LMFDB - Embedded newform 6017.2.a.c.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6017,2,Mod(1,6017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6017, 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("6017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6017 = 11 \cdot 547 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6017.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.0459868962$
Analytic rank:	$1$
Dimension:	$106$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	6017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.39408 q^{2} -0.179689 q^{3} +3.73161 q^{4} -1.83517 q^{5} +0.430189 q^{6} +0.373924 q^{7} -4.14560 q^{8} -2.96771 q^{9} +O(q^{10})$	\(q-2.39408 q^{2} -0.179689 q^{3} +3.73161 q^{4} -1.83517 q^{5} +0.430189 q^{6} +0.373924 q^{7} -4.14560 q^{8} -2.96771 q^{9} +4.39353 q^{10} +1.00000 q^{11} -0.670529 q^{12} +6.01413 q^{13} -0.895203 q^{14} +0.329759 q^{15} +2.46168 q^{16} +5.84884 q^{17} +7.10493 q^{18} -3.17074 q^{19} -6.84812 q^{20} -0.0671900 q^{21} -2.39408 q^{22} +0.679989 q^{23} +0.744919 q^{24} -1.63217 q^{25} -14.3983 q^{26} +1.07233 q^{27} +1.39534 q^{28} +5.00335 q^{29} -0.789469 q^{30} -9.34384 q^{31} +2.39776 q^{32} -0.179689 q^{33} -14.0026 q^{34} -0.686213 q^{35} -11.0743 q^{36} -3.30410 q^{37} +7.59100 q^{38} -1.08067 q^{39} +7.60787 q^{40} +0.161876 q^{41} +0.160858 q^{42} +3.21975 q^{43} +3.73161 q^{44} +5.44624 q^{45} -1.62795 q^{46} -5.62611 q^{47} -0.442336 q^{48} -6.86018 q^{49} +3.90753 q^{50} -1.05097 q^{51} +22.4424 q^{52} -3.08764 q^{53} -2.56725 q^{54} -1.83517 q^{55} -1.55014 q^{56} +0.569747 q^{57} -11.9784 q^{58} -8.99236 q^{59} +1.23053 q^{60} -2.58651 q^{61} +22.3699 q^{62} -1.10970 q^{63} -10.6638 q^{64} -11.0369 q^{65} +0.430189 q^{66} +7.79770 q^{67} +21.8256 q^{68} -0.122187 q^{69} +1.64285 q^{70} -11.9224 q^{71} +12.3029 q^{72} -5.11901 q^{73} +7.91026 q^{74} +0.293282 q^{75} -11.8320 q^{76} +0.373924 q^{77} +2.58721 q^{78} -1.78467 q^{79} -4.51758 q^{80} +8.71045 q^{81} -0.387545 q^{82} +13.2223 q^{83} -0.250727 q^{84} -10.7336 q^{85} -7.70833 q^{86} -0.899047 q^{87} -4.14560 q^{88} +17.1332 q^{89} -13.0387 q^{90} +2.24883 q^{91} +2.53745 q^{92} +1.67898 q^{93} +13.4693 q^{94} +5.81883 q^{95} -0.430851 q^{96} +15.6825 q^{97} +16.4238 q^{98} -2.96771 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 106 q - 13 q^{2} - 15 q^{3} + 93 q^{4} - 12 q^{5} - 22 q^{6} - 66 q^{7} - 39 q^{8} + 97 q^{9}+O(q^{10}) $ 106 * q - 13 * q^2 - 15 * q^3 + 93 * q^4 - 12 * q^5 - 22 * q^6 - 66 * q^7 - 39 * q^8 + 97 * q^9	\( 106 q - 13 q^{2} - 15 q^{3} + 93 q^{4} - 12 q^{5} - 22 q^{6} - 66 q^{7} - 39 q^{8} + 97 q^{9} - 30 q^{10} + 106 q^{11} - 26 q^{12} - 72 q^{13} + 3 q^{14} - 46 q^{15} + 75 q^{16} - 65 q^{17} - 37 q^{18} - 63 q^{19} - 25 q^{20} - 27 q^{21} - 13 q^{22} - 23 q^{23} - 56 q^{24} + 74 q^{25} + 2 q^{26} - 54 q^{27} - 115 q^{28} - 45 q^{29} - 14 q^{30} - 89 q^{31} - 96 q^{32} - 15 q^{33} - 26 q^{34} - 52 q^{35} + 91 q^{36} - 35 q^{37} + 7 q^{38} - 34 q^{39} - 74 q^{40} - 32 q^{41} - 94 q^{43} + 93 q^{44} - 46 q^{45} - 20 q^{46} - 105 q^{47} - 57 q^{48} + 80 q^{49} - 60 q^{50} - 36 q^{51} - 137 q^{52} - 61 q^{54} - 12 q^{55} + 32 q^{56} - 71 q^{57} - 28 q^{58} - 15 q^{59} - 21 q^{60} - 80 q^{61} - 84 q^{62} - 182 q^{63} + 55 q^{64} - 73 q^{65} - 22 q^{66} - 58 q^{67} - 145 q^{68} - 8 q^{69} - 39 q^{70} - 11 q^{71} - 100 q^{72} - 155 q^{73} - 15 q^{74} - 15 q^{75} - 132 q^{76} - 66 q^{77} - 45 q^{78} - 50 q^{79} - 28 q^{80} + 114 q^{81} - 57 q^{82} - 96 q^{83} - 27 q^{84} - 74 q^{85} + 54 q^{86} - 182 q^{87} - 39 q^{88} + 9 q^{89} - 53 q^{90} + 6 q^{91} - 18 q^{92} - 26 q^{93} - 33 q^{94} - 49 q^{95} - 56 q^{96} - 102 q^{97} - 76 q^{98} + 97 q^{99}+O(q^{100}) \) 106 * q - 13 * q^2 - 15 * q^3 + 93 * q^4 - 12 * q^5 - 22 * q^6 - 66 * q^7 - 39 * q^8 + 97 * q^9 - 30 * q^10 + 106 * q^11 - 26 * q^12 - 72 * q^13 + 3 * q^14 - 46 * q^15 + 75 * q^16 - 65 * q^17 - 37 * q^18 - 63 * q^19 - 25 * q^20 - 27 * q^21 - 13 * q^22 - 23 * q^23 - 56 * q^24 + 74 * q^25 + 2 * q^26 - 54 * q^27 - 115 * q^28 - 45 * q^29 - 14 * q^30 - 89 * q^31 - 96 * q^32 - 15 * q^33 - 26 * q^34 - 52 * q^35 + 91 * q^36 - 35 * q^37 + 7 * q^38 - 34 * q^39 - 74 * q^40 - 32 * q^41 - 94 * q^43 + 93 * q^44 - 46 * q^45 - 20 * q^46 - 105 * q^47 - 57 * q^48 + 80 * q^49 - 60 * q^50 - 36 * q^51 - 137 * q^52 - 61 * q^54 - 12 * q^55 + 32 * q^56 - 71 * q^57 - 28 * q^58 - 15 * q^59 - 21 * q^60 - 80 * q^61 - 84 * q^62 - 182 * q^63 + 55 * q^64 - 73 * q^65 - 22 * q^66 - 58 * q^67 - 145 * q^68 - 8 * q^69 - 39 * q^70 - 11 * q^71 - 100 * q^72 - 155 * q^73 - 15 * q^74 - 15 * q^75 - 132 * q^76 - 66 * q^77 - 45 * q^78 - 50 * q^79 - 28 * q^80 + 114 * q^81 - 57 * q^82 - 96 * q^83 - 27 * q^84 - 74 * q^85 + 54 * q^86 - 182 * q^87 - 39 * q^88 + 9 * q^89 - 53 * q^90 + 6 * q^91 - 18 * q^92 - 26 * q^93 - 33 * q^94 - 49 * q^95 - 56 * q^96 - 102 * q^97 - 76 * q^98 + 97 * 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 $

$2$	−2.39408	−1.69287	−0.846434	−	0.532493i	$-0.821255\pi$
$2$	−2.39408	−1.69287	−0.846434	+	0.532493i	$0.821255\pi$
$3$	−0.179689	−0.103743	−0.0518717	−	0.998654i	$-0.516519\pi$
$3$	−0.179689	−0.103743	−0.0518717	+	0.998654i	$0.516519\pi$
$4$	3.73161	1.86580
$5$	−1.83517	−0.820711	−0.410356	−	0.911926i	$-0.634595\pi$
$5$	−1.83517	−0.820711	−0.410356	+	0.911926i	$0.634595\pi$
$6$	0.430189	0.175624
$7$	0.373924	0.141330	0.0706650	−	0.997500i	$-0.477488\pi$
$7$	0.373924	0.141330	0.0706650	+	0.997500i	$0.477488\pi$
$8$	−4.14560	−1.46569
$9$	−2.96771	−0.989237
$10$	4.39353	1.38936
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−0.670529	−0.193565
$13$	6.01413	1.66802	0.834009	−	0.551750i	$-0.186040\pi$
$13$	6.01413	1.66802	0.834009	+	0.551750i	$0.186040\pi$
$14$	−0.895203	−0.239253
$15$	0.329759	0.0851434
$16$	2.46168	0.615419
$17$	5.84884	1.41855	0.709276	−	0.704931i	$-0.249022\pi$
$17$	5.84884	1.41855	0.709276	+	0.704931i	$0.249022\pi$
$18$	7.10493	1.67465
$19$	−3.17074	−0.727418	−0.363709	−	0.931513i	$-0.618490\pi$
$19$	−3.17074	−0.727418	−0.363709	+	0.931513i	$0.618490\pi$
$20$	−6.84812	−1.53129
$21$	−0.0671900	−0.0146621
$22$	−2.39408	−0.510419
$23$	0.679989	0.141788	0.0708938	−	0.997484i	$-0.477415\pi$
$23$	0.679989	0.141788	0.0708938	+	0.997484i	$0.477415\pi$
