LMFDB - Embedded newform 1859.2.a.k.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1859,2,Mod(1,1859)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1859, 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("1859.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1859 = 11 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1859.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:	$14.8441897358$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.28561300.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 9x^{4} - x^{3} + 22x^{2} + 4x - 12 $ x^6 - 9x^4 - x^3 + 22x^2 + 4*x - 12
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 143)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.58147$ of defining polynomial
Character	$\chi$	$=$	1859.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.498953 q^{2} -0.240597 q^{3} -1.75105 q^{4} +0.581470 q^{5} +0.120047 q^{6} +1.41017 q^{7} +1.87160 q^{8} -2.94211 q^{9} +O(q^{10})$	\(q-0.498953 q^{2} -0.240597 q^{3} -1.75105 q^{4} +0.581470 q^{5} +0.120047 q^{6} +1.41017 q^{7} +1.87160 q^{8} -2.94211 q^{9} -0.290126 q^{10} -1.00000 q^{11} +0.421296 q^{12} -0.703610 q^{14} -0.139900 q^{15} +2.56825 q^{16} +0.451517 q^{17} +1.46798 q^{18} +3.19052 q^{19} -1.01818 q^{20} -0.339283 q^{21} +0.498953 q^{22} -4.03454 q^{23} -0.450300 q^{24} -4.66189 q^{25} +1.42965 q^{27} -2.46928 q^{28} +10.2019 q^{29} +0.0698034 q^{30} -7.10174 q^{31} -5.02463 q^{32} +0.240597 q^{33} -0.225286 q^{34} +0.819973 q^{35} +5.15177 q^{36} +4.68112 q^{37} -1.59192 q^{38} +1.08828 q^{40} -8.86324 q^{41} +0.169286 q^{42} +4.41503 q^{43} +1.75105 q^{44} -1.71075 q^{45} +2.01304 q^{46} +3.77409 q^{47} -0.617913 q^{48} -5.01141 q^{49} +2.32607 q^{50} -0.108634 q^{51} -0.0779742 q^{53} -0.713330 q^{54} -0.581470 q^{55} +2.63927 q^{56} -0.767629 q^{57} -5.09029 q^{58} -7.70134 q^{59} +0.244971 q^{60} -4.32766 q^{61} +3.54344 q^{62} -4.14889 q^{63} -2.62945 q^{64} -0.120047 q^{66} -11.2317 q^{67} -0.790628 q^{68} +0.970696 q^{69} -0.409128 q^{70} -1.98509 q^{71} -5.50645 q^{72} -2.84192 q^{73} -2.33566 q^{74} +1.12164 q^{75} -5.58675 q^{76} -1.41017 q^{77} +14.6900 q^{79} +1.49336 q^{80} +8.48237 q^{81} +4.42234 q^{82} +4.03491 q^{83} +0.594100 q^{84} +0.262544 q^{85} -2.20289 q^{86} -2.45455 q^{87} -1.87160 q^{88} -10.2374 q^{89} +0.853584 q^{90} +7.06466 q^{92} +1.70866 q^{93} -1.88309 q^{94} +1.85519 q^{95} +1.20891 q^{96} -12.5156 q^{97} +2.50046 q^{98} +2.94211 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{3} + 8 q^{4} - 6 q^{5} - 12 q^{6} - 3 q^{7} + 3 q^{8} + 7 q^{9}+O(q^{10}) $ 6 * q + q^3 + 8 * q^4 - 6 * q^5 - 12 * q^6 - 3 * q^7 + 3 * q^8 + 7 * q^9	$ 6 q + q^{3} + 8 q^{4} - 6 q^{5} - 12 q^{6} - 3 q^{7} + 3 q^{8} + 7 q^{9} - 3 q^{10} - 6 q^{11} - 17 q^{12} + 12 q^{14} + 4 q^{15} + 8 q^{16} + 2 q^{17} + 6 q^{18} - 10 q^{19} - 15 q^{20} - 12 q^{21} + 3 q^{23} - 14 q^{24} - 6 q^{25} + 10 q^{27} - 16 q^{28} + 3 q^{29} + 19 q^{30} - 5 q^{31} + q^{32} - q^{33} + 5 q^{34} - 13 q^{35} + 20 q^{36} - 25 q^{37} - 27 q^{38} - 8 q^{40} - 24 q^{41} + 13 q^{42} - 8 q^{43} - 8 q^{44} - 27 q^{45} - 18 q^{46} - 10 q^{47} - 28 q^{48} - q^{49} + 26 q^{50} - 17 q^{51} + 10 q^{53} - 47 q^{54} + 6 q^{55} + 15 q^{56} - 6 q^{58} + 4 q^{59} + 61 q^{60} - 21 q^{61} - 5 q^{62} - 6 q^{63} - 27 q^{64} + 12 q^{66} - 21 q^{67} + 14 q^{68} + 5 q^{69} - 31 q^{70} + 3 q^{71} + 50 q^{72} - 13 q^{73} - 38 q^{74} - 23 q^{75} - 8 q^{76} + 3 q^{77} - 4 q^{79} - 44 q^{80} + 34 q^{81} - 33 q^{82} - 8 q^{83} - 47 q^{84} + 13 q^{85} + 11 q^{86} - 51 q^{87} - 3 q^{88} + 9 q^{89} - 70 q^{90} + 15 q^{92} + 21 q^{93} + 10 q^{94} + 27 q^{95} + 19 q^{96} - 15 q^{97} - 21 q^{98} - 7 q^{99}+O(q^{100}) $ 6 * q + q^3 + 8 * q^4 - 6 * q^5 - 12 * q^6 - 3 * q^7 + 3 * q^8 + 7 * q^9 - 3 * q^10 - 6 * q^11 - 17 * q^12 + 12 * q^14 + 4 * q^15 + 8 * q^16 + 2 * q^17 + 6 * q^18 - 10 * q^19 - 15 * q^20 - 12 * q^21 + 3 * q^23 - 14 * q^24 - 6 * q^25 + 10 * q^27 - 16 * q^28 + 3 * q^29 + 19 * q^30 - 5 * q^31 + q^32 - q^33 + 5 * q^34 - 13 * q^35 + 20 * q^36 - 25 * q^37 - 27 * q^38 - 8 * q^40 - 24 * q^41 + 13 * q^42 - 8 * q^43 - 8 * q^44 - 27 * q^45 - 18 * q^46 - 10 * q^47 - 28 * q^48 - q^49 + 26 * q^50 - 17 * q^51 + 10 * q^53 - 47 * q^54 + 6 * q^55 + 15 * q^56 - 6 * q^58 + 4 * q^59 + 61 * q^60 - 21 * q^61 - 5 * q^62 - 6 * q^63 - 27 * q^64 + 12 * q^66 - 21 * q^67 + 14 * q^68 + 5 * q^69 - 31 * q^70 + 3 * q^71 + 50 * q^72 - 13 * q^73 - 38 * q^74 - 23 * q^75 - 8 * q^76 + 3 * q^77 - 4 * q^79 - 44 * q^80 + 34 * q^81 - 33 * q^82 - 8 * q^83 - 47 * q^84 + 13 * q^85 + 11 * q^86 - 51 * q^87 - 3 * q^88 + 9 * q^89 - 70 * q^90 + 15 * q^92 + 21 * q^93 + 10 * q^94 + 27 * q^95 + 19 * q^96 - 15 * q^97 - 21 * q^98 - 7 * 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 $

$2$	−0.498953	−0.352813	−0.176407	−	0.984317i	$-0.556447\pi$
$2$	−0.498953	−0.352813	−0.176407	+	0.984317i	$0.556447\pi$
$3$	−0.240597	−0.138909	−0.0694543	−	0.997585i	$-0.522126\pi$
$3$	−0.240597	−0.138909	−0.0694543	+	0.997585i	$0.522126\pi$
$4$	−1.75105	−0.875523
$5$	0.581470	0.260041	0.130021	−	0.991511i	$-0.458496\pi$
$5$	0.581470	0.260041	0.130021	+	0.991511i	$0.458496\pi$
$6$	0.120047	0.0490088
$7$	1.41017	0.532995	0.266498	−	0.963836i	$-0.414134\pi$
$7$	1.41017	0.532995	0.266498	+	0.963836i	$0.414134\pi$
$8$	1.87160	0.661709
$9$	−2.94211	−0.980704
$10$	−0.290126	−0.0917460
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	0.421296	0.121618
$13$	0	0
$13$	0	0
$14$	−0.703610	−0.188048
$15$	−0.139900	−0.0361220
$16$	2.56825	0.642063
$17$	0.451517	0.109509	0.0547545	−	0.998500i	$-0.482562\pi$
$17$	0.451517	0.109509	0.0547545	+	0.998500i	$0.482562\pi$
$18$	1.46798	0.346005
$19$	3.19052	0.731956	0.365978	−	0.930624i	$-0.380735\pi$
$19$	3.19052	0.731956	0.365978	+	0.930624i	$0.380735\pi$
$20$	−1.01818	−0.227672
$21$	−0.339283	−0.0740376
$22$	0.498953	0.106377
$23$	−4.03454	−0.841259	−0.420629	−	0.907233i	$-0.638191\pi$
$23$	−4.03454	−0.841259	−0.420629	+	0.907233i	$0.638191\pi$
$24$	−0.450300	−0.0919171
$25$	−4.66189	−0.932379
$26$	0	0
$27$	1.42965	0.275137
$28$	−2.46928	−0.466649
