LMFDB - Embedded newform 6005.2.a.d.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6005,2,Mod(1,6005)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6005, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6005.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6005 = 5 \cdot 1201 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6005.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:	$47.9501664138$
Analytic rank:	$1$
Dimension:	$83$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	6005.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.55566 q^{2} -0.523024 q^{3} +0.420073 q^{4} -1.00000 q^{5} +0.813646 q^{6} +2.34977 q^{7} +2.45783 q^{8} -2.72645 q^{9} +O(q^{10})$	\(q-1.55566 q^{2} -0.523024 q^{3} +0.420073 q^{4} -1.00000 q^{5} +0.813646 q^{6} +2.34977 q^{7} +2.45783 q^{8} -2.72645 q^{9} +1.55566 q^{10} -1.32583 q^{11} -0.219708 q^{12} -6.82461 q^{13} -3.65544 q^{14} +0.523024 q^{15} -4.66368 q^{16} +3.25562 q^{17} +4.24142 q^{18} +2.86608 q^{19} -0.420073 q^{20} -1.22898 q^{21} +2.06254 q^{22} -2.71920 q^{23} -1.28550 q^{24} +1.00000 q^{25} +10.6168 q^{26} +2.99507 q^{27} +0.987074 q^{28} -2.99560 q^{29} -0.813646 q^{30} +7.08276 q^{31} +2.33945 q^{32} +0.693440 q^{33} -5.06463 q^{34} -2.34977 q^{35} -1.14531 q^{36} +6.14406 q^{37} -4.45865 q^{38} +3.56943 q^{39} -2.45783 q^{40} +6.04230 q^{41} +1.91188 q^{42} -4.85141 q^{43} -0.556945 q^{44} +2.72645 q^{45} +4.23015 q^{46} +5.15080 q^{47} +2.43922 q^{48} -1.47859 q^{49} -1.55566 q^{50} -1.70276 q^{51} -2.86684 q^{52} -6.38621 q^{53} -4.65930 q^{54} +1.32583 q^{55} +5.77532 q^{56} -1.49903 q^{57} +4.66012 q^{58} -6.87768 q^{59} +0.219708 q^{60} -1.20229 q^{61} -11.0184 q^{62} -6.40652 q^{63} +5.68799 q^{64} +6.82461 q^{65} -1.07876 q^{66} -1.33170 q^{67} +1.36760 q^{68} +1.42221 q^{69} +3.65544 q^{70} +15.3185 q^{71} -6.70113 q^{72} +3.70490 q^{73} -9.55806 q^{74} -0.523024 q^{75} +1.20396 q^{76} -3.11539 q^{77} -5.55282 q^{78} +6.54448 q^{79} +4.66368 q^{80} +6.61285 q^{81} -9.39975 q^{82} +10.8398 q^{83} -0.516263 q^{84} -3.25562 q^{85} +7.54714 q^{86} +1.56677 q^{87} -3.25866 q^{88} -3.89339 q^{89} -4.24142 q^{90} -16.0363 q^{91} -1.14226 q^{92} -3.70445 q^{93} -8.01289 q^{94} -2.86608 q^{95} -1.22359 q^{96} -15.2969 q^{97} +2.30018 q^{98} +3.61480 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 83 q + q^{2} - 4 q^{3} + 61 q^{4} - 83 q^{5} - 6 q^{6} + 2 q^{7} - 3 q^{8} + 61 q^{9}+O(q^{10}) $ 83 * q + q^2 - 4 * q^3 + 61 * q^4 - 83 * q^5 - 6 * q^6 + 2 * q^7 - 3 * q^8 + 61 * q^9	\( 83 q + q^{2} - 4 q^{3} + 61 q^{4} - 83 q^{5} - 6 q^{6} + 2 q^{7} - 3 q^{8} + 61 q^{9} - q^{10} - 26 q^{11} - 12 q^{12} - 15 q^{13} - 21 q^{14} + 4 q^{15} + 5 q^{16} + 8 q^{17} - 12 q^{18} - 79 q^{19} - 61 q^{20} - 34 q^{21} - 25 q^{22} + 31 q^{23} - 42 q^{24} + 83 q^{25} - 13 q^{26} - 25 q^{27} - 16 q^{28} - 16 q^{29} + 6 q^{30} - 40 q^{31} + 15 q^{32} - 33 q^{33} - 54 q^{34} - 2 q^{35} + 11 q^{36} - 45 q^{37} + 10 q^{38} - 54 q^{39} + 3 q^{40} - 27 q^{41} - 28 q^{42} - 101 q^{43} - 51 q^{44} - 61 q^{45} - 46 q^{46} + 71 q^{47} - 14 q^{48} + 23 q^{49} + q^{50} - 71 q^{51} - 34 q^{52} - 49 q^{53} - 25 q^{54} + 26 q^{55} - 41 q^{56} - 20 q^{57} - 43 q^{58} - 60 q^{59} + 12 q^{60} - 38 q^{61} - 2 q^{62} + 36 q^{63} - 113 q^{64} + 15 q^{65} - 42 q^{66} - 164 q^{67} + 10 q^{68} - 93 q^{69} + 21 q^{70} - 78 q^{71} + q^{72} - 18 q^{73} - 23 q^{74} - 4 q^{75} - 112 q^{76} - 35 q^{77} - 44 q^{78} - 124 q^{79} - 5 q^{80} - 45 q^{81} - 34 q^{82} + 5 q^{83} - 60 q^{84} - 8 q^{85} - 25 q^{86} + 12 q^{87} - 149 q^{88} - 44 q^{89} + 12 q^{90} - 192 q^{91} + 35 q^{92} - 13 q^{93} - 32 q^{94} + 79 q^{95} - 59 q^{96} - 31 q^{97} + 25 q^{98} - 134 q^{99}+O(q^{100}) \) 83 * q + q^2 - 4 * q^3 + 61 * q^4 - 83 * q^5 - 6 * q^6 + 2 * q^7 - 3 * q^8 + 61 * q^9 - q^10 - 26 * q^11 - 12 * q^12 - 15 * q^13 - 21 * q^14 + 4 * q^15 + 5 * q^16 + 8 * q^17 - 12 * q^18 - 79 * q^19 - 61 * q^20 - 34 * q^21 - 25 * q^22 + 31 * q^23 - 42 * q^24 + 83 * q^25 - 13 * q^26 - 25 * q^27 - 16 * q^28 - 16 * q^29 + 6 * q^30 - 40 * q^31 + 15 * q^32 - 33 * q^33 - 54 * q^34 - 2 * q^35 + 11 * q^36 - 45 * q^37 + 10 * q^38 - 54 * q^39 + 3 * q^40 - 27 * q^41 - 28 * q^42 - 101 * q^43 - 51 * q^44 - 61 * q^45 - 46 * q^46 + 71 * q^47 - 14 * q^48 + 23 * q^49 + q^50 - 71 * q^51 - 34 * q^52 - 49 * q^53 - 25 * q^54 + 26 * q^55 - 41 * q^56 - 20 * q^57 - 43 * q^58 - 60 * q^59 + 12 * q^60 - 38 * q^61 - 2 * q^62 + 36 * q^63 - 113 * q^64 + 15 * q^65 - 42 * q^66 - 164 * q^67 + 10 * q^68 - 93 * q^69 + 21 * q^70 - 78 * q^71 + q^72 - 18 * q^73 - 23 * q^74 - 4 * q^75 - 112 * q^76 - 35 * q^77 - 44 * q^78 - 124 * q^79 - 5 * q^80 - 45 * q^81 - 34 * q^82 + 5 * q^83 - 60 * q^84 - 8 * q^85 - 25 * q^86 + 12 * q^87 - 149 * q^88 - 44 * q^89 + 12 * q^90 - 192 * q^91 + 35 * q^92 - 13 * q^93 - 32 * q^94 + 79 * q^95 - 59 * q^96 - 31 * q^97 + 25 * q^98 - 134 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.55566	−1.10002	−0.550008	−	0.835159i	$-0.685375\pi$
$2$	−1.55566	−1.10002	−0.550008	+	0.835159i	$0.685375\pi$
$3$	−0.523024	−0.301968	−0.150984	−	0.988536i	$-0.548244\pi$
$3$	−0.523024	−0.301968	−0.150984	+	0.988536i	$0.548244\pi$
$4$	0.420073	0.210036
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.813646	0.332170
$7$	2.34977	0.888129	0.444064	−	0.895995i	$-0.353536\pi$
$7$	2.34977	0.888129	0.444064	+	0.895995i	$0.353536\pi$
$8$	2.45783	0.868973
$9$	−2.72645	−0.908815
$10$	1.55566	0.491942
$11$	−1.32583	−0.399753	−0.199876	−	0.979821i	$-0.564054\pi$
$11$	−1.32583	−0.399753	−0.199876	+	0.979821i	$0.564054\pi$
$12$	−0.219708	−0.0634243
$13$	−6.82461	−1.89281	−0.946404	−	0.322987i	$-0.895313\pi$
$13$	−6.82461	−1.89281	−0.946404	+	0.322987i	$0.895313\pi$
$14$	−3.65544	−0.976956
$15$	0.523024	0.135044
$16$	−4.66368	−1.16592
$17$	3.25562	0.789603	0.394801	−	0.918766i	$-0.370813\pi$
$17$	3.25562	0.789603	0.394801	+	0.918766i	$0.370813\pi$
$18$	4.24142	0.999712
$19$	2.86608	0.657525	0.328762	−	0.944413i	$-0.393369\pi$
$19$	2.86608	0.657525	0.328762	+	0.944413i	$0.393369\pi$
$20$	−0.420073	−0.0939312
$21$	−1.22898	−0.268186
$22$	2.06254	0.439734
$23$	−2.71920	−0.566993	−0.283497	−	0.958973i	$-0.591494\pi$
$23$	−2.71920	−0.566993	−0.283497	+	0.958973i	$0.591494\pi$
$24$	−1.28550	−0.262402
$25$	1.00000	0.200000
