LMFDB - Embedded newform 8035.2.a.c.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8035,2,Mod(1,8035)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8035, 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("8035.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8035 = 5 \cdot 1607 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8035.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$64.1597980241$
Analytic rank:	$0$
Dimension:	$127$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	8035.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.47063 q^{2} -2.44892 q^{3} +4.10400 q^{4} -1.00000 q^{5} +6.05037 q^{6} +0.863350 q^{7} -5.19820 q^{8} +2.99721 q^{9} +O(q^{10})$	\(q-2.47063 q^{2} -2.44892 q^{3} +4.10400 q^{4} -1.00000 q^{5} +6.05037 q^{6} +0.863350 q^{7} -5.19820 q^{8} +2.99721 q^{9} +2.47063 q^{10} -2.75641 q^{11} -10.0504 q^{12} -1.88663 q^{13} -2.13302 q^{14} +2.44892 q^{15} +4.63482 q^{16} +4.04453 q^{17} -7.40500 q^{18} -1.96067 q^{19} -4.10400 q^{20} -2.11427 q^{21} +6.81005 q^{22} +0.0529010 q^{23} +12.7300 q^{24} +1.00000 q^{25} +4.66115 q^{26} +0.00682633 q^{27} +3.54319 q^{28} -0.276838 q^{29} -6.05037 q^{30} -1.79194 q^{31} -1.05451 q^{32} +6.75022 q^{33} -9.99252 q^{34} -0.863350 q^{35} +12.3006 q^{36} -0.975732 q^{37} +4.84408 q^{38} +4.62020 q^{39} +5.19820 q^{40} -10.6593 q^{41} +5.22359 q^{42} +2.99758 q^{43} -11.3123 q^{44} -2.99721 q^{45} -0.130699 q^{46} +1.76711 q^{47} -11.3503 q^{48} -6.25463 q^{49} -2.47063 q^{50} -9.90472 q^{51} -7.74271 q^{52} +13.6335 q^{53} -0.0168653 q^{54} +2.75641 q^{55} -4.48787 q^{56} +4.80152 q^{57} +0.683964 q^{58} -5.66720 q^{59} +10.0504 q^{60} -9.51933 q^{61} +4.42721 q^{62} +2.58764 q^{63} -6.66433 q^{64} +1.88663 q^{65} -16.6773 q^{66} +2.82571 q^{67} +16.5987 q^{68} -0.129550 q^{69} +2.13302 q^{70} +9.53096 q^{71} -15.5801 q^{72} +0.614249 q^{73} +2.41067 q^{74} -2.44892 q^{75} -8.04659 q^{76} -2.37974 q^{77} -11.4148 q^{78} -15.7986 q^{79} -4.63482 q^{80} -9.00835 q^{81} +26.3352 q^{82} -0.299636 q^{83} -8.67698 q^{84} -4.04453 q^{85} -7.40591 q^{86} +0.677955 q^{87} +14.3284 q^{88} +16.1278 q^{89} +7.40500 q^{90} -1.62882 q^{91} +0.217106 q^{92} +4.38831 q^{93} -4.36586 q^{94} +1.96067 q^{95} +2.58242 q^{96} -18.8571 q^{97} +15.4529 q^{98} -8.26153 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 127 q + 19 q^{2} + 10 q^{3} + 125 q^{4} - 127 q^{5} + 13 q^{7} + 54 q^{8} + 123 q^{9}+O(q^{10}) $ 127 * q + 19 * q^2 + 10 * q^3 + 125 * q^4 - 127 * q^5 + 13 * q^7 + 54 * q^8 + 123 * q^9	\( 127 q + 19 q^{2} + 10 q^{3} + 125 q^{4} - 127 q^{5} + 13 q^{7} + 54 q^{8} + 123 q^{9} - 19 q^{10} + 30 q^{11} + 35 q^{12} + 30 q^{13} + 39 q^{14} - 10 q^{15} + 121 q^{16} + 63 q^{17} + 53 q^{18} - 35 q^{19} - 125 q^{20} + 33 q^{21} + 49 q^{22} + 61 q^{23} - 5 q^{24} + 127 q^{25} + 10 q^{26} + 40 q^{27} + 32 q^{28} + 134 q^{29} - 25 q^{31} + 122 q^{32} + 48 q^{33} - 21 q^{34} - 13 q^{35} + 133 q^{36} + 60 q^{37} + 33 q^{38} + 26 q^{39} - 54 q^{40} + 9 q^{41} + 45 q^{42} + 48 q^{43} + 85 q^{44} - 123 q^{45} - 11 q^{46} + 57 q^{47} + 71 q^{48} + 70 q^{49} + 19 q^{50} + 45 q^{51} + 68 q^{52} + 182 q^{53} - 29 q^{54} - 30 q^{55} + 96 q^{56} + 74 q^{57} + 47 q^{58} + 19 q^{59} - 35 q^{60} + 16 q^{61} + 43 q^{62} + 73 q^{63} + 110 q^{64} - 30 q^{65} + 8 q^{66} + 40 q^{67} + 129 q^{68} + 2 q^{69} - 39 q^{70} + 48 q^{71} + 151 q^{72} + 30 q^{73} + 117 q^{74} + 10 q^{75} - 98 q^{76} + 134 q^{77} + 54 q^{78} + 23 q^{79} - 121 q^{80} + 111 q^{81} + 4 q^{82} + 92 q^{83} + 48 q^{84} - 63 q^{85} + 42 q^{86} + 69 q^{87} + 121 q^{88} + 12 q^{89} - 53 q^{90} - 30 q^{91} + 175 q^{92} + 82 q^{93} - 23 q^{94} + 35 q^{95} + 6 q^{96} + 67 q^{97} + 122 q^{98} + 73 q^{99}+O(q^{100}) \) 127 * q + 19 * q^2 + 10 * q^3 + 125 * q^4 - 127 * q^5 + 13 * q^7 + 54 * q^8 + 123 * q^9 - 19 * q^10 + 30 * q^11 + 35 * q^12 + 30 * q^13 + 39 * q^14 - 10 * q^15 + 121 * q^16 + 63 * q^17 + 53 * q^18 - 35 * q^19 - 125 * q^20 + 33 * q^21 + 49 * q^22 + 61 * q^23 - 5 * q^24 + 127 * q^25 + 10 * q^26 + 40 * q^27 + 32 * q^28 + 134 * q^29 - 25 * q^31 + 122 * q^32 + 48 * q^33 - 21 * q^34 - 13 * q^35 + 133 * q^36 + 60 * q^37 + 33 * q^38 + 26 * q^39 - 54 * q^40 + 9 * q^41 + 45 * q^42 + 48 * q^43 + 85 * q^44 - 123 * q^45 - 11 * q^46 + 57 * q^47 + 71 * q^48 + 70 * q^49 + 19 * q^50 + 45 * q^51 + 68 * q^52 + 182 * q^53 - 29 * q^54 - 30 * q^55 + 96 * q^56 + 74 * q^57 + 47 * q^58 + 19 * q^59 - 35 * q^60 + 16 * q^61 + 43 * q^62 + 73 * q^63 + 110 * q^64 - 30 * q^65 + 8 * q^66 + 40 * q^67 + 129 * q^68 + 2 * q^69 - 39 * q^70 + 48 * q^71 + 151 * q^72 + 30 * q^73 + 117 * q^74 + 10 * q^75 - 98 * q^76 + 134 * q^77 + 54 * q^78 + 23 * q^79 - 121 * q^80 + 111 * q^81 + 4 * q^82 + 92 * q^83 + 48 * q^84 - 63 * q^85 + 42 * q^86 + 69 * q^87 + 121 * q^88 + 12 * q^89 - 53 * q^90 - 30 * q^91 + 175 * q^92 + 82 * q^93 - 23 * q^94 + 35 * q^95 + 6 * q^96 + 67 * q^97 + 122 * q^98 + 73 * 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 $

$2$	−2.47063	−1.74700	−0.873499	−	0.486826i	$-0.838154\pi$
$2$	−2.47063	−1.74700	−0.873499	+	0.486826i	$0.838154\pi$
$3$	−2.44892	−1.41389	−0.706943	−	0.707271i	$-0.749926\pi$
$3$	−2.44892	−1.41389	−0.706943	+	0.707271i	$0.749926\pi$
$4$	4.10400	2.05200
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	6.05037	2.47005
$7$	0.863350	0.326315	0.163158	−	0.986600i	$-0.447832\pi$
$7$	0.863350	0.326315	0.163158	+	0.986600i	$0.447832\pi$
$8$	−5.19820	−1.83784
$9$	2.99721	0.999071
$10$	2.47063	0.781281
$11$	−2.75641	−0.831087	−0.415544	−	0.909573i	$-0.636409\pi$
$11$	−2.75641	−0.831087	−0.415544	+	0.909573i	$0.636409\pi$
$12$	−10.0504	−2.90129
$13$	−1.88663	−0.523256	−0.261628	−	0.965169i	$-0.584259\pi$
$13$	−1.88663	−0.523256	−0.261628	+	0.965169i	$0.584259\pi$
$14$	−2.13302	−0.570072
$15$	2.44892	0.632309
$16$	4.63482	1.15871
$17$	4.04453	0.980942	0.490471	−	0.871458i	$-0.336825\pi$
$17$	4.04453	0.980942	0.490471	+	0.871458i	$0.336825\pi$
$18$	−7.40500	−1.74537
$19$	−1.96067	−0.449808	−0.224904	−	0.974381i	$-0.572207\pi$
$19$	−1.96067	−0.449808	−0.224904	+	0.974381i	$0.572207\pi$
$20$	−4.10400	−0.917682
$21$	−2.11427	−0.461373
$22$	6.81005	1.45191
$23$	0.0529010	0.0110306	0.00551531	−	0.999985i	$-0.498244\pi$
$23$	0.0529010	0.0110306	0.00551531	+	0.999985i	$0.498244\pi$
