LMFDB - Embedded newform 139.2.a.c.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [139,2,Mod(1,139)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(139, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("139.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 139 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	139.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:	$1.10992058810$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 11x^{5} + 8x^{4} + 35x^{3} - 10x^{2} - 32x - 8 $ x^7 - x^6 - 11x^5 + 8x^4 + 35x^3 - 10x^2 - 32*x - 8
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$2.47985$ of defining polynomial
Character	$\chi$	$=$	139.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.47985 q^{2} -0.245836 q^{3} +4.14965 q^{4} -2.31250 q^{5} -0.609636 q^{6} -0.326651 q^{7} +5.33082 q^{8} -2.93956 q^{9} +O(q^{10})$	\(q+2.47985 q^{2} -0.245836 q^{3} +4.14965 q^{4} -2.31250 q^{5} -0.609636 q^{6} -0.326651 q^{7} +5.33082 q^{8} -2.93956 q^{9} -5.73465 q^{10} +0.570671 q^{11} -1.02013 q^{12} +0.655030 q^{13} -0.810045 q^{14} +0.568496 q^{15} +4.92032 q^{16} +1.14453 q^{17} -7.28968 q^{18} -2.77067 q^{19} -9.59608 q^{20} +0.0803026 q^{21} +1.41518 q^{22} +7.23464 q^{23} -1.31051 q^{24} +0.347657 q^{25} +1.62438 q^{26} +1.46016 q^{27} -1.35549 q^{28} +7.86393 q^{29} +1.40978 q^{30} -8.91763 q^{31} +1.54002 q^{32} -0.140292 q^{33} +2.83826 q^{34} +0.755380 q^{35} -12.1982 q^{36} -4.69099 q^{37} -6.87084 q^{38} -0.161030 q^{39} -12.3275 q^{40} +9.63165 q^{41} +0.199138 q^{42} +11.2545 q^{43} +2.36809 q^{44} +6.79774 q^{45} +17.9408 q^{46} -8.96119 q^{47} -1.20959 q^{48} -6.89330 q^{49} +0.862137 q^{50} -0.281366 q^{51} +2.71815 q^{52} +7.21477 q^{53} +3.62098 q^{54} -1.31968 q^{55} -1.74132 q^{56} +0.681130 q^{57} +19.5014 q^{58} -5.58094 q^{59} +2.35906 q^{60} +10.8663 q^{61} -22.1144 q^{62} +0.960211 q^{63} -6.02163 q^{64} -1.51476 q^{65} -0.347902 q^{66} -3.89682 q^{67} +4.74939 q^{68} -1.77853 q^{69} +1.87323 q^{70} -4.74151 q^{71} -15.6703 q^{72} -5.98781 q^{73} -11.6329 q^{74} -0.0854666 q^{75} -11.4973 q^{76} -0.186410 q^{77} -0.399330 q^{78} +6.17739 q^{79} -11.3782 q^{80} +8.45973 q^{81} +23.8850 q^{82} -14.5135 q^{83} +0.333228 q^{84} -2.64672 q^{85} +27.9095 q^{86} -1.93324 q^{87} +3.04214 q^{88} +11.5467 q^{89} +16.8574 q^{90} -0.213966 q^{91} +30.0212 q^{92} +2.19228 q^{93} -22.2224 q^{94} +6.40717 q^{95} -0.378592 q^{96} -5.82160 q^{97} -17.0943 q^{98} -1.67752 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + q^{2} - 2 q^{3} + 9 q^{4} + 11 q^{5} - 7 q^{6} - 5 q^{7} + 6 q^{8} + 13 q^{9}+O(q^{10}) $ 7 * q + q^2 - 2 * q^3 + 9 * q^4 + 11 * q^5 - 7 * q^6 - 5 * q^7 + 6 * q^8 + 13 * q^9	\( 7 q + q^{2} - 2 q^{3} + 9 q^{4} + 11 q^{5} - 7 q^{6} - 5 q^{7} + 6 q^{8} + 13 q^{9} - 4 q^{10} + 2 q^{11} - 8 q^{12} + 6 q^{13} + 7 q^{14} - 3 q^{15} + 5 q^{16} + 5 q^{17} - 10 q^{18} - 10 q^{19} + 12 q^{20} - 5 q^{21} - 18 q^{22} - q^{23} - 21 q^{24} + 14 q^{25} - 8 q^{26} - 11 q^{27} - 28 q^{28} + 30 q^{29} - 41 q^{30} - 20 q^{31} - 12 q^{32} - 20 q^{33} - 17 q^{34} - 7 q^{35} + 2 q^{36} + 6 q^{37} + 6 q^{38} + 11 q^{39} - 22 q^{40} + 19 q^{41} + 6 q^{42} - 12 q^{43} + 25 q^{44} + 27 q^{45} + 22 q^{46} - 3 q^{47} + 15 q^{48} - 8 q^{49} + 12 q^{50} + 23 q^{51} - 8 q^{52} + 38 q^{53} - 7 q^{54} + 7 q^{55} + 21 q^{56} - 19 q^{57} - 21 q^{58} - 14 q^{59} - 8 q^{60} + 4 q^{61} - q^{62} - 18 q^{63} - 16 q^{64} + 10 q^{65} + 18 q^{66} + 9 q^{67} - 25 q^{68} + 9 q^{69} + 20 q^{70} + 24 q^{71} + 41 q^{72} - 5 q^{73} + 9 q^{74} - 21 q^{75} + 3 q^{76} - 13 q^{77} + 20 q^{78} + 8 q^{79} + 11 q^{80} + 39 q^{81} + 56 q^{82} - 9 q^{83} - q^{84} - 22 q^{85} + 39 q^{86} - 25 q^{87} - 29 q^{88} + 10 q^{89} + 72 q^{90} + 7 q^{91} + 29 q^{92} - 15 q^{93} - 36 q^{94} - 21 q^{95} - 11 q^{96} - 5 q^{97} - 49 q^{98} - 31 q^{99}+O(q^{100}) \) 7 * q + q^2 - 2 * q^3 + 9 * q^4 + 11 * q^5 - 7 * q^6 - 5 * q^7 + 6 * q^8 + 13 * q^9 - 4 * q^10 + 2 * q^11 - 8 * q^12 + 6 * q^13 + 7 * q^14 - 3 * q^15 + 5 * q^16 + 5 * q^17 - 10 * q^18 - 10 * q^19 + 12 * q^20 - 5 * q^21 - 18 * q^22 - q^23 - 21 * q^24 + 14 * q^25 - 8 * q^26 - 11 * q^27 - 28 * q^28 + 30 * q^29 - 41 * q^30 - 20 * q^31 - 12 * q^32 - 20 * q^33 - 17 * q^34 - 7 * q^35 + 2 * q^36 + 6 * q^37 + 6 * q^38 + 11 * q^39 - 22 * q^40 + 19 * q^41 + 6 * q^42 - 12 * q^43 + 25 * q^44 + 27 * q^45 + 22 * q^46 - 3 * q^47 + 15 * q^48 - 8 * q^49 + 12 * q^50 + 23 * q^51 - 8 * q^52 + 38 * q^53 - 7 * q^54 + 7 * q^55 + 21 * q^56 - 19 * q^57 - 21 * q^58 - 14 * q^59 - 8 * q^60 + 4 * q^61 - q^62 - 18 * q^63 - 16 * q^64 + 10 * q^65 + 18 * q^66 + 9 * q^67 - 25 * q^68 + 9 * q^69 + 20 * q^70 + 24 * q^71 + 41 * q^72 - 5 * q^73 + 9 * q^74 - 21 * q^75 + 3 * q^76 - 13 * q^77 + 20 * q^78 + 8 * q^79 + 11 * q^80 + 39 * q^81 + 56 * q^82 - 9 * q^83 - q^84 - 22 * q^85 + 39 * q^86 - 25 * q^87 - 29 * q^88 + 10 * q^89 + 72 * q^90 + 7 * q^91 + 29 * q^92 - 15 * q^93 - 36 * q^94 - 21 * q^95 - 11 * q^96 - 5 * q^97 - 49 * q^98 - 31 * 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 $

$2$	2.47985	1.75352	0.876759	−	0.480930i	$-0.159701\pi$
$2$	2.47985	1.75352	0.876759	+	0.480930i	$0.159701\pi$
$3$	−0.245836	−0.141934	−0.0709668	−	0.997479i	$-0.522608\pi$
$3$	−0.245836	−0.141934	−0.0709668	+	0.997479i	$0.522608\pi$
$4$	4.14965	2.07483
$5$	−2.31250	−1.03418	−0.517091	−	0.855931i	$-0.672985\pi$
$5$	−2.31250	−1.03418	−0.517091	+	0.855931i	$0.672985\pi$
$6$	−0.609636	−0.248883
$7$	−0.326651	−0.123462	−0.0617312	−	0.998093i	$-0.519662\pi$
$7$	−0.326651	−0.123462	−0.0617312	+	0.998093i	$0.519662\pi$
$8$	5.33082	1.88473
$9$	−2.93956	−0.979855
$10$	−5.73465	−1.81346
$11$	0.570671	0.172064	0.0860319	−	0.996292i	$-0.472581\pi$
$11$	0.570671	0.172064	0.0860319	+	0.996292i	$0.472581\pi$
$12$	−1.02013	−0.294487
$13$	0.655030	0.181673	0.0908364	−	0.995866i	$-0.471046\pi$
$13$	0.655030	0.181673	0.0908364	+	0.995866i	$0.471046\pi$
$14$	−0.810045	−0.216494
$15$	0.568496	0.146785
$16$	4.92032	1.23008
$17$	1.14453	0.277589	0.138794	−	0.990321i	$-0.455677\pi$
$17$	1.14453	0.277589	0.138794	+	0.990321i	$0.455677\pi$
$18$	−7.28968	−1.71819
$19$	−2.77067	−0.635634	−0.317817	−	0.948152i	$-0.602950\pi$
$19$	−2.77067	−0.635634	−0.317817	+	0.948152i	$0.602950\pi$
$20$	−9.59608	−2.14575
$21$	0.0803026	0.0175235
$22$	1.41518	0.301717
