LMFDB - Embedded newform 8015.2.a.i.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:	$1$
Dimension:	$44$
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)

$f(q)$	$=$	$q-2.32161 q^{2} -1.61048 q^{3} +3.38989 q^{4} +1.00000 q^{5} +3.73891 q^{6} -1.00000 q^{7} -3.22677 q^{8} -0.406353 q^{9} +O(q^{10})$	\(q-2.32161 q^{2} -1.61048 q^{3} +3.38989 q^{4} +1.00000 q^{5} +3.73891 q^{6} -1.00000 q^{7} -3.22677 q^{8} -0.406353 q^{9} -2.32161 q^{10} -1.92221 q^{11} -5.45934 q^{12} -2.65544 q^{13} +2.32161 q^{14} -1.61048 q^{15} +0.711551 q^{16} -1.71382 q^{17} +0.943394 q^{18} -6.17735 q^{19} +3.38989 q^{20} +1.61048 q^{21} +4.46264 q^{22} -3.52947 q^{23} +5.19666 q^{24} +1.00000 q^{25} +6.16489 q^{26} +5.48586 q^{27} -3.38989 q^{28} -3.98704 q^{29} +3.73891 q^{30} +0.382786 q^{31} +4.80160 q^{32} +3.09569 q^{33} +3.97882 q^{34} -1.00000 q^{35} -1.37749 q^{36} +1.71819 q^{37} +14.3414 q^{38} +4.27653 q^{39} -3.22677 q^{40} -3.97201 q^{41} -3.73891 q^{42} +4.07646 q^{43} -6.51609 q^{44} -0.406353 q^{45} +8.19407 q^{46} +12.2938 q^{47} -1.14594 q^{48} +1.00000 q^{49} -2.32161 q^{50} +2.76007 q^{51} -9.00162 q^{52} +0.976477 q^{53} -12.7361 q^{54} -1.92221 q^{55} +3.22677 q^{56} +9.94851 q^{57} +9.25636 q^{58} +13.5071 q^{59} -5.45934 q^{60} +4.81943 q^{61} -0.888682 q^{62} +0.406353 q^{63} -12.5706 q^{64} -2.65544 q^{65} -7.18699 q^{66} +10.9839 q^{67} -5.80964 q^{68} +5.68415 q^{69} +2.32161 q^{70} -14.7303 q^{71} +1.31121 q^{72} +10.8239 q^{73} -3.98896 q^{74} -1.61048 q^{75} -20.9405 q^{76} +1.92221 q^{77} -9.92844 q^{78} +13.3536 q^{79} +0.711551 q^{80} -7.61582 q^{81} +9.22147 q^{82} +9.80584 q^{83} +5.45934 q^{84} -1.71382 q^{85} -9.46395 q^{86} +6.42105 q^{87} +6.20255 q^{88} +16.3538 q^{89} +0.943394 q^{90} +2.65544 q^{91} -11.9645 q^{92} -0.616470 q^{93} -28.5414 q^{94} -6.17735 q^{95} -7.73289 q^{96} +11.0182 q^{97} -2.32161 q^{98} +0.781097 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 2 q^{2} + 30 q^{4} + 44 q^{5} - 7 q^{6} - 44 q^{7} - 3 q^{8} + 16 q^{9}+O(q^{10}) $ 44 * q - 2 * q^2 + 30 * q^4 + 44 * q^5 - 7 * q^6 - 44 * q^7 - 3 * q^8 + 16 * q^9	\( 44 q - 2 q^{2} + 30 q^{4} + 44 q^{5} - 7 q^{6} - 44 q^{7} - 3 q^{8} + 16 q^{9} - 2 q^{10} - 15 q^{11} - 3 q^{12} - 17 q^{13} + 2 q^{14} + 10 q^{16} - 7 q^{17} - 16 q^{18} - 32 q^{19} + 30 q^{20} - 14 q^{22} + 8 q^{23} - 35 q^{24} + 44 q^{25} - 27 q^{26} + 6 q^{27} - 30 q^{28} - 42 q^{29} - 7 q^{30} - 43 q^{31} - 8 q^{32} - 33 q^{33} - 33 q^{34} - 44 q^{35} - 11 q^{36} - 44 q^{37} + 4 q^{38} + 3 q^{39} - 3 q^{40} - 62 q^{41} + 7 q^{42} - 7 q^{43} - 45 q^{44} + 16 q^{45} - 15 q^{46} + 2 q^{47} - 26 q^{48} + 44 q^{49} - 2 q^{50} - 25 q^{51} - 35 q^{52} - 25 q^{53} - 76 q^{54} - 15 q^{55} + 3 q^{56} - 7 q^{57} - 2 q^{58} - 35 q^{59} - 3 q^{60} - 86 q^{61} - 23 q^{62} - 16 q^{63} - 5 q^{64} - 17 q^{65} - 6 q^{66} + 2 q^{67} - q^{68} - 75 q^{69} + 2 q^{70} - 54 q^{71} - 3 q^{72} - 52 q^{73} - 22 q^{74} - 77 q^{76} + 15 q^{77} + 2 q^{78} + 46 q^{79} + 10 q^{80} - 72 q^{81} - 16 q^{82} + 26 q^{83} + 3 q^{84} - 7 q^{85} - 33 q^{86} - 8 q^{87} - 23 q^{88} - 105 q^{89} - 16 q^{90} + 17 q^{91} - 41 q^{92} - 11 q^{93} - 47 q^{94} - 32 q^{95} - 39 q^{96} - 80 q^{97} - 2 q^{98} - 53 q^{99}+O(q^{100}) \) 44 * q - 2 * q^2 + 30 * q^4 + 44 * q^5 - 7 * q^6 - 44 * q^7 - 3 * q^8 + 16 * q^9 - 2 * q^10 - 15 * q^11 - 3 * q^12 - 17 * q^13 + 2 * q^14 + 10 * q^16 - 7 * q^17 - 16 * q^18 - 32 * q^19 + 30 * q^20 - 14 * q^22 + 8 * q^23 - 35 * q^24 + 44 * q^25 - 27 * q^26 + 6 * q^27 - 30 * q^28 - 42 * q^29 - 7 * q^30 - 43 * q^31 - 8 * q^32 - 33 * q^33 - 33 * q^34 - 44 * q^35 - 11 * q^36 - 44 * q^37 + 4 * q^38 + 3 * q^39 - 3 * q^40 - 62 * q^41 + 7 * q^42 - 7 * q^43 - 45 * q^44 + 16 * q^45 - 15 * q^46 + 2 * q^47 - 26 * q^48 + 44 * q^49 - 2 * q^50 - 25 * q^51 - 35 * q^52 - 25 * q^53 - 76 * q^54 - 15 * q^55 + 3 * q^56 - 7 * q^57 - 2 * q^58 - 35 * q^59 - 3 * q^60 - 86 * q^61 - 23 * q^62 - 16 * q^63 - 5 * q^64 - 17 * q^65 - 6 * q^66 + 2 * q^67 - q^68 - 75 * q^69 + 2 * q^70 - 54 * q^71 - 3 * q^72 - 52 * q^73 - 22 * q^74 - 77 * q^76 + 15 * q^77 + 2 * q^78 + 46 * q^79 + 10 * q^80 - 72 * q^81 - 16 * q^82 + 26 * q^83 + 3 * q^84 - 7 * q^85 - 33 * q^86 - 8 * q^87 - 23 * q^88 - 105 * q^89 - 16 * q^90 + 17 * q^91 - 41 * q^92 - 11 * q^93 - 47 * q^94 - 32 * q^95 - 39 * q^96 - 80 * q^97 - 2 * q^98 - 53 * 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 $

$2$	−2.32161	−1.64163	−0.820814	−	0.571196i	$-0.806480\pi$
$2$	−2.32161	−1.64163	−0.820814	+	0.571196i	$0.806480\pi$
$3$	−1.61048	−0.929811	−0.464906	−	0.885360i	$-0.653912\pi$
$3$	−1.61048	−0.929811	−0.464906	+	0.885360i	$0.653912\pi$
$4$	3.38989	1.69494
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	3.73891	1.52640
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−3.22677	−1.14084
$9$	−0.406353	−0.135451
$10$	−2.32161	−0.734158
$11$	−1.92221	−0.579569	−0.289785	−	0.957092i	$-0.593584\pi$
$11$	−1.92221	−0.579569	−0.289785	+	0.957092i	$0.593584\pi$
$12$	−5.45934	−1.57598
$13$	−2.65544	−0.736486	−0.368243	−	0.929730i	$-0.620040\pi$
$13$	−2.65544	−0.736486	−0.368243	+	0.929730i	$0.620040\pi$
$14$	2.32161	0.620477
$15$	−1.61048	−0.415824
$16$	0.711551	0.177888
$17$	−1.71382	−0.415662	−0.207831	−	0.978165i	$-0.566640\pi$
$17$	−1.71382	−0.415662	−0.207831	+	0.978165i	$0.566640\pi$
$18$	0.943394	0.222360
$19$	−6.17735	−1.41718	−0.708591	−	0.705619i	$-0.750669\pi$
$19$	−6.17735	−1.41718	−0.708591	+	0.705619i	$0.750669\pi$
$20$	3.38989	0.758001
$21$	1.61048	0.351436
$22$	4.46264	0.951437
$23$	−3.52947	−0.735946	−0.367973	−	0.929836i	$-0.619948\pi$
$23$	−3.52947	−0.735946	−0.367973	+	0.929836i	$0.619948\pi$
$24$	5.19666	1.06076
$25$	1.00000	0.200000
$26$	6.16489	1.20904
$27$	5.48586	1.05576
$28$	−3.38989	−0.640628
$29$	−3.98704	−0.740374	−0.370187	−	0.928957i	$-0.620706\pi$
$29$	−3.98704	−0.740374	−0.370187	+	0.928957i	$0.620706\pi$
$30$	3.73891	0.682629
$31$	0.382786	0.0687505	0.0343752	−	0.999409i	$-0.489056\pi$
$31$	0.382786	0.0687505	0.0343752	+	0.999409i	$0.489056\pi$
$32$	4.80160	0.848812
$33$	3.09569	0.538890
$34$	3.97882	0.682362
$35$	−1.00000	−0.169031
