LMFDB - Embedded newform 6019.2.a.e.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6019,2,Mod(1,6019)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6019, 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("6019.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6019 = 13 \cdot 463 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6019.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:	$48.0619569766$
Analytic rank:	$0$
Dimension:	$130$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	6019.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.49278 q^{2} -3.38832 q^{3} +4.21397 q^{4} +3.98474 q^{5} +8.44636 q^{6} +1.44276 q^{7} -5.51896 q^{8} +8.48073 q^{9} +O(q^{10})$	\(q-2.49278 q^{2} -3.38832 q^{3} +4.21397 q^{4} +3.98474 q^{5} +8.44636 q^{6} +1.44276 q^{7} -5.51896 q^{8} +8.48073 q^{9} -9.93310 q^{10} +6.59443 q^{11} -14.2783 q^{12} +1.00000 q^{13} -3.59648 q^{14} -13.5016 q^{15} +5.32963 q^{16} +2.82998 q^{17} -21.1406 q^{18} +6.37631 q^{19} +16.7916 q^{20} -4.88853 q^{21} -16.4385 q^{22} -2.05414 q^{23} +18.7000 q^{24} +10.8782 q^{25} -2.49278 q^{26} -18.5705 q^{27} +6.07974 q^{28} -1.54019 q^{29} +33.6566 q^{30} -5.96786 q^{31} -2.24769 q^{32} -22.3441 q^{33} -7.05454 q^{34} +5.74902 q^{35} +35.7376 q^{36} +3.25237 q^{37} -15.8948 q^{38} -3.38832 q^{39} -21.9916 q^{40} -9.07081 q^{41} +12.1860 q^{42} -3.19391 q^{43} +27.7888 q^{44} +33.7935 q^{45} +5.12054 q^{46} -10.6693 q^{47} -18.0585 q^{48} -4.91845 q^{49} -27.1169 q^{50} -9.58890 q^{51} +4.21397 q^{52} +1.02504 q^{53} +46.2922 q^{54} +26.2771 q^{55} -7.96252 q^{56} -21.6050 q^{57} +3.83935 q^{58} +3.31468 q^{59} -56.8954 q^{60} -4.31294 q^{61} +14.8766 q^{62} +12.2356 q^{63} -5.05624 q^{64} +3.98474 q^{65} +55.6989 q^{66} +1.19567 q^{67} +11.9255 q^{68} +6.96010 q^{69} -14.3311 q^{70} +6.88915 q^{71} -46.8048 q^{72} +13.2455 q^{73} -8.10746 q^{74} -36.8588 q^{75} +26.8696 q^{76} +9.51416 q^{77} +8.44636 q^{78} +5.09326 q^{79} +21.2372 q^{80} +37.4805 q^{81} +22.6116 q^{82} -4.03646 q^{83} -20.6001 q^{84} +11.2768 q^{85} +7.96174 q^{86} +5.21864 q^{87} -36.3944 q^{88} +8.94803 q^{89} -84.2399 q^{90} +1.44276 q^{91} -8.65611 q^{92} +20.2210 q^{93} +26.5963 q^{94} +25.4079 q^{95} +7.61591 q^{96} -9.53667 q^{97} +12.2606 q^{98} +55.9256 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 130 q + 10 q^{2} + 11 q^{3} + 146 q^{4} + 40 q^{5} + 4 q^{6} + 8 q^{7} + 24 q^{8} + 181 q^{9}+O(q^{10}) $ 130 * q + 10 * q^2 + 11 * q^3 + 146 * q^4 + 40 * q^5 + 4 * q^6 + 8 * q^7 + 24 * q^8 + 181 * q^9	\( 130 q + 10 q^{2} + 11 q^{3} + 146 q^{4} + 40 q^{5} + 4 q^{6} + 8 q^{7} + 24 q^{8} + 181 q^{9} + 5 q^{10} + 43 q^{11} + 28 q^{12} + 130 q^{13} + 47 q^{14} + 29 q^{15} + 170 q^{16} + 85 q^{17} + 20 q^{18} + 3 q^{19} + 73 q^{20} + 62 q^{21} + 12 q^{22} + 62 q^{23} - 5 q^{24} + 178 q^{25} + 10 q^{26} + 35 q^{27} - q^{28} + 134 q^{29} + 24 q^{30} + 14 q^{31} + 48 q^{32} + 4 q^{33} + 4 q^{34} + 50 q^{35} + 244 q^{36} + 32 q^{37} + 76 q^{38} + 11 q^{39} - 6 q^{40} + 48 q^{41} + 9 q^{42} + 34 q^{43} + 123 q^{44} + 115 q^{45} + 5 q^{46} + 25 q^{47} + 35 q^{48} + 210 q^{49} + 24 q^{50} + 20 q^{51} + 146 q^{52} + 193 q^{53} - 39 q^{54} + 32 q^{55} + 122 q^{56} + 7 q^{57} - 4 q^{58} + 50 q^{59} + 42 q^{60} + 57 q^{61} + 51 q^{62} + 8 q^{63} + 172 q^{64} + 40 q^{65} - 4 q^{66} + 21 q^{67} + 132 q^{68} + 92 q^{69} - 46 q^{70} + 58 q^{71} - 26 q^{72} + 15 q^{73} + 120 q^{74} + 23 q^{75} - 65 q^{76} + 192 q^{77} + 4 q^{78} + 32 q^{79} + 66 q^{80} + 326 q^{81} + 11 q^{82} + 33 q^{83} + 5 q^{84} + 43 q^{85} + 105 q^{86} + 31 q^{87} - 17 q^{88} + 84 q^{89} - 73 q^{90} + 8 q^{91} + 161 q^{92} + 52 q^{93} + 4 q^{94} + 59 q^{95} - 77 q^{96} + 9 q^{97} - 61 q^{98} + 100 q^{99}+O(q^{100}) \) 130 * q + 10 * q^2 + 11 * q^3 + 146 * q^4 + 40 * q^5 + 4 * q^6 + 8 * q^7 + 24 * q^8 + 181 * q^9 + 5 * q^10 + 43 * q^11 + 28 * q^12 + 130 * q^13 + 47 * q^14 + 29 * q^15 + 170 * q^16 + 85 * q^17 + 20 * q^18 + 3 * q^19 + 73 * q^20 + 62 * q^21 + 12 * q^22 + 62 * q^23 - 5 * q^24 + 178 * q^25 + 10 * q^26 + 35 * q^27 - q^28 + 134 * q^29 + 24 * q^30 + 14 * q^31 + 48 * q^32 + 4 * q^33 + 4 * q^34 + 50 * q^35 + 244 * q^36 + 32 * q^37 + 76 * q^38 + 11 * q^39 - 6 * q^40 + 48 * q^41 + 9 * q^42 + 34 * q^43 + 123 * q^44 + 115 * q^45 + 5 * q^46 + 25 * q^47 + 35 * q^48 + 210 * q^49 + 24 * q^50 + 20 * q^51 + 146 * q^52 + 193 * q^53 - 39 * q^54 + 32 * q^55 + 122 * q^56 + 7 * q^57 - 4 * q^58 + 50 * q^59 + 42 * q^60 + 57 * q^61 + 51 * q^62 + 8 * q^63 + 172 * q^64 + 40 * q^65 - 4 * q^66 + 21 * q^67 + 132 * q^68 + 92 * q^69 - 46 * q^70 + 58 * q^71 - 26 * q^72 + 15 * q^73 + 120 * q^74 + 23 * q^75 - 65 * q^76 + 192 * q^77 + 4 * q^78 + 32 * q^79 + 66 * q^80 + 326 * q^81 + 11 * q^82 + 33 * q^83 + 5 * q^84 + 43 * q^85 + 105 * q^86 + 31 * q^87 - 17 * q^88 + 84 * q^89 - 73 * q^90 + 8 * q^91 + 161 * q^92 + 52 * q^93 + 4 * q^94 + 59 * q^95 - 77 * q^96 + 9 * q^97 - 61 * q^98 + 100 * 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 $

$2$	−2.49278	−1.76266	−0.881332	−	0.472497i	$-0.843353\pi$
$2$	−2.49278	−1.76266	−0.881332	+	0.472497i	$0.843353\pi$
$3$	−3.38832	−1.95625	−0.978124	−	0.208021i	$-0.933298\pi$
$3$	−3.38832	−1.95625	−0.978124	+	0.208021i	$0.933298\pi$
$4$	4.21397	2.10699
$5$	3.98474	1.78203	0.891016	−	0.453973i	$-0.149994\pi$
$5$	3.98474	1.78203	0.891016	+	0.453973i	$0.149994\pi$
$6$	8.44636	3.44821
$7$	1.44276	0.545311	0.272656	−	0.962112i	$-0.412098\pi$
$7$	1.44276	0.545311	0.272656	+	0.962112i	$0.412098\pi$
$8$	−5.51896	−1.95125
$9$	8.48073	2.82691
$10$	−9.93310	−3.14112
$11$	6.59443	1.98830	0.994148	−	0.108027i	$-0.0344532\pi$
$11$	6.59443	1.98830	0.994148	+	0.108027i	$0.0344532\pi$
$12$	−14.2783	−4.12179
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−3.59648	−0.961200
$15$	−13.5016	−3.48610
$16$	5.32963	1.33241
$17$	2.82998	0.686372	0.343186	−	0.939267i	$-0.388494\pi$
$17$	2.82998	0.686372	0.343186	+	0.939267i	$0.388494\pi$
$18$	−21.1406	−4.98289
$19$	6.37631	1.46282	0.731412	−	0.681935i	$-0.238861\pi$
$19$	6.37631	1.46282	0.731412	+	0.681935i	$0.238861\pi$
$20$	16.7916	3.75472
$21$	−4.88853	−1.06676
$22$	−16.4385	−3.50470
$23$	−2.05414	−0.428319	−0.214159	−	0.976799i	$-0.568701\pi$
