LMFDB - Embedded newform 6019.2.a.c.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6019, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6019.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6019 = 13 \cdot 463 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6019.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$48.0619569766$
Analytic rank:	$1$
Dimension:	$108$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	6019.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.60952 q^{2} +3.26666 q^{3} +4.80961 q^{4} -2.76749 q^{5} -8.52442 q^{6} -0.615812 q^{7} -7.33173 q^{8} +7.67107 q^{9} +O(q^{10})$	\(q-2.60952 q^{2} +3.26666 q^{3} +4.80961 q^{4} -2.76749 q^{5} -8.52442 q^{6} -0.615812 q^{7} -7.33173 q^{8} +7.67107 q^{9} +7.22184 q^{10} -2.51197 q^{11} +15.7114 q^{12} -1.00000 q^{13} +1.60698 q^{14} -9.04046 q^{15} +9.51309 q^{16} +2.40142 q^{17} -20.0178 q^{18} -0.0503723 q^{19} -13.3106 q^{20} -2.01165 q^{21} +6.55503 q^{22} -3.59072 q^{23} -23.9503 q^{24} +2.65902 q^{25} +2.60952 q^{26} +15.2588 q^{27} -2.96181 q^{28} -5.79202 q^{29} +23.5913 q^{30} +3.35869 q^{31} -10.1612 q^{32} -8.20575 q^{33} -6.26655 q^{34} +1.70426 q^{35} +36.8948 q^{36} -3.26030 q^{37} +0.131448 q^{38} -3.26666 q^{39} +20.2905 q^{40} +7.71689 q^{41} +5.24945 q^{42} +10.4913 q^{43} -12.0816 q^{44} -21.2296 q^{45} +9.37005 q^{46} +6.11194 q^{47} +31.0761 q^{48} -6.62078 q^{49} -6.93877 q^{50} +7.84462 q^{51} -4.80961 q^{52} -6.99504 q^{53} -39.8182 q^{54} +6.95185 q^{55} +4.51497 q^{56} -0.164549 q^{57} +15.1144 q^{58} -4.10455 q^{59} -43.4811 q^{60} -6.39430 q^{61} -8.76458 q^{62} -4.72394 q^{63} +7.48962 q^{64} +2.76749 q^{65} +21.4131 q^{66} +1.21688 q^{67} +11.5499 q^{68} -11.7297 q^{69} -4.44730 q^{70} -12.1196 q^{71} -56.2422 q^{72} +8.15155 q^{73} +8.50782 q^{74} +8.68612 q^{75} -0.242271 q^{76} +1.54690 q^{77} +8.52442 q^{78} +2.11639 q^{79} -26.3274 q^{80} +26.8322 q^{81} -20.1374 q^{82} -16.3133 q^{83} -9.67524 q^{84} -6.64591 q^{85} -27.3772 q^{86} -18.9206 q^{87} +18.4171 q^{88} +6.90629 q^{89} +55.3992 q^{90} +0.615812 q^{91} -17.2699 q^{92} +10.9717 q^{93} -15.9493 q^{94} +0.139405 q^{95} -33.1931 q^{96} -17.3241 q^{97} +17.2771 q^{98} -19.2695 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 11 q^{2} + q^{3} + 95 q^{4} - 40 q^{5} - 10 q^{6} - 8 q^{7} - 33 q^{8} + 79 q^{9}+O(q^{10}) $ 108 * q - 11 * q^2 + q^3 + 95 * q^4 - 40 * q^5 - 10 * q^6 - 8 * q^7 - 33 * q^8 + 79 * q^9	\( 108 q - 11 q^{2} + q^{3} + 95 q^{4} - 40 q^{5} - 10 q^{6} - 8 q^{7} - 33 q^{8} + 79 q^{9} - q^{10} - 45 q^{11} - 6 q^{12} - 108 q^{13} - 31 q^{14} - 39 q^{15} + 73 q^{16} + 21 q^{17} - 35 q^{18} - 19 q^{19} - 79 q^{20} - 72 q^{21} - 26 q^{23} - 23 q^{24} + 92 q^{25} + 11 q^{26} + 7 q^{27} - 21 q^{28} - 94 q^{29} - 24 q^{30} - 36 q^{31} - 77 q^{32} - 32 q^{33} - 58 q^{34} - 10 q^{35} + 17 q^{36} - 54 q^{37} - 12 q^{38} - q^{39} - 4 q^{40} - 68 q^{41} - 11 q^{42} - 32 q^{43} - 151 q^{44} - 121 q^{45} - 33 q^{46} - 51 q^{47} - 27 q^{48} + 72 q^{49} - 45 q^{50} - 24 q^{51} - 95 q^{52} - 81 q^{53} - 29 q^{54} + 4 q^{55} - 68 q^{56} - 45 q^{57} - 30 q^{58} - 94 q^{59} - 108 q^{60} - 39 q^{61} - 9 q^{62} - 52 q^{63} + 31 q^{64} + 40 q^{65} - 40 q^{66} - 47 q^{67} + 24 q^{68} - 60 q^{69} - 66 q^{70} - 86 q^{71} - 91 q^{72} - 51 q^{73} - 110 q^{74} - 7 q^{75} - 51 q^{76} - 96 q^{77} + 10 q^{78} - 18 q^{79} - 136 q^{80} - 24 q^{81} - 33 q^{82} - 77 q^{83} - 113 q^{84} - 95 q^{85} - 137 q^{86} + 23 q^{87} + 19 q^{88} - 112 q^{89} - 19 q^{90} + 8 q^{91} - 111 q^{92} - 124 q^{93} - 20 q^{94} - 73 q^{95} - 77 q^{96} - 41 q^{97} - 80 q^{98} - 154 q^{99}+O(q^{100}) \) 108 * q - 11 * q^2 + q^3 + 95 * q^4 - 40 * q^5 - 10 * q^6 - 8 * q^7 - 33 * q^8 + 79 * q^9 - q^10 - 45 * q^11 - 6 * q^12 - 108 * q^13 - 31 * q^14 - 39 * q^15 + 73 * q^16 + 21 * q^17 - 35 * q^18 - 19 * q^19 - 79 * q^20 - 72 * q^21 - 26 * q^23 - 23 * q^24 + 92 * q^25 + 11 * q^26 + 7 * q^27 - 21 * q^28 - 94 * q^29 - 24 * q^30 - 36 * q^31 - 77 * q^32 - 32 * q^33 - 58 * q^34 - 10 * q^35 + 17 * q^36 - 54 * q^37 - 12 * q^38 - q^39 - 4 * q^40 - 68 * q^41 - 11 * q^42 - 32 * q^43 - 151 * q^44 - 121 * q^45 - 33 * q^46 - 51 * q^47 - 27 * q^48 + 72 * q^49 - 45 * q^50 - 24 * q^51 - 95 * q^52 - 81 * q^53 - 29 * q^54 + 4 * q^55 - 68 * q^56 - 45 * q^57 - 30 * q^58 - 94 * q^59 - 108 * q^60 - 39 * q^61 - 9 * q^62 - 52 * q^63 + 31 * q^64 + 40 * q^65 - 40 * q^66 - 47 * q^67 + 24 * q^68 - 60 * q^69 - 66 * q^70 - 86 * q^71 - 91 * q^72 - 51 * q^73 - 110 * q^74 - 7 * q^75 - 51 * q^76 - 96 * q^77 + 10 * q^78 - 18 * q^79 - 136 * q^80 - 24 * q^81 - 33 * q^82 - 77 * q^83 - 113 * q^84 - 95 * q^85 - 137 * q^86 + 23 * q^87 + 19 * q^88 - 112 * q^89 - 19 * q^90 + 8 * q^91 - 111 * q^92 - 124 * q^93 - 20 * q^94 - 73 * q^95 - 77 * q^96 - 41 * q^97 - 80 * q^98 - 154 * 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 $

$2$	−2.60952	−1.84521	−0.922605	−	0.385745i	$-0.873944\pi$
$2$	−2.60952	−1.84521	−0.922605	+	0.385745i	$0.873944\pi$
$3$	3.26666	1.88601	0.943004	−	0.332782i	$-0.107987\pi$
$3$	3.26666	1.88601	0.943004	+	0.332782i	$0.107987\pi$
$4$	4.80961	2.40480
$5$	−2.76749	−1.23766	−0.618830	−	0.785525i	$-0.712393\pi$
$5$	−2.76749	−1.23766	−0.618830	+	0.785525i	$0.712393\pi$
$6$	−8.52442	−3.48008
$7$	−0.615812	−0.232755	−0.116378	−	0.993205i	$-0.537128\pi$
$7$	−0.615812	−0.232755	−0.116378	+	0.993205i	$0.537128\pi$
$8$	−7.33173	−2.59216
$9$	7.67107	2.55702
$10$	7.22184	2.28374
$11$	−2.51197	−0.757387	−0.378693	−	0.925522i	$-0.623626\pi$
$11$	−2.51197	−0.757387	−0.378693	+	0.925522i	$0.623626\pi$
$12$	15.7114	4.53548
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	1.60698	0.429482
$15$	−9.04046	−2.33424
$16$	9.51309	2.37827
$17$	2.40142	0.582430	0.291215	−	0.956658i	$-0.405941\pi$
$17$	2.40142	0.582430	0.291215	+	0.956658i	$0.405941\pi$
$18$	−20.0178	−4.71825
$19$	−0.0503723	−0.0115562	−0.00577810	−	0.999983i	$-0.501839\pi$
$19$	−0.0503723	−0.0115562	−0.00577810	+	0.999983i	$0.501839\pi$
$20$	−13.3106	−2.97633
$21$	−2.01165	−0.438978
$22$	6.55503	1.39754
$23$	−3.59072	−0.748716	−0.374358	−	0.927284i	$-0.622137\pi$
$23$	−3.59072	−0.748716	−0.374358	+	0.927284i	$0.622137\pi$
$24$	−23.9503	−4.88883
