LMFDB - Embedded newform 5077.2.a.b.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5077,2,Mod(1,5077)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5077, 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("5077.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5077 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5077.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:	$40.5400491062$
Analytic rank:	$1$
Dimension:	$205$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	5077.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.54248 q^{2} +2.75174 q^{3} +4.46418 q^{4} -3.07759 q^{5} -6.99622 q^{6} -3.90745 q^{7} -6.26513 q^{8} +4.57206 q^{9} +O(q^{10})$	\(q-2.54248 q^{2} +2.75174 q^{3} +4.46418 q^{4} -3.07759 q^{5} -6.99622 q^{6} -3.90745 q^{7} -6.26513 q^{8} +4.57206 q^{9} +7.82470 q^{10} -1.66112 q^{11} +12.2843 q^{12} +0.441222 q^{13} +9.93461 q^{14} -8.46872 q^{15} +7.00056 q^{16} -6.23607 q^{17} -11.6243 q^{18} +8.14235 q^{19} -13.7389 q^{20} -10.7523 q^{21} +4.22336 q^{22} +7.85357 q^{23} -17.2400 q^{24} +4.47157 q^{25} -1.12180 q^{26} +4.32589 q^{27} -17.4436 q^{28} +4.42691 q^{29} +21.5315 q^{30} -1.06188 q^{31} -5.26851 q^{32} -4.57097 q^{33} +15.8550 q^{34} +12.0255 q^{35} +20.4105 q^{36} +1.90838 q^{37} -20.7017 q^{38} +1.21413 q^{39} +19.2815 q^{40} +3.64309 q^{41} +27.3374 q^{42} +0.714271 q^{43} -7.41554 q^{44} -14.0709 q^{45} -19.9675 q^{46} +0.372940 q^{47} +19.2637 q^{48} +8.26820 q^{49} -11.3689 q^{50} -17.1600 q^{51} +1.96970 q^{52} -6.28743 q^{53} -10.9985 q^{54} +5.11225 q^{55} +24.4807 q^{56} +22.4056 q^{57} -11.2553 q^{58} -8.98516 q^{59} -37.8059 q^{60} +3.69042 q^{61} +2.69979 q^{62} -17.8651 q^{63} -0.606061 q^{64} -1.35790 q^{65} +11.6216 q^{66} -9.52810 q^{67} -27.8389 q^{68} +21.6110 q^{69} -30.5747 q^{70} -6.69544 q^{71} -28.6445 q^{72} +0.902173 q^{73} -4.85202 q^{74} +12.3046 q^{75} +36.3490 q^{76} +6.49075 q^{77} -3.08689 q^{78} +16.0851 q^{79} -21.5449 q^{80} -1.81247 q^{81} -9.26246 q^{82} -8.84985 q^{83} -48.0002 q^{84} +19.1921 q^{85} -1.81602 q^{86} +12.1817 q^{87} +10.4071 q^{88} +2.04644 q^{89} +35.7750 q^{90} -1.72406 q^{91} +35.0598 q^{92} -2.92200 q^{93} -0.948190 q^{94} -25.0588 q^{95} -14.4976 q^{96} +2.83398 q^{97} -21.0217 q^{98} -7.59473 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 205 q - 25 q^{2} - 59 q^{3} + 195 q^{4} - 44 q^{5} - 26 q^{6} - 30 q^{7} - 75 q^{8} + 186 q^{9}+O(q^{10}) $ 205 * q - 25 * q^2 - 59 * q^3 + 195 * q^4 - 44 * q^5 - 26 * q^6 - 30 * q^7 - 75 * q^8 + 186 * q^9	\( 205 q - 25 q^{2} - 59 q^{3} + 195 q^{4} - 44 q^{5} - 26 q^{6} - 30 q^{7} - 75 q^{8} + 186 q^{9} - 28 q^{10} - 83 q^{11} - 108 q^{12} - 36 q^{13} - 67 q^{14} - 63 q^{15} + 187 q^{16} - 72 q^{17} - 57 q^{18} - 47 q^{19} - 132 q^{20} - 35 q^{21} - 40 q^{22} - 97 q^{23} - 49 q^{24} + 175 q^{25} - 78 q^{26} - 227 q^{27} - 59 q^{28} - 46 q^{29} + 30 q^{30} - 77 q^{31} - 175 q^{32} - 74 q^{33} - 28 q^{34} - 171 q^{35} + 171 q^{36} - 52 q^{37} - 144 q^{38} - 54 q^{39} - 49 q^{40} - 107 q^{41} + 7 q^{42} - 58 q^{43} - 139 q^{44} - 89 q^{45} - 33 q^{46} - 255 q^{47} - 202 q^{48} + 171 q^{49} - 74 q^{50} - 63 q^{51} - 90 q^{52} - 82 q^{53} - 51 q^{54} - 70 q^{55} - 180 q^{56} - 70 q^{57} - 50 q^{58} - 289 q^{59} - 105 q^{60} - 20 q^{61} - 143 q^{62} - 119 q^{63} + 201 q^{64} - 92 q^{65} - 3 q^{66} - 138 q^{67} - 177 q^{68} - 67 q^{69} + 4 q^{70} - 141 q^{71} - 138 q^{72} - 71 q^{73} - 26 q^{74} - 251 q^{75} - 42 q^{76} - 149 q^{77} - 6 q^{78} - 47 q^{79} - 294 q^{80} + 193 q^{81} - 70 q^{82} - 329 q^{83} - 40 q^{84} - 45 q^{85} - 83 q^{86} - 139 q^{87} - 45 q^{88} - 163 q^{89} - 116 q^{90} - 141 q^{91} - 204 q^{92} - 91 q^{93} - 8 q^{94} - 173 q^{95} - 53 q^{96} - 147 q^{97} - 156 q^{98} - 157 q^{99}+O(q^{100}) \) 205 * q - 25 * q^2 - 59 * q^3 + 195 * q^4 - 44 * q^5 - 26 * q^6 - 30 * q^7 - 75 * q^8 + 186 * q^9 - 28 * q^10 - 83 * q^11 - 108 * q^12 - 36 * q^13 - 67 * q^14 - 63 * q^15 + 187 * q^16 - 72 * q^17 - 57 * q^18 - 47 * q^19 - 132 * q^20 - 35 * q^21 - 40 * q^22 - 97 * q^23 - 49 * q^24 + 175 * q^25 - 78 * q^26 - 227 * q^27 - 59 * q^28 - 46 * q^29 + 30 * q^30 - 77 * q^31 - 175 * q^32 - 74 * q^33 - 28 * q^34 - 171 * q^35 + 171 * q^36 - 52 * q^37 - 144 * q^38 - 54 * q^39 - 49 * q^40 - 107 * q^41 + 7 * q^42 - 58 * q^43 - 139 * q^44 - 89 * q^45 - 33 * q^46 - 255 * q^47 - 202 * q^48 + 171 * q^49 - 74 * q^50 - 63 * q^51 - 90 * q^52 - 82 * q^53 - 51 * q^54 - 70 * q^55 - 180 * q^56 - 70 * q^57 - 50 * q^58 - 289 * q^59 - 105 * q^60 - 20 * q^61 - 143 * q^62 - 119 * q^63 + 201 * q^64 - 92 * q^65 - 3 * q^66 - 138 * q^67 - 177 * q^68 - 67 * q^69 + 4 * q^70 - 141 * q^71 - 138 * q^72 - 71 * q^73 - 26 * q^74 - 251 * q^75 - 42 * q^76 - 149 * q^77 - 6 * q^78 - 47 * q^79 - 294 * q^80 + 193 * q^81 - 70 * q^82 - 329 * q^83 - 40 * q^84 - 45 * q^85 - 83 * q^86 - 139 * q^87 - 45 * q^88 - 163 * q^89 - 116 * q^90 - 141 * q^91 - 204 * q^92 - 91 * q^93 - 8 * q^94 - 173 * q^95 - 53 * q^96 - 147 * q^97 - 156 * q^98 - 157 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.54248	−1.79780	−0.898901	−	0.438152i	$-0.855633\pi$
$2$	−2.54248	−1.79780	−0.898901	+	0.438152i	$0.855633\pi$
$3$	2.75174	1.58872	0.794358	−	0.607450i	$-0.207807\pi$
$3$	2.75174	1.58872	0.794358	+	0.607450i	$0.207807\pi$
$4$	4.46418	2.23209
$5$	−3.07759	−1.37634	−0.688170	−	0.725549i	$-0.741586\pi$
$5$	−3.07759	−1.37634	−0.688170	+	0.725549i	$0.741586\pi$
$6$	−6.99622	−2.85620
$7$	−3.90745	−1.47688	−0.738440	−	0.674320i	$-0.764437\pi$
$7$	−3.90745	−1.47688	−0.738440	+	0.674320i	$0.764437\pi$
$8$	−6.26513	−2.21506
$9$	4.57206	1.52402
$10$	7.82470	2.47439
$11$	−1.66112	−0.500847	−0.250423	−	0.968136i	$-0.580570\pi$
$11$	−1.66112	−0.500847	−0.250423	+	0.968136i	$0.580570\pi$
$12$	12.2843	3.54616
$13$	0.441222	0.122373	0.0611865	−	0.998126i	$-0.480512\pi$
$13$	0.441222	0.122373	0.0611865	+	0.998126i	$0.480512\pi$
$14$	9.93461	2.65514
$15$	−8.46872	−2.18661
$16$	7.00056	1.75014
$17$	−6.23607	−1.51247	−0.756234	−	0.654301i	$-0.772963\pi$
$17$	−6.23607	−1.51247	−0.756234	+	0.654301i	$0.772963\pi$
$18$	−11.6243	−2.73988
$19$	8.14235	1.86798	0.933992	−	0.357294i	$-0.116301\pi$
$19$	8.14235	1.86798	0.933992	+	0.357294i	$0.116301\pi$
$20$	−13.7389	−3.07212
