LMFDB - Embedded newform 8031.2.a.a.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8031,2,Mod(1,8031)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8031, 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("8031.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8031 = 3 \cdot 2677 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8031.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:	$64.1278578633$
Analytic rank:	$1$
Dimension:	$92$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	8031.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.49908 q^{2} +1.00000 q^{3} +4.24541 q^{4} -0.718338 q^{5} -2.49908 q^{6} -1.10283 q^{7} -5.61146 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.49908 q^{2} +1.00000 q^{3} +4.24541 q^{4} -0.718338 q^{5} -2.49908 q^{6} -1.10283 q^{7} -5.61146 q^{8} +1.00000 q^{9} +1.79519 q^{10} +3.34169 q^{11} +4.24541 q^{12} +3.56169 q^{13} +2.75606 q^{14} -0.718338 q^{15} +5.53268 q^{16} +3.38914 q^{17} -2.49908 q^{18} +3.65353 q^{19} -3.04964 q^{20} -1.10283 q^{21} -8.35117 q^{22} -1.81135 q^{23} -5.61146 q^{24} -4.48399 q^{25} -8.90095 q^{26} +1.00000 q^{27} -4.68196 q^{28} +5.01405 q^{29} +1.79519 q^{30} -10.9411 q^{31} -2.60370 q^{32} +3.34169 q^{33} -8.46974 q^{34} +0.792205 q^{35} +4.24541 q^{36} +6.93538 q^{37} -9.13047 q^{38} +3.56169 q^{39} +4.03093 q^{40} -1.59903 q^{41} +2.75606 q^{42} -11.3210 q^{43} +14.1869 q^{44} -0.718338 q^{45} +4.52672 q^{46} -0.808532 q^{47} +5.53268 q^{48} -5.78377 q^{49} +11.2059 q^{50} +3.38914 q^{51} +15.1208 q^{52} -9.45317 q^{53} -2.49908 q^{54} -2.40047 q^{55} +6.18849 q^{56} +3.65353 q^{57} -12.5305 q^{58} -3.95796 q^{59} -3.04964 q^{60} -7.97305 q^{61} +27.3428 q^{62} -1.10283 q^{63} -4.55850 q^{64} -2.55850 q^{65} -8.35117 q^{66} -15.5239 q^{67} +14.3883 q^{68} -1.81135 q^{69} -1.97978 q^{70} -6.10152 q^{71} -5.61146 q^{72} -10.6722 q^{73} -17.3321 q^{74} -4.48399 q^{75} +15.5107 q^{76} -3.68532 q^{77} -8.90095 q^{78} -7.94824 q^{79} -3.97434 q^{80} +1.00000 q^{81} +3.99610 q^{82} +1.23161 q^{83} -4.68196 q^{84} -2.43455 q^{85} +28.2922 q^{86} +5.01405 q^{87} -18.7518 q^{88} -8.02975 q^{89} +1.79519 q^{90} -3.92794 q^{91} -7.68994 q^{92} -10.9411 q^{93} +2.02059 q^{94} -2.62447 q^{95} -2.60370 q^{96} +18.7561 q^{97} +14.4541 q^{98} +3.34169 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 92 q - 6 q^{2} + 92 q^{3} + 70 q^{4} - 18 q^{5} - 6 q^{6} - 42 q^{7} - 15 q^{8} + 92 q^{9}+O(q^{10}) $ 92 * q - 6 * q^2 + 92 * q^3 + 70 * q^4 - 18 * q^5 - 6 * q^6 - 42 * q^7 - 15 * q^8 + 92 * q^9	\( 92 q - 6 q^{2} + 92 q^{3} + 70 q^{4} - 18 q^{5} - 6 q^{6} - 42 q^{7} - 15 q^{8} + 92 q^{9} - 44 q^{10} - 24 q^{11} + 70 q^{12} - 48 q^{13} - 29 q^{14} - 18 q^{15} + 26 q^{16} - 69 q^{17} - 6 q^{18} - 74 q^{19} - 42 q^{20} - 42 q^{21} - 62 q^{22} - 19 q^{23} - 15 q^{24} + 16 q^{25} - 27 q^{26} + 92 q^{27} - 101 q^{28} - 54 q^{29} - 44 q^{30} - 67 q^{31} - 36 q^{32} - 24 q^{33} - 63 q^{34} - 31 q^{35} + 70 q^{36} - 70 q^{37} - 18 q^{38} - 48 q^{39} - 125 q^{40} - 98 q^{41} - 29 q^{42} - 159 q^{43} - 52 q^{44} - 18 q^{45} - 68 q^{46} - 15 q^{47} + 26 q^{48} - 28 q^{49} - 7 q^{50} - 69 q^{51} - 98 q^{52} - 23 q^{53} - 6 q^{54} - 93 q^{55} - 48 q^{56} - 74 q^{57} - 37 q^{58} - 36 q^{59} - 42 q^{60} - 172 q^{61} - 26 q^{62} - 42 q^{63} - 23 q^{64} - 66 q^{65} - 62 q^{66} - 143 q^{67} - 74 q^{68} - 19 q^{69} - 30 q^{70} - 9 q^{71} - 15 q^{72} - 134 q^{73} - 19 q^{74} + 16 q^{75} - 157 q^{76} - 25 q^{77} - 27 q^{78} - 138 q^{79} - 29 q^{80} + 92 q^{81} - 61 q^{82} - 24 q^{83} - 101 q^{84} - 84 q^{85} + 14 q^{86} - 54 q^{87} - 140 q^{88} - 148 q^{89} - 44 q^{90} - 115 q^{91} - 12 q^{92} - 67 q^{93} - 79 q^{94} - 10 q^{95} - 36 q^{96} - 165 q^{97} + 36 q^{98} - 24 q^{99}+O(q^{100}) \) 92 * q - 6 * q^2 + 92 * q^3 + 70 * q^4 - 18 * q^5 - 6 * q^6 - 42 * q^7 - 15 * q^8 + 92 * q^9 - 44 * q^10 - 24 * q^11 + 70 * q^12 - 48 * q^13 - 29 * q^14 - 18 * q^15 + 26 * q^16 - 69 * q^17 - 6 * q^18 - 74 * q^19 - 42 * q^20 - 42 * q^21 - 62 * q^22 - 19 * q^23 - 15 * q^24 + 16 * q^25 - 27 * q^26 + 92 * q^27 - 101 * q^28 - 54 * q^29 - 44 * q^30 - 67 * q^31 - 36 * q^32 - 24 * q^33 - 63 * q^34 - 31 * q^35 + 70 * q^36 - 70 * q^37 - 18 * q^38 - 48 * q^39 - 125 * q^40 - 98 * q^41 - 29 * q^42 - 159 * q^43 - 52 * q^44 - 18 * q^45 - 68 * q^46 - 15 * q^47 + 26 * q^48 - 28 * q^49 - 7 * q^50 - 69 * q^51 - 98 * q^52 - 23 * q^53 - 6 * q^54 - 93 * q^55 - 48 * q^56 - 74 * q^57 - 37 * q^58 - 36 * q^59 - 42 * q^60 - 172 * q^61 - 26 * q^62 - 42 * q^63 - 23 * q^64 - 66 * q^65 - 62 * q^66 - 143 * q^67 - 74 * q^68 - 19 * q^69 - 30 * q^70 - 9 * q^71 - 15 * q^72 - 134 * q^73 - 19 * q^74 + 16 * q^75 - 157 * q^76 - 25 * q^77 - 27 * q^78 - 138 * q^79 - 29 * q^80 + 92 * q^81 - 61 * q^82 - 24 * q^83 - 101 * q^84 - 84 * q^85 + 14 * q^86 - 54 * q^87 - 140 * q^88 - 148 * q^89 - 44 * q^90 - 115 * q^91 - 12 * q^92 - 67 * q^93 - 79 * q^94 - 10 * q^95 - 36 * q^96 - 165 * q^97 + 36 * q^98 - 24 * 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 $

$2$	−2.49908	−1.76712	−0.883559	−	0.468320i	$-0.844859\pi$
$2$	−2.49908	−1.76712	−0.883559	+	0.468320i	$0.844859\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.24541	2.12270
$5$	−0.718338	−0.321251	−0.160625	−	0.987015i	$-0.551351\pi$
$5$	−0.718338	−0.321251	−0.160625	+	0.987015i	$0.551351\pi$
$6$	−2.49908	−1.02025
$7$	−1.10283	−0.416830	−0.208415	−	0.978040i	$-0.566831\pi$
$7$	−1.10283	−0.416830	−0.208415	+	0.978040i	$0.566831\pi$
$8$	−5.61146	−1.98395
$9$	1.00000	0.333333
$10$	1.79519	0.567688
$11$	3.34169	1.00756	0.503779	−	0.863832i	$-0.331942\pi$
$11$	3.34169	1.00756	0.503779	+	0.863832i	$0.331942\pi$
$12$	4.24541	1.22554
$13$	3.56169	0.987835	0.493918	−	0.869509i	$-0.335564\pi$
$13$	3.56169	0.987835	0.493918	+	0.869509i	$0.335564\pi$
$14$	2.75606	0.736588
$15$	−0.718338	−0.185474
$16$	5.53268	1.38317
$17$	3.38914	0.821988	0.410994	−	0.911638i	$-0.365182\pi$
$17$	3.38914	0.821988	0.410994	+	0.911638i	$0.365182\pi$
$18$	−2.49908	−0.589039
$19$	3.65353	0.838177	0.419089	−	0.907945i	$-0.362350\pi$
$19$	3.65353	0.838177	0.419089	+	0.907945i	$0.362350\pi$
$20$	−3.04964	−0.681920
$21$	−1.10283	−0.240657
$22$	−8.35117	−1.78047
$23$	−1.81135	−0.377693	−0.188847	−	0.982007i	$-0.560475\pi$