$25$	2.65902	0.531804
$26$	2.60952	0.511769
$27$	15.2588	2.93656
$28$	−2.96181	−0.559730
$29$	−5.79202	−1.07555	−0.537776	−	0.843088i	$-0.680735\pi$
$29$	−5.79202	−1.07555	−0.537776	+	0.843088i	$0.680735\pi$
$30$	23.5913	4.30716
$31$	3.35869	0.603239	0.301620	−	0.953428i	$-0.402473\pi$
$31$	3.35869	0.603239	0.301620	+	0.953428i	$0.402473\pi$
$32$	−10.1612	−1.79626
$33$	−8.20575	−1.42844
$34$	−6.26655	−1.07471
$35$	1.70426	0.288072
$36$	36.8948	6.14914
$37$	−3.26030	−0.535990	−0.267995	−	0.963420i	$-0.586361\pi$
$37$	−3.26030	−0.535990	−0.267995	+	0.963420i	$0.586361\pi$
$38$	0.131448	0.0213236
$39$	−3.26666	−0.523084
$40$	20.2905	3.20821
$41$	7.71689	1.20518	0.602588	−	0.798052i	$-0.294136\pi$
$41$	7.71689	1.20518	0.602588	+	0.798052i	$0.294136\pi$
$42$	5.24945	0.810007
$43$	10.4913	1.59990	0.799951	−	0.600065i	$-0.204859\pi$
$43$	10.4913	1.59990	0.799951	+	0.600065i	$0.204859\pi$
$44$	−12.0816	−1.82137
$45$	−21.2296	−3.16473
$46$	9.37005	1.38154
$47$	6.11194	0.891519	0.445759	−	0.895153i	$-0.352934\pi$
$47$	6.11194	0.891519	0.445759	+	0.895153i	$0.352934\pi$
$48$	31.0761	4.48544
$49$	−6.62078	−0.945825
$50$	−6.93877	−0.981290
$51$	7.84462	1.09847
$52$	−4.80961	−0.666972
$53$	−6.99504	−0.960843	−0.480421	−	0.877038i	$-0.659516\pi$
$53$	−6.99504	−0.960843	−0.480421	+	0.877038i	$0.659516\pi$
$54$	−39.8182	−5.41857
$55$	6.95185	0.937388
$56$	4.51497	0.603338
$57$	−0.164549	−0.0217951
$58$	15.1144	1.98462
$59$	−4.10455	−0.534367	−0.267183	−	0.963646i	$-0.586093\pi$
$59$	−4.10455	−0.534367	−0.267183	+	0.963646i	$0.586093\pi$
$60$	−43.4811	−5.61338
$61$	−6.39430	−0.818706	−0.409353	−	0.912376i	$-0.634246\pi$
$61$	−6.39430	−0.818706	−0.409353	+	0.912376i	$0.634246\pi$
$62$	−8.76458	−1.11310
$63$	−4.72394	−0.595161
$64$	7.48962	0.936202
$65$	2.76749	0.343265
$66$	21.4131	2.63577
$67$	1.21688	0.148665	0.0743327	−	0.997233i	$-0.476317\pi$
$67$	1.21688	0.148665	0.0743327	+	0.997233i	$0.476317\pi$
$68$	11.5499	1.40063
$69$	−11.7297	−1.41208
$70$	−4.44730	−0.531553
$71$	−12.1196	−1.43833	−0.719164	−	0.694840i	$-0.755475\pi$
$71$	−12.1196	−1.43833	−0.719164	+	0.694840i	$0.755475\pi$
$72$	−56.2422	−6.62821
$73$	8.15155	0.954067	0.477034	−	0.878885i	$-0.341712\pi$
$73$	8.15155	0.954067	0.477034	+	0.878885i	$0.341712\pi$
$74$	8.50782	0.989014
$75$	8.68612	1.00299
$76$	−0.242271	−0.0277904
$77$	1.54690	0.176286
$78$	8.52442	0.965201
$79$	2.11639	0.238112	0.119056	−	0.992888i	$-0.462013\pi$
$79$	2.11639	0.238112	0.119056	+	0.992888i	$0.462013\pi$
$80$	−26.3274	−2.94350
$81$	26.8322	2.98135
$82$	−20.1374	−2.22380
$83$	−16.3133	−1.79062	−0.895311	−	0.445442i	$-0.853047\pi$
$83$	−16.3133	−1.79062	−0.895311	+	0.445442i	$0.853047\pi$
$84$	−9.67524	−1.05566
$85$	−6.64591	−0.720850
$86$	−27.3772	−2.95216
$87$	−18.9206	−2.02850
$88$	18.4171	1.96327
$89$	6.90629	0.732065	0.366032	−	0.930602i	$-0.380716\pi$
$89$	6.90629	0.732065	0.366032	+	0.930602i	$0.380716\pi$
$90$	55.3992	5.83959
$91$	0.615812	0.0645547
$92$	−17.2699	−1.80051
$93$	10.9717	1.13771
$94$	−15.9493	−1.64504
$95$	0.139405	0.0143027
$96$	−33.1931	−3.38776
$97$	−17.3241	−1.75900	−0.879499	−	0.475901i	$-0.842122\pi$
$97$	−17.3241	−1.75900	−0.879499	+	0.475901i	$0.842122\pi$
$98$	17.2771	1.74525
$99$	−19.2695	−1.93666
$100$	12.7888	1.27888
$101$	5.91189	0.588255	0.294127	−	0.955766i	$-0.404971\pi$
$101$	5.91189	0.588255	0.294127	+	0.955766i	$0.404971\pi$
$102$	−20.4707	−2.02690
$103$	1.17555	0.115830	0.0579152	−	0.998322i	$-0.481555\pi$
$103$	1.17555	0.115830	0.0579152	+	0.998322i	$0.481555\pi$
$104$	7.33173	0.718935
$105$	5.56723	0.543306
$106$	18.2537	1.77296
$107$	−17.3840	−1.68058	−0.840290	−	0.542138i	$-0.817615\pi$
$107$	−17.3840	−1.68058	−0.840290	+	0.542138i	$0.817615\pi$
$108$	73.3889	7.06185
$109$	19.1539	1.83461	0.917306	−	0.398182i	$-0.130359\pi$
$109$	19.1539	1.83461	0.917306	+	0.398182i	$0.130359\pi$
$110$	−18.1410	−1.72968
$111$	−10.6503	−1.01088
$112$	−5.85828	−0.553556
$113$	−4.95444	−0.466075	−0.233037	−	0.972468i	$-0.574866\pi$
$113$	−4.95444	−0.466075	−0.233037	+	0.972468i	$0.574866\pi$
$114$	0.429395	0.0402165
$115$	9.93728	0.926656
$116$	−27.8574	−2.58649
$117$	−7.67107	−0.709191
$118$	10.7109	0.986020
$119$	−1.47882	−0.135564
$120$	66.2822	6.05071
$121$	−4.69002	−0.426366
$122$	16.6861	1.51069
$123$	25.2085	2.27297
$124$	16.1540	1.45067
$125$	6.47865	0.579468
$126$	12.3272	1.09820
$127$	−2.22713	−0.197626	−0.0988130	−	0.995106i	$-0.531505\pi$
$127$	−2.22713	−0.197626	−0.0988130	+	0.995106i	$0.531505\pi$
$128$	0.778024	0.0687683
$129$	34.2714	3.01743
$130$	−7.22184	−0.633397
$131$	−13.8689	−1.21174	−0.605868	−	0.795566i	$-0.707174\pi$
$131$	−13.8689	−1.21174	−0.605868	+	0.795566i	$0.707174\pi$
$132$	−39.4664	−3.43511
$133$	0.0310199	0.00268977
$134$	−3.17547	−0.274319
$135$	−42.2287	−3.63447
$136$	−17.6065	−1.50975
$137$	4.90087	0.418710	0.209355	−	0.977840i	$-0.432864\pi$
$137$	4.90087	0.418710	0.209355	+	0.977840i	$0.432864\pi$
$138$	30.6088	2.60559
$139$	10.2827	0.872171	0.436086	−	0.899905i	$-0.356364\pi$
$139$	10.2827	0.872171	0.436086	+	0.899905i	$0.356364\pi$
$140$	8.19680	0.692756
$141$	19.9656	1.68141
$142$	31.6263	2.65402
$143$	2.51197	0.210061
$144$	72.9756	6.08130
$145$	16.0294	1.33117
$146$	−21.2717	−1.76046
$147$	−21.6278	−1.78383
$148$	−15.6807	−1.28895
$149$	−16.3214	−1.33710	−0.668552	−	0.743665i	$-0.733086\pi$
$149$	−16.3214	−1.33710	−0.668552	+	0.743665i	$0.733086\pi$
$150$	−22.6666	−1.85072
$151$	3.97750	0.323684	0.161842	−	0.986817i	$-0.448256\pi$
$151$	3.97750	0.323684	0.161842	+	0.986817i	$0.448256\pi$
$152$	0.369316	0.0299555
$153$	18.4215	1.48929
$154$	−4.03667	−0.325284
$155$	−9.29516	−0.746605
$156$	−15.7114	−1.25791
$157$	−7.56584	−0.603820	−0.301910	−	0.953336i	$-0.597624\pi$
$157$	−7.56584	−0.603820	−0.301910	+	0.953336i	$0.597624\pi$
$158$	−5.52276	−0.439367
$159$	−22.8504	−1.81216
$160$	28.1210	2.22316
$161$	2.21121	0.174268
$162$	−70.0191	−5.50122
$163$	1.68690	0.132128	0.0660642	−	0.997815i	$-0.478956\pi$
$163$	1.68690	0.132128	0.0660642	+	0.997815i	$0.478956\pi$
$164$	37.1152	2.89821
$165$	22.7093	1.76792
$166$	42.5700	3.30407
$167$	−11.4356	−0.884915	−0.442457	−	0.896790i	$-0.645893\pi$