$24$	0.744919	0.152056
$25$	−1.63217	−0.326433
$26$	−14.3983	−2.82374
$27$	1.07233	0.206370
$28$	1.39534	0.263694
$29$	5.00335	0.929099	0.464549	−	0.885547i	$-0.346216\pi$
$29$	5.00335	0.929099	0.464549	+	0.885547i	$0.346216\pi$
$30$	−0.789469	−0.144137
$31$	−9.34384	−1.67820	−0.839101	−	0.543975i	$-0.816919\pi$
$31$	−9.34384	−1.67820	−0.839101	+	0.543975i	$0.816919\pi$
$32$	2.39776	0.423868
$33$	−0.179689	−0.0312798
$34$	−14.0026	−2.40142
$35$	−0.686213	−0.115991
$36$	−11.0743	−1.84572
$37$	−3.30410	−0.543190	−0.271595	−	0.962412i	$-0.587551\pi$
$37$	−3.30410	−0.543190	−0.271595	+	0.962412i	$0.587551\pi$
$38$	7.59100	1.23142
$39$	−1.08067	−0.173046
$40$	7.60787	1.20291
$41$	0.161876	0.0252809	0.0126404	−	0.999920i	$-0.495976\pi$
$41$	0.161876	0.0252809	0.0126404	+	0.999920i	$0.495976\pi$
$42$	0.160858	0.0248209
$43$	3.21975	0.491007	0.245504	−	0.969396i	$-0.421047\pi$
$43$	3.21975	0.491007	0.245504	+	0.969396i	$0.421047\pi$
$44$	3.73161	0.562561
$45$	5.44624	0.811878
$46$	−1.62795	−0.240028
$47$	−5.62611	−0.820652	−0.410326	−	0.911939i	$-0.634585\pi$
$47$	−5.62611	−0.820652	−0.410326	+	0.911939i	$0.634585\pi$
$48$	−0.442336	−0.0638457
$49$	−6.86018	−0.980026
$50$	3.90753	0.552608
$51$	−1.05097	−0.147165
$52$	22.4424	3.11220
$53$	−3.08764	−0.424120	−0.212060	−	0.977257i	$-0.568017\pi$
$53$	−3.08764	−0.424120	−0.212060	+	0.977257i	$0.568017\pi$
$54$	−2.56725	−0.349358
$55$	−1.83517	−0.247454
$56$	−1.55014	−0.207146
$57$	0.569747	0.0754648
$58$	−11.9784	−1.57284
$59$	−8.99236	−1.17071	−0.585353	−	0.810778i	$-0.699044\pi$
$59$	−8.99236	−1.17071	−0.585353	+	0.810778i	$0.699044\pi$
$60$	1.23053	0.158861
$61$	−2.58651	−0.331168	−0.165584	−	0.986196i	$-0.552951\pi$
$61$	−2.58651	−0.331168	−0.165584	+	0.986196i	$0.552951\pi$
$62$	22.3699	2.84098
$63$	−1.10970	−0.139809
$64$	−10.6638	−1.33297
$65$	−11.0369	−1.36896
$66$	0.430189	0.0529526
$67$	7.79770	0.952641	0.476320	−	0.879272i	$-0.341970\pi$
$67$	7.79770	0.952641	0.476320	+	0.879272i	$0.341970\pi$
$68$	21.8256	2.64674
$69$	−0.122187	−0.0147095
$70$	1.64285	0.196358
$71$	−11.9224	−1.41493	−0.707466	−	0.706748i	$-0.750162\pi$
$71$	−11.9224	−1.41493	−0.707466	+	0.706748i	$0.750162\pi$
$72$	12.3029	1.44992
$73$	−5.11901	−0.599135	−0.299567	−	0.954075i	$-0.596842\pi$
$73$	−5.11901	−0.599135	−0.299567	+	0.954075i	$0.596842\pi$
$74$	7.91026	0.919550
$75$	0.293282	0.0338653
$76$	−11.8320	−1.35722
$77$	0.373924	0.0426126
$78$	2.58721	0.292944
$79$	−1.78467	−0.200791	−0.100396	−	0.994948i	$-0.532011\pi$
$79$	−1.78467	−0.200791	−0.100396	+	0.994948i	$0.532011\pi$
$80$	−4.51758	−0.505081
$81$	8.71045	0.967828
$82$	−0.387545	−0.0427972
$83$	13.2223	1.45133	0.725666	−	0.688047i	$-0.241532\pi$
$83$	13.2223	1.45133	0.725666	+	0.688047i	$0.241532\pi$
$84$	−0.250727	−0.0273565
$85$	−10.7336	−1.16422
$86$	−7.70833	−0.831211
$87$	−0.899047	−0.0963879
$88$	−4.14560	−0.441923
$89$	17.1332	1.81612	0.908058	−	0.418844i	$-0.137565\pi$
$89$	17.1332	1.81612	0.908058	+	0.418844i	$0.137565\pi$
$90$	−13.0387	−1.37440
$91$	2.24883	0.235741
$92$	2.53745	0.264548
$93$	1.67898	0.174103
$94$	13.4693	1.38926
$95$	5.81883	0.597000
$96$	−0.430851	−0.0439735
$97$	15.6825	1.59231	0.796157	−	0.605090i	$-0.206863\pi$
$97$	15.6825	1.59231	0.796157	+	0.605090i	$0.206863\pi$
$98$	16.4238	1.65905
$99$	−2.96771	−0.298266
$100$	−6.09060	−0.609060
$101$	15.1463	1.50711	0.753555	−	0.657385i	$-0.228337\pi$
$101$	15.1463	1.50711	0.753555	+	0.657385i	$0.228337\pi$
$102$	2.51611	0.249132
$103$	−0.217065	−0.0213881	−0.0106940	−	0.999943i	$-0.503404\pi$
$103$	−0.217065	−0.0213881	−0.0106940	+	0.999943i	$0.503404\pi$
$104$	−24.9322	−2.44480
$105$	0.123305	0.0120333
$106$	7.39205	0.717979
$107$	−1.51562	−0.146521	−0.0732604	−	0.997313i	$-0.523340\pi$
$107$	−1.51562	−0.146521	−0.0732604	+	0.997313i	$0.523340\pi$
$108$	4.00152	0.385047
$109$	2.48417	0.237941	0.118970	−	0.992898i	$-0.462041\pi$
$109$	2.48417	0.237941	0.118970	+	0.992898i	$0.462041\pi$
$110$	4.39353	0.418907
$111$	0.593710	0.0563524
$112$	0.920479	0.0869771
$113$	−7.35374	−0.691781	−0.345891	−	0.938275i	$-0.612423\pi$
$113$	−7.35374	−0.691781	−0.345891	+	0.938275i	$0.612423\pi$
$114$	−1.36402	−0.127752
$115$	−1.24789	−0.116367
$116$	18.6705	1.73352
$117$	−17.8482	−1.65007
$118$	21.5284	1.98185
$119$	2.18702	0.200484
$120$	−1.36705	−0.124794
$121$	1.00000	0.0909091
$122$	6.19230	0.560624
$123$	−0.0290874	−0.00262272
$124$	−34.8675	−3.13120
$125$	12.1711	1.08862
$126$	2.65670	0.236678
$127$	10.4142	0.924114	0.462057	−	0.886850i	$-0.347112\pi$
$127$	10.4142	0.924114	0.462057	+	0.886850i	$0.347112\pi$
$128$	20.7344	1.83268
$129$	−0.578554	−0.0509388
$130$	26.4232	2.31747
$131$	−2.04204	−0.178413	−0.0892067	−	0.996013i	$-0.528433\pi$
$131$	−2.04204	−0.178413	−0.0892067	+	0.996013i	$0.528433\pi$
$132$	−0.670529	−0.0583620
$133$	−1.18562	−0.102806
$134$	−18.6683	−1.61270
$135$	−1.96791	−0.169371
$136$	−24.2469	−2.07916
$137$	14.0680	1.20191	0.600954	−	0.799283i	$-0.294787\pi$
$137$	14.0680	1.20191	0.600954	+	0.799283i	$0.294787\pi$
$138$	0.292524	0.0249013
$139$	−10.3244	−0.875706	−0.437853	−	0.899047i	$-0.644261\pi$
$139$	−10.3244	−0.875706	−0.437853	+	0.899047i	$0.644261\pi$
$140$	−2.56068	−0.216417
$141$	1.01095	0.0851373
$142$	28.5432	2.39529
$143$	6.01413	0.502927
$144$	−7.30554	−0.608795
$145$	−9.18198	−0.762522
$146$	12.2553	1.01426
$147$	1.23270	0.101671
$148$	−12.3296	−1.01349
$149$	−19.0969	−1.56448	−0.782238	−	0.622980i	$-0.785922\pi$
$149$	−19.0969	−1.56448	−0.782238	+	0.622980i	$0.785922\pi$
$150$	−0.702140	−0.0573295
$151$	−17.1066	−1.39212	−0.696059	−	0.717984i	$-0.745065\pi$
$151$	−17.1066	−1.39212	−0.696059	+	0.717984i	$0.745065\pi$
$152$	13.1446	1.06617
$153$	−17.3577	−1.40328
$154$	−0.895203	−0.0721375
$155$	17.1475	1.37732
$156$	−4.03264	−0.322870
$157$	−20.7553	−1.65646	−0.828228	−	0.560391i	$-0.810651\pi$
$157$	−20.7553	−1.65646	−0.828228	+	0.560391i	$0.810651\pi$
$158$	4.27264	0.339913
$159$	0.554815	0.0439997
$160$	−4.40029	−0.347873
$161$	0.254264	0.0200388
$162$	−20.8535	−1.63840
$163$	−16.2746	−1.27473	−0.637363	−	0.770564i	$-0.719975\pi$
$163$	−16.2746	−1.27473	−0.637363	+	0.770564i	$0.719975\pi$
$164$	0.604059	0.0471691
$165$	0.329759	0.0256717
$166$	−31.6551	−2.45692