$29$	10.2019	1.89445	0.947226	−	0.320567i	$-0.103873\pi$
$29$	10.2019	1.89445	0.947226	+	0.320567i	$0.103873\pi$
$30$	0.0698034	0.0127443
$31$	−7.10174	−1.27551	−0.637755	−	0.770239i	$-0.720137\pi$
$31$	−7.10174	−1.27551	−0.637755	+	0.770239i	$0.720137\pi$
$32$	−5.02463	−0.888237
$33$	0.240597	0.0418825
$34$	−0.225286	−0.0386362
$35$	0.819973	0.138601
$36$	5.15177	0.858629
$37$	4.68112	0.769571	0.384786	−	0.923006i	$-0.374275\pi$
$37$	4.68112	0.769571	0.384786	+	0.923006i	$0.374275\pi$
$38$	−1.59192	−0.258244
$39$	0	0
$40$	1.08828	0.172072
$41$	−8.86324	−1.38421	−0.692103	−	0.721799i	$-0.743315\pi$
$41$	−8.86324	−1.38421	−0.692103	+	0.721799i	$0.743315\pi$
$42$	0.169286	0.0261214
$43$	4.41503	0.673286	0.336643	−	0.941632i	$-0.390708\pi$
$43$	4.41503	0.673286	0.336643	+	0.941632i	$0.390708\pi$
$44$	1.75105	0.263980
$45$	−1.71075	−0.255024
$46$	2.01304	0.296807
$47$	3.77409	0.550507	0.275253	−	0.961372i	$-0.411238\pi$
$47$	3.77409	0.550507	0.275253	+	0.961372i	$0.411238\pi$
$48$	−0.617913	−0.0891881
$49$	−5.01141	−0.715916
$50$	2.32607	0.328955
$51$	−0.108634	−0.0152118
$52$	0	0
$53$	−0.0779742	−0.0107106	−0.00535529	−	0.999986i	$-0.501705\pi$
$53$	−0.0779742	−0.0107106	−0.00535529	+	0.999986i	$0.501705\pi$
$54$	−0.713330	−0.0970719
$55$	−0.581470	−0.0784054
$56$	2.63927	0.352688
$57$	−0.767629	−0.101675
$58$	−5.09029	−0.668387
$59$	−7.70134	−1.00263	−0.501315	−	0.865265i	$-0.667150\pi$
$59$	−7.70134	−1.00263	−0.501315	+	0.865265i	$0.667150\pi$
$60$	0.244971	0.0316256
$61$	−4.32766	−0.554100	−0.277050	−	0.960856i	$-0.589357\pi$
$61$	−4.32766	−0.554100	−0.277050	+	0.960856i	$0.589357\pi$
$62$	3.54344	0.450017
$63$	−4.14889	−0.522711
$64$	−2.62945	−0.328681
$65$	0	0
$66$	−0.120047	−0.0147767
$67$	−11.2317	−1.37217	−0.686085	−	0.727521i	$-0.740672\pi$
$67$	−11.2317	−1.37217	−0.686085	+	0.727521i	$0.740672\pi$
$68$	−0.790628	−0.0958777
$69$	0.970696	0.116858
$70$	−0.409128	−0.0489002
$71$	−1.98509	−0.235587	−0.117793	−	0.993038i	$-0.537582\pi$
$71$	−1.98509	−0.235587	−0.117793	+	0.993038i	$0.537582\pi$
$72$	−5.50645	−0.648941
$73$	−2.84192	−0.332622	−0.166311	−	0.986073i	$-0.553185\pi$
$73$	−2.84192	−0.332622	−0.166311	+	0.986073i	$0.553185\pi$
$74$	−2.33566	−0.271515
$75$	1.12164	0.129515
$76$	−5.58675	−0.640844
$77$	−1.41017	−0.160704
$78$	0	0
$79$	14.6900	1.65276	0.826379	−	0.563114i	$-0.190397\pi$
$79$	14.6900	1.65276	0.826379	+	0.563114i	$0.190397\pi$
$80$	1.49336	0.166963
$81$	8.48237	0.942485
$82$	4.42234	0.488366
$83$	4.03491	0.442889	0.221444	−	0.975173i	$-0.428923\pi$
$83$	4.03491	0.442889	0.221444	+	0.975173i	$0.428923\pi$
$84$	0.594100	0.0648216
$85$	0.262544	0.0284769
$86$	−2.20289	−0.237544
$87$	−2.45455	−0.263156
$88$	−1.87160	−0.199513
$89$	−10.2374	−1.08516	−0.542580	−	0.840004i	$-0.682552\pi$
$89$	−10.2374	−1.08516	−0.542580	+	0.840004i	$0.682552\pi$
$90$	0.853584	0.0899757
$91$	0	0
$92$	7.06466	0.736541
$93$	1.70866	0.177179
$94$	−1.88309	−0.194226
$95$	1.85519	0.190339
$96$	1.20891	0.123384
$97$	−12.5156	−1.27076	−0.635381	−	0.772199i	$-0.719157\pi$
$97$	−12.5156	−1.27076	−0.635381	+	0.772199i	$0.719157\pi$
$98$	2.50046	0.252585
$99$	2.94211	0.295694
$100$	8.16319	0.816319
$101$	9.00406	0.895937	0.447969	−	0.894049i	$-0.352148\pi$
$101$	9.00406	0.895937	0.447969	+	0.894049i	$0.352148\pi$
$102$	0.0542031	0.00536691
$103$	−14.3214	−1.41113	−0.705564	−	0.708646i	$-0.749306\pi$
$103$	−14.3214	−1.41113	−0.705564	+	0.708646i	$0.749306\pi$
$104$	0	0
$105$	−0.197283	−0.0192528
$106$	0.0389055	0.00377883
$107$	−6.27660	−0.606782	−0.303391	−	0.952866i	$-0.598119\pi$
$107$	−6.27660	−0.606782	−0.303391	+	0.952866i	$0.598119\pi$
$108$	−2.50339	−0.240889
$109$	−6.86332	−0.657387	−0.328693	−	0.944437i	$-0.606608\pi$
$109$	−6.86332	−0.657387	−0.328693	+	0.944437i	$0.606608\pi$
$110$	0.290126	0.0276624
$111$	−1.12626	−0.106900
$112$	3.62168	0.342217
$113$	−15.1061	−1.42106	−0.710531	−	0.703666i	$-0.751545\pi$
$113$	−15.1061	−1.42106	−0.710531	+	0.703666i	$0.751545\pi$
$114$	0.383011	0.0358723
$115$	−2.34596	−0.218762
$116$	−17.8641	−1.65864
$117$	0	0
$118$	3.84261	0.353741
$119$	0.636718	0.0583678
$120$	−0.261836	−0.0239022
$121$	1.00000	0.0909091
$122$	2.15930	0.195494
$123$	2.13247	0.192278
$124$	12.4355	1.11674
$125$	−5.61810	−0.502498
$126$	2.07010	0.184419
$127$	−2.24656	−0.199350	−0.0996748	−	0.995020i	$-0.531780\pi$
$127$	−2.24656	−0.199350	−0.0996748	+	0.995020i	$0.531780\pi$
$128$	11.3612	1.00420
$129$	−1.06224	−0.0935253
$130$	0	0
$131$	−6.82807	−0.596572	−0.298286	−	0.954477i	$-0.596415\pi$
$131$	−6.82807	−0.596572	−0.298286	+	0.954477i	$0.596415\pi$
$132$	−0.421296	−0.0366691
$133$	4.49919	0.390129
$134$	5.60409	0.484120
$135$	0.831300	0.0715469
$136$	0.845058	0.0724632
$137$	−18.8394	−1.60956	−0.804779	−	0.593575i	$-0.797716\pi$
$137$	−18.8394	−1.60956	−0.804779	+	0.593575i	$0.797716\pi$
$138$	−0.484332	−0.0412291
$139$	−14.0782	−1.19409	−0.597047	−	0.802206i	$-0.703659\pi$
$139$	−14.0782	−1.19409	−0.597047	+	0.802206i	$0.703659\pi$
$140$	−1.43581	−0.121348
$141$	−0.908033	−0.0764702
$142$	0.990467	0.0831181
$143$	0	0
$144$	−7.55609	−0.629674
$145$	5.93212	0.492636
$146$	1.41798	0.117353
$147$	1.20573	0.0994469
$148$	−8.19685	−0.673777
$149$	1.87272	0.153420	0.0767098	−	0.997053i	$-0.475559\pi$
$149$	1.87272	0.153420	0.0767098	+	0.997053i	$0.475559\pi$
$150$	−0.559644	−0.0456947
$151$	−14.7657	−1.20162	−0.600809	−	0.799393i	$-0.705155\pi$
$151$	−14.7657	−1.20162	−0.600809	+	0.799393i	$0.705155\pi$
$152$	5.97137	0.484342
$153$	−1.32842	−0.107396
$154$	0.703610	0.0566985
$155$	−4.12945	−0.331685
$156$	0	0
$157$	−6.92557	−0.552721	−0.276360	−	0.961054i	$-0.589128\pi$
$157$	−6.92557	−0.552721	−0.276360	+	0.961054i	$0.589128\pi$
$158$	−7.32964	−0.583115
$159$	0.0187603	0.00148779
$160$	−2.92167	−0.230978
$161$	−5.68939	−0.448387
$162$	−4.23230	−0.332521
$163$	12.3970	0.971004	0.485502	−	0.874236i	$-0.338637\pi$
$163$	12.3970	0.971004	0.485502	+	0.874236i	$0.338637\pi$
$164$	15.5199	1.21190
$165$	0.139900	0.0108912
$166$	−2.01323	−0.156257
$167$	−20.3701	−1.57628	−0.788142	−	0.615493i	$-0.788957\pi$
$167$	−20.3701	−1.57628	−0.788142	+	0.615493i	$0.788957\pi$