$24$	12.7300	2.59850
$25$	1.00000	0.200000
$26$	4.66115	0.914127
$27$	0.00682633	0.00131373
$28$	3.54319	0.669599
$29$	−0.276838	−0.0514075	−0.0257038	−	0.999670i	$-0.508183\pi$
$29$	−0.276838	−0.0514075	−0.0257038	+	0.999670i	$0.508183\pi$
$30$	−6.05037	−1.10464
$31$	−1.79194	−0.321841	−0.160921	−	0.986967i	$-0.551446\pi$
$31$	−1.79194	−0.321841	−0.160921	+	0.986967i	$0.551446\pi$
$32$	−1.05451	−0.186413
$33$	6.75022	1.17506
$34$	−9.99252	−1.71370
$35$	−0.863350	−0.145933
$36$	12.3006	2.05009
$37$	−0.975732	−0.160409	−0.0802046	−	0.996778i	$-0.525557\pi$
$37$	−0.975732	−0.160409	−0.0802046	+	0.996778i	$0.525557\pi$
$38$	4.84408	0.785814
$39$	4.62020	0.739824
$40$	5.19820	0.821908
$41$	−10.6593	−1.66470	−0.832352	−	0.554248i	$-0.813006\pi$
$41$	−10.6593	−1.66470	−0.832352	+	0.554248i	$0.813006\pi$
$42$	5.22359	0.806017
$43$	2.99758	0.457127	0.228564	−	0.973529i	$-0.426597\pi$
$43$	2.99758	0.457127	0.228564	+	0.973529i	$0.426597\pi$
$44$	−11.3123	−1.70539
$45$	−2.99721	−0.446798
$46$	−0.130699	−0.0192705
$47$	1.76711	0.257759	0.128880	−	0.991660i	$-0.458862\pi$
$47$	1.76711	0.257759	0.128880	+	0.991660i	$0.458862\pi$
$48$	−11.3503	−1.63828
$49$	−6.25463	−0.893518
$50$	−2.47063	−0.349400
$51$	−9.90472	−1.38694
$52$	−7.74271	−1.07372
$53$	13.6335	1.87271	0.936356	−	0.351053i	$-0.114176\pi$
$53$	13.6335	1.87271	0.936356	+	0.351053i	$0.114176\pi$
$54$	−0.0168653	−0.00229508
$55$	2.75641	0.371674
$56$	−4.48787	−0.599716
$57$	4.80152	0.635977
$58$	0.683964	0.0898089
$59$	−5.66720	−0.737806	−0.368903	−	0.929468i	$-0.620267\pi$
$59$	−5.66720	−0.737806	−0.368903	+	0.929468i	$0.620267\pi$
$60$	10.0504	1.29750
$61$	−9.51933	−1.21883	−0.609413	−	0.792853i	$-0.708595\pi$
$61$	−9.51933	−1.21883	−0.609413	+	0.792853i	$0.708595\pi$
$62$	4.42721	0.562256
$63$	2.58764	0.326012
$64$	−6.66433	−0.833042
$65$	1.88663	0.234007
$66$	−16.6773	−2.05283
$67$	2.82571	0.345215	0.172608	−	0.984991i	$-0.444781\pi$
$67$	2.82571	0.345215	0.172608	+	0.984991i	$0.444781\pi$
$68$	16.5987	2.01289
$69$	−0.129550	−0.0155960
$70$	2.13302	0.254944
$71$	9.53096	1.13112	0.565558	−	0.824708i	$-0.308661\pi$
$71$	9.53096	1.13112	0.565558	+	0.824708i	$0.308661\pi$
$72$	−15.5801	−1.83613
$73$	0.614249	0.0718924	0.0359462	−	0.999354i	$-0.488556\pi$
$73$	0.614249	0.0718924	0.0359462	+	0.999354i	$0.488556\pi$
$74$	2.41067	0.280235
$75$	−2.44892	−0.282777
$76$	−8.04659	−0.923007
$77$	−2.37974	−0.271197
$78$	−11.4148	−1.29247
$79$	−15.7986	−1.77748	−0.888741	−	0.458410i	$-0.848419\pi$
$79$	−15.7986	−1.77748	−0.888741	+	0.458410i	$0.848419\pi$
$80$	−4.63482	−0.518189
$81$	−9.00835	−1.00093
$82$	26.3352	2.90823
$83$	−0.299636	−0.0328893	−0.0164447	−	0.999865i	$-0.505235\pi$
$83$	−0.299636	−0.0328893	−0.0164447	+	0.999865i	$0.505235\pi$
$84$	−8.67698	−0.946737
$85$	−4.04453	−0.438690
$86$	−7.40591	−0.798600
$87$	0.677955	0.0726844
$88$	14.3284	1.52741
$89$	16.1278	1.70954	0.854771	−	0.519005i	$-0.173698\pi$
$89$	16.1278	1.70954	0.854771	+	0.519005i	$0.173698\pi$
$90$	7.40500	0.780555
$91$	−1.62882	−0.170746
$92$	0.217106	0.0226349
$93$	4.38831	0.455046
$94$	−4.36586	−0.450304
$95$	1.96067	0.201160
$96$	2.58242	0.263567
$97$	−18.8571	−1.91465	−0.957324	−	0.289016i	$-0.906672\pi$
$97$	−18.8571	−1.91465	−0.957324	+	0.289016i	$0.906672\pi$
$98$	15.4529	1.56097
$99$	−8.26153	−0.830315
$100$	4.10400	0.410400
$101$	16.6218	1.65393	0.826964	−	0.562255i	$-0.190066\pi$
$101$	16.6218	1.65393	0.826964	+	0.562255i	$0.190066\pi$
$102$	24.4709	2.42298
$103$	4.64020	0.457212	0.228606	−	0.973519i	$-0.426583\pi$
$103$	4.64020	0.457212	0.228606	+	0.973519i	$0.426583\pi$
$104$	9.80706	0.961662
$105$	2.11427	0.206332
$106$	−33.6834	−3.27162
$107$	−3.61450	−0.349427	−0.174713	−	0.984619i	$-0.555900\pi$
$107$	−3.61450	−0.349427	−0.174713	+	0.984619i	$0.555900\pi$
$108$	0.0280153	0.00269577
$109$	0.965927	0.0925191	0.0462595	−	0.998929i	$-0.485270\pi$
$109$	0.965927	0.0925191	0.0462595	+	0.998929i	$0.485270\pi$
$110$	−6.81005	−0.649313
$111$	2.38949	0.226800
$112$	4.00147	0.378103
$113$	10.7652	1.01270	0.506350	−	0.862328i	$-0.330994\pi$
$113$	10.7652	1.01270	0.506350	+	0.862328i	$0.330994\pi$
$114$	−11.8628	−1.11105
$115$	−0.0529010	−0.00493305
$116$	−1.13614	−0.105488
$117$	−5.65462	−0.522770
$118$	14.0015	1.28895
$119$	3.49184	0.320096
$120$	−12.7300	−1.16208
$121$	−3.40223	−0.309294
$122$	23.5187	2.12928
$123$	26.1038	2.35370
$124$	−7.35410	−0.660418
$125$	−1.00000	−0.0894427
$126$	−6.39310	−0.569543
$127$	−5.10018	−0.452568	−0.226284	−	0.974061i	$-0.572658\pi$
$127$	−5.10018	−0.452568	−0.226284	+	0.974061i	$0.572658\pi$
$128$	18.5741	1.64174
$129$	−7.34084	−0.646325
$130$	−4.66115	−0.408810
$131$	13.6374	1.19150	0.595752	−	0.803168i	$-0.296854\pi$
$131$	13.6374	1.19150	0.595752	+	0.803168i	$0.296854\pi$
$132$	27.7029	2.41123
$133$	−1.69274	−0.146779
$134$	−6.98128	−0.603090
$135$	−0.00682633	−0.000587517 0
$136$	−21.0243	−1.80282
$137$	−17.4093	−1.48738	−0.743688	−	0.668527i	$-0.766925\pi$
$137$	−17.4093	−1.48738	−0.743688	+	0.668527i	$0.766925\pi$
$138$	0.320071	0.0272462
$139$	−1.61558	−0.137032	−0.0685159	−	0.997650i	$-0.521826\pi$
$139$	−1.61558	−0.137032	−0.0685159	+	0.997650i	$0.521826\pi$
$140$	−3.54319	−0.299454
$141$	−4.32750	−0.364442
$142$	−23.5475	−1.97606
$143$	5.20030	0.434871
$144$	13.8915	1.15763
$145$	0.276838	0.0229902
$146$	−1.51758	−0.125596
$147$	15.3171	1.26333
$148$	−4.00440	−0.329160
$149$	11.5463	0.945909	0.472955	−	0.881087i	$-0.343187\pi$
$149$	11.5463	0.945909	0.472955	+	0.881087i	$0.343187\pi$
$150$	6.05037	0.494011
$151$	9.15326	0.744882	0.372441	−	0.928056i	$-0.378521\pi$
$151$	9.15326	0.744882	0.372441	+	0.928056i	$0.378521\pi$
$152$	10.1920	0.826677
$153$	12.1223	0.980030
$154$	5.87945	0.473780
$155$	1.79194	0.143932
$156$	18.9613	1.51812
$157$	6.83839	0.545763	0.272882	−	0.962048i	$-0.412023\pi$
$157$	6.83839	0.545763	0.272882	+	0.962048i	$0.412023\pi$
$158$	39.0325	3.10526
$159$	−33.3875	−2.64780
$160$	1.05451	0.0833665
$161$	0.0456721	0.00359946
$162$	22.2563	1.74862
$163$	1.52989	0.119830	0.0599150	−	0.998203i	$-0.480917\pi$
$163$	1.52989	0.119830	0.0599150	+	0.998203i	$0.480917\pi$
$164$	−43.7458	−3.41597
$165$	−6.75022	−0.525504
$166$	0.740289	0.0574576
$167$	−2.39128	−0.185043	−0.0925214	−	0.995711i	$-0.529493\pi$
