LMFDB - Embedded newform 2645.2.a.t.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2645,2,Mod(1,2645)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2645, 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("2645.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2645 = 5 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2645.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:	$21.1204313346$
Analytic rank:	$1$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 5x^{9} - 12x^{8} + 78x^{7} + 60x^{6} - 474x^{5} - 231x^{4} + 1353x^{3} + 770x^{2} - 1540x - 1199 $ x^10 - 5x^9 - 12x^8 + 78x^7 + 60x^6 - 474x^5 - 231x^4 + 1353x^3 + 770x^2 - 1540*x - 1199
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 115)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-2.23472$ of defining polynomial
Character	$\chi$	$=$	2645.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.91899 q^{2} +2.23472 q^{3} +1.68251 q^{4} -1.00000 q^{5} -4.28840 q^{6} -0.856675 q^{7} +0.609264 q^{8} +1.99398 q^{9} +O(q^{10})$	\(q-1.91899 q^{2} +2.23472 q^{3} +1.68251 q^{4} -1.00000 q^{5} -4.28840 q^{6} -0.856675 q^{7} +0.609264 q^{8} +1.99398 q^{9} +1.91899 q^{10} +1.35929 q^{11} +3.75994 q^{12} -3.70626 q^{13} +1.64395 q^{14} -2.23472 q^{15} -4.53418 q^{16} +1.08385 q^{17} -3.82643 q^{18} +2.60223 q^{19} -1.68251 q^{20} -1.91443 q^{21} -2.60847 q^{22} +1.36154 q^{24} +1.00000 q^{25} +7.11226 q^{26} -2.24816 q^{27} -1.44136 q^{28} -9.21258 q^{29} +4.28840 q^{30} +3.31499 q^{31} +7.48251 q^{32} +3.03765 q^{33} -2.07990 q^{34} +0.856675 q^{35} +3.35489 q^{36} +10.2432 q^{37} -4.99364 q^{38} -8.28246 q^{39} -0.609264 q^{40} -10.2850 q^{41} +3.67376 q^{42} -11.2047 q^{43} +2.28702 q^{44} -1.99398 q^{45} -1.15400 q^{47} -10.1326 q^{48} -6.26611 q^{49} -1.91899 q^{50} +2.42211 q^{51} -6.23581 q^{52} +5.25336 q^{53} +4.31420 q^{54} -1.35929 q^{55} -0.521941 q^{56} +5.81526 q^{57} +17.6788 q^{58} +4.01155 q^{59} -3.75994 q^{60} +8.59646 q^{61} -6.36142 q^{62} -1.70820 q^{63} -5.29046 q^{64} +3.70626 q^{65} -5.82920 q^{66} +5.67112 q^{67} +1.82359 q^{68} -1.64395 q^{70} +5.89785 q^{71} +1.21486 q^{72} -14.2223 q^{73} -19.6565 q^{74} +2.23472 q^{75} +4.37827 q^{76} -1.16447 q^{77} +15.8939 q^{78} -13.5878 q^{79} +4.53418 q^{80} -11.0060 q^{81} +19.7368 q^{82} -9.00151 q^{83} -3.22104 q^{84} -1.08385 q^{85} +21.5017 q^{86} -20.5876 q^{87} +0.828170 q^{88} -1.41667 q^{89} +3.82643 q^{90} +3.17506 q^{91} +7.40808 q^{93} +2.21450 q^{94} -2.60223 q^{95} +16.7213 q^{96} -6.89830 q^{97} +12.0246 q^{98} +2.71041 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 2 q^{2} - 5 q^{3} - 2 q^{4} - 10 q^{5} + q^{6} + 9 q^{7} + 19 q^{9}+O(q^{10}) $ 10 * q - 2 * q^2 - 5 * q^3 - 2 * q^4 - 10 * q^5 + q^6 + 9 * q^7 + 19 * q^9	$ 10 q - 2 q^{2} - 5 q^{3} - 2 q^{4} - 10 q^{5} + q^{6} + 9 q^{7} + 19 q^{9} + 2 q^{10} - 4 q^{11} + q^{12} - 17 q^{13} - 4 q^{14} + 5 q^{15} - 18 q^{16} + 12 q^{17} - 17 q^{18} + q^{19} + 2 q^{20} - 4 q^{21} + 3 q^{22} + 10 q^{25} + 10 q^{26} - 41 q^{27} - 4 q^{28} - 16 q^{29} - q^{30} - 28 q^{31} + 8 q^{32} + 25 q^{33} - 9 q^{34} - 9 q^{35} + 5 q^{36} + 2 q^{37} + 24 q^{38} - 15 q^{39} - 6 q^{41} + 25 q^{42} - 21 q^{43} + 3 q^{44} - 19 q^{45} - q^{47} + 9 q^{48} + 13 q^{49} - 2 q^{50} - 52 q^{51} + 10 q^{52} + 3 q^{53} + 28 q^{54} + 4 q^{55} + 22 q^{57} + 12 q^{58} - 40 q^{59} - q^{60} - q^{61} - 12 q^{62} + 21 q^{63} + 8 q^{64} + 17 q^{65} - 49 q^{66} + 34 q^{67} + 13 q^{68} + 4 q^{70} - 37 q^{71} - 41 q^{73} - 18 q^{74} - 5 q^{75} + 2 q^{76} - 21 q^{77} - 30 q^{78} + 8 q^{79} + 18 q^{80} - 38 q^{81} + 21 q^{82} + 17 q^{83} + 3 q^{84} - 12 q^{85} - 9 q^{86} - 15 q^{87} - 11 q^{88} + 3 q^{89} + 17 q^{90} - 42 q^{91} + 14 q^{93} + 9 q^{94} - q^{95} - 4 q^{96} - 46 q^{97} - 40 q^{98} - 24 q^{99}+O(q^{100}) $ 10 * q - 2 * q^2 - 5 * q^3 - 2 * q^4 - 10 * q^5 + q^6 + 9 * q^7 + 19 * q^9 + 2 * q^10 - 4 * q^11 + q^12 - 17 * q^13 - 4 * q^14 + 5 * q^15 - 18 * q^16 + 12 * q^17 - 17 * q^18 + q^19 + 2 * q^20 - 4 * q^21 + 3 * q^22 + 10 * q^25 + 10 * q^26 - 41 * q^27 - 4 * q^28 - 16 * q^29 - q^30 - 28 * q^31 + 8 * q^32 + 25 * q^33 - 9 * q^34 - 9 * q^35 + 5 * q^36 + 2 * q^37 + 24 * q^38 - 15 * q^39 - 6 * q^41 + 25 * q^42 - 21 * q^43 + 3 * q^44 - 19 * q^45 - q^47 + 9 * q^48 + 13 * q^49 - 2 * q^50 - 52 * q^51 + 10 * q^52 + 3 * q^53 + 28 * q^54 + 4 * q^55 + 22 * q^57 + 12 * q^58 - 40 * q^59 - q^60 - q^61 - 12 * q^62 + 21 * q^63 + 8 * q^64 + 17 * q^65 - 49 * q^66 + 34 * q^67 + 13 * q^68 + 4 * q^70 - 37 * q^71 - 41 * q^73 - 18 * q^74 - 5 * q^75 + 2 * q^76 - 21 * q^77 - 30 * q^78 + 8 * q^79 + 18 * q^80 - 38 * q^81 + 21 * q^82 + 17 * q^83 + 3 * q^84 - 12 * q^85 - 9 * q^86 - 15 * q^87 - 11 * q^88 + 3 * q^89 + 17 * q^90 - 42 * q^91 + 14 * q^93 + 9 * q^94 - q^95 - 4 * q^96 - 46 * q^97 - 40 * q^98 - 24 * 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 $

$2$	−1.91899	−1.35693	−0.678464	−	0.734634i	$-0.737354\pi$
$2$	−1.91899	−1.35693	−0.678464	+	0.734634i	$0.737354\pi$
$3$	2.23472	1.29022	0.645109	−	0.764091i	$-0.276812\pi$
$3$	2.23472	1.29022	0.645109	+	0.764091i	$0.276812\pi$
$4$	1.68251	0.841254
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−4.28840	−1.75073
$7$	−0.856675	−0.323793	−0.161896	−	0.986808i	$-0.551761\pi$
$7$	−0.856675	−0.323793	−0.161896	+	0.986808i	$0.551761\pi$
$8$	0.609264	0.215408
$9$	1.99398	0.664662
$10$	1.91899	0.606837
$11$	1.35929	0.409843	0.204921	−	0.978778i	$-0.434306\pi$
$11$	1.35929	0.409843	0.204921	+	0.978778i	$0.434306\pi$
$12$	3.75994	1.08540
$13$	−3.70626	−1.02793	−0.513965	−	0.857811i	$-0.671824\pi$
$13$	−3.70626	−1.02793	−0.513965	+	0.857811i	$0.671824\pi$
$14$	1.64395	0.439363
$15$	−2.23472	−0.577003
$16$	−4.53418	−1.13355
$17$	1.08385	0.262873	0.131436	−	0.991325i	$-0.458041\pi$
$17$	1.08385	0.262873	0.131436	+	0.991325i	$0.458041\pi$
$18$	−3.82643	−0.901898
$19$	2.60223	0.596992	0.298496	−	0.954411i	$-0.403515\pi$
$19$	2.60223	0.596992	0.298496	+	0.954411i	$0.403515\pi$
$20$	−1.68251	−0.376220
$21$	−1.91443	−0.417763
$22$	−2.60847	−0.556127
$23$	0	0
$23$	0	0
$24$	1.36154	0.277923
$25$	1.00000	0.200000
$26$	7.11226	1.39483
$27$	−2.24816	−0.432659
$28$	−1.44136	−0.272392
