LMFDB - Embedded newform 8033.2.a.d.1.15

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			1.15
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)

$f(q)$	$=$	$q-2.44996 q^{2} -1.86877 q^{3} +4.00229 q^{4} -1.18542 q^{5} +4.57841 q^{6} -4.60968 q^{7} -4.90553 q^{8} +0.492307 q^{9} +O(q^{10})$	\(q-2.44996 q^{2} -1.86877 q^{3} +4.00229 q^{4} -1.18542 q^{5} +4.57841 q^{6} -4.60968 q^{7} -4.90553 q^{8} +0.492307 q^{9} +2.90424 q^{10} -4.13288 q^{11} -7.47937 q^{12} +5.64639 q^{13} +11.2935 q^{14} +2.21529 q^{15} +4.01376 q^{16} -0.789075 q^{17} -1.20613 q^{18} +0.196589 q^{19} -4.74442 q^{20} +8.61443 q^{21} +10.1254 q^{22} +0.875963 q^{23} +9.16732 q^{24} -3.59477 q^{25} -13.8334 q^{26} +4.68631 q^{27} -18.4493 q^{28} +1.00000 q^{29} -5.42736 q^{30} +6.03265 q^{31} -0.0224789 q^{32} +7.72341 q^{33} +1.93320 q^{34} +5.46442 q^{35} +1.97036 q^{36} -5.16136 q^{37} -0.481635 q^{38} -10.5518 q^{39} +5.81514 q^{40} -6.94964 q^{41} -21.1050 q^{42} +7.59516 q^{43} -16.5410 q^{44} -0.583593 q^{45} -2.14607 q^{46} +3.48575 q^{47} -7.50080 q^{48} +14.2491 q^{49} +8.80703 q^{50} +1.47460 q^{51} +22.5985 q^{52} -5.06422 q^{53} -11.4813 q^{54} +4.89922 q^{55} +22.6129 q^{56} -0.367380 q^{57} -2.44996 q^{58} +5.84941 q^{59} +8.86623 q^{60} +8.42006 q^{61} -14.7797 q^{62} -2.26937 q^{63} -7.97245 q^{64} -6.69337 q^{65} -18.9220 q^{66} +8.01953 q^{67} -3.15811 q^{68} -1.63697 q^{69} -13.3876 q^{70} -9.87437 q^{71} -2.41503 q^{72} -10.9721 q^{73} +12.6451 q^{74} +6.71780 q^{75} +0.786808 q^{76} +19.0512 q^{77} +25.8515 q^{78} -7.78387 q^{79} -4.75801 q^{80} -10.2346 q^{81} +17.0263 q^{82} -7.81802 q^{83} +34.4775 q^{84} +0.935390 q^{85} -18.6078 q^{86} -1.86877 q^{87} +20.2740 q^{88} -5.40229 q^{89} +1.42978 q^{90} -26.0280 q^{91} +3.50586 q^{92} -11.2737 q^{93} -8.53993 q^{94} -0.233042 q^{95} +0.0420080 q^{96} -12.0522 q^{97} -34.9097 q^{98} -2.03465 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.44996	−1.73238	−0.866191	−	0.499713i	$-0.833439\pi$
$2$	−2.44996	−1.73238	−0.866191	+	0.499713i	$0.833439\pi$
$3$	−1.86877	−1.07894	−0.539468	−	0.842006i	$-0.681375\pi$
$3$	−1.86877	−1.07894	−0.539468	+	0.842006i	$0.681375\pi$
$4$	4.00229	2.00115
$5$	−1.18542	−0.530138	−0.265069	−	0.964229i	$-0.585395\pi$
$5$	−1.18542	−0.530138	−0.265069	+	0.964229i	$0.585395\pi$
$6$	4.57841	1.86913
$7$	−4.60968	−1.74229	−0.871147	−	0.491023i	$-0.836623\pi$
$7$	−4.60968	−1.74229	−0.871147	+	0.491023i	$0.836623\pi$
$8$	−4.90553	−1.73437
$9$	0.492307	0.164102
$10$	2.90424	0.918402
$11$	−4.13288	−1.24611	−0.623055	−	0.782178i	$-0.714109\pi$
$11$	−4.13288	−1.24611	−0.623055	+	0.782178i	$0.714109\pi$
$12$	−7.47937	−2.15911
$13$	5.64639	1.56603	0.783013	−	0.622006i	$-0.213682\pi$
$13$	5.64639	1.56603	0.783013	+	0.622006i	$0.213682\pi$
$14$	11.2935	3.01832
$15$	2.21529	0.571985
$16$	4.01376	1.00344
$17$	−0.789075	−0.191379	−0.0956894	−	0.995411i	$-0.530506\pi$
$17$	−0.789075	−0.191379	−0.0956894	+	0.995411i	$0.530506\pi$
$18$	−1.20613	−0.284288
$19$	0.196589	0.0451007	0.0225503	−	0.999746i	$-0.492821\pi$
$19$	0.196589	0.0451007	0.0225503	+	0.999746i	$0.492821\pi$
$20$	−4.74442	−1.06088
$21$	8.61443	1.87982
$22$	10.1254	2.15874
$23$	0.875963	0.182651	0.0913254	−	0.995821i	$-0.470890\pi$
$23$	0.875963	0.182651	0.0913254	+	0.995821i	$0.470890\pi$
$24$	9.16732	1.87127
$25$	−3.59477	−0.718954
$26$	−13.8334	−2.71295
$27$	4.68631	0.901880
$28$	−18.4493	−3.48658
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	−5.42736	−0.990896
$31$	6.03265	1.08350	0.541748	−	0.840541i	$-0.317763\pi$
$31$	6.03265	1.08350	0.541748	+	0.840541i	$0.317763\pi$
$32$	−0.0224789	−0.00397375
$33$	7.72341	1.34447
$34$	1.93320	0.331541
$35$	5.46442	0.923656
$36$	1.97036	0.328393
$37$	−5.16136	−0.848522	−0.424261	−	0.905540i	$-0.639466\pi$
$37$	−5.16136	−0.848522	−0.424261	+	0.905540i	$0.639466\pi$
$38$	−0.481635	−0.0781316
$39$	−10.5518	−1.68964
$40$	5.81514	0.919454
$41$	−6.94964	−1.08535	−0.542676	−	0.839942i	$-0.682589\pi$
$41$	−6.94964	−1.08535	−0.542676	+	0.839942i	$0.682589\pi$
$42$	−21.1050	−3.25657
$43$	7.59516	1.15825	0.579125	−	0.815239i	$-0.303394\pi$
$43$	7.59516	1.15825	0.579125	+	0.815239i	$0.303394\pi$
$44$	−16.5410	−2.49365
$45$	−0.583593	−0.0869968
$46$	−2.14607	−0.316421
$47$	3.48575	0.508448	0.254224	−	0.967145i	$-0.418180\pi$
$47$	3.48575	0.508448	0.254224	+	0.967145i	$0.418180\pi$
$48$	−7.50080	−1.08265
$49$	14.2491	2.03559
$50$	8.80703	1.24550
$51$	1.47460	0.206485
$52$	22.5985	3.13385
$53$	−5.06422	−0.695624	−0.347812	−	0.937564i	$-0.613075\pi$
$53$	−5.06422	−0.695624	−0.347812	+	0.937564i	$0.613075\pi$
$54$	−11.4813	−1.56240
$55$	4.89922	0.660611
$56$	22.6129	3.02178
$57$	−0.367380	−0.0486607
$58$	−2.44996	−0.321695
$59$	5.84941	0.761528	0.380764	−	0.924672i	$-0.375661\pi$
$59$	5.84941	0.761528	0.380764	+	0.924672i	$0.375661\pi$
$60$	8.86623	1.14463
$61$	8.42006	1.07808	0.539039	−	0.842281i	$-0.318788\pi$
$61$	8.42006	1.07808	0.539039	+	0.842281i	$0.318788\pi$
$62$	−14.7797	−1.87703
$63$	−2.26937	−0.285914
$64$	−7.97245	−0.996556
$65$	−6.69337	−0.830210
$66$	−18.9220	−2.32914
$67$	8.01953	0.979742	0.489871	−	0.871795i	$-0.337044\pi$
$67$	8.01953	0.979742	0.489871	+	0.871795i	$0.337044\pi$
$68$	−3.15811	−0.382977
$69$	−1.63697	−0.197068
$70$	−13.3876	−1.60013
$71$	−9.87437	−1.17187	−0.585936	−	0.810357i	$-0.699273\pi$
$71$	−9.87437	−1.17187	−0.585936	+	0.810357i	$0.699273\pi$
$72$	−2.41503	−0.284614
$73$	−10.9721	−1.28418	−0.642092	−	0.766628i	$-0.721933\pi$
$73$	−10.9721	−1.28418	−0.642092	+	0.766628i	$0.721933\pi$