$167$	−1.72474	−0.133464	−0.0667320	−	0.997771i	$-0.521257\pi$
$167$	−1.72474	−0.133464	−0.0667320	+	0.997771i	$0.521257\pi$
$168$	0.278543	0.0214901
$169$	23.1697	1.78229
$170$	25.6970	1.97087
$171$	9.40984	0.719589
$172$	12.0148	0.916123
$173$	9.09979	0.691844	0.345922	−	0.938263i	$-0.387566\pi$
$173$	9.09979	0.691844	0.345922	+	0.938263i	$0.387566\pi$
$174$	2.15239	0.163172
$175$	−0.610306	−0.0461348
$176$	2.46168	0.185556
$177$	1.61583	0.121453
$178$	−41.0182	−3.07445
$179$	−20.0313	−1.49721	−0.748605	−	0.663017i	$-0.769276\pi$
$179$	−20.0313	−1.49721	−0.748605	+	0.663017i	$0.769276\pi$
$180$	20.3232	1.51481
$181$	9.25128	0.687642	0.343821	−	0.939035i	$-0.388279\pi$
$181$	9.25128	0.687642	0.343821	+	0.939035i	$0.388279\pi$
$182$	−5.38386	−0.399079
$183$	0.464767	0.0343565
$184$	−2.81896	−0.207817
$185$	6.06357	0.445802
$186$	−4.01962	−0.294733
$187$	5.84884	0.427709
$188$	−20.9944	−1.53117
$189$	0.400971	0.0291663
$190$	−13.9307	−1.01064
$191$	11.0791	0.801657	0.400828	−	0.916153i	$-0.368722\pi$
$191$	11.0791	0.801657	0.400828	+	0.916153i	$0.368722\pi$
$192$	1.91616	0.138287
$193$	15.1622	1.09140	0.545699	−	0.837982i	$-0.316264\pi$
$193$	15.1622	1.09140	0.545699	+	0.837982i	$0.316264\pi$
$194$	−37.5451	−2.69558
$195$	1.98321	0.142021
$196$	−25.5995	−1.82854
$197$	−16.6652	−1.18735	−0.593673	−	0.804707i	$-0.702323\pi$
$197$	−16.6652	−1.18735	−0.593673	+	0.804707i	$0.702323\pi$
$198$	7.10493	0.504926
$199$	−22.9383	−1.62605	−0.813027	−	0.582226i	$-0.802182\pi$
$199$	−22.9383	−1.62605	−0.813027	+	0.582226i	$0.802182\pi$
$200$	6.76630	0.478450
$201$	−1.40116	−0.0988303
$202$	−36.2613	−2.55134
$203$	1.87087	0.131309
$204$	−3.92181	−0.274582
$205$	−0.297070	−0.0207483
$206$	0.519670	0.0362072
$207$	−2.01801	−0.140262
$208$	14.8048	1.02653
$209$	−3.17074	−0.219325
$210$	−0.295201	−0.0203708
$211$	2.81573	0.193843	0.0969213	−	0.995292i	$-0.469100\pi$
$211$	2.81573	0.193843	0.0969213	+	0.995292i	$0.469100\pi$
$212$	−11.5219	−0.791324
$213$	2.14233	0.146790
$214$	3.62852	0.248041
$215$	−5.90878	−0.402975
$216$	−4.44546	−0.302475
$217$	−3.49388	−0.237180
$218$	−5.94731	−0.402802
$219$	0.919830	0.0621563
$220$	−6.84812	−0.461700
$221$	35.1756	2.36617
$222$	−1.42139	−0.0953973
$223$	−23.4098	−1.56763	−0.783817	−	0.620992i	$-0.786730\pi$
$223$	−23.4098	−1.56763	−0.783817	+	0.620992i	$0.786730\pi$
$224$	0.896580	0.0599053
$225$	4.84380	0.322920
$226$	17.6054	1.17109
$227$	−9.86918	−0.655041	−0.327520	−	0.944844i	$-0.606213\pi$
$227$	−9.86918	−0.655041	−0.327520	+	0.944844i	$0.606213\pi$
$228$	2.12607	0.140803
$229$	−2.01835	−0.133376	−0.0666880	−	0.997774i	$-0.521243\pi$
$229$	−2.01835	−0.133376	−0.0666880	+	0.997774i	$0.521243\pi$
$230$	2.98755	0.196993
$231$	−0.0671900	−0.00442078
$232$	−20.7419	−1.36177
$233$	16.8723	1.10534	0.552670	−	0.833400i	$-0.313609\pi$
$233$	16.8723	1.10534	0.552670	+	0.833400i	$0.313609\pi$
$234$	42.7300	2.79335
$235$	10.3248	0.673518
$236$	−33.5560	−2.18431
$237$	0.320686	0.0208308
$238$	−5.23589	−0.339393
$239$	28.1658	1.82190	0.910948	−	0.412522i	$-0.135352\pi$
$239$	28.1658	1.82190	0.910948	+	0.412522i	$0.135352\pi$
$240$	0.811760	0.0523989
$241$	11.9948	0.772656	0.386328	−	0.922361i	$-0.373743\pi$
$241$	11.9948	0.772656	0.386328	+	0.922361i	$0.373743\pi$
$242$	−2.39408	−0.153897
$243$	−4.78217	−0.306776
$244$	−9.65182	−0.617895
$245$	12.5896	0.804318
$246$	0.0696375	0.00443993
$247$	−19.0692	−1.21335
$248$	38.7358	2.45973
$249$	−2.37590	−0.150566
$250$	−29.1386	−1.84289
$251$	−9.30790	−0.587509	−0.293755	−	0.955881i	$-0.594905\pi$
$251$	−9.30790	−0.587509	−0.293755	+	0.955881i	$0.594905\pi$
$252$	−4.14096	−0.260856
$253$	0.679989	0.0427506
$254$	−24.9325	−1.56440
$255$	1.92871	0.120780
$256$	−28.3122	−1.76951
$257$	12.7303	0.794092	0.397046	−	0.917799i	$-0.370035\pi$
$257$	12.7303	0.794092	0.397046	+	0.917799i	$0.370035\pi$
$258$	1.38510	0.0862327
$259$	−1.23548	−0.0767691
$260$	−41.1855	−2.55421
$261$	−14.8485	−0.919099
$262$	4.88879	0.302031
$263$	14.7742	0.911016	0.455508	−	0.890232i	$-0.349458\pi$
$263$	14.7742	0.911016	0.455508	+	0.890232i	$0.349458\pi$
$264$	0.744919	0.0458466
$265$	5.66633	0.348080
$266$	2.83846	0.174037
$267$	−3.07865	−0.188410
$268$	29.0980	1.77744
$269$	25.5398	1.55719	0.778594	−	0.627528i	$-0.215933\pi$
$269$	25.5398	1.55719	0.778594	+	0.627528i	$0.215933\pi$
$270$	4.71132	0.286722
$271$	1.65583	0.100584	0.0502922	−	0.998735i	$-0.483985\pi$
$271$	1.65583	0.100584	0.0502922	+	0.998735i	$0.483985\pi$
$272$	14.3979	0.873003
$273$	−0.404089	−0.0244566
$274$	−33.6798	−2.03467
$275$	−1.63217	−0.0984233
$276$	−0.455952	−0.0274451
$277$	−17.5359	−1.05363	−0.526815	−	0.849980i	$-0.676614\pi$
$277$	−17.5359	−1.05363	−0.526815	+	0.849980i	$0.676614\pi$
$278$	24.7175	1.48245
$279$	27.7298	1.66014
$280$	2.84476	0.170007
$281$	−19.5215	−1.16456	−0.582278	−	0.812990i	$-0.697839\pi$
$281$	−19.5215	−1.16456	−0.582278	+	0.812990i	$0.697839\pi$
$282$	−2.42029	−0.144126
$283$	−0.449425	−0.0267155	−0.0133578	−	0.999911i	$-0.504252\pi$
$283$	−0.449425	−0.0267155	−0.0133578	+	0.999911i	$0.504252\pi$
$284$	−44.4898	−2.63998
$285$	−1.04558	−0.0619348
$286$	−14.3983	−0.851389
$287$	0.0605295	0.00357294
$288$	−7.11586	−0.419306
$289$	17.2089	1.01229
$290$	21.9824	1.29085
$291$	−2.81797	−0.165192
$292$	−19.1021	−1.11787
$293$	2.21724	0.129533	0.0647663	−	0.997900i	$-0.479370\pi$
$293$	2.21724	0.129533	0.0647663	+	0.997900i	$0.479370\pi$
$294$	−2.95118	−0.172116
$295$	16.5025	0.960812
$296$	13.6975	0.796149
$297$	1.07233	0.0622230
$298$	45.7194	2.64845
$299$	4.08954	0.236504
$300$	1.09441	0.0631860
$301$	1.20394	0.0693940
$302$	40.9546	2.35667
$303$	−2.72162	−0.156353
$304$	−7.80533	−0.447666
$305$	4.74667	0.271793
$306$	41.5556	2.37557
$307$	−16.4096	−0.936544	−0.468272	−	0.883584i	$-0.655123\pi$
$307$	−16.4096	−0.936544	−0.468272	+	0.883584i	$0.655123\pi$
$308$	1.39534	0.0795067
$309$	0.0390042	0.00221887
$310$	−41.0524	−2.33162
$311$	29.3948	1.66683	0.833414	−	0.552648i	$-0.186383\pi$
$311$	29.3948	1.66683	0.833414	+	0.552648i	$0.186383\pi$
$312$	4.48004	0.253632
$313$	17.9042	1.01201	0.506003	−	0.862532i	$-0.331122\pi$
$313$	17.9042	1.01201	0.506003	+	0.862532i	$0.331122\pi$
$314$	49.6899	2.80416
$315$	2.03648	0.114743
$316$	−6.65969	−0.374637
$317$	−26.2139	−1.47232	−0.736159	−	0.676808i	$-0.763363\pi$
