LMFDB - Embedded newform 1805.2.a.h.1.2

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			1.2
Root			$-2.50702$ 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)

$f(q)$	$=$	$q+1.22188 q^{2} +2.28514 q^{3} -0.507019 q^{4} -1.00000 q^{5} +2.79216 q^{6} -1.28514 q^{7} -3.06327 q^{8} +2.22188 q^{9} +O(q^{10})$	\(q+1.22188 q^{2} +2.28514 q^{3} -0.507019 q^{4} -1.00000 q^{5} +2.79216 q^{6} -1.28514 q^{7} -3.06327 q^{8} +2.22188 q^{9} -1.22188 q^{10} +0.285142 q^{11} -1.15861 q^{12} -5.00000 q^{13} -1.57028 q^{14} -2.28514 q^{15} -2.72889 q^{16} -6.23591 q^{17} +2.71486 q^{18} +0.507019 q^{20} -2.93673 q^{21} +0.348409 q^{22} -5.23591 q^{23} -7.00000 q^{24} +1.00000 q^{25} -6.10938 q^{26} -1.77812 q^{27} +0.651591 q^{28} +1.28514 q^{29} -2.79216 q^{30} -1.22188 q^{31} +2.79216 q^{32} +0.651591 q^{33} -7.61951 q^{34} +1.28514 q^{35} -1.12653 q^{36} +10.8695 q^{37} -11.4257 q^{39} +3.06327 q^{40} -0.841390 q^{41} -3.58832 q^{42} -4.95077 q^{43} -0.144573 q^{44} -2.22188 q^{45} -6.39764 q^{46} +5.72889 q^{47} -6.23591 q^{48} -5.34841 q^{49} +1.22188 q^{50} -14.2500 q^{51} +2.53509 q^{52} +12.3624 q^{53} -2.17265 q^{54} -0.285142 q^{55} +3.93673 q^{56} +1.57028 q^{58} +5.72889 q^{59} +1.15861 q^{60} +4.45779 q^{61} -1.49298 q^{62} -2.85543 q^{63} +8.86946 q^{64} +5.00000 q^{65} +0.796164 q^{66} -0.985963 q^{67} +3.16172 q^{68} -11.9648 q^{69} +1.57028 q^{70} -2.92270 q^{71} -6.80620 q^{72} -0.764087 q^{73} +13.2811 q^{74} +2.28514 q^{75} -0.366449 q^{77} -13.9608 q^{78} -15.4578 q^{79} +2.72889 q^{80} -10.7289 q^{81} -1.02807 q^{82} +1.66563 q^{83} +1.48898 q^{84} +6.23591 q^{85} -6.04923 q^{86} +2.93673 q^{87} -0.873467 q^{88} -16.0281 q^{89} -2.71486 q^{90} +6.42571 q^{91} +2.65471 q^{92} -2.79216 q^{93} +7.00000 q^{94} +6.38049 q^{96} +11.7429 q^{97} -6.53509 q^{98} +0.633551 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.22188	0.863997	0.431998	−	0.901874i	$-0.357809\pi$
$2$	1.22188	0.863997	0.431998	+	0.901874i	$0.357809\pi$
$3$	2.28514	1.31933	0.659664	−	0.751561i	$-0.270699\pi$
$3$	2.28514	1.31933	0.659664	+	0.751561i	$0.270699\pi$
$4$	−0.507019	−0.253509
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	2.79216	1.13990
$7$	−1.28514	−0.485738	−0.242869	−	0.970059i	$-0.578089\pi$
$7$	−1.28514	−0.485738	−0.242869	+	0.970059i	$0.578089\pi$
$8$	−3.06327	−1.08303
$9$	2.22188	0.740625
$10$	−1.22188	−0.386391
$11$	0.285142	0.0859737	0.0429868	−	0.999076i	$-0.486313\pi$
$11$	0.285142	0.0859737	0.0429868	+	0.999076i	$0.486313\pi$
$12$	−1.15861	−0.334462
$13$	−5.00000	−1.38675	−0.693375	−	0.720577i	$-0.743877\pi$
$13$	−5.00000	−1.38675	−0.693375	+	0.720577i	$0.743877\pi$
$14$	−1.57028	−0.419676
$15$	−2.28514	−0.590021
$16$	−2.72889	−0.682224
$17$	−6.23591	−1.51243	−0.756216	−	0.654323i	$-0.772954\pi$
$17$	−6.23591	−1.51243	−0.756216	+	0.654323i	$0.772954\pi$
$18$	2.71486	0.639898
$19$	0	0
$19$	0	0
$20$	0.507019	0.113373
$21$	−2.93673	−0.640848
$22$	0.348409	0.0742810
$23$	−5.23591	−1.09176	−0.545882	−	0.837862i	$-0.683805\pi$
$23$	−5.23591	−1.09176	−0.545882	+	0.837862i	$0.683805\pi$
$24$	−7.00000	−1.42887
$25$	1.00000	0.200000
$26$	−6.10938	−1.19815
$27$	−1.77812	−0.342200
$28$	0.651591	0.123139
$29$	1.28514	0.238645	0.119322	−	0.992856i	$-0.461928\pi$
$29$	1.28514	0.238645	0.119322	+	0.992856i	$0.461928\pi$
$30$	−2.79216	−0.509777
$31$	−1.22188	−0.219455	−0.109728	−	0.993962i	$-0.534998\pi$
$31$	−1.22188	−0.219455	−0.109728	+	0.993962i	$0.534998\pi$
$32$	2.79216	0.493589
$33$	0.651591	0.113427
$34$	−7.61951	−1.30674
$35$	1.28514	0.217229
$36$	−1.12653	−0.187755
$37$	10.8695	1.78693	0.893464	−	0.449134i	$-0.148267\pi$
$37$	10.8695	1.78693	0.893464	+	0.449134i	$0.148267\pi$
$38$	0	0
$39$	−11.4257	−1.82958
$40$	3.06327	0.484345
$41$	−0.841390	−0.131403	−0.0657015	−	0.997839i	$-0.520929\pi$
$41$	−0.841390	−0.131403	−0.0657015	+	0.997839i	$0.520929\pi$
$42$	−3.58832	−0.553691
$43$	−4.95077	−0.754985	−0.377493	−	0.926013i	$-0.623214\pi$
$43$	−4.95077	−0.754985	−0.377493	+	0.926013i	$0.623214\pi$
$44$	−0.144573	−0.0217951
$45$	−2.22188	−0.331218
$46$	−6.39764	−0.943280
$47$	5.72889	0.835645	0.417823	−	0.908529i	$-0.362793\pi$
$47$	5.72889	0.835645	0.417823	+	0.908529i	$0.362793\pi$
$48$	−6.23591	−0.900077
$49$	−5.34841	−0.764058
$50$	1.22188	0.172799
$51$	−14.2500	−1.99539
$52$	2.53509	0.351554
$53$	12.3624	1.69811	0.849056	−	0.528302i	$-0.177171\pi$
$53$	12.3624	1.69811	0.849056	+	0.528302i	$0.177171\pi$
$54$	−2.17265	−0.295660
$55$	−0.285142	−0.0384486
$56$	3.93673	0.526068
$57$	0	0
$58$	1.57028	0.206189
$59$	5.72889	0.745839	0.372919	−	0.927864i	$-0.378357\pi$
$59$	5.72889	0.745839	0.372919	+	0.927864i	$0.378357\pi$
$60$	1.15861	0.149576
$61$	4.45779	0.570761	0.285381	−	0.958414i	$-0.407880\pi$
$61$	4.45779	0.570761	0.285381	+	0.958414i	$0.407880\pi$
$62$	−1.49298	−0.189609
$63$	−2.85543	−0.359750
$64$	8.86946	1.10868
$65$	5.00000	0.620174
$66$	0.796164	0.0980010
$67$	−0.985963	−0.120455	−0.0602273	−	0.998185i	$-0.519183\pi$
$67$	−0.985963	−0.120455	−0.0602273	+	0.998185i	$0.519183\pi$
$68$	3.16172	0.383415
$69$	−11.9648	−1.44039
$70$	1.57028	0.187685
$71$	−2.92270	−0.346860	−0.173430	−	0.984846i	$-0.555485\pi$
$71$	−2.92270	−0.346860	−0.173430	+	0.984846i	$0.555485\pi$
$72$	−6.80620	−0.802118
$73$	−0.764087	−0.0894296	−0.0447148	−	0.999000i	$-0.514238\pi$
$73$	−0.764087	−0.0894296	−0.0447148	+	0.999000i	$0.514238\pi$
$74$	13.2811	1.54390
$75$	2.28514	0.263866
$76$	0	0
$77$	−0.366449	−0.0417607
$78$	−13.9608	−1.58075
$79$	−15.4578	−1.73914	−0.869569	−	0.493812i	$-0.835603\pi$
