LMFDB - Embedded newform 4033.2.a.d.1.40

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4033,2,Mod(1,4033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4033, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4033 = 37 \cdot 109 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4033.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:	$32.2036671352$
Analytic rank:	$1$
Dimension:	$79$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.40
Character	$\chi$	$=$	4033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.202771 q^{2} +2.90713 q^{3} -1.95888 q^{4} -3.02225 q^{5} -0.589482 q^{6} +1.84810 q^{7} +0.802747 q^{8} +5.45141 q^{9} +O(q^{10})$	\(q-0.202771 q^{2} +2.90713 q^{3} -1.95888 q^{4} -3.02225 q^{5} -0.589482 q^{6} +1.84810 q^{7} +0.802747 q^{8} +5.45141 q^{9} +0.612824 q^{10} +1.93474 q^{11} -5.69473 q^{12} -4.45845 q^{13} -0.374741 q^{14} -8.78607 q^{15} +3.75499 q^{16} +2.58389 q^{17} -1.10539 q^{18} -2.66076 q^{19} +5.92023 q^{20} +5.37266 q^{21} -0.392309 q^{22} -8.93695 q^{23} +2.33369 q^{24} +4.13397 q^{25} +0.904045 q^{26} +7.12657 q^{27} -3.62021 q^{28} -6.15485 q^{29} +1.78156 q^{30} +0.361331 q^{31} -2.36690 q^{32} +5.62454 q^{33} -0.523937 q^{34} -5.58540 q^{35} -10.6787 q^{36} -1.00000 q^{37} +0.539526 q^{38} -12.9613 q^{39} -2.42610 q^{40} +0.339994 q^{41} -1.08942 q^{42} +9.77508 q^{43} -3.78993 q^{44} -16.4755 q^{45} +1.81215 q^{46} +10.4028 q^{47} +10.9163 q^{48} -3.58454 q^{49} -0.838250 q^{50} +7.51169 q^{51} +8.73358 q^{52} -6.70903 q^{53} -1.44506 q^{54} -5.84726 q^{55} +1.48355 q^{56} -7.73519 q^{57} +1.24803 q^{58} -14.5057 q^{59} +17.2109 q^{60} +12.5616 q^{61} -0.0732675 q^{62} +10.0747 q^{63} -7.03005 q^{64} +13.4745 q^{65} -1.14049 q^{66} -0.658183 q^{67} -5.06153 q^{68} -25.9809 q^{69} +1.13256 q^{70} -9.92857 q^{71} +4.37610 q^{72} +7.01372 q^{73} +0.202771 q^{74} +12.0180 q^{75} +5.21213 q^{76} +3.57558 q^{77} +2.62818 q^{78} -13.8658 q^{79} -11.3485 q^{80} +4.36364 q^{81} -0.0689410 q^{82} +6.04032 q^{83} -10.5244 q^{84} -7.80914 q^{85} -1.98210 q^{86} -17.8929 q^{87} +1.55311 q^{88} -7.86557 q^{89} +3.34076 q^{90} -8.23964 q^{91} +17.5064 q^{92} +1.05044 q^{93} -2.10939 q^{94} +8.04149 q^{95} -6.88088 q^{96} -11.6604 q^{97} +0.726841 q^{98} +10.5471 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9}+O(q^{10}) $ 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9} - 13 q^{10} - 5 q^{11} - 40 q^{12} - 18 q^{13} - 42 q^{14} - 49 q^{15} + 83 q^{16} - 62 q^{17} - 33 q^{18} - 25 q^{19} - 39 q^{20} - 15 q^{21} - 31 q^{22} - 94 q^{23} - 39 q^{24} + 71 q^{25} - 35 q^{26} - 47 q^{27} - 13 q^{28} - 17 q^{29} + 15 q^{30} - 37 q^{31} - 105 q^{32} - 60 q^{33} + 9 q^{34} - 60 q^{35} + 43 q^{36} - 79 q^{37} - 80 q^{38} - 41 q^{39} - 64 q^{40} - 37 q^{41} - 30 q^{42} - 20 q^{43} - 14 q^{44} - 8 q^{45} + 61 q^{46} - 148 q^{47} - 39 q^{48} + 82 q^{49} - 90 q^{50} - 45 q^{51} - 27 q^{52} - 70 q^{53} - 41 q^{54} - 105 q^{55} - 68 q^{56} - 31 q^{57} - 14 q^{58} - 96 q^{59} - 74 q^{60} - 21 q^{61} + 4 q^{62} - 60 q^{63} + 132 q^{64} - 15 q^{65} + 71 q^{66} - 44 q^{67} - 166 q^{68} - 72 q^{69} - 9 q^{70} - 55 q^{71} - 126 q^{72} - 27 q^{73} + 11 q^{74} - 39 q^{75} - 4 q^{76} - 104 q^{77} - 47 q^{78} - 49 q^{79} - 82 q^{80} + 55 q^{81} + 20 q^{82} - 52 q^{83} - 29 q^{84} + 3 q^{85} - 32 q^{86} - 113 q^{87} + 14 q^{88} - 68 q^{89} - 39 q^{90} - 30 q^{91} - 179 q^{92} - 53 q^{93} - 33 q^{94} - 86 q^{95} + 33 q^{96} - 57 q^{97} - 116 q^{98} + q^{99}+O(q^{100}) \) 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9 - 13 * q^10 - 5 * q^11 - 40 * q^12 - 18 * q^13 - 42 * q^14 - 49 * q^15 + 83 * q^16 - 62 * q^17 - 33 * q^18 - 25 * q^19 - 39 * q^20 - 15 * q^21 - 31 * q^22 - 94 * q^23 - 39 * q^24 + 71 * q^25 - 35 * q^26 - 47 * q^27 - 13 * q^28 - 17 * q^29 + 15 * q^30 - 37 * q^31 - 105 * q^32 - 60 * q^33 + 9 * q^34 - 60 * q^35 + 43 * q^36 - 79 * q^37 - 80 * q^38 - 41 * q^39 - 64 * q^40 - 37 * q^41 - 30 * q^42 - 20 * q^43 - 14 * q^44 - 8 * q^45 + 61 * q^46 - 148 * q^47 - 39 * q^48 + 82 * q^49 - 90 * q^50 - 45 * q^51 - 27 * q^52 - 70 * q^53 - 41 * q^54 - 105 * q^55 - 68 * q^56 - 31 * q^57 - 14 * q^58 - 96 * q^59 - 74 * q^60 - 21 * q^61 + 4 * q^62 - 60 * q^63 + 132 * q^64 - 15 * q^65 + 71 * q^66 - 44 * q^67 - 166 * q^68 - 72 * q^69 - 9 * q^70 - 55 * q^71 - 126 * q^72 - 27 * q^73 + 11 * q^74 - 39 * q^75 - 4 * q^76 - 104 * q^77 - 47 * q^78 - 49 * q^79 - 82 * q^80 + 55 * q^81 + 20 * q^82 - 52 * q^83 - 29 * q^84 + 3 * q^85 - 32 * q^86 - 113 * q^87 + 14 * q^88 - 68 * q^89 - 39 * q^90 - 30 * q^91 - 179 * q^92 - 53 * q^93 - 33 * q^94 - 86 * q^95 + 33 * q^96 - 57 * q^97 - 116 * q^98 + 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 $

$2$	−0.202771	−0.143381	−0.0716904	−	0.997427i	$-0.522839\pi$
$2$	−0.202771	−0.143381	−0.0716904	+	0.997427i	$0.522839\pi$
$3$	2.90713	1.67843	0.839216	−	0.543798i	$-0.183014\pi$
$3$	2.90713	1.67843	0.839216	+	0.543798i	$0.183014\pi$
$4$	−1.95888	−0.979442
$5$	−3.02225	−1.35159	−0.675795	−	0.737090i	$-0.736199\pi$
$5$	−3.02225	−1.35159	−0.675795	+	0.737090i	$0.736199\pi$
$6$	−0.589482	−0.240655
$7$	1.84810	0.698515	0.349257	−	0.937027i	$-0.386434\pi$
$7$	1.84810	0.698515	0.349257	+	0.937027i	$0.386434\pi$
$8$	0.802747	0.283814
$9$	5.45141	1.81714
$10$	0.612824	0.193792
$11$	1.93474	0.583346	0.291673	−	0.956518i	$-0.405788\pi$
$11$	1.93474	0.583346	0.291673	+	0.956518i	$0.405788\pi$
$12$	−5.69473	−1.64393
$13$	−4.45845	−1.23655	−0.618276	−	0.785961i	$-0.712168\pi$
$13$	−4.45845	−1.23655	−0.618276	+	0.785961i	$0.712168\pi$
$14$	−0.374741	−0.100154
$15$	−8.78607	−2.26855
$16$	3.75499	0.938748
$17$	2.58389	0.626684	0.313342	−	0.949640i	$-0.398551\pi$
$17$	2.58389	0.626684	0.313342	+	0.949640i	$0.398551\pi$
$18$	−1.10539	−0.260543
$19$	−2.66076	−0.610421	−0.305211	−	0.952285i	$-0.598727\pi$
$19$	−2.66076	−0.610421	−0.305211	+	0.952285i	$0.598727\pi$
$20$	5.92023	1.32380
$21$	5.37266	1.17241
$22$	−0.392309	−0.0836406
$23$	−8.93695	−1.86348	−0.931741	−	0.363123i	$-0.881710\pi$
$23$	−8.93695	−1.86348	−0.931741	+	0.363123i	$0.881710\pi$
$24$	2.33369	0.476363
$25$	4.13397	0.826795
$26$	0.904045	0.177298
$27$	7.12657	1.37151
$28$	−3.62021	−0.684155
