LMFDB - Embedded newform 6001.2.a.a.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6001,2,Mod(1,6001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6001, 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("6001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6001 = 17 \cdot 353 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6001.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:	$47.9182262530$
Analytic rank:	$1$
Dimension:	$113$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	6001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.30912 q^{2} -2.56184 q^{3} +3.33205 q^{4} -3.64906 q^{5} +5.91560 q^{6} -1.49745 q^{7} -3.07586 q^{8} +3.56301 q^{9} +O(q^{10})$	\(q-2.30912 q^{2} -2.56184 q^{3} +3.33205 q^{4} -3.64906 q^{5} +5.91560 q^{6} -1.49745 q^{7} -3.07586 q^{8} +3.56301 q^{9} +8.42614 q^{10} -3.48349 q^{11} -8.53617 q^{12} -6.84422 q^{13} +3.45779 q^{14} +9.34831 q^{15} +0.438451 q^{16} -1.00000 q^{17} -8.22743 q^{18} -4.85370 q^{19} -12.1589 q^{20} +3.83622 q^{21} +8.04381 q^{22} -3.52454 q^{23} +7.87986 q^{24} +8.31567 q^{25} +15.8041 q^{26} -1.44234 q^{27} -4.98957 q^{28} +0.257619 q^{29} -21.5864 q^{30} -10.5212 q^{31} +5.13929 q^{32} +8.92414 q^{33} +2.30912 q^{34} +5.46429 q^{35} +11.8721 q^{36} +9.05762 q^{37} +11.2078 q^{38} +17.5338 q^{39} +11.2240 q^{40} -8.20246 q^{41} -8.85830 q^{42} +2.07454 q^{43} -11.6072 q^{44} -13.0016 q^{45} +8.13860 q^{46} -9.47289 q^{47} -1.12324 q^{48} -4.75765 q^{49} -19.2019 q^{50} +2.56184 q^{51} -22.8053 q^{52} +1.76880 q^{53} +3.33053 q^{54} +12.7115 q^{55} +4.60595 q^{56} +12.4344 q^{57} -0.594873 q^{58} -4.14338 q^{59} +31.1490 q^{60} +8.79865 q^{61} +24.2947 q^{62} -5.33542 q^{63} -12.7442 q^{64} +24.9750 q^{65} -20.6069 q^{66} +0.775554 q^{67} -3.33205 q^{68} +9.02931 q^{69} -12.6177 q^{70} -15.9272 q^{71} -10.9593 q^{72} +12.4024 q^{73} -20.9152 q^{74} -21.3034 q^{75} -16.1728 q^{76} +5.21635 q^{77} -40.4876 q^{78} +1.78756 q^{79} -1.59994 q^{80} -6.99399 q^{81} +18.9405 q^{82} -14.5821 q^{83} +12.7825 q^{84} +3.64906 q^{85} -4.79038 q^{86} -0.659977 q^{87} +10.7148 q^{88} -10.9734 q^{89} +30.0224 q^{90} +10.2489 q^{91} -11.7440 q^{92} +26.9535 q^{93} +21.8741 q^{94} +17.7115 q^{95} -13.1660 q^{96} +10.9242 q^{97} +10.9860 q^{98} -12.4117 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 113 q - 11 q^{2} - 11 q^{3} + 103 q^{4} - 19 q^{5} - 13 q^{6} + 11 q^{7} - 36 q^{8} + 94 q^{9}+O(q^{10}) $ 113 * q - 11 * q^2 - 11 * q^3 + 103 * q^4 - 19 * q^5 - 13 * q^6 + 11 * q^7 - 36 * q^8 + 94 * q^9	\( 113 q - 11 q^{2} - 11 q^{3} + 103 q^{4} - 19 q^{5} - 13 q^{6} + 11 q^{7} - 36 q^{8} + 94 q^{9} - 5 q^{10} - 40 q^{11} - 19 q^{12} - 18 q^{13} - 48 q^{14} - 63 q^{15} + 79 q^{16} - 113 q^{17} - 32 q^{18} - 46 q^{19} - 56 q^{20} - 46 q^{21} + 14 q^{22} - 35 q^{23} - 42 q^{24} + 88 q^{25} - 89 q^{26} - 41 q^{27} + 20 q^{28} - 51 q^{29} - 18 q^{30} - 57 q^{31} - 93 q^{32} - 40 q^{33} + 11 q^{34} - 69 q^{35} + 18 q^{36} + 16 q^{37} - 74 q^{38} - 51 q^{39} + 2 q^{40} - 87 q^{41} - 23 q^{42} - 32 q^{43} - 110 q^{44} - 17 q^{45} - 17 q^{46} - 161 q^{47} - 36 q^{48} + 56 q^{49} - 69 q^{50} + 11 q^{51} - 49 q^{52} - 48 q^{53} - 38 q^{54} - 79 q^{55} - 171 q^{56} + 20 q^{57} + 13 q^{58} - 174 q^{59} - 146 q^{60} - 34 q^{61} - 34 q^{62} - 14 q^{63} + 62 q^{64} - 22 q^{65} - 60 q^{66} - 50 q^{67} - 103 q^{68} - 59 q^{69} - 58 q^{70} - 189 q^{71} - 123 q^{72} - 4 q^{73} - 24 q^{74} - 106 q^{75} - 92 q^{76} - 78 q^{77} - 42 q^{78} + 8 q^{79} - 150 q^{80} + 13 q^{81} + 6 q^{82} - 109 q^{83} - 114 q^{84} + 19 q^{85} - 116 q^{86} - 106 q^{87} + 54 q^{88} - 170 q^{89} - q^{90} - 43 q^{91} - 94 q^{92} - 69 q^{93} - 35 q^{94} - 78 q^{95} - 44 q^{96} - 3 q^{97} - 68 q^{98} - 119 q^{99}+O(q^{100}) \) 113 * q - 11 * q^2 - 11 * q^3 + 103 * q^4 - 19 * q^5 - 13 * q^6 + 11 * q^7 - 36 * q^8 + 94 * q^9 - 5 * q^10 - 40 * q^11 - 19 * q^12 - 18 * q^13 - 48 * q^14 - 63 * q^15 + 79 * q^16 - 113 * q^17 - 32 * q^18 - 46 * q^19 - 56 * q^20 - 46 * q^21 + 14 * q^22 - 35 * q^23 - 42 * q^24 + 88 * q^25 - 89 * q^26 - 41 * q^27 + 20 * q^28 - 51 * q^29 - 18 * q^30 - 57 * q^31 - 93 * q^32 - 40 * q^33 + 11 * q^34 - 69 * q^35 + 18 * q^36 + 16 * q^37 - 74 * q^38 - 51 * q^39 + 2 * q^40 - 87 * q^41 - 23 * q^42 - 32 * q^43 - 110 * q^44 - 17 * q^45 - 17 * q^46 - 161 * q^47 - 36 * q^48 + 56 * q^49 - 69 * q^50 + 11 * q^51 - 49 * q^52 - 48 * q^53 - 38 * q^54 - 79 * q^55 - 171 * q^56 + 20 * q^57 + 13 * q^58 - 174 * q^59 - 146 * q^60 - 34 * q^61 - 34 * q^62 - 14 * q^63 + 62 * q^64 - 22 * q^65 - 60 * q^66 - 50 * q^67 - 103 * q^68 - 59 * q^69 - 58 * q^70 - 189 * q^71 - 123 * q^72 - 4 * q^73 - 24 * q^74 - 106 * q^75 - 92 * q^76 - 78 * q^77 - 42 * q^78 + 8 * q^79 - 150 * q^80 + 13 * q^81 + 6 * q^82 - 109 * q^83 - 114 * q^84 + 19 * q^85 - 116 * q^86 - 106 * q^87 + 54 * q^88 - 170 * q^89 - q^90 - 43 * q^91 - 94 * q^92 - 69 * q^93 - 35 * q^94 - 78 * q^95 - 44 * q^96 - 3 * q^97 - 68 * q^98 - 119 * 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 $

$2$	−2.30912	−1.63280	−0.816398	−	0.577489i	$-0.804033\pi$
$2$	−2.30912	−1.63280	−0.816398	+	0.577489i	$0.804033\pi$
$3$	−2.56184	−1.47908	−0.739539	−	0.673114i	$-0.764956\pi$
$3$	−2.56184	−1.47908	−0.739539	+	0.673114i	$0.764956\pi$
$4$	3.33205	1.66602
$5$	−3.64906	−1.63191	−0.815955	−	0.578115i	$-0.803789\pi$
$5$	−3.64906	−1.63191	−0.815955	+	0.578115i	$0.803789\pi$
$6$	5.91560	2.41503
$7$	−1.49745	−0.565982	−0.282991	−	0.959123i	$-0.591327\pi$
$7$	−1.49745	−0.565982	−0.282991	+	0.959123i	$0.591327\pi$
$8$	−3.07586	−1.08748
$9$	3.56301	1.18767
$10$	8.42614	2.66458
$11$	−3.48349	−1.05031	−0.525156	−	0.851006i	$-0.675993\pi$
$11$	−3.48349	−1.05031	−0.525156	+	0.851006i	$0.675993\pi$
$12$	−8.53617	−2.46418
$13$	−6.84422	−1.89824	−0.949122	−	0.314908i	$-0.898026\pi$
$13$	−6.84422	−1.89824	−0.949122	+	0.314908i	$0.898026\pi$
$14$	3.45779	0.924134
$15$	9.34831	2.41372
$16$	0.438451	0.109613
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−8.22743	−1.93922
$19$	−4.85370	−1.11352	−0.556758	−	0.830675i	$-0.687955\pi$
$19$	−4.85370	−1.11352	−0.556758	+	0.830675i	$0.687955\pi$
$20$	−12.1589	−2.71880
$21$	3.83622	0.837132
$22$	8.04381	1.71495
