LMFDB - Embedded newform 6013.2.a.d.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6013, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6013 = 7 \cdot 859 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6013.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$48.0140467354$
Analytic rank:	$1$
Dimension:	$104$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	6013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.10979 q^{2} +2.86366 q^{3} +2.45121 q^{4} -1.33833 q^{5} -6.04172 q^{6} +1.00000 q^{7} -0.951963 q^{8} +5.20055 q^{9} +O(q^{10})$	\(q-2.10979 q^{2} +2.86366 q^{3} +2.45121 q^{4} -1.33833 q^{5} -6.04172 q^{6} +1.00000 q^{7} -0.951963 q^{8} +5.20055 q^{9} +2.82359 q^{10} -0.277490 q^{11} +7.01944 q^{12} -2.39425 q^{13} -2.10979 q^{14} -3.83251 q^{15} -2.89398 q^{16} -5.58083 q^{17} -10.9721 q^{18} +7.29105 q^{19} -3.28052 q^{20} +2.86366 q^{21} +0.585447 q^{22} -8.24433 q^{23} -2.72610 q^{24} -3.20888 q^{25} +5.05136 q^{26} +6.30163 q^{27} +2.45121 q^{28} -9.45722 q^{29} +8.08580 q^{30} +7.15524 q^{31} +8.00962 q^{32} -0.794638 q^{33} +11.7744 q^{34} -1.33833 q^{35} +12.7476 q^{36} +9.24030 q^{37} -15.3826 q^{38} -6.85632 q^{39} +1.27404 q^{40} +2.30324 q^{41} -6.04172 q^{42} +0.865266 q^{43} -0.680188 q^{44} -6.96004 q^{45} +17.3938 q^{46} +4.46556 q^{47} -8.28739 q^{48} +1.00000 q^{49} +6.77006 q^{50} -15.9816 q^{51} -5.86881 q^{52} +2.36592 q^{53} -13.2951 q^{54} +0.371373 q^{55} -0.951963 q^{56} +20.8791 q^{57} +19.9527 q^{58} -7.63369 q^{59} -9.39431 q^{60} +4.68376 q^{61} -15.0960 q^{62} +5.20055 q^{63} -11.1106 q^{64} +3.20429 q^{65} +1.67652 q^{66} -3.08316 q^{67} -13.6798 q^{68} -23.6090 q^{69} +2.82359 q^{70} -2.66394 q^{71} -4.95073 q^{72} -7.69011 q^{73} -19.4951 q^{74} -9.18914 q^{75} +17.8719 q^{76} -0.277490 q^{77} +14.4654 q^{78} -12.9100 q^{79} +3.87310 q^{80} +2.44407 q^{81} -4.85936 q^{82} +0.210392 q^{83} +7.01944 q^{84} +7.46898 q^{85} -1.82553 q^{86} -27.0823 q^{87} +0.264161 q^{88} -1.85567 q^{89} +14.6842 q^{90} -2.39425 q^{91} -20.2086 q^{92} +20.4902 q^{93} -9.42140 q^{94} -9.75782 q^{95} +22.9368 q^{96} -10.2249 q^{97} -2.10979 q^{98} -1.44310 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 104 q - 17 q^{2} - 34 q^{3} + 99 q^{4} - 46 q^{5} - 18 q^{6} + 104 q^{7} - 48 q^{8} + 98 q^{9}+O(q^{10}) $ 104 * q - 17 * q^2 - 34 * q^3 + 99 * q^4 - 46 * q^5 - 18 * q^6 + 104 * q^7 - 48 * q^8 + 98 * q^9	\( 104 q - 17 q^{2} - 34 q^{3} + 99 q^{4} - 46 q^{5} - 18 q^{6} + 104 q^{7} - 48 q^{8} + 98 q^{9} - 17 q^{10} - 46 q^{11} - 62 q^{12} - 37 q^{13} - 17 q^{14} - 17 q^{15} + 93 q^{16} - 75 q^{17} - 41 q^{18} - 40 q^{19} - 106 q^{20} - 34 q^{21} - 14 q^{22} - 57 q^{23} - 38 q^{24} + 102 q^{25} - 45 q^{26} - 121 q^{27} + 99 q^{28} - 29 q^{29} + 26 q^{30} - 42 q^{31} - 113 q^{32} - 42 q^{33} - 7 q^{34} - 46 q^{35} + 99 q^{36} - 31 q^{37} - 62 q^{38} - 9 q^{39} - 36 q^{40} - 106 q^{41} - 18 q^{42} - 29 q^{43} - 60 q^{44} - 121 q^{45} + 21 q^{46} - 141 q^{47} - 88 q^{48} + 104 q^{49} - 70 q^{50} - 2 q^{51} - 58 q^{52} - 70 q^{53} - 49 q^{54} - 14 q^{55} - 48 q^{56} - 11 q^{57} - 28 q^{58} - 202 q^{59} + 17 q^{60} - 79 q^{61} - 41 q^{62} + 98 q^{63} + 110 q^{64} - 34 q^{65} - 21 q^{66} - 57 q^{67} - 180 q^{68} - 99 q^{69} - 17 q^{70} - 109 q^{71} - 73 q^{72} - 46 q^{73} - 7 q^{74} - 146 q^{75} - 54 q^{76} - 46 q^{77} - 42 q^{78} - 12 q^{79} - 187 q^{80} + 100 q^{81} - 45 q^{82} - 156 q^{83} - 62 q^{84} - 13 q^{85} - 8 q^{86} - 76 q^{87} - 6 q^{88} - 140 q^{89} - 5 q^{90} - 37 q^{91} - 98 q^{92} - q^{93} - 17 q^{94} - 48 q^{95} - 12 q^{96} - 63 q^{97} - 17 q^{98} - 78 q^{99}+O(q^{100}) \) 104 * q - 17 * q^2 - 34 * q^3 + 99 * q^4 - 46 * q^5 - 18 * q^6 + 104 * q^7 - 48 * q^8 + 98 * q^9 - 17 * q^10 - 46 * q^11 - 62 * q^12 - 37 * q^13 - 17 * q^14 - 17 * q^15 + 93 * q^16 - 75 * q^17 - 41 * q^18 - 40 * q^19 - 106 * q^20 - 34 * q^21 - 14 * q^22 - 57 * q^23 - 38 * q^24 + 102 * q^25 - 45 * q^26 - 121 * q^27 + 99 * q^28 - 29 * q^29 + 26 * q^30 - 42 * q^31 - 113 * q^32 - 42 * q^33 - 7 * q^34 - 46 * q^35 + 99 * q^36 - 31 * q^37 - 62 * q^38 - 9 * q^39 - 36 * q^40 - 106 * q^41 - 18 * q^42 - 29 * q^43 - 60 * q^44 - 121 * q^45 + 21 * q^46 - 141 * q^47 - 88 * q^48 + 104 * q^49 - 70 * q^50 - 2 * q^51 - 58 * q^52 - 70 * q^53 - 49 * q^54 - 14 * q^55 - 48 * q^56 - 11 * q^57 - 28 * q^58 - 202 * q^59 + 17 * q^60 - 79 * q^61 - 41 * q^62 + 98 * q^63 + 110 * q^64 - 34 * q^65 - 21 * q^66 - 57 * q^67 - 180 * q^68 - 99 * q^69 - 17 * q^70 - 109 * q^71 - 73 * q^72 - 46 * q^73 - 7 * q^74 - 146 * q^75 - 54 * q^76 - 46 * q^77 - 42 * q^78 - 12 * q^79 - 187 * q^80 + 100 * q^81 - 45 * q^82 - 156 * q^83 - 62 * q^84 - 13 * q^85 - 8 * q^86 - 76 * q^87 - 6 * q^88 - 140 * q^89 - 5 * q^90 - 37 * q^91 - 98 * q^92 - q^93 - 17 * q^94 - 48 * q^95 - 12 * q^96 - 63 * q^97 - 17 * q^98 - 78 * 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 $

$2$	−2.10979	−1.49185	−0.745923	−	0.666032i	$-0.767991\pi$
$2$	−2.10979	−1.49185	−0.745923	+	0.666032i	$0.767991\pi$
$3$	2.86366	1.65333	0.826667	−	0.562691i	$-0.190234\pi$
$3$	2.86366	1.65333	0.826667	+	0.562691i	$0.190234\pi$
$4$	2.45121	1.22561
$5$	−1.33833	−0.598518	−0.299259	−	0.954172i	$-0.596739\pi$
$5$	−1.33833	−0.598518	−0.299259	+	0.954172i	$0.596739\pi$
$6$	−6.04172	−2.46652
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−0.951963	−0.336570
$9$	5.20055	1.73352
$10$	2.82359	0.892897
$11$	−0.277490	−0.0836665	−0.0418333	−	0.999125i	$-0.513320\pi$
$11$	−0.277490	−0.0836665	−0.0418333	+	0.999125i	$0.513320\pi$
$12$	7.01944	2.02634
$13$	−2.39425	−0.664045	−0.332023	−	0.943271i	$-0.607731\pi$
$13$	−2.39425	−0.664045	−0.332023	+	0.943271i	$0.607731\pi$
$14$	−2.10979	−0.563865
$15$	−3.83251	−0.989551
$16$	−2.89398	−0.723496
$17$	−5.58083	−1.35355	−0.676775	−	0.736190i	$-0.736623\pi$
$17$	−5.58083	−1.35355	−0.676775	+	0.736190i	$0.736623\pi$
$18$	−10.9721	−2.58614
$19$	7.29105	1.67268	0.836341	−	0.548209i	$-0.184690\pi$
$19$	7.29105	1.67268	0.836341	+	0.548209i	$0.184690\pi$
$20$	−3.28052	−0.733548
$21$	2.86366	0.624902
$22$	0.585447	0.124818
$23$	−8.24433	−1.71906	−0.859531	−	0.511084i	$-0.829244\pi$
$23$	−8.24433	−1.71906	−0.859531	+	0.511084i	$0.829244\pi$
$24$	−2.72610	−0.556462
