LMFDB - Embedded newform 547.2.a.b.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [547,2,Mod(1,547)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(547, 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("547.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 547 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	547.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:	$4.36781699056$
Analytic rank:	$1$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 4 x^{17} - 18 x^{16} + 84 x^{15} + 116 x^{14} - 708 x^{13} - 282 x^{12} + 3104 x^{11} + \cdots + 328 $ x^18 - 4x^17 - 18x^16 + 84x^15 + 116x^14 - 708x^13 - 282x^12 + 3104x^11 - 137x^10 - 7703x^9 + 2068x^8 + 11068x^7 - 4274x^6 - 9021x^5 + 4048x^4 + 3834x^3 - 1851x^2 - 654*x + 328
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$-0.735255$ of defining polynomial
Character	$\chi$	$=$	547.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.735255 q^{2} +0.544167 q^{3} -1.45940 q^{4} +0.962787 q^{5} +0.400102 q^{6} -3.25298 q^{7} -2.54354 q^{8} -2.70388 q^{9} +O(q^{10})$	\(q+0.735255 q^{2} +0.544167 q^{3} -1.45940 q^{4} +0.962787 q^{5} +0.400102 q^{6} -3.25298 q^{7} -2.54354 q^{8} -2.70388 q^{9} +0.707894 q^{10} -0.883096 q^{11} -0.794158 q^{12} -4.48154 q^{13} -2.39177 q^{14} +0.523917 q^{15} +1.04865 q^{16} -3.18294 q^{17} -1.98804 q^{18} +4.12466 q^{19} -1.40509 q^{20} -1.77017 q^{21} -0.649301 q^{22} +3.73970 q^{23} -1.38411 q^{24} -4.07304 q^{25} -3.29508 q^{26} -3.10387 q^{27} +4.74740 q^{28} +6.33388 q^{29} +0.385213 q^{30} -8.47939 q^{31} +5.85811 q^{32} -0.480552 q^{33} -2.34028 q^{34} -3.13193 q^{35} +3.94604 q^{36} +11.0375 q^{37} +3.03268 q^{38} -2.43871 q^{39} -2.44889 q^{40} +1.41138 q^{41} -1.30152 q^{42} -9.31097 q^{43} +1.28879 q^{44} -2.60326 q^{45} +2.74963 q^{46} -5.82191 q^{47} +0.570639 q^{48} +3.58188 q^{49} -2.99473 q^{50} -1.73205 q^{51} +6.54036 q^{52} -7.06826 q^{53} -2.28213 q^{54} -0.850233 q^{55} +8.27409 q^{56} +2.24450 q^{57} +4.65702 q^{58} +12.9274 q^{59} -0.764605 q^{60} -3.04777 q^{61} -6.23452 q^{62} +8.79567 q^{63} +2.20991 q^{64} -4.31477 q^{65} -0.353328 q^{66} -9.15218 q^{67} +4.64518 q^{68} +2.03502 q^{69} -2.30277 q^{70} -4.57601 q^{71} +6.87744 q^{72} -14.4453 q^{73} +8.11538 q^{74} -2.21642 q^{75} -6.01952 q^{76} +2.87269 q^{77} -1.79308 q^{78} +7.20620 q^{79} +1.00962 q^{80} +6.42262 q^{81} +1.03773 q^{82} +7.39056 q^{83} +2.58338 q^{84} -3.06450 q^{85} -6.84594 q^{86} +3.44669 q^{87} +2.24619 q^{88} +0.838265 q^{89} -1.91406 q^{90} +14.5784 q^{91} -5.45771 q^{92} -4.61421 q^{93} -4.28059 q^{94} +3.97117 q^{95} +3.18779 q^{96} +0.475381 q^{97} +2.63360 q^{98} +2.38779 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 4 q^{2} - 10 q^{3} + 16 q^{4} - 27 q^{5} - 3 q^{6} - 11 q^{7} - 12 q^{8} + 14 q^{9}+O(q^{10}) $ 18 * q - 4 * q^2 - 10 * q^3 + 16 * q^4 - 27 * q^5 - 3 * q^6 - 11 * q^7 - 12 * q^8 + 14 * q^9	\( 18 q - 4 q^{2} - 10 q^{3} + 16 q^{4} - 27 q^{5} - 3 q^{6} - 11 q^{7} - 12 q^{8} + 14 q^{9} - 5 q^{10} + 2 q^{11} - 32 q^{12} - 25 q^{13} - 7 q^{14} + 9 q^{15} + 8 q^{16} - 30 q^{17} - 10 q^{18} + 4 q^{19} - 41 q^{20} - 16 q^{21} - 24 q^{22} - 26 q^{23} - 12 q^{24} + 31 q^{25} - 18 q^{26} - 37 q^{27} - 16 q^{28} - 18 q^{29} + 8 q^{30} - 5 q^{31} - 28 q^{32} - 10 q^{33} + 5 q^{34} - 9 q^{35} + 31 q^{36} - 18 q^{37} - 45 q^{38} + 7 q^{39} + 7 q^{40} - 17 q^{41} + 4 q^{42} + 8 q^{43} + 12 q^{44} - 44 q^{45} + 30 q^{46} - 52 q^{47} - 7 q^{48} + 29 q^{49} + 13 q^{50} + 19 q^{51} - 14 q^{52} - 60 q^{53} + 11 q^{54} + 11 q^{55} + 7 q^{56} + 4 q^{57} + 14 q^{58} - 8 q^{59} + 86 q^{60} - 26 q^{61} + 4 q^{62} - q^{63} + 44 q^{64} - 6 q^{65} + 18 q^{66} + 12 q^{67} - 61 q^{68} - 38 q^{69} + 35 q^{70} - q^{71} + 28 q^{72} - 2 q^{73} + 16 q^{74} - 17 q^{75} + 66 q^{76} - 73 q^{77} + 115 q^{78} + 18 q^{79} - 32 q^{80} + 18 q^{81} + 44 q^{82} - 43 q^{83} + 41 q^{84} + 51 q^{85} + 4 q^{86} + 3 q^{87} - 17 q^{88} - 28 q^{89} + 58 q^{90} - q^{91} - 68 q^{92} - 60 q^{93} + 78 q^{94} - 18 q^{95} + 29 q^{96} - 34 q^{97} + 34 q^{98} + 15 q^{99}+O(q^{100}) \) 18 * q - 4 * q^2 - 10 * q^3 + 16 * q^4 - 27 * q^5 - 3 * q^6 - 11 * q^7 - 12 * q^8 + 14 * q^9 - 5 * q^10 + 2 * q^11 - 32 * q^12 - 25 * q^13 - 7 * q^14 + 9 * q^15 + 8 * q^16 - 30 * q^17 - 10 * q^18 + 4 * q^19 - 41 * q^20 - 16 * q^21 - 24 * q^22 - 26 * q^23 - 12 * q^24 + 31 * q^25 - 18 * q^26 - 37 * q^27 - 16 * q^28 - 18 * q^29 + 8 * q^30 - 5 * q^31 - 28 * q^32 - 10 * q^33 + 5 * q^34 - 9 * q^35 + 31 * q^36 - 18 * q^37 - 45 * q^38 + 7 * q^39 + 7 * q^40 - 17 * q^41 + 4 * q^42 + 8 * q^43 + 12 * q^44 - 44 * q^45 + 30 * q^46 - 52 * q^47 - 7 * q^48 + 29 * q^49 + 13 * q^50 + 19 * q^51 - 14 * q^52 - 60 * q^53 + 11 * q^54 + 11 * q^55 + 7 * q^56 + 4 * q^57 + 14 * q^58 - 8 * q^59 + 86 * q^60 - 26 * q^61 + 4 * q^62 - q^63 + 44 * q^64 - 6 * q^65 + 18 * q^66 + 12 * q^67 - 61 * q^68 - 38 * q^69 + 35 * q^70 - q^71 + 28 * q^72 - 2 * q^73 + 16 * q^74 - 17 * q^75 + 66 * q^76 - 73 * q^77 + 115 * q^78 + 18 * q^79 - 32 * q^80 + 18 * q^81 + 44 * q^82 - 43 * q^83 + 41 * q^84 + 51 * q^85 + 4 * q^86 + 3 * q^87 - 17 * q^88 - 28 * q^89 + 58 * q^90 - q^91 - 68 * q^92 - 60 * q^93 + 78 * q^94 - 18 * q^95 + 29 * q^96 - 34 * q^97 + 34 * q^98 + 15 * 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 $

$2$	0.735255	0.519904	0.259952	−	0.965622i	$-0.416293\pi$
$2$	0.735255	0.519904	0.259952	+	0.965622i	$0.416293\pi$
$3$	0.544167	0.314175	0.157088	−	0.987585i	$-0.449790\pi$
$3$	0.544167	0.314175	0.157088	+	0.987585i	$0.449790\pi$
$4$	−1.45940	−0.729700
$5$	0.962787	0.430571	0.215286	−	0.976551i	$-0.430932\pi$
$5$	0.962787	0.430571	0.215286	+	0.976551i	$0.430932\pi$
$6$	0.400102	0.163341
$7$	−3.25298	−1.22951	−0.614755	−	0.788718i	$-0.710745\pi$
$7$	−3.25298	−1.22951	−0.614755	+	0.788718i	$0.710745\pi$
$8$	−2.54354	−0.899278
$9$	−2.70388	−0.901294
$10$	0.707894	0.223856
$11$	−0.883096	−0.266263	−0.133132	−	0.991098i	$-0.542503\pi$
$11$	−0.883096	−0.266263	−0.133132	+	0.991098i	$0.542503\pi$
$12$	−0.794158	−0.229254
$13$	−4.48154	−1.24296	−0.621478	−	0.783431i	$-0.713468\pi$
$13$	−4.48154	−1.24296	−0.621478	+	0.783431i	$0.713468\pi$
$14$	−2.39177	−0.639228
$15$	0.523917	0.135275
$16$	1.04865	0.262161
$17$	−3.18294	−0.771977	−0.385988	−	0.922504i	$-0.626140\pi$
