LMFDB - Embedded newform 8007.2.a.g.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8007,2,Mod(1,8007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8007, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8007 = 3 \cdot 17 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8007.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:	$63.9362168984$
Analytic rank:	$0$
Dimension:	$56$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	8007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.76474 q^{2} -1.00000 q^{3} +5.64378 q^{4} -1.85589 q^{5} +2.76474 q^{6} +1.33970 q^{7} -10.0741 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.76474 q^{2} -1.00000 q^{3} +5.64378 q^{4} -1.85589 q^{5} +2.76474 q^{6} +1.33970 q^{7} -10.0741 q^{8} +1.00000 q^{9} +5.13105 q^{10} +4.23218 q^{11} -5.64378 q^{12} +2.39495 q^{13} -3.70392 q^{14} +1.85589 q^{15} +16.5647 q^{16} -1.00000 q^{17} -2.76474 q^{18} -1.09326 q^{19} -10.4742 q^{20} -1.33970 q^{21} -11.7009 q^{22} -1.76503 q^{23} +10.0741 q^{24} -1.55568 q^{25} -6.62142 q^{26} -1.00000 q^{27} +7.56097 q^{28} -7.57011 q^{29} -5.13105 q^{30} -9.07777 q^{31} -25.6488 q^{32} -4.23218 q^{33} +2.76474 q^{34} -2.48633 q^{35} +5.64378 q^{36} +2.01553 q^{37} +3.02257 q^{38} -2.39495 q^{39} +18.6964 q^{40} -4.16917 q^{41} +3.70392 q^{42} +8.04012 q^{43} +23.8855 q^{44} -1.85589 q^{45} +4.87986 q^{46} -7.10141 q^{47} -16.5647 q^{48} -5.20521 q^{49} +4.30104 q^{50} +1.00000 q^{51} +13.5166 q^{52} +6.44986 q^{53} +2.76474 q^{54} -7.85446 q^{55} -13.4963 q^{56} +1.09326 q^{57} +20.9294 q^{58} -3.43785 q^{59} +10.4742 q^{60} -0.676883 q^{61} +25.0977 q^{62} +1.33970 q^{63} +37.7829 q^{64} -4.44476 q^{65} +11.7009 q^{66} +8.47766 q^{67} -5.64378 q^{68} +1.76503 q^{69} +6.87406 q^{70} -3.75805 q^{71} -10.0741 q^{72} +2.20661 q^{73} -5.57241 q^{74} +1.55568 q^{75} -6.17011 q^{76} +5.66985 q^{77} +6.62142 q^{78} +5.76415 q^{79} -30.7422 q^{80} +1.00000 q^{81} +11.5267 q^{82} +13.4279 q^{83} -7.56097 q^{84} +1.85589 q^{85} -22.2288 q^{86} +7.57011 q^{87} -42.6354 q^{88} +15.6676 q^{89} +5.13105 q^{90} +3.20852 q^{91} -9.96146 q^{92} +9.07777 q^{93} +19.6336 q^{94} +2.02897 q^{95} +25.6488 q^{96} +14.6029 q^{97} +14.3910 q^{98} +4.23218 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + q^{2} - 56 q^{3} + 61 q^{4} + q^{5} - q^{6} + 19 q^{7} + 56 q^{9}+O(q^{10}) $ 56 * q + q^2 - 56 * q^3 + 61 * q^4 + q^5 - q^6 + 19 * q^7 + 56 * q^9	\( 56 q + q^{2} - 56 q^{3} + 61 q^{4} + q^{5} - q^{6} + 19 q^{7} + 56 q^{9} + 8 q^{10} - 7 q^{11} - 61 q^{12} + 8 q^{13} - 8 q^{14} - q^{15} + 71 q^{16} - 56 q^{17} + q^{18} - 2 q^{19} - 4 q^{20} - 19 q^{21} + 47 q^{22} + 16 q^{23} + 85 q^{25} - 11 q^{26} - 56 q^{27} + 52 q^{28} + 17 q^{29} - 8 q^{30} + 23 q^{31} + 11 q^{32} + 7 q^{33} - q^{34} - 41 q^{35} + 61 q^{36} + 58 q^{37} - 22 q^{38} - 8 q^{39} + 38 q^{40} - q^{41} + 8 q^{42} + 27 q^{43} + 2 q^{44} + q^{45} + 46 q^{46} + 5 q^{47} - 71 q^{48} + 59 q^{49} - 4 q^{50} + 56 q^{51} + 25 q^{52} + 15 q^{53} - q^{54} + 9 q^{55} - 36 q^{56} + 2 q^{57} + 89 q^{58} - 61 q^{59} + 4 q^{60} + 47 q^{61} + 8 q^{62} + 19 q^{63} + 88 q^{64} + 39 q^{65} - 47 q^{66} + 20 q^{67} - 61 q^{68} - 16 q^{69} + 36 q^{70} - 2 q^{71} + 93 q^{73} + 48 q^{74} - 85 q^{75} + 38 q^{76} + 26 q^{77} + 11 q^{78} + 72 q^{79} + 42 q^{80} + 56 q^{81} + 33 q^{82} - 11 q^{83} - 52 q^{84} - q^{85} - 4 q^{86} - 17 q^{87} + 130 q^{88} - 6 q^{89} + 8 q^{90} + 37 q^{91} + 132 q^{92} - 23 q^{93} - 32 q^{94} + 12 q^{95} - 11 q^{96} + 100 q^{97} + 42 q^{98} - 7 q^{99}+O(q^{100}) \) 56 * q + q^2 - 56 * q^3 + 61 * q^4 + q^5 - q^6 + 19 * q^7 + 56 * q^9 + 8 * q^10 - 7 * q^11 - 61 * q^12 + 8 * q^13 - 8 * q^14 - q^15 + 71 * q^16 - 56 * q^17 + q^18 - 2 * q^19 - 4 * q^20 - 19 * q^21 + 47 * q^22 + 16 * q^23 + 85 * q^25 - 11 * q^26 - 56 * q^27 + 52 * q^28 + 17 * q^29 - 8 * q^30 + 23 * q^31 + 11 * q^32 + 7 * q^33 - q^34 - 41 * q^35 + 61 * q^36 + 58 * q^37 - 22 * q^38 - 8 * q^39 + 38 * q^40 - q^41 + 8 * q^42 + 27 * q^43 + 2 * q^44 + q^45 + 46 * q^46 + 5 * q^47 - 71 * q^48 + 59 * q^49 - 4 * q^50 + 56 * q^51 + 25 * q^52 + 15 * q^53 - q^54 + 9 * q^55 - 36 * q^56 + 2 * q^57 + 89 * q^58 - 61 * q^59 + 4 * q^60 + 47 * q^61 + 8 * q^62 + 19 * q^63 + 88 * q^64 + 39 * q^65 - 47 * q^66 + 20 * q^67 - 61 * q^68 - 16 * q^69 + 36 * q^70 - 2 * q^71 + 93 * q^73 + 48 * q^74 - 85 * q^75 + 38 * q^76 + 26 * q^77 + 11 * q^78 + 72 * q^79 + 42 * q^80 + 56 * q^81 + 33 * q^82 - 11 * q^83 - 52 * q^84 - q^85 - 4 * q^86 - 17 * q^87 + 130 * q^88 - 6 * q^89 + 8 * q^90 + 37 * q^91 + 132 * q^92 - 23 * q^93 - 32 * q^94 + 12 * q^95 - 11 * q^96 + 100 * q^97 + 42 * q^98 - 7 * 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 $

$2$	−2.76474	−1.95497	−0.977483	−	0.211016i	$-0.932323\pi$
$2$	−2.76474	−1.95497	−0.977483	+	0.211016i	$0.932323\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	5.64378	2.82189
$5$	−1.85589	−0.829979	−0.414989	−	0.909826i	$-0.636215\pi$
$5$	−1.85589	−0.829979	−0.414989	+	0.909826i	$0.636215\pi$
$6$	2.76474	1.12870
$7$	1.33970	0.506359	0.253179	−	0.967419i	$-0.418524\pi$
$7$	1.33970	0.506359	0.253179	+	0.967419i	$0.418524\pi$
$8$	−10.0741	−3.56173
$9$	1.00000	0.333333
$10$	5.13105	1.62258
$11$	4.23218	1.27605	0.638026	−	0.770015i	$-0.279751\pi$
$11$	4.23218	1.27605	0.638026	+	0.770015i	$0.279751\pi$
$12$	−5.64378	−1.62922
$13$	2.39495	0.664240	0.332120	−	0.943237i	$-0.392236\pi$
$13$	2.39495	0.664240	0.332120	+	0.943237i	$0.392236\pi$
$14$	−3.70392	−0.989914
$15$	1.85589	0.479188
$16$	16.5647	4.14117
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−2.76474	−0.651655
$19$	−1.09326	−0.250811	−0.125405	−	0.992106i	$-0.540023\pi$
$19$	−1.09326	−0.250811	−0.125405	+	0.992106i	$0.540023\pi$
$20$	−10.4742	−2.34211
$21$	−1.33970	−0.292346
$22$	−11.7009	−2.49464
$23$	−1.76503	−0.368035	−0.184017	−	0.982923i	$-0.558910\pi$
$23$	−1.76503	−0.368035	−0.184017	+	0.982923i	$0.558910\pi$
$24$	10.0741	2.05637
$25$	−1.55568	−0.311136
$26$	−6.62142	−1.29857
$27$	−1.00000	−0.192450
$28$	7.56097	1.42889
$29$	−7.57011	−1.40573	−0.702867	−	0.711321i	$-0.748097\pi$
$29$	−7.57011	−1.40573	−0.702867	+	0.711321i	$0.748097\pi$