$167$	−2.39128	−0.185043	−0.0925214	+	0.995711i	$0.529493\pi$
$168$	10.9904	0.847930
$169$	−9.44064	−0.726203
$170$	9.99252	0.766391
$171$	−5.87654	−0.449390
$172$	12.3021	0.938025
$173$	−22.5245	−1.71251	−0.856255	−	0.516554i	$-0.827215\pi$
$173$	−22.5245	−1.71251	−0.856255	+	0.516554i	$0.827215\pi$
$174$	−1.67497	−0.126979
$175$	0.863350	0.0652631
$176$	−12.7754	−0.962985
$177$	13.8785	1.04317
$178$	−39.8458	−2.98657
$179$	9.59710	0.717321	0.358660	−	0.933468i	$-0.383234\pi$
$179$	9.59710	0.717321	0.358660	+	0.933468i	$0.383234\pi$
$180$	−12.3006	−0.916830
$181$	10.6394	0.790819	0.395409	−	0.918505i	$-0.370603\pi$
$181$	10.6394	0.790819	0.395409	+	0.918505i	$0.370603\pi$
$182$	4.02420	0.298294
$183$	23.3121	1.72328
$184$	−0.274990	−0.0202726
$185$	0.975732	0.0717372
$186$	−10.8419	−0.794965
$187$	−11.1484	−0.815248
$188$	7.25221	0.528922
$189$	0.00589351	0.000428690 0
$190$	−4.84408	−0.351427
$191$	−2.28508	−0.165343	−0.0826713	−	0.996577i	$-0.526345\pi$
$191$	−2.28508	−0.165343	−0.0826713	+	0.996577i	$0.526345\pi$
$192$	16.3204	1.17783
$193$	11.5468	0.831157	0.415579	−	0.909557i	$-0.363579\pi$
$193$	11.5468	0.831157	0.415579	+	0.909557i	$0.363579\pi$
$194$	46.5889	3.34489
$195$	−4.62020	−0.330859
$196$	−25.6690	−1.83350
$197$	0.637838	0.0454440	0.0227220	−	0.999742i	$-0.492767\pi$
$197$	0.637838	0.0454440	0.0227220	+	0.999742i	$0.492767\pi$
$198$	20.4112	1.45056
$199$	−27.1866	−1.92720	−0.963602	−	0.267341i	$-0.913855\pi$
$199$	−27.1866	−1.92720	−0.963602	+	0.267341i	$0.913855\pi$
$200$	−5.19820	−0.367568
$201$	−6.91994	−0.488095
$202$	−41.0662	−2.88941
$203$	−0.239008	−0.0167751
$204$	−40.6490	−2.84600
$205$	10.6593	0.744478
$206$	−11.4642	−0.798749
$207$	0.158556	0.0110204
$208$	−8.74417	−0.606299
$209$	5.40440	0.373830
$210$	−5.22359	−0.360462
$211$	15.6175	1.07515	0.537576	−	0.843215i	$-0.319340\pi$
$211$	15.6175	1.07515	0.537576	+	0.843215i	$0.319340\pi$
$212$	55.9521	3.84280
$213$	−23.3406	−1.59927
$214$	8.93009	0.610448
$215$	−2.99758	−0.204433
$216$	−0.0354847	−0.00241443
$217$	−1.54707	−0.105022
$218$	−2.38645	−0.161631
$219$	−1.50425	−0.101648
$220$	11.3123	0.762674
$221$	−7.63051	−0.513283
$222$	−5.90354	−0.396220
$223$	−23.9738	−1.60541	−0.802703	−	0.596378i	$-0.796606\pi$
$223$	−23.9738	−1.60541	−0.802703	+	0.596378i	$0.796606\pi$
$224$	−0.910413	−0.0608295
$225$	2.99721	0.199814
$226$	−26.5967	−1.76919
$227$	−22.5739	−1.49828	−0.749140	−	0.662411i	$-0.769533\pi$
$227$	−22.5739	−1.49828	−0.749140	+	0.662411i	$0.769533\pi$
$228$	19.7055	1.30503
$229$	15.4688	1.02221	0.511103	−	0.859519i	$-0.329237\pi$
$229$	15.4688	1.02221	0.511103	+	0.859519i	$0.329237\pi$
$230$	0.130699	0.00861802
$231$	5.82780	0.383441
$232$	1.43906	0.0944790
$233$	8.28892	0.543025	0.271513	−	0.962435i	$-0.412476\pi$
$233$	8.28892	0.543025	0.271513	+	0.962435i	$0.412476\pi$
$234$	13.9705	0.913277
$235$	−1.76711	−0.115273
$236$	−23.2582	−1.51398
$237$	38.6895	2.51315
$238$	−8.62704	−0.559208
$239$	−23.9112	−1.54669	−0.773343	−	0.633988i	$-0.781417\pi$
$239$	−23.9112	−1.54669	−0.773343	+	0.633988i	$0.781417\pi$
$240$	11.3503	0.732659
$241$	11.7198	0.754937	0.377469	−	0.926022i	$-0.376795\pi$
$241$	11.7198	0.754937	0.377469	+	0.926022i	$0.376795\pi$
$242$	8.40564	0.540335
$243$	22.0403	1.41388
$244$	−39.0673	−2.50103
$245$	6.25463	0.399593
$246$	−64.4927	−4.11191
$247$	3.69905	0.235365
$248$	9.31484	0.591493
$249$	0.733785	0.0465017
$250$	2.47063	0.156256
$251$	−22.6509	−1.42971	−0.714857	−	0.699271i	$-0.753508\pi$
$251$	−22.6509	−1.42971	−0.714857	+	0.699271i	$0.753508\pi$
$252$	10.6197	0.668977
$253$	−0.145817	−0.00916742
$254$	12.6007	0.790635
$255$	9.90472	0.620258
$256$	−32.5611	−2.03507
$257$	−3.96054	−0.247052	−0.123526	−	0.992341i	$-0.539420\pi$
$257$	−3.96054	−0.247052	−0.123526	+	0.992341i	$0.539420\pi$
$258$	18.1365	1.12913
$259$	−0.842397	−0.0523440
$260$	7.74271	0.480183
$261$	−0.829743	−0.0513598
$262$	−33.6929	−2.08155
$263$	−20.7922	−1.28210	−0.641051	−	0.767498i	$-0.721501\pi$
$263$	−20.7922	−1.28210	−0.641051	+	0.767498i	$0.721501\pi$
$264$	−35.0890	−2.15958
$265$	−13.6335	−0.837502
$266$	4.18214	0.256423
$267$	−39.4957	−2.41710
$268$	11.5967	0.708382
$269$	−25.6135	−1.56168	−0.780840	−	0.624731i	$-0.785209\pi$
$269$	−25.6135	−1.56168	−0.780840	+	0.624731i	$0.785209\pi$
$270$	0.0168653	0.00102639
$271$	9.06500	0.550660	0.275330	−	0.961350i	$-0.411213\pi$
$271$	9.06500	0.550660	0.275330	+	0.961350i	$0.411213\pi$
$272$	18.7457	1.13662
$273$	3.98884	0.241416
$274$	43.0119	2.59844
$275$	−2.75641	−0.166217
$276$	−0.531675	−0.0320031
$277$	20.4667	1.22973	0.614864	−	0.788633i	$-0.289211\pi$
$277$	20.4667	1.22973	0.614864	+	0.788633i	$0.289211\pi$
$278$	3.99150	0.239394
$279$	−5.37081	−0.321542
$280$	4.48787	0.268201
$281$	−8.04463	−0.479902	−0.239951	−	0.970785i	$-0.577131\pi$
$281$	−8.04463	−0.479902	−0.239951	+	0.970785i	$0.577131\pi$
$282$	10.6917	0.636679
$283$	−15.3420	−0.911990	−0.455995	−	0.889982i	$-0.650716\pi$
$283$	−15.3420	−0.911990	−0.455995	+	0.889982i	$0.650716\pi$
$284$	39.1151	2.32105
$285$	−4.80152	−0.284418
$286$	−12.8480	−0.759719
$287$	−9.20270	−0.543218
$288$	−3.16060	−0.186240
$289$	−0.641806	−0.0377533
$290$	−0.683964	−0.0401637
$291$	46.1795	2.70709
$292$	2.52088	0.147523
$293$	−12.9509	−0.756600	−0.378300	−	0.925683i	$-0.623491\pi$
$293$	−12.9509	−0.756600	−0.378300	+	0.925683i	$0.623491\pi$
$294$	−37.8428	−2.20704
$295$	5.66720	0.329957
$296$	5.07205	0.294807
$297$	−0.0188161	−0.00109182
$298$	−28.5266	−1.65250
$299$	−0.0998045	−0.00577184
$300$	−10.0504	−0.580259
$301$	2.58796	0.149168
$302$	−22.6143	−1.30131
$303$	−40.7054	−2.33846
$304$	−9.08735	−0.521195
$305$	9.51933	0.545075
$306$	−29.9497	−1.71211
$307$	−30.4348	−1.73701	−0.868504	−	0.495683i	$-0.834918\pi$
$307$	−30.4348	−1.73701	−0.868504	+	0.495683i	$0.834918\pi$
$308$	−9.76646	−0.556496
$309$	−11.3635	−0.646446
$310$	−4.42721	−0.251448
$311$	−29.2417	−1.65814	−0.829071	−	0.559143i	$-0.811130\pi$
$311$	−29.2417	−1.65814	−0.829071	+	0.559143i	$0.811130\pi$
$312$	−24.0167	−1.35968
$313$	−12.7365	−0.719911	−0.359956	−	0.932969i	$-0.617208\pi$
$313$	−12.7365	−0.719911	−0.359956	+	0.932969i	$0.617208\pi$
$314$	−16.8951	−0.953447
$315$	−2.58764	−0.145797
$316$	−64.8375	−3.64739