$25$	−3.20888	−0.641776
$26$	5.05136	0.990654
$27$	6.30163	1.21275
$28$	2.45121	0.463236
$29$	−9.45722	−1.75616	−0.878081	−	0.478513i	$-0.841176\pi$
$29$	−9.45722	−1.75616	−0.878081	+	0.478513i	$0.841176\pi$
$30$	8.08580	1.47626
$31$	7.15524	1.28512	0.642559	−	0.766236i	$-0.277873\pi$
$31$	7.15524	1.28512	0.642559	+	0.766236i	$0.277873\pi$
$32$	8.00962	1.41591
$33$	−0.794638	−0.138329
$34$	11.7744	2.01929
$35$	−1.33833	−0.226219
$36$	12.7476	2.12461
$37$	9.24030	1.51910	0.759548	−	0.650452i	$-0.225420\pi$
$37$	9.24030	1.51910	0.759548	+	0.650452i	$0.225420\pi$
$38$	−15.3826	−2.49539
$39$	−6.85632	−1.09789
$40$	1.27404	0.201443
$41$	2.30324	0.359706	0.179853	−	0.983693i	$-0.442438\pi$
$41$	2.30324	0.359706	0.179853	+	0.983693i	$0.442438\pi$
$42$	−6.04172	−0.932258
$43$	0.865266	0.131952	0.0659759	−	0.997821i	$-0.478984\pi$
$43$	0.865266	0.131952	0.0659759	+	0.997821i	$0.478984\pi$
$44$	−0.680188	−0.102542
$45$	−6.96004	−1.03754
$46$	17.3938	2.56458
$47$	4.46556	0.651369	0.325685	−	0.945478i	$-0.394405\pi$
$47$	4.46556	0.651369	0.325685	+	0.945478i	$0.394405\pi$
$48$	−8.28739	−1.19618
$49$	1.00000	0.142857
$50$	6.77006	0.957431
$51$	−15.9816	−2.23787
$52$	−5.86881	−0.813858
$53$	2.36592	0.324984	0.162492	−	0.986710i	$-0.448047\pi$
$53$	2.36592	0.324984	0.162492	+	0.986710i	$0.448047\pi$
$54$	−13.2951	−1.80923
$55$	0.371373	0.0500759
$56$	−0.951963	−0.127211
$57$	20.8791	2.76550
$58$	19.9527	2.61992
$59$	−7.63369	−0.993822	−0.496911	−	0.867802i	$-0.665532\pi$
$59$	−7.63369	−0.993822	−0.496911	+	0.867802i	$0.665532\pi$
$60$	−9.39431	−1.21280
$61$	4.68376	0.599694	0.299847	−	0.953987i	$-0.403064\pi$
$61$	4.68376	0.599694	0.299847	+	0.953987i	$0.403064\pi$
$62$	−15.0960	−1.91720
$63$	5.20055	0.655208
$64$	−11.1106	−1.38883
$65$	3.20429	0.397443
$66$	1.67652	0.206365
$67$	−3.08316	−0.376667	−0.188334	−	0.982105i	$-0.560309\pi$
$67$	−3.08316	−0.376667	−0.188334	+	0.982105i	$0.560309\pi$
$68$	−13.6798	−1.65892
$69$	−23.6090	−2.84218
$70$	2.82359	0.337483
$71$	−2.66394	−0.316151	−0.158075	−	0.987427i	$-0.550529\pi$
$71$	−2.66394	−0.316151	−0.158075	+	0.987427i	$0.550529\pi$
$72$	−4.95073	−0.583449
$73$	−7.69011	−0.900059	−0.450030	−	0.893014i	$-0.648587\pi$
$73$	−7.69011	−0.900059	−0.450030	+	0.893014i	$0.648587\pi$
$74$	−19.4951	−2.26626
$75$	−9.18914	−1.06107
$76$	17.8719	2.05005
$77$	−0.277490	−0.0316230
$78$	14.4654	1.63788
$79$	−12.9100	−1.45248	−0.726242	−	0.687439i	$-0.758735\pi$
$79$	−12.9100	−1.45248	−0.726242	+	0.687439i	$0.758735\pi$
$80$	3.87310	0.433025
$81$	2.44407	0.271563
$82$	−4.85936	−0.536626
$83$	0.210392	0.0230935	0.0115468	−	0.999933i	$-0.496324\pi$
$83$	0.210392	0.0230935	0.0115468	+	0.999933i	$0.496324\pi$
$84$	7.01944	0.765884
$85$	7.46898	0.810125
$86$	−1.82553	−0.196852
$87$	−27.0823	−2.90352
$88$	0.264161	0.0281596
$89$	−1.85567	−0.196700	−0.0983501	−	0.995152i	$-0.531356\pi$
$89$	−1.85567	−0.196700	−0.0983501	+	0.995152i	$0.531356\pi$
$90$	14.6842	1.54785
$91$	−2.39425	−0.250986
$92$	−20.2086	−2.10689
$93$	20.4902	2.12473
$94$	−9.42140	−0.971743
$95$	−9.75782	−1.00113
$96$	22.9368	2.34098
$97$	−10.2249	−1.03819	−0.519093	−	0.854718i	$-0.673730\pi$
$97$	−10.2249	−1.03819	−0.519093	+	0.854718i	$0.673730\pi$
$98$	−2.10979	−0.213121
$99$	−1.44310	−0.145037
$100$	−7.86564	−0.786564
$101$	3.58788	0.357008	0.178504	−	0.983939i	$-0.442874\pi$
$101$	3.58788	0.357008	0.178504	+	0.983939i	$0.442874\pi$
$102$	33.7178	3.33856
$103$	−8.43928	−0.831547	−0.415773	−	0.909468i	$-0.636489\pi$
$103$	−8.43928	−0.831547	−0.415773	+	0.909468i	$0.636489\pi$
$104$	2.27924	0.223497
$105$	−3.83251	−0.374015
$106$	−4.99159	−0.484826
$107$	−14.8949	−1.43994	−0.719972	−	0.694003i	$-0.755845\pi$
$107$	−14.8949	−1.43994	−0.719972	+	0.694003i	$0.755845\pi$
$108$	15.4466	1.48635
$109$	−9.34829	−0.895404	−0.447702	−	0.894183i	$-0.647757\pi$
$109$	−9.34829	−0.895404	−0.447702	+	0.894183i	$0.647757\pi$
$110$	−0.783519	−0.0747056
$111$	26.4611	2.51157
$112$	−2.89398	−0.273456
$113$	−16.5930	−1.56094	−0.780468	−	0.625195i	$-0.785019\pi$
$113$	−16.5930	−1.56094	−0.780468	+	0.625195i	$0.785019\pi$
$114$	−44.0505	−4.12571
$115$	11.0336	1.02889
$116$	−23.1816	−2.15236
$117$	−12.4514	−1.15113
$118$	16.1055	1.48263
$119$	−5.58083	−0.511594
$120$	3.64841	0.333053
$121$	−10.9230	−0.993000
$122$	−9.88174	−0.894651
$123$	6.59570	0.594715
$124$	17.5390	1.57505
$125$	10.9862	0.982633
$126$	−10.9721	−0.977469
$127$	−1.18131	−0.104825	−0.0524123	−	0.998626i	$-0.516691\pi$
$127$	−1.18131	−0.104825	−0.0524123	+	0.998626i	$0.516691\pi$
$128$	7.42189	0.656008
$129$	2.47783	0.218161
$130$	−6.76038	−0.592924
$131$	1.71993	0.150271	0.0751356	−	0.997173i	$-0.476061\pi$
$131$	1.71993	0.150271	0.0751356	+	0.997173i	$0.476061\pi$
$132$	−1.94783	−0.169537
$133$	7.29105	0.632214
$134$	6.50481	0.561930
$135$	−8.43364	−0.725852
$136$	5.31274	0.455564
$137$	−2.06512	−0.176435	−0.0882175	−	0.996101i	$-0.528117\pi$
$137$	−2.06512	−0.176435	−0.0882175	+	0.996101i	$0.528117\pi$
$138$	49.8099	4.24010
$139$	20.4252	1.73245	0.866224	−	0.499657i	$-0.166540\pi$
$139$	20.4252	1.73245	0.866224	+	0.499657i	$0.166540\pi$
$140$	−3.28052	−0.277255
$141$	12.7879	1.07693
$142$	5.62034	0.471649
$143$	0.664382	0.0555584
$144$	−15.0503	−1.25419
$145$	12.6569	1.05109
$146$	16.2245	1.34275
$147$	2.86366	0.236191
$148$	22.6499	1.86181
$149$	10.7736	0.882606	0.441303	−	0.897358i	$-0.354516\pi$
$149$	10.7736	0.882606	0.441303	+	0.897358i	$0.354516\pi$
$150$	19.3872	1.58295
$151$	−0.555355	−0.0451941	−0.0225971	−	0.999745i	$-0.507193\pi$
$151$	−0.555355	−0.0451941	−0.0225971	+	0.999745i	$0.507193\pi$
$152$	−6.94081	−0.562974
$153$	−29.0234	−2.34640
$154$	0.585447	0.0471766
$155$	−9.57605	−0.769167
$156$	−16.8063	−1.34558
$157$	−14.3121	−1.14223	−0.571115	−	0.820870i	$-0.693489\pi$
$157$	−14.3121	−1.14223	−0.571115	+	0.820870i	$0.693489\pi$
$158$	27.2373	2.16688
$159$	6.77519	0.537307
$160$	−10.7195	−0.847451
$161$	−8.24433	−0.649744
$162$	−5.15646	−0.405130
$163$	−3.11235	−0.243778	−0.121889	−	0.992544i	$-0.538895\pi$
$163$	−3.11235	−0.243778	−0.121889	+	0.992544i	$0.538895\pi$
$164$	5.64574	0.440858
$165$	1.06349	0.0827923
$166$	−0.443883	−0.0344520
$167$	4.67851	0.362034	0.181017	−	0.983480i	$-0.442061\pi$