$17$	−3.18294	−0.771977	−0.385988	+	0.922504i	$0.626140\pi$
$18$	−1.98804	−0.468586
$19$	4.12466	0.946261	0.473131	−	0.880992i	$-0.343124\pi$
$19$	4.12466	0.946261	0.473131	+	0.880992i	$0.343124\pi$
$20$	−1.40509	−0.314188
$21$	−1.77017	−0.386282
$22$	−0.649301	−0.138431
$23$	3.73970	0.779781	0.389890	−	0.920861i	$-0.372513\pi$
$23$	3.73970	0.779781	0.389890	+	0.920861i	$0.372513\pi$
$24$	−1.38411	−0.282531
$25$	−4.07304	−0.814608
$26$	−3.29508	−0.646218
$27$	−3.10387	−0.597339
$28$	4.74740	0.897174
$29$	6.33388	1.17617	0.588086	−	0.808798i	$-0.299881\pi$
$29$	6.33388	1.17617	0.588086	+	0.808798i	$0.299881\pi$
$30$	0.385213	0.0703300
$31$	−8.47939	−1.52294	−0.761472	−	0.648198i	$-0.775523\pi$
$31$	−8.47939	−1.52294	−0.761472	+	0.648198i	$0.775523\pi$
$32$	5.85811	1.03558
$33$	−0.480552	−0.0836533
$34$	−2.34028	−0.401354
$35$	−3.13193	−0.529392
$36$	3.94604	0.657674
$37$	11.0375	1.81455	0.907276	−	0.420535i	$-0.138158\pi$
$37$	11.0375	1.81455	0.907276	+	0.420535i	$0.138158\pi$
$38$	3.03268	0.491965
$39$	−2.43871	−0.390506
$40$	−2.44889	−0.387203
$41$	1.41138	0.220421	0.110210	−	0.993908i	$-0.464848\pi$
$41$	1.41138	0.220421	0.110210	+	0.993908i	$0.464848\pi$
$42$	−1.30152	−0.200829
$43$	−9.31097	−1.41991	−0.709955	−	0.704247i	$-0.751285\pi$
$43$	−9.31097	−1.41991	−0.709955	+	0.704247i	$0.751285\pi$
$44$	1.28879	0.194292
$45$	−2.60326	−0.388071
$46$	2.74963	0.405411
$47$	−5.82191	−0.849213	−0.424606	−	0.905378i	$-0.639587\pi$
$47$	−5.82191	−0.849213	−0.424606	+	0.905378i	$0.639587\pi$
$48$	0.570639	0.0823646
$49$	3.58188	0.511697
$50$	−2.99473	−0.423518
$51$	−1.73205	−0.242536
$52$	6.54036	0.906985
$53$	−7.06826	−0.970900	−0.485450	−	0.874264i	$-0.661344\pi$
$53$	−7.06826	−0.970900	−0.485450	+	0.874264i	$0.661344\pi$
$54$	−2.28213	−0.310559
$55$	−0.850233	−0.114645
$56$	8.27409	1.10567
$57$	2.24450	0.297292
$58$	4.65702	0.611497
$59$	12.9274	1.68301	0.841503	−	0.540252i	$-0.181671\pi$
$59$	12.9274	1.68301	0.841503	+	0.540252i	$0.181671\pi$
$60$	−0.764605	−0.0987100
$61$	−3.04777	−0.390227	−0.195114	−	0.980781i	$-0.562508\pi$
$61$	−3.04777	−0.390227	−0.195114	+	0.980781i	$0.562508\pi$
$62$	−6.23452	−0.791784
$63$	8.79567	1.10815
$64$	2.20991	0.276239
$65$	−4.31477	−0.535182
$66$	−0.353328	−0.0434917
$67$	−9.15218	−1.11812	−0.559059	−	0.829128i	$-0.688837\pi$
$67$	−9.15218	−1.11812	−0.559059	+	0.829128i	$0.688837\pi$
$68$	4.64518	0.563311
$69$	2.03502	0.244988
$70$	−2.30277	−0.275233
$71$	−4.57601	−0.543072	−0.271536	−	0.962428i	$-0.587532\pi$
$71$	−4.57601	−0.543072	−0.271536	+	0.962428i	$0.587532\pi$
$72$	6.87744	0.810514
$73$	−14.4453	−1.69070	−0.845349	−	0.534215i	$-0.820607\pi$
$73$	−14.4453	−1.69070	−0.845349	+	0.534215i	$0.820607\pi$
$74$	8.11538	0.943393
$75$	−2.21642	−0.255930
$76$	−6.01952	−0.690486
$77$	2.87269	0.327374
$78$	−1.79308	−0.203026
$79$	7.20620	0.810761	0.405381	−	0.914148i	$-0.367139\pi$
$79$	7.20620	0.810761	0.405381	+	0.914148i	$0.367139\pi$
$80$	1.00962	0.112879
$81$	6.42262	0.713625
$82$	1.03773	0.114598
$83$	7.39056	0.811219	0.405610	−	0.914046i	$-0.367059\pi$
$83$	7.39056	0.811219	0.405610	+	0.914046i	$0.367059\pi$
$84$	2.58338	0.281870
$85$	−3.06450	−0.332391
$86$	−6.84594	−0.738217
$87$	3.44669	0.369524
$88$	2.24619	0.239445
$89$	0.838265	0.0888559	0.0444280	−	0.999013i	$-0.485853\pi$
$89$	0.838265	0.0888559	0.0444280	+	0.999013i	$0.485853\pi$
$90$	−1.91406	−0.201760
$91$	14.5784	1.52823
$92$	−5.45771	−0.569006
$93$	−4.61421	−0.478471
$94$	−4.28059	−0.441509
$95$	3.97117	0.407433
$96$	3.18779	0.325353
$97$	0.475381	0.0482676	0.0241338	−	0.999709i	$-0.492317\pi$
$97$	0.475381	0.0482676	0.0241338	+	0.999709i	$0.492317\pi$
$98$	2.63360	0.266033
$99$	2.38779	0.239982
$100$	5.94419	0.594419
$101$	−3.07939	−0.306411	−0.153205	−	0.988194i	$-0.548960\pi$
$101$	−3.07939	−0.306411	−0.153205	+	0.988194i	$0.548960\pi$
$102$	−1.27350	−0.126095
$103$	−3.71378	−0.365929	−0.182965	−	0.983119i	$-0.558569\pi$
$103$	−3.71378	−0.365929	−0.182965	+	0.983119i	$0.558569\pi$
$104$	11.3990	1.11776
$105$	−1.70429	−0.166322
$106$	−5.19698	−0.504775
$107$	16.1036	1.55680	0.778398	−	0.627771i	$-0.216032\pi$
$107$	16.1036	1.55680	0.778398	+	0.627771i	$0.216032\pi$
$108$	4.52978	0.435878
$109$	2.61098	0.250087	0.125043	−	0.992151i	$-0.460093\pi$
$109$	2.61098	0.250087	0.125043	+	0.992151i	$0.460093\pi$
$110$	−0.625139	−0.0596046
$111$	6.00624	0.570087
$112$	−3.41122	−0.322330
$113$	−12.2204	−1.14960	−0.574798	−	0.818295i	$-0.694919\pi$
$113$	−12.2204	−1.14960	−0.574798	+	0.818295i	$0.694919\pi$
$114$	1.65028	0.154563
$115$	3.60053	0.335751
$116$	−9.24367	−0.858253
$117$	12.1176	1.12027
$118$	9.50495	0.875002
$119$	10.3540	0.949154
$120$	−1.33261	−0.121650
$121$	−10.2201	−0.929104
$122$	−2.24089	−0.202881
$123$	0.768028	0.0692508
$124$	12.3748	1.11129
$125$	−8.73541	−0.781318
$126$	6.46707	0.576132
$127$	5.90845	0.524290	0.262145	−	0.965028i	$-0.415570\pi$
$127$	5.90845	0.524290	0.262145	+	0.965028i	$0.415570\pi$
$128$	−10.0914	−0.891959
$129$	−5.06673	−0.446100
$130$	−3.17246	−0.278243
$131$	4.91027	0.429012	0.214506	−	0.976723i	$-0.431186\pi$
$131$	4.91027	0.429012	0.214506	+	0.976723i	$0.431186\pi$
$132$	0.701317	0.0610418
$133$	−13.4174	−1.16344
$134$	−6.72919	−0.581314
$135$	−2.98836	−0.257197
$136$	8.09595	0.694222
$137$	−8.29905	−0.709036	−0.354518	−	0.935049i	$-0.615355\pi$
$137$	−8.29905	−0.709036	−0.354518	+	0.935049i	$0.615355\pi$
$138$	1.49626	0.127370
$139$	21.0776	1.78778	0.893889	−	0.448288i	$-0.147966\pi$
$139$	21.0776	1.78778	0.893889	+	0.448288i	$0.147966\pi$
$140$	4.57073	0.386297
$141$	−3.16809	−0.266802
$142$	−3.36453	−0.282345
$143$	3.95763	0.330954
$144$	−2.83541	−0.236284
$145$	6.09818	0.506426
$146$	−10.6210	−0.879001
$147$	1.94914	0.160762
$148$	−16.1081	−1.32408
$149$	−20.9236	−1.71413	−0.857063	−	0.515212i	$-0.827713\pi$
$149$	−20.9236	−1.71413	−0.857063	+	0.515212i	$0.827713\pi$
$150$	−1.62963	−0.133059
$151$	−12.2666	−0.998241	−0.499121	−	0.866533i	$-0.666344\pi$
$151$	−12.2666	−0.998241	−0.499121	+	0.866533i	$0.666344\pi$
$152$	−10.4912	−0.850952
$153$	8.60630	0.695778
$154$	2.11216	0.170203
$155$	−8.16385	−0.655736
$156$	3.55905	0.284952
$157$	9.63793	0.769191	0.384595	−	0.923085i	$-0.374341\pi$
$157$	9.63793	0.769191	0.384595	+	0.923085i	$0.374341\pi$
$158$	5.29840	0.421518
$159$	−3.84632	−0.305033
