LMFDB - Embedded newform 8031.2.a.c.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8031,2,Mod(1,8031)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8031, 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("8031.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8031 = 3 \cdot 2677 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8031.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:	$64.1278578633$
Analytic rank:	$0$
Dimension:	$121$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	8031.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.47165 q^{2} -1.00000 q^{3} +4.10906 q^{4} -0.0868982 q^{5} +2.47165 q^{6} -4.58387 q^{7} -5.21287 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.47165 q^{2} -1.00000 q^{3} +4.10906 q^{4} -0.0868982 q^{5} +2.47165 q^{6} -4.58387 q^{7} -5.21287 q^{8} +1.00000 q^{9} +0.214782 q^{10} +1.33421 q^{11} -4.10906 q^{12} +5.46936 q^{13} +11.3297 q^{14} +0.0868982 q^{15} +4.66627 q^{16} -3.26907 q^{17} -2.47165 q^{18} +5.48038 q^{19} -0.357070 q^{20} +4.58387 q^{21} -3.29770 q^{22} +6.52318 q^{23} +5.21287 q^{24} -4.99245 q^{25} -13.5184 q^{26} -1.00000 q^{27} -18.8354 q^{28} +3.44362 q^{29} -0.214782 q^{30} +0.383849 q^{31} -1.10767 q^{32} -1.33421 q^{33} +8.08001 q^{34} +0.398330 q^{35} +4.10906 q^{36} +5.11145 q^{37} -13.5456 q^{38} -5.46936 q^{39} +0.452989 q^{40} +3.37977 q^{41} -11.3297 q^{42} -9.13227 q^{43} +5.48235 q^{44} -0.0868982 q^{45} -16.1230 q^{46} +11.6646 q^{47} -4.66627 q^{48} +14.0119 q^{49} +12.3396 q^{50} +3.26907 q^{51} +22.4739 q^{52} -0.255008 q^{53} +2.47165 q^{54} -0.115940 q^{55} +23.8951 q^{56} -5.48038 q^{57} -8.51144 q^{58} +8.41181 q^{59} +0.357070 q^{60} +1.40024 q^{61} -0.948741 q^{62} -4.58387 q^{63} -6.59479 q^{64} -0.475278 q^{65} +3.29770 q^{66} +2.16945 q^{67} -13.4328 q^{68} -6.52318 q^{69} -0.984534 q^{70} +0.196062 q^{71} -5.21287 q^{72} +7.44718 q^{73} -12.6337 q^{74} +4.99245 q^{75} +22.5192 q^{76} -6.11584 q^{77} +13.5184 q^{78} +1.99292 q^{79} -0.405491 q^{80} +1.00000 q^{81} -8.35361 q^{82} +6.37539 q^{83} +18.8354 q^{84} +0.284077 q^{85} +22.5718 q^{86} -3.44362 q^{87} -6.95506 q^{88} -7.00920 q^{89} +0.214782 q^{90} -25.0708 q^{91} +26.8041 q^{92} -0.383849 q^{93} -28.8308 q^{94} -0.476235 q^{95} +1.10767 q^{96} -1.49934 q^{97} -34.6325 q^{98} +1.33421 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 121 q + 7 q^{2} - 121 q^{3} + 123 q^{4} + 24 q^{5} - 7 q^{6} - 14 q^{7} + 18 q^{8} + 121 q^{9}+O(q^{10}) $ 121 * q + 7 * q^2 - 121 * q^3 + 123 * q^4 + 24 * q^5 - 7 * q^6 - 14 * q^7 + 18 * q^8 + 121 * q^9	\( 121 q + 7 q^{2} - 121 q^{3} + 123 q^{4} + 24 q^{5} - 7 q^{6} - 14 q^{7} + 18 q^{8} + 121 q^{9} + 18 q^{10} + 32 q^{11} - 123 q^{12} + 2 q^{13} + 37 q^{14} - 24 q^{15} + 131 q^{16} + 87 q^{17} + 7 q^{18} - 10 q^{19} + 60 q^{20} + 14 q^{21} - 22 q^{22} + 31 q^{23} - 18 q^{24} + 147 q^{25} + 37 q^{26} - 121 q^{27} - 29 q^{28} + 68 q^{29} - 18 q^{30} + 25 q^{31} + 43 q^{32} - 32 q^{33} + 27 q^{34} + 51 q^{35} + 123 q^{36} - 4 q^{37} + 36 q^{38} - 2 q^{39} + 61 q^{40} + 132 q^{41} - 37 q^{42} - 91 q^{43} + 94 q^{44} + 24 q^{45} + 39 q^{47} - 131 q^{48} + 217 q^{49} + 54 q^{50} - 87 q^{51} - 12 q^{52} + 55 q^{53} - 7 q^{54} + 7 q^{55} + 104 q^{56} + 10 q^{57} - 3 q^{58} + 58 q^{59} - 60 q^{60} + 126 q^{61} + 74 q^{62} - 14 q^{63} + 122 q^{64} + 128 q^{65} + 22 q^{66} - 139 q^{67} + 190 q^{68} - 31 q^{69} - 18 q^{70} + 37 q^{71} + 18 q^{72} + 84 q^{73} + 79 q^{74} - 147 q^{75} + 23 q^{76} + 95 q^{77} - 37 q^{78} - 14 q^{79} + 145 q^{80} + 121 q^{81} + 9 q^{82} + 58 q^{83} + 29 q^{84} + 32 q^{85} + 28 q^{86} - 68 q^{87} - 84 q^{88} + 198 q^{89} + 18 q^{90} + 5 q^{91} + 98 q^{92} - 25 q^{93} + 9 q^{94} + 42 q^{95} - 43 q^{96} + 73 q^{97} + 69 q^{98} + 32 q^{99}+O(q^{100}) \) 121 * q + 7 * q^2 - 121 * q^3 + 123 * q^4 + 24 * q^5 - 7 * q^6 - 14 * q^7 + 18 * q^8 + 121 * q^9 + 18 * q^10 + 32 * q^11 - 123 * q^12 + 2 * q^13 + 37 * q^14 - 24 * q^15 + 131 * q^16 + 87 * q^17 + 7 * q^18 - 10 * q^19 + 60 * q^20 + 14 * q^21 - 22 * q^22 + 31 * q^23 - 18 * q^24 + 147 * q^25 + 37 * q^26 - 121 * q^27 - 29 * q^28 + 68 * q^29 - 18 * q^30 + 25 * q^31 + 43 * q^32 - 32 * q^33 + 27 * q^34 + 51 * q^35 + 123 * q^36 - 4 * q^37 + 36 * q^38 - 2 * q^39 + 61 * q^40 + 132 * q^41 - 37 * q^42 - 91 * q^43 + 94 * q^44 + 24 * q^45 + 39 * q^47 - 131 * q^48 + 217 * q^49 + 54 * q^50 - 87 * q^51 - 12 * q^52 + 55 * q^53 - 7 * q^54 + 7 * q^55 + 104 * q^56 + 10 * q^57 - 3 * q^58 + 58 * q^59 - 60 * q^60 + 126 * q^61 + 74 * q^62 - 14 * q^63 + 122 * q^64 + 128 * q^65 + 22 * q^66 - 139 * q^67 + 190 * q^68 - 31 * q^69 - 18 * q^70 + 37 * q^71 + 18 * q^72 + 84 * q^73 + 79 * q^74 - 147 * q^75 + 23 * q^76 + 95 * q^77 - 37 * q^78 - 14 * q^79 + 145 * q^80 + 121 * q^81 + 9 * q^82 + 58 * q^83 + 29 * q^84 + 32 * q^85 + 28 * q^86 - 68 * q^87 - 84 * q^88 + 198 * q^89 + 18 * q^90 + 5 * q^91 + 98 * q^92 - 25 * q^93 + 9 * q^94 + 42 * q^95 - 43 * q^96 + 73 * q^97 + 69 * q^98 + 32 * 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 $

$2$	−2.47165	−1.74772	−0.873861	−	0.486176i	$-0.838391\pi$
$2$	−2.47165	−1.74772	−0.873861	+	0.486176i	$0.838391\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.10906	2.05453
$5$	−0.0868982	−0.0388621	−0.0194310	−	0.999811i	$-0.506185\pi$
$5$	−0.0868982	−0.0388621	−0.0194310	+	0.999811i	$0.506185\pi$
$6$	2.47165	1.00905
$7$	−4.58387	−1.73254	−0.866270	−	0.499576i	$-0.833489\pi$
$7$	−4.58387	−1.73254	−0.866270	+	0.499576i	$0.833489\pi$
$8$	−5.21287	−1.84303
$9$	1.00000	0.333333
$10$	0.214782	0.0679201
$11$	1.33421	0.402279	0.201140	−	0.979563i	$-0.435536\pi$
$11$	1.33421	0.402279	0.201140	+	0.979563i	$0.435536\pi$
$12$	−4.10906	−1.18618
$13$	5.46936	1.51693	0.758464	−	0.651715i	$-0.225950\pi$
$13$	5.46936	1.51693	0.758464	+	0.651715i	$0.225950\pi$
$14$	11.3297	3.02800
$15$	0.0868982	0.0224370
$16$	4.66627	1.16657
$17$	−3.26907	−0.792866	−0.396433	−	0.918064i	$-0.629752\pi$
$17$	−3.26907	−0.792866	−0.396433	+	0.918064i	$0.629752\pi$
$18$	−2.47165	−0.582574
$19$	5.48038	1.25728	0.628642	−	0.777695i	$-0.283611\pi$
$19$	5.48038	1.25728	0.628642	+	0.777695i	$0.283611\pi$
$20$	−0.357070	−0.0798434
$21$	4.58387	1.00028
$22$	−3.29770	−0.703072
$23$	6.52318	1.36018	0.680088	−	0.733130i	$-0.261941\pi$
