LMFDB - Embedded newform 8043.2.a.s.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8043,2,Mod(1,8043)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8043, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("8043.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8043 = 3 \cdot 7 \cdot 383 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8043.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:	$64.2236783457$
Analytic rank:	$0$
Dimension:	$50$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	8043.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.18460 q^{2} -1.00000 q^{3} -0.596731 q^{4} +3.79711 q^{5} +1.18460 q^{6} -1.00000 q^{7} +3.07608 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.18460 q^{2} -1.00000 q^{3} -0.596731 q^{4} +3.79711 q^{5} +1.18460 q^{6} -1.00000 q^{7} +3.07608 q^{8} +1.00000 q^{9} -4.49805 q^{10} +2.91794 q^{11} +0.596731 q^{12} +5.89933 q^{13} +1.18460 q^{14} -3.79711 q^{15} -2.45045 q^{16} +0.930186 q^{17} -1.18460 q^{18} -4.24122 q^{19} -2.26586 q^{20} +1.00000 q^{21} -3.45658 q^{22} +5.16580 q^{23} -3.07608 q^{24} +9.41807 q^{25} -6.98833 q^{26} -1.00000 q^{27} +0.596731 q^{28} -5.59647 q^{29} +4.49805 q^{30} -4.14269 q^{31} -3.24936 q^{32} -2.91794 q^{33} -1.10189 q^{34} -3.79711 q^{35} -0.596731 q^{36} -3.26039 q^{37} +5.02413 q^{38} -5.89933 q^{39} +11.6802 q^{40} +12.0644 q^{41} -1.18460 q^{42} +1.78801 q^{43} -1.74123 q^{44} +3.79711 q^{45} -6.11939 q^{46} +4.06893 q^{47} +2.45045 q^{48} +1.00000 q^{49} -11.1566 q^{50} -0.930186 q^{51} -3.52032 q^{52} +7.38438 q^{53} +1.18460 q^{54} +11.0797 q^{55} -3.07608 q^{56} +4.24122 q^{57} +6.62955 q^{58} +6.04653 q^{59} +2.26586 q^{60} -8.70272 q^{61} +4.90741 q^{62} -1.00000 q^{63} +8.75008 q^{64} +22.4004 q^{65} +3.45658 q^{66} -0.990051 q^{67} -0.555071 q^{68} -5.16580 q^{69} +4.49805 q^{70} +11.1066 q^{71} +3.07608 q^{72} +7.26130 q^{73} +3.86225 q^{74} -9.41807 q^{75} +2.53087 q^{76} -2.91794 q^{77} +6.98833 q^{78} +9.91047 q^{79} -9.30463 q^{80} +1.00000 q^{81} -14.2915 q^{82} -1.22433 q^{83} -0.596731 q^{84} +3.53202 q^{85} -2.11807 q^{86} +5.59647 q^{87} +8.97581 q^{88} +9.47455 q^{89} -4.49805 q^{90} -5.89933 q^{91} -3.08259 q^{92} +4.14269 q^{93} -4.82004 q^{94} -16.1044 q^{95} +3.24936 q^{96} -16.4472 q^{97} -1.18460 q^{98} +2.91794 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q - q^{2} - 50 q^{3} + 53 q^{4} + 11 q^{5} + q^{6} - 50 q^{7} - 6 q^{8} + 50 q^{9}+O(q^{10}) $ 50 * q - q^2 - 50 * q^3 + 53 * q^4 + 11 * q^5 + q^6 - 50 * q^7 - 6 * q^8 + 50 * q^9	\( 50 q - q^{2} - 50 q^{3} + 53 q^{4} + 11 q^{5} + q^{6} - 50 q^{7} - 6 q^{8} + 50 q^{9} + 16 q^{10} - 31 q^{11} - 53 q^{12} + 42 q^{13} + q^{14} - 11 q^{15} + 59 q^{16} + 44 q^{17} - q^{18} + 11 q^{19} + 7 q^{20} + 50 q^{21} + 19 q^{22} - 16 q^{23} + 6 q^{24} + 71 q^{25} + q^{26} - 50 q^{27} - 53 q^{28} + 3 q^{29} - 16 q^{30} + 13 q^{31} - 23 q^{32} + 31 q^{33} + q^{34} - 11 q^{35} + 53 q^{36} + 53 q^{37} + 28 q^{38} - 42 q^{39} + 50 q^{40} + 23 q^{41} - q^{42} + 9 q^{43} - 78 q^{44} + 11 q^{45} - 8 q^{46} + 26 q^{47} - 59 q^{48} + 50 q^{49} - 38 q^{50} - 44 q^{51} + 86 q^{52} + 58 q^{53} + q^{54} + 28 q^{55} + 6 q^{56} - 11 q^{57} - 4 q^{58} + 7 q^{59} - 7 q^{60} + 51 q^{61} + 7 q^{62} - 50 q^{63} + 74 q^{64} - 14 q^{65} - 19 q^{66} + 23 q^{67} + 98 q^{68} + 16 q^{69} - 16 q^{70} - 75 q^{71} - 6 q^{72} + 34 q^{73} - 68 q^{74} - 71 q^{75} + 31 q^{76} + 31 q^{77} - q^{78} - 18 q^{79} - 21 q^{80} + 50 q^{81} + 31 q^{82} + 40 q^{83} + 53 q^{84} + 30 q^{85} - 15 q^{86} - 3 q^{87} + 70 q^{88} + 63 q^{89} + 16 q^{90} - 42 q^{91} - 38 q^{92} - 13 q^{93} + q^{94} - 77 q^{95} + 23 q^{96} + 77 q^{97} - q^{98} - 31 q^{99}+O(q^{100}) \) 50 * q - q^2 - 50 * q^3 + 53 * q^4 + 11 * q^5 + q^6 - 50 * q^7 - 6 * q^8 + 50 * q^9 + 16 * q^10 - 31 * q^11 - 53 * q^12 + 42 * q^13 + q^14 - 11 * q^15 + 59 * q^16 + 44 * q^17 - q^18 + 11 * q^19 + 7 * q^20 + 50 * q^21 + 19 * q^22 - 16 * q^23 + 6 * q^24 + 71 * q^25 + q^26 - 50 * q^27 - 53 * q^28 + 3 * q^29 - 16 * q^30 + 13 * q^31 - 23 * q^32 + 31 * q^33 + q^34 - 11 * q^35 + 53 * q^36 + 53 * q^37 + 28 * q^38 - 42 * q^39 + 50 * q^40 + 23 * q^41 - q^42 + 9 * q^43 - 78 * q^44 + 11 * q^45 - 8 * q^46 + 26 * q^47 - 59 * q^48 + 50 * q^49 - 38 * q^50 - 44 * q^51 + 86 * q^52 + 58 * q^53 + q^54 + 28 * q^55 + 6 * q^56 - 11 * q^57 - 4 * q^58 + 7 * q^59 - 7 * q^60 + 51 * q^61 + 7 * q^62 - 50 * q^63 + 74 * q^64 - 14 * q^65 - 19 * q^66 + 23 * q^67 + 98 * q^68 + 16 * q^69 - 16 * q^70 - 75 * q^71 - 6 * q^72 + 34 * q^73 - 68 * q^74 - 71 * q^75 + 31 * q^76 + 31 * q^77 - q^78 - 18 * q^79 - 21 * q^80 + 50 * q^81 + 31 * q^82 + 40 * q^83 + 53 * q^84 + 30 * q^85 - 15 * q^86 - 3 * q^87 + 70 * q^88 + 63 * q^89 + 16 * q^90 - 42 * q^91 - 38 * q^92 - 13 * q^93 + q^94 - 77 * q^95 + 23 * q^96 + 77 * q^97 - q^98 - 31 * 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 $

$2$	−1.18460	−0.837636	−0.418818	−	0.908070i	$-0.637555\pi$
$2$	−1.18460	−0.837636	−0.418818	+	0.908070i	$0.637555\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.596731	−0.298366
$5$	3.79711	1.69812	0.849060	−	0.528296i	$-0.177169\pi$
$5$	3.79711	1.69812	0.849060	+	0.528296i	$0.177169\pi$
$6$	1.18460	0.483609
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	3.07608	1.08756
$9$	1.00000	0.333333
$10$	−4.49805	−1.42241
$11$	2.91794	0.879792	0.439896	−	0.898049i	$-0.355015\pi$
$11$	2.91794	0.879792	0.439896	+	0.898049i	$0.355015\pi$
$12$	0.596731	0.172262
$13$	5.89933	1.63618	0.818090	−	0.575090i	$-0.195033\pi$
$13$	5.89933	1.63618	0.818090	+	0.575090i	$0.195033\pi$
$14$	1.18460	0.316597
$15$	−3.79711	−0.980411
$16$	−2.45045	−0.612612
$17$	0.930186	0.225603	0.112802	−	0.993618i	$-0.464018\pi$
$17$	0.930186	0.225603	0.112802	+	0.993618i	$0.464018\pi$
$18$	−1.18460	−0.279212
$19$	−4.24122	−0.973002	−0.486501	−	0.873680i	$-0.661727\pi$
$19$	−4.24122	−0.973002	−0.486501	+	0.873680i	$0.661727\pi$
$20$	−2.26586	−0.506661
$21$	1.00000	0.218218
$22$	−3.45658	−0.736945
$23$	5.16580	1.07714	0.538572	−	0.842580i	$-0.318964\pi$
$23$	5.16580	1.07714	0.538572	+	0.842580i	$0.318964\pi$
$24$	−3.07608	−0.627902
$25$	9.41807	1.88361
$26$	−6.98833	−1.37052
$27$	−1.00000	−0.192450
