LMFDB - Embedded newform 8002.2.a.g.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8002,2,Mod(1,8002)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8002, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8002.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8002 = 2 \cdot 4001 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8002.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:	$63.8962916974$
Analytic rank:	$0$
Dimension:	$95$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	8002.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.24343 q^{3} +1.00000 q^{4} -3.17394 q^{5} -2.24343 q^{6} +1.39363 q^{7} +1.00000 q^{8} +2.03297 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.24343 q^{3} +1.00000 q^{4} -3.17394 q^{5} -2.24343 q^{6} +1.39363 q^{7} +1.00000 q^{8} +2.03297 q^{9} -3.17394 q^{10} +0.735237 q^{11} -2.24343 q^{12} +4.21295 q^{13} +1.39363 q^{14} +7.12051 q^{15} +1.00000 q^{16} -2.62009 q^{17} +2.03297 q^{18} +4.37119 q^{19} -3.17394 q^{20} -3.12651 q^{21} +0.735237 q^{22} +6.54733 q^{23} -2.24343 q^{24} +5.07390 q^{25} +4.21295 q^{26} +2.16946 q^{27} +1.39363 q^{28} +1.87223 q^{29} +7.12051 q^{30} +1.02762 q^{31} +1.00000 q^{32} -1.64945 q^{33} -2.62009 q^{34} -4.42331 q^{35} +2.03297 q^{36} -6.78086 q^{37} +4.37119 q^{38} -9.45145 q^{39} -3.17394 q^{40} -4.82955 q^{41} -3.12651 q^{42} -7.98546 q^{43} +0.735237 q^{44} -6.45252 q^{45} +6.54733 q^{46} -1.11312 q^{47} -2.24343 q^{48} -5.05779 q^{49} +5.07390 q^{50} +5.87799 q^{51} +4.21295 q^{52} +12.0340 q^{53} +2.16946 q^{54} -2.33360 q^{55} +1.39363 q^{56} -9.80645 q^{57} +1.87223 q^{58} +9.15709 q^{59} +7.12051 q^{60} -4.77680 q^{61} +1.02762 q^{62} +2.83321 q^{63} +1.00000 q^{64} -13.3717 q^{65} -1.64945 q^{66} -13.7355 q^{67} -2.62009 q^{68} -14.6885 q^{69} -4.42331 q^{70} +14.1531 q^{71} +2.03297 q^{72} -0.507181 q^{73} -6.78086 q^{74} -11.3829 q^{75} +4.37119 q^{76} +1.02465 q^{77} -9.45145 q^{78} -3.46645 q^{79} -3.17394 q^{80} -10.9659 q^{81} -4.82955 q^{82} -3.80344 q^{83} -3.12651 q^{84} +8.31602 q^{85} -7.98546 q^{86} -4.20021 q^{87} +0.735237 q^{88} -2.34743 q^{89} -6.45252 q^{90} +5.87130 q^{91} +6.54733 q^{92} -2.30540 q^{93} -1.11312 q^{94} -13.8739 q^{95} -2.24343 q^{96} +13.8745 q^{97} -5.05779 q^{98} +1.49471 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 95 q + 95 q^{2} + 24 q^{3} + 95 q^{4} + 36 q^{5} + 24 q^{6} + 21 q^{7} + 95 q^{8} + 121 q^{9}+O(q^{10}) $ 95 * q + 95 * q^2 + 24 * q^3 + 95 * q^4 + 36 * q^5 + 24 * q^6 + 21 * q^7 + 95 * q^8 + 121 * q^9	\( 95 q + 95 q^{2} + 24 q^{3} + 95 q^{4} + 36 q^{5} + 24 q^{6} + 21 q^{7} + 95 q^{8} + 121 q^{9} + 36 q^{10} + 40 q^{11} + 24 q^{12} + 52 q^{13} + 21 q^{14} + 15 q^{15} + 95 q^{16} + 84 q^{17} + 121 q^{18} + 37 q^{19} + 36 q^{20} + 36 q^{21} + 40 q^{22} + 37 q^{23} + 24 q^{24} + 133 q^{25} + 52 q^{26} + 93 q^{27} + 21 q^{28} + 66 q^{29} + 15 q^{30} + 10 q^{31} + 95 q^{32} + 63 q^{33} + 84 q^{34} + 55 q^{35} + 121 q^{36} + 49 q^{37} + 37 q^{38} + 14 q^{39} + 36 q^{40} + 98 q^{41} + 36 q^{42} + 37 q^{43} + 40 q^{44} + 97 q^{45} + 37 q^{46} + 91 q^{47} + 24 q^{48} + 170 q^{49} + 133 q^{50} + 22 q^{51} + 52 q^{52} + 70 q^{53} + 93 q^{54} - q^{55} + 21 q^{56} + 50 q^{57} + 66 q^{58} + 72 q^{59} + 15 q^{60} + 97 q^{61} + 10 q^{62} + 75 q^{63} + 95 q^{64} + 75 q^{65} + 63 q^{66} + 39 q^{67} + 84 q^{68} + 65 q^{69} + 55 q^{70} + 28 q^{71} + 121 q^{72} + 117 q^{73} + 49 q^{74} + 62 q^{75} + 37 q^{76} + 92 q^{77} + 14 q^{78} + q^{79} + 36 q^{80} + 155 q^{81} + 98 q^{82} + 117 q^{83} + 36 q^{84} + 81 q^{85} + 37 q^{86} + 46 q^{87} + 40 q^{88} + 90 q^{89} + 97 q^{90} + 65 q^{91} + 37 q^{92} + 36 q^{93} + 91 q^{94} + 38 q^{95} + 24 q^{96} + 111 q^{97} + 170 q^{98} + 97 q^{99}+O(q^{100}) \) 95 * q + 95 * q^2 + 24 * q^3 + 95 * q^4 + 36 * q^5 + 24 * q^6 + 21 * q^7 + 95 * q^8 + 121 * q^9 + 36 * q^10 + 40 * q^11 + 24 * q^12 + 52 * q^13 + 21 * q^14 + 15 * q^15 + 95 * q^16 + 84 * q^17 + 121 * q^18 + 37 * q^19 + 36 * q^20 + 36 * q^21 + 40 * q^22 + 37 * q^23 + 24 * q^24 + 133 * q^25 + 52 * q^26 + 93 * q^27 + 21 * q^28 + 66 * q^29 + 15 * q^30 + 10 * q^31 + 95 * q^32 + 63 * q^33 + 84 * q^34 + 55 * q^35 + 121 * q^36 + 49 * q^37 + 37 * q^38 + 14 * q^39 + 36 * q^40 + 98 * q^41 + 36 * q^42 + 37 * q^43 + 40 * q^44 + 97 * q^45 + 37 * q^46 + 91 * q^47 + 24 * q^48 + 170 * q^49 + 133 * q^50 + 22 * q^51 + 52 * q^52 + 70 * q^53 + 93 * q^54 - q^55 + 21 * q^56 + 50 * q^57 + 66 * q^58 + 72 * q^59 + 15 * q^60 + 97 * q^61 + 10 * q^62 + 75 * q^63 + 95 * q^64 + 75 * q^65 + 63 * q^66 + 39 * q^67 + 84 * q^68 + 65 * q^69 + 55 * q^70 + 28 * q^71 + 121 * q^72 + 117 * q^73 + 49 * q^74 + 62 * q^75 + 37 * q^76 + 92 * q^77 + 14 * q^78 + q^79 + 36 * q^80 + 155 * q^81 + 98 * q^82 + 117 * q^83 + 36 * q^84 + 81 * q^85 + 37 * q^86 + 46 * q^87 + 40 * q^88 + 90 * q^89 + 97 * q^90 + 65 * q^91 + 37 * q^92 + 36 * q^93 + 91 * q^94 + 38 * q^95 + 24 * q^96 + 111 * q^97 + 170 * q^98 + 97 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.24343	−1.29524	−0.647622	−	0.761962i	$-0.724236\pi$
$3$	−2.24343	−1.29524	−0.647622	+	0.761962i	$0.724236\pi$
$4$	1.00000	0.500000
$5$	−3.17394	−1.41943	−0.709715	−	0.704489i	$-0.751176\pi$
$5$	−3.17394	−1.41943	−0.709715	+	0.704489i	$0.751176\pi$
$6$	−2.24343	−0.915876
$7$	1.39363	0.526744	0.263372	−	0.964694i	$-0.415165\pi$
$7$	1.39363	0.526744	0.263372	+	0.964694i	$0.415165\pi$
$8$	1.00000	0.353553
$9$	2.03297	0.677656
$10$	−3.17394	−1.00369
$11$	0.735237	0.221682	0.110841	−	0.993838i	$-0.464646\pi$
$11$	0.735237	0.221682	0.110841	+	0.993838i	$0.464646\pi$
$12$	−2.24343	−0.647622
$13$	4.21295	1.16846	0.584231	−	0.811588i	$-0.301396\pi$
$13$	4.21295	1.16846	0.584231	+	0.811588i	$0.301396\pi$
$14$	1.39363	0.372464
$15$	7.12051	1.83851
$16$	1.00000	0.250000
$17$	−2.62009	−0.635466	−0.317733	−	0.948180i	$-0.602922\pi$
$17$	−2.62009	−0.635466	−0.317733	+	0.948180i	$0.602922\pi$
$18$	2.03297	0.479175
$19$	4.37119	1.00282	0.501410	−	0.865210i	$-0.332815\pi$
$19$	4.37119	1.00282	0.501410	+	0.865210i	$0.332815\pi$
$20$	−3.17394	−0.709715
$21$	−3.12651	−0.682261
$22$	0.735237	0.156753
$23$	6.54733	1.36521	0.682607	−	0.730786i	$-0.260846\pi$
$23$	6.54733	1.36521	0.682607	+	0.730786i	$0.260846\pi$
$24$	−2.24343	−0.457938