$23$	6.52318	1.36018	0.680088	+	0.733130i	$0.261941\pi$
$24$	5.21287	1.06407
$25$	−4.99245	−0.998490
$26$	−13.5184	−2.65117
$27$	−1.00000	−0.192450
$28$	−18.8354	−3.55956
$29$	3.44362	0.639465	0.319732	−	0.947508i	$-0.396407\pi$
$29$	3.44362	0.639465	0.319732	+	0.947508i	$0.396407\pi$
$30$	−0.214782	−0.0392137
$31$	0.383849	0.0689413	0.0344706	−	0.999406i	$-0.489025\pi$
$31$	0.383849	0.0689413	0.0344706	+	0.999406i	$0.489025\pi$
$32$	−1.10767	−0.195809
$33$	−1.33421	−0.232256
$34$	8.08001	1.38571
$35$	0.398330	0.0673301
$36$	4.10906	0.684844
$37$	5.11145	0.840318	0.420159	−	0.907451i	$-0.361974\pi$
$37$	5.11145	0.840318	0.420159	+	0.907451i	$0.361974\pi$
$38$	−13.5456	−2.19738
$39$	−5.46936	−0.875799
$40$	0.452989	0.0716239
$41$	3.37977	0.527831	0.263916	−	0.964546i	$-0.414986\pi$
$41$	3.37977	0.527831	0.263916	+	0.964546i	$0.414986\pi$
$42$	−11.3297	−1.74822
$43$	−9.13227	−1.39266	−0.696329	−	0.717723i	$-0.745185\pi$
$43$	−9.13227	−1.39266	−0.696329	+	0.717723i	$0.745185\pi$
$44$	5.48235	0.826495
$45$	−0.0868982	−0.0129540
$46$	−16.1230	−2.37721
$47$	11.6646	1.70145	0.850727	−	0.525608i	$-0.176162\pi$
$47$	11.6646	1.70145	0.850727	+	0.525608i	$0.176162\pi$
$48$	−4.66627	−0.673519
$49$	14.0119	2.00170
$50$	12.3396	1.74508
$51$	3.26907	0.457761
$52$	22.4739	3.11658
$53$	−0.255008	−0.0350280	−0.0175140	−	0.999847i	$-0.505575\pi$
$53$	−0.255008	−0.0350280	−0.0175140	+	0.999847i	$0.505575\pi$
$54$	2.47165	0.336349
$55$	−0.115940	−0.0156334
$56$	23.8951	3.19312
$57$	−5.48038	−0.725894
$58$	−8.51144	−1.11761
$59$	8.41181	1.09512	0.547562	−	0.836765i	$-0.315556\pi$
$59$	8.41181	1.09512	0.547562	+	0.836765i	$0.315556\pi$
$60$	0.357070	0.0460976
$61$	1.40024	0.179282	0.0896411	−	0.995974i	$-0.471428\pi$
$61$	1.40024	0.179282	0.0896411	+	0.995974i	$0.471428\pi$
$62$	−0.948741	−0.120490
$63$	−4.58387	−0.577513
$64$	−6.59479	−0.824348
$65$	−0.475278	−0.0589510
$66$	3.29770	0.405919
$67$	2.16945	0.265040	0.132520	−	0.991180i	$-0.457693\pi$
$67$	2.16945	0.265040	0.132520	+	0.991180i	$0.457693\pi$
$68$	−13.4328	−1.62897
$69$	−6.52318	−0.785298
$70$	−0.984534	−0.117674
$71$	0.196062	0.0232683	0.0116341	−	0.999932i	$-0.496297\pi$
$71$	0.196062	0.0232683	0.0116341	+	0.999932i	$0.496297\pi$
$72$	−5.21287	−0.614343
$73$	7.44718	0.871627	0.435813	−	0.900037i	$-0.356461\pi$
$73$	7.44718	0.871627	0.435813	+	0.900037i	$0.356461\pi$
$74$	−12.6337	−1.46864
$75$	4.99245	0.576478
$76$	22.5192	2.58313
$77$	−6.11584	−0.696965
$78$	13.5184	1.53065
$79$	1.99292	0.224221	0.112111	−	0.993696i	$-0.464239\pi$
$79$	1.99292	0.224221	0.112111	+	0.993696i	$0.464239\pi$
$80$	−0.405491	−0.0453353
$81$	1.00000	0.111111
$82$	−8.35361	−0.922502
$83$	6.37539	0.699789	0.349895	−	0.936789i	$-0.386217\pi$
$83$	6.37539	0.699789	0.349895	+	0.936789i	$0.386217\pi$
$84$	18.8354	2.05511
$85$	0.284077	0.0308124
$86$	22.5718	2.43398
$87$	−3.44362	−0.369195
$88$	−6.95506	−0.741412
$89$	−7.00920	−0.742974	−0.371487	−	0.928438i	$-0.621152\pi$
$89$	−7.00920	−0.742974	−0.371487	+	0.928438i	$0.621152\pi$
$90$	0.214782	0.0226400
$91$	−25.0708	−2.62814
$92$	26.8041	2.79453
$93$	−0.383849	−0.0398033
$94$	−28.8308	−2.97367
$95$	−0.476235	−0.0488607
$96$	1.10767	0.113051
$97$	−1.49934	−0.152235	−0.0761174	−	0.997099i	$-0.524252\pi$
$97$	−1.49934	−0.152235	−0.0761174	+	0.997099i	$0.524252\pi$
$98$	−34.6325	−3.49841
$99$	1.33421	0.134093
$100$	−20.5143	−2.05143
$101$	13.0179	1.29533	0.647665	−	0.761925i	$-0.275746\pi$
$101$	13.0179	1.29533	0.647665	+	0.761925i	$0.275746\pi$
$102$	−8.08001	−0.800040
$103$	−2.12095	−0.208983	−0.104492	−	0.994526i	$-0.533322\pi$
$103$	−2.12095	−0.208983	−0.104492	+	0.994526i	$0.533322\pi$
$104$	−28.5111	−2.79574
$105$	−0.398330	−0.0388731
$106$	0.630290	0.0612192
$107$	−13.7276	−1.32710	−0.663550	−	0.748132i	$-0.730951\pi$
$107$	−13.7276	−1.32710	−0.663550	+	0.748132i	$0.730951\pi$
$108$	−4.10906	−0.395395
$109$	14.7534	1.41312	0.706560	−	0.707654i	$-0.250246\pi$
$109$	14.7534	1.41312	0.706560	+	0.707654i	$0.250246\pi$
$110$	0.286564	0.0273228
$111$	−5.11145	−0.485158
$112$	−21.3896	−2.02113
$113$	−7.65851	−0.720452	−0.360226	−	0.932865i	$-0.617300\pi$
$113$	−7.65851	−0.720452	−0.360226	+	0.932865i	$0.617300\pi$
$114$	13.5456	1.26866
$115$	−0.566853	−0.0528593
$116$	14.1501	1.31380
$117$	5.46936	0.505643
$118$	−20.7911	−1.91397
$119$	14.9850	1.37367
$120$	−0.452989	−0.0413521
$121$	−9.21989	−0.838172
$122$	−3.46090	−0.313335
$123$	−3.37977	−0.304743
$124$	1.57726	0.141642
$125$	0.868326	0.0776655
$126$	11.3297	1.00933
$127$	0.948026	0.0841237	0.0420618	−	0.999115i	$-0.486607\pi$
$127$	0.948026	0.0841237	0.0420618	+	0.999115i	$0.486607\pi$
$128$	18.5153	1.63654
$129$	9.13227	0.804051
$130$	1.17472	0.103030
$131$	−2.61525	−0.228496	−0.114248	−	0.993452i	$-0.536446\pi$
$131$	−2.61525	−0.228496	−0.114248	+	0.993452i	$0.536446\pi$
$132$	−5.48235	−0.477177
$133$	−25.1213	−2.17830
$134$	−5.36212	−0.463217
$135$	0.0868982	0.00747901
$136$	17.0412	1.46127
$137$	−16.1623	−1.38083	−0.690417	−	0.723412i	$-0.742573\pi$
$137$	−16.1623	−1.38083	−0.690417	+	0.723412i	$0.742573\pi$
$138$	16.1230	1.37248
$139$	−18.8111	−1.59554	−0.797768	−	0.602965i	$-0.793986\pi$
$139$	−18.8111	−1.59554	−0.797768	+	0.602965i	$0.793986\pi$
$140$	1.63676	0.138332
$141$	−11.6646	−0.982335
$142$	−0.484596	−0.0406664
$143$	7.29727	0.610228
$144$	4.66627	0.388856
$145$	−0.299245	−0.0248509
$146$	−18.4068	−1.52336
$147$	−14.0119	−1.15568
$148$	21.0033	1.72646
$149$	16.1437	1.32254	0.661271	−	0.750147i	$-0.270017\pi$
$149$	16.1437	1.32254	0.661271	+	0.750147i	$0.270017\pi$
$150$	−12.3396	−1.00752
$151$	6.74736	0.549093	0.274546	−	0.961574i	$-0.411472\pi$
$151$	6.74736	0.549093	0.274546	+	0.961574i	$0.411472\pi$
$152$	−28.5685	−2.31721
$153$	−3.26907	−0.264289
$154$	15.1162	1.21810
$155$	−0.0333558	−0.00267920
$156$	−22.4739	−1.79936
$157$	−11.3748	−0.907810	−0.453905	−	0.891050i	$-0.649969\pi$
$157$	−11.3748	−0.907810	−0.453905	+	0.891050i	$0.649969\pi$
$158$	−4.92581	−0.391876
$159$	0.255008	0.0202234
$160$	0.0962542	0.00760956
$161$	−29.9014	−2.35656
$162$	−2.47165	−0.194191
$163$	−24.2440	−1.89893	−0.949466	−	0.313869i	$-0.898375\pi$
$163$	−24.2440	−1.89893	−0.949466	+	0.313869i	$0.898375\pi$
$164$	13.8877	1.08445
$165$	0.115940	0.00902595
$166$	−15.7577	−1.22304