$29$	−9.21258	−1.71073	−0.855366	−	0.518024i	$-0.826668\pi$
$29$	−9.21258	−1.71073	−0.855366	+	0.518024i	$0.826668\pi$
$30$	4.28840	0.782951
$31$	3.31499	0.595390	0.297695	−	0.954661i	$-0.403782\pi$
$31$	3.31499	0.595390	0.297695	+	0.954661i	$0.403782\pi$
$32$	7.48251	1.32273
$33$	3.03765	0.528786
$34$	−2.07990	−0.356700
$35$	0.856675	0.144804
$36$	3.35489	0.559149
$37$	10.2432	1.68397	0.841986	−	0.539500i	$-0.181387\pi$
$37$	10.2432	1.68397	0.841986	+	0.539500i	$0.181387\pi$
$38$	−4.99364	−0.810076
$39$	−8.28246	−1.32625
$40$	−0.609264	−0.0963332
$41$	−10.2850	−1.60625	−0.803123	−	0.595813i	$-0.796830\pi$
$41$	−10.2850	−1.60625	−0.803123	+	0.595813i	$0.796830\pi$
$42$	3.67376	0.566874
$43$	−11.2047	−1.70871	−0.854353	−	0.519693i	$-0.826046\pi$
$43$	−11.2047	−1.70871	−0.854353	+	0.519693i	$0.826046\pi$
$44$	2.28702	0.344782
$45$	−1.99398	−0.297246
$46$	0	0
$47$	−1.15400	−0.168328	−0.0841639	−	0.996452i	$-0.526822\pi$
$47$	−1.15400	−0.168328	−0.0841639	+	0.996452i	$0.526822\pi$
$48$	−10.1326	−1.46252
$49$	−6.26611	−0.895158
$50$	−1.91899	−0.271386
$51$	2.42211	0.339163
$52$	−6.23581	−0.864751
$53$	5.25336	0.721605	0.360802	−	0.932642i	$-0.382503\pi$
$53$	5.25336	0.721605	0.360802	+	0.932642i	$0.382503\pi$
$54$	4.31420	0.587088
$55$	−1.35929	−0.183287
$56$	−0.521941	−0.0697474
$57$	5.81526	0.770250
$58$	17.6788	2.32134
$59$	4.01155	0.522259	0.261129	−	0.965304i	$-0.415905\pi$
$59$	4.01155	0.522259	0.261129	+	0.965304i	$0.415905\pi$
$60$	−3.75994	−0.485406
$61$	8.59646	1.10066	0.550332	−	0.834946i	$-0.314501\pi$
$61$	8.59646	1.10066	0.550332	+	0.834946i	$0.314501\pi$
$62$	−6.36142	−0.807901
$63$	−1.70820	−0.215212
$64$	−5.29046	−0.661307
$65$	3.70626	0.459705
$66$	−5.82920	−0.717525
$67$	5.67112	0.692837	0.346419	−	0.938080i	$-0.387398\pi$
$67$	5.67112	0.692837	0.346419	+	0.938080i	$0.387398\pi$
$68$	1.82359	0.221143
$69$	0	0
$70$	−1.64395	−0.196489
$71$	5.89785	0.699946	0.349973	−	0.936760i	$-0.386191\pi$
$71$	5.89785	0.699946	0.349973	+	0.936760i	$0.386191\pi$
$72$	1.21486	0.143173
$73$	−14.2223	−1.66459	−0.832295	−	0.554333i	$-0.812974\pi$
$73$	−14.2223	−1.66459	−0.832295	+	0.554333i	$0.812974\pi$
$74$	−19.6565	−2.28503
$75$	2.23472	0.258044
$76$	4.37827	0.502222
$77$	−1.16447	−0.132704
$78$	15.8939	1.79963
$79$	−13.5878	−1.52875	−0.764376	−	0.644771i	$-0.776953\pi$
$79$	−13.5878	−1.52875	−0.764376	+	0.644771i	$0.776953\pi$
$80$	4.53418	0.506937
$81$	−11.0060	−1.22289
$82$	19.7368	2.17956
$83$	−9.00151	−0.988044	−0.494022	−	0.869449i	$-0.664474\pi$
$83$	−9.00151	−0.988044	−0.494022	+	0.869449i	$0.664474\pi$
$84$	−3.22104	−0.351445
$85$	−1.08385	−0.117560
$86$	21.5017	2.31859
$87$	−20.5876	−2.20722
$88$	0.828170	0.0882832
$89$	−1.41667	−0.150167	−0.0750834	−	0.997177i	$-0.523922\pi$
$89$	−1.41667	−0.150167	−0.0750834	+	0.997177i	$0.523922\pi$
$90$	3.82643	0.403341
$91$	3.17506	0.332836
$92$	0	0
$93$	7.40808	0.768183
$94$	2.21450	0.228409
$95$	−2.60223	−0.266983
$96$	16.7213	1.70661
$97$	−6.89830	−0.700416	−0.350208	−	0.936672i	$-0.613889\pi$
$97$	−6.89830	−0.700416	−0.350208	+	0.936672i	$0.613889\pi$
$98$	12.0246	1.21467
$99$	2.71041	0.272407
$100$	1.68251	0.168251
$101$	−2.63779	−0.262470	−0.131235	−	0.991351i	$-0.541894\pi$
$101$	−2.63779	−0.262470	−0.131235	+	0.991351i	$0.541894\pi$
$102$	−4.64800	−0.460220
$103$	−11.0900	−1.09273	−0.546366	−	0.837546i	$-0.683989\pi$
$103$	−11.0900	−1.09273	−0.546366	+	0.837546i	$0.683989\pi$
$104$	−2.25809	−0.221424
$105$	1.91443	0.186829
$106$	−10.0811	−0.979166
$107$	15.7763	1.52515	0.762577	−	0.646898i	$-0.223934\pi$
$107$	15.7763	1.52515	0.762577	+	0.646898i	$0.223934\pi$
$108$	−3.78255	−0.363976
$109$	−2.18221	−0.209017	−0.104509	−	0.994524i	$-0.533327\pi$
$109$	−2.18221	−0.209017	−0.104509	+	0.994524i	$0.533327\pi$
$110$	2.60847	0.248708
$111$	22.8907	2.17269
$112$	3.88432	0.367034
$113$	−7.48210	−0.703856	−0.351928	−	0.936027i	$-0.614474\pi$
$113$	−7.48210	−0.703856	−0.351928	+	0.936027i	$0.614474\pi$
$114$	−11.1594	−1.04517
$115$	0	0
$116$	−15.5002	−1.43916
$117$	−7.39022	−0.683226
$118$	−7.69810	−0.708668
$119$	−0.928509	−0.0851163
$120$	−1.36154	−0.124291
$121$	−9.15232	−0.832029
$122$	−16.4965	−1.49352
$123$	−22.9841	−2.07241
$124$	5.57750	0.500874
$125$	−1.00000	−0.0894427
$126$	3.27800	0.292028
$127$	0.197682	0.0175415	0.00877074	−	0.999962i	$-0.497208\pi$
$127$	0.197682	0.0175415	0.00877074	+	0.999962i	$0.497208\pi$
$128$	−4.81270	−0.425387
$129$	−25.0395	−2.20460
$130$	−7.11226	−0.623786
$131$	7.23872	0.632450	0.316225	−	0.948684i	$-0.397585\pi$
$131$	7.23872	0.632450	0.316225	+	0.948684i	$0.397585\pi$
$132$	5.11086	0.444843
$133$	−2.22926	−0.193302
$134$	−10.8828	−0.940131
$135$	2.24816	0.193491
$136$	0.660353	0.0566248
$137$	−12.1452	−1.03764	−0.518819	−	0.854884i	$-0.673628\pi$
$137$	−12.1452	−1.03764	−0.518819	+	0.854884i	$0.673628\pi$
$138$	0	0
$139$	−7.21823	−0.612242	−0.306121	−	0.951993i	$-0.599031\pi$
$139$	−7.21823	−0.612242	−0.306121	+	0.951993i	$0.599031\pi$
$140$	1.44136	0.121817
$141$	−2.57886	−0.217180
$142$	−11.3179	−0.949776
$143$	−5.03790	−0.421290
$144$	−9.04109	−0.753425
$145$	9.21258	0.765063
$146$	27.2923	2.25873
$147$	−14.0030	−1.15495
$148$	17.2342	1.41665
$149$	−13.1728	−1.07916	−0.539578	−	0.841935i	$-0.681416\pi$
$149$	−13.1728	−1.07916	−0.539578	+	0.841935i	$0.681416\pi$
$150$	−4.28840	−0.350146
$151$	−11.3404	−0.922872	−0.461436	−	0.887174i	$-0.652666\pi$
$151$	−11.3404	−0.922872	−0.461436	+	0.887174i	$0.652666\pi$
$152$	1.58545	0.128597
$153$	2.16119	0.174722
$154$	2.23461	0.180070
$155$	−3.31499	−0.266266
$156$	−13.9353	−1.11572
$157$	7.59488	0.606138	0.303069	−	0.952969i	$-0.401989\pi$
$157$	7.59488	0.606138	0.303069	+	0.952969i	$0.401989\pi$
$158$	26.0749	2.07441
$159$	11.7398	0.931027
$160$	−7.48251	−0.591544
$161$	0	0
$162$	21.1203	1.65937
$163$	−1.67640	−0.131306	−0.0656530	−	0.997843i	$-0.520913\pi$
$163$	−1.67640	−0.131306	−0.0656530	+	0.997843i	$0.520913\pi$
$164$	−17.3046	−1.35126
$165$	−3.03765	−0.236480
$166$	17.2738	1.34071
$167$	11.8195	0.914618	0.457309	−	0.889308i	$-0.348813\pi$
$167$	11.8195	0.914618	0.457309	+	0.889308i	$0.348813\pi$
$168$	−1.16639	−0.0899893
$169$	0.736347	0.0566421
