LMFDB - Embedded newform 6005.2.a.f.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6005,2,Mod(1,6005)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6005, 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("6005.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6005 = 5 \cdot 1201 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6005.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:	$47.9501664138$
Analytic rank:	$0$
Dimension:	$111$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	6005.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.32774 q^{2} +1.75930 q^{3} +3.41838 q^{4} +1.00000 q^{5} -4.09520 q^{6} +3.92990 q^{7} -3.30162 q^{8} +0.0951392 q^{9} +O(q^{10})$	\(q-2.32774 q^{2} +1.75930 q^{3} +3.41838 q^{4} +1.00000 q^{5} -4.09520 q^{6} +3.92990 q^{7} -3.30162 q^{8} +0.0951392 q^{9} -2.32774 q^{10} +4.21811 q^{11} +6.01395 q^{12} +0.471299 q^{13} -9.14779 q^{14} +1.75930 q^{15} +0.848551 q^{16} +1.41072 q^{17} -0.221459 q^{18} -0.0947343 q^{19} +3.41838 q^{20} +6.91387 q^{21} -9.81867 q^{22} -2.96829 q^{23} -5.80854 q^{24} +1.00000 q^{25} -1.09706 q^{26} -5.11052 q^{27} +13.4339 q^{28} +7.78383 q^{29} -4.09520 q^{30} -3.76526 q^{31} +4.62803 q^{32} +7.42093 q^{33} -3.28379 q^{34} +3.92990 q^{35} +0.325222 q^{36} +2.98053 q^{37} +0.220517 q^{38} +0.829156 q^{39} -3.30162 q^{40} -8.82492 q^{41} -16.0937 q^{42} -0.607675 q^{43} +14.4191 q^{44} +0.0951392 q^{45} +6.90941 q^{46} +3.58652 q^{47} +1.49286 q^{48} +8.44411 q^{49} -2.32774 q^{50} +2.48188 q^{51} +1.61108 q^{52} -7.16298 q^{53} +11.8960 q^{54} +4.21811 q^{55} -12.9750 q^{56} -0.166666 q^{57} -18.1187 q^{58} +0.0798648 q^{59} +6.01395 q^{60} +7.33114 q^{61} +8.76454 q^{62} +0.373887 q^{63} -12.4699 q^{64} +0.471299 q^{65} -17.2740 q^{66} -1.23787 q^{67} +4.82237 q^{68} -5.22211 q^{69} -9.14779 q^{70} +15.5384 q^{71} -0.314113 q^{72} +1.47143 q^{73} -6.93791 q^{74} +1.75930 q^{75} -0.323838 q^{76} +16.5768 q^{77} -1.93006 q^{78} +12.4912 q^{79} +0.848551 q^{80} -9.27637 q^{81} +20.5421 q^{82} +14.8932 q^{83} +23.6342 q^{84} +1.41072 q^{85} +1.41451 q^{86} +13.6941 q^{87} -13.9266 q^{88} -15.5444 q^{89} -0.221459 q^{90} +1.85216 q^{91} -10.1467 q^{92} -6.62422 q^{93} -8.34849 q^{94} -0.0947343 q^{95} +8.14209 q^{96} +10.0781 q^{97} -19.6557 q^{98} +0.401308 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 111 q + 20 q^{2} + 40 q^{3} + 136 q^{4} + 111 q^{5} + 3 q^{6} + 39 q^{7} + 45 q^{8} + 139 q^{9}+O(q^{10}) $ 111 * q + 20 * q^2 + 40 * q^3 + 136 * q^4 + 111 * q^5 + 3 * q^6 + 39 * q^7 + 45 * q^8 + 139 * q^9	\( 111 q + 20 q^{2} + 40 q^{3} + 136 q^{4} + 111 q^{5} + 3 q^{6} + 39 q^{7} + 45 q^{8} + 139 q^{9} + 20 q^{10} + 36 q^{11} + 80 q^{12} + 36 q^{13} + 7 q^{14} + 40 q^{15} + 190 q^{16} + 38 q^{17} + 48 q^{18} + 77 q^{19} + 136 q^{20} + 11 q^{21} + 39 q^{22} + 82 q^{23} - 3 q^{24} + 111 q^{25} - 3 q^{26} + 130 q^{27} + 87 q^{28} + 20 q^{29} + 3 q^{30} + 41 q^{31} + 85 q^{32} + 33 q^{33} + 7 q^{34} + 39 q^{35} + 191 q^{36} + 80 q^{37} + 42 q^{38} + 21 q^{39} + 45 q^{40} + 16 q^{41} + 33 q^{42} + 164 q^{43} + 37 q^{44} + 139 q^{45} + 32 q^{46} + 148 q^{47} + 149 q^{48} + 160 q^{49} + 20 q^{50} + 51 q^{51} + 87 q^{52} + 83 q^{53} - 6 q^{54} + 36 q^{55} - 10 q^{56} + 28 q^{57} + 47 q^{58} + 14 q^{59} + 80 q^{60} + 20 q^{61} + 14 q^{62} + 120 q^{63} + 231 q^{64} + 36 q^{65} - 4 q^{66} + 253 q^{67} + 80 q^{68} + 6 q^{69} + 7 q^{70} + 5 q^{71} + 124 q^{72} + 64 q^{73} - 37 q^{74} + 40 q^{75} + 92 q^{76} + 63 q^{77} + 29 q^{78} + 91 q^{79} + 190 q^{80} + 187 q^{81} - 7 q^{82} + 63 q^{83} - 69 q^{84} + 38 q^{85} - 22 q^{86} + 57 q^{87} + 121 q^{88} - 6 q^{89} + 48 q^{90} + 119 q^{91} + 104 q^{92} + 14 q^{93} - q^{94} + 77 q^{95} - 38 q^{96} + 96 q^{97} + 81 q^{98} + 106 q^{99}+O(q^{100}) \) 111 * q + 20 * q^2 + 40 * q^3 + 136 * q^4 + 111 * q^5 + 3 * q^6 + 39 * q^7 + 45 * q^8 + 139 * q^9 + 20 * q^10 + 36 * q^11 + 80 * q^12 + 36 * q^13 + 7 * q^14 + 40 * q^15 + 190 * q^16 + 38 * q^17 + 48 * q^18 + 77 * q^19 + 136 * q^20 + 11 * q^21 + 39 * q^22 + 82 * q^23 - 3 * q^24 + 111 * q^25 - 3 * q^26 + 130 * q^27 + 87 * q^28 + 20 * q^29 + 3 * q^30 + 41 * q^31 + 85 * q^32 + 33 * q^33 + 7 * q^34 + 39 * q^35 + 191 * q^36 + 80 * q^37 + 42 * q^38 + 21 * q^39 + 45 * q^40 + 16 * q^41 + 33 * q^42 + 164 * q^43 + 37 * q^44 + 139 * q^45 + 32 * q^46 + 148 * q^47 + 149 * q^48 + 160 * q^49 + 20 * q^50 + 51 * q^51 + 87 * q^52 + 83 * q^53 - 6 * q^54 + 36 * q^55 - 10 * q^56 + 28 * q^57 + 47 * q^58 + 14 * q^59 + 80 * q^60 + 20 * q^61 + 14 * q^62 + 120 * q^63 + 231 * q^64 + 36 * q^65 - 4 * q^66 + 253 * q^67 + 80 * q^68 + 6 * q^69 + 7 * q^70 + 5 * q^71 + 124 * q^72 + 64 * q^73 - 37 * q^74 + 40 * q^75 + 92 * q^76 + 63 * q^77 + 29 * q^78 + 91 * q^79 + 190 * q^80 + 187 * q^81 - 7 * q^82 + 63 * q^83 - 69 * q^84 + 38 * q^85 - 22 * q^86 + 57 * q^87 + 121 * q^88 - 6 * q^89 + 48 * q^90 + 119 * q^91 + 104 * q^92 + 14 * q^93 - q^94 + 77 * q^95 - 38 * q^96 + 96 * q^97 + 81 * q^98 + 106 * 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 $

$2$	−2.32774	−1.64596	−0.822981	−	0.568069i	$-0.807691\pi$
$2$	−2.32774	−1.64596	−0.822981	+	0.568069i	$0.807691\pi$
$3$	1.75930	1.01573	0.507866	−	0.861436i	$-0.330434\pi$
$3$	1.75930	1.01573	0.507866	+	0.861436i	$0.330434\pi$
$4$	3.41838	1.70919
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−4.09520	−1.67186
$7$	3.92990	1.48536	0.742681	−	0.669645i	$-0.233554\pi$
$7$	3.92990	1.48536	0.742681	+	0.669645i	$0.233554\pi$
$8$	−3.30162	−1.16730
$9$	0.0951392	0.0317131
$10$	−2.32774	−0.736096
$11$	4.21811	1.27181	0.635904	−	0.771768i	$-0.280627\pi$
$11$	4.21811	1.27181	0.635904	+	0.771768i	$0.280627\pi$
$12$	6.01395	1.73608
$13$	0.471299	0.130715	0.0653574	−	0.997862i	$-0.479181\pi$
$13$	0.471299	0.130715	0.0653574	+	0.997862i	$0.479181\pi$
$14$	−9.14779	−2.44485
$15$	1.75930	0.454250
$16$	0.848551	0.212138
$17$	1.41072	0.342150	0.171075	−	0.985258i	$-0.445276\pi$
$17$	1.41072	0.342150	0.171075	+	0.985258i	$0.445276\pi$
$18$	−0.221459	−0.0521985
$19$	−0.0947343	−0.0217335	−0.0108668	−	0.999941i	$-0.503459\pi$
$19$	−0.0947343	−0.0217335	−0.0108668	+	0.999941i	$0.503459\pi$
$20$	3.41838	0.764372
$21$	6.91387	1.50873
$22$	−9.81867	−2.09335
$23$	−2.96829	−0.618931	−0.309466	−	0.950911i	$-0.600150\pi$
