LMFDB - Embedded newform 8033.2.a.d.1.18

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			1.18
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)

$f(q)$	$=$	$q-2.40306 q^{2} +1.89974 q^{3} +3.77470 q^{4} -4.37204 q^{5} -4.56518 q^{6} -3.13994 q^{7} -4.26472 q^{8} +0.608994 q^{9} +O(q^{10})$	\(q-2.40306 q^{2} +1.89974 q^{3} +3.77470 q^{4} -4.37204 q^{5} -4.56518 q^{6} -3.13994 q^{7} -4.26472 q^{8} +0.608994 q^{9} +10.5063 q^{10} -4.79547 q^{11} +7.17094 q^{12} +4.83938 q^{13} +7.54547 q^{14} -8.30571 q^{15} +2.69898 q^{16} -3.48147 q^{17} -1.46345 q^{18} +5.61567 q^{19} -16.5031 q^{20} -5.96506 q^{21} +11.5238 q^{22} -2.60245 q^{23} -8.10184 q^{24} +14.1147 q^{25} -11.6293 q^{26} -4.54228 q^{27} -11.8524 q^{28} +1.00000 q^{29} +19.9591 q^{30} -7.37267 q^{31} +2.04363 q^{32} -9.11013 q^{33} +8.36620 q^{34} +13.7279 q^{35} +2.29877 q^{36} -9.76813 q^{37} -13.4948 q^{38} +9.19354 q^{39} +18.6455 q^{40} -7.25475 q^{41} +14.3344 q^{42} -8.89429 q^{43} -18.1015 q^{44} -2.66255 q^{45} +6.25385 q^{46} +0.153764 q^{47} +5.12735 q^{48} +2.85924 q^{49} -33.9185 q^{50} -6.61388 q^{51} +18.2672 q^{52} +1.76700 q^{53} +10.9154 q^{54} +20.9660 q^{55} +13.3910 q^{56} +10.6683 q^{57} -2.40306 q^{58} -4.05174 q^{59} -31.3516 q^{60} -7.07115 q^{61} +17.7170 q^{62} -1.91221 q^{63} -10.3089 q^{64} -21.1580 q^{65} +21.8922 q^{66} -6.57741 q^{67} -13.1415 q^{68} -4.94397 q^{69} -32.9891 q^{70} -6.48375 q^{71} -2.59719 q^{72} -7.02129 q^{73} +23.4734 q^{74} +26.8142 q^{75} +21.1975 q^{76} +15.0575 q^{77} -22.0926 q^{78} +14.9862 q^{79} -11.8000 q^{80} -10.4561 q^{81} +17.4336 q^{82} -15.8429 q^{83} -22.5163 q^{84} +15.2211 q^{85} +21.3735 q^{86} +1.89974 q^{87} +20.4514 q^{88} -5.69091 q^{89} +6.39826 q^{90} -15.1954 q^{91} -9.82349 q^{92} -14.0061 q^{93} -0.369505 q^{94} -24.5519 q^{95} +3.88236 q^{96} +14.6243 q^{97} -6.87092 q^{98} -2.92042 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.40306	−1.69922	−0.849610	−	0.527411i	$-0.823163\pi$
$2$	−2.40306	−1.69922	−0.849610	+	0.527411i	$0.823163\pi$
$3$	1.89974	1.09681	0.548406	−	0.836212i	$-0.315235\pi$
$3$	1.89974	1.09681	0.548406	+	0.836212i	$0.315235\pi$
$4$	3.77470	1.88735
$5$	−4.37204	−1.95523	−0.977617	−	0.210392i	$-0.932526\pi$
$5$	−4.37204	−1.95523	−0.977617	+	0.210392i	$0.932526\pi$
$6$	−4.56518	−1.86373
$7$	−3.13994	−1.18679	−0.593393	−	0.804913i	$-0.702212\pi$
$7$	−3.13994	−1.18679	−0.593393	+	0.804913i	$0.702212\pi$
$8$	−4.26472	−1.50781
$9$	0.608994	0.202998
$10$	10.5063	3.32237
$11$	−4.79547	−1.44589	−0.722945	−	0.690906i	$-0.757212\pi$
$11$	−4.79547	−1.44589	−0.722945	+	0.690906i	$0.757212\pi$
$12$	7.17094	2.07007
$13$	4.83938	1.34220	0.671101	−	0.741366i	$-0.265821\pi$
$13$	4.83938	1.34220	0.671101	+	0.741366i	$0.265821\pi$
$14$	7.54547	2.01661
$15$	−8.30571	−2.14453
$16$	2.69898	0.674745
$17$	−3.48147	−0.844382	−0.422191	−	0.906507i	$-0.638739\pi$
$17$	−3.48147	−0.844382	−0.422191	+	0.906507i	$0.638739\pi$
$18$	−1.46345	−0.344939
$19$	5.61567	1.28832	0.644162	−	0.764889i	$-0.277206\pi$
$19$	5.61567	1.28832	0.644162	+	0.764889i	$0.277206\pi$
$20$	−16.5031	−3.69021
$21$	−5.96506	−1.30168
$22$	11.5238	2.45689
$23$	−2.60245	−0.542649	−0.271324	−	0.962488i	$-0.587462\pi$
$23$	−2.60245	−0.542649	−0.271324	+	0.962488i	$0.587462\pi$
$24$	−8.10184	−1.65378
$25$	14.1147	2.82294
$26$	−11.6293	−2.28070
$27$	−4.54228	−0.874162
$28$	−11.8524	−2.23988
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	19.9591	3.64402
$31$	−7.37267	−1.32417	−0.662085	−	0.749429i	$-0.730328\pi$
$31$	−7.37267	−1.32417	−0.662085	+	0.749429i	$0.730328\pi$
$32$	2.04363	0.361266
$33$	−9.11013	−1.58587
$34$	8.36620	1.43479
$35$	13.7279	2.32045
$36$	2.29877	0.383129
$37$	−9.76813	−1.60587	−0.802935	−	0.596066i	$-0.796730\pi$
$37$	−9.76813	−1.60587	−0.802935	+	0.596066i	$0.796730\pi$
$38$	−13.4948	−2.18915
$39$	9.19354	1.47215
$40$	18.6455	2.94812
$41$	−7.25475	−1.13300	−0.566500	−	0.824061i	$-0.691703\pi$
$41$	−7.25475	−1.13300	−0.566500	+	0.824061i	$0.691703\pi$
$42$	14.3344	2.21185
$43$	−8.89429	−1.35637	−0.678183	−	0.734893i	$-0.737232\pi$
$43$	−8.89429	−1.35637	−0.678183	+	0.734893i	$0.737232\pi$
$44$	−18.1015	−2.72890
$45$	−2.66255	−0.396909
$46$	6.25385	0.922081
$47$	0.153764	0.0224288	0.0112144	−	0.999937i	$-0.496430\pi$
$47$	0.153764	0.0224288	0.0112144	+	0.999937i	$0.496430\pi$
$48$	5.12735	0.740069
$49$	2.85924	0.408462
$50$	−33.9185	−4.79680
$51$	−6.61388	−0.926128
$52$	18.2672	2.53321
$53$	1.76700	0.242716	0.121358	−	0.992609i	$-0.461275\pi$
$53$	1.76700	0.242716	0.121358	+	0.992609i	$0.461275\pi$
$54$	10.9154	1.48539
$55$	20.9660	2.82705
$56$	13.3910	1.78944
$57$	10.6683	1.41305
$58$	−2.40306	−0.315537
$59$	−4.05174	−0.527491	−0.263746	−	0.964592i	$-0.584958\pi$
$59$	−4.05174	−0.527491	−0.263746	+	0.964592i	$0.584958\pi$
$60$	−31.3516	−4.04747
$61$	−7.07115	−0.905369	−0.452684	−	0.891671i	$-0.649534\pi$
$61$	−7.07115	−0.905369	−0.452684	+	0.891671i	$0.649534\pi$
$62$	17.7170	2.25006
$63$	−1.91221	−0.240915
$64$	−10.3089	−1.28862
$65$	−21.1580	−2.62432
$66$	21.8922	2.69474
$67$	−6.57741	−0.803558	−0.401779	−	0.915737i	$-0.631608\pi$
$67$	−6.57741	−0.803558	−0.401779	+	0.915737i	$0.631608\pi$
$68$	−13.1415	−1.59364
$69$	−4.94397	−0.595184
$70$	−32.9891	−3.94295
$71$	−6.48375	−0.769479	−0.384740	−	0.923025i	$-0.625709\pi$
$71$	−6.48375	−0.769479	−0.384740	+	0.923025i	$0.625709\pi$
$72$	−2.59719	−0.306082
$73$	−7.02129	−0.821779	−0.410890	−	0.911685i	$-0.634782\pi$
$73$	−7.02129	−0.821779	−0.410890	+	0.911685i	$0.634782\pi$