$23$	−2.05414	−0.428319	−0.214159	+	0.976799i	$0.568701\pi$
$24$	18.7000	3.81712
$25$	10.8782	2.17563
$26$	−2.49278	−0.488875
$27$	−18.5705	−3.57389
$28$	6.07974	1.14896
$29$	−1.54019	−0.286005	−0.143003	−	0.989722i	$-0.545676\pi$
$29$	−1.54019	−0.286005	−0.143003	+	0.989722i	$0.545676\pi$
$30$	33.6566	6.14482
$31$	−5.96786	−1.07186	−0.535929	−	0.844263i	$-0.680039\pi$
$31$	−5.96786	−1.07186	−0.535929	+	0.844263i	$0.680039\pi$
$32$	−2.24769	−0.397340
$33$	−22.3441	−3.88960
$34$	−7.05454	−1.20984
$35$	5.74902	0.971761
$36$	35.7376	5.95626
$37$	3.25237	0.534687	0.267343	−	0.963601i	$-0.413854\pi$
$37$	3.25237	0.534687	0.267343	+	0.963601i	$0.413854\pi$
$38$	−15.8948	−2.57847
$39$	−3.38832	−0.542566
$40$	−21.9916	−3.47718
$41$	−9.07081	−1.41662	−0.708312	−	0.705900i	$-0.750543\pi$
$41$	−9.07081	−1.41662	−0.708312	+	0.705900i	$0.750543\pi$
$42$	12.1860	1.88035
$43$	−3.19391	−0.487067	−0.243534	−	0.969892i	$-0.578307\pi$
$43$	−3.19391	−0.487067	−0.243534	+	0.969892i	$0.578307\pi$
$44$	27.7888	4.18931
$45$	33.7935	5.03764
$46$	5.12054	0.754982
$47$	−10.6693	−1.55628	−0.778140	−	0.628091i	$-0.783836\pi$
$47$	−10.6693	−1.55628	−0.778140	+	0.628091i	$0.783836\pi$
$48$	−18.0585	−2.60652
$49$	−4.91845	−0.702636
$50$	−27.1169	−3.83491
$51$	−9.58890	−1.34271
$52$	4.21397	0.584373
$53$	1.02504	0.140800	0.0704001	−	0.997519i	$-0.477572\pi$
$53$	1.02504	0.140800	0.0704001	+	0.997519i	$0.477572\pi$
$54$	46.2922	6.29957
$55$	26.2771	3.54321
$56$	−7.96252	−1.06404
$57$	−21.6050	−2.86165
$58$	3.83935	0.504131
$59$	3.31468	0.431534	0.215767	−	0.976445i	$-0.430775\pi$
$59$	3.31468	0.431534	0.215767	+	0.976445i	$0.430775\pi$
$60$	−56.8954	−7.34516
$61$	−4.31294	−0.552216	−0.276108	−	0.961127i	$-0.589045\pi$
$61$	−4.31294	−0.552216	−0.276108	+	0.961127i	$0.589045\pi$
$62$	14.8766	1.88933
$63$	12.2356	1.54154
$64$	−5.05624	−0.632030
$65$	3.98474	0.494246
$66$	55.6989	6.85606
$67$	1.19567	0.146075	0.0730374	−	0.997329i	$-0.476731\pi$
$67$	1.19567	0.146075	0.0730374	+	0.997329i	$0.476731\pi$
$68$	11.9255	1.44618
$69$	6.96010	0.837898
$70$	−14.3311	−1.71289
$71$	6.88915	0.817592	0.408796	−	0.912626i	$-0.365949\pi$
$71$	6.88915	0.817592	0.408796	+	0.912626i	$0.365949\pi$
$72$	−46.8048	−5.51600
$73$	13.2455	1.55027	0.775136	−	0.631794i	$-0.217681\pi$
$73$	13.2455	1.55027	0.775136	+	0.631794i	$0.217681\pi$
$74$	−8.10746	−0.942473
$75$	−36.8588	−4.25608
$76$	26.8696	3.08215
$77$	9.51416	1.08424
$78$	8.44636	0.956362
$79$	5.09326	0.573036	0.286518	−	0.958075i	$-0.407502\pi$
$79$	5.09326	0.573036	0.286518	+	0.958075i	$0.407502\pi$
$80$	21.2372	2.37439
$81$	37.4805	4.16450
$82$	22.6116	2.49703
$83$	−4.03646	−0.443059	−0.221530	−	0.975154i	$-0.571105\pi$
$83$	−4.03646	−0.443059	−0.221530	+	0.975154i	$0.571105\pi$
$84$	−20.6001	−2.24766
$85$	11.2768	1.22314
$86$	7.96174	0.858536
$87$	5.21864	0.559497
$88$	−36.3944	−3.87966
$89$	8.94803	0.948490	0.474245	−	0.880393i	$-0.342721\pi$
$89$	8.94803	0.948490	0.474245	+	0.880393i	$0.342721\pi$
$90$	−84.2399	−8.87967
$91$	1.44276	0.151242
$92$	−8.65611	−0.902462
$93$	20.2210	2.09682
$94$	26.5963	2.74320
$95$	25.4079	2.60680
$96$	7.61591	0.777295
$97$	−9.53667	−0.968302	−0.484151	−	0.874984i	$-0.660871\pi$
$97$	−9.53667	−0.968302	−0.484151	+	0.874984i	$0.660871\pi$
$98$	12.2606	1.23851
$99$	55.9256	5.62073
$100$	45.8403	4.58403
$101$	10.7250	1.06718	0.533591	−	0.845743i	$-0.320842\pi$
$101$	10.7250	1.06718	0.533591	+	0.845743i	$0.320842\pi$
$102$	23.9031	2.36675
$103$	−1.49511	−0.147318	−0.0736590	−	0.997283i	$-0.523468\pi$
$103$	−1.49511	−0.147318	−0.0736590	+	0.997283i	$0.523468\pi$
$104$	−5.51896	−0.541178
$105$	−19.4795	−1.90101
$106$	−2.55521	−0.248184
$107$	−9.27286	−0.896441	−0.448221	−	0.893923i	$-0.647942\pi$
$107$	−9.27286	−0.896441	−0.448221	+	0.893923i	$0.647942\pi$
$108$	−78.2555	−7.53013
$109$	10.5049	1.00618	0.503091	−	0.864233i	$-0.332196\pi$
$109$	10.5049	1.00618	0.503091	+	0.864233i	$0.332196\pi$
$110$	−65.5032	−6.24548
$111$	−11.0201	−1.04598
$112$	7.68936	0.726576
$113$	1.26612	0.119107	0.0595533	−	0.998225i	$-0.481032\pi$
$113$	1.26612	0.119107	0.0595533	+	0.998225i	$0.481032\pi$
$114$	53.8566	5.04413
$115$	−8.18523	−0.763277
$116$	−6.49030	−0.602609
$117$	8.48073	0.784043
$118$	−8.26277	−0.760650
$119$	4.08298	0.374286
$120$	74.5147	6.80223
$121$	32.4865	2.95332
$122$	10.7512	0.973371
$123$	30.7348	2.77127
$124$	−25.1484	−2.25839
$125$	23.4230	2.09502
$126$	−30.5008	−2.71723
$127$	−10.0479	−0.891608	−0.445804	−	0.895131i	$-0.647082\pi$
$127$	−10.0479	−0.891608	−0.445804	+	0.895131i	$0.647082\pi$
$128$	17.0995	1.51140
$129$	10.8220	0.952825
$130$	−9.93310	−0.871191
$131$	−17.7152	−1.54778	−0.773891	−	0.633319i	$-0.781692\pi$
$131$	−17.7152	−1.54778	−0.773891	+	0.633319i	$0.781692\pi$
$132$	−94.1573	−8.19534
$133$	9.19946	0.797695
$134$	−2.98056	−0.257481
$135$	−73.9985	−6.36878
$136$	−15.6186	−1.33928
$137$	6.06215	0.517925	0.258962	−	0.965887i	$-0.416619\pi$
$137$	6.06215	0.517925	0.258962	+	0.965887i	$0.416619\pi$
$138$	−17.3500	−1.47693
$139$	−22.7294	−1.92788	−0.963942	−	0.266112i	$-0.914261\pi$
$139$	−22.7294	−1.92788	−0.963942	+	0.266112i	$0.914261\pi$
$140$	24.2262	2.04749
$141$	36.1511	3.04447
$142$	−17.1732	−1.44114
$143$	6.59443	0.551454
$144$	45.1991	3.76659
$145$	−6.13724	−0.509670
$146$	−33.0182	−2.73261
$147$	16.6653	1.37453
$148$	13.7054	1.12658
$149$	11.9933	0.982532	0.491266	−	0.871009i	$-0.336534\pi$
$149$	11.9933	0.982532	0.491266	+	0.871009i	$0.336534\pi$
$150$	91.8809	7.50205
$151$	15.1326	1.23148	0.615738	−	0.787951i	$-0.288858\pi$
$151$	15.1326	1.23148	0.615738	+	0.787951i	$0.288858\pi$
$152$	−35.1906	−2.85433
$153$	24.0003	1.94031
$154$	−23.7168	−1.91115
$155$	−23.7804	−1.91009
$156$	−14.2783	−1.14318
$157$	2.39354	0.191026	0.0955128	−	0.995428i	$-0.469551\pi$
$157$	2.39354	0.191026	0.0955128	+	0.995428i	$0.469551\pi$
$158$	−12.6964	−1.01007
$159$	−3.47317	−0.275440
$160$	−8.95648	−0.708072
$161$	−2.96363	−0.233567
$162$	−93.4309	−7.34063
$163$	8.58739	0.672617	0.336308	−	0.941752i	$-0.390822\pi$
$163$	8.58739	0.672617	0.336308	+	0.941752i	$0.390822\pi$
$164$	−38.2242	−2.98481
$165$	−89.0353	−6.93139
$166$	10.0620	0.780964
