LMFDB - Embedded newform 4033.2.a.d.1.18

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			1.18
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)

$f(q)$	$=$	$q-1.80025 q^{2} +1.41167 q^{3} +1.24090 q^{4} +0.213559 q^{5} -2.54136 q^{6} -2.54704 q^{7} +1.36657 q^{8} -1.00719 q^{9} +O(q^{10})$	\(q-1.80025 q^{2} +1.41167 q^{3} +1.24090 q^{4} +0.213559 q^{5} -2.54136 q^{6} -2.54704 q^{7} +1.36657 q^{8} -1.00719 q^{9} -0.384459 q^{10} +1.24725 q^{11} +1.75174 q^{12} +1.90462 q^{13} +4.58531 q^{14} +0.301474 q^{15} -4.94197 q^{16} -3.92660 q^{17} +1.81319 q^{18} +5.27048 q^{19} +0.265005 q^{20} -3.59558 q^{21} -2.24537 q^{22} +2.59275 q^{23} +1.92914 q^{24} -4.95439 q^{25} -3.42880 q^{26} -5.65683 q^{27} -3.16063 q^{28} +4.85757 q^{29} -0.542729 q^{30} +1.57742 q^{31} +6.16365 q^{32} +1.76071 q^{33} +7.06886 q^{34} -0.543942 q^{35} -1.24983 q^{36} -1.00000 q^{37} -9.48819 q^{38} +2.68870 q^{39} +0.291842 q^{40} -7.59622 q^{41} +6.47294 q^{42} -3.23107 q^{43} +1.54772 q^{44} -0.215094 q^{45} -4.66760 q^{46} -1.14828 q^{47} -6.97642 q^{48} -0.512597 q^{49} +8.91915 q^{50} -5.54305 q^{51} +2.36345 q^{52} +11.3924 q^{53} +10.1837 q^{54} +0.266362 q^{55} -3.48069 q^{56} +7.44018 q^{57} -8.74484 q^{58} +4.17419 q^{59} +0.374100 q^{60} +4.10910 q^{61} -2.83975 q^{62} +2.56535 q^{63} -1.21218 q^{64} +0.406749 q^{65} -3.16972 q^{66} -5.17598 q^{67} -4.87252 q^{68} +3.66010 q^{69} +0.979232 q^{70} -16.1412 q^{71} -1.37639 q^{72} -4.41986 q^{73} +1.80025 q^{74} -6.99396 q^{75} +6.54016 q^{76} -3.17680 q^{77} -4.84033 q^{78} -2.92425 q^{79} -1.05540 q^{80} -4.96400 q^{81} +13.6751 q^{82} +7.83025 q^{83} -4.46176 q^{84} -0.838558 q^{85} +5.81673 q^{86} +6.85727 q^{87} +1.70445 q^{88} +4.91950 q^{89} +0.387223 q^{90} -4.85115 q^{91} +3.21735 q^{92} +2.22679 q^{93} +2.06719 q^{94} +1.12556 q^{95} +8.70103 q^{96} +11.2210 q^{97} +0.922803 q^{98} -1.25622 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.80025	−1.27297	−0.636485	−	0.771289i	$-0.719612\pi$
$2$	−1.80025	−1.27297	−0.636485	+	0.771289i	$0.719612\pi$
$3$	1.41167	0.815028	0.407514	−	0.913199i	$-0.366396\pi$
$3$	1.41167	0.815028	0.407514	+	0.913199i	$0.366396\pi$
$4$	1.24090	0.620451
$5$	0.213559	0.0955063	0.0477532	−	0.998859i	$-0.484794\pi$
$5$	0.213559	0.0955063	0.0477532	+	0.998859i	$0.484794\pi$
$6$	−2.54136	−1.03751
$7$	−2.54704	−0.962690	−0.481345	−	0.876531i	$-0.659852\pi$
$7$	−2.54704	−0.962690	−0.481345	+	0.876531i	$0.659852\pi$
$8$	1.36657	0.483154
$9$	−1.00719	−0.335730
$10$	−0.384459	−0.121577
$11$	1.24725	0.376061	0.188030	−	0.982163i	$-0.439790\pi$
$11$	1.24725	0.376061	0.188030	+	0.982163i	$0.439790\pi$
$12$	1.75174	0.505685
$13$	1.90462	0.528247	0.264124	−	0.964489i	$-0.414917\pi$
$13$	1.90462	0.528247	0.264124	+	0.964489i	$0.414917\pi$
$14$	4.58531	1.22547
$15$	0.301474	0.0778403
$16$	−4.94197	−1.23549
$17$	−3.92660	−0.952339	−0.476170	−	0.879353i	$-0.657975\pi$
$17$	−3.92660	−0.952339	−0.476170	+	0.879353i	$0.657975\pi$
$18$	1.81319	0.427374
$19$	5.27048	1.20913	0.604566	−	0.796555i	$-0.293347\pi$
$19$	5.27048	1.20913	0.604566	+	0.796555i	$0.293347\pi$
$20$	0.265005	0.0592570
$21$	−3.59558	−0.784619
$22$	−2.24537	−0.478714
$23$	2.59275	0.540625	0.270313	−	0.962773i	$-0.412873\pi$
$23$	2.59275	0.540625	0.270313	+	0.962773i	$0.412873\pi$
$24$	1.92914	0.393784
$25$	−4.95439	−0.990879
$26$	−3.42880	−0.672443
$27$	−5.65683	−1.08866
$28$	−3.16063	−0.597302
$29$	4.85757	0.902027	0.451014	−	0.892517i	$-0.351063\pi$
$29$	4.85757	0.902027	0.451014	+	0.892517i	$0.351063\pi$
$30$	−0.542729	−0.0990883
$31$	1.57742	0.283313	0.141656	−	0.989916i	$-0.454757\pi$
$31$	1.57742	0.283313	0.141656	+	0.989916i	$0.454757\pi$
$32$	6.16365	1.08959
$33$	1.76071	0.306500
$34$	7.06886	1.21230
$35$	−0.543942	−0.0919430
$36$	−1.24983	−0.208304
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	−9.48819	−1.53919
$39$	2.68870	0.430536
$40$	0.291842	0.0461442
$41$	−7.59622	−1.18633	−0.593165	−	0.805081i	$-0.702122\pi$
$41$	−7.59622	−1.18633	−0.593165	+	0.805081i	$0.702122\pi$
$42$	6.47294	0.998796
$43$	−3.23107	−0.492733	−0.246366	−	0.969177i	$-0.579237\pi$
$43$	−3.23107	−0.492733	−0.246366	+	0.969177i	$0.579237\pi$
$44$	1.54772	0.233328
$45$	−0.215094	−0.0320643
$46$	−4.66760	−0.688199
$47$	−1.14828	−0.167494	−0.0837469	−	0.996487i	$-0.526689\pi$
$47$	−1.14828	−0.167494	−0.0837469	+	0.996487i	$0.526689\pi$
$48$	−6.97642	−1.00696
$49$	−0.512597	−0.0732282
$50$	8.91915	1.26136
$51$	−5.54305	−0.776183
$52$	2.36345	0.327752
$53$	11.3924	1.56486	0.782430	−	0.622738i	$-0.213980\pi$
$53$	11.3924	1.56486	0.782430	+	0.622738i	$0.213980\pi$
$54$	10.1837	1.38583
$55$	0.266362	0.0359162
$56$	−3.48069	−0.465127
$57$	7.44018	0.985476
$58$	−8.74484	−1.14825
$59$	4.17419	0.543434	0.271717	−	0.962377i	$-0.412409\pi$
$59$	4.17419	0.543434	0.271717	+	0.962377i	$0.412409\pi$
$60$	0.374100	0.0482961
$61$	4.10910	0.526117	0.263058	−	0.964780i	$-0.415269\pi$
$61$	4.10910	0.526117	0.263058	+	0.964780i	$0.415269\pi$
$62$	−2.83975	−0.360649
$63$	2.56535	0.323204
$64$	−1.21218	−0.151522
$65$	0.406749	0.0504510
$66$	−3.16972	−0.390165
$67$	−5.17598	−0.632346	−0.316173	−	0.948701i	$-0.602398\pi$
$67$	−5.17598	−0.632346	−0.316173	+	0.948701i	$0.602398\pi$
$68$	−4.87252	−0.590880
$69$	3.66010	0.440624
$70$	0.979232	0.117041
$71$	−16.1412	−1.91560	−0.957802	−	0.287429i	$-0.907199\pi$
$71$	−16.1412	−1.91560	−0.957802	+	0.287429i	$0.907199\pi$
$72$	−1.37639	−0.162209
$73$	−4.41986	−0.517305	−0.258653	−	0.965970i	$-0.583279\pi$
$73$	−4.41986	−0.517305	−0.258653	+	0.965970i	$0.583279\pi$