$74$	12.6451	1.46996
$75$	6.71780	0.775705
$76$	0.786808	0.0902530
$77$	19.0512	2.17109
$78$	25.8515	2.92710
$79$	−7.78387	−0.875753	−0.437877	−	0.899035i	$-0.644269\pi$
$79$	−7.78387	−0.875753	−0.437877	+	0.899035i	$0.644269\pi$
$80$	−4.75801	−0.531962
$81$	−10.2346	−1.13717
$82$	17.0263	1.88024
$83$	−7.81802	−0.858139	−0.429069	−	0.903272i	$-0.641158\pi$
$83$	−7.81802	−0.858139	−0.429069	+	0.903272i	$0.641158\pi$
$84$	34.4775	3.76180
$85$	0.935390	0.101457
$86$	−18.6078	−2.00653
$87$	−1.86877	−0.200353
$88$	20.2740	2.16121
$89$	−5.40229	−0.572642	−0.286321	−	0.958134i	$-0.592432\pi$
$89$	−5.40229	−0.572642	−0.286321	+	0.958134i	$0.592432\pi$
$90$	1.42978	0.150712
$91$	−26.0280	−2.72848
$92$	3.50586	0.365511
$93$	−11.2737	−1.16902
$94$	−8.53993	−0.880827
$95$	−0.233042	−0.0239096
$96$	0.0420080	0.00428742
$97$	−12.0522	−1.22371	−0.611857	−	0.790969i	$-0.709577\pi$
$97$	−12.0522	−1.22371	−0.611857	+	0.790969i	$0.709577\pi$
$98$	−34.9097	−3.52641
$99$	−2.03465	−0.204490
$100$	−14.3873	−1.43873
$101$	−4.29240	−0.427110	−0.213555	−	0.976931i	$-0.568504\pi$
$101$	−4.29240	−0.427110	−0.213555	+	0.976931i	$0.568504\pi$
$102$	−3.61271	−0.357712
$103$	1.31090	0.129167	0.0645835	−	0.997912i	$-0.479428\pi$
$103$	1.31090	0.129167	0.0645835	+	0.997912i	$0.479428\pi$
$104$	−27.6985	−2.71606
$105$	−10.2118	−0.996566
$106$	12.4071	1.20509
$107$	7.46033	0.721217	0.360608	−	0.932717i	$-0.382569\pi$
$107$	7.46033	0.721217	0.360608	+	0.932717i	$0.382569\pi$
$108$	18.7560	1.80479
$109$	−14.8435	−1.42175	−0.710873	−	0.703321i	$-0.751700\pi$
$109$	−14.8435	−1.42175	−0.710873	+	0.703321i	$0.751700\pi$
$110$	−12.0029	−1.14443
$111$	9.64539	0.915500
$112$	−18.5021	−1.74829
$113$	−8.10093	−0.762072	−0.381036	−	0.924560i	$-0.624433\pi$
$113$	−8.10093	−0.762072	−0.381036	+	0.924560i	$0.624433\pi$
$114$	0.900066	0.0842989
$115$	−1.03839	−0.0968302
$116$	4.00229	0.371604
$117$	2.77975	0.256988
$118$	−14.3308	−1.31926
$119$	3.63738	0.333438
$120$	−10.8672	−0.992032
$121$	6.08071	0.552792
$122$	−20.6288	−1.86764
$123$	12.9873	1.17102
$124$	24.1444	2.16824
$125$	10.1885	0.911283
$126$	5.55987	0.495313
$127$	6.64224	0.589404	0.294702	−	0.955589i	$-0.404780\pi$
$127$	6.64224	0.589404	0.294702	+	0.955589i	$0.404780\pi$
$128$	19.5771	1.73039
$129$	−14.1936	−1.24968
$130$	16.3985	1.43824
$131$	4.85471	0.424158	0.212079	−	0.977253i	$-0.431977\pi$
$131$	4.85471	0.424158	0.212079	+	0.977253i	$0.431977\pi$
$132$	30.9114	2.69049
$133$	−0.906213	−0.0785786
$134$	−19.6475	−1.69729
$135$	−5.55526	−0.478121
$136$	3.87083	0.331921
$137$	−11.3351	−0.968422	−0.484211	−	0.874951i	$-0.660893\pi$
$137$	−11.3351	−0.968422	−0.484211	+	0.874951i	$0.660893\pi$
$138$	4.01052	0.341398
$139$	−11.4225	−0.968844	−0.484422	−	0.874835i	$-0.660970\pi$
$139$	−11.4225	−0.968844	−0.484422	+	0.874835i	$0.660970\pi$
$140$	21.8702	1.84837
$141$	−6.51406	−0.548583
$142$	24.1918	2.03013
$143$	−23.3358	−1.95144
$144$	1.97600	0.164667
$145$	−1.18542	−0.0984442
$146$	26.8811	2.22470
$147$	−26.6283	−2.19627
$148$	−20.6573	−1.69802
$149$	−6.91529	−0.566523	−0.283261	−	0.959043i	$-0.591416\pi$
$149$	−6.91529	−0.566523	−0.283261	+	0.959043i	$0.591416\pi$
$150$	−16.4583	−1.34382
$151$	−1.02960	−0.0837874	−0.0418937	−	0.999122i	$-0.513339\pi$
$151$	−1.02960	−0.0837874	−0.0418937	+	0.999122i	$0.513339\pi$
$152$	−0.964375	−0.0782211
$153$	−0.388467	−0.0314057
$154$	−46.6747	−3.76116
$155$	−7.15126	−0.574403
$156$	−42.2314	−3.38122
$157$	12.2466	0.977388	0.488694	−	0.872455i	$-0.337474\pi$
$157$	12.2466	0.977388	0.488694	+	0.872455i	$0.337474\pi$
$158$	19.0701	1.51714
$159$	9.46386	0.750533
$160$	0.0266471	0.00210664
$161$	−4.03790	−0.318231
$162$	25.0742	1.97002
$163$	−2.23434	−0.175007	−0.0875034	−	0.996164i	$-0.527889\pi$
$163$	−2.23434	−0.175007	−0.0875034	+	0.996164i	$0.527889\pi$
$164$	−27.8145	−2.17195
$165$	−9.15552	−0.712757
$166$	19.1538	1.48662
$167$	−9.21915	−0.713399	−0.356699	−	0.934219i	$-0.616098\pi$
$167$	−9.21915	−0.713399	−0.356699	+	0.934219i	$0.616098\pi$
$168$	−42.2584	−3.26030
$169$	18.8817	1.45244
$170$	−2.29166	−0.175763
$171$	0.0967822	0.00740112
$172$	30.3980	2.31783
$173$	2.10227	0.159832	0.0799162	−	0.996802i	$-0.474535\pi$
$173$	2.10227	0.159832	0.0799162	+	0.996802i	$0.474535\pi$
$174$	4.57841	0.347088
$175$	16.5707	1.25263
$176$	−16.5884	−1.25040
$177$	−10.9312	−0.821640
$178$	13.2354	0.992035
$179$	−9.51161	−0.710931	−0.355466	−	0.934689i	$-0.615678\pi$
$179$	−9.51161	−0.710931	−0.355466	+	0.934689i	$0.615678\pi$
$180$	−2.33571	−0.174093
$181$	24.1894	1.79798	0.898992	−	0.437965i	$-0.144301\pi$
$181$	24.1894	1.79798	0.898992	+	0.437965i	$0.144301\pi$
$182$	63.7675	4.72676
$183$	−15.7352	−1.16318
$184$	−4.29706	−0.316784
$185$	6.11840	0.449834
$186$	27.6200	2.02519
$187$	3.26116	0.238479
$188$	13.9510	1.01748
$189$	−21.6024	−1.57134
$190$	0.570942	0.0414205
$191$	5.69160	0.411829	0.205915	−	0.978570i	$-0.433983\pi$
$191$	5.69160	0.411829	0.205915	+	0.978570i	$0.433983\pi$
$192$	14.8987	1.07522
$193$	17.3077	1.24584	0.622919	−	0.782286i	$-0.285947\pi$
$193$	17.3077	1.24584	0.622919	+	0.782286i	$0.285947\pi$
$194$	29.5273	2.11994
$195$	12.5084	0.895743
$196$	57.0291	4.07351
$197$	−3.74578	−0.266876	−0.133438	−	0.991057i	$-0.542602\pi$
$197$	−3.74578	−0.266876	−0.133438	+	0.991057i	$0.542602\pi$
$198$	4.98479	0.354254
$199$	−19.2447	−1.36422	−0.682111	−	0.731248i	$-0.738938\pi$
$199$	−19.2447	−1.36422	−0.682111	+	0.731248i	$0.738938\pi$
$200$	17.6342	1.24693
$201$	−14.9867	−1.05708