$28$	0.596731	0.112772
$29$	−5.59647	−1.03924	−0.519619	−	0.854398i	$-0.673926\pi$
$29$	−5.59647	−1.03924	−0.519619	+	0.854398i	$0.673926\pi$
$30$	4.49805	0.821227
$31$	−4.14269	−0.744049	−0.372024	−	0.928223i	$-0.621336\pi$
$31$	−4.14269	−0.744049	−0.372024	+	0.928223i	$0.621336\pi$
$32$	−3.24936	−0.574412
$33$	−2.91794	−0.507948
$34$	−1.10189	−0.188973
$35$	−3.79711	−0.641829
$36$	−0.596731	−0.0994552
$37$	−3.26039	−0.536005	−0.268003	−	0.963418i	$-0.586364\pi$
$37$	−3.26039	−0.536005	−0.268003	+	0.963418i	$0.586364\pi$
$38$	5.02413	0.815022
$39$	−5.89933	−0.944649
$40$	11.6802	1.84680
$41$	12.0644	1.88415	0.942075	−	0.335403i	$-0.108873\pi$
$41$	12.0644	1.88415	0.942075	+	0.335403i	$0.108873\pi$
$42$	−1.18460	−0.182787
$43$	1.78801	0.272669	0.136335	−	0.990663i	$-0.456468\pi$
$43$	1.78801	0.272669	0.136335	+	0.990663i	$0.456468\pi$
$44$	−1.74123	−0.262500
$45$	3.79711	0.566040
$46$	−6.11939	−0.902254
$47$	4.06893	0.593515	0.296757	−	0.954953i	$-0.404095\pi$
$47$	4.06893	0.593515	0.296757	+	0.954953i	$0.404095\pi$
$48$	2.45045	0.353692
$49$	1.00000	0.142857
$50$	−11.1566	−1.57778
$51$	−0.930186	−0.130252
$52$	−3.52032	−0.488180
$53$	7.38438	1.01432	0.507161	−	0.861851i	$-0.330695\pi$
$53$	7.38438	1.01432	0.507161	+	0.861851i	$0.330695\pi$
$54$	1.18460	0.161203
$55$	11.0797	1.49399
$56$	−3.07608	−0.411058
$57$	4.24122	0.561763
$58$	6.62955	0.870503
$59$	6.04653	0.787191	0.393596	−	0.919284i	$-0.371231\pi$
$59$	6.04653	0.787191	0.393596	+	0.919284i	$0.371231\pi$
$60$	2.26586	0.292521
$61$	−8.70272	−1.11427	−0.557135	−	0.830422i	$-0.688099\pi$
$61$	−8.70272	−1.11427	−0.557135	+	0.830422i	$0.688099\pi$
$62$	4.90741	0.623242
$63$	−1.00000	−0.125988
$64$	8.75008	1.09376
$65$	22.4004	2.77843
$66$	3.45658	0.425476
$67$	−0.990051	−0.120954	−0.0604770	−	0.998170i	$-0.519262\pi$
$67$	−0.990051	−0.120954	−0.0604770	+	0.998170i	$0.519262\pi$
$68$	−0.555071	−0.0673123
$69$	−5.16580	−0.621889
$70$	4.49805	0.537619
$71$	11.1066	1.31811	0.659053	−	0.752096i	$-0.270957\pi$
$71$	11.1066	1.31811	0.659053	+	0.752096i	$0.270957\pi$
$72$	3.07608	0.362519
$73$	7.26130	0.849871	0.424936	−	0.905224i	$-0.360297\pi$
$73$	7.26130	0.849871	0.424936	+	0.905224i	$0.360297\pi$
$74$	3.86225	0.448977
$75$	−9.41807	−1.08751
$76$	2.53087	0.290310
$77$	−2.91794	−0.332530
$78$	6.98833	0.791272
$79$	9.91047	1.11501	0.557507	−	0.830172i	$-0.311758\pi$
$79$	9.91047	1.11501	0.557507	+	0.830172i	$0.311758\pi$
$80$	−9.30463	−1.04029
$81$	1.00000	0.111111
$82$	−14.2915	−1.57823
$83$	−1.22433	−0.134387	−0.0671936	−	0.997740i	$-0.521405\pi$
$83$	−1.22433	−0.134387	−0.0671936	+	0.997740i	$0.521405\pi$
$84$	−0.596731	−0.0651087
$85$	3.53202	0.383102
$86$	−2.11807	−0.228397
$87$	5.59647	0.600004
$88$	8.97581	0.956825
$89$	9.47455	1.00430	0.502150	−	0.864780i	$-0.332542\pi$
$89$	9.47455	1.00430	0.502150	+	0.864780i	$0.332542\pi$
$90$	−4.49805	−0.474136
$91$	−5.89933	−0.618418
$92$	−3.08259	−0.321383
$93$	4.14269	0.429577
$94$	−4.82004	−0.497149
$95$	−16.1044	−1.65228
$96$	3.24936	0.331637
$97$	−16.4472	−1.66996	−0.834980	−	0.550281i	$-0.814521\pi$
$97$	−16.4472	−1.66996	−0.834980	+	0.550281i	$0.814521\pi$
$98$	−1.18460	−0.119662
$99$	2.91794	0.293264
$100$	−5.62006	−0.562006
$101$	4.13776	0.411722	0.205861	−	0.978581i	$-0.434001\pi$
$101$	4.13776	0.411722	0.205861	+	0.978581i	$0.434001\pi$
$102$	1.10189	0.109104
$103$	−15.2197	−1.49964	−0.749819	−	0.661643i	$-0.769860\pi$
$103$	−15.2197	−1.49964	−0.749819	+	0.661643i	$0.769860\pi$
$104$	18.1468	1.77944
$105$	3.79711	0.370560
$106$	−8.74750	−0.849633
$107$	−11.2189	−1.08457	−0.542284	−	0.840195i	$-0.682440\pi$
$107$	−11.2189	−1.08457	−0.542284	+	0.840195i	$0.682440\pi$
$108$	0.596731	0.0574205
$109$	−10.8243	−1.03678	−0.518388	−	0.855146i	$-0.673468\pi$
$109$	−10.8243	−1.03678	−0.518388	+	0.855146i	$0.673468\pi$
$110$	−13.1250	−1.25142
$111$	3.26039	0.309463
$112$	2.45045	0.231546
$113$	20.8291	1.95944	0.979721	−	0.200369i	$-0.0642140\pi$
$113$	20.8291	1.95944	0.979721	+	0.200369i	$0.0642140\pi$
$114$	−5.02413	−0.470553
$115$	19.6151	1.82912
$116$	3.33959	0.310073
$117$	5.89933	0.545394
$118$	−7.16270	−0.659380
$119$	−0.930186	−0.0852700
$120$	−11.6802	−1.06625
$121$	−2.48563	−0.225966
$122$	10.3092	0.933352
$123$	−12.0644	−1.08781
$124$	2.47207	0.221999
$125$	16.7759	1.50048
$126$	1.18460	0.105532
$127$	−16.8483	−1.49504	−0.747521	−	0.664238i	$-0.768756\pi$
$127$	−16.8483	−1.49504	−0.747521	+	0.664238i	$0.768756\pi$
$128$	−3.86659	−0.341761
$129$	−1.78801	−0.157426
$130$	−26.5355	−2.32732
$131$	18.6417	1.62873	0.814367	−	0.580350i	$-0.197084\pi$
$131$	18.6417	1.62873	0.814367	+	0.580350i	$0.197084\pi$
$132$	1.74123	0.151554
$133$	4.24122	0.367760
$134$	1.17281	0.101315
$135$	−3.79711	−0.326804
$136$	2.86132	0.245357
$137$	−14.2819	−1.22018	−0.610092	−	0.792331i	$-0.708867\pi$
$137$	−14.2819	−1.22018	−0.610092	+	0.792331i	$0.708867\pi$
$138$	6.11939	0.520917
$139$	1.88491	0.159876	0.0799379	−	0.996800i	$-0.474528\pi$
$139$	1.88491	0.159876	0.0799379	+	0.996800i	$0.474528\pi$
$140$	2.26586	0.191500
$141$	−4.06893	−0.342666
$142$	−13.1568	−1.10409
$143$	17.2139	1.43950
$144$	−2.45045	−0.204204
$145$	−21.2504	−1.76475
$146$	−8.60171	−0.711883
$147$	−1.00000	−0.0824786
$148$	1.94558	0.159926
$149$	13.0487	1.06899	0.534497	−	0.845171i	$-0.320501\pi$
$149$	13.0487	1.06899	0.534497	+	0.845171i	$0.320501\pi$
$150$	11.1566	0.910934
$151$	−16.9361	−1.37824	−0.689119	−	0.724648i	$-0.742002\pi$
$151$	−16.9361	−1.37824	−0.689119	+	0.724648i	$0.742002\pi$
$152$	−13.0463	−1.05820
$153$	0.930186	0.0752011
$154$	3.45658	0.278539
$155$	−15.7303	−1.26348
$156$	3.52032	0.281851
$157$	12.8706	1.02719	0.513594	−	0.858034i	$-0.328314\pi$
$157$	12.8706	1.02719	0.513594	+	0.858034i	$0.328314\pi$
$158$	−11.7399	−0.933977
$159$	−7.38438	−0.585619
$160$	−12.3382	−0.975421
$161$	−5.16580	−0.407122
$162$	−1.18460	−0.0930707
$163$	6.83242	0.535156	0.267578	−	0.963536i	$-0.413777\pi$
$163$	6.83242	0.535156	0.267578	+	0.963536i	$0.413777\pi$
$164$	−7.19923	−0.562166
$165$	−11.0797	−0.862557
$166$	1.45033	0.112568
$167$	2.63886	0.204201	0.102101	−	0.994774i	$-0.467444\pi$
$167$	2.63886	0.204201	0.102101	+	0.994774i	$0.467444\pi$