$23$	−2.96829	−0.618931	−0.309466	+	0.950911i	$0.600150\pi$
$24$	−5.80854	−1.18566
$25$	1.00000	0.200000
$26$	−1.09706	−0.215151
$27$	−5.11052	−0.983521
$28$	13.4339	2.53876
$29$	7.78383	1.44542	0.722711	−	0.691151i	$-0.242896\pi$
$29$	7.78383	1.44542	0.722711	+	0.691151i	$0.242896\pi$
$30$	−4.09520	−0.747677
$31$	−3.76526	−0.676260	−0.338130	−	0.941099i	$-0.609794\pi$
$31$	−3.76526	−0.676260	−0.338130	+	0.941099i	$0.609794\pi$
$32$	4.62803	0.818127
$33$	7.42093	1.29182
$34$	−3.28379	−0.563165
$35$	3.92990	0.664274
$36$	0.325222	0.0542036
$37$	2.98053	0.489997	0.244998	−	0.969523i	$-0.421213\pi$
$37$	2.98053	0.489997	0.244998	+	0.969523i	$0.421213\pi$
$38$	0.220517	0.0357726
$39$	0.829156	0.132771
$40$	−3.30162	−0.522031
$41$	−8.82492	−1.37822	−0.689110	−	0.724656i	$-0.741999\pi$
$41$	−8.82492	−1.37822	−0.689110	+	0.724656i	$0.741999\pi$
$42$	−16.0937	−2.48331
$43$	−0.607675	−0.0926696	−0.0463348	−	0.998926i	$-0.514754\pi$
$43$	−0.607675	−0.0926696	−0.0463348	+	0.998926i	$0.514754\pi$
$44$	14.4191	2.17376
$45$	0.0951392	0.0141825
$46$	6.90941	1.01874
$47$	3.58652	0.523148	0.261574	−	0.965183i	$-0.415758\pi$
$47$	3.58652	0.523148	0.261574	+	0.965183i	$0.415758\pi$
$48$	1.49286	0.215475
$49$	8.44411	1.20630
$50$	−2.32774	−0.329192
$51$	2.48188	0.347533
$52$	1.61108	0.223416
$53$	−7.16298	−0.983911	−0.491956	−	0.870620i	$-0.663718\pi$
$53$	−7.16298	−0.983911	−0.491956	+	0.870620i	$0.663718\pi$
$54$	11.8960	1.61884
$55$	4.21811	0.568770
$56$	−12.9750	−1.73386
$57$	−0.166666	−0.0220755
$58$	−18.1187	−2.37911
$59$	0.0798648	0.0103975	0.00519876	−	0.999986i	$-0.498345\pi$
$59$	0.0798648	0.0103975	0.00519876	+	0.999986i	$0.498345\pi$
$60$	6.01395	0.776398
$61$	7.33114	0.938656	0.469328	−	0.883024i	$-0.344496\pi$
$61$	7.33114	0.938656	0.469328	+	0.883024i	$0.344496\pi$
$62$	8.76454	1.11310
$63$	0.373887	0.0471054
$64$	−12.4699	−1.55874
$65$	0.471299	0.0584574
$66$	−17.2740	−2.12628
$67$	−1.23787	−0.151230	−0.0756150	−	0.997137i	$-0.524092\pi$
$67$	−1.23787	−0.151230	−0.0756150	+	0.997137i	$0.524092\pi$
$68$	4.82237	0.584798
$69$	−5.22211	−0.628669
$70$	−9.14779	−1.09337
$71$	15.5384	1.84407	0.922034	−	0.387109i	$-0.126526\pi$
$71$	15.5384	1.84407	0.922034	+	0.387109i	$0.126526\pi$
$72$	−0.314113	−0.0370186
$73$	1.47143	0.172218	0.0861091	−	0.996286i	$-0.472557\pi$
$73$	1.47143	0.172218	0.0861091	+	0.996286i	$0.472557\pi$
$74$	−6.93791	−0.806516
$75$	1.75930	0.203147
$76$	−0.323838	−0.0371467
$77$	16.5768	1.88910
$78$	−1.93006	−0.218536
$79$	12.4912	1.40537	0.702687	−	0.711499i	$-0.251983\pi$
$79$	12.4912	1.40537	0.702687	+	0.711499i	$0.251983\pi$
$80$	0.848551	0.0948709
$81$	−9.27637	−1.03071
$82$	20.5421	2.26850
$83$	14.8932	1.63474	0.817370	−	0.576113i	$-0.195431\pi$
$83$	14.8932	1.63474	0.817370	+	0.576113i	$0.195431\pi$
$84$	23.6342	2.57871
$85$	1.41072	0.153014
$86$	1.41451	0.152531
$87$	13.6941	1.46816
$88$	−13.9266	−1.48458
$89$	−15.5444	−1.64770	−0.823851	−	0.566806i	$-0.808179\pi$
$89$	−15.5444	−1.64770	−0.823851	+	0.566806i	$0.808179\pi$
$90$	−0.221459	−0.0233439
$91$	1.85216	0.194159
$92$	−10.1467	−1.05787
$93$	−6.62422	−0.686899
$94$	−8.34849	−0.861082
$95$	−0.0947343	−0.00971954
$96$	8.14209	0.830998
$97$	10.0781	1.02328	0.511638	−	0.859201i	$-0.329039\pi$
$97$	10.0781	1.02328	0.511638	+	0.859201i	$0.329039\pi$
$98$	−19.6557	−1.98552
$99$	0.401308	0.0403329
$100$	3.41838	0.341838
$101$	−9.13789	−0.909254	−0.454627	−	0.890682i	$-0.650227\pi$
$101$	−9.13789	−0.909254	−0.454627	+	0.890682i	$0.650227\pi$
$102$	−5.77717	−0.572025
$103$	3.13663	0.309061	0.154531	−	0.987988i	$-0.450613\pi$
$103$	3.13663	0.309061	0.154531	+	0.987988i	$0.450613\pi$
$104$	−1.55605	−0.152583
$105$	6.91387	0.674725
$106$	16.6736	1.61948
$107$	−19.6653	−1.90112	−0.950558	−	0.310546i	$-0.899488\pi$
$107$	−19.6653	−1.90112	−0.950558	+	0.310546i	$0.899488\pi$
$108$	−17.4697	−1.68102
$109$	12.4075	1.18842	0.594211	−	0.804310i	$-0.297465\pi$
$109$	12.4075	1.18842	0.594211	+	0.804310i	$0.297465\pi$
$110$	−9.81867	−0.936174
$111$	5.24366	0.497706
$112$	3.33472	0.315101
$113$	6.87749	0.646980	0.323490	−	0.946232i	$-0.395144\pi$
$113$	6.87749	0.646980	0.323490	+	0.946232i	$0.395144\pi$
$114$	0.387956	0.0363354
$115$	−2.96829	−0.276794
$116$	26.6081	2.47050
$117$	0.0448390	0.00414536
$118$	−0.185905	−0.0171139
$119$	5.54398	0.508216
$120$	−5.80854	−0.530244
$121$	6.79247	0.617497
$122$	−17.0650	−1.54499
$123$	−15.5257	−1.39990
$124$	−12.8711	−1.15586
$125$	1.00000	0.0894427
$126$	−0.870313	−0.0775336
$127$	1.00076	0.0888035	0.0444017	−	0.999014i	$-0.485862\pi$
$127$	1.00076	0.0888035	0.0444017	+	0.999014i	$0.485862\pi$
$128$	19.7708	1.74750
$129$	−1.06908	−0.0941275
$130$	−1.09706	−0.0962186
$131$	−5.20259	−0.454553	−0.227276	−	0.973830i	$-0.572982\pi$
$131$	−5.20259	−0.454553	−0.227276	+	0.973830i	$0.572982\pi$
$132$	25.3675	2.20796
$133$	−0.372296	−0.0322822
$134$	2.88144	0.248919
$135$	−5.11052	−0.439844
$136$	−4.65765	−0.399390
$137$	2.76225	0.235995	0.117997	−	0.993014i	$-0.462353\pi$
$137$	2.76225	0.235995	0.117997	+	0.993014i	$0.462353\pi$
$138$	12.1557	1.03476
$139$	18.6254	1.57978	0.789891	−	0.613247i	$-0.210137\pi$
$139$	18.6254	1.57978	0.789891	+	0.613247i	$0.210137\pi$
$140$	13.4339	1.13537
$141$	6.30977	0.531379
$142$	−36.1694	−3.03526
$143$	1.98799	0.166244
$144$	0.0807304	0.00672753
$145$	7.78383	0.646412
$146$	−3.42511	−0.283465
$147$	14.8557	1.22528
$148$	10.1886	0.837497
$149$	18.8329	1.54285	0.771424	−	0.636322i	$-0.219545\pi$
$149$	18.8329	1.54285	0.771424	+	0.636322i	$0.219545\pi$
$150$	−4.09520	−0.334371
$151$	8.89673	0.724005	0.362003	−	0.932177i	$-0.382093\pi$
$151$	8.89673	0.724005	0.362003	+	0.932177i	$0.382093\pi$
$152$	0.312776	0.0253695
$153$	0.134215	0.0108506
$154$	−38.5864	−3.10938
$155$	−3.76526	−0.302433
$156$	2.83437	0.226931
$157$	7.50989	0.599355	0.299677	−	0.954041i	$-0.403121\pi$
$157$	7.50989	0.599355	0.299677	+	0.954041i	$0.403121\pi$
$158$	−29.0764	−2.31319
$159$	−12.6018	−0.999391
$160$	4.62803	0.365878
$161$	−11.6651	−0.919337
$162$	21.5930	1.69650
$163$	−4.00069	−0.313358	−0.156679	−	0.987650i	$-0.550079\pi$
$163$	−4.00069	−0.313358	−0.156679	+	0.987650i	$0.550079\pi$
$164$	−30.1669	−2.35564
$165$	7.42093	0.577718
$166$	−34.6675	−2.69072
$167$	−7.21568	−0.558366	−0.279183	−	0.960238i	$-0.590064\pi$