$30$	−5.13105	−0.936797
$31$	−9.07777	−1.63042	−0.815208	−	0.579168i	$-0.803377\pi$
$31$	−9.07777	−1.63042	−0.815208	+	0.579168i	$0.803377\pi$
$32$	−25.6488	−4.53411
$33$	−4.23218	−0.736728
$34$	2.76474	0.474149
$35$	−2.48633	−0.420267
$36$	5.64378	0.940630
$37$	2.01553	0.331351	0.165675	−	0.986180i	$-0.447020\pi$
$37$	2.01553	0.331351	0.165675	+	0.986180i	$0.447020\pi$
$38$	3.02257	0.490326
$39$	−2.39495	−0.383499
$40$	18.6964	2.95616
$41$	−4.16917	−0.651115	−0.325557	−	0.945522i	$-0.605552\pi$
$41$	−4.16917	−0.651115	−0.325557	+	0.945522i	$0.605552\pi$
$42$	3.70392	0.571527
$43$	8.04012	1.22611	0.613053	−	0.790042i	$-0.289941\pi$
$43$	8.04012	1.22611	0.613053	+	0.790042i	$0.289941\pi$
$44$	23.8855	3.60088
$45$	−1.85589	−0.276660
$46$	4.87986	0.719495
$47$	−7.10141	−1.03585	−0.517924	−	0.855427i	$-0.673295\pi$
$47$	−7.10141	−1.03585	−0.517924	+	0.855427i	$0.673295\pi$
$48$	−16.5647	−2.39091
$49$	−5.20521	−0.743601
$50$	4.30104	0.608259
$51$	1.00000	0.140028
$52$	13.5166	1.87441
$53$	6.44986	0.885956	0.442978	−	0.896532i	$-0.353922\pi$
$53$	6.44986	0.885956	0.442978	+	0.896532i	$0.353922\pi$
$54$	2.76474	0.376233
$55$	−7.85446	−1.05910
$56$	−13.4963	−1.80351
$57$	1.09326	0.144806
$58$	20.9294	2.74816
$59$	−3.43785	−0.447570	−0.223785	−	0.974639i	$-0.571841\pi$
$59$	−3.43785	−0.447570	−0.223785	+	0.974639i	$0.571841\pi$
$60$	10.4742	1.35222
$61$	−0.676883	−0.0866660	−0.0433330	−	0.999061i	$-0.513798\pi$
$61$	−0.676883	−0.0866660	−0.0433330	+	0.999061i	$0.513798\pi$
$62$	25.0977	3.18741
$63$	1.33970	0.168786
$64$	37.7829	4.72286
$65$	−4.44476	−0.551305
$66$	11.7009	1.44028
$67$	8.47766	1.03571	0.517855	−	0.855468i	$-0.326731\pi$
$67$	8.47766	1.03571	0.517855	+	0.855468i	$0.326731\pi$
$68$	−5.64378	−0.684409
$69$	1.76503	0.212485
$70$	6.87406	0.821607
$71$	−3.75805	−0.445998	−0.222999	−	0.974819i	$-0.571585\pi$
$71$	−3.75805	−0.445998	−0.222999	+	0.974819i	$0.571585\pi$
$72$	−10.0741	−1.18724
$73$	2.20661	0.258264	0.129132	−	0.991627i	$-0.458781\pi$
$73$	2.20661	0.258264	0.129132	+	0.991627i	$0.458781\pi$
$74$	−5.57241	−0.647780
$75$	1.55568	0.179634
$76$	−6.17011	−0.707760
$77$	5.66985	0.646140
$78$	6.62142	0.749728
$79$	5.76415	0.648518	0.324259	−	0.945968i	$-0.394885\pi$
$79$	5.76415	0.648518	0.324259	+	0.945968i	$0.394885\pi$
$80$	−30.7422	−3.43708
$81$	1.00000	0.111111
$82$	11.5267	1.27291
$83$	13.4279	1.47390	0.736951	−	0.675946i	$-0.236265\pi$
$83$	13.4279	1.47390	0.736951	+	0.675946i	$0.236265\pi$
$84$	−7.56097	−0.824969
$85$	1.85589	0.201299
$86$	−22.2288	−2.39699
$87$	7.57011	0.811601
$88$	−42.6354	−4.54495
$89$	15.6676	1.66076	0.830382	−	0.557195i	$-0.188122\pi$
$89$	15.6676	1.66076	0.830382	+	0.557195i	$0.188122\pi$
$90$	5.13105	0.540860
$91$	3.20852	0.336344
$92$	−9.96146	−1.03855
$93$	9.07777	0.941321
$94$	19.6336	2.02505
$95$	2.02897	0.208168
$96$	25.6488	2.61777
$97$	14.6029	1.48270	0.741350	−	0.671118i	$-0.234186\pi$
$97$	14.6029	1.48270	0.741350	+	0.671118i	$0.234186\pi$
$98$	14.3910	1.45371
$99$	4.23218	0.425350
$100$	−8.77990	−0.877990
$101$	−18.6011	−1.85088	−0.925440	−	0.378893i	$-0.876305\pi$
$101$	−18.6011	−1.85088	−0.925440	+	0.378893i	$0.876305\pi$
$102$	−2.76474	−0.273750
$103$	2.35681	0.232224	0.116112	−	0.993236i	$-0.462957\pi$
$103$	2.35681	0.232224	0.116112	+	0.993236i	$0.462957\pi$
$104$	−24.1270	−2.36584
$105$	2.48633	0.242641
$106$	−17.8322	−1.73201
$107$	−10.6871	−1.03317	−0.516583	−	0.856237i	$-0.672796\pi$
$107$	−10.6871	−1.03317	−0.516583	+	0.856237i	$0.672796\pi$
$108$	−5.64378	−0.543073
$109$	−3.99249	−0.382411	−0.191206	−	0.981550i	$-0.561240\pi$
$109$	−3.99249	−0.382411	−0.191206	+	0.981550i	$0.561240\pi$
$110$	21.7155	2.07049
$111$	−2.01553	−0.191306
$112$	22.1917	2.09692
$113$	5.86657	0.551880	0.275940	−	0.961175i	$-0.411011\pi$
$113$	5.86657	0.551880	0.275940	+	0.961175i	$0.411011\pi$
$114$	−3.02257	−0.283090
$115$	3.27570	0.305461
$116$	−42.7240	−3.96683
$117$	2.39495	0.221413
$118$	9.50476	0.874984
$119$	−1.33970	−0.122810
$120$	−18.6964	−1.70674
$121$	6.91137	0.628307
$122$	1.87140	0.169429
$123$	4.16917	0.375921
$124$	−51.2329	−4.60085
$125$	12.1666	1.08821
$126$	−3.70392	−0.329971
$127$	−15.4757	−1.37325	−0.686624	−	0.727013i	$-0.740908\pi$
$127$	−15.4757	−1.37325	−0.686624	+	0.727013i	$0.740908\pi$
$128$	−53.1622	−4.69892
$129$	−8.04012	−0.707893
$130$	12.2886	1.07778
$131$	−7.55100	−0.659734	−0.329867	−	0.944027i	$-0.607004\pi$
$131$	−7.55100	−0.659734	−0.329867	+	0.944027i	$0.607004\pi$
$132$	−23.8855	−2.07897
$133$	−1.46464	−0.127000
$134$	−23.4385	−2.02478
$135$	1.85589	0.159729
$136$	10.0741	0.863846
$137$	8.04763	0.687555	0.343778	−	0.939051i	$-0.388293\pi$
$137$	8.04763	0.687555	0.343778	+	0.939051i	$0.388293\pi$
$138$	−4.87986	−0.415401
$139$	16.1340	1.36846	0.684232	−	0.729264i	$-0.260137\pi$
$139$	16.1340	1.36846	0.684232	+	0.729264i	$0.260137\pi$
$140$	−14.0323	−1.18595
$141$	7.10141	0.598047
$142$	10.3900	0.871911
$143$	10.1359	0.847605
$144$	16.5647	1.38039
$145$	14.0493	1.16673
$146$	−6.10069	−0.504897
$147$	5.20521	0.429318
$148$	11.3752	0.935036
$149$	−14.0933	−1.15456	−0.577282	−	0.816545i	$-0.695887\pi$
$149$	−14.0933	−1.15456	−0.577282	+	0.816545i	$0.695887\pi$
$150$	−4.30104	−0.351179
$151$	−17.0770	−1.38971	−0.694853	−	0.719152i	$-0.744530\pi$
$151$	−17.0770	−1.38971	−0.694853	+	0.719152i	$0.744530\pi$
$152$	11.0136	0.893320
$153$	−1.00000	−0.0808452
$154$	−15.6757	−1.26318
$155$	16.8473	1.35321
$156$	−13.5166	−1.08219
$157$	1.00000	0.0798087
$157$	1.00000	0.0798087
$158$	−15.9364	−1.26783
$159$	−6.44986	−0.511507
$160$	47.6013	3.76322
$161$	−2.36461	−0.186358
$162$	−2.76474	−0.217218
$163$	17.3537	1.35925	0.679625	−	0.733560i	$-0.262143\pi$
$163$	17.3537	1.35925	0.679625	+	0.733560i	$0.262143\pi$
$164$	−23.5299	−1.83737
$165$	7.85446	0.611469
$166$	−37.1246	−2.88143
$167$	−5.32748	−0.412253	−0.206126	−	0.978525i	$-0.566086\pi$
$167$	−5.32748	−0.412253	−0.206126	+	0.978525i	$0.566086\pi$
$168$	13.4963	1.04126
$169$	−7.26420	−0.558785
$170$	−5.13105	−0.393533
$171$	−1.09326	−0.0836036
$172$	45.3766	3.45994
$173$	4.53469	0.344766	0.172383	−	0.985030i	$-0.444853\pi$