$23$	−1.81135	−0.377693	−0.188847	+	0.982007i	$0.560475\pi$
$24$	−5.61146	−1.14543
$25$	−4.48399	−0.896798
$26$	−8.90095	−1.74562
$27$	1.00000	0.192450
$28$	−4.68196	−0.884808
$29$	5.01405	0.931085	0.465543	−	0.885026i	$-0.345859\pi$
$29$	5.01405	0.931085	0.465543	+	0.885026i	$0.345859\pi$
$30$	1.79519	0.327755
$31$	−10.9411	−1.96509	−0.982544	−	0.186031i	$-0.940437\pi$
$31$	−10.9411	−1.96509	−0.982544	+	0.186031i	$0.940437\pi$
$32$	−2.60370	−0.460274
$33$	3.34169	0.581714
$34$	−8.46974	−1.45255
$35$	0.792205	0.133907
$36$	4.24541	0.707568
$37$	6.93538	1.14017	0.570085	−	0.821586i	$-0.306910\pi$
$37$	6.93538	1.14017	0.570085	+	0.821586i	$0.306910\pi$
$38$	−9.13047	−1.48116
$39$	3.56169	0.570327
$40$	4.03093	0.637346
$41$	−1.59903	−0.249726	−0.124863	−	0.992174i	$-0.539849\pi$
$41$	−1.59903	−0.249726	−0.124863	+	0.992174i	$0.539849\pi$
$42$	2.75606	0.425270
$43$	−11.3210	−1.72644	−0.863222	−	0.504825i	$-0.831557\pi$
$43$	−11.3210	−1.72644	−0.863222	+	0.504825i	$0.831557\pi$
$44$	14.1869	2.13875
$45$	−0.718338	−0.107084
$46$	4.52672	0.667429
$47$	−0.808532	−0.117936	−0.0589682	−	0.998260i	$-0.518781\pi$
$47$	−0.808532	−0.117936	−0.0589682	+	0.998260i	$0.518781\pi$
$48$	5.53268	0.798574
$49$	−5.78377	−0.826252
$50$	11.2059	1.58475
$51$	3.38914	0.474575
$52$	15.1208	2.09688
$53$	−9.45317	−1.29849	−0.649246	−	0.760578i	$-0.724915\pi$
$53$	−9.45317	−1.29849	−0.649246	+	0.760578i	$0.724915\pi$
$54$	−2.49908	−0.340082
$55$	−2.40047	−0.323679
$56$	6.18849	0.826971
$57$	3.65353	0.483922
$58$	−12.5305	−1.64534
$59$	−3.95796	−0.515282	−0.257641	−	0.966241i	$-0.582945\pi$
$59$	−3.95796	−0.515282	−0.257641	+	0.966241i	$0.582945\pi$
$60$	−3.04964	−0.393707
$61$	−7.97305	−1.02084	−0.510422	−	0.859924i	$-0.670511\pi$
$61$	−7.97305	−1.02084	−0.510422	+	0.859924i	$0.670511\pi$
$62$	27.3428	3.47254
$63$	−1.10283	−0.138943
$64$	−4.55850	−0.569812
$65$	−2.55850	−0.317343
$66$	−8.35117	−1.02796
$67$	−15.5239	−1.89654	−0.948272	−	0.317459i	$-0.897170\pi$
$67$	−15.5239	−1.89654	−0.948272	+	0.317459i	$0.897170\pi$
$68$	14.3883	1.74484
$69$	−1.81135	−0.218061
$70$	−1.97978	−0.236630
$71$	−6.10152	−0.724117	−0.362058	−	0.932155i	$-0.617926\pi$
$71$	−6.10152	−0.724117	−0.362058	+	0.932155i	$0.617926\pi$
$72$	−5.61146	−0.661317
$73$	−10.6722	−1.24909	−0.624545	−	0.780989i	$-0.714715\pi$
$73$	−10.6722	−1.24909	−0.624545	+	0.780989i	$0.714715\pi$
$74$	−17.3321	−2.01481
$75$	−4.48399	−0.517767
$76$	15.5107	1.77920
$77$	−3.68532	−0.419981
$78$	−8.90095	−1.00783
$79$	−7.94824	−0.894247	−0.447123	−	0.894472i	$-0.647551\pi$
$79$	−7.94824	−0.894247	−0.447123	+	0.894472i	$0.647551\pi$
$80$	−3.97434	−0.444345
$81$	1.00000	0.111111
$82$	3.99610	0.441296
$83$	1.23161	0.135187	0.0675936	−	0.997713i	$-0.478468\pi$
$83$	1.23161	0.135187	0.0675936	+	0.997713i	$0.478468\pi$
$84$	−4.68196	−0.510844
$85$	−2.43455	−0.264064
$86$	28.2922	3.05083
$87$	5.01405	0.537562
$88$	−18.7518	−1.99895
$89$	−8.02975	−0.851152	−0.425576	−	0.904923i	$-0.639928\pi$
$89$	−8.02975	−0.851152	−0.425576	+	0.904923i	$0.639928\pi$
$90$	1.79519	0.189229
$91$	−3.92794	−0.411760
$92$	−7.68994	−0.801732
$93$	−10.9411	−1.13454
$94$	2.02059	0.208408
$95$	−2.62447	−0.269265
$96$	−2.60370	−0.265739
$97$	18.7561	1.90440	0.952198	−	0.305483i	$-0.0988178\pi$
$97$	18.7561	1.90440	0.952198	+	0.305483i	$0.0988178\pi$
$98$	14.4541	1.46009
$99$	3.34169	0.335853
$100$	−19.0364	−1.90364
$101$	6.79640	0.676267	0.338133	−	0.941098i	$-0.390204\pi$
$101$	6.79640	0.676267	0.338133	+	0.941098i	$0.390204\pi$
$102$	−8.46974	−0.838630
$103$	1.60603	0.158247	0.0791234	−	0.996865i	$-0.474788\pi$
$103$	1.60603	0.158247	0.0791234	+	0.996865i	$0.474788\pi$
$104$	−19.9863	−1.95982
$105$	0.792205	0.0773113
$106$	23.6242	2.29459
$107$	12.9820	1.25502	0.627511	−	0.778608i	$-0.284074\pi$
$107$	12.9820	1.25502	0.627511	+	0.778608i	$0.284074\pi$
$108$	4.24541	0.408515
$109$	−2.52439	−0.241793	−0.120896	−	0.992665i	$-0.538577\pi$
$109$	−2.52439	−0.241793	−0.120896	+	0.992665i	$0.538577\pi$
$110$	5.99896	0.571979
$111$	6.93538	0.658277
$112$	−6.10161	−0.576548
$113$	−18.9351	−1.78127	−0.890634	−	0.454721i	$-0.849739\pi$
$113$	−18.9351	−1.78127	−0.890634	+	0.454721i	$0.849739\pi$
$114$	−9.13047	−0.855147
$115$	1.30117	0.121334
$116$	21.2867	1.97642
$117$	3.56169	0.329278
$118$	9.89126	0.910564
$119$	−3.73765	−0.342630
$120$	4.03093	0.367972
$121$	0.166918	0.0151743
$122$	19.9253	1.80395
$123$	−1.59903	−0.144180
$124$	−46.4496	−4.17130
$125$	6.81271	0.609348
$126$	2.75606	0.245529
$127$	6.06920	0.538554	0.269277	−	0.963063i	$-0.413215\pi$
$127$	6.06920	0.538554	0.269277	+	0.963063i	$0.413215\pi$
$128$	16.5995	1.46720
$129$	−11.3210	−0.996762
$130$	6.39390	0.560782
$131$	10.6150	0.927434	0.463717	−	0.885983i	$-0.346515\pi$
$131$	10.6150	0.927434	0.463717	+	0.885983i	$0.346515\pi$
$132$	14.1869	1.23481
$133$	−4.02922	−0.349378
$134$	38.7954	3.35142
$135$	−0.718338	−0.0618247
$136$	−19.0180	−1.63078
$137$	−7.57690	−0.647339	−0.323669	−	0.946170i	$-0.604917\pi$
$137$	−7.57690	−0.647339	−0.323669	+	0.946170i	$0.604917\pi$
$138$	4.52672	0.385340
$139$	−3.09124	−0.262196	−0.131098	−	0.991369i	$-0.541850\pi$
$139$	−3.09124	−0.262196	−0.131098	+	0.991369i	$0.541850\pi$
$140$	3.36323	0.284245
$141$	−0.808532	−0.0680907
$142$	15.2482	1.27960
$143$	11.9021	0.995302
$144$	5.53268	0.461057
$145$	−3.60178	−0.299112
$146$	26.6708	2.20729
$147$	−5.78377	−0.477037
$148$	29.4435	2.42024
$149$	−14.9716	−1.22653	−0.613263	−	0.789879i	$-0.710143\pi$
$149$	−14.9716	−1.22653	−0.613263	+	0.789879i	$0.710143\pi$
$150$	11.2059	0.914954
$151$	11.4360	0.930651	0.465325	−	0.885140i	$-0.345937\pi$
$151$	11.4360	0.930651	0.465325	+	0.885140i	$0.345937\pi$
$152$	−20.5016	−1.66290
$153$	3.38914	0.273996
$154$	9.20991	0.742156
$155$	7.85944	0.631286
$156$	15.1208	1.21064
$157$	−12.5032	−0.997864	−0.498932	−	0.866641i	$-0.666274\pi$
$157$	−12.5032	−0.997864	−0.498932	+	0.866641i	$0.666274\pi$
$158$	19.8633	1.58024
$159$	−9.45317	−0.749685
$160$	1.87034	0.147863
$161$	1.99762	0.157434
$162$	−2.49908	−0.196346
$163$	−2.45177	−0.192038	−0.0960189	−	0.995380i	$-0.530611\pi$
$163$	−2.45177	−0.192038	−0.0960189	+	0.995380i	$0.530611\pi$
$164$	−6.78853	−0.530095
$165$	−2.40047	−0.186876
$166$	−3.07791	−0.238892
