LMFDB - Embedded newform 8041.2.a.g.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8041,2,Mod(1,8041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8041, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("8041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8041 = 11 \cdot 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8041.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:	$64.2077082653$
Analytic rank:	$1$
Dimension:	$69$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	8041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.12129 q^{2} +1.35005 q^{3} +2.49986 q^{4} -1.60395 q^{5} -2.86383 q^{6} -4.53308 q^{7} -1.06034 q^{8} -1.17738 q^{9} +O(q^{10})$	\(q-2.12129 q^{2} +1.35005 q^{3} +2.49986 q^{4} -1.60395 q^{5} -2.86383 q^{6} -4.53308 q^{7} -1.06034 q^{8} -1.17738 q^{9} +3.40244 q^{10} -1.00000 q^{11} +3.37492 q^{12} +0.894770 q^{13} +9.61596 q^{14} -2.16540 q^{15} -2.75042 q^{16} +1.00000 q^{17} +2.49755 q^{18} +5.74568 q^{19} -4.00965 q^{20} -6.11986 q^{21} +2.12129 q^{22} -5.62341 q^{23} -1.43151 q^{24} -2.42735 q^{25} -1.89806 q^{26} -5.63965 q^{27} -11.3321 q^{28} -3.02816 q^{29} +4.59344 q^{30} +6.20713 q^{31} +7.95513 q^{32} -1.35005 q^{33} -2.12129 q^{34} +7.27082 q^{35} -2.94328 q^{36} +6.17491 q^{37} -12.1882 q^{38} +1.20798 q^{39} +1.70074 q^{40} +11.3513 q^{41} +12.9820 q^{42} +1.00000 q^{43} -2.49986 q^{44} +1.88845 q^{45} +11.9289 q^{46} +3.38378 q^{47} -3.71320 q^{48} +13.5488 q^{49} +5.14910 q^{50} +1.35005 q^{51} +2.23680 q^{52} +3.66404 q^{53} +11.9633 q^{54} +1.60395 q^{55} +4.80662 q^{56} +7.75693 q^{57} +6.42359 q^{58} -8.84019 q^{59} -5.41320 q^{60} -10.1961 q^{61} -13.1671 q^{62} +5.33714 q^{63} -11.3743 q^{64} -1.43516 q^{65} +2.86383 q^{66} +2.85720 q^{67} +2.49986 q^{68} -7.59185 q^{69} -15.4235 q^{70} +0.715674 q^{71} +1.24843 q^{72} +9.17039 q^{73} -13.0988 q^{74} -3.27703 q^{75} +14.3634 q^{76} +4.53308 q^{77} -2.56247 q^{78} -15.9552 q^{79} +4.41154 q^{80} -4.08165 q^{81} -24.0793 q^{82} -12.3232 q^{83} -15.2988 q^{84} -1.60395 q^{85} -2.12129 q^{86} -4.08815 q^{87} +1.06034 q^{88} +6.18834 q^{89} -4.00595 q^{90} -4.05606 q^{91} -14.0577 q^{92} +8.37991 q^{93} -7.17797 q^{94} -9.21577 q^{95} +10.7398 q^{96} +18.0060 q^{97} -28.7409 q^{98} +1.17738 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 69 q - 11 q^{2} - 3 q^{3} + 65 q^{4} - 6 q^{5} - 10 q^{6} - 11 q^{7} - 33 q^{8} + 56 q^{9}+O(q^{10}) $ 69 * q - 11 * q^2 - 3 * q^3 + 65 * q^4 - 6 * q^5 - 10 * q^6 - 11 * q^7 - 33 * q^8 + 56 * q^9	\( 69 q - 11 q^{2} - 3 q^{3} + 65 q^{4} - 6 q^{5} - 10 q^{6} - 11 q^{7} - 33 q^{8} + 56 q^{9} - q^{10} - 69 q^{11} - 3 q^{12} - 28 q^{13} - 15 q^{14} - 45 q^{15} + 53 q^{16} + 69 q^{17} - 17 q^{18} - 32 q^{19} - 21 q^{20} - 38 q^{21} + 11 q^{22} - 41 q^{23} - 11 q^{24} + 67 q^{25} - 6 q^{26} - 3 q^{27} - 21 q^{28} - 22 q^{29} - 22 q^{30} - 27 q^{31} - 87 q^{32} + 3 q^{33} - 11 q^{34} - 44 q^{35} + 59 q^{36} + 24 q^{37} - 22 q^{38} - 59 q^{39} + q^{40} - 43 q^{41} - 15 q^{42} + 69 q^{43} - 65 q^{44} - 12 q^{45} - 21 q^{46} - 99 q^{47} + 2 q^{48} + 64 q^{49} - 78 q^{50} - 3 q^{51} - 57 q^{52} - 50 q^{53} + 20 q^{54} + 6 q^{55} - 59 q^{56} - 15 q^{57} + 22 q^{58} - 82 q^{59} - 86 q^{60} - 24 q^{61} + 15 q^{62} - 63 q^{63} + 63 q^{64} - 23 q^{65} + 10 q^{66} - 54 q^{67} + 65 q^{68} + 36 q^{69} + 9 q^{70} - 128 q^{71} - 69 q^{72} + 2 q^{73} - 58 q^{74} - 31 q^{75} - 76 q^{76} + 11 q^{77} - 19 q^{78} - 43 q^{79} - 19 q^{80} + 49 q^{81} - 2 q^{82} - 62 q^{83} - 82 q^{84} - 6 q^{85} - 11 q^{86} - 62 q^{87} + 33 q^{88} - 49 q^{89} - 37 q^{90} - 2 q^{91} - 96 q^{92} - 29 q^{93} - 75 q^{94} - 133 q^{95} - 86 q^{96} + 5 q^{97} - 72 q^{98} - 56 q^{99}+O(q^{100}) \) 69 * q - 11 * q^2 - 3 * q^3 + 65 * q^4 - 6 * q^5 - 10 * q^6 - 11 * q^7 - 33 * q^8 + 56 * q^9 - q^10 - 69 * q^11 - 3 * q^12 - 28 * q^13 - 15 * q^14 - 45 * q^15 + 53 * q^16 + 69 * q^17 - 17 * q^18 - 32 * q^19 - 21 * q^20 - 38 * q^21 + 11 * q^22 - 41 * q^23 - 11 * q^24 + 67 * q^25 - 6 * q^26 - 3 * q^27 - 21 * q^28 - 22 * q^29 - 22 * q^30 - 27 * q^31 - 87 * q^32 + 3 * q^33 - 11 * q^34 - 44 * q^35 + 59 * q^36 + 24 * q^37 - 22 * q^38 - 59 * q^39 + q^40 - 43 * q^41 - 15 * q^42 + 69 * q^43 - 65 * q^44 - 12 * q^45 - 21 * q^46 - 99 * q^47 + 2 * q^48 + 64 * q^49 - 78 * q^50 - 3 * q^51 - 57 * q^52 - 50 * q^53 + 20 * q^54 + 6 * q^55 - 59 * q^56 - 15 * q^57 + 22 * q^58 - 82 * q^59 - 86 * q^60 - 24 * q^61 + 15 * q^62 - 63 * q^63 + 63 * q^64 - 23 * q^65 + 10 * q^66 - 54 * q^67 + 65 * q^68 + 36 * q^69 + 9 * q^70 - 128 * q^71 - 69 * q^72 + 2 * q^73 - 58 * q^74 - 31 * q^75 - 76 * q^76 + 11 * q^77 - 19 * q^78 - 43 * q^79 - 19 * q^80 + 49 * q^81 - 2 * q^82 - 62 * q^83 - 82 * q^84 - 6 * q^85 - 11 * q^86 - 62 * q^87 + 33 * q^88 - 49 * q^89 - 37 * q^90 - 2 * q^91 - 96 * q^92 - 29 * q^93 - 75 * q^94 - 133 * q^95 - 86 * q^96 + 5 * q^97 - 72 * q^98 - 56 * 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 $

$2$	−2.12129	−1.49998	−0.749988	−	0.661451i	$-0.769941\pi$
$2$	−2.12129	−1.49998	−0.749988	+	0.661451i	$0.769941\pi$
$3$	1.35005	0.779449	0.389725	−	0.920931i	$-0.372570\pi$
$3$	1.35005	0.779449	0.389725	+	0.920931i	$0.372570\pi$
$4$	2.49986	1.24993
$5$	−1.60395	−0.717308	−0.358654	−	0.933471i	$-0.616764\pi$
$5$	−1.60395	−0.717308	−0.358654	+	0.933471i	$0.616764\pi$
$6$	−2.86383	−1.16916
$7$	−4.53308	−1.71334	−0.856671	−	0.515863i	$-0.827471\pi$
$7$	−4.53308	−1.71334	−0.856671	+	0.515863i	$0.827471\pi$
$8$	−1.06034	−0.374888
$9$	−1.17738	−0.392459
$10$	3.40244	1.07594
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	3.37492	0.974257
$13$	0.894770	0.248164	0.124082	−	0.992272i	$-0.460401\pi$
$13$	0.894770	0.248164	0.124082	+	0.992272i	$0.460401\pi$
$14$	9.61596	2.56997
$15$	−2.16540	−0.559105
$16$	−2.75042	−0.687606
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	2.49755	0.588679
$19$	5.74568	1.31815	0.659074	−	0.752078i	$-0.270948\pi$
$19$	5.74568	1.31815	0.659074	+	0.752078i	$0.270948\pi$
$20$	−4.00965	−0.896584
$21$	−6.11986	−1.33546
$22$	2.12129	0.452260
$23$	−5.62341	−1.17256	−0.586281	−	0.810108i	$-0.699408\pi$
$23$	−5.62341	−1.17256	−0.586281	+	0.810108i	$0.699408\pi$
$24$	−1.43151	−0.292206
$25$	−2.42735	−0.485470
