LMFDB - Embedded newform 1502.2.a.e.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1502,2,Mod(1,1502)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1502, 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("1502.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1502 = 2 \cdot 751 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1502.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:	$11.9935303836$
Analytic rank:	$1$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 4x^{10} - 9x^{9} + 58x^{8} - 40x^{7} - 146x^{6} + 237x^{5} - 47x^{4} - 89x^{3} + 39x^{2} - 1 $ x^11 - 4x^10 - 9x^9 + 58x^8 - 40x^7 - 146x^6 + 237x^5 - 47x^4 - 89x^3 + 39*x^2 - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-3.30464$ of defining polynomial
Character	$\chi$	$=$	1502.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.42377 q^{3} +1.00000 q^{4} +0.121552 q^{5} +1.42377 q^{6} +1.78140 q^{7} -1.00000 q^{8} -0.972877 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.42377 q^{3} +1.00000 q^{4} +0.121552 q^{5} +1.42377 q^{6} +1.78140 q^{7} -1.00000 q^{8} -0.972877 q^{9} -0.121552 q^{10} -0.545822 q^{11} -1.42377 q^{12} -0.139039 q^{13} -1.78140 q^{14} -0.173063 q^{15} +1.00000 q^{16} +2.24245 q^{17} +0.972877 q^{18} -2.50537 q^{19} +0.121552 q^{20} -2.53630 q^{21} +0.545822 q^{22} +0.638338 q^{23} +1.42377 q^{24} -4.98523 q^{25} +0.139039 q^{26} +5.65647 q^{27} +1.78140 q^{28} -1.37065 q^{29} +0.173063 q^{30} -6.29761 q^{31} -1.00000 q^{32} +0.777125 q^{33} -2.24245 q^{34} +0.216533 q^{35} -0.972877 q^{36} +5.38212 q^{37} +2.50537 q^{38} +0.197960 q^{39} -0.121552 q^{40} +2.63198 q^{41} +2.53630 q^{42} -5.88097 q^{43} -0.545822 q^{44} -0.118256 q^{45} -0.638338 q^{46} +10.1400 q^{47} -1.42377 q^{48} -3.82662 q^{49} +4.98523 q^{50} -3.19273 q^{51} -0.139039 q^{52} -10.8475 q^{53} -5.65647 q^{54} -0.0663460 q^{55} -1.78140 q^{56} +3.56707 q^{57} +1.37065 q^{58} +4.44925 q^{59} -0.173063 q^{60} +3.05171 q^{61} +6.29761 q^{62} -1.73308 q^{63} +1.00000 q^{64} -0.0169005 q^{65} -0.777125 q^{66} +2.06092 q^{67} +2.24245 q^{68} -0.908846 q^{69} -0.216533 q^{70} -0.564116 q^{71} +0.972877 q^{72} -9.39380 q^{73} -5.38212 q^{74} +7.09782 q^{75} -2.50537 q^{76} -0.972326 q^{77} -0.197960 q^{78} -9.19830 q^{79} +0.121552 q^{80} -5.13488 q^{81} -2.63198 q^{82} +5.37747 q^{83} -2.53630 q^{84} +0.272575 q^{85} +5.88097 q^{86} +1.95148 q^{87} +0.545822 q^{88} +9.06536 q^{89} +0.118256 q^{90} -0.247684 q^{91} +0.638338 q^{92} +8.96635 q^{93} -10.1400 q^{94} -0.304534 q^{95} +1.42377 q^{96} -13.9022 q^{97} +3.82662 q^{98} +0.531018 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - 11 q^{2} - 4 q^{3} + 11 q^{4} + q^{5} + 4 q^{6} - 6 q^{7} - 11 q^{8} + 3 q^{9}+O(q^{10}) $ 11 * q - 11 * q^2 - 4 * q^3 + 11 * q^4 + q^5 + 4 * q^6 - 6 * q^7 - 11 * q^8 + 3 * q^9	\( 11 q - 11 q^{2} - 4 q^{3} + 11 q^{4} + q^{5} + 4 q^{6} - 6 q^{7} - 11 q^{8} + 3 q^{9} - q^{10} + 4 q^{11} - 4 q^{12} - 19 q^{13} + 6 q^{14} + q^{15} + 11 q^{16} - 8 q^{17} - 3 q^{18} - 9 q^{19} + q^{20} - 6 q^{21} - 4 q^{22} + 2 q^{23} + 4 q^{24} - 2 q^{25} + 19 q^{26} - 16 q^{27} - 6 q^{28} + 13 q^{29} - q^{30} - 19 q^{31} - 11 q^{32} - 37 q^{33} + 8 q^{34} + 3 q^{35} + 3 q^{36} - 29 q^{37} + 9 q^{38} + 8 q^{39} - q^{40} - 23 q^{41} + 6 q^{42} - 13 q^{43} + 4 q^{44} - 6 q^{45} - 2 q^{46} - 16 q^{47} - 4 q^{48} - 5 q^{49} + 2 q^{50} + 33 q^{51} - 19 q^{52} - 25 q^{53} + 16 q^{54} - 14 q^{55} + 6 q^{56} + 4 q^{57} - 13 q^{58} + 6 q^{59} + q^{60} + 10 q^{61} + 19 q^{62} - 7 q^{63} + 11 q^{64} - 19 q^{65} + 37 q^{66} - 16 q^{67} - 8 q^{68} - 25 q^{69} - 3 q^{70} + 8 q^{71} - 3 q^{72} - 56 q^{73} + 29 q^{74} - 50 q^{75} - 9 q^{76} - 7 q^{77} - 8 q^{78} + 2 q^{79} + q^{80} - 5 q^{81} + 23 q^{82} + 21 q^{83} - 6 q^{84} - 55 q^{85} + 13 q^{86} - 11 q^{87} - 4 q^{88} - 24 q^{89} + 6 q^{90} - 43 q^{91} + 2 q^{92} + 10 q^{93} + 16 q^{94} + 25 q^{95} + 4 q^{96} - 84 q^{97} + 5 q^{98} + 14 q^{99}+O(q^{100}) \) 11 * q - 11 * q^2 - 4 * q^3 + 11 * q^4 + q^5 + 4 * q^6 - 6 * q^7 - 11 * q^8 + 3 * q^9 - q^10 + 4 * q^11 - 4 * q^12 - 19 * q^13 + 6 * q^14 + q^15 + 11 * q^16 - 8 * q^17 - 3 * q^18 - 9 * q^19 + q^20 - 6 * q^21 - 4 * q^22 + 2 * q^23 + 4 * q^24 - 2 * q^25 + 19 * q^26 - 16 * q^27 - 6 * q^28 + 13 * q^29 - q^30 - 19 * q^31 - 11 * q^32 - 37 * q^33 + 8 * q^34 + 3 * q^35 + 3 * q^36 - 29 * q^37 + 9 * q^38 + 8 * q^39 - q^40 - 23 * q^41 + 6 * q^42 - 13 * q^43 + 4 * q^44 - 6 * q^45 - 2 * q^46 - 16 * q^47 - 4 * q^48 - 5 * q^49 + 2 * q^50 + 33 * q^51 - 19 * q^52 - 25 * q^53 + 16 * q^54 - 14 * q^55 + 6 * q^56 + 4 * q^57 - 13 * q^58 + 6 * q^59 + q^60 + 10 * q^61 + 19 * q^62 - 7 * q^63 + 11 * q^64 - 19 * q^65 + 37 * q^66 - 16 * q^67 - 8 * q^68 - 25 * q^69 - 3 * q^70 + 8 * q^71 - 3 * q^72 - 56 * q^73 + 29 * q^74 - 50 * q^75 - 9 * q^76 - 7 * q^77 - 8 * q^78 + 2 * q^79 + q^80 - 5 * q^81 + 23 * q^82 + 21 * q^83 - 6 * q^84 - 55 * q^85 + 13 * q^86 - 11 * q^87 - 4 * q^88 - 24 * q^89 + 6 * q^90 - 43 * q^91 + 2 * q^92 + 10 * q^93 + 16 * q^94 + 25 * q^95 + 4 * q^96 - 84 * q^97 + 5 * q^98 + 14 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.42377	−0.822014	−0.411007	−	0.911632i	$-0.634823\pi$
$3$	−1.42377	−0.822014	−0.411007	+	0.911632i	$0.634823\pi$
$4$	1.00000	0.500000
$5$	0.121552	0.0543599	0.0271800	−	0.999631i	$-0.491347\pi$
$5$	0.121552	0.0543599	0.0271800	+	0.999631i	$0.491347\pi$
$6$	1.42377	0.581252
$7$	1.78140	0.673305	0.336652	−	0.941629i	$-0.390705\pi$
$7$	1.78140	0.673305	0.336652	+	0.941629i	$0.390705\pi$
$8$	−1.00000	−0.353553
$9$	−0.972877	−0.324292
$10$	−0.121552	−0.0384383
$11$	−0.545822	−0.164571	−0.0822857	−	0.996609i	$-0.526222\pi$
$11$	−0.545822	−0.164571	−0.0822857	+	0.996609i	$0.526222\pi$
$12$	−1.42377	−0.411007
$13$	−0.139039	−0.0385625	−0.0192812	−	0.999814i	$-0.506138\pi$
$13$	−0.139039	−0.0385625	−0.0192812	+	0.999814i	$0.506138\pi$
$14$	−1.78140	−0.476099
$15$	−0.173063	−0.0446846
$16$	1.00000	0.250000
$17$	2.24245	0.543874	0.271937	−	0.962315i	$-0.412336\pi$
$17$	2.24245	0.543874	0.271937	+	0.962315i	$0.412336\pi$
$18$	0.972877	0.229309
$19$	−2.50537	−0.574771	−0.287386	−	0.957815i	$-0.592786\pi$
$19$	−2.50537	−0.574771	−0.287386	+	0.957815i	$0.592786\pi$
$20$	0.121552	0.0271800
$21$	−2.53630	−0.553466
$22$	0.545822	0.116370
$23$	0.638338	0.133103	0.0665513	−	0.997783i	$-0.478800\pi$