$202$	10.5162	0.739917
$203$	−4.60968	−0.323536
$204$	5.90179	0.413208
$205$	8.23828	0.575386
$206$	−3.21166	−0.223767
$207$	0.431242	0.0299734
$208$	22.6632	1.57141
$209$	−0.812480	−0.0562004
$210$	25.0184	1.72643
$211$	19.0094	1.30866	0.654329	−	0.756210i	$-0.272951\pi$
$211$	19.0094	1.30866	0.654329	+	0.756210i	$0.272951\pi$
$212$	−20.2685	−1.39204
$213$	18.4529	1.26438
$214$	−18.2775	−1.24942
$215$	−9.00349	−0.614033
$216$	−22.9888	−1.56419
$217$	−27.8086	−1.88777
$218$	36.3658	2.46301
$219$	20.5043	1.38555
$220$	19.6081	1.32198
$221$	−4.45542	−0.299704
$222$	−23.6308	−1.58600
$223$	10.4320	0.698576	0.349288	−	0.937015i	$-0.386423\pi$
$223$	10.4320	0.698576	0.349288	+	0.937015i	$0.386423\pi$
$224$	0.103621	0.00692344
$225$	−1.76973	−0.117982
$226$	19.8469	1.32020
$227$	−18.8969	−1.25423	−0.627117	−	0.778925i	$-0.715765\pi$
$227$	−18.8969	−1.25423	−0.627117	+	0.778925i	$0.715765\pi$
$228$	−1.47036	−0.0973772
$229$	−7.97382	−0.526925	−0.263463	−	0.964670i	$-0.584865\pi$
$229$	−7.97382	−0.526925	−0.263463	+	0.964670i	$0.584865\pi$
$230$	2.54401	0.167747
$231$	−35.6024	−2.34247
$232$	−4.90553	−0.322064
$233$	−1.30350	−0.0853954	−0.0426977	−	0.999088i	$-0.513595\pi$
$233$	−1.30350	−0.0853954	−0.0426977	+	0.999088i	$0.513595\pi$
$234$	−6.81028	−0.445202
$235$	−4.13209	−0.269548
$236$	23.4110	1.52393
$237$	14.5463	0.944881
$238$	−8.91143	−0.577642
$239$	−21.8547	−1.41367	−0.706833	−	0.707381i	$-0.749877\pi$
$239$	−21.8547	−1.41367	−0.706833	+	0.707381i	$0.749877\pi$
$240$	8.89164	0.573953
$241$	−19.3236	−1.24474	−0.622372	−	0.782721i	$-0.713831\pi$
$241$	−19.3236	−1.24474	−0.622372	+	0.782721i	$0.713831\pi$
$242$	−14.8975	−0.957647
$243$	5.06712	0.325056
$244$	33.6995	2.15739
$245$	−16.8913	−1.07914
$246$	−31.8183	−2.02866
$247$	1.11002	0.0706288
$248$	−29.5934	−1.87918
$249$	14.6101	0.925877
$250$	−24.9613	−1.57869
$251$	−10.6584	−0.672749	−0.336375	−	0.941728i	$-0.609201\pi$
$251$	−10.6584	−0.672749	−0.336375	+	0.941728i	$0.609201\pi$
$252$	−9.08270	−0.572156
$253$	−3.62025	−0.227603
$254$	−16.2732	−1.02107
$255$	−1.74803	−0.109466
$256$	−32.0182	−2.00114
$257$	0.511226	0.0318894	0.0159447	−	0.999873i	$-0.494924\pi$
$257$	0.511226	0.0318894	0.0159447	+	0.999873i	$0.494924\pi$
$258$	34.7738	2.16492
$259$	23.7922	1.47837
$260$	−26.7888	−1.66137
$261$	0.492307	0.0304730
$262$	−11.8938	−0.734803
$263$	4.18456	0.258031	0.129016	−	0.991643i	$-0.458818\pi$
$263$	4.18456	0.258031	0.129016	+	0.991643i	$0.458818\pi$
$264$	−37.8874	−2.33181
$265$	6.00325	0.368777
$266$	2.22018	0.136128
$267$	10.0957	0.617844
$268$	32.0965	1.96061
$269$	−16.2658	−0.991742	−0.495871	−	0.868396i	$-0.665151\pi$
$269$	−16.2658	−0.991742	−0.495871	+	0.868396i	$0.665151\pi$
$270$	13.6102	0.828288
$271$	−28.4656	−1.72916	−0.864582	−	0.502492i	$-0.832417\pi$
$271$	−28.4656	−1.72916	−0.864582	+	0.502492i	$0.832417\pi$
$272$	−3.16716	−0.192037
$273$	48.6404	2.94385
$274$	27.7705	1.67768
$275$	14.8568	0.895896
$276$	−6.55165	−0.394363
$277$	−1.00000	−0.0600842
$277$	−1.00000	−0.0600842
$278$	27.9846	1.67841
$279$	2.96992	0.177804
$280$	−26.8059	−1.60196
$281$	16.2260	0.967960	0.483980	−	0.875079i	$-0.339191\pi$
$281$	16.2260	0.967960	0.483980	+	0.875079i	$0.339191\pi$
$282$	15.9592	0.950355
$283$	2.25736	0.134186	0.0670931	−	0.997747i	$-0.478628\pi$
$283$	2.25736	0.134186	0.0670931	+	0.997747i	$0.478628\pi$
$284$	−39.5201	−2.34509
$285$	0.435502	0.0257969
$286$	57.1718	3.38064
$287$	32.0356	1.89100
$288$	−0.0110665	−0.000652101 0
$289$	−16.3774	−0.963374
$290$	2.90424	0.170543
$291$	22.5228	1.32031
$292$	−43.9134	−2.56984
$293$	−5.74892	−0.335855	−0.167928	−	0.985799i	$-0.553707\pi$
$293$	−5.74892	−0.335855	−0.167928	+	0.985799i	$0.553707\pi$
$294$	65.2383	3.80477
$295$	−6.93403	−0.403715
$296$	25.3192	1.47165
$297$	−19.3679	−1.12384
$298$	16.9422	0.981434
$299$	4.94602	0.286036
$300$	26.8866	1.55230
$301$	−35.0112	−2.01801
$302$	2.52247	0.145152
$303$	8.02152	0.460824
$304$	0.789062	0.0452558
$305$	−9.98135	−0.571530
$306$	0.951728	0.0544067
$307$	28.3752	1.61946	0.809730	−	0.586803i	$-0.199614\pi$
$307$	28.3752	1.61946	0.809730	+	0.586803i	$0.199614\pi$
$308$	76.2487	4.34467
$309$	−2.44978	−0.139363
$310$	17.5203	0.995085
$311$	−12.8878	−0.730799	−0.365400	−	0.930851i	$-0.619068\pi$
$311$	−12.8878	−0.730799	−0.365400	+	0.930851i	$0.619068\pi$
$312$	51.7622	2.93046
$313$	−31.2822	−1.76817	−0.884086	−	0.467325i	$-0.845218\pi$
$313$	−31.2822	−1.76817	−0.884086	+	0.467325i	$0.845218\pi$
$314$	−30.0037	−1.69321
$315$	2.69017	0.151574
$316$	−31.1533	−1.75251
$317$	−0.811326	−0.0455686	−0.0227843	−	0.999740i	$-0.507253\pi$
$317$	−0.811326	−0.0455686	−0.0227843	+	0.999740i	$0.507253\pi$
$318$	−23.1861	−1.30021
$319$	−4.13288	−0.231397
$320$	9.45074	0.528312
$321$	−13.9416	−0.778147
$322$	9.89269	0.551298
$323$	−0.155124	−0.00863131
$324$	−40.9617	−2.27565
$325$	−20.2974	−1.12590
$326$	5.47403	0.303179
$327$	27.7390	1.53397
$328$	34.0917	1.88240
$329$	−16.0682	−0.885866
$330$	22.4306	1.23477
$331$	4.58280	0.251894	0.125947	−	0.992037i	$-0.459803\pi$
$331$	4.58280	0.251894	0.125947	+	0.992037i	$0.459803\pi$
$332$	−31.2900	−1.71726
$333$	−2.54097	−0.139244
$334$	22.5865	1.23588
$335$	−9.50656	−0.519399
$336$	34.5763	1.88629
$337$	8.84525	0.481831	0.240916	−	0.970546i	$-0.422552\pi$
$337$	8.84525	0.481831	0.240916	+	0.970546i	$0.422552\pi$
$338$	−46.2593	−2.51617
$339$	15.1388	0.822226
$340$	3.74370	0.203031
$341$	−24.9322	−1.35016
$342$	−0.237112	−0.0128216
$343$	−33.4161	−1.80430
$344$	−37.2583	−2.00883
$345$	1.94051	0.104474