$79$	−15.4578	−1.73914	−0.869569	+	0.493812i	$0.835603\pi$
$80$	2.72889	0.305100
$81$	−10.7289	−1.19210
$82$	−1.02807	−0.113532
$83$	1.66563	0.182826	0.0914132	−	0.995813i	$-0.470862\pi$
$83$	1.66563	0.182826	0.0914132	+	0.995813i	$0.470862\pi$
$84$	1.48898	0.162461
$85$	6.23591	0.676380
$86$	−6.04923	−0.652305
$87$	2.93673	0.314851
$88$	−0.873467	−0.0931119
$89$	−16.0281	−1.69897	−0.849486	−	0.527611i	$-0.823088\pi$
$89$	−16.0281	−1.69897	−0.849486	+	0.527611i	$0.823088\pi$
$90$	−2.71486	−0.286171
$91$	6.42571	0.673598
$92$	2.65471	0.276772
$93$	−2.79216	−0.289534
$94$	7.00000	0.721995
$95$	0	0
$96$	6.38049	0.651206
$97$	11.7429	1.19231	0.596157	−	0.802868i	$-0.296694\pi$
$97$	11.7429	1.19231	0.596157	+	0.802868i	$0.296694\pi$
$98$	−6.53509	−0.660144
$99$	0.633551	0.0636743
$100$	−0.507019	−0.0507019
$101$	−7.91869	−0.787939	−0.393970	−	0.919123i	$-0.628899\pi$
$101$	−7.91869	−0.787939	−0.393970	+	0.919123i	$0.628899\pi$
$102$	−17.4117	−1.72401
$103$	−12.8202	−1.26322	−0.631608	−	0.775288i	$-0.717605\pi$
$103$	−12.8202	−1.26322	−0.631608	+	0.775288i	$0.717605\pi$
$104$	15.3163	1.50189
$105$	2.93673	0.286596
$106$	15.1054	1.46716
$107$	13.8062	1.33470	0.667348	−	0.744746i	$-0.267429\pi$
$107$	13.8062	1.33470	0.667348	+	0.744746i	$0.267429\pi$
$108$	0.901542	0.0867509
$109$	−9.20384	−0.881568	−0.440784	−	0.897613i	$-0.645299\pi$
$109$	−9.20384	−0.881568	−0.440784	+	0.897613i	$0.645299\pi$
$110$	−0.348409	−0.0332195
$111$	24.8383	2.35754
$112$	3.50702	0.331382
$113$	−17.3273	−1.63001	−0.815005	−	0.579453i	$-0.803266\pi$
$113$	−17.3273	−1.63001	−0.815005	+	0.579453i	$0.803266\pi$
$114$	0	0
$115$	5.23591	0.488251
$116$	−0.651591	−0.0604987
$117$	−11.1094	−1.02706
$118$	7.00000	0.644402
$119$	8.01404	0.734646
$120$	7.00000	0.639010
$121$	−10.9187	−0.992609
$122$	5.44687	0.493136
$123$	−1.92270	−0.173364
$124$	0.619514	0.0556340
$125$	−1.00000	−0.0894427
$126$	−3.48898	−0.310823
$127$	9.33126	0.828015	0.414008	−	0.910273i	$-0.364129\pi$
$127$	9.33126	0.828015	0.414008	+	0.910273i	$0.364129\pi$
$128$	5.25307	0.464310
$129$	−11.3132	−0.996073
$130$	6.10938	0.535828
$131$	12.4257	1.08564	0.542820	−	0.839849i	$-0.317357\pi$
$131$	12.4257	1.08564	0.542820	+	0.839849i	$0.317357\pi$
$132$	−0.330369	−0.0287549
$133$	0	0
$134$	−1.20472	−0.104072
$135$	1.77812	0.153037
$136$	19.1023	1.63801
$137$	−18.5351	−1.58356	−0.791780	−	0.610806i	$-0.790845\pi$
$137$	−18.5351	−1.58356	−0.791780	+	0.610806i	$0.790845\pi$
$138$	−14.6195	−1.24450
$139$	−6.01404	−0.510104	−0.255052	−	0.966927i	$-0.582093\pi$
$139$	−6.01404	−0.510104	−0.255052	+	0.966927i	$0.582093\pi$
$140$	−0.651591	−0.0550695
$141$	13.0913	1.10249
$142$	−3.57117	−0.299686
$143$	−1.42571	−0.119224
$144$	−6.06327	−0.505272
$145$	−1.28514	−0.106725
$146$	−0.933619	−0.0772669
$147$	−12.2219	−1.00804
$148$	−5.51102	−0.453003
$149$	−6.79216	−0.556436	−0.278218	−	0.960518i	$-0.589744\pi$
$149$	−6.79216	−0.556436	−0.278218	+	0.960518i	$0.589744\pi$
$150$	2.79216	0.227979
$151$	−15.8875	−1.29291	−0.646453	−	0.762953i	$-0.723749\pi$
$151$	−15.8875	−1.29291	−0.646453	+	0.762953i	$0.723749\pi$
$152$	0	0
$153$	−13.8554	−1.12014
$154$	−0.447755	−0.0360811
$155$	1.22188	0.0981435
$156$	5.79305	0.463815
$157$	7.50702	0.599125	0.299563	−	0.954077i	$-0.403159\pi$
$157$	7.50702	0.599125	0.299563	+	0.954077i	$0.403159\pi$
$158$	−18.8875	−1.50261
$159$	28.2500	2.24037
$160$	−2.79216	−0.220740
$161$	6.72889	0.530311
$162$	−13.1094	−1.02997
$163$	21.8202	1.70909	0.854546	−	0.519375i	$-0.173835\pi$
$163$	21.8202	1.70909	0.854546	+	0.519375i	$0.173835\pi$
$164$	0.426600	0.0333119
$165$	−0.651591	−0.0507263
$166$	2.03519	0.157962
$167$	11.2851	0.873271	0.436635	−	0.899639i	$-0.356170\pi$
$167$	11.2851	0.873271	0.436635	+	0.899639i	$0.356170\pi$
$168$	8.99600	0.694056
$169$	12.0000	0.923077
$170$	7.61951	0.584390
$171$	0	0
$172$	2.51013	0.191396
$173$	−5.85543	−0.445180	−0.222590	−	0.974912i	$-0.571451\pi$
$173$	−5.85543	−0.445180	−0.222590	+	0.974912i	$0.571451\pi$
$174$	3.58832	0.272030
$175$	−1.28514	−0.0971476
$176$	−0.778124	−0.0586533
$177$	13.0913	0.984005
$178$	−19.5843	−1.46791
$179$	−18.7922	−1.40459	−0.702296	−	0.711885i	$-0.747842\pi$
$179$	−18.7922	−1.40459	−0.702296	+	0.711885i	$0.747842\pi$
$180$	1.12653	0.0839668
$181$	13.3453	0.991948	0.495974	−	0.868337i	$-0.334811\pi$
$181$	13.3453	0.991948	0.495974	+	0.868337i	$0.334811\pi$
$182$	7.85142	0.581986
$183$	10.1867	0.753021
$184$	16.0390	1.18241
$185$	−10.8695	−0.799139
$186$	−3.41168	−0.250156
$187$	−1.77812	−0.130029
$188$	−2.90466	−0.211844
$189$	2.28514	0.166220
$190$	0	0
$191$	−0.668743	−0.0483885	−0.0241943	−	0.999707i	$-0.507702\pi$
$191$	−0.668743	−0.0483885	−0.0241943	+	0.999707i	$0.507702\pi$
$192$	20.2680	1.46272
$193$	−3.76409	−0.270945	−0.135472	−	0.990781i	$-0.543255\pi$
$193$	−3.76409	−0.270945	−0.135472	+	0.990781i	$0.543255\pi$
$194$	14.3484	1.03016
$195$	11.4257	0.818212
$196$	2.71174	0.193696
$197$	14.6164	1.04138	0.520688	−	0.853747i	$-0.325676\pi$
$197$	14.6164	1.04138	0.520688	+	0.853747i	$0.325676\pi$
$198$	0.774121	0.0550144
$199$	11.5211	0.816706	0.408353	−	0.912824i	$-0.366103\pi$
$199$	11.5211	0.816706	0.408353	+	0.912824i	$0.366103\pi$
$200$	−3.06327	−0.216606
$201$	−2.25307	−0.158919
$202$	−9.67566	−0.680777
$203$	−1.65159	−0.115919
$204$	7.22499	0.505851
$205$	0.841390	0.0587652
$206$	−15.6647	−1.09141
$207$	−11.6336	−0.808588
$208$	13.6445	0.946074
$209$	0	0
$210$	3.58832	0.247618
$211$	−17.1406	−1.18001	−0.590003	−	0.807401i	$-0.700873\pi$
$211$	−17.1406	−1.18001	−0.590003	+	0.807401i	$0.700873\pi$