$23$	0.638338	0.133103	0.0665513	+	0.997783i	$0.478800\pi$
$24$	1.42377	0.290626
$25$	−4.98523	−0.997045
$26$	0.139039	0.0272678
$27$	5.65647	1.08859
$28$	1.78140	0.336652
$29$	−1.37065	−0.254522	−0.127261	−	0.991869i	$-0.540619\pi$
$29$	−1.37065	−0.254522	−0.127261	+	0.991869i	$0.540619\pi$
$30$	0.173063	0.0315968
$31$	−6.29761	−1.13108	−0.565542	−	0.824720i	$-0.691333\pi$
$31$	−6.29761	−1.13108	−0.565542	+	0.824720i	$0.691333\pi$
$32$	−1.00000	−0.176777
$33$	0.777125	0.135280
$34$	−2.24245	−0.384577
$35$	0.216533	0.0366008
$36$	−0.972877	−0.162146
$37$	5.38212	0.884814	0.442407	−	0.896814i	$-0.354125\pi$
$37$	5.38212	0.884814	0.442407	+	0.896814i	$0.354125\pi$
$38$	2.50537	0.406425
$39$	0.197960	0.0316989
$40$	−0.121552	−0.0192191
$41$	2.63198	0.411047	0.205523	−	0.978652i	$-0.434110\pi$
$41$	2.63198	0.411047	0.205523	+	0.978652i	$0.434110\pi$
$42$	2.53630	0.391360
$43$	−5.88097	−0.896840	−0.448420	−	0.893823i	$-0.648013\pi$
$43$	−5.88097	−0.896840	−0.448420	+	0.893823i	$0.648013\pi$
$44$	−0.545822	−0.0822857
$45$	−0.118256	−0.0176285
$46$	−0.638338	−0.0941178
$47$	10.1400	1.47907	0.739533	−	0.673120i	$-0.235046\pi$
$47$	10.1400	1.47907	0.739533	+	0.673120i	$0.235046\pi$
$48$	−1.42377	−0.205504
$49$	−3.82662	−0.546660
$50$	4.98523	0.705017
$51$	−3.19273	−0.447072
$52$	−0.139039	−0.0192812
$53$	−10.8475	−1.49002	−0.745012	−	0.667052i	$-0.767556\pi$
$53$	−10.8475	−1.49002	−0.745012	+	0.667052i	$0.767556\pi$
$54$	−5.65647	−0.769748
$55$	−0.0663460	−0.00894609
$56$	−1.78140	−0.238049
$57$	3.56707	0.472470
$58$	1.37065	0.179975
$59$	4.44925	0.579243	0.289622	−	0.957141i	$-0.406470\pi$
$59$	4.44925	0.579243	0.289622	+	0.957141i	$0.406470\pi$
$60$	−0.173063	−0.0223423
$61$	3.05171	0.390732	0.195366	−	0.980730i	$-0.437411\pi$
$61$	3.05171	0.390732	0.195366	+	0.980730i	$0.437411\pi$
$62$	6.29761	0.799797
$63$	−1.73308	−0.218348
$64$	1.00000	0.125000
$65$	−0.0169005	−0.00209625
$66$	−0.777125	−0.0956575
$67$	2.06092	0.251782	0.125891	−	0.992044i	$-0.459821\pi$
$67$	2.06092	0.251782	0.125891	+	0.992044i	$0.459821\pi$
$68$	2.24245	0.271937
$69$	−0.908846	−0.109412
$70$	−0.216533	−0.0258807
$71$	−0.564116	−0.0669482	−0.0334741	−	0.999440i	$-0.510657\pi$
$71$	−0.564116	−0.0669482	−0.0334741	+	0.999440i	$0.510657\pi$
$72$	0.972877	0.114655
$73$	−9.39380	−1.09946	−0.549730	−	0.835342i	$-0.685270\pi$
$73$	−9.39380	−1.09946	−0.549730	+	0.835342i	$0.685270\pi$
$74$	−5.38212	−0.625658
$75$	7.09782	0.819585
$76$	−2.50537	−0.287386
$77$	−0.972326	−0.110807
$78$	−0.197960	−0.0224145
$79$	−9.19830	−1.03489	−0.517445	−	0.855716i	$-0.673117\pi$
$79$	−9.19830	−1.03489	−0.517445	+	0.855716i	$0.673117\pi$
$80$	0.121552	0.0135900
$81$	−5.13488	−0.570542
$82$	−2.63198	−0.290654
$83$	5.37747	0.590254	0.295127	−	0.955458i	$-0.404638\pi$
$83$	5.37747	0.590254	0.295127	+	0.955458i	$0.404638\pi$
$84$	−2.53630	−0.276733
$85$	0.272575	0.0295649
$86$	5.88097	0.634162
$87$	1.95148	0.209221
$88$	0.545822	0.0581848
$89$	9.06536	0.960926	0.480463	−	0.877015i	$-0.340469\pi$
$89$	9.06536	0.960926	0.480463	+	0.877015i	$0.340469\pi$
$90$	0.118256	0.0124652
$91$	−0.247684	−0.0259643
$92$	0.638338	0.0665513
$93$	8.96635	0.929767
$94$	−10.1400	−1.04586
$95$	−0.304534	−0.0312445
$96$	1.42377	0.145313
$97$	−13.9022	−1.41155	−0.705775	−	0.708436i	$-0.749401\pi$
$97$	−13.9022	−1.41155	−0.705775	+	0.708436i	$0.749401\pi$
$98$	3.82662	0.386547
$99$	0.531018	0.0533693
$100$	−4.98523	−0.498523
$101$	−16.8947	−1.68109	−0.840545	−	0.541742i	$-0.817765\pi$
$101$	−16.8947	−1.68109	−0.840545	+	0.541742i	$0.817765\pi$
$102$	3.19273	0.316128
$103$	−18.6786	−1.84046	−0.920230	−	0.391379i	$-0.871998\pi$
$103$	−18.6786	−1.84046	−0.920230	+	0.391379i	$0.871998\pi$
$104$	0.139039	0.0136339
$105$	−0.308294	−0.0300864
$106$	10.8475	1.05361
$107$	−13.5509	−1.31001	−0.655007	−	0.755623i	$-0.727334\pi$
$107$	−13.5509	−1.31001	−0.655007	+	0.755623i	$0.727334\pi$
$108$	5.65647	0.544294
$109$	6.83452	0.654629	0.327314	−	0.944916i	$-0.393856\pi$
$109$	6.83452	0.654629	0.327314	+	0.944916i	$0.393856\pi$
$110$	0.0663460	0.00632584
$111$	−7.66290	−0.727330
$112$	1.78140	0.168326
$113$	−8.94386	−0.841367	−0.420684	−	0.907207i	$-0.638210\pi$
$113$	−8.94386	−0.841367	−0.420684	+	0.907207i	$0.638210\pi$
$114$	−3.56707	−0.334087
$115$	0.0775915	0.00723545
$116$	−1.37065	−0.127261
$117$	0.135268	0.0125055
$118$	−4.44925	−0.409587
$119$	3.99469	0.366193
$120$	0.173063	0.0157984
$121$	−10.7021	−0.972916
$122$	−3.05171	−0.276289
$123$	−3.74734	−0.337886
$124$	−6.29761	−0.565542
$125$	−1.21373	−0.108559
$126$	1.73308	0.154395
$127$	−19.9483	−1.77012	−0.885062	−	0.465472i	$-0.845884\pi$
$127$	−19.9483	−1.77012	−0.885062	+	0.465472i	$0.845884\pi$
$128$	−1.00000	−0.0883883
$129$	8.37316	0.737215
$130$	0.0169005	0.00148227
$131$	11.5570	1.00974	0.504870	−	0.863196i	$-0.331541\pi$
$131$	11.5570	1.00974	0.504870	+	0.863196i	$0.331541\pi$
$132$	0.777125	0.0676401
$133$	−4.46306	−0.386996
$134$	−2.06092	−0.178037
$135$	0.687557	0.0591755
$136$	−2.24245	−0.192288
$137$	−18.2809	−1.56184	−0.780922	−	0.624629i	$-0.785250\pi$
$137$	−18.2809	−1.56184	−0.780922	+	0.624629i	$0.785250\pi$
$138$	0.908846	0.0773662
$139$	0.880915	0.0747183	0.0373591	−	0.999302i	$-0.488105\pi$
$139$	0.880915	0.0747183	0.0373591	+	0.999302i	$0.488105\pi$
$140$	0.216533	0.0183004
$141$	−14.4370	−1.21581
$142$	0.564116	0.0473396
$143$	0.0758905	0.00634628
$144$	−0.972877	−0.0810731
$145$	−0.166605	−0.0138358
$146$	9.39380	0.777436
$147$	5.44823	0.449363
$148$	5.38212	0.442407
$149$	11.3363	0.928709	0.464355	−	0.885649i	$-0.346286\pi$
$149$	11.3363	0.928709	0.464355	+	0.885649i	$0.346286\pi$
$150$	−7.09782	−0.579534
$151$	13.0632	1.06307	0.531535	−	0.847036i	$-0.321615\pi$
$151$	13.0632	1.06307	0.531535	+	0.847036i	$0.321615\pi$
$152$	2.50537	0.203212
$153$	−2.18163	−0.176374
$154$	0.972326	0.0783522
$155$	−0.765490	−0.0614856
$156$	0.197960	0.0158495
$157$	−21.9809	−1.75427	−0.877133	−	0.480247i	$-0.840547\pi$
$157$	−21.9809	−1.75427	−0.877133	+	0.480247i	$0.840547\pi$
$158$	9.19830	0.731778
$159$	15.4444	1.22482
$160$	−0.121552	−0.00960956
$161$	1.13713	0.0896186
$162$	5.13488	0.403434
$163$	−4.86702	−0.381214	−0.190607	−	0.981666i	$-0.561046\pi$
$163$	−4.86702	−0.381214	−0.190607	+	0.981666i	$0.561046\pi$
$164$	2.63198	0.205523
$165$	0.0944615	0.00735381
