.897925i	$-0.645074\pi$
$937$	−26.9462	−0.880295	−0.440148	+	0.897925i	$0.645074\pi$
$938$	12.7615	0.416678
$939$	−65.6810	−2.14342
$940$	−12.5495	−0.409319
$941$	−6.13520	−0.200002	−0.100001	−	0.994987i	$-0.531885\pi$
$941$	−6.13520	−0.200002	−0.100001	+	0.994987i	$0.531885\pi$
$942$	11.0483	0.359972
$943$	3.26676	0.106380
$944$	−17.2404	−0.561126
$945$	−2.36250	−0.0768520
$946$	3.53568	0.114955
$947$	34.4367	1.11904	0.559521	−	0.828816i	$-0.310985\pi$
$947$	34.4367	1.11904	0.559521	+	0.828816i	$0.310985\pi$
$948$	−19.8071	−0.643304
$949$	9.07614	0.294624
$950$	7.64082	0.247901
$951$	−77.8487	−2.52442
$952$	26.2398	0.850436
$953$	−37.8762	−1.22693	−0.613465	−	0.789722i	$-0.710225\pi$
$953$	−37.8762	−1.22693	−0.613465	+	0.789722i	$0.710225\pi$
$954$	−34.0644	−1.10288
$955$	−60.5040	−1.95786
$956$	11.2331	0.363305
$957$	17.2734	0.558369
$958$	40.0630	1.29438
$959$	−36.0735	−1.16487
$960$	19.1004	0.616462
$961$	34.9248	1.12661
$962$	−4.12930	−0.133134
$963$	23.2128	0.748023
$964$	6.52742	0.210234
$965$	−75.1031	−2.41765
$966$	29.4123	0.946327
$967$	13.8100	0.444099	0.222050	−	0.975035i	$-0.428725\pi$
$967$	13.8100	0.444099	0.222050	+	0.975035i	$0.428725\pi$
$968$	1.88110	0.0604610
$969$	3.28743	0.105607
$970$	36.0553	1.15766
$971$	12.4732	0.400284	0.200142	−	0.979767i	$-0.435860\pi$
$971$	12.4732	0.400284	0.200142	+	0.979767i	$0.435860\pi$
$972$	19.6111	0.629027
$973$	58.4403	1.87351
$974$	35.2336	1.12896
$975$	−27.6191	−0.884520
$976$	−21.9842	−0.703698
$977$	−21.5045	−0.687990	−0.343995	−	0.938972i	$-0.611780\pi$
$977$	−21.5045	−0.687990	−0.343995	+	0.938972i	$0.611780\pi$
$978$	76.7054	2.45277
$979$	13.8034	0.441157
$980$	−35.4423	−1.13216
$981$	12.5996	0.402274
$982$	20.9524	0.668619
$983$	−9.51671	−0.303536	−0.151768	−	0.988416i	$-0.548497\pi$
$983$	−9.51671	−0.303536	−0.151768	+	0.988416i	$0.548497\pi$
$984$	−8.65792	−0.276005
$985$	−2.52147	−0.0803409
$986$	−41.0205	−1.30636
$987$	−34.7007	−1.10454
$988$	−0.354474	−0.0112773
$989$	3.59556	0.114332
$990$	−20.2229	−0.642726
$991$	3.63536	0.115481	0.0577405	−	0.998332i	$-0.481610\pi$
$991$	3.63536	0.115481	0.0577405	+	0.998332i	$0.481610\pi$
$992$	−38.3649	−1.21809
$993$	−12.8984	−0.409319
$994$	18.7311	0.594115
$995$	−47.9149	−1.51900
$996$	20.4402	0.647671
$997$	9.60165	0.304087	0.152044	−	0.988374i	$-0.451415\pi$
$997$	9.60165	0.304087	0.152044	+	0.988374i	$0.451415\pi$
$998$	8.84508	0.279986
$999$	0.346119	0.0109507