$168$	3.07608	0.237325
$169$	21.8021	1.67709
$170$	−4.18402	−0.320900
$171$	−4.24122	−0.324334
$172$	−1.06696	−0.0813551
$173$	−16.5137	−1.25551	−0.627757	−	0.778410i	$-0.716027\pi$
$173$	−16.5137	−1.25551	−0.627757	+	0.778410i	$0.716027\pi$
$174$	−6.62955	−0.502585
$175$	−9.41807	−0.711939
$176$	−7.15026	−0.538971
$177$	−6.04653	−0.454485
$178$	−11.2235	−0.841239
$179$	16.1259	1.20531	0.602655	−	0.798002i	$-0.294110\pi$
$179$	16.1259	1.20531	0.602655	+	0.798002i	$0.294110\pi$
$180$	−2.26586	−0.168887
$181$	15.1718	1.12771	0.563857	−	0.825873i	$-0.309317\pi$
$181$	15.1718	1.12771	0.563857	+	0.825873i	$0.309317\pi$
$182$	6.98833	0.518009
$183$	8.70272	0.643324
$184$	15.8904	1.17146
$185$	−12.3801	−0.910202
$186$	−4.90741	−0.359829
$187$	2.71423	0.198484
$188$	−2.42806	−0.177084
$189$	1.00000	0.0727393
$190$	19.0772	1.38401
$191$	2.33675	0.169081	0.0845407	−	0.996420i	$-0.473058\pi$
$191$	2.33675	0.169081	0.0845407	+	0.996420i	$0.473058\pi$
$192$	−8.75008	−0.631483
$193$	13.9366	1.00318	0.501589	−	0.865106i	$-0.332749\pi$
$193$	13.9366	1.00318	0.501589	+	0.865106i	$0.332749\pi$
$194$	19.4833	1.39882
$195$	−22.4004	−1.60413
$196$	−0.596731	−0.0426237
$197$	12.0055	0.855359	0.427679	−	0.903931i	$-0.359331\pi$
$197$	12.0055	0.855359	0.427679	+	0.903931i	$0.359331\pi$
$198$	−3.45658	−0.245648
$199$	13.3009	0.942873	0.471437	−	0.881900i	$-0.343736\pi$
$199$	13.3009	0.942873	0.471437	+	0.881900i	$0.343736\pi$
$200$	28.9707	2.04854
$201$	0.990051	0.0698328
$202$	−4.90157	−0.344873
$203$	5.59647	0.392795
$204$	0.555071	0.0388628
$205$	45.8101	3.19951
$206$	18.0292	1.25615
$207$	5.16580	0.359048
$208$	−14.4560	−1.00234
$209$	−12.3756	−0.856039
$210$	−4.49805	−0.310395
$211$	−25.1718	−1.73290	−0.866450	−	0.499264i	$-0.833604\pi$
$211$	−25.1718	−1.73290	−0.866450	+	0.499264i	$0.833604\pi$
$212$	−4.40649	−0.302639
$213$	−11.1066	−0.761009
$214$	13.2898	0.908473
$215$	6.78928	0.463025
$216$	−3.07608	−0.209301
$217$	4.14269	0.281224
$218$	12.8224	0.868441
$219$	−7.26130	−0.490673
$220$	−6.61163	−0.445756
$221$	5.48748	0.369128
$222$	−3.86225	−0.259217
$223$	−0.335382	−0.0224589	−0.0112294	−	0.999937i	$-0.503575\pi$
$223$	−0.335382	−0.0224589	−0.0112294	+	0.999937i	$0.503575\pi$
$224$	3.24936	0.217107
$225$	9.41807	0.627872
$226$	−24.6741	−1.64130
$227$	−24.9517	−1.65610	−0.828052	−	0.560651i	$-0.810551\pi$
$227$	−24.9517	−1.65610	−0.828052	+	0.560651i	$0.810551\pi$
$228$	−2.53087	−0.167611
$229$	2.32461	0.153615	0.0768073	−	0.997046i	$-0.475527\pi$
$229$	2.32461	0.153615	0.0768073	+	0.997046i	$0.475527\pi$
$230$	−23.2360	−1.53214
$231$	2.91794	0.191986
$232$	−17.2152	−1.13023
$233$	−24.3573	−1.59570	−0.797851	−	0.602855i	$-0.794030\pi$
$233$	−24.3573	−1.59570	−0.797851	+	0.602855i	$0.794030\pi$
$234$	−6.98833	−0.456841
$235$	15.4502	1.00786
$236$	−3.60815	−0.234871
$237$	−9.91047	−0.643754
$238$	1.10189	0.0714252
$239$	3.46881	0.224379	0.112189	−	0.993687i	$-0.464214\pi$
$239$	3.46881	0.224379	0.112189	+	0.993687i	$0.464214\pi$
$240$	9.30463	0.600611
$241$	−16.1160	−1.03812	−0.519060	−	0.854738i	$-0.673718\pi$
$241$	−16.1160	−1.03812	−0.519060	+	0.854738i	$0.673718\pi$
$242$	2.94447	0.189277
$243$	−1.00000	−0.0641500
$244$	5.19319	0.332460
$245$	3.79711	0.242589
$246$	14.2915	0.911192
$247$	−25.0204	−1.59201
$248$	−12.7432	−0.809196
$249$	1.22433	0.0775885
$250$	−19.8727	−1.25686
$251$	−9.69309	−0.611822	−0.305911	−	0.952060i	$-0.598961\pi$
$251$	−9.69309	−0.611822	−0.305911	+	0.952060i	$0.598961\pi$
$252$	0.596731	0.0375905
$253$	15.0735	0.947662
$254$	19.9584	1.25230
$255$	−3.53202	−0.221184
$256$	−12.9198	−0.807489
$257$	22.7736	1.42058	0.710290	−	0.703909i	$-0.248564\pi$
$257$	22.7736	1.42058	0.710290	+	0.703909i	$0.248564\pi$
$258$	2.11807	0.131865
$259$	3.26039	0.202591
$260$	−13.3670	−0.828989
$261$	−5.59647	−0.346412
$262$	−22.0829	−1.36429
$263$	−27.0285	−1.66665	−0.833325	−	0.552784i	$-0.813566\pi$
$263$	−27.0285	−1.66665	−0.833325	+	0.552784i	$0.813566\pi$
$264$	−8.97581	−0.552423
$265$	28.0393	1.72244
$266$	−5.02413	−0.308049
$267$	−9.47455	−0.579833
$268$	0.590795	0.0360885
$269$	−23.7743	−1.44954	−0.724772	−	0.688989i	$-0.758055\pi$
$269$	−23.7743	−1.44954	−0.724772	+	0.688989i	$0.758055\pi$
$270$	4.49805	0.273742
$271$	−8.07382	−0.490450	−0.245225	−	0.969466i	$-0.578862\pi$
$271$	−8.07382	−0.490450	−0.245225	+	0.969466i	$0.578862\pi$
$272$	−2.27937	−0.138207
$273$	5.89933	0.357044
$274$	16.9183	1.02207
$275$	27.4814	1.65719
$276$	3.08259	0.185550
$277$	−12.3202	−0.740247	−0.370124	−	0.928982i	$-0.620685\pi$
$277$	−12.3202	−0.740247	−0.370124	+	0.928982i	$0.620685\pi$
$278$	−2.23286	−0.133918
$279$	−4.14269	−0.248016
$280$	−11.6802	−0.698027
$281$	29.7537	1.77496	0.887479	−	0.460849i	$-0.152455\pi$
$281$	29.7537	1.77496	0.887479	+	0.460849i	$0.152455\pi$
$282$	4.82004	0.287029
$283$	−16.7093	−0.993265	−0.496633	−	0.867961i	$-0.665430\pi$
$283$	−16.7093	−0.993265	−0.496633	+	0.867961i	$0.665430\pi$
$284$	−6.62763	−0.393278
$285$	16.1044	0.953941
$286$	−20.3915	−1.20578
$287$	−12.0644	−0.712142
$288$	−3.24936	−0.191471
$289$	−16.1348	−0.949103
$290$	25.1732	1.47822
$291$	16.4472	0.964151
$292$	−4.33305	−0.253572
$293$	18.9931	1.10959	0.554793	−	0.831988i	$-0.312797\pi$
$293$	18.9931	1.10959	0.554793	+	0.831988i	$0.312797\pi$
$294$	1.18460	0.0690871
$295$	22.9594	1.33675
$296$	−10.0292	−0.582937
$297$	−2.91794	−0.169316
$298$	−15.4575	−0.895427
$299$	30.4748	1.76240
$300$	5.62006	0.324474
$301$	−1.78801	−0.103059
$302$	20.0624	1.15446
$303$	−4.13776	−0.237708
$304$	10.3929	0.596073
$305$	−33.0452	−1.89216
$306$	−1.10189	−0.0629911
$307$	24.6369	1.40610	0.703050	−	0.711140i	$-0.251821\pi$
$307$	24.6369	1.40610	0.703050	+	0.711140i	$0.251821\pi$
$308$	1.74123	0.0992156
$309$	15.2197	0.865817
$310$	18.6340	1.05834
$311$	1.08133	0.0613166	0.0306583	−	0.999530i	$-0.490240\pi$
$311$	1.08133	0.0613166	0.0306583	+	0.999530i	$0.490240\pi$
$312$	−18.1468	−1.02736
$313$	−24.0770	−1.36092	−0.680458	−	0.732788i	$-0.738219\pi$
$313$	−24.0770	−1.36092	−0.680458	+	0.732788i	$0.738219\pi$
$314$	−15.2465	−0.860409
$315$	−3.79711	−0.213943
$316$	−5.91389	−0.332682
$317$	20.8583	1.17152	0.585760	−	0.810485i	$-0.300796\pi$