$74$	23.4734	2.72873
$75$	26.8142	3.09624
$76$	21.1975	2.43152
$77$	15.0575	1.71596
$78$	−22.0926	−2.50150
$79$	14.9862	1.68608	0.843039	−	0.537852i	$-0.180764\pi$
$79$	14.9862	1.68608	0.843039	+	0.537852i	$0.180764\pi$
$80$	−11.8000	−1.31928
$81$	−10.4561	−1.16179
$82$	17.4336	1.92522
$83$	−15.8429	−1.73899	−0.869494	−	0.493944i	$-0.835555\pi$
$83$	−15.8429	−1.73899	−0.869494	+	0.493944i	$0.835555\pi$
$84$	−22.5163	−2.45673
$85$	15.2211	1.65096
$86$	21.3735	2.30477
$87$	1.89974	0.203673
$88$	20.4514	2.18012
$89$	−5.69091	−0.603235	−0.301617	−	0.953429i	$-0.597527\pi$
$89$	−5.69091	−0.603235	−0.301617	+	0.953429i	$0.597527\pi$
$90$	6.39826	0.674436
$91$	−15.1954	−1.59291
$92$	−9.82349	−1.02417
$93$	−14.0061	−1.45237
$94$	−0.369505	−0.0381115
$95$	−24.5519	−2.51898
$96$	3.88236	0.396241
$97$	14.6243	1.48487	0.742437	−	0.669915i	$-0.233670\pi$
$97$	14.6243	1.48487	0.742437	+	0.669915i	$0.233670\pi$
$98$	−6.87092	−0.694068
$99$	−2.92042	−0.293513
$100$	53.2788	5.32788
$101$	−6.44425	−0.641227	−0.320613	−	0.947210i	$-0.603889\pi$
$101$	−6.44425	−0.641227	−0.320613	+	0.947210i	$0.603889\pi$
$102$	15.8936	1.57370
$103$	11.6413	1.14705	0.573524	−	0.819189i	$-0.305576\pi$
$103$	11.6413	1.14705	0.573524	+	0.819189i	$0.305576\pi$
$104$	−20.6386	−2.02378
$105$	26.0795	2.54509
$106$	−4.24621	−0.412428
$107$	−6.70584	−0.648278	−0.324139	−	0.946009i	$-0.605075\pi$
$107$	−6.70584	−0.648278	−0.324139	+	0.946009i	$0.605075\pi$
$108$	−17.1458	−1.64985
$109$	−3.16747	−0.303388	−0.151694	−	0.988427i	$-0.548473\pi$
$109$	−3.16747	−0.303388	−0.151694	+	0.988427i	$0.548473\pi$
$110$	−50.3825	−4.80379
$111$	−18.5569	−1.76134
$112$	−8.47464	−0.800778
$113$	17.1970	1.61776	0.808881	−	0.587973i	$-0.200074\pi$
$113$	17.1970	1.61776	0.808881	+	0.587973i	$0.200074\pi$
$114$	−25.6366	−2.40108
$115$	11.3780	1.06101
$116$	3.77470	0.350472
$117$	2.94716	0.272465
$118$	9.73658	0.896325
$119$	10.9316	1.00210
$120$	35.4215	3.23353
$121$	11.9966	1.09060
$122$	16.9924	1.53842
$123$	−13.7821	−1.24269
$124$	−27.8296	−2.49917
$125$	−39.8498	−3.56428
$126$	4.59515	0.409369
$127$	−16.8794	−1.49781	−0.748903	−	0.662679i	$-0.769419\pi$
$127$	−16.8794	−1.49781	−0.748903	+	0.662679i	$0.769419\pi$
$128$	20.6857	1.82838
$129$	−16.8968	−1.48768
$130$	50.8439	4.45930
$131$	−7.69906	−0.672670	−0.336335	−	0.941742i	$-0.609187\pi$
$131$	−7.69906	−0.672670	−0.336335	+	0.941742i	$0.609187\pi$
$132$	−34.3880	−2.99309
$133$	−17.6329	−1.52897
$134$	15.8059	1.36542
$135$	19.8590	1.70919
$136$	14.8475	1.27316
$137$	−5.93571	−0.507122	−0.253561	−	0.967319i	$-0.581602\pi$
$137$	−5.93571	−0.507122	−0.253561	+	0.967319i	$0.581602\pi$
$138$	11.8807	1.01135
$139$	−18.8548	−1.59924	−0.799622	−	0.600504i	$-0.794967\pi$
$139$	−18.8548	−1.59924	−0.799622	+	0.600504i	$0.794967\pi$
$140$	51.8189	4.37950
$141$	0.292111	0.0246002
$142$	15.5808	1.30752
$143$	−23.2071	−1.94068
$144$	1.64366	0.136972
$145$	−4.37204	−0.363078
$146$	16.8726	1.39638
$147$	5.43179	0.448007
$148$	−36.8718	−3.03084
$149$	−0.491006	−0.0402248	−0.0201124	−	0.999798i	$-0.506402\pi$
$149$	−0.491006	−0.0402248	−0.0201124	+	0.999798i	$0.506402\pi$
$150$	−64.4362	−5.26119
$151$	6.78525	0.552175	0.276088	−	0.961132i	$-0.410962\pi$
$151$	6.78525	0.552175	0.276088	+	0.961132i	$0.410962\pi$
$152$	−23.9493	−1.94254
$153$	−2.12020	−0.171408
$154$	−36.1841	−2.91580
$155$	32.2336	2.58906
$156$	34.7029	2.77846
$157$	−0.648336	−0.0517428	−0.0258714	−	0.999665i	$-0.508236\pi$
$157$	−0.648336	−0.0517428	−0.0258714	+	0.999665i	$0.508236\pi$
$158$	−36.0127	−2.86502
$159$	3.35683	0.266214
$160$	−8.93482	−0.706360
$161$	8.17155	0.644009
$162$	25.1267	1.97414
$163$	5.78001	0.452725	0.226363	−	0.974043i	$-0.427317\pi$
$163$	5.78001	0.452725	0.226363	+	0.974043i	$0.427317\pi$
$164$	−27.3845	−2.13837
$165$	39.8298	3.10075
$166$	38.0715	2.95492
$167$	−4.20187	−0.325150	−0.162575	−	0.986696i	$-0.551980\pi$
$167$	−4.20187	−0.325150	−0.162575	+	0.986696i	$0.551980\pi$
$168$	25.4393	1.96269
$169$	10.4196	0.801509
$170$	−36.5773	−2.80535
$171$	3.41991	0.261527
$172$	−33.5733	−2.55994
$173$	3.84086	0.292015	0.146007	−	0.989283i	$-0.453358\pi$
$173$	3.84086	0.292015	0.146007	+	0.989283i	$0.453358\pi$
$174$	−4.56518	−0.346085
$175$	−44.3194	−3.35023
$176$	−12.9429	−0.975606
$177$	−7.69723	−0.578559
$178$	13.6756	1.02503
$179$	−17.8569	−1.33469	−0.667343	−	0.744750i	$-0.732569\pi$
$179$	−17.8569	−1.33469	−0.667343	+	0.744750i	$0.732569\pi$
$180$	−10.0503	−0.749107
$181$	−9.33835	−0.694114	−0.347057	−	0.937844i	$-0.612819\pi$
$181$	−9.33835	−0.694114	−0.347057	+	0.937844i	$0.612819\pi$
$182$	36.5154	2.70670
$183$	−13.4333	−0.993020
$184$	11.0987	0.818210
$185$	42.7066	3.13985
$186$	33.6575	2.46789
$187$	16.6953	1.22088
$188$	0.580414	0.0423311
$189$	14.2625	1.03744
$190$	58.9998	4.28030
$191$	−6.73304	−0.487186	−0.243593	−	0.969878i	$-0.578326\pi$
$191$	−6.73304	−0.487186	−0.243593	+	0.969878i	$0.578326\pi$
$192$	−19.5842	−1.41337
$193$	−27.2580	−1.96208	−0.981039	−	0.193813i	$-0.937915\pi$
$193$	−27.2580	−1.96208	−0.981039	+	0.193813i	$0.937915\pi$
$194$	−35.1431	−2.52313
$195$	−40.1945	−2.87839
$196$	10.7928	0.770912
$197$	−21.3173	−1.51879	−0.759396	−	0.650629i	$-0.774505\pi$
$197$	−21.3173	−1.51879	−0.759396	+	0.650629i	$0.774505\pi$
$198$	7.01794	0.498743
$199$	−4.77636	−0.338587	−0.169293	−	0.985566i	$-0.554149\pi$
$199$	−4.77636	−0.338587	−0.169293	+	0.985566i	$0.554149\pi$
$200$	−60.1953	−4.25645
$201$	−12.4953	−0.881353