$36$	−1.37749	−0.229582
$37$	1.71819	0.282468	0.141234	−	0.989976i	$-0.454893\pi$
$37$	1.71819	0.282468	0.141234	+	0.989976i	$0.454893\pi$
$38$	14.3414	2.32649
$39$	4.27653	0.684793
$40$	−3.22677	−0.510198
$41$	−3.97201	−0.620324	−0.310162	−	0.950684i	$-0.600383\pi$
$41$	−3.97201	−0.620324	−0.310162	+	0.950684i	$0.600383\pi$
$42$	−3.73891	−0.576927
$43$	4.07646	0.621654	0.310827	−	0.950467i	$-0.399394\pi$
$43$	4.07646	0.621654	0.310827	+	0.950467i	$0.399394\pi$
$44$	−6.51609	−0.982337
$45$	−0.406353	−0.0605755
$46$	8.19407	1.20815
$47$	12.2938	1.79323	0.896617	−	0.442808i	$-0.146018\pi$
$47$	12.2938	1.79323	0.896617	+	0.442808i	$0.146018\pi$
$48$	−1.14594	−0.165402
$49$	1.00000	0.142857
$50$	−2.32161	−0.328326
$51$	2.76007	0.386487
$52$	−9.00162	−1.24830
$53$	0.976477	0.134129	0.0670647	−	0.997749i	$-0.478637\pi$
$53$	0.976477	0.134129	0.0670647	+	0.997749i	$0.478637\pi$
$54$	−12.7361	−1.73316
$55$	−1.92221	−0.259191
$56$	3.22677	0.431196
$57$	9.94851	1.31771
$58$	9.25636	1.21542
$59$	13.5071	1.75847	0.879237	−	0.476384i	$-0.158053\pi$
$59$	13.5071	1.75847	0.879237	+	0.476384i	$0.158053\pi$
$60$	−5.45934	−0.704798
$61$	4.81943	0.617065	0.308532	−	0.951214i	$-0.400162\pi$
$61$	4.81943	0.617065	0.308532	+	0.951214i	$0.400162\pi$
$62$	−0.888682	−0.112863
$63$	0.406353	0.0511956
$64$	−12.5706	−1.57132
$65$	−2.65544	−0.329366
$66$	−7.18699	−0.884657
$67$	10.9839	1.34190	0.670949	−	0.741503i	$-0.265887\pi$
$67$	10.9839	1.34190	0.670949	+	0.741503i	$0.265887\pi$
$68$	−5.80964	−0.704523
$69$	5.68415	0.684291
$70$	2.32161	0.277486
$71$	−14.7303	−1.74817	−0.874084	−	0.485775i	$-0.838538\pi$
$71$	−14.7303	−1.74817	−0.874084	+	0.485775i	$0.838538\pi$
$72$	1.31121	0.154527
$73$	10.8239	1.26684	0.633420	−	0.773809i	$-0.281651\pi$
$73$	10.8239	1.26684	0.633420	+	0.773809i	$0.281651\pi$
$74$	−3.98896	−0.463707
$75$	−1.61048	−0.185962
$76$	−20.9405	−2.40204
$77$	1.92221	0.219057
$78$	−9.92844	−1.12417
$79$	13.3536	1.50240	0.751200	−	0.660074i	$-0.229475\pi$
$79$	13.3536	1.50240	0.751200	+	0.660074i	$0.229475\pi$
$80$	0.711551	0.0795538
$81$	−7.61582	−0.846202
$82$	9.22147	1.01834
$83$	9.80584	1.07633	0.538166	−	0.842839i	$-0.319118\pi$
$83$	9.80584	1.07633	0.538166	+	0.842839i	$0.319118\pi$
$84$	5.45934	0.595663
$85$	−1.71382	−0.185890
$86$	−9.46395	−1.02052
$87$	6.42105	0.688409
$88$	6.20255	0.661194
$89$	16.3538	1.73350	0.866750	−	0.498743i	$-0.166205\pi$
$89$	16.3538	1.73350	0.866750	+	0.498743i	$0.166205\pi$
$90$	0.943394	0.0994424
$91$	2.65544	0.278365
$92$	−11.9645	−1.24739
$93$	−0.616470	−0.0639250
$94$	−28.5414	−2.94382
$95$	−6.17735	−0.633783
$96$	−7.73289	−0.789235
$97$	11.0182	1.11872	0.559362	−	0.828923i	$-0.311046\pi$
$97$	11.0182	1.11872	0.559362	+	0.828923i	$0.311046\pi$
$98$	−2.32161	−0.234518
$99$	0.781097	0.0785032
$100$	3.38989	0.338989
$101$	−1.11777	−0.111222	−0.0556110	−	0.998453i	$-0.517711\pi$
$101$	−1.11777	−0.111222	−0.0556110	+	0.998453i	$0.517711\pi$
$102$	−6.40781	−0.634468
$103$	−16.8599	−1.66126	−0.830629	−	0.556827i	$-0.812019\pi$
$103$	−16.8599	−1.66126	−0.830629	+	0.556827i	$0.812019\pi$
$104$	8.56849	0.840210
$105$	1.61048	0.157167
$106$	−2.26700	−0.220191
$107$	−3.00106	−0.290123	−0.145062	−	0.989423i	$-0.546338\pi$
$107$	−3.00106	−0.290123	−0.145062	+	0.989423i	$0.546338\pi$
$108$	18.5965	1.78944
$109$	4.50197	0.431210	0.215605	−	0.976481i	$-0.430828\pi$
$109$	4.50197	0.431210	0.215605	+	0.976481i	$0.430828\pi$
$110$	4.46264	0.425496
$111$	−2.76710	−0.262642
$112$	−0.711551	−0.0672352
$113$	0.845924	0.0795779	0.0397889	−	0.999208i	$-0.487331\pi$
$113$	0.845924	0.0795779	0.0397889	+	0.999208i	$0.487331\pi$
$114$	−23.0966	−2.16319
$115$	−3.52947	−0.329125
$116$	−13.5156	−1.25489
$117$	1.07904	0.0997576
$118$	−31.3583	−2.88676
$119$	1.71382	0.157105
$120$	5.19666	0.474388
$121$	−7.30509	−0.664099
$122$	−11.1888	−1.01299
$123$	6.39685	0.576784
$124$	1.29760	0.116528
$125$	1.00000	0.0894427
$126$	−0.943394	−0.0840442
$127$	−1.35876	−0.120570	−0.0602850	−	0.998181i	$-0.519201\pi$
$127$	−1.35876	−0.120570	−0.0602850	+	0.998181i	$0.519201\pi$
$128$	19.5808	1.73071
$129$	−6.56505	−0.578021
$130$	6.16489	0.540697
$131$	−3.57188	−0.312076	−0.156038	−	0.987751i	$-0.549872\pi$
$131$	−3.57188	−0.312076	−0.156038	+	0.987751i	$0.549872\pi$
$132$	10.4940	0.913388
$133$	6.17735	0.535645
$134$	−25.5004	−2.20290
$135$	5.48586	0.472148
$136$	5.53010	0.474202
$137$	−16.2521	−1.38851	−0.694257	−	0.719727i	$-0.744267\pi$
$137$	−16.2521	−1.38851	−0.694257	+	0.719727i	$0.744267\pi$
$138$	−13.1964	−1.12335
$139$	−14.4254	−1.22354	−0.611772	−	0.791034i	$-0.709543\pi$
$139$	−14.4254	−1.22354	−0.611772	+	0.791034i	$0.709543\pi$
$140$	−3.38989	−0.286498
$141$	−19.7989	−1.66737
$142$	34.1981	2.86984
$143$	5.10432	0.426845
$144$	−0.289141	−0.0240951
$145$	−3.98704	−0.331106
$146$	−25.1289	−2.07968
$147$	−1.61048	−0.132830
$148$	5.82445	0.478767
$149$	1.02175	0.0837048	0.0418524	−	0.999124i	$-0.486674\pi$
$149$	1.02175	0.0837048	0.0418524	+	0.999124i	$0.486674\pi$
$150$	3.73891	0.305281
$151$	6.14242	0.499863	0.249931	−	0.968264i	$-0.419592\pi$
$151$	6.14242	0.499863	0.249931	+	0.968264i	$0.419592\pi$
$152$	19.9329	1.61677
$153$	0.696415	0.0563018
$154$	−4.46264	−0.359610
$155$	0.382786	0.0307461
$156$	14.4969	1.16068
$157$	−11.7765	−0.939869	−0.469934	−	0.882701i	$-0.655722\pi$
$157$	−11.7765	−0.939869	−0.469934	+	0.882701i	$0.655722\pi$
$158$	−31.0019	−2.46638
$159$	−1.57260	−0.124715
$160$	4.80160	0.379600
$161$	3.52947	0.278161
$162$	17.6810	1.38915
$163$	7.87684	0.616962	0.308481	−	0.951231i	$-0.400179\pi$
$163$	7.87684	0.616962	0.308481	+	0.951231i	$0.400179\pi$
$164$	−13.4647	−1.05141
$165$	3.09569	0.240999
$166$	−22.7654	−1.76694
$167$	0.388370	0.0300530	0.0150265	−	0.999887i	$-0.495217\pi$
$167$	0.388370	0.0300530	0.0150265	+	0.999887i	$0.495217\pi$
$168$	−5.19666	−0.400931
$169$	−5.94866	−0.457589
$170$	3.97882	0.305162
$171$	2.51019	0.191959
$172$	13.8187	1.05367
$173$	17.1175	1.30142	0.650708	−	0.759328i	$-0.274472\pi$
$173$	17.1175	1.30142	0.650708	+	0.759328i	$0.274472\pi$
$174$	−14.9072	−1.13011
$175$	−1.00000	−0.0755929
$176$	−1.36775	−0.103098
