LMFDB - Embedded newform 8033.2.a.d.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8033,2,Mod(1,8033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8033, 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("8033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8033 = 29 \cdot 277 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8033.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:	$64.1438279437$
Analytic rank:	$0$
Dimension:	$168$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	8033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.50804 q^{2} +0.217745 q^{3} +4.29026 q^{4} -0.0259578 q^{5} -0.546113 q^{6} -4.91509 q^{7} -5.74406 q^{8} -2.95259 q^{9} +O(q^{10})$	\(q-2.50804 q^{2} +0.217745 q^{3} +4.29026 q^{4} -0.0259578 q^{5} -0.546113 q^{6} -4.91509 q^{7} -5.74406 q^{8} -2.95259 q^{9} +0.0651033 q^{10} +1.34997 q^{11} +0.934183 q^{12} -2.16677 q^{13} +12.3272 q^{14} -0.00565219 q^{15} +5.82581 q^{16} +6.15149 q^{17} +7.40520 q^{18} -4.56297 q^{19} -0.111366 q^{20} -1.07024 q^{21} -3.38578 q^{22} +4.90959 q^{23} -1.25074 q^{24} -4.99933 q^{25} +5.43435 q^{26} -1.29615 q^{27} -21.0870 q^{28} +1.00000 q^{29} +0.0141759 q^{30} -3.05744 q^{31} -3.12323 q^{32} +0.293949 q^{33} -15.4282 q^{34} +0.127585 q^{35} -12.6674 q^{36} +0.549486 q^{37} +11.4441 q^{38} -0.471804 q^{39} +0.149103 q^{40} +8.84536 q^{41} +2.68419 q^{42} -1.58144 q^{43} +5.79172 q^{44} +0.0766428 q^{45} -12.3134 q^{46} -5.55928 q^{47} +1.26854 q^{48} +17.1581 q^{49} +12.5385 q^{50} +1.33946 q^{51} -9.29602 q^{52} -3.89747 q^{53} +3.25079 q^{54} -0.0350423 q^{55} +28.2326 q^{56} -0.993565 q^{57} -2.50804 q^{58} -10.0507 q^{59} -0.0242494 q^{60} -9.12224 q^{61} +7.66817 q^{62} +14.5122 q^{63} -3.81843 q^{64} +0.0562447 q^{65} -0.737237 q^{66} -3.39617 q^{67} +26.3915 q^{68} +1.06904 q^{69} -0.319988 q^{70} -0.0579752 q^{71} +16.9598 q^{72} -11.9792 q^{73} -1.37813 q^{74} -1.08858 q^{75} -19.5763 q^{76} -6.63522 q^{77} +1.18330 q^{78} +8.83426 q^{79} -0.151225 q^{80} +8.57553 q^{81} -22.1845 q^{82} +3.19686 q^{83} -4.59159 q^{84} -0.159679 q^{85} +3.96630 q^{86} +0.217745 q^{87} -7.75431 q^{88} -14.3899 q^{89} -0.192223 q^{90} +10.6499 q^{91} +21.0634 q^{92} -0.665742 q^{93} +13.9429 q^{94} +0.118445 q^{95} -0.680069 q^{96} -9.30421 q^{97} -43.0331 q^{98} -3.98590 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q + 12 q^{2} + 35 q^{3} + 184 q^{4} + 12 q^{5} + 10 q^{6} + 74 q^{7} + 39 q^{8} + 183 q^{9}+O(q^{10}) $ 168 * q + 12 * q^2 + 35 * q^3 + 184 * q^4 + 12 * q^5 + 10 * q^6 + 74 * q^7 + 39 * q^8 + 183 * q^9	\( 168 q + 12 q^{2} + 35 q^{3} + 184 q^{4} + 12 q^{5} + 10 q^{6} + 74 q^{7} + 39 q^{8} + 183 q^{9} + 41 q^{10} + 29 q^{11} + 82 q^{12} + 62 q^{13} + 23 q^{14} + 31 q^{15} + 204 q^{16} + 56 q^{17} + 35 q^{18} + 83 q^{19} + 6 q^{20} + 30 q^{21} + 56 q^{22} + 54 q^{23} + 28 q^{24} + 210 q^{25} + 21 q^{26} + 140 q^{27} + 151 q^{28} + 168 q^{29} + 29 q^{30} + 72 q^{31} + 40 q^{32} + 32 q^{33} + 34 q^{34} + 18 q^{35} + 152 q^{36} + 42 q^{37} + 29 q^{38} + 70 q^{39} + 97 q^{40} + 41 q^{41} - 20 q^{42} + 119 q^{43} + 37 q^{44} + 22 q^{45} + 24 q^{46} + 119 q^{47} + 135 q^{48} + 216 q^{49} + 38 q^{50} + 18 q^{51} + 154 q^{52} - 7 q^{53} + 35 q^{54} + 224 q^{55} + 46 q^{56} + 12 q^{57} + 12 q^{58} + 25 q^{59} + 13 q^{60} + 82 q^{61} + 27 q^{62} + 211 q^{63} + 217 q^{64} + 8 q^{65} - 6 q^{66} + 76 q^{67} + 132 q^{68} + 36 q^{69} + 39 q^{70} + 32 q^{71} + 39 q^{72} + 89 q^{73} - q^{74} + 123 q^{75} + 180 q^{76} + 68 q^{77} - 54 q^{78} + 176 q^{79} - 11 q^{80} + 192 q^{81} + 51 q^{82} + 76 q^{83} + 86 q^{84} + 65 q^{85} - 72 q^{86} + 35 q^{87} + 178 q^{88} + 55 q^{89} + 2 q^{90} + 80 q^{91} + 44 q^{92} + 39 q^{93} + 89 q^{94} + 77 q^{95} - 68 q^{96} + 82 q^{97} + 80 q^{98} + 67 q^{99}+O(q^{100}) \) 168 * q + 12 * q^2 + 35 * q^3 + 184 * q^4 + 12 * q^5 + 10 * q^6 + 74 * q^7 + 39 * q^8 + 183 * q^9 + 41 * q^10 + 29 * q^11 + 82 * q^12 + 62 * q^13 + 23 * q^14 + 31 * q^15 + 204 * q^16 + 56 * q^17 + 35 * q^18 + 83 * q^19 + 6 * q^20 + 30 * q^21 + 56 * q^22 + 54 * q^23 + 28 * q^24 + 210 * q^25 + 21 * q^26 + 140 * q^27 + 151 * q^28 + 168 * q^29 + 29 * q^30 + 72 * q^31 + 40 * q^32 + 32 * q^33 + 34 * q^34 + 18 * q^35 + 152 * q^36 + 42 * q^37 + 29 * q^38 + 70 * q^39 + 97 * q^40 + 41 * q^41 - 20 * q^42 + 119 * q^43 + 37 * q^44 + 22 * q^45 + 24 * q^46 + 119 * q^47 + 135 * q^48 + 216 * q^49 + 38 * q^50 + 18 * q^51 + 154 * q^52 - 7 * q^53 + 35 * q^54 + 224 * q^55 + 46 * q^56 + 12 * q^57 + 12 * q^58 + 25 * q^59 + 13 * q^60 + 82 * q^61 + 27 * q^62 + 211 * q^63 + 217 * q^64 + 8 * q^65 - 6 * q^66 + 76 * q^67 + 132 * q^68 + 36 * q^69 + 39 * q^70 + 32 * q^71 + 39 * q^72 + 89 * q^73 - q^74 + 123 * q^75 + 180 * q^76 + 68 * q^77 - 54 * q^78 + 176 * q^79 - 11 * q^80 + 192 * q^81 + 51 * q^82 + 76 * q^83 + 86 * q^84 + 65 * q^85 - 72 * q^86 + 35 * q^87 + 178 * q^88 + 55 * q^89 + 2 * q^90 + 80 * q^91 + 44 * q^92 + 39 * q^93 + 89 * q^94 + 77 * q^95 - 68 * q^96 + 82 * q^97 + 80 * q^98 + 67 * 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 $

$2$	−2.50804	−1.77345	−0.886726	−	0.462296i	$-0.847026\pi$
$2$	−2.50804	−1.77345	−0.886726	+	0.462296i	$0.847026\pi$
$3$	0.217745	0.125715	0.0628576	−	0.998023i	$-0.479979\pi$
$3$	0.217745	0.125715	0.0628576	+	0.998023i	$0.479979\pi$
$4$	4.29026	2.14513
$5$	−0.0259578	−0.0116087	−0.00580435	−	0.999983i	$-0.501848\pi$
$5$	−0.0259578	−0.0116087	−0.00580435	+	0.999983i	$0.501848\pi$
$6$	−0.546113	−0.222950
$7$	−4.91509	−1.85773	−0.928864	−	0.370421i	$-0.879213\pi$
$7$	−4.91509	−1.85773	−0.928864	+	0.370421i	$0.879213\pi$
$8$	−5.74406	−2.03083
$9$	−2.95259	−0.984196
$10$	0.0651033	0.0205875
$11$	1.34997	0.407031	0.203516	−	0.979072i	$-0.434763\pi$
$11$	1.34997	0.407031	0.203516	+	0.979072i	$0.434763\pi$
$12$	0.934183	0.269676
$13$	−2.16677	−0.600955	−0.300477	−	0.953789i	$-0.597146\pi$
$13$	−2.16677	−0.600955	−0.300477	+	0.953789i	$0.597146\pi$
$14$	12.3272	3.29459
$15$	−0.00565219	−0.00145939
$16$	5.82581	1.45645
$17$	6.15149	1.49196	0.745978	−	0.665971i	$-0.231983\pi$
$17$	6.15149	1.49196	0.745978	+	0.665971i	$0.231983\pi$
$18$	7.40520	1.74542
$19$	−4.56297	−1.04682	−0.523409	−	0.852082i	$-0.675340\pi$
$19$	−4.56297	−1.04682	−0.523409	+	0.852082i	$0.675340\pi$
$20$	−0.111366	−0.0249022
$21$	−1.07024	−0.233545
