LMFDB - Embedded newform 1805.2.a.h.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1805,2,Mod(1,1805)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1805, 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("1805.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1805 = 5 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1805.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:	$14.4129975648$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.361.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 6x + 7 $ x^3 - x^2 - 6*x + 7
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.28514$ of defining polynomial
Character	$\chi$	$=$	1805.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.50702 q^{2} +1.22188 q^{3} +4.28514 q^{4} -1.00000 q^{5} -3.06327 q^{6} -0.221876 q^{7} -5.72889 q^{8} -1.50702 q^{9} +O(q^{10})$	\(q-2.50702 q^{2} +1.22188 q^{3} +4.28514 q^{4} -1.00000 q^{5} -3.06327 q^{6} -0.221876 q^{7} -5.72889 q^{8} -1.50702 q^{9} +2.50702 q^{10} -0.778124 q^{11} +5.23591 q^{12} -5.00000 q^{13} +0.556248 q^{14} -1.22188 q^{15} +5.79216 q^{16} +7.07730 q^{17} +3.77812 q^{18} -4.28514 q^{20} -0.271105 q^{21} +1.95077 q^{22} +8.07730 q^{23} -7.00000 q^{24} +1.00000 q^{25} +12.5351 q^{26} -5.50702 q^{27} -0.950771 q^{28} +0.221876 q^{29} +3.06327 q^{30} +2.50702 q^{31} -3.06327 q^{32} -0.950771 q^{33} -17.7429 q^{34} +0.221876 q^{35} -6.45779 q^{36} -1.90466 q^{37} -6.10938 q^{39} +5.72889 q^{40} -7.23591 q^{41} +0.679666 q^{42} +7.29918 q^{43} -3.33437 q^{44} +1.50702 q^{45} -20.2500 q^{46} -2.79216 q^{47} +7.07730 q^{48} -6.95077 q^{49} -2.50702 q^{50} +8.64759 q^{51} -21.4257 q^{52} +4.38049 q^{53} +13.8062 q^{54} +0.778124 q^{55} +1.27111 q^{56} -0.556248 q^{58} -2.79216 q^{59} -5.23591 q^{60} -12.5843 q^{61} -6.28514 q^{62} +0.334372 q^{63} -3.90466 q^{64} +5.00000 q^{65} +2.38360 q^{66} -10.5703 q^{67} +30.3273 q^{68} +9.86946 q^{69} -0.556248 q^{70} -9.84139 q^{71} +8.63355 q^{72} -14.0773 q^{73} +4.77501 q^{74} +1.22188 q^{75} +0.172647 q^{77} +15.3163 q^{78} +1.58432 q^{79} -5.79216 q^{80} -2.20784 q^{81} +18.1406 q^{82} -9.52106 q^{83} -1.16172 q^{84} -7.07730 q^{85} -18.2992 q^{86} +0.271105 q^{87} +4.45779 q^{88} +3.14057 q^{89} -3.77812 q^{90} +1.10938 q^{91} +34.6124 q^{92} +3.06327 q^{93} +7.00000 q^{94} -3.74293 q^{96} -6.36245 q^{97} +17.4257 q^{98} +1.17265 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + q^{2} + q^{3} + 7 q^{4} - 3 q^{5} - 6 q^{6} + 2 q^{7} - 6 q^{8} + 4 q^{9}+O(q^{10}) $ 3 * q + q^2 + q^3 + 7 * q^4 - 3 * q^5 - 6 * q^6 + 2 * q^7 - 6 * q^8 + 4 * q^9	\( 3 q + q^{2} + q^{3} + 7 q^{4} - 3 q^{5} - 6 q^{6} + 2 q^{7} - 6 q^{8} + 4 q^{9} - q^{10} - 5 q^{11} - 4 q^{12} - 15 q^{13} + 7 q^{14} - q^{15} + 3 q^{16} + q^{17} + 14 q^{18} - 7 q^{20} - 12 q^{21} - 8 q^{22} + 4 q^{23} - 21 q^{24} + 3 q^{25} - 5 q^{26} - 8 q^{27} + 11 q^{28} - 2 q^{29} + 6 q^{30} - q^{31} - 6 q^{32} + 11 q^{33} - 25 q^{34} - 2 q^{35} + 3 q^{36} - 2 q^{37} - 5 q^{39} + 6 q^{40} - 2 q^{41} - 23 q^{42} - q^{43} - 18 q^{44} - 4 q^{45} - 24 q^{46} + 6 q^{47} + q^{48} - 7 q^{49} + q^{50} - 6 q^{51} - 35 q^{52} + 11 q^{53} + 10 q^{54} + 5 q^{55} + 15 q^{56} - 7 q^{58} + 6 q^{59} + 4 q^{60} - 9 q^{61} - 13 q^{62} + 9 q^{63} - 8 q^{64} + 15 q^{65} + 29 q^{66} - 20 q^{67} + 34 q^{68} - 5 q^{69} - 7 q^{70} - 29 q^{71} + 11 q^{72} - 22 q^{73} - 7 q^{74} + q^{75} - 16 q^{77} + 30 q^{78} - 24 q^{79} - 3 q^{80} - 21 q^{81} + 31 q^{82} - 3 q^{83} - 28 q^{84} - q^{85} - 32 q^{86} + 12 q^{87} - 9 q^{88} - 14 q^{89} - 14 q^{90} - 10 q^{91} + 41 q^{92} + 6 q^{93} + 21 q^{94} + 17 q^{96} + 7 q^{97} + 23 q^{98} - 13 q^{99}+O(q^{100}) \) 3 * q + q^2 + q^3 + 7 * q^4 - 3 * q^5 - 6 * q^6 + 2 * q^7 - 6 * q^8 + 4 * q^9 - q^10 - 5 * q^11 - 4 * q^12 - 15 * q^13 + 7 * q^14 - q^15 + 3 * q^16 + q^17 + 14 * q^18 - 7 * q^20 - 12 * q^21 - 8 * q^22 + 4 * q^23 - 21 * q^24 + 3 * q^25 - 5 * q^26 - 8 * q^27 + 11 * q^28 - 2 * q^29 + 6 * q^30 - q^31 - 6 * q^32 + 11 * q^33 - 25 * q^34 - 2 * q^35 + 3 * q^36 - 2 * q^37 - 5 * q^39 + 6 * q^40 - 2 * q^41 - 23 * q^42 - q^43 - 18 * q^44 - 4 * q^45 - 24 * q^46 + 6 * q^47 + q^48 - 7 * q^49 + q^50 - 6 * q^51 - 35 * q^52 + 11 * q^53 + 10 * q^54 + 5 * q^55 + 15 * q^56 - 7 * q^58 + 6 * q^59 + 4 * q^60 - 9 * q^61 - 13 * q^62 + 9 * q^63 - 8 * q^64 + 15 * q^65 + 29 * q^66 - 20 * q^67 + 34 * q^68 - 5 * q^69 - 7 * q^70 - 29 * q^71 + 11 * q^72 - 22 * q^73 - 7 * q^74 + q^75 - 16 * q^77 + 30 * q^78 - 24 * q^79 - 3 * q^80 - 21 * q^81 + 31 * q^82 - 3 * q^83 - 28 * q^84 - q^85 - 32 * q^86 + 12 * q^87 - 9 * q^88 - 14 * q^89 - 14 * q^90 - 10 * q^91 + 41 * q^92 + 6 * q^93 + 21 * q^94 + 17 * q^96 + 7 * q^97 + 23 * q^98 - 13 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.50702	−1.77273	−0.886365	−	0.462987i	$-0.846778\pi$
$2$	−2.50702	−1.77273	−0.886365	+	0.462987i	$0.846778\pi$
$3$	1.22188	0.705451	0.352725	−	0.935727i	$-0.385255\pi$
$3$	1.22188	0.705451	0.352725	+	0.935727i	$0.385255\pi$
$4$	4.28514	2.14257
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−3.06327	−1.25057
$7$	−0.221876	−0.0838613	−0.0419307	−	0.999121i	$-0.513351\pi$
$7$	−0.221876	−0.0838613	−0.0419307	+	0.999121i	$0.513351\pi$
$8$	−5.72889	−2.02547
$9$	−1.50702	−0.502340
$10$	2.50702	0.792789
$11$	−0.778124	−0.234613	−0.117307	−	0.993096i	$-0.537426\pi$
$11$	−0.778124	−0.234613	−0.117307	+	0.993096i	$0.537426\pi$
$12$	5.23591	1.51148
$13$	−5.00000	−1.38675	−0.693375	−	0.720577i	$-0.743877\pi$
$13$	−5.00000	−1.38675	−0.693375	+	0.720577i	$0.743877\pi$
$14$	0.556248	0.148663
$15$	−1.22188	−0.315487
$16$	5.79216	1.44804
$17$	7.07730	1.71650	0.858249	−	0.513233i	$-0.171552\pi$
$17$	7.07730	1.71650	0.858249	+	0.513233i	$0.171552\pi$
$18$	3.77812	0.890512
$19$	0	0
$19$	0	0
$20$	−4.28514	−0.958187
$21$	−0.271105	−0.0591600
$22$	1.95077	0.415906
$23$	8.07730	1.68423	0.842117	−	0.539295i	$-0.181309\pi$
$23$	8.07730	1.68423	0.842117	+	0.539295i	$0.181309\pi$
$24$	−7.00000	−1.42887
$25$	1.00000	0.200000
$26$	12.5351	2.45833
$27$	−5.50702	−1.05983
$28$	−0.950771	−0.179679
$29$	0.221876	0.0412014	0.0206007	−	0.999788i	$-0.493442\pi$
$29$	0.221876	0.0412014	0.0206007	+	0.999788i	$0.493442\pi$
$30$	3.06327	0.559273