$317$	20.8583	1.17152	0.585760	+	0.810485i	$0.300796\pi$
$318$	8.74750	0.490536
$319$	−16.3301	−0.914313
$320$	33.2251	1.85734
$321$	11.2189	0.626176
$322$	6.11939	0.341020
$323$	−3.94512	−0.219512
$324$	−0.596731	−0.0331517
$325$	55.5603	3.08193
$326$	−8.09366	−0.448266
$327$	10.8243	0.598583
$328$	37.1112	2.04912
$329$	−4.06893	−0.224327
$330$	13.1250	0.722509
$331$	−21.1567	−1.16288	−0.581440	−	0.813590i	$-0.697510\pi$
$331$	−21.1567	−1.16288	−0.581440	+	0.813590i	$0.697510\pi$
$332$	0.730594	0.0400965
$333$	−3.26039	−0.178668
$334$	−3.12598	−0.171046
$335$	−3.75934	−0.205394
$336$	−2.45045	−0.133683
$337$	−5.57167	−0.303508	−0.151754	−	0.988418i	$-0.548492\pi$
$337$	−5.57167	−0.303508	−0.151754	+	0.988418i	$0.548492\pi$
$338$	−25.8267	−1.40479
$339$	−20.8291	−1.13128
$340$	−2.10767	−0.114304
$341$	−12.0881	−0.654608
$342$	5.02413	0.271674
$343$	−1.00000	−0.0539949
$344$	5.50006	0.296543
$345$	−19.6151	−1.05604
$346$	19.5621	1.05166
$347$	−33.5343	−1.80021	−0.900107	−	0.435668i	$-0.856512\pi$
$347$	−33.5343	−1.80021	−0.900107	+	0.435668i	$0.856512\pi$
$348$	−3.33959	−0.179021
$349$	−8.34933	−0.446930	−0.223465	−	0.974712i	$-0.571737\pi$
$349$	−8.34933	−0.446930	−0.223465	+	0.974712i	$0.571737\pi$
$350$	11.1566	0.596346
$351$	−5.89933	−0.314883
$352$	−9.48145	−0.505363
$353$	5.03208	0.267831	0.133915	−	0.990993i	$-0.457245\pi$
$353$	5.03208	0.267831	0.133915	+	0.990993i	$0.457245\pi$
$354$	7.16270	0.380693
$355$	42.1729	2.23830
$356$	−5.65376	−0.299649
$357$	0.930186	0.0492307
$358$	−19.1027	−1.00961
$359$	−19.9020	−1.05039	−0.525194	−	0.850983i	$-0.676007\pi$
$359$	−19.9020	−1.05039	−0.525194	+	0.850983i	$0.676007\pi$
$360$	11.6802	0.615602
$361$	−1.01208	−0.0532671
$362$	−17.9725	−0.944614
$363$	2.48563	0.130462
$364$	3.52032	0.184515
$365$	27.5720	1.44318
$366$	−10.3092	−0.538871
$367$	12.9334	0.675120	0.337560	−	0.941304i	$-0.390398\pi$
$367$	12.9334	0.675120	0.337560	+	0.941304i	$0.390398\pi$
$368$	−12.6585	−0.659871
$369$	12.0644	0.628050
$370$	14.6654	0.762418
$371$	−7.38438	−0.383378
$372$	−2.47207	−0.128171
$373$	33.7862	1.74938	0.874690	−	0.484682i	$-0.161065\pi$
$373$	33.7862	1.74938	0.874690	+	0.484682i	$0.161065\pi$
$374$	−3.21526	−0.166257
$375$	−16.7759	−0.866305
$376$	12.5164	0.645482
$377$	−33.0154	−1.70038
$378$	−1.18460	−0.0609291
$379$	30.0545	1.54379	0.771897	−	0.635747i	$-0.219308\pi$
$379$	30.0545	1.54379	0.771897	+	0.635747i	$0.219308\pi$
$380$	9.60999	0.492982
$381$	16.8483	0.863163
$382$	−2.76811	−0.141629
$383$	1.00000	0.0510976
$383$	1.00000	0.0510976
$384$	3.86659	0.197316
$385$	−11.0797	−0.564676
$386$	−16.5092	−0.840298
$387$	1.78801	0.0908897
$388$	9.81456	0.498259
$389$	23.8803	1.21078	0.605390	−	0.795929i	$-0.293017\pi$
$389$	23.8803	1.21078	0.605390	+	0.795929i	$0.293017\pi$
$390$	26.5355	1.34368
$391$	4.80515	0.243007
$392$	3.07608	0.155365
$393$	−18.6417	−0.940350
$394$	−14.2217	−0.716479
$395$	37.6312	1.89343
$396$	−1.74123	−0.0874999
$397$	−9.50586	−0.477085	−0.238543	−	0.971132i	$-0.576670\pi$
$397$	−9.50586	−0.477085	−0.238543	+	0.971132i	$0.576670\pi$
$398$	−15.7562	−0.789785
$399$	−4.24122	−0.212326
$400$	−23.0785	−1.15393
$401$	2.29133	0.114423	0.0572117	−	0.998362i	$-0.481779\pi$
$401$	2.29133	0.114423	0.0572117	+	0.998362i	$0.481779\pi$
$402$	−1.17281	−0.0584945
$403$	−24.4391	−1.21740
$404$	−2.46913	−0.122844
$405$	3.79711	0.188680
$406$	−6.62955	−0.329019
$407$	−9.51363	−0.471573
$408$	−2.86132	−0.141657
$409$	39.1059	1.93366	0.966831	−	0.255419i	$-0.0822133\pi$
$409$	39.1059	1.93366	0.966831	+	0.255419i	$0.0822133\pi$
$410$	−54.2664	−2.68003
$411$	14.2819	0.704473
$412$	9.08205	0.447441
$413$	−6.04653	−0.297530
$414$	−6.11939	−0.300751
$415$	−4.64890	−0.228206
$416$	−19.1691	−0.939842
$417$	−1.88491	−0.0923044
$418$	14.6601	0.717049
$419$	−4.74554	−0.231835	−0.115917	−	0.993259i	$-0.536981\pi$
$419$	−4.74554	−0.231835	−0.115917	+	0.993259i	$0.536981\pi$
$420$	−2.26586	−0.110563
$421$	14.5623	0.709725	0.354862	−	0.934919i	$-0.384528\pi$
$421$	14.5623	0.709725	0.354862	+	0.934919i	$0.384528\pi$
$422$	29.8185	1.45154
$423$	4.06893	0.197838
$424$	22.7149	1.10313
$425$	8.76056	0.424949
$426$	13.1568	0.637449
$427$	8.70272	0.421154
$428$	6.69464	0.323598
$429$	−17.2139	−0.831095
$430$	−8.04256	−0.387846
$431$	−16.5033	−0.794937	−0.397469	−	0.917616i	$-0.630111\pi$
$431$	−16.5033	−0.794937	−0.397469	+	0.917616i	$0.630111\pi$
$432$	2.45045	0.117897
$433$	−12.5700	−0.604078	−0.302039	−	0.953296i	$-0.597667\pi$
$433$	−12.5700	−0.604078	−0.302039	+	0.953296i	$0.597667\pi$
$434$	−4.90741	−0.235563
$435$	21.2504	1.01888
$436$	6.45917	0.309338
$437$	−21.9093	−1.04806
$438$	8.60171	0.411006
$439$	−28.4027	−1.35559	−0.677794	−	0.735251i	$-0.737064\pi$
$439$	−28.4027	−1.35559	−0.677794	+	0.735251i	$0.737064\pi$
$440$	34.0822	1.62480
$441$	1.00000	0.0476190
$442$	−6.50044	−0.309195
$443$	−22.7049	−1.07874	−0.539371	−	0.842068i	$-0.681338\pi$
$443$	−22.7049	−1.07874	−0.539371	+	0.842068i	$0.681338\pi$
$444$	−1.94558	−0.0923331
$445$	35.9760	1.70542
$446$	0.397293	0.0188124
$447$	−13.0487	−0.617184
$448$	−8.75008	−0.413403
$449$	0.129690	0.00612044	0.00306022	−	0.999995i	$-0.499026\pi$
$449$	0.129690	0.00612044	0.00306022	+	0.999995i	$0.499026\pi$
$450$	−11.1566	−0.525928
$451$	35.2033	1.65766
$452$	−12.4294	−0.584630
$453$	16.9361	0.795726
$454$	29.5577	1.38721
$455$	−22.4004	−1.05015
$456$	13.0463	0.610950
$457$	12.5417	0.586674	0.293337	−	0.956009i	$-0.405234\pi$
$457$	12.5417	0.586674	0.293337	+	0.956009i	$0.405234\pi$
$458$	−2.75372	−0.128673
$459$	−0.930186	−0.0434174
$460$	−11.7050	−0.545747
$461$	2.24347	0.104489	0.0522443	−	0.998634i	$-0.483363\pi$
$461$	2.24347	0.104489	0.0522443	+	0.998634i	$0.483363\pi$
$462$	−3.45658	−0.160815
$463$	8.90873	0.414024	0.207012	−	0.978338i	$-0.433626\pi$
$463$	8.90873	0.414024	0.207012	+	0.978338i	$0.433626\pi$
$464$	13.7139	0.636650
$465$	15.7303	0.729473
$466$	28.8536	1.33662
$467$	−0.339196	−0.0156961	−0.00784806	−	0.999969i	$-0.502498\pi$
$467$	−0.339196	−0.0156961	−0.00784806	+	0.999969i	$0.502498\pi$
$468$	−3.52032	−0.162727
$469$	0.990051	0.0457163
$470$	−18.3022	−0.844220
$471$	−12.8706	−0.593047
$472$	18.5996	0.856116
$473$	5.21731	0.239892