$212$	−6.26799	−0.430487
$213$	−6.67878	−0.457622
$214$	16.8695	1.15317
$215$	4.95077	0.337640
$216$	5.44687	0.370612
$217$	1.57028	0.106598
$218$	−11.2459	−0.761672
$219$	−1.74605	−0.117987
$220$	0.144573	0.00974708
$221$	31.1796	2.09736
$222$	30.3493	2.03691
$223$	1.52417	0.102066	0.0510330	−	0.998697i	$-0.483749\pi$
$223$	1.52417	0.102066	0.0510330	+	0.998697i	$0.483749\pi$
$224$	−3.58832	−0.239755
$225$	2.22188	0.148125
$226$	−21.1718	−1.40832
$227$	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
$229$	18.4397	1.21853	0.609266	−	0.792966i	$-0.291464\pi$
$229$	18.4397	1.21853	0.609266	+	0.792966i	$0.291464\pi$
$230$	6.39764	0.421848
$231$	−0.837388	−0.0550961
$232$	−3.93673	−0.258459
$233$	12.7117	0.832774	0.416387	−	0.909187i	$-0.363296\pi$
$233$	12.7117	0.832774	0.416387	+	0.909187i	$0.363296\pi$
$234$	−13.5743	−0.887379
$235$	−5.72889	−0.373712
$236$	−2.90466	−0.189077
$237$	−35.3233	−2.29449
$238$	9.79216	0.634732
$239$	−10.8343	−0.700811	−0.350405	−	0.936598i	$-0.613956\pi$
$239$	−10.8343	−0.700811	−0.350405	+	0.936598i	$0.613956\pi$
$240$	6.23591	0.402526
$241$	−9.87347	−0.636006	−0.318003	−	0.948090i	$-0.603012\pi$
$241$	−9.87347	−0.636006	−0.318003	+	0.948090i	$0.603012\pi$
$242$	−13.3413	−0.857611
$243$	−19.1827	−1.23057
$244$	−2.26018	−0.144693
$245$	5.34841	0.341697
$246$	−2.34930	−0.149786
$247$	0	0
$248$	3.74293	0.237676
$249$	3.80620	0.241208
$250$	−1.22188	−0.0772782
$251$	17.7710	1.12170	0.560848	−	0.827919i	$-0.310475\pi$
$251$	17.7710	1.12170	0.560848	+	0.827919i	$0.310475\pi$
$252$	1.44775	0.0912000
$253$	−1.49298	−0.0938629
$254$	11.4016	0.715403
$255$	14.2500	0.892367
$256$	−11.3203	−0.707521
$257$	8.15861	0.508920	0.254460	−	0.967083i	$-0.418102\pi$
$257$	8.15861	0.508920	0.254460	+	0.967083i	$0.418102\pi$
$258$	−13.8234	−0.860604
$259$	−13.9688	−0.867980
$260$	−2.53509	−0.157220
$261$	2.85543	0.176747
$262$	15.1827	0.937989
$263$	6.31722	0.389536	0.194768	−	0.980849i	$-0.437605\pi$
$263$	6.31722	0.389536	0.194768	+	0.980849i	$0.437605\pi$
$264$	−1.99600	−0.122845
$265$	−12.3624	−0.759419
$266$	0	0
$267$	−36.6264	−2.24150
$268$	0.499901	0.0305363
$269$	8.23903	0.502342	0.251171	−	0.967943i	$-0.419184\pi$
$269$	8.23903	0.502342	0.251171	+	0.967943i	$0.419184\pi$
$270$	2.17265	0.132223
$271$	−4.22188	−0.256461	−0.128230	−	0.991744i	$-0.540930\pi$
$271$	−4.22188	−0.256461	−0.128230	+	0.991744i	$0.540930\pi$
$272$	17.0172	1.03182
$273$	14.6837	0.888696
$274$	−22.6476	−1.36819
$275$	0.285142	0.0171947
$276$	6.06638	0.365153
$277$	−9.83739	−0.591071	−0.295536	−	0.955332i	$-0.595498\pi$
$277$	−9.83739	−0.591071	−0.295536	+	0.955332i	$0.595498\pi$
$278$	−7.34841	−0.440728
$279$	−2.71486	−0.162534
$280$	−3.93673	−0.235265
$281$	5.38049	0.320973	0.160486	−	0.987038i	$-0.448694\pi$
$281$	5.38049	0.320973	0.160486	+	0.987038i	$0.448694\pi$
$282$	15.9960	0.952548
$283$	−4.96481	−0.295127	−0.147564	−	0.989053i	$-0.547143\pi$
$283$	−4.96481	−0.295127	−0.147564	+	0.989053i	$0.547143\pi$
$284$	1.48186	0.0879323
$285$	0	0
$286$	−1.74204	−0.103009
$287$	1.08131	0.0638275
$288$	6.20384	0.365565
$289$	21.8866	1.28745
$290$	−1.57028	−0.0922103
$291$	26.8343	1.57305
$292$	0.387406	0.0226712
$293$	−3.80620	−0.222360	−0.111180	−	0.993800i	$-0.535463\pi$
$293$	−3.80620	−0.222360	−0.111180	+	0.993800i	$0.535463\pi$
$294$	−14.9336	−0.870946
$295$	−5.72889	−0.333549
$296$	−33.2961	−1.93529
$297$	−0.507019	−0.0294202
$298$	−8.29918	−0.480759
$299$	26.1796	1.51400
$300$	−1.15861	−0.0668924
$301$	6.36245	0.366725
$302$	−19.4126	−1.11707
$303$	−18.0953	−1.03955
$304$	0	0
$305$	−4.45779	−0.255252
$306$	−16.9296	−0.967802
$307$	0.574288	0.0327763	0.0163882	−	0.999866i	$-0.494783\pi$
$307$	0.574288	0.0327763	0.0163882	+	0.999866i	$0.494783\pi$
$308$	0.185796	0.0105867
$309$	−29.2961	−1.66659
$310$	1.49298	0.0847956
$311$	−8.61640	−0.488591	−0.244296	−	0.969701i	$-0.578557\pi$
$311$	−8.61640	−0.488591	−0.244296	+	0.969701i	$0.578557\pi$
$312$	35.0000	1.98148
$313$	−34.1234	−1.92877	−0.964385	−	0.264503i	$-0.914792\pi$
$313$	−34.1234	−1.92877	−0.964385	+	0.264503i	$0.914792\pi$
$314$	9.17265	0.517642
$315$	2.85543	0.160885
$316$	7.83739	0.440887
$317$	−11.0773	−0.622163	−0.311082	−	0.950383i	$-0.600691\pi$
$317$	−11.0773	−0.622163	−0.311082	+	0.950383i	$0.600691\pi$
$318$	34.5179	1.93567
$319$	0.366449	0.0205172
$320$	−8.86946	−0.495818
$321$	31.5491	1.76090
$322$	8.22188	0.458187
$323$	0	0
$324$	5.43975	0.302208
$325$	−5.00000	−0.277350
$326$	26.6616	1.47665
$327$	−21.0321	−1.16308
$328$	2.57740	0.142313
$329$	−7.36245	−0.405905
$330$	−0.796164	−0.0438274
$331$	6.41168	0.352418	0.176209	−	0.984353i	$-0.443617\pi$
$331$	6.41168	0.352418	0.176209	+	0.984353i	$0.443617\pi$
$332$	−0.844505	−0.0463482
$333$	24.1506	1.32344
$334$	13.7890	0.754503
$335$	0.985963	0.0538689
$336$	8.01404	0.437202
$337$	−25.2671	−1.37639	−0.688193	−	0.725527i	$-0.741596\pi$
$337$	−25.2671	−1.37639	−0.688193	+	0.725527i	$0.741596\pi$
$338$	14.6625	0.797536
$339$	−39.5952	−2.15052
$340$	−3.16172	−0.171469
$341$	−0.348409	−0.0188674
$342$	0	0
$343$	15.8695	0.856871
$344$	15.1655	0.817671
$345$	11.9648	0.644164
$346$	−7.15461	−0.384634
$347$	12.4086	0.666126	0.333063	−	0.942904i	$-0.391918\pi$
$347$	12.4086	0.666126	0.333063	+	0.942904i	$0.391918\pi$
$348$	−1.48898	−0.0798176
$349$	6.20384	0.332084	0.166042	−	0.986119i	$-0.446901\pi$
$349$	6.20384	0.332084	0.166042	+	0.986119i	$0.446901\pi$
$350$	−1.57028	−0.0839353
$351$	8.89062	0.474546
$352$	0.796164	0.0424357
$353$	−23.3484	−1.24271	−0.621355	−	0.783529i	$-0.713418\pi$