$25$	5.07390	1.01478
$26$	4.21295	0.826227
$27$	2.16946	0.417514
$28$	1.39363	0.263372
$29$	1.87223	0.347664	0.173832	−	0.984775i	$-0.444385\pi$
$29$	1.87223	0.347664	0.173832	+	0.984775i	$0.444385\pi$
$30$	7.12051	1.30002
$31$	1.02762	0.184567	0.0922833	−	0.995733i	$-0.470583\pi$
$31$	1.02762	0.184567	0.0922833	+	0.995733i	$0.470583\pi$
$32$	1.00000	0.176777
$33$	−1.64945	−0.287133
$34$	−2.62009	−0.449342
$35$	−4.42331	−0.747675
$36$	2.03297	0.338828
$37$	−6.78086	−1.11477	−0.557384	−	0.830255i	$-0.688195\pi$
$37$	−6.78086	−1.11477	−0.557384	+	0.830255i	$0.688195\pi$
$38$	4.37119	0.709101
$39$	−9.45145	−1.51344
$40$	−3.17394	−0.501844
$41$	−4.82955	−0.754249	−0.377124	−	0.926163i	$-0.623087\pi$
$41$	−4.82955	−0.754249	−0.377124	+	0.926163i	$0.623087\pi$
$42$	−3.12651	−0.482432
$43$	−7.98546	−1.21777	−0.608885	−	0.793258i	$-0.708383\pi$
$43$	−7.98546	−1.21777	−0.608885	+	0.793258i	$0.708383\pi$
$44$	0.735237	0.110841
$45$	−6.45252	−0.961885
$46$	6.54733	0.965352
$47$	−1.11312	−0.162365	−0.0811824	−	0.996699i	$-0.525870\pi$
$47$	−1.11312	−0.162365	−0.0811824	+	0.996699i	$0.525870\pi$
$48$	−2.24343	−0.323811
$49$	−5.05779	−0.722541
$50$	5.07390	0.717558
$51$	5.87799	0.823083
$52$	4.21295	0.584231
$53$	12.0340	1.65300	0.826500	−	0.562937i	$-0.190329\pi$
$53$	12.0340	1.65300	0.826500	+	0.562937i	$0.190329\pi$
$54$	2.16946	0.295227
$55$	−2.33360	−0.314662
$56$	1.39363	0.186232
$57$	−9.80645	−1.29890
$58$	1.87223	0.245836
$59$	9.15709	1.19215	0.596076	−	0.802928i	$-0.296726\pi$
$59$	9.15709	1.19215	0.596076	+	0.802928i	$0.296726\pi$
$60$	7.12051	0.919254
$61$	−4.77680	−0.611606	−0.305803	−	0.952095i	$-0.598925\pi$
$61$	−4.77680	−0.611606	−0.305803	+	0.952095i	$0.598925\pi$
$62$	1.02762	0.130508
$63$	2.83321	0.356951
$64$	1.00000	0.125000
$65$	−13.3717	−1.65855
$66$	−1.64945	−0.203033
$67$	−13.7355	−1.67806	−0.839029	−	0.544087i	$-0.816876\pi$
$67$	−13.7355	−1.67806	−0.839029	+	0.544087i	$0.816876\pi$
$68$	−2.62009	−0.317733
$69$	−14.6885	−1.76828
$70$	−4.42331	−0.528686
$71$	14.1531	1.67966	0.839830	−	0.542850i	$-0.182655\pi$
$71$	14.1531	1.67966	0.839830	+	0.542850i	$0.182655\pi$
$72$	2.03297	0.239588
$73$	−0.507181	−0.0593611	−0.0296805	−	0.999559i	$-0.509449\pi$
$73$	−0.507181	−0.0593611	−0.0296805	+	0.999559i	$0.509449\pi$
$74$	−6.78086	−0.788259
$75$	−11.3829	−1.31439
$76$	4.37119	0.501410
$77$	1.02465	0.116770
$78$	−9.45145	−1.07017
$79$	−3.46645	−0.390006	−0.195003	−	0.980803i	$-0.562472\pi$
$79$	−3.46645	−0.390006	−0.195003	+	0.980803i	$0.562472\pi$
$80$	−3.17394	−0.354857
$81$	−10.9659	−1.21844
$82$	−4.82955	−0.533334
$83$	−3.80344	−0.417482	−0.208741	−	0.977971i	$-0.566937\pi$
$83$	−3.80344	−0.417482	−0.208741	+	0.977971i	$0.566937\pi$
$84$	−3.12651	−0.341131
$85$	8.31602	0.901999
$86$	−7.98546	−0.861094
$87$	−4.20021	−0.450310
$88$	0.735237	0.0783765
$89$	−2.34743	−0.248827	−0.124414	−	0.992230i	$-0.539705\pi$
$89$	−2.34743	−0.248827	−0.124414	+	0.992230i	$0.539705\pi$
$90$	−6.45252	−0.680156
$91$	5.87130	0.615480
$92$	6.54733	0.682607
$93$	−2.30540	−0.239059
$94$	−1.11312	−0.114809
$95$	−13.8739	−1.42343
$96$	−2.24343	−0.228969
$97$	13.8745	1.40874	0.704372	−	0.709831i	$-0.251229\pi$
$97$	13.8745	1.40874	0.704372	+	0.709831i	$0.251229\pi$
$98$	−5.05779	−0.510914
$99$	1.49471	0.150224
$100$	5.07390	0.507390
$101$	7.81978	0.778098	0.389049	−	0.921217i	$-0.372804\pi$
$101$	7.81978	0.778098	0.389049	+	0.921217i	$0.372804\pi$
$102$	5.87799	0.582008
$103$	9.10596	0.897237	0.448618	−	0.893723i	$-0.351916\pi$
$103$	9.10596	0.897237	0.448618	+	0.893723i	$0.351916\pi$
$104$	4.21295	0.413114
$105$	9.92337	0.968422
$106$	12.0340	1.16885
$107$	−6.55718	−0.633907	−0.316953	−	0.948441i	$-0.602660\pi$
$107$	−6.55718	−0.633907	−0.316953	+	0.948441i	$0.602660\pi$
$108$	2.16946	0.208757
$109$	−3.79582	−0.363574	−0.181787	−	0.983338i	$-0.558188\pi$
$109$	−3.79582	−0.363574	−0.181787	+	0.983338i	$0.558188\pi$
$110$	−2.33360	−0.222500
$111$	15.2124	1.44390
$112$	1.39363	0.131686
$113$	−19.1992	−1.80611	−0.903054	−	0.429527i	$-0.858680\pi$
$113$	−19.1992	−1.80611	−0.903054	+	0.429527i	$0.858680\pi$
$114$	−9.80645	−0.918458
$115$	−20.7809	−1.93782
$116$	1.87223	0.173832
$117$	8.56479	0.791816
$118$	9.15709	0.842978
$119$	−3.65145	−0.334728
$120$	7.12051	0.650010
$121$	−10.4594	−0.950857
$122$	−4.77680	−0.432471
$123$	10.8347	0.976936
$124$	1.02762	0.0922833
$125$	−0.234558	−0.0209795
$126$	2.83321	0.252403
$127$	16.1155	1.43002	0.715011	−	0.699113i	$-0.246422\pi$
$127$	16.1155	1.43002	0.715011	+	0.699113i	$0.246422\pi$
$128$	1.00000	0.0883883
$129$	17.9148	1.57731
$130$	−13.3717	−1.17277
$131$	17.4543	1.52499	0.762496	−	0.646992i	$-0.223973\pi$
$131$	17.4543	1.52499	0.762496	+	0.646992i	$0.223973\pi$
$132$	−1.64945	−0.143566
$133$	6.09183	0.528229
$134$	−13.7355	−1.18657
$135$	−6.88575	−0.592631
$136$	−2.62009	−0.224671
$137$	−17.7672	−1.51795	−0.758977	−	0.651117i	$-0.774301\pi$
$137$	−17.7672	−1.51795	−0.758977	+	0.651117i	$0.774301\pi$
$138$	−14.6885	−1.25037
$139$	−3.81319	−0.323431	−0.161715	−	0.986837i	$-0.551703\pi$
$139$	−3.81319	−0.323431	−0.161715	+	0.986837i	$0.551703\pi$
$140$	−4.42331	−0.373838
$141$	2.49720	0.210302
$142$	14.1531	1.18770
$143$	3.09752	0.259027
$144$	2.03297	0.169414
$145$	−5.94235	−0.493485
$146$	−0.507181	−0.0419746
$147$	11.3468	0.935867
$148$	−6.78086	−0.557384
$149$	−11.9880	−0.982095	−0.491048	−	0.871133i	$-0.663386\pi$
$149$	−11.9880	−0.982095	−0.491048	+	0.871133i	$0.663386\pi$
$150$	−11.3829	−0.929412
$151$	−4.99802	−0.406733	−0.203367	−	0.979103i	$-0.565188\pi$
$151$	−4.99802	−0.406733	−0.203367	+	0.979103i	$0.565188\pi$
$152$	4.37119	0.354550
$153$	−5.32657	−0.430627
$154$	1.02465	0.0825687
$155$	−3.26161	−0.261979
$156$	−9.45145	−0.756721
$157$	16.0318	1.27948	0.639739	−	0.768592i	$-0.279042\pi$
$157$	16.0318	1.27948	0.639739	+	0.768592i	$0.279042\pi$
$158$	−3.46645	−0.275776
$159$	−26.9974	−2.14104
$160$	−3.17394	−0.250922
$161$	9.12458	0.719118
$162$	−10.9659	−0.861566
$163$	2.17331	0.170227	0.0851134	−	0.996371i	$-0.472875\pi$
$163$	2.17331	0.170227	0.0851134	+	0.996371i	$0.472875\pi$
$164$	−4.82955	−0.377124
$165$	5.23526	0.407564
$166$	−3.80344	−0.295204
$167$	19.0830	1.47668	0.738342	−	0.674427i	$-0.235609\pi$
