LMFDB - Embedded newform 8041.2.a.i.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8041,2,Mod(1,8041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8041, 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("8041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8041 = 11 \cdot 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8041.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$64.2077082653$
Analytic rank:	$0$
Dimension:	$78$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	8041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.81193 q^{2} +3.07426 q^{3} +5.90697 q^{4} +1.69870 q^{5} -8.64463 q^{6} +0.0326130 q^{7} -10.9861 q^{8} +6.45110 q^{9} +O(q^{10})$	\(q-2.81193 q^{2} +3.07426 q^{3} +5.90697 q^{4} +1.69870 q^{5} -8.64463 q^{6} +0.0326130 q^{7} -10.9861 q^{8} +6.45110 q^{9} -4.77662 q^{10} +1.00000 q^{11} +18.1596 q^{12} -1.17718 q^{13} -0.0917056 q^{14} +5.22224 q^{15} +19.0784 q^{16} -1.00000 q^{17} -18.1401 q^{18} +1.55104 q^{19} +10.0341 q^{20} +0.100261 q^{21} -2.81193 q^{22} -2.46839 q^{23} -33.7743 q^{24} -2.11443 q^{25} +3.31015 q^{26} +10.6096 q^{27} +0.192644 q^{28} +8.97486 q^{29} -14.6846 q^{30} -0.677587 q^{31} -31.6748 q^{32} +3.07426 q^{33} +2.81193 q^{34} +0.0553996 q^{35} +38.1065 q^{36} -3.61383 q^{37} -4.36143 q^{38} -3.61896 q^{39} -18.6621 q^{40} -5.83154 q^{41} -0.281927 q^{42} -1.00000 q^{43} +5.90697 q^{44} +10.9585 q^{45} +6.94094 q^{46} +9.03871 q^{47} +58.6520 q^{48} -6.99894 q^{49} +5.94565 q^{50} -3.07426 q^{51} -6.95357 q^{52} -2.98614 q^{53} -29.8335 q^{54} +1.69870 q^{55} -0.358291 q^{56} +4.76832 q^{57} -25.2367 q^{58} +9.48257 q^{59} +30.8476 q^{60} +0.450285 q^{61} +1.90533 q^{62} +0.210390 q^{63} +50.9108 q^{64} -1.99967 q^{65} -8.64463 q^{66} +6.42090 q^{67} -5.90697 q^{68} -7.58847 q^{69} -0.155780 q^{70} +10.2825 q^{71} -70.8727 q^{72} +10.9510 q^{73} +10.1619 q^{74} -6.50032 q^{75} +9.16198 q^{76} +0.0326130 q^{77} +10.1763 q^{78} -8.83713 q^{79} +32.4084 q^{80} +13.2634 q^{81} +16.3979 q^{82} +16.2738 q^{83} +0.592239 q^{84} -1.69870 q^{85} +2.81193 q^{86} +27.5911 q^{87} -10.9861 q^{88} +11.5341 q^{89} -30.8144 q^{90} -0.0383914 q^{91} -14.5807 q^{92} -2.08308 q^{93} -25.4162 q^{94} +2.63475 q^{95} -97.3768 q^{96} +2.98376 q^{97} +19.6805 q^{98} +6.45110 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 78 q + 7 q^{2} + 10 q^{3} + 91 q^{4} + 17 q^{5} + 12 q^{6} + 11 q^{7} + 33 q^{8} + 102 q^{9}+O(q^{10}) $ 78 * q + 7 * q^2 + 10 * q^3 + 91 * q^4 + 17 * q^5 + 12 * q^6 + 11 * q^7 + 33 * q^8 + 102 * q^9	\( 78 q + 7 q^{2} + 10 q^{3} + 91 q^{4} + 17 q^{5} + 12 q^{6} + 11 q^{7} + 33 q^{8} + 102 q^{9} + 3 q^{10} + 78 q^{11} + 31 q^{12} - 16 q^{13} + 31 q^{14} + 38 q^{15} + 121 q^{16} - 78 q^{17} + 11 q^{18} + 51 q^{20} + 6 q^{21} + 7 q^{22} + 48 q^{23} + 11 q^{24} + 101 q^{25} + 18 q^{26} + 46 q^{27} + 27 q^{28} + 22 q^{29} + 14 q^{30} + 56 q^{31} + 83 q^{32} + 10 q^{33} - 7 q^{34} + 24 q^{35} + 139 q^{36} + 53 q^{37} + 10 q^{38} + 79 q^{39} - q^{40} + 23 q^{41} + 17 q^{42} - 78 q^{43} + 91 q^{44} + 76 q^{45} + 21 q^{46} + 57 q^{47} + 78 q^{48} + 115 q^{49} + 58 q^{50} - 10 q^{51} - 63 q^{52} + 22 q^{53} - 18 q^{54} + 17 q^{55} + 111 q^{56} - 11 q^{57} + 36 q^{58} + 71 q^{59} + 36 q^{60} + 4 q^{61} - 5 q^{62} + 71 q^{63} + 183 q^{64} + 47 q^{65} + 12 q^{66} + 11 q^{67} - 91 q^{68} + 31 q^{69} + 33 q^{70} + 159 q^{71} + 59 q^{72} + 2 q^{73} - 4 q^{74} + 83 q^{75} - 44 q^{76} + 11 q^{77} + 101 q^{78} + 35 q^{79} + 85 q^{80} + 170 q^{81} + 98 q^{82} - 32 q^{83} + 44 q^{84} - 17 q^{85} - 7 q^{86} - 6 q^{87} + 33 q^{88} + 50 q^{89} - 5 q^{90} + 86 q^{91} + 106 q^{92} + 68 q^{93} - q^{94} + 109 q^{95} - 50 q^{96} + 40 q^{97} + 106 q^{98} + 102 q^{99}+O(q^{100}) \) 78 * q + 7 * q^2 + 10 * q^3 + 91 * q^4 + 17 * q^5 + 12 * q^6 + 11 * q^7 + 33 * q^8 + 102 * q^9 + 3 * q^10 + 78 * q^11 + 31 * q^12 - 16 * q^13 + 31 * q^14 + 38 * q^15 + 121 * q^16 - 78 * q^17 + 11 * q^18 + 51 * q^20 + 6 * q^21 + 7 * q^22 + 48 * q^23 + 11 * q^24 + 101 * q^25 + 18 * q^26 + 46 * q^27 + 27 * q^28 + 22 * q^29 + 14 * q^30 + 56 * q^31 + 83 * q^32 + 10 * q^33 - 7 * q^34 + 24 * q^35 + 139 * q^36 + 53 * q^37 + 10 * q^38 + 79 * q^39 - q^40 + 23 * q^41 + 17 * q^42 - 78 * q^43 + 91 * q^44 + 76 * q^45 + 21 * q^46 + 57 * q^47 + 78 * q^48 + 115 * q^49 + 58 * q^50 - 10 * q^51 - 63 * q^52 + 22 * q^53 - 18 * q^54 + 17 * q^55 + 111 * q^56 - 11 * q^57 + 36 * q^58 + 71 * q^59 + 36 * q^60 + 4 * q^61 - 5 * q^62 + 71 * q^63 + 183 * q^64 + 47 * q^65 + 12 * q^66 + 11 * q^67 - 91 * q^68 + 31 * q^69 + 33 * q^70 + 159 * q^71 + 59 * q^72 + 2 * q^73 - 4 * q^74 + 83 * q^75 - 44 * q^76 + 11 * q^77 + 101 * q^78 + 35 * q^79 + 85 * q^80 + 170 * q^81 + 98 * q^82 - 32 * q^83 + 44 * q^84 - 17 * q^85 - 7 * q^86 - 6 * q^87 + 33 * q^88 + 50 * q^89 - 5 * q^90 + 86 * q^91 + 106 * q^92 + 68 * q^93 - q^94 + 109 * q^95 - 50 * q^96 + 40 * q^97 + 106 * q^98 + 102 * 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 $

$2$	−2.81193	−1.98834	−0.994169	−	0.107835i	$-0.965608\pi$
$2$	−2.81193	−1.98834	−0.994169	+	0.107835i	$0.965608\pi$
$3$	3.07426	1.77493	0.887464	−	0.460878i	$-0.152465\pi$
$3$	3.07426	1.77493	0.887464	+	0.460878i	$0.152465\pi$
$4$	5.90697	2.95349
$5$	1.69870	0.759680	0.379840	−	0.925052i	$-0.375979\pi$
$5$	1.69870	0.759680	0.379840	+	0.925052i	$0.375979\pi$
$6$	−8.64463	−3.52915
$7$	0.0326130	0.0123266	0.00616328	−	0.999981i	$-0.498038\pi$
$7$	0.0326130	0.0123266	0.00616328	+	0.999981i	$0.498038\pi$
$8$	−10.9861	−3.88419
$9$	6.45110	2.15037
$10$	−4.77662	−1.51050
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	18.1596	5.24222
$13$	−1.17718	−0.326491	−0.163245	−	0.986585i	$-0.552196\pi$
$13$	−1.17718	−0.326491	−0.163245	+	0.986585i	$0.552196\pi$
$14$	−0.0917056	−0.0245094
$15$	5.22224	1.34838
$16$	19.0784	4.76959
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−18.1401	−4.27565
$19$	1.55104	0.355834	0.177917	−	0.984045i	$-0.443064\pi$
$19$	1.55104	0.355834	0.177917	+	0.984045i	$0.443064\pi$
$20$	10.0341	2.24370
$21$	0.100261	0.0218787
$22$	−2.81193	−0.599506
$23$	−2.46839	−0.514694	−0.257347	−	0.966319i	$-0.582848\pi$
$23$	−2.46839	−0.514694	−0.257347	+	0.966319i	$0.582848\pi$
$24$	−33.7743	−6.89415
$25$	−2.11443	−0.422887