$317$	30.5069	1.71344	0.856719	−	0.515784i	$-0.172499\pi$
$317$	30.5069	1.71344	0.856719	+	0.515784i	$0.172499\pi$
$318$	82.4880	4.62570
$319$	0.763078	0.0427242
$320$	6.66433	0.372548
$321$	8.85163	0.494050
$322$	−0.112839	−0.00628826
$323$	−7.92998	−0.441236
$324$	−36.9703	−2.05391
$325$	−1.88663	−0.104651
$326$	−3.77978	−0.209343
$327$	−2.36548	−0.130811
$328$	55.4092	3.05946
$329$	1.52563	0.0841108
$330$	16.6773	0.918054
$331$	−14.8473	−0.816083	−0.408042	−	0.912963i	$-0.633788\pi$
$331$	−14.8473	−0.816083	−0.408042	+	0.912963i	$0.633788\pi$
$332$	−1.22971	−0.0674889
$333$	−2.92447	−0.160260
$334$	5.90796	0.323269
$335$	−2.82571	−0.154385
$336$	−9.79929	−0.534595
$337$	11.8323	0.644545	0.322272	−	0.946647i	$-0.395553\pi$
$337$	11.8323	0.644545	0.322272	+	0.946647i	$0.395553\pi$
$338$	23.3243	1.26868
$339$	−26.3630	−1.43184
$340$	−16.5987	−0.900193
$341$	4.93930	0.267478
$342$	14.5187	0.785084
$343$	−11.4434	−0.617884
$344$	−15.5820	−0.840127
$345$	0.129550	0.00697476
$346$	55.6498	2.99175
$347$	6.67286	0.358218	0.179109	−	0.983829i	$-0.442679\pi$
$347$	6.67286	0.358218	0.179109	+	0.983829i	$0.442679\pi$
$348$	2.78233	0.149148
$349$	13.3370	0.713913	0.356957	−	0.934121i	$-0.383814\pi$
$349$	13.3370	0.713913	0.356957	+	0.934121i	$0.383814\pi$
$350$	−2.13302	−0.114014
$351$	−0.0128787	−0.000687416 0
$352$	2.90666	0.154926
$353$	9.14662	0.486825	0.243413	−	0.969923i	$-0.421733\pi$
$353$	9.14662	0.486825	0.243413	+	0.969923i	$0.421733\pi$
$354$	−34.2886	−1.82242
$355$	−9.53096	−0.505851
$356$	66.1884	3.50798
$357$	−8.55124	−0.452580
$358$	−23.7109	−1.25316
$359$	3.41258	0.180109	0.0900545	−	0.995937i	$-0.471296\pi$
$359$	3.41258	0.180109	0.0900545	+	0.995937i	$0.471296\pi$
$360$	15.5801	0.821144
$361$	−15.1558	−0.797672
$362$	−26.2859	−1.38156
$363$	8.33179	0.437306
$364$	−6.68467	−0.350372
$365$	−0.614249	−0.0321512
$366$	−57.5955	−3.01056
$367$	9.42764	0.492119	0.246059	−	0.969255i	$-0.420864\pi$
$367$	9.42764	0.492119	0.246059	+	0.969255i	$0.420864\pi$
$368$	0.245187	0.0127812
$369$	−31.9482	−1.66316
$370$	−2.41067	−0.125325
$371$	11.7705	0.611095
$372$	18.0096	0.933755
$373$	5.84321	0.302550	0.151275	−	0.988492i	$-0.451662\pi$
$373$	5.84321	0.302550	0.151275	+	0.988492i	$0.451662\pi$
$374$	27.5434	1.42424
$375$	2.44892	0.126462
$376$	−9.18578	−0.473720
$377$	0.522290	0.0268993
$378$	−0.0145607	−0.000748920 0
$379$	28.8287	1.48083	0.740414	−	0.672151i	$-0.234629\pi$
$379$	28.8287	1.48083	0.740414	+	0.672151i	$0.234629\pi$
$380$	8.04659	0.412781
$381$	12.4899	0.639879
$382$	5.64558	0.288853
$383$	−6.12272	−0.312856	−0.156428	−	0.987689i	$-0.549998\pi$
$383$	−6.12272	−0.312856	−0.156428	+	0.987689i	$0.549998\pi$
$384$	−45.4865	−2.32123
$385$	2.37974	0.121283
$386$	−28.5279	−1.45203
$387$	8.98439	0.456702
$388$	−77.3896	−3.92886
$389$	−16.2516	−0.823988	−0.411994	−	0.911187i	$-0.635168\pi$
$389$	−16.2516	−0.823988	−0.411994	+	0.911187i	$0.635168\pi$
$390$	11.4148	0.578010
$391$	0.213960	0.0108204
$392$	32.5128	1.64215
$393$	−33.3969	−1.68465
$394$	−1.57586	−0.0793906
$395$	15.7986	0.794914
$396$	−33.9053	−1.70381
$397$	−13.7427	−0.689724	−0.344862	−	0.938653i	$-0.612074\pi$
$397$	−13.7427	−0.689724	−0.344862	+	0.938653i	$0.612074\pi$
$398$	67.1679	3.36682
$399$	4.14539	0.207529
$400$	4.63482	0.231741
$401$	−6.09407	−0.304323	−0.152162	−	0.988356i	$-0.548623\pi$
$401$	−6.09407	−0.304323	−0.152162	+	0.988356i	$0.548623\pi$
$402$	17.0966	0.852700
$403$	3.38071	0.168405
$404$	68.2158	3.39386
$405$	9.00835	0.447629
$406$	0.590500	0.0293060
$407$	2.68951	0.133314
$408$	51.4868	2.54897
$409$	25.5777	1.26473	0.632367	−	0.774669i	$-0.282084\pi$
$409$	25.5777	1.26473	0.632367	+	0.774669i	$0.282084\pi$
$410$	−26.3352	−1.30060
$411$	42.6340	2.10298
$412$	19.0434	0.938200
$413$	−4.89277	−0.240758
$414$	−0.391732	−0.0192526
$415$	0.299636	0.0147086
$416$	1.98947	0.0975418
$417$	3.95643	0.193747
$418$	−13.3523	−0.653080
$419$	15.9901	0.781169	0.390585	−	0.920567i	$-0.372273\pi$
$419$	15.9901	0.781169	0.390585	+	0.920567i	$0.372273\pi$
$420$	8.67698	0.423393
$421$	11.3420	0.552774	0.276387	−	0.961046i	$-0.410863\pi$
$421$	11.3420	0.552774	0.276387	+	0.961046i	$0.410863\pi$
$422$	−38.5850	−1.87829
$423$	5.29640	0.257520
$424$	−70.8699	−3.44175
$425$	4.04453	0.196188
$426$	57.6658	2.79392
$427$	−8.21851	−0.397722
$428$	−14.8339	−0.717024
$429$	−12.7351	−0.614858
$430$	7.40591	0.357145
$431$	27.4453	1.32199	0.660996	−	0.750390i	$-0.270134\pi$
$431$	27.4453	1.32199	0.660996	+	0.750390i	$0.270134\pi$
$432$	0.0316388	0.00152222
$433$	11.2255	0.539461	0.269730	−	0.962936i	$-0.413065\pi$
$433$	11.2255	0.539461	0.269730	+	0.962936i	$0.413065\pi$
$434$	3.82223	0.183473
$435$	−0.677955	−0.0325054
$436$	3.96417	0.189849
$437$	−0.103721	−0.00496167
$438$	3.71643	0.177578
$439$	−17.1781	−0.819867	−0.409934	−	0.912115i	$-0.634448\pi$
$439$	−17.1781	−0.819867	−0.409934	+	0.912115i	$0.634448\pi$
$440$	−14.3284	−0.683077
$441$	−18.7464	−0.892688
$442$	18.8521	0.896705
$443$	20.5257	0.975207	0.487603	−	0.873065i	$-0.337871\pi$
$443$	20.5257	0.975207	0.487603	+	0.873065i	$0.337871\pi$
$444$	9.80647	0.465394
$445$	−16.1278	−0.764530
$446$	59.2304	2.80464
$447$	−28.2760	−1.33741
$448$	−5.75365	−0.271834
$449$	−15.8229	−0.746730	−0.373365	−	0.927685i	$-0.621796\pi$
$449$	−15.8229	−0.746730	−0.373365	+	0.927685i	$0.621796\pi$
$450$	−7.40500	−0.349075
$451$	29.3814	1.38351
$452$	44.1802	2.07806
$453$	−22.4156	−1.05318
$454$	55.7716	2.61749
$455$	1.62882	0.0763601
$456$	−24.9593	−1.16883
$457$	−26.6977	−1.24887	−0.624434	−	0.781078i	$-0.714670\pi$
$457$	−26.6977	−1.24887	−0.624434	+	0.781078i	$0.714670\pi$
$458$	−38.2176	−1.78579
$459$	0.0276093	0.00128869
$460$	−0.217106	−0.0101226
$461$	−37.6376	−1.75296	−0.876478	−	0.481442i	$-0.840113\pi$
$461$	−37.6376	−1.75296	−0.876478	+	0.481442i	$0.840113\pi$
$462$	−14.3983	−0.669870
$463$	−34.0373	−1.58185	−0.790923	−	0.611916i	$-0.790399\pi$
$463$	−34.0373	−1.58185	−0.790923	+	0.611916i	$0.790399\pi$
$464$	−1.28310	−0.0595662
$465$	−4.38831	−0.203503
$466$	−20.4788	−0.948664
$467$	−13.6512	−0.631703	−0.315852	−	0.948809i	$-0.602290\pi$
$467$	−13.6512	−0.631703	−0.315852	+	0.948809i	$0.602290\pi$
$468$	−23.2066	−1.07272
$469$	2.43957	0.112649
$470$	4.36586	0.201382
