LMFDB - Embedded newform 8026.2.a.b.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8026,2,Mod(1,8026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8026, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8026 = 2 \cdot 4013 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8026.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.0879326623$
Analytic rank:	$1$
Dimension:	$81$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	8026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.51028 q^{3} +1.00000 q^{4} +0.572444 q^{5} +2.51028 q^{6} -2.83976 q^{7} -1.00000 q^{8} +3.30151 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.51028 q^{3} +1.00000 q^{4} +0.572444 q^{5} +2.51028 q^{6} -2.83976 q^{7} -1.00000 q^{8} +3.30151 q^{9} -0.572444 q^{10} -5.93756 q^{11} -2.51028 q^{12} +6.42133 q^{13} +2.83976 q^{14} -1.43699 q^{15} +1.00000 q^{16} +2.33519 q^{17} -3.30151 q^{18} +0.888912 q^{19} +0.572444 q^{20} +7.12860 q^{21} +5.93756 q^{22} +0.524657 q^{23} +2.51028 q^{24} -4.67231 q^{25} -6.42133 q^{26} -0.756885 q^{27} -2.83976 q^{28} +2.26089 q^{29} +1.43699 q^{30} -7.56734 q^{31} -1.00000 q^{32} +14.9050 q^{33} -2.33519 q^{34} -1.62560 q^{35} +3.30151 q^{36} -9.68846 q^{37} -0.888912 q^{38} -16.1193 q^{39} -0.572444 q^{40} +7.12012 q^{41} -7.12860 q^{42} +3.77483 q^{43} -5.93756 q^{44} +1.88993 q^{45} -0.524657 q^{46} -6.77085 q^{47} -2.51028 q^{48} +1.06425 q^{49} +4.67231 q^{50} -5.86199 q^{51} +6.42133 q^{52} -0.516803 q^{53} +0.756885 q^{54} -3.39892 q^{55} +2.83976 q^{56} -2.23142 q^{57} -2.26089 q^{58} +3.45403 q^{59} -1.43699 q^{60} +2.86298 q^{61} +7.56734 q^{62} -9.37551 q^{63} +1.00000 q^{64} +3.67585 q^{65} -14.9050 q^{66} +1.78930 q^{67} +2.33519 q^{68} -1.31704 q^{69} +1.62560 q^{70} +15.8679 q^{71} -3.30151 q^{72} -2.40290 q^{73} +9.68846 q^{74} +11.7288 q^{75} +0.888912 q^{76} +16.8613 q^{77} +16.1193 q^{78} +7.70080 q^{79} +0.572444 q^{80} -8.00455 q^{81} -7.12012 q^{82} -14.6083 q^{83} +7.12860 q^{84} +1.33677 q^{85} -3.77483 q^{86} -5.67546 q^{87} +5.93756 q^{88} +5.98353 q^{89} -1.88993 q^{90} -18.2350 q^{91} +0.524657 q^{92} +18.9962 q^{93} +6.77085 q^{94} +0.508852 q^{95} +2.51028 q^{96} +13.0873 q^{97} -1.06425 q^{98} -19.6029 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 81 q - 81 q^{2} - 10 q^{3} + 81 q^{4} - 26 q^{5} + 10 q^{6} + 3 q^{7} - 81 q^{8} + 59 q^{9}+O(q^{10}) $ 81 * q - 81 * q^2 - 10 * q^3 + 81 * q^4 - 26 * q^5 + 10 * q^6 + 3 * q^7 - 81 * q^8 + 59 * q^9	\( 81 q - 81 q^{2} - 10 q^{3} + 81 q^{4} - 26 q^{5} + 10 q^{6} + 3 q^{7} - 81 q^{8} + 59 q^{9} + 26 q^{10} - 41 q^{11} - 10 q^{12} + 33 q^{13} - 3 q^{14} - 7 q^{15} + 81 q^{16} - 9 q^{17} - 59 q^{18} - 32 q^{19} - 26 q^{20} - 23 q^{21} + 41 q^{22} - 28 q^{23} + 10 q^{24} + 81 q^{25} - 33 q^{26} - 37 q^{27} + 3 q^{28} - 35 q^{29} + 7 q^{30} - 29 q^{31} - 81 q^{32} - 7 q^{33} + 9 q^{34} - 67 q^{35} + 59 q^{36} + 13 q^{37} + 32 q^{38} - 42 q^{39} + 26 q^{40} - 66 q^{41} + 23 q^{42} - 22 q^{43} - 41 q^{44} - 65 q^{45} + 28 q^{46} - 71 q^{47} - 10 q^{48} + 64 q^{49} - 81 q^{50} - 43 q^{51} + 33 q^{52} - 37 q^{53} + 37 q^{54} + 12 q^{55} - 3 q^{56} - q^{57} + 35 q^{58} - 162 q^{59} - 7 q^{60} + 19 q^{61} + 29 q^{62} - 16 q^{63} + 81 q^{64} - 45 q^{65} + 7 q^{66} - 43 q^{67} - 9 q^{68} - 21 q^{69} + 67 q^{70} - 99 q^{71} - 59 q^{72} + 53 q^{73} - 13 q^{74} - 61 q^{75} - 32 q^{76} - 31 q^{77} + 42 q^{78} + 4 q^{79} - 26 q^{80} + q^{81} + 66 q^{82} - 112 q^{83} - 23 q^{84} + 17 q^{85} + 22 q^{86} - 15 q^{87} + 41 q^{88} - 111 q^{89} + 65 q^{90} - 49 q^{91} - 28 q^{92} - 19 q^{93} + 71 q^{94} - 53 q^{95} + 10 q^{96} + 50 q^{97} - 64 q^{98} - 97 q^{99}+O(q^{100}) \) 81 * q - 81 * q^2 - 10 * q^3 + 81 * q^4 - 26 * q^5 + 10 * q^6 + 3 * q^7 - 81 * q^8 + 59 * q^9 + 26 * q^10 - 41 * q^11 - 10 * q^12 + 33 * q^13 - 3 * q^14 - 7 * q^15 + 81 * q^16 - 9 * q^17 - 59 * q^18 - 32 * q^19 - 26 * q^20 - 23 * q^21 + 41 * q^22 - 28 * q^23 + 10 * q^24 + 81 * q^25 - 33 * q^26 - 37 * q^27 + 3 * q^28 - 35 * q^29 + 7 * q^30 - 29 * q^31 - 81 * q^32 - 7 * q^33 + 9 * q^34 - 67 * q^35 + 59 * q^36 + 13 * q^37 + 32 * q^38 - 42 * q^39 + 26 * q^40 - 66 * q^41 + 23 * q^42 - 22 * q^43 - 41 * q^44 - 65 * q^45 + 28 * q^46 - 71 * q^47 - 10 * q^48 + 64 * q^49 - 81 * q^50 - 43 * q^51 + 33 * q^52 - 37 * q^53 + 37 * q^54 + 12 * q^55 - 3 * q^56 - q^57 + 35 * q^58 - 162 * q^59 - 7 * q^60 + 19 * q^61 + 29 * q^62 - 16 * q^63 + 81 * q^64 - 45 * q^65 + 7 * q^66 - 43 * q^67 - 9 * q^68 - 21 * q^69 + 67 * q^70 - 99 * q^71 - 59 * q^72 + 53 * q^73 - 13 * q^74 - 61 * q^75 - 32 * q^76 - 31 * q^77 + 42 * q^78 + 4 * q^79 - 26 * q^80 + q^81 + 66 * q^82 - 112 * q^83 - 23 * q^84 + 17 * q^85 + 22 * q^86 - 15 * q^87 + 41 * q^88 - 111 * q^89 + 65 * q^90 - 49 * q^91 - 28 * q^92 - 19 * q^93 + 71 * q^94 - 53 * q^95 + 10 * q^96 + 50 * q^97 - 64 * q^98 - 97 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.51028	−1.44931	−0.724656	−	0.689111i	$-0.758001\pi$
$3$	−2.51028	−1.44931	−0.724656	+	0.689111i	$0.758001\pi$
$4$	1.00000	0.500000
$5$	0.572444	0.256005	0.128002	−	0.991774i	$-0.459144\pi$
$5$	0.572444	0.256005	0.128002	+	0.991774i	$0.459144\pi$
$6$	2.51028	1.02482
$7$	−2.83976	−1.07333	−0.536665	−	0.843796i	$-0.680316\pi$
$7$	−2.83976	−1.07333	−0.536665	+	0.843796i	$0.680316\pi$
$8$	−1.00000	−0.353553
$9$	3.30151	1.10050
$10$	−0.572444	−0.181023
$11$	−5.93756	−1.79024	−0.895121	−	0.445823i	$-0.852911\pi$
$11$	−5.93756	−1.79024	−0.895121	+	0.445823i	$0.852911\pi$
$12$	−2.51028	−0.724656
$13$	6.42133	1.78096	0.890478	−	0.455026i	$-0.150370\pi$
$13$	6.42133	1.78096	0.890478	+	0.455026i	$0.150370\pi$
$14$	2.83976	0.758958
$15$	−1.43699	−0.371030
$16$	1.00000	0.250000
$17$	2.33519	0.566367	0.283184	−	0.959066i	$-0.408609\pi$
$17$	2.33519	0.566367	0.283184	+	0.959066i	$0.408609\pi$
$18$	−3.30151	−0.778174
$19$	0.888912	0.203930	0.101965	−	0.994788i	$-0.467487\pi$
$19$	0.888912	0.203930	0.101965	+	0.994788i	$0.467487\pi$
$20$	0.572444	0.128002
$21$	7.12860	1.55559
$22$	5.93756	1.26589
$23$	0.524657	0.109399	0.0546993	−	0.998503i	$-0.482580\pi$
$23$	0.524657	0.109399	0.0546993	+	0.998503i	$0.482580\pi$
$24$	2.51028	0.512409
$25$	−4.67231	−0.934462
$26$	−6.42133	−1.25933
$27$	−0.756885	−0.145663
$28$	−2.83976	−0.536665