$168$	−0.635001	−0.0489914
$169$	0	0
$170$	−0.130997	−0.0100470
$171$	−9.38688	−0.717832
$172$	−7.73092	−0.589477
$173$	−1.08539	−0.0825204	−0.0412602	−	0.999148i	$-0.513137\pi$
$173$	−1.08539	−0.0825204	−0.0412602	+	0.999148i	$0.513137\pi$
$174$	1.22471	0.0928448
$175$	−6.57407	−0.496953
$176$	−2.56825	−0.193589
$177$	1.85292	0.139274
$178$	5.10797	0.382858
$179$	−6.97496	−0.521333	−0.260666	−	0.965429i	$-0.583942\pi$
$179$	−6.97496	−0.521333	−0.260666	+	0.965429i	$0.583942\pi$
$180$	2.99560	0.223279
$181$	7.09724	0.527534	0.263767	−	0.964586i	$-0.415035\pi$
$181$	7.09724	0.527534	0.263767	+	0.964586i	$0.415035\pi$
$182$	0	0
$183$	1.04122	0.0769692
$184$	−7.55102	−0.556669
$185$	2.72193	0.200120
$186$	−0.852539	−0.0625112
$187$	−0.451517	−0.0330182
$188$	−6.60860	−0.481981
$189$	2.01606	0.146647
$190$	−0.925654	−0.0671540
$191$	11.8298	0.855975	0.427987	−	0.903785i	$-0.359223\pi$
$191$	11.8298	0.855975	0.427987	+	0.903785i	$0.359223\pi$
$192$	0.632637	0.0456567
$193$	0.675979	0.0486581	0.0243290	−	0.999704i	$-0.492255\pi$
$193$	0.675979	0.0486581	0.0243290	+	0.999704i	$0.492255\pi$
$194$	6.24468	0.448342
$195$	0	0
$196$	8.77521	0.626801
$197$	10.5107	0.748855	0.374427	−	0.927256i	$-0.377839\pi$
$197$	10.5107	0.748855	0.374427	+	0.927256i	$0.377839\pi$
$198$	−1.46798	−0.104325
$199$	−20.2548	−1.43583	−0.717913	−	0.696133i	$-0.754902\pi$
$199$	−20.2548	−1.43583	−0.717913	+	0.696133i	$0.754902\pi$
$200$	−8.72518	−0.616963
$201$	2.70231	0.190606
$202$	−4.49260	−0.316098
$203$	14.3865	1.00973
$204$	0.190223	0.0133182
$205$	−5.15371	−0.359950
$206$	7.14570	0.497865
$207$	11.8701	0.825026
$208$	0	0
$209$	−3.19052	−0.220693
$210$	0.0984349	0.00679265
$211$	11.8794	0.817811	0.408905	−	0.912577i	$-0.365911\pi$
$211$	11.8794	0.817811	0.408905	+	0.912577i	$0.365911\pi$
$212$	0.136536	0.00937736
$213$	0.477606	0.0327250
$214$	3.13173	0.214081
$215$	2.56721	0.175082
$216$	2.67573	0.182061
$217$	−10.0147	−0.679841
$218$	3.42448	0.231935
$219$	0.683757	0.0462040
$220$	1.01818	0.0686457
$221$	0	0
$222$	0.561952	0.0377157
$223$	−9.84833	−0.659493	−0.329746	−	0.944070i	$-0.606963\pi$
$223$	−9.84833	−0.659493	−0.329746	+	0.944070i	$0.606963\pi$
$224$	−7.08560	−0.473426
$225$	13.7158	0.914388
$226$	7.53723	0.501369
$227$	0.0679654	0.00451102	0.00225551	−	0.999997i	$-0.499282\pi$
$227$	0.0679654	0.00451102	0.00225551	+	0.999997i	$0.499282\pi$
$228$	1.34415	0.0890188
$229$	13.1872	0.871434	0.435717	−	0.900084i	$-0.356495\pi$
$229$	13.1872	0.871434	0.435717	+	0.900084i	$0.356495\pi$
$230$	1.17052	0.0771821
$231$	0.339283	0.0223232
$232$	19.0939	1.25358
$233$	18.2397	1.19493	0.597463	−	0.801897i	$-0.296176\pi$
$233$	18.2397	1.19493	0.597463	+	0.801897i	$0.296176\pi$
$234$	0	0
$235$	2.19452	0.143155
$236$	13.4854	0.877825
$237$	−3.53438	−0.229582
$238$	−0.317692	−0.0205929
$239$	10.9341	0.707266	0.353633	−	0.935384i	$-0.384946\pi$
$239$	10.9341	0.707266	0.353633	+	0.935384i	$0.384946\pi$
$240$	−0.359298	−0.0231926
$241$	5.19412	0.334582	0.167291	−	0.985908i	$-0.446498\pi$
$241$	5.19412	0.334582	0.167291	+	0.985908i	$0.446498\pi$
$242$	−0.498953	−0.0320739
$243$	−6.32979	−0.406056
$244$	7.57792	0.485127
$245$	−2.91399	−0.186168
$246$	−1.06400	−0.0678382
$247$	0	0
$248$	−13.2916	−0.844017
$249$	−0.970786	−0.0615211
$250$	2.80317	0.177288
$251$	11.3143	0.714155	0.357077	−	0.934075i	$-0.383773\pi$
$251$	11.3143	0.714155	0.357077	+	0.934075i	$0.383773\pi$
$252$	7.26489	0.457645
$253$	4.03454	0.253649
$254$	1.12093	0.0703332
$255$	−0.0631672	−0.00395568
$256$	−0.409821	−0.0256138
$257$	−27.6497	−1.72474	−0.862370	−	0.506279i	$-0.831021\pi$
$257$	−27.6497	−1.72474	−0.862370	+	0.506279i	$0.831021\pi$
$258$	0.530009	0.0329969
$259$	6.60118	0.410178
$260$	0	0
$261$	−30.0152	−1.85790
$262$	3.40689	0.210478
$263$	5.15358	0.317783	0.158892	−	0.987296i	$-0.449208\pi$
$263$	5.15358	0.317783	0.158892	+	0.987296i	$0.449208\pi$
$264$	0.450300	0.0277141
$265$	−0.0453396	−0.00278519
$266$	−2.24488	−0.137643
$267$	2.46308	0.150738
$268$	19.6672	1.20137
$269$	22.6690	1.38215	0.691076	−	0.722782i	$-0.257137\pi$
$269$	22.6690	1.38215	0.691076	+	0.722782i	$0.257137\pi$
$270$	−0.414780	−0.0252427
$271$	−6.75010	−0.410040	−0.205020	−	0.978758i	$-0.565726\pi$
$271$	−6.75010	−0.410040	−0.205020	+	0.978758i	$0.565726\pi$
$272$	1.15961	0.0703117
$273$	0	0
$274$	9.39997	0.567873
$275$	4.66189	0.281123
$276$	−1.69973	−0.102312
$277$	−4.64457	−0.279065	−0.139533	−	0.990217i	$-0.544560\pi$
$277$	−4.64457	−0.279065	−0.139533	+	0.990217i	$0.544560\pi$
$278$	7.02434	0.421292
$279$	20.8941	1.25090
$280$	1.53466	0.0917134
$281$	−21.0948	−1.25841	−0.629206	−	0.777238i	$-0.716620\pi$
$281$	−21.0948	−1.25841	−0.629206	+	0.777238i	$0.716620\pi$
$282$	0.453066	0.0269797
$283$	27.3312	1.62467	0.812336	−	0.583190i	$-0.198196\pi$
$283$	27.3312	1.62467	0.812336	+	0.583190i	$0.198196\pi$
$284$	3.47598	0.206262
$285$	−0.446353	−0.0264397
$286$	0	0
$287$	−12.4987	−0.737775
$288$	14.7830	0.871098
$289$	−16.7961	−0.988008
$290$	−2.95985	−0.173808
$291$	3.01120	0.176520
$292$	4.97633	0.291218
$293$	30.0122	1.75333	0.876667	−	0.481098i	$-0.159762\pi$
$293$	30.0122	1.75333	0.876667	+	0.481098i	$0.159762\pi$
$294$	−0.601603	−0.0350862
$295$	−4.47810	−0.260725
$296$	8.76116	0.509232
$297$	−1.42965	−0.0829569
$298$	−0.934401	−0.0541284
$299$	0	0
$300$	−1.96404	−0.113394
$301$	6.22596	0.358858
$302$	7.36741	0.423947
$303$	−2.16635	−0.124453
$304$	8.19407	0.469962
$305$	−2.51640	−0.144089
$306$	0.662817	0.0378907
$307$	−28.9631	−1.65301	−0.826506	−	0.562927i	$-0.809675\pi$
$307$	−28.9631	−1.65301	−0.826506	+	0.562927i	$0.809675\pi$
$308$	2.46928	0.140700
$309$	3.44568	0.196018
$310$	2.06040	0.117023
$311$	10.3363	0.586117	0.293059	−	0.956094i	$-0.405327\pi$
$311$	10.3363	0.586117	0.293059	+	0.956094i	$0.405327\pi$
$312$	0	0
$313$	23.0075	1.30046	0.650230	−	0.759737i	$-0.274672\pi$
$313$	23.0075	1.30046	0.650230	+	0.759737i	$0.274672\pi$
$314$	3.45554	0.195007
$315$	−2.41245	−0.135926
$316$	−25.7229	−1.44703
$317$	−19.3410	−1.08630	−0.543149	−	0.839636i	$-0.682768\pi$