$167$	−11.4356	−0.884915	−0.442457	+	0.896790i	$0.645893\pi$
$168$	14.7489	1.13790
$169$	1.00000	0.0769231
$170$	17.3426	1.33012
$171$	−0.386410	−0.0295495
$172$	50.4588	3.84745
$173$	−3.56830	−0.271292	−0.135646	−	0.990757i	$-0.543311\pi$
$173$	−3.56830	−0.271292	−0.135646	+	0.990757i	$0.543311\pi$
$174$	49.3737	3.74301
$175$	−1.63746	−0.123780
$176$	−23.8966	−1.80127
$177$	−13.4082	−1.00782
$178$	−18.0221	−1.35081
$179$	8.50720	0.635858	0.317929	−	0.948114i	$-0.397013\pi$
$179$	8.50720	0.635858	0.317929	+	0.948114i	$0.397013\pi$
$180$	−102.106	−7.61055
$181$	−20.7162	−1.53982	−0.769912	−	0.638150i	$-0.779700\pi$
$181$	−20.7162	−1.53982	−0.769912	+	0.638150i	$0.779700\pi$
$182$	−1.60698	−0.119117
$183$	−20.8880	−1.54409
$184$	26.3261	1.94079
$185$	9.02285	0.663373
$186$	−28.6309	−2.09932
$187$	−6.03228	−0.441124
$188$	29.3960	2.14393
$189$	−9.39657	−0.683500
$190$	−0.363781	−0.0263914
$191$	3.85826	0.279174	0.139587	−	0.990210i	$-0.455423\pi$
$191$	3.85826	0.279174	0.139587	+	0.990210i	$0.455423\pi$
$192$	24.4660	1.76568
$193$	16.5723	1.19290	0.596451	−	0.802649i	$-0.296577\pi$
$193$	16.5723	1.19290	0.596451	+	0.802649i	$0.296577\pi$
$194$	45.2077	3.24572
$195$	9.04046	0.647401
$196$	−31.8433	−2.27452
$197$	−9.90716	−0.705856	−0.352928	−	0.935651i	$-0.614814\pi$
$197$	−9.90716	−0.705856	−0.352928	+	0.935651i	$0.614814\pi$
$198$	50.2842	3.57354
$199$	−2.28664	−0.162095	−0.0810477	−	0.996710i	$-0.525827\pi$
$199$	−2.28664	−0.162095	−0.0810477	+	0.996710i	$0.525827\pi$
$200$	−19.4952	−1.37852
$201$	3.97513	0.280384
$202$	−15.4272	−1.08545
$203$	3.56680	0.250340
$204$	37.7295	2.64160
$205$	−21.3564	−1.49160
$206$	−3.06762	−0.213731
$207$	−27.5446	−1.91449
$208$	−9.51309	−0.659614
$209$	0.126534	0.00875251
$210$	−14.5278	−1.00251
$211$	−9.32687	−0.642088	−0.321044	−	0.947064i	$-0.604034\pi$
$211$	−9.32687	−0.642088	−0.321044	+	0.947064i	$0.604034\pi$
$212$	−33.6434	−2.31064
$213$	−39.5905	−2.71270
$214$	45.3640	3.10102
$215$	−29.0345	−1.98014
$216$	−111.873	−7.61203
$217$	−2.06832	−0.140407
$218$	−49.9826	−3.38525
$219$	26.6284	1.79938
$220$	33.4357	2.25423
$221$	−2.40142	−0.161537
$222$	27.7922	1.86529
$223$	−24.0372	−1.60965	−0.804825	−	0.593512i	$-0.797741\pi$
$223$	−24.0372	−1.60965	−0.804825	+	0.593512i	$0.797741\pi$
$224$	6.25738	0.418089
$225$	20.3975	1.35984
$226$	12.9287	0.860006
$227$	−1.22477	−0.0812907	−0.0406453	−	0.999174i	$-0.512941\pi$
$227$	−1.22477	−0.0812907	−0.0406453	+	0.999174i	$0.512941\pi$
$228$	−0.791417	−0.0524129
$229$	−15.8136	−1.04499	−0.522495	−	0.852643i	$-0.674999\pi$
$229$	−15.8136	−1.04499	−0.522495	+	0.852643i	$0.674999\pi$
$230$	−25.9316	−1.70988
$231$	5.05320	0.332476
$232$	42.4655	2.78800
$233$	−22.1219	−1.44925	−0.724626	−	0.689143i	$-0.757987\pi$
$233$	−22.1219	−1.44925	−0.724626	+	0.689143i	$0.757987\pi$
$234$	20.0178	1.30861
$235$	−16.9148	−1.10340
$236$	−19.7413	−1.28505
$237$	6.91352	0.449082
$238$	3.85902	0.250143
$239$	−16.2539	−1.05138	−0.525690	−	0.850676i	$-0.676193\pi$
$239$	−16.2539	−1.05138	−0.525690	+	0.850676i	$0.676193\pi$
$240$	−86.0028	−5.55145
$241$	−17.1531	−1.10493	−0.552464	−	0.833537i	$-0.686312\pi$
$241$	−17.1531	−1.10493	−0.552464	+	0.833537i	$0.686312\pi$
$242$	12.2387	0.786734
$243$	41.8751	2.68629
$244$	−30.7541	−1.96883
$245$	18.3230	1.17061
$246$	−65.7821	−4.19411
$247$	0.0503723	0.00320511
$248$	−24.6250	−1.56369
$249$	−53.2902	−3.37713
$250$	−16.9062	−1.06924
$251$	−13.8074	−0.871517	−0.435758	−	0.900064i	$-0.643520\pi$
$251$	−13.8074	−0.871517	−0.435758	+	0.900064i	$0.643520\pi$
$252$	−22.7203	−1.43124
$253$	9.01976	0.567067
$254$	5.81175	0.364662
$255$	−21.7099	−1.35953
$256$	−17.0095	−1.06309
$257$	8.44661	0.526885	0.263442	−	0.964675i	$-0.415142\pi$
$257$	8.44661	0.526885	0.263442	+	0.964675i	$0.415142\pi$
$258$	−89.4320	−5.56779
$259$	2.00773	0.124754
$260$	13.3106	0.825485
$261$	−44.4311	−2.75021
$262$	36.1913	2.23591
$263$	−6.02822	−0.371716	−0.185858	−	0.982577i	$-0.559506\pi$
$263$	−6.02822	−0.371716	−0.185858	+	0.982577i	$0.559506\pi$
$264$	60.1623	3.70273
$265$	19.3587	1.18920
$266$	−0.0809471	−0.00496319
$267$	22.5605	1.38068
$268$	5.85271	0.357511
$269$	−25.3720	−1.54696	−0.773479	−	0.633822i	$-0.781485\pi$
$269$	−25.3720	−1.54696	−0.773479	+	0.633822i	$0.781485\pi$
$270$	110.197	6.70636
$271$	−0.766798	−0.0465797	−0.0232898	−	0.999729i	$-0.507414\pi$
$271$	−0.766798	−0.0465797	−0.0232898	+	0.999729i	$0.507414\pi$
$272$	22.8449	1.38518
$273$	2.01165	0.121751
$274$	−12.7889	−0.772608
$275$	−6.67937	−0.402781
$276$	−56.4150	−3.39578
$277$	15.6890	0.942659	0.471330	−	0.881957i	$-0.343774\pi$
$277$	15.6890	0.942659	0.471330	+	0.881957i	$0.343774\pi$
$278$	−26.8331	−1.60934
$279$	25.7648	1.54250
$280$	−12.4951	−0.746728
$281$	14.7101	0.877530	0.438765	−	0.898602i	$-0.355416\pi$
$281$	14.7101	0.877530	0.438765	+	0.898602i	$0.355416\pi$
$282$	−52.1008	−3.10256
$283$	3.78484	0.224985	0.112493	−	0.993653i	$-0.464117\pi$
$283$	3.78484	0.224985	0.112493	+	0.993653i	$0.464117\pi$
$284$	−58.2904	−3.45890
$285$	0.455389	0.0269749
$286$	−6.55503	−0.387607
$287$	−4.75216	−0.280511
$288$	−77.9471	−4.59308
$289$	−11.2332	−0.660776
$290$	−41.8290	−2.45629
$291$	−56.5920	−3.31748
$292$	39.2058	2.29434
$293$	−17.4072	−1.01694	−0.508469	−	0.861080i	$-0.669788\pi$
$293$	−17.4072	−1.01694	−0.508469	+	0.861080i	$0.669788\pi$
$294$	56.4383	3.29155
$295$	11.3593	0.661365
$296$	23.9036	1.38937
$297$	−38.3296	−2.22411
$298$	42.5912	2.46724
$299$	3.59072	0.207656
$300$	41.7768	2.41198
$301$	−6.46065	−0.372386
$302$	−10.3794	−0.597265
$303$	19.3121	1.10945
$304$	−0.479197	−0.0274838
$305$	17.6962	1.01328
$306$	−48.0712	−2.74805
$307$	−11.8849	−0.678305	−0.339153	−	0.940731i	$-0.610140\pi$
$307$	−11.8849	−0.678305	−0.339153	+	0.940731i	$0.610140\pi$
$308$	7.43998	0.423932
$309$	3.84012	0.218457
$310$	24.2559	1.37764
$311$	18.7705	1.06438	0.532190	−	0.846625i	$-0.321369\pi$
$311$	18.7705	1.06438	0.532190	+	0.846625i	$0.321369\pi$
$312$	23.9503	1.35592
$313$	19.8757	1.12344	0.561719	−	0.827328i	$-0.310140\pi$
$313$	19.8757	1.12344	0.561719	+	0.827328i	$0.310140\pi$
$314$	19.7432	1.11417
$315$	13.0735	0.736607
$316$	10.1790	0.572613
$317$	−3.92209	−0.220286	−0.110143	−	0.993916i	$-0.535131\pi$
