LMFDB - Embedded newform 6033.2.a.e.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6033,2,Mod(1,6033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6033, 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("6033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6033 = 3 \cdot 2011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6033.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:	$48.1737475394$
Analytic rank:	$0$
Dimension:	$97$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	6033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.88583 q^{2} +1.00000 q^{3} +1.55635 q^{4} -4.37058 q^{5} -1.88583 q^{6} +3.62055 q^{7} +0.836652 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.88583 q^{2} +1.00000 q^{3} +1.55635 q^{4} -4.37058 q^{5} -1.88583 q^{6} +3.62055 q^{7} +0.836652 q^{8} +1.00000 q^{9} +8.24216 q^{10} +0.290408 q^{11} +1.55635 q^{12} +4.42107 q^{13} -6.82773 q^{14} -4.37058 q^{15} -4.69048 q^{16} +1.55890 q^{17} -1.88583 q^{18} -3.34533 q^{19} -6.80214 q^{20} +3.62055 q^{21} -0.547660 q^{22} -4.26113 q^{23} +0.836652 q^{24} +14.1019 q^{25} -8.33737 q^{26} +1.00000 q^{27} +5.63483 q^{28} +5.28947 q^{29} +8.24216 q^{30} +1.01607 q^{31} +7.17213 q^{32} +0.290408 q^{33} -2.93981 q^{34} -15.8239 q^{35} +1.55635 q^{36} +9.00438 q^{37} +6.30872 q^{38} +4.42107 q^{39} -3.65665 q^{40} -1.13824 q^{41} -6.82773 q^{42} -2.02299 q^{43} +0.451976 q^{44} -4.37058 q^{45} +8.03576 q^{46} +5.97877 q^{47} -4.69048 q^{48} +6.10835 q^{49} -26.5938 q^{50} +1.55890 q^{51} +6.88072 q^{52} +0.270406 q^{53} -1.88583 q^{54} -1.26925 q^{55} +3.02914 q^{56} -3.34533 q^{57} -9.97503 q^{58} +7.93077 q^{59} -6.80214 q^{60} +1.92382 q^{61} -1.91613 q^{62} +3.62055 q^{63} -4.14445 q^{64} -19.3226 q^{65} -0.547660 q^{66} -13.3175 q^{67} +2.42619 q^{68} -4.26113 q^{69} +29.8411 q^{70} -11.0770 q^{71} +0.836652 q^{72} +16.4223 q^{73} -16.9807 q^{74} +14.1019 q^{75} -5.20650 q^{76} +1.05144 q^{77} -8.33737 q^{78} +13.1605 q^{79} +20.5001 q^{80} +1.00000 q^{81} +2.14652 q^{82} +2.38678 q^{83} +5.63483 q^{84} -6.81328 q^{85} +3.81501 q^{86} +5.28947 q^{87} +0.242970 q^{88} -12.7322 q^{89} +8.24216 q^{90} +16.0067 q^{91} -6.63180 q^{92} +1.01607 q^{93} -11.2749 q^{94} +14.6210 q^{95} +7.17213 q^{96} +5.92951 q^{97} -11.5193 q^{98} +0.290408 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 97 q + 12 q^{2} + 97 q^{3} + 120 q^{4} + 6 q^{5} + 12 q^{6} + 50 q^{7} + 30 q^{8} + 97 q^{9}+O(q^{10}) $ 97 * q + 12 * q^2 + 97 * q^3 + 120 * q^4 + 6 * q^5 + 12 * q^6 + 50 * q^7 + 30 * q^8 + 97 * q^9	\( 97 q + 12 q^{2} + 97 q^{3} + 120 q^{4} + 6 q^{5} + 12 q^{6} + 50 q^{7} + 30 q^{8} + 97 q^{9} + 35 q^{10} + 18 q^{11} + 120 q^{12} + 67 q^{13} - q^{14} + 6 q^{15} + 158 q^{16} + 25 q^{17} + 12 q^{18} + 51 q^{19} + 10 q^{20} + 50 q^{21} + 39 q^{22} + 87 q^{23} + 30 q^{24} + 149 q^{25} + 14 q^{26} + 97 q^{27} + 83 q^{28} + 23 q^{29} + 35 q^{30} + 72 q^{31} + 57 q^{32} + 18 q^{33} + 28 q^{34} + 45 q^{35} + 120 q^{36} + 72 q^{37} + 3 q^{38} + 67 q^{39} + 90 q^{40} + 5 q^{41} - q^{42} + 122 q^{43} + 11 q^{44} + 6 q^{45} + 56 q^{46} + 49 q^{47} + 158 q^{48} + 167 q^{49} + 13 q^{50} + 25 q^{51} + 128 q^{52} + 30 q^{53} + 12 q^{54} + 120 q^{55} - 21 q^{56} + 51 q^{57} + 37 q^{58} + 2 q^{59} + 10 q^{60} + 158 q^{61} + 17 q^{62} + 50 q^{63} + 212 q^{64} + q^{65} + 39 q^{66} + 77 q^{67} + 56 q^{68} + 87 q^{69} + 9 q^{70} + 38 q^{71} + 30 q^{72} + 82 q^{73} - 6 q^{74} + 149 q^{75} + 93 q^{76} + 49 q^{77} + 14 q^{78} + 134 q^{79} - 25 q^{80} + 97 q^{81} + 53 q^{82} + 69 q^{83} + 83 q^{84} + 72 q^{85} + 23 q^{87} + 107 q^{88} + 35 q^{90} + 84 q^{91} + 108 q^{92} + 72 q^{93} + 65 q^{94} + 89 q^{95} + 57 q^{96} + 65 q^{97} + 18 q^{99}+O(q^{100}) \) 97 * q + 12 * q^2 + 97 * q^3 + 120 * q^4 + 6 * q^5 + 12 * q^6 + 50 * q^7 + 30 * q^8 + 97 * q^9 + 35 * q^10 + 18 * q^11 + 120 * q^12 + 67 * q^13 - q^14 + 6 * q^15 + 158 * q^16 + 25 * q^17 + 12 * q^18 + 51 * q^19 + 10 * q^20 + 50 * q^21 + 39 * q^22 + 87 * q^23 + 30 * q^24 + 149 * q^25 + 14 * q^26 + 97 * q^27 + 83 * q^28 + 23 * q^29 + 35 * q^30 + 72 * q^31 + 57 * q^32 + 18 * q^33 + 28 * q^34 + 45 * q^35 + 120 * q^36 + 72 * q^37 + 3 * q^38 + 67 * q^39 + 90 * q^40 + 5 * q^41 - q^42 + 122 * q^43 + 11 * q^44 + 6 * q^45 + 56 * q^46 + 49 * q^47 + 158 * q^48 + 167 * q^49 + 13 * q^50 + 25 * q^51 + 128 * q^52 + 30 * q^53 + 12 * q^54 + 120 * q^55 - 21 * q^56 + 51 * q^57 + 37 * q^58 + 2 * q^59 + 10 * q^60 + 158 * q^61 + 17 * q^62 + 50 * q^63 + 212 * q^64 + q^65 + 39 * q^66 + 77 * q^67 + 56 * q^68 + 87 * q^69 + 9 * q^70 + 38 * q^71 + 30 * q^72 + 82 * q^73 - 6 * q^74 + 149 * q^75 + 93 * q^76 + 49 * q^77 + 14 * q^78 + 134 * q^79 - 25 * q^80 + 97 * q^81 + 53 * q^82 + 69 * q^83 + 83 * q^84 + 72 * q^85 + 23 * q^87 + 107 * q^88 + 35 * q^90 + 84 * q^91 + 108 * q^92 + 72 * q^93 + 65 * q^94 + 89 * q^95 + 57 * q^96 + 65 * q^97 + 18 * 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 $

$2$	−1.88583	−1.33348	−0.666741	−	0.745290i	$-0.732311\pi$
$2$	−1.88583	−1.33348	−0.666741	+	0.745290i	$0.732311\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.55635	0.778174
$5$	−4.37058	−1.95458	−0.977291	−	0.211903i	$-0.932034\pi$
$5$	−4.37058	−1.95458	−0.977291	+	0.211903i	$0.932034\pi$
$6$	−1.88583	−0.769886
$7$	3.62055	1.36844	0.684219	−	0.729277i	$-0.260143\pi$
$7$	3.62055	1.36844	0.684219	+	0.729277i	$0.260143\pi$
$8$	0.836652	0.295801
$9$	1.00000	0.333333
$10$	8.24216	2.60640
$11$	0.290408	0.0875613	0.0437807	−	0.999041i	$-0.486060\pi$
$11$	0.290408	0.0875613	0.0437807	+	0.999041i	$0.486060\pi$
$12$	1.55635	0.449279
$13$	4.42107	1.22618	0.613092	−	0.790012i	$-0.289926\pi$
$13$	4.42107	1.22618	0.613092	+	0.790012i	$0.289926\pi$
$14$	−6.82773	−1.82479
$15$	−4.37058	−1.12848
$16$	−4.69048	−1.17262
$17$	1.55890	0.378088	0.189044	−	0.981969i	$-0.439461\pi$
$17$	1.55890	0.378088	0.189044	+	0.981969i	$0.439461\pi$
$18$	−1.88583	−0.444494
$19$	−3.34533	−0.767471	−0.383736	−	0.923443i	$-0.625363\pi$
$19$	−3.34533	−0.767471	−0.383736	+	0.923443i	$0.625363\pi$
$20$	−6.80214	−1.52100
$21$	3.62055	0.790068
$22$	−0.547660	−0.116761
$23$	−4.26113	−0.888507	−0.444254	−	0.895901i	$-0.646531\pi$
$23$	−4.26113	−0.888507	−0.444254	+	0.895901i	$0.646531\pi$