$317$	−19.3410	−1.08630	−0.543149	+	0.839636i	$0.682768\pi$
$318$	−0.00936053	−0.000524913 0
$319$	−10.2019	−0.571199
$320$	−1.52895	−0.0854707
$321$	1.51013	0.0842872
$322$	2.83874	0.158197
$323$	1.44058	0.0801558
$324$	−14.8530	−0.825168
$325$	0	0
$326$	−6.18550	−0.342583
$327$	1.65129	0.0913167
$328$	−16.5884	−0.915941
$329$	5.32211	0.293418
$330$	−0.0698034	−0.00384255
$331$	15.8477	0.871068	0.435534	−	0.900172i	$-0.356560\pi$
$331$	15.8477	0.871068	0.435534	+	0.900172i	$0.356560\pi$
$332$	−7.06531	−0.387759
$333$	−13.7724	−0.754722
$334$	10.1637	0.556134
$335$	−6.53089	−0.356821
$336$	−0.871365	−0.0475368
$337$	5.84238	0.318254	0.159127	−	0.987258i	$-0.449132\pi$
$337$	5.84238	0.318254	0.159127	+	0.987258i	$0.449132\pi$
$338$	0	0
$339$	3.63448	0.197398
$340$	−0.459726	−0.0249322
$341$	7.10174	0.384581
$342$	4.68361	0.253261
$343$	−16.9382	−0.914575
$344$	8.26316	0.445520
$345$	0.564431	0.0303879
$346$	0.541557	0.0291143
$347$	−8.21192	−0.440839	−0.220420	−	0.975405i	$-0.570743\pi$
$347$	−8.21192	−0.440839	−0.220420	+	0.975405i	$0.570743\pi$
$348$	4.29803	0.230399
$349$	12.3503	0.661095	0.330548	−	0.943789i	$-0.392767\pi$
$349$	12.3503	0.661095	0.330548	+	0.943789i	$0.392767\pi$
$350$	3.28015	0.175332
$351$	0	0
$352$	5.02463	0.267814
$353$	16.3881	0.872250	0.436125	−	0.899886i	$-0.356351\pi$
$353$	16.3881	0.872250	0.436125	+	0.899886i	$0.356351\pi$
$354$	−0.924520	−0.0491377
$355$	−1.15427	−0.0612623
$356$	17.9261	0.950082
$357$	−0.153192	−0.00810779
$358$	3.48018	0.183933
$359$	−0.450004	−0.0237503	−0.0118751	−	0.999929i	$-0.503780\pi$
$359$	−0.450004	−0.0237503	−0.0118751	+	0.999929i	$0.503780\pi$
$360$	−3.20183	−0.168751
$361$	−8.82057	−0.464240
$362$	−3.54119	−0.186121
$363$	−0.240597	−0.0126281
$364$	0	0
$365$	−1.65249	−0.0864953
$366$	−0.519520	−0.0271557
$367$	−19.5901	−1.02260	−0.511298	−	0.859404i	$-0.670835\pi$
$367$	−19.5901	−1.02260	−0.511298	+	0.859404i	$0.670835\pi$
$368$	−10.3617	−0.540141
$369$	26.0767	1.35750
$370$	−1.35811	−0.0706050
$371$	−0.109957	−0.00570869
$372$	−2.99194	−0.155125
$373$	12.0789	0.625424	0.312712	−	0.949848i	$-0.398763\pi$
$373$	12.0789	0.625424	0.312712	+	0.949848i	$0.398763\pi$
$374$	0.225286	0.0116493
$375$	1.35170	0.0698013
$376$	7.06356	0.364275
$377$	0	0
$378$	−1.00592	−0.0517389
$379$	32.2247	1.65527	0.827636	−	0.561265i	$-0.189685\pi$
$379$	32.2247	1.65527	0.827636	+	0.561265i	$0.189685\pi$
$380$	−3.24853	−0.166646
$381$	0.540514	0.0276914
$382$	−5.90252	−0.301999
$383$	33.6591	1.71990	0.859950	−	0.510379i	$-0.170495\pi$
$383$	33.6591	1.71990	0.859950	+	0.510379i	$0.170495\pi$
$384$	−2.73348	−0.139492
$385$	−0.819973	−0.0417897
$386$	−0.337282	−0.0171672
$387$	−12.9895	−0.660295
$388$	21.9153	1.11258
$389$	9.54985	0.484197	0.242098	−	0.970252i	$-0.422164\pi$
$389$	9.54985	0.484197	0.242098	+	0.970252i	$0.422164\pi$
$390$	0	0
$391$	−1.82166	−0.0921255
$392$	−9.37934	−0.473728
$393$	1.64281	0.0828690
$394$	−5.24434	−0.264206
$395$	8.54181	0.429785
$396$	−5.15177	−0.258886
$397$	−19.5587	−0.981622	−0.490811	−	0.871266i	$-0.663299\pi$
$397$	−19.5587	−0.981622	−0.490811	+	0.871266i	$0.663299\pi$
$398$	10.1062	0.506578
$399$	−1.08249	−0.0541923
$400$	−11.9729	−0.598646
$401$	−25.3773	−1.26728	−0.633642	−	0.773627i	$-0.718441\pi$
$401$	−25.3773	−1.26728	−0.633642	+	0.773627i	$0.718441\pi$
$402$	−1.34833	−0.0672484
$403$	0	0
$404$	−15.7665	−0.784414
$405$	4.93224	0.245085
$406$	−7.17818	−0.356247
$407$	−4.68112	−0.232034
$408$	−0.203318	−0.0100658
$409$	−15.2320	−0.753174	−0.376587	−	0.926381i	$-0.622902\pi$
$409$	−15.2320	−0.753174	−0.376587	+	0.926381i	$0.622902\pi$
$410$	2.57146	0.126995
$411$	4.53270	0.223581
$412$	25.0774	1.23548
$413$	−10.8602	−0.534397
$414$	−5.92260	−0.291080
$415$	2.34618	0.115169
$416$	0	0
$417$	3.38716	0.165870
$418$	1.59192	0.0778634
$419$	−7.96179	−0.388959	−0.194480	−	0.980907i	$-0.562302\pi$
$419$	−7.96179	−0.388959	−0.194480	+	0.980907i	$0.562302\pi$
$420$	0.345451	0.0168563
$421$	−6.44783	−0.314248	−0.157124	−	0.987579i	$-0.550222\pi$
$421$	−6.44783	−0.314248	−0.157124	+	0.987579i	$0.550222\pi$
$422$	−5.92726	−0.288534
$423$	−11.1038	−0.539885
$424$	−0.145936	−0.00708729
$425$	−2.10493	−0.102104
$426$	−0.238303	−0.0115458
$427$	−6.10274	−0.295332
$428$	10.9906	0.531251
$429$	0	0
$430$	−1.28092	−0.0617713
$431$	40.8664	1.96846	0.984232	−	0.176882i	$-0.0566010\pi$
$431$	40.8664	1.96846	0.984232	+	0.176882i	$0.0566010\pi$
$432$	3.67171	0.176655
$433$	12.9814	0.623845	0.311923	−	0.950107i	$-0.399027\pi$
$433$	12.9814	0.623845	0.311923	+	0.950107i	$0.399027\pi$
$434$	4.99686	0.239857
$435$	−1.42725	−0.0684313
$436$	12.0180	0.575557
$437$	−12.8723	−0.615764
$438$	−0.341163	−0.0163014
$439$	21.0473	1.00453	0.502266	−	0.864713i	$-0.332500\pi$
$439$	21.0473	1.00453	0.502266	+	0.864713i	$0.332500\pi$
$440$	−1.08828	−0.0518816
$441$	14.7441	0.702102
$442$	0	0
$443$	18.8136	0.893862	0.446931	−	0.894569i	$-0.352517\pi$
$443$	18.8136	0.893862	0.446931	+	0.894569i	$0.352517\pi$
$444$	1.97214	0.0935934
$445$	−5.95272	−0.282186
$446$	4.91385	0.232678
$447$	−0.450571	−0.0213113
$448$	−3.70798	−0.175186
$449$	−16.0680	−0.758297	−0.379149	−	0.925336i	$-0.623783\pi$
$449$	−16.0680	−0.758297	−0.379149	+	0.925336i	$0.623783\pi$
$450$	−6.84355	−0.322608
$451$	8.86324	0.417354
$452$	26.4515	1.24417
$453$	3.55259	0.166915
$454$	−0.0339116	−0.00159155
$455$	0	0
$456$	−1.43669	−0.0672793
$457$	−35.4122	−1.65651	−0.828256	−	0.560350i	$-0.810667\pi$
$457$	−35.4122	−1.65651	−0.828256	+	0.560350i	$0.810667\pi$
$458$	−6.57979	−0.307453
$459$	0.645514	0.0301300
$460$	4.10788	0.191531
$461$	15.8599	0.738668	0.369334	−	0.929297i	$-0.379586\pi$
$461$	15.8599	0.738668	0.369334	+	0.929297i	$0.379586\pi$
$462$	−0.169286	−0.00787591
$463$	−16.8149	−0.781453	−0.390727	−	0.920507i	$-0.627776\pi$
$463$	−16.8149	−0.781453	−0.390727	+	0.920507i	$0.627776\pi$
$464$	26.2011	1.21636
$465$	0.993532	0.0460739
$466$	−9.10078	−0.421585
$467$	24.5686	1.13690	0.568449	−	0.822718i	$-0.307544\pi$
$467$	24.5686	1.13690	0.568449	+	0.822718i	$0.307544\pi$
$468$	0	0
$469$	−15.8386	−0.731360
$470$	−1.09496	−0.0505068
