LMFDB - Embedded newform 8015.2.a.m.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8015,2,Mod(1,8015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8015, 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("8015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8015 = 5 \cdot 7 \cdot 229 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8015.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:	$64.0000972201$
Analytic rank:	$0$
Dimension:	$67$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	8015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.66598 q^{2} +2.60914 q^{3} +5.10744 q^{4} +1.00000 q^{5} -6.95591 q^{6} -1.00000 q^{7} -8.28438 q^{8} +3.80761 q^{9} +O(q^{10})$	\(q-2.66598 q^{2} +2.60914 q^{3} +5.10744 q^{4} +1.00000 q^{5} -6.95591 q^{6} -1.00000 q^{7} -8.28438 q^{8} +3.80761 q^{9} -2.66598 q^{10} -1.73240 q^{11} +13.3260 q^{12} +5.33868 q^{13} +2.66598 q^{14} +2.60914 q^{15} +11.8711 q^{16} +5.43715 q^{17} -10.1510 q^{18} +4.98176 q^{19} +5.10744 q^{20} -2.60914 q^{21} +4.61854 q^{22} +5.38581 q^{23} -21.6151 q^{24} +1.00000 q^{25} -14.2328 q^{26} +2.10716 q^{27} -5.10744 q^{28} -10.6328 q^{29} -6.95591 q^{30} +9.82040 q^{31} -15.0793 q^{32} -4.52007 q^{33} -14.4953 q^{34} -1.00000 q^{35} +19.4471 q^{36} -5.85058 q^{37} -13.2813 q^{38} +13.9294 q^{39} -8.28438 q^{40} +10.1101 q^{41} +6.95591 q^{42} +0.168261 q^{43} -8.84814 q^{44} +3.80761 q^{45} -14.3585 q^{46} -11.7247 q^{47} +30.9733 q^{48} +1.00000 q^{49} -2.66598 q^{50} +14.1863 q^{51} +27.2670 q^{52} +3.95515 q^{53} -5.61764 q^{54} -1.73240 q^{55} +8.28438 q^{56} +12.9981 q^{57} +28.3469 q^{58} +4.56156 q^{59} +13.3260 q^{60} -5.22929 q^{61} -26.1810 q^{62} -3.80761 q^{63} +16.4590 q^{64} +5.33868 q^{65} +12.0504 q^{66} +11.9727 q^{67} +27.7699 q^{68} +14.0523 q^{69} +2.66598 q^{70} -1.91039 q^{71} -31.5437 q^{72} +11.4282 q^{73} +15.5975 q^{74} +2.60914 q^{75} +25.4441 q^{76} +1.73240 q^{77} -37.1354 q^{78} -10.1717 q^{79} +11.8711 q^{80} -5.92495 q^{81} -26.9533 q^{82} -5.65341 q^{83} -13.3260 q^{84} +5.43715 q^{85} -0.448580 q^{86} -27.7426 q^{87} +14.3519 q^{88} +13.5735 q^{89} -10.1510 q^{90} -5.33868 q^{91} +27.5077 q^{92} +25.6228 q^{93} +31.2578 q^{94} +4.98176 q^{95} -39.3441 q^{96} -1.52090 q^{97} -2.66598 q^{98} -6.59630 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 67 q + 3 q^{2} + 73 q^{4} + 67 q^{5} + 17 q^{6} - 67 q^{7} + 12 q^{8} + 97 q^{9}+O(q^{10}) $ 67 * q + 3 * q^2 + 73 * q^4 + 67 * q^5 + 17 * q^6 - 67 * q^7 + 12 * q^8 + 97 * q^9	\( 67 q + 3 q^{2} + 73 q^{4} + 67 q^{5} + 17 q^{6} - 67 q^{7} + 12 q^{8} + 97 q^{9} + 3 q^{10} + 11 q^{11} + 9 q^{12} + 19 q^{13} - 3 q^{14} + 93 q^{16} + 7 q^{17} + 9 q^{18} + 36 q^{19} + 73 q^{20} - 8 q^{22} - 2 q^{23} + 37 q^{24} + 67 q^{25} + 39 q^{26} + 6 q^{27} - 73 q^{28} + 56 q^{29} + 17 q^{30} + 63 q^{31} + 27 q^{32} + 51 q^{33} + 55 q^{34} - 67 q^{35} + 148 q^{36} + 28 q^{37} + 10 q^{38} + 7 q^{39} + 12 q^{40} + 84 q^{41} - 17 q^{42} - 11 q^{43} + 41 q^{44} + 97 q^{45} + 17 q^{46} - 10 q^{47} + 10 q^{48} + 67 q^{49} + 3 q^{50} - q^{51} + 49 q^{52} + 3 q^{53} + 20 q^{54} + 11 q^{55} - 12 q^{56} + 45 q^{57} + 22 q^{58} + 80 q^{59} + 9 q^{60} + 64 q^{61} - 37 q^{62} - 97 q^{63} + 110 q^{64} + 19 q^{65} + 75 q^{66} + 22 q^{67} + 7 q^{68} + 107 q^{69} - 3 q^{70} + 24 q^{71} + 72 q^{72} + 83 q^{73} + 52 q^{74} + 115 q^{76} - 11 q^{77} - 70 q^{78} - 32 q^{79} + 93 q^{80} + 183 q^{81} + 56 q^{82} - 58 q^{83} - 9 q^{84} + 7 q^{85} + 51 q^{86} + 20 q^{87} - 5 q^{88} + 129 q^{89} + 9 q^{90} - 19 q^{91} - 37 q^{92} + 33 q^{93} + 89 q^{94} + 36 q^{95} + 129 q^{96} + 126 q^{97} + 3 q^{98} - 27 q^{99}+O(q^{100}) \) 67 * q + 3 * q^2 + 73 * q^4 + 67 * q^5 + 17 * q^6 - 67 * q^7 + 12 * q^8 + 97 * q^9 + 3 * q^10 + 11 * q^11 + 9 * q^12 + 19 * q^13 - 3 * q^14 + 93 * q^16 + 7 * q^17 + 9 * q^18 + 36 * q^19 + 73 * q^20 - 8 * q^22 - 2 * q^23 + 37 * q^24 + 67 * q^25 + 39 * q^26 + 6 * q^27 - 73 * q^28 + 56 * q^29 + 17 * q^30 + 63 * q^31 + 27 * q^32 + 51 * q^33 + 55 * q^34 - 67 * q^35 + 148 * q^36 + 28 * q^37 + 10 * q^38 + 7 * q^39 + 12 * q^40 + 84 * q^41 - 17 * q^42 - 11 * q^43 + 41 * q^44 + 97 * q^45 + 17 * q^46 - 10 * q^47 + 10 * q^48 + 67 * q^49 + 3 * q^50 - q^51 + 49 * q^52 + 3 * q^53 + 20 * q^54 + 11 * q^55 - 12 * q^56 + 45 * q^57 + 22 * q^58 + 80 * q^59 + 9 * q^60 + 64 * q^61 - 37 * q^62 - 97 * q^63 + 110 * q^64 + 19 * q^65 + 75 * q^66 + 22 * q^67 + 7 * q^68 + 107 * q^69 - 3 * q^70 + 24 * q^71 + 72 * q^72 + 83 * q^73 + 52 * q^74 + 115 * q^76 - 11 * q^77 - 70 * q^78 - 32 * q^79 + 93 * q^80 + 183 * q^81 + 56 * q^82 - 58 * q^83 - 9 * q^84 + 7 * q^85 + 51 * q^86 + 20 * q^87 - 5 * q^88 + 129 * q^89 + 9 * q^90 - 19 * q^91 - 37 * q^92 + 33 * q^93 + 89 * q^94 + 36 * q^95 + 129 * q^96 + 126 * q^97 + 3 * q^98 - 27 * 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 $

$2$	−2.66598	−1.88513	−0.942566	−	0.334020i	$-0.891595\pi$
$2$	−2.66598	−1.88513	−0.942566	+	0.334020i	$0.891595\pi$
$3$	2.60914	1.50639	0.753194	−	0.657799i	$-0.228512\pi$
$3$	2.60914	1.50639	0.753194	+	0.657799i	$0.228512\pi$
$4$	5.10744	2.55372
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−6.95591	−2.83974
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−8.28438	−2.92897
$9$	3.80761	1.26920
$10$	−2.66598	−0.843057
$11$	−1.73240	−0.522338	−0.261169	−	0.965293i	$-0.584108\pi$
$11$	−1.73240	−0.522338	−0.261169	+	0.965293i	$0.584108\pi$
$12$	13.3260	3.84689
$13$	5.33868	1.48068	0.740342	−	0.672230i	$-0.234664\pi$
$13$	5.33868	1.48068	0.740342	+	0.672230i	$0.234664\pi$
$14$	2.66598	0.712513
$15$	2.60914	0.673677
$16$	11.8711	2.96777
$17$	5.43715	1.31870	0.659352	−	0.751835i	$-0.270831\pi$
$17$	5.43715	1.31870	0.659352	+	0.751835i	$0.270831\pi$
$18$	−10.1510	−2.39261
$19$	4.98176	1.14289	0.571447	−	0.820639i	$-0.306382\pi$
$19$	4.98176	1.14289	0.571447	+	0.820639i	$0.306382\pi$
$20$	5.10744	1.14206
$21$	−2.60914	−0.569361
$22$	4.61854	0.984677
$23$	5.38581	1.12302	0.561509	−	0.827470i	$-0.310221\pi$
$23$	5.38581	1.12302	0.561509	+	0.827470i	$0.310221\pi$
$24$	−21.6151	−4.41216
$25$	1.00000	0.200000
$26$	−14.2328	−2.79128
$27$	2.10716	0.405523
$28$	−5.10744	−0.965216
