LMFDB - Embedded newform 6019.2.a.c.1.5

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			1.5
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)

$f(q)$	$=$	$q-2.62196 q^{2} -0.813055 q^{3} +4.87469 q^{4} +0.562087 q^{5} +2.13180 q^{6} -5.01388 q^{7} -7.53732 q^{8} -2.33894 q^{9} +O(q^{10})$	\(q-2.62196 q^{2} -0.813055 q^{3} +4.87469 q^{4} +0.562087 q^{5} +2.13180 q^{6} -5.01388 q^{7} -7.53732 q^{8} -2.33894 q^{9} -1.47377 q^{10} -2.09845 q^{11} -3.96339 q^{12} -1.00000 q^{13} +13.1462 q^{14} -0.457007 q^{15} +10.0132 q^{16} +3.74319 q^{17} +6.13262 q^{18} -0.888994 q^{19} +2.74000 q^{20} +4.07656 q^{21} +5.50205 q^{22} +3.39137 q^{23} +6.12826 q^{24} -4.68406 q^{25} +2.62196 q^{26} +4.34085 q^{27} -24.4411 q^{28} +3.62001 q^{29} +1.19826 q^{30} -8.47651 q^{31} -11.1796 q^{32} +1.70615 q^{33} -9.81451 q^{34} -2.81823 q^{35} -11.4016 q^{36} +2.48870 q^{37} +2.33091 q^{38} +0.813055 q^{39} -4.23663 q^{40} -7.93225 q^{41} -10.6886 q^{42} +6.00589 q^{43} -10.2293 q^{44} -1.31469 q^{45} -8.89206 q^{46} +1.50624 q^{47} -8.14128 q^{48} +18.1390 q^{49} +12.2814 q^{50} -3.04342 q^{51} -4.87469 q^{52} -2.70934 q^{53} -11.3816 q^{54} -1.17951 q^{55} +37.7912 q^{56} +0.722801 q^{57} -9.49153 q^{58} +11.4174 q^{59} -2.22777 q^{60} -0.919060 q^{61} +22.2251 q^{62} +11.7272 q^{63} +9.28607 q^{64} -0.562087 q^{65} -4.47347 q^{66} -2.20779 q^{67} +18.2469 q^{68} -2.75737 q^{69} +7.38930 q^{70} +1.75234 q^{71} +17.6294 q^{72} +9.37638 q^{73} -6.52527 q^{74} +3.80840 q^{75} -4.33357 q^{76} +10.5214 q^{77} -2.13180 q^{78} +6.77830 q^{79} +5.62829 q^{80} +3.48747 q^{81} +20.7981 q^{82} +8.69805 q^{83} +19.8719 q^{84} +2.10400 q^{85} -15.7472 q^{86} -2.94327 q^{87} +15.8167 q^{88} -11.1990 q^{89} +3.44706 q^{90} +5.01388 q^{91} +16.5319 q^{92} +6.89187 q^{93} -3.94930 q^{94} -0.499691 q^{95} +9.08962 q^{96} -6.56447 q^{97} -47.5597 q^{98} +4.90815 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.62196	−1.85401	−0.927004	−	0.375052i	$-0.877625\pi$
$2$	−2.62196	−1.85401	−0.927004	+	0.375052i	$0.877625\pi$
$3$	−0.813055	−0.469417	−0.234709	−	0.972066i	$-0.575414\pi$
$3$	−0.813055	−0.469417	−0.234709	+	0.972066i	$0.575414\pi$
$4$	4.87469	2.43734
$5$	0.562087	0.251373	0.125686	−	0.992070i	$-0.459887\pi$
$5$	0.562087	0.251373	0.125686	+	0.992070i	$0.459887\pi$
$6$	2.13180	0.870303
$7$	−5.01388	−1.89507	−0.947534	−	0.319656i	$-0.896433\pi$
$7$	−5.01388	−1.89507	−0.947534	+	0.319656i	$0.896433\pi$
$8$	−7.53732	−2.66485
$9$	−2.33894	−0.779647
$10$	−1.47377	−0.466047
$11$	−2.09845	−0.632706	−0.316353	−	0.948642i	$-0.602458\pi$
$11$	−2.09845	−0.632706	−0.316353	+	0.948642i	$0.602458\pi$
$12$	−3.96339	−1.14413
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	13.1462	3.51347
$15$	−0.457007	−0.117999
$16$	10.0132	2.50330
$17$	3.74319	0.907858	0.453929	−	0.891038i	$-0.350022\pi$
$17$	3.74319	0.907858	0.453929	+	0.891038i	$0.350022\pi$
$18$	6.13262	1.44547
$19$	−0.888994	−0.203949	−0.101975	−	0.994787i	$-0.532516\pi$
$19$	−0.888994	−0.203949	−0.101975	+	0.994787i	$0.532516\pi$
$20$	2.74000	0.612682
$21$	4.07656	0.889578
$22$	5.50205	1.17304
$23$	3.39137	0.707151	0.353575	−	0.935406i	$-0.384966\pi$
$23$	3.39137	0.707151	0.353575	+	0.935406i	$0.384966\pi$
$24$	6.12826	1.25093
$25$	−4.68406	−0.936812
$26$	2.62196	0.514209
$27$	4.34085	0.835397
$28$	−24.4411	−4.61893
$29$	3.62001	0.672219	0.336110	−	0.941823i	$-0.390889\pi$
$29$	3.62001	0.672219	0.336110	+	0.941823i	$0.390889\pi$
$30$	1.19826	0.218771
$31$	−8.47651	−1.52243	−0.761213	−	0.648502i	$-0.775396\pi$
$31$	−8.47651	−1.52243	−0.761213	+	0.648502i	$0.775396\pi$
$32$	−11.1796	−1.97629
$33$	1.70615	0.297003
$34$	−9.81451	−1.68317
$35$	−2.81823	−0.476368
$36$	−11.4016	−1.90027
$37$	2.48870	0.409139	0.204570	−	0.978852i	$-0.434421\pi$
$37$	2.48870	0.409139	0.204570	+	0.978852i	$0.434421\pi$
$38$	2.33091	0.378123
$39$	0.813055	0.130193
$40$	−4.23663	−0.669870
$41$	−7.93225	−1.23881	−0.619405	−	0.785072i	$-0.712626\pi$
$41$	−7.93225	−1.23881	−0.619405	+	0.785072i	$0.712626\pi$
$42$	−10.6886	−1.64928
$43$	6.00589	0.915890	0.457945	−	0.888981i	$-0.348586\pi$
$43$	6.00589	0.915890	0.457945	+	0.888981i	$0.348586\pi$
$44$	−10.2293	−1.54212
$45$	−1.31469	−0.195982
$46$	−8.89206	−1.31106
$47$	1.50624	0.219708	0.109854	−	0.993948i	$-0.464962\pi$
$47$	1.50624	0.219708	0.109854	+	0.993948i	$0.464962\pi$
$48$	−8.14128	−1.17509
$49$	18.1390	2.59128
$50$	12.2814	1.73686
$51$	−3.04342	−0.426164
$52$	−4.87469	−0.675997
$53$	−2.70934	−0.372156	−0.186078	−	0.982535i	$-0.559578\pi$
$53$	−2.70934	−0.372156	−0.186078	+	0.982535i	$0.559578\pi$
$54$	−11.3816	−1.54883
$55$	−1.17951	−0.159045
$56$	37.7912	5.05006
$57$	0.722801	0.0957373
$58$	−9.49153	−1.24630
$59$	11.4174	1.48642	0.743212	−	0.669056i	$-0.233301\pi$
$59$	11.4174	1.48642	0.743212	+	0.669056i	$0.233301\pi$
$60$	−2.22777	−0.287604
$61$	−0.919060	−0.117674	−0.0588368	−	0.998268i	$-0.518739\pi$
$61$	−0.919060	−0.117674	−0.0588368	+	0.998268i	$0.518739\pi$
$62$	22.2251	2.82259
$63$	11.7272	1.47748
$64$	9.28607	1.16076
$65$	−0.562087	−0.0697183
$66$	−4.47347	−0.550646
$67$	−2.20779	−0.269724	−0.134862	−	0.990864i	$-0.543059\pi$
$67$	−2.20779	−0.269724	−0.134862	+	0.990864i	$0.543059\pi$
$68$	18.2469	2.21276
$69$	−2.75737	−0.331949
$70$	7.38930	0.883191
$71$	1.75234	0.207964	0.103982	−	0.994579i	$-0.466842\pi$
$71$	1.75234	0.207964	0.103982	+	0.994579i	$0.466842\pi$
$72$	17.6294	2.07764
$73$	9.37638	1.09742	0.548711	−	0.836012i	$-0.315119\pi$
$73$	9.37638	1.09742	0.548711	+	0.836012i	$0.315119\pi$
