LMFDB - Embedded newform 6019.2.a.b.1.17

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:	$101$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
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)

$f(q)$	$=$	$q-2.06993 q^{2} -2.73222 q^{3} +2.28462 q^{4} +1.87227 q^{5} +5.65552 q^{6} -2.93607 q^{7} -0.589152 q^{8} +4.46505 q^{9} +O(q^{10})$	\(q-2.06993 q^{2} -2.73222 q^{3} +2.28462 q^{4} +1.87227 q^{5} +5.65552 q^{6} -2.93607 q^{7} -0.589152 q^{8} +4.46505 q^{9} -3.87547 q^{10} -1.01740 q^{11} -6.24210 q^{12} +1.00000 q^{13} +6.07746 q^{14} -5.11545 q^{15} -3.34974 q^{16} -2.64297 q^{17} -9.24235 q^{18} +6.16886 q^{19} +4.27742 q^{20} +8.02199 q^{21} +2.10595 q^{22} +4.11167 q^{23} +1.60969 q^{24} -1.49462 q^{25} -2.06993 q^{26} -4.00284 q^{27} -6.70780 q^{28} -6.74682 q^{29} +10.5886 q^{30} -0.987381 q^{31} +8.11205 q^{32} +2.77977 q^{33} +5.47078 q^{34} -5.49710 q^{35} +10.2010 q^{36} +1.18847 q^{37} -12.7691 q^{38} -2.73222 q^{39} -1.10305 q^{40} -5.99939 q^{41} -16.6050 q^{42} -2.73177 q^{43} -2.32438 q^{44} +8.35976 q^{45} -8.51089 q^{46} +9.53457 q^{47} +9.15225 q^{48} +1.62048 q^{49} +3.09376 q^{50} +7.22120 q^{51} +2.28462 q^{52} +11.6452 q^{53} +8.28561 q^{54} -1.90485 q^{55} +1.72979 q^{56} -16.8547 q^{57} +13.9655 q^{58} -2.22747 q^{59} -11.6869 q^{60} +5.99243 q^{61} +2.04381 q^{62} -13.1097 q^{63} -10.0919 q^{64} +1.87227 q^{65} -5.75394 q^{66} +0.146809 q^{67} -6.03820 q^{68} -11.2340 q^{69} +11.3786 q^{70} -9.60903 q^{71} -2.63059 q^{72} -7.40854 q^{73} -2.46005 q^{74} +4.08363 q^{75} +14.0935 q^{76} +2.98716 q^{77} +5.65552 q^{78} -1.21755 q^{79} -6.27161 q^{80} -2.45849 q^{81} +12.4183 q^{82} +2.42706 q^{83} +18.3272 q^{84} -4.94835 q^{85} +5.65459 q^{86} +18.4338 q^{87} +0.599404 q^{88} -17.2757 q^{89} -17.3041 q^{90} -2.93607 q^{91} +9.39362 q^{92} +2.69775 q^{93} -19.7359 q^{94} +11.5498 q^{95} -22.1639 q^{96} +1.51239 q^{97} -3.35429 q^{98} -4.54275 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 101 q - 8 q^{2} - 13 q^{3} + 86 q^{4} - 43 q^{5} - 10 q^{6} - q^{7} - 24 q^{8} + 52 q^{9}+O(q^{10}) $ 101 * q - 8 * q^2 - 13 * q^3 + 86 * q^4 - 43 * q^5 - 10 * q^6 - q^7 - 24 * q^8 + 52 * q^9	\( 101 q - 8 q^{2} - 13 q^{3} + 86 q^{4} - 43 q^{5} - 10 q^{6} - q^{7} - 24 q^{8} + 52 q^{9} - 19 q^{10} - 42 q^{11} - 28 q^{12} + 101 q^{13} - 45 q^{14} - 15 q^{15} + 48 q^{16} - 83 q^{17} - 4 q^{18} - 18 q^{19} - 51 q^{20} - 50 q^{21} - 20 q^{22} - 64 q^{23} - 23 q^{24} + 46 q^{25} - 8 q^{26} - 37 q^{27} - 11 q^{28} - 117 q^{29} - 28 q^{30} - 10 q^{31} - 36 q^{32} - 20 q^{33} - 10 q^{34} - 53 q^{35} - 16 q^{36} - 27 q^{37} - 68 q^{38} - 13 q^{39} - 42 q^{40} - 60 q^{41} - 31 q^{42} - 16 q^{43} - 89 q^{44} - 56 q^{45} + 5 q^{46} - 23 q^{47} - 37 q^{48} + 48 q^{49} - 30 q^{50} - 68 q^{51} + 86 q^{52} - 189 q^{53} - 23 q^{54} + 3 q^{55} - 106 q^{56} - 25 q^{57} - 82 q^{59} + 6 q^{60} - 68 q^{61} - 57 q^{62} + 3 q^{63} - 2 q^{64} - 43 q^{65} - 40 q^{66} - 13 q^{67} - 138 q^{68} - 92 q^{69} + 18 q^{70} - 39 q^{71} - 20 q^{72} + 19 q^{73} - 88 q^{74} - 21 q^{75} - 53 q^{76} - 147 q^{77} - 10 q^{78} - 19 q^{79} - 104 q^{80} - 55 q^{81} + 27 q^{82} - 49 q^{83} - 59 q^{84} - 27 q^{85} - 99 q^{86} - 33 q^{87} - 41 q^{88} - 70 q^{89} - 49 q^{90} - q^{91} - 111 q^{92} - 84 q^{93} + 4 q^{94} - 82 q^{95} - 7 q^{96} + 25 q^{97} - 37 q^{98} - 41 q^{99}+O(q^{100}) \) 101 * q - 8 * q^2 - 13 * q^3 + 86 * q^4 - 43 * q^5 - 10 * q^6 - q^7 - 24 * q^8 + 52 * q^9 - 19 * q^10 - 42 * q^11 - 28 * q^12 + 101 * q^13 - 45 * q^14 - 15 * q^15 + 48 * q^16 - 83 * q^17 - 4 * q^18 - 18 * q^19 - 51 * q^20 - 50 * q^21 - 20 * q^22 - 64 * q^23 - 23 * q^24 + 46 * q^25 - 8 * q^26 - 37 * q^27 - 11 * q^28 - 117 * q^29 - 28 * q^30 - 10 * q^31 - 36 * q^32 - 20 * q^33 - 10 * q^34 - 53 * q^35 - 16 * q^36 - 27 * q^37 - 68 * q^38 - 13 * q^39 - 42 * q^40 - 60 * q^41 - 31 * q^42 - 16 * q^43 - 89 * q^44 - 56 * q^45 + 5 * q^46 - 23 * q^47 - 37 * q^48 + 48 * q^49 - 30 * q^50 - 68 * q^51 + 86 * q^52 - 189 * q^53 - 23 * q^54 + 3 * q^55 - 106 * q^56 - 25 * q^57 - 82 * q^59 + 6 * q^60 - 68 * q^61 - 57 * q^62 + 3 * q^63 - 2 * q^64 - 43 * q^65 - 40 * q^66 - 13 * q^67 - 138 * q^68 - 92 * q^69 + 18 * q^70 - 39 * q^71 - 20 * q^72 + 19 * q^73 - 88 * q^74 - 21 * q^75 - 53 * q^76 - 147 * q^77 - 10 * q^78 - 19 * q^79 - 104 * q^80 - 55 * q^81 + 27 * q^82 - 49 * q^83 - 59 * q^84 - 27 * q^85 - 99 * q^86 - 33 * q^87 - 41 * q^88 - 70 * q^89 - 49 * q^90 - q^91 - 111 * q^92 - 84 * q^93 + 4 * q^94 - 82 * q^95 - 7 * q^96 + 25 * q^97 - 37 * q^98 - 41 * 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 $

$2$	−2.06993	−1.46366	−0.731832	−	0.681485i	$-0.761334\pi$
$2$	−2.06993	−1.46366	−0.731832	+	0.681485i	$0.761334\pi$
$3$	−2.73222	−1.57745	−0.788725	−	0.614746i	$-0.789259\pi$
$3$	−2.73222	−1.57745	−0.788725	+	0.614746i	$0.789259\pi$
$4$	2.28462	1.14231
$5$	1.87227	0.837303	0.418652	−	0.908147i	$-0.362503\pi$
$5$	1.87227	0.837303	0.418652	+	0.908147i	$0.362503\pi$
$6$	5.65552	2.30886
$7$	−2.93607	−1.10973	−0.554864	−	0.831941i	$-0.687230\pi$
$7$	−2.93607	−1.10973	−0.554864	+	0.831941i	$0.687230\pi$
$8$	−0.589152	−0.208297
$9$	4.46505	1.48835
$10$	−3.87547	−1.22553
$11$	−1.01740	−0.306758	−0.153379	−	0.988167i	$-0.549016\pi$
$11$	−1.01740	−0.306758	−0.153379	+	0.988167i	$0.549016\pi$
$12$	−6.24210	−1.80194
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	6.07746	1.62427
$15$	−5.11545	−1.32080
$16$	−3.34974	−0.837436
$17$	−2.64297	−0.641015	−0.320508	−	0.947246i	$-0.603854\pi$
$17$	−2.64297	−0.641015	−0.320508	+	0.947246i	$0.603854\pi$
$18$	−9.24235	−2.17844
$19$	6.16886	1.41523	0.707617	−	0.706596i	$-0.249770\pi$
$19$	6.16886	1.41523	0.707617	+	0.706596i	$0.249770\pi$
$20$	4.27742	0.956461
$21$	8.02199	1.75054
$22$	2.10595	0.448991
$23$	4.11167	0.857343	0.428672	−	0.903460i	$-0.358982\pi$
$23$	4.11167	0.857343	0.428672	+	0.903460i	$0.358982\pi$
$24$	1.60969	0.328577
$25$	−1.49462	−0.298923
$26$	−2.06993	−0.405947
$27$	−4.00284	−0.770347
$28$	−6.70780	−1.26766
$29$	−6.74682	−1.25285	−0.626427	−	0.779480i	$-0.715483\pi$
$29$	−6.74682	−1.25285	−0.626427	+	0.779480i	$0.715483\pi$
$30$	10.5886	1.93321
$31$	−0.987381	−0.177339	−0.0886694	−	0.996061i	$-0.528261\pi$
