LMFDB - Embedded newform 6013.2.a.f.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6013,2,Mod(1,6013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6013, 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("6013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6013 = 7 \cdot 859 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6013.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:	$48.0140467354$
Analytic rank:	$0$
Dimension:	$110$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	6013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.24570 q^{2} -1.05382 q^{3} +3.04316 q^{4} +1.30809 q^{5} +2.36656 q^{6} -1.00000 q^{7} -2.34263 q^{8} -1.88947 q^{9} +O(q^{10})$	\(q-2.24570 q^{2} -1.05382 q^{3} +3.04316 q^{4} +1.30809 q^{5} +2.36656 q^{6} -1.00000 q^{7} -2.34263 q^{8} -1.88947 q^{9} -2.93757 q^{10} +2.40940 q^{11} -3.20694 q^{12} +2.54546 q^{13} +2.24570 q^{14} -1.37848 q^{15} -0.825481 q^{16} +4.00711 q^{17} +4.24318 q^{18} -1.00984 q^{19} +3.98072 q^{20} +1.05382 q^{21} -5.41078 q^{22} -3.85436 q^{23} +2.46871 q^{24} -3.28891 q^{25} -5.71634 q^{26} +5.15261 q^{27} -3.04316 q^{28} -4.64307 q^{29} +3.09566 q^{30} +7.89837 q^{31} +6.53905 q^{32} -2.53906 q^{33} -8.99876 q^{34} -1.30809 q^{35} -5.74996 q^{36} +0.386212 q^{37} +2.26779 q^{38} -2.68245 q^{39} -3.06437 q^{40} +5.01310 q^{41} -2.36656 q^{42} +9.35891 q^{43} +7.33219 q^{44} -2.47159 q^{45} +8.65574 q^{46} -6.61036 q^{47} +0.869906 q^{48} +1.00000 q^{49} +7.38590 q^{50} -4.22276 q^{51} +7.74625 q^{52} -7.31985 q^{53} -11.5712 q^{54} +3.15170 q^{55} +2.34263 q^{56} +1.06418 q^{57} +10.4269 q^{58} +3.16616 q^{59} -4.19495 q^{60} -2.28912 q^{61} -17.7374 q^{62} +1.88947 q^{63} -13.0338 q^{64} +3.32968 q^{65} +5.70197 q^{66} -13.2498 q^{67} +12.1943 q^{68} +4.06179 q^{69} +2.93757 q^{70} +3.79624 q^{71} +4.42633 q^{72} +15.2649 q^{73} -0.867316 q^{74} +3.46591 q^{75} -3.07310 q^{76} -2.40940 q^{77} +6.02398 q^{78} -2.81529 q^{79} -1.07980 q^{80} +0.238497 q^{81} -11.2579 q^{82} +2.79171 q^{83} +3.20694 q^{84} +5.24165 q^{85} -21.0173 q^{86} +4.89295 q^{87} -5.64433 q^{88} +1.94065 q^{89} +5.55044 q^{90} -2.54546 q^{91} -11.7295 q^{92} -8.32344 q^{93} +14.8449 q^{94} -1.32095 q^{95} -6.89096 q^{96} -13.0329 q^{97} -2.24570 q^{98} -4.55248 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 110 q + 16 q^{2} + 29 q^{3} + 118 q^{4} + 12 q^{6} - 110 q^{7} + 57 q^{8} + 127 q^{9}+O(q^{10}) $ 110 * q + 16 * q^2 + 29 * q^3 + 118 * q^4 + 12 * q^6 - 110 * q^7 + 57 * q^8 + 127 * q^9	\( 110 q + 16 q^{2} + 29 q^{3} + 118 q^{4} + 12 q^{6} - 110 q^{7} + 57 q^{8} + 127 q^{9} + 3 q^{10} + 52 q^{11} + 62 q^{12} - 9 q^{13} - 16 q^{14} + 39 q^{15} + 146 q^{16} + 11 q^{17} + 60 q^{18} + 14 q^{19} + 18 q^{20} - 29 q^{21} + 32 q^{22} + 73 q^{23} + 24 q^{24} + 132 q^{25} - 7 q^{26} + 116 q^{27} - 118 q^{28} + 35 q^{29} + 18 q^{30} + 36 q^{31} + 140 q^{32} + 42 q^{33} - 7 q^{34} + 180 q^{36} + 49 q^{37} + 45 q^{39} + 6 q^{40} - 14 q^{41} - 12 q^{42} + 58 q^{43} + 92 q^{44} + 17 q^{45} + 27 q^{46} + 87 q^{47} + 98 q^{48} + 110 q^{49} + 91 q^{50} + 42 q^{51} + 16 q^{52} + 95 q^{53} + 41 q^{54} + 8 q^{55} - 57 q^{56} + 61 q^{57} + 46 q^{58} + 114 q^{59} + 81 q^{60} - 47 q^{61} + 31 q^{62} - 127 q^{63} + 199 q^{64} + 62 q^{65} + 21 q^{66} + 95 q^{67} + 60 q^{68} - 39 q^{69} - 3 q^{70} + 131 q^{71} + 186 q^{72} + 31 q^{73} + 23 q^{74} + 121 q^{75} + 14 q^{76} - 52 q^{77} + 110 q^{78} + 9 q^{79} + 61 q^{80} + 194 q^{81} + 45 q^{82} + 73 q^{83} - 62 q^{84} + 59 q^{85} + 72 q^{86} + 64 q^{87} + 100 q^{88} - 17 q^{89} + 11 q^{90} + 9 q^{91} + 192 q^{92} + 85 q^{93} - 11 q^{94} + 108 q^{95} + 68 q^{96} + 32 q^{97} + 16 q^{98} + 160 q^{99}+O(q^{100}) \) 110 * q + 16 * q^2 + 29 * q^3 + 118 * q^4 + 12 * q^6 - 110 * q^7 + 57 * q^8 + 127 * q^9 + 3 * q^10 + 52 * q^11 + 62 * q^12 - 9 * q^13 - 16 * q^14 + 39 * q^15 + 146 * q^16 + 11 * q^17 + 60 * q^18 + 14 * q^19 + 18 * q^20 - 29 * q^21 + 32 * q^22 + 73 * q^23 + 24 * q^24 + 132 * q^25 - 7 * q^26 + 116 * q^27 - 118 * q^28 + 35 * q^29 + 18 * q^30 + 36 * q^31 + 140 * q^32 + 42 * q^33 - 7 * q^34 + 180 * q^36 + 49 * q^37 + 45 * q^39 + 6 * q^40 - 14 * q^41 - 12 * q^42 + 58 * q^43 + 92 * q^44 + 17 * q^45 + 27 * q^46 + 87 * q^47 + 98 * q^48 + 110 * q^49 + 91 * q^50 + 42 * q^51 + 16 * q^52 + 95 * q^53 + 41 * q^54 + 8 * q^55 - 57 * q^56 + 61 * q^57 + 46 * q^58 + 114 * q^59 + 81 * q^60 - 47 * q^61 + 31 * q^62 - 127 * q^63 + 199 * q^64 + 62 * q^65 + 21 * q^66 + 95 * q^67 + 60 * q^68 - 39 * q^69 - 3 * q^70 + 131 * q^71 + 186 * q^72 + 31 * q^73 + 23 * q^74 + 121 * q^75 + 14 * q^76 - 52 * q^77 + 110 * q^78 + 9 * q^79 + 61 * q^80 + 194 * q^81 + 45 * q^82 + 73 * q^83 - 62 * q^84 + 59 * q^85 + 72 * q^86 + 64 * q^87 + 100 * q^88 - 17 * q^89 + 11 * q^90 + 9 * q^91 + 192 * q^92 + 85 * q^93 - 11 * q^94 + 108 * q^95 + 68 * q^96 + 32 * q^97 + 16 * q^98 + 160 * 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 $

$2$	−2.24570	−1.58795	−0.793974	−	0.607951i	$-0.791992\pi$
$2$	−2.24570	−1.58795	−0.793974	+	0.607951i	$0.791992\pi$
$3$	−1.05382	−0.608422	−0.304211	−	0.952605i	$-0.598393\pi$
$3$	−1.05382	−0.608422	−0.304211	+	0.952605i	$0.598393\pi$
$4$	3.04316	1.52158
$5$	1.30809	0.584994	0.292497	−	0.956266i	$-0.405514\pi$
$5$	1.30809	0.584994	0.292497	+	0.956266i	$0.405514\pi$
$6$	2.36656	0.966143
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−2.34263	−0.828246
$9$	−1.88947	−0.629823
$10$	−2.93757	−0.928941
$11$	2.40940	0.726460	0.363230	−	0.931699i	$-0.381674\pi$
$11$	2.40940	0.726460	0.363230	+	0.931699i	$0.381674\pi$
$12$	−3.20694	−0.925764
$13$	2.54546	0.705984	0.352992	−	0.935626i	$-0.385164\pi$
$13$	2.54546	0.705984	0.352992	+	0.935626i	$0.385164\pi$
$14$	2.24570	0.600188
$15$	−1.37848	−0.355923
$16$	−0.825481	−0.206370
$17$	4.00711	0.971867	0.485934	−	0.873996i	$-0.338480\pi$
$17$	4.00711	0.971867	0.485934	+	0.873996i	$0.338480\pi$
$18$	4.24318	1.00013
$19$	−1.00984	−0.231672	−0.115836	−	0.993268i	$-0.536955\pi$
$19$	−1.00984	−0.231672	−0.115836	+	0.993268i	$0.536955\pi$
$20$	3.98072	0.890116
$21$	1.05382	0.229962
$22$	−5.41078	−1.15358
$23$	−3.85436	−0.803690	−0.401845	−	0.915708i	$-0.631631\pi$
$23$	−3.85436	−0.803690	−0.401845	+	0.915708i	$0.631631\pi$