$177$	−21.7529	−1.63505
$178$	−37.9672	−2.84576
$179$	7.84661	0.586483	0.293242	−	0.956038i	$-0.405266\pi$
$179$	7.84661	0.586483	0.293242	+	0.956038i	$0.405266\pi$
$180$	−1.37749	−0.102672
$181$	−13.7647	−1.02312	−0.511559	−	0.859248i	$-0.670932\pi$
$181$	−13.7647	−1.02312	−0.511559	+	0.859248i	$0.670932\pi$
$182$	−6.16489	−0.456972
$183$	−7.76160	−0.573754
$184$	11.3888	0.839595
$185$	1.71819	0.126323
$186$	1.43120	0.104941
$187$	3.29432	0.240905
$188$	41.6745	3.03943
$189$	−5.48586	−0.399038
$190$	14.3414	1.04044
$191$	8.56906	0.620036	0.310018	−	0.950731i	$-0.399665\pi$
$191$	8.56906	0.620036	0.310018	+	0.950731i	$0.399665\pi$
$192$	20.2447	1.46103
$193$	23.4830	1.69034	0.845172	−	0.534494i	$-0.179498\pi$
$193$	23.4830	1.69034	0.845172	+	0.534494i	$0.179498\pi$
$194$	−25.5799	−1.83653
$195$	4.27653	0.306249
$196$	3.38989	0.242135
$197$	−5.08898	−0.362575	−0.181287	−	0.983430i	$-0.558026\pi$
$197$	−5.08898	−0.362575	−0.181287	+	0.983430i	$0.558026\pi$
$198$	−1.81341	−0.128873
$199$	−27.8640	−1.97523	−0.987613	−	0.156911i	$-0.949846\pi$
$199$	−27.8640	−1.97523	−0.987613	+	0.156911i	$0.949846\pi$
$200$	−3.22677	−0.228167
$201$	−17.6894	−1.24771
$202$	2.59502	0.182585
$203$	3.98704	0.279835
$204$	9.35632	0.655073
$205$	−3.97201	−0.277417
$206$	39.1422	2.72717
$207$	1.43421	0.0996846
$208$	−1.88948	−0.131012
$209$	11.8742	0.821356
$210$	−3.73891	−0.258009
$211$	−28.6249	−1.97062	−0.985311	−	0.170771i	$-0.945374\pi$
$211$	−28.6249	−1.97062	−0.985311	+	0.170771i	$0.945374\pi$
$212$	3.31015	0.227342
$213$	23.7229	1.62547
$214$	6.96729	0.476274
$215$	4.07646	0.278012
$216$	−17.7016	−1.20444
$217$	−0.382786	−0.0259852
$218$	−10.4518	−0.707887
$219$	−17.4316	−1.17792
$220$	−6.51609	−0.439314
$221$	4.55093	0.306129
$222$	6.42414	0.431160
$223$	13.9935	0.937071	0.468536	−	0.883445i	$-0.344782\pi$
$223$	13.9935	0.937071	0.468536	+	0.883445i	$0.344782\pi$
$224$	−4.80160	−0.320821
$225$	−0.406353	−0.0270902
$226$	−1.96391	−0.130637
$227$	−19.0347	−1.26338	−0.631688	−	0.775222i	$-0.717638\pi$
$227$	−19.0347	−1.26338	−0.631688	+	0.775222i	$0.717638\pi$
$228$	33.7243	2.23345
$229$	1.00000	0.0660819
$229$	1.00000	0.0660819
$230$	8.19407	0.540301
$231$	−3.09569	−0.203681
$232$	12.8653	0.844647
$233$	19.9576	1.30746	0.653732	−	0.756726i	$-0.273202\pi$
$233$	19.9576	1.30746	0.653732	+	0.756726i	$0.273202\pi$
$234$	−2.50512	−0.163765
$235$	12.2938	0.801958
$236$	45.7875	2.98051
$237$	−21.5058	−1.39695
$238$	−3.97882	−0.257909
$239$	−2.46839	−0.159667	−0.0798335	−	0.996808i	$-0.525439\pi$
$239$	−2.46839	−0.159667	−0.0798335	+	0.996808i	$0.525439\pi$
$240$	−1.14594	−0.0739700
$241$	−4.17489	−0.268928	−0.134464	−	0.990918i	$-0.542931\pi$
$241$	−4.17489	−0.268928	−0.134464	+	0.990918i	$0.542931\pi$
$242$	16.9596	1.09020
$243$	−4.19247	−0.268947
$244$	16.3373	1.04589
$245$	1.00000	0.0638877
$246$	−14.8510	−0.946865
$247$	16.4036	1.04373
$248$	−1.23517	−0.0784331
$249$	−15.7921	−1.00078
$250$	−2.32161	−0.146832
$251$	−4.06800	−0.256770	−0.128385	−	0.991724i	$-0.540979\pi$
$251$	−4.06800	−0.256770	−0.128385	+	0.991724i	$0.540979\pi$
$252$	1.37749	0.0867737
$253$	6.78440	0.426532
$254$	3.15450	0.197931
$255$	2.76007	0.172842
$256$	−20.3178	−1.26987
$257$	−22.0870	−1.37775	−0.688874	−	0.724881i	$-0.741895\pi$
$257$	−22.0870	−1.37775	−0.688874	+	0.724881i	$0.741895\pi$
$258$	15.2415	0.948895
$259$	−1.71819	−0.106763
$260$	−9.00162	−0.558257
$261$	1.62014	0.100284
$262$	8.29251	0.512313
$263$	−3.60469	−0.222274	−0.111137	−	0.993805i	$-0.535449\pi$
$263$	−3.60469	−0.222274	−0.111137	+	0.993805i	$0.535449\pi$
$264$	−9.98909	−0.614786
$265$	0.976477	0.0599845
$266$	−14.3414	−0.879329
$267$	−26.3375	−1.61183
$268$	37.2342	2.27444
$269$	−20.1513	−1.22865	−0.614324	−	0.789054i	$-0.710571\pi$
$269$	−20.1513	−1.22865	−0.614324	+	0.789054i	$0.710571\pi$
$270$	−12.7361	−0.775091
$271$	24.6411	1.49684	0.748421	−	0.663224i	$-0.230812\pi$
$271$	24.6411	1.49684	0.748421	+	0.663224i	$0.230812\pi$
$272$	−1.21947	−0.0739411
$273$	−4.27653	−0.258827
$274$	37.7312	2.27942
$275$	−1.92221	−0.115914
$276$	19.2686	1.15983
$277$	−21.0394	−1.26414	−0.632068	−	0.774913i	$-0.717794\pi$
$277$	−21.0394	−1.26414	−0.632068	+	0.774913i	$0.717794\pi$
$278$	33.4901	2.00860
$279$	−0.155546	−0.00931231
$280$	3.22677	0.192837
$281$	2.29378	0.136836	0.0684178	−	0.997657i	$-0.478205\pi$
$281$	2.29378	0.136836	0.0684178	+	0.997657i	$0.478205\pi$
$282$	45.9654	2.73720
$283$	−8.24856	−0.490326	−0.245163	−	0.969482i	$-0.578841\pi$
$283$	−8.24856	−0.490326	−0.245163	+	0.969482i	$0.578841\pi$
$284$	−49.9341	−2.96304
$285$	9.94851	0.589299
$286$	−11.8502	−0.700720
$287$	3.97201	0.234460
$288$	−1.95115	−0.114972
$289$	−14.0628	−0.827225
$290$	9.25636	0.543552
$291$	−17.7445	−1.04020
$292$	36.6917	2.14722
$293$	5.69479	0.332693	0.166347	−	0.986067i	$-0.446803\pi$
$293$	5.69479	0.332693	0.166347	+	0.986067i	$0.446803\pi$
$294$	3.73891	0.218058
$295$	13.5071	0.786414
$296$	−5.54420	−0.322250
$297$	−10.5450	−0.611883
$298$	−2.37210	−0.137412
$299$	9.37229	0.542014
$300$	−5.45934	−0.315195
$301$	−4.07646	−0.234963
$302$	−14.2603	−0.820589
$303$	1.80014	0.103415
$304$	−4.39550	−0.252099
$305$	4.81943	0.275960
$306$	−1.61680	−0.0924266
$307$	16.1538	0.921947	0.460974	−	0.887414i	$-0.347500\pi$
$307$	16.1538	0.921947	0.460974	+	0.887414i	$0.347500\pi$
$308$	6.51609	0.371288
$309$	27.1526	1.54466
$310$	−0.888682	−0.0504737
$311$	30.7109	1.74146	0.870729	−	0.491764i	$-0.163648\pi$
$311$	30.7109	1.74146	0.870729	+	0.491764i	$0.163648\pi$
$312$	−13.7994	−0.781237
$313$	−20.3709	−1.15143	−0.575716	−	0.817650i	$-0.695277\pi$
$313$	−20.3709	−1.15143	−0.575716	+	0.817650i	$0.695277\pi$
$314$	27.3405	1.54292
$315$	0.406353	0.0228954
$316$	45.2673	2.54648
$317$	23.8492	1.33950	0.669751	−	0.742586i	$-0.266401\pi$
$317$	23.8492	1.33950	0.669751	+	0.742586i	$0.266401\pi$
$318$	3.65096	0.204736
$319$	7.66394	0.429098
$320$	−12.5706	−0.702716
$321$	4.83314	0.269760
$322$	−8.19407	−0.456638
$323$	10.5869	0.589069
$324$	−25.8168	−1.43426
$325$	−2.65544	−0.147297
$326$	−18.2870	−1.01282
$327$	−7.25033	−0.400944
$328$	12.8168	0.707689