$31$	−0.987381	−0.177339	−0.0886694	+	0.996061i	$0.528261\pi$
$32$	8.11205	1.43402
$33$	2.77977	0.483896
$34$	5.47078	0.938231
$35$	−5.49710	−0.929179
$36$	10.2010	1.70016
$37$	1.18847	0.195383	0.0976916	−	0.995217i	$-0.468854\pi$
$37$	1.18847	0.195383	0.0976916	+	0.995217i	$0.468854\pi$
$38$	−12.7691	−2.07143
$39$	−2.73222	−0.437506
$40$	−1.10305	−0.174407
$41$	−5.99939	−0.936948	−0.468474	−	0.883477i	$-0.655196\pi$
$41$	−5.99939	−0.936948	−0.468474	+	0.883477i	$0.655196\pi$
$42$	−16.6050	−2.56220
$43$	−2.73177	−0.416592	−0.208296	−	0.978066i	$-0.566792\pi$
$43$	−2.73177	−0.416592	−0.208296	+	0.978066i	$0.566792\pi$
$44$	−2.32438	−0.350414
$45$	8.35976	1.24620
$46$	−8.51089	−1.25486
$47$	9.53457	1.39076	0.695380	−	0.718642i	$-0.255236\pi$
$47$	9.53457	1.39076	0.695380	+	0.718642i	$0.255236\pi$
$48$	9.15225	1.32101
$49$	1.62048	0.231497
$50$	3.09376	0.437523
$51$	7.22120	1.01117
$52$	2.28462	0.316820
$53$	11.6452	1.59959	0.799794	−	0.600274i	$-0.204942\pi$
$53$	11.6452	1.59959	0.799794	+	0.600274i	$0.204942\pi$
$54$	8.28561	1.12753
$55$	−1.90485	−0.256850
$56$	1.72979	0.231153
$57$	−16.8547	−2.23246
$58$	13.9655	1.83376
$59$	−2.22747	−0.289992	−0.144996	−	0.989432i	$-0.546317\pi$
$59$	−2.22747	−0.289992	−0.144996	+	0.989432i	$0.546317\pi$
$60$	−11.6869	−1.50877
$61$	5.99243	0.767252	0.383626	−	0.923488i	$-0.374675\pi$
$61$	5.99243	0.767252	0.383626	+	0.923488i	$0.374675\pi$
$62$	2.04381	0.259564
$63$	−13.1097	−1.65166
$64$	−10.0919	−1.26149
$65$	1.87227	0.232226
$66$	−5.75394	−0.708261
$67$	0.146809	0.0179356	0.00896781	−	0.999960i	$-0.497145\pi$
$67$	0.146809	0.0179356	0.00896781	+	0.999960i	$0.497145\pi$
$68$	−6.03820	−0.732239
$69$	−11.2340	−1.35242
$70$	11.3786	1.36001
$71$	−9.60903	−1.14038	−0.570191	−	0.821512i	$-0.693131\pi$
$71$	−9.60903	−1.14038	−0.570191	+	0.821512i	$0.693131\pi$
$72$	−2.63059	−0.310018
$73$	−7.40854	−0.867104	−0.433552	−	0.901129i	$-0.642740\pi$
$73$	−7.40854	−0.867104	−0.433552	+	0.901129i	$0.642740\pi$
$74$	−2.46005	−0.285975
$75$	4.08363	0.471537
$76$	14.0935	1.61664
$77$	2.98716	0.340418
$78$	5.65552	0.640362
$79$	−1.21755	−0.136985	−0.0684925	−	0.997652i	$-0.521819\pi$
$79$	−1.21755	−0.136985	−0.0684925	+	0.997652i	$0.521819\pi$
$80$	−6.27161	−0.701187
$81$	−2.45849	−0.273165
$82$	12.4183	1.37138
$83$	2.42706	0.266405	0.133202	−	0.991089i	$-0.457474\pi$
$83$	2.42706	0.266405	0.133202	+	0.991089i	$0.457474\pi$
$84$	18.3272	1.99966
$85$	−4.94835	−0.536724
$86$	5.65459	0.609750
$87$	18.4338	1.97631
$88$	0.599404	0.0638967
$89$	−17.2757	−1.83122	−0.915608	−	0.402071i	$-0.868290\pi$
$89$	−17.2757	−1.83122	−0.915608	+	0.402071i	$0.868290\pi$
$90$	−17.3041	−1.82402
$91$	−2.93607	−0.307783
$92$	9.39362	0.979353
$93$	2.69775	0.279743
$94$	−19.7359	−2.03561
$95$	11.5498	1.18498
$96$	−22.1639	−2.26210
$97$	1.51239	0.153559	0.0767797	−	0.997048i	$-0.475536\pi$
$97$	1.51239	0.153559	0.0767797	+	0.997048i	$0.475536\pi$
$98$	−3.35429	−0.338834
$99$	−4.54275	−0.456564
$100$	−3.41464	−0.341464
$101$	−8.21100	−0.817025	−0.408513	−	0.912753i	$-0.633952\pi$
$101$	−8.21100	−0.817025	−0.408513	+	0.912753i	$0.633952\pi$
$102$	−14.9474	−1.48001
$103$	6.30583	0.621332	0.310666	−	0.950519i	$-0.399448\pi$
$103$	6.30583	0.621332	0.310666	+	0.950519i	$0.399448\pi$
$104$	−0.589152	−0.0577711
$105$	15.0193	1.46573
$106$	−24.1048	−2.34126
$107$	13.6889	1.32336	0.661680	−	0.749786i	$-0.269844\pi$
$107$	13.6889	1.32336	0.661680	+	0.749786i	$0.269844\pi$
$108$	−9.14498	−0.879977
$109$	−1.41684	−0.135709	−0.0678545	−	0.997695i	$-0.521615\pi$
$109$	−1.41684	−0.135709	−0.0678545	+	0.997695i	$0.521615\pi$
$110$	3.94291	0.375942
$111$	−3.24717	−0.308207
$112$	9.83506	0.929326
$113$	2.13177	0.200540	0.100270	−	0.994960i	$-0.468029\pi$
$113$	2.13177	0.200540	0.100270	+	0.994960i	$0.468029\pi$
$114$	34.8881	3.26757
$115$	7.69815	0.717856
$116$	−15.4140	−1.43115
$117$	4.46505	0.412794
$118$	4.61072	0.424452
$119$	7.75995	0.711353
$120$	3.01378	0.275119
$121$	−9.96489	−0.905899
$122$	−12.4039	−1.12300
$123$	16.3917	1.47799
$124$	−2.25579	−0.202576
$125$	−12.1597	−1.08759
$126$	27.1362	2.41748
$127$	−10.3004	−0.914015	−0.457008	−	0.889463i	$-0.651079\pi$
$127$	−10.3004	−0.914015	−0.457008	+	0.889463i	$0.651079\pi$
$128$	4.66548	0.412374
$129$	7.46382	0.657153
$130$	−3.87547	−0.339901
$131$	18.5191	1.61802	0.809011	−	0.587793i	$-0.200003\pi$
$131$	18.5191	1.61802	0.809011	+	0.587793i	$0.200003\pi$
$132$	6.35073	0.552760
$133$	−18.1122	−1.57053
$134$	−0.303885	−0.0262517
$135$	−7.49439	−0.645014
$136$	1.55711	0.133521
$137$	4.69653	0.401251	0.200626	−	0.979668i	$-0.435703\pi$
$137$	4.69653	0.401251	0.200626	+	0.979668i	$0.435703\pi$
$138$	23.2537	1.97948
$139$	−2.37960	−0.201835	−0.100918	−	0.994895i	$-0.532178\pi$
$139$	−2.37960	−0.201835	−0.100918	+	0.994895i	$0.532178\pi$
$140$	−12.5588	−1.06141
$141$	−26.0506	−2.19385
$142$	19.8900	1.66914
$143$	−1.01740	−0.0850794
$144$	−14.9568	−1.24640
$145$	−12.6319	−1.04902
$146$	15.3352	1.26915
$147$	−4.42752	−0.365176
$148$	2.71521	0.223189
$149$	−7.75757	−0.635525	−0.317763	−	0.948170i	$-0.602931\pi$
$149$	−7.75757	−0.635525	−0.317763	+	0.948170i	$0.602931\pi$
$150$	−8.45284	−0.690172
$151$	−2.92247	−0.237827	−0.118914	−	0.992905i	$-0.537941\pi$
$151$	−2.92247	−0.237827	−0.118914	+	0.992905i	$0.537941\pi$
$152$	−3.63439	−0.294788
$153$	−11.8010	−0.954055
$154$	−6.18322	−0.498258
$155$	−1.84864	−0.148486
$156$	−6.24210	−0.499768
$157$	1.51361	0.120800	0.0603998	−	0.998174i	$-0.480762\pi$
$157$	1.51361	0.120800	0.0603998	+	0.998174i	$0.480762\pi$
$158$	2.52024	0.200500
$159$	−31.8173	−2.52327
$160$	15.1879	1.20071
$161$	−12.0721	−0.951418
$162$	5.08890	0.399822
$163$	6.48378	0.507849	0.253924	−	0.967224i	$-0.418279\pi$
$163$	6.48378	0.507849	0.253924	+	0.967224i	$0.418279\pi$
$164$	−13.7064	−1.07029
$165$	5.20447	0.405168
$166$	−5.02386	−0.389927
$167$	17.1759	1.32911	0.664556	−	0.747238i	$-0.268621\pi$
$167$	17.1759	1.32911	0.664556	+	0.747238i	$0.268621\pi$
$168$	−4.72617	−0.364632
$169$	1.00000	0.0769231
$170$	10.2428	0.785584
$171$	27.5443	2.10636
$172$	−6.24108	−0.475878
$173$	8.17654	0.621651	0.310825	−	0.950467i	$-0.399395\pi$