$167$	−7.21568	−0.558366	−0.279183	+	0.960238i	$0.590064\pi$
$168$	−22.8270	−1.76114
$169$	−12.7779	−0.982914
$170$	−3.28379	−0.251855
$171$	−0.00901295	−0.000689237 0
$172$	−2.07726	−0.158390
$173$	1.73105	0.131609	0.0658046	−	0.997833i	$-0.479039\pi$
$173$	1.73105	0.131609	0.0658046	+	0.997833i	$0.479039\pi$
$174$	−31.8763	−2.41654
$175$	3.92990	0.297072
$176$	3.57928	0.269799
$177$	0.140506	0.0105611
$178$	36.1833	2.71205
$179$	−13.2214	−0.988214	−0.494107	−	0.869401i	$-0.664505\pi$
$179$	−13.2214	−0.988214	−0.494107	+	0.869401i	$0.664505\pi$
$180$	0.325222	0.0242406
$181$	14.9948	1.11456	0.557279	−	0.830325i	$-0.311845\pi$
$181$	14.9948	1.11456	0.557279	+	0.830325i	$0.311845\pi$
$182$	−4.31134	−0.319578
$183$	12.8977	0.953423
$184$	9.80015	0.722477
$185$	2.98053	0.219133
$186$	15.4195	1.13061
$187$	5.95057	0.435149
$188$	12.2601	0.894159
$189$	−20.0838	−1.46088
$190$	0.220517	0.0159980
$191$	−0.497515	−0.0359989	−0.0179995	−	0.999838i	$-0.505730\pi$
$191$	−0.497515	−0.0359989	−0.0179995	+	0.999838i	$0.505730\pi$
$192$	−21.9384	−1.58327
$193$	26.2307	1.88812	0.944062	−	0.329768i	$-0.106970\pi$
$193$	26.2307	1.88812	0.944062	+	0.329768i	$0.106970\pi$
$194$	−23.4592	−1.68427
$195$	0.829156	0.0593771
$196$	28.8651	2.06180
$197$	−15.3110	−1.09087	−0.545433	−	0.838154i	$-0.683635\pi$
$197$	−15.3110	−1.09087	−0.545433	+	0.838154i	$0.683635\pi$
$198$	−0.934140	−0.0663865
$199$	5.05508	0.358345	0.179173	−	0.983818i	$-0.442658\pi$
$199$	5.05508	0.358345	0.179173	+	0.983818i	$0.442658\pi$
$200$	−3.30162	−0.233459
$201$	−2.17779	−0.153609
$202$	21.2706	1.49660
$203$	30.5897	2.14697
$204$	8.48400	0.593999
$205$	−8.82492	−0.616359
$206$	−7.30126	−0.508703
$207$	−0.282401	−0.0196282
$208$	0.399921	0.0277295
$209$	−0.399600	−0.0276409
$210$	−16.0937	−1.11057
$211$	−1.34467	−0.0925708	−0.0462854	−	0.998928i	$-0.514738\pi$
$211$	−1.34467	−0.0925708	−0.0462854	+	0.998928i	$0.514738\pi$
$212$	−24.4858	−1.68169
$213$	27.3367	1.87308
$214$	45.7757	3.12916
$215$	−0.607675	−0.0414431
$216$	16.8730	1.14806
$217$	−14.7971	−1.00449
$218$	−28.8814	−1.95610
$219$	2.58869	0.174928
$220$	14.4191	0.972135
$221$	0.664870	0.0447240
$222$	−12.2059	−0.819205
$223$	6.87951	0.460686	0.230343	−	0.973109i	$-0.426015\pi$
$223$	6.87951	0.460686	0.230343	+	0.973109i	$0.426015\pi$
$224$	18.1877	1.21521
$225$	0.0951392	0.00634261
$226$	−16.0090	−1.06490
$227$	11.8152	0.784201	0.392101	−	0.919922i	$-0.371749\pi$
$227$	11.8152	0.784201	0.392101	+	0.919922i	$0.371749\pi$
$228$	−0.569728	−0.0377312
$229$	8.05365	0.532200	0.266100	−	0.963945i	$-0.414265\pi$
$229$	8.05365	0.532200	0.266100	+	0.963945i	$0.414265\pi$
$230$	6.90941	0.455593
$231$	29.1635	1.91882
$232$	−25.6992	−1.68724
$233$	−21.5042	−1.40879	−0.704395	−	0.709809i	$-0.748781\pi$
$233$	−21.5042	−1.40879	−0.704395	+	0.709809i	$0.748781\pi$
$234$	−0.104373	−0.00682311
$235$	3.58652	0.233959
$236$	0.273008	0.0177713
$237$	21.9758	1.42748
$238$	−12.9050	−0.836504
$239$	−2.75185	−0.178002	−0.0890012	−	0.996032i	$-0.528367\pi$
$239$	−2.75185	−0.178002	−0.0890012	+	0.996032i	$0.528367\pi$
$240$	1.49286	0.0963634
$241$	−13.3163	−0.857776	−0.428888	−	0.903358i	$-0.641095\pi$
$241$	−13.3163	−0.857776	−0.428888	+	0.903358i	$0.641095\pi$
$242$	−15.8111	−1.01638
$243$	−0.988346	−0.0634024
$244$	25.0606	1.60434
$245$	8.44411	0.539474
$246$	36.1398	2.30419
$247$	−0.0446482	−0.00284089
$248$	12.4314	0.789397
$249$	26.2016	1.66046
$250$	−2.32774	−0.147219
$251$	−19.6329	−1.23922	−0.619608	−	0.784911i	$-0.712709\pi$
$251$	−19.6329	−1.23922	−0.619608	+	0.784911i	$0.712709\pi$
$252$	1.27809	0.0805120
$253$	−12.5206	−0.787162
$254$	−2.32952	−0.146167
$255$	2.48188	0.155421
$256$	−21.0813	−1.31758
$257$	−0.318208	−0.0198493	−0.00992464	−	0.999951i	$-0.503159\pi$
$257$	−0.318208	−0.0198493	−0.00992464	+	0.999951i	$0.503159\pi$
$258$	2.48855	0.154930
$259$	11.7132	0.727823
$260$	1.61108	0.0999147
$261$	0.740547	0.0458387
$262$	12.1103	0.748176
$263$	23.2102	1.43120	0.715600	−	0.698510i	$-0.246153\pi$
$263$	23.2102	1.43120	0.715600	+	0.698510i	$0.246153\pi$
$264$	−24.5011	−1.50794
$265$	−7.16298	−0.440019
$266$	0.866609	0.0531352
$267$	−27.3473	−1.67363
$268$	−4.23151	−0.258481
$269$	−29.0879	−1.77352	−0.886759	−	0.462231i	$-0.847049\pi$
$269$	−29.0879	−1.77352	−0.886759	+	0.462231i	$0.847049\pi$
$270$	11.8960	0.723966
$271$	−10.7154	−0.650914	−0.325457	−	0.945557i	$-0.605518\pi$
$271$	−10.7154	−0.650914	−0.325457	+	0.945557i	$0.605518\pi$
$272$	1.19707	0.0725828
$273$	3.25850	0.197213
$274$	−6.42980	−0.388438
$275$	4.21811	0.254362
$276$	−17.8512	−1.07451
$277$	−7.91791	−0.475741	−0.237870	−	0.971297i	$-0.576449\pi$
$277$	−7.91791	−0.475741	−0.237870	+	0.971297i	$0.576449\pi$
$278$	−43.3550	−2.60026
$279$	−0.358223	−0.0214463
$280$	−12.9750	−0.775406
$281$	3.52004	0.209988	0.104994	−	0.994473i	$-0.466518\pi$
$281$	3.52004	0.209988	0.104994	+	0.994473i	$0.466518\pi$
$282$	−14.6875	−0.874629
$283$	13.5185	0.803590	0.401795	−	0.915730i	$-0.368386\pi$
$283$	13.5185	0.803590	0.401795	+	0.915730i	$0.368386\pi$
$284$	53.1161	3.15186
$285$	−0.166666	−0.00987245
$286$	−4.62753	−0.273631
$287$	−34.6810	−2.04716
$288$	0.440306	0.0259453
$289$	−15.0099	−0.882934
$290$	−18.1187	−1.06397
$291$	17.7304	1.03937
$292$	5.02991	0.294353
$293$	13.3939	0.782480	0.391240	−	0.920289i	$-0.372046\pi$
$293$	13.3939	0.782480	0.391240	+	0.920289i	$0.372046\pi$
$294$	−34.5803	−2.01676
$295$	0.0798648	0.00464991
$296$	−9.84058	−0.571972
$297$	−21.5568	−1.25085
$298$	−43.8380	−2.53947
$299$	−1.39895	−0.0809034
$300$	6.01395	0.347216
$301$	−2.38810	−0.137648
$302$	−20.7093	−1.19169
$303$	−16.0763	−0.923559
$304$	−0.0803869	−0.00461050
$305$	7.33114	0.419780
$306$	−0.312417	−0.0178597
$307$	19.5528	1.11594	0.557968	−	0.829863i	$-0.311581\pi$
$307$	19.5528	1.11594	0.557968	+	0.829863i	$0.311581\pi$
$308$	56.6656	3.22882
$309$	5.51828	0.313924
$310$	8.76454	0.497793
$311$	−5.70803	−0.323673	−0.161836	−	0.986818i	$-0.551742\pi$
$311$	−5.70803	−0.323673	−0.161836	+	0.986818i	$0.551742\pi$
$312$	−2.73755	−0.154984
$313$	−5.19529	−0.293655	−0.146828	−	0.989162i	$-0.546906\pi$
$313$	−5.19529	−0.293655	−0.146828	+	0.989162i	$0.546906\pi$
$314$	−17.4811	−0.986515
$315$	0.373887	0.0210662
$316$	42.6998	2.40205