$329$	−12.2938	−0.677778
$330$	−7.18699	−0.395631
$331$	−15.7018	−0.863050	−0.431525	−	0.902101i	$-0.642024\pi$
$331$	−15.7018	−0.863050	−0.431525	+	0.902101i	$0.642024\pi$
$332$	33.2407	1.82432
$333$	−0.698189	−0.0382605
$334$	−0.901645	−0.0493358
$335$	10.9839	0.600115
$336$	1.14594	0.0625161
$337$	−3.95217	−0.215288	−0.107644	−	0.994189i	$-0.534331\pi$
$337$	−3.95217	−0.215288	−0.107644	+	0.994189i	$0.534331\pi$
$338$	13.8105	0.751191
$339$	−1.36234	−0.0739924
$340$	−5.80964	−0.315072
$341$	−0.735798	−0.0398457
$342$	−5.82768	−0.315125
$343$	−1.00000	−0.0539949
$344$	−13.1538	−0.709206
$345$	5.68415	0.306024
$346$	−39.7401	−2.13644
$347$	26.2131	1.40719	0.703597	−	0.710599i	$-0.251576\pi$
$347$	26.2131	1.40719	0.703597	+	0.710599i	$0.251576\pi$
$348$	21.7666	1.16681
$349$	1.18602	0.0634861	0.0317430	−	0.999496i	$-0.489894\pi$
$349$	1.18602	0.0634861	0.0317430	+	0.999496i	$0.489894\pi$
$350$	2.32161	0.124095
$351$	−14.5674	−0.777548
$352$	−9.22971	−0.491945
$353$	−16.3860	−0.872139	−0.436069	−	0.899913i	$-0.643630\pi$
$353$	−16.3860	−0.872139	−0.436069	+	0.899913i	$0.643630\pi$
$354$	50.5019	2.68414
$355$	−14.7303	−0.781805
$356$	55.4375	2.93818
$357$	−2.76007	−0.146078
$358$	−18.2168	−0.962787
$359$	25.2086	1.33046	0.665230	−	0.746638i	$-0.268333\pi$
$359$	25.2086	1.33046	0.665230	+	0.746638i	$0.268333\pi$
$360$	1.31121	0.0691068
$361$	19.1597	1.00841
$362$	31.9562	1.67958
$363$	11.7647	0.617487
$364$	9.00162	0.471813
$365$	10.8239	0.566548
$366$	18.0194	0.941890
$367$	17.4286	0.909768	0.454884	−	0.890551i	$-0.349681\pi$
$367$	17.4286	0.909768	0.454884	+	0.890551i	$0.349681\pi$
$368$	−2.51140	−0.130916
$369$	1.61404	0.0840234
$370$	−3.98896	−0.207376
$371$	−0.976477	−0.0506962
$372$	−2.08976	−0.108349
$373$	8.77514	0.454360	0.227180	−	0.973853i	$-0.427049\pi$
$373$	8.77514	0.454360	0.227180	+	0.973853i	$0.427049\pi$
$374$	−7.64815	−0.395476
$375$	−1.61048	−0.0831649
$376$	−39.6693	−2.04579
$377$	10.5873	0.545275
$378$	12.7361	0.655072
$379$	−34.3727	−1.76561	−0.882804	−	0.469741i	$-0.844347\pi$
$379$	−34.3727	−1.76561	−0.882804	+	0.469741i	$0.844347\pi$
$380$	−20.9405	−1.07423
$381$	2.18825	0.112107
$382$	−19.8940	−1.01787
$383$	−30.5106	−1.55902	−0.779509	−	0.626391i	$-0.784531\pi$
$383$	−30.5106	−1.55902	−0.779509	+	0.626391i	$0.784531\pi$
$384$	−31.5345	−1.60924
$385$	1.92221	0.0979651
$386$	−54.5185	−2.77492
$387$	−1.65648	−0.0842036
$388$	37.3503	1.89617
$389$	27.4941	1.39401	0.697004	−	0.717067i	$-0.254516\pi$
$389$	27.4941	1.39401	0.697004	+	0.717067i	$0.254516\pi$
$390$	−9.92844	−0.502746
$391$	6.04887	0.305905
$392$	−3.22677	−0.162977
$393$	5.75244	0.290172
$394$	11.8146	0.595213
$395$	13.3536	0.671894
$396$	2.64783	0.133058
$397$	−24.6727	−1.23829	−0.619144	−	0.785278i	$-0.712520\pi$
$397$	−24.6727	−1.23829	−0.619144	+	0.785278i	$0.712520\pi$
$398$	64.6894	3.24259
$399$	−9.94851	−0.498048
$400$	0.711551	0.0355775
$401$	−1.76775	−0.0882770	−0.0441385	−	0.999025i	$-0.514054\pi$
$401$	−1.76775	−0.0882770	−0.0441385	+	0.999025i	$0.514054\pi$
$402$	41.0679	2.04828
$403$	−1.01646	−0.0506337
$404$	−3.78910	−0.188515
$405$	−7.61582	−0.378433
$406$	−9.25636	−0.459385
$407$	−3.30272	−0.163710
$408$	−8.90612	−0.440919
$409$	−7.97026	−0.394104	−0.197052	−	0.980393i	$-0.563137\pi$
$409$	−7.97026	−0.394104	−0.197052	+	0.980393i	$0.563137\pi$
$410$	9.22147	0.455416
$411$	26.1737	1.29106
$412$	−57.1532	−2.81574
$413$	−13.5071	−0.664641
$414$	−3.32968	−0.163645
$415$	9.80584	0.481350
$416$	−12.7504	−0.625138
$417$	23.2318	1.13767
$418$	−27.5673	−1.34836
$419$	−9.09113	−0.444131	−0.222065	−	0.975032i	$-0.571280\pi$
$419$	−9.09113	−0.444131	−0.222065	+	0.975032i	$0.571280\pi$
$420$	5.45934	0.266389
$421$	−2.04758	−0.0997929	−0.0498964	−	0.998754i	$-0.515889\pi$
$421$	−2.04758	−0.0997929	−0.0498964	+	0.998754i	$0.515889\pi$
$422$	66.4560	3.23503
$423$	−4.99561	−0.242895
$424$	−3.15087	−0.153020
$425$	−1.71382	−0.0831324
$426$	−55.0754	−2.66841
$427$	−4.81943	−0.233229
$428$	−10.1732	−0.491742
$429$	−8.22040	−0.396885
$430$	−9.46395	−0.456392
$431$	26.8991	1.29568	0.647842	−	0.761774i	$-0.275671\pi$
$431$	26.8991	1.29568	0.647842	+	0.761774i	$0.275671\pi$
$432$	3.90347	0.187806
$433$	−31.5899	−1.51811	−0.759056	−	0.651026i	$-0.774339\pi$
$433$	−31.5899	−1.51811	−0.759056	+	0.651026i	$0.774339\pi$
$434$	0.888682	0.0426581
$435$	6.42105	0.307866
$436$	15.2611	0.730876
$437$	21.8028	1.04297
$438$	40.4695	1.93371
$439$	11.1407	0.531715	0.265858	−	0.964012i	$-0.414345\pi$
$439$	11.1407	0.531715	0.265858	+	0.964012i	$0.414345\pi$
$440$	6.20255	0.295695
$441$	−0.406353	−0.0193501
$442$	−10.5655	−0.502550
$443$	−5.40320	−0.256714	−0.128357	−	0.991728i	$-0.540970\pi$
$443$	−5.40320	−0.256714	−0.128357	+	0.991728i	$0.540970\pi$
$444$	−9.38016	−0.445163
$445$	16.3538	0.775245
$446$	−32.4874	−1.53832
$447$	−1.64550	−0.0778296
$448$	12.5706	0.593903
$449$	16.5420	0.780665	0.390332	−	0.920674i	$-0.372360\pi$
$449$	16.5420	0.780665	0.390332	+	0.920674i	$0.372360\pi$
$450$	0.943394	0.0444720
$451$	7.63506	0.359521
$452$	2.86759	0.134880
$453$	−9.89224	−0.464778
$454$	44.1912	2.07399
$455$	2.65544	0.124489
$456$	−32.1016	−1.50330
$457$	−4.74237	−0.221839	−0.110919	−	0.993829i	$-0.535380\pi$
$457$	−4.74237	−0.221839	−0.110919	+	0.993829i	$0.535380\pi$
$458$	−2.32161	−0.108482
$459$	−9.40177	−0.438837
$460$	−11.9645	−0.557848
$461$	−2.78297	−0.129616	−0.0648078	−	0.997898i	$-0.520643\pi$
$461$	−2.78297	−0.129616	−0.0648078	+	0.997898i	$0.520643\pi$
$462$	7.18699	0.334369
$463$	3.49858	0.162593	0.0812963	−	0.996690i	$-0.474094\pi$
$463$	3.49858	0.162593	0.0812963	+	0.996690i	$0.474094\pi$
$464$	−2.83698	−0.131704
$465$	−0.616470	−0.0285881
$466$	−46.3337	−2.14637
$467$	−28.2381	−1.30670	−0.653351	−	0.757055i	$-0.726637\pi$
$467$	−28.2381	−1.30670	−0.653351	+	0.757055i	$0.726637\pi$
$468$	3.65784	0.169083
$469$	−10.9839	−0.507190
$470$	−28.5414	−1.31652
$471$	18.9659	0.873901
$472$	−43.5844	−2.00613
$473$	−7.83582	−0.360292
$474$	49.9280	2.29327
$475$	−6.17735	−0.283436
$476$	5.80964	0.266285
$477$	−0.396794	−0.0181680
$478$	5.73065	0.262114
$479$	12.3200	0.562914	0.281457	−	0.959574i	$-0.409182\pi$