$24$	0.836652	0.170781
$25$	14.1019	2.82039
$26$	−8.33737	−1.63509
$27$	1.00000	0.192450
$28$	5.63483	1.06488
$29$	5.28947	0.982230	0.491115	−	0.871095i	$-0.336589\pi$
$29$	5.28947	0.982230	0.491115	+	0.871095i	$0.336589\pi$
$30$	8.24216	1.50480
$31$	1.01607	0.182492	0.0912458	−	0.995828i	$-0.470915\pi$
$31$	1.01607	0.182492	0.0912458	+	0.995828i	$0.470915\pi$
$32$	7.17213	1.26787
$33$	0.290408	0.0505535
$34$	−2.93981	−0.504174
$35$	−15.8239	−2.67472
$36$	1.55635	0.259391
$37$	9.00438	1.48031	0.740155	−	0.672436i	$-0.234752\pi$
$37$	9.00438	1.48031	0.740155	+	0.672436i	$0.234752\pi$
$38$	6.30872	1.02341
$39$	4.42107	0.707937
$40$	−3.65665	−0.578167
$41$	−1.13824	−0.177763	−0.0888814	−	0.996042i	$-0.528329\pi$
$41$	−1.13824	−0.177763	−0.0888814	+	0.996042i	$0.528329\pi$
$42$	−6.82773	−1.05354
$43$	−2.02299	−0.308503	−0.154252	−	0.988032i	$-0.549297\pi$
$43$	−2.02299	−0.308503	−0.154252	+	0.988032i	$0.549297\pi$
$44$	0.451976	0.0681379
$45$	−4.37058	−0.651527
$46$	8.03576	1.18481
$47$	5.97877	0.872093	0.436046	−	0.899924i	$-0.356378\pi$
$47$	5.97877	0.872093	0.436046	+	0.899924i	$0.356378\pi$
$48$	−4.69048	−0.677012
$49$	6.10835	0.872621
$50$	−26.5938	−3.76094
$51$	1.55890	0.218289
$52$	6.88072	0.954184
$53$	0.270406	0.0371431	0.0185715	−	0.999828i	$-0.494088\pi$
$53$	0.270406	0.0371431	0.0185715	+	0.999828i	$0.494088\pi$
$54$	−1.88583	−0.256629
$55$	−1.26925	−0.171146
$56$	3.02914	0.404785
$57$	−3.34533	−0.443100
$58$	−9.97503	−1.30979
$59$	7.93077	1.03250	0.516249	−	0.856438i	$-0.327328\pi$
$59$	7.93077	1.03250	0.516249	+	0.856438i	$0.327328\pi$
$60$	−6.80214	−0.878152
$61$	1.92382	0.246320	0.123160	−	0.992387i	$-0.460697\pi$
$61$	1.92382	0.246320	0.123160	+	0.992387i	$0.460697\pi$
$62$	−1.91613	−0.243349
$63$	3.62055	0.456146
$64$	−4.14445	−0.518056
$65$	−19.3226	−2.39668
$66$	−0.547660	−0.0674122
$67$	−13.3175	−1.62699	−0.813493	−	0.581574i	$-0.802437\pi$
$67$	−13.3175	−1.62699	−0.813493	+	0.581574i	$0.802437\pi$
$68$	2.42619	0.294218
$69$	−4.26113	−0.512980
$70$	29.8411	3.56669
$71$	−11.0770	−1.31460	−0.657298	−	0.753631i	$-0.728301\pi$
$71$	−11.0770	−1.31460	−0.657298	+	0.753631i	$0.728301\pi$
$72$	0.836652	0.0986003
$73$	16.4223	1.92209	0.961044	−	0.276396i	$-0.0891403\pi$
$73$	16.4223	1.92209	0.961044	+	0.276396i	$0.0891403\pi$
$74$	−16.9807	−1.97397
$75$	14.1019	1.62835
$76$	−5.20650	−0.597226
$77$	1.05144	0.119822
$78$	−8.33737	−0.944022
$79$	13.1605	1.48068	0.740338	−	0.672235i	$-0.234666\pi$
$79$	13.1605	1.48068	0.740338	+	0.672235i	$0.234666\pi$
$80$	20.5001	2.29198
$81$	1.00000	0.111111
$82$	2.14652	0.237044
$83$	2.38678	0.261983	0.130992	−	0.991383i	$-0.458184\pi$
$83$	2.38678	0.261983	0.130992	+	0.991383i	$0.458184\pi$
$84$	5.63483	0.614810
$85$	−6.81328	−0.739004
$86$	3.81501	0.411383
$87$	5.28947	0.567091
$88$	0.242970	0.0259007
$89$	−12.7322	−1.34961	−0.674806	−	0.737996i	$-0.735773\pi$
$89$	−12.7322	−1.34961	−0.674806	+	0.737996i	$0.735773\pi$
$90$	8.24216	0.868800
$91$	16.0067	1.67796
$92$	−6.63180	−0.691413
$93$	1.01607	0.105362
$94$	−11.2749	−1.16292
$95$	14.6210	1.50008
$96$	7.17213	0.732003
$97$	5.92951	0.602051	0.301026	−	0.953616i	$-0.402671\pi$
$97$	5.92951	0.602051	0.301026	+	0.953616i	$0.402671\pi$
$98$	−11.5193	−1.16362
$99$	0.290408	0.0291871
$100$	21.9475	2.19475
$101$	1.24902	0.124282	0.0621409	−	0.998067i	$-0.480207\pi$
$101$	1.24902	0.124282	0.0621409	+	0.998067i	$0.480207\pi$
$102$	−2.93981	−0.291085
$103$	−14.7149	−1.44990	−0.724950	−	0.688802i	$-0.758137\pi$
$103$	−14.7149	−1.44990	−0.724950	+	0.688802i	$0.758137\pi$
$104$	3.69889	0.362706
$105$	−15.8239	−1.54425
$106$	−0.509939	−0.0495296
$107$	−0.151915	−0.0146862	−0.00734308	−	0.999973i	$-0.502337\pi$
$107$	−0.151915	−0.0146862	−0.00734308	+	0.999973i	$0.502337\pi$
$108$	1.55635	0.149760
$109$	0.804710	0.0770772	0.0385386	−	0.999257i	$-0.487730\pi$
$109$	0.804710	0.0770772	0.0385386	+	0.999257i	$0.487730\pi$
$110$	2.39359	0.228220
$111$	9.00438	0.854658
$112$	−16.9821	−1.60466
$113$	4.42629	0.416390	0.208195	−	0.978087i	$-0.433241\pi$
$113$	4.42629	0.416390	0.208195	+	0.978087i	$0.433241\pi$
$114$	6.30872	0.590865
$115$	18.6236	1.73666
$116$	8.23226	0.764346
$117$	4.42107	0.408728
$118$	−14.9561	−1.37682
$119$	5.64406	0.517390
$120$	−3.65665	−0.333805
$121$	−10.9157	−0.992333
$122$	−3.62800	−0.328464
$123$	−1.13824	−0.102631
$124$	1.58136	0.142010
$125$	−39.7807	−3.55810
$126$	−6.82773	−0.608262
$127$	−3.17042	−0.281330	−0.140665	−	0.990057i	$-0.544924\pi$
$127$	−3.17042	−0.281330	−0.140665	+	0.990057i	$0.544924\pi$
$128$	−6.52854	−0.577047
$129$	−2.02299	−0.178114
$130$	36.4391	3.19592
$131$	11.2570	0.983533	0.491766	−	0.870727i	$-0.336351\pi$
$131$	11.2570	0.983533	0.491766	+	0.870727i	$0.336351\pi$
$132$	0.451976	0.0393395
$133$	−12.1119	−1.05024
$134$	25.1144	2.16956
$135$	−4.37058	−0.376159
$136$	1.30425	0.111839
$137$	0.100739	0.00860668	0.00430334	−	0.999991i	$-0.498630\pi$
$137$	0.100739	0.00860668	0.00430334	+	0.999991i	$0.498630\pi$
$138$	8.03576	0.684049
$139$	−1.70366	−0.144503	−0.0722514	−	0.997386i	$-0.523018\pi$
$139$	−1.70366	−0.144503	−0.0722514	+	0.997386i	$0.523018\pi$
$140$	−24.6274	−2.08140
$141$	5.97877	0.503503
$142$	20.8893	1.75299
$143$	1.28391	0.107366
$144$	−4.69048	−0.390873
$145$	−23.1180	−1.91985
$146$	−30.9697	−2.56307
$147$	6.10835	0.503808
$148$	14.0139	1.15194
$149$	−13.5488	−1.10996	−0.554979	−	0.831864i	$-0.687274\pi$
$149$	−13.5488	−1.10996	−0.554979	+	0.831864i	$0.687274\pi$
$150$	−26.5938	−2.17138
$151$	7.69215	0.625978	0.312989	−	0.949757i	$-0.398670\pi$
$151$	7.69215	0.625978	0.312989	+	0.949757i	$0.398670\pi$
$152$	−2.79888	−0.227019
$153$	1.55890	0.126029
$154$	−1.98283	−0.159781
$155$	−4.44081	−0.356695
$156$	6.88072	0.550898
$157$	−17.5645	−1.40180	−0.700898	−	0.713262i	$-0.747217\pi$
$157$	−17.5645	−1.40180	−0.700898	+	0.713262i	$0.747217\pi$
$158$	−24.8185	−1.97445
$159$	0.270406	0.0214446
$160$	−31.3463	−2.47815
$161$	−15.4276	−1.21587
$162$	−1.88583	−0.148165
$163$	8.78432	0.688041	0.344020	−	0.938962i	$-0.388211\pi$
$163$	8.78432	0.688041	0.344020	+	0.938962i	$0.388211\pi$
$164$	−1.77149	−0.138330
$165$	−1.26925	−0.0988110
$166$	−4.50106	−0.349350
$167$	−14.3528	−1.11066	−0.555328	−	0.831632i	$-0.687407\pi$