$26$	10.6168	2.08212
$27$	2.99507	0.576401
$28$	0.987074	0.186539
$29$	−2.99560	−0.556268	−0.278134	−	0.960542i	$-0.589716\pi$
$29$	−2.99560	−0.556268	−0.278134	+	0.960542i	$0.589716\pi$
$30$	−0.813646	−0.148551
$31$	7.08276	1.27210	0.636051	−	0.771647i	$-0.280567\pi$
$31$	7.08276	1.27210	0.636051	+	0.771647i	$0.280567\pi$
$32$	2.33945	0.413560
$33$	0.693440	0.120712
$34$	−5.06463	−0.868576
$35$	−2.34977	−0.397183
$36$	−1.14531	−0.190884
$37$	6.14406	1.01008	0.505039	−	0.863097i	$-0.331478\pi$
$37$	6.14406	1.01008	0.505039	+	0.863097i	$0.331478\pi$
$38$	−4.45865	−0.723288
$39$	3.56943	0.571567
$40$	−2.45783	−0.388617
$41$	6.04230	0.943649	0.471824	−	0.881693i	$-0.343596\pi$
$41$	6.04230	0.943649	0.471824	+	0.881693i	$0.343596\pi$
$42$	1.91188	0.295009
$43$	−4.85141	−0.739833	−0.369917	−	0.929065i	$-0.620614\pi$
$43$	−4.85141	−0.739833	−0.369917	+	0.929065i	$0.620614\pi$
$44$	−0.556945	−0.0839626
$45$	2.72645	0.406435
$46$	4.23015	0.623702
$47$	5.15080	0.751322	0.375661	−	0.926757i	$-0.377416\pi$
$47$	5.15080	0.751322	0.375661	+	0.926757i	$0.377416\pi$
$48$	2.43922	0.352071
$49$	−1.47859	−0.211227
$50$	−1.55566	−0.220003
$51$	−1.70276	−0.238435
$52$	−2.86684	−0.397559
$53$	−6.38621	−0.877214	−0.438607	−	0.898679i	$-0.644528\pi$
$53$	−6.38621	−0.877214	−0.438607	+	0.898679i	$0.644528\pi$
$54$	−4.65930	−0.634051
$55$	1.32583	0.178775
$56$	5.77532	0.771760
$57$	−1.49903	−0.198551
$58$	4.66012	0.611904
$59$	−6.87768	−0.895398	−0.447699	−	0.894184i	$-0.647756\pi$
$59$	−6.87768	−0.895398	−0.447699	+	0.894184i	$0.647756\pi$
$60$	0.219708	0.0283642
$61$	−1.20229	−0.153937	−0.0769685	−	0.997034i	$-0.524524\pi$
$61$	−1.20229	−0.153937	−0.0769685	+	0.997034i	$0.524524\pi$
$62$	−11.0184	−1.39933
$63$	−6.40652	−0.807145
$64$	5.68799	0.710999
$65$	6.82461	0.846489
$66$	−1.07876	−0.132786
$67$	−1.33170	−0.162693	−0.0813464	−	0.996686i	$-0.525922\pi$
$67$	−1.33170	−0.162693	−0.0813464	+	0.996686i	$0.525922\pi$
$68$	1.36760	0.165845
$69$	1.42221	0.171214
$70$	3.65544	0.436908
$71$	15.3185	1.81797	0.908987	−	0.416825i	$-0.136857\pi$
$71$	15.3185	1.81797	0.908987	+	0.416825i	$0.136857\pi$
$72$	−6.70113	−0.789736
$73$	3.70490	0.433625	0.216813	−	0.976213i	$-0.430434\pi$
$73$	3.70490	0.433625	0.216813	+	0.976213i	$0.430434\pi$
$74$	−9.55806	−1.11110
$75$	−0.523024	−0.0603936
$76$	1.20396	0.138104
$77$	−3.11539	−0.355032
$78$	−5.55282	−0.628733
$79$	6.54448	0.736312	0.368156	−	0.929764i	$-0.379989\pi$
$79$	6.54448	0.736312	0.368156	+	0.929764i	$0.379989\pi$
$80$	4.66368	0.521416
$81$	6.61285	0.734761
$82$	−9.39975	−1.03803
$83$	10.8398	1.18983	0.594913	−	0.803790i	$-0.297186\pi$
$83$	10.8398	1.18983	0.594913	+	0.803790i	$0.297186\pi$
$84$	−0.516263	−0.0563289
$85$	−3.25562	−0.353121
$86$	7.54714	0.813829
$87$	1.56677	0.167975
$88$	−3.25866	−0.347374
$89$	−3.89339	−0.412698	−0.206349	−	0.978478i	$-0.566158\pi$
$89$	−3.89339	−0.412698	−0.206349	+	0.978478i	$0.566158\pi$
$90$	−4.24142	−0.447085
$91$	−16.0363	−1.68106
$92$	−1.14226	−0.119089
$93$	−3.70445	−0.384134
$94$	−8.01289	−0.826467
$95$	−2.86608	−0.294054
$96$	−1.22359	−0.124882
$97$	−15.2969	−1.55317	−0.776584	−	0.630014i	$-0.783049\pi$
$97$	−15.2969	−1.55317	−0.776584	+	0.630014i	$0.783049\pi$
$98$	2.30018	0.232354
$99$	3.61480	0.363301
$100$	0.420073	0.0420073
$101$	−16.6224	−1.65399	−0.826996	−	0.562208i	$-0.809952\pi$
$101$	−16.6224	−1.65399	−0.826996	+	0.562208i	$0.809952\pi$
$102$	2.64892	0.262282
$103$	−10.0653	−0.991766	−0.495883	−	0.868389i	$-0.665156\pi$
$103$	−10.0653	−0.991766	−0.495883	+	0.868389i	$0.665156\pi$
$104$	−16.7737	−1.64480
$105$	1.22898	0.119937
$106$	9.93477	0.964950
$107$	12.6218	1.22020	0.610100	−	0.792324i	$-0.291129\pi$
$107$	12.6218	1.22020	0.610100	+	0.792324i	$0.291129\pi$
$108$	1.25815	0.121065
$109$	7.20263	0.689887	0.344944	−	0.938623i	$-0.387898\pi$
$109$	7.20263	0.689887	0.344944	+	0.938623i	$0.387898\pi$
$110$	−2.06254	−0.196655
$111$	−3.21349	−0.305011
$112$	−10.9586	−1.03549
$113$	7.91142	0.744244	0.372122	−	0.928184i	$-0.378630\pi$
$113$	7.91142	0.744244	0.372122	+	0.928184i	$0.378630\pi$
$114$	2.33198	0.218410
$115$	2.71920	0.253567
$116$	−1.25837	−0.116837
$117$	18.6069	1.72021
$118$	10.6993	0.984952
$119$	7.64994	0.701269
$120$	1.28550	0.117350
$121$	−9.24218	−0.840198
$122$	1.87035	0.169333
$123$	−3.16027	−0.284952
$124$	2.97528	0.267188
$125$	−1.00000	−0.0894427
$126$	9.96635	0.887873
$127$	−7.51977	−0.667272	−0.333636	−	0.942702i	$-0.608276\pi$
$127$	−7.51977	−0.667272	−0.333636	+	0.942702i	$0.608276\pi$
$128$	−13.5275	−1.19567
$129$	2.53740	0.223406
$130$	−10.6168	−0.931152
$131$	−5.93529	−0.518568	−0.259284	−	0.965801i	$-0.583487\pi$
$131$	−5.93529	−0.518568	−0.259284	+	0.965801i	$0.583487\pi$
$132$	0.291295	0.0253540
$133$	6.73463	0.583966
$134$	2.07167	0.178965
$135$	−2.99507	−0.257774
$136$	8.00174	0.686144
$137$	−11.0014	−0.939913	−0.469957	−	0.882690i	$-0.655730\pi$
$137$	−11.0014	−0.939913	−0.469957	+	0.882690i	$0.655730\pi$
$138$	−2.21247	−0.188338
$139$	4.89245	0.414972	0.207486	−	0.978238i	$-0.433472\pi$
$139$	4.89245	0.414972	0.207486	+	0.978238i	$0.433472\pi$
$140$	−0.987074	−0.0834230
$141$	−2.69399	−0.226875
$142$	−23.8304	−1.99980
$143$	9.04827	0.756654
$144$	12.7153	1.05961
$145$	2.99560	0.248771
$146$	−5.76355	−0.476995
$147$	0.773338	0.0637839
$148$	2.58095	0.212153
$149$	−16.0500	−1.31487	−0.657435	−	0.753512i	$-0.728358\pi$
$149$	−16.0500	−1.31487	−0.657435	+	0.753512i	$0.728358\pi$
$150$	0.813646	0.0664339
$151$	−2.79725	−0.227637	−0.113818	−	0.993502i	$-0.536308\pi$
$151$	−2.79725	−0.227637	−0.113818	+	0.993502i	$0.536308\pi$
$152$	7.04434	0.571371
$153$	−8.87626	−0.717603
$154$	4.84648	0.390541
$155$	−7.08276	−0.568901
$156$	1.49942	0.120050
$157$	−1.32156	−0.105472	−0.0527359	−	0.998608i	$-0.516794\pi$
$157$	−1.32156	−0.105472	−0.0527359	+	0.998608i	$0.516794\pi$
$158$	−10.1810	−0.809955
$159$	3.34014	0.264890
$160$	−2.33945	−0.184949
$161$	−6.38950	−0.503563
$162$	−10.2873	−0.808249
$163$	3.24972	0.254538	0.127269	−	0.991868i	$-0.459379\pi$
$163$	3.24972	0.254538	0.127269	+	0.991868i	$0.459379\pi$
$164$	2.53821	0.198201
$165$	−0.693440	−0.0539842
$166$	−16.8631	−1.30883
$167$	22.0070	1.70295	0.851476	−	0.524393i	$-0.175708\pi$
$167$	22.0070	1.70295	0.851476	+	0.524393i	$0.175708\pi$