$74$	1.80025	0.209275
$75$	−6.99396	−0.807593
$76$	6.54016	0.750207
$77$	−3.17680	−0.362030
$78$	−4.84033	−0.548059
$79$	−2.92425	−0.329004	−0.164502	−	0.986377i	$-0.552602\pi$
$79$	−2.92425	−0.329004	−0.164502	+	0.986377i	$0.552602\pi$
$80$	−1.05540	−0.117997
$81$	−4.96400	−0.551555
$82$	13.6751	1.51016
$83$	7.83025	0.859482	0.429741	−	0.902952i	$-0.358605\pi$
$83$	7.83025	0.859482	0.429741	+	0.902952i	$0.358605\pi$
$84$	−4.46176	−0.486818
$85$	−0.838558	−0.0909544
$86$	5.81673	0.627234
$87$	6.85727	0.735177
$88$	1.70445	0.181695
$89$	4.91950	0.521466	0.260733	−	0.965411i	$-0.416036\pi$
$89$	4.91950	0.521466	0.260733	+	0.965411i	$0.416036\pi$
$90$	0.387223	0.0408169
$91$	−4.85115	−0.508538
$92$	3.21735	0.335432
$93$	2.22679	0.230908
$94$	2.06719	0.213214
$95$	1.12556	0.115480
$96$	8.70103	0.888045
$97$	11.2210	1.13932	0.569662	−	0.821879i	$-0.307074\pi$
$97$	11.2210	1.13932	0.569662	+	0.821879i	$0.307074\pi$
$98$	0.922803	0.0932172
$99$	−1.25622	−0.126255
$100$	−6.14792	−0.614792
$101$	6.77092	0.673732	0.336866	−	0.941553i	$-0.390633\pi$
$101$	6.77092	0.673732	0.336866	+	0.941553i	$0.390633\pi$
$102$	9.97889	0.988057
$103$	2.91963	0.287679	0.143840	−	0.989601i	$-0.454055\pi$
$103$	2.91963	0.287679	0.143840	+	0.989601i	$0.454055\pi$
$104$	2.60279	0.255225
$105$	−0.767866	−0.0749360
$106$	−20.5091	−1.99202
$107$	−8.02324	−0.775636	−0.387818	−	0.921736i	$-0.626771\pi$
$107$	−8.02324	−0.775636	−0.387818	+	0.921736i	$0.626771\pi$
$108$	−7.01957	−0.675459
$109$	−1.00000	−0.0957826
$109$	−1.00000	−0.0957826
$110$	−0.479518	−0.0457202
$111$	−1.41167	−0.133990
$112$	12.5874	1.18940
$113$	−11.1729	−1.05106	−0.525530	−	0.850775i	$-0.676133\pi$
$113$	−11.1729	−1.05106	−0.525530	+	0.850775i	$0.676133\pi$
$114$	−13.3942	−1.25448
$115$	0.553703	0.0516331
$116$	6.02777	0.559664
$117$	−1.91832	−0.177349
$118$	−7.51460	−0.691775
$119$	10.0012	0.916807
$120$	0.411984	0.0376088
$121$	−9.44436	−0.858578
$122$	−7.39742	−0.669731
$123$	−10.7234	−0.966892
$124$	1.95742	0.175782
$125$	−2.12585	−0.190141
$126$	−4.61828	−0.411429
$127$	−20.4583	−1.81538	−0.907690	−	0.419641i	$-0.862156\pi$
$127$	−20.4583	−1.81538	−0.907690	+	0.419641i	$0.862156\pi$
$128$	−10.1451	−0.896706
$129$	−4.56120	−0.401591
$130$	−0.732250	−0.0642225
$131$	−15.9608	−1.39450	−0.697250	−	0.716828i	$-0.745593\pi$
$131$	−15.9608	−1.39450	−0.697250	+	0.716828i	$0.745593\pi$
$132$	2.18487	0.190168
$133$	−13.4241	−1.16402
$134$	9.31806	0.804958
$135$	−1.20806	−0.103974
$136$	−5.36595	−0.460126
$137$	−13.2797	−1.13456	−0.567282	−	0.823524i	$-0.692005\pi$
$137$	−13.2797	−1.13456	−0.567282	+	0.823524i	$0.692005\pi$
$138$	−6.58910	−0.560901
$139$	21.2954	1.80625	0.903124	−	0.429380i	$-0.141268\pi$
$139$	21.2954	1.80625	0.903124	+	0.429380i	$0.141268\pi$
$140$	−0.674979	−0.0570461
$141$	−1.62099	−0.136512
$142$	29.0581	2.43851
$143$	2.37555	0.198653
$144$	4.97750	0.414792
$145$	1.03737	0.0861493
$146$	7.95686	0.658514
$147$	−0.723618	−0.0596830
$148$	−1.24090	−0.102002
$149$	−18.6716	−1.52963	−0.764817	−	0.644247i	$-0.777171\pi$
$149$	−18.6716	−1.52963	−0.764817	+	0.644247i	$0.777171\pi$
$150$	12.5909	1.02804
$151$	−1.68125	−0.136818	−0.0684090	−	0.997657i	$-0.521792\pi$
$151$	−1.68125	−0.136818	−0.0684090	+	0.997657i	$0.521792\pi$
$152$	7.20246	0.584196
$153$	3.95483	0.319729
$154$	5.71904	0.460853
$155$	0.336871	0.0270582
$156$	3.33641	0.267127
$157$	−20.7802	−1.65844	−0.829221	−	0.558921i	$-0.811216\pi$
$157$	−20.7802	−1.65844	−0.829221	+	0.558921i	$0.811216\pi$
$158$	5.26439	0.418812
$159$	16.0822	1.27540
$160$	1.31630	0.104063
$161$	−6.60383	−0.520454
$162$	8.93644	0.702113
$163$	−1.41071	−0.110495	−0.0552475	−	0.998473i	$-0.517595\pi$
$163$	−1.41071	−0.110495	−0.0552475	+	0.998473i	$0.517595\pi$
$164$	−9.42618	−0.736061
$165$	0.376014	0.0292727
$166$	−14.0964	−1.09409
$167$	17.5776	1.36020	0.680100	−	0.733120i	$-0.261937\pi$
$167$	17.5776	1.36020	0.680100	+	0.733120i	$0.261937\pi$
$168$	−4.91359	−0.379092
$169$	−9.37241	−0.720955
$170$	1.50961	0.115782
$171$	−5.30838	−0.405942
$172$	−4.00944	−0.305717
$173$	−14.5096	−1.10314	−0.551572	−	0.834127i	$-0.685972\pi$
$173$	−14.5096	−1.10314	−0.551572	+	0.834127i	$0.685972\pi$
$174$	−12.3448	−0.935858
$175$	12.6190	0.953909
$176$	−6.16388	−0.464620
$177$	5.89258	0.442914
$178$	−8.85634	−0.663810
$179$	12.3478	0.922918	0.461459	−	0.887161i	$-0.347326\pi$
$179$	12.3478	0.922918	0.461459	+	0.887161i	$0.347326\pi$
$180$	−0.266911	−0.0198944
$181$	22.1524	1.64657	0.823287	−	0.567626i	$-0.192138\pi$
$181$	22.1524	1.64657	0.823287	+	0.567626i	$0.192138\pi$
$182$	8.73328	0.647354
$183$	5.80069	0.428800
$184$	3.54316	0.261205
$185$	−0.213559	−0.0157011
$186$	−4.00879	−0.293938
$187$	−4.89746	−0.358138
$188$	−1.42490	−0.103922
$189$	14.4082	1.04804
$190$	−2.02628	−0.147002
$191$	15.1479	1.09607	0.548033	−	0.836456i	$-0.315377\pi$
$191$	15.1479	1.09607	0.548033	+	0.836456i	$0.315377\pi$
$192$	−1.71120	−0.123495
$193$	−23.5997	−1.69874	−0.849372	−	0.527794i	$-0.823019\pi$
$193$	−23.5997	−1.69874	−0.849372	+	0.527794i	$0.823019\pi$
$194$	−20.2007	−1.45032
$195$	0.574195	0.0411189
$196$	−0.636083	−0.0454345
$197$	−18.6758	−1.33060	−0.665298	−	0.746578i	$-0.731696\pi$
$197$	−18.6758	−1.33060	−0.665298	+	0.746578i	$0.731696\pi$
$198$	2.26151	0.160719
$199$	6.98773	0.495347	0.247674	−	0.968844i	$-0.420334\pi$
$199$	6.98773	0.495347	0.247674	+	0.968844i	$0.420334\pi$
$200$	−6.77050	−0.478747
$201$	−7.30677	−0.515380
$202$	−12.1894	−0.857640
$203$	−12.3724	−0.868372
$204$	−6.87839	−0.481584
$205$	−1.62224	−0.113302