$29$	2.26089	0.419836	0.209918	−	0.977719i	$-0.432680\pi$
$29$	2.26089	0.419836	0.209918	+	0.977719i	$0.432680\pi$
$30$	1.43699	0.262358
$31$	−7.56734	−1.35914	−0.679568	−	0.733613i	$-0.737833\pi$
$31$	−7.56734	−1.35914	−0.679568	+	0.733613i	$0.737833\pi$
$32$	−1.00000	−0.176777
$33$	14.9050	2.59462
$34$	−2.33519	−0.400482
$35$	−1.62560	−0.274777
$36$	3.30151	0.550252
$37$	−9.68846	−1.59277	−0.796386	−	0.604788i	$-0.793258\pi$
$37$	−9.68846	−1.59277	−0.796386	+	0.604788i	$0.793258\pi$
$38$	−0.888912	−0.144201
$39$	−16.1193	−2.58116
$40$	−0.572444	−0.0905113
$41$	7.12012	1.11198	0.555988	−	0.831190i	$-0.312340\pi$
$41$	7.12012	1.11198	0.555988	+	0.831190i	$0.312340\pi$
$42$	−7.12860	−1.09997
$43$	3.77483	0.575656	0.287828	−	0.957682i	$-0.407067\pi$
$43$	3.77483	0.575656	0.287828	+	0.957682i	$0.407067\pi$
$44$	−5.93756	−0.895121
$45$	1.88993	0.281734
$46$	−0.524657	−0.0773564
$47$	−6.77085	−0.987630	−0.493815	−	0.869567i	$-0.664398\pi$
$47$	−6.77085	−0.987630	−0.493815	+	0.869567i	$0.664398\pi$
$48$	−2.51028	−0.362328
$49$	1.06425	0.152035
$50$	4.67231	0.660764
$51$	−5.86199	−0.820843
$52$	6.42133	0.890478
$53$	−0.516803	−0.0709883	−0.0354942	−	0.999370i	$-0.511301\pi$
$53$	−0.516803	−0.0709883	−0.0354942	+	0.999370i	$0.511301\pi$
$54$	0.756885	0.102999
$55$	−3.39892	−0.458310
$56$	2.83976	0.379479
$57$	−2.23142	−0.295559
$58$	−2.26089	−0.296869
$59$	3.45403	0.449676	0.224838	−	0.974396i	$-0.427815\pi$
$59$	3.45403	0.449676	0.224838	+	0.974396i	$0.427815\pi$
$60$	−1.43699	−0.185515
$61$	2.86298	0.366567	0.183283	−	0.983060i	$-0.441327\pi$
$61$	2.86298	0.366567	0.183283	+	0.983060i	$0.441327\pi$
$62$	7.56734	0.961054
$63$	−9.37551	−1.18120
$64$	1.00000	0.125000
$65$	3.67585	0.455933
$66$	−14.9050	−1.83467
$67$	1.78930	0.218598	0.109299	−	0.994009i	$-0.465139\pi$
$67$	1.78930	0.218598	0.109299	+	0.994009i	$0.465139\pi$
$68$	2.33519	0.283184
$69$	−1.31704	−0.158553
$70$	1.62560	0.194297
$71$	15.8679	1.88317	0.941587	−	0.336770i	$-0.109335\pi$
$71$	15.8679	1.88317	0.941587	+	0.336770i	$0.109335\pi$
$72$	−3.30151	−0.389087
$73$	−2.40290	−0.281238	−0.140619	−	0.990064i	$-0.544909\pi$
$73$	−2.40290	−0.281238	−0.140619	+	0.990064i	$0.544909\pi$
$74$	9.68846	1.12626
$75$	11.7288	1.35433
$76$	0.888912	0.101965
$77$	16.8613	1.92152
$78$	16.1193	1.82516
$79$	7.70080	0.866408	0.433204	−	0.901296i	$-0.357383\pi$
$79$	7.70080	0.866408	0.433204	+	0.901296i	$0.357383\pi$
$80$	0.572444	0.0640011
$81$	−8.00455	−0.889394
$82$	−7.12012	−0.786286
$83$	−14.6083	−1.60347	−0.801735	−	0.597679i	$-0.796090\pi$
$83$	−14.6083	−1.60347	−0.801735	+	0.597679i	$0.796090\pi$
$84$	7.12860	0.777794
$85$	1.33677	0.144993
$86$	−3.77483	−0.407050
$87$	−5.67546	−0.608473
$88$	5.93756	0.632946
$89$	5.98353	0.634253	0.317126	−	0.948383i	$-0.397282\pi$
$89$	5.98353	0.634253	0.317126	+	0.948383i	$0.397282\pi$
$90$	−1.88993	−0.199216
$91$	−18.2350	−1.91155
$92$	0.524657	0.0546993
$93$	18.9962	1.96981
$94$	6.77085	0.698360
$95$	0.508852	0.0522071
$96$	2.51028	0.256205
$97$	13.0873	1.32881	0.664406	−	0.747372i	$-0.268685\pi$
$97$	13.0873	1.32881	0.664406	+	0.747372i	$0.268685\pi$
$98$	−1.06425	−0.107505
$99$	−19.6029	−1.97017
$100$	−4.67231	−0.467231
$101$	11.1767	1.11212	0.556060	−	0.831142i	$-0.312312\pi$
$101$	11.1767	1.11212	0.556060	+	0.831142i	$0.312312\pi$
$102$	5.86199	0.580423
$103$	−5.63346	−0.555081	−0.277541	−	0.960714i	$-0.589519\pi$
$103$	−5.63346	−0.555081	−0.277541	+	0.960714i	$0.589519\pi$
$104$	−6.42133	−0.629663
$105$	4.08072	0.398238
$106$	0.516803	0.0501963
$107$	14.7693	1.42780	0.713899	−	0.700249i	$-0.246928\pi$
$107$	14.7693	1.42780	0.713899	+	0.700249i	$0.246928\pi$
$108$	−0.756885	−0.0728313
$109$	−11.0324	−1.05671	−0.528355	−	0.849024i	$-0.677191\pi$
$109$	−11.0324	−1.05671	−0.528355	+	0.849024i	$0.677191\pi$
$110$	3.39892	0.324074
$111$	24.3208	2.30842
$112$	−2.83976	−0.268332
$113$	−6.67221	−0.627669	−0.313835	−	0.949478i	$-0.601614\pi$
$113$	−6.67221	−0.627669	−0.313835	+	0.949478i	$0.601614\pi$
$114$	2.23142	0.208992
$115$	0.300336	0.0280065
$116$	2.26089	0.209918
$117$	21.2001	1.95995
$118$	−3.45403	−0.317969
$119$	−6.63139	−0.607898
$120$	1.43699	0.131179
$121$	24.2547	2.20497
$122$	−2.86298	−0.259202
$123$	−17.8735	−1.61160
$124$	−7.56734	−0.679568
$125$	−5.53685	−0.495231
$126$	9.37551	0.835237
$127$	15.0226	1.33304	0.666519	−	0.745488i	$-0.267784\pi$
$127$	15.0226	1.33304	0.666519	+	0.745488i	$0.267784\pi$
$128$	−1.00000	−0.0883883
$129$	−9.47589	−0.834305
$130$	−3.67585	−0.322393
$131$	4.45250	0.389017	0.194508	−	0.980901i	$-0.437689\pi$
$131$	4.45250	0.389017	0.194508	+	0.980901i	$0.437689\pi$
$132$	14.9050	1.29731
$133$	−2.52430	−0.218884
$134$	−1.78930	−0.154572
$135$	−0.433274	−0.0372903
$136$	−2.33519	−0.200241
$137$	−17.1243	−1.46302	−0.731512	−	0.681828i	$-0.761185\pi$
$137$	−17.1243	−1.46302	−0.731512	+	0.681828i	$0.761185\pi$
$138$	1.31704	0.112114
$139$	14.3559	1.21765	0.608827	−	0.793303i	$-0.291640\pi$
$139$	14.3559	1.21765	0.608827	+	0.793303i	$0.291640\pi$
$140$	−1.62560	−0.137389
$141$	16.9967	1.43138
$142$	−15.8679	−1.33160
$143$	−38.1271	−3.18834
$144$	3.30151	0.275126
$145$	1.29423	0.107480
$146$	2.40290	0.198866
$147$	−2.67156	−0.220346
$148$	−9.68846	−0.796386
$149$	−2.58200	−0.211526	−0.105763	−	0.994391i	$-0.533728\pi$
$149$	−2.58200	−0.211526	−0.105763	+	0.994391i	$0.533728\pi$
$150$	−11.7288	−0.957653
$151$	−17.9534	−1.46102	−0.730512	−	0.682900i	$-0.760718\pi$
$151$	−17.9534	−1.46102	−0.730512	+	0.682900i	$0.760718\pi$
$152$	−0.888912	−0.0721003
$153$	7.70967	0.623290
$154$	−16.8613	−1.35872
$155$	−4.33188	−0.347945
$156$	−16.1193	−1.29058
$157$	14.5950	1.16481	0.582405	−	0.812899i	$-0.302112\pi$
$157$	14.5950	1.16481	0.582405	+	0.812899i	$0.302112\pi$
$158$	−7.70080	−0.612643
$159$	1.29732	0.102884
$160$	−0.572444	−0.0452556
$161$	−1.48990	−0.117421
$162$	8.00455	0.628897
$163$	13.4380	1.05254	0.526271	−	0.850317i	$-0.323590\pi$
$163$	13.4380	1.05254	0.526271	+	0.850317i	$0.323590\pi$
$164$	7.12012	0.555988
$165$	8.53225	0.664235
$166$	14.6083	1.13383
$167$	−11.2962	−0.874125	−0.437062	−	0.899431i	$-0.643981\pi$
$167$	−11.2962	−0.874125	−0.437062	+	0.899431i	$0.643981\pi$
$168$	−7.12860	−0.549984
$169$	28.2335	2.17181