$24$	2.46871	0.503923
$25$	−3.28891	−0.657782
$26$	−5.71634	−1.12107
$27$	5.15261	0.991620
$28$	−3.04316	−0.575104
$29$	−4.64307	−0.862197	−0.431099	−	0.902305i	$-0.641874\pi$
$29$	−4.64307	−0.862197	−0.431099	+	0.902305i	$0.641874\pi$
$30$	3.09566	0.565188
$31$	7.89837	1.41859	0.709295	−	0.704912i	$-0.249014\pi$
$31$	7.89837	1.41859	0.709295	+	0.704912i	$0.249014\pi$
$32$	6.53905	1.15595
$33$	−2.53906	−0.441994
$34$	−8.99876	−1.54328
$35$	−1.30809	−0.221107
$36$	−5.74996	−0.958327
$37$	0.386212	0.0634928	0.0317464	−	0.999496i	$-0.489893\pi$
$37$	0.386212	0.0634928	0.0317464	+	0.999496i	$0.489893\pi$
$38$	2.26779	0.367884
$39$	−2.68245	−0.429536
$40$	−3.06437	−0.484519
$41$	5.01310	0.782915	0.391457	−	0.920196i	$-0.371971\pi$
$41$	5.01310	0.782915	0.391457	+	0.920196i	$0.371971\pi$
$42$	−2.36656	−0.365168
$43$	9.35891	1.42722	0.713610	−	0.700543i	$-0.247059\pi$
$43$	9.35891	1.42722	0.713610	+	0.700543i	$0.247059\pi$
$44$	7.33219	1.10537
$45$	−2.47159	−0.368443
$46$	8.65574	1.27622
$47$	−6.61036	−0.964219	−0.482110	−	0.876111i	$-0.660129\pi$
$47$	−6.61036	−0.964219	−0.482110	+	0.876111i	$0.660129\pi$
$48$	0.869906	0.125560
$49$	1.00000	0.142857
$50$	7.38590	1.04452
$51$	−4.22276	−0.591305
$52$	7.74625	1.07421
$53$	−7.31985	−1.00546	−0.502730	−	0.864444i	$-0.667671\pi$
$53$	−7.31985	−1.00546	−0.502730	+	0.864444i	$0.667671\pi$
$54$	−11.5712	−1.57464
$55$	3.15170	0.424975
$56$	2.34263	0.313047
$57$	1.06418	0.140954
$58$	10.4269	1.36913
$59$	3.16616	0.412198	0.206099	−	0.978531i	$-0.433923\pi$
$59$	3.16616	0.412198	0.206099	+	0.978531i	$0.433923\pi$
$60$	−4.19495	−0.541566
$61$	−2.28912	−0.293092	−0.146546	−	0.989204i	$-0.546816\pi$
$61$	−2.28912	−0.293092	−0.146546	+	0.989204i	$0.546816\pi$
$62$	−17.7374	−2.25265
$63$	1.88947	0.238051
$64$	−13.0338	−1.62922
$65$	3.32968	0.412996
$66$	5.70197	0.701864
$67$	−13.2498	−1.61872	−0.809362	−	0.587310i	$-0.800187\pi$
$67$	−13.2498	−1.61872	−0.809362	+	0.587310i	$0.800187\pi$
$68$	12.1943	1.47878
$69$	4.06179	0.488983
$70$	2.93757	0.351107
$71$	3.79624	0.450530	0.225265	−	0.974297i	$-0.427675\pi$
$71$	3.79624	0.450530	0.225265	+	0.974297i	$0.427675\pi$
$72$	4.42633	0.521648
$73$	15.2649	1.78663	0.893313	−	0.449435i	$-0.148375\pi$
$73$	15.2649	1.78663	0.893313	+	0.449435i	$0.148375\pi$
$74$	−0.867316	−0.100823
$75$	3.46591	0.400209
$76$	−3.07310	−0.352508
$77$	−2.40940	−0.274576
$78$	6.02398	0.682081
$79$	−2.81529	−0.316745	−0.158373	−	0.987379i	$-0.550625\pi$
$79$	−2.81529	−0.316745	−0.158373	+	0.987379i	$0.550625\pi$
$80$	−1.07980	−0.120725
$81$	0.238497	0.0264997
$82$	−11.2579	−1.24323
$83$	2.79171	0.306429	0.153215	−	0.988193i	$-0.451037\pi$
$83$	2.79171	0.306429	0.153215	+	0.988193i	$0.451037\pi$
$84$	3.20694	0.349906
$85$	5.24165	0.568536
$86$	−21.0173	−2.26635
$87$	4.89295	0.524580
$88$	−5.64433	−0.601688
$89$	1.94065	0.205708	0.102854	−	0.994696i	$-0.467203\pi$
$89$	1.94065	0.205708	0.102854	+	0.994696i	$0.467203\pi$
$90$	5.55044	0.585068
$91$	−2.54546	−0.266837
$92$	−11.7295	−1.22288
$93$	−8.32344	−0.863101
$94$	14.8449	1.53113
$95$	−1.32095	−0.135527
$96$	−6.89096	−0.703306
$97$	−13.0329	−1.32330	−0.661648	−	0.749815i	$-0.730142\pi$
$97$	−13.0329	−1.32330	−0.661648	+	0.749815i	$0.730142\pi$
$98$	−2.24570	−0.226850
$99$	−4.55248	−0.457541
$100$	−10.0087	−1.00087
$101$	16.0784	1.59987	0.799933	−	0.600090i	$-0.204869\pi$
$101$	16.0784	1.59987	0.799933	+	0.600090i	$0.204869\pi$
$102$	9.48306	0.938962
$103$	5.15885	0.508317	0.254158	−	0.967163i	$-0.418202\pi$
$103$	5.15885	0.508317	0.254158	+	0.967163i	$0.418202\pi$
$104$	−5.96308	−0.584728
$105$	1.37848	0.134526
$106$	16.4382	1.59662
$107$	−0.151397	−0.0146361	−0.00731803	−	0.999973i	$-0.502329\pi$
$107$	−0.151397	−0.0146361	−0.00731803	+	0.999973i	$0.502329\pi$
$108$	15.6802	1.50883
$109$	8.44863	0.809232	0.404616	−	0.914487i	$-0.367405\pi$
$109$	8.44863	0.809232	0.404616	+	0.914487i	$0.367405\pi$
$110$	−7.07777	−0.674838
$111$	−0.406997	−0.0386304
$112$	0.825481	0.0780006
$113$	3.53447	0.332495	0.166247	−	0.986084i	$-0.446835\pi$
$113$	3.53447	0.332495	0.166247	+	0.986084i	$0.446835\pi$
$114$	−2.38983	−0.223828
$115$	−5.04184	−0.470154
$116$	−14.1296	−1.31190
$117$	−4.80957	−0.444645
$118$	−7.11023	−0.654550
$119$	−4.00711	−0.367331
$120$	3.22928	0.294792
$121$	−5.19481	−0.472255
$122$	5.14067	0.465415
$123$	−5.28289	−0.476343
$124$	24.0360	2.15850
$125$	−10.8426	−0.969793
$126$	−4.24318	−0.378012
$127$	6.87397	0.609967	0.304983	−	0.952358i	$-0.401349\pi$
$127$	6.87397	0.609967	0.304983	+	0.952358i	$0.401349\pi$
$128$	16.1918	1.43117
$129$	−9.86259	−0.868352
$130$	−7.47746	−0.655817
$131$	−11.9483	−1.04393	−0.521963	−	0.852968i	$-0.674800\pi$
$131$	−11.9483	−1.04393	−0.521963	+	0.852968i	$0.674800\pi$
$132$	−7.72679	−0.672531
$133$	1.00984	0.0875639
$134$	29.7551	2.57045
$135$	6.74006	0.580092
$136$	−9.38719	−0.804945
$137$	−9.83722	−0.840451	−0.420225	−	0.907420i	$-0.638049\pi$
$137$	−9.83722	−0.840451	−0.420225	+	0.907420i	$0.638049\pi$
$138$	−9.12157	−0.776480
$139$	19.8865	1.68675	0.843376	−	0.537324i	$-0.180565\pi$
$139$	19.8865	1.68675	0.843376	+	0.537324i	$0.180565\pi$
$140$	−3.98072	−0.336432
$141$	6.96611	0.586652
$142$	−8.52520	−0.715419
$143$	6.13302	0.512869
$144$	1.55972	0.129977
$145$	−6.07354	−0.504380
$146$	−34.2805	−2.83707
$147$	−1.05382	−0.0869174
$148$	1.17531	0.0966096
$149$	19.6724	1.61162	0.805812	−	0.592171i	$-0.201729\pi$
$149$	19.6724	1.61162	0.805812	+	0.592171i	$0.201729\pi$
$150$	−7.78339	−0.635511
$151$	−18.0192	−1.46638	−0.733191	−	0.680023i	$-0.761970\pi$
$151$	−18.0192	−1.46638	−0.733191	+	0.680023i	$0.761970\pi$
$152$	2.36567	0.191881
$153$	−7.57131	−0.612104
$154$	5.41078	0.436013
$155$	10.3318	0.829866
$156$	−8.16314	−0.653574
$157$	−2.29575	−0.183221	−0.0916104	−	0.995795i	$-0.529201\pi$
$157$	−2.29575	−0.183221	−0.0916104	+	0.995795i	$0.529201\pi$
$158$	6.32230	0.502975
$159$	7.71379	0.611743
$160$	8.55364	0.676224
$161$	3.85436	0.303766
$162$	−0.535592	−0.0420801
$163$	15.9713	1.25097	0.625483	−	0.780238i	$-0.284902\pi$
$163$	15.9713	1.25097	0.625483	+	0.780238i	$0.284902\pi$
$164$	15.2557	1.19127
$165$	−3.32132	−0.258564
$166$	−6.26933	−0.486594
$167$	17.3099	1.33948	0.669741	−	0.742594i	$-0.266405\pi$