$167$	−14.3528	−1.11066	−0.555328	+	0.831632i	$0.687407\pi$
$168$	3.02914	0.233703
$169$	6.54584	0.503526
$170$	12.8487	0.985448
$171$	−3.34533	−0.255824
$172$	−3.14848	−0.240069
$173$	−16.5047	−1.25483	−0.627413	−	0.778687i	$-0.715886\pi$
$173$	−16.5047	−1.25483	−0.627413	+	0.778687i	$0.715886\pi$
$174$	−9.97503	−0.756205
$175$	51.0567	3.85952
$176$	−1.36215	−0.102676
$177$	7.93077	0.596113
$178$	24.0108	1.79968
$179$	14.4367	1.07905	0.539524	−	0.841970i	$-0.318604\pi$
$179$	14.4367	1.07905	0.539524	+	0.841970i	$0.318604\pi$
$180$	−6.80214	−0.507001
$181$	−0.987542	−0.0734034	−0.0367017	−	0.999326i	$-0.511685\pi$
$181$	−0.987542	−0.0734034	−0.0367017	+	0.999326i	$0.511685\pi$
$182$	−30.1858	−2.23752
$183$	1.92382	0.142213
$184$	−3.56508	−0.262821
$185$	−39.3543	−2.89339
$186$	−1.91613	−0.140498
$187$	0.452716	0.0331059
$188$	9.30504	0.678640
$189$	3.62055	0.263356
$190$	−27.5727	−2.00034
$191$	−6.78905	−0.491239	−0.245619	−	0.969366i	$-0.578991\pi$
$191$	−6.78905	−0.491239	−0.245619	+	0.969366i	$0.578991\pi$
$192$	−4.14445	−0.299100
$193$	−23.9728	−1.72560	−0.862799	−	0.505547i	$-0.831291\pi$
$193$	−23.9728	−1.72560	−0.862799	+	0.505547i	$0.831291\pi$
$194$	−11.1820	−0.802824
$195$	−19.3226	−1.38372
$196$	9.50672	0.679051
$197$	6.25762	0.445837	0.222918	−	0.974837i	$-0.428442\pi$
$197$	6.25762	0.445837	0.222918	+	0.974837i	$0.428442\pi$
$198$	−0.547660	−0.0389205
$199$	16.3678	1.16028	0.580140	−	0.814516i	$-0.302998\pi$
$199$	16.3678	1.16028	0.580140	+	0.814516i	$0.302998\pi$
$200$	11.7984	0.834274
$201$	−13.3175	−0.939341
$202$	−2.35543	−0.165727
$203$	19.1508	1.34412
$204$	2.42619	0.169867
$205$	4.97476	0.347452
$206$	27.7497	1.93342
$207$	−4.26113	−0.296169
$208$	−20.7369	−1.43785
$209$	−0.971510	−0.0672008
$210$	29.8411	2.05923
$211$	18.7029	1.28756	0.643779	−	0.765211i	$-0.277365\pi$
$211$	18.7029	1.28756	0.643779	+	0.765211i	$0.277365\pi$
$212$	0.420845	0.0289038
$213$	−11.0770	−0.758983
$214$	0.286485	0.0195837
$215$	8.84163	0.602994
$216$	0.836652	0.0569269
$217$	3.67873	0.249728
$218$	−1.51754	−0.102781
$219$	16.4223	1.10972
$220$	−1.97540	−0.133181
$221$	6.89199	0.463605
$222$	−16.9807	−1.13967
$223$	−28.0965	−1.88148	−0.940739	−	0.339131i	$-0.889867\pi$
$223$	−28.0965	−1.88148	−0.940739	+	0.339131i	$0.889867\pi$
$224$	25.9670	1.73499
$225$	14.1019	0.940129
$226$	−8.34722	−0.555249
$227$	20.0495	1.33073	0.665365	−	0.746518i	$-0.268276\pi$
$227$	20.0495	1.33073	0.665365	+	0.746518i	$0.268276\pi$
$228$	−5.20650	−0.344809
$229$	2.09962	0.138747	0.0693734	−	0.997591i	$-0.477900\pi$
$229$	2.09962	0.138747	0.0693734	+	0.997591i	$0.477900\pi$
$230$	−35.1209	−2.31580
$231$	1.05144	0.0691794
$232$	4.42544	0.290545
$233$	5.62322	0.368389	0.184195	−	0.982890i	$-0.441032\pi$
$233$	5.62322	0.368389	0.184195	+	0.982890i	$0.441032\pi$
$234$	−8.33737	−0.545031
$235$	−26.1307	−1.70458
$236$	12.3430	0.803463
$237$	13.1605	0.854868
$238$	−10.6437	−0.689930
$239$	−2.79623	−0.180873	−0.0904364	−	0.995902i	$-0.528826\pi$
$239$	−2.79623	−0.180873	−0.0904364	+	0.995902i	$0.528826\pi$
$240$	20.5001	1.32328
$241$	25.7468	1.65849	0.829247	−	0.558882i	$-0.188770\pi$
$241$	25.7468	1.65849	0.829247	+	0.558882i	$0.188770\pi$
$242$	20.5851	1.32326
$243$	1.00000	0.0641500
$244$	2.99414	0.191680
$245$	−26.6970	−1.70561
$246$	2.14652	0.136857
$247$	−14.7899	−0.941060
$248$	0.850096	0.0539812
$249$	2.38678	0.151256
$250$	75.0196	4.74466
$251$	−6.66177	−0.420487	−0.210244	−	0.977649i	$-0.567426\pi$
$251$	−6.66177	−0.420487	−0.210244	+	0.977649i	$0.567426\pi$
$252$	5.63483	0.354961
$253$	−1.23747	−0.0777988
$254$	5.97887	0.375148
$255$	−6.81328	−0.426664
$256$	20.6006	1.28754
$257$	13.0290	0.812725	0.406362	−	0.913712i	$-0.366797\pi$
$257$	13.0290	0.812725	0.406362	+	0.913712i	$0.366797\pi$
$258$	3.81501	0.237512
$259$	32.6008	2.02571
$260$	−30.0727	−1.86503
$261$	5.28947	0.327410
$262$	−21.2289	−1.31152
$263$	9.07396	0.559524	0.279762	−	0.960069i	$-0.409744\pi$
$263$	9.07396	0.559524	0.279762	+	0.960069i	$0.409744\pi$
$264$	0.242970	0.0149538
$265$	−1.18183	−0.0725992
$266$	22.8410	1.40047
$267$	−12.7322	−0.779198
$268$	−20.7266	−1.26608
$269$	−5.39177	−0.328742	−0.164371	−	0.986399i	$-0.552559\pi$
$269$	−5.39177	−0.328742	−0.164371	+	0.986399i	$0.552559\pi$
$270$	8.24216	0.501602
$271$	29.0353	1.76377	0.881884	−	0.471466i	$-0.156275\pi$
$271$	29.0353	1.76377	0.881884	+	0.471466i	$0.156275\pi$
$272$	−7.31197	−0.443353
$273$	16.0067	0.968768
$274$	−0.189976	−0.0114769
$275$	4.09532	0.246957
$276$	−6.63180	−0.399188
$277$	3.62470	0.217787	0.108894	−	0.994053i	$-0.465269\pi$
$277$	3.62470	0.217787	0.108894	+	0.994053i	$0.465269\pi$
$278$	3.21282	0.192692
$279$	1.01607	0.0608305
$280$	−13.2391	−0.791186
$281$	3.62844	0.216455	0.108227	−	0.994126i	$-0.465483\pi$
$281$	3.62844	0.216455	0.108227	+	0.994126i	$0.465483\pi$
$282$	−11.2749	−0.671412
$283$	2.46733	0.146668	0.0733338	−	0.997307i	$-0.476636\pi$
$283$	2.46733	0.146668	0.0733338	+	0.997307i	$0.476636\pi$
$284$	−17.2396	−1.02298
$285$	14.6210	0.866074
$286$	−2.42124	−0.143171
$287$	−4.12104	−0.243257
$288$	7.17213	0.422622
$289$	−14.5698	−0.857049
$290$	43.5966	2.56008
$291$	5.92951	0.347594
$292$	25.5588	1.49572
$293$	13.6121	0.795226	0.397613	−	0.917553i	$-0.369839\pi$
$293$	13.6121	0.795226	0.397613	+	0.917553i	$0.369839\pi$
$294$	−11.5193	−0.671819
$295$	−34.6620	−2.01810
$296$	7.53353	0.437877
$297$	0.290408	0.0168512
$298$	25.5507	1.48011
$299$	−18.8387	−1.08947
$300$	21.9475	1.26714
$301$	−7.32433	−0.422167
$302$	−14.5061	−0.834731
$303$	1.24902	0.0717541
$304$	15.6912	0.899951
$305$	−8.40821	−0.481453
$306$	−2.93981	−0.168058
$307$	−29.1262	−1.66232	−0.831160	−	0.556034i	$-0.812322\pi$
$307$	−29.1262	−1.66232	−0.831160	+	0.556034i	$0.812322\pi$
$308$	1.63640	0.0932425
$309$	−14.7149	−0.837100
$310$	8.37461	0.475646
$311$	30.2957	1.71791	0.858956	−	0.512049i	$-0.171114\pi$
$311$	30.2957	1.71791	0.858956	+	0.512049i	$0.171114\pi$
$312$	3.69889	0.209409
$313$	13.3733	0.755905	0.377952	−	0.925825i	$-0.376628\pi$
$313$	13.3733	0.755905	0.377952	+	0.925825i	$0.376628\pi$
$314$	33.1235	1.86927
$315$	−15.8239	−0.891574
$316$	20.4824	1.15222
$317$	7.86307	0.441634	0.220817	−	0.975315i	$-0.429128\pi$
