LMFDB - Embedded newform 4034.2.a.c.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4034,2,Mod(1,4034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4034, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4034 = 2 \cdot 2017 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4034.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:	$32.2116521754$
Analytic rank:	$0$
Dimension:	$49$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	4034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.73587 q^{3} +1.00000 q^{4} -3.97663 q^{5} +2.73587 q^{6} +4.88134 q^{7} -1.00000 q^{8} +4.48496 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.73587 q^{3} +1.00000 q^{4} -3.97663 q^{5} +2.73587 q^{6} +4.88134 q^{7} -1.00000 q^{8} +4.48496 q^{9} +3.97663 q^{10} -1.47432 q^{11} -2.73587 q^{12} +0.404731 q^{13} -4.88134 q^{14} +10.8795 q^{15} +1.00000 q^{16} +4.76385 q^{17} -4.48496 q^{18} +2.11033 q^{19} -3.97663 q^{20} -13.3547 q^{21} +1.47432 q^{22} +0.955349 q^{23} +2.73587 q^{24} +10.8136 q^{25} -0.404731 q^{26} -4.06266 q^{27} +4.88134 q^{28} +3.00985 q^{29} -10.8795 q^{30} +9.00310 q^{31} -1.00000 q^{32} +4.03355 q^{33} -4.76385 q^{34} -19.4113 q^{35} +4.48496 q^{36} -1.65085 q^{37} -2.11033 q^{38} -1.10729 q^{39} +3.97663 q^{40} +3.13867 q^{41} +13.3547 q^{42} +10.0626 q^{43} -1.47432 q^{44} -17.8350 q^{45} -0.955349 q^{46} -5.48245 q^{47} -2.73587 q^{48} +16.8274 q^{49} -10.8136 q^{50} -13.0333 q^{51} +0.404731 q^{52} +4.10074 q^{53} +4.06266 q^{54} +5.86284 q^{55} -4.88134 q^{56} -5.77358 q^{57} -3.00985 q^{58} +0.277011 q^{59} +10.8795 q^{60} -11.8960 q^{61} -9.00310 q^{62} +21.8926 q^{63} +1.00000 q^{64} -1.60946 q^{65} -4.03355 q^{66} -7.25225 q^{67} +4.76385 q^{68} -2.61371 q^{69} +19.4113 q^{70} -14.7470 q^{71} -4.48496 q^{72} +9.01845 q^{73} +1.65085 q^{74} -29.5845 q^{75} +2.11033 q^{76} -7.19666 q^{77} +1.10729 q^{78} +0.856173 q^{79} -3.97663 q^{80} -2.34000 q^{81} -3.13867 q^{82} +0.687178 q^{83} -13.3547 q^{84} -18.9441 q^{85} -10.0626 q^{86} -8.23455 q^{87} +1.47432 q^{88} +4.02511 q^{89} +17.8350 q^{90} +1.97563 q^{91} +0.955349 q^{92} -24.6313 q^{93} +5.48245 q^{94} -8.39200 q^{95} +2.73587 q^{96} -6.53309 q^{97} -16.8274 q^{98} -6.61228 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 49 q - 49 q^{2} + 8 q^{3} + 49 q^{4} - 8 q^{5} - 8 q^{6} + 18 q^{7} - 49 q^{8} + 59 q^{9}+O(q^{10}) $ 49 * q - 49 * q^2 + 8 * q^3 + 49 * q^4 - 8 * q^5 - 8 * q^6 + 18 * q^7 - 49 * q^8 + 59 * q^9	\( 49 q - 49 q^{2} + 8 q^{3} + 49 q^{4} - 8 q^{5} - 8 q^{6} + 18 q^{7} - 49 q^{8} + 59 q^{9} + 8 q^{10} + q^{11} + 8 q^{12} + 9 q^{13} - 18 q^{14} + 15 q^{15} + 49 q^{16} - 27 q^{17} - 59 q^{18} + 27 q^{19} - 8 q^{20} + 13 q^{21} - q^{22} + 16 q^{23} - 8 q^{24} + 71 q^{25} - 9 q^{26} + 29 q^{27} + 18 q^{28} - 7 q^{29} - 15 q^{30} + 75 q^{31} - 49 q^{32} - 3 q^{33} + 27 q^{34} - 16 q^{35} + 59 q^{36} + 36 q^{37} - 27 q^{38} + 24 q^{39} + 8 q^{40} - 12 q^{41} - 13 q^{42} + 22 q^{43} + q^{44} + 5 q^{45} - 16 q^{46} + 26 q^{47} + 8 q^{48} + 107 q^{49} - 71 q^{50} + 35 q^{51} + 9 q^{52} - 10 q^{53} - 29 q^{54} + 76 q^{55} - 18 q^{56} - 10 q^{57} + 7 q^{58} + 9 q^{59} + 15 q^{60} + 87 q^{61} - 75 q^{62} + 68 q^{63} + 49 q^{64} - 6 q^{65} + 3 q^{66} + 46 q^{67} - 27 q^{68} + 70 q^{69} + 16 q^{70} + 40 q^{71} - 59 q^{72} + 6 q^{73} - 36 q^{74} + 69 q^{75} + 27 q^{76} - 12 q^{77} - 24 q^{78} + 76 q^{79} - 8 q^{80} + 77 q^{81} + 12 q^{82} - 32 q^{83} + 13 q^{84} + 19 q^{85} - 22 q^{86} + 36 q^{87} - q^{88} + 34 q^{89} - 5 q^{90} + 119 q^{91} + 16 q^{92} - 5 q^{93} - 26 q^{94} - 2 q^{95} - 8 q^{96} + 52 q^{97} - 107 q^{98} + 26 q^{99}+O(q^{100}) \) 49 * q - 49 * q^2 + 8 * q^3 + 49 * q^4 - 8 * q^5 - 8 * q^6 + 18 * q^7 - 49 * q^8 + 59 * q^9 + 8 * q^10 + q^11 + 8 * q^12 + 9 * q^13 - 18 * q^14 + 15 * q^15 + 49 * q^16 - 27 * q^17 - 59 * q^18 + 27 * q^19 - 8 * q^20 + 13 * q^21 - q^22 + 16 * q^23 - 8 * q^24 + 71 * q^25 - 9 * q^26 + 29 * q^27 + 18 * q^28 - 7 * q^29 - 15 * q^30 + 75 * q^31 - 49 * q^32 - 3 * q^33 + 27 * q^34 - 16 * q^35 + 59 * q^36 + 36 * q^37 - 27 * q^38 + 24 * q^39 + 8 * q^40 - 12 * q^41 - 13 * q^42 + 22 * q^43 + q^44 + 5 * q^45 - 16 * q^46 + 26 * q^47 + 8 * q^48 + 107 * q^49 - 71 * q^50 + 35 * q^51 + 9 * q^52 - 10 * q^53 - 29 * q^54 + 76 * q^55 - 18 * q^56 - 10 * q^57 + 7 * q^58 + 9 * q^59 + 15 * q^60 + 87 * q^61 - 75 * q^62 + 68 * q^63 + 49 * q^64 - 6 * q^65 + 3 * q^66 + 46 * q^67 - 27 * q^68 + 70 * q^69 + 16 * q^70 + 40 * q^71 - 59 * q^72 + 6 * q^73 - 36 * q^74 + 69 * q^75 + 27 * q^76 - 12 * q^77 - 24 * q^78 + 76 * q^79 - 8 * q^80 + 77 * q^81 + 12 * q^82 - 32 * q^83 + 13 * q^84 + 19 * q^85 - 22 * q^86 + 36 * q^87 - q^88 + 34 * q^89 - 5 * q^90 + 119 * q^91 + 16 * q^92 - 5 * q^93 - 26 * q^94 - 2 * q^95 - 8 * q^96 + 52 * q^97 - 107 * q^98 + 26 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.73587	−1.57955	−0.789776	−	0.613395i	$-0.789803\pi$
$3$	−2.73587	−1.57955	−0.789776	+	0.613395i	$0.789803\pi$
$4$	1.00000	0.500000
$5$	−3.97663	−1.77840	−0.889202	−	0.457515i	$-0.848739\pi$
$5$	−3.97663	−1.77840	−0.889202	+	0.457515i	$0.848739\pi$
$6$	2.73587	1.11691
$7$	4.88134	1.84497	0.922486	−	0.386031i	$-0.126154\pi$
$7$	4.88134	1.84497	0.922486	+	0.386031i	$0.126154\pi$
$8$	−1.00000	−0.353553
$9$	4.48496	1.49499
$10$	3.97663	1.25752
$11$	−1.47432	−0.444525	−0.222263	−	0.974987i	$-0.571344\pi$
$11$	−1.47432	−0.444525	−0.222263	+	0.974987i	$0.571344\pi$
$12$	−2.73587	−0.789776
$13$	0.404731	0.112252	0.0561260	−	0.998424i	$-0.482125\pi$
$13$	0.404731	0.112252	0.0561260	+	0.998424i	$0.482125\pi$
$14$	−4.88134	−1.30459
$15$	10.8795	2.80908
$16$	1.00000	0.250000
$17$	4.76385	1.15540	0.577702	−	0.816248i	$-0.303950\pi$
$17$	4.76385	1.15540	0.577702	+	0.816248i	$0.303950\pi$
$18$	−4.48496	−1.05712
$19$	2.11033	0.484143	0.242071	−	0.970258i	$-0.422173\pi$
$19$	2.11033	0.484143	0.242071	+	0.970258i	$0.422173\pi$
$20$	−3.97663	−0.889202
$21$	−13.3547	−2.91423
$22$	1.47432	0.314327
$23$	0.955349	0.199204	0.0996020	−	0.995027i	$-0.468243\pi$
$23$	0.955349	0.199204	0.0996020	+	0.995027i	$0.468243\pi$
$24$	2.73587	0.558456
$25$	10.8136	2.16272
$26$	−0.404731	−0.0793742
$27$	−4.06266	−0.781859
$28$	4.88134	0.922486