$22$	−3.38578	−0.721850
$23$	4.90959	1.02372	0.511860	−	0.859069i	$-0.328957\pi$
$23$	4.90959	1.02372	0.511860	+	0.859069i	$0.328957\pi$
$24$	−1.25074	−0.255307
$25$	−4.99933	−0.999865
$26$	5.43435	1.06576
$27$	−1.29615	−0.249444
$28$	−21.0870	−3.98507
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	0.0141759	0.00258816
$31$	−3.05744	−0.549132	−0.274566	−	0.961568i	$-0.588534\pi$
$31$	−3.05744	−0.549132	−0.274566	+	0.961568i	$0.588534\pi$
$32$	−3.12323	−0.552115
$33$	0.293949	0.0511700
$34$	−15.4282	−2.64591
$35$	0.127585	0.0215658
$36$	−12.6674	−2.11123
$37$	0.549486	0.0903349	0.0451674	−	0.998979i	$-0.485618\pi$
$37$	0.549486	0.0903349	0.0451674	+	0.998979i	$0.485618\pi$
$38$	11.4441	1.85648
$39$	−0.471804	−0.0755492
$40$	0.149103	0.0235753
$41$	8.84536	1.38141	0.690707	−	0.723135i	$-0.257300\pi$
$41$	8.84536	1.38141	0.690707	+	0.723135i	$0.257300\pi$
$42$	2.68419	0.414180
$43$	−1.58144	−0.241167	−0.120583	−	0.992703i	$-0.538476\pi$
$43$	−1.58144	−0.241167	−0.120583	+	0.992703i	$0.538476\pi$
$44$	5.79172	0.873135
$45$	0.0766428	0.0114252
$46$	−12.3134	−1.81552
$47$	−5.55928	−0.810904	−0.405452	−	0.914116i	$-0.632886\pi$
$47$	−5.55928	−0.810904	−0.405452	+	0.914116i	$0.632886\pi$
$48$	1.26854	0.183098
$49$	17.1581	2.45115
$50$	12.5385	1.77321
$51$	1.33946	0.187562
$52$	−9.29602	−1.28913
$53$	−3.89747	−0.535359	−0.267680	−	0.963508i	$-0.586257\pi$
$53$	−3.89747	−0.535359	−0.267680	+	0.963508i	$0.586257\pi$
$54$	3.25079	0.442376
$55$	−0.0350423	−0.00472510
$56$	28.2326	3.77273
$57$	−0.993565	−0.131601
$58$	−2.50804	−0.329322
$59$	−10.0507	−1.30849	−0.654246	−	0.756282i	$-0.727014\pi$
$59$	−10.0507	−1.30849	−0.654246	+	0.756282i	$0.727014\pi$
$60$	−0.0242494	−0.00313058
$61$	−9.12224	−1.16798	−0.583992	−	0.811760i	$-0.698510\pi$
$61$	−9.12224	−1.16798	−0.583992	+	0.811760i	$0.698510\pi$
$62$	7.66817	0.973858
$63$	14.5122	1.82837
$64$	−3.81843	−0.477303
$65$	0.0562447	0.00697630
$66$	−0.737237	−0.0907475
$67$	−3.39617	−0.414909	−0.207454	−	0.978245i	$-0.566518\pi$
$67$	−3.39617	−0.414909	−0.207454	+	0.978245i	$0.566518\pi$
$68$	26.3915	3.20044
$69$	1.06904	0.128697
$70$	−0.319988	−0.0382459
$71$	−0.0579752	−0.00688040	−0.00344020	−	0.999994i	$-0.501095\pi$
$71$	−0.0579752	−0.00688040	−0.00344020	+	0.999994i	$0.501095\pi$
$72$	16.9598	1.99874
$73$	−11.9792	−1.40206	−0.701032	−	0.713129i	$-0.747277\pi$
$73$	−11.9792	−1.40206	−0.701032	+	0.713129i	$0.747277\pi$
$74$	−1.37813	−0.160205
$75$	−1.08858	−0.125698
$76$	−19.5763	−2.24556
$77$	−6.63522	−0.756153
$78$	1.18330	0.133983
$79$	8.83426	0.993932	0.496966	−	0.867770i	$-0.334447\pi$
$79$	8.83426	0.993932	0.496966	+	0.867770i	$0.334447\pi$
$80$	−0.151225	−0.0169075
$81$	8.57553	0.952837
$82$	−22.1845	−2.44987
$83$	3.19686	0.350901	0.175450	−	0.984488i	$-0.443862\pi$
$83$	3.19686	0.350901	0.175450	+	0.984488i	$0.443862\pi$
$84$	−4.59159	−0.500984
$85$	−0.159679	−0.0173197
$86$	3.96630	0.427697
$87$	0.217745	0.0233447
$88$	−7.75431	−0.826612
$89$	−14.3899	−1.52533	−0.762664	−	0.646795i	$-0.776109\pi$
$89$	−14.3899	−1.52533	−0.762664	+	0.646795i	$0.776109\pi$
$90$	−0.192223	−0.0202621
$91$	10.6499	1.11641
$92$	21.0634	2.19601
$93$	−0.665742	−0.0690342
$94$	13.9429	1.43810
$95$	0.118445	0.0121522
$96$	−0.680069	−0.0694093
$97$	−9.30421	−0.944700	−0.472350	−	0.881411i	$-0.656594\pi$
$97$	−9.30421	−0.944700	−0.472350	+	0.881411i	$0.656594\pi$
$98$	−43.0331	−4.34700
$99$	−3.98590	−0.400598
$100$	−21.4484	−2.14484
$101$	−13.5149	−1.34479	−0.672393	−	0.740195i	$-0.734733\pi$
$101$	−13.5149	−1.34479	−0.672393	+	0.740195i	$0.734733\pi$
$102$	−3.35941	−0.332631
$103$	12.0865	1.19092	0.595458	−	0.803386i	$-0.296970\pi$
$103$	12.0865	1.19092	0.595458	+	0.803386i	$0.296970\pi$
$104$	12.4461	1.22044
$105$	0.0277810	0.00271115
$106$	9.77502	0.949434
$107$	−4.30494	−0.416174	−0.208087	−	0.978110i	$-0.566724\pi$
$107$	−4.30494	−0.416174	−0.208087	+	0.978110i	$0.566724\pi$
$108$	−5.56081	−0.535089
$109$	−4.59901	−0.440505	−0.220253	−	0.975443i	$-0.570688\pi$
$109$	−4.59901	−0.440505	−0.220253	+	0.975443i	$0.570688\pi$
$110$	0.0878874	0.00837974
$111$	0.119648	0.0113565
$112$	−28.6343	−2.70569
$113$	−6.08689	−0.572607	−0.286303	−	0.958139i	$-0.592427\pi$
$113$	−6.08689	−0.572607	−0.286303	+	0.958139i	$0.592427\pi$
$114$	2.49190	0.233388
$115$	−0.127442	−0.0118841
$116$	4.29026	0.398341
$117$	6.39759	0.591457
$118$	25.2076	2.32055
$119$	−30.2351	−2.77165
$120$	0.0324665	0.00296378
$121$	−9.17758	−0.834326
$122$	22.8789	2.07136
$123$	1.92603	0.173665
$124$	−13.1172	−1.17796
$125$	0.259561	0.0232158
$126$	−36.3972	−3.24252
$127$	−20.2720	−1.79885	−0.899426	−	0.437072i	$-0.856015\pi$
$127$	−20.2720	−1.79885	−0.899426	+	0.437072i	$0.856015\pi$
$128$	15.8232	1.39859
$129$	−0.344350	−0.0303183
$130$	−0.141064	−0.0123721
$131$	−14.0381	−1.22651	−0.613257	−	0.789884i	$-0.710141\pi$
$131$	−14.0381	−1.22651	−0.613257	+	0.789884i	$0.710141\pi$
$132$	1.26112	0.109766
$133$	22.4274	1.94470
$134$	8.51773	0.735820
$135$	0.0336452	0.00289572
$136$	−35.3345	−3.02991
$137$	9.63698	0.823342	0.411671	−	0.911332i	$-0.364945\pi$
$137$	9.63698	0.823342	0.411671	+	0.911332i	$0.364945\pi$
$138$	−2.68119	−0.228238
$139$	−18.9785	−1.60973	−0.804867	−	0.593455i	$-0.797764\pi$
$139$	−18.9785	−1.60973	−0.804867	+	0.593455i	$0.797764\pi$
$140$	0.547373	0.0462614
$141$	−1.21051	−0.101943
$142$	0.145404	0.0122020
$143$	−2.92508	−0.244607
$144$	−17.2012	−1.43343
$145$	−0.0259578	−0.00215568
$146$	30.0444	2.48649
$147$	3.73609	0.308147
$148$	2.35744	0.193780
$149$	−12.4932	−1.02348	−0.511740	−	0.859140i	$-0.670999\pi$
$149$	−12.4932	−1.02348	−0.511740	+	0.859140i	$0.670999\pi$
$150$	2.73020	0.222920
$151$	−3.18067	−0.258839	−0.129420	−	0.991590i	$-0.541311\pi$
$151$	−3.18067	−0.258839	−0.129420	+	0.991590i	$0.541311\pi$
$152$	26.2100	2.12591
$153$	−18.1628	−1.46838
$154$	16.6414	1.34100
$155$	0.0793644	0.00637470
$156$	−2.02416	−0.162063
$157$	−2.54028	−0.202737	−0.101368	−	0.994849i	$-0.532322\pi$
$157$	−2.54028	−0.202737	−0.101368	+	0.994849i	$0.532322\pi$
$158$	−22.1567	−1.76269
$159$	−0.848656	−0.0673028
$160$	0.0810724	0.00640933
$161$	−24.1311	−1.90179
$162$	−21.5078	−1.68981
$163$	−14.8051	−1.15962	−0.579811	−	0.814751i	$-0.696873\pi$
$163$	−14.8051	−1.15962	−0.579811	+	0.814751i	$0.696873\pi$
$164$	37.9489	2.96331