$29$	−6.15485	−1.14293	−0.571463	−	0.820628i	$-0.693624\pi$
$29$	−6.15485	−1.14293	−0.571463	+	0.820628i	$0.693624\pi$
$30$	1.78156	0.325267
$31$	0.361331	0.0648969	0.0324485	−	0.999473i	$-0.489670\pi$
$31$	0.361331	0.0648969	0.0324485	+	0.999473i	$0.489670\pi$
$32$	−2.36690	−0.418413
$33$	5.62454	0.979107
$34$	−0.523937	−0.0898545
$35$	−5.58540	−0.944105
$36$	−10.6787	−1.77978
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	0.539526	0.0875227
$39$	−12.9613	−2.07547
$40$	−2.42610	−0.383600
$41$	0.339994	0.0530982	0.0265491	−	0.999648i	$-0.491548\pi$
$41$	0.339994	0.0530982	0.0265491	+	0.999648i	$0.491548\pi$
$42$	−1.08942	−0.168101
$43$	9.77508	1.49069	0.745343	−	0.666681i	$-0.232286\pi$
$43$	9.77508	1.49069	0.745343	+	0.666681i	$0.232286\pi$
$44$	−3.78993	−0.571353
$45$	−16.4755	−2.45602
$46$	1.81215	0.267188
$47$	10.4028	1.51740	0.758701	−	0.651439i	$-0.225834\pi$
$47$	10.4028	1.51740	0.758701	+	0.651439i	$0.225834\pi$
$48$	10.9163	1.57563
$49$	−3.58454	−0.512077
$50$	−0.838250	−0.118547
$51$	7.51169	1.05185
$52$	8.73358	1.21113
$53$	−6.70903	−0.921556	−0.460778	−	0.887515i	$-0.652430\pi$
$53$	−6.70903	−0.921556	−0.460778	+	0.887515i	$0.652430\pi$
$54$	−1.44506	−0.196648
$55$	−5.84726	−0.788444
$56$	1.48355	0.198248
$57$	−7.73519	−1.02455
$58$	1.24803	0.163874
$59$	−14.5057	−1.88849	−0.944243	−	0.329249i	$-0.893204\pi$
$59$	−14.5057	−1.88849	−0.944243	+	0.329249i	$0.893204\pi$
$60$	17.2109	2.22192
$61$	12.5616	1.60835	0.804177	−	0.594390i	$-0.202607\pi$
$61$	12.5616	1.60835	0.804177	+	0.594390i	$0.202607\pi$
$62$	−0.0732675	−0.00930498
$63$	10.0747	1.26930
$64$	−7.03005	−0.878756
$65$	13.4745	1.67131
$66$	−1.14049	−0.140385
$67$	−0.658183	−0.0804098	−0.0402049	−	0.999191i	$-0.512801\pi$
$67$	−0.658183	−0.0804098	−0.0402049	+	0.999191i	$0.512801\pi$
$68$	−5.06153	−0.613801
$69$	−25.9809	−3.12773
$70$	1.13256	0.135367
$71$	−9.92857	−1.17830	−0.589152	−	0.808022i	$-0.700538\pi$
$71$	−9.92857	−1.17830	−0.589152	+	0.808022i	$0.700538\pi$
$72$	4.37610	0.515729
$73$	7.01372	0.820894	0.410447	−	0.911885i	$-0.365373\pi$
$73$	7.01372	0.820894	0.410447	+	0.911885i	$0.365373\pi$
$74$	0.202771	0.0235717
$75$	12.0180	1.38772
$76$	5.21213	0.597872
$77$	3.57558	0.407476
$78$	2.62818	0.297582
$79$	−13.8658	−1.56003	−0.780014	−	0.625762i	$-0.784788\pi$
$79$	−13.8658	−1.56003	−0.780014	+	0.625762i	$0.784788\pi$
$80$	−11.3485	−1.26880
$81$	4.36364	0.484849
$82$	−0.0689410	−0.00761326
$83$	6.04032	0.663011	0.331506	−	0.943453i	$-0.392443\pi$
$83$	6.04032	0.663011	0.331506	+	0.943453i	$0.392443\pi$
$84$	−10.5244	−1.14831
$85$	−7.80914	−0.847020
$86$	−1.98210	−0.213736
$87$	−17.8929	−1.91833
$88$	1.55311	0.165562
$89$	−7.86557	−0.833748	−0.416874	−	0.908964i	$-0.636874\pi$
$89$	−7.86557	−0.833748	−0.416874	+	0.908964i	$0.636874\pi$
$90$	3.34076	0.352147
$91$	−8.23964	−0.863749
$92$	17.5064	1.82517
$93$	1.05044	0.108925
$94$	−2.10939	−0.217566
$95$	8.04149	0.825039
$96$	−6.88088	−0.702277
$97$	−11.6604	−1.18394	−0.591968	−	0.805961i	$-0.701649\pi$
$97$	−11.6604	−1.18394	−0.591968	+	0.805961i	$0.701649\pi$
$98$	0.726841	0.0734221
$99$	10.5471	1.06002
$100$	−8.09797	−0.809797
$101$	−18.9004	−1.88066	−0.940328	−	0.340270i	$-0.889481\pi$
$101$	−18.9004	−1.88066	−0.940328	+	0.340270i	$0.889481\pi$
$102$	−1.52315	−0.150815
$103$	−1.76716	−0.174123	−0.0870617	−	0.996203i	$-0.527748\pi$
$103$	−1.76716	−0.174123	−0.0870617	+	0.996203i	$0.527748\pi$
$104$	−3.57901	−0.350951
$105$	−16.2375	−1.58462
$106$	1.36040	0.132133
$107$	−3.96485	−0.383296	−0.191648	−	0.981464i	$-0.561383\pi$
$107$	−3.96485	−0.383296	−0.191648	+	0.981464i	$0.561383\pi$
$108$	−13.9601	−1.34331
$109$	−1.00000	−0.0957826
$109$	−1.00000	−0.0957826
$110$	1.18566	0.113048
$111$	−2.90713	−0.275933
$112$	6.93959	0.655730
$113$	16.5359	1.55556	0.777782	−	0.628534i	$-0.216345\pi$
$113$	16.5359	1.55556	0.777782	+	0.628534i	$0.216345\pi$
$114$	1.56847	0.146901
$115$	27.0097	2.51866
$116$	12.0566	1.11943
$117$	−24.3048	−2.24698
$118$	2.94134	0.270773
$119$	4.77527	0.437748
$120$	−7.05299	−0.643847
$121$	−7.25678	−0.659708
$122$	−2.54714	−0.230607
$123$	0.988408	0.0891218
$124$	−0.707805	−0.0635628
$125$	2.61734	0.234102
$126$	−2.04286	−0.181993
$127$	−3.68420	−0.326920	−0.163460	−	0.986550i	$-0.552265\pi$
$127$	−3.68420	−0.326920	−0.163460	+	0.986550i	$0.552265\pi$
$128$	6.15929	0.544409
$129$	28.4175	2.50202
$130$	−2.73225	−0.239634
$131$	−10.5971	−0.925874	−0.462937	−	0.886391i	$-0.653204\pi$
$131$	−10.5971	−0.925874	−0.462937	+	0.886391i	$0.653204\pi$
$132$	−11.0178	−0.958978
$133$	−4.91735	−0.426388
$134$	0.133460	0.0115292
$135$	−21.5383	−1.85372
$136$	2.07421	0.177862
$137$	21.5984	1.84528	0.922640	−	0.385663i	$-0.126027\pi$
$137$	21.5984	1.84528	0.922640	+	0.385663i	$0.126027\pi$
$138$	5.26817	0.448456
$139$	−15.3312	−1.30038	−0.650190	−	0.759772i	$-0.725311\pi$
$139$	−15.3312	−1.30038	−0.650190	+	0.759772i	$0.725311\pi$
$140$	10.9412	0.924696
$141$	30.2423	2.54686
$142$	2.01323	0.168946
$143$	−8.62594	−0.721337
$144$	20.4700	1.70583
$145$	18.6015	1.54477
$146$	−1.42218	−0.117700
$147$	−10.4207	−0.859487
$148$	1.95888	0.161019
$149$	−16.4393	−1.34676	−0.673382	−	0.739295i	$-0.735159\pi$
$149$	−16.4393	−1.34676	−0.673382	+	0.739295i	$0.735159\pi$
$150$	−2.43690	−0.198972
$151$	−16.6104	−1.35173	−0.675867	−	0.737024i	$-0.736230\pi$
$151$	−16.6104	−1.35173	−0.675867	+	0.737024i	$0.736230\pi$
$152$	−2.13592	−0.173246
$153$	14.0858	1.13877
$154$	−0.725025	−0.0584242
$155$	−1.09203	−0.0877140
$156$	25.3897	2.03280
$157$	15.9961	1.27663	0.638313	−	0.769777i	$-0.279633\pi$
$157$	15.9961	1.27663	0.638313	+	0.769777i	$0.279633\pi$
$158$	2.81159	0.223678
$159$	−19.5040	−1.54677
$160$	7.15335	0.565522
$161$	−16.5163	−1.30167
$162$	−0.884821	−0.0695181
$163$	1.93273	0.151383	0.0756917	−	0.997131i	$-0.475884\pi$
$163$	1.93273	0.151383	0.0756917	+	0.997131i	$0.475884\pi$
$164$	−0.666010	−0.0520066
$165$	−16.9987	−1.32335
$166$	−1.22480	−0.0950631
$167$	−16.4562	−1.27342	−0.636709	−	0.771104i	$-0.719705\pi$
$167$	−16.4562	−1.27342	−0.636709	+	0.771104i	$0.719705\pi$
$168$	4.31289	0.332746
$169$	6.87776	0.529059
$170$	1.58347	0.121446
$171$	−14.5049	−1.10922