$346$	−5.15046	−0.276891
$347$	15.9721	0.857426	0.428713	−	0.903441i	$-0.358967\pi$
$347$	15.9721	0.857426	0.428713	+	0.903441i	$0.358967\pi$
$348$	−7.47937	−0.400936
$349$	−28.6956	−1.53604	−0.768021	−	0.640424i	$-0.778758\pi$
$349$	−28.6956	−1.53604	−0.768021	+	0.640424i	$0.778758\pi$
$350$	−40.5975	−2.17003
$351$	26.4607	1.41237
$352$	0.0929028	0.00495173
$353$	−15.5716	−0.828791	−0.414396	−	0.910097i	$-0.636007\pi$
$353$	−15.5716	−0.828791	−0.414396	+	0.910097i	$0.636007\pi$
$354$	26.7810	1.42339
$355$	11.7053	0.621254
$356$	−21.6216	−1.14594
$357$	−6.79743	−0.359758
$358$	23.3031	1.23160
$359$	−5.03866	−0.265930	−0.132965	−	0.991121i	$-0.542450\pi$
$359$	−5.03866	−0.265930	−0.132965	+	0.991121i	$0.542450\pi$
$360$	2.86283	0.150884
$361$	−18.9614	−0.997966
$362$	−59.2630	−3.11479
$363$	−11.3635	−0.596427
$364$	−104.172	−5.46008
$365$	13.0066	0.680795
$366$	38.5505	2.01507
$367$	4.79135	0.250107	0.125053	−	0.992150i	$-0.460090\pi$
$367$	4.79135	0.250107	0.125053	+	0.992150i	$0.460090\pi$
$368$	3.51590	0.183279
$369$	−3.42135	−0.178109
$370$	−14.9898	−0.779284
$371$	23.3444	1.21198
$372$	−45.1204	−2.33939
$373$	23.9877	1.24203	0.621017	−	0.783797i	$-0.286720\pi$
$373$	23.9877	1.24203	0.621017	+	0.783797i	$0.286720\pi$
$374$	−7.98969	−0.413137
$375$	−19.0399	−0.983216
$376$	−17.0994	−0.881836
$377$	5.64639	0.290804
$378$	52.9248	2.72216
$379$	5.10438	0.262194	0.131097	−	0.991370i	$-0.458150\pi$
$379$	5.10438	0.262194	0.131097	+	0.991370i	$0.458150\pi$
$380$	−0.932701	−0.0478466
$381$	−12.4128	−0.635929
$382$	−13.9442	−0.713446
$383$	34.1072	1.74279	0.871397	−	0.490578i	$-0.163214\pi$
$383$	34.1072	1.74279	0.871397	+	0.490578i	$0.163214\pi$
$384$	−36.5852	−1.86698
$385$	−22.5838	−1.15098
$386$	−42.4032	−2.15827
$387$	3.73915	0.190071
$388$	−48.2363	−2.44883
$389$	−15.7238	−0.797227	−0.398614	−	0.917119i	$-0.630509\pi$
$389$	−15.7238	−0.797227	−0.398614	+	0.917119i	$0.630509\pi$
$390$	−30.6450	−1.55177
$391$	−0.691200	−0.0349555
$392$	−69.8995	−3.53046
$393$	−9.07234	−0.457639
$394$	9.17701	0.462331
$395$	9.22719	0.464270
$396$	−8.14325	−0.409213
$397$	−6.02151	−0.302211	−0.151106	−	0.988518i	$-0.548283\pi$
$397$	−6.02151	−0.302211	−0.151106	+	0.988518i	$0.548283\pi$
$398$	47.1488	2.36335
$399$	1.69350	0.0847812
$400$	−14.4285	−0.721427
$401$	−23.8000	−1.18851	−0.594256	−	0.804276i	$-0.702554\pi$
$401$	−23.8000	−1.18851	−0.594256	+	0.804276i	$0.702554\pi$
$402$	36.7167	1.83126
$403$	34.0627	1.69678
$404$	−17.1794	−0.854709
$405$	12.1323	0.602859
$406$	11.2935	0.560488
$407$	21.3313	1.05735
$408$	−7.23370	−0.358122
$409$	11.0277	0.545284	0.272642	−	0.962115i	$-0.412102\pi$
$409$	11.0277	0.545284	0.272642	+	0.962115i	$0.412102\pi$
$410$	−20.1834	−0.996789
$411$	21.1827	1.04486
$412$	5.24662	0.258482
$413$	−26.9639	−1.32681
$414$	−1.05653	−0.0519254
$415$	9.26767	0.454932
$416$	−0.126925	−0.00622300
$417$	21.3460	1.04532
$418$	1.99054	0.0973606
$419$	24.9125	1.21705	0.608527	−	0.793533i	$-0.291761\pi$
$419$	24.9125	1.21705	0.608527	+	0.793533i	$0.291761\pi$
$420$	−40.8705	−1.99427
$421$	0.840738	0.0409751	0.0204875	−	0.999790i	$-0.493478\pi$
$421$	0.840738	0.0409751	0.0204875	+	0.999790i	$0.493478\pi$
$422$	−46.5721	−2.26710
$423$	1.71606	0.0834375
$424$	24.8427	1.20647
$425$	2.83654	0.137593
$426$	−45.2089	−2.19038
$427$	−38.8137	−1.87833
$428$	29.8584	1.44326
$429$	43.6094	2.10548
$430$	22.0582	1.06374
$431$	19.0215	0.916232	0.458116	−	0.888892i	$-0.348524\pi$
$431$	19.0215	0.916232	0.458116	+	0.888892i	$0.348524\pi$
$432$	18.8097	0.904982
$433$	20.5699	0.988528	0.494264	−	0.869312i	$-0.335438\pi$
$433$	20.5699	0.988528	0.494264	+	0.869312i	$0.335438\pi$
$434$	68.1298	3.27034
$435$	2.21529	0.106215
$436$	−59.4079	−2.84512
$437$	0.172205	0.00823767
$438$	−50.2347	−2.40031
$439$	−37.1799	−1.77450	−0.887249	−	0.461290i	$-0.847387\pi$
$439$	−37.1799	−1.77450	−0.887249	+	0.461290i	$0.847387\pi$
$440$	−24.0333	−1.14574
$441$	7.01493	0.334044
$442$	10.9156	0.519202
$443$	21.5919	1.02586	0.512931	−	0.858430i	$-0.328560\pi$
$443$	21.5919	1.02586	0.512931	+	0.858430i	$0.328560\pi$
$444$	38.6037	1.83205
$445$	6.40401	0.303579
$446$	−25.5579	−1.21020
$447$	12.9231	0.611242
$448$	36.7504	1.73629
$449$	27.1154	1.27966	0.639828	−	0.768518i	$-0.279005\pi$
$449$	27.1154	1.27966	0.639828	+	0.768518i	$0.279005\pi$
$450$	4.33576	0.204390
$451$	28.7220	1.35247
$452$	−32.4223	−1.52502
$453$	1.92408	0.0904013
$454$	46.2967	2.17281
$455$	30.8543	1.44647
$456$	1.80220	0.0843955
$457$	−2.31295	−0.108195	−0.0540977	−	0.998536i	$-0.517228\pi$
$457$	−2.31295	−0.108195	−0.0540977	+	0.998536i	$0.517228\pi$
$458$	19.5355	0.912835
$459$	−3.69785	−0.172601
$460$	−4.15593	−0.193771
$461$	−22.1095	−1.02974	−0.514871	−	0.857267i	$-0.672160\pi$
$461$	−22.1095	−1.02974	−0.514871	+	0.857267i	$0.672160\pi$
$462$	87.2244	4.05805
$463$	32.0191	1.48805	0.744027	−	0.668150i	$-0.232914\pi$
$463$	32.0191	1.48805	0.744027	+	0.668150i	$0.232914\pi$
$464$	4.01376	0.186334
$465$	13.3641	0.619744
$466$	3.19353	0.147937
$467$	−29.2633	−1.35414	−0.677072	−	0.735916i	$-0.736752\pi$
$467$	−29.2633	−1.35414	−0.677072	+	0.735916i	$0.736752\pi$
$468$	11.1254	0.514271
$469$	−36.9675	−1.70700
$470$	10.1234	0.466960
$471$	−22.8862	−1.05454
$472$	−28.6945	−1.32077
$473$	−31.3899	−1.44331
$474$	−35.6377	−1.63690
$475$	−0.706693	−0.0324253
$476$	14.5579	0.667259
$477$	−2.49315	−0.114153
$478$	53.5432	2.44901
$479$	−31.1005	−1.42102	−0.710509	−	0.703688i	$-0.751535\pi$
$479$	−31.1005	−1.42102	−0.710509	+	0.703688i	$0.751535\pi$