$168$	−3.02063	−0.233047
$169$	33.5753	2.58272
$170$	5.06463	0.388439
$171$	−7.81422	−0.597568
$172$	−2.03795	−0.155392
$173$	−1.00684	−0.0765489	−0.0382744	−	0.999267i	$-0.512186\pi$
$173$	−1.00684	−0.0765489	−0.0382744	+	0.999267i	$0.512186\pi$
$174$	−2.43736	−0.184775
$175$	2.34977	0.177626
$176$	6.18325	0.466080
$177$	3.59719	0.270381
$178$	6.05678	0.453975
$179$	10.6240	0.794075	0.397037	−	0.917802i	$-0.370038\pi$
$179$	10.6240	0.794075	0.397037	+	0.917802i	$0.370038\pi$
$180$	1.14531	0.0853661
$181$	11.4663	0.852282	0.426141	−	0.904657i	$-0.359873\pi$
$181$	11.4663	0.852282	0.426141	+	0.904657i	$0.359873\pi$
$182$	24.9469	1.84919
$183$	0.628825	0.0464841
$184$	−6.68333	−0.492702
$185$	−6.14406	−0.451721
$186$	5.76286	0.422553
$187$	−4.31639	−0.315646
$188$	2.16371	0.157805
$189$	7.03771	0.511918
$190$	4.45865	0.323464
$191$	17.0280	1.23210	0.616051	−	0.787706i	$-0.288731\pi$
$191$	17.0280	1.23210	0.616051	+	0.787706i	$0.288731\pi$
$192$	−2.97495	−0.214699
$193$	−0.0310591	−0.00223569	−0.00111784	−	0.999999i	$-0.500356\pi$
$193$	−0.0310591	−0.00223569	−0.00111784	+	0.999999i	$0.500356\pi$
$194$	23.7968	1.70851
$195$	−3.56943	−0.255613
$196$	−0.621116	−0.0443654
$197$	−2.65695	−0.189300	−0.0946499	−	0.995511i	$-0.530173\pi$
$197$	−2.65695	−0.189300	−0.0946499	+	0.995511i	$0.530173\pi$
$198$	−5.62340	−0.399637
$199$	−1.78754	−0.126715	−0.0633577	−	0.997991i	$-0.520181\pi$
$199$	−1.78754	−0.126715	−0.0633577	+	0.997991i	$0.520181\pi$
$200$	2.45783	0.173795
$201$	0.696510	0.0491280
$202$	25.8588	1.81942
$203$	−7.03895	−0.494038
$204$	−0.715285	−0.0500800
$205$	−6.04230	−0.422013
$206$	15.6582	1.09096
$207$	7.41376	0.515292
$208$	31.8278	2.20686
$209$	−3.79994	−0.262847
$210$	−1.91188	−0.131932
$211$	−0.124282	−0.00855592	−0.00427796	−	0.999991i	$-0.501362\pi$
$211$	−0.124282	−0.00855592	−0.00427796	+	0.999991i	$0.501362\pi$
$212$	−2.68268	−0.184247
$213$	−8.01195	−0.548970
$214$	−19.6353	−1.34224
$215$	4.85141	0.330864
$216$	7.36136	0.500877
$217$	16.6428	1.12979
$218$	−11.2048	−0.758887
$219$	−1.93775	−0.130941
$220$	0.556945	0.0375492
$221$	−22.2183	−1.49457
$222$	4.99909	0.335517
$223$	−1.42829	−0.0956457	−0.0478228	−	0.998856i	$-0.515228\pi$
$223$	−1.42829	−0.0956457	−0.0478228	+	0.998856i	$0.515228\pi$
$224$	5.49716	0.367294
$225$	−2.72645	−0.181763
$226$	−12.3075	−0.818681
$227$	18.6659	1.23890	0.619448	−	0.785037i	$-0.287356\pi$
$227$	18.6659	1.23890	0.619448	+	0.785037i	$0.287356\pi$
$228$	−0.629702	−0.0417030
$229$	−7.98535	−0.527687	−0.263843	−	0.964566i	$-0.584990\pi$
$229$	−7.98535	−0.527687	−0.263843	+	0.964566i	$0.584990\pi$
$230$	−4.23015	−0.278928
$231$	1.62942	0.107208
$232$	−7.36265	−0.483382
$233$	1.37990	0.0904003	0.0452002	−	0.998978i	$-0.485607\pi$
$233$	1.37990	0.0904003	0.0452002	+	0.998978i	$0.485607\pi$
$234$	−28.9460	−1.89226
$235$	−5.15080	−0.336001
$236$	−2.88913	−0.188066
$237$	−3.42292	−0.222342
$238$	−11.9007	−0.771407
$239$	−7.17965	−0.464413	−0.232206	−	0.972667i	$-0.574594\pi$
$239$	−7.17965	−0.464413	−0.232206	+	0.972667i	$0.574594\pi$
$240$	−2.43922	−0.157451
$241$	−4.61294	−0.297145	−0.148573	−	0.988901i	$-0.547468\pi$
$241$	−4.61294	−0.297145	−0.148573	+	0.988901i	$0.547468\pi$
$242$	14.3777	0.924232
$243$	−12.4439	−0.798275
$244$	−0.505048	−0.0323324
$245$	1.47859	0.0944637
$246$	4.91629	0.313451
$247$	−19.5599	−1.24457
$248$	17.4082	1.10542
$249$	−5.66949	−0.359289
$250$	1.55566	0.0983885
$251$	−24.0875	−1.52039	−0.760194	−	0.649697i	$-0.774896\pi$
$251$	−24.0875	−1.52039	−0.760194	+	0.649697i	$0.774896\pi$
$252$	−2.69120	−0.169530
$253$	3.60520	0.226657
$254$	11.6982	0.734010
$255$	1.70276	0.106631
$256$	9.66813	0.604258
$257$	22.9775	1.43330	0.716648	−	0.697435i	$-0.245676\pi$
$257$	22.9775	1.43330	0.716648	+	0.697435i	$0.245676\pi$
$258$	−3.94733	−0.245750
$259$	14.4371	0.897079
$260$	2.86684	0.177794
$261$	8.16733	0.505545
$262$	9.23328	0.570434
$263$	20.2015	1.24568	0.622838	−	0.782351i	$-0.285980\pi$
$263$	20.2015	1.24568	0.622838	+	0.782351i	$0.285980\pi$
$264$	1.70436	0.104896
$265$	6.38621	0.392302
$266$	−10.4768	−0.642373
$267$	2.03633	0.124622
$268$	−0.559411	−0.0341714
$269$	−3.18976	−0.194483	−0.0972415	−	0.995261i	$-0.531002\pi$
$269$	−3.18976	−0.194483	−0.0972415	+	0.995261i	$0.531002\pi$
$270$	4.65930	0.283556
$271$	−19.2843	−1.17144	−0.585719	−	0.810514i	$-0.699188\pi$
$271$	−19.2843	−1.17144	−0.585719	+	0.810514i	$0.699188\pi$
$272$	−15.1832	−0.920615
$273$	8.38734	0.507625
$274$	17.1144	1.03392
$275$	−1.32583	−0.0799505
$276$	0.597431	0.0359611
$277$	−24.1522	−1.45116	−0.725582	−	0.688136i	$-0.758429\pi$
$277$	−24.1522	−1.45116	−0.725582	+	0.688136i	$0.758429\pi$
$278$	−7.61098	−0.456477
$279$	−19.3108	−1.15611
$280$	−5.77532	−0.345142
$281$	−20.0209	−1.19435	−0.597174	−	0.802112i	$-0.703710\pi$
$281$	−20.0209	−1.19435	−0.597174	+	0.802112i	$0.703710\pi$
$282$	4.19093	0.249566
$283$	20.5555	1.22190	0.610950	−	0.791669i	$-0.290788\pi$
$283$	20.5555	1.22190	0.610950	+	0.791669i	$0.290788\pi$
$284$	6.43489	0.381841
$285$	1.49903	0.0887948
$286$	−14.0760	−0.832332
$287$	14.1980	0.838081
$288$	−6.37837	−0.375849
$289$	−6.40097	−0.376527
$290$	−4.66012	−0.273652
$291$	8.00066	0.469007
$292$	1.55633	0.0910771
$293$	−18.2287	−1.06493	−0.532467	−	0.846451i	$-0.678735\pi$
$293$	−18.2287	−1.06493	−0.532467	+	0.846451i	$0.678735\pi$
$294$	−1.20305	−0.0701633
$295$	6.87768	0.400434
$296$	15.1010	0.877730
$297$	−3.97095	−0.230418
$298$	24.9684	1.44638
$299$	18.5575	1.07321
$300$	−0.219708	−0.0126849
$301$	−11.3997	−0.657067
$302$	4.35156	0.250404
$303$	8.69392	0.499452
$304$	−13.3665	−0.766622
$305$	1.20229	0.0688427
$306$	13.8084	0.789375
$307$	28.7378	1.64015	0.820076	−	0.572255i	$-0.193931\pi$
$307$	28.7378	1.64015	0.820076	+	0.572255i	$0.193931\pi$
$308$	−1.30869	−0.0745696
$309$	5.26441	0.299482
$310$	11.0184	0.625800
$311$	−7.89830	−0.447871	−0.223936	−	0.974604i	$-0.571891\pi$
$311$	−7.89830	−0.447871	−0.223936	+	0.974604i	$0.571891\pi$
$312$	8.77305	0.496676
$313$	15.1564	0.856689	0.428345	−	0.903615i	$-0.359097\pi$
$313$	15.1564	0.856689	0.428345	+	0.903615i	$0.359097\pi$
$314$	2.05589	0.116021
$315$	6.40652	0.360966
$316$	2.74916	0.154652
$317$	8.51764	0.478398	0.239199	−	0.970971i	$-0.423115\pi$