$29$	−10.6328	−1.97447	−0.987234	−	0.159274i	$-0.949085\pi$
$29$	−10.6328	−1.97447	−0.987234	+	0.159274i	$0.949085\pi$
$30$	−6.95591	−1.26997
$31$	9.82040	1.76380	0.881898	−	0.471440i	$-0.156266\pi$
$31$	9.82040	1.76380	0.881898	+	0.471440i	$0.156266\pi$
$32$	−15.0793	−2.66567
$33$	−4.52007	−0.786844
$34$	−14.4953	−2.48593
$35$	−1.00000	−0.169031
$36$	19.4471	3.24119
$37$	−5.85058	−0.961830	−0.480915	−	0.876767i	$-0.659695\pi$
$37$	−5.85058	−0.961830	−0.480915	+	0.876767i	$0.659695\pi$
$38$	−13.2813	−2.15451
$39$	13.9294	2.23048
$40$	−8.28438	−1.30988
$41$	10.1101	1.57893	0.789465	−	0.613796i	$-0.210358\pi$
$41$	10.1101	1.57893	0.789465	+	0.613796i	$0.210358\pi$
$42$	6.95591	1.07332
$43$	0.168261	0.0256595	0.0128298	−	0.999918i	$-0.495916\pi$
$43$	0.168261	0.0256595	0.0128298	+	0.999918i	$0.495916\pi$
$44$	−8.84814	−1.33391
$45$	3.80761	0.567605
$46$	−14.3585	−2.11704
$47$	−11.7247	−1.71022	−0.855110	−	0.518446i	$-0.826511\pi$
$47$	−11.7247	−1.71022	−0.855110	+	0.518446i	$0.826511\pi$
$48$	30.9733	4.47062
$49$	1.00000	0.142857
$50$	−2.66598	−0.377026
$51$	14.1863	1.98648
$52$	27.2670	3.78126
$53$	3.95515	0.543282	0.271641	−	0.962399i	$-0.412434\pi$
$53$	3.95515	0.543282	0.271641	+	0.962399i	$0.412434\pi$
$54$	−5.61764	−0.764464
$55$	−1.73240	−0.233597
$56$	8.28438	1.10705
$57$	12.9981	1.72164
$58$	28.3469	3.72213
$59$	4.56156	0.593865	0.296933	−	0.954898i	$-0.404036\pi$
$59$	4.56156	0.593865	0.296933	+	0.954898i	$0.404036\pi$
$60$	13.3260	1.72038
$61$	−5.22929	−0.669542	−0.334771	−	0.942300i	$-0.608659\pi$
$61$	−5.22929	−0.669542	−0.334771	+	0.942300i	$0.608659\pi$
$62$	−26.1810	−3.32499
$63$	−3.80761	−0.479713
$64$	16.4590	2.05737
$65$	5.33868	0.662182
$66$	12.0504	1.48330
$67$	11.9727	1.46270	0.731348	−	0.682005i	$-0.238892\pi$
$67$	11.9727	1.46270	0.731348	+	0.682005i	$0.238892\pi$
$68$	27.7699	3.36760
$69$	14.0523	1.69170
$70$	2.66598	0.318645
$71$	−1.91039	−0.226722	−0.113361	−	0.993554i	$-0.536162\pi$
$71$	−1.91039	−0.226722	−0.113361	+	0.993554i	$0.536162\pi$
$72$	−31.5437	−3.71746
$73$	11.4282	1.33758	0.668788	−	0.743454i	$-0.266814\pi$
$73$	11.4282	1.33758	0.668788	+	0.743454i	$0.266814\pi$
$74$	15.5975	1.81318
$75$	2.60914	0.301277
$76$	25.4441	2.91864
$77$	1.73240	0.197425
$78$	−37.1354	−4.20476
$79$	−10.1717	−1.14440	−0.572201	−	0.820113i	$-0.693910\pi$
$79$	−10.1717	−1.14440	−0.572201	+	0.820113i	$0.693910\pi$
$80$	11.8711	1.32723
$81$	−5.92495	−0.658328
$82$	−26.9533	−2.97649
$83$	−5.65341	−0.620542	−0.310271	−	0.950648i	$-0.600420\pi$
$83$	−5.65341	−0.620542	−0.310271	+	0.950648i	$0.600420\pi$
$84$	−13.3260	−1.45399
$85$	5.43715	0.589742
$86$	−0.448580	−0.0483716
$87$	−27.7426	−2.97431
$88$	14.3519	1.52991
$89$	13.5735	1.43879	0.719394	−	0.694602i	$-0.244420\pi$
$89$	13.5735	1.43879	0.719394	+	0.694602i	$0.244420\pi$
$90$	−10.1510	−1.07001
$91$	−5.33868	−0.559646
$92$	27.5077	2.86788
$93$	25.6228	2.65696
$94$	31.2578	3.22399
$95$	4.98176	0.511118
$96$	−39.3441	−4.01554
$97$	−1.52090	−0.154424	−0.0772121	−	0.997015i	$-0.524602\pi$
$97$	−1.52090	−0.154424	−0.0772121	+	0.997015i	$0.524602\pi$
$98$	−2.66598	−0.269305
$99$	−6.59630	−0.662953
$100$	5.10744	0.510744
$101$	−3.46631	−0.344911	−0.172455	−	0.985017i	$-0.555170\pi$
$101$	−3.46631	−0.344911	−0.172455	+	0.985017i	$0.555170\pi$
$102$	−37.8203	−3.74477
$103$	10.7474	1.05897	0.529487	−	0.848318i	$-0.322384\pi$
$103$	10.7474	1.05897	0.529487	+	0.848318i	$0.322384\pi$
$104$	−44.2277	−4.33688
$105$	−2.60914	−0.254626
$106$	−10.5443	−1.02416
$107$	−15.4689	−1.49543	−0.747716	−	0.664019i	$-0.768849\pi$
$107$	−15.4689	−1.49543	−0.747716	+	0.664019i	$0.768849\pi$
$108$	10.7622	1.03559
$109$	1.98649	0.190271	0.0951356	−	0.995464i	$-0.469672\pi$
$109$	1.98649	0.190271	0.0951356	+	0.995464i	$0.469672\pi$
$110$	4.61854	0.440361
$111$	−15.2650	−1.44889
$112$	−11.8711	−1.12171
$113$	−6.88528	−0.647713	−0.323857	−	0.946106i	$-0.604980\pi$
$113$	−6.88528	−0.647713	−0.323857	+	0.946106i	$0.604980\pi$
$114$	−34.6527	−3.24552
$115$	5.38581	0.502229
$116$	−54.3066	−5.04224
$117$	20.3276	1.87929
$118$	−12.1610	−1.11951
$119$	−5.43715	−0.498423
$120$	−21.6151	−1.97318
$121$	−7.99879	−0.727163
$122$	13.9412	1.26217
$123$	26.3786	2.37848
$124$	50.1571	4.50424
$125$	1.00000	0.0894427
$126$	10.1510	0.904323
$127$	−1.37276	−0.121813	−0.0609065	−	0.998143i	$-0.519399\pi$
$127$	−1.37276	−0.121813	−0.0609065	+	0.998143i	$0.519399\pi$
$128$	−13.7206	−1.21275
$129$	0.439016	0.0386532
$130$	−14.2328	−1.24830
$131$	6.34145	0.554055	0.277028	−	0.960862i	$-0.410651\pi$
$131$	6.34145	0.554055	0.277028	+	0.960862i	$0.410651\pi$
$132$	−23.0860	−2.00938
$133$	−4.98176	−0.431974
$134$	−31.9189	−2.75737
$135$	2.10716	0.181355
$136$	−45.0434	−3.86244
$137$	11.5815	0.989471	0.494736	−	0.869044i	$-0.335265\pi$
$137$	11.5815	0.989471	0.494736	+	0.869044i	$0.335265\pi$
$138$	−37.4632	−3.18908
$139$	8.14723	0.691039	0.345519	−	0.938412i	$-0.387703\pi$
$139$	8.14723	0.691039	0.345519	+	0.938412i	$0.387703\pi$
$140$	−5.10744	−0.431658
$141$	−30.5913	−2.57625
$142$	5.09306	0.427400
$143$	−9.24873	−0.773418
$144$	45.2005	3.76671
$145$	−10.6328	−0.883009
$146$	−30.4675	−2.52151
$147$	2.60914	0.215198
$148$	−29.8815	−2.45625
$149$	−17.4080	−1.42612	−0.713060	−	0.701104i	$-0.752691\pi$
$149$	−17.4080	−1.42612	−0.713060	+	0.701104i	$0.752691\pi$
$150$	−6.95591	−0.567948
$151$	16.0303	1.30453	0.652263	−	0.757993i	$-0.273820\pi$
$151$	16.0303	1.30453	0.652263	+	0.757993i	$0.273820\pi$
$152$	−41.2708	−3.34751
$153$	20.7025	1.67370
$154$	−4.61854	−0.372173
$155$	9.82040	0.788794
$156$	71.1434	5.69603
$157$	−4.69434	−0.374649	−0.187325	−	0.982298i	$-0.559982\pi$
$157$	−4.69434	−0.374649	−0.187325	+	0.982298i	$0.559982\pi$
$158$	27.1175	2.15735
$159$	10.3195	0.818393
$160$	−15.0793	−1.19213
$161$	−5.38581	−0.424461
$162$	15.7958	1.24103
$163$	−16.1624	−1.26594	−0.632970	−	0.774176i	$-0.718164\pi$
$163$	−16.1624	−1.26594	−0.632970	+	0.774176i	$0.718164\pi$
$164$	51.6367	4.03215
$165$	−4.52007	−0.351887
$166$	15.0719	1.16980
$167$	−24.5511	−1.89982	−0.949911	−	0.312520i	$-0.898827\pi$
$167$	−24.5511	−1.89982	−0.949911	+	0.312520i	$0.898827\pi$