$26$	−1.89806	−0.372241
$27$	−5.63965	−1.08535
$28$	−11.3321	−2.14156
$29$	−3.02816	−0.562314	−0.281157	−	0.959662i	$-0.590718\pi$
$29$	−3.02816	−0.562314	−0.281157	+	0.959662i	$0.590718\pi$
$30$	4.59344	0.838644
$31$	6.20713	1.11483	0.557417	−	0.830233i	$-0.311793\pi$
$31$	6.20713	1.11483	0.557417	+	0.830233i	$0.311793\pi$
$32$	7.95513	1.40628
$33$	−1.35005	−0.235013
$34$	−2.12129	−0.363798
$35$	7.27082	1.22899
$36$	−2.94328	−0.490546
$37$	6.17491	1.01515	0.507575	−	0.861608i	$-0.330542\pi$
$37$	6.17491	1.01515	0.507575	+	0.861608i	$0.330542\pi$
$38$	−12.1882	−1.97719
$39$	1.20798	0.193432
$40$	1.70074	0.268910
$41$	11.3513	1.77277	0.886387	−	0.462946i	$-0.153208\pi$
$41$	11.3513	1.77277	0.886387	+	0.462946i	$0.153208\pi$
$42$	12.9820	2.00316
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	−2.49986	−0.376868
$45$	1.88845	0.281514
$46$	11.9289	1.75881
$47$	3.38378	0.493575	0.246788	−	0.969070i	$-0.420625\pi$
$47$	3.38378	0.493575	0.246788	+	0.969070i	$0.420625\pi$
$48$	−3.71320	−0.535954
$49$	13.5488	1.93554
$50$	5.14910	0.728193
$51$	1.35005	0.189044
$52$	2.23680	0.310188
$53$	3.66404	0.503294	0.251647	−	0.967819i	$-0.419028\pi$
$53$	3.66404	0.503294	0.251647	+	0.967819i	$0.419028\pi$
$54$	11.9633	1.62800
$55$	1.60395	0.216276
$56$	4.80662	0.642312
$57$	7.75693	1.02743
$58$	6.42359	0.843458
$59$	−8.84019	−1.15089	−0.575447	−	0.817839i	$-0.695172\pi$
$59$	−8.84019	−1.15089	−0.575447	+	0.817839i	$0.695172\pi$
$60$	−5.41320	−0.698842
$61$	−10.1961	−1.30548	−0.652739	−	0.757583i	$-0.726380\pi$
$61$	−10.1961	−1.30548	−0.652739	+	0.757583i	$0.726380\pi$
$62$	−13.1671	−1.67222
$63$	5.33714	0.672416
$64$	−11.3743	−1.42178
$65$	−1.43516	−0.178010
$66$	2.86383	0.352514
$67$	2.85720	0.349063	0.174532	−	0.984652i	$-0.444159\pi$
$67$	2.85720	0.349063	0.174532	+	0.984652i	$0.444159\pi$
$68$	2.49986	0.303152
$69$	−7.59185	−0.913952
$70$	−15.4235	−1.84346
$71$	0.715674	0.0849349	0.0424675	−	0.999098i	$-0.486478\pi$
$71$	0.715674	0.0849349	0.0424675	+	0.999098i	$0.486478\pi$
$72$	1.24843	0.147128
$73$	9.17039	1.07331	0.536657	−	0.843801i	$-0.319687\pi$
$73$	9.17039	1.07331	0.536657	+	0.843801i	$0.319687\pi$
$74$	−13.0988	−1.52270
$75$	−3.27703	−0.378399
$76$	14.3634	1.64759
$77$	4.53308	0.516592
$78$	−2.56247	−0.290143
$79$	−15.9552	−1.79510	−0.897550	−	0.440912i	$-0.854655\pi$
$79$	−15.9552	−1.79510	−0.897550	+	0.440912i	$0.854655\pi$
$80$	4.41154	0.493225
$81$	−4.08165	−0.453517
$82$	−24.0793	−2.65912
$83$	−12.3232	−1.35265	−0.676325	−	0.736603i	$-0.736429\pi$
$83$	−12.3232	−1.35265	−0.676325	+	0.736603i	$0.736429\pi$
$84$	−15.2988	−1.66923
$85$	−1.60395	−0.173973
$86$	−2.12129	−0.228744
$87$	−4.08815	−0.438295
$88$	1.06034	0.113033
$89$	6.18834	0.655963	0.327982	−	0.944684i	$-0.393632\pi$
$89$	6.18834	0.655963	0.327982	+	0.944684i	$0.393632\pi$
$90$	−4.00595	−0.422264
$91$	−4.05606	−0.425191
$92$	−14.0577	−1.46562
$93$	8.37991	0.868956
$94$	−7.17797	−0.740351
$95$	−9.21577	−0.945518
$96$	10.7398	1.09612
$97$	18.0060	1.82823	0.914114	−	0.405457i	$-0.132888\pi$
$97$	18.0060	1.82823	0.914114	+	0.405457i	$0.132888\pi$
$98$	−28.7409	−2.90327
$99$	1.17738	0.118331
$100$	−6.06803	−0.606803
$101$	10.1588	1.01084	0.505421	−	0.862873i	$-0.331337\pi$
$101$	10.1588	1.01084	0.505421	+	0.862873i	$0.331337\pi$
$102$	−2.86383	−0.283562
$103$	11.8307	1.16571	0.582857	−	0.812575i	$-0.301935\pi$
$103$	11.8307	1.16571	0.582857	+	0.812575i	$0.301935\pi$
$104$	−0.948764	−0.0930340
$105$	9.81594	0.957938
$106$	−7.77248	−0.754930
$107$	7.66772	0.741267	0.370633	−	0.928779i	$-0.379141\pi$
$107$	7.66772	0.741267	0.370633	+	0.928779i	$0.379141\pi$
$108$	−14.0983	−1.35661
$109$	1.24366	0.119121	0.0595607	−	0.998225i	$-0.481030\pi$
$109$	1.24366	0.119121	0.0595607	+	0.998225i	$0.481030\pi$
$110$	−3.40244	−0.324409
$111$	8.33641	0.791257
$112$	12.4679	1.17810
$113$	3.81585	0.358965	0.179483	−	0.983761i	$-0.442558\pi$
$113$	3.81585	0.358965	0.179483	+	0.983761i	$0.442558\pi$
$114$	−16.4547	−1.54112
$115$	9.01965	0.841087
$116$	−7.56996	−0.702853
$117$	−1.05348	−0.0973944
$118$	18.7526	1.72632
$119$	−4.53308	−0.415546
$120$	2.29607	0.209602
$121$	1.00000	0.0909091
$122$	21.6289	1.95819
$123$	15.3248	1.38179
$124$	15.5170	1.39346
$125$	11.9131	1.06554
$126$	−11.3216	−1.00861
$127$	−14.8361	−1.31649	−0.658243	−	0.752805i	$-0.728700\pi$
$127$	−14.8361	−1.31649	−0.658243	+	0.752805i	$0.728700\pi$
$128$	8.21782	0.726359
$129$	1.35005	0.118865
$130$	3.04440	0.267011
$131$	7.44224	0.650231	0.325116	−	0.945674i	$-0.394597\pi$
$131$	7.44224	0.650231	0.325116	+	0.945674i	$0.394597\pi$
$132$	−3.37492	−0.293749
$133$	−26.0456	−2.25844
$134$	−6.06095	−0.523586
$135$	9.04571	0.778531
$136$	−1.06034	−0.0909238
$137$	−21.9270	−1.87335	−0.936675	−	0.350201i	$-0.886113\pi$
$137$	−21.9270	−1.87335	−0.936675	+	0.350201i	$0.886113\pi$
$138$	16.1045	1.37091
$139$	7.16231	0.607499	0.303750	−	0.952752i	$-0.401761\pi$
$139$	7.16231	0.607499	0.303750	+	0.952752i	$0.401761\pi$
$140$	18.1760	1.53615
$141$	4.56826	0.384717
$142$	−1.51815	−0.127400
$143$	−0.894770	−0.0748244
$144$	3.23828	0.269857
$145$	4.85701	0.403352
$146$	−19.4530	−1.60994
$147$	18.2915	1.50866
$148$	15.4364	1.26886
$149$	8.18872	0.670846	0.335423	−	0.942068i	$-0.391121\pi$
$149$	8.18872	0.670846	0.335423	+	0.942068i	$0.391121\pi$
$150$	6.95153	0.567590
$151$	−18.1026	−1.47317	−0.736584	−	0.676347i	$-0.763562\pi$
$151$	−18.1026	−1.47317	−0.736584	+	0.676347i	$0.763562\pi$
$152$	−6.09240	−0.494159
$153$	−1.17738	−0.0951853
$154$	−9.61596	−0.774876
$155$	−9.95592	−0.799679
$156$	3.01978	0.241776
$157$	17.1521	1.36889	0.684444	−	0.729065i	$-0.260045\pi$
$157$	17.1521	1.36889	0.684444	+	0.729065i	$0.260045\pi$
$158$	33.8456	2.69261
$159$	4.94662	0.392292
$160$	−12.7596	−1.00874
$161$	25.4913	2.00900
$162$	8.65836	0.680265
$163$	0.737702	0.0577813	0.0288906	−	0.999583i	$-0.490803\pi$
$163$	0.737702	0.0577813	0.0288906	+	0.999583i	$0.490803\pi$
$164$	28.3766	2.21584
$165$	2.16540	0.168576
$166$	26.1411	2.02894
$167$	4.70137	0.363803	0.181901	−	0.983317i	$-0.441775\pi$
$167$	4.70137	0.363803	0.181901	+	0.983317i	$0.441775\pi$
$168$	6.48916	0.500650
$169$	−12.1994	−0.938414
$170$	3.40244	0.260955
$171$	−6.76483	−0.517319