$167$	21.4151	1.65715	0.828575	−	0.559879i	$-0.189152\pi$
$167$	21.4151	1.65715	0.828575	+	0.559879i	$0.189152\pi$
$168$	26.9796	2.08152
$169$	1.00000	0.0769231
$170$	−28.1105	−2.15598
$171$	54.0757	4.13527
$172$	−13.4591	−1.02624
$173$	−15.1522	−1.15200	−0.576002	−	0.817449i	$-0.695388\pi$
$173$	−15.1522	−1.15200	−0.576002	+	0.817449i	$0.695388\pi$
$174$	−13.0090	−0.986206
$175$	15.6946	1.18640
$176$	35.1459	2.64922
$177$	−11.2312	−0.844188
$178$	−22.3055	−1.67187
$179$	−8.46858	−0.632971	−0.316486	−	0.948597i	$-0.602503\pi$
$179$	−8.46858	−0.632971	−0.316486	+	0.948597i	$0.602503\pi$
$180$	142.405	10.6142
$181$	8.53674	0.634531	0.317265	−	0.948337i	$-0.397235\pi$
$181$	8.53674	0.634531	0.317265	+	0.948337i	$0.397235\pi$
$182$	−3.59648	−0.266589
$183$	14.6136	1.08027
$184$	11.3367	0.835755
$185$	12.9599	0.952828
$186$	−50.4066	−3.69599
$187$	18.6621	1.36471
$188$	−44.9602	−3.27906
$189$	−26.7927	−1.94888
$190$	−63.3365	−4.59491
$191$	20.3010	1.46893	0.734464	−	0.678648i	$-0.237434\pi$
$191$	20.3010	1.46893	0.734464	+	0.678648i	$0.237434\pi$
$192$	17.1322	1.23641
$193$	4.38213	0.315432	0.157716	−	0.987484i	$-0.449587\pi$
$193$	4.38213	0.315432	0.157716	+	0.987484i	$0.449587\pi$
$194$	23.7729	1.70679
$195$	−13.5016	−0.966869
$196$	−20.7262	−1.48044
$197$	−12.4745	−0.888771	−0.444386	−	0.895836i	$-0.646578\pi$
$197$	−12.4745	−0.888771	−0.444386	+	0.895836i	$0.646578\pi$
$198$	−139.410	−9.90746
$199$	−18.6701	−1.32349	−0.661744	−	0.749730i	$-0.730183\pi$
$199$	−18.6701	−1.32349	−0.661744	+	0.749730i	$0.730183\pi$
$200$	−60.0362	−4.24520
$201$	−4.05133	−0.285759
$202$	−26.7352	−1.88108
$203$	−2.22211	−0.155962
$204$	−40.4074	−2.82908
$205$	−36.1449	−2.52447
$206$	3.72700	0.259672
$207$	−17.4206	−1.21082
$208$	5.32963	0.369543
$209$	42.0481	2.90853
$210$	48.5582	3.35084
$211$	6.80183	0.468258	0.234129	−	0.972206i	$-0.424776\pi$
$211$	6.80183	0.468258	0.234129	+	0.972206i	$0.424776\pi$
$212$	4.31950	0.296664
$213$	−23.3427	−1.59941
$214$	23.1152	1.58013
$215$	−12.7269	−0.867969
$216$	102.490	6.97354
$217$	−8.61017	−0.584496
$218$	−26.1863	−1.77356
$219$	−44.8801	−3.03272
$220$	110.731	7.46549
$221$	2.82998	0.190365
$222$	27.4707	1.84371
$223$	−0.317178	−0.0212398	−0.0106199	−	0.999944i	$-0.503380\pi$
$223$	−0.317178	−0.0212398	−0.0106199	+	0.999944i	$0.503380\pi$
$224$	−3.24288	−0.216674
$225$	92.2548	6.15032
$226$	−3.15617	−0.209945
$227$	5.63366	0.373919	0.186960	−	0.982368i	$-0.440137\pi$
$227$	5.63366	0.373919	0.186960	+	0.982368i	$0.440137\pi$
$228$	−91.0428	−6.02946
$229$	−27.3015	−1.80413	−0.902066	−	0.431598i	$-0.857950\pi$
$229$	−27.3015	−1.80413	−0.902066	+	0.431598i	$0.857950\pi$
$230$	20.4040	1.34540
$231$	−32.2371	−2.12104
$232$	8.50022	0.558067
$233$	−9.90457	−0.648870	−0.324435	−	0.945908i	$-0.605174\pi$
$233$	−9.90457	−0.648870	−0.324435	+	0.945908i	$0.605174\pi$
$234$	−21.1406	−1.38201
$235$	−42.5145	−2.77334
$236$	13.9680	0.909236
$237$	−17.2576	−1.12100
$238$	−10.1780	−0.659741
$239$	26.9508	1.74330	0.871652	−	0.490125i	$-0.163049\pi$
$239$	26.9508	1.74330	0.871652	+	0.490125i	$0.163049\pi$
$240$	−71.9584	−4.64490
$241$	13.2632	0.854357	0.427179	−	0.904167i	$-0.359508\pi$
$241$	13.2632	0.854357	0.427179	+	0.904167i	$0.359508\pi$
$242$	−80.9819	−5.20571
$243$	−71.2847	−4.57292
$244$	−18.1746	−1.16351
$245$	−19.5988	−1.25212
$246$	−76.6153	−4.88482
$247$	6.37631	0.405715
$248$	32.9364	2.09146
$249$	13.6768	0.866734
$250$	−58.3885	−3.69281
$251$	−1.77879	−0.112276	−0.0561380	−	0.998423i	$-0.517879\pi$
$251$	−1.77879	−0.112276	−0.0561380	+	0.998423i	$0.517879\pi$
$252$	51.5606	3.24801
$253$	−13.5459	−0.851624
$254$	25.0473	1.57161
$255$	−38.2093	−2.39276
$256$	−32.5129	−2.03206
$257$	−0.921307	−0.0574695	−0.0287348	−	0.999587i	$-0.509148\pi$
$257$	−0.921307	−0.0574695	−0.0287348	+	0.999587i	$0.509148\pi$
$258$	−26.9769	−1.67951
$259$	4.69238	0.291571
$260$	16.7916	1.04137
$261$	−13.0619	−0.808511
$262$	44.1601	2.72822
$263$	−6.44605	−0.397480	−0.198740	−	0.980052i	$-0.563685\pi$
$263$	−6.44605	−0.397480	−0.198740	+	0.980052i	$0.563685\pi$
$264$	123.316	7.58957
$265$	4.08453	0.250910
$266$	−22.9323	−1.40607
$267$	−30.3188	−1.85548
$268$	5.03854	0.307778
$269$	12.6296	0.770042	0.385021	−	0.922908i	$-0.374194\pi$
$269$	12.6296	0.770042	0.385021	+	0.922908i	$0.374194\pi$
$270$	184.462	11.2260
$271$	17.0025	1.03283	0.516415	−	0.856338i	$-0.327266\pi$
$271$	17.0025	1.03283	0.516415	+	0.856338i	$0.327266\pi$
$272$	15.0828	0.914527
$273$	−4.88853	−0.295867
$274$	−15.1116	−0.912928
$275$	71.7354	4.32581
$276$	29.3297	1.76544
$277$	−7.76024	−0.466267	−0.233134	−	0.972445i	$-0.574898\pi$
$277$	−7.76024	−0.466267	−0.233134	+	0.972445i	$0.574898\pi$
$278$	56.6595	3.39821
$279$	−50.6118	−3.03005
$280$	−31.7286	−1.89615
$281$	21.3649	1.27452	0.637261	−	0.770648i	$-0.280067\pi$
$281$	21.3649	1.27452	0.637261	+	0.770648i	$0.280067\pi$
$282$	−90.1168	−5.36638
$283$	27.9652	1.66236	0.831178	−	0.556007i	$-0.187667\pi$
$283$	27.9652	1.66236	0.831178	+	0.556007i	$0.187667\pi$
$284$	29.0307	1.72266
$285$	−86.0903	−5.09955
$286$	−16.4385	−0.972029
$287$	−13.0870	−0.772500
$288$	−19.0621	−1.12324
$289$	−8.99119	−0.528894
$290$	15.2988	0.898378
$291$	32.3133	1.89424
$292$	55.8163	3.26640
$293$	4.25286	0.248455	0.124227	−	0.992254i	$-0.460355\pi$
$293$	4.25286	0.248455	0.124227	+	0.992254i	$0.460355\pi$
$294$	−41.5430	−2.42284
$295$	13.2081	0.769007
$296$	−17.9497	−1.04331
$297$	−122.462	−7.10595
$298$	−29.8968	−1.73188
$299$	−2.05414	−0.118794
$300$	−155.322	−8.96751
$301$	−4.60804	−0.265603
$302$	−37.7224	−2.17068
$303$	−36.3399	−2.08767
$304$	33.9833	1.94908
$305$	−17.1860	−0.984066
$306$	−59.8276	−3.42012
$307$	−16.3469	−0.932965	−0.466482	−	0.884531i	$-0.654479\pi$
$307$	−16.3469	−0.932965	−0.466482	+	0.884531i	$0.654479\pi$
$308$	40.0924	2.28448
$309$	5.06593	0.288191
$310$	59.2793	3.36684
$311$	−1.11684	−0.0633304	−0.0316652	−	0.999499i	$-0.510081\pi$
$311$	−1.11684	−0.0633304	−0.0316652	+	0.999499i	$0.510081\pi$
$312$	18.7000	1.05868
$313$	9.65432	0.545695	0.272847	−	0.962057i	$-0.412035\pi$
$313$	9.65432	0.545695	0.272847	+	0.962057i	$0.412035\pi$
$314$	−5.96659	−0.336714
$315$	48.7558	2.74708