$317$	7.86307	0.441634	0.220817	+	0.975315i	$0.429128\pi$
$318$	−0.509939	−0.0285959
$319$	1.53610	0.0860053
$320$	18.1136	1.01258
$321$	−0.151915	−0.00847905
$322$	29.0938	1.62134
$323$	−5.21503	−0.290172
$324$	1.55635	0.0864638
$325$	62.3456	3.45831
$326$	−16.5657	−0.917490
$327$	0.804710	0.0445006
$328$	−0.952309	−0.0525824
$329$	21.6464	1.19340
$330$	2.39359	0.131763
$331$	−24.5104	−1.34721	−0.673607	−	0.739089i	$-0.735256\pi$
$331$	−24.5104	−1.34721	−0.673607	+	0.739089i	$0.735256\pi$
$332$	3.71466	0.203868
$333$	9.00438	0.493437
$334$	27.0670	1.48104
$335$	58.2050	3.18008
$336$	−16.9821	−0.926449
$337$	28.4157	1.54790	0.773951	−	0.633246i	$-0.218278\pi$
$337$	28.4157	1.54790	0.773951	+	0.633246i	$0.218278\pi$
$338$	−12.3443	−0.671443
$339$	4.42629	0.240403
$340$	−10.6038	−0.575074
$341$	0.295075	0.0159792
$342$	6.30872	0.341136
$343$	−3.22826	−0.174310
$344$	−1.69254	−0.0912555
$345$	18.6236	1.00266
$346$	31.1250	1.67329
$347$	9.58552	0.514578	0.257289	−	0.966335i	$-0.417171\pi$
$347$	9.58552	0.514578	0.257289	+	0.966335i	$0.417171\pi$
$348$	8.23226	0.441295
$349$	16.3761	0.876594	0.438297	−	0.898830i	$-0.355582\pi$
$349$	16.3761	0.876594	0.438297	+	0.898830i	$0.355582\pi$
$350$	−96.2842	−5.14661
$351$	4.42107	0.235979
$352$	2.08284	0.111016
$353$	12.6011	0.670690	0.335345	−	0.942095i	$-0.391147\pi$
$353$	12.6011	0.670690	0.335345	+	0.942095i	$0.391147\pi$
$354$	−14.9561	−0.794906
$355$	48.4128	2.56949
$356$	−19.8157	−1.05023
$357$	5.64406	0.298715
$358$	−27.2251	−1.43889
$359$	24.8771	1.31296	0.656482	−	0.754342i	$-0.272044\pi$
$359$	24.8771	1.31296	0.656482	+	0.754342i	$0.272044\pi$
$360$	−3.65665	−0.192722
$361$	−7.80877	−0.410988
$362$	1.86233	0.0978821
$363$	−10.9157	−0.572924
$364$	24.9120	1.30574
$365$	−71.7750	−3.75688
$366$	−3.62800	−0.189639
$367$	18.9310	0.988188	0.494094	−	0.869408i	$-0.335500\pi$
$367$	18.9310	0.988188	0.494094	+	0.869408i	$0.335500\pi$
$368$	19.9867	1.04188
$369$	−1.13824	−0.0592543
$370$	74.2155	3.85828
$371$	0.979016	0.0508280
$372$	1.58136	0.0819896
$373$	20.5736	1.06526	0.532629	−	0.846349i	$-0.321204\pi$
$373$	20.5736	1.06526	0.532629	+	0.846349i	$0.321204\pi$
$374$	−0.853745	−0.0441461
$375$	−39.7807	−2.05427
$376$	5.00215	0.257966
$377$	23.3851	1.20439
$378$	−6.82773	−0.351180
$379$	27.8694	1.43156	0.715778	−	0.698327i	$-0.246072\pi$
$379$	27.8694	1.43156	0.715778	+	0.698327i	$0.246072\pi$
$380$	22.7554	1.16733
$381$	−3.17042	−0.162426
$382$	12.8030	0.655058
$383$	3.69948	0.189035	0.0945174	−	0.995523i	$-0.469869\pi$
$383$	3.69948	0.189035	0.0945174	+	0.995523i	$0.469869\pi$
$384$	−6.52854	−0.333158
$385$	−4.59538	−0.234202
$386$	45.2085	2.30105
$387$	−2.02299	−0.102834
$388$	9.22839	0.468500
$389$	−1.82369	−0.0924648	−0.0462324	−	0.998931i	$-0.514721\pi$
$389$	−1.82369	−0.0924648	−0.0462324	+	0.998931i	$0.514721\pi$
$390$	36.4391	1.84517
$391$	−6.64266	−0.335934
$392$	5.11056	0.258122
$393$	11.2570	0.567843
$394$	−11.8008	−0.594515
$395$	−57.5191	−2.89410
$396$	0.451976	0.0227126
$397$	8.27538	0.415329	0.207665	−	0.978200i	$-0.433414\pi$
$397$	8.27538	0.415329	0.207665	+	0.978200i	$0.433414\pi$
$398$	−30.8668	−1.54721
$399$	−12.1119	−0.606354
$400$	−66.1448	−3.30724
$401$	13.6715	0.682720	0.341360	−	0.939933i	$-0.389112\pi$
$401$	13.6715	0.682720	0.341360	+	0.939933i	$0.389112\pi$
$402$	25.1144	1.25259
$403$	4.49211	0.223768
$404$	1.94390	0.0967128
$405$	−4.37058	−0.217176
$406$	−36.1151	−1.79236
$407$	2.61494	0.129618
$408$	1.30425	0.0645702
$409$	−11.8779	−0.587326	−0.293663	−	0.955909i	$-0.594874\pi$
$409$	−11.8779	−0.587326	−0.293663	+	0.955909i	$0.594874\pi$
$410$	−9.38153	−0.463321
$411$	0.100739	0.00496907
$412$	−22.9015	−1.12827
$413$	28.7137	1.41291
$414$	8.03576	0.394936
$415$	−10.4316	−0.512067
$416$	31.7085	1.55464
$417$	−1.70366	−0.0834288
$418$	1.83210	0.0896110
$419$	−13.8886	−0.678502	−0.339251	−	0.940696i	$-0.610174\pi$
$419$	−13.8886	−0.678502	−0.339251	+	0.940696i	$0.610174\pi$
$420$	−24.6274	−1.20170
$421$	−33.5752	−1.63635	−0.818177	−	0.574967i	$-0.805015\pi$
$421$	−33.5752	−1.63635	−0.818177	+	0.574967i	$0.805015\pi$
$422$	−35.2704	−1.71694
$423$	5.97877	0.290698
$424$	0.226235	0.0109870
$425$	21.9835	1.06636
$426$	20.8893	1.01209
$427$	6.96529	0.337074
$428$	−0.236432	−0.0114284
$429$	1.28391	0.0619879
$430$	−16.6738	−0.804082
$431$	27.3317	1.31652	0.658261	−	0.752789i	$-0.271292\pi$
$431$	27.3317	1.31652	0.658261	+	0.752789i	$0.271292\pi$
$432$	−4.69048	−0.225671
$433$	15.4428	0.742133	0.371067	−	0.928606i	$-0.378992\pi$
$433$	15.4428	0.742133	0.371067	+	0.928606i	$0.378992\pi$
$434$	−6.93745	−0.333008
$435$	−23.1180	−1.10842
$436$	1.25241	0.0599795
$437$	14.2549	0.681904
$438$	−30.9697	−1.47979
$439$	−11.9089	−0.568383	−0.284191	−	0.958768i	$-0.591725\pi$
$439$	−11.9089	−0.568383	−0.284191	+	0.958768i	$0.591725\pi$
$440$	−1.06192	−0.0506251
$441$	6.10835	0.290874
$442$	−12.9971	−0.618209
$443$	35.8587	1.70370	0.851849	−	0.523787i	$-0.175481\pi$
$443$	35.8587	1.70370	0.851849	+	0.523787i	$0.175481\pi$
$444$	14.0139	0.665072
$445$	55.6471	2.63792
$446$	52.9851	2.50892
$447$	−13.5488	−0.640835
$448$	−15.0052	−0.708928
$449$	4.69942	0.221779	0.110890	−	0.993833i	$-0.464630\pi$
$449$	4.69942	0.221779	0.110890	+	0.993833i	$0.464630\pi$
$450$	−26.5938	−1.25365
$451$	−0.330553	−0.0155652
$452$	6.88884	0.324024
$453$	7.69215	0.361409
$454$	−37.8099	−1.77450
$455$	−69.9584	−3.27970
$456$	−2.79888	−0.131069
$457$	−42.2536	−1.97654	−0.988271	−	0.152711i	$-0.951200\pi$
$457$	−42.2536	−1.97654	−0.988271	+	0.152711i	$0.951200\pi$
$458$	−3.95952	−0.185016
$459$	1.55890	0.0727631
$460$	28.9848	1.35142
$461$	−13.6589	−0.636158	−0.318079	−	0.948064i	$-0.603038\pi$
$461$	−13.6589	−0.636158	−0.318079	+	0.948064i	$0.603038\pi$
$462$	−1.98283	−0.0922494
$463$	−2.70692	−0.125801	−0.0629006	−	0.998020i	$-0.520035\pi$
$463$	−2.70692	−0.125801	−0.0629006	+	0.998020i	$0.520035\pi$
$464$	−24.8101	−1.15178
$465$	−4.44081	−0.205938
$466$	−10.6044	−0.491240
$467$	−13.3379	−0.617206	−0.308603	−	0.951191i	$-0.599861\pi$
$467$	−13.3379	−0.617206	−0.308603	+	0.951191i	$0.599861\pi$
$468$	6.88072	0.318061
$469$	−48.2165	−2.22643
$470$	49.2779	2.27302
$471$	−17.5645	−0.809327
$472$	6.63529	0.305414