$21$	−10.7523	−2.34634
$22$	4.22336	0.900423
$23$	7.85357	1.63758	0.818792	−	0.574091i	$-0.194644\pi$
$23$	7.85357	1.63758	0.818792	+	0.574091i	$0.194644\pi$
$24$	−17.2400	−3.51910
$25$	4.47157	0.894314
$26$	−1.12180	−0.220002
$27$	4.32589	0.832517
$28$	−17.4436	−3.29653
$29$	4.42691	0.822057	0.411029	−	0.911622i	$-0.365170\pi$
$29$	4.42691	0.822057	0.411029	+	0.911622i	$0.365170\pi$
$30$	21.5315	3.93110
$31$	−1.06188	−0.190718	−0.0953592	−	0.995443i	$-0.530400\pi$
$31$	−1.06188	−0.190718	−0.0953592	+	0.995443i	$0.530400\pi$
$32$	−5.26851	−0.931350
$33$	−4.57097	−0.795703
$34$	15.8550	2.71912
$35$	12.0255	2.03269
$36$	20.4105	3.40175
$37$	1.90838	0.313736	0.156868	−	0.987620i	$-0.449860\pi$
$37$	1.90838	0.313736	0.156868	+	0.987620i	$0.449860\pi$
$38$	−20.7017	−3.35826
$39$	1.21413	0.194416
$40$	19.2815	3.04867
$41$	3.64309	0.568954	0.284477	−	0.958683i	$-0.408180\pi$
$41$	3.64309	0.568954	0.284477	+	0.958683i	$0.408180\pi$
$42$	27.3374	4.21826
$43$	0.714271	0.108925	0.0544627	−	0.998516i	$-0.482655\pi$
$43$	0.714271	0.108925	0.0544627	+	0.998516i	$0.482655\pi$
$44$	−7.41554	−1.11794
$45$	−14.0709	−2.09757
$46$	−19.9675	−2.94405
$47$	0.372940	0.0543988	0.0271994	−	0.999630i	$-0.491341\pi$
$47$	0.372940	0.0543988	0.0271994	+	0.999630i	$0.491341\pi$
$48$	19.2637	2.78048
$49$	8.26820	1.18117
$50$	−11.3689	−1.60780
$51$	−17.1600	−2.40288
$52$	1.96970	0.273148
$53$	−6.28743	−0.863645	−0.431822	−	0.901959i	$-0.642129\pi$
$53$	−6.28743	−0.863645	−0.431822	+	0.901959i	$0.642129\pi$
$54$	−10.9985	−1.49670
$55$	5.11225	0.689335
$56$	24.4807	3.27137
$57$	22.4056	2.96770
$58$	−11.2553	−1.47790
$59$	−8.98516	−1.16977	−0.584884	−	0.811117i	$-0.698860\pi$
$59$	−8.98516	−1.16977	−0.584884	+	0.811117i	$0.698860\pi$
$60$	−37.8059	−4.88072
$61$	3.69042	0.472510	0.236255	−	0.971691i	$-0.424080\pi$
$61$	3.69042	0.472510	0.236255	+	0.971691i	$0.424080\pi$
$62$	2.69979	0.342874
$63$	−17.8651	−2.25079
$64$	−0.606061	−0.0757576
$65$	−1.35790	−0.168427
$66$	11.6216	1.43052
$67$	−9.52810	−1.16404	−0.582021	−	0.813174i	$-0.697738\pi$
$67$	−9.52810	−1.16404	−0.582021	+	0.813174i	$0.697738\pi$
$68$	−27.8389	−3.37597
$69$	21.6110	2.60166
$70$	−30.5747	−3.65437
$71$	−6.69544	−0.794603	−0.397301	−	0.917688i	$-0.630053\pi$
$71$	−6.69544	−0.794603	−0.397301	+	0.917688i	$0.630053\pi$
$72$	−28.6445	−3.37579
$73$	0.902173	0.105591	0.0527957	−	0.998605i	$-0.483187\pi$
$73$	0.902173	0.105591	0.0527957	+	0.998605i	$0.483187\pi$
$74$	−4.85202	−0.564036
$75$	12.3046	1.42081
$76$	36.3490	4.16951
$77$	6.49075	0.739690
$78$	−3.08689	−0.349521
$79$	16.0851	1.80972	0.904859	−	0.425711i	$-0.139976\pi$
$79$	16.0851	1.80972	0.904859	+	0.425711i	$0.139976\pi$
$80$	−21.5449	−2.40879
$81$	−1.81247	−0.201385
$82$	−9.26246	−1.02287
$83$	−8.84985	−0.971397	−0.485699	−	0.874126i	$-0.661435\pi$
$83$	−8.84985	−0.971397	−0.485699	+	0.874126i	$0.661435\pi$
$84$	−48.0002	−5.23725
$85$	19.1921	2.08167
$86$	−1.81602	−0.195826
$87$	12.1817	1.30602
$88$	10.4071	1.10940
$89$	2.04644	0.216923	0.108461	−	0.994101i	$-0.465408\pi$
$89$	2.04644	0.216923	0.108461	+	0.994101i	$0.465408\pi$
$90$	35.7750	3.77101
$91$	−1.72406	−0.180730
$92$	35.0598	3.65524
$93$	−2.92200	−0.302997
$94$	−0.948190	−0.0977983
$95$	−25.0588	−2.57098
$96$	−14.4976	−1.47965
$97$	2.83398	0.287747	0.143873	−	0.989596i	$-0.454044\pi$
$97$	2.83398	0.287747	0.143873	+	0.989596i	$0.454044\pi$
$98$	−21.0217	−2.12351
$99$	−7.59473	−0.763300
$100$	19.9619	1.99619
$101$	3.06352	0.304831	0.152416	−	0.988316i	$-0.451295\pi$
$101$	3.06352	0.304831	0.152416	+	0.988316i	$0.451295\pi$
$102$	43.6289	4.31991
$103$	14.2848	1.40752	0.703762	−	0.710436i	$-0.251502\pi$
$103$	14.2848	1.40752	0.703762	+	0.710436i	$0.251502\pi$
$104$	−2.76431	−0.271063
$105$	33.0911	3.22937
$106$	15.9856	1.55266
$107$	7.54561	0.729462	0.364731	−	0.931113i	$-0.381161\pi$
$107$	7.54561	0.729462	0.364731	+	0.931113i	$0.381161\pi$
$108$	19.3115	1.85825
$109$	−1.06929	−0.102420	−0.0512098	−	0.998688i	$-0.516308\pi$
$109$	−1.06929	−0.102420	−0.0512098	+	0.998688i	$0.516308\pi$
$110$	−12.9978	−1.23929
$111$	5.25137	0.498438
$112$	−27.3544	−2.58475
$113$	−14.5365	−1.36748	−0.683741	−	0.729725i	$-0.739648\pi$
$113$	−14.5365	−1.36748	−0.683741	+	0.729725i	$0.739648\pi$
$114$	−56.9657	−5.33533
$115$	−24.1701	−2.25387
$116$	19.7625	1.83491
$117$	2.01729	0.186499
$118$	22.8445	2.10301
$119$	24.3671	2.23373
$120$	53.0576	4.84347
$121$	−8.24068	−0.749153
$122$	−9.38280	−0.849479
$123$	10.0248	0.903907
$124$	−4.74041	−0.425701
$125$	1.62630	0.145460
$126$	45.4216	4.04648
$127$	2.09262	0.185690	0.0928451	−	0.995681i	$-0.470404\pi$
$127$	2.09262	0.185690	0.0928451	+	0.995681i	$0.470404\pi$
$128$	12.0779	1.06755
$129$	1.96549	0.173051
$130$	3.45243	0.302798
$131$	−19.5938	−1.71191	−0.855957	−	0.517047i	$-0.827031\pi$
$131$	−19.5938	−1.71191	−0.855957	+	0.517047i	$0.827031\pi$
$132$	−20.4056	−1.77608
$133$	−31.8159	−2.75879
$134$	24.2250	2.09272
$135$	−13.3133	−1.14583
$136$	39.0697	3.35020
$137$	−5.77897	−0.493730	−0.246865	−	0.969050i	$-0.579401\pi$
$137$	−5.77897	−0.493730	−0.246865	+	0.969050i	$0.579401\pi$
$138$	−54.9454	−4.67726
$139$	2.74116	0.232502	0.116251	−	0.993220i	$-0.462912\pi$
$139$	2.74116	0.232502	0.116251	+	0.993220i	$0.462912\pi$
$140$	53.6843	4.53715
$141$	1.02623	0.0864243
$142$	17.0230	1.42854
$143$	−0.732923	−0.0612901
$144$	32.0070	2.66725
$145$	−13.6242	−1.13143
$146$	−2.29375	−0.189832
$147$	22.7519	1.87655
$148$	8.51938	0.700288
$149$	3.85012	0.315414	0.157707	−	0.987486i	$-0.449590\pi$
$149$	3.85012	0.315414	0.157707	+	0.987486i	$0.449590\pi$
$150$	−31.2841	−2.55434
$151$	18.6711	1.51943	0.759716	−	0.650255i	$-0.225338\pi$
$151$	18.6711	1.51943	0.759716	+	0.650255i	$0.225338\pi$
$152$	−51.0129	−4.13769
$153$	−28.5116	−2.30503
$154$	−16.5026	−1.32982
$155$	3.26802	0.262494
$156$	5.42009	0.433954
$157$	−9.61993	−0.767754	−0.383877	−	0.923384i	$-0.625411\pi$
$157$	−9.61993	−0.767754	−0.383877	+	0.923384i	$0.625411\pi$
$158$	−40.8961	−3.25352
$159$	−17.3014	−1.37209
$160$	16.2143	1.28186
$161$	−30.6875	−2.41851
$162$	4.60816	0.362051
$163$	−25.5206	−1.99892	−0.999462	−	0.0327838i	$-0.989563\pi$
$163$	−25.5206	−1.99892	−0.999462	+	0.0327838i	$0.989563\pi$
$164$	16.2634	1.26996