$317$	−26.2139	−1.47232	−0.736159	+	0.676808i	$0.763363\pi$
$318$	−1.32827	−0.0744857
$319$	5.00335	0.280134
$320$	19.5698	1.09398
$321$	0.272341	0.0152006
$322$	−0.608728	−0.0339231
$323$	−18.5451	−1.03188
$324$	32.5040	1.80578
$325$	−9.81605	−0.544496
$326$	38.9627	2.15794
$327$	−0.446379	−0.0246848
$328$	−0.671075	−0.0370539
$329$	−2.10374	−0.115983
$330$	−0.789469	−0.0434588
$331$	−6.00895	−0.330282	−0.165141	−	0.986270i	$-0.552808\pi$
$331$	−6.00895	−0.330282	−0.165141	+	0.986270i	$0.552808\pi$
$332$	49.3403	2.70790
$333$	9.80561	0.537344
$334$	4.12915	0.225937
$335$	−14.3101	−0.781843
$336$	−0.165400	−0.00902331
$337$	0.779994	0.0424890	0.0212445	−	0.999774i	$-0.493237\pi$
$337$	0.779994	0.0424890	0.0212445	+	0.999774i	$0.493237\pi$
$338$	−55.4701	−3.01718
$339$	1.32139	0.0717678
$340$	−40.0535	−2.17221
$341$	−9.34384	−0.505997
$342$	−22.5279	−1.21817
$343$	−5.18265	−0.279837
$344$	−13.3478	−0.719665
$345$	0.224233	0.0120723
$346$	−21.7856	−1.17120
$347$	14.2370	0.764280	0.382140	−	0.924104i	$-0.375187\pi$
$347$	14.2370	0.764280	0.382140	+	0.924104i	$0.375187\pi$
$348$	−3.35489	−0.179841
$349$	−32.3854	−1.73355	−0.866775	−	0.498700i	$-0.833811\pi$
$349$	−32.3854	−1.73355	−0.866775	+	0.498700i	$0.833811\pi$
$350$	1.46112	0.0781001
$351$	6.44914	0.344230
$352$	2.39776	0.127801
$353$	−9.89812	−0.526824	−0.263412	−	0.964683i	$-0.584848\pi$
$353$	−9.89812	−0.526824	−0.263412	+	0.964683i	$0.584848\pi$
$354$	−3.86842	−0.205604
$355$	21.8796	1.16125
$356$	63.9344	3.38852
$357$	−0.392983	−0.0207989
$358$	47.9565	2.53458
$359$	−21.5311	−1.13637	−0.568184	−	0.822902i	$-0.692354\pi$
$359$	−21.5311	−1.13637	−0.568184	+	0.822902i	$0.692354\pi$
$360$	−22.5780	−1.18996
$361$	−8.94641	−0.470864
$362$	−22.1483	−1.16409
$363$	−0.179689	−0.00943123
$364$	8.39174	0.439846
$365$	9.39424	0.491717
$366$	−1.11269	−0.0581611
$367$	−8.90435	−0.464803	−0.232402	−	0.972620i	$-0.574658\pi$
$367$	−8.90435	−0.464803	−0.232402	+	0.972620i	$0.574658\pi$
$368$	1.67391	0.0872587
$369$	−0.480403	−0.0250088
$370$	−14.5167	−0.754685
$371$	−1.15454	−0.0599409
$372$	6.26531	0.324841
$373$	−13.5296	−0.700534	−0.350267	−	0.936650i	$-0.613909\pi$
$373$	−13.5296	−0.700534	−0.350267	+	0.936650i	$0.613909\pi$
$374$	−14.0026	−0.724055
$375$	−2.18702	−0.112937
$376$	23.3236	1.20282
$377$	30.0908	1.54975
$378$	−0.959955	−0.0493747
$379$	−7.85566	−0.403518	−0.201759	−	0.979435i	$-0.564666\pi$
$379$	−7.85566	−0.403518	−0.201759	+	0.979435i	$0.564666\pi$
$380$	21.7136	1.11388
$381$	−1.87132	−0.0958708
$382$	−26.5243	−1.35710
$383$	4.79601	0.245065	0.122532	−	0.992465i	$-0.460898\pi$
$383$	4.79601	0.245065	0.122532	+	0.992465i	$0.460898\pi$
$384$	−3.72574	−0.190128
$385$	−0.686213	−0.0349726
$386$	−36.2994	−1.84759
$387$	−9.55529	−0.485723
$388$	58.5208	2.97095
$389$	5.34323	0.270913	0.135456	−	0.990783i	$-0.456750\pi$
$389$	5.34323	0.270913	0.135456	+	0.990783i	$0.456750\pi$
$390$	−4.74797	−0.240423
$391$	3.97715	0.201133
$392$	28.4396	1.43642
$393$	0.366931	0.0185092
$394$	39.8977	2.01002
$395$	3.27517	0.164792
$396$	−11.0743	−0.556506
$397$	−13.1684	−0.660901	−0.330451	−	0.943823i	$-0.607201\pi$
$397$	−13.1684	−0.660901	−0.330451	+	0.943823i	$0.607201\pi$
$398$	54.9161	2.75270
$399$	0.213042	0.0106654
$400$	−4.01786	−0.200893
$401$	−34.0103	−1.69839	−0.849197	−	0.528076i	$-0.822914\pi$
$401$	−34.0103	−1.69839	−0.849197	+	0.528076i	$0.822914\pi$
$402$	3.35449	0.167307
$403$	−56.1950	−2.79927
$404$	56.5199	2.81197
$405$	−15.9851	−0.794307
$406$	−4.47901	−0.222290
$407$	−3.30410	−0.163778
$408$	4.35691	0.215699
$409$	9.68204	0.478746	0.239373	−	0.970928i	$-0.423058\pi$
$409$	9.68204	0.478746	0.239373	+	0.970928i	$0.423058\pi$
$410$	0.711209	0.0351241
$411$	−2.52786	−0.124690
$412$	−0.810001	−0.0399059
$413$	−3.36246	−0.165456
$414$	4.83128	0.237444
$415$	−24.2651	−1.19113
$416$	14.4204	0.707020
$417$	1.85518	0.0908488
$418$	7.59100	0.371288
$419$	−13.2652	−0.648048	−0.324024	−	0.946049i	$-0.605036\pi$
$419$	−13.2652	−0.648048	−0.324024	+	0.946049i	$0.605036\pi$
$420$	0.460125	0.0224518
$421$	10.2365	0.498898	0.249449	−	0.968388i	$-0.419751\pi$
$421$	10.2365	0.498898	0.249449	+	0.968388i	$0.419751\pi$
$422$	−6.74107	−0.328150
$423$	16.6967	0.811819
$424$	12.8001	0.621629
$425$	−9.54627	−0.463062
$426$	−5.12890	−0.248496
$427$	−0.967157	−0.0468040
$428$	−5.65571	−0.273379
$429$	−1.08067	−0.0521754
$430$	14.1461	0.682184
$431$	19.1015	0.920085	0.460042	−	0.887897i	$-0.347834\pi$
$431$	19.1015	0.920085	0.460042	+	0.887897i	$0.347834\pi$
$432$	2.63973	0.127004
$433$	−27.6484	−1.32870	−0.664348	−	0.747423i	$-0.731291\pi$
$433$	−27.6484	−1.32870	−0.664348	+	0.747423i	$0.731291\pi$
$434$	8.36463	0.401515
$435$	1.64990	0.0791067
$436$	9.26996	0.443951
$437$	−2.15607	−0.103139
$438$	−2.20214	−0.105223
$439$	17.3620	0.828642	0.414321	−	0.910131i	$-0.364019\pi$
$439$	17.3620	0.828642	0.414321	+	0.910131i	$0.364019\pi$
$440$	7.60787	0.362691
$441$	20.3590	0.969478
$442$	−84.2132	−4.00561
$443$	−18.2415	−0.866680	−0.433340	−	0.901230i	$-0.642665\pi$
$443$	−18.2415	−0.866680	−0.433340	+	0.901230i	$0.642665\pi$
$444$	2.21549	0.105143
$445$	−31.4423	−1.49051
$446$	56.0448	2.65380
$447$	3.43150	0.162304
$448$	−3.98744	−0.188389
$449$	−20.2317	−0.954793	−0.477397	−	0.878688i	$-0.658419\pi$
$449$	−20.2317	−0.954793	−0.477397	+	0.878688i	$0.658419\pi$
$450$	−11.5964	−0.546661
$451$	0.161876	0.00762246
$452$	−27.4413	−1.29073
$453$	3.07388	0.144423
$454$	23.6276	1.10890
$455$	−4.12697	−0.193475
$456$	−2.36194	−0.110608
$457$	19.0925	0.893107	0.446554	−	0.894757i	$-0.352651\pi$
$457$	19.0925	0.893107	0.446554	+	0.894757i	$0.352651\pi$
$458$	4.83208	0.225788
$459$	6.27189	0.292747
$460$	−4.65665	−0.217117
$461$	−20.8789	−0.972429	−0.486214	−	0.873840i	$-0.661623\pi$
$461$	−20.8789	−0.972429	−0.486214	+	0.873840i	$0.661623\pi$
$462$	0.160858	0.00748380
$463$	15.7557	0.732227	0.366114	−	0.930570i	$-0.380688\pi$
$463$	15.7557	0.732227	0.366114	+	0.930570i	$0.380688\pi$
$464$	12.3166	0.571785
$465$	−3.08122	−0.142888
$466$	−40.3936	−1.87120
$467$	−13.7584	−0.636662	−0.318331	−	0.947980i	$-0.603122\pi$
$467$	−13.7584	−0.636662	−0.318331	+	0.947980i	$0.603122\pi$
$468$	−66.6025	−3.07870
$469$	2.91575	0.134637
$470$	−24.7185	−1.14018