$160$	5.64011	0.445890
$161$	−12.1652	−0.958749
$162$	4.72227	0.371016
$163$	11.8440	0.927693	0.463847	−	0.885915i	$-0.346469\pi$
$163$	11.8440	0.927693	0.463847	+	0.885915i	$0.346469\pi$
$164$	−2.05977	−0.160841
$165$	−0.462669	−0.0360187
$166$	5.43395	0.421756
$167$	−18.8572	−1.45922	−0.729609	−	0.683865i	$-0.760298\pi$
$167$	−18.8572	−1.45922	−0.729609	+	0.683865i	$0.760298\pi$
$168$	4.50249	0.347375
$169$	7.08424	0.544941
$170$	−2.25319	−0.172812
$171$	−11.1526	−0.852859
$172$	13.5884	1.03611
$173$	−15.1822	−1.15428	−0.577140	−	0.816645i	$-0.695831\pi$
$173$	−15.1822	−1.15428	−0.577140	+	0.816645i	$0.695831\pi$
$174$	2.53420	0.192117
$175$	13.2495	1.00157
$176$	−0.926054	−0.0698040
$177$	7.03468	0.528759
$178$	0.616339	0.0461966
$179$	−2.57897	−0.192761	−0.0963806	−	0.995345i	$-0.530727\pi$
$179$	−2.57897	−0.192761	−0.0963806	+	0.995345i	$0.530727\pi$
$180$	3.79920	0.283176
$181$	−9.50776	−0.706706	−0.353353	−	0.935490i	$-0.614959\pi$
$181$	−9.50776	−0.706706	−0.353353	+	0.935490i	$0.614959\pi$
$182$	10.7188	0.794532
$183$	−1.65850	−0.122600
$184$	−9.51208	−0.701240
$185$	10.6268	0.781295
$186$	−3.39262	−0.248759
$187$	2.81084	0.205549
$188$	8.49649	0.619670
$189$	10.0968	0.734435
$190$	2.91982	0.211826
$191$	6.20885	0.449257	0.224628	−	0.974444i	$-0.427883\pi$
$191$	6.20885	0.449257	0.224628	+	0.974444i	$0.427883\pi$
$192$	1.20256	0.0867875
$193$	−19.6307	−1.41305	−0.706526	−	0.707687i	$-0.749739\pi$
$193$	−19.6307	−1.41305	−0.706526	+	0.707687i	$0.749739\pi$
$194$	0.349526	0.0250945
$195$	−2.34796	−0.168141
$196$	−5.22739	−0.373385
$197$	26.3638	1.87834	0.939171	−	0.343449i	$-0.111595\pi$
$197$	26.3638	1.87834	0.939171	+	0.343449i	$0.111595\pi$
$198$	1.75563	0.124767
$199$	−5.17965	−0.367176	−0.183588	−	0.983003i	$-0.558771\pi$
$199$	−5.17965	−0.367176	−0.183588	+	0.983003i	$0.558771\pi$
$200$	10.3600	0.732559
$201$	−4.98032	−0.351285
$202$	−2.26414	−0.159304
$203$	−20.6040	−1.44612
$204$	2.52776	0.176978
$205$	1.35886	0.0949069
$206$	−2.73058	−0.190248
$207$	−10.1117	−0.702812
$208$	−4.69955	−0.325855
$209$	−3.64247	−0.251955
$210$	−1.25309	−0.0864714
$211$	11.3624	0.782217	0.391109	−	0.920344i	$-0.372092\pi$
$211$	11.3624	0.782217	0.391109	+	0.920344i	$0.372092\pi$
$212$	10.3154	0.708466
$213$	−2.49011	−0.170620
$214$	11.8403	0.809385
$215$	−8.96448	−0.611373
$216$	7.89482	0.537174
$217$	27.5833	1.87248
$218$	1.91974	0.130021
$219$	−7.86068	−0.531175
$220$	1.24083	0.0836567
$221$	14.2645	0.959534
$222$	4.41612	0.296391
$223$	18.9951	1.27201	0.636003	−	0.771686i	$-0.280587\pi$
$223$	18.9951	1.27201	0.636003	+	0.771686i	$0.280587\pi$
$224$	−19.0563	−1.27325
$225$	11.0130	0.734201
$226$	−8.98510	−0.597680
$227$	11.7708	0.781254	0.390627	−	0.920549i	$-0.372258\pi$
$227$	11.7708	0.781254	0.390627	+	0.920549i	$0.372258\pi$
$228$	−3.27563	−0.216934
$229$	6.31464	0.417283	0.208641	−	0.977992i	$-0.433096\pi$
$229$	6.31464	0.417283	0.208641	+	0.977992i	$0.433096\pi$
$230$	2.64731	0.174558
$231$	1.56323	0.102853
$232$	−16.1105	−1.05771
$233$	20.7839	1.36160	0.680799	−	0.732470i	$-0.261633\pi$
$233$	20.7839	1.36160	0.680799	+	0.732470i	$0.261633\pi$
$234$	8.90951	0.582433
$235$	−5.60526	−0.365647
$236$	−18.8663	−1.22809
$237$	3.92138	0.254721
$238$	7.61287	0.493469
$239$	−23.8405	−1.54212	−0.771058	−	0.636765i	$-0.780272\pi$
$239$	−23.8405	−1.54212	−0.771058	+	0.636765i	$0.780272\pi$
$240$	0.549403	0.0354638
$241$	1.62031	0.104374	0.0521868	−	0.998637i	$-0.483381\pi$
$241$	1.62031	0.104374	0.0521868	+	0.998637i	$0.483381\pi$
$242$	−7.51442	−0.483045
$243$	12.8066	0.821543
$244$	4.44792	0.284749
$245$	3.44859	0.220322
$246$	0.564697	0.0360038
$247$	−18.4848	−1.17616
$248$	21.5677	1.36955
$249$	4.02170	0.254865
$250$	−6.42276	−0.406211
$251$	−10.7109	−0.676064	−0.338032	−	0.941135i	$-0.609761\pi$
$251$	−10.7109	−0.676064	−0.338032	+	0.941135i	$0.609761\pi$
$252$	−12.8364	−0.808617
$253$	−3.30251	−0.207627
$254$	4.34422	0.272581
$255$	−1.66760	−0.104429
$256$	−11.8396	−0.739972
$257$	−28.7954	−1.79621	−0.898105	−	0.439781i	$-0.855056\pi$
$257$	−28.7954	−1.79621	−0.898105	+	0.439781i	$0.855056\pi$
$258$	−3.72534	−0.231929
$259$	−35.9047	−2.23101
$260$	6.29698	0.390522
$261$	−17.1261	−1.06008
$262$	3.61030	0.223045
$263$	−27.1652	−1.67508	−0.837539	−	0.546378i	$-0.816006\pi$
$263$	−27.1652	−1.67508	−0.837539	+	0.546378i	$0.816006\pi$
$264$	1.22230	0.0752276
$265$	−6.80523	−0.418042
$266$	−9.86523	−0.604876
$267$	0.456156	0.0279163
$268$	13.3567	0.815890
$269$	−19.2182	−1.17176	−0.585878	−	0.810399i	$-0.699250\pi$
$269$	−19.2182	−1.17176	−0.585878	+	0.810399i	$0.699250\pi$
$270$	−2.19721	−0.133718
$271$	−9.73786	−0.591533	−0.295766	−	0.955260i	$-0.595575\pi$
$271$	−9.73786	−0.591533	−0.295766	+	0.955260i	$0.595575\pi$
$272$	−3.33778	−0.202382
$273$	7.93308	0.480132
$274$	−6.10192	−0.368631
$275$	3.59689	0.216900
$276$	−2.96991	−0.178767
$277$	−26.8931	−1.61585	−0.807925	−	0.589285i	$-0.799409\pi$
$277$	−26.8931	−1.61585	−0.807925	+	0.589285i	$0.799409\pi$
$278$	15.4974	0.929474
$279$	22.9273	1.37262
$280$	7.96619	0.476071
$281$	−4.21282	−0.251316	−0.125658	−	0.992074i	$-0.540104\pi$
$281$	−4.21282	−0.251316	−0.125658	+	0.992074i	$0.540104\pi$
$282$	−2.32936	−0.138711
$283$	31.3587	1.86408	0.932039	−	0.362357i	$-0.118028\pi$
$283$	31.3587	1.86408	0.932039	+	0.362357i	$0.118028\pi$
$284$	6.67822	0.396280
$285$	2.16098	0.128005
$286$	2.90987	0.172064
$287$	−4.59120	−0.271010
$288$	−15.8396	−0.933359
$289$	−6.86888	−0.404052
$290$	4.48372	0.263293
$291$	0.258687	0.0151645
$292$	21.0815	1.23370
$293$	−15.8890	−0.928244	−0.464122	−	0.885771i	$-0.653630\pi$
$293$	−15.8890	−0.928244	−0.464122	+	0.885771i	$0.653630\pi$
$294$	1.43312	0.0835811
$295$	12.4463	0.724654
$296$	−28.0743	−1.63179
$297$	2.74101	0.159050
$298$	−15.3842	−0.891181
$299$	−16.7596	−0.969234
$300$	3.23464	0.186752
$301$	30.2884	1.74579
$302$	−9.01908	−0.518990
$303$	−1.67570	−0.0962667
$304$	4.32530	0.248073
$305$	−2.93436	−0.168021
$306$	6.32783	0.361738
$307$	−13.7030	−0.782070	−0.391035	−	0.920376i	$-0.627883\pi$
$307$	−13.7030	−0.782070	−0.391035	+	0.920376i	$0.627883\pi$
$308$	−4.19241	−0.238884
$309$	−2.02092	−0.114966
$310$	−6.00251	−0.340920
$311$	6.49422	0.368253	0.184127	−	0.982903i	$-0.441054\pi$
$311$	6.49422	0.368253	0.184127	+	0.982903i	$0.441054\pi$