$172$	−19.1483	−1.46004
$173$	24.5619	1.86740	0.933702	−	0.358052i	$-0.116559\pi$
$173$	24.5619	1.86740	0.933702	+	0.358052i	$0.116559\pi$
$174$	3.62817	0.275051
$175$	7.63998	0.577528
$176$	7.26493	0.547615
$177$	−42.1701	−3.16970
$178$	1.59491	0.119544
$179$	−0.168809	−0.0126174	−0.00630868	−	0.999980i	$-0.502008\pi$
$179$	−0.168809	−0.0126174	−0.00630868	+	0.999980i	$0.502008\pi$
$180$	32.2736	2.40553
$181$	5.08606	0.378043	0.189022	−	0.981973i	$-0.439468\pi$
$181$	5.08606	0.378043	0.189022	+	0.981973i	$0.439468\pi$
$182$	1.67076	0.123845
$183$	36.5183	2.69951
$184$	−7.17411	−0.528882
$185$	3.02225	0.222200
$186$	−0.212998	−0.0156178
$187$	4.99915	0.365574
$188$	−20.3779	−1.48621
$189$	13.1706	0.958019
$190$	−1.63058	−0.118295
$191$	2.35247	0.170219	0.0851095	−	0.996372i	$-0.472876\pi$
$191$	2.35247	0.170219	0.0851095	+	0.996372i	$0.472876\pi$
$192$	−20.4373	−1.47493
$193$	−19.3372	−1.39192	−0.695961	−	0.718079i	$-0.745021\pi$
$193$	−19.3372	−1.39192	−0.695961	+	0.718079i	$0.745021\pi$
$194$	2.36440	0.169754
$195$	39.1722	2.80518
$196$	7.02170	0.501550
$197$	3.96200	0.282281	0.141140	−	0.989990i	$-0.454923\pi$
$197$	3.96200	0.282281	0.141140	+	0.989990i	$0.454923\pi$
$198$	−2.13864	−0.151986
$199$	−10.7553	−0.762422	−0.381211	−	0.924488i	$-0.624493\pi$
$199$	−10.7553	−0.762422	−0.381211	+	0.924488i	$0.624493\pi$
$200$	3.31854	0.234656
$201$	−1.91342	−0.134962
$202$	3.83245	0.269650
$203$	−11.3747	−0.798351
$204$	−14.7145	−1.03022
$205$	−1.02755	−0.0717670
$206$	0.358329	0.0249660
$207$	−48.7190	−3.38620
$208$	−16.7414	−1.16081
$209$	−5.14789	−0.356087
$210$	3.29249	0.227204
$211$	−14.0952	−0.970357	−0.485178	−	0.874415i	$-0.661245\pi$
$211$	−14.0952	−0.970357	−0.485178	+	0.874415i	$0.661245\pi$
$212$	13.1422	0.902610
$213$	−28.8637	−1.97770
$214$	0.803957	0.0549573
$215$	−29.5427	−2.01480
$216$	5.72084	0.389254
$217$	0.667774	0.0453315
$218$	0.202771	0.0137334
$219$	20.3898	1.37781
$220$	11.4541	0.772235
$221$	−11.5201	−0.774927
$222$	0.589482	0.0395635
$223$	−28.2508	−1.89181	−0.945907	−	0.324439i	$-0.894824\pi$
$223$	−28.2508	−1.89181	−0.945907	+	0.324439i	$0.894824\pi$
$224$	−4.37426	−0.292267
$225$	22.5360	1.50240
$226$	−3.35300	−0.223038
$227$	−0.525794	−0.0348982	−0.0174491	−	0.999848i	$-0.505554\pi$
$227$	−0.525794	−0.0348982	−0.0174491	+	0.999848i	$0.505554\pi$
$228$	15.1523	1.00349
$229$	−0.909397	−0.0600947	−0.0300473	−	0.999548i	$-0.509566\pi$
$229$	−0.909397	−0.0600947	−0.0300473	+	0.999548i	$0.509566\pi$
$230$	−5.47678	−0.361128
$231$	10.3947	0.683921
$232$	−4.94079	−0.324379
$233$	5.87145	0.384651	0.192326	−	0.981331i	$-0.438397\pi$
$233$	5.87145	0.384651	0.192326	+	0.981331i	$0.438397\pi$
$234$	4.92832	0.322174
$235$	−31.4398	−2.05091
$236$	28.4151	1.84966
$237$	−40.3098	−2.61840
$238$	−0.968287	−0.0627647
$239$	10.7185	0.693321	0.346660	−	0.937991i	$-0.387316\pi$
$239$	10.7185	0.693321	0.346660	+	0.937991i	$0.387316\pi$
$240$	−32.9916	−2.12960
$241$	−17.5800	−1.13243	−0.566213	−	0.824259i	$-0.691592\pi$
$241$	−17.5800	−1.13243	−0.566213	+	0.824259i	$0.691592\pi$
$242$	1.47147	0.0945894
$243$	−8.69403	−0.557722
$244$	−24.6068	−1.57529
$245$	10.8334	0.692118
$246$	−0.200421	−0.0127784
$247$	11.8629	0.754817
$248$	0.290057	0.0184187
$249$	17.5600	1.11282
$250$	−0.530722	−0.0335658
$251$	5.57352	0.351797	0.175899	−	0.984408i	$-0.443717\pi$
$251$	5.57352	0.351797	0.175899	+	0.984408i	$0.443717\pi$
$252$	−19.7352	−1.24320
$253$	−17.2907	−1.08705
$254$	0.747049	0.0468741
$255$	−22.7022	−1.42167
$256$	12.8112	0.800698
$257$	9.11099	0.568328	0.284164	−	0.958776i	$-0.408284\pi$
$257$	9.11099	0.568328	0.284164	+	0.958776i	$0.408284\pi$
$258$	−5.76224	−0.358741
$259$	−1.84810	−0.114835
$260$	−26.3950	−1.63695
$261$	−33.5526	−2.07685
$262$	2.14879	0.132753
$263$	−18.9205	−1.16669	−0.583343	−	0.812226i	$-0.698256\pi$
$263$	−18.9205	−1.16669	−0.583343	+	0.812226i	$0.698256\pi$
$264$	4.51508	0.277884
$265$	20.2763	1.24557
$266$	0.997096	0.0611359
$267$	−22.8662	−1.39939
$268$	1.28930	0.0787567
$269$	−15.2746	−0.931309	−0.465655	−	0.884967i	$-0.654181\pi$
$269$	−15.2746	−0.931309	−0.465655	+	0.884967i	$0.654181\pi$
$270$	4.36734	0.265788
$271$	4.39832	0.267179	0.133590	−	0.991037i	$-0.457350\pi$
$271$	4.39832	0.267179	0.133590	+	0.991037i	$0.457350\pi$
$272$	9.70247	0.588299
$273$	−23.9537	−1.44974
$274$	−4.37954	−0.264578
$275$	7.99816	0.482307
$276$	50.8935	3.06343
$277$	23.5978	1.41786	0.708928	−	0.705280i	$-0.249179\pi$
$277$	23.5978	1.41786	0.708928	+	0.705280i	$0.249179\pi$
$278$	3.10873	0.186449
$279$	1.96976	0.117927
$280$	−4.48367	−0.267950
$281$	−24.5497	−1.46451	−0.732257	−	0.681028i	$-0.761533\pi$
$281$	−24.5497	−1.46451	−0.732257	+	0.681028i	$0.761533\pi$
$282$	−6.13226	−0.365171
$283$	16.0073	0.951536	0.475768	−	0.879571i	$-0.342170\pi$
$283$	16.0073	0.951536	0.475768	+	0.879571i	$0.342170\pi$
$284$	19.4489	1.15408
$285$	23.3777	1.38477
$286$	1.74909	0.103426
$287$	0.628342	0.0370899
$288$	−12.9029	−0.760313
$289$	−10.3235	−0.607267
$290$	−3.77184	−0.221490
$291$	−33.8984	−1.98716
$292$	−13.7391	−0.804018
$293$	0.574436	0.0335589	0.0167795	−	0.999859i	$-0.494659\pi$
$293$	0.574436	0.0335589	0.0167795	+	0.999859i	$0.494659\pi$
$294$	2.11302	0.123234
$295$	43.8399	2.55246
$296$	−0.802747	−0.0466587
$297$	13.7881	0.800064
$298$	3.33342	0.193100
$299$	39.8449	2.30429
$300$	−23.5419	−1.35919
$301$	18.0653	1.04127
$302$	3.36810	0.193813
$303$	−54.9458	−3.15655
$304$	−9.99115	−0.573032
$305$	−37.9644	−2.17383
$306$	−2.85620	−0.163278
$307$	18.9100	1.07925	0.539626	−	0.841905i	$-0.318566\pi$
$307$	18.9100	1.07925	0.539626	+	0.841905i	$0.318566\pi$
$308$	−7.00416	−0.399099
$309$	−5.13736	−0.292254
$310$	0.221432	0.0125765
$311$	1.98818	0.112739	0.0563697	−	0.998410i	$-0.482047\pi$
$311$	1.98818	0.112739	0.0563697	+	0.998410i	$0.482047\pi$
$312$	−10.4046	−0.589047
$313$	30.4897	1.72338	0.861689	−	0.507437i	$-0.169407\pi$
$313$	30.4897	1.72338	0.861689	+	0.507437i	$0.169407\pi$
$314$	−3.24354	−0.183044
$315$	−30.4483	−1.71557
$316$	27.1616	1.52796
$317$	−13.8535	−0.778093	−0.389046	−	0.921218i	$-0.627195\pi$
$317$	−13.8535	−0.778093	−0.389046	+	0.921218i	$0.627195\pi$
$318$	3.95485	0.221777