$170$	−1.33677	−0.102525
$171$	2.93476	0.224426
$172$	3.77483	0.287828
$173$	18.6328	1.41662	0.708311	−	0.705901i	$-0.249457\pi$
$173$	18.6328	1.41662	0.708311	+	0.705901i	$0.249457\pi$
$174$	5.67546	0.430256
$175$	13.2682	1.00298
$176$	−5.93756	−0.447561
$177$	−8.67059	−0.651721
$178$	−5.98353	−0.448485
$179$	−23.6038	−1.76423	−0.882116	−	0.471031i	$-0.843882\pi$
$179$	−23.6038	−1.76423	−0.882116	+	0.471031i	$0.843882\pi$
$180$	1.88993	0.140867
$181$	−9.38551	−0.697620	−0.348810	−	0.937194i	$-0.613414\pi$
$181$	−9.38551	−0.697620	−0.348810	+	0.937194i	$0.613414\pi$
$182$	18.2350	1.35167
$183$	−7.18688	−0.531269
$184$	−0.524657	−0.0386782
$185$	−5.54610	−0.407757
$186$	−18.9962	−1.39287
$187$	−13.8653	−1.01393
$188$	−6.77085	−0.493815
$189$	2.14937	0.156344
$190$	−0.508852	−0.0369160
$191$	−7.11336	−0.514704	−0.257352	−	0.966318i	$-0.582850\pi$
$191$	−7.11336	−0.514704	−0.257352	+	0.966318i	$0.582850\pi$
$192$	−2.51028	−0.181164
$193$	12.9109	0.929349	0.464674	−	0.885482i	$-0.346171\pi$
$193$	12.9109	0.929349	0.464674	+	0.885482i	$0.346171\pi$
$194$	−13.0873	−0.939612
$195$	−9.22742	−0.660789
$196$	1.06425	0.0760176
$197$	−19.3573	−1.37915	−0.689574	−	0.724215i	$-0.742202\pi$
$197$	−19.3573	−1.37915	−0.689574	+	0.724215i	$0.742202\pi$
$198$	19.6029	1.39312
$199$	22.4553	1.59181	0.795906	−	0.605421i	$-0.206995\pi$
$199$	22.4553	1.59181	0.795906	+	0.605421i	$0.206995\pi$
$200$	4.67231	0.330382
$201$	−4.49164	−0.316816
$202$	−11.1767	−0.786387
$203$	−6.42038	−0.450622
$204$	−5.86199	−0.410421
$205$	4.07587	0.284671
$206$	5.63346	0.392502
$207$	1.73216	0.120394
$208$	6.42133	0.445239
$209$	−5.27797	−0.365085
$210$	−4.08072	−0.281597
$211$	−19.3031	−1.32888	−0.664440	−	0.747342i	$-0.731330\pi$
$211$	−19.3031	−1.32888	−0.664440	+	0.747342i	$0.731330\pi$
$212$	−0.516803	−0.0354942
$213$	−39.8329	−2.72931
$214$	−14.7693	−1.00961
$215$	2.16088	0.147371
$216$	0.756885	0.0514995
$217$	21.4895	1.45880
$218$	11.0324	0.747206
$219$	6.03196	0.407602
$220$	−3.39892	−0.229155
$221$	14.9950	1.00868
$222$	−24.3208	−1.63230
$223$	26.9052	1.80171	0.900854	−	0.434122i	$-0.142941\pi$
$223$	26.9052	1.80171	0.900854	+	0.434122i	$0.142941\pi$
$224$	2.83976	0.189740
$225$	−15.4257	−1.02838
$226$	6.67221	0.443829
$227$	4.31593	0.286458	0.143229	−	0.989690i	$-0.454251\pi$
$227$	4.31593	0.286458	0.143229	+	0.989690i	$0.454251\pi$
$228$	−2.23142	−0.147779
$229$	24.0031	1.58617	0.793085	−	0.609111i	$-0.208474\pi$
$229$	24.0031	1.58617	0.793085	+	0.609111i	$0.208474\pi$
$230$	−0.300336	−0.0198036
$231$	−42.3265	−2.78488
$232$	−2.26089	−0.148434
$233$	15.3745	1.00722	0.503609	−	0.863932i	$-0.332005\pi$
$233$	15.3745	1.00722	0.503609	+	0.863932i	$0.332005\pi$
$234$	−21.2001	−1.38589
$235$	−3.87593	−0.252838
$236$	3.45403	0.224838
$237$	−19.3312	−1.25570
$238$	6.63139	0.429849
$239$	−23.2488	−1.50384	−0.751921	−	0.659253i	$-0.770873\pi$
$239$	−23.2488	−1.50384	−0.751921	+	0.659253i	$0.770873\pi$
$240$	−1.43699	−0.0927576
$241$	−18.3739	−1.18357	−0.591785	−	0.806096i	$-0.701576\pi$
$241$	−18.3739	−1.18357	−0.591785	+	0.806096i	$0.701576\pi$
$242$	−24.2547	−1.55915
$243$	22.3643	1.43467
$244$	2.86298	0.183283
$245$	0.609221	0.0389217
$246$	17.8735	1.13957
$247$	5.70800	0.363191
$248$	7.56734	0.480527
$249$	36.6710	2.32393
$250$	5.53685	0.350181
$251$	−1.35101	−0.0852749	−0.0426375	−	0.999091i	$-0.513576\pi$
$251$	−1.35101	−0.0852749	−0.0426375	+	0.999091i	$0.513576\pi$
$252$	−9.37551	−0.590602
$253$	−3.11518	−0.195850
$254$	−15.0226	−0.942600
$255$	−3.35566	−0.210139
$256$	1.00000	0.0625000
$257$	−4.14243	−0.258398	−0.129199	−	0.991619i	$-0.541241\pi$
$257$	−4.14243	−0.258398	−0.129199	+	0.991619i	$0.541241\pi$
$258$	9.47589	0.589943
$259$	27.5129	1.70957
$260$	3.67585	0.227967
$261$	7.46435	0.462031
$262$	−4.45250	−0.275076
$263$	−6.31890	−0.389640	−0.194820	−	0.980839i	$-0.562412\pi$
$263$	−6.31890	−0.389640	−0.194820	+	0.980839i	$0.562412\pi$
$264$	−14.9050	−0.917337
$265$	−0.295840	−0.0181733
$266$	2.52430	0.154775
$267$	−15.0203	−0.919230
$268$	1.78930	0.109299
$269$	25.8988	1.57908	0.789540	−	0.613699i	$-0.210319\pi$
$269$	25.8988	1.57908	0.789540	+	0.613699i	$0.210319\pi$
$270$	0.433274	0.0263682
$271$	−2.48249	−0.150800	−0.0754002	−	0.997153i	$-0.524023\pi$
$271$	−2.48249	−0.150800	−0.0754002	+	0.997153i	$0.524023\pi$
$272$	2.33519	0.141592
$273$	45.7751	2.77044
$274$	17.1243	1.03451
$275$	27.7421	1.67291
$276$	−1.31704	−0.0792763
$277$	26.7267	1.60585	0.802927	−	0.596077i	$-0.203275\pi$
$277$	26.7267	1.60585	0.802927	+	0.596077i	$0.203275\pi$
$278$	−14.3559	−0.861011
$279$	−24.9837	−1.49573
$280$	1.62560	0.0971484
$281$	−26.3278	−1.57058	−0.785291	−	0.619127i	$-0.787487\pi$
$281$	−26.3278	−1.57058	−0.785291	+	0.619127i	$0.787487\pi$
$282$	−16.9967	−1.01214
$283$	15.9767	0.949717	0.474858	−	0.880062i	$-0.342499\pi$
$283$	15.9767	0.949717	0.474858	+	0.880062i	$0.342499\pi$
$284$	15.8679	0.941587
$285$	−1.27736	−0.0756644
$286$	38.1271	2.25450
$287$	−20.2194	−1.19352
$288$	−3.30151	−0.194544
$289$	−11.5469	−0.679228
$290$	−1.29423	−0.0759998
$291$	−32.8528	−1.92586
$292$	−2.40290	−0.140619
$293$	1.81053	0.105773	0.0528863	−	0.998601i	$-0.483158\pi$
$293$	1.81053	0.105773	0.0528863	+	0.998601i	$0.483158\pi$
$294$	2.67156	0.155808
$295$	1.97724	0.115119
$296$	9.68846	0.563130
$297$	4.49405	0.260771
$298$	2.58200	0.149571
$299$	3.36899	0.194834
$300$	11.7288	0.677163
$301$	−10.7196	−0.617869
$302$	17.9534	1.03310
$303$	−28.0566	−1.61181
$304$	0.888912	0.0509826
$305$	1.63889	0.0938427
$306$	−7.70967	−0.440732
$307$	−32.5990	−1.86052	−0.930260	−	0.366900i	$-0.880419\pi$
$307$	−32.5990	−1.86052	−0.930260	+	0.366900i	$0.880419\pi$
$308$	16.8613	0.960760
$309$	14.1416	0.804486
$310$	4.33188	0.246034
$311$	−18.1529	−1.02936	−0.514678	−	0.857384i	$-0.672088\pi$
$311$	−18.1529	−1.02936	−0.514678	+	0.857384i	$0.672088\pi$
$312$	16.1193	0.912578
$313$	24.8111	1.40240	0.701202	−	0.712963i	$-0.252647\pi$
$313$	24.8111	1.40240	0.701202	+	0.712963i	$0.252647\pi$
$314$	−14.5950	−0.823644
$315$	−5.36695	−0.302394
$316$	7.70080	0.433204
$317$	−1.66060	−0.0932684	−0.0466342	−	0.998912i	$-0.514850\pi$
$317$	−1.66060	−0.0932684	−0.0466342	+	0.998912i	$0.514850\pi$
$318$	−1.29732	−0.0727501