$29$	3.00985	0.558915	0.279458	−	0.960158i	$-0.409845\pi$
$29$	3.00985	0.558915	0.279458	+	0.960158i	$0.409845\pi$
$30$	−10.8795	−1.98632
$31$	9.00310	1.61701	0.808503	−	0.588492i	$-0.200278\pi$
$31$	9.00310	1.61701	0.808503	+	0.588492i	$0.200278\pi$
$32$	−1.00000	−0.176777
$33$	4.03355	0.702151
$34$	−4.76385	−0.816993
$35$	−19.4113	−3.28110
$36$	4.48496	0.747494
$37$	−1.65085	−0.271398	−0.135699	−	0.990750i	$-0.543328\pi$
$37$	−1.65085	−0.271398	−0.135699	+	0.990750i	$0.543328\pi$
$38$	−2.11033	−0.342341
$39$	−1.10729	−0.177308
$40$	3.97663	0.628761
$41$	3.13867	0.490178	0.245089	−	0.969501i	$-0.421183\pi$
$41$	3.13867	0.490178	0.245089	+	0.969501i	$0.421183\pi$
$42$	13.3547	2.06067
$43$	10.0626	1.53453	0.767265	−	0.641330i	$-0.221617\pi$
$43$	10.0626	1.53453	0.767265	+	0.641330i	$0.221617\pi$
$44$	−1.47432	−0.222263
$45$	−17.8350	−2.65869
$46$	−0.955349	−0.140858
$47$	−5.48245	−0.799698	−0.399849	−	0.916581i	$-0.630937\pi$
$47$	−5.48245	−0.799698	−0.399849	+	0.916581i	$0.630937\pi$
$48$	−2.73587	−0.394888
$49$	16.8274	2.40392
$50$	−10.8136	−1.52927
$51$	−13.0333	−1.82502
$52$	0.404731	0.0561260
$53$	4.10074	0.563280	0.281640	−	0.959520i	$-0.409122\pi$
$53$	4.10074	0.563280	0.281640	+	0.959520i	$0.409122\pi$
$54$	4.06266	0.552858
$55$	5.86284	0.790545
$56$	−4.88134	−0.652296
$57$	−5.77358	−0.764729
$58$	−3.00985	−0.395213
$59$	0.277011	0.0360637	0.0180319	−	0.999837i	$-0.494260\pi$
$59$	0.277011	0.0360637	0.0180319	+	0.999837i	$0.494260\pi$
$60$	10.8795	1.40454
$61$	−11.8960	−1.52313	−0.761566	−	0.648087i	$-0.775569\pi$
$61$	−11.8960	−1.52313	−0.761566	+	0.648087i	$0.775569\pi$
$62$	−9.00310	−1.14340
$63$	21.8926	2.75821
$64$	1.00000	0.125000
$65$	−1.60946	−0.199629
$66$	−4.03355	−0.496496
$67$	−7.25225	−0.886004	−0.443002	−	0.896521i	$-0.646087\pi$
$67$	−7.25225	−0.886004	−0.443002	+	0.896521i	$0.646087\pi$
$68$	4.76385	0.577702
$69$	−2.61371	−0.314653
$70$	19.4113	2.32009
$71$	−14.7470	−1.75015	−0.875076	−	0.483985i	$-0.839189\pi$
$71$	−14.7470	−1.75015	−0.875076	+	0.483985i	$0.839189\pi$
$72$	−4.48496	−0.528558
$73$	9.01845	1.05553	0.527765	−	0.849391i	$-0.323030\pi$
$73$	9.01845	1.05553	0.527765	+	0.849391i	$0.323030\pi$
$74$	1.65085	0.191908
$75$	−29.5845	−3.41613
$76$	2.11033	0.242071
$77$	−7.19666	−0.820136
$78$	1.10729	0.125376
$79$	0.856173	0.0963270	0.0481635	−	0.998839i	$-0.484663\pi$
$79$	0.856173	0.0963270	0.0481635	+	0.998839i	$0.484663\pi$
$80$	−3.97663	−0.444601
$81$	−2.34000	−0.260000
$82$	−3.13867	−0.346608
$83$	0.687178	0.0754276	0.0377138	−	0.999289i	$-0.487992\pi$
$83$	0.687178	0.0754276	0.0377138	+	0.999289i	$0.487992\pi$
$84$	−13.3547	−1.45711
$85$	−18.9441	−2.05477
$86$	−10.0626	−1.08508
$87$	−8.23455	−0.882836
$88$	1.47432	0.157163
$89$	4.02511	0.426660	0.213330	−	0.976980i	$-0.431569\pi$
$89$	4.02511	0.426660	0.213330	+	0.976980i	$0.431569\pi$
$90$	17.8350	1.87998
$91$	1.97563	0.207102
$92$	0.955349	0.0996020
$93$	−24.6313	−2.55415
$94$	5.48245	0.565472
$95$	−8.39200	−0.861001
$96$	2.73587	0.279228
$97$	−6.53309	−0.663334	−0.331667	−	0.943396i	$-0.607611\pi$
$97$	−6.53309	−0.663334	−0.331667	+	0.943396i	$0.607611\pi$
$98$	−16.8274	−1.69983
$99$	−6.61228	−0.664559
$100$	10.8136	1.08136
$101$	9.80604	0.975737	0.487869	−	0.872917i	$-0.337774\pi$
$101$	9.80604	0.975737	0.487869	+	0.872917i	$0.337774\pi$
$102$	13.0333	1.29048
$103$	6.64406	0.654658	0.327329	−	0.944910i	$-0.393851\pi$
$103$	6.64406	0.654658	0.327329	+	0.944910i	$0.393851\pi$
$104$	−0.404731	−0.0396871
$105$	53.1066	5.18268
$106$	−4.10074	−0.398299
$107$	−2.95545	−0.285715	−0.142857	−	0.989743i	$-0.545629\pi$
$107$	−2.95545	−0.285715	−0.142857	+	0.989743i	$0.545629\pi$
$108$	−4.06266	−0.390929
$109$	8.40436	0.804992	0.402496	−	0.915422i	$-0.368143\pi$
$109$	8.40436	0.804992	0.402496	+	0.915422i	$0.368143\pi$
$110$	−5.86284	−0.559000
$111$	4.51651	0.428688
$112$	4.88134	0.461243
$113$	−2.89121	−0.271983	−0.135991	−	0.990710i	$-0.543422\pi$
$113$	−2.89121	−0.271983	−0.135991	+	0.990710i	$0.543422\pi$
$114$	5.77358	0.540745
$115$	−3.79907	−0.354265
$116$	3.00985	0.279458
$117$	1.81520	0.167815
$118$	−0.277011	−0.0255009
$119$	23.2539	2.13169
$120$	−10.8795	−0.993161
$121$	−8.82637	−0.802397
$122$	11.8960	1.07702
$123$	−8.58698	−0.774262
$124$	9.00310	0.808503
$125$	−23.1185	−2.06778
$126$	−21.8926	−1.95035
$127$	−11.0365	−0.979331	−0.489665	−	0.871910i	$-0.662881\pi$
$127$	−11.0365	−0.979331	−0.489665	+	0.871910i	$0.662881\pi$
$128$	−1.00000	−0.0883883
$129$	−27.5299	−2.42387
$130$	1.60946	0.141159
$131$	1.18092	0.103177	0.0515885	−	0.998668i	$-0.483572\pi$
$131$	1.18092	0.103177	0.0515885	+	0.998668i	$0.483572\pi$
$132$	4.03355	0.351075
$133$	10.3012	0.893230
$134$	7.25225	0.626499
$135$	16.1557	1.39046
$136$	−4.76385	−0.408497
$137$	−8.47053	−0.723686	−0.361843	−	0.932239i	$-0.617852\pi$
$137$	−8.47053	−0.723686	−0.361843	+	0.932239i	$0.617852\pi$
$138$	2.61371	0.222493
$139$	−13.4839	−1.14369	−0.571844	−	0.820362i	$-0.693772\pi$
$139$	−13.4839	−1.14369	−0.571844	+	0.820362i	$0.693772\pi$
$140$	−19.4113	−1.64055
$141$	14.9993	1.26317
$142$	14.7470	1.23754
$143$	−0.596704	−0.0498989
$144$	4.48496	0.373747
$145$	−11.9691	−0.993977
$146$	−9.01845	−0.746372
$147$	−46.0376	−3.79712
$148$	−1.65085	−0.135699
$149$	13.0760	1.07123	0.535614	−	0.844463i	$-0.320080\pi$
$149$	13.0760	1.07123	0.535614	+	0.844463i	$0.320080\pi$
$150$	29.5845	2.41557
$151$	0.390478	0.0317767	0.0158883	−	0.999874i	$-0.494942\pi$
$151$	0.390478	0.0317767	0.0158883	+	0.999874i	$0.494942\pi$
$152$	−2.11033	−0.171170
$153$	21.3657	1.72731
$154$	7.19666	0.579924
$155$	−35.8020	−2.87569
$156$	−1.10729	−0.0886540
$157$	−6.67542	−0.532757	−0.266378	−	0.963869i	$-0.585827\pi$
$157$	−6.67542	−0.532757	−0.266378	+	0.963869i	$0.585827\pi$
$158$	−0.856173	−0.0681134
$159$	−11.2191	−0.889730
$160$	3.97663	0.314380
$161$	4.66338	0.367526
$162$	2.34000	0.183848
$163$	−2.86183	−0.224156	−0.112078	−	0.993699i	$-0.535751\pi$
$163$	−2.86183	−0.224156	−0.112078	+	0.993699i	$0.535751\pi$
$164$	3.13867	0.245089
$165$	−16.0399	−1.24871
$166$	−0.687178	−0.0533353
$167$	5.90449	0.456903	0.228451	−	0.973555i	$-0.426634\pi$
$167$	5.90449	0.456903	0.228451	+	0.973555i	$0.426634\pi$
$168$	13.3547	1.03034