$353$	−23.3484	−1.24271	−0.621355	+	0.783529i	$0.713418\pi$
$354$	15.9960	0.850178
$355$	2.92270	0.155121
$356$	8.12653	0.430705
$357$	18.3132	0.969238
$358$	−22.9617	−1.21356
$359$	−37.7218	−1.99088	−0.995440	−	0.0953935i	$-0.969589\pi$
$359$	−37.7218	−1.99088	−0.995440	+	0.0953935i	$0.969589\pi$
$360$	6.80620	0.358718
$361$	0	0
$362$	16.3063	0.857040
$363$	−24.9508	−1.30958
$364$	−3.25796	−0.170763
$365$	0.764087	0.0399941
$366$	12.4469	0.650608
$367$	29.4077	1.53507	0.767534	−	0.641008i	$-0.221484\pi$
$367$	29.4077	1.53507	0.767534	+	0.641008i	$0.221484\pi$
$368$	14.2883	0.744827
$369$	−1.86946	−0.0973204
$370$	−13.2811	−0.690454
$371$	−15.8875	−0.824838
$372$	1.41568	0.0733995
$373$	−21.5491	−1.11577	−0.557886	−	0.829918i	$-0.688387\pi$
$373$	−21.5491	−1.11577	−0.557886	+	0.829918i	$0.688387\pi$
$374$	−2.17265	−0.112345
$375$	−2.28514	−0.118004
$376$	−17.5491	−0.905027
$377$	−6.42571	−0.330941
$378$	2.79216	0.143613
$379$	−19.3945	−0.996230	−0.498115	−	0.867111i	$-0.665974\pi$
$379$	−19.3945	−0.996230	−0.498115	+	0.867111i	$0.665974\pi$
$380$	0	0
$381$	21.3233	1.09242
$382$	−0.817121	−0.0418076
$383$	18.8866	0.965061	0.482531	−	0.875879i	$-0.339718\pi$
$383$	18.8866	0.965061	0.482531	+	0.875879i	$0.339718\pi$
$384$	12.0040	0.612577
$385$	0.366449	0.0186760
$386$	−4.59925	−0.234096
$387$	−11.0000	−0.559161
$388$	−5.95389	−0.302263
$389$	−9.08042	−0.460395	−0.230198	−	0.973144i	$-0.573937\pi$
$389$	−9.08042	−0.460395	−0.230198	+	0.973144i	$0.573937\pi$
$390$	13.9608	0.706933
$391$	32.6507	1.65122
$392$	16.3836	0.827497
$393$	28.3945	1.43231
$394$	17.8594	0.899745
$395$	15.4578	0.777766
$396$	−0.321222	−0.0161420
$397$	16.9960	0.853005	0.426502	−	0.904486i	$-0.359746\pi$
$397$	16.9960	0.853005	0.426502	+	0.904486i	$0.359746\pi$
$398$	14.0773	0.705631
$399$	0	0
$400$	−2.72889	−0.136445
$401$	1.59144	0.0794727	0.0397363	−	0.999210i	$-0.487348\pi$
$401$	1.59144	0.0794727	0.0397363	+	0.999210i	$0.487348\pi$
$402$	−2.75297	−0.137306
$403$	6.10938	0.304330
$404$	4.01493	0.199750
$405$	10.7289	0.533123
$406$	−2.01804	−0.100154
$407$	3.09935	0.153629
$408$	43.6514	2.16107
$409$	−1.99689	−0.0987396	−0.0493698	−	0.998781i	$-0.515721\pi$
$409$	−1.99689	−0.0987396	−0.0493698	+	0.998781i	$0.515721\pi$
$410$	1.02807	0.0507730
$411$	−42.3553	−2.08923
$412$	6.50010	0.320237
$413$	−7.36245	−0.362282
$414$	−14.2148	−0.698617
$415$	−1.66563	−0.0817625
$416$	−13.9608	−0.684485
$417$	−13.7429	−0.672994
$418$	0	0
$419$	−22.7781	−1.11278	−0.556392	−	0.830920i	$-0.687815\pi$
$419$	−22.7781	−1.11278	−0.556392	+	0.830920i	$0.687815\pi$
$420$	−1.48898	−0.0726547
$421$	−13.8414	−0.674588	−0.337294	−	0.941399i	$-0.609512\pi$
$421$	−13.8414	−0.674588	−0.337294	+	0.941399i	$0.609512\pi$
$422$	−20.9437	−1.01952
$423$	12.7289	0.618900
$424$	−37.8695	−1.83910
$425$	−6.23591	−0.302486
$426$	−8.16064	−0.395384
$427$	−5.72889	−0.277241
$428$	−7.00000	−0.338358
$429$	−3.25796	−0.157296
$430$	6.04923	0.291720
$431$	3.43975	0.165687	0.0828435	−	0.996563i	$-0.473600\pi$
$431$	3.43975	0.165687	0.0828435	+	0.996563i	$0.473600\pi$
$432$	4.85231	0.233457
$433$	−9.20072	−0.442158	−0.221079	−	0.975256i	$-0.570958\pi$
$433$	−9.20072	−0.442158	−0.221079	+	0.975256i	$0.570958\pi$
$434$	1.91869	0.0921002
$435$	−2.93673	−0.140806
$436$	4.66652	0.223486
$437$	0	0
$438$	−2.13345	−0.101940
$439$	−37.5099	−1.79025	−0.895126	−	0.445814i	$-0.852914\pi$
$439$	−37.5099	−1.79025	−0.895126	+	0.445814i	$0.852914\pi$
$440$	0.873467	0.0416409
$441$	−11.8835	−0.565881
$442$	38.0976	1.81212
$443$	14.6788	0.697410	0.348705	−	0.937233i	$-0.386622\pi$
$443$	14.6788	0.697410	0.348705	+	0.937233i	$0.386622\pi$
$444$	−12.5935	−0.597660
$445$	16.0281	0.759804
$446$	1.86235	0.0881847
$447$	−15.5211	−0.734121
$448$	−11.3985	−0.538530
$449$	−7.39052	−0.348780	−0.174390	−	0.984677i	$-0.555795\pi$
$449$	−7.39052	−0.348780	−0.174390	+	0.984677i	$0.555795\pi$
$450$	2.71486	0.127980
$451$	−0.239916	−0.0112972
$452$	8.78524	0.413223
$453$	−36.3052	−1.70577
$454$	4.88750	0.229382
$455$	−6.42571	−0.301242
$456$	0	0
$457$	2.30007	0.107593	0.0537963	−	0.998552i	$-0.482868\pi$
$457$	2.30007	0.107593	0.0537963	+	0.998552i	$0.482868\pi$
$458$	22.5311	1.05281
$459$	11.0882	0.517554
$460$	−2.65471	−0.123776
$461$	19.7570	0.920174	0.460087	−	0.887874i	$-0.347818\pi$
$461$	19.7570	0.920174	0.460087	+	0.887874i	$0.347818\pi$
$462$	−1.02318	−0.0476028
$463$	28.9468	1.34527	0.672635	−	0.739974i	$-0.265162\pi$
$463$	28.9468	1.34527	0.672635	+	0.739974i	$0.265162\pi$
$464$	−3.50702	−0.162809
$465$	2.79216	0.129483
$466$	15.5322	0.719514
$467$	−3.31722	−0.153503	−0.0767513	−	0.997050i	$-0.524455\pi$
$467$	−3.31722	−0.153503	−0.0767513	+	0.997050i	$0.524455\pi$
$468$	5.63266	0.260370
$469$	1.26710	0.0585094
$470$	−7.00000	−0.322886
$471$	17.1546	0.790443
$472$	−17.5491	−0.807764
$473$	−1.41168	−0.0649089
$474$	−43.1606	−1.98243
$475$	0	0
$476$	−4.06327	−0.186240
$477$	27.4678	1.25767
$478$	−13.2381	−0.605498
$479$	−39.5070	−1.80512	−0.902561	−	0.430562i	$-0.858315\pi$
$479$	−39.5070	−1.80512	−0.902561	+	0.430562i	$0.858315\pi$
$480$	−6.38049	−0.291228
$481$	−54.3473	−2.47802
$482$	−12.0642	−0.549507
$483$	15.3765	0.699654
$484$	5.53598	0.251636
$485$	−11.7429	−0.533219
$486$	−23.4389	−1.06321
$487$	−24.7781	−1.12280	−0.561402	−	0.827543i	$-0.689738\pi$
$487$	−24.7781	−1.12280	−0.561402	+	0.827543i	$0.689738\pi$
$488$	−13.6554	−0.618151
$489$	49.8623	2.25485
$490$	6.53509	0.295225
$491$	−13.6235	−0.614821	−0.307410	−	0.951577i	$-0.599462\pi$
$491$	−13.6235	−0.614821	−0.307410	+	0.951577i	$0.599462\pi$