$170$	2.07990	0.159521
$171$	5.18881	0.396798
$172$	−18.8521	−1.43746
$173$	17.6187	1.33952	0.669762	−	0.742576i	$-0.266396\pi$
$173$	17.6187	1.33952	0.669762	+	0.742576i	$0.266396\pi$
$174$	39.5072	2.99503
$175$	−0.856675	−0.0647585
$176$	−6.16329	−0.464576
$177$	8.96469	0.673828
$178$	2.71857	0.203766
$179$	19.3014	1.44266	0.721329	−	0.692593i	$-0.243532\pi$
$179$	19.3014	1.44266	0.721329	+	0.692593i	$0.243532\pi$
$180$	−3.35489	−0.250059
$181$	1.71741	0.127654	0.0638272	−	0.997961i	$-0.479669\pi$
$181$	1.71741	0.127654	0.0638272	+	0.997961i	$0.479669\pi$
$182$	−6.09289	−0.451635
$183$	19.2107	1.42010
$184$	0	0
$185$	−10.2432	−0.753095
$186$	−14.2160	−1.04237
$187$	1.47328	0.107737
$188$	−1.94161	−0.141606
$189$	1.92595	0.140092
$190$	4.99364	0.362277
$191$	−11.1167	−0.804373	−0.402187	−	0.915558i	$-0.631750\pi$
$191$	−11.1167	−0.804373	−0.402187	+	0.915558i	$0.631750\pi$
$192$	−11.8227	−0.853230
$193$	−11.7457	−0.845477	−0.422738	−	0.906252i	$-0.638931\pi$
$193$	−11.7457	−0.845477	−0.422738	+	0.906252i	$0.638931\pi$
$194$	13.2377	0.950414
$195$	8.28246	0.593119
$196$	−10.5428	−0.753055
$197$	6.67144	0.475320	0.237660	−	0.971348i	$-0.423620\pi$
$197$	6.67144	0.475320	0.237660	+	0.971348i	$0.423620\pi$
$198$	−5.20124	−0.369636
$199$	−4.85104	−0.343881	−0.171941	−	0.985107i	$-0.555004\pi$
$199$	−4.85104	−0.343881	−0.171941	+	0.985107i	$0.555004\pi$
$200$	0.609264	0.0430815
$201$	12.6734	0.893911
$202$	5.06187	0.356152
$203$	7.89218	0.553922
$204$	4.07522	0.285322
$205$	10.2850	0.718335
$206$	21.2816	1.48276
$207$	0	0
$208$	16.8049	1.16521
$209$	3.53720	0.244673
$210$	−3.67376	−0.253514
$211$	5.84576	0.402439	0.201219	−	0.979546i	$-0.435510\pi$
$211$	5.84576	0.402439	0.201219	+	0.979546i	$0.435510\pi$
$212$	8.83882	0.607053
$213$	13.1801	0.903082
$214$	−30.2745	−2.06952
$215$	11.2047	0.764157
$216$	−1.36973	−0.0931981
$217$	−2.83987	−0.192783
$218$	4.18762	0.283622
$219$	−31.7828	−2.14768
$220$	−2.28702	−0.154191
$221$	−4.01704	−0.270215
$222$	−43.9269	−2.94818
$223$	−10.1324	−0.678514	−0.339257	−	0.940694i	$-0.610176\pi$
$223$	−10.1324	−0.678514	−0.339257	+	0.940694i	$0.610176\pi$
$224$	−6.41007	−0.428291
$225$	1.99398	0.132932
$226$	14.3580	0.955083
$227$	19.6842	1.30649	0.653245	−	0.757147i	$-0.273407\pi$
$227$	19.6842	1.30649	0.653245	+	0.757147i	$0.273407\pi$
$228$	9.78422	0.647976
$229$	−26.1967	−1.73113	−0.865563	−	0.500801i	$-0.833039\pi$
$229$	−26.1967	−1.73113	−0.865563	+	0.500801i	$0.833039\pi$
$230$	0	0
$231$	−2.60227	−0.171217
$232$	−5.61290	−0.368505
$233$	1.23257	0.0807481	0.0403740	−	0.999185i	$-0.487145\pi$
$233$	1.23257	0.0807481	0.0403740	+	0.999185i	$0.487145\pi$
$234$	14.1817	0.927089
$235$	1.15400	0.0752785
$236$	6.74946	0.439352
$237$	−30.3651	−1.97242
$238$	1.78180	0.115497
$239$	8.71086	0.563459	0.281729	−	0.959494i	$-0.409092\pi$
$239$	8.71086	0.563459	0.281729	+	0.959494i	$0.409092\pi$
$240$	10.1326	0.654059
$241$	−5.61182	−0.361489	−0.180744	−	0.983530i	$-0.557851\pi$
$241$	−5.61182	−0.361489	−0.180744	+	0.983530i	$0.557851\pi$
$242$	17.5632	1.12900
$243$	−17.8508	−1.14513
$244$	14.4636	0.925938
$245$	6.26611	0.400327
$246$	44.1062	2.81211
$247$	−9.64453	−0.613667
$248$	2.01971	0.128251
$249$	−20.1159	−1.27479
$250$	1.91899	0.121367
$251$	−14.0394	−0.886156	−0.443078	−	0.896483i	$-0.646114\pi$
$251$	−14.0394	−0.886156	−0.443078	+	0.896483i	$0.646114\pi$
$252$	−2.87405	−0.181048
$253$	0	0
$254$	−0.379350	−0.0238025
$255$	−2.42211	−0.151678
$256$	19.8164	1.23853
$257$	−9.95527	−0.620992	−0.310496	−	0.950575i	$-0.600495\pi$
$257$	−9.95527	−0.620992	−0.310496	+	0.950575i	$0.600495\pi$
$258$	48.0504	2.99149
$259$	−8.77509	−0.545257
$260$	6.23581	0.386728
$261$	−18.3697	−1.13706
$262$	−13.8910	−0.858189
$263$	25.9402	1.59954	0.799770	−	0.600306i	$-0.204955\pi$
$263$	25.9402	1.59954	0.799770	+	0.600306i	$0.204955\pi$
$264$	1.85073	0.113905
$265$	−5.25336	−0.322711
$266$	4.27793	0.262296
$267$	−3.16587	−0.193748
$268$	9.54170	0.582852
$269$	−3.79380	−0.231312	−0.115656	−	0.993289i	$-0.536897\pi$
$269$	−3.79380	−0.231312	−0.115656	+	0.993289i	$0.536897\pi$
$270$	−4.31420	−0.262554
$271$	−5.02775	−0.305414	−0.152707	−	0.988272i	$-0.548799\pi$
$271$	−5.02775	−0.305414	−0.152707	+	0.988272i	$0.548799\pi$
$272$	−4.91439	−0.297979
$273$	7.09537	0.429431
$274$	23.3065	1.40800
$275$	1.35929	0.0819686
$276$	0	0
$277$	−28.7588	−1.72795	−0.863975	−	0.503535i	$-0.832032\pi$
$277$	−28.7588	−1.72795	−0.863975	+	0.503535i	$0.832032\pi$
$278$	13.8517	0.830769
$279$	6.61004	0.395733
$280$	0.521941	0.0311920
$281$	−22.9917	−1.37157	−0.685785	−	0.727804i	$-0.740541\pi$
$281$	−22.9917	−1.37157	−0.685785	+	0.727804i	$0.740541\pi$
$282$	4.94880	0.294697
$283$	−14.4862	−0.861112	−0.430556	−	0.902564i	$-0.641683\pi$
$283$	−14.4862	−0.861112	−0.430556	+	0.902564i	$0.641683\pi$
$284$	9.92317	0.588832
$285$	−5.81526	−0.344466
$286$	9.66765	0.571660
$287$	8.81090	0.520091
$288$	14.9200	0.879170
$289$	−15.8253	−0.930898
$290$	−17.6788	−1.03814
$291$	−15.4158	−0.903689
$292$	−23.9291	−1.40034
$293$	34.0730	1.99057	0.995283	−	0.0970188i	$-0.0309307\pi$
$293$	34.0730	1.99057	0.995283	+	0.0970188i	$0.0309307\pi$
$294$	26.8716	1.56718
$295$	−4.01155	−0.233561
$296$	6.24082	0.362740
$297$	−3.05592	−0.177322
$298$	25.2784	1.46434
$299$	0	0
$300$	3.75994	0.217080
$301$	9.59881	0.553266
$302$	21.7621	1.25227
$303$	−5.89472	−0.338643
$304$	−11.7990	−0.676718
$305$	−8.59646	−0.492232
$306$	−4.14729	−0.237085
$307$	−12.7963	−0.730325	−0.365163	−	0.930944i	$-0.618987\pi$
$307$	−12.7963	−0.730325	−0.365163	+	0.930944i	$0.618987\pi$
$308$	−1.95923	−0.111638
$309$	−24.7831	−1.40986
$310$	6.36142	0.361304
$311$	7.87598	0.446606	0.223303	−	0.974749i	$-0.428316\pi$
$311$	7.87598	0.446606	0.223303	+	0.974749i	$0.428316\pi$
$312$	−5.04621	−0.285685
$313$	7.90746	0.446956	0.223478	−	0.974709i	$-0.428259\pi$
$313$	7.90746	0.446956	0.223478	+	0.974709i	$0.428259\pi$
$314$	−14.5745	−0.822485
$315$	1.70820	0.0962460
$316$	−22.8616	−1.28607
$317$	10.8809	0.611134	0.305567	−	0.952171i	$-0.401154\pi$
$317$	10.8809	0.611134	0.305567	+	0.952171i	$0.401154\pi$
$318$	−22.5285	−1.26334
$319$	−12.5226	−0.701131