$169$	−12.8362	−0.987399
$170$	18.9441	1.45294
$171$	9.46475	0.723787
$172$	10.0626	0.767265
$173$	15.9426	1.21209	0.606047	−	0.795429i	$-0.292754\pi$
$173$	15.9426	1.21209	0.606047	+	0.795429i	$0.292754\pi$
$174$	8.23455	0.624260
$175$	52.7848	3.99015
$176$	−1.47432	−0.111131
$177$	−0.757864	−0.0569646
$178$	−4.02511	−0.301694
$179$	5.20820	0.389279	0.194640	−	0.980875i	$-0.437646\pi$
$179$	5.20820	0.389279	0.194640	+	0.980875i	$0.437646\pi$
$180$	−17.8350	−1.32935
$181$	13.5841	1.00970	0.504848	−	0.863208i	$-0.331549\pi$
$181$	13.5841	1.00970	0.504848	+	0.863208i	$0.331549\pi$
$182$	−1.97563	−0.146443
$183$	32.5460	2.40587
$184$	−0.955349	−0.0704292
$185$	6.56483	0.482656
$186$	24.6313	1.80605
$187$	−7.02345	−0.513606
$188$	−5.48245	−0.399849
$189$	−19.8312	−1.44251
$190$	8.39200	0.608820
$191$	24.5475	1.77620	0.888098	−	0.459655i	$-0.152027\pi$
$191$	24.5475	1.77620	0.888098	+	0.459655i	$0.152027\pi$
$192$	−2.73587	−0.197444
$193$	−16.3092	−1.17396	−0.586982	−	0.809600i	$-0.699684\pi$
$193$	−16.3092	−1.17396	−0.586982	+	0.809600i	$0.699684\pi$
$194$	6.53309	0.469048
$195$	4.40328	0.315325
$196$	16.8274	1.20196
$197$	11.4606	0.816530	0.408265	−	0.912863i	$-0.366134\pi$
$197$	11.4606	0.816530	0.408265	+	0.912863i	$0.366134\pi$
$198$	6.61228	0.469914
$199$	19.3940	1.37480	0.687400	−	0.726279i	$-0.258752\pi$
$199$	19.3940	1.37480	0.687400	+	0.726279i	$0.258752\pi$
$200$	−10.8136	−0.764637
$201$	19.8412	1.39949
$202$	−9.80604	−0.689951
$203$	14.6921	1.03118
$204$	−13.0333	−0.912510
$205$	−12.4813	−0.871734
$206$	−6.64406	−0.462913
$207$	4.28470	0.297807
$208$	0.404731	0.0280630
$209$	−3.11131	−0.215214
$210$	−53.1066	−3.66471
$211$	−5.46025	−0.375899	−0.187950	−	0.982179i	$-0.560184\pi$
$211$	−5.46025	−0.375899	−0.187950	+	0.982179i	$0.560184\pi$
$212$	4.10074	0.281640
$213$	40.3459	2.76446
$214$	2.95545	0.202031
$215$	−40.0152	−2.72901
$216$	4.06266	0.276429
$217$	43.9472	2.98333
$218$	−8.40436	−0.569215
$219$	−24.6733	−1.66727
$220$	5.86284	0.395272
$221$	1.92808	0.129696
$222$	−4.51651	−0.303128
$223$	1.20110	0.0804313	0.0402156	−	0.999191i	$-0.487196\pi$
$223$	1.20110	0.0804313	0.0402156	+	0.999191i	$0.487196\pi$
$224$	−4.88134	−0.326148
$225$	48.4986	3.23324
$226$	2.89121	0.192321
$227$	22.8427	1.51612	0.758060	−	0.652184i	$-0.226147\pi$
$227$	22.8427	1.51612	0.758060	+	0.652184i	$0.226147\pi$
$228$	−5.77358	−0.382365
$229$	−16.6260	−1.09868	−0.549339	−	0.835600i	$-0.685120\pi$
$229$	−16.6260	−1.09868	−0.549339	+	0.835600i	$0.685120\pi$
$230$	3.79907	0.250503
$231$	19.6891	1.29545
$232$	−3.00985	−0.197606
$233$	9.60505	0.629248	0.314624	−	0.949216i	$-0.398122\pi$
$233$	9.60505	0.629248	0.314624	+	0.949216i	$0.398122\pi$
$234$	−1.81520	−0.118663
$235$	21.8017	1.42219
$236$	0.277011	0.0180319
$237$	−2.34237	−0.152154
$238$	−23.2539	−1.50733
$239$	−18.4975	−1.19650	−0.598252	−	0.801308i	$-0.704138\pi$
$239$	−18.4975	−1.19650	−0.598252	+	0.801308i	$0.704138\pi$
$240$	10.8795	0.702271
$241$	8.38770	0.540299	0.270150	−	0.962818i	$-0.412927\pi$
$241$	8.38770	0.540299	0.270150	+	0.962818i	$0.412927\pi$
$242$	8.82637	0.567381
$243$	18.5899	1.19254
$244$	−11.8960	−0.761566
$245$	−66.9165	−4.27514
$246$	8.58698	0.547486
$247$	0.854115	0.0543460
$248$	−9.00310	−0.571698
$249$	−1.88003	−0.119142
$250$	23.1185	1.46214
$251$	−6.07463	−0.383427	−0.191714	−	0.981451i	$-0.561404\pi$
$251$	−6.07463	−0.383427	−0.191714	+	0.981451i	$0.561404\pi$
$252$	21.8926	1.37910
$253$	−1.40849	−0.0885512
$254$	11.0365	0.692491
$255$	51.8284	3.24562
$256$	1.00000	0.0625000
$257$	21.5927	1.34691	0.673456	−	0.739227i	$-0.264809\pi$
$257$	21.5927	1.34691	0.673456	+	0.739227i	$0.264809\pi$
$258$	27.5299	1.71394
$259$	−8.05836	−0.500722
$260$	−1.60946	−0.0998147
$261$	13.4991	0.835572
$262$	−1.18092	−0.0729572
$263$	−25.5332	−1.57445	−0.787223	−	0.616669i	$-0.788482\pi$
$263$	−25.5332	−1.57445	−0.787223	+	0.616669i	$0.788482\pi$
$264$	−4.03355	−0.248248
$265$	−16.3071	−1.00174
$266$	−10.3012	−0.631609
$267$	−11.0121	−0.673933
$268$	−7.25225	−0.443002
$269$	0.446408	0.0272180	0.0136090	−	0.999907i	$-0.495668\pi$
$269$	0.446408	0.0272180	0.0136090	+	0.999907i	$0.495668\pi$
$270$	−16.1557	−0.983204
$271$	−15.2254	−0.924877	−0.462439	−	0.886651i	$-0.653025\pi$
$271$	−15.2254	−0.924877	−0.462439	+	0.886651i	$0.653025\pi$
$272$	4.76385	0.288851
$273$	−5.40505	−0.327128
$274$	8.47053	0.511723
$275$	−15.9427	−0.961383
$276$	−2.61371	−0.157327
$277$	32.9420	1.97929	0.989647	−	0.143524i	$-0.0458435\pi$
$277$	32.9420	1.97929	0.989647	+	0.143524i	$0.0458435\pi$
$278$	13.4839	0.808710
$279$	40.3786	2.41740
$280$	19.4113	1.16005
$281$	31.6857	1.89021	0.945104	−	0.326769i	$-0.105960\pi$
$281$	31.6857	1.89021	0.945104	+	0.326769i	$0.105960\pi$
$282$	−14.9993	−0.893193
$283$	−9.37023	−0.557002	−0.278501	−	0.960436i	$-0.589838\pi$
$283$	−9.37023	−0.557002	−0.278501	+	0.960436i	$0.589838\pi$
$284$	−14.7470	−0.875076
$285$	22.9594	1.36000
$286$	0.596704	0.0352838
$287$	15.3209	0.904364
$288$	−4.48496	−0.264279
$289$	5.69426	0.334957
$290$	11.9691	0.702848
$291$	17.8736	1.04777
$292$	9.01845	0.527765
$293$	−22.8613	−1.33557	−0.667787	−	0.744353i	$-0.732758\pi$
$293$	−22.8613	−1.33557	−0.667787	+	0.744353i	$0.732758\pi$
$294$	46.0376	2.68497
$295$	−1.10157	−0.0641359
$296$	1.65085	0.0959538
$297$	5.98967	0.347556
$298$	−13.0760	−0.757472
$299$	0.386659	0.0223611
$300$	−29.5845	−1.70806
$301$	49.1189	2.83117
$302$	−0.390478	−0.0224695
$303$	−26.8280	−1.54123
$304$	2.11033	0.121036
$305$	47.3062	2.70874
$306$	−21.3657	−1.22139
$307$	31.6258	1.80498	0.902491	−	0.430708i	$-0.141736\pi$
$307$	31.6258	1.80498	0.902491	+	0.430708i	$0.141736\pi$
$308$	−7.19666	−0.410068
$309$	−18.1772	−1.03407
$310$	35.8020	2.03342
$311$	29.1949	1.65549	0.827746	−	0.561103i	$-0.189623\pi$
$311$	29.1949	1.65549	0.827746	+	0.561103i	$0.189623\pi$
$312$	1.10729	0.0626879
$313$	−6.85252	−0.387327	−0.193664	−	0.981068i	$-0.562037\pi$
$313$	−6.85252	−0.387327	−0.193664	+	0.981068i	$0.562037\pi$
$314$	6.67542	0.376716
$315$	−87.0588	−4.90521
$316$	0.856173	0.0481635
$317$	21.8134	1.22516	0.612582	−	0.790407i	$-0.290131\pi$
$317$	21.8134	1.22516	0.612582	+	0.790407i	$0.290131\pi$
$318$	11.2191	0.629134