$474$	11.7399	0.539232
$475$	−39.9441	−1.83276
$476$	0.555071	0.0254416
$477$	7.38438	0.338107
$478$	−4.10914	−0.187948
$479$	−40.6604	−1.85782	−0.928911	−	0.370303i	$-0.879254\pi$
$479$	−40.6604	−1.85782	−0.928911	+	0.370303i	$0.879254\pi$
$480$	12.3382	0.563160
$481$	−19.2341	−0.877001
$482$	19.0909	0.869567
$483$	5.16580	0.235052
$484$	1.48325	0.0674206
$485$	−62.4519	−2.83579
$486$	1.18460	0.0537344
$487$	21.8454	0.989909	0.494955	−	0.868919i	$-0.335185\pi$
$487$	21.8454	0.989909	0.494955	+	0.868919i	$0.335185\pi$
$488$	−26.7703	−1.21183
$489$	−6.83242	−0.308973
$490$	−4.49805	−0.203201
$491$	16.6537	0.751571	0.375786	−	0.926707i	$-0.377373\pi$
$491$	16.6537	0.751571	0.375786	+	0.926707i	$0.377373\pi$
$492$	7.19923	0.324566
$493$	−5.20575	−0.234455
$494$	29.6390	1.33352
$495$	11.0797	0.497998
$496$	10.1514	0.455813
$497$	−11.1066	−0.498197
$498$	−1.45033	−0.0649909
$499$	−2.99274	−0.133974	−0.0669868	−	0.997754i	$-0.521339\pi$
$499$	−2.99274	−0.133974	−0.0669868	+	0.997754i	$0.521339\pi$
$500$	−10.0107	−0.447693
$501$	−2.63886	−0.117896
$502$	11.4824	0.512485
$503$	26.3443	1.17463	0.587317	−	0.809357i	$-0.300184\pi$
$503$	26.3443	1.17463	0.587317	+	0.809357i	$0.300184\pi$
$504$	−3.07608	−0.137019
$505$	15.7115	0.699154
$506$	−17.8560	−0.793796
$507$	−21.8021	−0.968266
$508$	10.0539	0.446070
$509$	40.0220	1.77394	0.886972	−	0.461823i	$-0.152804\pi$
$509$	40.0220	1.77394	0.886972	+	0.461823i	$0.152804\pi$
$510$	4.18402	0.185272
$511$	−7.26130	−0.321221
$512$	23.0379	1.01814
$513$	4.24122	0.187254
$514$	−26.9776	−1.18993
$515$	−57.7908	−2.54657
$516$	1.06696	0.0469704
$517$	11.8729	0.522169
$518$	−3.86225	−0.169698
$519$	16.5137	0.724871
$520$	68.9055	3.02171
$521$	−15.4773	−0.678073	−0.339036	−	0.940773i	$-0.610101\pi$
$521$	−15.4773	−0.678073	−0.339036	+	0.940773i	$0.610101\pi$
$522$	6.62955	0.290168
$523$	2.50881	0.109703	0.0548513	−	0.998495i	$-0.482532\pi$
$523$	2.50881	0.109703	0.0548513	+	0.998495i	$0.482532\pi$
$524$	−11.1241	−0.485958
$525$	9.41807	0.411038
$526$	32.0179	1.39605
$527$	−3.85347	−0.167860
$528$	7.15026	0.311175
$529$	3.68547	0.160238
$530$	−33.2153	−1.44278
$531$	6.04653	0.262397
$532$	−2.53087	−0.109727
$533$	71.1722	3.08281
$534$	11.2235	0.485689
$535$	−42.5993	−1.84173
$536$	−3.04547	−0.131544
$537$	−16.1259	−0.695886
$538$	28.1629	1.21419
$539$	2.91794	0.125685
$540$	2.26586	0.0975070
$541$	−19.3874	−0.833528	−0.416764	−	0.909015i	$-0.636836\pi$
$541$	−19.3874	−0.833528	−0.416764	+	0.909015i	$0.636836\pi$
$542$	9.56422	0.410819
$543$	−15.1718	−0.651086
$544$	−3.02251	−0.129589
$545$	−41.1009	−1.76057
$546$	−6.98833	−0.299073
$547$	30.2590	1.29378	0.646890	−	0.762583i	$-0.276069\pi$
$547$	30.2590	1.29378	0.646890	+	0.762583i	$0.276069\pi$
$548$	8.52245	0.364061
$549$	−8.70272	−0.371423
$550$	−32.5543	−1.38812
$551$	23.7358	1.01118
$552$	−15.8904	−0.676340
$553$	−9.91047	−0.421436
$554$	14.5944	0.620058
$555$	12.3801	0.525505
$556$	−1.12478	−0.0477015
$557$	2.46969	0.104644	0.0523222	−	0.998630i	$-0.483338\pi$
$557$	2.46969	0.104644	0.0523222	+	0.998630i	$0.483338\pi$
$558$	4.90741	0.207747
$559$	10.5481	0.446136
$560$	9.30463	0.393192
$561$	−2.71423	−0.114595
$562$	−35.2461	−1.48677
$563$	5.68457	0.239576	0.119788	−	0.992799i	$-0.461779\pi$
$563$	5.68457	0.239576	0.119788	+	0.992799i	$0.461779\pi$
$564$	2.42806	0.102240
$565$	79.0906	3.32737
$566$	19.7938	0.831995
$567$	−1.00000	−0.0419961
$568$	34.1647	1.43352
$569$	22.3040	0.935032	0.467516	−	0.883985i	$-0.345149\pi$
$569$	22.3040	0.935032	0.467516	+	0.883985i	$0.345149\pi$
$570$	−19.0772	−0.799056
$571$	15.0924	0.631597	0.315799	−	0.948826i	$-0.397728\pi$
$571$	15.0924	0.631597	0.315799	+	0.948826i	$0.397728\pi$
$572$	−10.2721	−0.429497
$573$	−2.33675	−0.0976192
$574$	14.2915	0.596515
$575$	48.6519	2.02892
$576$	8.75008	0.364587
$577$	−14.5840	−0.607142	−0.303571	−	0.952809i	$-0.598179\pi$
$577$	−14.5840	−0.607142	−0.303571	+	0.952809i	$0.598179\pi$
$578$	19.1132	0.795003
$579$	−13.9366	−0.579185
$580$	12.6808	0.526541
$581$	1.22433	0.0507936
$582$	−19.4833	−0.807608
$583$	21.5472	0.892392
$584$	22.3363	0.924284
$585$	22.4004	0.926144
$586$	−22.4991	−0.929430
$587$	11.6401	0.480437	0.240218	−	0.970719i	$-0.422781\pi$
$587$	11.6401	0.480437	0.240218	+	0.970719i	$0.422781\pi$
$588$	0.596731	0.0246088
$589$	17.5700	0.723961
$590$	−27.1976	−1.11971
$591$	−12.0055	−0.493842
$592$	7.98943	0.328363
$593$	24.9237	1.02349	0.511746	−	0.859137i	$-0.328999\pi$
$593$	24.9237	1.02349	0.511746	+	0.859137i	$0.328999\pi$
$594$	3.45658	0.141825
$595$	−3.53202	−0.144799
$596$	−7.78659	−0.318951
$597$	−13.3009	−0.544368
$598$	−36.1003	−1.47625
$599$	33.8710	1.38393	0.691966	−	0.721930i	$-0.256745\pi$
$599$	33.8710	1.38393	0.691966	+	0.721930i	$0.256745\pi$
$600$	−28.9707	−1.18273
$601$	14.5415	0.593161	0.296581	−	0.955008i	$-0.404154\pi$
$601$	14.5415	0.593161	0.296581	+	0.955008i	$0.404154\pi$
$602$	2.11807	0.0863261
$603$	−0.990051	−0.0403180
$604$	10.1063	0.411219
$605$	−9.43821	−0.383718
$606$	4.90157	0.199113
$607$	11.0826	0.449828	0.224914	−	0.974379i	$-0.427790\pi$
$607$	11.0826	0.449828	0.224914	+	0.974379i	$0.427790\pi$
$608$	13.7813	0.558904
$609$	−5.59647	−0.226780
$610$	39.1452	1.58494
$611$	24.0040	0.971097
$612$	−0.555071	−0.0224374
$613$	−3.75973	−0.151854	−0.0759270	−	0.997113i	$-0.524192\pi$
$613$	−3.75973	−0.151854	−0.0759270	+	0.997113i	$0.524192\pi$
$614$	−29.1847	−1.17780
$615$	−45.8101	−1.84724
$616$	−8.97581	−0.361646
$617$	8.13631	0.327556	0.163778	−	0.986497i	$-0.447632\pi$
$617$	8.13631	0.327556	0.163778	+	0.986497i	$0.447632\pi$
$618$	−18.0292	−0.725239
$619$	−12.8620	−0.516968	−0.258484	−	0.966016i	$-0.583223\pi$
$619$	−12.8620	−0.516968	−0.258484	+	0.966016i	$0.583223\pi$
$620$	9.38674	0.376981
$621$	−5.16580	−0.207296
$622$	−1.28094	−0.0513610
$623$	−9.47455	−0.379590
$624$	14.4560	0.578704
$625$	16.6097	0.664389
$626$	28.5216	1.13995
$627$	12.3756	0.494235
$628$	−7.68030	−0.306478
$629$	−3.03277	−0.120925
$630$	4.49805	0.179206
$631$	−7.88425	−0.313867	−0.156933	−	0.987609i	$-0.550161\pi$
$631$	−7.88425	−0.313867	−0.156933	+	0.987609i	$0.550161\pi$
$632$	30.4854	1.21264
$633$	25.1718	1.00049
$634$	−24.7087	−0.981307