$202$	15.4859	1.08959
$203$	−3.13994	−0.220381
$204$	−24.9654	−1.74793
$205$	31.7180	2.21528
$206$	−27.9747	−1.94909
$207$	−1.58488	−0.110157
$208$	13.0614	0.905645
$209$	−26.9298	−1.86277
$210$	−62.6705	−4.32468
$211$	−14.9882	−1.03183	−0.515914	−	0.856641i	$-0.672547\pi$
$211$	−14.9882	−1.03183	−0.515914	+	0.856641i	$0.672547\pi$
$212$	6.66990	0.458091
$213$	−12.3174	−0.843974
$214$	16.1145	1.10157
$215$	38.8862	2.65201
$216$	19.3715	1.31807
$217$	23.1497	1.57151
$218$	7.61162	0.515524
$219$	−13.3386	−0.901338
$220$	79.1404	5.33564
$221$	−16.8482	−1.13333
$222$	44.5933	2.99290
$223$	−7.63520	−0.511291	−0.255645	−	0.966771i	$-0.582288\pi$
$223$	−7.63520	−0.511291	−0.255645	+	0.966771i	$0.582288\pi$
$224$	−6.41688	−0.428746
$225$	8.59578	0.573052
$226$	−41.3255	−2.74893
$227$	20.4981	1.36050	0.680252	−	0.732978i	$-0.261870\pi$
$227$	20.4981	1.36050	0.680252	+	0.732978i	$0.261870\pi$
$228$	40.2697	2.66692
$229$	−2.57449	−0.170127	−0.0850636	−	0.996376i	$-0.527109\pi$
$229$	−2.57449	−0.170127	−0.0850636	+	0.996376i	$0.527109\pi$
$230$	−27.3421	−1.80288
$231$	28.6053	1.88209
$232$	−4.26472	−0.279993
$233$	−12.1178	−0.793862	−0.396931	−	0.917849i	$-0.629925\pi$
$233$	−12.1178	−0.793862	−0.396931	+	0.917849i	$0.629925\pi$
$234$	−7.08220	−0.462978
$235$	−0.672263	−0.0438536
$236$	−15.2941	−0.995562
$237$	28.4698	1.84931
$238$	−26.2694	−1.70279
$239$	−12.5985	−0.814929	−0.407465	−	0.913221i	$-0.633587\pi$
$239$	−12.5985	−0.814929	−0.407465	+	0.913221i	$0.633587\pi$
$240$	−22.4169	−1.44701
$241$	7.74955	0.499192	0.249596	−	0.968350i	$-0.419702\pi$
$241$	7.74955	0.499192	0.249596	+	0.968350i	$0.419702\pi$
$242$	−28.8284	−1.85316
$243$	−6.23701	−0.400104
$244$	−26.6915	−1.70875
$245$	−12.5007	−0.798640
$246$	33.1192	2.11160
$247$	27.1764	1.72919
$248$	31.4424	1.99659
$249$	−30.0974	−1.90734
$250$	95.7616	6.05649
$251$	27.9715	1.76554	0.882772	−	0.469801i	$-0.155674\pi$
$251$	27.9715	1.76554	0.882772	+	0.469801i	$0.155674\pi$
$252$	−7.21802	−0.454692
$253$	12.4800	0.784610
$254$	40.5623	2.54510
$255$	28.9161	1.81080
$256$	−29.0912	−1.81820
$257$	16.6107	1.03615	0.518073	−	0.855337i	$-0.326650\pi$
$257$	16.6107	1.03615	0.518073	+	0.855337i	$0.326650\pi$
$258$	40.6040	2.52790
$259$	30.6714	1.90583
$260$	−79.8650	−4.95302
$261$	0.608994	0.0376958
$262$	18.5013	1.14301
$263$	32.2131	1.98634	0.993171	−	0.116667i	$-0.0372210\pi$
$263$	32.2131	1.98634	0.993171	+	0.116667i	$0.0372210\pi$
$264$	38.8522	2.39118
$265$	−7.72539	−0.474567
$266$	42.3729	2.59805
$267$	−10.8112	−0.661636
$268$	−24.8278	−1.51660
$269$	9.48746	0.578461	0.289230	−	0.957260i	$-0.406601\pi$
$269$	9.48746	0.578461	0.289230	+	0.957260i	$0.406601\pi$
$270$	−47.7224	−2.90429
$271$	18.3389	1.11401	0.557004	−	0.830510i	$-0.311951\pi$
$271$	18.3389	1.11401	0.557004	+	0.830510i	$0.311951\pi$
$272$	−9.39643	−0.569742
$273$	−28.8672	−1.74712
$274$	14.2639	0.861712
$275$	−67.6867	−4.08166
$276$	−18.6620	−1.12332
$277$	−1.00000	−0.0600842
$277$	−1.00000	−0.0600842
$278$	45.3092	2.71747
$279$	−4.48991	−0.268804
$280$	−58.5458	−3.49878
$281$	23.8333	1.42178	0.710889	−	0.703305i	$-0.248293\pi$
$281$	23.8333	1.42178	0.710889	+	0.703305i	$0.248293\pi$
$282$	−0.701961	−0.0418012
$283$	24.6304	1.46413	0.732064	−	0.681236i	$-0.238557\pi$
$283$	24.6304	1.46413	0.732064	+	0.681236i	$0.238557\pi$
$284$	−24.4742	−1.45228
$285$	−46.6422	−2.76284
$286$	55.7681	3.29764
$287$	22.7795	1.34463
$288$	1.24456	0.0733363
$289$	−4.87934	−0.287020
$290$	10.5063	0.616950
$291$	27.7823	1.62863
$292$	−26.5033	−1.55099
$293$	−20.7641	−1.21305	−0.606526	−	0.795064i	$-0.707437\pi$
$293$	−20.7641	−1.21305	−0.606526	+	0.795064i	$0.707437\pi$
$294$	−13.0529	−0.761262
$295$	17.7144	1.03137
$296$	41.6583	2.42134
$297$	21.7824	1.26394
$298$	1.17992	0.0683508
$299$	−12.5943	−0.728345
$300$	101.216	5.84369
$301$	27.9276	1.60972
$302$	−16.3054	−0.938268
$303$	−12.2424	−0.703306
$304$	15.1566	0.869290
$305$	30.9153	1.77021
$306$	5.09497	0.291260
$307$	−4.21639	−0.240642	−0.120321	−	0.992735i	$-0.538392\pi$
$307$	−4.21639	−0.240642	−0.120321	+	0.992735i	$0.538392\pi$
$308$	56.8376	3.23862
$309$	22.1153	1.25810
$310$	−77.4592	−4.39939
$311$	28.2716	1.60313	0.801567	−	0.597905i	$-0.204000\pi$
$311$	28.2716	1.60313	0.801567	+	0.597905i	$0.204000\pi$
$312$	−39.2079	−2.21971
$313$	−8.55254	−0.483418	−0.241709	−	0.970349i	$-0.577708\pi$
$313$	−8.55254	−0.483418	−0.241709	+	0.970349i	$0.577708\pi$
$314$	1.55799	0.0879225
$315$	8.36024	0.471046
$316$	56.5684	3.18222
$317$	−15.6972	−0.881642	−0.440821	−	0.897595i	$-0.645313\pi$
$317$	−15.6972	−0.881642	−0.440821	+	0.897595i	$0.645313\pi$
$318$	−8.06668	−0.452357
$319$	−4.79547	−0.268495
$320$	45.0710	2.51955
$321$	−12.7393	−0.711040
$322$	−19.6367	−1.09431
$323$	−19.5508	−1.08784
$324$	−39.4687	−2.19271
$325$	68.3064	3.78896
$326$	−13.8897	−0.769280
$327$	−6.01735	−0.332760
$328$	30.9395	1.70835
$329$	−0.482811	−0.0266182
$330$	−95.7135	−5.26885
$331$	10.8335	0.595462	0.297731	−	0.954650i	$-0.403770\pi$
$331$	10.8335	0.595462	0.297731	+	0.954650i	$0.403770\pi$
$332$	−59.8024	−3.28208
$333$	−5.94874	−0.325989
$334$	10.0974	0.552503
$335$	28.7567	1.57114
$336$	−16.0996	−0.878304
$337$	−12.1201	−0.660225	−0.330113	−	0.943942i	$-0.607087\pi$
$337$	−12.1201	−0.660225	−0.330113	+	0.943942i	$0.607087\pi$
$338$	−25.0390	−1.36194
$339$	32.6698	1.77438
$340$	57.4553	3.11595
$341$	35.3554	1.91460
$342$	−8.21826	−0.444393
$343$	13.0018	0.702029
$344$	37.9317	2.04514
$345$	21.6152	1.16372
$346$	−9.22981	−0.496198