$23$	7.23464	1.50853	0.754263	−	0.656572i	$-0.227994\pi$
$23$	7.23464	1.50853	0.754263	+	0.656572i	$0.227994\pi$
$24$	−1.31051	−0.267506
$25$	0.347657	0.0695314
$26$	1.62438	0.318567
$27$	1.46016	0.281008
$28$	−1.35549	−0.256163
$29$	7.86393	1.46029	0.730147	−	0.683290i	$-0.239451\pi$
$29$	7.86393	1.46029	0.730147	+	0.683290i	$0.239451\pi$
$30$	1.40978	0.257390
$31$	−8.91763	−1.60165	−0.800827	−	0.598896i	$-0.795606\pi$
$31$	−8.91763	−1.60165	−0.800827	+	0.598896i	$0.795606\pi$
$32$	1.54002	0.272239
$33$	−0.140292	−0.0244216
$34$	2.83826	0.486757
$35$	0.755380	0.127683
$36$	−12.1982	−2.03303
$37$	−4.69099	−0.771194	−0.385597	−	0.922667i	$-0.626004\pi$
$37$	−4.69099	−0.771194	−0.385597	+	0.922667i	$0.626004\pi$
$38$	−6.87084	−1.11460
$39$	−0.161030	−0.0257855
$40$	−12.3275	−1.94915
$41$	9.63165	1.50421	0.752105	−	0.659043i	$-0.229039\pi$
$41$	9.63165	1.50421	0.752105	+	0.659043i	$0.229039\pi$
$42$	0.199138	0.0307277
$43$	11.2545	1.71630	0.858148	−	0.513403i	$-0.171615\pi$
$43$	11.2545	1.71630	0.858148	+	0.513403i	$0.171615\pi$
$44$	2.36809	0.357003
$45$	6.79774	1.01335
$46$	17.9408	2.64523
$47$	−8.96119	−1.30712	−0.653562	−	0.756873i	$-0.726726\pi$
$47$	−8.96119	−1.30712	−0.653562	+	0.756873i	$0.726726\pi$
$48$	−1.20959	−0.174590
$49$	−6.89330	−0.984757
$50$	0.862137	0.121925
$51$	−0.281366	−0.0393991
$52$	2.71815	0.376940
$53$	7.21477	0.991025	0.495512	−	0.868601i	$-0.334980\pi$
$53$	7.21477	0.991025	0.495512	+	0.868601i	$0.334980\pi$
$54$	3.62098	0.492752
$55$	−1.31968	−0.177945
$56$	−1.74132	−0.232693
$57$	0.681130	0.0902178
$58$	19.5014	2.56065
$59$	−5.58094	−0.726577	−0.363288	−	0.931677i	$-0.618346\pi$
$59$	−5.58094	−0.726577	−0.363288	+	0.931677i	$0.618346\pi$
$60$	2.35906	0.304554
$61$	10.8663	1.39129	0.695646	−	0.718385i	$-0.255118\pi$
$61$	10.8663	1.39129	0.695646	+	0.718385i	$0.255118\pi$
$62$	−22.1144	−2.80853
$63$	0.960211	0.120975
$64$	−6.02163	−0.752704
$65$	−1.51476	−0.187883
$66$	−0.347902	−0.0428238
$67$	−3.89682	−0.476073	−0.238036	−	0.971256i	$-0.576504\pi$
$67$	−3.89682	−0.476073	−0.238036	+	0.971256i	$0.576504\pi$
$68$	4.74939	0.575949
$69$	−1.77853	−0.214110
$70$	1.87323	0.223894
$71$	−4.74151	−0.562713	−0.281357	−	0.959603i	$-0.590784\pi$
$71$	−4.74151	−0.562713	−0.281357	+	0.959603i	$0.590784\pi$
$72$	−15.6703	−1.84676
$73$	−5.98781	−0.700820	−0.350410	−	0.936596i	$-0.613958\pi$
$73$	−5.98781	−0.700820	−0.350410	+	0.936596i	$0.613958\pi$
$74$	−11.6329	−1.35230
$75$	−0.0854666	−0.00986883
$76$	−11.4973	−1.31883
$77$	−0.186410	−0.0212434
$78$	−0.399330	−0.0452153
$79$	6.17739	0.695010	0.347505	−	0.937678i	$-0.387029\pi$
$79$	6.17739	0.695010	0.347505	+	0.937678i	$0.387029\pi$
$80$	−11.3782	−1.27213
$81$	8.45973	0.939970
$82$	23.8850	2.63766
$83$	−14.5135	−1.59306	−0.796529	−	0.604600i	$-0.793333\pi$
$83$	−14.5135	−1.59306	−0.796529	+	0.604600i	$0.793333\pi$
$84$	0.333228	0.0363581
$85$	−2.64672	−0.287077
$86$	27.9095	3.00956
$87$	−1.93324	−0.207265
$88$	3.04214	0.324294
$89$	11.5467	1.22395	0.611975	−	0.790877i	$-0.290375\pi$
$89$	11.5467	1.22395	0.611975	+	0.790877i	$0.290375\pi$
$90$	16.8574	1.77692
$91$	−0.213966	−0.0224298
$92$	30.0212	3.12993
$93$	2.19228	0.227328
$94$	−22.2224	−2.29207
$95$	6.40717	0.657361
$96$	−0.378592	−0.0386399
$97$	−5.82160	−0.591094	−0.295547	−	0.955328i	$-0.595502\pi$
$97$	−5.82160	−0.591094	−0.295547	+	0.955328i	$0.595502\pi$
$98$	−17.0943	−1.72679
$99$	−1.67752	−0.168598
$100$	1.44266	0.144266
$101$	10.2902	1.02392	0.511958	−	0.859011i	$-0.328920\pi$
$101$	10.2902	1.02392	0.511958	+	0.859011i	$0.328920\pi$
$102$	−0.697746	−0.0690871
$103$	−0.0520725	−0.00513086	−0.00256543	−	0.999997i	$-0.500817\pi$
$103$	−0.0520725	−0.00513086	−0.00256543	+	0.999997i	$0.500817\pi$
$104$	3.49185	0.342404
$105$	−0.185700	−0.0181224
$106$	17.8915	1.73778
$107$	−8.26648	−0.799151	−0.399575	−	0.916700i	$-0.630842\pi$
$107$	−8.26648	−0.799151	−0.399575	+	0.916700i	$0.630842\pi$
$108$	6.05916	0.583042
$109$	−0.971231	−0.0930270	−0.0465135	−	0.998918i	$-0.514811\pi$
$109$	−0.971231	−0.0930270	−0.0465135	+	0.998918i	$0.514811\pi$
$110$	−3.27260	−0.312030
$111$	1.15321	0.109458
$112$	−1.60723	−0.151869
$113$	0.0781957	0.00735603	0.00367802	−	0.999993i	$-0.498829\pi$
$113$	0.0781957	0.00735603	0.00367802	+	0.999993i	$0.498829\pi$
$114$	1.68910	0.158199
$115$	−16.7301	−1.56009
$116$	32.6326	3.02986
$117$	−1.92550	−0.178013
$118$	−13.8399	−1.27407
$119$	−0.373861	−0.0342718
$120$	3.03055	0.276650
$121$	−10.6743	−0.970394
$122$	26.9469	2.43966
$123$	−2.36781	−0.213498
$124$	−37.0051	−3.32316
$125$	10.7585	0.962273
$126$	2.38118	0.212132
$127$	−3.90704	−0.346693	−0.173347	−	0.984861i	$-0.555458\pi$
$127$	−3.90704	−0.346693	−0.173347	+	0.984861i	$0.555458\pi$
$128$	−18.0128	−1.59212
$129$	−2.76676	−0.243600
$130$	−3.75637	−0.329456
$131$	−3.91653	−0.342189	−0.171095	−	0.985255i	$-0.554730\pi$
$131$	−3.91653	−0.342189	−0.171095	+	0.985255i	$0.554730\pi$
$132$	−0.582161	−0.0506706
$133$	0.905041	0.0784770
$134$	−9.66354	−0.834803
$135$	−3.37662	−0.290613
$136$	6.10127	0.523179
$137$	−19.5648	−1.67153	−0.835766	−	0.549086i	$-0.814976\pi$
$137$	−19.5648	−1.67153	−0.835766	+	0.549086i	$0.814976\pi$
$138$	−4.41050	−0.375447
$139$	1.00000	0.0848189
$139$	1.00000	0.0848189
$140$	3.13457	0.264919
$141$	2.20298	0.185525
$142$	−11.7582	−0.986728
$143$	0.373807	0.0312593
$144$	−14.4636	−1.20530
$145$	−18.1853	−1.51021
$146$	−14.8489	−1.22890
$147$	1.69462	0.139770
$148$	−19.4660	−1.60009
$149$	4.30582	0.352747	0.176373	−	0.984323i	$-0.443563\pi$
$149$	4.30582	0.352747	0.176373	+	0.984323i	$0.443563\pi$
$150$	−0.211944	−0.0173052
$151$	−15.8273	−1.28801	−0.644003	−	0.765023i	$-0.722728\pi$
$151$	−15.8273	−1.28801	−0.644003	+	0.765023i	$0.722728\pi$
$152$	−14.7699	−1.19800
$153$	−3.36441	−0.271997
$154$	−0.462269	−0.0372507
$155$	20.6220	1.65640
$156$	−0.668219	−0.0535004
$157$	1.14090	0.0910534	0.0455267	−	0.998963i	$-0.485503\pi$
$157$	1.14090	0.0910534	0.0455267	+	0.998963i	$0.485503\pi$
$158$	15.3190	1.21871
$159$	−1.77365	−0.140660
$160$	−3.56129	−0.281545
$161$	−2.36320	−0.186246
$162$	20.9789	1.64826
$163$	−2.94076	−0.230338	−0.115169	−	0.993346i	$-0.536741\pi$
$163$	−2.94076	−0.230338	−0.115169	+	0.993346i	$0.536741\pi$
$164$	39.9680	3.12098
$165$	0.324424	0.0252564
$166$	−35.9912	−2.79346
$167$	4.64987	0.359818	0.179909	−	0.983683i	$-0.442420\pi$