$480$	−0.0497973	−0.00227293
$481$	−29.1430	−1.32881
$482$	47.3421	2.15637
$483$	7.54592	0.343351
$484$	24.3368	1.10622
$485$	14.2870	0.648737
$486$	−12.4142	−0.563121
$487$	−43.8219	−1.98576	−0.992881	−	0.119112i	$-0.961995\pi$
$487$	−43.8219	−1.98576	−0.992881	+	0.119112i	$0.961995\pi$
$488$	−41.3049	−1.86978
$489$	4.17547	0.188821
$490$	41.3828	1.86949
$491$	−37.4499	−1.69009	−0.845046	−	0.534694i	$-0.820427\pi$
$491$	−37.4499	−1.69009	−0.845046	+	0.534694i	$0.820427\pi$
$492$	51.9789	2.34339
$493$	−0.789075	−0.0355382
$494$	−2.71950	−0.122356
$495$	2.41192	0.108408
$496$	24.2136	1.08722
$497$	45.5177	2.04175
$498$	−35.7941	−1.60397
$499$	3.06901	0.137388	0.0686940	−	0.997638i	$-0.478117\pi$
$499$	3.06901	0.137388	0.0686940	+	0.997638i	$0.478117\pi$
$500$	40.7772	1.82361
$501$	17.2285	0.769712
$502$	26.1125	1.16546
$503$	−10.6541	−0.475044	−0.237522	−	0.971382i	$-0.576335\pi$
$503$	−10.6541	−0.475044	−0.237522	+	0.971382i	$0.576335\pi$
$504$	11.1325	0.495880
$505$	5.08832	0.226427
$506$	8.86946	0.394296
$507$	−35.2855	−1.56709
$508$	26.5842	1.17948
$509$	−24.1603	−1.07088	−0.535442	−	0.844572i	$-0.679855\pi$
$509$	−24.1603	−1.07088	−0.535442	+	0.844572i	$0.679855\pi$
$510$	4.28260	0.189637
$511$	50.5777	2.23743
$512$	39.2890	1.73635
$513$	0.921277	0.0406754
$514$	−1.25248	−0.0552446
$515$	−1.55398	−0.0684764
$516$	−56.8070	−2.50079
$517$	−14.4062	−0.633583
$518$	−58.2898	−2.56111
$519$	−3.92865	−0.172449
$520$	32.8345	1.43989
$521$	4.32790	0.189609	0.0948044	−	0.995496i	$-0.469777\pi$
$521$	4.32790	0.189609	0.0948044	+	0.995496i	$0.469777\pi$
$522$	−1.20613	−0.0527909
$523$	8.71981	0.381291	0.190645	−	0.981659i	$-0.438942\pi$
$523$	8.71981	0.381291	0.190645	+	0.981659i	$0.438942\pi$
$524$	19.4300	0.848802
$525$	−30.9669	−1.35151
$526$	−10.2520	−0.447008
$527$	−4.76022	−0.207358
$528$	30.9999	1.34910
$529$	−22.2327	−0.966639
$530$	−14.7077	−0.638862
$531$	2.87970	0.124968
$532$	−3.62693	−0.157247
$533$	−39.2404	−1.69969
$534$	−24.7339	−1.07034
$535$	−8.84366	−0.382345
$536$	−39.3401	−1.69923
$537$	17.7750	0.767049
$538$	39.8505	1.71808
$539$	−58.8899	−2.53657
$540$	−22.2338	−0.956790
$541$	−1.51055	−0.0649438	−0.0324719	−	0.999473i	$-0.510338\pi$
$541$	−1.51055	−0.0649438	−0.0324719	+	0.999473i	$0.510338\pi$
$542$	69.7396	2.99557
$543$	−45.2045	−1.93991
$544$	0.0177376	0.000760492 0
$545$	17.5958	0.753721
$546$	−119.167	−5.09987
$547$	−5.54975	−0.237290	−0.118645	−	0.992937i	$-0.537855\pi$
$547$	−5.54975	−0.237290	−0.118645	+	0.992937i	$0.537855\pi$
$548$	−45.3663	−1.93795
$549$	4.14525	0.176915
$550$	−36.3984	−1.55203
$551$	0.196589	0.00837498
$552$	8.03023	0.341789
$553$	35.8811	1.52582
$554$	2.44996	0.104089
$555$	−11.4339	−0.485342
$556$	−45.7162	−1.93880
$557$	8.29316	0.351392	0.175696	−	0.984444i	$-0.443782\pi$
$557$	8.29316	0.351392	0.175696	+	0.984444i	$0.443782\pi$
$558$	−7.27617	−0.308025
$559$	42.8852	1.81385
$560$	21.9329	0.926834
$561$	−6.09435	−0.257304
$562$	−39.7529	−1.67688
$563$	3.37359	0.142180	0.0710899	−	0.997470i	$-0.477352\pi$
$563$	3.37359	0.142180	0.0710899	+	0.997470i	$0.477352\pi$
$564$	−26.0712	−1.09780
$565$	9.60305	0.404003
$566$	−5.53044	−0.232462
$567$	47.1780	1.98129
$568$	48.4391	2.03246
$569$	−32.3702	−1.35703	−0.678514	−	0.734588i	$-0.737376\pi$
$569$	−32.3702	−1.35703	−0.678514	+	0.734588i	$0.737376\pi$
$570$	−1.06696	−0.0446901
$571$	17.1680	0.718460	0.359230	−	0.933249i	$-0.383039\pi$
$571$	17.1680	0.718460	0.359230	+	0.933249i	$0.383039\pi$
$572$	−93.3969	−3.90512
$573$	−10.6363	−0.444337
$574$	−78.4858	−3.27594
$575$	−3.14888	−0.131317
$576$	−3.92489	−0.163537
$577$	−1.47492	−0.0614017	−0.0307008	−	0.999529i	$-0.509774\pi$
$577$	−1.47492	−0.0614017	−0.0307008	+	0.999529i	$0.509774\pi$
$578$	40.1238	1.66893
$579$	−32.3442	−1.34418
$580$	−4.74442	−0.197001
$581$	36.0385	1.49513
$582$	−55.1798	−2.28728
$583$	20.9298	0.866824
$584$	53.8239	2.22725
$585$	−3.29519	−0.136239
$586$	14.0846	0.581829
$587$	−14.4416	−0.596070	−0.298035	−	0.954555i	$-0.596331\pi$
$587$	−14.4416	−0.596070	−0.298035	+	0.954555i	$0.596331\pi$
$588$	−106.574	−4.39505
$589$	1.18595	0.0488664
$590$	16.9881	0.699388
$591$	7.00001	0.287942
$592$	−20.7164	−0.851441
$593$	3.10964	0.127698	0.0638489	−	0.997960i	$-0.479662\pi$
$593$	3.10964	0.127698	0.0638489	+	0.997960i	$0.479662\pi$
$594$	47.4507	1.94692
$595$	−4.31184	−0.176768
$596$	−27.6770	−1.13370
$597$	35.9640	1.47191
$598$	−12.1175	−0.495523
$599$	−29.8125	−1.21811	−0.609053	−	0.793129i	$-0.708451\pi$
$599$	−29.8125	−1.21811	−0.609053	+	0.793129i	$0.708451\pi$
$600$	−32.9544	−1.34536
$601$	14.5229	0.592403	0.296201	−	0.955125i	$-0.404280\pi$
$601$	14.5229	0.592403	0.296201	+	0.955125i	$0.404280\pi$
$602$	85.7760	3.49597
$603$	3.94807	0.160778
$604$	−4.12075	−0.167671
$605$	−7.20823	−0.293056
$606$	−19.6524	−0.798323
$607$	35.4494	1.43885	0.719424	−	0.694571i	$-0.244406\pi$
$607$	35.4494	1.43885	0.719424	+	0.694571i	$0.244406\pi$
$608$	−0.00441912	−0.000179219 0
$609$	8.61443	0.349074
$610$	24.4539	0.990109
$611$	19.6819	0.796243
$612$	−1.55476	−0.0628474
$613$	−7.69752	−0.310900	−0.155450	−	0.987844i	$-0.549683\pi$
$613$	−7.69752	−0.310900	−0.155450	+	0.987844i	$0.549683\pi$
$614$	−69.5181	−2.80552
$615$	−15.3955	−0.620805
$616$	−93.4565	−3.76547
$617$	−9.84304	−0.396266	−0.198133	−	0.980175i	$-0.563488\pi$
$617$	−9.84304	−0.396266	−0.198133	+	0.980175i	$0.563488\pi$
$618$	6.00185	0.241430
$619$	30.4224	1.22278	0.611390	−	0.791329i	$-0.290611\pi$
$619$	30.4224	1.22278	0.611390	+	0.791329i	$0.290611\pi$
