LMFDB - Embedded newform 103.2.a.b.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [103,2,Mod(1,103)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(103, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("103.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	103.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:	$0.822459140819$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.6999257.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 6x^{4} + 7x^{3} + 11x^{2} + x - 1 $ x^6 - 2x^5 - 6x^4 + 7x^3 + 11x^2 + x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-0.833273$ of defining polynomial
Character	$\chi$	$=$	103.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.83327 q^{2} +0.860083 q^{3} +1.36089 q^{4} -3.15863 q^{5} +1.57677 q^{6} +2.30447 q^{7} -1.17166 q^{8} -2.26026 q^{9} +O(q^{10})$	\(q+1.83327 q^{2} +0.860083 q^{3} +1.36089 q^{4} -3.15863 q^{5} +1.57677 q^{6} +2.30447 q^{7} -1.17166 q^{8} -2.26026 q^{9} -5.79063 q^{10} +4.75234 q^{11} +1.17048 q^{12} -6.46310 q^{13} +4.22472 q^{14} -2.71668 q^{15} -4.86976 q^{16} +6.20284 q^{17} -4.14367 q^{18} -1.72770 q^{19} -4.29855 q^{20} +1.98204 q^{21} +8.71234 q^{22} +7.50139 q^{23} -1.00773 q^{24} +4.97694 q^{25} -11.8486 q^{26} -4.52426 q^{27} +3.13613 q^{28} +0.513841 q^{29} -4.98042 q^{30} -1.19354 q^{31} -6.58427 q^{32} +4.08741 q^{33} +11.3715 q^{34} -7.27897 q^{35} -3.07596 q^{36} -1.39046 q^{37} -3.16735 q^{38} -5.55880 q^{39} +3.70085 q^{40} +6.48242 q^{41} +3.63361 q^{42} +1.09089 q^{43} +6.46741 q^{44} +7.13931 q^{45} +13.7521 q^{46} -6.86458 q^{47} -4.18840 q^{48} -1.68941 q^{49} +9.12409 q^{50} +5.33496 q^{51} -8.79557 q^{52} -1.24331 q^{53} -8.29420 q^{54} -15.0109 q^{55} -2.70006 q^{56} -1.48597 q^{57} +0.942010 q^{58} +9.79832 q^{59} -3.69711 q^{60} -1.04557 q^{61} -2.18808 q^{62} -5.20870 q^{63} -2.33125 q^{64} +20.4145 q^{65} +7.49333 q^{66} +4.24442 q^{67} +8.44139 q^{68} +6.45182 q^{69} -13.3443 q^{70} -5.53386 q^{71} +2.64826 q^{72} -5.11686 q^{73} -2.54909 q^{74} +4.28058 q^{75} -2.35121 q^{76} +10.9516 q^{77} -10.1908 q^{78} +9.28318 q^{79} +15.3818 q^{80} +2.88953 q^{81} +11.8840 q^{82} -8.19673 q^{83} +2.69733 q^{84} -19.5925 q^{85} +1.99990 q^{86} +0.441946 q^{87} -5.56814 q^{88} -18.0403 q^{89} +13.0883 q^{90} -14.8940 q^{91} +10.2086 q^{92} -1.02654 q^{93} -12.5846 q^{94} +5.45718 q^{95} -5.66302 q^{96} +4.11714 q^{97} -3.09716 q^{98} -10.7415 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 4 q^{2} + 6 q^{4} + 3 q^{5} - 3 q^{6} - 2 q^{7} + 9 q^{8} + 8 q^{9}+O(q^{10}) $ 6 * q + 4 * q^2 + 6 * q^4 + 3 * q^5 - 3 * q^6 - 2 * q^7 + 9 * q^8 + 8 * q^9	\( 6 q + 4 q^{2} + 6 q^{4} + 3 q^{5} - 3 q^{6} - 2 q^{7} + 9 q^{8} + 8 q^{9} - 10 q^{10} - q^{11} - 13 q^{12} - q^{13} - 9 q^{14} - 9 q^{15} + 2 q^{16} + 21 q^{17} - 3 q^{18} - 7 q^{19} - 9 q^{20} - 14 q^{21} - 11 q^{22} + 12 q^{23} - 36 q^{24} + q^{25} - 5 q^{26} - 10 q^{28} + 12 q^{29} + 2 q^{30} - 16 q^{31} + 27 q^{32} + 15 q^{33} + 10 q^{34} + 5 q^{35} - 3 q^{36} - 8 q^{38} + 5 q^{39} - q^{40} + 14 q^{41} + 25 q^{42} - 6 q^{43} - 4 q^{44} + 8 q^{45} + 19 q^{46} + q^{47} - 41 q^{48} - 2 q^{49} + q^{50} - 5 q^{51} - 5 q^{52} + 19 q^{53} + 23 q^{54} - 10 q^{55} - 13 q^{56} + 23 q^{57} + 4 q^{58} + 3 q^{59} + 17 q^{60} + q^{61} + 23 q^{62} - 20 q^{63} + 61 q^{64} + 23 q^{65} + q^{66} - 12 q^{67} + 14 q^{68} - 22 q^{69} - 14 q^{70} - 27 q^{71} + 31 q^{72} - 7 q^{73} + 15 q^{74} - 17 q^{75} - 38 q^{76} + 27 q^{77} - 20 q^{78} - 21 q^{79} - 28 q^{80} - 2 q^{81} + 53 q^{82} - 9 q^{83} + 61 q^{84} - 9 q^{85} - 11 q^{86} - 12 q^{87} - 31 q^{88} - 14 q^{89} - 22 q^{90} - 33 q^{91} + 30 q^{92} - 32 q^{93} - 6 q^{95} - 33 q^{96} - 8 q^{97} + 2 q^{98} - 54 q^{99}+O(q^{100}) \) 6 * q + 4 * q^2 + 6 * q^4 + 3 * q^5 - 3 * q^6 - 2 * q^7 + 9 * q^8 + 8 * q^9 - 10 * q^10 - q^11 - 13 * q^12 - q^13 - 9 * q^14 - 9 * q^15 + 2 * q^16 + 21 * q^17 - 3 * q^18 - 7 * q^19 - 9 * q^20 - 14 * q^21 - 11 * q^22 + 12 * q^23 - 36 * q^24 + q^25 - 5 * q^26 - 10 * q^28 + 12 * q^29 + 2 * q^30 - 16 * q^31 + 27 * q^32 + 15 * q^33 + 10 * q^34 + 5 * q^35 - 3 * q^36 - 8 * q^38 + 5 * q^39 - q^40 + 14 * q^41 + 25 * q^42 - 6 * q^43 - 4 * q^44 + 8 * q^45 + 19 * q^46 + q^47 - 41 * q^48 - 2 * q^49 + q^50 - 5 * q^51 - 5 * q^52 + 19 * q^53 + 23 * q^54 - 10 * q^55 - 13 * q^56 + 23 * q^57 + 4 * q^58 + 3 * q^59 + 17 * q^60 + q^61 + 23 * q^62 - 20 * q^63 + 61 * q^64 + 23 * q^65 + q^66 - 12 * q^67 + 14 * q^68 - 22 * q^69 - 14 * q^70 - 27 * q^71 + 31 * q^72 - 7 * q^73 + 15 * q^74 - 17 * q^75 - 38 * q^76 + 27 * q^77 - 20 * q^78 - 21 * q^79 - 28 * q^80 - 2 * q^81 + 53 * q^82 - 9 * q^83 + 61 * q^84 - 9 * q^85 - 11 * q^86 - 12 * q^87 - 31 * q^88 - 14 * q^89 - 22 * q^90 - 33 * q^91 + 30 * q^92 - 32 * q^93 - 6 * q^95 - 33 * q^96 - 8 * q^97 + 2 * q^98 - 54 * 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 $

$2$	1.83327	1.29632	0.648160	−	0.761504i	$-0.275539\pi$
$2$	1.83327	1.29632	0.648160	+	0.761504i	$0.275539\pi$
$3$	0.860083	0.496569	0.248285	−	0.968687i	$-0.420133\pi$
$3$	0.860083	0.496569	0.248285	+	0.968687i	$0.420133\pi$
$4$	1.36089	0.680445
$5$	−3.15863	−1.41258	−0.706291	−	0.707922i	$-0.749633\pi$
$5$	−3.15863	−1.41258	−0.706291	+	0.707922i	$0.749633\pi$
$6$	1.57677	0.643712
$7$	2.30447	0.871008	0.435504	−	0.900187i	$-0.356570\pi$
$7$	2.30447	0.871008	0.435504	+	0.900187i	$0.356570\pi$
$8$	−1.17166	−0.414246
$9$	−2.26026	−0.753419
$10$	−5.79063	−1.83116
$11$	4.75234	1.43288	0.716442	−	0.697646i	$-0.245769\pi$
$11$	4.75234	1.43288	0.716442	+	0.697646i	$0.245769\pi$
$12$	1.17048	0.337888
$13$	−6.46310	−1.79254	−0.896271	−	0.443507i	$-0.853734\pi$
$13$	−6.46310	−1.79254	−0.896271	+	0.443507i	$0.853734\pi$
$14$	4.22472	1.12910
$15$	−2.71668	−0.701445
$16$	−4.86976	−1.21744
$17$	6.20284	1.50441	0.752205	−	0.658929i	$-0.228990\pi$
$17$	6.20284	1.50441	0.752205	+	0.658929i	$0.228990\pi$
$18$	−4.14367	−0.976672
$19$	−1.72770	−0.396362	−0.198181	−	0.980165i	$-0.563503\pi$
$19$	−1.72770	−0.396362	−0.198181	+	0.980165i	$0.563503\pi$
$20$	−4.29855	−0.961184
$21$	1.98204	0.432516
$22$	8.71234	1.85748
$23$	7.50139	1.56415	0.782074	−	0.623186i	$-0.214162\pi$
$23$	7.50139	1.56415	0.782074	+	0.623186i	$0.214162\pi$
$24$	−1.00773	−0.205702