$319$	−4.43749	−0.248452
$320$	−3.97663	−0.222300
$321$	8.08573	0.451301
$322$	−4.66338	−0.259880
$323$	10.0533	0.559380
$324$	−2.34000	−0.130000
$325$	4.37659	0.242770
$326$	2.86183	0.158502
$327$	−22.9932	−1.27153
$328$	−3.13867	−0.173304
$329$	−26.7617	−1.47542
$330$	16.0399	0.882970
$331$	22.6563	1.24530	0.622651	−	0.782500i	$-0.286056\pi$
$331$	22.6563	1.24530	0.622651	+	0.782500i	$0.286056\pi$
$332$	0.687178	0.0377138
$333$	−7.40401	−0.405737
$334$	−5.90449	−0.323079
$335$	28.8395	1.57567
$336$	−13.3547	−0.728557
$337$	−23.4290	−1.27626	−0.638131	−	0.769928i	$-0.720292\pi$
$337$	−23.4290	−1.27626	−0.638131	+	0.769928i	$0.720292\pi$
$338$	12.8362	0.698197
$339$	7.90997	0.429611
$340$	−18.9441	−1.02739
$341$	−13.2735	−0.718799
$342$	−9.46475	−0.511795
$343$	47.9710	2.59019
$344$	−10.0626	−0.542538
$345$	10.3937	0.559580
$346$	−15.9426	−0.857080
$347$	−33.2320	−1.78399	−0.891993	−	0.452049i	$-0.850693\pi$
$347$	−33.2320	−1.78399	−0.891993	+	0.452049i	$0.850693\pi$
$348$	−8.23455	−0.441418
$349$	−22.5018	−1.20450	−0.602248	−	0.798309i	$-0.705728\pi$
$349$	−22.5018	−1.20450	−0.602248	+	0.798309i	$0.705728\pi$
$350$	−52.7848	−2.82147
$351$	−1.64428	−0.0877653
$352$	1.47432	0.0785817
$353$	−26.1441	−1.39151	−0.695756	−	0.718278i	$-0.744930\pi$
$353$	−26.1441	−1.39151	−0.695756	+	0.718278i	$0.744930\pi$
$354$	0.757864	0.0402800
$355$	58.6436	3.11248
$356$	4.02511	0.213330
$357$	−63.6197	−3.36711
$358$	−5.20820	−0.275262
$359$	22.0057	1.16142	0.580709	−	0.814111i	$-0.302775\pi$
$359$	22.0057	1.16142	0.580709	+	0.814111i	$0.302775\pi$
$360$	17.8350	0.939989
$361$	−14.5465	−0.765606
$362$	−13.5841	−0.713963
$363$	24.1478	1.26743
$364$	1.97563	0.103551
$365$	−35.8630	−1.87716
$366$	−32.5460	−1.70121
$367$	26.6998	1.39372	0.696860	−	0.717207i	$-0.254580\pi$
$367$	26.6998	1.39372	0.696860	+	0.717207i	$0.254580\pi$
$368$	0.955349	0.0498010
$369$	14.0768	0.732809
$370$	−6.56483	−0.341289
$371$	20.0171	1.03923
$372$	−24.6313	−1.27707
$373$	−10.9592	−0.567448	−0.283724	−	0.958906i	$-0.591570\pi$
$373$	−10.9592	−0.567448	−0.283724	+	0.958906i	$0.591570\pi$
$374$	7.02345	0.363174
$375$	63.2492	3.26617
$376$	5.48245	0.282736
$377$	1.21818	0.0627394
$378$	19.8312	1.02001
$379$	17.3254	0.889947	0.444974	−	0.895544i	$-0.353213\pi$
$379$	17.3254	0.889947	0.444974	+	0.895544i	$0.353213\pi$
$380$	−8.39200	−0.430501
$381$	30.1944	1.54690
$382$	−24.5475	−1.25596
$383$	−5.76915	−0.294790	−0.147395	−	0.989078i	$-0.547089\pi$
$383$	−5.76915	−0.294790	−0.147395	+	0.989078i	$0.547089\pi$
$384$	2.73587	0.139614
$385$	28.6185	1.45853
$386$	16.3092	0.830118
$387$	45.1303	2.29410
$388$	−6.53309	−0.331667
$389$	23.8703	1.21027	0.605137	−	0.796121i	$-0.293118\pi$
$389$	23.8703	1.21027	0.605137	+	0.796121i	$0.293118\pi$
$390$	−4.40328	−0.222969
$391$	4.55114	0.230161
$392$	−16.8274	−0.849914
$393$	−3.23083	−0.162974
$394$	−11.4606	−0.577374
$395$	−3.40468	−0.171308
$396$	−6.61228	−0.332280
$397$	−31.9687	−1.60446	−0.802231	−	0.597014i	$-0.796354\pi$
$397$	−31.9687	−1.60446	−0.802231	+	0.597014i	$0.796354\pi$
$398$	−19.3940	−0.972131
$399$	−28.1828	−1.41090
$400$	10.8136	0.540680
$401$	−33.8532	−1.69055	−0.845275	−	0.534332i	$-0.820563\pi$
$401$	−33.8532	−1.69055	−0.845275	+	0.534332i	$0.820563\pi$
$402$	−19.8412	−0.989589
$403$	3.64383	0.181512
$404$	9.80604	0.487869
$405$	9.30532	0.462385
$406$	−14.6921	−0.729156
$407$	2.43389	0.120643
$408$	13.0333	0.645242
$409$	33.0756	1.63548	0.817742	−	0.575585i	$-0.195226\pi$
$409$	33.0756	1.63548	0.817742	+	0.575585i	$0.195226\pi$
$410$	12.4813	0.616409
$411$	23.1742	1.14310
$412$	6.64406	0.327329
$413$	1.35218	0.0665366
$414$	−4.28470	−0.210582
$415$	−2.73265	−0.134141
$416$	−0.404731	−0.0198435
$417$	36.8901	1.80652
$418$	3.11131	0.152179
$419$	−5.82701	−0.284668	−0.142334	−	0.989819i	$-0.545461\pi$
$419$	−5.82701	−0.284668	−0.142334	+	0.989819i	$0.545461\pi$
$420$	53.1066	2.59134
$421$	16.3584	0.797261	0.398630	−	0.917112i	$-0.369486\pi$
$421$	16.3584	0.797261	0.398630	+	0.917112i	$0.369486\pi$
$422$	5.46025	0.265801
$423$	−24.5886	−1.19554
$424$	−4.10074	−0.199149
$425$	51.5143	2.49881
$426$	−40.3459	−1.95477
$427$	−58.0686	−2.81014
$428$	−2.95545	−0.142857
$429$	1.63250	0.0788179
$430$	40.0152	1.92970
$431$	−6.68804	−0.322152	−0.161076	−	0.986942i	$-0.551496\pi$
$431$	−6.68804	−0.322152	−0.161076	+	0.986942i	$0.551496\pi$
$432$	−4.06266	−0.195465
$433$	−22.7147	−1.09160	−0.545799	−	0.837916i	$-0.683774\pi$
$433$	−22.7147	−1.09160	−0.545799	+	0.837916i	$0.683774\pi$
$434$	−43.9472	−2.10953
$435$	32.7458	1.57004
$436$	8.40436	0.402496
$437$	2.01610	0.0964432
$438$	24.6733	1.17893
$439$	23.1104	1.10300	0.551501	−	0.834174i	$-0.314055\pi$
$439$	23.1104	1.10300	0.551501	+	0.834174i	$0.314055\pi$
$440$	−5.86284	−0.279500
$441$	75.4704	3.59383
$442$	−1.92808	−0.0917092
$443$	−40.3154	−1.91544	−0.957721	−	0.287698i	$-0.907110\pi$
$443$	−40.3154	−1.91544	−0.957721	+	0.287698i	$0.907110\pi$
$444$	4.51651	0.214344
$445$	−16.0064	−0.758774
$446$	−1.20110	−0.0568735
$447$	−35.7742	−1.69206
$448$	4.88134	0.230621
$449$	−22.8297	−1.07740	−0.538699	−	0.842498i	$-0.681084\pi$
$449$	−22.8297	−1.07740	−0.538699	+	0.842498i	$0.681084\pi$
$450$	−48.4986	−2.28624
$451$	−4.62741	−0.217896
$452$	−2.89121	−0.135991
$453$	−1.06830	−0.0501929
$454$	−22.8427	−1.07206
$455$	−7.85633	−0.368311
$456$	5.77358	0.270373
$457$	−26.1099	−1.22137	−0.610684	−	0.791875i	$-0.709105\pi$
$457$	−26.1099	−1.22137	−0.610684	+	0.791875i	$0.709105\pi$
$458$	16.6260	0.776882
$459$	−19.3539	−0.903362
$460$	−3.79907	−0.177133
$461$	−26.3571	−1.22757	−0.613786	−	0.789472i	$-0.710354\pi$
$461$	−26.3571	−1.22757	−0.613786	+	0.789472i	$0.710354\pi$
$462$	−19.6891	−0.916020
$463$	12.3730	0.575023	0.287512	−	0.957777i	$-0.407172\pi$
$463$	12.3730	0.575023	0.287512	+	0.957777i	$0.407172\pi$
$464$	3.00985	0.139729
$465$	97.9495	4.54230
$466$	−9.60505	−0.444945
$467$	−29.7862	−1.37834	−0.689171	−	0.724599i	$-0.742025\pi$
$467$	−29.7862	−1.37834	−0.689171	+	0.724599i	$0.742025\pi$
$468$	1.81520	0.0839077
$469$	−35.4007	−1.63465
$470$	−21.8017	−1.00564
$471$	18.2631	0.841518
$472$	−0.277011	−0.0127505
$473$	−14.8355	−0.682137
$474$	2.34237	0.107589
$475$	22.8202	1.04706