$319$	−11.9080	−0.666721
$320$	21.2465	1.18772
$321$	−11.5263	−0.643337
$322$	3.34904	0.186634
$323$	−6.87511	−0.382541
$324$	−8.54787	−0.474882
$325$	−18.4311	−1.02237
$326$	−0.391903	−0.0217055
$327$	−2.90713	−0.160765
$328$	0.272930	0.0150700
$329$	19.2254	1.05993
$330$	3.44686	0.189743
$331$	20.6747	1.13638	0.568192	−	0.822896i	$-0.307643\pi$
$331$	20.6747	1.13638	0.568192	+	0.822896i	$0.307643\pi$
$332$	−11.8323	−0.649381
$333$	−5.45141	−0.298735
$334$	3.33684	0.182584
$335$	1.98919	0.108681
$336$	20.1743	1.10060
$337$	27.8482	1.51699	0.758494	−	0.651680i	$-0.225936\pi$
$337$	27.8482	1.51699	0.758494	+	0.651680i	$0.225936\pi$
$338$	−1.39461	−0.0758569
$339$	48.0720	2.61091
$340$	15.2972	0.829607
$341$	0.699081	0.0378574
$342$	2.94118	0.159041
$343$	−19.5612	−1.05621
$344$	7.84692	0.423078
$345$	78.5206	4.22741
$346$	−4.98044	−0.267750
$347$	−31.8840	−1.71162	−0.855812	−	0.517287i	$-0.826942\pi$
$347$	−31.8840	−1.71162	−0.855812	+	0.517287i	$0.826942\pi$
$348$	35.0502	1.87889
$349$	26.8636	1.43798	0.718988	−	0.695022i	$-0.244605\pi$
$349$	26.8636	1.43798	0.718988	+	0.695022i	$0.244605\pi$
$350$	−1.54917	−0.0828065
$351$	−31.7735	−1.69594
$352$	−4.57933	−0.244079
$353$	−1.56789	−0.0834505	−0.0417253	−	0.999129i	$-0.513285\pi$
$353$	−1.56789	−0.0834505	−0.0417253	+	0.999129i	$0.513285\pi$
$354$	8.55087	0.454474
$355$	30.0066	1.59258
$356$	15.4077	0.816608
$357$	13.8823	0.734731
$358$	0.0342295	0.00180909
$359$	8.63511	0.455743	0.227872	−	0.973691i	$-0.426823\pi$
$359$	8.63511	0.455743	0.227872	+	0.973691i	$0.426823\pi$
$360$	−13.2257	−0.697054
$361$	−11.9203	−0.627386
$362$	−1.03130	−0.0542042
$363$	−21.0964	−1.10727
$364$	16.1405	0.845992
$365$	−21.1972	−1.10951
$366$	−7.40486	−0.387058
$367$	25.5800	1.33527	0.667634	−	0.744490i	$-0.267307\pi$
$367$	25.5800	1.33527	0.667634	+	0.744490i	$0.267307\pi$
$368$	−33.5582	−1.74934
$369$	1.85345	0.0964867
$370$	−0.612824	−0.0318592
$371$	−12.3989	−0.643720
$372$	−2.05768	−0.106686
$373$	−8.35696	−0.432707	−0.216353	−	0.976315i	$-0.569416\pi$
$373$	−8.35696	−0.432707	−0.216353	+	0.976315i	$0.569416\pi$
$374$	−1.01368	−0.0524163
$375$	7.60896	0.392925
$376$	8.35081	0.430660
$377$	27.4411	1.41329
$378$	−2.67061	−0.137362
$379$	11.7270	0.602378	0.301189	−	0.953565i	$-0.402617\pi$
$379$	11.7270	0.602378	0.301189	+	0.953565i	$0.402617\pi$
$380$	−15.7523	−0.808078
$381$	−10.7105	−0.548713
$382$	−0.477013	−0.0244061
$383$	−23.4096	−1.19617	−0.598087	−	0.801431i	$-0.704072\pi$
$383$	−23.4096	−1.19617	−0.598087	+	0.801431i	$0.704072\pi$
$384$	17.9059	0.913754
$385$	−10.8063	−0.550740
$386$	3.92103	0.199575
$387$	53.2880	2.70878
$388$	22.8414	1.15960
$389$	−29.0821	−1.47452	−0.737261	−	0.675608i	$-0.763881\pi$
$389$	−29.0821	−1.47452	−0.737261	+	0.675608i	$0.763881\pi$
$390$	−7.94300	−0.402209
$391$	−23.0920	−1.16781
$392$	−2.87748	−0.145335
$393$	−30.8072	−1.55402
$394$	−0.803379	−0.0404737
$395$	41.9060	2.10852
$396$	−20.6605	−1.03823
$397$	−7.98929	−0.400971	−0.200486	−	0.979697i	$-0.564252\pi$
$397$	−7.98929	−0.400971	−0.200486	+	0.979697i	$0.564252\pi$
$398$	2.18086	0.109317
$399$	−14.2954	−0.715664
$400$	15.5230	0.776152
$401$	0.990428	0.0494596	0.0247298	−	0.999694i	$-0.492127\pi$
$401$	0.990428	0.0494596	0.0247298	+	0.999694i	$0.492127\pi$
$402$	0.387987	0.0193510
$403$	−1.61098	−0.0802484
$404$	37.0236	1.84199
$405$	−13.1880	−0.655317
$406$	2.30647	0.114468
$407$	−1.93474	−0.0959015
$408$	6.02999	0.298529
$409$	−20.0385	−0.990842	−0.495421	−	0.868653i	$-0.664986\pi$
$409$	−20.0385	−0.990842	−0.495421	+	0.868653i	$0.664986\pi$
$410$	0.208357	0.0102900
$411$	62.7895	3.09718
$412$	3.46166	0.170544
$413$	−26.8080	−1.31914
$414$	9.87880	0.485516
$415$	−18.2553	−0.896119
$416$	10.5527	0.517389
$417$	−44.5699	−2.18260
$418$	1.04384	0.0510560
$419$	24.8175	1.21241	0.606206	−	0.795308i	$-0.292691\pi$
$419$	24.8175	1.21241	0.606206	+	0.795308i	$0.292691\pi$
$420$	31.8074	1.55204
$421$	14.2645	0.695210	0.347605	−	0.937641i	$-0.386995\pi$
$421$	14.2645	0.695210	0.347605	+	0.937641i	$0.386995\pi$
$422$	2.85811	0.139131
$423$	56.7099	2.75733
$424$	−5.38565	−0.261550
$425$	10.6817	0.518139
$426$	5.85271	0.283565
$427$	23.2151	1.12346
$428$	7.76668	0.375417
$429$	−25.0767	−1.21072
$430$	5.99041	0.288883
$431$	38.7019	1.86421	0.932103	−	0.362193i	$-0.117972\pi$
$431$	38.7019	1.86421	0.932103	+	0.362193i	$0.117972\pi$
$432$	26.7602	1.28750
$433$	31.2169	1.50019	0.750094	−	0.661331i	$-0.230008\pi$
$433$	31.2169	1.50019	0.750094	+	0.661331i	$0.230008\pi$
$434$	−0.135405	−0.00649966
$435$	54.0769	2.59279
$436$	1.95888	0.0938135
$437$	23.7791	1.13751
$438$	−4.13446	−0.197552
$439$	20.7161	0.988728	0.494364	−	0.869255i	$-0.335401\pi$
$439$	20.7161	0.988728	0.494364	+	0.869255i	$0.335401\pi$
$440$	−4.69387	−0.223772
$441$	−19.5408	−0.930514
$442$	2.33595	0.111110
$443$	12.1354	0.576572	0.288286	−	0.957544i	$-0.406915\pi$
$443$	12.1354	0.576572	0.288286	+	0.957544i	$0.406915\pi$
$444$	5.69473	0.270260
$445$	23.7717	1.12689
$446$	5.72844	0.271250
$447$	−47.7913	−2.26045
$448$	−12.9922	−0.613824
$449$	0.477122	0.0225168	0.0112584	−	0.999937i	$-0.496416\pi$
$449$	0.477122	0.0225168	0.0112584	+	0.999937i	$0.496416\pi$
$450$	−4.56965	−0.215415
$451$	0.657801	0.0309746
$452$	−32.3919	−1.52359
$453$	−48.2885	−2.26879
$454$	0.106616	0.00500373
$455$	24.9022	1.16743
$456$	−6.20940	−0.290782
$457$	0.310769	0.0145371	0.00726857	−	0.999974i	$-0.497686\pi$
$457$	0.310769	0.0145371	0.00726857	+	0.999974i	$0.497686\pi$
$458$	0.184399	0.00861642
$459$	18.4142	0.859503
$460$	−52.9088	−2.46688
$461$	−5.28005	−0.245916	−0.122958	−	0.992412i	$-0.539238\pi$
$461$	−5.28005	−0.245916	−0.122958	+	0.992412i	$0.539238\pi$
$462$	−2.10774	−0.0980611
$463$	27.5860	1.28203	0.641016	−	0.767527i	$-0.278513\pi$
$463$	27.5860	1.28203	0.641016	+	0.767527i	$0.278513\pi$
$464$	−23.1114	−1.07292
$465$	−3.17468	−0.147222
$466$	−1.19056	−0.0551516
$467$	7.09897	0.328501	0.164251	−	0.986419i	$-0.447479\pi$
$467$	7.09897	0.328501	0.164251	+	0.986419i	$0.447479\pi$
$468$	47.6103	2.20079
$469$	−1.21639	−0.0561674
$470$	6.37508	0.294061
$471$	46.5027	2.14273
$472$	−11.6444	−0.535979
$473$	18.9122	0.869586
$474$	8.17366	0.375429