$206$	−5.25606	−0.366207
$207$	−2.61139	−0.181504
$208$	−9.41258	−0.652645
$209$	6.57363	0.454707
$210$	1.38235	0.0953913
$211$	−12.7140	−0.875266	−0.437633	−	0.899154i	$-0.644183\pi$
$211$	−12.7140	−0.875266	−0.437633	+	0.899154i	$0.644183\pi$
$212$	14.1368	0.970920
$213$	−22.7860	−1.56127
$214$	14.4438	0.987361
$215$	−0.690022	−0.0470591
$216$	−7.73042	−0.525989
$217$	−4.01775	−0.272742
$218$	1.80025	0.121928
$219$	−6.23938	−0.421618
$220$	0.330529	0.0222843
$221$	−7.47868	−0.503071
$222$	2.54136	0.170565
$223$	16.6781	1.11685	0.558425	−	0.829555i	$-0.311406\pi$
$223$	16.6781	1.11685	0.558425	+	0.829555i	$0.311406\pi$
$224$	−15.6990	−1.04894
$225$	4.99002	0.332668
$226$	20.1140	1.33797
$227$	−13.6199	−0.903982	−0.451991	−	0.892023i	$-0.649286\pi$
$227$	−13.6199	−0.903982	−0.451991	+	0.892023i	$0.649286\pi$
$228$	9.23254	0.611440
$229$	−15.5217	−1.02571	−0.512853	−	0.858477i	$-0.671411\pi$
$229$	−15.5217	−1.02571	−0.512853	+	0.858477i	$0.671411\pi$
$230$	−0.996805	−0.0657274
$231$	−4.48459	−0.295065
$232$	6.63818	0.435818
$233$	−0.525509	−0.0344273	−0.0172136	−	0.999852i	$-0.505480\pi$
$233$	−0.525509	−0.0344273	−0.0172136	+	0.999852i	$0.505480\pi$
$234$	3.45345	0.225759
$235$	−0.245225	−0.0159967
$236$	5.17977	0.337174
$237$	−4.12808	−0.268148
$238$	−18.0046	−1.16707
$239$	−25.9358	−1.67765	−0.838824	−	0.544403i	$-0.816756\pi$
$239$	−25.9358	−1.67765	−0.838824	+	0.544403i	$0.816756\pi$
$240$	−1.48987	−0.0961710
$241$	−1.29649	−0.0835143	−0.0417572	−	0.999128i	$-0.513296\pi$
$241$	−1.29649	−0.0835143	−0.0417572	+	0.999128i	$0.513296\pi$
$242$	17.0022	1.09294
$243$	9.96296	0.639124
$244$	5.09900	0.326430
$245$	−0.109470	−0.00699375
$246$	19.3047	1.23082
$247$	10.0383	0.638721
$248$	2.15565	0.136884
$249$	11.0537	0.700501
$250$	3.82706	0.242044
$251$	22.6741	1.43117	0.715587	−	0.698524i	$-0.246159\pi$
$251$	22.6741	1.43117	0.715587	+	0.698524i	$0.246159\pi$
$252$	3.18335	0.200532
$253$	3.23381	0.203308
$254$	36.8301	2.31092
$255$	−1.18377	−0.0741303
$256$	20.6880	1.29300
$257$	5.53155	0.345049	0.172524	−	0.985005i	$-0.444808\pi$
$257$	5.53155	0.345049	0.172524	+	0.985005i	$0.444808\pi$
$258$	8.21130	0.511213
$259$	2.54704	0.158265
$260$	0.504736	0.0313024
$261$	−4.89249	−0.302838
$262$	28.7334	1.77516
$263$	−24.3064	−1.49880	−0.749398	−	0.662119i	$-0.769657\pi$
$263$	−24.3064	−1.49880	−0.749398	+	0.662119i	$0.769657\pi$
$264$	2.40612	0.148087
$265$	2.43293	0.149454
$266$	24.1668	1.48176
$267$	6.94471	0.425009
$268$	−6.42289	−0.392340
$269$	2.16670	0.132106	0.0660531	−	0.997816i	$-0.478959\pi$
$269$	2.16670	0.132106	0.0660531	+	0.997816i	$0.478959\pi$
$270$	2.17482	0.132355
$271$	−5.39620	−0.327796	−0.163898	−	0.986477i	$-0.552407\pi$
$271$	−5.39620	−0.327796	−0.163898	+	0.986477i	$0.552407\pi$
$272$	19.4051	1.17661
$273$	−6.84822	−0.414473
$274$	23.9068	1.44426
$275$	−6.17938	−0.372631
$276$	4.54183	0.273386
$277$	3.88107	0.233191	0.116595	−	0.993179i	$-0.462802\pi$
$277$	3.88107	0.233191	0.116595	+	0.993179i	$0.462802\pi$
$278$	−38.3370	−2.29930
$279$	−1.58876	−0.0951166
$280$	−0.743332	−0.0444226
$281$	−10.8055	−0.644603	−0.322302	−	0.946637i	$-0.604457\pi$
$281$	−10.8055	−0.644603	−0.322302	+	0.946637i	$0.604457\pi$
$282$	2.91819	0.173776
$283$	5.45346	0.324175	0.162087	−	0.986776i	$-0.448177\pi$
$283$	5.45346	0.324175	0.162087	+	0.986776i	$0.448177\pi$
$284$	−20.0296	−1.18854
$285$	1.58891	0.0941191
$286$	−4.27658	−0.252880
$287$	19.3479	1.14207
$288$	−6.20797	−0.365808
$289$	−1.58185	−0.0930500
$290$	−1.86753	−0.109665
$291$	15.8404	0.928580
$292$	−5.48462	−0.320963
$293$	6.74315	0.393939	0.196970	−	0.980410i	$-0.436890\pi$
$293$	6.74315	0.393939	0.196970	+	0.980410i	$0.436890\pi$
$294$	1.30269	0.0759746
$295$	0.891435	0.0519014
$296$	−1.36657	−0.0794300
$297$	−7.05550	−0.409401
$298$	33.6135	1.94718
$299$	4.93821	0.285584
$300$	−8.67883	−0.501072
$301$	8.22965	0.474349
$302$	3.02667	0.174165
$303$	9.55830	0.549110
$304$	−26.0465	−1.49387
$305$	0.877534	0.0502475
$306$	−7.11968	−0.407005
$307$	−7.00194	−0.399622	−0.199811	−	0.979834i	$-0.564033\pi$
$307$	−7.00194	−0.399622	−0.199811	+	0.979834i	$0.564033\pi$
$308$	−3.94210	−0.224622
$309$	4.12155	0.234467
$310$	−0.606453	−0.0344442
$311$	6.95327	0.394284	0.197142	−	0.980375i	$-0.436834\pi$
$311$	6.95327	0.394284	0.197142	+	0.980375i	$0.436834\pi$
$312$	3.67428	0.208015
$313$	23.7959	1.34502	0.672512	−	0.740086i	$-0.265215\pi$
$313$	23.7959	1.34502	0.672512	+	0.740086i	$0.265215\pi$
$314$	37.4096	2.11115
$315$	0.547853	0.0308680
$316$	−3.62872	−0.204131
$317$	0.222151	0.0124773	0.00623863	−	0.999981i	$-0.498014\pi$
$317$	0.222151	0.0124773	0.00623863	+	0.999981i	$0.498014\pi$
$318$	−28.9521	−1.62355
$319$	6.05861	0.339217
$320$	−0.258871	−0.0144713
$321$	−11.3262	−0.632165
$322$	11.8885	0.662523
$323$	−20.6950	−1.15150
$324$	−6.15984	−0.342213
$325$	−9.43625	−0.523429
$326$	2.53962	0.140657
$327$	−1.41167	−0.0780655
$328$	−10.3807	−0.573180
$329$	2.92471	0.161245
$330$	−0.676920	−0.0372632
$331$	−28.7581	−1.58069	−0.790343	−	0.612665i	$-0.790098\pi$
$331$	−28.7581	−1.58069	−0.790343	+	0.612665i	$0.790098\pi$
$332$	9.71658	0.533267
$333$	1.00719	0.0551937
$334$	−31.6442	−1.73149
$335$	−1.10537	−0.0603931
$336$	17.7692	0.969390
$337$	1.70024	0.0926181	0.0463090	−	0.998927i	$-0.485254\pi$
$337$	1.70024	0.0926181	0.0463090	+	0.998927i	$0.485254\pi$
$338$	16.8727	0.917753
$339$	−15.7725	−0.856642
$340$	−1.04057	−0.0564328
$341$	1.96744	0.106543
$342$	9.55641	0.516752
$343$	19.1349	1.03319
$344$	−4.41546	−0.238066
$345$	0.781646	0.0420824