$168$	21.6151	1.66764
$169$	15.5015	1.19243
$170$	−14.4953	−1.11174
$171$	18.9686	1.45056
$172$	0.859383	0.0655273
$173$	14.2046	1.07996	0.539979	−	0.841679i	$-0.318432\pi$
$173$	14.2046	1.07996	0.539979	+	0.841679i	$0.318432\pi$
$174$	73.9611	5.60697
$175$	−1.00000	−0.0755929
$176$	−20.5655	−1.55018
$177$	11.9018	0.894591
$178$	−36.1867	−2.71230
$179$	10.2048	0.762740	0.381370	−	0.924423i	$-0.375452\pi$
$179$	10.2048	0.762740	0.381370	+	0.924423i	$0.375452\pi$
$180$	19.4471	1.44950
$181$	−15.0087	−1.11559	−0.557794	−	0.829979i	$-0.688352\pi$
$181$	−15.0087	−1.11559	−0.557794	+	0.829979i	$0.688352\pi$
$182$	14.2328	1.05501
$183$	−13.6439	−1.00859
$184$	−44.6181	−3.28929
$185$	−5.85058	−0.430143
$186$	−68.3098	−5.00872
$187$	−9.41932	−0.688809
$188$	−59.8832	−4.36743
$189$	−2.10716	−0.153273
$190$	−13.2813	−0.963525
$191$	−5.05279	−0.365607	−0.182804	−	0.983149i	$-0.558517\pi$
$191$	−5.05279	−0.365607	−0.182804	+	0.983149i	$0.558517\pi$
$192$	42.9438	3.09920
$193$	−5.32069	−0.382992	−0.191496	−	0.981493i	$-0.561334\pi$
$193$	−5.32069	−0.382992	−0.191496	+	0.981493i	$0.561334\pi$
$194$	4.05469	0.291110
$195$	13.9294	0.997502
$196$	5.10744	0.364817
$197$	−14.1312	−1.00681	−0.503404	−	0.864051i	$-0.667919\pi$
$197$	−14.1312	−1.00681	−0.503404	+	0.864051i	$0.667919\pi$
$198$	17.5856	1.24975
$199$	−2.02115	−0.143275	−0.0716376	−	0.997431i	$-0.522823\pi$
$199$	−2.02115	−0.143275	−0.0716376	+	0.997431i	$0.522823\pi$
$200$	−8.28438	−0.585794
$201$	31.2384	2.20339
$202$	9.24110	0.650202
$203$	10.6328	0.746279
$204$	72.4557	5.07291
$205$	10.1101	0.706119
$206$	−28.6524	−1.99631
$207$	20.5070	1.42534
$208$	63.3760	4.39434
$209$	−8.63041	−0.596978
$210$	6.95591	0.480003
$211$	11.2521	0.774623	0.387312	−	0.921949i	$-0.373404\pi$
$211$	11.2521	0.774623	0.387312	+	0.921949i	$0.373404\pi$
$212$	20.2007	1.38739
$213$	−4.98448	−0.341531
$214$	41.2397	2.81909
$215$	0.168261	0.0114753
$216$	−17.4565	−1.18776
$217$	−9.82040	−0.666652
$218$	−5.29594	−0.358686
$219$	29.8179	2.01491
$220$	−8.84814	−0.596541
$221$	29.0272	1.95258
$222$	40.6961	2.73135
$223$	15.8100	1.05871	0.529357	−	0.848399i	$-0.322433\pi$
$223$	15.8100	1.05871	0.529357	+	0.848399i	$0.322433\pi$
$224$	15.0793	1.00753
$225$	3.80761	0.253840
$226$	18.3560	1.22102
$227$	−12.7087	−0.843507	−0.421754	−	0.906710i	$-0.638585\pi$
$227$	−12.7087	−0.843507	−0.421754	+	0.906710i	$0.638585\pi$
$228$	66.3871	4.39660
$229$	−1.00000	−0.0660819
$229$	−1.00000	−0.0660819
$230$	−14.3585	−0.946768
$231$	4.52007	0.297399
$232$	88.0865	5.78316
$233$	16.7763	1.09905	0.549527	−	0.835476i	$-0.314808\pi$
$233$	16.7763	1.09905	0.549527	+	0.835476i	$0.314808\pi$
$234$	−54.1930	−3.54270
$235$	−11.7247	−0.764834
$236$	23.2979	1.51657
$237$	−26.5393	−1.72391
$238$	14.4953	0.939593
$239$	3.18232	0.205847	0.102924	−	0.994689i	$-0.467180\pi$
$239$	3.18232	0.205847	0.102924	+	0.994689i	$0.467180\pi$
$240$	30.9733	1.99932
$241$	5.09317	0.328080	0.164040	−	0.986454i	$-0.447547\pi$
$241$	5.09317	0.328080	0.164040	+	0.986454i	$0.447547\pi$
$242$	21.3246	1.37080
$243$	−21.7805	−1.39722
$244$	−26.7083	−1.70982
$245$	1.00000	0.0638877
$246$	−70.3248	−4.48375
$247$	26.5961	1.69227
$248$	−81.3559	−5.16611
$249$	−14.7505	−0.934777
$250$	−2.66598	−0.168611
$251$	20.9631	1.32318	0.661588	−	0.749867i	$-0.269883\pi$
$251$	20.9631	1.32318	0.661588	+	0.749867i	$0.269883\pi$
$252$	−19.4471	−1.22505
$253$	−9.33038	−0.586596
$254$	3.65975	0.229633
$255$	14.1863	0.888380
$256$	3.66099	0.228812
$257$	10.8415	0.676274	0.338137	−	0.941097i	$-0.390203\pi$
$257$	10.8415	0.676274	0.338137	+	0.941097i	$0.390203\pi$
$258$	−1.17041	−0.0728664
$259$	5.85058	0.363538
$260$	27.2670	1.69103
$261$	−40.4857	−2.50600
$262$	−16.9062	−1.04447
$263$	−7.28201	−0.449028	−0.224514	−	0.974471i	$-0.572079\pi$
$263$	−7.28201	−0.449028	−0.224514	+	0.974471i	$0.572079\pi$
$264$	37.4460	2.30464
$265$	3.95515	0.242963
$266$	13.2813	0.814327
$267$	35.4151	2.16737
$268$	61.1498	3.73532
$269$	7.36840	0.449259	0.224630	−	0.974444i	$-0.427883\pi$
$269$	7.36840	0.449259	0.224630	+	0.974444i	$0.427883\pi$
$270$	−5.61764	−0.341879
$271$	20.9285	1.27132	0.635658	−	0.771971i	$-0.280729\pi$
$271$	20.9285	1.27132	0.635658	+	0.771971i	$0.280729\pi$
$272$	64.5449	3.91361
$273$	−13.9294	−0.843043
$274$	−30.8759	−1.86528
$275$	−1.73240	−0.104468
$276$	71.7714	4.32013
$277$	−12.9988	−0.781024	−0.390512	−	0.920598i	$-0.627702\pi$
$277$	−12.9988	−0.781024	−0.390512	+	0.920598i	$0.627702\pi$
$278$	−21.7203	−1.30270
$279$	37.3922	2.23861
$280$	8.28438	0.495086
$281$	−12.9135	−0.770355	−0.385178	−	0.922842i	$-0.625860\pi$
$281$	−12.9135	−0.770355	−0.385178	+	0.922842i	$0.625860\pi$
$282$	81.5558	4.85658
$283$	−17.8921	−1.06358	−0.531788	−	0.846878i	$-0.678480\pi$
$283$	−17.8921	−1.06358	−0.531788	+	0.846878i	$0.678480\pi$
$284$	−9.75722	−0.578984
$285$	12.9981	0.769942
$286$	24.6569	1.45799
$287$	−10.1101	−0.596779
$288$	−57.4162	−3.38328
$289$	12.5626	0.738978
$290$	28.3469	1.66459
$291$	−3.96825	−0.232623
$292$	58.3691	3.41579
$293$	−26.7325	−1.56173	−0.780865	−	0.624699i	$-0.785221\pi$
$293$	−26.7325	−1.56173	−0.780865	+	0.624699i	$0.785221\pi$
$294$	−6.95591	−0.405677
$295$	4.56156	0.265585
$296$	48.4685	2.81717
$297$	−3.65044	−0.211820
$298$	46.4094	2.68842
$299$	28.7531	1.66284
$300$	13.3260	0.769379
$301$	−0.168261	−0.00969839
$302$	−42.7364	−2.45920
$303$	−9.04408	−0.519569
$304$	59.1390	3.39185
$305$	−5.22929	−0.299428
$306$	−55.1925	−3.15515
$307$	−6.36432	−0.363231	−0.181616	−	0.983370i	$-0.558133\pi$
$307$	−6.36432	−0.363231	−0.181616	+	0.983370i	$0.558133\pi$
$308$	8.84814	0.504169
$309$	28.0415	1.59523
$310$	−26.1810	−1.48698
$311$	−12.0795	−0.684965	−0.342483	−	0.939524i	$-0.611268\pi$
$311$	−12.0795	−0.684965	−0.342483	+	0.939524i	$0.611268\pi$
$312$	−115.396	−6.53302
$313$	11.6585	0.658979	0.329490	−	0.944159i	$-0.393123\pi$
$313$	11.6585	0.658979	0.329490	+	0.944159i	$0.393123\pi$
$314$	12.5150	0.706263
$315$	−3.80761	−0.214534
$316$	−51.9513	−2.92249
$317$	−3.48127	−0.195528	−0.0977639	−	0.995210i	$-0.531169\pi$
$317$	−3.48127	−0.195528	−0.0977639	+	0.995210i	$0.531169\pi$
$318$	−27.5117	−1.54278