$26$	3.31015	0.649174
$27$	10.6096	2.04182
$28$	0.192644	0.0364063
$29$	8.97486	1.66659	0.833295	−	0.552829i	$-0.186452\pi$
$29$	8.97486	1.66659	0.833295	+	0.552829i	$0.186452\pi$
$30$	−14.6846	−2.68103
$31$	−0.677587	−0.121698	−0.0608492	−	0.998147i	$-0.519381\pi$
$31$	−0.677587	−0.121698	−0.0608492	+	0.998147i	$0.519381\pi$
$32$	−31.6748	−5.59937
$33$	3.07426	0.535161
$34$	2.81193	0.482243
$35$	0.0553996	0.00936424
$36$	38.1065	6.35108
$37$	−3.61383	−0.594111	−0.297055	−	0.954860i	$-0.596005\pi$
$37$	−3.61383	−0.594111	−0.297055	+	0.954860i	$0.596005\pi$
$38$	−4.36143	−0.707518
$39$	−3.61896	−0.579498
$40$	−18.6621	−2.95074
$41$	−5.83154	−0.910734	−0.455367	−	0.890304i	$-0.650492\pi$
$41$	−5.83154	−0.910734	−0.455367	+	0.890304i	$0.650492\pi$
$42$	−0.281927	−0.0435023
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	5.90697	0.890510
$45$	10.9585	1.63359
$46$	6.94094	1.02339
$47$	9.03871	1.31843	0.659215	−	0.751954i	$-0.270889\pi$
$47$	9.03871	1.31843	0.659215	+	0.751954i	$0.270889\pi$
$48$	58.6520	8.46568
$49$	−6.99894	−0.999848
$50$	5.94565	0.840841
$51$	−3.07426	−0.430483
$52$	−6.95357	−0.964287
$53$	−2.98614	−0.410178	−0.205089	−	0.978743i	$-0.565748\pi$
$53$	−2.98614	−0.410178	−0.205089	+	0.978743i	$0.565748\pi$
$54$	−29.8335	−4.05982
$55$	1.69870	0.229052
$56$	−0.358291	−0.0478787
$57$	4.76832	0.631579
$58$	−25.2367	−3.31374
$59$	9.48257	1.23453	0.617263	−	0.786757i	$-0.288242\pi$
$59$	9.48257	1.23453	0.617263	+	0.786757i	$0.288242\pi$
$60$	30.8476	3.98241
$61$	0.450285	0.0576531	0.0288266	−	0.999584i	$-0.490823\pi$
$61$	0.450285	0.0576531	0.0288266	+	0.999584i	$0.490823\pi$
$62$	1.90533	0.241977
$63$	0.210390	0.0265066
$64$	50.9108	6.36385
$65$	−1.99967	−0.248029
$66$	−8.64463	−1.06408
$67$	6.42090	0.784438	0.392219	−	0.919872i	$-0.371707\pi$
$67$	6.42090	0.784438	0.392219	+	0.919872i	$0.371707\pi$
$68$	−5.90697	−0.716326
$69$	−7.58847	−0.913544
$70$	−0.155780	−0.0186193
$71$	10.2825	1.22031	0.610153	−	0.792284i	$-0.291108\pi$
$71$	10.2825	1.22031	0.610153	+	0.792284i	$0.291108\pi$
$72$	−70.8727	−8.35243
$73$	10.9510	1.28172	0.640858	−	0.767659i	$-0.278579\pi$
$73$	10.9510	1.28172	0.640858	+	0.767659i	$0.278579\pi$
$74$	10.1619	1.18129
$75$	−6.50032	−0.750593
$76$	9.16198	1.05095
$77$	0.0326130	0.00371660
$78$	10.1763	1.15224
$79$	−8.83713	−0.994255	−0.497127	−	0.867678i	$-0.665612\pi$
$79$	−8.83713	−0.994255	−0.497127	+	0.867678i	$0.665612\pi$
$80$	32.4084	3.62336
$81$	13.2634	1.47371
$82$	16.3979	1.81085
$83$	16.2738	1.78628	0.893142	−	0.449774i	$-0.148495\pi$
$83$	16.2738	1.78628	0.893142	+	0.449774i	$0.148495\pi$
$84$	0.592239	0.0646186
$85$	−1.69870	−0.184249
$86$	2.81193	0.303219
$87$	27.5911	2.95808
$88$	−10.9861	−1.17113
$89$	11.5341	1.22262	0.611308	−	0.791392i	$-0.290643\pi$
$89$	11.5341	1.22262	0.611308	+	0.791392i	$0.290643\pi$
$90$	−30.8144	−3.24813
$91$	−0.0383914	−0.00402451
$92$	−14.5807	−1.52014
$93$	−2.08308	−0.216006
$94$	−25.4162	−2.62149
$95$	2.63475	0.270320
$96$	−97.3768	−9.93848
$97$	2.98376	0.302955	0.151478	−	0.988461i	$-0.451597\pi$
$97$	2.98376	0.302955	0.151478	+	0.988461i	$0.451597\pi$
$98$	19.6805	1.98804
$99$	6.45110	0.648360
$100$	−12.4899	−1.24899
$101$	15.8751	1.57963	0.789814	−	0.613346i	$-0.210177\pi$
$101$	15.8751	1.57963	0.789814	+	0.613346i	$0.210177\pi$
$102$	8.64463	0.855946
$103$	−2.64399	−0.260520	−0.130260	−	0.991480i	$-0.541581\pi$
$103$	−2.64399	−0.260520	−0.130260	+	0.991480i	$0.541581\pi$
$104$	12.9327	1.26815
$105$	0.170313	0.0166208
$106$	8.39682	0.815572
$107$	0.540692	0.0522707	0.0261354	−	0.999658i	$-0.491680\pi$
$107$	0.540692	0.0522707	0.0261354	+	0.999658i	$0.491680\pi$
$108$	62.6705	6.03048
$109$	3.08817	0.295793	0.147897	−	0.989003i	$-0.452750\pi$
$109$	3.08817	0.295793	0.147897	+	0.989003i	$0.452750\pi$
$110$	−4.77662	−0.455433
$111$	−11.1099	−1.05450
$112$	0.622203	0.0587927
$113$	13.9382	1.31119	0.655596	−	0.755112i	$-0.272417\pi$
$113$	13.9382	1.31119	0.655596	+	0.755112i	$0.272417\pi$
$114$	−13.4082	−1.25579
$115$	−4.19304	−0.391003
$116$	53.0142	4.92225
$117$	−7.59410	−0.702075
$118$	−26.6644	−2.45465
$119$	−0.0326130	−0.00298963
$120$	−57.3723	−5.23735
$121$	1.00000	0.0909091
$122$	−1.26617	−0.114634
$123$	−17.9277	−1.61649
$124$	−4.00249	−0.359434
$125$	−12.0853	−1.08094
$126$	−0.591602	−0.0527041
$127$	−6.74189	−0.598246	−0.299123	−	0.954215i	$-0.596694\pi$
$127$	−6.74189	−0.598246	−0.299123	+	0.954215i	$0.596694\pi$
$128$	−79.8081	−7.05411
$129$	−3.07426	−0.270674
$130$	5.62294	0.493165
$131$	−20.3984	−1.78222	−0.891108	−	0.453791i	$-0.850071\pi$
$131$	−20.3984	−1.78222	−0.891108	+	0.453791i	$0.850071\pi$
$132$	18.1596	1.58059
$133$	0.0505842	0.00438621
$134$	−18.0552	−1.55973
$135$	18.0225	1.55113
$136$	10.9861	0.942054
$137$	4.73957	0.404928	0.202464	−	0.979290i	$-0.435105\pi$
$137$	4.73957	0.404928	0.202464	+	0.979290i	$0.435105\pi$
$138$	21.3383	1.81643
$139$	2.72694	0.231296	0.115648	−	0.993290i	$-0.463106\pi$
$139$	2.72694	0.231296	0.115648	+	0.993290i	$0.463106\pi$
$140$	0.327244	0.0276571
$141$	27.7874	2.34012
$142$	−28.9136	−2.42638
$143$	−1.17718	−0.0984407
$144$	123.076	10.2564
$145$	15.2456	1.26607
$146$	−30.7935	−2.54848
$147$	−21.5166	−1.77466
$148$	−21.3468	−1.75470
$149$	−4.21569	−0.345363	−0.172682	−	0.984978i	$-0.555243\pi$
$149$	−4.21569	−0.345363	−0.172682	+	0.984978i	$0.555243\pi$
$150$	18.2785	1.49243
$151$	6.20840	0.505232	0.252616	−	0.967567i	$-0.418709\pi$
$151$	6.20840	0.505232	0.252616	+	0.967567i	$0.418709\pi$
$152$	−17.0400	−1.38213
$153$	−6.45110	−0.521540
$154$	−0.0917056	−0.00738985
$155$	−1.15101	−0.0924517
$156$	−21.3771	−1.71154
$157$	−17.3047	−1.38106	−0.690532	−	0.723302i	$-0.742623\pi$
$157$	−17.3047	−1.38106	−0.690532	+	0.723302i	$0.742623\pi$
$158$	24.8494	1.97691
$159$	−9.18018	−0.728035
$160$	−53.8059	−4.25373
$161$	−0.0805015	−0.00634441
$162$	−37.2957	−2.93023
$163$	−8.23562	−0.645064	−0.322532	−	0.946559i	$-0.604534\pi$
$163$	−8.23562	−0.645064	−0.322532	+	0.946559i	$0.604534\pi$
$164$	−34.4468	−2.68984
$165$	5.22224	0.406551
$166$	−45.7609	−3.55174
$167$	−2.78341	−0.215387	−0.107693	−	0.994184i	$-0.534346\pi$
$167$	−2.78341	−0.215387	−0.107693	+	0.994184i	$0.534346\pi$
$168$	−1.10148	−0.0849812