$167$	4.67851	0.362034	0.181017	+	0.983480i	$0.442061\pi$
$168$	−2.72610	−0.210323
$169$	−7.26757	−0.559044
$170$	−15.7580	−1.20858
$171$	37.9175	2.89962
$172$	2.12095	0.161721
$173$	11.4540	0.870832	0.435416	−	0.900229i	$-0.356601\pi$
$173$	11.4540	0.870832	0.435416	+	0.900229i	$0.356601\pi$
$174$	57.1379	4.33161
$175$	−3.20888	−0.242569
$176$	0.803053	0.0605324
$177$	−21.8603	−1.64312
$178$	3.91506	0.293446
$179$	22.4854	1.68064	0.840320	−	0.542090i	$-0.182367\pi$
$179$	22.4854	1.68064	0.840320	+	0.542090i	$0.182367\pi$
$180$	−17.0605	−1.27162
$181$	16.8930	1.25564	0.627822	−	0.778357i	$-0.283947\pi$
$181$	16.8930	1.25564	0.627822	+	0.778357i	$0.283947\pi$
$182$	5.05136	0.374432
$183$	13.4127	0.991494
$184$	7.84829	0.578584
$185$	−12.3665	−0.909206
$186$	−43.2299	−3.16977
$187$	1.54863	0.113247
$188$	10.9460	0.798322
$189$	6.30163	0.458376
$190$	20.5869	1.49353
$191$	−23.0025	−1.66440	−0.832201	−	0.554474i	$-0.812919\pi$
$191$	−23.0025	−1.66440	−0.832201	+	0.554474i	$0.812919\pi$
$192$	−31.8171	−2.29620
$193$	−18.2913	−1.31664	−0.658318	−	0.752740i	$-0.728732\pi$
$193$	−18.2913	−1.31664	−0.658318	+	0.752740i	$0.728732\pi$
$194$	21.5725	1.54881
$195$	9.17600	0.657107
$196$	2.45121	0.175087
$197$	6.88209	0.490328	0.245164	−	0.969482i	$-0.421158\pi$
$197$	6.88209	0.490328	0.245164	+	0.969482i	$0.421158\pi$
$198$	3.04464	0.216373
$199$	−21.5071	−1.52460	−0.762299	−	0.647225i	$-0.775929\pi$
$199$	−21.5071	−1.52460	−0.762299	+	0.647225i	$0.775929\pi$
$200$	3.05473	0.216002
$201$	−8.82911	−0.622757
$202$	−7.56967	−0.532600
$203$	−9.45722	−0.663766
$204$	−39.1743	−2.74275
$205$	−3.08249	−0.215291
$206$	17.8051	1.24054
$207$	−42.8750	−2.98002
$208$	6.92892	0.480434
$209$	−2.02320	−0.139948
$210$	8.08580	0.557973
$211$	−13.6432	−0.939238	−0.469619	−	0.882869i	$-0.655609\pi$
$211$	−13.6432	−0.939238	−0.469619	+	0.882869i	$0.655609\pi$
$212$	5.79937	0.398302
$213$	−7.62861	−0.522703
$214$	31.4251	2.14818
$215$	−1.15801	−0.0789756
$216$	−5.99891	−0.408174
$217$	7.15524	0.485729
$218$	19.7229	1.33581
$219$	−22.0219	−1.48810
$220$	0.910314	0.0613734
$221$	13.3619	0.898819
$222$	−55.8273	−3.74688
$223$	14.3448	0.960599	0.480299	−	0.877105i	$-0.340528\pi$
$223$	14.3448	0.960599	0.480299	+	0.877105i	$0.340528\pi$
$224$	8.00962	0.535165
$225$	−16.6879	−1.11253
$226$	35.0077	2.32868
$227$	1.60074	0.106245	0.0531224	−	0.998588i	$-0.483083\pi$
$227$	1.60074	0.106245	0.0531224	+	0.998588i	$0.483083\pi$
$228$	51.1791	3.38942
$229$	23.1372	1.52895	0.764475	−	0.644654i	$-0.222999\pi$
$229$	23.1372	1.52895	0.764475	+	0.644654i	$0.222999\pi$
$230$	−23.2786	−1.53495
$231$	−0.794638	−0.0522834
$232$	9.00292	0.591070
$233$	−23.9096	−1.56637	−0.783184	−	0.621789i	$-0.786406\pi$
$233$	−23.9096	−1.56637	−0.783184	+	0.621789i	$0.786406\pi$
$234$	26.2699	1.71731
$235$	−5.97638	−0.389856
$236$	−18.7118	−1.21803
$237$	−36.9697	−2.40144
$238$	11.7744	0.763220
$239$	3.31288	0.214292	0.107146	−	0.994243i	$-0.465829\pi$
$239$	3.31288	0.214292	0.107146	+	0.994243i	$0.465829\pi$
$240$	11.0912	0.715936
$241$	−12.9443	−0.833819	−0.416909	−	0.908948i	$-0.636887\pi$
$241$	−12.9443	−0.833819	−0.416909	+	0.908948i	$0.636887\pi$
$242$	23.0452	1.48140
$243$	−11.9059	−0.763764
$244$	11.4809	0.734988
$245$	−1.33833	−0.0855026
$246$	−13.9155	−0.887223
$247$	−17.4566	−1.11074
$248$	−6.81152	−0.432532
$249$	0.602492	0.0381814
$250$	−23.1785	−1.46594
$251$	22.3418	1.41020	0.705101	−	0.709106i	$-0.250901\pi$
$251$	22.3418	1.41020	0.705101	+	0.709106i	$0.250901\pi$
$252$	12.7476	0.803026
$253$	2.28772	0.143828
$254$	2.49232	0.156382
$255$	21.3886	1.33941
$256$	6.56267	0.410167
$257$	−18.7144	−1.16737	−0.583686	−	0.811979i	$-0.698390\pi$
$257$	−18.7144	−1.16737	−0.583686	+	0.811979i	$0.698390\pi$
$258$	−5.22770	−0.325462
$259$	9.24030	0.574164
$260$	7.85439	0.487109
$261$	−49.1827	−3.04433
$262$	−3.62870	−0.224182
$263$	4.17069	0.257176	0.128588	−	0.991698i	$-0.458956\pi$
$263$	4.17069	0.257176	0.128588	+	0.991698i	$0.458956\pi$
$264$	0.756466	0.0465573
$265$	−3.16637	−0.194509
$266$	−15.3826	−0.943167
$267$	−5.31399	−0.325211
$268$	−7.55747	−0.461646
$269$	−18.7435	−1.14281	−0.571407	−	0.820667i	$-0.693602\pi$
$269$	−18.7435	−1.14281	−0.571407	+	0.820667i	$0.693602\pi$
$270$	17.7932	1.08286
$271$	−8.49108	−0.515796	−0.257898	−	0.966172i	$-0.583030\pi$
$271$	−8.49108	−0.515796	−0.257898	+	0.966172i	$0.583030\pi$
$272$	16.1508	0.979288
$273$	−6.85632	−0.414963
$274$	4.35697	0.263214
$275$	0.890434	0.0536952
$276$	−57.8706	−3.48340
$277$	12.7132	0.763863	0.381931	−	0.924191i	$-0.375259\pi$
$277$	12.7132	0.763863	0.381931	+	0.924191i	$0.375259\pi$
$278$	−43.0930	−2.58455
$279$	37.2112	2.22777
$280$	1.27404	0.0761383
$281$	−0.531485	−0.0317057	−0.0158529	−	0.999874i	$-0.505046\pi$
$281$	−0.531485	−0.0317057	−0.0158529	+	0.999874i	$0.505046\pi$
$282$	−26.9797	−1.60662
$283$	17.9582	1.06750	0.533752	−	0.845641i	$-0.320782\pi$
$283$	17.9582	1.06750	0.533752	+	0.845641i	$0.320782\pi$
$284$	−6.52987	−0.387477
$285$	−27.9431	−1.65520
$286$	−1.40171	−0.0828846
$287$	2.30324	0.135956
$288$	41.6544	2.45451
$289$	14.1457	0.832100
$290$	−26.7033	−1.56807
$291$	−29.2807	−1.71647
$292$	−18.8501	−1.10312
$293$	−8.97808	−0.524505	−0.262252	−	0.964999i	$-0.584465\pi$
$293$	−8.97808	−0.524505	−0.262252	+	0.964999i	$0.584465\pi$
$294$	−6.04172	−0.352360
$295$	10.2164	0.594820
$296$	−8.79642	−0.511281
$297$	−1.74864	−0.101466
$298$	−22.7300	−1.31671
$299$	19.7390	1.14153
$300$	−22.5245	−1.30045
$301$	0.865266	0.0498731
$302$	1.17168	0.0674227
$303$	10.2745	0.590253
$304$	−21.1002	−1.21018
$305$	−6.26840	−0.358927
$306$	61.2333	3.50047
$307$	−2.71632	−0.155029	−0.0775144	−	0.996991i	$-0.524698\pi$
$307$	−2.71632	−0.155029	−0.0775144	+	0.996991i	$0.524698\pi$
$308$	−0.680188	−0.0387573
$309$	−24.1672	−1.37483
$310$	20.2034	1.14748
$311$	−10.5024	−0.595536	−0.297768	−	0.954638i	$-0.596242\pi$
$311$	−10.5024	−0.595536	−0.297768	+	0.954638i	$0.596242\pi$
$312$	6.52696	0.369516
$313$	−34.2912	−1.93825	−0.969127	−	0.246563i	$-0.920699\pi$
$313$	−34.2912	−1.93825	−0.969127	+	0.246563i	$0.920699\pi$
$314$	30.1955	1.70403
$315$	−6.96004	−0.392154
$316$	−31.6450	−1.78017
$317$	−29.9712	−1.68335	−0.841674	−	0.539985i	$-0.818430\pi$