$167$	19.0830	1.47668	0.738342	+	0.674427i	$0.235609\pi$
$168$	−3.12651	−0.241216
$169$	4.74894	0.365303
$170$	8.31602	0.637809
$171$	8.88650	0.679567
$172$	−7.98546	−0.608885
$173$	8.24584	0.626920	0.313460	−	0.949601i	$-0.398512\pi$
$173$	8.24584	0.626920	0.313460	+	0.949601i	$0.398512\pi$
$174$	−4.20021	−0.318417
$175$	7.07115	0.534529
$176$	0.735237	0.0554206
$177$	−20.5433	−1.54413
$178$	−2.34743	−0.175948
$179$	9.12516	0.682046	0.341023	−	0.940055i	$-0.389227\pi$
$179$	9.12516	0.682046	0.341023	+	0.940055i	$0.389227\pi$
$180$	−6.45252	−0.480943
$181$	0.0412025	0.00306256	0.00153128	−	0.999999i	$-0.499513\pi$
$181$	0.0412025	0.00306256	0.00153128	+	0.999999i	$0.499513\pi$
$182$	5.87130	0.435210
$183$	10.7164	0.792179
$184$	6.54733	0.482676
$185$	21.5221	1.58233
$186$	−2.30540	−0.169040
$187$	−1.92639	−0.140871
$188$	−1.11312	−0.0811824
$189$	3.02344	0.219923
$190$	−13.8739	−1.00652
$191$	22.6830	1.64128	0.820642	−	0.571443i	$-0.193616\pi$
$191$	22.6830	1.64128	0.820642	+	0.571443i	$0.193616\pi$
$192$	−2.24343	−0.161905
$193$	17.4192	1.25386	0.626931	−	0.779075i	$-0.284311\pi$
$193$	17.4192	1.25386	0.626931	+	0.779075i	$0.284311\pi$
$194$	13.8745	0.996133
$195$	29.9983	2.14823
$196$	−5.05779	−0.361271
$197$	7.06810	0.503581	0.251791	−	0.967782i	$-0.418981\pi$
$197$	7.06810	0.503581	0.251791	+	0.967782i	$0.418981\pi$
$198$	1.49471	0.106225
$199$	−8.25644	−0.585283	−0.292642	−	0.956222i	$-0.594534\pi$
$199$	−8.25644	−0.585283	−0.292642	+	0.956222i	$0.594534\pi$
$200$	5.07390	0.358779
$201$	30.8146	2.17349
$202$	7.81978	0.550198
$203$	2.60920	0.183130
$204$	5.87799	0.411541
$205$	15.3287	1.07060
$206$	9.10596	0.634442
$207$	13.3105	0.925146
$208$	4.21295	0.292115
$209$	3.21386	0.222307
$210$	9.92337	0.684778
$211$	5.51064	0.379368	0.189684	−	0.981845i	$-0.439254\pi$
$211$	5.51064	0.379368	0.189684	+	0.981845i	$0.439254\pi$
$212$	12.0340	0.826500
$213$	−31.7514	−2.17557
$214$	−6.55718	−0.448240
$215$	25.3454	1.72854
$216$	2.16946	0.147613
$217$	1.43213	0.0972192
$218$	−3.79582	−0.257086
$219$	1.13782	0.0768871
$220$	−2.33360	−0.157331
$221$	−11.0383	−0.742517
$222$	15.2124	1.02099
$223$	16.7113	1.11907	0.559535	−	0.828807i	$-0.310980\pi$
$223$	16.7113	1.11907	0.559535	+	0.828807i	$0.310980\pi$
$224$	1.39363	0.0931160
$225$	10.3151	0.687672
$226$	−19.1992	−1.27711
$227$	−1.23980	−0.0822886	−0.0411443	−	0.999153i	$-0.513100\pi$
$227$	−1.23980	−0.0822886	−0.0411443	+	0.999153i	$0.513100\pi$
$228$	−9.80645	−0.649448
$229$	25.2635	1.66946	0.834731	−	0.550658i	$-0.185623\pi$
$229$	25.2635	1.66946	0.834731	+	0.550658i	$0.185623\pi$
$230$	−20.7809	−1.37025
$231$	−2.29873	−0.151245
$232$	1.87223	0.122918
$233$	−7.69379	−0.504037	−0.252018	−	0.967722i	$-0.581094\pi$
$233$	−7.69379	−0.504037	−0.252018	+	0.967722i	$0.581094\pi$
$234$	8.56479	0.559898
$235$	3.53297	0.230465
$236$	9.15709	0.596076
$237$	7.77673	0.505153
$238$	−3.65145	−0.236688
$239$	−19.7435	−1.27710	−0.638549	−	0.769581i	$-0.720465\pi$
$239$	−19.7435	−1.27710	−0.638549	+	0.769581i	$0.720465\pi$
$240$	7.12051	0.459627
$241$	−8.09276	−0.521300	−0.260650	−	0.965433i	$-0.583937\pi$
$241$	−8.09276	−0.521300	−0.260650	+	0.965433i	$0.583937\pi$
$242$	−10.4594	−0.672357
$243$	18.0929	1.16066
$244$	−4.77680	−0.305803
$245$	16.0531	1.02560
$246$	10.8347	0.690798
$247$	18.4156	1.17176
$248$	1.02762	0.0652541
$249$	8.53274	0.540741
$250$	−0.234558	−0.0148347
$251$	−6.27716	−0.396211	−0.198105	−	0.980181i	$-0.563479\pi$
$251$	−6.27716	−0.396211	−0.198105	+	0.980181i	$0.563479\pi$
$252$	2.83321	0.178476
$253$	4.81384	0.302644
$254$	16.1155	1.01118
$255$	−18.6564	−1.16831
$256$	1.00000	0.0625000
$257$	−15.9198	−0.993052	−0.496526	−	0.868022i	$-0.665391\pi$
$257$	−15.9198	−0.993052	−0.496526	+	0.868022i	$0.665391\pi$
$258$	17.9148	1.11533
$259$	−9.45003	−0.587197
$260$	−13.3717	−0.829275
$261$	3.80619	0.235597
$262$	17.4543	1.07833
$263$	19.1316	1.17971	0.589853	−	0.807511i	$-0.299186\pi$
$263$	19.1316	1.17971	0.589853	+	0.807511i	$0.299186\pi$
$264$	−1.64945	−0.101517
$265$	−38.1953	−2.34632
$266$	6.09183	0.373514
$267$	5.26630	0.322292
$268$	−13.7355	−0.839029
$269$	17.0598	1.04015	0.520077	−	0.854119i	$-0.325903\pi$
$269$	17.0598	1.04015	0.520077	+	0.854119i	$0.325903\pi$
$270$	−6.88575	−0.419053
$271$	−14.4218	−0.876065	−0.438032	−	0.898959i	$-0.644324\pi$
$271$	−14.4218	−0.876065	−0.438032	+	0.898959i	$0.644324\pi$
$272$	−2.62009	−0.158866
$273$	−13.1718	−0.797196
$274$	−17.7672	−1.07336
$275$	3.73052	0.224959
$276$	−14.6885	−0.884142
$277$	17.8690	1.07365	0.536823	−	0.843695i	$-0.319624\pi$
$277$	17.8690	1.07365	0.536823	+	0.843695i	$0.319624\pi$
$278$	−3.81319	−0.228700
$279$	2.08913	0.125073
$280$	−4.42331	−0.264343
$281$	15.8335	0.944548	0.472274	−	0.881452i	$-0.343433\pi$
$281$	15.8335	0.944548	0.472274	+	0.881452i	$0.343433\pi$
$282$	2.49720	0.148706
$283$	−2.22872	−0.132484	−0.0662419	−	0.997804i	$-0.521101\pi$
$283$	−2.22872	−0.132484	−0.0662419	+	0.997804i	$0.521101\pi$
$284$	14.1531	0.839830
$285$	31.1251	1.84369
$286$	3.09752	0.183160
$287$	−6.73062	−0.397296
$288$	2.03297	0.119794
$289$	−10.1351	−0.596183
$290$	−5.94235	−0.348947
$291$	−31.1265	−1.82467
$292$	−0.507181	−0.0296805
$293$	−10.1898	−0.595294	−0.297647	−	0.954676i	$-0.596202\pi$
$293$	−10.1898	−0.595294	−0.297647	+	0.954676i	$0.596202\pi$
$294$	11.3468	0.661758
$295$	−29.0641	−1.69217
$296$	−6.78086	−0.394130
$297$	1.59507	0.0925553
$298$	−11.9880	−0.694446
$299$	27.5836	1.59520
$300$	−11.3829	−0.657194
$301$	−11.1288	−0.641453
$302$	−4.99802	−0.287604
$303$	−17.5431	−1.00783
$304$	4.37119	0.250705
$305$	15.1613	0.868132
$306$	−5.32657	−0.304500
$307$	−8.93716	−0.510070	−0.255035	−	0.966932i	$-0.582087\pi$
$307$	−8.93716	−0.510070	−0.255035	+	0.966932i	$0.582087\pi$
$308$	1.02465	0.0583849
$309$	−20.4286	−1.16214
$310$	−3.26161	−0.185247
$311$	18.7735	1.06455	0.532273	−	0.846573i	$-0.321338\pi$
$311$	18.7735	1.06455	0.532273	+	0.846573i	$0.321338\pi$
$312$	−9.45145	−0.535083
$313$	2.91942	0.165015	0.0825077	−	0.996590i	$-0.473707\pi$
$313$	2.91942	0.165015	0.0825077	+	0.996590i	$0.473707\pi$
$314$	16.0318	0.904728
$315$	−8.99245	−0.506667
$316$	−3.46645	−0.195003
$317$	30.3048	1.70209	0.851043	−	0.525096i	$-0.175970\pi$