$23$	−3.52454	−0.734918	−0.367459	−	0.930040i	$-0.619772\pi$
$23$	−3.52454	−0.734918	−0.367459	+	0.930040i	$0.619772\pi$
$24$	7.87986	1.60847
$25$	8.31567	1.66313
$26$	15.8041	3.09945
$27$	−1.44234	−0.277578
$28$	−4.98957	−0.942940
$29$	0.257619	0.0478386	0.0239193	−	0.999714i	$-0.492386\pi$
$29$	0.257619	0.0478386	0.0239193	+	0.999714i	$0.492386\pi$
$30$	−21.5864	−3.94112
$31$	−10.5212	−1.88966	−0.944830	−	0.327561i	$-0.893773\pi$
$31$	−10.5212	−1.88966	−0.944830	+	0.327561i	$0.893773\pi$
$32$	5.13929	0.908507
$33$	8.92414	1.55349
$34$	2.30912	0.396011
$35$	5.46429	0.923633
$36$	11.8721	1.97869
$37$	9.05762	1.48906	0.744532	−	0.667587i	$-0.232673\pi$
$37$	9.05762	1.48906	0.744532	+	0.667587i	$0.232673\pi$
$38$	11.2078	1.81814
$39$	17.5338	2.80765
$40$	11.2240	1.77467
$41$	−8.20246	−1.28101	−0.640505	−	0.767954i	$-0.721275\pi$
$41$	−8.20246	−1.28101	−0.640505	+	0.767954i	$0.721275\pi$
$42$	−8.85830	−1.36687
$43$	2.07454	0.316365	0.158183	−	0.987410i	$-0.449437\pi$
$43$	2.07454	0.316365	0.158183	+	0.987410i	$0.449437\pi$
$44$	−11.6072	−1.74985
$45$	−13.0016	−1.93817
$46$	8.13860	1.19997
$47$	−9.47289	−1.38176	−0.690882	−	0.722968i	$-0.742777\pi$
$47$	−9.47289	−1.38176	−0.690882	+	0.722968i	$0.742777\pi$
$48$	−1.12324	−0.162126
$49$	−4.75765	−0.679664
$50$	−19.2019	−2.71556
$51$	2.56184	0.358729
$52$	−22.8053	−3.16252
$53$	1.76880	0.242963	0.121481	−	0.992594i	$-0.461236\pi$
$53$	1.76880	0.242963	0.121481	+	0.992594i	$0.461236\pi$
$54$	3.33053	0.453228
$55$	12.7115	1.71402
$56$	4.60595	0.615496
$57$	12.4344	1.64698
$58$	−0.594873	−0.0781106
$59$	−4.14338	−0.539422	−0.269711	−	0.962941i	$-0.586928\pi$
$59$	−4.14338	−0.539422	−0.269711	+	0.962941i	$0.586928\pi$
$60$	31.1490	4.02132
$61$	8.79865	1.12655	0.563276	−	0.826269i	$-0.309541\pi$
$61$	8.79865	1.12655	0.563276	+	0.826269i	$0.309541\pi$
$62$	24.2947	3.08543
$63$	−5.33542	−0.672200
$64$	−12.7442	−1.59302
$65$	24.9750	3.09777
$66$	−20.6069	−2.53654
$67$	0.775554	0.0947491	0.0473745	−	0.998877i	$-0.484915\pi$
$67$	0.775554	0.0947491	0.0473745	+	0.998877i	$0.484915\pi$
$68$	−3.33205	−0.404070
$69$	9.02931	1.08700
$70$	−12.6177	−1.50810
$71$	−15.9272	−1.89021	−0.945107	−	0.326762i	$-0.894042\pi$
$71$	−15.9272	−1.89021	−0.945107	+	0.326762i	$0.894042\pi$
$72$	−10.9593	−1.29157
$73$	12.4024	1.45159	0.725793	−	0.687913i	$-0.241473\pi$
$73$	12.4024	1.45159	0.725793	+	0.687913i	$0.241473\pi$
$74$	−20.9152	−2.43134
$75$	−21.3034	−2.45990
$76$	−16.1728	−1.85514
$77$	5.21635	0.594458
$78$	−40.4876	−4.58432
$79$	1.78756	0.201116	0.100558	−	0.994931i	$-0.467937\pi$
$79$	1.78756	0.201116	0.100558	+	0.994931i	$0.467937\pi$
$80$	−1.59994	−0.178878
$81$	−6.99399	−0.777110
$82$	18.9405	2.09163
$83$	−14.5821	−1.60059	−0.800294	−	0.599607i	$-0.795323\pi$
$83$	−14.5821	−1.60059	−0.800294	+	0.599607i	$0.795323\pi$
$84$	12.7825	1.39468
$85$	3.64906	0.395797
$86$	−4.79038	−0.516560
$87$	−0.659977	−0.0707569
$88$	10.7148	1.14220
$89$	−10.9734	−1.16318	−0.581590	−	0.813482i	$-0.697569\pi$
$89$	−10.9734	−1.16318	−0.581590	+	0.813482i	$0.697569\pi$
$90$	30.0224	3.16464
$91$	10.2489	1.07437
$92$	−11.7440	−1.22439
$93$	26.9535	2.79495
$94$	21.8741	2.25614
$95$	17.7115	1.81716
$96$	−13.1660	−1.34375
$97$	10.9242	1.10919	0.554594	−	0.832121i	$-0.312874\pi$
$97$	10.9242	1.10919	0.554594	+	0.832121i	$0.312874\pi$
$98$	10.9860	1.10975
$99$	−12.4117	−1.24742
$100$	27.7082	2.77082
$101$	3.79515	0.377631	0.188816	−	0.982013i	$-0.439535\pi$
$101$	3.79515	0.377631	0.188816	+	0.982013i	$0.439535\pi$
$102$	−5.91560	−0.585731
$103$	0.673794	0.0663909	0.0331955	−	0.999449i	$-0.489432\pi$
$103$	0.673794	0.0663909	0.0331955	+	0.999449i	$0.489432\pi$
$104$	21.0519	2.06431
$105$	−13.9986	−1.36612
$106$	−4.08437	−0.396709
$107$	4.69255	0.453646	0.226823	−	0.973936i	$-0.427166\pi$
$107$	4.69255	0.453646	0.226823	+	0.973936i	$0.427166\pi$
$108$	−4.80594	−0.462452
$109$	−16.7869	−1.60789	−0.803945	−	0.594704i	$-0.797269\pi$
$109$	−16.7869	−1.60789	−0.803945	+	0.594704i	$0.797269\pi$
$110$	−29.3524	−2.79864
$111$	−23.2042	−2.20244
$112$	−0.656558	−0.0620389
$113$	5.49015	0.516470	0.258235	−	0.966082i	$-0.416859\pi$
$113$	5.49015	0.516470	0.258235	+	0.966082i	$0.416859\pi$
$114$	−28.7125	−2.68918
$115$	12.8613	1.19932
$116$	0.858398	0.0797002
$117$	−24.3860	−2.25449
$118$	9.56757	0.880766
$119$	1.49745	0.137271
$120$	−28.7541	−2.62488
$121$	1.13472	0.103157
$122$	−20.3172	−1.83943
$123$	21.0134	1.89471
$124$	−35.0571	−3.14822
$125$	−12.0991	−1.08217
$126$	12.3201	1.09757
$127$	−18.8335	−1.67121	−0.835604	−	0.549333i	$-0.814882\pi$
$127$	−18.8335	−1.67121	−0.835604	+	0.549333i	$0.814882\pi$
$128$	19.1492	1.69257
$129$	−5.31465	−0.467928
$130$	−57.6703	−5.05802
$131$	20.4316	1.78511	0.892557	−	0.450935i	$-0.148909\pi$
$131$	20.4316	1.78511	0.892557	+	0.450935i	$0.148909\pi$
$132$	29.7357	2.58816
$133$	7.26817	0.630230
$134$	−1.79085	−0.154706
$135$	5.26318	0.452982
$136$	3.07586	0.263753
$137$	3.94979	0.337453	0.168727	−	0.985663i	$-0.446035\pi$
$137$	3.94979	0.337453	0.168727	+	0.985663i	$0.446035\pi$
$138$	−20.8498	−1.77485
$139$	23.2945	1.97582	0.987909	−	0.155037i	$-0.0495496\pi$
$139$	23.2945	1.97582	0.987909	+	0.155037i	$0.0495496\pi$
$140$	18.2073	1.53879
$141$	24.2680	2.04373
$142$	36.7779	3.08633
$143$	23.8418	1.99375
$144$	1.56220	0.130184
$145$	−0.940066	−0.0780683
$146$	−28.6386	−2.37014
$147$	12.1883	1.00528
$148$	30.1804	2.48082
$149$	−7.77384	−0.636858	−0.318429	−	0.947947i	$-0.603155\pi$
$149$	−7.77384	−0.636858	−0.318429	+	0.947947i	$0.603155\pi$
$150$	49.1921	4.01652
$151$	8.41967	0.685183	0.342592	−	0.939484i	$-0.388695\pi$
$151$	8.41967	0.685183	0.342592	+	0.939484i	$0.388695\pi$
$152$	14.9293	1.21093
$153$	−3.56301	−0.288052
$154$	−12.0452	−0.970630
$155$	38.3925	3.08376
$156$	58.4234	4.67761
$157$	9.78727	0.781109	0.390555	−	0.920580i	$-0.372283\pi$
$157$	9.78727	0.781109	0.390555	+	0.920580i	$0.372283\pi$
$158$	−4.12770	−0.328382
$159$	−4.53137	−0.359361
$160$	−18.7536	−1.48260
$161$	5.27782	0.415951
$162$	16.1500	1.26886
$163$	21.0012	1.64494	0.822471	−	0.568807i	$-0.192595\pi$
$163$	21.0012	1.64494	0.822471	+	0.568807i	$0.192595\pi$
$164$	−27.3310	−2.13419
$165$	−32.5648	−2.53516
$166$	33.6718	2.61344