$479$	12.3200	0.562914	0.281457	+	0.959574i	$0.409182\pi$
$480$	−7.73289	−0.352956
$481$	−4.56253	−0.208034
$482$	9.69247	0.441480
$483$	−5.68415	−0.258638
$484$	−24.7634	−1.12561
$485$	11.0182	0.500309
$486$	9.73328	0.441511
$487$	−18.7531	−0.849785	−0.424892	−	0.905244i	$-0.639688\pi$
$487$	−18.7531	−0.849785	−0.424892	+	0.905244i	$0.639688\pi$
$488$	−15.5512	−0.703970
$489$	−12.6855	−0.573658
$490$	−2.32161	−0.104880
$491$	9.48762	0.428170	0.214085	−	0.976815i	$-0.431323\pi$
$491$	9.48762	0.428170	0.214085	+	0.976815i	$0.431323\pi$
$492$	21.6846	0.977616
$493$	6.83306	0.307745
$494$	−38.0827	−1.71342
$495$	0.781097	0.0351077
$496$	0.272372	0.0122299
$497$	14.7303	0.660745
$498$	36.6632	1.64292
$499$	37.4337	1.67576	0.837882	−	0.545851i	$-0.183793\pi$
$499$	37.4337	1.67576	0.837882	+	0.545851i	$0.183793\pi$
$500$	3.38989	0.151600
$501$	−0.625463	−0.0279436
$502$	9.44431	0.421520
$503$	23.4102	1.04381	0.521904	−	0.853004i	$-0.325222\pi$
$503$	23.4102	1.04381	0.521904	+	0.853004i	$0.325222\pi$
$504$	−1.31121	−0.0584059
$505$	−1.11777	−0.0497400
$506$	−15.7508	−0.700207
$507$	9.58020	0.425472
$508$	−4.60602	−0.204359
$509$	−29.1272	−1.29104	−0.645519	−	0.763744i	$-0.723359\pi$
$509$	−29.1272	−1.29104	−0.645519	+	0.763744i	$0.723359\pi$
$510$	−6.40781	−0.283743
$511$	−10.8239	−0.478820
$512$	8.00862	0.353934
$513$	−33.8881	−1.49620
$514$	51.2774	2.26175
$515$	−16.8599	−0.742937
$516$	−22.2548	−0.979712
$517$	−23.6313	−1.03930
$518$	3.98896	0.175265
$519$	−27.5673	−1.21007
$520$	8.56849	0.375753
$521$	−25.2269	−1.10521	−0.552604	−	0.833444i	$-0.686366\pi$
$521$	−25.2269	−1.10521	−0.552604	+	0.833444i	$0.686366\pi$
$522$	−3.76135	−0.164630
$523$	32.3592	1.41497	0.707484	−	0.706729i	$-0.249830\pi$
$523$	32.3592	1.41497	0.707484	+	0.706729i	$0.249830\pi$
$524$	−12.1082	−0.528951
$525$	1.61048	0.0702871
$526$	8.36868	0.364892
$527$	−0.656026	−0.0285769
$528$	2.20274	0.0958620
$529$	−10.5428	−0.458383
$530$	−2.26700	−0.0984723
$531$	−5.48865	−0.238187
$532$	20.9405	0.907887
$533$	10.5474	0.456860
$534$	61.1454	2.64602
$535$	−3.00106	−0.129747
$536$	−35.4426	−1.53089
$537$	−12.6368	−0.545319
$538$	46.7836	2.01698
$539$	−1.92221	−0.0827956
$540$	18.5965	0.800264
$541$	−14.1219	−0.607149	−0.303575	−	0.952808i	$-0.598180\pi$
$541$	−14.1219	−0.607149	−0.303575	+	0.952808i	$0.598180\pi$
$542$	−57.2072	−2.45726
$543$	22.1677	0.951307
$544$	−8.22907	−0.352819
$545$	4.50197	0.192843
$546$	9.92844	0.424898
$547$	−19.8041	−0.846763	−0.423381	−	0.905952i	$-0.639157\pi$
$547$	−19.8041	−0.846763	−0.423381	+	0.905952i	$0.639157\pi$
$548$	−55.0929	−2.35345
$549$	−1.95839	−0.0835820
$550$	4.46264	0.190287
$551$	24.6294	1.04925
$552$	−18.3415	−0.780665
$553$	−13.3536	−0.567854
$554$	48.8454	2.07524
$555$	−2.76710	−0.117457
$556$	−48.9004	−2.07384
$557$	8.14110	0.344950	0.172475	−	0.985014i	$-0.444824\pi$
$557$	8.14110	0.344950	0.172475	+	0.985014i	$0.444824\pi$
$558$	0.361118	0.0152874
$559$	−10.8248	−0.457839
$560$	−0.711551	−0.0300685
$561$	−5.30545	−0.223996
$562$	−5.32528	−0.224633
$563$	33.7690	1.42319	0.711597	−	0.702588i	$-0.247972\pi$
$563$	33.7690	1.42319	0.711597	+	0.702588i	$0.247972\pi$
$564$	−67.1160	−2.82609
$565$	0.845924	0.0355883
$566$	19.1500	0.804933
$567$	7.61582	0.319834
$568$	47.5314	1.99438
$569$	2.65851	0.111451	0.0557253	−	0.998446i	$-0.482253\pi$
$569$	2.65851	0.111451	0.0557253	+	0.998446i	$0.482253\pi$
$570$	−23.0966	−0.967409
$571$	22.6128	0.946316	0.473158	−	0.880978i	$-0.343114\pi$
$571$	22.6128	0.946316	0.473158	+	0.880978i	$0.343114\pi$
$572$	17.3031	0.723477
$573$	−13.8003	−0.576516
$574$	−9.22147	−0.384897
$575$	−3.52947	−0.147189
$576$	5.10808	0.212837
$577$	−29.1524	−1.21363	−0.606816	−	0.794842i	$-0.707553\pi$
$577$	−29.1524	−1.21363	−0.606816	+	0.794842i	$0.707553\pi$
$578$	32.6484	1.35800
$579$	−37.8189	−1.57170
$580$	−13.5156	−0.561205
$581$	−9.80584	−0.406815
$582$	41.1959	1.70763
$583$	−1.87700	−0.0777374
$584$	−34.9262	−1.44526
$585$	1.07904	0.0446130
$586$	−13.2211	−0.546159
$587$	−9.49647	−0.391961	−0.195981	−	0.980608i	$-0.562789\pi$
$587$	−9.49647	−0.391961	−0.195981	+	0.980608i	$0.562789\pi$
$588$	−5.45934	−0.225140
$589$	−2.36461	−0.0974320
$590$	−31.3583	−1.29100
$591$	8.19571	0.337126
$592$	1.22258	0.0502476
$593$	33.3188	1.36824	0.684119	−	0.729371i	$-0.260187\pi$
$593$	33.3188	1.36824	0.684119	+	0.729371i	$0.260187\pi$
$594$	24.4814	1.00448
$595$	1.71382	0.0702597
$596$	3.46360	0.141875
$597$	44.8744	1.83659
$598$	−21.7588	−0.889785
$599$	−2.69357	−0.110056	−0.0550281	−	0.998485i	$-0.517525\pi$
$599$	−2.69357	−0.110056	−0.0550281	+	0.998485i	$0.517525\pi$
$600$	5.19666	0.212153
$601$	−45.4585	−1.85429	−0.927146	−	0.374700i	$-0.877746\pi$
$601$	−45.4585	−1.85429	−0.927146	+	0.374700i	$0.877746\pi$
$602$	9.46395	0.385722
$603$	−4.46334	−0.181761
$604$	20.8221	0.847238
$605$	−7.30509	−0.296994
$606$	−4.17923	−0.169770
$607$	30.8509	1.25220	0.626100	−	0.779743i	$-0.284650\pi$
$607$	30.8509	1.25220	0.626100	+	0.779743i	$0.284650\pi$
$608$	−29.6612	−1.20292
$609$	−6.42105	−0.260194
$610$	−11.1888	−0.453023
$611$	−32.6454	−1.32069
$612$	2.36077	0.0954283
$613$	−19.7730	−0.798626	−0.399313	−	0.916815i	$-0.630751\pi$
$613$	−19.7730	−0.798626	−0.399313	+	0.916815i	$0.630751\pi$
$614$	−37.5029	−1.51349
$615$	6.39685	0.257946
$616$	−6.20255	−0.249908
$617$	11.5940	0.466757	0.233379	−	0.972386i	$-0.425022\pi$
$617$	11.5940	0.466757	0.233379	+	0.972386i	$0.425022\pi$
$618$	−63.0378	−2.53575
$619$	2.63248	0.105808	0.0529041	−	0.998600i	$-0.483152\pi$
$619$	2.63248	0.105808	0.0529041	+	0.998600i	$0.483152\pi$
$620$	1.29760	0.0521129
$621$	−19.3622	−0.776979
$622$	−71.2989	−2.85883
$623$	−16.3538	−0.655201
$624$	3.04297	0.121816
$625$	1.00000	0.0400000
$626$	47.2934	1.89022
$627$	−19.1232	−0.763706
$628$	−39.9211	−1.59302
$629$	−2.94466	−0.117411
$630$	−0.943394	−0.0375857
$631$	−7.16320	−0.285162	−0.142581	−	0.989783i	$-0.545540\pi$
$631$	−7.16320	−0.285162	−0.142581	+	0.989783i	$0.545540\pi$
$632$	−43.0891	−1.71399
$633$	46.0999	1.83231
$634$	−55.3685	−2.19896
$635$	−1.35876	−0.0539206
$636$	−5.33093	−0.211385