$166$	−5.37747	−0.417373
$167$	−8.99876	−0.696345	−0.348173	−	0.937430i	$-0.613198\pi$
$167$	−8.99876	−0.696345	−0.348173	+	0.937430i	$0.613198\pi$
$168$	2.53630	0.195680
$169$	−12.9807	−0.998513
$170$	−0.272575	−0.0209056
$171$	2.43742	0.186394
$172$	−5.88097	−0.448420
$173$	−21.8896	−1.66424	−0.832119	−	0.554597i	$-0.812872\pi$
$173$	−21.8896	−1.66424	−0.832119	+	0.554597i	$0.812872\pi$
$174$	−1.95148	−0.147942
$175$	−8.88067	−0.671315
$176$	−0.545822	−0.0411429
$177$	−6.33472	−0.476146
$178$	−9.06536	−0.679477
$179$	3.89045	0.290786	0.145393	−	0.989374i	$-0.453555\pi$
$179$	3.89045	0.290786	0.145393	+	0.989374i	$0.453555\pi$
$180$	−0.118256	−0.00881425
$181$	−0.729596	−0.0542305	−0.0271152	−	0.999632i	$-0.508632\pi$
$181$	−0.729596	−0.0542305	−0.0271152	+	0.999632i	$0.508632\pi$
$182$	0.247684	0.0183595
$183$	−4.34494	−0.321187
$184$	−0.638338	−0.0470589
$185$	0.654209	0.0480984
$186$	−8.96635	−0.657445
$187$	−1.22398	−0.0895061
$188$	10.1400	0.739533
$189$	10.0764	0.732951
$190$	0.304534	0.0220932
$191$	7.44350	0.538592	0.269296	−	0.963057i	$-0.413209\pi$
$191$	7.44350	0.538592	0.269296	+	0.963057i	$0.413209\pi$
$192$	−1.42377	−0.102752
$193$	16.3430	1.17639	0.588196	−	0.808718i	$-0.299838\pi$
$193$	16.3430	1.17639	0.588196	+	0.808718i	$0.299838\pi$
$194$	13.9022	0.998117
$195$	0.0240625	0.00172315
$196$	−3.82662	−0.273330
$197$	5.31064	0.378367	0.189184	−	0.981942i	$-0.439416\pi$
$197$	5.31064	0.378367	0.189184	+	0.981942i	$0.439416\pi$
$198$	−0.531018	−0.0377378
$199$	20.7946	1.47409	0.737045	−	0.675843i	$-0.236220\pi$
$199$	20.7946	1.47409	0.737045	+	0.675843i	$0.236220\pi$
$200$	4.98523	0.352509
$201$	−2.93428	−0.206968
$202$	16.8947	1.18871
$203$	−2.44166	−0.171371
$204$	−3.19273	−0.223536
$205$	0.319924	0.0223445
$206$	18.6786	1.30140
$207$	−0.621024	−0.0431642
$208$	−0.139039	−0.00964062
$209$	1.36749	0.0945910
$210$	0.308294	0.0212743
$211$	3.89554	0.268180	0.134090	−	0.990969i	$-0.457189\pi$
$211$	3.89554	0.268180	0.134090	+	0.990969i	$0.457189\pi$
$212$	−10.8475	−0.745012
$213$	0.803172	0.0550324
$214$	13.5509	0.926319
$215$	−0.714847	−0.0487521
$216$	−5.65647	−0.384874
$217$	−11.2185	−0.761564
$218$	−6.83452	−0.462892
$219$	13.3746	0.903773
$220$	−0.0663460	−0.00447304
$221$	−0.311788	−0.0209731
$222$	7.66290	0.514300
$223$	9.16642	0.613829	0.306914	−	0.951737i	$-0.400703\pi$
$223$	9.16642	0.613829	0.306914	+	0.951737i	$0.400703\pi$
$224$	−1.78140	−0.119025
$225$	4.85001	0.323334
$226$	8.94386	0.594936
$227$	22.4244	1.48836	0.744181	−	0.667978i	$-0.232840\pi$
$227$	22.4244	1.48836	0.744181	+	0.667978i	$0.232840\pi$
$228$	3.56707	0.236235
$229$	−0.142438	−0.00941257	−0.00470629	−	0.999989i	$-0.501498\pi$
$229$	−0.142438	−0.00941257	−0.00470629	+	0.999989i	$0.501498\pi$
$230$	−0.0775915	−0.00511623
$231$	1.38437	0.0910848
$232$	1.37065	0.0899873
$233$	4.37921	0.286891	0.143446	−	0.989658i	$-0.454182\pi$
$233$	4.37921	0.286891	0.143446	+	0.989658i	$0.454182\pi$
$234$	−0.135268	−0.00884274
$235$	1.23254	0.0804019
$236$	4.44925	0.289622
$237$	13.0963	0.850694
$238$	−3.99469	−0.258938
$239$	−28.0928	−1.81717	−0.908586	−	0.417699i	$-0.862837\pi$
$239$	−28.0928	−1.81717	−0.908586	+	0.417699i	$0.862837\pi$
$240$	−0.173063	−0.0111712
$241$	−15.8579	−1.02150	−0.510750	−	0.859729i	$-0.670632\pi$
$241$	−15.8579	−1.02150	−0.510750	+	0.859729i	$0.670632\pi$
$242$	10.7021	0.687956
$243$	−9.65851	−0.619594
$244$	3.05171	0.195366
$245$	−0.465135	−0.0297164
$246$	3.74734	0.238922
$247$	0.348344	0.0221646
$248$	6.29761	0.399899
$249$	−7.65629	−0.485197
$250$	1.21373	0.0767629
$251$	−11.1574	−0.704252	−0.352126	−	0.935953i	$-0.614541\pi$
$251$	−11.1574	−0.704252	−0.352126	+	0.935953i	$0.614541\pi$
$252$	−1.73308	−0.109174
$253$	−0.348419	−0.0219049
$254$	19.9483	1.25167
$255$	−0.388085	−0.0243028
$256$	1.00000	0.0625000
$257$	23.9756	1.49556	0.747778	−	0.663949i	$-0.231121\pi$
$257$	23.9756	1.49556	0.747778	+	0.663949i	$0.231121\pi$
$258$	−8.37316	−0.521290
$259$	9.58769	0.595750
$260$	−0.0169005	−0.00104813
$261$	1.33347	0.0825397
$262$	−11.5570	−0.713994
$263$	−3.75174	−0.231342	−0.115671	−	0.993288i	$-0.536902\pi$
$263$	−3.75174	−0.231342	−0.115671	+	0.993288i	$0.536902\pi$
$264$	−0.777125	−0.0478287
$265$	−1.31854	−0.0809975
$266$	4.46306	0.273648
$267$	−12.9070	−0.789895
$268$	2.06092	0.125891
$269$	−7.96903	−0.485881	−0.242940	−	0.970041i	$-0.578112\pi$
$269$	−7.96903	−0.485881	−0.242940	+	0.970041i	$0.578112\pi$
$270$	−0.687557	−0.0418434
$271$	5.83224	0.354283	0.177142	−	0.984185i	$-0.443315\pi$
$271$	5.83224	0.354283	0.177142	+	0.984185i	$0.443315\pi$
$272$	2.24245	0.135968
$273$	0.352645	0.0213430
$274$	18.2809	1.10439
$275$	2.72104	0.164085
$276$	−0.908846	−0.0547061
$277$	22.5858	1.35705	0.678526	−	0.734577i	$-0.262619\pi$
$277$	22.5858	1.35705	0.678526	+	0.734577i	$0.262619\pi$
$278$	−0.880915	−0.0528338
$279$	6.12680	0.366802
$280$	−0.216533	−0.0129403
$281$	11.3865	0.679260	0.339630	−	0.940559i	$-0.389698\pi$
$281$	11.3865	0.679260	0.339630	+	0.940559i	$0.389698\pi$
$282$	14.4370	0.859710
$283$	15.3113	0.910161	0.455080	−	0.890450i	$-0.349611\pi$
$283$	15.3113	0.910161	0.455080	+	0.890450i	$0.349611\pi$
$284$	−0.564116	−0.0334741
$285$	0.433586	0.0256834
$286$	−0.0758905	−0.00448750
$287$	4.68861	0.276760
$288$	0.972877	0.0573273
$289$	−11.9714	−0.704201
$290$	0.166605	0.00978340
$291$	19.7935	1.16031
$292$	−9.39380	−0.549730
$293$	−26.5206	−1.54935	−0.774674	−	0.632360i	$-0.782086\pi$
$293$	−26.5206	−1.54935	−0.774674	+	0.632360i	$0.782086\pi$
$294$	−5.44823	−0.317747
$295$	0.540818	0.0314876
$296$	−5.38212	−0.312829
$297$	−3.08742	−0.179150
$298$	−11.3363	−0.656696
$299$	−0.0887538	−0.00513277
$300$	7.09782	0.409793
$301$	−10.4763	−0.603847
$302$	−13.0632	−0.751704
$303$	24.0542	1.38188
$304$	−2.50537	−0.143693
$305$	0.370943	0.0212401
$306$	2.18163	0.124715
$307$	−15.8941	−0.907123	−0.453561	−	0.891225i	$-0.649847\pi$
$307$	−15.8941	−0.907123	−0.453561	+	0.891225i	$0.649847\pi$
$308$	−0.972326	−0.0554034
$309$	26.5941	1.51288
$310$	0.765490	0.0434769
$311$	25.2547	1.43207	0.716033	−	0.698067i	$-0.245956\pi$
$311$	25.2547	1.43207	0.716033	+	0.698067i	$0.245956\pi$
$312$	−0.197960	−0.0112073
$313$	−16.5991	−0.938236	−0.469118	−	0.883135i	$-0.655428\pi$
$313$	−16.5991	−0.938236	−0.469118	+	0.883135i	$0.655428\pi$