$320$	5.29046	0.295746
$321$	35.2557	1.96778
$322$	0	0
$323$	2.82043	0.156933
$324$	−18.5176	−1.02876
$325$	−3.70626	−0.205586
$326$	3.21699	0.178173
$327$	−4.87663	−0.269678
$328$	−6.26628	−0.345998
$329$	0.988600	0.0545033
$330$	5.82920	0.320887
$331$	−30.8140	−1.69369	−0.846847	−	0.531837i	$-0.821502\pi$
$331$	−30.8140	−1.69369	−0.846847	+	0.531837i	$0.821502\pi$
$332$	−15.1451	−0.831196
$333$	20.4248	1.11927
$334$	−22.6814	−1.24107
$335$	−5.67112	−0.309846
$336$	8.68038	0.473553
$337$	30.4353	1.65792	0.828959	−	0.559309i	$-0.188934\pi$
$337$	30.4353	1.65792	0.828959	+	0.559309i	$0.188934\pi$
$338$	−1.41304	−0.0768593
$339$	−16.7204	−0.908128
$340$	−1.82359	−0.0988981
$341$	4.50605	0.244016
$342$	−9.95725	−0.538426
$343$	11.3647	0.613638
$344$	−6.82665	−0.368068
$345$	0	0
$346$	−33.8100	−1.81764
$347$	−18.9273	−1.01607	−0.508034	−	0.861337i	$-0.669628\pi$
$347$	−18.9273	−1.01607	−0.508034	+	0.861337i	$0.669628\pi$
$348$	−34.6387	−1.85683
$349$	−34.8245	−1.86412	−0.932058	−	0.362310i	$-0.881988\pi$
$349$	−34.8245	−1.86412	−0.932058	+	0.362310i	$0.881988\pi$
$350$	1.64395	0.0878726
$351$	8.33228	0.444744
$352$	10.1709	0.542112
$353$	−19.1478	−1.01913	−0.509567	−	0.860431i	$-0.670194\pi$
$353$	−19.1478	−1.01913	−0.509567	+	0.860431i	$0.670194\pi$
$354$	−17.2031	−0.914336
$355$	−5.89785	−0.313025
$356$	−2.38356	−0.126328
$357$	−2.07496	−0.109819
$358$	−37.0392	−1.95758
$359$	−31.2032	−1.64684	−0.823421	−	0.567430i	$-0.807938\pi$
$359$	−31.2032	−1.64684	−0.823421	+	0.567430i	$0.807938\pi$
$360$	−1.21486	−0.0640290
$361$	−12.2284	−0.643600
$362$	−3.29569	−0.173218
$363$	−20.4529	−1.07350
$364$	5.34206	0.280000
$365$	14.2223	0.744427
$366$	−36.8651	−1.92697
$367$	30.9084	1.61340	0.806702	−	0.590958i	$-0.201250\pi$
$367$	30.9084	1.61340	0.806702	+	0.590958i	$0.201250\pi$
$368$	0	0
$369$	−20.5081	−1.06761
$370$	19.6565	1.02190
$371$	−4.50042	−0.233650
$372$	12.4642	0.646236
$373$	−0.282768	−0.0146411	−0.00732057	−	0.999973i	$-0.502330\pi$
$373$	−0.282768	−0.0146411	−0.00732057	+	0.999973i	$0.502330\pi$
$374$	−2.82719	−0.146191
$375$	−2.23472	−0.115401
$376$	−0.703090	−0.0362591
$377$	34.1442	1.75851
$378$	−3.69586	−0.190095
$379$	1.51561	0.0778519	0.0389259	−	0.999242i	$-0.487606\pi$
$379$	1.51561	0.0778519	0.0389259	+	0.999242i	$0.487606\pi$
$380$	−4.37827	−0.224600
$381$	0.441765	0.0226323
$382$	21.3327	1.09148
$383$	32.6210	1.66686	0.833429	−	0.552627i	$-0.186375\pi$
$383$	32.6210	1.66686	0.833429	+	0.552627i	$0.186375\pi$
$384$	−10.7551	−0.548841
$385$	1.16447	0.0593471
$386$	22.5399	1.14725
$387$	−22.3421	−1.13571
$388$	−11.6064	−0.589228
$389$	−3.82954	−0.194165	−0.0970827	−	0.995276i	$-0.530951\pi$
$389$	−3.82954	−0.194165	−0.0970827	+	0.995276i	$0.530951\pi$
$390$	−15.8939	−0.804820
$391$	0	0
$392$	−3.81772	−0.192824
$393$	16.1765	0.815998
$394$	−12.8024	−0.644975
$395$	13.5878	0.683678
$396$	4.56029	0.229163
$397$	−1.13061	−0.0567435	−0.0283717	−	0.999597i	$-0.509032\pi$
$397$	−1.13061	−0.0567435	−0.0283717	+	0.999597i	$0.509032\pi$
$398$	9.30908	0.466622
$399$	−4.98179	−0.249401
$400$	−4.53418	−0.226709
$401$	−5.81333	−0.290304	−0.145152	−	0.989409i	$-0.546367\pi$
$401$	−5.81333	−0.290304	−0.145152	+	0.989409i	$0.546367\pi$
$402$	−24.3200	−1.21297
$403$	−12.2862	−0.612020
$404$	−4.43809	−0.220803
$405$	11.0060	0.546891
$406$	−15.1450	−0.751633
$407$	13.9235	0.690163
$408$	1.47571	0.0730583
$409$	10.7847	0.533271	0.266635	−	0.963797i	$-0.414088\pi$
$409$	10.7847	0.533271	0.266635	+	0.963797i	$0.414088\pi$
$410$	−19.7368	−0.974730
$411$	−27.1412	−1.33878
$412$	−18.6590	−0.919265
$413$	−3.43659	−0.169104
$414$	0	0
$415$	9.00151	0.441867
$416$	−27.7321	−1.35968
$417$	−16.1307	−0.789926
$418$	−6.78783	−0.332004
$419$	−20.4484	−0.998969	−0.499484	−	0.866323i	$-0.666477\pi$
$419$	−20.4484	−0.998969	−0.499484	+	0.866323i	$0.666477\pi$
$420$	3.22104	0.157171
$421$	34.1378	1.66378	0.831888	−	0.554943i	$-0.187260\pi$
$421$	34.1378	1.66378	0.831888	+	0.554943i	$0.187260\pi$
$422$	−11.2179	−0.546080
$423$	−2.30105	−0.111881
$424$	3.20069	0.155439
$425$	1.08385	0.0525746
$426$	−25.2923	−1.22542
$427$	−7.36437	−0.356387
$428$	26.5437	1.28304
$429$	−11.2583	−0.543556
$430$	−21.5017	−1.03691
$431$	−11.2154	−0.540229	−0.270114	−	0.962828i	$-0.587062\pi$
$431$	−11.2154	−0.540229	−0.270114	+	0.962828i	$0.587062\pi$
$432$	10.1936	0.490439
$433$	−30.2222	−1.45239	−0.726194	−	0.687490i	$-0.758713\pi$
$433$	−30.2222	−1.45239	−0.726194	+	0.687490i	$0.758713\pi$
$434$	5.44967	0.261592
$435$	20.5876	0.987098
$436$	−3.67158	−0.175837
$437$	0	0
$438$	60.9908	2.91425
$439$	3.70814	0.176980	0.0884899	−	0.996077i	$-0.471796\pi$
$439$	3.70814	0.176980	0.0884899	+	0.996077i	$0.471796\pi$
$440$	−0.828170	−0.0394815
$441$	−12.4945	−0.594977
$442$	7.70864	0.366663
$443$	29.3087	1.39250	0.696249	−	0.717800i	$-0.254851\pi$
$443$	29.3087	1.39250	0.696249	+	0.717800i	$0.254851\pi$
$444$	38.5138	1.82778
$445$	1.41667	0.0671566
$446$	19.4439	0.920694
$447$	−29.4375	−1.39235
$448$	4.53220	0.214126
$449$	22.1291	1.04434	0.522169	−	0.852842i	$-0.325123\pi$
$449$	22.1291	1.04434	0.522169	+	0.852842i	$0.325123\pi$
$450$	−3.82643	−0.180380
$451$	−13.9803	−0.658309
$452$	−12.5887	−0.592122
$453$	−25.3427	−1.19071
$454$	−37.7738	−1.77281
$455$	−3.17506	−0.148849
$456$	3.54303	0.165918
$457$	−10.2800	−0.480879	−0.240440	−	0.970664i	$-0.577292\pi$
$457$	−10.2800	−0.480879	−0.240440	+	0.970664i	$0.577292\pi$
$458$	50.2711	2.34901
$459$	−2.43668	−0.113734
$460$	0	0
$461$	−21.0411	−0.979981	−0.489991	−	0.871728i	$-0.663000\pi$
$461$	−21.0411	−0.979981	−0.489991	+	0.871728i	$0.663000\pi$
$462$	4.99373	0.232329
$463$	1.01012	0.0469442	0.0234721	−	0.999724i	$-0.492528\pi$
$463$	1.01012	0.0469442	0.0234721	+	0.999724i	$0.492528\pi$
$464$	41.7715	1.93919
$465$	−7.40808	−0.343542
$466$	−2.36528	−0.109569
$467$	20.1840	0.934006	0.467003	−	0.884256i	$-0.345334\pi$
$467$	20.1840	0.934006	0.467003	+	0.884256i	$0.345334\pi$
$468$	−12.4341	−0.574767
$469$	−4.85830	−0.224336
$470$	−2.21450	−0.102147
$471$	16.9725	0.782049
$472$	2.44409	0.112498
$473$	−15.2305	−0.700301
$474$	58.2701	2.67643
$475$	2.60223	0.119398
$476$	−1.56222	−0.0716044