$167$	0.574794	0.0444789	0.0222395	−	0.999753i	$-0.492920\pi$
$167$	0.574794	0.0444789	0.0222395	+	0.999753i	$0.492920\pi$
$168$	−11.7997	−0.910366
$169$	33.8433	2.60333
$170$	−8.42614	−0.646255
$171$	−17.2938	−1.32249
$172$	6.91248	0.527072
$173$	6.68565	0.508301	0.254150	−	0.967165i	$-0.418204\pi$
$173$	6.68565	0.508301	0.254150	+	0.967165i	$0.418204\pi$
$174$	1.52397	0.115532
$175$	−12.4523	−0.941304
$176$	−1.52734	−0.115128
$177$	10.6147	0.797847
$178$	25.3390	1.89924
$179$	8.59297	0.642269	0.321134	−	0.947034i	$-0.395936\pi$
$179$	8.59297	0.642269	0.321134	+	0.947034i	$0.395936\pi$
$180$	−43.3221	−3.22904
$181$	8.97075	0.666791	0.333395	−	0.942787i	$-0.391806\pi$
$181$	8.97075	0.666791	0.333395	+	0.942787i	$0.391806\pi$
$182$	−23.6659	−1.75423
$183$	−22.5407	−1.66626
$184$	10.8410	0.799210
$185$	−33.0518	−2.43002
$186$	−62.2391	−4.56359
$187$	3.48349	0.254738
$188$	−31.5641	−2.30205
$189$	2.15983	0.157104
$190$	−40.8980	−2.96705
$191$	22.8167	1.65096	0.825478	−	0.564435i	$-0.190906\pi$
$191$	22.8167	1.65096	0.825478	+	0.564435i	$0.190906\pi$
$192$	32.6485	2.35620
$193$	−4.58486	−0.330026	−0.165013	−	0.986291i	$-0.552767\pi$
$193$	−4.58486	−0.330026	−0.165013	+	0.986291i	$0.552767\pi$
$194$	−25.2254	−1.81108
$195$	−63.9818	−4.58183
$196$	−15.8527	−1.13234
$197$	14.0861	1.00359	0.501795	−	0.864986i	$-0.332673\pi$
$197$	14.0861	1.00359	0.501795	+	0.864986i	$0.332673\pi$
$198$	28.6602	2.03679
$199$	−22.9916	−1.62983	−0.814914	−	0.579582i	$-0.803216\pi$
$199$	−22.9916	−1.62983	−0.814914	+	0.579582i	$0.803216\pi$
$200$	−25.5779	−1.80863
$201$	−1.98684	−0.140141
$202$	−8.76346	−0.616595
$203$	−0.385771	−0.0270758
$204$	8.53617	0.597651
$205$	29.9313	2.09049
$206$	−1.55587	−0.108403
$207$	−12.5580	−0.872840
$208$	−3.00085	−0.208072
$209$	16.9078	1.16954
$210$	32.3245	2.23060
$211$	14.3859	0.990368	0.495184	−	0.868788i	$-0.335101\pi$
$211$	14.3859	0.990368	0.495184	+	0.868788i	$0.335101\pi$
$212$	5.89371	0.404782
$213$	40.8029	2.79577
$214$	−10.8357	−0.740711
$215$	−7.57015	−0.516280
$216$	4.43643	0.301861
$217$	15.7549	1.06951
$218$	38.7629	2.62536
$219$	−31.7728	−2.14701
$220$	42.3553	2.85559
$221$	6.84422	0.460392
$222$	53.5812	3.59614
$223$	−7.62441	−0.510568	−0.255284	−	0.966866i	$-0.582169\pi$
$223$	−7.62441	−0.510568	−0.255284	+	0.966866i	$0.582169\pi$
$224$	−7.69582	−0.514199
$225$	29.6288	1.97525
$226$	−12.6774	−0.843291
$227$	−16.8693	−1.11966	−0.559828	−	0.828609i	$-0.689133\pi$
$227$	−16.8693	−1.11966	−0.559828	+	0.828609i	$0.689133\pi$
$228$	41.4320	2.74390
$229$	−12.5587	−0.829900	−0.414950	−	0.909844i	$-0.636201\pi$
$229$	−12.5587	−0.829900	−0.414950	+	0.909844i	$0.636201\pi$
$230$	−29.6983	−1.95825
$231$	−13.3634	−0.879250
$232$	−0.792400	−0.0520236
$233$	−9.14685	−0.599230	−0.299615	−	0.954060i	$-0.596858\pi$
$233$	−9.14685	−0.599230	−0.299615	+	0.954060i	$0.596858\pi$
$234$	56.3103	3.68112
$235$	34.5672	2.25491
$236$	−13.8059	−0.898690
$237$	−4.57944	−0.297467
$238$	−3.45779	−0.224135
$239$	−24.0337	−1.55461	−0.777304	−	0.629125i	$-0.783413\pi$
$239$	−24.0337	−1.55461	−0.777304	+	0.629125i	$0.783413\pi$
$240$	4.09877	0.264575
$241$	−5.94699	−0.383079	−0.191540	−	0.981485i	$-0.561348\pi$
$241$	−5.94699	−0.383079	−0.191540	+	0.981485i	$0.561348\pi$
$242$	−2.62021	−0.168434
$243$	22.2445	1.42698
$244$	29.3175	1.87686
$245$	17.3610	1.10915
$246$	−48.5225	−3.09368
$247$	33.2198	2.11372
$248$	32.3617	2.05497
$249$	37.3569	2.36739
$250$	27.9383	1.76697
$251$	9.11959	0.575623	0.287812	−	0.957687i	$-0.407072\pi$
$251$	9.11959	0.575623	0.287812	+	0.957687i	$0.407072\pi$
$252$	−17.7779	−1.11990
$253$	12.2777	0.771894
$254$	43.4890	2.72874
$255$	−9.34831	−0.585414
$256$	−18.7296	−1.17060
$257$	−6.90176	−0.430520	−0.215260	−	0.976557i	$-0.569060\pi$
$257$	−6.90176	−0.430520	−0.215260	+	0.976557i	$0.569060\pi$
$258$	12.2722	0.764032
$259$	−13.5633	−0.842784
$260$	83.2179	5.16095
$261$	0.917897	0.0568164
$262$	−47.1790	−2.91473
$263$	−2.12604	−0.131097	−0.0655487	−	0.997849i	$-0.520880\pi$
$263$	−2.12604	−0.131097	−0.0655487	+	0.997849i	$0.520880\pi$
$264$	−27.4494	−1.68940
$265$	−6.45445	−0.396494
$266$	−16.7831	−1.02904
$267$	28.1121	1.72043
$268$	2.58419	0.157854
$269$	−13.8243	−0.842881	−0.421440	−	0.906856i	$-0.638475\pi$
$269$	−13.8243	−0.842881	−0.421440	+	0.906856i	$0.638475\pi$
$270$	−12.1533	−0.739628
$271$	24.0480	1.46081	0.730407	−	0.683012i	$-0.239331\pi$
$271$	24.0480	1.46081	0.730407	+	0.683012i	$0.239331\pi$
$272$	−0.438451	−0.0265850
$273$	−26.2559	−1.58908
$274$	−9.12055	−0.550992
$275$	−28.9676	−1.74681
$276$	30.0861	1.81097
$277$	−5.63419	−0.338526	−0.169263	−	0.985571i	$-0.554139\pi$
$277$	−5.63419	−0.338526	−0.169263	+	0.985571i	$0.554139\pi$
$278$	−53.7900	−3.22611
$279$	−37.4871	−2.24429
$280$	−16.8074	−1.00443
$281$	−23.3461	−1.39271	−0.696356	−	0.717697i	$-0.745196\pi$
$281$	−23.3461	−1.39271	−0.696356	+	0.717697i	$0.745196\pi$
$282$	−56.0378	−3.33700
$283$	−23.8214	−1.41603	−0.708017	−	0.706195i	$-0.750410\pi$
$283$	−23.8214	−1.41603	−0.708017	+	0.706195i	$0.750410\pi$
$284$	−53.0703	−3.14914
$285$	−45.3739	−2.68772
$286$	−55.0536	−3.25539
$287$	12.2828	0.725029
$288$	18.3113	1.07901
$289$	1.00000	0.0588235
$290$	2.17073	0.127470
$291$	−27.9861	−1.64057
$292$	41.3253	2.41838
$293$	−3.67793	−0.214867	−0.107434	−	0.994212i	$-0.534263\pi$
$293$	−3.67793	−0.214867	−0.107434	+	0.994212i	$0.534263\pi$
$294$	−28.1443	−1.64141
$295$	15.1195	0.880289
$296$	−27.8600	−1.61933
$297$	5.02437	0.291544
$298$	17.9507	1.03986
$299$	24.1227	1.39505
$300$	−70.9839	−4.09826
$301$	−3.10652	−0.179057
$302$	−19.4421	−1.11876
$303$	−9.72255	−0.558546
$304$	−2.12811	−0.122055
$305$	−32.1069	−1.83843
$306$	8.22743	0.470331
$307$	21.0777	1.20297	0.601485	−	0.798884i	$-0.294576\pi$
$307$	21.0777	1.20297	0.601485	+	0.798884i	$0.294576\pi$
$308$	17.3811	0.990382
$309$	−1.72615	−0.0981973
$310$	−88.6529	−5.03515
$311$	−14.6991	−0.833509	−0.416755	−	0.909019i	$-0.636833\pi$
$311$	−14.6991	−0.833509	−0.416755	+	0.909019i	$0.636833\pi$
$312$	−53.9315	−3.05327
$313$	29.5056	1.66776	0.833878	−	0.551948i	$-0.186115\pi$
$313$	29.5056	1.66776	0.833878	+	0.551948i	$0.186115\pi$
$314$	−22.6000	−1.27539
$315$	19.4693	1.09697
$316$	5.95624	0.335065