$317$	30.3048	1.70209	0.851043	+	0.525096i	$0.175970\pi$
$318$	−26.9974	−1.51394
$319$	1.37653	0.0770710
$320$	−3.17394	−0.177429
$321$	14.7106	0.821064
$322$	9.12458	0.508493
$323$	−11.4529	−0.637258
$324$	−10.9659	−0.609219
$325$	21.3761	1.18573
$326$	2.17331	0.120369
$327$	8.51565	0.470917
$328$	−4.82955	−0.266667
$329$	−1.55128	−0.0855246
$330$	5.23526	0.288192
$331$	−25.1243	−1.38096	−0.690479	−	0.723353i	$-0.742600\pi$
$331$	−25.1243	−1.38096	−0.690479	+	0.723353i	$0.742600\pi$
$332$	−3.80344	−0.208741
$333$	−13.7853	−0.755429
$334$	19.0830	1.04417
$335$	43.5957	2.38188
$336$	−3.12651	−0.170565
$337$	13.1666	0.717232	0.358616	−	0.933485i	$-0.383249\pi$
$337$	13.1666	0.717232	0.358616	+	0.933485i	$0.383249\pi$
$338$	4.74894	0.258308
$339$	43.0720	2.33935
$340$	8.31602	0.450999
$341$	0.755546	0.0409151
$342$	8.88650	0.480527
$343$	−16.8041	−0.907338
$344$	−7.98546	−0.430547
$345$	46.6203	2.50996
$346$	8.24584	0.443299
$347$	−4.60247	−0.247073	−0.123537	−	0.992340i	$-0.539424\pi$
$347$	−4.60247	−0.247073	−0.123537	+	0.992340i	$0.539424\pi$
$348$	−4.20021	−0.225155
$349$	−20.1123	−1.07659	−0.538294	−	0.842757i	$-0.680931\pi$
$349$	−20.1123	−1.07659	−0.538294	+	0.842757i	$0.680931\pi$
$350$	7.07115	0.377969
$351$	9.13984	0.487849
$352$	0.735237	0.0391883
$353$	−8.47566	−0.451114	−0.225557	−	0.974230i	$-0.572420\pi$
$353$	−8.47566	−0.451114	−0.225557	+	0.974230i	$0.572420\pi$
$354$	−20.5433	−1.09186
$355$	−44.9210	−2.38416
$356$	−2.34743	−0.124414
$357$	8.19176	0.433554
$358$	9.12516	0.482280
$359$	−35.8652	−1.89289	−0.946447	−	0.322859i	$-0.895356\pi$
$359$	−35.8652	−1.89289	−0.946447	+	0.322859i	$0.895356\pi$
$360$	−6.45252	−0.340078
$361$	0.107308	0.00564778
$362$	0.0412025	0.00216555
$363$	23.4650	1.23159
$364$	5.87130	0.307740
$365$	1.60976	0.0842589
$366$	10.7164	0.560155
$367$	−31.6351	−1.65134	−0.825669	−	0.564155i	$-0.809202\pi$
$367$	−31.6351	−1.65134	−0.825669	+	0.564155i	$0.809202\pi$
$368$	6.54733	0.341303
$369$	−9.81832	−0.511121
$370$	21.5221	1.11888
$371$	16.7710	0.870707
$372$	−2.30540	−0.119529
$373$	−21.7276	−1.12501	−0.562507	−	0.826792i	$-0.690163\pi$
$373$	−21.7276	−1.12501	−0.562507	+	0.826792i	$0.690163\pi$
$374$	−1.92639	−0.0996112
$375$	0.526213	0.0271735
$376$	−1.11312	−0.0574046
$377$	7.88761	0.406233
$378$	3.02344	0.155509
$379$	18.9843	0.975157	0.487578	−	0.873079i	$-0.337880\pi$
$379$	18.9843	0.975157	0.487578	+	0.873079i	$0.337880\pi$
$380$	−13.8739	−0.711716
$381$	−36.1540	−1.85223
$382$	22.6830	1.16056
$383$	38.2293	1.95343	0.976714	−	0.214547i	$-0.0688275\pi$
$383$	38.2293	1.95343	0.976714	+	0.214547i	$0.0688275\pi$
$384$	−2.24343	−0.114484
$385$	−3.25218	−0.165746
$386$	17.4192	0.886614
$387$	−16.2342	−0.825230
$388$	13.8745	0.704372
$389$	23.8169	1.20757	0.603783	−	0.797149i	$-0.293659\pi$
$389$	23.8169	1.20757	0.603783	+	0.797149i	$0.293659\pi$
$390$	29.9983	1.51902
$391$	−17.1546	−0.867546
$392$	−5.05779	−0.255457
$393$	−39.1576	−1.97524
$394$	7.06810	0.356086
$395$	11.0023	0.553586
$396$	1.49471	0.0751122
$397$	16.0530	0.805679	0.402839	−	0.915271i	$-0.368023\pi$
$397$	16.0530	0.805679	0.402839	+	0.915271i	$0.368023\pi$
$398$	−8.25644	−0.413858
$399$	−13.6666	−0.684185
$400$	5.07390	0.253695
$401$	39.8493	1.98998	0.994990	−	0.0999788i	$-0.0318775\pi$
$401$	39.8493	1.98998	0.994990	+	0.0999788i	$0.0318775\pi$
$402$	30.8146	1.53689
$403$	4.32932	0.215659
$404$	7.81978	0.389049
$405$	34.8053	1.72949
$406$	2.60920	0.129492
$407$	−4.98554	−0.247124
$408$	5.87799	0.291004
$409$	−25.9293	−1.28212	−0.641062	−	0.767489i	$-0.721506\pi$
$409$	−25.9293	−1.28212	−0.641062	+	0.767489i	$0.721506\pi$
$410$	15.3287	0.757031
$411$	39.8594	1.96612
$412$	9.10596	0.448618
$413$	12.7616	0.627958
$414$	13.3105	0.654177
$415$	12.0719	0.592586
$416$	4.21295	0.206557
$417$	8.55462	0.418921
$418$	3.21386	0.157195
$419$	22.6406	1.10607	0.553034	−	0.833159i	$-0.313470\pi$
$419$	22.6406	1.10607	0.553034	+	0.833159i	$0.313470\pi$
$420$	9.92337	0.484211
$421$	−3.70951	−0.180791	−0.0903953	−	0.995906i	$-0.528813\pi$
$421$	−3.70951	−0.180791	−0.0903953	+	0.995906i	$0.528813\pi$
$422$	5.51064	0.268254
$423$	−2.26293	−0.110028
$424$	12.0340	0.584423
$425$	−13.2941	−0.644858
$426$	−31.7514	−1.53836
$427$	−6.65710	−0.322160
$428$	−6.55718	−0.316953
$429$	−6.94905	−0.335503
$430$	25.3454	1.22226
$431$	−1.36738	−0.0658646	−0.0329323	−	0.999458i	$-0.510485\pi$
$431$	−1.36738	−0.0658646	−0.0329323	+	0.999458i	$0.510485\pi$
$432$	2.16946	0.104378
$433$	36.0994	1.73483	0.867414	−	0.497586i	$-0.165780\pi$
$433$	36.0994	1.73483	0.867414	+	0.497586i	$0.165780\pi$
$434$	1.43213	0.0687444
$435$	13.3312	0.639184
$436$	−3.79582	−0.181787
$437$	28.6196	1.36906
$438$	1.13782	0.0543674
$439$	24.8534	1.18619	0.593094	−	0.805133i	$-0.297906\pi$
$439$	24.8534	1.18619	0.593094	+	0.805133i	$0.297906\pi$
$440$	−2.33360	−0.111250
$441$	−10.2823	−0.489635
$442$	−11.0383	−0.525039
$443$	23.7960	1.13058	0.565292	−	0.824891i	$-0.308763\pi$
$443$	23.7960	1.13058	0.565292	+	0.824891i	$0.308763\pi$
$444$	15.2124	0.721948
$445$	7.45062	0.353193
$446$	16.7113	0.791302
$447$	26.8942	1.27205
$448$	1.39363	0.0658430
$449$	16.7475	0.790364	0.395182	−	0.918603i	$-0.370681\pi$
$449$	16.7475	0.790364	0.395182	+	0.918603i	$0.370681\pi$
$450$	10.3151	0.486258
$451$	−3.55086	−0.167204
$452$	−19.1992	−0.903054
$453$	11.2127	0.526818
$454$	−1.23980	−0.0581868
$455$	−18.6352	−0.873630
$456$	−9.80645	−0.459229
$457$	−14.8356	−0.693978	−0.346989	−	0.937869i	$-0.612796\pi$
$457$	−14.8356	−0.693978	−0.346989	+	0.937869i	$0.612796\pi$
$458$	25.2635	1.18049
$459$	−5.68420	−0.265316
$460$	−20.7809	−0.968912
$461$	8.97844	0.418167	0.209084	−	0.977898i	$-0.432952\pi$
$461$	8.97844	0.418167	0.209084	+	0.977898i	$0.432952\pi$
$462$	−2.29873	−0.106947
$463$	14.5634	0.676819	0.338410	−	0.940999i	$-0.390111\pi$
$463$	14.5634	0.676819	0.338410	+	0.940999i	$0.390111\pi$
$464$	1.87223	0.0869161
$465$	7.31720	0.339327
$466$	−7.69379	−0.356408
$467$	26.2854	1.21634	0.608171	−	0.793806i	$-0.291904\pi$
$467$	26.2854	1.21634	0.608171	+	0.793806i	$0.291904\pi$
$468$	8.56479	0.395908
$469$	−19.1422	−0.883906
$470$	3.53297	0.162964
$471$	−35.9662	−1.65724
$472$	9.15709	0.421489
$473$	−5.87120	−0.269958
$474$	7.77673	0.357197
$475$	22.1790	1.01764