$477$	10.4751	0.479623
$478$	−16.7160	−0.764573
$479$	2.56293	0.117103	0.0585517	−	0.998284i	$-0.481352\pi$
$479$	2.56293	0.117103	0.0585517	+	0.998284i	$0.481352\pi$
$480$	−16.7213	−0.763221
$481$	−37.9639	−1.73101
$482$	10.7690	0.490514
$483$	0	0
$484$	−15.3988	−0.699947
$485$	6.89830	0.313236
$486$	34.2555	1.55386
$487$	24.5376	1.11191	0.555953	−	0.831214i	$-0.312354\pi$
$487$	24.5376	1.11191	0.555953	+	0.831214i	$0.312354\pi$
$488$	5.23752	0.237091
$489$	−3.74630	−0.169413
$490$	−12.0246	−0.543215
$491$	−33.1883	−1.49777	−0.748884	−	0.662701i	$-0.769410\pi$
$491$	−33.1883	−1.49777	−0.748884	+	0.662701i	$0.769410\pi$
$492$	−38.6709	−1.74342
$493$	−9.98508	−0.449705
$494$	18.5077	0.832702
$495$	−2.71041	−0.121824
$496$	−15.0308	−0.674902
$497$	−5.05254	−0.226637
$498$	38.6021	1.72980
$499$	15.3500	0.687162	0.343581	−	0.939123i	$-0.388360\pi$
$499$	15.3500	0.687162	0.343581	+	0.939123i	$0.388360\pi$
$500$	−1.68251	−0.0752440
$501$	26.4132	1.18006
$502$	26.9413	1.20245
$503$	−13.3657	−0.595948	−0.297974	−	0.954574i	$-0.596311\pi$
$503$	−13.3657	−0.595948	−0.297974	+	0.954574i	$0.596311\pi$
$504$	−1.04074	−0.0463584
$505$	2.63779	0.117380
$506$	0	0
$507$	1.64553	0.0730806
$508$	0.332602	0.0147568
$509$	1.20496	0.0534088	0.0267044	−	0.999643i	$-0.491499\pi$
$509$	1.20496	0.0534088	0.0267044	+	0.999643i	$0.491499\pi$
$510$	4.64800	0.205817
$511$	12.1839	0.538982
$512$	−28.4020	−1.25520
$513$	−5.85024	−0.258294
$514$	19.1040	0.842642
$515$	11.0900	0.488685
$516$	−42.1291	−1.85463
$517$	−1.56862	−0.0689879
$518$	16.8393	0.739875
$519$	39.3729	1.72828
$520$	2.25809	0.0990239
$521$	−8.30860	−0.364006	−0.182003	−	0.983298i	$-0.558258\pi$
$521$	−8.30860	−0.364006	−0.182003	+	0.983298i	$0.558258\pi$
$522$	35.2513	1.54291
$523$	−14.3563	−0.627756	−0.313878	−	0.949463i	$-0.601628\pi$
$523$	−14.3563	−0.627756	−0.313878	+	0.949463i	$0.601628\pi$
$524$	12.1792	0.532051
$525$	−1.91443	−0.0835526
$526$	−49.7789	−2.17046
$527$	3.59296	0.156512
$528$	−13.7732	−0.599404
$529$	0	0
$530$	10.0811	0.437896
$531$	7.99896	0.347125
$532$	−3.75075	−0.162616
$533$	38.1189	1.65111
$534$	6.07525	0.262902
$535$	−15.7763	−0.682069
$536$	3.45521	0.149242
$537$	43.1334	1.86134
$538$	7.28025	0.313874
$539$	−8.51749	−0.366874
$540$	3.78255	0.162775
$541$	25.9615	1.11617	0.558087	−	0.829783i	$-0.311536\pi$
$541$	25.9615	1.11617	0.558087	+	0.829783i	$0.311536\pi$
$542$	9.64818	0.414425
$543$	3.83794	0.164702
$544$	8.10994	0.347711
$545$	2.18221	0.0934755
$546$	−13.6159	−0.582707
$547$	−10.1303	−0.433139	−0.216570	−	0.976267i	$-0.569487\pi$
$547$	−10.1303	−0.433139	−0.216570	+	0.976267i	$0.569487\pi$
$548$	−20.4344	−0.872916
$549$	17.1412	0.731569
$550$	−2.60847	−0.111225
$551$	−23.9732	−1.02129
$552$	0	0
$553$	11.6404	0.494998
$554$	55.1878	2.34470
$555$	−22.8907	−0.971656
$556$	−12.1447	−0.515051
$557$	−29.2269	−1.23838	−0.619192	−	0.785240i	$-0.712540\pi$
$557$	−29.2269	−1.23838	−0.619192	+	0.785240i	$0.712540\pi$
$558$	−12.6846	−0.536981
$559$	41.5277	1.75643
$560$	−3.88432	−0.164142
$561$	3.29236	0.139004
$562$	44.1208	1.86112
$563$	37.0527	1.56159	0.780793	−	0.624790i	$-0.214815\pi$
$563$	37.0527	1.56159	0.780793	+	0.624790i	$0.214815\pi$
$564$	−4.33896	−0.182703
$565$	7.48210	0.314774
$566$	27.7987	1.16847
$567$	9.42854	0.395962
$568$	3.59335	0.150774
$569$	18.1900	0.762563	0.381281	−	0.924459i	$-0.375483\pi$
$569$	18.1900	0.762563	0.381281	+	0.924459i	$0.375483\pi$
$570$	11.1594	0.467416
$571$	33.2279	1.39055	0.695273	−	0.718746i	$-0.255283\pi$
$571$	33.2279	1.39055	0.695273	+	0.718746i	$0.255283\pi$
$572$	−8.47630	−0.354412
$573$	−24.8427	−1.03782
$574$	−16.9080	−0.705726
$575$	0	0
$576$	−10.5491	−0.439545
$577$	3.37247	0.140398	0.0701990	−	0.997533i	$-0.477637\pi$
$577$	3.37247	0.140398	0.0701990	+	0.997533i	$0.477637\pi$
$578$	30.3685	1.26316
$579$	−26.2485	−1.09085
$580$	15.5002	0.643612
$581$	7.71137	0.319921
$582$	29.5827	1.22624
$583$	7.14087	0.295744
$584$	−8.66512	−0.358565
$585$	7.39022	0.305548
$586$	−65.3856	−2.70105
$587$	−23.1114	−0.953910	−0.476955	−	0.878928i	$-0.658260\pi$
$587$	−23.1114	−0.953910	−0.476955	+	0.878928i	$0.658260\pi$
$588$	−23.5602	−0.971605
$589$	8.62637	0.355443
$590$	7.69810	0.316926
$591$	14.9088	0.613266
$592$	−46.4445	−1.90886
$593$	−5.27431	−0.216590	−0.108295	−	0.994119i	$-0.534539\pi$
$593$	−5.27431	−0.216590	−0.108295	+	0.994119i	$0.534539\pi$
$594$	5.86426	0.240614
$595$	0.928509	0.0380652
$596$	−22.1633	−0.907845
$597$	−10.8407	−0.443681
$598$	0	0
$599$	34.9630	1.42855	0.714276	−	0.699865i	$-0.246756\pi$
$599$	34.9630	1.42855	0.714276	+	0.699865i	$0.246756\pi$
$600$	1.36154	0.0555845
$601$	19.3584	0.789648	0.394824	−	0.918757i	$-0.370806\pi$
$601$	19.3584	0.789648	0.394824	+	0.918757i	$0.370806\pi$
$602$	−18.4200	−0.750743
$603$	11.3081	0.460502
$604$	−19.0804	−0.776369
$605$	9.15232	0.372095
$606$	11.3119	0.459514
$607$	30.5099	1.23836	0.619180	−	0.785249i	$-0.287465\pi$
$607$	30.5099	1.23836	0.619180	+	0.785249i	$0.287465\pi$
$608$	19.4712	0.789661
$609$	17.6368	0.714681
$610$	16.4965	0.667924
$611$	4.27701	0.173029
$612$	3.63621	0.146985
$613$	42.9686	1.73549	0.867744	−	0.497012i	$-0.165570\pi$
$613$	42.9686	1.73549	0.867744	+	0.497012i	$0.165570\pi$
$614$	24.5560	0.990999
$615$	22.9841	0.926809
$616$	−0.709472	−0.0285854
$617$	−22.2943	−0.897534	−0.448767	−	0.893649i	$-0.648137\pi$
$617$	−22.2943	−0.897534	−0.448767	+	0.893649i	$0.648137\pi$
$618$	47.5585	1.91308
$619$	18.6604	0.750026	0.375013	−	0.927020i	$-0.377638\pi$
$619$	18.6604	0.750026	0.375013	+	0.927020i	$0.377638\pi$
$620$	−5.57750	−0.223998
$621$	0	0
$622$	−15.1139	−0.606012
$623$	1.21363	0.0486229
$624$	37.5542	1.50337
$625$	1.00000	0.0400000
$626$	−15.1743	−0.606487
$627$	7.90465	0.315681
$628$	12.7784	0.509915
$629$	11.1021	0.442670
$630$	−3.27800	−0.130599
$631$	−28.3494	−1.12857	−0.564285	−	0.825580i	$-0.690848\pi$
$631$	−28.3494	−1.12857	−0.564285	+	0.825580i	$0.690848\pi$
$632$	−8.27859	−0.329305
$633$	13.0636	0.519233
$634$	−20.8803	−0.829265
$635$	−0.197682	−0.00784478
$636$	19.7523	0.783230
$637$	23.2238	0.920161
$638$	24.0307	0.951385
$639$	11.7602	0.465227
$640$	4.81270	0.190239
