LMFDB - Embedded newform 6031.2.a.e.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6031,2,Mod(1,6031)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6031, 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("6031.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6031 = 37 \cdot 163 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6031.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:	$48.1577774590$
Analytic rank:	$0$
Dimension:	$134$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	6031.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.23037 q^{2} +2.48760 q^{3} +2.97457 q^{4} +3.37158 q^{5} -5.54828 q^{6} -3.17676 q^{7} -2.17365 q^{8} +3.18815 q^{9} +O(q^{10})$	\(q-2.23037 q^{2} +2.48760 q^{3} +2.97457 q^{4} +3.37158 q^{5} -5.54828 q^{6} -3.17676 q^{7} -2.17365 q^{8} +3.18815 q^{9} -7.51989 q^{10} +2.90148 q^{11} +7.39953 q^{12} +5.00487 q^{13} +7.08536 q^{14} +8.38715 q^{15} -1.10108 q^{16} -1.28083 q^{17} -7.11076 q^{18} +3.14485 q^{19} +10.0290 q^{20} -7.90250 q^{21} -6.47138 q^{22} +1.16024 q^{23} -5.40717 q^{24} +6.36757 q^{25} -11.1627 q^{26} +0.468039 q^{27} -9.44949 q^{28} +5.14553 q^{29} -18.7065 q^{30} -3.74356 q^{31} +6.80312 q^{32} +7.21771 q^{33} +2.85673 q^{34} -10.7107 q^{35} +9.48337 q^{36} +1.00000 q^{37} -7.01420 q^{38} +12.4501 q^{39} -7.32865 q^{40} -7.47355 q^{41} +17.6255 q^{42} +8.31474 q^{43} +8.63064 q^{44} +10.7491 q^{45} -2.58777 q^{46} +0.971484 q^{47} -2.73904 q^{48} +3.09180 q^{49} -14.2021 q^{50} -3.18619 q^{51} +14.8873 q^{52} +5.20496 q^{53} -1.04390 q^{54} +9.78257 q^{55} +6.90517 q^{56} +7.82313 q^{57} -11.4765 q^{58} +5.42144 q^{59} +24.9481 q^{60} +11.3588 q^{61} +8.34953 q^{62} -10.1280 q^{63} -12.9714 q^{64} +16.8743 q^{65} -16.0982 q^{66} -11.8698 q^{67} -3.80991 q^{68} +2.88621 q^{69} +23.8889 q^{70} -5.06347 q^{71} -6.92993 q^{72} +10.7790 q^{73} -2.23037 q^{74} +15.8400 q^{75} +9.35458 q^{76} -9.21729 q^{77} -27.7684 q^{78} -5.14697 q^{79} -3.71238 q^{80} -8.40015 q^{81} +16.6688 q^{82} -8.85962 q^{83} -23.5065 q^{84} -4.31842 q^{85} -18.5450 q^{86} +12.8000 q^{87} -6.30680 q^{88} +5.41610 q^{89} -23.9745 q^{90} -15.8993 q^{91} +3.45121 q^{92} -9.31247 q^{93} -2.16677 q^{94} +10.6031 q^{95} +16.9234 q^{96} +4.75336 q^{97} -6.89588 q^{98} +9.25034 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 134 q + 9 q^{2} + 7 q^{3} + 149 q^{4} + 22 q^{5} + 20 q^{6} + 11 q^{7} + 27 q^{8} + 181 q^{9}+O(q^{10}) $ 134 * q + 9 * q^2 + 7 * q^3 + 149 * q^4 + 22 * q^5 + 20 * q^6 + 11 * q^7 + 27 * q^8 + 181 * q^9	\( 134 q + 9 q^{2} + 7 q^{3} + 149 q^{4} + 22 q^{5} + 20 q^{6} + 11 q^{7} + 27 q^{8} + 181 q^{9} + 15 q^{10} + 20 q^{11} + 28 q^{12} + 11 q^{13} + 17 q^{14} - 13 q^{15} + 143 q^{16} + 76 q^{17} + 23 q^{18} + 15 q^{19} + 67 q^{20} + 63 q^{21} + 2 q^{22} + 22 q^{23} + 33 q^{24} + 160 q^{25} + 65 q^{26} + 31 q^{27} + 10 q^{28} + 73 q^{29} + 20 q^{30} + 10 q^{31} + 53 q^{32} + 72 q^{33} - 7 q^{34} + 52 q^{35} + 201 q^{36} + 134 q^{37} + 70 q^{38} + 6 q^{39} + 11 q^{40} + 182 q^{41} - 15 q^{42} + 12 q^{43} + 33 q^{44} + 29 q^{45} + 24 q^{46} + 80 q^{47} + 21 q^{48} + 229 q^{49} + 37 q^{50} + 57 q^{51} - 15 q^{52} + 75 q^{53} + 95 q^{54} - 9 q^{55} + 39 q^{56} + 19 q^{57} - 21 q^{58} + 91 q^{59} + 62 q^{60} + 58 q^{61} + 108 q^{62} + 9 q^{63} + 167 q^{64} + 76 q^{65} + 105 q^{66} - 17 q^{67} + 109 q^{68} + 48 q^{69} - 55 q^{70} + 56 q^{71} + 48 q^{72} + 54 q^{73} + 9 q^{74} + 28 q^{75} + 82 q^{76} + 156 q^{77} + 16 q^{78} - 2 q^{79} + 98 q^{80} + 270 q^{81} - 42 q^{82} + 130 q^{83} + 229 q^{84} + 22 q^{85} + 72 q^{86} + 22 q^{87} + 61 q^{88} + 157 q^{89} + 176 q^{90} + 31 q^{91} - 18 q^{92} + 36 q^{93} + 83 q^{94} + 98 q^{95} + 111 q^{96} + 35 q^{97} + 53 q^{98} + 55 q^{99}+O(q^{100}) \) 134 * q + 9 * q^2 + 7 * q^3 + 149 * q^4 + 22 * q^5 + 20 * q^6 + 11 * q^7 + 27 * q^8 + 181 * q^9 + 15 * q^10 + 20 * q^11 + 28 * q^12 + 11 * q^13 + 17 * q^14 - 13 * q^15 + 143 * q^16 + 76 * q^17 + 23 * q^18 + 15 * q^19 + 67 * q^20 + 63 * q^21 + 2 * q^22 + 22 * q^23 + 33 * q^24 + 160 * q^25 + 65 * q^26 + 31 * q^27 + 10 * q^28 + 73 * q^29 + 20 * q^30 + 10 * q^31 + 53 * q^32 + 72 * q^33 - 7 * q^34 + 52 * q^35 + 201 * q^36 + 134 * q^37 + 70 * q^38 + 6 * q^39 + 11 * q^40 + 182 * q^41 - 15 * q^42 + 12 * q^43 + 33 * q^44 + 29 * q^45 + 24 * q^46 + 80 * q^47 + 21 * q^48 + 229 * q^49 + 37 * q^50 + 57 * q^51 - 15 * q^52 + 75 * q^53 + 95 * q^54 - 9 * q^55 + 39 * q^56 + 19 * q^57 - 21 * q^58 + 91 * q^59 + 62 * q^60 + 58 * q^61 + 108 * q^62 + 9 * q^63 + 167 * q^64 + 76 * q^65 + 105 * q^66 - 17 * q^67 + 109 * q^68 + 48 * q^69 - 55 * q^70 + 56 * q^71 + 48 * q^72 + 54 * q^73 + 9 * q^74 + 28 * q^75 + 82 * q^76 + 156 * q^77 + 16 * q^78 - 2 * q^79 + 98 * q^80 + 270 * q^81 - 42 * q^82 + 130 * q^83 + 229 * q^84 + 22 * q^85 + 72 * q^86 + 22 * q^87 + 61 * q^88 + 157 * q^89 + 176 * q^90 + 31 * q^91 - 18 * q^92 + 36 * q^93 + 83 * q^94 + 98 * q^95 + 111 * q^96 + 35 * q^97 + 53 * q^98 + 55 * 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 $

$2$	−2.23037	−1.57711	−0.788556	−	0.614963i	$-0.789171\pi$
$2$	−2.23037	−1.57711	−0.788556	+	0.614963i	$0.789171\pi$
$3$	2.48760	1.43622	0.718108	−	0.695932i	$-0.245008\pi$
$3$	2.48760	1.43622	0.718108	+	0.695932i	$0.245008\pi$
$4$	2.97457	1.48728
$5$	3.37158	1.50782	0.753909	−	0.656979i	$-0.228166\pi$
$5$	3.37158	1.50782	0.753909	+	0.656979i	$0.228166\pi$
$6$	−5.54828	−2.26507
$7$	−3.17676	−1.20070	−0.600351	−	0.799737i	$-0.704973\pi$
$7$	−3.17676	−1.20070	−0.600351	+	0.799737i	$0.704973\pi$
$8$	−2.17365	−0.768502
$9$	3.18815	1.06272
$10$	−7.51989	−2.37800
$11$	2.90148	0.874828	0.437414	−	0.899260i	$-0.355894\pi$
$11$	2.90148	0.874828	0.437414	+	0.899260i	$0.355894\pi$
$12$	7.39953	2.13606
$13$	5.00487	1.38810	0.694051	−	0.719926i	$-0.255824\pi$
$13$	5.00487	1.38810	0.694051	+	0.719926i	$0.255824\pi$
$14$	7.08536	1.89364
$15$	8.38715	2.16555
$16$	−1.10108	−0.275270
$17$	−1.28083	−0.310646	−0.155323	−	0.987864i	$-0.549642\pi$
$17$	−1.28083	−0.310646	−0.155323	+	0.987864i	$0.549642\pi$
$18$	−7.11076	−1.67602
$19$	3.14485	0.721478	0.360739	−	0.932667i	$-0.382524\pi$
$19$	3.14485	0.721478	0.360739	+	0.932667i	$0.382524\pi$
$20$	10.0290	2.24255
$21$	−7.90250	−1.72447