$317$	−29.9712	−1.68335	−0.841674	+	0.539985i	$0.818430\pi$
$318$	−14.2942	−0.801580
$319$	2.62429	0.146932
$320$	14.8697	0.831241
$321$	−42.6539	−2.38071
$322$	17.3938	0.969319
$323$	−40.6901	−2.26406
$324$	5.99092	0.332829
$325$	7.68286	0.426168
$326$	6.56640	0.363679
$327$	−26.7703	−1.48040
$328$	−2.19260	−0.121066
$329$	4.46556	0.246194
$330$	−2.24373	−0.123513
$331$	−9.12802	−0.501721	−0.250861	−	0.968023i	$-0.580714\pi$
$331$	−9.12802	−0.501721	−0.250861	+	0.968023i	$0.580714\pi$
$332$	0.515716	0.0283036
$333$	48.0546	2.63338
$334$	−9.87066	−0.540099
$335$	4.12627	0.225442
$336$	−8.28739	−0.452114
$337$	19.3332	1.05315	0.526573	−	0.850130i	$-0.323477\pi$
$337$	19.3332	1.05315	0.526573	+	0.850130i	$0.323477\pi$
$338$	15.3330	0.834007
$339$	−47.5167	−2.58075
$340$	18.3081	0.992894
$341$	−1.98551	−0.107521
$342$	−79.9979	−4.32579
$343$	1.00000	0.0539949
$344$	−0.823701	−0.0444110
$345$	31.5965	1.70110
$346$	−24.1656	−1.29915
$347$	−10.6416	−0.571269	−0.285635	−	0.958339i	$-0.592204\pi$
$347$	−10.6416	−0.571269	−0.285635	+	0.958339i	$0.592204\pi$
$348$	−66.3843	−3.55857
$349$	−5.30244	−0.283833	−0.141916	−	0.989879i	$-0.545326\pi$
$349$	−5.30244	−0.283833	−0.141916	+	0.989879i	$0.545326\pi$
$350$	6.77006	0.361875
$351$	−15.0877	−0.805320
$352$	−2.22259	−0.118465
$353$	−7.50293	−0.399341	−0.199670	−	0.979863i	$-0.563987\pi$
$353$	−7.50293	−0.399341	−0.199670	+	0.979863i	$0.563987\pi$
$354$	46.1206	2.45128
$355$	3.56522	0.189222
$356$	−4.54863	−0.241077
$357$	−15.9816	−0.845836
$358$	−47.4395	−2.50726
$359$	27.1911	1.43509	0.717545	−	0.696513i	$-0.245266\pi$
$359$	27.1911	1.43509	0.717545	+	0.696513i	$0.245266\pi$
$360$	6.62570	0.349205
$361$	34.1595	1.79787
$362$	−35.6406	−1.87323
$363$	−31.2798	−1.64176
$364$	−5.86881	−0.307609
$365$	10.2919	0.538702
$366$	−28.2979	−1.47916
$367$	26.9344	1.40596	0.702981	−	0.711209i	$-0.251852\pi$
$367$	26.9344	1.40596	0.702981	+	0.711209i	$0.251852\pi$
$368$	23.8590	1.24373
$369$	11.9781	0.623556
$370$	26.0908	1.35640
$371$	2.36592	0.122832
$372$	50.2257	2.60408
$373$	−4.10325	−0.212458	−0.106229	−	0.994342i	$-0.533878\pi$
$373$	−4.10325	−0.212458	−0.106229	+	0.994342i	$0.533878\pi$
$374$	−3.26728	−0.168947
$375$	31.4607	1.62462
$376$	−4.25105	−0.219231
$377$	22.6429	1.16617
$378$	−13.2951	−0.683826
$379$	31.7923	1.63306	0.816532	−	0.577301i	$-0.195894\pi$
$379$	31.7923	1.63306	0.816532	+	0.577301i	$0.195894\pi$
$380$	−23.9185	−1.22699
$381$	−3.38288	−0.173310
$382$	48.5304	2.48303
$383$	15.0494	0.768990	0.384495	−	0.923127i	$-0.374376\pi$
$383$	15.0494	0.768990	0.384495	+	0.923127i	$0.374376\pi$
$384$	21.2538	1.08460
$385$	0.371373	0.0189269
$386$	38.5908	1.96422
$387$	4.49986	0.228741
$388$	−25.0635	−1.27241
$389$	−8.60834	−0.436460	−0.218230	−	0.975897i	$-0.570028\pi$
$389$	−8.60834	−0.436460	−0.218230	+	0.975897i	$0.570028\pi$
$390$	−19.3594	−0.980303
$391$	46.0102	2.32684
$392$	−0.951963	−0.0480814
$393$	4.92530	0.248449
$394$	−14.5198	−0.731495
$395$	17.2778	0.869338
$396$	−3.53735	−0.177759
$397$	0.606215	0.0304250	0.0152125	−	0.999884i	$-0.495158\pi$
$397$	0.606215	0.0304250	0.0152125	+	0.999884i	$0.495158\pi$
$398$	45.3754	2.27447
$399$	20.8791	1.04526
$400$	9.28645	0.464322
$401$	−38.8499	−1.94007	−0.970035	−	0.242965i	$-0.921880\pi$
$401$	−38.8499	−1.94007	−0.970035	+	0.242965i	$0.921880\pi$
$402$	18.6276	0.929058
$403$	−17.1314	−0.853377
$404$	8.79466	0.437551
$405$	−3.27096	−0.162535
$406$	19.9527	0.990238
$407$	−2.56409	−0.127097
$408$	15.2139	0.753200
$409$	4.14804	0.205107	0.102554	−	0.994727i	$-0.467299\pi$
$409$	4.14804	0.205107	0.102554	+	0.994727i	$0.467299\pi$
$410$	6.50341	0.321181
$411$	−5.91380	−0.291706
$412$	−20.6865	−1.01915
$413$	−7.63369	−0.375629
$414$	90.4573	4.44573
$415$	−0.281574	−0.0138219
$416$	−19.1770	−0.940231
$417$	58.4910	2.86432
$418$	4.26852	0.208780
$419$	7.77483	0.379825	0.189913	−	0.981801i	$-0.439180\pi$
$419$	7.77483	0.379825	0.189913	+	0.981801i	$0.439180\pi$
$420$	−9.39431	−0.458395
$421$	−14.8598	−0.724223	−0.362112	−	0.932135i	$-0.617944\pi$
$421$	−14.8598	−0.724223	−0.362112	+	0.932135i	$0.617944\pi$
$422$	28.7843	1.40120
$423$	23.2234	1.12916
$424$	−2.25227	−0.109380
$425$	17.9082	0.868676
$426$	16.0948	0.779793
$427$	4.68376	0.226663
$428$	−36.5106	−1.76480
$429$	1.90256	0.0918566
$430$	2.44316	0.117819
$431$	0.751104	0.0361794	0.0180897	−	0.999836i	$-0.494242\pi$
$431$	0.751104	0.0361794	0.0180897	+	0.999836i	$0.494242\pi$
$432$	−18.2368	−0.877418
$433$	−21.0949	−1.01376	−0.506879	−	0.862017i	$-0.669201\pi$
$433$	−21.0949	−1.01376	−0.506879	+	0.862017i	$0.669201\pi$
$434$	−15.0960	−0.724633
$435$	36.2449	1.73781
$436$	−22.9147	−1.09741
$437$	−60.1098	−2.87544
$438$	46.4615	2.22002
$439$	22.7254	1.08462	0.542312	−	0.840177i	$-0.317549\pi$
$439$	22.7254	1.08462	0.542312	+	0.840177i	$0.317549\pi$
$440$	−0.353533	−0.0168540
$441$	5.20055	0.247645
$442$	−28.1908	−1.34090
$443$	15.9560	0.758093	0.379046	−	0.925378i	$-0.376252\pi$
$443$	15.9560	0.758093	0.379046	+	0.925378i	$0.376252\pi$
$444$	64.8617	3.07820
$445$	2.48349	0.117729
$446$	−30.2645	−1.43307
$447$	30.8519	1.45924
$448$	−11.1106	−0.524929
$449$	−11.1960	−0.528374	−0.264187	−	0.964471i	$-0.585104\pi$
$449$	−11.1960	−0.528374	−0.264187	+	0.964471i	$0.585104\pi$
$450$	35.2080	1.65972
$451$	−0.639128	−0.0300954
$452$	−40.6729	−1.91309
$453$	−1.59035	−0.0747210
$454$	−3.37722	−0.158501
$455$	3.20429	0.150219
$456$	−19.8761	−0.930785
$457$	−22.2382	−1.04026	−0.520129	−	0.854088i	$-0.674116\pi$
$457$	−22.2382	−1.04026	−0.520129	+	0.854088i	$0.674116\pi$
$458$	−48.8146	−2.28096
$459$	−35.1683	−1.64152
$460$	27.0457	1.26101
$461$	−18.2739	−0.851099	−0.425550	−	0.904935i	$-0.639919\pi$
$461$	−18.2739	−0.851099	−0.425550	+	0.904935i	$0.639919\pi$
$462$	1.67652	0.0779988
$463$	1.55627	0.0723259	0.0361630	−	0.999346i	$-0.488486\pi$
$463$	1.55627	0.0723259	0.0361630	+	0.999346i	$0.488486\pi$
$464$	27.3690	1.27058
$465$	−27.4226	−1.27169
$466$	50.4442	2.33678
$467$	29.2809	1.35496	0.677478	−	0.735543i	$-0.263073\pi$
$467$	29.2809	1.35496	0.677478	+	0.735543i	$0.263073\pi$
$468$	−30.5211	−1.41084
$469$	−3.08316	−0.142367
$470$	12.6089	0.581606
$471$	−40.9850	−1.88849
$472$	7.26699	0.334490