$492$	0.974843	0.0439493
$493$	−8.01404	−0.360934
$494$	0	0
$495$	−0.633551	−0.0284760
$496$	3.33437	0.149718
$497$	3.75608	0.168483
$498$	4.65070	0.208403
$499$	8.18980	0.366626	0.183313	−	0.983055i	$-0.441318\pi$
$499$	8.18980	0.366626	0.183313	+	0.983055i	$0.441318\pi$
$500$	0.507019	0.0226746
$501$	25.7882	1.15213
$502$	21.7140	0.969142
$503$	18.2851	0.815294	0.407647	−	0.913140i	$-0.366349\pi$
$503$	18.2851	0.815294	0.407647	+	0.913140i	$0.366349\pi$
$504$	8.74693	0.389619
$505$	7.91869	0.352377
$506$	−1.82424	−0.0810973
$507$	27.4217	1.21784
$508$	−4.73112	−0.209910
$509$	11.8844	0.526766	0.263383	−	0.964691i	$-0.415162\pi$
$509$	11.8844	0.526766	0.263383	+	0.964691i	$0.415162\pi$
$510$	17.4117	0.771002
$511$	0.981960	0.0434394
$512$	−24.3382	−1.07561
$513$	0	0
$514$	9.96881	0.439705
$515$	12.8202	0.564927
$516$	5.73601	0.252514
$517$	1.63355	0.0718435
$518$	−17.0682	−0.749932
$519$	−13.3805	−0.587338
$520$	−15.3163	−0.671666
$521$	21.3725	0.936345	0.468173	−	0.883637i	$-0.344913\pi$
$521$	21.3725	0.936345	0.468173	+	0.883637i	$0.344913\pi$
$522$	3.48898	0.152708
$523$	−5.77724	−0.252621	−0.126310	−	0.991991i	$-0.540314\pi$
$523$	−5.77724	−0.252621	−0.126310	+	0.991991i	$0.540314\pi$
$524$	−6.30007	−0.275220
$525$	−2.93673	−0.128170
$526$	7.71886	0.336558
$527$	7.61951	0.331911
$528$	−1.77812	−0.0773829
$529$	4.41479	0.191947
$530$	−15.1054	−0.656136
$531$	12.7289	0.552387
$532$	0	0
$533$	4.20695	0.182223
$534$	−44.7530	−1.93665
$535$	−13.8062	−0.596894
$536$	3.02027	0.130456
$537$	−42.9428	−1.85312
$538$	10.0671	0.434022
$539$	−1.52506	−0.0656889
$540$	−0.901542	−0.0387962
$541$	2.63355	0.113225	0.0566126	−	0.998396i	$-0.481970\pi$
$541$	2.63355	0.113225	0.0566126	+	0.998396i	$0.481970\pi$
$542$	−5.15861	−0.221581
$543$	30.4959	1.30870
$544$	−17.4117	−0.746519
$545$	9.20384	0.394249
$546$	17.9416	0.767831
$547$	−36.3624	−1.55475	−0.777373	−	0.629040i	$-0.783448\pi$
$547$	−36.3624	−1.55475	−0.777373	+	0.629040i	$0.783448\pi$
$548$	9.39764	0.401447
$549$	9.90466	0.422720
$550$	0.348409	0.0148562
$551$	0	0
$552$	36.6514	1.55999
$553$	19.8655	0.844765
$554$	−12.0201	−0.510684
$555$	−24.8383	−1.05433
$556$	3.04923	0.129316
$557$	23.9648	1.01542	0.507711	−	0.861528i	$-0.330492\pi$
$557$	23.9648	1.01542	0.507711	+	0.861528i	$0.330492\pi$
$558$	−3.31722	−0.140429
$559$	24.7539	1.04698
$560$	−3.50702	−0.148199
$561$	−4.06327	−0.171551
$562$	6.57429	0.277320
$563$	−8.52017	−0.359082	−0.179541	−	0.983750i	$-0.557461\pi$
$563$	−8.52017	−0.359082	−0.179541	+	0.983750i	$0.557461\pi$
$564$	−6.63755	−0.279491
$565$	17.3273	0.728963
$566$	−6.06638	−0.254989
$567$	13.7882	0.579048
$568$	8.95300	0.375659
$569$	16.3734	0.686407	0.343204	−	0.939261i	$-0.388488\pi$
$569$	16.3734	0.686407	0.343204	+	0.939261i	$0.388488\pi$
$570$	0	0
$571$	−5.21876	−0.218398	−0.109199	−	0.994020i	$-0.534829\pi$
$571$	−5.21876	−0.218398	−0.109199	+	0.994020i	$0.534829\pi$
$572$	0.722863	0.0302244
$573$	−1.52817	−0.0638403
$574$	1.32122	0.0551468
$575$	−5.23591	−0.218353
$576$	19.7069	0.821119
$577$	−32.0390	−1.33380	−0.666900	−	0.745147i	$-0.732379\pi$
$577$	−32.0390	−1.33380	−0.666900	+	0.745147i	$0.732379\pi$
$578$	26.7427	1.11235
$579$	−8.60147	−0.357465
$580$	0.651591	0.0270559
$581$	−2.14057	−0.0888058
$582$	32.7882	1.35911
$583$	3.52506	0.145993
$584$	2.34060	0.0968547
$585$	11.1094	0.459316
$586$	−4.65070	−0.192119
$587$	−3.34441	−0.138038	−0.0690192	−	0.997615i	$-0.521987\pi$
$587$	−3.34441	−0.138038	−0.0690192	+	0.997615i	$0.521987\pi$
$588$	6.19672	0.255548
$589$	0	0
$590$	−7.00000	−0.288185
$591$	33.4006	1.37392
$592$	−29.6616	−1.21909
$593$	42.2108	1.73339	0.866694	−	0.498840i	$-0.166241\pi$
$593$	42.2108	1.73339	0.866694	+	0.498840i	$0.166241\pi$
$594$	−0.619514	−0.0254190
$595$	−8.01404	−0.328543
$596$	3.44375	0.141062
$597$	26.3273	1.07750
$598$	31.9882	1.30809
$599$	−5.21876	−0.213233	−0.106616	−	0.994300i	$-0.534002\pi$
$599$	−5.21876	−0.213233	−0.106616	+	0.994300i	$0.534002\pi$
$600$	−7.00000	−0.285774
$601$	−10.1546	−0.414215	−0.207108	−	0.978318i	$-0.566405\pi$
$601$	−10.1546	−0.414215	−0.207108	+	0.978318i	$0.566405\pi$
$602$	7.77412	0.316850
$603$	−2.19069	−0.0892117
$604$	8.05526	0.327764
$605$	10.9187	0.443908
$606$	−22.1103	−0.898168
$607$	42.8764	1.74030	0.870149	−	0.492788i	$-0.164022\pi$
$607$	42.8764	1.74030	0.870149	+	0.492788i	$0.164022\pi$
$608$	0	0
$609$	−3.77412	−0.152935
$610$	−5.44687	−0.220537
$611$	−28.6445	−1.15883
$612$	7.02496	0.283967
$613$	25.0733	1.01270	0.506351	−	0.862328i	$-0.330994\pi$
$613$	25.0733	1.01270	0.506351	+	0.862328i	$0.330994\pi$
$614$	0.701708	0.0283186
$615$	1.92270	0.0775306
$616$	1.12253	0.0452280
$617$	−5.49698	−0.221300	−0.110650	−	0.993859i	$-0.535293\pi$
$617$	−5.49698	−0.221300	−0.110650	+	0.993859i	$0.535293\pi$
$618$	−35.7962	−1.43993
$619$	15.4899	0.622590	0.311295	−	0.950313i	$-0.399237\pi$
$619$	15.4899	0.622590	0.311295	+	0.950313i	$0.399237\pi$
$620$	−0.619514	−0.0248803
$621$	9.31010	0.373602
$622$	−10.5282	−0.422141
$623$	20.5984	0.825256
$624$	31.1796	1.24818
$625$	1.00000	0.0400000
$626$	−41.6946	−1.66645
$627$	0	0
$628$	−3.80620	−0.151884
$629$	−67.7810	−2.70261
$630$	3.48898	0.139004
$631$	41.3233	1.64505	0.822526	−	0.568727i	$-0.192564\pi$
$631$	41.3233	1.64505	0.822526	+	0.568727i	$0.192564\pi$
$632$	47.3513	1.88353
$633$	−39.1686	−1.55681
$634$	−13.5351	−0.537547
$635$	−9.33126	−0.370300
$636$	−14.3233	−0.567954
$637$	26.7420	1.05956
$638$	0.447755	0.0177268
$639$	−6.49387	−0.256894
$640$	−5.25307	−0.207646
$641$	−30.6717	−1.21146	−0.605729	−	0.795671i	$-0.707118\pi$