$476$	23.2539	1.06584
$477$	18.3917	0.842096
$478$	18.4975	0.846056
$479$	9.04329	0.413199	0.206599	−	0.978426i	$-0.433760\pi$
$479$	9.04329	0.413199	0.206599	+	0.978426i	$0.433760\pi$
$480$	−10.8795	−0.496580
$481$	−0.668150	−0.0304650
$482$	−8.38770	−0.382049
$483$	−12.7584	−0.580526
$484$	−8.82637	−0.401199
$485$	25.9797	1.17968
$486$	−18.5899	−0.843255
$487$	−21.8519	−0.990204	−0.495102	−	0.868835i	$-0.664869\pi$
$487$	−21.8519	−0.990204	−0.495102	+	0.868835i	$0.664869\pi$
$488$	11.8960	0.538509
$489$	7.82958	0.354066
$490$	66.9165	3.02298
$491$	36.1502	1.63144	0.815719	−	0.578449i	$-0.196342\pi$
$491$	36.1502	1.63144	0.815719	+	0.578449i	$0.196342\pi$
$492$	−8.58698	−0.387131
$493$	14.3385	0.645773
$494$	−0.854115	−0.0384284
$495$	26.2946	1.18185
$496$	9.00310	0.404251
$497$	−71.9853	−3.22898
$498$	1.88003	0.0842460
$499$	42.5255	1.90370	0.951852	−	0.306559i	$-0.0991777\pi$
$499$	42.5255	1.90370	0.951852	+	0.306559i	$0.0991777\pi$
$500$	−23.1185	−1.03389
$501$	−16.1539	−0.721702
$502$	6.07463	0.271124
$503$	−0.620222	−0.0276543	−0.0138272	−	0.999904i	$-0.504401\pi$
$503$	−0.620222	−0.0276543	−0.0138272	+	0.999904i	$0.504401\pi$
$504$	−21.8926	−0.975174
$505$	−38.9950	−1.73525
$506$	1.40849	0.0626151
$507$	35.1181	1.55965
$508$	−11.0365	−0.489665
$509$	7.29393	0.323298	0.161649	−	0.986848i	$-0.448319\pi$
$509$	7.29393	0.323298	0.161649	+	0.986848i	$0.448319\pi$
$510$	−51.8284	−2.29500
$511$	44.0221	1.94742
$512$	−1.00000	−0.0441942
$513$	−8.57355	−0.378531
$514$	−21.5927	−0.952411
$515$	−26.4210	−1.16425
$516$	−27.5299	−1.21194
$517$	8.08291	0.355486
$518$	8.05836	0.354064
$519$	−43.6168	−1.91457
$520$	1.60946	0.0705797
$521$	37.9276	1.66164	0.830819	−	0.556543i	$-0.187873\pi$
$521$	37.9276	1.66164	0.830819	+	0.556543i	$0.187873\pi$
$522$	−13.4991	−0.590838
$523$	36.1332	1.58000	0.789998	−	0.613110i	$-0.210082\pi$
$523$	36.1332	1.58000	0.789998	+	0.613110i	$0.210082\pi$
$524$	1.18092	0.0515885
$525$	−144.412	−6.30266
$526$	25.5332	1.11330
$527$	42.8894	1.86829
$528$	4.03355	0.175538
$529$	−22.0873	−0.960318
$530$	16.3071	0.708336
$531$	1.24238	0.0539148
$532$	10.3012	0.446615
$533$	1.27032	0.0550235
$534$	11.0121	0.476542
$535$	11.7528	0.508116
$536$	7.25225	0.313250
$537$	−14.2489	−0.614887
$538$	−0.446408	−0.0192460
$539$	−24.8091	−1.06860
$540$	16.1557	0.695230
$541$	−3.66699	−0.157656	−0.0788282	−	0.996888i	$-0.525118\pi$
$541$	−3.66699	−0.157656	−0.0788282	+	0.996888i	$0.525118\pi$
$542$	15.2254	0.653987
$543$	−37.1642	−1.59487
$544$	−4.76385	−0.204248
$545$	−33.4210	−1.43160
$546$	5.40505	0.231315
$547$	19.7384	0.843953	0.421976	−	0.906607i	$-0.361337\pi$
$547$	19.7384	0.843953	0.421976	+	0.906607i	$0.361337\pi$
$548$	−8.47053	−0.361843
$549$	−53.3533	−2.27706
$550$	15.9427	0.679800
$551$	6.35178	0.270595
$552$	2.61371	0.111247
$553$	4.17927	0.177720
$554$	−32.9420	−1.39957
$555$	−17.9605	−0.762381
$556$	−13.4839	−0.571844
$557$	−44.7960	−1.89807	−0.949034	−	0.315175i	$-0.897937\pi$
$557$	−44.7960	−1.89807	−0.949034	+	0.315175i	$0.897937\pi$
$558$	−40.3786	−1.70936
$559$	4.07264	0.172254
$560$	−19.4113	−0.820276
$561$	19.2152	0.811267
$562$	−31.6857	−1.33658
$563$	15.0773	0.635431	0.317715	−	0.948186i	$-0.397084\pi$
$563$	15.0773	0.635431	0.317715	+	0.948186i	$0.397084\pi$
$564$	14.9993	0.631583
$565$	11.4973	0.483695
$566$	9.37023	0.393860
$567$	−11.4223	−0.479693
$568$	14.7470	0.618772
$569$	−3.60246	−0.151023	−0.0755114	−	0.997145i	$-0.524059\pi$
$569$	−3.60246	−0.151023	−0.0755114	+	0.997145i	$0.524059\pi$
$570$	−22.9594	−0.961663
$571$	−5.75194	−0.240711	−0.120356	−	0.992731i	$-0.538403\pi$
$571$	−5.75194	−0.240711	−0.120356	+	0.992731i	$0.538403\pi$
$572$	−0.596704	−0.0249494
$573$	−67.1587	−2.80559
$574$	−15.3209	−0.639482
$575$	10.3308	0.430822
$576$	4.48496	0.186873
$577$	−28.0022	−1.16575	−0.582874	−	0.812562i	$-0.698072\pi$
$577$	−28.0022	−1.16575	−0.582874	+	0.812562i	$0.698072\pi$
$578$	−5.69426	−0.236850
$579$	44.6199	1.85434
$580$	−11.9691	−0.496989
$581$	3.35435	0.139162
$582$	−17.8736	−0.740887
$583$	−6.04581	−0.250392
$584$	−9.01845	−0.373186
$585$	−7.21839	−0.298444
$586$	22.8613	0.944393
$587$	23.0676	0.952102	0.476051	−	0.879418i	$-0.342068\pi$
$587$	23.0676	0.952102	0.476051	+	0.879418i	$0.342068\pi$
$588$	−46.0376	−1.89856
$589$	18.9995	0.782862
$590$	1.10157	0.0453509
$591$	−31.3545	−1.28975
$592$	−1.65085	−0.0678496
$593$	10.3013	0.423023	0.211512	−	0.977375i	$-0.432161\pi$
$593$	10.3013	0.423023	0.211512	+	0.977375i	$0.432161\pi$
$594$	−5.98967	−0.245759
$595$	−92.4724	−3.79100
$596$	13.0760	0.535614
$597$	−53.0592	−2.17157
$598$	−0.386659	−0.0158117
$599$	−19.2354	−0.785938	−0.392969	−	0.919552i	$-0.628552\pi$
$599$	−19.2354	−0.785938	−0.392969	+	0.919552i	$0.628552\pi$
$600$	29.5845	1.20778
$601$	−3.83667	−0.156501	−0.0782505	−	0.996934i	$-0.524933\pi$
$601$	−3.83667	−0.156501	−0.0782505	+	0.996934i	$0.524933\pi$
$602$	−49.1189	−2.00194
$603$	−32.5261	−1.32456
$604$	0.390478	0.0158883
$605$	35.0992	1.42699
$606$	26.8280	1.08981
$607$	−25.2050	−1.02304	−0.511520	−	0.859271i	$-0.670917\pi$
$607$	−25.2050	−1.02304	−0.511520	+	0.859271i	$0.670917\pi$
$608$	−2.11033	−0.0855852
$609$	−40.1956	−1.62881
$610$	−47.3062	−1.91537
$611$	−2.21892	−0.0897677
$612$	21.3657	0.863657
$613$	−33.6493	−1.35908	−0.679541	−	0.733637i	$-0.737821\pi$
$613$	−33.6493	−1.35908	−0.679541	+	0.733637i	$0.737821\pi$
$614$	−31.6258	−1.27632
$615$	34.1472	1.37695
$616$	7.19666	0.289962
$617$	−28.7861	−1.15888	−0.579442	−	0.815013i	$-0.696729\pi$
$617$	−28.7861	−1.15888	−0.579442	+	0.815013i	$0.696729\pi$
$618$	18.1772	0.731196
$619$	36.4542	1.46522	0.732610	−	0.680649i	$-0.238302\pi$
$619$	36.4542	1.46522	0.732610	+	0.680649i	$0.238302\pi$
$620$	−35.8020	−1.43784
$621$	−3.88125	−0.155749
$622$	−29.1949	−1.17061
$623$	19.6479	0.787176
$624$	−1.10729	−0.0443270
$625$	37.8658	1.51463
$626$	6.85252	0.273882
$627$	8.51212	0.339941
$628$	−6.67542	−0.266378
$629$	−7.86441	−0.313575
$630$	87.0588	3.46851
$631$	9.49358	0.377933	0.188967	−	0.981984i	$-0.439486\pi$
$631$	9.49358	0.377933	0.188967	+	0.981984i	$0.439486\pi$
$632$	−0.856173	−0.0340567
$633$	14.9385	0.593753
$634$	−21.8134	−0.866322
$635$	43.8881	1.74165