$25$	4.97694	0.995388
$26$	−11.8486	−2.32371
$27$	−4.52426	−0.870694
$28$	3.13613	0.592673
$29$	0.513841	0.0954178	0.0477089	−	0.998861i	$-0.484808\pi$
$29$	0.513841	0.0954178	0.0477089	+	0.998861i	$0.484808\pi$
$30$	−4.98042	−0.909297
$31$	−1.19354	−0.214366	−0.107183	−	0.994239i	$-0.534183\pi$
$31$	−1.19354	−0.214366	−0.107183	+	0.994239i	$0.534183\pi$
$32$	−6.58427	−1.16395
$33$	4.08741	0.711526
$34$	11.3715	1.95020
$35$	−7.27897	−1.23037
$36$	−3.07596	−0.512660
$37$	−1.39046	−0.228590	−0.114295	−	0.993447i	$-0.536461\pi$
$37$	−1.39046	−0.228590	−0.114295	+	0.993447i	$0.536461\pi$
$38$	−3.16735	−0.513812
$39$	−5.55880	−0.890121
$40$	3.70085	0.585156
$41$	6.48242	1.01238	0.506192	−	0.862421i	$-0.331053\pi$
$41$	6.48242	1.01238	0.506192	+	0.862421i	$0.331053\pi$
$42$	3.63361	0.560679
$43$	1.09089	0.166359	0.0831796	−	0.996535i	$-0.473492\pi$
$43$	1.09089	0.166359	0.0831796	+	0.996535i	$0.473492\pi$
$44$	6.46741	0.974999
$45$	7.13931	1.06427
$46$	13.7521	2.02764
$47$	−6.86458	−1.00130	−0.500651	−	0.865649i	$-0.666906\pi$
$47$	−6.86458	−1.00130	−0.500651	+	0.865649i	$0.666906\pi$
$48$	−4.18840	−0.604543
$49$	−1.68941	−0.241345
$50$	9.12409	1.29034
$51$	5.33496	0.747044
$52$	−8.79557	−1.21973
$53$	−1.24331	−0.170782	−0.0853911	−	0.996348i	$-0.527214\pi$
$53$	−1.24331	−0.170782	−0.0853911	+	0.996348i	$0.527214\pi$
$54$	−8.29420	−1.12870
$55$	−15.0109	−2.02407
$56$	−2.70006	−0.360811
$57$	−1.48597	−0.196821
$58$	0.942010	0.123692
$59$	9.79832	1.27563	0.637817	−	0.770188i	$-0.279838\pi$
$59$	9.79832	1.27563	0.637817	+	0.770188i	$0.279838\pi$
$60$	−3.69711	−0.477294
$61$	−1.04557	−0.133871	−0.0669354	−	0.997757i	$-0.521322\pi$
$61$	−1.04557	−0.133871	−0.0669354	+	0.997757i	$0.521322\pi$
$62$	−2.18808	−0.277886
$63$	−5.20870	−0.656234
$64$	−2.33125	−0.291406
$65$	20.4145	2.53211
$66$	7.49333	0.922366
$67$	4.24442	0.518539	0.259269	−	0.965805i	$-0.416518\pi$
$67$	4.24442	0.518539	0.259269	+	0.965805i	$0.416518\pi$
$68$	8.44139	1.02367
$69$	6.45182	0.776708
$70$	−13.3443	−1.59495
$71$	−5.53386	−0.656748	−0.328374	−	0.944548i	$-0.606501\pi$
$71$	−5.53386	−0.656748	−0.328374	+	0.944548i	$0.606501\pi$
$72$	2.64826	0.312101
$73$	−5.11686	−0.598883	−0.299441	−	0.954115i	$-0.596800\pi$
$73$	−5.11686	−0.598883	−0.299441	+	0.954115i	$0.596800\pi$
$74$	−2.54909	−0.296325
$75$	4.28058	0.494279
$76$	−2.35121	−0.269703
$77$	10.9516	1.24805
$78$	−10.1908	−1.15388
$79$	9.28318	1.04444	0.522220	−	0.852811i	$-0.325104\pi$
$79$	9.28318	1.04444	0.522220	+	0.852811i	$0.325104\pi$
$80$	15.3818	1.71973
$81$	2.88953	0.321059
$82$	11.8840	1.31237
$83$	−8.19673	−0.899708	−0.449854	−	0.893102i	$-0.648524\pi$
$83$	−8.19673	−0.899708	−0.449854	+	0.893102i	$0.648524\pi$
$84$	2.69733	0.294303
$85$	−19.5925	−2.12510
$86$	1.99990	0.215655
$87$	0.441946	0.0473815
$88$	−5.56814	−0.593566
$89$	−18.0403	−1.91227	−0.956136	−	0.292924i	$-0.905372\pi$
$89$	−18.0403	−1.91227	−0.956136	+	0.292924i	$0.905372\pi$
$90$	13.0883	1.37963
$91$	−14.8940	−1.56132
$92$	10.2086	1.06432
$93$	−1.02654	−0.106447
$94$	−12.5846	−1.29801
$95$	5.45718	0.559894
$96$	−5.66302	−0.577979
$97$	4.11714	0.418032	0.209016	−	0.977912i	$-0.432974\pi$
$97$	4.11714	0.418032	0.209016	+	0.977912i	$0.432974\pi$
$98$	−3.09716	−0.312860
$99$	−10.7415	−1.07956
$100$	6.77307	0.677307
$101$	−12.6169	−1.25543	−0.627717	−	0.778442i	$-0.716010\pi$
$101$	−12.6169	−1.25543	−0.627717	+	0.778442i	$0.716010\pi$
$102$	9.78044	0.968408
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	7.57258	0.742553
$105$	−6.26052	−0.610964
$106$	−2.27933	−0.221388
$107$	−8.09095	−0.782181	−0.391091	−	0.920352i	$-0.627902\pi$
$107$	−8.09095	−0.782181	−0.391091	+	0.920352i	$0.627902\pi$
$108$	−6.15702	−0.592459
$109$	−6.28670	−0.602156	−0.301078	−	0.953599i	$-0.597347\pi$
$109$	−6.28670	−0.602156	−0.301078	+	0.953599i	$0.597347\pi$
$110$	−27.5190	−2.62384
$111$	−1.19591	−0.113511
$112$	−11.2222	−1.06040
$113$	5.30928	0.499455	0.249728	−	0.968316i	$-0.419659\pi$
$113$	5.30928	0.499455	0.249728	+	0.968316i	$0.419659\pi$
$114$	−2.72419	−0.255143
$115$	−23.6941	−2.20949
$116$	0.699280	0.0649266
$117$	14.6083	1.35053
$118$	17.9630	1.65363
$119$	14.2943	1.31035
$120$	3.18304	0.290570
$121$	11.5847	1.05316
$122$	−1.91681	−0.173539
$123$	5.57542	0.502718
$124$	−1.62427	−0.145864
$125$	0.0728347	0.00651454
$126$	−9.54896	−0.850689
$127$	−10.9536	−0.971977	−0.485988	−	0.873965i	$-0.661540\pi$
$127$	−10.9536	−0.971977	−0.485988	+	0.873965i	$0.661540\pi$
$128$	8.89473	0.786190
$129$	0.938256	0.0826089
$130$	37.4254	3.28243
$131$	−5.44040	−0.475330	−0.237665	−	0.971347i	$-0.576382\pi$
$131$	−5.44040	−0.475330	−0.237665	+	0.971347i	$0.576382\pi$
$132$	5.56251	0.484154
$133$	−3.98144	−0.345235
$134$	7.78119	0.672192
$135$	14.2905	1.22993
$136$	−7.26765	−0.623196
$137$	10.9542	0.935878	0.467939	−	0.883761i	$-0.344997\pi$
$137$	10.9542	0.935878	0.467939	+	0.883761i	$0.344997\pi$
$138$	11.8279	1.00686
$139$	1.45268	0.123215	0.0616075	−	0.998100i	$-0.480377\pi$
$139$	1.45268	0.123215	0.0616075	+	0.998100i	$0.480377\pi$
$140$	−9.90587	−0.837199
$141$	−5.90411	−0.497215
$142$	−10.1451	−0.851355
$143$	−30.7149	−2.56851
$144$	11.0069	0.917242
$145$	−1.62303	−0.134785
$146$	−9.38060	−0.776344
$147$	−1.45304	−0.119844
$148$	−1.89226	−0.155543
$149$	1.58293	0.129679	0.0648394	−	0.997896i	$-0.479346\pi$
$149$	1.58293	0.129679	0.0648394	+	0.997896i	$0.479346\pi$
$150$	7.84748	0.640744
$151$	0.0192144	0.00156365	0.000781824	−	1.00000i	$-0.499751\pi$
$151$	0.0192144	0.00156365	0.000781824		1.00000i	$0.499751\pi$
$152$	2.02429	0.164191
$153$	−14.0200	−1.13345
$154$	20.0773	1.61788
$155$	3.76994	0.302809
$156$	−7.56492	−0.605678
$157$	4.31226	0.344156	0.172078	−	0.985083i	$-0.444952\pi$
$157$	4.31226	0.344156	0.172078	+	0.985083i	$0.444952\pi$
$158$	17.0186	1.35393
$159$	−1.06935	−0.0848052
$160$	20.7973	1.64417
$161$	17.2867	1.36239
$162$	5.29730	0.416195
$163$	21.0318	1.64734	0.823668	−	0.567072i	$-0.191924\pi$
$163$	21.0318	1.64734	0.823668	+	0.567072i	$0.191924\pi$
$164$	8.82185	0.688871
$165$	−12.9106	−1.00509
$166$	−15.0268	−1.16631
$167$	17.6735	1.36762	0.683809	−	0.729661i	$-0.260322\pi$
$167$	17.6735	1.36762	0.683809	+	0.729661i	$0.260322\pi$
