LMFDB - Embedded newform 8047.2.a.c.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8047,2,Mod(1,8047)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8047, 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("8047.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8047 = 13 \cdot 619 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8047.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:	$64.2556185065$
Analytic rank:	$1$
Dimension:	$151$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	8047.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.76685 q^{2} +2.61084 q^{3} +5.65545 q^{4} +1.02194 q^{5} -7.22381 q^{6} +1.46189 q^{7} -10.1141 q^{8} +3.81650 q^{9} +O(q^{10})$	\(q-2.76685 q^{2} +2.61084 q^{3} +5.65545 q^{4} +1.02194 q^{5} -7.22381 q^{6} +1.46189 q^{7} -10.1141 q^{8} +3.81650 q^{9} -2.82754 q^{10} -5.55985 q^{11} +14.7655 q^{12} -1.00000 q^{13} -4.04481 q^{14} +2.66811 q^{15} +16.6732 q^{16} +0.0770610 q^{17} -10.5597 q^{18} -2.93911 q^{19} +5.77950 q^{20} +3.81675 q^{21} +15.3833 q^{22} +0.624072 q^{23} -26.4063 q^{24} -3.95565 q^{25} +2.76685 q^{26} +2.13176 q^{27} +8.26762 q^{28} +2.85853 q^{29} -7.38227 q^{30} +6.99649 q^{31} -25.9041 q^{32} -14.5159 q^{33} -0.213216 q^{34} +1.49395 q^{35} +21.5840 q^{36} -5.15344 q^{37} +8.13206 q^{38} -2.61084 q^{39} -10.3359 q^{40} +6.49342 q^{41} -10.5604 q^{42} +6.19452 q^{43} -31.4434 q^{44} +3.90022 q^{45} -1.72671 q^{46} -8.73637 q^{47} +43.5311 q^{48} -4.86289 q^{49} +10.9447 q^{50} +0.201194 q^{51} -5.65545 q^{52} -13.3953 q^{53} -5.89826 q^{54} -5.68181 q^{55} -14.7856 q^{56} -7.67355 q^{57} -7.90911 q^{58} -1.28889 q^{59} +15.0894 q^{60} +7.02732 q^{61} -19.3582 q^{62} +5.57929 q^{63} +38.3263 q^{64} -1.02194 q^{65} +40.1633 q^{66} +0.145107 q^{67} +0.435815 q^{68} +1.62936 q^{69} -4.13354 q^{70} -0.935284 q^{71} -38.6004 q^{72} +4.10344 q^{73} +14.2588 q^{74} -10.3276 q^{75} -16.6220 q^{76} -8.12786 q^{77} +7.22381 q^{78} -13.2846 q^{79} +17.0389 q^{80} -5.88381 q^{81} -17.9663 q^{82} -6.46113 q^{83} +21.5855 q^{84} +0.0787514 q^{85} -17.1393 q^{86} +7.46317 q^{87} +56.2327 q^{88} -12.3340 q^{89} -10.7913 q^{90} -1.46189 q^{91} +3.52941 q^{92} +18.2667 q^{93} +24.1722 q^{94} -3.00358 q^{95} -67.6316 q^{96} -5.54152 q^{97} +13.4549 q^{98} -21.2192 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 151 q - 13 q^{2} - 16 q^{3} + 151 q^{4} - 43 q^{5} - 17 q^{6} - 18 q^{7} - 39 q^{8} + 135 q^{9}+O(q^{10}) $ 151 * q - 13 * q^2 - 16 * q^3 + 151 * q^4 - 43 * q^5 - 17 * q^6 - 18 * q^7 - 39 * q^8 + 135 * q^9	\( 151 q - 13 q^{2} - 16 q^{3} + 151 q^{4} - 43 q^{5} - 17 q^{6} - 18 q^{7} - 39 q^{8} + 135 q^{9} - 3 q^{10} - 27 q^{11} - 52 q^{12} - 151 q^{13} - 9 q^{14} - 14 q^{15} + 143 q^{16} - 111 q^{17} - 37 q^{18} - 17 q^{19} - 107 q^{20} - 29 q^{21} - 16 q^{22} - 47 q^{23} - 46 q^{24} + 122 q^{25} + 13 q^{26} - 55 q^{27} - 44 q^{28} + 37 q^{29} - 14 q^{30} - 27 q^{31} - 86 q^{32} - 94 q^{33} - 10 q^{34} - 47 q^{35} + 124 q^{36} - 59 q^{37} - 80 q^{38} + 16 q^{39} + 5 q^{40} - 129 q^{41} - 77 q^{42} - 11 q^{43} - 99 q^{44} - 122 q^{45} - 17 q^{46} - 130 q^{47} - 111 q^{48} + 99 q^{49} - 72 q^{50} + 15 q^{51} - 151 q^{52} - 43 q^{53} - 49 q^{54} - 40 q^{55} - 50 q^{56} - 85 q^{57} - 73 q^{58} - 74 q^{59} - 43 q^{60} - 7 q^{61} - 110 q^{62} - 70 q^{63} + 141 q^{64} + 43 q^{65} - 16 q^{66} - 39 q^{67} - 222 q^{68} + 19 q^{69} - 52 q^{70} - 72 q^{71} - 106 q^{72} - 143 q^{73} + 20 q^{74} - 73 q^{75} - 88 q^{76} - 86 q^{77} + 17 q^{78} + 10 q^{79} - 239 q^{80} + 103 q^{81} - 96 q^{82} - 96 q^{83} - 75 q^{84} - 24 q^{85} - 109 q^{86} - 65 q^{87} - 45 q^{88} - 237 q^{89} - 79 q^{90} + 18 q^{91} - 153 q^{92} - 137 q^{93} - 23 q^{94} + 10 q^{95} - 109 q^{96} - 160 q^{97} - 119 q^{98} - 86 q^{99}+O(q^{100}) \) 151 * q - 13 * q^2 - 16 * q^3 + 151 * q^4 - 43 * q^5 - 17 * q^6 - 18 * q^7 - 39 * q^8 + 135 * q^9 - 3 * q^10 - 27 * q^11 - 52 * q^12 - 151 * q^13 - 9 * q^14 - 14 * q^15 + 143 * q^16 - 111 * q^17 - 37 * q^18 - 17 * q^19 - 107 * q^20 - 29 * q^21 - 16 * q^22 - 47 * q^23 - 46 * q^24 + 122 * q^25 + 13 * q^26 - 55 * q^27 - 44 * q^28 + 37 * q^29 - 14 * q^30 - 27 * q^31 - 86 * q^32 - 94 * q^33 - 10 * q^34 - 47 * q^35 + 124 * q^36 - 59 * q^37 - 80 * q^38 + 16 * q^39 + 5 * q^40 - 129 * q^41 - 77 * q^42 - 11 * q^43 - 99 * q^44 - 122 * q^45 - 17 * q^46 - 130 * q^47 - 111 * q^48 + 99 * q^49 - 72 * q^50 + 15 * q^51 - 151 * q^52 - 43 * q^53 - 49 * q^54 - 40 * q^55 - 50 * q^56 - 85 * q^57 - 73 * q^58 - 74 * q^59 - 43 * q^60 - 7 * q^61 - 110 * q^62 - 70 * q^63 + 141 * q^64 + 43 * q^65 - 16 * q^66 - 39 * q^67 - 222 * q^68 + 19 * q^69 - 52 * q^70 - 72 * q^71 - 106 * q^72 - 143 * q^73 + 20 * q^74 - 73 * q^75 - 88 * q^76 - 86 * q^77 + 17 * q^78 + 10 * q^79 - 239 * q^80 + 103 * q^81 - 96 * q^82 - 96 * q^83 - 75 * q^84 - 24 * q^85 - 109 * q^86 - 65 * q^87 - 45 * q^88 - 237 * q^89 - 79 * q^90 + 18 * q^91 - 153 * q^92 - 137 * q^93 - 23 * q^94 + 10 * q^95 - 109 * q^96 - 160 * q^97 - 119 * q^98 - 86 * 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 $

$2$	−2.76685	−1.95646	−0.978229	−	0.207530i	$-0.933457\pi$
$2$	−2.76685	−1.95646	−0.978229	+	0.207530i	$0.933457\pi$
$3$	2.61084	1.50737	0.753686	−	0.657235i	$-0.228274\pi$
$3$	2.61084	1.50737	0.753686	+	0.657235i	$0.228274\pi$
$4$	5.65545	2.82772
$5$	1.02194	0.457023	0.228512	−	0.973541i	$-0.426614\pi$
$5$	1.02194	0.457023	0.228512	+	0.973541i	$0.426614\pi$
$6$	−7.22381	−2.94911
$7$	1.46189	0.552541	0.276270	−	0.961080i	$-0.410901\pi$
$7$	1.46189	0.552541	0.276270	+	0.961080i	$0.410901\pi$
$8$	−10.1141	−3.57587
$9$	3.81650	1.27217
$10$	−2.82754	−0.894147
$11$	−5.55985	−1.67636	−0.838179	−	0.545396i	$-0.816379\pi$
$11$	−5.55985	−1.67636	−0.838179	+	0.545396i	$0.816379\pi$
$12$	14.7655	4.26243
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−4.04481	−1.08102
$15$	2.66811	0.688904
$16$	16.6732	4.16830
$17$	0.0770610	0.0186900	0.00934502	−	0.999956i	$-0.497025\pi$
$17$	0.0770610	0.0186900	0.00934502	+	0.999956i	$0.497025\pi$
$18$	−10.5597	−2.48894
$19$	−2.93911	−0.674277	−0.337139	−	0.941455i	$-0.609459\pi$
$19$	−2.93911	−0.674277	−0.337139	+	0.941455i	$0.609459\pi$
$20$	5.77950	1.29234
$21$	3.81675	0.832884
$22$	15.3833	3.27972