$314$	21.9809	1.24045
$315$	−0.210660	−0.0118694
$316$	−9.19830	−0.517445
$317$	−5.25615	−0.295215	−0.147607	−	0.989046i	$-0.547157\pi$
$317$	−5.25615	−0.295215	−0.147607	+	0.989046i	$0.547157\pi$
$318$	−15.4444	−0.866079
$319$	0.748128	0.0418871
$320$	0.121552	0.00679499
$321$	19.2933	1.07685
$322$	−1.13713	−0.0633700
$323$	−5.61817	−0.312603
$324$	−5.13488	−0.285271
$325$	0.693141	0.0384485
$326$	4.86702	0.269559
$327$	−9.73079	−0.538114
$328$	−2.63198	−0.145327
$329$	18.0633	0.995862
$330$	−0.0944615	−0.00519993
$331$	28.7508	1.58028	0.790142	−	0.612923i	$-0.210007\pi$
$331$	28.7508	1.58028	0.790142	+	0.612923i	$0.210007\pi$
$332$	5.37747	0.295127
$333$	−5.23614	−0.286939
$334$	8.99876	0.492390
$335$	0.250510	0.0136868
$336$	−2.53630	−0.138367
$337$	18.6050	1.01348	0.506741	−	0.862098i	$-0.330850\pi$
$337$	18.6050	1.01348	0.506741	+	0.862098i	$0.330850\pi$
$338$	12.9807	0.706055
$339$	12.7340	0.691616
$340$	0.272575	0.0147825
$341$	3.43737	0.186144
$342$	−2.43742	−0.131800
$343$	−19.2865	−1.04137
$344$	5.88097	0.317081
$345$	−0.110473	−0.00594764
$346$	21.8896	1.17679
$347$	12.9766	0.696621	0.348311	−	0.937379i	$-0.386755\pi$
$347$	12.9766	0.696621	0.348311	+	0.937379i	$0.386755\pi$
$348$	1.95148	0.104611
$349$	−29.8967	−1.60033	−0.800167	−	0.599778i	$-0.795256\pi$
$349$	−29.8967	−1.60033	−0.800167	+	0.599778i	$0.795256\pi$
$350$	8.88067	0.474692
$351$	−0.786469	−0.0419786
$352$	0.545822	0.0290924
$353$	−9.43292	−0.502064	−0.251032	−	0.967979i	$-0.580770\pi$
$353$	−9.43292	−0.502064	−0.251032	+	0.967979i	$0.580770\pi$
$354$	6.33472	0.336686
$355$	−0.0685697	−0.00363930
$356$	9.06536	0.480463
$357$	−5.68753	−0.301016
$358$	−3.89045	−0.205617
$359$	29.4680	1.55526	0.777629	−	0.628723i	$-0.216422\pi$
$359$	29.4680	1.55526	0.777629	+	0.628723i	$0.216422\pi$
$360$	0.118256	0.00623262
$361$	−12.7231	−0.669638
$362$	0.729596	0.0383467
$363$	15.2373	0.799751
$364$	−0.247684	−0.0129822
$365$	−1.14184	−0.0597666
$366$	4.34494	0.227114
$367$	−1.09425	−0.0571196	−0.0285598	−	0.999592i	$-0.509092\pi$
$367$	−1.09425	−0.0571196	−0.0285598	+	0.999592i	$0.509092\pi$
$368$	0.638338	0.0332757
$369$	−2.56060	−0.133299
$370$	−0.654209	−0.0340107
$371$	−19.3238	−1.00324
$372$	8.96635	0.464884
$373$	−4.66625	−0.241609	−0.120805	−	0.992676i	$-0.538547\pi$
$373$	−4.66625	−0.241609	−0.120805	+	0.992676i	$0.538547\pi$
$374$	1.22398	0.0632904
$375$	1.72807	0.0892372
$376$	−10.1400	−0.522929
$377$	0.190573	0.00981502
$378$	−10.0764	−0.518275
$379$	31.0167	1.59322	0.796610	−	0.604494i	$-0.206625\pi$
$379$	31.0167	1.59322	0.796610	+	0.604494i	$0.206625\pi$
$380$	−0.304534	−0.0156223
$381$	28.4018	1.45507
$382$	−7.44350	−0.380842
$383$	7.45470	0.380918	0.190459	−	0.981695i	$-0.439002\pi$
$383$	7.45470	0.380918	0.190459	+	0.981695i	$0.439002\pi$
$384$	1.42377	0.0726565
$385$	−0.118189	−0.00602345
$386$	−16.3430	−0.831835
$387$	5.72146	0.290838
$388$	−13.9022	−0.705775
$389$	11.3980	0.577904	0.288952	−	0.957344i	$-0.406693\pi$
$389$	11.3980	0.577904	0.288952	+	0.957344i	$0.406693\pi$
$390$	−0.0240625	−0.00121845
$391$	1.43144	0.0723910
$392$	3.82662	0.193274
$393$	−16.4545	−0.830020
$394$	−5.31064	−0.267546
$395$	−1.11808	−0.0562565
$396$	0.531018	0.0266846
$397$	26.8534	1.34773	0.673867	−	0.738853i	$-0.264632\pi$
$397$	26.8534	1.34773	0.673867	+	0.738853i	$0.264632\pi$
$398$	−20.7946	−1.04234
$399$	6.35438	0.318117
$400$	−4.98523	−0.249261
$401$	−4.82298	−0.240848	−0.120424	−	0.992723i	$-0.538425\pi$
$401$	−4.82298	−0.240848	−0.120424	+	0.992723i	$0.538425\pi$
$402$	2.93428	0.146349
$403$	0.875613	0.0436174
$404$	−16.8947	−0.840545
$405$	−0.624157	−0.0310146
$406$	2.44166	0.121178
$407$	−2.93768	−0.145615
$408$	3.19273	0.158064
$409$	−5.86729	−0.290119	−0.145059	−	0.989423i	$-0.546337\pi$
$409$	−5.86729	−0.290119	−0.145059	+	0.989423i	$0.546337\pi$
$410$	−0.319924	−0.0157999
$411$	26.0278	1.28386
$412$	−18.6786	−0.920230
$413$	7.92589	0.390007
$414$	0.621024	0.0305217
$415$	0.653645	0.0320862
$416$	0.139039	0.00681695
$417$	−1.25422	−0.0614195
$418$	−1.36749	−0.0668859
$419$	11.0633	0.540478	0.270239	−	0.962793i	$-0.412897\pi$
$419$	11.0633	0.540478	0.270239	+	0.962793i	$0.412897\pi$
$420$	−0.308294	−0.0150432
$421$	16.3284	0.795799	0.397900	−	0.917429i	$-0.369739\pi$
$421$	16.3284	0.795799	0.397900	+	0.917429i	$0.369739\pi$
$422$	−3.89554	−0.189632
$423$	−9.86494	−0.479650
$424$	10.8475	0.526803
$425$	−11.1791	−0.542267
$426$	−0.803172	−0.0389138
$427$	5.43631	0.263082
$428$	−13.5509	−0.655007
$429$	−0.108051	−0.00521674
$430$	0.714847	0.0344730
$431$	−30.0797	−1.44889	−0.724444	−	0.689334i	$-0.757903\pi$
$431$	−30.0797	−1.44889	−0.724444	+	0.689334i	$0.757903\pi$
$432$	5.65647	0.272147
$433$	1.02856	0.0494293	0.0247147	−	0.999695i	$-0.492132\pi$
$433$	1.02856	0.0494293	0.0247147	+	0.999695i	$0.492132\pi$
$434$	11.2185	0.538507
$435$	0.237208	0.0113732
$436$	6.83452	0.327314
$437$	−1.59927	−0.0765036
$438$	−13.3746	−0.639064
$439$	−18.6322	−0.889264	−0.444632	−	0.895713i	$-0.646666\pi$
$439$	−18.6322	−0.889264	−0.444632	+	0.895713i	$0.646666\pi$
$440$	0.0663460	0.00316292
$441$	3.72283	0.177278
$442$	0.311788	0.0148302
$443$	31.1259	1.47884	0.739419	−	0.673246i	$-0.235101\pi$
$443$	31.1259	1.47884	0.739419	+	0.673246i	$0.235101\pi$
$444$	−7.66290	−0.363665
$445$	1.10192	0.0522358
$446$	−9.16642	−0.434043
$447$	−16.1403	−0.763412
$448$	1.78140	0.0841631
$449$	−23.7286	−1.11982	−0.559910	−	0.828553i	$-0.689164\pi$
$449$	−23.7286	−1.11982	−0.559910	+	0.828553i	$0.689164\pi$
$450$	−4.85001	−0.228632
$451$	−1.43659	−0.0676466
$452$	−8.94386	−0.420684
$453$	−18.5990	−0.873859
$454$	−22.4244	−1.05243
$455$	−0.0301066	−0.00141142
$456$	−3.56707	−0.167044
$457$	−27.5244	−1.28754	−0.643768	−	0.765221i	$-0.722630\pi$
$457$	−27.5244	−1.28754	−0.643768	+	0.765221i	$0.722630\pi$
$458$	0.142438	0.00665569
$459$	12.6843	0.592054
$460$	0.0775915	0.00361772
$461$	−0.100308	−0.00467182	−0.00233591	−	0.999997i	$-0.500744\pi$
$461$	−0.100308	−0.00467182	−0.00233591	+	0.999997i	$0.500744\pi$
$462$	−1.38437	−0.0644067
$463$	−1.20112	−0.0558206	−0.0279103	−	0.999610i	$-0.508885\pi$
$463$	−1.20112	−0.0558206	−0.0279103	+	0.999610i	$0.508885\pi$
$464$	−1.37065	−0.0636306
$465$	1.08988	0.0505421
$466$	−4.37921	−0.202863
$467$	12.8183	0.593159	0.296579	−	0.955008i	$-0.404154\pi$