$165$	−0.00763029	−0.000594017 0
$166$	−8.01784	−0.622305
$167$	13.6597	1.05702	0.528508	−	0.848928i	$-0.322752\pi$
$167$	13.6597	1.05702	0.528508	+	0.848928i	$0.322752\pi$
$168$	6.14750	0.474290
$169$	−8.30509	−0.638853
$170$	0.400482	0.0307156
$171$	13.4726	1.03027
$172$	−6.78477	−0.517334
$173$	5.31271	0.403918	0.201959	−	0.979394i	$-0.435269\pi$
$173$	5.31271	0.403918	0.201959	+	0.979394i	$0.435269\pi$
$174$	−0.546113	−0.0414008
$175$	24.5721	1.85748
$176$	7.86466	0.592821
$177$	−2.18850	−0.164497
$178$	36.0905	2.70509
$179$	13.8939	1.03848	0.519241	−	0.854628i	$-0.326215\pi$
$179$	13.8939	1.03848	0.519241	+	0.854628i	$0.326215\pi$
$180$	0.328817	0.0245086
$181$	−18.5863	−1.38151	−0.690753	−	0.723091i	$-0.742721\pi$
$181$	−18.5863	−1.38151	−0.690753	+	0.723091i	$0.742721\pi$
$182$	−26.7103	−1.97990
$183$	−1.98632	−0.146833
$184$	−28.2010	−2.07900
$185$	−0.0142635	−0.00104867
$186$	1.66971	0.122429
$187$	8.30432	0.607272
$188$	−23.8507	−1.73949
$189$	6.37068	0.463398
$190$	−0.297064	−0.0215513
$191$	22.5169	1.62926	0.814632	−	0.579979i	$-0.196939\pi$
$191$	22.5169	1.62926	0.814632	+	0.579979i	$0.196939\pi$
$192$	−0.831444	−0.0600043
$193$	23.5576	1.69572	0.847858	−	0.530223i	$-0.177892\pi$
$193$	23.5576	1.69572	0.847858	+	0.530223i	$0.177892\pi$
$194$	23.3353	1.67538
$195$	0.0122470	0.000877027 0
$196$	73.6126	5.25804
$197$	2.84853	0.202950	0.101475	−	0.994838i	$-0.467644\pi$
$197$	2.84853	0.202950	0.101475	+	0.994838i	$0.467644\pi$
$198$	9.99680	0.710442
$199$	8.38569	0.594446	0.297223	−	0.954808i	$-0.403940\pi$
$199$	8.38569	0.594446	0.297223	+	0.954808i	$0.403940\pi$
$200$	28.7164	2.03056
$201$	−0.739500	−0.0521603
$202$	33.8960	2.38491
$203$	−4.91509	−0.344971
$204$	5.74662	0.402344
$205$	−0.229606	−0.0160364
$206$	−30.3134	−2.11203
$207$	−14.4960	−1.00754
$208$	−12.6232	−0.875262
$209$	−6.15987	−0.426087
$210$	−0.0696759	−0.00480809
$211$	21.6680	1.49168	0.745842	−	0.666122i	$-0.232047\pi$
$211$	21.6680	1.49168	0.745842	+	0.666122i	$0.232047\pi$
$212$	−16.7212	−1.14842
$213$	−0.0126238	−0.000864971 0
$214$	10.7970	0.738065
$215$	0.0410506	0.00279963
$216$	7.44515	0.506578
$217$	15.0276	1.02014
$218$	11.5345	0.781214
$219$	−2.60842	−0.176261
$220$	−0.150341	−0.0101360
$221$	−13.3289	−0.896598
$222$	−0.300081	−0.0201401
$223$	25.1853	1.68653	0.843267	−	0.537495i	$-0.180629\pi$
$223$	25.1853	1.68653	0.843267	+	0.537495i	$0.180629\pi$
$224$	15.3510	1.02568
$225$	14.7609	0.984063
$226$	15.2662	1.01549
$227$	9.42117	0.625305	0.312652	−	0.949868i	$-0.398782\pi$
$227$	9.42117	0.625305	0.312652	+	0.949868i	$0.398782\pi$
$228$	−4.26265	−0.282301
$229$	−16.4164	−1.08482	−0.542412	−	0.840113i	$-0.682489\pi$
$229$	−16.4164	−1.08482	−0.542412	+	0.840113i	$0.682489\pi$
$230$	0.319630	0.0210758
$231$	−1.44479	−0.0950600
$232$	−5.74406	−0.377116
$233$	−2.87511	−0.188354	−0.0941772	−	0.995555i	$-0.530022\pi$
$233$	−2.87511	−0.188354	−0.0941772	+	0.995555i	$0.530022\pi$
$234$	−16.0454	−1.04892
$235$	0.144307	0.00941354
$236$	−43.1202	−2.80689
$237$	1.92362	0.124952
$238$	75.8308	4.91538
$239$	7.75548	0.501660	0.250830	−	0.968031i	$-0.419296\pi$
$239$	7.75548	0.501660	0.250830	+	0.968031i	$0.419296\pi$
$240$	−0.0329286	−0.00212553
$241$	23.2100	1.49509	0.747543	−	0.664213i	$-0.231233\pi$
$241$	23.2100	1.49509	0.747543	+	0.664213i	$0.231233\pi$
$242$	23.0177	1.47964
$243$	5.75572	0.369230
$244$	−39.1368	−2.50548
$245$	−0.445386	−0.0284547
$246$	−4.83057	−0.307986
$247$	9.88693	0.629090
$248$	17.5621	1.11519
$249$	0.696100	0.0441136
$250$	−0.650989	−0.0411721
$251$	22.0438	1.39139	0.695697	−	0.718336i	$-0.255096\pi$
$251$	22.0438	1.39139	0.695697	+	0.718336i	$0.255096\pi$
$252$	62.2612	3.92209
$253$	6.62780	0.416686
$254$	50.8431	3.19018
$255$	−0.0347694	−0.00217734
$256$	−32.0484	−2.00303
$257$	20.1914	1.25950	0.629752	−	0.776796i	$-0.283156\pi$
$257$	20.1914	1.25950	0.629752	+	0.776796i	$0.283156\pi$
$258$	0.863643	0.0537681
$259$	−2.70077	−0.167818
$260$	0.241305	0.0149651
$261$	−2.95259	−0.182761
$262$	35.2081	2.17516
$263$	4.84835	0.298962	0.149481	−	0.988765i	$-0.452240\pi$
$263$	4.84835	0.298962	0.149481	+	0.988765i	$0.452240\pi$
$264$	−1.68846	−0.103918
$265$	0.101170	0.00621482
$266$	−56.2488	−3.44883
$267$	−3.13333	−0.191757
$268$	−14.5705	−0.890033
$269$	−16.2545	−0.991053	−0.495527	−	0.868593i	$-0.665025\pi$
$269$	−16.2545	−0.991053	−0.495527	+	0.868593i	$0.665025\pi$
$270$	−0.0843834	−0.00513541
$271$	24.2924	1.47566	0.737830	−	0.674987i	$-0.235851\pi$
$271$	24.2924	1.47566	0.737830	+	0.674987i	$0.235851\pi$
$272$	35.8374	2.17296
$273$	2.31896	0.140350
$274$	−24.1699	−1.46016
$275$	−6.74894	−0.406976
$276$	4.58646	0.276072
$277$	−1.00000	−0.0600842
$277$	−1.00000	−0.0600842
$278$	47.5988	2.85479
$279$	9.02735	0.540453
$280$	−0.732856	−0.0437965
$281$	−15.7333	−0.938571	−0.469286	−	0.883046i	$-0.655488\pi$
$281$	−15.7333	−0.938571	−0.469286	+	0.883046i	$0.655488\pi$
$282$	3.03599	0.180791
$283$	24.6663	1.46626	0.733129	−	0.680090i	$-0.238059\pi$
$283$	24.6663	1.46626	0.733129	+	0.680090i	$0.238059\pi$
$284$	−0.248729	−0.0147593
$285$	0.0257908	0.00152772
$286$	7.33621	0.433799
$287$	−43.4757	−2.56629
$288$	9.22162	0.543389
$289$	20.8408	1.22593
$290$	0.0651033	0.00382300
$291$	−2.02595	−0.118763
$292$	−51.3941	−3.00761
$293$	−23.5594	−1.37635	−0.688177	−	0.725543i	$-0.741589\pi$
$293$	−23.5594	−1.37635	−0.688177	+	0.725543i	$0.741589\pi$
$294$	−9.37025	−0.546484
$295$	0.260895	0.0151899
$296$	−3.15628	−0.183455
$297$	−1.74976	−0.101531
$298$	31.3334	1.81509
$299$	−10.6380	−0.615210
$300$	−4.67029	−0.269639
$301$	7.77289	0.448022
$302$	7.97724	0.459039
$303$	−2.94281	−0.169060
$304$	−26.5830	−1.52464
$305$	0.236794	0.0135588
$306$	45.5530	2.60409
$307$	−5.72821	−0.326926	−0.163463	−	0.986549i	$-0.552266\pi$
$307$	−5.72821	−0.326926	−0.163463	+	0.986549i	$0.552266\pi$
$308$	−28.4668	−1.62205
$309$	2.63177	0.149716
$310$	−0.199049	−0.0113052
$311$	2.21037	0.125339	0.0626694	−	0.998034i	$-0.480039\pi$
$311$	2.21037	0.125339	0.0626694	+	0.998034i	$0.480039\pi$
$312$	2.71007	0.153428
$313$	11.7678	0.665155	0.332577	−	0.943076i	$-0.392082\pi$
$313$	11.7678	0.665155	0.332577	+	0.943076i	$0.392082\pi$
$314$	6.37113	0.359544
$315$	−0.376706	−0.0212250
$316$	37.9013	2.13211
$317$	10.4187	0.585171	0.292585	−	0.956239i	$-0.405484\pi$