$167$	13.0133	1.00700	0.503499	−	0.863996i	$-0.332046\pi$
$167$	13.0133	1.00700	0.503499	+	0.863996i	$0.332046\pi$
$168$	6.18849	0.477452
$169$	−0.314366	−0.0241820
$170$	6.08414	0.466632
$171$	3.65353	0.279392
$172$	−48.0625	−3.66473
$173$	15.6871	1.19267	0.596333	−	0.802737i	$-0.296624\pi$
$173$	15.6871	1.19267	0.596333	+	0.802737i	$0.296624\pi$
$174$	−12.5305	−0.949936
$175$	4.94508	0.373813
$176$	18.4885	1.39363
$177$	−3.95796	−0.297498
$178$	20.0670	1.50409
$179$	25.2376	1.88635	0.943174	−	0.332300i	$-0.107825\pi$
$179$	25.2376	1.88635	0.943174	+	0.332300i	$0.107825\pi$
$180$	−3.04964	−0.227307
$181$	−11.5133	−0.855774	−0.427887	−	0.903832i	$-0.640742\pi$
$181$	−11.5133	−0.855774	−0.427887	+	0.903832i	$0.640742\pi$
$182$	9.81624	0.727628
$183$	−7.97305	−0.589384
$184$	10.1643	0.749325
$185$	−4.98195	−0.366280
$186$	27.3428	2.00487
$187$	11.3255	0.828201
$188$	−3.43255	−0.250344
$189$	−1.10283	−0.0802191
$190$	6.55877	0.475823
$191$	5.22203	0.377853	0.188926	−	0.981991i	$-0.439499\pi$
$191$	5.22203	0.377853	0.188926	+	0.981991i	$0.439499\pi$
$192$	−4.55850	−0.328981
$193$	4.16545	0.299836	0.149918	−	0.988698i	$-0.452099\pi$
$193$	4.16545	0.299836	0.149918	+	0.988698i	$0.452099\pi$
$194$	−46.8731	−3.36529
$195$	−2.55850	−0.183218
$196$	−24.5545	−1.75389
$197$	−3.30895	−0.235753	−0.117876	−	0.993028i	$-0.537609\pi$
$197$	−3.30895	−0.235753	−0.117876	+	0.993028i	$0.537609\pi$
$198$	−8.35117	−0.593492
$199$	16.8370	1.19355	0.596773	−	0.802410i	$-0.296449\pi$
$199$	16.8370	1.19355	0.596773	+	0.802410i	$0.296449\pi$
$200$	25.1617	1.77920
$201$	−15.5239	−1.09497
$202$	−16.9848	−1.19504
$203$	−5.52964	−0.388105
$204$	14.3883	1.00738
$205$	1.14864	0.0802247
$206$	−4.01360	−0.279641
$207$	−1.81135	−0.125898
$208$	19.7057	1.36634
$209$	12.2090	0.844513
$210$	−1.97978	−0.136618
$211$	−7.74096	−0.532910	−0.266455	−	0.963847i	$-0.585852\pi$
$211$	−7.74096	−0.532910	−0.266455	+	0.963847i	$0.585852\pi$
$212$	−40.1326	−2.75632
$213$	−6.10152	−0.418069
$214$	−32.4432	−2.21777
$215$	8.13234	0.554621
$216$	−5.61146	−0.381812
$217$	12.0662	0.819108
$218$	6.30865	0.427276
$219$	−10.6722	−0.721162
$220$	−10.1910	−0.687075
$221$	12.0711	0.811988
$222$	−17.3321	−1.16325
$223$	−8.10207	−0.542555	−0.271277	−	0.962501i	$-0.587446\pi$
$223$	−8.10207	−0.542555	−0.271277	+	0.962501i	$0.587446\pi$
$224$	2.87144	0.191856
$225$	−4.48399	−0.298933
$226$	47.3205	3.14771
$227$	6.62935	0.440006	0.220003	−	0.975499i	$-0.429393\pi$
$227$	6.62935	0.440006	0.220003	+	0.975499i	$0.429393\pi$
$228$	15.5107	1.02722
$229$	−13.4120	−0.886290	−0.443145	−	0.896450i	$-0.646137\pi$
$229$	−13.4120	−0.886290	−0.443145	+	0.896450i	$0.646137\pi$
$230$	−3.25172	−0.214412
$231$	−3.68532	−0.242476
$232$	−28.1361	−1.84723
$233$	−12.0481	−0.789299	−0.394649	−	0.918832i	$-0.629134\pi$
$233$	−12.0481	−0.789299	−0.394649	+	0.918832i	$0.629134\pi$
$234$	−8.90095	−0.581874
$235$	0.580799	0.0378872
$236$	−16.8032	−1.09379
$237$	−7.94824	−0.516293
$238$	9.34069	0.605467
$239$	−20.7963	−1.34520	−0.672600	−	0.740006i	$-0.734823\pi$
$239$	−20.7963	−1.34520	−0.672600	+	0.740006i	$0.734823\pi$
$240$	−3.97434	−0.256542
$241$	−14.6354	−0.942752	−0.471376	−	0.881932i	$-0.656243\pi$
$241$	−14.6354	−0.942752	−0.471376	+	0.881932i	$0.656243\pi$
$242$	−0.417141	−0.0268148
$243$	1.00000	0.0641500
$244$	−33.8488	−2.16695
$245$	4.15470	0.265434
$246$	3.99610	0.254782
$247$	13.0127	0.827981
$248$	61.3958	3.89864
$249$	1.23161	0.0780504
$250$	−17.0255	−1.07679
$251$	−19.7788	−1.24843	−0.624214	−	0.781253i	$-0.714581\pi$
$251$	−19.7788	−1.24843	−0.624214	+	0.781253i	$0.714581\pi$
$252$	−4.68196	−0.294936
$253$	−6.05299	−0.380548
$254$	−15.1674	−0.951688
$255$	−2.43455	−0.152458
$256$	−32.3664	−2.02290
$257$	−22.2097	−1.38540	−0.692701	−	0.721225i	$-0.743579\pi$
$257$	−22.2097	−1.38540	−0.692701	+	0.721225i	$0.743579\pi$
$258$	28.2922	1.76140
$259$	−7.64855	−0.475257
$260$	−10.8619	−0.673625
$261$	5.01405	0.310362
$262$	−26.5277	−1.63889
$263$	−20.9233	−1.29019	−0.645093	−	0.764104i	$-0.723181\pi$
$263$	−20.9233	−1.29019	−0.645093	+	0.764104i	$0.723181\pi$
$264$	−18.7518	−1.15409
$265$	6.79057	0.417141
$266$	10.0694	0.617392
$267$	−8.02975	−0.491413
$268$	−65.9052	−4.02580
$269$	0.824030	0.0502420	0.0251210	−	0.999684i	$-0.492003\pi$
$269$	0.824030	0.0502420	0.0251210	+	0.999684i	$0.492003\pi$
$270$	1.79519	0.109252
$271$	−6.64432	−0.403613	−0.201807	−	0.979425i	$-0.564681\pi$
$271$	−6.64432	−0.403613	−0.201807	+	0.979425i	$0.564681\pi$
$272$	18.7511	1.13695
$273$	−3.92794	−0.237730
$274$	18.9353	1.14392
$275$	−14.9841	−0.903577
$276$	−7.68994	−0.462880
$277$	7.79045	0.468083	0.234041	−	0.972227i	$-0.424805\pi$
$277$	7.79045	0.468083	0.234041	+	0.972227i	$0.424805\pi$
$278$	7.72527	0.463331
$279$	−10.9411	−0.655029
$280$	−4.44543	−0.265665
$281$	−11.3010	−0.674160	−0.337080	−	0.941476i	$-0.609439\pi$
$281$	−11.3010	−0.674160	−0.337080	+	0.941476i	$0.609439\pi$
$282$	2.02059	0.120324
$283$	29.8724	1.77573	0.887864	−	0.460105i	$-0.152188\pi$
$283$	29.8724	1.77573	0.887864	+	0.460105i	$0.152188\pi$
$284$	−25.9034	−1.53709
$285$	−2.62447	−0.155460
$286$	−29.7443	−1.75882
$287$	1.76346	0.104094
$288$	−2.60370	−0.153425
$289$	−5.51371	−0.324336
$290$	9.00115	0.528566
$291$	18.7561	1.09950
$292$	−45.3079	−2.65145
$293$	−13.5014	−0.788761	−0.394381	−	0.918947i	$-0.629041\pi$
$293$	−13.5014	−0.788761	−0.394381	+	0.918947i	$0.629041\pi$
$294$	14.4541	0.842981
$295$	2.84315	0.165535
$296$	−38.9176	−2.26204
$297$	3.34169	0.193905
$298$	37.4154	2.16741
$299$	−6.45148	−0.373099
$300$	−19.0364	−1.09907
$301$	12.4852	0.719634
$302$	−28.5796	−1.64457
$303$	6.79640	0.390443
$304$	20.2138	1.15934
$305$	5.72734	0.327947
$306$	−8.46974	−0.484183
$307$	−5.11999	−0.292213	−0.146107	−	0.989269i	$-0.546674\pi$
$307$	−5.11999	−0.292213	−0.146107	+	0.989269i	$0.546674\pi$
$308$	−15.6457	−0.891496
$309$	1.60603	0.0913639
$310$	−19.6414	−1.11556
$311$	32.5137	1.84368	0.921842	−	0.387566i	$-0.126684\pi$
$311$	32.5137	1.84368	0.921842	+	0.387566i	$0.126684\pi$
$312$	−19.9863	−1.13150
$313$	28.5054	1.61122	0.805612	−	0.592444i	$-0.201837\pi$
$313$	28.5054	1.61122	0.805612	+	0.592444i	$0.201837\pi$
$314$	31.2465	1.76334
$315$	0.792205	0.0446357
$316$	−33.7435	−1.89822