$471$	3.72951	0.171847
$472$	37.2788	1.71589
$473$	3.21975	0.148044
$474$	−0.767746	−0.0352638
$475$	5.17517	0.237453
$476$	8.16110	0.374063
$477$	9.16322	0.419555
$478$	−67.4312	−3.08423
$479$	−4.62159	−0.211166	−0.105583	−	0.994411i	$-0.533671\pi$
$479$	−4.62159	−0.211166	−0.105583	+	0.994411i	$0.533671\pi$
$480$	0.790683	0.0360896
$481$	−19.8713	−0.906052
$482$	−28.7166	−1.30800
$483$	−0.0456885	−0.00207890
$484$	3.73161	0.169618
$485$	−28.7800	−1.30683
$486$	11.4489	0.519332
$487$	−11.0234	−0.499519	−0.249759	−	0.968308i	$-0.580352\pi$
$487$	−11.0234	−0.499519	−0.249759	+	0.968308i	$0.580352\pi$
$488$	10.7226	0.485390
$489$	2.92437	0.132244
$490$	−30.1404	−1.36160
$491$	25.9101	1.16931	0.584653	−	0.811284i	$-0.301231\pi$
$491$	25.9101	1.16931	0.584653	+	0.811284i	$0.301231\pi$
$492$	−0.108543	−0.00489349
$493$	29.2638	1.31797
$494$	45.6532	2.05404
$495$	5.44624	0.244790
$496$	−23.0015	−1.03280
$497$	−4.45808	−0.199972
$498$	5.68808	0.254889
$499$	−0.375967	−0.0168306	−0.00841530	−	0.999965i	$-0.502679\pi$
$499$	−0.375967	−0.0168306	−0.00841530	+	0.999965i	$0.502679\pi$
$500$	45.4179	2.03115
$501$	0.309916	0.0138460
$502$	22.2838	0.994576
$503$	7.27713	0.324471	0.162236	−	0.986752i	$-0.448130\pi$
$503$	7.27713	0.324471	0.162236	+	0.986752i	$0.448130\pi$
$504$	4.60037	0.204917
$505$	−27.7959	−1.23690
$506$	−1.62795	−0.0723711
$507$	−4.16335	−0.184901
$508$	38.8618	1.72421
$509$	−11.5444	−0.511696	−0.255848	−	0.966717i	$-0.582355\pi$
$509$	−11.5444	−0.511696	−0.255848	+	0.966717i	$0.582355\pi$
$510$	−4.61747	−0.204465
$511$	−1.91412	−0.0846757
$512$	26.3128	1.16287
$513$	−3.40009	−0.150117
$514$	−30.4772	−1.34429
$515$	0.398350	0.0175534
$516$	−2.15893	−0.0950418
$517$	−5.62611	−0.247436
$518$	2.95784	0.129960
$519$	−1.63513	−0.0717743
$520$	45.7547	2.00648
$521$	30.7442	1.34693	0.673465	−	0.739219i	$-0.264805\pi$
$521$	30.7442	1.34693	0.673465	+	0.739219i	$0.264805\pi$
$522$	35.5485	1.55591
$523$	17.6245	0.770666	0.385333	−	0.922778i	$-0.374087\pi$
$523$	17.6245	0.770666	0.385333	+	0.922778i	$0.374087\pi$
$524$	−7.62007	−0.332884
$525$	0.109665	0.00478618
$526$	−35.3706	−1.54223
$527$	−54.6506	−2.38062
$528$	−0.442336	−0.0192502
$529$	−22.5376	−0.979896
$530$	−13.5656	−0.589254
$531$	26.6867	1.15811
$532$	−4.42425	−0.191816
$533$	0.973546	0.0421689
$534$	7.37052	0.318954
$535$	2.78142	0.120251
$536$	−32.3262	−1.39628
$537$	3.59940	0.155326
$538$	−61.1442	−2.63611
$539$	−6.86018	−0.295489
$540$	−7.34346	−0.316012
$541$	20.1138	0.864759	0.432380	−	0.901692i	$-0.357674\pi$
$541$	20.1138	0.864759	0.432380	+	0.901692i	$0.357674\pi$
$542$	−3.96418	−0.170276
$543$	−1.66235	−0.0713384
$544$	14.0241	0.601278
$545$	−4.55887	−0.195281
$546$	0.967421	0.0414018
$547$	1.00000	0.0427569
$547$	1.00000	0.0427569
$548$	52.4962	2.24252
$549$	7.67600	0.327604
$550$	3.90753	0.166618
$551$	−15.8643	−0.675843
$552$	0.506537	0.0215596
$553$	−0.667331	−0.0283778
$554$	41.9823	1.78366
$555$	−1.08956	−0.0462491
$556$	−38.5267	−1.63389
$557$	25.4636	1.07893	0.539464	−	0.842009i	$-0.318627\pi$
$557$	25.4636	1.07893	0.539464	+	0.842009i	$0.318627\pi$
$558$	−66.3873	−2.81040
$559$	19.3640	0.819009
$560$	−1.68923	−0.0713831
$561$	−1.05097	−0.0443720
$562$	46.7360	1.97144
$563$	−39.2615	−1.65467	−0.827337	−	0.561706i	$-0.810145\pi$
$563$	−39.2615	−1.65467	−0.827337	+	0.561706i	$0.810145\pi$
$564$	3.77246	0.158849
$565$	13.4953	0.567753
$566$	1.07596	0.0452259
$567$	3.25705	0.136783
$568$	49.4256	2.07385
$569$	−33.7635	−1.41544	−0.707720	−	0.706493i	$-0.750276\pi$
$569$	−33.7635	−1.41544	−0.707720	+	0.706493i	$0.750276\pi$
$570$	2.50320	0.104848
$571$	29.8914	1.25092	0.625458	−	0.780257i	$-0.284912\pi$
$571$	29.8914	1.25092	0.625458	+	0.780257i	$0.284912\pi$
$572$	22.4424	0.938362
$573$	−1.99080	−0.0831667
$574$	−0.144912	−0.00604852
$575$	−1.10985	−0.0462841
$576$	31.6470	1.31863
$577$	−9.61989	−0.400481	−0.200241	−	0.979747i	$-0.564172\pi$
$577$	−9.61989	−0.400481	−0.200241	+	0.979747i	$0.564172\pi$
$578$	−41.1994	−1.71367
$579$	−2.72448	−0.113225
$580$	−34.2635	−1.42272
$581$	4.94412	0.205117
$582$	6.74644	0.279649
$583$	−3.08764	−0.127877
$584$	21.2214	0.878147
$585$	32.7544	1.35423
$586$	−5.30824	−0.219282
$587$	−16.7346	−0.690711	−0.345355	−	0.938472i	$-0.612242\pi$
$587$	−16.7346	−0.690711	−0.345355	+	0.938472i	$0.612242\pi$
$588$	4.59995	0.189699
$589$	29.6269	1.22075
$590$	−39.5082	−1.62653
$591$	2.99455	0.123179
$592$	−8.13361	−0.334290
$593$	−9.13613	−0.375176	−0.187588	−	0.982248i	$-0.560067\pi$
$593$	−9.13613	−0.375176	−0.187588	+	0.982248i	$0.560067\pi$
$594$	−2.56725	−0.105335
$595$	−4.01354	−0.164539
$596$	−71.2620	−2.91900
$597$	4.12176	0.168692
$598$	−9.79068	−0.400371
$599$	15.4926	0.633009	0.316505	−	0.948591i	$-0.397491\pi$
$599$	15.4926	0.633009	0.316505	+	0.948591i	$0.397491\pi$
$600$	−1.21583	−0.0496361
$601$	−24.0874	−0.982547	−0.491273	−	0.871005i	$-0.663468\pi$
$601$	−24.0874	−0.982547	−0.491273	+	0.871005i	$0.663468\pi$
$602$	−2.88233	−0.117475
$603$	−23.1413	−0.942388
$604$	−63.8353	−2.59742
$605$	−1.83517	−0.0746101
$606$	6.51576	0.264685
$607$	−19.9915	−0.811432	−0.405716	−	0.913999i	$-0.632978\pi$
$607$	−19.9915	−0.811432	−0.405716	+	0.913999i	$0.632978\pi$
$608$	−7.60267	−0.308329
$609$	−0.336175	−0.0136225
$610$	−11.3639	−0.460111
$611$	−33.8361	−1.36886
$612$	−64.7720	−2.61825
$613$	−4.93254	−0.199223	−0.0996117	−	0.995026i	$-0.531760\pi$
$613$	−4.93254	−0.199223	−0.0996117	+	0.995026i	$0.531760\pi$
$614$	39.2858	1.58545
$615$	0.0533802	0.00215250
$616$	−1.55014	−0.0624569
$617$	−1.73132	−0.0697004	−0.0348502	−	0.999393i	$-0.511095\pi$
$617$	−1.73132	−0.0697004	−0.0348502	+	0.999393i	$0.511095\pi$
$618$	−0.0933791	−0.00375626
$619$	−7.82980	−0.314706	−0.157353	−	0.987542i	$-0.550296\pi$
$619$	−7.82980	−0.314706	−0.157353	+	0.987542i	$0.550296\pi$
$620$	63.9877	2.56981
$621$	0.729174	0.0292608
$622$	−70.3735	−2.82172
$623$	6.40652	0.256672
$624$	−2.66026	−0.106496
$625$	−14.1752	−0.567008
$626$	−42.8641	−1.71319
$627$	0.569747	0.0227535
$628$	−77.4508	−3.09062
$629$	−19.3251	−0.770543
$630$	−4.87549	−0.194244
$631$	−46.0076	−1.83154	−0.915768	−	0.401708i	$-0.868417\pi$
$631$	−46.0076	−1.83154	−0.915768	+	0.401708i	$0.868417\pi$
$632$	7.39853	0.294298
$633$	−0.505955	−0.0201099