$473$	−0.587492	−0.0270129
$474$	−24.8185	−1.13995
$475$	−47.1756	−2.16457
$476$	8.78412	0.402619
$477$	0.270406	0.0123810
$478$	5.27320	0.241191
$479$	27.1999	1.24279	0.621397	−	0.783496i	$-0.286565\pi$
$479$	27.1999	1.24279	0.621397	+	0.783496i	$0.286565\pi$
$480$	−31.3463	−1.43076
$481$	39.8090	1.81513
$482$	−48.5540	−2.21157
$483$	−15.4276	−0.701981
$484$	−16.9886	−0.772208
$485$	−25.9154	−1.17676
$486$	−1.88583	−0.0855429
$487$	8.31402	0.376744	0.188372	−	0.982098i	$-0.439679\pi$
$487$	8.31402	0.376744	0.188372	+	0.982098i	$0.439679\pi$
$488$	1.60957	0.0728618
$489$	8.78432	0.397241
$490$	50.3460	2.27440
$491$	1.10354	0.0498020	0.0249010	−	0.999690i	$-0.492073\pi$
$491$	1.10354	0.0498020	0.0249010	+	0.999690i	$0.492073\pi$
$492$	−1.77149	−0.0798651
$493$	8.24574	0.371369
$494$	27.8913	1.25489
$495$	−1.26925	−0.0570486
$496$	−4.76585	−0.213993
$497$	−40.1047	−1.79894
$498$	−4.50106	−0.201697
$499$	16.6326	0.744578	0.372289	−	0.928117i	$-0.378573\pi$
$499$	16.6326	0.744578	0.372289	+	0.928117i	$0.378573\pi$
$500$	−61.9126	−2.76882
$501$	−14.3528	−0.641237
$502$	12.5630	0.560712
$503$	16.3109	0.727267	0.363633	−	0.931542i	$-0.381536\pi$
$503$	16.3109	0.727267	0.363633	+	0.931542i	$0.381536\pi$
$504$	3.02914	0.134928
$505$	−5.45892	−0.242919
$506$	2.33365	0.103743
$507$	6.54584	0.290711
$508$	−4.93428	−0.218923
$509$	31.5543	1.39862	0.699310	−	0.714818i	$-0.253491\pi$
$509$	31.5543	1.39862	0.699310	+	0.714818i	$0.253491\pi$
$510$	12.8487	0.568949
$511$	59.4578	2.63026
$512$	−25.7921	−1.13986
$513$	−3.34533	−0.147700
$514$	−24.5704	−1.08375
$515$	64.3125	2.83395
$516$	−3.14848	−0.138604
$517$	1.73628	0.0763616
$518$	−61.4794	−2.70125
$519$	−16.5047	−0.724474
$520$	−16.1663	−0.708939
$521$	−33.9015	−1.48525	−0.742625	−	0.669707i	$-0.766420\pi$
$521$	−33.9015	−1.48525	−0.742625	+	0.669707i	$0.766420\pi$
$522$	−9.97503	−0.436595
$523$	−30.2400	−1.32230	−0.661152	−	0.750252i	$-0.729932\pi$
$523$	−30.2400	−1.32230	−0.661152	+	0.750252i	$0.729932\pi$
$524$	17.5199	0.765360
$525$	51.0567	2.22830
$526$	−17.1119	−0.746116
$527$	1.58395	0.0689979
$528$	−1.36215	−0.0592801
$529$	−4.84277	−0.210555
$530$	2.22873	0.0968097
$531$	7.93077	0.344166
$532$	−18.8504	−0.817267
$533$	−5.03223	−0.217970
$534$	24.0108	1.03905
$535$	0.663955	0.0287053
$536$	−11.1421	−0.481264
$537$	14.4367	0.622989
$538$	10.1679	0.438371
$539$	1.77391	0.0764079
$540$	−6.80214	−0.292717
$541$	−18.0947	−0.777952	−0.388976	−	0.921248i	$-0.627171\pi$
$541$	−18.0947	−0.777952	−0.388976	+	0.921248i	$0.627171\pi$
$542$	−54.7556	−2.35195
$543$	−0.987542	−0.0423795
$544$	11.1806	0.479365
$545$	−3.51705	−0.150654
$546$	−30.1858	−1.29183
$547$	16.7824	0.717564	0.358782	−	0.933421i	$-0.383192\pi$
$547$	16.7824	0.717564	0.358782	+	0.933421i	$0.383192\pi$
$548$	0.156784	0.00669750
$549$	1.92382	0.0821067
$550$	−7.72306	−0.329312
$551$	−17.6950	−0.753833
$552$	−3.56508	−0.151740
$553$	47.6483	2.02621
$554$	−6.83557	−0.290415
$555$	−39.3543	−1.67050
$556$	−2.65149	−0.112448
$557$	−44.6654	−1.89253	−0.946267	−	0.323388i	$-0.895178\pi$
$557$	−44.6654	−1.89253	−0.946267	+	0.323388i	$0.895178\pi$
$558$	−1.91613	−0.0811164
$559$	−8.94377	−0.378281
$560$	74.2215	3.13643
$561$	0.452716	0.0191137
$562$	−6.84262	−0.288639
$563$	−29.4614	−1.24165	−0.620824	−	0.783950i	$-0.713202\pi$
$563$	−29.4614	−1.24165	−0.620824	+	0.783950i	$0.713202\pi$
$564$	9.30504	0.391813
$565$	−19.3454	−0.813868
$566$	−4.65296	−0.195579
$567$	3.62055	0.152049
$568$	−9.26758	−0.388859
$569$	−10.5622	−0.442791	−0.221395	−	0.975184i	$-0.571061\pi$
$569$	−10.5622	−0.442791	−0.221395	+	0.975184i	$0.571061\pi$
$570$	−27.5727	−1.15489
$571$	−11.5437	−0.483090	−0.241545	−	0.970390i	$-0.577654\pi$
$571$	−11.5437	−0.483090	−0.241545	+	0.970390i	$0.577654\pi$
$572$	1.99822	0.0835496
$573$	−6.78905	−0.283617
$574$	7.77158	0.324379
$575$	−60.0902	−2.50593
$576$	−4.14445	−0.172685
$577$	−8.94104	−0.372220	−0.186110	−	0.982529i	$-0.559588\pi$
$577$	−8.94104	−0.372220	−0.186110	+	0.982529i	$0.559588\pi$
$578$	27.4762	1.14286
$579$	−23.9728	−0.996275
$580$	−35.9797	−1.49398
$581$	8.64144	0.358508
$582$	−11.1820	−0.463511
$583$	0.0785280	0.00325230
$584$	13.7398	0.568555
$585$	−19.3226	−0.798892
$586$	−25.6700	−1.06042
$587$	38.9064	1.60584	0.802920	−	0.596087i	$-0.203278\pi$
$587$	38.9064	1.60584	0.802920	+	0.596087i	$0.203278\pi$
$588$	9.50672	0.392050
$589$	−3.39909	−0.140057
$590$	65.3666	2.69110
$591$	6.25762	0.257404
$592$	−42.2348	−1.73584
$593$	16.7164	0.686462	0.343231	−	0.939251i	$-0.388479\pi$
$593$	16.7164	0.686462	0.343231	+	0.939251i	$0.388479\pi$
$594$	−0.547660	−0.0224707
$595$	−24.6678	−1.01128
$596$	−21.0866	−0.863741
$597$	16.3678	0.669888
$598$	35.5266	1.45279
$599$	3.95858	0.161743	0.0808716	−	0.996725i	$-0.474230\pi$
$599$	3.95858	0.161743	0.0808716	+	0.996725i	$0.474230\pi$
$600$	11.7984	0.481668
$601$	16.8945	0.689142	0.344571	−	0.938760i	$-0.388024\pi$
$601$	16.8945	0.689142	0.344571	+	0.938760i	$0.388024\pi$
$602$	13.8124	0.562952
$603$	−13.3175	−0.542329
$604$	11.9717	0.487120
$605$	47.7077	1.93960
$606$	−2.35543	−0.0956828
$607$	−27.7624	−1.12684	−0.563420	−	0.826171i	$-0.690515\pi$
$607$	−27.7624	−1.12684	−0.563420	+	0.826171i	$0.690515\pi$
$608$	−23.9931	−0.973050
$609$	19.1508	0.776028
$610$	15.8564	0.642009
$611$	26.4325	1.06935
$612$	2.42619	0.0980728
$613$	−34.7452	−1.40335	−0.701673	−	0.712499i	$-0.747563\pi$
$613$	−34.7452	−1.40335	−0.701673	+	0.712499i	$0.747563\pi$
$614$	54.9270	2.21667
$615$	4.97476	0.200602
$616$	0.879685	0.0354435
$617$	45.4899	1.83135	0.915676	−	0.401916i	$-0.131656\pi$
$617$	45.4899	1.83135	0.915676	+	0.401916i	$0.131656\pi$
$618$	27.7497	1.11626
$619$	21.6799	0.871390	0.435695	−	0.900094i	$-0.356503\pi$
$619$	21.6799	0.871390	0.435695	+	0.900094i	$0.356503\pi$
$620$	−6.91145	−0.277570
$621$	−4.26113	−0.170993
$622$	−57.1325	−2.29080
$623$	−46.0975	−1.84686
$624$	−20.7369	−0.830141
$625$	103.355	4.13420
$626$	−25.2198	−1.00799
$627$	−0.971510	−0.0387984
$628$	−27.3364	−1.09084
$629$	14.0369	0.559688
$630$	29.8411	1.18890
$631$	39.4585	1.57082	0.785408	−	0.618978i	$-0.212453\pi$
$631$	39.4585	1.57082	0.785408	+	0.618978i	$0.212453\pi$
$632$	11.0108	0.437985
$633$	18.7029	0.743372
$634$	−14.8284	−0.588911