$22$	−6.47138	−1.37970
$23$	1.16024	0.241927	0.120963	−	0.992657i	$-0.461402\pi$
$23$	1.16024	0.241927	0.120963	+	0.992657i	$0.461402\pi$
$24$	−5.40717	−1.10373
$25$	6.36757	1.27351
$26$	−11.1627	−2.18919
$27$	0.468039	0.0900742
$28$	−9.44949	−1.78579
$29$	5.14553	0.955502	0.477751	−	0.878495i	$-0.341452\pi$
$29$	5.14553	0.955502	0.477751	+	0.878495i	$0.341452\pi$
$30$	−18.7065	−3.41532
$31$	−3.74356	−0.672363	−0.336181	−	0.941797i	$-0.609136\pi$
$31$	−3.74356	−0.672363	−0.336181	+	0.941797i	$0.609136\pi$
$32$	6.80312	1.20263
$33$	7.21771	1.25644
$34$	2.85673	0.489924
$35$	−10.7107	−1.81044
$36$	9.48337	1.58056
$37$	1.00000	0.164399
$37$	1.00000	0.164399
$38$	−7.01420	−1.13785
$39$	12.4501	1.99361
$40$	−7.32865	−1.15876
$41$	−7.47355	−1.16717	−0.583586	−	0.812051i	$-0.698351\pi$
$41$	−7.47355	−1.16717	−0.583586	+	0.812051i	$0.698351\pi$
$42$	17.6255	2.71968
$43$	8.31474	1.26799	0.633993	−	0.773339i	$-0.281415\pi$
$43$	8.31474	1.26799	0.633993	+	0.773339i	$0.281415\pi$
$44$	8.63064	1.30112
$45$	10.7491	1.60238
$46$	−2.58777	−0.381545
$47$	0.971484	0.141706	0.0708528	−	0.997487i	$-0.477428\pi$
$47$	0.971484	0.141706	0.0708528	+	0.997487i	$0.477428\pi$
$48$	−2.73904	−0.395347
$49$	3.09180	0.441686
$50$	−14.2021	−2.00848
$51$	−3.18619	−0.446155
$52$	14.8873	2.06450
$53$	5.20496	0.714956	0.357478	−	0.933921i	$-0.383637\pi$
$53$	5.20496	0.714956	0.357478	+	0.933921i	$0.383637\pi$
$54$	−1.04390	−0.142057
$55$	9.78257	1.31908
$56$	6.90517	0.922742
$57$	7.82313	1.03620
$58$	−11.4765	−1.50693
$59$	5.42144	0.705811	0.352906	−	0.935659i	$-0.385194\pi$
$59$	5.42144	0.705811	0.352906	+	0.935659i	$0.385194\pi$
$60$	24.9481	3.22079
$61$	11.3588	1.45435	0.727176	−	0.686451i	$-0.240833\pi$
$61$	11.3588	1.45435	0.727176	+	0.686451i	$0.240833\pi$
$62$	8.34953	1.06039
$63$	−10.1280	−1.27601
$64$	−12.9714	−1.62142
$65$	16.8743	2.09300
$66$	−16.0982	−1.98155
$67$	−11.8698	−1.45013	−0.725065	−	0.688680i	$-0.758190\pi$
$67$	−11.8698	−1.45013	−0.725065	+	0.688680i	$0.758190\pi$
$68$	−3.80991	−0.462020
$69$	2.88621	0.347459
$70$	23.8889	2.85527
$71$	−5.06347	−0.600924	−0.300462	−	0.953794i	$-0.597141\pi$
$71$	−5.06347	−0.600924	−0.300462	+	0.953794i	$0.597141\pi$
$72$	−6.92993	−0.816700
$73$	10.7790	1.26159	0.630794	−	0.775950i	$-0.282729\pi$
$73$	10.7790	1.26159	0.630794	+	0.775950i	$0.282729\pi$
$74$	−2.23037	−0.259276
$75$	15.8400	1.82904
$76$	9.35458	1.07304
$77$	−9.21729	−1.05041
$78$	−27.7684	−3.14415
$79$	−5.14697	−0.579079	−0.289540	−	0.957166i	$-0.593502\pi$
$79$	−5.14697	−0.579079	−0.289540	+	0.957166i	$0.593502\pi$
$80$	−3.71238	−0.415057
$81$	−8.40015	−0.933350
$82$	16.6688	1.84076
$83$	−8.85962	−0.972470	−0.486235	−	0.873828i	$-0.661630\pi$
$83$	−8.85962	−0.972470	−0.486235	+	0.873828i	$0.661630\pi$
$84$	−23.5065	−2.56477
$85$	−4.31842	−0.468398
$86$	−18.5450	−1.99976
$87$	12.8000	1.37231
$88$	−6.30680	−0.672307
$89$	5.41610	0.574106	0.287053	−	0.957915i	$-0.407324\pi$
$89$	5.41610	0.574106	0.287053	+	0.957915i	$0.407324\pi$
$90$	−23.9745	−2.52714
$91$	−15.8993	−1.66670
$92$	3.45121	0.359814
$93$	−9.31247	−0.965658
$94$	−2.16677	−0.223486
$95$	10.6031	1.08786
$96$	16.9234	1.72724
$97$	4.75336	0.482631	0.241315	−	0.970447i	$-0.422421\pi$
$97$	4.75336	0.482631	0.241315	+	0.970447i	$0.422421\pi$
$98$	−6.89588	−0.696589
$99$	9.25034	0.929694
$100$	18.9408	1.89408
$101$	−2.85167	−0.283752	−0.141876	−	0.989884i	$-0.545313\pi$
$101$	−2.85167	−0.283752	−0.141876	+	0.989884i	$0.545313\pi$
$102$	7.10639	0.703637
$103$	3.20163	0.315466	0.157733	−	0.987482i	$-0.449581\pi$
$103$	3.20163	0.315466	0.157733	+	0.987482i	$0.449581\pi$
$104$	−10.8788	−1.06676
$105$	−26.6440	−2.60018
$106$	−11.6090	−1.12757
$107$	−5.43122	−0.525056	−0.262528	−	0.964924i	$-0.584556\pi$
$107$	−5.43122	−0.525056	−0.262528	+	0.964924i	$0.584556\pi$
$108$	1.39221	0.133966
$109$	1.69427	0.162282	0.0811408	−	0.996703i	$-0.474144\pi$
$109$	1.69427	0.162282	0.0811408	+	0.996703i	$0.474144\pi$
$110$	−21.8188	−2.08034
$111$	2.48760	0.236112
$112$	3.49787	0.330517
$113$	−1.53767	−0.144651	−0.0723257	−	0.997381i	$-0.523042\pi$
$113$	−1.53767	−0.144651	−0.0723257	+	0.997381i	$0.523042\pi$
$114$	−17.4485	−1.63420
$115$	3.91184	0.364781
$116$	15.3057	1.42110
$117$	15.9563	1.47516
$118$	−12.0918	−1.11314
$119$	4.06888	0.372994
$120$	−18.2307	−1.66423
$121$	−2.58144	−0.234676
$122$	−25.3345	−2.29368
$123$	−18.5912	−1.67631
$124$	−11.1355	−0.999995
$125$	4.61089	0.412411
$126$	22.5892	2.01241
$127$	−2.58307	−0.229210	−0.114605	−	0.993411i	$-0.536560\pi$
$127$	−2.58307	−0.229210	−0.114605	+	0.993411i	$0.536560\pi$
$128$	15.3247	1.35453
$129$	20.6837	1.82110
$130$	−37.6361	−3.30090
$131$	2.02919	0.177291	0.0886454	−	0.996063i	$-0.471746\pi$
$131$	2.02919	0.177291	0.0886454	+	0.996063i	$0.471746\pi$
$132$	21.4696	1.86869
$133$	−9.99044	−0.866281
$134$	26.4742	2.28702
$135$	1.57803	0.135815
$136$	2.78407	0.238732
$137$	−4.77791	−0.408204	−0.204102	−	0.978950i	$-0.565427\pi$
$137$	−4.77791	−0.408204	−0.204102	+	0.978950i	$0.565427\pi$
$138$	−6.43733	−0.547982
$139$	1.08245	0.0918122	0.0459061	−	0.998946i	$-0.485382\pi$
$139$	1.08245	0.0918122	0.0459061	+	0.998946i	$0.485382\pi$
$140$	−31.8597	−2.69264
$141$	2.41666	0.203520
$142$	11.2934	0.947724
$143$	14.5215	1.21435
$144$	−3.51041	−0.292534
$145$	17.3486	1.44072
$146$	−24.0412	−1.98967
$147$	7.69116	0.634356
$148$	2.97457	0.244508
$149$	1.24979	0.102387	0.0511933	−	0.998689i	$-0.483698\pi$
$149$	1.24979	0.102387	0.0511933	+	0.998689i	$0.483698\pi$
$150$	−35.3291	−2.88461
$151$	−5.75141	−0.468043	−0.234021	−	0.972231i	$-0.575189\pi$
$151$	−5.75141	−0.468043	−0.234021	+	0.972231i	$0.575189\pi$
$152$	−6.83581	−0.554458
$153$	−4.08347	−0.330129
$154$	20.5580	1.65661
$155$	−12.6217	−1.01380
$156$	37.0337	2.96507
$157$	17.4020	1.38883	0.694415	−	0.719575i	$-0.255663\pi$
$157$	17.4020	1.38883	0.694415	+	0.719575i	$0.255663\pi$
$158$	11.4797	0.913273
$159$	12.9479	1.02683
$160$	22.9373	1.81335
$161$	−3.68580	−0.290482
$162$	18.7355	1.47200
$163$	−1.00000	−0.0783260
$163$	−1.00000	−0.0783260
$164$	−22.2306	−1.73592
$165$	24.3351	1.89449
$166$	19.7603	1.53369
$167$	−16.4263	−1.27111	−0.635554	−	0.772056i	$-0.719228\pi$
$167$	−16.4263	−1.27111	−0.635554	+	0.772056i	$0.719228\pi$