$23$	0.624072	0.130128	0.0650640	−	0.997881i	$-0.479275\pi$
$23$	0.624072	0.130128	0.0650640	+	0.997881i	$0.479275\pi$
$24$	−26.4063	−5.39016
$25$	−3.95565	−0.791130
$26$	2.76685	0.542624
$27$	2.13176	0.410258
$28$	8.26762	1.56243
$29$	2.85853	0.530815	0.265408	−	0.964136i	$-0.414493\pi$
$29$	2.85853	0.530815	0.265408	+	0.964136i	$0.414493\pi$
$30$	−7.38227	−1.34781
$31$	6.99649	1.25661	0.628303	−	0.777969i	$-0.283750\pi$
$31$	6.99649	1.25661	0.628303	+	0.777969i	$0.283750\pi$
$32$	−25.9041	−4.57924
$33$	−14.5159	−2.52689
$34$	−0.213216	−0.0365663
$35$	1.49395	0.252524
$36$	21.5840	3.59734
$37$	−5.15344	−0.847220	−0.423610	−	0.905845i	$-0.639237\pi$
$37$	−5.15344	−0.847220	−0.423610	+	0.905845i	$0.639237\pi$
$38$	8.13206	1.31919
$39$	−2.61084	−0.418070
$40$	−10.3359	−1.63425
$41$	6.49342	1.01410	0.507051	−	0.861916i	$-0.330736\pi$
$41$	6.49342	1.01410	0.507051	+	0.861916i	$0.330736\pi$
$42$	−10.5604	−1.62950
$43$	6.19452	0.944655	0.472328	−	0.881423i	$-0.343414\pi$
$43$	6.19452	0.944655	0.472328	+	0.881423i	$0.343414\pi$
$44$	−31.4434	−4.74028
$45$	3.90022	0.581410
$46$	−1.72671	−0.254590
$47$	−8.73637	−1.27433	−0.637166	−	0.770727i	$-0.719893\pi$
$47$	−8.73637	−1.27433	−0.637166	+	0.770727i	$0.719893\pi$
$48$	43.5311	6.28318
$49$	−4.86289	−0.694699
$50$	10.9447	1.54781
$51$	0.201194	0.0281728
$52$	−5.65545	−0.784270
$53$	−13.3953	−1.83998	−0.919990	−	0.391941i	$-0.871804\pi$
$53$	−13.3953	−1.83998	−0.919990	+	0.391941i	$0.871804\pi$
$54$	−5.89826	−0.802652
$55$	−5.68181	−0.766135
$56$	−14.7856	−1.97581
$57$	−7.67355	−1.01639
$58$	−7.90911	−1.03852
$59$	−1.28889	−0.167799	−0.0838997	−	0.996474i	$-0.526738\pi$
$59$	−1.28889	−0.167799	−0.0838997	+	0.996474i	$0.526738\pi$
$60$	15.0894	1.94803
$61$	7.02732	0.899756	0.449878	−	0.893090i	$-0.351467\pi$
$61$	7.02732	0.899756	0.449878	+	0.893090i	$0.351467\pi$
$62$	−19.3582	−2.45850
$63$	5.57929	0.702924
$64$	38.3263	4.79079
$65$	−1.02194	−0.126755
$66$	40.1633	4.94376
$67$	0.145107	0.0177276	0.00886381	−	0.999961i	$-0.497179\pi$
$67$	0.145107	0.0177276	0.00886381	+	0.999961i	$0.497179\pi$
$68$	0.435815	0.0528503
$69$	1.62936	0.196151
$70$	−4.13354	−0.494052
$71$	−0.935284	−0.110998	−0.0554989	−	0.998459i	$-0.517675\pi$
$71$	−0.935284	−0.110998	−0.0554989	+	0.998459i	$0.517675\pi$
$72$	−38.6004	−4.54910
$73$	4.10344	0.480272	0.240136	−	0.970739i	$-0.422808\pi$
$73$	4.10344	0.480272	0.240136	+	0.970739i	$0.422808\pi$
$74$	14.2588	1.65755
$75$	−10.3276	−1.19253
$76$	−16.6220	−1.90667
$77$	−8.12786	−0.926255
$78$	7.22381	0.817935
$79$	−13.2846	−1.49463	−0.747317	−	0.664468i	$-0.768658\pi$
$79$	−13.2846	−1.49463	−0.747317	+	0.664468i	$0.768658\pi$
$80$	17.0389	1.90501
$81$	−5.88381	−0.653757
$82$	−17.9663	−1.98405
$83$	−6.46113	−0.709201	−0.354601	−	0.935018i	$-0.615383\pi$
$83$	−6.46113	−0.709201	−0.354601	+	0.935018i	$0.615383\pi$
$84$	21.5855	2.35517
$85$	0.0787514	0.00854179
$86$	−17.1393	−1.84818
$87$	7.46317	0.800135
$88$	56.2327	5.99443
$89$	−12.3340	−1.30740	−0.653700	−	0.756754i	$-0.726784\pi$
$89$	−12.3340	−1.30740	−0.653700	+	0.756754i	$0.726784\pi$
$90$	−10.7913	−1.13750
$91$	−1.46189	−0.153247
$92$	3.52941	0.367966
$93$	18.2667	1.89417
$94$	24.1722	2.49317
$95$	−3.00358	−0.308161
$96$	−67.6316	−6.90262
$97$	−5.54152	−0.562656	−0.281328	−	0.959612i	$-0.590775\pi$
$97$	−5.54152	−0.562656	−0.281328	+	0.959612i	$0.590775\pi$
$98$	13.4549	1.35915
$99$	−21.2192	−2.13261
$100$	−22.3710	−2.23710
$101$	6.00385	0.597406	0.298703	−	0.954346i	$-0.403446\pi$
$101$	6.00385	0.597406	0.298703	+	0.954346i	$0.403446\pi$
$102$	−0.556674	−0.0551189
$103$	18.7107	1.84362	0.921809	−	0.387644i	$-0.126711\pi$
$103$	18.7107	1.84362	0.921809	+	0.387644i	$0.126711\pi$
$104$	10.1141	0.991767
$105$	3.90048	0.380647
$106$	37.0626	3.59984
$107$	17.1510	1.65805	0.829024	−	0.559213i	$-0.188897\pi$
$107$	17.1510	1.65805	0.829024	+	0.559213i	$0.188897\pi$
$108$	12.0561	1.16010
$109$	−5.28214	−0.505937	−0.252968	−	0.967475i	$-0.581407\pi$
$109$	−5.28214	−0.505937	−0.252968	+	0.967475i	$0.581407\pi$
$110$	15.7207	1.49891
$111$	−13.4548	−1.27707
$112$	24.3743	2.30316
$113$	−1.18297	−0.111285	−0.0556423	−	0.998451i	$-0.517721\pi$
$113$	−1.18297	−0.111285	−0.0556423	+	0.998451i	$0.517721\pi$
$114$	21.2315	1.98852
$115$	0.637762	0.0594716
$116$	16.1663	1.50100
$117$	−3.81650	−0.352836
$118$	3.56617	0.328292
$119$	0.112654	0.0103270
$120$	−26.9855	−2.46343
$121$	19.9119	1.81017
$122$	−19.4435	−1.76033
$123$	16.9533	1.52863
$124$	39.5683	3.55334
$125$	−9.15209	−0.818588
$126$	−15.4370	−1.37524
$127$	−13.1129	−1.16358	−0.581791	−	0.813338i	$-0.697648\pi$
$127$	−13.1129	−1.16358	−0.581791	+	0.813338i	$0.697648\pi$
$128$	−54.2348	−4.79373
$129$	16.1729	1.42395
$130$	2.82754	0.247992
$131$	−9.01124	−0.787316	−0.393658	−	0.919257i	$-0.628791\pi$
$131$	−9.01124	−0.787316	−0.393658	+	0.919257i	$0.628791\pi$
$132$	−82.0939	−7.14536
$133$	−4.29664	−0.372566
$134$	−0.401488	−0.0346833
$135$	2.17852	0.187497
$136$	−0.779401	−0.0668331
$137$	−15.0957	−1.28971	−0.644856	−	0.764304i	$-0.723083\pi$
$137$	−15.0957	−1.28971	−0.644856	+	0.764304i	$0.723083\pi$
$138$	−4.50818	−0.383762
$139$	−4.56022	−0.386793	−0.193396	−	0.981121i	$-0.561950\pi$
$139$	−4.56022	−0.386793	−0.193396	+	0.981121i	$0.561950\pi$
$140$	8.44897	0.714068
$141$	−22.8093	−1.92089
$142$	2.58779	0.217163
$143$	5.55985	0.464938
$144$	63.6334	5.30278
$145$	2.92123	0.242595
$146$	−11.3536	−0.939631
$147$	−12.6962	−1.04717
$148$	−29.1450	−2.39570
$149$	18.5587	1.52039	0.760195	−	0.649695i	$-0.225104\pi$
$149$	18.5587	1.52039	0.760195	+	0.649695i	$0.225104\pi$
$150$	28.5748	2.33313
$151$	−4.88699	−0.397697	−0.198849	−	0.980030i	$-0.563720\pi$
$151$	−4.88699	−0.397697	−0.198849	+	0.980030i	$0.563720\pi$
$152$	29.7263	2.41113
$153$	0.294104	0.0237769
$154$	22.4886	1.81218
$155$	7.14996	0.574299
$156$	−14.7655	−1.18219
$157$	14.2691	1.13879	0.569397	−	0.822062i	$-0.307177\pi$
$157$	14.2691	1.13879	0.569397	+	0.822062i	$0.307177\pi$
$158$	36.7565	2.92419
$159$	−34.9729	−2.77353
$160$	−26.4723	−2.09282
$161$	0.912322	0.0719011
$162$	16.2796	1.27905
$163$	−6.25609	−0.490015	−0.245007	−	0.969521i	$-0.578790\pi$
$163$	−6.25609	−0.490015	−0.245007	+	0.969521i	$0.578790\pi$
$164$	36.7232	2.86760
$165$	−14.8343	−1.15485
$166$	17.8770	1.38752