$476$	−3.65145	−0.167364
$477$	24.4648	1.12017
$478$	−19.7435	−0.903044
$479$	13.9443	0.637131	0.318566	−	0.947901i	$-0.396799\pi$
$479$	13.9443	0.637131	0.318566	+	0.947901i	$0.396799\pi$
$480$	7.12051	0.325005
$481$	−28.5674	−1.30256
$482$	−8.09276	−0.368615
$483$	−20.4703	−0.931433
$484$	−10.4594	−0.475428
$485$	−44.0369	−1.99961
$486$	18.0929	0.820711
$487$	−33.3184	−1.50980	−0.754901	−	0.655839i	$-0.772315\pi$
$487$	−33.3184	−1.50980	−0.754901	+	0.655839i	$0.772315\pi$
$488$	−4.77680	−0.216235
$489$	−4.87567	−0.220485
$490$	16.0531	0.725206
$491$	−18.0203	−0.813247	−0.406623	−	0.913596i	$-0.633294\pi$
$491$	−18.0203	−0.813247	−0.406623	+	0.913596i	$0.633294\pi$
$492$	10.8347	0.488468
$493$	−4.90542	−0.220929
$494$	18.4156	0.828557
$495$	−4.74413	−0.213233
$496$	1.02762	0.0461416
$497$	19.7242	0.884750
$498$	8.53274	0.382361
$499$	22.9001	1.02515	0.512575	−	0.858642i	$-0.328692\pi$
$499$	22.9001	1.02515	0.512575	+	0.858642i	$0.328692\pi$
$500$	−0.234558	−0.0104897
$501$	−42.8112	−1.91267
$502$	−6.27716	−0.280163
$503$	−4.49848	−0.200577	−0.100289	−	0.994958i	$-0.531977\pi$
$503$	−4.49848	−0.200577	−0.100289	+	0.994958i	$0.531977\pi$
$504$	2.83321	0.126201
$505$	−24.8195	−1.10445
$506$	4.81384	0.214001
$507$	−10.6539	−0.473156
$508$	16.1155	0.715011
$509$	12.1000	0.536325	0.268162	−	0.963374i	$-0.413584\pi$
$509$	12.1000	0.536325	0.268162	+	0.963374i	$0.413584\pi$
$510$	−18.6564	−0.826119
$511$	−0.706824	−0.0312681
$512$	1.00000	0.0441942
$513$	9.48314	0.418691
$514$	−15.9198	−0.702194
$515$	−28.9018	−1.27356
$516$	17.9148	0.788655
$517$	−0.818404	−0.0359934
$518$	−9.45003	−0.415211
$519$	−18.4989	−0.812014
$520$	−13.3717	−0.586386
$521$	14.7374	0.645657	0.322829	−	0.946457i	$-0.395366\pi$
$521$	14.7374	0.645657	0.322829	+	0.946457i	$0.395366\pi$
$522$	3.80619	0.166592
$523$	−12.1585	−0.531654	−0.265827	−	0.964021i	$-0.585645\pi$
$523$	−12.1585	−0.531654	−0.265827	+	0.964021i	$0.585645\pi$
$524$	17.4543	0.762496
$525$	−15.8636	−0.692345
$526$	19.1316	0.834178
$527$	−2.69247	−0.117286
$528$	−1.64945	−0.0717831
$529$	19.8676	0.863808
$530$	−38.1953	−1.65910
$531$	18.6161	0.807869
$532$	6.09183	0.264115
$533$	−20.3466	−0.881311
$534$	5.26630	0.227895
$535$	20.8121	0.899786
$536$	−13.7355	−0.593283
$537$	−20.4716	−0.883416
$538$	17.0598	0.735500
$539$	−3.71867	−0.160175
$540$	−6.88575	−0.296316
$541$	39.4657	1.69676	0.848382	−	0.529385i	$-0.177577\pi$
$541$	39.4657	1.69676	0.848382	+	0.529385i	$0.177577\pi$
$542$	−14.4218	−0.619471
$543$	−0.0924348	−0.00396676
$544$	−2.62009	−0.112336
$545$	12.0477	0.516067
$546$	−13.1718	−0.563703
$547$	34.5006	1.47514	0.737570	−	0.675271i	$-0.235973\pi$
$547$	34.5006	1.47514	0.737570	+	0.675271i	$0.235973\pi$
$548$	−17.7672	−0.758977
$549$	−9.71108	−0.414459
$550$	3.73052	0.159070
$551$	8.18387	0.348645
$552$	−14.6885	−0.625183
$553$	−4.83096	−0.205433
$554$	17.8690	0.759182
$555$	−48.2832	−2.04951
$556$	−3.81319	−0.161715
$557$	33.1805	1.40590	0.702951	−	0.711239i	$-0.251865\pi$
$557$	33.1805	1.40590	0.702951	+	0.711239i	$0.251865\pi$
$558$	2.08913	0.0884397
$559$	−33.6423	−1.42292
$560$	−4.42331	−0.186919
$561$	4.32171	0.182463
$562$	15.8335	0.667896
$563$	−24.0599	−1.01401	−0.507003	−	0.861944i	$-0.669247\pi$
$563$	−24.0599	−1.01401	−0.507003	+	0.861944i	$0.669247\pi$
$564$	2.49720	0.105151
$565$	60.9371	2.56364
$566$	−2.22872	−0.0936802
$567$	−15.2825	−0.641805
$568$	14.1531	0.593849
$569$	−36.4448	−1.52785	−0.763923	−	0.645307i	$-0.776729\pi$
$569$	−36.4448	−1.52785	−0.763923	+	0.645307i	$0.776729\pi$
$570$	31.1251	1.30369
$571$	−26.7660	−1.12012	−0.560062	−	0.828451i	$-0.689223\pi$
$571$	−26.7660	−1.12012	−0.560062	+	0.828451i	$0.689223\pi$
$572$	3.09752	0.129514
$573$	−50.8877	−2.12586
$574$	−6.73062	−0.280930
$575$	33.2205	1.38539
$576$	2.03297	0.0847070
$577$	−25.1217	−1.04583	−0.522914	−	0.852385i	$-0.675155\pi$
$577$	−25.1217	−1.04583	−0.522914	+	0.852385i	$0.675155\pi$
$578$	−10.1351	−0.421565
$579$	−39.0787	−1.62406
$580$	−5.94235	−0.246743
$581$	−5.30060	−0.219906
$582$	−31.1265	−1.29023
$583$	8.84785	0.366441
$584$	−0.507181	−0.0209873
$585$	−27.1842	−1.12393
$586$	−10.1898	−0.420937
$587$	29.7885	1.22950	0.614752	−	0.788721i	$-0.289256\pi$
$587$	29.7885	1.22950	0.614752	+	0.788721i	$0.289256\pi$
$588$	11.3468	0.467933
$589$	4.49194	0.185087
$590$	−29.0641	−1.19655
$591$	−15.8568	−0.652260
$592$	−6.78086	−0.278692
$593$	−5.79205	−0.237851	−0.118925	−	0.992903i	$-0.537945\pi$
$593$	−5.79205	−0.237851	−0.118925	+	0.992903i	$0.537945\pi$
$594$	1.59507	0.0654465
$595$	11.5895	0.475122
$596$	−11.9880	−0.491048
$597$	18.5227	0.758085
$598$	27.5836	1.12798
$599$	24.8158	1.01394	0.506972	−	0.861962i	$-0.330765\pi$
$599$	24.8158	1.01394	0.506972	+	0.861962i	$0.330765\pi$
$600$	−11.3829	−0.464706
$601$	27.4033	1.11780	0.558902	−	0.829233i	$-0.311223\pi$
$601$	27.4033	1.11780	0.558902	+	0.829233i	$0.311223\pi$
$602$	−11.1288	−0.453576
$603$	−27.9238	−1.13715
$604$	−4.99802	−0.203367
$605$	33.1976	1.34967
$606$	−17.5431	−0.712641
$607$	−29.4417	−1.19500	−0.597501	−	0.801868i	$-0.703840\pi$
$607$	−29.4417	−1.19500	−0.597501	+	0.801868i	$0.703840\pi$
$608$	4.37119	0.177275
$609$	−5.85355	−0.237198
$610$	15.1613	0.613862
$611$	−4.68950	−0.189717
$612$	−5.32657	−0.215314
$613$	−26.2597	−1.06062	−0.530309	−	0.847804i	$-0.677924\pi$
$613$	−26.2597	−1.06062	−0.530309	+	0.847804i	$0.677924\pi$
$614$	−8.93716	−0.360674
$615$	−34.3888	−1.38669
$616$	1.02465	0.0412843
$617$	0.985988	0.0396944	0.0198472	−	0.999803i	$-0.493682\pi$
$617$	0.985988	0.0396944	0.0198472	+	0.999803i	$0.493682\pi$
$618$	−20.4286	−0.821757
$619$	41.4488	1.66597	0.832983	−	0.553298i	$-0.186631\pi$
$619$	41.4488	1.66597	0.832983	+	0.553298i	$0.186631\pi$
$620$	−3.26161	−0.130990
$621$	14.2042	0.569995
$622$	18.7735	0.752748
$623$	−3.27146	−0.131068
$624$	−9.45145	−0.378361
$625$	−24.6250	−0.985001
$626$	2.91942	0.116683
$627$	−7.21006	−0.287942
$628$	16.0318	0.639739
$629$	17.7665	0.708396
$630$	−8.99245	−0.358268
$631$	45.8468	1.82513	0.912565	−	0.408931i	$-0.134098\pi$
$631$	45.8468	1.82513	0.912565	+	0.408931i	$0.134098\pi$
$632$	−3.46645	−0.137888
$633$	−12.3627	−0.491374
$634$	30.3048	1.20356
$635$	−51.1498	−2.02982
$636$	−26.9974	−1.07052