$172$	2.49986	0.190612
$173$	−17.7514	−1.34962	−0.674809	−	0.737993i	$-0.735774\pi$
$173$	−17.7514	−1.34962	−0.674809	+	0.737993i	$0.735774\pi$
$174$	8.67214	0.657433
$175$	11.0034	0.831776
$176$	2.75042	0.207321
$177$	−11.9347	−0.897064
$178$	−13.1273	−0.983929
$179$	4.16077	0.310991	0.155495	−	0.987837i	$-0.450303\pi$
$179$	4.16077	0.310991	0.155495	+	0.987837i	$0.450303\pi$
$180$	4.72086	0.351872
$181$	17.0430	1.26680	0.633399	−	0.773826i	$-0.281659\pi$
$181$	17.0430	1.26680	0.633399	+	0.773826i	$0.281659\pi$
$182$	8.60407	0.637776
$183$	−13.7652	−1.01755
$184$	5.96275	0.439580
$185$	−9.90424	−0.728174
$186$	−17.7762	−1.30341
$187$	−1.00000	−0.0731272
$188$	8.45898	0.616934
$189$	25.5650	1.85958
$190$	19.5493	1.41825
$191$	9.68610	0.700861	0.350431	−	0.936589i	$-0.386035\pi$
$191$	9.68610	0.700861	0.350431	+	0.936589i	$0.386035\pi$
$192$	−15.3558	−1.10821
$193$	6.74611	0.485596	0.242798	−	0.970077i	$-0.421935\pi$
$193$	6.74611	0.485596	0.242798	+	0.970077i	$0.421935\pi$
$194$	−38.1958	−2.74230
$195$	−1.93754	−0.138750
$196$	33.8701	2.41929
$197$	−7.49347	−0.533888	−0.266944	−	0.963712i	$-0.586014\pi$
$197$	−7.49347	−0.533888	−0.266944	+	0.963712i	$0.586014\pi$
$198$	−2.49755	−0.177493
$199$	−16.1205	−1.14275	−0.571375	−	0.820689i	$-0.693590\pi$
$199$	−16.1205	−1.14275	−0.571375	+	0.820689i	$0.693590\pi$
$200$	2.57383	0.181997
$201$	3.85736	0.272077
$202$	−21.5498	−1.51624
$203$	13.7269	0.963437
$204$	3.37492	0.236292
$205$	−18.2069	−1.27162
$206$	−25.0963	−1.74854
$207$	6.62087	0.460182
$208$	−2.46100	−0.170639
$209$	−5.74568	−0.397437
$210$	−20.8224	−1.43688
$211$	−19.7117	−1.35701	−0.678504	−	0.734597i	$-0.737371\pi$
$211$	−19.7117	−1.35701	−0.678504	+	0.734597i	$0.737371\pi$
$212$	9.15958	0.629082
$213$	0.966193	0.0662025
$214$	−16.2654	−1.11188
$215$	−1.60395	−0.109388
$216$	5.97997	0.406885
$217$	−28.1374	−1.91009
$218$	−2.63817	−0.178679
$219$	12.3804	0.836593
$220$	4.00965	0.270330
$221$	0.894770	0.0601887
$222$	−17.6839	−1.18687
$223$	12.4905	0.836428	0.418214	−	0.908348i	$-0.362656\pi$
$223$	12.4905	0.836428	0.418214	+	0.908348i	$0.362656\pi$
$224$	−36.0612	−2.40944
$225$	2.85790	0.190527
$226$	−8.09452	−0.538440
$227$	−11.3312	−0.752081	−0.376041	−	0.926603i	$-0.622715\pi$
$227$	−11.3312	−0.752081	−0.376041	+	0.926603i	$0.622715\pi$
$228$	19.3912	1.28421
$229$	0.800643	0.0529080	0.0264540	−	0.999650i	$-0.491578\pi$
$229$	0.800643	0.0529080	0.0264540	+	0.999650i	$0.491578\pi$
$230$	−19.1333	−1.26161
$231$	6.11986	0.402657
$232$	3.21089	0.210805
$233$	−0.607229	−0.0397809	−0.0198904	−	0.999802i	$-0.506332\pi$
$233$	−0.607229	−0.0397809	−0.0198904	+	0.999802i	$0.506332\pi$
$234$	2.23474	0.146089
$235$	−5.42741	−0.354045
$236$	−22.0992	−1.43854
$237$	−21.5403	−1.39919
$238$	9.61596	0.623310
$239$	−11.4642	−0.741556	−0.370778	−	0.928722i	$-0.620909\pi$
$239$	−11.4642	−0.741556	−0.370778	+	0.928722i	$0.620909\pi$
$240$	5.95578	0.384444
$241$	−11.3964	−0.734105	−0.367053	−	0.930200i	$-0.619633\pi$
$241$	−11.3964	−0.734105	−0.367053	+	0.930200i	$0.619633\pi$
$242$	−2.12129	−0.136361
$243$	11.4085	0.731858
$244$	−25.4888	−1.63175
$245$	−21.7316	−1.38838
$246$	−32.5082	−2.07265
$247$	5.14106	0.327118
$248$	−6.58170	−0.417938
$249$	−16.6369	−1.05432
$250$	−25.2711	−1.59828
$251$	−14.0964	−0.889757	−0.444879	−	0.895591i	$-0.646753\pi$
$251$	−14.0964	−0.889757	−0.444879	+	0.895591i	$0.646753\pi$
$252$	13.3421	0.840473
$253$	5.62341	0.353541
$254$	31.4715	1.97470
$255$	−2.16540	−0.135603
$256$	5.31617	0.332260
$257$	−24.3319	−1.51778	−0.758890	−	0.651219i	$-0.774258\pi$
$257$	−24.3319	−1.51778	−0.758890	+	0.651219i	$0.774258\pi$
$258$	−2.86383	−0.178295
$259$	−27.9913	−1.73930
$260$	−3.58771	−0.222500
$261$	3.56528	0.220685
$262$	−15.7871	−0.975332
$263$	8.06694	0.497429	0.248714	−	0.968577i	$-0.419992\pi$
$263$	8.06694	0.497429	0.248714	+	0.968577i	$0.419992\pi$
$264$	1.43151	0.0881036
$265$	−5.87693	−0.361017
$266$	55.2502	3.38761
$267$	8.35455	0.511290
$268$	7.14261	0.436304
$269$	−5.22515	−0.318583	−0.159292	−	0.987232i	$-0.550921\pi$
$269$	−5.22515	−0.318583	−0.159292	+	0.987232i	$0.550921\pi$
$270$	−19.1885	−1.16778
$271$	−16.8716	−1.02488	−0.512438	−	0.858724i	$-0.671258\pi$
$271$	−16.8716	−1.02488	−0.512438	+	0.858724i	$0.671258\pi$
$272$	−2.75042	−0.166769
$273$	−5.47587	−0.331414
$274$	46.5134	2.80998
$275$	2.42735	0.146375
$276$	−18.9786	−1.14238
$277$	21.8995	1.31581	0.657905	−	0.753101i	$-0.271443\pi$
$277$	21.8995	1.31581	0.657905	+	0.753101i	$0.271443\pi$
$278$	−15.1933	−0.911235
$279$	−7.30813	−0.437526
$280$	−7.70958	−0.460735
$281$	9.16234	0.546579	0.273290	−	0.961932i	$-0.411888\pi$
$281$	9.16234	0.546579	0.273290	+	0.961932i	$0.411888\pi$
$282$	−9.69059	−0.577066
$283$	−2.28900	−0.136067	−0.0680336	−	0.997683i	$-0.521673\pi$
$283$	−2.28900	−0.136067	−0.0680336	+	0.997683i	$0.521673\pi$
$284$	1.78909	0.106163
$285$	−12.4417	−0.736983
$286$	1.89806	0.112235
$287$	−51.4563	−3.03737
$288$	−9.36618	−0.551908
$289$	1.00000	0.0588235
$290$	−10.3031	−0.605019
$291$	24.3089	1.42501
$292$	22.9247	1.34157
$293$	−21.8462	−1.27627	−0.638134	−	0.769925i	$-0.720293\pi$
$293$	−21.8462	−1.27627	−0.638134	+	0.769925i	$0.720293\pi$
$294$	−38.8015	−2.26295
$295$	14.1792	0.825546
$296$	−6.54753	−0.380568
$297$	5.63965	0.327246
$298$	−17.3706	−1.00625
$299$	−5.03165	−0.290988
$300$	−8.19212	−0.472972
$301$	−4.53308	−0.261282
$302$	38.4008	2.20972
$303$	13.7149	0.787900
$304$	−15.8030	−0.906367
$305$	16.3540	0.936429
$306$	2.49755	0.142776
$307$	−27.0810	−1.54559	−0.772797	−	0.634653i	$-0.781143\pi$
$307$	−27.0810	−1.54559	−0.772797	+	0.634653i	$0.781143\pi$
$308$	11.3321	0.645704
$309$	15.9720	0.908614
$310$	21.1194	1.19950
$311$	−1.20649	−0.0684139	−0.0342069	−	0.999415i	$-0.510891\pi$
$311$	−1.20649	−0.0684139	−0.0342069	+	0.999415i	$0.510891\pi$
$312$	−1.28087	−0.0725153
$313$	9.18903	0.519395	0.259697	−	0.965690i	$-0.416377\pi$
$313$	9.18903	0.519395	0.259697	+	0.965690i	$0.416377\pi$
$314$	−36.3846	−2.05330
$315$	−8.56050	−0.482329
$316$	−39.8858	−2.24375
$317$	4.75104	0.266845	0.133422	−	0.991059i	$-0.457403\pi$
$317$	4.75104	0.266845	0.133422	+	0.991059i	$0.457403\pi$
$318$	−10.4932	−0.588429