$167$	17.3099	1.33948	0.669741	+	0.742594i	$0.266405\pi$
$168$	−2.46871	−0.190465
$169$	−6.52063	−0.501587
$170$	−11.7712	−0.902807
$171$	1.90805	0.145912
$172$	28.4807	2.17163
$173$	16.2683	1.23685	0.618427	−	0.785842i	$-0.287770\pi$
$173$	16.2683	1.23685	0.618427	+	0.785842i	$0.287770\pi$
$174$	−10.9881	−0.833006
$175$	3.28891	0.248618
$176$	−1.98891	−0.149920
$177$	−3.33655	−0.250791
$178$	−4.35811	−0.326654
$179$	−6.31316	−0.471867	−0.235934	−	0.971769i	$-0.575815\pi$
$179$	−6.31316	−0.471867	−0.235934	+	0.971769i	$0.575815\pi$
$180$	−7.52145	−0.560616
$181$	−4.20451	−0.312519	−0.156259	−	0.987716i	$-0.549944\pi$
$181$	−4.20451	−0.312519	−0.156259	+	0.987716i	$0.549944\pi$
$182$	5.71634	0.423723
$183$	2.41232	0.178323
$184$	9.02935	0.665653
$185$	0.505199	0.0371429
$186$	18.6920	1.37056
$187$	9.65472	0.706023
$188$	−20.1164	−1.46714
$189$	−5.15261	−0.374797
$190$	2.96646	0.215210
$191$	−26.2982	−1.90287	−0.951437	−	0.307844i	$-0.900393\pi$
$191$	−26.2982	−1.90287	−0.951437	+	0.307844i	$0.900393\pi$
$192$	13.7352	0.991254
$193$	−7.43672	−0.535307	−0.267653	−	0.963515i	$-0.586248\pi$
$193$	−7.43672	−0.535307	−0.267653	+	0.963515i	$0.586248\pi$
$194$	29.2681	2.10133
$195$	−3.50888	−0.251276
$196$	3.04316	0.217369
$197$	−10.7833	−0.768278	−0.384139	−	0.923275i	$-0.625502\pi$
$197$	−10.7833	−0.768278	−0.384139	+	0.923275i	$0.625502\pi$
$198$	10.2235	0.726552
$199$	22.6444	1.60522	0.802609	−	0.596506i	$-0.203445\pi$
$199$	22.6444	1.60522	0.802609	+	0.596506i	$0.203445\pi$
$200$	7.70471	0.544805
$201$	13.9629	0.984868
$202$	−36.1073	−2.54050
$203$	4.64307	0.325880
$204$	−12.8506	−0.899719
$205$	6.55757	0.458001
$206$	−11.5852	−0.807181
$207$	7.28270	0.506182
$208$	−2.10123	−0.145694
$209$	−2.43309	−0.168301
$210$	−3.09566	−0.213621
$211$	−19.3615	−1.33290	−0.666451	−	0.745548i	$-0.732188\pi$
$211$	−19.3615	−1.33290	−0.666451	+	0.745548i	$0.732188\pi$
$212$	−22.2755	−1.52989
$213$	−4.00054	−0.274113
$214$	0.339991	0.0232413
$215$	12.2423	0.834916
$216$	−12.0707	−0.821305
$217$	−7.89837	−0.536176
$218$	−18.9731	−1.28502
$219$	−16.0865	−1.08702
$220$	9.59113	0.646634
$221$	10.1999	0.686122
$222$	0.913992	0.0613432
$223$	−0.717083	−0.0480195	−0.0240097	−	0.999712i	$-0.507643\pi$
$223$	−0.717083	−0.0480195	−0.0240097	+	0.999712i	$0.507643\pi$
$224$	−6.53905	−0.436908
$225$	6.21429	0.414286
$226$	−7.93735	−0.527985
$227$	28.1341	1.86733	0.933663	−	0.358153i	$-0.116594\pi$
$227$	28.1341	1.86733	0.933663	+	0.358153i	$0.116594\pi$
$228$	3.23848	0.214474
$229$	−6.35205	−0.419755	−0.209878	−	0.977728i	$-0.567307\pi$
$229$	−6.35205	−0.419755	−0.209878	+	0.977728i	$0.567307\pi$
$230$	11.3225	0.746580
$231$	2.53906	0.167058
$232$	10.8770	0.714111
$233$	2.05914	0.134899	0.0674495	−	0.997723i	$-0.478514\pi$
$233$	2.05914	0.134899	0.0674495	+	0.997723i	$0.478514\pi$
$234$	10.8008	0.706073
$235$	−8.64692	−0.564063
$236$	9.63513	0.627194
$237$	2.96681	0.192715
$238$	8.99876	0.583303
$239$	−13.6241	−0.881271	−0.440636	−	0.897686i	$-0.645247\pi$
$239$	−13.6241	−0.881271	−0.440636	+	0.897686i	$0.645247\pi$
$240$	1.13791	0.0734519
$241$	1.59335	0.102636	0.0513182	−	0.998682i	$-0.483658\pi$
$241$	1.59335	0.102636	0.0513182	+	0.998682i	$0.483658\pi$
$242$	11.6660	0.749918
$243$	−15.7092	−1.00774
$244$	−6.96617	−0.445963
$245$	1.30809	0.0835706
$246$	11.8638	0.756408
$247$	−2.57050	−0.163557
$248$	−18.5030	−1.17494
$249$	−2.94195	−0.186438
$250$	24.3492	1.53998
$251$	13.7058	0.865101	0.432551	−	0.901610i	$-0.357614\pi$
$251$	13.7058	0.865101	0.432551	+	0.901610i	$0.357614\pi$
$252$	5.74996	0.362214
$253$	−9.28669	−0.583849
$254$	−15.4369	−0.968596
$255$	−5.52374	−0.345910
$256$	−10.2944	−0.643402
$257$	16.9015	1.05429	0.527144	−	0.849776i	$-0.323263\pi$
$257$	16.9015	1.05429	0.527144	+	0.849776i	$0.323263\pi$
$258$	22.1484	1.37890
$259$	−0.386212	−0.0239980
$260$	10.1328	0.628408
$261$	8.77294	0.543032
$262$	26.8322	1.65770
$263$	3.61158	0.222699	0.111350	−	0.993781i	$-0.464483\pi$
$263$	3.61158	0.222699	0.111350	+	0.993781i	$0.464483\pi$
$264$	5.94809	0.366080
$265$	−9.57500	−0.588188
$266$	−2.26779	−0.139047
$267$	−2.04509	−0.125157
$268$	−40.3214	−2.46302
$269$	−13.6297	−0.831021	−0.415510	−	0.909588i	$-0.636397\pi$
$269$	−13.6297	−0.831021	−0.415510	+	0.909588i	$0.636397\pi$
$270$	−15.1361	−0.921156
$271$	−16.4063	−0.996609	−0.498305	−	0.867002i	$-0.666044\pi$
$271$	−16.4063	−0.996609	−0.498305	+	0.867002i	$0.666044\pi$
$272$	−3.30779	−0.200564
$273$	2.68245	0.162349
$274$	22.0914	1.33459
$275$	−7.92429	−0.477852
$276$	12.3607	0.744027
$277$	−22.2496	−1.33685	−0.668423	−	0.743781i	$-0.733030\pi$
$277$	−22.2496	−1.33685	−0.668423	+	0.743781i	$0.733030\pi$
$278$	−44.6591	−2.67848
$279$	−14.9237	−0.893460
$280$	3.06437	0.183131
$281$	0.392516	0.0234155	0.0117078	−	0.999931i	$-0.496273\pi$
$281$	0.392516	0.0234155	0.0117078	+	0.999931i	$0.496273\pi$
$282$	−15.6438	−0.931574
$283$	−0.572895	−0.0340551	−0.0170275	−	0.999855i	$-0.505420\pi$
$283$	−0.572895	−0.0340551	−0.0170275	+	0.999855i	$0.505420\pi$
$284$	11.5526	0.685519
$285$	1.39204	0.0824575
$286$	−13.7729	−0.814410
$287$	−5.01310	−0.295914
$288$	−12.3553	−0.728044
$289$	−0.943064	−0.0554743
$290$	13.6393	0.800930
$291$	13.7343	0.805122
$292$	46.4537	2.71850
$293$	−6.28135	−0.366960	−0.183480	−	0.983023i	$-0.558736\pi$
$293$	−6.28135	−0.366960	−0.183480	+	0.983023i	$0.558736\pi$
$294$	2.36656	0.138020
$295$	4.14161	0.241134
$296$	−0.904752	−0.0525877
$297$	12.4147	0.720372
$298$	−44.1782	−2.55918
$299$	−9.81113	−0.567392
$300$	10.5473	0.608951
$301$	−9.35891	−0.539439
$302$	40.4657	2.32854
$303$	−16.9437	−0.973393
$304$	0.833600	0.0478102
$305$	−2.99437	−0.171457
$306$	17.0029	0.971990
$307$	−14.4480	−0.824589	−0.412294	−	0.911051i	$-0.635272\pi$
$307$	−14.4480	−0.824589	−0.412294	+	0.911051i	$0.635272\pi$
$308$	−7.33219	−0.417790
$309$	−5.43649	−0.309271
$310$	−23.2020	−1.31779
$311$	−28.2457	−1.60167	−0.800834	−	0.598887i	$-0.795610\pi$
$311$	−28.2457	−1.60167	−0.800834	+	0.598887i	$0.795610\pi$
$312$	6.28400	0.355761
$313$	−6.07053	−0.343127	−0.171563	−	0.985173i	$-0.554882\pi$
$313$	−6.07053	−0.343127	−0.171563	+	0.985173i	$0.554882\pi$
$314$	5.15557	0.290945
$315$	2.47159	0.139258
$316$	−8.56740	−0.481954