$167$	4.64987	0.359818	0.179909	+	0.983683i	$0.442420\pi$
$168$	0.428078	0.0330270
$169$	−12.5709	−0.966995
$170$	−6.56347	−0.503395
$171$	8.14455	0.622830
$172$	46.7023	3.56102
$173$	2.04281	0.155312	0.0776559	−	0.996980i	$-0.475256\pi$
$173$	2.04281	0.155312	0.0776559	+	0.996980i	$0.475256\pi$
$174$	−4.79414	−0.363443
$175$	−0.113562	−0.00858451
$176$	2.80788	0.211652
$177$	1.37200	0.103126
$178$	28.6341	2.14622
$179$	−18.4289	−1.37744	−0.688719	−	0.725029i	$-0.741827\pi$
$179$	−18.4289	−1.37744	−0.688719	+	0.725029i	$0.741827\pi$
$180$	28.2083	2.10252
$181$	1.48337	0.110258	0.0551290	−	0.998479i	$-0.482443\pi$
$181$	1.48337	0.110258	0.0551290	+	0.998479i	$0.482443\pi$
$182$	−0.530604	−0.0393310
$183$	−2.67134	−0.197471
$184$	38.5665	2.84316
$185$	10.8479	0.797554
$186$	5.43651	0.398625
$187$	0.653149	0.0477630
$188$	−37.1859	−2.71206
$189$	−0.476962	−0.0346939
$190$	15.8888	1.15270
$191$	15.1176	1.09387	0.546937	−	0.837174i	$-0.315794\pi$
$191$	15.1176	1.09387	0.546937	+	0.837174i	$0.315794\pi$
$192$	1.48033	0.106834
$193$	12.6498	0.910553	0.455276	−	0.890350i	$-0.349540\pi$
$193$	12.6498	0.910553	0.455276	+	0.890350i	$0.349540\pi$
$194$	−14.4367	−1.03649
$195$	0.372382	0.0266668
$196$	−28.6048	−2.04320
$197$	20.0054	1.42532	0.712662	−	0.701508i	$-0.247489\pi$
$197$	20.0054	1.42532	0.712662	+	0.701508i	$0.247489\pi$
$198$	−4.16001	−0.295639
$199$	−11.0064	−0.780220	−0.390110	−	0.920768i	$-0.627563\pi$
$199$	−11.0064	−0.780220	−0.390110	+	0.920768i	$0.627563\pi$
$200$	1.85330	0.131048
$201$	0.957980	0.0675707
$202$	25.5182	1.79546
$203$	−2.56876	−0.180292
$204$	−1.16757	−0.0817464
$205$	−22.2732	−1.55563
$206$	−0.129132	−0.00899705
$207$	−21.2667	−1.47814
$208$	3.22296	0.223472
$209$	−1.58114	−0.109370
$210$	−0.460507	−0.0317780
$211$	9.89782	0.681394	0.340697	−	0.940173i	$-0.389337\pi$
$211$	9.89782	0.681394	0.340697	+	0.940173i	$0.389337\pi$
$212$	29.9388	2.05621
$213$	1.16563	0.0798679
$214$	−20.4996	−1.40133
$215$	−26.0260	−1.77496
$216$	7.78384	0.529623
$217$	2.91295	0.197744
$218$	−2.40851	−0.163125
$219$	1.47202	0.0994698
$220$	−5.47620	−0.369205
$221$	0.749700	0.0504303
$222$	2.85980	0.191937
$223$	6.88052	0.460753	0.230377	−	0.973102i	$-0.426004\pi$
$223$	6.88052	0.460753	0.230377	+	0.973102i	$0.426004\pi$
$224$	−0.503048	−0.0336113
$225$	−1.02196	−0.0681307
$226$	0.193914	0.0128989
$227$	28.2205	1.87306	0.936529	−	0.350591i	$-0.114019\pi$
$227$	28.2205	1.87306	0.936529	+	0.350591i	$0.114019\pi$
$228$	2.82645	0.187186
$229$	24.7429	1.63505	0.817527	−	0.575890i	$-0.195344\pi$
$229$	24.7429	1.63505	0.817527	+	0.575890i	$0.195344\pi$
$230$	−41.4881	−2.73565
$231$	0.0458263	0.00301515
$232$	41.9212	2.75226
$233$	−18.1608	−1.18975	−0.594877	−	0.803817i	$-0.702799\pi$
$233$	−18.1608	−1.18975	−0.594877	+	0.803817i	$0.702799\pi$
$234$	−4.77496	−0.312149
$235$	20.7228	1.35180
$236$	−23.1590	−1.50752
$237$	−1.51862	−0.0986452
$238$	−0.927119	−0.0600962
$239$	22.9960	1.48748	0.743742	−	0.668466i	$-0.233049\pi$
$239$	22.9960	1.48748	0.743742	+	0.668466i	$0.233049\pi$
$240$	2.79718	0.180557
$241$	29.9171	1.92713	0.963564	−	0.267477i	$-0.0861900\pi$
$241$	29.9171	1.92713	0.963564	+	0.267477i	$0.0861900\pi$
$242$	−26.4707	−1.70160
$243$	−6.46019	−0.414421
$244$	45.0915	2.88669
$245$	15.9408	1.01842
$246$	−5.87180	−0.374372
$247$	−1.81487	−0.115477
$248$	−47.5383	−3.01868
$249$	3.56793	0.226108
$250$	26.6796	1.68736
$251$	14.5346	0.917416	0.458708	−	0.888587i	$-0.348312\pi$
$251$	14.5346	0.917416	0.458708	+	0.888587i	$0.348312\pi$
$252$	3.98455	0.251003
$253$	4.12860	0.259563
$254$	−9.68886	−0.607933
$255$	0.650659	0.0407459
$256$	−32.6257	−2.03911
$257$	0.986686	0.0615478	0.0307739	−	0.999526i	$-0.490203\pi$
$257$	0.986686	0.0615478	0.0307739	+	0.999526i	$0.490203\pi$
$258$	−6.86116	−0.427157
$259$	1.53232	0.0952134
$260$	−6.28572	−0.389824
$261$	−23.1165	−1.43088
$262$	−9.71241	−0.600035
$263$	−9.74159	−0.600692	−0.300346	−	0.953830i	$-0.597102\pi$
$263$	−9.74159	−0.600692	−0.300346	+	0.953830i	$0.597102\pi$
$264$	−0.747869	−0.0460281
$265$	−16.6842	−1.02490
$266$	2.24437	0.137611
$267$	−2.83860	−0.173720
$268$	−16.1705	−0.987769
$269$	2.53822	0.154758	0.0773791	−	0.997002i	$-0.475345\pi$
$269$	2.53822	0.154758	0.0773791	+	0.997002i	$0.475345\pi$
$270$	−8.37351	−0.509595
$271$	13.1783	0.800527	0.400263	−	0.916400i	$-0.368919\pi$
$271$	13.1783	0.800527	0.400263	+	0.916400i	$0.368919\pi$
$272$	5.63144	0.341456
$273$	0.0526006	0.00318354
$274$	−48.5177	−2.93106
$275$	0.198398	0.0119638
$276$	−7.38030	−0.444242
$277$	14.6123	0.877967	0.438983	−	0.898495i	$-0.355339\pi$
$277$	14.6123	0.877967	0.438983	+	0.898495i	$0.355339\pi$
$278$	2.47985	0.148731
$279$	26.2140	1.56939
$280$	4.02680	0.240647
$281$	3.35534	0.200163	0.100081	−	0.994979i	$-0.468090\pi$
$281$	3.35534	0.200163	0.100081	+	0.994979i	$0.468090\pi$
$282$	5.46307	0.325321
$283$	11.8499	0.704403	0.352202	−	0.935924i	$-0.385433\pi$
$283$	11.8499	0.704403	0.352202	+	0.935924i	$0.385433\pi$
$284$	−19.6756	−1.16753
$285$	−1.57511	−0.0933016
$286$	0.926985	0.0548138
$287$	−3.14619	−0.185713
$288$	−4.52698	−0.266755
$289$	−15.6901	−0.922945
$290$	−45.0969	−2.64818
$291$	1.43116	0.0838960
$292$	−24.8473	−1.45408
$293$	13.7232	0.801717	0.400859	−	0.916140i	$-0.368712\pi$
$293$	13.7232	0.801717	0.400859	+	0.916140i	$0.368712\pi$
$294$	4.20241	0.245089
$295$	12.9059	0.751412
$296$	−25.0068	−1.45349
$297$	0.833270	0.0483513
$298$	10.6778	0.618548
$299$	4.73891	0.274058
$300$	−0.354657	−0.0204761
$301$	−3.67629	−0.211898
$302$	−39.2493	−2.25854
$303$	−2.52971	−0.145328
$304$	−13.6326	−0.781881
$305$	−25.1284	−1.43885
$306$	−8.34324	−0.476951
$307$	−19.3132	−1.10226	−0.551131	−	0.834419i	$-0.685803\pi$
$307$	−19.3132	−1.10226	−0.551131	+	0.834419i	$0.685803\pi$
$308$	−0.773538	−0.0440764
$309$	0.0128013	0.000728241 0
$310$	51.1395	2.90453
$311$	20.7756	1.17807	0.589037	−	0.808106i	$-0.299507\pi$
$311$	20.7756	1.17807	0.589037	+	0.808106i	$0.299507\pi$
$312$	−0.858422	−0.0485986
$313$	−27.5648	−1.55805	−0.779026	−	0.626991i	$-0.784286\pi$
$313$	−27.5648	−1.55805	−0.779026	+	0.626991i	$0.784286\pi$
$314$	2.82925	0.159664
$315$	−2.22049	−0.125110
$316$	25.6340	1.44203
$317$	−18.7677	−1.05410	−0.527049	−	0.849835i	$-0.676702\pi$
$317$	−18.7677	−1.05410	−0.527049	+	0.849835i	$0.676702\pi$