$641$	−30.6717	−1.21146	−0.605729	+	0.795671i	$0.707118\pi$
$642$	38.5491	1.52141
$643$	−8.01804	−0.316201	−0.158100	−	0.987423i	$-0.550537\pi$
$643$	−8.01804	−0.316201	−0.158100	+	0.987423i	$0.550537\pi$
$644$	−3.41168	−0.134439
$645$	11.3132	0.445457
$646$	0	0
$647$	10.0272	0.394209	0.197105	−	0.980382i	$-0.436846\pi$
$647$	10.0272	0.394209	0.197105	+	0.980382i	$0.436846\pi$
$648$	32.8655	1.29108
$649$	1.63355	0.0641225
$650$	−6.10938	−0.239630
$651$	3.58832	0.140638
$652$	−11.0633	−0.433271
$653$	20.4117	0.798771	0.399385	−	0.916783i	$-0.369224\pi$
$653$	20.4117	0.798771	0.399385	+	0.916783i	$0.369224\pi$
$654$	−25.6986	−1.00489
$655$	−12.4257	−0.485513
$656$	2.29607	0.0896463
$657$	−1.69771	−0.0662338
$658$	−8.99600	−0.350700
$659$	−36.9748	−1.44034	−0.720168	−	0.693800i	$-0.755935\pi$
$659$	−36.9748	−1.44034	−0.720168	+	0.693800i	$0.755935\pi$
$660$	0.330369	0.0128596
$661$	3.19291	0.124190	0.0620950	−	0.998070i	$-0.480222\pi$
$661$	3.19291	0.124190	0.0620950	+	0.998070i	$0.480222\pi$
$662$	7.83427	0.304488
$663$	71.2498	2.76711
$664$	−5.10226	−0.198006
$665$	0	0
$666$	29.5090	1.14345
$667$	−6.72889	−0.260544
$668$	−5.72178	−0.221382
$669$	3.48295	0.134658
$670$	1.20472	0.0465426
$671$	1.27111	0.0490705
$672$	−8.19983	−0.316315
$673$	−15.0742	−0.581067	−0.290534	−	0.956865i	$-0.593833\pi$
$673$	−15.0742	−0.581067	−0.290534	+	0.956865i	$0.593833\pi$
$674$	−30.8733	−1.18919
$675$	−1.77812	−0.0684400
$676$	−6.08422	−0.234009
$677$	17.9648	0.690444	0.345222	−	0.938521i	$-0.387804\pi$
$677$	17.9648	0.690444	0.345222	+	0.938521i	$0.387804\pi$
$678$	−48.3805	−1.85804
$679$	−15.0913	−0.579153
$680$	−19.1023	−0.732538
$681$	9.14057	0.350267
$682$	−0.425712	−0.0163014
$683$	−3.78524	−0.144838	−0.0724191	−	0.997374i	$-0.523072\pi$
$683$	−3.78524	−0.144838	−0.0724191	+	0.997374i	$0.523072\pi$
$684$	0	0
$685$	18.5351	0.708190
$686$	19.3905	0.740334
$687$	42.1375	1.60764
$688$	13.5101	0.515069
$689$	−61.8122	−2.35486
$690$	14.6195	0.556555
$691$	−10.3335	−0.393104	−0.196552	−	0.980493i	$-0.562974\pi$
$691$	−10.3335	−0.393104	−0.196552	+	0.980493i	$0.562974\pi$
$692$	2.96881	0.112857
$693$	−0.814204	−0.0309290
$694$	15.1617	0.575531
$695$	6.01404	0.228125
$696$	−8.99600	−0.340992
$697$	5.24684	0.198738
$698$	7.58032	0.286919
$699$	29.0481	1.09870
$700$	0.651591	0.0246278
$701$	35.9960	1.35955	0.679775	−	0.733421i	$-0.262077\pi$
$701$	35.9960	1.35955	0.679775	+	0.733421i	$0.262077\pi$
$702$	10.8632	0.410006
$703$	0	0
$704$	2.52906	0.0953176
$705$	−13.0913	−0.493048
$706$	−28.5289	−1.07370
$707$	10.1766	0.382732
$708$	−6.63755	−0.249455
$709$	8.80531	0.330690	0.165345	−	0.986236i	$-0.447126\pi$
$709$	8.80531	0.330690	0.165345	+	0.986236i	$0.447126\pi$
$710$	3.57117	0.134024
$711$	−34.3453	−1.28805
$712$	49.0983	1.84004
$713$	6.39764	0.239593
$714$	22.3765	0.837419
$715$	1.42571	0.0533186
$716$	9.52798	0.356077
$717$	−24.7579	−0.924599
$718$	−46.0913	−1.72011
$719$	18.9920	0.708282	0.354141	−	0.935192i	$-0.384773\pi$
$719$	18.9920	0.708282	0.354141	+	0.935192i	$0.384773\pi$
$720$	6.06327	0.225965
$721$	16.4758	0.613592
$722$	0	0
$723$	−22.5623	−0.839100
$724$	−6.76631	−0.251468
$725$	1.28514	0.0477290
$726$	−30.4868	−1.13147
$727$	4.09134	0.151739	0.0758697	−	0.997118i	$-0.475827\pi$
$727$	4.09134	0.151739	0.0758697	+	0.997118i	$0.475827\pi$
$728$	−19.6837	−0.729525
$729$	−11.6485	−0.431425
$730$	0.933619	0.0345548
$731$	30.8726	1.14186
$732$	−5.16484	−0.190898
$733$	−50.4678	−1.86407	−0.932036	−	0.362366i	$-0.881969\pi$
$733$	−50.4678	−1.86407	−0.932036	+	0.362366i	$0.881969\pi$
$734$	35.9325	1.32629
$735$	12.2219	0.450811
$736$	−14.6195	−0.538882
$737$	−0.281140	−0.0103559
$738$	−2.28425	−0.0840846
$739$	34.2297	1.25916	0.629580	−	0.776936i	$-0.283227\pi$
$739$	34.2297	1.25916	0.629580	+	0.776936i	$0.283227\pi$
$740$	5.51102	0.202589
$741$	0	0
$742$	−19.4126	−0.712658
$743$	22.5992	0.829086	0.414543	−	0.910030i	$-0.363941\pi$
$743$	22.5992	0.829086	0.414543	+	0.910030i	$0.363941\pi$
$744$	8.55313	0.313573
$745$	6.79216	0.248846
$746$	−26.3304	−0.964023
$747$	3.70082	0.135406
$748$	0.901542	0.0329636
$749$	−17.7429	−0.648313
$750$	−2.79216	−0.101955
$751$	−25.4397	−0.928310	−0.464155	−	0.885754i	$-0.653642\pi$
$751$	−25.4397	−0.928310	−0.464155	+	0.885754i	$0.653642\pi$
$752$	−15.6336	−0.570097
$753$	40.6093	1.47988
$754$	−7.85142	−0.285932
$755$	15.8875	0.578205
$756$	−1.15861	−0.0421382
$757$	42.8031	1.55570	0.777852	−	0.628447i	$-0.216309\pi$
$757$	42.8031	1.55570	0.777852	+	0.628447i	$0.216309\pi$
$758$	−23.6977	−0.860739
$759$	−3.41168	−0.123836
$760$	0	0
$761$	−29.8944	−1.08367	−0.541836	−	0.840484i	$-0.682271\pi$
$761$	−29.8944	−1.08367	−0.541836	+	0.840484i	$0.682271\pi$
$762$	26.0544	0.943850
$763$	11.8282	0.428211
$764$	0.339065	0.0122669
$765$	13.8554	0.500944
$766$	23.0771	0.833810
$767$	−28.6445	−1.03429
$768$	−25.8686	−0.933452
$769$	−16.6436	−0.600183	−0.300092	−	0.953910i	$-0.597017\pi$
$769$	−16.6436	−0.600183	−0.300092	+	0.953910i	$0.597017\pi$
$770$	0.447755	0.0161360
$771$	18.6436	0.671432
$772$	1.90846	0.0686871
$773$	6.11338	0.219883	0.109942	−	0.993938i	$-0.464934\pi$
$773$	6.11338	0.219883	0.109942	+	0.993938i	$0.464934\pi$
$774$	−13.4406	−0.483114
$775$	−1.22188	−0.0438911
$776$	−35.9717	−1.29131
$777$	−31.9207	−1.14515
$778$	−11.0951	−0.397780
$779$	0	0
$780$	−5.79305	−0.207424
$781$	−0.833385	−0.0298209
$782$	39.8951	1.42665
$783$	−2.28514	−0.0816643
$784$	14.5952	0.521259
$785$	−7.50702	−0.267937
$786$	34.6946	1.23752
$787$	−18.7781	−0.669368	−0.334684	−	0.942330i	$-0.608630\pi$