$167$	−12.1701	−0.941747	−0.470874	−	0.882201i	$-0.656061\pi$
$167$	−12.1701	−0.941747	−0.470874	+	0.882201i	$0.656061\pi$
$168$	−38.6029	−2.97828
$169$	1.00000	0.0769231
$170$	−0.217893	−0.0167116
$171$	−11.2171	−0.857794
$172$	35.0328	2.67122
$173$	7.98711	0.607249	0.303624	−	0.952792i	$-0.401803\pi$
$173$	7.98711	0.607249	0.303624	+	0.952792i	$0.401803\pi$
$174$	−20.6494	−1.56543
$175$	−5.78270	−0.437131
$176$	−92.7005	−6.98756
$177$	−3.36510	−0.252936
$178$	34.1263	2.55787
$179$	−0.840316	−0.0628082	−0.0314041	−	0.999507i	$-0.509998\pi$
$179$	−0.840316	−0.0628082	−0.0314041	+	0.999507i	$0.509998\pi$
$180$	22.0575	1.64407
$181$	2.44728	0.181905	0.0909526	−	0.995855i	$-0.471009\pi$
$181$	2.44728	0.181905	0.0909526	+	0.995855i	$0.471009\pi$
$182$	4.04481	0.299822
$183$	18.3472	1.35627
$184$	−6.31191	−0.465321
$185$	−5.26648	−0.387199
$186$	−50.5413	−3.70587
$187$	−0.428447	−0.0313312
$188$	−49.4081	−3.60346
$189$	3.11639	0.226684
$190$	8.31044	0.602903
$191$	−15.4204	−1.11578	−0.557889	−	0.829915i	$-0.688389\pi$
$191$	−15.4204	−1.11578	−0.557889	+	0.829915i	$0.688389\pi$
$192$	100.064	7.22149
$193$	0.539106	0.0388057	0.0194028	−	0.999812i	$-0.493823\pi$
$193$	0.539106	0.0388057	0.0194028	+	0.999812i	$0.493823\pi$
$194$	15.3325	1.10081
$195$	−2.66811	−0.191068
$196$	−27.5018	−1.96442
$197$	−23.3222	−1.66164	−0.830819	−	0.556543i	$-0.812127\pi$
$197$	−23.3222	−1.66164	−0.830819	+	0.556543i	$0.812127\pi$
$198$	58.7102	4.17236
$199$	0.927258	0.0657316	0.0328658	−	0.999460i	$-0.489537\pi$
$199$	0.927258	0.0657316	0.0328658	+	0.999460i	$0.489537\pi$
$200$	40.0077	2.82897
$201$	0.378851	0.0267221
$202$	−16.6118	−1.16880
$203$	4.17884	0.293297
$204$	1.13784	0.0796650
$205$	6.63586	0.463469
$206$	−51.7696	−3.60696
$207$	2.38177	0.165545
$208$	−16.6732	−1.15608
$209$	16.3410	1.13033
$210$	−10.7920	−0.744720
$211$	21.8475	1.50404	0.752021	−	0.659139i	$-0.229079\pi$
$211$	21.8475	1.50404	0.752021	+	0.659139i	$0.229079\pi$
$212$	−75.7562	−5.20296
$213$	−2.44188	−0.167315
$214$	−47.4542	−3.24390
$215$	6.33040	0.431730
$216$	−21.5608	−1.46703
$217$	10.2281	0.694326
$218$	14.6149	0.989844
$219$	10.7134	0.723948
$220$	−32.1332	−2.16642
$221$	−0.0770610	−0.00518368
$222$	37.2274	2.49854
$223$	−29.6306	−1.98421	−0.992104	−	0.125414i	$-0.959974\pi$
$223$	−29.6306	−1.98421	−0.992104	+	0.125414i	$0.959974\pi$
$224$	−37.8688	−2.53022
$225$	−15.0967	−1.00645
$226$	3.27310	0.217724
$227$	−6.89840	−0.457863	−0.228931	−	0.973443i	$-0.573523\pi$
$227$	−6.89840	−0.457863	−0.228931	+	0.973443i	$0.573523\pi$
$228$	−43.3974	−2.87406
$229$	−24.6808	−1.63095	−0.815476	−	0.578791i	$-0.803525\pi$
$229$	−24.6808	−1.63095	−0.815476	+	0.578791i	$0.803525\pi$
$230$	−1.76459	−0.116354
$231$	−21.2206	−1.39621
$232$	−28.9114	−1.89812
$233$	−11.0659	−0.724951	−0.362475	−	0.931993i	$-0.618068\pi$
$233$	−11.0659	−0.724951	−0.362475	+	0.931993i	$0.618068\pi$
$234$	10.5597	0.690308
$235$	−8.92801	−0.582399
$236$	−7.28926	−0.474491
$237$	−34.6840	−2.25297
$238$	−0.311697	−0.0202043
$239$	−8.40649	−0.543771	−0.271885	−	0.962330i	$-0.587647\pi$
$239$	−8.40649	−0.543771	−0.271885	+	0.962330i	$0.587647\pi$
$240$	44.4860	2.87156
$241$	21.3044	1.37234	0.686169	−	0.727442i	$-0.259291\pi$
$241$	21.3044	1.37234	0.686169	+	0.727442i	$0.259291\pi$
$242$	−55.0932	−3.54153
$243$	−21.7570	−1.39571
$244$	39.7427	2.54426
$245$	−4.96956	−0.317494
$246$	−46.9072	−2.99070
$247$	2.93911	0.187011
$248$	−70.7630	−4.49346
$249$	−16.8690	−1.06903
$250$	25.3225	1.60153
$251$	−22.9935	−1.45133	−0.725667	−	0.688046i	$-0.758469\pi$
$251$	−22.9935	−1.45133	−0.725667	+	0.688046i	$0.758469\pi$
$252$	31.5534	1.98768
$253$	−3.46975	−0.218141
$254$	36.2814	2.27650
$255$	0.205608	0.0128756
$256$	73.4070	4.58794
$257$	−3.84698	−0.239968	−0.119984	−	0.992776i	$-0.538284\pi$
$257$	−3.84698	−0.239968	−0.119984	+	0.992776i	$0.538284\pi$
$258$	−44.7480	−2.78589
$259$	−7.53373	−0.468123
$260$	−5.77950	−0.358430
$261$	10.9096	0.675286
$262$	24.9327	1.54035
$263$	6.29102	0.387921	0.193960	−	0.981009i	$-0.437867\pi$
$263$	6.29102	0.387921	0.193960	+	0.981009i	$0.437867\pi$
$264$	146.815	9.03583
$265$	−13.6891	−0.840914
$266$	11.8881	0.728909
$267$	−32.2021	−1.97074
$268$	0.820644	0.0501288
$269$	−20.3966	−1.24360	−0.621800	−	0.783176i	$-0.713598\pi$
$269$	−20.3966	−1.24360	−0.621800	+	0.783176i	$0.713598\pi$
$270$	−6.02764	−0.366831
$271$	21.9954	1.33612	0.668062	−	0.744106i	$-0.267124\pi$
$271$	21.9954	1.33612	0.668062	+	0.744106i	$0.267124\pi$
$272$	1.28485	0.0779058
$273$	−3.81675	−0.231000
$274$	41.7675	2.52327
$275$	21.9928	1.32622
$276$	9.21474	0.554662
$277$	8.79204	0.528262	0.264131	−	0.964487i	$-0.414915\pi$
$277$	8.79204	0.528262	0.264131	+	0.964487i	$0.414915\pi$
$278$	12.6174	0.756744
$279$	26.7021	1.59861
$280$	−15.1099	−0.902992
$281$	3.62298	0.216129	0.108064	−	0.994144i	$-0.465535\pi$
$281$	3.62298	0.216129	0.108064	+	0.994144i	$0.465535\pi$
$282$	63.1099	3.75814
$283$	−15.8461	−0.941953	−0.470977	−	0.882146i	$-0.656098\pi$
$283$	−15.8461	−0.941953	−0.470977	+	0.882146i	$0.656098\pi$
$284$	−5.28945	−0.313871
$285$	−7.84187	−0.464512
$286$	−15.3833	−0.909631
$287$	9.49264	0.560333
$288$	−98.8631	−5.82556
$289$	−16.9941	−0.999651
$290$	−8.08260	−0.474627
$291$	−14.4680	−0.848132
$292$	23.2068	1.35808
$293$	−7.60780	−0.444452	−0.222226	−	0.974995i	$-0.571332\pi$
$293$	−7.60780	−0.444452	−0.222226	+	0.974995i	$0.571332\pi$
$294$	35.1286	2.04874
$295$	−1.31716	−0.0766883
$296$	52.1222	3.02954
$297$	−11.8523	−0.687739
$298$	−51.3492	−2.97458
$299$	−0.624072	−0.0360910
$300$	−58.4071	−3.37214
$301$	9.05567	0.521960
$302$	13.5216	0.778078
$303$	15.6751	0.900512
$304$	−49.0044	−2.81059
$305$	7.18147	0.411210
$306$	−0.813740	−0.0465184
$307$	−5.93481	−0.338717	−0.169359	−	0.985554i	$-0.554170\pi$
$307$	−5.93481	−0.338717	−0.169359	+	0.985554i	$0.554170\pi$
$308$	−45.9667	−2.61920
$309$	48.8507	2.77902
$310$	−19.7829	−1.12359
$311$	−16.4754	−0.934232	−0.467116	−	0.884196i	$-0.654707\pi$
$311$	−16.4754	−0.934232	−0.467116	+	0.884196i	$0.654707\pi$
$312$	26.4063	1.49496
$313$	−17.9330	−1.01363	−0.506817	−	0.862054i	$-0.669178\pi$
$313$	−17.9330	−1.01363	−0.506817	+	0.862054i	$0.669178\pi$
$314$	−39.4803	−2.22800
$315$	5.70167	0.321253