$165$	14.0676	1.09516
$166$	22.5005	1.74638
$167$	−21.3828	−1.65465	−0.827325	−	0.561723i	$-0.810139\pi$
$167$	−21.3828	−1.65465	−0.827325	+	0.561723i	$0.810139\pi$
$168$	67.3644	5.19728
$169$	−12.8053	−0.985025
$170$	−48.7954	−3.74243
$171$	37.2273	2.84684
$172$	3.18864	0.243131
$173$	9.29481	0.706672	0.353336	−	0.935497i	$-0.385047\pi$
$173$	9.29481	0.706672	0.353336	+	0.935497i	$0.385047\pi$
$174$	−30.9717	−2.34796
$175$	−17.4725	−1.32079
$176$	−11.6288	−0.876552
$177$	−24.7248	−1.85843
$178$	−5.20304	−0.389984
$179$	−15.0934	−1.12813	−0.564067	−	0.825729i	$-0.690764\pi$
$179$	−15.0934	−1.12813	−0.564067	+	0.825729i	$0.690764\pi$
$180$	−62.8152	−4.68197
$181$	−17.5596	−1.30520	−0.652598	−	0.757704i	$-0.726321\pi$
$181$	−17.5596	−1.30520	−0.652598	+	0.757704i	$0.726321\pi$
$182$	4.38337	0.324917
$183$	10.1551	0.750684
$184$	−49.2036	−3.62734
$185$	−5.87323	−0.431808
$186$	7.42912	0.544729
$187$	10.3589	0.757515
$188$	1.66487	0.121423
$189$	−16.9032	−1.22953
$190$	63.7115	4.62212
$191$	14.3059	1.03514	0.517568	−	0.855642i	$-0.326837\pi$
$191$	14.3059	1.03514	0.517568	+	0.855642i	$0.326837\pi$
$192$	−1.66772	−0.120357
$193$	5.06961	0.364918	0.182459	−	0.983213i	$-0.441594\pi$
$193$	5.06961	0.364918	0.182459	+	0.983213i	$0.441594\pi$
$194$	−7.20532	−0.517312
$195$	−3.73659	−0.267583
$196$	36.9108	2.63648
$197$	−12.9774	−0.924604	−0.462302	−	0.886722i	$-0.652976\pi$
$197$	−12.9774	−0.924604	−0.462302	+	0.886722i	$0.652976\pi$
$198$	19.3094	1.37226
$199$	12.3284	0.873940	0.436970	−	0.899476i	$-0.356052\pi$
$199$	12.3284	0.873940	0.436970	+	0.899476i	$0.356052\pi$
$200$	−28.0149	−1.98096
$201$	−26.2188	−1.84933
$202$	−7.78892	−0.548027
$203$	−17.2980	−1.21408
$204$	−76.6055	−5.36345
$205$	−11.2119	−0.783075
$206$	−36.3188	−2.53045
$207$	35.9070	2.49571
$208$	3.08880	0.214170
$209$	−13.5254	−0.935573
$210$	−84.1334	−5.80576
$211$	−3.60225	−0.247989	−0.123995	−	0.992283i	$-0.539571\pi$
$211$	−3.60225	−0.247989	−0.123995	+	0.992283i	$0.539571\pi$
$212$	−28.0682	−1.92773
$213$	−18.4241	−1.26240
$214$	−19.1845	−1.31143
$215$	−2.19823	−0.149918
$216$	−27.1022	−1.84407
$217$	4.14923	0.281668
$218$	2.71865	0.184130
$219$	2.48254	0.167755
$220$	22.8220	1.53866
$221$	−2.75149	−0.185085
$222$	−13.3515	−0.896093
$223$	−8.66379	−0.580170	−0.290085	−	0.957001i	$-0.593684\pi$
$223$	−8.66379	−0.580170	−0.290085	+	0.957001i	$0.593684\pi$
$224$	20.5865	1.37549
$225$	20.4443	1.36295
$226$	36.9588	2.45846
$227$	−8.58657	−0.569910	−0.284955	−	0.958541i	$-0.591979\pi$
$227$	−8.58657	−0.569910	−0.284955	+	0.958541i	$0.591979\pi$
$228$	100.023	6.62417
$229$	−12.7222	−0.840707	−0.420354	−	0.907360i	$-0.638094\pi$
$229$	−12.7222	−0.840707	−0.420354	+	0.907360i	$0.638094\pi$
$230$	61.4519	4.05202
$231$	17.8608	1.17516
$232$	−27.7352	−1.82090
$233$	−20.0537	−1.31376	−0.656881	−	0.753995i	$-0.728124\pi$
$233$	−20.0537	−1.31376	−0.656881	+	0.753995i	$0.728124\pi$
$234$	−5.12892	−0.335288
$235$	−1.14776	−0.0748713
$236$	−40.1114	−2.61103
$237$	44.2621	2.87513
$238$	−61.9529	−4.01581
$239$	−14.6305	−0.946367	−0.473183	−	0.880964i	$-0.656895\pi$
$239$	−14.6305	−0.946367	−0.473183	+	0.880964i	$0.656895\pi$
$240$	−59.2858	−3.82688
$241$	−15.6810	−1.01010	−0.505051	−	0.863089i	$-0.668526\pi$
$241$	−15.6810	−1.01010	−0.505051	+	0.863089i	$0.668526\pi$
$242$	20.9517	1.34683
$243$	−17.9651	−1.15246
$244$	16.4747	1.05468
$245$	−25.4461	−1.62569
$246$	−25.4878	−1.62505
$247$	3.59259	0.228591
$248$	6.65278	0.422452
$249$	−24.3525	−1.54327
$250$	−4.13482	−0.261509
$251$	28.7687	1.81587	0.907933	−	0.419115i	$-0.137660\pi$
$251$	28.7687	1.81587	0.907933	+	0.419115i	$0.137660\pi$
$252$	−79.7531	−5.02397
$253$	−13.0457	−0.820178
$254$	−5.32044	−0.333834
$255$	52.8115	3.30719
$256$	−29.4957	−1.84348
$257$	9.31176	0.580851	0.290426	−	0.956898i	$-0.406203\pi$
$257$	9.31176	0.580851	0.290426	+	0.956898i	$0.406203\pi$
$258$	−4.99720	−0.311112
$259$	−7.45692	−0.463351
$260$	−6.06192	−0.375944
$261$	20.2401	1.25283
$262$	49.8167	3.07768
$263$	−16.2715	−1.00335	−0.501673	−	0.865058i	$-0.667282\pi$
$263$	−16.2715	−1.00335	−0.501673	+	0.865058i	$0.667282\pi$
$264$	28.6377	1.76253
$265$	19.3501	1.18867
$266$	80.8911	4.95975
$267$	5.63128	0.344629
$268$	−42.5352	−2.59825
$269$	−1.92431	−0.117327	−0.0586637	−	0.998278i	$-0.518684\pi$
$269$	−1.92431	−0.117327	−0.0586637	+	0.998278i	$0.518684\pi$
$270$	33.8488	2.05997
$271$	−22.8006	−1.38504	−0.692520	−	0.721399i	$-0.743499\pi$
$271$	−22.8006	−1.38504	−0.692520	+	0.721399i	$0.743499\pi$
$272$	−43.6560	−2.64703
$273$	−4.74415	−0.287129
$274$	14.6929	0.887630
$275$	−7.42781	−0.447914
$276$	96.4753	5.80713
$277$	4.81124	0.289079	0.144540	−	0.989499i	$-0.453830\pi$
$277$	4.81124	0.289079	0.144540	+	0.989499i	$0.453830\pi$
$278$	−6.96934	−0.417993
$279$	−4.85495	−0.290659
$280$	−75.3416	−4.50252
$281$	4.59406	0.274059	0.137029	−	0.990567i	$-0.456245\pi$
$281$	4.59406	0.274059	0.137029	+	0.990567i	$0.456245\pi$
$282$	−2.60917	−0.155374
$283$	24.9487	1.48304	0.741522	−	0.670928i	$-0.234104\pi$
$283$	24.9487	1.48304	0.741522	+	0.670928i	$0.234104\pi$
$284$	−29.8897	−1.77363
$285$	−68.9553	−4.08456
$286$	1.86344	0.110187
$287$	−14.2352	−0.840277
$288$	−24.0879	−1.41940
$289$	21.8885	1.28756
$290$	34.6393	2.03409
$291$	7.79836	0.457148
$292$	4.02746	0.235690
$293$	−23.9925	−1.40166	−0.700828	−	0.713330i	$-0.747186\pi$
$293$	−23.9925	−1.40166	−0.700828	+	0.713330i	$0.747186\pi$
$294$	−57.8462	−3.37366
$295$	27.6526	1.61000
$296$	−11.9563	−0.694944
$297$	−7.18582	−0.416963
$298$	−9.78885	−0.567053
$299$	3.46517	0.200396
$300$	54.9299	3.17138
$301$	−2.79098	−0.160870
$302$	−47.4708	−2.73164
$303$	8.43000	0.484291
$304$	57.0011	3.26924
$305$	−11.3576	−0.650334
$306$	72.4902	4.14399
$307$	2.29236	0.130832	0.0654159	−	0.997858i	$-0.479163\pi$
$307$	2.29236	0.130832	0.0654159	+	0.997858i	$0.479163\pi$
$308$	28.9759	1.65106
$309$	39.3080	2.23615
$310$	−8.30886	−0.471911
$311$	−3.32327	−0.188445	−0.0942227	−	0.995551i	$-0.530037\pi$
$311$	−3.32327	−0.188445	−0.0942227	+	0.995551i	$0.530037\pi$
$312$	−7.60666	−0.430642
$313$	−0.629013	−0.0355539	−0.0177770	−	0.999842i	$-0.505659\pi$
$313$	−0.629013	−0.0355539	−0.0177770	+	0.999842i	$0.505659\pi$
$314$	24.4584	1.38027