$319$	3.02816	0.169544
$320$	18.2437	1.01986
$321$	10.3518	0.577780
$322$	−54.0744	−3.01345
$323$	5.74568	0.319698
$324$	−10.2036	−0.566864
$325$	−2.17192	−0.120476
$326$	−1.56488	−0.0866706
$327$	1.67900	0.0928491
$328$	−12.0363	−0.664592
$329$	−15.3389	−0.845663
$330$	−4.59344	−0.252861
$331$	27.1099	1.49009	0.745047	−	0.667012i	$-0.232427\pi$
$331$	27.1099	1.49009	0.745047	+	0.667012i	$0.232427\pi$
$332$	−30.8063	−1.69072
$333$	−7.27020	−0.398404
$334$	−9.97295	−0.545696
$335$	−4.58281	−0.250386
$336$	16.8322	0.918272
$337$	−11.5539	−0.629380	−0.314690	−	0.949195i	$-0.601901\pi$
$337$	−11.5539	−0.629380	−0.314690	+	0.949195i	$0.601901\pi$
$338$	25.8784	1.40760
$339$	5.15158	0.279795
$340$	−4.00965	−0.217454
$341$	−6.20713	−0.336135
$342$	14.3501	0.775967
$343$	−29.6862	−1.60290
$344$	−1.06034	−0.0571699
$345$	12.1769	0.655585
$346$	37.6559	2.02439
$347$	22.9132	1.23004	0.615022	−	0.788510i	$-0.289147\pi$
$347$	22.9132	1.23004	0.615022	+	0.788510i	$0.289147\pi$
$348$	−10.2198	−0.547838
$349$	−26.0383	−1.39380	−0.696898	−	0.717170i	$-0.745437\pi$
$349$	−26.0383	−1.39380	−0.696898	+	0.717170i	$0.745437\pi$
$350$	−23.3413	−1.24764
$351$	−5.04619	−0.269346
$352$	−7.95513	−0.424010
$353$	−0.901560	−0.0479852	−0.0239926	−	0.999712i	$-0.507638\pi$
$353$	−0.901560	−0.0479852	−0.0239926	+	0.999712i	$0.507638\pi$
$354$	25.3168	1.34558
$355$	−1.14790	−0.0609245
$356$	15.4700	0.819908
$357$	−6.11986	−0.323897
$358$	−8.82619	−0.466479
$359$	−17.8974	−0.944588	−0.472294	−	0.881441i	$-0.656574\pi$
$359$	−17.8974	−0.944588	−0.472294	+	0.881441i	$0.656574\pi$
$360$	−2.00241	−0.105536
$361$	14.0128	0.737516
$362$	−36.1531	−1.90017
$363$	1.35005	0.0708590
$364$	−10.1396	−0.531458
$365$	−14.7088	−0.769896
$366$	29.2000	1.52631
$367$	35.5802	1.85727	0.928635	−	0.370995i	$-0.120983\pi$
$367$	35.5802	1.85727	0.928635	+	0.370995i	$0.120983\pi$
$368$	15.4667	0.806260
$369$	−13.3647	−0.695741
$370$	21.0097	1.09224
$371$	−16.6094	−0.862315
$372$	20.9486	1.08613
$373$	35.2062	1.82291	0.911455	−	0.411401i	$-0.134960\pi$
$373$	35.2062	1.82291	0.911455	+	0.411401i	$0.134960\pi$
$374$	2.12129	0.109689
$375$	16.0832	0.830533
$376$	−3.58797	−0.185036
$377$	−2.70950	−0.139546
$378$	−54.2306	−2.78932
$379$	18.9428	0.973026	0.486513	−	0.873673i	$-0.338269\pi$
$379$	18.9428	0.973026	0.486513	+	0.873673i	$0.338269\pi$
$380$	−23.0381	−1.18183
$381$	−20.0293	−1.02613
$382$	−20.5470	−1.05128
$383$	−4.24810	−0.217068	−0.108534	−	0.994093i	$-0.534616\pi$
$383$	−4.24810	−0.217068	−0.108534	+	0.994093i	$0.534616\pi$
$384$	11.0944	0.566160
$385$	−7.27082	−0.370555
$386$	−14.3104	−0.728382
$387$	−1.17738	−0.0598494
$388$	45.0124	2.28516
$389$	−28.5944	−1.44979	−0.724897	−	0.688857i	$-0.758113\pi$
$389$	−28.5944	−1.44979	−0.724897	+	0.688857i	$0.758113\pi$
$390$	4.11007	0.208122
$391$	−5.62341	−0.284388
$392$	−14.3664	−0.725612
$393$	10.0474	0.506822
$394$	15.8958	0.800819
$395$	25.5913	1.28764
$396$	2.94328	0.147905
$397$	−21.7445	−1.09133	−0.545664	−	0.838004i	$-0.683722\pi$
$397$	−21.7445	−1.09133	−0.545664	+	0.838004i	$0.683722\pi$
$398$	34.1961	1.71410
$399$	−35.1627	−1.76034
$400$	6.67624	0.333812
$401$	−20.6726	−1.03234	−0.516169	−	0.856487i	$-0.672643\pi$
$401$	−20.6726	−1.03234	−0.516169	+	0.856487i	$0.672643\pi$
$402$	−8.18256	−0.408109
$403$	5.55395	0.276662
$404$	25.3957	1.26348
$405$	6.54676	0.325311
$406$	−29.1186	−1.44513
$407$	−6.17491	−0.306079
$408$	−1.43151	−0.0708705
$409$	−14.9278	−0.738131	−0.369066	−	0.929403i	$-0.620322\pi$
$409$	−14.9278	−0.738131	−0.369066	+	0.929403i	$0.620322\pi$
$410$	38.6220	1.90741
$411$	−29.6024	−1.46018
$412$	29.5751	1.45706
$413$	40.0733	1.97188
$414$	−14.0448	−0.690262
$415$	19.7658	0.970267
$416$	7.11801	0.348989
$417$	9.66945	0.473515
$418$	12.1882	0.596146
$419$	−20.0504	−0.979528	−0.489764	−	0.871855i	$-0.662917\pi$
$419$	−20.0504	−0.979528	−0.489764	+	0.871855i	$0.662917\pi$
$420$	24.5385	1.19735
$421$	−26.6335	−1.29804	−0.649018	−	0.760773i	$-0.724820\pi$
$421$	−26.6335	−1.29804	−0.649018	+	0.760773i	$0.724820\pi$
$422$	41.8141	2.03548
$423$	−3.98399	−0.193708
$424$	−3.88514	−0.188679
$425$	−2.42735	−0.117744
$426$	−2.04957	−0.0993021
$427$	46.2197	2.23673
$428$	19.1682	0.926531
$429$	−1.20798	−0.0583218
$430$	3.40244	0.164080
$431$	−38.6023	−1.85941	−0.929704	−	0.368307i	$-0.879937\pi$
$431$	−38.6023	−1.85941	−0.929704	+	0.368307i	$0.879937\pi$
$432$	15.5114	0.746294
$433$	15.3579	0.738056	0.369028	−	0.929418i	$-0.379691\pi$
$433$	15.3579	0.738056	0.369028	+	0.929418i	$0.379691\pi$
$434$	59.6875	2.86509
$435$	6.55718	0.314393
$436$	3.10898	0.148893
$437$	−32.3103	−1.54561
$438$	−26.2625	−1.25487
$439$	17.0823	0.815292	0.407646	−	0.913140i	$-0.366350\pi$
$439$	17.0823	0.815292	0.407646	+	0.913140i	$0.366350\pi$
$440$	−1.70074	−0.0810795
$441$	−15.9520	−0.759620
$442$	−1.89806	−0.0902817
$443$	0.699711	0.0332443	0.0166221	−	0.999862i	$-0.494709\pi$
$443$	0.699711	0.0332443	0.0166221	+	0.999862i	$0.494709\pi$
$444$	20.8399	0.989016
$445$	−9.92578	−0.470527
$446$	−26.4960	−1.25462
$447$	11.0552	0.522891
$448$	51.5604	2.43600
$449$	20.5926	0.971827	0.485913	−	0.874007i	$-0.338487\pi$
$449$	20.5926	0.971827	0.485913	+	0.874007i	$0.338487\pi$
$450$	−6.06244	−0.285786
$451$	−11.3513	−0.534511
$452$	9.53910	0.448681
$453$	−24.4393	−1.14826
$454$	24.0368	1.12810
$455$	6.50571	0.304992
$456$	−8.22501	−0.385172
$457$	7.34008	0.343354	0.171677	−	0.985153i	$-0.445081\pi$
$457$	7.34008	0.343354	0.171677	+	0.985153i	$0.445081\pi$
$458$	−1.69839	−0.0793608
$459$	−5.63965	−0.263236
$460$	22.5479	1.05130
$461$	−22.4511	−1.04565	−0.522827	−	0.852439i	$-0.675122\pi$
$461$	−22.4511	−1.04565	−0.522827	+	0.852439i	$0.675122\pi$
$462$	−12.9820	−0.603976
$463$	−32.2725	−1.49983	−0.749915	−	0.661534i	$-0.769906\pi$
$463$	−32.2725	−1.49983	−0.749915	+	0.661534i	$0.769906\pi$
$464$	8.32871	0.386651
$465$	−13.4409	−0.623309
$466$	1.28811	0.0596704
$467$	1.93299	0.0894482	0.0447241	−	0.998999i	$-0.485759\pi$
$467$	1.93299	0.0894482	0.0447241	+	0.998999i	$0.485759\pi$
$468$	−2.63355	−0.121736
$469$	−12.9519	−0.598065
$470$	11.5131	0.531060
$471$	23.1561	1.06698
$472$	9.37365	0.431457
$473$	−1.00000	−0.0459800
$474$	45.6931	2.09875