$637$	−21.3082	−0.844262
$638$	1.37653	0.0544974
$639$	28.7727	1.13823
$640$	−3.17394	−0.125461
$641$	4.87529	0.192562	0.0962812	−	0.995354i	$-0.469305\pi$
$641$	4.87529	0.192562	0.0962812	+	0.995354i	$0.469305\pi$
$642$	14.7106	0.580580
$643$	−6.79183	−0.267844	−0.133922	−	0.990992i	$-0.542757\pi$
$643$	−6.79183	−0.267844	−0.133922	+	0.990992i	$0.542757\pi$
$644$	9.12458	0.359559
$645$	−56.8605	−2.23888
$646$	−11.4529	−0.450609
$647$	−11.5755	−0.455079	−0.227540	−	0.973769i	$-0.573068\pi$
$647$	−11.5755	−0.455079	−0.227540	+	0.973769i	$0.573068\pi$
$648$	−10.9659	−0.430783
$649$	6.73263	0.264279
$650$	21.3761	0.838439
$651$	−3.21288	−0.125923
$652$	2.17331	0.0851134
$653$	−9.33831	−0.365436	−0.182718	−	0.983165i	$-0.558490\pi$
$653$	−9.33831	−0.365436	−0.182718	+	0.983165i	$0.558490\pi$
$654$	8.51565	0.332988
$655$	−55.3990	−2.16462
$656$	−4.82955	−0.188562
$657$	−1.03108	−0.0402264
$658$	−1.55128	−0.0604750
$659$	1.55454	0.0605561	0.0302781	−	0.999542i	$-0.490361\pi$
$659$	1.55454	0.0605561	0.0302781	+	0.999542i	$0.490361\pi$
$660$	5.23526	0.203782
$661$	27.7456	1.07918	0.539589	−	0.841928i	$-0.318580\pi$
$661$	27.7456	1.07918	0.539589	+	0.841928i	$0.318580\pi$
$662$	−25.1243	−0.976484
$663$	24.7637	0.961741
$664$	−3.80344	−0.147602
$665$	−19.3351	−0.749784
$666$	−13.7853	−0.534169
$667$	12.2581	0.474636
$668$	19.0830	0.738342
$669$	−37.4905	−1.44947
$670$	43.5957	1.68425
$671$	−3.51208	−0.135582
$672$	−3.12651	−0.120608
$673$	2.85955	0.110228	0.0551138	−	0.998480i	$-0.482448\pi$
$673$	2.85955	0.110228	0.0551138	+	0.998480i	$0.482448\pi$
$674$	13.1666	0.507159
$675$	11.0076	0.423685
$676$	4.74894	0.182651
$677$	10.8690	0.417728	0.208864	−	0.977945i	$-0.433023\pi$
$677$	10.8690	0.417728	0.208864	+	0.977945i	$0.433023\pi$
$678$	43.0720	1.65417
$679$	19.3360	0.742047
$680$	8.31602	0.318905
$681$	2.78141	0.106584
$682$	0.755546	0.0289314
$683$	−13.6378	−0.521837	−0.260919	−	0.965361i	$-0.584025\pi$
$683$	−13.6378	−0.521837	−0.260919	+	0.965361i	$0.584025\pi$
$684$	8.88650	0.339784
$685$	56.3920	2.15463
$686$	−16.8041	−0.641585
$687$	−56.6769	−2.16236
$688$	−7.98546	−0.304443
$689$	50.6987	1.93147
$690$	46.6203	1.77481
$691$	−21.0719	−0.801612	−0.400806	−	0.916163i	$-0.631270\pi$
$691$	−21.0719	−0.801612	−0.400806	+	0.916163i	$0.631270\pi$
$692$	8.24584	0.313460
$693$	2.08308	0.0791297
$694$	−4.60247	−0.174707
$695$	12.1028	0.459087
$696$	−4.20021	−0.159209
$697$	12.6539	0.479299
$698$	−20.1123	−0.761263
$699$	17.2605	0.652850
$700$	7.07115	0.267265
$701$	3.98454	0.150494	0.0752469	−	0.997165i	$-0.476026\pi$
$701$	3.98454	0.150494	0.0752469	+	0.997165i	$0.476026\pi$
$702$	9.13984	0.344961
$703$	−29.6405	−1.11791
$704$	0.735237	0.0277103
$705$	−7.92596	−0.298509
$706$	−8.47566	−0.318986
$707$	10.8979	0.409858
$708$	−20.5433	−0.772063
$709$	−38.1959	−1.43448	−0.717239	−	0.696827i	$-0.754594\pi$
$709$	−38.1959	−1.43448	−0.717239	+	0.696827i	$0.754594\pi$
$710$	−44.9210	−1.68585
$711$	−7.04718	−0.264290
$712$	−2.34743	−0.0879738
$713$	6.72819	0.251973
$714$	8.19176	0.306569
$715$	−9.83133	−0.367671
$716$	9.12516	0.341023
$717$	44.2930	1.65415
$718$	−35.8652	−1.33848
$719$	−50.9645	−1.90066	−0.950328	−	0.311251i	$-0.899252\pi$
$719$	−50.9645	−1.90066	−0.950328	+	0.311251i	$0.899252\pi$
$720$	−6.45252	−0.240471
$721$	12.6904	0.472614
$722$	0.107308	0.00399358
$723$	18.1555	0.675211
$724$	0.0412025	0.00153128
$725$	9.49951	0.352803
$726$	23.4650	0.870867
$727$	−15.2180	−0.564403	−0.282202	−	0.959355i	$-0.591065\pi$
$727$	−15.2180	−0.564403	−0.282202	+	0.959355i	$0.591065\pi$
$728$	5.87130	0.217605
$729$	−7.69232	−0.284901
$730$	1.60976	0.0595800
$731$	20.9226	0.773852
$732$	10.7164	0.396089
$733$	24.1523	0.892086	0.446043	−	0.895011i	$-0.352833\pi$
$733$	24.1523	0.892086	0.446043	+	0.895011i	$0.352833\pi$
$734$	−31.6351	−1.16767
$735$	−36.0140	−1.32840
$736$	6.54733	0.241338
$737$	−10.0988	−0.371996
$738$	−9.81832	−0.361417
$739$	48.3002	1.77675	0.888375	−	0.459119i	$-0.151835\pi$
$739$	48.3002	1.77675	0.888375	+	0.459119i	$0.151835\pi$
$740$	21.5221	0.791167
$741$	−41.3141	−1.51771
$742$	16.7710	0.615683
$743$	−31.8614	−1.16888	−0.584441	−	0.811436i	$-0.698686\pi$
$743$	−31.8614	−1.16888	−0.584441	+	0.811436i	$0.698686\pi$
$744$	−2.30540	−0.0845200
$745$	38.0492	1.39402
$746$	−21.7276	−0.795506
$747$	−7.73227	−0.282909
$748$	−1.92639	−0.0704357
$749$	−9.13831	−0.333906
$750$	0.526213	0.0192146
$751$	11.6013	0.423339	0.211669	−	0.977341i	$-0.432110\pi$
$751$	11.6013	0.423339	0.211669	+	0.977341i	$0.432110\pi$
$752$	−1.11312	−0.0405912
$753$	14.0824	0.513189
$754$	7.88761	0.287250
$755$	15.8634	0.577329
$756$	3.02344	0.109961
$757$	−11.3184	−0.411376	−0.205688	−	0.978618i	$-0.565943\pi$
$757$	−11.3184	−0.411376	−0.205688	+	0.978618i	$0.565943\pi$
$758$	18.9843	0.689540
$759$	−10.7995	−0.391997
$760$	−13.8739	−0.503259
$761$	26.3920	0.956710	0.478355	−	0.878166i	$-0.341233\pi$
$761$	26.3920	0.956710	0.478355	+	0.878166i	$0.341233\pi$
$762$	−36.1540	−1.30972
$763$	−5.28998	−0.191510
$764$	22.6830	0.820642
$765$	16.9062	0.611245
$766$	38.2293	1.38128
$767$	38.5783	1.39298
$768$	−2.24343	−0.0809527
$769$	−26.6480	−0.960951	−0.480476	−	0.877008i	$-0.659536\pi$
$769$	−26.6480	−0.960951	−0.480476	+	0.877008i	$0.659536\pi$
$770$	−3.25218	−0.117200
$771$	35.7150	1.28624
$772$	17.4192	0.626931
$773$	26.9964	0.970993	0.485497	−	0.874238i	$-0.338639\pi$
$773$	26.9964	0.970993	0.485497	+	0.874238i	$0.338639\pi$
$774$	−16.2342	−0.583526
$775$	5.21406	0.187294
$776$	13.8745	0.498066
$777$	21.2005	0.760563
$778$	23.8169	0.853878
$779$	−21.1109	−0.756376
$780$	29.9983	1.07411
$781$	10.4059	0.372351
$782$	−17.1546	−0.613448
$783$	4.06174	0.145155
$784$	−5.05779	−0.180635
$785$	−50.8840	−1.81613
$786$	−39.1576	−1.39670
$787$	22.2721	0.793916	0.396958	−	0.917837i	$-0.370066\pi$
$787$	22.2721	0.793916	0.396958	+	0.917837i	$0.370066\pi$
$788$	7.06810	0.251791
$789$	−42.9204	−1.52801
$790$	11.0023	0.391444
$791$	−26.7566	−0.951356
$792$	1.49471	0.0531123
$793$	−20.1244	−0.714638
$794$	16.0530	0.569701
$795$	85.6883	3.03905
$796$	−8.25644	−0.292642
$797$	−14.5266	−0.514560	−0.257280	−	0.966337i	$-0.582826\pi$
$797$	−14.5266	−0.514560	−0.257280	+	0.966337i	$0.582826\pi$
$798$	−13.6666	−0.483792