$475$	−10.9995	−0.504693
$476$	−9.35420	−0.428749
$477$	−36.5737	−1.67459
$478$	−2.17340	−0.0994089
$479$	2.86583	0.130943	0.0654716	−	0.997854i	$-0.479145\pi$
$479$	2.86583	0.130943	0.0654716	+	0.997854i	$0.479145\pi$
$480$	20.7957	0.949191
$481$	4.45845	0.203288
$482$	3.56471	0.162368
$483$	−48.0152	−2.18477
$484$	14.2152	0.646145
$485$	35.2407	1.60020
$486$	1.76290	0.0799667
$487$	22.8762	1.03662	0.518310	−	0.855193i	$-0.326561\pi$
$487$	22.8762	1.03662	0.518310	+	0.855193i	$0.326561\pi$
$488$	10.0838	0.456473
$489$	5.61871	0.254087
$490$	−2.19669	−0.0992365
$491$	29.7151	1.34102	0.670512	−	0.741898i	$-0.266074\pi$
$491$	29.7151	1.34102	0.670512	+	0.741898i	$0.266074\pi$
$492$	−1.93618	−0.0872896
$493$	−15.9034	−0.716254
$494$	−2.40545	−0.108226
$495$	−31.8758	−1.43271
$496$	1.35680	0.0609219
$497$	−18.3490	−0.823063
$498$	−3.56066	−0.159557
$499$	−12.8121	−0.573549	−0.286775	−	0.957998i	$-0.592583\pi$
$499$	−12.8121	−0.573549	−0.286775	+	0.957998i	$0.592583\pi$
$500$	−5.12707	−0.229290
$501$	−47.8403	−2.13735
$502$	−1.13015	−0.0504410
$503$	−7.78369	−0.347058	−0.173529	−	0.984829i	$-0.555517\pi$
$503$	−7.78369	−0.347058	−0.173529	+	0.984829i	$0.555517\pi$
$504$	8.08746	0.360244
$505$	57.1215	2.54187
$506$	3.50605	0.155863
$507$	19.9946	0.887990
$508$	7.21692	0.320199
$509$	21.1404	0.937032	0.468516	−	0.883455i	$-0.344789\pi$
$509$	21.1404	0.937032	0.468516	+	0.883455i	$0.344789\pi$
$510$	4.60335	0.203840
$511$	12.9620	0.573406
$512$	−14.9163	−0.659214
$513$	−18.9621	−0.837198
$514$	−1.84745	−0.0814873
$515$	5.34079	0.235343
$516$	−55.6665	−2.45058
$517$	20.1267	0.885171
$518$	0.374741	0.0164652
$519$	71.4045	3.13431
$520$	10.8166	0.474341
$521$	−26.3966	−1.15646	−0.578228	−	0.815875i	$-0.696256\pi$
$521$	−26.3966	−1.15646	−0.578228	+	0.815875i	$0.696256\pi$
$522$	6.80350	0.297781
$523$	31.0575	1.35805	0.679025	−	0.734115i	$-0.262403\pi$
$523$	31.0575	1.35805	0.679025	+	0.734115i	$0.262403\pi$
$524$	20.7585	0.906839
$525$	22.2104	0.969342
$526$	3.83652	0.167280
$527$	0.933638	0.0406699
$528$	21.1201	0.919135
$529$	56.8690	2.47257
$530$	−4.11145	−0.178590
$531$	−79.0767	−3.43164
$532$	9.63251	0.417622
$533$	−1.51585	−0.0656587
$534$	4.63661	0.200646
$535$	11.9827	0.518059
$536$	−0.528354	−0.0228214
$537$	−0.490749	−0.0211774
$538$	3.09725	0.133532
$539$	−6.93515	−0.298718
$540$	42.1909	1.81561
$541$	−0.799564	−0.0343759	−0.0171880	−	0.999852i	$-0.505471\pi$
$541$	−0.799564	−0.0343759	−0.0171880	+	0.999852i	$0.505471\pi$
$542$	−0.891853	−0.0383084
$543$	14.7858	0.634521
$544$	−6.11580	−0.262213
$545$	3.02225	0.129459
$546$	4.85712	0.207866
$547$	27.2334	1.16441	0.582207	−	0.813041i	$-0.302189\pi$
$547$	27.2334	1.16441	0.582207	+	0.813041i	$0.302189\pi$
$548$	−42.3088	−1.80734
$549$	68.4787	2.92260
$550$	−1.62180	−0.0691536
$551$	16.3766	0.697666
$552$	−20.8561	−0.887694
$553$	−25.6254	−1.08970
$554$	−4.78496	−0.203293
$555$	8.78607	0.372948
$556$	30.0321	1.27365
$557$	45.3423	1.92122	0.960608	−	0.277908i	$-0.0896409\pi$
$557$	45.3423	1.92122	0.960608	+	0.277908i	$0.0896409\pi$
$558$	−0.399411	−0.0169084
$559$	−43.5817	−1.84331
$560$	−20.9732	−0.886277
$561$	14.5332	0.613591
$562$	4.97798	0.209983
$563$	−5.52087	−0.232677	−0.116339	−	0.993210i	$-0.537116\pi$
$563$	−5.52087	−0.232677	−0.116339	+	0.993210i	$0.537116\pi$
$564$	−59.2411	−2.49450
$565$	−49.9755	−2.10249
$566$	−3.24582	−0.136432
$567$	8.06443	0.338674
$568$	−7.97013	−0.334419
$569$	−11.6417	−0.488045	−0.244022	−	0.969770i	$-0.578467\pi$
$569$	−11.6417	−0.488045	−0.244022	+	0.969770i	$0.578467\pi$
$570$	−4.74031	−0.198550
$571$	−13.8591	−0.579984	−0.289992	−	0.957029i	$-0.593653\pi$
$571$	−13.8591	−0.579984	−0.289992	+	0.957029i	$0.593653\pi$
$572$	16.8972	0.706508
$573$	6.83895	0.285701
$574$	−0.127410	−0.00531798
$575$	−36.9451	−1.54072
$576$	−38.3237	−1.59682
$577$	−1.13167	−0.0471119	−0.0235560	−	0.999723i	$-0.507499\pi$
$577$	−1.13167	−0.0471119	−0.0235560	+	0.999723i	$0.507499\pi$
$578$	2.09331	0.0870704
$579$	−56.2158	−2.33625
$580$	−36.4381	−1.51301
$581$	11.1631	0.463123
$582$	6.87361	0.284920
$583$	−12.9802	−0.537586
$584$	5.63024	0.232981
$585$	73.4552	3.03700
$586$	−0.116479	−0.00481171
$587$	11.5529	0.476838	0.238419	−	0.971162i	$-0.423371\pi$
$587$	11.5529	0.476838	0.238419	+	0.971162i	$0.423371\pi$
$588$	20.4130	0.841818
$589$	−0.961416	−0.0396145
$590$	−8.88947	−0.365974
$591$	11.5181	0.473789
$592$	−3.75499	−0.154329
$593$	−32.4185	−1.33127	−0.665633	−	0.746279i	$-0.731838\pi$
$593$	−32.4185	−1.33127	−0.665633	+	0.746279i	$0.731838\pi$
$594$	−2.79582	−0.114714
$595$	−14.4320	−0.591656
$596$	32.2028	1.31908
$597$	−31.2670	−1.27967
$598$	−8.07940	−0.330391
$599$	−38.4628	−1.57155	−0.785775	−	0.618513i	$-0.787735\pi$
$599$	−38.4628	−1.57155	−0.785775	+	0.618513i	$0.787735\pi$
$600$	9.64742	0.393854
$601$	40.7632	1.66277	0.831383	−	0.555701i	$-0.187550\pi$
$601$	40.7632	1.66277	0.831383	+	0.555701i	$0.187550\pi$
$602$	−3.66312	−0.149298
$603$	−3.58802	−0.146116
$604$	32.5378	1.32394
$605$	21.9318	0.891654
$606$	11.1414	0.452589
$607$	−31.7458	−1.28852	−0.644262	−	0.764805i	$-0.722835\pi$
$607$	−31.7458	−1.28852	−0.644262	+	0.764805i	$0.722835\pi$
$608$	6.29776	0.255408
$609$	−33.0679	−1.33998
$610$	7.69808	0.311686
$611$	−46.3803	−1.87635
$612$	−27.5925	−1.11536
$613$	−5.19296	−0.209742	−0.104871	−	0.994486i	$-0.533443\pi$
$613$	−5.19296	−0.209742	−0.104871	+	0.994486i	$0.533443\pi$
$614$	−3.83441	−0.154744
$615$	−2.98721	−0.120456
$616$	2.87029	0.115647
$617$	−42.8519	−1.72515	−0.862575	−	0.505929i	$-0.831150\pi$
$617$	−42.8519	−1.72515	−0.862575	+	0.505929i	$0.831150\pi$
$618$	1.04171	0.0419037
$619$	39.7668	1.59836	0.799181	−	0.601090i	$-0.205267\pi$
$619$	39.7668	1.59836	0.799181	+	0.601090i	$0.205267\pi$
$620$	2.13916	0.0859108
$621$	−63.6898	−2.55578
$622$	−0.403146	−0.0161647
$623$	−14.5363	−0.582385
$624$	−48.6696	−1.94834
$625$	−28.5801	−1.14321
$626$	−6.18242	−0.247099
$627$	−14.9656	−0.597668
$628$	−31.3344	−1.25038
$629$	−2.58389	−0.103026
$630$	6.17404	0.245980
$631$	29.6206	1.17918	0.589589	−	0.807703i	$-0.299290\pi$
$631$	29.6206	1.17918	0.589589	+	0.807703i	$0.299290\pi$
$632$	−11.1308	−0.442758
$633$	−40.9767	−1.62868