$317$	1.19299	0.0670053	0.0335026	−	0.999439i	$-0.489334\pi$
$317$	1.19299	0.0670053	0.0335026	+	0.999439i	$0.489334\pi$
$318$	29.3338	1.64496
$319$	32.8331	1.83830
$320$	−12.4699	−0.697091
$321$	−34.5972	−1.93103
$322$	27.1533	1.51319
$323$	−0.133644	−0.00743612
$324$	−31.7101	−1.76167
$325$	0.471299	0.0261429
$326$	9.31257	0.515775
$327$	21.8285	1.20712
$328$	29.1365	1.60879
$329$	14.0947	0.777064
$330$	−17.2740	−0.950902
$331$	−25.5494	−1.40432	−0.702161	−	0.712018i	$-0.747782\pi$
$331$	−25.5494	−1.40432	−0.702161	+	0.712018i	$0.747782\pi$
$332$	50.9106	2.79408
$333$	0.283566	0.0155393
$334$	16.7962	0.919050
$335$	−1.23787	−0.0676321
$336$	5.86677	0.320059
$337$	0.113556	0.00618581	0.00309290	−	0.999995i	$-0.499015\pi$
$337$	0.113556	0.00618581	0.00309290	+	0.999995i	$0.499015\pi$
$338$	29.7436	1.61784
$339$	12.0996	0.657159
$340$	4.82237	0.261530
$341$	−15.8823	−0.860073
$342$	0.0209798	0.00113446
$343$	5.67520	0.306432
$344$	2.00631	0.108173
$345$	−5.22211	−0.281149
$346$	−4.02943	−0.216624
$347$	−12.8783	−0.691346	−0.345673	−	0.938355i	$-0.612349\pi$
$347$	−12.8783	−0.691346	−0.345673	+	0.938355i	$0.612349\pi$
$348$	46.8116	2.50937
$349$	−16.1049	−0.862074	−0.431037	−	0.902334i	$-0.641852\pi$
$349$	−16.1049	−0.862074	−0.431037	+	0.902334i	$0.641852\pi$
$350$	−9.14779	−0.488970
$351$	−2.40858	−0.128561
$352$	19.5215	1.04050
$353$	9.77672	0.520362	0.260181	−	0.965560i	$-0.416218\pi$
$353$	9.77672	0.520362	0.260181	+	0.965560i	$0.416218\pi$
$354$	−0.327062	−0.0173832
$355$	15.5384	0.824692
$356$	−53.1366	−2.81623
$357$	9.75353	0.516212
$358$	30.7760	1.62656
$359$	−26.5056	−1.39891	−0.699457	−	0.714675i	$-0.746575\pi$
$359$	−26.5056	−1.39891	−0.699457	+	0.714675i	$0.746575\pi$
$360$	−0.314113	−0.0165552
$361$	−18.9910	−0.999528
$362$	−34.9041	−1.83452
$363$	11.9500	0.627212
$364$	6.33137	0.331854
$365$	1.47143	0.0770183
$366$	−30.0224	−1.56930
$367$	−38.1899	−1.99349	−0.996747	−	0.0805925i	$-0.974319\pi$
$367$	−38.1899	−1.99349	−0.996747	+	0.0805925i	$0.974319\pi$
$368$	−2.51874	−0.131299
$369$	−0.839595	−0.0437076
$370$	−6.93791	−0.360685
$371$	−28.1498	−1.46146
$372$	−22.6441	−1.17404
$373$	12.0108	0.621894	0.310947	−	0.950427i	$-0.399354\pi$
$373$	12.0108	0.621894	0.310947	+	0.950427i	$0.399354\pi$
$374$	−13.8514	−0.716238
$375$	1.75930	0.0908499
$376$	−11.8413	−0.610669
$377$	3.66851	0.188938
$378$	46.7500	2.40456
$379$	1.65222	0.0848688	0.0424344	−	0.999099i	$-0.486489\pi$
$379$	1.65222	0.0848688	0.0424344	+	0.999099i	$0.486489\pi$
$380$	−0.323838	−0.0166125
$381$	1.76065	0.0902006
$382$	1.15809	0.0592528
$383$	−2.85664	−0.145968	−0.0729838	−	0.997333i	$-0.523252\pi$
$383$	−2.85664	−0.145968	−0.0729838	+	0.997333i	$0.523252\pi$
$384$	34.7827	1.77500
$385$	16.5768	0.844830
$386$	−61.0582	−3.10778
$387$	−0.0578137	−0.00293884
$388$	34.4507	1.74897
$389$	16.3440	0.828672	0.414336	−	0.910124i	$-0.364014\pi$
$389$	16.3440	0.828672	0.414336	+	0.910124i	$0.364014\pi$
$390$	−1.93006	−0.0977324
$391$	−4.18742	−0.211767
$392$	−27.8792	−1.40811
$393$	−9.15293	−0.461704
$394$	35.6401	1.79552
$395$	12.4912	0.628502
$396$	1.37182	0.0689366
$397$	7.68663	0.385781	0.192890	−	0.981220i	$-0.438214\pi$
$397$	7.68663	0.385781	0.192890	+	0.981220i	$0.438214\pi$
$398$	−11.7669	−0.589822
$399$	−0.654981	−0.0327901
$400$	0.848551	0.0424275
$401$	−31.0487	−1.55050	−0.775249	−	0.631656i	$-0.782375\pi$
$401$	−31.0487	−1.55050	−0.775249	+	0.631656i	$0.782375\pi$
$402$	5.06933	0.252835
$403$	−1.77456	−0.0883971
$404$	−31.2367	−1.55409
$405$	−9.27637	−0.460946
$406$	−71.2048	−3.53384
$407$	12.5722	0.623182
$408$	−8.19421	−0.405674
$409$	37.8098	1.86957	0.934787	−	0.355208i	$-0.115590\pi$
$409$	37.8098	1.86957	0.934787	+	0.355208i	$0.115590\pi$
$410$	20.5421	1.01450
$411$	4.85963	0.239708
$412$	10.7222	0.528244
$413$	0.313861	0.0154441
$414$	0.657355	0.0323073
$415$	14.8932	0.731078
$416$	2.18118	0.106941
$417$	32.7676	1.60464
$418$	0.930165	0.0454959
$419$	−17.7596	−0.867613	−0.433806	−	0.901006i	$-0.642830\pi$
$419$	−17.7596	−0.867613	−0.433806	+	0.901006i	$0.642830\pi$
$420$	23.6342	1.15323
$421$	−22.8089	−1.11164	−0.555820	−	0.831303i	$-0.687596\pi$
$421$	−22.8089	−1.11164	−0.555820	+	0.831303i	$0.687596\pi$
$422$	3.13004	0.152368
$423$	0.341219	0.0165906
$424$	23.6494	1.14852
$425$	1.41072	0.0684299
$426$	−63.6328	−3.08302
$427$	28.8106	1.39424
$428$	−67.2234	−3.24937
$429$	3.49747	0.168860
$430$	1.41451	0.0682137
$431$	−34.3395	−1.65407	−0.827037	−	0.562148i	$-0.809975\pi$
$431$	−34.3395	−1.65407	−0.827037	+	0.562148i	$0.809975\pi$
$432$	−4.33654	−0.208642
$433$	−17.7851	−0.854699	−0.427350	−	0.904086i	$-0.640553\pi$
$433$	−17.7851	−0.854699	−0.427350	+	0.904086i	$0.640553\pi$
$434$	34.4438	1.65335
$435$	13.6941	0.656582
$436$	42.4135	2.03124
$437$	0.281199	0.0134516
$438$	−6.02581	−0.287924
$439$	22.9535	1.09551	0.547754	−	0.836639i	$-0.315483\pi$
$439$	22.9535	1.09551	0.547754	+	0.836639i	$0.315483\pi$
$440$	−13.9266	−0.663924
$441$	0.803365	0.0382555
$442$	−1.54764	−0.0736140
$443$	28.9992	1.37780	0.688898	−	0.724859i	$-0.258095\pi$
$443$	28.9992	1.37780	0.688898	+	0.724859i	$0.258095\pi$
$444$	17.9248	0.850673
$445$	−15.5444	−0.736875
$446$	−16.0137	−0.758272
$447$	33.1327	1.56712
$448$	−49.0056	−2.31530
$449$	8.74997	0.412937	0.206468	−	0.978453i	$-0.433803\pi$
$449$	8.74997	0.412937	0.206468	+	0.978453i	$0.433803\pi$
$450$	−0.221459	−0.0104397
$451$	−37.2245	−1.75283
$452$	23.5099	1.10581
$453$	15.6520	0.735396
$454$	−27.5027	−1.29076
$455$	1.85216	0.0868304
$456$	0.550268	0.0257686
$457$	−15.4910	−0.724640	−0.362320	−	0.932054i	$-0.618015\pi$
$457$	−15.4910	−0.724640	−0.362320	+	0.932054i	$0.618015\pi$
$458$	−18.7468	−0.875981
$459$	−7.20951	−0.336511
$460$	−10.1467	−0.473094
$461$	−19.1507	−0.891936	−0.445968	−	0.895049i	$-0.647141\pi$
$461$	−19.1507	−0.891936	−0.445968	+	0.895049i	$0.647141\pi$
$462$	−67.8851	−3.15830
$463$	−18.1066	−0.841485	−0.420742	−	0.907180i	$-0.638230\pi$
$463$	−18.1066	−0.841485	−0.420742	+	0.907180i	$0.638230\pi$
$464$	6.60498	0.306628
$465$	−6.62422	−0.307191
$466$	50.0563	2.31881
$467$	−38.1164	−1.76382	−0.881908	−	0.471422i	$-0.843741\pi$
$467$	−38.1164	−1.76382	−0.881908	+	0.471422i	$0.843741\pi$
$468$	0.153276	0.00708521
$469$	−4.86471	−0.224631
$470$	−8.34849	−0.385087
$471$	13.2122	0.608784