$635$	−63.9748	−2.53876
$636$	4.40649	0.174729
$637$	5.89933	0.233740
$638$	19.3446	0.765861
$639$	11.1066	0.439369
$640$	−14.6819	−0.580352
$641$	−41.4478	−1.63709	−0.818545	−	0.574443i	$-0.805219\pi$
$641$	−41.4478	−1.63709	−0.818545	+	0.574443i	$0.805219\pi$
$642$	−13.2898	−0.524507
$643$	0.594062	0.0234275	0.0117138	−	0.999931i	$-0.496271\pi$
$643$	0.594062	0.0234275	0.0117138	+	0.999931i	$0.496271\pi$
$644$	3.08259	0.121471
$645$	−6.78928	−0.267328
$646$	4.67338	0.183871
$647$	−17.4325	−0.685341	−0.342670	−	0.939456i	$-0.611331\pi$
$647$	−17.4325	−0.685341	−0.342670	+	0.939456i	$0.611331\pi$
$648$	3.07608	0.120840
$649$	17.6434	0.692565
$650$	−65.8166	−2.58154
$651$	−4.14269	−0.162365
$652$	−4.07712	−0.159672
$653$	5.28094	0.206659	0.103330	−	0.994647i	$-0.467050\pi$
$653$	5.28094	0.206659	0.103330	+	0.994647i	$0.467050\pi$
$654$	−12.8224	−0.501394
$655$	70.7847	2.76579
$656$	−29.5633	−1.15425
$657$	7.26130	0.283290
$658$	4.82004	0.187905
$659$	−17.7849	−0.692800	−0.346400	−	0.938087i	$-0.612596\pi$
$659$	−17.7849	−0.692800	−0.346400	+	0.938087i	$0.612596\pi$
$660$	6.61163	0.257358
$661$	−27.8510	−1.08328	−0.541639	−	0.840611i	$-0.682196\pi$
$661$	−27.8510	−1.08328	−0.541639	+	0.840611i	$0.682196\pi$
$662$	25.0622	0.974070
$663$	−5.48748	−0.213116
$664$	−3.76612	−0.146154
$665$	16.1044	0.624501
$666$	3.86225	0.149659
$667$	−28.9102	−1.11941
$668$	−1.57469	−0.0609266
$669$	0.335382	0.0129666
$670$	4.45330	0.172046
$671$	−25.3940	−0.980325
$672$	−3.24936	−0.125347
$673$	10.8668	0.418883	0.209442	−	0.977821i	$-0.432835\pi$
$673$	10.8668	0.418883	0.209442	+	0.977821i	$0.432835\pi$
$674$	6.60018	0.254230
$675$	−9.41807	−0.362502
$676$	−13.0100	−0.500385
$677$	0.405624	0.0155894	0.00779471	−	0.999970i	$-0.497519\pi$
$677$	0.405624	0.0155894	0.00779471	+	0.999970i	$0.497519\pi$
$678$	24.6741	0.947604
$679$	16.4472	0.631185
$680$	10.8648	0.416645
$681$	24.9517	0.956153
$682$	14.3195	0.548323
$683$	−23.7978	−0.910599	−0.455299	−	0.890338i	$-0.650468\pi$
$683$	−23.7978	−0.910599	−0.455299	+	0.890338i	$0.650468\pi$
$684$	2.53087	0.0967701
$685$	−54.2299	−2.07202
$686$	1.18460	0.0452281
$687$	−2.32461	−0.0886894
$688$	−4.38143	−0.167040
$689$	43.5629	1.65961
$690$	23.2360	0.884580
$691$	−13.5963	−0.517227	−0.258613	−	0.965981i	$-0.583266\pi$
$691$	−13.5963	−0.517227	−0.258613	+	0.965981i	$0.583266\pi$
$692$	9.85424	0.374602
$693$	−2.91794	−0.110843
$694$	39.7246	1.50793
$695$	7.15721	0.271489
$696$	17.2152	0.652539
$697$	11.2222	0.425070
$698$	9.89059	0.374364
$699$	24.3573	0.921279
$700$	5.62006	0.212418
$701$	19.7905	0.747476	0.373738	−	0.927534i	$-0.378076\pi$
$701$	19.7905	0.747476	0.373738	+	0.927534i	$0.378076\pi$
$702$	6.98833	0.263757
$703$	13.8280	0.521534
$704$	25.5322	0.962282
$705$	−15.4502	−0.581888
$706$	−5.96098	−0.224345
$707$	−4.13776	−0.155616
$708$	3.60815	0.135603
$709$	8.49693	0.319109	0.159555	−	0.987189i	$-0.448994\pi$
$709$	8.49693	0.319109	0.159555	+	0.987189i	$0.448994\pi$
$710$	−49.9578	−1.87488
$711$	9.91047	0.371672
$712$	29.1445	1.09224
$713$	−21.4003	−0.801447
$714$	−1.10189	−0.0412374
$715$	65.3631	2.44444
$716$	−9.62286	−0.359623
$717$	−3.46881	−0.129545
$718$	23.5759	0.879843
$719$	−41.9125	−1.56307	−0.781537	−	0.623859i	$-0.785564\pi$
$719$	−41.9125	−1.56307	−0.781537	+	0.623859i	$0.785564\pi$
$720$	−9.30463	−0.346763
$721$	15.2197	0.566810
$722$	1.19890	0.0446185
$723$	16.1160	0.599359
$724$	−9.05351	−0.336471
$725$	−52.7079	−1.95752
$726$	−2.94447	−0.109279
$727$	20.0690	0.744316	0.372158	−	0.928169i	$-0.378618\pi$
$727$	20.0690	0.744316	0.372158	+	0.928169i	$0.378618\pi$
$728$	−18.1468	−0.672566
$729$	1.00000	0.0370370
$730$	−32.6617	−1.20886
$731$	1.66318	0.0615150
$732$	−5.19319	−0.191946
$733$	19.1990	0.709131	0.354566	−	0.935031i	$-0.384629\pi$
$733$	19.1990	0.709131	0.354566	+	0.935031i	$0.384629\pi$
$734$	−15.3209	−0.565505
$735$	−3.79711	−0.140059
$736$	−16.7856	−0.618724
$737$	−2.88891	−0.106414
$738$	−14.2915	−0.526077
$739$	−32.2304	−1.18561	−0.592807	−	0.805345i	$-0.701980\pi$
$739$	−32.2304	−1.18561	−0.592807	+	0.805345i	$0.701980\pi$
$740$	7.38759	0.271573
$741$	25.0204	0.919146
$742$	8.74750	0.321131
$743$	32.7080	1.19994	0.599970	−	0.800023i	$-0.295179\pi$
$743$	32.7080	1.19994	0.599970	+	0.800023i	$0.295179\pi$
$744$	12.7432	0.467190
$745$	49.5475	1.81528
$746$	−40.0230	−1.46534
$747$	−1.22433	−0.0447957
$748$	−1.61966	−0.0592208
$749$	11.2189	0.409928
$750$	19.8727	0.725648
$751$	36.7223	1.34002	0.670008	−	0.742354i	$-0.266290\pi$
$751$	36.7223	1.34002	0.670008	+	0.742354i	$0.266290\pi$
$752$	−9.97071	−0.363594
$753$	9.69309	0.353236
$754$	39.1099	1.42430
$755$	−64.3082	−2.34041
$756$	−0.596731	−0.0217029
$757$	37.0291	1.34585	0.672924	−	0.739712i	$-0.265038\pi$
$757$	37.0291	1.34585	0.672924	+	0.739712i	$0.265038\pi$
$758$	−35.6024	−1.29314
$759$	−15.0735	−0.547133
$760$	−49.5384	−1.79694
$761$	11.9837	0.434408	0.217204	−	0.976126i	$-0.430306\pi$
$761$	11.9837	0.434408	0.217204	+	0.976126i	$0.430306\pi$
$762$	−19.9584	−0.723017
$763$	10.8243	0.391864
$764$	−1.39441	−0.0504481
$765$	3.53202	0.127701
$766$	−1.18460	−0.0428012
$767$	35.6705	1.28799
$768$	12.9198	0.466204
$769$	−47.3878	−1.70885	−0.854423	−	0.519577i	$-0.826089\pi$
$769$	−47.3878	−1.70885	−0.854423	+	0.519577i	$0.826089\pi$
$770$	13.1250	0.472993
$771$	−22.7736	−0.820173
$772$	−8.31640	−0.299314
$773$	−31.2559	−1.12420	−0.562098	−	0.827071i	$-0.690006\pi$
$773$	−31.2559	−1.12420	−0.562098	+	0.827071i	$0.690006\pi$
$774$	−2.11807	−0.0761325
$775$	−39.0161	−1.40150
$776$	−50.5929	−1.81618
$777$	−3.26039	−0.116966
$778$	−28.2885	−1.01419
$779$	−51.1679	−1.83328
$780$	13.3670	0.478617
$781$	32.4083	1.15966
$782$	−5.69217	−0.203551
$783$	5.59647	0.200001
$784$	−2.45045	−0.0875160
$785$	48.8712	1.74429
$786$	22.0829	0.787671
$787$	26.1410	0.931828	0.465914	−	0.884830i	$-0.345726\pi$
$787$	26.1410	0.931828	0.465914	+	0.884830i	$0.345726\pi$
$788$	−7.16408	−0.255210
$789$	27.0285	0.962240
$790$	−44.5778	−1.58601
$791$	−20.8291	−0.740599
$792$	8.97581	0.318942
$793$	−51.3402	−1.82315
$794$	11.2606	0.399624
$795$	−28.0393	−0.994452
$796$	−7.93705	−0.281321
$797$	35.8632	1.27034	0.635169	−	0.772373i	$-0.280930\pi$