$318$	−4.39839	−0.246649
$319$	4.48772	0.251264
$320$	13.9250	0.778432
$321$	2.03220	0.113426
$322$	−5.86038	−0.326586
$323$	−3.17110	−0.176445
$324$	35.1050	1.95028
$325$	0.227726	0.0126320
$326$	−7.29264	−0.403902
$327$	0.238764	0.0132037
$328$	51.3446	2.83503
$329$	2.92718	0.161381
$330$	0.804523	0.0442875
$331$	−0.0825219	−0.00453581	−0.00226791	−	0.999997i	$-0.500722\pi$
$331$	−0.0825219	−0.00453581	−0.00226791	+	0.999997i	$0.500722\pi$
$332$	−60.2258	−3.30532
$333$	13.7895	0.755658
$334$	11.5310	0.630947
$335$	9.01141	0.492346
$336$	0.395114	0.0215553
$337$	13.5611	0.738718	0.369359	−	0.929287i	$-0.379577\pi$
$337$	13.5611	0.738718	0.369359	+	0.929287i	$0.379577\pi$
$338$	−31.1740	−1.69564
$339$	−0.0192233	−0.00104407
$340$	−10.9830	−0.595635
$341$	−5.08903	−0.275587
$342$	20.1973	1.09214
$343$	4.53826	0.245043
$344$	59.9957	3.23475
$345$	4.11286	0.221429
$346$	5.06586	0.272342
$347$	−14.0479	−0.754130	−0.377065	−	0.926187i	$-0.623067\pi$
$347$	−14.0479	−0.754130	−0.377065	+	0.926187i	$0.623067\pi$
$348$	−8.02226	−0.430038
$349$	29.7905	1.59465	0.797323	−	0.603553i	$-0.206249\pi$
$349$	29.7905	1.59465	0.797323	+	0.603553i	$0.206249\pi$
$350$	−0.281618	−0.0150531
$351$	0.956449	0.0510515
$352$	0.878843	0.0468425
$353$	1.66236	0.0884787	0.0442394	−	0.999021i	$-0.485914\pi$
$353$	1.66236	0.0884787	0.0442394	+	0.999021i	$0.485914\pi$
$354$	3.40235	0.180833
$355$	10.9647	0.581948
$356$	47.9149	2.53949
$357$	0.0919085	0.00486431
$358$	−45.7008	−2.41536
$359$	−19.7653	−1.04317	−0.521586	−	0.853198i	$-0.674660\pi$
$359$	−19.7653	−1.04317	−0.521586	+	0.853198i	$0.674660\pi$
$360$	36.2375	1.90989
$361$	−11.3234	−0.595969
$362$	3.67854	0.193340
$363$	2.62414	0.137731
$364$	−0.887886	−0.0465379
$365$	13.8468	0.724775
$366$	−6.62451	−0.346269
$367$	−20.9268	−1.09237	−0.546185	−	0.837665i	$-0.683920\pi$
$367$	−20.9268	−1.09237	−0.546185	+	0.837665i	$0.683920\pi$
$368$	35.5967	1.85561
$369$	−28.3128	−1.47391
$370$	26.9012	1.39853
$371$	−2.35671	−0.122354
$372$	9.09719	0.471667
$373$	11.5715	0.599147	0.299574	−	0.954073i	$-0.403156\pi$
$373$	11.5715	0.599147	0.299574	+	0.954073i	$0.403156\pi$
$374$	1.61971	0.0837532
$375$	−2.64484	−0.136579
$376$	−47.7705	−2.46358
$377$	5.15111	0.265296
$378$	−1.18279	−0.0608364
$379$	20.9839	1.07787	0.538935	−	0.842347i	$-0.318827\pi$
$379$	20.9839	1.07787	0.538935	+	0.842347i	$0.318827\pi$
$380$	26.5875	1.36391
$381$	0.960490	0.0492074
$382$	37.4895	1.91813
$383$	−15.1795	−0.775639	−0.387819	−	0.921735i	$-0.626772\pi$
$383$	−15.1795	−0.775639	−0.387819	+	0.921735i	$0.626772\pi$
$384$	4.42819	0.225975
$385$	0.431074	0.0219695
$386$	31.3696	1.59667
$387$	−33.0833	−1.68172
$388$	−24.1576	−1.22642
$389$	2.64861	0.134290	0.0671450	−	0.997743i	$-0.478611\pi$
$389$	2.64861	0.134290	0.0671450	+	0.997743i	$0.478611\pi$
$390$	0.923452	0.0467608
$391$	8.28024	0.418750
$392$	−36.7469	−1.85600
$393$	0.962825	0.0485681
$394$	49.6103	2.49933
$395$	−14.2852	−0.718767
$396$	−6.96115	−0.349811
$397$	−24.5634	−1.23280	−0.616400	−	0.787433i	$-0.711410\pi$
$397$	−24.5634	−1.23280	−0.616400	+	0.787433i	$0.711410\pi$
$398$	−27.2941	−1.36813
$399$	−0.222492	−0.0111385
$400$	1.71058	0.0855292
$401$	36.8459	1.84000	0.919998	−	0.391923i	$-0.128190\pi$
$401$	36.8459	1.84000	0.919998	+	0.391923i	$0.128190\pi$
$402$	2.37565	0.118486
$403$	−5.84132	−0.290977
$404$	42.7009	2.12445
$405$	−19.5631	−0.972100
$406$	−6.37014	−0.316145
$407$	−2.67701	−0.132694
$408$	−1.49991	−0.0742567
$409$	−6.96504	−0.344399	−0.172199	−	0.985062i	$-0.555087\pi$
$409$	−6.96504	−0.344399	−0.172199	+	0.985062i	$0.555087\pi$
$410$	−55.2341	−2.72782
$411$	4.80973	0.237246
$412$	−0.216083	−0.0106456
$413$	1.82302	0.0897049
$414$	−52.7382	−2.59194
$415$	33.5624	1.64751
$416$	1.00876	0.0494585
$417$	−0.245836	−0.0120386
$418$	−3.92099	−0.191782
$419$	−1.96945	−0.0962140	−0.0481070	−	0.998842i	$-0.515319\pi$
$419$	−1.96945	−0.0962140	−0.0481070	+	0.998842i	$0.515319\pi$
$420$	−0.770590	−0.0376009
$421$	−35.7362	−1.74168	−0.870838	−	0.491570i	$-0.836423\pi$
$421$	−35.7362	−1.74168	−0.870838	+	0.491570i	$0.836423\pi$
$422$	24.5451	1.19484
$423$	26.3420	1.28079
$424$	38.4606	1.86781
$425$	0.397903	0.0193011
$426$	2.89060	0.140050
$427$	−3.54950	−0.171772
$428$	−34.3030	−1.65810
$429$	−0.0918952	−0.00443674
$430$	−64.5407	−3.11243
$431$	−28.8284	−1.38862	−0.694308	−	0.719678i	$-0.744289\pi$
$431$	−28.8284	−1.38862	−0.694308	+	0.719678i	$0.744289\pi$
$432$	7.18445	0.345662
$433$	−28.0446	−1.34774	−0.673869	−	0.738851i	$-0.735369\pi$
$433$	−28.0446	−1.34774	−0.673869	+	0.738851i	$0.735369\pi$
$434$	7.22369	0.346748
$435$	4.47061	0.214349
$436$	−4.03027	−0.193015
$437$	−20.0448	−0.958871
$438$	3.65039	0.174422
$439$	27.0360	1.29036	0.645180	−	0.764031i	$-0.276782\pi$
$439$	27.0360	1.29036	0.645180	+	0.764031i	$0.276782\pi$
$440$	−7.03496	−0.335378
$441$	20.2633	0.964919
$442$	1.85914	0.0884305
$443$	−8.67760	−0.412285	−0.206143	−	0.978522i	$-0.566091\pi$
$443$	−8.67760	−0.412285	−0.206143	+	0.978522i	$0.566091\pi$
$444$	4.78544	0.227107
$445$	−26.7018	−1.26579
$446$	17.0626	0.807940
$447$	−1.05853	−0.0500666
$448$	1.96697	0.0929306
$449$	−14.6027	−0.689142	−0.344571	−	0.938760i	$-0.611976\pi$
$449$	−14.6027	−0.689142	−0.344571	+	0.938760i	$0.611976\pi$
$450$	−2.53431	−0.119468
$451$	5.49650	0.258820
$452$	0.324485	0.0152625
$453$	3.89092	0.182811
$454$	69.9825	3.28444
$455$	0.494797	0.0231964
$456$	3.63098	0.170036
$457$	13.1688	0.616010	0.308005	−	0.951385i	$-0.400339\pi$
$457$	13.1688	0.616010	0.308005	+	0.951385i	$0.400339\pi$
$458$	61.3586	2.86710
$459$	1.67119	0.0780046
$460$	−69.4241	−3.23692
$461$	−4.68827	−0.218354	−0.109177	−	0.994022i	$-0.534822\pi$
$461$	−4.68827	−0.218354	−0.109177	+	0.994022i	$0.534822\pi$
$462$	0.113642	0.00528713
$463$	25.1950	1.17091	0.585454	−	0.810705i	$-0.300916\pi$
$463$	25.1950	1.17091	0.585454	+	0.810705i	$0.300916\pi$
$464$	38.6930	1.79628
$465$	−5.06964	−0.235099
$466$	−45.0360	−2.08625
$467$	−24.2118	−1.12039	−0.560193	−	0.828362i	$-0.689273\pi$
$467$	−24.2118	−1.12039	−0.560193	+	0.828362i	$0.689273\pi$
$468$	−7.99018	−0.369346
$469$	1.27290	0.0587771
$470$	51.3893	2.37041
$471$	−0.280473	−0.0129235
$472$	−29.7510	−1.36940
$473$	6.42262	0.295312
$474$	−3.76596	−0.172976
$475$	−0.963241	−0.0441965