$312$	6.20296	0.351174
$313$	8.26403	0.467111	0.233555	−	0.972344i	$-0.424964\pi$
$313$	8.26403	0.467111	0.233555	+	0.972344i	$0.424964\pi$
$314$	7.08634	0.399905
$315$	8.46836	0.477138
$316$	−10.5167	−0.591612
$317$	−28.1441	−1.58073	−0.790364	−	0.612638i	$-0.790108\pi$
$317$	−28.1441	−1.58073	−0.790364	+	0.612638i	$0.790108\pi$
$318$	−2.82803	−0.158588
$319$	−5.59343	−0.313172
$320$	2.12768	0.118941
$321$	8.76307	0.489107
$322$	−8.94450	−0.498457
$323$	−13.1285	−0.730492
$324$	−9.37317	−0.520732
$325$	18.2535	1.01252
$326$	8.70836	0.482312
$327$	1.42081	0.0785710
$328$	−3.58991	−0.198220
$329$	18.9386	1.04412
$330$	−0.340180	−0.0187263
$331$	−1.78319	−0.0980130	−0.0490065	−	0.998798i	$-0.515606\pi$
$331$	−1.78319	−0.0980130	−0.0490065	+	0.998798i	$0.515606\pi$
$332$	−10.7858	−0.591947
$333$	−29.8441	−1.63545
$334$	−13.8649	−0.758653
$335$	−8.81160	−0.481429
$336$	−1.85628	−0.101268
$337$	17.5528	0.956160	0.478080	−	0.878316i	$-0.341333\pi$
$337$	17.5528	0.956160	0.478080	+	0.878316i	$0.341333\pi$
$338$	5.20873	0.283317
$339$	−6.64993	−0.361175
$340$	4.47232	0.242546
$341$	7.48811	0.405504
$342$	−8.20000	−0.443405
$343$	11.1191	0.600374
$344$	23.6829	1.27689
$345$	1.95929	0.105485
$346$	−11.1628	−0.600115
$347$	14.8308	0.796160	0.398080	−	0.917351i	$-0.369677\pi$
$347$	14.8308	0.796160	0.398080	+	0.917351i	$0.369677\pi$
$348$	−5.03010	−0.269642
$349$	−34.3697	−1.83977	−0.919884	−	0.392190i	$-0.871718\pi$
$349$	−34.3697	−1.83977	−0.919884	+	0.392190i	$0.871718\pi$
$350$	9.74178	0.520720
$351$	13.9101	0.742467
$352$	−5.17327	−0.275736
$353$	−16.1758	−0.860949	−0.430474	−	0.902603i	$-0.641654\pi$
$353$	−16.1758	−0.860949	−0.430474	+	0.902603i	$0.641654\pi$
$354$	5.17229	0.274904
$355$	−4.40572	−0.233831
$356$	−1.22336	−0.0648381
$357$	5.63433	0.298201
$358$	−1.89620	−0.100217
$359$	17.7167	0.935053	0.467526	−	0.883979i	$-0.345145\pi$
$359$	17.7167	0.935053	0.467526	+	0.883979i	$0.345145\pi$
$360$	6.62151	0.348984
$361$	−1.98721	−0.104590
$362$	−6.99063	−0.367419
$363$	−5.56147	−0.291901
$364$	−21.2757	−1.11515
$365$	−13.9078	−0.727966
$366$	−1.21942	−0.0637401
$367$	7.29148	0.380612	0.190306	−	0.981725i	$-0.439052\pi$
$367$	7.29148	0.380612	0.190306	+	0.981725i	$0.439052\pi$
$368$	3.92162	0.204428
$369$	−3.81621	−0.198664
$370$	7.81338	0.406198
$371$	22.9929	1.19373
$372$	6.73397	0.349140
$373$	19.4135	1.00520	0.502598	−	0.864520i	$-0.332378\pi$
$373$	19.4135	1.00520	0.502598	+	0.864520i	$0.332378\pi$
$374$	2.06669	0.106866
$375$	−4.75352	−0.245471
$376$	14.8083	0.763678
$377$	−28.3856	−1.46193
$378$	7.42374	0.381836
$379$	21.5543	1.10717	0.553586	−	0.832792i	$-0.313259\pi$
$379$	21.5543	1.10717	0.553586	+	0.832792i	$0.313259\pi$
$380$	−5.79552	−0.297304
$381$	3.21519	0.164719
$382$	4.56509	0.233571
$383$	−8.69462	−0.444274	−0.222137	−	0.975015i	$-0.571303\pi$
$383$	−8.69462	−0.444274	−0.222137	+	0.975015i	$0.571303\pi$
$384$	−5.49139	−0.280231
$385$	2.76579	0.140958
$386$	−14.4336	−0.734652
$387$	25.1758	1.27976
$388$	−0.693771	−0.0352209
$389$	20.0986	1.01904	0.509520	−	0.860459i	$-0.329823\pi$
$389$	20.0986	1.01904	0.509520	+	0.860459i	$0.329823\pi$
$390$	−1.72635	−0.0874171
$391$	−11.9032	−0.601973
$392$	−9.11066	−0.460158
$393$	2.67201	0.134785
$394$	19.3841	0.976558
$395$	6.93804	0.349091
$396$	−3.48473	−0.175114
$397$	−22.3318	−1.12080	−0.560402	−	0.828221i	$-0.689353\pi$
$397$	−22.3318	−1.12080	−0.560402	+	0.828221i	$0.689353\pi$
$398$	−3.80836	−0.190896
$399$	−7.30132	−0.365523
$400$	−4.27118	−0.213559
$401$	−1.95708	−0.0977321	−0.0488661	−	0.998805i	$-0.515561\pi$
$401$	−1.95708	−0.0977321	−0.0488661	+	0.998805i	$0.515561\pi$
$402$	−3.66181	−0.182634
$403$	38.0008	1.89295
$404$	4.49406	0.223588
$405$	6.18362	0.307266
$406$	−15.1492	−0.751842
$407$	−9.74716	−0.483149
$408$	4.40555	0.218107
$409$	14.4716	0.715576	0.357788	−	0.933803i	$-0.383531\pi$
$409$	14.4716	0.715576	0.357788	+	0.933803i	$0.383531\pi$
$410$	0.999110	0.0493425
$411$	−4.51607	−0.222761
$412$	5.41989	0.267019
$413$	−42.0526	−2.06927
$414$	−7.43468	−0.365395
$415$	7.11554	0.349288
$416$	−26.2534	−1.28718
$417$	11.4697	0.561676
$418$	−2.67814	−0.130992
$419$	−4.92102	−0.240408	−0.120204	−	0.992749i	$-0.538355\pi$
$419$	−4.92102	−0.240408	−0.120204	+	0.992749i	$0.538355\pi$
$420$	2.48724	0.121365
$421$	16.7810	0.817857	0.408928	−	0.912566i	$-0.365903\pi$
$421$	16.7810	0.817857	0.408928	+	0.912566i	$0.365903\pi$
$422$	8.35424	0.406678
$423$	15.7418	0.765390
$424$	17.9784	0.873109
$425$	12.9643	0.628859
$426$	−1.83087	−0.0887059
$427$	9.91435	0.479789
$428$	−23.5016	−1.13599
$429$	2.15361	0.103977
$430$	−6.59119	−0.317855
$431$	10.5214	0.506800	0.253400	−	0.967362i	$-0.418451\pi$
$431$	10.5214	0.506800	0.253400	+	0.967362i	$0.418451\pi$
$432$	−3.25486	−0.156599
$433$	−11.8135	−0.567721	−0.283860	−	0.958866i	$-0.591615\pi$
$433$	−11.8135	−0.567721	−0.283860	+	0.958866i	$0.591615\pi$
$434$	20.2808	0.973508
$435$	3.31843	0.159107
$436$	−3.81047	−0.182488
$437$	15.4250	0.737876
$438$	−5.77961	−0.276160
$439$	8.18885	0.390833	0.195416	−	0.980720i	$-0.437394\pi$
$439$	8.18885	0.390833	0.195416	+	0.980720i	$0.437394\pi$
$440$	2.16260	0.103098
$441$	−9.68497	−0.461189
$442$	10.4880	0.498866
$443$	−15.7119	−0.746496	−0.373248	−	0.927732i	$-0.621756\pi$
$443$	−15.7119	−0.746496	−0.373248	+	0.927732i	$0.621756\pi$
$444$	−8.76551	−0.415993
$445$	0.807071	0.0382588
$446$	13.9663	0.661321
$447$	−11.3859	−0.538536
$448$	−7.18881	−0.339639
$449$	9.89465	0.466957	0.233479	−	0.972362i	$-0.424989\pi$
$449$	9.89465	0.466957	0.233479	+	0.972362i	$0.424989\pi$
$450$	8.09738	0.381714
$451$	−1.24639	−0.0586900
$452$	17.8344	0.838860
$453$	−6.67508	−0.313623
$454$	8.65453	0.406177
$455$	14.0359	0.658012
$456$	−5.70899	−0.267348
$457$	19.4319	0.908985	0.454492	−	0.890751i	$-0.349821\pi$
$457$	19.4319	0.908985	0.454492	+	0.890751i	$0.349821\pi$
$458$	4.64287	0.216947
$459$	9.87943	0.461132
$460$	−5.25461	−0.244998
$461$	28.4760	1.32626	0.663130	−	0.748504i	$-0.269228\pi$
$461$	28.4760	1.32626	0.663130	+	0.748504i	$0.269228\pi$
$462$	1.14937	0.0534735
$463$	−10.8095	−0.502361	−0.251181	−	0.967940i	$-0.580819\pi$
$463$	−10.8095	−0.502361	−0.251181	+	0.967940i	$0.580819\pi$
$464$	6.64200	0.308347
$465$	−4.44250	−0.206016
$466$	15.2815	0.707901