$317$	−3.92209	−0.220286	−0.110143	+	0.993916i	$0.535131\pi$
$318$	59.6287	3.34381
$319$	14.5494	0.814609
$320$	−20.7275	−1.15870
$321$	−56.7878	−3.16958
$322$	−5.77019	−0.321560
$323$	−0.120965	−0.00673067
$324$	129.052	7.16956
$325$	−2.65902	−0.147496
$326$	−4.40201	−0.243805
$327$	62.5694	3.46009
$328$	−56.5781	−3.12401
$329$	−3.76381	−0.207506
$330$	−59.2605	−3.26219
$331$	17.1731	0.943917	0.471959	−	0.881621i	$-0.343547\pi$
$331$	17.1731	0.943917	0.471959	+	0.881621i	$0.343547\pi$
$332$	−78.4607	−4.30609
$333$	−25.0100	−1.37054
$334$	29.8415	1.63285
$335$	−3.36771	−0.183997
$336$	−19.1370	−1.04401
$337$	13.1360	0.715561	0.357781	−	0.933806i	$-0.383534\pi$
$337$	13.1360	0.715561	0.357781	+	0.933806i	$0.383534\pi$
$338$	−2.60952	−0.141939
$339$	−16.1845	−0.879020
$340$	−31.9642	−1.73350
$341$	−8.43693	−0.456885
$342$	1.00835	0.0545251
$343$	8.38784	0.452901
$344$	−76.9191	−4.14720
$345$	32.4617	1.74768
$346$	9.31155	0.500592
$347$	21.1558	1.13570	0.567852	−	0.823131i	$-0.307775\pi$
$347$	21.1558	1.13570	0.567852	+	0.823131i	$0.307775\pi$
$348$	−91.0005	−4.87814
$349$	21.7016	1.16166	0.580830	−	0.814025i	$-0.302728\pi$
$349$	21.7016	1.16166	0.580830	+	0.814025i	$0.302728\pi$
$350$	4.27298	0.228400
$351$	−15.2588	−0.814455
$352$	25.5245	1.36046
$353$	34.9332	1.85931	0.929653	−	0.368437i	$-0.120107\pi$
$353$	34.9332	1.85931	0.929653	+	0.368437i	$0.120107\pi$
$354$	34.9889	1.85964
$355$	33.5408	1.78016
$356$	33.2165	1.76047
$357$	−4.83081	−0.255674
$358$	−22.1997	−1.17329
$359$	−20.1761	−1.06485	−0.532427	−	0.846476i	$-0.678720\pi$
$359$	−20.1761	−1.06485	−0.532427	+	0.846476i	$0.678720\pi$
$360$	155.650	8.20347
$361$	−18.9975	−0.999866
$362$	54.0594	2.84130
$363$	−15.3207	−0.804129
$364$	2.96181	0.155241
$365$	−22.5594	−1.18081
$366$	54.5077	2.84916
$367$	−20.2178	−1.05536	−0.527679	−	0.849444i	$-0.676938\pi$
$367$	−20.2178	−1.05536	−0.527679	+	0.849444i	$0.676938\pi$
$368$	−34.1588	−1.78065
$369$	59.1969	3.08167
$370$	−23.5453	−1.22406
$371$	4.30763	0.223641
$372$	52.7696	2.73598
$373$	−6.74751	−0.349373	−0.174686	−	0.984624i	$-0.555891\pi$
$373$	−6.74751	−0.349373	−0.174686	+	0.984624i	$0.555891\pi$
$374$	15.7414	0.813967
$375$	21.1635	1.09288
$376$	−44.8111	−2.31096
$377$	5.79202	0.298304
$378$	24.5206	1.26120
$379$	3.83115	0.196793	0.0983964	−	0.995147i	$-0.468629\pi$
$379$	3.83115	0.196793	0.0983964	+	0.995147i	$0.468629\pi$
$380$	0.670483	0.0343951
$381$	−7.27529	−0.372724
$382$	−10.0682	−0.515134
$383$	19.9158	1.01765	0.508824	−	0.860870i	$-0.330080\pi$
$383$	19.9158	1.01765	0.508824	+	0.860870i	$0.330080\pi$
$384$	2.54154	0.129697
$385$	−4.28104	−0.218182
$386$	−43.2458	−2.20116
$387$	80.4792	4.09099
$388$	−83.3222	−4.23004
$389$	0.904447	0.0458573	0.0229286	−	0.999737i	$-0.492701\pi$
$389$	0.904447	0.0458573	0.0229286	+	0.999737i	$0.492701\pi$
$390$	−23.5913	−1.19459
$391$	−8.62281	−0.436074
$392$	48.5417	2.45173
$393$	−45.3051	−2.28534
$394$	25.8529	1.30245
$395$	−5.85709	−0.294702
$396$	−92.6786	−4.65728
$397$	−14.1047	−0.707897	−0.353949	−	0.935265i	$-0.615161\pi$
$397$	−14.1047	−0.707897	−0.353949	+	0.935265i	$0.615161\pi$
$398$	5.96703	0.299100
$399$	0.101332	0.00507292
$400$	25.2955	1.26478
$401$	−7.03623	−0.351372	−0.175686	−	0.984446i	$-0.556214\pi$
$401$	−7.03623	−0.351372	−0.175686	+	0.984446i	$0.556214\pi$
$402$	−10.3732	−0.517368
$403$	−3.35869	−0.167308
$404$	28.4338	1.41464
$405$	−74.2578	−3.68990
$406$	−9.30765	−0.461931
$407$	8.18976	0.405951
$408$	−57.5146	−2.84740
$409$	−26.2638	−1.29866	−0.649331	−	0.760506i	$-0.724951\pi$
$409$	−26.2638	−1.29866	−0.649331	+	0.760506i	$0.724951\pi$
$410$	55.7301	2.75231
$411$	16.0095	0.789690
$412$	5.65393	0.278549
$413$	2.52763	0.124377
$414$	71.8784	3.53263
$415$	45.1471	2.21618
$416$	10.1612	0.498192
$417$	33.5903	1.64492
$418$	−0.330192	−0.0161502
$419$	−12.3762	−0.604617	−0.302308	−	0.953210i	$-0.597757\pi$
$419$	−12.3762	−0.604617	−0.302308	+	0.953210i	$0.597757\pi$
$420$	26.7762	1.30654
$421$	−35.8535	−1.74739	−0.873697	−	0.486470i	$-0.838284\pi$
$421$	−35.8535	−1.74739	−0.873697	+	0.486470i	$0.838284\pi$
$422$	24.3387	1.18479
$423$	46.8852	2.27963
$424$	51.2857	2.49066
$425$	6.38542	0.309738
$426$	103.312	5.00550
$427$	3.93769	0.190558
$428$	−83.6104	−4.04146
$429$	8.20575	0.396177
$430$	75.7662	3.65377
$431$	−4.09900	−0.197442	−0.0987209	−	0.995115i	$-0.531475\pi$
$431$	−4.09900	−0.197442	−0.0987209	+	0.995115i	$0.531475\pi$
$432$	145.159	6.98394
$433$	26.8547	1.29056	0.645278	−	0.763948i	$-0.276742\pi$
$433$	26.8547	1.29056	0.645278	+	0.763948i	$0.276742\pi$
$434$	5.39734	0.259081
$435$	52.3626	2.51059
$436$	92.1228	4.41188
$437$	0.180873	0.00865231
$438$	−69.4873	−3.32023
$439$	19.8292	0.946396	0.473198	−	0.880956i	$-0.343100\pi$
$439$	19.8292	0.946396	0.473198	+	0.880956i	$0.343100\pi$
$440$	−50.9691	−2.42986
$441$	−50.7885	−2.41850
$442$	6.26655	0.298070
$443$	−15.5489	−0.738751	−0.369376	−	0.929280i	$-0.620428\pi$
$443$	−15.5489	−0.738751	−0.369376	+	0.929280i	$0.620428\pi$
$444$	−51.2237	−2.43097
$445$	−19.1131	−0.906048
$446$	62.7256	2.97014
$447$	−53.3166	−2.52179
$448$	−4.61220	−0.217906
$449$	−17.8517	−0.842475	−0.421238	−	0.906950i	$-0.638404\pi$
$449$	−17.8517	−0.842475	−0.421238	+	0.906950i	$0.638404\pi$
$450$	−53.2278	−2.50918
$451$	−19.3846	−0.912784
$452$	−23.8289	−1.12082
$453$	12.9931	0.610471
$454$	3.19606	0.149998
$455$	−1.70426	−0.0798968
$456$	1.20643	0.0564963
$457$	0.611560	0.0286076	0.0143038	−	0.999898i	$-0.495447\pi$
$457$	0.611560	0.0286076	0.0143038	+	0.999898i	$0.495447\pi$
$458$	41.2658	1.92823
$459$	36.6428	1.71034
$460$	47.7944	2.22843
$461$	23.3553	1.08776	0.543882	−	0.839162i	$-0.316954\pi$
$461$	23.3553	1.08776	0.543882	+	0.839162i	$0.316954\pi$
$462$	−13.1864	−0.613489
$463$	−1.00000	−0.0464739
$463$	−1.00000	−0.0464739
$464$	−55.1001	−2.55796
$465$	−30.3641	−1.40810
$466$	57.7275	2.67417
$467$	−28.3940	−1.31392	−0.656959	−	0.753926i	$-0.728158\pi$
$467$	−28.3940	−1.31392	−0.656959	+	0.753926i	$0.728158\pi$
$468$	−36.8948	−1.70546
$469$	−0.749369	−0.0346027
$470$	44.1394	2.03600
$471$	−24.7150	−1.13881
$472$	30.0934	1.38516
$473$	−26.3537	−1.21174
$474$	−18.0410	−0.828650