$636$	−11.2191	−0.444865
$637$	6.81058	0.269845
$638$	4.43749	0.175682
$639$	−66.1400	−2.61646
$640$	3.97663	0.157190
$641$	35.1283	1.38748	0.693742	−	0.720223i	$-0.255961\pi$
$641$	35.1283	1.38748	0.693742	+	0.720223i	$0.255961\pi$
$642$	−8.08573	−0.319118
$643$	35.2262	1.38919	0.694593	−	0.719403i	$-0.255585\pi$
$643$	35.2262	1.38919	0.694593	+	0.719403i	$0.255585\pi$
$644$	4.66338	0.183763
$645$	109.476	4.31062
$646$	−10.0533	−0.395542
$647$	−19.7343	−0.775835	−0.387917	−	0.921694i	$-0.626805\pi$
$647$	−19.7343	−0.775835	−0.387917	+	0.921694i	$0.626805\pi$
$648$	2.34000	0.0919239
$649$	−0.408403	−0.0160312
$650$	−4.37659	−0.171664
$651$	−120.234	−4.71233
$652$	−2.86183	−0.112078
$653$	29.4076	1.15081	0.575404	−	0.817869i	$-0.304845\pi$
$653$	29.4076	1.15081	0.575404	+	0.817869i	$0.304845\pi$
$654$	22.9932	0.899106
$655$	−4.69606	−0.183490
$656$	3.13867	0.122544
$657$	40.4474	1.57800
$658$	26.7617	1.04328
$659$	9.09542	0.354307	0.177154	−	0.984183i	$-0.443311\pi$
$659$	9.09542	0.354307	0.177154	+	0.984183i	$0.443311\pi$
$660$	−16.0399	−0.624354
$661$	27.1096	1.05444	0.527221	−	0.849728i	$-0.323234\pi$
$661$	27.1096	1.05444	0.527221	+	0.849728i	$0.323234\pi$
$662$	−22.6563	−0.880561
$663$	−5.27496	−0.204862
$664$	−0.687178	−0.0266677
$665$	−40.9642	−1.58852
$666$	7.40401	0.286900
$667$	2.87546	0.111338
$668$	5.90449	0.228451
$669$	−3.28603	−0.127045
$670$	−28.8395	−1.11417
$671$	17.5386	0.677070
$672$	13.3547	0.515168
$673$	20.5776	0.793209	0.396604	−	0.917990i	$-0.370189\pi$
$673$	20.5776	0.793209	0.396604	+	0.917990i	$0.370189\pi$
$674$	23.4290	0.902453
$675$	−43.9319	−1.69094
$676$	−12.8362	−0.493700
$677$	−5.15958	−0.198299	−0.0991494	−	0.995073i	$-0.531612\pi$
$677$	−5.15958	−0.198299	−0.0991494	+	0.995073i	$0.531612\pi$
$678$	−7.90997	−0.303781
$679$	−31.8902	−1.22383
$680$	18.9441	0.726472
$681$	−62.4945	−2.39479
$682$	13.2735	0.508268
$683$	−29.3594	−1.12341	−0.561704	−	0.827338i	$-0.689854\pi$
$683$	−29.3594	−1.12341	−0.561704	+	0.827338i	$0.689854\pi$
$684$	9.46475	0.361894
$685$	33.6842	1.28701
$686$	−47.9710	−1.83154
$687$	45.4865	1.73542
$688$	10.0626	0.383633
$689$	1.65969	0.0632293
$690$	−10.3937	−0.395683
$691$	35.7261	1.35909	0.679543	−	0.733635i	$-0.262178\pi$
$691$	35.7261	1.35909	0.679543	+	0.733635i	$0.262178\pi$
$692$	15.9426	0.606047
$693$	−32.2768	−1.22609
$694$	33.2320	1.26147
$695$	53.6205	2.03394
$696$	8.23455	0.312130
$697$	14.9521	0.566353
$698$	22.5018	0.851708
$699$	−26.2781	−0.993930
$700$	52.7848	1.99508
$701$	−8.52460	−0.321970	−0.160985	−	0.986957i	$-0.551467\pi$
$701$	−8.52460	−0.321970	−0.160985	+	0.986957i	$0.551467\pi$
$702$	1.64428	0.0620594
$703$	−3.48384	−0.131396
$704$	−1.47432	−0.0555656
$705$	−59.6465	−2.24642
$706$	26.1441	0.983948
$707$	47.8666	1.80021
$708$	−0.757864	−0.0284823
$709$	−27.1043	−1.01792	−0.508962	−	0.860789i	$-0.669971\pi$
$709$	−27.1043	−1.01792	−0.508962	+	0.860789i	$0.669971\pi$
$710$	−58.6436	−2.20085
$711$	3.83990	0.144008
$712$	−4.02511	−0.150847
$713$	8.60111	0.322114
$714$	63.6197	2.38091
$715$	2.37287	0.0887403
$716$	5.20820	0.194640
$717$	50.6067	1.88994
$718$	−22.0057	−0.821247
$719$	33.6781	1.25598	0.627991	−	0.778221i	$-0.283877\pi$
$719$	33.6781	1.25598	0.627991	+	0.778221i	$0.283877\pi$
$720$	−17.8350	−0.664673
$721$	32.4319	1.20783
$722$	14.5465	0.541365
$723$	−22.9476	−0.853431
$724$	13.5841	0.504848
$725$	32.5473	1.20878
$726$	−24.1478	−0.896208
$727$	12.7870	0.474245	0.237123	−	0.971480i	$-0.423796\pi$
$727$	12.7870	0.474245	0.237123	+	0.971480i	$0.423796\pi$
$728$	−1.97563	−0.0732216
$729$	−43.8395	−1.62368
$730$	35.8630	1.32735
$731$	47.9367	1.77300
$732$	32.5460	1.20293
$733$	−10.8129	−0.399385	−0.199693	−	0.979859i	$-0.563994\pi$
$733$	−10.8129	−0.399385	−0.199693	+	0.979859i	$0.563994\pi$
$734$	−26.6998	−0.985509
$735$	183.075	6.75281
$736$	−0.955349	−0.0352146
$737$	10.6922	0.393851
$738$	−14.0768	−0.518175
$739$	−13.2784	−0.488454	−0.244227	−	0.969718i	$-0.578534\pi$
$739$	−13.2784	−0.488454	−0.244227	+	0.969718i	$0.578534\pi$
$740$	6.56483	0.241328
$741$	−2.33674	−0.0858424
$742$	−20.0171	−0.734850
$743$	−4.96628	−0.182195	−0.0910977	−	0.995842i	$-0.529038\pi$
$743$	−4.96628	−0.182195	−0.0910977	+	0.995842i	$0.529038\pi$
$744$	24.6313	0.903027
$745$	−51.9984	−1.90507
$746$	10.9592	0.401246
$747$	3.08197	0.112763
$748$	−7.02345	−0.256803
$749$	−14.4266	−0.527135
$750$	−63.2492	−2.30953
$751$	0.311325	0.0113604	0.00568021	−	0.999984i	$-0.498192\pi$
$751$	0.311325	0.0113604	0.00568021	+	0.999984i	$0.498192\pi$
$752$	−5.48245	−0.199925
$753$	16.6194	0.605644
$754$	−1.21818	−0.0443635
$755$	−1.55279	−0.0565118
$756$	−19.8312	−0.721254
$757$	16.7158	0.607545	0.303773	−	0.952745i	$-0.401754\pi$
$757$	16.7158	0.607545	0.303773	+	0.952745i	$0.401754\pi$
$758$	−17.3254	−0.629288
$759$	3.85345	0.139871
$760$	8.39200	0.304410
$761$	3.17302	0.115022	0.0575109	−	0.998345i	$-0.481684\pi$
$761$	3.17302	0.115022	0.0575109	+	0.998345i	$0.481684\pi$
$762$	−30.1944	−1.09383
$763$	41.0245	1.48519
$764$	24.5475	0.888098
$765$	−84.9634	−3.07186
$766$	5.76915	0.208448
$767$	0.112115	0.00404823
$768$	−2.73587	−0.0987221
$769$	22.6547	0.816948	0.408474	−	0.912770i	$-0.366061\pi$
$769$	22.6547	0.816948	0.408474	+	0.912770i	$0.366061\pi$
$770$	−28.6185	−1.03134
$771$	−59.0746	−2.12752
$772$	−16.3092	−0.586982
$773$	−30.4052	−1.09360	−0.546799	−	0.837264i	$-0.684154\pi$
$773$	−30.4052	−1.09360	−0.546799	+	0.837264i	$0.684154\pi$
$774$	−45.1303	−1.62218
$775$	97.3559	3.49713
$776$	6.53309	0.234524
$777$	22.0466	0.790917
$778$	−23.8703	−0.855793
$779$	6.62363	0.237316
$780$	4.40328	0.157663
$781$	21.7419	0.777987
$782$	−4.55114	−0.162748
$783$	−12.2280	−0.436993
$784$	16.8274	0.600980
$785$	26.5457	0.947457
$786$	3.23083	0.115240
$787$	1.75377	0.0625150	0.0312575	−	0.999511i	$-0.490049\pi$
$787$	1.75377	0.0625150	0.0312575	+	0.999511i	$0.490049\pi$
$788$	11.4606	0.408265
$789$	69.8554	2.48692
$790$	3.40468	0.121133
$791$	−14.1130	−0.501800
$792$	6.61228	0.234957
$793$	−4.81469	−0.170975
$794$	31.9687	1.13453
$795$	44.6141	1.58230
$796$	19.3940	0.687400
$797$	−7.36674	−0.260943	−0.130472	−	0.991452i	$-0.541649\pi$
$797$	−7.36674	−0.260943	−0.130472	+	0.991452i	$0.541649\pi$