$467$	26.3662	1.22008	0.610041	−	0.792369i	$-0.291153\pi$
$467$	26.3662	1.22008	0.610041	+	0.792369i	$0.291153\pi$
$468$	−17.6844	−0.817460
$469$	29.7719	1.37474
$470$	−4.12130	−0.190101
$471$	5.24465	0.241661
$472$	−32.8814	−1.51349
$473$	8.22248	0.378070
$474$	2.88322	0.132431
$475$	−16.7999	−0.770832
$476$	−15.1107	−0.692597
$477$	19.1117	0.875067
$478$	−17.5289	−0.801752
$479$	−0.194030	−0.00886547	−0.00443274	−	0.999990i	$-0.501411\pi$
$479$	−0.194030	−0.00886547	−0.00443274	+	0.999990i	$0.501411\pi$
$480$	3.06916	0.140088
$481$	−49.4650	−2.25541
$482$	1.19134	0.0542642
$483$	−6.61988	−0.301215
$484$	14.9153	0.677967
$485$	0.457691	0.0207827
$486$	9.41611	0.427123
$487$	−2.65682	−0.120392	−0.0601959	−	0.998187i	$-0.519173\pi$
$487$	−2.65682	−0.120392	−0.0601959	+	0.998187i	$0.519173\pi$
$488$	7.75214	0.350923
$489$	6.44512	0.291458
$490$	2.53559	0.114546
$491$	11.0398	0.498219	0.249109	−	0.968475i	$-0.419862\pi$
$491$	11.0398	0.498219	0.249109	+	0.968475i	$0.419862\pi$
$492$	−1.12086	−0.0505323
$493$	−20.1604	−0.907978
$494$	−13.5911	−0.611491
$495$	2.29893	0.103329
$496$	−8.89187	−0.399257
$497$	14.8857	0.667713
$498$	2.95698	0.132505
$499$	30.9966	1.38760	0.693799	−	0.720168i	$-0.255935\pi$
$499$	30.9966	1.38760	0.693799	+	0.720168i	$0.255935\pi$
$500$	12.7484	0.570128
$501$	−10.2615	−0.458450
$502$	−7.87523	−0.351489
$503$	−37.0982	−1.65413	−0.827063	−	0.562109i	$-0.809990\pi$
$503$	−37.0982	−1.65413	−0.827063	+	0.562109i	$0.809990\pi$
$504$	−22.3722	−0.996536
$505$	−2.96480	−0.131932
$506$	−2.42819	−0.107946
$507$	3.85501	0.171207
$508$	−8.62279	−0.382575
$509$	−8.10275	−0.359148	−0.179574	−	0.983744i	$-0.557472\pi$
$509$	−8.10275	−0.359148	−0.179574	+	0.983744i	$0.557472\pi$
$510$	−1.22611	−0.0542931
$511$	46.9904	2.07873
$512$	11.4776	0.507244
$513$	−12.8024	−0.565239
$514$	−21.1720	−0.933857
$515$	−3.57558	−0.157559
$516$	7.39438	0.325519
$517$	5.14130	0.226114
$518$	−26.3992	−1.15991
$519$	−8.26165	−0.362646
$520$	10.9748	0.481277
$521$	9.96721	0.436671	0.218336	−	0.975874i	$-0.429937\pi$
$521$	9.96721	0.436671	0.218336	+	0.975874i	$0.429937\pi$
$522$	−12.5920	−0.551139
$523$	−7.12073	−0.311368	−0.155684	−	0.987807i	$-0.549758\pi$
$523$	−7.12073	−0.311368	−0.155684	+	0.987807i	$0.549758\pi$
$524$	−7.16604	−0.313050
$525$	7.20996	0.314668
$526$	−19.9734	−0.870879
$527$	26.9894	1.17568
$528$	−0.503929	−0.0219307
$529$	−9.01467	−0.391942
$530$	−5.00358	−0.217342
$531$	−34.9542	−1.51688
$532$	19.5814	0.848961
$533$	−6.32517	−0.273974
$534$	0.335392	0.0145138
$535$	15.5044	0.670312
$536$	23.2790	1.00550
$537$	−1.40339	−0.0605608
$538$	−14.1303	−0.609201
$539$	−3.16314	−0.136246
$540$	4.36121	0.187677
$541$	39.1006	1.68107	0.840533	−	0.541760i	$-0.182242\pi$
$541$	39.1006	1.68107	0.840533	+	0.541760i	$0.182242\pi$
$542$	−7.15981	−0.307540
$543$	−5.17381	−0.222030
$544$	−18.6460	−0.799441
$545$	2.51382	0.107680
$546$	5.83284	0.249622
$547$	−1.00000	−0.0427569
$547$	−1.00000	−0.0427569
$548$	12.1116	0.517383
$549$	8.24082	0.351710
$550$	2.64463	0.112767
$551$	26.1251	1.11297
$552$	−5.17616	−0.220312
$553$	−23.4416	−0.996840
$554$	−19.7733	−0.840087
$555$	5.78273	0.245463
$556$	−30.7606	−1.30454
$557$	39.1227	1.65768	0.828841	−	0.559485i	$-0.189001\pi$
$557$	39.1227	1.65768	0.828841	+	0.559485i	$0.189001\pi$
$558$	16.8574	0.713631
$559$	41.7275	1.76489
$560$	−3.28428	−0.138786
$561$	1.52957	0.0645784
$562$	−3.09750	−0.130660
$563$	32.3381	1.36289	0.681445	−	0.731869i	$-0.261352\pi$
$563$	32.3381	1.36289	0.681445	+	0.731869i	$0.261352\pi$
$564$	4.62351	0.194685
$565$	−11.7656	−0.494983
$566$	23.0566	0.969142
$567$	−20.8927	−0.877409
$568$	11.6393	0.488373
$569$	0.316254	0.0132581	0.00662903	−	0.999978i	$-0.497890\pi$
$569$	0.316254	0.0132581	0.00662903	+	0.999978i	$0.497890\pi$
$570$	1.58887	0.0665505
$571$	4.67642	0.195702	0.0978511	−	0.995201i	$-0.468803\pi$
$571$	4.67642	0.195702	0.0978511	+	0.995201i	$0.468803\pi$
$572$	−5.77577	−0.241497
$573$	3.37866	0.141145
$574$	−3.37570	−0.140899
$575$	−15.2319	−0.635216
$576$	−5.97535	−0.248973
$577$	38.4107	1.59906	0.799529	−	0.600627i	$-0.205082\pi$
$577$	38.4107	1.59906	0.799529	+	0.600627i	$0.205082\pi$
$578$	−5.05038	−0.210068
$579$	−10.6824	−0.443946
$580$	−8.89968	−0.369539
$581$	−24.0413	−0.997403
$582$	0.190201	0.00788408
$583$	6.24195	0.258515
$584$	36.7423	1.52041
$585$	11.6666	0.482356
$586$	−11.6825	−0.482598
$587$	6.56995	0.271171	0.135586	−	0.990766i	$-0.456708\pi$
$587$	6.56995	0.271171	0.135586	+	0.990766i	$0.456708\pi$
$588$	−2.84458	−0.117308
$589$	−34.9746	−1.44110
$590$	9.15125	0.376751
$591$	14.3463	0.590129
$592$	11.5744	0.475706
$593$	−0.570902	−0.0234441	−0.0117221	−	0.999931i	$-0.503731\pi$
$593$	−0.570902	−0.0234441	−0.0117221	+	0.999931i	$0.503731\pi$
$594$	2.01534	0.0826905
$595$	9.96874	0.408679
$596$	30.5359	1.25080
$597$	−2.81860	−0.115357
$598$	−12.3226	−0.503909
$599$	8.95352	0.365831	0.182915	−	0.983129i	$-0.441447\pi$
$599$	8.95352	0.365831	0.182915	+	0.983129i	$0.441447\pi$
$600$	5.63755	0.230152
$601$	−12.7284	−0.519202	−0.259601	−	0.965716i	$-0.583591\pi$
$601$	−12.7284	−0.519202	−0.259601	+	0.965716i	$0.583591\pi$
$602$	22.2697	0.907646
$603$	24.7464	1.00775
$604$	17.9019	0.728416
$605$	−9.83982	−0.400046
$606$	−1.23207	−0.0500495
$607$	26.7859	1.08721	0.543603	−	0.839342i	$-0.317060\pi$
$607$	26.7859	1.08721	0.543603	+	0.839342i	$0.317060\pi$
$608$	24.1627	0.979926
$609$	−11.2120	−0.454334
$610$	−2.15750	−0.0873547
$611$	26.0911	1.05553
$612$	−12.5600	−0.507709
$613$	31.3273	1.26530	0.632649	−	0.774439i	$-0.281968\pi$
$613$	31.3273	1.26530	0.632649	+	0.774439i	$0.281968\pi$
$614$	−10.0752	−0.406602
$615$	0.739448	0.0298174
$616$	−7.30682	−0.294400
$617$	−31.6103	−1.27258	−0.636292	−	0.771448i	$-0.719533\pi$
$617$	−31.6103	−1.27258	−0.636292	+	0.771448i	$0.719533\pi$
$618$	−1.48589	−0.0597713
$619$	7.99712	0.321431	0.160716	−	0.987001i	$-0.448620\pi$
$619$	7.99712	0.321431	0.160716	+	0.987001i	$0.448620\pi$
$620$	11.9143	0.478490
$621$	−11.6075	−0.465794
$622$	4.77491	0.191457
$623$	−2.72686	−0.109249
$624$	−2.55734	−0.102376
$625$	11.9549	0.478195
$626$	6.07617	0.242853
$627$	−1.98211	−0.0791579
$628$	−14.0656	−0.561278
$629$	−35.1317	−1.40079
$630$	6.22641	0.248066
$631$	−44.2164	−1.76023	−0.880113	−	0.474764i	$-0.842534\pi$