$173$	8.17654	0.621651	0.310825	+	0.950467i	$0.399395\pi$
$174$	−38.1568	−2.89266
$175$	4.38830	0.331724
$176$	3.40804	0.256890
$177$	6.08596	0.457449
$178$	35.7595	2.68029
$179$	9.48881	0.709227	0.354614	−	0.935013i	$-0.384612\pi$
$179$	9.48881	0.709227	0.354614	+	0.935013i	$0.384612\pi$
$180$	19.0989	1.42355
$181$	1.04691	0.0778165	0.0389082	−	0.999243i	$-0.487612\pi$
$181$	1.04691	0.0778165	0.0389082	+	0.999243i	$0.487612\pi$
$182$	6.07746	0.450491
$183$	−16.3727	−1.21030
$184$	−2.42240	−0.178582
$185$	2.22513	0.163595
$186$	−5.58415	−0.409450
$187$	2.68897	0.196637
$188$	21.7829	1.58868
$189$	11.7526	0.854876
$190$	−23.9072	−1.73441
$191$	16.5115	1.19473	0.597364	−	0.801970i	$-0.296215\pi$
$191$	16.5115	1.19473	0.597364	+	0.801970i	$0.296215\pi$
$192$	27.5734	1.98994
$193$	15.6819	1.12881	0.564406	−	0.825498i	$-0.309105\pi$
$193$	15.6819	1.12881	0.564406	+	0.825498i	$0.309105\pi$
$194$	−3.13054	−0.224759
$195$	−5.11545	−0.366325
$196$	3.70219	0.264442
$197$	−3.68510	−0.262553	−0.131276	−	0.991346i	$-0.541907\pi$
$197$	−3.68510	−0.262553	−0.131276	+	0.991346i	$0.541907\pi$
$198$	9.40319	0.668256
$199$	−10.6953	−0.758167	−0.379084	−	0.925362i	$-0.623761\pi$
$199$	−10.6953	−0.758167	−0.379084	+	0.925362i	$0.623761\pi$
$200$	0.880556	0.0622647
$201$	−0.401116	−0.0282925
$202$	16.9962	1.19585
$203$	19.8091	1.39033
$204$	16.4977	1.15507
$205$	−11.2325	−0.784509
$206$	−13.0527	−0.909421
$207$	18.3588	1.27603
$208$	−3.34974	−0.232263
$209$	−6.27621	−0.434135
$210$	−31.0890	−2.14534
$211$	20.0458	1.38001	0.690006	−	0.723804i	$-0.257608\pi$
$211$	20.0458	1.38001	0.690006	+	0.723804i	$0.257608\pi$
$212$	26.6049	1.82723
$213$	26.2540	1.79890
$214$	−28.3352	−1.93696
$215$	−5.11461	−0.348814
$216$	2.35828	0.160461
$217$	2.89901	0.196798
$218$	2.93277	0.198632
$219$	20.2418	1.36781
$220$	−4.35186	−0.293402
$221$	−2.64297	−0.177786
$222$	6.72142	0.451112
$223$	0.168810	0.0113044	0.00565218	−	0.999984i	$-0.498201\pi$
$223$	0.168810	0.0113044	0.00565218	+	0.999984i	$0.498201\pi$
$224$	−23.8175	−1.59137
$225$	−6.67354	−0.444903
$226$	−4.41263	−0.293524
$227$	−6.70747	−0.445190	−0.222595	−	0.974911i	$-0.571453\pi$
$227$	−6.70747	−0.445190	−0.222595	+	0.974911i	$0.571453\pi$
$228$	−38.5067	−2.55017
$229$	17.6439	1.16594	0.582969	−	0.812494i	$-0.301891\pi$
$229$	17.6439	1.16594	0.582969	+	0.812494i	$0.301891\pi$
$230$	−15.9347	−1.05070
$231$	−8.16159	−0.536993
$232$	3.97490	0.260965
$233$	4.81124	0.315195	0.157598	−	0.987503i	$-0.449625\pi$
$233$	4.81124	0.315195	0.157598	+	0.987503i	$0.449625\pi$
$234$	−9.24235	−0.604191
$235$	17.8513	1.16449
$236$	−5.08894	−0.331262
$237$	3.32662	0.216087
$238$	−16.0626	−1.04118
$239$	13.0456	0.843851	0.421926	−	0.906630i	$-0.361354\pi$
$239$	13.0456	0.843851	0.421926	+	0.906630i	$0.361354\pi$
$240$	17.1354	1.10609
$241$	13.9752	0.900223	0.450112	−	0.892972i	$-0.351384\pi$
$241$	13.9752	0.900223	0.450112	+	0.892972i	$0.351384\pi$
$242$	20.6267	1.32593
$243$	18.7257	1.20125
$244$	13.6905	0.876441
$245$	3.03397	0.193834
$246$	−33.9297	−2.16328
$247$	6.16886	0.392515
$248$	0.581717	0.0369391
$249$	−6.63128	−0.420240
$250$	25.1697	1.59187
$251$	6.56751	0.414538	0.207269	−	0.978284i	$-0.433543\pi$
$251$	6.56751	0.414538	0.207269	+	0.978284i	$0.433543\pi$
$252$	−29.9507	−1.88672
$253$	−4.18322	−0.262997
$254$	21.3212	1.33781
$255$	13.5200	0.846656
$256$	10.5266	0.657911
$257$	−7.75018	−0.483443	−0.241721	−	0.970346i	$-0.577712\pi$
$257$	−7.75018	−0.483443	−0.241721	+	0.970346i	$0.577712\pi$
$258$	−15.4496	−0.961851
$259$	−3.48943	−0.216822
$260$	4.27742	0.265275
$261$	−30.1249	−1.86468
$262$	−38.3333	−2.36824
$263$	7.10681	0.438225	0.219112	−	0.975700i	$-0.429684\pi$
$263$	7.10681	0.438225	0.219112	+	0.975700i	$0.429684\pi$
$264$	−1.63771	−0.100794
$265$	21.8029	1.33934
$266$	37.4910	2.29872
$267$	47.2010	2.88865
$268$	0.335404	0.0204881
$269$	−2.72904	−0.166392	−0.0831962	−	0.996533i	$-0.526513\pi$
$269$	−2.72904	−0.166392	−0.0831962	+	0.996533i	$0.526513\pi$
$270$	15.5129	0.944084
$271$	12.0128	0.729726	0.364863	−	0.931061i	$-0.381116\pi$
$271$	12.0128	0.729726	0.364863	+	0.931061i	$0.381116\pi$
$272$	8.85328	0.536809
$273$	8.02199	0.485513
$274$	−9.72149	−0.587297
$275$	1.52063	0.0916973
$276$	−25.6655	−1.54488
$277$	26.9781	1.62096	0.810479	−	0.585767i	$-0.199207\pi$
$277$	26.9781	1.62096	0.810479	+	0.585767i	$0.199207\pi$
$278$	4.92562	0.295419
$279$	−4.40870	−0.263942
$280$	3.23862	0.193545
$281$	−2.40828	−0.143666	−0.0718330	−	0.997417i	$-0.522885\pi$
$281$	−2.40828	−0.143666	−0.0718330	+	0.997417i	$0.522885\pi$
$282$	53.9230	3.21107
$283$	−0.0124177	−0.000738153 0	−0.000369077	−	1.00000i	$-0.500117\pi$
$283$	−0.0124177	−0.000738153 0	−0.000369077		1.00000i	$0.500117\pi$
$284$	−21.9530	−1.30267
$285$	−31.5565	−1.86925
$286$	2.10595	0.124528
$287$	17.6146	1.03976
$288$	36.2207	2.13432
$289$	−10.0147	−0.589099
$290$	26.1471	1.53541
$291$	−4.13218	−0.242232
$292$	−16.9257	−0.990502
$293$	−19.0323	−1.11188	−0.555940	−	0.831222i	$-0.687642\pi$
$293$	−19.0323	−1.11188	−0.555940	+	0.831222i	$0.687642\pi$
$294$	9.16467	0.534494
$295$	−4.17043	−0.242812
$296$	−0.700189	−0.0406977
$297$	4.07250	0.236310
$298$	16.0577	0.930195
$299$	4.11167	0.237784
$300$	9.32956	0.538642
$301$	8.02067	0.462304
$302$	6.04931	0.348099
$303$	22.4343	1.28882
$304$	−20.6641	−1.18517
$305$	11.2194	0.642423
$306$	24.4273	1.39642
$307$	−21.0346	−1.20051	−0.600254	−	0.799810i	$-0.704934\pi$
$307$	−21.0346	−1.20051	−0.600254	+	0.799810i	$0.704934\pi$
$308$	6.82454	0.388864
$309$	−17.2289	−0.980121
$310$	3.82656	0.217334
$311$	−17.9420	−1.01740	−0.508699	−	0.860944i	$-0.669873\pi$
$311$	−17.9420	−1.01740	−0.508699	+	0.860944i	$0.669873\pi$
$312$	1.60969	0.0911310
$313$	−31.1822	−1.76252	−0.881260	−	0.472631i	$-0.843304\pi$
$313$	−31.1822	−1.76252	−0.881260	+	0.472631i	$0.843304\pi$
$314$	−3.13308	−0.176810
$315$	−24.5448	−1.38294
$316$	−2.78164	−0.156479
$317$	12.0231	0.675283	0.337642	−	0.941275i	$-0.390371\pi$
$317$	12.0231	0.675283	0.337642	+	0.941275i	$0.390371\pi$
$318$	65.8596	3.69322
$319$	6.86423	0.384323
$320$	−18.8947	−1.05625
$321$	−37.4013	−2.08754
$322$	24.9885	1.39256
$323$	−16.3041	−0.907187