$316$	21.4629	1.20738
$317$	12.8431	0.721340	0.360670	−	0.932693i	$-0.382548\pi$
$317$	12.8431	0.721340	0.360670	+	0.932693i	$0.382548\pi$
$318$	8.65787	0.485509
$319$	−10.1566	−0.568663
$320$	−20.1478	−1.12630
$321$	31.4194	1.75366
$322$	7.38769	0.411700
$323$	18.0448	1.00404
$324$	157.942	8.77456
$325$	10.8782	0.603412
$326$	−21.4065	−1.18560
$327$	−35.5938	−1.96834
$328$	50.0615	2.76418
$329$	−15.3932	−0.848656
$330$	221.946	12.2177
$331$	14.1019	0.775110	0.387555	−	0.921847i	$-0.373320\pi$
$331$	14.1019	0.775110	0.387555	+	0.921847i	$0.373320\pi$
$332$	−17.0095	−0.933520
$333$	27.5825	1.51151
$334$	−53.3832	−2.92100
$335$	4.76446	0.260310
$336$	−26.0540	−1.42136
$337$	19.5119	1.06288	0.531442	−	0.847095i	$-0.321651\pi$
$337$	19.5119	1.06288	0.531442	+	0.847095i	$0.321651\pi$
$338$	−2.49278	−0.135590
$339$	−4.29003	−0.233002
$340$	47.5200	2.57713
$341$	−39.3546	−2.13117
$342$	−134.799	−7.28910
$343$	−17.1954	−0.928466
$344$	17.6271	0.950389
$345$	27.7342	1.49316
$346$	37.7713	2.03060
$347$	0.315450	0.0169343	0.00846713	−	0.999964i	$-0.497305\pi$
$347$	0.315450	0.0169343	0.00846713	+	0.999964i	$0.497305\pi$
$348$	21.9912	1.17885
$349$	9.42431	0.504472	0.252236	−	0.967666i	$-0.418834\pi$
$349$	9.42431	0.504472	0.252236	+	0.967666i	$0.418834\pi$
$350$	−39.1232	−2.09122
$351$	−18.5705	−0.991218
$352$	−14.8223	−0.790029
$353$	27.2936	1.45269	0.726346	−	0.687329i	$-0.241217\pi$
$353$	27.2936	1.45269	0.726346	+	0.687329i	$0.241217\pi$
$354$	27.9969	1.48802
$355$	27.4515	1.45697
$356$	37.7068	1.99846
$357$	−13.8345	−0.732197
$358$	21.1103	1.11572
$359$	15.3691	0.811151	0.405576	−	0.914061i	$-0.367071\pi$
$359$	15.3691	0.811151	0.405576	+	0.914061i	$0.367071\pi$
$360$	−186.505	−9.82968
$361$	21.6573	1.13986
$362$	−21.2802	−1.11846
$363$	−110.075	−5.77743
$364$	6.07974	0.318665
$365$	52.7800	2.76263
$366$	−36.4286	−1.90416
$367$	−27.0763	−1.41337	−0.706686	−	0.707527i	$-0.749811\pi$
$367$	−27.0763	−1.41337	−0.706686	+	0.707527i	$0.749811\pi$
$368$	−10.9478	−0.570695
$369$	−76.9271	−4.00466
$370$	−32.3062	−1.67952
$371$	1.47889	0.0767799
$372$	85.2108	4.41798
$373$	−4.16591	−0.215703	−0.107851	−	0.994167i	$-0.534397\pi$
$373$	−4.16591	−0.215703	−0.107851	+	0.994167i	$0.534397\pi$
$374$	−46.5207	−2.40553
$375$	−79.3647	−4.09838
$376$	58.8835	3.03668
$377$	−1.54019	−0.0793236
$378$	66.7884	3.43522
$379$	−24.0134	−1.23349	−0.616743	−	0.787164i	$-0.711548\pi$
$379$	−24.0134	−1.23349	−0.616743	+	0.787164i	$0.711548\pi$
$380$	107.068	5.49249
$381$	34.0456	1.74421
$382$	−50.6060	−2.58923
$383$	24.7571	1.26503	0.632514	−	0.774549i	$-0.282023\pi$
$383$	24.7571	1.26503	0.632514	+	0.774549i	$0.282023\pi$
$384$	−57.9386	−2.95667
$385$	37.9115	1.93215
$386$	−10.9237	−0.556002
$387$	−27.0867	−1.37689
$388$	−40.1873	−2.04020
$389$	25.2390	1.27967	0.639833	−	0.768514i	$-0.279003\pi$
$389$	25.2390	1.27967	0.639833	+	0.768514i	$0.279003\pi$
$390$	33.6566	1.70427
$391$	−5.81319	−0.293986
$392$	27.1447	1.37102
$393$	60.0247	3.02785
$394$	31.0962	1.56661
$395$	20.2953	1.02117
$396$	235.669	11.8428
$397$	13.1992	0.662448	0.331224	−	0.943552i	$-0.392538\pi$
$397$	13.1992	0.662448	0.331224	+	0.943552i	$0.392538\pi$
$398$	46.5405	2.33286
$399$	−31.1707	−1.56049
$400$	57.9766	2.89883
$401$	33.0991	1.65289	0.826445	−	0.563018i	$-0.190360\pi$
$401$	33.0991	1.65289	0.826445	+	0.563018i	$0.190360\pi$
$402$	10.0991	0.503697
$403$	−5.96786	−0.297280
$404$	45.1951	2.24854
$405$	149.350	7.42128
$406$	5.53925	0.274908
$407$	21.4475	1.06312
$408$	52.9207	2.61997
$409$	9.45905	0.467720	0.233860	−	0.972270i	$-0.424864\pi$
$409$	9.45905	0.467720	0.233860	+	0.972270i	$0.424864\pi$
$410$	90.1013	4.44979
$411$	−20.5405	−1.01319
$412$	−6.30037	−0.310397
$413$	4.78227	0.235320
$414$	43.4259	2.13427
$415$	−16.0843	−0.789545
$416$	−2.24769	−0.110202
$417$	77.0146	3.77142
$418$	−104.817	−5.12676
$419$	−1.38131	−0.0674816	−0.0337408	−	0.999431i	$-0.510742\pi$
$419$	−1.38131	−0.0674816	−0.0337408	+	0.999431i	$0.510742\pi$
$420$	−82.0862	−4.00540
$421$	−36.3285	−1.77054	−0.885271	−	0.465076i	$-0.846027\pi$
$421$	−36.3285	−1.77054	−0.885271	+	0.465076i	$0.846027\pi$
$422$	−16.9555	−0.825381
$423$	−90.4835	−4.39946
$424$	−5.65716	−0.274736
$425$	30.7851	1.49329
$426$	58.1882	2.81923
$427$	−6.22253	−0.301129
$428$	−39.0756	−1.88879
$429$	−22.3441	−1.07878
$430$	31.7255	1.52994
$431$	−14.8392	−0.714777	−0.357389	−	0.933956i	$-0.616333\pi$
$431$	−14.8392	−0.714777	−0.357389	+	0.933956i	$0.616333\pi$
$432$	−98.9737	−4.76187
$433$	−24.1228	−1.15927	−0.579635	−	0.814876i	$-0.696805\pi$
$433$	−24.1228	−1.15927	−0.579635	+	0.814876i	$0.696805\pi$
$434$	21.4633	1.03027
$435$	20.7950	0.997042
$436$	44.2672	2.12001
$437$	−13.0978	−0.626555
$438$	111.876	5.34566
$439$	−6.32488	−0.301870	−0.150935	−	0.988544i	$-0.548228\pi$
$439$	−6.32488	−0.301870	−0.150935	+	0.988544i	$0.548228\pi$
$440$	−145.022	−6.91367
$441$	−41.7120	−1.98629
$442$	−7.05454	−0.335550
$443$	−39.2485	−1.86475	−0.932377	−	0.361488i	$-0.882269\pi$
$443$	−39.2485	−1.86475	−0.932377	+	0.361488i	$0.882269\pi$
$444$	−46.4383	−2.20387
$445$	35.6556	1.69024
$446$	0.790657	0.0374387
$447$	−40.6373	−1.92208
$448$	−7.29493	−0.344653
$449$	28.8019	1.35925	0.679623	−	0.733561i	$-0.262143\pi$
$449$	28.8019	1.35925	0.679623	+	0.733561i	$0.262143\pi$
$450$	−229.971	−10.8410
$451$	−59.8169	−2.81667
$452$	5.33540	0.250956
$453$	−51.2743	−2.40908
$454$	−14.0435	−0.659095
$455$	5.74902	0.269518
$456$	119.237	5.58378
$457$	18.6992	0.874710	0.437355	−	0.899289i	$-0.355915\pi$
$457$	18.6992	0.874710	0.437355	+	0.899289i	$0.355915\pi$
$458$	68.0567	3.18008
$459$	−52.5541	−2.45302
$460$	−34.4924	−1.60821
$461$	−30.7939	−1.43422	−0.717108	−	0.696962i	$-0.754535\pi$
$461$	−30.7939	−1.43422	−0.717108	+	0.696962i	$0.754535\pi$
$462$	80.3600	3.73869
$463$	−1.00000	−0.0464739
$463$	−1.00000	−0.0464739
$464$	−8.20861	−0.381075
$465$	80.5756	3.73660
$466$	24.6900	1.14374
$467$	27.9992	1.29565	0.647823	−	0.761791i	$-0.275679\pi$
$467$	27.9992	1.29565	0.647823	+	0.761791i	$0.275679\pi$
$468$	35.7376	1.65197
$469$	1.72507	0.0796562
$470$	105.979	4.88846
$471$	−8.11010	−0.373694
$472$	−18.2936	−0.842029
$473$	−21.0620	−0.968434