$476$	−1.55139	−0.0711080
$477$	−21.2083	−0.971060
$478$	57.0265	2.60833
$479$	−22.0171	−1.00599	−0.502994	−	0.864290i	$-0.667768\pi$
$479$	−22.0171	−1.00599	−0.502994	+	0.864290i	$0.667768\pi$
$480$	0.875494	0.0399606
$481$	−3.07274	−0.140105
$482$	74.1899	3.37926
$483$	0.580960	0.0264346
$484$	−44.2948	−2.01340
$485$	13.4625	0.611298
$486$	−16.0203	−0.726695
$487$	−35.4094	−1.60455	−0.802276	−	0.596953i	$-0.796378\pi$
$487$	−35.4094	−1.60455	−0.802276	+	0.596953i	$0.796378\pi$
$488$	57.9265	2.62221
$489$	0.722944	0.0326927
$490$	39.5307	1.78581
$491$	43.9214	1.98214	0.991072	−	0.133328i	$-0.0425663\pi$
$491$	43.9214	1.98214	0.991072	+	0.133328i	$0.0425663\pi$
$492$	−9.82557	−0.442971
$493$	9.00048	0.405361
$494$	−4.50061	−0.202492
$495$	3.87928	0.174360
$496$	−43.8776	−1.97016
$497$	1.54882	0.0694740
$498$	8.84793	0.396485
$499$	6.73789	0.301630	0.150815	−	0.988562i	$-0.451810\pi$
$499$	6.73789	0.301630	0.150815	+	0.988562i	$0.451810\pi$
$500$	44.6442	1.99655
$501$	−1.14311	−0.0510702
$502$	36.0436	1.60871
$503$	−0.982907	−0.0438257	−0.0219128	−	0.999760i	$-0.506976\pi$
$503$	−0.982907	−0.0438257	−0.0219128	+	0.999760i	$0.506976\pi$
$504$	5.11871	0.228006
$505$	−23.7962	−1.05891
$506$	10.2383	0.455148
$507$	3.09039	0.137249
$508$	−16.2129	−0.719329
$509$	−32.6107	−1.44544	−0.722721	−	0.691140i	$-0.757109\pi$
$509$	−32.6107	−1.44544	−0.722721	+	0.691140i	$0.757109\pi$
$510$	1.61354	0.0714486
$511$	1.95592	0.0865249
$512$	−44.8813	−1.98349
$513$	−4.04561	−0.178618
$514$	2.44683	0.107925
$515$	0.120418	0.00530624
$516$	−11.4811	−0.505428
$517$	−5.11389	−0.224909
$518$	3.79991	0.166959
$519$	−0.502196	−0.0220440
$520$	−8.07490	−0.354108
$521$	8.76803	0.384134	0.192067	−	0.981382i	$-0.438481\pi$
$521$	8.76803	0.384134	0.192067	+	0.981382i	$0.438481\pi$
$522$	−57.3255	−2.50907
$523$	−28.4574	−1.24436	−0.622178	−	0.782876i	$-0.713752\pi$
$523$	−28.4574	−1.24436	−0.622178	+	0.782876i	$0.713752\pi$
$524$	−16.2523	−0.709983
$525$	0.0279177	0.00121843
$526$	−24.1577	−1.05332
$527$	−10.2065	−0.444601
$528$	−0.690279	−0.0300405
$529$	29.3400	1.27565
$530$	−41.3742	−1.79718
$531$	16.4055	0.711940
$532$	3.75561	0.162826
$533$	6.30902	0.273274
$534$	−7.03930	−0.304620
$535$	19.1162	0.826467
$536$	−20.7733	−0.897268
$537$	4.53048	0.195505
$538$	6.29441	0.271371
$539$	−3.93381	−0.169441
$540$	−14.0118	−0.602972
$541$	25.4795	1.09545	0.547725	−	0.836658i	$-0.315494\pi$
$541$	25.4795	1.09545	0.547725	+	0.836658i	$0.315494\pi$
$542$	32.6803	1.40374
$543$	−0.364666	−0.0156493
$544$	1.76259	0.0755705
$545$	2.24597	0.0962068
$546$	0.130442	0.00558239
$547$	−10.7278	−0.458689	−0.229344	−	0.973345i	$-0.573658\pi$
$547$	−10.7278	−0.458689	−0.229344	+	0.973345i	$0.573658\pi$
$548$	−81.1870	−3.46814
$549$	−31.9423	−1.36326
$550$	0.491996	0.0209788
$551$	−21.7883	−0.928214
$552$	−9.48105	−0.403540
$553$	−2.01785	−0.0858077
$554$	36.2363	1.53953
$555$	−2.66681	−0.113200
$556$	4.14965	0.175985
$557$	31.2761	1.32521	0.662606	−	0.748968i	$-0.269450\pi$
$557$	31.2761	1.32521	0.662606	+	0.748968i	$0.269450\pi$
$558$	65.0067	2.75195
$559$	7.37204	0.311804
$560$	3.71671	0.157060
$561$	−0.160567	−0.00677916
$562$	8.32074	0.350989
$563$	18.9842	0.800090	0.400045	−	0.916496i	$-0.368995\pi$
$563$	18.9842	0.800090	0.400045	+	0.916496i	$0.368995\pi$
$564$	9.14162	0.384932
$565$	−0.180828	−0.00760747
$566$	29.3860	1.23518
$567$	−2.76338	−0.116051
$568$	−25.2761	−1.06056
$569$	20.9669	0.878978	0.439489	−	0.898248i	$-0.355159\pi$
$569$	20.9669	0.878978	0.439489	+	0.898248i	$0.355159\pi$
$570$	−3.90604	−0.163606
$571$	−10.2145	−0.427464	−0.213732	−	0.976892i	$-0.568562\pi$
$571$	−10.2145	−0.427464	−0.213732	+	0.976892i	$0.568562\pi$
$572$	1.55117	0.0648576
$573$	−3.71646	−0.155257
$574$	−7.80207	−0.325652
$575$	2.51517	0.104890
$576$	17.7010	0.737540
$577$	−3.73780	−0.155607	−0.0778033	−	0.996969i	$-0.524791\pi$
$577$	−3.73780	−0.155607	−0.0778033	+	0.996969i	$0.524791\pi$
$578$	−38.9090	−1.61840
$579$	−3.10978	−0.129238
$580$	−75.4628	−3.13342
$581$	4.74083	0.196683
$582$	3.54906	0.147113
$583$	4.11726	0.170519
$584$	−31.9199	−1.32086
$585$	4.45273	0.184098
$586$	34.0315	1.40583
$587$	−15.3677	−0.634293	−0.317147	−	0.948377i	$-0.602725\pi$
$587$	−15.3677	−0.634293	−0.317147	+	0.948377i	$0.602725\pi$
$588$	7.03209	0.289999
$589$	24.7078	1.01807
$590$	32.0048	1.31762
$591$	−4.91804	−0.202301
$592$	−23.0812	−0.948630
$593$	−34.5495	−1.41878	−0.709389	−	0.704817i	$-0.751029\pi$
$593$	−34.5495	−1.41878	−0.709389	+	0.704817i	$0.751029\pi$
$594$	2.06639	0.0847848
$595$	0.864554	0.0354432
$596$	17.8677	0.731889
$597$	2.70576	0.110739
$598$	11.7518	0.480566
$599$	46.5366	1.90143	0.950717	−	0.310060i	$-0.100349\pi$
$599$	46.5366	1.90143	0.950717	+	0.310060i	$0.100349\pi$
$600$	−0.455607	−0.0186001
$601$	−30.4861	−1.24356	−0.621778	−	0.783194i	$-0.713589\pi$
$601$	−30.4861	−1.24356	−0.621778	+	0.783194i	$0.713589\pi$
$602$	−9.11666	−0.371567
$603$	11.4550	0.466482
$604$	−65.6778	−2.67239
$605$	24.6844	1.00356
$606$	−6.27330	−0.254835
$607$	−13.2182	−0.536511	−0.268256	−	0.963348i	$-0.586447\pi$
$607$	−13.2182	−0.536511	−0.268256	+	0.963348i	$0.586447\pi$
$608$	−4.26688	−0.173045
$609$	0.631494	0.0255894
$610$	−62.3146	−2.52305
$611$	−5.86986	−0.237469
$612$	−13.9611	−0.564346
$613$	−16.8823	−0.681869	−0.340935	−	0.940087i	$-0.610743\pi$
$613$	−16.8823	−0.681869	−0.340935	+	0.940087i	$0.610743\pi$
$614$	−47.8938	−1.93284
$615$	5.47555	0.220796
$616$	−0.993719	−0.0400381
$617$	−16.5346	−0.665659	−0.332829	−	0.942987i	$-0.608003\pi$
$617$	−16.5346	−0.665659	−0.332829	+	0.942987i	$0.608003\pi$
$618$	0.0317453	0.00127698
$619$	19.1064	0.767952	0.383976	−	0.923343i	$-0.374555\pi$
$619$	19.1064	0.767952	0.383976	+	0.923343i	$0.374555\pi$
$620$	85.5743	3.43675
$621$	10.5637	0.423908
$622$	51.5202	2.06577
$623$	−3.77175	−0.151112
$624$	−0.792320	−0.0317182
$625$	−26.6174	−1.06470
$626$	−68.3565	−2.73207
$627$	0.388701	0.0155232
$628$	4.73432	0.188920
$629$	−5.36896	−0.214075
$630$	−5.50648	−0.219383
$631$	−20.1170	−0.800844	−0.400422	−	0.916331i	$-0.631136\pi$
$631$	−20.1170	−0.800844	−0.400422	+	0.916331i	$0.631136\pi$
$632$	32.9305	1.30991
$633$	−2.43324	−0.0967127
$634$	−46.5410	−1.84838
$635$	9.03502	0.358544
$636$	−7.36004	−0.291844
$637$	−4.51532	−0.178904
$638$	11.1289	0.440596