$317$	−3.51756	−0.197566	−0.0987828	−	0.995109i	$-0.531495\pi$
$317$	−3.51756	−0.197566	−0.0987828	+	0.995109i	$0.531495\pi$
$318$	10.4635	0.586763
$319$	−0.897412	−0.0502454
$320$	46.5042	2.59967
$321$	−12.0215	−0.670977
$322$	−12.1871	−0.679163
$323$	4.85370	0.270067
$324$	−23.3043	−1.29468
$325$	−56.9142	−3.15703
$326$	−48.4944	−2.68586
$327$	43.0052	2.37819
$328$	25.2297	1.39307
$329$	14.1852	0.782054
$330$	75.1960	4.13941
$331$	9.14988	0.502923	0.251462	−	0.967867i	$-0.419089\pi$
$331$	9.14988	0.502923	0.251462	+	0.967867i	$0.419089\pi$
$332$	−48.5881	−2.66662
$333$	32.2724	1.76852
$334$	−1.32727	−0.0726250
$335$	−2.83005	−0.154622
$336$	1.68199	0.0917603
$337$	31.1959	1.69935	0.849674	−	0.527308i	$-0.176799\pi$
$337$	31.1959	1.69935	0.849674	+	0.527308i	$0.176799\pi$
$338$	−78.1483	−4.25071
$339$	−14.0649	−0.763899
$340$	12.1589	0.659407
$341$	36.6505	1.98473
$342$	39.9335	2.15936
$343$	17.6065	0.950660
$344$	−6.38102	−0.344041
$345$	−32.9485	−1.77389
$346$	−15.4380	−0.829952
$347$	25.8642	1.38846	0.694232	−	0.719752i	$-0.255744\pi$
$347$	25.8642	1.38846	0.694232	+	0.719752i	$0.255744\pi$
$348$	−2.19907	−0.117883
$349$	−24.2935	−1.30040	−0.650202	−	0.759762i	$-0.725316\pi$
$349$	−24.2935	−1.30040	−0.650202	+	0.759762i	$0.725316\pi$
$350$	28.7538	1.53696
$351$	9.87167	0.526911
$352$	−17.9027	−0.954216
$353$	−1.00000	−0.0532246
$353$	−1.00000	−0.0532246
$354$	−24.5106	−1.30272
$355$	58.1194	3.08466
$356$	−36.5640	−1.93789
$357$	−3.83622	−0.203034
$358$	−19.8422	−1.04869
$359$	−9.11539	−0.481092	−0.240546	−	0.970638i	$-0.577326\pi$
$359$	−9.11539	−0.481092	−0.240546	+	0.970638i	$0.577326\pi$
$360$	39.9913	2.10773
$361$	4.55843	0.239918
$362$	−20.7146	−1.08873
$363$	−2.90697	−0.152576
$364$	34.1497	1.78993
$365$	−45.2570	−2.36886
$366$	52.0493	2.72066
$367$	13.5739	0.708553	0.354276	−	0.935141i	$-0.384727\pi$
$367$	13.5739	0.708553	0.354276	+	0.935141i	$0.384727\pi$
$368$	−1.54534	−0.0805564
$369$	−29.2254	−1.52142
$370$	76.3208	3.96773
$371$	−2.64868	−0.137513
$372$	89.8105	4.65646
$373$	−3.63303	−0.188111	−0.0940555	−	0.995567i	$-0.529983\pi$
$373$	−3.63303	−0.188111	−0.0940555	+	0.995567i	$0.529983\pi$
$374$	−8.04381	−0.415936
$375$	30.9959	1.60062
$376$	29.1373	1.50264
$377$	−1.76320	−0.0908093
$378$	−4.98730	−0.256519
$379$	27.2845	1.40151	0.700755	−	0.713402i	$-0.252847\pi$
$379$	27.2845	1.40151	0.700755	+	0.713402i	$0.252847\pi$
$380$	59.0155	3.02743
$381$	48.2485	2.47184
$382$	−52.6865	−2.69567
$383$	0.767520	0.0392184	0.0196092	−	0.999808i	$-0.493758\pi$
$383$	0.767520	0.0392184	0.0196092	+	0.999808i	$0.493758\pi$
$384$	−49.0572	−2.50344
$385$	−19.0348	−0.970103
$386$	10.5870	0.538865
$387$	7.39162	0.375737
$388$	36.4001	1.84793
$389$	13.4355	0.681205	0.340602	−	0.940207i	$-0.389369\pi$
$389$	13.4355	0.681205	0.340602	+	0.940207i	$0.389369\pi$
$390$	147.742	7.48120
$391$	3.52454	0.178244
$392$	14.6339	0.739122
$393$	−52.3423	−2.64032
$394$	−32.5265	−1.63866
$395$	−6.52293	−0.328204
$396$	−41.3564	−2.07824
$397$	−16.4452	−0.825362	−0.412681	−	0.910876i	$-0.635407\pi$
$397$	−16.4452	−0.825362	−0.412681	+	0.910876i	$0.635407\pi$
$398$	53.0903	2.66118
$399$	−18.6199	−0.932159
$400$	3.64601	0.182301
$401$	19.7553	0.986534	0.493267	−	0.869878i	$-0.335803\pi$
$401$	19.7553	0.986534	0.493267	+	0.869878i	$0.335803\pi$
$402$	4.58787	0.228822
$403$	72.0092	3.58704
$404$	12.6456	0.629143
$405$	25.5215	1.26818
$406$	0.890792	0.0442092
$407$	−31.5522	−1.56398
$408$	−7.87986	−0.390111
$409$	−20.8827	−1.03258	−0.516291	−	0.856413i	$-0.672688\pi$
$409$	−20.8827	−1.03258	−0.516291	+	0.856413i	$0.672688\pi$
$410$	−69.1151	−3.41335
$411$	−10.1187	−0.499119
$412$	2.24512	0.110609
$413$	6.20450	0.305303
$414$	28.9979	1.42517
$415$	53.2109	2.61202
$416$	−35.1744	−1.72457
$417$	−59.6768	−2.92239
$418$	−39.0423	−1.90962
$419$	−31.1082	−1.51973	−0.759867	−	0.650079i	$-0.774736\pi$
$419$	−31.1082	−1.51973	−0.759867	+	0.650079i	$0.774736\pi$
$420$	−46.6440	−2.27600
$421$	32.1011	1.56451	0.782257	−	0.622956i	$-0.214069\pi$
$421$	32.1011	1.56451	0.782257	+	0.622956i	$0.214069\pi$
$422$	−33.2189	−1.61707
$423$	−33.7520	−1.64108
$424$	−5.44057	−0.264218
$425$	−8.31567	−0.403369
$426$	−94.2190	−4.56493
$427$	−13.1755	−0.637609
$428$	15.6358	0.755785
$429$	−61.0788	−2.94891
$430$	17.4804	0.842980
$431$	5.58008	0.268783	0.134391	−	0.990928i	$-0.457092\pi$
$431$	5.58008	0.268783	0.134391	+	0.990928i	$0.457092\pi$
$432$	−0.632394	−0.0304261
$433$	5.82127	0.279753	0.139876	−	0.990169i	$-0.455330\pi$
$433$	5.82127	0.279753	0.139876	+	0.990169i	$0.455330\pi$
$434$	−36.3801	−1.74630
$435$	2.40830	0.115469
$436$	−55.9346	−2.67878
$437$	17.1071	0.818343
$438$	73.3673	3.50563
$439$	−8.56672	−0.408867	−0.204434	−	0.978880i	$-0.565535\pi$
$439$	−8.56672	−0.408867	−0.204434	+	0.978880i	$0.565535\pi$
$440$	−39.0988	−1.86396
$441$	−16.9515	−0.807216
$442$	−15.8041	−0.751726
$443$	−39.6410	−1.88340	−0.941700	−	0.336454i	$-0.890772\pi$
$443$	−39.6410	−1.88340	−0.941700	+	0.336454i	$0.890772\pi$
$444$	−77.3174	−3.66932
$445$	40.0427	1.89821
$446$	17.6057	0.833654
$447$	19.9153	0.941962
$448$	19.0837	0.901621
$449$	20.6015	0.972243	0.486122	−	0.873891i	$-0.338411\pi$
$449$	20.6015	0.972243	0.486122	+	0.873891i	$0.338411\pi$
$450$	−68.4165	−3.22519
$451$	28.5732	1.34546
$452$	18.2935	0.860452
$453$	−21.5698	−1.01344
$454$	38.9533	1.82817
$455$	−37.3988	−1.75328
$456$	−38.2465	−1.79106
$457$	−4.01128	−0.187640	−0.0938199	−	0.995589i	$-0.529908\pi$
$457$	−4.01128	−0.187640	−0.0938199	+	0.995589i	$0.529908\pi$
$458$	28.9995	1.35506
$459$	1.44234	0.0673225
$460$	42.8544	1.99810
$461$	24.2369	1.12883	0.564413	−	0.825493i	$-0.309103\pi$
$461$	24.2369	1.12883	0.564413	+	0.825493i	$0.309103\pi$
$462$	30.8578	1.43564
$463$	24.7970	1.15241	0.576207	−	0.817304i	$-0.304532\pi$
$463$	24.7970	1.15241	0.576207	+	0.817304i	$0.304532\pi$
$464$	0.112953	0.00524372
$465$	−98.3552	−4.56111
$466$	21.1212	0.978421
$467$	28.4656	1.31723	0.658615	−	0.752480i	$-0.271143\pi$
$467$	28.4656	1.31723	0.658615	+	0.752480i	$0.271143\pi$
$468$	−81.2554	−3.75603
$469$	−1.16135	−0.0536263
$470$	−79.8199	−3.68182
$471$	−25.0734	−1.15532
$472$	12.7445	0.586612
$473$	−7.22666	−0.332282