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.2.a.c.1.2	✓	6
3.2	odd	2		1287.2.a.q.1.5		6
4.3	odd	2		2288.2.a.z.1.6		6
5.4	even	2		3575.2.a.p.1.5		6
7.6	odd	2		7007.2.a.r.1.2		6
8.3	odd	2		9152.2.a.cs.1.1		6
8.5	even	2		9152.2.a.cm.1.6		6
11.10	odd	2		1573.2.a.m.1.5		6
13.12	even	2		1859.2.a.m.1.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.2.a.c.1.2	✓	6	1.1	even	1	trivial
1287.2.a.q.1.5		6	3.2	odd	2
1573.2.a.m.1.5		6	11.10	odd	2
1859.2.a.m.1.5		6	13.12	even	2
2288.2.a.z.1.6		6	4.3	odd	2
3575.2.a.p.1.5		6	5.4	even	2
7007.2.a.r.1.2		6	7.6	odd	2
9152.2.a.cm.1.6		6	8.5	even	2
9152.2.a.cs.1.1		6	8.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	143.a (trivial)

\(f(q)\)	\(=\)	\(q-1.70126 q^{2} -2.43752 q^{3} +0.894288 q^{4} -4.04114 q^{5} +4.14685 q^{6} +4.09965 q^{7} +1.88110 q^{8} +2.94150 q^{9} +O(q^{10})\)	\(q-1.70126 q^{2} -2.43752 q^{3} +0.894288 q^{4} -4.04114 q^{5} +4.14685 q^{6} +4.09965 q^{7} +1.88110 q^{8} +2.94150 q^{9} +6.87504 q^{10} -1.00000 q^{11} -2.17984 q^{12} +1.00000 q^{13} -6.97457 q^{14} +9.85036 q^{15} -4.98882 q^{16} +3.40252 q^{17} -5.00425 q^{18} -0.396376 q^{19} -3.61395 q^{20} -9.99296 q^{21} +1.70126 q^{22} +1.73007 q^{23} -4.58523 q^{24} +11.3308 q^{25} -1.70126 q^{26} +0.142600 q^{27} +3.66626 q^{28} +7.08646 q^{29} -16.7580 q^{30} -8.11941 q^{31} +4.72508 q^{32} +2.43752 q^{33} -5.78858 q^{34} -16.5673 q^{35} +2.63055 q^{36} +2.42720 q^{37} +0.674339 q^{38} -2.43752 q^{39} -7.60181 q^{40} +1.88822 q^{41} +17.0006 q^{42} +2.07827 q^{43} -0.894288 q^{44} -11.8870 q^{45} -2.94331 q^{46} +3.47252 q^{47} +12.1604 q^{48} +9.80709 q^{49} -19.2767 q^{50} -8.29371 q^{51} +0.894288 q^{52} +6.80709 q^{53} -0.242600 q^{54} +4.04114 q^{55} +7.71186 q^{56} +0.966174 q^{57} -12.0559 q^{58} +3.45580 q^{59} +8.80906 q^{60} +4.40670 q^{61} +13.8132 q^{62} +12.0591 q^{63} +1.93905 q^{64} -4.04114 q^{65} -4.14685 q^{66} -1.82972 q^{67} +3.04283 q^{68} -4.21709 q^{69} +28.1852 q^{70} -2.68563 q^{71} +5.53326 q^{72} +9.07614 q^{73} -4.12930 q^{74} -27.6191 q^{75} -0.354474 q^{76} -4.09965 q^{77} +4.14685 q^{78} +9.08646 q^{79} +20.1606 q^{80} -9.17208 q^{81} -3.21236 q^{82} -9.37689 q^{83} -8.93659 q^{84} -13.7501 q^{85} -3.53568 q^{86} -17.2734 q^{87} -1.88110 q^{88} -13.8034 q^{89} +20.2229 q^{90} +4.09965 q^{91} +1.54718 q^{92} +19.7912 q^{93} -5.90766 q^{94} +1.60181 q^{95} -11.5175 q^{96} +5.24437 q^{97} -16.6844 q^{98} -2.94150 