$316$	−75.1304	−4.22641
$317$	−16.2325	−0.911710	−0.455855	−	0.890054i	$-0.650667\pi$
$317$	−16.2325	−0.911710	−0.455855	+	0.890054i	$0.650667\pi$
$318$	96.7648	5.42630
$319$	−15.8930	−0.889836
$320$	39.1670	2.18950
$321$	44.7785	2.49929
$322$	−2.52426	−0.140671
$323$	−0.226491	−0.0126023
$324$	−33.2756	−1.84864
$325$	3.95565	0.219420
$326$	17.3096	0.958693
$327$	−13.7908	−0.762635
$328$	−65.6750	−3.62629
$329$	−12.7716	−0.704120
$330$	41.0443	2.25941
$331$	−1.77764	−0.0977079	−0.0488540	−	0.998806i	$-0.515557\pi$
$331$	−1.77764	−0.0977079	−0.0488540	+	0.998806i	$0.515557\pi$
$332$	−36.5406	−2.00543
$333$	−19.6681	−1.07781
$334$	33.6727	1.84249
$335$	0.148290	0.00810193
$336$	63.6375	3.47171
$337$	5.88775	0.320726	0.160363	−	0.987058i	$-0.448733\pi$
$337$	5.88775	0.320726	0.160363	+	0.987058i	$0.448733\pi$
$338$	−2.76685	−0.150497
$339$	−3.08856	−0.167747
$340$	0.445374	0.0241538
$341$	−38.8994	−2.10652
$342$	31.0360	1.67824
$343$	−17.3422	−0.936390
$344$	−62.6518	−3.37796
$345$	1.66510	0.0896458
$346$	−22.0991	−1.18806
$347$	8.23098	0.441862	0.220931	−	0.975289i	$-0.429090\pi$
$347$	8.23098	0.441862	0.220931	+	0.975289i	$0.429090\pi$
$348$	42.2076	2.26256
$349$	35.9747	1.92568	0.962842	−	0.270065i	$-0.0870453\pi$
$349$	35.9747	1.92568	0.962842	+	0.270065i	$0.0870453\pi$
$350$	15.9999	0.855229
$351$	−2.13176	−0.113785
$352$	144.023	7.67644
$353$	6.66657	0.354826	0.177413	−	0.984136i	$-0.443227\pi$
$353$	6.66657	0.354826	0.177413	+	0.984136i	$0.443227\pi$
$354$	9.31071	0.494859
$355$	−0.955800	−0.0507286
$356$	−69.7543	−3.69697
$357$	0.294123	0.0155666
$358$	2.32503	0.122881
$359$	−20.8099	−1.09830	−0.549152	−	0.835723i	$-0.685049\pi$
$359$	−20.8099	−1.09830	−0.549152	+	0.835723i	$0.685049\pi$
$360$	−39.4471	−2.07905
$361$	−10.3617	−0.545350
$362$	−6.77126	−0.355890
$363$	51.9869	2.72860
$364$	−8.26762	−0.433341
$365$	4.19345	0.219495
$366$	−50.7640	−2.65348
$367$	11.4259	0.596425	0.298213	−	0.954499i	$-0.403610\pi$
$367$	11.4259	0.596425	0.298213	+	0.954499i	$0.403610\pi$
$368$	10.4053	0.542413
$369$	24.7822	1.29011
$370$	14.5715	0.757539
$371$	−19.5823	−1.01666
$372$	103.307	5.35620
$373$	−31.2412	−1.61761	−0.808803	−	0.588080i	$-0.799884\pi$
$373$	−31.2412	−1.61761	−0.808803	+	0.588080i	$0.799884\pi$
$374$	1.18545	0.0612981
$375$	−23.8947	−1.23392
$376$	88.3603	4.55684
$377$	−2.85853	−0.147222
$378$	−8.62258	−0.443498
$379$	−1.86639	−0.0958700	−0.0479350	−	0.998850i	$-0.515264\pi$
$379$	−1.86639	−0.0958700	−0.0479350	+	0.998850i	$0.515264\pi$
$380$	−16.9866	−0.871393
$381$	−34.2357	−1.75395
$382$	42.6658	2.18297
$383$	34.6810	1.77212	0.886059	−	0.463573i	$-0.153433\pi$
$383$	34.6810	1.77212	0.886059	+	0.463573i	$0.153433\pi$
$384$	−141.599	−7.22593
$385$	−8.30615	−0.423320
$386$	−1.49162	−0.0759216
$387$	23.6414	1.20176
$388$	−31.3398	−1.59104
$389$	−3.44322	−0.174578	−0.0872891	−	0.996183i	$-0.527820\pi$
$389$	−3.44322	−0.174578	−0.0872891	+	0.996183i	$0.527820\pi$
$390$	7.38227	0.373816
$391$	0.0480916	0.00243210
$392$	49.1837	2.48415
$393$	−23.5269	−1.18678
$394$	64.5290	3.25092
$395$	−13.5760	−0.683083
$396$	−120.004	−6.03043
$397$	−8.34110	−0.418628	−0.209314	−	0.977848i	$-0.567123\pi$
$397$	−8.34110	−0.418628	−0.209314	+	0.977848i	$0.567123\pi$
$398$	−2.56558	−0.128601
$399$	−11.2178	−0.561595
$400$	−65.9534	−3.29767
$401$	21.5606	1.07668	0.538342	−	0.842726i	$-0.319051\pi$
$401$	21.5606	1.07668	0.538342	+	0.842726i	$0.319051\pi$
$402$	−1.04822	−0.0522806
$403$	−6.99649	−0.348520
$404$	33.9545	1.68930
$405$	−6.01288	−0.298782
$406$	−11.5622	−0.573823
$407$	28.6523	1.42024
$408$	−2.03489	−0.100742
$409$	−6.31826	−0.312418	−0.156209	−	0.987724i	$-0.549927\pi$
$409$	−6.31826	−0.312418	−0.156209	+	0.987724i	$0.549927\pi$
$410$	−18.3604	−0.906756
$411$	−39.4125	−1.94408
$412$	105.817	5.21325
$413$	−1.88421	−0.0927160
$414$	−6.59001	−0.323881
$415$	−6.60286	−0.324122
$416$	25.9041	1.27005
$417$	−11.9060	−0.583040
$418$	−45.2130	−2.21144
$419$	−23.0343	−1.12530	−0.562650	−	0.826695i	$-0.690218\pi$
$419$	−23.0343	−1.12530	−0.562650	+	0.826695i	$0.690218\pi$
$420$	22.0589	1.07637
$421$	−1.36606	−0.0665775	−0.0332887	−	0.999446i	$-0.510598\pi$
$421$	−1.36606	−0.0665775	−0.0332887	+	0.999446i	$0.510598\pi$
$422$	−60.4487	−2.94260
$423$	−33.3424	−1.62116
$424$	135.481	6.57952
$425$	−0.304826	−0.0147862
$426$	6.75631	0.327344
$427$	10.2731	0.497152
$428$	96.9965	4.68850
$429$	14.5159	0.700834
$430$	−17.5152	−0.844660
$431$	−5.91836	−0.285077	−0.142539	−	0.989789i	$-0.545527\pi$
$431$	−5.91836	−0.285077	−0.142539	+	0.989789i	$0.545527\pi$
$432$	35.5433	1.71008
$433$	30.4934	1.46542	0.732709	−	0.680542i	$-0.238256\pi$
$433$	30.4934	1.46542	0.732709	+	0.680542i	$0.238256\pi$
$434$	−28.2995	−1.35842
$435$	7.62687	0.365681
$436$	−29.8729	−1.43065
$437$	−1.83422	−0.0877424
$438$	−29.6425	−1.41637
$439$	−34.0572	−1.62546	−0.812731	−	0.582640i	$-0.802020\pi$
$439$	−34.0572	−1.62546	−0.812731	+	0.582640i	$0.802020\pi$
$440$	57.4662	2.73959
$441$	−18.5592	−0.883773
$442$	0.213216	0.0101417
$443$	−7.83742	−0.372367	−0.186183	−	0.982515i	$-0.559612\pi$
$443$	−7.83742	−0.372367	−0.186183	+	0.982515i	$0.559612\pi$
$444$	−76.0930	−3.61121
$445$	−12.6045	−0.597513
$446$	81.9833	3.88202
$447$	48.4539	2.29179
$448$	56.0286	2.64710
$449$	−1.19408	−0.0563519	−0.0281759	−	0.999603i	$-0.508970\pi$
$449$	−1.19408	−0.0563519	−0.0281759	+	0.999603i	$0.508970\pi$
$450$	41.7704	1.96908
$451$	−36.1024	−1.70000
$452$	−6.69024	−0.314682
$453$	−12.7592	−0.599478
$454$	19.0868	0.895789
$455$	−1.49395	−0.0700376
$456$	77.6108	3.63446
$457$	18.2070	0.851687	0.425844	−	0.904797i	$-0.359977\pi$
$457$	18.2070	0.851687	0.425844	+	0.904797i	$0.359977\pi$
$458$	68.2880	3.19089
$459$	0.164276	0.00766773
$460$	3.60683	0.168169
$461$	−17.8193	−0.829926	−0.414963	−	0.909838i	$-0.636205\pi$
$461$	−17.8193	−0.829926	−0.414963	+	0.909838i	$0.636205\pi$
$462$	58.7141	2.73163
$463$	30.9991	1.44065	0.720326	−	0.693636i	$-0.243992\pi$
$463$	30.9991	1.44065	0.720326	+	0.693636i	$0.243992\pi$
$464$	47.6608	2.21260
$465$	18.6674	0.865681
$466$	30.6176	1.41834
$467$	28.5145	1.31949	0.659747	−	0.751488i	$-0.270663\pi$
$467$	28.5145	1.31949	0.659747	+	0.751488i	$0.270663\pi$
$468$	−21.5840	−0.997723
$469$	0.212129	0.00979523