$315$	54.9815	3.09786
$316$	71.8070	4.03946
$317$	−19.9329	−1.11954	−0.559771	−	0.828647i	$-0.689111\pi$
$317$	−19.9329	−1.11954	−0.559771	+	0.828647i	$0.689111\pi$
$318$	43.9883	2.46674
$319$	−7.35363	−0.411724
$320$	1.86521	0.104268
$321$	20.7635	1.15891
$322$	78.0222	4.34801
$323$	−50.7763	−2.82527
$324$	−8.09119	−0.449511
$325$	1.97295	0.109440
$326$	64.8854	3.59367
$327$	−2.94241	−0.162716
$328$	−22.8244	−1.26027
$329$	−1.45724	−0.0803405
$330$	−35.7664	−1.96888
$331$	−9.38618	−0.515911	−0.257956	−	0.966157i	$-0.583049\pi$
$331$	−9.38618	−0.515911	−0.257956	+	0.966157i	$0.583049\pi$
$332$	−39.5074	−2.16825
$333$	8.72524	0.478140
$334$	54.3652	2.97473
$335$	29.3236	1.60212
$336$	−75.2721	−4.10643
$337$	7.66911	0.417763	0.208881	−	0.977941i	$-0.433018\pi$
$337$	7.66911	0.417763	0.208881	+	0.977941i	$0.433018\pi$
$338$	32.5572	1.77088
$339$	−40.0007	−2.17254
$340$	85.6769	4.64648
$341$	1.76390	0.0955207
$342$	−94.6495	−5.11806
$343$	−4.95544	−0.267569
$344$	−4.47500	−0.241276
$345$	−66.5097	−3.58076
$346$	−23.6318	−1.27046
$347$	−16.2129	−0.870352	−0.435176	−	0.900346i	$-0.643314\pi$
$347$	−16.2129	−0.870352	−0.435176	+	0.900346i	$0.643314\pi$
$348$	54.3813	2.91515
$349$	17.3681	0.929692	0.464846	−	0.885392i	$-0.346110\pi$
$349$	17.3681	0.929692	0.464846	+	0.885392i	$0.346110\pi$
$350$	44.4233	2.37452
$351$	1.90868	0.101878
$352$	8.75163	0.466464
$353$	15.2509	0.811723	0.405861	−	0.913935i	$-0.366972\pi$
$353$	15.2509	0.811723	0.405861	+	0.913935i	$0.366972\pi$
$354$	62.8622	3.34109
$355$	20.6058	1.09364
$356$	9.13570	0.484191
$357$	67.0520	3.54877
$358$	38.3746	2.02816
$359$	30.7007	1.62032	0.810161	−	0.586207i	$-0.199379\pi$
$359$	30.7007	1.62032	0.810161	+	0.586207i	$0.199379\pi$
$360$	88.1561	4.64623
$361$	47.2979	2.48936
$362$	44.6449	2.34648
$363$	−22.6762	−1.19019
$364$	−7.69650	−0.403406
$365$	−2.77652	−0.145330
$366$	−25.8190	−1.34958
$367$	14.5564	0.759836	0.379918	−	0.925020i	$-0.375952\pi$
$367$	14.5564	0.759836	0.379918	+	0.925020i	$0.375952\pi$
$368$	54.9794	2.86600
$369$	16.6564	0.867097
$370$	14.9325	0.776306
$371$	24.5678	1.27550
$372$	−13.0444	−0.676318
$373$	−2.75664	−0.142733	−0.0713667	−	0.997450i	$-0.522736\pi$
$373$	−2.75664	−0.142733	−0.0713667	+	0.997450i	$0.522736\pi$
$374$	−26.3371	−1.36186
$375$	4.47514	0.231095
$376$	−2.33651	−0.120496
$377$	1.95325	0.100598
$378$	42.9760	2.21045
$379$	12.9165	0.663477	0.331739	−	0.943371i	$-0.392365\pi$
$379$	12.9165	0.663477	0.331739	+	0.943371i	$0.392365\pi$
$380$	−111.867	−5.73867
$381$	5.75835	0.295009
$382$	−36.3723	−1.86097
$383$	14.0783	0.719369	0.359684	−	0.933074i	$-0.382884\pi$
$383$	14.0783	0.719369	0.359684	+	0.933074i	$0.382884\pi$
$384$	33.2353	1.69603
$385$	−19.9759	−1.01807
$386$	−12.8894	−0.656051
$387$	3.26569	0.166004
$388$	12.6514	0.642277
$389$	−30.4913	−1.54597	−0.772984	−	0.634425i	$-0.781237\pi$
$389$	−30.4913	−1.54597	−0.772984	+	0.634425i	$0.781237\pi$
$390$	9.50018	0.481060
$391$	−48.9754	−2.47679
$392$	−51.8013	−2.61636
$393$	−53.9169	−2.71975
$394$	32.9948	1.66226
$395$	−49.5035	−2.49079
$396$	−33.9043	−1.70375
$397$	−34.2981	−1.72137	−0.860685	−	0.509138i	$-0.829964\pi$
$397$	−34.2981	−1.72137	−0.860685	+	0.509138i	$0.829964\pi$
$398$	−31.3448	−1.57117
$399$	−87.5489	−4.38293
$400$	31.3035	1.56518
$401$	−34.8748	−1.74156	−0.870782	−	0.491670i	$-0.836387\pi$
$401$	−34.8748	−1.74156	−0.870782	+	0.491670i	$0.836387\pi$
$402$	66.6607	3.32473
$403$	−0.468523	−0.0233388
$404$	13.6761	0.680412
$405$	5.57804	0.277175
$406$	43.9796	2.18267
$407$	−3.17006	−0.157134
$408$	107.510	5.32252
$409$	35.9588	1.77805	0.889025	−	0.457858i	$-0.151383\pi$
$409$	35.9588	1.77805	0.889025	+	0.457858i	$0.151383\pi$
$410$	28.5061	1.40781
$411$	−15.9022	−0.784398
$412$	63.7700	3.14172
$413$	35.1091	1.72761
$414$	−91.2926	−4.48679
$415$	27.2362	1.33697
$416$	−2.32458	−0.113972
$417$	7.54296	0.369380
$418$	34.3881	1.68198
$419$	−33.8275	−1.65258	−0.826290	−	0.563246i	$-0.809553\pi$
$419$	−33.8275	−1.65258	−0.826290	+	0.563246i	$0.809553\pi$
$420$	147.725	7.20824
$421$	−32.7752	−1.59736	−0.798682	−	0.601753i	$-0.794469\pi$
$421$	−32.7752	−1.59736	−0.798682	+	0.601753i	$0.794469\pi$
$422$	9.15863	0.445835
$423$	1.70510	0.0829048
$424$	39.3915	1.91302
$425$	−27.8850	−1.35262
$426$	46.8428	2.26954
$427$	−14.4201	−0.697840
$428$	33.6850	1.62823
$429$	−2.01681	−0.0973725
$430$	5.58896	0.269524
$431$	34.2424	1.64940	0.824699	−	0.565573i	$-0.191345\pi$
$431$	34.2424	1.64940	0.824699	+	0.565573i	$0.191345\pi$
$432$	30.2836	1.45702
$433$	−11.4269	−0.549144	−0.274572	−	0.961567i	$-0.588536\pi$
$433$	−11.4269	−0.549144	−0.274572	+	0.961567i	$0.588536\pi$
$434$	−10.5493	−0.506383
$435$	−37.4903	−1.79752
$436$	−4.77352	−0.228610
$437$	63.9466	3.05898
$438$	−6.31180	−0.301590
$439$	−38.8213	−1.85284	−0.926419	−	0.376494i	$-0.877130\pi$
$439$	−38.8213	−1.85284	−0.926419	+	0.376494i	$0.877130\pi$
$440$	−32.0289	−1.52692
$441$	37.8027	1.80013
$442$	6.99560	0.332747
$443$	7.82989	0.372009	0.186005	−	0.982549i	$-0.440446\pi$
$443$	7.82989	0.372009	0.186005	+	0.982549i	$0.440446\pi$
$444$	23.4431	1.11256
$445$	−6.29812	−0.298560
$446$	22.0275	1.04303
$447$	10.5945	0.501104
$448$	2.36815	0.111885
$449$	1.71701	0.0810309	0.0405154	−	0.999179i	$-0.487100\pi$
$449$	1.71701	0.0810309	0.0405154	+	0.999179i	$0.487100\pi$
$450$	−51.9790	−2.45032
$451$	−6.05160	−0.284959
$452$	−64.8937	−3.05234
$453$	51.3780	2.41395
$454$	21.8311	1.02459
$455$	5.30594	0.248746
$456$	−140.374	−6.57361
$457$	−30.5899	−1.43094	−0.715468	−	0.698645i	$-0.753787\pi$
$457$	−30.5899	−1.43094	−0.715468	+	0.698645i	$0.753787\pi$
$458$	32.3459	1.51142
$459$	−26.9765	−1.25916
$460$	−107.900	−5.03085
$461$	0.0298074	0.00138827	0.000694135	−	1.00000i	$-0.499779\pi$
$461$	0.0298074	0.00138827	0.000694135		1.00000i	$0.499779\pi$
$462$	−45.4108	−2.11270
$463$	−35.7331	−1.66066	−0.830329	−	0.557273i	$-0.811848\pi$
$463$	−35.7331	−1.66066	−0.830329	+	0.557273i	$0.811848\pi$
$464$	30.9909	1.43872
$465$	8.99273	0.417028
$466$	50.9860	2.36188
$467$	8.56575	0.396376	0.198188	−	0.980164i	$-0.436494\pi$
$467$	8.56575	0.396376	0.198188	+	0.980164i	$0.436494\pi$
$468$	9.00556	0.416282
$469$	37.2306	1.71915
$470$	2.91814	0.134604