$173$	4.53469	0.344766	0.172383	+	0.985030i	$0.444853\pi$
$174$	−20.9294	−1.58665
$175$	−2.08414	−0.157546
$176$	70.1048	5.28434
$177$	3.43785	0.258405
$178$	−43.3168	−3.24673
$179$	20.9355	1.56480	0.782398	−	0.622779i	$-0.213996\pi$
$179$	20.9355	1.56480	0.782398	+	0.622779i	$0.213996\pi$
$180$	−10.4742	−0.780703
$181$	−9.92791	−0.737936	−0.368968	−	0.929442i	$-0.620289\pi$
$181$	−9.92791	−0.737936	−0.368968	+	0.929442i	$0.620289\pi$
$182$	−8.87071	−0.657541
$183$	0.676883	0.0500366
$184$	17.7811	1.31084
$185$	−3.74060	−0.275014
$186$	−25.0977	−1.84025
$187$	−4.23218	−0.309488
$188$	−40.0788	−2.92305
$189$	−1.33970	−0.0974488
$190$	−5.60956	−0.406960
$191$	−13.4258	−0.971458	−0.485729	−	0.874109i	$-0.661446\pi$
$191$	−13.4258	−0.971458	−0.485729	+	0.874109i	$0.661446\pi$
$192$	−37.7829	−2.72675
$193$	−16.9752	−1.22190	−0.610950	−	0.791669i	$-0.709213\pi$
$193$	−16.9752	−1.22190	−0.610950	+	0.791669i	$0.709213\pi$
$194$	−40.3732	−2.89863
$195$	4.44476	0.318296
$196$	−29.3770	−2.09836
$197$	13.1858	0.939450	0.469725	−	0.882813i	$-0.344353\pi$
$197$	13.1858	0.939450	0.469725	+	0.882813i	$0.344353\pi$
$198$	−11.7009	−0.831545
$199$	26.5511	1.88216	0.941078	−	0.338189i	$-0.109814\pi$
$199$	26.5511	1.88216	0.941078	+	0.338189i	$0.109814\pi$
$200$	15.6720	1.10818
$201$	−8.47766	−0.597968
$202$	51.4272	3.61841
$203$	−10.1417	−0.711806
$204$	5.64378	0.395144
$205$	7.73751	0.540411
$206$	−6.51597	−0.453989
$207$	−1.76503	−0.122678
$208$	39.6716	2.75073
$209$	−4.62687	−0.320047
$210$	−6.87406	−0.474355
$211$	21.0144	1.44669	0.723344	−	0.690487i	$-0.242604\pi$
$211$	21.0144	1.44669	0.723344	+	0.690487i	$0.242604\pi$
$212$	36.4016	2.50007
$213$	3.75805	0.257497
$214$	29.5472	2.01980
$215$	−14.9216	−1.01764
$216$	10.0741	0.685455
$217$	−12.1615	−0.825575
$218$	11.0382	0.747601
$219$	−2.20661	−0.149109
$220$	−44.3288	−2.98865
$221$	−2.39495	−0.161102
$222$	5.57241	0.373996
$223$	−25.1729	−1.68570	−0.842852	−	0.538145i	$-0.819125\pi$
$223$	−25.1729	−1.68570	−0.842852	+	0.538145i	$0.819125\pi$
$224$	−34.3617	−2.29589
$225$	−1.55568	−0.103712
$226$	−16.2195	−1.07891
$227$	22.5963	1.49977	0.749883	−	0.661570i	$-0.230110\pi$
$227$	22.5963	1.49977	0.749883	+	0.661570i	$0.230110\pi$
$228$	6.17011	0.408626
$229$	9.93904	0.656790	0.328395	−	0.944540i	$-0.393492\pi$
$229$	9.93904	0.656790	0.328395	+	0.944540i	$0.393492\pi$
$230$	−9.05647	−0.597166
$231$	−5.66985	−0.373049
$232$	76.2620	5.00685
$233$	16.1146	1.05570	0.527852	−	0.849336i	$-0.322998\pi$
$233$	16.1146	1.05570	0.527852	+	0.849336i	$0.322998\pi$
$234$	−6.62142	−0.432856
$235$	13.1794	0.859731
$236$	−19.4025	−1.26299
$237$	−5.76415	−0.374422
$238$	3.70392	0.240089
$239$	1.82612	0.118122	0.0590609	−	0.998254i	$-0.481189\pi$
$239$	1.82612	0.118122	0.0590609	+	0.998254i	$0.481189\pi$
$240$	30.7422	1.98440
$241$	22.4713	1.44750	0.723752	−	0.690060i	$-0.242416\pi$
$241$	22.4713	1.44750	0.723752	+	0.690060i	$0.242416\pi$
$242$	−19.1081	−1.22832
$243$	−1.00000	−0.0641500
$244$	−3.82018	−0.244562
$245$	9.66028	0.617173
$246$	−11.5267	−0.734913
$247$	−2.61830	−0.166599
$248$	91.4503	5.80710
$249$	−13.4279	−0.850958
$250$	−33.6375	−2.12742
$251$	12.7082	0.802132	0.401066	−	0.916049i	$-0.368640\pi$
$251$	12.7082	0.802132	0.401066	+	0.916049i	$0.368640\pi$
$252$	7.56097	0.476296
$253$	−7.46994	−0.469631
$254$	42.7863	2.68465
$255$	−1.85589	−0.116220
$256$	71.4138	4.46337
$257$	−9.06473	−0.565442	−0.282721	−	0.959202i	$-0.591237\pi$
$257$	−9.06473	−0.565442	−0.282721	+	0.959202i	$0.591237\pi$
$258$	22.2288	1.38391
$259$	2.70020	0.167782
$260$	−25.0853	−1.55572
$261$	−7.57011	−0.468578
$262$	20.8766	1.28976
$263$	20.5223	1.26546	0.632729	−	0.774374i	$-0.281935\pi$
$263$	20.5223	1.26546	0.632729	+	0.774374i	$0.281935\pi$
$264$	42.6354	2.62403
$265$	−11.9702	−0.735325
$266$	4.04934	0.248281
$267$	−15.6676	−0.958842
$268$	47.8460	2.92266
$269$	−8.22100	−0.501243	−0.250622	−	0.968085i	$-0.580635\pi$
$269$	−8.22100	−0.501243	−0.250622	+	0.968085i	$0.580635\pi$
$270$	−5.13105	−0.312266
$271$	−2.69383	−0.163638	−0.0818191	−	0.996647i	$-0.526073\pi$
$271$	−2.69383	−0.163638	−0.0818191	+	0.996647i	$0.526073\pi$
$272$	−16.5647	−1.00438
$273$	−3.20852	−0.194188
$274$	−22.2496	−1.34415
$275$	−6.58391	−0.397025
$276$	9.96146	0.599609
$277$	−19.1129	−1.14838	−0.574191	−	0.818722i	$-0.694683\pi$
$277$	−19.1129	−1.14838	−0.574191	+	0.818722i	$0.694683\pi$
$278$	−44.6062	−2.67530
$279$	−9.07777	−0.543472
$280$	25.0475	1.49688
$281$	−18.2385	−1.08802	−0.544008	−	0.839080i	$-0.683094\pi$
$281$	−18.2385	−1.08802	−0.544008	+	0.839080i	$0.683094\pi$
$282$	−19.6336	−1.16916
$283$	6.09903	0.362550	0.181275	−	0.983432i	$-0.441978\pi$
$283$	6.09903	0.362550	0.181275	+	0.983432i	$0.441978\pi$
$284$	−21.2096	−1.25856
$285$	−2.02897	−0.120186
$286$	−28.0230	−1.65704
$287$	−5.58543	−0.329698
$288$	−25.6488	−1.51137
$289$	1.00000	0.0588235
$290$	−38.8426	−2.28091
$291$	−14.6029	−0.856038
$292$	12.4536	0.728792
$293$	4.54238	0.265369	0.132684	−	0.991158i	$-0.457640\pi$
$293$	4.54238	0.265369	0.132684	+	0.991158i	$0.457640\pi$
$294$	−14.3910	−0.839302
$295$	6.38027	0.371474
$296$	−20.3046	−1.18018
$297$	−4.23218	−0.245576
$298$	38.9642	2.25713
$299$	−4.22717	−0.244464
$300$	8.77990	0.506908
$301$	10.7713	0.620850
$302$	47.2134	2.71683
$303$	18.6011	1.06861
$304$	−18.1095	−1.03865
$305$	1.25622	0.0719309
$306$	2.76474	0.158050
$307$	5.40621	0.308549	0.154274	−	0.988028i	$-0.450696\pi$
$307$	5.40621	0.308549	0.154274	+	0.988028i	$0.450696\pi$
$308$	31.9994	1.82333
$309$	−2.35681	−0.134074
$310$	−46.5785	−2.64548
$311$	−5.58264	−0.316562	−0.158281	−	0.987394i	$-0.550595\pi$
$311$	−5.58264	−0.316562	−0.158281	+	0.987394i	$0.550595\pi$
$312$	24.1270	1.36592
$313$	−9.53177	−0.538767	−0.269384	−	0.963033i	$-0.586820\pi$
$313$	−9.53177	−0.538767	−0.269384	+	0.963033i	$0.586820\pi$
$314$	−2.76474	−0.156023
$315$	−2.48633	−0.140089
$316$	32.5316	1.83005
$317$	17.0936	0.960072	0.480036	−	0.877249i	$-0.340624\pi$
$317$	17.0936	0.960072	0.480036	+	0.877249i	$0.340624\pi$
$318$	17.8322	0.999979
$319$	−32.0381	−1.79379
$320$	−70.1209	−3.91988