$347$	−9.67364	−0.519308	−0.259654	−	0.965702i	$-0.583609\pi$
$347$	−9.67364	−0.519308	−0.259654	+	0.965702i	$0.583609\pi$
$348$	7.17094	0.384403
$349$	−18.6726	−0.999522	−0.499761	−	0.866163i	$-0.666579\pi$
$349$	−18.6726	−0.999522	−0.499761	+	0.866163i	$0.666579\pi$
$350$	106.502	5.69278
$351$	−21.9818	−1.17330
$352$	−9.80017	−0.522351
$353$	18.5398	0.986776	0.493388	−	0.869809i	$-0.335758\pi$
$353$	18.5398	0.986776	0.493388	+	0.869809i	$0.335758\pi$
$354$	18.4969	0.983100
$355$	28.3472	1.50451
$356$	−21.4815	−1.13852
$357$	20.7672	1.09912
$358$	42.9112	2.26793
$359$	23.0331	1.21564	0.607819	−	0.794075i	$-0.292045\pi$
$359$	23.0331	1.21564	0.607819	+	0.794075i	$0.292045\pi$
$360$	11.3550	0.598462
$361$	12.5358	0.659779
$362$	22.4406	1.17945
$363$	22.7903	1.19618
$364$	−57.3580	−3.00638
$365$	30.6973	1.60677
$366$	32.2811	1.68736
$367$	1.01863	0.0531722	0.0265861	−	0.999647i	$-0.491536\pi$
$367$	1.01863	0.0531722	0.0265861	+	0.999647i	$0.491536\pi$
$368$	−7.02397	−0.366150
$369$	−4.41810	−0.229997
$370$	−102.627	−5.33530
$371$	−5.54828	−0.288052
$372$	−52.8689	−2.74113
$373$	26.7852	1.38688	0.693442	−	0.720512i	$-0.256093\pi$
$373$	26.7852	1.38688	0.693442	+	0.720512i	$0.256093\pi$
$374$	−40.1199	−2.07455
$375$	−75.7041	−3.90934
$376$	−0.655762	−0.0338183
$377$	4.83938	0.249241
$378$	−34.2736	−1.76285
$379$	14.3644	0.737848	0.368924	−	0.929459i	$-0.379726\pi$
$379$	14.3644	0.737848	0.368924	+	0.929459i	$0.379726\pi$
$380$	−92.6763	−4.75419
$381$	−32.0664	−1.64281
$382$	16.1799	0.827836
$383$	−33.7866	−1.72641	−0.863206	−	0.504852i	$-0.831547\pi$
$383$	−33.7866	−1.72641	−0.863206	+	0.504852i	$0.831547\pi$
$384$	39.2974	2.00539
$385$	−65.8320	−3.35511
$386$	65.5028	3.33400
$387$	−5.41657	−0.275340
$388$	55.2025	2.80248
$389$	24.5706	1.24578	0.622891	−	0.782309i	$-0.285958\pi$
$389$	24.5706	1.24578	0.622891	+	0.782309i	$0.285958\pi$
$390$	96.5899	4.89102
$391$	9.06037	0.458203
$392$	−12.1938	−0.615882
$393$	−14.6262	−0.737793
$394$	51.2267	2.58076
$395$	−65.5202	−3.29668
$396$	−11.0237	−0.553962
$397$	31.5557	1.58374	0.791868	−	0.610693i	$-0.209109\pi$
$397$	31.5557	1.58374	0.791868	+	0.610693i	$0.209109\pi$
$398$	11.4779	0.575334
$399$	−33.4978	−1.67699
$400$	38.0953	1.90476
$401$	−16.1441	−0.806199	−0.403099	−	0.915156i	$-0.632067\pi$
$401$	−16.1441	−0.806199	−0.403099	+	0.915156i	$0.632067\pi$
$402$	30.0271	1.49761
$403$	−35.6791	−1.77730
$404$	−24.3251	−1.21022
$405$	45.7145	2.27157
$406$	7.54547	0.374476
$407$	46.8428	2.32191
$408$	28.2064	1.39642
$409$	−35.5346	−1.75708	−0.878538	−	0.477673i	$-0.841480\pi$
$409$	−35.5346	−1.75708	−0.878538	+	0.477673i	$0.841480\pi$
$410$	−76.2203	−3.76425
$411$	−11.2763	−0.556218
$412$	43.9423	2.16488
$413$	12.7222	0.626020
$414$	3.80856	0.187181
$415$	69.2659	3.40013
$416$	9.88990	0.484892
$417$	−35.8191	−1.75407
$418$	64.7140	3.16526
$419$	−32.2167	−1.57389	−0.786944	−	0.617024i	$-0.788338\pi$
$419$	−32.2167	−1.57389	−0.786944	+	0.617024i	$0.788338\pi$
$420$	98.4422	4.80349
$421$	−11.6252	−0.566580	−0.283290	−	0.959034i	$-0.591426\pi$
$421$	−11.6252	−0.566580	−0.283290	+	0.959034i	$0.591426\pi$
$422$	36.0175	1.75330
$423$	0.0936416	0.00455301
$424$	−7.53576	−0.365969
$425$	−49.1400	−2.38364
$426$	29.5995	1.43410
$427$	22.2030	1.07448
$428$	−25.3126	−1.22353
$429$	−44.0874	−2.12856
$430$	−93.4458	−4.50636
$431$	−7.34526	−0.353809	−0.176904	−	0.984228i	$-0.556608\pi$
$431$	−7.34526	−0.353809	−0.176904	+	0.984228i	$0.556608\pi$
$432$	−12.2595	−0.589836
$433$	−21.7693	−1.04617	−0.523084	−	0.852281i	$-0.675219\pi$
$433$	−21.7693	−1.04617	−0.523084	+	0.852281i	$0.675219\pi$
$434$	−55.6302	−2.67034
$435$	−8.30571	−0.398228
$436$	−11.9562	−0.572600
$437$	−14.6145	−0.699108
$438$	32.0534	1.53157
$439$	1.59090	0.0759296	0.0379648	−	0.999279i	$-0.487913\pi$
$439$	1.59090	0.0759296	0.0379648	+	0.999279i	$0.487913\pi$
$440$	−89.4141	−4.26265
$441$	1.74126	0.0829171
$442$	40.4872	1.92578
$443$	−14.7982	−0.703082	−0.351541	−	0.936173i	$-0.614342\pi$
$443$	−14.7982	−0.703082	−0.351541	+	0.936173i	$0.614342\pi$
$444$	−70.0466	−3.32427
$445$	24.8809	1.17947
$446$	18.3478	0.868796
$447$	−0.932782	−0.0441191
$448$	32.3694	1.52931
$449$	28.4444	1.34237	0.671186	−	0.741289i	$-0.265785\pi$
$449$	28.4444	1.34237	0.671186	+	0.741289i	$0.265785\pi$
$450$	−20.6562	−0.973742
$451$	34.7899	1.63819
$452$	64.9137	3.05329
$453$	12.8902	0.605633
$454$	−49.2581	−2.31180
$455$	66.4347	3.11451
$456$	−45.4973	−2.13061
$457$	5.99015	0.280208	0.140104	−	0.990137i	$-0.455256\pi$
$457$	5.99015	0.280208	0.140104	+	0.990137i	$0.455256\pi$
$458$	6.18666	0.289084
$459$	15.8138	0.738126
$460$	42.9487	2.00249
$461$	−16.8763	−0.786008	−0.393004	−	0.919537i	$-0.628564\pi$
$461$	−16.8763	−0.786008	−0.393004	+	0.919537i	$0.628564\pi$
$462$	−68.7402	−3.19808
$463$	7.07571	0.328836	0.164418	−	0.986391i	$-0.447425\pi$
$463$	7.07571	0.328836	0.164418	+	0.986391i	$0.447425\pi$
$464$	2.69898	0.125297
$465$	61.2352	2.83972
$466$	29.1197	1.34895
$467$	30.3809	1.40586	0.702929	−	0.711260i	$-0.251875\pi$
$467$	30.3809	1.40586	0.702929	+	0.711260i	$0.251875\pi$
$468$	11.1246	0.514237
$469$	20.6527	0.953652
$470$	1.61549	0.0745169
$471$	−1.23167	−0.0567522
$472$	17.2795	0.795355
$473$	42.6523	1.96116
$474$	−68.4147	−3.14239
$475$	79.2636	3.63686
$476$	41.2637	1.89132
$477$	1.07609	0.0492709
$478$	30.2750	1.38474
$479$	39.3056	1.79592	0.897959	−	0.440078i	$-0.145049\pi$
$479$	39.3056	1.79592	0.897959	+	0.440078i	$0.145049\pi$
$480$	−16.9738	−0.774744