$467$	12.8183	0.593159	0.296579	+	0.955008i	$0.404154\pi$
$468$	0.135268	0.00625276
$469$	3.67132	0.169526
$470$	−1.23254	−0.0568527
$471$	31.2958	1.44203
$472$	−4.44925	−0.204793
$473$	3.20996	0.147594
$474$	−13.0963	−0.601532
$475$	12.4898	0.573073
$476$	3.99469	0.183096
$477$	10.5533	0.483203
$478$	28.0928	1.28493
$479$	26.4736	1.20961	0.604805	−	0.796374i	$-0.293251\pi$
$479$	26.4736	1.20961	0.604805	+	0.796374i	$0.293251\pi$
$480$	0.173063	0.00789920
$481$	−0.748324	−0.0341206
$482$	15.8579	0.722310
$483$	−1.61902	−0.0736678
$484$	−10.7021	−0.486458
$485$	−1.68984	−0.0767317
$486$	9.65851	0.438119
$487$	16.4323	0.744617	0.372309	−	0.928109i	$-0.378566\pi$
$487$	16.4323	0.744617	0.372309	+	0.928109i	$0.378566\pi$
$488$	−3.05171	−0.138144
$489$	6.92952	0.313364
$490$	0.465135	0.0210127
$491$	17.7368	0.800451	0.400226	−	0.916417i	$-0.368932\pi$
$491$	17.7368	0.800451	0.400226	+	0.916417i	$0.368932\pi$
$492$	−3.74734	−0.168943
$493$	−3.07360	−0.138428
$494$	−0.348344	−0.0156727
$495$	0.0645465	0.00290115
$496$	−6.29761	−0.282771
$497$	−1.00491	−0.0450766
$498$	7.65629	0.343086
$499$	37.3562	1.67229	0.836146	−	0.548507i	$-0.184804\pi$
$499$	37.3562	1.67229	0.836146	+	0.548507i	$0.184804\pi$
$500$	−1.21373	−0.0542796
$501$	12.8122	0.572406
$502$	11.1574	0.497981
$503$	−17.3138	−0.771986	−0.385993	−	0.922502i	$-0.626141\pi$
$503$	−17.3138	−0.771986	−0.385993	+	0.922502i	$0.626141\pi$
$504$	1.73308	0.0771976
$505$	−2.05360	−0.0913839
$506$	0.348419	0.0154891
$507$	18.4815	0.820792
$508$	−19.9483	−0.885062
$509$	−26.8448	−1.18987	−0.594937	−	0.803772i	$-0.702823\pi$
$509$	−26.8448	−1.18987	−0.594937	+	0.803772i	$0.702823\pi$
$510$	0.388085	0.0171847
$511$	−16.7341	−0.740272
$512$	−1.00000	−0.0441942
$513$	−14.1715	−0.625689
$514$	−23.9756	−1.05752
$515$	−2.27043	−0.100047
$516$	8.37316	0.368608
$517$	−5.53461	−0.243412
$518$	−9.58769	−0.421259
$519$	31.1658	1.36803
$520$	0.0169005	0.000741137 0
$521$	15.4516	0.676948	0.338474	−	0.940976i	$-0.390089\pi$
$521$	15.4516	0.676948	0.338474	+	0.940976i	$0.390089\pi$
$522$	−1.33347	−0.0583644
$523$	19.5643	0.855486	0.427743	−	0.903901i	$-0.359309\pi$
$523$	19.5643	0.855486	0.427743	+	0.903901i	$0.359309\pi$
$524$	11.5570	0.504870
$525$	12.6440	0.551831
$526$	3.75174	0.163584
$527$	−14.1221	−0.615167
$528$	0.777125	0.0338200
$529$	−22.5925	−0.982284
$530$	1.31854	0.0572739
$531$	−4.32858	−0.187844
$532$	−4.46306	−0.193498
$533$	−0.365948	−0.0158510
$534$	12.9070	0.558540
$535$	−1.64714	−0.0712122
$536$	−2.06092	−0.0890183
$537$	−5.53911	−0.239030
$538$	7.96903	0.343569
$539$	2.08865	0.0899647
$540$	0.687557	0.0295878
$541$	−6.94106	−0.298419	−0.149210	−	0.988806i	$-0.547673\pi$
$541$	−6.94106	−0.298419	−0.149210	+	0.988806i	$0.547673\pi$
$542$	−5.83224	−0.250516
$543$	1.03878	0.0445782
$544$	−2.24245	−0.0961442
$545$	0.830753	0.0355855
$546$	−0.352645	−0.0150918
$547$	−35.0893	−1.50031	−0.750155	−	0.661262i	$-0.770021\pi$
$547$	−35.0893	−1.50031	−0.750155	+	0.661262i	$0.770021\pi$
$548$	−18.2809	−0.780922
$549$	−2.96894	−0.126711
$550$	−2.72104	−0.116026
$551$	3.43397	0.146292
$552$	0.908846	0.0386831
$553$	−16.3858	−0.696797
$554$	−22.5858	−0.959580
$555$	−0.931444	−0.0395376
$556$	0.880915	0.0373591
$557$	2.90671	0.123161	0.0615807	−	0.998102i	$-0.480386\pi$
$557$	2.90671	0.123161	0.0615807	+	0.998102i	$0.480386\pi$
$558$	−6.12680	−0.259368
$559$	0.817685	0.0345844
$560$	0.216533	0.00915020
$561$	1.74266	0.0735753
$562$	−11.3865	−0.480309
$563$	−16.7056	−0.704057	−0.352028	−	0.935989i	$-0.614508\pi$
$563$	−16.7056	−0.704057	−0.352028	+	0.935989i	$0.614508\pi$
$564$	−14.4370	−0.607907
$565$	−1.08715	−0.0457366
$566$	−15.3113	−0.643581
$567$	−9.14726	−0.384149
$568$	0.564116	0.0236698
$569$	28.0605	1.17636	0.588178	−	0.808732i	$-0.299845\pi$
$569$	28.0605	1.17636	0.588178	+	0.808732i	$0.299845\pi$
$570$	−0.433586	−0.0181609
$571$	−12.5628	−0.525737	−0.262869	−	0.964832i	$-0.584669\pi$
$571$	−12.5628	−0.525737	−0.262869	+	0.964832i	$0.584669\pi$
$572$	0.0758905	0.00317314
$573$	−10.5978	−0.442731
$574$	−4.68861	−0.195699
$575$	−3.18226	−0.132709
$576$	−0.972877	−0.0405365
$577$	5.09785	0.212226	0.106113	−	0.994354i	$-0.466159\pi$
$577$	5.09785	0.212226	0.106113	+	0.994354i	$0.466159\pi$
$578$	11.9714	0.497945
$579$	−23.2686	−0.967011
$580$	−0.166605	−0.00691791
$581$	9.57942	0.397421
$582$	−19.7935	−0.820466
$583$	5.92082	0.245215
$584$	9.39380	0.388718
$585$	0.0164421	0.000679799 0
$586$	26.5206	1.09556
$587$	3.48193	0.143715	0.0718574	−	0.997415i	$-0.477107\pi$
$587$	3.48193	0.143715	0.0718574	+	0.997415i	$0.477107\pi$
$588$	5.44823	0.224681
$589$	15.7778	0.650115
$590$	−0.540818	−0.0222651
$591$	−7.56113	−0.311023
$592$	5.38212	0.221204
$593$	47.3309	1.94365	0.971824	−	0.235708i	$-0.0757410\pi$
$593$	47.3309	1.94365	0.971824	+	0.235708i	$0.0757410\pi$
$594$	3.08742	0.126678
$595$	0.485565	0.0199062
$596$	11.3363	0.464355
$597$	−29.6068	−1.21172
$598$	0.0887538	0.00362941
$599$	−22.6659	−0.926104	−0.463052	−	0.886331i	$-0.653246\pi$
$599$	−22.6659	−0.926104	−0.463052	+	0.886331i	$0.653246\pi$
$600$	−7.09782	−0.289767
$601$	−35.5617	−1.45059	−0.725296	−	0.688437i	$-0.758297\pi$
$601$	−35.5617	−1.45059	−0.725296	+	0.688437i	$0.758297\pi$
$602$	10.4763	0.426984
$603$	−2.00502	−0.0816509
$604$	13.0632	0.531535
$605$	−1.30086	−0.0528876
$606$	−24.0542	−0.977137
$607$	−10.4548	−0.424346	−0.212173	−	0.977232i	$-0.568054\pi$
$607$	−10.4548	−0.424346	−0.212173	+	0.977232i	$0.568054\pi$
$608$	2.50537	0.101606
$609$	3.47637	0.140870
$610$	−0.370943	−0.0150190
$611$	−1.40985	−0.0570365
$612$	−2.18163	−0.0881871
$613$	−18.5698	−0.750025	−0.375013	−	0.927020i	$-0.622362\pi$
$613$	−18.5698	−0.750025	−0.375013	+	0.927020i	$0.622362\pi$
$614$	15.8941	0.641433
$615$	−0.455498	−0.0183675
$616$	0.972326	0.0391761
$617$	−19.8105	−0.797543	−0.398771	−	0.917050i	$-0.630563\pi$
$617$	−19.8105	−0.797543	−0.398771	+	0.917050i	$0.630563\pi$
$618$	−26.5941	−1.06977
$619$	9.26449	0.372371	0.186186	−	0.982515i	$-0.440387\pi$
$619$	9.26449	0.372371	0.186186	+	0.982515i	$0.440387\pi$
$620$	−0.765490	−0.0307428
$621$	3.61074	0.144894
$622$	−25.2547	−1.01262
$623$	16.1490	0.646996
$624$	0.197960	0.00792473
$625$	24.7786	0.991144
$626$	16.5991	0.663433
$627$	−1.94699	−0.0777551
$628$	−21.9809	−0.877133
$629$	12.0691	0.481227