$475$	−0.133941	−0.00614563
$476$	−7.11256	−0.326004
$477$	−53.6595	−2.45690
$478$	42.4150	1.94002
$479$	18.1246	0.828132	0.414066	−	0.910247i	$-0.364108\pi$
$479$	18.1246	0.828132	0.414066	+	0.910247i	$0.364108\pi$
$480$	91.8617	4.19289
$481$	3.26030	0.148657
$482$	44.7614	2.03883
$483$	7.22326	0.328670
$484$	−22.5571	−1.02532
$485$	47.9444	2.17704
$486$	−109.274	−4.95677
$487$	−2.82231	−0.127891	−0.0639455	−	0.997953i	$-0.520368\pi$
$487$	−2.82231	−0.127891	−0.0639455	+	0.997953i	$0.520368\pi$
$488$	46.8813	2.12222
$489$	5.51054	0.249195
$490$	−47.8141	−2.16002
$491$	39.0553	1.76254	0.881272	−	0.472610i	$-0.156688\pi$
$491$	39.0553	1.76254	0.881272	+	0.472610i	$0.156688\pi$
$492$	121.243	5.46605
$493$	−13.9091	−0.626433
$494$	−0.131448	−0.00591411
$495$	53.3282	2.39692
$496$	31.9516	1.43467
$497$	7.46338	0.334779
$498$	139.062	6.23151
$499$	−19.8755	−0.889751	−0.444876	−	0.895592i	$-0.646752\pi$
$499$	−19.8755	−0.889751	−0.444876	+	0.895592i	$0.646752\pi$
$500$	31.1597	1.39351
$501$	−37.3563	−1.66896
$502$	36.0308	1.60813
$503$	−15.2846	−0.681509	−0.340754	−	0.940152i	$-0.610682\pi$
$503$	−15.2846	−0.681509	−0.340754	+	0.940152i	$0.610682\pi$
$504$	34.6347	1.54275
$505$	−16.3611	−0.728060
$506$	−23.5373	−1.04636
$507$	3.26666	0.145078
$508$	−10.7116	−0.475252
$509$	13.9304	0.617454	0.308727	−	0.951151i	$-0.400097\pi$
$509$	13.9304	0.617454	0.308727	+	0.951151i	$0.400097\pi$
$510$	56.6526	2.50862
$511$	−5.01983	−0.222064
$512$	42.8306	1.89286
$513$	−0.768622	−0.0339355
$514$	−22.0416	−0.972214
$515$	−3.25333	−0.143359
$516$	164.832	7.25632
$517$	−15.3530	−0.675224
$518$	−5.23922	−0.230198
$519$	−11.6564	−0.511660
$520$	−20.2905	−0.889798
$521$	−21.0940	−0.924146	−0.462073	−	0.886842i	$-0.652894\pi$
$521$	−21.0940	−0.924146	−0.462073	+	0.886842i	$0.652894\pi$
$522$	115.944	5.07472
$523$	−14.8324	−0.648576	−0.324288	−	0.945958i	$-0.605125\pi$
$523$	−14.8324	−0.648576	−0.324288	+	0.945958i	$0.605125\pi$
$524$	−66.7041	−2.91398
$525$	−5.34902	−0.233450
$526$	15.7308	0.685895
$527$	8.06563	0.351344
$528$	−78.0620	−3.39721
$529$	−10.1068	−0.439424
$530$	−50.5170	−2.19432
$531$	−31.4863	−1.36639
$532$	0.149193	0.00646836
$533$	−7.71689	−0.334256
$534$	−58.8721	−2.54765
$535$	48.1102	2.07999
$536$	−8.92183	−0.385364
$537$	27.7902	1.19923
$538$	66.2088	2.85446
$539$	16.6312	0.716355
$540$	−203.103	−8.74017
$541$	−27.0274	−1.16200	−0.580999	−	0.813904i	$-0.697338\pi$
$541$	−27.0274	−1.16200	−0.580999	+	0.813904i	$0.697338\pi$
$542$	2.00098	0.0859493
$543$	−67.6729	−2.90412
$544$	−24.4012	−1.04619
$545$	−53.0083	−2.27063
$546$	−5.24945	−0.224656
$547$	20.7389	0.886729	0.443365	−	0.896341i	$-0.353785\pi$
$547$	20.7389	0.886729	0.443365	+	0.896341i	$0.353785\pi$
$548$	23.5713	1.00691
$549$	−49.0512	−2.09345
$550$	17.4300	0.743216
$551$	0.291758	0.0124293
$552$	85.9986	3.66034
$553$	−1.30330	−0.0554219
$554$	−40.9407	−1.73940
$555$	29.4746	1.25113
$556$	49.4560	2.09740
$557$	10.6497	0.451241	0.225621	−	0.974215i	$-0.427559\pi$
$557$	10.6497	0.451241	0.225621	+	0.974215i	$0.427559\pi$
$558$	−67.2338	−2.84623
$559$	−10.4913	−0.443733
$560$	16.2128	0.685114
$561$	−19.7054	−0.831964
$562$	−38.3863	−1.61923
$563$	30.4639	1.28390	0.641950	−	0.766746i	$-0.278125\pi$
$563$	30.4639	1.28390	0.641950	+	0.766746i	$0.278125\pi$
$564$	96.0269	4.04346
$565$	13.7114	0.576842
$566$	−9.87662	−0.415145
$567$	−16.5236	−0.693925
$568$	88.8574	3.72837
$569$	30.1392	1.26350	0.631750	−	0.775172i	$-0.282337\pi$
$569$	30.1392	1.26350	0.631750	+	0.775172i	$0.282337\pi$
$570$	−1.18835	−0.0497744
$571$	−1.53762	−0.0643473	−0.0321736	−	0.999482i	$-0.510243\pi$
$571$	−1.53762	−0.0643473	−0.0321736	+	0.999482i	$0.510243\pi$
$572$	12.0816	0.505156
$573$	12.6036	0.526524
$574$	12.4009	0.517602
$575$	−9.54778	−0.398170
$576$	57.4534	2.39389
$577$	−28.6279	−1.19180	−0.595898	−	0.803060i	$-0.703204\pi$
$577$	−28.6279	−1.19180	−0.595898	+	0.803060i	$0.703204\pi$
$578$	29.3133	1.21927
$579$	54.1362	2.24982
$580$	77.0950	3.20120
$581$	10.0460	0.416777
$582$	147.678	6.12145
$583$	17.5713	0.727730
$584$	−59.7650	−2.47309
$585$	21.2296	0.877738
$586$	45.4244	1.87646
$587$	−35.9026	−1.48186	−0.740930	−	0.671582i	$-0.765615\pi$
$587$	−35.9026	−1.48186	−0.740930	+	0.671582i	$0.765615\pi$
$588$	−104.021	−4.28977
$589$	−0.169185	−0.00697115
$590$	−29.6424	−1.22036
$591$	−32.3633	−1.33125
$592$	−31.0155	−1.27473
$593$	30.3410	1.24596	0.622978	−	0.782239i	$-0.285922\pi$
$593$	30.3410	1.24596	0.622978	+	0.782239i	$0.285922\pi$
$594$	100.022	4.10396
$595$	4.09263	0.167782
$596$	−78.4997	−3.21547
$597$	−7.46967	−0.305713
$598$	−9.37005	−0.383170
$599$	27.3815	1.11878	0.559389	−	0.828905i	$-0.311036\pi$
$599$	27.3815	1.11878	0.559389	+	0.828905i	$0.311036\pi$
$600$	−63.6842	−2.59990
$601$	−4.51174	−0.184038	−0.0920189	−	0.995757i	$-0.529332\pi$
$601$	−4.51174	−0.184038	−0.0920189	+	0.995757i	$0.529332\pi$
$602$	16.8592	0.687130
$603$	9.33477	0.380141
$604$	19.1302	0.778396
$605$	12.9796	0.527696
$606$	−50.3954	−2.04717
$607$	9.67083	0.392527	0.196263	−	0.980551i	$-0.437119\pi$
$607$	9.67083	0.392527	0.196263	+	0.980551i	$0.437119\pi$
$608$	0.511842	0.0207579
$609$	11.6515	0.472144
$610$	−46.1786	−1.86972
$611$	−6.11194	−0.247263
$612$	88.6000	3.58144
$613$	30.2232	1.22071	0.610353	−	0.792130i	$-0.291028\pi$
$613$	30.2232	1.22071	0.610353	+	0.792130i	$0.291028\pi$
$614$	31.0138	1.25162
$615$	−69.7643	−2.81317
$616$	−11.3415	−0.456960
$617$	−25.8703	−1.04150	−0.520750	−	0.853709i	$-0.674348\pi$
$617$	−25.8703	−1.04150	−0.520750	+	0.853709i	$0.674348\pi$
$618$	−10.0209	−0.403099
$619$	−11.8793	−0.477468	−0.238734	−	0.971085i	$-0.576732\pi$
$619$	−11.8793	−0.477468	−0.238734	+	0.971085i	$0.576732\pi$
$620$	−44.7061	−1.79544
$621$	−54.7901	−2.19865
$622$	−48.9821	−1.96400
$623$	−4.25298	−0.170392
$624$	−31.0761	−1.24404
$625$	−31.2247	−1.24899
$626$	−51.8660	−2.07298
$627$	0.413342	0.0165073
$628$	−36.3887	−1.45207
$629$	−7.82934	−0.312176
$630$	−34.1155	−1.35920
$631$	−2.17469	−0.0865730	−0.0432865	−	0.999063i	$-0.513783\pi$
$631$	−2.17469	−0.0865730	−0.0432865	+	0.999063i	$0.513783\pi$
$632$	−15.5168	−0.617224
$633$	−30.4677	−1.21098
$634$	10.2348	0.406475