$481$	−47.2717	−2.15540
$482$	−18.6226	−0.848238
$483$	15.5238	0.706357
$484$	45.2834	2.05834
$485$	−63.9381	−2.90328
$486$	14.9879	0.679865
$487$	28.9191	1.31045	0.655226	−	0.755433i	$-0.272574\pi$
$487$	28.9191	1.31045	0.655226	+	0.755433i	$0.272574\pi$
$488$	30.1565	1.36512
$489$	10.9805	0.496555
$490$	30.0399	1.35707
$491$	11.1180	0.501747	0.250874	−	0.968020i	$-0.419282\pi$
$491$	11.1180	0.501747	0.250874	+	0.968020i	$0.419282\pi$
$492$	−52.0233	−2.34539
$493$	−3.48147	−0.156798
$494$	−65.3065	−2.93828
$495$	12.7682	0.573886
$496$	−19.8987	−0.893477
$497$	20.3586	0.913207
$498$	72.3259	3.24100
$499$	11.2519	0.503705	0.251853	−	0.967766i	$-0.418960\pi$
$499$	11.2519	0.503705	0.251853	+	0.967766i	$0.418960\pi$
$500$	−150.421	−6.72704
$501$	−7.98244	−0.356629
$502$	−67.2172	−3.00005
$503$	15.7754	0.703390	0.351695	−	0.936115i	$-0.385605\pi$
$503$	15.7754	0.703390	0.351695	+	0.936115i	$0.385605\pi$
$504$	8.15503	0.363254
$505$	28.1745	1.25375
$506$	−29.9902	−1.33323
$507$	19.7945	0.879105
$508$	−63.7148	−2.82689
$509$	−20.3183	−0.900595	−0.450297	−	0.892879i	$-0.648682\pi$
$509$	−20.3183	−0.900595	−0.450297	+	0.892879i	$0.648682\pi$
$510$	−69.4872	−3.07695
$511$	22.0464	0.975277
$512$	28.5365	1.26115
$513$	−25.5080	−1.12620
$514$	−39.9165	−1.76064
$515$	−50.8960	−2.24275
$516$	−63.7804	−2.80778
$517$	−0.737372	−0.0324296
$518$	−73.7052	−3.23842
$519$	7.29661	0.320286
$520$	90.2328	3.95697
$521$	−17.1489	−0.751308	−0.375654	−	0.926760i	$-0.622582\pi$
$521$	−17.1489	−0.751308	−0.375654	+	0.926760i	$0.622582\pi$
$522$	−1.46345	−0.0640535
$523$	−17.5127	−0.765776	−0.382888	−	0.923795i	$-0.625070\pi$
$523$	−17.5127	−0.765776	−0.382888	+	0.923795i	$0.625070\pi$
$524$	−29.0617	−1.26956
$525$	−84.1950	−3.67457
$526$	−77.4099	−3.37523
$527$	25.6677	1.11810
$528$	−24.5880	−1.07006
$529$	−16.2272	−0.705532
$530$	18.5646	0.806394
$531$	−2.46749	−0.107080
$532$	−66.5589	−2.88570
$533$	−35.1085	−1.52072
$534$	25.9800	1.12427
$535$	29.3182	1.26754
$536$	28.0508	1.21161
$537$	−33.9234	−1.46390
$538$	−22.7989	−0.982932
$539$	−13.7114	−0.590591
$540$	74.9619	3.22584
$541$	−12.3038	−0.528980	−0.264490	−	0.964388i	$-0.585204\pi$
$541$	−12.3038	−0.528980	−0.264490	+	0.964388i	$0.585204\pi$
$542$	−44.0695	−1.89295
$543$	−17.7404	−0.761313
$544$	−7.11484	−0.305046
$545$	13.8483	0.593195
$546$	69.3696	2.96875
$547$	−2.79321	−0.119429	−0.0597144	−	0.998216i	$-0.519019\pi$
$547$	−2.79321	−0.119429	−0.0597144	+	0.998216i	$0.519019\pi$
$548$	−22.4055	−0.957118
$549$	−4.30629	−0.183788
$550$	162.655	6.93564
$551$	5.61567	0.239236
$552$	21.0847	0.897423
$553$	−47.0558	−2.00102
$554$	2.40306	0.102096
$555$	81.1313	3.44383
$556$	−71.1713	−3.01834
$557$	18.2340	0.772598	0.386299	−	0.922374i	$-0.373753\pi$
$557$	18.2340	0.772598	0.386299	+	0.922374i	$0.373753\pi$
$558$	10.7895	0.456757
$559$	−43.0429	−1.82052
$560$	37.0514	1.56571
$561$	31.7167	1.33908
$562$	−57.2729	−2.41591
$563$	−40.8975	−1.72362	−0.861811	−	0.507229i	$-0.830670\pi$
$563$	−40.8975	−1.72362	−0.861811	+	0.507229i	$0.830670\pi$
$564$	1.10263	0.0464293
$565$	−75.1861	−3.16310
$566$	−59.1884	−2.48788
$567$	32.8316	1.37880
$568$	27.6514	1.16023
$569$	8.48401	0.355668	0.177834	−	0.984060i	$-0.443091\pi$
$569$	8.48401	0.355668	0.177834	+	0.984060i	$0.443091\pi$
$570$	112.084	4.69468
$571$	39.3581	1.64708	0.823542	−	0.567255i	$-0.191995\pi$
$571$	39.3581	1.64708	0.823542	+	0.567255i	$0.191995\pi$
$572$	−87.6000	−3.66274
$573$	−12.7910	−0.534351
$574$	−54.7405	−2.28482
$575$	−36.7329	−1.53187
$576$	−6.27808	−0.261587
$577$	−30.3600	−1.26390	−0.631951	−	0.775008i	$-0.717746\pi$
$577$	−30.3600	−1.26390	−0.631951	+	0.775008i	$0.717746\pi$
$578$	11.7253	0.487710
$579$	−51.7831	−2.15203
$580$	−16.5031	−0.685256
$581$	49.7459	2.06381
$582$	−66.7627	−2.76740
$583$	−8.47360	−0.350941
$584$	29.9438	1.23908
$585$	−12.8851	−0.532732
$586$	49.8974	2.06124
$587$	−14.0648	−0.580516	−0.290258	−	0.956948i	$-0.593741\pi$
$587$	−14.0648	−0.580516	−0.290258	+	0.956948i	$0.593741\pi$
$588$	20.5034	0.845546
$589$	−41.4025	−1.70596
$590$	−42.5687	−1.75252
$591$	−40.4971	−1.66583
$592$	−26.3640	−1.08355
$593$	29.5543	1.21365	0.606824	−	0.794836i	$-0.292443\pi$
$593$	29.5543	1.21365	0.606824	+	0.794836i	$0.292443\pi$
$594$	−52.3444	−2.14772
$595$	−47.7935	−1.95934
$596$	−1.85340	−0.0759184
$597$	−9.07381	−0.371366
$598$	30.2648	1.23762
$599$	−27.2320	−1.11267	−0.556335	−	0.830958i	$-0.687793\pi$
$599$	−27.2320	−1.11267	−0.556335	+	0.830958i	$0.687793\pi$
$600$	−114.355	−4.66853
$601$	−9.33212	−0.380665	−0.190333	−	0.981720i	$-0.560957\pi$
$601$	−9.33212	−0.380665	−0.190333	+	0.981720i	$0.560957\pi$
$602$	−67.1116	−2.73527
$603$	−4.00561	−0.163121
$604$	25.6123	1.04215
$605$	−52.4494	−2.13237
$606$	29.4192	1.19507
$607$	20.2937	0.823696	0.411848	−	0.911253i	$-0.364884\pi$
$607$	20.2937	0.823696	0.411848	+	0.911253i	$0.364884\pi$
$608$	11.4764	0.465428
$609$	−5.96506	−0.241716
$610$	−74.2915	−3.00797
$611$	0.744124	0.0301040
$612$	−8.00312	−0.323507
$613$	0.716617	0.0289439	0.0144719	−	0.999895i	$-0.495393\pi$
$613$	0.716617	0.0289439	0.0144719	+	0.999895i	$0.495393\pi$
$614$	10.1322	0.408904
$615$	60.2558	2.42975
$616$	−64.2161	−2.58734
$617$	3.01553	0.121401	0.0607003	−	0.998156i	$-0.480667\pi$
$617$	3.01553	0.121401	0.0607003	+	0.998156i	$0.480667\pi$
$618$	−53.1444	−2.13778
$619$	39.5385	1.58919	0.794594	−	0.607141i	$-0.207684\pi$
$619$	39.5385	1.58919	0.794594	+	0.607141i	$0.207684\pi$
$620$	121.672	4.88647
$621$	11.8211	0.474363