$620$	−28.6214	−1.14946
$621$	4.10503	0.164729
$622$	31.5745	1.26602
$623$	24.9028	0.997711
$624$	−42.3524	−1.69545
$625$	5.89619	0.235848
$626$	76.6399	3.06315
$627$	1.51834	0.0606366
$628$	49.0146	1.95590
$629$	4.07270	0.162389
$630$	−6.59081	−0.262584
$631$	19.5761	0.779310	0.389655	−	0.920961i	$-0.372594\pi$
$631$	19.5761	0.779310	0.389655	+	0.920961i	$0.372594\pi$
$632$	38.1840	1.51888
$633$	−35.5242	−1.41196
$634$	1.98771	0.0789422
$635$	−7.87388	−0.312465
$636$	37.8771	1.50193
$637$	80.4560	3.18778
$638$	10.1254	0.400868
$639$	−4.86122	−0.192307
$640$	−23.2072	−0.917345
$641$	14.4528	0.570851	0.285425	−	0.958401i	$-0.407865\pi$
$641$	14.4528	0.570851	0.285425	+	0.958401i	$0.407865\pi$
$642$	34.1564	1.34805
$643$	5.66491	0.223402	0.111701	−	0.993742i	$-0.464370\pi$
$643$	5.66491	0.223402	0.111701	+	0.993742i	$0.464370\pi$
$644$	−16.1609	−0.636828
$645$	16.8255	0.662502
$646$	0.380046	0.0149527
$647$	−9.20297	−0.361806	−0.180903	−	0.983501i	$-0.557902\pi$
$647$	−9.20297	−0.361806	−0.180903	+	0.983501i	$0.557902\pi$
$648$	50.2059	1.97228
$649$	−24.1749	−0.948948
$650$	49.7279	1.95049
$651$	51.9679	2.03678
$652$	−8.94247	−0.350214
$653$	27.4742	1.07515	0.537574	−	0.843216i	$-0.319341\pi$
$653$	27.4742	1.07515	0.537574	+	0.843216i	$0.319341\pi$
$654$	−67.9594	−2.65742
$655$	−5.75489	−0.224862
$656$	−27.8942	−1.08909
$657$	−5.40162	−0.210737
$658$	39.3663	1.53466
$659$	30.0458	1.17042	0.585210	−	0.810882i	$-0.301012\pi$
$659$	30.0458	1.17042	0.585210	+	0.810882i	$0.301012\pi$
$660$	−36.6431	−1.42633
$661$	−12.6320	−0.491328	−0.245664	−	0.969355i	$-0.579006\pi$
$661$	−12.6320	−0.491328	−0.245664	+	0.969355i	$0.579006\pi$
$662$	−11.2277	−0.436376
$663$	8.32617	0.323362
$664$	38.3515	1.48833
$665$	1.07425	0.0416575
$666$	6.22527	0.241224
$667$	0.875963	0.0339174
$668$	−36.8977	−1.42762
$669$	−19.4950	−0.753719
$670$	23.2907	0.899797
$671$	−34.7991	−1.34340
$672$	−0.193643	−0.00746995
$673$	−32.6889	−1.26007	−0.630033	−	0.776568i	$-0.716959\pi$
$673$	−32.6889	−1.26007	−0.630033	+	0.776568i	$0.716959\pi$
$674$	−21.6705	−0.834716
$675$	−16.8462	−0.648410
$676$	75.5700	2.90654
$677$	−14.3932	−0.553174	−0.276587	−	0.960989i	$-0.589203\pi$
$677$	−14.3932	−0.553174	−0.276587	+	0.960989i	$0.589203\pi$
$678$	−37.0894	−1.42441
$679$	55.5566	2.13207
$680$	−4.58858	−0.175964
$681$	35.3141	1.35324
$682$	61.0829	2.33899
$683$	12.1869	0.466321	0.233160	−	0.972438i	$-0.425093\pi$
$683$	12.1869	0.466321	0.233160	+	0.972438i	$0.425093\pi$
$684$	0.387351	0.0148107
$685$	13.4369	0.513397
$686$	81.8679	3.12573
$687$	14.9013	0.568518
$688$	30.4851	1.16224
$689$	−28.5945	−1.08936
$690$	−4.75417	−0.180988
$691$	12.6139	0.479856	0.239928	−	0.970791i	$-0.422876\pi$
$691$	12.6139	0.479856	0.239928	+	0.970791i	$0.422876\pi$
$692$	8.41388	0.319848
$693$	9.37905	0.356281
$694$	−39.1309	−1.48539
$695$	13.5405	0.513621
$696$	9.16732	0.347486
$697$	5.48379	0.207713
$698$	70.3031	2.66101
$699$	2.43595	0.0921361
$700$	66.3208	2.50669
$701$	40.9024	1.54486	0.772431	−	0.635099i	$-0.219041\pi$
$701$	40.9024	1.54486	0.772431	+	0.635099i	$0.219041\pi$
$702$	−64.8276	−2.44676
$703$	−1.01467	−0.0382689
$704$	32.9492	1.24182
$705$	7.72193	0.290825
$706$	38.1497	1.43578
$707$	19.7866	0.744151
$708$	−43.7499	−1.64422
$709$	−32.9772	−1.23848	−0.619242	−	0.785200i	$-0.712560\pi$
$709$	−32.9772	−1.23848	−0.619242	+	0.785200i	$0.712560\pi$
$710$	−28.6776	−1.07625
$711$	−3.83205	−0.143713
$712$	26.5011	0.993172
$713$	5.28438	0.197902
$714$	16.6534	0.623239
$715$	27.6629	1.03453
$716$	−38.0683	−1.42268
$717$	40.8415	1.52525
$718$	12.3445	0.460692
$719$	−21.1769	−0.789766	−0.394883	−	0.918731i	$-0.629215\pi$
$719$	−21.1769	−0.789766	−0.394883	+	0.918731i	$0.629215\pi$
$720$	−2.34240	−0.0872961
$721$	−6.04284	−0.225047
$722$	46.4545	1.72886
$723$	36.1115	1.34300
$724$	96.8131	3.59803
$725$	−3.59477	−0.133506
$726$	27.8400	1.03324
$727$	30.4974	1.13109	0.565544	−	0.824718i	$-0.308666\pi$
$727$	30.4974	1.13109	0.565544	+	0.824718i	$0.308666\pi$
$728$	127.681	4.73218
$729$	21.2344	0.786458
$730$	−31.8655	−1.17940
$731$	−5.99315	−0.221665
$732$	−62.9767	−2.32769
$733$	22.9490	0.847640	0.423820	−	0.905746i	$-0.360689\pi$
$733$	22.9490	0.847640	0.423820	+	0.905746i	$0.360689\pi$
$734$	−11.7386	−0.433280
$735$	31.5659	1.16433
$736$	−0.0196907	−0.000725809 0
$737$	−33.1438	−1.22087
$738$	8.38217	0.308552
$739$	13.8779	0.510508	0.255254	−	0.966874i	$-0.417841\pi$
$739$	13.8779	0.510508	0.255254	+	0.966874i	$0.417841\pi$
$740$	24.4876	0.900183
$741$	−2.07437	−0.0762039
$742$	−57.1928	−2.09961
$743$	29.0919	1.06728	0.533640	−	0.845712i	$-0.320824\pi$
$743$	29.0919	1.06728	0.533640	+	0.845712i	$0.320824\pi$
$744$	55.3033	2.02752
$745$	8.19756	0.300335
$746$	−58.7687	−2.15168
$747$	−3.84886	−0.140822
$748$	13.0521	0.477232
$749$	−34.3897	−1.25657
$750$	46.6469	1.70330
$751$	−2.66574	−0.0972743	−0.0486372	−	0.998817i	$-0.515488\pi$
$751$	−2.66574	−0.0972743	−0.0486372	+	0.998817i	$0.515488\pi$
$752$	13.9910	0.510198
$753$	19.9180	0.725853
$754$	−13.8334	−0.503783
$755$	1.22051	0.0444189
$756$	−86.4589	−3.14448
$757$	28.0407	1.01916	0.509579	−	0.860424i	$-0.329801\pi$
$757$	28.0407	1.01916	0.509579	+	0.860424i	$0.329801\pi$
$758$	−12.5055	−0.454220
$759$	6.76542	0.245569
$760$	1.14319	0.0414680
$761$	−14.2512	−0.516607	−0.258304	−	0.966064i	$-0.583163\pi$
$761$	−14.2512	−0.516607	−0.258304	+	0.966064i	$0.583163\pi$
$762$	30.4109	1.10167
$763$	68.4235	2.47710
$764$	22.7794	0.824131
$765$	0.460498	0.0166494