$473$	−0.240103	−0.0110400
$474$	77.9984	3.58258
$475$	−23.3961	−1.07349
$476$	−13.6798	−0.627013
$477$	12.3041	0.563365
$478$	−6.98948	−0.319691
$479$	14.1150	0.644933	0.322466	−	0.946581i	$-0.395488\pi$
$479$	14.1150	0.644933	0.322466	+	0.946581i	$0.395488\pi$
$480$	−30.6970	−1.40112
$481$	−22.1236	−1.00875
$482$	27.3098	1.24393
$483$	−23.6090	−1.07424
$484$	−26.7746	−1.21703
$485$	13.6843	0.621373
$486$	25.1190	1.13942
$487$	19.9614	0.904536	0.452268	−	0.891882i	$-0.350615\pi$
$487$	19.9614	0.904536	0.452268	+	0.891882i	$0.350615\pi$
$488$	−4.45876	−0.201839
$489$	−8.91271	−0.403047
$490$	2.82359	0.127557
$491$	26.6200	1.20134	0.600671	−	0.799496i	$-0.294900\pi$
$491$	26.6200	1.20134	0.600671	+	0.799496i	$0.294900\pi$
$492$	16.1675	0.728886
$493$	52.7791	2.37705
$494$	36.8298	1.65705
$495$	1.93134	0.0868075
$496$	−20.7071	−0.929778
$497$	−2.66394	−0.119494
$498$	−1.27113	−0.0569607
$499$	−26.2778	−1.17635	−0.588177	−	0.808732i	$-0.700154\pi$
$499$	−26.2778	−1.17635	−0.588177	+	0.808732i	$0.700154\pi$
$500$	26.9294	1.20432
$501$	13.3977	0.598563
$502$	−47.1365	−2.10381
$503$	0.320830	0.0143051	0.00715255	−	0.999974i	$-0.497723\pi$
$503$	0.320830	0.0143051	0.00715255	+	0.999974i	$0.497723\pi$
$504$	−4.95073	−0.220523
$505$	−4.80176	−0.213676
$506$	−4.82661	−0.214569
$507$	−20.8118	−0.924286
$508$	−2.89565	−0.128474
$509$	13.3536	0.591887	0.295943	−	0.955206i	$-0.404366\pi$
$509$	13.3536	0.591887	0.295943	+	0.955206i	$0.404366\pi$
$510$	−45.1255	−1.99819
$511$	−7.69011	−0.340191
$512$	−28.6896	−1.26791
$513$	45.9455	2.02854
$514$	39.4835	1.74154
$515$	11.2945	0.497696
$516$	6.07368	0.267379
$517$	−1.23915	−0.0544978
$518$	−19.4951	−0.856565
$519$	32.8004	1.43978
$520$	−3.05036	−0.133767
$521$	0.358381	0.0157009	0.00785047	−	0.999969i	$-0.497501\pi$
$521$	0.358381	0.0157009	0.00785047	+	0.999969i	$0.497501\pi$
$522$	103.765	4.54168
$523$	−42.0579	−1.83906	−0.919532	−	0.393016i	$-0.871432\pi$
$523$	−42.0579	−1.83906	−0.919532	+	0.393016i	$0.871432\pi$
$524$	4.21592	0.184173
$525$	−9.18914	−0.401047
$526$	−8.79929	−0.383667
$527$	−39.9322	−1.73947
$528$	2.29967	0.100080
$529$	44.9690	1.95517
$530$	6.68038	0.290177
$531$	−39.6994	−1.72281
$532$	17.8719	0.774846
$533$	−5.51454	−0.238861
$534$	11.2114	0.485165
$535$	19.9343	0.861833
$536$	2.93505	0.126775
$537$	64.3907	2.77866
$538$	39.5449	1.70490
$539$	−0.277490	−0.0119524
$540$	−20.6726	−0.889609
$541$	33.8512	1.45538	0.727688	−	0.685908i	$-0.240595\pi$
$541$	33.8512	1.45538	0.727688	+	0.685908i	$0.240595\pi$
$542$	17.9144	0.769489
$543$	48.3757	2.07600
$544$	−44.7004	−1.91651
$545$	12.5111	0.535916
$546$	14.4654	0.619061
$547$	−9.63084	−0.411785	−0.205893	−	0.978575i	$-0.566010\pi$
$547$	−9.63084	−0.411785	−0.205893	+	0.978575i	$0.566010\pi$
$548$	−5.06205	−0.216240
$549$	24.3581	1.03958
$550$	−1.87863	−0.0801049
$551$	−68.9531	−2.93750
$552$	22.4748	0.956593
$553$	−12.9100	−0.548987
$554$	−26.8222	−1.13957
$555$	−35.4136	−1.50322
$556$	50.0666	2.12330
$557$	5.42557	0.229889	0.114944	−	0.993372i	$-0.463331\pi$
$557$	5.42557	0.229889	0.114944	+	0.993372i	$0.463331\pi$
$558$	−78.5077	−3.32350
$559$	−2.07166	−0.0876221
$560$	3.87310	0.163668
$561$	4.43474	0.187235
$562$	1.12132	0.0473001
$563$	16.2919	0.686623	0.343311	−	0.939222i	$-0.388451\pi$
$563$	16.2919	0.686623	0.343311	+	0.939222i	$0.388451\pi$
$564$	31.3457	1.31989
$565$	22.2068	0.934249
$566$	−37.8880	−1.59255
$567$	2.44407	0.102641
$568$	2.53597	0.106407
$569$	−8.79795	−0.368829	−0.184415	−	0.982849i	$-0.559039\pi$
$569$	−8.79795	−0.368829	−0.184415	+	0.982849i	$0.559039\pi$
$570$	58.9540	2.46931
$571$	−32.0440	−1.34100	−0.670500	−	0.741909i	$-0.733920\pi$
$571$	−32.0440	−1.34100	−0.670500	+	0.741909i	$0.733920\pi$
$572$	1.62854	0.0680927
$573$	−65.8713	−2.75181
$574$	−4.85936	−0.202826
$575$	26.4551	1.10325
$576$	−57.7815	−2.40756
$577$	38.6865	1.61054	0.805269	−	0.592909i	$-0.202021\pi$
$577$	38.6865	1.61054	0.805269	+	0.592909i	$0.202021\pi$
$578$	−29.8444	−1.24137
$579$	−52.3800	−2.17684
$580$	31.0246	1.28823
$581$	0.210392	0.00872854
$582$	61.7762	2.56071
$583$	−0.656520	−0.0271903
$584$	7.32070	0.302933
$585$	16.6641	0.688974
$586$	18.9419	0.782481
$587$	−31.7510	−1.31050	−0.655251	−	0.755411i	$-0.727437\pi$
$587$	−31.7510	−1.31050	−0.655251	+	0.755411i	$0.727437\pi$
$588$	7.01944	0.289477
$589$	52.1692	2.14959
$590$	−21.5544	−0.887381
$591$	19.7080	0.810677
$592$	−26.7413	−1.09906
$593$	6.43197	0.264130	0.132065	−	0.991241i	$-0.457839\pi$
$593$	6.43197	0.264130	0.132065	+	0.991241i	$0.457839\pi$
$594$	3.68926	0.151372
$595$	7.46898	0.306198
$596$	26.4083	1.08173
$597$	−61.5890	−2.52067
$598$	−41.6451	−1.70299
$599$	−12.4849	−0.510118	−0.255059	−	0.966926i	$-0.582095\pi$
$599$	−12.4849	−0.510118	−0.255059	+	0.966926i	$0.582095\pi$
$600$	8.74772	0.357124
$601$	−4.94577	−0.201742	−0.100871	−	0.994899i	$-0.532163\pi$
$601$	−4.94577	−0.201742	−0.100871	+	0.994899i	$0.532163\pi$
$602$	−1.82553	−0.0744031
$603$	−16.0341	−0.652959
$604$	−1.36129	−0.0553902
$605$	14.6185	0.594329
$606$	−21.6770	−0.880567
$607$	−40.9390	−1.66166	−0.830831	−	0.556525i	$-0.812134\pi$
$607$	−40.9390	−1.66166	−0.830831	+	0.556525i	$0.812134\pi$
$608$	58.3986	2.36837
$609$	−27.0823	−1.09743
$610$	13.2250	0.535465
$611$	−10.6917	−0.432539
$612$	−71.1425	−2.87577
$613$	−43.6487	−1.76296	−0.881478	−	0.472225i	$-0.843451\pi$
$613$	−43.6487	−1.76296	−0.881478	+	0.472225i	$0.843451\pi$
$614$	5.73087	0.231279
$615$	−8.82721	−0.355947
$616$	0.264161	0.0106433
$617$	−21.7751	−0.876634	−0.438317	−	0.898821i	$-0.644425\pi$
$617$	−21.7751	−0.876634	−0.438317	+	0.898821i	$0.644425\pi$
$618$	50.9878	2.05103
$619$	−4.82852	−0.194075	−0.0970373	−	0.995281i	$-0.530937\pi$
$619$	−4.82852	−0.194075	−0.0970373	+	0.995281i	$0.530937\pi$
$620$	−23.4729	−0.942695
$621$	−51.9527	−2.08479
$622$	22.1578	0.888448
$623$	−1.85567	−0.0743457
$624$	19.8421	0.794318
$625$	1.34131	0.0536523
$626$	72.3472	2.89158
$627$	−5.79375	−0.231380
$628$	−35.0820	−1.39992
$629$	−51.5685	−2.05617
$630$	14.6842	0.585033
$631$	15.0552	0.599337	0.299669	−	0.954043i	$-0.403124\pi$
$631$	15.0552	0.599337	0.299669	+	0.954043i	$0.403124\pi$
$632$	12.2898	0.488862
$633$	−39.0696	−1.55288