$317$	−18.2715	−1.02623	−0.513115	−	0.858320i	$-0.671508\pi$
$317$	−18.2715	−1.02623	−0.513115	+	0.858320i	$0.671508\pi$
$318$	23.6242	1.32478
$319$	16.7554	0.938123
$320$	3.27454	0.183053
$321$	12.9820	0.724587
$322$	−4.99220	−0.278205
$323$	12.3823	0.688972
$324$	4.24541	0.235856
$325$	−15.9706	−0.885888
$326$	6.12718	0.339353
$327$	−2.52439	−0.139599
$328$	8.97289	0.495445
$329$	0.891673	0.0491595
$330$	5.99896	0.330232
$331$	−25.0751	−1.37825	−0.689127	−	0.724640i	$-0.742006\pi$
$331$	−25.0751	−1.37825	−0.689127	+	0.724640i	$0.742006\pi$
$332$	5.22871	0.286963
$333$	6.93538	0.380057
$334$	−32.5213	−1.77948
$335$	11.1514	0.609266
$336$	−6.10161	−0.332870
$337$	11.3762	0.619701	0.309851	−	0.950785i	$-0.399721\pi$
$337$	11.3762	0.619701	0.309851	+	0.950785i	$0.399721\pi$
$338$	0.785626	0.0427324
$339$	−18.9351	−1.02842
$340$	−10.3357	−0.560530
$341$	−36.5620	−1.97994
$342$	−9.13047	−0.493719
$343$	14.0983	0.761238
$344$	63.5276	3.42518
$345$	1.30117	0.0700524
$346$	−39.2033	−2.10758
$347$	−2.89374	−0.155344	−0.0776721	−	0.996979i	$-0.524749\pi$
$347$	−2.89374	−0.155344	−0.0776721	+	0.996979i	$0.524749\pi$
$348$	21.2867	1.14109
$349$	22.0506	1.18034	0.590171	−	0.807278i	$-0.299060\pi$
$349$	22.0506	1.18034	0.590171	+	0.807278i	$0.299060\pi$
$350$	−12.3582	−0.660571
$351$	3.56169	0.190109
$352$	−8.70078	−0.463753
$353$	31.7567	1.69024	0.845120	−	0.534576i	$-0.179529\pi$
$353$	31.7567	1.69024	0.845120	+	0.534576i	$0.179529\pi$
$354$	9.89126	0.525715
$355$	4.38295	0.232623
$356$	−34.0896	−1.80674
$357$	−3.73765	−0.197817
$358$	−63.0709	−3.33340
$359$	22.3879	1.18159	0.590794	−	0.806823i	$-0.298815\pi$
$359$	22.3879	1.18159	0.590794	+	0.806823i	$0.298815\pi$
$360$	4.03093	0.212449
$361$	−5.65171	−0.297459
$362$	28.7726	1.51225
$363$	0.166918	0.00876090
$364$	−16.6757	−0.874044
$365$	7.66627	0.401271
$366$	19.9253	1.04151
$367$	0.858738	0.0448258	0.0224129	−	0.999749i	$-0.492865\pi$
$367$	0.858738	0.0448258	0.0224129	+	0.999749i	$0.492865\pi$
$368$	−10.0216	−0.522415
$369$	−1.59903	−0.0832421
$370$	12.4503	0.647260
$371$	10.4252	0.541251
$372$	−46.4496	−2.40830
$373$	−30.5378	−1.58119	−0.790595	−	0.612340i	$-0.790229\pi$
$373$	−30.5378	−1.58119	−0.790595	+	0.612340i	$0.790229\pi$
$374$	−28.3033	−1.46353
$375$	6.81271	0.351807
$376$	4.53705	0.233980
$377$	17.8585	0.919758
$378$	2.75606	0.141757
$379$	−24.2002	−1.24308	−0.621540	−	0.783382i	$-0.713493\pi$
$379$	−24.2002	−1.24308	−0.621540	+	0.783382i	$0.713493\pi$
$380$	−11.1420	−0.571570
$381$	6.06920	0.310934
$382$	−13.0503	−0.667710
$383$	11.2428	0.574482	0.287241	−	0.957858i	$-0.407262\pi$
$383$	11.2428	0.574482	0.287241	+	0.957858i	$0.407262\pi$
$384$	16.5995	0.847088
$385$	2.64731	0.134919
$386$	−10.4098	−0.529845
$387$	−11.3210	−0.575481
$388$	79.6274	4.04247
$389$	21.2495	1.07739	0.538697	−	0.842499i	$-0.318917\pi$
$389$	21.2495	1.07739	0.538697	+	0.842499i	$0.318917\pi$
$390$	6.39390	0.323768
$391$	−6.13894	−0.310459
$392$	32.4554	1.63924
$393$	10.6150	0.535454
$394$	8.26933	0.416603
$395$	5.70952	0.287277
$396$	14.1869	0.712916
$397$	17.1263	0.859547	0.429773	−	0.902937i	$-0.358593\pi$
$397$	17.1263	0.859547	0.429773	+	0.902937i	$0.358593\pi$
$398$	−42.0771	−2.10914
$399$	−4.02922	−0.201713
$400$	−24.8085	−1.24042
$401$	7.74776	0.386905	0.193452	−	0.981110i	$-0.438032\pi$
$401$	7.74776	0.386905	0.193452	+	0.981110i	$0.438032\pi$
$402$	38.7954	1.93494
$403$	−38.9690	−1.94118
$404$	28.8535	1.43552
$405$	−0.718338	−0.0356945
$406$	13.8190	0.685827
$407$	23.1759	1.14879
$408$	−19.0180	−0.941534
$409$	−1.53659	−0.0759794	−0.0379897	−	0.999278i	$-0.512095\pi$
$409$	−1.53659	−0.0759794	−0.0379897	+	0.999278i	$0.512095\pi$
$410$	−2.87055	−0.141767
$411$	−7.57690	−0.373741
$412$	6.81826	0.335911
$413$	4.36495	0.214785
$414$	4.52672	0.222476
$415$	−0.884716	−0.0434290
$416$	−9.27358	−0.454675
$417$	−3.09124	−0.151379
$418$	−30.5112	−1.49235
$419$	7.10393	0.347050	0.173525	−	0.984829i	$-0.444484\pi$
$419$	7.10393	0.347050	0.173525	+	0.984829i	$0.444484\pi$
$420$	3.36323	0.164109
$421$	−12.4860	−0.608528	−0.304264	−	0.952588i	$-0.598411\pi$
$421$	−12.4860	−0.608528	−0.304264	+	0.952588i	$0.598411\pi$
$422$	19.3453	0.941715
$423$	−0.808532	−0.0393122
$424$	53.0461	2.57615
$425$	−15.1969	−0.737157
$426$	15.2482	0.738777
$427$	8.79291	0.425519
$428$	55.1141	2.66404
$429$	11.9021	0.574638
$430$	−20.3234	−0.980081
$431$	−18.0556	−0.869707	−0.434853	−	0.900501i	$-0.643200\pi$
$431$	−18.0556	−0.869707	−0.434853	+	0.900501i	$0.643200\pi$
$432$	5.53268	0.266191
$433$	−12.9800	−0.623781	−0.311891	−	0.950118i	$-0.600962\pi$
$433$	−12.9800	−0.623781	−0.311891	+	0.950118i	$0.600962\pi$
$434$	−30.1545	−1.44746
$435$	−3.60178	−0.172692
$436$	−10.7171	−0.513254
$437$	−6.61784	−0.316574
$438$	26.6708	1.27438
$439$	−39.0506	−1.86378	−0.931892	−	0.362737i	$-0.881842\pi$
$439$	−39.0506	−1.86378	−0.931892	+	0.362737i	$0.881842\pi$
$440$	13.4701	0.642163
$441$	−5.78377	−0.275417
$442$	−30.1666	−1.43488
$443$	19.2358	0.913922	0.456961	−	0.889487i	$-0.348938\pi$
$443$	19.2358	0.913922	0.456961	+	0.889487i	$0.348938\pi$
$444$	29.4435	1.39733
$445$	5.76808	0.273433
$446$	20.2477	0.958758
$447$	−14.9716	−0.708135
$448$	5.02725	0.237515
$449$	−19.9528	−0.941632	−0.470816	−	0.882231i	$-0.656041\pi$
$449$	−19.9528	−0.941632	−0.470816	+	0.882231i	$0.656041\pi$
$450$	11.2059	0.528249
$451$	−5.34346	−0.251614
$452$	−80.3874	−3.78111
$453$	11.4360	0.537312
$454$	−16.5673	−0.777542
$455$	2.82159	0.132278
$456$	−20.5016	−0.960078
$457$	0.137499	0.00643192	0.00321596	−	0.999995i	$-0.498976\pi$
$457$	0.137499	0.00643192	0.00321596	+	0.999995i	$0.498976\pi$
$458$	33.5177	1.56618
$459$	3.38914	0.158192
$460$	5.52398	0.257557
$461$	5.01545	0.233593	0.116796	−	0.993156i	$-0.462738\pi$
$461$	5.01545	0.233593	0.116796	+	0.993156i	$0.462738\pi$
$462$	9.20991	0.428484
$463$	10.0893	0.468890	0.234445	−	0.972129i	$-0.424673\pi$
$463$	10.0893	0.468890	0.234445	+	0.972129i	$0.424673\pi$
$464$	27.7411	1.28785
$465$	7.85944	0.364473
$466$	30.1092	1.39478
$467$	−18.3628	−0.849727	−0.424864	−	0.905257i	$-0.639678\pi$
$467$	−18.3628	−0.849727	−0.424864	+	0.905257i	$0.639678\pi$
$468$	15.1208	0.698961
$469$	17.1202	0.790537
$470$	−1.45147	−0.0669511
$471$	−12.5032	−0.576117