$74$	−6.52527	−0.758547
$75$	3.80840	0.439756
$76$	−4.33357	−0.497094
$77$	10.5214	1.19902
$78$	−2.13180	−0.241379
$79$	6.77830	0.762618	0.381309	−	0.924448i	$-0.375473\pi$
$79$	6.77830	0.762618	0.381309	+	0.924448i	$0.375473\pi$
$80$	5.62829	0.629262
$81$	3.48747	0.387497
$82$	20.7981	2.29676
$83$	8.69805	0.954735	0.477367	−	0.878704i	$-0.341591\pi$
$83$	8.69805	0.954735	0.477367	+	0.878704i	$0.341591\pi$
$84$	19.8719	2.16821
$85$	2.10400	0.228211
$86$	−15.7472	−1.69807
$87$	−2.94327	−0.315551
$88$	15.8167	1.68606
$89$	−11.1990	−1.18710	−0.593548	−	0.804799i	$-0.702273\pi$
$89$	−11.1990	−1.18710	−0.593548	+	0.804799i	$0.702273\pi$
$90$	3.44706	0.363352
$91$	5.01388	0.525597
$92$	16.5319	1.72357
$93$	6.89187	0.714653
$94$	−3.94930	−0.407340
$95$	−0.499691	−0.0512673
$96$	9.08962	0.927706
$97$	−6.56447	−0.666521	−0.333261	−	0.942835i	$-0.608149\pi$
$97$	−6.56447	−0.666521	−0.333261	+	0.942835i	$0.608149\pi$
$98$	−47.5597	−4.80425
$99$	4.90815	0.493288
$100$	−22.8333	−2.28333
$101$	−2.20644	−0.219549	−0.109774	−	0.993957i	$-0.535013\pi$
$101$	−2.20644	−0.219549	−0.109774	+	0.993957i	$0.535013\pi$
$102$	7.97974	0.790112
$103$	8.75090	0.862252	0.431126	−	0.902292i	$-0.358116\pi$
$103$	8.75090	0.862252	0.431126	+	0.902292i	$0.358116\pi$
$104$	7.53732	0.739095
$105$	2.29138	0.223616
$106$	7.10378	0.689980
$107$	10.2031	0.986374	0.493187	−	0.869923i	$-0.335832\pi$
$107$	10.2031	0.986374	0.493187	+	0.869923i	$0.335832\pi$
$108$	21.1603	2.03615
$109$	15.6191	1.49604	0.748018	−	0.663678i	$-0.231005\pi$
$109$	15.6191	1.49604	0.748018	+	0.663678i	$0.231005\pi$
$110$	3.09263	0.294871
$111$	−2.02345	−0.192057
$112$	−50.2050	−4.74392
$113$	−11.8151	−1.11147	−0.555734	−	0.831360i	$-0.687563\pi$
$113$	−11.8151	−1.11147	−0.555734	+	0.831360i	$0.687563\pi$
$114$	−1.89516	−0.177498
$115$	1.90625	0.177758
$116$	17.6464	1.63843
$117$	2.33894	0.216235
$118$	−29.9361	−2.75584
$119$	−18.7679	−1.72045
$120$	3.44461	0.314449
$121$	−6.59651	−0.599683
$122$	2.40974	0.218168
$123$	6.44936	0.581519
$124$	−41.3203	−3.71067
$125$	−5.44328	−0.486862
$126$	−30.7482	−2.73927
$127$	14.2707	1.26632	0.633158	−	0.774023i	$-0.281758\pi$
$127$	14.2707	1.26632	0.633158	+	0.774023i	$0.281758\pi$
$128$	−1.98855	−0.175765
$129$	−4.88312	−0.429935
$130$	1.47377	0.129258
$131$	−1.93359	−0.168938	−0.0844692	−	0.996426i	$-0.526919\pi$
$131$	−1.93359	−0.168938	−0.0844692	+	0.996426i	$0.526919\pi$
$132$	8.31697	0.723899
$133$	4.45731	0.386497
$134$	5.78873	0.500070
$135$	2.43994	0.209996
$136$	−28.2137	−2.41930
$137$	−9.68430	−0.827386	−0.413693	−	0.910417i	$-0.635761\pi$
$137$	−9.68430	−0.827386	−0.413693	+	0.910417i	$0.635761\pi$
$138$	7.22973	0.615436
$139$	2.19805	0.186436	0.0932181	−	0.995646i	$-0.470285\pi$
$139$	2.19805	0.186436	0.0932181	+	0.995646i	$0.470285\pi$
$140$	−13.7380	−1.16107
$141$	−1.22466	−0.103135
$142$	−4.59456	−0.385567
$143$	2.09845	0.175481
$144$	−23.4203	−1.95169
$145$	2.03476	0.168978
$146$	−24.5845	−2.03463
$147$	−14.7480	−1.21639
$148$	12.1316	0.997213
$149$	−10.2179	−0.837079	−0.418540	−	0.908199i	$-0.637458\pi$
$149$	−10.2179	−0.837079	−0.418540	+	0.908199i	$0.637458\pi$
$150$	−9.98547	−0.815310
$151$	−8.30980	−0.676242	−0.338121	−	0.941103i	$-0.609791\pi$
$151$	−8.30980	−0.676242	−0.338121	+	0.941103i	$0.609791\pi$
$152$	6.70063	0.543493
$153$	−8.75511	−0.707809
$154$	−27.5866	−2.22299
$155$	−4.76453	−0.382696
$156$	3.96339	0.317325
$157$	13.7126	1.09438	0.547191	−	0.837008i	$-0.315697\pi$
$157$	13.7126	1.09438	0.547191	+	0.837008i	$0.315697\pi$
$158$	−17.7725	−1.41390
$159$	2.20284	0.174697
$160$	−6.28390	−0.496786
$161$	−17.0039	−1.34010
$162$	−9.14403	−0.718423
$163$	19.7219	1.54474	0.772368	−	0.635175i	$-0.219072\pi$
$163$	19.7219	1.54474	0.772368	+	0.635175i	$0.219072\pi$
$164$	−38.6673	−3.01941
$165$	0.959006	0.0746585
$166$	−22.8060	−1.77009
$167$	6.83061	0.528568	0.264284	−	0.964445i	$-0.414864\pi$
$167$	6.83061	0.528568	0.264284	+	0.964445i	$0.414864\pi$
$168$	−30.7263	−2.37059
$169$	1.00000	0.0769231
$170$	−5.51661	−0.423104
$171$	2.07930	0.159008
$172$	29.2768	2.23234
$173$	−21.7859	−1.65635	−0.828176	−	0.560468i	$-0.810621\pi$
$173$	−21.7859	−1.65635	−0.828176	+	0.560468i	$0.810621\pi$
$174$	7.71714	0.585035
$175$	23.4853	1.77532
$176$	−21.0122	−1.58385
$177$	−9.28301	−0.697753
$178$	29.3635	2.20089
$179$	2.06612	0.154429	0.0772146	−	0.997014i	$-0.475397\pi$
$179$	2.06612	0.154429	0.0772146	+	0.997014i	$0.475397\pi$
$180$	−6.40869	−0.477676
$181$	−1.16015	−0.0862336	−0.0431168	−	0.999070i	$-0.513729\pi$
$181$	−1.16015	−0.0862336	−0.0431168	+	0.999070i	$0.513729\pi$
$182$	−13.1462	−0.974461
$183$	0.747246	0.0552380
$184$	−25.5619	−1.88445
$185$	1.39886	0.102846
$186$	−18.0702	−1.32497
$187$	−7.85490	−0.574407
$188$	7.34245	0.535503
$189$	−21.7645	−1.58313
$190$	1.31017	0.0950499
$191$	2.49479	0.180517	0.0902584	−	0.995918i	$-0.471231\pi$
$191$	2.49479	0.180517	0.0902584	+	0.995918i	$0.471231\pi$
$192$	−7.55009	−0.544881
$193$	14.0195	1.00915	0.504574	−	0.863369i	$-0.331650\pi$
$193$	14.0195	1.00915	0.504574	+	0.863369i	$0.331650\pi$
$194$	17.2118	1.23573
$195$	0.457007	0.0327270
$196$	88.4218	6.31584
$197$	−21.9338	−1.56272	−0.781359	−	0.624082i	$-0.785473\pi$
$197$	−21.9338	−1.56272	−0.781359	+	0.624082i	$0.785473\pi$
$198$	−12.8690	−0.914559
$199$	−15.6165	−1.10702	−0.553512	−	0.832841i	$-0.686713\pi$
$199$	−15.6165	−1.10702	−0.553512	+	0.832841i	$0.686713\pi$
$200$	35.3053	2.49646
$201$	1.79505	0.126613
$202$	5.78519	0.407045
$203$	−18.1503	−1.27390