$346$	26.1209	1.40427
$347$	−28.8999	−1.55143	−0.775714	−	0.631085i	$-0.782610\pi$
$347$	−28.8999	−1.55143	−0.775714	+	0.631085i	$0.782610\pi$
$348$	8.50921	0.456142
$349$	14.5565	0.779194	0.389597	−	0.920985i	$-0.372614\pi$
$349$	14.5565	0.779194	0.389597	+	0.920985i	$0.372614\pi$
$350$	−22.7174	−1.21430
$351$	−10.7741	−0.575080
$352$	7.68763	0.409752
$353$	0.608885	0.0324077	0.0162038	−	0.999869i	$-0.494842\pi$
$353$	0.608885	0.0324077	0.0162038	+	0.999869i	$0.494842\pi$
$354$	−10.6081	−0.563815
$355$	−3.44708	−0.182952
$356$	6.10462	0.323544
$357$	14.1184	0.747223
$358$	−22.2291	−1.17485
$359$	4.48611	0.236768	0.118384	−	0.992968i	$-0.462229\pi$
$359$	4.48611	0.236768	0.118384	+	0.992968i	$0.462229\pi$
$360$	−0.293940	−0.0154920
$361$	8.77798	0.461999
$362$	−39.8798	−2.09604
$363$	−13.3323	−0.699765
$364$	−6.01980	−0.315523
$365$	−0.943899	−0.0494059
$366$	−10.4427	−0.545849
$367$	−11.0145	−0.574952	−0.287476	−	0.957788i	$-0.592816\pi$
$367$	−11.0145	−0.574952	−0.287476	+	0.957788i	$0.592816\pi$
$368$	−12.8133	−0.667938
$369$	7.65084	0.398287
$370$	0.384459	0.0199871
$371$	−29.0168	−1.50648
$372$	2.76323	0.143267
$373$	7.38632	0.382449	0.191225	−	0.981546i	$-0.438754\pi$
$373$	7.38632	0.382449	0.191225	+	0.981546i	$0.438754\pi$
$374$	8.81665	0.455898
$375$	−3.00099	−0.154971
$376$	−1.56920	−0.0809252
$377$	9.25183	0.476494
$378$	−25.9383	−1.33412
$379$	22.1161	1.13603	0.568013	−	0.823019i	$-0.307712\pi$
$379$	22.1161	1.13603	0.568013	+	0.823019i	$0.307712\pi$
$380$	1.39671	0.0716495
$381$	−28.8803	−1.47959
$382$	−27.2701	−1.39526
$383$	−17.9409	−0.916735	−0.458367	−	0.888763i	$-0.651566\pi$
$383$	−17.9409	−0.916735	−0.458367	+	0.888763i	$0.651566\pi$
$384$	−14.3215	−0.730840
$385$	−0.678433	−0.0345762
$386$	42.4854	2.16245
$387$	3.25430	0.165425
$388$	13.9242	0.706895
$389$	−2.56891	−0.130249	−0.0651244	−	0.997877i	$-0.520744\pi$
$389$	−2.56891	−0.130249	−0.0651244	+	0.997877i	$0.520744\pi$
$390$	−1.03369	−0.0523431
$391$	−10.1807	−0.514859
$392$	−0.700497	−0.0353805
$393$	−22.5313	−1.13656
$394$	33.6211	1.69381
$395$	−0.624500	−0.0314220
$396$	−1.55885	−0.0783351
$397$	−5.25847	−0.263915	−0.131958	−	0.991255i	$-0.542126\pi$
$397$	−5.25847	−0.263915	−0.131958	+	0.991255i	$0.542126\pi$
$398$	−12.5797	−0.630562
$399$	−18.9504	−0.948707
$400$	24.4844	1.22422
$401$	−26.7064	−1.33366	−0.666828	−	0.745212i	$-0.732348\pi$
$401$	−26.7064	−1.33366	−0.666828	+	0.745212i	$0.732348\pi$
$402$	13.1540	0.656063
$403$	3.00439	0.149659
$404$	8.40205	0.418018
$405$	−1.06010	−0.0526770
$406$	22.2734	1.10541
$407$	−1.24725	−0.0618240
$408$	−7.57494	−0.375016
$409$	7.22754	0.357379	0.178689	−	0.983906i	$-0.442814\pi$
$409$	7.22754	0.357379	0.178689	+	0.983906i	$0.442814\pi$
$410$	2.92044	0.144230
$411$	−18.7466	−0.924701
$412$	3.62297	0.178491
$413$	−10.6318	−0.523158
$414$	4.70116	0.231049
$415$	1.67222	0.0820859
$416$	11.7394	0.575573
$417$	30.0620	1.47214
$418$	−11.8342	−0.578828
$419$	−30.1586	−1.47335	−0.736673	−	0.676249i	$-0.763604\pi$
$419$	−30.1586	−1.47335	−0.736673	+	0.676249i	$0.763604\pi$
$420$	−0.952847	−0.0464942
$421$	−38.2342	−1.86342	−0.931711	−	0.363201i	$-0.881684\pi$
$421$	−38.2342	−1.86342	−0.931711	+	0.363201i	$0.881684\pi$
$422$	22.8883	1.11419
$423$	1.15654	0.0562327
$424$	15.5684	0.756068
$425$	19.4539	0.943652
$426$	41.0205	1.98745
$427$	−10.4660	−0.506487
$428$	−9.95606	−0.481244
$429$	3.35349	0.161908
$430$	1.24221	0.0599048
$431$	29.8305	1.43688	0.718441	−	0.695588i	$-0.244856\pi$
$431$	29.8305	1.43688	0.718441	+	0.695588i	$0.244856\pi$
$432$	27.9558	1.34503
$433$	−39.4970	−1.89810	−0.949052	−	0.315120i	$-0.897955\pi$
$433$	−39.4970	−1.89810	−0.949052	+	0.315120i	$0.897955\pi$
$434$	7.23295	0.347193
$435$	1.46443	0.0702140
$436$	−1.24090	−0.0594285
$437$	13.6650	0.653687
$438$	11.2324	0.536707
$439$	−6.49411	−0.309947	−0.154974	−	0.987919i	$-0.549529\pi$
$439$	−6.49411	−0.309947	−0.154974	+	0.987919i	$0.549529\pi$
$440$	0.364001	0.0173530
$441$	0.516283	0.0245849
$442$	13.4635	0.640394
$443$	−30.9260	−1.46934	−0.734669	−	0.678426i	$-0.762663\pi$
$443$	−30.9260	−1.46934	−0.734669	+	0.678426i	$0.762663\pi$
$444$	−1.75174	−0.0831341
$445$	1.05060	0.0498033
$446$	−30.0248	−1.42172
$447$	−26.3581	−1.24669
$448$	3.08747	0.145869
$449$	−25.2817	−1.19312	−0.596559	−	0.802570i	$-0.703466\pi$
$449$	−25.2817	−1.19312	−0.596559	+	0.802570i	$0.703466\pi$
$450$	−8.98328	−0.423476
$451$	−9.47441	−0.446133
$452$	−13.8645	−0.652131
$453$	−2.37336	−0.111510
$454$	24.5192	1.15074
$455$	−1.03600	−0.0485686
$456$	10.1675	0.476136
$457$	38.5460	1.80310	0.901552	−	0.432671i	$-0.142429\pi$
$457$	38.5460	1.80310	0.901552	+	0.432671i	$0.142429\pi$
$458$	27.9430	1.30569
$459$	22.2121	1.03677
$460$	0.687092	0.0320358
$461$	−37.5321	−1.74805	−0.874023	−	0.485884i	$-0.838498\pi$
$461$	−37.5321	−1.74805	−0.874023	+	0.485884i	$0.838498\pi$
$462$	8.07339	0.375608
$463$	40.8846	1.90007	0.950033	−	0.312149i	$-0.101049\pi$
$463$	40.8846	1.90007	0.950033	+	0.312149i	$0.101049\pi$
$464$	−24.0059	−1.11445
$465$	0.475551	0.0220531
$466$	0.946049	0.0438249
$467$	23.3733	1.08159	0.540794	−	0.841155i	$-0.318124\pi$
$467$	23.3733	1.08159	0.540794	+	0.841155i	$0.318124\pi$
$468$	−2.38045	−0.110036
$469$	13.1834	0.608753
$470$	0.441466	0.0203633
$471$	−29.3348	−1.35168
$472$	5.70431	0.262562
$473$	−4.02996	−0.185298
$474$	7.43158	0.341344
$475$	−26.1120	−1.19810
$476$	12.4105	0.568834
$477$	−11.4743	−0.525371
$478$	46.6909	2.13559
$479$	−38.0047	−1.73648	−0.868240	−	0.496144i	$-0.834749\pi$