$317$	8.51764	0.478398	0.239199	+	0.970971i	$0.423115\pi$
$318$	−5.19612	−0.291384
$319$	3.97165	0.222370
$320$	−5.68799	−0.317968
$321$	−6.60153	−0.368461
$322$	9.93988	0.553928
$323$	9.33087	0.519183
$324$	2.77788	0.154327
$325$	−6.82461	−0.378561
$326$	−5.05546	−0.279996
$327$	−3.76715	−0.208324
$328$	14.8509	0.820005
$329$	12.1032	0.667271
$330$	1.07876	0.0593836
$331$	−9.73305	−0.534977	−0.267488	−	0.963561i	$-0.586194\pi$
$331$	−9.73305	−0.534977	−0.267488	+	0.963561i	$0.586194\pi$
$332$	4.55352	0.249907
$333$	−16.7515	−0.917974
$334$	−34.2354	−1.87328
$335$	1.33170	0.0727585
$336$	5.73160	0.312684
$337$	−12.3190	−0.671061	−0.335531	−	0.942029i	$-0.608916\pi$
$337$	−12.3190	−0.671061	−0.335531	+	0.942029i	$0.608916\pi$
$338$	−52.2318	−2.84103
$339$	−4.13786	−0.224738
$340$	−1.36760	−0.0741683
$341$	−9.39053	−0.508526
$342$	12.1563	0.657335
$343$	−19.9227	−1.07573
$344$	−11.9239	−0.642895
$345$	−1.42221	−0.0765691
$346$	1.56630	0.0842050
$347$	−35.8176	−1.92279	−0.961395	−	0.275172i	$-0.911265\pi$
$347$	−35.8176	−1.92279	−0.961395	+	0.275172i	$0.911265\pi$
$348$	0.658157	0.0352809
$349$	−15.6629	−0.838416	−0.419208	−	0.907890i	$-0.637692\pi$
$349$	−15.6629	−0.838416	−0.419208	+	0.907890i	$0.637692\pi$
$350$	−3.65544	−0.195391
$351$	−20.4402	−1.09102
$352$	−3.10171	−0.165322
$353$	3.35379	0.178504	0.0892521	−	0.996009i	$-0.471552\pi$
$353$	3.35379	0.178504	0.0892521	+	0.996009i	$0.471552\pi$
$354$	−5.59600	−0.297424
$355$	−15.3185	−0.813022
$356$	−1.63551	−0.0866817
$357$	−4.00110	−0.211761
$358$	−16.5273	−0.873496
$359$	8.06817	0.425822	0.212911	−	0.977072i	$-0.431706\pi$
$359$	8.06817	0.425822	0.212911	+	0.977072i	$0.431706\pi$
$360$	6.70113	0.353181
$361$	−10.7856	−0.567661
$362$	−17.8376	−0.937524
$363$	4.83388	0.253713
$364$	−6.73640	−0.353083
$365$	−3.70490	−0.193923
$366$	−0.978236	−0.0511332
$367$	19.2316	1.00388	0.501940	−	0.864903i	$-0.332620\pi$
$367$	19.2316	1.00388	0.501940	+	0.864903i	$0.332620\pi$
$368$	12.6815	0.661070
$369$	−16.4740	−0.857602
$370$	9.55806	0.496900
$371$	−15.0061	−0.779079
$372$	−1.55614	−0.0806821
$373$	−0.285533	−0.0147843	−0.00739217	−	0.999973i	$-0.502353\pi$
$373$	−0.285533	−0.0147843	−0.00739217	+	0.999973i	$0.502353\pi$
$374$	6.71483	0.347216
$375$	0.523024	0.0270088
$376$	12.6598	0.652879
$377$	20.4438	1.05291
$378$	−10.9483	−0.563119
$379$	−9.88435	−0.507725	−0.253863	−	0.967240i	$-0.581701\pi$
$379$	−9.88435	−0.507725	−0.253863	+	0.967240i	$0.581701\pi$
$380$	−1.20396	−0.0617620
$381$	3.93302	0.201495
$382$	−26.4897	−1.35533
$383$	−3.29812	−0.168526	−0.0842631	−	0.996444i	$-0.526854\pi$
$383$	−3.29812	−0.168526	−0.0842631	+	0.996444i	$0.526854\pi$
$384$	7.07518	0.361054
$385$	3.11539	0.158775
$386$	0.0483174	0.00245929
$387$	13.2271	0.672372
$388$	−6.42583	−0.326222
$389$	−14.1163	−0.715727	−0.357863	−	0.933774i	$-0.616495\pi$
$389$	−14.1163	−0.715727	−0.357863	+	0.933774i	$0.616495\pi$
$390$	5.55282	0.281178
$391$	−8.85269	−0.447700
$392$	−3.63412	−0.183551
$393$	3.10430	0.156591
$394$	4.13330	0.208233
$395$	−6.54448	−0.329289
$396$	1.51848	0.0763065
$397$	−16.0627	−0.806165	−0.403082	−	0.915164i	$-0.632061\pi$
$397$	−16.0627	−0.806165	−0.403082	+	0.915164i	$0.632061\pi$
$398$	2.78080	0.139389
$399$	−3.52237	−0.176339
$400$	−4.66368	−0.233184
$401$	−29.2705	−1.46170	−0.730849	−	0.682539i	$-0.760876\pi$
$401$	−29.2705	−1.46170	−0.730849	+	0.682539i	$0.760876\pi$
$402$	−1.08353	−0.0540417
$403$	−48.3371	−2.40784
$404$	−6.98263	−0.347399
$405$	−6.61285	−0.328595
$406$	10.9502	0.543450
$407$	−8.14598	−0.403781
$408$	−4.18510	−0.207193
$409$	−32.4842	−1.60624	−0.803121	−	0.595816i	$-0.796829\pi$
$409$	−32.4842	−1.60624	−0.803121	+	0.595816i	$0.796829\pi$
$410$	9.39975	0.464221
$411$	5.75399	0.283824
$412$	−4.22817	−0.208307
$413$	−16.1610	−0.795229
$414$	−11.5333	−0.566830
$415$	−10.8398	−0.532107
$416$	−15.9658	−0.782789
$417$	−2.55887	−0.125308
$418$	5.91140	0.289136
$419$	−21.4559	−1.04819	−0.524095	−	0.851660i	$-0.675596\pi$
$419$	−21.4559	−1.04819	−0.524095	+	0.851660i	$0.675596\pi$
$420$	0.516263	0.0251911
$421$	7.47888	0.364498	0.182249	−	0.983252i	$-0.441662\pi$
$421$	7.47888	0.364498	0.182249	+	0.983252i	$0.441662\pi$
$422$	0.193340	0.00941165
$423$	−14.0434	−0.682813
$424$	−15.6962	−0.762275
$425$	3.25562	0.157921
$426$	12.4639	0.603876
$427$	−2.82509	−0.136716
$428$	5.30210	0.256286
$429$	−4.73246	−0.228485
$430$	−7.54714	−0.363955
$431$	8.35256	0.402329	0.201164	−	0.979558i	$-0.435527\pi$
$431$	8.35256	0.402329	0.201164	+	0.979558i	$0.435527\pi$
$432$	−13.9681	−0.672038
$433$	−32.4443	−1.55917	−0.779586	−	0.626295i	$-0.784571\pi$
$433$	−32.4443	−1.55917	−0.779586	+	0.626295i	$0.784571\pi$
$434$	−25.8906	−1.24279
$435$	−1.56677	−0.0751208
$436$	3.02563	0.144901
$437$	−7.79347	−0.372812
$438$	3.01447	0.144037
$439$	−1.70020	−0.0811463	−0.0405732	−	0.999177i	$-0.512918\pi$
$439$	−1.70020	−0.0811463	−0.0405732	+	0.999177i	$0.512918\pi$
$440$	3.25866	0.155350
$441$	4.03130	0.191967
$442$	34.5641	1.64405
$443$	−22.0578	−1.04800	−0.524000	−	0.851718i	$-0.675561\pi$
$443$	−22.0578	−1.04800	−0.524000	+	0.851718i	$0.675561\pi$
$444$	−1.34990	−0.0640635
$445$	3.89339	0.184564
$446$	2.22194	0.105212
$447$	8.39455	0.397048
$448$	13.3655	0.631458
$449$	4.93124	0.232719	0.116360	−	0.993207i	$-0.462877\pi$
$449$	4.93124	0.232719	0.116360	+	0.993207i	$0.462877\pi$
$450$	4.24142	0.199942
$451$	−8.01106	−0.377226
$452$	3.32337	0.156318
$453$	1.46303	0.0687390
$454$	−29.0377	−1.36281
$455$	16.0363	0.751791
$456$	−3.68435	−0.172536
$457$	−2.71787	−0.127137	−0.0635683	−	0.997977i	$-0.520248\pi$
$457$	−2.71787	−0.127137	−0.0635683	+	0.997977i	$0.520248\pi$
$458$	12.4225	0.580464
$459$	9.75079	0.455128
$460$	1.14226	0.0532583
$461$	−3.04119	−0.141642	−0.0708211	−	0.997489i	$-0.522562\pi$
$461$	−3.04119	−0.141642	−0.0708211	+	0.997489i	$0.522562\pi$
$462$	−2.53483	−0.117931
$463$	14.6796	0.682218	0.341109	−	0.940024i	$-0.389198\pi$
$463$	14.6796	0.682218	0.341109	+	0.940024i	$0.389198\pi$
$464$	13.9705	0.648565
$465$	3.70445	0.171790
$466$	−2.14665	−0.0994418
$467$	−3.40792	−0.157700	−0.0788498	−	0.996887i	$-0.525125\pi$
$467$	−3.40792	−0.157700	−0.0788498	+	0.996887i	$0.525125\pi$
$468$	7.81627	0.361307
$469$	−3.12918	−0.144492
$470$	8.01289	0.369607