$317$	−1.52173	−0.0854688	−0.0427344	−	0.999086i	$-0.513607\pi$
$317$	−1.52173	−0.0854688	−0.0427344	+	0.999086i	$0.513607\pi$
$318$	−17.3229	−0.971417
$319$	−11.1870	−0.626352
$320$	−17.0493	−0.953085
$321$	0.159544	0.00890490
$322$	−8.65574	−0.482365
$323$	−4.04652	−0.225155
$324$	0.725785	0.0403214
$325$	−8.37179	−0.464383
$326$	−35.8667	−1.98647
$327$	−8.90332	−0.492355
$328$	−11.7439	−0.648446
$329$	6.61036	0.364441
$330$	7.45867	0.410586
$331$	−18.1324	−0.996649	−0.498324	−	0.866991i	$-0.666051\pi$
$331$	−18.1324	−0.996649	−0.498324	+	0.866991i	$0.666051\pi$
$332$	8.49562	0.466258
$333$	−0.729735	−0.0399892
$334$	−38.8729	−2.12703
$335$	−17.3319	−0.946944
$336$	−0.869906	−0.0474573
$337$	25.6027	1.39467	0.697335	−	0.716745i	$-0.254369\pi$
$337$	25.6027	1.39467	0.697335	+	0.716745i	$0.254369\pi$
$338$	14.6434	0.796495
$339$	−3.72468	−0.202297
$340$	15.9512	0.865075
$341$	19.0303	1.03055
$342$	−4.28491	−0.231702
$343$	−1.00000	−0.0539949
$344$	−21.9245	−1.18209
$345$	5.31318	0.286052
$346$	−36.5336	−1.96406
$347$	3.64105	0.195462	0.0977308	−	0.995213i	$-0.468842\pi$
$347$	3.64105	0.195462	0.0977308	+	0.995213i	$0.468842\pi$
$348$	14.8901	0.798191
$349$	−2.91568	−0.156073	−0.0780363	−	0.996951i	$-0.524865\pi$
$349$	−2.91568	−0.156073	−0.0780363	+	0.996951i	$0.524865\pi$
$350$	−7.38590	−0.394793
$351$	13.1158	0.700067
$352$	15.7552	0.839752
$353$	15.8764	0.845013	0.422507	−	0.906360i	$-0.361150\pi$
$353$	15.8764	0.845013	0.422507	+	0.906360i	$0.361150\pi$
$354$	7.49289	0.398243
$355$	4.96581	0.263558
$356$	5.90571	0.313002
$357$	4.22276	0.223492
$358$	14.1774	0.749302
$359$	29.5144	1.55771	0.778856	−	0.627203i	$-0.215801\pi$
$359$	29.5144	1.55771	0.778856	+	0.627203i	$0.215801\pi$
$360$	5.79002	0.305161
$361$	−17.9802	−0.946328
$362$	9.44207	0.496264
$363$	5.47438	0.287331
$364$	−7.74625	−0.406014
$365$	19.9679	1.04517
$366$	−5.41733	−0.283169
$367$	29.3983	1.53458	0.767290	−	0.641300i	$-0.221604\pi$
$367$	29.3983	1.53458	0.767290	+	0.641300i	$0.221604\pi$
$368$	3.18170	0.165858
$369$	−9.47210	−0.493098
$370$	−1.13452	−0.0589811
$371$	7.31985	0.380028
$372$	−25.3296	−1.31328
$373$	−1.95314	−0.101130	−0.0505649	−	0.998721i	$-0.516102\pi$
$373$	−1.95314	−0.101130	−0.0505649	+	0.998721i	$0.516102\pi$
$374$	−21.6816	−1.12113
$375$	11.4261	0.590043
$376$	15.4856	0.798610
$377$	−11.8188	−0.608697
$378$	11.5712	0.595159
$379$	−9.01112	−0.462870	−0.231435	−	0.972850i	$-0.574342\pi$
$379$	−9.01112	−0.462870	−0.231435	+	0.972850i	$0.574342\pi$
$380$	−4.01987	−0.206215
$381$	−7.24391	−0.371117
$382$	59.0579	3.02167
$383$	16.0692	0.821100	0.410550	−	0.911838i	$-0.365337\pi$
$383$	16.0692	0.821100	0.410550	+	0.911838i	$0.365337\pi$
$384$	−17.0632	−0.870754
$385$	−3.15170	−0.160625
$386$	16.7006	0.850040
$387$	−17.6834	−0.898896
$388$	−39.6614	−2.01350
$389$	−3.27220	−0.165907	−0.0829536	−	0.996553i	$-0.526435\pi$
$389$	−3.27220	−0.165907	−0.0829536	+	0.996553i	$0.526435\pi$
$390$	7.87988	0.399013
$391$	−15.4449	−0.781080
$392$	−2.34263	−0.118321
$393$	12.5913	0.635147
$394$	24.2160	1.21999
$395$	−3.68265	−0.185294
$396$	−13.8539	−0.696187
$397$	−9.81464	−0.492582	−0.246291	−	0.969196i	$-0.579212\pi$
$397$	−9.81464	−0.492582	−0.246291	+	0.969196i	$0.579212\pi$
$398$	−50.8525	−2.54900
$399$	−1.06418	−0.0532758
$400$	2.71493	0.135747
$401$	27.8751	1.39202	0.696008	−	0.718034i	$-0.254958\pi$
$401$	27.8751	1.39202	0.696008	+	0.718034i	$0.254958\pi$
$402$	−31.3565	−1.56392
$403$	20.1050	1.00150
$404$	48.9293	2.43433
$405$	0.311975	0.0155021
$406$	−10.4269	−0.517481
$407$	0.930537	0.0461250
$408$	9.89238	0.489746
$409$	−0.717812	−0.0354935	−0.0177467	−	0.999843i	$-0.505649\pi$
$409$	−0.717812	−0.0354935	−0.0177467	+	0.999843i	$0.505649\pi$
$410$	−14.7263	−0.727281
$411$	10.3666	0.511349
$412$	15.6992	0.773446
$413$	−3.16616	−0.155796
$414$	−16.3547	−0.803792
$415$	3.65179	0.179259
$416$	16.6449	0.816082
$417$	−20.9568	−1.02626
$418$	5.46400	0.267253
$419$	20.4117	0.997177	0.498589	−	0.866839i	$-0.333852\pi$
$419$	20.4117	0.997177	0.498589	+	0.866839i	$0.333852\pi$
$420$	4.19495	0.204693
$421$	−22.7437	−1.10846	−0.554231	−	0.832363i	$-0.686988\pi$
$421$	−22.7437	−1.10846	−0.554231	+	0.832363i	$0.686988\pi$
$422$	43.4802	2.11658
$423$	12.4901	0.607287
$424$	17.1477	0.832767
$425$	−13.1790	−0.639277
$426$	8.98401	0.435277
$427$	2.28912	0.110778
$428$	−0.460725	−0.0222700
$429$	−6.46309	−0.312041
$430$	−27.4924	−1.32580
$431$	15.8654	0.764212	0.382106	−	0.924119i	$-0.375199\pi$
$431$	15.8654	0.764212	0.382106	+	0.924119i	$0.375199\pi$
$432$	−4.25338	−0.204641
$433$	17.3625	0.834390	0.417195	−	0.908817i	$-0.363013\pi$
$433$	17.3625	0.834390	0.417195	+	0.908817i	$0.363013\pi$
$434$	17.7374	0.851421
$435$	6.40041	0.306876
$436$	25.7106	1.23131
$437$	3.89227	0.186193
$438$	36.1253	1.72614
$439$	13.2872	0.634161	0.317081	−	0.948399i	$-0.397297\pi$
$439$	13.2872	0.634161	0.317081	+	0.948399i	$0.397297\pi$
$440$	−7.38327	−0.351984
$441$	−1.88947	−0.0899747
$442$	−22.9060	−1.08953
$443$	22.8564	1.08594	0.542970	−	0.839752i	$-0.317300\pi$
$443$	22.8564	1.08594	0.542970	+	0.839752i	$0.317300\pi$
$444$	−1.23856	−0.0587794
$445$	2.53854	0.120338
$446$	1.61035	0.0762525
$447$	−20.7311	−0.980547
$448$	13.0338	0.615788
$449$	−26.1359	−1.23343	−0.616714	−	0.787188i	$-0.711536\pi$
$449$	−26.1359	−1.23343	−0.616714	+	0.787188i	$0.711536\pi$
$450$	−13.9554	−0.657865
$451$	12.0785	0.568757
$452$	10.7560	0.505918
$453$	18.9890	0.892179
$454$	−63.1807	−2.96522
$455$	−3.32968	−0.156098
$456$	−2.49299	−0.116745
$457$	8.09950	0.378879	0.189439	−	0.981892i	$-0.439333\pi$
$457$	8.09950	0.378879	0.189439	+	0.981892i	$0.439333\pi$
$458$	14.2648	0.666550
$459$	20.6471	0.963723
$460$	−15.3431	−0.715378
$461$	19.6462	0.915017	0.457508	−	0.889205i	$-0.348742\pi$
$461$	19.6462	0.915017	0.457508	+	0.889205i	$0.348742\pi$
$462$	−5.70197	−0.265280
$463$	18.7203	0.870007	0.435004	−	0.900429i	$-0.356747\pi$
$463$	18.7203	0.870007	0.435004	+	0.900429i	$0.356747\pi$
$464$	3.83277	0.177932
$465$	−10.8878	−0.504909
$466$	−4.62421	−0.214213
$467$	16.4114	0.759428	0.379714	−	0.925104i	$-0.376022\pi$
$467$	16.4114	0.759428	0.379714	+	0.925104i	$0.376022\pi$
$468$	−14.6363	−0.676563
$469$	13.2498	0.611820