$474$	10.5745	0.485703
$475$	−40.3618	−1.85193
$476$	4.98957	0.228697
$477$	6.30223	0.288559
$478$	55.4967	2.53836
$479$	12.1444	0.554893	0.277447	−	0.960741i	$-0.410512\pi$
$479$	12.1444	0.554893	0.277447	+	0.960741i	$0.410512\pi$
$480$	48.0437	2.19288
$481$	−61.9923	−2.82661
$482$	13.7323	0.625491
$483$	−13.5209	−0.615223
$484$	3.78095	0.171861
$485$	−39.8632	−1.81009
$486$	−51.3652	−2.32998
$487$	−1.20765	−0.0547237	−0.0273619	−	0.999626i	$-0.508711\pi$
$487$	−1.20765	−0.0547237	−0.0273619	+	0.999626i	$0.508711\pi$
$488$	−27.0635	−1.22511
$489$	−53.8017	−2.43300
$490$	−40.0886	−1.81102
$491$	−38.1387	−1.72117	−0.860587	−	0.509304i	$-0.829903\pi$
$491$	−38.1387	−1.72117	−0.860587	+	0.509304i	$0.829903\pi$
$492$	70.0176	3.15664
$493$	−0.257619	−0.0116026
$494$	−76.7086	−3.45128
$495$	45.2911	2.03569
$496$	−4.61302	−0.207131
$497$	23.8502	1.06983
$498$	−86.2616	−3.86547
$499$	−31.6833	−1.41834	−0.709171	−	0.705037i	$-0.750930\pi$
$499$	−31.6833	−1.41834	−0.709171	+	0.705037i	$0.750930\pi$
$500$	−40.3147	−1.80293
$501$	−1.47253	−0.0657878
$502$	−21.0583	−0.939876
$503$	−40.8882	−1.82311	−0.911556	−	0.411175i	$-0.865119\pi$
$503$	−40.8882	−1.82311	−0.911556	+	0.411175i	$0.865119\pi$
$504$	16.4110	0.731006
$505$	−13.8487	−0.616261
$506$	−28.3508	−1.26035
$507$	−86.7010	−3.85053
$508$	−62.7543	−2.78427
$509$	−35.5649	−1.57638	−0.788192	−	0.615429i	$-0.788983\pi$
$509$	−35.5649	−1.57638	−0.788192	+	0.615429i	$0.788983\pi$
$510$	21.5864	0.955861
$511$	−18.5719	−0.821572
$512$	4.95056	0.218786
$513$	7.00068	0.309087
$514$	15.9370	0.702952
$515$	−2.45872	−0.108344
$516$	−17.7087	−0.779580
$517$	32.9988	1.45128
$518$	31.3194	1.37609
$519$	−17.1276	−0.751816
$520$	−76.8196	−3.36876
$521$	34.2199	1.49920	0.749601	−	0.661890i	$-0.230245\pi$
$521$	34.2199	1.49920	0.749601	+	0.661890i	$0.230245\pi$
$522$	−2.11954	−0.0927696
$523$	−7.24758	−0.316915	−0.158457	−	0.987366i	$-0.550652\pi$
$523$	−7.24758	−0.316915	−0.158457	+	0.987366i	$0.550652\pi$
$524$	68.0789	2.97404
$525$	31.9007	1.39226
$526$	4.90930	0.214056
$527$	10.5212	0.458310
$528$	3.91280	0.170283
$529$	−10.5776	−0.459895
$530$	14.9041	0.647393
$531$	−14.7629	−0.640655
$532$	24.2179	1.04998
$533$	56.1394	2.43167
$534$	−64.9143	−2.80912
$535$	−17.1234	−0.740310
$536$	−2.38550	−0.103038
$537$	−22.0138	−0.949965
$538$	31.9219	1.37625
$539$	16.5732	0.713860
$540$	17.5372	0.754680
$541$	−19.6874	−0.846427	−0.423214	−	0.906030i	$-0.639098\pi$
$541$	−19.6874	−0.846427	−0.423214	+	0.906030i	$0.639098\pi$
$542$	−55.5298	−2.38521
$543$	−22.9816	−0.986235
$544$	−5.13929	−0.220345
$545$	61.2563	2.62393
$546$	60.6281	2.59464
$547$	−14.6812	−0.627724	−0.313862	−	0.949469i	$-0.601623\pi$
$547$	−14.6812	−0.627724	−0.313862	+	0.949469i	$0.601623\pi$
$548$	13.1609	0.562205
$549$	31.3497	1.33797
$550$	66.8897	2.85218
$551$	−1.25040	−0.0532690
$552$	−27.7729	−1.18209
$553$	−2.67678	−0.113828
$554$	13.0100	0.552743
$555$	84.6734	3.59419
$556$	77.6186	3.29176
$557$	−26.3781	−1.11767	−0.558837	−	0.829277i	$-0.688752\pi$
$557$	−26.3781	−1.11767	−0.558837	+	0.829277i	$0.688752\pi$
$558$	86.5622	3.66447
$559$	−14.1986	−0.600538
$560$	2.39582	0.101242
$561$	−8.92414	−0.376778
$562$	53.9090	2.27401
$563$	−44.7185	−1.88466	−0.942330	−	0.334684i	$-0.891370\pi$
$563$	−44.7185	−1.88466	−0.942330	+	0.334684i	$0.891370\pi$
$564$	80.8622	3.40491
$565$	−20.0339	−0.842833
$566$	55.0065	2.31210
$567$	10.4731	0.439831
$568$	48.9900	2.05557
$569$	−3.69040	−0.154710	−0.0773548	−	0.997004i	$-0.524647\pi$
$569$	−3.69040	−0.154710	−0.0773548	+	0.997004i	$0.524647\pi$
$570$	104.774	4.38850
$571$	−31.8871	−1.33443	−0.667216	−	0.744864i	$-0.732514\pi$
$571$	−31.8871	−1.33443	−0.667216	+	0.744864i	$0.732514\pi$
$572$	79.4420	3.32164
$573$	−58.4526	−2.44189
$574$	−28.3624	−1.18382
$575$	−29.3089	−1.22227
$576$	−45.4075	−1.89198
$577$	−22.5777	−0.939923	−0.469961	−	0.882687i	$-0.655732\pi$
$577$	−22.5777	−0.939923	−0.469961	+	0.882687i	$0.655732\pi$
$578$	−2.30912	−0.0960469
$579$	11.7457	0.488133
$580$	−3.13235	−0.130064
$581$	21.8359	0.905905
$582$	64.6233	2.67872
$583$	−6.16159	−0.255187
$584$	−38.1480	−1.57857
$585$	88.9861	3.67912
$586$	8.49280	0.350834
$587$	−12.6124	−0.520569	−0.260285	−	0.965532i	$-0.583816\pi$
$587$	−12.6124	−0.520569	−0.260285	+	0.965532i	$0.583816\pi$
$588$	40.6121	1.67481
$589$	51.0667	2.10417
$590$	−34.9127	−1.43733
$591$	−36.0862	−1.48439
$592$	3.97132	0.163220
$593$	8.35891	0.343259	0.171630	−	0.985162i	$-0.445097\pi$
$593$	8.35891	0.343259	0.171630	+	0.985162i	$0.445097\pi$
$594$	−11.6019	−0.476031
$595$	−5.46429	−0.224014
$596$	−25.9028	−1.06102
$597$	58.9006	2.41064
$598$	−55.7024	−2.27784
$599$	−39.2464	−1.60356	−0.801781	−	0.597617i	$-0.796114\pi$
$599$	−39.2464	−1.60356	−0.801781	+	0.597617i	$0.796114\pi$
$600$	65.5263	2.67510
$601$	−33.8652	−1.38139	−0.690695	−	0.723146i	$-0.742695\pi$
$601$	−33.8652	−1.38139	−0.690695	+	0.723146i	$0.742695\pi$
$602$	7.17335	0.292364
$603$	2.76331	0.112531
$604$	28.0548	1.14153
$605$	−4.14067	−0.168342
$606$	22.4506	0.911992
$607$	43.3780	1.76066	0.880329	−	0.474363i	$-0.157322\pi$
$607$	43.3780	1.76066	0.880329	+	0.474363i	$0.157322\pi$
$608$	−24.9446	−1.01164
$609$	0.988281	0.0400472
$610$	74.1387	3.00179
$611$	64.8345	2.62292
$612$	−11.8721	−0.479902
$613$	12.4888	0.504420	0.252210	−	0.967673i	$-0.418843\pi$
$613$	12.4888	0.504420	0.252210	+	0.967673i	$0.418843\pi$
$614$	−48.6710	−1.96420
$615$	−76.6791	−3.09200
$616$	−16.0448	−0.646463
$617$	12.1206	0.487955	0.243978	−	0.969781i	$-0.421548\pi$
$617$	12.1206	0.487955	0.243978	+	0.969781i	$0.421548\pi$
$618$	3.98590	0.160336
$619$	−27.3827	−1.10060	−0.550301	−	0.834966i	$-0.685487\pi$
$619$	−27.3827	−1.10060	−0.550301	+	0.834966i	$0.685487\pi$
$620$	127.926	5.13761
$621$	5.08358	0.203997
$622$	33.9420	1.36095
$623$	16.4321	0.658339
$624$	7.68770	0.307754
$625$	2.57197	0.102879
$626$	−68.1321	−2.72311
$627$	−43.3151	−1.72984
$628$	32.6117	1.30135
$629$	−9.05762	−0.361151
$630$	−44.9570	−1.79113
$631$	11.4977	0.457717	0.228858	−	0.973460i	$-0.426501\pi$
$631$	11.4977	0.457717	0.228858	+	0.973460i	$0.426501\pi$
$632$	−5.49830	−0.218710
$633$	−36.8544	−1.46483
$634$	8.12247	0.322585
$635$	68.7248	2.72726