$471$	−16.7467	−0.771646
$472$	29.4592	1.35597
$473$	−8.26255	−0.379913
$474$	−95.5874	−4.39048
$475$	−1.96067	−0.0899617
$476$	14.3305	0.656838
$477$	40.8626	1.87097
$478$	59.0756	2.70206
$479$	10.1022	0.461582	0.230791	−	0.973003i	$-0.425869\pi$
$479$	10.1022	0.461582	0.230791	+	0.973003i	$0.425869\pi$
$480$	−2.58242	−0.117871
$481$	1.84084	0.0839351
$482$	−28.9552	−1.31887
$483$	−0.111847	−0.00508923
$484$	−13.9628	−0.634671
$485$	18.8571	0.856257
$486$	−54.4533	−2.47005
$487$	−36.1443	−1.63785	−0.818927	−	0.573898i	$-0.805431\pi$
$487$	−36.1443	−1.63785	−0.818927	+	0.573898i	$0.805431\pi$
$488$	49.4834	2.24001
$489$	−3.74657	−0.169426
$490$	−15.4529	−0.698089
$491$	−17.8166	−0.804051	−0.402026	−	0.915628i	$-0.631694\pi$
$491$	−17.8166	−0.804051	−0.402026	+	0.915628i	$0.631694\pi$
$492$	107.130	4.82979
$493$	−1.11968	−0.0504278
$494$	−9.13897	−0.411182
$495$	8.26153	0.371328
$496$	−8.30530	−0.372919
$497$	8.22855	0.369101
$498$	−1.81291	−0.0812384
$499$	−14.0005	−0.626748	−0.313374	−	0.949630i	$-0.601459\pi$
$499$	−14.0005	−0.626748	−0.313374	+	0.949630i	$0.601459\pi$
$500$	−4.10400	−0.183536
$501$	5.85605	0.261629
$502$	55.9620	2.49771
$503$	42.0177	1.87348	0.936738	−	0.350033i	$-0.113829\pi$
$503$	42.0177	1.87348	0.936738	+	0.350033i	$0.113829\pi$
$504$	−13.4511	−0.599159
$505$	−16.6218	−0.739659
$506$	0.360259	0.0160155
$507$	23.1194	1.02677
$508$	−20.9312	−0.928670
$509$	−26.9050	−1.19254	−0.596270	−	0.802784i	$-0.703351\pi$
$509$	−26.9050	−1.19254	−0.596270	+	0.802784i	$0.703351\pi$
$510$	−24.4709	−1.08359
$511$	0.530311	0.0234596
$512$	43.2980	1.91352
$513$	−0.0133842	−0.000590926 0
$514$	9.78502	0.431599
$515$	−4.64020	−0.204472
$516$	−30.1268	−1.32626
$517$	−4.87086	−0.214220
$518$	2.08125	0.0914449
$519$	55.1608	2.42129
$520$	−9.80706	−0.430068
$521$	17.0619	0.747493	0.373747	−	0.927531i	$-0.378073\pi$
$521$	17.0619	0.747493	0.373747	+	0.927531i	$0.378073\pi$
$522$	2.04999	0.0897254
$523$	3.66548	0.160280	0.0801401	−	0.996784i	$-0.474463\pi$
$523$	3.66548	0.160280	0.0801401	+	0.996784i	$0.474463\pi$
$524$	55.9678	2.44497
$525$	−2.11427	−0.0922745
$526$	51.3698	2.23983
$527$	−7.24753	−0.315707
$528$	31.2861	1.36155
$529$	−22.9972	−0.999878
$530$	33.6834	1.46311
$531$	−16.9858	−0.737121
$532$	−6.94702	−0.301191
$533$	20.1101	0.871065
$534$	97.5791	4.22266
$535$	3.61450	0.156268
$536$	−14.6886	−0.634451
$537$	−23.5025	−1.01421
$538$	63.2813	2.72825
$539$	17.2403	0.742592
$540$	−0.0280153	−0.00120559
$541$	35.5884	1.53006	0.765032	−	0.643992i	$-0.222723\pi$
$541$	35.5884	1.53006	0.765032	+	0.643992i	$0.222723\pi$
$542$	−22.3963	−0.962001
$543$	−26.0550	−1.11813
$544$	−4.26500	−0.182861
$545$	−0.965927	−0.0413758
$546$	−9.85495	−0.421753
$547$	7.05023	0.301446	0.150723	−	0.988576i	$-0.451840\pi$
$547$	7.05023	0.301446	0.150723	+	0.988576i	$0.451840\pi$
$548$	−71.4477	−3.05209
$549$	−28.5315	−1.21769
$550$	6.81005	0.290382
$551$	0.542788	0.0231235
$552$	0.673429	0.0286631
$553$	−13.6397	−0.580020
$554$	−50.5657	−2.14833
$555$	−2.38949	−0.101428
$556$	−6.63034	−0.281189
$557$	−29.9895	−1.27070	−0.635348	−	0.772226i	$-0.719143\pi$
$557$	−29.9895	−1.27070	−0.635348	+	0.772226i	$0.719143\pi$
$558$	13.2693	0.561733
$559$	−5.65532	−0.239194
$560$	−4.00147	−0.169093
$561$	27.3014	1.15267
$562$	19.8753	0.838388
$563$	17.8365	0.751718	0.375859	−	0.926677i	$-0.377348\pi$
$563$	17.8365	0.751718	0.375859	+	0.926677i	$0.377348\pi$
$564$	−17.7601	−0.747834
$565$	−10.7652	−0.452893
$566$	37.9045	1.59324
$567$	−7.77736	−0.326618
$568$	−49.5439	−2.07881
$569$	44.2380	1.85455	0.927276	−	0.374379i	$-0.122144\pi$
$569$	44.2380	1.85455	0.927276	+	0.374379i	$0.122144\pi$
$570$	11.8628	0.496877
$571$	−17.2750	−0.722934	−0.361467	−	0.932385i	$-0.617724\pi$
$571$	−17.2750	−0.722934	−0.361467	+	0.932385i	$0.617724\pi$
$572$	21.3421	0.892356
$573$	5.59598	0.233775
$574$	22.7364	0.949001
$575$	0.0529010	0.00220613
$576$	−19.9744	−0.832268
$577$	13.8109	0.574957	0.287478	−	0.957787i	$-0.407183\pi$
$577$	13.8109	0.574957	0.287478	+	0.957787i	$0.407183\pi$
$578$	1.58566	0.0659549
$579$	−28.2772	−1.17516
$580$	1.13614	0.0471758
$581$	−0.258691	−0.0107323
$582$	−114.092	−4.72928
$583$	−37.5796	−1.55639
$584$	−3.19299	−0.132127
$585$	5.65462	0.233790
$586$	31.9969	1.32178
$587$	28.2773	1.16713	0.583564	−	0.812067i	$-0.301658\pi$
$587$	28.2773	1.16713	0.583564	+	0.812067i	$0.301658\pi$
$588$	62.8613	2.59236
$589$	3.51339	0.144767
$590$	−14.0015	−0.576434
$591$	−1.56201	−0.0642527
$592$	−4.52234	−0.185867
$593$	10.7800	0.442680	0.221340	−	0.975197i	$-0.428957\pi$
$593$	10.7800	0.442680	0.221340	+	0.975197i	$0.428957\pi$
$594$	0.0464877	0.00190741
$595$	−3.49184	−0.143151
$596$	47.3860	1.94101
$597$	66.5777	2.72484
$598$	0.246580	0.0100834
$599$	−39.4848	−1.61331	−0.806653	−	0.591025i	$-0.798723\pi$
$599$	−39.4848	−1.61331	−0.806653	+	0.591025i	$0.798723\pi$
$600$	12.7300	0.519700
$601$	0.761173	0.0310489	0.0155245	−	0.999879i	$-0.495058\pi$
$601$	0.761173	0.0310489	0.0155245	+	0.999879i	$0.495058\pi$
$602$	−6.39389	−0.260595
$603$	8.46925	0.344895
$604$	37.5650	1.52850
$605$	3.40223	0.138320
$606$	100.568	4.08529
$607$	4.83981	0.196442	0.0982209	−	0.995165i	$-0.468685\pi$
$607$	4.83981	0.196442	0.0982209	+	0.995165i	$0.468685\pi$
$608$	2.06755	0.0838502
$609$	0.585312	0.0237180
$610$	−23.5187	−0.952245
$611$	−3.33387	−0.134874
$612$	49.7500	2.01102
$613$	−5.18795	−0.209539	−0.104770	−	0.994497i	$-0.533411\pi$
$613$	−5.18795	−0.209539	−0.104770	+	0.994497i	$0.533411\pi$
$614$	75.1931	3.03455
$615$	−26.1038	−1.05261
$616$	12.3704	0.498417
$617$	16.9296	0.681560	0.340780	−	0.940143i	$-0.389309\pi$
$617$	16.9296	0.681560	0.340780	+	0.940143i	$0.389309\pi$
$618$	28.0749	1.12934
$619$	−10.1144	−0.406533	−0.203266	−	0.979123i	$-0.565156\pi$
$619$	−10.1144	−0.406533	−0.203266	+	0.979123i	$0.565156\pi$
$620$	7.35410	0.295348
$621$	0.000361120 0	1.44913e−5 0
$622$	72.2453	2.89677
$623$	13.9239	0.557850
$624$	21.4138	0.857237
$625$	1.00000	0.0400000
$626$	31.4672	1.25768
$627$	−13.2349	−0.528553
$628$	28.0648	1.11991
$629$	−3.94637	−0.157352
$630$	6.39310	0.254707
$631$	−36.4230	−1.44998	−0.724988	−	0.688761i	$-0.758155\pi$
$631$	−36.4230	−1.44998	−0.724988	+	0.688761i	$0.758155\pi$
$632$	82.1243	3.26673
$633$	−38.2460	−1.52014