$204$	−14.8357	−1.03871
$205$	−4.45861	−0.311403
$206$	−22.9445	−1.59862
$207$	−7.93223	−0.551328
$208$	−10.0132	−0.694291
$209$	1.86551	0.129040
$210$	−6.00791	−0.414585
$211$	10.7220	0.738135	0.369067	−	0.929403i	$-0.379677\pi$
$211$	10.7220	0.738135	0.369067	+	0.929403i	$0.379677\pi$
$212$	−13.2072	−0.907073
$213$	−1.42474	−0.0976219
$214$	−26.7522	−1.82875
$215$	3.37583	0.230230
$216$	−32.7184	−2.22621
$217$	42.5002	2.88510
$218$	−40.9526	−2.77366
$219$	−7.62351	−0.515149
$220$	−5.74974	−0.387648
$221$	−3.74319	−0.251794
$222$	5.30540	0.356075
$223$	16.4526	1.10175	0.550873	−	0.834589i	$-0.314295\pi$
$223$	16.4526	1.10175	0.550873	+	0.834589i	$0.314295\pi$
$224$	56.0531	3.74521
$225$	10.9557	0.730383
$226$	30.9787	2.06067
$227$	24.7655	1.64374	0.821872	−	0.569672i	$-0.192930\pi$
$227$	24.7655	1.64374	0.821872	+	0.569672i	$0.192930\pi$
$228$	3.52343	0.233345
$229$	18.5878	1.22832	0.614158	−	0.789183i	$-0.289496\pi$
$229$	18.5878	1.22832	0.614158	+	0.789183i	$0.289496\pi$
$230$	−4.99811	−0.329565
$231$	−8.55445	−0.562841
$232$	−27.2852	−1.79136
$233$	−23.9474	−1.56885	−0.784424	−	0.620224i	$-0.787042\pi$
$233$	−23.9474	−1.56885	−0.784424	+	0.620224i	$0.787042\pi$
$234$	−6.13262	−0.400902
$235$	0.846637	0.0552285
$236$	55.6565	3.62293
$237$	−5.51113	−0.357986
$238$	49.2088	3.18973
$239$	−9.32840	−0.603404	−0.301702	−	0.953402i	$-0.597555\pi$
$239$	−9.32840	−0.603404	−0.301702	+	0.953402i	$0.597555\pi$
$240$	−4.57611	−0.295386
$241$	−26.5400	−1.70959	−0.854797	−	0.518962i	$-0.826319\pi$
$241$	−26.5400	−1.70959	−0.854797	+	0.518962i	$0.826319\pi$
$242$	17.2958	1.11182
$243$	−15.8581	−1.01730
$244$	−4.48013	−0.286811
$245$	10.1957	0.651377
$246$	−16.9100	−1.07814
$247$	0.888994	0.0565653
$248$	63.8902	4.05703
$249$	−7.07199	−0.448169
$250$	14.2721	0.902645
$251$	−6.99970	−0.441817	−0.220909	−	0.975295i	$-0.570902\pi$
$251$	−6.99970	−0.441817	−0.220909	+	0.975295i	$0.570902\pi$
$252$	57.1663	3.60114
$253$	−7.11663	−0.447418
$254$	−37.4171	−2.34776
$255$	−1.71067	−0.107126
$256$	−13.3582	−0.834890
$257$	28.6673	1.78821	0.894107	−	0.447853i	$-0.147811\pi$
$257$	28.6673	1.78821	0.894107	+	0.447853i	$0.147811\pi$
$258$	12.8034	0.797102
$259$	−12.4780	−0.775346
$260$	−2.74000	−0.169927
$261$	−8.46700	−0.524094
$262$	5.06980	0.313213
$263$	−4.80013	−0.295989	−0.147994	−	0.988988i	$-0.547282\pi$
$263$	−4.80013	−0.295989	−0.147994	+	0.988988i	$0.547282\pi$
$264$	−12.8598	−0.791468
$265$	−1.52288	−0.0935499
$266$	−11.6869	−0.716569
$267$	9.10544	0.557244
$268$	−10.7623	−0.657410
$269$	0.988540	0.0602724	0.0301362	−	0.999546i	$-0.490406\pi$
$269$	0.988540	0.0602724	0.0301362	+	0.999546i	$0.490406\pi$
$270$	−6.39742	−0.389334
$271$	14.4614	0.878467	0.439233	−	0.898373i	$-0.355250\pi$
$271$	14.4614	0.878467	0.439233	+	0.898373i	$0.355250\pi$
$272$	37.4813	2.27264
$273$	−4.07656	−0.246724
$274$	25.3919	1.53398
$275$	9.82926	0.592727
$276$	−13.4413	−0.809073
$277$	−4.12998	−0.248147	−0.124073	−	0.992273i	$-0.539596\pi$
$277$	−4.12998	−0.248147	−0.124073	+	0.992273i	$0.539596\pi$
$278$	−5.76320	−0.345654
$279$	19.8261	1.18696
$280$	21.2419	1.26945
$281$	−18.1710	−1.08399	−0.541994	−	0.840382i	$-0.682330\pi$
$281$	−18.1710	−1.08399	−0.541994	+	0.840382i	$0.682330\pi$
$282$	3.21100	0.191212
$283$	11.0345	0.655931	0.327966	−	0.944690i	$-0.393637\pi$
$283$	11.0345	0.655931	0.327966	+	0.944690i	$0.393637\pi$
$284$	8.54209	0.506880
$285$	0.406277	0.0240657
$286$	−5.50205	−0.325343
$287$	39.7713	2.34763
$288$	26.1484	1.54081
$289$	−2.98850	−0.175794
$290$	−5.33506	−0.313286
$291$	5.33727	0.312877
$292$	45.7069	2.67480
$293$	1.02235	0.0597265	0.0298633	−	0.999554i	$-0.490493\pi$
$293$	1.02235	0.0597265	0.0298633	+	0.999554i	$0.490493\pi$
$294$	38.6686	2.25520
$295$	6.41759	0.373647
$296$	−18.7581	−1.09029
$297$	−9.10906	−0.528561
$298$	26.7908	1.55195
$299$	−3.39137	−0.196128
$300$	18.5647	1.07184
$301$	−30.1128	−1.73567
$302$	21.7880	1.25376
$303$	1.79395	0.103060
$304$	−8.90167	−0.510546
$305$	−0.516591	−0.0295799
$306$	22.9556	1.31228
$307$	−33.2990	−1.90047	−0.950236	−	0.311530i	$-0.899159\pi$
$307$	−33.2990	−1.90047	−0.950236	+	0.311530i	$0.899159\pi$
$308$	51.2884	2.92243
$309$	−7.11496	−0.404756
$310$	12.4924	0.709522
$311$	1.63927	0.0929547	0.0464773	−	0.998919i	$-0.485200\pi$
$311$	1.63927	0.0929547	0.0464773	+	0.998919i	$0.485200\pi$
$312$	−6.12826	−0.346944
$313$	−27.2970	−1.54292	−0.771460	−	0.636278i	$-0.780473\pi$
$313$	−27.2970	−1.54292	−0.771460	+	0.636278i	$0.780473\pi$
$314$	−35.9538	−2.02899
$315$	6.59168	0.371399
$316$	33.0421	1.85876
$317$	23.6522	1.32844	0.664221	−	0.747536i	$-0.268763\pi$
$317$	23.6522	1.32844	0.664221	+	0.747536i	$0.268763\pi$
$318$	−5.77577	−0.323889
$319$	−7.59641	−0.425317
$320$	5.21958	0.291783
$321$	−8.29571	−0.463021
$322$	44.5837	2.48455
$323$	−3.32768	−0.185157
$324$	17.0003	0.944464
$325$	4.68406	0.259825
$326$	−51.7100	−2.86395
$327$	−12.6992	−0.702266
$328$	59.7880	3.30124
$329$	−7.55210	−0.416361
$330$	−2.51448	−0.138418
$331$	−1.34847	−0.0741188	−0.0370594	−	0.999313i	$-0.511799\pi$
$331$	−1.34847	−0.0741188	−0.0370594	+	0.999313i	$0.511799\pi$
$332$	42.4003	2.32702
$333$	−5.82092	−0.318984
$334$	−17.9096	−0.979969
$335$	−1.24097	−0.0678013
$336$	40.8194	2.22688
$337$	−11.3712	−0.619431	−0.309715	−	0.950829i	$-0.600234\pi$
$337$	−11.3712	−0.619431	−0.309715	+	0.950829i	$0.600234\pi$
$338$	−2.62196	−0.142616
$339$	9.60630	0.521743
$340$	10.2563	0.556228
$341$	17.7875	0.963248
$342$	−5.45186	−0.294803
$343$	−55.8494	−3.01558