$471$	1.66627	0.0767777
$472$	−14.4138	−0.663449
$473$	−4.41503	−0.203003
$474$	1.76349	0.0809997
$475$	−14.8739	−0.682460
$476$	−1.11492	−0.0511024
$477$	0.229409	0.0105039
$478$	−5.45558	−0.249533
$479$	33.4182	1.52692	0.763458	−	0.645858i	$-0.223500\pi$
$479$	33.4182	1.52692	0.763458	+	0.645858i	$0.223500\pi$
$480$	0.702945	0.0320849
$481$	0	0
$482$	−2.59162	−0.118045
$483$	1.36885	0.0622848
$484$	−1.75105	−0.0795930
$485$	−7.27742	−0.330451
$486$	3.15827	0.143262
$487$	12.1531	0.550709	0.275354	−	0.961343i	$-0.411205\pi$
$487$	12.1531	0.550709	0.275354	+	0.961343i	$0.411205\pi$
$488$	−8.09962	−0.366653
$489$	−2.98267	−0.134881
$490$	1.45394	0.0656824
$491$	3.04976	0.137634	0.0688169	−	0.997629i	$-0.478078\pi$
$491$	3.04976	0.137634	0.0688169	+	0.997629i	$0.478078\pi$
$492$	−3.73405	−0.168344
$493$	4.60635	0.207460
$494$	0	0
$495$	1.71075	0.0768925
$496$	−18.2391	−0.818958
$497$	−2.79932	−0.125567
$498$	0.484377	0.0217054
$499$	−17.6401	−0.789678	−0.394839	−	0.918750i	$-0.629200\pi$
$499$	−17.6401	−0.789678	−0.394839	+	0.918750i	$0.629200\pi$
$500$	9.83755	0.439949
$501$	4.90098	0.218960
$502$	−5.64533	−0.251963
$503$	−35.8363	−1.59786	−0.798931	−	0.601423i	$-0.794601\pi$
$503$	−35.8363	−1.59786	−0.798931	+	0.601423i	$0.794601\pi$
$504$	−7.76504	−0.345882
$505$	5.23559	0.232981
$506$	−2.01304	−0.0894907
$507$	0	0
$508$	3.93382	0.174535
$509$	−19.4380	−0.861572	−0.430786	−	0.902454i	$-0.641764\pi$
$509$	−19.4380	−0.861572	−0.430786	+	0.902454i	$0.641764\pi$
$510$	0.0315175	0.00139562
$511$	−4.00760	−0.177286
$512$	−22.5180	−0.995164
$513$	4.56134	0.201388
$514$	13.7959	0.608511
$515$	−8.32746	−0.366952
$516$	1.86004	0.0818835
$517$	−3.77409	−0.165984
$518$	−3.29368	−0.144716
$519$	0.261140	0.0114628
$520$	0	0
$521$	15.3874	0.674132	0.337066	−	0.941481i	$-0.390565\pi$
$521$	15.3874	0.674132	0.337066	+	0.941481i	$0.390565\pi$
$522$	14.9762	0.655491
$523$	−10.4642	−0.457567	−0.228784	−	0.973477i	$-0.573475\pi$
$523$	−10.4642	−0.457567	−0.228784	+	0.973477i	$0.573475\pi$
$524$	11.9563	0.522312
$525$	1.58170	0.0690311
$526$	−2.57140	−0.112118
$527$	−3.20656	−0.139680
$528$	0.617913	0.0268912
$529$	−6.72252	−0.292284
$530$	0.0226224	0.000982652 0
$531$	22.6582	0.983283
$532$	−7.87828	−0.341567
$533$	0	0
$534$	−1.22896	−0.0531823
$535$	−3.64965	−0.157788
$536$	−21.0212	−0.907977
$537$	1.67815	0.0724176
$538$	−11.3108	−0.487642
$539$	5.01141	0.215857
$540$	−1.45564	−0.0626410
$541$	6.85555	0.294743	0.147372	−	0.989081i	$-0.452919\pi$
$541$	6.85555	0.294743	0.147372	+	0.989081i	$0.452919\pi$
$542$	3.36799	0.144667
$543$	−1.70757	−0.0732790
$544$	−2.26871	−0.0972701
$545$	−3.99081	−0.170948
$546$	0	0
$547$	−36.9564	−1.58014	−0.790070	−	0.613016i	$-0.789956\pi$
$547$	−36.9564	−1.58014	−0.790070	+	0.613016i	$0.789956\pi$
$548$	32.9886	1.40920
$549$	12.7325	0.543408
$550$	−2.32607	−0.0991838
$551$	32.5495	1.38666
$552$	1.81675	0.0773261
$553$	20.7155	0.880912
$554$	2.31742	0.0984579
$555$	−0.654887	−0.0277984
$556$	24.6515	1.04546
$557$	18.0232	0.763668	0.381834	−	0.924231i	$-0.375293\pi$
$557$	18.0232	0.763668	0.381834	+	0.924231i	$0.375293\pi$
$558$	−10.4252	−0.441334
$559$	0	0
$560$	2.10590	0.0889904
$561$	0.108634	0.00458652
$562$	10.5253	0.443984
$563$	28.9340	1.21942	0.609712	−	0.792623i	$-0.291285\pi$
$563$	28.9340	1.21942	0.609712	+	0.792623i	$0.291285\pi$
$564$	1.59001	0.0669514
$565$	−8.78374	−0.369535
$566$	−13.6370	−0.573205
$567$	11.9616	0.502340
$568$	−3.71529	−0.155890
$569$	15.0882	0.632531	0.316265	−	0.948671i	$-0.397571\pi$
$569$	15.0882	0.632531	0.316265	+	0.948671i	$0.397571\pi$
$570$	0.222709	0.00932827
$571$	17.5630	0.734988	0.367494	−	0.930026i	$-0.380216\pi$
$571$	17.5630	0.734988	0.367494	+	0.930026i	$0.380216\pi$
$572$	0	0
$573$	−2.84621	−0.118902
$574$	6.23626	0.260297
$575$	18.8086	0.784372
$576$	7.73614	0.322339
$577$	−38.7780	−1.61435	−0.807174	−	0.590314i	$-0.799004\pi$
$577$	−38.7780	−1.61435	−0.807174	+	0.590314i	$0.799004\pi$
$578$	8.38048	0.348582
$579$	−0.162638	−0.00675903
$580$	−10.3874	−0.431314
$581$	5.68992	0.236058
$582$	−1.50245	−0.0622785
$583$	0.0779742	0.00322936
$584$	−5.31893	−0.220099
$585$	0	0
$586$	−14.9747	−0.618599
$587$	44.2206	1.82518	0.912591	−	0.408874i	$-0.134079\pi$
$587$	44.2206	1.82518	0.912591	+	0.408874i	$0.134079\pi$
$588$	−2.11129	−0.0870681
$589$	−22.6583	−0.933617
$590$	2.23436	0.0919872
$591$	−2.52884	−0.104022
$592$	12.0223	0.494113
$593$	10.0591	0.413077	0.206538	−	0.978439i	$-0.433780\pi$
$593$	10.0591	0.413077	0.206538	+	0.978439i	$0.433780\pi$
$594$	0.713330	0.0292683
$595$	0.370232	0.0151780
$596$	−3.27922	−0.134322
$597$	4.87324	0.199449
$598$	0	0
$599$	42.4291	1.73360	0.866802	−	0.498652i	$-0.166172\pi$
$599$	42.4291	1.73360	0.866802	+	0.498652i	$0.166172\pi$
$600$	2.09925	0.0857015
$601$	−34.6678	−1.41413	−0.707064	−	0.707150i	$-0.749981\pi$
$601$	−34.6678	−1.41413	−0.707064	+	0.707150i	$0.749981\pi$
$602$	−3.10646	−0.126610
$603$	33.0449	1.34569
$604$	25.8555	1.05204
$605$	0.581470	0.0236401
$606$	1.08091	0.0439088
$607$	47.1052	1.91194	0.955971	−	0.293461i	$-0.0948072\pi$
$607$	47.1052	1.91194	0.955971	+	0.293461i	$0.0948072\pi$
$608$	−16.0312	−0.650151
$609$	−3.46134	−0.140261
$610$	1.25557	0.0508364
$611$	0	0
$612$	2.32612	0.0940277
$613$	−46.7560	−1.88846	−0.944229	−	0.329288i	$-0.893191\pi$
$613$	−46.7560	−1.88846	−0.944229	+	0.329288i	$0.893191\pi$
$614$	14.4512	0.583205
$615$	1.23997	0.0500002
$616$	−2.63927	−0.106339
$617$	−1.47586	−0.0594158	−0.0297079	−	0.999559i	$-0.509458\pi$
$617$	−1.47586	−0.0594158	−0.0297079	+	0.999559i	$0.509458\pi$
$618$	−1.71923	−0.0691577
$619$	−26.4523	−1.06321	−0.531603	−	0.846994i	$-0.678410\pi$
$619$	−26.4523	−1.06321	−0.531603	+	0.846994i	$0.678410\pi$
$620$	7.23085	0.290398
$621$	−5.76799	−0.231461
$622$	−5.15732	−0.206790
$623$	−14.4365	−0.578385
$624$	0	0
$625$	20.0427	0.801708
$626$	−11.4797	−0.458820
$627$	0.767629	0.0306562
$628$	12.1270	0.483920
$629$	2.11361	0.0842750
$630$	1.20370	0.0479566
$631$	3.54962	0.141308	0.0706540	−	0.997501i	$-0.477491\pi$
$631$	3.54962	0.141308	0.0706540	+	0.997501i	$0.477491\pi$