$470$	24.7025	1.13944
$471$	37.2543	1.71659
$472$	13.0360	0.600028
$473$	−34.4406	−1.58358
$474$	95.9654	4.40784
$475$	11.6261	0.533441
$476$	0.637111	0.0292019
$477$	−51.1230	−2.34076
$478$	23.2595	1.06386
$479$	24.2737	1.10909	0.554547	−	0.832153i	$-0.312892\pi$
$479$	24.2737	1.10909	0.554547	+	0.832153i	$0.312892\pi$
$480$	−69.1151	−3.15466
$481$	5.15344	0.234976
$482$	−58.9461	−2.68492
$483$	2.38193	0.108382
$484$	112.611	5.11867
$485$	−5.66308	−0.257147
$486$	60.1983	2.73065
$487$	−2.35556	−0.106741	−0.0533703	−	0.998575i	$-0.516996\pi$
$487$	−2.35556	−0.106741	−0.0533703	+	0.998575i	$0.516996\pi$
$488$	−71.0749	−3.21741
$489$	−16.3337	−0.738634
$490$	13.7500	0.621163
$491$	41.3110	1.86434	0.932169	−	0.362023i	$-0.117914\pi$
$491$	41.3110	1.86434	0.932169	+	0.362023i	$0.117914\pi$
$492$	95.8786	4.32254
$493$	0.220281	0.00992096
$494$	−8.13206	−0.365879
$495$	−21.6846	−0.974652
$496$	116.654	5.23792
$497$	−1.36728	−0.0613308
$498$	46.6740	2.09151
$499$	18.7274	0.838352	0.419176	−	0.907905i	$-0.362319\pi$
$499$	18.7274	0.838352	0.419176	+	0.907905i	$0.362319\pi$
$500$	−51.7592	−2.31474
$501$	−31.7741	−1.41956
$502$	63.6194	2.83947
$503$	−40.0398	−1.78529	−0.892644	−	0.450762i	$-0.851152\pi$
$503$	−40.0398	−1.78529	−0.892644	+	0.450762i	$0.851152\pi$
$504$	−56.4293	−2.51356
$505$	6.13555	0.273028
$506$	9.60026	0.426784
$507$	2.61084	0.115952
$508$	−74.1594	−3.29029
$509$	17.8216	0.789929	0.394964	−	0.918696i	$-0.370757\pi$
$509$	17.8216	0.789929	0.394964	+	0.918696i	$0.370757\pi$
$510$	−0.568885	−0.0251906
$511$	5.99876	0.265370
$512$	−94.6363	−4.18237
$513$	−6.26548	−0.276628
$514$	10.6440	0.469487
$515$	19.1211	0.842577
$516$	91.4651	4.02653
$517$	48.5729	2.13623
$518$	20.8447	0.915863
$519$	20.8531	0.915349
$520$	10.3359	0.453261
$521$	12.7906	0.560368	0.280184	−	0.959946i	$-0.409604\pi$
$521$	12.7906	0.560368	0.280184	+	0.959946i	$0.409604\pi$
$522$	−30.1851	−1.32117
$523$	−27.4134	−1.19870	−0.599352	−	0.800485i	$-0.704575\pi$
$523$	−27.4134	−1.19870	−0.599352	+	0.800485i	$0.704575\pi$
$524$	−50.9626	−2.22631
$525$	−15.0977	−0.658919
$526$	−17.4063	−0.758950
$527$	0.539156	0.0234860
$528$	−242.027	−10.5329
$529$	−22.6105	−0.983067
$530$	37.8756	1.64521
$531$	−4.91906	−0.213469
$532$	−24.2994	−1.05351
$533$	−6.49342	−0.281261
$534$	89.0984	3.85566
$535$	17.5272	0.757767
$536$	−1.46762	−0.0633916
$537$	−2.19393	−0.0946752
$538$	56.4342	2.43305
$539$	27.0369	1.16456
$540$	12.3205	0.530191
$541$	12.7417	0.547809	0.273905	−	0.961757i	$-0.411685\pi$
$541$	12.7417	0.547809	0.273905	+	0.961757i	$0.411685\pi$
$542$	−60.8578	−2.61407
$543$	6.38947	0.274199
$544$	−1.99620	−0.0855862
$545$	−5.39800	−0.231225
$546$	10.5604	0.451942
$547$	−14.4638	−0.618427	−0.309214	−	0.950993i	$-0.600066\pi$
$547$	−14.4638	−0.618427	−0.309214	+	0.950993i	$0.600066\pi$
$548$	−85.3730	−3.64695
$549$	26.8198	1.14464
$550$	−60.8507	−2.59468
$551$	−8.40152	−0.357917
$552$	−16.4794	−0.701411
$553$	−19.4206	−0.825846
$554$	−24.3262	−1.03352
$555$	−13.7500	−0.583653
$556$	−25.7901	−1.09374
$557$	39.1696	1.65967	0.829835	−	0.558009i	$-0.188435\pi$
$557$	39.1696	1.65967	0.829835	+	0.558009i	$0.188435\pi$
$558$	−73.8807	−3.12762
$559$	−6.19452	−0.262000
$560$	24.9090	1.05260
$561$	−1.11861	−0.0472277
$562$	−10.0242	−0.422846
$563$	−46.8078	−1.97271	−0.986357	−	0.164621i	$-0.947360\pi$
$563$	−46.8078	−1.97271	−0.986357	+	0.164621i	$0.947360\pi$
$564$	−128.997	−5.43175
$565$	−1.20892	−0.0508597
$566$	43.8438	1.84289
$567$	−8.60146	−0.361227
$568$	9.45954	0.396913
$569$	8.12417	0.340583	0.170291	−	0.985394i	$-0.445529\pi$
$569$	8.12417	0.340583	0.170291	+	0.985394i	$0.445529\pi$
$570$	21.6973	0.908799
$571$	23.7144	0.992416	0.496208	−	0.868204i	$-0.334725\pi$
$571$	23.7144	0.992416	0.496208	+	0.868204i	$0.334725\pi$
$572$	31.4434	1.31472
$573$	−40.2602	−1.68189
$574$	−26.2647	−1.09627
$575$	−2.46861	−0.102948
$576$	146.272	6.09468
$577$	20.7241	0.862755	0.431378	−	0.902171i	$-0.358028\pi$
$577$	20.7241	0.862755	0.431378	+	0.902171i	$0.358028\pi$
$578$	47.0200	1.95577
$579$	1.40752	0.0584946
$580$	16.5209	0.685992
$581$	−9.44543	−0.391862
$582$	40.0309	1.65933
$583$	74.4756	3.08446
$584$	−41.5025	−1.71739
$585$	−3.90022	−0.161254
$586$	21.0496	0.869552
$587$	16.1781	0.667743	0.333871	−	0.942619i	$-0.391645\pi$
$587$	16.1781	0.667743	0.333871	+	0.942619i	$0.391645\pi$
$588$	−71.8030	−2.96111
$589$	−20.5634	−0.847301
$590$	3.64439	0.150037
$591$	−60.8906	−2.50470
$592$	−85.9243	−3.53147
$593$	15.2698	0.627056	0.313528	−	0.949579i	$-0.398489\pi$
$593$	15.2698	0.627056	0.313528	+	0.949579i	$0.398489\pi$
$594$	32.7934	1.34553
$595$	0.115125	0.00471968
$596$	104.958	4.29924
$597$	2.42093	0.0990819
$598$	1.72671	0.0706106
$599$	−7.13380	−0.291479	−0.145740	−	0.989323i	$-0.546556\pi$
$599$	−7.13380	−0.291479	−0.145740	+	0.989323i	$0.546556\pi$
$600$	104.454	4.26431
$601$	−14.0833	−0.574470	−0.287235	−	0.957860i	$-0.592736\pi$
$601$	−14.0833	−0.574470	−0.287235	+	0.957860i	$0.592736\pi$
$602$	−25.0557	−1.02119
$603$	0.553800	0.0225525
$604$	−27.6381	−1.12458
$605$	20.3487	0.827292
$606$	−43.3707	−1.76181
$607$	21.1823	0.859763	0.429881	−	0.902885i	$-0.358555\pi$
$607$	21.1823	0.859763	0.429881	+	0.902885i	$0.358555\pi$
$608$	76.1349	3.08768
$609$	10.9103	0.442107
$610$	−19.8700	−0.804514
$611$	8.73637	0.353436
$612$	1.66329	0.0672344
$613$	−43.7007	−1.76505	−0.882527	−	0.470262i	$-0.844159\pi$
$613$	−43.7007	−1.76505	−0.882527	+	0.470262i	$0.844159\pi$
$614$	16.4207	0.662686
$615$	17.3252	0.698619
$616$	82.2058	3.31216
$617$	−10.6807	−0.429989	−0.214995	−	0.976615i	$-0.568973\pi$
$617$	−10.6807	−0.429989	−0.214995	+	0.976615i	$0.568973\pi$
$618$	−135.162	−5.43703
$619$	−1.00000	−0.0401934
$619$	−1.00000	−0.0401934
$620$	40.4362	1.62396
$621$	1.33037	0.0533861
$622$	45.5848	1.82778
$623$	−18.0309	−0.722392
$624$	−43.5311	−1.74264
$625$	10.4254	0.417016
$626$	49.6179	1.98313
$627$	42.6638	1.70383
$628$	80.6979	3.22020
$629$	−0.397129	−0.0158346
$630$	−15.7757	−0.628518
$631$	−4.28209	−0.170467	−0.0852337	−	0.996361i	$-0.527164\pi$
$631$	−4.28209	−0.170467	−0.0852337	+	0.996361i	$0.527164\pi$
$632$	134.361	5.34461
$633$	57.0404	2.26715
$634$	44.9130	1.78372
$635$	−13.4005	−0.531784