$798$	28.1828	0.997660
$799$	−26.1176	−0.923974
$800$	−10.8136	−0.382318
$801$	18.0524	0.637852
$802$	33.8532	1.19540
$803$	−13.2961	−0.469209
$804$	19.8412	0.699745
$805$	−18.5445	−0.653609
$806$	−3.64383	−0.128348
$807$	−1.22131	−0.0429922
$808$	−9.80604	−0.344975
$809$	11.0917	0.389963	0.194982	−	0.980807i	$-0.437535\pi$
$809$	11.0917	0.389963	0.194982	+	0.980807i	$0.437535\pi$
$810$	−9.30532	−0.326956
$811$	−17.0057	−0.597151	−0.298576	−	0.954386i	$-0.596511\pi$
$811$	−17.0057	−0.597151	−0.298576	+	0.954386i	$0.596511\pi$
$812$	14.6921	0.515591
$813$	41.6547	1.46089
$814$	−2.43389	−0.0853078
$815$	11.3804	0.398639
$816$	−13.0333	−0.456255
$817$	21.2354	0.742932
$818$	−33.0756	−1.15646
$819$	8.86061	0.309615
$820$	−12.4813	−0.435867
$821$	21.5837	0.753275	0.376637	−	0.926361i	$-0.377080\pi$
$821$	21.5837	0.753275	0.376637	+	0.926361i	$0.377080\pi$
$822$	−23.1742	−0.808294
$823$	45.3151	1.57958	0.789792	−	0.613375i	$-0.210188\pi$
$823$	45.3151	1.57958	0.789792	+	0.613375i	$0.210188\pi$
$824$	−6.64406	−0.231457
$825$	43.6172	1.51855
$826$	−1.35218	−0.0470485
$827$	−11.4938	−0.399678	−0.199839	−	0.979829i	$-0.564042\pi$
$827$	−11.4938	−0.399678	−0.199839	+	0.979829i	$0.564042\pi$
$828$	4.28470	0.148904
$829$	31.6385	1.09885	0.549425	−	0.835543i	$-0.314847\pi$
$829$	31.6385	1.09885	0.549425	+	0.835543i	$0.314847\pi$
$830$	2.73265	0.0948518
$831$	−90.1249	−3.12640
$832$	0.404731	0.0140315
$833$	80.1634	2.77750
$834$	−36.8901	−1.27740
$835$	−23.4800	−0.812558
$836$	−3.11131	−0.107607
$837$	−36.5765	−1.26427
$838$	5.82701	0.201291
$839$	50.5266	1.74437	0.872185	−	0.489175i	$-0.162702\pi$
$839$	50.5266	1.74437	0.872185	+	0.489175i	$0.162702\pi$
$840$	−53.1066	−1.83235
$841$	−19.9408	−0.687614
$842$	−16.3584	−0.563748
$843$	−86.6877	−2.98568
$844$	−5.46025	−0.187950
$845$	51.0448	1.75599
$846$	24.5886	0.845373
$847$	−43.0845	−1.48040
$848$	4.10074	0.140820
$849$	25.6357	0.879814
$850$	−51.5143	−1.76693
$851$	−1.57714	−0.0540636
$852$	40.3459	1.38223
$853$	−45.1702	−1.54660	−0.773299	−	0.634041i	$-0.781395\pi$
$853$	−45.1702	−1.54660	−0.773299	+	0.634041i	$0.781395\pi$
$854$	58.0686	1.98707
$855$	−37.6378	−1.28719
$856$	2.95545	0.101015
$857$	−56.3655	−1.92541	−0.962704	−	0.270556i	$-0.912792\pi$
$857$	−56.3655	−1.92541	−0.962704	+	0.270556i	$0.912792\pi$
$858$	−1.63250	−0.0557327
$859$	7.86572	0.268375	0.134187	−	0.990956i	$-0.457158\pi$
$859$	7.86572	0.268375	0.134187	+	0.990956i	$0.457158\pi$
$860$	−40.0152	−1.36451
$861$	−41.9159	−1.42849
$862$	6.68804	0.227796
$863$	37.7831	1.28615	0.643075	−	0.765803i	$-0.277658\pi$
$863$	37.7831	1.28615	0.643075	+	0.765803i	$0.277658\pi$
$864$	4.06266	0.138214
$865$	−63.3979	−2.15559
$866$	22.7147	0.771876
$867$	−15.5787	−0.529082
$868$	43.9472	1.49166
$869$	−1.26228	−0.0428197
$870$	−32.7458	−1.11019
$871$	−2.93521	−0.0994557
$872$	−8.40436	−0.284608
$873$	−29.3006	−0.991677
$874$	−2.01610	−0.0681956
$875$	−112.849	−3.81500
$876$	−24.6733	−0.833633
$877$	−34.0747	−1.15062	−0.575310	−	0.817936i	$-0.695118\pi$
$877$	−34.0747	−1.15062	−0.575310	+	0.817936i	$0.695118\pi$
$878$	−23.1104	−0.779940
$879$	62.5455	2.10961
$880$	5.86284	0.197636
$881$	28.7207	0.967625	0.483812	−	0.875172i	$-0.339252\pi$
$881$	28.7207	0.967625	0.483812	+	0.875172i	$0.339252\pi$
$882$	−75.4704	−2.54122
$883$	−24.8300	−0.835597	−0.417799	−	0.908540i	$-0.637198\pi$
$883$	−24.8300	−0.835597	−0.417799	+	0.908540i	$0.637198\pi$
$884$	1.92808	0.0648482
$885$	3.01375	0.101306
$886$	40.3154	1.35442
$887$	50.7448	1.70384	0.851921	−	0.523670i	$-0.175437\pi$
$887$	50.7448	1.70384	0.851921	+	0.523670i	$0.175437\pi$
$888$	−4.51651	−0.151564
$889$	−53.8729	−1.80684
$890$	16.0064	0.536534
$891$	3.44992	0.115577
$892$	1.20110	0.0402156
$893$	−11.5698	−0.387168
$894$	35.7742	1.19647
$895$	−20.7111	−0.692295
$896$	−4.88134	−0.163074
$897$	−1.05785	−0.0353205
$898$	22.8297	0.761835
$899$	27.0980	0.903769
$900$	48.4986	1.61662
$901$	19.5353	0.650815
$902$	4.62741	0.154076
$903$	−134.383	−4.47197
$904$	2.89121	0.0961603
$905$	−54.0188	−1.79565
$906$	1.06830	0.0354918
$907$	−5.88682	−0.195469	−0.0977343	−	0.995213i	$-0.531160\pi$
$907$	−5.88682	−0.195469	−0.0977343	+	0.995213i	$0.531160\pi$
$908$	22.8427	0.758060
$909$	43.9797	1.45872
$910$	7.85633	0.260435
$911$	−10.3963	−0.344445	−0.172222	−	0.985058i	$-0.555095\pi$
$911$	−10.3963	−0.344445	−0.172222	+	0.985058i	$0.555095\pi$
$912$	−5.77358	−0.191182
$913$	−1.01312	−0.0335294
$914$	26.1099	0.863637
$915$	−129.423	−4.27860
$916$	−16.6260	−0.549339
$917$	5.76444	0.190359
$918$	19.3539	0.638773
$919$	−42.1338	−1.38987	−0.694933	−	0.719074i	$-0.744566\pi$
$919$	−42.1338	−1.38987	−0.694933	+	0.719074i	$0.744566\pi$
$920$	3.79907	0.125252
$921$	−86.5241	−2.85107
$922$	26.3571	0.868025
$923$	−5.96858	−0.196458
$924$	19.6891	0.647724
$925$	−17.8516	−0.586958
$926$	−12.3730	−0.406603
$927$	29.7983	0.978706
$928$	−3.00985	−0.0988032
$929$	2.49871	0.0819800	0.0409900	−	0.999160i	$-0.486949\pi$
$929$	2.49871	0.0819800	0.0409900	+	0.999160i	$0.486949\pi$
$930$	−97.9495	−3.21189
$931$	35.5114	1.16384
$932$	9.60505	0.314624
$933$	−79.8734	−2.61494
$934$	29.7862	0.974635
$935$	27.9297	0.913398
$936$	−1.81520	−0.0593317
$937$	20.8383	0.680758	0.340379	−	0.940288i	$-0.389445\pi$
$937$	20.8383	0.680758	0.340379	+	0.940288i	$0.389445\pi$
$938$	35.4007	1.15587
$939$	18.7476	0.611804
$940$	21.8017	0.711093
$941$	34.5191	1.12529	0.562646	−	0.826698i	$-0.309784\pi$
$941$	34.5191	1.12529	0.562646	+	0.826698i	$0.309784\pi$
$942$	−18.2631	−0.595043
$943$	2.99852	0.0976453
$944$	0.277011	0.00901593
$945$	78.8613	2.56536
$946$	14.8355	0.482344
$947$	−6.04765	−0.196522	−0.0982611	−	0.995161i	$-0.531328\pi$
$947$	−6.04765	−0.196522	−0.0982611	+	0.995161i	$0.531328\pi$
$948$	−2.34237	−0.0760768
$949$	3.65004	0.118485
$950$	−22.8202	−0.740387
$951$	−59.6786	−1.93521
$952$	−23.2539	−0.753665
$953$	17.1318	0.554955	0.277477	−	0.960732i	$-0.410502\pi$
$953$	17.1318	0.554955	0.277477	+	0.960732i	$0.410502\pi$
$954$	−18.3917	−0.595452
$955$	−97.6164	−3.15879
$956$	−18.4975	−0.598252
$957$	12.1404	0.392443
$958$	−9.04329	−0.292176
$959$	−41.3475	−1.33518
$960$	10.8795	0.351135
$961$	50.0559	1.61471