$635$	6.16357	0.244594
$636$	−109.902	−4.35788
$637$	6.62078	0.262325
$638$	−37.9669	−1.50312
$639$	−92.9702	−3.67784
$640$	−2.15318	−0.0851118
$641$	31.5362	1.24561	0.622803	−	0.782379i	$-0.285994\pi$
$641$	31.5362	1.24561	0.622803	+	0.782379i	$0.285994\pi$
$642$	148.189	5.84855
$643$	−27.2396	−1.07423	−0.537113	−	0.843510i	$-0.680485\pi$
$643$	−27.2396	−1.07423	−0.537113	+	0.843510i	$0.680485\pi$
$644$	10.6350	0.419079
$645$	−94.8458	−3.73455
$646$	0.315661	0.0124195
$647$	15.1717	0.596461	0.298230	−	0.954494i	$-0.403604\pi$
$647$	15.1717	0.596461	0.298230	+	0.954494i	$0.403604\pi$
$648$	−196.726	−7.72813
$649$	10.3105	0.404722
$650$	6.93877	0.272161
$651$	−6.75652	−0.264809
$652$	8.11333	0.317743
$653$	23.9750	0.938215	0.469107	−	0.883141i	$-0.344576\pi$
$653$	23.9750	0.938215	0.469107	+	0.883141i	$0.344576\pi$
$654$	−163.276	−6.38460
$655$	38.3822	1.49972
$656$	73.4115	2.86624
$657$	62.5312	2.43957
$658$	9.82175	0.382892
$659$	−35.1953	−1.37102	−0.685508	−	0.728065i	$-0.740420\pi$
$659$	−35.1953	−1.37102	−0.685508	+	0.728065i	$0.740420\pi$
$660$	109.223	4.25150
$661$	−15.2007	−0.591238	−0.295619	−	0.955306i	$-0.595526\pi$
$661$	−15.2007	−0.591238	−0.295619	+	0.955306i	$0.595526\pi$
$662$	−44.8135	−1.74173
$663$	−7.84462	−0.304660
$664$	119.605	4.64157
$665$	−0.0858474	−0.00332902
$666$	65.2641	2.52893
$667$	20.7975	0.805283
$668$	−55.0008	−2.12805
$669$	−78.5214	−3.03581
$670$	8.78810	0.339514
$671$	16.0623	0.620077
$672$	20.4407	0.788518
$673$	24.5823	0.947580	0.473790	−	0.880638i	$-0.342886\pi$
$673$	24.5823	0.947580	0.473790	+	0.880638i	$0.342886\pi$
$674$	−34.2786	−1.32036
$675$	40.5735	1.56167
$676$	4.80961	0.184985
$677$	46.3490	1.78134	0.890669	−	0.454653i	$-0.150237\pi$
$677$	46.3490	1.78134	0.890669	+	0.454653i	$0.150237\pi$
$678$	42.2337	1.62198
$679$	10.6684	0.409416
$680$	48.7260	1.86856
$681$	−4.00090	−0.153315
$682$	22.0163	0.843049
$683$	−26.8348	−1.02681	−0.513403	−	0.858148i	$-0.671615\pi$
$683$	−26.8348	−1.02681	−0.513403	+	0.858148i	$0.671615\pi$
$684$	−1.85848	−0.0710607
$685$	−13.5631	−0.518221
$686$	−21.8883	−0.835698
$687$	−51.6575	−1.97086
$688$	99.8043	3.80500
$689$	6.99504	0.266490
$690$	−84.7096	−3.22484
$691$	4.79554	0.182431	0.0912155	−	0.995831i	$-0.470925\pi$
$691$	4.79554	0.182431	0.0912155	+	0.995831i	$0.470925\pi$
$692$	−17.1621	−0.652405
$693$	11.8664	0.450767
$694$	−55.2066	−2.09561
$695$	−28.4574	−1.07945
$696$	138.721	5.25819
$697$	18.5315	0.701930
$698$	−56.6308	−2.14351
$699$	−72.2646	−2.73330
$700$	−7.87552	−0.297667
$701$	−9.24177	−0.349057	−0.174528	−	0.984652i	$-0.555840\pi$
$701$	−9.24177	−0.349057	−0.174528	+	0.984652i	$0.555840\pi$
$702$	39.8182	1.50284
$703$	0.164229	0.00619400
$704$	−18.8137	−0.709067
$705$	−55.2548	−2.08102
$706$	−91.1589	−3.43081
$707$	−3.64061	−0.136919
$708$	−64.4880	−2.42361
$709$	−42.8216	−1.60820	−0.804100	−	0.594494i	$-0.797352\pi$
$709$	−42.8216	−1.60820	−0.804100	+	0.594494i	$0.797352\pi$
$710$	−87.5256	−3.28478
$711$	16.2350	0.608859
$712$	−50.6350	−1.89763
$713$	−12.0601	−0.451655
$714$	12.6061	0.471772
$715$	−6.95185	−0.259985
$716$	40.9163	1.52911
$717$	−53.0961	−1.98291
$718$	52.6500	1.96488
$719$	11.1499	0.415821	0.207911	−	0.978148i	$-0.433334\pi$
$719$	11.1499	0.415821	0.207911	+	0.978148i	$0.433334\pi$
$720$	−201.960	−7.52659
$721$	−0.723918	−0.0269601
$722$	49.5743	1.84496
$723$	−56.0334	−2.08390
$724$	−99.6368	−3.70297
$725$	−15.4011	−0.571983
$726$	39.9797	1.48379
$727$	−12.3545	−0.458203	−0.229101	−	0.973403i	$-0.573579\pi$
$727$	−12.3545	−0.458203	−0.229101	+	0.973403i	$0.573579\pi$
$728$	−4.51497	−0.167336
$729$	56.2954	2.08501
$730$	58.8692	2.17885
$731$	25.1939	0.931830
$732$	−100.463	−3.71322
$733$	−0.603646	−0.0222962	−0.0111481	−	0.999938i	$-0.503549\pi$
$733$	−0.603646	−0.0222962	−0.0111481	+	0.999938i	$0.503549\pi$
$734$	52.7587	1.94736
$735$	59.8549	2.20778
$736$	36.4859	1.34489
$737$	−3.05676	−0.112597
$738$	−154.476	−5.68632
$739$	−14.4452	−0.531374	−0.265687	−	0.964059i	$-0.585599\pi$
$739$	−14.4452	−0.531374	−0.265687	+	0.964059i	$0.585599\pi$
$740$	43.3964	1.59528
$741$	0.164549	0.00604487
$742$	−11.2409	−0.412665
$743$	−8.15550	−0.299196	−0.149598	−	0.988747i	$-0.547798\pi$
$743$	−8.15550	−0.299196	−0.149598	+	0.988747i	$0.547798\pi$
$744$	−80.4416	−2.94913
$745$	45.1695	1.65488
$746$	17.6078	0.644666
$747$	−125.141	−4.57866
$748$	−29.0129	−1.06082
$749$	10.7053	0.391164
$750$	−55.2267	−2.01660
$751$	−3.75818	−0.137138	−0.0685690	−	0.997646i	$-0.521843\pi$
$751$	−3.75818	−0.137138	−0.0685690	+	0.997646i	$0.521843\pi$
$752$	58.1435	2.12027
$753$	−45.1042	−1.64369
$754$	−15.1144	−0.550435
$755$	−11.0077	−0.400611
$756$	−45.1938	−1.64368
$757$	−21.0061	−0.763481	−0.381741	−	0.924270i	$-0.624675\pi$
$757$	−21.0061	−0.763481	−0.381741	+	0.924270i	$0.624675\pi$
$758$	−9.99746	−0.363124
$759$	29.4645	1.06949
$760$	−1.02208	−0.0370747
$761$	−31.4829	−1.14126	−0.570628	−	0.821209i	$-0.693300\pi$
$761$	−31.4829	−1.14126	−0.570628	+	0.821209i	$0.693300\pi$
$762$	18.9850	0.687755
$763$	−11.7952	−0.427016
$764$	18.5567	0.671358
$765$	−50.9813	−1.84323
$766$	−51.9707	−1.87778
$767$	4.10455	0.148207
$768$	−55.5643	−2.00500
$769$	32.2935	1.16453	0.582266	−	0.812998i	$-0.302166\pi$
$769$	32.2935	1.16453	0.582266	+	0.812998i	$0.302166\pi$
$770$	11.1715	0.402591
$771$	27.5922	0.993709
$772$	79.7063	2.86869
$773$	41.5918	1.49595	0.747976	−	0.663726i	$-0.231026\pi$
$773$	41.5918	1.49595	0.747976	+	0.663726i	$0.231026\pi$
$774$	−210.012	−7.54874
$775$	8.93083	0.320805
$776$	127.016	4.55960
$777$	6.55858	0.235288
$778$	−2.36017	−0.0846163
$779$	−0.388718	−0.0139273
$780$	43.4811	1.55687
$781$	30.4440	1.08937
$782$	22.5014	0.804649
$783$	−88.3795	−3.15842
$784$	−62.9841	−2.24943
$785$	20.9384	0.747324
$786$	118.225	4.21694
$787$	17.3676	0.619088	0.309544	−	0.950885i	$-0.399824\pi$
$787$	17.3676	0.619088	0.309544	+	0.950885i	$0.399824\pi$
$788$	−47.6495	−1.69744
$789$	−19.6922	−0.701060
$790$	15.2842	0.543788
$791$	3.05101	0.108481
$792$	141.279	5.02012
$793$	6.39430	0.227068
$794$	36.8067	1.30622
$795$	63.2384	2.24284
$796$	−10.9978	−0.389807
$797$	−40.9934	−1.45206	−0.726031	−	0.687662i	$-0.758637\pi$