$479$	−38.0047	−1.73648	−0.868240	+	0.496144i	$0.834749\pi$
$480$	1.85818	0.0848139
$481$	−1.90462	−0.0868433
$482$	2.33401	0.106311
$483$	−9.32242	−0.424185
$484$	−11.7195	−0.532706
$485$	2.39635	0.108813
$486$	−17.9358	−0.813586
$487$	−13.8591	−0.628015	−0.314007	−	0.949421i	$-0.601672\pi$
$487$	−13.8591	−0.628015	−0.314007	+	0.949421i	$0.601672\pi$
$488$	5.61536	0.254195
$489$	−1.99145	−0.0900565
$490$	0.197073	0.00890283
$491$	29.9389	1.35112	0.675562	−	0.737303i	$-0.263901\pi$
$491$	29.9389	1.35112	0.675562	+	0.737303i	$0.263901\pi$
$492$	−13.3066	−0.599910
$493$	−19.0737	−0.859036
$494$	−18.0714	−0.813072
$495$	−0.268277	−0.0120581
$496$	−7.79555	−0.350030
$497$	41.1122	1.84413
$498$	−19.8995	−0.891717
$499$	−16.9268	−0.757745	−0.378873	−	0.925449i	$-0.623688\pi$
$499$	−16.9268	−0.757745	−0.378873	+	0.925449i	$0.623688\pi$
$500$	−2.63797	−0.117974
$501$	24.8138	1.10860
$502$	−40.8190	−1.82184
$503$	−38.7637	−1.72839	−0.864193	−	0.503161i	$-0.832170\pi$
$503$	−38.7637	−1.72839	−0.864193	+	0.503161i	$0.832170\pi$
$504$	3.50572	0.156157
$505$	1.44599	0.0643456
$506$	−5.82167	−0.258805
$507$	−13.2307	−0.587598
$508$	−25.3868	−1.12636
$509$	−17.6837	−0.783816	−0.391908	−	0.920004i	$-0.628185\pi$
$509$	−17.6837	−0.783816	−0.391908	+	0.920004i	$0.628185\pi$
$510$	2.13108	0.0943657
$511$	11.2575	0.498005
$512$	−16.9535	−0.749246
$513$	−29.8142	−1.31633
$514$	−9.95818	−0.439237
$515$	0.623511	0.0274752
$516$	−5.66000	−0.249168
$517$	−1.43220	−0.0629879
$518$	−4.58531	−0.201467
$519$	−20.4827	−0.899092
$520$	0.555849	0.0243756
$521$	5.32183	0.233154	0.116577	−	0.993182i	$-0.462808\pi$
$521$	5.32183	0.233154	0.116577	+	0.993182i	$0.462808\pi$
$522$	8.80771	0.385503
$523$	8.01136	0.350312	0.175156	−	0.984541i	$-0.443957\pi$
$523$	8.01136	0.350312	0.175156	+	0.984541i	$0.443957\pi$
$524$	−19.8058	−0.865219
$525$	17.8139	0.777462
$526$	43.7576	1.90792
$527$	−6.19388	−0.269810
$528$	−8.70136	−0.378678
$529$	−16.2777	−0.707724
$530$	−4.37989	−0.190250
$531$	−4.20421	−0.182447
$532$	−16.6580	−0.722217
$533$	−14.4679	−0.626676
$534$	−12.5022	−0.541024
$535$	−1.71343	−0.0740781
$536$	−7.07331	−0.305521
$537$	17.4310	0.752204
$538$	−3.90061	−0.168167
$539$	−0.639338	−0.0275383
$540$	−1.49909	−0.0645106
$541$	41.5949	1.78831	0.894153	−	0.447762i	$-0.147779\pi$
$541$	41.5949	1.78831	0.894153	+	0.447762i	$0.147779\pi$
$542$	9.71451	0.417274
$543$	31.2718	1.34200
$544$	−24.2021	−1.03766
$545$	−0.213559	−0.00914784
$546$	12.3285	0.527611
$547$	−2.56527	−0.109683	−0.0548416	−	0.998495i	$-0.517465\pi$
$547$	−2.56527	−0.109683	−0.0548416	+	0.998495i	$0.517465\pi$
$548$	−16.4789	−0.703942
$549$	−4.13865	−0.176633
$550$	11.1244	0.474348
$551$	25.6017	1.09067
$552$	5.00177	0.212889
$553$	7.44819	0.316729
$554$	−6.98690	−0.296845
$555$	−0.301474	−0.0127969
$556$	26.4255	1.12069
$557$	4.01493	0.170118	0.0850590	−	0.996376i	$-0.472892\pi$
$557$	4.01493	0.170118	0.0850590	+	0.996376i	$0.472892\pi$
$558$	2.86017	0.121081
$559$	−6.15396	−0.260285
$560$	2.68814	0.113595
$561$	−6.91359	−0.291892
$562$	19.4526	0.820560
$563$	5.53414	0.233236	0.116618	−	0.993177i	$-0.462795\pi$
$563$	5.53414	0.233236	0.116618	+	0.993177i	$0.462795\pi$
$564$	−2.01149	−0.0846991
$565$	−2.38607	−0.100383
$566$	−9.81760	−0.412665
$567$	12.6435	0.530977
$568$	−22.0580	−0.925531
$569$	−4.96786	−0.208263	−0.104132	−	0.994564i	$-0.533206\pi$
$569$	−4.96786	−0.208263	−0.104132	+	0.994564i	$0.533206\pi$
$570$	−2.86044	−0.119811
$571$	0.262219	0.0109735	0.00548676	−	0.999985i	$-0.498253\pi$
$571$	0.262219	0.0109735	0.00548676	+	0.999985i	$0.498253\pi$
$572$	2.94782	0.123255
$573$	21.3839	0.893325
$574$	−34.8310	−1.45382
$575$	−12.8455	−0.535694
$576$	1.22090	0.0508706
$577$	−27.1979	−1.13226	−0.566131	−	0.824315i	$-0.691560\pi$
$577$	−27.1979	−1.13226	−0.566131	+	0.824315i	$0.691560\pi$
$578$	2.84773	0.118450
$579$	−33.3150	−1.38452
$580$	1.28728	0.0534514
$581$	−19.9439	−0.827414
$582$	−28.5167	−1.18205
$583$	14.2091	0.588483
$584$	−6.04003	−0.249938
$585$	−0.409673	−0.0169379
$586$	−12.1394	−0.501472
$587$	−39.4103	−1.62664	−0.813319	−	0.581818i	$-0.802341\pi$
$587$	−39.4103	−1.62664	−0.813319	+	0.581818i	$0.802341\pi$
$588$	−0.897939	−0.0370304
$589$	8.31376	0.342562
$590$	−1.60481	−0.0660688
$591$	−26.3641	−1.08447
$592$	4.94197	0.203114
$593$	41.0366	1.68517	0.842586	−	0.538562i	$-0.181032\pi$
$593$	41.0366	1.68517	0.842586	+	0.538562i	$0.181032\pi$
$594$	12.7017	0.521155
$595$	2.13584	0.0875609
$596$	−23.1696	−0.949064
$597$	9.86437	0.403722
$598$	−8.89001	−0.363540
$599$	−30.6206	−1.25112	−0.625562	−	0.780175i	$-0.715130\pi$
$599$	−30.6206	−1.25112	−0.625562	+	0.780175i	$0.715130\pi$
$600$	−9.55771	−0.390192
$601$	19.2508	0.785257	0.392629	−	0.919697i	$-0.371566\pi$
$601$	19.2508	0.785257	0.392629	+	0.919697i	$0.371566\pi$
$602$	−14.8154	−0.603832
$603$	5.21319	0.212298
$604$	−2.08626	−0.0848889
$605$	−2.01692	−0.0819996
$606$	−17.2073	−0.699000
$607$	−15.0844	−0.612257	−0.306128	−	0.951990i	$-0.599034\pi$
$607$	−15.0844	−0.612257	−0.306128	+	0.951990i	$0.599034\pi$
$608$	32.4854	1.31746
$609$	−17.4657	−0.707747
$610$	−1.57978	−0.0639635
$611$	−2.18704	−0.0884782
$612$	4.90756	0.198376
$613$	−11.2684	−0.455128	−0.227564	−	0.973763i	$-0.573076\pi$
$613$	−11.2684	−0.455128	−0.227564	+	0.973763i	$0.573076\pi$
$614$	12.6053	0.508707
$615$	−2.29006	−0.0923443
$616$	−4.34131	−0.174916
$617$	−46.9949	−1.89194	−0.945972	−	0.324247i	$-0.894889\pi$
$617$	−46.9949	−1.89194	−0.945972	+	0.324247i	$0.894889\pi$
$618$	−7.41982	−0.298469
$619$	−41.6769	−1.67514	−0.837569	−	0.546332i	$-0.816024\pi$