$324$	−5.61672	−0.312040
$325$	−1.49462	−0.0829065
$326$	−13.4210	−0.743320
$327$	3.87113	0.214074
$328$	3.53455	0.195163
$329$	−27.9941	−1.54337
$330$	−10.7729	−0.593029
$331$	−9.30133	−0.511247	−0.255624	−	0.966776i	$-0.582281\pi$
$331$	−9.30133	−0.511247	−0.255624	+	0.966776i	$0.582281\pi$
$332$	5.54492	0.304317
$333$	5.30658	0.290799
$334$	−35.5530	−1.94537
$335$	0.274866	0.0150175
$336$	−26.8716	−1.46597
$337$	1.80119	0.0981169	0.0490584	−	0.998796i	$-0.484378\pi$
$337$	1.80119	0.0981169	0.0490584	+	0.998796i	$0.484378\pi$
$338$	−2.06993	−0.112590
$339$	−5.82449	−0.316343
$340$	−11.3051	−0.613106
$341$	1.00456	0.0544001
$342$	−57.0148	−3.08301
$343$	15.7946	0.852829
$344$	1.60943	0.0867746
$345$	−21.0331	−1.13238
$346$	−16.9249	−0.909888
$347$	−18.3114	−0.983008	−0.491504	−	0.870875i	$-0.663553\pi$
$347$	−18.3114	−0.983008	−0.491504	+	0.870875i	$0.663553\pi$
$348$	42.1144	2.25757
$349$	26.5618	1.42182	0.710911	−	0.703282i	$-0.248283\pi$
$349$	26.5618	1.42182	0.710911	+	0.703282i	$0.248283\pi$
$350$	−9.08348	−0.485532
$351$	−4.00284	−0.213656
$352$	−8.25321	−0.439898
$353$	−28.2549	−1.50385	−0.751927	−	0.659246i	$-0.770876\pi$
$353$	−28.2549	−1.50385	−0.751927	+	0.659246i	$0.770876\pi$
$354$	−12.5975	−0.669551
$355$	−17.9907	−0.954845
$356$	−39.4684	−2.09182
$357$	−21.2019	−1.12212
$358$	−19.6412	−1.03807
$359$	−26.5703	−1.40233	−0.701164	−	0.713000i	$-0.747336\pi$
$359$	−26.5703	−1.40233	−0.701164	+	0.713000i	$0.747336\pi$
$360$	−4.92517	−0.259579
$361$	19.0549	1.00289
$362$	−2.16704	−0.113897
$363$	27.2263	1.42901
$364$	−6.70780	−0.351584
$365$	−13.8708	−0.726028
$366$	33.8903	1.77148
$367$	−17.7988	−0.929092	−0.464546	−	0.885549i	$-0.653782\pi$
$367$	−17.7988	−0.929092	−0.464546	+	0.885549i	$0.653782\pi$
$368$	−13.7730	−0.717970
$369$	−26.7876	−1.39451
$370$	−4.60588	−0.239448
$371$	−34.1910	−1.77511
$372$	6.16333	0.319554
$373$	−0.390200	−0.0202038	−0.0101019	−	0.999949i	$-0.503216\pi$
$373$	−0.390200	−0.0202038	−0.0101019	+	0.999949i	$0.503216\pi$
$374$	−5.56598	−0.287810
$375$	33.2229	1.71562
$376$	−5.61731	−0.289690
$377$	−6.74682	−0.347479
$378$	−24.3271	−1.25125
$379$	−18.8758	−0.969586	−0.484793	−	0.874629i	$-0.661105\pi$
$379$	−18.8758	−0.969586	−0.484793	+	0.874629i	$0.661105\pi$
$380$	26.3868	1.35362
$381$	28.1431	1.44181
$382$	−34.1776	−1.74868
$383$	4.88558	0.249641	0.124821	−	0.992179i	$-0.460164\pi$
$383$	4.88558	0.249641	0.124821	+	0.992179i	$0.460164\pi$
$384$	−12.7471	−0.650500
$385$	5.59276	0.285033
$386$	−32.4606	−1.65220
$387$	−12.1975	−0.620034
$388$	3.45523	0.175413
$389$	−1.48085	−0.0750820	−0.0375410	−	0.999295i	$-0.511952\pi$
$389$	−1.48085	−0.0750820	−0.0375410	+	0.999295i	$0.511952\pi$
$390$	10.5886	0.536177
$391$	−10.8670	−0.549570
$392$	−0.954709	−0.0482201
$393$	−50.5984	−2.55235
$394$	7.62791	0.384289
$395$	−2.27958	−0.114698
$396$	−10.3785	−0.521538
$397$	39.0456	1.95964	0.979822	−	0.199873i	$-0.0640528\pi$
$397$	39.0456	1.95964	0.979822	+	0.199873i	$0.0640528\pi$
$398$	22.1385	1.10970
$399$	49.4865	2.47743
$400$	5.00658	0.250329
$401$	−13.1855	−0.658454	−0.329227	−	0.944251i	$-0.606788\pi$
$401$	−13.1855	−0.658454	−0.329227	+	0.944251i	$0.606788\pi$
$402$	0.830283	0.0414108
$403$	−0.987381	−0.0491849
$404$	−18.7591	−0.933298
$405$	−4.60294	−0.228722
$406$	−41.0035	−2.03497
$407$	−1.20915	−0.0599354
$408$	−4.25438	−0.210623
$409$	4.70711	0.232752	0.116376	−	0.993205i	$-0.462872\pi$
$409$	4.70711	0.232752	0.116376	+	0.993205i	$0.462872\pi$
$410$	23.2504	1.14826
$411$	−12.8320	−0.632954
$412$	14.4065	0.709755
$413$	6.54001	0.321813
$414$	−38.0015	−1.86767
$415$	4.54411	0.223061
$416$	8.11205	0.397726
$417$	6.50161	0.318385
$418$	12.9913	0.635427
$419$	4.51230	0.220440	0.110220	−	0.993907i	$-0.464844\pi$
$419$	4.51230	0.220440	0.110220	+	0.993907i	$0.464844\pi$
$420$	34.3135	1.67433
$421$	−1.41745	−0.0690825	−0.0345412	−	0.999403i	$-0.510997\pi$
$421$	−1.41745	−0.0690825	−0.0345412	+	0.999403i	$0.510997\pi$
$422$	−41.4935	−2.01987
$423$	42.5723	2.06994
$424$	−6.86078	−0.333189
$425$	3.95024	0.191615
$426$	−54.3440	−2.63298
$427$	−17.5942	−0.851442
$428$	31.2741	1.51169
$429$	2.77977	0.134209
$430$	10.5869	0.510546
$431$	−2.74555	−0.132249	−0.0661243	−	0.997811i	$-0.521063\pi$
$431$	−2.74555	−0.132249	−0.0661243	+	0.997811i	$0.521063\pi$
$432$	13.4085	0.645116
$433$	−0.175926	−0.00845444	−0.00422722	−	0.999991i	$-0.501346\pi$
$433$	−0.175926	−0.00845444	−0.00422722	+	0.999991i	$0.501346\pi$
$434$	−6.00077	−0.288046
$435$	34.5131	1.65477
$436$	−3.23695	−0.155022
$437$	25.3643	1.21334
$438$	−41.8991	−2.00202
$439$	8.21793	0.392221	0.196110	−	0.980582i	$-0.437169\pi$
$439$	8.21793	0.392221	0.196110	+	0.980582i	$0.437169\pi$
$440$	1.12224	0.0535009
$441$	7.23553	0.344549
$442$	5.47078	0.260218
$443$	−25.3164	−1.20282	−0.601409	−	0.798942i	$-0.705394\pi$
$443$	−25.3164	−1.20282	−0.601409	+	0.798942i	$0.705394\pi$
$444$	−7.41855	−0.352069
$445$	−32.3447	−1.53328
$446$	−0.349426	−0.0165458
$447$	21.1954	1.00251
$448$	29.6305	1.39991
$449$	−7.21017	−0.340269	−0.170135	−	0.985421i	$-0.554420\pi$
$449$	−7.21017	−0.340269	−0.170135	+	0.985421i	$0.554420\pi$
$450$	13.8138	0.651188
$451$	6.10379	0.287416
$452$	4.87030	0.229080
$453$	7.98484	0.375160
$454$	13.8840	0.651609
$455$	−5.49710	−0.257708
$456$	9.92998	0.465014
$457$	−6.19374	−0.289731	−0.144866	−	0.989451i	$-0.546275\pi$
$457$	−6.19374	−0.289731	−0.144866	+	0.989451i	$0.546275\pi$
$458$	−36.5216	−1.70654
$459$	10.5794	0.493804
$460$	17.5874	0.820015
$461$	−7.64593	−0.356106	−0.178053	−	0.984021i	$-0.556980\pi$
$461$	−7.64593	−0.356106	−0.178053	+	0.984021i	$0.556980\pi$
$462$	16.8939	0.785977
$463$	1.00000	0.0464739
$463$	1.00000	0.0464739
$464$	22.6001	1.04918
$465$	5.05090	0.234230
$466$	−9.95895	−0.461340
$467$	−21.3721	−0.988981	−0.494490	−	0.869183i	$-0.664645\pi$
$467$	−21.3721	−0.988981	−0.494490	+	0.869183i	$0.664645\pi$
$468$	10.2010	0.471539
$469$	−0.431042	−0.0199037
$470$	−36.9509	−1.70442
$471$	−4.13553	−0.190555
$472$	1.31232	0.0604044
$473$	2.77931	0.127793
$474$	−6.88587	−0.316279
$475$	−9.22009	−0.423047
$476$	17.7286	0.812587
$477$	51.9963	2.38075
$478$	−27.0036	−1.23511