$634$	63.2329	2.51130
$635$	1.58098	0.0627394
$636$	16.6074	0.658527
$637$	−2.39425	−0.0948636
$638$	−5.53669	−0.219200
$639$	−13.8539	−0.548053
$640$	−9.93292	−0.392633
$641$	−35.9322	−1.41924	−0.709619	−	0.704586i	$-0.751133\pi$
$641$	−35.9322	−1.41924	−0.709619	+	0.704586i	$0.751133\pi$
$642$	89.9908	3.55165
$643$	34.7301	1.36962	0.684812	−	0.728720i	$-0.259885\pi$
$643$	34.7301	1.36962	0.684812	+	0.728720i	$0.259885\pi$
$644$	−20.2086	−0.796330
$645$	−3.31615	−0.130573
$646$	85.8476	3.37763
$647$	−12.8615	−0.505636	−0.252818	−	0.967514i	$-0.581357\pi$
$647$	−12.8615	−0.505636	−0.252818	+	0.967514i	$0.581357\pi$
$648$	−2.32666	−0.0913998
$649$	2.11828	0.0831496
$650$	−16.2092	−0.635778
$651$	20.4902	0.803073
$652$	−7.62903	−0.298776
$653$	−10.6259	−0.415825	−0.207913	−	0.978147i	$-0.566667\pi$
$653$	−10.6259	−0.415825	−0.207913	+	0.978147i	$0.566667\pi$
$654$	56.4798	2.20853
$655$	−2.30183	−0.0899401
$656$	−6.66555	−0.260246
$657$	−39.9928	−1.56027
$658$	−9.42140	−0.367284
$659$	−38.9682	−1.51799	−0.758993	−	0.651099i	$-0.774308\pi$
$659$	−38.9682	−1.51799	−0.758993	+	0.651099i	$0.774308\pi$
$660$	2.60683	0.101471
$661$	29.2705	1.13849	0.569245	−	0.822168i	$-0.307235\pi$
$661$	29.2705	1.13849	0.569245	+	0.822168i	$0.307235\pi$
$662$	19.2582	0.748491
$663$	38.2640	1.48605
$664$	−0.200285	−0.00777258
$665$	−9.75782	−0.378392
$666$	−101.385	−3.92859
$667$	77.9684	3.01895
$668$	11.4680	0.443711
$669$	41.0786	1.58819
$670$	−8.70556	−0.336325
$671$	−1.29970	−0.0501743
$672$	22.9368	0.884808
$673$	24.7700	0.954814	0.477407	−	0.878682i	$-0.341577\pi$
$673$	24.7700	0.954814	0.477407	+	0.878682i	$0.341577\pi$
$674$	−40.7889	−1.57113
$675$	−20.2212	−0.778313
$676$	−17.8144	−0.685167
$677$	19.5756	0.752351	0.376176	−	0.926548i	$-0.377239\pi$
$677$	19.5756	0.752351	0.376176	+	0.926548i	$0.377239\pi$
$678$	100.250	3.85008
$679$	−10.2249	−0.392397
$680$	−7.11019	−0.272663
$681$	4.58397	0.175658
$682$	4.18901	0.160405
$683$	−16.7258	−0.639994	−0.319997	−	0.947419i	$-0.603682\pi$
$683$	−16.7258	−0.639994	−0.319997	+	0.947419i	$0.603682\pi$
$684$	92.9438	3.55379
$685$	2.76381	0.105600
$686$	−2.10979	−0.0805521
$687$	66.2571	2.52787
$688$	−2.50407	−0.0954667
$689$	−5.66460	−0.215804
$690$	−66.6620	−2.53778
$691$	−5.36855	−0.204229	−0.102115	−	0.994773i	$-0.532561\pi$
$691$	−5.36855	−0.204229	−0.102115	+	0.994773i	$0.532561\pi$
$692$	28.0762	1.06730
$693$	−1.44310	−0.0548189
$694$	22.4515	0.852246
$695$	−27.3357	−1.03690
$696$	25.7813	0.977237
$697$	−12.8540	−0.486880
$698$	11.1870	0.423435
$699$	−68.4689	−2.58973
$700$	−7.86564	−0.297293
$701$	29.6689	1.12058	0.560290	−	0.828297i	$-0.310690\pi$
$701$	29.6689	1.12058	0.560290	+	0.828297i	$0.310690\pi$
$702$	31.8318	1.20141
$703$	67.3715	2.54096
$704$	3.08310	0.116199
$705$	−17.1143	−0.644563
$706$	15.8296	0.595755
$707$	3.58788	0.134936
$708$	−53.5842	−2.01382
$709$	14.3378	0.538467	0.269234	−	0.963075i	$-0.413230\pi$
$709$	14.3378	0.538467	0.269234	+	0.963075i	$0.413230\pi$
$710$	−7.52186	−0.282290
$711$	−67.1389	−2.51790
$712$	1.76652	0.0662033
$713$	−58.9901	−2.20920
$714$	33.7178	1.26186
$715$	−0.889160	−0.0332527
$716$	55.1166	2.05980
$717$	9.48696	0.354297
$718$	−57.3674	−2.14093
$719$	20.2791	0.756281	0.378141	−	0.925748i	$-0.376564\pi$
$719$	20.2791	0.756281	0.378141	+	0.925748i	$0.376564\pi$
$720$	20.1422	0.750657
$721$	−8.43928	−0.314295
$722$	−72.0693	−2.68214
$723$	−37.0682	−1.37858
$724$	41.4082	1.53893
$725$	30.3471	1.12706
$726$	65.9937	2.44926
$727$	−36.5775	−1.35659	−0.678293	−	0.734792i	$-0.737280\pi$
$727$	−36.5775	−1.35659	−0.678293	+	0.734792i	$0.737280\pi$
$728$	2.27924	0.0844741
$729$	−41.4267	−1.53432
$730$	−21.7137	−0.803661
$731$	−4.82891	−0.178604
$732$	32.8773	1.21518
$733$	20.9376	0.773346	0.386673	−	0.922217i	$-0.373624\pi$
$733$	20.9376	0.773346	0.386673	+	0.922217i	$0.373624\pi$
$734$	−56.8258	−2.09748
$735$	−3.83251	−0.141364
$736$	−66.0340	−2.43404
$737$	0.855546	0.0315144
$738$	−25.2713	−0.930250
$739$	6.20320	0.228188	0.114094	−	0.993470i	$-0.463603\pi$
$739$	6.20320	0.228188	0.114094	+	0.993470i	$0.463603\pi$
$740$	−30.3130	−1.11433
$741$	−49.9898	−1.83642
$742$	−4.99159	−0.183247
$743$	23.4338	0.859703	0.429852	−	0.902900i	$-0.358566\pi$
$743$	23.4338	0.859703	0.429852	+	0.902900i	$0.358566\pi$
$744$	−19.5059	−0.715120
$745$	−14.4186	−0.528256
$746$	8.65699	0.316955
$747$	1.09415	0.0400330
$748$	3.79602	0.138796
$749$	−14.8949	−0.544248
$750$	−66.3754	−2.42369
$751$	−15.6731	−0.571920	−0.285960	−	0.958242i	$-0.592312\pi$
$751$	−15.6731	−0.571920	−0.285960	+	0.958242i	$0.592312\pi$
$752$	−12.9233	−0.471263
$753$	63.9794	2.33154
$754$	−47.7718	−1.73975
$755$	0.743246	0.0270495
$756$	15.4466	0.561788
$757$	5.27571	0.191749	0.0958744	−	0.995393i	$-0.469435\pi$
$757$	5.27571	0.191749	0.0958744	+	0.995393i	$0.469435\pi$
$758$	−67.0752	−2.43628
$759$	6.55126	0.237796
$760$	9.28908	0.336950
$761$	−33.0034	−1.19637	−0.598186	−	0.801357i	$-0.704112\pi$
$761$	−33.0034	−1.19637	−0.598186	+	0.801357i	$0.704112\pi$
$762$	7.13716	0.258552
$763$	−9.34829	−0.338431
$764$	−56.3840	−2.03990
$765$	38.8428	1.40436
$766$	−31.7511	−1.14721
$767$	18.2770	0.659943
$768$	18.7933	0.678144
$769$	−14.7116	−0.530516	−0.265258	−	0.964178i	$-0.585457\pi$
$769$	−14.7116	−0.530516	−0.265258	+	0.964178i	$0.585457\pi$
$770$	−0.783519	−0.0282361
$771$	−53.5917	−1.93006
$772$	−44.8358	−1.61368
$773$	20.1861	0.726043	0.363021	−	0.931781i	$-0.381745\pi$
$773$	20.1861	0.726043	0.363021	+	0.931781i	$0.381745\pi$
$774$	−9.49376	−0.341246
$775$	−22.9603	−0.824758
$776$	9.73376	0.349422
$777$	26.4611	0.949286
$778$	18.1618	0.651132
$779$	16.7931	0.601674
$780$	22.4923	0.805354
$781$	0.739217	0.0264513
$782$	−97.0719	−3.47128
$783$	−59.5958	−2.12978
$784$	−2.89398	−0.103357
$785$	19.1543	0.683645
$786$	−10.3914	−0.370647
$787$	28.5450	1.01752	0.508760	−	0.860908i	$-0.330104\pi$
$787$	28.5450	1.01752	0.508760	+	0.860908i	$0.330104\pi$
$788$	16.8695	0.600950
$789$	11.9434	0.425198
$790$	−36.4524	−1.29692
$791$	−16.5930	−0.589979
$792$	1.37378	0.0488151
$793$	−11.2141	−0.398224
$794$	−1.27899	−0.0453895
$795$	−9.06742	−0.321588
$796$	−52.7184	−1.86856
$797$	13.5498	0.479958	0.239979	−	0.970778i	$-0.422859\pi$