$472$	22.2099	1.02230
$473$	−37.8315	−1.73949
$474$	19.8633	0.912351
$475$	−16.3824	−0.751676
$476$	−15.8678	−0.727301
$477$	−9.45317	−0.432831
$478$	51.9716	2.37713
$479$	14.8941	0.680530	0.340265	−	0.940330i	$-0.389483\pi$
$479$	14.8941	0.680530	0.340265	+	0.940330i	$0.389483\pi$
$480$	1.87034	0.0853689
$481$	24.7017	1.12630
$482$	36.5752	1.66595
$483$	1.99762	0.0908946
$484$	0.708634	0.0322106
$485$	−13.4732	−0.611788
$486$	−2.49908	−0.113361
$487$	18.1049	0.820412	0.410206	−	0.911993i	$-0.365457\pi$
$487$	18.1049	0.820412	0.410206	+	0.911993i	$0.365457\pi$
$488$	44.7404	2.02530
$489$	−2.45177	−0.110873
$490$	−10.3829	−0.469053
$491$	−7.24338	−0.326889	−0.163445	−	0.986553i	$-0.552261\pi$
$491$	−7.24338	−0.326889	−0.163445	+	0.986553i	$0.552261\pi$
$492$	−6.78853	−0.306051
$493$	16.9933	0.765341
$494$	−32.5199	−1.46314
$495$	−2.40047	−0.107893
$496$	−60.5339	−2.71805
$497$	6.72893	0.301834
$498$	−3.07791	−0.137924
$499$	2.45289	0.109807	0.0549033	−	0.998492i	$-0.482515\pi$
$499$	2.45289	0.109807	0.0549033	+	0.998492i	$0.482515\pi$
$500$	28.9228	1.29347
$501$	13.0133	0.581391
$502$	49.4289	2.20612
$503$	−11.1779	−0.498397	−0.249199	−	0.968452i	$-0.580167\pi$
$503$	−11.1779	−0.498397	−0.249199	+	0.968452i	$0.580167\pi$
$504$	6.18849	0.275657
$505$	−4.88211	−0.217251
$506$	15.1269	0.672474
$507$	−0.314366	−0.0139615
$508$	25.7662	1.14319
$509$	−3.73395	−0.165504	−0.0827522	−	0.996570i	$-0.526371\pi$
$509$	−3.73395	−0.165504	−0.0827522	+	0.996570i	$0.526371\pi$
$510$	6.08414	0.269410
$511$	11.7696	0.520658
$512$	47.6874	2.10751
$513$	3.65353	0.161307
$514$	55.5038	2.44817
$515$	−1.15367	−0.0508369
$516$	−48.0625	−2.11583
$517$	−2.70187	−0.118828
$518$	19.1143	0.839836
$519$	15.6871	0.688586
$520$	14.3569	0.629592
$521$	−44.0031	−1.92781	−0.963906	−	0.266243i	$-0.914217\pi$
$521$	−44.0031	−1.92781	−0.963906	+	0.266243i	$0.914217\pi$
$522$	−12.5305	−0.548446
$523$	−27.8287	−1.21686	−0.608432	−	0.793606i	$-0.708201\pi$
$523$	−27.8287	−1.21686	−0.608432	+	0.793606i	$0.708201\pi$
$524$	45.0649	1.96867
$525$	4.94508	0.215821
$526$	52.2890	2.27991
$527$	−37.0811	−1.61528
$528$	18.4885	0.804610
$529$	−19.7190	−0.857348
$530$	−16.9702	−0.737138
$531$	−3.95796	−0.171761
$532$	−17.1057	−0.741626
$533$	−5.69524	−0.246688
$534$	20.0670	0.868384
$535$	−9.32550	−0.403177
$536$	87.1117	3.76265
$537$	25.2376	1.08908
$538$	−2.05932	−0.0887835
$539$	−19.3276	−0.832498
$540$	−3.04964	−0.131236
$541$	−2.49151	−0.107119	−0.0535593	−	0.998565i	$-0.517057\pi$
$541$	−2.49151	−0.107119	−0.0535593	+	0.998565i	$0.517057\pi$
$542$	16.6047	0.713232
$543$	−11.5133	−0.494081
$544$	−8.82432	−0.378340
$545$	1.81336	0.0776760
$546$	9.81624	0.420096
$547$	7.02980	0.300573	0.150286	−	0.988643i	$-0.451980\pi$
$547$	7.02980	0.300573	0.150286	+	0.988643i	$0.451980\pi$
$548$	−32.1671	−1.37411
$549$	−7.97305	−0.340281
$550$	37.4465	1.59673
$551$	18.3190	0.780414
$552$	10.1643	0.432623
$553$	8.76555	0.372749
$554$	−19.4690	−0.827157
$555$	−4.98195	−0.211472
$556$	−13.1236	−0.556564
$557$	−6.80517	−0.288344	−0.144172	−	0.989553i	$-0.546052\pi$
$557$	−6.80517	−0.288344	−0.144172	+	0.989553i	$0.546052\pi$
$558$	27.3428	1.15751
$559$	−40.3221	−1.70544
$560$	4.38302	0.185216
$561$	11.3255	0.478162
$562$	28.2421	1.19132
$563$	5.19595	0.218983	0.109492	−	0.993988i	$-0.465078\pi$
$563$	5.19595	0.218983	0.109492	+	0.993988i	$0.465078\pi$
$564$	−3.43255	−0.144536
$565$	13.6018	0.572234
$566$	−74.6535	−3.13792
$567$	−1.10283	−0.0463145
$568$	34.2384	1.43661
$569$	28.0543	1.17610	0.588049	−	0.808825i	$-0.299896\pi$
$569$	28.0543	1.17610	0.588049	+	0.808825i	$0.299896\pi$
$570$	6.55877	0.274717
$571$	−31.2661	−1.30845	−0.654224	−	0.756301i	$-0.727004\pi$
$571$	−31.2661	−1.30845	−0.654224	+	0.756301i	$0.727004\pi$
$572$	50.5292	2.11273
$573$	5.22203	0.218153
$574$	−4.40702	−0.183946
$575$	8.12209	0.338715
$576$	−4.55850	−0.189937
$577$	−29.0774	−1.21051	−0.605254	−	0.796032i	$-0.706929\pi$
$577$	−29.0774	−1.21051	−0.605254	+	0.796032i	$0.706929\pi$
$578$	13.7792	0.573140
$579$	4.16545	0.173110
$580$	−15.2910	−0.634926
$581$	−1.35826	−0.0563502
$582$	−46.8731	−1.94295
$583$	−31.5896	−1.30831
$584$	59.8868	2.47813
$585$	−2.55850	−0.105781
$586$	33.7412	1.39383
$587$	36.4130	1.50293	0.751463	−	0.659775i	$-0.229348\pi$
$587$	36.4130	1.50293	0.751463	+	0.659775i	$0.229348\pi$
$588$	−24.5545	−1.01261
$589$	−39.9738	−1.64709
$590$	−7.10527	−0.292519
$591$	−3.30895	−0.136112
$592$	38.3713	1.57705
$593$	30.1437	1.23786	0.618928	−	0.785448i	$-0.287567\pi$
$593$	30.1437	1.23786	0.618928	+	0.785448i	$0.287567\pi$
$594$	−8.35117	−0.342652
$595$	2.68490	0.110070
$596$	−63.5608	−2.60355
$597$	16.8370	0.689094
$598$	16.1228	0.659309
$599$	13.5964	0.555534	0.277767	−	0.960649i	$-0.410406\pi$
$599$	13.5964	0.555534	0.277767	+	0.960649i	$0.410406\pi$
$600$	25.1617	1.02722
$601$	29.5956	1.20723	0.603616	−	0.797275i	$-0.293726\pi$
$601$	29.5956	1.20723	0.603616	+	0.797275i	$0.293726\pi$
$602$	−31.2015	−1.27168
$603$	−15.5239	−0.632181
$604$	48.5506	1.97550
$605$	−0.119903	−0.00487476
$606$	−16.9848	−0.689959
$607$	4.82707	0.195925	0.0979623	−	0.995190i	$-0.468768\pi$
$607$	4.82707	0.195925	0.0979623	+	0.995190i	$0.468768\pi$
$608$	−9.51271	−0.385791
$609$	−5.52964	−0.224072
$610$	−14.3131	−0.579521
$611$	−2.87974	−0.116502
$612$	14.3883	0.581613
$613$	−12.8984	−0.520960	−0.260480	−	0.965479i	$-0.583881\pi$
$613$	−12.8984	−0.520960	−0.260480	+	0.965479i	$0.583881\pi$
$614$	12.7953	0.516376
$615$	1.14864	0.0463178
$616$	20.6800	0.833222
$617$	8.52291	0.343120	0.171560	−	0.985174i	$-0.445119\pi$
$617$	8.52291	0.343120	0.171560	+	0.985174i	$0.445119\pi$
$618$	−4.01360	−0.161451
$619$	44.9756	1.80772	0.903861	−	0.427826i	$-0.140720\pi$
$619$	44.9756	1.80772	0.903861	+	0.427826i	$0.140720\pi$
$620$	33.3666	1.34003
$621$	−1.81135	−0.0726871
$622$	−81.2544	−3.25801
$623$	8.85545	0.354786
$624$	19.7057	0.788859
$625$	17.5261	0.701045
$626$	−71.2374	−2.84722
$627$	12.2090	0.487580
$628$	−53.0812	−2.11817
$629$	23.5050	0.937206
$630$	−1.97978	−0.0788765
$631$	25.8793	1.03024	0.515119	−	0.857119i	$-0.327748\pi$
$631$	25.8793	1.03024	0.515119	+	0.857119i	$0.327748\pi$
$632$	44.6012	1.77414
$633$	−7.74096	−0.307676
$634$	45.6620	1.81347
$635$	−4.35974	−0.173011