$169$	−11.6142	−0.893404
$170$	4.77662	0.366350
$171$	10.0059	0.765173
$172$	−5.90697	−0.450402
$173$	13.1682	1.00116	0.500579	−	0.865691i	$-0.333120\pi$
$173$	13.1682	1.00116	0.500579	+	0.865691i	$0.333120\pi$
$174$	−77.5843	−5.88165
$175$	−0.0689580	−0.00521274
$176$	19.0784	1.43809
$177$	29.1519	2.19119
$178$	−32.4333	−2.43098
$179$	−1.33522	−0.0997991	−0.0498995	−	0.998754i	$-0.515890\pi$
$179$	−1.33522	−0.0997991	−0.0498995	+	0.998754i	$0.515890\pi$
$180$	64.7313	4.82478
$181$	17.2141	1.27951	0.639756	−	0.768578i	$-0.279035\pi$
$181$	17.2141	1.27951	0.639756	+	0.768578i	$0.279035\pi$
$182$	0.107954	0.00800209
$183$	1.38430	0.102330
$184$	27.1180	1.99917
$185$	−6.13881	−0.451334
$186$	5.85749	0.429492
$187$	−1.00000	−0.0731272
$188$	53.3914	3.89397
$189$	0.346011	0.0251686
$190$	−7.40875	−0.537487
$191$	19.6559	1.42225	0.711125	−	0.703065i	$-0.248186\pi$
$191$	19.6559	1.42225	0.711125	+	0.703065i	$0.248186\pi$
$192$	156.513	11.2954
$193$	17.1004	1.23091	0.615457	−	0.788170i	$-0.288971\pi$
$193$	17.1004	1.23091	0.615457	+	0.788170i	$0.288971\pi$
$194$	−8.39015	−0.602377
$195$	−6.14751	−0.440233
$196$	−41.3425	−2.95304
$197$	10.4384	0.743704	0.371852	−	0.928292i	$-0.378723\pi$
$197$	10.4384	0.743704	0.371852	+	0.928292i	$0.378723\pi$
$198$	−18.1401	−1.28916
$199$	10.0793	0.714499	0.357250	−	0.934009i	$-0.383715\pi$
$199$	10.0793	0.714499	0.357250	+	0.934009i	$0.383715\pi$
$200$	23.2295	1.64257
$201$	19.7396	1.39232
$202$	−44.6396	−3.14083
$203$	0.292697	0.0205433
$204$	−18.1596	−1.27143
$205$	−9.90602	−0.691866
$206$	7.43473	0.518002
$207$	−15.9238	−1.10678
$208$	−22.4587	−1.55723
$209$	1.55104	0.107288
$210$	−0.478909	−0.0330478
$211$	13.2565	0.912612	0.456306	−	0.889823i	$-0.349172\pi$
$211$	13.2565	0.912612	0.456306	+	0.889823i	$0.349172\pi$
$212$	−17.6390	−1.21145
$213$	31.6110	2.16595
$214$	−1.52039	−0.103932
$215$	−1.69870	−0.115850
$216$	−116.559	−7.93080
$217$	−0.0220982	−0.00150012
$218$	−8.68373	−0.588136
$219$	33.6662	2.27495
$220$	10.0341	0.676502
$221$	1.17718	0.0791857
$222$	31.2403	2.09671
$223$	8.69610	0.582334	0.291167	−	0.956672i	$-0.405956\pi$
$223$	8.69610	0.582334	0.291167	+	0.956672i	$0.405956\pi$
$224$	−1.03301	−0.0690210
$225$	−13.6404	−0.909361
$226$	−39.1932	−2.60709
$227$	−26.5657	−1.76322	−0.881612	−	0.471974i	$-0.843541\pi$
$227$	−26.5657	−1.76322	−0.881612	+	0.471974i	$0.843541\pi$
$228$	28.1663	1.86536
$229$	11.8858	0.785439	0.392719	−	0.919658i	$-0.371534\pi$
$229$	11.8858	0.785439	0.392719	+	0.919658i	$0.371534\pi$
$230$	11.7905	0.777445
$231$	0.100261	0.00659669
$232$	−98.5991	−6.47335
$233$	13.6653	0.895246	0.447623	−	0.894222i	$-0.352271\pi$
$233$	13.6653	0.895246	0.447623	+	0.894222i	$0.352271\pi$
$234$	21.3541	1.39596
$235$	15.3540	1.00159
$236$	56.0133	3.64615
$237$	−27.1677	−1.76473
$238$	0.0917056	0.00594439
$239$	29.6433	1.91746	0.958732	−	0.284312i	$-0.0917652\pi$
$239$	29.6433	1.91746	0.958732	+	0.284312i	$0.0917652\pi$
$240$	99.6318	6.43121
$241$	−5.38697	−0.347005	−0.173503	−	0.984833i	$-0.555508\pi$
$241$	−5.38697	−0.347005	−0.173503	+	0.984833i	$0.555508\pi$
$242$	−2.81193	−0.180758
$243$	8.94636	0.573909
$244$	2.65982	0.170278
$245$	−11.8891	−0.759564
$246$	50.4115	3.21412
$247$	−1.82586	−0.116177
$248$	7.44408	0.472699
$249$	50.0301	3.17053
$250$	33.9829	2.14927
$251$	−11.6181	−0.733328	−0.366664	−	0.930353i	$-0.619500\pi$
$251$	−11.6181	−0.733328	−0.366664	+	0.930353i	$0.619500\pi$
$252$	1.24277	0.0782869
$253$	−2.46839	−0.155186
$254$	18.9578	1.18952
$255$	−5.22224	−0.327029
$256$	122.594	7.66210
$257$	−24.0147	−1.49799	−0.748997	−	0.662573i	$-0.769464\pi$
$257$	−24.0147	−1.49799	−0.748997	+	0.662573i	$0.769464\pi$
$258$	8.64463	0.538191
$259$	−0.117858	−0.00732334
$260$	−11.8120	−0.732549
$261$	57.8977	3.58378
$262$	57.3590	3.54365
$263$	−12.4444	−0.767357	−0.383678	−	0.923467i	$-0.625343\pi$
$263$	−12.4444	−0.767357	−0.383678	+	0.923467i	$0.625343\pi$
$264$	−33.7743	−2.07867
$265$	−5.07254	−0.311604
$266$	−0.142240	−0.00872126
$267$	35.4590	2.17006
$268$	37.9281	2.31683
$269$	25.4060	1.54903	0.774516	−	0.632554i	$-0.217993\pi$
$269$	25.4060	1.54903	0.774516	+	0.632554i	$0.217993\pi$
$270$	−50.6780	−3.08416
$271$	5.23651	0.318095	0.159048	−	0.987271i	$-0.449158\pi$
$271$	5.23651	0.318095	0.159048	+	0.987271i	$0.449158\pi$
$272$	−19.0784	−1.15680
$273$	−0.118025	−0.00714321
$274$	−13.3273	−0.805134
$275$	−2.11443	−0.127505
$276$	−44.8249	−2.69814
$277$	−3.10858	−0.186776	−0.0933882	−	0.995630i	$-0.529770\pi$
$277$	−3.10858	−0.186776	−0.0933882	+	0.995630i	$0.529770\pi$
$278$	−7.66797	−0.459894
$279$	−4.37118	−0.261696
$280$	−0.608628	−0.0363725
$281$	13.2004	0.787470	0.393735	−	0.919224i	$-0.371183\pi$
$281$	13.2004	0.787470	0.393735	+	0.919224i	$0.371183\pi$
$282$	−78.1362	−4.65295
$283$	0.683904	0.0406539	0.0203269	−	0.999793i	$-0.493529\pi$
$283$	0.683904	0.0406539	0.0203269	+	0.999793i	$0.493529\pi$
$284$	60.7383	3.60416
$285$	8.09992	0.479798
$286$	3.31015	0.195733
$287$	−0.190184	−0.0112262
$288$	−204.338	−12.0407
$289$	1.00000	0.0588235
$290$	−42.8695	−2.51738
$291$	9.17288	0.537724
$292$	64.6872	3.78553
$293$	3.34223	0.195255	0.0976276	−	0.995223i	$-0.468875\pi$
$293$	3.34223	0.195255	0.0976276	+	0.995223i	$0.468875\pi$
$294$	60.5032	3.52862
$295$	16.1080	0.937844
$296$	39.7021	2.30764
$297$	10.6096	0.615631
$298$	11.8543	0.686698
$299$	2.90573	0.168043
$300$	−38.3972	−2.21687
$301$	−0.0326130	−0.00187978
$302$	−17.4576	−1.00457
$303$	48.8041	2.80372
$304$	29.5914	1.69718
$305$	0.764898	0.0437979
$306$	18.1401	1.03700
$307$	−32.4504	−1.85204	−0.926021	−	0.377473i	$-0.876793\pi$
$307$	−32.4504	−1.85204	−0.926021	+	0.377473i	$0.876793\pi$
$308$	0.192644	0.0109769
$309$	−8.12833	−0.462405
$310$	3.23658	0.183825
$311$	−25.7160	−1.45822	−0.729109	−	0.684398i	$-0.760065\pi$
$311$	−25.7160	−1.45822	−0.729109	+	0.684398i	$0.760065\pi$
$312$	39.7585	2.25088
$313$	−10.3094	−0.582720	−0.291360	−	0.956614i	$-0.594108\pi$
$313$	−10.3094	−0.582720	−0.291360	+	0.956614i	$0.594108\pi$
$314$	48.6596	2.74602
$315$	0.357388	0.0201365
$316$	−52.2007	−2.93652
$317$	−24.9625	−1.40204	−0.701018	−	0.713143i	$-0.747271\pi$
$317$	−24.9625	−1.40204	−0.701018	+	0.713143i	$0.747271\pi$
$318$	25.8141	1.44758