$630$	0.210660	0.00839290
$631$	−34.9785	−1.39247	−0.696237	−	0.717812i	$-0.745144\pi$
$631$	−34.9785	−1.39247	−0.696237	+	0.717812i	$0.745144\pi$
$632$	9.19830	0.365889
$633$	−5.54635	−0.220448
$634$	5.25615	0.208748
$635$	−2.42476	−0.0962238
$636$	15.4444	0.612410
$637$	0.532050	0.0210806
$638$	−0.748128	−0.0296187
$639$	0.548816	0.0217108
$640$	−0.121552	−0.00480478
$641$	3.28090	0.129588	0.0647939	−	0.997899i	$-0.479361\pi$
$641$	3.28090	0.129588	0.0647939	+	0.997899i	$0.479361\pi$
$642$	−19.2933	−0.761448
$643$	18.4176	0.726318	0.363159	−	0.931727i	$-0.381698\pi$
$643$	18.4176	0.726318	0.363159	+	0.931727i	$0.381698\pi$
$644$	1.13713	0.0448093
$645$	1.01778	0.0400750
$646$	5.61817	0.221044
$647$	7.97753	0.313629	0.156815	−	0.987628i	$-0.449877\pi$
$647$	7.97753	0.313629	0.156815	+	0.987628i	$0.449877\pi$
$648$	5.13488	0.201717
$649$	−2.42850	−0.0953269
$650$	−0.693141	−0.0271872
$651$	15.9726	0.626017
$652$	−4.86702	−0.190607
$653$	38.9753	1.52522	0.762611	−	0.646857i	$-0.223917\pi$
$653$	38.9753	1.52522	0.762611	+	0.646857i	$0.223917\pi$
$654$	9.73079	0.380504
$655$	1.40478	0.0548893
$656$	2.63198	0.102762
$657$	9.13901	0.356547
$658$	−18.0633	−0.704181
$659$	13.9734	0.544324	0.272162	−	0.962251i	$-0.412261\pi$
$659$	13.9734	0.544324	0.272162	+	0.962251i	$0.412261\pi$
$660$	0.0944615	0.00367691
$661$	−33.3895	−1.29870	−0.649351	−	0.760489i	$-0.724959\pi$
$661$	−33.3895	−1.29870	−0.649351	+	0.760489i	$0.724959\pi$
$662$	−28.7508	−1.11743
$663$	0.443915	0.0172402
$664$	−5.37747	−0.208686
$665$	−0.542496	−0.0210371
$666$	5.23614	0.202896
$667$	−0.874935	−0.0338776
$668$	−8.99876	−0.348173
$669$	−13.0509	−0.504576
$670$	−0.250510	−0.00967805
$671$	−1.66569	−0.0643033
$672$	2.53630	0.0978400
$673$	3.09538	0.119318	0.0596591	−	0.998219i	$-0.480999\pi$
$673$	3.09538	0.119318	0.0596591	+	0.998219i	$0.480999\pi$
$674$	−18.6050	−0.716640
$675$	−28.1988	−1.08537
$676$	−12.9807	−0.499256
$677$	−13.4482	−0.516855	−0.258428	−	0.966031i	$-0.583204\pi$
$677$	−13.4482	−0.516855	−0.258428	+	0.966031i	$0.583204\pi$
$678$	−12.7340	−0.489046
$679$	−24.7653	−0.950404
$680$	−0.272575	−0.0104528
$681$	−31.9273	−1.22346
$682$	−3.43737	−0.131624
$683$	−14.1811	−0.542626	−0.271313	−	0.962491i	$-0.587458\pi$
$683$	−14.1811	−0.542626	−0.271313	+	0.962491i	$0.587458\pi$
$684$	2.43742	0.0931970
$685$	−2.22209	−0.0849017
$686$	19.2865	0.736363
$687$	0.202799	0.00773727
$688$	−5.88097	−0.224210
$689$	1.50823	0.0574590
$690$	0.110473	0.00420562
$691$	−26.7077	−1.01601	−0.508004	−	0.861355i	$-0.669616\pi$
$691$	−26.7077	−1.01601	−0.508004	+	0.861355i	$0.669616\pi$
$692$	−21.8896	−0.832119
$693$	0.945953	0.0359338
$694$	−12.9766	−0.492586
$695$	0.107077	0.00406168
$696$	−1.95148	−0.0739708
$697$	5.90209	0.223558
$698$	29.8967	1.13161
$699$	−6.23498	−0.235829
$700$	−8.88067	−0.335658
$701$	−13.1497	−0.496658	−0.248329	−	0.968676i	$-0.579881\pi$
$701$	−13.1497	−0.496658	−0.248329	+	0.968676i	$0.579881\pi$
$702$	0.786469	0.0296834
$703$	−13.4842	−0.508566
$704$	−0.545822	−0.0205714
$705$	−1.75485	−0.0660915
$706$	9.43292	0.355013
$707$	−30.0962	−1.13189
$708$	−6.33472	−0.238073
$709$	44.2738	1.66274	0.831369	−	0.555721i	$-0.187558\pi$
$709$	44.2738	1.66274	0.831369	+	0.555721i	$0.187558\pi$
$710$	0.0685697	0.00257337
$711$	8.94882	0.335607
$712$	−9.06536	−0.339739
$713$	−4.02000	−0.150550
$714$	5.68753	0.212850
$715$	0.00922468	0.000344983 0
$716$	3.89045	0.145393
$717$	39.9977	1.49374
$718$	−29.4680	−1.09973
$719$	−45.0100	−1.67859	−0.839294	−	0.543677i	$-0.817032\pi$
$719$	−45.0100	−1.67859	−0.839294	+	0.543677i	$0.817032\pi$
$720$	−0.118256	−0.00440713
$721$	−33.2740	−1.23919
$722$	12.7231	0.473505
$723$	22.5781	0.839688
$724$	−0.729596	−0.0271152
$725$	6.83297	0.253770
$726$	−15.2373	−0.565509
$727$	−9.28660	−0.344421	−0.172210	−	0.985060i	$-0.555091\pi$
$727$	−9.28660	−0.344421	−0.172210	+	0.985060i	$0.555091\pi$
$728$	0.247684	0.00917977
$729$	29.1561	1.07986
$730$	1.14184	0.0422614
$731$	−13.1878	−0.487768
$732$	−4.34494	−0.160594
$733$	−5.29599	−0.195612	−0.0978059	−	0.995206i	$-0.531182\pi$
$733$	−5.29599	−0.195612	−0.0978059	+	0.995206i	$0.531182\pi$
$734$	1.09425	0.0403896
$735$	0.662246	0.0244273
$736$	−0.638338	−0.0235294
$737$	−1.12490	−0.0414361
$738$	2.56060	0.0942569
$739$	−28.9026	−1.06320	−0.531599	−	0.846996i	$-0.678409\pi$
$739$	−28.9026	−1.06320	−0.531599	+	0.846996i	$0.678409\pi$
$740$	0.654209	0.0240492
$741$	−0.495962	−0.0182196
$742$	19.3238	0.709398
$743$	−12.0144	−0.440767	−0.220384	−	0.975413i	$-0.570731\pi$
$743$	−12.0144	−0.440767	−0.220384	+	0.975413i	$0.570731\pi$
$744$	−8.96635	−0.328722
$745$	1.37796	0.0504845
$746$	4.66625	0.170844
$747$	−5.23162	−0.191415
$748$	−1.22398	−0.0447531
$749$	−24.1395	−0.882038
$750$	−1.72807	−0.0631002
$751$	−1.00000	−0.0364905
$751$	−1.00000	−0.0364905
$752$	10.1400	0.369766
$753$	15.8856	0.578905
$754$	−0.190573	−0.00694027
$755$	1.58787	0.0577884
$756$	10.0764	0.366476
$757$	30.7740	1.11850	0.559250	−	0.828999i	$-0.311089\pi$
$757$	30.7740	1.11850	0.559250	+	0.828999i	$0.311089\pi$
$758$	−31.0167	−1.12658
$759$	0.496068	0.0180061
$760$	0.304534	0.0110466
$761$	20.5362	0.744435	0.372218	−	0.928145i	$-0.378597\pi$
$761$	20.5362	0.744435	0.372218	+	0.928145i	$0.378597\pi$
$762$	−28.4018	−1.02889
$763$	12.1750	0.440765
$764$	7.44350	0.269296
$765$	−0.265182	−0.00958768
$766$	−7.45470	−0.269349
$767$	−0.618620	−0.0223371
$768$	−1.42377	−0.0513759
$769$	35.4991	1.28013	0.640065	−	0.768320i	$-0.278907\pi$
$769$	35.4991	1.28013	0.640065	+	0.768320i	$0.278907\pi$
$770$	0.118189	0.00425922
$771$	−34.1357	−1.22937
$772$	16.3430	0.588196
$773$	29.1609	1.04884	0.524422	−	0.851459i	$-0.324282\pi$
$773$	29.1609	1.04884	0.524422	+	0.851459i	$0.324282\pi$
$774$	−5.72146	−0.205654
$775$	31.3950	1.12774
$776$	13.9022	0.499058
$777$	−13.6507	−0.489715
$778$	−11.3980	−0.408640
$779$	−6.59409	−0.236258
$780$	0.0240625	0.000861575 0
$781$	0.307907	0.0110178
$782$	−1.43144	−0.0511882
$783$	−7.75301	−0.277070
$784$	−3.82662	−0.136665
$785$	−2.67183	−0.0953618
$786$	16.4545	0.586913
$787$	−21.8872	−0.780196	−0.390098	−	0.920773i	$-0.627559\pi$
$787$	−21.8872	−0.780196	−0.390098	+	0.920773i	$0.627559\pi$
$788$	5.31064	0.189184
$789$	5.34162	0.190167
$790$	1.11808	0.0397794
$791$	−15.9326	−0.566497
$792$	−0.531018	−0.0188689