$168$	−2.32228	−0.179168
$169$	28.7717	2.21321
$170$	−35.9184	−2.75481
$171$	3.90505	0.298627
$172$	1.48458	0.113198
$173$	10.7088	0.814177	0.407089	−	0.913389i	$-0.366544\pi$
$173$	10.7088	0.814177	0.407089	+	0.913389i	$0.366544\pi$
$174$	0.810207	0.0614216
$175$	11.4692	0.866991
$176$	−23.1428	−1.74445
$177$	8.42737	0.633440
$178$	−33.0729	−2.47892
$179$	−7.55826	−0.564931	−0.282465	−	0.959277i	$-0.591152\pi$
$179$	−7.55826	−0.564931	−0.282465	+	0.959277i	$0.591152\pi$
$180$	9.71582	0.724174
$181$	5.83804	0.433938	0.216969	−	0.976179i	$-0.430383\pi$
$181$	5.83804	0.433938	0.216969	+	0.976179i	$0.430383\pi$
$182$	−27.3048	−2.02397
$183$	−0.899273	−0.0664762
$184$	−8.78911	−0.647941
$185$	4.39194	0.322902
$186$	−1.88193	−0.137990
$187$	29.4780	2.15565
$188$	−9.34193	−0.681330
$189$	−10.4260	−0.758381
$190$	10.0045	0.725802
$191$	5.78525	0.418606	0.209303	−	0.977851i	$-0.432880\pi$
$191$	5.78525	0.418606	0.209303	+	0.977851i	$0.432880\pi$
$192$	−2.00507	−0.144703
$193$	−20.3810	−1.46706	−0.733528	−	0.679659i	$-0.762128\pi$
$193$	−20.3810	−1.46706	−0.733528	+	0.679659i	$0.762128\pi$
$194$	7.54784	0.541903
$195$	17.5582	1.25737
$196$	−2.29911	−0.164222
$197$	11.7544	0.837464	0.418732	−	0.908110i	$-0.362475\pi$
$197$	11.7544	0.837464	0.418732	+	0.908110i	$0.362475\pi$
$198$	−19.6921	−1.39946
$199$	4.13479	0.293108	0.146554	−	0.989203i	$-0.453182\pi$
$199$	4.13479	0.293108	0.146554	+	0.989203i	$0.453182\pi$
$200$	−5.83130	−0.412335
$201$	3.65056	0.257490
$202$	−23.1303	−1.62744
$203$	1.18413	0.0831097
$204$	7.26029	0.508322
$205$	−20.4755	−1.43007
$206$	1.83327	0.127730
$207$	−16.9551	−1.17846
$208$	31.4737	2.18231
$209$	−8.21064	−0.567942
$210$	−11.4772	−0.792005
$211$	0.154963	0.0106681	0.00533406	−	0.999986i	$-0.498302\pi$
$211$	0.154963	0.0106681	0.00533406	+	0.999986i	$0.498302\pi$
$212$	−1.69201	−0.116208
$213$	−4.75958	−0.326121
$214$	−14.8329	−1.01396
$215$	−3.44572	−0.234996
$216$	5.30091	0.360681
$217$	−2.75047	−0.186714
$218$	−11.5252	−0.780587
$219$	−4.40092	−0.297387
$220$	−20.4282	−1.37727
$221$	−40.0896	−2.69672
$222$	−2.19243	−0.147146
$223$	7.87875	0.527600	0.263800	−	0.964577i	$-0.415024\pi$
$223$	7.87875	0.527600	0.263800	+	0.964577i	$0.415024\pi$
$224$	−15.1733	−1.01381
$225$	−11.2492	−0.749944
$226$	9.73337	0.647454
$227$	3.53751	0.234793	0.117397	−	0.993085i	$-0.462545\pi$
$227$	3.53751	0.234793	0.117397	+	0.993085i	$0.462545\pi$
$228$	−2.02224	−0.133926
$229$	−12.0223	−0.794454	−0.397227	−	0.917720i	$-0.630027\pi$
$229$	−12.0223	−0.794454	−0.397227	+	0.917720i	$0.630027\pi$
$230$	−43.4378	−2.86420
$231$	9.41931	0.619745
$232$	−0.602048	−0.0395264
$233$	10.7934	0.707097	0.353548	−	0.935416i	$-0.384975\pi$
$233$	10.7934	0.707097	0.353548	+	0.935416i	$0.384975\pi$
$234$	26.7809	1.75073
$235$	21.6827	1.41442
$236$	13.3344	0.867998
$237$	7.98431	0.518636
$238$	26.2053	1.69864
$239$	−23.8149	−1.54046	−0.770229	−	0.637768i	$-0.779858\pi$
$239$	−23.8149	−1.54046	−0.770229	+	0.637768i	$0.779858\pi$
$240$	13.2296	0.853967
$241$	−8.85676	−0.570514	−0.285257	−	0.958451i	$-0.592079\pi$
$241$	−8.85676	−0.570514	−0.285257	+	0.958451i	$0.592079\pi$
$242$	21.2380	1.36523
$243$	16.0580	1.03012
$244$	−1.42290	−0.0910918
$245$	5.33623	0.340919
$246$	10.2213	0.651684
$247$	11.1663	0.710496
$248$	1.39842	0.0888000
$249$	−7.04987	−0.446767
$250$	0.133526	0.00844492
$251$	−11.2021	−0.707068	−0.353534	−	0.935422i	$-0.615020\pi$
$251$	−11.2021	−0.707068	−0.353534	+	0.935422i	$0.615020\pi$
$252$	−7.08846	−0.446531
$253$	35.6492	2.24124
$254$	−20.0810	−1.25999
$255$	−16.8512	−1.05526
$256$	20.9690	1.31056
$257$	26.6166	1.66030	0.830148	−	0.557544i	$-0.188256\pi$
$257$	26.6166	1.66030	0.830148	+	0.557544i	$0.188256\pi$
$258$	1.72008	0.107087
$259$	−3.20427	−0.199103
$260$	27.7819	1.72296
$261$	−1.16141	−0.0718896
$262$	−9.97375	−0.616180
$263$	11.4785	0.707793	0.353897	−	0.935285i	$-0.384856\pi$
$263$	11.4785	0.707793	0.353897	+	0.935285i	$0.384856\pi$
$264$	−4.78907	−0.294747
$265$	3.92717	0.241244
$266$	−7.29907	−0.447535
$267$	−15.5162	−0.949575
$268$	5.77619	0.352837
$269$	−14.7392	−0.898664	−0.449332	−	0.893365i	$-0.648338\pi$
$269$	−14.7392	−0.898664	−0.449332	+	0.893365i	$0.648338\pi$
$270$	26.1983	1.59438
$271$	−8.53562	−0.518502	−0.259251	−	0.965810i	$-0.583476\pi$
$271$	−8.53562	−0.518502	−0.259251	+	0.965810i	$0.583476\pi$
$272$	−30.2064	−1.83153
$273$	−12.8101	−0.775303
$274$	20.0820	1.21320
$275$	23.6521	1.42628
$276$	8.78021	0.528507
$277$	−10.1024	−0.606993	−0.303496	−	0.952833i	$-0.598154\pi$
$277$	−10.1024	−0.606993	−0.303496	+	0.952833i	$0.598154\pi$
$278$	2.66316	0.159726
$279$	2.69770	0.161507
$280$	8.52850	0.509676
$281$	22.4709	1.34050	0.670250	−	0.742135i	$-0.266187\pi$
$281$	22.4709	1.34050	0.670250	+	0.742135i	$0.266187\pi$
$282$	−10.8238	−0.644550
$283$	11.4337	0.679663	0.339831	−	0.940486i	$-0.389630\pi$
$283$	11.4337	0.679663	0.339831	+	0.940486i	$0.389630\pi$
$284$	−7.53097	−0.446881
$285$	4.69363	0.278026
$286$	−56.3087	−3.32960
$287$	14.9385	0.881794
$288$	14.8821	0.876939
$289$	21.4753	1.26325
$290$	−2.97546	−0.174725
$291$	3.54108	0.207582
$292$	−6.96348	−0.407507
$293$	−10.7653	−0.628917	−0.314458	−	0.949271i	$-0.601823\pi$
$293$	−10.7653	−0.628917	−0.314458	+	0.949271i	$0.601823\pi$
$294$	−2.66381	−0.155357
$295$	−30.9493	−1.80194
$296$	1.62915	0.0946922
$297$	−21.5008	−1.24760
$298$	2.90194	0.168105
$299$	−48.4822	−2.80380
$300$	5.82540	0.336330
$301$	2.51392	0.144900
$302$	0.0352253	0.00202699
$303$	−10.8516	−0.623409
$304$	8.41350	0.482547
$305$	3.30255	0.189104
$306$	−25.7025	−1.46932
$307$	14.8402	0.846973	0.423487	−	0.905902i	$-0.360806\pi$
$307$	14.8402	0.846973	0.423487	+	0.905902i	$0.360806\pi$
$308$	14.9040	0.849232
$309$	0.860083	0.0489284
$310$	6.91133	0.392537
$311$	3.55828	0.201772	0.100886	−	0.994898i	$-0.467832\pi$
$311$	3.55828	0.201772	0.100886	+	0.994898i	$0.467832\pi$
$312$	6.51305	0.368729
$313$	24.6150	1.39132	0.695662	−	0.718369i	$-0.255111\pi$
$313$	24.6150	1.39132	0.695662	+	0.718369i	$0.255111\pi$
$314$	7.90556	0.446136
$315$	16.4523	0.926984
$316$	12.6334	0.710683
$317$	9.14888	0.513852	0.256926	−	0.966431i	$-0.417290\pi$
$317$	9.14888	0.513852	0.256926	+	0.966431i	$0.417290\pi$