$474$	43.0195	1.97595
$475$	69.3626	3.18257
$476$	17.2056	0.788616
$477$	8.69310	0.398030
$478$	−67.1826	−3.07286
$479$	−23.3114	−1.06513	−0.532564	−	0.846390i	$-0.678771\pi$
$479$	−23.3114	−1.06513	−0.532564	+	0.846390i	$0.678771\pi$
$480$	30.3474	1.38516
$481$	3.25237	0.148295
$482$	−33.0623	−1.50595
$483$	10.0417	0.456915
$484$	136.897	6.22261
$485$	−38.0012	−1.72554
$486$	177.698	8.06052
$487$	11.0541	0.500908	0.250454	−	0.968129i	$-0.419420\pi$
$487$	11.0541	0.500908	0.250454	+	0.968129i	$0.419420\pi$
$488$	23.8030	1.07751
$489$	−29.0969	−1.31581
$490$	48.8555	2.20707
$491$	−23.5632	−1.06339	−0.531696	−	0.846935i	$-0.678445\pi$
$491$	−23.5632	−1.06339	−0.531696	+	0.846935i	$0.678445\pi$
$492$	129.516	5.83902
$493$	−4.35870	−0.196306
$494$	−15.8948	−0.715139
$495$	222.849	10.0163
$496$	−31.8064	−1.42815
$497$	9.93937	0.445842
$498$	−34.0934	−1.52776
$499$	10.0244	0.448754	0.224377	−	0.974502i	$-0.427965\pi$
$499$	10.0244	0.448754	0.224377	+	0.974502i	$0.427965\pi$
$500$	98.7039	4.41417
$501$	−72.5612	−3.24180
$502$	4.43413	0.197905
$503$	6.85518	0.305657	0.152829	−	0.988253i	$-0.451162\pi$
$503$	6.85518	0.305657	0.152829	+	0.988253i	$0.451162\pi$
$504$	−67.5279	−3.00793
$505$	42.7366	1.90175
$506$	33.7670	1.50113
$507$	−3.38832	−0.150481
$508$	−42.3416	−1.87861
$509$	15.5528	0.689364	0.344682	−	0.938720i	$-0.387987\pi$
$509$	15.5528	0.689364	0.344682	+	0.938720i	$0.387987\pi$
$510$	95.2475	4.21763
$511$	19.1101	0.845380
$512$	46.8486	2.07044
$513$	−118.411	−5.22797
$514$	2.29662	0.101300
$515$	−5.95765	−0.262525
$516$	45.6037	2.00759
$517$	−70.3580	−3.09434
$518$	−11.6971	−0.513941
$519$	51.3407	2.25360
$520$	−21.9916	−0.964397
$521$	31.6765	1.38777	0.693885	−	0.720085i	$-0.255897\pi$
$521$	31.6765	1.38777	0.693885	+	0.720085i	$0.255897\pi$
$522$	32.5605	1.42513
$523$	18.6427	0.815187	0.407593	−	0.913164i	$-0.366368\pi$
$523$	18.6427	0.815187	0.407593	+	0.913164i	$0.366368\pi$
$524$	−74.6513	−3.26116
$525$	−53.1782	−2.32089
$526$	16.0686	0.700625
$527$	−16.8889	−0.735694
$528$	−119.086	−5.18253
$529$	−18.7805	−0.816543
$530$	−10.1818	−0.442271
$531$	28.1109	1.21991
$532$	38.7663	1.68073
$533$	−9.07081	−0.392901
$534$	75.5783	3.27059
$535$	−36.9500	−1.59749
$536$	−6.59888	−0.285028
$537$	28.6943	1.23825
$538$	−31.4829	−1.35733
$539$	−32.4344	−1.39705
$540$	−311.828	−13.4189
$541$	9.21673	0.396258	0.198129	−	0.980176i	$-0.436513\pi$
$541$	9.21673	0.396258	0.198129	+	0.980176i	$0.436513\pi$
$542$	−42.3836	−1.82053
$543$	−28.9252	−1.24130
$544$	−6.36094	−0.272723
$545$	41.8591	1.79305
$546$	12.1860	0.521514
$547$	−6.10912	−0.261207	−0.130604	−	0.991435i	$-0.541691\pi$
$547$	−6.10912	−0.261207	−0.130604	+	0.991435i	$0.541691\pi$
$548$	25.5458	1.09126
$549$	−36.5769	−1.56106
$550$	−178.821	−7.62495
$551$	−9.82069	−0.418376
$552$	−38.4125	−1.63495
$553$	7.34833	0.312483
$554$	19.3446	0.821873
$555$	−43.9122	−1.86397
$556$	−95.7812	−4.06203
$557$	41.6129	1.76319	0.881597	−	0.472003i	$-0.156469\pi$
$557$	41.6129	1.76319	0.881597	+	0.472003i	$0.156469\pi$
$558$	126.164	5.34096
$559$	−3.19391	−0.135088
$560$	30.6401	1.29478
$561$	−63.2333	−2.66971
$562$	−53.2580	−2.24655
$563$	37.3230	1.57298	0.786489	−	0.617604i	$-0.211897\pi$
$563$	37.3230	1.57298	0.786489	+	0.617604i	$0.211897\pi$
$564$	152.340	6.41466
$565$	5.04517	0.212252
$566$	−69.7111	−2.93018
$567$	54.0753	2.27095
$568$	−38.0209	−1.59532
$569$	−34.7772	−1.45794	−0.728968	−	0.684547i	$-0.760000\pi$
$569$	−34.7772	−1.45794	−0.728968	+	0.684547i	$0.760000\pi$
$570$	214.604	8.98879
$571$	−9.22165	−0.385914	−0.192957	−	0.981207i	$-0.561808\pi$
$571$	−9.22165	−0.385914	−0.192957	+	0.981207i	$0.561808\pi$
$572$	27.7888	1.16191
$573$	−68.7863	−2.87359
$574$	32.6230	1.36166
$575$	−22.3453	−0.931865
$576$	−42.8806	−1.78669
$577$	26.1703	1.08948	0.544741	−	0.838604i	$-0.316628\pi$
$577$	26.1703	1.08948	0.544741	+	0.838604i	$0.316628\pi$
$578$	22.4131	0.932262
$579$	−14.8481	−0.617064
$580$	−25.8622	−1.07387
$581$	−5.82363	−0.241605
$582$	−80.5501	−3.33891
$583$	6.75957	0.279953
$584$	−73.1015	−3.02496
$585$	33.7935	1.39719
$586$	−10.6015	−0.437942
$587$	42.7246	1.76343	0.881717	−	0.471778i	$-0.156388\pi$
$587$	42.7246	1.76343	0.881717	+	0.471778i	$0.156388\pi$
$588$	70.2271	2.89612
$589$	−38.0529	−1.56794
$590$	−32.9250	−1.35550
$591$	42.2676	1.73866
$592$	17.3339	0.712420
$593$	−15.8331	−0.650189	−0.325094	−	0.945682i	$-0.605396\pi$
$593$	−15.8331	−0.650189	−0.325094	+	0.945682i	$0.605396\pi$
$594$	305.271	12.5254
$595$	16.2696	0.666990
$596$	50.5396	2.07018
$597$	63.2603	2.58907
$598$	5.12054	0.209394
$599$	17.2758	0.705870	0.352935	−	0.935648i	$-0.385184\pi$
$599$	17.2758	0.705870	0.352935	+	0.935648i	$0.385184\pi$
$600$	203.422	8.30467
$601$	−2.24362	−0.0915190	−0.0457595	−	0.998952i	$-0.514571\pi$
$601$	−2.24362	−0.0915190	−0.0457595	+	0.998952i	$0.514571\pi$
$602$	11.4869	0.468169
$603$	10.1402	0.412940
$604$	63.7686	2.59471
$605$	129.450	5.26291
$606$	90.5876	3.67987
$607$	−46.1904	−1.87481	−0.937404	−	0.348243i	$-0.886779\pi$
$607$	−46.1904	−1.87481	−0.937404	+	0.348243i	$0.886779\pi$
$608$	−14.3320	−0.581238
$609$	7.52924	0.305100
$610$	42.8409	1.73458
$611$	−10.6693	−0.431634
$612$	101.137	4.08821
$613$	6.64918	0.268558	0.134279	−	0.990944i	$-0.457128\pi$
$613$	6.64918	0.268558	0.134279	+	0.990944i	$0.457128\pi$
$614$	40.7492	1.64450
$615$	122.470	4.93848
$616$	−52.5083	−2.11562
$617$	18.5564	0.747052	0.373526	−	0.927620i	$-0.378149\pi$
$617$	18.5564	0.747052	0.373526	+	0.927620i	$0.378149\pi$
$618$	−12.6283	−0.507984
$619$	−42.6948	−1.71605	−0.858024	−	0.513609i	$-0.828308\pi$
$619$	−42.6948	−1.71605	−0.858024	+	0.513609i	$0.828308\pi$
$620$	−100.210	−4.02452
$621$	38.1464	1.53076
$622$	2.78405	0.111630
$623$	12.9098	0.517222
$624$	−18.0585	−0.722918
$625$	38.9438	1.55775
$626$	−24.0661	−0.961877
$627$	−142.473	−5.68981
$628$	10.0863	0.402488
$629$	9.20416	0.366994
$630$	−121.538	−4.84218
$631$	−2.93178	−0.116712	−0.0583561	−	0.998296i	$-0.518586\pi$
$631$	−2.93178	−0.116712	−0.0583561	+	0.998296i	$0.518586\pi$
$632$	−28.1095	−1.11814
$633$	−23.0468	−0.916028
$634$	−32.0151	−1.27148
$635$	−40.0384	−1.58887
$636$	−14.6359	−0.580349