$319$	8.97486	0.502496
$320$	86.4820	4.83449
$321$	1.66223	0.0927767
$322$	0.226365	0.0126148
$323$	−1.55104	−0.0863024
$324$	78.3464	4.35258
$325$	2.48907	0.138069
$326$	23.1580	1.28260
$327$	9.49385	0.525011
$328$	64.0662	3.53746
$329$	0.294779	0.0162517
$330$	−14.6846	−0.808360
$331$	4.43030	0.243511	0.121756	−	0.992560i	$-0.461148\pi$
$331$	4.43030	0.243511	0.121756	+	0.992560i	$0.461148\pi$
$332$	96.1291	5.27577
$333$	−23.3132	−1.27756
$334$	7.82676	0.428261
$335$	10.9072	0.595922
$336$	1.91282	0.104353
$337$	17.5446	0.955717	0.477858	−	0.878437i	$-0.341413\pi$
$337$	17.5446	0.955717	0.477858	+	0.878437i	$0.341413\pi$
$338$	32.6585	1.77639
$339$	42.8496	2.32727
$340$	−10.0341	−0.544178
$341$	−0.677587	−0.0366934
$342$	−28.1360	−1.52142
$343$	−0.456547	−0.0246512
$344$	10.9861	0.592333
$345$	−12.8905	−0.694001
$346$	−37.0281	−1.99064
$347$	−27.3480	−1.46812	−0.734060	−	0.679085i	$-0.762377\pi$
$347$	−27.3480	−1.46812	−0.734060	+	0.679085i	$0.762377\pi$
$348$	162.980	8.73663
$349$	−21.4694	−1.14923	−0.574616	−	0.818423i	$-0.694849\pi$
$349$	−21.4694	−1.14923	−0.574616	+	0.818423i	$0.694849\pi$
$350$	0.193905	0.0103647
$351$	−12.4894	−0.666635
$352$	−31.6748	−1.68827
$353$	−0.280768	−0.0149438	−0.00747189	−	0.999972i	$-0.502378\pi$
$353$	−0.280768	−0.0149438	−0.00747189	+	0.999972i	$0.502378\pi$
$354$	−81.9733	−4.35683
$355$	17.4668	0.927042
$356$	68.1319	3.61098
$357$	−0.100261	−0.00530638
$358$	3.75455	0.198434
$359$	16.9686	0.895569	0.447785	−	0.894141i	$-0.352213\pi$
$359$	16.9686	0.895569	0.447785	+	0.894141i	$0.352213\pi$
$360$	−120.391	−6.34517
$361$	−16.5943	−0.873382
$362$	−48.4049	−2.54410
$363$	3.07426	0.161357
$364$	−0.226777	−0.0118863
$365$	18.6024	0.973694
$366$	−3.89255	−0.203467
$367$	2.64662	0.138152	0.0690762	−	0.997611i	$-0.477995\pi$
$367$	2.64662	0.138152	0.0690762	+	0.997611i	$0.477995\pi$
$368$	−47.0928	−2.45488
$369$	−37.6199	−1.95841
$370$	17.2619	0.897404
$371$	−0.0973870	−0.00505608
$372$	−12.3047	−0.637970
$373$	−11.7339	−0.607560	−0.303780	−	0.952742i	$-0.598249\pi$
$373$	−11.7339	−0.607560	−0.303780	+	0.952742i	$0.598249\pi$
$374$	2.81193	0.145402
$375$	−37.1533	−1.91859
$376$	−99.3006	−5.12104
$377$	−10.5650	−0.544126
$378$	−0.972959	−0.0500436
$379$	−13.3780	−0.687183	−0.343592	−	0.939119i	$-0.611644\pi$
$379$	−13.3780	−0.687183	−0.343592	+	0.939119i	$0.611644\pi$
$380$	15.5634	0.798386
$381$	−20.7264	−1.06184
$382$	−55.2711	−2.82791
$383$	11.9949	0.612909	0.306455	−	0.951885i	$-0.400857\pi$
$383$	11.9949	0.612909	0.306455	+	0.951885i	$0.400857\pi$
$384$	−245.351	−12.5205
$385$	0.0553996	0.00282342
$386$	−48.0852	−2.44747
$387$	−6.45110	−0.327928
$388$	17.6250	0.894774
$389$	13.0047	0.659364	0.329682	−	0.944092i	$-0.393058\pi$
$389$	13.0047	0.659364	0.329682	+	0.944092i	$0.393058\pi$
$390$	17.2864	0.875331
$391$	2.46839	0.124832
$392$	76.8914	3.88360
$393$	−62.7101	−3.16330
$394$	−29.3521	−1.47874
$395$	−15.0116	−0.755315
$396$	38.1065	1.91492
$397$	−6.23401	−0.312876	−0.156438	−	0.987688i	$-0.550001\pi$
$397$	−6.23401	−0.312876	−0.156438	+	0.987688i	$0.550001\pi$
$398$	−28.3422	−1.42067
$399$	0.155509	0.00778520
$400$	−40.3399	−2.01700
$401$	4.45609	0.222527	0.111263	−	0.993791i	$-0.464510\pi$
$401$	4.45609	0.222527	0.111263	+	0.993791i	$0.464510\pi$
$402$	−55.5063	−2.76840
$403$	0.797642	0.0397334
$404$	93.7736	4.66541
$405$	22.5304	1.11955
$406$	−0.823045	−0.0408470
$407$	−3.61383	−0.179131
$408$	33.7743	1.67208
$409$	20.9966	1.03821	0.519107	−	0.854709i	$-0.326265\pi$
$409$	20.9966	1.03821	0.519107	+	0.854709i	$0.326265\pi$
$410$	27.8551	1.37566
$411$	14.5707	0.718718
$412$	−15.6180	−0.769443
$413$	0.309255	0.0152174
$414$	44.7767	2.20065
$415$	27.6443	1.35700
$416$	37.2870	1.82814
$417$	8.38333	0.410533
$418$	−4.36143	−0.213325
$419$	−5.35864	−0.261787	−0.130893	−	0.991396i	$-0.541785\pi$
$419$	−5.35864	−0.261787	−0.130893	+	0.991396i	$0.541785\pi$
$420$	1.00603	0.0490894
$421$	−25.4388	−1.23981	−0.619906	−	0.784676i	$-0.712829\pi$
$421$	−25.4388	−1.23981	−0.619906	+	0.784676i	$0.712829\pi$
$422$	−37.2763	−1.81458
$423$	58.3096	2.83511
$424$	32.8062	1.59321
$425$	2.11443	0.102565
$426$	−88.8882	−4.30665
$427$	0.0146852	0.000710665 0
$428$	3.19386	0.154381
$429$	−3.61896	−0.174725
$430$	4.77662	0.230349
$431$	−0.0597797	−0.00287949	−0.00143974	−	0.999999i	$-0.500458\pi$
$431$	−0.0597797	−0.00287949	−0.00143974	+	0.999999i	$0.500458\pi$
$432$	202.414	9.73864
$433$	−5.52660	−0.265591	−0.132796	−	0.991143i	$-0.542395\pi$
$433$	−5.52660	−0.265591	−0.132796	+	0.991143i	$0.542395\pi$
$434$	0.0621386	0.00298275
$435$	46.8689	2.24719
$436$	18.2417	0.873621
$437$	−3.82858	−0.183146
$438$	−94.6672	−4.52337
$439$	−18.1528	−0.866387	−0.433194	−	0.901301i	$-0.642613\pi$
$439$	−18.1528	−0.866387	−0.433194	+	0.901301i	$0.642613\pi$
$440$	−18.6621	−0.889682
$441$	−45.1508	−2.15004
$442$	−3.31015	−0.157448
$443$	−8.33141	−0.395837	−0.197919	−	0.980218i	$-0.563418\pi$
$443$	−8.33141	−0.395837	−0.197919	+	0.980218i	$0.563418\pi$
$444$	−65.6258	−3.11446
$445$	19.5930	0.928797
$446$	−24.4529	−1.15788
$447$	−12.9602	−0.612994
$448$	1.66035	0.0784444
$449$	30.1074	1.42086	0.710428	−	0.703770i	$-0.248501\pi$
$449$	30.1074	1.42086	0.710428	+	0.703770i	$0.248501\pi$
$450$	38.3559	1.80812
$451$	−5.83154	−0.274597
$452$	82.3324	3.87259
$453$	19.0863	0.896750
$454$	74.7009	3.50589
$455$	−0.0652153	−0.00305734
$456$	−52.3855	−2.45317
$457$	42.0445	1.96676	0.983378	−	0.181568i	$-0.0581171\pi$
$457$	42.0445	1.96676	0.983378	+	0.181568i	$0.0581171\pi$
$458$	−33.4222	−1.56172
$459$	−10.6096	−0.495213
$460$	−24.7681	−1.15482
$461$	−13.4748	−0.627586	−0.313793	−	0.949491i	$-0.601600\pi$
$461$	−13.4748	−0.627586	−0.313793	+	0.949491i	$0.601600\pi$
$462$	−0.281927	−0.0131164
$463$	−42.7892	−1.98858	−0.994292	−	0.106697i	$-0.965972\pi$
$463$	−42.7892	−1.98858	−0.994292	+	0.106697i	$0.965972\pi$
$464$	171.226	7.94896
$465$	−3.53852	−0.164095
$466$	−38.4260	−1.78005
$467$	−21.0739	−0.975182	−0.487591	−	0.873072i	$-0.662124\pi$
$467$	−21.0739	−0.975182	−0.487591	+	0.873072i	$0.662124\pi$
$468$	−44.8582	−2.07357
$469$	0.209405	0.00966943
$470$	−43.1745	−1.99149
$471$	−53.1992	−2.45129
$472$	−104.177	−4.79513
$473$	−1.00000	−0.0459800
$474$	76.3937	3.50888