$167$	−18.5175	−1.43292	−0.716462	−	0.697626i	$-0.754240\pi$
$167$	−18.5175	−1.43292	−0.716462	+	0.697626i	$0.754240\pi$
$168$	−23.8951	−1.84355
$169$	16.9139	1.30107
$170$	−0.702138	−0.0538515
$171$	5.48038	0.419095
$172$	−37.5251	−2.86126
$173$	21.4866	1.63360	0.816799	−	0.576923i	$-0.195747\pi$
$173$	21.4866	1.63360	0.816799	+	0.576923i	$0.195747\pi$
$174$	8.51144	0.645251
$175$	22.8847	1.72992
$176$	6.22578	0.469286
$177$	−8.41181	−0.632271
$178$	17.3243	1.29851
$179$	8.66890	0.647944	0.323972	−	0.946067i	$-0.394982\pi$
$179$	8.66890	0.647944	0.323972	+	0.946067i	$0.394982\pi$
$180$	−0.357070	−0.0266145
$181$	3.97527	0.295479	0.147740	−	0.989026i	$-0.452800\pi$
$181$	3.97527	0.295479	0.147740	+	0.989026i	$0.452800\pi$
$182$	61.9664	4.59326
$183$	−1.40024	−0.103509
$184$	−34.0045	−2.50684
$185$	−0.444176	−0.0326565
$186$	0.948741	0.0695650
$187$	−4.36162	−0.318953
$188$	47.9305	3.49569
$189$	4.58387	0.333428
$190$	1.17709	0.0853949
$191$	19.1688	1.38700	0.693502	−	0.720455i	$-0.256067\pi$
$191$	19.1688	1.38700	0.693502	+	0.720455i	$0.256067\pi$
$192$	6.59479	0.475938
$193$	7.61825	0.548373	0.274187	−	0.961676i	$-0.411591\pi$
$193$	7.61825	0.548373	0.274187	+	0.961676i	$0.411591\pi$
$194$	3.70585	0.266064
$195$	0.475278	0.0340353
$196$	57.5757	4.11255
$197$	13.5833	0.967769	0.483884	−	0.875132i	$-0.339225\pi$
$197$	13.5833	0.967769	0.483884	+	0.875132i	$0.339225\pi$
$198$	−3.29770	−0.234357
$199$	12.2654	0.869474	0.434737	−	0.900557i	$-0.356841\pi$
$199$	12.2654	0.869474	0.434737	+	0.900557i	$0.356841\pi$
$200$	26.0250	1.84024
$201$	−2.16945	−0.153021
$202$	−32.1757	−2.26388
$203$	−15.7851	−1.10790
$204$	13.4328	0.940485
$205$	−0.293696	−0.0205126
$206$	5.24225	0.365245
$207$	6.52318	0.453392
$208$	25.5215	1.76960
$209$	7.31197	0.505779
$210$	0.984534	0.0679393
$211$	−18.9781	−1.30650	−0.653252	−	0.757140i	$-0.726596\pi$
$211$	−18.9781	−1.30650	−0.653252	+	0.757140i	$0.726596\pi$
$212$	−1.04784	−0.0719661
$213$	−0.196062	−0.0134339
$214$	33.9299	2.31940
$215$	0.793578	0.0541216
$216$	5.21287	0.354691
$217$	−1.75951	−0.119444
$218$	−36.4653	−2.46974
$219$	−7.44718	−0.503234
$220$	−0.476406	−0.0321193
$221$	−17.8797	−1.20272
$222$	12.6337	0.847921
$223$	−18.9660	−1.27006	−0.635029	−	0.772488i	$-0.719012\pi$
$223$	−18.9660	−1.27006	−0.635029	+	0.772488i	$0.719012\pi$
$224$	5.07740	0.339248
$225$	−4.99245	−0.332830
$226$	18.9292	1.25915
$227$	19.3807	1.28635	0.643173	−	0.765721i	$-0.277618\pi$
$227$	19.3807	1.28635	0.643173	+	0.765721i	$0.277618\pi$
$228$	−22.5192	−1.49137
$229$	6.30548	0.416678	0.208339	−	0.978057i	$-0.433194\pi$
$229$	6.30548	0.416678	0.208339	+	0.978057i	$0.433194\pi$
$230$	1.40106	0.0923833
$231$	6.11584	0.402393
$232$	−17.9512	−1.17855
$233$	−2.45172	−0.160618	−0.0803088	−	0.996770i	$-0.525591\pi$
$233$	−2.45172	−0.160618	−0.0803088	+	0.996770i	$0.525591\pi$
$234$	−13.5184	−0.883723
$235$	−1.01363	−0.0661220
$236$	34.5647	2.24997
$237$	−1.99292	−0.129454
$238$	−37.0377	−2.40080
$239$	11.6821	0.755651	0.377826	−	0.925877i	$-0.376672\pi$
$239$	11.6821	0.755651	0.377826	+	0.925877i	$0.376672\pi$
$240$	0.405491	0.0261743
$241$	−8.58314	−0.552889	−0.276444	−	0.961030i	$-0.589156\pi$
$241$	−8.58314	−0.552889	−0.276444	+	0.961030i	$0.589156\pi$
$242$	22.7884	1.46489
$243$	−1.00000	−0.0641500
$244$	5.75367	0.368341
$245$	−1.21761	−0.0777901
$246$	8.35361	0.532607
$247$	29.9742	1.90721
$248$	−2.00095	−0.127061
$249$	−6.37539	−0.404024
$250$	−2.14620	−0.135738
$251$	12.2984	0.776268	0.388134	−	0.921603i	$-0.373120\pi$
$251$	12.2984	0.776268	0.388134	+	0.921603i	$0.373120\pi$
$252$	−18.8354	−1.18652
$253$	8.70328	0.547171
$254$	−2.34319	−0.147025
$255$	−0.284077	−0.0177896
$256$	−32.5739	−2.03587
$257$	−12.1338	−0.756886	−0.378443	−	0.925625i	$-0.623540\pi$
$257$	−12.1338	−0.756886	−0.378443	+	0.925625i	$0.623540\pi$
$258$	−22.5718	−1.40526
$259$	−23.4302	−1.45588
$260$	−1.95295	−0.121117
$261$	3.44362	0.213155
$262$	6.46400	0.399347
$263$	−3.23452	−0.199449	−0.0997245	−	0.995015i	$-0.531796\pi$
$263$	−3.23452	−0.199449	−0.0997245	+	0.995015i	$0.531796\pi$
$264$	6.95506	0.428054
$265$	0.0221597	0.00136126
$266$	62.0912	3.80706
$267$	7.00920	0.428956
$268$	8.91440	0.544534
$269$	15.9532	0.972684	0.486342	−	0.873769i	$-0.338331\pi$
$269$	15.9532	0.972684	0.486342	+	0.873769i	$0.338331\pi$
$270$	−0.214782	−0.0130712
$271$	−21.5609	−1.30973	−0.654866	−	0.755745i	$-0.727275\pi$
$271$	−21.5609	−1.30973	−0.654866	+	0.755745i	$0.727275\pi$
$272$	−15.2544	−0.924933
$273$	25.0708	1.51736
$274$	39.9475	2.41331
$275$	−6.66097	−0.401672
$276$	−26.8041	−1.61342
$277$	30.0935	1.80815	0.904073	−	0.427379i	$-0.140563\pi$
$277$	30.0935	1.80815	0.904073	+	0.427379i	$0.140563\pi$
$278$	46.4944	2.78855
$279$	0.383849	0.0229804
$280$	−2.07644	−0.124091
$281$	2.93501	0.175088	0.0875441	−	0.996161i	$-0.472098\pi$
$281$	2.93501	0.175088	0.0875441	+	0.996161i	$0.472098\pi$
$282$	28.8308	1.71685
$283$	−31.0725	−1.84707	−0.923535	−	0.383515i	$-0.874714\pi$
$283$	−31.0725	−1.84707	−0.923535	+	0.383515i	$0.874714\pi$
$284$	0.805630	0.0478054
$285$	0.476235	0.0282097
$286$	−18.0363	−1.06651
$287$	−15.4924	−0.914489
$288$	−1.10767	−0.0652698
$289$	−6.31317	−0.371363
$290$	0.739629	0.0434325
$291$	1.49934	0.0878928
$292$	30.6009	1.79078
$293$	−4.31919	−0.252330	−0.126165	−	0.992009i	$-0.540267\pi$
$293$	−4.31919	−0.252330	−0.126165	+	0.992009i	$0.540267\pi$
$294$	34.6325	2.01981
$295$	−0.730972	−0.0425588
$296$	−26.6453	−1.54873
$297$	−1.33421	−0.0774186
$298$	−39.9016	−2.31143
$299$	35.6776	2.06329
$300$	20.5143	1.18439
$301$	41.8611	2.41284
$302$	−16.6771	−0.959661
$303$	−13.0179	−0.747859
$304$	25.5729	1.46671
$305$	−0.121678	−0.00696728
$306$	8.08001	0.461903
$307$	−22.5302	−1.28587	−0.642933	−	0.765922i	$-0.722283\pi$
$307$	−22.5302	−1.28587	−0.642933	+	0.765922i	$0.722283\pi$
$308$	−25.1304	−1.43194
$309$	2.12095	0.120657
$310$	0.0824439	0.00468250
$311$	−15.1719	−0.860320	−0.430160	−	0.902753i	$-0.641543\pi$
$311$	−15.1719	−0.860320	−0.430160	+	0.902753i	$0.641543\pi$
$312$	28.5111	1.61412
$313$	−15.5035	−0.876310	−0.438155	−	0.898899i	$-0.644368\pi$
$313$	−15.5035	−0.876310	−0.438155	+	0.898899i	$0.644368\pi$
$314$	28.1146	1.58660
$315$	0.398330	0.0224434
$316$	8.18904	0.460670