$479$	−17.7657	−0.811734	−0.405867	−	0.913932i	$-0.633030\pi$
$479$	−17.7657	−0.811734	−0.405867	+	0.913932i	$0.633030\pi$
$480$	−41.4968	−1.89406
$481$	1.18847	0.0541896
$482$	−28.9278	−1.31762
$483$	32.9838	1.50081
$484$	−22.7660	−1.03482
$485$	2.83159	0.128576
$486$	−38.7609	−1.75823
$487$	25.2731	1.14523	0.572617	−	0.819823i	$-0.305928\pi$
$487$	25.2731	1.14523	0.572617	+	0.819823i	$0.305928\pi$
$488$	−3.53045	−0.159816
$489$	−17.7151	−0.801106
$490$	−6.28013	−0.283707
$491$	24.4137	1.10177	0.550887	−	0.834580i	$-0.314290\pi$
$491$	24.4137	1.10177	0.550887	+	0.834580i	$0.314290\pi$
$492$	37.4488	1.68832
$493$	17.8317	0.803098
$494$	−12.7691	−0.574510
$495$	−8.50524	−0.382282
$496$	3.30747	0.148510
$497$	28.2127	1.26551
$498$	13.7263	0.615090
$499$	−6.70984	−0.300374	−0.150187	−	0.988658i	$-0.547988\pi$
$499$	−6.70984	−0.300374	−0.150187	+	0.988658i	$0.547988\pi$
$500$	−27.7802	−1.24237
$501$	−46.9285	−2.09661
$502$	−13.5943	−0.606744
$503$	−31.1648	−1.38957	−0.694785	−	0.719218i	$-0.744500\pi$
$503$	−31.1648	−1.38957	−0.694785	+	0.719218i	$0.744500\pi$
$504$	7.72359	0.344036
$505$	−15.3732	−0.684098
$506$	8.65900	0.384939
$507$	−2.73222	−0.121342
$508$	−23.5326	−1.04409
$509$	−21.6616	−0.960133	−0.480066	−	0.877232i	$-0.659387\pi$
$509$	−21.6616	−0.960133	−0.480066	+	0.877232i	$0.659387\pi$
$510$	−27.9855	−1.23922
$511$	21.7519	0.962250
$512$	−31.1203	−1.37534
$513$	−24.6930	−1.09022
$514$	16.0423	0.707598
$515$	11.8062	0.520243
$516$	17.0520	0.750673
$517$	−9.70049	−0.426627
$518$	7.22288	0.317355
$519$	−22.3401	−0.980623
$520$	−1.10305	−0.0483719
$521$	−36.4710	−1.59782	−0.798911	−	0.601449i	$-0.794590\pi$
$521$	−36.4710	−1.59782	−0.798911	+	0.601449i	$0.794590\pi$
$522$	62.3565	2.72927
$523$	−32.5159	−1.42182	−0.710910	−	0.703283i	$-0.751717\pi$
$523$	−32.5159	−1.42182	−0.710910	+	0.703283i	$0.751717\pi$
$524$	42.3092	1.84829
$525$	−11.9898	−0.523278
$526$	−14.7106	−0.641414
$527$	2.60962	0.113677
$528$	−9.31152	−0.405232
$529$	−6.09415	−0.264963
$530$	−45.1305	−1.96034
$531$	−9.94578	−0.431610
$532$	−41.3795	−1.79403
$533$	−5.99939	−0.259863
$534$	−97.7029	−4.22802
$535$	25.6294	1.10805
$536$	−0.0864929	−0.00373593
$537$	−25.9256	−1.11877
$538$	5.64893	0.243542
$539$	−1.64868	−0.0710138
$540$	−17.1218	−0.736807
$541$	29.7304	1.27821	0.639106	−	0.769119i	$-0.279305\pi$
$541$	29.7304	1.27821	0.639106	+	0.769119i	$0.279305\pi$
$542$	−24.8657	−1.06807
$543$	−2.86040	−0.122752
$544$	−21.4399	−0.919229
$545$	−2.65271	−0.113629
$546$	−16.6050	−0.710628
$547$	−11.0921	−0.474264	−0.237132	−	0.971477i	$-0.576207\pi$
$547$	−11.0921	−0.474264	−0.237132	+	0.971477i	$0.576207\pi$
$548$	10.7298	0.458354
$549$	26.7565	1.14194
$550$	−3.14760	−0.134214
$551$	−41.6202	−1.77308
$552$	6.61853	0.281704
$553$	3.57480	0.152016
$554$	−55.8429	−2.37254
$555$	−6.07956	−0.258063
$556$	−5.43650	−0.230559
$557$	−4.59096	−0.194525	−0.0972627	−	0.995259i	$-0.531009\pi$
$557$	−4.59096	−0.194525	−0.0972627	+	0.995259i	$0.531009\pi$
$558$	9.12572	0.386323
$559$	−2.73177	−0.115542
$560$	18.4139	0.778128
$561$	−7.34686	−0.310185
$562$	4.98498	0.210279
$563$	−32.5926	−1.37361	−0.686807	−	0.726840i	$-0.740988\pi$
$563$	−32.5926	−1.37361	−0.686807	+	0.726840i	$0.740988\pi$
$564$	−59.5158	−2.50607
$565$	3.99125	0.167913
$566$	0.0257037	0.00108041
$567$	7.21828	0.303139
$568$	5.66117	0.237537
$569$	2.64228	0.110770	0.0553850	−	0.998465i	$-0.482361\pi$
$569$	2.64228	0.110770	0.0553850	+	0.998465i	$0.482361\pi$
$570$	65.3199	2.73595
$571$	16.6586	0.697142	0.348571	−	0.937282i	$-0.386667\pi$
$571$	16.6586	0.697142	0.348571	+	0.937282i	$0.386667\pi$
$572$	−2.32438	−0.0971872
$573$	−45.1130	−1.88462
$574$	−36.4611	−1.52186
$575$	−6.14538	−0.256280
$576$	−45.0609	−1.87754
$577$	8.00854	0.333400	0.166700	−	0.986008i	$-0.446689\pi$
$577$	8.00854	0.333400	0.166700	+	0.986008i	$0.446689\pi$
$578$	20.7297	0.862243
$579$	−42.8466	−1.78064
$580$	−28.8590	−1.19831
$581$	−7.12601	−0.295637
$582$	8.55333	0.354547
$583$	−11.8478	−0.490687
$584$	4.36475	0.180615
$585$	8.35976	0.345634
$586$	39.3956	1.62742
$587$	−5.94883	−0.245535	−0.122767	−	0.992435i	$-0.539177\pi$
$587$	−5.94883	−0.245535	−0.122767	+	0.992435i	$0.539177\pi$
$588$	−10.1152	−0.417145
$589$	−6.09101	−0.250976
$590$	8.63250	0.355395
$591$	10.0685	0.414164
$592$	−3.98107	−0.163621
$593$	20.8141	0.854733	0.427366	−	0.904079i	$-0.359441\pi$
$593$	20.8141	0.854733	0.427366	+	0.904079i	$0.359441\pi$
$594$	−8.42980	−0.345879
$595$	14.5287	0.595618
$596$	−17.7231	−0.725968
$597$	29.2219	1.19597
$598$	−8.51089	−0.348036
$599$	−41.8010	−1.70794	−0.853971	−	0.520321i	$-0.825812\pi$
$599$	−41.8010	−1.70794	−0.853971	+	0.520321i	$0.825812\pi$
$600$	−2.40588	−0.0982195
$601$	5.32166	0.217075	0.108537	−	0.994092i	$-0.465383\pi$
$601$	5.32166	0.217075	0.108537	+	0.994092i	$0.465383\pi$
$602$	−16.6023	−0.676657
$603$	0.655511	0.0266945
$604$	−6.67674	−0.271673
$605$	−18.6569	−0.758512
$606$	−46.4375	−1.88639
$607$	20.3148	0.824551	0.412276	−	0.911059i	$-0.364734\pi$
$607$	20.3148	0.824551	0.412276	+	0.911059i	$0.364734\pi$
$608$	50.0421	2.02947
$609$	−54.1229	−2.19317
$610$	−23.2235	−0.940291
$611$	9.53457	0.385727
$612$	−26.9609	−1.08983
$613$	−41.8296	−1.68948	−0.844741	−	0.535175i	$-0.820246\pi$
$613$	−41.8296	−1.68948	−0.844741	+	0.535175i	$0.820246\pi$
$614$	43.5402	1.75714
$615$	30.6896	1.23752
$616$	−1.75989	−0.0709080
$617$	−25.4750	−1.02558	−0.512792	−	0.858513i	$-0.671389\pi$
$617$	−25.4750	−1.02558	−0.512792	+	0.858513i	$0.671389\pi$
$618$	35.6628	1.43457
$619$	21.8611	0.878672	0.439336	−	0.898323i	$-0.355214\pi$
$619$	21.8611	0.878672	0.439336	+	0.898323i	$0.355214\pi$
$620$	−4.22345	−0.169618
$621$	−16.4584	−0.660452
$622$	37.1388	1.48913
$623$	50.7225	2.03215
$624$	9.15225	0.366383
$625$	−15.2930	−0.611721
$626$	64.5450	2.57974
$627$	17.1480	0.684826
$628$	3.45804	0.137991
$629$	−3.14110	−0.125244
$630$	50.8061	2.02416
$631$	−14.2869	−0.568752	−0.284376	−	0.958713i	$-0.591786\pi$
$631$	−14.2869	−0.568752	−0.284376	+	0.958713i	$0.591786\pi$
$632$	0.717321	0.0285335
$633$	−54.7697	−2.17690
$634$	−24.8870	−0.988388
$635$	−19.2851	−0.765308
$636$	−72.6904	−2.88236
$637$	1.62048	0.0642058