$471$	0.691206	0.0318491
$472$	−16.9041	−0.778076
$473$	6.43214	0.295750
$474$	5.32489	0.244580
$475$	2.86608	0.131505
$476$	3.21353	0.147292
$477$	17.4117	0.797225
$478$	11.1691	0.510862
$479$	30.1094	1.37573	0.687867	−	0.725837i	$-0.258547\pi$
$479$	30.1094	1.37573	0.687867	+	0.725837i	$0.258547\pi$
$480$	1.22359	0.0558488
$481$	−41.9309	−1.91188
$482$	7.17616	0.326865
$483$	3.34186	0.152060
$484$	−3.88239	−0.176472
$485$	15.2969	0.694598
$486$	19.3584	0.878116
$487$	−26.4430	−1.19825	−0.599124	−	0.800656i	$-0.704485\pi$
$487$	−26.4430	−1.19825	−0.599124	+	0.800656i	$0.704485\pi$
$488$	−2.95501	−0.133767
$489$	−1.69968	−0.0768623
$490$	−2.30018	−0.103912
$491$	32.7980	1.48015	0.740077	−	0.672523i	$-0.234789\pi$
$491$	32.7980	1.48015	0.740077	+	0.672523i	$0.234789\pi$
$492$	−1.32754	−0.0598502
$493$	−9.75251	−0.439231
$494$	30.4285	1.36904
$495$	−3.61480	−0.162473
$496$	−33.0318	−1.48317
$497$	35.9950	1.61459
$498$	8.81979	0.395224
$499$	−35.9101	−1.60756	−0.803779	−	0.594928i	$-0.797180\pi$
$499$	−35.9101	−1.60756	−0.803779	+	0.594928i	$0.797180\pi$
$500$	−0.420073	−0.0187862
$501$	−11.5102	−0.514237
$502$	37.4719	1.67245
$503$	−13.4274	−0.598699	−0.299350	−	0.954144i	$-0.596770\pi$
$503$	−13.4274	−0.598699	−0.299350	+	0.954144i	$0.596770\pi$
$504$	−15.7461	−0.701387
$505$	16.6224	0.739688
$506$	−5.60846	−0.249326
$507$	−17.5607	−0.779898
$508$	−3.15885	−0.140151
$509$	−28.8123	−1.27708	−0.638542	−	0.769587i	$-0.720462\pi$
$509$	−28.8123	−1.27708	−0.638542	+	0.769587i	$0.720462\pi$
$510$	−2.64892	−0.117296
$511$	8.70564	0.385115
$512$	12.0146	0.530976
$513$	8.58411	0.378998
$514$	−35.7451	−1.57665
$515$	10.0653	0.443531
$516$	1.06589	0.0469234
$517$	−6.82909	−0.300343
$518$	−22.4592	−0.986802
$519$	0.526603	0.0231153
$520$	16.7737	0.735576
$521$	−34.5922	−1.51551	−0.757755	−	0.652539i	$-0.773704\pi$
$521$	−34.5922	−1.51551	−0.757755	+	0.652539i	$0.773704\pi$
$522$	−12.7056	−0.556108
$523$	−36.6442	−1.60234	−0.801171	−	0.598436i	$-0.795789\pi$
$523$	−36.6442	−1.60234	−0.801171	+	0.598436i	$0.795789\pi$
$524$	−2.49325	−0.108918
$525$	−1.22898	−0.0536373
$526$	−31.4266	−1.37026
$527$	23.0587	1.00445
$528$	−3.23399	−0.140741
$529$	−15.6059	−0.678519
$530$	−9.93477	−0.431539
$531$	18.7516	0.813751
$532$	2.82904	0.122654
$533$	−41.2364	−1.78614
$534$	−3.16784	−0.137086
$535$	−12.6218	−0.545690
$536$	−3.27308	−0.141376
$537$	−5.55660	−0.239785
$538$	4.96217	0.213935
$539$	1.96036	0.0844387
$540$	−1.25815	−0.0541420
$541$	−40.6554	−1.74791	−0.873957	−	0.486004i	$-0.838454\pi$
$541$	−40.6554	−1.74791	−0.873957	+	0.486004i	$0.838454\pi$
$542$	29.9998	1.28860
$543$	−5.99714	−0.257362
$544$	7.61634	0.326548
$545$	−7.20263	−0.308527
$546$	−13.0478	−0.558396
$547$	10.7259	0.458606	0.229303	−	0.973355i	$-0.426355\pi$
$547$	10.7259	0.458606	0.229303	+	0.973355i	$0.426355\pi$
$548$	−4.62139	−0.197416
$549$	3.27797	0.139900
$550$	2.06254	0.0879469
$551$	−8.58562	−0.365760
$552$	3.49554	0.148780
$553$	15.3780	0.653939
$554$	37.5725	1.59630
$555$	3.21349	0.136405
$556$	2.05519	0.0871593
$557$	−38.0840	−1.61367	−0.806836	−	0.590776i	$-0.798822\pi$
$557$	−38.0840	−1.61367	−0.806836	+	0.590776i	$0.798822\pi$
$558$	30.0409	1.27173
$559$	33.1090	1.40036
$560$	10.9586	0.463084
$561$	2.25757	0.0953149
$562$	31.1457	1.31380
$563$	14.7504	0.621656	0.310828	−	0.950466i	$-0.399394\pi$
$563$	14.7504	0.621656	0.310828	+	0.950466i	$0.399394\pi$
$564$	−1.13167	−0.0476521
$565$	−7.91142	−0.332836
$566$	−31.9774	−1.34411
$567$	15.5387	0.652562
$568$	37.6503	1.57977
$569$	−13.8678	−0.581367	−0.290683	−	0.956819i	$-0.593883\pi$
$569$	−13.8678	−0.581367	−0.290683	+	0.956819i	$0.593883\pi$
$570$	−2.33198	−0.0976758
$571$	−19.4480	−0.813875	−0.406937	−	0.913456i	$-0.633403\pi$
$571$	−19.4480	−0.813875	−0.406937	+	0.913456i	$0.633403\pi$
$572$	3.80093	0.158925
$573$	−8.90605	−0.372055
$574$	−22.0872	−0.921904
$575$	−2.71920	−0.113399
$576$	−15.5080	−0.646167
$577$	−24.5936	−1.02385	−0.511923	−	0.859031i	$-0.671067\pi$
$577$	−24.5936	−1.02385	−0.511923	+	0.859031i	$0.671067\pi$
$578$	9.95772	0.414186
$579$	0.0162447	0.000675106 0
$580$	1.25837	0.0522509
$581$	25.4711	1.05672
$582$	−12.4463	−0.515915
$583$	8.46703	0.350668
$584$	9.10599	0.376809
$585$	−18.6069	−0.769302
$586$	28.3577	1.17144
$587$	39.6994	1.63857	0.819285	−	0.573387i	$-0.194371\pi$
$587$	39.6994	1.63857	0.819285	+	0.573387i	$0.194371\pi$
$588$	0.324859	0.0133969
$589$	20.2998	0.836438
$590$	−10.6993	−0.440484
$591$	1.38965	0.0571625
$592$	−28.6540	−1.17767
$593$	33.7793	1.38715	0.693574	−	0.720386i	$-0.256035\pi$
$593$	33.7793	1.38715	0.693574	+	0.720386i	$0.256035\pi$
$594$	6.17744	0.253463
$595$	−7.64994	−0.313617
$596$	−6.74218	−0.276171
$597$	0.934926	0.0382640
$598$	−28.8692	−1.18055
$599$	23.9916	0.980270	0.490135	−	0.871646i	$-0.336947\pi$
$599$	23.9916	0.980270	0.490135	+	0.871646i	$0.336947\pi$
$600$	−1.28550	−0.0524804
$601$	−11.1306	−0.454025	−0.227013	−	0.973892i	$-0.572896\pi$
$601$	−11.1306	−0.454025	−0.227013	+	0.973892i	$0.572896\pi$
$602$	17.7340	0.722785
$603$	3.63080	0.147858
$604$	−1.17505	−0.0478120
$605$	9.24218	0.375748
$606$	−13.5248	−0.549406
$607$	36.1636	1.46783	0.733917	−	0.679239i	$-0.237690\pi$
$607$	36.1636	1.46783	0.733917	+	0.679239i	$0.237690\pi$
$608$	6.70505	0.271926
$609$	3.68154	0.149184
$610$	−1.87035	−0.0757282
$611$	−35.1522	−1.42211
$612$	−3.72868	−0.150723
$613$	−19.8807	−0.802975	−0.401487	−	0.915865i	$-0.631507\pi$
$613$	−19.8807	−0.802975	−0.401487	+	0.915865i	$0.631507\pi$
$614$	−44.7062	−1.80419
$615$	3.16027	0.127434
$616$	−7.65709	−0.308513
$617$	28.5458	1.14921	0.574606	−	0.818430i	$-0.305155\pi$
$617$	28.5458	1.14921	0.574606	+	0.818430i	$0.305155\pi$
$618$	−8.18962	−0.329435
$619$	−22.8255	−0.917435	−0.458718	−	0.888582i	$-0.651691\pi$
$619$	−22.8255	−0.917435	−0.458718	+	0.888582i	$0.651691\pi$
$620$	−2.97528	−0.119490
$621$	−8.14420	−0.326816
$622$	12.2871	0.492666
$623$	−9.14856	−0.366529
$624$	−16.6467	−0.666402
$625$	1.00000	0.0400000
$626$	−23.5782	−0.942373
$627$	1.98746	0.0793714
$628$	−0.555150	−0.0221529
$629$	20.0027	0.797560
$630$	−9.96635	−0.397069
$631$	4.81838	0.191817	0.0959083	−	0.995390i	$-0.469424\pi$
$631$	4.81838	0.191817	0.0959083	+	0.995390i	$0.469424\pi$
$632$	16.0852	0.639835