$319$	18.4203	1.03134
$320$	16.4590	0.920085
$321$	−40.3604	−2.25270
$322$	14.3585	0.800165
$323$	27.0866	1.50714
$324$	−30.2614	−1.68119
$325$	5.33868	0.296137
$326$	43.0887	2.38646
$327$	5.18303	0.286622
$328$	−83.7558	−4.62464
$329$	11.7247	0.646403
$330$	12.0504	0.663354
$331$	−5.22879	−0.287400	−0.143700	−	0.989621i	$-0.545900\pi$
$331$	−5.22879	−0.287400	−0.143700	+	0.989621i	$0.545900\pi$
$332$	−28.8745	−1.58469
$333$	−22.2767	−1.22076
$334$	65.4528	3.58142
$335$	11.9727	0.654138
$336$	−30.9733	−1.68973
$337$	−34.6378	−1.88684	−0.943422	−	0.331595i	$-0.892413\pi$
$337$	−34.6378	−1.88684	−0.943422	+	0.331595i	$0.892413\pi$
$338$	−41.3267	−2.24788
$339$	−17.9647	−0.975707
$340$	27.7699	1.50604
$341$	−17.0129	−0.921298
$342$	−50.5699	−2.73451
$343$	−1.00000	−0.0539949
$344$	−1.39394	−0.0751560
$345$	14.0523	0.756552
$346$	−37.8692	−2.03586
$347$	15.8333	0.849978	0.424989	−	0.905198i	$-0.360278\pi$
$347$	15.8333	0.849978	0.424989	+	0.905198i	$0.360278\pi$
$348$	−141.694	−7.59557
$349$	26.0678	1.39538	0.697689	−	0.716401i	$-0.254212\pi$
$349$	26.0678	1.39538	0.697689	+	0.716401i	$0.254212\pi$
$350$	2.66598	0.142503
$351$	11.2494	0.600451
$352$	26.1234	1.39238
$353$	7.14347	0.380208	0.190104	−	0.981764i	$-0.439117\pi$
$353$	7.14347	0.380208	0.190104	+	0.981764i	$0.439117\pi$
$354$	−31.7298	−1.68642
$355$	−1.91039	−0.101393
$356$	69.3259	3.67426
$357$	−14.1863	−0.750818
$358$	−27.2057	−1.43787
$359$	29.5839	1.56138	0.780689	−	0.624919i	$-0.214868\pi$
$359$	29.5839	1.56138	0.780689	+	0.624919i	$0.214868\pi$
$360$	−31.5437	−1.66250
$361$	5.81797	0.306209
$362$	40.0129	2.10303
$363$	−20.8700	−1.09539
$364$	−27.2670	−1.42918
$365$	11.4282	0.598182
$366$	36.3745	1.90132
$367$	−2.05983	−0.107522	−0.0537611	−	0.998554i	$-0.517121\pi$
$367$	−2.05983	−0.107522	−0.0537611	+	0.998554i	$0.517121\pi$
$368$	63.9354	3.33287
$369$	38.4952	2.00398
$370$	15.5975	0.810877
$371$	−3.95515	−0.205341
$372$	130.867	6.78514
$373$	2.74502	0.142132	0.0710658	−	0.997472i	$-0.477360\pi$
$373$	2.74502	0.142132	0.0710658	+	0.997472i	$0.477360\pi$
$374$	25.1117	1.29850
$375$	2.60914	0.134735
$376$	97.1317	5.00919
$377$	−56.7654	−2.92356
$378$	5.61764	0.288940
$379$	22.3935	1.15028	0.575139	−	0.818056i	$-0.304948\pi$
$379$	22.3935	1.15028	0.575139	+	0.818056i	$0.304948\pi$
$380$	25.4441	1.30525
$381$	−3.58173	−0.183497
$382$	13.4706	0.689218
$383$	−23.4653	−1.19902	−0.599511	−	0.800367i	$-0.704638\pi$
$383$	−23.4653	−1.19902	−0.599511	+	0.800367i	$0.704638\pi$
$384$	−35.7991	−1.82686
$385$	1.73240	0.0882913
$386$	14.1849	0.721990
$387$	0.640671	0.0325671
$388$	−7.76792	−0.394357
$389$	36.8408	1.86790	0.933952	−	0.357399i	$-0.116336\pi$
$389$	36.8408	1.86790	0.933952	+	0.357399i	$0.116336\pi$
$390$	−37.1354	−1.88042
$391$	29.2835	1.48093
$392$	−8.28438	−0.418424
$393$	16.5457	0.834622
$394$	37.6735	1.89796
$395$	−10.1717	−0.511793
$396$	−33.6902	−1.69300
$397$	11.9577	0.600139	0.300069	−	0.953917i	$-0.402990\pi$
$397$	11.9577	0.600139	0.300069	+	0.953917i	$0.402990\pi$
$398$	5.38833	0.270093
$399$	−12.9981	−0.650720
$400$	11.8711	0.593555
$401$	−16.8635	−0.842122	−0.421061	−	0.907032i	$-0.638342\pi$
$401$	−16.8635	−0.842122	−0.421061	+	0.907032i	$0.638342\pi$
$402$	−83.2809	−4.15367
$403$	52.4280	2.61162
$404$	−17.7040	−0.880806
$405$	−5.92495	−0.294413
$406$	−28.3469	−1.40683
$407$	10.1356	0.502401
$408$	−117.525	−5.81833
$409$	3.75966	0.185903	0.0929516	−	0.995671i	$-0.470370\pi$
$409$	3.75966	0.185903	0.0929516	+	0.995671i	$0.470370\pi$
$410$	−26.9533	−1.33113
$411$	30.2177	1.49053
$412$	54.8919	2.70433
$413$	−4.56156	−0.224460
$414$	−54.6713	−2.68695
$415$	−5.65341	−0.277515
$416$	−80.5037	−3.94702
$417$	21.2573	1.04097
$418$	23.0085	1.12538
$419$	−15.4638	−0.755458	−0.377729	−	0.925916i	$-0.623295\pi$
$419$	−15.4638	−0.755458	−0.377729	+	0.925916i	$0.623295\pi$
$420$	−13.3260	−0.650244
$421$	30.0997	1.46697	0.733485	−	0.679706i	$-0.237893\pi$
$421$	30.0997	1.46697	0.733485	+	0.679706i	$0.237893\pi$
$422$	−29.9977	−1.46027
$423$	−44.6430	−2.17062
$424$	−32.7660	−1.59126
$425$	5.43715	0.263741
$426$	13.2885	0.643830
$427$	5.22929	0.253063
$428$	−79.0063	−3.81892
$429$	−24.1312	−1.16507
$430$	−0.448580	−0.0216324
$431$	−32.9130	−1.58536	−0.792681	−	0.609636i	$-0.791316\pi$
$431$	−32.9130	−1.58536	−0.792681	+	0.609636i	$0.791316\pi$
$432$	25.0143	1.20350
$433$	22.4578	1.07925	0.539627	−	0.841904i	$-0.318565\pi$
$433$	22.4578	1.07925	0.539627	+	0.841904i	$0.318565\pi$
$434$	26.1810	1.25673
$435$	−27.7426	−1.33015
$436$	10.1459	0.485900
$437$	26.8308	1.28349
$438$	−79.4939	−3.79836
$439$	−8.67514	−0.414042	−0.207021	−	0.978336i	$-0.566377\pi$
$439$	−8.67514	−0.414042	−0.207021	+	0.978336i	$0.566377\pi$
$440$	14.3519	0.684198
$441$	3.80761	0.181315
$442$	−77.3860	−3.68088
$443$	−12.5903	−0.598185	−0.299093	−	0.954224i	$-0.596684\pi$
$443$	−12.5903	−0.598185	−0.299093	+	0.954224i	$0.596684\pi$
$444$	−77.9651	−3.70006
$445$	13.5735	0.643445
$446$	−42.1490	−1.99581
$447$	−45.4199	−2.14829
$448$	−16.4590	−0.777614
$449$	33.3785	1.57523	0.787615	−	0.616168i	$-0.211316\pi$
$449$	33.3785	1.57523	0.787615	+	0.616168i	$0.211316\pi$
$450$	−10.1510	−0.478523
$451$	−17.5147	−0.824735
$452$	−35.1662	−1.65408
$453$	41.8252	1.96512
$454$	33.8812	1.59012
$455$	−5.33868	−0.250281
$456$	−107.681	−5.04264
$457$	−11.3052	−0.528835	−0.264418	−	0.964408i	$-0.585180\pi$
$457$	−11.3052	−0.528835	−0.264418	+	0.964408i	$0.585180\pi$
$458$	2.66598	0.124573
$459$	11.4569	0.534764
$460$	27.5077	1.28255
$461$	1.05608	0.0491864	0.0245932	−	0.999698i	$-0.492171\pi$
$461$	1.05608	0.0491864	0.0245932	+	0.999698i	$0.492171\pi$
$462$	−12.0504	−0.560636
$463$	12.5107	0.581420	0.290710	−	0.956811i	$-0.406108\pi$
$463$	12.5107	0.581420	0.290710	+	0.956811i	$0.406108\pi$
$464$	−126.223	−5.85978
$465$	25.6228	1.18823
$466$	−44.7254	−2.07186
$467$	−10.2008	−0.472036	−0.236018	−	0.971749i	$-0.575842\pi$
$467$	−10.2008	−0.472036	−0.236018	+	0.971749i	$0.575842\pi$
$468$	103.822	4.79918
$469$	−11.9727	−0.552847
$470$	31.2578	1.44181
$471$	−12.2482	−0.564367
$472$	−37.7897	−1.73941
$473$	−0.291495	−0.0134030
$474$	70.7533	3.24980
$475$	4.98176	0.228579