$168$	17.1773	1.32526
$169$	12.0487	0.926826
$170$	9.63169	0.738717
$171$	10.0263	0.766727
$172$	24.7328	1.88586
$173$	−5.93268	−0.451054	−0.225527	−	0.974237i	$-0.572410\pi$
$173$	−5.93268	−0.451054	−0.225527	+	0.974237i	$0.572410\pi$
$174$	−28.5488	−2.16428
$175$	−20.2283	−1.52911
$176$	−3.19476	−0.240814
$177$	13.4864	1.01370
$178$	−12.0799	−0.905430
$179$	−3.29398	−0.246203	−0.123102	−	0.992394i	$-0.539284\pi$
$179$	−3.29398	−0.246203	−0.123102	+	0.992394i	$0.539284\pi$
$180$	31.9740	2.38320
$181$	4.70602	0.349795	0.174898	−	0.984587i	$-0.444041\pi$
$181$	4.70602	0.349795	0.174898	+	0.984587i	$0.444041\pi$
$182$	35.4613	2.62857
$183$	28.2563	2.08876
$184$	−2.52196	−0.185921
$185$	3.37158	0.247884
$186$	20.7703	1.52295
$187$	−3.71629	−0.271762
$188$	2.88975	0.210756
$189$	−1.48685	−0.108152
$190$	−23.6489	−1.71567
$191$	0.192802	0.0139507	0.00697533	−	0.999976i	$-0.497780\pi$
$191$	0.192802	0.0139507	0.00697533	+	0.999976i	$0.497780\pi$
$192$	−32.2675	−2.32871
$193$	10.2083	0.734809	0.367405	−	0.930061i	$-0.380246\pi$
$193$	10.2083	0.734809	0.367405	+	0.930061i	$0.380246\pi$
$194$	−10.6018	−0.761163
$195$	41.9766	3.00601
$196$	9.19678	0.656913
$197$	26.7962	1.90915	0.954574	−	0.297973i	$-0.0963106\pi$
$197$	26.7962	1.90915	0.954574	+	0.297973i	$0.0963106\pi$
$198$	−20.6317	−1.46623
$199$	18.3117	1.29808	0.649041	−	0.760753i	$-0.275170\pi$
$199$	18.3117	1.29808	0.649041	+	0.760753i	$0.275170\pi$
$200$	−13.8409	−0.978699
$201$	−29.5274	−2.08270
$202$	6.36030	0.447509
$203$	−16.3461	−1.14727
$204$	−9.47753	−0.663560
$205$	−25.1977	−1.75988
$206$	−7.14083	−0.497525
$207$	3.69902	0.257099
$208$	−5.51076	−0.382103
$209$	9.12471	0.631170
$210$	59.4260	4.10078
$211$	21.0273	1.44758	0.723790	−	0.690020i	$-0.242398\pi$
$211$	21.0273	1.44758	0.723790	+	0.690020i	$0.242398\pi$
$212$	15.4825	1.06334
$213$	−12.5959	−0.863056
$214$	12.1137	0.828073
$215$	28.0338	1.91189
$216$	−1.01735	−0.0692222
$217$	11.8924	0.807308
$218$	−3.77886	−0.255936
$219$	26.8139	1.81191
$220$	29.0989	1.96185
$221$	−6.41038	−0.431209
$222$	−5.54828	−0.372376
$223$	−21.3464	−1.42946	−0.714731	−	0.699400i	$-0.753451\pi$
$223$	−21.3464	−1.42946	−0.714731	+	0.699400i	$0.753451\pi$
$224$	−21.6119	−1.44401
$225$	20.3008	1.35339
$226$	3.42957	0.228132
$227$	5.41501	0.359407	0.179703	−	0.983721i	$-0.442486\pi$
$227$	5.41501	0.359407	0.179703	+	0.983721i	$0.442486\pi$
$228$	23.2704	1.54112
$229$	2.43369	0.160823	0.0804115	−	0.996762i	$-0.474377\pi$
$229$	2.43369	0.160823	0.0804115	+	0.996762i	$0.474377\pi$
$230$	−8.72487	−0.575301
$231$	−22.9289	−1.50861
$232$	−11.1846	−0.734305
$233$	16.4130	1.07525	0.537626	−	0.843183i	$-0.319321\pi$
$233$	16.4130	1.07525	0.537626	+	0.843183i	$0.319321\pi$
$234$	−35.5885	−2.32649
$235$	3.27544	0.213666
$236$	16.1264	1.04974
$237$	−12.8036	−0.831683
$238$	−9.07513	−0.588253
$239$	9.65862	0.624764	0.312382	−	0.949957i	$-0.398873\pi$
$239$	9.65862	0.624764	0.312382	+	0.949957i	$0.398873\pi$
$240$	−9.23492	−0.596111
$241$	−15.8199	−1.01905	−0.509523	−	0.860457i	$-0.670178\pi$
$241$	−15.8199	−1.01905	−0.509523	+	0.860457i	$0.670178\pi$
$242$	5.75757	0.370111
$243$	−22.3003	−1.43057
$244$	33.7877	2.16303
$245$	10.4243	0.665982
$246$	41.4653	2.64373
$247$	15.7396	1.00149
$248$	8.13719	0.516712
$249$	−22.0392	−1.39668
$250$	−10.2840	−0.650418
$251$	−9.93070	−0.626820	−0.313410	−	0.949618i	$-0.601471\pi$
$251$	−9.93070	−0.626820	−0.313410	+	0.949618i	$0.601471\pi$
$252$	−30.1264	−1.89778
$253$	3.36641	0.211644
$254$	5.76121	0.361490
$255$	−10.7425	−0.672721
$256$	−8.23715	−0.514822
$257$	1.52458	0.0951009	0.0475505	−	0.998869i	$-0.484859\pi$
$257$	1.52458	0.0951009	0.0475505	+	0.998869i	$0.484859\pi$
$258$	−46.1325	−2.87208
$259$	−3.17676	−0.197394
$260$	50.1939	3.11289
$261$	16.4047	1.01543
$262$	−4.52584	−0.279608
$263$	4.57454	0.282078	0.141039	−	0.990004i	$-0.454956\pi$
$263$	4.57454	0.282078	0.141039	+	0.990004i	$0.454956\pi$
$264$	−15.6888	−0.965578
$265$	17.5490	1.07802
$266$	22.2824	1.36622
$267$	13.4731	0.824540
$268$	−35.3076	−2.15676
$269$	−16.3615	−0.997576	−0.498788	−	0.866724i	$-0.666221\pi$
$269$	−16.3615	−0.997576	−0.498788	+	0.866724i	$0.666221\pi$
$270$	−3.51960	−0.214196
$271$	31.3509	1.90443	0.952217	−	0.305423i	$-0.0987978\pi$
$271$	31.3509	1.90443	0.952217	+	0.305423i	$0.0987978\pi$
$272$	1.41029	0.0855116
$273$	−39.5510	−2.39374
$274$	10.6565	0.643784
$275$	18.4754	1.11411
$276$	8.58523	0.516770
$277$	−2.88630	−0.173421	−0.0867105	−	0.996234i	$-0.527636\pi$
$277$	−2.88630	−0.173421	−0.0867105	+	0.996234i	$0.527636\pi$
$278$	−2.41427	−0.144798
$279$	−11.9350	−0.714531
$280$	23.2814	1.39133
$281$	30.6320	1.82735	0.913675	−	0.406445i	$-0.133232\pi$
$281$	30.6320	1.82735	0.913675	+	0.406445i	$0.133232\pi$
$282$	−5.39006	−0.320974
$283$	−1.65151	−0.0981721	−0.0490860	−	0.998795i	$-0.515631\pi$
$283$	−1.65151	−0.0981721	−0.0490860	+	0.998795i	$0.515631\pi$
$284$	−15.0616	−0.893744
$285$	26.3763	1.56240
$286$	−32.3884	−1.91517
$287$	23.7417	1.40143
$288$	21.6894	1.27806
$289$	−15.3595	−0.903499
$290$	−38.6939	−2.27218
$291$	11.8245	0.693162
$292$	32.0629	1.87634
$293$	5.28278	0.308623	0.154312	−	0.988022i	$-0.450684\pi$
$293$	5.28278	0.308623	0.154312	+	0.988022i	$0.450684\pi$
$294$	−17.1542	−1.00045
$295$	18.2788	1.06423
$296$	−2.17365	−0.126341
$297$	1.35800	0.0787994
$298$	−2.78749	−0.161475
$299$	5.80685	0.335819
$300$	47.1171	2.72031
$301$	−26.4139	−1.52247
$302$	12.8278	0.738156
$303$	−7.09382	−0.407529
$304$	−3.46273	−0.198601
$305$	38.2973	2.19290
$306$	9.10767	0.520651
$307$	−23.9257	−1.36551	−0.682757	−	0.730645i	$-0.739219\pi$
$307$	−23.9257	−1.36551	−0.682757	+	0.730645i	$0.739219\pi$
$308$	−27.4175	−1.56226
$309$	7.96437	0.453077
$310$	28.1512	1.59888
$311$	−31.8697	−1.80717	−0.903583	−	0.428412i	$-0.859073\pi$
$311$	−31.8697	−1.80717	−0.903583	+	0.428412i	$0.859073\pi$
$312$	−27.0622	−1.53210
$313$	6.75497	0.381814	0.190907	−	0.981608i	$-0.438857\pi$
$313$	6.75497	0.381814	0.190907	+	0.981608i	$0.438857\pi$
$314$	−38.8129	−2.19034
$315$	−34.1473	−1.92398
$316$	−15.3100	−0.861256
$317$	−28.8778	−1.62194	−0.810968	−	0.585090i	$-0.801059\pi$
$317$	−28.8778	−1.62194	−0.810968	+	0.585090i	$0.801059\pi$