$475$	−13.9468	−0.639921
$476$	−11.3321	−0.519404
$477$	−4.31395	−0.197522
$478$	24.3188	1.11232
$479$	−30.1508	−1.37763	−0.688813	−	0.724939i	$-0.741868\pi$
$479$	−30.1508	−1.37763	−0.688813	+	0.724939i	$0.741868\pi$
$480$	−17.2261	−0.786258
$481$	5.52512	0.251924
$482$	24.1750	1.10114
$483$	34.4145	1.56591
$484$	2.49986	0.113630
$485$	−28.8806	−1.31140
$486$	−24.2008	−1.09777
$487$	21.3503	0.967473	0.483736	−	0.875214i	$-0.339279\pi$
$487$	21.3503	0.967473	0.483736	+	0.875214i	$0.339279\pi$
$488$	10.8114	0.489408
$489$	0.995932	0.0450376
$490$	46.0989	2.08253
$491$	4.90253	0.221248	0.110624	−	0.993862i	$-0.464715\pi$
$491$	4.90253	0.221248	0.110624	+	0.993862i	$0.464715\pi$
$492$	38.3097	1.72714
$493$	−3.02816	−0.136381
$494$	−10.9057	−0.490669
$495$	−1.88845	−0.0848796
$496$	−17.0722	−0.766566
$497$	−3.24421	−0.145523
$498$	35.2917	1.58146
$499$	25.7276	1.15172	0.575862	−	0.817547i	$-0.304666\pi$
$499$	25.7276	1.15172	0.575862	+	0.817547i	$0.304666\pi$
$500$	29.7810	1.33185
$501$	6.34706	0.283566
$502$	29.9025	1.33462
$503$	2.70094	0.120429	0.0602144	−	0.998185i	$-0.480822\pi$
$503$	2.70094	0.120429	0.0602144	+	0.998185i	$0.480822\pi$
$504$	−5.65921	−0.252081
$505$	−16.2943	−0.725085
$506$	−11.9289	−0.530302
$507$	−16.4697	−0.731446
$508$	−37.0880	−1.64552
$509$	−40.2878	−1.78572	−0.892862	−	0.450331i	$-0.851306\pi$
$509$	−40.2878	−1.78572	−0.892862	+	0.450331i	$0.851306\pi$
$510$	4.59344	0.203401
$511$	−41.5701	−1.83895
$512$	−27.7128	−1.22474
$513$	−32.4036	−1.43065
$514$	51.6149	2.27663
$515$	−18.9758	−0.836175
$516$	3.37492	0.148573
$517$	−3.38378	−0.148819
$518$	59.3777	2.60891
$519$	−23.9653	−1.05196
$520$	1.52177	0.0667340
$521$	−37.5481	−1.64501	−0.822506	−	0.568756i	$-0.807425\pi$
$521$	−37.5481	−1.64501	−0.822506	+	0.568756i	$0.807425\pi$
$522$	−7.56298	−0.331023
$523$	10.6478	0.465597	0.232799	−	0.972525i	$-0.425212\pi$
$523$	10.6478	0.465597	0.232799	+	0.972525i	$0.425212\pi$
$524$	18.6045	0.812743
$525$	14.8550	0.648327
$526$	−17.1123	−0.746131
$527$	6.20713	0.270387
$528$	3.71320	0.161596
$529$	8.62269	0.374900
$530$	12.4667	0.541517
$531$	10.4082	0.451679
$532$	−65.1103	−2.82289
$533$	10.1568	0.439939
$534$	−17.7224	−0.766923
$535$	−12.2986	−0.531716
$536$	−3.02962	−0.130860
$537$	5.61723	0.242401
$538$	11.0840	0.477867
$539$	−13.5488	−0.583588
$540$	22.6130	0.973108
$541$	9.70174	0.417110	0.208555	−	0.978011i	$-0.433124\pi$
$541$	9.70174	0.417110	0.208555	+	0.978011i	$0.433124\pi$
$542$	35.7895	1.53729
$543$	23.0089	0.987404
$544$	7.95513	0.341073
$545$	−1.99477	−0.0854467
$546$	11.6159	0.497114
$547$	−14.2489	−0.609241	−0.304620	−	0.952474i	$-0.598530\pi$
$547$	−14.2489	−0.609241	−0.304620	+	0.952474i	$0.598530\pi$
$548$	−54.8144	−2.34155
$549$	12.0047	0.512346
$550$	−5.14910	−0.219559
$551$	−17.3988	−0.741214
$552$	8.04998	0.342630
$553$	72.3262	3.07562
$554$	−46.4550	−1.97368
$555$	−13.3712	−0.567575
$556$	17.9048	0.759331
$557$	−4.01900	−0.170291	−0.0851453	−	0.996369i	$-0.527135\pi$
$557$	−4.01900	−0.170291	−0.0851453	+	0.996369i	$0.527135\pi$
$558$	15.5026	0.656279
$559$	0.894770	0.0378447
$560$	−19.9978	−0.845063
$561$	−1.35005	−0.0569990
$562$	−19.4360	−0.819856
$563$	24.5602	1.03509	0.517544	−	0.855657i	$-0.326846\pi$
$563$	24.5602	1.03509	0.517544	+	0.855657i	$0.326846\pi$
$564$	11.4200	0.480869
$565$	−6.12044	−0.257489
$566$	4.85564	0.204098
$567$	18.5024	0.777030
$568$	−0.758861	−0.0318411
$569$	−8.81938	−0.369728	−0.184864	−	0.982764i	$-0.559184\pi$
$569$	−8.81938	−0.369728	−0.184864	+	0.982764i	$0.559184\pi$
$570$	26.3924	1.10546
$571$	−36.1769	−1.51396	−0.756978	−	0.653440i	$-0.773325\pi$
$571$	−36.1769	−1.51396	−0.756978	+	0.653440i	$0.773325\pi$
$572$	−2.23680	−0.0935252
$573$	13.0767	0.546286
$574$	109.153	4.55598
$575$	13.6500	0.569243
$576$	13.3918	0.557991
$577$	−4.71121	−0.196130	−0.0980652	−	0.995180i	$-0.531265\pi$
$577$	−4.71121	−0.196130	−0.0980652	+	0.995180i	$0.531265\pi$
$578$	−2.12129	−0.0882339
$579$	9.10756	0.378497
$580$	12.1418	0.504162
$581$	55.8622	2.31755
$582$	−51.5661	−2.13748
$583$	−3.66404	−0.151749
$584$	−9.72377	−0.402373
$585$	1.68973	0.0698617
$586$	46.3420	1.91437
$587$	23.8581	0.984729	0.492364	−	0.870389i	$-0.336133\pi$
$587$	23.8581	0.984729	0.492364	+	0.870389i	$0.336133\pi$
$588$	45.7261	1.88571
$589$	35.6642	1.46952
$590$	−30.0782	−1.23830
$591$	−10.1165	−0.416138
$592$	−16.9836	−0.698022
$593$	36.8701	1.51408	0.757038	−	0.653371i	$-0.226646\pi$
$593$	36.8701	1.51408	0.757038	+	0.653371i	$0.226646\pi$
$594$	−11.9633	−0.490861
$595$	7.27082	0.298075
$596$	20.4707	0.838511
$597$	−21.7634	−0.890715
$598$	10.6736	0.436475
$599$	−3.24023	−0.132392	−0.0661962	−	0.997807i	$-0.521086\pi$
$599$	−3.24023	−0.132392	−0.0661962	+	0.997807i	$0.521086\pi$
$600$	3.47478	0.141857
$601$	19.1314	0.780386	0.390193	−	0.920733i	$-0.372408\pi$
$601$	19.1314	0.780386	0.390193	+	0.920733i	$0.372408\pi$
$602$	9.61596	0.391917
$603$	−3.36401	−0.136993
$604$	−45.2539	−1.84135
$605$	−1.60395	−0.0652098
$606$	−29.0932	−1.18183
$607$	−20.9200	−0.849117	−0.424558	−	0.905401i	$-0.639571\pi$
$607$	−20.9200	−0.849117	−0.424558	+	0.905401i	$0.639571\pi$
$608$	45.7076	1.85369
$609$	18.5319	0.750950
$610$	−34.6916	−1.40462
$611$	3.02771	0.122488
$612$	−2.94328	−0.118975
$613$	−34.5619	−1.39594	−0.697971	−	0.716126i	$-0.745913\pi$
$613$	−34.5619	−1.39594	−0.697971	+	0.716126i	$0.745913\pi$
$614$	57.4466	2.31835
$615$	−24.5801	−0.991166
$616$	−4.80662	−0.193664
$617$	−19.9308	−0.802384	−0.401192	−	0.915994i	$-0.631404\pi$
$617$	−19.9308	−0.802384	−0.401192	+	0.915994i	$0.631404\pi$
$618$	−33.8812	−1.36290
$619$	30.8898	1.24157	0.620784	−	0.783982i	$-0.286815\pi$
$619$	30.8898	1.24157	0.620784	+	0.783982i	$0.286815\pi$
$620$	−24.8884	−0.999542
$621$	31.7140	1.27264
$622$	2.55931	0.102619
$623$	−28.0522	−1.12389
$624$	−3.32246	−0.133005
$625$	−6.97123	−0.278849
$626$	−19.4926	−0.779080
$627$	−7.75693	−0.309782
$628$	42.8779	1.71101
$629$	6.17491	0.246210
$630$	18.1593	0.723483
$631$	8.18195	0.325718	0.162859	−	0.986649i	$-0.447928\pi$
$631$	8.18195	0.325718	0.162859	+	0.986649i	$0.447928\pi$
$632$	16.9180	0.672962
$633$	−26.6117	−1.05772
$634$	−10.0783	−0.400261
$635$	23.7963	0.944326