$634$	62.7581	2.49244
$635$	−19.1118	−0.758430
$636$	2.07035	0.0820947
$637$	−41.2580	−1.63470
$638$	−11.9784	−0.474230
$639$	35.3823	1.39970
$640$	−38.0510	−1.50410
$641$	−12.4823	−0.493022	−0.246511	−	0.969140i	$-0.579284\pi$
$641$	−12.4823	−0.493022	−0.246511	+	0.969140i	$0.579284\pi$
$642$	−0.652005	−0.0257326
$643$	18.6708	0.736304	0.368152	−	0.929766i	$-0.379991\pi$
$643$	18.6708	0.736304	0.368152	+	0.929766i	$0.379991\pi$
$644$	0.948814	0.0373885
$645$	1.06174	0.0418060
$646$	44.3985	1.74684
$647$	−9.76447	−0.383881	−0.191940	−	0.981407i	$-0.561478\pi$
$647$	−9.76447	−0.383881	−0.191940	+	0.981407i	$0.561478\pi$
$648$	−36.1100	−1.41854
$649$	−8.99236	−0.352981
$650$	23.5004	0.921761
$651$	0.627813	0.0246059
$652$	−60.7304	−2.37839
$653$	22.2247	0.869719	0.434859	−	0.900498i	$-0.356798\pi$
$653$	22.2247	0.869719	0.434859	+	0.900498i	$0.356798\pi$
$654$	1.06867	0.0417881
$655$	3.74747	0.146426
$656$	0.398487	0.0155583
$657$	15.1917	0.592687
$658$	5.03651	0.196343
$659$	−4.16800	−0.162362	−0.0811812	−	0.996699i	$-0.525869\pi$
$659$	−4.16800	−0.162362	−0.0811812	+	0.996699i	$0.525869\pi$
$660$	1.23053	0.0478984
$661$	−41.1100	−1.59900	−0.799498	−	0.600669i	$-0.794901\pi$
$661$	−41.1100	−1.59900	−0.799498	+	0.600669i	$0.794901\pi$
$662$	14.3859	0.559123
$663$	−6.32068	−0.245475
$664$	−54.8143	−2.12721
$665$	2.17580	0.0843740
$666$	−23.4754	−0.909653
$667$	3.40222	0.131735
$668$	−6.43604	−0.249018
$669$	4.20648	0.162632
$670$	34.2594	1.32356
$671$	−2.58651	−0.0998510
$672$	−0.161106	−0.00621478
$673$	−42.9971	−1.65742	−0.828709	−	0.559680i	$-0.810924\pi$
$673$	−42.9971	−1.65742	−0.828709	+	0.559680i	$0.810924\pi$
$674$	−1.86737	−0.0719282
$675$	−1.75022	−0.0673661
$676$	86.4603	3.32540
$677$	−9.36046	−0.359752	−0.179876	−	0.983689i	$-0.557570\pi$
$677$	−9.36046	−0.359752	−0.179876	+	0.983689i	$0.557570\pi$
$678$	−3.16350	−0.121493
$679$	5.86405	0.225042
$680$	44.4972	1.70639
$681$	1.77338	0.0679562
$682$	22.3699	0.856587
$683$	−45.6073	−1.74512	−0.872558	−	0.488511i	$-0.837540\pi$
$683$	−45.6073	−1.74512	−0.872558	+	0.488511i	$0.837540\pi$
$684$	35.1138	1.34261
$685$	−25.8171	−0.986420
$686$	12.4077	0.473727
$687$	0.362675	0.0138369
$688$	7.92598	0.302175
$689$	−18.5695	−0.707440
$690$	−0.536830	−0.0204368
$691$	−48.4304	−1.84238	−0.921190	−	0.389113i	$-0.872782\pi$
$691$	−48.4304	−1.84238	−0.921190	+	0.389113i	$0.872782\pi$
$692$	33.9568	1.29085
$693$	−1.10970	−0.0421540
$694$	−34.0844	−1.29383
$695$	18.9470	0.718702
$696$	3.72709	0.141275
$697$	0.946789	0.0358622
$698$	77.5331	2.93467
$699$	−3.03177	−0.114672
$700$	−2.27742	−0.0860784
$701$	−36.7901	−1.38954	−0.694771	−	0.719231i	$-0.744494\pi$
$701$	−36.7901	−1.38954	−0.694771	+	0.719231i	$0.744494\pi$
$702$	−15.4397	−0.582736
$703$	10.4764	0.395126
$704$	−10.6638	−0.401906
$705$	−1.85526	−0.0698731
$706$	23.6969	0.891843
$707$	5.66355	0.213000
$708$	6.02964	0.226608
$709$	−40.0097	−1.50260	−0.751299	−	0.659962i	$-0.770572\pi$
$709$	−40.0097	−1.50260	−0.751299	+	0.659962i	$0.770572\pi$
$710$	−52.3815	−1.96584
$711$	5.29639	0.198630
$712$	−71.0274	−2.66187
$713$	−6.35371	−0.237948
$714$	0.940833	0.0352098
$715$	−11.0369	−0.412758
$716$	−74.7489	−2.79350
$717$	−5.06109	−0.189010
$718$	51.5471	1.92372
$719$	−42.4355	−1.58258	−0.791288	−	0.611444i	$-0.790589\pi$
$719$	−42.4355	−1.58258	−0.791288	+	0.611444i	$0.790589\pi$
$720$	13.4069	0.499645
$721$	−0.0811658	−0.00302277
$722$	21.4184	0.797110
$723$	−2.15534	−0.0801580
$724$	34.5221	1.28300
$725$	−8.16629	−0.303288
$726$	0.430189	0.0159658
$727$	−35.7945	−1.32754	−0.663772	−	0.747935i	$-0.731045\pi$
$727$	−35.7945	−1.32754	−0.663772	+	0.747935i	$0.731045\pi$
$728$	−9.32274	−0.345524
$729$	−25.2720	−0.936002
$730$	−22.4905	−0.832412
$731$	18.8318	0.696519
$732$	1.73433	0.0641025
$733$	−28.8373	−1.06513	−0.532565	−	0.846389i	$-0.678772\pi$
$733$	−28.8373	−1.06513	−0.532565	+	0.846389i	$0.678772\pi$
$734$	21.3177	0.786851
$735$	−2.26221	−0.0834428
$736$	1.63045	0.0600992
$737$	7.79770	0.287232
$738$	1.15012	0.0423365
$739$	36.9636	1.35973	0.679864	−	0.733338i	$-0.262039\pi$
$739$	36.9636	1.35973	0.679864	+	0.733338i	$0.262039\pi$
$740$	22.6269	0.831780
$741$	3.42653	0.125877
$742$	2.76406	0.101472
$743$	11.5690	0.424426	0.212213	−	0.977223i	$-0.431933\pi$
$743$	11.5690	0.424426	0.212213	+	0.977223i	$0.431933\pi$
$744$	−6.96040	−0.255181
$745$	35.0459	1.28398
$746$	32.3908	1.18591
$747$	−39.2399	−1.43571
$748$	21.8256	0.798021
$749$	−0.566728	−0.0207078
$750$	5.23589	0.191188
$751$	−26.6400	−0.972107	−0.486054	−	0.873929i	$-0.661564\pi$
$751$	−26.6400	−0.972107	−0.486054	+	0.873929i	$0.661564\pi$
$752$	−13.8496	−0.505045
$753$	1.67253	0.0609503
$754$	−72.0397	−2.62353
$755$	31.3935	1.14253
$756$	1.49626	0.0544186
$757$	14.0705	0.511401	0.255701	−	0.966756i	$-0.417694\pi$
$757$	14.0705	0.511401	0.255701	+	0.966756i	$0.417694\pi$
$758$	18.8071	0.683103
$759$	−0.122187	−0.00443509
$760$	−24.1226	−0.875017
$761$	24.4898	0.887755	0.443878	−	0.896087i	$-0.353602\pi$
$761$	24.4898	0.887755	0.443878	+	0.896087i	$0.353602\pi$
$762$	4.48009	0.162297
$763$	0.928892	0.0336282
$764$	41.3429	1.49573
$765$	31.8542	1.15169
$766$	−11.4820	−0.414862
$767$	−54.0812	−1.95276
$768$	5.08738	0.183575
$769$	24.9108	0.898306	0.449153	−	0.893455i	$-0.351726\pi$
$769$	24.9108	0.898306	0.449153	+	0.893455i	$0.351726\pi$
$770$	1.64285	0.0592041
$771$	−2.28749	−0.0823819
$772$	56.5793	2.03633
$773$	7.70709	0.277205	0.138602	−	0.990348i	$-0.455739\pi$
$773$	7.70709	0.277205	0.138602	+	0.990348i	$0.455739\pi$
$774$	22.8761	0.822264
$775$	15.2507	0.547821
$776$	−65.0133	−2.33384
$777$	0.222002	0.00796429
$778$	−12.7921	−0.458619
$779$	−0.513268	−0.0183897
$780$	7.40057	0.264983
$781$	−11.9224	−0.426618
$782$	−9.52159	−0.340492
$783$	5.36525	0.191738
$784$	−16.8875	−0.603126
$785$	38.0895	1.35947
$786$	−0.878462	−0.0313337
$787$	16.1483	0.575626	0.287813	−	0.957687i	$-0.407072\pi$
$787$	16.1483	0.575626	0.287813	+	0.957687i	$0.407072\pi$
$788$	−62.1879	−2.21535
$789$	−2.65476	−0.0945119
$790$	−7.84101	−0.278970
$791$	−2.74974	−0.0977694
$792$	12.3029	0.437166
$793$	−15.5556	−0.552395
$794$	31.5261	1.11882
$795$	−1.01818	−0.0361110
$796$	−85.5968	−3.03390
$797$	26.0244	0.921832	0.460916	−	0.887444i	$-0.347521\pi$