$475$	−3.27958	−0.150477
$476$	−0.192644	−0.00882983
$477$	−19.2639	−0.882032
$478$	−83.3549	−3.81256
$479$	−25.4396	−1.16237	−0.581183	−	0.813773i	$-0.697410\pi$
$479$	−25.4396	−1.16237	−0.581183	+	0.813773i	$0.697410\pi$
$480$	−165.414	−7.55006
$481$	4.25413	0.193972
$482$	15.1478	0.689963
$483$	−0.247483	−0.0112609
$484$	5.90697	0.268499
$485$	5.06851	0.230149
$486$	−25.1566	−1.14113
$487$	−11.8702	−0.537891	−0.268946	−	0.963155i	$-0.586675\pi$
$487$	−11.8702	−0.537891	−0.268946	+	0.963155i	$0.586675\pi$
$488$	−4.94690	−0.223936
$489$	−25.3185	−1.14494
$490$	33.4313	1.51027
$491$	0.816766	0.0368601	0.0184301	−	0.999830i	$-0.494133\pi$
$491$	0.816766	0.0368601	0.0184301	+	0.999830i	$0.494133\pi$
$492$	−105.898	−4.77427
$493$	−8.97486	−0.404207
$494$	5.13419	0.230998
$495$	10.9585	0.492546
$496$	−12.9273	−0.580452
$497$	0.335343	0.0150422
$498$	−140.681	−6.30408
$499$	31.6757	1.41800	0.709000	−	0.705208i	$-0.249146\pi$
$499$	31.6757	1.41800	0.709000	+	0.705208i	$0.249146\pi$
$500$	−71.3873	−3.19254
$501$	−8.55693	−0.382296
$502$	32.6693	1.45810
$503$	25.7796	1.14946	0.574729	−	0.818344i	$-0.305108\pi$
$503$	25.7796	1.14946	0.574729	+	0.818344i	$0.305108\pi$
$504$	−2.31137	−0.102957
$505$	26.9669	1.20001
$506$	6.94094	0.308562
$507$	−35.7053	−1.58573
$508$	−39.8242	−1.76691
$509$	−4.79531	−0.212548	−0.106274	−	0.994337i	$-0.533892\pi$
$509$	−4.79531	−0.212548	−0.106274	+	0.994337i	$0.533892\pi$
$510$	14.6846	0.650245
$511$	0.357145	0.0157991
$512$	−185.109	−8.18073
$513$	16.4559	0.726548
$514$	67.5277	2.97852
$515$	−4.49134	−0.197912
$516$	−18.1596	−0.799431
$517$	9.03871	0.397522
$518$	0.331409	0.0145613
$519$	40.4825	1.77698
$520$	21.9687	0.963390
$521$	−13.8061	−0.604856	−0.302428	−	0.953172i	$-0.597797\pi$
$521$	−13.8061	−0.604856	−0.302428	+	0.953172i	$0.597797\pi$
$522$	−162.805	−7.12576
$523$	8.39846	0.367239	0.183620	−	0.982997i	$-0.441219\pi$
$523$	8.39846	0.367239	0.183620	+	0.982997i	$0.441219\pi$
$524$	−120.493	−5.26375
$525$	−0.211995	−0.00925223
$526$	34.9929	1.52576
$527$	0.677587	0.0295162
$528$	58.6520	2.55250
$529$	−16.9071	−0.735090
$530$	14.2636	0.619573
$531$	61.1730	2.65468
$532$	0.298800	0.0129546
$533$	6.86477	0.297346
$534$	−99.7084	−4.31480
$535$	0.918472	0.0397090
$536$	−70.5410	−3.04691
$537$	−4.10482	−0.177136
$538$	−71.4400	−3.08000
$539$	−6.99894	−0.301466
$540$	106.458	4.58123
$541$	42.1260	1.81114	0.905569	−	0.424199i	$-0.139444\pi$
$541$	42.1260	1.81114	0.905569	+	0.424199i	$0.139444\pi$
$542$	−14.7247	−0.632481
$543$	52.9206	2.27104
$544$	31.6748	1.35805
$545$	5.24586	0.224708
$546$	0.331879	0.0142031
$547$	−3.75042	−0.160356	−0.0801782	−	0.996781i	$-0.525549\pi$
$547$	−3.75042	−0.160356	−0.0801782	+	0.996781i	$0.525549\pi$
$548$	27.9965	1.19595
$549$	2.90483	0.123975
$550$	5.94565	0.253523
$551$	13.9204	0.593029
$552$	83.3680	3.54838
$553$	−0.288205	−0.0122557
$554$	8.74112	0.371374
$555$	−18.8723	−0.801085
$556$	16.1079	0.683129
$557$	−13.1217	−0.555983	−0.277991	−	0.960584i	$-0.589669\pi$
$557$	−13.1217	−0.555983	−0.277991	+	0.960584i	$0.589669\pi$
$558$	12.2915	0.520340
$559$	1.17718	0.0497894
$560$	1.05693	0.0446636
$561$	−3.07426	−0.129796
$562$	−37.1187	−1.56576
$563$	26.1975	1.10409	0.552046	−	0.833814i	$-0.313847\pi$
$563$	26.1975	1.10409	0.552046	+	0.833814i	$0.313847\pi$
$564$	164.139	6.91151
$565$	23.6767	0.996086
$566$	−1.92309	−0.0808337
$567$	0.432559	0.0181658
$568$	−112.965	−4.73990
$569$	−37.2159	−1.56017	−0.780087	−	0.625672i	$-0.784825\pi$
$569$	−37.2159	−1.56017	−0.780087	+	0.625672i	$0.784825\pi$
$570$	−22.7765	−0.954001
$571$	−16.8575	−0.705464	−0.352732	−	0.935724i	$-0.614747\pi$
$571$	−16.8575	−0.705464	−0.352732	+	0.935724i	$0.614747\pi$
$572$	−6.95357	−0.290743
$573$	60.4274	2.52439
$574$	0.534785	0.0223215
$575$	5.21924	0.217657
$576$	328.431	13.6846
$577$	−10.6421	−0.443037	−0.221519	−	0.975156i	$-0.571101\pi$
$577$	−10.6421	−0.443037	−0.221519	+	0.975156i	$0.571101\pi$
$578$	−2.81193	−0.116961
$579$	52.5712	2.18478
$580$	90.0551	3.73933
$581$	0.530739	0.0220187
$582$	−25.7935	−1.06918
$583$	−2.98614	−0.123673
$584$	−120.309	−4.97843
$585$	−12.9001	−0.533352
$586$	−9.39814	−0.388233
$587$	38.2763	1.57983	0.789915	−	0.613216i	$-0.210124\pi$
$587$	38.2763	1.57983	0.789915	+	0.613216i	$0.210124\pi$
$588$	−127.098	−5.24143
$589$	−1.05097	−0.0433044
$590$	−45.2946	−1.86475
$591$	32.0904	1.32002
$592$	−68.9461	−2.83367
$593$	−24.3197	−0.998690	−0.499345	−	0.866403i	$-0.666426\pi$
$593$	−24.3197	−0.998690	−0.499345	+	0.866403i	$0.666426\pi$
$594$	−29.8335	−1.22408
$595$	−0.0553996	−0.00227116
$596$	−24.9020	−1.02002
$597$	30.9863	1.26818
$598$	−8.17073	−0.334126
$599$	−37.1737	−1.51888	−0.759439	−	0.650578i	$-0.774527\pi$
$599$	−37.1737	−1.51888	−0.759439	+	0.650578i	$0.774527\pi$
$600$	71.4135	2.91545
$601$	−45.3423	−1.84955	−0.924776	−	0.380513i	$-0.875747\pi$
$601$	−45.3423	−1.84955	−0.924776	+	0.380513i	$0.875747\pi$
$602$	0.0917056	0.00373764
$603$	41.4219	1.68683
$604$	36.6728	1.49220
$605$	1.69870	0.0690618
$606$	−137.234	−5.57475
$607$	−23.3124	−0.946219	−0.473110	−	0.881004i	$-0.656869\pi$
$607$	−23.3124	−0.946219	−0.473110	+	0.881004i	$0.656869\pi$
$608$	−49.1291	−1.99245
$609$	0.899828	0.0364629
$610$	−2.15084	−0.0870850
$611$	−10.6402	−0.430456
$612$	−38.1065	−1.54036
$613$	−12.0420	−0.486372	−0.243186	−	0.969980i	$-0.578193\pi$
$613$	−12.0420	−0.486372	−0.243186	+	0.969980i	$0.578193\pi$
$614$	91.2483	3.68248
$615$	−30.4537	−1.22801
$616$	−0.358291	−0.0144360
$617$	13.4782	0.542611	0.271306	−	0.962493i	$-0.412545\pi$
$617$	13.4782	0.542611	0.271306	+	0.962493i	$0.412545\pi$
$618$	22.8563	0.919416
$619$	−9.94513	−0.399728	−0.199864	−	0.979824i	$-0.564050\pi$
$619$	−9.94513	−0.399728	−0.199864	+	0.979824i	$0.564050\pi$
$620$	−6.79901	−0.273055
$621$	−26.1886	−1.05091
$622$	72.3116	2.89943
$623$	0.376163	0.0150707
$624$	−69.0439	−2.76397
$625$	−9.95701	−0.398280
$626$	28.9893	1.15864
$627$	4.76832	0.190428
$628$	−102.218	−4.07895
$629$	3.61383	0.144093
$630$	−1.00495	−0.0400382
$631$	−7.73143	−0.307783	−0.153892	−	0.988088i	$-0.549181\pi$
$631$	−7.73143	−0.307783	−0.153892	+	0.988088i	$0.549181\pi$
$632$	97.0860	3.86187
$633$	40.7538	1.61982
$634$	70.1930	2.78772