$787$	−18.7781	−0.669368	−0.334684	+	0.942330i	$0.608630\pi$
$788$	−7.41079	−0.263998
$789$	14.4357	0.513926
$790$	18.8875	0.671987
$791$	22.2680	0.791759
$792$	−1.94074	−0.0689611
$793$	−22.2889	−0.791504
$794$	20.7670	0.736993
$795$	−28.2500	−1.00192
$796$	−5.84139	−0.207043
$797$	30.2851	1.07275	0.536377	−	0.843978i	$-0.319792\pi$
$797$	30.2851	1.07275	0.536377	+	0.843978i	$0.319792\pi$
$798$	0	0
$799$	−35.7249	−1.26386
$800$	2.79216	0.0987178
$801$	−35.6124	−1.25830
$802$	1.94454	0.0686642
$803$	−0.217874	−0.00768859
$804$	1.14235	0.0402874
$805$	−6.72889	−0.237162
$806$	7.46491	0.262940
$807$	18.8274	0.662754
$808$	24.2571	0.853361
$809$	13.6015	0.478202	0.239101	−	0.970995i	$-0.423147\pi$
$809$	13.6015	0.478202	0.239101	+	0.970995i	$0.423147\pi$
$810$	13.1094	0.460617
$811$	1.59836	0.0561260	0.0280630	−	0.999606i	$-0.491066\pi$
$811$	1.59836	0.0561260	0.0280630	+	0.999606i	$0.491066\pi$
$812$	0.837388	0.0293865
$813$	−9.64759	−0.338356
$814$	3.78702	0.132735
$815$	−21.8202	−0.764330
$816$	38.8866	1.36130
$817$	0	0
$818$	−2.43995	−0.0853107
$819$	14.2771	0.498884
$820$	−0.426600	−0.0148975
$821$	−18.8022	−0.656201	−0.328101	−	0.944643i	$-0.606408\pi$
$821$	−18.8022	−0.656201	−0.328101	+	0.944643i	$0.606408\pi$
$822$	−51.7530	−1.80509
$823$	53.1967	1.85432	0.927161	−	0.374664i	$-0.122242\pi$
$823$	53.1967	1.85432	0.927161	+	0.374664i	$0.122242\pi$
$824$	39.2718	1.36810
$825$	0.651591	0.0226855
$826$	−8.99600	−0.313011
$827$	−25.0742	−0.871915	−0.435957	−	0.899967i	$-0.643590\pi$
$827$	−25.0742	−0.871915	−0.435957	+	0.899967i	$0.643590\pi$
$828$	5.89843	0.204985
$829$	−28.2740	−0.981997	−0.490999	−	0.871160i	$-0.663368\pi$
$829$	−28.2740	−0.981997	−0.490999	+	0.871160i	$0.663368\pi$
$830$	−2.03519	−0.0706425
$831$	−22.4798	−0.779817
$832$	−44.3473	−1.53747
$833$	33.3522	1.15559
$834$	−16.7922	−0.581465
$835$	−11.2851	−0.390538
$836$	0	0
$837$	2.17265	0.0750977
$838$	−27.8320	−0.961442
$839$	14.6797	0.506798	0.253399	−	0.967362i	$-0.418451\pi$
$839$	14.6797	0.506798	0.253399	+	0.967362i	$0.418451\pi$
$840$	−8.99600	−0.310391
$841$	−27.3484	−0.943049
$842$	−16.9125	−0.582842
$843$	12.2952	0.423468
$844$	8.69059	0.299142
$845$	−12.0000	−0.412813
$846$	15.5531	0.534728
$847$	14.0321	0.482148
$848$	−33.7358	−1.15849
$849$	−11.3453	−0.389369
$850$	−7.61951	−0.261347
$851$	−56.9116	−1.95090
$852$	3.38626	0.116012
$853$	−25.9047	−0.886959	−0.443479	−	0.896285i	$-0.646256\pi$
$853$	−25.9047	−0.886959	−0.443479	+	0.896285i	$0.646256\pi$
$854$	−7.00000	−0.239535
$855$	0	0
$856$	−42.2921	−1.44551
$857$	−12.9055	−0.440845	−0.220423	−	0.975404i	$-0.570744\pi$
$857$	−12.9055	−0.440845	−0.220423	+	0.975404i	$0.570744\pi$
$858$	−3.98082	−0.135903
$859$	−28.7178	−0.979838	−0.489919	−	0.871768i	$-0.662974\pi$
$859$	−28.7178	−0.979838	−0.489919	+	0.871768i	$0.662974\pi$
$860$	−2.51013	−0.0855948
$861$	2.47094	0.0842094
$862$	4.20295	0.143153
$863$	−3.04300	−0.103585	−0.0517925	−	0.998658i	$-0.516493\pi$
$863$	−3.04300	−0.103585	−0.0517925	+	0.998658i	$0.516493\pi$
$864$	−4.96481	−0.168906
$865$	5.85543	0.199091
$866$	−11.2421	−0.382024
$867$	50.0140	1.69857
$868$	−0.796164	−0.0270236
$869$	−4.40767	−0.149520
$870$	−3.58832	−0.121656
$871$	4.92981	0.167040
$872$	28.1938	0.954763
$873$	26.0913	0.883058
$874$	0	0
$875$	1.28514	0.0434457
$876$	0.885278	0.0299108
$877$	11.3694	0.383916	0.191958	−	0.981403i	$-0.438516\pi$
$877$	11.3694	0.383916	0.191958	+	0.981403i	$0.438516\pi$
$878$	−45.8325	−1.54677
$879$	−8.69771	−0.293366
$880$	0.778124	0.0262305
$881$	36.4014	1.22640	0.613198	−	0.789929i	$-0.289883\pi$
$881$	36.4014	1.22640	0.613198	+	0.789929i	$0.289883\pi$
$882$	−14.5202	−0.488919
$883$	−49.7679	−1.67482	−0.837411	−	0.546573i	$-0.815932\pi$
$883$	−49.7679	−1.67482	−0.837411	+	0.546573i	$0.815932\pi$
$884$	−15.8086	−0.531701
$885$	−13.0913	−0.440061
$886$	17.9356	0.602560
$887$	−15.6977	−0.527077	−0.263539	−	0.964649i	$-0.584890\pi$
$887$	−15.6977	−0.527077	−0.263539	+	0.964649i	$0.584890\pi$
$888$	−76.0863	−2.55329
$889$	−11.9920	−0.402199
$890$	19.5843	0.656468
$891$	−3.05926	−0.102489
$892$	−0.772783	−0.0258747
$893$	0	0
$894$	−18.9648	−0.634278
$895$	18.7922	0.628153
$896$	−6.75094	−0.225533
$897$	59.8240	1.99747
$898$	−9.03030	−0.301345
$899$	−1.57028	−0.0523719
$900$	−1.12653	−0.0375511
$901$	−77.0911	−2.56828
$902$	−0.293148	−0.00976075
$903$	14.5391	0.483831
$904$	53.0780	1.76535
$905$	−13.3453	−0.443613
$906$	−44.3605	−1.47378
$907$	−32.9156	−1.09294	−0.546472	−	0.837477i	$-0.684029\pi$
$907$	−32.9156	−1.09294	−0.546472	+	0.837477i	$0.684029\pi$
$908$	−2.02807	−0.0673040
$909$	−17.5944	−0.583568
$910$	−7.85142	−0.260272
$911$	−18.7109	−0.619918	−0.309959	−	0.950750i	$-0.600315\pi$
$911$	−18.7109	−0.619918	−0.309959	+	0.950750i	$0.600315\pi$
$912$	0	0
$913$	0.474941	0.0157183
$914$	2.81040	0.0929597
$915$	−10.1867	−0.336761
$916$	−9.34930	−0.308909
$917$	−15.9688	−0.527337
$918$	13.5484	0.447165
$919$	−50.9506	−1.68070	−0.840352	−	0.542041i	$-0.817652\pi$
$919$	−50.9506	−1.68070	−0.840352	+	0.542041i	$0.817652\pi$
$920$	−16.0390	−0.528790
$921$	1.31233	0.0432427
$922$	24.1406	0.795027
$923$	14.6135	0.481009
$924$	0.424571	0.0139674
$925$	10.8695	0.357386
$926$	35.3694	1.16231
$927$	−28.4850	−0.935569
$928$	3.58832	0.117793
$929$	11.4850	0.376810	0.188405	−	0.982091i	$-0.439668\pi$
$929$	11.4850	0.376810	0.188405	+	0.982091i	$0.439668\pi$
$930$	3.41168	0.111873
$931$	0	0
$932$	−6.44509	−0.211116
$933$	−19.6897	−0.644612
$934$	−4.05323	−0.132626
$935$	1.77812	0.0581509