$793$	−0.424307	−0.0150676
$794$	−26.8534	−0.952992
$795$	1.87730	0.0665811
$796$	20.7946	0.737045
$797$	−26.0908	−0.924182	−0.462091	−	0.886832i	$-0.652901\pi$
$797$	−26.0908	−0.924182	−0.462091	+	0.886832i	$0.652901\pi$
$798$	−6.35438	−0.224942
$799$	22.7384	0.804425
$800$	4.98523	0.176254
$801$	−8.81948	−0.311621
$802$	4.82298	0.170305
$803$	5.12734	0.180940
$804$	−2.93428	−0.103484
$805$	0.138221	0.00487166
$806$	−0.875613	−0.0308422
$807$	11.3461	0.399401
$808$	16.8947	0.594355
$809$	5.93340	0.208607	0.104304	−	0.994545i	$-0.466739\pi$
$809$	5.93340	0.208607	0.104304	+	0.994545i	$0.466739\pi$
$810$	0.624157	0.0219306
$811$	43.0650	1.51222	0.756108	−	0.654447i	$-0.227099\pi$
$811$	43.0650	1.51222	0.756108	+	0.654447i	$0.227099\pi$
$812$	−2.44166	−0.0856856
$813$	−8.30377	−0.291226
$814$	2.93768	0.102966
$815$	−0.591598	−0.0207228
$816$	−3.19273	−0.111768
$817$	14.7340	0.515478
$818$	5.86729	0.205145
$819$	0.240966	0.00842003
$820$	0.319924	0.0111722
$821$	27.5456	0.961346	0.480673	−	0.876900i	$-0.340392\pi$
$821$	27.5456	0.961346	0.480673	+	0.876900i	$0.340392\pi$
$822$	−26.0278	−0.907824
$823$	22.4713	0.783302	0.391651	−	0.920114i	$-0.371904\pi$
$823$	22.4713	0.783302	0.391651	+	0.920114i	$0.371904\pi$
$824$	18.6786	0.650701
$825$	−3.87414	−0.134880
$826$	−7.92589	−0.275777
$827$	31.7800	1.10510	0.552549	−	0.833481i	$-0.313655\pi$
$827$	31.7800	1.10510	0.552549	+	0.833481i	$0.313655\pi$
$828$	−0.621024	−0.0215821
$829$	51.0512	1.77308	0.886540	−	0.462651i	$-0.153102\pi$
$829$	51.0512	1.77308	0.886540	+	0.462651i	$0.153102\pi$
$830$	−0.653645	−0.0226883
$831$	−32.1571	−1.11552
$832$	−0.139039	−0.00482031
$833$	−8.58101	−0.297314
$834$	1.25422	0.0434301
$835$	−1.09382	−0.0378533
$836$	1.36749	0.0472955
$837$	−35.6222	−1.23128
$838$	−11.0633	−0.382176
$839$	41.1367	1.42020	0.710099	−	0.704102i	$-0.248650\pi$
$839$	41.1367	1.42020	0.710099	+	0.704102i	$0.248650\pi$
$840$	0.308294	0.0106371
$841$	−27.1213	−0.935218
$842$	−16.3284	−0.562715
$843$	−16.2117	−0.558362
$844$	3.89554	0.134090
$845$	−1.57783	−0.0542791
$846$	9.86494	0.339164
$847$	−19.0647	−0.655069
$848$	−10.8475	−0.372506
$849$	−21.7997	−0.748165
$850$	11.1791	0.383440
$851$	3.43561	0.117771
$852$	0.803172	0.0275162
$853$	−32.5402	−1.11415	−0.557077	−	0.830461i	$-0.688077\pi$
$853$	−32.5402	−1.11415	−0.557077	+	0.830461i	$0.688077\pi$
$854$	−5.43631	−0.186027
$855$	0.296274	0.0101324
$856$	13.5509	0.463160
$857$	1.29806	0.0443409	0.0221705	−	0.999754i	$-0.492942\pi$
$857$	1.29806	0.0443409	0.0221705	+	0.999754i	$0.492942\pi$
$858$	0.108051	0.00368879
$859$	−43.2036	−1.47409	−0.737045	−	0.675844i	$-0.763779\pi$
$859$	−43.2036	−1.47409	−0.737045	+	0.675844i	$0.763779\pi$
$860$	−0.714847	−0.0243761
$861$	−6.67550	−0.227501
$862$	30.0797	1.02452
$863$	−3.19802	−0.108862	−0.0544309	−	0.998518i	$-0.517334\pi$
$863$	−3.19802	−0.108862	−0.0544309	+	0.998518i	$0.517334\pi$
$864$	−5.65647	−0.192437
$865$	−2.66074	−0.0904678
$866$	−1.02856	−0.0349518
$867$	17.0446	0.578864
$868$	−11.2185	−0.380782
$869$	5.02063	0.170313
$870$	−0.237208	−0.00804209
$871$	−0.286549	−0.00970933
$872$	−6.83452	−0.231446
$873$	13.5251	0.457755
$874$	1.59927	0.0540962
$875$	−2.16213	−0.0730934
$876$	13.3746	0.451886
$877$	22.2171	0.750218	0.375109	−	0.926981i	$-0.377605\pi$
$877$	22.2171	0.750218	0.375109	+	0.926981i	$0.377605\pi$
$878$	18.6322	0.628805
$879$	37.7592	1.27359
$880$	−0.0663460	−0.00223652
$881$	4.76347	0.160485	0.0802426	−	0.996775i	$-0.474430\pi$
$881$	4.76347	0.160485	0.0802426	+	0.996775i	$0.474430\pi$
$882$	−3.72283	−0.125354
$883$	−10.6749	−0.359239	−0.179619	−	0.983736i	$-0.557487\pi$
$883$	−10.6749	−0.359239	−0.179619	+	0.983736i	$0.557487\pi$
$884$	−0.311788	−0.0104866
$885$	−0.770000	−0.0258833
$886$	−31.1259	−1.04570
$887$	−56.1101	−1.88399	−0.941997	−	0.335622i	$-0.891053\pi$
$887$	−56.1101	−1.88399	−0.941997	+	0.335622i	$0.891053\pi$
$888$	7.66290	0.257150
$889$	−35.5358	−1.19183
$890$	−1.10192	−0.0369363
$891$	2.80273	0.0938949
$892$	9.16642	0.306914
$893$	−25.4044	−0.850125
$894$	16.1403	0.539814
$895$	0.472894	0.0158071
$896$	−1.78140	−0.0595123
$897$	0.126365	0.00421921
$898$	23.7286	0.791832
$899$	8.63179	0.287886
$900$	4.85001	0.161667
$901$	−24.3250	−0.810385
$902$	1.43659	0.0478333
$903$	14.9159	0.496371
$904$	8.94386	0.297468
$905$	−0.0886842	−0.00294796
$906$	18.5990	0.617911
$907$	−51.5559	−1.71188	−0.855942	−	0.517071i	$-0.827022\pi$
$907$	−51.5559	−1.71188	−0.855942	+	0.517071i	$0.827022\pi$
$908$	22.4244	0.744181
$909$	16.4365	0.545165
$910$	0.0301066	0.000998023 0
$911$	7.80189	0.258488	0.129244	−	0.991613i	$-0.458745\pi$
$911$	7.80189	0.258488	0.129244	+	0.991613i	$0.458745\pi$
$912$	3.56707	0.118118
$913$	−2.93514	−0.0971390
$914$	27.5244	0.910426
$915$	−0.528138	−0.0174597
$916$	−0.142438	−0.00470629
$917$	20.5876	0.679862
$918$	−12.6843	−0.418646
$919$	23.6456	0.779997	0.389999	−	0.920815i	$-0.372475\pi$
$919$	23.6456	0.779997	0.389999	+	0.920815i	$0.372475\pi$
$920$	−0.0775915	−0.00255812
$921$	22.6295	0.745668
$922$	0.100308	0.00330347
$923$	0.0784341	0.00258169
$924$	1.38437	0.0455424
$925$	−26.8311	−0.882200
$926$	1.20112	0.0394711
$927$	18.1720	0.596847
$928$	1.37065	0.0449936
$929$	−2.44755	−0.0803014	−0.0401507	−	0.999194i	$-0.512784\pi$
$929$	−2.44755	−0.0803014	−0.0401507	+	0.999194i	$0.512784\pi$
$930$	−1.08988	−0.0357386
$931$	9.58711	0.314205
$932$	4.37921	0.143446
$933$	−35.9570	−1.17718
$934$	−12.8183	−0.419427
$935$	−0.148777	−0.00486554
$936$	−0.135268	−0.00442137
$937$	3.79015	0.123819	0.0619095	−	0.998082i	$-0.480281\pi$
$937$	3.79015	0.123819	0.0619095	+	0.998082i	$0.480281\pi$
$938$	−3.67132	−0.119873
$939$	23.6333	0.771244
$940$	1.23254	0.0402009
$941$	18.6286	0.607275	0.303638	−	0.952788i	$-0.401799\pi$
$941$	18.6286	0.607275	0.303638	+	0.952788i	$0.401799\pi$
$942$	−31.2958	−1.01967
$943$	1.68009	0.0547114
$944$	4.44925	0.144811
$945$	1.22481	0.0398432
$946$	−3.20996	−0.104365
$947$	−12.1364	−0.394380	−0.197190	−	0.980365i	$-0.563182\pi$
$947$	−12.1364	−0.394380	−0.197190	+	0.980365i	$0.563182\pi$
$948$	13.0963	0.425347
$949$	1.30610	0.0423979
$950$	−12.4898	−0.405224
$951$	7.48355	0.242671
$952$	−3.99469	−0.129469
$953$	−19.5710	−0.633968	−0.316984	−	0.948431i	$-0.602670\pi$
$953$	−19.5710	−0.633968	−0.316984	+	0.948431i	$0.602670\pi$