$636$	−40.1326	−1.59136
$637$	−20.6000	−0.816201
$638$	−41.8731	−1.65777
$639$	−6.10152	−0.241372
$640$	−11.9240	−0.471339
$641$	−17.6235	−0.696086	−0.348043	−	0.937479i	$-0.613154\pi$
$641$	−17.6235	−0.696086	−0.348043	+	0.937479i	$0.613154\pi$
$642$	−32.4432	−1.28043
$643$	33.1987	1.30923	0.654614	−	0.755963i	$-0.272831\pi$
$643$	33.1987	1.30923	0.654614	+	0.755963i	$0.272831\pi$
$644$	8.48069	0.334186
$645$	8.13234	0.320211
$646$	−30.9445	−1.21749
$647$	−26.9537	−1.05966	−0.529830	−	0.848104i	$-0.677744\pi$
$647$	−26.9537	−1.05966	−0.529830	+	0.848104i	$0.677744\pi$
$648$	−5.61146	−0.220439
$649$	−13.2263	−0.519177
$650$	39.9118	1.56547
$651$	12.0662	0.472912
$652$	−10.4088	−0.407639
$653$	8.79790	0.344288	0.172144	−	0.985072i	$-0.444931\pi$
$653$	8.79790	0.344288	0.172144	+	0.985072i	$0.444931\pi$
$654$	6.30865	0.246688
$655$	−7.62514	−0.297939
$656$	−8.84692	−0.345414
$657$	−10.6722	−0.416363
$658$	−2.22836	−0.0868707
$659$	2.92629	0.113992	0.0569961	−	0.998374i	$-0.481848\pi$
$659$	2.92629	0.113992	0.0569961	+	0.998374i	$0.481848\pi$
$660$	−10.1910	−0.396683
$661$	−17.8140	−0.692885	−0.346443	−	0.938071i	$-0.612610\pi$
$661$	−17.8140	−0.692885	−0.346443	+	0.938071i	$0.612610\pi$
$662$	62.6648	2.43554
$663$	12.0711	0.468802
$664$	−6.91116	−0.268205
$665$	2.89434	0.112238
$666$	−17.3321	−0.671605
$667$	−9.08221	−0.351665
$668$	55.2467	2.13756
$669$	−8.10207	−0.313244
$670$	−27.8683	−1.07664
$671$	−26.6435	−1.02856
$672$	2.87144	0.110768
$673$	47.0211	1.81253	0.906266	−	0.422708i	$-0.138921\pi$
$673$	47.0211	1.81253	0.906266	+	0.422708i	$0.138921\pi$
$674$	−28.4301	−1.09508
$675$	−4.48399	−0.172589
$676$	−1.33461	−0.0513312
$677$	46.8943	1.80229	0.901147	−	0.433514i	$-0.142727\pi$
$677$	46.8943	1.80229	0.901147	+	0.433514i	$0.142727\pi$
$678$	47.3205	1.81733
$679$	−20.6848	−0.793810
$680$	13.6614	0.523890
$681$	6.62935	0.254037
$682$	91.3713	3.49879
$683$	−37.9705	−1.45290	−0.726451	−	0.687218i	$-0.758832\pi$
$683$	−37.9705	−1.45290	−0.726451	+	0.687218i	$0.758832\pi$
$684$	15.5107	0.593068
$685$	5.44278	0.207958
$686$	−35.2328	−1.34520
$687$	−13.4120	−0.511700
$688$	−62.6358	−2.38797
$689$	−33.6692	−1.28270
$690$	−3.25172	−0.123791
$691$	43.6660	1.66113	0.830567	−	0.556918i	$-0.188016\pi$
$691$	43.6660	1.66113	0.830567	+	0.556918i	$0.188016\pi$
$692$	66.5981	2.53168
$693$	−3.68532	−0.139994
$694$	7.23170	0.274511
$695$	2.22056	0.0842306
$696$	−28.1361	−1.06650
$697$	−5.41934	−0.205272
$698$	−55.1063	−2.08580
$699$	−12.0481	−0.455702
$700$	20.9939	0.793494
$701$	−27.7486	−1.04805	−0.524025	−	0.851703i	$-0.675570\pi$
$701$	−27.7486	−1.04805	−0.524025	+	0.851703i	$0.675570\pi$
$702$	−8.90095	−0.335945
$703$	25.3386	0.955664
$704$	−15.2331	−0.574119
$705$	0.580799	0.0218742
$706$	−79.3627	−2.98685
$707$	−7.49527	−0.281889
$708$	−16.8032	−0.631501
$709$	−10.1557	−0.381404	−0.190702	−	0.981648i	$-0.561076\pi$
$709$	−10.1557	−0.381404	−0.190702	+	0.981648i	$0.561076\pi$
$710$	−10.9534	−0.411072
$711$	−7.94824	−0.298082
$712$	45.0586	1.68864
$713$	19.8183	0.742201
$714$	9.34069	0.349566
$715$	−8.54972	−0.319741
$716$	107.144	4.00416
$717$	−20.7963	−0.776652
$718$	−55.9492	−2.08800
$719$	21.1461	0.788616	0.394308	−	0.918978i	$-0.370984\pi$
$719$	21.1461	0.788616	0.394308	+	0.918978i	$0.370984\pi$
$720$	−3.97434	−0.148115
$721$	−1.77118	−0.0659621
$722$	14.1241	0.525644
$723$	−14.6354	−0.544298
$724$	−48.8785	−1.81656
$725$	−22.4829	−0.834995
$726$	−0.417141	−0.0154815
$727$	14.5800	0.540741	0.270371	−	0.962756i	$-0.412854\pi$
$727$	14.5800	0.540741	0.270371	+	0.962756i	$0.412854\pi$
$728$	22.0415	0.816911
$729$	1.00000	0.0370370
$730$	−19.1586	−0.709093
$731$	−38.3686	−1.41912
$732$	−33.8488	−1.25109
$733$	40.0557	1.47949	0.739746	−	0.672887i	$-0.234946\pi$
$733$	40.0557	1.47949	0.739746	+	0.672887i	$0.234946\pi$
$734$	−2.14606	−0.0792124
$735$	4.15470	0.153248
$736$	4.71623	0.173842
$737$	−51.8761	−1.91088
$738$	3.99610	0.147099
$739$	−39.0631	−1.43696	−0.718479	−	0.695548i	$-0.755162\pi$
$739$	−39.0631	−1.43696	−0.718479	+	0.695548i	$0.755162\pi$
$740$	−21.1504	−0.777505
$741$	13.0127	0.478035
$742$	−26.0535	−0.956454
$743$	−30.0575	−1.10270	−0.551351	−	0.834274i	$-0.685887\pi$
$743$	−30.0575	−1.10270	−0.551351	+	0.834274i	$0.685887\pi$
$744$	61.3958	2.25088
$745$	10.7547	0.394022
$746$	76.3166	2.79415
$747$	1.23161	0.0450624
$748$	48.0813	1.75803
$749$	−14.3170	−0.523131
$750$	−17.0255	−0.621684
$751$	8.32624	0.303829	0.151914	−	0.988394i	$-0.451456\pi$
$751$	8.32624	0.303829	0.151914	+	0.988394i	$0.451456\pi$
$752$	−4.47335	−0.163126
$753$	−19.7788	−0.720781
$754$	−44.6298	−1.62532
$755$	−8.21494	−0.298972
$756$	−4.68196	−0.170281
$757$	−23.5943	−0.857549	−0.428774	−	0.903412i	$-0.641055\pi$
$757$	−23.5943	−0.857549	−0.428774	+	0.903412i	$0.641055\pi$
$758$	60.4782	2.19667
$759$	−6.05299	−0.219710
$760$	14.7271	0.534209
$761$	−19.6102	−0.710868	−0.355434	−	0.934701i	$-0.615667\pi$
$761$	−19.6102	−0.710868	−0.355434	+	0.934701i	$0.615667\pi$
$762$	−15.1674	−0.549458
$763$	2.78397	0.100787
$764$	22.1696	0.802069
$765$	−2.43455	−0.0880214
$766$	−28.0967	−1.01518
$767$	−14.0970	−0.509014
$768$	−32.3664	−1.16792
$769$	−18.8533	−0.679867	−0.339934	−	0.940449i	$-0.610405\pi$
$769$	−18.8533	−0.679867	−0.339934	+	0.940449i	$0.610405\pi$
$770$	−6.61583	−0.238418
$771$	−22.2097	−0.799862
$772$	17.6841	0.636463
$773$	−6.24006	−0.224439	−0.112220	−	0.993683i	$-0.535796\pi$
$773$	−6.24006	−0.224439	−0.112220	+	0.993683i	$0.535796\pi$
$774$	28.2922	1.01694
$775$	49.0600	1.76229
$776$	−105.249	−3.77823
$777$	−7.64855	−0.274390
$778$	−53.1043	−1.90388
$779$	−5.84210	−0.209315
$780$	−10.8619	−0.388917
$781$	−20.3894	−0.729590
$782$	15.3417	0.548618
$783$	5.01405	0.179187
$784$	−31.9997	−1.14285
$785$	8.98153	0.320564
$786$	−26.5277	−0.946211
$787$	−19.6982	−0.702164	−0.351082	−	0.936345i	$-0.614186\pi$
$787$	−19.6982	−0.702164	−0.351082	+	0.936345i	$0.614186\pi$
$788$	−14.0478	−0.500433
$789$	−20.9233	−0.744889
$790$	−14.2686	−0.507653
$791$	20.8822	0.742487
$792$	−18.7518	−0.666316
$793$	−28.3975	−1.00843
$794$	−42.8001	−1.51892
$795$	6.79057	0.240837
$796$	71.4801	2.53355
$797$	−1.98048	−0.0701521	−0.0350761	−	0.999385i	$-0.511167\pi$
$797$	−1.98048	−0.0701521	−0.0350761	+	0.999385i	$0.511167\pi$