$635$	−11.4524	−0.454476
$636$	−54.2271	−2.15024
$637$	8.23901	0.326441
$638$	−25.2367	−0.999131
$639$	66.3333	2.62410
$640$	−135.570	−5.35886
$641$	−41.8758	−1.65400	−0.826998	−	0.562205i	$-0.809953\pi$
$641$	−41.8758	−1.65400	−0.826998	+	0.562205i	$0.809953\pi$
$642$	−4.67408	−0.184471
$643$	−38.1218	−1.50338	−0.751688	−	0.659519i	$-0.770760\pi$
$643$	−38.1218	−1.50338	−0.751688	+	0.659519i	$0.770760\pi$
$644$	−0.475520	−0.0187381
$645$	−5.22224	−0.205625
$646$	4.36143	0.171598
$647$	−22.9790	−0.903397	−0.451698	−	0.892171i	$-0.649182\pi$
$647$	−22.9790	−0.903397	−0.451698	+	0.892171i	$0.649182\pi$
$648$	−145.713	−5.72416
$649$	9.48257	0.372223
$650$	−6.99909	−0.274527
$651$	−0.0679356	−0.00266261
$652$	−48.6476	−1.90519
$653$	−15.0408	−0.588592	−0.294296	−	0.955714i	$-0.595085\pi$
$653$	−15.0408	−0.588592	−0.294296	+	0.955714i	$0.595085\pi$
$654$	−26.6961	−1.04390
$655$	−34.6507	−1.35391
$656$	−111.256	−4.34383
$657$	70.6459	2.75616
$658$	−0.828900	−0.0323139
$659$	20.6144	0.803024	0.401512	−	0.915854i	$-0.368485\pi$
$659$	20.6144	0.803024	0.401512	+	0.915854i	$0.368485\pi$
$660$	30.8476	1.20074
$661$	−26.2738	−1.02193	−0.510966	−	0.859601i	$-0.670712\pi$
$661$	−26.2738	−1.02193	−0.510966	+	0.859601i	$0.670712\pi$
$662$	−12.4577	−0.484182
$663$	3.61896	0.140549
$664$	−178.787	−6.93827
$665$	0.0859272	0.00333211
$666$	65.5552	2.54021
$667$	−22.1534	−0.857784
$668$	−16.4415	−0.636142
$669$	26.7341	1.03360
$670$	−30.6702	−1.18489
$671$	0.450285	0.0173831
$672$	−3.17575	−0.122507
$673$	−0.975638	−0.0376081	−0.0188040	−	0.999823i	$-0.505986\pi$
$673$	−0.975638	−0.0376081	−0.0188040	+	0.999823i	$0.505986\pi$
$674$	−49.3343	−1.90029
$675$	−22.4333	−0.863457
$676$	−68.6050	−2.63866
$677$	40.5937	1.56014	0.780071	−	0.625691i	$-0.215183\pi$
$677$	40.5937	1.56014	0.780071	+	0.625691i	$0.215183\pi$
$678$	−120.490	−4.62740
$679$	0.0973095	0.00373440
$680$	18.6621	0.715660
$681$	−81.6698	−3.12960
$682$	1.90533	0.0729589
$683$	−26.9547	−1.03139	−0.515696	−	0.856772i	$-0.672467\pi$
$683$	−26.9547	−1.03139	−0.515696	+	0.856772i	$0.672467\pi$
$684$	59.1048	2.25993
$685$	8.05108	0.307616
$686$	1.28378	0.0490150
$687$	36.5402	1.39410
$688$	−19.0784	−0.727356
$689$	3.51522	0.133919
$690$	36.2472	1.37991
$691$	−25.2803	−0.961709	−0.480855	−	0.876800i	$-0.659673\pi$
$691$	−25.2803	−0.961709	−0.480855	+	0.876800i	$0.659673\pi$
$692$	77.7841	2.95691
$693$	0.210390	0.00799205
$694$	76.9009	2.91912
$695$	4.63224	0.175711
$696$	−303.120	−11.4897
$697$	5.83154	0.220885
$698$	60.3706	2.28506
$699$	42.0109	1.58900
$700$	−0.407333	−0.0153957
$701$	26.5820	1.00399	0.501994	−	0.864871i	$-0.332600\pi$
$701$	26.5820	1.00399	0.501994	+	0.864871i	$0.332600\pi$
$702$	35.1194	1.32549
$703$	−5.60522	−0.211405
$704$	50.9108	1.91877
$705$	47.2023	1.77774
$706$	0.789501	0.0297133
$707$	0.517734	0.0194714
$708$	172.200	6.47166
$709$	−30.6910	−1.15263	−0.576313	−	0.817229i	$-0.695509\pi$
$709$	−30.6910	−1.15263	−0.576313	+	0.817229i	$0.695509\pi$
$710$	−49.1155	−1.84327
$711$	−57.0092	−2.13801
$712$	−126.716	−4.74888
$713$	1.67255	0.0626374
$714$	0.281927	0.0105509
$715$	−1.99967	−0.0747834
$716$	−7.88711	−0.294755
$717$	91.1312	3.40336
$718$	−47.7146	−1.78069
$719$	−22.6373	−0.844229	−0.422114	−	0.906543i	$-0.638712\pi$
$719$	−22.6373	−0.844229	−0.422114	+	0.906543i	$0.638712\pi$
$720$	209.070	7.79156
$721$	−0.0862286	−0.00321132
$722$	46.6620	1.73658
$723$	−16.5610	−0.615909
$724$	101.683	3.77902
$725$	−18.9767	−0.704778
$726$	−8.64463	−0.320832
$727$	−53.3661	−1.97924	−0.989619	−	0.143717i	$-0.954094\pi$
$727$	−53.3661	−1.97924	−0.989619	+	0.143717i	$0.954094\pi$
$728$	0.421773	0.0156320
$729$	−12.2867	−0.455061
$730$	−52.3087	−1.93603
$731$	1.00000	0.0369863
$732$	8.17700	0.302231
$733$	−13.7982	−0.509648	−0.254824	−	0.966987i	$-0.582018\pi$
$733$	−13.7982	−0.509648	−0.254824	+	0.966987i	$0.582018\pi$
$734$	−7.44212	−0.274694
$735$	−36.5501	−1.34817
$736$	78.1857	2.88196
$737$	6.42090	0.236517
$738$	105.785	3.89398
$739$	23.3295	0.858188	0.429094	−	0.903260i	$-0.358833\pi$
$739$	23.3295	0.858188	0.429094	+	0.903260i	$0.358833\pi$
$740$	−36.2618	−1.33301
$741$	−5.61317	−0.206205
$742$	0.273846	0.0100532
$743$	15.7367	0.577323	0.288662	−	0.957431i	$-0.406790\pi$
$743$	15.7367	0.577323	0.288662	+	0.957431i	$0.406790\pi$
$744$	22.8851	0.839007
$745$	−7.16118	−0.262365
$746$	32.9951	1.20803
$747$	104.984	3.84117
$748$	−5.90697	−0.215980
$749$	0.0176336	0.000644318 0
$750$	104.473	3.81480
$751$	7.73250	0.282163	0.141081	−	0.989998i	$-0.454942\pi$
$751$	7.73250	0.282163	0.141081	+	0.989998i	$0.454942\pi$
$752$	172.444	6.28838
$753$	−35.7171	−1.30160
$754$	29.7082	1.08191
$755$	10.5462	0.383815
$756$	2.04388	0.0743350
$757$	−13.1416	−0.477638	−0.238819	−	0.971064i	$-0.576760\pi$
$757$	−13.1416	−0.477638	−0.238819	+	0.971064i	$0.576760\pi$
$758$	37.6181	1.36635
$759$	−7.58847	−0.275444
$760$	−28.9458	−1.04997
$761$	9.76954	0.354146	0.177073	−	0.984198i	$-0.443337\pi$
$761$	9.76954	0.354146	0.177073	+	0.984198i	$0.443337\pi$
$762$	58.2811	2.11130
$763$	0.100715	0.00364611
$764$	116.107	4.20060
$765$	−10.9585	−0.396204
$766$	−33.7288	−1.21867
$767$	−11.1627	−0.403061
$768$	376.885	13.5997
$769$	18.0080	0.649385	0.324693	−	0.945820i	$-0.394739\pi$
$769$	18.0080	0.649385	0.324693	+	0.945820i	$0.394739\pi$
$770$	−0.155780	−0.00561392
$771$	−73.8275	−2.65883
$772$	101.012	3.63549
$773$	27.8734	1.00254	0.501268	−	0.865292i	$-0.332867\pi$
$773$	27.8734	1.00254	0.501268	+	0.865292i	$0.332867\pi$
$774$	18.1401	0.652031
$775$	1.43271	0.0514646
$776$	−32.7801	−1.17674
$777$	−0.362327	−0.0129984
$778$	−36.5683	−1.31104
$779$	−9.04498	−0.324070
$780$	−36.3132	−1.30022
$781$	10.2825	0.367936
$782$	−6.94094	−0.248207
$783$	95.2196	3.40287
$784$	−133.528	−4.76887
$785$	−29.3954	−1.04917
$786$	176.337	6.28972
$787$	37.5912	1.33998	0.669990	−	0.742370i	$-0.266298\pi$
$787$	37.5912	1.33998	0.669990	+	0.742370i	$0.266298\pi$
$788$	61.6593	2.19652
$789$	−38.2575	−1.36200
$790$	42.2116	1.50182
$791$	0.454566	0.0161625
$792$	−70.8727	−2.51835
$793$	−0.530067	−0.0188232
$794$	17.5296	0.622103
$795$	−15.5943	−0.553074
$796$	59.5379	2.11026
$797$	−23.8503	−0.844821	−0.422411	−	0.906405i	$-0.638816\pi$