$31$	2.50702	0.450274	0.225137	−	0.974327i	$-0.427717\pi$
$31$	2.50702	0.450274	0.225137	+	0.974327i	$0.427717\pi$
$32$	−3.06327	−0.541514
$33$	−0.950771	−0.165508
$34$	−17.7429	−3.04289
$35$	0.221876	0.0375039
$36$	−6.45779	−1.07630
$37$	−1.90466	−0.313124	−0.156562	−	0.987668i	$-0.550041\pi$
$37$	−1.90466	−0.313124	−0.156562	+	0.987668i	$0.550041\pi$
$38$	0	0
$39$	−6.10938	−0.978284
$40$	5.72889	0.905818
$41$	−7.23591	−1.13006	−0.565030	−	0.825070i	$-0.691135\pi$
$41$	−7.23591	−1.13006	−0.565030	+	0.825070i	$0.691135\pi$
$42$	0.679666	0.104875
$43$	7.29918	1.11311	0.556557	−	0.830809i	$-0.312122\pi$
$43$	7.29918	1.11311	0.556557	+	0.830809i	$0.312122\pi$
$44$	−3.33437	−0.502675
$45$	1.50702	0.224653
$46$	−20.2500	−2.98569
$47$	−2.79216	−0.407279	−0.203639	−	0.979046i	$-0.565277\pi$
$47$	−2.79216	−0.407279	−0.203639	+	0.979046i	$0.565277\pi$
$48$	7.07730	1.02152
$49$	−6.95077	−0.992967
$50$	−2.50702	−0.354546
$51$	8.64759	1.21090
$52$	−21.4257	−2.97121
$53$	4.38049	0.601706	0.300853	−	0.953671i	$-0.402729\pi$
$53$	4.38049	0.601706	0.300853	+	0.953671i	$0.402729\pi$
$54$	13.8062	1.87879
$55$	0.778124	0.104922
$56$	1.27111	0.169859
$57$	0	0
$58$	−0.556248	−0.0730389
$59$	−2.79216	−0.363508	−0.181754	−	0.983344i	$-0.558178\pi$
$59$	−2.79216	−0.363508	−0.181754	+	0.983344i	$0.558178\pi$
$60$	−5.23591	−0.675954
$61$	−12.5843	−1.61126	−0.805629	−	0.592421i	$-0.798172\pi$
$61$	−12.5843	−1.61126	−0.805629	+	0.592421i	$0.798172\pi$
$62$	−6.28514	−0.798214
$63$	0.334372	0.0421269
$64$	−3.90466	−0.488082
$65$	5.00000	0.620174
$66$	2.38360	0.293401
$67$	−10.5703	−1.29137	−0.645683	−	0.763606i	$-0.723427\pi$
$67$	−10.5703	−1.29137	−0.645683	+	0.763606i	$0.723427\pi$
$68$	30.3273	3.67772
$69$	9.86946	1.18814
$70$	−0.556248	−0.0664843
$71$	−9.84139	−1.16796	−0.583979	−	0.811769i	$-0.698505\pi$
$71$	−9.84139	−1.16796	−0.583979	+	0.811769i	$0.698505\pi$
$72$	8.63355	1.01747
$73$	−14.0773	−1.64762	−0.823812	−	0.566863i	$-0.808157\pi$
$73$	−14.0773	−1.64762	−0.823812	+	0.566863i	$0.808157\pi$
$74$	4.77501	0.555084
$75$	1.22188	0.141090
$76$	0	0
$77$	0.172647	0.0196750
$78$	15.3163	1.73423
$79$	1.58432	0.178250	0.0891251	−	0.996020i	$-0.471593\pi$
$79$	1.58432	0.178250	0.0891251	+	0.996020i	$0.471593\pi$
$80$	−5.79216	−0.647583
$81$	−2.20784	−0.245315
$82$	18.1406	2.00329
$83$	−9.52106	−1.04507	−0.522536	−	0.852617i	$-0.675014\pi$
$83$	−9.52106	−1.04507	−0.522536	+	0.852617i	$0.675014\pi$
$84$	−1.16172	−0.126755
$85$	−7.07730	−0.767641
$86$	−18.2992	−1.97325
$87$	0.271105	0.0290655
$88$	4.45779	0.475202
$89$	3.14057	0.332900	0.166450	−	0.986050i	$-0.446770\pi$
$89$	3.14057	0.332900	0.166450	+	0.986050i	$0.446770\pi$
$90$	−3.77812	−0.398249
$91$	1.10938	0.116295
$92$	34.6124	3.60859
$93$	3.06327	0.317646
$94$	7.00000	0.721995
$95$	0	0
$96$	−3.74293	−0.382011
$97$	−6.36245	−0.646009	−0.323004	−	0.946398i	$-0.604693\pi$
$97$	−6.36245	−0.646009	−0.323004	+	0.946398i	$0.604693\pi$
$98$	17.4257	1.76026
$99$	1.17265	0.117855
$100$	4.28514	0.428514
$101$	−7.39452	−0.735783	−0.367891	−	0.929869i	$-0.619920\pi$
$101$	−7.39452	−0.735783	−0.367891	+	0.929869i	$0.619920\pi$
$102$	−21.6797	−2.14661
$103$	12.2038	1.20248	0.601240	−	0.799069i	$-0.294674\pi$
$103$	12.2038	1.20248	0.601240	+	0.799069i	$0.294674\pi$
$104$	28.6445	2.80882
$105$	0.271105	0.0264572
$106$	−10.9820	−1.06666
$107$	−1.63355	−0.157921	−0.0789607	−	0.996878i	$-0.525160\pi$
$107$	−1.63355	−0.157921	−0.0789607	+	0.996878i	$0.525160\pi$
$108$	−23.5984	−2.27075
$109$	−7.61640	−0.729519	−0.364759	−	0.931102i	$-0.618849\pi$
$109$	−7.61640	−0.729519	−0.364759	+	0.931102i	$0.618849\pi$
$110$	−1.95077	−0.185999
$111$	−2.32725	−0.220893
$112$	−1.28514	−0.121435
$113$	12.4890	1.17486	0.587432	−	0.809273i	$-0.300139\pi$
$113$	12.4890	1.17486	0.587432	+	0.809273i	$0.300139\pi$
$114$	0	0
$115$	−8.07730	−0.753212
$116$	0.950771	0.0882769
$117$	7.53509	0.696620
$118$	7.00000	0.644402
$119$	−1.57028	−0.143948
$120$	7.00000	0.639010
$121$	−10.3945	−0.944957
$122$	31.5491	2.85632
$123$	−8.84139	−0.797201
$124$	10.7429	0.964744
$125$	−1.00000	−0.0894427
$126$	−0.838276	−0.0746795
$127$	−13.0421	−1.15730	−0.578650	−	0.815576i	$-0.696420\pi$
$127$	−13.0421	−1.15730	−0.578650	+	0.815576i	$0.696420\pi$
$128$	15.9156	1.40675
$129$	8.91869	0.785247
$130$	−12.5351	−1.09940
$131$	7.10938	0.621149	0.310575	−	0.950549i	$-0.399478\pi$
$131$	7.10938	0.621149	0.310575	+	0.950549i	$0.399478\pi$
$132$	−4.07419	−0.354613
$133$	0	0
$134$	26.4999	2.28924
$135$	5.50702	0.473969
$136$	−40.5451	−3.47672
$137$	5.42571	0.463550	0.231775	−	0.972769i	$-0.425547\pi$
$137$	5.42571	0.463550	0.231775	+	0.972769i	$0.425547\pi$
$138$	−24.7429	−2.10626
$139$	3.57028	0.302828	0.151414	−	0.988470i	$-0.451617\pi$
$139$	3.57028	0.302828	0.151414	+	0.988470i	$0.451617\pi$
$140$	0.950771	0.0803548
$141$	−3.41168	−0.287315
$142$	24.6725	2.07047
$143$	3.89062	0.325350
$144$	−8.72889	−0.727408
$145$	−0.221876	−0.0184258
$146$	35.2921	2.92079
$147$	−8.49298	−0.700489
$148$	−8.16172	−0.670890
$149$	−0.936734	−0.0767402	−0.0383701	−	0.999264i	$-0.512217\pi$
$149$	−0.936734	−0.0767402	−0.0383701	+	0.999264i	$0.512217\pi$
$150$	−3.06327	−0.250115
$151$	−0.971925	−0.0790942	−0.0395471	−	0.999218i	$-0.512592\pi$
$151$	−0.971925	−0.0790942	−0.0395471	+	0.999218i	$0.512592\pi$
$152$	0	0
$153$	−10.6656	−0.862265
$154$	−0.432830	−0.0348784
$155$	−2.50702	−0.201369
$156$	−26.1796	−2.09604
$157$	2.71486	0.216669	0.108335	−	0.994114i	$-0.465448\pi$
$157$	2.71486	0.216669	0.108335	+	0.994114i	$0.465448\pi$
$158$	−3.97193	−0.315989
$159$	5.35241	0.424474
$160$	3.06327	0.242172
$161$	−1.79216	−0.141242
$162$	5.53509	0.434878
$163$	−3.20384	−0.250944	−0.125472	−	0.992097i	$-0.540044\pi$
$163$	−3.20384	−0.250944	−0.125472	+	0.992097i	$0.540044\pi$
$164$	−31.0069	−2.42123
$165$	0.950771	0.0740174
$166$	23.8695	1.85263
$167$	10.2219	0.790993	0.395496	−	0.918468i	$-0.370573\pi$
$167$	10.2219	0.790993	0.395496	+	0.918468i	$0.370573\pi$
$168$	1.55313	0.119827
$169$	12.0000	0.923077
$170$	17.7429	1.36082
$171$	0	0
$172$	31.2780	2.38493
$173$	−2.66563	−0.202664	−0.101332	−	0.994853i	$-0.532310\pi$
$173$	−2.66563	−0.202664	−0.101332	+	0.994853i	$0.532310\pi$