$798$	10.0694	0.356451
$799$	−2.74023	−0.0969424
$800$	11.6750	0.412773
$801$	−8.02975	−0.283717
$802$	−19.3623	−0.683706
$803$	−35.6633	−1.25853
$804$	−65.9052	−2.32430
$805$	−1.43496	−0.0505758
$806$	97.3866	3.43030
$807$	0.824030	0.0290072
$808$	−38.1377	−1.34168
$809$	−0.858860	−0.0301959	−0.0150979	−	0.999886i	$-0.504806\pi$
$809$	−0.858860	−0.0301959	−0.0150979	+	0.999886i	$0.504806\pi$
$810$	1.79519	0.0630764
$811$	2.94088	0.103268	0.0516342	−	0.998666i	$-0.483557\pi$
$811$	2.94088	0.103268	0.0516342	+	0.998666i	$0.483557\pi$
$812$	−23.4756	−0.823832
$813$	−6.64432	−0.233026
$814$	−57.9185	−2.03004
$815$	1.76120	0.0616923
$816$	18.7511	0.656418
$817$	−41.3618	−1.44707
$818$	3.84006	0.134264
$819$	−3.92794	−0.137253
$820$	4.87646	0.170293
$821$	38.5970	1.34704	0.673522	−	0.739167i	$-0.264780\pi$
$821$	38.5970	1.34704	0.673522	+	0.739167i	$0.264780\pi$
$822$	18.9353	0.660445
$823$	40.6651	1.41750	0.708749	−	0.705461i	$-0.249260\pi$
$823$	40.6651	1.41750	0.708749	+	0.705461i	$0.249260\pi$
$824$	−9.01218	−0.313954
$825$	−14.9841	−0.521680
$826$	−10.9084	−0.379551
$827$	57.1097	1.98590	0.992950	−	0.118534i	$-0.0378194\pi$
$827$	57.1097	1.98590	0.992950	+	0.118534i	$0.0378194\pi$
$828$	−7.68994	−0.267244
$829$	7.28594	0.253051	0.126526	−	0.991963i	$-0.459617\pi$
$829$	7.28594	0.253051	0.126526	+	0.991963i	$0.459617\pi$
$830$	2.21098	0.0767441
$831$	7.79045	0.270248
$832$	−16.2360	−0.562881
$833$	−19.6020	−0.679169
$834$	7.72527	0.267504
$835$	−9.34794	−0.323499
$836$	51.8321	1.79265
$837$	−10.9411	−0.378181
$838$	−17.7533	−0.613278
$839$	5.81219	0.200659	0.100330	−	0.994954i	$-0.468010\pi$
$839$	5.81219	0.200659	0.100330	+	0.994954i	$0.468010\pi$
$840$	−4.44543	−0.153382
$841$	−3.85934	−0.133081
$842$	31.2034	1.07534
$843$	−11.3010	−0.389227
$844$	−32.8636	−1.13121
$845$	0.225821	0.00776848
$846$	2.02059	0.0694692
$847$	−0.184082	−0.00632512
$848$	−52.3014	−1.79604
$849$	29.8724	1.02522
$850$	37.9783	1.30264
$851$	−12.5624	−0.430635
$852$	−25.9034	−0.887437
$853$	−14.1812	−0.485555	−0.242777	−	0.970082i	$-0.578058\pi$
$853$	−14.1812	−0.485555	−0.242777	+	0.970082i	$0.578058\pi$
$854$	−21.9742	−0.751942
$855$	−2.62447	−0.0897550
$856$	−72.8483	−2.48990
$857$	31.6450	1.08097	0.540486	−	0.841353i	$-0.318241\pi$
$857$	31.6450	1.08097	0.540486	+	0.841353i	$0.318241\pi$
$858$	−29.7443	−1.01545
$859$	−36.1910	−1.23482	−0.617410	−	0.786641i	$-0.711818\pi$
$859$	−36.1910	−1.23482	−0.617410	+	0.786641i	$0.711818\pi$
$860$	34.5251	1.17730
$861$	1.76346	0.0600984
$862$	45.1224	1.53687
$863$	17.0595	0.580713	0.290356	−	0.956919i	$-0.406226\pi$
$863$	17.0595	0.580713	0.290356	+	0.956919i	$0.406226\pi$
$864$	−2.60370	−0.0885798
$865$	−11.2686	−0.383145
$866$	32.4382	1.10229
$867$	−5.51371	−0.187255
$868$	51.2260	1.73873
$869$	−26.5606	−0.901006
$870$	9.00115	0.305167
$871$	−55.2913	−1.87347
$872$	14.1655	0.479705
$873$	18.7561	0.634798
$874$	16.5385	0.559424
$875$	−7.51326	−0.253995
$876$	−45.3079	−1.53081
$877$	22.4157	0.756925	0.378462	−	0.925617i	$-0.376453\pi$
$877$	22.4157	0.756925	0.378462	+	0.925617i	$0.376453\pi$
$878$	97.5906	3.29352
$879$	−13.5014	−0.455392
$880$	−13.2810	−0.447703
$881$	−37.7226	−1.27091	−0.635453	−	0.772140i	$-0.719186\pi$
$881$	−37.7226	−1.27091	−0.635453	+	0.772140i	$0.719186\pi$
$882$	14.4541	0.486695
$883$	9.40445	0.316485	0.158242	−	0.987400i	$-0.449417\pi$
$883$	9.40445	0.316485	0.158242	+	0.987400i	$0.449417\pi$
$884$	51.2467	1.72361
$885$	2.84315	0.0955716
$886$	−48.0719	−1.61501
$887$	−47.5732	−1.59735	−0.798676	−	0.601762i	$-0.794466\pi$
$887$	−47.5732	−1.59735	−0.798676	+	0.601762i	$0.794466\pi$
$888$	−38.9176	−1.30599
$889$	−6.69329	−0.224486
$890$	−14.4149	−0.483188
$891$	3.34169	0.111951
$892$	−34.3966	−1.15168
$893$	−2.95400	−0.0988517
$894$	37.4154	1.25136
$895$	−18.1291	−0.605990
$896$	−18.3064	−0.611573
$897$	−6.45148	−0.215409
$898$	49.8638	1.66398
$899$	−54.8594	−1.82966
$900$	−19.0364	−0.634546
$901$	−32.0381	−1.06734
$902$	13.3538	0.444631
$903$	12.4852	0.415481
$904$	106.254	3.53395
$905$	8.27042	0.274918
$906$	−28.5796	−0.949493
$907$	20.2057	0.670919	0.335460	−	0.942055i	$-0.391108\pi$
$907$	20.2057	0.670919	0.335460	+	0.942055i	$0.391108\pi$
$908$	28.1443	0.934002
$909$	6.79640	0.225422
$910$	−7.05138	−0.233751
$911$	−25.2732	−0.837338	−0.418669	−	0.908139i	$-0.637503\pi$
$911$	−25.2732	−0.837338	−0.418669	+	0.908139i	$0.637503\pi$
$912$	20.2138	0.669347
$913$	4.11568	0.136209
$914$	−0.343621	−0.0113660
$915$	5.72734	0.189340
$916$	−56.9394	−1.88133
$917$	−11.7065	−0.386583
$918$	−8.46974	−0.279543
$919$	−39.9976	−1.31940	−0.659700	−	0.751529i	$-0.729317\pi$
$919$	−39.9976	−1.31940	−0.659700	+	0.751529i	$0.729317\pi$
$920$	−7.30144	−0.240721
$921$	−5.11999	−0.168710
$922$	−12.5340	−0.412786
$923$	−21.7317	−0.715308
$924$	−15.6457	−0.514705
$925$	−31.0982	−1.02250
$926$	−25.2140	−0.828583
$927$	1.60603	0.0527489
$928$	−13.0551	−0.428554
$929$	21.2173	0.696117	0.348059	−	0.937473i	$-0.386841\pi$
$929$	21.2173	0.696117	0.348059	+	0.937473i	$0.386841\pi$
$930$	−19.6414	−0.644067
$931$	−21.1312	−0.692546
$932$	−51.1492	−1.67545
$933$	32.5137	1.06445
$934$	45.8900	1.50157
$935$	−8.13552	−0.266060
$936$	−19.9863	−0.653272
$937$	−51.1769	−1.67188	−0.835939	−	0.548823i	$-0.815076\pi$
$937$	−51.1769	−1.67188	−0.835939	+	0.548823i	$0.815076\pi$
$938$	−42.7848	−1.39697
$939$	28.5054	0.930240
$940$	2.46573	0.0804233
$941$	32.8742	1.07167	0.535834	−	0.844323i	$-0.319997\pi$
$941$	32.8742	1.07167	0.535834	+	0.844323i	$0.319997\pi$
$942$	31.2465	1.01807
$943$	2.89641	0.0943200
$944$	−21.8981	−0.712723
$945$	0.792205	0.0257704
$946$	94.5439	3.07389
$947$	−6.58514	−0.213988	−0.106994	−	0.994260i	$-0.534123\pi$
$947$	−6.58514	−0.213988	−0.106994	+	0.994260i	$0.534123\pi$
$948$	−33.7435	−1.09594
$949$	−38.0111	−1.23389
$950$	40.9409	1.32830
$951$	−18.2715	−0.592494
$952$	20.9737	0.679760
$953$	−60.7032	−1.96637	−0.983185	−	0.182612i	$-0.941545\pi$
$953$	−60.7032	−1.96637	−0.983185	+	0.182612i	$0.941545\pi$
$954$	23.6242	0.764863
$955$	−3.75118	−0.121385
$956$	−88.2888	−2.85546
$957$	16.7554	0.541625
$958$	−37.2216	−1.20258
$959$	8.35604	0.269830
$960$	3.27454	0.105685
$961$	88.7087	2.86157
$962$	−61.7315	−1.99030
