LMFDB - Embedded newform 4015.2.a.h.1.28

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4015,2,Mod(1,4015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4015, 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("4015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4015 = 5 \cdot 11 \cdot 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4015.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:	$32.0599364115$
Analytic rank:	$0$
Dimension:	$37$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.28
Character	$\chi$	$=$	4015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.91950 q^{2} -0.260789 q^{3} +1.68450 q^{4} +1.00000 q^{5} -0.500585 q^{6} -5.05939 q^{7} -0.605613 q^{8} -2.93199 q^{9} +O(q^{10})$	\(q+1.91950 q^{2} -0.260789 q^{3} +1.68450 q^{4} +1.00000 q^{5} -0.500585 q^{6} -5.05939 q^{7} -0.605613 q^{8} -2.93199 q^{9} +1.91950 q^{10} +1.00000 q^{11} -0.439297 q^{12} -1.62207 q^{13} -9.71152 q^{14} -0.260789 q^{15} -4.53147 q^{16} +8.05028 q^{17} -5.62796 q^{18} +2.76332 q^{19} +1.68450 q^{20} +1.31943 q^{21} +1.91950 q^{22} +6.01036 q^{23} +0.157937 q^{24} +1.00000 q^{25} -3.11357 q^{26} +1.54700 q^{27} -8.52252 q^{28} +9.05396 q^{29} -0.500585 q^{30} +3.49816 q^{31} -7.48694 q^{32} -0.260789 q^{33} +15.4526 q^{34} -5.05939 q^{35} -4.93892 q^{36} -2.75291 q^{37} +5.30419 q^{38} +0.423017 q^{39} -0.605613 q^{40} -2.96672 q^{41} +2.53265 q^{42} -8.50985 q^{43} +1.68450 q^{44} -2.93199 q^{45} +11.5369 q^{46} -1.94959 q^{47} +1.18175 q^{48} +18.5974 q^{49} +1.91950 q^{50} -2.09942 q^{51} -2.73237 q^{52} +8.90378 q^{53} +2.96946 q^{54} +1.00000 q^{55} +3.06403 q^{56} -0.720641 q^{57} +17.3791 q^{58} -8.85846 q^{59} -0.439297 q^{60} +8.65733 q^{61} +6.71474 q^{62} +14.8341 q^{63} -5.30828 q^{64} -1.62207 q^{65} -0.500585 q^{66} -4.09260 q^{67} +13.5607 q^{68} -1.56743 q^{69} -9.71152 q^{70} +0.239302 q^{71} +1.77565 q^{72} +1.00000 q^{73} -5.28422 q^{74} -0.260789 q^{75} +4.65479 q^{76} -5.05939 q^{77} +0.811983 q^{78} +0.231708 q^{79} -4.53147 q^{80} +8.39253 q^{81} -5.69463 q^{82} +16.6802 q^{83} +2.22258 q^{84} +8.05028 q^{85} -16.3347 q^{86} -2.36117 q^{87} -0.605613 q^{88} +16.9646 q^{89} -5.62796 q^{90} +8.20668 q^{91} +10.1244 q^{92} -0.912281 q^{93} -3.74225 q^{94} +2.76332 q^{95} +1.95251 q^{96} -2.05323 q^{97} +35.6978 q^{98} -2.93199 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9}+O(q^{10}) $ 37 * q + 5 * q^2 + 3 * q^3 + 43 * q^4 + 37 * q^5 + 9 * q^6 + 6 * q^7 + 12 * q^8 + 50 * q^9	\( 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9} + 5 q^{10} + 37 q^{11} + 6 q^{12} + 11 q^{13} + 11 q^{14} + 3 q^{15} + 43 q^{16} + 38 q^{17} + 11 q^{18} + 34 q^{19} + 43 q^{20} + 39 q^{21} + 5 q^{22} + 4 q^{23} + 25 q^{24} + 37 q^{25} - 9 q^{26} + 3 q^{27} + 14 q^{28} + 58 q^{29} + 9 q^{30} + 8 q^{31} + 14 q^{32} + 3 q^{33} + 8 q^{34} + 6 q^{35} + 20 q^{36} + 2 q^{37} + 15 q^{38} + 14 q^{39} + 12 q^{40} + 62 q^{41} - 13 q^{42} + 