$797$	−40.9934	−1.45206	−0.726031	+	0.687662i	$0.758637\pi$
$798$	−0.264427	−0.00936061
$799$	14.6773	0.519247
$800$	−27.0188	−0.955257
$801$	52.9786	1.87191
$802$	18.3612	0.648356
$803$	−20.4764	−0.722598
$804$	19.1188	0.674269
$805$	−6.11950	−0.215684
$806$	8.76458	0.308719
$807$	−82.8817	−2.91757
$808$	−43.3443	−1.52485
$809$	1.99775	0.0702373	0.0351186	−	0.999383i	$-0.488819\pi$
$809$	1.99775	0.0702373	0.0351186	+	0.999383i	$0.488819\pi$
$810$	193.777	6.80865
$811$	31.4712	1.10510	0.552552	−	0.833479i	$-0.313654\pi$
$811$	31.4712	1.10510	0.552552	+	0.833479i	$0.313654\pi$
$812$	17.1549	0.602019
$813$	−2.50487	−0.0878496
$814$	−21.3714	−0.749066
$815$	−4.66849	−0.163530
$816$	74.6266	2.61245
$817$	−0.528469	−0.0184888
$818$	68.5360	2.39631
$819$	4.72394	0.165068
$820$	−102.716	−3.58700
$821$	−50.5937	−1.76573	−0.882867	−	0.469623i	$-0.844390\pi$
$821$	−50.5937	−1.76573	−0.882867	+	0.469623i	$0.844390\pi$
$822$	−41.7771	−1.45714
$823$	24.3057	0.847243	0.423622	−	0.905839i	$-0.360759\pi$
$823$	24.3057	0.847243	0.423622	+	0.905839i	$0.360759\pi$
$824$	−8.61881	−0.300250
$825$	−21.8192	−0.759648
$826$	−6.59591	−0.229501
$827$	49.4208	1.71853	0.859265	−	0.511530i	$-0.170921\pi$
$827$	49.4208	1.71853	0.859265	+	0.511530i	$0.170921\pi$
$828$	−132.479	−4.60396
$829$	−26.2785	−0.912690	−0.456345	−	0.889803i	$-0.650842\pi$
$829$	−26.2785	−0.912690	−0.456345	+	0.889803i	$0.650842\pi$
$830$	−117.812	−4.08932
$831$	51.2506	1.77786
$832$	−7.48962	−0.259656
$833$	−15.8993	−0.550876
$834$	−87.6545	−3.03523
$835$	31.6480	1.09522
$836$	0.608577	0.0210481
$837$	51.2497	1.77145
$838$	32.2960	1.11565
$839$	7.79347	0.269060	0.134530	−	0.990909i	$-0.457047\pi$
$839$	7.79347	0.269060	0.134530	+	0.990909i	$0.457047\pi$
$840$	−40.8174	−1.40833
$841$	4.54755	0.156812
$842$	93.5606	3.22431
$843$	48.0529	1.65503
$844$	−44.8586	−1.54410
$845$	−2.76749	−0.0952047
$846$	−122.348	−4.20641
$847$	2.88817	0.0992388
$848$	−66.5445	−2.28515
$849$	12.3638	0.424324
$850$	−16.6629	−0.571533
$851$	11.7068	0.401304
$852$	−190.415	−6.52351
$853$	49.0249	1.67858	0.839290	−	0.543684i	$-0.182971\pi$
$853$	49.0249	1.67858	0.839290	+	0.543684i	$0.182971\pi$
$854$	−10.2755	−0.351620
$855$	1.06939	0.0365723
$856$	127.455	4.35632
$857$	20.2675	0.692323	0.346162	−	0.938175i	$-0.387485\pi$
$857$	20.2675	0.692323	0.346162	+	0.938175i	$0.387485\pi$
$858$	−21.4131	−0.731030
$859$	7.07694	0.241462	0.120731	−	0.992685i	$-0.461476\pi$
$859$	7.07694	0.241462	0.120731	+	0.992685i	$0.461476\pi$
$860$	−139.644	−4.76184
$861$	−15.5237	−0.529046
$862$	10.6964	0.364322
$863$	−35.3743	−1.20415	−0.602077	−	0.798438i	$-0.705660\pi$
$863$	−35.3743	−1.20415	−0.602077	+	0.798438i	$0.705660\pi$
$864$	−155.047	−5.27482
$865$	9.87523	0.335768
$866$	−70.0780	−2.38135
$867$	−36.6950	−1.24623
$868$	−9.94782	−0.337651
$869$	−5.31630	−0.180343
$870$	−136.641	−4.63257
$871$	−1.21688	−0.0412324
$872$	−140.431	−4.75560
$873$	−132.895	−4.49780
$874$	−0.471991	−0.0159653
$875$	−3.98963	−0.134874
$876$	128.072	4.32715
$877$	50.8543	1.71723	0.858614	−	0.512622i	$-0.171326\pi$
$877$	50.8543	1.71723	0.858614	+	0.512622i	$0.171326\pi$
$878$	−51.7447	−1.74630
$879$	−56.8633	−1.91795
$880$	66.1336	2.22936
$881$	54.3883	1.83239	0.916193	−	0.400736i	$-0.131246\pi$
$881$	54.3883	1.83239	0.916193	+	0.400736i	$0.131246\pi$
$882$	132.534	4.46264
$883$	52.8574	1.77879	0.889397	−	0.457137i	$-0.151125\pi$
$883$	52.8574	1.77879	0.889397	+	0.457137i	$0.151125\pi$
$884$	−11.5499	−0.388464
$885$	37.1070	1.24734
$886$	40.5752	1.36315
$887$	−27.7353	−0.931259	−0.465630	−	0.884980i	$-0.654172\pi$
$887$	−27.7353	−0.931259	−0.465630	+	0.884980i	$0.654172\pi$
$888$	78.0850	2.62036
$889$	1.37150	0.0459985
$890$	49.8761	1.67185
$891$	−67.4015	−2.25804
$892$	−115.609	−3.87089
$893$	−0.307873	−0.0103026
$894$	139.131	4.65323
$895$	−23.5436	−0.786977
$896$	−0.479117	−0.0160062
$897$	11.7297	0.391642
$898$	46.5845	1.55454
$899$	−19.4536	−0.648815
$900$	98.1041	3.27014
$901$	−16.7980	−0.559623
$902$	50.5845	1.68428
$903$	−21.1047	−0.702322
$904$	36.3246	1.20814
$905$	57.3320	1.90578
$906$	−33.9059	−1.12645
$907$	−16.5779	−0.550459	−0.275229	−	0.961379i	$-0.588754\pi$
$907$	−16.5779	−0.550459	−0.275229	+	0.961379i	$0.588754\pi$
$908$	−5.89065	−0.195488
$909$	45.3505	1.50418
$910$	4.44730	0.147426
$911$	−49.3067	−1.63360	−0.816802	−	0.576918i	$-0.804255\pi$
$911$	−49.3067	−1.63360	−0.816802	+	0.576918i	$0.804255\pi$
$912$	−1.56537	−0.0518347
$913$	40.9786	1.35619
$914$	−1.59588	−0.0527870
$915$	57.8074	1.91105
$916$	−76.0570	−2.51299
$917$	8.54067	0.282038
$918$	−95.6202	−3.15594
$919$	−28.3388	−0.934810	−0.467405	−	0.884043i	$-0.654811\pi$
$919$	−28.3388	−0.934810	−0.467405	+	0.884043i	$0.654811\pi$
$920$	−72.8574	−2.40204
$921$	−38.8238	−1.27929
$922$	−60.9462	−2.00715
$923$	12.1196	0.398921
$924$	24.3039	0.799540
$925$	−8.66919	−0.285041
$926$	2.60952	0.0857542
$927$	9.01773	0.296181
$928$	58.8538	1.93197
$929$	50.2592	1.64895	0.824476	−	0.565897i	$-0.191470\pi$
$929$	50.2592	1.64895	0.824476	+	0.565897i	$0.191470\pi$
$930$	79.2359	2.59825
$931$	0.333504	0.0109301
$932$	−106.397	−3.48516
$933$	61.3170	2.00743
$934$	74.0948	2.42446
$935$	16.6943	0.545962
$936$	56.2422	1.83833
$937$	−54.2013	−1.77068	−0.885339	−	0.464945i	$-0.846074\pi$
$937$	−54.2013	−1.77068	−0.885339	+	0.464945i	$0.846074\pi$
$938$	1.95550	0.0638492
$939$	64.9270	2.11881
$940$	−81.3533	−2.65345
$941$	−27.6544	−0.901509	−0.450755	−	0.892648i	$-0.648845\pi$
$941$	−27.6544	−0.901509	−0.450755	+	0.892648i	$0.648845\pi$
$942$	64.4944	2.10134
$943$	−27.7092	−0.902335
$944$	−39.0470	−1.27087
$945$	26.0049	0.845941
$946$	68.7706	2.23592
$947$	54.6218	1.77497	0.887485	−	0.460837i	$-0.152451\pi$
$947$	54.6218	1.77497	0.887485	+	0.460837i	$0.152451\pi$
$948$	33.2513	1.07995
$949$	−8.15155	−0.264611
$950$	0.349522	0.0113400
$951$	−12.8121	−0.415462
$952$	10.8423	0.351402
$953$	−20.0508	−0.649508	−0.324754	−	0.945799i	$-0.605281\pi$
$953$	−20.0508	−0.649508	−0.324754	+	0.945799i	$0.605281\pi$
$954$	140.026	4.53350
$955$	−10.6777	−0.345522
$956$	−78.1751	−2.52836
$957$	47.5279	1.53636
$958$	−47.2964	−1.52808
$959$	−3.01802	−0.0974569
$960$	−67.7096	−2.18532
$961$	−19.7192	−0.636103