$962$	0.668150	0.0215420
$963$	−13.2551	−0.427140
$964$	8.38770	0.270150
$965$	64.8558	2.08778
$966$	12.7584	0.410494
$967$	20.4416	0.657357	0.328679	−	0.944442i	$-0.393397\pi$
$967$	20.4416	0.657357	0.328679	+	0.944442i	$0.393397\pi$
$968$	8.82637	0.283690
$969$	−27.5045	−0.883571
$970$	−25.9797	−0.834157
$971$	−30.2187	−0.969764	−0.484882	−	0.874579i	$-0.661138\pi$
$971$	−30.2187	−0.969764	−0.484882	+	0.874579i	$0.661138\pi$
$972$	18.5899	0.596271
$973$	−65.8194	−2.11007
$974$	21.8519	0.700180
$975$	−11.9738	−0.383467
$976$	−11.8960	−0.380783
$977$	14.6546	0.468842	0.234421	−	0.972135i	$-0.424681\pi$
$977$	14.6546	0.468842	0.234421	+	0.972135i	$0.424681\pi$
$978$	−7.82958	−0.250362
$979$	−5.93431	−0.189661
$980$	−66.9165	−2.13757
$981$	37.6932	1.20345
$982$	−36.1502	−1.15360
$983$	−49.2664	−1.57135	−0.785677	−	0.618637i	$-0.787685\pi$
$983$	−49.2664	−1.57135	−0.785677	+	0.618637i	$0.787685\pi$
$984$	8.58698	0.273743
$985$	−45.5744	−1.45212
$986$	−14.3385	−0.456630
$987$	73.2164	2.33050
$988$	0.854115	0.0271730
$989$	9.61328	0.305685
$990$	−26.2946	−0.835697
$991$	−37.5879	−1.19402	−0.597010	−	0.802234i	$-0.703645\pi$
$991$	−37.5879	−1.19402	−0.597010	+	0.802234i	$0.703645\pi$
$992$	−9.00310	−0.285849
$993$	−61.9845	−1.96702
$994$	71.9853	2.28323
$995$	−77.1226	−2.44495
$996$	−1.88003	−0.0595709
$997$	1.07070	0.0339095	0.0169547	−	0.999856i	$-0.494603\pi$
$997$	1.07070	0.0339095	0.0169547	+	0.999856i	$0.494603\pi$
$998$	−42.5255	−1.34612
$999$	6.70685	0.212195

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4034.2.a.c.1.6	✓	49

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4034.2.a.c.1.6	✓	49	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:	\( N \)	\(=\)	\( 4034 = 2 \cdot 2017 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4034.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.73587 q^{3} +1.00000 q^{4} -3.97663 q^{5} +2.73587 q^{6} +4.88134 q^{7} -1.00000 q^{8} +4.48496 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.73587 q^{3} +1.00000 q^{4} -3.97663 q^{5} +2.73587 q^{6} +4.88134 q^{7} -1.00000 q^{8} +4.48496 q^{9} +3.97663 q^{10} -1.47432 q^{11} -2.73587 q^{12} +0.404731 q^{13} -4.88134 q^{14} +10.8795 q^{15} +1.00000 q^{16} +4.76385 q^{17} -4.48496 q^{18} +2.11033 q^{19} -3.97663 q^{20} -13.3547 q^{21} +1.47432 q^{22} +0.955349 q^{23} +2.73587 q^{24} +10.8136 q^{25} -0.404731 q^{26} -4.06266 q^{27} +4.88134 q^{28} +3.00985 q^{29} -10.8795 q^{30} +9.00310 q^{31} -1.00000 q^{32} +4.03355 q^{33} -4.76385 q^{34} -19.4113 q^{35} +4.48496 q^{36} -1.65085 q^{37} -2.11033 q^{38} -1.10729 q^{39} +3.97663 q^{40} +3.13867 q^{41} +13.3547 q^{42} +10.0626 q^{43} -1.47432 q^{44} -17.8350 q^{45} -0.955349 q^{46} -5.48245 q^{47} -2.73587 q^{48} +16.8274 q^{49} -10.8136 q^{50} -13.0333 q^{51} +0.404731 q^{52} +4.10074 q^{53} +4.06266 q^{54} +5.86284 q^{55} -4.88134 q^{56} -5.77358 q^{57} -3.00985 q^{58} +0.277011 q^{59} +10.8795 q^{60} -11.8960 q^{61} -9.00310 q^{62} +21.8926 q^{63} +1.00000 q^{64} -1.60946 q^{65} -4.03355 q^{66} -7.25225 q^{67} +4.76385 q^{68} -2.61371 q^{69} +19.4113 q^{70} -14.7470 q^{71} -4.48496 q^{72} +9.01845 q^{73} +1.65085 q^{74} -29.5845 q^{75} +2.11033 q^{76} -7.19666 q^{77} +1.10729 q^{78} +0.856173 q^{79} -3.97663 q^{80} -2.34000 q^{81} -3.13867 q^{82} +0.687178 q^{83} -13.3547 q^{84} -18.9441 q^{85} -10.0626 q^{86} -8.23455 q^{87} +1.47432 q^{88} +4.02511 q^{89} +17.8350 q^{90} +1.97563 q^{91} +0.955349 q^{92} -24.6313 q^{93} +5.48245 q^{94} -8.39200 q^{95} +2.73587 q^{96} -6.53309 q^{97} -16.8274 q^{98} -6.61228 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 49 q - 49 q^{2} + 8 q^{3} + 49 q^{4} - 8 q^{5} - 8 q^{6} + 18 q^{7} - 49 q^{8} + 59 q^{9}+O(q^{10}) \) 49 * q - 49 * q^2 + 8 * q^3 + 49 * q^4 - 8 * q^5 - 8 * q^6 + 18 * q^7 - 49 * q^8 + 59 * q^9	\( 49 q - 49 q^{2} + 8 q^{3} + 49 q^{4} - 8 q^{5} - 8 q^{6} + 18 q^{7} - 49 q^{8} + 59 q^{9} + 8 q^{10} + q^{11} + 8 q^{12} + 9 q^{13} - 18 q^{14} + 15 q^{15} + 49 q^{16} - 27 q^{17} - 59 q^{18} + 27 q^{19} - 8 q^{20} + 13 q^{21} - q^{22} + 16 q^{23} - 8 q^{24} + 71 q^{25} - 9 q^{26} + 29 q^{27} + 18 q^{28} - 7 q^{29} - 15 q^{30} + 75 q^{31} - 49 q^{32} - 3 q^{33} + 27 q^{34} - 16 q^{35} + 59 q^{36} + 36 q^{37} - 27 q^{38} + 24 q^{39} + 8 q^{40} - 12 q^{41} - 13 q^{42} + 22 q^{43} + q^{44} + 5 q^{45} - 16 q^{46} + 26 q^{47} + 8 q^{48} + 107 q^{49} - 71 q^{50} + 35 q^{51} + 9 q^{52} - 10 q^{53} - 29 q^{54} + 76 q^{55} - 18 q^{56} - 10 q^{57} + 7 q^{58} + 9 q^{59} + 15 q^{60} + 87 q^{61} - 75 q^{62} + 68 q^{63} + 49 q^{64} - 6 q^{65} + 3 q^{66} + 46 q^{67} - 27 q^{68} + 70 q^{69} + 16 q^{70} + 40 q^{71} - 59 q^{72} + 6 q^{73} - 36 q^{74} + 69 q^{75} + 27 q^{76} - 12 q^{77} - 24 q^{78} + 76 q^{79} - 8 q^{80} + 77 q^{81} + 12 q^{82} - 32 q^{83} + 13 q^{84} + 19 q^{85} - 22 q^{86} + 36 q^{87} - q^{88} + 34 q^{89} - 5 q^{90} + 119 q^{91} + 16 q^{92} - 5 q^{93} - 26 q^{94} - 2 q^{95} - 8 q^{96} + 52 q^{97} - 107 q^{98} + 26 q^{99}+O(q^{100}) \) 49 * q - 49 * q^2 + 8 * q^3 + 49 * q^4 - 8 * q^5 - 8 * q^6 + 18 * q^7 - 49 * q^8 + 59 * q^9 + 8 * q^10 + q^11 + 8 * q^12 + 9 * q^13 - 18 * q^14 + 15 * q^15 + 49 * q^16 - 27 * q^17 - 59 * q^18 + 27 * q^19 - 8 * q^20 + 13 * q^21 - q^22 + 16 * q^23 - 8 * q^24 + 71 * q^25 - 9 * q^26 + 29 * q^27 + 18 * q^28 - 7 * q^29 - 15 * q^30 + 75 * q^31 - 49 * q^32 - 3 * q^33 + 27 * q^34 - 16 * q^35 + 59 * q^36 + 36 * q^37 - 27 * q^38 + 24 * q^39 + 8 * q^40 - 12 * q^41 - 13 * q^42 + 22 * q^43 + q^44 + 5 * q^45 - 16 * q^46 + 26 * q^47 + 8 * q^48 + 107 * q^49 - 71 * q^50 + 35 * q^51 + 9 * q^52 - 10 * q^53 - 29 * q^54 + 76 * q^55 - 18 * q^56 - 10 * q^57 + 7 * q^58 + 9 * q^59 + 15 * q^60 + 87 * q^61 - 75 * q^62 + 68 * q^63 + 49 * q^64 - 6 * q^65 + 3 * q^66 + 46 * q^67 - 27 * q^68 + 70 * q^69 + 16 * q^70 + 40 * q^71 - 59 * q^72 + 6 * q^73 - 36 * q^74 + 69 * q^75 + 27 * q^76 - 12 * q^77 - 24 * q^78 + 76 * q^79 - 8 * q^80 + 77 * q^81 + 12 * q^82 - 32 * q^83 + 13 * q^84 + 19 * q^85 - 22 * q^86 + 36 * q^87 - q^88 + 34 * q^89 - 5 * q^90 + 119 * q^91 + 16 * q^92 - 5 * q^93 - 26 * q^94 - 2 * q^95 - 8 * q^96 + 52 * q^97 - 107 * q^98 + 26 * q^99

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