$636$	12.3658	0.490338
$637$	12.1230	0.480332
$638$	−6.42359	−0.254312
$639$	−0.842619	−0.0333335
$640$	−13.1810	−0.521023
$641$	45.0270	1.77846	0.889229	−	0.457462i	$-0.151241\pi$
$641$	45.0270	1.77846	0.889229	+	0.457462i	$0.151241\pi$
$642$	−21.9591	−0.866656
$643$	3.21875	0.126935	0.0634675	−	0.997984i	$-0.479784\pi$
$643$	3.21875	0.126935	0.0634675	+	0.997984i	$0.479784\pi$
$644$	63.7247	2.51111
$645$	−2.16540	−0.0852627
$646$	−12.1882	−0.479539
$647$	−29.7823	−1.17086	−0.585432	−	0.810721i	$-0.699075\pi$
$647$	−29.7823	−1.17086	−0.585432	+	0.810721i	$0.699075\pi$
$648$	4.32796	0.170018
$649$	8.84019	0.347008
$650$	4.60726	0.180712
$651$	−37.9868	−1.48882
$652$	1.84415	0.0722226
$653$	16.2837	0.637232	0.318616	−	0.947884i	$-0.396782\pi$
$653$	16.2837	0.637232	0.318616	+	0.947884i	$0.396782\pi$
$654$	−3.56165	−0.139271
$655$	−11.9370	−0.466416
$656$	−31.2208	−1.21897
$657$	−10.7970	−0.421231
$658$	32.5383	1.26848
$659$	−1.47647	−0.0575149	−0.0287575	−	0.999586i	$-0.509155\pi$
$659$	−1.47647	−0.0575149	−0.0287575	+	0.999586i	$0.509155\pi$
$660$	5.41320	0.210709
$661$	29.7457	1.15697	0.578487	−	0.815692i	$-0.303643\pi$
$661$	29.7457	1.15697	0.578487	+	0.815692i	$0.303643\pi$
$662$	−57.5078	−2.23511
$663$	1.20798	0.0469141
$664$	13.0669	0.507093
$665$	41.7758	1.62000
$666$	15.4222	0.597597
$667$	17.0285	0.659348
$668$	11.7528	0.454728
$669$	16.8628	0.651953
$670$	9.72146	0.375573
$671$	10.1961	0.393616
$672$	−48.6843	−1.87804
$673$	6.11258	0.235623	0.117811	−	0.993036i	$-0.462412\pi$
$673$	6.11258	0.235623	0.117811	+	0.993036i	$0.462412\pi$
$674$	24.5091	0.944055
$675$	13.6894	0.526905
$676$	−30.4967	−1.17295
$677$	−40.0929	−1.54090	−0.770448	−	0.637503i	$-0.779968\pi$
$677$	−40.0929	−1.54090	−0.770448	+	0.637503i	$0.779968\pi$
$678$	−10.9280	−0.419686
$679$	−81.6224	−3.13238
$680$	1.70074	0.0652203
$681$	−15.2977	−0.586209
$682$	13.1671	0.504195
$683$	24.9039	0.952921	0.476461	−	0.879196i	$-0.341919\pi$
$683$	24.9039	0.952921	0.476461	+	0.879196i	$0.341919\pi$
$684$	−16.9111	−0.646613
$685$	35.1698	1.34377
$686$	62.9729	2.40431
$687$	1.08091	0.0412391
$688$	−2.75042	−0.104859
$689$	3.27847	0.124900
$690$	−25.8308	−0.983362
$691$	16.5740	0.630504	0.315252	−	0.949008i	$-0.397911\pi$
$691$	16.5740	0.630504	0.315252	+	0.949008i	$0.397911\pi$
$692$	−44.3761	−1.68693
$693$	−5.33714	−0.202741
$694$	−48.6054	−1.84504
$695$	−11.4880	−0.435764
$696$	4.33484	0.164312
$697$	11.3513	0.429961
$698$	55.2346	2.09066
$699$	−0.819787	−0.0310072
$700$	27.5068	1.03966
$701$	−11.7750	−0.444737	−0.222369	−	0.974963i	$-0.571379\pi$
$701$	−11.7750	−0.444737	−0.222369	+	0.974963i	$0.571379\pi$
$702$	10.7044	0.404012
$703$	35.4790	1.33812
$704$	11.3743	0.428684
$705$	−7.32725	−0.275960
$706$	1.91247	0.0719766
$707$	−46.0508	−1.73192
$708$	−29.8350	−1.12127
$709$	30.7825	1.15606	0.578031	−	0.816015i	$-0.303821\pi$
$709$	30.7825	1.15606	0.578031	+	0.816015i	$0.303821\pi$
$710$	2.43504	0.0913853
$711$	18.7853	0.704503
$712$	−6.56177	−0.245913
$713$	−34.9052	−1.30721
$714$	12.9820	0.485838
$715$	1.43516	0.0536721
$716$	10.4013	0.388716
$717$	−15.4772	−0.578005
$718$	37.9655	1.41686
$719$	6.01929	0.224482	0.112241	−	0.993681i	$-0.464197\pi$
$719$	6.01929	0.224482	0.112241	+	0.993681i	$0.464197\pi$
$720$	−5.19404	−0.193571
$721$	−53.6295	−1.99727
$722$	−29.7252	−1.10626
$723$	−15.3856	−0.572198
$724$	42.6051	1.58341
$725$	7.35039	0.272987
$726$	−2.86383	−0.106287
$727$	−42.3690	−1.57138	−0.785690	−	0.618621i	$-0.787692\pi$
$727$	−42.3690	−1.57138	−0.785690	+	0.618621i	$0.787692\pi$
$728$	4.30082	0.159399
$729$	27.6470	1.02396
$730$	31.2017	1.15483
$731$	1.00000	0.0369863
$732$	−34.4111	−1.27187
$733$	11.1677	0.412487	0.206243	−	0.978501i	$-0.433876\pi$
$733$	11.1677	0.412487	0.206243	+	0.978501i	$0.433876\pi$
$734$	−75.4757	−2.78586
$735$	−29.3386	−1.08217
$736$	−44.7349	−1.64895
$737$	−2.85720	−0.105246
$738$	28.3505	1.04359
$739$	27.3680	1.00675	0.503374	−	0.864069i	$-0.332092\pi$
$739$	27.3680	1.00675	0.503374	+	0.864069i	$0.332092\pi$
$740$	−24.7592	−0.910167
$741$	6.94066	0.254972
$742$	35.2332	1.29345
$743$	−35.1915	−1.29105	−0.645525	−	0.763739i	$-0.723361\pi$
$743$	−35.1915	−1.29105	−0.645525	+	0.763739i	$0.723361\pi$
$744$	−8.88559	−0.325762
$745$	−13.1343	−0.481203
$746$	−74.6825	−2.73432
$747$	14.5091	0.530860
$748$	−2.49986	−0.0914039
$749$	−34.7584	−1.27004
$750$	−34.1171	−1.24578
$751$	−17.4790	−0.637819	−0.318910	−	0.947785i	$-0.603317\pi$
$751$	−17.4790	−0.637819	−0.318910	+	0.947785i	$0.603317\pi$
$752$	−9.30683	−0.339385
$753$	−19.0308	−0.693521
$754$	5.74763	0.209316
$755$	29.0356	1.05671
$756$	63.9088	2.32434
$757$	−37.1050	−1.34860	−0.674302	−	0.738456i	$-0.735555\pi$
$757$	−37.1050	−1.34860	−0.674302	+	0.738456i	$0.735555\pi$
$758$	−40.1831	−1.45952
$759$	7.59185	0.275567
$760$	9.77189	0.354464
$761$	−22.6338	−0.820476	−0.410238	−	0.911978i	$-0.634554\pi$
$761$	−22.6338	−0.820476	−0.410238	+	0.911978i	$0.634554\pi$
$762$	42.4880	1.53918
$763$	−5.63762	−0.204096
$764$	24.2139	0.876027
$765$	1.88845	0.0682771
$766$	9.01144	0.325596
$767$	−7.90994	−0.285611
$768$	7.17707	0.258980
$769$	12.5856	0.453848	0.226924	−	0.973912i	$-0.427133\pi$
$769$	12.5856	0.453848	0.226924	+	0.973912i	$0.427133\pi$
$770$	15.4235	0.555824
$771$	−32.8491	−1.18303
$772$	16.8643	0.606960
$773$	16.3638	0.588566	0.294283	−	0.955718i	$-0.404919\pi$
$773$	16.3638	0.588566	0.294283	+	0.955718i	$0.404919\pi$
$774$	2.49755	0.0897727
$775$	−15.0669	−0.541218
$776$	−19.0925	−0.685382
$777$	−37.7896	−1.35569
$778$	60.6570	2.17466
$779$	65.2208	2.33678
$780$	−4.84357	−0.173428
$781$	−0.715674	−0.0256088
$782$	11.9289	0.426575
$783$	17.0777	0.610308
$784$	−37.2649	−1.33089
$785$	−27.5111	−0.981914
$786$	−21.3133	−0.760222
$787$	1.59031	0.0566884	0.0283442	−	0.999598i	$-0.490977\pi$
$787$	1.59031	0.0566884	0.0283442	+	0.999598i	$0.490977\pi$
$788$	−18.7326	−0.667322
$789$	10.8907	0.387720
$790$	−54.2865	−1.93143
$791$	−17.2976	−0.615031
$792$	−1.24843	−0.0443609
$793$	−9.12317	−0.323973
$794$	46.1264	1.63697
$795$	−7.93412	−0.281394
$796$	−40.2989	−1.42836
$797$	−23.4033	−0.828987	−0.414494	−	0.910052i	$-0.636041\pi$
$797$	−23.4033	−0.828987	−0.414494	+	0.910052i	$0.636041\pi$