$317$	18.0294	1.01263	0.506315	−	0.862349i	$-0.331007\pi$
$317$	18.0294	1.01263	0.506315	+	0.862349i	$0.331007\pi$
$318$	−0.630290	−0.0353449
$319$	4.59451	0.257243
$320$	0.573075	0.0320359
$321$	13.7276	0.766202
$322$	73.9059	4.11861
$323$	−17.9157	−0.996858
$324$	4.10906	0.228281
$325$	−27.3055	−1.51464
$326$	59.9226	3.31881
$327$	−14.7534	−0.815865
$328$	−17.6183	−0.972807
$329$	−53.4689	−2.94784
$330$	−0.286564	−0.0157748
$331$	13.0770	0.718779	0.359389	−	0.933188i	$-0.382985\pi$
$331$	13.0770	0.718779	0.359389	+	0.933188i	$0.382985\pi$
$332$	26.1969	1.43774
$333$	5.11145	0.280106
$334$	45.7687	2.50435
$335$	−0.188521	−0.0103000
$336$	21.3896	1.16690
$337$	20.3442	1.10822	0.554110	−	0.832444i	$-0.313059\pi$
$337$	20.3442	1.10822	0.554110	+	0.832444i	$0.313059\pi$
$338$	−41.8053	−2.27391
$339$	7.65851	0.415953
$340$	1.16729	0.0633051
$341$	0.512134	0.0277336
$342$	−13.5456	−0.732461
$343$	−32.1415	−1.73548
$344$	47.6053	2.56671
$345$	0.566853	0.0305183
$346$	−53.1074	−2.85507
$347$	−6.54336	−0.351266	−0.175633	−	0.984456i	$-0.556197\pi$
$347$	−6.54336	−0.351266	−0.175633	+	0.984456i	$0.556197\pi$
$348$	−14.1501	−0.758523
$349$	−21.1951	−1.13455	−0.567274	−	0.823529i	$-0.692002\pi$
$349$	−21.1951	−1.13455	−0.567274	+	0.823529i	$0.692002\pi$
$350$	−56.5631	−3.02343
$351$	−5.46936	−0.291933
$352$	−1.47786	−0.0787700
$353$	−35.7986	−1.90536	−0.952682	−	0.303968i	$-0.901689\pi$
$353$	−35.7986	−1.90536	−0.952682	+	0.303968i	$0.901689\pi$
$354$	20.7911	1.10503
$355$	−0.0170374	−0.000904252 0
$356$	−28.8013	−1.52646
$357$	−14.9850	−0.793090
$358$	−21.4265	−1.13243
$359$	−21.4392	−1.13152	−0.565758	−	0.824572i	$-0.691416\pi$
$359$	−21.4392	−1.13152	−0.565758	+	0.824572i	$0.691416\pi$
$360$	0.452989	0.0238746
$361$	11.0345	0.580765
$362$	−9.82548	−0.516416
$363$	9.21989	0.483919
$364$	−103.018	−5.39959
$365$	−0.647147	−0.0338732
$366$	3.46090	0.180904
$367$	17.4269	0.909677	0.454838	−	0.890574i	$-0.349697\pi$
$367$	17.4269	0.909677	0.454838	+	0.890574i	$0.349697\pi$
$368$	30.4389	1.58674
$369$	3.37977	0.175944
$370$	1.09785	0.0570745
$371$	1.16892	0.0606874
$372$	−1.57726	−0.0817771
$373$	0.371380	0.0192293	0.00961467	−	0.999954i	$-0.496940\pi$
$373$	0.371380	0.0192293	0.00961467	+	0.999954i	$0.496940\pi$
$374$	10.7804	0.557442
$375$	−0.868326	−0.0448402
$376$	−60.8059	−3.13583
$377$	18.8344	0.970022
$378$	−11.3297	−0.582739
$379$	18.1760	0.933640	0.466820	−	0.884352i	$-0.345400\pi$
$379$	18.1760	0.933640	0.466820	+	0.884352i	$0.345400\pi$
$380$	−1.95688	−0.100386
$381$	−0.948026	−0.0485688
$382$	−47.3786	−2.42410
$383$	19.8117	1.01233	0.506165	−	0.862437i	$-0.331063\pi$
$383$	19.8117	1.01233	0.506165	+	0.862437i	$0.331063\pi$
$384$	−18.5153	−0.944857
$385$	0.531456	0.0270855
$386$	−18.8297	−0.958404
$387$	−9.13227	−0.464219
$388$	−6.16088	−0.312771
$389$	−11.3597	−0.575957	−0.287979	−	0.957637i	$-0.592983\pi$
$389$	−11.3597	−0.575957	−0.287979	+	0.957637i	$0.592983\pi$
$390$	−1.17472	−0.0594843
$391$	−21.3247	−1.07844
$392$	−73.0421	−3.68918
$393$	2.61525	0.131922
$394$	−33.5732	−1.69139
$395$	−0.173181	−0.00871371
$396$	5.48235	0.275498
$397$	−25.9968	−1.30474	−0.652372	−	0.757899i	$-0.726226\pi$
$397$	−25.9968	−1.30474	−0.652372	+	0.757899i	$0.726226\pi$
$398$	−30.3159	−1.51960
$399$	25.1213	1.25764
$400$	−23.2961	−1.16481
$401$	6.42955	0.321076	0.160538	−	0.987030i	$-0.448677\pi$
$401$	6.42955	0.321076	0.160538	+	0.987030i	$0.448677\pi$
$402$	5.36212	0.267438
$403$	2.09941	0.104579
$404$	53.4914	2.66130
$405$	−0.0868982	−0.00431801
$406$	39.0153	1.93630
$407$	6.81975	0.338042
$408$	−17.0412	−0.843667
$409$	13.8399	0.684338	0.342169	−	0.939639i	$-0.388839\pi$
$409$	13.8399	0.684338	0.342169	+	0.939639i	$0.388839\pi$
$410$	0.725914	0.0358503
$411$	16.1623	0.797225
$412$	−8.71512	−0.429363
$413$	−38.5587	−1.89735
$414$	−16.1230	−0.792403
$415$	−0.554010	−0.0271953
$416$	−6.05822	−0.297029
$417$	18.8111	0.921183
$418$	−18.0726	−0.883962
$419$	10.3879	0.507484	0.253742	−	0.967272i	$-0.418339\pi$
$419$	10.3879	0.507484	0.253742	+	0.967272i	$0.418339\pi$
$420$	−1.63676	−0.0798659
$421$	10.5753	0.515410	0.257705	−	0.966224i	$-0.417034\pi$
$421$	10.5753	0.515410	0.257705	+	0.966224i	$0.417034\pi$
$422$	46.9072	2.28341
$423$	11.6646	0.567151
$424$	1.32932	0.0645576
$425$	16.3207	0.791669
$426$	0.484596	0.0234788
$427$	−6.41851	−0.310614
$428$	−56.4077	−2.72657
$429$	−7.29727	−0.352315
$430$	−1.96145	−0.0945895
$431$	−5.82979	−0.280811	−0.140406	−	0.990094i	$-0.544841\pi$
$431$	−5.82979	−0.280811	−0.140406	+	0.990094i	$0.544841\pi$
$432$	−4.66627	−0.224506
$433$	−26.3592	−1.26674	−0.633370	−	0.773849i	$-0.718329\pi$
$433$	−26.3592	−1.26674	−0.633370	+	0.773849i	$0.718329\pi$
$434$	4.34891	0.208754
$435$	0.299245	0.0143477
$436$	60.6226	2.90330
$437$	35.7495	1.71013
$438$	18.4068	0.879513
$439$	37.7230	1.80042	0.900210	−	0.435456i	$-0.143413\pi$
$439$	37.7230	1.80042	0.900210	+	0.435456i	$0.143413\pi$
$440$	0.604382	0.0288128
$441$	14.0119	0.667232
$442$	44.1925	2.10202
$443$	19.1726	0.910918	0.455459	−	0.890257i	$-0.349475\pi$
$443$	19.1726	0.910918	0.455459	+	0.890257i	$0.349475\pi$
$444$	−21.0033	−0.996772
$445$	0.609087	0.0288735
$446$	46.8774	2.21971
$447$	−16.1437	−0.763570
$448$	30.2296	1.42822
$449$	26.4140	1.24656	0.623278	−	0.782000i	$-0.285801\pi$
$449$	26.4140	1.24656	0.623278	+	0.782000i	$0.285801\pi$
$450$	12.3396	0.581694
$451$	4.50932	0.212335
$452$	−31.4693	−1.48019
$453$	−6.74736	−0.317019
$454$	−47.9025	−2.24817
$455$	2.17861	0.102135
$456$	28.5685	1.33784
$457$	−38.0172	−1.77837	−0.889184	−	0.457550i	$-0.848727\pi$
$457$	−38.0172	−1.77837	−0.889184	+	0.457550i	$0.848727\pi$
$458$	−15.5849	−0.728237
$459$	3.26907	0.152587
$460$	−2.32923	−0.108601
$461$	16.5430	0.770484	0.385242	−	0.922816i	$-0.374118\pi$
$461$	16.5430	0.770484	0.385242	+	0.922816i	$0.374118\pi$
$462$	−15.1162	−0.703271
$463$	10.4486	0.485587	0.242794	−	0.970078i	$-0.421936\pi$
$463$	10.4486	0.485587	0.242794	+	0.970078i	$0.421936\pi$
$464$	16.0689	0.745980
$465$	0.0333558	0.00154684
$466$	6.05980	0.280715
$467$	18.8300	0.871346	0.435673	−	0.900105i	$-0.356510\pi$
$467$	18.8300	0.871346	0.435673	+	0.900105i	$0.356510\pi$
$468$	22.4739	1.03886
$469$	−9.94447	−0.459193
$470$	2.50534	0.115563
$471$	11.3748	0.524124