$797$	−23.8503	−0.844821	−0.422411	+	0.906405i	$0.638816\pi$
$798$	−0.437282	−0.0154796
$799$	−9.03871	−0.319766
$800$	66.9743	2.36790
$801$	74.4079	2.62907
$802$	−12.5302	−0.442458
$803$	10.9510	0.386452
$804$	116.601	4.11220
$805$	−0.136748	−0.00481972
$806$	−2.24292	−0.0790034
$807$	78.1048	2.74942
$808$	−174.406	−6.13558
$809$	11.2649	0.396052	0.198026	−	0.980197i	$-0.436547\pi$
$809$	11.2649	0.396052	0.198026	+	0.980197i	$0.436547\pi$
$810$	−63.3541	−2.22604
$811$	14.6532	0.514542	0.257271	−	0.966339i	$-0.417177\pi$
$811$	14.6532	0.514542	0.257271	+	0.966339i	$0.417177\pi$
$812$	1.72895	0.0606744
$813$	16.0984	0.564596
$814$	10.1619	0.356173
$815$	−13.9898	−0.490042
$816$	−58.6520	−2.05323
$817$	−1.55104	−0.0542642
$818$	−59.0410	−2.06432
$819$	−0.247667	−0.00865417
$820$	−58.5146	−2.04342
$821$	−1.75764	−0.0613420	−0.0306710	−	0.999530i	$-0.509764\pi$
$821$	−1.75764	−0.0613420	−0.0306710	+	0.999530i	$0.509764\pi$
$822$	−40.9718	−1.42905
$823$	42.5583	1.48349	0.741745	−	0.670682i	$-0.233999\pi$
$823$	42.5583	1.48349	0.741745	+	0.670682i	$0.233999\pi$
$824$	29.0473	1.01191
$825$	−6.50032	−0.226312
$826$	−0.869605	−0.0302574
$827$	−3.52560	−0.122597	−0.0612986	−	0.998119i	$-0.519524\pi$
$827$	−3.52560	−0.122597	−0.0612986	+	0.998119i	$0.519524\pi$
$828$	−94.0614	−3.26886
$829$	35.4349	1.23070	0.615352	−	0.788252i	$-0.289014\pi$
$829$	35.4349	1.23070	0.615352	+	0.788252i	$0.289014\pi$
$830$	−77.7339	−2.69818
$831$	−9.55659	−0.331514
$832$	−59.9312	−2.07774
$833$	6.99894	0.242499
$834$	−23.5734	−0.816279
$835$	−4.72817	−0.163625
$836$	9.16198	0.316874
$837$	−7.18892	−0.248486
$838$	15.0681	0.520520
$839$	38.0672	1.31423	0.657113	−	0.753792i	$-0.271777\pi$
$839$	38.0672	1.31423	0.657113	+	0.753792i	$0.271777\pi$
$840$	−1.87108	−0.0645585
$841$	51.5481	1.77752
$842$	71.5322	2.46516
$843$	40.5815	1.39770
$844$	78.3055	2.69539
$845$	−19.7291	−0.678701
$846$	−163.963	−5.63715
$847$	0.0326130	0.00112060
$848$	−56.9707	−1.95638
$849$	2.10250	0.0721577
$850$	−5.94565	−0.203934
$851$	8.92034	0.305785
$852$	186.726	6.39711
$853$	−42.4803	−1.45450	−0.727248	−	0.686375i	$-0.759201\pi$
$853$	−42.4803	−1.45450	−0.727248	+	0.686375i	$0.759201\pi$
$854$	−0.0412937	−0.00141304
$855$	16.9970	0.581287
$856$	−5.94013	−0.203029
$857$	−42.7923	−1.46176	−0.730879	−	0.682507i	$-0.760890\pi$
$857$	−42.7923	−1.46176	−0.730879	+	0.682507i	$0.760890\pi$
$858$	10.1763	0.347413
$859$	6.92457	0.236263	0.118132	−	0.992998i	$-0.462310\pi$
$859$	6.92457	0.236263	0.118132	+	0.992998i	$0.462310\pi$
$860$	−10.0341	−0.342162
$861$	−0.584676	−0.0199257
$862$	0.168097	0.00572539
$863$	34.3960	1.17085	0.585427	−	0.810725i	$-0.300927\pi$
$863$	34.3960	1.17085	0.585427	+	0.810725i	$0.300927\pi$
$864$	−336.057	−11.4329
$865$	22.3687	0.760560
$866$	15.5404	0.528085
$867$	3.07426	0.104407
$868$	−0.130533	−0.00443059
$869$	−8.83713	−0.299779
$870$	−131.792	−4.46817
$871$	−7.55856	−0.256112
$872$	−33.9271	−1.14892
$873$	19.2486	0.651465
$874$	10.7657	0.364155
$875$	−0.394137	−0.0133242
$876$	198.865	6.71904
$877$	−9.57617	−0.323364	−0.161682	−	0.986843i	$-0.551692\pi$
$877$	−9.57617	−0.323364	−0.161682	+	0.986843i	$0.551692\pi$
$878$	51.0446	1.72267
$879$	10.2749	0.346564
$880$	32.4084	1.09249
$881$	−5.46537	−0.184133	−0.0920664	−	0.995753i	$-0.529347\pi$
$881$	−5.46537	−0.184133	−0.0920664	+	0.995753i	$0.529347\pi$
$882$	126.961	4.27500
$883$	−45.4479	−1.52944	−0.764722	−	0.644360i	$-0.777124\pi$
$883$	−45.4479	−1.52944	−0.764722	+	0.644360i	$0.777124\pi$
$884$	6.95357	0.233874
$885$	49.5202	1.66460
$886$	23.4274	0.787058
$887$	−34.7881	−1.16807	−0.584035	−	0.811729i	$-0.698527\pi$
$887$	−34.7881	−1.16807	−0.584035	+	0.811729i	$0.698527\pi$
$888$	122.055	4.09589
$889$	−0.219873	−0.00737432
$890$	−55.0942	−1.84676
$891$	13.2634	0.444340
$892$	51.3676	1.71992
$893$	14.0194	0.469143
$894$	36.4431	1.21884
$895$	−2.26813	−0.0758154
$896$	−2.60278	−0.0869529
$897$	8.93299	0.298264
$898$	−84.6600	−2.82514
$899$	−6.08125	−0.202821
$900$	−80.5736	−2.68579
$901$	2.98614	0.0994827
$902$	16.3979	0.545991
$903$	−0.100261	−0.00333648
$904$	−153.127	−5.09292
$905$	29.2415	0.972020
$906$	−53.6693	−1.78304
$907$	−17.3796	−0.577081	−0.288540	−	0.957468i	$-0.593170\pi$
$907$	−17.3796	−0.577081	−0.288540	+	0.957468i	$0.593170\pi$
$908$	−156.923	−5.20766
$909$	102.412	3.39678
$910$	0.183381	0.00607902
$911$	52.8274	1.75025	0.875125	−	0.483898i	$-0.160779\pi$
$911$	52.8274	1.75025	0.875125	+	0.483898i	$0.160779\pi$
$912$	90.9718	3.01238
$913$	16.2738	0.538585
$914$	−118.226	−3.91058
$915$	2.35150	0.0777381
$916$	70.2094	2.31978
$917$	−0.665253	−0.0219686
$918$	29.8335	0.984651
$919$	−55.5962	−1.83395	−0.916975	−	0.398944i	$-0.869377\pi$
$919$	−55.5962	−1.83395	−0.916975	+	0.398944i	$0.869377\pi$
$920$	46.0653	1.51873
$921$	−99.7610	−3.28724
$922$	37.8904	1.24785
$923$	−12.1043	−0.398419
$924$	0.592239	0.0194832
$925$	7.64121	0.251241
$926$	120.320	3.95397
$927$	−17.0567	−0.560214
$928$	−284.277	−9.33186
$929$	−16.0534	−0.526696	−0.263348	−	0.964701i	$-0.584827\pi$
$929$	−16.0534	−0.526696	−0.263348	+	0.964701i	$0.584827\pi$
$930$	9.95009	0.326276
$931$	−10.8557	−0.355780
$932$	80.7208	2.64410
$933$	−79.0576	−2.58823
$934$	59.2583	1.93899
$935$	−1.69870	−0.0555533
$936$	83.4300	2.72699
$937$	30.0948	0.983154	0.491577	−	0.870834i	$-0.336421\pi$
$937$	30.0948	0.983154	0.491577	+	0.870834i	$0.336421\pi$
$938$	−0.588833	−0.0192261
$939$	−31.6937	−1.03429
$940$	90.6957	2.95817
$941$	−38.9713	−1.27043	−0.635214	−	0.772336i	$-0.719088\pi$
$941$	−38.9713	−1.27043	−0.635214	+	0.772336i	$0.719088\pi$
$942$	149.592	4.87399
$943$	14.3945	0.468749
$944$	180.912	5.88818
$945$	0.587767	0.0191201
$946$	2.81193	0.0914239
$947$	25.7207	0.835810	0.417905	−	0.908491i	$-0.362764\pi$
$947$	25.7207	0.835810	0.417905	+	0.908491i	$0.362764\pi$
$948$	−160.479	−5.21210
$949$	−12.8913	−0.418469
$950$	9.22196	0.299200
$951$	−76.7415	−2.48851
$952$	0.358291	0.0116123
$953$	−25.5181	−0.826612	−0.413306	−	0.910592i	$-0.635626\pi$
$953$	−25.5181	−0.826612	−0.413306	+	0.910592i	$0.635626\pi$
$954$	54.1687	1.75378
$955$	33.3894	1.08045
$956$	175.102	5.66320
$957$	27.5911	0.891893
$958$	71.5345	2.31117
$959$	0.154571	0.00499137
$960$	265.868	8.58086