$344$	−45.2683	−2.44070
$345$	−1.54988	−0.0834429
$346$	57.1219	3.07089
$347$	22.9134	1.23006	0.615029	−	0.788504i	$-0.289144\pi$
$347$	22.9134	1.23006	0.615029	+	0.788504i	$0.289144\pi$
$348$	−14.3475	−0.769107
$349$	31.5274	1.68763	0.843813	−	0.536638i	$-0.180306\pi$
$349$	31.5274	1.68763	0.843813	+	0.536638i	$0.180306\pi$
$350$	−61.5776	−3.29146
$351$	−4.34085	−0.231698
$352$	23.4598	1.25041
$353$	20.9025	1.11253	0.556263	−	0.831007i	$-0.312235\pi$
$353$	20.9025	1.11253	0.556263	+	0.831007i	$0.312235\pi$
$354$	24.3397	1.29364
$355$	0.984964	0.0522765
$356$	−54.5918	−2.89336
$357$	15.2593	0.807610
$358$	−5.41729	−0.286313
$359$	−10.0267	−0.529187	−0.264593	−	0.964360i	$-0.585238\pi$
$359$	−10.0267	−0.529187	−0.264593	+	0.964360i	$0.585238\pi$
$360$	9.90923	0.522262
$361$	−18.2097	−0.958405
$362$	3.04188	0.159878
$363$	5.36333	0.281502
$364$	24.4411	1.28106
$365$	5.27034	0.275862
$366$	−1.95925	−0.102412
$367$	−37.6234	−1.96392	−0.981962	−	0.189079i	$-0.939450\pi$
$367$	−37.6234	−1.96392	−0.981962	+	0.189079i	$0.939450\pi$
$368$	33.9585	1.77021
$369$	18.5531	0.965835
$370$	−3.66777	−0.190678
$371$	13.5843	0.705261
$372$	33.5957	1.74186
$373$	4.63586	0.240036	0.120018	−	0.992772i	$-0.461705\pi$
$373$	4.63586	0.240036	0.120018	+	0.992772i	$0.461705\pi$
$374$	20.5953	1.06496
$375$	4.42569	0.228541
$376$	−11.3530	−0.585487
$377$	−3.62001	−0.186440
$378$	57.0657	2.93514
$379$	14.7956	0.760000	0.380000	−	0.924987i	$-0.375924\pi$
$379$	14.7956	0.760000	0.380000	+	0.924987i	$0.375924\pi$
$380$	−2.43584	−0.124956
$381$	−11.6028	−0.594431
$382$	−6.54125	−0.334680
$383$	0.137910	0.00704685	0.00352343	−	0.999994i	$-0.498878\pi$
$383$	0.137910	0.00704685	0.00352343	+	0.999994i	$0.498878\pi$
$384$	1.61680	0.0825070
$385$	5.91392	0.301401
$386$	−36.7587	−1.87097
$387$	−14.0474	−0.714071
$388$	−31.9997	−1.62454
$389$	9.66166	0.489866	0.244933	−	0.969540i	$-0.421234\pi$
$389$	9.66166	0.489866	0.244933	+	0.969540i	$0.421234\pi$
$390$	−1.19826	−0.0606760
$391$	12.6946	0.641992
$392$	−136.719	−6.90536
$393$	1.57211	0.0793027
$394$	57.5095	2.89729
$395$	3.80999	0.191702
$396$	23.9257	1.20231
$397$	−20.2037	−1.01400	−0.506998	−	0.861947i	$-0.669245\pi$
$397$	−20.2037	−1.01400	−0.506998	+	0.861947i	$0.669245\pi$
$398$	40.9459	2.05243
$399$	−3.62403	−0.181429
$400$	−46.9024	−2.34512
$401$	6.18166	0.308697	0.154349	−	0.988016i	$-0.450672\pi$
$401$	6.18166	0.308697	0.154349	+	0.988016i	$0.450672\pi$
$402$	−4.70656	−0.234742
$403$	8.47651	0.422245
$404$	−10.7557	−0.535115
$405$	1.96026	0.0974062
$406$	47.5894	2.36182
$407$	−5.22240	−0.258865
$408$	22.9392	1.13566
$409$	7.26938	0.359448	0.179724	−	0.983717i	$-0.442480\pi$
$409$	7.26938	0.359448	0.179724	+	0.983717i	$0.442480\pi$
$410$	11.6903	0.577344
$411$	7.87387	0.388389
$412$	42.6579	2.10160
$413$	−57.2456	−2.81687
$414$	20.7980	1.02217
$415$	4.88906	0.239994
$416$	11.1796	0.548125
$417$	−1.78714	−0.0875164
$418$	−4.89129	−0.239241
$419$	24.0786	1.17632	0.588159	−	0.808745i	$-0.299853\pi$
$419$	24.0786	1.17632	0.588159	+	0.808745i	$0.299853\pi$
$420$	11.1698	0.545028
$421$	−3.07000	−0.149623	−0.0748114	−	0.997198i	$-0.523835\pi$
$421$	−3.07000	−0.149623	−0.0748114	+	0.997198i	$0.523835\pi$
$422$	−28.1128	−1.36851
$423$	−3.52301	−0.171294
$424$	20.4212	0.991739
$425$	−17.5333	−0.850492
$426$	3.73563	0.180992
$427$	4.60805	0.222999
$428$	49.7371	2.40413
$429$	−1.70615	−0.0823739
$430$	−8.85130	−0.426848
$431$	−33.3033	−1.60416	−0.802081	−	0.597215i	$-0.796274\pi$
$431$	−33.3033	−1.60416	−0.802081	+	0.597215i	$0.796274\pi$
$432$	43.4658	2.09125
$433$	18.3355	0.881148	0.440574	−	0.897716i	$-0.354775\pi$
$433$	18.3355	0.881148	0.440574	+	0.897716i	$0.354775\pi$
$434$	−111.434	−5.34900
$435$	−1.65437	−0.0793210
$436$	76.1381	3.64636
$437$	−3.01491	−0.144223
$438$	19.9886	0.955090
$439$	−9.67746	−0.461880	−0.230940	−	0.972968i	$-0.574180\pi$
$439$	−9.67746	−0.461880	−0.230940	+	0.972968i	$0.574180\pi$
$440$	8.89035	0.423831
$441$	−42.4260	−2.02028
$442$	9.81451	0.466829
$443$	−17.5548	−0.834055	−0.417027	−	0.908894i	$-0.636928\pi$
$443$	−17.5548	−0.834055	−0.417027	+	0.908894i	$0.636928\pi$
$444$	−9.86367	−0.468109
$445$	−6.29483	−0.298404
$446$	−43.1381	−2.04265
$447$	8.30768	0.392940
$448$	−46.5592	−2.19972
$449$	−34.1608	−1.61215	−0.806075	−	0.591814i	$-0.798412\pi$
$449$	−34.1608	−1.61215	−0.806075	+	0.591814i	$0.798412\pi$
$450$	−28.7255	−1.35413
$451$	16.6454	0.783803
$452$	−57.5948	−2.70903
$453$	6.75632	0.317440
$454$	−64.9342	−3.04751
$455$	2.81823	0.132121
$456$	−5.44798	−0.255125
$457$	0.967106	0.0452393	0.0226196	−	0.999744i	$-0.492799\pi$
$457$	0.967106	0.0452393	0.0226196	+	0.999744i	$0.492799\pi$
$458$	−48.7365	−2.27731
$459$	16.2487	0.758422
$460$	9.29236	0.433258
$461$	−31.5041	−1.46729	−0.733647	−	0.679531i	$-0.762183\pi$
$461$	−31.5041	−1.46729	−0.733647	+	0.679531i	$0.762183\pi$
$462$	22.4294	1.04351
$463$	−1.00000	−0.0464739
$463$	−1.00000	−0.0464739
$464$	36.2479	1.68277
$465$	3.87383	0.179644
$466$	62.7893	2.90866
$467$	−9.75935	−0.451609	−0.225804	−	0.974173i	$-0.572501\pi$
$467$	−9.75935	−0.451609	−0.225804	+	0.974173i	$0.572501\pi$
$468$	11.4016	0.527040
$469$	11.0696	0.511145
$470$	−2.21985	−0.102394
$471$	−11.1491	−0.513722
$472$	−86.0569	−3.96109
$473$	−12.6031	−0.579489
$474$	14.4500	0.663709
$475$	4.16410	0.191062
$476$	−91.4877	−4.19333
$477$	6.33698	0.290151
$478$	24.4587	1.11872
$479$	9.44267	0.431447	0.215723	−	0.976455i	$-0.430789\pi$
$479$	9.44267	0.431447	0.215723	+	0.976455i	$0.430789\pi$
$480$	5.10916	0.233200