$636$	−197.788	−7.84279
$637$	4.86289	0.192675
$638$	43.9734	1.74093
$639$	−3.56952	−0.141208
$640$	−55.4245	−2.19085
$641$	−13.8357	−0.546477	−0.273239	−	0.961946i	$-0.588095\pi$
$641$	−13.8357	−0.546477	−0.273239	+	0.961946i	$0.588095\pi$
$642$	−123.895	−4.88976
$643$	24.8171	0.978689	0.489345	−	0.872091i	$-0.337236\pi$
$643$	24.8171	0.978689	0.489345	+	0.872091i	$0.337236\pi$
$644$	5.15959	0.203316
$645$	16.5277	0.650777
$646$	0.626665	0.0246558
$647$	30.8563	1.21309	0.606544	−	0.795050i	$-0.292556\pi$
$647$	30.8563	1.21309	0.606544	+	0.795050i	$0.292556\pi$
$648$	59.5093	2.33775
$649$	7.16604	0.281292
$650$	−10.9447	−0.429286
$651$	26.7039	1.04661
$652$	−35.3810	−1.38563
$653$	40.2685	1.57583	0.787915	−	0.615784i	$-0.211161\pi$
$653$	40.2685	1.57583	0.787915	+	0.615784i	$0.211161\pi$
$654$	38.1571	1.49206
$655$	−9.20891	−0.359822
$656$	108.266	4.22709
$657$	15.6608	0.610986
$658$	35.3370	1.37758
$659$	37.8272	1.47354	0.736768	−	0.676145i	$-0.236351\pi$
$659$	37.8272	1.47354	0.736768	+	0.676145i	$0.236351\pi$
$660$	−83.8947	−3.26560
$661$	14.2314	0.553539	0.276769	−	0.960936i	$-0.410736\pi$
$661$	14.2314	0.553539	0.276769	+	0.960936i	$0.410736\pi$
$662$	4.91846	0.191161
$663$	−0.201194	−0.00781374
$664$	65.3484	2.53601
$665$	−4.39089	−0.170271
$666$	54.4187	2.10868
$667$	1.78393	0.0690740
$668$	−68.8271	−2.66300
$669$	−77.3607	−2.99094
$670$	−0.410295	−0.0158511
$671$	−39.0708	−1.50831
$672$	−98.8696	−3.81398
$673$	−31.0859	−1.19827	−0.599136	−	0.800647i	$-0.704489\pi$
$673$	−31.0859	−1.19827	−0.599136	+	0.800647i	$0.704489\pi$
$674$	−16.2905	−0.627487
$675$	−8.43250	−0.324567
$676$	5.65545	0.217517
$677$	38.8847	1.49446	0.747230	−	0.664566i	$-0.231384\pi$
$677$	38.8847	1.49446	0.747230	+	0.664566i	$0.231384\pi$
$678$	8.54556	0.328190
$679$	−8.10107	−0.310890
$680$	−0.796497	−0.0305443
$681$	−18.0106	−0.690169
$682$	107.629	4.12132
$683$	40.7868	1.56066	0.780331	−	0.625367i	$-0.215051\pi$
$683$	40.7868	1.56066	0.780331	+	0.625367i	$0.215051\pi$
$684$	−63.4378	−2.42561
$685$	−15.4268	−0.589429
$686$	47.9832	1.83201
$687$	−64.4377	−2.45845
$688$	103.283	3.93761
$689$	13.3953	0.510319
$690$	−4.60707	−0.175388
$691$	40.1419	1.52707	0.763534	−	0.645767i	$-0.223462\pi$
$691$	40.1419	1.52707	0.763534	+	0.645767i	$0.223462\pi$
$692$	45.1707	1.71713
$693$	−31.0200	−1.17835
$694$	−22.7739	−0.864484
$695$	−4.66025	−0.176773
$696$	−75.4830	−2.86118
$697$	0.500390	0.0189536
$698$	−99.5367	−3.76752
$699$	−28.8913	−1.09277
$700$	−32.7038	−1.23609
$701$	−8.48209	−0.320364	−0.160182	−	0.987087i	$-0.551208\pi$
$701$	−8.48209	−0.320364	−0.160182	+	0.987087i	$0.551208\pi$
$702$	5.89826	0.222616
$703$	15.1465	0.571261
$704$	−213.088	−8.03107
$705$	−23.3096	−0.877892
$706$	−18.4454	−0.694202
$707$	8.77694	0.330091
$708$	−19.0311	−0.715234
$709$	−51.4763	−1.93323	−0.966617	−	0.256227i	$-0.917520\pi$
$709$	−51.4763	−1.93323	−0.966617	+	0.256227i	$0.917520\pi$
$710$	2.64455	0.0992484
$711$	−50.7007	−1.90143
$712$	124.747	4.67509
$713$	4.36631	0.163520
$714$	−0.813793	−0.0304554
$715$	5.68181	0.212487
$716$	−4.75236	−0.177604
$717$	−21.9480	−0.819664
$718$	57.5778	2.14878
$719$	−10.0913	−0.376341	−0.188171	−	0.982136i	$-0.560256\pi$
$719$	−10.0913	−0.376341	−0.188171	+	0.982136i	$0.560256\pi$
$720$	65.0292	2.42350
$721$	27.3529	1.01867
$722$	28.6691	1.06695
$723$	55.6225	2.06862
$724$	13.8405	0.514378
$725$	−11.3073	−0.419944
$726$	−143.840	−5.33840
$727$	23.8300	0.883806	0.441903	−	0.897063i	$-0.354304\pi$
$727$	23.8300	0.883806	0.441903	+	0.897063i	$0.354304\pi$
$728$	14.7856	0.547991
$729$	−39.1527	−1.45010
$730$	−11.6027	−0.429433
$731$	0.477356	0.0176556
$732$	103.762	3.83515
$733$	−15.5560	−0.574573	−0.287287	−	0.957845i	$-0.592753\pi$
$733$	−15.5560	−0.574573	−0.287287	+	0.957845i	$0.592753\pi$
$734$	−31.6136	−1.16688
$735$	−12.9747	−0.478581
$736$	−16.1660	−0.595888
$737$	−0.806771	−0.0297178
$738$	−68.5685	−2.52404
$739$	−31.4674	−1.15755	−0.578774	−	0.815488i	$-0.696469\pi$
$739$	−31.4674	−1.15755	−0.578774	+	0.815488i	$0.696469\pi$
$740$	−29.7843	−1.09489
$741$	7.67355	0.281895
$742$	54.1813	1.98906
$743$	9.01052	0.330564	0.165282	−	0.986246i	$-0.447147\pi$
$743$	9.01052	0.330564	0.165282	+	0.986246i	$0.447147\pi$
$744$	−184.751	−6.77330
$745$	18.9658	0.694854
$746$	86.4395	3.16478
$747$	−24.6589	−0.902223
$748$	−2.42306	−0.0885960
$749$	25.0728	0.916139
$750$	66.1130	2.41410
$751$	−12.9890	−0.473976	−0.236988	−	0.971513i	$-0.576160\pi$
$751$	−12.9890	−0.473976	−0.236988	+	0.971513i	$0.576160\pi$
$752$	−145.663	−5.31180
$753$	−60.0323	−2.18770
$754$	7.90911	0.288033
$755$	−4.99419	−0.181757
$756$	17.6246	0.641000
$757$	−17.8684	−0.649437	−0.324719	−	0.945811i	$-0.605270\pi$
$757$	−17.8684	−0.649437	−0.324719	+	0.945811i	$0.605270\pi$
$758$	5.16402	0.187566
$759$	−9.05897	−0.328820
$760$	30.3784	1.10194
$761$	33.9858	1.23198	0.615992	−	0.787752i	$-0.288755\pi$
$761$	33.9858	1.23198	0.615992	+	0.787752i	$0.288755\pi$
$762$	94.7251	3.43153
$763$	−7.72188	−0.279551
$764$	−87.2091	−3.15511
$765$	0.300555	0.0108666
$766$	−95.9571	−3.46707
$767$	1.28889	0.0465392
$768$	191.654	6.91572
$769$	−11.1624	−0.402526	−0.201263	−	0.979537i	$-0.564505\pi$
$769$	−11.1624	−0.402526	−0.201263	+	0.979537i	$0.564505\pi$
$770$	22.9818	0.828208
$771$	−10.0439	−0.361721
$772$	3.04888	0.109732
$773$	−14.5676	−0.523959	−0.261980	−	0.965073i	$-0.584375\pi$
$773$	−14.5676	−0.523959	−0.261980	+	0.965073i	$0.584375\pi$
$774$	−65.4122	−2.35119
$775$	−27.6756	−0.994138
$776$	56.0474	2.01198
$777$	−19.6694	−0.705635
$778$	9.52686	0.341555
$779$	−19.0849	−0.683786
$780$	−15.0894	−0.540287
$781$	5.20004	0.186072
$782$	−0.133062	−0.00475830
$783$	6.09370	0.217771
$784$	−81.0800	−2.89572
$785$	14.5821	0.520456
$786$	65.0955	2.32188
$787$	31.0096	1.10537	0.552686	−	0.833390i	$-0.313603\pi$
$787$	31.0096	1.10537	0.552686	+	0.833390i	$0.313603\pi$
$788$	−131.897	−4.69865
$789$	16.4249	0.584740
$790$	37.5627	1.33642
$791$	−1.72937	−0.0614893
$792$	214.612	7.62592
$793$	−7.02732	−0.249548
$794$	23.0786	0.819028
$795$	−35.7401	−1.26757
$796$	5.24406	0.185871
$797$	0.668163	0.0236676	0.0118338	−	0.999930i	$-0.496233\pi$
$797$	0.668163	0.0236676	0.0118338	+	0.999930i	$0.496233\pi$
$798$	31.0381	1.09874
$799$	−0.673234	−0.0238173