$963$	12.9820	0.418341
$964$	−62.1335	−2.00118
$965$	−2.99221	−0.0963225
$966$	−4.99220	−0.160622
$967$	34.6141	1.11311	0.556557	−	0.830810i	$-0.312122\pi$
$967$	34.6141	1.11311	0.556557	+	0.830810i	$0.312122\pi$
$968$	−0.936652	−0.0301051
$969$	12.3823	0.397778
$970$	33.6707	1.08110
$971$	−14.2504	−0.457318	−0.228659	−	0.973507i	$-0.573434\pi$
$971$	−14.2504	−0.457318	−0.228659	+	0.973507i	$0.573434\pi$
$972$	4.24541	0.136172
$973$	3.40912	0.109291
$974$	−45.2457	−1.44976
$975$	−15.9706	−0.511468
$976$	−44.1123	−1.41200
$977$	−18.0133	−0.576298	−0.288149	−	0.957586i	$-0.593040\pi$
$977$	−18.0133	−0.576298	−0.288149	+	0.957586i	$0.593040\pi$
$978$	6.12718	0.195926
$979$	−26.8330	−0.857585
$980$	17.6384	0.563438
$981$	−2.52439	−0.0805975
$982$	18.1018	0.577652
$983$	42.6780	1.36122	0.680608	−	0.732648i	$-0.261716\pi$
$983$	42.6780	1.36122	0.680608	+	0.732648i	$0.261716\pi$
$984$	8.97289	0.286045
$985$	2.37694	0.0757357
$986$	−42.4677	−1.35245
$987$	0.891673	0.0283823
$988$	55.2444	1.75756
$989$	20.5064	0.652066
$990$	5.99896	0.190660
$991$	54.0085	1.71564	0.857819	−	0.513952i	$-0.171819\pi$
$991$	54.0085	1.71564	0.857819	+	0.513952i	$0.171819\pi$
$992$	28.4875	0.904479
$993$	−25.0751	−0.795736
$994$	−16.8162	−0.533376
$995$	−12.0947	−0.383427
$996$	5.22871	0.165678
$997$	−35.9742	−1.13932	−0.569658	−	0.821882i	$-0.692924\pi$
$997$	−35.9742	−1.13932	−0.569658	+	0.821882i	$0.692924\pi$
$998$	−6.12998	−0.194041
$999$	6.93538	0.219426

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8031.2.a.a.1.6	✓	92

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8031.2.a.a.1.6	✓	92	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:	\( N \)	\(=\)	\( 8031 = 3 \cdot 2677 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8031.a (trivial)

\(f(q)\)	\(=\)	\(q-2.49908 q^{2} +1.00000 q^{3} +4.24541 q^{4} -0.718338 q^{5} -2.49908 q^{6} -1.10283 q^{7} -5.61146 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.49908 q^{2} +1.00000 q^{3} +4.24541 q^{4} -0.718338 q^{5} -2.49908 q^{6} -1.10283 q^{7} -5.61146 q^{8} +1.00000 q^{9} +1.79519 q^{10} +3.34169 q^{11} +4.24541 q^{12} +3.56169 q^{13} +2.75606 q^{14} -0.718338 q^{15} +5.53268 q^{16} +3.38914 q^{17} -2.49908 q^{18} +3.65353 q^{19} -3.04964 q^{20} -1.10283 q^{21} -8.35117 q^{22} -1.81135 q^{23} -5.61146 q^{24} -4.48399 q^{25} -8.90095 q^{26} +1.00000 q^{27} -4.68196 q^{28} +5.01405 q^{29} +1.79519 q^{30} -10.9411 q^{31} -2.60370 q^{32} +3.34169 q^{33} -8.46974 q^{34} +0.792205 q^{35} +4.24541 q^{36} +6.93538 q^{37} -9.13047 q^{38} +3.56169 q^{39} +4.03093 q^{40} -1.59903 q^{41} +2.75606 q^{42} -11.3210 q^{43} +14.1869 q^{44} -0.718338 q^{45} +4.52672 q^{46} -0.808532 q^{47} +5.53268 q^{48} -5.78377 q^{49} +11.2059 q^{50} +3.38914 q^{51} +15.1208 q^{52} -9.45317 q^{53} -2.49908 q^{54} -2.40047 q^{55} +6.18849 q^{56} +3.65353 q^{57} -12.5305 q^{58} -3.95796 q^{59} -3.04964 q^{60} -7.97305 q^{61} +27.3428 q^{62} -1.10283 q^{63} -4.55850 q^{64} -2.55850 q^{65} -8.35117 q^{66} -15.5239 q^{67} +14.3883 q^{68} -1.81135 q^{69} -1.97978 q^{70} -6.10152 q^{71} -5.61146 q^{72} -10.6722 q^{73} -17.3321 q^{74} -4.48399 q^{75} +15.5107 q^{76} -3.68532 q^{77} -8.90095 q^{78} -7.94824 q^{79} -3.97434 q^{80} +1.00000 q^{81} +3.99610 q^{82} +1.23161 q^{83} -4.68196 q^{84} -2.43455 q^{85} +28.2922 q^{86} +5.01405 q^{87} -18.7518 q^{88} -8.02975 q^{89} +1.79519 q^{90} -3.92794 q^{91} -7.68994 q^{92} -10.9411 q^{93} +2.02059 q^{94} -2.62447 q^{95} -2.60370 q^{96} +18.7561 q^{97} +14.4541 q^{98} +3.34169 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 92 q - 6 q^{2} + 92 q^{3} + 70 q^{4} - 18 q^{5} - 6 q^{6} - 42 q^{7} - 15 q^{8} + 92 q^{9}+O(q^{10}) \) 92 * q - 6 * q^2 + 92 * q^3 + 70 * q^4 - 18 * q^5 - 6 * q^6 - 42 * q^7 - 15 * q^8 + 92 * q^9	\( 92 q - 6 q^{2} + 92 q^{3} + 70 q^{4} - 18 q^{5} - 6 q^{6} - 42 q^{7} - 15 q^{8} + 92 q^{9} - 44 q^{10} - 24 q^{11} + 70 q^{12} - 48 q^{13} - 29 q^{14} - 18 q^{15} + 26 q^{16} - 69 q^{17} - 6 q^{18} - 74 q^{19} - 42 q^{20} - 42 q^{21} - 62 q^{22} - 19 q^{23} - 15 q^{24} + 16 q^{25} - 27 q^{26} + 92 q^{27} - 101 q^{28} - 54 q^{29} - 44 q^{30} - 67 q^{31} - 36 q^{32} - 24 q^{33} - 63 q^{34} - 31 q^{35} + 70 q^{36} - 70 q^{37} - 18 q^{38} - 48 q^{39} - 125 q^{40} - 98 q^{41} - 29 q^{42} - 159 q^{43} - 52 q^{44} - 18 q^{45} - 68 q^{46} - 15 q^{47} + 26 q^{48} - 28 q^{49} - 7 q^{50} - 69 q^{51} - 98 q^{52} - 23 q^{53} - 6 q^{54} - 93 q^{55} - 48 q^{56} - 74 q^{57} - 37 q^{58} - 36 q^{59} - 42 q^{60} - 172 q^{61} - 26 q^{62} - 42 q^{63} - 23 q^{64} - 66 q^{65} - 62 q^{66} - 143 q^{67} - 74 q^{68} - 19 q^{69} - 30 q^{70} - 9 q^{71} - 15 q^{72} - 134 q^{73} - 19 q^{74} + 16 q^{75} - 157 q^{76} - 25 q^{77} - 27 q^{78} - 138 q^{79} - 29 q^{80} + 92 q^{81} - 61 q^{82} - 24 q^{83} - 101 q^{84} - 84 q^{85} + 14 q^{86} - 54 q^{87} - 140 q^{88} - 148 q^{89} - 44 q^{90} - 115 q^{91} - 12 q^{92} - 67 q^{93} - 79 q^{94} - 10 q^{95} - 36 q^{96} - 165 q^{97} + 36 q^{98} - 24 q^{99}+O(q^{100}) \) 92 * q - 6 * q^2 + 92 * q^3 + 70 * q^4 - 18 * q^5 - 6 * q^6 - 42 * q^7 - 15 * q^8 + 92 * q^9 - 44 * q^10 - 24 * q^11 + 70 * q^12 - 48 * q^13 - 29 * q^14 - 18 * q^15 + 26 * q^16 - 69 * q^17 - 6 * q^18 - 74 * q^19 - 42 * q^20 - 42 * q^21 - 62 * q^22 - 19 * q^23 - 15 * q^24 + 16 * q^25 - 27 * q^26 + 92 * q^27 - 101 * q^28 - 54 * q^29 - 44 * q^30 - 67 * q^31 - 36 * q^32 - 24 * q^33 - 63 * q^34 - 31 * q^35 + 70 * q^36 - 70 * q^37 - 18 * q^38 - 48 * q^39 - 125 * q^40 - 98 * q^41 - 29 * q^42 - 159 * q^43 - 52 * q^44 - 18 * q^45 - 68 * q^46 - 15 * q^47 + 26 * q^48 - 28 * q^49 - 7 * q^50 - 69 * q^51 - 98 * q^52 - 23 * q^53 - 6 * q^54 - 93 * q^55 - 48 * q^56 - 74 * q^57 - 37 * q^58 - 36 * q^59 - 42 * q^60 - 172 * q^61 - 26 * q^62 - 42 * q^63 - 23 * q^64 - 66 * q^65 - 62 * q^66 - 143 * q^67 - 74 * q^68 - 19 * q^69 - 30 * q^70 - 9 * q^71 - 15 * q^72 - 134 * q^73 - 19 * q^74 + 16 * q^75 - 157 * q^76 - 25 * q^77 - 27 * q^78 - 138 * q^79 - 29 * q^80 + 92 * q^81 - 61 * q^82 - 24 * q^83 - 101 * q^84 - 84 * q^85 + 14 * q^86 - 54 * q^87 - 140 * q^88 - 148 * q^89 - 44 * q^90 - 115 * q^91 - 12 * q^92 - 67 * q^93 - 79 * q^94 - 10 * q^95 - 36 * q^96 - 165 * q^97 + 36 * q^98 - 24 * q^99

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