$174$	−0.679666	−0.0515253
$175$	−0.221876	−0.0167723
$176$	−4.50702	−0.339729
$177$	−3.41168	−0.256437
$178$	−7.87347	−0.590141
$179$	−12.9367	−0.966937	−0.483468	−	0.875362i	$-0.660623\pi$
$179$	−12.9367	−0.966937	−0.483468	+	0.875362i	$0.660623\pi$
$180$	6.45779	0.481335
$181$	−18.6124	−1.38345	−0.691724	−	0.722162i	$-0.743149\pi$
$181$	−18.6124	−1.38345	−0.691724	+	0.722162i	$0.743149\pi$
$182$	−2.78124	−0.206159
$183$	−15.3765	−1.13666
$184$	−46.2740	−3.41137
$185$	1.90466	0.140033
$186$	−7.67967	−0.563100
$187$	−5.50702	−0.402713
$188$	−11.9648	−0.872623
$189$	1.22188	0.0888784
$190$	0	0
$191$	−23.0421	−1.66727	−0.833634	−	0.552317i	$-0.813744\pi$
$191$	−23.0421	−1.66727	−0.833634	+	0.552317i	$0.813744\pi$
$192$	−4.77101	−0.344318
$193$	−17.0773	−1.22925	−0.614626	−	0.788819i	$-0.710693\pi$
$193$	−17.0773	−1.22925	−0.614626	+	0.788819i	$0.710693\pi$
$194$	15.9508	1.14520
$195$	6.10938	0.437502
$196$	−29.7850	−2.12750
$197$	−8.82024	−0.628416	−0.314208	−	0.949354i	$-0.601739\pi$
$197$	−8.82024	−0.628416	−0.314208	+	0.949354i	$0.601739\pi$
$198$	−2.93985	−0.208926
$199$	−2.85543	−0.202416	−0.101208	−	0.994865i	$-0.532271\pi$
$199$	−2.85543	−0.202416	−0.101208	+	0.994865i	$0.532271\pi$
$200$	−5.72889	−0.405094
$201$	−12.9156	−0.910995
$202$	18.5382	1.30434
$203$	−0.0492290	−0.00345520
$204$	37.0561	2.59445
$205$	7.23591	0.505378
$206$	−30.5952	−2.13167
$207$	−12.1726	−0.846057
$208$	−28.9608	−2.00807
$209$	0	0
$210$	−0.679666	−0.0469014
$211$	−12.8875	−0.887212	−0.443606	−	0.896222i	$-0.646301\pi$
$211$	−12.8875	−0.887212	−0.443606	+	0.896222i	$0.646301\pi$
$212$	18.7710	1.28920
$213$	−12.0250	−0.823937
$214$	4.09534	0.279952
$215$	−7.29918	−0.497800
$216$	31.5491	2.14665
$217$	−0.556248	−0.0377606
$218$	19.0945	1.29324
$219$	−17.2007	−1.16232
$220$	3.33437	0.224803
$221$	−35.3865	−2.38035
$222$	5.83447	0.391584
$223$	20.7077	1.38669	0.693346	−	0.720604i	$-0.256136\pi$
$223$	20.7077	1.38669	0.693346	+	0.720604i	$0.256136\pi$
$224$	0.679666	0.0454121
$225$	−1.50702	−0.100468
$226$	−31.3101	−2.08272
$227$	4.00000	0.265489	0.132745	−	0.991150i	$-0.457621\pi$
$227$	4.00000	0.265489	0.132745	+	0.991150i	$0.457621\pi$
$228$	0	0
$229$	3.53910	0.233870	0.116935	−	0.993140i	$-0.462693\pi$
$229$	3.53910	0.233870	0.116935	+	0.993140i	$0.462693\pi$
$230$	20.2500	1.33524
$231$	0.210953	0.0138797
$232$	−1.27111	−0.0834521
$233$	−19.7850	−1.29616	−0.648081	−	0.761572i	$-0.724428\pi$
$233$	−19.7850	−1.29616	−0.648081	+	0.761572i	$0.724428\pi$
$234$	−18.8906	−1.23492
$235$	2.79216	0.182141
$236$	−11.9648	−0.778843
$237$	1.93585	0.125747
$238$	3.93673	0.255181
$239$	23.7741	1.53782	0.768910	−	0.639357i	$-0.220799\pi$
$239$	23.7741	1.53782	0.768910	+	0.639357i	$0.220799\pi$
$240$	−7.07730	−0.456838
$241$	−4.54221	−0.292589	−0.146295	−	0.989241i	$-0.546735\pi$
$241$	−4.54221	−0.292589	−0.146295	+	0.989241i	$0.546735\pi$
$242$	26.0593	1.67515
$243$	13.8234	0.886768
$244$	−53.9256	−3.45223
$245$	6.95077	0.444068
$246$	22.1655	1.41322
$247$	0	0
$248$	−14.3624	−0.912016
$249$	−11.6336	−0.737246
$250$	2.50702	0.158558
$251$	−19.5030	−1.23102	−0.615510	−	0.788129i	$-0.711050\pi$
$251$	−19.5030	−1.23102	−0.615510	+	0.788129i	$0.711050\pi$
$252$	1.43283	0.0902598
$253$	−6.28514	−0.395144
$254$	32.6968	2.05158
$255$	−8.64759	−0.541533
$256$	−32.0913	−2.00571
$257$	1.76409	0.110041	0.0550203	−	0.998485i	$-0.482478\pi$
$257$	1.76409	0.110041	0.0550203	+	0.998485i	$0.482478\pi$
$258$	−22.3593	−1.39203
$259$	0.422598	0.0262590
$260$	21.4257	1.32877
$261$	−0.334372	−0.0206971
$262$	−17.8234	−1.10113
$263$	−6.47183	−0.399070	−0.199535	−	0.979891i	$-0.563943\pi$
$263$	−6.47183	−0.399070	−0.199535	+	0.979891i	$0.563943\pi$
$264$	5.44687	0.335231
$265$	−4.38049	−0.269091
$266$	0	0
$267$	3.83739	0.234844
$268$	−45.2952	−2.76684
$269$	28.4859	1.73681	0.868407	−	0.495852i	$-0.165144\pi$
$269$	28.4859	1.73681	0.868407	+	0.495852i	$0.165144\pi$
$270$	−13.8062	−0.840218
$271$	−0.492981	−0.0299465	−0.0149732	−	0.999888i	$-0.504766\pi$
$271$	−0.492981	−0.0299465	−0.0149732	+	0.999888i	$0.504766\pi$
$272$	40.9929	2.48556
$273$	1.35553	0.0820402
$274$	−13.6024	−0.821749
$275$	−0.778124	−0.0469226
$276$	42.2921	2.54568
$277$	−8.78905	−0.528083	−0.264041	−	0.964511i	$-0.585056\pi$
$277$	−8.78905	−0.528083	−0.264041	+	0.964511i	$0.585056\pi$
$278$	−8.95077	−0.536832
$279$	−3.77812	−0.226190
$280$	−1.27111	−0.0759631
$281$	−4.74293	−0.282940	−0.141470	−	0.989943i	$-0.545183\pi$
$281$	−4.74293	−0.282940	−0.141470	+	0.989943i	$0.545183\pi$
$282$	8.55313	0.509332
$283$	16.8695	1.00279	0.501393	−	0.865220i	$-0.332821\pi$
$283$	16.8695	1.00279	0.501393	+	0.865220i	$0.332821\pi$
$284$	−42.1718	−2.50243
$285$	0	0
$286$	−9.75385	−0.576758
$287$	1.60548	0.0947683
$288$	4.61640	0.272024
$289$	33.0882	1.94637
$290$	0.556248	0.0326640
$291$	−7.77412	−0.455727
$292$	−60.3233	−3.53015
$293$	11.6336	0.679639	0.339820	−	0.940491i	$-0.389634\pi$
$293$	11.6336	0.679639	0.339820	+	0.940491i	$0.389634\pi$
$294$	21.2921	1.24178
$295$	2.79216	0.162566
$296$	10.9116	0.634223
$297$	4.28514	0.248649
$298$	2.34841	0.136040
$299$	−40.3865	−2.33561
$300$	5.23591	0.302296
$301$	−1.61951	−0.0933472
$302$	2.43664	0.140213
$303$	−9.03519	−0.519058
$304$	0	0
$305$	12.5843	0.720576
$306$	26.7389	1.52856
$307$	5.89062	0.336195	0.168098	−	0.985770i	$-0.446238\pi$
$307$	5.89062	0.336195	0.168098	+	0.985770i	$0.446238\pi$
$308$	0.739818	0.0421550
$309$	14.9116	0.848290
$310$	6.28514	0.356972
$311$	14.8202	0.840378	0.420189	−	0.907437i	$-0.361964\pi$
$311$	14.8202	0.840378	0.420189	+	0.907437i	$0.361964\pi$
$312$	35.0000	1.98148
$313$	−5.89462	−0.333184	−0.166592	−	0.986026i	$-0.553276\pi$
$313$	−5.89462	−0.333184	−0.166592	+	0.986026i	$0.553276\pi$
$314$	−6.80620	−0.384096
$315$	−0.334372	−0.0188397
$316$	6.78905	0.381914
$317$	−4.15861	−0.233571	−0.116785	−	0.993157i	$-0.537259\pi$
$317$	−4.15861	−0.233571	−0.116785	+	0.993157i	$0.537259\pi$
$318$	−13.4186	−0.752477
$319$	−0.172647	−0.00966638
$320$	3.90466	0.218277
$321$	−1.99600	−0.111406
$322$	4.49298	0.250384
$323$	0	0
$324$	−9.46090	−0.525606
$325$	−5.00000	−0.277350
$326$	8.03208	0.444856
$327$	−9.30630	−0.514639
$328$	41.4538	2.28890