$633$	0.0650024	0.00258361
$634$	−13.2505	−0.526246
$635$	7.51977	0.298413
$636$	1.40310	0.0556366
$637$	10.0908	0.399813
$638$	−6.17853	−0.244610
$639$	−41.7651	−1.65220
$640$	13.5275	0.534720
$641$	26.5023	1.04678	0.523389	−	0.852094i	$-0.324668\pi$
$641$	26.5023	1.04678	0.523389	+	0.852094i	$0.324668\pi$
$642$	10.2697	0.405313
$643$	−41.5322	−1.63787	−0.818934	−	0.573888i	$-0.805435\pi$
$643$	−41.5322	−1.63787	−0.818934	+	0.573888i	$0.805435\pi$
$644$	−2.68406	−0.105767
$645$	−2.53740	−0.0999102
$646$	−14.5156	−0.571110
$647$	22.6561	0.890703	0.445351	−	0.895356i	$-0.353079\pi$
$647$	22.6561	0.890703	0.445351	+	0.895356i	$0.353079\pi$
$648$	16.2532	0.638487
$649$	9.11863	0.357938
$650$	10.6168	0.416424
$651$	−8.70460	−0.341160
$652$	1.36512	0.0534623
$653$	28.9077	1.13124	0.565622	−	0.824665i	$-0.308636\pi$
$653$	28.9077	1.13124	0.565622	+	0.824665i	$0.308636\pi$
$654$	5.86040	0.229160
$655$	5.93529	0.231911
$656$	−28.1794	−1.10022
$657$	−10.1012	−0.394085
$658$	−18.8284	−0.734009
$659$	14.9277	0.581501	0.290751	−	0.956799i	$-0.406095\pi$
$659$	14.9277	0.581501	0.290751	+	0.956799i	$0.406095\pi$
$660$	−0.291295	−0.0113387
$661$	−18.6279	−0.724541	−0.362270	−	0.932073i	$-0.617998\pi$
$661$	−18.6279	−0.724541	−0.362270	+	0.932073i	$0.617998\pi$
$662$	15.1413	0.588483
$663$	11.6207	0.451311
$664$	26.6424	1.03393
$665$	−6.73463	−0.261158
$666$	26.0595	1.00979
$667$	8.14564	0.315400
$668$	9.24454	0.357682
$669$	0.747032	0.0288819
$670$	−2.07167	−0.0800355
$671$	1.59403	0.0615367
$672$	−2.87514	−0.110911
$673$	−18.4553	−0.711401	−0.355701	−	0.934600i	$-0.615758\pi$
$673$	−18.4553	−0.711401	−0.355701	+	0.934600i	$0.615758\pi$
$674$	19.1642	0.738178
$675$	2.99507	0.115280
$676$	14.1041	0.542465
$677$	28.2720	1.08658	0.543291	−	0.839544i	$-0.317178\pi$
$677$	28.2720	1.08658	0.543291	+	0.839544i	$0.317178\pi$
$678$	6.43710	0.247215
$679$	−35.9442	−1.37941
$680$	−8.00174	−0.306853
$681$	−9.76269	−0.374107
$682$	14.6085	0.559387
$683$	−22.7836	−0.871791	−0.435895	−	0.899997i	$-0.643568\pi$
$683$	−22.7836	−0.871791	−0.435895	+	0.899997i	$0.643568\pi$
$684$	−3.28254	−0.125511
$685$	11.0014	0.420342
$686$	30.9929	1.18332
$687$	4.17653	0.159344
$688$	22.6255	0.862587
$689$	43.5834	1.66040
$690$	2.21247	0.0842273
$691$	−0.215207	−0.00818687	−0.00409343	−	0.999992i	$-0.501303\pi$
$691$	−0.215207	−0.00818687	−0.00409343	+	0.999992i	$0.501303\pi$
$692$	−0.422948	−0.0160781
$693$	8.49394	0.322658
$694$	55.7200	2.11510
$695$	−4.89245	−0.185581
$696$	3.85084	0.145966
$697$	19.6714	0.745108
$698$	24.3661	0.922271
$699$	−0.721721	−0.0272980
$700$	0.987074	0.0373079
$701$	34.6090	1.30716	0.653582	−	0.756856i	$-0.273265\pi$
$701$	34.6090	1.30716	0.653582	+	0.756856i	$0.273265\pi$
$702$	31.7979	1.20014
$703$	17.6094	0.664151
$704$	−7.54130	−0.284224
$705$	2.69399	0.101462
$706$	−5.21735	−0.196358
$707$	−39.0588	−1.46896
$708$	1.51108	0.0567900
$709$	−39.7815	−1.49403	−0.747013	−	0.664810i	$-0.768513\pi$
$709$	−39.7815	−1.49403	−0.747013	+	0.664810i	$0.768513\pi$
$710$	23.8304	0.894338
$711$	−17.8432	−0.669171
$712$	−9.56927	−0.358624
$713$	−19.2595	−0.721273
$714$	6.22435	0.232940
$715$	−9.04827	−0.338386
$716$	4.46285	0.166785
$717$	3.75513	0.140238
$718$	−12.5513	−0.468411
$719$	−21.1803	−0.789893	−0.394947	−	0.918704i	$-0.629237\pi$
$719$	−21.1803	−0.789893	−0.394947	+	0.918704i	$0.629237\pi$
$720$	−12.7153	−0.473871
$721$	−23.6512	−0.880816
$722$	16.7787	0.624437
$723$	2.41268	0.0897284
$724$	4.81667	0.179010
$725$	−2.99560	−0.111254
$726$	−7.51986	−0.279088
$727$	−42.7860	−1.58684	−0.793422	−	0.608672i	$-0.791703\pi$
$727$	−42.7860	−1.58684	−0.793422	+	0.608672i	$0.791703\pi$
$728$	−39.4143	−1.46079
$729$	−13.3301	−0.493707
$730$	5.76355	0.213319
$731$	−15.7943	−0.584175
$732$	0.264152	0.00976335
$733$	−9.25648	−0.341896	−0.170948	−	0.985280i	$-0.554683\pi$
$733$	−9.25648	−0.341896	−0.170948	+	0.985280i	$0.554683\pi$
$734$	−29.9177	−1.10428
$735$	−0.773338	−0.0285250
$736$	−6.36143	−0.234486
$737$	1.76561	0.0650369
$738$	25.6279	0.943377
$739$	17.3691	0.638933	0.319467	−	0.947598i	$-0.396496\pi$
$739$	17.3691	0.638933	0.319467	+	0.947598i	$0.396496\pi$
$740$	−2.58095	−0.0948778
$741$	10.2303	0.375819
$742$	23.3444	0.857000
$743$	16.1668	0.593102	0.296551	−	0.955017i	$-0.404164\pi$
$743$	16.1668	0.593102	0.296551	+	0.955017i	$0.404164\pi$
$744$	−9.10490	−0.333802
$745$	16.0500	0.588027
$746$	0.444192	0.0162630
$747$	−29.5542	−1.08133
$748$	−1.81320	−0.0662971
$749$	29.6584	1.08369
$750$	−0.813646	−0.0297102
$751$	5.90615	0.215518	0.107759	−	0.994177i	$-0.465632\pi$
$751$	5.90615	0.215518	0.107759	+	0.994177i	$0.465632\pi$
$752$	−24.0217	−0.875982
$753$	12.5983	0.459108
$754$	−31.8035	−1.15822
$755$	2.79725	0.101802
$756$	2.95635	0.107522
$757$	34.4921	1.25364	0.626819	−	0.779165i	$-0.284357\pi$
$757$	34.4921	1.25364	0.626819	+	0.779165i	$0.284357\pi$
$758$	15.3767	0.558506
$759$	−1.88561	−0.0684431
$760$	−7.04434	−0.255525
$761$	−43.3109	−1.57002	−0.785010	−	0.619483i	$-0.787342\pi$
$761$	−43.3109	−1.57002	−0.785010	+	0.619483i	$0.787342\pi$
$762$	−6.11843	−0.221647
$763$	16.9245	0.612709
$764$	7.15300	0.258786
$765$	8.87626	0.320922
$766$	5.13075	0.185382
$767$	46.9375	1.69482
$768$	−5.05666	−0.182467
$769$	−19.9118	−0.718037	−0.359018	−	0.933330i	$-0.616888\pi$
$769$	−19.9118	−0.718037	−0.359018	+	0.933330i	$0.616888\pi$
$770$	−4.84648	−0.174655
$771$	−12.0178	−0.432809
$772$	−0.0130471	−0.000469576 0
$773$	−3.38116	−0.121612	−0.0608059	−	0.998150i	$-0.519367\pi$
$773$	−3.38116	−0.121612	−0.0608059	+	0.998150i	$0.519367\pi$
$774$	−20.5769	−0.739620
$775$	7.08276	0.254420
$776$	−37.5972	−1.34966
$777$	−7.55096	−0.270889
$778$	21.9602	0.787311
$779$	17.3177	0.620472
$780$	−1.49942	−0.0536880
$781$	−20.3097	−0.726739
$782$	13.7718	0.492477
$783$	−8.97201	−0.320633
$784$	6.89568	0.246274
$785$	1.32156	0.0471684
$786$	−4.82922	−0.172253
$787$	22.2487	0.793081	0.396540	−	0.918017i	$-0.370211\pi$
$787$	22.2487	0.793081	0.396540	+	0.918017i	$0.370211\pi$
$788$	−1.11611	−0.0397599
$789$	−10.5658	−0.376154
$790$	10.1810	0.362223
$791$	18.5900	0.660984
$792$	8.88456	0.315699
$793$	8.20514	0.291373
$794$	24.9881	0.886795
$795$	−3.34014	−0.118463
$796$	−0.750897	−0.0266148
$797$	−11.9967	−0.424946	−0.212473	−	0.977167i	$-0.568152\pi$