$954$	−10.5533	−0.341676
$955$	0.904775	0.0292778
$956$	−28.0928	−0.908586
$957$	−1.06516	−0.0344318
$958$	−26.4736	−0.855323
$959$	−32.5656	−1.05160
$960$	−0.173063	−0.00558558
$961$	8.65987	0.279351
$962$	0.748324	0.0241269
$963$	13.1833	0.424827
$964$	−15.8579	−0.510750
$965$	1.98653	0.0639486
$966$	1.61902	0.0520910
$967$	4.51288	0.145125	0.0725623	−	0.997364i	$-0.476882\pi$
$967$	4.51288	0.145125	0.0725623	+	0.997364i	$0.476882\pi$
$968$	10.7021	0.343978
$969$	7.99898	0.256964
$970$	1.68984	0.0542575
$971$	9.42735	0.302538	0.151269	−	0.988493i	$-0.451664\pi$
$971$	9.42735	0.302538	0.151269	+	0.988493i	$0.451664\pi$
$972$	−9.65851	−0.309797
$973$	1.56926	0.0503082
$974$	−16.4323	−0.526524
$975$	−0.986873	−0.0316052
$976$	3.05171	0.0976829
$977$	−18.7300	−0.599225	−0.299613	−	0.954061i	$-0.596857\pi$
$977$	−18.7300	−0.599225	−0.299613	+	0.954061i	$0.596857\pi$
$978$	−6.92952	−0.221582
$979$	−4.94807	−0.158141
$980$	−0.465135	−0.0148582
$981$	−6.64915	−0.212291
$982$	−17.7368	−0.566004
$983$	4.05307	0.129273	0.0646365	−	0.997909i	$-0.479411\pi$
$983$	4.05307	0.129273	0.0646365	+	0.997909i	$0.479411\pi$
$984$	3.74734	0.119461
$985$	0.645521	0.0205680
$986$	3.07360	0.0978834
$987$	−25.7180	−0.818613
$988$	0.348344	0.0110823
$989$	−3.75405	−0.119372
$990$	−0.0645465	−0.00205142
$991$	36.0829	1.14621	0.573105	−	0.819482i	$-0.305739\pi$
$991$	36.0829	1.14621	0.573105	+	0.819482i	$0.305739\pi$
$992$	6.29761	0.199949
$993$	−40.9345	−1.29902
$994$	1.00491	0.0318740
$995$	2.52764	0.0801314
$996$	−7.65629	−0.242599
$997$	21.1491	0.669800	0.334900	−	0.942254i	$-0.391298\pi$
$997$	21.1491	0.669800	0.334900	+	0.942254i	$0.391298\pi$
$998$	−37.3562	−1.18249
$999$	30.4438	0.963198

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1502.2.a.e.1.4	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1502.2.a.e.1.4	✓	11	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1502 = 2 \cdot 751 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1502.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.42377 q^{3} +1.00000 q^{4} +0.121552 q^{5} +1.42377 q^{6} +1.78140 q^{7} -1.00000 q^{8} -0.972877 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.42377 q^{3} +1.00000 q^{4} +0.121552 q^{5} +1.42377 q^{6} +1.78140 q^{7} -1.00000 q^{8} -0.972877 q^{9} -0.121552 q^{10} -0.545822 q^{11} -1.42377 q^{12} -0.139039 q^{13} -1.78140 q^{14} -0.173063 q^{15} +1.00000 q^{16} +2.24245 q^{17} +0.972877 q^{18} -2.50537 q^{19} +0.121552 q^{20} -2.53630 q^{21} +0.545822 q^{22} +0.638338 q^{23} +1.42377 q^{24} -4.98523 q^{25} +0.139039 q^{26} +5.65647 q^{27} +1.78140 q^{28} -1.37065 q^{29} +0.173063 q^{30} -6.29761 q^{31} -1.00000 q^{32} +0.777125 q^{33} -2.24245 q^{34} +0.216533 q^{35} -0.972877 q^{36} +5.38212 q^{37} +2.50537 q^{38} +0.197960 q^{39} -0.121552 q^{40} +2.63198 q^{41} +2.53630 q^{42} -5.88097 q^{43} -0.545822 q^{44} -0.118256 q^{45} -0.638338 q^{46} +10.1400 q^{47} -1.42377 q^{48} -3.82662 q^{49} +4.98523 q^{50} -3.19273 q^{51} -0.139039 q^{52} -10.8475 q^{53} -5.65647 q^{54} -0.0663460 q^{55} -1.78140 q^{56} +3.56707 q^{57} +1.37065 q^{58} +4.44925 q^{59} -0.173063 q^{60} +3.05171 q^{61} +6.29761 q^{62} -1.73308 q^{63} +1.00000 q^{64} -0.0169005 q^{65} -0.777125 q^{66} +2.06092 q^{67} +2.24245 q^{68} -0.908846 q^{69} -0.216533 q^{70} -0.564116 q^{71} +0.972877 q^{72} -9.39380 q^{73} -5.38212 q^{74} +7.09782 q^{75} -2.50537 q^{76} -0.972326 q^{77} -0.197960 q^{78} -9.19830 q^{79} +0.121552 q^{80} -5.13488 q^{81} -2.63198 q^{82} +5.37747 q^{83} -2.53630 q^{84} +0.272575 q^{85} +5.88097 q^{86} +1.95148 q^{87} +0.545822 q^{88} +9.06536 q^{89} +0.118256 q^{90} -0.247684 q^{91} +0.638338 q^{92} +8.96635 q^{93} -10.1400 q^{94} -0.304534 q^{95} +1.42377 q^{96} -13.9022 q^{97} +3.82662 q^{98} +0.531018 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 11 q^{2} - 4 q^{3} + 11 q^{4} + q^{5} + 4 q^{6} - 6 q^{7} - 11 q^{8} + 3 q^{9}+O(q^{10}) \) 11 * q - 11 * q^2 - 4 * q^3 + 11 * q^4 + q^5 + 4 * q^6 - 6 * q^7 - 11 * q^8 + 3 * q^9	\( 11 q - 11 q^{2} - 4 q^{3} + 11 q^{4} + q^{5} + 4 q^{6} - 6 q^{7} - 11 q^{8} + 3 q^{9} - q^{10} + 4 q^{11} - 4 q^{12} - 19 q^{13} + 6 q^{14} + q^{15} + 11 q^{16} - 8 q^{17} - 3 q^{18} - 9 q^{19} + q^{20} - 6 q^{21} - 4 q^{22} + 2 q^{23} + 4 q^{24} - 2 q^{25} + 19 q^{26} - 16 q^{27} - 6 q^{28} + 13 q^{29} - q^{30} - 19 q^{31} - 11 q^{32} - 37 q^{33} + 8 q^{34} + 3 q^{35} + 3 q^{36} - 29 q^{37} + 9 q^{38} + 8 q^{39} - q^{40} - 23 q^{41} + 6 q^{42} - 13 q^{43} + 4 q^{44} - 6 q^{45} - 2 q^{46} - 16 q^{47} - 4 q^{48} - 5 q^{49} + 2 q^{50} + 33 q^{51} - 19 q^{52} - 25 q^{53} + 16 q^{54} - 14 q^{55} + 6 q^{56} + 4 q^{57} - 13 q^{58} + 6 q^{59} + q^{60} + 10 q^{61} + 19 q^{62} - 7 q^{63} + 11 q^{64} - 19 q^{65} + 37 q^{66} - 16 q^{67} - 8 q^{68} - 25 q^{69} - 3 q^{70} + 8 q^{71} - 3 q^{72} - 56 q^{73} + 29 q^{74} - 50 q^{75} - 9 q^{76} - 7 q^{77} - 8 q^{78} + 2 q^{79} + q^{80} - 5 q^{81} + 23 q^{82} + 21 q^{83} - 6 q^{84} - 55 q^{85} + 13 q^{86} - 11 q^{87} - 4 q^{88} - 24 q^{89} + 6 q^{90} - 43 q^{91} + 2 q^{92} + 10 q^{93} + 16 q^{94} + 25 q^{95} + 4 q^{96} - 84 q^{97} + 5 q^{98} + 14 q^{99}+O(q^{100}) \) 11 * q - 11 * q^2 - 4 * q^3 + 11 * q^4 + q^5 + 4 * q^6 - 6 * q^7 - 11 * q^8 + 3 * q^9 - q^10 + 4 * q^11 - 4 * q^12 - 19 * q^13 + 6 * q^14 + q^15 + 11 * q^16 - 8 * q^17 - 3 * q^18 - 9 * q^19 + q^20 - 6 * q^21 - 4 * q^22 + 2 * q^23 + 4 * q^24 - 2 * q^25 + 19 * q^26 - 16 * q^27 - 6 * q^28 + 13 * q^29 - q^30 - 19 * q^31 - 11 * q^32 - 37 * q^33 + 8 * q^34 + 3 * q^35 + 3 * q^36 - 29 * q^37 + 9 * q^38 + 8 * q^39 - q^40 - 23 * q^41 + 6 * q^42 - 13 * q^43 + 4 * q^44 - 6 * q^45 - 2 * q^46 - 16 * q^47 - 4 * q^48 - 5 * q^49 + 2 * q^50 + 33 * q^51 - 19 * q^52 - 25 * q^53 + 16 * q^54 - 14 * q^55 + 6 * q^56 + 4 * q^57 - 13 * q^58 + 6 * q^59 + q^60 + 10 * q^61 + 19 * q^62 - 7 * q^63 + 11 * q^64 - 19 * q^65 + 37 * q^66 - 16 * q^67 - 8 * q^68 - 25 * q^69 - 3 * q^70 + 8 * q^71 - 3 * q^72 - 56 * q^73 + 29 * q^74 - 50 * q^75 - 9 * q^76 - 7 * q^77 - 8 * q^78 + 2 * q^79 + q^80 - 5 * q^81 + 23 * q^82 + 21 * q^83 - 6 * q^84 - 55 * q^85 + 13 * q^86 - 11 * q^87 - 4 * q^88 - 24 * q^89 + 6 * q^90 - 43 * q^91 + 2 * q^92 + 10 * q^93 + 16 * q^94 + 25 * q^95 + 4 * q^96 - 84 * q^97 + 5 * q^98 + 14 * q^99

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