$766$	−83.5611	−3.01918
$767$	33.0280	1.19257
$768$	59.8347	2.15910
$769$	0.217443	0.00784121	0.00392061	−	0.999992i	$-0.498752\pi$
$769$	0.217443	0.00784121	0.00392061	+	0.999992i	$0.498752\pi$
$770$	55.3294	1.99393
$771$	−0.955364	−0.0344066
$772$	69.2706	2.49310
$773$	23.7696	0.854934	0.427467	−	0.904031i	$-0.359406\pi$
$773$	23.7696	0.854934	0.427467	+	0.904031i	$0.359406\pi$
$774$	−9.16075	−0.329276
$775$	−21.6860	−0.778984
$776$	59.1223	2.12237
$777$	−44.4621	−1.59507
$778$	38.5226	1.38110
$779$	−1.36622	−0.0489501
$780$	50.0622	1.79251
$781$	40.8096	1.46028
$782$	1.69341	0.0605563
$783$	4.68631	0.167475
$784$	57.1925	2.04259
$785$	−14.5175	−0.518150
$786$	22.2269	0.792806
$787$	−16.7012	−0.595334	−0.297667	−	0.954670i	$-0.596209\pi$
$787$	−16.7012	−0.595334	−0.297667	+	0.954670i	$0.596209\pi$
$788$	−14.9917	−0.534058
$789$	−7.81999	−0.278399
$790$	−22.6062	−0.804293
$791$	37.3427	1.32775
$792$	9.98102	0.354660
$793$	47.5429	1.68830
$794$	14.7525	0.523545
$795$	−11.2187	−0.397886
$796$	−77.0230	−2.73001
$797$	−17.8560	−0.632492	−0.316246	−	0.948677i	$-0.602422\pi$
$797$	−17.8560	−0.632492	−0.316246	+	0.948677i	$0.602422\pi$
$798$	−4.14901	−0.146873
$799$	−2.75052	−0.0973063
$800$	0.0808065	0.00285694
$801$	−2.65959	−0.0939718
$802$	58.3089	2.05896
$803$	45.3463	1.60024
$804$	−59.9811	−2.11537
$805$	4.78663	0.168707
$806$	−83.4522	−2.93948
$807$	30.3970	1.07003
$808$	21.0565	0.740765
$809$	19.5282	0.686575	0.343288	−	0.939230i	$-0.388459\pi$
$809$	19.5282	0.686575	0.343288	+	0.939230i	$0.388459\pi$
$810$	−29.7236	−1.04438
$811$	11.1216	0.390533	0.195266	−	0.980750i	$-0.437443\pi$
$811$	11.1216	0.390533	0.195266	+	0.980750i	$0.437443\pi$
$812$	−18.4493	−0.647442
$813$	53.1958	1.86566
$814$	−52.2607	−1.83174
$815$	2.64864	0.0927778
$816$	5.91870	0.207196
$817$	1.49313	0.0522379
$818$	−27.0174	−0.944641
$819$	−12.8138	−0.447749
$820$	32.9720	1.15143
$821$	−28.1038	−0.980828	−0.490414	−	0.871489i	$-0.663155\pi$
$821$	−28.1038	−0.980828	−0.490414	+	0.871489i	$0.663155\pi$
$822$	−51.8967	−1.81010
$823$	38.5454	1.34361	0.671804	−	0.740729i	$-0.265520\pi$
$823$	38.5454	1.34361	0.671804	+	0.740729i	$0.265520\pi$
$824$	−6.43068	−0.224023
$825$	−27.7639	−0.966614
$826$	66.0603	2.29853
$827$	29.8522	1.03806	0.519031	−	0.854755i	$-0.326293\pi$
$827$	29.8522	1.03806	0.519031	+	0.854755i	$0.326293\pi$
$828$	1.72596	0.0599812
$829$	21.7048	0.753838	0.376919	−	0.926246i	$-0.376983\pi$
$829$	21.7048	0.753838	0.376919	+	0.926246i	$0.376983\pi$
$830$	−22.7054	−0.788116
$831$	1.86877	0.0648270
$832$	−45.0155	−1.56063
$833$	−11.2436	−0.389568
$834$	−52.2969	−1.81089
$835$	10.9286	0.378200
$836$	−3.25178	−0.112465
$837$	28.2709	0.977184
$838$	−61.0345	−2.10840
$839$	14.4623	0.499295	0.249648	−	0.968337i	$-0.419685\pi$
$839$	14.4623	0.499295	0.249648	+	0.968337i	$0.419685\pi$
$840$	50.0941	1.72841
$841$	1.00000	0.0344828
$842$	−2.05977	−0.0709845
$843$	−30.3226	−1.04437
$844$	76.0811	2.61882
$845$	−22.3828	−0.769992
$846$	−4.20427	−0.144546
$847$	−28.0301	−0.963126
$848$	−20.3266	−0.698017
$849$	−4.21849	−0.144778
$850$	−6.94941	−0.238363
$851$	−4.52115	−0.154983
$852$	73.8541	2.53020
$853$	−25.9306	−0.887846	−0.443923	−	0.896065i	$-0.646414\pi$
$853$	−25.9306	−0.887846	−0.443923	+	0.896065i	$0.646414\pi$
$854$	95.0920	3.25398
$855$	−0.114728	−0.00392361
$856$	−36.5969	−1.25086
$857$	12.7285	0.434796	0.217398	−	0.976083i	$-0.430243\pi$
$857$	12.7285	0.434796	0.217398	+	0.976083i	$0.430243\pi$
$858$	−106.841	−3.64749
$859$	−21.2895	−0.726390	−0.363195	−	0.931713i	$-0.618314\pi$
$859$	−21.2895	−0.726390	−0.363195	+	0.931713i	$0.618314\pi$
$860$	−36.0346	−1.22877
$861$	−59.8672	−2.04027
$862$	−46.6018	−1.58726
$863$	5.30338	0.180529	0.0902645	−	0.995918i	$-0.471229\pi$
$863$	5.30338	0.180529	0.0902645	+	0.995918i	$0.471229\pi$
$864$	−0.105343	−0.00358385
$865$	−2.49208	−0.0847332
$866$	−50.3955	−1.71251
$867$	30.6055	1.03942
$868$	−111.298	−3.77770
$869$	32.1698	1.09129
$870$	−5.42736	−0.184005
$871$	45.2814	1.53430
$872$	72.8150	2.46583
$873$	−5.93337	−0.200814
$874$	−0.421894	−0.0142708
$875$	−46.9655	−1.58772
$876$	82.0642	2.77269
$877$	25.7881	0.870804	0.435402	−	0.900236i	$-0.356606\pi$
$877$	25.7881	0.870804	0.435402	+	0.900236i	$0.356606\pi$
$878$	91.0891	3.07411
$879$	10.7434	0.362366
$880$	19.6643	0.662883
$881$	−8.31050	−0.279988	−0.139994	−	0.990152i	$-0.544708\pi$
$881$	−8.31050	−0.279988	−0.139994	+	0.990152i	$0.544708\pi$
$882$	−17.1863	−0.578692
$883$	22.6927	0.763669	0.381835	−	0.924231i	$-0.375292\pi$
$883$	22.6927	0.763669	0.381835	+	0.924231i	$0.375292\pi$
$884$	−17.8319	−0.599752
$885$	12.9581	0.435582
$886$	−52.8992	−1.77718
$887$	−34.7840	−1.16793	−0.583966	−	0.811778i	$-0.698500\pi$
$887$	−34.7840	−1.16793	−0.583966	+	0.811778i	$0.698500\pi$
$888$	−47.3158	−1.58781
$889$	−30.6186	−1.02691
$890$	−15.6896	−0.525915
$891$	42.2982	1.41704
$892$	41.7518	1.39795
$893$	0.685260	0.0229314
$894$	−31.6611	−1.05890
$895$	11.2753	0.376892
$896$	−90.2442	−3.01485
$897$	−9.24299	−0.308614
$898$	−66.4317	−2.21685
$899$	6.03265	0.201200
$900$	−7.08297	−0.236099
$901$	3.99605	0.133128
$902$	−70.3678	−2.34299
$903$	65.4280	2.17731
$904$	39.7394	1.32171
$905$	−28.6747	−0.953180
$906$	−4.71392	−0.156609
$907$	30.3555	1.00794	0.503969	−	0.863722i	$-0.331873\pi$
$907$	30.3555	1.00794	0.503969	+	0.863722i	$0.331873\pi$
$908$	−75.6311	−2.50991
$909$	−2.11318	−0.0700897
$910$	−75.5916	−2.50584
$911$	−3.23578	−0.107206	−0.0536031	−	0.998562i	$-0.517071\pi$