$634$	−75.3712	−2.99337
$635$	5.10018	0.202395
$636$	−137.022	−5.43328
$637$	11.8001	0.467539
$638$	−1.88528	−0.0746390
$639$	28.5663	1.13007
$640$	−18.5741	−0.734206
$641$	45.6252	1.80209	0.901043	−	0.433730i	$-0.142803\pi$
$641$	45.6252	1.80209	0.901043	+	0.433730i	$0.142803\pi$
$642$	−21.8691	−0.863103
$643$	38.3345	1.51176	0.755882	−	0.654708i	$-0.227208\pi$
$643$	38.3345	1.51176	0.755882	+	0.654708i	$0.227208\pi$
$644$	0.187438	0.00738610
$645$	7.34084	0.289045
$646$	19.5920	0.770838
$647$	43.9189	1.72663	0.863315	−	0.504666i	$-0.168384\pi$
$647$	43.9189	1.72663	0.863315	+	0.504666i	$0.168384\pi$
$648$	46.8273	1.83955
$649$	15.6211	0.613181
$650$	4.66115	0.182825
$651$	3.78864	0.148489
$652$	6.27866	0.245891
$653$	10.3958	0.406817	0.203409	−	0.979094i	$-0.434798\pi$
$653$	10.3958	0.406817	0.203409	+	0.979094i	$0.434798\pi$
$654$	5.84422	0.228527
$655$	−13.6374	−0.532857
$656$	−49.4040	−1.92890
$657$	1.84103	0.0718256
$658$	−3.76927	−0.146941
$659$	−14.2544	−0.555274	−0.277637	−	0.960686i	$-0.589551\pi$
$659$	−14.2544	−0.555274	−0.277637	+	0.960686i	$0.589551\pi$
$660$	−27.7029	−1.07833
$661$	29.0449	1.12972	0.564858	−	0.825188i	$-0.308931\pi$
$661$	29.0449	1.12972	0.564858	+	0.825188i	$0.308931\pi$
$662$	36.6822	1.42570
$663$	18.6865	0.725724
$664$	1.55757	0.0604454
$665$	1.69274	0.0656418
$666$	7.22529	0.279974
$667$	−0.0146450	−0.000567058 0
$668$	−9.81381	−0.379708
$669$	58.7100	2.26986
$670$	6.98128	0.269710
$671$	26.2391	1.01295
$672$	2.22953	0.0860060
$673$	45.0878	1.73801	0.869003	−	0.494807i	$-0.164761\pi$
$673$	45.0878	1.73801	0.869003	+	0.494807i	$0.164761\pi$
$674$	−29.2331	−1.12602
$675$	0.00682633	0.000262746 0
$676$	−38.7444	−1.49017
$677$	36.7352	1.41185	0.705924	−	0.708288i	$-0.250532\pi$
$677$	36.7352	1.41185	0.705924	+	0.708288i	$0.250532\pi$
$678$	65.1332	2.50142
$679$	−16.2803	−0.624779
$680$	21.0243	0.806244
$681$	55.2816	2.11840
$682$	−12.2032	−0.467284
$683$	37.9372	1.45163	0.725813	−	0.687892i	$-0.241464\pi$
$683$	37.9372	1.45163	0.725813	+	0.687892i	$0.241464\pi$
$684$	−24.1173	−0.922149
$685$	17.4093	0.665174
$686$	28.2723	1.07944
$687$	−37.8818	−1.44528
$688$	13.8933	0.529676
$689$	−25.7214	−0.979907
$690$	−0.320071	−0.0121849
$691$	18.8738	0.717992	0.358996	−	0.933339i	$-0.383119\pi$
$691$	18.8738	0.717992	0.358996	+	0.933339i	$0.383119\pi$
$692$	−92.4407	−3.51407
$693$	−7.13259	−0.270945
$694$	−16.4861	−0.625805
$695$	1.61558	0.0612825
$696$	−3.52415	−0.133582
$697$	−43.1118	−1.63298
$698$	−32.9508	−1.24721
$699$	−20.2989	−0.767775
$700$	3.54319	0.133920
$701$	2.60449	0.0983702	0.0491851	−	0.998790i	$-0.484338\pi$
$701$	2.60449	0.0983702	0.0491851	+	0.998790i	$0.484338\pi$
$702$	0.0318186	0.00120091
$703$	1.91309	0.0721534
$704$	18.3696	0.692331
$705$	4.32750	0.162983
$706$	−22.5979	−0.850483
$707$	14.3504	0.539702
$708$	56.9574	2.14059
$709$	−21.5464	−0.809191	−0.404595	−	0.914496i	$-0.632588\pi$
$709$	−21.5464	−0.809191	−0.404595	+	0.914496i	$0.632588\pi$
$710$	23.5475	0.883720
$711$	−47.3518	−1.77583
$712$	−83.8355	−3.14187
$713$	−0.0947953	−0.00355011
$714$	21.1269	0.790655
$715$	−5.20030	−0.194480
$716$	39.3865	1.47194
$717$	58.5566	2.18684
$718$	−8.43121	−0.314650
$719$	31.3235	1.16817	0.584085	−	0.811693i	$-0.301454\pi$
$719$	31.3235	1.16817	0.584085	+	0.811693i	$0.301454\pi$
$720$	−13.8915	−0.517707
$721$	4.00611	0.149195
$722$	37.4443	1.39353
$723$	−28.7008	−1.06739
$724$	43.6640	1.62276
$725$	−0.276838	−0.0102815
$726$	−20.5848	−0.763972
$727$	−4.13663	−0.153419	−0.0767095	−	0.997053i	$-0.524441\pi$
$727$	−4.13663	−0.153419	−0.0767095	+	0.997053i	$0.524441\pi$
$728$	8.46692	0.313805
$729$	−26.9498	−0.998141
$730$	1.51758	0.0561682
$731$	12.1238	0.448415
$732$	95.6728	3.53617
$733$	19.1708	0.708091	0.354046	−	0.935228i	$-0.384806\pi$
$733$	19.1708	0.708091	0.354046	+	0.935228i	$0.384806\pi$
$734$	−23.2922	−0.859730
$735$	−15.3171	−0.564979
$736$	−0.0557848	−0.00205626
$737$	−7.78880	−0.286904
$738$	78.9321	2.90553
$739$	−24.7619	−0.910882	−0.455441	−	0.890266i	$-0.650518\pi$
$739$	−24.7619	−0.910882	−0.455441	+	0.890266i	$0.650518\pi$
$740$	4.00440	0.147205
$741$	−9.05868	−0.332779
$742$	−29.0806	−1.06758
$743$	−23.5033	−0.862253	−0.431127	−	0.902291i	$-0.641884\pi$
$743$	−23.5033	−0.862253	−0.431127	+	0.902291i	$0.641884\pi$
$744$	−22.8113	−0.836303
$745$	−11.5463	−0.423024
$746$	−14.4364	−0.528554
$747$	−0.898073	−0.0328588
$748$	−45.7529	−1.67289
$749$	−3.12058	−0.114023
$750$	−6.05037	−0.220928
$751$	−30.0826	−1.09773	−0.548866	−	0.835911i	$-0.684940\pi$
$751$	−30.0826	−1.09773	−0.548866	+	0.835911i	$0.684940\pi$
$752$	8.19023	0.298667
$753$	55.4703	2.02145
$754$	−1.29038	−0.0469930
$755$	−9.15326	−0.333121
$756$	0.0241870	0.000879672 0
$757$	17.5100	0.636412	0.318206	−	0.948022i	$-0.396920\pi$
$757$	17.5100	0.636412	0.318206	+	0.948022i	$0.396920\pi$
$758$	−71.2249	−2.58700
$759$	0.357094	0.0129617
$760$	−10.1920	−0.369701
$761$	−40.9317	−1.48377	−0.741886	−	0.670526i	$-0.766069\pi$
$761$	−40.9317	−1.48377	−0.741886	+	0.670526i	$0.766069\pi$
$762$	−30.8580	−1.11787
$763$	0.833933	0.0301904
$764$	−9.37797	−0.339283
$765$	−12.1223	−0.438283
$766$	15.1270	0.546559
$767$	10.6919	0.386061
$768$	79.7394	2.87735
$769$	22.0487	0.795096	0.397548	−	0.917581i	$-0.369861\pi$
$769$	22.0487	0.795096	0.397548	+	0.917581i	$0.369861\pi$
$770$	−5.87945	−0.211881
$771$	9.69905	0.349303
$772$	47.3881	1.70553
$773$	−21.2861	−0.765607	−0.382804	−	0.923830i	$-0.625041\pi$
$773$	−21.2861	−0.765607	−0.382804	+	0.923830i	$0.625041\pi$
$774$	−22.1971	−0.797858
$775$	−1.79194	−0.0643682
$776$	98.0230	3.51882
$777$	2.06296	0.0740084
$778$	40.1516	1.43951
$779$	20.8994	0.748797
$780$	−18.9613	−0.678923
$781$	−26.2712	−0.940057
$782$	−0.528615	−0.0189032
$783$	−0.00188979	−6.75356e−5 0
$784$	−28.9891	−1.03532
$785$	−6.83839	−0.244073
$786$	82.5113	2.94308
$787$	27.1081	0.966299	0.483149	−	0.875538i	$-0.339493\pi$
$787$	27.1081	0.966299	0.483149	+	0.875538i	$0.339493\pi$
$788$	2.61769	0.0932512
$789$	50.9185	1.81275
$790$	−39.0325	−1.38871
$791$	9.29409	0.330460
$792$	42.9451	1.52599
$793$	17.9594	0.637757
$794$	33.9530	1.20495
$795$	33.3875	1.18413
$796$	−111.574	−3.95462
$797$	10.8758	0.385240	0.192620	−	0.981273i	$-0.438302\pi$