$321$	10.6871	0.596498
$322$	6.53754	0.364323
$323$	1.09326	0.0608305
$324$	5.64378	0.313543
$325$	−3.72577	−0.206669
$326$	−47.9785	−2.65729
$327$	3.99249	0.220785
$328$	42.0006	2.31909
$329$	−9.51376	−0.524510
$330$	−21.7155	−1.19540
$331$	−6.75979	−0.371552	−0.185776	−	0.982592i	$-0.559480\pi$
$331$	−6.75979	−0.371552	−0.185776	+	0.982592i	$0.559480\pi$
$332$	75.7841	4.15919
$333$	2.01553	0.110450
$334$	14.7291	0.805940
$335$	−15.7336	−0.859618
$336$	−22.1917	−1.21066
$337$	26.7458	1.45694	0.728469	−	0.685079i	$-0.240232\pi$
$337$	26.7458	1.45694	0.728469	+	0.685079i	$0.240232\pi$
$338$	20.0836	1.09241
$339$	−5.86657	−0.318628
$340$	10.4742	0.568045
$341$	−38.4188	−2.08049
$342$	3.02257	0.163442
$343$	−16.3513	−0.882887
$344$	−80.9969	−4.36706
$345$	−3.27570	−0.176358
$346$	−12.5372	−0.674006
$347$	31.9907	1.71735	0.858674	−	0.512522i	$-0.171289\pi$
$347$	31.9907	1.71735	0.858674	+	0.512522i	$0.171289\pi$
$348$	42.7240	2.29025
$349$	−34.5621	−1.85007	−0.925034	−	0.379885i	$-0.875964\pi$
$349$	−34.5621	−1.85007	−0.925034	+	0.379885i	$0.875964\pi$
$350$	5.76210	0.307997
$351$	−2.39495	−0.127833
$352$	−108.550	−5.78576
$353$	−1.87433	−0.0997603	−0.0498801	−	0.998755i	$-0.515884\pi$
$353$	−1.87433	−0.0997603	−0.0498801	+	0.998755i	$0.515884\pi$
$354$	−9.50476	−0.505172
$355$	6.97452	0.370169
$356$	88.4245	4.68649
$357$	1.33970	0.0709044
$358$	−57.8813	−3.05912
$359$	14.1536	0.747000	0.373500	−	0.927630i	$-0.378158\pi$
$359$	14.1536	0.747000	0.373500	+	0.927630i	$0.378158\pi$
$360$	18.6964	0.985387
$361$	−17.8048	−0.937094
$362$	27.4481	1.44264
$363$	−6.91137	−0.362753
$364$	18.1082	0.949125
$365$	−4.09521	−0.214353
$366$	−1.87140	−0.0978199
$367$	35.8717	1.87249	0.936244	−	0.351350i	$-0.114277\pi$
$367$	35.8717	1.87249	0.936244	+	0.351350i	$0.114277\pi$
$368$	−29.2372	−1.52409
$369$	−4.16917	−0.217038
$370$	10.3418	0.537643
$371$	8.64087	0.448612
$372$	51.2329	2.65630
$373$	−26.8765	−1.39161	−0.695805	−	0.718230i	$-0.744952\pi$
$373$	−26.8765	−1.39161	−0.695805	+	0.718230i	$0.744952\pi$
$374$	11.7009	0.605038
$375$	−12.1666	−0.628281
$376$	71.5403	3.68941
$377$	−18.1300	−0.933745
$378$	3.70392	0.190509
$379$	−9.10520	−0.467703	−0.233851	−	0.972272i	$-0.575133\pi$
$379$	−9.10520	−0.467703	−0.233851	+	0.972272i	$0.575133\pi$
$380$	11.4510	0.587426
$381$	15.4757	0.792845
$382$	37.1189	1.89917
$383$	−13.6982	−0.699947	−0.349973	−	0.936760i	$-0.613809\pi$
$383$	−13.6982	−0.699947	−0.349973	+	0.936760i	$0.613809\pi$
$384$	53.1622	2.71292
$385$	−10.5226	−0.536282
$386$	46.9320	2.38877
$387$	8.04012	0.408702
$388$	82.4156	4.18402
$389$	20.7060	1.04983	0.524917	−	0.851153i	$-0.324096\pi$
$389$	20.7060	1.04983	0.524917	+	0.851153i	$0.324096\pi$
$390$	−12.2886	−0.622258
$391$	1.76503	0.0892616
$392$	52.4377	2.64851
$393$	7.55100	0.380898
$394$	−36.4553	−1.83659
$395$	−10.6976	−0.538256
$396$	23.8855	1.20029
$397$	−32.7977	−1.64607	−0.823034	−	0.567993i	$-0.807720\pi$
$397$	−32.7977	−1.64607	−0.823034	+	0.567993i	$0.807720\pi$
$398$	−73.4068	−3.67955
$399$	1.46464	0.0733236
$400$	−25.7693	−1.28847
$401$	10.9811	0.548372	0.274186	−	0.961677i	$-0.411592\pi$
$401$	10.9811	0.548372	0.274186	+	0.961677i	$0.411592\pi$
$402$	23.4385	1.16901
$403$	−21.7408	−1.08299
$404$	−104.981	−5.22298
$405$	−1.85589	−0.0922198
$406$	28.0391	1.39156
$407$	8.53009	0.422821
$408$	−10.0741	−0.498742
$409$	30.8283	1.52436	0.762182	−	0.647363i	$-0.224128\pi$
$409$	30.8283	1.52436	0.762182	+	0.647363i	$0.224128\pi$
$410$	−21.3922	−1.05649
$411$	−8.04763	−0.396960
$412$	13.3013	0.655310
$413$	−4.60569	−0.226631
$414$	4.87986	0.239832
$415$	−24.9207	−1.22331
$416$	−61.4277	−3.01174
$417$	−16.1340	−0.790083
$418$	12.7921	0.625682
$419$	−19.7749	−0.966066	−0.483033	−	0.875602i	$-0.660465\pi$
$419$	−19.7749	−0.966066	−0.483033	+	0.875602i	$0.660465\pi$
$420$	14.0323	0.684707
$421$	−15.9936	−0.779482	−0.389741	−	0.920925i	$-0.627435\pi$
$421$	−15.9936	−0.779482	−0.389741	+	0.920925i	$0.627435\pi$
$422$	−58.0992	−2.82823
$423$	−7.10141	−0.345283
$424$	−64.9765	−3.15554
$425$	1.55568	0.0754615
$426$	−10.3900	−0.503398
$427$	−0.906820	−0.0438841
$428$	−60.3159	−2.91548
$429$	−10.1359	−0.489365
$430$	41.2542	1.98945
$431$	−8.03580	−0.387071	−0.193536	−	0.981093i	$-0.561995\pi$
$431$	−8.03580	−0.387071	−0.193536	+	0.981093i	$0.561995\pi$
$432$	−16.5647	−0.796969
$433$	−3.09785	−0.148873	−0.0744366	−	0.997226i	$-0.523716\pi$
$433$	−3.09785	−0.148873	−0.0744366	+	0.997226i	$0.523716\pi$
$434$	33.6233	1.61397
$435$	−14.0493	−0.673611
$436$	−22.5327	−1.07912
$437$	1.92964	0.0923071
$438$	6.10069	0.291502
$439$	5.64570	0.269455	0.134727	−	0.990883i	$-0.456984\pi$
$439$	5.64570	0.269455	0.134727	+	0.990883i	$0.456984\pi$
$440$	79.1266	3.77221
$441$	−5.20521	−0.247867
$442$	6.62142	0.314949
$443$	−29.0216	−1.37886	−0.689429	−	0.724353i	$-0.742139\pi$
$443$	−29.0216	−1.37886	−0.689429	+	0.724353i	$0.742139\pi$
$444$	−11.3752	−0.539843
$445$	−29.0773	−1.37840
$446$	69.5966	3.29549
$447$	14.0933	0.666588
$448$	50.6177	2.39146
$449$	−37.9646	−1.79166	−0.895829	−	0.444398i	$-0.853418\pi$
$449$	−37.9646	−1.79166	−0.895829	+	0.444398i	$0.853418\pi$
$450$	4.30104	0.202753
$451$	−17.6447	−0.830856
$452$	33.1096	1.55735
$453$	17.0770	0.802347
$454$	−62.4727	−2.93199
$455$	−5.95465	−0.279158
$456$	−11.0136	−0.515759
$457$	17.9237	0.838436	0.419218	−	0.907886i	$-0.362304\pi$
$457$	17.9237	0.838436	0.419218	+	0.907886i	$0.362304\pi$
$458$	−27.4789	−1.28400
$459$	1.00000	0.0466760
$460$	18.4874	0.861977
$461$	36.6793	1.70833	0.854163	−	0.520006i	$-0.174070\pi$
$461$	36.6793	1.70833	0.854163	+	0.520006i	$0.174070\pi$
$462$	15.6757	0.729298
$463$	20.2521	0.941196	0.470598	−	0.882348i	$-0.344038\pi$
$463$	20.2521	0.941196	0.470598	+	0.882348i	$0.344038\pi$
$464$	−125.396	−5.82138
$465$	−16.8473	−0.781276
$466$	−44.5527	−2.06386
$467$	−3.13362	−0.145007	−0.0725033	−	0.997368i	$-0.523099\pi$
$467$	−3.13362	−0.145007	−0.0725033	+	0.997368i	$0.523099\pi$
$468$	13.5166	0.624804
$469$	11.3575	0.524441
$470$	−36.4377	−1.68074
$471$	−1.00000	−0.0460776
$472$	34.6332	1.59412
$473$	34.0272	1.56457
$474$	15.9364	0.731982