$638$	−14.2085	−0.562520
$639$	−42.9048	−1.69729
$640$	8.73503	0.345282
$641$	38.3317	1.51401	0.757005	−	0.653409i	$-0.226662\pi$
$641$	38.3317	1.51401	0.757005	+	0.653409i	$0.226662\pi$
$642$	77.4181	3.05545
$643$	0.938739	0.0370202	0.0185101	−	0.999829i	$-0.494108\pi$
$643$	0.938739	0.0370202	0.0185101	+	0.999829i	$0.494108\pi$
$644$	−27.5803	−1.08682
$645$	13.9743	0.550236
$646$	33.7485	1.32782
$647$	32.7370	1.28702	0.643512	−	0.765436i	$-0.277477\pi$
$647$	32.7370	1.28702	0.643512	+	0.765436i	$0.277477\pi$
$648$	1.44842	0.0568994
$649$	2.26624	0.0889576
$650$	3.09376	0.121347
$651$	−7.92076	−0.310439
$652$	14.8130	0.580121
$653$	−32.9652	−1.29003	−0.645014	−	0.764171i	$-0.723149\pi$
$653$	−32.9652	−1.29003	−0.645014	+	0.764171i	$0.723149\pi$
$654$	−8.01298	−0.313332
$655$	34.6727	1.35478
$656$	20.0964	0.784633
$657$	−33.0795	−1.29055
$658$	57.9460	2.25897
$659$	5.81815	0.226643	0.113321	−	0.993558i	$-0.463851\pi$
$659$	5.81815	0.226643	0.113321	+	0.993558i	$0.463851\pi$
$660$	11.8903	0.462828
$661$	21.9905	0.855331	0.427665	−	0.903937i	$-0.359336\pi$
$661$	21.9905	0.855331	0.427665	+	0.903937i	$0.359336\pi$
$662$	19.2531	0.748294
$663$	7.22120	0.280448
$664$	−1.42991	−0.0554912
$665$	−33.9108	−1.31501
$666$	−10.9843	−0.425631
$667$	−27.7407	−1.07413
$668$	39.2405	1.51826
$669$	−0.461227	−0.0178321
$670$	−0.568955	−0.0219806
$671$	−6.09671	−0.235361
$672$	65.0748	2.51031
$673$	−10.1911	−0.392837	−0.196418	−	0.980520i	$-0.562931\pi$
$673$	−10.1911	−0.392837	−0.196418	+	0.980520i	$0.562931\pi$
$674$	−3.72834	−0.143610
$675$	5.98272	0.230275
$676$	2.28462	0.0878701
$677$	−46.3065	−1.77970	−0.889852	−	0.456249i	$-0.849193\pi$
$677$	−46.3065	−1.77970	−0.889852	+	0.456249i	$0.849193\pi$
$678$	12.0563	0.463019
$679$	−4.44046	−0.170409
$680$	2.91533	0.111798
$681$	18.3263	0.702266
$682$	−2.07938	−0.0796235
$683$	12.1553	0.465110	0.232555	−	0.972583i	$-0.425291\pi$
$683$	12.1553	0.465110	0.232555	+	0.972583i	$0.425291\pi$
$684$	62.9283	2.40612
$685$	8.79315	0.335969
$686$	−32.6938	−1.24826
$687$	−48.2070	−1.83921
$688$	9.15074	0.348869
$689$	11.6452	0.443646
$690$	43.5370	1.65743
$691$	−24.1478	−0.918626	−0.459313	−	0.888274i	$-0.651904\pi$
$691$	−24.1478	−0.918626	−0.459313	+	0.888274i	$0.651904\pi$
$692$	18.6803	0.710119
$693$	13.3378	0.506662
$694$	37.9034	1.43879
$695$	−4.45525	−0.168997
$696$	−10.8603	−0.411659
$697$	15.8562	0.600598
$698$	−54.9812	−2.08107
$699$	−13.1454	−0.497205
$700$	10.0256	0.378932
$701$	47.7144	1.80215	0.901073	−	0.433667i	$-0.142781\pi$
$701$	47.7144	1.80215	0.901073	+	0.433667i	$0.142781\pi$
$702$	8.28561	0.312720
$703$	7.33151	0.276513
$704$	10.2675	0.386972
$705$	−48.7736	−1.83692
$706$	58.4857	2.20114
$707$	24.1080	0.906676
$708$	13.9041	0.522549
$709$	−25.7437	−0.966827	−0.483413	−	0.875392i	$-0.660603\pi$
$709$	−25.7437	−0.966827	−0.483413	+	0.875392i	$0.660603\pi$
$710$	37.2395	1.39757
$711$	−5.43641	−0.203881
$712$	10.1780	0.381436
$713$	−4.05979	−0.152040
$714$	43.8865	1.64241
$715$	−1.90485	−0.0712373
$716$	21.6784	0.810159
$717$	−35.6436	−1.33113
$718$	54.9988	2.05254
$719$	−3.62655	−0.135247	−0.0676237	−	0.997711i	$-0.521542\pi$
$719$	−3.62655	−0.135247	−0.0676237	+	0.997711i	$0.521542\pi$
$720$	−28.0030	−1.04361
$721$	−18.5143	−0.689510
$722$	−39.4423	−1.46789
$723$	−38.1834	−1.42006
$724$	2.39180	0.0888906
$725$	10.0839	0.374507
$726$	−56.3567	−2.09159
$727$	−3.93161	−0.145815	−0.0729076	−	0.997339i	$-0.523228\pi$
$727$	−3.93161	−0.145815	−0.0729076	+	0.997339i	$0.523228\pi$
$728$	1.72979	0.0641102
$729$	−43.7872	−1.62175
$730$	28.7115	1.06266
$731$	7.22001	0.267042
$732$	−37.4054	−1.38254
$733$	−5.52637	−0.204121	−0.102061	−	0.994778i	$-0.532544\pi$
$733$	−5.52637	−0.204121	−0.102061	+	0.994778i	$0.532544\pi$
$734$	36.8424	1.35988
$735$	−8.28950	−0.305763
$736$	33.3541	1.22945
$737$	−0.149364	−0.00550190
$738$	55.4485	2.04109
$739$	−2.65082	−0.0975120	−0.0487560	−	0.998811i	$-0.515526\pi$
$739$	−2.65082	−0.0975120	−0.0487560	+	0.998811i	$0.515526\pi$
$740$	5.08359	0.186876
$741$	−16.8547	−0.619173
$742$	70.7731	2.59816
$743$	22.1289	0.811830	0.405915	−	0.913911i	$-0.366953\pi$
$743$	22.1289	0.811830	0.405915	+	0.913911i	$0.366953\pi$
$744$	−1.58938	−0.0582695
$745$	−14.5242	−0.532127
$746$	0.807689	0.0295716
$747$	10.8370	0.396503
$748$	6.14328	0.224620
$749$	−40.1917	−1.46857
$750$	−68.7692	−2.51110
$751$	4.38099	0.159865	0.0799323	−	0.996800i	$-0.474530\pi$
$751$	4.38099	0.159865	0.0799323	+	0.996800i	$0.474530\pi$
$752$	−31.9384	−1.16467
$753$	−17.9439	−0.653912
$754$	13.9655	0.508593
$755$	−5.47164	−0.199133
$756$	26.8503	0.976535
$757$	−19.7932	−0.719398	−0.359699	−	0.933068i	$-0.617121\pi$
$757$	−19.7932	−0.719398	−0.359699	+	0.933068i	$0.617121\pi$
$758$	39.0717	1.41915
$759$	11.4295	0.414865
$760$	−6.80456	−0.246827
$761$	−27.2626	−0.988270	−0.494135	−	0.869385i	$-0.664515\pi$
$761$	−27.2626	−0.988270	−0.494135	+	0.869385i	$0.664515\pi$
$762$	−58.2543	−2.11033
$763$	4.15994	0.150600
$764$	37.7225	1.36475
$765$	−22.0946	−0.798833
$766$	−10.1128	−0.365391
$767$	−2.22747	−0.0804294
$768$	−28.7610	−1.03782
$769$	−25.4533	−0.917870	−0.458935	−	0.888470i	$-0.651769\pi$
$769$	−25.4533	−0.917870	−0.458935	+	0.888470i	$0.651769\pi$
$770$	−11.5766	−0.417193
$771$	21.1752	0.762607
$772$	35.8273	1.28945
$773$	−47.9485	−1.72459	−0.862294	−	0.506408i	$-0.830973\pi$
$773$	−47.9485	−1.72459	−0.862294	+	0.506408i	$0.830973\pi$
$774$	25.2480	0.907522
$775$	1.47576	0.0530107
$776$	−0.891024	−0.0319859
$777$	9.53389	0.342027
$778$	3.06526	0.109895
$779$	−37.0094	−1.32600
$780$	−11.6869	−0.418457
$781$	9.77624	0.349821
$782$	22.4941	0.804386
$783$	27.0065	0.965132
$784$	−5.42820	−0.193864
$785$	2.83389	0.101146
$786$	104.735	3.73578
$787$	31.7610	1.13216	0.566079	−	0.824351i	$-0.308460\pi$
$787$	31.7610	1.13216	0.566079	+	0.824351i	$0.308460\pi$
$788$	−8.41907	−0.299917
$789$	−19.4174	−0.691278
$790$	4.71857	0.167879
$791$	−6.25903	−0.222546
$792$	2.67637	0.0951006
$793$	5.99243	0.212798
$794$	−80.8218	−2.86826
$795$	−59.5704	−2.11274
$796$	−24.4347	−0.866063
$797$	24.9072	0.882260	0.441130	−	0.897443i	$-0.354578\pi$
$797$	24.9072	0.882260	0.441130	+	0.897443i	$0.354578\pi$