$797$	10.8758	0.385240	0.192620	+	0.981273i	$0.438302\pi$
$798$	−10.2417	−0.362553
$799$	7.14711	0.252847
$800$	−1.05451	−0.0372827
$801$	48.3384	1.70795
$802$	15.0562	0.531652
$803$	−1.69312	−0.0597489
$804$	−28.3994	−1.00157
$805$	−0.0456721	−0.00160973
$806$	−8.35248	−0.294204
$807$	62.7254	2.20804
$808$	−86.4033	−3.03966
$809$	−1.95007	−0.0685608	−0.0342804	−	0.999412i	$-0.510914\pi$
$809$	−1.95007	−0.0685608	−0.0342804	+	0.999412i	$0.510914\pi$
$810$	−22.2563	−0.782006
$811$	−16.7621	−0.588597	−0.294298	−	0.955714i	$-0.595086\pi$
$811$	−16.7621	−0.588597	−0.294298	+	0.955714i	$0.595086\pi$
$812$	−0.980889	−0.0344225
$813$	−22.1995	−0.778570
$814$	−6.64478	−0.232899
$815$	−1.52989	−0.0535896
$816$	−45.9066	−1.60705
$817$	−5.87727	−0.205620
$818$	−63.1929	−2.20949
$819$	−4.88191	−0.170588
$820$	43.7458	1.52767
$821$	19.9009	0.694545	0.347272	−	0.937764i	$-0.387108\pi$
$821$	19.9009	0.694545	0.347272	+	0.937764i	$0.387108\pi$
$822$	−105.333	−3.67390
$823$	−2.12966	−0.0742351	−0.0371176	−	0.999311i	$-0.511818\pi$
$823$	−2.12966	−0.0742351	−0.0371176	+	0.999311i	$0.511818\pi$
$824$	−24.1207	−0.840284
$825$	6.75022	0.235012
$826$	12.0882	0.420603
$827$	44.7800	1.55715	0.778577	−	0.627549i	$-0.215942\pi$
$827$	44.7800	1.55715	0.778577	+	0.627549i	$0.215942\pi$
$828$	0.650713	0.0226138
$829$	−28.2890	−0.982517	−0.491258	−	0.871014i	$-0.663463\pi$
$829$	−28.2890	−0.982517	−0.491258	+	0.871014i	$0.663463\pi$
$830$	−0.740289	−0.0256958
$831$	−50.1214	−1.73869
$832$	12.5731	0.435894
$833$	−25.2970	−0.876489
$834$	−9.77486	−0.338476
$835$	2.39128	0.0827536
$836$	22.1797	0.767099
$837$	−0.0122324	−0.000422812 0
$838$	−39.5057	−1.36470
$839$	−42.5905	−1.47039	−0.735194	−	0.677857i	$-0.762909\pi$
$839$	−42.5905	−1.47039	−0.735194	+	0.677857i	$0.762909\pi$
$840$	−10.9904	−0.379206
$841$	−28.9234	−0.997357
$842$	−28.0218	−0.965696
$843$	19.7007	0.678527
$844$	64.0942	2.20621
$845$	9.44064	0.324768
$846$	−13.0854	−0.449886
$847$	−2.93731	−0.100927
$848$	63.1890	2.16992
$849$	37.5714	1.28945
$850$	−9.99252	−0.342741
$851$	−0.0516172	−0.00176942
$852$	−95.7897	−3.28170
$853$	−18.5677	−0.635747	−0.317873	−	0.948133i	$-0.602969\pi$
$853$	−18.5677	−0.635747	−0.317873	+	0.948133i	$0.602969\pi$
$854$	20.3049	0.694819
$855$	5.87654	0.200974
$856$	18.7889	0.642192
$857$	−18.9879	−0.648614	−0.324307	−	0.945952i	$-0.605131\pi$
$857$	−18.9879	−0.648614	−0.324307	+	0.945952i	$0.605131\pi$
$858$	31.4638	1.07416
$859$	11.1785	0.381405	0.190702	−	0.981648i	$-0.438923\pi$
$859$	11.1785	0.381405	0.190702	+	0.981648i	$0.438923\pi$
$860$	−12.3021	−0.419497
$861$	22.5367	0.768048
$862$	−67.8070	−2.30952
$863$	−2.44917	−0.0833706	−0.0416853	−	0.999131i	$-0.513273\pi$
$863$	−2.44917	−0.0833706	−0.0416853	+	0.999131i	$0.513273\pi$
$864$	−0.00719846	−0.000244896 0
$865$	22.5245	0.765857
$866$	−27.7339	−0.942437
$867$	1.57173	0.0533788
$868$	−6.34916	−0.215505
$869$	43.5474	1.47724
$870$	1.67497	0.0567869
$871$	−5.33106	−0.180636
$872$	−5.02109	−0.170035
$873$	−56.5187	−1.91287
$874$	0.256257	0.00866802
$875$	−0.863350	−0.0291865
$876$	−6.17343	−0.208581
$877$	42.1984	1.42494	0.712470	−	0.701703i	$-0.247576\pi$
$877$	42.1984	1.42494	0.712470	+	0.701703i	$0.247576\pi$
$878$	42.4407	1.43231
$879$	31.7158	1.06975
$880$	12.7754	0.430660
$881$	4.23811	0.142785	0.0713927	−	0.997448i	$-0.477256\pi$
$881$	4.23811	0.142785	0.0713927	+	0.997448i	$0.477256\pi$
$882$	46.3155	1.55952
$883$	46.9817	1.58106	0.790530	−	0.612424i	$-0.209805\pi$
$883$	46.9817	1.58106	0.790530	+	0.612424i	$0.209805\pi$
$884$	−31.3156	−1.05326
$885$	−13.8785	−0.466521
$886$	−50.7114	−1.70368
$887$	40.2146	1.35027	0.675136	−	0.737693i	$-0.264085\pi$
$887$	40.2146	1.35027	0.675136	+	0.737693i	$0.264085\pi$
$888$	−12.4210	−0.416823
$889$	−4.40324	−0.147680
$890$	39.8458	1.33563
$891$	24.8307	0.831859
$892$	−98.3886	−3.29430
$893$	−3.46471	−0.115942
$894$	69.8594	2.33645
$895$	−9.59710	−0.320796
$896$	16.0360	0.535724
$897$	0.244413	0.00816072
$898$	39.0925	1.30454
$899$	0.496076	0.0165451
$900$	12.3006	0.410019
$901$	55.1412	1.83702
$902$	−72.5904	−2.41700
$903$	−6.33771	−0.210906
$904$	−55.9595	−1.86118
$905$	−10.6394	−0.353665
$906$	55.3806	1.83990
$907$	35.8746	1.19120	0.595599	−	0.803282i	$-0.296915\pi$
$907$	35.8746	1.19120	0.595599	+	0.803282i	$0.296915\pi$
$908$	−92.6432	−3.07447
$909$	49.8190	1.65239
$910$	−4.02420	−0.133401
$911$	37.4748	1.24160	0.620799	−	0.783970i	$-0.286808\pi$
$911$	37.4748	1.24160	0.620799	+	0.783970i	$0.286808\pi$
$912$	22.2542	0.736910
$913$	0.825918	0.0273339
$914$	65.9601	2.18177
$915$	−23.3121	−0.770674
$916$	63.4839	2.09757
$917$	11.7738	0.388806
$918$	−0.0682123	−0.00225134
$919$	12.3990	0.409006	0.204503	−	0.978866i	$-0.434442\pi$
$919$	12.3990	0.409006	0.204503	+	0.978866i	$0.434442\pi$
$920$	0.274990	0.00906616
$921$	74.5325	2.45593
$922$	92.9884	3.06241
$923$	−17.9814	−0.591863
$924$	23.9173	0.786821
$925$	−0.975732	−0.0320819
$926$	84.0934	2.76348
$927$	13.9077	0.456787
$928$	0.291929	0.00958305
$929$	25.2164	0.827322	0.413661	−	0.910431i	$-0.364250\pi$
$929$	25.2164	0.827322	0.413661	+	0.910431i	$0.364250\pi$
$930$	10.8419	0.355519
$931$	12.2633	0.401912
$932$	34.0177	1.11429
$933$	71.6105	2.34442
$934$	33.7271	1.10358
$935$	11.1484	0.364590
$936$	29.3938	0.960768
$937$	−1.40530	−0.0459093	−0.0229546	−	0.999737i	$-0.507307\pi$
$937$	−1.40530	−0.0459093	−0.0229546	+	0.999737i	$0.507307\pi$
$938$	−6.02728	−0.196798
$939$	31.1908	1.01787
$940$	−7.25221	−0.236541
$941$	−24.0910	−0.785346	−0.392673	−	0.919678i	$-0.628450\pi$
$941$	−24.0910	−0.785346	−0.392673	+	0.919678i	$0.628450\pi$
$942$	41.3748	1.34806
$943$	−0.563888	−0.0183627
$944$	−26.2664	−0.854900
$945$	−0.00589351	−0.000191716 0
$946$	20.4137	0.663706
$947$	−43.4723	−1.41266	−0.706329	−	0.707883i	$-0.749650\pi$
$947$	−43.4723	−1.41266	−0.706329	+	0.707883i	$0.749650\pi$
$948$	158.782	5.15699
$949$	−1.15886	−0.0376181
$950$	4.84408	0.157163
$951$	−74.7090	−2.42260
$952$	−18.1513	−0.588287
$953$	−37.1366	−1.20297	−0.601486	−	0.798883i	$-0.705424\pi$
$953$	−37.1366	−1.20297	−0.601486	+	0.798883i	$0.705424\pi$
$954$	−100.956	−3.26858
$955$	2.28508	0.0739434
$956$	−98.1315	−3.17380
$957$	−1.86872	−0.0604071
$958$	−24.9588	−0.806382
$959$	−15.0303	−0.485354
$960$	−16.3204	−0.526740