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{3} + 8 q^{4} + q^{5} - 3 q^{6} + 4 q^{7} - 6 q^{8} + 13 q^{9}+O(q^{10}) \) 6 * q + 3 * q^3 + 8 * q^4 + q^5 - 3 * q^6 + 4 * q^7 - 6 * q^8 + 13 * q^9	\( 6 q + 3 q^{3} + 8 q^{4} + q^{5} - 3 q^{6} + 4 q^{7} - 6 q^{8} + 13 q^{9} + 6 q^{10} - 6 q^{11} - 6 q^{12} + 6 q^{13} - 12 q^{14} + 3 q^{15} + 8 q^{16} + 6 q^{18} - 10 q^{19} + 4 q^{20} - 12 q^{21} + 11 q^{23} - 38 q^{24} + 23 q^{25} + 9 q^{27} + 9 q^{28} + 2 q^{29} - 56 q^{30} - 9 q^{31} - 17 q^{32} - 3 q^{33} - 40 q^{34} - 24 q^{35} + 11 q^{36} + 15 q^{37} - 9 q^{38} + 3 q^{39} + 16 q^{40} - 4 q^{41} + 19 q^{42} - 2 q^{43} - 8 q^{44} - 26 q^{45} - 6 q^{46} + 6 q^{47} + 19 q^{48} + 20 q^{49} - 4 q^{50} + 6 q^{51} + 8 q^{52} + 2 q^{53} + 37 q^{54} - q^{55} - 39 q^{56} + 22 q^{57} + 18 q^{58} + 11 q^{59} - 24 q^{60} + 16 q^{61} + 16 q^{62} - 26 q^{63} + 36 q^{64} + q^{65} + 3 q^{66} + 9 q^{67} + 12 q^{68} - 3 q^{69} + 32 q^{70} - 15 q^{71} + 5 q^{72} + 32 q^{73} + 22 q^{74} + 4 q^{75} - 26 q^{76} - 4 q^{77} - 3 q^{78} + 14 q^{79} + 56 q^{80} - 2 q^{81} - 24 q^{82} - 26 q^{83} + 43 q^{84} - 12 q^{85} - 10 q^{86} - 38 q^{87} + 6 q^{88} - 23 q^{89} - 10 q^{90} + 4 q^{91} + 83 q^{92} + 23 q^{93} + 46 q^{94} - 52 q^{95} - 56 q^{96} + 27 q^{97} - 3 q^{98} - 13 q^{99}+O(q^{100}) \) 6 * q + 3 * q^3 + 8 * q^4 + q^5 - 3 * q^6 + 4 * q^7 - 6 * q^8 + 13 * q^9 + 6 * q^10 - 6 * q^11 - 6 * q^12 + 6 * q^13 - 12 * q^14 + 3 * q^15 + 8 * q^16 + 6 * q^18 - 10 * q^19 + 4 * q^20 - 12 * q^21 + 11 * q^23 - 38 * q^24 + 23 * q^25 + 9 * q^27 + 9 * q^28 + 2 * q^29 - 56 * q^30 - 9 * q^31 - 17 * q^32 - 3 * q^33 - 40 * q^34 - 24 * q^35 + 11 * q^36 + 15 * q^37 - 9 * q^38 + 3 * q^39 + 16 * q^40 - 4 * q^41 + 19 * q^42 - 2 * q^43 - 8 * q^44 - 26 * q^45 - 6 * q^46 + 6 * q^47 + 19 * q^48 + 20 * q^49 - 4 * q^50 + 6 * q^51 + 8 * q^52 + 2 * q^53 + 37 * q^54 - q^55 - 39 * q^56 + 22 * q^57 + 18 * q^58 + 11 * q^59 - 24 * q^60 + 16 * q^61 + 16 * q^62 - 26 * q^63 + 36 * q^64 + q^65 + 3 * q^66 + 9 * q^67 + 12 * q^68 - 3 * q^69 + 32 * q^70 - 15 * q^71 + 5 * q^72 + 32 * q^73 + 22 * q^74 + 4 * q^75 - 26 * q^76 - 4 * q^77 - 3 * q^78 + 14 * q^79 + 56 * q^80 - 2 * q^81 - 24 * q^82 - 26 * q^83 + 43 * q^84 - 12 * q^85 - 10 * q^86 - 38 * q^87 + 6 * q^88 - 23 * q^89 - 10 * q^90 + 4 * q^91 + 83 * q^92 + 23 * q^93 + 46 * q^94 - 52 * q^95 - 56 * q^96 + 27 * q^97 - 3 * q^98 - 13 * q^99

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