$476$	−27.7699	−1.27283
$477$	15.0597	0.689534
$478$	−8.48401	−0.388049
$479$	9.98072	0.456031	0.228015	−	0.973658i	$-0.426776\pi$
$479$	9.98072	0.456031	0.228015	+	0.973658i	$0.426776\pi$
$480$	−39.3441	−1.79580
$481$	−31.2344	−1.42417
$482$	−13.5783	−0.618474
$483$	−14.0523	−0.639403
$484$	−40.8534	−1.85697
$485$	−1.52090	−0.0690606
$486$	58.0663	2.63394
$487$	−10.0502	−0.455418	−0.227709	−	0.973729i	$-0.573123\pi$
$487$	−10.0502	−0.455418	−0.227709	+	0.973729i	$0.573123\pi$
$488$	43.3214	1.96107
$489$	−42.1700	−1.90700
$490$	−2.66598	−0.120437
$491$	32.0264	1.44533	0.722666	−	0.691197i	$-0.242916\pi$
$491$	32.0264	1.44533	0.722666	+	0.691197i	$0.242916\pi$
$492$	134.727	6.07397
$493$	−57.8124	−2.60374
$494$	−70.9045	−3.19014
$495$	−6.59630	−0.296482
$496$	116.579	5.23455
$497$	1.91039	0.0856928
$498$	39.3246	1.76218
$499$	35.3195	1.58112	0.790559	−	0.612386i	$-0.209790\pi$
$499$	35.3195	1.58112	0.790559	+	0.612386i	$0.209790\pi$
$500$	5.10744	0.228412
$501$	−64.0573	−2.86187
$502$	−55.8871	−2.49436
$503$	−25.2531	−1.12598	−0.562991	−	0.826463i	$-0.690349\pi$
$503$	−25.2531	−1.12598	−0.562991	+	0.826463i	$0.690349\pi$
$504$	31.5437	1.40507
$505$	−3.46631	−0.154249
$506$	24.8746	1.10581
$507$	40.4456	1.79625
$508$	−7.01130	−0.311076
$509$	−32.9904	−1.46227	−0.731136	−	0.682231i	$-0.761010\pi$
$509$	−32.9904	−1.46227	−0.731136	+	0.682231i	$0.761010\pi$
$510$	−37.8203	−1.67471
$511$	−11.4282	−0.505556
$512$	17.6812	0.781405
$513$	10.4974	0.463470
$514$	−28.9032	−1.27487
$515$	10.7474	0.473588
$516$	2.24225	0.0987095
$517$	20.3118	0.893314
$518$	−15.5975	−0.685316
$519$	37.0618	1.62683
$520$	−44.2277	−1.93951
$521$	16.7802	0.735152	0.367576	−	0.929994i	$-0.380188\pi$
$521$	16.7802	0.735152	0.367576	+	0.929994i	$0.380188\pi$
$522$	107.934	4.72414
$523$	−0.441211	−0.0192928	−0.00964640	−	0.999953i	$-0.503071\pi$
$523$	−0.441211	−0.0192928	−0.00964640	+	0.999953i	$0.503071\pi$
$524$	32.3886	1.41490
$525$	−2.60914	−0.113872
$526$	19.4137	0.846477
$527$	53.3950	2.32592
$528$	−53.6582	−2.33517
$529$	6.00693	0.261171
$530$	−10.5443	−0.458017
$531$	17.3686	0.753735
$532$	−25.4441	−1.10314
$533$	53.9745	2.33790
$534$	−94.4160	−4.08578
$535$	−15.4689	−0.668777
$536$	−99.1862	−4.28419
$537$	26.6256	1.14898
$538$	−19.6440	−0.846913
$539$	−1.73240	−0.0746198
$540$	10.7622	0.463131
$541$	−13.5988	−0.584660	−0.292330	−	0.956318i	$-0.594431\pi$
$541$	−13.5988	−0.584660	−0.292330	+	0.956318i	$0.594431\pi$
$542$	−55.7949	−2.39660
$543$	−39.1598	−1.68051
$544$	−81.9886	−3.51523
$545$	1.98649	0.0850919
$546$	37.1354	1.58925
$547$	−15.3345	−0.655654	−0.327827	−	0.944738i	$-0.606316\pi$
$547$	−15.3345	−0.655654	−0.327827	+	0.944738i	$0.606316\pi$
$548$	59.1517	2.52683
$549$	−19.9111	−0.849784
$550$	4.61854	0.196935
$551$	−52.9703	−2.25661
$552$	−116.415	−4.95494
$553$	10.1717	0.432544
$554$	34.6546	1.47233
$555$	−15.2650	−0.647963
$556$	41.6115	1.76472
$557$	1.75492	0.0743584	0.0371792	−	0.999309i	$-0.488163\pi$
$557$	1.75492	0.0743584	0.0371792	+	0.999309i	$0.488163\pi$
$558$	−99.6869	−4.22008
$559$	0.898291	0.0379937
$560$	−11.8711	−0.501645
$561$	−24.5763	−1.03761
$562$	34.4271	1.45222
$563$	−34.0502	−1.43504	−0.717522	−	0.696535i	$-0.754724\pi$
$563$	−34.0502	−1.43504	−0.717522	+	0.696535i	$0.754724\pi$
$564$	−156.243	−6.57904
$565$	−6.88528	−0.289666
$566$	47.7000	2.00498
$567$	5.92495	0.248825
$568$	15.8264	0.664061
$569$	−0.671021	−0.0281307	−0.0140653	−	0.999901i	$-0.504477\pi$
$569$	−0.671021	−0.0281307	−0.0140653	+	0.999901i	$0.504477\pi$
$570$	−34.6527	−1.45144
$571$	17.3108	0.724436	0.362218	−	0.932093i	$-0.382020\pi$
$571$	17.3108	0.724436	0.362218	+	0.932093i	$0.382020\pi$
$572$	−47.2374	−1.97509
$573$	−13.1834	−0.550746
$574$	26.9533	1.12501
$575$	5.38581	0.224604
$576$	62.6693	2.61122
$577$	−0.691743	−0.0287976	−0.0143988	−	0.999896i	$-0.504583\pi$
$577$	−0.691743	−0.0287976	−0.0143988	+	0.999896i	$0.504583\pi$
$578$	−33.4917	−1.39307
$579$	−13.8824	−0.576934
$580$	−54.3066	−2.25496
$581$	5.65341	0.234543
$582$	10.5793	0.438524
$583$	−6.85190	−0.283777
$584$	−94.6759	−3.91772
$585$	20.3276	0.840443
$586$	71.2683	2.94407
$587$	−16.1596	−0.666978	−0.333489	−	0.942754i	$-0.608226\pi$
$587$	−16.1596	−0.666978	−0.333489	+	0.942754i	$0.608226\pi$
$588$	13.3260	0.549556
$589$	48.9229	2.01583
$590$	−12.1610	−0.500662
$591$	−36.8703	−1.51664
$592$	−69.4528	−2.85449
$593$	42.2008	1.73298	0.866489	−	0.499196i	$-0.166371\pi$
$593$	42.2008	1.73298	0.866489	+	0.499196i	$0.166371\pi$
$594$	9.73200	0.399309
$595$	−5.43715	−0.222902
$596$	−88.9104	−3.64191
$597$	−5.27345	−0.215828
$598$	−76.6552	−3.13466
$599$	−12.2774	−0.501642	−0.250821	−	0.968034i	$-0.580701\pi$
$599$	−12.2774	−0.501642	−0.250821	+	0.968034i	$0.580701\pi$
$600$	−21.6151	−0.882433
$601$	−35.7188	−1.45700	−0.728501	−	0.685045i	$-0.759783\pi$
$601$	−35.7188	−1.45700	−0.728501	+	0.685045i	$0.759783\pi$
$602$	0.448580	0.0182827
$603$	45.5873	1.85646
$604$	81.8738	3.33140
$605$	−7.99879	−0.325197
$606$	24.1113	0.979456
$607$	−0.646823	−0.0262538	−0.0131269	−	0.999914i	$-0.504179\pi$
$607$	−0.646823	−0.0262538	−0.0131269	+	0.999914i	$0.504179\pi$
$608$	−75.1217	−3.04659
$609$	27.7426	1.12419
$610$	13.9412	0.564462
$611$	−62.5943	−2.53230
$612$	105.737	4.27417
$613$	6.45106	0.260556	0.130278	−	0.991478i	$-0.458413\pi$
$613$	6.45106	0.260556	0.130278	+	0.991478i	$0.458413\pi$
$614$	16.9671	0.684738
$615$	26.3786	1.06369
$616$	−14.3519	−0.578253
$617$	14.4828	0.583056	0.291528	−	0.956562i	$-0.405836\pi$
$617$	14.4828	0.583056	0.291528	+	0.956562i	$0.405836\pi$
$618$	−74.7581	−3.00721
$619$	−26.6892	−1.07273	−0.536366	−	0.843986i	$-0.680203\pi$
$619$	−26.6892	−1.07273	−0.536366	+	0.843986i	$0.680203\pi$
$620$	50.1571	2.01436
$621$	11.3488	0.455410
$622$	32.2037	1.29125
$623$	−13.5735	−0.543811
$624$	165.357	6.61957
$625$	1.00000	0.0400000
$626$	−31.0814	−1.24226
$627$	−22.5179	−0.899280
$628$	−23.9761	−0.956750
$629$	−31.8105	−1.26837
$630$	10.1510	0.404426
$631$	41.1671	1.63884	0.819418	−	0.573197i	$-0.194297\pi$
$631$	41.1671	1.63884	0.819418	+	0.573197i	$0.194297\pi$
$632$	84.2660	3.35192
$633$	29.3582	1.16688