$472$	−43.8497	−2.01835
$473$	−12.1844	−0.560237
$474$	4.92581	0.226250
$475$	−27.3605	−1.25539
$476$	61.5743	2.82225
$477$	−0.255008	−0.0116760
$478$	−28.8740	−1.32067
$479$	−29.9588	−1.36885	−0.684427	−	0.729082i	$-0.739947\pi$
$479$	−29.9588	−1.36885	−0.684427	+	0.729082i	$0.739947\pi$
$480$	−0.0962542	−0.00439338
$481$	27.9564	1.27470
$482$	21.2145	0.966296
$483$	29.9014	1.36056
$484$	−37.8851	−1.72205
$485$	0.130290	0.00591616
$486$	2.47165	0.112116
$487$	−27.9004	−1.26429	−0.632145	−	0.774850i	$-0.717825\pi$
$487$	−27.9004	−1.26429	−0.632145	+	0.774850i	$0.717825\pi$
$488$	−7.29926	−0.330422
$489$	24.2440	1.09635
$490$	3.00950	0.135955
$491$	−30.8606	−1.39272	−0.696360	−	0.717693i	$-0.745198\pi$
$491$	−30.8606	−1.39272	−0.696360	+	0.717693i	$0.745198\pi$
$492$	−13.8877	−0.626105
$493$	−11.2575	−0.507010
$494$	−74.0857	−3.33327
$495$	−0.115940	−0.00521113
$496$	1.79114	0.0804247
$497$	−0.898722	−0.0403132
$498$	15.7577	0.706121
$499$	9.65522	0.432227	0.216114	−	0.976368i	$-0.430662\pi$
$499$	9.65522	0.432227	0.216114	+	0.976368i	$0.430662\pi$
$500$	3.56801	0.159566
$501$	18.5175	0.827299
$502$	−30.3974	−1.35670
$503$	8.61468	0.384109	0.192055	−	0.981384i	$-0.438485\pi$
$503$	8.61468	0.384109	0.192055	+	0.981384i	$0.438485\pi$
$504$	23.8951	1.06437
$505$	−1.13123	−0.0503392
$506$	−21.5115	−0.956302
$507$	−16.9139	−0.751173
$508$	3.89550	0.172835
$509$	0.513897	0.0227781	0.0113890	−	0.999935i	$-0.496375\pi$
$509$	0.513897	0.0227781	0.0113890	+	0.999935i	$0.496375\pi$
$510$	0.702138	0.0310912
$511$	−34.1369	−1.51013
$512$	43.4807	1.92159
$513$	−5.48038	−0.241965
$514$	29.9905	1.32283
$515$	0.184307	0.00812153
$516$	37.5251	1.65195
$517$	15.5630	0.684459
$518$	57.9114	2.54448
$519$	−21.4866	−0.943158
$520$	2.47756	0.108648
$521$	−8.86118	−0.388215	−0.194108	−	0.980980i	$-0.562181\pi$
$521$	−8.86118	−0.388215	−0.194108	+	0.980980i	$0.562181\pi$
$522$	−8.51144	−0.372536
$523$	−40.3659	−1.76508	−0.882539	−	0.470240i	$-0.844168\pi$
$523$	−40.3659	−1.76508	−0.882539	+	0.470240i	$0.844168\pi$
$524$	−10.7462	−0.469452
$525$	−22.8847	−0.998772
$526$	7.99460	0.348581
$527$	−1.25483	−0.0546612
$528$	−6.22578	−0.270942
$529$	19.5518	0.850080
$530$	−0.0547711	−0.00237911
$531$	8.41181	0.365042
$532$	−103.225	−4.47538
$533$	18.4852	0.800681
$534$	−17.3243	−0.749696
$535$	1.19291	0.0515739
$536$	−11.3091	−0.488477
$537$	−8.66890	−0.374091
$538$	−39.4308	−1.69998
$539$	18.6948	0.805241
$540$	0.357070	0.0153659
$541$	−29.0980	−1.25102	−0.625511	−	0.780215i	$-0.715110\pi$
$541$	−29.0980	−1.25102	−0.625511	+	0.780215i	$0.715110\pi$
$542$	53.2910	2.28905
$543$	−3.97527	−0.170595
$544$	3.62104	0.155251
$545$	−1.28204	−0.0549167
$546$	−61.9664	−2.65192
$547$	30.5510	1.30627	0.653133	−	0.757244i	$-0.273454\pi$
$547$	30.5510	1.30627	0.653133	+	0.757244i	$0.273454\pi$
$548$	−66.4117	−2.83697
$549$	1.40024	0.0597607
$550$	16.4636	0.702010
$551$	18.8724	0.803989
$552$	34.0045	1.44733
$553$	−9.13530	−0.388472
$554$	−74.3808	−3.16014
$555$	0.444176	0.0188542
$556$	−77.2959	−3.27808
$557$	6.78698	0.287574	0.143787	−	0.989609i	$-0.454072\pi$
$557$	6.78698	0.287574	0.143787	+	0.989609i	$0.454072\pi$
$558$	−0.948741	−0.0401634
$559$	−49.9477	−2.11256
$560$	1.85872	0.0785452
$561$	4.36162	0.184148
$562$	−7.25433	−0.306005
$563$	44.0976	1.85849	0.929247	−	0.369460i	$-0.120457\pi$
$563$	44.0976	1.85849	0.929247	+	0.369460i	$0.120457\pi$
$564$	−47.9305	−2.01824
$565$	0.665511	0.0279983
$566$	76.8005	3.22816
$567$	−4.58387	−0.192504
$568$	−1.02204	−0.0428840
$569$	28.0928	1.17771	0.588856	−	0.808238i	$-0.299579\pi$
$569$	28.0928	1.17771	0.588856	+	0.808238i	$0.299579\pi$
$570$	−1.17709	−0.0493028
$571$	42.9695	1.79822	0.899109	−	0.437724i	$-0.144215\pi$
$571$	42.9695	1.79822	0.899109	+	0.437724i	$0.144215\pi$
$572$	29.9849	1.25373
$573$	−19.1688	−0.800787
$574$	38.2919	1.59827
$575$	−32.5666	−1.35812
$576$	−6.59479	−0.274783
$577$	33.1213	1.37886	0.689429	−	0.724353i	$-0.257861\pi$
$577$	33.1213	1.37886	0.689429	+	0.724353i	$0.257861\pi$
$578$	15.6040	0.649040
$579$	−7.61825	−0.316604
$580$	−1.22962	−0.0510570
$581$	−29.2239	−1.21241
$582$	−3.70585	−0.153612
$583$	−0.340234	−0.0140910
$584$	−38.8212	−1.60643
$585$	−0.475278	−0.0196503
$586$	10.6755	0.441003
$587$	−20.6303	−0.851503	−0.425752	−	0.904840i	$-0.639990\pi$
$587$	−20.6303	−0.851503	−0.425752	+	0.904840i	$0.639990\pi$
$588$	−57.5757	−2.37438
$589$	2.10364	0.0866788
$590$	1.80671	0.0743810
$591$	−13.5833	−0.558742
$592$	23.8514	0.980288
$593$	−21.3502	−0.876749	−0.438374	−	0.898792i	$-0.644446\pi$
$593$	−21.3502	−0.876749	−0.438374	+	0.898792i	$0.644446\pi$
$594$	3.29770	0.135306
$595$	−1.30217	−0.0533838
$596$	66.3354	2.71720
$597$	−12.2654	−0.501991
$598$	−88.1826	−3.60606
$599$	−35.3441	−1.44412	−0.722060	−	0.691830i	$-0.756805\pi$
$599$	−35.3441	−1.44412	−0.722060	+	0.691830i	$0.756805\pi$
$600$	−26.0250	−1.06247
$601$	−13.7515	−0.560936	−0.280468	−	0.959863i	$-0.590490\pi$
$601$	−13.7515	−0.560936	−0.280468	+	0.959863i	$0.590490\pi$
$602$	−103.466	−4.21697
$603$	2.16945	0.0883467
$604$	27.7253	1.12813
$605$	0.801192	0.0325731
$606$	32.1757	1.30705
$607$	−5.35738	−0.217449	−0.108725	−	0.994072i	$-0.534677\pi$
$607$	−5.35738	−0.217449	−0.108725	+	0.994072i	$0.534677\pi$
$608$	−6.07043	−0.246188
$609$	15.7851	0.639646
$610$	0.300746	0.0121769
$611$	63.7978	2.58098
$612$	−13.4328	−0.542990
$613$	23.7126	0.957742	0.478871	−	0.877885i	$-0.341046\pi$
$613$	23.7126	0.957742	0.478871	+	0.877885i	$0.341046\pi$
$614$	55.6868	2.24734
$615$	0.293696	0.0118430
$616$	31.8811	1.28453
$617$	5.53891	0.222988	0.111494	−	0.993765i	$-0.464436\pi$
$617$	5.53891	0.222988	0.111494	+	0.993765i	$0.464436\pi$
$618$	−5.24225	−0.210874
$619$	−24.8560	−0.999046	−0.499523	−	0.866301i	$-0.666491\pi$
$619$	−24.8560	−0.999046	−0.499523	+	0.866301i	$0.666491\pi$
$620$	−0.137061	−0.00550450
$621$	−6.52318	−0.261766
$622$	37.4997	1.50360
$623$	32.1293	1.28723
$624$	−25.5215	−1.02168
$625$	24.8868	0.995471
$626$	38.3193	1.53155
$627$	−7.31197	−0.292012
$628$	−46.7399	−1.86512
$629$	−16.7097	−0.666260
$630$	−0.984534	−0.0392248
$631$	−29.8976	−1.19021	−0.595103	−	0.803649i	$-0.702889\pi$
$631$	−29.8976	−1.19021	−0.595103	+	0.803649i	$0.702889\pi$
$632$	−10.3888	−0.413246