$632$	27.4938	1.09364
$633$	−2.85814	−0.113601
$634$	9.65024	0.383260
$635$	−1.30630	−0.0518391
$636$	−0.0328502	−0.00130260
$637$	0	0
$638$	5.09029	0.201526
$639$	5.84036	0.231041
$640$	6.60621	0.261134
$641$	−29.3537	−1.15940	−0.579700	−	0.814830i	$-0.696830\pi$
$641$	−29.3537	−1.15940	−0.579700	+	0.814830i	$0.696830\pi$
$642$	−0.753484	−0.0297376
$643$	5.32527	0.210008	0.105004	−	0.994472i	$-0.466514\pi$
$643$	5.32527	0.210008	0.105004	+	0.994472i	$0.466514\pi$
$644$	9.96239	0.392573
$645$	−0.617662	−0.0243204
$646$	−0.718780	−0.0282800
$647$	18.4157	0.723997	0.361998	−	0.932179i	$-0.382095\pi$
$647$	18.4157	0.723997	0.361998	+	0.932179i	$0.382095\pi$
$648$	15.8756	0.623651
$649$	7.70134	0.302304
$650$	0	0
$651$	2.40950	0.0944358
$652$	−21.7076	−0.850136
$653$	24.0351	0.940565	0.470283	−	0.882516i	$-0.344152\pi$
$653$	24.0351	0.940565	0.470283	+	0.882516i	$0.344152\pi$
$654$	−0.823918	−0.0322177
$655$	−3.97032	−0.155133
$656$	−22.7630	−0.888747
$657$	8.36125	0.326203
$658$	−2.65548	−0.103522
$659$	−23.4568	−0.913746	−0.456873	−	0.889532i	$-0.651031\pi$
$659$	−23.4568	−0.913746	−0.456873	+	0.889532i	$0.651031\pi$
$660$	−0.244971	−0.00953548
$661$	−39.3316	−1.52982	−0.764911	−	0.644137i	$-0.777217\pi$
$661$	−39.3316	−1.52982	−0.764911	+	0.644137i	$0.777217\pi$
$662$	−7.90726	−0.307324
$663$	0	0
$664$	7.55172	0.293064
$665$	2.61614	0.101450
$666$	6.87177	0.266276
$667$	−41.1601	−1.59372
$668$	35.6690	1.38007
$669$	2.36948	0.0916092
$670$	3.25861	0.125891
$671$	4.32766	0.167067
$672$	1.70477	0.0657630
$673$	−29.6199	−1.14176	−0.570882	−	0.821032i	$-0.693399\pi$
$673$	−29.6199	−1.14176	−0.570882	+	0.821032i	$0.693399\pi$
$674$	−2.91507	−0.112284
$675$	−6.66489	−0.256532
$676$	0	0
$677$	−39.7317	−1.52701	−0.763507	−	0.645800i	$-0.776524\pi$
$677$	−39.7317	−1.52701	−0.763507	+	0.645800i	$0.776524\pi$
$678$	−1.81343	−0.0696445
$679$	−17.6491	−0.677310
$680$	0.491376	0.0188434
$681$	−0.0163523	−0.000626620 0
$682$	−3.54344	−0.135685
$683$	28.2766	1.08197	0.540986	−	0.841031i	$-0.318051\pi$
$683$	28.2766	1.08197	0.540986	+	0.841031i	$0.318051\pi$
$684$	16.4369	0.628479
$685$	−10.9545	−0.418551
$686$	8.45135	0.322674
$687$	−3.17280	−0.121050
$688$	11.3389	0.432292
$689$	0	0
$690$	−0.281624	−0.0107213
$691$	−27.1212	−1.03174	−0.515869	−	0.856667i	$-0.672531\pi$
$691$	−27.1212	−1.03174	−0.515869	+	0.856667i	$0.672531\pi$
$692$	1.90056	0.0722485
$693$	4.14889	0.157603
$694$	4.09736	0.155534
$695$	−8.18602	−0.310514
$696$	−4.59393	−0.174133
$697$	−4.00191	−0.151583
$698$	−6.16221	−0.233243
$699$	−4.38842	−0.165985
$700$	11.5115	0.435094
$701$	26.8389	1.01369	0.506845	−	0.862037i	$-0.330812\pi$
$701$	26.8389	1.01369	0.506845	+	0.862037i	$0.330812\pi$
$702$	0	0
$703$	14.9352	0.563292
$704$	2.62945	0.0991012
$705$	−0.527994	−0.0198854
$706$	−8.17688	−0.307741
$707$	12.6973	0.477530
$708$	−3.24455	−0.121937
$709$	−25.0089	−0.939229	−0.469614	−	0.882872i	$-0.655607\pi$
$709$	−25.0089	−0.939229	−0.469614	+	0.882872i	$0.655607\pi$
$710$	0.575926	0.0216141
$711$	−43.2197	−1.62087
$712$	−19.1602	−0.718060
$713$	28.6522	1.07303
$714$	0.0764357	0.00286054
$715$	0	0
$716$	12.2135	0.456439
$717$	−2.63070	−0.0982453
$718$	0.224531	0.00837941
$719$	28.2484	1.05349	0.526743	−	0.850024i	$-0.323413\pi$
$719$	28.2484	1.05349	0.526743	+	0.850024i	$0.323413\pi$
$720$	−4.39364	−0.163741
$721$	−20.1956	−0.752125
$722$	4.40105	0.163790
$723$	−1.24969	−0.0464764
$724$	−12.4276	−0.461868
$725$	−47.5603	−1.76635
$726$	0.120047	0.00445534
$727$	−10.0496	−0.372718	−0.186359	−	0.982482i	$-0.559669\pi$
$727$	−10.0496	−0.372718	−0.186359	+	0.982482i	$0.559669\pi$
$728$	0	0
$729$	−23.9242	−0.886081
$730$	0.824515	0.0305167
$731$	1.99346	0.0737309
$732$	−1.82322	−0.0673883
$733$	−17.7381	−0.655171	−0.327586	−	0.944822i	$-0.606235\pi$
$733$	−17.7381	−0.655171	−0.327586	+	0.944822i	$0.606235\pi$
$734$	9.77455	0.360785
$735$	0.701096	0.0258603
$736$	20.2720	0.747238
$737$	11.2317	0.413725
$738$	−13.0110	−0.478943
$739$	−50.2035	−1.84676	−0.923382	−	0.383882i	$-0.874587\pi$
$739$	−50.2035	−1.84676	−0.923382	+	0.383882i	$0.874587\pi$
$740$	−4.76622	−0.175210
$741$	0	0
$742$	0.0548634	0.00201410
$743$	3.73178	0.136906	0.0684529	−	0.997654i	$-0.478194\pi$
$743$	3.73178	0.136906	0.0684529	+	0.997654i	$0.478194\pi$
$744$	3.19791	0.117241
$745$	1.08893	0.0398954
$746$	−6.02682	−0.220658
$747$	−11.8712	−0.434343
$748$	0.790628	0.0289082
$749$	−8.85109	−0.323412
$750$	−0.674433	−0.0246268
$751$	30.2206	1.10277	0.551384	−	0.834252i	$-0.314100\pi$
$751$	30.2206	1.10277	0.551384	+	0.834252i	$0.314100\pi$
$752$	9.69281	0.353460
$753$	−2.72219	−0.0992023
$754$	0	0
$755$	−8.58583	−0.312470
$756$	−3.53021	−0.128393
$757$	29.7763	1.08224	0.541120	−	0.840946i	$-0.318001\pi$
$757$	29.7763	1.08224	0.541120	+	0.840946i	$0.318001\pi$
$758$	−16.0786	−0.584002
$759$	−0.970696	−0.0352340
$760$	3.47217	0.125949
$761$	−47.4141	−1.71876	−0.859381	−	0.511336i	$-0.829151\pi$
$761$	−47.4141	−1.71876	−0.859381	+	0.511336i	$0.829151\pi$
$762$	−0.269691	−0.00976989
$763$	−9.67847	−0.350384
$764$	−20.7145	−0.749426
$765$	−0.772434	−0.0279274
$766$	−16.7943	−0.606803
$767$	0	0
$768$	0.0986016	0.00355798
$769$	−5.29889	−0.191083	−0.0955415	−	0.995425i	$-0.530458\pi$
$769$	−5.29889	−0.191083	−0.0955415	+	0.995425i	$0.530458\pi$
$770$	0.409128	0.0147440
$771$	6.65242	0.239581
$772$	−1.18367	−0.0426013
$773$	−26.9573	−0.969586	−0.484793	−	0.874629i	$-0.661105\pi$
$773$	−26.9573	−0.969586	−0.484793	+	0.874629i	$0.661105\pi$
$774$	6.48116	0.232961
$775$	33.1076	1.18926
$776$	−23.4241	−0.840875
$777$	−1.58822	−0.0569772
$778$	−4.76493	−0.170831
$779$	−28.2784	−1.01318
$780$	0	0
$781$	1.98509	0.0710321
$782$	0.908925	0.0325031
$783$	14.5852	0.521234
$784$	−12.8706	−0.459663
$785$	−4.02701	−0.143730
$786$	−0.819687	−0.0292373
$787$	31.7594	1.13210	0.566050	−	0.824371i	$-0.308471\pi$
$787$	31.7594	1.13210	0.566050	+	0.824371i	$0.308471\pi$
$788$	−18.4047	−0.655640
$789$	−1.23994	−0.0441429
$790$	−4.26196	−0.151634
$791$	−21.3022	−0.757419
$792$	5.50645	0.195663
$793$	0	0
$794$	9.75886	0.346329
$795$	0.0109086	0.000386887 0