$639$	13.9380	0.551378
$640$	41.6545	1.64654
$641$	−19.2938	−0.762061	−0.381031	−	0.924562i	$-0.624431\pi$
$641$	−19.2938	−0.762061	−0.381031	+	0.924562i	$0.624431\pi$
$642$	5.03955	0.198895
$643$	29.2745	1.15447	0.577237	−	0.816577i	$-0.304131\pi$
$643$	29.2745	1.15447	0.577237	+	0.816577i	$0.304131\pi$
$644$	−9.80647	−0.386429
$645$	6.39814	0.251926
$646$	−7.86386	−0.309399
$647$	19.8266	0.779466	0.389733	−	0.920928i	$-0.372567\pi$
$647$	19.8266	0.779466	0.389733	+	0.920928i	$0.372567\pi$
$648$	45.0973	1.77159
$649$	−3.18488	−0.125018
$650$	0.564726	0.0221504
$651$	−0.716109	−0.0280665
$652$	−12.2031	−0.477911
$653$	−35.7848	−1.40037	−0.700183	−	0.713963i	$-0.746898\pi$
$653$	−35.7848	−1.40037	−0.700183	+	0.713963i	$0.746898\pi$
$654$	0.592098	0.0231529
$655$	9.05698	0.353886
$656$	47.3908	1.85030
$657$	17.6015	0.686702
$658$	7.25897	0.282984
$659$	−21.1886	−0.825389	−0.412695	−	0.910869i	$-0.635412\pi$
$659$	−21.1886	−0.825389	−0.412695	+	0.910869i	$0.635412\pi$
$660$	1.34625	0.0524026
$661$	8.67722	0.337505	0.168752	−	0.985658i	$-0.446026\pi$
$661$	8.67722	0.337505	0.168752	+	0.985658i	$0.446026\pi$
$662$	−0.204642	−0.00795363
$663$	−0.184303	−0.00715775
$664$	−77.3686	−3.00248
$665$	−2.09291	−0.0811594
$666$	34.1958	1.32506
$667$	56.8927	2.20289
$668$	19.2953	0.746559
$669$	−1.69148	−0.0653964
$670$	22.3469	0.863337
$671$	6.20110	0.239391
$672$	0.123667	0.00477057
$673$	−7.11219	−0.274155	−0.137077	−	0.990560i	$-0.543771\pi$
$673$	−7.11219	−0.274155	−0.137077	+	0.990560i	$0.543771\pi$
$674$	33.6294	1.29536
$675$	0.507634	0.0195389
$676$	−52.1650	−2.00635
$677$	−16.7747	−0.644704	−0.322352	−	0.946620i	$-0.604473\pi$
$677$	−16.7747	−0.644704	−0.322352	+	0.946620i	$0.604473\pi$
$678$	−0.0476709	−0.00183079
$679$	1.90163	0.0729779
$680$	−14.1092	−0.541063
$681$	−6.93760	−0.265850
$682$	−12.6200	−0.483246
$683$	47.7431	1.82684	0.913419	−	0.407020i	$-0.133432\pi$
$683$	47.7431	1.82684	0.913419	+	0.407020i	$0.133432\pi$
$684$	33.7971	1.29226
$685$	45.2435	1.72867
$686$	11.2542	0.429687
$687$	−6.08269	−0.232069
$688$	55.3758	2.11118
$689$	4.72589	0.180042
$690$	10.1993	0.388280
$691$	−30.4574	−1.15865	−0.579327	−	0.815095i	$-0.696685\pi$
$691$	−30.4574	−1.15865	−0.579327	+	0.815095i	$0.696685\pi$
$692$	8.47695	0.322245
$693$	0.547965	0.0208155
$694$	−34.8367	−1.32238
$695$	−2.31250	−0.0877181
$696$	−10.3057	−0.390638
$697$	11.0237	0.417552
$698$	73.8758	2.79624
$699$	4.46458	0.168866
$700$	−0.471245	−0.0178114
$701$	−19.6196	−0.741020	−0.370510	−	0.928828i	$-0.620817\pi$
$701$	−19.6196	−0.741020	−0.370510	+	0.928828i	$0.620817\pi$
$702$	2.37185	0.0895197
$703$	12.9972	0.490197
$704$	−3.43637	−0.129513
$705$	−5.09440	−0.191866
$706$	4.12241	0.155149
$707$	−3.36131	−0.126415
$708$	5.69331	0.213968
$709$	11.6038	0.435790	0.217895	−	0.975972i	$-0.430081\pi$
$709$	11.6038	0.435790	0.217895	+	0.975972i	$0.430081\pi$
$710$	27.1909	1.02046
$711$	−18.1588	−0.681009
$712$	61.5535	2.30681
$713$	−64.5158	−2.41614
$714$	0.227919	0.00852966
$715$	−0.864429	−0.0323278
$716$	−76.4734	−2.85794
$717$	−5.65323	−0.211124
$718$	−49.0150	−1.82922
$719$	26.2649	0.979514	0.489757	−	0.871859i	$-0.337085\pi$
$719$	26.2649	0.979514	0.489757	+	0.871859i	$0.337085\pi$
$720$	33.4471	1.24650
$721$	0.0170095	0.000633468 0
$722$	−28.0803	−1.04504
$723$	−7.35470	−0.273524
$724$	6.15548	0.228766
$725$	2.73395	0.101536
$726$	6.50746	0.241515
$727$	0.451096	0.0167302	0.00836512	−	0.999965i	$-0.497337\pi$
$727$	0.451096	0.0167302	0.00836512	+	0.999965i	$0.497337\pi$
$728$	−1.14062	−0.0422740
$729$	−23.7911	−0.881150
$730$	34.3380	1.27091
$731$	12.8811	0.476424
$732$	−11.0851	−0.409718
$733$	36.4971	1.34805	0.674025	−	0.738708i	$-0.264564\pi$
$733$	36.4971	1.34805	0.674025	+	0.738708i	$0.264564\pi$
$734$	−51.8953	−1.91549
$735$	−3.91881	−0.144548
$736$	11.1415	0.410680
$737$	−2.22380	−0.0819149
$738$	−70.2116	−2.58452
$739$	−15.0007	−0.551811	−0.275905	−	0.961185i	$-0.588978\pi$
$739$	−15.0007	−0.551811	−0.275905	+	0.961185i	$0.588978\pi$
$740$	45.0151	1.65479
$741$	0.446161	0.0163901
$742$	−5.84429	−0.214551
$743$	−28.6822	−1.05225	−0.526125	−	0.850407i	$-0.676356\pi$
$743$	−28.6822	−1.05225	−0.526125	+	0.850407i	$0.676356\pi$
$744$	11.6866	0.428452
$745$	−9.95722	−0.364804
$746$	28.6955	1.05062
$747$	42.6632	1.56097
$748$	2.71034	0.0990999
$749$	2.70025	0.0986651
$750$	−6.55880	−0.239494
$751$	30.4351	1.11059	0.555297	−	0.831652i	$-0.312605\pi$
$751$	30.4351	1.11059	0.555297	+	0.831652i	$0.312605\pi$
$752$	−44.0919	−1.60787
$753$	−3.57313	−0.130212
$754$	12.7740	0.465201
$755$	36.6006	1.33203
$756$	−1.97923	−0.0719838
$757$	51.7252	1.87998	0.939992	−	0.341197i	$-0.110832\pi$
$757$	51.7252	1.87998	0.939992	+	0.341197i	$0.110832\pi$
$758$	52.0369	1.89007
$759$	−1.01496	−0.0368406
$760$	34.1554	1.23895
$761$	29.6807	1.07593	0.537963	−	0.842969i	$-0.319194\pi$
$761$	29.6807	1.07593	0.537963	+	0.842969i	$0.319194\pi$
$762$	2.38187	0.0862861
$763$	0.317253	0.0114853
$764$	62.7330	2.26960
$765$	7.78020	0.281294
$766$	−37.6430	−1.36010
$767$	−3.65569	−0.131999
$768$	8.02057	0.289418
$769$	−3.68318	−0.132819	−0.0664095	−	0.997792i	$-0.521154\pi$
$769$	−3.68318	−0.132819	−0.0664095	+	0.997792i	$0.521154\pi$
$770$	1.06900	0.0385240
$771$	−0.242563	−0.00873570
$772$	52.4923	1.88924
$773$	24.8227	0.892809	0.446405	−	0.894831i	$-0.352704\pi$
$773$	24.8227	0.892809	0.446405	+	0.894831i	$0.352704\pi$
$774$	−82.0417	−2.94893
$775$	−3.10028	−0.111365
$776$	−31.0339	−1.11405
$777$	−0.376698	−0.0135140
$778$	6.56816	0.235480
$779$	−26.6861	−0.956128
$780$	1.54526	0.0553291
$781$	−2.70584	−0.0968226
$782$	20.5338	0.734285
$783$	11.4826	0.410354
$784$	−33.9172	−1.21133
$785$	−2.63832	−0.0941657
$786$	2.38766	0.0851650
$787$	−21.0833	−0.751538	−0.375769	−	0.926713i	$-0.622621\pi$
$787$	−21.0833	−0.751538	−0.375769	+	0.926713i	$0.622621\pi$
$788$	83.0154	2.95730
$789$	2.39483	0.0852583
$790$	−35.4252	−1.26037
$791$	−0.0255427	−0.000908194 0
$792$	−8.94258	−0.317761
$793$	7.11778	0.252760
$794$	−60.9135	−2.16174
$795$	4.10157	0.145468
$796$	−45.6726	−1.61882
$797$	−24.3975	−0.864204	−0.432102	−	0.901825i	$-0.642228\pi$
$797$	−24.3975	−0.864204	−0.432102	+	0.901825i	$0.642228\pi$
$798$	−0.551746	−0.0195316
$799$	−10.2563	−0.362843
$800$	0.535398	0.0189292
$801$	−33.9423	−1.19929
$802$	91.3723	3.22647