$329$	0.619514	0.0341549
$330$	−2.38360	−0.131213
$331$	10.6797	0.587008	0.293504	−	0.955958i	$-0.405179\pi$
$331$	10.6797	0.587008	0.293504	+	0.955958i	$0.405179\pi$
$332$	−40.7991	−2.23914
$333$	2.87035	0.157294
$334$	−25.6264	−1.40222
$335$	10.5703	0.577516
$336$	−1.57028	−0.0856661
$337$	−26.3453	−1.43512	−0.717560	−	0.696497i	$-0.754741\pi$
$337$	−26.3453	−1.43512	−0.717560	+	0.696497i	$0.754741\pi$
$338$	−30.0842	−1.63637
$339$	15.2600	0.828809
$340$	−30.3273	−1.64473
$341$	−1.95077	−0.105640
$342$	0	0
$343$	3.09534	0.167133
$344$	−41.8162	−2.25458
$345$	−9.86946	−0.531354
$346$	6.68278	0.359268
$347$	−16.8835	−0.906354	−0.453177	−	0.891421i	$-0.649709\pi$
$347$	−16.8835	−0.906354	−0.453177	+	0.891421i	$0.649709\pi$
$348$	1.16172	0.0622750
$349$	4.61640	0.247110	0.123555	−	0.992338i	$-0.460570\pi$
$349$	4.61640	0.247110	0.123555	+	0.992338i	$0.460570\pi$
$350$	0.556248	0.0297327
$351$	27.5351	1.46971
$352$	2.38360	0.127046
$353$	−24.9508	−1.32800	−0.663998	−	0.747735i	$-0.731142\pi$
$353$	−24.9508	−1.32800	−0.663998	+	0.747735i	$0.731142\pi$
$354$	8.55313	0.454594
$355$	9.84139	0.522327
$356$	13.4578	0.713261
$357$	−1.91869	−0.101548
$358$	32.4326	1.71412
$359$	11.8022	0.622896	0.311448	−	0.950263i	$-0.399186\pi$
$359$	11.8022	0.622896	0.311448	+	0.950263i	$0.399186\pi$
$360$	−8.63355	−0.455028
$361$	0	0
$362$	46.6616	2.45248
$363$	−12.7008	−0.666620
$364$	4.75385	0.249170
$365$	14.0773	0.736840
$366$	38.5491	2.01500
$367$	26.2328	1.36934	0.684670	−	0.728853i	$-0.259946\pi$
$367$	26.2328	1.36934	0.684670	+	0.728853i	$0.259946\pi$
$368$	46.7850	2.43884
$369$	10.9047	0.567674
$370$	−4.77501	−0.248241
$371$	−0.971925	−0.0504599
$372$	13.1265	0.680579
$373$	11.9960	0.621129	0.310565	−	0.950552i	$-0.399482\pi$
$373$	11.9960	0.621129	0.310565	+	0.950552i	$0.399482\pi$
$374$	13.8062	0.713902
$375$	−1.22188	−0.0630974
$376$	15.9960	0.824931
$377$	−1.10938	−0.0571360
$378$	−3.06327	−0.157557
$379$	0.313217	0.0160889	0.00804444	−	0.999968i	$-0.497439\pi$
$379$	0.313217	0.0160889	0.00804444	+	0.999968i	$0.497439\pi$
$380$	0	0
$381$	−15.9358	−0.816418
$382$	57.7670	2.95562
$383$	30.0882	1.53744	0.768718	−	0.639588i	$-0.220895\pi$
$383$	30.0882	1.53744	0.768718	+	0.639588i	$0.220895\pi$
$384$	19.4469	0.992394
$385$	−0.172647	−0.00879891
$386$	42.8131	2.17913
$387$	−11.0000	−0.559161
$388$	−27.2640	−1.38412
$389$	−35.7218	−1.81117	−0.905583	−	0.424169i	$-0.860566\pi$
$389$	−35.7218	−1.81117	−0.905583	+	0.424169i	$0.860566\pi$
$390$	−15.3163	−0.775573
$391$	57.1655	2.89099
$392$	39.8202	2.01123
$393$	8.68678	0.438190
$394$	22.1125	1.11401
$395$	−1.58432	−0.0797159
$396$	5.02496	0.252514
$397$	9.55313	0.479458	0.239729	−	0.970840i	$-0.422941\pi$
$397$	9.55313	0.479458	0.239729	+	0.970840i	$0.422941\pi$
$398$	7.15861	0.358829
$399$	0	0
$400$	5.79216	0.289608
$401$	30.8835	1.54225	0.771124	−	0.636685i	$-0.219695\pi$
$401$	30.8835	1.54225	0.771124	+	0.636685i	$0.219695\pi$
$402$	32.3796	1.61495
$403$	−12.5351	−0.624417
$404$	−31.6866	−1.57647
$405$	2.20784	0.109708
$406$	0.123418	0.00612514
$407$	1.48206	0.0734629
$408$	−49.5411	−2.45265
$409$	31.5632	1.56070	0.780349	−	0.625344i	$-0.215041\pi$
$409$	31.5632	1.56070	0.780349	+	0.625344i	$0.215041\pi$
$410$	−18.1406	−0.895899
$411$	6.62955	0.327012
$412$	52.2952	2.57640
$413$	0.619514	0.0304843
$414$	30.5171	1.49983
$415$	9.52106	0.467370
$416$	15.3163	0.750945
$417$	4.36245	0.213630
$418$	0	0
$419$	−26.5070	−1.29495	−0.647476	−	0.762086i	$-0.724176\pi$
$419$	−26.5070	−1.29495	−0.647476	+	0.762086i	$0.724176\pi$
$420$	1.16172	0.0566863
$421$	−20.2359	−0.986238	−0.493119	−	0.869962i	$-0.664143\pi$
$421$	−20.2359	−0.986238	−0.493119	+	0.869962i	$0.664143\pi$
$422$	32.3092	1.57279
$423$	4.20784	0.204592
$424$	−25.0953	−1.21874
$425$	7.07730	0.343300
$426$	30.1468	1.46062
$427$	2.79216	0.135122
$428$	−7.00000	−0.338358
$429$	4.75385	0.229518
$430$	18.2992	0.882465
$431$	−11.4609	−0.552052	−0.276026	−	0.961150i	$-0.589018\pi$
$431$	−11.4609	−0.552052	−0.276026	+	0.961150i	$0.589018\pi$
$432$	−31.8975	−1.53467
$433$	25.9468	1.24692	0.623461	−	0.781854i	$-0.285726\pi$
$433$	25.9468	1.24692	0.623461	+	0.781854i	$0.285726\pi$
$434$	1.39452	0.0669393
$435$	−0.271105	−0.0129985
$436$	−32.6374	−1.56305
$437$	0	0
$438$	43.1225	2.06047
$439$	25.3123	1.20809	0.604046	−	0.796950i	$-0.293554\pi$
$439$	25.3123	1.20809	0.604046	+	0.796950i	$0.293554\pi$
$440$	−4.45779	−0.212517
$441$	10.4749	0.498807
$442$	88.7147	4.21973
$443$	20.0250	0.951415	0.475707	−	0.879604i	$-0.342192\pi$
$443$	20.0250	0.951415	0.475707	+	0.879604i	$0.342192\pi$
$444$	−9.97262	−0.473279
$445$	−3.14057	−0.148877
$446$	−51.9147	−2.45823
$447$	−1.14457	−0.0541364
$448$	0.866350	0.0409312
$449$	19.7601	0.932536	0.466268	−	0.884644i	$-0.345598\pi$
$449$	19.7601	0.932536	0.466268	+	0.884644i	$0.345598\pi$
$450$	3.77812	0.178102
$451$	5.63044	0.265127
$452$	53.5171	2.51723
$453$	−1.18757	−0.0557970
$454$	−10.0281	−0.470641
$455$	−1.10938	−0.0520086
$456$	0	0
$457$	−34.4647	−1.61219	−0.806096	−	0.591785i	$-0.798423\pi$
$457$	−34.4647	−1.61219	−0.806096	+	0.591785i	$0.798423\pi$
$458$	−8.87258	−0.414588
$459$	−38.9748	−1.81919
$460$	−34.6124	−1.61381
$461$	−7.93273	−0.369464	−0.184732	−	0.982789i	$-0.559142\pi$
$461$	−7.93273	−0.369464	−0.184732	+	0.982789i	$0.559142\pi$
$462$	−0.528864	−0.0246050
$463$	9.25395	0.430068	0.215034	−	0.976607i	$-0.431014\pi$
$463$	9.25395	0.430068	0.215034	+	0.976607i	$0.431014\pi$
$464$	1.28514	0.0596612
$465$	−3.06327	−0.142056
$466$	49.6015	2.29774
$467$	9.47183	0.438304	0.219152	−	0.975691i	$-0.429671\pi$
$467$	9.47183	0.438304	0.219152	+	0.975691i	$0.429671\pi$
$468$	32.2889	1.49256
$469$	2.34529	0.108296
$470$	−7.00000	−0.322886
$471$	3.31722	0.152849
$472$	15.9960	0.736275
$473$	−5.67967	−0.261151
$474$	−4.85320	−0.222915
$475$	0	0
$476$	−6.72889	−0.308418
$477$	−6.60147	−0.302261
$478$	−59.6022	−2.72614
$479$	−34.7149	−1.58616	−0.793081	−	0.609116i	$-0.791524\pi$
$479$	−34.7149	−1.58616	−0.793081	+	0.609116i	$0.791524\pi$
$480$	3.74293	0.170841
$481$	9.52328	0.434224
$482$	11.3874	0.518682
$483$	−2.18980	−0.0996393
$484$	−44.5420	−2.02464
$485$	6.36245	0.288904