$317$	10.4187	0.585171	0.292585	+	0.956239i	$0.405484\pi$
$318$	2.12846	0.119358
$319$	1.34997	0.0755838
$320$	0.0991181	0.00554087
$321$	−0.937380	−0.0523195
$322$	60.5216	3.37274
$323$	−28.0691	−1.56180
$324$	36.7913	2.04396
$325$	10.8324	0.600874
$326$	37.1316	2.05653
$327$	−1.00141	−0.0553782
$328$	−50.8083	−2.80542
$329$	27.3243	1.50644
$330$	0.0191371	0.00105346
$331$	−10.1051	−0.555426	−0.277713	−	0.960664i	$-0.589576\pi$
$331$	−10.1051	−0.555426	−0.277713	+	0.960664i	$0.589576\pi$
$332$	13.7153	0.752727
$333$	−1.62240	−0.0889072
$334$	−34.2589	−1.87457
$335$	0.0881573	0.00481655
$336$	−6.23499	−0.340147
$337$	25.3767	1.38236	0.691179	−	0.722684i	$-0.257092\pi$
$337$	25.3767	1.38236	0.691179	+	0.722684i	$0.257092\pi$
$338$	20.8295	1.13298
$339$	−1.32539	−0.0719854
$340$	−0.685066	−0.0371529
$341$	−4.12745	−0.223514
$342$	−33.7897	−1.82714
$343$	−49.9278	−2.69585
$344$	9.08386	0.489769
$345$	−0.0277500	−0.00149401
$346$	−13.3245	−0.716328
$347$	−22.5267	−1.20930	−0.604648	−	0.796493i	$-0.706686\pi$
$347$	−22.5267	−1.20930	−0.604648	+	0.796493i	$0.706686\pi$
$348$	0.934183	0.0500775
$349$	−22.7402	−1.21726	−0.608628	−	0.793455i	$-0.708280\pi$
$349$	−22.7402	−1.21726	−0.608628	+	0.793455i	$0.708280\pi$
$350$	−61.6278	−3.29415
$351$	2.80846	0.149904
$352$	−4.21627	−0.224728
$353$	−17.6414	−0.938956	−0.469478	−	0.882944i	$-0.655558\pi$
$353$	−17.6414	−0.938956	−0.469478	+	0.882944i	$0.655558\pi$
$354$	5.48883	0.291728
$355$	0.00150491	7.98724e−5 0
$356$	−61.7365	−3.27203
$357$	−6.58355	−0.348438
$358$	−34.8466	−1.84170
$359$	33.4432	1.76507	0.882533	−	0.470250i	$-0.155836\pi$
$359$	33.4432	1.76507	0.882533	+	0.470250i	$0.155836\pi$
$360$	−0.440241	−0.0232027
$361$	1.82071	0.0958271
$362$	46.6150	2.45003
$363$	−1.99837	−0.104887
$364$	45.6907	2.39485
$365$	0.310955	0.0162761
$366$	4.98178	0.260402
$367$	21.8195	1.13897	0.569485	−	0.822002i	$-0.307143\pi$
$367$	21.8195	1.13897	0.569485	+	0.822002i	$0.307143\pi$
$368$	28.6023	1.49100
$369$	−26.1167	−1.35958
$370$	0.0357733	0.00185977
$371$	19.1564	0.994552
$372$	−2.85621	−0.148087
$373$	16.5960	0.859308	0.429654	−	0.902994i	$-0.358636\pi$
$373$	16.5960	0.859308	0.429654	+	0.902994i	$0.358636\pi$
$374$	−20.8276	−1.07697
$375$	0.0565181	0.00291858
$376$	31.9328	1.64681
$377$	−2.16677	−0.111594
$378$	−15.9779	−0.821815
$379$	−33.7692	−1.73461	−0.867303	−	0.497780i	$-0.834149\pi$
$379$	−33.7692	−1.73461	−0.867303	+	0.497780i	$0.834149\pi$
$380$	0.508159	0.0260680
$381$	−4.41414	−0.226143
$382$	−56.4732	−2.88942
$383$	22.3276	1.14089	0.570444	−	0.821337i	$-0.306771\pi$
$383$	22.3276	1.14089	0.570444	+	0.821337i	$0.306771\pi$
$384$	3.44543	0.175824
$385$	0.172236	0.00877795
$386$	−59.0835	−3.00727
$387$	4.66932	0.237355
$388$	−39.9175	−2.02650
$389$	7.64536	0.387635	0.193818	−	0.981038i	$-0.437913\pi$
$389$	7.64536	0.387635	0.193818	+	0.981038i	$0.437913\pi$
$390$	−0.0307160	−0.00155537
$391$	30.2013	1.52735
$392$	−98.5570	−4.97788
$393$	−3.05673	−0.154191
$394$	−7.14423	−0.359921
$395$	−0.229318	−0.0115383
$396$	−17.1006	−0.859335
$397$	1.62752	0.0816827	0.0408414	−	0.999166i	$-0.486996\pi$
$397$	1.62752	0.0816827	0.0408414	+	0.999166i	$0.486996\pi$
$398$	−21.0316	−1.05422
$399$	4.88346	0.244479
$400$	−29.1251	−1.45626
$401$	−19.5884	−0.978197	−0.489098	−	0.872229i	$-0.662674\pi$
$401$	−19.5884	−0.978197	−0.489098	+	0.872229i	$0.662674\pi$
$402$	1.85470	0.0925038
$403$	6.62477	0.330003
$404$	−57.9825	−2.88474
$405$	−0.222602	−0.0110612
$406$	12.3272	0.611790
$407$	0.741789	0.0367691
$408$	−7.69392	−0.380906
$409$	−31.4854	−1.55685	−0.778427	−	0.627735i	$-0.783982\pi$
$409$	−31.4854	−1.55685	−0.778427	+	0.627735i	$0.783982\pi$
$410$	0.575862	0.0284398
$411$	2.09840	0.103507
$412$	51.8542	2.55467
$413$	49.4002	2.43082
$414$	36.3565	1.78683
$415$	−0.0829835	−0.00407350
$416$	6.76734	0.331796
$417$	−4.13248	−0.202368
$418$	15.4492	0.755645
$419$	−9.68421	−0.473105	−0.236552	−	0.971619i	$-0.576017\pi$
$419$	−9.68421	−0.473105	−0.236552	+	0.971619i	$0.576017\pi$
$420$	0.119188	0.00581577
$421$	−9.11963	−0.444464	−0.222232	−	0.974994i	$-0.571334\pi$
$421$	−9.11963	−0.444464	−0.222232	+	0.974994i	$0.571334\pi$
$422$	−54.3441	−2.64543
$423$	16.4142	0.798088
$424$	22.3873	1.08722
$425$	−30.7533	−1.49175
$426$	0.0316611	0.00153398
$427$	44.8366	2.16980
$428$	−18.4693	−0.892748
$429$	−0.636922	−0.0307509
$430$	−0.102957	−0.00496501
$431$	2.45179	0.118098	0.0590492	−	0.998255i	$-0.481193\pi$
$431$	2.45179	0.118098	0.0590492	+	0.998255i	$0.481193\pi$
$432$	−7.55110	−0.363303
$433$	17.2912	0.830963	0.415482	−	0.909602i	$-0.363613\pi$
$433$	17.2912	0.830963	0.415482	+	0.909602i	$0.363613\pi$
$434$	−37.6897	−1.80916
$435$	−0.00565219	−0.000271002 0
$436$	−19.7309	−0.944940
$437$	−22.4023	−1.07165
$438$	6.54203	0.312590
$439$	29.6365	1.41447	0.707236	−	0.706978i	$-0.249942\pi$
$439$	29.6365	1.41447	0.707236	+	0.706978i	$0.249942\pi$
$440$	0.201285	0.00959589
$441$	−50.6607	−2.41241
$442$	33.4294	1.59007
$443$	−40.4302	−1.92089	−0.960447	−	0.278462i	$-0.910175\pi$
$443$	−40.4302	−1.92089	−0.960447	+	0.278462i	$0.910175\pi$
$444$	0.513320	0.0243611
$445$	0.373531	0.0177071
$446$	−63.1658	−2.99099
$447$	−2.72033	−0.128667
$448$	18.7679	0.886699
$449$	−2.60513	−0.122944	−0.0614718	−	0.998109i	$-0.519579\pi$
$449$	−2.60513	−0.122944	−0.0614718	+	0.998109i	$0.519579\pi$
$450$	−37.0210	−1.74519
$451$	11.9410	0.562278
$452$	−26.1143	−1.22832
$453$	−0.692576	−0.0325400
$454$	−23.6287	−1.10895
$455$	−0.276448	−0.0129601
$456$	5.70710	0.267259
$457$	28.7323	1.34404	0.672020	−	0.740533i	$-0.265427\pi$
$457$	28.7323	1.34404	0.672020	+	0.740533i	$0.265427\pi$
$458$	41.1729	1.92388
$459$	−7.97324	−0.372159
$460$	−0.546761	−0.0254929
$461$	15.9894	0.744701	0.372351	−	0.928092i	$-0.378552\pi$
$461$	15.9894	0.744701	0.372351	+	0.928092i	$0.378552\pi$
$462$	3.62358	0.168584
$463$	−28.6536	−1.33165	−0.665823	−	0.746110i	$-0.731919\pi$
$463$	−28.6536	−1.33165	−0.665823	+	0.746110i	$0.731919\pi$
$464$	5.82581	0.270456
$465$	0.0172812	0.000801398 0
$466$	7.21088	0.334037
$467$	16.6344	0.769749	0.384874	−	0.922969i	$-0.374245\pi$
$467$	16.6344	0.769749	0.384874	+	0.922969i	$0.374245\pi$
$468$	27.4473	1.26875
$469$	16.6925	0.770787
$470$	−0.361927	−0.0166944
$471$	−0.553134	−0.0254871
$472$	57.7320	2.65733