$318$	−28.8786	−1.61943
$319$	14.9296	0.835899
$320$	−43.7340	−2.44480
$321$	−13.5107	−0.754094
$322$	8.22072	0.458123
$323$	−4.02801	−0.224125
$324$	−24.9868	−1.38816
$325$	31.8689	1.76777
$326$	2.23037	0.123529
$327$	4.21466	0.233071
$328$	16.2449	0.896974
$329$	−3.08617	−0.170146
$330$	−54.2764	−2.98782
$331$	−11.4068	−0.626977	−0.313489	−	0.949592i	$-0.601498\pi$
$331$	−11.4068	−0.626977	−0.313489	+	0.949592i	$0.601498\pi$
$332$	−26.3536	−1.44634
$333$	3.18815	0.174709
$334$	36.6369	2.00468
$335$	−40.0201	−2.18653
$336$	8.70129	0.474694
$337$	−22.3864	−1.21947	−0.609733	−	0.792607i	$-0.708724\pi$
$337$	−22.3864	−1.21947	−0.609733	+	0.792607i	$0.708724\pi$
$338$	−26.8732	−1.46171
$339$	−3.82510	−0.207751
$340$	−12.8454	−0.696641
$341$	−10.8618	−0.588202
$342$	−22.3623	−1.20921
$343$	12.4154	0.670369
$344$	−18.0734	−0.974450
$345$	9.73110	0.523905
$346$	13.2321	0.711362
$347$	−7.26829	−0.390182	−0.195091	−	0.980785i	$-0.562500\pi$
$347$	−7.26829	−0.390182	−0.195091	+	0.980785i	$0.562500\pi$
$348$	38.0745	2.04101
$349$	−23.2449	−1.24427	−0.622135	−	0.782910i	$-0.713735\pi$
$349$	−23.2449	−1.24427	−0.622135	+	0.782910i	$0.713735\pi$
$350$	45.1166	2.41158
$351$	2.34248	0.125032
$352$	19.7391	1.05210
$353$	−18.5164	−0.985528	−0.492764	−	0.870163i	$-0.664013\pi$
$353$	−18.5164	−0.985528	−0.492764	+	0.870163i	$0.664013\pi$
$354$	−30.0796	−1.59871
$355$	−17.0719	−0.906083
$356$	16.1106	0.853859
$357$	10.1218	0.535700
$358$	7.34680	0.388290
$359$	−8.47621	−0.447357	−0.223679	−	0.974663i	$-0.571807\pi$
$359$	−8.47621	−0.447357	−0.223679	+	0.974663i	$0.571807\pi$
$360$	−23.3648	−1.23143
$361$	−9.10991	−0.479469
$362$	−10.4962	−0.551667
$363$	−6.42158	−0.337046
$364$	−47.2935	−2.47885
$365$	36.3424	1.90225
$366$	−63.0220	−3.29421
$367$	14.0924	0.735616	0.367808	−	0.929902i	$-0.380108\pi$
$367$	14.0924	0.735616	0.367808	+	0.929902i	$0.380108\pi$
$368$	−1.27752	−0.0665951
$369$	−23.8268	−1.24037
$370$	−7.51989	−0.390941
$371$	−16.5349	−0.858450
$372$	−27.7006	−1.43621
$373$	−28.2807	−1.46432	−0.732160	−	0.681132i	$-0.761488\pi$
$373$	−28.2807	−1.46432	−0.732160	+	0.681132i	$0.761488\pi$
$374$	8.28872	0.428600
$375$	11.4700	0.592311
$376$	−2.11167	−0.108901
$377$	25.7527	1.32633
$378$	3.31623	0.170568
$379$	19.6334	1.00850	0.504250	−	0.863558i	$-0.331769\pi$
$379$	19.6334	1.00850	0.504250	+	0.863558i	$0.331769\pi$
$380$	31.5397	1.61795
$381$	−6.42564	−0.329195
$382$	−0.430020	−0.0220017
$383$	−5.15291	−0.263301	−0.131651	−	0.991296i	$-0.542028\pi$
$383$	−5.15291	−0.263301	−0.131651	+	0.991296i	$0.542028\pi$
$384$	38.1218	1.94539
$385$	−31.0769	−1.58382
$386$	−22.7683	−1.15888
$387$	26.5086	1.34751
$388$	14.1392	0.717809
$389$	8.87073	0.449764	0.224882	−	0.974386i	$-0.427800\pi$
$389$	8.87073	0.449764	0.224882	+	0.974386i	$0.427800\pi$
$390$	−93.6235	−4.74081
$391$	−1.48607	−0.0751536
$392$	−6.72050	−0.339437
$393$	5.04780	0.254628
$394$	−59.7655	−3.01094
$395$	−17.3534	−0.873146
$396$	27.5158	1.38272
$397$	−30.4247	−1.52697	−0.763487	−	0.645824i	$-0.776514\pi$
$397$	−30.4247	−1.52697	−0.763487	+	0.645824i	$0.776514\pi$
$398$	−40.8419	−2.04722
$399$	−24.8522	−1.24417
$400$	−7.01121	−0.350560
$401$	28.5586	1.42615	0.713075	−	0.701088i	$-0.247302\pi$
$401$	28.5586	1.42615	0.713075	+	0.701088i	$0.247302\pi$
$402$	65.8571	3.28465
$403$	−18.7360	−0.933308
$404$	−8.48250	−0.422020
$405$	−28.3218	−1.40732
$406$	36.4580	1.80938
$407$	2.90148	0.143821
$408$	6.92566	0.342871
$409$	34.5098	1.70640	0.853199	−	0.521586i	$-0.174659\pi$
$409$	34.5098	1.70640	0.853199	+	0.521586i	$0.174659\pi$
$410$	56.2003	2.77553
$411$	−11.8855	−0.586270
$412$	9.52347	0.469188
$413$	−17.2226	−0.847469
$414$	−8.25019	−0.405475
$415$	−29.8710	−1.46631
$416$	34.0488	1.66938
$417$	2.69270	0.131862
$418$	−20.3515	−0.995425
$419$	35.4172	1.73024	0.865122	−	0.501561i	$-0.167241\pi$
$419$	35.4172	1.73024	0.865122	+	0.501561i	$0.167241\pi$
$420$	−79.2543	−3.86721
$421$	−11.2506	−0.548322	−0.274161	−	0.961684i	$-0.588400\pi$
$421$	−11.2506	−0.548322	−0.274161	+	0.961684i	$0.588400\pi$
$422$	−46.8988	−2.28300
$423$	3.09724	0.150593
$424$	−11.3138	−0.549446
$425$	−8.15577	−0.395613
$426$	28.0935	1.36114
$427$	−36.0843	−1.74624
$428$	−16.1555	−0.780908
$429$	36.1237	1.74407
$430$	−62.5260	−3.01527
$431$	39.3729	1.89653	0.948263	−	0.317485i	$-0.102838\pi$
$431$	39.3729	1.89653	0.948263	+	0.317485i	$0.102838\pi$
$432$	−0.515348	−0.0247947
$433$	−4.08286	−0.196210	−0.0981049	−	0.995176i	$-0.531278\pi$
$433$	−4.08286	−0.196210	−0.0981049	+	0.995176i	$0.531278\pi$
$434$	−26.5245	−1.27322
$435$	43.1563	2.06919
$436$	5.03972	0.241359
$437$	3.64878	0.174545
$438$	−59.8050	−2.85759
$439$	−5.96162	−0.284533	−0.142266	−	0.989828i	$-0.545439\pi$
$439$	−5.96162	−0.284533	−0.142266	+	0.989828i	$0.545439\pi$
$440$	−21.2639	−1.01372
$441$	9.85713	0.469387
$442$	14.2975	0.680065
$443$	−0.284662	−0.0135247	−0.00676236	−	0.999977i	$-0.502153\pi$
$443$	−0.284662	−0.0135247	−0.00676236	+	0.999977i	$0.502153\pi$
$444$	7.39953	0.351166
$445$	18.2608	0.865647
$446$	47.6105	2.25442
$447$	3.10897	0.147049
$448$	41.2069	1.94684
$449$	−10.4329	−0.492359	−0.246180	−	0.969224i	$-0.579175\pi$
$449$	−10.4329	−0.492359	−0.246180	+	0.969224i	$0.579175\pi$
$450$	−45.2783	−2.13444
$451$	−21.6843	−1.02107
$452$	−4.57389	−0.215138
$453$	−14.3072	−0.672211
$454$	−12.0775	−0.566825
$455$	−53.6057	−2.51307
$456$	−17.0048	−0.796321
$457$	−13.3178	−0.622982	−0.311491	−	0.950249i	$-0.600828\pi$
$457$	−13.3178	−0.622982	−0.311491	+	0.950249i	$0.600828\pi$
$458$	−5.42805	−0.253636
$459$	−0.599478	−0.0279812
$460$	11.6360	0.542533
$461$	23.7641	1.10681	0.553403	−	0.832914i	$-0.313329\pi$
$461$	23.7641	1.10681	0.553403	+	0.832914i	$0.313329\pi$
$462$	51.1401	2.37925
$463$	0.632912	0.0294139	0.0147070	−	0.999892i	$-0.495318\pi$
$463$	0.632912	0.0294139	0.0147070	+	0.999892i	$0.495318\pi$
$464$	−5.66564	−0.263021
$465$	−31.3978	−1.45604
$466$	−36.6072	−1.69579
$467$	15.6541	0.724387	0.362193	−	0.932103i	$-0.382028\pi$
$467$	15.6541	0.724387	0.362193	+	0.932103i	$0.382028\pi$
$468$	47.4630	2.19398
$469$	37.7076	1.74117
$470$	−7.30546	−0.336976
$471$	43.2892	1.99466
$472$	−11.7843	−0.542417
$473$	24.1250	1.10927