$472$	−0.263683	−0.0121370
$473$	−2.56324	−0.117858
$474$	−51.1541	−2.34958
$475$	−0.0947343	−0.00434671
$476$	18.9514	0.868637
$477$	−0.681480	−0.0312028
$478$	6.40559	0.292985
$479$	−16.0177	−0.731869	−0.365935	−	0.930641i	$-0.619251\pi$
$479$	−16.0177	−0.731869	−0.365935	+	0.930641i	$0.619251\pi$
$480$	8.14209	0.371634
$481$	1.40472	0.0640498
$482$	30.9968	1.41187
$483$	−20.5224	−0.933801
$484$	23.2192	1.05542
$485$	10.0781	0.457623
$486$	2.30061	0.104358
$487$	38.8838	1.76199	0.880996	−	0.473123i	$-0.156873\pi$
$487$	38.8838	1.76199	0.880996	+	0.473123i	$0.156873\pi$
$488$	−24.2046	−1.09569
$489$	−7.03842	−0.318288
$490$	−19.6557	−0.887954
$491$	−34.8048	−1.57072	−0.785359	−	0.619041i	$-0.787522\pi$
$491$	−34.8048	−1.57072	−0.785359	+	0.619041i	$0.787522\pi$
$492$	−53.0727	−2.39270
$493$	10.9808	0.494550
$494$	0.103929	0.00467600
$495$	0.401308	0.0180374
$496$	−3.19501	−0.143460
$497$	61.0643	2.73911
$498$	−60.9905	−2.73305
$499$	−6.16861	−0.276145	−0.138073	−	0.990422i	$-0.544091\pi$
$499$	−6.16861	−0.276145	−0.138073	+	0.990422i	$0.544091\pi$
$500$	3.41838	0.152874
$501$	−12.6946	−0.567151
$502$	45.7003	2.03970
$503$	17.3122	0.771913	0.385957	−	0.922517i	$-0.373871\pi$
$503$	17.3122	0.771913	0.385957	+	0.922517i	$0.373871\pi$
$504$	−1.23443	−0.0549860
$505$	−9.13789	−0.406631
$506$	29.1447	1.29564
$507$	−22.4801	−0.998378
$508$	3.42099	0.151782
$509$	24.3778	1.08053	0.540264	−	0.841495i	$-0.318324\pi$
$509$	24.3778	1.08053	0.540264	+	0.841495i	$0.318324\pi$
$510$	−5.77717	−0.255817
$511$	5.78258	0.255806
$512$	9.53029	0.421183
$513$	0.484142	0.0213754
$514$	0.740706	0.0326711
$515$	3.13663	0.138216
$516$	−3.65453	−0.160882
$517$	15.1284	0.665344
$518$	−27.2653	−1.19797
$519$	3.04543	0.133680
$520$	−1.55605	−0.0682372
$521$	29.4723	1.29120	0.645602	−	0.763674i	$-0.276606\pi$
$521$	29.4723	1.29120	0.645602	+	0.763674i	$0.276606\pi$
$522$	−1.72380	−0.0754488
$523$	−6.39300	−0.279546	−0.139773	−	0.990184i	$-0.544637\pi$
$523$	−6.39300	−0.279546	−0.139773	+	0.990184i	$0.544637\pi$
$524$	−17.7844	−0.776916
$525$	6.91387	0.301746
$526$	−54.0273	−2.35570
$527$	−5.31172	−0.231382
$528$	6.29703	0.274043
$529$	−14.1893	−0.616924
$530$	16.6736	0.724254
$531$	0.00759827	0.000329737 0
$532$	−1.27265	−0.0551764
$533$	−4.15917	−0.180154
$534$	63.6573	2.75472
$535$	−19.6653	−0.850205
$536$	4.08698	0.176530
$537$	−23.2604	−1.00376
$538$	67.7090	2.91914
$539$	35.6182	1.53418
$540$	−17.4697	−0.751776
$541$	−0.531717	−0.0228603	−0.0114301	−	0.999935i	$-0.503638\pi$
$541$	−0.531717	−0.0228603	−0.0114301	+	0.999935i	$0.503638\pi$
$542$	24.9427	1.07138
$543$	26.3804	1.13209
$544$	6.52884	0.279922
$545$	12.4075	0.531478
$546$	−7.58494	−0.324606
$547$	43.2601	1.84967	0.924834	−	0.380371i	$-0.124204\pi$
$547$	43.2601	1.84967	0.924834	+	0.380371i	$0.124204\pi$
$548$	9.44241	0.403360
$549$	0.697478	0.0297676
$550$	−9.81867	−0.418670
$551$	−0.737396	−0.0314141
$552$	17.2414	0.733843
$553$	49.0893	2.08749
$554$	18.4308	0.783051
$555$	5.24366	0.222581
$556$	63.6685	2.70015
$557$	8.05739	0.341403	0.170701	−	0.985323i	$-0.445397\pi$
$557$	8.05739	0.341403	0.170701	+	0.985323i	$0.445397\pi$
$558$	0.833851	0.0352997
$559$	−0.286396	−0.0121133
$560$	3.33472	0.140918
$561$	10.4688	0.441995
$562$	−8.19374	−0.345632
$563$	−24.8406	−1.04691	−0.523453	−	0.852055i	$-0.675356\pi$
$563$	−24.8406	−1.04691	−0.523453	+	0.852055i	$0.675356\pi$
$564$	21.5692	0.908226
$565$	6.87749	0.289338
$566$	−31.4675	−1.32268
$567$	−36.4552	−1.53097
$568$	−51.3018	−2.15258
$569$	14.7752	0.619410	0.309705	−	0.950833i	$-0.399770\pi$
$569$	14.7752	0.619410	0.309705	+	0.950833i	$0.399770\pi$
$570$	0.387956	0.0162497
$571$	−31.7842	−1.33013	−0.665063	−	0.746787i	$-0.731595\pi$
$571$	−31.7842	−1.33013	−0.665063	+	0.746787i	$0.731595\pi$
$572$	6.79570	0.284143
$573$	−0.875278	−0.0365653
$574$	80.7285	3.36954
$575$	−2.96829	−0.123786
$576$	−1.18638	−0.0494325
$577$	6.08385	0.253274	0.126637	−	0.991949i	$-0.459582\pi$
$577$	6.08385	0.253274	0.126637	+	0.991949i	$0.459582\pi$
$578$	34.9391	1.45327
$579$	46.1476	1.91783
$580$	26.6081	1.10484
$581$	58.5287	2.42818
$582$	−41.2718	−1.71077
$583$	−30.2143	−1.25135
$584$	−4.85811	−0.201030
$585$	0.0448390	0.00185386
$586$	−31.1775	−1.28793
$587$	4.26689	0.176113	0.0880567	−	0.996115i	$-0.471934\pi$
$587$	4.26689	0.176113	0.0880567	+	0.996115i	$0.471934\pi$
$588$	50.7825	2.09423
$589$	0.356699	0.0146975
$590$	−0.185905	−0.00765357
$591$	−26.9367	−1.10803
$592$	2.52914	0.103947
$593$	34.7994	1.42904	0.714519	−	0.699616i	$-0.246645\pi$
$593$	34.7994	1.42904	0.714519	+	0.699616i	$0.246645\pi$
$594$	50.1786	2.05885
$595$	5.54398	0.227281
$596$	64.3778	2.63702
$597$	8.89341	0.363983
$598$	3.25639	0.133164
$599$	10.3094	0.421232	0.210616	−	0.977569i	$-0.432453\pi$
$599$	10.3094	0.421232	0.210616	+	0.977569i	$0.432453\pi$
$600$	−5.80854	−0.237132
$601$	−13.5138	−0.551238	−0.275619	−	0.961267i	$-0.588883\pi$
$601$	−13.5138	−0.551238	−0.275619	+	0.961267i	$0.588883\pi$
$602$	5.55888	0.226563
$603$	−0.117770	−0.00479597
$604$	30.4124	1.23746
$605$	6.79247	0.276153
$606$	37.4214	1.52014
$607$	−1.35072	−0.0548242	−0.0274121	−	0.999624i	$-0.508727\pi$
$607$	−1.35072	−0.0548242	−0.0274121	+	0.999624i	$0.508727\pi$
$608$	−0.438433	−0.0177808
$609$	53.8164	2.18075
$610$	−17.0650	−0.690941
$611$	1.69032	0.0683831
$612$	0.458796	0.0185457
$613$	14.9142	0.602377	0.301189	−	0.953565i	$-0.402617\pi$
$613$	14.9142	0.602377	0.301189	+	0.953565i	$0.402617\pi$
$614$	−45.5138	−1.83679
$615$	−15.5257	−0.626056
$616$	−54.7301	−2.20514
$617$	39.2030	1.57825	0.789127	−	0.614230i	$-0.210533\pi$
$617$	39.2030	1.57825	0.789127	+	0.614230i	$0.210533\pi$
$618$	−12.8451	−0.516706
$619$	5.03155	0.202235	0.101118	−	0.994874i	$-0.467758\pi$
$619$	5.03155	0.202235	0.101118	+	0.994874i	$0.467758\pi$
$620$	−12.8711	−0.516915
$621$	15.1695	0.608732
$622$	13.2868	0.532753
$623$	−61.0879	−2.44743
$624$	0.703581	0.0281658
$625$	1.00000	0.0400000
$626$	12.0933	0.483345
$627$	−0.703017	−0.0280758
$628$	25.6716	1.02441
$629$	4.20470	0.167652
$630$	−0.870313	−0.0346741
$631$	−1.23983	−0.0493567	−0.0246784	−	0.999695i	$-0.507856\pi$
$631$	−1.23983	−0.0493567	−0.0246784	+	0.999695i	$0.507856\pi$
$632$	−41.2413	−1.64049
$633$	−2.36568	−0.0940272
$634$	−2.77698	−0.110288