$622$	−67.9383	−2.72408
$623$	17.8691	0.715911
$624$	24.8132	0.993322
$625$	103.651	4.14605
$626$	20.5523	0.821434
$627$	−51.1595	−2.04311
$628$	−2.44728	−0.0976569
$629$	34.0075	1.35597
$630$	−20.0902	−0.800412
$631$	−0.478687	−0.0190562	−0.00952812	−	0.999955i	$-0.503033\pi$
$631$	−0.478687	−0.0190562	−0.00952812	+	0.999955i	$0.503033\pi$
$632$	−63.9119	−2.54228
$633$	−28.4735	−1.13172
$634$	37.7213	1.49810
$635$	73.7974	2.92856
$636$	12.6710	0.502440
$637$	13.8369	0.548239
$638$	11.5238	0.456232
$639$	−3.94857	−0.156203
$640$	−90.4387	−3.57490
$641$	−15.2480	−0.602260	−0.301130	−	0.953583i	$-0.597364\pi$
$641$	−15.2480	−0.602260	−0.301130	+	0.953583i	$0.597364\pi$
$642$	30.6134	1.20821
$643$	−19.8172	−0.781512	−0.390756	−	0.920494i	$-0.627786\pi$
$643$	−19.8172	−0.781512	−0.390756	+	0.920494i	$0.627786\pi$
$644$	30.8452	1.21547
$645$	73.8734	2.90876
$646$	46.9818	1.84848
$647$	4.31331	0.169574	0.0847869	−	0.996399i	$-0.472979\pi$
$647$	4.31331	0.169574	0.0847869	+	0.996399i	$0.472979\pi$
$648$	44.5924	1.75175
$649$	19.4300	0.762694
$650$	−164.145	−6.43828
$651$	43.9784	1.72365
$652$	21.8178	0.854452
$653$	−27.7687	−1.08668	−0.543338	−	0.839514i	$-0.682840\pi$
$653$	−27.7687	−1.08668	−0.543338	+	0.839514i	$0.682840\pi$
$654$	14.4601	0.565433
$655$	33.6606	1.31523
$656$	−19.5804	−0.764487
$657$	−4.27592	−0.166820
$658$	1.16022	0.0452302
$659$	29.1463	1.13538	0.567689	−	0.823243i	$-0.307838\pi$
$659$	29.1463	1.13538	0.567689	+	0.823243i	$0.307838\pi$
$660$	150.346	5.85220
$661$	−36.6544	−1.42569	−0.712845	−	0.701322i	$-0.752594\pi$
$661$	−36.6544	−1.42569	−0.712845	+	0.701322i	$0.752594\pi$
$662$	−26.0335	−1.01182
$663$	−32.0071	−1.24305
$664$	67.5657	2.62206
$665$	77.0917	2.98949
$666$	14.2952	0.553927
$667$	−2.60245	−0.100767
$668$	−15.8608	−0.613673
$669$	−14.5049	−0.560790
$670$	−69.1040	−2.66972
$671$	33.9095	1.30906
$672$	−12.1904	−0.470254
$673$	−48.2760	−1.86090	−0.930452	−	0.366413i	$-0.880586\pi$
$673$	−48.2760	−1.86090	−0.930452	+	0.366413i	$0.880586\pi$
$674$	29.1254	1.12187
$675$	−64.1129	−2.46771
$676$	39.3309	1.51273
$677$	−8.95857	−0.344306	−0.172153	−	0.985070i	$-0.555072\pi$
$677$	−8.95857	−0.344306	−0.172153	+	0.985070i	$0.555072\pi$
$678$	−78.5076	−3.01507
$679$	−45.9195	−1.76223
$680$	−64.9139	−2.48933
$681$	38.9409	1.49222
$682$	−84.9612	−3.25333
$683$	14.2648	0.545829	0.272914	−	0.962038i	$-0.412012\pi$
$683$	14.2648	0.545829	0.272914	+	0.962038i	$0.412012\pi$
$684$	12.9092	0.493594
$685$	25.9511	0.991542
$686$	−31.2440	−1.19290
$687$	−4.89086	−0.186598
$688$	−24.0055	−0.915201
$689$	8.55119	0.325774
$690$	−51.9427	−1.97743
$691$	−9.55122	−0.363345	−0.181673	−	0.983359i	$-0.558151\pi$
$691$	−9.55122	−0.363345	−0.181673	+	0.983359i	$0.558151\pi$
$692$	14.4981	0.551135
$693$	9.16994	0.348337
$694$	23.2464	0.882420
$695$	82.4339	3.12690
$696$	−8.10184	−0.307100
$697$	25.2572	0.956685
$698$	44.8715	1.69841
$699$	−23.0206	−0.870718
$700$	−167.292	−6.32306
$701$	6.76920	0.255669	0.127835	−	0.991796i	$-0.459197\pi$
$701$	6.76920	0.255669	0.127835	+	0.991796i	$0.459197\pi$
$702$	52.8236	1.99370
$703$	−54.8546	−2.06888
$704$	49.4362	1.86320
$705$	−1.27712	−0.0480992
$706$	−44.5524	−1.67675
$707$	20.2346	0.760999
$708$	−29.0548	−1.09195
$709$	−2.62482	−0.0985772	−0.0492886	−	0.998785i	$-0.515695\pi$
$709$	−2.62482	−0.0985772	−0.0492886	+	0.998785i	$0.515695\pi$
$710$	−68.1200	−2.55650
$711$	9.12651	0.342271
$712$	24.2701	0.909562
$713$	19.1870	0.718559
$714$	−49.9049	−1.86764
$715$	101.462	3.79448
$716$	−67.4044	−2.51902
$717$	−23.9338	−0.893825
$718$	−55.3498	−2.06564
$719$	11.0074	0.410506	0.205253	−	0.978709i	$-0.434198\pi$
$719$	11.0074	0.410506	0.205253	+	0.978709i	$0.434198\pi$
$720$	−7.18616	−0.267812
$721$	−36.5529	−1.36130
$722$	−30.1243	−1.12111
$723$	14.7221	0.547520
$724$	−35.2495	−1.31004
$725$	14.1147	0.524207
$726$	−54.7664	−2.03257
$727$	−4.92131	−0.182521	−0.0912607	−	0.995827i	$-0.529090\pi$
$727$	−4.92131	−0.182521	−0.0912607	+	0.995827i	$0.529090\pi$
$728$	64.8040	2.40180
$729$	19.5197	0.722951
$730$	−73.7675	−2.73026
$731$	30.9652	1.14529
$732$	−50.7068	−1.87418
$733$	43.0827	1.59130	0.795648	−	0.605760i	$-0.207131\pi$
$733$	43.0827	1.59130	0.795648	+	0.605760i	$0.207131\pi$
$734$	−2.44784	−0.0903513
$735$	−23.7480	−0.875958
$736$	−5.31845	−0.196041
$737$	31.5418	1.16186
$738$	10.6170	0.390816
$739$	−13.0272	−0.479215	−0.239607	−	0.970870i	$-0.577019\pi$
$739$	−13.0272	−0.479215	−0.239607	+	0.970870i	$0.577019\pi$
$740$	161.205	5.92601
$741$	51.6280	1.89660
$742$	13.3329	0.489464
$743$	−34.4501	−1.26385	−0.631925	−	0.775029i	$-0.717735\pi$
$743$	−34.4501	−1.26385	−0.631925	+	0.775029i	$0.717735\pi$
$744$	59.7322	2.18989
$745$	2.14670	0.0786489
$746$	−64.3665	−2.35662
$747$	−9.64826	−0.353011
$748$	63.0198	2.30423
$749$	21.0559	0.769368
$750$	181.922	6.64284
$751$	−27.8340	−1.01568	−0.507838	−	0.861452i	$-0.669555\pi$
$751$	−27.8340	−1.01568	−0.507838	+	0.861452i	$0.669555\pi$
$752$	0.415006	0.0151337
$753$	53.1384	1.93647
$754$	−11.6293	−0.423515
$755$	−29.6653	−1.07963
$756$	53.8367	1.95802
$757$	0.930589	0.0338228	0.0169114	−	0.999857i	$-0.494617\pi$
$757$	0.930589	0.0338228	0.0169114	+	0.999857i	$0.494617\pi$
$758$	−34.5185	−1.25377
$759$	23.7087	0.860571
$760$	104.707	3.79813
$761$	−39.7617	−1.44136	−0.720681	−	0.693267i	$-0.756171\pi$
$761$	−39.7617	−1.44136	−0.720681	+	0.693267i	$0.756171\pi$
$762$	77.0576	2.79150
$763$	9.94566	0.360057
$764$	−25.4152	−0.919490
$765$	9.26959	0.335143