$474$	28.5568	1.31166
$475$	20.0251	0.918814
$476$	12.1032	0.554748
$477$	16.5942	0.759796
$478$	−21.5423	−0.985324
$479$	−11.3277	−0.517574	−0.258787	−	0.965934i	$-0.583323\pi$
$479$	−11.3277	−0.517574	−0.258787	+	0.965934i	$0.583323\pi$
$480$	57.0588	2.60437
$481$	5.00487	0.228202
$482$	35.2842	1.60715
$483$	−9.16880	−0.417195
$484$	−7.67866	−0.349030
$485$	16.0264	0.727719
$486$	49.7381	2.25617
$487$	−9.64566	−0.437086	−0.218543	−	0.975827i	$-0.570130\pi$
$487$	−9.64566	−0.437086	−0.218543	+	0.975827i	$0.570130\pi$
$488$	−24.6902	−1.11767
$489$	−2.48760	−0.112493
$490$	−23.2500	−1.05033
$491$	34.9969	1.57939	0.789693	−	0.613502i	$-0.210240\pi$
$491$	34.9969	1.57939	0.789693	+	0.613502i	$0.210240\pi$
$492$	−55.3008	−2.49315
$493$	−6.59054	−0.296823
$494$	−35.1051	−1.57946
$495$	31.1883	1.40181
$496$	4.12196	0.185081
$497$	16.0854	0.721530
$498$	49.1556	2.20272
$499$	−28.6167	−1.28106	−0.640530	−	0.767933i	$-0.721285\pi$
$499$	−28.6167	−1.28106	−0.640530	+	0.767933i	$0.721285\pi$
$500$	13.7154	0.613372
$501$	−40.8621	−1.82559
$502$	22.1492	0.988566
$503$	8.13878	0.362890	0.181445	−	0.983401i	$-0.441923\pi$
$503$	8.13878	0.362890	0.181445	+	0.983401i	$0.441923\pi$
$504$	22.0147	0.980613
$505$	−9.61466	−0.427847
$506$	−7.50835	−0.333787
$507$	29.9724	1.33112
$508$	−7.68351	−0.340901
$509$	8.89734	0.394368	0.197184	−	0.980367i	$-0.436820\pi$
$509$	8.89734	0.394368	0.197184	+	0.980367i	$0.436820\pi$
$510$	23.9598	1.06096
$511$	−34.2424	−1.51479
$512$	−12.2775	−0.542594
$513$	1.47191	0.0649866
$514$	−3.40039	−0.149985
$515$	10.7946	0.475665
$516$	61.5252	2.70850
$517$	2.81874	0.123968
$518$	7.08536	0.311313
$519$	−14.7581	−0.647810
$520$	−36.6789	−1.60848
$521$	−33.8939	−1.48492	−0.742460	−	0.669890i	$-0.766341\pi$
$521$	−33.8939	−1.48492	−0.742460	+	0.669890i	$0.766341\pi$
$522$	−36.5887	−1.60144
$523$	−25.7180	−1.12457	−0.562284	−	0.826944i	$-0.690077\pi$
$523$	−25.7180	−1.12457	−0.562284	+	0.826944i	$0.690077\pi$
$524$	6.03595	0.263682
$525$	−50.3198	−2.19614
$526$	−10.2029	−0.444869
$527$	4.79485	0.208867
$528$	−7.94727	−0.345861
$529$	−21.6538	−0.941472
$530$	−39.1407	−1.70017
$531$	17.2844	0.750077
$532$	−29.7172	−1.28841
$533$	−37.4041	−1.62015
$534$	−30.0500	−1.30039
$535$	−18.3118	−0.791689
$536$	25.8009	1.11443
$537$	−8.19409	−0.353601
$538$	36.4922	1.57329
$539$	8.97079	0.386399
$540$	4.69397	0.201996
$541$	17.6751	0.759911	0.379955	−	0.925005i	$-0.375939\pi$
$541$	17.6751	0.759911	0.379955	+	0.925005i	$0.375939\pi$
$542$	−69.9243	−3.00351
$543$	11.7067	0.502382
$544$	−8.71363	−0.373594
$545$	5.71237	0.244691
$546$	88.2136	3.77519
$547$	−1.72154	−0.0736077	−0.0368039	−	0.999323i	$-0.511718\pi$
$547$	−1.72154	−0.0736077	−0.0368039	+	0.999323i	$0.511718\pi$
$548$	−14.2122	−0.607116
$549$	36.2137	1.54556
$550$	−41.2070	−1.75707
$551$	16.1819	0.689374
$552$	−6.27362	−0.267023
$553$	16.3507	0.695302
$554$	6.43753	0.273504
$555$	8.38715	0.356015
$556$	3.21982	0.136551
$557$	14.7923	0.626769	0.313385	−	0.949626i	$-0.398537\pi$
$557$	14.7923	0.626769	0.313385	+	0.949626i	$0.398537\pi$
$558$	26.6196	1.12690
$559$	41.6142	1.76009
$560$	11.7933	0.498360
$561$	−9.24465	−0.390309
$562$	−68.3208	−2.88194
$563$	25.7805	1.08652	0.543259	−	0.839565i	$-0.317190\pi$
$563$	25.7805	1.08652	0.543259	+	0.839565i	$0.317190\pi$
$564$	7.18853	0.302692
$565$	−5.18437	−0.218108
$566$	3.68349	0.154828
$567$	26.6853	1.12068
$568$	11.0062	0.461811
$569$	21.8227	0.914854	0.457427	−	0.889247i	$-0.348771\pi$
$569$	21.8227	0.914854	0.457427	+	0.889247i	$0.348771\pi$
$570$	−58.8291	−2.46408
$571$	−21.2545	−0.889473	−0.444737	−	0.895661i	$-0.646703\pi$
$571$	−21.2545	−0.889473	−0.444737	+	0.895661i	$0.646703\pi$
$572$	43.1952	1.80608
$573$	0.479614	0.0200361
$574$	−52.9528	−2.21021
$575$	7.38791	0.308097
$576$	−41.3546	−1.72311
$577$	14.5826	0.607081	0.303540	−	0.952819i	$-0.401831\pi$
$577$	14.5826	0.607081	0.303540	+	0.952819i	$0.401831\pi$
$578$	34.2574	1.42492
$579$	25.3941	1.05534
$580$	51.6046	2.14276
$581$	28.1449	1.16765
$582$	−26.3730	−1.09319
$583$	15.1021	0.625464
$584$	−23.4298	−0.969534
$585$	53.7979	2.22427
$586$	−11.7826	−0.486733
$587$	−33.5227	−1.38363	−0.691815	−	0.722075i	$-0.743189\pi$
$587$	−33.5227	−1.38363	−0.691815	+	0.722075i	$0.743189\pi$
$588$	22.8779	0.943468
$589$	−11.7729	−0.485095
$590$	−40.7686	−1.67842
$591$	66.6581	2.74195
$592$	−1.10108	−0.0452541
$593$	10.0004	0.410666	0.205333	−	0.978692i	$-0.434172\pi$
$593$	10.0004	0.410666	0.205333	+	0.978692i	$0.434172\pi$
$594$	−3.02886	−0.124276
$595$	13.7186	0.562407
$596$	3.71758	0.152278
$597$	45.5522	1.86433
$598$	−12.9514	−0.529624
$599$	3.25535	0.133010	0.0665051	−	0.997786i	$-0.478815\pi$
$599$	3.25535	0.133010	0.0665051	+	0.997786i	$0.478815\pi$
$600$	−34.4306	−1.40562
$601$	−40.9982	−1.67235	−0.836176	−	0.548462i	$-0.815214\pi$
$601$	−40.9982	−1.67235	−0.836176	+	0.548462i	$0.815214\pi$
$602$	58.9130	2.40111
$603$	−37.8428	−1.54108
$604$	−17.1080	−0.696113
$605$	−8.70353	−0.353849
$606$	15.8219	0.642720
$607$	−2.94867	−0.119683	−0.0598415	−	0.998208i	$-0.519060\pi$
$607$	−2.94867	−0.119683	−0.0598415	+	0.998208i	$0.519060\pi$
$608$	21.3948	0.867674
$609$	−40.6626	−1.64773
$610$	−85.4173	−3.45845
$611$	4.86215	0.196702
$612$	−12.1466	−0.490996
$613$	12.0635	0.487241	0.243621	−	0.969871i	$-0.421665\pi$
$613$	12.0635	0.487241	0.243621	+	0.969871i	$0.421665\pi$
$614$	53.3634	2.15357
$615$	−62.6817	−2.52757
$616$	20.0352	0.807241
$617$	26.8344	1.08031	0.540157	−	0.841564i	$-0.318365\pi$
$617$	26.8344	1.08031	0.540157	+	0.841564i	$0.318365\pi$
$618$	−17.7635	−0.714554
$619$	32.8813	1.32161	0.660805	−	0.750558i	$-0.270215\pi$
$619$	32.8813	1.32161	0.660805	+	0.750558i	$0.270215\pi$
$620$	−37.5442	−1.50781
$621$	0.543037	0.0217913
$622$	71.0814	2.85011
$623$	−17.2057	−0.689330
$624$	−13.7086	−0.548782
$625$	−16.2919	−0.651675
$626$	−15.0661	−0.602163
$627$	22.6986	0.906496
$628$	51.7634	2.06558
$629$	−1.28083	−0.0510700
$630$	76.1613	3.03434
$631$	5.94787	0.236781	0.118391	−	0.992967i	$-0.462227\pi$
$631$	5.94787	0.236781	0.118391	+	0.992967i	$0.462227\pi$
$632$	11.1877	0.445024
$633$	52.3076	2.07904
$634$	64.4082	2.55798
$635$	−8.70903	−0.345607
$636$	38.5143	1.52719
$637$	15.4741	0.613105