$962$	−8.50782	−0.274303
$963$	−133.354	−4.29728
$964$	−82.4996	−2.65713
$965$	−45.8638	−1.47641
$966$	−18.8493	−0.606465
$967$	−22.7688	−0.732195	−0.366097	−	0.930577i	$-0.619306\pi$
$967$	−22.7688	−0.732195	−0.366097	+	0.930577i	$0.619306\pi$
$968$	34.3860	1.10521
$969$	−0.395152	−0.0126941
$970$	−125.112	−4.01710
$971$	−43.9279	−1.40971	−0.704857	−	0.709350i	$-0.748989\pi$
$971$	−43.9279	−1.40971	−0.704857	+	0.709350i	$0.748989\pi$
$972$	201.403	6.46000
$973$	−6.33224	−0.203002
$974$	7.36487	0.235986
$975$	−8.68612	−0.278178
$976$	−60.8296	−1.94711
$977$	44.5207	1.42434	0.712172	−	0.702005i	$-0.247711\pi$
$977$	44.5207	1.42434	0.712172	+	0.702005i	$0.247711\pi$
$978$	−14.3799	−0.459818
$979$	−17.3484	−0.554456
$980$	88.1262	2.81509
$981$	146.931	4.69115
$982$	−101.916	−3.25226
$983$	−14.0394	−0.447787	−0.223894	−	0.974614i	$-0.571877\pi$
$983$	−14.0394	−0.447787	−0.223894	+	0.974614i	$0.571877\pi$
$984$	−184.822	−5.89190
$985$	27.4180	0.873610
$986$	36.2960	1.15590
$987$	−12.2951	−0.391357
$988$	0.242271	0.00770767
$989$	−37.6711	−1.19787
$990$	−139.161	−4.42283
$991$	19.6219	0.623310	0.311655	−	0.950195i	$-0.399117\pi$
$991$	19.6219	0.623310	0.311655	+	0.950195i	$0.399117\pi$
$992$	−34.1283	−1.08357
$993$	56.0986	1.78023
$994$	−19.4759	−0.617737
$995$	6.32825	0.200619
$996$	−256.305	−8.12132
$997$	−4.48042	−0.141896	−0.0709482	−	0.997480i	$-0.522602\pi$
$997$	−4.48042	−0.141896	−0.0709482	+	0.997480i	$0.522602\pi$
$998$	51.8656	1.64178
$999$	−49.7483	−1.57397

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6019.2.a.c.1.7	✓	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6019.2.a.c.1.7	✓	108	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6019 = 13 \cdot 463 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6019.a (trivial)

\(f(q)\)	\(=\)	\(q-2.60952 q^{2} +3.26666 q^{3} +4.80961 q^{4} -2.76749 q^{5} -8.52442 q^{6} -0.615812 q^{7} -7.33173 q^{8} +7.67107 q^{9} +O(q^{10})\)	\(q-2.60952 q^{2} +3.26666 q^{3} +4.80961 q^{4} -2.76749 q^{5} -8.52442 q^{6} -0.615812 q^{7} -7.33173 q^{8} +7.67107 q^{9} +7.22184 q^{10} -2.51197 q^{11} +15.7114 q^{12} -1.00000 q^{13} +1.60698 q^{14} -9.04046 q^{15} +9.51309 q^{16} +2.40142 q^{17} -20.0178 q^{18} -0.0503723 q^{19} -13.3106 q^{20} -2.01165 q^{21} +6.55503 q^{22} -3.59072 q^{23} -23.9503 q^{24} +2.65902 q^{25} +2.60952 q^{26} +15.2588 q^{27} -2.96181 q^{28} -5.79202 q^{29} +23.5913 q^{30} +3.35869 q^{31} -10.1612 q^{32} -8.20575 q^{33} -6.26655 q^{34} +1.70426 q^{35} +36.8948 q^{36} -3.26030 q^{37} +0.131448 q^{38} -3.26666 q^{39} +20.2905 q^{40} +7.71689 q^{41} +5.24945 q^{42} +10.4913 q^{43} -12.0816 q^{44} -21.2296 q^{45} +9.37005 q^{46} +6.11194 q^{47} +31.0761 q^{48} -6.62078 q^{49} -6.93877 q^{50} +7.84462 q^{51} -4.80961 q^{52} -6.99504 q^{53} -39.8182 q^{54} +6.95185 q^{55} +4.51497 q^{56} -0.164549 q^{57} +15.1144 q^{58} -4.10455 q^{59} -43.4811 q^{60} -6.39430 q^{61} -8.76458 q^{62} -4.72394 q^{63} +7.48962 q^{64} +2.76749 q^{65} +21.4131 q^{66} +1.21688 q^{67} +11.5499 q^{68} -11.7297 q^{69} -4.44730 q^{70} -12.1196 q^{71} -56.2422 q^{72} +8.15155 q^{73} +8.50782 q^{74} +8.68612 q^{75} -0.242271 q^{76} +1.54690 q^{77} +8.52442 q^{78} +2.11639 q^{79} -26.3274 q^{80} +26.8322 q^{81} -20.1374 q^{82} -16.3133 q^{83} -9.67524 q^{84} -6.64591 q^{85} -27.3772 q^{86} -18.9206 q^{87} +18.4171 q^{88} +6.90629 q^{89} +55.3992 q^{90} +0.615812 q^{91} -17.2699 q^{92} +10.9717 q^{93} -15.9493 q^{94} +0.139405 q^{95} -33.1931 q^{96} -17.3241 q^{97} +17.2771 q^{98} -19.2695 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 11 q^{2} + q^{3} + 95 q^{4} - 40 q^{5} - 10 q^{6} - 8 q^{7} - 33 q^{8} + 79 q^{9}+O(q^{10}) \) 108 * q - 11 * q^2 + q^3 + 95 * q^4 - 40 * q^5 - 10 * q^6 - 8 * q^7 - 33 * q^8 + 79 * q^9	\( 108 q - 11 q^{2} + q^{3} + 95 q^{4} - 40 q^{5} - 10 q^{6} - 8 q^{7} - 33 q^{8} + 79 q^{9} - q^{10} - 45 q^{11} - 6 q^{12} - 108 q^{13} - 31 q^{14} - 39 q^{15} + 73 q^{16} + 21 q^{17} - 35 q^{18} - 19 q^{19} - 79 q^{20} - 72 q^{21} - 26 q^{23} - 23 q^{24} + 92 q^{25} + 11 q^{26} + 7 q^{27} - 21 q^{28} - 94 q^{29} - 24 q^{30} - 36 q^{31} - 77 q^{32} - 32 q^{33} - 58 q^{34} - 10 q^{35} + 17 q^{36} - 54 q^{37} - 12 q^{38} - q^{39} - 4 q^{40} - 68 q^{41} - 11 q^{42} - 32 q^{43} - 151 q^{44} - 121 q^{45} - 33 q^{46} - 51 q^{47} - 27 q^{48} + 72 q^{49} - 45 q^{50} - 24 q^{51} - 95 q^{52} - 81 q^{53} - 29 q^{54} + 4 q^{55} - 68 q^{56} - 45 q^{57} - 30 q^{58} - 94 q^{59} - 108 q^{60} - 39 q^{61} - 9 q^{62} - 52 q^{63} + 31 q^{64} + 40 q^{65} - 40 q^{66} - 47 q^{67} + 24 q^{68} - 60 q^{69} - 66 q^{70} - 86 q^{71} - 91 q^{72} - 51 q^{73} - 110 q^{74} - 7 q^{75} - 51 q^{76} - 96 q^{77} + 10 q^{78} - 18 q^{79} - 136 q^{80} - 24 q^{81} - 33 q^{82} - 77 q^{83} - 113 q^{84} - 95 q^{85} - 137 q^{86} + 23 q^{87} + 19 q^{88} - 112 q^{89} - 19 q^{90} + 8 q^{91} - 111 q^{92} - 124 q^{93} - 20 q^{94} - 73 q^{95} - 77 q^{96} - 41 q^{97} - 80 q^{98} - 154 q^{99}+O(q^{100}) \) 108 * q - 11 * q^2 + q^3 + 95 * q^4 - 40 * q^5 - 10 * q^6 - 8 * q^7 - 33 * q^8 + 79 * q^9 - q^10 - 45 * q^11 - 6 * q^12 - 108 * q^13 - 31 * q^14 - 39 * q^15 + 73 * q^16 + 21 * q^17 - 35 * q^18 - 19 * q^19 - 79 * q^20 - 72 * q^21 - 26 * q^23 - 23 * q^24 + 92 * q^25 + 11 * q^26 + 7 * q^27 - 21 * q^28 - 94 * q^29 - 24 * q^30 - 36 * q^31 - 77 * q^32 - 32 * q^33 - 58 * q^34 - 10 * q^35 + 17 * q^36 - 54 * q^37 - 12 * q^38 - q^39 - 4 * q^40 - 68 * q^41 - 11 * q^42 - 32 * q^43 - 151 * q^44 - 121 * q^45 - 33 * q^46 - 51 * q^47 - 27 * q^48 + 72 * q^49 - 45 * q^50 - 24 * q^51 - 95 * q^52 - 81 * q^53 - 29 * q^54 + 4 * q^55 - 68 * q^56 - 45 * q^57 - 30 * q^58 - 94 * q^59 - 108 * q^60 - 39 * q^61 - 9 * q^62 - 52 * q^63 + 31 * q^64 + 40 * q^65 - 40 * q^66 - 47 * q^67 + 24 * q^68 - 60 * q^69 - 66 * q^70 - 86 * q^71 - 91 * q^72 - 51 * q^73 - 110 * q^74 - 7 * q^75 - 51 * q^76 - 96 * q^77 + 10 * q^78 - 18 * q^79 - 136 * q^80 - 24 * q^81 - 33 * q^82 - 77 * q^83 - 113 * q^84 - 95 * q^85 - 137 * q^86 + 23 * q^87 + 19 * q^88 - 112 * q^89 - 19 * q^90 + 8 * q^91 - 111 * q^92 - 124 * q^93 - 20 * q^94 - 73 * q^95 - 77 * q^96 - 41 * q^97 - 80 * q^98 - 154 * q^99

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