$936$	34.0310	1.11234
$937$	16.1695	0.528236	0.264118	−	0.964490i	$-0.414919\pi$
$937$	16.1695	0.528236	0.264118	+	0.964490i	$0.414919\pi$
$938$	1.54824	0.0505519
$939$	−77.9769	−2.54468
$940$	2.90466	0.0947394
$941$	−25.3874	−0.827606	−0.413803	−	0.910367i	$-0.635800\pi$
$941$	−25.3874	−0.827606	−0.413803	+	0.910367i	$0.635800\pi$
$942$	20.9608	0.682940
$943$	4.40545	0.143461
$944$	−15.6336	−0.508829
$945$	−2.28514	−0.0743357
$946$	−1.72489	−0.0560811
$947$	23.3805	0.759764	0.379882	−	0.925035i	$-0.375965\pi$
$947$	23.3805	0.759764	0.379882	+	0.925035i	$0.375965\pi$
$948$	17.9095	0.581675
$949$	3.82043	0.124016
$950$	0	0
$951$	−25.3132	−0.820837
$952$	−24.5491	−0.795642
$953$	−22.1787	−0.718438	−0.359219	−	0.933253i	$-0.616957\pi$
$953$	−22.1787	−0.718438	−0.359219	+	0.933253i	$0.616957\pi$
$954$	33.5623	1.08662
$955$	0.668743	0.0216400
$956$	5.49318	0.177662
$957$	0.837388	0.0270689
$958$	−48.2727	−1.55962
$959$	23.8202	0.769196
$960$	−20.2680	−0.654147
$961$	−29.5070	−0.951839
$962$	−66.4057	−2.14101
$963$	30.6757	0.988509
$964$	5.00603	0.161233
$965$	3.76409	0.121170
$966$	18.7882	0.604499
$967$	−40.8594	−1.31395	−0.656975	−	0.753912i	$-0.728164\pi$
$967$	−40.8594	−1.31395	−0.656975	+	0.753912i	$0.728164\pi$
$968$	33.4469	1.07502
$969$	0	0
$970$	−14.3484	−0.460700
$971$	24.6476	0.790979	0.395489	−	0.918471i	$-0.370575\pi$
$971$	24.6476	0.790979	0.395489	+	0.918471i	$0.370575\pi$
$972$	9.72598	0.311961
$973$	7.72889	0.247777
$974$	−30.2758	−0.970099
$975$	−11.4257	−0.365916
$976$	−12.1648	−0.389387
$977$	−13.7077	−0.438549	−0.219275	−	0.975663i	$-0.570369\pi$
$977$	−13.7077	−0.438549	−0.219275	+	0.975663i	$0.570369\pi$
$978$	60.9256	1.94819
$979$	−4.57028	−0.146067
$980$	−2.71174	−0.0866235
$981$	−20.4498	−0.652911
$982$	−16.6463	−0.531203
$983$	0.282028	0.00899529	0.00449765	−	0.999990i	$-0.498568\pi$
$983$	0.282028	0.00899529	0.00449765	+	0.999990i	$0.498568\pi$
$984$	5.88973	0.187758
$985$	−14.6164	−0.465717
$986$	−9.79216	−0.311846
$987$	−16.8242	−0.535521
$988$	0	0
$989$	25.9218	0.824266
$990$	−0.774121	−0.0246032
$991$	24.5984	0.781393	0.390696	−	0.920520i	$-0.372234\pi$
$991$	24.5984	0.781393	0.390696	+	0.920520i	$0.372234\pi$
$992$	−3.41168	−0.108321
$993$	14.6516	0.464954
$994$	4.58947	0.145569
$995$	−11.5211	−0.365242
$996$	−1.92981	−0.0611485
$997$	−23.1827	−0.734203	−0.367101	−	0.930181i	$-0.619650\pi$
$997$	−23.1827	−0.734203	−0.367101	+	0.930181i	$0.619650\pi$
$998$	10.0069	0.316764
$999$	−19.3273	−0.611487

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1805.2.a.h.1.2		3
5.4	even	2		9025.2.a.z.1.2		3
19.7	even	3		95.2.e.b.11.2	✓	6
19.11	even	3		95.2.e.b.26.2	yes	6
19.18	odd	2		1805.2.a.g.1.2		3
57.11	odd	6		855.2.k.g.406.2		6
57.26	odd	6		855.2.k.g.676.2		6
76.7	odd	6		1520.2.q.j.961.3		6
76.11	odd	6		1520.2.q.j.881.3		6
95.7	odd	12		475.2.j.b.49.3		12
95.49	even	6		475.2.e.d.26.2		6
95.64	even	6		475.2.e.d.201.2		6
95.68	odd	12		475.2.j.b.349.3		12
95.83	odd	12		475.2.j.b.49.4		12
95.87	odd	12		475.2.j.b.349.4		12
95.94	odd	2		9025.2.a.ba.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.e.b.11.2	✓	6	19.7	even	3
95.2.e.b.26.2	yes	6	19.11	even	3
475.2.e.d.26.2		6	95.49	even	6
475.2.e.d.201.2		6	95.64	even	6
475.2.j.b.49.3		12	95.7	odd	12
475.2.j.b.49.4		12	95.83	odd	12
475.2.j.b.349.3		12	95.68	odd	12
475.2.j.b.349.4		12	95.87	odd	12
855.2.k.g.406.2		6	57.11	odd	6
855.2.k.g.676.2		6	57.26	odd	6
1520.2.q.j.881.3		6	76.11	odd	6
1520.2.q.j.961.3		6	76.7	odd	6
1805.2.a.g.1.2		3	19.18	odd	2
1805.2.a.h.1.2		3	1.1	even	1	trivial
9025.2.a.z.1.2		3	5.4	even	2
9025.2.a.ba.1.2		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)

\(f(q)\)	\(=\)	\(q+1.22188 q^{2} +2.28514 q^{3} -0.507019 q^{4} -1.00000 q^{5} +2.79216 q^{6} -1.28514 q^{7} -3.06327 q^{8} +2.22188 q^{9} +O(q^{10})\)	\(q+1.22188 q^{2} +2.28514 q^{3} -0.507019 q^{4} -1.00000 q^{5} +2.79216 q^{6} -1.28514 q^{7} -3.06327 q^{8} +2.22188 q^{9} -1.22188 q^{10} +0.285142 q^{11} -1.15861 q^{12} -5.00000 q^{13} -1.57028 q^{14} -2.28514 q^{15} -2.72889 q^{16} -6.23591 q^{17} +2.71486 q^{18} +0.507019 q^{20} -2.93673 q^{21} +0.348409 q^{22} -5.23591 q^{23} -7.00000 q^{24} +1.00000 q^{25} -6.10938 q^{26} -1.77812 q^{27} +0.651591 q^{28} +1.28514 q^{29} -2.79216 q^{30} -1.22188 q^{31} +2.79216 q^{32} +0.651591 q^{33} -7.61951 q^{34} +1.28514 q^{35} -1.12653 q^{36} +10.8695 q^{37} -11.4257 q^{39} +3.06327 q^{40} -0.841390 q^{41} -3.58832 q^{42} -4.95077 q^{43} -0.144573 q^{44} -2.22188 q^{45} -6.39764 q^{46} +5.72889 q^{47} -6.23591 q^{48} -5.34841 q^{49} +1.22188 q^{50} -14.2500 q^{51} +2.53509 q^{52} +12.3624 q^{53} -2.17265 q^{54} -0.285142 q^{55} +3.93673 q^{56} +1.57028 q^{58} +5.72889 q^{59} +1.15861 q^{60} +4.45779 q^{61} -1.49298 q^{62} -2.85543 q^{63} +8.86946 q^{64} +5.00000 q^{65} +0.796164 q^{66} -0.985963 q^{67} +3.16172 q^{68} -11.9648 q^{69} +1.57028 q^{70} -2.92270 q^{71} -6.80620 q^{72} -0.764087 q^{73} +13.2811 q^{74} +2.28514 q^{75} -0.366449 q^{77} -13.9608 q^{78} -15.4578 q^{79} +2.72889 q^{80} -10.7289 q^{81} -1.02807 q^{82} +1.66563 q^{83} +1.48898 q^{84} +6.23591 q^{85} -6.04923 q^{86} +2.93673 q^{87} -0.873467 q^{88} -16.0281 q^{89} -2.71486 q^{90} +6.42571 q^{91} +2.65471 q^{92} -2.79216 q^{93} +7.00000 q^{94} +6.38049 q^{96} +11.7429 q^{97} -6.53509 q^{98} +0.633551 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + q^{2} + q^{3} + 7 q^{4} - 3 q^{5} - 6 q^{6} + 2 q^{7} - 6 q^{8} + 4 q^{9}+O(q^{10}) \) 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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