$318$	−1.96042	−0.109935
$319$	2.44195	0.136723
$320$	7.36354	0.411635
$321$	−6.95889	−0.388407
$322$	31.6913	1.76609
$323$	−10.7167	−0.596292
$324$	3.93234	0.218463
$325$	−32.1665	−1.78427
$326$	38.5570	2.13547
$327$	−5.40708	−0.299012
$328$	−7.59521	−0.419375
$329$	−15.8192	−0.872142
$330$	−23.6687	−1.30292
$331$	−11.1143	−0.610896	−0.305448	−	0.952209i	$-0.598806\pi$
$331$	−11.1143	−0.610896	−0.305448	+	0.952209i	$0.598806\pi$
$332$	−11.1548	−0.612202
$333$	3.14279	0.172224
$334$	32.4004	1.77287
$335$	−13.4066	−0.732479
$336$	−9.65204	−0.526562
$337$	−26.6108	−1.44958	−0.724791	−	0.688969i	$-0.758064\pi$
$337$	−26.6108	−1.44958	−0.724791	+	0.688969i	$0.758064\pi$
$338$	52.7463	2.86902
$339$	4.56643	0.248014
$340$	−26.6632	−1.44602
$341$	−5.67210	−0.307161
$342$	7.15903	0.387116
$343$	−20.0245	−1.08122
$344$	−1.27816	−0.0689136
$345$	−20.3789	−1.09716
$346$	19.6322	1.05543
$347$	10.9038	0.585346	0.292673	−	0.956213i	$-0.405455\pi$
$347$	10.9038	0.585346	0.292673	+	0.956213i	$0.405455\pi$
$348$	0.601439	0.0322405
$349$	−28.1512	−1.50690	−0.753449	−	0.657506i	$-0.771612\pi$
$349$	−28.1512	−1.50690	−0.753449	+	0.657506i	$0.771612\pi$
$350$	21.0262	1.12390
$351$	29.2407	1.56075
$352$	−31.2907	−1.66780
$353$	26.9861	1.43632	0.718161	−	0.695877i	$-0.244984\pi$
$353$	26.9861	1.43632	0.718161	+	0.695877i	$0.244984\pi$
$354$	15.4497	0.821141
$355$	17.4794	0.927710
$356$	−24.5509	−1.30120
$357$	12.2943	0.650681
$358$	−13.8564	−0.732331
$359$	22.3930	1.18185	0.590927	−	0.806725i	$-0.298762\pi$
$359$	22.3930	1.18185	0.590927	+	0.806725i	$0.298762\pi$
$360$	−8.36488	−0.440868
$361$	−16.0150	−0.842897
$362$	10.7027	0.562522
$363$	9.96384	0.522966
$364$	−20.2691	−1.06239
$365$	16.1623	0.845971
$366$	−1.64861	−0.0861744
$367$	−15.6050	−0.814575	−0.407287	−	0.913300i	$-0.633525\pi$
$367$	−15.6050	−0.814575	−0.407287	+	0.913300i	$0.633525\pi$
$368$	−36.5300	−1.90426
$369$	−14.6519	−0.762749
$370$	8.05162	0.418584
$371$	−2.86518	−0.148753
$372$	−1.39701	−0.0724316
$373$	14.2418	0.737412	0.368706	−	0.929546i	$-0.379801\pi$
$373$	14.2418	0.737412	0.368706	+	0.929546i	$0.379801\pi$
$374$	54.0413	2.79441
$375$	0.0626439	0.00323492
$376$	8.04297	0.414785
$377$	−3.32100	−0.171040
$378$	−19.1137	−0.983105
$379$	−15.1257	−0.776955	−0.388477	−	0.921458i	$-0.626999\pi$
$379$	−15.1257	−0.776955	−0.388477	+	0.921458i	$0.626999\pi$
$380$	7.42661	0.380977
$381$	−9.42102	−0.482654
$382$	10.6059	0.542647
$383$	25.3522	1.29544	0.647719	−	0.761879i	$-0.275723\pi$
$383$	25.3522	1.29544	0.647719	+	0.761879i	$0.275723\pi$
$384$	7.65021	0.390398
$385$	−34.5921	−1.76298
$386$	−37.3639	−1.90177
$387$	−2.46569	−0.125338
$388$	5.60297	0.284448
$389$	22.5206	1.14184	0.570919	−	0.821006i	$-0.306587\pi$
$389$	22.5206	1.14184	0.570919	+	0.821006i	$0.306587\pi$
$390$	32.1890	1.62995
$391$	46.5299	2.35312
$392$	1.97943	0.0999761
$393$	−4.67920	−0.236034
$394$	21.5490	1.08562
$395$	−29.3221	−1.47536
$396$	−14.6180	−0.734583
$397$	−30.5766	−1.53459	−0.767297	−	0.641292i	$-0.778399\pi$
$397$	−30.5766	−1.53459	−0.767297	+	0.641292i	$0.778399\pi$
$398$	7.58020	0.379961
$399$	−3.42437	−0.171433
$400$	−24.2365	−1.21183
$401$	−37.2066	−1.85801	−0.929005	−	0.370067i	$-0.879335\pi$
$401$	−37.2066	−1.85801	−0.929005	+	0.370067i	$0.879335\pi$
$402$	6.69247	0.333790
$403$	7.71395	0.384259
$404$	−17.1703	−0.854253
$405$	−9.12696	−0.453523
$406$	2.17083	0.107737
$407$	−6.60792	−0.327543
$408$	−6.25078	−0.309460
$409$	15.8367	0.783075	0.391538	−	0.920162i	$-0.371943\pi$
$409$	15.8367	0.783075	0.391538	+	0.920162i	$0.371943\pi$
$410$	−37.5373	−1.85383
$411$	9.42150	0.464728
$412$	1.36089	0.0670462
$413$	22.5799	1.11109
$414$	−31.0833	−1.52766
$415$	25.8904	1.27091
$416$	42.5548	2.08642
$417$	1.24943	0.0611847
$418$	−15.0523	−0.736234
$419$	−2.02953	−0.0991490	−0.0495745	−	0.998770i	$-0.515787\pi$
$419$	−2.02953	−0.0991490	−0.0495745	+	0.998770i	$0.515787\pi$
$420$	−8.51988	−0.415727
$421$	−8.82234	−0.429975	−0.214987	−	0.976617i	$-0.568971\pi$
$421$	−8.82234	−0.429975	−0.214987	+	0.976617i	$0.568971\pi$
$422$	0.284090	0.0138293
$423$	15.5157	0.754400
$424$	1.45674	0.0707458
$425$	30.8712	1.49747
$426$	−8.72560	−0.422757
$427$	−2.40947	−0.116603
$428$	−11.0109	−0.532231
$429$	−26.4173	−1.27544
$430$	−6.31694	−0.304630
$431$	−22.6436	−1.09070	−0.545351	−	0.838208i	$-0.683604\pi$
$431$	−22.6436	−1.09070	−0.545351	+	0.838208i	$0.683604\pi$
$432$	22.0320	1.06002
$433$	−8.79535	−0.422678	−0.211339	−	0.977413i	$-0.567782\pi$
$433$	−8.79535	−0.422678	−0.211339	+	0.977413i	$0.567782\pi$
$434$	−5.04237	−0.242041
$435$	−1.39594	−0.0669303
$436$	−8.55550	−0.409734
$437$	−12.9602	−0.619969
$438$	−8.06809	−0.385508
$439$	17.8100	0.850023	0.425011	−	0.905188i	$-0.360270\pi$
$439$	17.8100	0.850023	0.425011	+	0.905188i	$0.360270\pi$
$440$	17.5877	0.838461
$441$	3.81851	0.181834
$442$	−73.4952	−3.49581
$443$	−32.0935	−1.52481	−0.762404	−	0.647101i	$-0.775981\pi$
$443$	−32.0935	−1.52481	−0.762404	+	0.647101i	$0.775981\pi$
$444$	−1.62750	−0.0772377
$445$	56.9827	2.70124
$446$	14.4439	0.683939
$447$	1.36145	0.0643945
$448$	−5.37229	−0.253817
$449$	−32.1260	−1.51612	−0.758061	−	0.652184i	$-0.773853\pi$
$449$	−32.1260	−1.51612	−0.758061	+	0.652184i	$0.773853\pi$
$450$	−20.6228	−0.972168
$451$	30.8066	1.45063
$452$	7.22535	0.339852
$453$	0.0165260	0.000776459 0
$454$	6.48523	0.304367
$455$	47.0447	2.20549
$456$	1.74106	0.0815324
$457$	−23.5992	−1.10393	−0.551963	−	0.833869i	$-0.686121\pi$
$457$	−23.5992	−1.10393	−0.551963	+	0.833869i	$0.686121\pi$
$458$	−22.0401	−1.02987
$459$	−28.0633	−1.30988
$460$	−32.2451	−1.50343
$461$	17.1609	0.799264	0.399632	−	0.916676i	$-0.369138\pi$
$461$	17.1609	0.799264	0.399632	+	0.916676i	$0.369138\pi$
$462$	17.2682	0.803388
$463$	−39.3784	−1.83007	−0.915036	−	0.403373i	$-0.867838\pi$
$463$	−39.3784	−1.83007	−0.915036	+	0.403373i	$0.867838\pi$
$464$	−2.50228	−0.116165
$465$	3.24246	0.150366
$466$	19.7872	0.916623
$467$	−27.5136	−1.27318	−0.636589	−	0.771203i	$-0.719655\pi$
$467$	−27.5136	−1.27318	−0.636589	+	0.771203i	$0.719655\pi$
$468$	19.8802	0.918964
$469$	9.78115	0.451652
$470$	39.7502	1.83354
$471$	3.70891	0.170897
$472$	−11.4803	−0.528425
$473$	5.18428	0.238374
$474$	14.6374	0.672319