$473$	−2.13489	−0.0981623
$474$	−4.82451	−0.221597
$475$	22.8118	1.04668
$476$	−129.716	−5.94554
$477$	11.5076	0.526898
$478$	−19.4510	−0.889670
$479$	0.256937	0.0117397	0.00586987	−	0.999983i	$-0.498132\pi$
$479$	0.256937	0.0117397	0.00586987	+	0.999983i	$0.498132\pi$
$480$	0.0176531	0.000805751 0
$481$	−1.19061	−0.0542872
$482$	−58.2115	−2.65146
$483$	−5.25442	−0.239085
$484$	−39.3742	−1.78974
$485$	0.241517	0.0109667
$486$	−14.4356	−0.654811
$487$	−10.7608	−0.487616	−0.243808	−	0.969824i	$-0.578397\pi$
$487$	−10.7608	−0.487616	−0.243808	+	0.969824i	$0.578397\pi$
$488$	52.3987	2.37198
$489$	−3.22373	−0.145782
$490$	1.11705	0.0504630
$491$	−31.1453	−1.40557	−0.702784	−	0.711403i	$-0.748060\pi$
$491$	−31.1453	−1.40557	−0.702784	+	0.711403i	$0.748060\pi$
$492$	8.26319	0.372533
$493$	6.15149	0.277049
$494$	−24.7968	−1.11566
$495$	0.103465	0.00465042
$496$	−17.8120	−0.799784
$497$	0.284953	0.0127819
$498$	−1.74585	−0.0782332
$499$	−3.64340	−0.163101	−0.0815504	−	0.996669i	$-0.525987\pi$
$499$	−3.64340	−0.163101	−0.0815504	+	0.996669i	$0.525987\pi$
$500$	1.11358	0.0498010
$501$	2.97432	0.132883
$502$	−55.2867	−2.46757
$503$	−33.8591	−1.50970	−0.754852	−	0.655896i	$-0.772291\pi$
$503$	−33.8591	−1.50970	−0.754852	+	0.655896i	$0.772291\pi$
$504$	−83.3591	−3.71311
$505$	0.350818	0.0156112
$506$	−16.6228	−0.738973
$507$	−1.80839	−0.0803136
$508$	−86.9723	−3.85877
$509$	39.8870	1.76796	0.883979	−	0.467526i	$-0.154854\pi$
$509$	39.8870	1.76796	0.883979	+	0.467526i	$0.154854\pi$
$510$	0.0872030	0.00386142
$511$	58.8790	2.60465
$512$	48.7322	2.15368
$513$	5.91428	0.261122
$514$	−50.6408	−2.23367
$515$	−0.313739	−0.0138250
$516$	−1.47735	−0.0650367
$517$	−7.50485	−0.330063
$518$	6.77363	0.297616
$519$	1.15682	0.0507786
$520$	−0.323073	−0.0141677
$521$	23.9433	1.04898	0.524488	−	0.851418i	$-0.324257\pi$
$521$	23.9433	1.04898	0.524488	+	0.851418i	$0.324257\pi$
$522$	7.40520	0.324117
$523$	24.7544	1.08243	0.541217	−	0.840883i	$-0.317964\pi$
$523$	24.7544	1.08243	0.541217	+	0.840883i	$0.317964\pi$
$524$	−60.2270	−2.63103
$525$	5.35046	0.233513
$526$	−12.1598	−0.530194
$527$	−18.8078	−0.819280
$528$	1.71249	0.0745267
$529$	1.10408	0.0480036
$530$	−0.253738	−0.0110217
$531$	29.6756	1.28781
$532$	96.2194	4.17164
$533$	−19.1659	−0.830167
$534$	7.85852	0.340072
$535$	0.111747	0.00483124
$536$	19.5078	0.842610
$537$	3.02534	0.130553
$538$	40.7669	1.75758
$539$	23.1629	0.997696
$540$	0.144347	0.00621169
$541$	30.4956	1.31111	0.655554	−	0.755148i	$-0.272435\pi$
$541$	30.4956	1.31111	0.655554	+	0.755148i	$0.272435\pi$
$542$	−60.9263	−2.61701
$543$	−4.04707	−0.173676
$544$	−19.2125	−0.823731
$545$	0.119380	0.00511369
$546$	−5.81604	−0.248904
$547$	4.86562	0.208039	0.104019	−	0.994575i	$-0.466830\pi$
$547$	4.86562	0.208039	0.104019	+	0.994575i	$0.466830\pi$
$548$	41.3451	1.76618
$549$	26.9342	1.14952
$550$	16.9266	0.721753
$551$	−4.56297	−0.194389
$552$	−6.14063	−0.261363
$553$	−43.4212	−1.84646
$554$	2.50804	0.106556
$555$	−0.00310580	−0.000131834 0
$556$	−81.4227	−3.45309
$557$	−21.5534	−0.913249	−0.456624	−	0.889660i	$-0.650942\pi$
$557$	−21.5534	−0.913249	−0.456624	+	0.889660i	$0.650942\pi$
$558$	−22.6409	−0.958467
$559$	3.42661	0.144930
$560$	0.743286	0.0314096
$561$	1.80823	0.0763434
$562$	39.4598	1.66451
$563$	26.7461	1.12721	0.563606	−	0.826044i	$-0.309414\pi$
$563$	26.7461	1.12721	0.563606	+	0.826044i	$0.309414\pi$
$564$	−5.19338	−0.218681
$565$	0.158003	0.00664722
$566$	−61.8640	−2.60034
$567$	−42.1495	−1.77011
$568$	0.333013	0.0139729
$569$	1.95491	0.0819541	0.0409771	−	0.999160i	$-0.486953\pi$
$569$	1.95491	0.0819541	0.0409771	+	0.999160i	$0.486953\pi$
$570$	−0.0646843	−0.00270933
$571$	11.4943	0.481023	0.240511	−	0.970646i	$-0.422685\pi$
$571$	11.4943	0.481023	0.240511	+	0.970646i	$0.422685\pi$
$572$	−12.5493	−0.524714
$573$	4.90294	0.204823
$574$	109.039	4.55119
$575$	−24.5446	−1.02358
$576$	11.2742	0.469760
$577$	6.99985	0.291408	0.145704	−	0.989328i	$-0.453455\pi$
$577$	6.99985	0.291408	0.145704	+	0.989328i	$0.453455\pi$
$578$	−52.2696	−2.17413
$579$	5.12956	0.213177
$580$	−0.111366	−0.00462422
$581$	−15.7128	−0.651878
$582$	5.08116	0.210621
$583$	−5.26147	−0.217908
$584$	68.8095	2.84736
$585$	−0.166068	−0.00686605
$586$	59.0878	2.44090
$587$	37.2054	1.53563	0.767816	−	0.640670i	$-0.221343\pi$
$587$	37.2054	1.53563	0.767816	+	0.640670i	$0.221343\pi$
$588$	16.0288	0.661016
$589$	13.9510	0.574841
$590$	−0.654335	−0.0269385
$591$	0.620254	0.0255139
$592$	3.20120	0.131568
$593$	27.2448	1.11881	0.559404	−	0.828895i	$-0.311030\pi$
$593$	27.2448	1.11881	0.559404	+	0.828895i	$0.311030\pi$
$594$	4.38846	0.180061
$595$	0.784838	0.0321752
$596$	−53.5990	−2.19550
$597$	1.82594	0.0747309
$598$	26.6804	1.09104
$599$	−22.5863	−0.922850	−0.461425	−	0.887179i	$-0.652662\pi$
$599$	−22.5863	−0.922850	−0.461425	+	0.887179i	$0.652662\pi$
$600$	6.25286	0.255272
$601$	38.2187	1.55897	0.779487	−	0.626418i	$-0.215480\pi$
$601$	38.2187	1.55897	0.779487	+	0.626418i	$0.215480\pi$
$602$	−19.4947	−0.794545
$603$	10.0275	0.408351
$604$	−13.6459	−0.555244
$605$	0.238230	0.00968543
$606$	7.38068	0.299820
$607$	14.6495	0.594606	0.297303	−	0.954783i	$-0.403913\pi$
$607$	14.6495	0.594606	0.297303	+	0.954783i	$0.403913\pi$
$608$	14.2512	0.577964
$609$	−1.07024	−0.0433682
$610$	−0.593888	−0.0240458
$611$	12.0457	0.487316
$612$	−77.9232	−3.14986
$613$	−12.4521	−0.502935	−0.251467	−	0.967866i	$-0.580913\pi$
$613$	−12.4521	−0.502935	−0.251467	+	0.967866i	$0.580913\pi$
$614$	14.3666	0.579787
$615$	−0.0499957	−0.00201602
$616$	38.1131	1.53562
$617$	21.6577	0.871906	0.435953	−	0.899969i	$-0.356411\pi$
$617$	21.6577	0.871906	0.435953	+	0.899969i	$0.356411\pi$
$618$	−6.60059	−0.265515
$619$	−40.9420	−1.64560	−0.822798	−	0.568333i	$-0.807588\pi$
$619$	−40.9420	−1.64560	−0.822798	+	0.568333i	$0.807588\pi$
$620$	0.340494	0.0136746
$621$	−6.36355	−0.255361
$622$	−5.54371	−0.222282
$623$	70.7277	2.83364
$624$	−2.74864	−0.110034
$625$	24.9899	0.999596
$626$	−29.5141	−1.17962
$627$	−1.34128	−0.0535657
$628$	−10.8985	−0.434896
$629$	3.38015	0.134776
$630$	0.944793	0.0376415
$631$	35.0763	1.39637	0.698184	−	0.715919i	$-0.253992\pi$
$631$	35.0763	1.39637	0.698184	+	0.715919i	$0.253992\pi$
$632$	−50.7445	−2.01851
$633$	4.71810	0.187528
$634$	−26.1304	−1.03777
$635$	0.526218	0.0208823