$641$	42.9590	1.69678	0.848390	−	0.529372i	$-0.177573\pi$
$641$	42.9590	1.69678	0.848390	+	0.529372i	$0.177573\pi$
$642$	−67.6551	−2.67014
$643$	−17.3713	−0.685058	−0.342529	−	0.939507i	$-0.611283\pi$
$643$	−17.3713	−0.685058	−0.342529	+	0.939507i	$0.611283\pi$
$644$	0	0
$645$	25.0395	0.985929
$646$	−5.41237	−0.212947
$647$	37.1578	1.46082	0.730411	−	0.683008i	$-0.239329\pi$
$647$	37.1578	1.46082	0.730411	+	0.683008i	$0.239329\pi$
$648$	−6.70555	−0.263419
$649$	5.45287	0.214044
$650$	7.11226	0.278966
$651$	−6.34632	−0.248732
$652$	−2.82056	−0.110462
$653$	−3.84464	−0.150452	−0.0752261	−	0.997167i	$-0.523968\pi$
$653$	−3.84464	−0.150452	−0.0752261	+	0.997167i	$0.523968\pi$
$654$	9.35818	0.365934
$655$	−7.23872	−0.282840
$656$	46.6341	1.82075
$657$	−28.3590	−1.10639
$658$	−1.89711	−0.0739570
$659$	−20.9110	−0.814575	−0.407288	−	0.913300i	$-0.633525\pi$
$659$	−20.9110	−0.814575	−0.407288	+	0.913300i	$0.633525\pi$
$660$	−5.11086	−0.198940
$661$	11.5884	0.450736	0.225368	−	0.974274i	$-0.427642\pi$
$661$	11.5884	0.450736	0.225368	+	0.974274i	$0.427642\pi$
$662$	59.1317	2.29822
$663$	−8.97697	−0.348636
$664$	−5.48430	−0.212832
$665$	2.22926	0.0864471
$666$	−39.1949	−1.51877
$667$	0	0
$668$	19.8863	0.769425
$669$	−22.6430	−0.875430
$670$	10.8828	0.420439
$671$	11.6851	0.451099
$672$	−14.3247	−0.552589
$673$	27.4775	1.05918	0.529589	−	0.848254i	$-0.322346\pi$
$673$	27.4775	1.05918	0.529589	+	0.848254i	$0.322346\pi$
$674$	−58.4050	−2.24968
$675$	−2.24816	−0.0865319
$676$	1.23891	0.0476504
$677$	−6.24112	−0.239866	−0.119933	−	0.992782i	$-0.538268\pi$
$677$	−6.24112	−0.239866	−0.119933	+	0.992782i	$0.538268\pi$
$678$	32.0862	1.23226
$679$	5.90960	0.226790
$680$	−0.660353	−0.0253234
$681$	43.9888	1.68566
$682$	−8.64705	−0.331112
$683$	−16.0866	−0.615538	−0.307769	−	0.951461i	$-0.599582\pi$
$683$	−16.0866	−0.615538	−0.307769	+	0.951461i	$0.599582\pi$
$684$	8.73020	0.333808
$685$	12.1452	0.464046
$686$	−21.8088	−0.832663
$687$	−58.5423	−2.23353
$688$	50.8043	1.93690
$689$	−19.4703	−0.741760
$690$	0	0
$691$	51.7962	1.97042	0.985211	−	0.171347i	$-0.0548118\pi$
$691$	51.7962	1.97042	0.985211	+	0.171347i	$0.0548118\pi$
$692$	29.6436	1.12688
$693$	−2.32194	−0.0882033
$694$	36.3211	1.37873
$695$	7.21823	0.273803
$696$	−12.5433	−0.475451
$697$	−11.1474	−0.422239
$698$	66.8278	2.52947
$699$	2.75444	0.104183
$700$	−1.44136	−0.0544783
$701$	−19.9328	−0.752853	−0.376426	−	0.926447i	$-0.622847\pi$
$701$	−19.9328	−0.752853	−0.376426	+	0.926447i	$0.622847\pi$
$702$	−15.9895	−0.603486
$703$	26.6551	1.00532
$704$	−7.19129	−0.271032
$705$	2.57886	0.0971256
$706$	36.7443	1.38289
$707$	2.25972	0.0849857
$708$	15.0832	0.566860
$709$	19.6922	0.739555	0.369777	−	0.929120i	$-0.379434\pi$
$709$	19.6922	0.739555	0.369777	+	0.929120i	$0.379434\pi$
$710$	11.3179	0.424753
$711$	−27.0939	−1.01610
$712$	−0.863127	−0.0323471
$713$	0	0
$714$	3.98182	0.149016
$715$	5.03790	0.188407
$716$	32.4748	1.21364
$717$	19.4664	0.726984
$718$	59.8785	2.23465
$719$	25.9108	0.966311	0.483155	−	0.875535i	$-0.339491\pi$
$719$	25.9108	0.966311	0.483155	+	0.875535i	$0.339491\pi$
$720$	9.04109	0.336942
$721$	9.50054	0.353819
$722$	23.4661	0.873319
$723$	−12.5409	−0.466399
$724$	2.88956	0.107390
$725$	−9.21258	−0.342146
$726$	39.2488	1.45666
$727$	29.5781	1.09699	0.548495	−	0.836154i	$-0.315201\pi$
$727$	29.5781	1.09699	0.548495	+	0.836154i	$0.315201\pi$
$728$	1.93445	0.0716955
$729$	−6.87368	−0.254581
$730$	−27.2923	−1.01013
$731$	−12.1443	−0.449173
$732$	32.3222	1.19466
$733$	4.80280	0.177395	0.0886976	−	0.996059i	$-0.471730\pi$
$733$	4.80280	0.177395	0.0886976	+	0.996059i	$0.471730\pi$
$734$	−59.3127	−2.18927
$735$	14.0030	0.516509
$736$	0	0
$737$	7.70872	0.283954
$738$	39.3548	1.44867
$739$	−3.24445	−0.119349	−0.0596745	−	0.998218i	$-0.519006\pi$
$739$	−3.24445	−0.119349	−0.0596745	+	0.998218i	$0.519006\pi$
$740$	−17.2342	−0.633544
$741$	−21.5529	−0.791764
$742$	8.63625	0.317047
$743$	49.2183	1.80564	0.902822	−	0.430015i	$-0.141492\pi$
$743$	49.2183	1.80564	0.902822	+	0.430015i	$0.141492\pi$
$744$	4.51348	0.165472
$745$	13.1728	0.482614
$746$	0.542627	0.0198670
$747$	−17.9489	−0.656715
$748$	2.47880	0.0906338
$749$	−13.5152	−0.493833
$750$	4.28840	0.156590
$751$	−32.1484	−1.17311	−0.586556	−	0.809909i	$-0.699517\pi$
$751$	−32.1484	−1.17311	−0.586556	+	0.809909i	$0.699517\pi$
$752$	5.23244	0.190807
$753$	−31.3741	−1.14333
$754$	−65.5222	−2.38618
$755$	11.3404	0.412721
$756$	3.24042	0.117853
$757$	−6.47875	−0.235474	−0.117737	−	0.993045i	$-0.537564\pi$
$757$	−6.47875	−0.235474	−0.117737	+	0.993045i	$0.537564\pi$
$758$	−2.90844	−0.105639
$759$	0	0
$760$	−1.58545	−0.0575102
$761$	−7.67911	−0.278367	−0.139184	−	0.990267i	$-0.544448\pi$
$761$	−7.67911	−0.278367	−0.139184	+	0.990267i	$0.544448\pi$
$762$	−0.847741	−0.0307104
$763$	1.86944	0.0676783
$764$	−18.7039	−0.676682
$765$	−2.16119	−0.0781379
$766$	−62.5993	−2.26180
$767$	−14.8678	−0.536846
$768$	44.2842	1.59797
$769$	−5.54976	−0.200129	−0.100065	−	0.994981i	$-0.531905\pi$
$769$	−5.54976	−0.200129	−0.100065	+	0.994981i	$0.531905\pi$
$770$	−2.23461	−0.0805297
$771$	−22.2473	−0.801215
$772$	−19.7623	−0.711261
$773$	−32.1994	−1.15813	−0.579066	−	0.815280i	$-0.696583\pi$
$773$	−32.1994	−1.15813	−0.579066	+	0.815280i	$0.696583\pi$
$774$	42.8741	1.54108
$775$	3.31499	0.119078
$776$	−4.20289	−0.150875
$777$	−19.6099	−0.703501
$778$	7.34883	0.263468
$779$	−26.7639	−0.958917
$780$	13.9353	0.498964
$781$	8.01691	0.286868
$782$	0	0
$783$	20.7114	0.740165
$784$	28.4117	1.01470
$785$	−7.59488	−0.271073
$786$	−31.0425	−1.10725
$787$	23.4789	0.836934	0.418467	−	0.908232i	$-0.362568\pi$
$787$	23.4789	0.836934	0.418467	+	0.908232i	$0.362568\pi$
$788$	11.2247	0.399865
$789$	57.9691	2.06376
$790$	−26.0749	−0.927702
$791$	6.40972	0.227903
$792$	1.65136	0.0586785
$793$	−31.8607	−1.13141
$794$	2.16962	0.0769968
$795$	−11.7398	−0.416368
$796$	−8.16191	−0.289291
$797$	26.4437	0.936682	0.468341	−	0.883548i	$-0.344852\pi$
$797$	26.4437	0.936682	0.468341	+	0.883548i	$0.344852\pi$
$798$	9.55998	0.338420
$799$	−1.25076	−0.0442488
$800$	7.48251	0.264547
$801$	−2.82482	−0.0998101
$802$	11.1557	0.393921
$803$	−19.3323	−0.682220
$804$	21.3230	0.752006