$475$	−8.59868	−0.394534
$476$	19.4529	0.891623
$477$	2.81021	0.128671
$478$	−43.6592	−1.99693
$479$	−19.3130	−0.882433	−0.441216	−	0.897401i	$-0.645453\pi$
$479$	−19.3130	−0.882433	−0.441216	+	0.897401i	$0.645453\pi$
$480$	17.8874	0.816443
$481$	8.98666	0.409756
$482$	−16.2369	−0.739568
$483$	14.8680	0.676519
$484$	15.7656	0.716616
$485$	−13.0045	−0.590505
$486$	29.4387	1.33537
$487$	−18.9101	−0.856900	−0.428450	−	0.903566i	$-0.640940\pi$
$487$	−18.9101	−0.856900	−0.428450	+	0.903566i	$0.640940\pi$
$488$	1.22505	0.0554554
$489$	18.0891	0.818016
$490$	9.78277	0.441941
$491$	20.0000	0.902589	0.451295	−	0.892375i	$-0.350962\pi$
$491$	20.0000	0.902589	0.451295	+	0.892375i	$0.350962\pi$
$492$	7.58753	0.342072
$493$	3.18727	0.143548
$494$	20.4709	0.921030
$495$	33.9285	1.52497
$496$	5.81224	0.260977
$497$	−12.7526	−0.572033
$498$	−12.9243	−0.579153
$499$	−18.9045	−0.846282	−0.423141	−	0.906064i	$-0.639073\pi$
$499$	−18.9045	−0.846282	−0.423141	+	0.906064i	$0.639073\pi$
$500$	0.0991201	0.00443278
$501$	15.2007	0.679117
$502$	−20.5365	−0.916587
$503$	39.0236	1.73998	0.869988	−	0.493072i	$-0.164126\pi$
$503$	39.0236	1.73998	0.869988	+	0.493072i	$0.164126\pi$
$504$	6.10284	0.271842
$505$	39.8523	1.77340
$506$	65.3546	2.90537
$507$	24.7460	1.09901
$508$	−14.9067	−0.661376
$509$	−35.0187	−1.55218	−0.776088	−	0.630624i	$-0.782799\pi$
$509$	−35.0187	−1.55218	−0.776088	+	0.630624i	$0.782799\pi$
$510$	−30.8928	−1.36796
$511$	−11.7916	−0.521632
$512$	20.6524	0.912714
$513$	7.81658	0.345110
$514$	48.7954	2.15227
$515$	−3.15863	−0.139186
$516$	1.27686	0.0562108
$517$	−32.6228	−1.43475
$518$	−5.87429	−0.258102
$519$	9.21048	0.404295
$520$	−23.9190	−1.04892
$521$	14.6043	0.639828	0.319914	−	0.947447i	$-0.396346\pi$
$521$	14.6043	0.639828	0.319914	+	0.947447i	$0.396346\pi$
$522$	−2.12918	−0.0931919
$523$	−7.00829	−0.306451	−0.153225	−	0.988191i	$-0.548966\pi$
$523$	−7.00829	−0.306451	−0.153225	+	0.988191i	$0.548966\pi$
$524$	−7.40379	−0.323436
$525$	9.86448	0.430521
$526$	21.0432	0.917527
$527$	−7.40332	−0.322494
$528$	−19.9047	−0.866240
$529$	33.2709	1.44656
$530$	7.19957	0.312729
$531$	−22.1467	−0.961086
$532$	−5.41830	−0.234913
$533$	−41.8965	−1.81474
$534$	−28.4454	−1.23095
$535$	25.5563	1.10490
$536$	−4.97304	−0.214803
$537$	−6.50073	−0.280527
$538$	−27.0210	−1.16496
$539$	−8.02867	−0.345819
$540$	19.4477	0.836897
$541$	−8.34301	−0.358694	−0.179347	−	0.983786i	$-0.557398\pi$
$541$	−8.34301	−0.358694	−0.179347	+	0.983786i	$0.557398\pi$
$542$	−15.6481	−0.672144
$543$	5.02120	0.215480
$544$	−40.8412	−1.75105
$545$	19.8574	0.850595
$546$	−23.4844	−1.00504
$547$	−16.0590	−0.686634	−0.343317	−	0.939220i	$-0.611551\pi$
$547$	−16.0590	−0.686634	−0.343317	+	0.939220i	$0.611551\pi$
$548$	14.9074	0.636813
$549$	2.36325	0.100861
$550$	43.3608	1.84891
$551$	−0.887764	−0.0378200
$552$	−7.55936	−0.321748
$553$	21.3928	0.909715
$554$	−18.5204	−0.786857
$555$	3.77743	0.160343
$556$	1.97694	0.0838410
$557$	44.1684	1.87147	0.935737	−	0.352698i	$-0.114736\pi$
$557$	44.1684	1.87147	0.935737	+	0.352698i	$0.114736\pi$
$558$	4.94562	0.209365
$559$	−7.05053	−0.298206
$560$	35.4468	1.49790
$561$	25.3536	1.07043
$562$	41.1953	1.73772
$563$	11.6427	0.490680	0.245340	−	0.969437i	$-0.421100\pi$
$563$	11.6427	0.490680	0.245340	+	0.969437i	$0.421100\pi$
$564$	−8.03484	−0.338328
$565$	−16.7701	−0.705522
$566$	20.9611	0.881060
$567$	6.65884	0.279645
$568$	6.48382	0.272055
$569$	−17.4820	−0.732884	−0.366442	−	0.930441i	$-0.619424\pi$
$569$	−17.4820	−0.732884	−0.366442	+	0.930441i	$0.619424\pi$
$570$	8.60470	0.360411
$571$	4.66273	0.195129	0.0975645	−	0.995229i	$-0.468895\pi$
$571$	4.66273	0.195129	0.0975645	+	0.995229i	$0.468895\pi$
$572$	−41.7995	−1.74773
$573$	4.97580	0.207867
$574$	27.3864	1.14309
$575$	37.3340	1.55693
$576$	5.26921	0.219551
$577$	30.4075	1.26588	0.632940	−	0.774201i	$-0.281848\pi$
$577$	30.4075	1.26588	0.632940	+	0.774201i	$0.281848\pi$
$578$	39.3700	1.63758
$579$	−17.5294	−0.728495
$580$	−2.20877	−0.0917141
$581$	−18.8891	−0.783653
$582$	6.49177	0.269093
$583$	−5.90865	−0.244711
$584$	5.99524	0.248085
$585$	−46.1421	−1.90774
$586$	−19.7358	−0.815277
$587$	24.0377	0.992144	0.496072	−	0.868281i	$-0.334775\pi$
$587$	24.0377	0.992144	0.496072	+	0.868281i	$0.334775\pi$
$588$	−1.97742	−0.0815475
$589$	2.06208	0.0849665
$590$	−56.7385	−2.33589
$591$	10.1097	0.415859
$592$	6.77119	0.278294
$593$	−35.4197	−1.45451	−0.727256	−	0.686367i	$-0.759204\pi$
$593$	−35.4197	−1.45451	−0.727256	+	0.686367i	$0.759204\pi$
$594$	−39.4169	−1.61729
$595$	−45.1503	−1.85098
$596$	2.15419	0.0882393
$597$	3.55627	0.145548
$598$	−88.8812	−3.63462
$599$	−41.2300	−1.68461	−0.842305	−	0.539001i	$-0.818802\pi$
$599$	−41.2300	−1.68461	−0.842305	+	0.539001i	$0.818802\pi$
$600$	−5.01540	−0.204753
$601$	5.91875	0.241431	0.120715	−	0.992687i	$-0.461481\pi$
$601$	5.91875	0.241431	0.120715	+	0.992687i	$0.461481\pi$
$602$	4.60871	0.187837
$603$	−9.59349	−0.390677
$604$	0.0261487	0.00106398
$605$	−36.5919	−1.48767
$606$	−19.8940	−0.808138
$607$	0.847542	0.0344007	0.0172003	−	0.999852i	$-0.494525\pi$
$607$	0.847542	0.0344007	0.0172003	+	0.999852i	$0.494525\pi$
$608$	11.3757	0.461344
$609$	1.01845	0.0412697
$610$	6.05448	0.245139
$611$	44.3664	1.79487
$612$	−19.0797	−0.771251
$613$	13.1885	0.532679	0.266339	−	0.963879i	$-0.414186\pi$
$613$	13.1885	0.532679	0.266339	+	0.963879i	$0.414186\pi$
$614$	27.2061	1.09795
$615$	−17.6107	−0.710131
$616$	−12.8316	−0.517001
$617$	14.7334	0.593144	0.296572	−	0.955011i	$-0.404157\pi$
$617$	14.7334	0.593144	0.296572	+	0.955011i	$0.404157\pi$
$618$	1.57677	0.0634269
$619$	10.7113	0.430525	0.215263	−	0.976556i	$-0.430939\pi$
$619$	10.7113	0.430525	0.215263	+	0.976556i	$0.430939\pi$
$620$	5.13048	0.206045
$621$	−33.9382	−1.36189
$622$	6.52330	0.261561
$623$	−41.5734	−1.66560
$624$	27.0700	1.08367
$625$	−25.1148	−1.00459
$626$	45.1261	1.80360
$627$	−7.06183	−0.282022
$628$	5.86852	0.234179
$629$	−8.62478	−0.343893
$630$	30.1616	1.20167
$631$	−19.0460	−0.758210	−0.379105	−	0.925354i	$-0.623768\pi$
$631$	−19.0460	−0.758210	−0.379105	+	0.925354i	$0.623768\pi$
$632$	−10.8768	−0.432654
$633$	0.133281	0.00529746
$634$	16.7724	0.666117
$635$	34.5984	1.37300
$636$	−1.45527	−0.0577052