$633$	18.9781	0.754311
$634$	−44.5623	−1.76979
$635$	−0.0823818	−0.00326922
$636$	1.04784	0.0415497
$637$	76.6360	3.03643
$638$	−11.3560	−0.449590
$639$	0.196062	0.00775608
$640$	−1.60895	−0.0635994
$641$	47.0567	1.85863	0.929315	−	0.369289i	$-0.120399\pi$
$641$	47.0567	1.85863	0.929315	+	0.369289i	$0.120399\pi$
$642$	−33.9299	−1.33911
$643$	−28.8810	−1.13896	−0.569479	−	0.822006i	$-0.692855\pi$
$643$	−28.8810	−1.13896	−0.569479	+	0.822006i	$0.692855\pi$
$644$	−122.867	−4.84163
$645$	−0.793578	−0.0312471
$646$	44.2815	1.74223
$647$	−43.5396	−1.71172	−0.855859	−	0.517209i	$-0.826971\pi$
$647$	−43.5396	−1.71172	−0.855859	+	0.517209i	$0.826971\pi$
$648$	−5.21287	−0.204781
$649$	11.2231	0.440546
$650$	67.4897	2.64716
$651$	1.75951	0.0689608
$652$	−99.6199	−3.90142
$653$	−10.0035	−0.391468	−0.195734	−	0.980657i	$-0.562709\pi$
$653$	−10.0035	−0.391468	−0.195734	+	0.980657i	$0.562709\pi$
$654$	36.4653	1.42590
$655$	0.227261	0.00887982
$656$	15.7709	0.615751
$657$	7.44718	0.290542
$658$	132.157	5.15200
$659$	10.1870	0.396828	0.198414	−	0.980118i	$-0.436421\pi$
$659$	10.1870	0.396828	0.198414	+	0.980118i	$0.436421\pi$
$660$	0.476406	0.0185441
$661$	43.4623	1.69049	0.845244	−	0.534381i	$-0.179455\pi$
$661$	43.4623	1.69049	0.845244	+	0.534381i	$0.179455\pi$
$662$	−32.3219	−1.25623
$663$	17.8797	0.694391
$664$	−33.2341	−1.28973
$665$	2.18300	0.0846531
$666$	−12.6337	−0.489547
$667$	22.4634	0.869785
$668$	−76.0894	−2.94399
$669$	18.9660	0.733268
$670$	0.465959	0.0180016
$671$	1.86821	0.0721215
$672$	−5.07740	−0.195865
$673$	40.6180	1.56571	0.782855	−	0.622205i	$-0.213763\pi$
$673$	40.6180	1.56571	0.782855	+	0.622205i	$0.213763\pi$
$674$	−50.2838	−1.93686
$675$	4.99245	0.192159
$676$	69.5003	2.67309
$677$	−11.6730	−0.448629	−0.224314	−	0.974517i	$-0.572014\pi$
$677$	−11.6730	−0.448629	−0.224314	+	0.974517i	$0.572014\pi$
$678$	−18.9292	−0.726970
$679$	6.87278	0.263753
$680$	−1.48085	−0.0567882
$681$	−19.3807	−0.742672
$682$	−1.26582	−0.0484707
$683$	28.6990	1.09814	0.549068	−	0.835778i	$-0.314983\pi$
$683$	28.6990	1.09814	0.549068	+	0.835778i	$0.314983\pi$
$684$	22.5192	0.861044
$685$	1.40447	0.0536621
$686$	79.4427	3.03314
$687$	−6.30548	−0.240569
$688$	−42.6137	−1.62463
$689$	−1.39473	−0.0531349
$690$	−1.40106	−0.0533375
$691$	24.1721	0.919549	0.459775	−	0.888036i	$-0.347930\pi$
$691$	24.1721	0.919549	0.459775	+	0.888036i	$0.347930\pi$
$692$	88.2899	3.35628
$693$	−6.11584	−0.232322
$694$	16.1729	0.613915
$695$	1.63465	0.0620058
$696$	17.9512	0.680437
$697$	−11.0487	−0.418499
$698$	52.3869	1.98287
$699$	2.45172	0.0927326
$700$	94.0349	3.55418
$701$	38.4413	1.45191	0.725953	−	0.687744i	$-0.241399\pi$
$701$	38.4413	1.45191	0.725953	+	0.687744i	$0.241399\pi$
$702$	13.5184	0.510217
$703$	28.0127	1.05652
$704$	−8.79882	−0.331618
$705$	1.01363	0.0381756
$706$	88.4816	3.33005
$707$	−59.6724	−2.24421
$708$	−34.5647	−1.29902
$709$	−11.5194	−0.432619	−0.216310	−	0.976325i	$-0.569402\pi$
$709$	−11.5194	−0.432619	−0.216310	+	0.976325i	$0.569402\pi$
$710$	0.0421106	0.00158038
$711$	1.99292	0.0747404
$712$	36.5381	1.36932
$713$	2.50391	0.0937723
$714$	37.0377	1.38610
$715$	−0.634120	−0.0237147
$716$	35.6211	1.33122
$717$	−11.6821	−0.436275
$718$	52.9901	1.97757
$719$	−13.4065	−0.499977	−0.249988	−	0.968249i	$-0.580427\pi$
$719$	−13.4065	−0.499977	−0.249988	+	0.968249i	$0.580427\pi$
$720$	−0.405491	−0.0151118
$721$	9.72216	0.362072
$722$	−27.2735	−1.01502
$723$	8.58314	0.319211
$724$	16.3346	0.607072
$725$	−17.1921	−0.638499
$726$	−22.7884	−0.845755
$727$	17.9101	0.664250	0.332125	−	0.943235i	$-0.392234\pi$
$727$	17.9101	0.664250	0.332125	+	0.943235i	$0.392234\pi$
$728$	130.691	4.84373
$729$	1.00000	0.0370370
$730$	1.59952	0.0592010
$731$	29.8540	1.10419
$732$	−5.75367	−0.212662
$733$	35.8657	1.32473	0.662366	−	0.749181i	$-0.269553\pi$
$733$	35.8657	1.32473	0.662366	+	0.749181i	$0.269553\pi$
$734$	−43.0732	−1.58986
$735$	1.21761	0.0449121
$736$	−7.22550	−0.266335
$737$	2.89450	0.106620
$738$	−8.35361	−0.307501
$739$	−4.04625	−0.148844	−0.0744219	−	0.997227i	$-0.523711\pi$
$739$	−4.04625	−0.148844	−0.0744219	+	0.997227i	$0.523711\pi$
$740$	−1.82515	−0.0670938
$741$	−29.9742	−1.10113
$742$	−2.88917	−0.106065
$743$	−6.73607	−0.247123	−0.123561	−	0.992337i	$-0.539432\pi$
$743$	−6.73607	−0.247123	−0.123561	+	0.992337i	$0.539432\pi$
$744$	2.00095	0.0733585
$745$	−1.40286	−0.0513967
$746$	−0.917923	−0.0336076
$747$	6.37539	0.233263
$748$	−17.9222	−0.655300
$749$	62.9257	2.29926
$750$	2.14620	0.0783682
$751$	34.2050	1.24816	0.624078	−	0.781362i	$-0.285475\pi$
$751$	34.2050	1.24816	0.624078	+	0.781362i	$0.285475\pi$
$752$	54.4301	1.98486
$753$	−12.2984	−0.448179
$754$	−46.5521	−1.69533
$755$	−0.586334	−0.0213389
$756$	18.8354	0.685037
$757$	35.0273	1.27309	0.636544	−	0.771240i	$-0.280363\pi$
$757$	35.0273	1.27309	0.636544	+	0.771240i	$0.280363\pi$
$758$	−44.9248	−1.63174
$759$	−8.70328	−0.315909
$760$	2.48255	0.0900516
$761$	45.1235	1.63573	0.817863	−	0.575413i	$-0.195159\pi$
$761$	45.1235	1.63573	0.817863	+	0.575413i	$0.195159\pi$
$762$	2.34319	0.0848848
$763$	−67.6277	−2.44829
$764$	78.7657	2.84964
$765$	0.284077	0.0102708
$766$	−48.9676	−1.76927
$767$	46.0072	1.66123
$768$	32.5739	1.17541
$769$	30.1901	1.08868	0.544341	−	0.838864i	$-0.316780\pi$
$769$	30.1901	1.08868	0.544341	+	0.838864i	$0.316780\pi$
$770$	−1.31357	−0.0473379
$771$	12.1338	0.436988
$772$	31.3039	1.12665
$773$	−32.1589	−1.15668	−0.578338	−	0.815797i	$-0.696299\pi$
$773$	−32.1589	−1.15668	−0.578338	+	0.815797i	$0.696299\pi$
$774$	22.5718	0.811326
$775$	−1.91635	−0.0688372
$776$	7.81586	0.280573
$777$	23.4302	0.840555
$778$	28.0771	1.00661
$779$	18.5224	0.663634
$780$	1.95295	0.0699267
$781$	0.261587	0.00936033
$782$	52.7073	1.88481
$783$	−3.44362	−0.123065
$784$	65.3833	2.33512
$785$	0.988453	0.0352794
$786$	−6.46400	−0.230563
$787$	−15.7132	−0.560116	−0.280058	−	0.959983i	$-0.590354\pi$
$787$	−15.7132	−0.560116	−0.280058	+	0.959983i	$0.590354\pi$
$788$	55.8146	1.98831
$789$	3.23452	0.115152
$790$	0.428044	0.0152291
$791$	35.1056	1.24821
$792$	−6.95506	−0.247137
$793$	7.65841	0.271958
$794$	64.2551	2.28033
$795$	−0.0221597	−0.000785924 0
$796$	50.3995	1.78636
$797$	49.0999	1.73921	0.869604	−	0.493750i	$-0.164374\pi$
$797$	49.0999	1.73921	0.869604	+	0.493750i	$0.164374\pi$