$631$	−44.2164	−1.76023	−0.880113	+	0.474764i	$0.842534\pi$
$632$	−18.3293	−0.729100
$633$	6.18303	0.245753
$634$	−20.6931	−0.821827
$635$	5.68858	0.225744
$636$	5.61331	0.222582
$637$	−16.0523	−0.636017
$638$	−4.11260	−0.162819
$639$	12.3730	0.489468
$640$	−9.71583	−0.384052
$641$	−16.8320	−0.664824	−0.332412	−	0.943134i	$-0.607862\pi$
$641$	−16.8320	−0.664824	−0.332412	+	0.943134i	$0.607862\pi$
$642$	6.44310	0.254289
$643$	−12.4597	−0.491362	−0.245681	−	0.969351i	$-0.579012\pi$
$643$	−12.4597	−0.491362	−0.245681	+	0.969351i	$0.579012\pi$
$644$	17.7538	0.699599
$645$	−4.87818	−0.192078
$646$	−9.65283	−0.379786
$647$	−48.1533	−1.89310	−0.946551	−	0.322555i	$-0.895458\pi$
$647$	−48.1533	−1.89310	−0.946551	+	0.322555i	$0.895458\pi$
$648$	−16.3362	−0.641747
$649$	−11.4161	−0.448123
$650$	13.4210	0.526415
$651$	15.0099	0.588285
$652$	−17.2851	−0.676938
$653$	−12.7505	−0.498967	−0.249484	−	0.968379i	$-0.580261\pi$
$653$	−12.7505	−0.498967	−0.249484	+	0.968379i	$0.580261\pi$
$654$	1.04466	0.0408494
$655$	4.72754	0.184720
$656$	1.48004	0.0577858
$657$	39.0585	1.52382
$658$	13.9247	0.542840
$659$	−29.8939	−1.16450	−0.582250	−	0.813010i	$-0.697828\pi$
$659$	−29.8939	−1.16450	−0.582250	+	0.813010i	$0.697828\pi$
$660$	0.675219	0.0262829
$661$	22.0815	0.858872	0.429436	−	0.903097i	$-0.358712\pi$
$661$	22.0815	0.858872	0.429436	+	0.903097i	$0.358712\pi$
$662$	−1.31110	−0.0509574
$663$	7.76227	0.301462
$664$	−18.7982	−0.729512
$665$	−12.9181	−0.500943
$666$	−21.9430	−0.850275
$667$	23.6868	0.917157
$668$	27.5203	1.06479
$669$	10.3365	0.399633
$670$	−6.47878	−0.250297
$671$	2.69148	0.103903
$672$	−10.3698	−0.400024
$673$	24.6133	0.948772	0.474386	−	0.880317i	$-0.342670\pi$
$673$	24.6133	0.948772	0.474386	+	0.880317i	$0.342670\pi$
$674$	12.9058	0.497112
$675$	12.6422	0.486598
$676$	−10.3387	−0.397644
$677$	15.1930	0.583913	0.291956	−	0.956432i	$-0.405694\pi$
$677$	15.1930	0.583913	0.291956	+	0.956432i	$0.405694\pi$
$678$	−4.88940	−0.187776
$679$	−1.54640	−0.0593456
$680$	7.79467	0.298912
$681$	6.40527	0.245451
$682$	5.50568	0.210823
$683$	−23.5519	−0.901189	−0.450594	−	0.892729i	$-0.648788\pi$
$683$	−23.5519	−0.901189	−0.450594	+	0.892729i	$0.648788\pi$
$684$	16.2761	0.622331
$685$	−7.99022	−0.305291
$686$	8.17537	0.312137
$687$	3.43622	0.131100
$688$	−9.76391	−0.372245
$689$	31.6767	1.20679
$690$	1.44058	0.0548419
$691$	−37.0300	−1.40869	−0.704343	−	0.709860i	$-0.748758\pi$
$691$	−37.0300	−1.40869	−0.704343	+	0.709860i	$0.748758\pi$
$692$	22.1569	0.842278
$693$	−7.76742	−0.295060
$694$	10.9044	0.413927
$695$	20.2932	0.769766
$696$	−8.76681	−0.332305
$697$	−4.49235	−0.170160
$698$	−25.2705	−0.956503
$699$	11.3099	0.427781
$700$	−19.3363	−0.730845
$701$	35.5829	1.34395	0.671973	−	0.740576i	$-0.265447\pi$
$701$	35.5829	1.34395	0.671973	+	0.740576i	$0.265447\pi$
$702$	10.2275	0.386012
$703$	45.5259	1.71704
$704$	−1.95157	−0.0735524
$705$	−3.05020	−0.114877
$706$	−11.8933	−0.447611
$707$	10.0172	0.376736
$708$	−10.2664	−0.385835
$709$	40.5125	1.52148	0.760739	−	0.649058i	$-0.224837\pi$
$709$	40.5125	1.52148	0.760739	+	0.649058i	$0.224837\pi$
$710$	−3.23933	−0.121570
$711$	−19.4847	−0.730734
$712$	−2.13216	−0.0799062
$713$	−31.7103	−1.18756
$714$	4.14267	0.155036
$715$	3.81036	0.142499
$716$	3.76375	0.140658
$717$	−12.9732	−0.484494
$718$	13.0263	0.486138
$719$	6.36743	0.237465	0.118733	−	0.992926i	$-0.462117\pi$
$719$	6.36743	0.237465	0.118733	+	0.992926i	$0.462117\pi$
$720$	−2.72990	−0.101737
$721$	12.0808	0.449914
$722$	−1.46111	−0.0543767
$723$	0.881722	0.0327916
$724$	13.8756	0.515683
$725$	−25.7982	−0.958120
$726$	−4.08910	−0.151761
$727$	−35.1164	−1.30240	−0.651198	−	0.758908i	$-0.725733\pi$
$727$	−35.1164	−1.30240	−0.651198	+	0.758908i	$0.725733\pi$
$728$	−37.0807	−1.37430
$729$	−12.2989	−0.455516
$730$	−10.2258	−0.378473
$731$	29.6363	1.09614
$732$	2.42041	0.0894610
$733$	26.1891	0.967315	0.483658	−	0.875257i	$-0.339308\pi$
$733$	26.1891	0.967315	0.483658	+	0.875257i	$0.339308\pi$
$734$	5.36110	0.197882
$735$	1.87661	0.0692197
$736$	21.9075	0.807523
$737$	8.08225	0.297714
$738$	−2.80589	−0.103286
$739$	15.8483	0.582988	0.291494	−	0.956573i	$-0.405848\pi$
$739$	15.8483	0.582988	0.291494	+	0.956573i	$0.405848\pi$
$740$	−15.5087	−0.570110
$741$	−10.0588	−0.369521
$742$	16.9057	0.620626
$743$	13.1980	0.484189	0.242095	−	0.970253i	$-0.422166\pi$
$743$	13.1980	0.484189	0.242095	+	0.970253i	$0.422166\pi$
$744$	11.7364	0.430278
$745$	−20.1449	−0.738054
$746$	14.2739	0.522605
$747$	−19.9832	−0.731147
$748$	−4.10214	−0.149989
$749$	−52.3848	−1.91410
$750$	−3.49505	−0.127621
$751$	−17.3729	−0.633945	−0.316973	−	0.948435i	$-0.602666\pi$
$751$	−17.3729	−0.633945	−0.316973	+	0.948435i	$0.602666\pi$
$752$	−6.10512	−0.222631
$753$	−5.82851	−0.212403
$754$	−20.8707	−0.760064
$755$	−11.8101	−0.429814
$756$	−14.7353	−0.535917
$757$	−38.7514	−1.40844	−0.704222	−	0.709980i	$-0.748704\pi$
$757$	−38.7514	−1.40844	−0.704222	+	0.709980i	$0.748704\pi$
$758$	15.8479	0.575623
$759$	−1.79712	−0.0652313
$760$	−10.1008	−0.366396
$761$	−29.0280	−1.05226	−0.526132	−	0.850403i	$-0.676358\pi$
$761$	−29.0280	−1.05226	−0.526132	+	0.850403i	$0.676358\pi$
$762$	2.36398	0.0856381
$763$	−8.49347	−0.307484
$764$	−9.06120	−0.327823
$765$	8.28603	0.299582
$766$	−6.39277	−0.230980
$767$	−57.9348	−2.09190
$768$	−6.44270	−0.232481
$769$	−8.49451	−0.306320	−0.153160	−	0.988201i	$-0.548945\pi$
$769$	−8.49451	−0.306320	−0.153160	+	0.988201i	$0.548945\pi$
$770$	2.03356	0.0732845
$771$	−15.6695	−0.564325
$772$	28.6491	1.03110
$773$	−30.2676	−1.08865	−0.544325	−	0.838875i	$-0.683214\pi$
$773$	−30.2676	−1.08865	−0.544325	+	0.838875i	$0.683214\pi$
$774$	18.5106	0.665351
$775$	34.5369	1.24060
$776$	−1.20915	−0.0434060
$777$	−19.5382	−0.700929
$778$	14.7776	0.529803
$779$	5.82147	0.208576
$780$	3.42661	0.122692
$781$	4.04105	0.144600
$782$	−8.75192	−0.312968
$783$	−19.6595	−0.702574
$784$	3.75612	0.134147
$785$	9.27927	0.331191
$786$	1.96461	0.0700752
$787$	−25.5339	−0.910185	−0.455093	−	0.890444i	$-0.650394\pi$
$787$	−25.5339	−0.910185	−0.455093	+	0.890444i	$0.650394\pi$
$788$	−38.4753	−1.37063
$789$	−14.7824	−0.526268
$790$	5.10123	0.181494
$791$	39.7526	1.41344
$792$	−6.07344	−0.215810
$793$	13.6587	0.485036
$794$	−16.4196	−0.582710
$795$	−3.70318	−0.131338
$796$	7.55918	0.267928