$319$	−13.4242	−0.751608
$320$	0.572444	0.0320006
$321$	−37.0750	−2.06932
$322$	1.48990	0.0830289
$323$	2.07578	0.115499
$324$	−8.00455	−0.444697
$325$	−30.0024	−1.66424
$326$	−13.4380	−0.744260
$327$	27.6944	1.53150
$328$	−7.12012	−0.393143
$329$	19.2276	1.06005
$330$	−8.53225	−0.469685
$331$	−6.80573	−0.374077	−0.187038	−	0.982353i	$-0.559889\pi$
$331$	−6.80573	−0.374077	−0.187038	+	0.982353i	$0.559889\pi$
$332$	−14.6083	−0.801735
$333$	−31.9866	−1.75285
$334$	11.2962	0.618100
$335$	1.02427	0.0559620
$336$	7.12860	0.388897
$337$	−2.67013	−0.145451	−0.0727256	−	0.997352i	$-0.523170\pi$
$337$	−2.67013	−0.145451	−0.0727256	+	0.997352i	$0.523170\pi$
$338$	−28.2335	−1.53570
$339$	16.7491	0.909688
$340$	1.33677	0.0724963
$341$	44.9316	2.43318
$342$	−2.93476	−0.158693
$343$	16.8561	0.910145
$344$	−3.77483	−0.203525
$345$	−0.753929	−0.0405902
$346$	−18.6328	−1.00170
$347$	−16.0486	−0.861534	−0.430767	−	0.902463i	$-0.641757\pi$
$347$	−16.0486	−0.861534	−0.430767	+	0.902463i	$0.641757\pi$
$348$	−5.67546	−0.304237
$349$	2.69879	0.144463	0.0722314	−	0.997388i	$-0.476988\pi$
$349$	2.69879	0.144463	0.0722314	+	0.997388i	$0.476988\pi$
$350$	−13.2682	−0.709217
$351$	−4.86021	−0.259419
$352$	5.93756	0.316473
$353$	12.6410	0.672810	0.336405	−	0.941717i	$-0.390789\pi$
$353$	12.6410	0.672810	0.336405	+	0.941717i	$0.390789\pi$
$354$	8.67059	0.460836
$355$	9.08348	0.482101
$356$	5.98353	0.317126
$357$	16.6467	0.881034
$358$	23.6038	1.24750
$359$	−24.6226	−1.29953	−0.649765	−	0.760135i	$-0.725133\pi$
$359$	−24.6226	−1.29953	−0.649765	+	0.760135i	$0.725133\pi$
$360$	−1.88993	−0.0996081
$361$	−18.2098	−0.958412
$362$	9.38551	0.493291
$363$	−60.8860	−3.19569
$364$	−18.2350	−0.955776
$365$	−1.37553	−0.0719983
$366$	7.18688	0.375664
$367$	29.3186	1.53042	0.765209	−	0.643782i	$-0.222636\pi$
$367$	29.3186	1.53042	0.765209	+	0.643782i	$0.222636\pi$
$368$	0.524657	0.0273496
$369$	23.5072	1.22373
$370$	5.54610	0.288328
$371$	1.46760	0.0761938
$372$	18.9962	0.984905
$373$	−7.42114	−0.384252	−0.192126	−	0.981370i	$-0.561538\pi$
$373$	−7.42114	−0.384252	−0.192126	+	0.981370i	$0.561538\pi$
$374$	13.8653	0.716960
$375$	13.8991	0.717744
$376$	6.77085	0.349180
$377$	14.5179	0.747710
$378$	−2.14937	−0.110552
$379$	−14.9987	−0.770433	−0.385217	−	0.922826i	$-0.625873\pi$
$379$	−14.9987	−0.770433	−0.385217	+	0.922826i	$0.625873\pi$
$380$	0.508852	0.0261036
$381$	−37.7109	−1.93199
$382$	7.11336	0.363951
$383$	−2.00276	−0.102336	−0.0511680	−	0.998690i	$-0.516294\pi$
$383$	−2.00276	−0.102336	−0.0511680	+	0.998690i	$0.516294\pi$
$384$	2.51028	0.128102
$385$	9.65212	0.491918
$386$	−12.9109	−0.657149
$387$	12.4627	0.633512
$388$	13.0873	0.664406
$389$	17.1209	0.868063	0.434032	−	0.900898i	$-0.357091\pi$
$389$	17.1209	0.868063	0.434032	+	0.900898i	$0.357091\pi$
$390$	9.22742	0.467248
$391$	1.22517	0.0619597
$392$	−1.06425	−0.0537526
$393$	−11.1770	−0.563807
$394$	19.3573	0.975205
$395$	4.40828	0.221804
$396$	−19.6029	−0.985085
$397$	−18.8168	−0.944390	−0.472195	−	0.881494i	$-0.656538\pi$
$397$	−18.8168	−0.944390	−0.472195	+	0.881494i	$0.656538\pi$
$398$	−22.4553	−1.12558
$399$	6.33670	0.317232
$400$	−4.67231	−0.233615
$401$	−32.7639	−1.63615	−0.818076	−	0.575110i	$-0.804959\pi$
$401$	−32.7639	−1.63615	−0.818076	+	0.575110i	$0.804959\pi$
$402$	4.49164	0.224023
$403$	−48.5924	−2.42056
$404$	11.1767	0.556060
$405$	−4.58215	−0.227689
$406$	6.42038	0.318638
$407$	57.5258	2.85145
$408$	5.86199	0.290212
$409$	21.2010	1.04832	0.524161	−	0.851619i	$-0.324379\pi$
$409$	21.2010	1.04832	0.524161	+	0.851619i	$0.324379\pi$
$410$	−4.07587	−0.201293
$411$	42.9867	2.12038
$412$	−5.63346	−0.277541
$413$	−9.80862	−0.482651
$414$	−1.73216	−0.0851311
$415$	−8.36244	−0.410496
$416$	−6.42133	−0.314832
$417$	−36.0374	−1.76476
$418$	5.27797	0.258154
$419$	−5.12065	−0.250160	−0.125080	−	0.992147i	$-0.539919\pi$
$419$	−5.12065	−0.250160	−0.125080	+	0.992147i	$0.539919\pi$
$420$	4.08072	0.199119
$421$	3.11161	0.151651	0.0758253	−	0.997121i	$-0.475841\pi$
$421$	3.11161	0.151651	0.0758253	+	0.997121i	$0.475841\pi$
$422$	19.3031	0.939660
$423$	−22.3541	−1.08689
$424$	0.516803	0.0250982
$425$	−10.9107	−0.529248
$426$	39.8329	1.92991
$427$	−8.13017	−0.393447
$428$	14.7693	0.713899
$429$	95.7096	4.62090
$430$	−2.16088	−0.104207
$431$	5.83074	0.280857	0.140428	−	0.990091i	$-0.455152\pi$
$431$	5.83074	0.280857	0.140428	+	0.990091i	$0.455152\pi$
$432$	−0.756885	−0.0364156
$433$	31.8773	1.53193	0.765963	−	0.642885i	$-0.222263\pi$
$433$	31.8773	1.53193	0.765963	+	0.642885i	$0.222263\pi$
$434$	−21.4895	−1.03153
$435$	−3.24888	−0.155772
$436$	−11.0324	−0.528355
$437$	0.466374	0.0223097
$438$	−6.03196	−0.288218
$439$	2.58104	0.123186	0.0615931	−	0.998101i	$-0.480382\pi$
$439$	2.58104	0.123186	0.0615931	+	0.998101i	$0.480382\pi$
$440$	3.39892	0.162037
$441$	3.51363	0.167316
$442$	−14.9950	−0.713241
$443$	16.9202	0.803903	0.401951	−	0.915661i	$-0.368332\pi$
$443$	16.9202	0.803903	0.401951	+	0.915661i	$0.368332\pi$
$444$	24.3208	1.15421
$445$	3.42523	0.162372
$446$	−26.9052	−1.27400
$447$	6.48156	0.306567
$448$	−2.83976	−0.134166
$449$	−28.9062	−1.36417	−0.682083	−	0.731275i	$-0.738926\pi$
$449$	−28.9062	−1.36417	−0.682083	+	0.731275i	$0.738926\pi$
$450$	15.4257	0.727174
$451$	−42.2762	−1.99071
$452$	−6.67221	−0.313835
$453$	45.0680	2.11748
$454$	−4.31593	−0.202556
$455$	−10.4385	−0.489366
$456$	2.23142	0.104496
$457$	−31.7821	−1.48670	−0.743351	−	0.668901i	$-0.766765\pi$
$457$	−31.7821	−1.48670	−0.743351	+	0.668901i	$0.766765\pi$
$458$	−24.0031	−1.12159
$459$	−1.76747	−0.0824985
$460$	0.300336	0.0140033
$461$	−35.4674	−1.65188	−0.825942	−	0.563755i	$-0.809356\pi$
$461$	−35.4674	−1.65188	−0.825942	+	0.563755i	$0.809356\pi$
$462$	42.3265	1.96921
$463$	7.93900	0.368957	0.184478	−	0.982837i	$-0.440940\pi$
$463$	7.93900	0.368957	0.184478	+	0.982837i	$0.440940\pi$
$464$	2.26089	0.104959
$465$	10.8742	0.504281
$466$	−15.3745	−0.712210
$467$	17.5219	0.810817	0.405408	−	0.914136i	$-0.367129\pi$
$467$	17.5219	0.810817	0.405408	+	0.914136i	$0.367129\pi$
$468$	21.2001	0.979975
$469$	−5.08118	−0.234627
$470$	3.87593	0.178783
$471$	−36.6376	−1.68817
$472$	−3.45403	−0.158985
$473$	−22.4133	−1.03056
$474$	19.3312	0.887911
$475$	−4.15327	−0.190565