$796$	35.4671	1.25710
$797$	39.1785	1.38777	0.693887	−	0.720083i	$-0.255897\pi$
$797$	39.1785	1.38777	0.693887	+	0.720083i	$0.255897\pi$
$798$	0.540112	0.0191198
$799$	1.70407	0.0602855
$800$	23.4243	0.828174
$801$	30.1195	1.06422
$802$	12.6621	0.447114
$803$	2.84192	0.100289
$804$	−4.73187	−0.166880
$805$	−3.30821	−0.116599
$806$	0	0
$807$	−5.45409	−0.191993
$808$	16.8520	0.592850
$809$	6.29260	0.221236	0.110618	−	0.993863i	$-0.464717\pi$
$809$	6.29260	0.221236	0.110618	+	0.993863i	$0.464717\pi$
$810$	−2.46096	−0.0864692
$811$	1.88117	0.0660569	0.0330284	−	0.999454i	$-0.489485\pi$
$811$	1.88117	0.0660569	0.0330284	+	0.999454i	$0.489485\pi$
$812$	−25.1914	−0.884045
$813$	1.62405	0.0569580
$814$	2.33566	0.0818648
$815$	7.20845	0.252501
$816$	−0.278999	−0.00976691
$817$	14.0863	0.492816
$818$	7.60005	0.265730
$819$	0	0
$820$	9.02438	0.315145
$821$	−37.1928	−1.29804	−0.649019	−	0.760772i	$-0.724820\pi$
$821$	−37.1928	−1.29804	−0.649019	+	0.760772i	$0.724820\pi$
$822$	−2.26160	−0.0788825
$823$	32.6301	1.13741	0.568706	−	0.822541i	$-0.307444\pi$
$823$	32.6301	1.13741	0.568706	+	0.822541i	$0.307444\pi$
$824$	−26.8039	−0.933756
$825$	−1.12164	−0.0390504
$826$	5.41874	0.188542
$827$	24.7521	0.860713	0.430357	−	0.902659i	$-0.358388\pi$
$827$	24.7521	0.860713	0.430357	+	0.902659i	$0.358388\pi$
$828$	−20.7850	−0.722329
$829$	26.8337	0.931972	0.465986	−	0.884792i	$-0.345700\pi$
$829$	26.8337	0.931972	0.465986	+	0.884792i	$0.345700\pi$
$830$	−1.17063	−0.0406333
$831$	1.11747	0.0387646
$832$	0	0
$833$	−2.26274	−0.0783993
$834$	−1.69003	−0.0585211
$835$	−11.8446	−0.409899
$836$	5.58675	0.193222
$837$	−10.1530	−0.350940
$838$	3.97256	0.137230
$839$	−0.234629	−0.00810031	−0.00405015	−	0.999992i	$-0.501289\pi$
$839$	−0.234629	−0.00810031	−0.00405015	+	0.999992i	$0.501289\pi$
$840$	−0.369234	−0.0127398
$841$	75.0795	2.58895
$842$	3.21717	0.110871
$843$	5.07535	0.174804
$844$	−20.8013	−0.716012
$845$	0	0
$846$	5.54027	0.190478
$847$	1.41017	0.0484541
$848$	−0.200257	−0.00687687
$849$	−6.57580	−0.225681
$850$	1.05026	0.0360236
$851$	−18.8861	−0.647408
$852$	−0.836310	−0.0286515
$853$	−34.3397	−1.17577	−0.587884	−	0.808945i	$-0.700039\pi$
$853$	−34.3397	−1.17577	−0.587884	+	0.808945i	$0.700039\pi$
$854$	3.04498	0.104197
$855$	−5.45819	−0.186666
$856$	−11.7473	−0.401513
$857$	−52.5142	−1.79385	−0.896925	−	0.442182i	$-0.854205\pi$
$857$	−52.5142	−1.79385	−0.896925	+	0.442182i	$0.854205\pi$
$858$	0	0
$859$	−4.82353	−0.164577	−0.0822883	−	0.996609i	$-0.526223\pi$
$859$	−4.82353	−0.164577	−0.0822883	+	0.996609i	$0.526223\pi$
$860$	−4.49530	−0.153288
$861$	3.00715	0.102483
$862$	−20.3904	−0.694500
$863$	−22.2969	−0.758997	−0.379498	−	0.925192i	$-0.623903\pi$
$863$	−22.2969	−0.758997	−0.379498	+	0.925192i	$0.623903\pi$
$864$	−7.18348	−0.244387
$865$	−0.631119	−0.0214587
$866$	−6.47710	−0.220101
$867$	4.04110	0.137243
$868$	17.5362	0.595216
$869$	−14.6900	−0.498325
$870$	0.712130	0.0241435
$871$	0	0
$872$	−12.8454	−0.434999
$873$	36.8222	1.24624
$874$	6.42266	0.217250
$875$	−7.92249	−0.267829
$876$	−1.19729	−0.0404527
$877$	−17.5328	−0.592039	−0.296019	−	0.955182i	$-0.595659\pi$
$877$	−17.5328	−0.592039	−0.296019	+	0.955182i	$0.595659\pi$
$878$	−10.5016	−0.354412
$879$	−7.22085	−0.243553
$880$	−1.49336	−0.0503412
$881$	0.943503	0.0317874	0.0158937	−	0.999874i	$-0.494941\pi$
$881$	0.943503	0.0317874	0.0158937	+	0.999874i	$0.494941\pi$
$882$	−7.35664	−0.247711
$883$	−43.2575	−1.45573	−0.727866	−	0.685719i	$-0.759488\pi$
$883$	−43.2575	−1.45573	−0.727866	+	0.685719i	$0.759488\pi$
$884$	0	0
$885$	1.07742	0.0362170
$886$	−9.38711	−0.315366
$887$	36.0485	1.21039	0.605195	−	0.796077i	$-0.293095\pi$
$887$	36.0485	1.21039	0.605195	+	0.796077i	$0.293095\pi$
$888$	−2.10791	−0.0707367
$889$	−3.16803	−0.106252
$890$	2.97013	0.0995590
$891$	−8.48237	−0.284170
$892$	17.2449	0.577401
$893$	12.0413	0.402947
$894$	0.224814	0.00751890
$895$	−4.05573	−0.135568
$896$	16.0213	0.535234
$897$	0	0
$898$	8.01719	0.267537
$899$	−72.4515	−2.41639
$900$	−24.0170	−0.800567
$901$	−0.0352067	−0.00117291
$902$	−4.42234	−0.147248
$903$	−1.49795	−0.0498485
$904$	−28.2725	−0.940330
$905$	4.12683	0.137181
$906$	−1.77257	−0.0588898
$907$	36.0344	1.19650	0.598250	−	0.801309i	$-0.295863\pi$
$907$	36.0344	1.19650	0.598250	+	0.801309i	$0.295863\pi$
$908$	−0.119011	−0.00394951
$909$	−26.4910	−0.878650
$910$	0	0
$911$	−26.9133	−0.891677	−0.445839	−	0.895113i	$-0.647094\pi$
$911$	−26.9133	−0.891677	−0.445839	+	0.895113i	$0.647094\pi$
$912$	−1.97147	−0.0652818
$913$	−4.03491	−0.133536
$914$	17.6690	0.584439
$915$	0.605438	0.0200152
$916$	−23.0914	−0.762960
$917$	−9.62876	−0.317970
$918$	−0.322081	−0.0106303
$919$	−46.0399	−1.51872	−0.759359	−	0.650672i	$-0.774487\pi$
$919$	−46.0399	−1.51872	−0.759359	+	0.650672i	$0.774487\pi$
$920$	−4.39069	−0.144757
$921$	6.96843	0.229618
$922$	−7.91333	−0.260612
$923$	0	0
$924$	−0.594100	−0.0195445
$925$	−21.8229	−0.717532
$926$	8.38983	0.275707
$927$	42.1351	1.38390
$928$	−51.2609	−1.68272
$929$	−8.45239	−0.277314	−0.138657	−	0.990340i	$-0.544279\pi$
$929$	−8.45239	−0.277314	−0.138657	+	0.990340i	$0.544279\pi$
$930$	−0.495726	−0.0162555
$931$	−15.9890	−0.524019
$932$	−31.9386	−1.04618
$933$	−2.48688	−0.0814167
$934$	−12.2586	−0.401113
$935$	−0.262544	−0.00858610
$936$	0	0
$937$	30.6941	1.00273	0.501366	−	0.865236i	$-0.332831\pi$
$937$	30.6941	1.00273	0.501366	+	0.865236i	$0.332831\pi$
$938$	7.90273	0.258033
$939$	−5.53553	−0.180645
$940$	−3.84270	−0.125335
$941$	−8.73917	−0.284889	−0.142444	−	0.989803i	$-0.545496\pi$
$941$	−8.73917	−0.284889	−0.142444	+	0.989803i	$0.545496\pi$
$942$	−0.831391	−0.0270882
$943$	35.7591	1.16447
$944$	−19.7790	−0.643752
$945$	1.17228	0.0381342
$946$	2.20289	0.0716223
$947$	1.28286	0.0416875	0.0208437	−	0.999783i	$-0.493365\pi$
$947$	1.28286	0.0416875	0.0208437	+	0.999783i	$0.493365\pi$
$948$	6.18885	0.201005
$949$	0	0
$950$	7.42137	0.240781
$951$	4.65338	0.150896
$952$	1.19168	0.0386225
$953$	28.3044	0.916871	0.458435	−	0.888728i	$-0.348410\pi$
$953$	28.3044	0.916871	0.458435	+	0.888728i	$0.348410\pi$
$954$	−0.114464	−0.00370592