$637$	−4.91845	−0.194876
$638$	25.3183	1.00236
$639$	58.4250	2.31126
$640$	68.1371	2.69336
$641$	−48.3222	−1.90861	−0.954306	−	0.298830i	$-0.903404\pi$
$641$	−48.3222	−1.90861	−0.954306	+	0.298830i	$0.903404\pi$
$642$	−78.3219	−3.09112
$643$	21.4888	0.847435	0.423718	−	0.905794i	$-0.360725\pi$
$643$	21.4888	0.847435	0.423718	+	0.905794i	$0.360725\pi$
$644$	−12.4887	−0.492122
$645$	43.1229	1.69796
$646$	−44.9819	−1.76979
$647$	33.0508	1.29936	0.649681	−	0.760207i	$-0.274903\pi$
$647$	33.0508	1.29936	0.649681	+	0.760207i	$0.274903\pi$
$648$	−206.854	−8.12598
$649$	21.8584	0.858017
$650$	−27.1169	−1.06361
$651$	29.1740	1.14342
$652$	36.1871	1.41719
$653$	13.8265	0.541072	0.270536	−	0.962710i	$-0.412799\pi$
$653$	13.8265	0.541072	0.270536	+	0.962710i	$0.412799\pi$
$654$	88.7277	3.46953
$655$	−70.5904	−2.75820
$656$	−48.3441	−1.88752
$657$	112.332	4.38248
$658$	38.3720	1.49590
$659$	32.1861	1.25379	0.626897	−	0.779102i	$-0.284325\pi$
$659$	32.1861	1.25379	0.626897	+	0.779102i	$0.284325\pi$
$660$	−375.193	−14.6043
$661$	14.0383	0.546028	0.273014	−	0.962010i	$-0.411979\pi$
$661$	14.0383	0.546028	0.273014	+	0.962010i	$0.411979\pi$
$662$	−35.1530	−1.36626
$663$	−9.58890	−0.372402
$664$	22.2771	0.864517
$665$	36.6575	1.42152
$666$	−68.7572	−2.66429
$667$	3.16376	0.122501
$668$	90.2426	3.49159
$669$	1.07470	0.0415504
$670$	−11.8768	−0.458839
$671$	−28.4414	−1.09797
$672$	10.9879	0.423868
$673$	−15.3714	−0.592522	−0.296261	−	0.955107i	$-0.595740\pi$
$673$	−15.3714	−0.592522	−0.296261	+	0.955107i	$0.595740\pi$
$674$	−48.6391	−1.87351
$675$	−202.013	−7.77547
$676$	4.21397	0.162076
$677$	19.6830	0.756480	0.378240	−	0.925708i	$-0.376529\pi$
$677$	19.6830	0.756480	0.378240	+	0.925708i	$0.376529\pi$
$678$	10.6941	0.410705
$679$	−13.7591	−0.528026
$680$	−62.2360	−2.38664
$681$	−19.0887	−0.731479
$682$	98.1026	3.75654
$683$	44.8451	1.71595	0.857974	−	0.513692i	$-0.171723\pi$
$683$	44.8451	1.71595	0.857974	+	0.513692i	$0.171723\pi$
$684$	227.874	8.71296
$685$	24.1561	0.922958
$686$	42.8645	1.63657
$687$	92.5062	3.52933
$688$	−17.0224	−0.648972
$689$	1.02504	0.0390510
$690$	−69.1354	−2.63194
$691$	−22.4793	−0.855152	−0.427576	−	0.903979i	$-0.640632\pi$
$691$	−22.4793	−0.855152	−0.427576	+	0.903979i	$0.640632\pi$
$692$	−63.8511	−2.42726
$693$	80.6870	3.06505
$694$	−0.786349	−0.0298494
$695$	−90.5709	−3.43555
$696$	−28.8015	−1.09172
$697$	−25.6703	−0.972330
$698$	−23.4928	−0.889215
$699$	33.5599	1.26935
$700$	66.1365	2.49972
$701$	50.3652	1.90227	0.951134	−	0.308777i	$-0.0999198\pi$
$701$	50.3652	1.90227	0.951134	+	0.308777i	$0.0999198\pi$
$702$	46.2922	1.74719
$703$	20.7381	0.782153
$704$	−33.3430	−1.25666
$705$	144.053	5.42534
$706$	−68.0371	−2.56061
$707$	15.4736	0.581946
$708$	−47.3279	−1.77869
$709$	5.29635	0.198909	0.0994543	−	0.995042i	$-0.468290\pi$
$709$	5.29635	0.198909	0.0994543	+	0.995042i	$0.468290\pi$
$710$	−68.4307	−2.56816
$711$	43.1945	1.61992
$712$	−49.3838	−1.85074
$713$	12.2588	0.459097
$714$	34.4863	1.29062
$715$	26.2771	0.982708
$716$	−35.6864	−1.33366
$717$	−91.3181	−3.41034
$718$	−38.3119	−1.42979
$719$	−29.6581	−1.10606	−0.553031	−	0.833161i	$-0.686529\pi$
$719$	−29.6581	−1.10606	−0.553031	+	0.833161i	$0.686529\pi$
$720$	180.107	6.71218
$721$	−2.15709	−0.0803342
$722$	−53.9869	−2.00919
$723$	−44.9400	−1.67134
$724$	35.9736	1.33695
$725$	−16.7544	−0.622243
$726$	274.393	10.1837
$727$	−33.7143	−1.25039	−0.625197	−	0.780467i	$-0.714981\pi$
$727$	−33.7143	−1.25039	−0.625197	+	0.780467i	$0.714981\pi$
$728$	−7.96252	−0.295111
$729$	129.094	4.78126
$730$	−131.569	−4.86960
$731$	−9.03873	−0.334309
$732$	61.5815	2.27612
$733$	−19.3305	−0.713988	−0.356994	−	0.934107i	$-0.616198\pi$
$733$	−19.3305	−0.713988	−0.356994	+	0.934107i	$0.616198\pi$
$734$	67.4954	2.49130
$735$	66.4069	2.44946
$736$	4.61708	0.170188
$737$	7.88479	0.290440
$738$	191.763	7.05888
$739$	−8.69899	−0.319998	−0.159999	−	0.987117i	$-0.551149\pi$
$739$	−8.69899	−0.319998	−0.159999	+	0.987117i	$0.551149\pi$
$740$	54.6125	2.00760
$741$	−21.6050	−0.793679
$742$	−3.68654	−0.135337
$743$	2.89216	0.106103	0.0530515	−	0.998592i	$-0.483105\pi$
$743$	2.89216	0.106103	0.0530515	+	0.998592i	$0.483105\pi$
$744$	−111.599	−4.09142
$745$	47.7904	1.75090
$746$	10.3847	0.380211
$747$	−34.2321	−1.25249
$748$	78.6418	2.87543
$749$	−13.3785	−0.488839
$750$	197.839	7.22406
$751$	−30.1287	−1.09941	−0.549707	−	0.835358i	$-0.685261\pi$
$751$	−30.1287	−1.09941	−0.549707	+	0.835358i	$0.685261\pi$
$752$	−56.8635	−2.07360
$753$	6.02710	0.219640
$754$	3.83935	0.139821
$755$	60.2997	2.19453
$756$	−112.904	−4.10627
$757$	4.90111	0.178134	0.0890670	−	0.996026i	$-0.471611\pi$
$757$	4.90111	0.178134	0.0890670	+	0.996026i	$0.471611\pi$
$758$	59.8603	2.17422
$759$	45.8979	1.66599
$760$	−140.225	−5.08651
$761$	−35.1530	−1.27430	−0.637148	−	0.770742i	$-0.719886\pi$
$761$	−35.1530	−1.27430	−0.637148	+	0.770742i	$0.719886\pi$
$762$	−84.8683	−3.07445
$763$	15.1560	0.548682
$764$	85.5478	3.09501
$765$	95.6351	3.45769
$766$	−61.7141	−2.22982
$767$	3.31468	0.119686
$768$	110.164	3.97521
$769$	−9.33776	−0.336728	−0.168364	−	0.985725i	$-0.553848\pi$
$769$	−9.33776	−0.336728	−0.168364	+	0.985725i	$0.553848\pi$
$770$	−94.5052	−3.40573
$771$	3.12168	0.112425
$772$	18.4662	0.664612
$773$	−6.66513	−0.239728	−0.119864	−	0.992790i	$-0.538246\pi$
$773$	−6.66513	−0.239728	−0.119864	+	0.992790i	$0.538246\pi$
$774$	67.5213	2.42700
$775$	−64.9194	−2.33197
$776$	52.6325	1.88940
$777$	−15.8993	−0.570385
$778$	−62.9153	−2.25562
$779$	−57.8383	−2.07227
$780$	−56.8954	−2.03718
$781$	45.4300	1.62561
$782$	14.4910	0.518198
$783$	28.6020	1.02215
$784$	−26.2135	−0.936197
$785$	9.53766	0.340414
$786$	−149.629	−5.33708
$787$	28.2208	1.00596	0.502982	−	0.864297i	$-0.332236\pi$
$787$	28.2208	1.00596	0.502982	+	0.864297i	$0.332236\pi$
$788$	−52.5672	−1.87263
$789$	21.8413	0.777571
$790$	−50.5919	−1.79998
$791$	1.82671	0.0649502
$792$	−308.651	−10.9674
$793$	−4.31294	−0.153157
$794$	−32.9027	−1.16767
$795$	−13.8397	−0.490843
$796$	−78.6753	−2.78857
$797$	41.6494	1.47530	0.737649	−	0.675185i	$-0.235936\pi$
$797$	41.6494	1.47530	0.737649	+	0.675185i	$0.235936\pi$
$798$	77.7019	2.75062
$799$	−30.1940	−1.06819