$476$	−6.63139	−0.303949
$477$	−1.70623	−0.0781230
$478$	23.2488	1.06338
$479$	33.2920	1.52115	0.760575	−	0.649251i	$-0.224917\pi$
$479$	33.2920	1.52115	0.760575	+	0.649251i	$0.224917\pi$
$480$	1.43699	0.0655895
$481$	−62.2128	−2.83666
$482$	18.3739	0.836910
$483$	3.74007	0.170179
$484$	24.2547	1.10248
$485$	7.49173	0.340182
$486$	−22.3643	−1.01447
$487$	−11.1132	−0.503589	−0.251794	−	0.967781i	$-0.581021\pi$
$487$	−11.1132	−0.503589	−0.251794	+	0.967781i	$0.581021\pi$
$488$	−2.86298	−0.129601
$489$	−33.7331	−1.52546
$490$	−0.609221	−0.0275218
$491$	3.20830	0.144789	0.0723943	−	0.997376i	$-0.476936\pi$
$491$	3.20830	0.144789	0.0723943	+	0.997376i	$0.476936\pi$
$492$	−17.8735	−0.805800
$493$	5.27960	0.237781
$494$	−5.70800	−0.256815
$495$	−11.2216	−0.504373
$496$	−7.56734	−0.339784
$497$	−45.0611	−2.02127
$498$	−36.6710	−1.64327
$499$	26.7315	1.19667	0.598334	−	0.801247i	$-0.295830\pi$
$499$	26.7315	1.19667	0.598334	+	0.801247i	$0.295830\pi$
$500$	−5.53685	−0.247616
$501$	28.3566	1.26688
$502$	1.35101	0.0602985
$503$	−26.1958	−1.16801	−0.584006	−	0.811750i	$-0.698515\pi$
$503$	−26.1958	−1.16801	−0.584006	+	0.811750i	$0.698515\pi$
$504$	9.37551	0.417619
$505$	6.39801	0.284708
$506$	3.11518	0.138487
$507$	−70.8740	−3.14762
$508$	15.0226	0.666519
$509$	−33.7950	−1.49794	−0.748968	−	0.662606i	$-0.769451\pi$
$509$	−33.7950	−1.49794	−0.748968	+	0.662606i	$0.769451\pi$
$510$	3.35566	0.148591
$511$	6.82367	0.301861
$512$	−1.00000	−0.0441942
$513$	−0.672804	−0.0297050
$514$	4.14243	0.182715
$515$	−3.22484	−0.142103
$516$	−9.47589	−0.417153
$517$	40.2023	1.76810
$518$	−27.5129	−1.20885
$519$	−46.7735	−2.05313
$520$	−3.67585	−0.161197
$521$	12.8900	0.564721	0.282360	−	0.959308i	$-0.408883\pi$
$521$	12.8900	0.564721	0.282360	+	0.959308i	$0.408883\pi$
$522$	−7.46435	−0.326706
$523$	−27.0814	−1.18419	−0.592093	−	0.805870i	$-0.701698\pi$
$523$	−27.0814	−1.18419	−0.592093	+	0.805870i	$0.701698\pi$
$524$	4.45250	0.194508
$525$	−33.3070	−1.45364
$526$	6.31890	0.275517
$527$	−17.6712	−0.769770
$528$	14.9050	0.648655
$529$	−22.7247	−0.988032
$530$	0.295840	0.0128505
$531$	11.4035	0.494871
$532$	−2.52430	−0.109442
$533$	45.7206	1.98038
$534$	15.0203	0.649994
$535$	8.45457	0.365523
$536$	−1.78930	−0.0772859
$537$	59.2523	2.55692
$538$	−25.8988	−1.11658
$539$	−6.31903	−0.272180
$540$	−0.433274	−0.0186451
$541$	−31.6424	−1.36041	−0.680206	−	0.733021i	$-0.738110\pi$
$541$	−31.6424	−1.36041	−0.680206	+	0.733021i	$0.738110\pi$
$542$	2.48249	0.106632
$543$	23.5603	1.01107
$544$	−2.33519	−0.100121
$545$	−6.31541	−0.270522
$546$	−45.7751	−1.95899
$547$	−6.71368	−0.287056	−0.143528	−	0.989646i	$-0.545845\pi$
$547$	−6.71368	−0.287056	−0.143528	+	0.989646i	$0.545845\pi$
$548$	−17.1243	−0.731512
$549$	9.45216	0.403408
$550$	−27.7421	−1.18293
$551$	2.00973	0.0856173
$552$	1.31704	0.0560568
$553$	−21.8685	−0.929941
$554$	−26.7267	−1.13551
$555$	13.9223	0.590967
$556$	14.3559	0.608827
$557$	−13.8186	−0.585514	−0.292757	−	0.956187i	$-0.594573\pi$
$557$	−13.8186	−0.585514	−0.292757	+	0.956187i	$0.594573\pi$
$558$	24.9837	1.05764
$559$	24.2394	1.02522
$560$	−1.62560	−0.0686943
$561$	34.8059	1.46951
$562$	26.3278	1.11057
$563$	32.7454	1.38006	0.690028	−	0.723783i	$-0.257598\pi$
$563$	32.7454	1.38006	0.690028	+	0.723783i	$0.257598\pi$
$564$	16.9967	0.715692
$565$	−3.81947	−0.160686
$566$	−15.9767	−0.671551
$567$	22.7310	0.954613
$568$	−15.8679	−0.665802
$569$	−14.4309	−0.604975	−0.302487	−	0.953153i	$-0.597817\pi$
$569$	−14.4309	−0.604975	−0.302487	+	0.953153i	$0.597817\pi$
$570$	1.27736	0.0535028
$571$	−22.6015	−0.945842	−0.472921	−	0.881105i	$-0.656800\pi$
$571$	−22.6015	−0.945842	−0.472921	+	0.881105i	$0.656800\pi$
$572$	−38.1271	−1.59417
$573$	17.8565	0.745967
$574$	20.2194	0.843943
$575$	−2.45136	−0.102229
$576$	3.30151	0.137563
$577$	−31.7916	−1.32350	−0.661750	−	0.749724i	$-0.730186\pi$
$577$	−31.7916	−1.32350	−0.661750	+	0.749724i	$0.730186\pi$
$578$	11.5469	0.480287
$579$	−32.4101	−1.34692
$580$	1.29423	0.0537400
$581$	41.4841	1.72105
$582$	32.8528	1.36179
$583$	3.06855	0.127086
$584$	2.40290	0.0994328
$585$	12.1359	0.501756
$586$	−1.81053	−0.0747925
$587$	−22.3530	−0.922605	−0.461302	−	0.887243i	$-0.652618\pi$
$587$	−22.3530	−0.922605	−0.461302	+	0.887243i	$0.652618\pi$
$588$	−2.67156	−0.110173
$589$	−6.72670	−0.277169
$590$	−1.97724	−0.0814016
$591$	48.5922	1.99881
$592$	−9.68846	−0.398193
$593$	28.6196	1.17527	0.587633	−	0.809127i	$-0.300060\pi$
$593$	28.6196	1.17527	0.587633	+	0.809127i	$0.300060\pi$
$594$	−4.49405	−0.184393
$595$	−3.79610	−0.155625
$596$	−2.58200	−0.105763
$597$	−56.3690	−2.30703
$598$	−3.36899	−0.137768
$599$	−9.00199	−0.367811	−0.183906	−	0.982944i	$-0.558874\pi$
$599$	−9.00199	−0.367811	−0.183906	+	0.982944i	$0.558874\pi$
$600$	−11.7288	−0.478827
$601$	−11.3369	−0.462440	−0.231220	−	0.972901i	$-0.574272\pi$
$601$	−11.3369	−0.462440	−0.231220	+	0.972901i	$0.574272\pi$
$602$	10.7196	0.436899
$603$	5.90739	0.240568
$604$	−17.9534	−0.730512
$605$	13.8844	0.564482
$606$	28.0566	1.13972
$607$	11.1488	0.452514	0.226257	−	0.974068i	$-0.427351\pi$
$607$	11.1488	0.452514	0.226257	+	0.974068i	$0.427351\pi$
$608$	−0.888912	−0.0360501
$609$	16.1170	0.653092
$610$	−1.63889	−0.0663568
$611$	−43.4779	−1.75893
$612$	7.70967	0.311645
$613$	−39.9831	−1.61490	−0.807452	−	0.589934i	$-0.799154\pi$
$613$	−39.9831	−1.61490	−0.807452	+	0.589934i	$0.799154\pi$
$614$	32.5990	1.31559
$615$	−10.2316	−0.412577
$616$	−16.8613	−0.679360
$617$	12.9179	0.520055	0.260027	−	0.965601i	$-0.416268\pi$
$617$	12.9179	0.520055	0.260027	+	0.965601i	$0.416268\pi$
$618$	−14.1416	−0.568858
$619$	−29.7008	−1.19378	−0.596888	−	0.802325i	$-0.703596\pi$
$619$	−29.7008	−1.19378	−0.596888	+	0.802325i	$0.703596\pi$
$620$	−4.33188	−0.173972
$621$	−0.397105	−0.0159353
$622$	18.1529	0.727864
$623$	−16.9918	−0.680762
$624$	−16.1193	−0.645290
$625$	20.1920	0.807680
$626$	−24.8111	−0.991649
$627$	13.2492	0.529122
$628$	14.5950	0.582405
$629$	−22.6244	−0.902094
$630$	5.36695	0.213825
$631$	−27.0845	−1.07822	−0.539108	−	0.842237i	$-0.681238\pi$
$631$	−27.0845	−1.07822	−0.539108	+	0.842237i	$0.681238\pi$
$632$	−7.70080	−0.306322
$633$	48.4562	1.92596
$634$	1.66060	0.0659507
$635$	8.59957	0.341264
$636$	1.29732	0.0514421