$481$	−2.48870	−0.113475
$482$	69.5870	3.16960
$483$	13.8251	0.629065
$484$	−32.1559	−1.46163
$485$	−3.68980	−0.167545
$486$	41.5793	1.88607
$487$	−4.62842	−0.209734	−0.104867	−	0.994486i	$-0.533442\pi$
$487$	−4.62842	−0.209734	−0.104867	+	0.994486i	$0.533442\pi$
$488$	6.92725	0.313582
$489$	−16.0350	−0.725126
$490$	−26.7327	−1.20766
$491$	−0.442718	−0.0199796	−0.00998978	−	0.999950i	$-0.503180\pi$
$491$	−0.442718	−0.0199796	−0.00998978	+	0.999950i	$0.503180\pi$
$492$	31.4386	1.41736
$493$	13.5504	0.610279
$494$	−2.33091	−0.104873
$495$	2.75881	0.123999
$496$	−84.8770	−3.81109
$497$	−8.78599	−0.394106
$498$	18.5425	0.830909
$499$	23.1224	1.03510	0.517551	−	0.855653i	$-0.326844\pi$
$499$	23.1224	1.03510	0.517551	+	0.855653i	$0.326844\pi$
$500$	−26.5343	−1.18665
$501$	−5.55366	−0.248119
$502$	18.3530	0.819133
$503$	23.9471	1.06775	0.533873	−	0.845564i	$-0.320736\pi$
$503$	23.9471	1.06775	0.533873	+	0.845564i	$0.320736\pi$
$504$	−88.3914	−3.93727
$505$	−1.24021	−0.0551885
$506$	18.6595	0.829517
$507$	−0.813055	−0.0361090
$508$	69.5650	3.08645
$509$	−15.7555	−0.698351	−0.349175	−	0.937057i	$-0.613538\pi$
$509$	−15.7555	−0.698351	−0.349175	+	0.937057i	$0.613538\pi$
$510$	4.48530	0.198613
$511$	−47.0120	−2.07969
$512$	39.0019	1.72366
$513$	−3.85899	−0.170379
$514$	−75.1645	−3.31536
$515$	4.91876	0.216747
$516$	−23.8037	−1.04790
$517$	−3.16077	−0.139010
$518$	32.7169	1.43750
$519$	17.7131	0.777521
$520$	4.23663	0.185788
$521$	−5.89432	−0.258235	−0.129117	−	0.991629i	$-0.541214\pi$
$521$	−5.89432	−0.258235	−0.129117	+	0.991629i	$0.541214\pi$
$522$	22.2001	0.971674
$523$	21.5755	0.943432	0.471716	−	0.881751i	$-0.343635\pi$
$523$	21.5755	0.943432	0.471716	+	0.881751i	$0.343635\pi$
$524$	−9.42564	−0.411761
$525$	−19.0948	−0.833367
$526$	12.5858	0.548765
$527$	−31.7292	−1.38215
$528$	17.0841	0.743488
$529$	−11.4986	−0.499938
$530$	3.99294	0.173442
$531$	−26.7047	−1.15889
$532$	21.7280	0.942027
$533$	7.93225	0.343584
$534$	−23.8741	−1.03313
$535$	5.73505	0.247948
$536$	16.6408	0.718773
$537$	−1.67987	−0.0724918
$538$	−2.59192	−0.111745
$539$	−38.0637	−1.63952
$540$	11.8939	0.511833
$541$	11.6991	0.502982	0.251491	−	0.967860i	$-0.419079\pi$
$541$	11.6991	0.502982	0.251491	+	0.967860i	$0.419079\pi$
$542$	−37.9172	−1.62868
$543$	0.943270	0.0404796
$544$	−41.8474	−1.79419
$545$	8.77928	0.376063
$546$	10.6886	0.457429
$547$	−17.9749	−0.768552	−0.384276	−	0.923218i	$-0.625549\pi$
$547$	−17.9749	−0.768552	−0.384276	+	0.923218i	$0.625549\pi$
$548$	−47.2079	−2.01662
$549$	2.14963	0.0917439
$550$	−25.7719	−1.09892
$551$	−3.21817	−0.137099
$552$	20.7832	0.884592
$553$	−33.9856	−1.44521
$554$	10.8287	0.460066
$555$	−1.13735	−0.0482779
$556$	10.7148	0.454409
$557$	31.7006	1.34320	0.671599	−	0.740915i	$-0.265608\pi$
$557$	31.7006	1.34320	0.671599	+	0.740915i	$0.265608\pi$
$558$	−51.9832	−2.20062
$559$	−6.00589	−0.254022
$560$	−28.2195	−1.19249
$561$	6.38646	0.269637
$562$	47.6436	2.00972
$563$	−24.2265	−1.02102	−0.510512	−	0.859870i	$-0.670544\pi$
$563$	−24.2265	−1.02102	−0.510512	+	0.859870i	$0.670544\pi$
$564$	−5.96981	−0.251374
$565$	−6.64109	−0.279393
$566$	−28.9320	−1.21610
$567$	−17.4858	−0.734333
$568$	−13.2079	−0.554192
$569$	14.8480	0.622462	0.311231	−	0.950334i	$-0.399259\pi$
$569$	14.8480	0.622462	0.311231	+	0.950334i	$0.399259\pi$
$570$	−1.06524	−0.0446181
$571$	16.6210	0.695568	0.347784	−	0.937575i	$-0.386934\pi$
$571$	16.6210	0.695568	0.347784	+	0.937575i	$0.386934\pi$
$572$	10.2293	0.427708
$573$	−2.02840	−0.0847378
$574$	−104.279	−4.35252
$575$	−15.8854	−0.662467
$576$	−21.7196	−0.904983
$577$	−25.3377	−1.05482	−0.527411	−	0.849610i	$-0.676837\pi$
$577$	−25.3377	−1.05482	−0.527411	+	0.849610i	$0.676837\pi$
$578$	7.83575	0.325924
$579$	−11.3986	−0.473712
$580$	9.91882	0.411857
$581$	−43.6110	−1.80929
$582$	−13.9941	−0.580076
$583$	5.68541	0.235466
$584$	−70.6728	−2.92446
$585$	1.31469	0.0543557
$586$	−2.68057	−0.110733
$587$	15.6762	0.647027	0.323514	−	0.946224i	$-0.395136\pi$
$587$	15.6762	0.647027	0.323514	+	0.946224i	$0.395136\pi$
$588$	−71.8918	−2.96477
$589$	7.53556	0.310497
$590$	−16.8267	−0.692744
$591$	17.8334	0.733567
$592$	24.9198	1.02420
$593$	−34.0661	−1.39893	−0.699464	−	0.714668i	$-0.746578\pi$
$593$	−34.0661	−1.39893	−0.699464	+	0.714668i	$0.746578\pi$
$594$	23.8836	0.979956
$595$	−10.5492	−0.432475
$596$	−49.8089	−2.04025
$597$	12.6971	0.519657
$598$	8.89206	0.363623
$599$	−25.0885	−1.02509	−0.512543	−	0.858661i	$-0.671297\pi$
$599$	−25.0885	−1.02509	−0.512543	+	0.858661i	$0.671297\pi$
$600$	−28.7051	−1.17188
$601$	42.8553	1.74810	0.874052	−	0.485832i	$-0.161483\pi$
$601$	42.8553	1.74810	0.874052	+	0.485832i	$0.161483\pi$
$602$	78.9546	3.21795
$603$	5.16388	0.210290
$604$	−40.5077	−1.64823
$605$	−3.70781	−0.150744
$606$	−4.70368	−0.191074
$607$	20.5538	0.834253	0.417126	−	0.908849i	$-0.363037\pi$
$607$	20.5538	0.834253	0.417126	+	0.908849i	$0.363037\pi$
$608$	9.93859	0.403063
$609$	14.7572	0.597991
$610$	1.35448	0.0548414
$611$	−1.50624	−0.0609359
$612$	−42.6784	−1.72517
$613$	7.10589	0.287004	0.143502	−	0.989650i	$-0.454164\pi$
$613$	7.10589	0.287004	0.143502	+	0.989650i	$0.454164\pi$
$614$	87.3086	3.52349
$615$	3.62510	0.146178
$616$	−79.3029	−3.19521
$617$	24.8158	0.999045	0.499522	−	0.866301i	$-0.333509\pi$
$617$	24.8158	0.999045	0.499522	+	0.866301i	$0.333509\pi$
$618$	18.6552	0.750421
$619$	13.1195	0.527317	0.263658	−	0.964616i	$-0.415071\pi$
$619$	13.1195	0.527317	0.263658	+	0.964616i	$0.415071\pi$
$620$	−23.2256	−0.932763
$621$	14.7215	0.590752