$797$	−11.9967	−0.424946	−0.212473	+	0.977167i	$0.568152\pi$
$798$	5.47961	0.193976
$799$	16.7690	0.593246
$800$	2.33945	0.0827119
$801$	10.6151	0.375067
$802$	45.5349	1.60789
$803$	−4.91206	−0.173343
$804$	0.292585	0.0103187
$805$	6.38950	0.225200
$806$	75.1960	2.64867
$807$	1.66832	0.0587276
$808$	−40.8550	−1.43727
$809$	41.7641	1.46835	0.734173	−	0.678962i	$-0.237570\pi$
$809$	41.7641	1.46835	0.734173	+	0.678962i	$0.237570\pi$
$810$	10.2873	0.361460
$811$	−26.9611	−0.946733	−0.473367	−	0.880866i	$-0.656961\pi$
$811$	−26.9611	−0.946733	−0.473367	+	0.880866i	$0.656961\pi$
$812$	−2.95687	−0.103766
$813$	10.0862	0.353737
$814$	12.6724	0.444166
$815$	−3.24972	−0.113833
$816$	7.94116	0.277996
$817$	−13.9045	−0.486459
$818$	50.5344	1.76689
$819$	43.7220	1.52777
$820$	−2.53821	−0.0886380
$821$	−4.59884	−0.160501	−0.0802503	−	0.996775i	$-0.525572\pi$
$821$	−4.59884	−0.160501	−0.0802503	+	0.996775i	$0.525572\pi$
$822$	−8.95125	−0.312211
$823$	−3.75326	−0.130831	−0.0654153	−	0.997858i	$-0.520837\pi$
$823$	−3.75326	−0.130831	−0.0654153	+	0.997858i	$0.520837\pi$
$824$	−24.7388	−0.861818
$825$	0.693440	0.0241425
$826$	25.1409	0.874765
$827$	15.9962	0.556241	0.278121	−	0.960546i	$-0.410289\pi$
$827$	15.9962	0.556241	0.278121	+	0.960546i	$0.410289\pi$
$828$	3.11432	0.108230
$829$	26.7703	0.929770	0.464885	−	0.885371i	$-0.346096\pi$
$829$	26.7703	0.929770	0.464885	+	0.885371i	$0.346096\pi$
$830$	16.8631	0.585326
$831$	12.6322	0.438205
$832$	−38.8183	−1.34578
$833$	−4.81373	−0.166786
$834$	3.98073	0.137841
$835$	−22.0070	−0.761583
$836$	−1.59625	−0.0552075
$837$	21.2133	0.733240
$838$	33.3781	1.15303
$839$	−42.3987	−1.46377	−0.731883	−	0.681431i	$-0.761358\pi$
$839$	−42.3987	−1.46377	−0.731883	+	0.681431i	$0.761358\pi$
$840$	3.02063	0.104222
$841$	−20.0264	−0.690566
$842$	−11.6346	−0.400954
$843$	10.4714	0.360655
$844$	−0.0522075	−0.00179706
$845$	−33.5753	−1.15503
$846$	21.8467	0.751106
$847$	−21.7170	−0.746204
$848$	29.7833	1.02276
$849$	−10.7510	−0.368975
$850$	−5.06463	−0.173715
$851$	−16.7070	−0.572707
$852$	−3.36560	−0.115304
$853$	−17.2945	−0.592152	−0.296076	−	0.955164i	$-0.595678\pi$
$853$	−17.2945	−0.592152	−0.296076	+	0.955164i	$0.595678\pi$
$854$	4.39488	0.150390
$855$	7.81422	0.267241
$856$	31.0223	1.06032
$857$	−11.8679	−0.405399	−0.202699	−	0.979241i	$-0.564971\pi$
$857$	−11.8679	−0.405399	−0.202699	+	0.979241i	$0.564971\pi$
$858$	7.36209	0.251338
$859$	36.5351	1.24656	0.623280	−	0.781998i	$-0.285800\pi$
$859$	36.5351	1.24656	0.623280	+	0.781998i	$0.285800\pi$
$860$	2.03795	0.0694934
$861$	−7.42589	−0.253074
$862$	−12.9937	−0.442568
$863$	57.2352	1.94831	0.974154	−	0.225886i	$-0.0725275\pi$
$863$	57.2352	1.94831	0.974154	+	0.225886i	$0.0725275\pi$
$864$	7.00680	0.238376
$865$	1.00684	0.0342337
$866$	50.4722	1.71512
$867$	3.34786	0.113699
$868$	6.99121	0.237297
$869$	−8.67686	−0.294342
$870$	2.43736	0.0826341
$871$	9.08833	0.307946
$872$	17.7028	0.599493
$873$	41.7063	1.41154
$874$	12.1240	0.410099
$875$	−2.34977	−0.0794366
$876$	−0.813996	−0.0275024
$877$	−29.2500	−0.987701	−0.493851	−	0.869547i	$-0.664411\pi$
$877$	−29.2500	−0.987701	−0.493851	+	0.869547i	$0.664411\pi$
$878$	2.64494	0.0892623
$879$	9.53406	0.321576
$880$	−6.18325	−0.208437
$881$	−48.2783	−1.62654	−0.813269	−	0.581889i	$-0.802314\pi$
$881$	−48.2783	−1.62654	−0.813269	+	0.581889i	$0.802314\pi$
$882$	−6.27133	−0.211166
$883$	50.6387	1.70413	0.852065	−	0.523437i	$-0.175350\pi$
$883$	50.6387	1.70413	0.852065	+	0.523437i	$0.175350\pi$
$884$	−9.33331	−0.313913
$885$	−3.59719	−0.120918
$886$	34.3145	1.15282
$887$	−51.0857	−1.71529	−0.857645	−	0.514242i	$-0.828073\pi$
$887$	−51.0857	−1.71529	−0.857645	+	0.514242i	$0.828073\pi$
$888$	−7.89821	−0.265046
$889$	−17.6697	−0.592623
$890$	−6.05678	−0.203024
$891$	−8.76751	−0.293722
$892$	−0.599988	−0.0200891
$893$	14.7626	0.494013
$894$	−13.0590	−0.436760
$895$	−10.6240	−0.355121
$896$	−31.7864	−1.06191
$897$	−9.70602	−0.324075
$898$	−7.67132	−0.255995
$899$	−21.2171	−0.707629
$900$	−1.14531	−0.0381769
$901$	−20.7911	−0.692650
$902$	12.4625	0.414955
$903$	5.96231	0.198413
$904$	19.4449	0.646728
$905$	−11.4663	−0.381152
$906$	−2.27597	−0.0756141
$907$	−21.9890	−0.730132	−0.365066	−	0.930982i	$-0.618954\pi$
$907$	−21.9890	−0.730132	−0.365066	+	0.930982i	$0.618954\pi$
$908$	7.84102	0.260214
$909$	45.3201	1.50317
$910$	−24.9469	−0.826983
$911$	7.47833	0.247768	0.123884	−	0.992297i	$-0.460465\pi$
$911$	7.47833	0.247768	0.123884	+	0.992297i	$0.460465\pi$
$912$	6.99100	0.231495
$913$	−14.3718	−0.475636
$914$	4.22808	0.139852
$915$	−0.628825	−0.0207883
$916$	−3.35443	−0.110833
$917$	−13.9465	−0.460556
$918$	−15.1689	−0.500648
$919$	−7.04314	−0.232332	−0.116166	−	0.993230i	$-0.537060\pi$
$919$	−7.04314	−0.232332	−0.116166	+	0.993230i	$0.537060\pi$
$920$	6.68333	0.220343
$921$	−15.0305	−0.495273
$922$	4.73105	0.155809
$923$	−104.543	−3.44107
$924$	0.684477	0.0225176
$925$	6.14406	0.202016
$926$	−22.8364	−0.750451
$927$	27.4426	0.901333
$928$	−7.00804	−0.230050
$929$	−2.95612	−0.0969870	−0.0484935	−	0.998823i	$-0.515442\pi$
$929$	−2.95612	−0.0969870	−0.0484935	+	0.998823i	$0.515442\pi$
$930$	−5.76286	−0.188972
$931$	−4.23777	−0.138887
$932$	0.579659	0.0189874
$933$	4.13100	0.135243
$934$	5.30156	0.173472
$935$	4.31639	0.141161
$936$	45.7326	1.49482
$937$	−19.8935	−0.649894	−0.324947	−	0.945732i	$-0.605346\pi$
$937$	−19.8935	−0.649894	−0.324947	+	0.945732i	$0.605346\pi$
$938$	4.86794	0.158944
$939$	−7.92715	−0.258693
$940$	−2.16371	−0.0705726
$941$	−29.7446	−0.969646	−0.484823	−	0.874612i	$-0.661116\pi$
$941$	−29.7446	−0.969646	−0.484823	+	0.874612i	$0.661116\pi$
$942$	−1.07528	−0.0350345
$943$	−16.4302	−0.535042
$944$	32.0753	1.04396
$945$	−7.03771	−0.228937
$946$	−10.0062	−0.325330
$947$	1.96343	0.0638029	0.0319015	−	0.999491i	$-0.489844\pi$
$947$	1.96343	0.0638029	0.0319015	+	0.999491i	$0.489844\pi$
$948$	−1.43788	−0.0467000
$949$	−25.2845	−0.820769
$950$	−4.45865	−0.144658
$951$	−4.45493	−0.144461
$952$	18.8022	0.609384
$953$	35.7977	1.15960	0.579801	−	0.814758i	$-0.303130\pi$
$953$	35.7977	1.15960	0.579801	+	0.814758i	$0.303130\pi$
$954$	−27.0866	−0.876961
$955$	−17.0280	−0.551013
$956$	−3.01597	−0.0975436
$957$	−2.07727	−0.0671485
$958$	−46.8400	−1.51333