$635$	13.8566	0.549882
$636$	0.420845	0.0166876
$637$	27.0054	1.06999
$638$	−2.89683	−0.114687
$639$	−11.0770	−0.438199
$640$	28.5335	1.12788
$641$	28.6939	1.13334	0.566671	−	0.823944i	$-0.308231\pi$
$641$	28.6939	1.13334	0.566671	+	0.823944i	$0.308231\pi$
$642$	0.286485	0.0113067
$643$	−23.5519	−0.928796	−0.464398	−	0.885626i	$-0.653729\pi$
$643$	−23.5519	−0.928796	−0.464398	+	0.885626i	$0.653729\pi$
$644$	−24.0107	−0.946156
$645$	8.84163	0.348139
$646$	9.83464	0.386939
$647$	19.2099	0.755221	0.377610	−	0.925965i	$-0.376746\pi$
$647$	19.2099	0.755221	0.377610	+	0.925965i	$0.376746\pi$
$648$	0.836652	0.0328668
$649$	2.30316	0.0904069
$650$	−117.573	−4.61160
$651$	3.67873	0.144181
$652$	13.6715	0.535416
$653$	1.61346	0.0631397	0.0315699	−	0.999502i	$-0.489949\pi$
$653$	1.61346	0.0631397	0.0315699	+	0.999502i	$0.489949\pi$
$654$	−1.51754	−0.0593407
$655$	−49.1998	−1.92239
$656$	5.33888	0.208448
$657$	16.4223	0.640696
$658$	−40.8214	−1.59138
$659$	13.4904	0.525512	0.262756	−	0.964862i	$-0.415369\pi$
$659$	13.4904	0.525512	0.262756	+	0.964862i	$0.415369\pi$
$660$	−1.97540	−0.0768922
$661$	43.1498	1.67833	0.839166	−	0.543875i	$-0.183043\pi$
$661$	43.1498	1.67833	0.839166	+	0.543875i	$0.183043\pi$
$662$	46.2224	1.79649
$663$	6.89199	0.267663
$664$	1.99690	0.0774949
$665$	52.9361	2.05277
$666$	−16.9807	−0.657989
$667$	−22.5391	−0.872718
$668$	−22.3380	−0.864283
$669$	−28.0965	−1.08627
$670$	−109.765	−4.24058
$671$	0.558693	0.0215681
$672$	25.9670	1.00170
$673$	4.59530	0.177136	0.0885678	−	0.996070i	$-0.471771\pi$
$673$	4.59530	0.177136	0.0885678	+	0.996070i	$0.471771\pi$
$674$	−53.5871	−2.06410
$675$	14.1019	0.542784
$676$	10.1876	0.391831
$677$	−44.2853	−1.70202	−0.851012	−	0.525147i	$-0.824010\pi$
$677$	−44.2853	−1.70202	−0.851012	+	0.525147i	$0.824010\pi$
$678$	−8.34722	−0.320573
$679$	21.4681	0.823869
$680$	−5.70034	−0.218598
$681$	20.0495	0.768297
$682$	−0.556460	−0.0213080
$683$	−14.6702	−0.561340	−0.280670	−	0.959804i	$-0.590557\pi$
$683$	−14.6702	−0.561340	−0.280670	+	0.959804i	$0.590557\pi$
$684$	−5.20650	−0.199075
$685$	−0.440286	−0.0168225
$686$	6.08795	0.232439
$687$	2.09962	0.0801055
$688$	9.48879	0.361757
$689$	1.19548	0.0455442
$690$	−35.1209	−1.33703
$691$	−10.5737	−0.402241	−0.201120	−	0.979567i	$-0.564458\pi$
$691$	−10.5737	−0.402241	−0.201120	+	0.979567i	$0.564458\pi$
$692$	−25.6870	−0.976473
$693$	1.05144	0.0399407
$694$	−18.0766	−0.686180
$695$	7.44599	0.282443
$696$	4.42544	0.167746
$697$	−1.77440	−0.0672100
$698$	−30.8826	−1.16892
$699$	5.62322	0.212690
$700$	79.4620	3.00338
$701$	−1.61179	−0.0608765	−0.0304382	−	0.999537i	$-0.509690\pi$
$701$	−1.61179	−0.0608765	−0.0304382	+	0.999537i	$0.509690\pi$
$702$	−8.33737	−0.314674
$703$	−30.1226	−1.13610
$704$	−1.20358	−0.0453617
$705$	−26.1307	−0.984138
$706$	−23.7635	−0.894353
$707$	4.52212	0.170072
$708$	12.3430	0.463880
$709$	39.7220	1.49179	0.745895	−	0.666064i	$-0.232022\pi$
$709$	39.7220	1.49179	0.745895	+	0.666064i	$0.232022\pi$
$710$	−91.2983	−3.42636
$711$	13.1605	0.493558
$712$	−10.6524	−0.399216
$713$	−4.32961	−0.162145
$714$	−10.6437	−0.398331
$715$	−5.61144	−0.209856
$716$	22.4685	0.839688
$717$	−2.79623	−0.104427
$718$	−46.9140	−1.75081
$719$	24.3386	0.907677	0.453839	−	0.891084i	$-0.350054\pi$
$719$	24.3386	0.907677	0.453839	+	0.891084i	$0.350054\pi$
$720$	20.5001	0.763993
$721$	−53.2759	−1.98410
$722$	14.7260	0.548045
$723$	25.7468	0.957532
$724$	−1.53696	−0.0571206
$725$	74.5918	2.77027
$726$	20.5851	0.763983
$727$	31.0774	1.15260	0.576299	−	0.817239i	$-0.304496\pi$
$727$	31.0774	1.15260	0.576299	+	0.817239i	$0.304496\pi$
$728$	13.3920	0.496341
$729$	1.00000	0.0370370
$730$	135.355	5.00973
$731$	−3.15363	−0.116641
$732$	2.99414	0.110666
$733$	−0.408959	−0.0151052	−0.00755262	−	0.999971i	$-0.502404\pi$
$733$	−0.408959	−0.0151052	−0.00755262	+	0.999971i	$0.502404\pi$
$734$	−35.7005	−1.31773
$735$	−26.6970	−0.984734
$736$	−30.5614	−1.12651
$737$	−3.86750	−0.142461
$738$	2.14652	0.0790145
$739$	25.3860	0.933841	0.466920	−	0.884299i	$-0.345363\pi$
$739$	25.3860	0.933841	0.466920	+	0.884299i	$0.345363\pi$
$740$	−61.2490	−2.25156
$741$	−14.7899	−0.543322
$742$	−1.84626	−0.0677782
$743$	36.7126	1.34686	0.673428	−	0.739253i	$-0.264821\pi$
$743$	36.7126	1.34686	0.673428	+	0.739253i	$0.264821\pi$
$744$	0.850096	0.0311660
$745$	59.2159	2.16950
$746$	−38.7982	−1.42050
$747$	2.38678	0.0873277
$748$	0.704584	0.0257621
$749$	−0.550014	−0.0200971
$750$	75.0196	2.73933
$751$	24.1130	0.879897	0.439949	−	0.898023i	$-0.354997\pi$
$751$	24.1130	0.879897	0.439949	+	0.898023i	$0.354997\pi$
$752$	−28.0433	−1.02263
$753$	−6.66177	−0.242768
$754$	−44.1003	−1.60604
$755$	−33.6191	−1.22353
$756$	5.63483	0.204937
$757$	9.73344	0.353768	0.176884	−	0.984232i	$-0.443398\pi$
$757$	9.73344	0.353768	0.176884	+	0.984232i	$0.443398\pi$
$758$	−52.5570	−1.90896
$759$	−1.23747	−0.0449172
$760$	12.2327	0.443727
$761$	43.0665	1.56116	0.780579	−	0.625057i	$-0.214924\pi$
$761$	43.0665	1.56116	0.780579	+	0.625057i	$0.214924\pi$
$762$	5.97887	0.216592
$763$	2.91349	0.105475
$764$	−10.5661	−0.382269
$765$	−6.81328	−0.246335
$766$	−6.97659	−0.252074
$767$	35.0625	1.26603
$768$	20.6006	0.743360
$769$	−19.3593	−0.698114	−0.349057	−	0.937101i	$-0.613498\pi$
$769$	−19.3593	−0.698114	−0.349057	+	0.937101i	$0.613498\pi$
$770$	8.66610	0.312304
$771$	13.0290	0.469227
$772$	−37.3100	−1.34282
$773$	2.32389	0.0835847	0.0417923	−	0.999126i	$-0.486693\pi$
$773$	2.32389	0.0835847	0.0417923	+	0.999126i	$0.486693\pi$
$774$	3.81501	0.137128
$775$	14.3286	0.514697
$776$	4.96094	0.178087
$777$	32.6008	1.16955
$778$	3.43917	0.123300
$779$	3.80778	0.136428
$780$	−30.0727	−1.07678
$781$	−3.21685	−0.115108
$782$	12.5269	0.447962
$783$	5.28947	0.189030
$784$	−28.6511	−1.02325
$785$	76.7668	2.73992
$786$	−21.2289	−0.757208
$787$	−40.7149	−1.45133	−0.725665	−	0.688049i	$-0.758468\pi$
$787$	−40.7149	−1.45133	−0.725665	+	0.688049i	$0.758468\pi$
$788$	9.73903	0.346939
$789$	9.07396	0.323042
$790$	108.471	3.85923
$791$	16.0256	0.569804
$792$	0.242970	0.00863357
$793$	8.50535	0.302034
$794$	−15.6059	−0.553834
$795$	−1.18183	−0.0419151
$796$	25.4740	0.902900
$797$	−13.7695	−0.487740	−0.243870	−	0.969808i	$-0.578417\pi$