$637$	10.9189	0.432621
$638$	4.47675	0.177236
$639$	12.5079	0.494806
$640$	−28.0952	−1.11056
$641$	−7.47507	−0.295247	−0.147624	−	0.989044i	$-0.547162\pi$
$641$	−7.47507	−0.295247	−0.147624	+	0.989044i	$0.547162\pi$
$642$	−12.7575	−0.503500
$643$	−29.8503	−1.17718	−0.588589	−	0.808432i	$-0.700317\pi$
$643$	−29.8503	−1.17718	−0.588589	+	0.808432i	$0.700317\pi$
$644$	23.5253	0.927028
$645$	−2.96360	−0.116692
$646$	−19.6466	−0.772985
$647$	13.4392	0.528349	0.264174	−	0.964475i	$-0.414901\pi$
$647$	13.4392	0.528349	0.264174	+	0.964475i	$0.414901\pi$
$648$	−3.38556	−0.132997
$649$	46.5650	1.82783
$650$	−58.9699	−2.31299
$651$	−2.36563	−0.0927165
$652$	28.6219	1.12092
$653$	32.7397	1.28120	0.640602	−	0.767873i	$-0.278685\pi$
$653$	32.7397	1.28120	0.640602	+	0.767873i	$0.278685\pi$
$654$	−9.91266	−0.387616
$655$	17.1842	0.671443
$656$	−31.5678	−1.23252
$657$	11.5654	0.451210
$658$	−29.0009	−1.13057
$659$	−38.5260	−1.50076	−0.750380	−	0.661007i	$-0.770129\pi$
$659$	−38.5260	−1.50076	−0.750380	+	0.661007i	$0.770129\pi$
$660$	−17.5699	−0.683908
$661$	−24.5572	−0.955166	−0.477583	−	0.878587i	$-0.658487\pi$
$661$	−24.5572	−0.955166	−0.477583	+	0.878587i	$0.658487\pi$
$662$	−20.3755	−0.791917
$663$	−34.4804	−1.33911
$664$	9.60381	0.372700
$665$	12.5759	0.487673
$666$	5.76159	0.223257
$667$	3.85452	0.149248
$668$	24.0517	0.930589
$669$	6.77638	0.261990
$670$	−24.5779	−0.949527
$671$	−4.96888	−0.191822
$672$	−13.0503	−0.503425
$673$	43.6914	1.68418	0.842090	−	0.539337i	$-0.181325\pi$
$673$	43.6914	1.68418	0.842090	+	0.539337i	$0.181325\pi$
$674$	−48.7848	−1.87912
$675$	−22.5170	−0.866678
$676$	39.1551	1.50596
$677$	32.3720	1.24416	0.622079	−	0.782955i	$-0.286288\pi$
$677$	32.3720	1.24416	0.622079	+	0.782955i	$0.286288\pi$
$678$	8.37150	0.321506
$679$	9.48783	0.364110
$680$	22.9558	0.880315
$681$	3.04256	0.116591
$682$	−10.3985	−0.398179
$683$	−47.1388	−1.80371	−0.901857	−	0.432034i	$-0.857796\pi$
$683$	−47.1388	−1.80371	−0.901857	+	0.432034i	$0.857796\pi$
$684$	5.31435	0.203199
$685$	−34.6002	−1.32200
$686$	−36.7104	−1.40161
$687$	−10.3401	−0.394501
$688$	−5.31237	−0.202532
$689$	8.03566	0.306134
$690$	−37.3601	−1.42227
$691$	44.3229	1.68612	0.843062	−	0.537817i	$-0.180751\pi$
$691$	44.3229	1.68612	0.843062	+	0.537817i	$0.180751\pi$
$692$	14.5735	0.554003
$693$	−24.7535	−0.940308
$694$	19.9896	0.758795
$695$	−4.58849	−0.174051
$696$	−0.517812	−0.0196276
$697$	40.2094	1.52304
$698$	−51.6088	−1.95342
$699$	9.28319	0.351122
$700$	15.6083	0.589940
$701$	10.6787	0.403330	0.201665	−	0.979455i	$-0.435365\pi$
$701$	10.6787	0.403330	0.201665	+	0.979455i	$0.435365\pi$
$702$	53.6062	2.02324
$703$	2.40230	0.0906043
$704$	−11.0789	−0.417551
$705$	18.6489	0.702358
$706$	49.4728	1.86193
$707$	−29.0754	−1.09349
$708$	11.4687	0.431021
$709$	17.2970	0.649604	0.324802	−	0.945782i	$-0.394702\pi$
$709$	17.2970	0.649604	0.324802	+	0.945782i	$0.394702\pi$
$710$	32.0445	1.20261
$711$	−20.9824	−0.786901
$712$	21.1372	0.792150
$713$	−8.95319	−0.335300
$714$	22.5387	0.843491
$715$	97.0169	3.62822
$716$	−10.2860	−0.384404
$717$	−20.4828	−0.764944
$718$	41.0524	1.53206
$719$	30.0654	1.12125	0.560624	−	0.828070i	$-0.310561\pi$
$719$	30.0654	1.12125	0.560624	+	0.828070i	$0.310561\pi$
$720$	−34.7667	−1.29568
$721$	2.30447	0.0858230
$722$	−29.3599	−1.09266
$723$	−7.61755	−0.283300
$724$	7.94492	0.295271
$725$	2.55735	0.0949778
$726$	18.2664	0.677931
$727$	−19.9497	−0.739893	−0.369946	−	0.929053i	$-0.620624\pi$
$727$	−19.9497	−0.739893	−0.369946	+	0.929053i	$0.620624\pi$
$728$	17.4508	0.646769
$729$	5.14263	0.190468
$730$	29.6298	1.09665
$731$	6.76662	0.250273
$732$	−1.22381	−0.0452334
$733$	6.99405	0.258331	0.129166	−	0.991623i	$-0.458770\pi$
$733$	6.99405	0.258331	0.129166	+	0.991623i	$0.458770\pi$
$734$	−28.6082	−1.05595
$735$	4.58960	0.169290
$736$	−49.3912	−1.82058
$737$	20.1710	0.743007
$738$	−26.8610	−0.988766
$739$	10.5049	0.386430	0.193215	−	0.981156i	$-0.438109\pi$
$739$	10.5049	0.386430	0.193215	+	0.981156i	$0.438109\pi$
$740$	5.97694	0.219717
$741$	9.60397	0.352810
$742$	−5.25265	−0.192831
$743$	10.4318	0.382705	0.191352	−	0.981521i	$-0.438713\pi$
$743$	10.4318	0.382705	0.191352	+	0.981521i	$0.438713\pi$
$744$	1.20276	0.0440954
$745$	−4.99989	−0.183182
$746$	26.1091	0.955922
$747$	18.5267	0.677857
$748$	40.1163	1.46680
$749$	−18.6453	−0.681286
$750$	0.114843	0.00419349
$751$	34.2232	1.24882	0.624411	−	0.781096i	$-0.285339\pi$
$751$	34.2232	1.24882	0.624411	+	0.781096i	$0.285339\pi$
$752$	33.4288	1.21902
$753$	−9.63471	−0.351108
$754$	−6.08831	−0.221723
$755$	−0.0606912	−0.00220878
$756$	−14.1887	−0.516037
$757$	−10.5262	−0.382583	−0.191291	−	0.981533i	$-0.561268\pi$
$757$	−10.5262	−0.382583	−0.191291	+	0.981533i	$0.561268\pi$
$758$	−27.7295	−1.00718
$759$	30.6612	1.11293
$760$	−6.39397	−0.231934
$761$	30.5687	1.10811	0.554057	−	0.832479i	$-0.313079\pi$
$761$	30.5687	1.10811	0.554057	+	0.832479i	$0.313079\pi$
$762$	−17.2713	−0.625673
$763$	−14.4875	−0.524483
$764$	7.87309	0.284838
$765$	44.2841	1.60109
$766$	46.4776	1.67930
$767$	−63.3275	−2.28663
$768$	18.0350	0.650784
$769$	−19.3406	−0.697439	−0.348719	−	0.937227i	$-0.613383\pi$
$769$	−19.3406	−0.697439	−0.348719	+	0.937227i	$0.613383\pi$
$770$	−63.4168	−2.28538
$771$	22.8924	0.824451
$772$	−27.7363	−0.998251
$773$	17.5619	0.631656	0.315828	−	0.948816i	$-0.397718\pi$
$773$	17.5619	0.631656	0.315828	+	0.948816i	$0.397718\pi$
$774$	−4.52029	−0.162478
$775$	−5.94016	−0.213377
$776$	−4.82390	−0.173168
$777$	−2.75594	−0.0988686
$778$	41.2863	1.48019
$779$	−11.1997	−0.401271
$780$	23.8948	0.855570
$781$	−26.2988	−0.941044
$782$	85.3021	3.05040
$783$	−2.32475	−0.0830797
$784$	8.22704	0.293823
$785$	−13.6208	−0.486149
$786$	−8.57825	−0.305976
$787$	−42.8157	−1.52621	−0.763107	−	0.646272i	$-0.776327\pi$
$787$	−42.8157	−1.52621	−0.763107	+	0.646272i	$0.776327\pi$
$788$	15.9964	0.569848
$789$	9.87245	0.351468
$790$	−53.7555	−1.91253
$791$	12.2351	0.435030
$792$	12.5854	0.447204
$793$	6.75759	0.239969
$794$	−56.0552	−1.98932
$795$	3.37769	0.119794
$796$	5.62700	0.199444
$797$	21.7217	0.769422	0.384711	−	0.923037i	$-0.374301\pi$
$797$	21.7217	0.769422	0.384711	+	0.923037i	$0.374301\pi$
$798$	−6.27781	−0.222232
$799$	−42.5799	−1.50637