$959$	−25.8507	−0.834764
$960$	2.97495	0.0960162
$961$	19.1655	0.618241
$962$	65.2301	2.10310
$963$	−34.4128	−1.10894
$964$	−1.93777	−0.0624114
$965$	0.0310591	0.000999829 0
$966$	−5.19879	−0.167268
$967$	11.8416	0.380802	0.190401	−	0.981706i	$-0.439021\pi$
$967$	11.8416	0.380802	0.190401	+	0.981706i	$0.439021\pi$
$968$	−22.7157	−0.730109
$969$	−4.88026	−0.156777
$970$	−23.7968	−0.764069
$971$	−24.1713	−0.775693	−0.387847	−	0.921724i	$-0.626781\pi$
$971$	−24.1713	−0.775693	−0.387847	+	0.921724i	$0.626781\pi$
$972$	−5.22734	−0.167667
$973$	11.4961	0.368549
$974$	41.1364	1.31809
$975$	3.56943	0.114313
$976$	5.60709	0.179478
$977$	9.43501	0.301853	0.150926	−	0.988545i	$-0.451774\pi$
$977$	9.43501	0.301853	0.150926	+	0.988545i	$0.451774\pi$
$978$	2.64413	0.0845498
$979$	5.16197	0.164977
$980$	0.621116	0.0198408
$981$	−19.6376	−0.626980
$982$	−51.0225	−1.62819
$983$	30.5385	0.974025	0.487013	−	0.873395i	$-0.338087\pi$
$983$	30.5385	0.974025	0.487013	+	0.873395i	$0.338087\pi$
$984$	−7.76739	−0.247615
$985$	2.65695	0.0846574
$986$	15.1716	0.483161
$987$	−6.33026	−0.201494
$988$	−8.21659	−0.261404
$989$	13.1920	0.419481
$990$	5.62340	0.178723
$991$	8.56061	0.271937	0.135968	−	0.990713i	$-0.456585\pi$
$991$	8.56061	0.271937	0.135968	+	0.990713i	$0.456585\pi$
$992$	16.5697	0.526090
$993$	5.09062	0.161546
$994$	−55.9959	−1.77608
$995$	1.78754	0.0566688
$996$	−2.38160	−0.0754639
$997$	−40.4711	−1.28173	−0.640866	−	0.767653i	$-0.721425\pi$
$997$	−40.4711	−1.28173	−0.640866	+	0.767653i	$0.721425\pi$
$998$	55.8639	1.76834
$999$	18.4019	0.582210

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6005.2.a.d.1.20	✓	83

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6005.2.a.d.1.20	✓	83	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:	\( N \)	\(=\)	\( 6005 = 5 \cdot 1201 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6005.a (trivial)

\(f(q)\)	\(=\)	\(q-1.55566 q^{2} -0.523024 q^{3} +0.420073 q^{4} -1.00000 q^{5} +0.813646 q^{6} +2.34977 q^{7} +2.45783 q^{8} -2.72645 q^{9} +O(q^{10})\)	\(q-1.55566 q^{2} -0.523024 q^{3} +0.420073 q^{4} -1.00000 q^{5} +0.813646 q^{6} +2.34977 q^{7} +2.45783 q^{8} -2.72645 q^{9} +1.55566 q^{10} -1.32583 q^{11} -0.219708 q^{12} -6.82461 q^{13} -3.65544 q^{14} +0.523024 q^{15} -4.66368 q^{16} +3.25562 q^{17} +4.24142 q^{18} +2.86608 q^{19} -0.420073 q^{20} -1.22898 q^{21} +2.06254 q^{22} -2.71920 q^{23} -1.28550 q^{24} +1.00000 q^{25} +10.6168 q^{26} +2.99507 q^{27} +0.987074 q^{28} -2.99560 q^{29} -0.813646 q^{30} +7.08276 q^{31} +2.33945 q^{32} +0.693440 q^{33} -5.06463 q^{34} -2.34977 q^{35} -1.14531 q^{36} +6.14406 q^{37} -4.45865 q^{38} +3.56943 q^{39} -2.45783 q^{40} +6.04230 q^{41} +1.91188 q^{42} -4.85141 q^{43} -0.556945 q^{44} +2.72645 q^{45} +4.23015 q^{46} +5.15080 q^{47} +2.43922 q^{48} -1.47859 q^{49} -1.55566 q^{50} -1.70276 q^{51} -2.86684 q^{52} -6.38621 q^{53} -4.65930 q^{54} +1.32583 q^{55} +5.77532 q^{56} -1.49903 q^{57} +4.66012 q^{58} -6.87768 q^{59} +0.219708 q^{60} -1.20229 q^{61} -11.0184 q^{62} -6.40652 q^{63} +5.68799 q^{64} +6.82461 q^{65} -1.07876 q^{66} -1.33170 q^{67} +1.36760 q^{68} +1.42221 q^{69} +3.65544 q^{70} +15.3185 q^{71} -6.70113 q^{72} +3.70490 q^{73} -9.55806 q^{74} -0.523024 q^{75} +1.20396 q^{76} -3.11539 q^{77} -5.55282 q^{78} +6.54448 q^{79} +4.66368 q^{80} +6.61285 q^{81} -9.39975 q^{82} +10.8398 q^{83} -0.516263 q^{84} -3.25562 q^{85} +7.54714 q^{86} +1.56677 q^{87} -3.25866 q^{88} -3.89339 q^{89} -4.24142 q^{90} -16.0363 q^{91} -1.14226 q^{92} -3.70445 q^{93} -8.01289 q^{94} -2.86608 q^{95} -1.22359 q^{96} -15.2969 q^{97} +2.30018 q^{98} +3.61480 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 83 q + q^{2} - 4 q^{3} + 61 q^{4} - 83 q^{5} - 6 q^{6} + 2 q^{7} - 3 q^{8} + 61 q^{9}+O(q^{10}) \) 83 * q + q^2 - 4 * q^3 + 61 * q^4 - 83 * q^5 - 6 * q^6 + 2 * q^7 - 3 * q^8 + 61 * q^9	\( 83 q + q^{2} - 4 q^{3} + 61 q^{4} - 83 q^{5} - 6 q^{6} + 2 q^{7} - 3 q^{8} + 61 q^{9} - q^{10} - 26 q^{11} - 12 q^{12} - 15 q^{13} - 21 q^{14} + 4 q^{15} + 5 q^{16} + 8 q^{17} - 12 q^{18} - 79 q^{19} - 61 q^{20} - 34 q^{21} - 25 q^{22} + 31 q^{23} - 42 q^{24} + 83 q^{25} - 13 q^{26} - 25 q^{27} - 16 q^{28} - 16 q^{29} + 6 q^{30} - 40 q^{31} + 15 q^{32} - 33 q^{33} - 54 q^{34} - 2 q^{35} + 11 q^{36} - 45 q^{37} + 10 q^{38} - 54 q^{39} + 3 q^{40} - 27 q^{41} - 28 q^{42} - 101 q^{43} - 51 q^{44} - 61 q^{45} - 46 q^{46} + 71 q^{47} - 14 q^{48} + 23 q^{49} + q^{50} - 71 q^{51} - 34 q^{52} - 49 q^{53} - 25 q^{54} + 26 q^{55} - 41 q^{56} - 20 q^{57} - 43 q^{58} - 60 q^{59} + 12 q^{60} - 38 q^{61} - 2 q^{62} + 36 q^{63} - 113 q^{64} + 15 q^{65} - 42 q^{66} - 164 q^{67} + 10 q^{68} - 93 q^{69} + 21 q^{70} - 78 q^{71} + q^{72} - 18 q^{73} - 23 q^{74} - 4 q^{75} - 112 q^{76} - 35 q^{77} - 44 q^{78} - 124 q^{79} - 5 q^{80} - 45 q^{81} - 34 q^{82} + 5 q^{83} - 60 q^{84} - 8 q^{85} - 25 q^{86} + 12 q^{87} - 149 q^{88} - 44 q^{89} + 12 q^{90} - 192 q^{91} + 35 q^{92} - 13 q^{93} - 32 q^{94} + 79 q^{95} - 59 q^{96} - 31 q^{97} + 25 q^{98} - 134 q^{99}+O(q^{100}) \) 83 * q + q^2 - 4 * q^3 + 61 * q^4 - 83 * q^5 - 6 * q^6 + 2 * q^7 - 3 * q^8 + 61 * q^9 - q^10 - 26 * q^11 - 12 * q^12 - 15 * q^13 - 21 * q^14 + 4 * q^15 + 5 * q^16 + 8 * q^17 - 12 * q^18 - 79 * q^19 - 61 * q^20 - 34 * q^21 - 25 * q^22 + 31 * q^23 - 42 * q^24 + 83 * q^25 - 13 * q^26 - 25 * q^27 - 16 * q^28 - 16 * q^29 + 6 * q^30 - 40 * q^31 + 15 * q^32 - 33 * q^33 - 54 * q^34 - 2 * q^35 + 11 * q^36 - 45 * q^37 + 10 * q^38 - 54 * q^39 + 3 * q^40 - 27 * q^41 - 28 * q^42 - 101 * q^43 - 51 * q^44 - 61 * q^45 - 46 * q^46 + 71 * q^47 - 14 * q^48 + 23 * q^49 + q^50 - 71 * q^51 - 34 * q^52 - 49 * q^53 - 25 * q^54 + 26 * q^55 - 41 * q^56 - 20 * q^57 - 43 * q^58 - 60 * q^59 + 12 * q^60 - 38 * q^61 - 2 * q^62 + 36 * q^63 - 113 * q^64 + 15 * q^65 - 42 * q^66 - 164 * q^67 + 10 * q^68 - 93 * q^69 + 21 * q^70 - 78 * q^71 + q^72 - 18 * q^73 - 23 * q^74 - 4 * q^75 - 112 * q^76 - 35 * q^77 - 44 * q^78 - 124 * q^79 - 5 * q^80 - 45 * q^81 - 34 * q^82 + 5 * q^83 - 60 * q^84 - 8 * q^85 - 25 * q^86 + 12 * q^87 - 149 * q^88 - 44 * q^89 + 12 * q^90 - 192 * q^91 + 35 * q^92 - 13 * q^93 - 32 * q^94 + 79 * q^95 - 59 * q^96 - 31 * q^97 + 25 * q^98 - 134 * q^99

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