$622$	−4.29811	−0.172339
$623$	56.1506	2.24963
$624$	8.14128	0.325912
$625$	20.3607	0.814428
$626$	71.5718	2.86059
$627$	−1.51676	−0.0605736
$628$	66.8445	2.66738
$629$	9.31567	0.371440
$630$	−17.2831	−0.688577
$631$	−45.4849	−1.81072	−0.905362	−	0.424640i	$-0.860401\pi$
$631$	−45.4849	−1.81072	−0.905362	+	0.424640i	$0.860401\pi$
$632$	−51.0902	−2.03226
$633$	−8.71760	−0.346493
$634$	−62.0153	−2.46294
$635$	8.02134	0.318317
$636$	10.7382	0.425796
$637$	−18.1390	−0.718692
$638$	19.9175	0.788541
$639$	−4.09861	−0.162139
$640$	−1.11774	−0.0441824
$641$	−41.4687	−1.63791	−0.818957	−	0.573855i	$-0.805447\pi$
$641$	−41.4687	−1.63791	−0.818957	+	0.573855i	$0.805447\pi$
$642$	21.7510	0.858445
$643$	−11.4282	−0.450683	−0.225342	−	0.974280i	$-0.572350\pi$
$643$	−11.4282	−0.450683	−0.225342	+	0.974280i	$0.572350\pi$
$644$	−82.8889	−3.26628
$645$	−2.74474	−0.108074
$646$	8.72504	0.343282
$647$	−28.1813	−1.10792	−0.553960	−	0.832544i	$-0.686884\pi$
$647$	−28.1813	−1.10792	−0.553960	+	0.832544i	$0.686884\pi$
$648$	−26.2862	−1.03262
$649$	−23.9589	−0.940470
$650$	−12.2814	−0.481717
$651$	−34.5550	−1.35432
$652$	96.1379	3.76505
$653$	9.95814	0.389692	0.194846	−	0.980834i	$-0.437579\pi$
$653$	9.95814	0.389692	0.194846	+	0.980834i	$0.437579\pi$
$654$	33.2967	1.30201
$655$	−1.08684	−0.0424665
$656$	−79.4273	−3.10111
$657$	−21.9308	−0.855602
$658$	19.8013	0.771936
$659$	−15.6540	−0.609792	−0.304896	−	0.952386i	$-0.598622\pi$
$659$	−15.6540	−0.609792	−0.304896	+	0.952386i	$0.598622\pi$
$660$	4.67486	0.181969
$661$	−6.97540	−0.271312	−0.135656	−	0.990756i	$-0.543314\pi$
$661$	−6.97540	−0.271312	−0.135656	+	0.990756i	$0.543314\pi$
$662$	3.53565	0.137417
$663$	3.04342	0.118197
$664$	−65.5600	−2.54422
$665$	2.50539	0.0971549
$666$	15.2622	0.591399
$667$	12.2768	0.475360
$668$	33.2971	1.28830
$669$	−13.3769	−0.517179
$670$	3.25377	0.125704
$671$	1.92860	0.0744528
$672$	−45.5743	−1.75807
$673$	44.0869	1.69943	0.849713	−	0.527245i	$-0.176775\pi$
$673$	44.0869	1.69943	0.849713	+	0.527245i	$0.176775\pi$
$674$	29.8149	1.14843
$675$	−20.3328	−0.782610
$676$	4.87469	0.187488
$677$	−33.0623	−1.27069	−0.635345	−	0.772229i	$-0.719142\pi$
$677$	−33.0623	−1.27069	−0.635345	+	0.772229i	$0.719142\pi$
$678$	−25.1874	−0.967315
$679$	32.9135	1.26310
$680$	−15.8585	−0.608146
$681$	−20.1357	−0.771602
$682$	−46.6382	−1.78587
$683$	39.7278	1.52014	0.760072	−	0.649839i	$-0.225164\pi$
$683$	39.7278	1.52014	0.760072	+	0.649839i	$0.225164\pi$
$684$	10.1360	0.387558
$685$	−5.44342	−0.207982
$686$	146.435	5.59092
$687$	−15.1129	−0.576593
$688$	60.1382	2.29275
$689$	2.70934	0.103218
$690$	4.06373	0.154704
$691$	−2.89062	−0.109964	−0.0549822	−	0.998487i	$-0.517510\pi$
$691$	−2.89062	−0.109964	−0.0549822	+	0.998487i	$0.517510\pi$
$692$	−106.200	−4.03710
$693$	−24.6089	−0.934813
$694$	−60.0782	−2.28054
$695$	1.23549	0.0468650
$696$	22.1844	0.840896
$697$	−29.6920	−1.12466
$698$	−82.6638	−3.12887
$699$	19.4706	0.736445
$700$	114.483	4.32707
$701$	3.01235	0.113775	0.0568874	−	0.998381i	$-0.481882\pi$
$701$	3.01235	0.113775	0.0568874	+	0.998381i	$0.481882\pi$
$702$	11.3816	0.429569
$703$	−2.21244	−0.0834436
$704$	−19.4864	−0.734420
$705$	−0.688362	−0.0259252
$706$	−54.8054	−2.06263
$707$	11.0628	0.416059
$708$	−45.2517	−1.70066
$709$	−28.9013	−1.08541	−0.542705	−	0.839923i	$-0.682600\pi$
$709$	−28.9013	−1.08541	−0.542705	+	0.839923i	$0.682600\pi$
$710$	−2.58254	−0.0969210
$711$	−15.8541	−0.594573
$712$	84.4108	3.16343
$713$	−28.7470	−1.07658
$714$	−40.0094	−1.49731
$715$	1.17951	0.0441112
$716$	10.0717	0.376397
$717$	7.58450	0.283248
$718$	26.2895	0.981116
$719$	−42.2809	−1.57681	−0.788405	−	0.615156i	$-0.789093\pi$
$719$	−42.2809	−1.57681	−0.788405	+	0.615156i	$0.789093\pi$
$720$	−13.1642	−0.490602
$721$	−43.8759	−1.63403
$722$	47.7451	1.77689
$723$	21.5785	0.802513
$724$	−5.65539	−0.210181
$725$	−16.9563	−0.629743
$726$	−14.0624	−0.521906
$727$	27.2812	1.01180	0.505902	−	0.862591i	$-0.331160\pi$
$727$	27.2812	1.01180	0.505902	+	0.862591i	$0.331160\pi$
$728$	−37.7912	−1.40064
$729$	2.43106	0.0900391
$730$	−13.8186	−0.511450
$731$	22.4812	0.831497
$732$	3.64259	0.134634
$733$	−3.17902	−0.117420	−0.0587099	−	0.998275i	$-0.518699\pi$
$733$	−3.17902	−0.117420	−0.0587099	+	0.998275i	$0.518699\pi$
$734$	98.6471	3.64113
$735$	−8.28964	−0.305768
$736$	−37.9142	−1.39754
$737$	4.63293	0.170656
$738$	−48.6455	−1.79066
$739$	−39.4584	−1.45150	−0.725750	−	0.687958i	$-0.758507\pi$
$739$	−39.4584	−1.45150	−0.725750	+	0.687958i	$0.758507\pi$
$740$	6.81902	0.250672
$741$	−0.722801	−0.0265527
$742$	−35.6175	−1.30756
$743$	10.3307	0.378996	0.189498	−	0.981881i	$-0.439314\pi$
$743$	10.3307	0.378996	0.189498	+	0.981881i	$0.439314\pi$
$744$	−51.9462	−1.90444
$745$	−5.74332	−0.210419
$746$	−12.1551	−0.445028
$747$	−20.3442	−0.744357
$748$	−38.2902	−1.40003
$749$	−51.1573	−1.86925
$750$	−11.6040	−0.423717
$751$	−36.0409	−1.31515	−0.657576	−	0.753388i	$-0.728418\pi$
$751$	−36.0409	−1.31515	−0.657576	+	0.753388i	$0.728418\pi$
$752$	15.0823	0.549994
$753$	5.69114	0.207397
$754$	9.49153	0.345661
$755$	−4.67082	−0.169989
$756$	−106.095	−3.85864
$757$	−10.1689	−0.369593	−0.184797	−	0.982777i	$-0.559163\pi$
$757$	−10.1689	−0.369593	−0.184797	+	0.982777i	$0.559163\pi$
$758$	−38.7935	−1.40905
$759$	5.78621	0.210026
$760$	3.76634	0.136619
$761$	7.27332	0.263658	0.131829	−	0.991272i	$-0.457915\pi$
$761$	7.27332	0.263658	0.131829	+	0.991272i	$0.457915\pi$
$762$	30.4222	1.10208
$763$	−78.3122	−2.83509
$764$	12.1613	0.439982
$765$	−4.92113	−0.177924