$637$	6.83388	0.270768
$638$	13.4242	0.531467
$639$	52.3881	2.07244
$640$	−0.572444	−0.0226278
$641$	−38.1283	−1.50598	−0.752989	−	0.658033i	$-0.771389\pi$
$641$	−38.1283	−1.50598	−0.752989	+	0.658033i	$0.771389\pi$
$642$	37.0750	1.46323
$643$	−3.09479	−0.122046	−0.0610232	−	0.998136i	$-0.519436\pi$
$643$	−3.09479	−0.122046	−0.0610232	+	0.998136i	$0.519436\pi$
$644$	−1.48990	−0.0587103
$645$	−5.42441	−0.213586
$646$	−2.07578	−0.0816705
$647$	−13.5389	−0.532269	−0.266135	−	0.963936i	$-0.585747\pi$
$647$	−13.5389	−0.532269	−0.266135	+	0.963936i	$0.585747\pi$
$648$	8.00455	0.314448
$649$	−20.5085	−0.805030
$650$	30.0024	1.17679
$651$	−53.9446	−2.11426
$652$	13.4380	0.526271
$653$	−23.4281	−0.916812	−0.458406	−	0.888743i	$-0.651579\pi$
$653$	−23.4281	−0.916812	−0.458406	+	0.888743i	$0.651579\pi$
$654$	−27.6944	−1.08293
$655$	2.54881	0.0995901
$656$	7.12012	0.277994
$657$	−7.93321	−0.309504
$658$	−19.2276	−0.749570
$659$	−40.6304	−1.58274	−0.791368	−	0.611340i	$-0.790631\pi$
$659$	−40.6304	−1.58274	−0.791368	+	0.611340i	$0.790631\pi$
$660$	8.53225	0.332117
$661$	−11.1135	−0.432265	−0.216132	−	0.976364i	$-0.569344\pi$
$661$	−11.1135	−0.432265	−0.216132	+	0.976364i	$0.569344\pi$
$662$	6.80573	0.264512
$663$	−37.6418	−1.46188
$664$	14.6083	0.566913
$665$	−1.44502	−0.0560354
$666$	31.9866	1.23945
$667$	1.18619	0.0459294
$668$	−11.2962	−0.437062
$669$	−67.5397	−2.61124
$670$	−1.02427	−0.0395711
$671$	−16.9991	−0.656243
$672$	−7.12860	−0.274992
$673$	−6.45540	−0.248837	−0.124419	−	0.992230i	$-0.539707\pi$
$673$	−6.45540	−0.248837	−0.124419	+	0.992230i	$0.539707\pi$
$674$	2.67013	0.102849
$675$	3.53640	0.136116
$676$	28.2335	1.08590
$677$	6.60096	0.253696	0.126848	−	0.991922i	$-0.459514\pi$
$677$	6.60096	0.253696	0.126848	+	0.991922i	$0.459514\pi$
$678$	−16.7491	−0.643247
$679$	−37.1648	−1.42625
$680$	−1.33677	−0.0512626
$681$	−10.8342	−0.415167
$682$	−44.9316	−1.72052
$683$	−0.685625	−0.0262347	−0.0131174	−	0.999914i	$-0.504176\pi$
$683$	−0.685625	−0.0262347	−0.0131174	+	0.999914i	$0.504176\pi$
$684$	2.93476	0.112213
$685$	−9.80268	−0.374541
$686$	−16.8561	−0.643570
$687$	−60.2546	−2.29885
$688$	3.77483	0.143914
$689$	−3.31856	−0.126427
$690$	0.753929	0.0287016
$691$	20.0973	0.764537	0.382269	−	0.924051i	$-0.375143\pi$
$691$	20.0973	0.764537	0.382269	+	0.924051i	$0.375143\pi$
$692$	18.6328	0.708311
$693$	55.6677	2.11464
$694$	16.0486	0.609197
$695$	8.21796	0.311725
$696$	5.67546	0.215128
$697$	16.6268	0.629787
$698$	−2.69879	−0.102151
$699$	−38.5943	−1.45977
$700$	13.2682	0.501492
$701$	−24.8212	−0.937484	−0.468742	−	0.883335i	$-0.655293\pi$
$701$	−24.8212	−0.937484	−0.468742	+	0.883335i	$0.655293\pi$
$702$	4.86021	0.183437
$703$	−8.61218	−0.324815
$704$	−5.93756	−0.223780
$705$	9.72967	0.366441
$706$	−12.6410	−0.475749
$707$	−31.7391	−1.19367
$708$	−8.67059	−0.325861
$709$	24.8320	0.932586	0.466293	−	0.884630i	$-0.345589\pi$
$709$	24.8320	0.932586	0.466293	+	0.884630i	$0.345589\pi$
$710$	−9.08348	−0.340897
$711$	25.4243	0.953486
$712$	−5.98353	−0.224242
$713$	−3.97026	−0.148687
$714$	−16.6467	−0.622985
$715$	−21.8256	−0.816231
$716$	−23.6038	−0.882116
$717$	58.3611	2.17954
$718$	24.6226	0.918906
$719$	−35.7066	−1.33163	−0.665816	−	0.746116i	$-0.731916\pi$
$719$	−35.7066	−1.33163	−0.665816	+	0.746116i	$0.731916\pi$
$720$	1.88993	0.0704336
$721$	15.9977	0.595785
$722$	18.2098	0.677700
$723$	46.1238	1.71536
$724$	−9.38551	−0.348810
$725$	−10.5636	−0.392321
$726$	60.8860	2.25969
$727$	−5.86615	−0.217564	−0.108782	−	0.994066i	$-0.534695\pi$
$727$	−5.86615	−0.217564	−0.108782	+	0.994066i	$0.534695\pi$
$728$	18.2350	0.675836
$729$	−32.1271	−1.18989
$730$	1.37553	0.0509105
$731$	8.81495	0.326033
$732$	−7.18688	−0.265635
$733$	19.3456	0.714546	0.357273	−	0.934000i	$-0.383707\pi$
$733$	19.3456	0.714546	0.357273	+	0.934000i	$0.383707\pi$
$734$	−29.3186	−1.08217
$735$	−1.52932	−0.0564097
$736$	−0.524657	−0.0193391
$737$	−10.6241	−0.391343
$738$	−23.5072	−0.865311
$739$	−1.71153	−0.0629595	−0.0314798	−	0.999504i	$-0.510022\pi$
$739$	−1.71153	−0.0629595	−0.0314798	+	0.999504i	$0.510022\pi$
$740$	−5.54610	−0.203879
$741$	−14.3287	−0.526377
$742$	−1.46760	−0.0538772
$743$	−27.5385	−1.01029	−0.505144	−	0.863035i	$-0.668561\pi$
$743$	−27.5385	−1.01029	−0.505144	+	0.863035i	$0.668561\pi$
$744$	−18.9962	−0.696433
$745$	−1.47805	−0.0541516
$746$	7.42114	0.271707
$747$	−48.2296	−1.76463
$748$	−13.8653	−0.506967
$749$	−41.9412	−1.53250
$750$	−13.8991	−0.507522
$751$	1.24533	0.0454427	0.0227214	−	0.999742i	$-0.492767\pi$
$751$	1.24533	0.0454427	0.0227214	+	0.999742i	$0.492767\pi$
$752$	−6.77085	−0.246907
$753$	3.39141	0.123590
$754$	−14.5179	−0.528711
$755$	−10.2773	−0.374029
$756$	2.14937	0.0781719
$757$	34.1439	1.24098	0.620491	−	0.784214i	$-0.286934\pi$
$757$	34.1439	1.24098	0.620491	+	0.784214i	$0.286934\pi$
$758$	14.9987	0.544779
$759$	7.81999	0.283848
$760$	−0.508852	−0.0184580
$761$	−27.7197	−1.00484	−0.502419	−	0.864624i	$-0.667557\pi$
$761$	−27.7197	−1.00484	−0.502419	+	0.864624i	$0.667557\pi$
$762$	37.7109	1.36612
$763$	31.3293	1.13420
$764$	−7.11336	−0.257352
$765$	4.41335	0.159565
$766$	2.00276	0.0723625
$767$	22.1795	0.800854
$768$	−2.51028	−0.0905820
$769$	38.4090	1.38507	0.692533	−	0.721387i	$-0.256495\pi$
$769$	38.4090	1.38507	0.692533	+	0.721387i	$0.256495\pi$
$770$	−9.65212	−0.347838
$771$	10.3987	0.374499
$772$	12.9109	0.464674
$773$	−21.3072	−0.766365	−0.383183	−	0.923673i	$-0.625172\pi$
$773$	−21.3072	−0.766365	−0.383183	+	0.923673i	$0.625172\pi$
$774$	−12.4627	−0.447961
$775$	35.3570	1.27006
$776$	−13.0873	−0.469806
$777$	−69.0651	−2.47770
$778$	−17.1209	−0.613813
$779$	6.32916	0.226766
$780$	−9.22742	−0.330395
$781$	−94.2167	−3.37134
$782$	−1.22517	−0.0438121
$783$	−1.71123	−0.0611544
$784$	1.06425	0.0380088
$785$	8.35482	0.298196
$786$	11.1770	0.398672
$787$	20.8147	0.741966	0.370983	−	0.928640i	$-0.379021\pi$
$787$	20.8147	0.741966	0.370983	+	0.928640i	$0.379021\pi$
$788$	−19.3573	−0.689574
$789$	15.8622	0.564710
$790$	−4.40828	−0.156839
$791$	18.9475	0.673696
$792$	19.6029	0.696560
$793$	18.3841	0.652839
$794$	18.8168	0.667785
$795$	0.742643	0.0263388
$796$	22.4553	0.795906
$797$	−23.8215	−0.843802	−0.421901	−	0.906642i	$-0.638637\pi$