$634$	9.28100	0.368596
$635$	−1.37276	−0.0544764
$636$	52.7065	2.08995
$637$	5.33868	0.211526
$638$	−49.1082	−1.94421
$639$	−7.27402	−0.287756
$640$	−13.7206	−0.542356
$641$	29.5787	1.16829	0.584144	−	0.811650i	$-0.301430\pi$
$641$	29.5787	1.16829	0.584144	+	0.811650i	$0.301430\pi$
$642$	107.600	4.24663
$643$	−13.4707	−0.531233	−0.265617	−	0.964079i	$-0.585576\pi$
$643$	−13.4707	−0.531233	−0.265617	+	0.964079i	$0.585576\pi$
$644$	−27.5077	−1.08396
$645$	0.439016	0.0172862
$646$	−72.2123	−2.84116
$647$	24.4706	0.962039	0.481019	−	0.876710i	$-0.340267\pi$
$647$	24.4706	0.962039	0.481019	+	0.876710i	$0.340267\pi$
$648$	49.0845	1.92822
$649$	−7.90246	−0.310199
$650$	−14.2328	−0.558257
$651$	−25.6228	−1.00424
$652$	−82.5487	−3.23286
$653$	−17.9376	−0.701954	−0.350977	−	0.936384i	$-0.614150\pi$
$653$	−17.9376	−0.701954	−0.350977	+	0.936384i	$0.614150\pi$
$654$	−13.8178	−0.540321
$655$	6.34145	0.247781
$656$	120.018	4.68591
$657$	43.5143	1.69765
$658$	−31.2578	−1.21855
$659$	−15.1706	−0.590962	−0.295481	−	0.955349i	$-0.595480\pi$
$659$	−15.1706	−0.590962	−0.295481	+	0.955349i	$0.595480\pi$
$660$	−23.0860	−0.898622
$661$	2.89838	0.112734	0.0563670	−	0.998410i	$-0.482048\pi$
$661$	2.89838	0.112734	0.0563670	+	0.998410i	$0.482048\pi$
$662$	13.9398	0.541787
$663$	75.7361	2.94135
$664$	46.8350	1.81755
$665$	−4.98176	−0.193184
$666$	59.3893	2.30129
$667$	−57.2664	−2.21737
$668$	−125.393	−4.85162
$669$	41.2504	1.59483
$670$	−31.9189	−1.23314
$671$	9.05922	0.349727
$672$	39.3441	1.51773
$673$	10.2177	0.393862	0.196931	−	0.980417i	$-0.436902\pi$
$673$	10.2177	0.393862	0.196931	+	0.980417i	$0.436902\pi$
$674$	92.3438	3.55695
$675$	2.10716	0.0811046
$676$	79.1732	3.04512
$677$	−11.5666	−0.444542	−0.222271	−	0.974985i	$-0.571347\pi$
$677$	−11.5666	−0.444542	−0.222271	+	0.974985i	$0.571347\pi$
$678$	47.8934	1.83934
$679$	1.52090	0.0583669
$680$	−45.0434	−1.72734
$681$	−33.1588	−1.27065
$682$	45.3559	1.73677
$683$	23.5443	0.900898	0.450449	−	0.892802i	$-0.351264\pi$
$683$	23.5443	0.900898	0.450449	+	0.892802i	$0.351264\pi$
$684$	96.8810	3.70434
$685$	11.5815	0.442505
$686$	2.66598	0.101788
$687$	−2.60914	−0.0995449
$688$	1.99744	0.0761517
$689$	21.1153	0.804429
$690$	−37.4632	−1.42620
$691$	45.7708	1.74120	0.870601	−	0.491990i	$-0.163730\pi$
$691$	45.7708	1.74120	0.870601	+	0.491990i	$0.163730\pi$
$692$	72.5493	2.75791
$693$	6.59630	0.250573
$694$	−42.2113	−1.60232
$695$	8.14723	0.309042
$696$	229.830	8.71168
$697$	54.9701	2.08214
$698$	−69.4962	−2.63047
$699$	43.7718	1.65560
$700$	−5.10744	−0.193043
$701$	21.0192	0.793885	0.396942	−	0.917844i	$-0.370071\pi$
$701$	21.0192	0.793885	0.396942	+	0.917844i	$0.370071\pi$
$702$	−29.9908	−1.13193
$703$	−29.1462	−1.09927
$704$	−28.5136	−1.07464
$705$	−30.5913	−1.15214
$706$	−19.0443	−0.716743
$707$	3.46631	0.130364
$708$	60.7876	2.28454
$709$	−31.3454	−1.17720	−0.588601	−	0.808424i	$-0.700321\pi$
$709$	−31.3454	−1.17720	−0.588601	+	0.808424i	$0.700321\pi$
$710$	5.09306	0.191139
$711$	−38.7297	−1.45248
$712$	−112.448	−4.21417
$713$	52.8908	1.98078
$714$	37.8203	1.41539
$715$	−9.24873	−0.345883
$716$	52.1203	1.94783
$717$	8.30312	0.310086
$718$	−78.8701	−2.94340
$719$	−26.9823	−1.00627	−0.503136	−	0.864207i	$-0.667820\pi$
$719$	−26.9823	−1.00627	−0.503136	+	0.864207i	$0.667820\pi$
$720$	45.2005	1.68452
$721$	−10.7474	−0.400255
$722$	−15.5106	−0.577244
$723$	13.2888	0.494215
$724$	−76.6561	−2.84890
$725$	−10.6328	−0.394894
$726$	55.6389	2.06495
$727$	24.5451	0.910327	0.455163	−	0.890408i	$-0.349581\pi$
$727$	24.5451	0.910327	0.455163	+	0.890408i	$0.349581\pi$
$728$	44.2277	1.63919
$729$	−39.0535	−1.44643
$730$	−30.4675	−1.12765
$731$	0.914860	0.0338373
$732$	−69.6857	−2.57566
$733$	10.6464	0.393232	0.196616	−	0.980481i	$-0.437005\pi$
$733$	10.6464	0.393232	0.196616	+	0.980481i	$0.437005\pi$
$734$	5.49146	0.202693
$735$	2.60914	0.0962395
$736$	−81.2144	−2.99360
$737$	−20.7415	−0.764022
$738$	−102.627	−3.77777
$739$	−32.9569	−1.21234	−0.606169	−	0.795336i	$-0.707295\pi$
$739$	−32.9569	−1.21234	−0.606169	+	0.795336i	$0.707295\pi$
$740$	−29.8815	−1.09847
$741$	69.3928	2.54921
$742$	10.5443	0.387095
$743$	5.41432	0.198632	0.0993161	−	0.995056i	$-0.468335\pi$
$743$	5.41432	0.198632	0.0993161	+	0.995056i	$0.468335\pi$
$744$	−212.269	−7.78216
$745$	−17.4080	−0.637780
$746$	−7.31815	−0.267937
$747$	−21.5260	−0.787594
$748$	−48.1087	−1.75903
$749$	15.4689	0.565220
$750$	−6.95591	−0.253994
$751$	21.8713	0.798095	0.399047	−	0.916930i	$-0.369341\pi$
$751$	21.8713	0.798095	0.399047	+	0.916930i	$0.369341\pi$
$752$	−139.185	−5.07555
$753$	54.6955	1.99322
$754$	151.335	5.51130
$755$	16.0303	0.583402
$756$	−10.7622	−0.391417
$757$	−38.1294	−1.38584	−0.692918	−	0.721017i	$-0.743675\pi$
$757$	−38.1294	−1.38584	−0.692918	+	0.721017i	$0.743675\pi$
$758$	−59.7006	−2.16842
$759$	−24.3442	−0.883640
$760$	−41.2708	−1.49705
$761$	−0.158026	−0.00572843	−0.00286422	−	0.999996i	$-0.500912\pi$
$761$	−0.158026	−0.00572843	−0.00286422	+	0.999996i	$0.500912\pi$
$762$	9.54881	0.345917
$763$	−1.98649	−0.0719158
$764$	−25.8069	−0.933659
$765$	20.7025	0.748502
$766$	62.5580	2.26031
$767$	24.3527	0.879327
$768$	9.55204	0.344680
$769$	11.6922	0.421631	0.210816	−	0.977526i	$-0.432388\pi$
$769$	11.6922	0.421631	0.210816	+	0.977526i	$0.432388\pi$
$770$	−4.61854	−0.166441
$771$	28.2870	1.01873
$772$	−27.1751	−0.978054
$773$	23.8192	0.856718	0.428359	−	0.903609i	$-0.359092\pi$
$773$	23.8192	0.856718	0.428359	+	0.903609i	$0.359092\pi$
$774$	−1.70802	−0.0613933
$775$	9.82040	0.352759
$776$	12.5997	0.452304
$777$	15.2650	0.547628
$778$	−98.2169	−3.52124
$779$	50.3660	1.80455
$780$	71.1434	2.54734
$781$	3.30956	0.118425
$782$	−78.0691	−2.79174
$783$	−22.4051	−0.800692
$784$	11.8711	0.423968
$785$	−4.69434	−0.167548
$786$	−44.1106	−1.57337
$787$	−53.2029	−1.89648	−0.948239	−	0.317559i	$-0.897137\pi$
$787$	−53.2029	−1.89648	−0.948239	+	0.317559i	$0.897137\pi$
$788$	−72.1744	−2.57111
$789$	−18.9998	−0.676410
$790$	27.1175	0.964796
$791$	6.88528	0.244813
$792$	54.6462	1.94177
$793$	−27.9175	−0.991380
$794$	−31.8789	−1.13134
$795$	10.3195	0.365996
$796$	−10.3229	−0.365885
$797$	6.37463	0.225801	0.112900	−	0.993606i	$-0.463986\pi$