$797$	−13.7695	−0.487740	−0.243870	+	0.969808i	$0.578417\pi$
$798$	22.8410	0.808562
$799$	9.32028	0.329728
$800$	101.141	3.57587
$801$	−12.7322	−0.449870
$802$	−25.7820	−0.910395
$803$	4.76917	0.168300
$804$	−20.7266	−0.730971
$805$	67.4276	2.37651
$806$	−8.47135	−0.298391
$807$	−5.39177	−0.189799
$808$	1.04499	0.0367627
$809$	38.3675	1.34893	0.674464	−	0.738308i	$-0.264375\pi$
$809$	38.3675	1.34893	0.674464	+	0.738308i	$0.264375\pi$
$810$	8.24216	0.289600
$811$	−18.9724	−0.666212	−0.333106	−	0.942889i	$-0.608097\pi$
$811$	−18.9724	−0.666212	−0.333106	+	0.942889i	$0.608097\pi$
$812$	29.8053	1.04596
$813$	29.0353	1.01831
$814$	−4.93133	−0.172843
$815$	−38.3925	−1.34483
$816$	−7.31197	−0.255970
$817$	6.76757	0.236767
$818$	22.3998	0.783189
$819$	16.0067	0.559319
$820$	7.74245	0.270378
$821$	12.7828	0.446124	0.223062	−	0.974804i	$-0.428395\pi$
$821$	12.7828	0.446124	0.223062	+	0.974804i	$0.428395\pi$
$822$	−0.189976	−0.00662616
$823$	−3.03809	−0.105901	−0.0529506	−	0.998597i	$-0.516863\pi$
$823$	−3.03809	−0.105901	−0.0529506	+	0.998597i	$0.516863\pi$
$824$	−12.3112	−0.428882
$825$	4.09532	0.142581
$826$	−54.1491	−1.88409
$827$	−29.8404	−1.03765	−0.518826	−	0.854880i	$-0.673631\pi$
$827$	−29.8404	−1.03765	−0.518826	+	0.854880i	$0.673631\pi$
$828$	−6.63180	−0.230471
$829$	−19.0396	−0.661274	−0.330637	−	0.943758i	$-0.607264\pi$
$829$	−19.0396	−0.661274	−0.330637	+	0.943758i	$0.607264\pi$
$830$	19.6722	0.682832
$831$	3.62470	0.125740
$832$	−18.3229	−0.635232
$833$	9.52229	0.329928
$834$	3.21282	0.111251
$835$	62.7301	2.17087
$836$	−1.51201	−0.0522939
$837$	1.01607	0.0351205
$838$	26.1915	0.904770
$839$	−18.4783	−0.637943	−0.318972	−	0.947764i	$-0.603338\pi$
$839$	−18.4783	−0.637943	−0.318972	+	0.947764i	$0.603338\pi$
$840$	−13.2391	−0.456791
$841$	−1.02151	−0.0352244
$842$	63.3170	2.18205
$843$	3.62844	0.124970
$844$	29.1082	1.00194
$845$	−28.6091	−0.984182
$846$	−11.2749	−0.387640
$847$	−39.5207	−1.35795
$848$	−1.26833	−0.0435547
$849$	2.46733	0.0846786
$850$	−41.4571	−1.42197
$851$	−38.3688	−1.31527
$852$	−17.2396	−0.590621
$853$	3.28360	0.112428	0.0562142	−	0.998419i	$-0.482097\pi$
$853$	3.28360	0.112428	0.0562142	+	0.998419i	$0.482097\pi$
$854$	−13.1353	−0.449482
$855$	14.6210	0.500028
$856$	−0.127100	−0.00434418
$857$	30.8452	1.05365	0.526825	−	0.849974i	$-0.323382\pi$
$857$	30.8452	1.05365	0.526825	+	0.849974i	$0.323382\pi$
$858$	−2.42124	−0.0826598
$859$	−0.714373	−0.0243741	−0.0121871	−	0.999926i	$-0.503879\pi$
$859$	−0.714373	−0.0243741	−0.0121871	+	0.999926i	$0.503879\pi$
$860$	13.7607	0.469234
$861$	−4.12104	−0.140445
$862$	−51.5429	−1.75556
$863$	37.2257	1.26718	0.633589	−	0.773670i	$-0.281581\pi$
$863$	37.2257	1.26718	0.633589	+	0.773670i	$0.281581\pi$
$864$	7.17213	0.244001
$865$	72.1349	2.45266
$866$	−29.1225	−0.989621
$867$	−14.5698	−0.494818
$868$	5.72538	0.194332
$869$	3.82192	0.129650
$870$	43.5966	1.47806
$871$	−58.8774	−1.99498
$872$	0.673262	0.0227995
$873$	5.92951	0.200684
$874$	−26.8823	−0.909306
$875$	−144.028	−4.86903
$876$	25.5588	0.863553
$877$	−35.1447	−1.18675	−0.593376	−	0.804925i	$-0.702205\pi$
$877$	−35.1447	−1.18675	−0.593376	+	0.804925i	$0.702205\pi$
$878$	22.4582	0.757928
$879$	13.6121	0.459124
$880$	5.95339	0.200689
$881$	29.0073	0.977282	0.488641	−	0.872485i	$-0.337493\pi$
$881$	29.0073	0.977282	0.488641	+	0.872485i	$0.337493\pi$
$882$	−11.5193	−0.387875
$883$	−3.72672	−0.125414	−0.0627071	−	0.998032i	$-0.519973\pi$
$883$	−3.72672	−0.125414	−0.0627071	+	0.998032i	$0.519973\pi$
$884$	10.7263	0.360766
$885$	−34.6620	−1.16515
$886$	−67.6234	−2.27185
$887$	25.9695	0.871971	0.435985	−	0.899954i	$-0.356400\pi$
$887$	25.9695	0.871971	0.435985	+	0.899954i	$0.356400\pi$
$888$	7.53353	0.252809
$889$	−11.4787	−0.384982
$890$	−104.941	−3.51762
$891$	0.290408	0.00972903
$892$	−43.7279	−1.46412
$893$	−20.0009	−0.669306
$894$	25.5507	0.854542
$895$	−63.0967	−2.10909
$896$	−23.6369	−0.789652
$897$	−18.8387	−0.629007
$898$	−8.86229	−0.295738
$899$	5.37447	0.179249
$900$	21.9475	0.731584
$901$	0.421535	0.0140434
$902$	0.623367	0.0207558
$903$	−7.32433	−0.243738
$904$	3.70326	0.123169
$905$	4.31613	0.143473
$906$	−14.5061	−0.481932
$907$	1.63570	0.0543126	0.0271563	−	0.999631i	$-0.491355\pi$
$907$	1.63570	0.0543126	0.0271563	+	0.999631i	$0.491355\pi$
$908$	31.2040	1.03554
$909$	1.24902	0.0414272
$910$	131.930	4.37342
$911$	−27.4668	−0.910014	−0.455007	−	0.890488i	$-0.650363\pi$
$911$	−27.4668	−0.910014	−0.455007	+	0.890488i	$0.650363\pi$
$912$	15.6912	0.519587
$913$	0.693140	0.0229396
$914$	79.6831	2.63568
$915$	−8.40821	−0.277967
$916$	3.26774	0.107969
$917$	40.7567	1.34590
$918$	−2.93981	−0.0970283
$919$	31.3853	1.03530	0.517652	−	0.855591i	$-0.326806\pi$
$919$	31.3853	1.03530	0.517652	+	0.855591i	$0.326806\pi$
$920$	15.5815	0.513706
$921$	−29.1262	−0.959740
$922$	25.7583	0.848305
$923$	−48.9721	−1.61194
$924$	1.63640	0.0538336
$925$	126.979	4.17505
$926$	5.10479	0.167754
$927$	−14.7149	−0.483300
$928$	37.9368	1.24534
$929$	−22.1077	−0.725329	−0.362664	−	0.931920i	$-0.618133\pi$
$929$	−22.1077	−0.725329	−0.362664	+	0.931920i	$0.618133\pi$
$930$	8.37461	0.274614
$931$	−20.4344	−0.669712
$932$	8.75168	0.286671
$933$	30.2957	0.991837
$934$	25.1531	0.823033
$935$	−1.97863	−0.0647082
$936$	3.69889	0.120902
$937$	−39.0995	−1.27732	−0.638662	−	0.769487i	$-0.720512\pi$
$937$	−39.0995	−1.27732	−0.638662	+	0.769487i	$0.720512\pi$
$938$	90.9280	2.96890
$939$	13.3733	0.436422
$940$	−40.6684	−1.32646
$941$	−12.2935	−0.400756	−0.200378	−	0.979719i	$-0.564217\pi$
$941$	−12.2935	−0.400756	−0.200378	+	0.979719i	$0.564217\pi$
$942$	33.1235	1.07922
$943$	4.85018	0.157944
$944$	−37.1991	−1.21073
$945$	−15.8239	−0.514751
$946$	1.10791	0.0360213
$947$	−5.10408	−0.165860	−0.0829301	−	0.996555i	$-0.526428\pi$
$947$	−5.10408	−0.165860	−0.0829301	+	0.996555i	$0.526428\pi$
$948$	20.4824	0.665236
$949$	72.6042	2.35683
$950$	88.9651	2.88641
$951$	7.86307	0.254977
$952$	4.72211	0.153044
$953$	8.27256	0.267975	0.133987	−	0.990983i	$-0.457222\pi$
$953$	8.27256	0.267975	0.133987	+	0.990983i	$0.457222\pi$
$954$	−0.509939	−0.0165099
$955$	29.6721	0.960166
$956$	−4.35190	−0.140751
$957$	1.53610	0.0496552
$958$	−51.2943	−1.65724
$959$	0.364729	0.0117777
$960$	18.1136	0.584615