$805$	0	0
$806$	23.5771	0.830467
$807$	−8.47809	−0.298443
$808$	−1.60711	−0.0565379
$809$	−7.02549	−0.247003	−0.123501	−	0.992344i	$-0.539412\pi$
$809$	−7.02549	−0.247003	−0.123501	+	0.992344i	$0.539412\pi$
$810$	−21.1203	−0.742092
$811$	4.27148	0.149992	0.0749960	−	0.997184i	$-0.476106\pi$
$811$	4.27148	0.149992	0.0749960	+	0.997184i	$0.476106\pi$
$812$	13.2786	0.465989
$813$	−11.2356	−0.394050
$814$	−26.7190	−0.936502
$815$	1.67640	0.0587218
$816$	−10.9823	−0.384457
$817$	−29.1573	−1.02008
$818$	−20.6958	−0.723610
$819$	6.33102	0.221224
$820$	17.3046	0.604302
$821$	−6.11360	−0.213366	−0.106683	−	0.994293i	$-0.534023\pi$
$821$	−6.11360	−0.213366	−0.106683	+	0.994293i	$0.534023\pi$
$822$	52.0836	1.81663
$823$	−2.72171	−0.0948727	−0.0474364	−	0.998874i	$-0.515105\pi$
$823$	−2.72171	−0.0948727	−0.0474364	+	0.998874i	$0.515105\pi$
$824$	−6.75676	−0.235383
$825$	3.03765	0.105757
$826$	6.59477	0.229461
$827$	25.6382	0.891527	0.445764	−	0.895151i	$-0.352932\pi$
$827$	25.6382	0.891527	0.445764	+	0.895151i	$0.352932\pi$
$828$	0	0
$829$	−13.0685	−0.453887	−0.226943	−	0.973908i	$-0.572873\pi$
$829$	−13.0685	−0.453887	−0.226943	+	0.973908i	$0.572873\pi$
$830$	−17.2738	−0.599582
$831$	−64.2680	−2.22943
$832$	19.6078	0.679778
$833$	−6.79154	−0.235313
$834$	30.9547	1.07187
$835$	−11.8195	−0.409029
$836$	5.95136	0.205832
$837$	−7.45265	−0.257601
$838$	39.2402	1.35553
$839$	6.39079	0.220634	0.110317	−	0.993896i	$-0.464813\pi$
$839$	6.39079	0.220634	0.110317	+	0.993896i	$0.464813\pi$
$840$	1.16639	0.0402444
$841$	55.8716	1.92661
$842$	−65.5100	−2.25762
$843$	−51.3801	−1.76962
$844$	9.83553	0.338553
$845$	−0.736347	−0.0253311
$846$	4.41569	0.151815
$847$	7.84056	0.269405
$848$	−23.8197	−0.817972
$849$	−32.3725	−1.11102
$850$	−2.07990	−0.0713399
$851$	0	0
$852$	22.1755	0.759721
$853$	37.7956	1.29410	0.647049	−	0.762448i	$-0.276003\pi$
$853$	37.7956	1.29410	0.647049	+	0.762448i	$0.276003\pi$
$854$	14.1321	0.483591
$855$	−5.18881	−0.177453
$856$	9.61194	0.328529
$857$	−2.26923	−0.0775154	−0.0387577	−	0.999249i	$-0.512340\pi$
$857$	−2.26923	−0.0775154	−0.0387577	+	0.999249i	$0.512340\pi$
$858$	21.6045	0.737566
$859$	30.6258	1.04494	0.522469	−	0.852659i	$-0.325011\pi$
$859$	30.6258	1.04494	0.522469	+	0.852659i	$0.325011\pi$
$860$	18.8521	0.642850
$861$	19.6899	0.671030
$862$	21.5223	0.733051
$863$	−16.4827	−0.561076	−0.280538	−	0.959843i	$-0.590513\pi$
$863$	−16.4827	−0.561076	−0.280538	+	0.959843i	$0.590513\pi$
$864$	−16.8219	−0.572293
$865$	−17.6187	−0.599054
$866$	57.9961	1.97079
$867$	−35.3651	−1.20106
$868$	−4.77810	−0.162179
$869$	−18.4699	−0.626548
$870$	−39.5072	−1.33942
$871$	−21.0186	−0.712189
$872$	−1.32954	−0.0450239
$873$	−13.7551	−0.465540
$874$	0	0
$875$	0.856675	0.0289609
$876$	−53.4748	−1.80675
$877$	−43.0763	−1.45458	−0.727291	−	0.686329i	$-0.759221\pi$
$877$	−43.0763	−1.45458	−0.727291	+	0.686329i	$0.759221\pi$
$878$	−7.11587	−0.240149
$879$	76.1437	2.56826
$880$	6.16329	0.207765
$881$	−20.6944	−0.697211	−0.348605	−	0.937270i	$-0.613345\pi$
$881$	−20.6944	−0.697211	−0.348605	+	0.937270i	$0.613345\pi$
$882$	23.9768	0.807342
$883$	−1.45188	−0.0488598	−0.0244299	−	0.999702i	$-0.507777\pi$
$883$	−1.45188	−0.0488598	−0.0244299	+	0.999702i	$0.507777\pi$
$884$	−6.75870	−0.227320
$885$	−8.96469	−0.301345
$886$	−56.2430	−1.88952
$887$	43.0886	1.44677	0.723386	−	0.690444i	$-0.242585\pi$
$887$	43.0886	1.44677	0.723386	+	0.690444i	$0.242585\pi$
$888$	13.9465	0.468014
$889$	−0.169349	−0.00567980
$890$	−2.71857	−0.0911267
$891$	−14.9604	−0.501191
$892$	−17.0478	−0.570802
$893$	−3.00297	−0.100490
$894$	56.4902	1.88931
$895$	−19.3014	−0.645176
$896$	4.12292	0.137737
$897$	0	0
$898$	−42.4655	−1.41709
$899$	−30.5396	−1.01855
$900$	3.35489	0.111830
$901$	5.69387	0.189690
$902$	26.8281	0.893278
$903$	21.4507	0.713834
$904$	−4.55858	−0.151616
$905$	−1.71741	−0.0570888
$906$	48.6323	1.61570
$907$	13.9051	0.461711	0.230856	−	0.972988i	$-0.425847\pi$
$907$	13.9051	0.461711	0.230856	+	0.972988i	$0.425847\pi$
$908$	33.1189	1.09909
$909$	−5.25971	−0.174453
$910$	6.09289	0.201977
$911$	46.7788	1.54985	0.774925	−	0.632054i	$-0.217788\pi$
$911$	46.7788	1.54985	0.774925	+	0.632054i	$0.217788\pi$
$912$	−26.3675	−0.873114
$913$	−12.2357	−0.404943
$914$	19.7272	0.652518
$915$	−19.2107	−0.635087
$916$	−44.0761	−1.45632
$917$	−6.20123	−0.204783
$918$	4.67595	0.154329
$919$	19.2142	0.633819	0.316909	−	0.948456i	$-0.397355\pi$
$919$	19.2142	0.633819	0.316909	+	0.948456i	$0.397355\pi$
$920$	0	0
$921$	−28.5963	−0.942279
$922$	40.3776	1.32976
$923$	−21.8589	−0.719496
$924$	−4.37835	−0.144037
$925$	10.2432	0.336794
$926$	−1.93840	−0.0636999
$927$	−22.1133	−0.726297
$928$	−68.9332	−2.26284
$929$	51.5790	1.69225	0.846126	−	0.532983i	$-0.178929\pi$
$929$	51.5790	1.69225	0.846126	+	0.532983i	$0.178929\pi$
$930$	14.2160	0.466161
$931$	−16.3059	−0.534403
$932$	2.07380	0.0679296
$933$	17.6006	0.576219
$934$	−38.7329	−1.26738
$935$	−1.47328	−0.0481813
$936$	−4.50260	−0.147172
$937$	25.2422	0.824626	0.412313	−	0.911042i	$-0.364721\pi$
$937$	25.2422	0.824626	0.412313	+	0.911042i	$0.364721\pi$
$938$	9.32302	0.304407
$939$	17.6710	0.576671
$940$	1.94161	0.0633283
$941$	6.59264	0.214914	0.107457	−	0.994210i	$-0.465729\pi$
$941$	6.59264	0.214914	0.107457	+	0.994210i	$0.465729\pi$
$942$	−32.5699	−1.06118
$943$	0	0
$944$	−18.1891	−0.592004
$945$	−1.92595	−0.0626510
$946$	29.2272	0.950258
$947$	27.5264	0.894487	0.447244	−	0.894412i	$-0.352406\pi$
$947$	27.5264	0.894487	0.447244	+	0.894412i	$0.352406\pi$
$948$	−51.0894	−1.65931
$949$	52.7114	1.71108
$950$	−4.99364	−0.162015
$951$	24.3159	0.788496
$952$	−0.565708	−0.0183347
$953$	24.3938	0.790191	0.395096	−	0.918640i	$-0.370711\pi$
$953$	24.3938	0.790191	0.395096	+	0.918640i	$0.370711\pi$
$954$	−20.1016	−0.650814
$955$	11.1167	0.359727
$956$	14.6561	0.474012
$957$	−27.9846	−0.904612
$958$	−4.91823	−0.158901
$959$	10.4045	0.335979
$960$	11.8227	0.381576
$961$	−20.0108	−0.645511
$962$	72.8522	2.34885
$963$	31.4577	1.01371
$964$	−9.44192	−0.304104
$965$	11.7457	0.378109
$966$	0	0
$967$	−15.9088	−0.511592	−0.255796	−	0.966731i	$-0.582337\pi$
$967$	−15.9088	−0.511592	−0.255796	+	0.966731i	$0.582337\pi$