$798$	−102.434	−3.62612
$799$	−25.1996	−0.891499
$800$	−12.1244	−0.428662
$801$	−77.1367	−2.72549
$802$	27.2932	0.963755
$803$	7.53746	0.265991
$804$	−0.916399	−0.0323189
$805$	−22.6023	−0.796625
$806$	2.04381	0.0719902
$807$	7.45634	0.262476
$808$	4.83752	0.170184
$809$	−9.91231	−0.348498	−0.174249	−	0.984702i	$-0.555750\pi$
$809$	−9.91231	−0.348498	−0.174249	+	0.984702i	$0.555750\pi$
$810$	9.52779	0.334772
$811$	7.22600	0.253739	0.126870	−	0.991919i	$-0.459507\pi$
$811$	7.22600	0.253739	0.126870	+	0.991919i	$0.459507\pi$
$812$	45.2564	1.58819
$813$	−32.8217	−1.15111
$814$	2.50286	0.0877253
$815$	12.1394	0.425223
$816$	−24.1892	−0.846790
$817$	−16.8519	−0.589575
$818$	−9.74341	−0.340670
$819$	−13.1097	−0.458089
$820$	−25.6619	−0.896154
$821$	25.9888	0.907014	0.453507	−	0.891253i	$-0.350173\pi$
$821$	25.9888	0.907014	0.453507	+	0.891253i	$0.350173\pi$
$822$	26.5613	0.926432
$823$	18.6888	0.651450	0.325725	−	0.945465i	$-0.394392\pi$
$823$	18.6888	0.651450	0.325725	+	0.945465i	$0.394392\pi$
$824$	−3.71509	−0.129421
$825$	−4.15469	−0.144648
$826$	−13.5374	−0.471026
$827$	−16.4154	−0.570819	−0.285410	−	0.958406i	$-0.592130\pi$
$827$	−16.4154	−0.570819	−0.285410	+	0.958406i	$0.592130\pi$
$828$	41.9430	1.45762
$829$	−1.34460	−0.0466999	−0.0233500	−	0.999727i	$-0.507433\pi$
$829$	−1.34460	−0.0466999	−0.0233500	+	0.999727i	$0.507433\pi$
$830$	−9.40600	−0.326487
$831$	−73.7103	−2.55698
$832$	−10.0919	−0.349874
$833$	−4.28289	−0.148393
$834$	−13.4579	−0.466009
$835$	32.1579	1.11287
$836$	−14.3388	−0.495917
$837$	3.95233	0.136612
$838$	−9.34016	−0.322650
$839$	17.6087	0.607919	0.303959	−	0.952685i	$-0.401691\pi$
$839$	17.6087	0.607919	0.303959	+	0.952685i	$0.401691\pi$
$840$	−8.84865	−0.305307
$841$	16.5196	0.569642
$842$	2.93403	0.101113
$843$	6.57996	0.226626
$844$	45.7972	1.57640
$845$	1.87227	0.0644079
$846$	−88.1219	−3.02969
$847$	29.2576	1.00530
$848$	−39.0084	−1.33955
$849$	0.0339278	0.00116440
$850$	−8.17672	−0.280459
$851$	4.88660	0.167510
$852$	59.9805	2.05490
$853$	−9.93437	−0.340146	−0.170073	−	0.985431i	$-0.554400\pi$
$853$	−9.93437	−0.340146	−0.170073	+	0.985431i	$0.554400\pi$
$854$	36.4188	1.24622
$855$	51.5702	1.76366
$856$	−8.06486	−0.275651
$857$	33.3534	1.13933	0.569664	−	0.821877i	$-0.307073\pi$
$857$	33.3534	1.13933	0.569664	+	0.821877i	$0.307073\pi$
$858$	−5.75394	−0.196436
$859$	29.9746	1.02272	0.511360	−	0.859367i	$-0.329142\pi$
$859$	29.9746	1.02272	0.511360	+	0.859367i	$0.329142\pi$
$860$	−11.6850	−0.398454
$861$	−48.1271	−1.64017
$862$	5.68311	0.193567
$863$	−54.1014	−1.84163	−0.920817	−	0.389996i	$-0.872476\pi$
$863$	−54.1014	−1.84163	−0.920817	+	0.389996i	$0.872476\pi$
$864$	−32.4712	−1.10469
$865$	15.3087	0.520510
$866$	0.364154	0.0123745
$867$	27.3624	0.929275
$868$	6.62316	0.224805
$869$	1.23874	0.0420213
$870$	−71.4397	−2.42203
$871$	0.146809	0.00497444
$872$	0.834735	0.0282677
$873$	6.75287	0.228550
$874$	−52.5025	−1.77592
$875$	35.7015	1.20693
$876$	46.2448	1.56247
$877$	−39.8086	−1.34424	−0.672121	−	0.740441i	$-0.734617\pi$
$877$	−39.8086	−1.34424	−0.672121	+	0.740441i	$0.734617\pi$
$878$	−17.0106	−0.574079
$879$	52.0006	1.75394
$880$	6.38075	0.215095
$881$	−55.7164	−1.87713	−0.938566	−	0.345099i	$-0.887845\pi$
$881$	−55.7164	−1.87713	−0.938566	+	0.345099i	$0.887845\pi$
$882$	−14.9771	−0.504304
$883$	−12.5154	−0.421178	−0.210589	−	0.977575i	$-0.567538\pi$
$883$	−12.5154	−0.421178	−0.210589	+	0.977575i	$0.567538\pi$
$884$	−6.03820	−0.203087
$885$	11.3945	0.383023
$886$	52.4032	1.76052
$887$	−8.28981	−0.278344	−0.139172	−	0.990268i	$-0.544444\pi$
$887$	−8.28981	−0.278344	−0.139172	+	0.990268i	$0.544444\pi$
$888$	1.91307	0.0641985
$889$	30.2427	1.01431
$890$	66.9513	2.24421
$891$	2.50127	0.0837957
$892$	0.385668	0.0129131
$893$	58.8174	1.96825
$894$	−43.8731	−1.46734
$895$	17.7656	0.593838
$896$	−13.6982	−0.457624
$897$	−11.2340	−0.375093
$898$	14.9246	0.498039
$899$	6.66168	0.222180
$900$	−15.2465	−0.508217
$901$	−30.7779	−1.02536
$902$	−12.6344	−0.420681
$903$	−21.9143	−0.729261
$904$	−1.25594	−0.0417719
$905$	1.96010	0.0651560
$906$	−16.5281	−0.549109
$907$	−8.64417	−0.287025	−0.143512	−	0.989649i	$-0.545840\pi$
$907$	−8.64417	−0.287025	−0.143512	+	0.989649i	$0.545840\pi$
$908$	−15.3240	−0.508546
$909$	−36.6625	−1.21602
$910$	11.3786	0.377198
$911$	−32.2802	−1.06949	−0.534746	−	0.845013i	$-0.679593\pi$
$911$	−32.2802	−1.06949	−0.534746	+	0.845013i	$0.679593\pi$
$912$	56.4589	1.86954
$913$	−2.46930	−0.0817218
$914$	12.8206	0.424069
$915$	−30.6540	−1.01339
$916$	40.3096	1.33187
$917$	−54.3733	−1.79557
$918$	−21.8987	−0.722764
$919$	−30.6214	−1.01011	−0.505053	−	0.863088i	$-0.668527\pi$
$919$	−30.6214	−1.01011	−0.505053	+	0.863088i	$0.668527\pi$
$920$	−4.53538	−0.149527
$921$	57.4712	1.89374
$922$	15.8266	0.521220
$923$	−9.60903	−0.316285
$924$	−18.6462	−0.613414
$925$	−1.77631	−0.0584046
$926$	−2.06993	−0.0680222
$927$	28.1558	0.924759
$928$	−54.7305	−1.79662
$929$	−4.79739	−0.157397	−0.0786986	−	0.996898i	$-0.525076\pi$
$929$	−4.79739	−0.157397	−0.0786986	+	0.996898i	$0.525076\pi$
$930$	−10.4550	−0.342834
$931$	9.99653	0.327623
$932$	10.9919	0.360051
$933$	49.0216	1.60489
$934$	44.2387	1.44754
$935$	5.03446	0.164645
$936$	−2.63059	−0.0859835
$937$	−33.2357	−1.08576	−0.542881	−	0.839810i	$-0.682667\pi$
$937$	−33.2357	−1.08576	−0.542881	+	0.839810i	$0.682667\pi$
$938$	0.892228	0.0291323
$939$	85.1967	2.78029
$940$	40.7834	1.33021
$941$	−36.5421	−1.19124	−0.595619	−	0.803267i	$-0.703093\pi$
$941$	−36.5421	−1.19124	−0.595619	+	0.803267i	$0.703093\pi$
$942$	8.56028	0.278909
$943$	−24.6675	−0.803286
$944$	7.46147	0.242850
$945$	22.0040	0.715790
$946$	−5.75299	−0.187046
$947$	1.41652	0.0460306	0.0230153	−	0.999735i	$-0.492673\pi$
$947$	1.41652	0.0460306	0.0230153	+	0.999735i	$0.492673\pi$
$948$	7.60006	0.246839
$949$	−7.40854	−0.240491
$950$	19.0850	0.619198
$951$	−32.8497	−1.06523
$952$	−4.57178	−0.148172
$953$	−6.35261	−0.205781	−0.102891	−	0.994693i	$-0.532809\pi$
$953$	−6.35261	−0.205781	−0.102891	+	0.994693i	$0.532809\pi$
$954$	−107.629	−3.48461
$955$	30.9139	1.00035
$956$	29.8043	0.963941
$957$	−18.7546	−0.606251
$958$	36.7737	1.18811