$798$	−62.0912	−2.19801
$799$	−38.1323	−1.34903
$800$	5.52996	0.195514
$801$	−7.00920	−0.247658
$802$	−15.8916	−0.561152
$803$	9.93609	0.350637
$804$	−8.91440	−0.314387
$805$	2.59838	0.0915808
$806$	−5.18900	−0.182775
$807$	−15.9532	−0.561579
$808$	−67.8607	−2.38733
$809$	21.0573	0.740335	0.370167	−	0.928965i	$-0.379300\pi$
$809$	21.0573	0.740335	0.370167	+	0.928965i	$0.379300\pi$
$810$	0.214782	0.00754668
$811$	28.1050	0.986900	0.493450	−	0.869774i	$-0.335736\pi$
$811$	28.1050	0.986900	0.493450	+	0.869774i	$0.335736\pi$
$812$	−64.8621	−2.27621
$813$	21.5609	0.756174
$814$	−16.8560	−0.590804
$815$	2.10676	0.0737965
$816$	15.2544	0.534010
$817$	−50.0483	−1.75097
$818$	−34.2073	−1.19603
$819$	−25.0708	−0.876046
$820$	−1.20681	−0.0421438
$821$	33.7147	1.17665	0.588326	−	0.808624i	$-0.299787\pi$
$821$	33.7147	1.17665	0.588326	+	0.808624i	$0.299787\pi$
$822$	−39.9475	−1.39333
$823$	0.288753	0.0100653	0.00503265	−	0.999987i	$-0.498398\pi$
$823$	0.288753	0.0100653	0.00503265	+	0.999987i	$0.498398\pi$
$824$	11.0562	0.385162
$825$	6.66097	0.231905
$826$	95.3036	3.31604
$827$	35.2643	1.22626	0.613130	−	0.789982i	$-0.289910\pi$
$827$	35.2643	1.22626	0.613130	+	0.789982i	$0.289910\pi$
$828$	26.8041	0.931509
$829$	5.40442	0.187703	0.0938516	−	0.995586i	$-0.470082\pi$
$829$	5.40442	0.187703	0.0938516	+	0.995586i	$0.470082\pi$
$830$	1.36932	0.0475298
$831$	−30.0935	−1.04393
$832$	−36.0693	−1.25048
$833$	−45.8058	−1.58708
$834$	−46.4944	−1.60997
$835$	1.60914	0.0556864
$836$	30.0453	1.03914
$837$	−0.383849	−0.0132678
$838$	−25.6754	−0.886942
$839$	−2.27909	−0.0786829	−0.0393414	−	0.999226i	$-0.512526\pi$
$839$	−2.27909	−0.0786829	−0.0393414	+	0.999226i	$0.512526\pi$
$840$	2.07644	0.0716441
$841$	−17.1415	−0.591085
$842$	−26.1385	−0.900793
$843$	−2.93501	−0.101087
$844$	−77.9821	−2.68425
$845$	−1.46979	−0.0505623
$846$	−28.8308	−0.991223
$847$	42.2628	1.45217
$848$	−1.18994	−0.0408626
$849$	31.0725	1.06641
$850$	−40.3390	−1.38362
$851$	33.3429	1.14298
$852$	−0.805630	−0.0276004
$853$	39.5587	1.35446	0.677232	−	0.735769i	$-0.263179\pi$
$853$	39.5587	1.35446	0.677232	+	0.735769i	$0.263179\pi$
$854$	15.8643	0.542866
$855$	−0.476235	−0.0162869
$856$	71.5604	2.44588
$857$	−19.1035	−0.652564	−0.326282	−	0.945273i	$-0.605796\pi$
$857$	−19.1035	−0.652564	−0.326282	+	0.945273i	$0.605796\pi$
$858$	18.0363	0.615749
$859$	−23.5518	−0.803576	−0.401788	−	0.915733i	$-0.631611\pi$
$859$	−23.5518	−0.803576	−0.401788	+	0.915733i	$0.631611\pi$
$860$	3.26086	0.111194
$861$	15.4924	0.527980
$862$	14.4092	0.490780
$863$	−26.3758	−0.897841	−0.448921	−	0.893572i	$-0.648191\pi$
$863$	−26.3758	−0.897841	−0.448921	+	0.893572i	$0.648191\pi$
$864$	1.10767	0.0376835
$865$	−1.86715	−0.0634850
$866$	65.1507	2.21391
$867$	6.31317	0.214407
$868$	−7.22995	−0.245401
$869$	2.65897	0.0901995
$870$	−0.739629	−0.0250758
$871$	11.8655	0.402047
$872$	−76.9075	−2.60442
$873$	−1.49934	−0.0507450
$874$	−88.3602	−2.98883
$875$	−3.98030	−0.134559
$876$	−30.6009	−1.03391
$877$	4.28590	0.144724	0.0723622	−	0.997378i	$-0.476946\pi$
$877$	4.28590	0.144724	0.0723622	+	0.997378i	$0.476946\pi$
$878$	−93.2381	−3.14663
$879$	4.31919	0.145683
$880$	−0.541010	−0.0182374
$881$	−33.2848	−1.12139	−0.560696	−	0.828022i	$-0.689466\pi$
$881$	−33.2848	−1.12139	−0.560696	+	0.828022i	$0.689466\pi$
$882$	−34.6325	−1.16614
$883$	27.9003	0.938919	0.469459	−	0.882954i	$-0.344449\pi$
$883$	27.9003	0.938919	0.469459	+	0.882954i	$0.344449\pi$
$884$	−73.4689	−2.47103
$885$	0.730972	0.0245713
$886$	−47.3880	−1.59203
$887$	26.0012	0.873033	0.436517	−	0.899696i	$-0.356212\pi$
$887$	26.0012	0.873033	0.436517	+	0.899696i	$0.356212\pi$
$888$	26.6453	0.894159
$889$	−4.34563	−0.145748
$890$	−1.50545	−0.0504629
$891$	1.33421	0.0446977
$892$	−77.9326	−2.60937
$893$	63.9263	2.13921
$894$	39.9016	1.33451
$895$	−0.753312	−0.0251805
$896$	−84.8720	−2.83537
$897$	−35.6776	−1.19124
$898$	−65.2863	−2.17863
$899$	1.32183	0.0440855
$900$	−20.5143	−0.683810
$901$	0.833638	0.0277725
$902$	−11.1455	−0.371103
$903$	−41.8611	−1.39305
$904$	39.9228	1.32781
$905$	−0.345444	−0.0114829
$906$	16.6771	0.554061
$907$	48.0270	1.59471	0.797354	−	0.603511i	$-0.206232\pi$
$907$	48.0270	1.59471	0.797354	+	0.603511i	$0.206232\pi$
$908$	79.6367	2.64284
$909$	13.0179	0.431777
$910$	−5.38477	−0.178503
$911$	−32.4519	−1.07518	−0.537591	−	0.843206i	$-0.680665\pi$
$911$	−32.4519	−1.07518	−0.537591	+	0.843206i	$0.680665\pi$
$912$	−25.5729	−0.846805
$913$	8.50610	0.281511
$914$	93.9652	3.10809
$915$	0.121678	0.00402256
$916$	25.9096	0.856078
$917$	11.9880	0.395878
$918$	−8.08001	−0.266680
$919$	24.4621	0.806930	0.403465	−	0.914995i	$-0.367806\pi$
$919$	24.4621	0.806930	0.403465	+	0.914995i	$0.367806\pi$
$920$	2.95493	0.0974211
$921$	22.5302	0.742395
$922$	−40.8885	−1.34659
$923$	1.07233	0.0352963
$924$	25.1304	0.826729
$925$	−25.5187	−0.839049
$926$	−25.8253	−0.848672
$927$	−2.12095	−0.0696611
$928$	−3.81438	−0.125213
$929$	−49.0278	−1.60855	−0.804275	−	0.594257i	$-0.797446\pi$
$929$	−49.0278	−1.60855	−0.804275	+	0.594257i	$0.797446\pi$
$930$	−0.0824439	−0.00270344
$931$	76.7904	2.51670
$932$	−10.0743	−0.329994
$933$	15.1719	0.496706
$934$	−46.5411	−1.52287
$935$	0.379017	0.0123952
$936$	−28.5111	−0.931913
$937$	22.4573	0.733647	0.366823	−	0.930291i	$-0.380445\pi$
$937$	22.4573	0.733647	0.366823	+	0.930291i	$0.380445\pi$
$938$	24.5793	0.802542
$939$	15.5035	0.505938
$940$	−4.16508	−0.135850
$941$	33.2174	1.08286	0.541429	−	0.840747i	$-0.317884\pi$
$941$	33.2174	1.08286	0.541429	+	0.840747i	$0.317884\pi$
$942$	−28.1146	−0.916024
$943$	22.0468	0.717943
$944$	39.2518	1.27754
$945$	−0.398330	−0.0129577
$946$	30.1155	0.979139
$947$	25.9221	0.842354	0.421177	−	0.906978i	$-0.361617\pi$
$947$	25.9221	0.842354	0.421177	+	0.906978i	$0.361617\pi$
$948$	−8.18904	−0.265968
$949$	40.7313	1.32219
$950$	67.6256	2.19407
$951$	−18.0294	−0.584642
$952$	−78.1149	−2.53172
$953$	21.9327	0.710470	0.355235	−	0.934777i	$-0.384401\pi$
$953$	21.9327	0.710470	0.355235	+	0.934777i	$0.384401\pi$
$954$	0.630290	0.0204064
$955$	−1.66573	−0.0539019
$956$	48.0024	1.55251
$957$	−4.59451	−0.148520
$958$	74.0478	2.39238
$959$	74.0857	2.39235
$960$	−0.573075	−0.0184959
$961$	−30.8527	−0.995247
$962$	−69.0984	−2.22782