$619$	−41.6769	−1.67514	−0.837569	+	0.546332i	$0.816024\pi$
$620$	0.418025	0.0167883
$621$	−14.6667	−0.588555
$622$	−12.5176	−0.501911
$623$	−12.5302	−0.502010
$624$	−13.2875	−0.531924
$625$	24.3180	0.972719
$626$	−42.8386	−1.71217
$627$	9.27978	0.370599
$628$	−25.7862	−1.02898
$629$	3.92660	0.156564
$630$	−0.986273	−0.0392940
$631$	45.7407	1.82091	0.910454	−	0.413610i	$-0.135732\pi$
$631$	45.7407	1.82091	0.910454	+	0.413610i	$0.135732\pi$
$632$	−3.99618	−0.158960
$633$	−17.9479	−0.713366
$634$	−0.399928	−0.0158832
$635$	−4.36904	−0.173380
$636$	19.9565	0.791326
$637$	−0.976305	−0.0386826
$638$	−10.9070	−0.431813
$639$	16.2572	0.643126
$640$	−2.16657	−0.0856411
$641$	−21.0365	−0.830893	−0.415447	−	0.909618i	$-0.636375\pi$
$641$	−21.0365	−0.830893	−0.415447	+	0.909618i	$0.636375\pi$
$642$	20.3899	0.804726
$643$	46.3141	1.82645	0.913224	−	0.407458i	$-0.133585\pi$
$643$	46.3141	1.82645	0.913224	+	0.407458i	$0.133585\pi$
$644$	−8.19471	−0.322917
$645$	−0.974083	−0.0383545
$646$	37.2563	1.46583
$647$	40.7174	1.60077	0.800383	−	0.599489i	$-0.204630\pi$
$647$	40.7174	1.60077	0.800383	+	0.599489i	$0.204630\pi$
$648$	−6.78363	−0.266486
$649$	5.20628	0.204364
$650$	16.9876	0.666309
$651$	−5.67173	−0.222293
$652$	−1.75055	−0.0685568
$653$	−46.9420	−1.83698	−0.918491	−	0.395442i	$-0.870591\pi$
$653$	−46.9420	−1.83698	−0.918491	+	0.395442i	$0.870591\pi$
$654$	2.54136	0.0993750
$655$	−3.40856	−0.133184
$656$	37.5403	1.46570
$657$	4.45164	0.173675
$658$	−5.26521	−0.205259
$659$	15.0726	0.587147	0.293573	−	0.955937i	$-0.405156\pi$
$659$	15.0726	0.587147	0.293573	+	0.955937i	$0.405156\pi$
$660$	0.466597	0.0181623
$661$	14.8072	0.575933	0.287967	−	0.957640i	$-0.407021\pi$
$661$	14.8072	0.575933	0.287967	+	0.957640i	$0.407021\pi$
$662$	51.7717	2.01216
$663$	−10.5574	−0.410017
$664$	10.7005	0.415262
$665$	−2.86684	−0.111171
$666$	−1.81319	−0.0702599
$667$	12.5944	0.487659
$668$	21.8122	0.843938
$669$	23.5440	0.910263
$670$	1.98995	0.0768785
$671$	5.12509	0.197852
$672$	−22.1619	−0.854912
$673$	46.0429	1.77482	0.887412	−	0.460978i	$-0.152501\pi$
$673$	46.0429	1.77482	0.887412	+	0.460978i	$0.152501\pi$
$674$	−3.06086	−0.117900
$675$	28.0261	1.07873
$676$	−11.6303	−0.447317
$677$	20.6941	0.795339	0.397669	−	0.917529i	$-0.369819\pi$
$677$	20.6941	0.795339	0.397669	+	0.917529i	$0.369819\pi$
$678$	28.3944	1.09048
$679$	−28.5804	−1.09682
$680$	−1.14594	−0.0439450
$681$	−19.2267	−0.736770
$682$	−3.54189	−0.135626
$683$	−20.2855	−0.776202	−0.388101	−	0.921617i	$-0.626869\pi$
$683$	−20.2855	−0.776202	−0.388101	+	0.921617i	$0.626869\pi$
$684$	−6.58718	−0.251867
$685$	−2.83600	−0.108358
$686$	−34.4476	−1.31521
$687$	−21.9116	−0.835978
$688$	15.9678	0.608767
$689$	21.6981	0.826633
$690$	−1.40716	−0.0535696
$691$	3.13865	0.119400	0.0596999	−	0.998216i	$-0.480986\pi$
$691$	3.13865	0.119400	0.0596999	+	0.998216i	$0.480986\pi$
$692$	−18.0050	−0.684447
$693$	3.19964	0.121544
$694$	52.0271	1.97492
$695$	4.54781	0.172508
$696$	9.37091	0.355204
$697$	29.8273	1.12979
$698$	−26.2054	−0.991890
$699$	−0.741845	−0.0280592
$700$	15.6590	0.591854
$701$	−2.61768	−0.0988684	−0.0494342	−	0.998777i	$-0.515742\pi$
$701$	−2.61768	−0.0988684	−0.0494342	+	0.998777i	$0.515742\pi$
$702$	19.3961	0.732060
$703$	−5.27048	−0.198780
$704$	−1.51189	−0.0569817
$705$	−0.346176	−0.0130378
$706$	−1.09615	−0.0412540
$707$	−17.2458	−0.648595
$708$	7.31212	0.274806
$709$	3.07494	0.115482	0.0577408	−	0.998332i	$-0.481610\pi$
$709$	3.07494	0.115482	0.0577408	+	0.998332i	$0.481610\pi$
$710$	6.20562	0.232893
$711$	2.94528	0.110457
$712$	6.72282	0.251948
$713$	4.08985	0.153166
$714$	−25.4166	−0.951192
$715$	0.507319	0.0189726
$716$	15.3224	0.572626
$717$	−36.6128	−1.36733
$718$	−8.07612	−0.301398
$719$	−46.9200	−1.74982	−0.874910	−	0.484285i	$-0.839080\pi$
$719$	−46.9200	−1.74982	−0.874910	+	0.484285i	$0.839080\pi$
$720$	1.06299	0.0396152
$721$	−7.43640	−0.276946
$722$	−15.8026	−0.588111
$723$	−1.83022	−0.0680665
$724$	27.4889	1.02162
$725$	−24.0663	−0.893799
$726$	24.0015	0.890779
$727$	23.0194	0.853743	0.426871	−	0.904312i	$-0.359616\pi$
$727$	23.0194	0.853743	0.426871	+	0.904312i	$0.359616\pi$
$728$	−6.62941	−0.245702
$729$	28.9564	1.07246
$730$	1.69925	0.0628922
$731$	12.6871	0.469249
$732$	7.19810	0.266049
$733$	−14.8495	−0.548478	−0.274239	−	0.961662i	$-0.588426\pi$
$733$	−14.8495	−0.548478	−0.274239	+	0.961662i	$0.588426\pi$
$734$	19.8288	0.731896
$735$	−0.154535	−0.00570010
$736$	15.9808	0.589059
$737$	−6.45576	−0.237801
$738$	−13.7734	−0.507007
$739$	18.8250	0.692488	0.346244	−	0.938145i	$-0.387457\pi$
$739$	18.8250	0.692488	0.346244	+	0.938145i	$0.387457\pi$
$740$	−0.265005	−0.00974179
$741$	14.1707	0.520575
$742$	52.2374	1.91770
$743$	13.5052	0.495458	0.247729	−	0.968829i	$-0.420316\pi$
$743$	13.5052	0.495458	0.247729	+	0.968829i	$0.420316\pi$
$744$	3.04306	0.111564
$745$	−3.98747	−0.146090
$746$	−13.2972	−0.486846
$747$	−7.88655	−0.288554
$748$	−6.07727	−0.222207
$749$	20.4355	0.746697
$750$	5.40254	0.197273
$751$	−24.1608	−0.881640	−0.440820	−	0.897596i	$-0.645312\pi$
$751$	−24.1608	−0.881640	−0.440820	+	0.897596i	$0.645312\pi$
$752$	5.67476	0.206937
$753$	32.0083	1.16645
$754$	−16.6556	−0.606562
$755$	−0.359045	−0.0130670
$756$	17.8791	0.650257
$757$	17.1605	0.623710	0.311855	−	0.950130i	$-0.399050\pi$
$757$	17.1605	0.623710	0.311855	+	0.950130i	$0.399050\pi$
$758$	−39.8145	−1.44613
$759$	4.56507	0.165702
$760$	1.53815	0.0557944
$761$	−8.22391	−0.298117	−0.149058	−	0.988828i	$-0.547624\pi$
$761$	−8.22391	−0.298117	−0.149058	+	0.988828i	$0.547624\pi$