$798$	74.5903	2.64047
$799$	3.38378	0.119710
$800$	−19.3099	−0.682707
$801$	−7.28601	−0.257439
$802$	43.8525	1.54848
$803$	−9.17039	−0.323616
$804$	9.64285	0.340077
$805$	−40.8868	−1.44107
$806$	−11.7815	−0.414987
$807$	−7.05419	−0.248319
$808$	−10.7719	−0.378953
$809$	34.6676	1.21885	0.609424	−	0.792844i	$-0.291401\pi$
$809$	34.6676	1.21885	0.609424	+	0.792844i	$0.291401\pi$
$810$	−13.8876	−0.487959
$811$	−25.8975	−0.909384	−0.454692	−	0.890649i	$-0.650251\pi$
$811$	−25.8975	−0.909384	−0.454692	+	0.890649i	$0.650251\pi$
$812$	34.3152	1.20423
$813$	−22.7774	−0.798839
$814$	13.0988	0.459111
$815$	−1.18324	−0.0414470
$816$	−3.71320	−0.129988
$817$	5.74568	0.201016
$818$	31.6661	1.10718
$819$	4.77551	0.166870
$820$	−45.5146	−1.58944
$821$	47.8939	1.67151	0.835755	−	0.549103i	$-0.185030\pi$
$821$	47.8939	1.67151	0.835755	+	0.549103i	$0.185030\pi$
$822$	62.7953	2.19024
$823$	−21.5145	−0.749949	−0.374975	−	0.927035i	$-0.622349\pi$
$823$	−21.5145	−0.749949	−0.374975	+	0.927035i	$0.622349\pi$
$824$	−12.5446	−0.437012
$825$	3.27703	0.114092
$826$	−85.0069	−2.95777
$827$	−50.8283	−1.76747	−0.883737	−	0.467983i	$-0.844981\pi$
$827$	−50.8283	−1.76747	−0.883737	+	0.467983i	$0.844981\pi$
$828$	16.5512	0.575195
$829$	−1.79519	−0.0623494	−0.0311747	−	0.999514i	$-0.509925\pi$
$829$	−1.79519	−0.0623494	−0.0311747	+	0.999514i	$0.509925\pi$
$830$	−41.9290	−1.45538
$831$	29.5653	1.02561
$832$	−10.1773	−0.352836
$833$	13.5488	0.469438
$834$	−20.5117	−0.710261
$835$	−7.54075	−0.260958
$836$	−14.3634	−0.496768
$837$	−35.0060	−1.20999
$838$	42.5328	1.46927
$839$	−52.1184	−1.79933	−0.899664	−	0.436582i	$-0.856189\pi$
$839$	−52.1184	−1.79933	−0.899664	+	0.436582i	$0.856189\pi$
$840$	−10.4083	−0.359120
$841$	−19.8303	−0.683803
$842$	56.4972	1.94702
$843$	12.3696	0.426031
$844$	−49.2764	−1.69616
$845$	19.5672	0.673132
$846$	8.45118	0.290558
$847$	−4.53308	−0.155758
$848$	−10.0777	−0.346068
$849$	−3.09026	−0.106057
$850$	5.14910	0.176613
$851$	−34.7240	−1.19032
$852$	2.41535	0.0827484
$853$	−14.2140	−0.486678	−0.243339	−	0.969941i	$-0.578243\pi$
$853$	−14.2140	−0.486678	−0.243339	+	0.969941i	$0.578243\pi$
$854$	−98.0453	−3.35504
$855$	10.8504	0.371077
$856$	−8.13042	−0.277892
$857$	−8.13322	−0.277825	−0.138913	−	0.990305i	$-0.544361\pi$
$857$	−8.13322	−0.277825	−0.138913	+	0.990305i	$0.544361\pi$
$858$	2.56247	0.0874814
$859$	14.3524	0.489698	0.244849	−	0.969561i	$-0.421262\pi$
$859$	14.3524	0.489698	0.244849	+	0.969561i	$0.421262\pi$
$860$	−4.00965	−0.136728
$861$	−69.4683	−2.36747
$862$	81.8866	2.78907
$863$	55.1946	1.87885	0.939423	−	0.342760i	$-0.111362\pi$
$863$	55.1946	1.87885	0.939423	+	0.342760i	$0.111362\pi$
$864$	−44.8641	−1.52631
$865$	28.4724	0.968091
$866$	−32.5786	−1.10707
$867$	1.35005	0.0458500
$868$	−70.3395	−2.38748
$869$	15.9552	0.541243
$870$	−13.9097	−0.471582
$871$	2.55654	0.0866251
$872$	−1.31871	−0.0446572
$873$	−21.1998	−0.717505
$874$	68.5394	2.31838
$875$	−54.0029	−1.82563
$876$	30.9494	1.04568
$877$	53.2848	1.79930	0.899650	−	0.436611i	$-0.143822\pi$
$877$	53.2848	1.79930	0.899650	+	0.436611i	$0.143822\pi$
$878$	−36.2364	−1.22292
$879$	−29.4933	−0.994786
$880$	−4.41154	−0.148713
$881$	−9.74148	−0.328199	−0.164099	−	0.986444i	$-0.552472\pi$
$881$	−9.74148	−0.328199	−0.164099	+	0.986444i	$0.552472\pi$
$882$	33.8388	1.13941
$883$	−1.20413	−0.0405222	−0.0202611	−	0.999795i	$-0.506450\pi$
$883$	−1.20413	−0.0405222	−0.0202611	+	0.999795i	$0.506450\pi$
$884$	2.23680	0.0752317
$885$	19.1426	0.643471
$886$	−1.48429	−0.0498656
$887$	−27.4999	−0.923356	−0.461678	−	0.887048i	$-0.652752\pi$
$887$	−27.4999	−0.923356	−0.461678	+	0.887048i	$0.652752\pi$
$888$	−8.83947	−0.296633
$889$	67.2530	2.25559
$890$	21.0554	0.705780
$891$	4.08165	0.136741
$892$	31.2246	1.04548
$893$	19.4421	0.650606
$894$	−23.4512	−0.784324
$895$	−6.67366	−0.223076
$896$	−37.2520	−1.24450
$897$	−6.79296	−0.226810
$898$	−43.6829	−1.45772
$899$	−18.7962	−0.626887
$900$	7.14436	0.238145
$901$	3.66404	0.122067
$902$	24.0793	0.801754
$903$	−6.11986	−0.203656
$904$	−4.04612	−0.134572
$905$	−27.3361	−0.908683
$906$	51.8428	1.72236
$907$	5.75278	0.191018	0.0955089	−	0.995429i	$-0.469552\pi$
$907$	5.75278	0.191018	0.0955089	+	0.995429i	$0.469552\pi$
$908$	−28.3265	−0.940049
$909$	−11.9608	−0.396714
$910$	−13.8005	−0.457482
$911$	−25.8306	−0.855806	−0.427903	−	0.903825i	$-0.640748\pi$
$911$	−25.8306	−0.855806	−0.427903	+	0.903825i	$0.640748\pi$
$912$	−21.3348	−0.706467
$913$	12.3232	0.407840
$914$	−15.5704	−0.515023
$915$	22.0787	0.729899
$916$	2.00150	0.0661313
$917$	−33.7362	−1.11407
$918$	11.9633	0.394848
$919$	59.1823	1.95224	0.976122	−	0.217224i	$-0.0697003\pi$
$919$	59.1823	1.95224	0.976122	+	0.217224i	$0.0697003\pi$
$920$	−9.56394	−0.315314
$921$	−36.5606	−1.20471
$922$	47.6253	1.56846
$923$	0.640364	0.0210778
$924$	15.2988	0.503293
$925$	−14.9887	−0.492824
$926$	68.4592	2.24971
$927$	−13.9292	−0.457495
$928$	−24.0894	−0.790772
$929$	53.6562	1.76040	0.880201	−	0.474602i	$-0.157408\pi$
$929$	53.6562	1.76040	0.880201	+	0.474602i	$0.157408\pi$
$930$	28.5121	0.934949
$931$	77.8469	2.55133
$932$	−1.51799	−0.0497233
$933$	−1.62882	−0.0533251
$934$	−4.10043	−0.134170
$935$	1.60395	0.0524547
$936$	1.11705	0.0365120
$937$	21.5314	0.703401	0.351701	−	0.936113i	$-0.385604\pi$
$937$	21.5314	0.703401	0.351701	+	0.936113i	$0.385604\pi$
$938$	27.4748	0.897083
$939$	12.4056	0.404842
$940$	−13.5678	−0.442532
$941$	−7.49397	−0.244296	−0.122148	−	0.992512i	$-0.538978\pi$
$941$	−7.49397	−0.244296	−0.122148	+	0.992512i	$0.538978\pi$
$942$	−49.1208	−1.60044
$943$	−63.8329	−2.07869
$944$	24.3143	0.791362
$945$	−41.0049	−1.33389
$946$	2.12129	0.0689690
$947$	−61.1766	−1.98797	−0.993987	−	0.109500i	$-0.965075\pi$
$947$	−61.1766	−1.98797	−0.993987	+	0.109500i	$0.965075\pi$
$948$	−53.8476	−1.74889
$949$	8.20539	0.266358
$950$	29.5851	0.959867
$951$	6.41411	0.207992
$952$	4.80662	0.155784
$953$	−34.1480	−1.10616	−0.553082	−	0.833127i	$-0.686548\pi$
$953$	−34.1480	−1.10616	−0.553082	+	0.833127i	$0.686548\pi$
$954$	9.15113	0.296279
$955$	−15.5360	−0.502733
$956$	−28.6588	−0.926892
$957$	4.08815	0.132151
$958$	63.9585	2.06641
$959$	99.3967	3.20969
$960$	24.6299	0.794925
$961$	7.52848	0.242854