$638$	−33.2987	−1.31831
$639$	−16.1431	−0.638611
$640$	51.6686	2.04238
$641$	36.6738	1.44853	0.724263	−	0.689523i	$-0.242180\pi$
$641$	36.6738	1.44853	0.724263	+	0.689523i	$0.242180\pi$
$642$	30.1339	1.18929
$643$	−11.6526	−0.459535	−0.229767	−	0.973246i	$-0.573797\pi$
$643$	−11.6526	−0.459535	−0.229767	+	0.973246i	$0.573797\pi$
$644$	−10.9637	−0.432029
$645$	69.7370	2.74589
$646$	8.98398	0.353470
$647$	26.8829	1.05688	0.528438	−	0.848972i	$-0.322778\pi$
$647$	26.8829	1.05688	0.528438	+	0.848972i	$0.322778\pi$
$648$	18.2590	0.717282
$649$	15.7302	0.617463
$650$	−71.0795	−2.78797
$651$	29.5835	1.15947
$652$	−2.97457	−0.116493
$653$	23.4745	0.918628	0.459314	−	0.888274i	$-0.348095\pi$
$653$	23.4745	0.918628	0.459314	+	0.888274i	$0.348095\pi$
$654$	−9.40028	−0.367580
$655$	6.84157	0.267322
$656$	8.22897	0.321287
$657$	34.3651	1.34071
$658$	6.88332	0.268340
$659$	9.19551	0.358206	0.179103	−	0.983830i	$-0.442680\pi$
$659$	9.19551	0.358206	0.179103	+	0.983830i	$0.442680\pi$
$660$	72.3864	2.81764
$661$	−38.5512	−1.49947	−0.749733	−	0.661740i	$-0.769818\pi$
$661$	−38.5512	−1.49947	−0.749733	+	0.661740i	$0.769818\pi$
$662$	25.4415	0.988813
$663$	−15.9465	−0.619309
$664$	19.2577	0.747345
$665$	−33.6836	−1.30619
$666$	−7.11076	−0.275537
$667$	5.97005	0.231161
$668$	−48.8613	−1.89050
$669$	−53.1013	−2.05302
$670$	89.2598	3.44841
$671$	32.9574	1.27231
$672$	−53.7617	−2.07390
$673$	−23.0822	−0.889752	−0.444876	−	0.895592i	$-0.646752\pi$
$673$	−23.0822	−0.889752	−0.444876	+	0.895592i	$0.646752\pi$
$674$	49.9301	1.92324
$675$	2.98027	0.114711
$676$	35.8398	1.37845
$677$	−19.1289	−0.735182	−0.367591	−	0.929988i	$-0.619817\pi$
$677$	−19.1289	−0.735182	−0.367591	+	0.929988i	$0.619817\pi$
$678$	8.53139	0.327646
$679$	−15.1003	−0.579496
$680$	9.38674	0.359965
$681$	13.4704	0.516185
$682$	24.2260	0.927660
$683$	−24.7838	−0.948325	−0.474163	−	0.880437i	$-0.657249\pi$
$683$	−24.7838	−0.948325	−0.474163	+	0.880437i	$0.657249\pi$
$684$	29.8238	1.14034
$685$	−16.1091	−0.615498
$686$	−27.6910	−1.05725
$687$	6.05406	0.230977
$688$	−9.15519	−0.349038
$689$	26.0502	0.992432
$690$	−21.7040	−0.826257
$691$	−5.42879	−0.206521	−0.103260	−	0.994654i	$-0.532927\pi$
$691$	−5.42879	−0.206521	−0.103260	+	0.994654i	$0.532927\pi$
$692$	−17.6472	−0.670845
$693$	−29.3861	−1.11629
$694$	16.2110	0.615361
$695$	3.64957	0.138436
$696$	−27.8228	−1.05462
$697$	9.57233	0.362578
$698$	51.8448	1.96236
$699$	40.8290	1.54429
$700$	−60.1703	−2.27422
$701$	8.38776	0.316801	0.158401	−	0.987375i	$-0.449366\pi$
$701$	8.38776	0.316801	0.158401	+	0.987375i	$0.449366\pi$
$702$	−5.22460	−0.197190
$703$	3.14485	0.118610
$704$	−37.6361	−1.41846
$705$	8.14798	0.306871
$706$	41.2985	1.55429
$707$	9.05908	0.340702
$708$	40.1161	1.50766
$709$	−0.151901	−0.00570477	−0.00285239	−	0.999996i	$-0.500908\pi$
$709$	−0.151901	−0.00570477	−0.00285239	+	0.999996i	$0.500908\pi$
$710$	38.0768	1.42900
$711$	−16.4093	−0.615397
$712$	−11.7727	−0.441202
$713$	−4.34342	−0.162662
$714$	−22.5753	−0.844859
$715$	48.9605	1.83102
$716$	−9.79816	−0.366174
$717$	24.0268	0.897296
$718$	18.9051	0.705533
$719$	−29.4455	−1.09813	−0.549065	−	0.835779i	$-0.685016\pi$
$719$	−29.4455	−1.09813	−0.549065	+	0.835779i	$0.685016\pi$
$720$	−11.8356	−0.441088
$721$	−10.1708	−0.378781
$722$	20.3185	0.756176
$723$	−39.3535	−1.46357
$724$	13.9984	0.520245
$725$	32.7646	1.21685
$726$	14.3225	0.531559
$727$	−16.0489	−0.595220	−0.297610	−	0.954687i	$-0.596190\pi$
$727$	−16.0489	−0.595220	−0.297610	+	0.954687i	$0.596190\pi$
$728$	34.5595	1.28086
$729$	−30.2738	−1.12125
$730$	−81.0571	−3.00006
$731$	−10.6498	−0.393895
$732$	84.0502	3.10658
$733$	−6.29611	−0.232552	−0.116276	−	0.993217i	$-0.537096\pi$
$733$	−6.29611	−0.232552	−0.116276	+	0.993217i	$0.537096\pi$
$734$	−31.4313	−1.16015
$735$	25.9314	0.956494
$736$	7.89325	0.290949
$737$	−34.4400	−1.26861
$738$	53.1426	1.95621
$739$	47.6694	1.75355	0.876773	−	0.480904i	$-0.159692\pi$
$739$	47.6694	1.75355	0.876773	+	0.480904i	$0.159692\pi$
$740$	10.0290	0.368674
$741$	39.1538	1.43835
$742$	36.8790	1.35387
$743$	−20.3361	−0.746059	−0.373030	−	0.927819i	$-0.621681\pi$
$743$	−20.3361	−0.746059	−0.373030	+	0.927819i	$0.621681\pi$
$744$	20.2421	0.742110
$745$	4.21376	0.154380
$746$	63.0766	2.30940
$747$	−28.2458	−1.03346
$748$	−11.0544	−0.404188
$749$	17.2537	0.630436
$750$	−25.5825	−0.934141
$751$	7.61815	0.277990	0.138995	−	0.990293i	$-0.455613\pi$
$751$	7.61815	0.277990	0.138995	+	0.990293i	$0.455613\pi$
$752$	−1.06968	−0.0390073
$753$	−24.7036	−0.900250
$754$	−57.4382	−2.09178
$755$	−19.3913	−0.705723
$756$	−4.42273	−0.160853
$757$	−42.1052	−1.53034	−0.765170	−	0.643828i	$-0.777345\pi$
$757$	−42.1052	−1.53034	−0.765170	+	0.643828i	$0.777345\pi$
$758$	−43.7898	−1.59052
$759$	8.37427	0.303967
$760$	−23.0475	−0.836021
$761$	−5.42461	−0.196642	−0.0983210	−	0.995155i	$-0.531347\pi$
$761$	−5.42461	−0.196642	−0.0983210	+	0.995155i	$0.531347\pi$
$762$	14.3316	0.519178
$763$	−5.38229	−0.194852
$764$	0.573502	0.0207486
$765$	−13.7678	−0.497775
$766$	11.4929	0.415256
$767$	27.1336	0.979738
$768$	−20.4907	−0.739395
$769$	35.4046	1.27672	0.638360	−	0.769738i	$-0.279613\pi$
$769$	35.4046	1.27672	0.638360	+	0.769738i	$0.279613\pi$
$770$	69.3130	2.49787
$771$	3.79255	0.136585
$772$	30.3653	1.09287
$773$	15.3651	0.552645	0.276322	−	0.961065i	$-0.410884\pi$
$773$	15.3651	0.552645	0.276322	+	0.961065i	$0.410884\pi$
$774$	−59.1242	−2.12517
$775$	−23.8374	−0.856264
$776$	−10.3322	−0.370903
$777$	−7.90250	−0.283501
$778$	−19.7851	−0.709328
$779$	−23.5032	−0.842089
$780$	124.862	4.47079
$781$	−14.6915	−0.525705
$782$	3.31449	0.118526
$783$	2.40831	0.0860660
$784$	−3.40432	−0.121583
$785$	58.6722	2.09410
$786$	−11.2585	−0.401577
$787$	12.1321	0.432461	0.216231	−	0.976342i	$-0.430624\pi$
$787$	12.1321	0.432461	0.216231	+	0.976342i	$0.430624\pi$
$788$	79.7071	2.83945
$789$	11.3796	0.405125
$790$	38.7047	1.37705
$791$	4.88479	0.173683
$792$	−20.1070	−0.714472
$793$	56.8496	2.01879
$794$	67.8585	2.40821
$795$	43.6548	1.54828
$796$	54.4694	1.93062
$797$	19.1888	0.679703	0.339851	−	0.940479i	$-0.389623\pi$
$797$	19.1888	0.679703	0.339851	+	0.940479i	$0.389623\pi$
$798$	55.4297	1.96219
$799$	−1.24430	−0.0440203