$635$	1.00076	0.0397141
$636$	−43.0779	−1.70815
$637$	3.97970	0.157681
$638$	−76.4269	−3.02577
$639$	1.47831	0.0584810
$640$	19.7708	0.781508
$641$	6.90062	0.272558	0.136279	−	0.990671i	$-0.456486\pi$
$641$	6.90062	0.272558	0.136279	+	0.990671i	$0.456486\pi$
$642$	80.5333	3.17840
$643$	2.21128	0.0872042	0.0436021	−	0.999049i	$-0.486117\pi$
$643$	2.21128	0.0872042	0.0436021	+	0.999049i	$0.486117\pi$
$644$	−39.8756	−1.57132
$645$	−1.06908	−0.0420951
$646$	0.311087	0.0122396
$647$	−24.8831	−0.978254	−0.489127	−	0.872212i	$-0.662685\pi$
$647$	−24.8831	−0.978254	−0.489127	+	0.872212i	$0.662685\pi$
$648$	30.6270	1.20314
$649$	0.336879	0.0132236
$650$	−1.09706	−0.0430303
$651$	−26.0325	−1.02029
$652$	−13.6759	−0.535588
$653$	−16.6908	−0.653162	−0.326581	−	0.945169i	$-0.605897\pi$
$653$	−16.6908	−0.653162	−0.326581	+	0.945169i	$0.605897\pi$
$654$	−50.8111	−1.98687
$655$	−5.20259	−0.203282
$656$	−7.48839	−0.292373
$657$	0.139991	0.00546157
$658$	−32.8087	−1.27902
$659$	−32.0480	−1.24841	−0.624206	−	0.781260i	$-0.714577\pi$
$659$	−32.0480	−1.24841	−0.624206	+	0.781260i	$0.714577\pi$
$660$	25.3675	0.987430
$661$	−11.4863	−0.446765	−0.223383	−	0.974731i	$-0.571710\pi$
$661$	−11.4863	−0.446765	−0.223383	+	0.974731i	$0.571710\pi$
$662$	59.4724	2.31146
$663$	1.16971	0.0454276
$664$	−49.1716	−1.90823
$665$	−0.372296	−0.0144370
$666$	−0.660067	−0.0255771
$667$	−23.1047	−0.894616
$668$	−24.6659	−0.954354
$669$	12.1031	0.467934
$670$	2.88144	0.111320
$671$	30.9236	1.19379
$672$	31.9976	1.23433
$673$	−8.18425	−0.315480	−0.157740	−	0.987481i	$-0.550421\pi$
$673$	−8.18425	−0.315480	−0.157740	+	0.987481i	$0.550421\pi$
$674$	−0.264330	−0.0101816
$675$	−5.11052	−0.196704
$676$	−43.6796	−1.67999
$677$	17.2502	0.662977	0.331489	−	0.943459i	$-0.392449\pi$
$677$	17.2502	0.662977	0.331489	+	0.943459i	$0.392449\pi$
$678$	−28.1647	−1.08166
$679$	39.6059	1.51993
$680$	−4.65765	−0.178613
$681$	20.7865	0.796539
$682$	36.9698	1.41565
$683$	4.98122	0.190601	0.0953005	−	0.995449i	$-0.469619\pi$
$683$	4.98122	0.190601	0.0953005	+	0.995449i	$0.469619\pi$
$684$	−0.0308097	−0.00117804
$685$	2.76225	0.105540
$686$	−13.2104	−0.504375
$687$	14.1688	0.540573
$688$	−0.515643	−0.0196587
$689$	−3.37590	−0.128612
$690$	12.1557	0.462761
$691$	−18.3623	−0.698537	−0.349268	−	0.937023i	$-0.613570\pi$
$691$	−18.3623	−0.698537	−0.349268	+	0.937023i	$0.613570\pi$
$692$	5.91737	0.224945
$693$	1.57710	0.0599090
$694$	29.9775	1.13793
$695$	18.6254	0.706500
$696$	−45.2127	−1.71378
$697$	−12.4495	−0.471558
$698$	37.4879	1.41894
$699$	−37.8324	−1.43095
$700$	13.4339	0.507753
$701$	−36.3448	−1.37272	−0.686362	−	0.727260i	$-0.740793\pi$
$701$	−36.3448	−1.37272	−0.686362	+	0.727260i	$0.740793\pi$
$702$	5.60656	0.211606
$703$	−0.282359	−0.0106494
$704$	−52.5996	−1.98242
$705$	6.30977	0.237640
$706$	−22.7577	−0.856497
$707$	−35.9110	−1.35057
$708$	0.480303	0.0180509
$709$	43.3311	1.62733	0.813667	−	0.581332i	$-0.197468\pi$
$709$	43.3311	1.62733	0.813667	+	0.581332i	$0.197468\pi$
$710$	−36.1694	−1.35741
$711$	1.18841	0.0445687
$712$	51.3216	1.92336
$713$	11.1764	0.418558
$714$	−22.7037	−0.849665
$715$	1.98799	0.0743466
$716$	−45.1958	−1.68904
$717$	−4.84133	−0.180803
$718$	61.6982	2.30256
$719$	−29.6663	−1.10637	−0.553184	−	0.833059i	$-0.686587\pi$
$719$	−29.6663	−1.10637	−0.553184	+	0.833059i	$0.686587\pi$
$720$	0.0807304	0.00300864
$721$	12.3266	0.459068
$722$	44.2062	1.64518
$723$	−23.4273	−0.871271
$724$	51.2580	1.90499
$725$	7.78383	0.289084
$726$	−27.8165	−1.03237
$727$	−3.24524	−0.120359	−0.0601796	−	0.998188i	$-0.519167\pi$
$727$	−3.24524	−0.120359	−0.0601796	+	0.998188i	$0.519167\pi$
$728$	−6.11511	−0.226641
$729$	26.0903	0.966307
$730$	−3.42511	−0.126769
$731$	−0.857259	−0.0317069
$732$	44.0891	1.62958
$733$	21.0326	0.776857	0.388428	−	0.921479i	$-0.373018\pi$
$733$	21.0326	0.776857	0.388428	+	0.921479i	$0.373018\pi$
$734$	88.8961	3.28121
$735$	14.8557	0.547962
$736$	−13.7373	−0.506364
$737$	−5.22148	−0.192336
$738$	1.95436	0.0719410
$739$	2.87018	0.105581	0.0527907	−	0.998606i	$-0.483188\pi$
$739$	2.87018	0.105581	0.0527907	+	0.998606i	$0.483188\pi$
$740$	10.1886	0.374540
$741$	−0.0785495	−0.00288559
$742$	65.5254	2.40551
$743$	24.3195	0.892196	0.446098	−	0.894984i	$-0.352813\pi$
$743$	24.3195	0.892196	0.446098	+	0.894984i	$0.352813\pi$
$744$	21.8706	0.801816
$745$	18.8329	0.689982
$746$	−27.9579	−1.02361
$747$	1.41693	0.0518426
$748$	20.3413	0.743751
$749$	−77.2827	−2.82385
$750$	−4.09520	−0.149535
$751$	10.4537	0.381460	0.190730	−	0.981642i	$-0.438914\pi$
$751$	10.4537	0.381460	0.190730	+	0.981642i	$0.438914\pi$
$752$	3.04335	0.110979
$753$	−34.5401	−1.25871
$754$	−8.53934	−0.310984
$755$	8.89673	0.323785
$756$	−68.6542	−2.49693
$757$	21.2144	0.771050	0.385525	−	0.922697i	$-0.374020\pi$
$757$	21.2144	0.771050	0.385525	+	0.922697i	$0.374020\pi$
$758$	−3.84594	−0.139691
$759$	−22.0275	−0.799546
$760$	0.312776	0.0113456
$761$	16.5103	0.598497	0.299249	−	0.954175i	$-0.403264\pi$
$761$	16.5103	0.598497	0.299249	+	0.954175i	$0.403264\pi$
$762$	−4.09833	−0.148467
$763$	48.7601	1.76524
$764$	−1.70069	−0.0615289
$765$	0.134215	0.00485254
$766$	6.64952	0.240257
$767$	0.0376402	0.00135911
$768$	−37.0883	−1.33831
$769$	30.7008	1.10710	0.553550	−	0.832816i	$-0.313273\pi$
$769$	30.7008	1.10710	0.553550	+	0.832816i	$0.313273\pi$
$770$	−38.5864	−1.39056
$771$	−0.559824	−0.0201616
$772$	89.6663	3.22716
$773$	18.7307	0.673697	0.336848	−	0.941559i	$-0.390639\pi$
$773$	18.7307	0.673697	0.336848	+	0.941559i	$0.390639\pi$
$774$	0.134575	0.00483721
$775$	−3.76526	−0.135252
$776$	−33.2740	−1.19447
$777$	20.6070	0.739274
$778$	−38.0445	−1.36396
$779$	0.836023	0.0299536
$780$	2.83437	0.101487
$781$	65.5427	2.34530
$782$	9.74723	0.348560
$783$	−39.7795	−1.42160
$784$	7.16525	0.255902
$785$	7.50989	0.268040
$786$	21.3056	0.759947
$787$	14.3668	0.512121	0.256060	−	0.966661i	$-0.417575\pi$
$787$	14.3668	0.512121	0.256060	+	0.966661i	$0.417575\pi$
$788$	−52.3389	−1.86450
$789$	40.8337	1.45372
$790$	−29.0764	−1.03449
$791$	27.0279	0.961000
$792$	−1.32496	−0.0470805
$793$	3.45515	0.122696
$794$	−17.8925	−0.634981
$795$	−12.6018	−0.446941
$796$	17.2802	0.612480
$797$	−31.6576	−1.12137	−0.560685	−	0.828029i	$-0.689462\pi$
$797$	−31.6576	−1.12137	−0.560685	+	0.828029i	$0.689462\pi$