$762$	51.9919	1.88347
$763$	2.54704	0.0922090
$764$	18.7971	0.680056
$765$	0.844588	0.0305361
$766$	32.2980	1.16698
$767$	7.95027	0.287068
$768$	29.2046	1.05383
$769$	31.8215	1.14751	0.573757	−	0.819026i	$-0.305485\pi$
$769$	31.8215	1.14751	0.573757	+	0.819026i	$0.305485\pi$
$770$	1.22135	0.0440144
$771$	7.80872	0.281224
$772$	−29.2849	−1.05399
$773$	36.9921	1.33051	0.665257	−	0.746614i	$-0.268322\pi$
$773$	36.9921	1.33051	0.665257	+	0.746614i	$0.268322\pi$
$774$	−5.85855	−0.210581
$775$	−7.81515	−0.280729
$776$	15.3343	0.550468
$777$	3.59558	0.128991
$778$	4.62468	0.165803
$779$	−40.0358	−1.43443
$780$	0.712520	0.0255123
$781$	−20.1321	−0.720384
$782$	18.3278	0.655399
$783$	−27.4784	−0.981998
$784$	2.53324	0.0904728
$785$	−4.43779	−0.158392
$786$	40.5621	1.44680
$787$	39.0593	1.39231	0.696156	−	0.717890i	$-0.254892\pi$
$787$	39.0593	1.39231	0.696156	+	0.717890i	$0.254892\pi$
$788$	−23.1749	−0.825570
$789$	−34.3126	−1.22156
$790$	1.12426	0.0399992
$791$	28.4578	1.01184
$792$	−1.71671	−0.0610006
$793$	7.82629	0.277920
$794$	9.46657	0.335956
$795$	3.43450	0.121809
$796$	8.67110	0.307339
$797$	−33.8021	−1.19733	−0.598666	−	0.800999i	$-0.704302\pi$
$797$	−33.8021	−1.19733	−0.598666	+	0.800999i	$0.704302\pi$
$798$	34.1155	1.20768
$799$	4.50883	0.159511
$800$	−30.5371	−1.07965
$801$	−4.95487	−0.175072
$802$	48.0783	1.69770
$803$	−5.51268	−0.194538
$804$	−9.06699	−0.319768
$805$	−1.41030	−0.0497067
$806$	−5.40865	−0.190512
$807$	3.05867	0.107670
$808$	9.25290	0.325516
$809$	16.1064	0.566272	0.283136	−	0.959080i	$-0.408625\pi$
$809$	16.1064	0.566272	0.283136	+	0.959080i	$0.408625\pi$
$810$	1.90845	0.0670562
$811$	−19.2934	−0.677482	−0.338741	−	0.940880i	$-0.610001\pi$
$811$	−19.2934	−0.677482	−0.338741	+	0.940880i	$0.610001\pi$
$812$	−15.3530	−0.538783
$813$	−7.61765	−0.267163
$814$	2.24537	0.0787001
$815$	−0.301268	−0.0105530
$816$	27.3936	0.958967
$817$	−17.0293	−0.595779
$818$	−13.0114	−0.454932
$819$	4.88603	0.170732
$820$	−2.01304	−0.0702984
$821$	17.1033	0.596908	0.298454	−	0.954424i	$-0.403529\pi$
$821$	17.1033	0.596908	0.298454	+	0.954424i	$0.403529\pi$
$822$	33.7485	1.17712
$823$	19.2070	0.669516	0.334758	−	0.942304i	$-0.391345\pi$
$823$	19.2070	0.669516	0.334758	+	0.942304i	$0.391345\pi$
$824$	3.98986	0.138993
$825$	−8.72324	−0.303704
$826$	19.1400	0.665964
$827$	8.31783	0.289239	0.144620	−	0.989487i	$-0.453804\pi$
$827$	8.31783	0.289239	0.144620	+	0.989487i	$0.453804\pi$
$828$	−3.24048	−0.112614
$829$	35.2352	1.22377	0.611884	−	0.790947i	$-0.290412\pi$
$829$	35.2352	1.22377	0.611884	+	0.790947i	$0.290412\pi$
$830$	−3.01041	−0.104493
$831$	5.47879	0.190057
$832$	−2.30875	−0.0800413
$833$	2.01276	0.0697381
$834$	−54.1191	−1.87399
$835$	3.75386	0.129908
$836$	8.15723	0.282124
$837$	−8.92318	−0.308430
$838$	54.2931	1.87552
$839$	52.8401	1.82424	0.912122	−	0.409919i	$-0.134443\pi$
$839$	52.8401	1.82424	0.912122	+	0.409919i	$0.134443\pi$
$840$	−1.04934	−0.0362056
$841$	−5.40406	−0.186347
$842$	68.8312	2.37208
$843$	−15.2538	−0.525369
$844$	−15.7768	−0.543060
$845$	−2.00156	−0.0688557
$846$	−2.08205	−0.0715825
$847$	24.0551	0.826545
$848$	−56.3006	−1.93337
$849$	7.69849	0.264211
$850$	−35.0219	−1.20124
$851$	−2.59275	−0.0888782
$852$	−28.2752	−0.968692
$853$	36.0002	1.23262	0.616311	−	0.787503i	$-0.288626\pi$
$853$	36.0002	1.23262	0.616311	+	0.787503i	$0.288626\pi$
$854$	18.8415	0.644743
$855$	−1.13365	−0.0387700
$856$	−10.9643	−0.374751
$857$	14.7071	0.502386	0.251193	−	0.967937i	$-0.419177\pi$
$857$	14.7071	0.502386	0.251193	+	0.967937i	$0.419177\pi$
$858$	−6.03712	−0.206104
$859$	−1.52695	−0.0520990	−0.0260495	−	0.999661i	$-0.508293\pi$
$859$	−1.52695	−0.0520990	−0.0260495	+	0.999661i	$0.508293\pi$
$860$	−0.856250	−0.0291979
$861$	27.3128	0.930818
$862$	−53.7023	−1.82911
$863$	−33.0974	−1.12665	−0.563324	−	0.826236i	$-0.690478\pi$
$863$	−33.0974	−1.12665	−0.563324	+	0.826236i	$0.690478\pi$
$864$	−34.8667	−1.18619
$865$	−3.09865	−0.105357
$866$	71.1045	2.41623
$867$	−2.23305	−0.0758384
$868$	−4.98563	−0.169223
$869$	−3.64729	−0.123726
$870$	−2.63634	−0.0893803
$871$	−9.85829	−0.334035
$872$	−1.36657	−0.0462777
$873$	−11.3017	−0.382505
$874$	−24.6005	−0.832124
$875$	5.41461	0.183047
$876$	−7.74246	−0.261594
$877$	41.9607	1.41691	0.708457	−	0.705754i	$-0.249392\pi$
$877$	41.9607	1.41691	0.708457	+	0.705754i	$0.249392\pi$
$878$	11.6910	0.394553
$879$	9.51910	0.321071
$880$	−1.31635	−0.0443741
$881$	12.1140	0.408130	0.204065	−	0.978957i	$-0.434585\pi$
$881$	12.1140	0.408130	0.204065	+	0.978957i	$0.434585\pi$
$882$	−0.929439	−0.0312958
$883$	6.11719	0.205860	0.102930	−	0.994689i	$-0.467178\pi$
$883$	6.11719	0.205860	0.102930	+	0.994689i	$0.467178\pi$
$884$	−9.28032	−0.312131
$885$	1.25841	0.0423010
$886$	55.6745	1.87042
$887$	−42.9961	−1.44367	−0.721834	−	0.692066i	$-0.756701\pi$
$887$	−42.9961	−1.44367	−0.721834	+	0.692066i	$0.756701\pi$
$888$	−1.92914	−0.0647376
$889$	52.1081	1.74765
$890$	−1.89135	−0.0633981
$891$	−6.19136	−0.207418
$892$	20.6959	0.692951
$893$	−6.05199	−0.202522
$894$	47.4511	1.58700
$895$	2.63698	0.0881445
$896$	25.8399	0.863250
$897$	6.97111	0.232759
$898$	45.5134	1.51880
$899$	7.66241	0.255556
$900$	6.19213	0.206404
$901$	−44.7332	−1.49028
$902$	17.0563	0.567913
$903$	11.6175	0.386608
$904$	−15.2685	−0.507823
$905$	4.73083	0.157258
$906$	4.27265	0.141949
$907$	−46.6362	−1.54853	−0.774265	−	0.632861i	$-0.781880\pi$
$907$	−46.6362	−1.54853	−0.774265	+	0.632861i	$0.781880\pi$
$908$	−16.9009	−0.560877
$909$	−6.81961	−0.226192
$910$	1.86507	0.0618264