$636$	−3.64096	−0.144373
$637$	−37.1776	−1.47303
$638$	−3.38578	−0.134044
$639$	0.171177	0.00677166
$640$	−0.410737	−0.0162358
$641$	−15.5083	−0.612540	−0.306270	−	0.951945i	$-0.599081\pi$
$641$	−15.5083	−0.612540	−0.306270	+	0.951945i	$0.599081\pi$
$642$	2.35099	0.0927860
$643$	−10.6367	−0.419471	−0.209736	−	0.977758i	$-0.567260\pi$
$643$	−10.6367	−0.419471	−0.209736	+	0.977758i	$0.567260\pi$
$644$	−103.529	−4.07960
$645$	0.00893858	0.000351956 0
$646$	70.3983	2.76979
$647$	23.4369	0.921401	0.460701	−	0.887556i	$-0.347598\pi$
$647$	23.4369	0.921401	0.460701	+	0.887556i	$0.347598\pi$
$648$	−49.2584	−1.93505
$649$	−13.5682	−0.532597
$650$	−27.1681	−1.06562
$651$	3.27218	0.128247
$652$	−63.5175	−2.48754
$653$	27.0401	1.05816	0.529080	−	0.848572i	$-0.322537\pi$
$653$	27.0401	1.05816	0.529080	+	0.848572i	$0.322537\pi$
$654$	2.51158	0.0982105
$655$	0.364398	0.0142382
$656$	51.5314	2.01196
$657$	35.3698	1.37991
$658$	−68.5305	−2.67160
$659$	−7.19608	−0.280320	−0.140160	−	0.990129i	$-0.544762\pi$
$659$	−7.19608	−0.280320	−0.140160	+	0.990129i	$0.544762\pi$
$660$	−0.0327359	−0.00127424
$661$	−50.9236	−1.98070	−0.990350	−	0.138590i	$-0.955743\pi$
$661$	−50.9236	−1.98070	−0.990350	+	0.138590i	$0.955743\pi$
$662$	25.3440	0.985021
$663$	−2.90230	−0.112716
$664$	−18.3629	−0.712620
$665$	−0.582167	−0.0225755
$666$	4.06905	0.157673
$667$	4.90959	0.190100
$668$	58.6035	2.26744
$669$	5.48398	0.212023
$670$	−0.221102	−0.00854191
$671$	−12.3148	−0.475406
$672$	3.34260	0.128944
$673$	6.11784	0.235825	0.117913	−	0.993024i	$-0.462380\pi$
$673$	6.11784	0.235825	0.117913	+	0.993024i	$0.462380\pi$
$674$	−63.6458	−2.45154
$675$	6.47986	0.249410
$676$	−35.6310	−1.37042
$677$	−16.0690	−0.617583	−0.308792	−	0.951130i	$-0.599925\pi$
$677$	−16.0690	−0.617583	−0.308792	+	0.951130i	$0.599925\pi$
$678$	3.32413	0.127663
$679$	45.7310	1.75500
$680$	0.917208	0.0351733
$681$	2.05141	0.0786104
$682$	10.3518	0.396391
$683$	−21.9974	−0.841708	−0.420854	−	0.907128i	$-0.638270\pi$
$683$	−21.9974	−0.841708	−0.420854	+	0.907128i	$0.638270\pi$
$684$	57.8008	2.21007
$685$	−0.250155	−0.00955793
$686$	125.221	4.78096
$687$	−3.57458	−0.136379
$688$	−9.21314	−0.351248
$689$	8.44494	0.321727
$690$	0.0695980	0.00264955
$691$	43.1712	1.64231	0.821155	−	0.570705i	$-0.193330\pi$
$691$	43.1712	1.64231	0.821155	+	0.570705i	$0.193330\pi$
$692$	22.7929	0.866456
$693$	19.5911	0.744203
$694$	56.4978	2.14463
$695$	0.492641	0.0186869
$696$	−1.25074	−0.0474092
$697$	54.4121	2.06101
$698$	57.0334	2.15875
$699$	−0.626040	−0.0236790
$700$	105.421	3.98453
$701$	19.9026	0.751711	0.375855	−	0.926678i	$-0.377349\pi$
$701$	19.9026	0.751711	0.375855	+	0.926678i	$0.377349\pi$
$702$	−7.04372	−0.265848
$703$	−2.50729	−0.0945641
$704$	−5.15476	−0.194277
$705$	0.0314221	0.00118342
$706$	44.2453	1.66519
$707$	66.4270	2.49825
$708$	−9.38922	−0.352868
$709$	−44.7986	−1.68245	−0.841224	−	0.540687i	$-0.818164\pi$
$709$	−44.7986	−1.68245	−0.841224	+	0.540687i	$0.818164\pi$
$710$	−0.00377438	−0.000141650 0
$711$	−26.0839	−0.978224
$712$	82.6565	3.09768
$713$	−15.0108	−0.562157
$714$	16.5118	0.617938
$715$	0.0759287	0.00283957
$716$	59.6086	2.22768
$717$	1.68872	0.0630663
$718$	−83.8770	−3.13026
$719$	11.2425	0.419274	0.209637	−	0.977779i	$-0.432772\pi$
$719$	11.2425	0.419274	0.209637	+	0.977779i	$0.432772\pi$
$720$	0.446506	0.0166403
$721$	−59.4061	−2.21240
$722$	−4.56642	−0.169945
$723$	5.05386	0.187955
$724$	−79.7399	−2.96351
$725$	−4.99933	−0.185670
$726$	5.01200	0.186013
$727$	−3.50191	−0.129879	−0.0649394	−	0.997889i	$-0.520685\pi$
$727$	−3.50191	−0.129879	−0.0649394	+	0.997889i	$0.520685\pi$
$728$	−61.1735	−2.26724
$729$	−24.4733	−0.906419
$730$	−0.779888	−0.0288650
$731$	−9.72818	−0.359810
$732$	−8.52185	−0.314977
$733$	34.0231	1.25667	0.628335	−	0.777942i	$-0.283737\pi$
$733$	34.0231	1.25667	0.628335	+	0.777942i	$0.283737\pi$
$734$	−54.7242	−2.01991
$735$	−0.0969808	−0.00357719
$736$	−15.3338	−0.565211
$737$	−4.58473	−0.168881
$738$	65.5017	2.41115
$739$	−35.9687	−1.32313	−0.661564	−	0.749889i	$-0.730107\pi$
$739$	−35.9687	−1.32313	−0.661564	+	0.749889i	$0.730107\pi$
$740$	−0.0611939	−0.00224953
$741$	2.15283	0.0790862
$742$	−48.0451	−1.76379
$743$	4.41153	0.161843	0.0809217	−	0.996720i	$-0.474214\pi$
$743$	4.41153	0.161843	0.0809217	+	0.996720i	$0.474214\pi$
$744$	3.82406	0.140197
$745$	0.324296	0.0118813
$746$	−41.6234	−1.52394
$747$	−9.43900	−0.345355
$748$	35.6277	1.30268
$749$	21.1592	0.773139
$750$	−0.141750	−0.00517597
$751$	8.56727	0.312624	0.156312	−	0.987708i	$-0.450039\pi$
$751$	8.56727	0.312624	0.156312	+	0.987708i	$0.450039\pi$
$752$	−32.3873	−1.18104
$753$	4.79993	0.174919
$754$	5.43435	0.197907
$755$	0.0825633	0.00300479
$756$	27.3319	0.994050
$757$	−23.6866	−0.860904	−0.430452	−	0.902613i	$-0.641646\pi$
$757$	−23.6866	−0.860904	−0.430452	+	0.902613i	$0.641646\pi$
$758$	84.6944	3.07624
$759$	1.44317	0.0523838
$760$	−0.680355	−0.0246791
$761$	−35.4246	−1.28414	−0.642070	−	0.766646i	$-0.721924\pi$
$761$	−35.4246	−1.28414	−0.642070	+	0.766646i	$0.721924\pi$
$762$	11.0708	0.401054
$763$	22.6045	0.818338
$764$	96.6032	3.49498
$765$	0.471467	0.0170459
$766$	−55.9985	−2.02331
$767$	21.7776	0.786345
$768$	−6.97839	−0.251811
$769$	−14.9470	−0.539001	−0.269501	−	0.963000i	$-0.586859\pi$
$769$	−14.9470	−0.539001	−0.269501	+	0.963000i	$0.586859\pi$
$770$	−0.431974	−0.0155673
$771$	4.39658	0.158339
$772$	101.068	3.63753
$773$	−28.3023	−1.01796	−0.508981	−	0.860778i	$-0.669978\pi$
$773$	−28.3023	−1.01796	−0.508981	+	0.860778i	$0.669978\pi$
$774$	−11.7108	−0.420938
$775$	15.2851	0.549058
$776$	53.4440	1.91853
$777$	−0.588079	−0.0210972
$778$	−19.1749	−0.687452
$779$	−40.3611	−1.44609
$780$	0.0525429	0.00188134
$781$	−0.0782648	−0.00280054
$782$	−75.7460	−2.70867
$783$	−1.29615	−0.0463205
$784$	99.9596	3.56999
$785$	0.0659402	0.00235351
$786$	7.66639	0.273451
$787$	−53.9512	−1.92315	−0.961577	−	0.274536i	$-0.911476\pi$
$787$	−53.9512	−1.92315	−0.961577	+	0.274536i	$0.911476\pi$
$788$	12.2209	0.435353
$789$	1.05570	0.0375841
$790$	0.575139	0.0204625
$791$	29.9176	1.06375
$792$	22.8953	0.813548
$793$	19.7658	0.701905
$794$	−4.08188	−0.144860
$795$	0.0220293	0.000781298 0
$796$	35.9768	1.27516
$797$	−19.8213	−0.702106	−0.351053	−	0.936356i	$-0.614176\pi$
$797$	−19.8213	−0.702106	−0.351053	+	0.936356i	$0.614176\pi$