$797$	6.37463	0.225801	0.112900	+	0.993606i	$0.463986\pi$
$798$	34.6527	1.22669
$799$	−63.7489	−2.25527
$800$	−15.0793	−0.533135
$801$	51.6825	1.82611
$802$	44.9577	1.58751
$803$	−19.7983	−0.698667
$804$	159.548	5.62684
$805$	−5.38581	−0.189825
$806$	−139.772	−4.92326
$807$	19.2252	0.676758
$808$	28.7162	1.01023
$809$	−36.9023	−1.29741	−0.648707	−	0.761038i	$-0.724690\pi$
$809$	−36.9023	−1.29741	−0.648707	+	0.761038i	$0.724690\pi$
$810$	15.7958	0.555008
$811$	−10.5688	−0.371121	−0.185561	−	0.982633i	$-0.559410\pi$
$811$	−10.5688	−0.371121	−0.185561	+	0.982633i	$0.559410\pi$
$812$	54.3066	1.90579
$813$	54.6053	1.91509
$814$	−27.0212	−0.947091
$815$	−16.1624	−0.566145
$816$	168.407	5.89542
$817$	0.838236	0.0293261
$818$	−10.0232	−0.350452
$819$	−20.3276	−0.710304
$820$	51.6367	1.80323
$821$	53.2448	1.85826	0.929128	−	0.369758i	$-0.120559\pi$
$821$	53.2448	1.85826	0.929128	+	0.369758i	$0.120559\pi$
$822$	−80.5596	−2.80984
$823$	41.0193	1.42984	0.714922	−	0.699205i	$-0.246462\pi$
$823$	41.0193	1.42984	0.714922	+	0.699205i	$0.246462\pi$
$824$	−89.0357	−3.10171
$825$	−4.52007	−0.157369
$826$	12.1610	0.423137
$827$	−24.1207	−0.838758	−0.419379	−	0.907811i	$-0.637752\pi$
$827$	−24.1207	−0.838758	−0.419379	+	0.907811i	$0.637752\pi$
$828$	104.739	3.63992
$829$	53.5829	1.86101	0.930506	−	0.366278i	$-0.119368\pi$
$829$	53.5829	1.86101	0.930506	+	0.366278i	$0.119368\pi$
$830$	15.0719	0.523152
$831$	−33.9157	−1.17652
$832$	87.8693	3.04632
$833$	5.43715	0.188386
$834$	−56.6714	−1.96237
$835$	−24.5511	−0.849626
$836$	−44.0793	−1.52452
$837$	20.6931	0.715260
$838$	41.2263	1.42414
$839$	47.9461	1.65528	0.827641	−	0.561257i	$-0.189682\pi$
$839$	47.9461	1.65528	0.827641	+	0.561257i	$0.189682\pi$
$840$	21.6151	0.745792
$841$	84.0573	2.89853
$842$	−80.2451	−2.76543
$843$	−33.6931	−1.16045
$844$	57.4692	1.97817
$845$	15.5015	0.533269
$846$	119.017	4.09190
$847$	7.99879	0.274842
$848$	46.9520	1.61234
$849$	−46.6830	−1.60216
$850$	−14.4953	−0.497186
$851$	−31.5101	−1.08015
$852$	−25.4579	−0.872174
$853$	18.7168	0.640852	0.320426	−	0.947274i	$-0.396174\pi$
$853$	18.7168	0.640852	0.320426	+	0.947274i	$0.396174\pi$
$854$	−13.9412	−0.477057
$855$	18.9686	0.648712
$856$	128.150	4.38007
$857$	5.36281	0.183190	0.0915951	−	0.995796i	$-0.470803\pi$
$857$	5.36281	0.183190	0.0915951	+	0.995796i	$0.470803\pi$
$858$	64.3334	2.19630
$859$	14.7613	0.503647	0.251824	−	0.967773i	$-0.418970\pi$
$859$	14.7613	0.503647	0.251824	+	0.967773i	$0.418970\pi$
$860$	0.859383	0.0293047
$861$	−26.3786	−0.898981
$862$	87.7453	2.98862
$863$	−21.0511	−0.716589	−0.358294	−	0.933609i	$-0.616642\pi$
$863$	−21.0511	−0.716589	−0.358294	+	0.933609i	$0.616642\pi$
$864$	−31.7745	−1.08099
$865$	14.2046	0.482972
$866$	−59.8721	−2.03454
$867$	32.7776	1.11319
$868$	−50.1571	−1.70244
$869$	17.6214	0.597766
$870$	73.9611	2.50752
$871$	63.9183	2.16579
$872$	−16.4568	−0.557299
$873$	−5.79100	−0.195996
$874$	−71.5304	−2.41955
$875$	−1.00000	−0.0338062
$876$	152.293	5.14551
$877$	38.8545	1.31202	0.656012	−	0.754750i	$-0.272242\pi$
$877$	38.8545	1.31202	0.656012	+	0.754750i	$0.272242\pi$
$878$	23.1278	0.780524
$879$	−69.7489	−2.35257
$880$	−20.5655	−0.693262
$881$	−4.80681	−0.161945	−0.0809727	−	0.996716i	$-0.525803\pi$
$881$	−4.80681	−0.161945	−0.0809727	+	0.996716i	$0.525803\pi$
$882$	−10.1510	−0.341802
$883$	−49.5170	−1.66638	−0.833190	−	0.552986i	$-0.813488\pi$
$883$	−49.5170	−1.66638	−0.833190	+	0.552986i	$0.813488\pi$
$884$	148.255	4.98635
$885$	11.9018	0.400073
$886$	33.5656	1.12766
$887$	−52.5788	−1.76542	−0.882712	−	0.469914i	$-0.844285\pi$
$887$	−52.5788	−1.76542	−0.882712	+	0.469914i	$0.844285\pi$
$888$	126.461	4.24375
$889$	1.37276	0.0460410
$890$	−36.1867	−1.21298
$891$	10.2644	0.343870
$892$	80.7485	2.70366
$893$	−58.4096	−1.95460
$894$	121.088	4.04980
$895$	10.2048	0.341108
$896$	13.7206	0.458375
$897$	75.0209	2.50487
$898$	−88.9864	−2.96951
$899$	−104.419	−3.48256
$900$	19.4471	0.648238
$901$	21.5048	0.716427
$902$	46.6938	1.55474
$903$	−0.439016	−0.0146095
$904$	57.0403	1.89713
$905$	−15.0087	−0.498906
$906$	−111.505	−3.70451
$907$	−12.5440	−0.416516	−0.208258	−	0.978074i	$-0.566779\pi$
$907$	−12.5440	−0.416516	−0.208258	+	0.978074i	$0.566779\pi$
$908$	−64.9091	−2.15408
$909$	−13.1983	−0.437761
$910$	14.2328	0.471813
$911$	−32.8723	−1.08911	−0.544554	−	0.838726i	$-0.683301\pi$
$911$	−32.8723	−1.08911	−0.544554	+	0.838726i	$0.683301\pi$
$912$	154.302	5.10944
$913$	9.79397	0.324133
$914$	30.1394	0.996924
$915$	−13.6439	−0.451055
$916$	−5.10744	−0.168755
$917$	−6.34145	−0.209413
$918$	−30.5440	−1.00810
$919$	−22.9318	−0.756452	−0.378226	−	0.925713i	$-0.623466\pi$
$919$	−22.9318	−0.756452	−0.378226	+	0.925713i	$0.623466\pi$
$920$	−44.6181	−1.47101
$921$	−16.6054	−0.547167
$922$	−2.81548	−0.0927229
$923$	−10.1990	−0.335703
$924$	23.0860	0.759474
$925$	−5.85058	−0.192366
$926$	−33.3532	−1.09605
$927$	40.9220	1.34405
$928$	160.336	5.26329
$929$	50.4059	1.65376	0.826882	−	0.562375i	$-0.190112\pi$
$929$	50.4059	1.65376	0.826882	+	0.562375i	$0.190112\pi$
$930$	−68.3098	−2.23997
$931$	4.98176	0.163271
$932$	85.6842	2.80668
$933$	−31.5171	−1.03182
$934$	27.1951	0.889850
$935$	−9.41932	−0.308045
$936$	−168.402	−5.50438
$937$	34.0424	1.11212	0.556058	−	0.831143i	$-0.312313\pi$
$937$	34.0424	1.11212	0.556058	+	0.831143i	$0.312313\pi$
$938$	31.9189	1.04219
$939$	30.4187	0.992678
$940$	−59.8832	−1.95317
$941$	−18.4053	−0.599994	−0.299997	−	0.953940i	$-0.596986\pi$
$941$	−18.4053	−0.599994	−0.299997	+	0.953940i	$0.596986\pi$
$942$	32.6534	1.06391
$943$	54.4510	1.77317
$944$	54.1508	1.76246
$945$	−2.10716	−0.0685459
$946$	0.777120	0.0252663
$947$	19.1307	0.621664	0.310832	−	0.950465i	$-0.399392\pi$
$947$	19.1307	0.621664	0.310832	+	0.950465i	$0.399392\pi$
$948$	−135.548	−4.40240
$949$	61.0118	1.98053
$950$	−13.2813	−0.430902
$951$	−9.08312	−0.294540
$952$	45.0434	1.45987
$953$	−24.8037	−0.803472	−0.401736	−	0.915756i	$-0.631593\pi$
$953$	−24.8037	−0.803472	−0.401736	+	0.915756i	$0.631593\pi$
$954$	−40.1487	−1.29986
$955$	−5.05279	−0.163505
$956$	16.2535	0.525677
$957$	48.0612	1.55360
$958$	−26.6084	−0.859678