$798$	1.52463	0.0539712
$799$	5.05958	0.178995
$800$	4.62803	0.163625
$801$	−1.47888	−0.0522537
$802$	72.2733	2.55206
$803$	6.20667	0.219029
$804$	−7.44450	−0.262547
$805$	−11.6651	−0.411140
$806$	4.13072	0.145498
$807$	−51.1743	−1.80142
$808$	30.1698	1.06137
$809$	18.6508	0.655728	0.327864	−	0.944725i	$-0.393671\pi$
$809$	18.6508	0.655728	0.327864	+	0.944725i	$0.393671\pi$
$810$	21.5930	0.758700
$811$	−29.2437	−1.02688	−0.513442	−	0.858124i	$-0.671630\pi$
$811$	−29.2437	−1.02688	−0.513442	+	0.858124i	$0.671630\pi$
$812$	104.567	3.66958
$813$	−18.8516	−0.661155
$814$	−29.2649	−1.02573
$815$	−4.00069	−0.140138
$816$	2.10600	0.0737248
$817$	0.0575677	0.00201404
$818$	−88.0114	−3.07725
$819$	0.176213	0.00615737
$820$	−30.1669	−1.05347
$821$	9.33244	0.325704	0.162852	−	0.986650i	$-0.447931\pi$
$821$	9.33244	0.325704	0.162852	+	0.986650i	$0.447931\pi$
$822$	−11.3120	−0.394550
$823$	47.2659	1.64759	0.823793	−	0.566891i	$-0.191854\pi$
$823$	47.2659	1.64759	0.823793	+	0.566891i	$0.191854\pi$
$824$	−10.3560	−0.360767
$825$	7.42093	0.258364
$826$	−0.730586	−0.0254203
$827$	24.7821	0.861758	0.430879	−	0.902410i	$-0.358204\pi$
$827$	24.7821	0.861758	0.430879	+	0.902410i	$0.358204\pi$
$828$	−0.965352	−0.0335483
$829$	−5.24258	−0.182082	−0.0910412	−	0.995847i	$-0.529019\pi$
$829$	−5.24258	−0.182082	−0.0910412	+	0.995847i	$0.529019\pi$
$830$	−34.6675	−1.20333
$831$	−13.9300	−0.483226
$832$	−5.87707	−0.203751
$833$	11.9123	0.412735
$834$	−76.2745	−2.64117
$835$	−7.21568	−0.249709
$836$	−1.36598	−0.0472435
$837$	19.2424	0.665116
$838$	41.3397	1.42806
$839$	−1.64281	−0.0567161	−0.0283580	−	0.999598i	$-0.509028\pi$
$839$	−1.64281	−0.0567161	−0.0283580	+	0.999598i	$0.509028\pi$
$840$	−22.8270	−0.787605
$841$	31.5880	1.08924
$842$	53.0933	1.82972
$843$	6.19281	0.213292
$844$	−4.59658	−0.158221
$845$	−12.7779	−0.439572
$846$	−0.794269	−0.0273075
$847$	26.6937	0.917207
$848$	−6.07816	−0.208725
$849$	23.7831	0.816233
$850$	−3.28379	−0.112633
$851$	−8.84709	−0.303274
$852$	93.4472	3.20145
$853$	−19.6884	−0.674118	−0.337059	−	0.941483i	$-0.609432\pi$
$853$	−19.6884	−0.674118	−0.337059	+	0.941483i	$0.609432\pi$
$854$	−67.0637	−2.29487
$855$	−0.00901295	−0.000308236 0
$856$	64.9273	2.21917
$857$	−0.139879	−0.00477819	−0.00238909	−	0.999997i	$-0.500760\pi$
$857$	−0.139879	−0.00477819	−0.00238909	+	0.999997i	$0.500760\pi$
$858$	−8.14121	−0.277936
$859$	11.2591	0.384156	0.192078	−	0.981380i	$-0.438477\pi$
$859$	11.2591	0.384156	0.192078	+	0.981380i	$0.438477\pi$
$860$	−2.07726	−0.0708341
$861$	−61.0144	−2.07936
$862$	79.9333	2.72254
$863$	42.5030	1.44682	0.723410	−	0.690418i	$-0.242574\pi$
$863$	42.5030	1.44682	0.723410	+	0.690418i	$0.242574\pi$
$864$	−23.6516	−0.804645
$865$	1.73105	0.0588574
$866$	41.3992	1.40680
$867$	−26.4069	−0.896825
$868$	−50.5820	−1.71687
$869$	52.6894	1.78737
$870$	−31.8763	−1.08071
$871$	−0.583407	−0.0197680
$872$	−40.9647	−1.38724
$873$	0.958821	0.0324512
$874$	−0.654558	−0.0221408
$875$	3.92990	0.132855
$876$	8.84913	0.298984
$877$	−38.2210	−1.29063	−0.645316	−	0.763916i	$-0.723274\pi$
$877$	−38.2210	−1.29063	−0.645316	+	0.763916i	$0.723274\pi$
$878$	−53.4297	−1.80317
$879$	23.5639	0.794791
$880$	3.57928	0.120658
$881$	0.143935	0.00484929	0.00242464	−	0.999997i	$-0.499228\pi$
$881$	0.143935	0.00484929	0.00242464	+	0.999997i	$0.499228\pi$
$882$	−1.87003	−0.0629671
$883$	34.5704	1.16339	0.581693	−	0.813409i	$-0.302391\pi$
$883$	34.5704	1.16339	0.581693	+	0.813409i	$0.302391\pi$
$884$	2.27278	0.0764417
$885$	0.140506	0.00472306
$886$	−67.5027	−2.26780
$887$	0.00429134	0.000144089 0	7.20445e−5	−	1.00000i	$-0.499977\pi$
$887$	0.00429134	0.000144089 0	7.20445e−5		1.00000i	$0.499977\pi$
$888$	−17.3125	−0.580971
$889$	3.93290	0.131905
$890$	36.1833	1.21287
$891$	−39.1287	−1.31086
$892$	23.5168	0.787400
$893$	−0.339767	−0.0113699
$894$	−77.1242	−2.57942
$895$	−13.2214	−0.441943
$896$	77.6971	2.59568
$897$	−2.46117	−0.0821762
$898$	−20.3677	−0.679678
$899$	−29.3081	−0.977481
$900$	0.325222	0.0108407
$901$	−10.1050	−0.336645
$902$	86.6490	2.88510
$903$	−4.20139	−0.139814
$904$	−22.7068	−0.755218
$905$	14.9948	0.498445
$906$	−36.4338	−1.21043
$907$	55.2918	1.83594	0.917968	−	0.396655i	$-0.129829\pi$
$907$	55.2918	1.83594	0.917968	+	0.396655i	$0.129829\pi$
$908$	40.3887	1.34035
$909$	−0.869371	−0.0288352
$910$	−4.31134	−0.142919
$911$	11.4843	0.380490	0.190245	−	0.981737i	$-0.439072\pi$
$911$	11.4843	0.380490	0.190245	+	0.981737i	$0.439072\pi$
$912$	−0.141425	−0.00468304
$913$	62.8211	2.07908
$914$	36.0591	1.19273
$915$	12.8977	0.426384
$916$	27.5304	0.909631
$917$	−20.4457	−0.675175
$918$	16.7819	0.553885
$919$	−43.3238	−1.42912	−0.714561	−	0.699573i	$-0.753373\pi$
$919$	−43.3238	−1.42912	−0.714561	+	0.699573i	$0.753373\pi$
$920$	9.80015	0.323101
$921$	34.3992	1.13349
$922$	44.5778	1.46809
$923$	7.32322	0.241047
$924$	99.6918	3.27962
$925$	2.98053	0.0979994
$926$	42.1475	1.38505
$927$	0.298416	0.00980128
$928$	36.0238	1.18254
$929$	−25.0378	−0.821464	−0.410732	−	0.911756i	$-0.634727\pi$
$929$	−25.0378	−0.821464	−0.410732	+	0.911756i	$0.634727\pi$
$930$	15.4195	0.505624
$931$	−0.799947	−0.0262172
$932$	−73.5096	−2.40789
$933$	−10.0421	−0.328765
$934$	88.7251	2.90317
$935$	5.95057	0.194604
$936$	−0.148041	−0.00483887
$937$	27.4963	0.898266	0.449133	−	0.893465i	$-0.351733\pi$
$937$	27.4963	0.898266	0.449133	+	0.893465i	$0.351733\pi$
$938$	11.3238	0.369735
$939$	−9.14009	−0.298275
$940$	12.2601	0.399880
$941$	26.5566	0.865720	0.432860	−	0.901461i	$-0.357504\pi$
$941$	26.5566	0.865720	0.432860	+	0.901461i	$0.357504\pi$
$942$	−30.7545	−1.00204
$943$	26.1949	0.853024
$944$	0.0677693	0.00220570
$945$	−20.0838	−0.653327
$946$	5.96656	0.193990
$947$	−51.1918	−1.66351	−0.831756	−	0.555142i	$-0.812664\pi$
$947$	−51.1918	−1.66351	−0.831756	+	0.555142i	$0.812664\pi$
$948$	75.1217	2.43984
$949$	0.693484	0.0225115
$950$	0.220517	0.00715452
$951$	2.09884	0.0680594
$952$	−18.3041	−0.593239
$953$	−30.5032	−0.988095	−0.494047	−	0.869435i	$-0.664483\pi$
$953$	−30.5032	−0.988095	−0.494047	+	0.869435i	$0.664483\pi$
$954$	1.58631	0.0513587
$955$	−0.497515	−0.0160992
$956$	−9.40686	−0.304240
$957$	57.7633	1.86722
$958$	37.2851	1.20463
$959$	10.8554	0.350538
$960$	−21.9384	−0.708058
$961$	−16.8228	−0.542672
$962$	−3.26983	−0.105424