$803$	−3.41707	−0.120586
$804$	3.97529	0.140198
$805$	5.46490	0.192612
$806$	−14.4856	−0.510233
$807$	−0.623987	−0.0219654
$808$	54.8553	1.92980
$809$	9.84260	0.346048	0.173024	−	0.984918i	$-0.444646\pi$
$809$	9.84260	0.346048	0.173024	+	0.984918i	$0.444646\pi$
$810$	−48.5136	−1.70460
$811$	−46.1782	−1.62154	−0.810769	−	0.585367i	$-0.800951\pi$
$811$	−46.1782	−1.62154	−0.810769	+	0.585367i	$0.800951\pi$
$812$	−10.6595	−0.374074
$813$	−3.23971	−0.113622
$814$	−6.63858	−0.232682
$815$	6.80050	0.238211
$816$	−1.38441	−0.0484641
$817$	−31.1825	−1.09094
$818$	−17.2722	−0.603910
$819$	0.628968	0.0219779
$820$	−92.4260	−3.22766
$821$	−3.25038	−0.113439	−0.0567195	−	0.998390i	$-0.518064\pi$
$821$	−3.25038	−0.113439	−0.0567195	+	0.998390i	$0.518064\pi$
$822$	11.9274	0.416016
$823$	−1.80449	−0.0629005	−0.0314503	−	0.999505i	$-0.510013\pi$
$823$	−1.80449	−0.0629005	−0.0314503	+	0.999505i	$0.510013\pi$
$824$	−0.277589	−0.00967028
$825$	−0.0487733	−0.00169807
$826$	4.52081	0.157299
$827$	−8.40455	−0.292255	−0.146127	−	0.989266i	$-0.546681\pi$
$827$	−8.40455	−0.292255	−0.146127	+	0.989266i	$0.546681\pi$
$828$	−88.2494	−3.06688
$829$	−11.0909	−0.385205	−0.192602	−	0.981277i	$-0.561693\pi$
$829$	−11.0909	−0.385205	−0.192602	+	0.981277i	$0.561693\pi$
$830$	83.2296	2.88894
$831$	−3.59223	−0.124613
$832$	−3.94435	−0.136746
$833$	−7.88957	−0.273357
$834$	−0.609636	−0.0211100
$835$	−10.7528	−0.372117
$836$	−6.56118	−0.226923
$837$	−13.0212	−0.450077
$838$	−4.88394	−0.168713
$839$	−49.3189	−1.70268	−0.851339	−	0.524617i	$-0.824209\pi$
$839$	−49.3189	−1.70268	−0.851339	+	0.524617i	$0.824209\pi$
$840$	−0.989931	−0.0341559
$841$	32.8413	1.13246
$842$	−88.6204	−3.05406
$843$	−0.824864	−0.0284098
$844$	41.0725	1.41378
$845$	29.0703	1.00005
$846$	65.3242	2.24589
$847$	3.48678	0.119807
$848$	35.4990	1.21904
$849$	−2.91313	−0.0999784
$850$	0.986739	0.0338449
$851$	−33.9376	−1.16337
$852$	4.83698	0.165712
$853$	−7.86042	−0.269136	−0.134568	−	0.990904i	$-0.542965\pi$
$853$	−7.86042	−0.269136	−0.134568	+	0.990904i	$0.542965\pi$
$854$	−8.80222	−0.301206
$855$	−18.8343	−0.644119
$856$	−44.0671	−1.50618
$857$	3.23243	0.110418	0.0552088	−	0.998475i	$-0.482418\pi$
$857$	3.23243	0.110418	0.0552088	+	0.998475i	$0.482418\pi$
$858$	−0.227886	−0.00777991
$859$	−3.07827	−0.105029	−0.0525146	−	0.998620i	$-0.516724\pi$
$859$	−3.07827	−0.105029	−0.0525146	+	0.998620i	$0.516724\pi$
$860$	−107.999	−3.68274
$861$	0.773446	0.0263590
$862$	−71.4901	−2.43496
$863$	−50.4748	−1.71818	−0.859091	−	0.511822i	$-0.828971\pi$
$863$	−50.4748	−1.71818	−0.859091	+	0.511822i	$0.828971\pi$
$864$	2.24867	0.0765013
$865$	−4.72399	−0.160621
$866$	−69.5464	−2.36328
$867$	3.85718	0.130997
$868$	12.0877	0.410285
$869$	3.52525	0.119586
$870$	11.0864	0.375866
$871$	−2.55254	−0.0864895
$872$	−5.17746	−0.175331
$873$	17.1130	0.579186
$874$	−49.7080	−1.68140
$875$	−3.51429	−0.118805
$876$	6.10837	0.206383
$877$	−21.1020	−0.712563	−0.356281	−	0.934379i	$-0.615956\pi$
$877$	−21.1020	−0.712563	−0.356281	+	0.934379i	$0.615956\pi$
$878$	67.0453	2.26267
$879$	−3.37366	−0.113791
$880$	−6.49323	−0.218887
$881$	27.3881	0.922730	0.461365	−	0.887210i	$-0.347360\pi$
$881$	27.3881	0.922730	0.461365	+	0.887210i	$0.347360\pi$
$882$	50.2499	1.69200
$883$	23.3136	0.784567	0.392283	−	0.919844i	$-0.371685\pi$
$883$	23.3136	0.784567	0.392283	+	0.919844i	$0.371685\pi$
$884$	3.11100	0.104634
$885$	−3.17274	−0.106651
$886$	−21.5191	−0.722950
$887$	30.1658	1.01287	0.506435	−	0.862278i	$-0.330963\pi$
$887$	30.1658	1.01287	0.506435	+	0.862278i	$0.330963\pi$
$888$	6.14757	0.206299
$889$	1.27624	0.0428036
$890$	−66.2164	−2.21958
$891$	4.82772	0.161735
$892$	28.5518	0.955984
$893$	24.8285	0.830853
$894$	−2.62499	−0.0877927
$895$	42.6167	1.42452
$896$	5.88389	0.196567
$897$	−1.16499	−0.0388980
$898$	−36.2124	−1.20842
$899$	−70.1276	−2.33889
$900$	−4.24078	−0.141359
$901$	8.25750	0.275097
$902$	13.6305	0.453846
$903$	0.903766	0.0300754
$904$	0.416847	0.0138641
$905$	−3.43029	−0.114027
$906$	9.64889	0.320563
$907$	−26.8143	−0.890353	−0.445176	−	0.895443i	$-0.646859\pi$
$907$	−26.8143	−0.890353	−0.445176	+	0.895443i	$0.646859\pi$
$908$	117.105	3.88627
$909$	−30.2488	−1.00329
$910$	1.22702	0.0406754
$911$	24.7438	0.819798	0.409899	−	0.912131i	$-0.365564\pi$
$911$	24.7438	0.819798	0.409899	+	0.912131i	$0.365564\pi$
$912$	3.35138	0.110975
$913$	−8.28241	−0.274108
$914$	32.6566	1.08018
$915$	6.17747	0.204221
$916$	102.674	3.39246
$917$	1.27934	0.0422475
$918$	4.14431	0.136782
$919$	−27.2810	−0.899916	−0.449958	−	0.893050i	$-0.648561\pi$
$919$	−27.2810	−0.899916	−0.449958	+	0.893050i	$0.648561\pi$
$920$	−89.1851	−2.94035
$921$	4.74788	0.156448
$922$	−11.6262	−0.382888
$923$	−3.10583	−0.102230
$924$	0.190163	0.00625592
$925$	−1.63085	−0.0536221
$926$	62.4797	2.05321
$927$	0.153071	0.00502750
$928$	12.1106	0.397549
$929$	31.6186	1.03737	0.518687	−	0.854964i	$-0.326421\pi$
$929$	31.6186	1.03737	0.518687	+	0.854964i	$0.326421\pi$
$930$	−12.5719	−0.412250
$931$	19.0990	0.625946
$932$	−75.3610	−2.46853
$933$	−5.10738	−0.167208
$934$	−60.0415	−1.96462
$935$	−1.51041	−0.0493956
$936$	−10.2645	−0.335506
$937$	35.8451	1.17101	0.585504	−	0.810670i	$-0.300897\pi$
$937$	35.8451	1.17101	0.585504	+	0.810670i	$0.300897\pi$
$938$	3.15660	0.103067
$939$	6.77641	0.221140
$940$	85.9923	2.80476
$941$	49.3069	1.60736	0.803679	−	0.595063i	$-0.202873\pi$
$941$	49.3069	1.60736	0.803679	+	0.595063i	$0.202873\pi$
$942$	−0.695531	−0.0226616
$943$	69.6815	2.26914
$944$	−27.4600	−0.893748
$945$	1.10298	0.0358798
$946$	15.9271	0.517836
$947$	−43.3960	−1.41018	−0.705090	−	0.709118i	$-0.749093\pi$
$947$	−43.3960	−1.41018	−0.705090	+	0.709118i	$0.749093\pi$
$948$	−6.30176	−0.204672
$949$	−3.92220	−0.127320
$950$	−2.38869	−0.0774995
$951$	4.61377	0.149612
$952$	−1.99299	−0.0645930
$953$	46.8528	1.51771	0.758856	−	0.651259i	$-0.225759\pi$
$953$	46.8528	1.51771	0.758856	+	0.651259i	$0.225759\pi$
$954$	−52.5933	−1.70277
$955$	−34.9596	−1.13126
$956$	95.4253	3.08627
$957$	−1.10324	−0.0356628
$958$	−54.5991	−1.76402
$959$	6.39085	0.206371
$960$	−3.42327	−0.110486
$961$	48.5242	1.56530
$962$	−7.61993	−0.245676
$963$	24.2999	0.783052
$964$	124.146	3.99846
$965$	−29.2527	−0.941677
$966$	1.44069	0.0463535
$967$	−9.07659	−0.291884	−0.145942	−	0.989293i	$-0.546621\pi$