$486$	−34.6554	−1.57200
$487$	−28.5070	−1.29178	−0.645888	−	0.763432i	$-0.723513\pi$
$487$	−28.5070	−1.29178	−0.645888	+	0.763432i	$0.723513\pi$
$488$	72.0943	3.26355
$489$	−3.91469	−0.177028
$490$	−17.4257	−0.787213
$491$	−31.1898	−1.40758	−0.703788	−	0.710410i	$-0.748509\pi$
$491$	−31.1898	−1.40758	−0.703788	+	0.710410i	$0.748509\pi$
$492$	−37.8866	−1.70806
$493$	1.57028	0.0707221
$494$	0	0
$495$	−1.17265	−0.0527066
$496$	14.5211	0.652015
$497$	2.18357	0.0979465
$498$	29.1655	1.30694
$499$	16.1867	0.724616	0.362308	−	0.932059i	$-0.381989\pi$
$499$	16.1867	0.724616	0.362308	+	0.932059i	$0.381989\pi$
$500$	−4.28514	−0.191637
$501$	12.4899	0.558006
$502$	48.8944	2.18226
$503$	17.2219	0.767886	0.383943	−	0.923357i	$-0.374566\pi$
$503$	17.2219	0.767886	0.383943	+	0.923357i	$0.374566\pi$
$504$	−1.91558	−0.0853267
$505$	7.39452	0.329052
$506$	15.7570	0.700483
$507$	14.6625	0.651185
$508$	−55.8873	−2.47960
$509$	−36.5912	−1.62188	−0.810939	−	0.585130i	$-0.801043\pi$
$509$	−36.5912	−1.62188	−0.810939	+	0.585130i	$0.801043\pi$
$510$	21.6797	0.959992
$511$	3.12342	0.138172
$512$	48.6224	2.14883
$513$	0	0
$514$	−4.42260	−0.195072
$515$	−12.2038	−0.537765
$516$	38.2179	1.68245
$517$	2.17265	0.0955529
$518$	−1.05946	−0.0465500
$519$	−3.25707	−0.142969
$520$	−28.6445	−1.25614
$521$	−3.63667	−0.159325	−0.0796626	−	0.996822i	$-0.525384\pi$
$521$	−3.63667	−0.159325	−0.0796626	+	0.996822i	$0.525384\pi$
$522$	0.838276	0.0366903
$523$	−35.6233	−1.55770	−0.778850	−	0.627211i	$-0.784196\pi$
$523$	−35.6233	−1.55770	−0.778850	+	0.627211i	$0.784196\pi$
$524$	30.4647	1.33086
$525$	−0.271105	−0.0118320
$526$	16.2250	0.707443
$527$	17.7429	0.772894
$528$	−5.50702	−0.239662
$529$	42.2428	1.83664
$530$	10.9820	0.477026
$531$	4.20784	0.182605
$532$	0	0
$533$	36.1796	1.56711
$534$	−9.62040	−0.416316
$535$	1.63355	0.0706246
$536$	60.5561	2.61562
$537$	−15.8071	−0.682126
$538$	−71.4146	−3.07890
$539$	5.40856	0.232963
$540$	23.5984	1.01551
$541$	3.17265	0.136403	0.0682014	−	0.997672i	$-0.478274\pi$
$541$	3.17265	0.136403	0.0682014	+	0.997672i	$0.478274\pi$
$542$	1.23591	0.0530870
$543$	−22.7420	−0.975955
$544$	−21.6797	−0.929508
$545$	7.61640	0.326251
$546$	−3.39833	−0.145435
$547$	−28.3805	−1.21346	−0.606731	−	0.794907i	$-0.707519\pi$
$547$	−28.3805	−1.21346	−0.606731	+	0.794907i	$0.707519\pi$
$548$	23.2500	0.993189
$549$	18.9648	0.809398
$550$	1.95077	0.0831812
$551$	0	0
$552$	−56.5411	−2.40655
$553$	−0.351523	−0.0149483
$554$	22.0343	0.936148
$555$	2.32725	0.0987864
$556$	15.2992	0.648830
$557$	2.13054	0.0902737	0.0451368	−	0.998981i	$-0.485628\pi$
$557$	2.13054	0.0902737	0.0451368	+	0.998981i	$0.485628\pi$
$558$	9.47183	0.400974
$559$	−36.4959	−1.54361
$560$	1.28514	0.0543072
$561$	−6.72889	−0.284094
$562$	11.8906	0.501575
$563$	−20.2609	−0.853894	−0.426947	−	0.904277i	$-0.640411\pi$
$563$	−20.2609	−0.853894	−0.426947	+	0.904277i	$0.640411\pi$
$564$	−14.6195	−0.615593
$565$	−12.4890	−0.525415
$566$	−42.2921	−1.77767
$567$	0.489867	0.0205725
$568$	56.3803	2.36566
$569$	−34.7530	−1.45692	−0.728460	−	0.685088i	$-0.759764\pi$
$569$	−34.7530	−1.45692	−0.728460	+	0.685088i	$0.759764\pi$
$570$	0	0
$571$	32.0702	1.34210	0.671048	−	0.741414i	$-0.265845\pi$
$571$	32.0702	1.34210	0.671048	+	0.741414i	$0.265845\pi$
$572$	16.6719	0.697085
$573$	−28.1546	−1.17618
$574$	−4.02496	−0.167999
$575$	8.07730	0.336847
$576$	5.88439	0.245183
$577$	30.2740	1.26032	0.630162	−	0.776464i	$-0.282988\pi$
$577$	30.2740	1.26032	0.630162	+	0.776464i	$0.282988\pi$
$578$	−82.9528	−3.45038
$579$	−20.8664	−0.867176
$580$	−0.950771	−0.0394786
$581$	2.11250	0.0876411
$582$	19.4899	0.807881
$583$	−3.40856	−0.141168
$584$	80.6474	3.33721
$585$	−7.53509	−0.311538
$586$	−29.1655	−1.20482
$587$	2.49610	0.103025	0.0515125	−	0.998672i	$-0.483596\pi$
$587$	2.49610	0.103025	0.0515125	+	0.998672i	$0.483596\pi$
$588$	−36.3936	−1.50085
$589$	0	0
$590$	−7.00000	−0.288185
$591$	−10.7772	−0.443316
$592$	−11.0321	−0.453416
$593$	−9.96392	−0.409169	−0.204585	−	0.978849i	$-0.565584\pi$
$593$	−9.96392	−0.409169	−0.204585	+	0.978849i	$0.565584\pi$
$594$	−10.7429	−0.440788
$595$	1.57028	0.0643754
$596$	−4.01404	−0.164421
$597$	−3.48898	−0.142794
$598$	101.250	4.14041
$599$	32.0702	1.31035	0.655176	−	0.755476i	$-0.272594\pi$
$599$	32.0702	1.31035	0.655176	+	0.755476i	$0.272594\pi$
$600$	−7.00000	−0.285774
$601$	3.68278	0.150224	0.0751119	−	0.997175i	$-0.476069\pi$
$601$	3.68278	0.150224	0.0751119	+	0.997175i	$0.476069\pi$
$602$	4.06015	0.165479
$603$	15.9296	0.648704
$604$	−4.16484	−0.169465
$605$	10.3945	0.422597
$606$	22.6514	0.920150
$607$	−20.4850	−0.831460	−0.415730	−	0.909488i	$-0.636474\pi$
$607$	−20.4850	−0.831460	−0.415730	+	0.909488i	$0.636474\pi$
$608$	0	0
$609$	−0.0601518	−0.00243747
$610$	−31.5491	−1.27739
$611$	13.9608	0.564794
$612$	−45.7037	−1.84746
$613$	10.7117	0.432643	0.216322	−	0.976322i	$-0.430594\pi$
$613$	10.7117	0.432643	0.216322	+	0.976322i	$0.430594\pi$
$614$	−14.7679	−0.595984
$615$	8.84139	0.356519
$616$	−0.989077	−0.0398511
$617$	−17.7320	−0.713864	−0.356932	−	0.934130i	$-0.616177\pi$
$617$	−17.7320	−0.713864	−0.356932	+	0.934130i	$0.616177\pi$
$618$	−37.3836	−1.50379
$619$	−13.2780	−0.533689	−0.266844	−	0.963740i	$-0.585981\pi$
$619$	−13.2780	−0.533689	−0.266844	+	0.963740i	$0.585981\pi$
$620$	−10.7429	−0.431447
$621$	−44.4819	−1.78500
$622$	−37.1546	−1.48976
$623$	−0.696818	−0.0279174
$624$	−35.3865	−1.41659
$625$	1.00000	0.0400000
$626$	14.7779	0.590645
$627$	0	0
$628$	11.6336	0.464229
$629$	−13.4798	−0.537476
$630$	0.838276	0.0333977
$631$	4.06415	0.161791	0.0808957	−	0.996723i	$-0.474222\pi$
$631$	4.06415	0.161791	0.0808957	+	0.996723i	$0.474222\pi$
$632$	−9.07642	−0.361040
$633$	−15.7469	−0.625884
$634$	10.4257	0.414058
$635$	13.0421	0.517560
$636$	22.9358	0.909465
$637$	34.7539	1.37700
$638$	0.432830	0.0171359
$639$	14.8312	0.586712
$640$	−15.9156	−0.629119
$641$	4.98507	0.196899	0.0984493	−	0.995142i	$-0.468612\pi$
$641$	4.98507	0.196899	0.0984493	+	0.995142i	$0.468612\pi$
$642$	5.00400	0.197492
$643$	−5.87658	−0.231750	−0.115875	−	0.993264i	$-0.536967\pi$
$643$	−5.87658	−0.231750	−0.115875	+	0.993264i	$0.536967\pi$
$644$	−7.67967	−0.302621
$645$	−8.91869	−0.351173