$471$	−26.4715	−1.21974
$472$	56.2932	2.59110
$473$	−1.18649	−0.0545549
$474$	−112.535	−5.16891
$475$	36.4091	1.67056
$476$	108.779	4.98590
$477$	−28.7465	−1.31621
$478$	37.1976	1.70138
$479$	23.1227	1.05650	0.528251	−	0.849088i	$-0.322848\pi$
$479$	23.1227	1.05650	0.528251	+	0.849088i	$0.322848\pi$
$480$	44.6176	2.03650
$481$	0.842021	0.0383929
$482$	39.8686	1.81596
$483$	−84.4439	−3.84233
$484$	−36.7879	−1.67218
$485$	−8.72182	−0.396038
$486$	45.6758	2.07190
$487$	−3.89507	−0.176502	−0.0882511	−	0.996098i	$-0.528128\pi$
$487$	−3.89507	−0.176502	−0.0882511	+	0.996098i	$0.528128\pi$
$488$	−23.1209	−1.04664
$489$	−70.2259	−3.17572
$490$	64.6962	2.92268
$491$	9.33609	0.421332	0.210666	−	0.977558i	$-0.432437\pi$
$491$	9.33609	0.421332	0.210666	+	0.977558i	$0.432437\pi$
$492$	44.7526	2.01760
$493$	−27.6065	−1.24334
$494$	−9.13406	−0.410961
$495$	23.3735	1.05056
$496$	−7.43373	−0.333784
$497$	26.1621	1.17353
$498$	61.9155	2.77450
$499$	−2.20194	−0.0985723	−0.0492862	−	0.998785i	$-0.515695\pi$
$499$	−2.20194	−0.0985723	−0.0492862	+	0.998785i	$0.515695\pi$
$500$	7.26008	0.324681
$501$	−58.8398	−2.62877
$502$	−73.1438	−3.26457
$503$	17.2466	0.768988	0.384494	−	0.923128i	$-0.374376\pi$
$503$	17.2466	0.768988	0.384494	+	0.923128i	$0.374376\pi$
$504$	111.927	4.98563
$505$	−9.42826	−0.419552
$506$	33.1684	1.47452
$507$	−35.2369	−1.56492
$508$	9.34185	0.414478
$509$	31.3902	1.39135	0.695674	−	0.718358i	$-0.255106\pi$
$509$	31.3902	1.39135	0.695674	+	0.718358i	$0.255106\pi$
$510$	−134.272	−5.94566
$511$	−3.52520	−0.155946
$512$	50.8363	2.24667
$513$	35.2229	1.55513
$514$	−23.6749	−1.04426
$515$	−43.9628	−1.93723
$516$	8.77429	0.386267
$517$	−0.619497	−0.0272455
$518$	18.9590	0.833013
$519$	25.5769	1.12270
$520$	8.50742	0.373075
$521$	19.4535	0.852272	0.426136	−	0.904659i	$-0.359874\pi$
$521$	19.4535	0.852272	0.426136	+	0.904659i	$0.359874\pi$
$522$	−51.4600	−2.25234
$523$	19.0828	0.834433	0.417217	−	0.908807i	$-0.363006\pi$
$523$	19.0828	0.834433	0.417217	+	0.908807i	$0.363006\pi$
$524$	−87.4701	−3.82115
$525$	−48.0796	−2.09837
$526$	41.3700	1.80382
$527$	6.62193	0.288456
$528$	−31.9993	−1.39259
$529$	38.6786	1.68168
$530$	−49.1973	−2.13699
$531$	−41.0807	−1.78275
$532$	−142.032	−6.15786
$533$	1.60741	0.0696246
$534$	−14.3174	−0.619574
$535$	−23.2223	−1.00399
$536$	59.6947	2.57842
$537$	−41.5331	−1.79228
$538$	4.89252	0.210932
$539$	−13.7345	−0.591586
$540$	−59.4330	−2.55759
$541$	30.4314	1.30835	0.654174	−	0.756344i	$-0.273016\pi$
$541$	30.4314	1.30835	0.654174	+	0.756344i	$0.273016\pi$
$542$	57.9700	2.49003
$543$	−48.3195	−2.07359
$544$	32.8548	1.40864
$545$	3.29085	0.140964
$546$	12.0619	0.516201
$547$	0.908719	0.0388540	0.0194270	−	0.999811i	$-0.493816\pi$
$547$	0.908719	0.0388540	0.0194270	+	0.999811i	$0.493816\pi$
$548$	−25.7984	−1.10205
$549$	16.8728	0.720114
$550$	18.8850	0.805261
$551$	36.0455	1.53559
$552$	−135.395	−5.76281
$553$	−62.8519	−2.67274
$554$	−12.2325	−0.519707
$555$	−16.1616	−0.686021
$556$	12.2370	0.518966
$557$	31.4382	1.33208	0.666039	−	0.745917i	$-0.267989\pi$
$557$	31.4382	1.33208	0.666039	+	0.745917i	$0.267989\pi$
$558$	12.3436	0.522546
$559$	0.315152	0.0133295
$560$	84.1856	3.55749
$561$	28.5048	1.20348
$562$	−11.6803	−0.492704
$563$	−38.0565	−1.60389	−0.801946	−	0.597397i	$-0.796202\pi$
$563$	−38.0565	−1.60389	−0.801946	+	0.597397i	$0.796202\pi$
$564$	4.58129	0.192907
$565$	44.7375	1.88212
$566$	−63.4314	−2.66622
$567$	7.08214	0.297422
$568$	41.9478	1.76009
$569$	−43.9669	−1.84319	−0.921594	−	0.388156i	$-0.873112\pi$
$569$	−43.9669	−1.84319	−0.921594	+	0.388156i	$0.873112\pi$
$570$	175.317	7.34323
$571$	10.2268	0.427977	0.213989	−	0.976836i	$-0.431354\pi$
$571$	10.2268	0.427977	0.213989	+	0.976836i	$0.431354\pi$
$572$	−3.27190	−0.136805
$573$	39.3660	1.64454
$574$	36.1926	1.51065
$575$	35.1178	1.46451
$576$	−2.77094	−0.115456
$577$	−15.9978	−0.665998	−0.332999	−	0.942927i	$-0.608061\pi$
$577$	−15.9978	−0.665998	−0.332999	+	0.942927i	$0.608061\pi$
$578$	−55.6511	−2.31478
$579$	13.9502	0.579752
$580$	−60.8210	−2.52546
$581$	34.5804	1.43464
$582$	−19.8271	−0.821861
$583$	10.4442	0.432554
$584$	−5.65223	−0.233891
$585$	−6.20840	−0.256686
$586$	61.0003	2.51990
$587$	−6.27706	−0.259082	−0.129541	−	0.991574i	$-0.541350\pi$
$587$	−6.27706	−0.259082	−0.129541	+	0.991574i	$0.541350\pi$
$588$	101.569	4.18862
$589$	−8.64616	−0.356259
$590$	−70.3062	−2.89446
$591$	−35.7105	−1.46893
$592$	13.3598	0.549083
$593$	19.8163	0.813759	0.406880	−	0.913482i	$-0.366617\pi$
$593$	19.8163	0.813759	0.406880	+	0.913482i	$0.366617\pi$
$594$	18.2698	0.749617
$595$	−74.9921	−3.07438
$596$	17.1877	0.704034
$597$	33.9246	1.38844
$598$	−8.81011	−0.360272
$599$	2.72172	0.111207	0.0556033	−	0.998453i	$-0.482292\pi$
$599$	2.72172	0.111207	0.0556033	+	0.998453i	$0.482292\pi$
$600$	−77.0897	−3.14718
$601$	−24.3253	−0.992252	−0.496126	−	0.868251i	$-0.665245\pi$
$601$	−24.3253	−0.992252	−0.496126	+	0.868251i	$0.665245\pi$
$602$	7.09600	0.289212
$603$	−43.5630	−1.77402
$604$	83.3512	3.39151
$605$	25.3614	1.03109
$606$	−21.4331	−0.870659
$607$	−17.4586	−0.708622	−0.354311	−	0.935128i	$-0.615285\pi$
$607$	−17.4586	−0.708622	−0.354311	+	0.935128i	$0.615285\pi$
$608$	−42.8981	−1.73975
$609$	−47.5994	−1.92883
$610$	28.8764	1.16917
$611$	0.164549	0.00665695
$612$	−127.281	−5.14504
$613$	10.0867	0.407399	0.203700	−	0.979033i	$-0.434703\pi$
$613$	10.0867	0.407399	0.203700	+	0.979033i	$0.434703\pi$
$614$	−5.82827	−0.235210
$615$	−30.8523	−1.24408
$616$	−40.6654	−1.63845
$617$	−9.50185	−0.382530	−0.191265	−	0.981538i	$-0.561259\pi$
$617$	−9.50185	−0.382530	−0.191265	+	0.981538i	$0.561259\pi$
$618$	−99.9397	−4.02016
$619$	−39.7078	−1.59599	−0.797996	−	0.602663i	$-0.794106\pi$
$619$	−39.7078	−1.59599	−0.797996	+	0.602663i	$0.794106\pi$
$620$	14.5890	0.585910
$621$	33.9737	1.36332
$622$	8.44934	0.338787
$623$	−7.99639	−0.320369
$624$	8.49957	0.340255
$625$	−27.3629	−1.09452
$626$	1.59925	0.0639189
$627$	−37.2184	−1.48636
$628$	−42.9451	−1.71370
$629$	−11.9008	−0.474516
$630$	−139.789	−5.56933
$631$	−13.2697	−0.528260	−0.264130	−	0.964487i	$-0.585085\pi$
$631$	−13.2697	−0.528260	−0.264130	+	0.964487i	$0.585085\pi$
$632$	−100.775	−4.00863
$633$	−9.91244	−0.393984
$634$	50.6789	2.01272