$911$	−3.23578	−0.107206	−0.0536031	+	0.998562i	$0.517071\pi$
$912$	−1.47458	−0.0488281
$913$	32.3109	1.06934
$914$	5.66664	0.187436
$915$	18.6529	0.616644
$916$	−31.9136	−1.05445
$917$	−22.3786	−0.739008
$918$	9.05957	0.299010
$919$	20.2262	0.667199	0.333600	−	0.942715i	$-0.391737\pi$
$919$	20.2262	0.667199	0.333600	+	0.942715i	$0.391737\pi$
$920$	5.09384	0.167939
$921$	−53.0268	−1.74729
$922$	54.1674	1.78391
$923$	−55.7545	−1.83518
$924$	−142.491	−4.68762
$925$	18.5539	0.610048
$926$	−78.4454	−2.57788
$927$	0.645366	0.0211966
$928$	−0.0224789	−0.000737907 0
$929$	24.3864	0.800091	0.400045	−	0.916495i	$-0.368994\pi$
$929$	24.3864	0.800091	0.400045	+	0.916495i	$0.368994\pi$
$930$	−32.7414	−1.07363
$931$	2.80122	0.0918063
$932$	−5.21700	−0.170889
$933$	24.0843	0.788485
$934$	71.6939	2.34590
$935$	−3.86585	−0.126427
$936$	−13.6362	−0.445712
$937$	−59.8830	−1.95629	−0.978146	−	0.207918i	$-0.933331\pi$
$937$	−59.8830	−1.95629	−0.978146	+	0.207918i	$0.933331\pi$
$938$	90.5687	2.95717
$939$	58.4592	1.90774
$940$	−16.5378	−0.539405
$941$	22.1181	0.721029	0.360514	−	0.932754i	$-0.382601\pi$
$941$	22.1181	0.721029	0.360514	+	0.932754i	$0.382601\pi$
$942$	56.0701	1.82686
$943$	−6.08762	−0.198240
$944$	23.4781	0.764148
$945$	25.6080	0.833027
$946$	76.9039	2.50036
$947$	−18.6664	−0.606577	−0.303289	−	0.952899i	$-0.598085\pi$
$947$	−18.6664	−0.606577	−0.303289	+	0.952899i	$0.598085\pi$
$948$	58.2184	1.89085
$949$	−61.9526	−2.01107
$950$	1.73137	0.0561730
$951$	1.51618	0.0491656
$952$	−17.8433	−0.578304
$953$	−23.1429	−0.749673	−0.374836	−	0.927091i	$-0.622301\pi$
$953$	−23.1429	−0.749673	−0.374836	+	0.927091i	$0.622301\pi$
$954$	6.10811	0.197757
$955$	−6.74696	−0.218326
$956$	−87.4691	−2.82895
$957$	7.72341	0.249662
$958$	76.1949	2.46174
$959$	52.2511	1.68728
$960$	−17.6613	−0.570015
$961$	5.39291	0.173965
$962$	71.3991	2.30200
$963$	3.67277	0.118353
$964$	−77.3389	−2.49092
$965$	−20.5170	−0.660466
$966$	−18.4872	−0.594815
$967$	22.4983	0.723498	0.361749	−	0.932276i	$-0.382180\pi$
$967$	22.4983	0.723498	0.361749	+	0.932276i	$0.382180\pi$
$968$	−29.8291	−0.958745
$969$	0.289891	0.00931263
$970$	−35.0024	−1.12386
$971$	8.83307	0.283467	0.141733	−	0.989905i	$-0.454732\pi$
$971$	8.83307	0.283467	0.141733	+	0.989905i	$0.454732\pi$
$972$	20.2801	0.650485
$973$	52.6540	1.68801
$974$	107.362	3.44010
$975$	37.9313	1.21477
$976$	33.7961	1.08179
$977$	−40.0555	−1.28149	−0.640745	−	0.767754i	$-0.721374\pi$
$977$	−40.0555	−1.28149	−0.640745	+	0.767754i	$0.721374\pi$
$978$	−10.2297	−0.327110
$979$	22.3270	0.713575
$980$	−67.6037	−2.15952
$981$	−7.30753	−0.233312
$982$	91.7508	2.92788
$983$	11.8552	0.378124	0.189062	−	0.981965i	$-0.439455\pi$
$983$	11.8552	0.378124	0.189062	+	0.981965i	$0.439455\pi$
$984$	−63.7096	−2.03099
$985$	4.44035	0.141481
$986$	1.93320	0.0615657
$987$	30.0277	0.955793
$988$	4.44262	0.141339
$989$	6.65307	0.211555
$990$	−5.90910	−0.187804
$991$	−4.62981	−0.147071	−0.0735354	−	0.997293i	$-0.523428\pi$
$991$	−4.62981	−0.147071	−0.0735354	+	0.997293i	$0.523428\pi$
$992$	−0.135608	−0.00430555
$993$	−8.56421	−0.271777
$994$	−111.516	−3.53708
$995$	22.8132	0.723227
$996$	58.4738	1.85281
$997$	−52.3393	−1.65760	−0.828802	−	0.559543i	$-0.810977\pi$
$997$	−52.3393	−1.65760	−0.828802	+	0.559543i	$0.810977\pi$
$998$	−7.51895	−0.238008
$999$	−24.1877	−0.765265

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8033.2.a.d.1.15	✓	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8033.2.a.d.1.15	✓	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)

\(f(q)\)	\(=\)	\(q-2.44996 q^{2} -1.86877 q^{3} +4.00229 q^{4} -1.18542 q^{5} +4.57841 q^{6} -4.60968 q^{7} -4.90553 q^{8} +0.492307 q^{9} +O(q^{10})\)	\(q-2.44996 q^{2} -1.86877 q^{3} +4.00229 q^{4} -1.18542 q^{5} +4.57841 q^{6} -4.60968 q^{7} -4.90553 q^{8} +0.492307 q^{9} +2.90424 q^{10} -4.13288 q^{11} -7.47937 q^{12} +5.64639 q^{13} +11.2935 q^{14} +2.21529 q^{15} +4.01376 q^{16} -0.789075 q^{17} -1.20613 q^{18} +0.196589 q^{19} -4.74442 q^{20} +8.61443 q^{21} +10.1254 q^{22} +0.875963 q^{23} +9.16732 q^{24} -3.59477 q^{25} -13.8334 q^{26} +4.68631 q^{27} -18.4493 q^{28} +1.00000 q^{29} -5.42736 q^{30} +6.03265 q^{31} -0.0224789 q^{32} +7.72341 q^{33} +1.93320 q^{34} +5.46442 q^{35} +1.97036 q^{36} -5.16136 q^{37} -0.481635 q^{38} -10.5518 q^{39} +5.81514 q^{40} -6.94964 q^{41} -21.1050 q^{42} +7.59516 q^{43} -16.5410 q^{44} -0.583593 q^{45} -2.14607 q^{46} +3.48575 q^{47} -7.50080 q^{48} +14.2491 q^{49} +8.80703 q^{50} +1.47460 q^{51} +22.5985 q^{52} -5.06422 q^{53} -11.4813 q^{54} +4.89922 q^{55} +22.6129 q^{56} -0.367380 q^{57} -2.44996 q^{58} +5.84941 q^{59} +8.86623 q^{60} +8.42006 q^{61} -14.7797 q^{62} -2.26937 q^{63} -7.97245 q^{64} -6.69337 q^{65} -18.9220 q^{66} +8.01953 q^{67} -3.15811 q^{68} -1.63697 q^{69} -13.3876 q^{70} -9.87437 q^{71} -2.41503 q^{72} -10.9721 q^{73} +12.6451 q^{74} +6.71780 q^{75} +0.786808 q^{76} +19.0512 q^{77} +25.8515 q^{78} -7.78387 q^{79} -4.75801 q^{80} -10.2346 q^{81} +17.0263 q^{82} -7.81802 q^{83} +34.4775 q^{84} +0.935390 q^{85} -18.6078 q^{86} -1.86877 q^{87} +20.2740 q^{88} -5.40229 q^{89} +1.42978 q^{90} -26.0280 q^{91} +3.50586 q^{92} -11.2737 q^{93} -8.53993 q^{94} -0.233042 q^{95} +0.0420080 q^{96} -12.0522 q^{97} -34.9097 q^{98} -2.03465 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q + 12 q^{2} + 35 q^{3} + 184 q^{4} + 12 q^{5} + 10 q^{6} + 74 q^{7} + 39 q^{8} + 183 q^{9}+O(q^{10}) \) 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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