30 q^{43} + 43 q^{44} + 50 q^{45} + 31 q^{46} + 5 q^{47} - 25 q^{48} + 59 q^{49} + 5 q^{50} + 23 q^{51} - q^{52} + 18 q^{53} + 13 q^{54} + 37 q^{55} + 22 q^{56} + 5 q^{57} - 40 q^{58} + 15 q^{59} + 6 q^{60} + 57 q^{61} + 20 q^{62} - 29 q^{63} + 10 q^{64} + 11 q^{65} + 9 q^{66} - 14 q^{67} + 53 q^{68} + 24 q^{69} + 11 q^{70} + 8 q^{71} + 15 q^{72} + 37 q^{73} + 7 q^{74} + 3 q^{75} + 59 q^{76} + 6 q^{77} + q^{78} + 42 q^{79} + 43 q^{80} + 61 q^{81} - 22 q^{82} + 44 q^{83} + 66 q^{84} + 38 q^{85} - q^{86} - 26 q^{87} + 12 q^{88} + 69 q^{89} + 11 q^{90} - 10 q^{91} - 21 q^{92} - 26 q^{93} + 29 q^{94} + 34 q^{95} - 9 q^{96} + 37 q^{97} - 15 q^{98} + 50 q^{99}+O(q^{100}) \) 37 * q + 5 * q^2 + 3 * q^3 + 43 * q^4 + 37 * q^5 + 9 * q^6 + 6 * q^7 + 12 * q^8 + 50 * q^9 + 5 * q^10 + 37 * q^11 + 6 * q^12 + 11 * q^13 + 11 * q^14 + 3 * q^15 + 43 * q^16 + 38 * q^17 + 11 * q^18 + 34 * q^19 + 43 * q^20 + 39 * q^21 + 5 * q^22 + 4 * q^23 + 25 * q^24 + 37 * q^25 - 9 * q^26 + 3 * q^27 + 14 * q^28 + 58 * q^29 + 9 * q^30 + 8 * q^31 + 14 * q^32 + 3 * q^33 + 8 * q^34 + 6 * q^35 + 20 * q^36 + 2 * q^37 + 15 * q^38 + 14 * q^39 + 12 * q^40 + 62 * q^41 - 13 * q^42 + 30 * q^43 + 43 * q^44 + 50 * q^45 + 31 * q^46 + 5 * q^47 - 25 * q^48 + 59 * q^49 + 5 * q^50 + 23 * q^51 - q^52 + 18 * q^53 + 13 * q^54 + 37 * q^55 + 22 * q^56 + 5 * q^57 - 40 * q^58 + 15 * q^59 + 6 * q^60 + 57 * q^61 + 20 * q^62 - 29 * q^63 + 10 * q^64 + 11 * q^65 + 9 * q^66 - 14 * q^67 + 53 * q^68 + 24 * q^69 + 11 * q^70 + 8 * q^71 + 15 * q^72 + 37 * q^73 + 7 * q^74 + 3 * q^75 + 59 * q^76 + 6 * q^77 + q^78 + 42 * q^79 + 43 * q^80 + 61 * q^81 - 22 * q^82 + 44 * q^83 + 66 * q^84 + 38 * q^85 - q^86 - 26 * q^87 + 12 * q^88 + 69 * q^89 + 11 * q^90 - 10 * q^91 - 21 * q^92 - 26 * q^93 + 29 * q^94 + 34 * q^95 - 9 * q^96 + 37 * q^97 - 15 * q^98 + 50 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.91950	1.35729	0.678647	−	0.734464i	$-0.262567\pi$
$2$	1.91950	1.35729	0.678647	+	0.734464i	$0.262567\pi$
$3$	−0.260789	−0.150566	−0.0752832	−	0.997162i	$-0.523986\pi$
$3$	−0.260789	−0.150566	−0.0752832	+	0.997162i	$0.523986\pi$
$4$	1.68450	0.842248
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.500585	−0.204363
$7$	−5.05939	−1.91227	−0.956135	−	0.292927i	$-0.905371\pi$
$7$	−5.05939	−1.91227	−0.956135	+	0.292927i	$0.905371\pi$
$8$	−0.605613	−0.214116
$9$	−2.93199	−0.977330
$10$	1.91950	0.607000
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−0.439297	−0.126814
$13$	−1.62207	−0.449881	−0.224941	−	0.974372i	$-0.572219\pi$
$13$	−1.62207	−0.449881	−0.224941	+	0.974372i	$0.572219\pi$
$14$	−9.71152	−2.59551
$15$	−0.260789	−0.0673353
$16$	−4.53147	−1.13287
$17$	8.05028	1.95248	0.976240	−	0.216691i	$-0.0695264\pi$
$17$	8.05028	1.95248	0.976240	+	0.216691i	$0.0695264\pi$
$18$	−5.62796	−1.32652
$19$	2.76332	0.633948	0.316974	−	0.948434i	$-0.397333\pi$
$19$	2.76332	0.633948	0.316974	+	0.948434i	$0.397333\pi$
$20$	1.68450	0.376665
$21$	1.31943	0.287923