$635$	−6.44024	−0.255573
$636$	−77.2364	−3.06262
$637$	3.64811	0.144544
$638$	18.6964	0.740199
$639$	−30.6119	−1.21099
$640$	−37.1709	−1.46931
$641$	8.98395	0.354845	0.177422	−	0.984135i	$-0.443224\pi$
$641$	8.98395	0.354845	0.177422	+	0.984135i	$0.443224\pi$
$642$	−52.7908	−2.08349
$643$	−21.9173	−0.864333	−0.432166	−	0.901794i	$-0.642251\pi$
$643$	−21.9173	−0.864333	−0.432166	+	0.901794i	$0.642251\pi$
$644$	−136.995	−5.39834
$645$	−6.04896	−0.238178
$646$	129.097	5.07927
$647$	−15.7615	−0.619650	−0.309825	−	0.950794i	$-0.600271\pi$
$647$	−15.7615	−0.619650	−0.309825	+	0.950794i	$0.600271\pi$
$648$	11.3553	0.446080
$649$	14.9254	0.585874
$650$	−5.01619	−0.196751
$651$	11.4176	0.447491
$652$	−113.928	−4.46178
$653$	9.64920	0.377602	0.188801	−	0.982015i	$-0.439540\pi$
$653$	9.64920	0.377602	0.188801	+	0.982015i	$0.439540\pi$
$654$	7.48101	0.292531
$655$	60.3016	2.35618
$656$	25.5037	0.995750
$657$	4.12478	0.160923
$658$	3.70501	0.144436
$659$	42.2003	1.64389	0.821945	−	0.569566i	$-0.192889\pi$
$659$	42.2003	1.64389	0.821945	+	0.569566i	$0.192889\pi$
$660$	62.8002	2.44449
$661$	−4.75840	−0.185080	−0.0925402	−	0.995709i	$-0.529499\pi$
$661$	−4.75840	−0.185080	−0.0925402	+	0.995709i	$0.529499\pi$
$662$	23.8641	0.927506
$663$	−7.57138	−0.294048
$664$	55.4454	2.15170
$665$	97.9163	3.79703
$666$	−22.1837	−0.859601
$667$	34.7671	1.34619
$668$	−95.4567	−3.69333
$669$	−23.8405	−0.921726
$670$	−74.5545	−2.88029
$671$	−6.13023	−0.236655
$672$	56.6486	2.18527
$673$	−15.7392	−0.606701	−0.303351	−	0.952879i	$-0.598105\pi$
$673$	−15.7392	−0.606701	−0.303351	+	0.952879i	$0.598105\pi$
$674$	−19.4985	−0.751055
$675$	19.3435	0.744532
$676$	−57.1653	−2.19867
$677$	25.0571	0.963022	0.481511	−	0.876440i	$-0.340088\pi$
$677$	25.0571	0.963022	0.481511	+	0.876440i	$0.340088\pi$
$678$	101.701	3.90580
$679$	−11.0736	−0.424967
$680$	−120.241	−4.61102
$681$	−23.6280	−0.905426
$682$	−4.48468	−0.171727
$683$	−24.6790	−0.944314	−0.472157	−	0.881514i	$-0.656525\pi$
$683$	−24.6790	−0.944314	−0.472157	+	0.881514i	$0.656525\pi$
$684$	166.189	6.35441
$685$	17.7853	0.679541
$686$	12.5991	0.481036
$687$	−35.0082	−1.33564
$688$	5.00030	0.190635
$689$	−2.77415	−0.105687
$690$	169.099	6.43750
$691$	19.2423	0.732010	0.366005	−	0.930613i	$-0.380725\pi$
$691$	19.2423	0.732010	0.366005	+	0.930613i	$0.380725\pi$
$692$	41.4937	1.57736
$693$	29.6761	1.12730
$694$	41.2208	1.56472
$695$	−8.43618	−0.320002
$696$	−76.3199	−2.89290
$697$	−22.7185	−0.860525
$698$	−44.1579	−1.67140
$699$	−55.1825	−2.08719
$700$	−78.0002	−2.94813
$701$	−31.4480	−1.18777	−0.593887	−	0.804548i	$-0.702407\pi$
$701$	−31.4480	−1.18777	−0.593887	+	0.804548i	$0.702407\pi$
$702$	−4.85276	−0.183156
$703$	15.5387	0.586055
$704$	1.00674	0.0379429
$705$	−3.15832	−0.118949
$706$	−38.7750	−1.45932
$707$	−11.9706	−0.450199
$708$	−110.376	−4.14818
$709$	−1.82761	−0.0686373	−0.0343187	−	0.999411i	$-0.510926\pi$
$709$	−1.82761	−0.0686373	−0.0343187	+	0.999411i	$0.510926\pi$
$710$	−52.3898	−1.96616
$711$	73.5421	2.75805
$712$	−12.8212	−0.480496
$713$	−8.33952	−0.312317
$714$	−170.478	−6.37998
$715$	2.25564	0.0843560
$716$	−67.3797	−2.51810
$717$	−40.2592	−1.50351
$718$	−78.0559	−2.91302
$719$	31.7708	1.18485	0.592425	−	0.805626i	$-0.298171\pi$
$719$	31.7708	1.18485	0.592425	+	0.805626i	$0.298171\pi$
$720$	−98.5044	−3.67104
$721$	−55.8172	−2.07874
$722$	−120.254	−4.47538
$723$	−43.1500	−1.60477
$724$	−78.3894	−2.91332
$725$	19.7952	0.735177
$726$	57.6536	2.13973
$727$	40.9351	1.51820	0.759100	−	0.650974i	$-0.225639\pi$
$727$	40.9351	1.51820	0.759100	+	0.650974i	$0.225639\pi$
$728$	10.8014	0.400327
$729$	−43.9978	−1.62955
$730$	7.05923	0.261274
$731$	−4.45424	−0.164746
$732$	45.3340	1.67559
$733$	49.4597	1.82684	0.913418	−	0.407022i	$-0.133433\pi$
$733$	49.4597	1.82684	0.913418	+	0.407022i	$0.133433\pi$
$734$	−37.0092	−1.36604
$735$	−70.0211	−2.58277
$736$	−41.3767	−1.52516
$737$	15.8273	0.583007
$738$	−42.3485	−1.55887
$739$	53.2218	1.95780	0.978898	−	0.204349i	$-0.0655077\pi$
$739$	53.2218	1.95780	0.978898	+	0.204349i	$0.0655077\pi$
$740$	−26.2192	−0.963835
$741$	9.88585	0.363166
$742$	−62.4632	−2.29309
$743$	−39.9969	−1.46734	−0.733672	−	0.679504i	$-0.762195\pi$
$743$	−39.9969	−1.46734	−0.733672	+	0.679504i	$0.762195\pi$
$744$	18.3067	0.671157
$745$	−11.8491	−0.434118
$746$	7.00869	0.256606
$747$	−40.4620	−1.48043
$748$	46.2438	1.69084
$749$	−29.4841	−1.07733
$750$	−11.3779	−0.415463
$751$	11.0336	0.402622	0.201311	−	0.979527i	$-0.435480\pi$
$751$	11.0336	0.402622	0.201311	+	0.979527i	$0.435480\pi$
$752$	2.61079	0.0952056
$753$	79.1640	2.88490
$754$	−4.96609	−0.180855
$755$	−57.4620	−2.09126
$756$	−75.4590	−2.74442
$757$	42.7189	1.55264	0.776322	−	0.630336i	$-0.217083\pi$
$757$	42.7189	1.55264	0.776322	+	0.630336i	$0.217083\pi$
$758$	−32.8399	−1.19280
$759$	−35.8984	−1.30303
$760$	156.997	5.69487
$761$	−32.0455	−1.16165	−0.580823	−	0.814030i	$-0.697269\pi$
$761$	−32.0455	−1.16165	−0.580823	+	0.814030i	$0.697269\pi$
$762$	−14.6405	−0.530368
$763$	4.17821	0.151261
$764$	63.8640	2.31052
$765$	87.7472	3.17251
$766$	−35.7938	−1.29328
$767$	−3.96445	−0.143148
$768$	−81.1644	−2.92877
$769$	8.19338	0.295461	0.147730	−	0.989028i	$-0.452803\pi$
$769$	8.19338	0.295461	0.147730	+	0.989028i	$0.452803\pi$
$770$	50.7882	1.83028
$771$	25.6235	0.922808
$772$	22.6317	0.814531
$773$	−26.6125	−0.957185	−0.478593	−	0.878037i	$-0.658853\pi$
$773$	−26.6125	−0.957185	−0.478593	+	0.878037i	$0.658853\pi$
$774$	−8.30293	−0.298443
$775$	−4.74825	−0.170562
$776$	−17.7552	−0.637375
$777$	−20.5195	−0.736133
$778$	77.5233	2.77934
$779$	29.6633	1.06280
$780$	−16.6808	−0.597269
$781$	11.1219	0.397974
$782$	124.519	4.45278
$783$	19.1503	0.684377
$784$	57.8821	2.06722
$785$	29.6062	1.05669
$786$	137.082	4.88956
$787$	−48.5399	−1.73026	−0.865131	−	0.501546i	$-0.832765\pi$
$787$	−48.5399	−1.73026	−0.865131	+	0.501546i	$0.832765\pi$
$788$	−57.9337	−2.06380
$789$	−44.7750	−1.59403
$790$	125.861	4.47795
$791$	56.8008	2.01960
$792$	47.5820	1.69075
$793$	1.62829	0.0578224
$794$	87.2020	3.09468
$795$	53.2465	1.88846
$796$	55.0364	1.95071
$797$	−1.25473	−0.0444447	−0.0222223	−	0.999753i	$-0.507074\pi$
$797$	−1.25473	−0.0444447	−0.0222223	+	0.999753i	$0.507074\pi$
$798$	222.591	7.87964