$961$	−30.5409	−0.985190
$962$	−11.9623	−0.385681
$963$	3.48806	0.112401
$964$	−31.8207	−1.02487
$965$	29.0484	0.935101
$966$	0.695905	0.0223904
$967$	−18.0109	−0.579193	−0.289596	−	0.957149i	$-0.593521\pi$
$967$	−18.0109	−0.579193	−0.289596	+	0.957149i	$0.593521\pi$
$968$	−10.9861	−0.353108
$969$	−4.76832	−0.153181
$970$	−14.2523	−0.457614
$971$	−10.5123	−0.337354	−0.168677	−	0.985671i	$-0.553950\pi$
$971$	−10.5123	−0.337354	−0.168677	+	0.985671i	$0.553950\pi$
$972$	52.8459	1.69503
$973$	0.0889336	0.00285108
$974$	33.3783	1.06951
$975$	7.65205	0.245062
$976$	8.59071	0.274982
$977$	−14.7191	−0.470907	−0.235454	−	0.971886i	$-0.575658\pi$
$977$	−14.7191	−0.470907	−0.235454	+	0.971886i	$0.575658\pi$
$978$	71.1939	2.27653
$979$	11.5341	0.368633
$980$	−70.2284	−2.24336
$981$	19.9221	0.636063
$982$	−2.29669	−0.0732904
$983$	33.8125	1.07845	0.539226	−	0.842161i	$-0.318717\pi$
$983$	33.8125	1.07845	0.539226	+	0.842161i	$0.318717\pi$
$984$	196.956	6.27874
$985$	17.7316	0.564977
$986$	25.2367	0.803701
$987$	0.906230	0.0288456
$988$	−10.7853	−0.343126
$989$	2.46839	0.0784901
$990$	−30.8144	−0.979347
$991$	30.6661	0.974142	0.487071	−	0.873362i	$-0.338065\pi$
$991$	30.6661	0.974142	0.487071	+	0.873362i	$0.338065\pi$
$992$	21.4625	0.681434
$993$	13.6199	0.432215
$994$	−0.942961	−0.0299089
$995$	17.1216	0.542791
$996$	295.526	9.36410
$997$	12.6168	0.399578	0.199789	−	0.979839i	$-0.435974\pi$
$997$	12.6168	0.399578	0.199789	+	0.979839i	$0.435974\pi$
$998$	−89.0701	−2.81946
$999$	−38.3413	−1.21306

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.i.1.1	✓	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.i.1.1	✓	78	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:	\( N \)	\(=\)	\( 8041 = 11 \cdot 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8041.a (trivial)

\(f(q)\)	\(=\)	\(q-2.81193 q^{2} +3.07426 q^{3} +5.90697 q^{4} +1.69870 q^{5} -8.64463 q^{6} +0.0326130 q^{7} -10.9861 q^{8} +6.45110 q^{9} +O(q^{10})\)	\(q-2.81193 q^{2} +3.07426 q^{3} +5.90697 q^{4} +1.69870 q^{5} -8.64463 q^{6} +0.0326130 q^{7} -10.9861 q^{8} +6.45110 q^{9} -4.77662 q^{10} +1.00000 q^{11} +18.1596 q^{12} -1.17718 q^{13} -0.0917056 q^{14} +5.22224 q^{15} +19.0784 q^{16} -1.00000 q^{17} -18.1401 q^{18} +1.55104 q^{19} +10.0341 q^{20} +0.100261 q^{21} -2.81193 q^{22} -2.46839 q^{23} -33.7743 q^{24} -2.11443 q^{25} +3.31015 q^{26} +10.6096 q^{27} +0.192644 q^{28} +8.97486 q^{29} -14.6846 q^{30} -0.677587 q^{31} -31.6748 q^{32} +3.07426 q^{33} +2.81193 q^{34} +0.0553996 q^{35} +38.1065 q^{36} -3.61383 q^{37} -4.36143 q^{38} -3.61896 q^{39} -18.6621 q^{40} -5.83154 q^{41} -0.281927 q^{42} -1.00000 q^{43} +5.90697 q^{44} +10.9585 q^{45} +6.94094 q^{46} +9.03871 q^{47} +58.6520 q^{48} -6.99894 q^{49} +5.94565 q^{50} -3.07426 q^{51} -6.95357 q^{52} -2.98614 q^{53} -29.8335 q^{54} +1.69870 q^{55} -0.358291 q^{56} +4.76832 q^{57} -25.2367 q^{58} +9.48257 q^{59} +30.8476 q^{60} +0.450285 q^{61} +1.90533 q^{62} +0.210390 q^{63} +50.9108 q^{64} -1.99967 q^{65} -8.64463 q^{66} +6.42090 q^{67} -5.90697 q^{68} -7.58847 q^{69} -0.155780 q^{70} +10.2825 q^{71} -70.8727 q^{72} +10.9510 q^{73} +10.1619 q^{74} -6.50032 q^{75} +9.16198 q^{76} +0.0326130 q^{77} +10.1763 q^{78} -8.83713 q^{79} +32.4084 q^{80} +13.2634 q^{81} +16.3979 q^{82} +16.2738 q^{83} +0.592239 q^{84} -1.69870 q^{85} +2.81193 q^{86} +27.5911 q^{87} -10.9861 q^{88} +11.5341 q^{89} -30.8144 q^{90} -0.0383914 q^{91} -14.5807 q^{92} -2.08308 q^{93} -25.4162 q^{94} +2.63475 q^{95} -97.3768 q^{96} +2.98376 q^{97} +19.6805 q^{98} +6.45110 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 78 q + 7 q^{2} + 10 q^{3} + 91 q^{4} + 17 q^{5} + 12 q^{6} + 11 q^{7} + 33 q^{8} + 102 q^{9}+O(q^{10}) \) 78 * q + 7 * q^2 + 10 * q^3 + 91 * q^4 + 17 * q^5 + 12 * q^6 + 11 * q^7 + 33 * q^8 + 102 * q^9	\( 78 q + 7 q^{2} + 10 q^{3} + 91 q^{4} + 17 q^{5} + 12 q^{6} + 11 q^{7} + 33 q^{8} + 102 q^{9} + 3 q^{10} + 78 q^{11} + 31 q^{12} - 16 q^{13} + 31 q^{14} + 38 q^{15} + 121 q^{16} - 78 q^{17} + 11 q^{18} + 51 q^{20} + 6 q^{21} + 7 q^{22} + 48 q^{23} + 11 q^{24} + 101 q^{25} + 18 q^{26} + 46 q^{27} + 27 q^{28} + 22 q^{29} + 14 q^{30} + 56 q^{31} + 83 q^{32} + 10 q^{33} - 7 q^{34} + 24 q^{35} + 139 q^{36} + 53 q^{37} + 10 q^{38} + 79 q^{39} - q^{40} + 23 q^{41} + 17 q^{42} - 78 q^{43} + 91 q^{44} + 76 q^{45} + 21 q^{46} + 57 q^{47} + 78 q^{48} + 115 q^{49} + 58 q^{50} - 10 q^{51} - 63 q^{52} + 22 q^{53} - 18 q^{54} + 17 q^{55} + 111 q^{56} - 11 q^{57} + 36 q^{58} + 71 q^{59} + 36 q^{60} + 4 q^{61} - 5 q^{62} + 71 q^{63} + 183 q^{64} + 47 q^{65} + 12 q^{66} + 11 q^{67} - 91 q^{68} + 31 q^{69} + 33 q^{70} + 159 q^{71} + 59 q^{72} + 2 q^{73} - 4 q^{74} + 83 q^{75} - 44 q^{76} + 11 q^{77} + 101 q^{78} + 35 q^{79} + 85 q^{80} + 170 q^{81} + 98 q^{82} - 32 q^{83} + 44 q^{84} - 17 q^{85} - 7 q^{86} - 6 q^{87} + 33 q^{88} + 50 q^{89} - 5 q^{90} + 86 q^{91} + 106 q^{92} + 68 q^{93} - q^{94} + 109 q^{95} - 50 q^{96} + 40 q^{97} + 106 q^{98} + 102 q^{99}+O(q^{100}) \) 78 * q + 7 * q^2 + 10 * q^3 + 91 * q^4 + 17 * q^5 + 12 * q^6 + 11 * q^7 + 33 * q^8 + 102 * q^9 + 3 * q^10 + 78 * q^11 + 31 * q^12 - 16 * q^13 + 31 * q^14 + 38 * q^15 + 121 * q^16 - 78 * q^17 + 11 * q^18 + 51 * q^20 + 6 * q^21 + 7 * q^22 + 48 * q^23 + 11 * q^24 + 101 * q^25 + 18 * q^26 + 46 * q^27 + 27 * q^28 + 22 * q^29 + 14 * q^30 + 56 * q^31 + 83 * q^32 + 10 * q^33 - 7 * q^34 + 24 * q^35 + 139 * q^36 + 53 * q^37 + 10 * q^38 + 79 * q^39 - q^40 + 23 * q^41 + 17 * q^42 - 78 * q^43 + 91 * q^44 + 76 * q^45 + 21 * q^46 + 57 * q^47 + 78 * q^48 + 115 * q^49 + 58 * q^50 - 10 * q^51 - 63 * q^52 + 22 * q^53 - 18 * q^54 + 17 * q^55 + 111 * q^56 - 11 * q^57 + 36 * q^58 + 71 * q^59 + 36 * q^60 + 4 * q^61 - 5 * q^62 + 71 * q^63 + 183 * q^64 + 47 * q^65 + 12 * q^66 + 11 * q^67 - 91 * q^68 + 31 * q^69 + 33 * q^70 + 159 * q^71 + 59 * q^72 + 2 * q^73 - 4 * q^74 + 83 * q^75 - 44 * q^76 + 11 * q^77 + 101 * q^78 + 35 * q^79 + 85 * q^80 + 170 * q^81 + 98 * q^82 - 32 * q^83 + 44 * q^84 - 17 * q^85 - 7 * q^86 - 6 * q^87 + 33 * q^88 + 50 * q^89 - 5 * q^90 + 86 * q^91 + 106 * q^92 + 68 * q^93 - q^94 + 109 * q^95 - 50 * q^96 + 40 * q^97 + 106 * q^98 + 102 * q^99

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