$637$	−2.65544	−0.105212
$638$	−17.7927	−0.704420
$639$	5.98571	0.236791
$640$	19.5808	0.773998
$641$	−17.5685	−0.693915	−0.346957	−	0.937881i	$-0.612785\pi$
$641$	−17.5685	−0.693915	−0.346957	+	0.937881i	$0.612785\pi$
$642$	−11.2207	−0.442845
$643$	38.2766	1.50948	0.754741	−	0.656023i	$-0.227763\pi$
$643$	38.2766	1.50948	0.754741	+	0.656023i	$0.227763\pi$
$644$	11.9645	0.471468
$645$	−6.56505	−0.258499
$646$	−24.5786	−0.967031
$647$	−2.71231	−0.106632	−0.0533159	−	0.998578i	$-0.516979\pi$
$647$	−2.71231	−0.106632	−0.0533159	+	0.998578i	$0.516979\pi$
$648$	24.5745	0.965379
$649$	−25.9635	−1.01916
$650$	6.16489	0.241807
$651$	0.616470	0.0241614
$652$	26.7016	1.04572
$653$	9.89553	0.387242	0.193621	−	0.981076i	$-0.437977\pi$
$653$	9.89553	0.387242	0.193621	+	0.981076i	$0.437977\pi$
$654$	16.8325	0.658201
$655$	−3.57188	−0.139565
$656$	−2.82629	−0.110348
$657$	−4.39831	−0.171595
$658$	28.5414	1.11266
$659$	11.8596	0.461986	0.230993	−	0.972955i	$-0.425803\pi$
$659$	11.8596	0.461986	0.230993	+	0.972955i	$0.425803\pi$
$660$	10.4940	0.408480
$661$	42.6616	1.65934	0.829672	−	0.558251i	$-0.188527\pi$
$661$	42.6616	1.65934	0.829672	+	0.558251i	$0.188527\pi$
$662$	36.4535	1.41681
$663$	−7.32919	−0.284642
$664$	−31.6412	−1.22792
$665$	6.17735	0.239548
$666$	1.62093	0.0628096
$667$	14.0721	0.544876
$668$	1.31653	0.0509381
$669$	−22.5362	−0.871299
$670$	−25.5004	−0.985166
$671$	−9.26398	−0.357632
$672$	7.73289	0.298303
$673$	−34.4855	−1.32932	−0.664659	−	0.747147i	$-0.731423\pi$
$673$	−34.4855	−1.32932	−0.664659	+	0.747147i	$0.731423\pi$
$674$	9.17540	0.353423
$675$	5.48586	0.211151
$676$	−20.1653	−0.775587
$677$	−15.0257	−0.577486	−0.288743	−	0.957407i	$-0.593237\pi$
$677$	−15.0257	−0.577486	−0.288743	+	0.957407i	$0.593237\pi$
$678$	3.16284	0.121468
$679$	−11.0182	−0.422838
$680$	5.53010	0.212070
$681$	30.6550	1.17470
$682$	1.70824	0.0654118
$683$	8.53764	0.326684	0.163342	−	0.986570i	$-0.447773\pi$
$683$	8.53764	0.326684	0.163342	+	0.986570i	$0.447773\pi$
$684$	8.50924	0.325359
$685$	−16.2521	−0.620962
$686$	2.32161	0.0886396
$687$	−1.61048	−0.0614437
$688$	2.90061	0.110585
$689$	−2.59297	−0.0987844
$690$	−13.1964	−0.502378
$691$	−2.72755	−0.103761	−0.0518805	−	0.998653i	$-0.516522\pi$
$691$	−2.72755	−0.103761	−0.0518805	+	0.998653i	$0.516522\pi$
$692$	58.0262	2.20583
$693$	−0.781097	−0.0296714
$694$	−60.8567	−2.31009
$695$	−14.4254	−0.547186
$696$	−20.7193	−0.785362
$697$	6.80730	0.257845
$698$	−2.75347	−0.104221
$699$	−32.1413	−1.21569
$700$	−3.38989	−0.128126
$701$	−32.5697	−1.23014	−0.615069	−	0.788473i	$-0.710872\pi$
$701$	−32.5697	−1.23014	−0.615069	+	0.788473i	$0.710872\pi$
$702$	33.8198	1.27645
$703$	−10.6138	−0.400309
$704$	24.1633	0.910690
$705$	−19.7989	−0.745670
$706$	38.0420	1.43173
$707$	1.11777	0.0420379
$708$	−73.7399	−2.77131
$709$	−52.0263	−1.95389	−0.976945	−	0.213491i	$-0.931516\pi$
$709$	−52.0263	−1.95389	−0.976945	+	0.213491i	$0.931516\pi$
$710$	34.1981	1.28343
$711$	−5.42628	−0.203502
$712$	−52.7700	−1.97764
$713$	−1.35103	−0.0505966
$714$	6.40781	0.239806
$715$	5.10432	0.190891
$716$	26.5991	0.994056
$717$	3.97530	0.148460
$718$	−58.5247	−2.18412
$719$	11.1537	0.415961	0.207981	−	0.978133i	$-0.433311\pi$
$719$	11.1537	0.415961	0.207981	+	0.978133i	$0.433311\pi$
$720$	−0.289141	−0.0107756
$721$	16.8599	0.627896
$722$	−44.4814	−1.65543
$723$	6.72357	0.250052
$724$	−46.6606	−1.73413
$725$	−3.98704	−0.148075
$726$	−27.3131	−1.01368
$727$	−31.7664	−1.17815	−0.589075	−	0.808078i	$-0.700508\pi$
$727$	−31.7664	−1.17815	−0.589075	+	0.808078i	$0.700508\pi$
$728$	−8.56849	−0.317570
$729$	29.5993	1.09627
$730$	−25.1289	−0.930061
$731$	−6.98630	−0.258398
$732$	−26.3109	−0.972480
$733$	−51.8429	−1.91486	−0.957430	−	0.288665i	$-0.906789\pi$
$733$	−51.8429	−1.91486	−0.957430	+	0.288665i	$0.906789\pi$
$734$	−40.4626	−1.49350
$735$	−1.61048	−0.0594035
$736$	−16.9471	−0.624680
$737$	−21.1134	−0.777723
$738$	−3.74717	−0.137935
$739$	12.7220	0.467985	0.233992	−	0.972238i	$-0.424821\pi$
$739$	12.7220	0.467985	0.233992	+	0.972238i	$0.424821\pi$
$740$	5.82445	0.214111
$741$	−26.4176	−0.970476
$742$	2.26700	0.0832243
$743$	2.33921	0.0858172	0.0429086	−	0.999079i	$-0.486338\pi$
$743$	2.33921	0.0858172	0.0429086	+	0.999079i	$0.486338\pi$
$744$	1.98921	0.0729280
$745$	1.02175	0.0374339
$746$	−20.3725	−0.745890
$747$	−3.98463	−0.145790
$748$	11.1674	0.408320
$749$	3.00106	0.109656
$750$	3.73891	0.136526
$751$	−14.0407	−0.512353	−0.256177	−	0.966630i	$-0.582463\pi$
$751$	−14.0407	−0.512353	−0.256177	+	0.966630i	$0.582463\pi$
$752$	8.74766	0.318994
$753$	6.55143	0.238747
$754$	−24.5797	−0.895139
$755$	6.14242	0.223545
$756$	−18.5965	−0.676346
$757$	−49.3867	−1.79499	−0.897494	−	0.441026i	$-0.854615\pi$
$757$	−49.3867	−1.79499	−0.897494	+	0.441026i	$0.854615\pi$
$758$	79.8001	2.89847
$759$	−10.9262	−0.396594
$760$	19.9329	0.723044
$761$	35.0571	1.27082	0.635409	−	0.772176i	$-0.280832\pi$
$761$	35.0571	1.27082	0.635409	+	0.772176i	$0.280832\pi$
$762$	−5.08027	−0.184039
$763$	−4.50197	−0.162982
$764$	29.0481	1.05092
$765$	0.696415	0.0251789
$766$	70.8338	2.55933
$767$	−35.8672	−1.29509
$768$	32.7215	1.18074
$769$	−21.2589	−0.766617	−0.383309	−	0.923620i	$-0.625215\pi$
$769$	−21.2589	−0.766617	−0.383309	+	0.923620i	$0.625215\pi$
$770$	−4.46264	−0.160822
$771$	35.5707	1.28105
$772$	79.6047	2.86504
$773$	10.1879	0.366435	0.183218	−	0.983072i	$-0.441349\pi$
$773$	10.1879	0.366435	0.183218	+	0.983072i	$0.441349\pi$
$774$	3.84570	0.138231
$775$	0.382786	0.0137501
$776$	−35.5531	−1.27628
$777$	2.76710	0.0992693
$778$	−63.8307	−2.28844
$779$	24.5365	0.879112
$780$	14.4969	0.519074
$781$	28.3148	1.01318
$782$	−14.0431	−0.502182
$783$	−21.8724	−0.781654
$784$	0.711551	0.0254125
$785$	−11.7765	−0.420322
$786$	−13.3549	−0.476354
$787$	−0.0423361	−0.00150912	−0.000754559	−	1.00000i	$-0.500240\pi$
$787$	−0.0423361	−0.00150912	−0.000754559		1.00000i	$0.500240\pi$
$788$	−17.2511	−0.614544
$789$	5.80528	0.206673
$790$	−31.0019	−1.10300
$791$	−0.845924	−0.0300776
$792$	−2.52042	−0.0895594
$793$	−12.7977	−0.454459
$794$	57.2805	2.03281
$795$	−1.57260	−0.0557743
$796$	−94.4557	−3.34789