$799$	2.91647	0.103177
$800$	5.07390	0.179389
$801$	−4.77226	−0.168620
$802$	39.8493	1.40713
$803$	−0.372898	−0.0131593
$804$	30.8146	1.08675
$805$	−28.9609	−1.02074
$806$	4.32932	0.152494
$807$	−38.2724	−1.34725
$808$	7.81978	0.275099
$809$	−22.7403	−0.799506	−0.399753	−	0.916623i	$-0.630904\pi$
$809$	−22.7403	−0.799506	−0.399753	+	0.916623i	$0.630904\pi$
$810$	34.8053	1.22293
$811$	25.5685	0.897830	0.448915	−	0.893574i	$-0.351811\pi$
$811$	25.5685	0.897830	0.448915	+	0.893574i	$0.351811\pi$
$812$	2.60920	0.0915650
$813$	32.3544	1.13472
$814$	−4.98554	−0.174743
$815$	−6.89796	−0.241625
$816$	5.87799	0.205771
$817$	−34.9060	−1.22120
$818$	−25.9293	−0.906598
$819$	11.9362	0.417084
$820$	15.3287	0.535301
$821$	28.0453	0.978787	0.489393	−	0.872063i	$-0.337218\pi$
$821$	28.0453	0.978787	0.489393	+	0.872063i	$0.337218\pi$
$822$	39.8594	1.39026
$823$	−0.844917	−0.0294519	−0.0147260	−	0.999892i	$-0.504688\pi$
$823$	−0.844917	−0.0294519	−0.0147260	+	0.999892i	$0.504688\pi$
$824$	9.10596	0.317221
$825$	−8.36915	−0.291376
$826$	12.7616	0.444033
$827$	−39.7703	−1.38295	−0.691474	−	0.722401i	$-0.743038\pi$
$827$	−39.7703	−1.38295	−0.691474	+	0.722401i	$0.743038\pi$
$828$	13.3105	0.462573
$829$	45.6530	1.58559	0.792797	−	0.609486i	$-0.208624\pi$
$829$	45.6530	1.58559	0.792797	+	0.609486i	$0.208624\pi$
$830$	12.0719	0.419021
$831$	−40.0878	−1.39063
$832$	4.21295	0.146058
$833$	13.2519	0.459150
$834$	8.55462	0.296222
$835$	−60.5682	−2.09605
$836$	3.21386	0.111154
$837$	2.22939	0.0770590
$838$	22.6406	0.782108
$839$	18.6393	0.643500	0.321750	−	0.946825i	$-0.395729\pi$
$839$	18.6393	0.643500	0.321750	+	0.946825i	$0.395729\pi$
$840$	9.92337	0.342389
$841$	−25.4948	−0.879129
$842$	−3.70951	−0.127838
$843$	−35.5213	−1.22342
$844$	5.51064	0.189684
$845$	−15.0728	−0.518522
$846$	−2.26293	−0.0778012
$847$	−14.5766	−0.500858
$848$	12.0340	0.413250
$849$	4.99998	0.171599
$850$	−13.2941	−0.455983
$851$	−44.3966	−1.52190
$852$	−31.7514	−1.08778
$853$	20.6337	0.706483	0.353242	−	0.935532i	$-0.385079\pi$
$853$	20.6337	0.706483	0.353242	+	0.935532i	$0.385079\pi$
$854$	−6.65710	−0.227801
$855$	−28.2052	−0.964598
$856$	−6.55718	−0.224120
$857$	14.3342	0.489646	0.244823	−	0.969568i	$-0.421270\pi$
$857$	14.3342	0.489646	0.244823	+	0.969568i	$0.421270\pi$
$858$	−6.94905	−0.237237
$859$	−35.8791	−1.22418	−0.612090	−	0.790788i	$-0.709671\pi$
$859$	−35.8791	−1.22418	−0.612090	+	0.790788i	$0.709671\pi$
$860$	25.3454	0.864270
$861$	15.0997	0.514595
$862$	−1.36738	−0.0465733
$863$	28.9470	0.985367	0.492684	−	0.870209i	$-0.336016\pi$
$863$	28.9470	0.985367	0.492684	+	0.870209i	$0.336016\pi$
$864$	2.16946	0.0738067
$865$	−26.1718	−0.889868
$866$	36.0994	1.22671
$867$	22.7374	0.772203
$868$	1.43213	0.0486096
$869$	−2.54866	−0.0864574
$870$	13.3312	0.451971
$871$	−57.8669	−1.96075
$872$	−3.79582	−0.128543
$873$	28.2065	0.954645
$874$	28.6196	0.968074
$875$	−0.326887	−0.0110508
$876$	1.13782	0.0384435
$877$	−22.7511	−0.768250	−0.384125	−	0.923281i	$-0.625497\pi$
$877$	−22.7511	−0.768250	−0.384125	+	0.923281i	$0.625497\pi$
$878$	24.8534	0.838762
$879$	22.8601	0.771051
$880$	−2.33360	−0.0786656
$881$	−20.7253	−0.698252	−0.349126	−	0.937076i	$-0.613521\pi$
$881$	−20.7253	−0.698252	−0.349126	+	0.937076i	$0.613521\pi$
$882$	−10.2823	−0.346224
$883$	−30.6070	−1.03001	−0.515004	−	0.857188i	$-0.672210\pi$
$883$	−30.6070	−1.03001	−0.515004	+	0.857188i	$0.672210\pi$
$884$	−11.0383	−0.371259
$885$	65.2031	2.19178
$886$	23.7960	0.799444
$887$	14.3389	0.481453	0.240727	−	0.970593i	$-0.422614\pi$
$887$	14.3389	0.481453	0.240727	+	0.970593i	$0.422614\pi$
$888$	15.2124	0.510494
$889$	22.4591	0.753255
$890$	7.45062	0.249745
$891$	−8.06257	−0.270106
$892$	16.7113	0.559535
$893$	−4.86565	−0.162823
$894$	26.8942	0.899477
$895$	−28.9627	−0.968117
$896$	1.39363	0.0465580
$897$	−61.8818	−2.06617
$898$	16.7475	0.558872
$899$	1.92395	0.0641672
$900$	10.3151	0.343836
$901$	−31.5302	−1.05042
$902$	−3.55086	−0.118231
$903$	24.9667	0.830838
$904$	−19.1992	−0.638556
$905$	−0.130774	−0.00434708
$906$	11.2127	0.372517
$907$	−31.2583	−1.03792	−0.518958	−	0.854800i	$-0.673680\pi$
$907$	−31.2583	−1.03792	−0.518958	+	0.854800i	$0.673680\pi$
$908$	−1.23980	−0.0411443
$909$	15.8974	0.527283
$910$	−18.6352	−0.617750
$911$	1.87049	0.0619721	0.0309861	−	0.999520i	$-0.490135\pi$
$911$	1.87049	0.0619721	0.0309861	+	0.999520i	$0.490135\pi$
$912$	−9.80645	−0.324724
$913$	−2.79643	−0.0925483
$914$	−14.8356	−0.490717
$915$	−34.0132	−1.12444
$916$	25.2635	0.834731
$917$	24.3249	0.803280
$918$	−5.68420	−0.187606
$919$	−23.5075	−0.775441	−0.387721	−	0.921777i	$-0.626738\pi$
$919$	−23.5075	−0.775441	−0.387721	+	0.921777i	$0.626738\pi$
$920$	−20.7809	−0.685124
$921$	20.0499	0.660665
$922$	8.97844	0.295689
$923$	59.6261	1.96262
$924$	−2.29873	−0.0756226
$925$	−34.4054	−1.13124
$926$	14.5634	0.478583
$927$	18.5121	0.608018
$928$	1.87223	0.0614590
$929$	0.851999	0.0279532	0.0139766	−	0.999902i	$-0.495551\pi$
$929$	0.851999	0.0279532	0.0139766	+	0.999902i	$0.495551\pi$
$930$	7.31720	0.239940
$931$	−22.1086	−0.724579
$932$	−7.69379	−0.252018
$933$	−42.1169	−1.37885
$934$	26.2854	0.860084
$935$	6.11424	0.199957
$936$	8.56479	0.279949
$937$	11.3343	0.370277	0.185138	−	0.982712i	$-0.440727\pi$
$937$	11.3343	0.370277	0.185138	+	0.982712i	$0.440727\pi$
$938$	−19.1422	−0.625016
$939$	−6.54951	−0.213735
$940$	3.53297	0.115233
$941$	10.2361	0.333688	0.166844	−	0.985983i	$-0.446642\pi$
$941$	10.2361	0.333688	0.166844	+	0.985983i	$0.446642\pi$
$942$	−35.9662	−1.17184
$943$	−31.6207	−1.02971
$944$	9.15709	0.298038
$945$	−9.59621	−0.312165
$946$	−5.87120	−0.190889
$947$	−47.2059	−1.53399	−0.766993	−	0.641655i	$-0.778248\pi$
$947$	−47.2059	−1.53399	−0.766993	+	0.641655i	$0.778248\pi$
$948$	7.77673	0.252576
$949$	−2.13673	−0.0693611
$950$	22.1790	0.719581
$951$	−67.9866	−2.20462
$952$	−3.65145	−0.118344
$953$	55.9131	1.81120	0.905602	−	0.424130i	$-0.139420\pi$
$953$	55.9131	1.81120	0.905602	+	0.424130i	$0.139420\pi$
$954$	24.4648	0.792077
$955$	−71.9945	−2.32969
$956$	−19.7435	−0.638549
$957$	−3.08815	−0.0998258
$958$	13.9443	0.450520
$959$	−24.7610	−0.799573
$960$	7.12051	0.229813
$961$	−29.9440	−0.965935
$962$	−28.5674	−0.921051
$963$	−13.3306	−0.429571