$475$	1.70076	0.0780362
$476$	−7.56097	−0.346556
$477$	6.44986	0.295319
$478$	−5.04874	−0.230924
$479$	0.677061	0.0309357	0.0154679	−	0.999880i	$-0.495076\pi$
$479$	0.677061	0.0309357	0.0154679	+	0.999880i	$0.495076\pi$
$480$	−47.6013	−2.17269
$481$	4.82710	0.220097
$482$	−62.1273	−2.82982
$483$	2.36461	0.107594
$484$	39.0063	1.77301
$485$	−27.1014	−1.23061
$486$	2.76474	0.125411
$487$	−37.9994	−1.72192	−0.860958	−	0.508675i	$-0.830135\pi$
$487$	−37.9994	−1.72192	−0.860958	+	0.508675i	$0.830135\pi$
$488$	6.81899	0.308681
$489$	−17.3537	−0.784763
$490$	−26.7082	−1.20655
$491$	0.986072	0.0445008	0.0222504	−	0.999752i	$-0.492917\pi$
$491$	0.986072	0.0445008	0.0222504	+	0.999752i	$0.492917\pi$
$492$	23.5299	1.06081
$493$	7.57011	0.340941
$494$	7.23892	0.325695
$495$	−7.85446	−0.353032
$496$	−150.370	−6.75183
$497$	−5.03465	−0.225835
$498$	37.1246	1.66359
$499$	13.0690	0.585047	0.292523	−	0.956258i	$-0.405505\pi$
$499$	13.0690	0.585047	0.292523	+	0.956258i	$0.405505\pi$
$500$	68.6656	3.07082
$501$	5.32748	0.238014
$502$	−35.1348	−1.56814
$503$	−0.868514	−0.0387251	−0.0193626	−	0.999813i	$-0.506164\pi$
$503$	−0.868514	−0.0387251	−0.0193626	+	0.999813i	$0.506164\pi$
$504$	−13.4963	−0.601171
$505$	34.5216	1.53619
$506$	20.6524	0.918113
$507$	7.26420	0.322615
$508$	−87.3415	−3.87515
$509$	26.9511	1.19459	0.597293	−	0.802023i	$-0.296243\pi$
$509$	26.9511	1.19459	0.597293	+	0.802023i	$0.296243\pi$
$510$	5.13105	0.227207
$511$	2.95619	0.130774
$512$	−91.1161	−4.02680
$513$	1.09326	0.0482686
$514$	25.0616	1.10542
$515$	−4.37398	−0.192741
$516$	−45.3766	−1.99759
$517$	−30.0545	−1.32179
$518$	−7.46535	−0.328009
$519$	−4.53469	−0.199051
$520$	44.7770	1.96360
$521$	37.9899	1.66437	0.832184	−	0.554500i	$-0.187090\pi$
$521$	37.9899	1.66437	0.832184	+	0.554500i	$0.187090\pi$
$522$	20.9294	0.916054
$523$	−2.77240	−0.121228	−0.0606142	−	0.998161i	$-0.519306\pi$
$523$	−2.77240	−0.121228	−0.0606142	+	0.998161i	$0.519306\pi$
$524$	−42.6162	−1.86170
$525$	2.08414	0.0909594
$526$	−56.7387	−2.47393
$527$	9.07777	0.395434
$528$	−70.1048	−3.05092
$529$	−19.8847	−0.864550
$530$	33.0945	1.43753
$531$	−3.43785	−0.149190
$532$	−8.26609	−0.358381
$533$	−9.98496	−0.432497
$534$	43.3168	1.87450
$535$	19.8342	0.857505
$536$	−85.4047	−3.68892
$537$	−20.9355	−0.903435
$538$	22.7289	0.979913
$539$	−22.0294	−0.948873
$540$	10.4742	0.450739
$541$	39.1343	1.68252	0.841258	−	0.540634i	$-0.181816\pi$
$541$	39.1343	1.68252	0.841258	+	0.540634i	$0.181816\pi$
$542$	7.44772	0.319907
$543$	9.92791	0.426047
$544$	25.6488	1.09968
$545$	7.40962	0.317393
$546$	8.87071	0.379631
$547$	24.5115	1.04804	0.524019	−	0.851707i	$-0.324432\pi$
$547$	24.5115	1.04804	0.524019	+	0.851707i	$0.324432\pi$
$548$	45.4190	1.94020
$549$	−0.676883	−0.0288887
$550$	18.2028	0.776170
$551$	8.27609	0.352573
$552$	−17.7811	−0.756814
$553$	7.72223	0.328383
$554$	52.8421	2.24505
$555$	3.74060	0.158779
$556$	91.0565	3.86166
$557$	0.909945	0.0385556	0.0192778	−	0.999814i	$-0.493863\pi$
$557$	0.909945	0.0385556	0.0192778	+	0.999814i	$0.493863\pi$
$558$	25.0977	1.06247
$559$	19.2557	0.814429
$560$	−41.1853	−1.74040
$561$	4.23218	0.178683
$562$	50.4246	2.12703
$563$	17.3411	0.730841	0.365420	−	0.930843i	$-0.380925\pi$
$563$	17.3411	0.730841	0.365420	+	0.930843i	$0.380925\pi$
$564$	40.0788	1.68762
$565$	−10.8877	−0.458049
$566$	−16.8622	−0.708772
$567$	1.33970	0.0562621
$568$	37.8589	1.58853
$569$	14.9112	0.625108	0.312554	−	0.949900i	$-0.398815\pi$
$569$	14.9112	0.625108	0.312554	+	0.949900i	$0.398815\pi$
$570$	5.60956	0.234959
$571$	18.8331	0.788143	0.394071	−	0.919080i	$-0.371066\pi$
$571$	18.8331	0.788143	0.394071	+	0.919080i	$0.371066\pi$
$572$	57.2046	2.39185
$573$	13.4258	0.560872
$574$	15.4423	0.644547
$575$	2.74582	0.114509
$576$	37.7829	1.57429
$577$	20.7631	0.864379	0.432189	−	0.901783i	$-0.357741\pi$
$577$	20.7631	0.864379	0.432189	+	0.901783i	$0.357741\pi$
$578$	−2.76474	−0.114998
$579$	16.9752	0.705465
$580$	79.2910	3.29238
$581$	17.9893	0.746324
$582$	40.3732	1.67352
$583$	27.2970	1.13053
$584$	−22.2296	−0.919866
$585$	−4.44476	−0.183768
$586$	−12.5585	−0.518787
$587$	27.2867	1.12624	0.563121	−	0.826375i	$-0.309601\pi$
$587$	27.2867	1.12624	0.563121	+	0.826375i	$0.309601\pi$
$588$	29.3770	1.21149
$589$	9.92435	0.408926
$590$	−17.6398	−0.726218
$591$	−13.1858	−0.542391
$592$	33.3866	1.37218
$593$	−25.2167	−1.03553	−0.517763	−	0.855524i	$-0.673235\pi$
$593$	−25.2167	−1.03553	−0.517763	+	0.855524i	$0.673235\pi$
$594$	11.7009	0.480093
$595$	2.48633	0.101930
$596$	−79.5392	−3.25805
$597$	−26.5511	−1.08666
$598$	11.6870	0.477918
$599$	10.8512	0.443368	0.221684	−	0.975119i	$-0.428845\pi$
$599$	10.8512	0.443368	0.221684	+	0.975119i	$0.428845\pi$
$600$	−15.6720	−0.639809
$601$	−9.47939	−0.386673	−0.193336	−	0.981133i	$-0.561931\pi$
$601$	−9.47939	−0.386673	−0.193336	+	0.981133i	$0.561931\pi$
$602$	−29.7799	−1.21374
$603$	8.47766	0.345237
$604$	−96.3787	−3.92160
$605$	−12.8267	−0.521481
$606$	−51.4272	−2.08909
$607$	12.6900	0.515070	0.257535	−	0.966269i	$-0.417090\pi$
$607$	12.6900	0.515070	0.257535	+	0.966269i	$0.417090\pi$
$608$	28.0408	1.13720
$609$	10.1417	0.410961
$610$	−3.47312	−0.140622
$611$	−17.0075	−0.688052
$612$	−5.64378	−0.228136
$613$	28.8159	1.16386	0.581931	−	0.813238i	$-0.302297\pi$
$613$	28.8159	1.16386	0.581931	+	0.813238i	$0.302297\pi$
$614$	−14.9468	−0.603202
$615$	−7.73751	−0.312007
$616$	−57.1186	−2.30138
$617$	4.96560	0.199908	0.0999539	−	0.994992i	$-0.468130\pi$
$617$	4.96560	0.199908	0.0999539	+	0.994992i	$0.468130\pi$
$618$	6.51597	0.262111
$619$	−30.6050	−1.23012	−0.615060	−	0.788481i	$-0.710868\pi$
$619$	−30.6050	−1.23012	−0.615060	+	0.788481i	$0.710868\pi$
$620$	95.0826	3.81861
$621$	1.76503	0.0708283
$622$	15.4345	0.618868
$623$	20.9899	0.840942
$624$	−39.6716	−1.58814
$625$	−14.8015	−0.592059
$626$	26.3528	1.05327
$627$	4.62687	0.184779
$628$	5.64378	0.225211
$629$	−2.01553	−0.0803644
$630$	6.87406	0.273869
$631$	10.2465	0.407905	0.203952	−	0.978981i	$-0.434621\pi$
$631$	10.2465	0.407905	0.203952	+	0.978981i	$0.434621\pi$
$632$	−58.0686	−2.30985
$633$	−21.0144	−0.835246
$634$	−47.2593	−1.87691