$766$	−0.361594	−0.0130649
$767$	−11.4174	−0.412260
$768$	10.8610	0.391912
$769$	46.5104	1.67721	0.838603	−	0.544743i	$-0.183373\pi$
$769$	46.5104	1.67721	0.838603	+	0.544743i	$0.183373\pi$
$770$	−15.5061	−0.558800
$771$	−23.3081	−0.839419
$772$	68.3408	2.45964
$773$	−41.2119	−1.48229	−0.741145	−	0.671345i	$-0.765717\pi$
$773$	−41.2119	−1.48229	−0.741145	+	0.671345i	$0.765717\pi$
$774$	36.8318	1.32389
$775$	39.7045	1.42623
$776$	49.4785	1.77618
$777$	10.1453	0.363961
$778$	−25.3325	−0.908215
$779$	7.05172	0.252654
$780$	2.22777	0.0797669
$781$	−3.67719	−0.131580
$782$	−33.2847	−1.19026
$783$	15.7139	0.561570
$784$	181.629	6.48675
$785$	7.70765	0.275098
$786$	−4.12202	−0.147028
$787$	−15.7266	−0.560594	−0.280297	−	0.959913i	$-0.590433\pi$
$787$	−15.7266	−0.560594	−0.280297	+	0.959913i	$0.590433\pi$
$788$	−106.920	−3.80888
$789$	3.90277	0.138942
$790$	−9.98966	−0.355416
$791$	59.2393	2.10631
$792$	−36.9943	−1.31454
$793$	0.919060	0.0326368
$794$	52.9734	1.87996
$795$	1.23819	0.0439140
$796$	−76.1256	−2.69820
$797$	−42.4618	−1.50407	−0.752037	−	0.659120i	$-0.770929\pi$
$797$	−42.4618	−1.50407	−0.752037	+	0.659120i	$0.770929\pi$
$798$	9.50208	0.336370
$799$	5.63815	0.199463
$800$	52.3659	1.85141
$801$	26.1939	0.925516
$802$	−16.2081	−0.572327
$803$	−19.6759	−0.694346
$804$	8.75032	0.308600
$805$	−9.55769	−0.336864
$806$	−22.2251	−0.782845
$807$	−0.803737	−0.0282929
$808$	16.6306	0.585063
$809$	−10.0531	−0.353449	−0.176724	−	0.984260i	$-0.556550\pi$
$809$	−10.0531	−0.353449	−0.176724	+	0.984260i	$0.556550\pi$
$810$	−5.13973	−0.180592
$811$	−2.61121	−0.0916919	−0.0458460	−	0.998949i	$-0.514598\pi$
$811$	−2.61121	−0.0916919	−0.0458460	+	0.998949i	$0.514598\pi$
$812$	−88.4770	−3.10493
$813$	−11.7579	−0.412368
$814$	13.6929	0.479937
$815$	11.0854	0.388305
$816$	−30.4744	−1.06682
$817$	−5.33920	−0.186795
$818$	−19.0601	−0.666419
$819$	−11.7272	−0.409780
$820$	−21.7343	−0.758996
$821$	5.35399	0.186855	0.0934277	−	0.995626i	$-0.470218\pi$
$821$	5.35399	0.186855	0.0934277	+	0.995626i	$0.470218\pi$
$822$	−20.6450	−0.720077
$823$	1.24345	0.0433439	0.0216719	−	0.999765i	$-0.493101\pi$
$823$	1.24345	0.0433439	0.0216719	+	0.999765i	$0.493101\pi$
$824$	−65.9584	−2.29777
$825$	−7.99173	−0.278236
$826$	150.096	5.22251
$827$	5.43062	0.188841	0.0944206	−	0.995532i	$-0.469900\pi$
$827$	5.43062	0.188841	0.0944206	+	0.995532i	$0.469900\pi$
$828$	−38.6671	−1.34378
$829$	−19.9964	−0.694502	−0.347251	−	0.937772i	$-0.612885\pi$
$829$	−19.9964	−0.694502	−0.347251	+	0.937772i	$0.612885\pi$
$830$	−12.8189	−0.444951
$831$	3.35790	0.116484
$832$	−9.28607	−0.321937
$833$	67.8976	2.35251
$834$	4.68580	0.162256
$835$	3.83939	0.132868
$836$	9.09377	0.314515
$837$	−36.7953	−1.27183
$838$	−63.1333	−2.18090
$839$	−9.14555	−0.315740	−0.157870	−	0.987460i	$-0.550463\pi$
$839$	−9.14555	−0.315740	−0.157870	+	0.987460i	$0.550463\pi$
$840$	−17.2709	−0.595901
$841$	−15.8955	−0.548121
$842$	8.04943	0.277402
$843$	14.7740	0.508843
$844$	52.2665	1.79909
$845$	0.562087	0.0193364
$846$	9.23719	0.317581
$847$	33.0741	1.13644
$848$	−27.1291	−0.931619
$849$	−8.97163	−0.307906
$850$	45.9718	1.57682
$851$	8.44010	0.289323
$852$	−6.94519	−0.237938
$853$	21.2739	0.728404	0.364202	−	0.931320i	$-0.381342\pi$
$853$	21.2739	0.728404	0.364202	+	0.931320i	$0.381342\pi$
$854$	−12.0821	−0.413442
$855$	1.16875	0.0399704
$856$	−76.9043	−2.62854
$857$	10.3519	0.353613	0.176806	−	0.984246i	$-0.443423\pi$
$857$	10.3519	0.353613	0.176806	+	0.984246i	$0.443423\pi$
$858$	4.47347	0.152722
$859$	−35.8691	−1.22384	−0.611919	−	0.790920i	$-0.709602\pi$
$859$	−35.8691	−1.22384	−0.611919	+	0.790920i	$0.709602\pi$
$860$	16.4561	0.561149
$861$	−32.3363	−1.10202
$862$	87.3199	2.97413
$863$	−25.9306	−0.882689	−0.441344	−	0.897338i	$-0.645498\pi$
$863$	−25.9306	−0.882689	−0.441344	+	0.897338i	$0.645498\pi$
$864$	−48.5290	−1.65099
$865$	−12.2456	−0.416362
$866$	−48.0750	−1.63366
$867$	2.42982	0.0825209
$868$	207.175	7.03198
$869$	−14.2239	−0.482513
$870$	4.33770	0.147062
$871$	2.20779	0.0748080
$872$	−117.726	−3.98671
$873$	15.3539	0.519651
$874$	7.90498	0.267390
$875$	27.2919	0.922636
$876$	−37.1622	−1.25560
$877$	51.0176	1.72274	0.861372	−	0.507975i	$-0.169606\pi$
$877$	51.0176	1.72274	0.861372	+	0.507975i	$0.169606\pi$
$878$	25.3739	0.856329
$879$	−0.831229	−0.0280367
$880$	−11.8107	−0.398138
$881$	32.8067	1.10528	0.552642	−	0.833418i	$-0.313620\pi$
$881$	32.8067	1.10528	0.552642	+	0.833418i	$0.313620\pi$
$882$	111.239	3.74562
$883$	27.7138	0.932644	0.466322	−	0.884615i	$-0.345579\pi$
$883$	27.7138	0.932644	0.466322	+	0.884615i	$0.345579\pi$
$884$	−18.2469	−0.613710
$885$	−5.21785	−0.175396
$886$	46.0281	1.54634
$887$	−1.16562	−0.0391378	−0.0195689	−	0.999809i	$-0.506229\pi$
$887$	−1.16562	−0.0391378	−0.0195689	+	0.999809i	$0.506229\pi$
$888$	15.2514	0.511803
$889$	−71.5513	−2.39975
$890$	16.5048	0.553243
$891$	−7.31829	−0.245172
$892$	80.2012	2.68534
$893$	−1.33904	−0.0448092
$894$	−21.7824	−0.728513
$895$	1.16134	0.0388193
$896$	9.97034	0.333086
$897$	2.75737	0.0920660
$898$	89.5684	2.98894
$899$	−30.6851	−1.02340
$900$	53.4058	1.78019
$901$	−10.1416	−0.337865
$902$	−43.6437	−1.45318
$903$	24.4834	0.814755
$904$	89.0540	2.96189
$905$	−0.652108	−0.0216768
$906$	−17.7148	−0.588535
$907$	19.6835	0.653578	0.326789	−	0.945097i	$-0.394033\pi$
$907$	19.6835	0.653578	0.326789	+	0.945097i	$0.394033\pi$
$908$	120.724	4.00637
$909$	5.16073	0.171170
$910$	−7.38930	−0.244953
$911$	35.2446	1.16771	0.583853	−	0.811859i	$-0.301544\pi$