$955$	6.87868	0.222589
$956$	−19.1460	−0.619227
$957$	2.45455	0.0793444
$958$	−16.6741	−0.538716
$959$	−26.5668	−0.857886
$960$	0.367860	0.0118726
$961$	19.4347	0.626927
$962$	0	0
$963$	18.4665	0.595073
$964$	−9.09513	−0.292935
$965$	0.393062	0.0126531
$966$	−0.682992	−0.0219749
$967$	53.1966	1.71069	0.855343	−	0.518062i	$-0.173346\pi$
$967$	53.1966	1.71069	0.855343	+	0.518062i	$0.173346\pi$
$968$	1.87160	0.0601554
$969$	−0.346598	−0.0111343
$970$	3.63109	0.116587
$971$	−47.2817	−1.51734	−0.758671	−	0.651474i	$-0.774151\pi$
$971$	−47.2817	−1.51734	−0.758671	+	0.651474i	$0.774151\pi$
$972$	11.0838	0.355512
$973$	−19.8526	−0.636446
$974$	−6.06382	−0.194297
$975$	0	0
$976$	−11.1145	−0.355767
$977$	5.45529	0.174530	0.0872651	−	0.996185i	$-0.472187\pi$
$977$	5.45529	0.174530	0.0872651	+	0.996185i	$0.472187\pi$
$978$	1.48821	0.0475877
$979$	10.2374	0.327188
$980$	5.10252	0.162994
$981$	20.1927	0.644702
$982$	−1.52169	−0.0485590
$983$	40.9873	1.30729	0.653645	−	0.756801i	$-0.273239\pi$
$983$	40.9873	1.30729	0.653645	+	0.756801i	$0.273239\pi$
$984$	3.99112	0.127232
$985$	6.11164	0.194733
$986$	−2.29835	−0.0731945
$987$	−1.28048	−0.0407582
$988$	0	0
$989$	−17.8126	−0.566408
$990$	−0.853584	−0.0271287
$991$	−48.1942	−1.53094	−0.765469	−	0.643472i	$-0.777493\pi$
$991$	−48.1942	−1.53094	−0.765469	+	0.643472i	$0.777493\pi$
$992$	35.6836	1.13296
$993$	−3.81291	−0.120999
$994$	1.39673	0.0443016
$995$	−11.7776	−0.373374
$996$	1.69989	0.0538631
$997$	2.54972	0.0807504	0.0403752	−	0.999185i	$-0.487145\pi$
$997$	2.54972	0.0807504	0.0403752	+	0.999185i	$0.487145\pi$
$998$	8.80157	0.278609
$999$	6.69238	0.211737

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.2.a.k.1.3		6
13.3	even	3		143.2.e.c.100.4	✓	12
13.9	even	3		143.2.e.c.133.4	yes	12
13.12	even	2		1859.2.a.l.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.2.e.c.100.4	✓	12	13.3	even	3
143.2.e.c.133.4	yes	12	13.9	even	3
1859.2.a.k.1.3		6	1.1	even	1	trivial
1859.2.a.l.1.4		6	13.12	even	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:	\( N \)	\(=\)	\( 1859 = 11 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1859.a (trivial)

\(f(q)\)	\(=\)	\(q-0.498953 q^{2} -0.240597 q^{3} -1.75105 q^{4} +0.581470 q^{5} +0.120047 q^{6} +1.41017 q^{7} +1.87160 q^{8} -2.94211 q^{9} +O(q^{10})\)	\(q-0.498953 q^{2} -0.240597 q^{3} -1.75105 q^{4} +0.581470 q^{5} +0.120047 q^{6} +1.41017 q^{7} +1.87160 q^{8} -2.94211 q^{9} -0.290126 q^{10} -1.00000 q^{11} +0.421296 q^{12} -0.703610 q^{14} -0.139900 q^{15} +2.56825 q^{16} +0.451517 q^{17} +1.46798 q^{18} +3.19052 q^{19} -1.01818 q^{20} -0.339283 q^{21} +0.498953 q^{22} -4.03454 q^{23} -0.450300 q^{24} -4.66189 q^{25} +1.42965 q^{27} -2.46928 q^{28} +10.2019 q^{29} +0.0698034 q^{30} -7.10174 q^{31} -5.02463 q^{32} +0.240597 q^{33} -0.225286 q^{34} +0.819973 q^{35} +5.15177 q^{36} +4.68112 q^{37} -1.59192 q^{38} +1.08828 q^{40} -8.86324 q^{41} +0.169286 q^{42} +4.41503 q^{43} +1.75105 q^{44} -1.71075 q^{45} +2.01304 q^{46} +3.77409 q^{47} -0.617913 q^{48} -5.01141 q^{49} +2.32607 q^{50} -0.108634 q^{51} -0.0779742 q^{53} -0.713330 q^{54} -0.581470 q^{55} +2.63927 q^{56} -0.767629 q^{57} -5.09029 q^{58} -7.70134 q^{59} +0.244971 q^{60} -4.32766 q^{61} +3.54344 q^{62} -4.14889 q^{63} -2.62945 q^{64} -0.120047 q^{66} -11.2317 q^{67} -0.790628 q^{68} +0.970696 q^{69} -0.409128 q^{70} -1.98509 q^{71} -5.50645 q^{72} -2.84192 q^{73} -2.33566 q^{74} +1.12164 q^{75} -5.58675 q^{76} -1.41017 q^{77} +14.6900 q^{79} +1.49336 q^{80} +8.48237 q^{81} +4.42234 q^{82} +4.03491 q^{83} +0.594100 q^{84} +0.262544 q^{85} -2.20289 q^{86} -2.45455 q^{87} -1.87160 q^{88} -10.2374 q^{89} +0.853584 q^{90} +7.06466 q^{92} +1.70866 q^{93} -1.88309 q^{94} +1.85519 q^{95} +1.20891 q^{96} -12.5156 q^{97} +2.50046 q^{98} +2.94211 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{3} + 8 q^{4} - 6 q^{5} - 12 q^{6} - 3 q^{7} + 3 q^{8} + 7 q^{9}+O(q^{10}) \) 6 * q + q^3 + 8 * q^4 - 6 * q^5 - 12 * q^6 - 3 * q^7 + 3 * q^8 + 7 * q^9	\( 6 q + q^{3} + 8 q^{4} - 6 q^{5} - 12 q^{6} - 3 q^{7} + 3 q^{8} + 7 q^{9} - 3 q^{10} - 6 q^{11} - 17 q^{12} + 12 q^{14} + 4 q^{15} + 8 q^{16} + 2 q^{17} + 6 q^{18} - 10 q^{19} - 15 q^{20} - 12 q^{21} + 3 q^{23} - 14 q^{24} - 6 q^{25} + 10 q^{27} - 16 q^{28} + 3 q^{29} + 19 q^{30} - 5 q^{31} + q^{32} - q^{33} + 5 q^{34} - 13 q^{35} + 20 q^{36} - 25 q^{37} - 27 q^{38} - 8 q^{40} - 24 q^{41} + 13 q^{42} - 8 q^{43} - 8 q^{44} - 27 q^{45} - 18 q^{46} - 10 q^{47} - 28 q^{48} - q^{49} + 26 q^{50} - 17 q^{51} + 10 q^{53} - 47 q^{54} + 6 q^{55} + 15 q^{56} - 6 q^{58} + 4 q^{59} + 61 q^{60} - 21 q^{61} - 5 q^{62} - 6 q^{63} - 27 q^{64} + 12 q^{66} - 21 q^{67} + 14 q^{68} + 5 q^{69} - 31 q^{70} + 3 q^{71} + 50 q^{72} - 13 q^{73} - 38 q^{74} - 23 q^{75} - 8 q^{76} + 3 q^{77} - 4 q^{79} - 44 q^{80} + 34 q^{81} - 33 q^{82} - 8 q^{83} - 47 q^{84} + 13 q^{85} + 11 q^{86} - 51 q^{87} - 3 q^{88} + 9 q^{89} - 70 q^{90} + 15 q^{92} + 21 q^{93} + 10 q^{94} + 27 q^{95} + 19 q^{96} - 15 q^{97} - 21 q^{98} - 7 q^{99}+O(q^{100}) \) 6 * q + q^3 + 8 * q^4 - 6 * q^5 - 12 * q^6 - 3 * q^7 + 3 * q^8 + 7 * q^9 - 3 * q^10 - 6 * q^11 - 17 * q^12 + 12 * q^14 + 4 * q^15 + 8 * q^16 + 2 * q^17 + 6 * q^18 - 10 * q^19 - 15 * q^20 - 12 * q^21 + 3 * q^23 - 14 * q^24 - 6 * q^25 + 10 * q^27 - 16 * q^28 + 3 * q^29 + 19 * q^30 - 5 * q^31 + q^32 - q^33 + 5 * q^34 - 13 * q^35 + 20 * q^36 - 25 * q^37 - 27 * q^38 - 8 * q^40 - 24 * q^41 + 13 * q^42 - 8 * q^43 - 8 * q^44 - 27 * q^45 - 18 * q^46 - 10 * q^47 - 28 * q^48 - q^49 + 26 * q^50 - 17 * q^51 + 10 * q^53 - 47 * q^54 + 6 * q^55 + 15 * q^56 - 6 * q^58 + 4 * q^59 + 61 * q^60 - 21 * q^61 - 5 * q^62 - 6 * q^63 - 27 * q^64 + 12 * q^66 - 21 * q^67 + 14 * q^68 + 5 * q^69 - 31 * q^70 + 3 * q^71 + 50 * q^72 - 13 * q^73 - 38 * q^74 - 23 * q^75 - 8 * q^76 + 3 * q^77 - 4 * q^79 - 44 * q^80 + 34 * q^81 - 33 * q^82 - 8 * q^83 - 47 * q^84 + 13 * q^85 + 11 * q^86 - 51 * q^87 - 3 * q^88 + 9 * q^89 - 70 * q^90 + 15 * q^92 + 21 * q^93 + 10 * q^94 + 27 * q^95 + 19 * q^96 - 15 * q^97 - 21 * q^98 - 7 * q^99

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