$646$	0	0
$647$	16.9757	0.667385	0.333692	−	0.942682i	$-0.391705\pi$
$647$	16.9757	0.667385	0.333692	+	0.942682i	$0.391705\pi$
$648$	12.6485	0.496879
$649$	2.17265	0.0852839
$650$	12.5351	0.491667
$651$	−0.679666	−0.0266382
$652$	−13.7289	−0.537665
$653$	24.6797	0.965790	0.482895	−	0.875678i	$-0.339585\pi$
$653$	24.6797	0.965790	0.482895	+	0.875678i	$0.339585\pi$
$654$	23.3311	0.912317
$655$	−7.10938	−0.277786
$656$	−41.9116	−1.63637
$657$	21.2148	0.827667
$658$	−1.55313	−0.0605474
$659$	1.88662	0.0734921	0.0367461	−	0.999325i	$-0.488301\pi$
$659$	1.88662	0.0734921	0.0367461	+	0.999325i	$0.488301\pi$
$660$	4.07419	0.158588
$661$	44.7499	1.74057	0.870284	−	0.492551i	$-0.163935\pi$
$661$	44.7499	1.74057	0.870284	+	0.492551i	$0.163935\pi$
$662$	−26.7741	−1.04061
$663$	−43.2379	−1.67922
$664$	54.5451	2.11676
$665$	0	0
$666$	−7.19603	−0.278840
$667$	1.79216	0.0693928
$668$	43.8022	1.69476
$669$	25.3023	0.978243
$670$	−26.4999	−1.02378
$671$	9.79216	0.378022
$672$	0.830467	0.0320360
$673$	25.4046	0.979274	0.489637	−	0.871926i	$-0.337129\pi$
$673$	25.4046	0.979274	0.489637	+	0.871926i	$0.337129\pi$
$674$	66.0481	2.54408
$675$	−5.50702	−0.211965
$676$	51.4217	1.97776
$677$	−3.86946	−0.148716	−0.0743578	−	0.997232i	$-0.523691\pi$
$677$	−3.86946	−0.148716	−0.0743578	+	0.997232i	$0.523691\pi$
$678$	−38.2571	−1.46925
$679$	1.41168	0.0541751
$680$	40.5451	1.55483
$681$	4.88750	0.187290
$682$	4.89062	0.187271
$683$	−48.5171	−1.85645	−0.928227	−	0.372015i	$-0.878667\pi$
$683$	−48.5171	−1.85645	−0.928227	+	0.372015i	$0.878667\pi$
$684$	0	0
$685$	−5.42571	−0.207306
$686$	−7.76008	−0.296281
$687$	4.32434	0.164984
$688$	42.2780	1.61183
$689$	−21.9024	−0.834416
$690$	24.7429	0.941947
$691$	−47.6374	−1.81221	−0.906105	−	0.423052i	$-0.860959\pi$
$691$	−47.6374	−1.81221	−0.906105	+	0.423052i	$0.860959\pi$
$692$	−11.4226	−0.434222
$693$	−0.260182	−0.00988351
$694$	42.3273	1.60672
$695$	−3.57028	−0.135429
$696$	−1.55313	−0.0588714
$697$	−51.2108	−1.93975
$698$	−11.5734	−0.438060
$699$	−24.1749	−0.914378
$700$	−0.950771	−0.0359358
$701$	28.5531	1.07844	0.539218	−	0.842166i	$-0.318720\pi$
$701$	28.5531	1.07844	0.539218	+	0.842166i	$0.318720\pi$
$702$	−69.0310	−2.60541
$703$	0	0
$704$	3.03831	0.114510
$705$	3.41168	0.128491
$706$	62.5520	2.35418
$707$	1.64067	0.0617037
$708$	−14.6195	−0.549435
$709$	19.4827	0.731690	0.365845	−	0.930676i	$-0.380780\pi$
$709$	19.4827	0.731690	0.365845	+	0.930676i	$0.380780\pi$
$710$	−24.6725	−0.925944
$711$	−2.38760	−0.0895421
$712$	−17.9920	−0.674279
$713$	20.2500	0.758367
$714$	4.81020	0.180017
$715$	−3.89062	−0.145501
$716$	−55.4357	−2.07173
$717$	29.0490	1.08486
$718$	−29.5883	−1.10423
$719$	4.10627	0.153138	0.0765689	−	0.997064i	$-0.475603\pi$
$719$	4.10627	0.153138	0.0765689	+	0.997064i	$0.475603\pi$
$720$	8.72889	0.325307
$721$	−2.70774	−0.100842
$722$	0	0
$723$	−5.55002	−0.206407
$724$	−79.7568	−2.96414
$725$	0.221876	0.00824027
$726$	31.8412	1.18174
$727$	−12.4117	−0.460324	−0.230162	−	0.973152i	$-0.573926\pi$
$727$	−12.4117	−0.460324	−0.230162	+	0.973152i	$0.573926\pi$
$728$	−6.35553	−0.235551
$729$	23.5139	0.870887
$730$	−35.2921	−1.30622
$731$	51.6585	1.91066
$732$	−65.8904	−2.43538
$733$	−16.3985	−0.605693	−0.302847	−	0.953039i	$-0.597937\pi$
$733$	−16.3985	−0.605693	−0.302847	+	0.953039i	$0.597937\pi$
$734$	−65.7661	−2.42747
$735$	8.49298	0.313268
$736$	−24.7429	−0.912037
$737$	8.22499	0.302971
$738$	−27.3382	−1.00633
$739$	−46.2036	−1.69963	−0.849814	−	0.527082i	$-0.823286\pi$
$739$	−46.2036	−1.69963	−0.849814	+	0.527082i	$0.823286\pi$
$740$	8.16172	0.300031
$741$	0	0
$742$	2.43664	0.0894517
$743$	−24.8131	−0.910305	−0.455153	−	0.890413i	$-0.650415\pi$
$743$	−24.8131	−0.910305	−0.455153	+	0.890413i	$0.650415\pi$
$744$	−17.5491	−0.643382
$745$	0.936734	0.0343193
$746$	−30.0742	−1.10109
$747$	14.3484	0.524981
$748$	−23.5984	−0.862841
$749$	0.362446	0.0132435
$750$	3.06327	0.111855
$751$	−10.5391	−0.384577	−0.192289	−	0.981338i	$-0.561591\pi$
$751$	−10.5391	−0.384577	−0.192289	+	0.981338i	$0.561591\pi$
$752$	−16.1726	−0.589756
$753$	−23.8303	−0.868423
$754$	2.78124	0.101287
$755$	0.971925	0.0353720
$756$	5.23591	0.190428
$757$	−6.19672	−0.225224	−0.112612	−	0.993639i	$-0.535922\pi$
$757$	−6.19672	−0.225224	−0.112612	+	0.993639i	$0.535922\pi$
$758$	−0.785241	−0.0285212
$759$	−7.67967	−0.278754
$760$	0	0
$761$	35.6084	1.29080	0.645402	−	0.763843i	$-0.276690\pi$
$761$	35.6084	1.29080	0.645402	+	0.763843i	$0.276690\pi$
$762$	39.9515	1.44729
$763$	1.68990	0.0611784
$764$	−98.7387	−3.57224
$765$	10.6656	0.385617
$766$	−75.4317	−2.72546
$767$	13.9608	0.504095
$768$	−39.2116	−1.41493
$769$	−0.155495	−0.00560730	−0.00280365	−	0.999996i	$-0.500892\pi$
$769$	−0.155495	−0.00560730	−0.00280365	+	0.999996i	$0.500892\pi$
$770$	0.432830	0.0155981
$771$	2.15550	0.0776283
$772$	−73.1787	−2.63376
$773$	−5.08823	−0.183011	−0.0915054	−	0.995805i	$-0.529168\pi$
$773$	−5.08823	−0.183011	−0.0915054	+	0.995805i	$0.529168\pi$
$774$	27.5772	0.991242
$775$	2.50702	0.0900548
$776$	36.4498	1.30847
$777$	0.516362	0.0185244
$778$	89.5552	3.21071
$779$	0	0
$780$	26.1796	0.937379
$781$	7.65782	0.274018
$782$	−143.315	−5.12494
$783$	−1.22188	−0.0436663
$784$	−40.2600	−1.43786
$785$	−2.71486	−0.0968974
$786$	−21.7779	−0.776793
$787$	−22.5070	−0.802289	−0.401144	−	0.916015i	$-0.631387\pi$
$787$	−22.5070	−0.802289	−0.401144	+	0.916015i	$0.631387\pi$
$788$	−37.7960	−1.34643
$789$	−7.90777	−0.281524
$790$	3.97193	0.141315
$791$	−2.77101	−0.0985257
$792$	−6.71797	−0.238713
$793$	62.9216	2.23441
$794$	−23.9499	−0.849950
$795$	−5.35241	−0.189830
$796$	−12.2359	−0.433690
$797$	29.2219	1.03509	0.517546	−	0.855655i	$-0.326846\pi$
$797$	29.2219	1.03509	0.517546	+	0.855655i	$0.326846\pi$
$798$	0	0
$799$	−19.7610	−0.699093
$800$	−3.06327	−0.108303
$801$	−4.73290	−0.167229
$802$	−77.4255	−2.73399
$803$	10.9539	0.386554
$804$	−55.3451	−1.95187
$805$	1.79216	0.0631654
$806$	31.4257	1.10692
$807$	34.8062	1.22524
$808$	42.3624	1.49031
$809$	25.8664	0.909412	0.454706	−	0.890641i	$-0.349744\pi$
$809$	25.8664	0.909412	0.454706	+	0.890641i	$0.349744\pi$
$810$	−5.53509	−0.194483
$811$	−19.6968	−0.691649	−0.345824	−	0.938299i	$-0.612401\pi$