$800$	−32.7695	−1.15858
$801$	40.7758	1.44074
$802$	−68.2099	−2.40857
$803$	−24.3171	−0.858130
$804$	4.96801	0.175208
$805$	−54.6024	−1.92448
$806$	14.1418	0.498123
$807$	−12.6769	−0.446249
$808$	14.7828	0.520058
$809$	36.3521	1.27807	0.639036	−	0.769177i	$-0.279333\pi$
$809$	36.3521	1.27807	0.639036	+	0.769177i	$0.279333\pi$
$810$	−16.7322	−0.587910
$811$	32.6168	1.14533	0.572665	−	0.819790i	$-0.305910\pi$
$811$	32.6168	1.14533	0.572665	+	0.819790i	$0.305910\pi$
$812$	1.61147	0.0565516
$813$	−7.34134	−0.257472
$814$	−12.1141	−0.424600
$815$	−66.4316	−2.32700
$816$	−25.9800	−0.909481
$817$	−1.88474	−0.0659385
$818$	29.0330	1.01512
$819$	33.6643	1.17633
$820$	−27.8650	−0.973087
$821$	−15.3986	−0.537415	−0.268707	−	0.963222i	$-0.586596\pi$
$821$	−15.3986	−0.537415	−0.268707	+	0.963222i	$0.586596\pi$
$822$	17.2722	0.602436
$823$	44.7193	1.55882	0.779408	−	0.626517i	$-0.215520\pi$
$823$	44.7193	1.55882	0.779408	+	0.626517i	$0.215520\pi$
$824$	−1.17166	−0.0408168
$825$	20.3428	0.708245
$826$	41.3952	1.44032
$827$	−46.2796	−1.60930	−0.804650	−	0.593750i	$-0.797647\pi$
$827$	−46.2796	−1.60930	−0.804650	+	0.593750i	$0.797647\pi$
$828$	−23.0740	−0.801876
$829$	46.8140	1.62592	0.812958	−	0.582322i	$-0.197856\pi$
$829$	46.8140	1.62592	0.812958	+	0.582322i	$0.197856\pi$
$830$	47.4642	1.64751
$831$	−8.68888	−0.301414
$832$	15.0671	0.522357
$833$	−10.4792	−0.363082
$834$	2.29054	0.0793150
$835$	−55.8241	−1.93187
$836$	−11.1738	−0.386453
$837$	5.39987	0.186647
$838$	−3.72068	−0.128529
$839$	12.4136	0.428567	0.214283	−	0.976772i	$-0.431258\pi$
$839$	12.4136	0.428567	0.214283	+	0.976772i	$0.431258\pi$
$840$	7.33522	0.253089
$841$	−28.7360	−0.990895
$842$	−16.1738	−0.557384
$843$	19.3268	0.665651
$844$	0.210888	0.00725907
$845$	−90.8790	−3.12633
$846$	28.4445	0.977943
$847$	26.6967	0.917310
$848$	6.05463	0.207917
$849$	9.83393	0.337500
$850$	56.5953	1.94120
$851$	−10.4304	−0.357548
$852$	−6.47726	−0.221907
$853$	35.0631	1.20054	0.600269	−	0.799798i	$-0.295060\pi$
$853$	35.0631	1.20054	0.600269	+	0.799798i	$0.295060\pi$
$854$	−4.41722	−0.151154
$855$	−12.3346	−0.421835
$856$	9.47987	0.324015
$857$	8.68396	0.296639	0.148319	−	0.988940i	$-0.452614\pi$
$857$	8.68396	0.296639	0.148319	+	0.988940i	$0.452614\pi$
$858$	−48.4302	−1.65338
$859$	−28.7863	−0.982174	−0.491087	−	0.871110i	$-0.663400\pi$
$859$	−28.7863	−0.982174	−0.491087	+	0.871110i	$0.663400\pi$
$860$	−4.68924	−0.159902
$861$	12.8484	0.437872
$862$	−41.5118	−1.41390
$863$	−35.8378	−1.21993	−0.609966	−	0.792427i	$-0.708817\pi$
$863$	−35.8378	−1.21993	−0.609966	+	0.792427i	$0.708817\pi$
$864$	29.7889	1.01344
$865$	−33.8252	−1.15009
$866$	−16.1243	−0.547925
$867$	18.4705	0.627292
$868$	−3.74309	−0.127049
$869$	44.1168	1.49656
$870$	−2.55914	−0.0867631
$871$	−27.4321	−0.929503
$872$	7.36590	0.249441
$873$	−9.30580	−0.314953
$874$	−23.7595	−0.803679
$875$	0.167846	0.00567422
$876$	−5.98917	−0.202355
$877$	11.0555	0.373317	0.186658	−	0.982425i	$-0.440234\pi$
$877$	11.0555	0.373317	0.186658	+	0.982425i	$0.440234\pi$
$878$	32.6505	1.10190
$879$	−9.25907	−0.312301
$880$	73.0994	2.46418
$881$	47.3888	1.59657	0.798285	−	0.602279i	$-0.205741\pi$
$881$	47.3888	1.59657	0.798285	+	0.602279i	$0.205741\pi$
$882$	7.00037	0.235715
$883$	8.36438	0.281484	0.140742	−	0.990046i	$-0.455051\pi$
$883$	8.36438	0.281484	0.140742	+	0.990046i	$0.455051\pi$
$884$	−54.5575	−1.83497
$885$	−26.6189	−0.894786
$886$	−58.8361	−1.97664
$887$	−20.6392	−0.692997	−0.346499	−	0.938050i	$-0.612630\pi$
$887$	−20.6392	−0.692997	−0.346499	+	0.938050i	$0.612630\pi$
$888$	1.40120	0.0470213
$889$	−25.2423	−0.846599
$890$	104.465	3.50167
$891$	13.7320	0.460041
$892$	10.7221	0.359003
$893$	11.8600	0.396878
$894$	2.49591	0.0834758
$895$	23.8737	0.798011
$896$	20.4976	0.684778
$897$	−41.6988	−1.39228
$898$	−58.8958	−1.96538
$899$	−0.613288	−0.0204543
$900$	−15.3089	−0.510296
$901$	−7.71208	−0.256926
$902$	56.4770	1.88048
$903$	2.16218	0.0719530
$904$	−6.22069	−0.206897
$905$	−18.4402	−0.612973
$906$	0.0302967	0.00100654
$907$	23.8350	0.791430	0.395715	−	0.918373i	$-0.370497\pi$
$907$	23.8350	0.791430	0.395715	+	0.918373i	$0.370497\pi$
$908$	4.81417	0.159764
$909$	28.5175	0.945867
$910$	86.2458	2.85902
$911$	−26.5737	−0.880427	−0.440214	−	0.897893i	$-0.645097\pi$
$911$	−26.5737	−0.880427	−0.440214	+	0.897893i	$0.645097\pi$
$912$	7.23631	0.239618
$913$	−38.9536	−1.28918
$914$	−43.2639	−1.43104
$915$	2.84047	0.0939030
$916$	−16.3610	−0.540582
$917$	−12.5373	−0.414017
$918$	−51.4476	−1.69802
$919$	32.2187	1.06280	0.531398	−	0.847122i	$-0.321667\pi$
$919$	32.2187	1.06280	0.531398	+	0.847122i	$0.321667\pi$
$920$	27.7615	0.915271
$921$	12.7638	0.420581
$922$	31.4607	1.03610
$923$	35.7659	1.17725
$924$	12.8186	0.421702
$925$	−6.92022	−0.227535
$926$	−72.1914	−2.37236
$927$	−2.26026	−0.0742366
$928$	−3.38326	−0.111061
$929$	−36.7516	−1.20578	−0.602890	−	0.797824i	$-0.705984\pi$
$929$	−36.7516	−1.20578	−0.602890	+	0.797824i	$0.705984\pi$
$930$	5.94432	0.194922
$931$	2.91881	0.0956600
$932$	14.6886	0.481140
$933$	3.06042	0.100194
$934$	−50.4399	−1.65045
$935$	−93.1102	−3.04503
$936$	−17.1160	−0.559453
$937$	−34.6767	−1.13284	−0.566420	−	0.824117i	$-0.691672\pi$
$937$	−34.6767	−1.13284	−0.566420	+	0.824117i	$0.691672\pi$
$938$	17.9315	0.585485
$939$	21.1710	0.690889
$940$	29.5077	0.962435
$941$	−6.11312	−0.199282	−0.0996410	−	0.995023i	$-0.531769\pi$
$941$	−6.11312	−0.199282	−0.0996410	+	0.995023i	$0.531769\pi$
$942$	6.79944	0.221538
$943$	48.6271	1.58352
$944$	−47.7155	−1.55301
$945$	32.9319	1.07128
$946$	9.50420	0.309008
$947$	15.4830	0.503131	0.251565	−	0.967840i	$-0.419055\pi$
$947$	15.4830	0.503131	0.251565	+	0.967840i	$0.419055\pi$
$948$	10.8658	0.352904
$949$	33.0708	1.07352
$950$	−15.7637	−0.511443
$951$	7.86879	0.255163
$952$	−16.7481	−0.542808
$953$	11.4444	0.370721	0.185361	−	0.982671i	$-0.440655\pi$
$953$	11.4444	0.370721	0.185361	+	0.982671i	$0.440655\pi$
$954$	5.15188	0.166798
$955$	−18.2735	−0.591315
$956$	−32.4094	−1.04820
$957$	2.10028	0.0678923
$958$	−35.4060	−1.14391
$959$	25.2436	0.815157
$960$	6.33326	0.204405
$961$	−29.5755	−0.954047
$962$	16.4750	0.531175
$963$	18.2876	0.589310
$964$	−12.0531	−0.388203
$965$	64.3760	2.07234