$797$	−48.5429	−1.71948	−0.859738	−	0.510735i	$-0.829373\pi$
$797$	−48.5429	−1.71948	−0.859738	+	0.510735i	$0.829373\pi$
$798$	−5.36834	−0.190037
$799$	18.5308	0.655573
$800$	−23.8603	−0.843589
$801$	−2.26657	−0.0800853
$802$	−1.43896	−0.0508113
$803$	12.7566	0.450171
$804$	7.26828	0.256332
$805$	−11.7125	−0.412810
$806$	27.9403	0.984154
$807$	−10.4579	−0.368137
$808$	7.83256	0.275549
$809$	30.1082	1.05855	0.529274	−	0.848451i	$-0.322464\pi$
$809$	30.1082	1.05855	0.529274	+	0.848451i	$0.322464\pi$
$810$	4.54654	0.159749
$811$	−26.6166	−0.934634	−0.467317	−	0.884090i	$-0.654779\pi$
$811$	−26.6166	−0.934634	−0.467317	+	0.884090i	$0.654779\pi$
$812$	30.0695	1.05523
$813$	−5.29902	−0.185845
$814$	−7.16665	−0.251191
$815$	11.4032	0.399438
$816$	−1.81631	−0.0635836
$817$	−38.4046	−1.34361
$818$	10.6403	0.372031
$819$	−39.4182	−1.37738
$820$	−1.98312	−0.0692536
$821$	−52.7820	−1.84210	−0.921052	−	0.389440i	$-0.872668\pi$
$821$	−52.7820	−1.84210	−0.921052	+	0.389440i	$0.872668\pi$
$822$	−3.32047	−0.115815
$823$	−20.7992	−0.725014	−0.362507	−	0.931981i	$-0.618079\pi$
$823$	−20.7992	−0.725014	−0.362507	+	0.931981i	$0.618079\pi$
$824$	9.44615	0.329072
$825$	1.95731	0.0681447
$826$	−30.9194	−1.07582
$827$	12.6722	0.440654	0.220327	−	0.975426i	$-0.429287\pi$
$827$	12.6722	0.440654	0.220327	+	0.975426i	$0.429287\pi$
$828$	14.7570	0.512841
$829$	24.4262	0.848357	0.424179	−	0.905579i	$-0.360563\pi$
$829$	24.4262	0.848357	0.424179	+	0.905579i	$0.360563\pi$
$830$	5.23174	0.181596
$831$	−14.6343	−0.507660
$832$	−9.90383	−0.343354
$833$	−11.4009	−0.395018
$834$	8.43319	0.292018
$835$	−18.1555	−0.628297
$836$	5.31581	0.183851
$837$	26.3189	0.909714
$838$	−3.61821	−0.124989
$839$	41.6208	1.43691	0.718455	−	0.695574i	$-0.244850\pi$
$839$	41.6208	1.43691	0.718455	+	0.695574i	$0.244850\pi$
$840$	4.33494	0.149570
$841$	11.1181	0.383383
$842$	12.3383	0.425207
$843$	−2.29248	−0.0789572
$844$	−16.5822	−0.570784
$845$	6.82061	0.234636
$846$	11.5742	0.397930
$847$	33.2459	1.14234
$848$	−7.41210	−0.254533
$849$	17.0644	0.585647
$850$	9.53204	0.326946
$851$	41.2769	1.41495
$852$	3.63407	0.124501
$853$	11.9436	0.408942	0.204471	−	0.978873i	$-0.434453\pi$
$853$	11.9436	0.408942	0.204471	+	0.978873i	$0.434453\pi$
$854$	7.28958	0.249444
$855$	−10.7376	−0.367217
$856$	−40.9603	−1.39999
$857$	−17.0803	−0.583452	−0.291726	−	0.956502i	$-0.594229\pi$
$857$	−17.0803	−0.583452	−0.291726	+	0.956502i	$0.594229\pi$
$858$	1.58346	0.0540583
$859$	−45.1499	−1.54049	−0.770247	−	0.637745i	$-0.779867\pi$
$859$	−45.1499	−1.54049	−0.770247	+	0.637745i	$0.779867\pi$
$860$	13.0828	0.446118
$861$	−2.49838	−0.0851446
$862$	7.73595	0.263487
$863$	−42.9192	−1.46099	−0.730494	−	0.682919i	$-0.760710\pi$
$863$	−42.9192	−1.46099	−0.730494	+	0.682919i	$0.760710\pi$
$864$	−18.1828	−0.618591
$865$	−14.6172	−0.497000
$866$	−8.68594	−0.295160
$867$	−3.73782	−0.126943
$868$	−40.2550	−1.36634
$869$	−6.36377	−0.215876
$870$	2.43990	0.0827202
$871$	41.0159	1.38977
$872$	−6.64114	−0.224897
$873$	−1.28537	−0.0435033
$874$	11.3413	0.383625
$875$	28.4161	0.960640
$876$	11.4719	0.387598
$877$	−22.1529	−0.748050	−0.374025	−	0.927419i	$-0.622023\pi$
$877$	−22.1529	−0.748050	−0.374025	+	0.927419i	$0.622023\pi$
$878$	6.02090	0.203196
$879$	−8.64627	−0.291631
$880$	−0.891593	−0.0300556
$881$	−8.84872	−0.298121	−0.149060	−	0.988828i	$-0.547625\pi$
$881$	−8.84872	−0.298121	−0.149060	+	0.988828i	$0.547625\pi$
$882$	−7.12093	−0.239774
$883$	14.6632	0.493455	0.246728	−	0.969085i	$-0.420645\pi$
$883$	14.6632	0.493455	0.246728	+	0.969085i	$0.420645\pi$
$884$	−20.8176	−0.700172
$885$	6.77290	0.227668
$886$	−11.5523	−0.388107
$887$	17.3973	0.584143	0.292072	−	0.956396i	$-0.405655\pi$
$887$	17.3973	0.584143	0.292072	+	0.956396i	$0.405655\pi$
$888$	−15.2771	−0.512667
$889$	−19.2201	−0.644621
$890$	0.593403	0.0198909
$891$	−5.67179	−0.190012
$892$	−27.7214	−0.928183
$893$	−24.0134	−0.803577
$894$	−8.37157	−0.279987
$895$	−2.48300	−0.0829975
$896$	32.8270	1.09667
$897$	−9.12004	−0.304509
$898$	7.27509	0.242773
$899$	−53.7075	−1.79124
$900$	−16.0724	−0.535747
$901$	22.4979	0.749512
$902$	−0.916412	−0.0305132
$903$	16.4820	0.548485
$904$	31.0830	1.03381
$905$	−9.15395	−0.304288
$906$	−4.90789	−0.163054
$907$	−33.7438	−1.12045	−0.560223	−	0.828342i	$-0.689285\pi$
$907$	−33.7438	−1.12045	−0.560223	+	0.828342i	$0.689285\pi$
$908$	−17.1783	−0.570081
$909$	8.32631	0.276166
$910$	10.3199	0.342103
$911$	12.1001	0.400895	0.200447	−	0.979704i	$-0.435760\pi$
$911$	12.1001	0.400895	0.200447	+	0.979704i	$0.435760\pi$
$912$	2.35369	0.0779384
$913$	−6.52657	−0.215998
$914$	14.2874	0.472585
$915$	−1.59678	−0.0527880
$916$	−9.21557	−0.304491
$917$	−15.9730	−0.527475
$918$	7.26390	0.239745
$919$	−31.4919	−1.03882	−0.519412	−	0.854524i	$-0.673849\pi$
$919$	−31.4919	−1.03882	−0.519412	+	0.854524i	$0.673849\pi$
$920$	−9.15811	−0.301934
$921$	−7.45671	−0.245707
$922$	20.9371	0.689528
$923$	20.5076	0.675015
$924$	−2.28137	−0.0750516
$925$	−44.9562	−1.47815
$926$	−7.94777	−0.261180
$927$	10.0416	0.329810
$928$	37.1046	1.21802
$929$	28.6545	0.940123	0.470061	−	0.882634i	$-0.344232\pi$
$929$	28.6545	0.940123	0.470061	+	0.882634i	$0.344232\pi$
$930$	−3.26637	−0.107109
$931$	14.7740	0.484199
$932$	−30.3320	−0.993558
$933$	3.53394	0.115696
$934$	19.3859	0.634326
$935$	2.70624	0.0885036
$936$	−30.8215	−1.00743
$937$	6.14354	0.200701	0.100350	−	0.994952i	$-0.468004\pi$
$937$	6.14354	0.200701	0.100350	+	0.994952i	$0.468004\pi$
$938$	21.8899	0.714731
$939$	4.49702	0.146755
$940$	8.18031	0.266812
$941$	−25.9528	−0.846038	−0.423019	−	0.906121i	$-0.639030\pi$
$941$	−25.9528	−0.846038	−0.423019	+	0.906121i	$0.639030\pi$
$942$	3.85616	0.125640
$943$	5.27814	0.171880
$944$	13.5563	0.441219
$945$	9.72108	0.316227
$946$	6.04562	0.196560
$947$	45.1337	1.46665	0.733324	−	0.679880i	$-0.237968\pi$
$947$	45.1337	1.46665	0.733324	+	0.679880i	$0.237968\pi$
$948$	−5.72286	−0.185870
$949$	64.7374	2.10146
$950$	−12.3522	−0.400759
$951$	−15.3151	−0.496625
$952$	−26.3360	−0.853553
$953$	−6.09060	−0.197294	−0.0986469	−	0.995122i	$-0.531451\pi$
$953$	−6.09060	−0.197294	−0.0986469	+	0.995122i	$0.531451\pi$
$954$	14.0520	0.454951
$955$	5.97781	0.193437
$956$	34.7929	1.12528
$957$	−3.04376	−0.0983908
$958$	−0.142662	−0.00460920
$959$	26.9966	0.871767
$960$	1.15781	0.0373682