$797$	35.8632	1.27034	0.635169	+	0.772373i	$0.280930\pi$
$798$	5.02413	0.177852
$799$	3.78486	0.133899
$800$	−30.6028	−1.08197
$801$	9.47455	0.334767
$802$	−2.71430	−0.0958451
$803$	21.1880	0.747710
$804$	−0.590795	−0.0208357
$805$	−19.6151	−0.691342
$806$	28.9505	1.01974
$807$	23.7743	0.836895
$808$	12.7281	0.447772
$809$	42.6633	1.49996	0.749980	−	0.661460i	$-0.230063\pi$
$809$	42.6633	1.49996	0.749980	+	0.661460i	$0.230063\pi$
$810$	−4.49805	−0.158045
$811$	−4.78067	−0.167872	−0.0839361	−	0.996471i	$-0.526749\pi$
$811$	−4.78067	−0.167872	−0.0839361	+	0.996471i	$0.526749\pi$
$812$	−3.33959	−0.117197
$813$	8.07382	0.283161
$814$	11.2698	0.395007
$815$	25.9435	0.908760
$816$	2.27937	0.0797940
$817$	−7.58334	−0.265308
$818$	−46.3247	−1.61970
$819$	−5.89933	−0.206139
$820$	−27.3363	−0.954625
$821$	15.2024	0.530569	0.265285	−	0.964170i	$-0.414534\pi$
$821$	15.2024	0.530569	0.265285	+	0.964170i	$0.414534\pi$
$822$	−16.9183	−0.590092
$823$	20.0988	0.700600	0.350300	−	0.936638i	$-0.386080\pi$
$823$	20.0988	0.700600	0.350300	+	0.936638i	$0.386080\pi$
$824$	−46.8169	−1.63094
$825$	−27.4814	−0.956778
$826$	7.16270	0.249222
$827$	26.3534	0.916397	0.458199	−	0.888850i	$-0.348495\pi$
$827$	26.3534	0.916397	0.458199	+	0.888850i	$0.348495\pi$
$828$	−3.08259	−0.107128
$829$	10.1440	0.352314	0.176157	−	0.984362i	$-0.443633\pi$
$829$	10.1440	0.352314	0.176157	+	0.984362i	$0.443633\pi$
$830$	5.50707	0.191153
$831$	12.3202	0.427382
$832$	51.6197	1.78959
$833$	0.930186	0.0322290
$834$	2.23286	0.0773175
$835$	10.0201	0.346758
$836$	7.38492	0.255413
$837$	4.14269	0.143192
$838$	5.62155	0.194193
$839$	−15.7257	−0.542910	−0.271455	−	0.962451i	$-0.587505\pi$
$839$	−15.7257	−0.542910	−0.271455	+	0.962451i	$0.587505\pi$
$840$	11.6802	0.403006
$841$	2.32042	0.0800146
$842$	−17.2505	−0.594491
$843$	−29.7537	−1.02477
$844$	15.0208	0.517038
$845$	82.7852	2.84790
$846$	−4.82004	−0.165716
$847$	2.48563	0.0854072
$848$	−18.0950	−0.621386
$849$	16.7093	0.573462
$850$	−10.3777	−0.355953
$851$	−16.8425	−0.577355
$852$	6.62763	0.227059
$853$	16.8443	0.576737	0.288368	−	0.957520i	$-0.406887\pi$
$853$	16.8443	0.576737	0.288368	+	0.957520i	$0.406887\pi$
$854$	−10.3092	−0.352774
$855$	−16.1044	−0.550758
$856$	−34.5101	−1.17953
$857$	30.8261	1.05300	0.526500	−	0.850175i	$-0.323504\pi$
$857$	30.8261	1.05300	0.526500	+	0.850175i	$0.323504\pi$
$858$	20.3915	0.696155
$859$	−16.8123	−0.573627	−0.286814	−	0.957986i	$-0.592596\pi$
$859$	−16.8123	−0.573627	−0.286814	+	0.957986i	$0.592596\pi$
$860$	−4.05138	−0.138151
$861$	12.0644	0.411155
$862$	19.5498	0.665868
$863$	23.4128	0.796979	0.398490	−	0.917173i	$-0.369534\pi$
$863$	23.4128	0.796979	0.398490	+	0.917173i	$0.369534\pi$
$864$	3.24936	0.110546
$865$	−62.7044	−2.13201
$866$	14.8904	0.505998
$867$	16.1348	0.547965
$868$	−2.47207	−0.0839076
$869$	28.9182	0.980981
$870$	−25.1732	−0.853450
$871$	−5.84064	−0.197903
$872$	−33.2963	−1.12755
$873$	−16.4472	−0.556653
$874$	25.9536	0.877895
$875$	−16.7759	−0.567130
$876$	4.33305	0.146400
$877$	49.1261	1.65887	0.829436	−	0.558602i	$-0.188662\pi$
$877$	49.1261	1.65887	0.829436	+	0.558602i	$0.188662\pi$
$878$	33.6458	1.13549
$879$	−18.9931	−0.640620
$880$	−27.1504	−0.915238
$881$	21.0740	0.710003	0.355001	−	0.934866i	$-0.384480\pi$
$881$	21.0740	0.710003	0.355001	+	0.934866i	$0.384480\pi$
$882$	−1.18460	−0.0398874
$883$	6.13728	0.206536	0.103268	−	0.994654i	$-0.467070\pi$
$883$	6.13728	0.206536	0.103268	+	0.994654i	$0.467070\pi$
$884$	−3.27455	−0.110135
$885$	−22.9594	−0.771771
$886$	26.8962	0.903594
$887$	4.01118	0.134682	0.0673411	−	0.997730i	$-0.478548\pi$
$887$	4.01118	0.134682	0.0673411	+	0.997730i	$0.478548\pi$
$888$	10.0292	0.336559
$889$	16.8483	0.565073
$890$	−42.6170	−1.42852
$891$	2.91794	0.0977547
$892$	0.200133	0.00670096
$893$	−17.2572	−0.577491
$894$	15.4575	0.516975
$895$	61.2321	2.04676
$896$	3.86659	0.129174
$897$	−30.4748	−1.01752
$898$	−0.153630	−0.00512670
$899$	23.1844	0.773243
$900$	−5.62006	−0.187335
$901$	6.86884	0.228834
$902$	−41.7017	−1.38852
$903$	1.78801	0.0595013
$904$	64.0721	2.13101
$905$	57.6092	1.91499
$906$	−20.0624	−0.666529
$907$	16.4267	0.545438	0.272719	−	0.962094i	$-0.412077\pi$
$907$	16.4267	0.545438	0.272719	+	0.962094i	$0.412077\pi$
$908$	14.8895	0.494125
$909$	4.13776	0.137241
$910$	26.5355	0.879642
$911$	−55.3243	−1.83298	−0.916488	−	0.400062i	$-0.868989\pi$
$911$	−55.3243	−1.83298	−0.916488	+	0.400062i	$0.868989\pi$
$912$	−10.3929	−0.344143
$913$	−3.57251	−0.118233
$914$	−14.8568	−0.491419
$915$	33.0452	1.09244
$916$	−1.38717	−0.0458333
$917$	−18.6417	−0.615604
$918$	1.10189	0.0363679
$919$	21.7995	0.719099	0.359550	−	0.933126i	$-0.382930\pi$
$919$	21.7995	0.719099	0.359550	+	0.933126i	$0.382930\pi$
$920$	60.3377	1.98927
$921$	−24.6369	−0.811812
$922$	−2.65760	−0.0875235
$923$	65.5213	2.15666
$924$	−1.74123	−0.0572821
$925$	−30.7066	−1.00963
$926$	−10.5533	−0.346801
$927$	−15.2197	−0.499879
$928$	18.1850	0.596950
$929$	41.7886	1.37104	0.685520	−	0.728054i	$-0.259575\pi$
$929$	41.7886	1.37104	0.685520	+	0.728054i	$0.259575\pi$
$930$	−18.6340	−0.611033
$931$	−4.24122	−0.139000
$932$	14.5348	0.476103
$933$	−1.08133	−0.0354011
$934$	0.401811	0.0131476
$935$	10.3062	0.337050
$936$	18.1468	0.593147
$937$	−26.2182	−0.856510	−0.428255	−	0.903658i	$-0.640871\pi$
$937$	−26.2182	−0.856510	−0.428255	+	0.903658i	$0.640871\pi$
$938$	−1.17281	−0.0382936
$939$	24.0770	0.785725
$940$	−9.21962	−0.300711
$941$	35.8366	1.16824	0.584120	−	0.811667i	$-0.301440\pi$
$941$	35.8366	1.16824	0.584120	+	0.811667i	$0.301440\pi$
$942$	15.2465	0.496758
$943$	62.3225	2.02950
$944$	−14.8167	−0.482243
$945$	3.79711	0.123520
$946$	−6.18040	−0.200942
$947$	−9.70399	−0.315337	−0.157669	−	0.987492i	$-0.550398\pi$
$947$	−9.70399	−0.315337	−0.157669	+	0.987492i	$0.550398\pi$
$948$	5.91389	0.192074
$949$	42.8368	1.39054
$950$	47.3176	1.53519
$951$	−20.8583	−0.676377
$952$	−2.86132	−0.0927361
$953$	23.8796	0.773537	0.386768	−	0.922177i	$-0.373591\pi$
$953$	23.8796	0.773537	0.386768	+	0.922177i	$0.373591\pi$
$954$	−8.74750	−0.283211
$955$	8.87291	0.287121
$956$	−2.06995	−0.0669469
$957$	16.3301	0.527879
$958$	48.1662	1.55618
$959$	14.2819	0.461186