$470$	19.4184	0.895703
$471$	2.41930	0.111476
$472$	−7.41714	−0.341402
$473$	22.5493	1.03682
$474$	−6.66255	−0.306021
$475$	3.32126	0.152390
$476$	−12.1943	−0.558925
$477$	13.8306	0.633261
$478$	30.5957	1.39941
$479$	−0.373222	−0.0170529	−0.00852647	−	0.999964i	$-0.502714\pi$
$479$	−0.373222	−0.0170529	−0.00852647	+	0.999964i	$0.502714\pi$
$480$	−9.01397	−0.411430
$481$	0.983087	0.0448249
$482$	−3.57818	−0.162981
$483$	−4.06179	−0.184818
$484$	−15.8087	−0.718575
$485$	−17.0482	−0.774120
$486$	35.2780	1.60024
$487$	4.40189	0.199469	0.0997344	−	0.995014i	$-0.468201\pi$
$487$	4.40189	0.199469	0.0997344	+	0.995014i	$0.468201\pi$
$488$	5.36257	0.242752
$489$	−16.8308	−0.761115
$490$	−2.93757	−0.132706
$491$	40.4871	1.82716	0.913578	−	0.406663i	$-0.133308\pi$
$491$	40.4871	1.82716	0.913578	+	0.406663i	$0.133308\pi$
$492$	−16.0767	−0.724794
$493$	−18.6053	−0.837941
$494$	5.77256	0.259720
$495$	−5.95503	−0.267659
$496$	−6.51996	−0.292755
$497$	−3.79624	−0.170284
$498$	6.60673	0.296055
$499$	16.0510	0.718542	0.359271	−	0.933233i	$-0.383025\pi$
$499$	16.0510	0.718542	0.359271	+	0.933233i	$0.383025\pi$
$500$	−32.9958	−1.47562
$501$	−18.2415	−0.814970
$502$	−30.7791	−1.37374
$503$	17.4383	0.777535	0.388767	−	0.921336i	$-0.372901\pi$
$503$	17.4383	0.777535	0.388767	+	0.921336i	$0.372901\pi$
$504$	−4.42633	−0.197164
$505$	21.0320	0.935912
$506$	20.8551	0.927122
$507$	6.87156	0.305177
$508$	20.9186	0.928114
$509$	−4.92598	−0.218340	−0.109170	−	0.994023i	$-0.534819\pi$
$509$	−4.92598	−0.218340	−0.109170	+	0.994023i	$0.534819\pi$
$510$	12.4047	0.549287
$511$	−15.2649	−0.675281
$512$	−9.26545	−0.409479
$513$	−5.20329	−0.229731
$514$	−37.9557	−1.67416
$515$	6.74822	0.297362
$516$	−30.0135	−1.32127
$517$	−15.9270	−0.700467
$518$	0.867316	0.0381077
$519$	−17.1438	−0.752529
$520$	−7.80022	−0.342062
$521$	−10.5341	−0.461509	−0.230754	−	0.973012i	$-0.574119\pi$
$521$	−10.5341	−0.461509	−0.230754	+	0.973012i	$0.574119\pi$
$522$	−19.7014	−0.862306
$523$	38.3887	1.67862	0.839311	−	0.543652i	$-0.182959\pi$
$523$	38.3887	1.67862	0.839311	+	0.543652i	$0.182959\pi$
$524$	−36.3606	−1.58842
$525$	−3.46591	−0.151265
$526$	−8.11052	−0.353635
$527$	31.6497	1.37868
$528$	2.09595	0.0912145
$529$	−8.14389	−0.354082
$530$	21.5026	0.934012
$531$	−5.98235	−0.259612
$532$	3.07310	0.133236
$533$	12.7606	0.552725
$534$	4.59265	0.198744
$535$	−0.198040	−0.00856201
$536$	31.0395	1.34070
$537$	6.65292	0.287094
$538$	30.6083	1.31962
$539$	2.40940	0.103780
$540$	20.5111	0.882657
$541$	−36.5514	−1.57147	−0.785733	−	0.618566i	$-0.787714\pi$
$541$	−36.5514	−1.57147	−0.785733	+	0.618566i	$0.787714\pi$
$542$	36.8435	1.58256
$543$	4.43079	0.190143
$544$	26.2027	1.12343
$545$	11.0515	0.473396
$546$	−6.02398	−0.257802
$547$	19.0464	0.814366	0.407183	−	0.913347i	$-0.366511\pi$
$547$	19.0464	0.814366	0.407183	+	0.913347i	$0.366511\pi$
$548$	−29.9363	−1.27881
$549$	4.32522	0.184596
$550$	17.7956	0.758805
$551$	4.68874	0.199747
$552$	−9.51529	−0.404998
$553$	2.81529	0.119718
$554$	49.9658	2.12284
$555$	−0.532387	−0.0225986
$556$	60.5179	2.56653
$557$	9.14173	0.387348	0.193674	−	0.981066i	$-0.437960\pi$
$557$	9.14173	0.387348	0.193674	+	0.981066i	$0.437960\pi$
$558$	33.5142	1.41877
$559$	23.8227	1.00759
$560$	1.07980	0.0456299
$561$	−10.1743	−0.429560
$562$	−0.881472	−0.0371826
$563$	37.8185	1.59386	0.796930	−	0.604072i	$-0.206456\pi$
$563$	37.8185	1.59386	0.796930	+	0.604072i	$0.206456\pi$
$564$	21.1990	0.892639
$565$	4.62339	0.194507
$566$	1.28655	0.0540777
$567$	−0.238497	−0.0100159
$568$	−8.89319	−0.373150
$569$	26.1655	1.09691	0.548457	−	0.836179i	$-0.315215\pi$
$569$	26.1655	1.09691	0.548457	+	0.836179i	$0.315215\pi$
$570$	−3.12611	−0.130938
$571$	30.1014	1.25970	0.629851	−	0.776716i	$-0.283116\pi$
$571$	30.1014	1.25970	0.629851	+	0.776716i	$0.283116\pi$
$572$	18.6638	0.780372
$573$	27.7135	1.15775
$574$	11.2579	0.469896
$575$	12.6767	0.528653
$576$	24.6269	1.02612
$577$	21.3113	0.887199	0.443600	−	0.896225i	$-0.353701\pi$
$577$	21.3113	0.887199	0.443600	+	0.896225i	$0.353701\pi$
$578$	2.11784	0.0880904
$579$	7.83695	0.325692
$580$	−18.4828	−0.767456
$581$	−2.79171	−0.115819
$582$	−30.8432	−1.27849
$583$	−17.6364	−0.730426
$584$	−35.7601	−1.47976
$585$	−6.29133	−0.260114
$586$	14.1060	0.582714
$587$	−9.72811	−0.401522	−0.200761	−	0.979640i	$-0.564341\pi$
$587$	−9.72811	−0.401522	−0.200761	+	0.979640i	$0.564341\pi$
$588$	−3.20694	−0.132252
$589$	−7.97606	−0.328648
$590$	−9.30080	−0.382908
$591$	11.3636	0.467437
$592$	−0.318810	−0.0131030
$593$	8.53522	0.350499	0.175250	−	0.984524i	$-0.443927\pi$
$593$	8.53522	0.350499	0.175250	+	0.984524i	$0.443927\pi$
$594$	−27.8796	−1.14391
$595$	−5.24165	−0.214887
$596$	59.8663	2.45222
$597$	−23.8631	−0.976650
$598$	22.0328	0.900990
$599$	−8.67312	−0.354374	−0.177187	−	0.984177i	$-0.556700\pi$
$599$	−8.67312	−0.354374	−0.177187	+	0.984177i	$0.556700\pi$
$600$	−8.11936	−0.331471
$601$	25.8851	1.05587	0.527937	−	0.849283i	$-0.322966\pi$
$601$	25.8851	1.05587	0.527937	+	0.849283i	$0.322966\pi$
$602$	21.0173	0.856601
$603$	25.0351	1.01951
$604$	−54.8354	−2.23122
$605$	−6.79526	−0.276267
$606$	38.0506	1.54570
$607$	−24.2205	−0.983080	−0.491540	−	0.870855i	$-0.663566\pi$
$607$	−24.2205	−0.983080	−0.491540	+	0.870855i	$0.663566\pi$
$608$	−6.60336	−0.267802
$609$	−4.89295	−0.198272
$610$	6.72445	0.272265
$611$	−16.8264	−0.680723
$612$	−23.0407	−0.931367
$613$	10.1849	0.411365	0.205683	−	0.978619i	$-0.434059\pi$
$613$	10.1849	0.411365	0.205683	+	0.978619i	$0.434059\pi$
$614$	32.4458	1.30940
$615$	−6.91048	−0.278658
$616$	5.64433	0.227417
$617$	25.9787	1.04586	0.522932	−	0.852374i	$-0.324838\pi$
$617$	25.9787	1.04586	0.522932	+	0.852374i	$0.324838\pi$
$618$	12.2087	0.491107
$619$	−6.82137	−0.274174	−0.137087	−	0.990559i	$-0.543774\pi$
$619$	−6.82137	−0.274174	−0.137087	+	0.990559i	$0.543774\pi$
$620$	31.4412	1.26271
$621$	−19.8600	−0.796955
$622$	63.4314	2.54337
$623$	−1.94065	−0.0777504
$624$	2.21431	0.0886434
$625$	2.26148	0.0904592
$626$	13.6326	0.544868
$627$	2.56404	0.102398
$628$	−6.98635	−0.278786
$629$	1.54759	0.0617066
$630$	−5.55044	−0.221135
$631$	−4.84818	−0.193003	−0.0965015	−	0.995333i	$-0.530765\pi$
$631$	−4.84818	−0.193003	−0.0965015	+	0.995333i	$0.530765\pi$