$798$	−12.2479	−0.433571
$799$	−34.1978	−1.20983
$800$	15.6141	0.552040
$801$	42.4875	1.50122
$802$	49.1284	1.73478
$803$	−16.1716	−0.570684
$804$	−3.17265	−0.111891
$805$	0.626390	0.0220774
$806$	−16.6152	−0.585245
$807$	−3.53934	−0.124591
$808$	77.6306	2.73103
$809$	27.6413	0.971818	0.485909	−	0.874009i	$-0.338489\pi$
$809$	27.6413	0.971818	0.485909	+	0.874009i	$0.338489\pi$
$810$	0.558295	0.0196165
$811$	−46.9011	−1.64692	−0.823461	−	0.567373i	$-0.807960\pi$
$811$	−46.9011	−1.64692	−0.823461	+	0.567373i	$0.807960\pi$
$812$	−21.0870	−0.740008
$813$	5.28956	0.185513
$814$	−1.86044	−0.0652082
$815$	0.384307	0.0134617
$816$	7.80342	0.273174
$817$	7.21604	0.252457
$818$	78.9667	2.76101
$819$	−31.4447	−1.09877
$820$	−0.985071	−0.0344002
$821$	6.73685	0.235118	0.117559	−	0.993066i	$-0.462493\pi$
$821$	6.73685	0.235118	0.117559	+	0.993066i	$0.462493\pi$
$822$	−5.26288	−0.183564
$823$	−23.4068	−0.815911	−0.407956	−	0.913002i	$-0.633758\pi$
$823$	−23.4068	−0.815911	−0.407956	+	0.913002i	$0.633758\pi$
$824$	−69.4255	−2.41855
$825$	−1.46955	−0.0511631
$826$	−123.898	−4.31095
$827$	27.3038	0.949447	0.474723	−	0.880135i	$-0.342548\pi$
$827$	27.3038	0.949447	0.474723	+	0.880135i	$0.342548\pi$
$828$	−62.1916	−2.16131
$829$	17.7486	0.616434	0.308217	−	0.951316i	$-0.400268\pi$
$829$	17.7486	0.616434	0.308217	+	0.951316i	$0.400268\pi$
$830$	0.208126	0.00722415
$831$	−0.217745	−0.00755350
$832$	8.27366	0.286838
$833$	105.548	3.65701
$834$	10.3644	0.358890
$835$	−0.354575	−0.0122706
$836$	−26.4275	−0.914013
$837$	3.96289	0.136977
$838$	24.2884	0.839028
$839$	−8.91443	−0.307760	−0.153880	−	0.988090i	$-0.549177\pi$
$839$	−8.91443	−0.307760	−0.153880	+	0.988090i	$0.549177\pi$
$840$	−0.159576	−0.00550589
$841$	1.00000	0.0344828
$842$	22.8724	0.788235
$843$	−3.42585	−0.117993
$844$	92.9612	3.19986
$845$	0.215582	0.00741626
$846$	−41.1676	−1.41537
$847$	45.1086	1.54995
$848$	−22.7059	−0.779725
$849$	5.37096	0.184331
$850$	77.1305	2.64555
$851$	2.69775	0.0924777
$852$	−0.0541595	−0.00185547
$853$	7.91211	0.270905	0.135453	−	0.990784i	$-0.456751\pi$
$853$	7.91211	0.270905	0.135453	+	0.990784i	$0.456751\pi$
$854$	−112.452	−3.84803
$855$	−0.349719	−0.0119601
$856$	24.7278	0.845180
$857$	35.4672	1.21154	0.605768	−	0.795641i	$-0.292866\pi$
$857$	35.4672	1.21154	0.605768	+	0.795641i	$0.292866\pi$
$858$	1.59742	0.0545352
$859$	39.2465	1.33907	0.669536	−	0.742780i	$-0.266493\pi$
$859$	39.2465	1.33907	0.669536	+	0.742780i	$0.266493\pi$
$860$	0.176118	0.00600557
$861$	−9.46663	−0.322622
$862$	−6.14918	−0.209442
$863$	−23.1605	−0.788391	−0.394195	−	0.919027i	$-0.628977\pi$
$863$	−23.1605	−0.788391	−0.394195	+	0.919027i	$0.628977\pi$
$864$	4.04817	0.137722
$865$	−0.137906	−0.00468896
$866$	−43.3671	−1.47367
$867$	4.53799	0.154118
$868$	64.4721	2.18833
$869$	11.9260	0.404561
$870$	0.0141759	0.000480609 0
$871$	7.35874	0.249341
$872$	26.4170	0.894592
$873$	27.4715	0.929769
$874$	56.1859	1.90052
$875$	−1.27576	−0.0431287
$876$	−11.1908	−0.378103
$877$	27.3998	0.925224	0.462612	−	0.886561i	$-0.346912\pi$
$877$	27.3998	0.925224	0.462612	+	0.886561i	$0.346912\pi$
$878$	−74.3294	−2.50850
$879$	−5.12994	−0.173029
$880$	−0.204150	−0.00688188
$881$	35.1383	1.18384	0.591920	−	0.805997i	$-0.298370\pi$
$881$	35.1383	1.18384	0.591920	+	0.805997i	$0.298370\pi$
$882$	127.059	4.27830
$883$	−57.8746	−1.94763	−0.973817	−	0.227334i	$-0.926999\pi$
$883$	−57.8746	−1.94763	−0.973817	+	0.227334i	$0.926999\pi$
$884$	−57.1844	−1.92332
$885$	0.0568086	0.00190960
$886$	101.400	3.40661
$887$	31.8260	1.06861	0.534307	−	0.845291i	$-0.320573\pi$
$887$	31.8260	1.06861	0.534307	+	0.845291i	$0.320573\pi$
$888$	−0.687264	−0.0230631
$889$	99.6388	3.34178
$890$	−0.936830	−0.0314026
$891$	11.5767	0.387834
$892$	108.052	3.61783
$893$	25.3668	0.848868
$894$	6.82269	0.228185
$895$	−0.360657	−0.0120554
$896$	−77.7725	−2.59820
$897$	−2.31637	−0.0773412
$898$	6.53377	0.218035
$899$	−3.05744	−0.101971
$900$	63.3283	2.11094
$901$	−23.9753	−0.798732
$902$	−29.9484	−0.997173
$903$	1.69251	0.0563232
$904$	34.9635	1.16287
$905$	0.482459	0.0160375
$906$	1.73701	0.0577082
$907$	−31.7368	−1.05380	−0.526902	−	0.849926i	$-0.676646\pi$
$907$	−31.7368	−1.05380	−0.526902	+	0.849926i	$0.676646\pi$
$908$	40.4193	1.34136
$909$	39.9040	1.32353
$910$	0.693342	0.0229841
$911$	58.7326	1.94590	0.972950	−	0.231018i	$-0.0742055\pi$
$911$	58.7326	1.94590	0.972950	+	0.231018i	$0.0742055\pi$
$912$	−5.78832	−0.191670
$913$	4.31566	0.142827
$914$	−72.0617	−2.38359
$915$	0.0515607	0.00170454
$916$	−70.4305	−2.32709
$917$	68.9984	2.27853
$918$	19.9972	0.660005
$919$	−3.14912	−0.103880	−0.0519400	−	0.998650i	$-0.516540\pi$
$919$	−3.14912	−0.103880	−0.0519400	+	0.998650i	$0.516540\pi$
$920$	0.732037	0.0241345
$921$	−1.24729	−0.0410996
$922$	−40.1021	−1.32069
$923$	0.125619	0.00413481
$924$	−6.19851	−0.203916
$925$	−2.74706	−0.0903227
$926$	71.8643	2.36161
$927$	−35.6864	−1.17210
$928$	−3.12323	−0.102525
$929$	−3.85250	−0.126396	−0.0631982	−	0.998001i	$-0.520130\pi$
$929$	−3.85250	−0.126396	−0.0631982	+	0.998001i	$0.520130\pi$
$930$	−0.0433420	−0.00142124
$931$	−78.2918	−2.56591
$932$	−12.3350	−0.404045
$933$	0.481298	0.0157570
$934$	−41.7198	−1.36511
$935$	−0.215562	−0.00704964
$936$	−36.7481	−1.20115
$937$	10.8115	0.353196	0.176598	−	0.984283i	$-0.443491\pi$
$937$	10.8115	0.353196	0.176598	+	0.984283i	$0.443491\pi$
$938$	−41.8654	−1.36695
$939$	2.56238	0.0836201
$940$	0.619113	0.0201933
$941$	37.5873	1.22531	0.612655	−	0.790351i	$-0.290102\pi$
$941$	37.5873	1.22531	0.612655	+	0.790351i	$0.290102\pi$
$942$	1.38728	0.0452001
$943$	43.4271	1.41418
$944$	−58.5536	−1.90576
$945$	−0.165369	−0.00537945
$946$	5.35439	0.174086
$947$	43.6069	1.41703	0.708516	−	0.705694i	$-0.249365\pi$
$947$	43.6069	1.41703	0.708516	+	0.705694i	$0.249365\pi$
$948$	8.25282	0.268039
$949$	25.9563	0.842577
$950$	−57.2128	−1.85623
$951$	2.26862	0.0735649
$952$	173.672	5.62875
$953$	−0.729759	−0.0236392	−0.0118196	−	0.999930i	$-0.503762\pi$
$953$	−0.729759	−0.0236392	−0.0118196	+	0.999930i	$0.503762\pi$
$954$	−28.8616	−0.934429
$955$	−0.584489	−0.0189136
$956$	33.2730	1.07613
$957$	0.293949	0.00950203
$958$	−0.644407	−0.0208199
$959$	−47.3666	−1.52955
$960$	0.0215825	0.000696572 0
$961$	−21.6521	−0.698454
$962$	2.98610	0.0962757