$799$	−2.32568	−0.0822765
$800$	−23.5585	−0.832919
$801$	9.35646	0.330594
$802$	88.6683	3.13099
$803$	−1.49862	−0.0528851
$804$	−117.046	−4.12788
$805$	94.4435	3.32870
$806$	1.19121	0.0419585
$807$	−5.29520	−0.186400
$808$	−19.1933	−0.675219
$809$	5.87648	0.206606	0.103303	−	0.994650i	$-0.467059\pi$
$809$	5.87648	0.206606	0.103303	+	0.994650i	$0.467059\pi$
$810$	−14.1820	−0.498306
$811$	22.6358	0.794852	0.397426	−	0.917634i	$-0.369904\pi$
$811$	22.6358	0.794852	0.397426	+	0.917634i	$0.369904\pi$
$812$	−77.2213	−2.70994
$813$	−62.7413	−2.20043
$814$	8.05979	0.282495
$815$	78.5419	2.75120
$816$	−120.130	−4.20538
$817$	5.81585	0.203471
$818$	−91.4245	−3.19658
$819$	−7.88248	−0.275436
$820$	−50.0521	−1.74790
$821$	−29.1499	−1.01734	−0.508669	−	0.860962i	$-0.669862\pi$
$821$	−29.1499	−1.01734	−0.508669	+	0.860962i	$0.669862\pi$
$822$	40.4310	1.41019
$823$	27.7253	0.966443	0.483221	−	0.875498i	$-0.339467\pi$
$823$	27.7253	0.966443	0.483221	+	0.875498i	$0.339467\pi$
$824$	−89.4961	−3.11774
$825$	−20.4394	−0.711608
$826$	−89.2640	−3.10589
$827$	13.0389	0.453407	0.226704	−	0.973964i	$-0.427205\pi$
$827$	13.0389	0.453407	0.226704	+	0.973964i	$0.427205\pi$
$828$	160.295	5.57065
$829$	−51.7530	−1.79746	−0.898728	−	0.438507i	$-0.855507\pi$
$829$	−51.7530	−1.79746	−0.898728	+	0.438507i	$0.855507\pi$
$830$	−69.2474	−2.40361
$831$	13.2393	0.459265
$832$	−0.267407	−0.00927068
$833$	−51.5611	−1.78648
$834$	−19.1778	−0.664072
$835$	65.8075	2.27736
$836$	−60.3800	−2.08829
$837$	−4.59355	−0.158776
$838$	86.0055	2.97101
$839$	−4.02174	−0.138846	−0.0694230	−	0.997587i	$-0.522116\pi$
$839$	−4.02174	−0.138846	−0.0694230	+	0.997587i	$0.522116\pi$
$840$	−207.320	−7.15323
$841$	−9.40244	−0.324222
$842$	83.3301	2.87174
$843$	12.6417	0.435402
$844$	−16.0811	−0.553534
$845$	39.4096	1.35573
$846$	−4.33518	−0.149046
$847$	32.2001	1.10641
$848$	−44.0156	−1.51150
$849$	68.6522	2.35614
$850$	70.8969	2.43174
$851$	14.9876	0.513770
$852$	−82.2486	−2.81779
$853$	−41.0541	−1.40567	−0.702833	−	0.711355i	$-0.748082\pi$
$853$	−41.0541	−1.40567	−0.702833	+	0.711355i	$0.748082\pi$
$854$	36.6629	1.25458
$855$	−114.570	−3.91823
$856$	−47.2742	−1.61580
$857$	−32.2180	−1.10055	−0.550274	−	0.834984i	$-0.685477\pi$
$857$	−32.2180	−1.10055	−0.550274	+	0.834984i	$0.685477\pi$
$858$	5.12769	0.175057
$859$	−1.34066	−0.0457427	−0.0228714	−	0.999738i	$-0.507281\pi$
$859$	−1.34066	−0.0457427	−0.0228714	+	0.999738i	$0.507281\pi$
$860$	−9.81332	−0.334632
$861$	−39.1715	−1.33496
$862$	−87.0604	−2.96529
$863$	29.9649	1.02002	0.510008	−	0.860169i	$-0.329642\pi$
$863$	29.9649	1.02002	0.510008	+	0.860169i	$0.329642\pi$
$864$	−22.7910	−0.775365
$865$	−28.6056	−0.972621
$866$	29.0527	0.987251
$867$	60.2315	2.04557
$868$	18.5229	0.628709
$869$	−26.7193	−0.906391
$870$	95.3182	3.23159
$871$	−4.20401	−0.142447
$872$	6.69925	0.226865
$873$	12.9571	0.438531
$874$	−162.583	−5.49944
$875$	−6.35468	−0.214827
$876$	11.0825	0.374444
$877$	15.5880	0.526370	0.263185	−	0.964745i	$-0.415227\pi$
$877$	15.5880	0.526370	0.263185	+	0.964745i	$0.415227\pi$
$878$	98.7022	3.33104
$879$	−66.0210	−2.22683
$880$	35.7886	1.20643
$881$	48.7623	1.64284	0.821422	−	0.570322i	$-0.193181\pi$
$881$	48.7623	1.64284	0.821422	+	0.570322i	$0.193181\pi$
$882$	−96.1124	−3.23627
$883$	−27.9642	−0.941071	−0.470535	−	0.882381i	$-0.655939\pi$
$883$	−27.9642	−0.941071	−0.470535	+	0.882381i	$0.655939\pi$
$884$	−12.2832	−0.413127
$885$	76.0928	2.55783
$886$	−19.9073	−0.668799
$887$	−30.2703	−1.01638	−0.508188	−	0.861246i	$-0.669684\pi$
$887$	−30.2703	−1.01638	−0.508188	+	0.861246i	$0.669684\pi$
$888$	−32.9005	−1.10407
$889$	−8.17683	−0.274242
$890$	16.0128	0.536751
$891$	3.01073	0.100863
$892$	−38.6767	−1.29499
$893$	3.03661	0.101616
$894$	−26.9363	−0.900886
$895$	46.4513	1.55270
$896$	−47.1939	−1.57664
$897$	9.53524	0.318372
$898$	−4.36546	−0.145677
$899$	−4.70083	−0.156781
$900$	91.2669	3.04223
$901$	39.2088	1.30624
$902$	15.3861	0.512300
$903$	−7.68005	−0.255576
$904$	91.0732	3.02905
$905$	54.0413	1.79640
$906$	−130.627	−4.33980
$907$	32.9004	1.09244	0.546220	−	0.837642i	$-0.316066\pi$
$907$	32.9004	1.09244	0.546220	+	0.837642i	$0.316066\pi$
$908$	−38.3320	−1.27209
$909$	14.0066	0.464569
$910$	−13.4902	−0.447196
$911$	−27.6539	−0.916214	−0.458107	−	0.888897i	$-0.651472\pi$
$911$	−27.6539	−0.916214	−0.458107	+	0.888897i	$0.651472\pi$
$912$	156.852	5.19389
$913$	14.7007	0.486521
$914$	77.7742	2.57254
$915$	−31.2531	−1.03320
$916$	−56.7943	−1.87654
$917$	76.5617	2.52829
$918$	68.5871	2.26371
$919$	−34.2549	−1.12997	−0.564983	−	0.825103i	$-0.691117\pi$
$919$	−34.2549	−1.12997	−0.564983	+	0.825103i	$0.691117\pi$
$920$	151.429	4.99246
$921$	6.30797	0.207855
$922$	−0.0757846	−0.00249583
$923$	−2.95418	−0.0972379
$924$	79.7341	2.62306
$925$	8.53347	0.280579
$926$	90.8505	2.98553
$927$	65.3109	2.14509
$928$	−23.3232	−0.765623
$929$	−28.8870	−0.947751	−0.473876	−	0.880592i	$-0.657145\pi$
$929$	−28.8870	−0.947751	−0.473876	+	0.880592i	$0.657145\pi$
$930$	−22.8638	−0.749733
$931$	67.3226	2.20641
$932$	−89.5234	−2.93243
$933$	−9.14477	−0.299386
$934$	−21.7782	−0.712605
$935$	−31.8803	−1.04260
$936$	−12.6386	−0.413105
$937$	−31.0161	−1.01325	−0.506626	−	0.862166i	$-0.669108\pi$
$937$	−31.0161	−1.01325	−0.506626	+	0.862166i	$0.669108\pi$
$938$	−94.6579	−3.09069
$939$	−1.73088	−0.0564851
$940$	−5.12379	−0.167120
$941$	−26.9816	−0.879574	−0.439787	−	0.898102i	$-0.644946\pi$
$941$	−26.9816	−0.879574	−0.439787	+	0.898102i	$0.644946\pi$
$942$	67.3032	2.19286
$943$	28.6112	0.931710
$944$	−62.9012	−2.04726
$945$	52.0212	1.69225
$946$	3.01662	0.0980789
$947$	6.65149	0.216145	0.108072	−	0.994143i	$-0.465532\pi$
$947$	6.65149	0.216145	0.108072	+	0.994143i	$0.465532\pi$
$948$	197.594	6.41755
$949$	0.398059	0.0129215
$950$	−92.5692	−3.00334
$951$	−54.8501	−1.77864
$952$	−152.663	−4.94784
$953$	43.3367	1.40381	0.701907	−	0.712268i	$-0.252332\pi$
$953$	43.3367	1.40381	0.701907	+	0.712268i	$0.252332\pi$
$954$	73.0872	2.36629
$955$	−44.0276	−1.42470
$956$	−65.3131	−2.11238
$957$	−20.2353	−0.654113
$958$	−58.7889	−1.89938
$959$	22.5811	0.729180
$960$	5.13256	0.165653
$961$	−29.8724	−0.963626
$962$	−2.14082	−0.0690228
$963$	34.4990	1.11171
$964$	−70.0029	−2.25464