$800$	−24.4508	−0.864466
$801$	75.8858	2.68129
$802$	−82.5089	−2.91349
$803$	87.3467	3.08240
$804$	−17.0722	−0.602090
$805$	−11.8093	−0.416223
$806$	14.8766	0.524005
$807$	−42.7933	−1.50639
$808$	−59.1911	−2.08234
$809$	−9.65649	−0.339504	−0.169752	−	0.985487i	$-0.554297\pi$
$809$	−9.65649	−0.339504	−0.169752	+	0.985487i	$0.554297\pi$
$810$	−372.298	−13.0812
$811$	31.1698	1.09452	0.547260	−	0.836963i	$-0.315671\pi$
$811$	31.1698	1.09452	0.547260	+	0.836963i	$0.315671\pi$
$812$	−9.36393	−0.328609
$813$	−57.6101	−2.02047
$814$	−53.4641	−1.87392
$815$	34.2186	1.19862
$816$	−51.1052	−1.78904
$817$	−20.3654	−0.712494
$818$	−23.5794	−0.824433
$819$	12.2356	0.427548
$820$	−152.313	−5.31902
$821$	27.6762	0.965907	0.482954	−	0.875646i	$-0.339564\pi$
$821$	27.6762	0.965907	0.482954	+	0.875646i	$0.339564\pi$
$822$	51.2031	1.78591
$823$	12.0292	0.419312	0.209656	−	0.977775i	$-0.432766\pi$
$823$	12.0292	0.419312	0.209656	+	0.977775i	$0.432766\pi$
$824$	8.25148	0.287454
$825$	−243.063	−8.46235
$826$	−11.9212	−0.414791
$827$	32.7201	1.13779	0.568894	−	0.822411i	$-0.307371\pi$
$827$	32.7201	1.13779	0.568894	+	0.822411i	$0.307371\pi$
$828$	−73.4101	−2.55118
$829$	−0.481722	−0.0167309	−0.00836545	−	0.999965i	$-0.502663\pi$
$829$	−0.481722	−0.0167309	−0.00836545	+	0.999965i	$0.502663\pi$
$830$	40.0946	1.39170
$831$	26.2942	0.912135
$832$	−5.05624	−0.175294
$833$	−13.9191	−0.482270
$834$	−191.981	−6.64775
$835$	85.3336	2.95309
$836$	177.190	6.12823
$837$	110.826	3.83070
$838$	3.44332	0.118947
$839$	−1.48559	−0.0512883	−0.0256442	−	0.999671i	$-0.508164\pi$
$839$	−1.48559	−0.0512883	−0.0256442	+	0.999671i	$0.508164\pi$
$840$	107.507	3.70933
$841$	−26.6278	−0.918201
$842$	90.5591	3.12087
$843$	−72.3911	−2.49328
$844$	28.6628	0.986613
$845$	3.98474	0.137079
$846$	225.556	7.75477
$847$	46.8702	1.61048
$848$	5.46309	0.187603
$849$	−94.7549	−3.25198
$850$	−76.7405	−2.63218
$851$	−6.68084	−0.229016
$852$	−98.3654	−3.36994
$853$	−7.60822	−0.260500	−0.130250	−	0.991481i	$-0.541578\pi$
$853$	−7.60822	−0.260500	−0.130250	+	0.991481i	$0.541578\pi$
$854$	15.5114	0.530790
$855$	215.478	7.36918
$856$	51.1765	1.74918
$857$	−20.2184	−0.690647	−0.345324	−	0.938484i	$-0.612231\pi$
$857$	−20.2184	−0.690647	−0.345324	+	0.938484i	$0.612231\pi$
$858$	55.6989	1.90153
$859$	−19.1426	−0.653138	−0.326569	−	0.945173i	$-0.605893\pi$
$859$	−19.1426	−0.653138	−0.326569	+	0.945173i	$0.605893\pi$
$860$	−53.6309	−1.82880
$861$	44.3429	1.51120
$862$	36.9908	1.25991
$863$	−46.4419	−1.58090	−0.790450	−	0.612526i	$-0.790153\pi$
$863$	−46.4419	−1.58090	−0.790450	+	0.612526i	$0.790153\pi$
$864$	41.7407	1.42005
$865$	−60.3778	−2.05291
$866$	60.1330	2.04340
$867$	30.4650	1.03465
$868$	−36.2830	−1.23153
$869$	33.5871	1.13937
$870$	−51.8373	−1.75745
$871$	1.19567	0.0405139
$872$	−57.9758	−1.96331
$873$	−80.8779	−2.73730
$874$	32.6501	1.10441
$875$	33.7937	1.14244
$876$	−189.124	−6.38990
$877$	−3.73165	−0.126009	−0.0630044	−	0.998013i	$-0.520068\pi$
$877$	−3.73165	−0.126009	−0.0630044	+	0.998013i	$0.520068\pi$
$878$	15.7666	0.532096
$879$	−14.4100	−0.486039
$880$	140.047	4.72099
$881$	−30.9133	−1.04150	−0.520748	−	0.853710i	$-0.674347\pi$
$881$	−30.9133	−1.04150	−0.520748	+	0.853710i	$0.674347\pi$
$882$	103.979	3.50116
$883$	−16.9682	−0.571026	−0.285513	−	0.958375i	$-0.592164\pi$
$883$	−16.9682	−0.571026	−0.285513	+	0.958375i	$0.592164\pi$
$884$	11.9255	0.401097
$885$	−44.7534	−1.50437
$886$	97.8381	3.28693
$887$	18.0355	0.605572	0.302786	−	0.953059i	$-0.402083\pi$
$887$	18.0355	0.605572	0.302786	+	0.953059i	$0.402083\pi$
$888$	60.8194	2.04097
$889$	−14.4967	−0.486204
$890$	−88.8818	−2.97932
$891$	247.163	8.28027
$892$	−1.33658	−0.0447520
$893$	−68.0308	−2.27656
$894$	101.300	3.38798
$895$	−33.7451	−1.12797
$896$	24.6704	0.824181
$897$	6.96010	0.232391
$898$	−71.7970	−2.39590
$899$	9.19160	0.306557
$900$	388.759	12.9586
$901$	2.90085	0.0966414
$902$	149.111	4.96484
$903$	15.6135	0.519586
$904$	−6.98767	−0.232406
$905$	34.0167	1.13075
$906$	127.816	4.24639
$907$	−31.5672	−1.04817	−0.524086	−	0.851666i	$-0.675593\pi$
$907$	−31.5672	−1.04817	−0.524086	+	0.851666i	$0.675593\pi$
$908$	23.7401	0.787843
$909$	90.9562	3.01683
$910$	−14.3311	−0.475070
$911$	−43.8800	−1.45381	−0.726904	−	0.686739i	$-0.759042\pi$
$911$	−43.8800	−1.45381	−0.726904	+	0.686739i	$0.759042\pi$
$912$	−115.146	−3.81288
$913$	−26.6182	−0.880932
$914$	−46.6130	−1.54182
$915$	58.2316	1.92508
$916$	−115.048	−3.80128
$917$	−25.5587	−0.844023
$918$	131.006	4.32385
$919$	39.2483	1.29468	0.647342	−	0.762200i	$-0.275881\pi$
$919$	39.2483	1.29468	0.647342	+	0.762200i	$0.275881\pi$
$920$	45.1740	1.48934
$921$	55.3884	1.82511
$922$	76.7626	2.52804
$923$	6.88915	0.226759
$924$	−135.846	−4.46901
$925$	35.3799	1.16328
$926$	2.49278	0.0819180
$927$	−12.6797	−0.416455
$928$	3.46186	0.113641
$929$	−37.6959	−1.23676	−0.618382	−	0.785878i	$-0.712211\pi$
$929$	−37.6959	−1.23676	−0.618382	+	0.785878i	$0.712211\pi$
$930$	−200.857	−6.58638
$931$	−31.3615	−1.02783
$932$	−41.7376	−1.36716
$933$	3.78423	0.123890
$934$	−69.7959	−2.28379
$935$	74.3638	2.43196
$936$	−46.8048	−1.52986
$937$	−12.4775	−0.407622	−0.203811	−	0.979010i	$-0.565333\pi$
$937$	−12.4775	−0.407622	−0.203811	+	0.979010i	$0.565333\pi$
$938$	−4.30022	−0.140407
$939$	−32.7120	−1.06751
$940$	−179.155	−5.84339
$941$	−30.5189	−0.994888	−0.497444	−	0.867496i	$-0.665728\pi$
$941$	−30.5189	−0.994888	−0.497444	+	0.867496i	$0.665728\pi$
$942$	20.2167	0.658697
$943$	18.6328	0.606766
$944$	17.6660	0.574979
$945$	−106.762	−3.47297
$946$	52.5031	1.70702
$947$	27.6524	0.898583	0.449292	−	0.893385i	$-0.351676\pi$
$947$	27.6524	0.898583	0.449292	+	0.893385i	$0.351676\pi$
$948$	−72.7231	−2.36194
$949$	13.2455	0.429968
$950$	−172.906	−5.60981
$951$	−43.5166	−1.41112
$952$	−22.5338	−0.730325
$953$	−29.2747	−0.948300	−0.474150	−	0.880444i	$-0.657244\pi$
$953$	−29.2747	−0.948300	−0.474150	+	0.880444i	$0.657244\pi$
$954$	−21.6700	−0.701593
$955$	80.8942	2.61768
$956$	113.570	3.67312
$957$	34.4140	1.11245
$958$	58.1104	1.87746
$959$	8.74622	0.282430
$960$	68.2673	2.20332
$961$	4.61530	0.148881
$962$	−8.10746	−0.261395
$963$	−78.6406	−2.53416
$964$	55.8907	1.80012