$632$	6.59520	0.262343
$633$	20.4035	0.810967
$634$	3.41734	0.135720
$635$	8.99175	0.356827
$636$	23.4743	0.930818
$637$	2.54546	0.100855
$638$	25.1226	0.994615
$639$	−7.17287	−0.283754
$640$	21.1803	0.837225
$641$	38.0222	1.50179	0.750894	−	0.660423i	$-0.229623\pi$
$641$	38.0222	1.50179	0.750894	+	0.660423i	$0.229623\pi$
$642$	−0.358289	−0.0141405
$643$	−10.6806	−0.421203	−0.210602	−	0.977572i	$-0.567542\pi$
$643$	−10.6806	−0.421203	−0.210602	+	0.977572i	$0.567542\pi$
$644$	11.7295	0.462205
$645$	−12.9011	−0.507981
$646$	9.08727	0.357534
$647$	42.6121	1.67525	0.837627	−	0.546242i	$-0.183942\pi$
$647$	42.6121	1.67525	0.837627	+	0.546242i	$0.183942\pi$
$648$	−0.558711	−0.0219482
$649$	7.62852	0.299446
$650$	18.8005	0.737417
$651$	8.32344	0.326221
$652$	48.6032	1.90345
$653$	16.2881	0.637403	0.318701	−	0.947855i	$-0.396753\pi$
$653$	16.2881	0.637403	0.318701	+	0.947855i	$0.396753\pi$
$654$	19.9942	0.781834
$655$	−15.6294	−0.610690
$656$	−4.13822	−0.161570
$657$	−28.8426	−1.12526
$658$	−14.8449	−0.578713
$659$	5.79831	0.225870	0.112935	−	0.993602i	$-0.463975\pi$
$659$	5.79831	0.225870	0.112935	+	0.993602i	$0.463975\pi$
$660$	−10.1073	−0.393426
$661$	26.9742	1.04917	0.524587	−	0.851357i	$-0.324220\pi$
$661$	26.9742	1.04917	0.524587	+	0.851357i	$0.324220\pi$
$662$	40.7200	1.58263
$663$	−10.7489	−0.417452
$664$	−6.53994	−0.253799
$665$	1.32095	0.0512243
$666$	1.63877	0.0635009
$667$	17.8961	0.692940
$668$	52.6770	2.03813
$669$	0.755675	0.0292161
$670$	38.9223	1.50370
$671$	−5.51540	−0.212920
$672$	6.89096	0.265825
$673$	−40.8041	−1.57288	−0.786441	−	0.617665i	$-0.788079\pi$
$673$	−40.8041	−1.57288	−0.786441	+	0.617665i	$0.788079\pi$
$674$	−57.4960	−2.21466
$675$	−16.9465	−0.652270
$676$	−19.8434	−0.763206
$677$	4.29826	0.165196	0.0825978	−	0.996583i	$-0.473678\pi$
$677$	4.29826	0.165196	0.0825978	+	0.996583i	$0.473678\pi$
$678$	8.36452	0.321237
$679$	13.0329	0.500159
$680$	−12.2793	−0.470888
$681$	−29.6482	−1.13612
$682$	−42.7363	−1.63646
$683$	44.1034	1.68757	0.843786	−	0.536680i	$-0.180322\pi$
$683$	44.1034	1.68757	0.843786	+	0.536680i	$0.180322\pi$
$684$	5.80652	0.222018
$685$	−12.8679	−0.491659
$686$	2.24570	0.0857412
$687$	6.69390	0.255388
$688$	−7.72560	−0.294536
$689$	−18.6324	−0.709838
$690$	−11.9318	−0.454236
$691$	−38.5907	−1.46806	−0.734030	−	0.679117i	$-0.762363\pi$
$691$	−38.5907	−1.46806	−0.734030	+	0.679117i	$0.762363\pi$
$692$	49.5070	1.88197
$693$	4.55248	0.172934
$694$	−8.17669	−0.310383
$695$	26.0133	0.986740
$696$	−11.4624	−0.434481
$697$	20.0881	0.760889
$698$	6.54773	0.247835
$699$	−2.16996	−0.0820755
$700$	10.0087	0.378293
$701$	−14.3068	−0.540361	−0.270180	−	0.962810i	$-0.587083\pi$
$701$	−14.3068	−0.540361	−0.270180	+	0.962810i	$0.587083\pi$
$702$	−29.4540	−1.11167
$703$	−0.390011	−0.0147095
$704$	−31.4035	−1.18356
$705$	9.11227	0.343188
$706$	−35.6535	−1.34184
$707$	−16.0784	−0.604692
$708$	−10.1537	−0.381598
$709$	−7.10431	−0.266808	−0.133404	−	0.991062i	$-0.542591\pi$
$709$	−7.10431	−0.266808	−0.133404	+	0.991062i	$0.542591\pi$
$710$	−11.1517	−0.418516
$711$	5.31941	0.199493
$712$	−4.54622	−0.170377
$713$	−30.4432	−1.14011
$714$	−9.48306	−0.354894
$715$	8.02252	0.300025
$716$	−19.2120	−0.717985
$717$	14.3573	0.536185
$718$	−66.2805	−2.47357
$719$	10.9095	0.406856	0.203428	−	0.979090i	$-0.434792\pi$
$719$	10.9095	0.406856	0.203428	+	0.979090i	$0.434792\pi$
$720$	2.04025	0.0760356
$721$	−5.15885	−0.192126
$722$	40.3782	1.50272
$723$	−1.67910	−0.0624463
$724$	−12.7950	−0.475523
$725$	15.2707	0.567138
$726$	−12.2938	−0.456266
$727$	36.1596	1.34109	0.670543	−	0.741871i	$-0.266061\pi$
$727$	36.1596	1.34109	0.670543	+	0.741871i	$0.266061\pi$
$728$	5.96308	0.221006
$729$	15.8391	0.586633
$730$	−44.8418	−1.65967
$731$	37.5022	1.38707
$732$	7.34107	0.271334
$733$	−35.1906	−1.29980	−0.649898	−	0.760022i	$-0.725188\pi$
$733$	−35.1906	−1.29980	−0.649898	+	0.760022i	$0.725188\pi$
$734$	−66.0198	−2.43684
$735$	−1.37848	−0.0508462
$736$	−25.2039	−0.929026
$737$	−31.9241	−1.17594
$738$	21.2715	0.783014
$739$	−3.70512	−0.136295	−0.0681476	−	0.997675i	$-0.521709\pi$
$739$	−3.70512	−0.136295	−0.0681476	+	0.997675i	$0.521709\pi$
$740$	1.53740	0.0565160
$741$	2.70883	0.0995115
$742$	−16.4382	−0.603465
$743$	46.3390	1.70001	0.850006	−	0.526773i	$-0.176598\pi$
$743$	46.3390	1.70001	0.850006	+	0.526773i	$0.176598\pi$
$744$	19.4988	0.714860
$745$	25.7332	0.942791
$746$	4.38617	0.160589
$747$	−5.27484	−0.192996
$748$	29.3809	1.07427
$749$	0.151397	0.00553191
$750$	−25.6597	−0.936958
$751$	−7.11355	−0.259577	−0.129789	−	0.991542i	$-0.541430\pi$
$751$	−7.11355	−0.259577	−0.129789	+	0.991542i	$0.541430\pi$
$752$	5.45672	0.198986
$753$	−14.4434	−0.526347
$754$	26.5414	0.966580
$755$	−23.5707	−0.857825
$756$	−15.6802	−0.570284
$757$	−20.2040	−0.734328	−0.367164	−	0.930156i	$-0.619671\pi$
$757$	−20.2040	−0.734328	−0.367164	+	0.930156i	$0.619671\pi$
$758$	20.2363	0.735014
$759$	9.78647	0.355226
$760$	3.09451	0.112250
$761$	38.0176	1.37814	0.689068	−	0.724697i	$-0.258020\pi$
$761$	38.0176	1.37814	0.689068	+	0.724697i	$0.258020\pi$
$762$	16.2677	0.589315
$763$	−8.44863	−0.305861
$764$	−80.0299	−2.89538
$765$	−9.90393	−0.358077
$766$	−36.0867	−1.30386
$767$	8.05932	0.291005
$768$	10.8485	0.391460
$769$	8.72429	0.314606	0.157303	−	0.987550i	$-0.449720\pi$
$769$	8.72429	0.314606	0.157303	+	0.987550i	$0.449720\pi$
$770$	7.07777	0.255065
$771$	−17.8111	−0.641452
$772$	−22.6312	−0.814513
$773$	22.2302	0.799564	0.399782	−	0.916610i	$-0.369086\pi$
$773$	22.2302	0.799564	0.399782	+	0.916610i	$0.369086\pi$
$774$	39.7115	1.42740
$775$	−25.9770	−0.933123
$776$	30.5314	1.09601
$777$	0.406997	0.0146009
$778$	7.34838	0.263452
$779$	−5.06241	−0.181380
$780$	−10.6781	−0.382337
$781$	9.14664	0.327292
$782$	34.6845	1.24032
$783$	−23.9239	−0.854972
$784$	−0.825481	−0.0294815
$785$	−3.00304	−0.107183
$786$	−28.2763	−1.00858
$787$	30.8073	1.09816	0.549081	−	0.835769i	$-0.314978\pi$
$787$	30.8073	1.09816	0.549081	+	0.835769i	$0.314978\pi$
$788$	−32.8153	−1.16900
$789$	−3.80595	−0.135495
$790$	8.27012	0.294238
$791$	−3.53447	−0.125671
$792$	10.6648	0.378957
$793$	−5.82686	−0.206918
$794$	22.0407	0.782196
$795$	10.0903	0.357866
$796$	68.9106	2.44247