$963$	−1.87094	−0.0602902
$964$	−45.5200	−1.46610
$965$	26.2307	0.844395
$966$	47.7708	1.53700
$967$	−9.36696	−0.301221	−0.150611	−	0.988593i	$-0.548124\pi$
$967$	−9.36696	−0.301221	−0.150611	+	0.988593i	$0.548124\pi$
$968$	−22.4261	−0.720803
$969$	−0.235119	−0.00755312
$970$	−23.4592	−0.753229
$971$	−27.1448	−0.871117	−0.435559	−	0.900160i	$-0.643449\pi$
$971$	−27.1448	−0.871117	−0.435559	+	0.900160i	$0.643449\pi$
$972$	−3.37854	−0.108367
$973$	73.1958	2.34655
$974$	−90.5114	−2.90017
$975$	0.829156	0.0265542
$976$	6.22084	0.199124
$977$	20.6227	0.659780	0.329890	−	0.944019i	$-0.392988\pi$
$977$	20.6227	0.659780	0.329890	+	0.944019i	$0.392988\pi$
$978$	16.3836	0.523890
$979$	−65.5680	−2.09556
$980$	28.8651	0.922063
$981$	1.18044	0.0376885
$982$	81.0165	2.58534
$983$	31.3395	0.999574	0.499787	−	0.866148i	$-0.333412\pi$
$983$	31.3395	0.999574	0.499787	+	0.866148i	$0.333412\pi$
$984$	51.2599	1.63410
$985$	−15.3110	−0.487850
$986$	−25.5605	−0.814011
$987$	24.7968	0.789290
$988$	−0.152624	−0.00485562
$989$	1.80376	0.0573561
$990$	−0.934140	−0.0296889
$991$	7.76819	0.246765	0.123382	−	0.992359i	$-0.460626\pi$
$991$	7.76819	0.246765	0.123382	+	0.992359i	$0.460626\pi$
$992$	−17.4257	−0.553267
$993$	−44.9491	−1.42642
$994$	−142.142	−4.50847
$995$	5.05508	0.160257
$996$	89.5670	2.83804
$997$	−45.8873	−1.45326	−0.726632	−	0.687027i	$-0.758915\pi$
$997$	−45.8873	−1.45326	−0.726632	+	0.687027i	$0.758915\pi$
$998$	14.3589	0.454524
$999$	−15.2321	−0.481922

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6005.2.a.f.1.13	✓	111

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6005.2.a.f.1.13	✓	111	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:	\( N \)	\(=\)	\( 6005 = 5 \cdot 1201 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6005.a (trivial)

\(f(q)\)	\(=\)	\(q-2.32774 q^{2} +1.75930 q^{3} +3.41838 q^{4} +1.00000 q^{5} -4.09520 q^{6} +3.92990 q^{7} -3.30162 q^{8} +0.0951392 q^{9} +O(q^{10})\)	\(q-2.32774 q^{2} +1.75930 q^{3} +3.41838 q^{4} +1.00000 q^{5} -4.09520 q^{6} +3.92990 q^{7} -3.30162 q^{8} +0.0951392 q^{9} -2.32774 q^{10} +4.21811 q^{11} +6.01395 q^{12} +0.471299 q^{13} -9.14779 q^{14} +1.75930 q^{15} +0.848551 q^{16} +1.41072 q^{17} -0.221459 q^{18} -0.0947343 q^{19} +3.41838 q^{20} +6.91387 q^{21} -9.81867 q^{22} -2.96829 q^{23} -5.80854 q^{24} +1.00000 q^{25} -1.09706 q^{26} -5.11052 q^{27} +13.4339 q^{28} +7.78383 q^{29} -4.09520 q^{30} -3.76526 q^{31} +4.62803 q^{32} +7.42093 q^{33} -3.28379 q^{34} +3.92990 q^{35} +0.325222 q^{36} +2.98053 q^{37} +0.220517 q^{38} +0.829156 q^{39} -3.30162 q^{40} -8.82492 q^{41} -16.0937 q^{42} -0.607675 q^{43} +14.4191 q^{44} +0.0951392 q^{45} +6.90941 q^{46} +3.58652 q^{47} +1.49286 q^{48} +8.44411 q^{49} -2.32774 q^{50} +2.48188 q^{51} +1.61108 q^{52} -7.16298 q^{53} +11.8960 q^{54} +4.21811 q^{55} -12.9750 q^{56} -0.166666 q^{57} -18.1187 q^{58} +0.0798648 q^{59} +6.01395 q^{60} +7.33114 q^{61} +8.76454 q^{62} +0.373887 q^{63} -12.4699 q^{64} +0.471299 q^{65} -17.2740 q^{66} -1.23787 q^{67} +4.82237 q^{68} -5.22211 q^{69} -9.14779 q^{70} +15.5384 q^{71} -0.314113 q^{72} +1.47143 q^{73} -6.93791 q^{74} +1.75930 q^{75} -0.323838 q^{76} +16.5768 q^{77} -1.93006 q^{78} +12.4912 q^{79} +0.848551 q^{80} -9.27637 q^{81} +20.5421 q^{82} +14.8932 q^{83} +23.6342 q^{84} +1.41072 q^{85} +1.41451 q^{86} +13.6941 q^{87} -13.9266 q^{88} -15.5444 q^{89} -0.221459 q^{90} +1.85216 q^{91} -10.1467 q^{92} -6.62422 q^{93} -8.34849 q^{94} -0.0947343 q^{95} +8.14209 q^{96} +10.0781 q^{97} -19.6557 q^{98} +0.401308 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 111 q + 20 q^{2} + 40 q^{3} + 136 q^{4} + 111 q^{5} + 3 q^{6} + 39 q^{7} + 45 q^{8} + 139 q^{9}+O(q^{10}) \) 111 * q + 20 * q^2 + 40 * q^3 + 136 * q^4 + 111 * q^5 + 3 * q^6 + 39 * q^7 + 45 * q^8 + 139 * q^9	\( 111 q + 20 q^{2} + 40 q^{3} + 136 q^{4} + 111 q^{5} + 3 q^{6} + 39 q^{7} + 45 q^{8} + 139 q^{9} + 20 q^{10} + 36 q^{11} + 80 q^{12} + 36 q^{13} + 7 q^{14} + 40 q^{15} + 190 q^{16} + 38 q^{17} + 48 q^{18} + 77 q^{19} + 136 q^{20} + 11 q^{21} + 39 q^{22} + 82 q^{23} - 3 q^{24} + 111 q^{25} - 3 q^{26} + 130 q^{27} + 87 q^{28} + 20 q^{29} + 3 q^{30} + 41 q^{31} + 85 q^{32} + 33 q^{33} + 7 q^{34} + 39 q^{35} + 191 q^{36} + 80 q^{37} + 42 q^{38} + 21 q^{39} + 45 q^{40} + 16 q^{41} + 33 q^{42} + 164 q^{43} + 37 q^{44} + 139 q^{45} + 32 q^{46} + 148 q^{47} + 149 q^{48} + 160 q^{49} + 20 q^{50} + 51 q^{51} + 87 q^{52} + 83 q^{53} - 6 q^{54} + 36 q^{55} - 10 q^{56} + 28 q^{57} + 47 q^{58} + 14 q^{59} + 80 q^{60} + 20 q^{61} + 14 q^{62} + 120 q^{63} + 231 q^{64} + 36 q^{65} - 4 q^{66} + 253 q^{67} + 80 q^{68} + 6 q^{69} + 7 q^{70} + 5 q^{71} + 124 q^{72} + 64 q^{73} - 37 q^{74} + 40 q^{75} + 92 q^{76} + 63 q^{77} + 29 q^{78} + 91 q^{79} + 190 q^{80} + 187 q^{81} - 7 q^{82} + 63 q^{83} - 69 q^{84} + 38 q^{85} - 22 q^{86} + 57 q^{87} + 121 q^{88} - 6 q^{89} + 48 q^{90} + 119 q^{91} + 104 q^{92} + 14 q^{93} - q^{94} + 77 q^{95} - 38 q^{96} + 96 q^{97} + 81 q^{98} + 106 q^{99}+O(q^{100}) \) 111 * q + 20 * q^2 + 40 * q^3 + 136 * q^4 + 111 * q^5 + 3 * q^6 + 39 * q^7 + 45 * q^8 + 139 * q^9 + 20 * q^10 + 36 * q^11 + 80 * q^12 + 36 * q^13 + 7 * q^14 + 40 * q^15 + 190 * q^16 + 38 * q^17 + 48 * q^18 + 77 * q^19 + 136 * q^20 + 11 * q^21 + 39 * q^22 + 82 * q^23 - 3 * q^24 + 111 * q^25 - 3 * q^26 + 130 * q^27 + 87 * q^28 + 20 * q^29 + 3 * q^30 + 41 * q^31 + 85 * q^32 + 33 * q^33 + 7 * q^34 + 39 * q^35 + 191 * q^36 + 80 * q^37 + 42 * q^38 + 21 * q^39 + 45 * q^40 + 16 * q^41 + 33 * q^42 + 164 * q^43 + 37 * q^44 + 139 * q^45 + 32 * q^46 + 148 * q^47 + 149 * q^48 + 160 * q^49 + 20 * q^50 + 51 * q^51 + 87 * q^52 + 83 * q^53 - 6 * q^54 + 36 * q^55 - 10 * q^56 + 28 * q^57 + 47 * q^58 + 14 * q^59 + 80 * q^60 + 20 * q^61 + 14 * q^62 + 120 * q^63 + 231 * q^64 + 36 * q^65 - 4 * q^66 + 253 * q^67 + 80 * q^68 + 6 * q^69 + 7 * q^70 + 5 * q^71 + 124 * q^72 + 64 * q^73 - 37 * q^74 + 40 * q^75 + 92 * q^76 + 63 * q^77 + 29 * q^78 + 91 * q^79 + 190 * q^80 + 187 * q^81 - 7 * q^82 + 63 * q^83 - 69 * q^84 + 38 * q^85 - 22 * q^86 + 57 * q^87 + 121 * q^88 - 6 * q^89 + 48 * q^90 + 119 * q^91 + 104 * q^92 + 14 * q^93 - q^94 + 77 * q^95 - 38 * q^96 + 96 * q^97 + 81 * q^98 + 106 * q^99

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