$961$	−29.9676	−0.966697
$962$	−75.0729	−2.42045
$963$	−0.151915	−0.00489538
$964$	40.0709	1.29060
$965$	104.775	3.37282
$966$	29.0938	0.936079
$967$	47.9755	1.54279	0.771394	−	0.636357i	$-0.219560\pi$
$967$	47.9755	1.54279	0.771394	+	0.636357i	$0.219560\pi$
$968$	−9.13261	−0.293533
$969$	−5.21503	−0.167531
$970$	48.8720	1.56918
$971$	−41.6389	−1.33626	−0.668128	−	0.744047i	$-0.732904\pi$
$971$	−41.6389	−1.33626	−0.668128	+	0.744047i	$0.732904\pi$
$972$	1.55635	0.0499199
$973$	−6.16819	−0.197743
$974$	−15.6788	−0.502382
$975$	62.3456	1.99666
$976$	−9.02364	−0.288840
$977$	−10.1848	−0.325841	−0.162921	−	0.986639i	$-0.552091\pi$
$977$	−10.1848	−0.325841	−0.162921	+	0.986639i	$0.552091\pi$
$978$	−16.5657	−0.529713
$979$	−3.69753	−0.118174
$980$	−41.5498	−1.32726
$981$	0.804710	0.0256924
$982$	−2.08108	−0.0664100
$983$	20.1803	0.643652	0.321826	−	0.946799i	$-0.395703\pi$
$983$	20.1803	0.643652	0.321826	+	0.946799i	$0.395703\pi$
$984$	−0.952309	−0.0303585
$985$	−27.3494	−0.871424
$986$	−15.5501	−0.495214
$987$	21.6464	0.689012
$988$	−23.0183	−0.732309
$989$	8.62022	0.274107
$990$	2.39359	0.0760732
$991$	40.7803	1.29543	0.647714	−	0.761884i	$-0.275725\pi$
$991$	40.7803	1.29543	0.647714	+	0.761884i	$0.275725\pi$
$992$	7.28739	0.231375
$993$	−24.5104	−0.777815
$994$	75.6306	2.39886
$995$	−71.5366	−2.26786
$996$	3.71466	0.117703
$997$	17.7620	0.562527	0.281263	−	0.959631i	$-0.409247\pi$
$997$	17.7620	0.562527	0.281263	+	0.959631i	$0.409247\pi$
$998$	−31.3663	−0.992882
$999$	9.00438	0.284886

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6033.2.a.e.1.20	✓	97

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6033.2.a.e.1.20	✓	97	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:	\( N \)	\(=\)	\( 6033 = 3 \cdot 2011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6033.a (trivial)

\(f(q)\)	\(=\)	\(q-1.88583 q^{2} +1.00000 q^{3} +1.55635 q^{4} -4.37058 q^{5} -1.88583 q^{6} +3.62055 q^{7} +0.836652 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.88583 q^{2} +1.00000 q^{3} +1.55635 q^{4} -4.37058 q^{5} -1.88583 q^{6} +3.62055 q^{7} +0.836652 q^{8} +1.00000 q^{9} +8.24216 q^{10} +0.290408 q^{11} +1.55635 q^{12} +4.42107 q^{13} -6.82773 q^{14} -4.37058 q^{15} -4.69048 q^{16} +1.55890 q^{17} -1.88583 q^{18} -3.34533 q^{19} -6.80214 q^{20} +3.62055 q^{21} -0.547660 q^{22} -4.26113 q^{23} +0.836652 q^{24} +14.1019 q^{25} -8.33737 q^{26} +1.00000 q^{27} +5.63483 q^{28} +5.28947 q^{29} +8.24216 q^{30} +1.01607 q^{31} +7.17213 q^{32} +0.290408 q^{33} -2.93981 q^{34} -15.8239 q^{35} +1.55635 q^{36} +9.00438 q^{37} +6.30872 q^{38} +4.42107 q^{39} -3.65665 q^{40} -1.13824 q^{41} -6.82773 q^{42} -2.02299 q^{43} +0.451976 q^{44} -4.37058 q^{45} +8.03576 q^{46} +5.97877 q^{47} -4.69048 q^{48} +6.10835 q^{49} -26.5938 q^{50} +1.55890 q^{51} +6.88072 q^{52} +0.270406 q^{53} -1.88583 q^{54} -1.26925 q^{55} +3.02914 q^{56} -3.34533 q^{57} -9.97503 q^{58} +7.93077 q^{59} -6.80214 q^{60} +1.92382 q^{61} -1.91613 q^{62} +3.62055 q^{63} -4.14445 q^{64} -19.3226 q^{65} -0.547660 q^{66} -13.3175 q^{67} +2.42619 q^{68} -4.26113 q^{69} +29.8411 q^{70} -11.0770 q^{71} +0.836652 q^{72} +16.4223 q^{73} -16.9807 q^{74} +14.1019 q^{75} -5.20650 q^{76} +1.05144 q^{77} -8.33737 q^{78} +13.1605 q^{79} +20.5001 q^{80} +1.00000 q^{81} +2.14652 q^{82} +2.38678 q^{83} +5.63483 q^{84} -6.81328 q^{85} +3.81501 q^{86} +5.28947 q^{87} +0.242970 q^{88} -12.7322 q^{89} +8.24216 q^{90} +16.0067 q^{91} -6.63180 q^{92} +1.01607 q^{93} -11.2749 q^{94} +14.6210 q^{95} +7.17213 q^{96} +5.92951 q^{97} -11.5193 q^{98} +0.290408 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 97 q + 12 q^{2} + 97 q^{3} + 120 q^{4} + 6 q^{5} + 12 q^{6} + 50 q^{7} + 30 q^{8} + 97 q^{9}+O(q^{10}) \) 97 * q + 12 * q^2 + 97 * q^3 + 120 * q^4 + 6 * q^5 + 12 * q^6 + 50 * q^7 + 30 * q^8 + 97 * q^9	\( 97 q + 12 q^{2} + 97 q^{3} + 120 q^{4} + 6 q^{5} + 12 q^{6} + 50 q^{7} + 30 q^{8} + 97 q^{9} + 35 q^{10} + 18 q^{11} + 120 q^{12} + 67 q^{13} - q^{14} + 6 q^{15} + 158 q^{16} + 25 q^{17} + 12 q^{18} + 51 q^{19} + 10 q^{20} + 50 q^{21} + 39 q^{22} + 87 q^{23} + 30 q^{24} + 149 q^{25} + 14 q^{26} + 97 q^{27} + 83 q^{28} + 23 q^{29} + 35 q^{30} + 72 q^{31} + 57 q^{32} + 18 q^{33} + 28 q^{34} + 45 q^{35} + 120 q^{36} + 72 q^{37} + 3 q^{38} + 67 q^{39} + 90 q^{40} + 5 q^{41} - q^{42} + 122 q^{43} + 11 q^{44} + 6 q^{45} + 56 q^{46} + 49 q^{47} + 158 q^{48} + 167 q^{49} + 13 q^{50} + 25 q^{51} + 128 q^{52} + 30 q^{53} + 12 q^{54} + 120 q^{55} - 21 q^{56} + 51 q^{57} + 37 q^{58} + 2 q^{59} + 10 q^{60} + 158 q^{61} + 17 q^{62} + 50 q^{63} + 212 q^{64} + q^{65} + 39 q^{66} + 77 q^{67} + 56 q^{68} + 87 q^{69} + 9 q^{70} + 38 q^{71} + 30 q^{72} + 82 q^{73} - 6 q^{74} + 149 q^{75} + 93 q^{76} + 49 q^{77} + 14 q^{78} + 134 q^{79} - 25 q^{80} + 97 q^{81} + 53 q^{82} + 69 q^{83} + 83 q^{84} + 72 q^{85} + 23 q^{87} + 107 q^{88} + 35 q^{90} + 84 q^{91} + 108 q^{92} + 72 q^{93} + 65 q^{94} + 89 q^{95} + 57 q^{96} + 65 q^{97} + 18 q^{99}+O(q^{100}) \) 97 * q + 12 * q^2 + 97 * q^3 + 120 * q^4 + 6 * q^5 + 12 * q^6 + 50 * q^7 + 30 * q^8 + 97 * q^9 + 35 * q^10 + 18 * q^11 + 120 * q^12 + 67 * q^13 - q^14 + 6 * q^15 + 158 * q^16 + 25 * q^17 + 12 * q^18 + 51 * q^19 + 10 * q^20 + 50 * q^21 + 39 * q^22 + 87 * q^23 + 30 * q^24 + 149 * q^25 + 14 * q^26 + 97 * q^27 + 83 * q^28 + 23 * q^29 + 35 * q^30 + 72 * q^31 + 57 * q^32 + 18 * q^33 + 28 * q^34 + 45 * q^35 + 120 * q^36 + 72 * q^37 + 3 * q^38 + 67 * q^39 + 90 * q^40 + 5 * q^41 - q^42 + 122 * q^43 + 11 * q^44 + 6 * q^45 + 56 * q^46 + 49 * q^47 + 158 * q^48 + 167 * q^49 + 13 * q^50 + 25 * q^51 + 128 * q^52 + 30 * q^53 + 12 * q^54 + 120 * q^55 - 21 * q^56 + 51 * q^57 + 37 * q^58 + 2 * q^59 + 10 * q^60 + 158 * q^61 + 17 * q^62 + 50 * q^63 + 212 * q^64 + q^65 + 39 * q^66 + 77 * q^67 + 56 * q^68 + 87 * q^69 + 9 * q^70 + 38 * q^71 + 30 * q^72 + 82 * q^73 - 6 * q^74 + 149 * q^75 + 93 * q^76 + 49 * q^77 + 14 * q^78 + 134 * q^79 - 25 * q^80 + 97 * q^81 + 53 * q^82 + 69 * q^83 + 83 * q^84 + 72 * q^85 + 23 * q^87 + 107 * q^88 + 35 * q^90 + 84 * q^91 + 108 * q^92 + 72 * q^93 + 65 * q^94 + 89 * q^95 + 57 * q^96 + 65 * q^97 + 18 * q^99

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