$635$	28.7212	1.13977
$636$	−36.4016	−1.44342
$637$	−12.4662	−0.493930
$638$	88.5769	3.50679
$639$	−3.75805	−0.148666
$640$	98.6632	3.90000
$641$	27.1352	1.07178	0.535888	−	0.844289i	$-0.319977\pi$
$641$	27.1352	1.07178	0.535888	+	0.844289i	$0.319977\pi$
$642$	−29.5472	−1.16613
$643$	−40.3504	−1.59127	−0.795633	−	0.605779i	$-0.792861\pi$
$643$	−40.3504	−1.59127	−0.795633	+	0.605779i	$0.792861\pi$
$644$	−13.3454	−0.525881
$645$	14.9216	0.587536
$646$	−3.02257	−0.118922
$647$	27.7689	1.09171	0.545854	−	0.837881i	$-0.316205\pi$
$647$	27.7689	1.09171	0.545854	+	0.837881i	$0.316205\pi$
$648$	−10.0741	−0.395748
$649$	−14.5496	−0.571122
$650$	10.3008	0.404030
$651$	12.1615	0.476646
$652$	97.9406	3.83565
$653$	26.3190	1.02994	0.514970	−	0.857208i	$-0.327803\pi$
$653$	26.3190	1.02994	0.514970	+	0.857208i	$0.327803\pi$
$654$	−11.0382	−0.431628
$655$	14.0138	0.547565
$656$	−69.0609	−2.69638
$657$	2.20661	0.0860879
$658$	26.3031	1.02540
$659$	14.7604	0.574985	0.287493	−	0.957783i	$-0.407178\pi$
$659$	14.7604	0.574985	0.287493	+	0.957783i	$0.407178\pi$
$660$	44.3288	1.72550
$661$	−28.6801	−1.11553	−0.557763	−	0.830000i	$-0.688340\pi$
$661$	−28.6801	−1.11553	−0.557763	+	0.830000i	$0.688340\pi$
$662$	18.6890	0.726370
$663$	2.39495	0.0930122
$664$	−135.274	−5.24964
$665$	2.71820	0.105407
$666$	−5.57241	−0.215927
$667$	13.3615	0.517359
$668$	−30.0671	−1.16333
$669$	25.1729	0.973242
$670$	43.4992	1.68052
$671$	−2.86469	−0.110590
$672$	34.3617	1.32553
$673$	−29.3322	−1.13067	−0.565337	−	0.824860i	$-0.691254\pi$
$673$	−29.3322	−1.13067	−0.565337	+	0.824860i	$0.691254\pi$
$674$	−73.9452	−2.84826
$675$	1.55568	0.0598781
$676$	−40.9976	−1.57683
$677$	29.6506	1.13956	0.569782	−	0.821796i	$-0.307028\pi$
$677$	29.6506	1.13956	0.569782	+	0.821796i	$0.307028\pi$
$678$	16.2195	0.622907
$679$	19.5635	0.750778
$680$	−18.6964	−0.716974
$681$	−22.5963	−0.865890
$682$	106.218	4.06729
$683$	−6.85818	−0.262421	−0.131210	−	0.991355i	$-0.541886\pi$
$683$	−6.85818	−0.262421	−0.131210	+	0.991355i	$0.541886\pi$
$684$	−6.17011	−0.235920
$685$	−14.9355	−0.570656
$686$	45.2071	1.72601
$687$	−9.93904	−0.379198
$688$	133.182	5.07751
$689$	15.4471	0.588488
$690$	9.05647	0.344774
$691$	30.0551	1.14335	0.571675	−	0.820480i	$-0.306294\pi$
$691$	30.0551	1.14335	0.571675	+	0.820480i	$0.306294\pi$
$692$	25.5928	0.972893
$693$	5.66985	0.215380
$694$	−88.4458	−3.35736
$695$	−29.9428	−1.13580
$696$	−76.2620	−2.89070
$697$	4.16917	0.157918
$698$	95.5552	3.61682
$699$	−16.1146	−0.609511
$700$	−11.7624	−0.444578
$701$	28.7971	1.08765	0.543825	−	0.839199i	$-0.316976\pi$
$701$	28.7971	1.08765	0.543825	+	0.839199i	$0.316976\pi$
$702$	6.62142	0.249909
$703$	−2.20349	−0.0831064
$704$	159.904	6.02662
$705$	−13.1794	−0.496366
$706$	5.18202	0.195028
$707$	−24.9199	−0.937210
$708$	19.4025	0.729189
$709$	5.81316	0.218318	0.109159	−	0.994024i	$-0.465184\pi$
$709$	5.81316	0.218318	0.109159	+	0.994024i	$0.465184\pi$
$710$	−19.2827	−0.723667
$711$	5.76415	0.216173
$712$	−157.837	−5.91519
$713$	16.0226	0.600050
$714$	−3.70392	−0.138616
$715$	−18.8111	−0.703494
$716$	118.156	4.41568
$717$	−1.82612	−0.0681976
$718$	−39.1311	−1.46036
$719$	−18.4222	−0.687033	−0.343517	−	0.939147i	$-0.611618\pi$
$719$	−18.4222	−0.687033	−0.343517	+	0.939147i	$0.611618\pi$
$720$	−30.7422	−1.14569
$721$	3.15742	0.117588
$722$	49.2256	1.83199
$723$	−22.4713	−0.835717
$724$	−56.0309	−2.08237
$725$	11.7767	0.437374
$726$	19.1081	0.709170
$727$	−33.1194	−1.22833	−0.614166	−	0.789177i	$-0.710507\pi$
$727$	−33.1194	−1.22833	−0.614166	+	0.789177i	$0.710507\pi$
$728$	−32.3229	−1.19797
$729$	1.00000	0.0370370
$730$	11.3222	0.419053
$731$	−8.04012	−0.297374
$732$	3.82018	0.141198
$733$	7.04825	0.260333	0.130167	−	0.991492i	$-0.458449\pi$
$733$	7.04825	0.260333	0.130167	+	0.991492i	$0.458449\pi$
$734$	−99.1759	−3.66065
$735$	−9.66028	−0.356325
$736$	45.2710	1.66871
$737$	35.8790	1.32162
$738$	11.5267	0.424302
$739$	−20.4237	−0.751296	−0.375648	−	0.926762i	$-0.622580\pi$
$739$	−20.4237	−0.751296	−0.375648	+	0.926762i	$0.622580\pi$
$740$	−21.1111	−0.776059
$741$	2.61830	0.0961858
$742$	−23.8897	−0.877020
$743$	14.2766	0.523757	0.261878	−	0.965101i	$-0.415658\pi$
$743$	14.2766	0.523757	0.261878	+	0.965101i	$0.415658\pi$
$744$	−91.4503	−3.35273
$745$	26.1555	0.958264
$746$	74.3064	2.72055
$747$	13.4279	0.491301
$748$	−23.8855	−0.873341
$749$	−14.3176	−0.523152
$750$	33.6375	1.22827
$751$	15.1271	0.551997	0.275998	−	0.961158i	$-0.410992\pi$
$751$	15.1271	0.551997	0.275998	+	0.961158i	$0.410992\pi$
$752$	−117.633	−4.28962
$753$	−12.7082	−0.463111
$754$	50.1248	1.82544
$755$	31.6930	1.15343
$756$	−7.56097	−0.274990
$757$	12.7804	0.464512	0.232256	−	0.972655i	$-0.425389\pi$
$757$	12.7804	0.464512	0.232256	+	0.972655i	$0.425389\pi$
$758$	25.1735	0.914343
$759$	7.46994	0.271142
$760$	−20.4400	−0.741437
$761$	−20.6474	−0.748467	−0.374233	−	0.927335i	$-0.622094\pi$
$761$	−20.6474	−0.748467	−0.374233	+	0.927335i	$0.622094\pi$
$762$	−42.7863	−1.54998
$763$	−5.34874	−0.193637
$764$	−75.7723	−2.74135
$765$	1.85589	0.0670998
$766$	37.8720	1.36837
$767$	−8.23349	−0.297294
$768$	−71.4138	−2.57693
$769$	−8.60072	−0.310150	−0.155075	−	0.987903i	$-0.549562\pi$
$769$	−8.60072	−0.310150	−0.155075	+	0.987903i	$0.549562\pi$
$770$	29.0923	1.04841
$771$	9.06473	0.326458
$772$	−95.8042	−3.44807
$773$	1.75674	0.0631856	0.0315928	−	0.999501i	$-0.489942\pi$
$773$	1.75674	0.0631856	0.0315928	+	0.999501i	$0.489942\pi$
$774$	−22.2288	−0.798998
$775$	14.1221	0.507280
$776$	−147.111	−5.28098
$777$	−2.70020	−0.0968692
$778$	−57.2466	−2.05239
$779$	4.55798	0.163307
$780$	25.0853	0.898197
$781$	−15.9047	−0.569117
$782$	−4.87986	−0.174503
$783$	7.57011	0.270534
$784$	−86.2226	−3.07938
$785$	−1.85589	−0.0662395
$786$	−20.8766	−0.744642
$787$	−31.2555	−1.11414	−0.557070	−	0.830466i	$-0.688074\pi$
$787$	−31.2555	−1.11414	−0.557070	+	0.830466i	$0.688074\pi$
$788$	74.4178	2.65102
$789$	−20.5223	−0.730612
$790$	29.5761	1.05227
$791$	7.85944	0.279449
$792$	−42.6354	−1.51498
$793$	−1.62110	−0.0575671
$794$	90.6769	3.21800
$795$	11.9702	0.424540
$796$	149.848	5.31124