$966$	27.2572	0.876985
$967$	−53.2569	−1.71263	−0.856313	−	0.516457i	$-0.827251\pi$
$967$	−53.2569	−1.71263	−0.856313	+	0.516457i	$0.827251\pi$
$968$	−13.5734	−0.436266
$969$	−9.21723	−0.296100
$970$	−23.8408	−0.765483
$971$	4.22288	0.135519	0.0677593	−	0.997702i	$-0.478415\pi$
$971$	4.22288	0.135519	0.0677593	+	0.997702i	$0.478415\pi$
$972$	21.8532	0.700941
$973$	3.34767	0.107321
$974$	−34.6674	−1.11082
$975$	−27.6658	−0.886016
$976$	5.09165	0.162980
$977$	−8.72391	−0.279103	−0.139551	−	0.990215i	$-0.544566\pi$
$977$	−8.72391	−0.279103	−0.139551	+	0.990215i	$0.544566\pi$
$978$	33.1622	1.06041
$979$	−85.7338	−2.74006
$980$	7.26203	0.231977
$981$	14.2096	0.453676
$982$	36.6655	1.17004
$983$	19.9047	0.634860	0.317430	−	0.948282i	$-0.397180\pi$
$983$	19.9047	0.634860	0.317430	+	0.948282i	$0.397180\pi$
$984$	−6.53251	−0.208249
$985$	−37.1277	−1.18299
$986$	5.84314	0.186084
$987$	−13.6058	−0.433079
$988$	15.1961	0.483453
$989$	8.18319	0.260210
$990$	62.2001	1.97685
$991$	29.0571	0.923029	0.461515	−	0.887133i	$-0.347306\pi$
$991$	29.0571	0.923029	0.461515	+	0.887133i	$0.347306\pi$
$992$	7.85857	0.249510
$993$	−9.55920	−0.303352
$994$	−23.3790	−0.741537
$995$	−13.0603	−0.414039
$996$	−9.59409	−0.304000
$997$	56.0663	1.77564	0.887819	−	0.460193i	$-0.152220\pi$
$997$	56.0663	1.77564	0.887819	+	0.460193i	$0.152220\pi$
$998$	−34.6571	−1.09705
$999$	6.29078	0.199032

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	103.2.a.b.1.5	✓	6
3.2	odd	2		927.2.a.f.1.2		6
4.3	odd	2		1648.2.a.m.1.3		6
5.4	even	2		2575.2.a.k.1.2		6
7.6	odd	2		5047.2.a.d.1.5		6
8.3	odd	2		6592.2.a.be.1.4		6
8.5	even	2		6592.2.a.bd.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
103.2.a.b.1.5	✓	6	1.1	even	1	trivial
927.2.a.f.1.2		6	3.2	odd	2
1648.2.a.m.1.3		6	4.3	odd	2
2575.2.a.k.1.2		6	5.4	even	2
5047.2.a.d.1.5		6	7.6	odd	2
6592.2.a.bd.1.3		6	8.5	even	2
6592.2.a.be.1.4		6	8.3	odd	2

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:	\( N \)	\(=\)	\( 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	103.a (trivial)

\(f(q)\)	\(=\)	\(q+1.83327 q^{2} +0.860083 q^{3} +1.36089 q^{4} -3.15863 q^{5} +1.57677 q^{6} +2.30447 q^{7} -1.17166 q^{8} -2.26026 q^{9} +O(q^{10})\)	\(q+1.83327 q^{2} +0.860083 q^{3} +1.36089 q^{4} -3.15863 q^{5} +1.57677 q^{6} +2.30447 q^{7} -1.17166 q^{8} -2.26026 q^{9} -5.79063 q^{10} +4.75234 q^{11} +1.17048 q^{12} -6.46310 q^{13} +4.22472 q^{14} -2.71668 q^{15} -4.86976 q^{16} +6.20284 q^{17} -4.14367 q^{18} -1.72770 q^{19} -4.29855 q^{20} +1.98204 q^{21} +8.71234 q^{22} +7.50139 q^{23} -1.00773 q^{24} +4.97694 q^{25} -11.8486 q^{26} -4.52426 q^{27} +3.13613 q^{28} +0.513841 q^{29} -4.98042 q^{30} -1.19354 q^{31} -6.58427 q^{32} +4.08741 q^{33} +11.3715 q^{34} -7.27897 q^{35} -3.07596 q^{36} -1.39046 q^{37} -3.16735 q^{38} -5.55880 q^{39} +3.70085 q^{40} +6.48242 q^{41} +3.63361 q^{42} +1.09089 q^{43} +6.46741 q^{44} +7.13931 q^{45} +13.7521 q^{46} -6.86458 q^{47} -4.18840 q^{48} -1.68941 q^{49} +9.12409 q^{50} +5.33496 q^{51} -8.79557 q^{52} -1.24331 q^{53} -8.29420 q^{54} -15.0109 q^{55} -2.70006 q^{56} -1.48597 q^{57} +0.942010 q^{58} +9.79832 q^{59} -3.69711 q^{60} -1.04557 q^{61} -2.18808 q^{62} -5.20870 q^{63} -2.33125 q^{64} +20.4145 q^{65} +7.49333 q^{66} +4.24442 q^{67} +8.44139 q^{68} +6.45182 q^{69} -13.3443 q^{70} -5.53386 q^{71} +2.64826 q^{72} -5.11686 q^{73} -2.54909 q^{74} +4.28058 q^{75} -2.35121 q^{76} +10.9516 q^{77} -10.1908 q^{78} +9.28318 q^{79} +15.3818 q^{80} +2.88953 q^{81} +11.8840 q^{82} -8.19673 q^{83} +2.69733 q^{84} -19.5925 q^{85} +1.99990 q^{86} +0.441946 q^{87} -5.56814 q^{88} -18.0403 q^{89} +13.0883 q^{90} -14.8940 q^{91} +10.2086 q^{92} -1.02654 q^{93} -12.5846 q^{94} +5.45718 q^{95} -5.66302 q^{96} +4.11714 q^{97} -3.09716 q^{98} -10.7415 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 4 q^{2} + 6 q^{4} + 3 q^{5} - 3 q^{6} - 2 q^{7} + 9 q^{8} + 8 q^{9}+O(q^{10}) \) 6 * q + 4 * q^2 + 6 * q^4 + 3 * q^5 - 3 * q^6 - 2 * q^7 + 9 * q^8 + 8 * q^9	\( 6 q + 4 q^{2} + 6 q^{4} + 3 q^{5} - 3 q^{6} - 2 q^{7} + 9 q^{8} + 8 q^{9} - 10 q^{10} - q^{11} - 13 q^{12} - q^{13} - 9 q^{14} - 9 q^{15} + 2 q^{16} + 21 q^{17} - 3 q^{18} - 7 q^{19} - 9 q^{20} - 14 q^{21} - 11 q^{22} + 12 q^{23} - 36 q^{24} + q^{25} - 5 q^{26} - 10 q^{28} + 12 q^{29} + 2 q^{30} - 16 q^{31} + 27 q^{32} + 15 q^{33} + 10 q^{34} + 5 q^{35} - 3 q^{36} - 8 q^{38} + 5 q^{39} - q^{40} + 14 q^{41} + 25 q^{42} - 6 q^{43} - 4 q^{44} + 8 q^{45} + 19 q^{46} + q^{47} - 41 q^{48} - 2 q^{49} + q^{50} - 5 q^{51} - 5 q^{52} + 19 q^{53} + 23 q^{54} - 10 q^{55} - 13 q^{56} + 23 q^{57} + 4 q^{58} + 3 q^{59} + 17 q^{60} + q^{61} + 23 q^{62} - 20 q^{63} + 61 q^{64} + 23 q^{65} + q^{66} - 12 q^{67} + 14 q^{68} - 22 q^{69} - 14 q^{70} - 27 q^{71} + 31 q^{72} - 7 q^{73} + 15 q^{74} - 17 q^{75} - 38 q^{76} + 27 q^{77} - 20 q^{78} - 21 q^{79} - 28 q^{80} - 2 q^{81} + 53 q^{82} - 9 q^{83} + 61 q^{84} - 9 q^{85} - 11 q^{86} - 12 q^{87} - 31 q^{88} - 14 q^{89} - 22 q^{90} - 33 q^{91} + 30 q^{92} - 32 q^{93} - 6 q^{95} - 33 q^{96} - 8 q^{97} + 2 q^{98} - 54 q^{99}+O(q^{100}) \) 6 * q + 4 * q^2 + 6 * q^4 + 3 * q^5 - 3 * q^6 - 2 * q^7 + 9 * q^8 + 8 * q^9 - 10 * q^10 - q^11 - 13 * q^12 - q^13 - 9 * q^14 - 9 * q^15 + 2 * q^16 + 21 * q^17 - 3 * q^18 - 7 * q^19 - 9 * q^20 - 14 * q^21 - 11 * q^22 + 12 * q^23 - 36 * q^24 + q^25 - 5 * q^26 - 10 * q^28 + 12 * q^29 + 2 * q^30 - 16 * q^31 + 27 * q^32 + 15 * q^33 + 10 * q^34 + 5 * q^35 - 3 * q^36 - 8 * q^38 + 5 * q^39 - q^40 + 14 * q^41 + 25 * q^42 - 6 * q^43 - 4 * q^44 + 8 * q^45 + 19 * q^46 + q^47 - 41 * q^48 - 2 * q^49 + q^50 - 5 * q^51 - 5 * q^52 + 19 * q^53 + 23 * q^54 - 10 * q^55 - 13 * q^56 + 23 * q^57 + 4 * q^58 + 3 * q^59 + 17 * q^60 + q^61 + 23 * q^62 - 20 * q^63 + 61 * q^64 + 23 * q^65 + q^66 - 12 * q^67 + 14 * q^68 - 22 * q^69 - 14 * q^70 - 27 * q^71 + 31 * q^72 - 7 * q^73 + 15 * q^74 - 17 * q^75 - 38 * q^76 + 27 * q^77 - 20 * q^78 - 21 * q^79 - 28 * q^80 - 2 * q^81 + 53 * q^82 - 9 * q^83 + 61 * q^84 - 9 * q^85 - 11 * q^86 - 12 * q^87 - 31 * q^88 - 14 * q^89 - 22 * q^90 - 33 * q^91 + 30 * q^92 - 32 * q^93 - 6 * q^95 - 33 * q^96 - 8 * q^97 + 2 * q^98 - 54 * q^99

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