$959$	−11.5815	−0.373985
$960$	42.9438	1.38600
$961$	65.4403	2.11098
$962$	83.2703	2.68474
$963$	−58.8993	−1.89800
$964$	26.0131	0.837824
$965$	−5.32069	−0.171279
$966$	37.4632	1.20536
$967$	38.9800	1.25351	0.626757	−	0.779215i	$-0.284382\pi$
$967$	38.9800	1.25351	0.626757	+	0.779215i	$0.284382\pi$
$968$	66.2650	2.12984
$969$	70.6727	2.27033
$970$	4.05469	0.130188
$971$	−51.5259	−1.65354	−0.826772	−	0.562537i	$-0.809825\pi$
$971$	−51.5259	−1.65354	−0.826772	+	0.562537i	$0.809825\pi$
$972$	−111.243	−3.56811
$973$	−8.14723	−0.261188
$974$	26.7936	0.858522
$975$	13.9294	0.446097
$976$	−62.0774	−1.98705
$977$	9.27677	0.296790	0.148395	−	0.988928i	$-0.452589\pi$
$977$	9.27677	0.296790	0.148395	+	0.988928i	$0.452589\pi$
$978$	112.424	3.59494
$979$	−23.5147	−0.751534
$980$	5.10744	0.163151
$981$	7.56377	0.241493
$982$	−85.3818	−2.72464
$983$	−31.6542	−1.00961	−0.504806	−	0.863233i	$-0.668436\pi$
$983$	−31.6542	−1.00961	−0.504806	+	0.863233i	$0.668436\pi$
$984$	−218.530	−6.96650
$985$	−14.1312	−0.450258
$986$	154.127	4.90839
$987$	30.5913	0.973733
$988$	135.838	4.32158
$989$	0.906220	0.0288161
$990$	17.5856	0.558907
$991$	1.47714	0.0469227	0.0234614	−	0.999725i	$-0.492531\pi$
$991$	1.47714	0.0469227	0.0234614	+	0.999725i	$0.492531\pi$
$992$	−148.085	−4.70171
$993$	−13.6426	−0.432936
$994$	−5.09306	−0.161542
$995$	−2.02115	−0.0640746
$996$	−75.3375	−2.38716
$997$	−19.7908	−0.626780	−0.313390	−	0.949625i	$-0.601465\pi$
$997$	−19.7908	−0.626780	−0.313390	+	0.949625i	$0.601465\pi$
$998$	−94.1610	−2.98062
$999$	−12.3281	−0.390044

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.m.1.3	✓	67

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.m.1.3	✓	67	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:	\( N \)	\(=\)	\( 8015 = 5 \cdot 7 \cdot 229 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8015.a (trivial)

\(f(q)\)	\(=\)	\(q-2.66598 q^{2} +2.60914 q^{3} +5.10744 q^{4} +1.00000 q^{5} -6.95591 q^{6} -1.00000 q^{7} -8.28438 q^{8} +3.80761 q^{9} +O(q^{10})\)	\(q-2.66598 q^{2} +2.60914 q^{3} +5.10744 q^{4} +1.00000 q^{5} -6.95591 q^{6} -1.00000 q^{7} -8.28438 q^{8} +3.80761 q^{9} -2.66598 q^{10} -1.73240 q^{11} +13.3260 q^{12} +5.33868 q^{13} +2.66598 q^{14} +2.60914 q^{15} +11.8711 q^{16} +5.43715 q^{17} -10.1510 q^{18} +4.98176 q^{19} +5.10744 q^{20} -2.60914 q^{21} +4.61854 q^{22} +5.38581 q^{23} -21.6151 q^{24} +1.00000 q^{25} -14.2328 q^{26} +2.10716 q^{27} -5.10744 q^{28} -10.6328 q^{29} -6.95591 q^{30} +9.82040 q^{31} -15.0793 q^{32} -4.52007 q^{33} -14.4953 q^{34} -1.00000 q^{35} +19.4471 q^{36} -5.85058 q^{37} -13.2813 q^{38} +13.9294 q^{39} -8.28438 q^{40} +10.1101 q^{41} +6.95591 q^{42} +0.168261 q^{43} -8.84814 q^{44} +3.80761 q^{45} -14.3585 q^{46} -11.7247 q^{47} +30.9733 q^{48} +1.00000 q^{49} -2.66598 q^{50} +14.1863 q^{51} +27.2670 q^{52} +3.95515 q^{53} -5.61764 q^{54} -1.73240 q^{55} +8.28438 q^{56} +12.9981 q^{57} +28.3469 q^{58} +4.56156 q^{59} +13.3260 q^{60} -5.22929 q^{61} -26.1810 q^{62} -3.80761 q^{63} +16.4590 q^{64} +5.33868 q^{65} +12.0504 q^{66} +11.9727 q^{67} +27.7699 q^{68} +14.0523 q^{69} +2.66598 q^{70} -1.91039 q^{71} -31.5437 q^{72} +11.4282 q^{73} +15.5975 q^{74} +2.60914 q^{75} +25.4441 q^{76} +1.73240 q^{77} -37.1354 q^{78} -10.1717 q^{79} +11.8711 q^{80} -5.92495 q^{81} -26.9533 q^{82} -5.65341 q^{83} -13.3260 q^{84} +5.43715 q^{85} -0.448580 q^{86} -27.7426 q^{87} +14.3519 q^{88} +13.5735 q^{89} -10.1510 q^{90} -5.33868 q^{91} +27.5077 q^{92} +25.6228 q^{93} +31.2578 q^{94} +4.98176 q^{95} -39.3441 q^{96} -1.52090 q^{97} -2.66598 q^{98} -6.59630 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 67 q + 3 q^{2} + 73 q^{4} + 67 q^{5} + 17 q^{6} - 67 q^{7} + 12 q^{8} + 97 q^{9}+O(q^{10}) \) 67 * q + 3 * q^2 + 73 * q^4 + 67 * q^5 + 17 * q^6 - 67 * q^7 + 12 * q^8 + 97 * q^9	\( 67 q + 3 q^{2} + 73 q^{4} + 67 q^{5} + 17 q^{6} - 67 q^{7} + 12 q^{8} + 97 q^{9} + 3 q^{10} + 11 q^{11} + 9 q^{12} + 19 q^{13} - 3 q^{14} + 93 q^{16} + 7 q^{17} + 9 q^{18} + 36 q^{19} + 73 q^{20} - 8 q^{22} - 2 q^{23} + 37 q^{24} + 67 q^{25} + 39 q^{26} + 6 q^{27} - 73 q^{28} + 56 q^{29} + 17 q^{30} + 63 q^{31} + 27 q^{32} + 51 q^{33} + 55 q^{34} - 67 q^{35} + 148 q^{36} + 28 q^{37} + 10 q^{38} + 7 q^{39} + 12 q^{40} + 84 q^{41} - 17 q^{42} - 11 q^{43} + 41 q^{44} + 97 q^{45} + 17 q^{46} - 10 q^{47} + 10 q^{48} + 67 q^{49} + 3 q^{50} - q^{51} + 49 q^{52} + 3 q^{53} + 20 q^{54} + 11 q^{55} - 12 q^{56} + 45 q^{57} + 22 q^{58} + 80 q^{59} + 9 q^{60} + 64 q^{61} - 37 q^{62} - 97 q^{63} + 110 q^{64} + 19 q^{65} + 75 q^{66} + 22 q^{67} + 7 q^{68} + 107 q^{69} - 3 q^{70} + 24 q^{71} + 72 q^{72} + 83 q^{73} + 52 q^{74} + 115 q^{76} - 11 q^{77} - 70 q^{78} - 32 q^{79} + 93 q^{80} + 183 q^{81} + 56 q^{82} - 58 q^{83} - 9 q^{84} + 7 q^{85} + 51 q^{86} + 20 q^{87} - 5 q^{88} + 129 q^{89} + 9 q^{90} - 19 q^{91} - 37 q^{92} + 33 q^{93} + 89 q^{94} + 36 q^{95} + 129 q^{96} + 126 q^{97} + 3 q^{98} - 27 q^{99}+O(q^{100}) \) 67 * q + 3 * q^2 + 73 * q^4 + 67 * q^5 + 17 * q^6 - 67 * q^7 + 12 * q^8 + 97 * q^9 + 3 * q^10 + 11 * q^11 + 9 * q^12 + 19 * q^13 - 3 * q^14 + 93 * q^16 + 7 * q^17 + 9 * q^18 + 36 * q^19 + 73 * q^20 - 8 * q^22 - 2 * q^23 + 37 * q^24 + 67 * q^25 + 39 * q^26 + 6 * q^27 - 73 * q^28 + 56 * q^29 + 17 * q^30 + 63 * q^31 + 27 * q^32 + 51 * q^33 + 55 * q^34 - 67 * q^35 + 148 * q^36 + 28 * q^37 + 10 * q^38 + 7 * q^39 + 12 * q^40 + 84 * q^41 - 17 * q^42 - 11 * q^43 + 41 * q^44 + 97 * q^45 + 17 * q^46 - 10 * q^47 + 10 * q^48 + 67 * q^49 + 3 * q^50 - q^51 + 49 * q^52 + 3 * q^53 + 20 * q^54 + 11 * q^55 - 12 * q^56 + 45 * q^57 + 22 * q^58 + 80 * q^59 + 9 * q^60 + 64 * q^61 - 37 * q^62 - 97 * q^63 + 110 * q^64 + 19 * q^65 + 75 * q^66 + 22 * q^67 + 7 * q^68 + 107 * q^69 - 3 * q^70 + 24 * q^71 + 72 * q^72 + 83 * q^73 + 52 * q^74 + 115 * q^76 - 11 * q^77 - 70 * q^78 - 32 * q^79 + 93 * q^80 + 183 * q^81 + 56 * q^82 - 58 * q^83 - 9 * q^84 + 7 * q^85 + 51 * q^86 + 20 * q^87 - 5 * q^88 + 129 * q^89 + 9 * q^90 - 19 * q^91 - 37 * q^92 + 33 * q^93 + 89 * q^94 + 36 * q^95 + 129 * q^96 + 126 * q^97 + 3 * q^98 - 27 * q^99

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