$797$	−38.7400	−1.37224	−0.686121	−	0.727487i	$-0.740688\pi$
$797$	−38.7400	−1.37224	−0.686121	+	0.727487i	$0.740688\pi$
$798$	−4.04934	−0.143345
$799$	7.10141	0.251230
$800$	39.9013	1.41072
$801$	15.6676	0.553588
$802$	−30.3600	−1.07205
$803$	9.33876	0.329558
$804$	−47.8460	−1.68740
$805$	4.38846	0.154673
$806$	60.1077	2.11720
$807$	8.22100	0.289393
$808$	187.389	6.59234
$809$	25.5296	0.897572	0.448786	−	0.893639i	$-0.351857\pi$
$809$	25.5296	0.897572	0.448786	+	0.893639i	$0.351857\pi$
$810$	5.13105	0.180287
$811$	−3.95999	−0.139054	−0.0695271	−	0.997580i	$-0.522149\pi$
$811$	−3.95999	−0.139054	−0.0695271	+	0.997580i	$0.522149\pi$
$812$	−57.2373	−2.00864
$813$	2.69383	0.0944766
$814$	−23.5835	−0.826600
$815$	−32.2066	−1.12815
$816$	16.5647	0.579880
$817$	−8.78993	−0.307521
$818$	−85.2323	−2.98008
$819$	3.20852	0.112115
$820$	43.6688	1.52498
$821$	0.464405	0.0162079	0.00810393	−	0.999967i	$-0.497420\pi$
$821$	0.464405	0.0162079	0.00810393	+	0.999967i	$0.497420\pi$
$822$	22.2496	0.776043
$823$	−8.37946	−0.292090	−0.146045	−	0.989278i	$-0.546654\pi$
$823$	−8.37946	−0.292090	−0.146045	+	0.989278i	$0.546654\pi$
$824$	−23.7428	−0.827118
$825$	6.58391	0.229222
$826$	12.7335	0.443056
$827$	0.194587	0.00676644	0.00338322	−	0.999994i	$-0.498923\pi$
$827$	0.194587	0.00676644	0.00338322	+	0.999994i	$0.498923\pi$
$828$	−9.96146	−0.346185
$829$	20.9860	0.728873	0.364437	−	0.931228i	$-0.381262\pi$
$829$	20.9860	0.728873	0.364437	+	0.931228i	$0.381262\pi$
$830$	68.8991	2.39152
$831$	19.1129	0.663018
$832$	90.4883	3.13712
$833$	5.20521	0.180350
$834$	44.6062	1.54459
$835$	9.88721	0.342161
$836$	−26.1130	−0.903138
$837$	9.07777	0.313774
$838$	54.6724	1.88863
$839$	−17.0932	−0.590124	−0.295062	−	0.955478i	$-0.595340\pi$
$839$	−17.0932	−0.590124	−0.295062	+	0.955478i	$0.595340\pi$
$840$	−25.0475	−0.864222
$841$	28.3065	0.976088
$842$	44.2182	1.52386
$843$	18.2385	0.628166
$844$	118.600	4.08240
$845$	13.4816	0.463779
$846$	19.6336	0.675015
$847$	9.25916	0.318149
$848$	106.840	3.66890
$849$	−6.09903	−0.209318
$850$	−4.30104	−0.147525
$851$	−3.55748	−0.121949
$852$	21.2096	0.726629
$853$	−25.1329	−0.860534	−0.430267	−	0.902702i	$-0.641581\pi$
$853$	−25.1329	−0.860534	−0.430267	+	0.902702i	$0.641581\pi$
$854$	2.50712	0.0857919
$855$	2.02897	0.0693892
$856$	107.663	3.67986
$857$	31.1187	1.06299	0.531497	−	0.847060i	$-0.321630\pi$
$857$	31.1187	1.06299	0.531497	+	0.847060i	$0.321630\pi$
$858$	28.0230	0.956691
$859$	−40.1203	−1.36889	−0.684443	−	0.729067i	$-0.739954\pi$
$859$	−40.1203	−1.36889	−0.684443	+	0.729067i	$0.739954\pi$
$860$	−84.2140	−2.87167
$861$	5.58543	0.190351
$862$	22.2169	0.756710
$863$	9.66177	0.328890	0.164445	−	0.986386i	$-0.447417\pi$
$863$	9.66177	0.328890	0.164445	+	0.986386i	$0.447417\pi$
$864$	25.6488	0.872590
$865$	−8.41589	−0.286149
$866$	8.56475	0.291042
$867$	−1.00000	−0.0339618
$868$	−68.6367	−2.32968
$869$	24.3949	0.827542
$870$	38.8426	1.31689
$871$	20.3036	0.687961
$872$	40.2207	1.36205
$873$	14.6029	0.494234
$874$	−5.33494	−0.180457
$875$	16.2996	0.551027
$876$	−12.4536	−0.420768
$877$	−12.8725	−0.434673	−0.217337	−	0.976097i	$-0.569737\pi$
$877$	−12.8725	−0.434673	−0.217337	+	0.976097i	$0.569737\pi$
$878$	−15.6089	−0.526774
$879$	−4.54238	−0.153211
$880$	−130.107	−4.38589
$881$	9.72854	0.327763	0.163881	−	0.986480i	$-0.447599\pi$
$881$	9.72854	0.327763	0.163881	+	0.986480i	$0.447599\pi$
$882$	14.3910	0.484571
$883$	−9.46736	−0.318602	−0.159301	−	0.987230i	$-0.550924\pi$
$883$	−9.46736	−0.318602	−0.159301	+	0.987230i	$0.550924\pi$
$884$	−13.5166	−0.454612
$885$	−6.38027	−0.214470
$886$	80.2372	2.69562
$887$	−14.8333	−0.498054	−0.249027	−	0.968497i	$-0.580111\pi$
$887$	−14.8333	−0.498054	−0.249027	+	0.968497i	$0.580111\pi$
$888$	20.3046	0.681379
$889$	−20.7328	−0.695356
$890$	80.3912	2.69472
$891$	4.23218	0.141783
$892$	−142.070	−4.75687
$893$	7.76368	0.259802
$894$	−38.9642	−1.30316
$895$	−38.8540	−1.29875
$896$	−71.2214	−2.37934
$897$	4.22717	0.141141
$898$	104.962	3.50263
$899$	68.7197	2.29193
$900$	−8.77990	−0.292663
$901$	−6.44986	−0.214876
$902$	48.7829	1.62429
$903$	−10.7713	−0.358448
$904$	−59.1004	−1.96565
$905$	18.4251	0.612471
$906$	−47.2134	−1.56856
$907$	44.9542	1.49268	0.746341	−	0.665564i	$-0.231809\pi$
$907$	44.9542	1.49268	0.746341	+	0.665564i	$0.231809\pi$
$908$	127.528	4.23217
$909$	−18.6011	−0.616960
$910$	16.4630	0.545745
$911$	5.74440	0.190321	0.0951603	−	0.995462i	$-0.469664\pi$
$911$	5.74440	0.190321	0.0951603	+	0.995462i	$0.469664\pi$
$912$	18.1095	0.599665
$913$	56.8293	1.88078
$914$	−49.5544	−1.63911
$915$	−1.25622	−0.0415293
$916$	56.0938	1.85339
$917$	−10.1161	−0.334062
$918$	−2.76474	−0.0912500
$919$	49.3836	1.62902	0.814508	−	0.580153i	$-0.197007\pi$
$919$	49.3836	1.62902	0.814508	+	0.580153i	$0.197007\pi$
$920$	−32.9998	−1.08797
$921$	−5.40621	−0.178141
$922$	−101.409	−3.33972
$923$	−9.00034	−0.296250
$924$	−31.9994	−1.05270
$925$	−3.13551	−0.103095
$926$	−55.9918	−1.84001
$927$	2.35681	0.0774079
$928$	194.164	6.37376
$929$	44.6139	1.46373	0.731867	−	0.681448i	$-0.238649\pi$
$929$	44.6139	1.46373	0.731867	+	0.681448i	$0.238649\pi$
$930$	46.5785	1.52737
$931$	5.69064	0.186503
$932$	90.9473	2.97908
$933$	5.58264	0.182767
$934$	8.66364	0.283483
$935$	7.85446	0.256868
$936$	−24.1270	−0.788615
$937$	16.4818	0.538438	0.269219	−	0.963079i	$-0.413234\pi$
$937$	16.4818	0.538438	0.269219	+	0.963079i	$0.413234\pi$
$938$	−31.4005	−1.02526
$939$	9.53177	0.311058
$940$	74.3818	2.42607
$941$	−11.3005	−0.368385	−0.184193	−	0.982890i	$-0.558967\pi$
$941$	−11.3005	−0.368385	−0.184193	+	0.982890i	$0.558967\pi$
$942$	2.76474	0.0900800
$943$	7.35872	0.239633
$944$	−56.9469	−1.85346
$945$	2.48633	0.0808804
$946$	−94.0764	−3.05869
$947$	35.2200	1.14449	0.572247	−	0.820081i	$-0.306072\pi$
$947$	35.2200	1.14449	0.572247	+	0.820081i	$0.306072\pi$
$948$	−32.5316	−1.05658
$949$	5.28472	0.171549
$950$	−4.70215	−0.152558
$951$	−17.0936	−0.554298
$952$	13.4963	0.437416
$953$	15.6248	0.506138	0.253069	−	0.967448i	$-0.418560\pi$
$953$	15.6248	0.506138	0.253069	+	0.967448i	$0.418560\pi$
$954$	−17.8322	−0.577338
$955$	24.9168	0.806289