$766$	81.1912	2.93356
$767$	−19.6079	−0.708001
$768$	−55.2656	−1.99423
$769$	−2.59654	−0.0936337	−0.0468169	−	0.998903i	$-0.514908\pi$
$769$	−2.59654	−0.0936337	−0.0468169	+	0.998903i	$0.514908\pi$
$770$	158.198	5.70107
$771$	31.5559	1.13646
$772$	−102.891	−3.70313
$773$	46.0576	1.65658	0.828288	−	0.560303i	$-0.189315\pi$
$773$	46.0576	1.65658	0.828288	+	0.560303i	$0.189315\pi$
$774$	13.0164	0.467863
$775$	−104.063	−3.73805
$776$	−62.3687	−2.23890
$777$	58.2675	2.09033
$778$	−59.0448	−2.11686
$779$	−40.7403	−1.45967
$780$	−151.722	−5.43253
$781$	31.0926	1.11258
$782$	−21.7726	−0.778588
$783$	−4.54228	−0.162328
$784$	7.71702	0.275608
$785$	2.83455	0.101169
$786$	35.1476	1.25367
$787$	5.22251	0.186162	0.0930812	−	0.995659i	$-0.470328\pi$
$787$	5.22251	0.186162	0.0930812	+	0.995659i	$0.470328\pi$
$788$	−80.4663	−2.86649
$789$	61.1963	2.17865
$790$	157.449	5.60178
$791$	−53.9977	−1.91994
$792$	12.4548	0.442561
$793$	−34.2200	−1.21519
$794$	−75.8303	−2.69112
$795$	−14.6762	−0.520511
$796$	−18.0293	−0.639032
$797$	28.0367	0.993109	0.496555	−	0.868005i	$-0.334598\pi$
$797$	28.0367	0.993109	0.496555	+	0.868005i	$0.334598\pi$
$798$	80.4973	2.84957
$799$	−0.535326	−0.0189385
$800$	28.8452	1.01983
$801$	−3.46573	−0.122456
$802$	38.7953	1.36991
$803$	33.6704	1.18820
$804$	−47.1662	−1.66342
$805$	−35.7263	−1.25919
$806$	85.7392	3.02003
$807$	18.0237	0.634463
$808$	27.4829	0.966846
$809$	15.2187	0.535061	0.267530	−	0.963549i	$-0.413792\pi$
$809$	15.2187	0.535061	0.267530	+	0.963549i	$0.413792\pi$
$810$	−109.855	−3.85990
$811$	−38.9368	−1.36726	−0.683628	−	0.729831i	$-0.739599\pi$
$811$	−38.9368	−1.36726	−0.683628	+	0.729831i	$0.739599\pi$
$812$	−11.8524	−0.415936
$813$	34.8390	1.22186
$814$	−112.566	−3.94544
$815$	−25.2704	−0.885184
$816$	−17.8507	−0.624900
$817$	−49.9474	−1.74744
$818$	85.3919	2.98566
$819$	−9.25390	−0.323357
$820$	119.726	4.18102
$821$	29.0817	1.01496	0.507479	−	0.861664i	$-0.330577\pi$
$821$	29.0817	1.01496	0.507479	+	0.861664i	$0.330577\pi$
$822$	27.0976	0.945137
$823$	−0.749160	−0.0261141	−0.0130570	−	0.999915i	$-0.504156\pi$
$823$	−0.749160	−0.0261141	−0.0130570	+	0.999915i	$0.504156\pi$
$824$	−49.6467	−1.72953
$825$	−128.587	−4.47682
$826$	−30.5723	−1.06375
$827$	−4.24551	−0.147631	−0.0738154	−	0.997272i	$-0.523518\pi$
$827$	−4.24551	−0.147631	−0.0738154	+	0.997272i	$0.523518\pi$
$828$	−5.98245	−0.207905
$829$	−17.0011	−0.590471	−0.295236	−	0.955424i	$-0.595398\pi$
$829$	−17.0011	−0.590471	−0.295236	+	0.955424i	$0.595398\pi$
$830$	−166.450	−5.77757
$831$	−1.89974	−0.0659011
$832$	−49.8888	−1.72958
$833$	−9.95436	−0.344898
$834$	86.0756	2.98055
$835$	18.3707	0.635745
$836$	−101.652	−3.51571
$837$	33.4887	1.15754
$838$	77.4187	2.67438
$839$	53.6565	1.85243	0.926213	−	0.377000i	$-0.123044\pi$
$839$	53.6565	1.85243	0.926213	+	0.377000i	$0.123044\pi$
$840$	−111.222	−3.83751
$841$	1.00000	0.0344828
$842$	27.9362	0.962744
$843$	45.2770	1.55942
$844$	−56.5758	−1.94742
$845$	−45.5549	−1.56714
$846$	−0.225026	−0.00773657
$847$	−37.6685	−1.29430
$848$	4.76910	0.163771
$849$	46.7913	1.60587
$850$	118.086	4.05033
$851$	25.4211	0.871424
$852$	−46.4945	−1.59288
$853$	−15.7846	−0.540454	−0.270227	−	0.962797i	$-0.587099\pi$
$853$	−15.7846	−0.540454	−0.270227	+	0.962797i	$0.587099\pi$
$854$	−53.3552	−1.82578
$855$	−14.9520	−0.511347
$856$	28.5985	0.977478
$857$	−33.2230	−1.13487	−0.567437	−	0.823417i	$-0.692065\pi$
$857$	−33.2230	−1.13487	−0.567437	+	0.823417i	$0.692065\pi$
$858$	105.945	3.61689
$859$	22.6071	0.771344	0.385672	−	0.922636i	$-0.373970\pi$
$859$	22.6071	0.771344	0.385672	+	0.922636i	$0.373970\pi$
$860$	146.784	5.00528
$861$	43.2750	1.47481
$862$	17.6511	0.601199
$863$	34.5576	1.17635	0.588176	−	0.808733i	$-0.299846\pi$
$863$	34.5576	1.17635	0.588176	+	0.808733i	$0.299846\pi$
$864$	−9.28273	−0.315805
$865$	−16.7924	−0.570958
$866$	52.3131	1.77767
$867$	−9.26945	−0.314807
$868$	87.3834	2.96599
$869$	−71.8659	−2.43788
$870$	19.9591	0.676678
$871$	−31.8306	−1.07854
$872$	13.5084	0.457451
$873$	8.90613	0.301427
$874$	35.1196	1.18794
$875$	125.126	4.23004
$876$	−50.3492	−1.70114
$877$	34.4867	1.16453	0.582267	−	0.812998i	$-0.302166\pi$
$877$	34.4867	1.16453	0.582267	+	0.812998i	$0.302166\pi$
$878$	−3.82303	−0.129021
$879$	−39.4463	−1.33049
$880$	56.5867	1.90754
$881$	−21.2753	−0.716782	−0.358391	−	0.933572i	$-0.616675\pi$
$881$	−21.2753	−0.716782	−0.358391	+	0.933572i	$0.616675\pi$
$882$	−4.18435	−0.140894
$883$	3.67876	0.123800	0.0619000	−	0.998082i	$-0.480284\pi$
$883$	3.67876	0.123800	0.0619000	+	0.998082i	$0.480284\pi$
$884$	−63.5969	−2.13899
$885$	33.6526	1.13122
$886$	35.5609	1.19469
$887$	3.10783	0.104351	0.0521754	−	0.998638i	$-0.483384\pi$
$887$	3.10783	0.104351	0.0521754	+	0.998638i	$0.483384\pi$
$888$	79.1398	2.65576
$889$	53.0004	1.77758
$890$	−59.7902	−2.00417
$891$	50.1420	1.67982
$892$	−28.8206	−0.964985
$893$	0.863490	0.0288956
$894$	2.24153	0.0749681
$895$	78.0710	2.60962
$896$	−64.9520	−2.16989
$897$	−23.9258	−0.798858
$898$	−68.3536	−2.28099
$899$	−7.37267	−0.245892
$900$	32.4465	1.08155
$901$	−6.15177	−0.204945
$902$	−83.6023	−2.78365
$903$	53.0550	1.76556
$904$	−73.3406	−2.43927
$905$	40.8276	1.35716
$906$	−30.9759	−1.02910
$907$	−13.8830	−0.460978	−0.230489	−	0.973075i	$-0.574033\pi$
$907$	−13.8830	−0.460978	−0.230489	+	0.973075i	$0.574033\pi$
$908$	77.3741	2.56775
$909$	−3.92451	−0.130168
$910$	−159.647	−5.29224
$911$	−38.9734	−1.29125	−0.645623	−	0.763656i	$-0.723402\pi$
$911$	−38.9734	−1.29125	−0.645623	+	0.763656i	$0.723402\pi$