$911$	35.2446	1.16771	0.583853	+	0.811859i	$0.301544\pi$
$912$	7.23755	0.239659
$913$	−18.2524	−0.604067
$914$	−2.53571	−0.0838740
$915$	0.420017	0.0138853
$916$	90.6097	2.99383
$917$	9.69478	0.320150
$918$	−42.6034	−1.40612
$919$	15.7467	0.519435	0.259718	−	0.965685i	$-0.416371\pi$
$919$	15.7467	0.519435	0.259718	+	0.965685i	$0.416371\pi$
$920$	−14.3680	−0.473699
$921$	27.0739	0.892115
$922$	82.6026	2.72037
$923$	−1.75234	−0.0576788
$924$	−41.7003	−1.37184
$925$	−11.6572	−0.383286
$926$	2.62196	0.0861630
$927$	−20.4678	−0.672252
$928$	−40.4703	−1.32850
$929$	−29.4776	−0.967129	−0.483564	−	0.875309i	$-0.660658\pi$
$929$	−29.4776	−0.967129	−0.483564	+	0.875309i	$0.660658\pi$
$930$	−10.1570	−0.333062
$931$	−16.1254	−0.528489
$932$	−116.736	−3.82382
$933$	−1.33282	−0.0436346
$934$	25.5887	0.837286
$935$	−4.41513	−0.144390
$936$	−17.6294	−0.576234
$937$	39.6974	1.29686	0.648428	−	0.761276i	$-0.275427\pi$
$937$	39.6974	1.29686	0.648428	+	0.761276i	$0.275427\pi$
$938$	−29.0240	−0.947667
$939$	22.1940	0.724274
$940$	4.12709	0.134611
$941$	27.4728	0.895587	0.447793	−	0.894137i	$-0.352210\pi$
$941$	27.4728	0.895587	0.447793	+	0.894137i	$0.352210\pi$
$942$	29.2324	0.952444
$943$	−26.9012	−0.876025
$944$	114.325	3.72097
$945$	−12.2335	−0.397957
$946$	33.0447	1.07438
$947$	18.9899	0.617088	0.308544	−	0.951210i	$-0.400158\pi$
$947$	18.9899	0.617088	0.308544	+	0.951210i	$0.400158\pi$
$948$	−26.8650	−0.872536
$949$	−9.37638	−0.304370
$950$	−10.9181	−0.354230
$951$	−19.2306	−0.623594
$952$	141.460	4.58474
$953$	−20.1527	−0.652811	−0.326405	−	0.945230i	$-0.605837\pi$
$953$	−20.1527	−0.652811	−0.326405	+	0.945230i	$0.605837\pi$
$954$	−16.6153	−0.537941
$955$	1.40229	0.0453770
$956$	−45.4730	−1.47070
$957$	6.17630	0.199651
$958$	−24.7583	−0.799905
$959$	48.5559	1.56795
$960$	−4.24380	−0.136968
$961$	40.8512	1.31778
$962$	6.52527	0.210383
$963$	−23.8645	−0.769024
$964$	−129.374	−4.16687
$965$	7.88019	0.253672
$966$	−36.2490	−1.16629
$967$	−34.2769	−1.10227	−0.551135	−	0.834416i	$-0.685805\pi$
$967$	−34.2769	−1.10227	−0.551135	+	0.834416i	$0.685805\pi$
$968$	49.7200	1.59806
$969$	2.70558	0.0869158
$970$	9.67452	0.310630
$971$	−44.1526	−1.41692	−0.708462	−	0.705749i	$-0.750611\pi$
$971$	−44.1526	−1.41692	−0.708462	+	0.705749i	$0.750611\pi$
$972$	−77.3031	−2.47950
$973$	−11.0208	−0.353309
$974$	12.1355	0.388848
$975$	−3.80840	−0.121966
$976$	−9.20273	−0.294572
$977$	−53.3340	−1.70630	−0.853152	−	0.521662i	$-0.825312\pi$
$977$	−53.3340	−1.70630	−0.853152	+	0.521662i	$0.825312\pi$
$978$	42.0431	1.34439
$979$	23.5006	0.751083
$980$	49.7007	1.58763
$981$	−36.5321	−1.16638
$982$	1.16079	0.0370423
$983$	−34.2230	−1.09155	−0.545773	−	0.837933i	$-0.683764\pi$
$983$	−34.2230	−1.09155	−0.545773	+	0.837933i	$0.683764\pi$
$984$	−48.6109	−1.54966
$985$	−12.3287	−0.392825
$986$	−35.5286	−1.13146
$987$	6.14027	0.195447
$988$	4.33357	0.137869
$989$	20.3682	0.647672
$990$	−7.23348	−0.229895
$991$	44.9566	1.42809	0.714047	−	0.700098i	$-0.246860\pi$
$991$	44.9566	1.42809	0.714047	+	0.700098i	$0.246860\pi$
$992$	94.7639	3.00876
$993$	1.09638	0.0347926
$994$	23.0365	0.730675
$995$	−8.77783	−0.278276
$996$	−34.4737	−1.09234
$997$	21.1207	0.668899	0.334450	−	0.942414i	$-0.391450\pi$
$997$	21.1207	0.668899	0.334450	+	0.942414i	$0.391450\pi$
$998$	−60.6261	−1.91909
$999$	10.8031	0.341794

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6019.2.a.c.1.5	✓	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6019.2.a.c.1.5	✓	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)

\(f(q)\)	\(=\)	\(q-2.62196 q^{2} -0.813055 q^{3} +4.87469 q^{4} +0.562087 q^{5} +2.13180 q^{6} -5.01388 q^{7} -7.53732 q^{8} -2.33894 q^{9} +O(q^{10})\)	\(q-2.62196 q^{2} -0.813055 q^{3} +4.87469 q^{4} +0.562087 q^{5} +2.13180 q^{6} -5.01388 q^{7} -7.53732 q^{8} -2.33894 q^{9} -1.47377 q^{10} -2.09845 q^{11} -3.96339 q^{12} -1.00000 q^{13} +13.1462 q^{14} -0.457007 q^{15} +10.0132 q^{16} +3.74319 q^{17} +6.13262 q^{18} -0.888994 q^{19} +2.74000 q^{20} +4.07656 q^{21} +5.50205 q^{22} +3.39137 q^{23} +6.12826 q^{24} -4.68406 q^{25} +2.62196 q^{26} +4.34085 q^{27} -24.4411 q^{28} +3.62001 q^{29} +1.19826 q^{30} -8.47651 q^{31} -11.1796 q^{32} +1.70615 q^{33} -9.81451 q^{34} -2.81823 q^{35} -11.4016 q^{36} +2.48870 q^{37} +2.33091 q^{38} +0.813055 q^{39} -4.23663 q^{40} -7.93225 q^{41} -10.6886 q^{42} +6.00589 q^{43} -10.2293 q^{44} -1.31469 q^{45} -8.89206 q^{46} +1.50624 q^{47} -8.14128 q^{48} +18.1390 q^{49} +12.2814 q^{50} -3.04342 q^{51} -4.87469 q^{52} -2.70934 q^{53} -11.3816 q^{54} -1.17951 q^{55} +37.7912 q^{56} +0.722801 q^{57} -9.49153 q^{58} +11.4174 q^{59} -2.22777 q^{60} -0.919060 q^{61} +22.2251 q^{62} +11.7272 q^{63} +9.28607 q^{64} -0.562087 q^{65} -4.47347 q^{66} -2.20779 q^{67} +18.2469 q^{68} -2.75737 q^{69} +7.38930 q^{70} +1.75234 q^{71} +17.6294 q^{72} +9.37638 q^{73} -6.52527 q^{74} +3.80840 q^{75} -4.33357 q^{76} +10.5214 q^{77} -2.13180 q^{78} +6.77830 q^{79} +5.62829 q^{80} +3.48747 q^{81} +20.7981 q^{82} +8.69805 q^{83} +19.8719 q^{84} +2.10400 q^{85} -15.7472 q^{86} -2.94327 q^{87} +15.8167 q^{88} -11.1990 q^{89} +3.44706 q^{90} +5.01388 q^{91} +16.5319 q^{92} +6.89187 q^{93} -3.94930 q^{94} -0.499691 q^{95} +9.08962 q^{96} -6.56447 q^{97} -47.5597 q^{98} +4.90815 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 11 q^{2} + q^{3} + 95 q^{4} - 40 q^{5} - 10 q^{6} - 8 q^{7} - 33 q^{8} + 79 q^{9}+O(q^{10}) \) 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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