$960$	−33.2251	−1.07233
$961$	−13.8381	−0.446391
$962$	22.7847	0.734608
$963$	−11.2189	−0.361523
$964$	9.61690	0.309740
$965$	52.9188	1.70352
$966$	−6.11939	−0.196888
$967$	−41.6729	−1.34011	−0.670054	−	0.742312i	$-0.733729\pi$
$967$	−41.6729	−1.34011	−0.670054	+	0.742312i	$0.733729\pi$
$968$	−7.64599	−0.245751
$969$	3.94512	0.126736
$970$	73.9802	2.37536
$971$	−30.3807	−0.974962	−0.487481	−	0.873133i	$-0.662084\pi$
$971$	−30.3807	−0.974962	−0.487481	+	0.873133i	$0.662084\pi$
$972$	0.596731	0.0191402
$973$	−1.88491	−0.0604274
$974$	−25.8780	−0.829184
$975$	−55.5603	−1.77936
$976$	21.3256	0.682615
$977$	−52.0323	−1.66466	−0.832331	−	0.554279i	$-0.812994\pi$
$977$	−52.0323	−1.66466	−0.832331	+	0.554279i	$0.812994\pi$
$978$	8.09366	0.258807
$979$	27.6462	0.883576
$980$	−2.26586	−0.0723802
$981$	−10.8243	−0.345592
$982$	−19.7279	−0.629543
$983$	28.4295	0.906760	0.453380	−	0.891317i	$-0.350218\pi$
$983$	28.4295	0.906760	0.453380	+	0.891317i	$0.350218\pi$
$984$	−37.1112	−1.18306
$985$	45.5864	1.45250
$986$	6.16672	0.196388
$987$	4.06893	0.129516
$988$	14.9304	0.475000
$989$	9.23650	0.293704
$990$	−13.1250	−0.417141
$991$	41.0465	1.30389	0.651943	−	0.758268i	$-0.273954\pi$
$991$	41.0465	1.30389	0.651943	+	0.758268i	$0.273954\pi$
$992$	13.4611	0.427391
$993$	21.1567	0.671389
$994$	13.1568	0.417308
$995$	50.5049	1.60111
$996$	−0.730594	−0.0231497
$997$	−50.2680	−1.59200	−0.796002	−	0.605294i	$-0.793055\pi$
$997$	−50.2680	−1.59200	−0.796002	+	0.605294i	$0.793055\pi$
$998$	3.54519	0.112221
$999$	3.26039	0.103154

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8043.2.a.s.1.17	✓	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8043.2.a.s.1.17	✓	50	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:	\( N \)	\(=\)	\( 8043 = 3 \cdot 7 \cdot 383 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8043.a (trivial)

\(f(q)\)	\(=\)	\(q-1.18460 q^{2} -1.00000 q^{3} -0.596731 q^{4} +3.79711 q^{5} +1.18460 q^{6} -1.00000 q^{7} +3.07608 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.18460 q^{2} -1.00000 q^{3} -0.596731 q^{4} +3.79711 q^{5} +1.18460 q^{6} -1.00000 q^{7} +3.07608 q^{8} +1.00000 q^{9} -4.49805 q^{10} +2.91794 q^{11} +0.596731 q^{12} +5.89933 q^{13} +1.18460 q^{14} -3.79711 q^{15} -2.45045 q^{16} +0.930186 q^{17} -1.18460 q^{18} -4.24122 q^{19} -2.26586 q^{20} +1.00000 q^{21} -3.45658 q^{22} +5.16580 q^{23} -3.07608 q^{24} +9.41807 q^{25} -6.98833 q^{26} -1.00000 q^{27} +0.596731 q^{28} -5.59647 q^{29} +4.49805 q^{30} -4.14269 q^{31} -3.24936 q^{32} -2.91794 q^{33} -1.10189 q^{34} -3.79711 q^{35} -0.596731 q^{36} -3.26039 q^{37} +5.02413 q^{38} -5.89933 q^{39} +11.6802 q^{40} +12.0644 q^{41} -1.18460 q^{42} +1.78801 q^{43} -1.74123 q^{44} +3.79711 q^{45} -6.11939 q^{46} +4.06893 q^{47} +2.45045 q^{48} +1.00000 q^{49} -11.1566 q^{50} -0.930186 q^{51} -3.52032 q^{52} +7.38438 q^{53} +1.18460 q^{54} +11.0797 q^{55} -3.07608 q^{56} +4.24122 q^{57} +6.62955 q^{58} +6.04653 q^{59} +2.26586 q^{60} -8.70272 q^{61} +4.90741 q^{62} -1.00000 q^{63} +8.75008 q^{64} +22.4004 q^{65} +3.45658 q^{66} -0.990051 q^{67} -0.555071 q^{68} -5.16580 q^{69} +4.49805 q^{70} +11.1066 q^{71} +3.07608 q^{72} +7.26130 q^{73} +3.86225 q^{74} -9.41807 q^{75} +2.53087 q^{76} -2.91794 q^{77} +6.98833 q^{78} +9.91047 q^{79} -9.30463 q^{80} +1.00000 q^{81} -14.2915 q^{82} -1.22433 q^{83} -0.596731 q^{84} +3.53202 q^{85} -2.11807 q^{86} +5.59647 q^{87} +8.97581 q^{88} +9.47455 q^{89} -4.49805 q^{90} -5.89933 q^{91} -3.08259 q^{92} +4.14269 q^{93} -4.82004 q^{94} -16.1044 q^{95} +3.24936 q^{96} -16.4472 q^{97} -1.18460 q^{98} +2.91794 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q - q^{2} - 50 q^{3} + 53 q^{4} + 11 q^{5} + q^{6} - 50 q^{7} - 6 q^{8} + 50 q^{9}+O(q^{10}) \) 50 * q - q^2 - 50 * q^3 + 53 * q^4 + 11 * q^5 + q^6 - 50 * q^7 - 6 * q^8 + 50 * q^9	\( 50 q - q^{2} - 50 q^{3} + 53 q^{4} + 11 q^{5} + q^{6} - 50 q^{7} - 6 q^{8} + 50 q^{9} + 16 q^{10} - 31 q^{11} - 53 q^{12} + 42 q^{13} + q^{14} - 11 q^{15} + 59 q^{16} + 44 q^{17} - q^{18} + 11 q^{19} + 7 q^{20} + 50 q^{21} + 19 q^{22} - 16 q^{23} + 6 q^{24} + 71 q^{25} + q^{26} - 50 q^{27} - 53 q^{28} + 3 q^{29} - 16 q^{30} + 13 q^{31} - 23 q^{32} + 31 q^{33} + q^{34} - 11 q^{35} + 53 q^{36} + 53 q^{37} + 28 q^{38} - 42 q^{39} + 50 q^{40} + 23 q^{41} - q^{42} + 9 q^{43} - 78 q^{44} + 11 q^{45} - 8 q^{46} + 26 q^{47} - 59 q^{48} + 50 q^{49} - 38 q^{50} - 44 q^{51} + 86 q^{52} + 58 q^{53} + q^{54} + 28 q^{55} + 6 q^{56} - 11 q^{57} - 4 q^{58} + 7 q^{59} - 7 q^{60} + 51 q^{61} + 7 q^{62} - 50 q^{63} + 74 q^{64} - 14 q^{65} - 19 q^{66} + 23 q^{67} + 98 q^{68} + 16 q^{69} - 16 q^{70} - 75 q^{71} - 6 q^{72} + 34 q^{73} - 68 q^{74} - 71 q^{75} + 31 q^{76} + 31 q^{77} - q^{78} - 18 q^{79} - 21 q^{80} + 50 q^{81} + 31 q^{82} + 40 q^{83} + 53 q^{84} + 30 q^{85} - 15 q^{86} - 3 q^{87} + 70 q^{88} + 63 q^{89} + 16 q^{90} - 42 q^{91} - 38 q^{92} - 13 q^{93} + q^{94} - 77 q^{95} + 23 q^{96} + 77 q^{97} - q^{98} - 31 q^{99}+O(q^{100}) \) 50 * q - q^2 - 50 * q^3 + 53 * q^4 + 11 * q^5 + q^6 - 50 * q^7 - 6 * q^8 + 50 * q^9 + 16 * q^10 - 31 * q^11 - 53 * q^12 + 42 * q^13 + q^14 - 11 * q^15 + 59 * q^16 + 44 * q^17 - q^18 + 11 * q^19 + 7 * q^20 + 50 * q^21 + 19 * q^22 - 16 * q^23 + 6 * q^24 + 71 * q^25 + q^26 - 50 * q^27 - 53 * q^28 + 3 * q^29 - 16 * q^30 + 13 * q^31 - 23 * q^32 + 31 * q^33 + q^34 - 11 * q^35 + 53 * q^36 + 53 * q^37 + 28 * q^38 - 42 * q^39 + 50 * q^40 + 23 * q^41 - q^42 + 9 * q^43 - 78 * q^44 + 11 * q^45 - 8 * q^46 + 26 * q^47 - 59 * q^48 + 50 * q^49 - 38 * q^50 - 44 * q^51 + 86 * q^52 + 58 * q^53 + q^54 + 28 * q^55 + 6 * q^56 - 11 * q^57 - 4 * q^58 + 7 * q^59 - 7 * q^60 + 51 * q^61 + 7 * q^62 - 50 * q^63 + 74 * q^64 - 14 * q^65 - 19 * q^66 + 23 * q^67 + 98 * q^68 + 16 * q^69 - 16 * q^70 - 75 * q^71 - 6 * q^72 + 34 * q^73 - 68 * q^74 - 71 * q^75 + 31 * q^76 + 31 * q^77 - q^78 - 18 * q^79 - 21 * q^80 + 50 * q^81 + 31 * q^82 + 40 * q^83 + 53 * q^84 + 30 * q^85 - 15 * q^86 - 3 * q^87 + 70 * q^88 + 63 * q^89 + 16 * q^90 - 42 * q^91 - 38 * q^92 - 13 * q^93 + q^94 - 77 * q^95 + 23 * q^96 + 77 * q^97 - q^98 - 31 * q^99

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