$963$	−13.7276	−0.442367
$964$	−35.2687	−1.13593
$965$	−0.662012	−0.0213109
$966$	−73.9059	−2.37788
$967$	−11.0775	−0.356229	−0.178115	−	0.984010i	$-0.557000\pi$
$967$	−11.0775	−0.356229	−0.178115	+	0.984010i	$0.557000\pi$
$968$	48.0621	1.54477
$969$	17.9157	0.575537
$970$	−0.322031	−0.0103398
$971$	2.74943	0.0882334	0.0441167	−	0.999026i	$-0.485953\pi$
$971$	2.74943	0.0882334	0.0441167	+	0.999026i	$0.485953\pi$
$972$	−4.10906	−0.131798
$973$	86.2276	2.76433
$974$	68.9602	2.20963
$975$	27.3055	0.874476
$976$	6.53390	0.209145
$977$	41.7614	1.33607	0.668033	−	0.744131i	$-0.267136\pi$
$977$	41.7614	1.33607	0.668033	+	0.744131i	$0.267136\pi$
$978$	−59.9226	−1.91611
$979$	−9.35174	−0.298883
$980$	−5.00323	−0.159822
$981$	14.7534	0.471040
$982$	76.2766	2.43409
$983$	−17.0051	−0.542379	−0.271189	−	0.962526i	$-0.587417\pi$
$983$	−17.0051	−0.542379	−0.271189	+	0.962526i	$0.587417\pi$
$984$	17.6183	0.561651
$985$	−1.18036	−0.0376095
$986$	27.8245	0.886113
$987$	53.4689	1.70193
$988$	123.166	3.91842
$989$	−59.5714	−1.89426
$990$	0.286564	0.00910761
$991$	−18.5430	−0.589038	−0.294519	−	0.955646i	$-0.595159\pi$
$991$	−18.5430	−0.589038	−0.294519	+	0.955646i	$0.595159\pi$
$992$	−0.425176	−0.0134994
$993$	−13.0770	−0.414987
$994$	2.22133	0.0704562
$995$	−1.06585	−0.0337896
$996$	−26.1969	−0.830079
$997$	44.7575	1.41748	0.708742	−	0.705468i	$-0.249263\pi$
$997$	44.7575	1.41748	0.708742	+	0.705468i	$0.249263\pi$
$998$	−23.8644	−0.755413
$999$	−5.11145	−0.161719

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8031.2.a.c.1.7	✓	121

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8031.2.a.c.1.7	✓	121	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:	\( N \)	\(=\)	\( 8031 = 3 \cdot 2677 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8031.a (trivial)

\(f(q)\)	\(=\)	\(q-2.47165 q^{2} -1.00000 q^{3} +4.10906 q^{4} -0.0868982 q^{5} +2.47165 q^{6} -4.58387 q^{7} -5.21287 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.47165 q^{2} -1.00000 q^{3} +4.10906 q^{4} -0.0868982 q^{5} +2.47165 q^{6} -4.58387 q^{7} -5.21287 q^{8} +1.00000 q^{9} +0.214782 q^{10} +1.33421 q^{11} -4.10906 q^{12} +5.46936 q^{13} +11.3297 q^{14} +0.0868982 q^{15} +4.66627 q^{16} -3.26907 q^{17} -2.47165 q^{18} +5.48038 q^{19} -0.357070 q^{20} +4.58387 q^{21} -3.29770 q^{22} +6.52318 q^{23} +5.21287 q^{24} -4.99245 q^{25} -13.5184 q^{26} -1.00000 q^{27} -18.8354 q^{28} +3.44362 q^{29} -0.214782 q^{30} +0.383849 q^{31} -1.10767 q^{32} -1.33421 q^{33} +8.08001 q^{34} +0.398330 q^{35} +4.10906 q^{36} +5.11145 q^{37} -13.5456 q^{38} -5.46936 q^{39} +0.452989 q^{40} +3.37977 q^{41} -11.3297 q^{42} -9.13227 q^{43} +5.48235 q^{44} -0.0868982 q^{45} -16.1230 q^{46} +11.6646 q^{47} -4.66627 q^{48} +14.0119 q^{49} +12.3396 q^{50} +3.26907 q^{51} +22.4739 q^{52} -0.255008 q^{53} +2.47165 q^{54} -0.115940 q^{55} +23.8951 q^{56} -5.48038 q^{57} -8.51144 q^{58} +8.41181 q^{59} +0.357070 q^{60} +1.40024 q^{61} -0.948741 q^{62} -4.58387 q^{63} -6.59479 q^{64} -0.475278 q^{65} +3.29770 q^{66} +2.16945 q^{67} -13.4328 q^{68} -6.52318 q^{69} -0.984534 q^{70} +0.196062 q^{71} -5.21287 q^{72} +7.44718 q^{73} -12.6337 q^{74} +4.99245 q^{75} +22.5192 q^{76} -6.11584 q^{77} +13.5184 q^{78} +1.99292 q^{79} -0.405491 q^{80} +1.00000 q^{81} -8.35361 q^{82} +6.37539 q^{83} +18.8354 q^{84} +0.284077 q^{85} +22.5718 q^{86} -3.44362 q^{87} -6.95506 q^{88} -7.00920 q^{89} +0.214782 q^{90} -25.0708 q^{91} +26.8041 q^{92} -0.383849 q^{93} -28.8308 q^{94} -0.476235 q^{95} +1.10767 q^{96} -1.49934 q^{97} -34.6325 q^{98} +1.33421 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 121 q + 7 q^{2} - 121 q^{3} + 123 q^{4} + 24 q^{5} - 7 q^{6} - 14 q^{7} + 18 q^{8} + 121 q^{9}+O(q^{10}) \) 121 * q + 7 * q^2 - 121 * q^3 + 123 * q^4 + 24 * q^5 - 7 * q^6 - 14 * q^7 + 18 * q^8 + 121 * q^9	\( 121 q + 7 q^{2} - 121 q^{3} + 123 q^{4} + 24 q^{5} - 7 q^{6} - 14 q^{7} + 18 q^{8} + 121 q^{9} + 18 q^{10} + 32 q^{11} - 123 q^{12} + 2 q^{13} + 37 q^{14} - 24 q^{15} + 131 q^{16} + 87 q^{17} + 7 q^{18} - 10 q^{19} + 60 q^{20} + 14 q^{21} - 22 q^{22} + 31 q^{23} - 18 q^{24} + 147 q^{25} + 37 q^{26} - 121 q^{27} - 29 q^{28} + 68 q^{29} - 18 q^{30} + 25 q^{31} + 43 q^{32} - 32 q^{33} + 27 q^{34} + 51 q^{35} + 123 q^{36} - 4 q^{37} + 36 q^{38} - 2 q^{39} + 61 q^{40} + 132 q^{41} - 37 q^{42} - 91 q^{43} + 94 q^{44} + 24 q^{45} + 39 q^{47} - 131 q^{48} + 217 q^{49} + 54 q^{50} - 87 q^{51} - 12 q^{52} + 55 q^{53} - 7 q^{54} + 7 q^{55} + 104 q^{56} + 10 q^{57} - 3 q^{58} + 58 q^{59} - 60 q^{60} + 126 q^{61} + 74 q^{62} - 14 q^{63} + 122 q^{64} + 128 q^{65} + 22 q^{66} - 139 q^{67} + 190 q^{68} - 31 q^{69} - 18 q^{70} + 37 q^{71} + 18 q^{72} + 84 q^{73} + 79 q^{74} - 147 q^{75} + 23 q^{76} + 95 q^{77} - 37 q^{78} - 14 q^{79} + 145 q^{80} + 121 q^{81} + 9 q^{82} + 58 q^{83} + 29 q^{84} + 32 q^{85} + 28 q^{86} - 68 q^{87} - 84 q^{88} + 198 q^{89} + 18 q^{90} + 5 q^{91} + 98 q^{92} - 25 q^{93} + 9 q^{94} + 42 q^{95} - 43 q^{96} + 73 q^{97} + 69 q^{98} + 32 q^{99}+O(q^{100}) \) 121 * q + 7 * q^2 - 121 * q^3 + 123 * q^4 + 24 * q^5 - 7 * q^6 - 14 * q^7 + 18 * q^8 + 121 * q^9 + 18 * q^10 + 32 * q^11 - 123 * q^12 + 2 * q^13 + 37 * q^14 - 24 * q^15 + 131 * q^16 + 87 * q^17 + 7 * q^18 - 10 * q^19 + 60 * q^20 + 14 * q^21 - 22 * q^22 + 31 * q^23 - 18 * q^24 + 147 * q^25 + 37 * q^26 - 121 * q^27 - 29 * q^28 + 68 * q^29 - 18 * q^30 + 25 * q^31 + 43 * q^32 - 32 * q^33 + 27 * q^34 + 51 * q^35 + 123 * q^36 - 4 * q^37 + 36 * q^38 - 2 * q^39 + 61 * q^40 + 132 * q^41 - 37 * q^42 - 91 * q^43 + 94 * q^44 + 24 * q^45 + 39 * q^47 - 131 * q^48 + 217 * q^49 + 54 * q^50 - 87 * q^51 - 12 * q^52 + 55 * q^53 - 7 * q^54 + 7 * q^55 + 104 * q^56 + 10 * q^57 - 3 * q^58 + 58 * q^59 - 60 * q^60 + 126 * q^61 + 74 * q^62 - 14 * q^63 + 122 * q^64 + 128 * q^65 + 22 * q^66 - 139 * q^67 + 190 * q^68 - 31 * q^69 - 18 * q^70 + 37 * q^71 + 18 * q^72 + 84 * q^73 + 79 * q^74 - 147 * q^75 + 23 * q^76 + 95 * q^77 - 37 * q^78 - 14 * q^79 + 145 * q^80 + 121 * q^81 + 9 * q^82 + 58 * q^83 + 29 * q^84 + 32 * q^85 + 28 * q^86 - 68 * q^87 - 84 * q^88 + 198 * q^89 + 18 * q^90 + 5 * q^91 + 98 * q^92 - 25 * q^93 + 9 * q^94 + 42 * q^95 - 43 * q^96 + 73 * q^97 + 69 * q^98 + 32 * q^99

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