$636$	−15.0987	−0.598704
$637$	32.5624	1.29017
$638$	2.07224	0.0820406
$639$	−56.7488	−2.24495
$640$	−69.8768	−2.76212
$641$	−15.5911	−0.615812	−0.307906	−	0.951417i	$-0.599628\pi$
$641$	−15.5911	−0.615812	−0.307906	+	0.951417i	$0.599628\pi$
$642$	27.7592	1.09557
$643$	−21.9751	−0.866615	−0.433308	−	0.901246i	$-0.642654\pi$
$643$	−21.9751	−0.866615	−0.433308	+	0.901246i	$0.642654\pi$
$644$	17.5860	0.692984
$645$	19.3935	0.763617
$646$	−11.2078	−0.440965
$647$	7.53796	0.296348	0.148174	−	0.988961i	$-0.452660\pi$
$647$	7.53796	0.296348	0.148174	+	0.988961i	$0.452660\pi$
$648$	21.5126	0.845094
$649$	14.4334	0.566562
$650$	131.422	5.15479
$651$	−40.3616	−1.58189
$652$	69.9771	2.74051
$653$	−9.42288	−0.368746	−0.184373	−	0.982856i	$-0.559025\pi$
$653$	−9.42288	−0.368746	−0.184373	+	0.982856i	$0.559025\pi$
$654$	−99.3043	−3.88311
$655$	−74.5561	−2.91315
$656$	−3.59638	−0.140415
$657$	44.1897	1.72400
$658$	−32.7553	−1.27693
$659$	24.3252	0.947577	0.473788	−	0.880639i	$-0.342886\pi$
$659$	24.3252	0.947577	0.473788	+	0.880639i	$0.342886\pi$
$660$	−108.507	−4.22364
$661$	16.9884	0.660773	0.330386	−	0.943846i	$-0.392821\pi$
$661$	16.9884	0.660773	0.330386	+	0.943846i	$0.392821\pi$
$662$	−21.1282	−0.821171
$663$	−17.5338	−0.680955
$664$	44.8524	1.74061
$665$	−26.5220	−1.02848
$666$	−74.5209	−2.88763
$667$	−0.907988	−0.0351574
$668$	1.91524	0.0741030
$669$	19.5325	0.755170
$670$	6.53493	0.252466
$671$	−30.6500	−1.18323
$672$	19.7154	0.760540
$673$	9.60265	0.370155	0.185078	−	0.982724i	$-0.440746\pi$
$673$	9.60265	0.370155	0.185078	+	0.982724i	$0.440746\pi$
$674$	−72.0351	−2.77469
$675$	−11.9940	−0.461649
$676$	112.768	4.33721
$677$	1.57534	0.0605453	0.0302726	−	0.999542i	$-0.490362\pi$
$677$	1.57534	0.0605453	0.0302726	+	0.999542i	$0.490362\pi$
$678$	32.4775	1.24729
$679$	−16.3585	−0.627780
$680$	−11.2240	−0.430422
$681$	43.2164	1.65606
$682$	−84.6304	−3.24067
$683$	4.48393	0.171573	0.0857865	−	0.996314i	$-0.472660\pi$
$683$	4.48393	0.171573	0.0857865	+	0.996314i	$0.472660\pi$
$684$	−57.6237	−2.20330
$685$	−14.4130	−0.550694
$686$	−40.6555	−1.55223
$687$	32.1732	1.22749
$688$	0.909586	0.0346776
$689$	−12.1060	−0.461203
$690$	76.0822	2.89640
$691$	4.98889	0.189786	0.0948931	−	0.995487i	$-0.469749\pi$
$691$	4.98889	0.189786	0.0948931	+	0.995487i	$0.469749\pi$
$692$	22.2769	0.846842
$693$	18.5859	0.706020
$694$	−59.7236	−2.26708
$695$	−85.0033	−3.22436
$696$	2.03000	0.0769469
$697$	8.20246	0.310690
$698$	56.0968	2.12329
$699$	23.4327	0.886308
$700$	−41.4916	−1.56824
$701$	45.6486	1.72412	0.862062	−	0.506802i	$-0.169173\pi$
$701$	45.6486	1.72412	0.862062	+	0.506802i	$0.169173\pi$
$702$	−22.7949	−0.860338
$703$	−43.9630	−1.65810
$704$	44.3942	1.67317
$705$	−88.5555	−3.33519
$706$	2.30912	0.0869050
$707$	−5.68304	−0.213733
$708$	35.3686	1.32923
$709$	−12.9810	−0.487510	−0.243755	−	0.969837i	$-0.578379\pi$
$709$	−12.9810	−0.487510	−0.243755	+	0.969837i	$0.578379\pi$
$710$	−134.205	−5.03662
$711$	6.36910	0.238860
$712$	33.7527	1.26494
$713$	37.0824	1.38875
$714$	8.85830	0.331514
$715$	−87.0002	−3.25362
$716$	28.6322	1.07004
$717$	61.5703	2.29939
$718$	21.0486	0.785525
$719$	−19.9910	−0.745538	−0.372769	−	0.927924i	$-0.621592\pi$
$719$	−19.9910	−0.745538	−0.372769	+	0.927924i	$0.621592\pi$
$720$	−5.70058	−0.212448
$721$	−1.00897	−0.0375761
$722$	−10.5260	−0.391736
$723$	15.2352	0.566604
$724$	29.8910	1.11089
$725$	2.14227	0.0795619
$726$	6.71256	0.249126
$727$	−16.7412	−0.620895	−0.310448	−	0.950590i	$-0.600479\pi$
$727$	−16.7412	−0.620895	−0.310448	+	0.950590i	$0.600479\pi$
$728$	−31.5241	−1.16836
$729$	−36.0048	−1.33351
$730$	104.504	3.86786
$731$	−2.07454	−0.0767298
$732$	−75.1068	−2.77603
$733$	−18.1403	−0.670026	−0.335013	−	0.942213i	$-0.608741\pi$
$733$	−18.1403	−0.670026	−0.335013	+	0.942213i	$0.608741\pi$
$734$	−31.3439	−1.15692
$735$	−44.4760	−1.64052
$736$	−18.1137	−0.667678
$737$	−2.70164	−0.0995161
$738$	67.4851	2.48416
$739$	20.1204	0.740142	0.370071	−	0.929003i	$-0.379333\pi$
$739$	20.1204	0.740142	0.370071	+	0.929003i	$0.379333\pi$
$740$	−110.130	−4.04847
$741$	−85.1037	−3.12636
$742$	6.11613	0.224530
$743$	−14.4646	−0.530654	−0.265327	−	0.964158i	$-0.585480\pi$
$743$	−14.4646	−0.530654	−0.265327	+	0.964158i	$0.585480\pi$
$744$	−82.9055	−3.03946
$745$	28.3672	1.03929
$746$	8.38911	0.307147
$747$	−51.9560	−1.90097
$748$	11.6072	0.424400
$749$	−7.02685	−0.256756
$750$	−71.5733	−2.61349
$751$	0.843350	0.0307743	0.0153871	−	0.999882i	$-0.495102\pi$
$751$	0.843350	0.0307743	0.0153871	+	0.999882i	$0.495102\pi$
$752$	−4.15340	−0.151459
$753$	−23.3629	−0.851392
$754$	4.07144	0.148273
$755$	−30.7239	−1.11816
$756$	7.19664	0.261739
$757$	−10.1330	−0.368290	−0.184145	−	0.982899i	$-0.558952\pi$
$757$	−10.1330	−0.368290	−0.184145	+	0.982899i	$0.558952\pi$
$758$	−63.0033	−2.28838
$759$	−31.4535	−1.14169
$760$	−54.4781	−1.97613
$761$	27.7194	1.00483	0.502414	−	0.864627i	$-0.332445\pi$
$761$	27.7194	1.00483	0.502414	+	0.864627i	$0.332445\pi$
$762$	−111.412	−4.03602
$763$	25.1375	0.910037
$764$	76.0262	2.75053
$765$	13.0016	0.470076
$766$	−1.77230	−0.0640357
$767$	28.3582	1.02395
$768$	47.9823	1.73141
$769$	1.94791	0.0702434	0.0351217	−	0.999383i	$-0.488818\pi$
$769$	1.94791	0.0702434	0.0351217	+	0.999383i	$0.488818\pi$
$770$	43.9537	1.58398
$771$	17.6812	0.636772
$772$	−15.2770	−0.549831
$773$	8.47858	0.304953	0.152477	−	0.988307i	$-0.451275\pi$
$773$	8.47858	0.304953	0.152477	+	0.988307i	$0.451275\pi$
$774$	−17.0682	−0.613502
$775$	−87.4906	−3.14276
$776$	−33.6014	−1.20622
$777$	34.7470	1.24654
$778$	−31.0241	−1.11227
$779$	39.8123	1.42642
$780$	−213.191	−7.63345
$781$	55.4824	1.98531
$782$	−8.13860	−0.291036
$783$	−0.371573	−0.0132789
$784$	−2.08599	−0.0744998
$785$	−35.7144	−1.27470
$786$	120.865	4.31111
$787$	−15.3984	−0.548894	−0.274447	−	0.961602i	$-0.588495\pi$
$787$	−15.3984	−0.548894	−0.274447	+	0.961602i	$0.588495\pi$
$788$	46.9355	1.67201
$789$	5.44658	0.193903
$790$	15.0622	0.535890
$791$	−8.22122	−0.292313
$792$	38.1768	1.35655
$793$	−60.2199	−2.13847
$794$	37.9740	1.34765
$795$	16.5352	0.586445
$796$	−76.6090	−2.71533
$797$	−8.64188	−0.306111	−0.153056	−	0.988218i	$-0.548911\pi$
$797$	−8.64188	−0.306111	−0.153056	+	0.988218i	$0.548911\pi$