$797$	26.0244	0.921832	0.460916	+	0.887444i	$0.347521\pi$
$798$	−0.510039	−0.0180552
$799$	−32.9062	−1.16414
$800$	−3.91354	−0.138365
$801$	−50.8464	−1.79657
$802$	81.4233	2.87516
$803$	−5.11901	−0.180646
$804$	−5.22858	−0.184398
$805$	−0.466617	−0.0164461
$806$	134.535	4.73880
$807$	−4.58922	−0.161548
$808$	−62.7904	−2.20896
$809$	24.2338	0.852016	0.426008	−	0.904720i	$-0.359920\pi$
$809$	24.2338	0.852016	0.426008	+	0.904720i	$0.359920\pi$
$810$	38.2696	1.34466
$811$	29.1767	1.02453	0.512267	−	0.858826i	$-0.328806\pi$
$811$	29.1767	1.02453	0.512267	+	0.858826i	$0.328806\pi$
$812$	6.98136	0.244998
$813$	−0.297534	−0.0104350
$814$	7.91026	0.277255
$815$	29.8666	1.04618
$816$	−2.58715	−0.0905684
$817$	−10.2090	−0.357167
$818$	−23.1795	−0.810454
$819$	−6.67387	−0.233204
$820$	−1.10855	−0.0387122
$821$	10.4657	0.365255	0.182627	−	0.983182i	$-0.441540\pi$
$821$	10.4657	0.365255	0.182627	+	0.983182i	$0.441540\pi$
$822$	6.05189	0.211084
$823$	37.0842	1.29267	0.646337	−	0.763052i	$-0.276300\pi$
$823$	37.0842	1.29267	0.646337	+	0.763052i	$0.276300\pi$
$824$	0.899865	0.0313483
$825$	0.293282	0.0102108
$826$	8.04999	0.280095
$827$	−23.1002	−0.803274	−0.401637	−	0.915799i	$-0.631559\pi$
$827$	−23.1002	−0.803274	−0.401637	+	0.915799i	$0.631559\pi$
$828$	−7.53043	−0.261700
$829$	26.6561	0.925804	0.462902	−	0.886410i	$-0.346808\pi$
$829$	26.6561	0.925804	0.462902	+	0.886410i	$0.346808\pi$
$830$	58.0924	2.01642
$831$	3.15101	0.109307
$832$	−64.1333	−2.22342
$833$	−40.1241	−1.39022
$834$	−4.44145	−0.153795
$835$	3.16518	0.109535
$836$	−11.8320	−0.409217
$837$	−10.0197	−0.346331
$838$	31.7579	1.09706
$839$	28.1012	0.970163	0.485081	−	0.874469i	$-0.338790\pi$
$839$	28.1012	0.970163	0.485081	+	0.874469i	$0.338790\pi$
$840$	−0.511173	−0.0176371
$841$	−3.96650	−0.136776
$842$	−24.5070	−0.844568
$843$	3.50780	0.120815
$844$	10.5072	0.361672
$845$	−42.5203	−1.46274
$846$	−39.9731	−1.37430
$847$	0.373924	0.0128482
$848$	−7.60077	−0.261011
$849$	0.0807566	0.00277156
$850$	22.8545	0.783903
$851$	−2.24675	−0.0770176
$852$	7.99433	0.273881
$853$	6.03852	0.206755	0.103377	−	0.994642i	$-0.467035\pi$
$853$	6.03852	0.206755	0.103377	+	0.994642i	$0.467035\pi$
$854$	2.31545	0.0792330
$855$	−17.2686	−0.590574
$856$	6.28317	0.214754
$857$	−27.8148	−0.950135	−0.475068	−	0.879949i	$-0.657576\pi$
$857$	−27.8148	−0.950135	−0.475068	+	0.879949i	$0.657576\pi$
$858$	2.58721	0.0883260
$859$	33.1787	1.13204	0.566022	−	0.824390i	$-0.308482\pi$
$859$	33.1787	1.13204	0.566022	+	0.824390i	$0.308482\pi$
$860$	−22.0492	−0.751872
$861$	−0.0108765	−0.000370669 0
$862$	−45.7304	−1.55758
$863$	9.26982	0.315548	0.157774	−	0.987475i	$-0.449568\pi$
$863$	9.26982	0.315548	0.157774	+	0.987475i	$0.449568\pi$
$864$	2.57119	0.0874738
$865$	−16.6996	−0.567804
$866$	66.1924	2.24931
$867$	−3.09225	−0.105018
$868$	−13.0378	−0.442532
$869$	−1.78467	−0.0605408
$870$	−3.94999	−0.133917
$871$	46.8964	1.58902
$872$	−10.2984	−0.348748
$873$	−46.5411	−1.57518
$874$	5.16180	0.174600
$875$	4.55108	0.153854
$876$	3.43244	0.115972
$877$	−33.5835	−1.13403	−0.567017	−	0.823706i	$-0.691903\pi$
$877$	−33.5835	−1.13403	−0.567017	+	0.823706i	$0.691903\pi$
$878$	−41.5659	−1.40278
$879$	−0.398414	−0.0134382
$880$	−4.51758	−0.152288
$881$	−27.8492	−0.938264	−0.469132	−	0.883128i	$-0.655433\pi$
$881$	−27.8492	−0.938264	−0.469132	+	0.883128i	$0.655433\pi$
$882$	−48.7411	−1.64120
$883$	55.4365	1.86559	0.932794	−	0.360410i	$-0.117363\pi$
$883$	55.4365	1.86559	0.932794	+	0.360410i	$0.117363\pi$
$884$	131.262	4.41481
$885$	−2.96531	−0.0996780
$886$	43.6716	1.46718
$887$	−22.4463	−0.753673	−0.376837	−	0.926280i	$-0.622988\pi$
$887$	−22.4463	−0.753673	−0.376837	+	0.926280i	$0.622988\pi$
$888$	−2.46128	−0.0825953
$889$	3.89413	0.130605
$890$	75.2753	2.52323
$891$	8.71045	0.291811
$892$	−87.3560	−2.92490
$893$	17.8389	0.596957
$894$	−8.21527	−0.274760
$895$	36.7608	1.22878
$896$	7.75308	0.259012
$897$	−0.734846	−0.0245358
$898$	48.4363	1.61634
$899$	−46.7505	−1.55922
$900$	18.0751	0.602505
$901$	−18.0591	−0.601636
$902$	−0.387545	−0.0129038
$903$	−0.216335	−0.00719918
$904$	30.4857	1.01394
$905$	−16.9776	−0.564356
$906$	−7.35909	−0.244490
$907$	−54.4198	−1.80698	−0.903490	−	0.428609i	$-0.859004\pi$
$907$	−54.4198	−1.80698	−0.903490	+	0.428609i	$0.859004\pi$
$908$	−36.8279	−1.22218
$909$	−44.9497	−1.49089
$910$	9.88029	0.327528
$911$	−33.5387	−1.11119	−0.555594	−	0.831454i	$-0.687509\pi$
$911$	−33.5387	−1.11119	−0.555594	+	0.831454i	$0.687509\pi$
$912$	1.40253	0.0464425
$913$	13.2223	0.437593
$914$	−45.7088	−1.51191
$915$	−0.852924	−0.0281968
$916$	−7.53167	−0.248854
$917$	−0.763566	−0.0252152
$918$	−15.0154	−0.495582
$919$	−25.1655	−0.830132	−0.415066	−	0.909791i	$-0.636241\pi$
$919$	−25.1655	−0.830132	−0.415066	+	0.909791i	$0.636241\pi$
$920$	5.17327	0.170558
$921$	2.94862	0.0971603
$922$	49.9858	1.64619
$923$	−71.7030	−2.36013
$924$	−0.250727	−0.00824830
$925$	5.39283	0.177315
$926$	−37.7203	−1.23956
$927$	0.644186	0.0211579
$928$	11.9968	0.393815
$929$	−28.1816	−0.924609	−0.462305	−	0.886721i	$-0.652977\pi$
$929$	−28.1816	−0.924609	−0.462305	+	0.886721i	$0.652977\pi$
$930$	7.37667	0.241891
$931$	21.7518	0.712888
$932$	62.9608	2.06235
$933$	−5.28193	−0.172923
$934$	32.9386	1.07779
$935$	−10.7336	−0.351026
$936$	73.9915	2.41849
$937$	−7.64808	−0.249852	−0.124926	−	0.992166i	$-0.539869\pi$
$937$	−7.64808	−0.249852	−0.124926	+	0.992166i	$0.539869\pi$
$938$	−6.98053	−0.227922
$939$	−3.21719	−0.104989
$940$	38.5282	1.25665
$941$	−9.55744	−0.311564	−0.155782	−	0.987791i	$-0.549790\pi$
$941$	−9.55744	−0.311564	−0.155782	+	0.987791i	$0.549790\pi$
$942$	−8.92873	−0.290914
$943$	0.110074	0.00358451
$944$	−22.1363	−0.720475
$945$	−0.735848	−0.0239371
$946$	−7.70833	−0.250619
$947$	−0.547314	−0.0177853	−0.00889265	−	0.999960i	$-0.502831\pi$
$947$	−0.547314	−0.0177853	−0.00889265	+	0.999960i	$0.502831\pi$
$948$	1.19667	0.0388661
$949$	−30.7864	−0.999368
$950$	−12.3898	−0.401977
$951$	4.71035	0.152743
$952$	−9.06651	−0.293847
$953$	−37.2177	−1.20560	−0.602800	−	0.797892i	$-0.705948\pi$
$953$	−37.2177	−1.20560	−0.602800	+	0.797892i	$0.705948\pi$
$954$	−21.9375	−0.710252
$955$	−20.3320	−0.657929
$956$	105.104	3.39930
$957$	−0.899047	−0.0290621
$958$	11.0644	0.357476
$959$	5.26035	0.169866