$797$	−23.8215	−0.843802	−0.421901	+	0.906642i	$0.638637\pi$
$798$	−6.33670	−0.224317
$799$	−15.8112	−0.559361
$800$	4.67231	0.165191
$801$	19.7547	0.697998
$802$	32.7639	1.15693
$803$	14.2674	0.503485
$804$	−4.49164	−0.158408
$805$	−0.852884	−0.0300602
$806$	48.5924	1.71159
$807$	−65.0134	−2.28858
$808$	−11.1767	−0.393194
$809$	22.2382	0.781855	0.390927	−	0.920422i	$-0.372154\pi$
$809$	22.2382	0.781855	0.390927	+	0.920422i	$0.372154\pi$
$810$	4.58215	0.161000
$811$	17.7381	0.622868	0.311434	−	0.950268i	$-0.399191\pi$
$811$	17.7381	0.622868	0.311434	+	0.950268i	$0.399191\pi$
$812$	−6.42038	−0.225311
$813$	6.23174	0.218557
$814$	−57.5258	−2.01628
$815$	7.69248	0.269456
$816$	−5.86199	−0.205211
$817$	3.35549	0.117394
$818$	−21.2010	−0.741275
$819$	−60.2033	−2.10367
$820$	4.07587	0.142335
$821$	34.5598	1.20614	0.603072	−	0.797687i	$-0.293943\pi$
$821$	34.5598	1.20614	0.603072	+	0.797687i	$0.293943\pi$
$822$	−42.9867	−1.49933
$823$	39.1076	1.36321	0.681603	−	0.731722i	$-0.261283\pi$
$823$	39.1076	1.36321	0.681603	+	0.731722i	$0.261283\pi$
$824$	5.63346	0.196251
$825$	−69.6405	−2.42457
$826$	9.80862	0.341286
$827$	−1.12761	−0.0392109	−0.0196055	−	0.999808i	$-0.506241\pi$
$827$	−1.12761	−0.0392109	−0.0196055	+	0.999808i	$0.506241\pi$
$828$	1.73216	0.0601968
$829$	−37.2264	−1.29293	−0.646463	−	0.762945i	$-0.723753\pi$
$829$	−37.2264	−1.29293	−0.646463	+	0.762945i	$0.723753\pi$
$830$	8.36244	0.290264
$831$	−67.0917	−2.32738
$832$	6.42133	0.222620
$833$	2.48522	0.0861078
$834$	36.0374	1.24787
$835$	−6.46643	−0.223780
$836$	−5.27797	−0.182542
$837$	5.72761	0.197975
$838$	5.12065	0.176890
$839$	−22.2889	−0.769499	−0.384749	−	0.923021i	$-0.625712\pi$
$839$	−22.2889	−0.769499	−0.384749	+	0.923021i	$0.625712\pi$
$840$	−4.08072	−0.140798
$841$	−23.8884	−0.823738
$842$	−3.11161	−0.107233
$843$	66.0901	2.27626
$844$	−19.3031	−0.664440
$845$	16.1621	0.555992
$846$	22.3541	0.768548
$847$	−68.8774	−2.36666
$848$	−0.516803	−0.0177471
$849$	−40.1060	−1.37644
$850$	10.9107	0.374235
$851$	−5.08311	−0.174247
$852$	−39.8329	−1.36465
$853$	−13.6122	−0.466072	−0.233036	−	0.972468i	$-0.574866\pi$
$853$	−13.6122	−0.466072	−0.233036	+	0.972468i	$0.574866\pi$
$854$	8.13017	0.278209
$855$	1.67998	0.0574542
$856$	−14.7693	−0.504803
$857$	2.02387	0.0691341	0.0345671	−	0.999402i	$-0.488995\pi$
$857$	2.02387	0.0691341	0.0345671	+	0.999402i	$0.488995\pi$
$858$	−95.7096	−3.26747
$859$	−15.3570	−0.523975	−0.261988	−	0.965071i	$-0.584378\pi$
$859$	−15.3570	−0.523975	−0.261988	+	0.965071i	$0.584378\pi$
$860$	2.16088	0.0736853
$861$	50.7565	1.72978
$862$	−5.83074	−0.198596
$863$	−26.1658	−0.890693	−0.445346	−	0.895358i	$-0.646919\pi$
$863$	−26.1658	−0.890693	−0.445346	+	0.895358i	$0.646919\pi$
$864$	0.756885	0.0257497
$865$	10.6662	0.362662
$866$	−31.8773	−1.08323
$867$	28.9859	0.984413
$868$	21.4895	0.729400
$869$	−45.7240	−1.55108
$870$	3.24888	0.110147
$871$	11.4897	0.389313
$872$	11.0324	0.373603
$873$	43.2078	1.46236
$874$	−0.466374	−0.0157753
$875$	15.7233	0.531546
$876$	6.03196	0.203801
$877$	7.80568	0.263579	0.131790	−	0.991278i	$-0.457928\pi$
$877$	7.80568	0.263579	0.131790	+	0.991278i	$0.457928\pi$
$878$	−2.58104	−0.0871058
$879$	−4.54495	−0.153297
$880$	−3.39892	−0.114578
$881$	40.3403	1.35910	0.679549	−	0.733630i	$-0.262175\pi$
$881$	40.3403	1.35910	0.679549	+	0.733630i	$0.262175\pi$
$882$	−3.51363	−0.118310
$883$	16.8391	0.566680	0.283340	−	0.959020i	$-0.408557\pi$
$883$	16.8391	0.566680	0.283340	+	0.959020i	$0.408557\pi$
$884$	14.9950	0.504338
$885$	−4.96342	−0.166844
$886$	−16.9202	−0.568445
$887$	−36.9246	−1.23981	−0.619903	−	0.784678i	$-0.712828\pi$
$887$	−36.9246	−1.23981	−0.619903	+	0.784678i	$0.712828\pi$
$888$	−24.3208	−0.816151
$889$	−42.6605	−1.43079
$890$	−3.42523	−0.114814
$891$	47.5275	1.59223
$892$	26.9052	0.900854
$893$	−6.01869	−0.201408
$894$	−6.48156	−0.216776
$895$	−13.5119	−0.451652
$896$	2.83976	0.0948698
$897$	−8.45712	−0.282375
$898$	28.9062	0.964611
$899$	−17.1089	−0.570614
$900$	−15.4257	−0.514190
$901$	−1.20683	−0.0402054
$902$	42.2762	1.40764
$903$	26.9093	0.895484
$904$	6.67221	0.221915
$905$	−5.37268	−0.178594
$906$	−45.0680	−1.49728
$907$	25.9861	0.862855	0.431427	−	0.902148i	$-0.358010\pi$
$907$	25.9861	0.862855	0.431427	+	0.902148i	$0.358010\pi$
$908$	4.31593	0.143229
$909$	36.8999	1.22389
$910$	10.4385	0.346034
$911$	40.1049	1.32873	0.664367	−	0.747406i	$-0.268701\pi$
$911$	40.1049	1.32873	0.664367	+	0.747406i	$0.268701\pi$
$912$	−2.23142	−0.0738897
$913$	86.7378	2.87060
$914$	31.7821	1.05126
$915$	−4.11408	−0.136007
$916$	24.0031	0.793085
$917$	−12.6440	−0.417543
$918$	1.76747	0.0583352
$919$	−33.7335	−1.11277	−0.556383	−	0.830926i	$-0.687811\pi$
$919$	−33.7335	−1.11277	−0.556383	+	0.830926i	$0.687811\pi$
$920$	−0.300336	−0.00990180
$921$	81.8326	2.69647
$922$	35.4674	1.16806
$923$	101.893	3.35385
$924$	−42.3265	−1.39244
$925$	45.2675	1.48838
$926$	−7.93900	−0.260892
$927$	−18.5990	−0.610870
$928$	−2.26089	−0.0742172
$929$	34.4675	1.13084	0.565421	−	0.824802i	$-0.308714\pi$
$929$	34.4675	1.13084	0.565421	+	0.824802i	$0.308714\pi$
$930$	−10.8742	−0.356580
$931$	0.946022	0.0310046
$932$	15.3745	0.503609
$933$	45.5689	1.49186
$934$	−17.5219	−0.573334
$935$	−7.93713	−0.259572
$936$	−21.2001	−0.692947
$937$	−15.4512	−0.504770	−0.252385	−	0.967627i	$-0.581215\pi$
$937$	−15.4512	−0.504770	−0.252385	+	0.967627i	$0.581215\pi$
$938$	5.08118	0.165906
$939$	−62.2827	−2.03252
$940$	−3.87593	−0.126419
$941$	−28.6196	−0.932973	−0.466487	−	0.884528i	$-0.654480\pi$
$941$	−28.6196	−0.932973	−0.466487	+	0.884528i	$0.654480\pi$
$942$	36.6376	1.19372
$943$	3.73562	0.121648
$944$	3.45403	0.112419
$945$	1.23039	0.0400248
$946$	22.4133	0.728719
$947$	−58.6315	−1.90527	−0.952634	−	0.304118i	$-0.901638\pi$
$947$	−58.6315	−1.90527	−0.952634	+	0.304118i	$0.901638\pi$
$948$	−19.3312	−0.627848
$949$	−15.4298	−0.500873
$950$	4.15327	0.134750
$951$	4.16857	0.135175
$952$	6.63139	0.214925
$953$	−37.0557	−1.20035	−0.600176	−	0.799868i	$-0.704903\pi$
$953$	−37.0557	−1.20035	−0.600176	+	0.799868i	$0.704903\pi$
$954$	1.70623	0.0552413
$955$	−4.07200	−0.131767
$956$	−23.2488	−0.751921
$957$	33.6984	1.08931
$958$	−33.2920	−1.07561
$959$	48.6288	1.57031
$960$	−1.43699	−0.0463788