$959$	−13.7893	−0.445280
$960$	51.6247	1.66618
$961$	−30.0251	−0.968551
$962$	−2.46005	−0.0793153
$963$	61.1218	1.96962
$964$	31.9281	1.02834
$965$	29.3608	0.945157
$966$	−68.2743	−2.19669
$967$	−18.1292	−0.582995	−0.291497	−	0.956572i	$-0.594154\pi$
$967$	−18.1292	−0.582995	−0.291497	+	0.956572i	$0.594154\pi$
$968$	5.87083	0.188696
$969$	44.5466	1.43104
$970$	−5.86120	−0.188192
$971$	−24.6527	−0.791144	−0.395572	−	0.918435i	$-0.629454\pi$
$971$	−24.6527	−0.791144	−0.395572	+	0.918435i	$0.629454\pi$
$972$	42.7811	1.37220
$973$	6.98668	0.223983
$974$	−52.3137	−1.67624
$975$	4.08363	0.130781
$976$	−20.0731	−0.642525
$977$	−41.9853	−1.34323	−0.671615	−	0.740900i	$-0.734399\pi$
$977$	−41.9853	−1.34323	−0.671615	+	0.740900i	$0.734399\pi$
$978$	36.6691	1.17255
$979$	17.5763	0.561741
$980$	6.93149	0.221418
$981$	−6.32627	−0.201982
$982$	−50.5347	−1.61263
$983$	−16.7321	−0.533672	−0.266836	−	0.963742i	$-0.585978\pi$
$983$	−16.7321	−0.533672	−0.266836	+	0.963742i	$0.585978\pi$
$984$	−9.65719	−0.307860
$985$	−6.89949	−0.219836
$986$	−36.9104	−1.17547
$987$	76.4862	2.43458
$988$	14.0935	0.448375
$989$	−11.2322	−0.357162
$990$	17.6053	0.559532
$991$	−25.5438	−0.811425	−0.405713	−	0.914001i	$-0.632977\pi$
$991$	−25.5438	−0.811425	−0.405713	+	0.914001i	$0.632977\pi$
$992$	−8.00968	−0.254308
$993$	25.4133	0.806467
$994$	−58.3985	−1.85229
$995$	−20.0244	−0.634816
$996$	−15.1500	−0.480045
$997$	38.6099	1.22279	0.611393	−	0.791327i	$-0.290609\pi$
$997$	38.6099	1.22279	0.611393	+	0.791327i	$0.290609\pi$
$998$	13.8889	0.439646
$999$	−4.75726	−0.150513

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6019.2.a.b.1.17	✓	101

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6019.2.a.b.1.17	✓	101	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)

\(f(q)\)	\(=\)	\(q-2.06993 q^{2} -2.73222 q^{3} +2.28462 q^{4} +1.87227 q^{5} +5.65552 q^{6} -2.93607 q^{7} -0.589152 q^{8} +4.46505 q^{9} +O(q^{10})\)	\(q-2.06993 q^{2} -2.73222 q^{3} +2.28462 q^{4} +1.87227 q^{5} +5.65552 q^{6} -2.93607 q^{7} -0.589152 q^{8} +4.46505 q^{9} -3.87547 q^{10} -1.01740 q^{11} -6.24210 q^{12} +1.00000 q^{13} +6.07746 q^{14} -5.11545 q^{15} -3.34974 q^{16} -2.64297 q^{17} -9.24235 q^{18} +6.16886 q^{19} +4.27742 q^{20} +8.02199 q^{21} +2.10595 q^{22} +4.11167 q^{23} +1.60969 q^{24} -1.49462 q^{25} -2.06993 q^{26} -4.00284 q^{27} -6.70780 q^{28} -6.74682 q^{29} +10.5886 q^{30} -0.987381 q^{31} +8.11205 q^{32} +2.77977 q^{33} +5.47078 q^{34} -5.49710 q^{35} +10.2010 q^{36} +1.18847 q^{37} -12.7691 q^{38} -2.73222 q^{39} -1.10305 q^{40} -5.99939 q^{41} -16.6050 q^{42} -2.73177 q^{43} -2.32438 q^{44} +8.35976 q^{45} -8.51089 q^{46} +9.53457 q^{47} +9.15225 q^{48} +1.62048 q^{49} +3.09376 q^{50} +7.22120 q^{51} +2.28462 q^{52} +11.6452 q^{53} +8.28561 q^{54} -1.90485 q^{55} +1.72979 q^{56} -16.8547 q^{57} +13.9655 q^{58} -2.22747 q^{59} -11.6869 q^{60} +5.99243 q^{61} +2.04381 q^{62} -13.1097 q^{63} -10.0919 q^{64} +1.87227 q^{65} -5.75394 q^{66} +0.146809 q^{67} -6.03820 q^{68} -11.2340 q^{69} +11.3786 q^{70} -9.60903 q^{71} -2.63059 q^{72} -7.40854 q^{73} -2.46005 q^{74} +4.08363 q^{75} +14.0935 q^{76} +2.98716 q^{77} +5.65552 q^{78} -1.21755 q^{79} -6.27161 q^{80} -2.45849 q^{81} +12.4183 q^{82} +2.42706 q^{83} +18.3272 q^{84} -4.94835 q^{85} +5.65459 q^{86} +18.4338 q^{87} +0.599404 q^{88} -17.2757 q^{89} -17.3041 q^{90} -2.93607 q^{91} +9.39362 q^{92} +2.69775 q^{93} -19.7359 q^{94} +11.5498 q^{95} -22.1639 q^{96} +1.51239 q^{97} -3.35429 q^{98} -4.54275 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 101 q - 8 q^{2} - 13 q^{3} + 86 q^{4} - 43 q^{5} - 10 q^{6} - q^{7} - 24 q^{8} + 52 q^{9}+O(q^{10}) \) 101 * q - 8 * q^2 - 13 * q^3 + 86 * q^4 - 43 * q^5 - 10 * q^6 - q^7 - 24 * q^8 + 52 * q^9	\( 101 q - 8 q^{2} - 13 q^{3} + 86 q^{4} - 43 q^{5} - 10 q^{6} - q^{7} - 24 q^{8} + 52 q^{9} - 19 q^{10} - 42 q^{11} - 28 q^{12} + 101 q^{13} - 45 q^{14} - 15 q^{15} + 48 q^{16} - 83 q^{17} - 4 q^{18} - 18 q^{19} - 51 q^{20} - 50 q^{21} - 20 q^{22} - 64 q^{23} - 23 q^{24} + 46 q^{25} - 8 q^{26} - 37 q^{27} - 11 q^{28} - 117 q^{29} - 28 q^{30} - 10 q^{31} - 36 q^{32} - 20 q^{33} - 10 q^{34} - 53 q^{35} - 16 q^{36} - 27 q^{37} - 68 q^{38} - 13 q^{39} - 42 q^{40} - 60 q^{41} - 31 q^{42} - 16 q^{43} - 89 q^{44} - 56 q^{45} + 5 q^{46} - 23 q^{47} - 37 q^{48} + 48 q^{49} - 30 q^{50} - 68 q^{51} + 86 q^{52} - 189 q^{53} - 23 q^{54} + 3 q^{55} - 106 q^{56} - 25 q^{57} - 82 q^{59} + 6 q^{60} - 68 q^{61} - 57 q^{62} + 3 q^{63} - 2 q^{64} - 43 q^{65} - 40 q^{66} - 13 q^{67} - 138 q^{68} - 92 q^{69} + 18 q^{70} - 39 q^{71} - 20 q^{72} + 19 q^{73} - 88 q^{74} - 21 q^{75} - 53 q^{76} - 147 q^{77} - 10 q^{78} - 19 q^{79} - 104 q^{80} - 55 q^{81} + 27 q^{82} - 49 q^{83} - 59 q^{84} - 27 q^{85} - 99 q^{86} - 33 q^{87} - 41 q^{88} - 70 q^{89} - 49 q^{90} - q^{91} - 111 q^{92} - 84 q^{93} + 4 q^{94} - 82 q^{95} - 7 q^{96} + 25 q^{97} - 37 q^{98} - 41 q^{99}+O(q^{100}) \) 101 * q - 8 * q^2 - 13 * q^3 + 86 * q^4 - 43 * q^5 - 10 * q^6 - q^7 - 24 * q^8 + 52 * q^9 - 19 * q^10 - 42 * q^11 - 28 * q^12 + 101 * q^13 - 45 * q^14 - 15 * q^15 + 48 * q^16 - 83 * q^17 - 4 * q^18 - 18 * q^19 - 51 * q^20 - 50 * q^21 - 20 * q^22 - 64 * q^23 - 23 * q^24 + 46 * q^25 - 8 * q^26 - 37 * q^27 - 11 * q^28 - 117 * q^29 - 28 * q^30 - 10 * q^31 - 36 * q^32 - 20 * q^33 - 10 * q^34 - 53 * q^35 - 16 * q^36 - 27 * q^37 - 68 * q^38 - 13 * q^39 - 42 * q^40 - 60 * q^41 - 31 * q^42 - 16 * q^43 - 89 * q^44 - 56 * q^45 + 5 * q^46 - 23 * q^47 - 37 * q^48 + 48 * q^49 - 30 * q^50 - 68 * q^51 + 86 * q^52 - 189 * q^53 - 23 * q^54 + 3 * q^55 - 106 * q^56 - 25 * q^57 - 82 * q^59 + 6 * q^60 - 68 * q^61 - 57 * q^62 + 3 * q^63 - 2 * q^64 - 43 * q^65 - 40 * q^66 - 13 * q^67 - 138 * q^68 - 92 * q^69 + 18 * q^70 - 39 * q^71 - 20 * q^72 + 19 * q^73 - 88 * q^74 - 21 * q^75 - 53 * q^76 - 147 * q^77 - 10 * q^78 - 19 * q^79 - 104 * q^80 - 55 * q^81 + 27 * q^82 - 49 * q^83 - 59 * q^84 - 27 * q^85 - 99 * q^86 - 33 * q^87 - 41 * q^88 - 70 * q^89 - 49 * q^90 - q^91 - 111 * q^92 - 84 * q^93 + 4 * q^94 - 82 * q^95 - 7 * q^96 + 25 * q^97 - 37 * q^98 - 41 * q^99

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