$811$	−19.6968	−0.691649	−0.345824	+	0.938299i	$0.612401\pi$
$812$	−0.210953	−0.00740301
$813$	−0.602362	−0.0211258
$814$	−3.71555	−0.130230
$815$	3.20384	0.112225
$816$	50.0882	1.75344
$817$	0	0
$818$	−79.1295	−2.76670
$819$	−1.67186	−0.0584194
$820$	31.0069	1.08281
$821$	4.08042	0.142408	0.0712038	−	0.997462i	$-0.477316\pi$
$821$	4.08042	0.142408	0.0712038	+	0.997462i	$0.477316\pi$
$822$	−16.6204	−0.579703
$823$	10.6064	0.369715	0.184857	−	0.982765i	$-0.440818\pi$
$823$	10.6064	0.369715	0.184857	+	0.982765i	$0.440818\pi$
$824$	−69.9145	−2.43559
$825$	−0.950771	−0.0331016
$826$	−1.55313	−0.0540404
$827$	15.4046	0.535669	0.267834	−	0.963465i	$-0.413692\pi$
$827$	15.4046	0.535669	0.267834	+	0.963465i	$0.413692\pi$
$828$	−52.1615	−1.81274
$829$	21.2350	0.737523	0.368761	−	0.929524i	$-0.379782\pi$
$829$	21.2350	0.737523	0.368761	+	0.929524i	$0.379782\pi$
$830$	−23.8695	−0.828521
$831$	−10.7391	−0.372536
$832$	19.5233	0.676848
$833$	−49.1927	−1.70443
$834$	−10.9367	−0.378708
$835$	−10.2219	−0.353743
$836$	0	0
$837$	−13.8062	−0.477212
$838$	66.4536	2.29560
$839$	−6.09134	−0.210296	−0.105148	−	0.994457i	$-0.533532\pi$
$839$	−6.09134	−0.210296	−0.105148	+	0.994457i	$0.533532\pi$
$840$	−1.55313	−0.0535882
$841$	−28.9508	−0.998302
$842$	50.7318	1.74833
$843$	−5.79528	−0.199600
$844$	−55.2248	−1.90092
$845$	−12.0000	−0.412813
$846$	−10.5491	−0.362687
$847$	2.30630	0.0792453
$848$	25.3725	0.871295
$849$	20.6124	0.707416
$850$	−17.7429	−0.608578
$851$	−15.3845	−0.527373
$852$	−51.5287	−1.76534
$853$	−34.9648	−1.19717	−0.598586	−	0.801058i	$-0.704271\pi$
$853$	−34.9648	−1.19717	−0.598586	+	0.801058i	$0.704271\pi$
$854$	−7.00000	−0.239535
$855$	0	0
$856$	9.35844	0.319865
$857$	4.15149	0.141812	0.0709061	−	0.997483i	$-0.477411\pi$
$857$	4.15149	0.141812	0.0709061	+	0.997483i	$0.477411\pi$
$858$	−11.9180	−0.406874
$859$	28.2491	0.963846	0.481923	−	0.876214i	$-0.339939\pi$
$859$	28.2491	0.963846	0.481923	+	0.876214i	$0.339939\pi$
$860$	−31.2780	−1.06657
$861$	1.96169	0.0668543
$862$	28.7327	0.978640
$863$	51.8272	1.76422	0.882108	−	0.471046i	$-0.156124\pi$
$863$	51.8272	1.76422	0.882108	+	0.471046i	$0.156124\pi$
$864$	16.8695	0.573911
$865$	2.66563	0.0906341
$866$	−65.0490	−2.21046
$867$	40.4297	1.37307
$868$	−2.38360	−0.0809047
$869$	−1.23280	−0.0418198
$870$	0.679666	0.0230428
$871$	52.8514	1.79080
$872$	43.6336	1.47762
$873$	9.58832	0.324516
$874$	0	0
$875$	0.221876	0.00750078
$876$	−73.7075	−2.49035
$877$	−47.1998	−1.59383	−0.796913	−	0.604095i	$-0.793535\pi$
$877$	−47.1998	−1.59383	−0.796913	+	0.604095i	$0.793535\pi$
$878$	−63.4585	−2.14162
$879$	14.2148	0.479452
$880$	4.50702	0.151932
$881$	−33.8935	−1.14190	−0.570951	−	0.820984i	$-0.693425\pi$
$881$	−33.8935	−1.14190	−0.570951	+	0.820984i	$0.693425\pi$
$882$	−26.2609	−0.884250
$883$	21.0662	0.708934	0.354467	−	0.935069i	$-0.384662\pi$
$883$	21.0662	0.708934	0.354467	+	0.935069i	$0.384662\pi$
$884$	−151.636	−5.10008
$885$	3.41168	0.114682
$886$	−50.2029	−1.68660
$887$	7.21476	0.242248	0.121124	−	0.992637i	$-0.461350\pi$
$887$	7.21476	0.242248	0.121124	+	0.992637i	$0.461350\pi$
$888$	13.3326	0.447413
$889$	2.89373	0.0970527
$890$	7.87347	0.263919
$891$	1.71797	0.0575542
$892$	88.7356	2.97109
$893$	0	0
$894$	2.86946	0.0959693
$895$	12.9367	0.432427
$896$	−3.53129	−0.117972
$897$	−49.3473	−1.64766
$898$	−49.5389	−1.65313
$899$	0.556248	0.0185519
$900$	−6.45779	−0.215260
$901$	31.0020	1.03283
$902$	−14.1156	−0.469998
$903$	−1.97885	−0.0658519
$904$	−71.5480	−2.37965
$905$	18.6124	0.618697
$906$	2.97727	0.0989131
$907$	1.16864	0.0388042	0.0194021	−	0.999812i	$-0.493824\pi$
$907$	1.16864	0.0388042	0.0194021	+	0.999812i	$0.493824\pi$
$908$	17.1406	0.568830
$909$	11.1437	0.369613
$910$	2.78124	0.0921972
$911$	−12.3313	−0.408553	−0.204276	−	0.978913i	$-0.565484\pi$
$911$	−12.3313	−0.408553	−0.204276	+	0.978913i	$0.565484\pi$
$912$	0	0
$913$	7.40856	0.245188
$914$	86.4037	2.85798
$915$	15.3765	0.508331
$916$	15.1655	0.501083
$917$	−1.57740	−0.0520904
$918$	97.7107	3.22493
$919$	52.8895	1.74466	0.872332	−	0.488913i	$-0.162607\pi$
$919$	52.8895	1.74466	0.872332	+	0.488913i	$0.162607\pi$
$920$	46.2740	1.52561
$921$	7.19761	0.237169
$922$	19.8875	0.654960
$923$	49.2070	1.61967
$924$	0.903965	0.0297383
$925$	−1.90466	−0.0626247
$926$	−23.1998	−0.762394
$927$	−18.3914	−0.604053
$928$	−0.679666	−0.0223111
$929$	1.39141	0.0456506	0.0228253	−	0.999739i	$-0.492734\pi$
$929$	1.39141	0.0456506	0.0228253	+	0.999739i	$0.492734\pi$
$930$	7.67967	0.251826
$931$	0	0
$932$	−84.7817	−2.77712
$933$	18.1085	0.592845
$934$	−23.7460	−0.776994
$935$	5.50702	0.180099
$936$	−43.1678	−1.41098
$937$	−33.3694	−1.09013	−0.545065	−	0.838394i	$-0.683495\pi$
$937$	−33.3694	−1.09013	−0.545065	+	0.838394i	$0.683495\pi$
$938$	−5.87970	−0.191979
$939$	−7.20250	−0.235045
$940$	11.9648	0.390249
$941$	35.3233	1.15151	0.575753	−	0.817624i	$-0.304709\pi$
$941$	35.3233	1.15151	0.575753	+	0.817624i	$0.304709\pi$
$942$	−8.31633	−0.270961
$943$	−58.4467	−1.90329
$944$	−16.1726	−0.526375
$945$	−1.22188	−0.0397476
$946$	14.2390	0.462951
$947$	13.2571	0.430797	0.215398	−	0.976526i	$-0.430895\pi$
$947$	13.2571	0.430797	0.215398	+	0.976526i	$0.430895\pi$
$948$	8.29537	0.269421
$949$	70.3865	2.28484
$950$	0	0
$951$	−5.08131	−0.164773
$952$	8.99600	0.291562
$953$	18.2702	0.591830	0.295915	−	0.955214i	$-0.404375\pi$
$953$	18.2702	0.591830	0.295915	+	0.955214i	$0.404375\pi$
$954$	16.5500	0.535827
$955$	23.0421	0.745625
$956$	101.875	3.29489
$957$	−0.210953	−0.00681916
$958$	87.0308	2.81184
$959$	−1.20384	−0.0388739
$960$	4.77101	0.153984
$961$	−24.7149	−0.797253
$962$	−23.8750	−0.769762
$963$	2.46179	0.0793301
$964$	−19.4640	−0.626894
$965$	17.0773	0.549738
$966$	5.48987	0.176634
$967$	−45.1125	−1.45072	−0.725360	−	0.688370i	$-0.758327\pi$
$967$	−45.1125	−1.45072	−0.725360	+	0.688370i	$0.758327\pi$
$968$	59.5491	1.91398
$969$	0	0
$970$	−15.9508	−0.512148
$971$	15.6024	0.500704	0.250352	−	0.968155i	$-0.419454\pi$
$971$	15.6024	0.500704	0.250352	+	0.968155i	$0.419454\pi$
$972$	59.2350	1.89996
$973$	−0.792161	−0.0253955
$974$	71.4676	2.28997
$975$	−6.10938	−0.195657
$976$	−72.8904	−2.33317
$977$	26.2319	0.839233	0.419617	−	0.907701i	$-0.362165\pi$