$967$	−9.07659	−0.291884	−0.145942	+	0.989293i	$0.546621\pi$
$968$	−56.9029	−1.82893
$969$	0.779572	0.0250435
$970$	33.3849	1.07192
$971$	−40.2761	−1.29252	−0.646260	−	0.763117i	$-0.723668\pi$
$971$	−40.2761	−1.29252	−0.646260	+	0.763117i	$0.723668\pi$
$972$	−26.8075	−0.859852
$973$	−0.326651	−0.0104719
$974$	−87.8099	−2.81361
$975$	−0.0559832	−0.00179290
$976$	53.4658	1.71140
$977$	−22.5984	−0.722987	−0.361493	−	0.932375i	$-0.617733\pi$
$977$	−22.5984	−0.722987	−0.361493	+	0.932375i	$0.617733\pi$
$978$	1.79279	0.0573272
$979$	6.58938	0.210598
$980$	66.1486	2.11304
$981$	2.85500	0.0911530
$982$	108.918	3.47573
$983$	36.5906	1.16706	0.583530	−	0.812092i	$-0.301671\pi$
$983$	36.5906	1.16706	0.583530	+	0.812092i	$0.301671\pi$
$984$	−12.6223	−0.402386
$985$	−46.2624	−1.47404
$986$	22.3198	0.710808
$987$	−0.719607	−0.0229053
$988$	−7.53109	−0.239596
$989$	81.4222	2.58908
$990$	9.62002	0.305744
$991$	−3.42163	−0.108692	−0.0543458	−	0.998522i	$-0.517307\pi$
$991$	−3.42163	−0.108692	−0.0543458	+	0.998522i	$0.517307\pi$
$992$	−13.7333	−0.436033
$993$	0.0202868	0.000643784 0
$994$	3.84084	0.121824
$995$	25.4522	0.806889
$996$	14.8057	0.469136
$997$	57.7784	1.82986	0.914930	−	0.403613i	$-0.132246\pi$
$997$	57.7784	1.82986	0.914930	+	0.403613i	$0.132246\pi$
$998$	16.7090	0.528913
$999$	−6.84959	−0.216711

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	139.2.a.c.1.7	✓	7
3.2	odd	2		1251.2.a.k.1.1		7
4.3	odd	2		2224.2.a.o.1.4		7
5.4	even	2		3475.2.a.e.1.1		7
7.6	odd	2		6811.2.a.p.1.7		7
8.3	odd	2		8896.2.a.bd.1.4		7
8.5	even	2		8896.2.a.be.1.4		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
139.2.a.c.1.7	✓	7	1.1	even	1	trivial
1251.2.a.k.1.1		7	3.2	odd	2
2224.2.a.o.1.4		7	4.3	odd	2
3475.2.a.e.1.1		7	5.4	even	2
6811.2.a.p.1.7		7	7.6	odd	2
8896.2.a.bd.1.4		7	8.3	odd	2
8896.2.a.be.1.4		7	8.5	even	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:	\( N \)	\(=\)	\( 139 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	139.a (trivial)

\(f(q)\)	\(=\)	\(q+2.47985 q^{2} -0.245836 q^{3} +4.14965 q^{4} -2.31250 q^{5} -0.609636 q^{6} -0.326651 q^{7} +5.33082 q^{8} -2.93956 q^{9} +O(q^{10})\)	\(q+2.47985 q^{2} -0.245836 q^{3} +4.14965 q^{4} -2.31250 q^{5} -0.609636 q^{6} -0.326651 q^{7} +5.33082 q^{8} -2.93956 q^{9} -5.73465 q^{10} +0.570671 q^{11} -1.02013 q^{12} +0.655030 q^{13} -0.810045 q^{14} +0.568496 q^{15} +4.92032 q^{16} +1.14453 q^{17} -7.28968 q^{18} -2.77067 q^{19} -9.59608 q^{20} +0.0803026 q^{21} +1.41518 q^{22} +7.23464 q^{23} -1.31051 q^{24} +0.347657 q^{25} +1.62438 q^{26} +1.46016 q^{27} -1.35549 q^{28} +7.86393 q^{29} +1.40978 q^{30} -8.91763 q^{31} +1.54002 q^{32} -0.140292 q^{33} +2.83826 q^{34} +0.755380 q^{35} -12.1982 q^{36} -4.69099 q^{37} -6.87084 q^{38} -0.161030 q^{39} -12.3275 q^{40} +9.63165 q^{41} +0.199138 q^{42} +11.2545 q^{43} +2.36809 q^{44} +6.79774 q^{45} +17.9408 q^{46} -8.96119 q^{47} -1.20959 q^{48} -6.89330 q^{49} +0.862137 q^{50} -0.281366 q^{51} +2.71815 q^{52} +7.21477 q^{53} +3.62098 q^{54} -1.31968 q^{55} -1.74132 q^{56} +0.681130 q^{57} +19.5014 q^{58} -5.58094 q^{59} +2.35906 q^{60} +10.8663 q^{61} -22.1144 q^{62} +0.960211 q^{63} -6.02163 q^{64} -1.51476 q^{65} -0.347902 q^{66} -3.89682 q^{67} +4.74939 q^{68} -1.77853 q^{69} +1.87323 q^{70} -4.74151 q^{71} -15.6703 q^{72} -5.98781 q^{73} -11.6329 q^{74} -0.0854666 q^{75} -11.4973 q^{76} -0.186410 q^{77} -0.399330 q^{78} +6.17739 q^{79} -11.3782 q^{80} +8.45973 q^{81} +23.8850 q^{82} -14.5135 q^{83} +0.333228 q^{84} -2.64672 q^{85} +27.9095 q^{86} -1.93324 q^{87} +3.04214 q^{88} +11.5467 q^{89} +16.8574 q^{90} -0.213966 q^{91} +30.0212 q^{92} +2.19228 q^{93} -22.2224 q^{94} +6.40717 q^{95} -0.378592 q^{96} -5.82160 q^{97} -17.0943 q^{98} -1.67752 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + q^{2} - 2 q^{3} + 9 q^{4} + 11 q^{5} - 7 q^{6} - 5 q^{7} + 6 q^{8} + 13 q^{9}+O(q^{10}) \) 7 * q + q^2 - 2 * q^3 + 9 * q^4 + 11 * q^5 - 7 * q^6 - 5 * q^7 + 6 * q^8 + 13 * q^9	\( 7 q + q^{2} - 2 q^{3} + 9 q^{4} + 11 q^{5} - 7 q^{6} - 5 q^{7} + 6 q^{8} + 13 q^{9} - 4 q^{10} + 2 q^{11} - 8 q^{12} + 6 q^{13} + 7 q^{14} - 3 q^{15} + 5 q^{16} + 5 q^{17} - 10 q^{18} - 10 q^{19} + 12 q^{20} - 5 q^{21} - 18 q^{22} - q^{23} - 21 q^{24} + 14 q^{25} - 8 q^{26} - 11 q^{27} - 28 q^{28} + 30 q^{29} - 41 q^{30} - 20 q^{31} - 12 q^{32} - 20 q^{33} - 17 q^{34} - 7 q^{35} + 2 q^{36} + 6 q^{37} + 6 q^{38} + 11 q^{39} - 22 q^{40} + 19 q^{41} + 6 q^{42} - 12 q^{43} + 25 q^{44} + 27 q^{45} + 22 q^{46} - 3 q^{47} + 15 q^{48} - 8 q^{49} + 12 q^{50} + 23 q^{51} - 8 q^{52} + 38 q^{53} - 7 q^{54} + 7 q^{55} + 21 q^{56} - 19 q^{57} - 21 q^{58} - 14 q^{59} - 8 q^{60} + 4 q^{61} - q^{62} - 18 q^{63} - 16 q^{64} + 10 q^{65} + 18 q^{66} + 9 q^{67} - 25 q^{68} + 9 q^{69} + 20 q^{70} + 24 q^{71} + 41 q^{72} - 5 q^{73} + 9 q^{74} - 21 q^{75} + 3 q^{76} - 13 q^{77} + 20 q^{78} + 8 q^{79} + 11 q^{80} + 39 q^{81} + 56 q^{82} - 9 q^{83} - q^{84} - 22 q^{85} + 39 q^{86} - 25 q^{87} - 29 q^{88} + 10 q^{89} + 72 q^{90} + 7 q^{91} + 29 q^{92} - 15 q^{93} - 36 q^{94} - 21 q^{95} - 11 q^{96} - 5 q^{97} - 49 q^{98} - 31 q^{99}+O(q^{100}) \) 7 * q + q^2 - 2 * q^3 + 9 * q^4 + 11 * q^5 - 7 * q^6 - 5 * q^7 + 6 * q^8 + 13 * q^9 - 4 * q^10 + 2 * q^11 - 8 * q^12 + 6 * q^13 + 7 * q^14 - 3 * q^15 + 5 * q^16 + 5 * q^17 - 10 * q^18 - 10 * q^19 + 12 * q^20 - 5 * q^21 - 18 * q^22 - q^23 - 21 * q^24 + 14 * q^25 - 8 * q^26 - 11 * q^27 - 28 * q^28 + 30 * q^29 - 41 * q^30 - 20 * q^31 - 12 * q^32 - 20 * q^33 - 17 * q^34 - 7 * q^35 + 2 * q^36 + 6 * q^37 + 6 * q^38 + 11 * q^39 - 22 * q^40 + 19 * q^41 + 6 * q^42 - 12 * q^43 + 25 * q^44 + 27 * q^45 + 22 * q^46 - 3 * q^47 + 15 * q^48 - 8 * q^49 + 12 * q^50 + 23 * q^51 - 8 * q^52 + 38 * q^53 - 7 * q^54 + 7 * q^55 + 21 * q^56 - 19 * q^57 - 21 * q^58 - 14 * q^59 - 8 * q^60 + 4 * q^61 - q^62 - 18 * q^63 - 16 * q^64 + 10 * q^65 + 18 * q^66 + 9 * q^67 - 25 * q^68 + 9 * q^69 + 20 * q^70 + 24 * q^71 + 41 * q^72 - 5 * q^73 + 9 * q^74 - 21 * q^75 + 3 * q^76 - 13 * q^77 + 20 * q^78 + 8 * q^79 + 11 * q^80 + 39 * q^81 + 56 * q^82 - 9 * q^83 - q^84 - 22 * q^85 + 39 * q^86 - 25 * q^87 - 29 * q^88 + 10 * q^89 + 72 * q^90 + 7 * q^91 + 29 * q^92 - 15 * q^93 - 36 * q^94 - 21 * q^95 - 11 * q^96 - 5 * q^97 - 49 * q^98 - 31 * q^99

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