$797$	−1.09697	−0.0388566	−0.0194283	−	0.999811i	$-0.506185\pi$
$797$	−1.09697	−0.0388566	−0.0194283	+	0.999811i	$0.506185\pi$
$798$	23.0966	0.817610
$799$	−21.0693	−0.745378
$800$	4.80160	0.169762
$801$	−6.64541	−0.234804
$802$	4.10402	0.144918
$803$	−20.8058	−0.734221
$804$	−59.9649	−2.11480
$805$	3.52947	0.124398
$806$	2.35984	0.0831217
$807$	32.4533	1.14241
$808$	3.60678	0.126886
$809$	−39.4375	−1.38655	−0.693275	−	0.720673i	$-0.743833\pi$
$809$	−39.4375	−1.38655	−0.693275	+	0.720673i	$0.743833\pi$
$810$	17.6810	0.621246
$811$	−6.74360	−0.236800	−0.118400	−	0.992966i	$-0.537776\pi$
$811$	−6.74360	−0.236800	−0.118400	+	0.992966i	$0.537776\pi$
$812$	13.5156	0.474305
$813$	−39.6841	−1.39178
$814$	7.66764	0.268751
$815$	7.87684	0.275914
$816$	1.96393	0.0687513
$817$	−25.1817	−0.880997
$818$	18.5039	0.646972
$819$	−1.07904	−0.0377048
$820$	−13.4647	−0.470206
$821$	13.5197	0.471840	0.235920	−	0.971772i	$-0.424190\pi$
$821$	13.5197	0.471840	0.235920	+	0.971772i	$0.424190\pi$
$822$	−60.7653	−2.11943
$823$	−17.5113	−0.610405	−0.305202	−	0.952288i	$-0.598724\pi$
$823$	−17.5113	−0.610405	−0.305202	+	0.952288i	$0.598724\pi$
$824$	54.4032	1.89522
$825$	3.09569	0.107778
$826$	31.3583	1.09109
$827$	−5.30049	−0.184316	−0.0921581	−	0.995744i	$-0.529377\pi$
$827$	−5.30049	−0.184316	−0.0921581	+	0.995744i	$0.529377\pi$
$828$	4.86181	0.168960
$829$	33.4807	1.16283	0.581416	−	0.813607i	$-0.302499\pi$
$829$	33.4807	1.16283	0.581416	+	0.813607i	$0.302499\pi$
$830$	−22.7654	−0.790197
$831$	33.8836	1.17541
$832$	33.3803	1.15725
$833$	−1.71382	−0.0593803
$834$	−53.9352	−1.86762
$835$	0.388370	0.0134401
$836$	40.2522	1.39215
$837$	2.09991	0.0725837
$838$	21.1061	0.729097
$839$	18.9310	0.653569	0.326785	−	0.945099i	$-0.394035\pi$
$839$	18.9310	0.653569	0.326785	+	0.945099i	$0.394035\pi$
$840$	−5.19666	−0.179302
$841$	−13.1035	−0.451846
$842$	4.75368	0.163823
$843$	−3.69409	−0.127231
$844$	−97.0352	−3.34009
$845$	−5.94866	−0.204640
$846$	11.5979	0.398743
$847$	7.30509	0.251006
$848$	0.694813	0.0238600
$849$	13.2841	0.455911
$850$	3.97882	0.136472
$851$	−6.06429	−0.207881
$852$	80.4179	2.75507
$853$	31.8541	1.09066	0.545332	−	0.838220i	$-0.316404\pi$
$853$	31.8541	1.09066	0.545332	+	0.838220i	$0.316404\pi$
$854$	11.1888	0.382875
$855$	2.51019	0.0858465
$856$	9.68374	0.330983
$857$	1.28886	0.0440265	0.0220133	−	0.999758i	$-0.492992\pi$
$857$	1.28886	0.0440265	0.0220133	+	0.999758i	$0.492992\pi$
$858$	19.0846	0.651537
$859$	13.7258	0.468319	0.234159	−	0.972198i	$-0.424766\pi$
$859$	13.7258	0.468319	0.234159	+	0.972198i	$0.424766\pi$
$860$	13.8187	0.471214
$861$	−6.39685	−0.218004
$862$	−62.4493	−2.12703
$863$	35.8513	1.22039	0.610196	−	0.792250i	$-0.291091\pi$
$863$	35.8513	1.22039	0.610196	+	0.792250i	$0.291091\pi$
$864$	26.3409	0.896137
$865$	17.1175	0.582011
$866$	73.3394	2.49217
$867$	22.6479	0.769163
$868$	−1.29760	−0.0440435
$869$	−25.6685	−0.870745
$870$	−14.9072	−0.505401
$871$	−29.1671	−0.988289
$872$	−14.5268	−0.491941
$873$	−4.47726	−0.151532
$874$	−50.6177	−1.71217
$875$	−1.00000	−0.0338062
$876$	−59.0913	−1.99651
$877$	−9.36088	−0.316094	−0.158047	−	0.987432i	$-0.550520\pi$
$877$	−9.36088	−0.316094	−0.158047	+	0.987432i	$0.550520\pi$
$878$	−25.8643	−0.872879
$879$	−9.17135	−0.309342
$880$	−1.36775	−0.0461070
$881$	−30.0130	−1.01116	−0.505582	−	0.862779i	$-0.668722\pi$
$881$	−30.0130	−1.01116	−0.505582	+	0.862779i	$0.668722\pi$
$882$	0.943394	0.0317657
$883$	36.2654	1.22043	0.610214	−	0.792236i	$-0.291083\pi$
$883$	36.2654	1.22043	0.610214	+	0.792236i	$0.291083\pi$
$884$	15.4271	0.518871
$885$	−21.7529	−0.731216
$886$	12.5441	0.421428
$887$	−11.0449	−0.370852	−0.185426	−	0.982658i	$-0.559366\pi$
$887$	−11.0449	−0.370852	−0.185426	+	0.982658i	$0.559366\pi$
$888$	8.92882	0.299632
$889$	1.35876	0.0455712
$890$	−37.9672	−1.27266
$891$	14.6392	0.490433
$892$	47.4362	1.58828
$893$	−75.9431	−2.54134
$894$	3.82022	0.127767
$895$	7.84661	0.262283
$896$	−19.5808	−0.654148
$897$	−15.0939	−0.503970
$898$	−38.4041	−1.28156
$899$	−1.52618	−0.0509011
$900$	−1.37749	−0.0459163
$901$	−1.67350	−0.0557525
$902$	−17.7256	−0.590199
$903$	6.56505	0.218471
$904$	−2.72961	−0.0907854
$905$	−13.7647	−0.457553
$906$	22.9659	0.762992
$907$	2.31271	0.0767923	0.0383962	−	0.999263i	$-0.487775\pi$
$907$	2.31271	0.0767923	0.0383962	+	0.999263i	$0.487775\pi$
$908$	−64.5254	−2.14135
$909$	0.454208	0.0150651
$910$	−6.16489	−0.204364
$911$	−55.7095	−1.84574	−0.922869	−	0.385113i	$-0.874162\pi$
$911$	−55.7095	−1.84574	−0.922869	+	0.385113i	$0.874162\pi$
$912$	7.07887	0.234405
$913$	−18.8489	−0.623809
$914$	11.0099	0.364177
$915$	−7.76160	−0.256590
$916$	3.38989	0.112005
$917$	3.57188	0.117954
$918$	21.8273	0.720407
$919$	18.1417	0.598440	0.299220	−	0.954184i	$-0.403273\pi$
$919$	18.1417	0.598440	0.299220	+	0.954184i	$0.403273\pi$
$920$	11.3888	0.375478
$921$	−26.0154	−0.857237
$922$	6.46097	0.212781
$923$	39.1154	1.28750
$924$	−10.4940	−0.345228
$925$	1.71819	0.0564936
$926$	−8.12234	−0.266917
$927$	6.85108	0.225019
$928$	−19.1442	−0.628438
$929$	−45.5780	−1.49537	−0.747683	−	0.664056i	$-0.768834\pi$
$929$	−45.5780	−1.49537	−0.747683	+	0.664056i	$0.768834\pi$
$930$	1.43120	0.0469310
$931$	−6.17735	−0.202455
$932$	67.6539	2.21608
$933$	−49.4594	−1.61923
$934$	65.5579	2.14512
$935$	3.29432	0.107736
$936$	−3.48183	−0.113807
$937$	−43.1827	−1.41072	−0.705359	−	0.708850i	$-0.749214\pi$
$937$	−43.1827	−1.41072	−0.705359	+	0.708850i	$0.749214\pi$
$938$	25.5004	0.832617
$939$	32.8070	1.07062
$940$	41.6745	1.35927
$941$	−35.0212	−1.14166	−0.570830	−	0.821068i	$-0.693378\pi$
$941$	−35.0212	−1.14166	−0.570830	+	0.821068i	$0.693378\pi$
$942$	−44.0314	−1.43462
$943$	14.0191	0.456525
$944$	9.61099	0.312811
$945$	−5.48586	−0.178455
$946$	18.1917	0.591465
$947$	18.7720	0.610007	0.305003	−	0.952351i	$-0.401342\pi$
$947$	18.7720	0.610007	0.305003	+	0.952351i	$0.401342\pi$
$948$	−72.9020	−2.36775
$949$	−28.7421	−0.933009
$950$	14.3414	0.465297
$951$	−38.4086	−1.24548
$952$	−5.53010	−0.179232
$953$	28.6024	0.926523	0.463262	−	0.886222i	$-0.346679\pi$
$953$	28.6024	0.926523	0.463262	+	0.886222i	$0.346679\pi$