$797$	13.5498	0.479958	0.239979	+	0.970778i	$0.422859\pi$
$798$	−44.0505	−1.55937
$799$	−24.9216	−0.881661
$800$	−25.7019	−0.908700
$801$	−9.65048	−0.340983
$802$	81.9651	2.89429
$803$	2.13393	0.0753049
$804$	−21.6420	−0.763255
$805$	11.0336	0.388884
$806$	36.1437	1.27311
$807$	−53.6752	−1.88945
$808$	−3.41553	−0.120158
$809$	20.5392	0.722120	0.361060	−	0.932543i	$-0.382415\pi$
$809$	20.5392	0.722120	0.361060	+	0.932543i	$0.382415\pi$
$810$	6.90104	0.242478
$811$	−43.2243	−1.51781	−0.758906	−	0.651201i	$-0.774266\pi$
$811$	−43.2243	−1.51781	−0.758906	+	0.651201i	$0.774266\pi$
$812$	−23.1816	−0.813516
$813$	−24.3156	−0.852784
$814$	5.40970	0.189610
$815$	4.16534	0.145906
$816$	46.2505	1.61909
$817$	6.30870	0.220714
$818$	−8.75149	−0.305989
$819$	−12.4514	−0.435088
$820$	−7.55584	−0.263861
$821$	−1.83457	−0.0640270	−0.0320135	−	0.999487i	$-0.510192\pi$
$821$	−1.83457	−0.0640270	−0.0320135	+	0.999487i	$0.510192\pi$
$822$	12.4769	0.435181
$823$	−13.3061	−0.463822	−0.231911	−	0.972737i	$-0.574498\pi$
$823$	−13.3061	−0.463822	−0.231911	+	0.972737i	$0.574498\pi$
$824$	8.03388	0.279873
$825$	2.54990	0.0887761
$826$	16.1055	0.560381
$827$	36.7199	1.27687	0.638437	−	0.769674i	$-0.279581\pi$
$827$	36.7199	1.27687	0.638437	+	0.769674i	$0.279581\pi$
$828$	−105.096	−3.65233
$829$	−34.7115	−1.20558	−0.602789	−	0.797900i	$-0.705944\pi$
$829$	−34.7115	−1.20558	−0.602789	+	0.797900i	$0.705944\pi$
$830$	0.594061	0.0206202
$831$	36.4063	1.26292
$832$	26.6017	0.922247
$833$	−5.58083	−0.193364
$834$	−123.404	−4.27312
$835$	−6.26137	−0.216684
$836$	−4.95929	−0.171521
$837$	45.0896	1.55853
$838$	−16.4033	−0.566641
$839$	14.5640	0.502804	0.251402	−	0.967883i	$-0.419108\pi$
$839$	14.5640	0.502804	0.251402	+	0.967883i	$0.419108\pi$
$840$	3.64841	0.125882
$841$	60.4389	2.08410
$842$	31.3511	1.08043
$843$	−1.52199	−0.0524202
$844$	−33.4424	−1.15114
$845$	9.72639	0.334598
$846$	−48.9964	−1.68453
$847$	−10.9230	−0.375319
$848$	−6.84693	−0.235124
$849$	51.4261	1.76494
$850$	−37.7826	−1.29593
$851$	−76.1800	−2.61142
$852$	−18.6993	−0.640629
$853$	14.7568	0.505262	0.252631	−	0.967563i	$-0.418704\pi$
$853$	14.7568	0.505262	0.252631	+	0.967563i	$0.418704\pi$
$854$	−9.88174	−0.338146
$855$	−50.7460	−1.73548
$856$	14.1794	0.484642
$857$	−4.06613	−0.138896	−0.0694482	−	0.997586i	$-0.522124\pi$
$857$	−4.06613	−0.138896	−0.0694482	+	0.997586i	$0.522124\pi$
$858$	−4.01401	−0.137036
$859$	1.00000	0.0341196
$859$	1.00000	0.0341196
$860$	−2.83853	−0.0967930
$861$	6.59570	0.224781
$862$	−1.58467	−0.0539741
$863$	0.509088	0.0173295	0.00866477	−	0.999962i	$-0.497242\pi$
$863$	0.509088	0.0173295	0.00866477	+	0.999962i	$0.497242\pi$
$864$	50.4736	1.71715
$865$	−15.3292	−0.521209
$866$	44.5059	1.51237
$867$	40.5085	1.37574
$868$	17.5390	0.595313
$869$	3.58239	0.121524
$870$	−76.4692	−2.59255
$871$	7.38184	0.250124
$872$	8.89923	0.301366
$873$	−53.1753	−1.79971
$874$	126.819	4.28972
$875$	10.9862	0.371400
$876$	−53.9803	−1.82382
$877$	−26.2762	−0.887283	−0.443641	−	0.896204i	$-0.646314\pi$
$877$	−26.2762	−0.887283	−0.443641	+	0.896204i	$0.646314\pi$
$878$	−47.9458	−1.61809
$879$	−25.7102	−0.867182
$880$	−1.07475	−0.0362297
$881$	−34.7995	−1.17242	−0.586212	−	0.810157i	$-0.699382\pi$
$881$	−34.7995	−1.17242	−0.586212	+	0.810157i	$0.699382\pi$
$882$	−10.9721	−0.369449
$883$	44.1185	1.48471	0.742353	−	0.670009i	$-0.233710\pi$
$883$	44.1185	1.48471	0.742353	+	0.670009i	$0.233710\pi$
$884$	32.7529	1.10160
$885$	29.2562	0.983438
$886$	−33.6638	−1.13096
$887$	−28.3011	−0.950258	−0.475129	−	0.879916i	$-0.657599\pi$
$887$	−28.3011	−0.950258	−0.475129	+	0.879916i	$0.657599\pi$
$888$	−25.1899	−0.845319
$889$	−1.18131	−0.0396200
$890$	−5.23964	−0.175633
$891$	−0.678205	−0.0227207
$892$	35.1621	1.17732
$893$	32.5586	1.08953
$894$	−65.0909	−2.17697
$895$	−30.0929	−1.00589
$896$	7.42189	0.247948
$897$	56.5257	1.88734
$898$	23.6213	0.788253
$899$	−67.6686	−2.25687
$900$	−40.9057	−1.36352
$901$	−13.2038	−0.439882
$902$	1.34843	0.0448976
$903$	2.47783	0.0824570
$904$	15.7959	0.525364
$905$	−22.6083	−0.751526
$906$	3.35530	0.111472
$907$	31.7953	1.05574	0.527872	−	0.849324i	$-0.322990\pi$
$907$	31.7953	1.05574	0.527872	+	0.849324i	$0.322990\pi$
$908$	3.92375	0.130214
$909$	18.6590	0.618878
$910$	−6.76038	−0.224104
$911$	−8.39214	−0.278044	−0.139022	−	0.990289i	$-0.544396\pi$
$911$	−8.39214	−0.278044	−0.139022	+	0.990289i	$0.544396\pi$
$912$	−60.4238	−2.00083
$913$	−0.0583818	−0.00193216
$914$	46.9178	1.55190
$915$	−17.9506	−0.593427
$916$	56.7142	1.87389
$917$	1.71993	0.0567972
$918$	74.1978	2.44889
$919$	15.3142	0.505168	0.252584	−	0.967575i	$-0.418720\pi$
$919$	15.3142	0.505168	0.252584	+	0.967575i	$0.418720\pi$
$920$	−10.5036	−0.346293
$921$	−7.77863	−0.256314
$922$	38.5540	1.26971
$923$	6.37813	0.209939
$924$	−1.94783	−0.0640788
$925$	−29.6510	−0.974919
$926$	−3.28340	−0.107899
$927$	−43.8889	−1.44150
$928$	−75.7487	−2.48657
$929$	−14.8196	−0.486215	−0.243107	−	0.969999i	$-0.578167\pi$
$929$	−14.8196	−0.486215	−0.243107	+	0.969999i	$0.578167\pi$
$930$	57.8558	1.89717
$931$	7.29105	0.238955
$932$	−58.6075	−1.91975
$933$	−30.0753	−0.984621
$934$	−61.7765	−2.02139
$935$	−2.07257	−0.0677803
$936$	11.8533	0.387437
$937$	15.9547	0.521217	0.260608	−	0.965445i	$-0.416077\pi$
$937$	15.9547	0.521217	0.260608	+	0.965445i	$0.416077\pi$
$938$	6.50481	0.212390
$939$	−98.1984	−3.20458
$940$	−14.6494	−0.477810
$941$	−32.0896	−1.04609	−0.523046	−	0.852305i	$-0.675204\pi$
$941$	−32.0896	−1.04609	−0.523046	+	0.852305i	$0.675204\pi$
$942$	86.4696	2.81733
$943$	−18.9887	−0.618357
$944$	22.0918	0.719026
$945$	−8.43364	−0.274346
$946$	0.506567	0.0164699
$947$	−44.5792	−1.44863	−0.724315	−	0.689470i	$-0.757844\pi$
$947$	−44.5792	−1.44863	−0.724315	+	0.689470i	$0.757844\pi$
$948$	−90.6207	−2.94322
$949$	18.4120	0.597680
$950$	49.3609	1.60148
$951$	−85.8273	−2.78314
$952$	5.31274	0.172187
$953$	33.1176	1.07278	0.536392	−	0.843969i	$-0.319787\pi$
$953$	33.1176	1.07278	0.536392	+	0.843969i	$0.319787\pi$
$954$	−25.9590	−0.840454
$955$	30.7849	0.996175
$956$	8.12057	0.262638
$957$	7.51507	0.242928
$958$	−29.7798	−0.962141
$959$	−2.06512	−0.0666862
$960$	42.5817	1.37432
$961$	20.1974	0.651529
$962$	46.6761	1.50490
$963$	−77.4617	−2.49617