$912$	28.7935	0.953448
$913$	75.9743	2.51438
$914$	−14.3947	−0.476135
$915$	58.7310	1.94159
$916$	−9.71795	−0.321090
$917$	24.1746	0.798316
$918$	−38.0016	−1.25424
$919$	54.4044	1.79463	0.897317	−	0.441387i	$-0.145513\pi$
$919$	54.4044	1.79463	0.897317	+	0.441387i	$0.145513\pi$
$920$	−48.5241	−1.59979
$921$	−8.01002	−0.263939
$922$	40.5548	1.33560
$923$	−31.3773	−1.03280
$924$	107.976	3.55216
$925$	−137.874	−4.53328
$926$	−17.0034	−0.558765
$927$	7.08946	0.232848
$928$	2.04363	0.0670854
$929$	54.4935	1.78787	0.893937	−	0.448194i	$-0.147932\pi$
$929$	54.4935	1.78787	0.893937	+	0.448194i	$0.147932\pi$
$930$	−147.152	−4.82531
$931$	16.0565	0.526232
$932$	−45.7410	−1.49830
$933$	53.7085	1.75834
$934$	−73.0071	−2.38886
$935$	−72.9925	−2.38711
$936$	−12.5688	−0.410824
$937$	−18.7531	−0.612638	−0.306319	−	0.951929i	$-0.599097\pi$
$937$	−18.7531	−0.612638	−0.306319	+	0.951929i	$0.599097\pi$
$938$	−49.6297	−1.62047
$939$	−16.2476	−0.530219
$940$	−2.53759	−0.0827671
$941$	5.93241	0.193391	0.0966955	−	0.995314i	$-0.469173\pi$
$941$	5.93241	0.193391	0.0966955	+	0.995314i	$0.469173\pi$
$942$	2.95977	0.0964345
$943$	18.8801	0.614822
$944$	−10.9356	−0.355922
$945$	−62.3561	−2.02844
$946$	−102.496	−3.33244
$947$	9.90411	0.321840	0.160920	−	0.986967i	$-0.448554\pi$
$947$	9.90411	0.321840	0.160920	+	0.986967i	$0.448554\pi$
$948$	107.465	3.49030
$949$	−33.9787	−1.10299
$950$	−190.475	−6.17983
$951$	−29.8205	−0.966996
$952$	−46.6203	−1.51097
$953$	−35.3315	−1.14450	−0.572249	−	0.820080i	$-0.693929\pi$
$953$	−35.3315	−1.14450	−0.572249	+	0.820080i	$0.693929\pi$
$954$	−2.58592	−0.0837222
$955$	29.4371	0.952562
$956$	−47.5556	−1.53806
$957$	−9.11013	−0.294489
$958$	−94.4538	−3.05166
$959$	18.6378	0.601846
$960$	85.6230	2.76347
$961$	23.3562	0.753426
$962$	113.597	3.66251
$963$	−4.08382	−0.131599
$964$	29.2522	0.942151
$965$	119.173	3.83632
$966$	−37.3046	−1.20026
$967$	25.6392	0.824502	0.412251	−	0.911070i	$-0.364743\pi$
$967$	25.6392	0.824502	0.412251	+	0.911070i	$0.364743\pi$
$968$	−51.1619	−1.64441
$969$	−37.1414	−1.19315
$970$	153.647	4.93331
$971$	−17.5242	−0.562378	−0.281189	−	0.959652i	$-0.590729\pi$
$971$	−17.5242	−0.562378	−0.281189	+	0.959652i	$0.590729\pi$
$972$	−23.5429	−0.755137
$973$	59.2030	1.89796
$974$	−69.4945	−2.22675
$975$	129.764	4.15578
$976$	−19.0849	−0.610893
$977$	−31.8854	−1.02010	−0.510052	−	0.860144i	$-0.670374\pi$
$977$	−31.8854	−1.02010	−0.510052	+	0.860144i	$0.670374\pi$
$978$	−26.3868	−0.843756
$979$	27.2906	0.872211
$980$	−47.1864	−1.50731
$981$	−1.92897	−0.0615873
$982$	−26.7172	−0.852579
$983$	−35.8915	−1.14476	−0.572380	−	0.819988i	$-0.693980\pi$
$983$	−35.8915	−1.14476	−0.572380	+	0.819988i	$0.693980\pi$
$984$	58.7768	1.87374
$985$	93.1998	2.96959
$986$	8.36620	0.266434
$987$	−0.917213	−0.0291952
$988$	102.583	3.26359
$989$	23.1470	0.736031
$990$	−30.6827	−0.975160
$991$	18.1624	0.576946	0.288473	−	0.957488i	$-0.406852\pi$
$991$	18.1624	0.576946	0.288473	+	0.957488i	$0.406852\pi$
$992$	−15.0670	−0.478378
$993$	20.5807	0.653110
$994$	−48.9229	−1.55174
$995$	20.8824	0.662017
$996$	−113.609	−3.59983
$997$	10.7238	0.339628	0.169814	−	0.985476i	$-0.445683\pi$
$997$	10.7238	0.339628	0.169814	+	0.985476i	$0.445683\pi$
$998$	−27.0391	−0.855907
$999$	44.3696	1.40379

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8033.2.a.d.1.18	✓	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8033.2.a.d.1.18	✓	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)

\(f(q)\)	\(=\)	\(q-2.40306 q^{2} +1.89974 q^{3} +3.77470 q^{4} -4.37204 q^{5} -4.56518 q^{6} -3.13994 q^{7} -4.26472 q^{8} +0.608994 q^{9} +O(q^{10})\)	\(q-2.40306 q^{2} +1.89974 q^{3} +3.77470 q^{4} -4.37204 q^{5} -4.56518 q^{6} -3.13994 q^{7} -4.26472 q^{8} +0.608994 q^{9} +10.5063 q^{10} -4.79547 q^{11} +7.17094 q^{12} +4.83938 q^{13} +7.54547 q^{14} -8.30571 q^{15} +2.69898 q^{16} -3.48147 q^{17} -1.46345 q^{18} +5.61567 q^{19} -16.5031 q^{20} -5.96506 q^{21} +11.5238 q^{22} -2.60245 q^{23} -8.10184 q^{24} +14.1147 q^{25} -11.6293 q^{26} -4.54228 q^{27} -11.8524 q^{28} +1.00000 q^{29} +19.9591 q^{30} -7.37267 q^{31} +2.04363 q^{32} -9.11013 q^{33} +8.36620 q^{34} +13.7279 q^{35} +2.29877 q^{36} -9.76813 q^{37} -13.4948 q^{38} +9.19354 q^{39} +18.6455 q^{40} -7.25475 q^{41} +14.3344 q^{42} -8.89429 q^{43} -18.1015 q^{44} -2.66255 q^{45} +6.25385 q^{46} +0.153764 q^{47} +5.12735 q^{48} +2.85924 q^{49} -33.9185 q^{50} -6.61388 q^{51} +18.2672 q^{52} +1.76700 q^{53} +10.9154 q^{54} +20.9660 q^{55} +13.3910 q^{56} +10.6683 q^{57} -2.40306 q^{58} -4.05174 q^{59} -31.3516 q^{60} -7.07115 q^{61} +17.7170 q^{62} -1.91221 q^{63} -10.3089 q^{64} -21.1580 q^{65} +21.8922 q^{66} -6.57741 q^{67} -13.1415 q^{68} -4.94397 q^{69} -32.9891 q^{70} -6.48375 q^{71} -2.59719 q^{72} -7.02129 q^{73} +23.4734 q^{74} +26.8142 q^{75} +21.1975 q^{76} +15.0575 q^{77} -22.0926 q^{78} +14.9862 q^{79} -11.8000 q^{80} -10.4561 q^{81} +17.4336 q^{82} -15.8429 q^{83} -22.5163 q^{84} +15.2211 q^{85} +21.3735 q^{86} +1.89974 q^{87} +20.4514 q^{88} -5.69091 q^{89} +6.39826 q^{90} -15.1954 q^{91} -9.82349 q^{92} -14.0061 q^{93} -0.369505 q^{94} -24.5519 q^{95} +3.88236 q^{96} +14.6243 q^{97} -6.87092 q^{98} -2.92042 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q + 12 q^{2} + 35 q^{3} + 184 q^{4} + 12 q^{5} + 10 q^{6} + 74 q^{7} + 39 q^{8} + 183 q^{9}+O(q^{10}) \) 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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