$954$	0.921203	0.0298250
$955$	8.56906	0.277288
$956$	−8.36757	−0.270627
$957$	−12.3426	−0.398981
$958$	−28.6022	−0.924096
$959$	16.2521	0.524809
$960$	20.2447	0.653393
$961$	−30.8535	−0.995273
$962$	10.5924	0.341514
$963$	1.21949	0.0392975
$964$	−14.1524	−0.455818
$965$	23.4830	0.755945
$966$	13.1964	0.424587
$967$	−59.2802	−1.90632	−0.953161	−	0.302465i	$-0.902191\pi$
$967$	−59.2802	−1.90632	−0.953161	+	0.302465i	$0.902191\pi$
$968$	23.5719	0.757629
$969$	−17.0499	−0.547723
$970$	−25.5799	−0.821321
$971$	−45.8919	−1.47274	−0.736371	−	0.676578i	$-0.763462\pi$
$971$	−45.8919	−1.47274	−0.736371	+	0.676578i	$0.763462\pi$
$972$	−14.2120	−0.455849
$973$	14.4254	0.462456
$974$	43.5375	1.39503
$975$	4.27653	0.136959
$976$	3.42927	0.109768
$977$	−19.6492	−0.628633	−0.314316	−	0.949318i	$-0.601775\pi$
$977$	−19.6492	−0.628633	−0.314316	+	0.949318i	$0.601775\pi$
$978$	29.4508	0.941733
$979$	−31.4355	−1.00468
$980$	3.38989	0.108286
$981$	−1.82939	−0.0584078
$982$	−22.0266	−0.702896
$983$	−23.9866	−0.765055	−0.382528	−	0.923944i	$-0.624946\pi$
$983$	−23.9866	−0.765055	−0.382528	+	0.923944i	$0.624946\pi$
$984$	−20.6412	−0.658017
$985$	−5.08898	−0.162148
$986$	−15.8637	−0.505203
$987$	19.7989	0.630206
$988$	55.6062	1.76907
$989$	−14.3877	−0.457504
$990$	−1.81341	−0.0576338
$991$	47.2523	1.50102	0.750510	−	0.660859i	$-0.229808\pi$
$991$	47.2523	1.50102	0.750510	+	0.660859i	$0.229808\pi$
$992$	1.83799	0.0583562
$993$	25.2875	0.802474
$994$	−34.1981	−1.08470
$995$	−27.8640	−0.883348
$996$	−53.5335	−1.69627
$997$	40.7734	1.29131	0.645653	−	0.763631i	$-0.276585\pi$
$997$	40.7734	1.29131	0.645653	+	0.763631i	$0.276585\pi$
$998$	−86.9067	−2.75098
$999$	9.42573	0.298217

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.i.1.3	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.i.1.3	✓	44	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)

\(f(q)\)	\(=\)	\(q-2.32161 q^{2} -1.61048 q^{3} +3.38989 q^{4} +1.00000 q^{5} +3.73891 q^{6} -1.00000 q^{7} -3.22677 q^{8} -0.406353 q^{9} +O(q^{10})\)	\(q-2.32161 q^{2} -1.61048 q^{3} +3.38989 q^{4} +1.00000 q^{5} +3.73891 q^{6} -1.00000 q^{7} -3.22677 q^{8} -0.406353 q^{9} -2.32161 q^{10} -1.92221 q^{11} -5.45934 q^{12} -2.65544 q^{13} +2.32161 q^{14} -1.61048 q^{15} +0.711551 q^{16} -1.71382 q^{17} +0.943394 q^{18} -6.17735 q^{19} +3.38989 q^{20} +1.61048 q^{21} +4.46264 q^{22} -3.52947 q^{23} +5.19666 q^{24} +1.00000 q^{25} +6.16489 q^{26} +5.48586 q^{27} -3.38989 q^{28} -3.98704 q^{29} +3.73891 q^{30} +0.382786 q^{31} +4.80160 q^{32} +3.09569 q^{33} +3.97882 q^{34} -1.00000 q^{35} -1.37749 q^{36} +1.71819 q^{37} +14.3414 q^{38} +4.27653 q^{39} -3.22677 q^{40} -3.97201 q^{41} -3.73891 q^{42} +4.07646 q^{43} -6.51609 q^{44} -0.406353 q^{45} +8.19407 q^{46} +12.2938 q^{47} -1.14594 q^{48} +1.00000 q^{49} -2.32161 q^{50} +2.76007 q^{51} -9.00162 q^{52} +0.976477 q^{53} -12.7361 q^{54} -1.92221 q^{55} +3.22677 q^{56} +9.94851 q^{57} +9.25636 q^{58} +13.5071 q^{59} -5.45934 q^{60} +4.81943 q^{61} -0.888682 q^{62} +0.406353 q^{63} -12.5706 q^{64} -2.65544 q^{65} -7.18699 q^{66} +10.9839 q^{67} -5.80964 q^{68} +5.68415 q^{69} +2.32161 q^{70} -14.7303 q^{71} +1.31121 q^{72} +10.8239 q^{73} -3.98896 q^{74} -1.61048 q^{75} -20.9405 q^{76} +1.92221 q^{77} -9.92844 q^{78} +13.3536 q^{79} +0.711551 q^{80} -7.61582 q^{81} +9.22147 q^{82} +9.80584 q^{83} +5.45934 q^{84} -1.71382 q^{85} -9.46395 q^{86} +6.42105 q^{87} +6.20255 q^{88} +16.3538 q^{89} +0.943394 q^{90} +2.65544 q^{91} -11.9645 q^{92} -0.616470 q^{93} -28.5414 q^{94} -6.17735 q^{95} -7.73289 q^{96} +11.0182 q^{97} -2.32161 q^{98} +0.781097 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 2 q^{2} + 30 q^{4} + 44 q^{5} - 7 q^{6} - 44 q^{7} - 3 q^{8} + 16 q^{9}+O(q^{10}) \) 44 * q - 2 * q^2 + 30 * q^4 + 44 * q^5 - 7 * q^6 - 44 * q^7 - 3 * q^8 + 16 * q^9	\( 44 q - 2 q^{2} + 30 q^{4} + 44 q^{5} - 7 q^{6} - 44 q^{7} - 3 q^{8} + 16 q^{9} - 2 q^{10} - 15 q^{11} - 3 q^{12} - 17 q^{13} + 2 q^{14} + 10 q^{16} - 7 q^{17} - 16 q^{18} - 32 q^{19} + 30 q^{20} - 14 q^{22} + 8 q^{23} - 35 q^{24} + 44 q^{25} - 27 q^{26} + 6 q^{27} - 30 q^{28} - 42 q^{29} - 7 q^{30} - 43 q^{31} - 8 q^{32} - 33 q^{33} - 33 q^{34} - 44 q^{35} - 11 q^{36} - 44 q^{37} + 4 q^{38} + 3 q^{39} - 3 q^{40} - 62 q^{41} + 7 q^{42} - 7 q^{43} - 45 q^{44} + 16 q^{45} - 15 q^{46} + 2 q^{47} - 26 q^{48} + 44 q^{49} - 2 q^{50} - 25 q^{51} - 35 q^{52} - 25 q^{53} - 76 q^{54} - 15 q^{55} + 3 q^{56} - 7 q^{57} - 2 q^{58} - 35 q^{59} - 3 q^{60} - 86 q^{61} - 23 q^{62} - 16 q^{63} - 5 q^{64} - 17 q^{65} - 6 q^{66} + 2 q^{67} - q^{68} - 75 q^{69} + 2 q^{70} - 54 q^{71} - 3 q^{72} - 52 q^{73} - 22 q^{74} - 77 q^{76} + 15 q^{77} + 2 q^{78} + 46 q^{79} + 10 q^{80} - 72 q^{81} - 16 q^{82} + 26 q^{83} + 3 q^{84} - 7 q^{85} - 33 q^{86} - 8 q^{87} - 23 q^{88} - 105 q^{89} - 16 q^{90} + 17 q^{91} - 41 q^{92} - 11 q^{93} - 47 q^{94} - 32 q^{95} - 39 q^{96} - 80 q^{97} - 2 q^{98} - 53 q^{99}+O(q^{100}) \) 44 * q - 2 * q^2 + 30 * q^4 + 44 * q^5 - 7 * q^6 - 44 * q^7 - 3 * q^8 + 16 * q^9 - 2 * q^10 - 15 * q^11 - 3 * q^12 - 17 * q^13 + 2 * q^14 + 10 * q^16 - 7 * q^17 - 16 * q^18 - 32 * q^19 + 30 * q^20 - 14 * q^22 + 8 * q^23 - 35 * q^24 + 44 * q^25 - 27 * q^26 + 6 * q^27 - 30 * q^28 - 42 * q^29 - 7 * q^30 - 43 * q^31 - 8 * q^32 - 33 * q^33 - 33 * q^34 - 44 * q^35 - 11 * q^36 - 44 * q^37 + 4 * q^38 + 3 * q^39 - 3 * q^40 - 62 * q^41 + 7 * q^42 - 7 * q^43 - 45 * q^44 + 16 * q^45 - 15 * q^46 + 2 * q^47 - 26 * q^48 + 44 * q^49 - 2 * q^50 - 25 * q^51 - 35 * q^52 - 25 * q^53 - 76 * q^54 - 15 * q^55 + 3 * q^56 - 7 * q^57 - 2 * q^58 - 35 * q^59 - 3 * q^60 - 86 * q^61 - 23 * q^62 - 16 * q^63 - 5 * q^64 - 17 * q^65 - 6 * q^66 + 2 * q^67 - q^68 - 75 * q^69 + 2 * q^70 - 54 * q^71 - 3 * q^72 - 52 * q^73 - 22 * q^74 - 77 * q^76 + 15 * q^77 + 2 * q^78 + 46 * q^79 + 10 * q^80 - 72 * q^81 - 16 * q^82 + 26 * q^83 + 3 * q^84 - 7 * q^85 - 33 * q^86 - 8 * q^87 - 23 * q^88 - 105 * q^89 - 16 * q^90 + 17 * q^91 - 41 * q^92 - 11 * q^93 - 47 * q^94 - 32 * q^95 - 39 * q^96 - 80 * q^97 - 2 * q^98 - 53 * q^99

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