$965$	17.4617	0.562110
$966$	−25.0319	−0.805388
$967$	−1.00306	−0.0322561	−0.0161281	−	0.999870i	$-0.505134\pi$
$967$	−1.00306	−0.0322561	−0.0161281	+	0.999870i	$0.505134\pi$
$968$	−179.292	−5.76266
$969$	−61.1417	−1.96416
$970$	94.7287	3.04156
$971$	−29.6796	−0.952465	−0.476233	−	0.879319i	$-0.657998\pi$
$971$	−29.6796	−0.952465	−0.476233	+	0.879319i	$0.657998\pi$
$972$	−300.392	−9.63508
$973$	−32.7930	−1.05130
$974$	−27.5554	−0.882932
$975$	−36.8588	−1.18042
$976$	−22.9864	−0.735776
$977$	23.9269	0.765488	0.382744	−	0.923854i	$-0.374979\pi$
$977$	23.9269	0.765488	0.382744	+	0.923854i	$0.374979\pi$
$978$	72.5322	2.31932
$979$	59.0072	1.88588
$980$	−82.5887	−2.63820
$981$	89.0888	2.84439
$982$	58.7379	1.87440
$983$	−50.1778	−1.60042	−0.800211	−	0.599718i	$-0.795279\pi$
$983$	−50.1778	−1.60042	−0.800211	+	0.599718i	$0.795279\pi$
$984$	−169.624	−5.40743
$985$	−49.7077	−1.58382
$986$	10.8653	0.346022
$987$	52.1572	1.66018
$988$	26.8696	0.854835
$989$	6.56076	0.208620
$990$	−555.515	−17.6554
$991$	11.4203	0.362777	0.181388	−	0.983412i	$-0.441941\pi$
$991$	11.4203	0.362777	0.181388	+	0.983412i	$0.441941\pi$
$992$	13.4139	0.425892
$993$	−47.7818	−1.51631
$994$	−24.7767	−0.785870
$995$	−74.3955	−2.35850
$996$	57.6338	1.82620
$997$	35.9825	1.13958	0.569789	−	0.821791i	$-0.307025\pi$
$997$	35.9825	1.13958	0.569789	+	0.821791i	$0.307025\pi$
$998$	−24.9887	−0.791003
$999$	−60.3981	−1.91091

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6019.2.a.e.1.12	✓	130

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6019.2.a.e.1.12	✓	130	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:	\( N \)	\(=\)	\( 6019 = 13 \cdot 463 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6019.a (trivial)

\(f(q)\)	\(=\)	\(q-2.49278 q^{2} -3.38832 q^{3} +4.21397 q^{4} +3.98474 q^{5} +8.44636 q^{6} +1.44276 q^{7} -5.51896 q^{8} +8.48073 q^{9} +O(q^{10})\)	\(q-2.49278 q^{2} -3.38832 q^{3} +4.21397 q^{4} +3.98474 q^{5} +8.44636 q^{6} +1.44276 q^{7} -5.51896 q^{8} +8.48073 q^{9} -9.93310 q^{10} +6.59443 q^{11} -14.2783 q^{12} +1.00000 q^{13} -3.59648 q^{14} -13.5016 q^{15} +5.32963 q^{16} +2.82998 q^{17} -21.1406 q^{18} +6.37631 q^{19} +16.7916 q^{20} -4.88853 q^{21} -16.4385 q^{22} -2.05414 q^{23} +18.7000 q^{24} +10.8782 q^{25} -2.49278 q^{26} -18.5705 q^{27} +6.07974 q^{28} -1.54019 q^{29} +33.6566 q^{30} -5.96786 q^{31} -2.24769 q^{32} -22.3441 q^{33} -7.05454 q^{34} +5.74902 q^{35} +35.7376 q^{36} +3.25237 q^{37} -15.8948 q^{38} -3.38832 q^{39} -21.9916 q^{40} -9.07081 q^{41} +12.1860 q^{42} -3.19391 q^{43} +27.7888 q^{44} +33.7935 q^{45} +5.12054 q^{46} -10.6693 q^{47} -18.0585 q^{48} -4.91845 q^{49} -27.1169 q^{50} -9.58890 q^{51} +4.21397 q^{52} +1.02504 q^{53} +46.2922 q^{54} +26.2771 q^{55} -7.96252 q^{56} -21.6050 q^{57} +3.83935 q^{58} +3.31468 q^{59} -56.8954 q^{60} -4.31294 q^{61} +14.8766 q^{62} +12.2356 q^{63} -5.05624 q^{64} +3.98474 q^{65} +55.6989 q^{66} +1.19567 q^{67} +11.9255 q^{68} +6.96010 q^{69} -14.3311 q^{70} +6.88915 q^{71} -46.8048 q^{72} +13.2455 q^{73} -8.10746 q^{74} -36.8588 q^{75} +26.8696 q^{76} +9.51416 q^{77} +8.44636 q^{78} +5.09326 q^{79} +21.2372 q^{80} +37.4805 q^{81} +22.6116 q^{82} -4.03646 q^{83} -20.6001 q^{84} +11.2768 q^{85} +7.96174 q^{86} +5.21864 q^{87} -36.3944 q^{88} +8.94803 q^{89} -84.2399 q^{90} +1.44276 q^{91} -8.65611 q^{92} +20.2210 q^{93} +26.5963 q^{94} +25.4079 q^{95} +7.61591 q^{96} -9.53667 q^{97} +12.2606 q^{98} +55.9256 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 130 q + 10 q^{2} + 11 q^{3} + 146 q^{4} + 40 q^{5} + 4 q^{6} + 8 q^{7} + 24 q^{8} + 181 q^{9}+O(q^{10}) \) 130 * q + 10 * q^2 + 11 * q^3 + 146 * q^4 + 40 * q^5 + 4 * q^6 + 8 * q^7 + 24 * q^8 + 181 * q^9	\( 130 q + 10 q^{2} + 11 q^{3} + 146 q^{4} + 40 q^{5} + 4 q^{6} + 8 q^{7} + 24 q^{8} + 181 q^{9} + 5 q^{10} + 43 q^{11} + 28 q^{12} + 130 q^{13} + 47 q^{14} + 29 q^{15} + 170 q^{16} + 85 q^{17} + 20 q^{18} + 3 q^{19} + 73 q^{20} + 62 q^{21} + 12 q^{22} + 62 q^{23} - 5 q^{24} + 178 q^{25} + 10 q^{26} + 35 q^{27} - q^{28} + 134 q^{29} + 24 q^{30} + 14 q^{31} + 48 q^{32} + 4 q^{33} + 4 q^{34} + 50 q^{35} + 244 q^{36} + 32 q^{37} + 76 q^{38} + 11 q^{39} - 6 q^{40} + 48 q^{41} + 9 q^{42} + 34 q^{43} + 123 q^{44} + 115 q^{45} + 5 q^{46} + 25 q^{47} + 35 q^{48} + 210 q^{49} + 24 q^{50} + 20 q^{51} + 146 q^{52} + 193 q^{53} - 39 q^{54} + 32 q^{55} + 122 q^{56} + 7 q^{57} - 4 q^{58} + 50 q^{59} + 42 q^{60} + 57 q^{61} + 51 q^{62} + 8 q^{63} + 172 q^{64} + 40 q^{65} - 4 q^{66} + 21 q^{67} + 132 q^{68} + 92 q^{69} - 46 q^{70} + 58 q^{71} - 26 q^{72} + 15 q^{73} + 120 q^{74} + 23 q^{75} - 65 q^{76} + 192 q^{77} + 4 q^{78} + 32 q^{79} + 66 q^{80} + 326 q^{81} + 11 q^{82} + 33 q^{83} + 5 q^{84} + 43 q^{85} + 105 q^{86} + 31 q^{87} - 17 q^{88} + 84 q^{89} - 73 q^{90} + 8 q^{91} + 161 q^{92} + 52 q^{93} + 4 q^{94} + 59 q^{95} - 77 q^{96} + 9 q^{97} - 61 q^{98} + 100 q^{99}+O(q^{100}) \) 130 * q + 10 * q^2 + 11 * q^3 + 146 * q^4 + 40 * q^5 + 4 * q^6 + 8 * q^7 + 24 * q^8 + 181 * q^9 + 5 * q^10 + 43 * q^11 + 28 * q^12 + 130 * q^13 + 47 * q^14 + 29 * q^15 + 170 * q^16 + 85 * q^17 + 20 * q^18 + 3 * q^19 + 73 * q^20 + 62 * q^21 + 12 * q^22 + 62 * q^23 - 5 * q^24 + 178 * q^25 + 10 * q^26 + 35 * q^27 - q^28 + 134 * q^29 + 24 * q^30 + 14 * q^31 + 48 * q^32 + 4 * q^33 + 4 * q^34 + 50 * q^35 + 244 * q^36 + 32 * q^37 + 76 * q^38 + 11 * q^39 - 6 * q^40 + 48 * q^41 + 9 * q^42 + 34 * q^43 + 123 * q^44 + 115 * q^45 + 5 * q^46 + 25 * q^47 + 35 * q^48 + 210 * q^49 + 24 * q^50 + 20 * q^51 + 146 * q^52 + 193 * q^53 - 39 * q^54 + 32 * q^55 + 122 * q^56 + 7 * q^57 - 4 * q^58 + 50 * q^59 + 42 * q^60 + 57 * q^61 + 51 * q^62 + 8 * q^63 + 172 * q^64 + 40 * q^65 - 4 * q^66 + 21 * q^67 + 132 * q^68 + 92 * q^69 - 46 * q^70 + 58 * q^71 - 26 * q^72 + 15 * q^73 + 120 * q^74 + 23 * q^75 - 65 * q^76 + 192 * q^77 + 4 * q^78 + 32 * q^79 + 66 * q^80 + 326 * q^81 + 11 * q^82 + 33 * q^83 + 5 * q^84 + 43 * q^85 + 105 * q^86 + 31 * q^87 - 17 * q^88 + 84 * q^89 - 73 * q^90 + 8 * q^91 + 161 * q^92 + 52 * q^93 + 4 * q^94 + 59 * q^95 - 77 * q^96 + 9 * q^97 - 61 * q^98 + 100 * q^99

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