$963$	12.7107	0.409597
$964$	99.5768	3.20715
$965$	−0.611505	−0.0196851
$966$	13.1783	0.424005
$967$	41.9897	1.35030	0.675149	−	0.737681i	$-0.264079\pi$
$967$	41.9897	1.35030	0.675149	+	0.737681i	$0.264079\pi$
$968$	52.7166	1.69438
$969$	−6.11191	−0.196343
$970$	−0.605735	−0.0194490
$971$	−34.8135	−1.11722	−0.558610	−	0.829431i	$-0.688665\pi$
$971$	−34.8135	−1.11722	−0.558610	+	0.829431i	$0.688665\pi$
$972$	24.6935	0.792046
$973$	93.2809	2.99045
$974$	26.9884	0.864764
$975$	2.35870	0.0755390
$976$	−53.1444	−1.70111
$977$	−20.9184	−0.669238	−0.334619	−	0.942353i	$-0.608608\pi$
$977$	−20.9184	−0.669238	−0.334619	+	0.942353i	$0.608608\pi$
$978$	8.08524	0.258537
$979$	−19.4259	−0.620856
$980$	−1.91082	−0.0610390
$981$	13.5790	0.433543
$982$	78.1137	2.49271
$983$	36.1899	1.15428	0.577139	−	0.816646i	$-0.304169\pi$
$983$	36.1899	1.15428	0.577139	+	0.816646i	$0.304169\pi$
$984$	−11.0633	−0.352684
$985$	−0.0739418	−0.00235598
$986$	−15.4282	−0.491333
$987$	5.94974	0.189382
$988$	42.4175	1.34948
$989$	−7.76420	−0.246887
$990$	−0.259495	−0.00824730
$991$	−11.8361	−0.375987	−0.187993	−	0.982170i	$-0.560198\pi$
$991$	−11.8361	−0.375987	−0.187993	+	0.982170i	$0.560198\pi$
$992$	9.54909	0.303184
$993$	−2.20033	−0.0698255
$994$	−0.714674	−0.0226681
$995$	−0.217674	−0.00690074
$996$	2.98645	0.0946293
$997$	−15.9715	−0.505822	−0.252911	−	0.967490i	$-0.581388\pi$
$997$	−15.9715	−0.505822	−0.252911	+	0.967490i	$0.581388\pi$
$998$	9.13778	0.289251
$999$	−0.712214	−0.0225335

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8033.2.a.d.1.12	✓	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8033.2.a.d.1.12	✓	168	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:	\( N \)	\(=\)	\( 8033 = 29 \cdot 277 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8033.a (trivial)

\(f(q)\)	\(=\)	\(q-2.50804 q^{2} +0.217745 q^{3} +4.29026 q^{4} -0.0259578 q^{5} -0.546113 q^{6} -4.91509 q^{7} -5.74406 q^{8} -2.95259 q^{9} +O(q^{10})\)	\(q-2.50804 q^{2} +0.217745 q^{3} +4.29026 q^{4} -0.0259578 q^{5} -0.546113 q^{6} -4.91509 q^{7} -5.74406 q^{8} -2.95259 q^{9} +0.0651033 q^{10} +1.34997 q^{11} +0.934183 q^{12} -2.16677 q^{13} +12.3272 q^{14} -0.00565219 q^{15} +5.82581 q^{16} +6.15149 q^{17} +7.40520 q^{18} -4.56297 q^{19} -0.111366 q^{20} -1.07024 q^{21} -3.38578 q^{22} +4.90959 q^{23} -1.25074 q^{24} -4.99933 q^{25} +5.43435 q^{26} -1.29615 q^{27} -21.0870 q^{28} +1.00000 q^{29} +0.0141759 q^{30} -3.05744 q^{31} -3.12323 q^{32} +0.293949 q^{33} -15.4282 q^{34} +0.127585 q^{35} -12.6674 q^{36} +0.549486 q^{37} +11.4441 q^{38} -0.471804 q^{39} +0.149103 q^{40} +8.84536 q^{41} +2.68419 q^{42} -1.58144 q^{43} +5.79172 q^{44} +0.0766428 q^{45} -12.3134 q^{46} -5.55928 q^{47} +1.26854 q^{48} +17.1581 q^{49} +12.5385 q^{50} +1.33946 q^{51} -9.29602 q^{52} -3.89747 q^{53} +3.25079 q^{54} -0.0350423 q^{55} +28.2326 q^{56} -0.993565 q^{57} -2.50804 q^{58} -10.0507 q^{59} -0.0242494 q^{60} -9.12224 q^{61} +7.66817 q^{62} +14.5122 q^{63} -3.81843 q^{64} +0.0562447 q^{65} -0.737237 q^{66} -3.39617 q^{67} +26.3915 q^{68} +1.06904 q^{69} -0.319988 q^{70} -0.0579752 q^{71} +16.9598 q^{72} -11.9792 q^{73} -1.37813 q^{74} -1.08858 q^{75} -19.5763 q^{76} -6.63522 q^{77} +1.18330 q^{78} +8.83426 q^{79} -0.151225 q^{80} +8.57553 q^{81} -22.1845 q^{82} +3.19686 q^{83} -4.59159 q^{84} -0.159679 q^{85} +3.96630 q^{86} +0.217745 q^{87} -7.75431 q^{88} -14.3899 q^{89} -0.192223 q^{90} +10.6499 q^{91} +21.0634 q^{92} -0.665742 q^{93} +13.9429 q^{94} +0.118445 q^{95} -0.680069 q^{96} -9.30421 q^{97} -43.0331 q^{98} -3.98590 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q + 12 q^{2} + 35 q^{3} + 184 q^{4} + 12 q^{5} + 10 q^{6} + 74 q^{7} + 39 q^{8} + 183 q^{9}+O(q^{10}) \) 168 * q + 12 * q^2 + 35 * q^3 + 184 * q^4 + 12 * q^5 + 10 * q^6 + 74 * q^7 + 39 * q^8 + 183 * q^9	\( 168 q + 12 q^{2} + 35 q^{3} + 184 q^{4} + 12 q^{5} + 10 q^{6} + 74 q^{7} + 39 q^{8} + 183 q^{9} + 41 q^{10} + 29 q^{11} + 82 q^{12} + 62 q^{13} + 23 q^{14} + 31 q^{15} + 204 q^{16} + 56 q^{17} + 35 q^{18} + 83 q^{19} + 6 q^{20} + 30 q^{21} + 56 q^{22} + 54 q^{23} + 28 q^{24} + 210 q^{25} + 21 q^{26} + 140 q^{27} + 151 q^{28} + 168 q^{29} + 29 q^{30} + 72 q^{31} + 40 q^{32} + 32 q^{33} + 34 q^{34} + 18 q^{35} + 152 q^{36} + 42 q^{37} + 29 q^{38} + 70 q^{39} + 97 q^{40} + 41 q^{41} - 20 q^{42} + 119 q^{43} + 37 q^{44} + 22 q^{45} + 24 q^{46} + 119 q^{47} + 135 q^{48} + 216 q^{49} + 38 q^{50} + 18 q^{51} + 154 q^{52} - 7 q^{53} + 35 q^{54} + 224 q^{55} + 46 q^{56} + 12 q^{57} + 12 q^{58} + 25 q^{59} + 13 q^{60} + 82 q^{61} + 27 q^{62} + 211 q^{63} + 217 q^{64} + 8 q^{65} - 6 q^{66} + 76 q^{67} + 132 q^{68} + 36 q^{69} + 39 q^{70} + 32 q^{71} + 39 q^{72} + 89 q^{73} - q^{74} + 123 q^{75} + 180 q^{76} + 68 q^{77} - 54 q^{78} + 176 q^{79} - 11 q^{80} + 192 q^{81} + 51 q^{82} + 76 q^{83} + 86 q^{84} + 65 q^{85} - 72 q^{86} + 35 q^{87} + 178 q^{88} + 55 q^{89} + 2 q^{90} + 80 q^{91} + 44 q^{92} + 39 q^{93} + 89 q^{94} + 77 q^{95} - 68 q^{96} + 82 q^{97} + 80 q^{98} + 67 q^{99}+O(q^{100}) \) 168 * q + 12 * q^2 + 35 * q^3 + 184 * q^4 + 12 * q^5 + 10 * q^6 + 74 * q^7 + 39 * q^8 + 183 * q^9 + 41 * q^10 + 29 * q^11 + 82 * q^12 + 62 * q^13 + 23 * q^14 + 31 * q^15 + 204 * q^16 + 56 * q^17 + 35 * q^18 + 83 * q^19 + 6 * q^20 + 30 * q^21 + 56 * q^22 + 54 * q^23 + 28 * q^24 + 210 * q^25 + 21 * q^26 + 140 * q^27 + 151 * q^28 + 168 * q^29 + 29 * q^30 + 72 * q^31 + 40 * q^32 + 32 * q^33 + 34 * q^34 + 18 * q^35 + 152 * q^36 + 42 * q^37 + 29 * q^38 + 70 * q^39 + 97 * q^40 + 41 * q^41 - 20 * q^42 + 119 * q^43 + 37 * q^44 + 22 * q^45 + 24 * q^46 + 119 * q^47 + 135 * q^48 + 216 * q^49 + 38 * q^50 + 18 * q^51 + 154 * q^52 - 7 * q^53 + 35 * q^54 + 224 * q^55 + 46 * q^56 + 12 * q^57 + 12 * q^58 + 25 * q^59 + 13 * q^60 + 82 * q^61 + 27 * q^62 + 211 * q^63 + 217 * q^64 + 8 * q^65 - 6 * q^66 + 76 * q^67 + 132 * q^68 + 36 * q^69 + 39 * q^70 + 32 * q^71 + 39 * q^72 + 89 * q^73 - q^74 + 123 * q^75 + 180 * q^76 + 68 * q^77 - 54 * q^78 + 176 * q^79 - 11 * q^80 + 192 * q^81 + 51 * q^82 + 76 * q^83 + 86 * q^84 + 65 * q^85 - 72 * q^86 + 35 * q^87 + 178 * q^88 + 55 * q^89 + 2 * q^90 + 80 * q^91 + 44 * q^92 + 39 * q^93 + 89 * q^94 + 77 * q^95 - 68 * q^96 + 82 * q^97 + 80 * q^98 + 67 * q^99

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