$797$	−15.5856	−0.552072	−0.276036	−	0.961147i	$-0.589021\pi$
$797$	−15.5856	−0.552072	−0.276036	+	0.961147i	$0.589021\pi$
$798$	2.38983	0.0845992
$799$	−26.4884	−0.937093
$800$	−21.5063	−0.760364
$801$	−3.66679	−0.129560
$802$	−62.5991	−2.21045
$803$	36.7793	1.29791
$804$	42.4914	1.49856
$805$	5.04184	0.177701
$806$	−45.1498	−1.59033
$807$	14.3633	0.505611
$808$	−37.6659	−1.32508
$809$	−0.558769	−0.0196453	−0.00982264	−	0.999952i	$-0.503127\pi$
$809$	−0.558769	−0.0196453	−0.00982264	+	0.999952i	$0.503127\pi$
$810$	−0.700601	−0.0246166
$811$	−1.76741	−0.0620623	−0.0310312	−	0.999518i	$-0.509879\pi$
$811$	−1.76741	−0.0620623	−0.0310312	+	0.999518i	$0.509879\pi$
$812$	14.1296	0.495853
$813$	17.2892	0.606359
$814$	−2.08971	−0.0732442
$815$	20.8918	0.731808
$816$	3.48581	0.122028
$817$	−9.45096	−0.330647
$818$	1.61199	0.0563619
$819$	4.80957	0.168060
$820$	19.9558	0.696885
$821$	−10.5187	−0.367104	−0.183552	−	0.983010i	$-0.558760\pi$
$821$	−10.5187	−0.367104	−0.183552	+	0.983010i	$0.558760\pi$
$822$	−23.2803	−0.811995
$823$	36.8771	1.28545	0.642727	−	0.766095i	$-0.277803\pi$
$823$	36.8771	1.28545	0.642727	+	0.766095i	$0.277803\pi$
$824$	−12.0853	−0.421011
$825$	8.35075	0.290736
$826$	7.11023	0.247397
$827$	37.2797	1.29634	0.648172	−	0.761494i	$-0.275534\pi$
$827$	37.2797	1.29634	0.648172	+	0.761494i	$0.275534\pi$
$828$	22.1624	0.770198
$829$	−13.2650	−0.460711	−0.230355	−	0.973107i	$-0.573989\pi$
$829$	−13.2650	−0.460711	−0.230355	+	0.973107i	$0.573989\pi$
$830$	−8.20082	−0.284655
$831$	23.4470	0.813366
$832$	−33.1769	−1.15020
$833$	4.00711	0.138838
$834$	47.0626	1.62964
$835$	22.6429	0.783589
$836$	−7.40431	−0.256083
$837$	40.6972	1.40670
$838$	−45.8385	−1.58347
$839$	−37.1225	−1.28161	−0.640805	−	0.767704i	$-0.721399\pi$
$839$	−37.1225	−1.28161	−0.640805	+	0.767704i	$0.721399\pi$
$840$	−3.22928	−0.111421
$841$	−7.44186	−0.256616
$842$	51.0756	1.76018
$843$	−0.413640	−0.0142465
$844$	−58.9203	−2.02812
$845$	−8.52955	−0.293425
$846$	−28.0489	−0.964341
$847$	5.19481	0.178496
$848$	6.04240	0.207497
$849$	0.603727	0.0207199
$850$	29.5961	1.01514
$851$	−1.48860	−0.0510286
$852$	−12.1743	−0.417085
$853$	10.2327	0.350361	0.175181	−	0.984536i	$-0.443949\pi$
$853$	10.2327	0.350361	0.175181	+	0.984536i	$0.443949\pi$
$854$	−5.14067	−0.175910
$855$	2.49590	0.0853579
$856$	0.354666	0.0121223
$857$	−16.0518	−0.548318	−0.274159	−	0.961684i	$-0.588400\pi$
$857$	−16.0518	−0.548318	−0.274159	+	0.961684i	$0.588400\pi$
$858$	14.5141	0.495505
$859$	1.00000	0.0341196
$859$	1.00000	0.0341196
$860$	37.2552	1.27039
$861$	5.28289	0.180041
$862$	−35.6290	−1.21353
$863$	36.9408	1.25748	0.628740	−	0.777616i	$-0.283571\pi$
$863$	36.9408	1.25748	0.628740	+	0.777616i	$0.283571\pi$
$864$	33.6931	1.14626
$865$	21.2803	0.723552
$866$	−38.9910	−1.32497
$867$	0.993817	0.0337518
$868$	−24.0360	−0.815837
$869$	−6.78316	−0.230103
$870$	−14.3734	−0.487303
$871$	−33.7269	−1.14279
$872$	−19.7920	−0.670243
$873$	24.6253	0.833441
$874$	−8.74087	−0.295664
$875$	10.8426	0.366547
$876$	−48.9537	−1.65399
$877$	−44.8256	−1.51365	−0.756826	−	0.653616i	$-0.773251\pi$
$877$	−44.8256	−1.51365	−0.756826	+	0.653616i	$0.773251\pi$
$878$	−29.8389	−1.00702
$879$	6.61939	0.223267
$880$	−2.60167	−0.0877022
$881$	10.6540	0.358941	0.179471	−	0.983763i	$-0.442561\pi$
$881$	10.6540	0.358941	0.179471	+	0.983763i	$0.442561\pi$
$882$	4.24318	0.142875
$883$	8.85212	0.297898	0.148949	−	0.988845i	$-0.452411\pi$
$883$	8.85212	0.297898	0.148949	+	0.988845i	$0.452411\pi$
$884$	31.0401	1.04399
$885$	−4.36450	−0.146711
$886$	−51.3286	−1.72442
$887$	−19.8221	−0.665559	−0.332780	−	0.943005i	$-0.607987\pi$
$887$	−19.8221	−0.665559	−0.332780	+	0.943005i	$0.607987\pi$
$888$	0.953444	0.0319955
$889$	−6.87397	−0.230546
$890$	−5.70079	−0.191091
$891$	0.574634	0.0192510
$892$	−2.18220	−0.0730655
$893$	6.67537	0.223383
$894$	46.5558	1.55706
$895$	−8.25815	−0.276040
$896$	−16.1918	−0.540931
$897$	10.3391	0.345214
$898$	58.6933	1.95862
$899$	−36.6727	−1.22310
$900$	18.9111	0.630370
$901$	−29.3315	−0.977173
$902$	−27.1248	−0.903156
$903$	9.86259	0.328206
$904$	−8.27996	−0.275387
$905$	−5.49986	−0.182822
$906$	−42.6435	−1.41673
$907$	55.2896	1.83586	0.917930	−	0.396742i	$-0.129859\pi$
$907$	55.2896	1.83586	0.917930	+	0.396742i	$0.129859\pi$
$908$	85.6167	2.84129
$909$	−30.3797	−1.00763
$910$	7.47746	0.247875
$911$	−54.5017	−1.80572	−0.902860	−	0.429934i	$-0.858537\pi$
$911$	−54.5017	−1.80572	−0.902860	+	0.429934i	$0.858537\pi$
$912$	−0.878462	−0.0290888
$913$	6.72632	0.222609
$914$	−18.1890	−0.601640
$915$	3.15552	0.104318
$916$	−19.3303	−0.638692
$917$	11.9483	0.394567
$918$	−46.3671	−1.53034
$919$	49.5138	1.63331	0.816654	−	0.577127i	$-0.195826\pi$
$919$	49.5138	1.63331	0.816654	+	0.577127i	$0.195826\pi$
$920$	11.8112	0.389403
$921$	15.2255	0.501698
$922$	−44.1195	−1.45300
$923$	9.66317	0.318067
$924$	7.72679	0.254193
$925$	−1.27022	−0.0417644
$926$	−42.0402	−1.38153
$927$	−9.74749	−0.320150
$928$	−30.3613	−0.996658
$929$	−13.1096	−0.430111	−0.215055	−	0.976602i	$-0.568993\pi$
$929$	−13.1096	−0.430111	−0.215055	+	0.976602i	$0.568993\pi$
$930$	24.4507	0.801770
$931$	−1.00984	−0.0330960
$932$	6.26631	0.205260
$933$	29.7658	0.974489
$934$	−36.8550	−1.20593
$935$	12.6292	0.413019
$936$	11.2670	0.368275
$937$	32.1850	1.05144	0.525720	−	0.850658i	$-0.323796\pi$
$937$	32.1850	1.05144	0.525720	+	0.850658i	$0.323796\pi$
$938$	−29.7551	−0.971540
$939$	6.39723	0.208766
$940$	−26.3140	−0.858267
$941$	15.7322	0.512857	0.256428	−	0.966563i	$-0.417454\pi$
$941$	15.7322	0.512857	0.256428	+	0.966563i	$0.417454\pi$
$942$	−5.43303	−0.177018
$943$	−19.3223	−0.629221
$944$	−2.61360	−0.0850655
$945$	−6.74006	−0.219254
$946$	−50.6390	−1.64642
$947$	−38.7262	−1.25843	−0.629217	−	0.777230i	$-0.716624\pi$
$947$	−38.7262	−1.25843	−0.629217	+	0.777230i	$0.716624\pi$
$948$	9.02848	0.293231
$949$	38.8563	1.26133
$950$	−7.45855	−0.241987
$951$	1.60362	0.0520011
$952$	9.38719	0.304240
$953$	0.560316	0.0181504	0.00907521	−	0.999959i	$-0.497111\pi$
$953$	0.560316	0.0181504	0.00907521	+	0.999959i	$0.497111\pi$
$954$	−31.0594	−1.00559
$955$	−34.4004	−1.11317
$956$	−41.4604	−1.34093
$957$	11.7891	0.381086
$958$	0.838144	0.0270792
$959$	9.83722	0.317660
$960$	17.9668	0.579877