$634$	2.80910	0.111564
$635$	11.1346	0.441862
$636$	38.2061	1.51497
$637$	15.9815	0.633210
$638$	2.41460	0.0955951
$639$	−54.1247	−2.14114
$640$	−18.6149	−0.735818
$641$	−21.2915	−0.840965	−0.420483	−	0.907301i	$-0.638139\pi$
$641$	−21.2915	−0.840965	−0.420483	+	0.907301i	$0.638139\pi$
$642$	2.33721	0.0922422
$643$	−14.6295	−0.576932	−0.288466	−	0.957490i	$-0.593145\pi$
$643$	−14.6295	−0.576932	−0.288466	+	0.957490i	$0.593145\pi$
$644$	32.3536	1.27491
$645$	−85.8845	−3.38170
$646$	1.39407	0.0548491
$647$	−0.481905	−0.0189456	−0.00947282	−	0.999955i	$-0.503015\pi$
$647$	−0.481905	−0.0189456	−0.00947282	+	0.999955i	$0.503015\pi$
$648$	3.50290	0.137607
$649$	−28.0648	−1.10164
$650$	3.73730	0.146589
$651$	1.94131	0.0760858
$652$	−3.78600	−0.148271
$653$	6.46940	0.253167	0.126584	−	0.991956i	$-0.459599\pi$
$653$	6.46940	0.253167	0.126584	+	0.991956i	$0.459599\pi$
$654$	0.589482	0.0230506
$655$	32.0271	1.25140
$656$	1.27668	0.0498459
$657$	38.2347	1.49168
$658$	−3.89835	−0.151973
$659$	−30.4249	−1.18519	−0.592593	−	0.805502i	$-0.701896\pi$
$659$	−30.4249	−1.18519	−0.592593	+	0.805502i	$0.701896\pi$
$660$	33.2986	1.29615
$661$	23.2339	0.903696	0.451848	−	0.892095i	$-0.350765\pi$
$661$	23.2339	0.903696	0.451848	+	0.892095i	$0.350765\pi$
$662$	−4.19223	−0.162936
$663$	−33.4905	−1.30066
$664$	4.84885	0.188172
$665$	14.8614	0.576302
$666$	1.10539	0.0428329
$667$	55.0055	2.12982
$668$	32.2357	1.24724
$669$	−82.1288	−3.17528
$670$	−0.403350	−0.0155828
$671$	24.3035	0.938226
$672$	−12.7165	−0.490551
$673$	−4.52900	−0.174580	−0.0872901	−	0.996183i	$-0.527821\pi$
$673$	−4.52900	−0.174580	−0.0872901	+	0.996183i	$0.527821\pi$
$674$	−5.64681	−0.217507
$675$	29.4611	1.13396
$676$	−13.4727	−0.518182
$677$	−47.4650	−1.82423	−0.912114	−	0.409936i	$-0.865551\pi$
$677$	−47.4650	−1.82423	−0.912114	+	0.409936i	$0.865551\pi$
$678$	−9.74760	−0.374355
$679$	−21.5496	−0.826997
$680$	−6.26876	−0.240396
$681$	−1.52855	−0.0585742
$682$	−0.141753	−0.00542802
$683$	−34.3250	−1.31341	−0.656705	−	0.754147i	$-0.728050\pi$
$683$	−34.3250	−1.31341	−0.656705	+	0.754147i	$0.728050\pi$
$684$	28.4134	1.08642
$685$	−65.2758	−2.49406
$686$	3.96646	0.151440
$687$	−2.64374	−0.100865
$688$	36.7054	1.39938
$689$	29.9119	1.13955
$690$	−15.9217	−0.606129
$691$	5.07322	0.192994	0.0964972	−	0.995333i	$-0.469236\pi$
$691$	5.07322	0.192994	0.0964972	+	0.995333i	$0.469236\pi$
$692$	−48.1138	−1.82901
$693$	19.4920	0.740439
$694$	6.46516	0.245414
$695$	46.3348	1.75758
$696$	−14.3635	−0.544448
$697$	0.878507	0.0332758
$698$	−5.44717	−0.206178
$699$	17.0691	0.645612
$700$	−14.9658	−0.565655
$701$	28.3838	1.07204	0.536020	−	0.844205i	$-0.319927\pi$
$701$	28.3838	1.07204	0.536020	+	0.844205i	$0.319927\pi$
$702$	6.44274	0.243165
$703$	2.66076	0.100353
$704$	−13.6013	−0.512619
$705$	−91.3996	−3.44231
$706$	0.317923	0.0119652
$707$	−34.9297	−1.31367
$708$	82.6063	3.10453
$709$	6.60398	0.248018	0.124009	−	0.992281i	$-0.460425\pi$
$709$	6.60398	0.248018	0.124009	+	0.992281i	$0.460425\pi$
$710$	−6.08447	−0.228346
$711$	−75.5884	−2.83478
$712$	−6.31406	−0.236629
$713$	−3.22919	−0.120934
$714$	−2.81494	−0.105346
$715$	26.0697	0.974952
$716$	0.330677	0.0123580
$717$	31.1600	1.16369
$718$	−1.75095	−0.0653449
$719$	−29.7344	−1.10890	−0.554452	−	0.832215i	$-0.687072\pi$
$719$	−29.7344	−1.10890	−0.554452	+	0.832215i	$0.687072\pi$
$720$	−61.8654	−2.30559
$721$	−3.26588	−0.121628
$722$	2.41710	0.0899551
$723$	−51.1073	−1.90070
$724$	−9.96299	−0.370272
$725$	−25.4440	−0.944966
$726$	4.27774	0.158762
$727$	−11.9768	−0.444194	−0.222097	−	0.975025i	$-0.571290\pi$
$727$	−11.9768	−0.444194	−0.222097	+	0.975025i	$0.571290\pi$
$728$	−6.61435	−0.245144
$729$	−38.3656	−1.42095
$730$	4.29818	0.159083
$731$	25.2577	0.934190
$732$	−71.5352	−2.64402
$733$	18.9512	0.699977	0.349988	−	0.936754i	$-0.386186\pi$
$733$	18.9512	0.699977	0.349988	+	0.936754i	$0.386186\pi$
$734$	−5.18689	−0.191452
$735$	31.4940	1.16167
$736$	21.1528	0.779704
$737$	−1.27341	−0.0469067
$738$	−0.375826	−0.0138343
$739$	1.18411	0.0435584	0.0217792	−	0.999763i	$-0.493067\pi$
$739$	1.18411	0.0435584	0.0217792	+	0.999763i	$0.493067\pi$
$740$	−5.92023	−0.217632
$741$	34.4869	1.26691
$742$	2.51414	0.0922971
$743$	0.992442	0.0364092	0.0182046	−	0.999834i	$-0.494205\pi$
$743$	0.992442	0.0364092	0.0182046	+	0.999834i	$0.494205\pi$
$744$	0.843235	0.0309145
$745$	49.6838	1.82027
$746$	1.69455	0.0620419
$747$	32.9283	1.20478
$748$	−9.79274	−0.358058
$749$	−7.32742	−0.267738
$750$	−1.54288	−0.0563379
$751$	4.83178	0.176314	0.0881571	−	0.996107i	$-0.471902\pi$
$751$	4.83178	0.176314	0.0881571	+	0.996107i	$0.471902\pi$
$752$	39.0624	1.42446
$753$	16.2029	0.590468
$754$	−5.56426	−0.202638
$755$	50.2007	1.82699
$756$	−25.7997	−0.938324
$757$	50.3532	1.83012	0.915059	−	0.403320i	$-0.132144\pi$
$757$	50.3532	1.83012	0.915059	+	0.403320i	$0.132144\pi$
$758$	−2.37790	−0.0863694
$759$	−50.2662	−1.82455
$760$	6.45528	0.234158
$761$	17.6651	0.640360	0.320180	−	0.947357i	$-0.396257\pi$
$761$	17.6651	0.640360	0.320180	+	0.947357i	$0.396257\pi$
$762$	2.17177	0.0786749
$763$	−1.84810	−0.0669056
$764$	−4.60822	−0.166720
$765$	−42.5708	−1.53915
$766$	4.74679	0.171508
$767$	64.6731	2.33521
$768$	37.2438	1.34392
$769$	−47.3615	−1.70790	−0.853950	−	0.520355i	$-0.825800\pi$
$769$	−47.3615	−1.70790	−0.853950	+	0.520355i	$0.825800\pi$
$770$	2.19120	0.0789655
$771$	26.4868	0.953900
$772$	37.8793	1.36331
$773$	−2.36032	−0.0848947	−0.0424474	−	0.999099i	$-0.513515\pi$
$773$	−2.36032	−0.0848947	−0.0424474	+	0.999099i	$0.513515\pi$
$774$	−10.8053	−0.388387
$775$	1.49373	0.0536565
$776$	−9.36037	−0.336018
$777$	−5.37266	−0.192743
$778$	5.89702	0.211418
$779$	−0.904645	−0.0324123
$780$	−76.7338	−2.74751
$781$	−19.2092	−0.687359
$782$	4.68240	0.167442
$783$	−43.8630	−1.56753
$784$	−13.4599	−0.480712
$785$	−48.3441	−1.72547
$786$	6.24681	0.222816
$787$	39.7251	1.41605	0.708024	−	0.706189i	$-0.249587\pi$
$787$	39.7251	1.41605	0.708024	+	0.706189i	$0.249587\pi$
$788$	−7.76110	−0.276478
$789$	−55.0043	−1.95820
$790$	−8.49732	−0.302321
$791$	30.5599	1.08658
$792$	8.46662	0.300848
$793$	−56.0054	−1.98881
$794$	1.62000	0.0574916
$795$	58.9460	2.09060