$956$	10.3062	0.333326
$957$	32.0381	1.03564
$958$	−1.87190	−0.0604783
$959$	10.7814	0.348150
$960$	70.1209	2.26314
$961$	51.4059	1.65826
$962$	−13.3457	−0.430281
$963$	−10.6871	−0.344388
$964$	126.823	4.08470
$965$	31.5041	1.01415
$966$	−6.53754	−0.210342
$967$	46.9538	1.50993	0.754966	−	0.655764i	$-0.227653\pi$
$967$	46.9538	1.50993	0.754966	+	0.655764i	$0.227653\pi$
$968$	−69.6258	−2.23786
$969$	−1.09326	−0.0351205
$970$	74.9282	2.40580
$971$	1.68158	0.0539643	0.0269822	−	0.999636i	$-0.491410\pi$
$971$	1.68158	0.0539643	0.0269822	+	0.999636i	$0.491410\pi$
$972$	−5.64378	−0.181024
$973$	21.6147	0.692934
$974$	105.058	3.36629
$975$	3.72577	0.119320
$976$	−11.2124	−0.358899
$977$	−34.9870	−1.11933	−0.559666	−	0.828718i	$-0.689071\pi$
$977$	−34.9870	−1.11933	−0.559666	+	0.828718i	$0.689071\pi$
$978$	47.9785	1.53418
$979$	66.3082	2.11922
$980$	54.5205	1.74159
$981$	−3.99249	−0.127470
$982$	−2.72623	−0.0869976
$983$	−32.9918	−1.05228	−0.526138	−	0.850399i	$-0.676360\pi$
$983$	−32.9918	−1.05228	−0.526138	+	0.850399i	$0.676360\pi$
$984$	−42.0006	−1.33893
$985$	−24.4714	−0.779723
$986$	−20.9294	−0.666527
$987$	9.51376	0.302826
$988$	−14.7771	−0.470123
$989$	−14.1911	−0.451250
$990$	21.7155	0.690165
$991$	51.2329	1.62747	0.813733	−	0.581238i	$-0.197432\pi$
$991$	51.2329	1.62747	0.813733	+	0.581238i	$0.197432\pi$
$992$	232.834	7.39249
$993$	6.75979	0.214515
$994$	13.9195	0.441500
$995$	−49.2758	−1.56215
$996$	−75.7841	−2.40131
$997$	−14.5863	−0.461954	−0.230977	−	0.972959i	$-0.574192\pi$
$997$	−14.5863	−0.461954	−0.230977	+	0.972959i	$0.574192\pi$
$998$	−36.1322	−1.14375
$999$	−2.01553	−0.0637685

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.g.1.1	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.g.1.1	✓	56	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:	\( N \)	\(=\)	\( 8007 = 3 \cdot 17 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8007.a (trivial)

\(f(q)\)	\(=\)	\(q-2.76474 q^{2} -1.00000 q^{3} +5.64378 q^{4} -1.85589 q^{5} +2.76474 q^{6} +1.33970 q^{7} -10.0741 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.76474 q^{2} -1.00000 q^{3} +5.64378 q^{4} -1.85589 q^{5} +2.76474 q^{6} +1.33970 q^{7} -10.0741 q^{8} +1.00000 q^{9} +5.13105 q^{10} +4.23218 q^{11} -5.64378 q^{12} +2.39495 q^{13} -3.70392 q^{14} +1.85589 q^{15} +16.5647 q^{16} -1.00000 q^{17} -2.76474 q^{18} -1.09326 q^{19} -10.4742 q^{20} -1.33970 q^{21} -11.7009 q^{22} -1.76503 q^{23} +10.0741 q^{24} -1.55568 q^{25} -6.62142 q^{26} -1.00000 q^{27} +7.56097 q^{28} -7.57011 q^{29} -5.13105 q^{30} -9.07777 q^{31} -25.6488 q^{32} -4.23218 q^{33} +2.76474 q^{34} -2.48633 q^{35} +5.64378 q^{36} +2.01553 q^{37} +3.02257 q^{38} -2.39495 q^{39} +18.6964 q^{40} -4.16917 q^{41} +3.70392 q^{42} +8.04012 q^{43} +23.8855 q^{44} -1.85589 q^{45} +4.87986 q^{46} -7.10141 q^{47} -16.5647 q^{48} -5.20521 q^{49} +4.30104 q^{50} +1.00000 q^{51} +13.5166 q^{52} +6.44986 q^{53} +2.76474 q^{54} -7.85446 q^{55} -13.4963 q^{56} +1.09326 q^{57} +20.9294 q^{58} -3.43785 q^{59} +10.4742 q^{60} -0.676883 q^{61} +25.0977 q^{62} +1.33970 q^{63} +37.7829 q^{64} -4.44476 q^{65} +11.7009 q^{66} +8.47766 q^{67} -5.64378 q^{68} +1.76503 q^{69} +6.87406 q^{70} -3.75805 q^{71} -10.0741 q^{72} +2.20661 q^{73} -5.57241 q^{74} +1.55568 q^{75} -6.17011 q^{76} +5.66985 q^{77} +6.62142 q^{78} +5.76415 q^{79} -30.7422 q^{80} +1.00000 q^{81} +11.5267 q^{82} +13.4279 q^{83} -7.56097 q^{84} +1.85589 q^{85} -22.2288 q^{86} +7.57011 q^{87} -42.6354 q^{88} +15.6676 q^{89} +5.13105 q^{90} +3.20852 q^{91} -9.96146 q^{92} +9.07777 q^{93} +19.6336 q^{94} +2.02897 q^{95} +25.6488 q^{96} +14.6029 q^{97} +14.3910 q^{98} +4.23218 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + q^{2} - 56 q^{3} + 61 q^{4} + q^{5} - q^{6} + 19 q^{7} + 56 q^{9}+O(q^{10}) \) 56 * q + q^2 - 56 * q^3 + 61 * q^4 + q^5 - q^6 + 19 * q^7 + 56 * q^9	\( 56 q + q^{2} - 56 q^{3} + 61 q^{4} + q^{5} - q^{6} + 19 q^{7} + 56 q^{9} + 8 q^{10} - 7 q^{11} - 61 q^{12} + 8 q^{13} - 8 q^{14} - q^{15} + 71 q^{16} - 56 q^{17} + q^{18} - 2 q^{19} - 4 q^{20} - 19 q^{21} + 47 q^{22} + 16 q^{23} + 85 q^{25} - 11 q^{26} - 56 q^{27} + 52 q^{28} + 17 q^{29} - 8 q^{30} + 23 q^{31} + 11 q^{32} + 7 q^{33} - q^{34} - 41 q^{35} + 61 q^{36} + 58 q^{37} - 22 q^{38} - 8 q^{39} + 38 q^{40} - q^{41} + 8 q^{42} + 27 q^{43} + 2 q^{44} + q^{45} + 46 q^{46} + 5 q^{47} - 71 q^{48} + 59 q^{49} - 4 q^{50} + 56 q^{51} + 25 q^{52} + 15 q^{53} - q^{54} + 9 q^{55} - 36 q^{56} + 2 q^{57} + 89 q^{58} - 61 q^{59} + 4 q^{60} + 47 q^{61} + 8 q^{62} + 19 q^{63} + 88 q^{64} + 39 q^{65} - 47 q^{66} + 20 q^{67} - 61 q^{68} - 16 q^{69} + 36 q^{70} - 2 q^{71} + 93 q^{73} + 48 q^{74} - 85 q^{75} + 38 q^{76} + 26 q^{77} + 11 q^{78} + 72 q^{79} + 42 q^{80} + 56 q^{81} + 33 q^{82} - 11 q^{83} - 52 q^{84} - q^{85} - 4 q^{86} - 17 q^{87} + 130 q^{88} - 6 q^{89} + 8 q^{90} + 37 q^{91} + 132 q^{92} - 23 q^{93} - 32 q^{94} + 12 q^{95} - 11 q^{96} + 100 q^{97} + 42 q^{98} - 7 q^{99}+O(q^{100}) \) 56 * q + q^2 - 56 * q^3 + 61 * q^4 + q^5 - q^6 + 19 * q^7 + 56 * q^9 + 8 * q^10 - 7 * q^11 - 61 * q^12 + 8 * q^13 - 8 * q^14 - q^15 + 71 * q^16 - 56 * q^17 + q^18 - 2 * q^19 - 4 * q^20 - 19 * q^21 + 47 * q^22 + 16 * q^23 + 85 * q^25 - 11 * q^26 - 56 * q^27 + 52 * q^28 + 17 * q^29 - 8 * q^30 + 23 * q^31 + 11 * q^32 + 7 * q^33 - q^34 - 41 * q^35 + 61 * q^36 + 58 * q^37 - 22 * q^38 - 8 * q^39 + 38 * q^40 - q^41 + 8 * q^42 + 27 * q^43 + 2 * q^44 + q^45 + 46 * q^46 + 5 * q^47 - 71 * q^48 + 59 * q^49 - 4 * q^50 + 56 * q^51 + 25 * q^52 + 15 * q^53 - q^54 + 9 * q^55 - 36 * q^56 + 2 * q^57 + 89 * q^58 - 61 * q^59 + 4 * q^60 + 47 * q^61 + 8 * q^62 + 19 * q^63 + 88 * q^64 + 39 * q^65 - 47 * q^66 + 20 * q^67 - 61 * q^68 - 16 * q^69 + 36 * q^70 - 2 * q^71 + 93 * q^73 + 48 * q^74 - 85 * q^75 + 38 * q^76 + 26 * q^77 + 11 * q^78 + 72 * q^79 + 42 * q^80 + 56 * q^81 + 33 * q^82 - 11 * q^83 - 52 * q^84 - q^85 - 4 * q^86 - 17 * q^87 + 130 * q^88 - 6 * q^89 + 8 * q^90 + 37 * q^91 + 132 * q^92 - 23 * q^93 - 32 * q^94 + 12 * q^95 - 11 * q^96 + 100 * q^97 + 42 * q^98 - 7 * q^99

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