$977$	26.2319	0.839233	0.419617	+	0.907701i	$0.362165\pi$
$978$	9.81420	0.313824
$979$	−2.44375	−0.0781027
$980$	29.7850	0.951448
$981$	11.4781	0.366466
$982$	78.1934	2.49525
$983$	−34.3413	−1.09532	−0.547659	−	0.836702i	$-0.684481\pi$
$983$	−34.3413	−1.09532	−0.547659	+	0.836702i	$0.684481\pi$
$984$	50.6514	1.61471
$985$	8.82024	0.281036
$986$	−3.93673	−0.125371
$987$	0.756969	0.0240946
$988$	0	0
$989$	58.9577	1.87475
$990$	2.93985	0.0934345
$991$	3.30318	0.104929	0.0524645	−	0.998623i	$-0.483292\pi$
$991$	3.30318	0.104929	0.0524645	+	0.998623i	$0.483292\pi$
$992$	−7.67967	−0.243830
$993$	13.0492	0.414105
$994$	−5.47425	−0.173633
$995$	2.85543	0.0905231
$996$	−49.8514	−1.57960
$997$	9.82335	0.311109	0.155554	−	0.987827i	$-0.450284\pi$
$997$	9.82335	0.311109	0.155554	+	0.987827i	$0.450284\pi$
$998$	−40.5803	−1.28455
$999$	10.4890	0.331857

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1805.2.a.h.1.1		3
5.4	even	2		9025.2.a.z.1.3		3
19.7	even	3		95.2.e.b.11.3	✓	6
19.11	even	3		95.2.e.b.26.3	yes	6
19.18	odd	2		1805.2.a.g.1.3		3
57.11	odd	6		855.2.k.g.406.1		6
57.26	odd	6		855.2.k.g.676.1		6
76.7	odd	6		1520.2.q.j.961.2		6
76.11	odd	6		1520.2.q.j.881.2		6
95.7	odd	12		475.2.j.b.49.6		12
95.49	even	6		475.2.e.d.26.1		6
95.64	even	6		475.2.e.d.201.1		6
95.68	odd	12		475.2.j.b.349.6		12
95.83	odd	12		475.2.j.b.49.1		12
95.87	odd	12		475.2.j.b.349.1		12
95.94	odd	2		9025.2.a.ba.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.e.b.11.3	✓	6	19.7	even	3
95.2.e.b.26.3	yes	6	19.11	even	3
475.2.e.d.26.1		6	95.49	even	6
475.2.e.d.201.1		6	95.64	even	6
475.2.j.b.49.1		12	95.83	odd	12
475.2.j.b.49.6		12	95.7	odd	12
475.2.j.b.349.1		12	95.87	odd	12
475.2.j.b.349.6		12	95.68	odd	12
855.2.k.g.406.1		6	57.11	odd	6
855.2.k.g.676.1		6	57.26	odd	6
1520.2.q.j.881.2		6	76.11	odd	6
1520.2.q.j.961.2		6	76.7	odd	6
1805.2.a.g.1.3		3	19.18	odd	2
1805.2.a.h.1.1		3	1.1	even	1	trivial
9025.2.a.z.1.3		3	5.4	even	2
9025.2.a.ba.1.1		3	95.94	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:	\( N \)	\(=\)	\( 1805 = 5 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1805.a (trivial)

\(f(q)\)	\(=\)	\(q-2.50702 q^{2} +1.22188 q^{3} +4.28514 q^{4} -1.00000 q^{5} -3.06327 q^{6} -0.221876 q^{7} -5.72889 q^{8} -1.50702 q^{9} +O(q^{10})\)	\(q-2.50702 q^{2} +1.22188 q^{3} +4.28514 q^{4} -1.00000 q^{5} -3.06327 q^{6} -0.221876 q^{7} -5.72889 q^{8} -1.50702 q^{9} +2.50702 q^{10} -0.778124 q^{11} +5.23591 q^{12} -5.00000 q^{13} +0.556248 q^{14} -1.22188 q^{15} +5.79216 q^{16} +7.07730 q^{17} +3.77812 q^{18} -4.28514 q^{20} -0.271105 q^{21} +1.95077 q^{22} +8.07730 q^{23} -7.00000 q^{24} +1.00000 q^{25} +12.5351 q^{26} -5.50702 q^{27} -0.950771 q^{28} +0.221876 q^{29} +3.06327 q^{30} +2.50702 q^{31} -3.06327 q^{32} -0.950771 q^{33} -17.7429 q^{34} +0.221876 q^{35} -6.45779 q^{36} -1.90466 q^{37} -6.10938 q^{39} +5.72889 q^{40} -7.23591 q^{41} +0.679666 q^{42} +7.29918 q^{43} -3.33437 q^{44} +1.50702 q^{45} -20.2500 q^{46} -2.79216 q^{47} +7.07730 q^{48} -6.95077 q^{49} -2.50702 q^{50} +8.64759 q^{51} -21.4257 q^{52} +4.38049 q^{53} +13.8062 q^{54} +0.778124 q^{55} +1.27111 q^{56} -0.556248 q^{58} -2.79216 q^{59} -5.23591 q^{60} -12.5843 q^{61} -6.28514 q^{62} +0.334372 q^{63} -3.90466 q^{64} +5.00000 q^{65} +2.38360 q^{66} -10.5703 q^{67} +30.3273 q^{68} +9.86946 q^{69} -0.556248 q^{70} -9.84139 q^{71} +8.63355 q^{72} -14.0773 q^{73} +4.77501 q^{74} +1.22188 q^{75} +0.172647 q^{77} +15.3163 q^{78} +1.58432 q^{79} -5.79216 q^{80} -2.20784 q^{81} +18.1406 q^{82} -9.52106 q^{83} -1.16172 q^{84} -7.07730 q^{85} -18.2992 q^{86} +0.271105 q^{87} +4.45779 q^{88} +3.14057 q^{89} -3.77812 q^{90} +1.10938 q^{91} +34.6124 q^{92} +3.06327 q^{93} +7.00000 q^{94} -3.74293 q^{96} -6.36245 q^{97} +17.4257 q^{98} +1.17265 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + q^{2} + q^{3} + 7 q^{4} - 3 q^{5} - 6 q^{6} + 2 q^{7} - 6 q^{8} + 4 q^{9}+O(q^{10}) \) 3 * q + q^2 + q^3 + 7 * q^4 - 3 * q^5 - 6 * q^6 + 2 * q^7 - 6 * q^8 + 4 * q^9	\( 3 q + q^{2} + q^{3} + 7 q^{4} - 3 q^{5} - 6 q^{6} + 2 q^{7} - 6 q^{8} + 4 q^{9} - q^{10} - 5 q^{11} - 4 q^{12} - 15 q^{13} + 7 q^{14} - q^{15} + 3 q^{16} + q^{17} + 14 q^{18} - 7 q^{20} - 12 q^{21} - 8 q^{22} + 4 q^{23} - 21 q^{24} + 3 q^{25} - 5 q^{26} - 8 q^{27} + 11 q^{28} - 2 q^{29} + 6 q^{30} - q^{31} - 6 q^{32} + 11 q^{33} - 25 q^{34} - 2 q^{35} + 3 q^{36} - 2 q^{37} - 5 q^{39} + 6 q^{40} - 2 q^{41} - 23 q^{42} - q^{43} - 18 q^{44} - 4 q^{45} - 24 q^{46} + 6 q^{47} + q^{48} - 7 q^{49} + q^{50} - 6 q^{51} - 35 q^{52} + 11 q^{53} + 10 q^{54} + 5 q^{55} + 15 q^{56} - 7 q^{58} + 6 q^{59} + 4 q^{60} - 9 q^{61} - 13 q^{62} + 9 q^{63} - 8 q^{64} + 15 q^{65} + 29 q^{66} - 20 q^{67} + 34 q^{68} - 5 q^{69} - 7 q^{70} - 29 q^{71} + 11 q^{72} - 22 q^{73} - 7 q^{74} + q^{75} - 16 q^{77} + 30 q^{78} - 24 q^{79} - 3 q^{80} - 21 q^{81} + 31 q^{82} - 3 q^{83} - 28 q^{84} - q^{85} - 32 q^{86} + 12 q^{87} - 9 q^{88} - 14 q^{89} - 14 q^{90} - 10 q^{91} + 41 q^{92} + 6 q^{93} + 21 q^{94} + 17 q^{96} + 7 q^{97} + 23 q^{98} - 13 q^{99}+O(q^{100}) \) 3 * q + q^2 + q^3 + 7 * q^4 - 3 * q^5 - 6 * q^6 + 2 * q^7 - 6 * q^8 + 4 * q^9 - q^10 - 5 * q^11 - 4 * q^12 - 15 * q^13 + 7 * q^14 - q^15 + 3 * q^16 + q^17 + 14 * q^18 - 7 * q^20 - 12 * q^21 - 8 * q^22 + 4 * q^23 - 21 * q^24 + 3 * q^25 - 5 * q^26 - 8 * q^27 + 11 * q^28 - 2 * q^29 + 6 * q^30 - q^31 - 6 * q^32 + 11 * q^33 - 25 * q^34 - 2 * q^35 + 3 * q^36 - 2 * q^37 - 5 * q^39 + 6 * q^40 - 2 * q^41 - 23 * q^42 - q^43 - 18 * q^44 - 4 * q^45 - 24 * q^46 + 6 * q^47 + q^48 - 7 * q^49 + q^50 - 6 * q^51 - 35 * q^52 + 11 * q^53 + 10 * q^54 + 5 * q^55 + 15 * q^56 - 7 * q^58 + 6 * q^59 + 4 * q^60 - 9 * q^61 - 13 * q^62 + 9 * q^63 - 8 * q^64 + 15 * q^65 + 29 * q^66 - 20 * q^67 + 34 * q^68 - 5 * q^69 - 7 * q^70 - 29 * q^71 + 11 * q^72 - 22 * q^73 - 7 * q^74 + q^75 - 16 * q^77 + 30 * q^78 - 24 * q^79 - 3 * q^80 - 21 * q^81 + 31 * q^82 - 3 * q^83 - 28 * q^84 - q^85 - 32 * q^86 + 12 * q^87 - 9 * q^88 - 14 * q^89 - 14 * q^90 - 10 * q^91 + 41 * q^92 + 6 * q^93 + 21 * q^94 + 17 * q^96 + 7 * q^97 + 23 * q^98 - 13 * q^99

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