$800$	102.468	3.62277
$801$	−47.0727	−1.66323
$802$	−59.6549	−2.10649
$803$	−22.8145	−0.805107
$804$	2.14257	0.0755627
$805$	0.932334	0.0328605
$806$	19.3582	0.681864
$807$	−53.2522	−1.87457
$808$	−60.7234	−2.13624
$809$	−28.8176	−1.01317	−0.506586	−	0.862189i	$-0.669093\pi$
$809$	−28.8176	−1.01317	−0.506586	+	0.862189i	$0.669093\pi$
$810$	16.6367	0.584555
$811$	40.1729	1.41066	0.705330	−	0.708879i	$-0.250799\pi$
$811$	40.1729	1.41066	0.705330	+	0.708879i	$0.250799\pi$
$812$	23.6332	0.829363
$813$	57.4265	2.01403
$814$	−79.2766	−2.77864
$815$	−6.39332	−0.223948
$816$	3.35455	0.117433
$817$	−18.2063	−0.636960
$818$	17.4817	0.611232
$819$	−5.57929	−0.194956
$820$	37.5288	1.31056
$821$	−19.8366	−0.692301	−0.346150	−	0.938179i	$-0.612511\pi$
$821$	−19.8366	−0.692301	−0.346150	+	0.938179i	$0.612511\pi$
$822$	109.048	3.80350
$823$	0.448284	0.0156262	0.00781311	−	0.999969i	$-0.497513\pi$
$823$	0.448284	0.0156262	0.00781311	+	0.999969i	$0.497513\pi$
$824$	−189.241	−6.59253
$825$	57.4198	1.99910
$826$	5.21333	0.181395
$827$	−37.6065	−1.30771	−0.653854	−	0.756621i	$-0.726849\pi$
$827$	−37.6065	−1.30771	−0.653854	+	0.756621i	$0.726849\pi$
$828$	13.4700	0.468115
$829$	−25.1797	−0.874526	−0.437263	−	0.899334i	$-0.644052\pi$
$829$	−25.1797	−0.874526	−0.437263	+	0.899334i	$0.644052\pi$
$830$	18.2691	0.634130
$831$	22.9546	0.796287
$832$	−38.3263	−1.32873
$833$	−0.374739	−0.0129839
$834$	32.9422	1.14069
$835$	−12.4370	−0.430400
$836$	92.4156	3.19626
$837$	14.9148	0.515533
$838$	63.7325	2.20160
$839$	51.4126	1.77496	0.887479	−	0.460847i	$-0.152454\pi$
$839$	51.4126	1.77496	0.887479	+	0.460847i	$0.152454\pi$
$840$	−39.4497	−1.36114
$841$	−20.8288	−0.718235
$842$	3.77967	0.130256
$843$	9.45902	0.325786
$844$	123.557	4.25302
$845$	1.02194	0.0351556
$846$	92.2534	3.17174
$847$	29.1089	1.00019
$848$	−223.342	−7.66960
$849$	−41.3717	−1.41987
$850$	0.843408	0.0289287
$851$	−3.21612	−0.110247
$852$	−13.8099	−0.473121
$853$	−20.0110	−0.685164	−0.342582	−	0.939488i	$-0.611301\pi$
$853$	−20.0110	−0.685164	−0.342582	+	0.939488i	$0.611301\pi$
$854$	−28.4242	−0.972657
$855$	−11.4632	−0.392032
$856$	−173.466	−5.92896
$857$	−1.33672	−0.0456613	−0.0228307	−	0.999739i	$-0.507268\pi$
$857$	−1.33672	−0.0456613	−0.0228307	+	0.999739i	$0.507268\pi$
$858$	−40.1633	−1.37115
$859$	3.53277	0.120536	0.0602682	−	0.998182i	$-0.480804\pi$
$859$	3.53277	0.120536	0.0602682	+	0.998182i	$0.480804\pi$
$860$	35.8012	1.22081
$861$	24.7838	0.844629
$862$	16.3752	0.557741
$863$	−10.2524	−0.348994	−0.174497	−	0.984658i	$-0.555830\pi$
$863$	−10.2524	−0.348994	−0.174497	+	0.984658i	$0.555830\pi$
$864$	−55.2214	−1.87867
$865$	8.16231	0.277527
$866$	−84.3705	−2.86703
$867$	−44.3688	−1.50684
$868$	57.8443	1.96336
$869$	73.8603	2.50554
$870$	−21.1024	−0.715438
$871$	−0.145107	−0.00491675
$872$	53.4239	1.80916
$873$	−21.1492	−0.715793
$874$	5.07500	0.171664
$875$	−13.3793	−0.452303
$876$	60.5894	2.04712
$877$	−16.1799	−0.546357	−0.273178	−	0.961963i	$-0.588075\pi$
$877$	−16.1799	−0.546357	−0.273178	+	0.961963i	$0.588075\pi$
$878$	94.2311	3.18015
$879$	−19.8628	−0.669954
$880$	−94.7340	−3.19348
$881$	34.0855	1.14837	0.574184	−	0.818726i	$-0.305319\pi$
$881$	34.0855	1.14837	0.574184	+	0.818726i	$0.305319\pi$
$882$	51.3506	1.72907
$883$	−17.2944	−0.582003	−0.291001	−	0.956723i	$-0.593988\pi$
$883$	−17.2944	−0.582003	−0.291001	+	0.956723i	$0.593988\pi$
$884$	−0.435815	−0.0146580
$885$	−3.43891	−0.115598
$886$	21.6849	0.728520
$887$	−12.8317	−0.430848	−0.215424	−	0.976521i	$-0.569113\pi$
$887$	−12.8317	−0.430848	−0.215424	+	0.976521i	$0.569113\pi$
$888$	136.083	4.56665
$889$	−19.1696	−0.642926
$890$	34.8749	1.16901
$891$	32.7131	1.09593
$892$	−167.574	−5.61080
$893$	25.6771	0.859253
$894$	−134.065	−4.48379
$895$	−0.858749	−0.0287048
$896$	−79.2851	−2.64873
$897$	−1.62936	−0.0544026
$898$	3.30382	0.110250
$899$	19.9996	0.667026
$900$	−85.3789	−2.84596
$901$	−1.03225	−0.0343893
$902$	99.8900	3.32597
$903$	23.6429	0.786788
$904$	11.9647	0.397939
$905$	2.50097	0.0831349
$906$	35.3027	1.17285
$907$	24.2928	0.806630	0.403315	−	0.915061i	$-0.367858\pi$
$907$	24.2928	0.806630	0.403315	+	0.915061i	$0.367858\pi$
$908$	−39.0135	−1.29471
$909$	22.9137	0.760000
$910$	4.13354	0.137025
$911$	−3.94119	−0.130578	−0.0652888	−	0.997866i	$-0.520797\pi$
$911$	−3.94119	−0.130578	−0.0652888	+	0.997866i	$0.520797\pi$
$912$	−127.943	−4.23661
$913$	35.9229	1.18887
$914$	−50.3760	−1.66629
$915$	18.7497	0.619846
$916$	−139.581	−4.61188
$917$	−13.1734	−0.435024
$918$	−0.454526	−0.0150016
$919$	27.4879	0.906741	0.453371	−	0.891322i	$-0.350221\pi$
$919$	27.4879	0.906741	0.453371	+	0.891322i	$0.350221\pi$
$920$	−6.45037	−0.212662
$921$	−15.4948	−0.510573
$922$	49.3032	1.62371
$923$	0.935284	0.0307853
$924$	−120.012	−3.94810
$925$	20.3852	0.670260
$926$	−85.7699	−2.81857
$927$	71.4094	2.34539
$928$	−74.0476	−2.43073
$929$	17.9513	0.588964	0.294482	−	0.955657i	$-0.404853\pi$
$929$	17.9513	0.588964	0.294482	+	0.955657i	$0.404853\pi$
$930$	−51.6499	−1.69367
$931$	14.2926	0.468420
$932$	−62.5826	−2.04996
$933$	−43.0146	−1.40823
$934$	−78.8953	−2.58153
$935$	−0.437846	−0.0143191
$936$	38.6004	1.26169
$937$	−22.1673	−0.724174	−0.362087	−	0.932144i	$-0.617936\pi$
$937$	−22.1673	−0.724174	−0.362087	+	0.932144i	$0.617936\pi$
$938$	−0.586930	−0.0191639
$939$	−46.8203	−1.52792
$940$	−50.4919	−1.64686
$941$	−20.0248	−0.652790	−0.326395	−	0.945233i	$-0.605834\pi$
$941$	−20.0248	−0.652790	−0.326395	+	0.945233i	$0.605834\pi$
$942$	−103.077	−3.35843
$943$	4.05237	0.131963
$944$	−21.4900	−0.699439
$945$	3.18475	0.103600
$946$	95.2918	3.09821
$947$	17.6982	0.575115	0.287558	−	0.957763i	$-0.407157\pi$
$947$	17.6982	0.575115	0.287558	+	0.957763i	$0.407157\pi$
$948$	−196.154	−6.37077
$949$	−4.10344	−0.133203
$950$	−32.1676	−1.04365
$951$	−42.3806	−1.37429
$952$	−1.13939	−0.0369280
$953$	−3.71919	−0.120476	−0.0602382	−	0.998184i	$-0.519186\pi$
$953$	−3.71919	−0.120476	−0.0602382	+	0.998184i	$0.519186\pi$
$954$	141.450	4.57960
$955$	−15.7586	−0.509937
$956$	−47.5425	−1.53763
$957$	−41.4941	−1.34131
$958$	−67.1616	−2.16989
$959$	−22.0682	−0.712619
$960$	102.259	3.30039
$961$	17.9508	0.579059
$962$	−14.2588	−0.459721
$963$	65.4568	2.10932
$964$	120.486	3.88060