$800$	43.3194	1.53157
$801$	17.2673	0.610112
$802$	−63.6964	−2.24920
$803$	31.2751	1.10367
$804$	−87.8312	−3.09757
$805$	−12.4270	−0.437994
$806$	41.7883	1.47193
$807$	−40.7008	−1.43273
$808$	6.19855	0.218064
$809$	36.8696	1.29626	0.648132	−	0.761528i	$-0.275550\pi$
$809$	36.8696	1.29626	0.648132	+	0.761528i	$0.275550\pi$
$810$	63.1682	2.21951
$811$	−30.2047	−1.06063	−0.530315	−	0.847801i	$-0.677926\pi$
$811$	−30.2047	−1.06063	−0.530315	+	0.847801i	$0.677926\pi$
$812$	−48.6227	−1.70632
$813$	77.9886	2.73518
$814$	−6.47138	−0.226822
$815$	−3.37158	−0.118101
$816$	3.50825	0.122813
$817$	26.1486	0.914825
$818$	−76.9697	−2.69118
$819$	−50.6892	−1.77123
$820$	−74.9522	−2.61745
$821$	−28.2609	−0.986311	−0.493155	−	0.869941i	$-0.664157\pi$
$821$	−28.2609	−0.986311	−0.493155	+	0.869941i	$0.664157\pi$
$822$	26.5092	0.924613
$823$	−21.8441	−0.761439	−0.380720	−	0.924691i	$-0.624324\pi$
$823$	−21.8441	−0.761439	−0.380720	+	0.924691i	$0.624324\pi$
$824$	−6.95923	−0.242436
$825$	45.9593	1.60010
$826$	38.4129	1.33655
$827$	−47.9014	−1.66569	−0.832847	−	0.553503i	$-0.813291\pi$
$827$	−47.9014	−1.66569	−0.832847	+	0.553503i	$0.813291\pi$
$828$	11.0030	0.382380
$829$	−12.4204	−0.431377	−0.215689	−	0.976462i	$-0.569200\pi$
$829$	−12.4204	−0.431377	−0.215689	+	0.976462i	$0.569200\pi$
$830$	66.6234	2.31253
$831$	−7.17996	−0.249070
$832$	−64.9199	−2.25069
$833$	−3.96007	−0.137208
$834$	−6.00573	−0.207961
$835$	−55.3828	−1.91660
$836$	27.1421	0.938728
$837$	−1.75213	−0.0605625
$838$	−78.9936	−2.72879
$839$	25.5169	0.880941	0.440471	−	0.897767i	$-0.354812\pi$
$839$	25.5169	0.880941	0.440471	+	0.897767i	$0.354812\pi$
$840$	57.9147	1.99825
$841$	−2.52348	−0.0870167
$842$	25.0931	0.864765
$843$	76.2001	2.62447
$844$	62.5472	2.15296
$845$	40.6233	1.39748
$846$	−6.90800	−0.237502
$847$	8.20060	0.281776
$848$	−5.73108	−0.196806
$849$	−4.10830	−0.140996
$850$	18.1904	0.623926
$851$	1.16024	0.0397725
$852$	−37.4673	−1.28361
$853$	−41.2828	−1.41350	−0.706748	−	0.707465i	$-0.749839\pi$
$853$	−41.2828	−1.41350	−0.706748	+	0.707465i	$0.749839\pi$
$854$	80.4815	2.75402
$855$	33.8044	1.15608
$856$	11.8056	0.403507
$857$	46.1219	1.57549	0.787747	−	0.615999i	$-0.211247\pi$
$857$	46.1219	1.57549	0.787747	+	0.615999i	$0.211247\pi$
$858$	−80.5694	−2.75059
$859$	−15.4879	−0.528442	−0.264221	−	0.964462i	$-0.585115\pi$
$859$	−15.4879	−0.528442	−0.264221	+	0.964462i	$0.585115\pi$
$860$	83.3886	2.84353
$861$	59.0597	2.01275
$862$	−87.8163	−2.99104
$863$	−16.2975	−0.554775	−0.277387	−	0.960758i	$-0.589469\pi$
$863$	−16.2975	−0.554775	−0.277387	+	0.960758i	$0.589469\pi$
$864$	3.18413	0.108326
$865$	−20.0025	−0.680107
$866$	9.10630	0.309445
$867$	−38.2082	−1.29762
$868$	35.3747	1.20070
$869$	−14.9338	−0.506595
$870$	−96.2548	−3.26334
$871$	−59.4069	−2.01293
$872$	−3.68275	−0.124714
$873$	15.1544	0.512900
$874$	−8.13814	−0.275277
$875$	−14.6477	−0.495182
$876$	79.7597	2.69483
$877$	−6.51721	−0.220071	−0.110035	−	0.993928i	$-0.535096\pi$
$877$	−6.51721	−0.220071	−0.110035	+	0.993928i	$0.535096\pi$
$878$	13.2966	0.448740
$879$	13.1414	0.443249
$880$	−10.7714	−0.363103
$881$	53.2834	1.79516	0.897582	−	0.440848i	$-0.145322\pi$
$881$	53.2834	1.79516	0.897582	+	0.440848i	$0.145322\pi$
$882$	−21.9851	−0.740276
$883$	−0.452011	−0.0152114	−0.00760569	−	0.999971i	$-0.502421\pi$
$883$	−0.452011	−0.0152114	−0.00760569	+	0.999971i	$0.502421\pi$
$884$	−19.0681	−0.641330
$885$	45.4704	1.52847
$886$	0.634903	0.0213300
$887$	3.05320	0.102516	0.0512582	−	0.998685i	$-0.483677\pi$
$887$	3.05320	0.102516	0.0512582	+	0.998685i	$0.483677\pi$
$888$	−5.40717	−0.181453
$889$	8.20579	0.275213
$890$	−40.7285	−1.36522
$891$	−24.3728	−0.816521
$892$	−63.4964	−2.12602
$893$	3.05517	0.102238
$894$	−6.93417	−0.231913
$895$	−11.1059	−0.371230
$896$	−48.6829	−1.62638
$897$	14.4451	0.482308
$898$	23.2693	0.776506
$899$	−19.2626	−0.642444
$900$	60.3860	2.01287
$901$	−6.66666	−0.222099
$902$	48.3641	1.61035
$903$	−65.7073	−2.18660
$904$	3.34235	0.111165
$905$	15.8667	0.527428
$906$	31.9104	1.06015
$907$	37.5872	1.24806	0.624032	−	0.781399i	$-0.285494\pi$
$907$	37.5872	1.24806	0.624032	+	0.781399i	$0.285494\pi$
$908$	16.1073	0.534540
$909$	−9.09156	−0.301548
$910$	119.561	3.96340
$911$	−21.4309	−0.710039	−0.355019	−	0.934859i	$-0.615526\pi$
$911$	−21.4309	−0.710039	−0.355019	+	0.934859i	$0.615526\pi$
$912$	−8.61389	−0.285234
$913$	−25.7060	−0.850744
$914$	29.7038	0.982513
$915$	95.2683	3.14947
$916$	7.23919	0.239190
$917$	−6.44624	−0.212874
$918$	1.33706	0.0441295
$919$	−0.339778	−0.0112082	−0.00560412	−	0.999984i	$-0.501784\pi$
$919$	−0.339778	−0.0112082	−0.00560412	+	0.999984i	$0.501784\pi$
$920$	−8.50299	−0.280335
$921$	−59.5177	−1.96117
$922$	−53.0029	−1.74556
$923$	−25.3420	−0.834143
$924$	−68.2037	−2.24374
$925$	6.36757	0.209365
$926$	−1.41163	−0.0463891
$927$	10.2073	0.335251
$928$	35.0057	1.14912
$929$	−14.7674	−0.484503	−0.242251	−	0.970214i	$-0.577886\pi$
$929$	−14.7674	−0.484503	−0.242251	+	0.970214i	$0.577886\pi$
$930$	70.0288	2.29633
$931$	9.72326	0.318667
$932$	48.8216	1.59921
$933$	−79.2791	−2.59548
$934$	−34.9146	−1.14244
$935$	−12.5298	−0.409768
$936$	−34.6834	−1.13366
$937$	−28.7884	−0.940475	−0.470238	−	0.882540i	$-0.655832\pi$
$937$	−28.7884	−0.940475	−0.470238	+	0.882540i	$0.655832\pi$
$938$	−84.1020	−2.74603
$939$	16.8037	0.548367
$940$	9.74302	0.317782
$941$	32.0289	1.04411	0.522056	−	0.852911i	$-0.325165\pi$
$941$	32.0289	1.04411	0.522056	+	0.852911i	$0.325165\pi$
$942$	−96.5510	−3.14580
$943$	−8.67110	−0.282370
$944$	−5.96944	−0.194289
$945$	−5.01303	−0.163074
$946$	−53.8078	−1.74944
$947$	−5.91802	−0.192310	−0.0961550	−	0.995366i	$-0.530654\pi$
$947$	−5.91802	−0.192310	−0.0961550	+	0.995366i	$0.530654\pi$
$948$	−38.0852	−1.23695
$949$	53.9476	1.75121
$950$	−44.6634	−1.44907
$951$	−71.8363	−2.32945
$952$	−8.84434	−0.286647
$953$	15.1319	0.490169	0.245085	−	0.969502i	$-0.421184\pi$
$953$	15.1319	0.490169	0.245085	+	0.969502i	$0.421184\pi$
$954$	−37.0113	−1.19828
$955$	0.650047	0.0210350
$956$	28.7302	0.929202
$957$	37.1390	1.20053
$958$	25.2649	0.816272
$959$	15.1783	0.490132
$960$	−108.793	−3.51127
$961$	−16.9858	−0.547928
$962$	−11.1627	−0.359901
$963$	−17.3155	−0.557986
$964$	−47.0573	−1.51561