$965$	−15.6022	−0.502252
$966$	214.697	6.90775
$967$	−40.2547	−1.29450	−0.647251	−	0.762277i	$-0.724082\pi$
$967$	−40.2547	−1.29450	−0.647251	+	0.762277i	$0.724082\pi$
$968$	51.6289	1.65942
$969$	−139.723	−4.48855
$970$	22.1750	0.711997
$971$	14.7481	0.473288	0.236644	−	0.971596i	$-0.423953\pi$
$971$	14.7481	0.473288	0.236644	+	0.971596i	$0.423953\pi$
$972$	−80.1995	−2.57240
$973$	−10.7110	−0.343378
$974$	9.90311	0.317316
$975$	5.42905	0.173869
$976$	25.8350	0.826958
$977$	41.6282	1.33180	0.665902	−	0.746039i	$-0.268047\pi$
$977$	41.6282	1.33180	0.665902	+	0.746039i	$0.268047\pi$
$978$	178.548	5.70932
$979$	−3.39939	−0.108645
$980$	−113.596	−3.62870
$981$	−4.88887	−0.156089
$982$	−23.7368	−0.757471
$983$	2.57232	0.0820444	0.0410222	−	0.999158i	$-0.486939\pi$
$983$	2.57232	0.0820444	0.0410222	+	0.999158i	$0.486939\pi$
$984$	−62.8067	−2.00220
$985$	39.9393	1.27257
$986$	70.1889	2.23527
$987$	−4.00995	−0.127638
$988$	16.0380	0.510236
$989$	5.60958	0.178374
$990$	−59.4265	−1.88870
$991$	23.7961	0.755907	0.377953	−	0.925825i	$-0.376628\pi$
$991$	23.7961	0.755907	0.377953	+	0.925825i	$0.376628\pi$
$992$	5.59450	0.177626
$993$	−25.8283	−0.819636
$994$	−66.5166	−2.10978
$995$	−37.9419	−1.20284
$996$	−108.714	−3.44473
$997$	7.59339	0.240485	0.120242	−	0.992745i	$-0.461633\pi$
$997$	7.59339	0.240485	0.120242	+	0.992745i	$0.461633\pi$
$998$	5.59838	0.177213
$999$	8.25545	0.261191

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5077.2.a.b.1.16	✓	205

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5077.2.a.b.1.16	✓	205	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:	\( N \)	\(=\)	\( 5077 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5077.a (trivial)

\(f(q)\)	\(=\)	\(q-2.54248 q^{2} +2.75174 q^{3} +4.46418 q^{4} -3.07759 q^{5} -6.99622 q^{6} -3.90745 q^{7} -6.26513 q^{8} +4.57206 q^{9} +O(q^{10})\)	\(q-2.54248 q^{2} +2.75174 q^{3} +4.46418 q^{4} -3.07759 q^{5} -6.99622 q^{6} -3.90745 q^{7} -6.26513 q^{8} +4.57206 q^{9} +7.82470 q^{10} -1.66112 q^{11} +12.2843 q^{12} +0.441222 q^{13} +9.93461 q^{14} -8.46872 q^{15} +7.00056 q^{16} -6.23607 q^{17} -11.6243 q^{18} +8.14235 q^{19} -13.7389 q^{20} -10.7523 q^{21} +4.22336 q^{22} +7.85357 q^{23} -17.2400 q^{24} +4.47157 q^{25} -1.12180 q^{26} +4.32589 q^{27} -17.4436 q^{28} +4.42691 q^{29} +21.5315 q^{30} -1.06188 q^{31} -5.26851 q^{32} -4.57097 q^{33} +15.8550 q^{34} +12.0255 q^{35} +20.4105 q^{36} +1.90838 q^{37} -20.7017 q^{38} +1.21413 q^{39} +19.2815 q^{40} +3.64309 q^{41} +27.3374 q^{42} +0.714271 q^{43} -7.41554 q^{44} -14.0709 q^{45} -19.9675 q^{46} +0.372940 q^{47} +19.2637 q^{48} +8.26820 q^{49} -11.3689 q^{50} -17.1600 q^{51} +1.96970 q^{52} -6.28743 q^{53} -10.9985 q^{54} +5.11225 q^{55} +24.4807 q^{56} +22.4056 q^{57} -11.2553 q^{58} -8.98516 q^{59} -37.8059 q^{60} +3.69042 q^{61} +2.69979 q^{62} -17.8651 q^{63} -0.606061 q^{64} -1.35790 q^{65} +11.6216 q^{66} -9.52810 q^{67} -27.8389 q^{68} +21.6110 q^{69} -30.5747 q^{70} -6.69544 q^{71} -28.6445 q^{72} +0.902173 q^{73} -4.85202 q^{74} +12.3046 q^{75} +36.3490 q^{76} +6.49075 q^{77} -3.08689 q^{78} +16.0851 q^{79} -21.5449 q^{80} -1.81247 q^{81} -9.26246 q^{82} -8.84985 q^{83} -48.0002 q^{84} +19.1921 q^{85} -1.81602 q^{86} +12.1817 q^{87} +10.4071 q^{88} +2.04644 q^{89} +35.7750 q^{90} -1.72406 q^{91} +35.0598 q^{92} -2.92200 q^{93} -0.948190 q^{94} -25.0588 q^{95} -14.4976 q^{96} +2.83398 q^{97} -21.0217 q^{98} -7.59473 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 205 q - 25 q^{2} - 59 q^{3} + 195 q^{4} - 44 q^{5} - 26 q^{6} - 30 q^{7} - 75 q^{8} + 186 q^{9}+O(q^{10}) \) 205 * q - 25 * q^2 - 59 * q^3 + 195 * q^4 - 44 * q^5 - 26 * q^6 - 30 * q^7 - 75 * q^8 + 186 * q^9	\( 205 q - 25 q^{2} - 59 q^{3} + 195 q^{4} - 44 q^{5} - 26 q^{6} - 30 q^{7} - 75 q^{8} + 186 q^{9} - 28 q^{10} - 83 q^{11} - 108 q^{12} - 36 q^{13} - 67 q^{14} - 63 q^{15} + 187 q^{16} - 72 q^{17} - 57 q^{18} - 47 q^{19} - 132 q^{20} - 35 q^{21} - 40 q^{22} - 97 q^{23} - 49 q^{24} + 175 q^{25} - 78 q^{26} - 227 q^{27} - 59 q^{28} - 46 q^{29} + 30 q^{30} - 77 q^{31} - 175 q^{32} - 74 q^{33} - 28 q^{34} - 171 q^{35} + 171 q^{36} - 52 q^{37} - 144 q^{38} - 54 q^{39} - 49 q^{40} - 107 q^{41} + 7 q^{42} - 58 q^{43} - 139 q^{44} - 89 q^{45} - 33 q^{46} - 255 q^{47} - 202 q^{48} + 171 q^{49} - 74 q^{50} - 63 q^{51} - 90 q^{52} - 82 q^{53} - 51 q^{54} - 70 q^{55} - 180 q^{56} - 70 q^{57} - 50 q^{58} - 289 q^{59} - 105 q^{60} - 20 q^{61} - 143 q^{62} - 119 q^{63} + 201 q^{64} - 92 q^{65} - 3 q^{66} - 138 q^{67} - 177 q^{68} - 67 q^{69} + 4 q^{70} - 141 q^{71} - 138 q^{72} - 71 q^{73} - 26 q^{74} - 251 q^{75} - 42 q^{76} - 149 q^{77} - 6 q^{78} - 47 q^{79} - 294 q^{80} + 193 q^{81} - 70 q^{82} - 329 q^{83} - 40 q^{84} - 45 q^{85} - 83 q^{86} - 139 q^{87} - 45 q^{88} - 163 q^{89} - 116 q^{90} - 141 q^{91} - 204 q^{92} - 91 q^{93} - 8 q^{94} - 173 q^{95} - 53 q^{96} - 147 q^{97} - 156 q^{98} - 157 q^{99}+O(q^{100}) \) 205 * q - 25 * q^2 - 59 * q^3 + 195 * q^4 - 44 * q^5 - 26 * q^6 - 30 * q^7 - 75 * q^8 + 186 * q^9 - 28 * q^10 - 83 * q^11 - 108 * q^12 - 36 * q^13 - 67 * q^14 - 63 * q^15 + 187 * q^16 - 72 * q^17 - 57 * q^18 - 47 * q^19 - 132 * q^20 - 35 * q^21 - 40 * q^22 - 97 * q^23 - 49 * q^24 + 175 * q^25 - 78 * q^26 - 227 * q^27 - 59 * q^28 - 46 * q^29 + 30 * q^30 - 77 * q^31 - 175 * q^32 - 74 * q^33 - 28 * q^34 - 171 * q^35 + 171 * q^36 - 52 * q^37 - 144 * q^38 - 54 * q^39 - 49 * q^40 - 107 * q^41 + 7 * q^42 - 58 * q^43 - 139 * q^44 - 89 * q^45 - 33 * q^46 - 255 * q^47 - 202 * q^48 + 171 * q^49 - 74 * q^50 - 63 * q^51 - 90 * q^52 - 82 * q^53 - 51 * q^54 - 70 * q^55 - 180 * q^56 - 70 * q^57 - 50 * q^58 - 289 * q^59 - 105 * q^60 - 20 * q^61 - 143 * q^62 - 119 * q^63 + 201 * q^64 - 92 * q^65 - 3 * q^66 - 138 * q^67 - 177 * q^68 - 67 * q^69 + 4 * q^70 - 141 * q^71 - 138 * q^72 - 71 * q^73 - 26 * q^74 - 251 * q^75 - 42 * q^76 - 149 * q^77 - 6 * q^78 - 47 * q^79 - 294 * q^80 + 193 * q^81 - 70 * q^82 - 329 * q^83 - 40 * q^84 - 45 * q^85 - 83 * q^86 - 139 * q^87 - 45 * q^88 - 163 * q^89 - 116 * q^90 - 141 * q^91 - 204 * q^92 - 91 * q^93 - 8 * q^94 - 173 * q^95 - 53 * q^96 - 147 * q^97 - 156 * q^98 - 157 * q^99

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