$961$	31.3843	1.01240
$962$	−2.20772	−0.0711797
$963$	0.286059	0.00921812
$964$	4.84881	0.156170
$965$	−9.72787	−0.313151
$966$	9.12157	0.293482
$967$	11.9897	0.385561	0.192781	−	0.981242i	$-0.438249\pi$
$967$	11.9897	0.385561	0.192781	+	0.981242i	$0.438249\pi$
$968$	12.1695	0.391144
$969$	4.26430	0.136989
$970$	38.2852	1.22926
$971$	−4.31136	−0.138358	−0.0691791	−	0.997604i	$-0.522038\pi$
$971$	−4.31136	−0.138358	−0.0691791	+	0.997604i	$0.522038\pi$
$972$	−47.8055	−1.53336
$973$	−19.8865	−0.637532
$974$	−9.88533	−0.316746
$975$	8.82234	0.282541
$976$	1.88962	0.0604854
$977$	30.2853	0.968914	0.484457	−	0.874815i	$-0.339017\pi$
$977$	30.2853	0.968914	0.484457	+	0.874815i	$0.339017\pi$
$978$	37.7969	1.20861
$979$	4.67579	0.149439
$980$	3.98072	0.127159
$981$	−15.9634	−0.509673
$982$	−90.9218	−2.90143
$983$	22.2247	0.708857	0.354429	−	0.935083i	$-0.384675\pi$
$983$	22.2247	0.708857	0.354429	+	0.935083i	$0.384675\pi$
$984$	12.3759	0.394529
$985$	−14.1055	−0.449438
$986$	41.7819	1.33061
$987$	−6.96611	−0.221734
$988$	−7.82244	−0.248865
$989$	−36.0726	−1.14704
$990$	13.3732	0.425029
$991$	−54.5061	−1.73144	−0.865722	−	0.500526i	$-0.833140\pi$
$991$	−54.5061	−1.73144	−0.865722	+	0.500526i	$0.833140\pi$
$992$	51.6478	1.63982
$993$	19.1083	0.606383
$994$	8.52520	0.270403
$995$	29.6208	0.939043
$996$	−8.95283	−0.283681
$997$	−20.0683	−0.635569	−0.317785	−	0.948163i	$-0.602939\pi$
$997$	−20.0683	−0.635569	−0.317785	+	0.948163i	$0.602939\pi$
$998$	−36.0457	−1.14101
$999$	1.99000	0.0629608

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6013.2.a.f.1.12	✓	110

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6013.2.a.f.1.12	✓	110	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:	\( N \)	\(=\)	\( 6013 = 7 \cdot 859 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6013.a (trivial)

\(f(q)\)	\(=\)	\(q-2.24570 q^{2} -1.05382 q^{3} +3.04316 q^{4} +1.30809 q^{5} +2.36656 q^{6} -1.00000 q^{7} -2.34263 q^{8} -1.88947 q^{9} +O(q^{10})\)	\(q-2.24570 q^{2} -1.05382 q^{3} +3.04316 q^{4} +1.30809 q^{5} +2.36656 q^{6} -1.00000 q^{7} -2.34263 q^{8} -1.88947 q^{9} -2.93757 q^{10} +2.40940 q^{11} -3.20694 q^{12} +2.54546 q^{13} +2.24570 q^{14} -1.37848 q^{15} -0.825481 q^{16} +4.00711 q^{17} +4.24318 q^{18} -1.00984 q^{19} +3.98072 q^{20} +1.05382 q^{21} -5.41078 q^{22} -3.85436 q^{23} +2.46871 q^{24} -3.28891 q^{25} -5.71634 q^{26} +5.15261 q^{27} -3.04316 q^{28} -4.64307 q^{29} +3.09566 q^{30} +7.89837 q^{31} +6.53905 q^{32} -2.53906 q^{33} -8.99876 q^{34} -1.30809 q^{35} -5.74996 q^{36} +0.386212 q^{37} +2.26779 q^{38} -2.68245 q^{39} -3.06437 q^{40} +5.01310 q^{41} -2.36656 q^{42} +9.35891 q^{43} +7.33219 q^{44} -2.47159 q^{45} +8.65574 q^{46} -6.61036 q^{47} +0.869906 q^{48} +1.00000 q^{49} +7.38590 q^{50} -4.22276 q^{51} +7.74625 q^{52} -7.31985 q^{53} -11.5712 q^{54} +3.15170 q^{55} +2.34263 q^{56} +1.06418 q^{57} +10.4269 q^{58} +3.16616 q^{59} -4.19495 q^{60} -2.28912 q^{61} -17.7374 q^{62} +1.88947 q^{63} -13.0338 q^{64} +3.32968 q^{65} +5.70197 q^{66} -13.2498 q^{67} +12.1943 q^{68} +4.06179 q^{69} +2.93757 q^{70} +3.79624 q^{71} +4.42633 q^{72} +15.2649 q^{73} -0.867316 q^{74} +3.46591 q^{75} -3.07310 q^{76} -2.40940 q^{77} +6.02398 q^{78} -2.81529 q^{79} -1.07980 q^{80} +0.238497 q^{81} -11.2579 q^{82} +2.79171 q^{83} +3.20694 q^{84} +5.24165 q^{85} -21.0173 q^{86} +4.89295 q^{87} -5.64433 q^{88} +1.94065 q^{89} +5.55044 q^{90} -2.54546 q^{91} -11.7295 q^{92} -8.32344 q^{93} +14.8449 q^{94} -1.32095 q^{95} -6.89096 q^{96} -13.0329 q^{97} -2.24570 q^{98} -4.55248 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 110 q + 16 q^{2} + 29 q^{3} + 118 q^{4} + 12 q^{6} - 110 q^{7} + 57 q^{8} + 127 q^{9}+O(q^{10}) \) 110 * q + 16 * q^2 + 29 * q^3 + 118 * q^4 + 12 * q^6 - 110 * q^7 + 57 * q^8 + 127 * q^9	\( 110 q + 16 q^{2} + 29 q^{3} + 118 q^{4} + 12 q^{6} - 110 q^{7} + 57 q^{8} + 127 q^{9} + 3 q^{10} + 52 q^{11} + 62 q^{12} - 9 q^{13} - 16 q^{14} + 39 q^{15} + 146 q^{16} + 11 q^{17} + 60 q^{18} + 14 q^{19} + 18 q^{20} - 29 q^{21} + 32 q^{22} + 73 q^{23} + 24 q^{24} + 132 q^{25} - 7 q^{26} + 116 q^{27} - 118 q^{28} + 35 q^{29} + 18 q^{30} + 36 q^{31} + 140 q^{32} + 42 q^{33} - 7 q^{34} + 180 q^{36} + 49 q^{37} + 45 q^{39} + 6 q^{40} - 14 q^{41} - 12 q^{42} + 58 q^{43} + 92 q^{44} + 17 q^{45} + 27 q^{46} + 87 q^{47} + 98 q^{48} + 110 q^{49} + 91 q^{50} + 42 q^{51} + 16 q^{52} + 95 q^{53} + 41 q^{54} + 8 q^{55} - 57 q^{56} + 61 q^{57} + 46 q^{58} + 114 q^{59} + 81 q^{60} - 47 q^{61} + 31 q^{62} - 127 q^{63} + 199 q^{64} + 62 q^{65} + 21 q^{66} + 95 q^{67} + 60 q^{68} - 39 q^{69} - 3 q^{70} + 131 q^{71} + 186 q^{72} + 31 q^{73} + 23 q^{74} + 121 q^{75} + 14 q^{76} - 52 q^{77} + 110 q^{78} + 9 q^{79} + 61 q^{80} + 194 q^{81} + 45 q^{82} + 73 q^{83} - 62 q^{84} + 59 q^{85} + 72 q^{86} + 64 q^{87} + 100 q^{88} - 17 q^{89} + 11 q^{90} + 9 q^{91} + 192 q^{92} + 85 q^{93} - 11 q^{94} + 108 q^{95} + 68 q^{96} + 32 q^{97} + 16 q^{98} + 160 q^{99}+O(q^{100}) \) 110 * q + 16 * q^2 + 29 * q^3 + 118 * q^4 + 12 * q^6 - 110 * q^7 + 57 * q^8 + 127 * q^9 + 3 * q^10 + 52 * q^11 + 62 * q^12 - 9 * q^13 - 16 * q^14 + 39 * q^15 + 146 * q^16 + 11 * q^17 + 60 * q^18 + 14 * q^19 + 18 * q^20 - 29 * q^21 + 32 * q^22 + 73 * q^23 + 24 * q^24 + 132 * q^25 - 7 * q^26 + 116 * q^27 - 118 * q^28 + 35 * q^29 + 18 * q^30 + 36 * q^31 + 140 * q^32 + 42 * q^33 - 7 * q^34 + 180 * q^36 + 49 * q^37 + 45 * q^39 + 6 * q^40 - 14 * q^41 - 12 * q^42 + 58 * q^43 + 92 * q^44 + 17 * q^45 + 27 * q^46 + 87 * q^47 + 98 * q^48 + 110 * q^49 + 91 * q^50 + 42 * q^51 + 16 * q^52 + 95 * q^53 + 41 * q^54 + 8 * q^55 - 57 * q^56 + 61 * q^57 + 46 * q^58 + 114 * q^59 + 81 * q^60 - 47 * q^61 + 31 * q^62 - 127 * q^63 + 199 * q^64 + 62 * q^65 + 21 * q^66 + 95 * q^67 + 60 * q^68 - 39 * q^69 - 3 * q^70 + 131 * q^71 + 186 * q^72 + 31 * q^73 + 23 * q^74 + 121 * q^75 + 14 * q^76 - 52 * q^77 + 110 * q^78 + 9 * q^79 + 61 * q^80 + 194 * q^81 + 45 * q^82 + 73 * q^83 - 62 * q^84 + 59 * q^85 + 72 * q^86 + 64 * q^87 + 100 * q^88 - 17 * q^89 + 11 * q^90 + 9 * q^91 + 192 * q^92 + 85 * q^93 - 11 * q^94 + 108 * q^95 + 68 * q^96 + 32 * q^97 + 16 * q^98 + 160 * q^99

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