$965$	34.4181	1.10796
$966$	20.4498	0.657963
$967$	−30.2493	−0.972753	−0.486377	−	0.873749i	$-0.661682\pi$
$967$	−30.2493	−0.972753	−0.486377	+	0.873749i	$0.661682\pi$
$968$	5.61115	0.180349
$969$	−10.0201	−0.321892
$970$	−35.7448	−1.14770
$971$	−6.26895	−0.201180	−0.100590	−	0.994928i	$-0.532073\pi$
$971$	−6.26895	−0.201180	−0.100590	+	0.994928i	$0.532073\pi$
$972$	−66.3339	−2.12766
$973$	−3.43868	−0.110239
$974$	21.5134	0.689334
$975$	79.2770	2.53890
$976$	−12.5070	−0.400339
$977$	10.0272	0.320799	0.160400	−	0.987052i	$-0.448722\pi$
$977$	10.0272	0.320799	0.160400	+	0.987052i	$0.448722\pi$
$978$	5.54828	0.177414
$979$	15.7147	0.502244
$980$	31.0077	0.990505
$981$	5.40159	0.172459
$982$	−78.0561	−2.49087
$983$	−34.8746	−1.11233	−0.556163	−	0.831073i	$-0.687727\pi$
$983$	−34.8746	−1.11233	−0.556163	+	0.831073i	$0.687727\pi$
$984$	40.4108	1.28825
$985$	90.3455	2.87865
$986$	14.6994	0.468124
$987$	−7.67716	−0.244367
$988$	46.8184	1.48949
$989$	9.64709	0.306760
$990$	−69.5615	−2.21081
$991$	−55.1717	−1.75259	−0.876294	−	0.481777i	$-0.839992\pi$
$991$	−55.1717	−1.75259	−0.876294	+	0.481777i	$0.839992\pi$
$992$	−25.4679	−0.808606
$993$	−28.3757	−0.900474
$994$	−35.8765	−1.13793
$995$	61.7394	1.95727
$996$	−65.5571	−2.07726
$997$	0.955539	0.0302622	0.0151311	−	0.999886i	$-0.495183\pi$
$997$	0.955539	0.0302622	0.0151311	+	0.999886i	$0.495183\pi$
$998$	63.8260	2.02038
$999$	0.468039	0.0148081

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6031.2.a.e.1.17	✓	134

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6031.2.a.e.1.17	✓	134	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:	\( N \)	\(=\)	\( 6031 = 37 \cdot 163 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6031.a (trivial)

\(f(q)\)	\(=\)	\(q-2.23037 q^{2} +2.48760 q^{3} +2.97457 q^{4} +3.37158 q^{5} -5.54828 q^{6} -3.17676 q^{7} -2.17365 q^{8} +3.18815 q^{9} +O(q^{10})\)	\(q-2.23037 q^{2} +2.48760 q^{3} +2.97457 q^{4} +3.37158 q^{5} -5.54828 q^{6} -3.17676 q^{7} -2.17365 q^{8} +3.18815 q^{9} -7.51989 q^{10} +2.90148 q^{11} +7.39953 q^{12} +5.00487 q^{13} +7.08536 q^{14} +8.38715 q^{15} -1.10108 q^{16} -1.28083 q^{17} -7.11076 q^{18} +3.14485 q^{19} +10.0290 q^{20} -7.90250 q^{21} -6.47138 q^{22} +1.16024 q^{23} -5.40717 q^{24} +6.36757 q^{25} -11.1627 q^{26} +0.468039 q^{27} -9.44949 q^{28} +5.14553 q^{29} -18.7065 q^{30} -3.74356 q^{31} +6.80312 q^{32} +7.21771 q^{33} +2.85673 q^{34} -10.7107 q^{35} +9.48337 q^{36} +1.00000 q^{37} -7.01420 q^{38} +12.4501 q^{39} -7.32865 q^{40} -7.47355 q^{41} +17.6255 q^{42} +8.31474 q^{43} +8.63064 q^{44} +10.7491 q^{45} -2.58777 q^{46} +0.971484 q^{47} -2.73904 q^{48} +3.09180 q^{49} -14.2021 q^{50} -3.18619 q^{51} +14.8873 q^{52} +5.20496 q^{53} -1.04390 q^{54} +9.78257 q^{55} +6.90517 q^{56} +7.82313 q^{57} -11.4765 q^{58} +5.42144 q^{59} +24.9481 q^{60} +11.3588 q^{61} +8.34953 q^{62} -10.1280 q^{63} -12.9714 q^{64} +16.8743 q^{65} -16.0982 q^{66} -11.8698 q^{67} -3.80991 q^{68} +2.88621 q^{69} +23.8889 q^{70} -5.06347 q^{71} -6.92993 q^{72} +10.7790 q^{73} -2.23037 q^{74} +15.8400 q^{75} +9.35458 q^{76} -9.21729 q^{77} -27.7684 q^{78} -5.14697 q^{79} -3.71238 q^{80} -8.40015 q^{81} +16.6688 q^{82} -8.85962 q^{83} -23.5065 q^{84} -4.31842 q^{85} -18.5450 q^{86} +12.8000 q^{87} -6.30680 q^{88} +5.41610 q^{89} -23.9745 q^{90} -15.8993 q^{91} +3.45121 q^{92} -9.31247 q^{93} -2.16677 q^{94} +10.6031 q^{95} +16.9234 q^{96} +4.75336 q^{97} -6.89588 q^{98} +9.25034 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 134 q + 9 q^{2} + 7 q^{3} + 149 q^{4} + 22 q^{5} + 20 q^{6} + 11 q^{7} + 27 q^{8} + 181 q^{9}+O(q^{10}) \) 134 * q + 9 * q^2 + 7 * q^3 + 149 * q^4 + 22 * q^5 + 20 * q^6 + 11 * q^7 + 27 * q^8 + 181 * q^9	\( 134 q + 9 q^{2} + 7 q^{3} + 149 q^{4} + 22 q^{5} + 20 q^{6} + 11 q^{7} + 27 q^{8} + 181 q^{9} + 15 q^{10} + 20 q^{11} + 28 q^{12} + 11 q^{13} + 17 q^{14} - 13 q^{15} + 143 q^{16} + 76 q^{17} + 23 q^{18} + 15 q^{19} + 67 q^{20} + 63 q^{21} + 2 q^{22} + 22 q^{23} + 33 q^{24} + 160 q^{25} + 65 q^{26} + 31 q^{27} + 10 q^{28} + 73 q^{29} + 20 q^{30} + 10 q^{31} + 53 q^{32} + 72 q^{33} - 7 q^{34} + 52 q^{35} + 201 q^{36} + 134 q^{37} + 70 q^{38} + 6 q^{39} + 11 q^{40} + 182 q^{41} - 15 q^{42} + 12 q^{43} + 33 q^{44} + 29 q^{45} + 24 q^{46} + 80 q^{47} + 21 q^{48} + 229 q^{49} + 37 q^{50} + 57 q^{51} - 15 q^{52} + 75 q^{53} + 95 q^{54} - 9 q^{55} + 39 q^{56} + 19 q^{57} - 21 q^{58} + 91 q^{59} + 62 q^{60} + 58 q^{61} + 108 q^{62} + 9 q^{63} + 167 q^{64} + 76 q^{65} + 105 q^{66} - 17 q^{67} + 109 q^{68} + 48 q^{69} - 55 q^{70} + 56 q^{71} + 48 q^{72} + 54 q^{73} + 9 q^{74} + 28 q^{75} + 82 q^{76} + 156 q^{77} + 16 q^{78} - 2 q^{79} + 98 q^{80} + 270 q^{81} - 42 q^{82} + 130 q^{83} + 229 q^{84} + 22 q^{85} + 72 q^{86} + 22 q^{87} + 61 q^{88} + 157 q^{89} + 176 q^{90} + 31 q^{91} - 18 q^{92} + 36 q^{93} + 83 q^{94} + 98 q^{95} + 111 q^{96} + 35 q^{97} + 53 q^{98} + 55 q^{99}+O(q^{100}) \) 134 * q + 9 * q^2 + 7 * q^3 + 149 * q^4 + 22 * q^5 + 20 * q^6 + 11 * q^7 + 27 * q^8 + 181 * q^9 + 15 * q^10 + 20 * q^11 + 28 * q^12 + 11 * q^13 + 17 * q^14 - 13 * q^15 + 143 * q^16 + 76 * q^17 + 23 * q^18 + 15 * q^19 + 67 * q^20 + 63 * q^21 + 2 * q^22 + 22 * q^23 + 33 * q^24 + 160 * q^25 + 65 * q^26 + 31 * q^27 + 10 * q^28 + 73 * q^29 + 20 * q^30 + 10 * q^31 + 53 * q^32 + 72 * q^33 - 7 * q^34 + 52 * q^35 + 201 * q^36 + 134 * q^37 + 70 * q^38 + 6 * q^39 + 11 * q^40 + 182 * q^41 - 15 * q^42 + 12 * q^43 + 33 * q^44 + 29 * q^45 + 24 * q^46 + 80 * q^47 + 21 * q^48 + 229 * q^49 + 37 * q^50 + 57 * q^51 - 15 * q^52 + 75 * q^53 + 95 * q^54 - 9 * q^55 + 39 * q^56 + 19 * q^57 - 21 * q^58 + 91 * q^59 + 62 * q^60 + 58 * q^61 + 108 * q^62 + 9 * q^63 + 167 * q^64 + 76 * q^65 + 105 * q^66 - 17 * q^67 + 109 * q^68 + 48 * q^69 - 55 * q^70 + 56 * q^71 + 48 * q^72 + 54 * q^73 + 9 * q^74 + 28 * q^75 + 82 * q^76 + 156 * q^77 + 16 * q^78 - 2 * q^79 + 98 * q^80 + 270 * q^81 - 42 * q^82 + 130 * q^83 + 229 * q^84 + 22 * q^85 + 72 * q^86 + 22 * q^87 + 61 * q^88 + 157 * q^89 + 176 * q^90 + 31 * q^91 - 18 * q^92 + 36 * q^93 + 83 * q^94 + 98 * q^95 + 111 * q^96 + 35 * q^97 + 53 * q^98 + 55 * q^99

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