$961$	−27.7890	−0.896418
$962$	−4.54803	−0.146634
$963$	−10.8334	−0.349102
$964$	48.0980	1.54913
$965$	−11.5468	−0.371705
$966$	0.276333	0.00889087
$967$	54.3627	1.74819	0.874093	−	0.485758i	$-0.161456\pi$
$967$	54.3627	1.74819	0.874093	+	0.485758i	$0.161456\pi$
$968$	17.6855	0.568433
$969$	19.4199	0.623857
$970$	−46.5889	−1.49588
$971$	−35.3116	−1.13320	−0.566601	−	0.823992i	$-0.691742\pi$
$971$	−35.3116	−1.13320	−0.566601	+	0.823992i	$0.691742\pi$
$972$	90.4533	2.90129
$973$	−1.39481	−0.0447156
$974$	89.2991	2.86133
$975$	4.62020	0.147965
$976$	−44.1204	−1.41226
$977$	58.7939	1.88098	0.940491	−	0.339818i	$-0.110366\pi$
$977$	58.7939	1.88098	0.940491	+	0.339818i	$0.110366\pi$
$978$	9.25639	0.295987
$979$	−44.4547	−1.42078
$980$	25.6690	0.819966
$981$	2.89509	0.0924331
$982$	44.0181	1.40468
$983$	−12.6862	−0.404625	−0.202313	−	0.979321i	$-0.564846\pi$
$983$	−12.6862	−0.404625	−0.202313	+	0.979321i	$0.564846\pi$
$984$	−135.693	−4.32573
$985$	−0.637838	−0.0203232
$986$	2.76631	0.0880973
$987$	−3.73615	−0.118923
$988$	15.1809	0.482969
$989$	0.158575	0.00504240
$990$	−20.4112	−0.648710
$991$	17.0233	0.540762	0.270381	−	0.962753i	$-0.412850\pi$
$991$	17.0233	0.540762	0.270381	+	0.962753i	$0.412850\pi$
$992$	1.88962	0.0599955
$993$	36.3599	1.15385
$994$	−20.3297	−0.644818
$995$	27.1866	0.861872
$996$	3.01145	0.0954216
$997$	25.2389	0.799325	0.399662	−	0.916662i	$-0.369127\pi$
$997$	25.2389	0.799325	0.399662	+	0.916662i	$0.369127\pi$
$998$	34.5900	1.09493
$999$	−0.00666067	−0.000210734 0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8035.2.a.c.1.5	✓	127

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8035.2.a.c.1.5	✓	127	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:	\( N \)	\(=\)	\( 8035 = 5 \cdot 1607 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8035.a (trivial)

\(f(q)\)	\(=\)	\(q-2.47063 q^{2} -2.44892 q^{3} +4.10400 q^{4} -1.00000 q^{5} +6.05037 q^{6} +0.863350 q^{7} -5.19820 q^{8} +2.99721 q^{9} +O(q^{10})\)	\(q-2.47063 q^{2} -2.44892 q^{3} +4.10400 q^{4} -1.00000 q^{5} +6.05037 q^{6} +0.863350 q^{7} -5.19820 q^{8} +2.99721 q^{9} +2.47063 q^{10} -2.75641 q^{11} -10.0504 q^{12} -1.88663 q^{13} -2.13302 q^{14} +2.44892 q^{15} +4.63482 q^{16} +4.04453 q^{17} -7.40500 q^{18} -1.96067 q^{19} -4.10400 q^{20} -2.11427 q^{21} +6.81005 q^{22} +0.0529010 q^{23} +12.7300 q^{24} +1.00000 q^{25} +4.66115 q^{26} +0.00682633 q^{27} +3.54319 q^{28} -0.276838 q^{29} -6.05037 q^{30} -1.79194 q^{31} -1.05451 q^{32} +6.75022 q^{33} -9.99252 q^{34} -0.863350 q^{35} +12.3006 q^{36} -0.975732 q^{37} +4.84408 q^{38} +4.62020 q^{39} +5.19820 q^{40} -10.6593 q^{41} +5.22359 q^{42} +2.99758 q^{43} -11.3123 q^{44} -2.99721 q^{45} -0.130699 q^{46} +1.76711 q^{47} -11.3503 q^{48} -6.25463 q^{49} -2.47063 q^{50} -9.90472 q^{51} -7.74271 q^{52} +13.6335 q^{53} -0.0168653 q^{54} +2.75641 q^{55} -4.48787 q^{56} +4.80152 q^{57} +0.683964 q^{58} -5.66720 q^{59} +10.0504 q^{60} -9.51933 q^{61} +4.42721 q^{62} +2.58764 q^{63} -6.66433 q^{64} +1.88663 q^{65} -16.6773 q^{66} +2.82571 q^{67} +16.5987 q^{68} -0.129550 q^{69} +2.13302 q^{70} +9.53096 q^{71} -15.5801 q^{72} +0.614249 q^{73} +2.41067 q^{74} -2.44892 q^{75} -8.04659 q^{76} -2.37974 q^{77} -11.4148 q^{78} -15.7986 q^{79} -4.63482 q^{80} -9.00835 q^{81} +26.3352 q^{82} -0.299636 q^{83} -8.67698 q^{84} -4.04453 q^{85} -7.40591 q^{86} +0.677955 q^{87} +14.3284 q^{88} +16.1278 q^{89} +7.40500 q^{90} -1.62882 q^{91} +0.217106 q^{92} +4.38831 q^{93} -4.36586 q^{94} +1.96067 q^{95} +2.58242 q^{96} -18.8571 q^{97} +15.4529 q^{98} -8.26153 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 127 q + 19 q^{2} + 10 q^{3} + 125 q^{4} - 127 q^{5} + 13 q^{7} + 54 q^{8} + 123 q^{9}+O(q^{10}) \) 127 * q + 19 * q^2 + 10 * q^3 + 125 * q^4 - 127 * q^5 + 13 * q^7 + 54 * q^8 + 123 * q^9	\( 127 q + 19 q^{2} + 10 q^{3} + 125 q^{4} - 127 q^{5} + 13 q^{7} + 54 q^{8} + 123 q^{9} - 19 q^{10} + 30 q^{11} + 35 q^{12} + 30 q^{13} + 39 q^{14} - 10 q^{15} + 121 q^{16} + 63 q^{17} + 53 q^{18} - 35 q^{19} - 125 q^{20} + 33 q^{21} + 49 q^{22} + 61 q^{23} - 5 q^{24} + 127 q^{25} + 10 q^{26} + 40 q^{27} + 32 q^{28} + 134 q^{29} - 25 q^{31} + 122 q^{32} + 48 q^{33} - 21 q^{34} - 13 q^{35} + 133 q^{36} + 60 q^{37} + 33 q^{38} + 26 q^{39} - 54 q^{40} + 9 q^{41} + 45 q^{42} + 48 q^{43} + 85 q^{44} - 123 q^{45} - 11 q^{46} + 57 q^{47} + 71 q^{48} + 70 q^{49} + 19 q^{50} + 45 q^{51} + 68 q^{52} + 182 q^{53} - 29 q^{54} - 30 q^{55} + 96 q^{56} + 74 q^{57} + 47 q^{58} + 19 q^{59} - 35 q^{60} + 16 q^{61} + 43 q^{62} + 73 q^{63} + 110 q^{64} - 30 q^{65} + 8 q^{66} + 40 q^{67} + 129 q^{68} + 2 q^{69} - 39 q^{70} + 48 q^{71} + 151 q^{72} + 30 q^{73} + 117 q^{74} + 10 q^{75} - 98 q^{76} + 134 q^{77} + 54 q^{78} + 23 q^{79} - 121 q^{80} + 111 q^{81} + 4 q^{82} + 92 q^{83} + 48 q^{84} - 63 q^{85} + 42 q^{86} + 69 q^{87} + 121 q^{88} + 12 q^{89} - 53 q^{90} - 30 q^{91} + 175 q^{92} + 82 q^{93} - 23 q^{94} + 35 q^{95} + 6 q^{96} + 67 q^{97} + 122 q^{98} + 73 q^{99}+O(q^{100}) \) 127 * q + 19 * q^2 + 10 * q^3 + 125 * q^4 - 127 * q^5 + 13 * q^7 + 54 * q^8 + 123 * q^9 - 19 * q^10 + 30 * q^11 + 35 * q^12 + 30 * q^13 + 39 * q^14 - 10 * q^15 + 121 * q^16 + 63 * q^17 + 53 * q^18 - 35 * q^19 - 125 * q^20 + 33 * q^21 + 49 * q^22 + 61 * q^23 - 5 * q^24 + 127 * q^25 + 10 * q^26 + 40 * q^27 + 32 * q^28 + 134 * q^29 - 25 * q^31 + 122 * q^32 + 48 * q^33 - 21 * q^34 - 13 * q^35 + 133 * q^36 + 60 * q^37 + 33 * q^38 + 26 * q^39 - 54 * q^40 + 9 * q^41 + 45 * q^42 + 48 * q^43 + 85 * q^44 - 123 * q^45 - 11 * q^46 + 57 * q^47 + 71 * q^48 + 70 * q^49 + 19 * q^50 + 45 * q^51 + 68 * q^52 + 182 * q^53 - 29 * q^54 - 30 * q^55 + 96 * q^56 + 74 * q^57 + 47 * q^58 + 19 * q^59 - 35 * q^60 + 16 * q^61 + 43 * q^62 + 73 * q^63 + 110 * q^64 - 30 * q^65 + 8 * q^66 + 40 * q^67 + 129 * q^68 + 2 * q^69 - 39 * q^70 + 48 * q^71 + 151 * q^72 + 30 * q^73 + 117 * q^74 + 10 * q^75 - 98 * q^76 + 134 * q^77 + 54 * q^78 + 23 * q^79 - 121 * q^80 + 111 * q^81 + 4 * q^82 + 92 * q^83 + 48 * q^84 - 63 * q^85 + 42 * q^86 + 69 * q^87 + 121 * q^88 + 12 * q^89 - 53 * q^90 - 30 * q^91 + 175 * q^92 + 82 * q^93 - 23 * q^94 + 35 * q^95 + 6 * q^96 + 67 * q^97 + 122 * q^98 + 73 * q^99

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