$960$	−3.51648	−0.113494
$961$	56.3073	1.81636
$962$	47.5733	1.53383
$963$	4.49794	0.144944
$964$	44.7600	1.44162
$965$	−27.8251	−0.895722
$966$	0.109382	0.00351930
$967$	51.6346	1.66046	0.830228	−	0.557424i	$-0.188210\pi$
$967$	51.6346	1.66046	0.830228	+	0.557424i	$0.188210\pi$
$968$	−4.14560	−0.133245
$969$	3.33236	0.107051
$970$	68.9014	2.21229
$971$	12.3419	0.396070	0.198035	−	0.980195i	$-0.436544\pi$
$971$	12.3419	0.396070	0.198035	+	0.980195i	$0.436544\pi$
$972$	−17.8452	−0.572384
$973$	−3.86055	−0.123763
$974$	26.3909	0.845619
$975$	1.76384	0.0564880
$976$	−6.36714	−0.203807
$977$	−27.9991	−0.895772	−0.447886	−	0.894091i	$-0.647823\pi$
$977$	−27.9991	−0.895772	−0.447886	+	0.894091i	$0.647823\pi$
$978$	−7.00116	−0.223873
$979$	17.1332	0.547580
$980$	46.9793	1.50070
$981$	−7.37231	−0.235380
$982$	−62.0307	−1.97948
$983$	26.0186	0.829864	0.414932	−	0.909852i	$-0.363805\pi$
$983$	26.0186	0.829864	0.414932	+	0.909852i	$0.363805\pi$
$984$	0.120585	0.00384410
$985$	30.5834	0.974468
$986$	−70.0597	−2.23116
$987$	0.378018	0.0120324
$988$	−71.1589	−2.26387
$989$	2.18940	0.0696187
$990$	−13.0387	−0.414398
$991$	−7.37456	−0.234260	−0.117130	−	0.993117i	$-0.537369\pi$
$991$	−7.37456	−0.234260	−0.117130	+	0.993117i	$0.537369\pi$
$992$	−22.4043	−0.711337
$993$	1.07974	0.0342646
$994$	10.6730	0.338527
$995$	42.0956	1.33452
$996$	−8.86591	−0.280927
$997$	9.38484	0.297221	0.148610	−	0.988896i	$-0.452520\pi$
$997$	9.38484	0.297221	0.148610	+	0.988896i	$0.452520\pi$
$998$	0.900094	0.0284920
$999$	−3.54309	−0.112098

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6017.2.a.c.1.12	✓	106

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6017.2.a.c.1.12	✓	106	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6017 = 11 \cdot 547 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6017.a (trivial)

\(f(q)\)	\(=\)	\(q-2.39408 q^{2} -0.179689 q^{3} +3.73161 q^{4} -1.83517 q^{5} +0.430189 q^{6} +0.373924 q^{7} -4.14560 q^{8} -2.96771 q^{9} +O(q^{10})\)	\(q-2.39408 q^{2} -0.179689 q^{3} +3.73161 q^{4} -1.83517 q^{5} +0.430189 q^{6} +0.373924 q^{7} -4.14560 q^{8} -2.96771 q^{9} +4.39353 q^{10} +1.00000 q^{11} -0.670529 q^{12} +6.01413 q^{13} -0.895203 q^{14} +0.329759 q^{15} +2.46168 q^{16} +5.84884 q^{17} +7.10493 q^{18} -3.17074 q^{19} -6.84812 q^{20} -0.0671900 q^{21} -2.39408 q^{22} +0.679989 q^{23} +0.744919 q^{24} -1.63217 q^{25} -14.3983 q^{26} +1.07233 q^{27} +1.39534 q^{28} +5.00335 q^{29} -0.789469 q^{30} -9.34384 q^{31} +2.39776 q^{32} -0.179689 q^{33} -14.0026 q^{34} -0.686213 q^{35} -11.0743 q^{36} -3.30410 q^{37} +7.59100 q^{38} -1.08067 q^{39} +7.60787 q^{40} +0.161876 q^{41} +0.160858 q^{42} +3.21975 q^{43} +3.73161 q^{44} +5.44624 q^{45} -1.62795 q^{46} -5.62611 q^{47} -0.442336 q^{48} -6.86018 q^{49} +3.90753 q^{50} -1.05097 q^{51} +22.4424 q^{52} -3.08764 q^{53} -2.56725 q^{54} -1.83517 q^{55} -1.55014 q^{56} +0.569747 q^{57} -11.9784 q^{58} -8.99236 q^{59} +1.23053 q^{60} -2.58651 q^{61} +22.3699 q^{62} -1.10970 q^{63} -10.6638 q^{64} -11.0369 q^{65} +0.430189 q^{66} +7.79770 q^{67} +21.8256 q^{68} -0.122187 q^{69} +1.64285 q^{70} -11.9224 q^{71} +12.3029 q^{72} -5.11901 q^{73} +7.91026 q^{74} +0.293282 q^{75} -11.8320 q^{76} +0.373924 q^{77} +2.58721 q^{78} -1.78467 q^{79} -4.51758 q^{80} +8.71045 q^{81} -0.387545 q^{82} +13.2223 q^{83} -0.250727 q^{84} -10.7336 q^{85} -7.70833 q^{86} -0.899047 q^{87} -4.14560 q^{88} +17.1332 q^{89} -13.0387 q^{90} +2.24883 q^{91} +2.53745 q^{92} +1.67898 q^{93} +13.4693 q^{94} +5.81883 q^{95} -0.430851 q^{96} +15.6825 q^{97} +16.4238 q^{98} -2.96771 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 106 q - 13 q^{2} - 15 q^{3} + 93 q^{4} - 12 q^{5} - 22 q^{6} - 66 q^{7} - 39 q^{8} + 97 q^{9}+O(q^{10}) \) 106 * q - 13 * q^2 - 15 * q^3 + 93 * q^4 - 12 * q^5 - 22 * q^6 - 66 * q^7 - 39 * q^8 + 97 * q^9	\( 106 q - 13 q^{2} - 15 q^{3} + 93 q^{4} - 12 q^{5} - 22 q^{6} - 66 q^{7} - 39 q^{8} + 97 q^{9} - 30 q^{10} + 106 q^{11} - 26 q^{12} - 72 q^{13} + 3 q^{14} - 46 q^{15} + 75 q^{16} - 65 q^{17} - 37 q^{18} - 63 q^{19} - 25 q^{20} - 27 q^{21} - 13 q^{22} - 23 q^{23} - 56 q^{24} + 74 q^{25} + 2 q^{26} - 54 q^{27} - 115 q^{28} - 45 q^{29} - 14 q^{30} - 89 q^{31} - 96 q^{32} - 15 q^{33} - 26 q^{34} - 52 q^{35} + 91 q^{36} - 35 q^{37} + 7 q^{38} - 34 q^{39} - 74 q^{40} - 32 q^{41} - 94 q^{43} + 93 q^{44} - 46 q^{45} - 20 q^{46} - 105 q^{47} - 57 q^{48} + 80 q^{49} - 60 q^{50} - 36 q^{51} - 137 q^{52} - 61 q^{54} - 12 q^{55} + 32 q^{56} - 71 q^{57} - 28 q^{58} - 15 q^{59} - 21 q^{60} - 80 q^{61} - 84 q^{62} - 182 q^{63} + 55 q^{64} - 73 q^{65} - 22 q^{66} - 58 q^{67} - 145 q^{68} - 8 q^{69} - 39 q^{70} - 11 q^{71} - 100 q^{72} - 155 q^{73} - 15 q^{74} - 15 q^{75} - 132 q^{76} - 66 q^{77} - 45 q^{78} - 50 q^{79} - 28 q^{80} + 114 q^{81} - 57 q^{82} - 96 q^{83} - 27 q^{84} - 74 q^{85} + 54 q^{86} - 182 q^{87} - 39 q^{88} + 9 q^{89} - 53 q^{90} + 6 q^{91} - 18 q^{92} - 26 q^{93} - 33 q^{94} - 49 q^{95} - 56 q^{96} - 102 q^{97} - 76 q^{98} + 97 q^{99}+O(q^{100}) \) 106 * q - 13 * q^2 - 15 * q^3 + 93 * q^4 - 12 * q^5 - 22 * q^6 - 66 * q^7 - 39 * q^8 + 97 * q^9 - 30 * q^10 + 106 * q^11 - 26 * q^12 - 72 * q^13 + 3 * q^14 - 46 * q^15 + 75 * q^16 - 65 * q^17 - 37 * q^18 - 63 * q^19 - 25 * q^20 - 27 * q^21 - 13 * q^22 - 23 * q^23 - 56 * q^24 + 74 * q^25 + 2 * q^26 - 54 * q^27 - 115 * q^28 - 45 * q^29 - 14 * q^30 - 89 * q^31 - 96 * q^32 - 15 * q^33 - 26 * q^34 - 52 * q^35 + 91 * q^36 - 35 * q^37 + 7 * q^38 - 34 * q^39 - 74 * q^40 - 32 * q^41 - 94 * q^43 + 93 * q^44 - 46 * q^45 - 20 * q^46 - 105 * q^47 - 57 * q^48 + 80 * q^49 - 60 * q^50 - 36 * q^51 - 137 * q^52 - 61 * q^54 - 12 * q^55 + 32 * q^56 - 71 * q^57 - 28 * q^58 - 15 * q^59 - 21 * q^60 - 80 * q^61 - 84 * q^62 - 182 * q^63 + 55 * q^64 - 73 * q^65 - 22 * q^66 - 58 * q^67 - 145 * q^68 - 8 * q^69 - 39 * q^70 - 11 * q^71 - 100 * q^72 - 155 * q^73 - 15 * q^74 - 15 * q^75 - 132 * q^76 - 66 * q^77 - 45 * q^78 - 50 * q^79 - 28 * q^80 + 114 * q^81 - 57 * q^82 - 96 * q^83 - 27 * q^84 - 74 * q^85 + 54 * q^86 - 182 * q^87 - 39 * q^88 + 9 * q^89 - 53 * q^90 + 6 * q^91 - 18 * q^92 - 26 * q^93 - 33 * q^94 - 49 * q^95 - 56 * q^96 - 102 * q^97 - 76 * q^98 + 97 * q^99

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