$796$	21.0684	0.746748
$797$	−22.9085	−0.811459	−0.405729	−	0.913993i	$-0.632982\pi$
$797$	−22.9085	−0.811459	−0.405729	+	0.913993i	$0.632982\pi$
$798$	2.89869	0.102612
$799$	26.8796	0.950932
$800$	−9.78470	−0.345941
$801$	−42.8784	−1.51503
$802$	−0.200830	−0.00709156
$803$	13.5697	0.478865
$804$	3.74817	0.132188
$805$	49.9164	1.75932
$806$	0.326659	0.0115061
$807$	−44.4053	−1.56314
$808$	−15.1722	−0.533756
$809$	7.05107	0.247902	0.123951	−	0.992288i	$-0.460443\pi$
$809$	7.05107	0.247902	0.123951	+	0.992288i	$0.460443\pi$
$810$	2.67415	0.0939600
$811$	8.19022	0.287597	0.143799	−	0.989607i	$-0.454068\pi$
$811$	8.19022	0.287597	0.143799	+	0.989607i	$0.454068\pi$
$812$	22.2818	0.781938
$813$	12.7865	0.448442
$814$	0.392309	0.0137504
$815$	−5.84120	−0.204608
$816$	28.2064	0.987420
$817$	−26.0092	−0.909946
$818$	4.06324	0.142068
$819$	−44.9177	−1.56955
$820$	2.01285	0.0702916
$821$	−44.7016	−1.56010	−0.780048	−	0.625720i	$-0.784805\pi$
$821$	−44.7016	−1.56010	−0.780048	+	0.625720i	$0.784805\pi$
$822$	−12.7319	−0.444076
$823$	29.1605	1.01647	0.508236	−	0.861218i	$-0.330298\pi$
$823$	29.1605	1.01647	0.508236	+	0.861218i	$0.330298\pi$
$824$	−1.41858	−0.0494187
$825$	23.2517	0.809520
$826$	5.43589	0.189139
$827$	17.4524	0.606879	0.303439	−	0.952851i	$-0.401865\pi$
$827$	17.4524	0.606879	0.303439	+	0.952851i	$0.401865\pi$
$828$	95.4348	3.31659
$829$	−9.77051	−0.339344	−0.169672	−	0.985501i	$-0.554271\pi$
$829$	−9.77051	−0.339344	−0.169672	+	0.985501i	$0.554271\pi$
$830$	3.70166	0.128486
$831$	68.6020	2.37978
$832$	31.3431	1.08663
$833$	−9.26204	−0.320911
$834$	9.03750	0.312943
$835$	49.7346	1.72114
$836$	10.0841	0.348766
$837$	2.57505	0.0890068
$838$	−5.03226	−0.173837
$839$	37.2611	1.28640	0.643198	−	0.765700i	$-0.277607\pi$
$839$	37.2611	1.28640	0.643198	+	0.765700i	$0.277607\pi$
$840$	−13.0346	−0.449737
$841$	8.88214	0.306281
$842$	−2.89243	−0.0996798
$843$	−71.3693	−2.45809
$844$	27.6109	0.950408
$845$	−20.7863	−0.715070
$846$	−11.4991	−0.395348
$847$	−13.4112	−0.460815
$848$	−25.1924	−0.865109
$849$	46.5354	1.59709
$850$	−2.16594	−0.0742912
$851$	8.93695	0.306355
$852$	56.5405	1.93705
$853$	−2.61233	−0.0894444	−0.0447222	−	0.998999i	$-0.514240\pi$
$853$	−2.61233	−0.0894444	−0.0447222	+	0.998999i	$0.514240\pi$
$854$	−4.70736	−0.161082
$855$	43.8374	1.49921
$856$	−3.18277	−0.108785
$857$	45.6263	1.55856	0.779282	−	0.626673i	$-0.215584\pi$
$857$	45.6263	1.55856	0.779282	+	0.626673i	$0.215584\pi$
$858$	5.08484	0.173593
$859$	−36.4911	−1.24506	−0.622530	−	0.782596i	$-0.713895\pi$
$859$	−36.4911	−1.24506	−0.622530	+	0.782596i	$0.713895\pi$
$860$	57.8707	1.97338
$861$	1.82667	0.0622529
$862$	−7.84763	−0.267291
$863$	29.6182	1.00821	0.504107	−	0.863641i	$-0.331822\pi$
$863$	29.6182	1.00821	0.504107	+	0.863641i	$0.331822\pi$
$864$	−16.8679	−0.573857
$865$	−74.2320	−2.52396
$866$	−6.32989	−0.215098
$867$	−30.0119	−1.01926
$868$	−1.30809	−0.0443995
$869$	−26.8268	−0.910036
$870$	−10.9652	−0.371756
$871$	2.93447	0.0994309
$872$	−0.802747	−0.0271845
$873$	−63.5658	−2.15137
$874$	−4.82172	−0.163097
$875$	4.83710	0.163524
$876$	−39.9412	−1.34949
$877$	6.42826	0.217067	0.108533	−	0.994093i	$-0.465385\pi$
$877$	6.42826	0.217067	0.108533	+	0.994093i	$0.465385\pi$
$878$	−4.20064	−0.141765
$879$	1.66996	0.0563264
$880$	−21.9564	−0.740151
$881$	19.7736	0.666190	0.333095	−	0.942893i	$-0.391907\pi$
$881$	19.7736	0.666190	0.333095	+	0.942893i	$0.391907\pi$
$882$	3.96231	0.133418
$883$	50.5883	1.70243	0.851216	−	0.524816i	$-0.175866\pi$
$883$	50.5883	1.70243	0.851216	+	0.524816i	$0.175866\pi$
$884$	22.5666	0.758996
$885$	127.448	4.28413
$886$	−2.46072	−0.0826694
$887$	−16.4849	−0.553508	−0.276754	−	0.960941i	$-0.589259\pi$
$887$	−16.4849	−0.553508	−0.276754	+	0.960941i	$0.589259\pi$
$888$	−2.33369	−0.0783136
$889$	−6.80876	−0.228358
$890$	−4.82021	−0.161574
$891$	8.44252	0.282835
$892$	55.3400	1.85292
$893$	−27.6794	−0.926255
$894$	9.69070	0.324106
$895$	0.510181	0.0170535
$896$	11.3830	0.380278
$897$	115.834	3.86760
$898$	−0.0967465	−0.00322847
$899$	−2.22394	−0.0741724
$900$	−44.1454	−1.47151
$901$	−17.3354	−0.577525
$902$	−0.133383	−0.00444117
$903$	52.5182	1.74770
$904$	13.2741	0.441491
$905$	−15.3713	−0.510960
$906$	9.79152	0.325302
$907$	−22.6380	−0.751684	−0.375842	−	0.926684i	$-0.622646\pi$
$907$	−22.6380	−0.751684	−0.375842	+	0.926684i	$0.622646\pi$
$908$	1.02997	0.0341807
$909$	−103.034	−3.41741
$910$	−5.04945	−0.167388
$911$	−40.7750	−1.35094	−0.675468	−	0.737389i	$-0.736059\pi$
$911$	−40.7750	−1.35094	−0.675468	+	0.737389i	$0.736059\pi$
$912$	−29.0456	−0.961796
$913$	11.6864	0.386765
$914$	−0.0630149	−0.00208435
$915$	−110.367	−3.64863
$916$	1.78140	0.0588592
$917$	−19.5845	−0.646736
$918$	−3.73388	−0.123236
$919$	−22.3610	−0.737621	−0.368810	−	0.929505i	$-0.620235\pi$
$919$	−22.3610	−0.737621	−0.368810	+	0.929505i	$0.620235\pi$
$920$	21.6819	0.714832
$921$	54.9739	1.81145
$922$	1.07064	0.0352597
$923$	44.2660	1.45703
$924$	−20.3620	−0.669860
$925$	−4.13397	−0.135924
$926$	−5.59365	−0.183819
$927$	−9.63351	−0.316406
$928$	14.5679	0.478215
$929$	12.1543	0.398769	0.199384	−	0.979921i	$-0.436106\pi$
$929$	12.1543	0.398769	0.199384	+	0.979921i	$0.436106\pi$
$930$	0.643733	0.0211088
$931$	9.53762	0.312583
$932$	−11.5015	−0.376744
$933$	5.77991	0.189226
$934$	−1.43947	−0.0471008
$935$	−15.1086	−0.494106
$936$	−19.5106	−0.637725
$937$	18.3473	0.599379	0.299689	−	0.954037i	$-0.403117\pi$
$937$	18.3473	0.599379	0.299689	+	0.954037i	$0.403117\pi$
$938$	0.246648	0.00805333
$939$	88.6374	2.89257
$940$	61.5869	2.00874
$941$	−14.6078	−0.476200	−0.238100	−	0.971241i	$-0.576525\pi$
$941$	−14.6078	−0.476200	−0.238100	+	0.971241i	$0.576525\pi$
$942$	−9.42940	−0.307226
$943$	−3.03851	−0.0989476
$944$	−54.4689	−1.77281
$945$	−39.8048	−1.29485
$946$	−3.83486	−0.124682
$947$	−46.7440	−1.51898	−0.759488	−	0.650521i	$-0.774551\pi$
$947$	−46.7440	−1.51898	−0.759488	+	0.650521i	$0.774551\pi$
$948$	78.9622	2.56457
$949$	−31.2703	−1.01508
$950$	2.23039	0.0723633
$951$	−40.2741	−1.30598
$952$	3.83333	0.124239
$953$	11.2252	0.363618	0.181809	−	0.983334i	$-0.441805\pi$
$953$	11.2252	0.363618	0.181809	+	0.983334i	$0.441805\pi$
$954$	7.41608	0.240105