$911$	−4.25752	−0.141058	−0.0705289	−	0.997510i	$-0.522469\pi$
$911$	−4.25752	−0.141058	−0.0705289	+	0.997510i	$0.522469\pi$
$912$	−36.7691	−1.21755
$913$	9.76630	0.323217
$914$	−69.3924	−2.29530
$915$	1.23879	0.0409531
$916$	−19.2610	−0.636400
$917$	40.6527	1.34247
$918$	−39.9873	−1.31978
$919$	−53.8262	−1.77556	−0.887782	−	0.460264i	$-0.847755\pi$
$919$	−53.8262	−1.77556	−0.887782	+	0.460264i	$0.847755\pi$
$920$	0.756672	0.0249467
$921$	−9.88443	−0.325703
$922$	67.5673	2.22521
$923$	−30.7428	−1.01191
$924$	−5.56494	−0.183073
$925$	4.95439	0.162899
$926$	−73.6025	−2.41873
$927$	−2.94062	−0.0965826
$928$	29.9403	0.982839
$929$	4.32903	0.142031	0.0710154	−	0.997475i	$-0.477376\pi$
$929$	4.32903	0.142031	0.0710154	+	0.997475i	$0.477376\pi$
$930$	−0.856111	−0.0280730
$931$	−2.70163	−0.0885425
$932$	−0.652106	−0.0213604
$933$	9.81571	0.321352
$934$	−42.0778	−1.37683
$935$	−1.04589	−0.0342044
$936$	−2.62151	−0.0856866
$937$	9.44016	0.308397	0.154198	−	0.988040i	$-0.450721\pi$
$937$	9.44016	0.308397	0.154198	+	0.988040i	$0.450721\pi$
$938$	−23.7335	−0.774925
$939$	33.5919	1.09623
$940$	−0.304300	−0.00992518
$941$	54.0288	1.76129	0.880644	−	0.473779i	$-0.157110\pi$
$941$	54.0288	1.76129	0.880644	+	0.473779i	$0.157110\pi$
$942$	52.8100	1.72064
$943$	−19.6951	−0.641360
$944$	−20.6287	−0.671408
$945$	3.07698	0.100094
$946$	7.25493	0.235878
$947$	−13.1895	−0.428602	−0.214301	−	0.976768i	$-0.568747\pi$
$947$	−13.1895	−0.428602	−0.214301	+	0.976768i	$0.568747\pi$
$948$	−5.12255	−0.166373
$949$	−8.41817	−0.273265
$950$	47.0082	1.52515
$951$	0.313604	0.0101693
$952$	13.6673	0.442959
$953$	40.4313	1.30970	0.654850	−	0.755759i	$-0.272732\pi$
$953$	40.4313	1.30970	0.654850	+	0.755759i	$0.272732\pi$
$954$	20.6566	0.668781
$955$	3.23497	0.104681
$956$	−32.1838	−1.04090
$957$	8.55276	0.276471
$958$	68.4180	2.21049
$959$	33.8240	1.09223
$960$	−0.365441	−0.0117945
$961$	−28.5118	−0.919734
$962$	3.42880	0.110549
$963$	8.08093	0.260404
$964$	−1.60882	−0.0518166
$965$	−5.03992	−0.162241
$966$	16.7827	0.539974
$967$	−16.8395	−0.541522	−0.270761	−	0.962647i	$-0.587275\pi$
$967$	−16.8395	−0.541522	−0.270761	+	0.962647i	$0.587275\pi$
$968$	−12.9063	−0.414825
$969$	−29.2146	−0.938507
$970$	−4.31403	−0.138515
$971$	13.1838	0.423087	0.211544	−	0.977369i	$-0.432151\pi$
$971$	13.1838	0.423087	0.211544	+	0.977369i	$0.432151\pi$
$972$	12.3631	0.396545
$973$	−54.2401	−1.73886
$974$	24.9498	0.799444
$975$	−13.3209	−0.426609
$976$	−20.3070	−0.650013
$977$	−47.5642	−1.52171	−0.760856	−	0.648921i	$-0.775221\pi$
$977$	−47.5642	−1.52171	−0.760856	+	0.648921i	$0.775221\pi$
$978$	3.58511	0.114639
$979$	6.13586	0.196103
$980$	−0.135841	−0.00433928
$981$	1.00719	0.0321571
$982$	−53.8976	−1.71994
$983$	−47.5978	−1.51813	−0.759067	−	0.651013i	$-0.774344\pi$
$983$	−47.5978	−1.51813	−0.759067	+	0.651013i	$0.774344\pi$
$984$	−14.6542	−0.467158
$985$	−3.98838	−0.127080
$986$	34.3374	1.09353
$987$	4.12872	0.131419
$988$	12.4565	0.396295
$989$	−8.37734	−0.266384
$990$	0.482966	0.0153497
$991$	12.2593	0.389429	0.194715	−	0.980860i	$-0.437622\pi$
$991$	12.2593	0.389429	0.194715	+	0.980860i	$0.437622\pi$
$992$	9.72265	0.308695
$993$	−40.5969	−1.28830
$994$	−74.0122	−2.34752
$995$	1.49229	0.0473088
$996$	13.7166	0.434627
$997$	21.3222	0.675281	0.337641	−	0.941275i	$-0.390371\pi$
$997$	21.3222	0.675281	0.337641	+	0.941275i	$0.390371\pi$
$998$	30.4724	0.964587
$999$	5.65683	0.178974

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4033.2.a.d.1.18	✓	79

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4033.2.a.d.1.18	✓	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)

\(f(q)\)	\(=\)	\(q-1.80025 q^{2} +1.41167 q^{3} +1.24090 q^{4} +0.213559 q^{5} -2.54136 q^{6} -2.54704 q^{7} +1.36657 q^{8} -1.00719 q^{9} +O(q^{10})\)	\(q-1.80025 q^{2} +1.41167 q^{3} +1.24090 q^{4} +0.213559 q^{5} -2.54136 q^{6} -2.54704 q^{7} +1.36657 q^{8} -1.00719 q^{9} -0.384459 q^{10} +1.24725 q^{11} +1.75174 q^{12} +1.90462 q^{13} +4.58531 q^{14} +0.301474 q^{15} -4.94197 q^{16} -3.92660 q^{17} +1.81319 q^{18} +5.27048 q^{19} +0.265005 q^{20} -3.59558 q^{21} -2.24537 q^{22} +2.59275 q^{23} +1.92914 q^{24} -4.95439 q^{25} -3.42880 q^{26} -5.65683 q^{27} -3.16063 q^{28} +4.85757 q^{29} -0.542729 q^{30} +1.57742 q^{31} +6.16365 q^{32} +1.76071 q^{33} +7.06886 q^{34} -0.543942 q^{35} -1.24983 q^{36} -1.00000 q^{37} -9.48819 q^{38} +2.68870 q^{39} +0.291842 q^{40} -7.59622 q^{41} +6.47294 q^{42} -3.23107 q^{43} +1.54772 q^{44} -0.215094 q^{45} -4.66760 q^{46} -1.14828 q^{47} -6.97642 q^{48} -0.512597 q^{49} +8.91915 q^{50} -5.54305 q^{51} +2.36345 q^{52} +11.3924 q^{53} +10.1837 q^{54} +0.266362 q^{55} -3.48069 q^{56} +7.44018 q^{57} -8.74484 q^{58} +4.17419 q^{59} +0.374100 q^{60} +4.10910 q^{61} -2.83975 q^{62} +2.56535 q^{63} -1.21218 q^{64} +0.406749 q^{65} -3.16972 q^{66} -5.17598 q^{67} -4.87252 q^{68} +3.66010 q^{69} +0.979232 q^{70} -16.1412 q^{71} -1.37639 q^{72} -4.41986 q^{73} +1.80025 q^{74} -6.99396 q^{75} +6.54016 q^{76} -3.17680 q^{77} -4.84033 q^{78} -2.92425 q^{79} -1.05540 q^{80} -4.96400 q^{81} +13.6751 q^{82} +7.83025 q^{83} -4.46176 q^{84} -0.838558 q^{85} +5.81673 q^{86} +6.85727 q^{87} +1.70445 q^{88} +4.91950 q^{89} +0.387223 q^{90} -4.85115 q^{91} +3.21735 q^{92} +2.22679 q^{93} +2.06719 q^{94} +1.12556 q^{95} +8.70103 q^{96} +11.2210 q^{97} +0.922803 q^{98} -1.25622 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9}+O(q^{10}) \) 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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