$962$	−11.7204	−0.377880
$963$	−9.02780	−0.290917
$964$	−28.4893	−0.917580
$965$	−10.8204	−0.348321
$966$	−73.0030	−2.34883
$967$	−21.5863	−0.694169	−0.347084	−	0.937834i	$-0.612828\pi$
$967$	−21.5863	−0.694169	−0.347084	+	0.937834i	$0.612828\pi$
$968$	−1.06034	−0.0340808
$969$	7.75693	0.249188
$970$	61.2641	1.96707
$971$	−21.9094	−0.703106	−0.351553	−	0.936168i	$-0.614346\pi$
$971$	−21.9094	−0.703106	−0.351553	+	0.936168i	$0.614346\pi$
$972$	28.5197	0.914770
$973$	−32.4673	−1.04085
$974$	−45.2900	−1.45119
$975$	−2.93219	−0.0939052
$976$	28.0436	0.897654
$977$	6.59345	0.210943	0.105472	−	0.994422i	$-0.466365\pi$
$977$	6.59345	0.210943	0.105472	+	0.994422i	$0.466365\pi$
$978$	−2.11266	−0.0675553
$979$	−6.18834	−0.197780
$980$	−54.3258	−1.73537
$981$	−1.46426	−0.0467503
$982$	−10.3997	−0.331867
$983$	−17.2978	−0.551713	−0.275857	−	0.961199i	$-0.588962\pi$
$983$	−17.2978	−0.551713	−0.275857	+	0.961199i	$0.588962\pi$
$984$	−16.2495	−0.518016
$985$	12.0191	0.382962
$986$	6.42359	0.204569
$987$	−20.7083	−0.659152
$988$	12.8519	0.408874
$989$	−5.62341	−0.178814
$990$	4.00595	0.127317
$991$	34.2575	1.08823	0.544113	−	0.839012i	$-0.316866\pi$
$991$	34.2575	1.08823	0.544113	+	0.839012i	$0.316866\pi$
$992$	49.3785	1.56777
$993$	36.5996	1.16145
$994$	6.88189	0.218280
$995$	25.8564	0.819703
$996$	−41.5900	−1.31783
$997$	8.48372	0.268682	0.134341	−	0.990935i	$-0.457108\pi$
$997$	8.48372	0.268682	0.134341	+	0.990935i	$0.457108\pi$
$998$	−54.5756	−1.72756
$999$	−34.8243	−1.10179

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.g.1.12	✓	69

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.g.1.12	✓	69	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:	\( N \)	\(=\)	\( 8041 = 11 \cdot 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8041.a (trivial)

\(f(q)\)	\(=\)	\(q-2.12129 q^{2} +1.35005 q^{3} +2.49986 q^{4} -1.60395 q^{5} -2.86383 q^{6} -4.53308 q^{7} -1.06034 q^{8} -1.17738 q^{9} +O(q^{10})\)	\(q-2.12129 q^{2} +1.35005 q^{3} +2.49986 q^{4} -1.60395 q^{5} -2.86383 q^{6} -4.53308 q^{7} -1.06034 q^{8} -1.17738 q^{9} +3.40244 q^{10} -1.00000 q^{11} +3.37492 q^{12} +0.894770 q^{13} +9.61596 q^{14} -2.16540 q^{15} -2.75042 q^{16} +1.00000 q^{17} +2.49755 q^{18} +5.74568 q^{19} -4.00965 q^{20} -6.11986 q^{21} +2.12129 q^{22} -5.62341 q^{23} -1.43151 q^{24} -2.42735 q^{25} -1.89806 q^{26} -5.63965 q^{27} -11.3321 q^{28} -3.02816 q^{29} +4.59344 q^{30} +6.20713 q^{31} +7.95513 q^{32} -1.35005 q^{33} -2.12129 q^{34} +7.27082 q^{35} -2.94328 q^{36} +6.17491 q^{37} -12.1882 q^{38} +1.20798 q^{39} +1.70074 q^{40} +11.3513 q^{41} +12.9820 q^{42} +1.00000 q^{43} -2.49986 q^{44} +1.88845 q^{45} +11.9289 q^{46} +3.38378 q^{47} -3.71320 q^{48} +13.5488 q^{49} +5.14910 q^{50} +1.35005 q^{51} +2.23680 q^{52} +3.66404 q^{53} +11.9633 q^{54} +1.60395 q^{55} +4.80662 q^{56} +7.75693 q^{57} +6.42359 q^{58} -8.84019 q^{59} -5.41320 q^{60} -10.1961 q^{61} -13.1671 q^{62} +5.33714 q^{63} -11.3743 q^{64} -1.43516 q^{65} +2.86383 q^{66} +2.85720 q^{67} +2.49986 q^{68} -7.59185 q^{69} -15.4235 q^{70} +0.715674 q^{71} +1.24843 q^{72} +9.17039 q^{73} -13.0988 q^{74} -3.27703 q^{75} +14.3634 q^{76} +4.53308 q^{77} -2.56247 q^{78} -15.9552 q^{79} +4.41154 q^{80} -4.08165 q^{81} -24.0793 q^{82} -12.3232 q^{83} -15.2988 q^{84} -1.60395 q^{85} -2.12129 q^{86} -4.08815 q^{87} +1.06034 q^{88} +6.18834 q^{89} -4.00595 q^{90} -4.05606 q^{91} -14.0577 q^{92} +8.37991 q^{93} -7.17797 q^{94} -9.21577 q^{95} +10.7398 q^{96} +18.0060 q^{97} -28.7409 q^{98} +1.17738 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 69 q - 11 q^{2} - 3 q^{3} + 65 q^{4} - 6 q^{5} - 10 q^{6} - 11 q^{7} - 33 q^{8} + 56 q^{9}+O(q^{10}) \) 69 * q - 11 * q^2 - 3 * q^3 + 65 * q^4 - 6 * q^5 - 10 * q^6 - 11 * q^7 - 33 * q^8 + 56 * q^9	\( 69 q - 11 q^{2} - 3 q^{3} + 65 q^{4} - 6 q^{5} - 10 q^{6} - 11 q^{7} - 33 q^{8} + 56 q^{9} - q^{10} - 69 q^{11} - 3 q^{12} - 28 q^{13} - 15 q^{14} - 45 q^{15} + 53 q^{16} + 69 q^{17} - 17 q^{18} - 32 q^{19} - 21 q^{20} - 38 q^{21} + 11 q^{22} - 41 q^{23} - 11 q^{24} + 67 q^{25} - 6 q^{26} - 3 q^{27} - 21 q^{28} - 22 q^{29} - 22 q^{30} - 27 q^{31} - 87 q^{32} + 3 q^{33} - 11 q^{34} - 44 q^{35} + 59 q^{36} + 24 q^{37} - 22 q^{38} - 59 q^{39} + q^{40} - 43 q^{41} - 15 q^{42} + 69 q^{43} - 65 q^{44} - 12 q^{45} - 21 q^{46} - 99 q^{47} + 2 q^{48} + 64 q^{49} - 78 q^{50} - 3 q^{51} - 57 q^{52} - 50 q^{53} + 20 q^{54} + 6 q^{55} - 59 q^{56} - 15 q^{57} + 22 q^{58} - 82 q^{59} - 86 q^{60} - 24 q^{61} + 15 q^{62} - 63 q^{63} + 63 q^{64} - 23 q^{65} + 10 q^{66} - 54 q^{67} + 65 q^{68} + 36 q^{69} + 9 q^{70} - 128 q^{71} - 69 q^{72} + 2 q^{73} - 58 q^{74} - 31 q^{75} - 76 q^{76} + 11 q^{77} - 19 q^{78} - 43 q^{79} - 19 q^{80} + 49 q^{81} - 2 q^{82} - 62 q^{83} - 82 q^{84} - 6 q^{85} - 11 q^{86} - 62 q^{87} + 33 q^{88} - 49 q^{89} - 37 q^{90} - 2 q^{91} - 96 q^{92} - 29 q^{93} - 75 q^{94} - 133 q^{95} - 86 q^{96} + 5 q^{97} - 72 q^{98} - 56 q^{99}+O(q^{100}) \) 69 * q - 11 * q^2 - 3 * q^3 + 65 * q^4 - 6 * q^5 - 10 * q^6 - 11 * q^7 - 33 * q^8 + 56 * q^9 - q^10 - 69 * q^11 - 3 * q^12 - 28 * q^13 - 15 * q^14 - 45 * q^15 + 53 * q^16 + 69 * q^17 - 17 * q^18 - 32 * q^19 - 21 * q^20 - 38 * q^21 + 11 * q^22 - 41 * q^23 - 11 * q^24 + 67 * q^25 - 6 * q^26 - 3 * q^27 - 21 * q^28 - 22 * q^29 - 22 * q^30 - 27 * q^31 - 87 * q^32 + 3 * q^33 - 11 * q^34 - 44 * q^35 + 59 * q^36 + 24 * q^37 - 22 * q^38 - 59 * q^39 + q^40 - 43 * q^41 - 15 * q^42 + 69 * q^43 - 65 * q^44 - 12 * q^45 - 21 * q^46 - 99 * q^47 + 2 * q^48 + 64 * q^49 - 78 * q^50 - 3 * q^51 - 57 * q^52 - 50 * q^53 + 20 * q^54 + 6 * q^55 - 59 * q^56 - 15 * q^57 + 22 * q^58 - 82 * q^59 - 86 * q^60 - 24 * q^61 + 15 * q^62 - 63 * q^63 + 63 * q^64 - 23 * q^65 + 10 * q^66 - 54 * q^67 + 65 * q^68 + 36 * q^69 + 9 * q^70 - 128 * q^71 - 69 * q^72 + 2 * q^73 - 58 * q^74 - 31 * q^75 - 76 * q^76 + 11 * q^77 - 19 * q^78 - 43 * q^79 - 19 * q^80 + 49 * q^81 - 2 * q^82 - 62 * q^83 - 82 * q^84 - 6 * q^85 - 11 * q^86 - 62 * q^87 + 33 * q^88 - 49 * q^89 - 37 * q^90 - 2 * q^91 - 96 * q^92 - 29 * q^93 - 75 * q^94 - 133 * q^95 - 86 * q^96 + 5 * q^97 - 72 * q^98 - 56 * q^99

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