$955$	−7.10975	−0.230066
$956$	−20.9963	−0.679068
$957$	−34.6182	−1.11905
$958$	−0.581108	−0.0187748
$959$	39.9160	1.28895
$960$	61.7665	1.99350
$961$	−30.8694	−0.995788
$962$	−0.904045	−0.0291476
$963$	−21.6140	−0.696502
$964$	34.4372	1.10915
$965$	58.4418	1.88131
$966$	9.73609	0.313253
$967$	2.86788	0.0922249	0.0461125	−	0.998936i	$-0.485317\pi$
$967$	2.86788	0.0922249	0.0461125	+	0.998936i	$0.485317\pi$
$968$	−5.82536	−0.187234
$969$	−19.9868	−0.642070
$970$	−7.14579	−0.229437
$971$	14.5717	0.467629	0.233814	−	0.972281i	$-0.424879\pi$
$971$	14.5717	0.467629	0.233814	+	0.972281i	$0.424879\pi$
$972$	17.0306	0.546256
$973$	−28.3336	−0.908334
$974$	−4.63863	−0.148631
$975$	−53.5817	−1.71599
$976$	47.1689	1.50984
$977$	−8.91247	−0.285135	−0.142568	−	0.989785i	$-0.545536\pi$
$977$	−8.91247	−0.285135	−0.142568	+	0.989785i	$0.545536\pi$
$978$	−1.13931	−0.0364312
$979$	−15.2178	−0.486364
$980$	−21.2213	−0.677890
$981$	−5.45141	−0.174050
$982$	−6.02537	−0.192277
$983$	10.8171	0.345011	0.172506	−	0.985009i	$-0.444814\pi$
$983$	10.8171	0.345011	0.172506	+	0.985009i	$0.444814\pi$
$984$	0.793442	0.0252940
$985$	−11.9741	−0.381528
$986$	3.22475	0.102697
$987$	55.8906	1.77902
$988$	−23.2380	−0.739299
$989$	−87.3594	−2.77787
$990$	6.46349	0.205423
$991$	−1.01860	−0.0323569	−0.0161785	−	0.999869i	$-0.505150\pi$
$991$	−1.01860	−0.0323569	−0.0161785	+	0.999869i	$0.505150\pi$
$992$	−0.855234	−0.0271537
$993$	60.1041	1.90734
$994$	3.72064	0.118011
$995$	32.5051	1.03048
$996$	−34.3980	−1.08994
$997$	−40.3871	−1.27907	−0.639537	−	0.768760i	$-0.720874\pi$
$997$	−40.3871	−1.27907	−0.639537	+	0.768760i	$0.720874\pi$
$998$	2.59793	0.0822360
$999$	−7.12657	−0.225475

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4033.2.a.d.1.40	✓	79

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4033.2.a.d.1.40	✓	79	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:	\( N \)	\(=\)	\( 4033 = 37 \cdot 109 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4033.a (trivial)

\(f(q)\)	\(=\)	\(q-0.202771 q^{2} +2.90713 q^{3} -1.95888 q^{4} -3.02225 q^{5} -0.589482 q^{6} +1.84810 q^{7} +0.802747 q^{8} +5.45141 q^{9} +O(q^{10})\)	\(q-0.202771 q^{2} +2.90713 q^{3} -1.95888 q^{4} -3.02225 q^{5} -0.589482 q^{6} +1.84810 q^{7} +0.802747 q^{8} +5.45141 q^{9} +0.612824 q^{10} +1.93474 q^{11} -5.69473 q^{12} -4.45845 q^{13} -0.374741 q^{14} -8.78607 q^{15} +3.75499 q^{16} +2.58389 q^{17} -1.10539 q^{18} -2.66076 q^{19} +5.92023 q^{20} +5.37266 q^{21} -0.392309 q^{22} -8.93695 q^{23} +2.33369 q^{24} +4.13397 q^{25} +0.904045 q^{26} +7.12657 q^{27} -3.62021 q^{28} -6.15485 q^{29} +1.78156 q^{30} +0.361331 q^{31} -2.36690 q^{32} +5.62454 q^{33} -0.523937 q^{34} -5.58540 q^{35} -10.6787 q^{36} -1.00000 q^{37} +0.539526 q^{38} -12.9613 q^{39} -2.42610 q^{40} +0.339994 q^{41} -1.08942 q^{42} +9.77508 q^{43} -3.78993 q^{44} -16.4755 q^{45} +1.81215 q^{46} +10.4028 q^{47} +10.9163 q^{48} -3.58454 q^{49} -0.838250 q^{50} +7.51169 q^{51} +8.73358 q^{52} -6.70903 q^{53} -1.44506 q^{54} -5.84726 q^{55} +1.48355 q^{56} -7.73519 q^{57} +1.24803 q^{58} -14.5057 q^{59} +17.2109 q^{60} +12.5616 q^{61} -0.0732675 q^{62} +10.0747 q^{63} -7.03005 q^{64} +13.4745 q^{65} -1.14049 q^{66} -0.658183 q^{67} -5.06153 q^{68} -25.9809 q^{69} +1.13256 q^{70} -9.92857 q^{71} +4.37610 q^{72} +7.01372 q^{73} +0.202771 q^{74} +12.0180 q^{75} +5.21213 q^{76} +3.57558 q^{77} +2.62818 q^{78} -13.8658 q^{79} -11.3485 q^{80} +4.36364 q^{81} -0.0689410 q^{82} +6.04032 q^{83} -10.5244 q^{84} -7.80914 q^{85} -1.98210 q^{86} -17.8929 q^{87} +1.55311 q^{88} -7.86557 q^{89} +3.34076 q^{90} -8.23964 q^{91} +17.5064 q^{92} +1.05044 q^{93} -2.10939 q^{94} +8.04149 q^{95} -6.88088 q^{96} -11.6604 q^{97} +0.726841 q^{98} +10.5471 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9}+O(q^{10}) \) 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9} - 13 q^{10} - 5 q^{11} - 40 q^{12} - 18 q^{13} - 42 q^{14} - 49 q^{15} + 83 q^{16} - 62 q^{17} - 33 q^{18} - 25 q^{19} - 39 q^{20} - 15 q^{21} - 31 q^{22} - 94 q^{23} - 39 q^{24} + 71 q^{25} - 35 q^{26} - 47 q^{27} - 13 q^{28} - 17 q^{29} + 15 q^{30} - 37 q^{31} - 105 q^{32} - 60 q^{33} + 9 q^{34} - 60 q^{35} + 43 q^{36} - 79 q^{37} - 80 q^{38} - 41 q^{39} - 64 q^{40} - 37 q^{41} - 30 q^{42} - 20 q^{43} - 14 q^{44} - 8 q^{45} + 61 q^{46} - 148 q^{47} - 39 q^{48} + 82 q^{49} - 90 q^{50} - 45 q^{51} - 27 q^{52} - 70 q^{53} - 41 q^{54} - 105 q^{55} - 68 q^{56} - 31 q^{57} - 14 q^{58} - 96 q^{59} - 74 q^{60} - 21 q^{61} + 4 q^{62} - 60 q^{63} + 132 q^{64} - 15 q^{65} + 71 q^{66} - 44 q^{67} - 166 q^{68} - 72 q^{69} - 9 q^{70} - 55 q^{71} - 126 q^{72} - 27 q^{73} + 11 q^{74} - 39 q^{75} - 4 q^{76} - 104 q^{77} - 47 q^{78} - 49 q^{79} - 82 q^{80} + 55 q^{81} + 20 q^{82} - 52 q^{83} - 29 q^{84} + 3 q^{85} - 32 q^{86} - 113 q^{87} + 14 q^{88} - 68 q^{89} - 39 q^{90} - 30 q^{91} - 179 q^{92} - 53 q^{93} - 33 q^{94} - 86 q^{95} + 33 q^{96} - 57 q^{97} - 116 q^{98} + q^{99}+O(q^{100}) \) 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9 - 13 * q^10 - 5 * q^11 - 40 * q^12 - 18 * q^13 - 42 * q^14 - 49 * q^15 + 83 * q^16 - 62 * q^17 - 33 * q^18 - 25 * q^19 - 39 * q^20 - 15 * q^21 - 31 * q^22 - 94 * q^23 - 39 * q^24 + 71 * q^25 - 35 * q^26 - 47 * q^27 - 13 * q^28 - 17 * q^29 + 15 * q^30 - 37 * q^31 - 105 * q^32 - 60 * q^33 + 9 * q^34 - 60 * q^35 + 43 * q^36 - 79 * q^37 - 80 * q^38 - 41 * q^39 - 64 * q^40 - 37 * q^41 - 30 * q^42 - 20 * q^43 - 14 * q^44 - 8 * q^45 + 61 * q^46 - 148 * q^47 - 39 * q^48 + 82 * q^49 - 90 * q^50 - 45 * q^51 - 27 * q^52 - 70 * q^53 - 41 * q^54 - 105 * q^55 - 68 * q^56 - 31 * q^57 - 14 * q^58 - 96 * q^59 - 74 * q^60 - 21 * q^61 + 4 * q^62 - 60 * q^63 + 132 * q^64 - 15 * q^65 + 71 * q^66 - 44 * q^67 - 166 * q^68 - 72 * q^69 - 9 * q^70 - 55 * q^71 - 126 * q^72 - 27 * q^73 + 11 * q^74 - 39 * q^75 - 4 * q^76 - 104 * q^77 - 47 * q^78 - 49 * q^79 - 82 * q^80 + 55 * q^81 + 20 * q^82 - 52 * q^83 - 29 * q^84 + 3 * q^85 - 32 * q^86 - 113 * q^87 + 14 * q^88 - 68 * q^89 - 39 * q^90 - 30 * q^91 - 179 * q^92 - 53 * q^93 - 33 * q^94 - 86 * q^95 + 33 * q^96 - 57 * q^97 - 116 * q^98 + q^99

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