$964$	−8.09276	−0.260650
$965$	−55.2875	−1.77977
$966$	−20.4703	−0.658622
$967$	−23.7103	−0.762471	−0.381235	−	0.924478i	$-0.624501\pi$
$967$	−23.7103	−0.762471	−0.381235	+	0.924478i	$0.624501\pi$
$968$	−10.4594	−0.336179
$969$	25.6938	0.825404
$970$	−44.0369	−1.41394
$971$	−7.83790	−0.251530	−0.125765	−	0.992060i	$-0.540139\pi$
$971$	−7.83790	−0.251530	−0.125765	+	0.992060i	$0.540139\pi$
$972$	18.0929	0.580330
$973$	−5.31419	−0.170365
$974$	−33.3184	−1.06759
$975$	−47.9557	−1.53581
$976$	−4.77680	−0.152902
$977$	−15.0500	−0.481492	−0.240746	−	0.970588i	$-0.577392\pi$
$977$	−15.0500	−0.481492	−0.240746	+	0.970588i	$0.577392\pi$
$978$	−4.87567	−0.155907
$979$	−1.72592	−0.0551606
$980$	16.0531	0.512798
$981$	−7.71679	−0.246378
$982$	−18.0203	−0.575052
$983$	11.6680	0.372153	0.186076	−	0.982535i	$-0.440423\pi$
$983$	11.6680	0.372153	0.186076	+	0.982535i	$0.440423\pi$
$984$	10.8347	0.345399
$985$	−22.4337	−0.714798
$986$	−4.90542	−0.156220
$987$	3.48018	0.110775
$988$	18.4156	0.585878
$989$	−52.2835	−1.66252
$990$	−4.74413	−0.150778
$991$	−50.2414	−1.59597	−0.797986	−	0.602676i	$-0.794101\pi$
$991$	−50.2414	−1.59597	−0.797986	+	0.602676i	$0.794101\pi$
$992$	1.02762	0.0326271
$993$	56.3646	1.78868
$994$	19.7242	0.625613
$995$	26.2054	0.830769
$996$	8.53274	0.270370
$997$	54.4368	1.72403	0.862016	−	0.506882i	$-0.169202\pi$
$997$	54.4368	1.72403	0.862016	+	0.506882i	$0.169202\pi$
$998$	22.9001	0.724891
$999$	−14.7108	−0.465430

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8002.2.a.g.1.14	✓	95

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8002.2.a.g.1.14	✓	95	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:	\( N \)	\(=\)	\( 8002 = 2 \cdot 4001 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8002.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.24343 q^{3} +1.00000 q^{4} -3.17394 q^{5} -2.24343 q^{6} +1.39363 q^{7} +1.00000 q^{8} +2.03297 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.24343 q^{3} +1.00000 q^{4} -3.17394 q^{5} -2.24343 q^{6} +1.39363 q^{7} +1.00000 q^{8} +2.03297 q^{9} -3.17394 q^{10} +0.735237 q^{11} -2.24343 q^{12} +4.21295 q^{13} +1.39363 q^{14} +7.12051 q^{15} +1.00000 q^{16} -2.62009 q^{17} +2.03297 q^{18} +4.37119 q^{19} -3.17394 q^{20} -3.12651 q^{21} +0.735237 q^{22} +6.54733 q^{23} -2.24343 q^{24} +5.07390 q^{25} +4.21295 q^{26} +2.16946 q^{27} +1.39363 q^{28} +1.87223 q^{29} +7.12051 q^{30} +1.02762 q^{31} +1.00000 q^{32} -1.64945 q^{33} -2.62009 q^{34} -4.42331 q^{35} +2.03297 q^{36} -6.78086 q^{37} +4.37119 q^{38} -9.45145 q^{39} -3.17394 q^{40} -4.82955 q^{41} -3.12651 q^{42} -7.98546 q^{43} +0.735237 q^{44} -6.45252 q^{45} +6.54733 q^{46} -1.11312 q^{47} -2.24343 q^{48} -5.05779 q^{49} +5.07390 q^{50} +5.87799 q^{51} +4.21295 q^{52} +12.0340 q^{53} +2.16946 q^{54} -2.33360 q^{55} +1.39363 q^{56} -9.80645 q^{57} +1.87223 q^{58} +9.15709 q^{59} +7.12051 q^{60} -4.77680 q^{61} +1.02762 q^{62} +2.83321 q^{63} +1.00000 q^{64} -13.3717 q^{65} -1.64945 q^{66} -13.7355 q^{67} -2.62009 q^{68} -14.6885 q^{69} -4.42331 q^{70} +14.1531 q^{71} +2.03297 q^{72} -0.507181 q^{73} -6.78086 q^{74} -11.3829 q^{75} +4.37119 q^{76} +1.02465 q^{77} -9.45145 q^{78} -3.46645 q^{79} -3.17394 q^{80} -10.9659 q^{81} -4.82955 q^{82} -3.80344 q^{83} -3.12651 q^{84} +8.31602 q^{85} -7.98546 q^{86} -4.20021 q^{87} +0.735237 q^{88} -2.34743 q^{89} -6.45252 q^{90} +5.87130 q^{91} +6.54733 q^{92} -2.30540 q^{93} -1.11312 q^{94} -13.8739 q^{95} -2.24343 q^{96} +13.8745 q^{97} -5.05779 q^{98} +1.49471 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 95 q + 95 q^{2} + 24 q^{3} + 95 q^{4} + 36 q^{5} + 24 q^{6} + 21 q^{7} + 95 q^{8} + 121 q^{9}+O(q^{10}) \) 95 * q + 95 * q^2 + 24 * q^3 + 95 * q^4 + 36 * q^5 + 24 * q^6 + 21 * q^7 + 95 * q^8 + 121 * q^9	\( 95 q + 95 q^{2} + 24 q^{3} + 95 q^{4} + 36 q^{5} + 24 q^{6} + 21 q^{7} + 95 q^{8} + 121 q^{9} + 36 q^{10} + 40 q^{11} + 24 q^{12} + 52 q^{13} + 21 q^{14} + 15 q^{15} + 95 q^{16} + 84 q^{17} + 121 q^{18} + 37 q^{19} + 36 q^{20} + 36 q^{21} + 40 q^{22} + 37 q^{23} + 24 q^{24} + 133 q^{25} + 52 q^{26} + 93 q^{27} + 21 q^{28} + 66 q^{29} + 15 q^{30} + 10 q^{31} + 95 q^{32} + 63 q^{33} + 84 q^{34} + 55 q^{35} + 121 q^{36} + 49 q^{37} + 37 q^{38} + 14 q^{39} + 36 q^{40} + 98 q^{41} + 36 q^{42} + 37 q^{43} + 40 q^{44} + 97 q^{45} + 37 q^{46} + 91 q^{47} + 24 q^{48} + 170 q^{49} + 133 q^{50} + 22 q^{51} + 52 q^{52} + 70 q^{53} + 93 q^{54} - q^{55} + 21 q^{56} + 50 q^{57} + 66 q^{58} + 72 q^{59} + 15 q^{60} + 97 q^{61} + 10 q^{62} + 75 q^{63} + 95 q^{64} + 75 q^{65} + 63 q^{66} + 39 q^{67} + 84 q^{68} + 65 q^{69} + 55 q^{70} + 28 q^{71} + 121 q^{72} + 117 q^{73} + 49 q^{74} + 62 q^{75} + 37 q^{76} + 92 q^{77} + 14 q^{78} + q^{79} + 36 q^{80} + 155 q^{81} + 98 q^{82} + 117 q^{83} + 36 q^{84} + 81 q^{85} + 37 q^{86} + 46 q^{87} + 40 q^{88} + 90 q^{89} + 97 q^{90} + 65 q^{91} + 37 q^{92} + 36 q^{93} + 91 q^{94} + 38 q^{95} + 24 q^{96} + 111 q^{97} + 170 q^{98} + 97 q^{99}+O(q^{100}) \) 95 * q + 95 * q^2 + 24 * q^3 + 95 * q^4 + 36 * q^5 + 24 * q^6 + 21 * q^7 + 95 * q^8 + 121 * q^9 + 36 * q^10 + 40 * q^11 + 24 * q^12 + 52 * q^13 + 21 * q^14 + 15 * q^15 + 95 * q^16 + 84 * q^17 + 121 * q^18 + 37 * q^19 + 36 * q^20 + 36 * q^21 + 40 * q^22 + 37 * q^23 + 24 * q^24 + 133 * q^25 + 52 * q^26 + 93 * q^27 + 21 * q^28 + 66 * q^29 + 15 * q^30 + 10 * q^31 + 95 * q^32 + 63 * q^33 + 84 * q^34 + 55 * q^35 + 121 * q^36 + 49 * q^37 + 37 * q^38 + 14 * q^39 + 36 * q^40 + 98 * q^41 + 36 * q^42 + 37 * q^43 + 40 * q^44 + 97 * q^45 + 37 * q^46 + 91 * q^47 + 24 * q^48 + 170 * q^49 + 133 * q^50 + 22 * q^51 + 52 * q^52 + 70 * q^53 + 93 * q^54 - q^55 + 21 * q^56 + 50 * q^57 + 66 * q^58 + 72 * q^59 + 15 * q^60 + 97 * q^61 + 10 * q^62 + 75 * q^63 + 95 * q^64 + 75 * q^65 + 63 * q^66 + 39 * q^67 + 84 * q^68 + 65 * q^69 + 55 * q^70 + 28 * q^71 + 121 * q^72 + 117 * q^73 + 49 * q^74 + 62 * q^75 + 37 * q^76 + 92 * q^77 + 14 * q^78 + q^79 + 36 * q^80 + 155 * q^81 + 98 * q^82 + 117 * q^83 + 36 * q^84 + 81 * q^85 + 37 * q^86 + 46 * q^87 + 40 * q^88 + 90 * q^89 + 97 * q^90 + 65 * q^91 + 37 * q^92 + 36 * q^93 + 91 * q^94 + 38 * q^95 + 24 * q^96 + 111 * q^97 + 170 * q^98 + 97 * q^99

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