$964$	−31.7293	−1.02193
$965$	24.4797	0.788030
$966$	49.8099	1.60261
$967$	51.8920	1.66873	0.834367	−	0.551209i	$-0.185833\pi$
$967$	51.8920	1.66873	0.834367	+	0.551209i	$0.185833\pi$
$968$	10.3983	0.334214
$969$	−116.523	−3.74325
$970$	−28.8710	−0.926993
$971$	44.8457	1.43917	0.719584	−	0.694405i	$-0.244332\pi$
$971$	44.8457	1.43917	0.719584	+	0.694405i	$0.244332\pi$
$972$	−29.1839	−0.936074
$973$	20.4252	0.654803
$974$	−42.1143	−1.34943
$975$	22.0011	0.704599
$976$	−13.5547	−0.433876
$977$	−5.46656	−0.174891	−0.0874453	−	0.996169i	$-0.527870\pi$
$977$	−5.46656	−0.174891	−0.0874453	+	0.996169i	$0.527870\pi$
$978$	18.8039	0.601284
$979$	0.514929	0.0164572
$980$	−3.28052	−0.104793
$981$	−48.6163	−1.55220
$982$	−56.1625	−1.79222
$983$	−27.1740	−0.866717	−0.433358	−	0.901222i	$-0.642672\pi$
$983$	−27.1740	−0.866717	−0.433358	+	0.901222i	$0.642672\pi$
$984$	−6.27886	−0.200163
$985$	−9.21049	−0.293471
$986$	−111.353	−3.54620
$987$	12.7879	0.407042
$988$	−42.7898	−1.36133
$989$	−7.13354	−0.226833
$990$	−4.07473	−0.129503
$991$	24.8100	0.788115	0.394058	−	0.919086i	$-0.371071\pi$
$991$	24.8100	0.788115	0.394058	+	0.919086i	$0.371071\pi$
$992$	57.3107	1.81962
$993$	−26.1395	−0.829513
$994$	5.62034	0.178266
$995$	28.7835	0.912499
$996$	1.47683	0.0467953
$997$	−9.71932	−0.307814	−0.153907	−	0.988085i	$-0.549186\pi$
$997$	−9.71932	−0.307814	−0.153907	+	0.988085i	$0.549186\pi$
$998$	55.4405	1.75494
$999$	58.2289	1.84228

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6013.2.a.d.1.19	✓	104

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6013.2.a.d.1.19	✓	104	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6013 = 7 \cdot 859 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6013.a (trivial)

\(f(q)\)	\(=\)	\(q-2.10979 q^{2} +2.86366 q^{3} +2.45121 q^{4} -1.33833 q^{5} -6.04172 q^{6} +1.00000 q^{7} -0.951963 q^{8} +5.20055 q^{9} +O(q^{10})\)	\(q-2.10979 q^{2} +2.86366 q^{3} +2.45121 q^{4} -1.33833 q^{5} -6.04172 q^{6} +1.00000 q^{7} -0.951963 q^{8} +5.20055 q^{9} +2.82359 q^{10} -0.277490 q^{11} +7.01944 q^{12} -2.39425 q^{13} -2.10979 q^{14} -3.83251 q^{15} -2.89398 q^{16} -5.58083 q^{17} -10.9721 q^{18} +7.29105 q^{19} -3.28052 q^{20} +2.86366 q^{21} +0.585447 q^{22} -8.24433 q^{23} -2.72610 q^{24} -3.20888 q^{25} +5.05136 q^{26} +6.30163 q^{27} +2.45121 q^{28} -9.45722 q^{29} +8.08580 q^{30} +7.15524 q^{31} +8.00962 q^{32} -0.794638 q^{33} +11.7744 q^{34} -1.33833 q^{35} +12.7476 q^{36} +9.24030 q^{37} -15.3826 q^{38} -6.85632 q^{39} +1.27404 q^{40} +2.30324 q^{41} -6.04172 q^{42} +0.865266 q^{43} -0.680188 q^{44} -6.96004 q^{45} +17.3938 q^{46} +4.46556 q^{47} -8.28739 q^{48} +1.00000 q^{49} +6.77006 q^{50} -15.9816 q^{51} -5.86881 q^{52} +2.36592 q^{53} -13.2951 q^{54} +0.371373 q^{55} -0.951963 q^{56} +20.8791 q^{57} +19.9527 q^{58} -7.63369 q^{59} -9.39431 q^{60} +4.68376 q^{61} -15.0960 q^{62} +5.20055 q^{63} -11.1106 q^{64} +3.20429 q^{65} +1.67652 q^{66} -3.08316 q^{67} -13.6798 q^{68} -23.6090 q^{69} +2.82359 q^{70} -2.66394 q^{71} -4.95073 q^{72} -7.69011 q^{73} -19.4951 q^{74} -9.18914 q^{75} +17.8719 q^{76} -0.277490 q^{77} +14.4654 q^{78} -12.9100 q^{79} +3.87310 q^{80} +2.44407 q^{81} -4.85936 q^{82} +0.210392 q^{83} +7.01944 q^{84} +7.46898 q^{85} -1.82553 q^{86} -27.0823 q^{87} +0.264161 q^{88} -1.85567 q^{89} +14.6842 q^{90} -2.39425 q^{91} -20.2086 q^{92} +20.4902 q^{93} -9.42140 q^{94} -9.75782 q^{95} +22.9368 q^{96} -10.2249 q^{97} -2.10979 q^{98} -1.44310 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 104 q - 17 q^{2} - 34 q^{3} + 99 q^{4} - 46 q^{5} - 18 q^{6} + 104 q^{7} - 48 q^{8} + 98 q^{9}+O(q^{10}) \) 104 * q - 17 * q^2 - 34 * q^3 + 99 * q^4 - 46 * q^5 - 18 * q^6 + 104 * q^7 - 48 * q^8 + 98 * q^9	\( 104 q - 17 q^{2} - 34 q^{3} + 99 q^{4} - 46 q^{5} - 18 q^{6} + 104 q^{7} - 48 q^{8} + 98 q^{9} - 17 q^{10} - 46 q^{11} - 62 q^{12} - 37 q^{13} - 17 q^{14} - 17 q^{15} + 93 q^{16} - 75 q^{17} - 41 q^{18} - 40 q^{19} - 106 q^{20} - 34 q^{21} - 14 q^{22} - 57 q^{23} - 38 q^{24} + 102 q^{25} - 45 q^{26} - 121 q^{27} + 99 q^{28} - 29 q^{29} + 26 q^{30} - 42 q^{31} - 113 q^{32} - 42 q^{33} - 7 q^{34} - 46 q^{35} + 99 q^{36} - 31 q^{37} - 62 q^{38} - 9 q^{39} - 36 q^{40} - 106 q^{41} - 18 q^{42} - 29 q^{43} - 60 q^{44} - 121 q^{45} + 21 q^{46} - 141 q^{47} - 88 q^{48} + 104 q^{49} - 70 q^{50} - 2 q^{51} - 58 q^{52} - 70 q^{53} - 49 q^{54} - 14 q^{55} - 48 q^{56} - 11 q^{57} - 28 q^{58} - 202 q^{59} + 17 q^{60} - 79 q^{61} - 41 q^{62} + 98 q^{63} + 110 q^{64} - 34 q^{65} - 21 q^{66} - 57 q^{67} - 180 q^{68} - 99 q^{69} - 17 q^{70} - 109 q^{71} - 73 q^{72} - 46 q^{73} - 7 q^{74} - 146 q^{75} - 54 q^{76} - 46 q^{77} - 42 q^{78} - 12 q^{79} - 187 q^{80} + 100 q^{81} - 45 q^{82} - 156 q^{83} - 62 q^{84} - 13 q^{85} - 8 q^{86} - 76 q^{87} - 6 q^{88} - 140 q^{89} - 5 q^{90} - 37 q^{91} - 98 q^{92} - q^{93} - 17 q^{94} - 48 q^{95} - 12 q^{96} - 63 q^{97} - 17 q^{98} - 78 q^{99}+O(q^{100}) \) 104 * q - 17 * q^2 - 34 * q^3 + 99 * q^4 - 46 * q^5 - 18 * q^6 + 104 * q^7 - 48 * q^8 + 98 * q^9 - 17 * q^10 - 46 * q^11 - 62 * q^12 - 37 * q^13 - 17 * q^14 - 17 * q^15 + 93 * q^16 - 75 * q^17 - 41 * q^18 - 40 * q^19 - 106 * q^20 - 34 * q^21 - 14 * q^22 - 57 * q^23 - 38 * q^24 + 102 * q^25 - 45 * q^26 - 121 * q^27 + 99 * q^28 - 29 * q^29 + 26 * q^30 - 42 * q^31 - 113 * q^32 - 42 * q^33 - 7 * q^34 - 46 * q^35 + 99 * q^36 - 31 * q^37 - 62 * q^38 - 9 * q^39 - 36 * q^40 - 106 * q^41 - 18 * q^42 - 29 * q^43 - 60 * q^44 - 121 * q^45 + 21 * q^46 - 141 * q^47 - 88 * q^48 + 104 * q^49 - 70 * q^50 - 2 * q^51 - 58 * q^52 - 70 * q^53 - 49 * q^54 - 14 * q^55 - 48 * q^56 - 11 * q^57 - 28 * q^58 - 202 * q^59 + 17 * q^60 - 79 * q^61 - 41 * q^62 + 98 * q^63 + 110 * q^64 - 34 * q^65 - 21 * q^66 - 57 * q^67 - 180 * q^68 - 99 * q^69 - 17 * q^70 - 109 * q^71 - 73 * q^72 - 46 * q^73 - 7 * q^74 - 146 * q^75 - 54 * q^76 - 46 * q^77 - 42 * q^78 - 12 * q^79 - 187 * q^80 + 100 * q^81 - 45 * q^82 - 156 * q^83 - 62 * q^84 - 13 * q^85 - 8 * q^86 - 76 * q^87 - 6 * q^88 - 140 * q^89 - 5 * q^90 - 37 * q^91 - 98 * q^92 - q^93 - 17 * q^94 - 48 * q^95 - 12 * q^96 - 63 * q^97 - 17 * q^98 - 78 * q^99

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