$798$	42.9956	1.52203
$799$	9.47289	0.335127
$800$	42.7366	1.51097
$801$	−39.0984	−1.38147
$802$	−45.6175	−1.61081
$803$	−43.2035	−1.52462
$804$	−6.62026	−0.233479
$805$	−19.2591	−0.678795
$806$	−166.278	−5.85690
$807$	35.4155	1.24669
$808$	−11.6734	−0.410667
$809$	38.8969	1.36754	0.683772	−	0.729696i	$-0.260338\pi$
$809$	38.8969	1.36754	0.683772	+	0.729696i	$0.260338\pi$
$810$	−58.9324	−2.07067
$811$	5.99010	0.210341	0.105170	−	0.994454i	$-0.466461\pi$
$811$	5.99010	0.210341	0.105170	+	0.994454i	$0.466461\pi$
$812$	−1.28541	−0.0451089
$813$	−61.6071	−2.16066
$814$	72.8578	2.55367
$815$	−76.6348	−2.68440
$816$	1.12324	0.0393213
$817$	−10.0692	−0.352278
$818$	48.2206	1.68600
$819$	36.5168	1.27600
$820$	99.7326	3.48281
$821$	2.33058	0.0813377	0.0406689	−	0.999173i	$-0.487051\pi$
$821$	2.33058	0.0813377	0.0406689	+	0.999173i	$0.487051\pi$
$822$	23.3654	0.814960
$823$	−5.46723	−0.190576	−0.0952878	−	0.995450i	$-0.530377\pi$
$823$	−5.46723	−0.190576	−0.0952878	+	0.995450i	$0.530377\pi$
$824$	−2.07250	−0.0721989
$825$	74.2102	2.58367
$826$	−14.3269	−0.498498
$827$	−9.92201	−0.345022	−0.172511	−	0.985008i	$-0.555188\pi$
$827$	−9.92201	−0.345022	−0.172511	+	0.985008i	$0.555188\pi$
$828$	−41.8438	−1.45417
$829$	17.7453	0.616319	0.308160	−	0.951335i	$-0.400287\pi$
$829$	17.7453	0.616319	0.308160	+	0.951335i	$0.400287\pi$
$830$	−122.870	−4.26489
$831$	14.4339	0.500705
$832$	87.2238	3.02394
$833$	4.75765	0.164843
$834$	137.801	4.77166
$835$	−2.09746	−0.0725856
$836$	56.3377	1.94848
$837$	15.1751	0.524528
$838$	71.8326	2.48142
$839$	16.4743	0.568756	0.284378	−	0.958712i	$-0.408213\pi$
$839$	16.4743	0.568756	0.284378	+	0.958712i	$0.408213\pi$
$840$	43.0578	1.48564
$841$	−28.9336	−0.997711
$842$	−74.1255	−2.55453
$843$	59.8089	2.05993
$844$	47.9346	1.64998
$845$	−123.496	−4.24840
$846$	77.9375	2.67955
$847$	−1.69919	−0.0583848
$848$	0.775530	0.0266318
$849$	61.0265	2.09443
$850$	19.2019	0.658620
$851$	−31.9240	−1.09434
$852$	135.957	4.65782
$853$	12.4408	0.425963	0.212982	−	0.977056i	$-0.431683\pi$
$853$	12.4408	0.425963	0.212982	+	0.977056i	$0.431683\pi$
$854$	30.4239	1.04109
$855$	63.1061	2.15818
$856$	−14.4336	−0.493332
$857$	−41.3994	−1.41418	−0.707088	−	0.707125i	$-0.749992\pi$
$857$	−41.3994	−1.41418	−0.707088	+	0.707125i	$0.749992\pi$
$858$	141.038	4.81497
$859$	31.8145	1.08550	0.542749	−	0.839895i	$-0.317384\pi$
$859$	31.8145	1.08550	0.542749	+	0.839895i	$0.317384\pi$
$860$	−25.2241	−0.860134
$861$	−31.4664	−1.07237
$862$	−12.8851	−0.438868
$863$	14.7534	0.502211	0.251106	−	0.967960i	$-0.419206\pi$
$863$	14.7534	0.502211	0.251106	+	0.967960i	$0.419206\pi$
$864$	−7.41259	−0.252181
$865$	−24.3964	−0.829502
$866$	−13.4420	−0.456779
$867$	−2.56184	−0.0870045
$868$	52.4962	1.78184
$869$	−6.22696	−0.211235
$870$	−5.56105	−0.188537
$871$	−5.30806	−0.179857
$872$	51.6341	1.74855
$873$	38.9231	1.31735
$874$	−39.5024	−1.33619
$875$	18.1177	0.612492
$876$	−105.869	−3.57697
$877$	45.8325	1.54765	0.773827	−	0.633398i	$-0.218340\pi$
$877$	45.8325	1.54765	0.773827	+	0.633398i	$0.218340\pi$
$878$	19.7816	0.667597
$879$	9.42226	0.317805
$880$	5.57336	0.187878
$881$	7.33502	0.247123	0.123562	−	0.992337i	$-0.460568\pi$
$881$	7.33502	0.247123	0.123562	+	0.992337i	$0.460568\pi$
$882$	39.1432	1.31802
$883$	−13.9038	−0.467898	−0.233949	−	0.972249i	$-0.575165\pi$
$883$	−13.9038	−0.467898	−0.233949	+	0.972249i	$0.575165\pi$
$884$	22.8053	0.767024
$885$	−38.7336	−1.30201
$886$	91.5359	3.07521
$887$	−48.0058	−1.61188	−0.805939	−	0.591999i	$-0.798339\pi$
$887$	−48.0058	−1.61188	−0.805939	+	0.591999i	$0.798339\pi$
$888$	71.3728	2.39512
$889$	28.2023	0.945874
$890$	−92.4635	−3.09938
$891$	24.3635	0.816209
$892$	−25.4049	−0.850619
$893$	45.9786	1.53862
$894$	−45.9869	−1.53803
$895$	−31.3563	−1.04813
$896$	−28.6750	−0.957965
$897$	−61.7985	−2.06339
$898$	−47.5713	−1.58748
$899$	−2.71045	−0.0903986
$900$	98.7246	3.29082
$901$	−1.76880	−0.0589271
$902$	−65.9791	−2.19686
$903$	7.95841	0.264839
$904$	−16.8870	−0.561652
$905$	−32.7348	−1.08814
$906$	49.8074	1.65474
$907$	−20.8859	−0.693505	−0.346752	−	0.937957i	$-0.612716\pi$
$907$	−20.8859	−0.693505	−0.346752	+	0.937957i	$0.612716\pi$
$908$	−56.2094	−1.86537
$909$	13.5221	0.448501
$910$	86.3583	2.86275
$911$	15.5342	0.514670	0.257335	−	0.966322i	$-0.417156\pi$
$911$	15.5342	0.514670	0.257335	+	0.966322i	$0.417156\pi$
$912$	5.45187	0.180530
$913$	50.7965	1.68112
$914$	9.26255	0.306378
$915$	82.2525	2.71918
$916$	−41.8461	−1.38263
$917$	−30.5952	−1.01034
$918$	−3.33053	−0.109924
$919$	−22.5667	−0.744407	−0.372203	−	0.928151i	$-0.621398\pi$
$919$	−22.5667	−0.744407	−0.372203	+	0.928151i	$0.621398\pi$
$920$	−39.5596	−1.30424
$921$	−53.9977	−1.77928
$922$	−55.9660	−1.84314
$923$	109.009	3.58809
$924$	−44.5276	−1.46485
$925$	75.3202	2.47651
$926$	−57.2593	−1.88166
$927$	2.40074	0.0788505
$928$	1.32398	0.0434617
$929$	36.8657	1.20952	0.604762	−	0.796406i	$-0.293268\pi$
$929$	36.8657	1.20952	0.604762	+	0.796406i	$0.293268\pi$
$930$	227.114	7.44737
$931$	23.0922	0.756817
$932$	−30.4778	−0.998332
$933$	37.6567	1.23282
$934$	−65.7305	−2.15077
$935$	−12.7115	−0.415710
$936$	75.0080	2.45171
$937$	−51.7830	−1.69168	−0.845839	−	0.533439i	$-0.820899\pi$
$937$	−51.7830	−1.69168	−0.845839	+	0.533439i	$0.820899\pi$
$938$	2.68171	0.0875608
$939$	−75.5886	−2.46674
$940$	115.180	3.75674
$941$	−6.71582	−0.218929	−0.109465	−	0.993991i	$-0.534914\pi$
$941$	−6.71582	−0.218929	−0.109465	+	0.993991i	$0.534914\pi$
$942$	57.8975	1.88640
$943$	28.9099	0.941437
$944$	−1.81667	−0.0591275
$945$	−7.88134	−0.256380
$946$	16.6872	0.542549
$947$	37.3223	1.21281	0.606406	−	0.795155i	$-0.292611\pi$
$947$	37.3223	1.21281	0.606406	+	0.795155i	$0.292611\pi$
$948$	−15.2589	−0.495587
$949$	−84.8844	−2.75546
$950$	93.2003	3.02382
$951$	9.01141	0.292215
$952$	−4.60595	−0.149280
$953$	19.6806	0.637518	0.318759	−	0.947836i	$-0.396734\pi$
$953$	19.6806	0.637518	0.318759	+	0.947836i	$0.396734\pi$
$954$	−14.5526	−0.471159
$955$	−83.2594	−2.69421
$956$	−80.0813	−2.59002
$957$	2.29902	0.0743169
$958$	−28.0430	−0.906027
$959$	−5.91460	−0.190993
$960$	−119.136	−3.84511
$961$	79.6952	2.57081
$962$	143.148	4.61527
$963$	16.7196	0.538781
$964$	−19.8157	−0.638220