$965$	0.550931	0.0177351
$966$	−6.59044	−0.212044
$967$	−20.3086	−0.653081	−0.326540	−	0.945183i	$-0.605883\pi$
$967$	−20.3086	−0.653081	−0.326540	+	0.945183i	$0.605883\pi$
$968$	−201.391	−6.47294
$969$	−0.591331	−0.0189963
$970$	15.6689	0.503097
$971$	−58.4891	−1.87701	−0.938503	−	0.345272i	$-0.887787\pi$
$971$	−58.4891	−1.87701	−0.938503	+	0.345272i	$0.887787\pi$
$972$	−123.046	−3.94669
$973$	−6.66652	−0.213719
$974$	6.51747	0.208833
$975$	10.3276	0.330747
$976$	117.168	3.75046
$977$	50.9152	1.62892	0.814461	−	0.580219i	$-0.197033\pi$
$977$	50.9152	1.62892	0.814461	+	0.580219i	$0.197033\pi$
$978$	45.1928	1.44511
$979$	68.5751	2.19167
$980$	−28.1051	−0.897785
$981$	−20.1593	−0.643637
$982$	−114.301	−3.64750
$983$	−44.3390	−1.41419	−0.707097	−	0.707117i	$-0.749995\pi$
$983$	−44.3390	−1.41419	−0.707097	+	0.707117i	$0.749995\pi$
$984$	−171.467	−5.46617
$985$	−23.8338	−0.759407
$986$	−0.609484	−0.0194099
$987$	−33.3446	−1.06137
$988$	16.6220	0.528815
$989$	3.86583	0.122926
$990$	59.9981	1.90686
$991$	−18.7743	−0.596386	−0.298193	−	0.954506i	$-0.596384\pi$
$991$	−18.7743	−0.596386	−0.298193	+	0.954506i	$0.596384\pi$
$992$	−181.238	−5.75430
$993$	−4.64114	−0.147282
$994$	3.78305	0.119991
$995$	0.947598	0.0300409
$996$	−95.4018	−3.02292
$997$	−17.1787	−0.544054	−0.272027	−	0.962290i	$-0.587694\pi$
$997$	−17.1787	−0.544054	−0.272027	+	0.962290i	$0.587694\pi$
$998$	−51.8158	−1.64020
$999$	−10.9859	−0.347578

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8047.2.a.c.1.2	✓	151

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8047.2.a.c.1.2	✓	151	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:	\( N \)	\(=\)	\( 8047 = 13 \cdot 619 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8047.a (trivial)

\(f(q)\)	\(=\)	\(q-2.76685 q^{2} +2.61084 q^{3} +5.65545 q^{4} +1.02194 q^{5} -7.22381 q^{6} +1.46189 q^{7} -10.1141 q^{8} +3.81650 q^{9} +O(q^{10})\)	\(q-2.76685 q^{2} +2.61084 q^{3} +5.65545 q^{4} +1.02194 q^{5} -7.22381 q^{6} +1.46189 q^{7} -10.1141 q^{8} +3.81650 q^{9} -2.82754 q^{10} -5.55985 q^{11} +14.7655 q^{12} -1.00000 q^{13} -4.04481 q^{14} +2.66811 q^{15} +16.6732 q^{16} +0.0770610 q^{17} -10.5597 q^{18} -2.93911 q^{19} +5.77950 q^{20} +3.81675 q^{21} +15.3833 q^{22} +0.624072 q^{23} -26.4063 q^{24} -3.95565 q^{25} +2.76685 q^{26} +2.13176 q^{27} +8.26762 q^{28} +2.85853 q^{29} -7.38227 q^{30} +6.99649 q^{31} -25.9041 q^{32} -14.5159 q^{33} -0.213216 q^{34} +1.49395 q^{35} +21.5840 q^{36} -5.15344 q^{37} +8.13206 q^{38} -2.61084 q^{39} -10.3359 q^{40} +6.49342 q^{41} -10.5604 q^{42} +6.19452 q^{43} -31.4434 q^{44} +3.90022 q^{45} -1.72671 q^{46} -8.73637 q^{47} +43.5311 q^{48} -4.86289 q^{49} +10.9447 q^{50} +0.201194 q^{51} -5.65545 q^{52} -13.3953 q^{53} -5.89826 q^{54} -5.68181 q^{55} -14.7856 q^{56} -7.67355 q^{57} -7.90911 q^{58} -1.28889 q^{59} +15.0894 q^{60} +7.02732 q^{61} -19.3582 q^{62} +5.57929 q^{63} +38.3263 q^{64} -1.02194 q^{65} +40.1633 q^{66} +0.145107 q^{67} +0.435815 q^{68} +1.62936 q^{69} -4.13354 q^{70} -0.935284 q^{71} -38.6004 q^{72} +4.10344 q^{73} +14.2588 q^{74} -10.3276 q^{75} -16.6220 q^{76} -8.12786 q^{77} +7.22381 q^{78} -13.2846 q^{79} +17.0389 q^{80} -5.88381 q^{81} -17.9663 q^{82} -6.46113 q^{83} +21.5855 q^{84} +0.0787514 q^{85} -17.1393 q^{86} +7.46317 q^{87} +56.2327 q^{88} -12.3340 q^{89} -10.7913 q^{90} -1.46189 q^{91} +3.52941 q^{92} +18.2667 q^{93} +24.1722 q^{94} -3.00358 q^{95} -67.6316 q^{96} -5.54152 q^{97} +13.4549 q^{98} -21.2192 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 151 q - 13 q^{2} - 16 q^{3} + 151 q^{4} - 43 q^{5} - 17 q^{6} - 18 q^{7} - 39 q^{8} + 135 q^{9}+O(q^{10}) \) 151 * q - 13 * q^2 - 16 * q^3 + 151 * q^4 - 43 * q^5 - 17 * q^6 - 18 * q^7 - 39 * q^8 + 135 * q^9	\( 151 q - 13 q^{2} - 16 q^{3} + 151 q^{4} - 43 q^{5} - 17 q^{6} - 18 q^{7} - 39 q^{8} + 135 q^{9} - 3 q^{10} - 27 q^{11} - 52 q^{12} - 151 q^{13} - 9 q^{14} - 14 q^{15} + 143 q^{16} - 111 q^{17} - 37 q^{18} - 17 q^{19} - 107 q^{20} - 29 q^{21} - 16 q^{22} - 47 q^{23} - 46 q^{24} + 122 q^{25} + 13 q^{26} - 55 q^{27} - 44 q^{28} + 37 q^{29} - 14 q^{30} - 27 q^{31} - 86 q^{32} - 94 q^{33} - 10 q^{34} - 47 q^{35} + 124 q^{36} - 59 q^{37} - 80 q^{38} + 16 q^{39} + 5 q^{40} - 129 q^{41} - 77 q^{42} - 11 q^{43} - 99 q^{44} - 122 q^{45} - 17 q^{46} - 130 q^{47} - 111 q^{48} + 99 q^{49} - 72 q^{50} + 15 q^{51} - 151 q^{52} - 43 q^{53} - 49 q^{54} - 40 q^{55} - 50 q^{56} - 85 q^{57} - 73 q^{58} - 74 q^{59} - 43 q^{60} - 7 q^{61} - 110 q^{62} - 70 q^{63} + 141 q^{64} + 43 q^{65} - 16 q^{66} - 39 q^{67} - 222 q^{68} + 19 q^{69} - 52 q^{70} - 72 q^{71} - 106 q^{72} - 143 q^{73} + 20 q^{74} - 73 q^{75} - 88 q^{76} - 86 q^{77} + 17 q^{78} + 10 q^{79} - 239 q^{80} + 103 q^{81} - 96 q^{82} - 96 q^{83} - 75 q^{84} - 24 q^{85} - 109 q^{86} - 65 q^{87} - 45 q^{88} - 237 q^{89} - 79 q^{90} + 18 q^{91} - 153 q^{92} - 137 q^{93} - 23 q^{94} + 10 q^{95} - 109 q^{96} - 160 q^{97} - 119 q^{98} - 86 q^{99}+O(q^{100}) \) 151 * q - 13 * q^2 - 16 * q^3 + 151 * q^4 - 43 * q^5 - 17 * q^6 - 18 * q^7 - 39 * q^8 + 135 * q^9 - 3 * q^10 - 27 * q^11 - 52 * q^12 - 151 * q^13 - 9 * q^14 - 14 * q^15 + 143 * q^16 - 111 * q^17 - 37 * q^18 - 17 * q^19 - 107 * q^20 - 29 * q^21 - 16 * q^22 - 47 * q^23 - 46 * q^24 + 122 * q^25 + 13 * q^26 - 55 * q^27 - 44 * q^28 + 37 * q^29 - 14 * q^30 - 27 * q^31 - 86 * q^32 - 94 * q^33 - 10 * q^34 - 47 * q^35 + 124 * q^36 - 59 * q^37 - 80 * q^38 + 16 * q^39 + 5 * q^40 - 129 * q^41 - 77 * q^42 - 11 * q^43 - 99 * q^44 - 122 * q^45 - 17 * q^46 - 130 * q^47 - 111 * q^48 + 99 * q^49 - 72 * q^50 + 15 * q^51 - 151 * q^52 - 43 * q^53 - 49 * q^54 - 40 * q^55 - 50 * q^56 - 85 * q^57 - 73 * q^58 - 74 * q^59 - 43 * q^60 - 7 * q^61 - 110 * q^62 - 70 * q^63 + 141 * q^64 + 43 * q^65 - 16 * q^66 - 39 * q^67 - 222 * q^68 + 19 * q^69 - 52 * q^70 - 72 * q^71 - 106 * q^72 - 143 * q^73 + 20 * q^74 - 73 * q^75 - 88 * q^76 - 86 * q^77 + 17 * q^78 + 10 * q^79 - 239 * q^80 + 103 * q^81 - 96 * q^82 - 96 * q^83 - 75 * q^84 - 24 * q^85 - 109 * q^86 - 65 * q^87 - 45 * q^88 - 237 * q^89 - 79 * q^90 + 18 * q^91 - 153 * q^92 - 137 * q^93 - 23 * q^94 + 10 * q^95 - 109 * q^96 - 160 * q^97 - 119 * q^98 - 86 * q^99

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