$961$	26.2647	0.847248
$962$	62.2128	2.00582
$963$	48.7609	1.57130
$964$	−18.3739	−0.591785
$965$	7.39078	0.237918
$966$	−3.74007	−0.120335
$967$	54.6473	1.75734	0.878670	−	0.477430i	$-0.158432\pi$
$967$	54.6473	1.75734	0.878670	+	0.477430i	$0.158432\pi$
$968$	−24.2547	−0.779574
$969$	−5.21079	−0.167395
$970$	−7.49173	−0.240545
$971$	12.5973	0.404266	0.202133	−	0.979358i	$-0.435213\pi$
$971$	12.5973	0.404266	0.202133	+	0.979358i	$0.435213\pi$
$972$	22.3643	0.717336
$973$	−40.7674	−1.30694
$974$	11.1132	0.356091
$975$	75.3146	2.41200
$976$	2.86298	0.0916417
$977$	21.1377	0.676254	0.338127	−	0.941101i	$-0.390207\pi$
$977$	21.1377	0.676254	0.338127	+	0.941101i	$0.390207\pi$
$978$	33.7331	1.07867
$979$	−35.5276	−1.13547
$980$	0.609221	0.0194609
$981$	−36.4235	−1.16291
$982$	−3.20830	−0.102381
$983$	−39.2279	−1.25118	−0.625588	−	0.780154i	$-0.715141\pi$
$983$	−39.2279	−1.25118	−0.625588	+	0.780154i	$0.715141\pi$
$984$	17.8735	0.569786
$985$	−11.0809	−0.353068
$986$	−5.27960	−0.168137
$987$	−48.2667	−1.53635
$988$	5.70800	0.181596
$989$	1.98049	0.0629759
$990$	11.2216	0.356645
$991$	−30.0979	−0.956091	−0.478045	−	0.878335i	$-0.658655\pi$
$991$	−30.0979	−0.956091	−0.478045	+	0.878335i	$0.658655\pi$
$992$	7.56734	0.240263
$993$	17.0843	0.542154
$994$	45.0611	1.42925
$995$	12.8544	0.407511
$996$	36.6710	1.16196
$997$	−52.6930	−1.66880	−0.834402	−	0.551157i	$-0.814187\pi$
$997$	−52.6930	−1.66880	−0.834402	+	0.551157i	$0.814187\pi$
$998$	−26.7315	−0.846172
$999$	7.33305	0.232007

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8026.2.a.b.1.12	✓	81

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8026.2.a.b.1.12	✓	81	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8026 = 2 \cdot 4013 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8026.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.51028 q^{3} +1.00000 q^{4} +0.572444 q^{5} +2.51028 q^{6} -2.83976 q^{7} -1.00000 q^{8} +3.30151 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.51028 q^{3} +1.00000 q^{4} +0.572444 q^{5} +2.51028 q^{6} -2.83976 q^{7} -1.00000 q^{8} +3.30151 q^{9} -0.572444 q^{10} -5.93756 q^{11} -2.51028 q^{12} +6.42133 q^{13} +2.83976 q^{14} -1.43699 q^{15} +1.00000 q^{16} +2.33519 q^{17} -3.30151 q^{18} +0.888912 q^{19} +0.572444 q^{20} +7.12860 q^{21} +5.93756 q^{22} +0.524657 q^{23} +2.51028 q^{24} -4.67231 q^{25} -6.42133 q^{26} -0.756885 q^{27} -2.83976 q^{28} +2.26089 q^{29} +1.43699 q^{30} -7.56734 q^{31} -1.00000 q^{32} +14.9050 q^{33} -2.33519 q^{34} -1.62560 q^{35} +3.30151 q^{36} -9.68846 q^{37} -0.888912 q^{38} -16.1193 q^{39} -0.572444 q^{40} +7.12012 q^{41} -7.12860 q^{42} +3.77483 q^{43} -5.93756 q^{44} +1.88993 q^{45} -0.524657 q^{46} -6.77085 q^{47} -2.51028 q^{48} +1.06425 q^{49} +4.67231 q^{50} -5.86199 q^{51} +6.42133 q^{52} -0.516803 q^{53} +0.756885 q^{54} -3.39892 q^{55} +2.83976 q^{56} -2.23142 q^{57} -2.26089 q^{58} +3.45403 q^{59} -1.43699 q^{60} +2.86298 q^{61} +7.56734 q^{62} -9.37551 q^{63} +1.00000 q^{64} +3.67585 q^{65} -14.9050 q^{66} +1.78930 q^{67} +2.33519 q^{68} -1.31704 q^{69} +1.62560 q^{70} +15.8679 q^{71} -3.30151 q^{72} -2.40290 q^{73} +9.68846 q^{74} +11.7288 q^{75} +0.888912 q^{76} +16.8613 q^{77} +16.1193 q^{78} +7.70080 q^{79} +0.572444 q^{80} -8.00455 q^{81} -7.12012 q^{82} -14.6083 q^{83} +7.12860 q^{84} +1.33677 q^{85} -3.77483 q^{86} -5.67546 q^{87} +5.93756 q^{88} +5.98353 q^{89} -1.88993 q^{90} -18.2350 q^{91} +0.524657 q^{92} +18.9962 q^{93} +6.77085 q^{94} +0.508852 q^{95} +2.51028 q^{96} +13.0873 q^{97} -1.06425 q^{98} -19.6029 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 81 q - 81 q^{2} - 10 q^{3} + 81 q^{4} - 26 q^{5} + 10 q^{6} + 3 q^{7} - 81 q^{8} + 59 q^{9}+O(q^{10}) \) 81 * q - 81 * q^2 - 10 * q^3 + 81 * q^4 - 26 * q^5 + 10 * q^6 + 3 * q^7 - 81 * q^8 + 59 * q^9	\( 81 q - 81 q^{2} - 10 q^{3} + 81 q^{4} - 26 q^{5} + 10 q^{6} + 3 q^{7} - 81 q^{8} + 59 q^{9} + 26 q^{10} - 41 q^{11} - 10 q^{12} + 33 q^{13} - 3 q^{14} - 7 q^{15} + 81 q^{16} - 9 q^{17} - 59 q^{18} - 32 q^{19} - 26 q^{20} - 23 q^{21} + 41 q^{22} - 28 q^{23} + 10 q^{24} + 81 q^{25} - 33 q^{26} - 37 q^{27} + 3 q^{28} - 35 q^{29} + 7 q^{30} - 29 q^{31} - 81 q^{32} - 7 q^{33} + 9 q^{34} - 67 q^{35} + 59 q^{36} + 13 q^{37} + 32 q^{38} - 42 q^{39} + 26 q^{40} - 66 q^{41} + 23 q^{42} - 22 q^{43} - 41 q^{44} - 65 q^{45} + 28 q^{46} - 71 q^{47} - 10 q^{48} + 64 q^{49} - 81 q^{50} - 43 q^{51} + 33 q^{52} - 37 q^{53} + 37 q^{54} + 12 q^{55} - 3 q^{56} - q^{57} + 35 q^{58} - 162 q^{59} - 7 q^{60} + 19 q^{61} + 29 q^{62} - 16 q^{63} + 81 q^{64} - 45 q^{65} + 7 q^{66} - 43 q^{67} - 9 q^{68} - 21 q^{69} + 67 q^{70} - 99 q^{71} - 59 q^{72} + 53 q^{73} - 13 q^{74} - 61 q^{75} - 32 q^{76} - 31 q^{77} + 42 q^{78} + 4 q^{79} - 26 q^{80} + q^{81} + 66 q^{82} - 112 q^{83} - 23 q^{84} + 17 q^{85} + 22 q^{86} - 15 q^{87} + 41 q^{88} - 111 q^{89} + 65 q^{90} - 49 q^{91} - 28 q^{92} - 19 q^{93} + 71 q^{94} - 53 q^{95} + 10 q^{96} + 50 q^{97} - 64 q^{98} - 97 q^{99}+O(q^{100}) \) 81 * q - 81 * q^2 - 10 * q^3 + 81 * q^4 - 26 * q^5 + 10 * q^6 + 3 * q^7 - 81 * q^8 + 59 * q^9 + 26 * q^10 - 41 * q^11 - 10 * q^12 + 33 * q^13 - 3 * q^14 - 7 * q^15 + 81 * q^16 - 9 * q^17 - 59 * q^18 - 32 * q^19 - 26 * q^20 - 23 * q^21 + 41 * q^22 - 28 * q^23 + 10 * q^24 + 81 * q^25 - 33 * q^26 - 37 * q^27 + 3 * q^28 - 35 * q^29 + 7 * q^30 - 29 * q^31 - 81 * q^32 - 7 * q^33 + 9 * q^34 - 67 * q^35 + 59 * q^36 + 13 * q^37 + 32 * q^38 - 42 * q^39 + 26 * q^40 - 66 * q^41 + 23 * q^42 - 22 * q^43 - 41 * q^44 - 65 * q^45 + 28 * q^46 - 71 * q^47 - 10 * q^48 + 64 * q^49 - 81 * q^50 - 43 * q^51 + 33 * q^52 - 37 * q^53 + 37 * q^54 + 12 * q^55 - 3 * q^56 - q^57 + 35 * q^58 - 162 * q^59 - 7 * q^60 + 19 * q^61 + 29 * q^62 - 16 * q^63 + 81 * q^64 - 45 * q^65 + 7 * q^66 - 43 * q^67 - 9 * q^68 - 21 * q^69 + 67 * q^70 - 99 * q^71 - 59 * q^72 + 53 * q^73 - 13 * q^74 - 61 * q^75 - 32 * q^76 - 31 * q^77 + 42 * q^78 + 4 * q^79 - 26 * q^80 + q^81 + 66 * q^82 - 112 * q^83 - 23 * q^84 + 17 * q^85 + 22 * q^86 - 15 * q^87 + 41 * q^88 - 111 * q^89 + 65 * q^90 - 49 * q^91 - 28 * q^92 - 19 * q^93 + 71 * q^94 - 53 * q^95 + 10 * q^96 + 50 * q^97 - 64 * q^98 - 97 * q^99

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