$965$	16.7305	0.538572
$966$	31.2215	1.00453
$967$	−10.9726	−0.352856	−0.176428	−	0.984314i	$-0.556454\pi$
$967$	−10.9726	−0.352856	−0.176428	+	0.984314i	$0.556454\pi$
$968$	−3.49025	−0.112181
$969$	−12.4344	−0.399450
$970$	92.0490	2.95552
$971$	−46.5795	−1.49481	−0.747404	−	0.664369i	$-0.768700\pi$
$971$	−46.5795	−1.49481	−0.747404	+	0.664369i	$0.768700\pi$
$972$	74.1197	2.37739
$973$	−34.8824	−1.11828
$974$	2.78861	0.0893527
$975$	145.805	4.66950
$976$	3.85778	0.123484
$977$	−54.0820	−1.73024	−0.865119	−	0.501567i	$-0.832757\pi$
$977$	−54.0820	−1.73024	−0.865119	+	0.501567i	$0.832757\pi$
$978$	124.235	3.97259
$979$	38.2258	1.22170
$980$	57.8476	1.84787
$981$	−59.8117	−1.90964
$982$	88.0668	2.81033
$983$	−40.8441	−1.30272	−0.651362	−	0.758767i	$-0.725802\pi$
$983$	−40.8441	−1.30272	−0.651362	+	0.758767i	$0.725802\pi$
$984$	−64.6343	−2.06047
$985$	−51.4010	−1.63777
$986$	0.594873	0.0189446
$987$	−36.3401	−1.15672
$988$	110.690	3.52152
$989$	−7.31182	−0.232502
$990$	−104.583	−3.32386
$991$	13.3924	0.425424	0.212712	−	0.977115i	$-0.431770\pi$
$991$	13.3924	0.425424	0.212712	+	0.977115i	$0.431770\pi$
$992$	−54.0714	−1.71677
$993$	−23.4405	−0.743862
$994$	−55.0730	−1.74681
$995$	83.8977	2.65973
$996$	124.475	3.94414
$997$	−37.5304	−1.18860	−0.594299	−	0.804244i	$-0.702570\pi$
$997$	−37.5304	−1.18860	−0.594299	+	0.804244i	$0.702570\pi$
$998$	73.1607	2.31586
$999$	−13.0641	−0.413331

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6001.2.a.a.1.13	✓	113

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6001.2.a.a.1.13	✓	113	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:	\( N \)	\(=\)	\( 6001 = 17 \cdot 353 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6001.a (trivial)

\(f(q)\)	\(=\)	\(q-2.30912 q^{2} -2.56184 q^{3} +3.33205 q^{4} -3.64906 q^{5} +5.91560 q^{6} -1.49745 q^{7} -3.07586 q^{8} +3.56301 q^{9} +O(q^{10})\)	\(q-2.30912 q^{2} -2.56184 q^{3} +3.33205 q^{4} -3.64906 q^{5} +5.91560 q^{6} -1.49745 q^{7} -3.07586 q^{8} +3.56301 q^{9} +8.42614 q^{10} -3.48349 q^{11} -8.53617 q^{12} -6.84422 q^{13} +3.45779 q^{14} +9.34831 q^{15} +0.438451 q^{16} -1.00000 q^{17} -8.22743 q^{18} -4.85370 q^{19} -12.1589 q^{20} +3.83622 q^{21} +8.04381 q^{22} -3.52454 q^{23} +7.87986 q^{24} +8.31567 q^{25} +15.8041 q^{26} -1.44234 q^{27} -4.98957 q^{28} +0.257619 q^{29} -21.5864 q^{30} -10.5212 q^{31} +5.13929 q^{32} +8.92414 q^{33} +2.30912 q^{34} +5.46429 q^{35} +11.8721 q^{36} +9.05762 q^{37} +11.2078 q^{38} +17.5338 q^{39} +11.2240 q^{40} -8.20246 q^{41} -8.85830 q^{42} +2.07454 q^{43} -11.6072 q^{44} -13.0016 q^{45} +8.13860 q^{46} -9.47289 q^{47} -1.12324 q^{48} -4.75765 q^{49} -19.2019 q^{50} +2.56184 q^{51} -22.8053 q^{52} +1.76880 q^{53} +3.33053 q^{54} +12.7115 q^{55} +4.60595 q^{56} +12.4344 q^{57} -0.594873 q^{58} -4.14338 q^{59} +31.1490 q^{60} +8.79865 q^{61} +24.2947 q^{62} -5.33542 q^{63} -12.7442 q^{64} +24.9750 q^{65} -20.6069 q^{66} +0.775554 q^{67} -3.33205 q^{68} +9.02931 q^{69} -12.6177 q^{70} -15.9272 q^{71} -10.9593 q^{72} +12.4024 q^{73} -20.9152 q^{74} -21.3034 q^{75} -16.1728 q^{76} +5.21635 q^{77} -40.4876 q^{78} +1.78756 q^{79} -1.59994 q^{80} -6.99399 q^{81} +18.9405 q^{82} -14.5821 q^{83} +12.7825 q^{84} +3.64906 q^{85} -4.79038 q^{86} -0.659977 q^{87} +10.7148 q^{88} -10.9734 q^{89} +30.0224 q^{90} +10.2489 q^{91} -11.7440 q^{92} +26.9535 q^{93} +21.8741 q^{94} +17.7115 q^{95} -13.1660 q^{96} +10.9242 q^{97} +10.9860 q^{98} -12.4117 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 113 q - 11 q^{2} - 11 q^{3} + 103 q^{4} - 19 q^{5} - 13 q^{6} + 11 q^{7} - 36 q^{8} + 94 q^{9}+O(q^{10}) \) 113 * q - 11 * q^2 - 11 * q^3 + 103 * q^4 - 19 * q^5 - 13 * q^6 + 11 * q^7 - 36 * q^8 + 94 * q^9	\( 113 q - 11 q^{2} - 11 q^{3} + 103 q^{4} - 19 q^{5} - 13 q^{6} + 11 q^{7} - 36 q^{8} + 94 q^{9} - 5 q^{10} - 40 q^{11} - 19 q^{12} - 18 q^{13} - 48 q^{14} - 63 q^{15} + 79 q^{16} - 113 q^{17} - 32 q^{18} - 46 q^{19} - 56 q^{20} - 46 q^{21} + 14 q^{22} - 35 q^{23} - 42 q^{24} + 88 q^{25} - 89 q^{26} - 41 q^{27} + 20 q^{28} - 51 q^{29} - 18 q^{30} - 57 q^{31} - 93 q^{32} - 40 q^{33} + 11 q^{34} - 69 q^{35} + 18 q^{36} + 16 q^{37} - 74 q^{38} - 51 q^{39} + 2 q^{40} - 87 q^{41} - 23 q^{42} - 32 q^{43} - 110 q^{44} - 17 q^{45} - 17 q^{46} - 161 q^{47} - 36 q^{48} + 56 q^{49} - 69 q^{50} + 11 q^{51} - 49 q^{52} - 48 q^{53} - 38 q^{54} - 79 q^{55} - 171 q^{56} + 20 q^{57} + 13 q^{58} - 174 q^{59} - 146 q^{60} - 34 q^{61} - 34 q^{62} - 14 q^{63} + 62 q^{64} - 22 q^{65} - 60 q^{66} - 50 q^{67} - 103 q^{68} - 59 q^{69} - 58 q^{70} - 189 q^{71} - 123 q^{72} - 4 q^{73} - 24 q^{74} - 106 q^{75} - 92 q^{76} - 78 q^{77} - 42 q^{78} + 8 q^{79} - 150 q^{80} + 13 q^{81} + 6 q^{82} - 109 q^{83} - 114 q^{84} + 19 q^{85} - 116 q^{86} - 106 q^{87} + 54 q^{88} - 170 q^{89} - q^{90} - 43 q^{91} - 94 q^{92} - 69 q^{93} - 35 q^{94} - 78 q^{95} - 44 q^{96} - 3 q^{97} - 68 q^{98} - 119 q^{99}+O(q^{100}) \) 113 * q - 11 * q^2 - 11 * q^3 + 103 * q^4 - 19 * q^5 - 13 * q^6 + 11 * q^7 - 36 * q^8 + 94 * q^9 - 5 * q^10 - 40 * q^11 - 19 * q^12 - 18 * q^13 - 48 * q^14 - 63 * q^15 + 79 * q^16 - 113 * q^17 - 32 * q^18 - 46 * q^19 - 56 * q^20 - 46 * q^21 + 14 * q^22 - 35 * q^23 - 42 * q^24 + 88 * q^25 - 89 * q^26 - 41 * q^27 + 20 * q^28 - 51 * q^29 - 18 * q^30 - 57 * q^31 - 93 * q^32 - 40 * q^33 + 11 * q^34 - 69 * q^35 + 18 * q^36 + 16 * q^37 - 74 * q^38 - 51 * q^39 + 2 * q^40 - 87 * q^41 - 23 * q^42 - 32 * q^43 - 110 * q^44 - 17 * q^45 - 17 * q^46 - 161 * q^47 - 36 * q^48 + 56 * q^49 - 69 * q^50 + 11 * q^51 - 49 * q^52 - 48 * q^53 - 38 * q^54 - 79 * q^55 - 171 * q^56 + 20 * q^57 + 13 * q^58 - 174 * q^59 - 146 * q^60 - 34 * q^61 - 34 * q^62 - 14 * q^63 + 62 * q^64 - 22 * q^65 - 60 * q^66 - 50 * q^67 - 103 * q^68 - 59 * q^69 - 58 * q^70 - 189 * q^71 - 123 * q^72 - 4 * q^73 - 24 * q^74 - 106 * q^75 - 92 * q^76 - 78 * q^77 - 42 * q^78 + 8 * q^79 - 150 * q^80 + 13 * q^81 + 6 * q^82 - 109 * q^83 - 114 * q^84 + 19 * q^85 - 116 * q^86 - 106 * q^87 + 54 * q^88 - 170 * q^89 - q^90 - 43 * q^91 - 94 * q^92 - 69 * q^93 - 35 * q^94 - 78 * q^95 - 44 * q^96 - 3 * q^97 - 68 * q^98 - 119 * q^99

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