$968$	−5.57618	−0.179225
$969$	6.30289	0.202478
$970$	−13.2377	−0.425038
$971$	−50.5990	−1.62380	−0.811900	−	0.583797i	$-0.801567\pi$
$971$	−50.5990	−1.62380	−0.811900	+	0.583797i	$0.801567\pi$
$972$	−30.0341	−0.963345
$973$	6.18367	0.198239
$974$	−47.0873	−1.50878
$975$	−8.28246	−0.265251
$976$	−38.9780	−1.24765
$977$	26.5359	0.848960	0.424480	−	0.905437i	$-0.360457\pi$
$977$	26.5359	0.848960	0.424480	+	0.905437i	$0.360457\pi$
$978$	7.18909	0.229882
$979$	−1.92567	−0.0615448
$980$	10.5428	0.336777
$981$	−4.35129	−0.138926
$982$	63.6879	2.03236
$983$	−27.4665	−0.876044	−0.438022	−	0.898964i	$-0.644321\pi$
$983$	−27.4665	−0.876044	−0.438022	+	0.898964i	$0.644321\pi$
$984$	−14.0034	−0.446412
$985$	−6.67144	−0.212570
$986$	19.1612	0.610218
$987$	2.20925	0.0703211
$988$	−16.2270	−0.516249
$989$	0	0
$990$	5.20124	0.165306
$991$	40.6729	1.29202	0.646009	−	0.763330i	$-0.276437\pi$
$991$	40.6729	1.29202	0.646009	+	0.763330i	$0.276437\pi$
$992$	24.8044	0.787542
$993$	−68.8608	−2.18523
$994$	9.69575	0.307530
$995$	4.85104	0.153788
$996$	−33.8451	−1.07242
$997$	37.3987	1.18443	0.592214	−	0.805781i	$-0.298254\pi$
$997$	37.3987	1.18443	0.592214	+	0.805781i	$0.298254\pi$
$998$	−29.4565	−0.932430
$999$	−23.0284	−0.728586

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2645.2.a.t.1.2		10
23.13	even	11		115.2.g.b.31.2	yes	20
23.16	even	11		115.2.g.b.26.2	✓	20
23.22	odd	2		2645.2.a.u.1.2		10
115.13	odd	44		575.2.p.c.399.1		40
115.39	even	22		575.2.k.c.26.1		20
115.59	even	22		575.2.k.c.376.1		20
115.62	odd	44		575.2.p.c.49.1		40
115.82	odd	44		575.2.p.c.399.4		40
115.108	odd	44		575.2.p.c.49.4		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.g.b.26.2	✓	20	23.16	even	11
115.2.g.b.31.2	yes	20	23.13	even	11
575.2.k.c.26.1		20	115.39	even	22
575.2.k.c.376.1		20	115.59	even	22
575.2.p.c.49.1		40	115.62	odd	44
575.2.p.c.49.4		40	115.108	odd	44
575.2.p.c.399.1		40	115.13	odd	44
575.2.p.c.399.4		40	115.82	odd	44
2645.2.a.t.1.2		10	1.1	even	1	trivial
2645.2.a.u.1.2		10	23.22	odd	2

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:	\( N \)	\(=\)	\( 2645 = 5 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2645.a (trivial)

\(f(q)\)	\(=\)	\(q-1.91899 q^{2} +2.23472 q^{3} +1.68251 q^{4} -1.00000 q^{5} -4.28840 q^{6} -0.856675 q^{7} +0.609264 q^{8} +1.99398 q^{9} +O(q^{10})\)	\(q-1.91899 q^{2} +2.23472 q^{3} +1.68251 q^{4} -1.00000 q^{5} -4.28840 q^{6} -0.856675 q^{7} +0.609264 q^{8} +1.99398 q^{9} +1.91899 q^{10} +1.35929 q^{11} +3.75994 q^{12} -3.70626 q^{13} +1.64395 q^{14} -2.23472 q^{15} -4.53418 q^{16} +1.08385 q^{17} -3.82643 q^{18} +2.60223 q^{19} -1.68251 q^{20} -1.91443 q^{21} -2.60847 q^{22} +1.36154 q^{24} +1.00000 q^{25} +7.11226 q^{26} -2.24816 q^{27} -1.44136 q^{28} -9.21258 q^{29} +4.28840 q^{30} +3.31499 q^{31} +7.48251 q^{32} +3.03765 q^{33} -2.07990 q^{34} +0.856675 q^{35} +3.35489 q^{36} +10.2432 q^{37} -4.99364 q^{38} -8.28246 q^{39} -0.609264 q^{40} -10.2850 q^{41} +3.67376 q^{42} -11.2047 q^{43} +2.28702 q^{44} -1.99398 q^{45} -1.15400 q^{47} -10.1326 q^{48} -6.26611 q^{49} -1.91899 q^{50} +2.42211 q^{51} -6.23581 q^{52} +5.25336 q^{53} +4.31420 q^{54} -1.35929 q^{55} -0.521941 q^{56} +5.81526 q^{57} +17.6788 q^{58} +4.01155 q^{59} -3.75994 q^{60} +8.59646 q^{61} -6.36142 q^{62} -1.70820 q^{63} -5.29046 q^{64} +3.70626 q^{65} -5.82920 q^{66} +5.67112 q^{67} +1.82359 q^{68} -1.64395 q^{70} +5.89785 q^{71} +1.21486 q^{72} -14.2223 q^{73} -19.6565 q^{74} +2.23472 q^{75} +4.37827 q^{76} -1.16447 q^{77} +15.8939 q^{78} -13.5878 q^{79} +4.53418 q^{80} -11.0060 q^{81} +19.7368 q^{82} -9.00151 q^{83} -3.22104 q^{84} -1.08385 q^{85} +21.5017 q^{86} -20.5876 q^{87} +0.828170 q^{88} -1.41667 q^{89} +3.82643 q^{90} +3.17506 q^{91} +7.40808 q^{93} +2.21450 q^{94} -2.60223 q^{95} +16.7213 q^{96} -6.89830 q^{97} +12.0246 q^{98} +2.71041 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{2} - 5 q^{3} - 2 q^{4} - 10 q^{5} + q^{6} + 9 q^{7} + 19 q^{9}+O(q^{10}) \) 10 * q - 2 * q^2 - 5 * q^3 - 2 * q^4 - 10 * q^5 + q^6 + 9 * q^7 + 19 * q^9	\( 10 q - 2 q^{2} - 5 q^{3} - 2 q^{4} - 10 q^{5} + q^{6} + 9 q^{7} + 19 q^{9} + 2 q^{10} - 4 q^{11} + q^{12} - 17 q^{13} - 4 q^{14} + 5 q^{15} - 18 q^{16} + 12 q^{17} - 17 q^{18} + q^{19} + 2 q^{20} - 4 q^{21} + 3 q^{22} + 10 q^{25} + 10 q^{26} - 41 q^{27} - 4 q^{28} - 16 q^{29} - q^{30} - 28 q^{31} + 8 q^{32} + 25 q^{33} - 9 q^{34} - 9 q^{35} + 5 q^{36} + 2 q^{37} + 24 q^{38} - 15 q^{39} - 6 q^{41} + 25 q^{42} - 21 q^{43} + 3 q^{44} - 19 q^{45} - q^{47} + 9 q^{48} + 13 q^{49} - 2 q^{50} - 52 q^{51} + 10 q^{52} + 3 q^{53} + 28 q^{54} + 4 q^{55} + 22 q^{57} + 12 q^{58} - 40 q^{59} - q^{60} - q^{61} - 12 q^{62} + 21 q^{63} + 8 q^{64} + 17 q^{65} - 49 q^{66} + 34 q^{67} + 13 q^{68} + 4 q^{70} - 37 q^{71} - 41 q^{73} - 18 q^{74} - 5 q^{75} + 2 q^{76} - 21 q^{77} - 30 q^{78} + 8 q^{79} + 18 q^{80} - 38 q^{81} + 21 q^{82} + 17 q^{83} + 3 q^{84} - 12 q^{85} - 9 q^{86} - 15 q^{87} - 11 q^{88} + 3 q^{89} + 17 q^{90} - 42 q^{91} + 14 q^{93} + 9 q^{94} - q^{95} - 4 q^{96} - 46 q^{97} - 40 q^{98} - 24 q^{99}+O(q^{100}) \) 10 * q - 2 * q^2 - 5 * q^3 - 2 * q^4 - 10 * q^5 + q^6 + 9 * q^7 + 19 * q^9 + 2 * q^10 - 4 * q^11 + q^12 - 17 * q^13 - 4 * q^14 + 5 * q^15 - 18 * q^16 + 12 * q^17 - 17 * q^18 + q^19 + 2 * q^20 - 4 * q^21 + 3 * q^22 + 10 * q^25 + 10 * q^26 - 41 * q^27 - 4 * q^28 - 16 * q^29 - q^30 - 28 * q^31 + 8 * q^32 + 25 * q^33 - 9 * q^34 - 9 * q^35 + 5 * q^36 + 2 * q^37 + 24 * q^38 - 15 * q^39 - 6 * q^41 + 25 * q^42 - 21 * q^43 + 3 * q^44 - 19 * q^45 - q^47 + 9 * q^48 + 13 * q^49 - 2 * q^50 - 52 * q^51 + 10 * q^52 + 3 * q^53 + 28 * q^54 + 4 * q^55 + 22 * q^57 + 12 * q^58 - 40 * q^59 - q^60 - q^61 - 12 * q^62 + 21 * q^63 + 8 * q^64 + 17 * q^65 - 49 * q^66 + 34 * q^67 + 13 * q^68 + 4 * q^70 - 37 * q^71 - 41 * q^73 - 18 * q^74 - 5 * q^75 + 2 * q^76 - 21 * q^77 - 30 * q^78 + 8 * q^79 + 18 * q^80 - 38 * q^81 + 21 * q^82 + 17 * q^83 + 3 * q^84 - 12 * q^85 - 9 * q^86 - 15 * q^87 - 11 * q^88 + 3 * q^89 + 17 * q^90 - 42 * q^91 + 14 * q^93 + 9 * q^94 - q^95 - 4 * q^96 - 46 * q^97 - 40 * q^98 - 24 * q^99

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