$961$	40.9000	1.31936
$962$	−36.3694	−1.17260
$963$	−43.5423	−1.40313
$964$	−2.36468	−0.0761614
$965$	−18.9002	−0.608420
$966$	−4.86731	−0.156603
$967$	−32.8474	−1.05630	−0.528151	−	0.849150i	$-0.677115\pi$
$967$	−32.8474	−1.05630	−0.528151	+	0.849150i	$0.677115\pi$
$968$	25.9954	0.835523
$969$	−7.14412	−0.229502
$970$	0.336519	0.0108050
$971$	45.3642	1.45581	0.727903	−	0.685680i	$-0.240495\pi$
$971$	45.3642	1.45581	0.727903	+	0.685680i	$0.240495\pi$
$972$	−18.6899	−0.599479
$973$	−68.5650	−2.19809
$974$	−1.95344	−0.0625922
$975$	9.93297	0.318110
$976$	−3.19603	−0.102303
$977$	9.96515	0.318813	0.159407	−	0.987213i	$-0.449042\pi$
$977$	9.96515	0.318813	0.159407	+	0.987213i	$0.449042\pi$
$978$	4.73881	0.151530
$979$	−0.740268	−0.0236591
$980$	−5.03286	−0.160769
$981$	−7.05979	−0.225402
$982$	8.11707	0.259026
$983$	−8.37150	−0.267009	−0.133505	−	0.991048i	$-0.542623\pi$
$983$	−8.37150	−0.267009	−0.133505	+	0.991048i	$0.542623\pi$
$984$	−1.95351	−0.0622757
$985$	25.3827	0.808761
$986$	−14.8230	−0.472062
$987$	10.3057	0.328035
$988$	26.9768	0.858245
$989$	−34.8202	−1.10722
$990$	1.69030	0.0537213
$991$	28.8111	0.915215	0.457608	−	0.889154i	$-0.348706\pi$
$991$	28.8111	0.915215	0.457608	+	0.889154i	$0.348706\pi$
$992$	−49.6732	−1.57712
$993$	−0.970354	−0.0307933
$994$	10.9448	0.347147
$995$	−4.98690	−0.158095
$996$	−5.86927	−0.185975
$997$	12.3708	0.391788	0.195894	−	0.980625i	$-0.437239\pi$
$997$	12.3708	0.391788	0.195894	+	0.980625i	$0.437239\pi$
$998$	22.7904	0.721418
$999$	−34.2589	−1.08390

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.2.a.b.1.11	✓	18
3.2	odd	2		4923.2.a.l.1.8		18
4.3	odd	2		8752.2.a.s.1.6		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.2.a.b.1.11	✓	18	1.1	even	1	trivial
4923.2.a.l.1.8		18	3.2	odd	2
8752.2.a.s.1.6		18	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 547 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	547.a (trivial)

\(f(q)\)	\(=\)	\(q+0.735255 q^{2} +0.544167 q^{3} -1.45940 q^{4} +0.962787 q^{5} +0.400102 q^{6} -3.25298 q^{7} -2.54354 q^{8} -2.70388 q^{9} +O(q^{10})\)	\(q+0.735255 q^{2} +0.544167 q^{3} -1.45940 q^{4} +0.962787 q^{5} +0.400102 q^{6} -3.25298 q^{7} -2.54354 q^{8} -2.70388 q^{9} +0.707894 q^{10} -0.883096 q^{11} -0.794158 q^{12} -4.48154 q^{13} -2.39177 q^{14} +0.523917 q^{15} +1.04865 q^{16} -3.18294 q^{17} -1.98804 q^{18} +4.12466 q^{19} -1.40509 q^{20} -1.77017 q^{21} -0.649301 q^{22} +3.73970 q^{23} -1.38411 q^{24} -4.07304 q^{25} -3.29508 q^{26} -3.10387 q^{27} +4.74740 q^{28} +6.33388 q^{29} +0.385213 q^{30} -8.47939 q^{31} +5.85811 q^{32} -0.480552 q^{33} -2.34028 q^{34} -3.13193 q^{35} +3.94604 q^{36} +11.0375 q^{37} +3.03268 q^{38} -2.43871 q^{39} -2.44889 q^{40} +1.41138 q^{41} -1.30152 q^{42} -9.31097 q^{43} +1.28879 q^{44} -2.60326 q^{45} +2.74963 q^{46} -5.82191 q^{47} +0.570639 q^{48} +3.58188 q^{49} -2.99473 q^{50} -1.73205 q^{51} +6.54036 q^{52} -7.06826 q^{53} -2.28213 q^{54} -0.850233 q^{55} +8.27409 q^{56} +2.24450 q^{57} +4.65702 q^{58} +12.9274 q^{59} -0.764605 q^{60} -3.04777 q^{61} -6.23452 q^{62} +8.79567 q^{63} +2.20991 q^{64} -4.31477 q^{65} -0.353328 q^{66} -9.15218 q^{67} +4.64518 q^{68} +2.03502 q^{69} -2.30277 q^{70} -4.57601 q^{71} +6.87744 q^{72} -14.4453 q^{73} +8.11538 q^{74} -2.21642 q^{75} -6.01952 q^{76} +2.87269 q^{77} -1.79308 q^{78} +7.20620 q^{79} +1.00962 q^{80} +6.42262 q^{81} +1.03773 q^{82} +7.39056 q^{83} +2.58338 q^{84} -3.06450 q^{85} -6.84594 q^{86} +3.44669 q^{87} +2.24619 q^{88} +0.838265 q^{89} -1.91406 q^{90} +14.5784 q^{91} -5.45771 q^{92} -4.61421 q^{93} -4.28059 q^{94} +3.97117 q^{95} +3.18779 q^{96} +0.475381 q^{97} +2.63360 q^{98} +2.38779 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 4 q^{2} - 10 q^{3} + 16 q^{4} - 27 q^{5} - 3 q^{6} - 11 q^{7} - 12 q^{8} + 14 q^{9}+O(q^{10}) \) 18 * q - 4 * q^2 - 10 * q^3 + 16 * q^4 - 27 * q^5 - 3 * q^6 - 11 * q^7 - 12 * q^8 + 14 * q^9	\( 18 q - 4 q^{2} - 10 q^{3} + 16 q^{4} - 27 q^{5} - 3 q^{6} - 11 q^{7} - 12 q^{8} + 14 q^{9} - 5 q^{10} + 2 q^{11} - 32 q^{12} - 25 q^{13} - 7 q^{14} + 9 q^{15} + 8 q^{16} - 30 q^{17} - 10 q^{18} + 4 q^{19} - 41 q^{20} - 16 q^{21} - 24 q^{22} - 26 q^{23} - 12 q^{24} + 31 q^{25} - 18 q^{26} - 37 q^{27} - 16 q^{28} - 18 q^{29} + 8 q^{30} - 5 q^{31} - 28 q^{32} - 10 q^{33} + 5 q^{34} - 9 q^{35} + 31 q^{36} - 18 q^{37} - 45 q^{38} + 7 q^{39} + 7 q^{40} - 17 q^{41} + 4 q^{42} + 8 q^{43} + 12 q^{44} - 44 q^{45} + 30 q^{46} - 52 q^{47} - 7 q^{48} + 29 q^{49} + 13 q^{50} + 19 q^{51} - 14 q^{52} - 60 q^{53} + 11 q^{54} + 11 q^{55} + 7 q^{56} + 4 q^{57} + 14 q^{58} - 8 q^{59} + 86 q^{60} - 26 q^{61} + 4 q^{62} - q^{63} + 44 q^{64} - 6 q^{65} + 18 q^{66} + 12 q^{67} - 61 q^{68} - 38 q^{69} + 35 q^{70} - q^{71} + 28 q^{72} - 2 q^{73} + 16 q^{74} - 17 q^{75} + 66 q^{76} - 73 q^{77} + 115 q^{78} + 18 q^{79} - 32 q^{80} + 18 q^{81} + 44 q^{82} - 43 q^{83} + 41 q^{84} + 51 q^{85} + 4 q^{86} + 3 q^{87} - 17 q^{88} - 28 q^{89} + 58 q^{90} - q^{91} - 68 q^{92} - 60 q^{93} + 78 q^{94} - 18 q^{95} + 29 q^{96} - 34 q^{97} + 34 q^{98} + 15 q^{99}+O(q^{100}) \) 18 * q - 4 * q^2 - 10 * q^3 + 16 * q^4 - 27 * q^5 - 3 * q^6 - 11 * q^7 - 12 * q^8 + 14 * q^9 - 5 * q^10 + 2 * q^11 - 32 * q^12 - 25 * q^13 - 7 * q^14 + 9 * q^15 + 8 * q^16 - 30 * q^17 - 10 * q^18 + 4 * q^19 - 41 * q^20 - 16 * q^21 - 24 * q^22 - 26 * q^23 - 12 * q^24 + 31 * q^25 - 18 * q^26 - 37 * q^27 - 16 * q^28 - 18 * q^29 + 8 * q^30 - 5 * q^31 - 28 * q^32 - 10 * q^33 + 5 * q^34 - 9 * q^35 + 31 * q^36 - 18 * q^37 - 45 * q^38 + 7 * q^39 + 7 * q^40 - 17 * q^41 + 4 * q^42 + 8 * q^43 + 12 * q^44 - 44 * q^45 + 30 * q^46 - 52 * q^47 - 7 * q^48 + 29 * q^49 + 13 * q^50 + 19 * q^51 - 14 * q^52 - 60 * q^53 + 11 * q^54 + 11 * q^55 + 7 * q^56 + 4 * q^57 + 14 * q^58 - 8 * q^59 + 86 * q^60 - 26 * q^61 + 4 * q^62 - q^63 + 44 * q^64 - 6 * q^65 + 18 * q^66 + 12 * q^67 - 61 * q^68 - 38 * q^69 + 35 * q^70 - q^71 + 28 * q^72 - 2 * q^73 + 16 * q^74 - 17 * q^75 + 66 * q^76 - 73 * q^77 + 115 * q^78 + 18 * q^79 - 32 * q^80 + 18 * q^81 + 44 * q^82 - 43 * q^83 + 41 * q^84 + 51 * q^85 + 4 * q^86 + 3 * q^87 - 17 * q^88 - 28 * q^89 + 58 * q^90 - q^91 - 68 * q^92 - 60 * q^93 + 78 * q^94 - 18 * q^95 + 29 * q^96 - 34 * q^97 + 34 * q^98 + 15 * q^99

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