$22$	1.91950	0.409240
$23$	6.01036	1.25325	0.626624	−	0.779322i	$-0.284436\pi$
$23$	6.01036	1.25325	0.626624	+	0.779322i	$0.284436\pi$
$24$	0.157937	0.0322387
$25$	1.00000	0.200000
$26$	−3.11357	−0.610621
$27$	1.54700	0.297719
$28$	−8.52252	−1.61060
$29$	9.05396	1.68128	0.840639	−	0.541596i	$-0.182180\pi$
$29$	9.05396	1.68128	0.840639	+	0.541596i	$0.182180\pi$
$30$	−0.500585	−0.0913938
$31$	3.49816	0.628289	0.314144	−	0.949375i	$-0.398282\pi$
$31$	3.49816	0.628289	0.314144	+	0.949375i	$0.398282\pi$
$32$	−7.48694	−1.32352
$33$	−0.260789	−0.0453975
$34$	15.4526	2.65009
$35$	−5.05939	−0.855193
$36$	−4.93892	−0.823154
$37$	−2.75291	−0.452576	−0.226288	−	0.974060i	$-0.572659\pi$
$37$	−2.75291	−0.452576	−0.226288	+	0.974060i	$0.572659\pi$
$38$	5.30419	0.860454
$39$	0.423017	0.0677370
$40$	−0.605613	−0.0957558
$41$	−2.96672	−0.463324	−0.231662	−	0.972796i	$-0.574416\pi$
$41$	−2.96672	−0.463324	−0.231662	+	0.972796i	$0.574416\pi$
$42$	2.53265	0.390797
$43$	−8.50985	−1.29774	−0.648870	−	0.760899i	$-0.724758\pi$
$43$	−8.50985	−1.29774	−0.648870	+	0.760899i	$0.724758\pi$
$44$	1.68450	0.253947
$45$	−2.93199	−0.437075
$46$	11.5369	1.70102
$47$	−1.94959	−0.284377	−0.142189	−	0.989840i	$-0.545414\pi$
$47$	−1.94959	−0.284377	−0.142189	+	0.989840i	$0.545414\pi$
$48$	1.18175	0.170572
$49$	18.5974	2.65678
$50$	1.91950	0.271459
$51$	−2.09942	−0.293978
$52$	−2.73237	−0.378911
$53$	8.90378	1.22303	0.611514	−	0.791234i	$-0.290561\pi$
$53$	8.90378	1.22303	0.611514	+	0.791234i	$0.290561\pi$
$54$	2.96946	0.404093
$55$	1.00000	0.134840
$56$	3.06403	0.409448
$57$	−0.720641	−0.0954512
$58$	17.3791	2.28199
$59$	−8.85846	−1.15327	−0.576637	−	0.817001i	$-0.695635\pi$
$59$	−8.85846	−1.15327	−0.576637	+	0.817001i	$0.695635\pi$
$60$	−0.439297	−0.0567130
$61$	8.65733	1.10846	0.554229	−	0.832364i	$-0.313013\pi$
$61$	8.65733	1.10846	0.554229	+	0.832364i	$0.313013\pi$
$62$	6.71474	0.852773
$63$	14.8341	1.86892
$64$	−5.30828	−0.663535
$65$	−1.62207	−0.201193
$66$	−0.500585	−0.0616177
$67$	−4.09260	−0.499991	−0.249996	−	0.968247i	$-0.580429\pi$
$67$	−4.09260	−0.499991	−0.249996	+	0.968247i	$0.580429\pi$
$68$	13.5607	1.64447
$69$	−1.56743	−0.188697
$70$	−9.71152	−1.16075
$71$	0.239302	0.0283999	0.0141999	−	0.999899i	$-0.495480\pi$
$71$	0.239302	0.0283999	0.0141999	+	0.999899i	$0.495480\pi$
$72$	1.77565	0.209262
$73$	1.00000	0.117041
$73$	1.00000	0.117041
$74$	−5.28422	−0.614279
$75$	−0.260789	−0.0301133
$76$	4.65479	0.533941
$77$	−5.05939	−0.576571
$78$	0.811983	0.0919390
$79$	0.231708	0.0260692	0.0130346	−	0.999915i	$-0.495851\pi$
$79$	0.231708	0.0260692	0.0130346	+	0.999915i	$0.495851\pi$
$80$	−4.53147	−0.506633
$81$	8.39253	0.932503
$82$	−5.69463	−0.628867
$83$	16.6802	1.83089	0.915443	−	0.402447i	$-0.131840\pi$
$83$	16.6802	1.83089	0.915443	+	0.402447i	$0.131840\pi$
$84$	2.22258	0.242503
$85$	8.05028	0.873176
$86$	−16.3347	−1.76142
$87$	−2.36117	−0.253144
$88$	−0.605613	−0.0645585
$89$	16.9646	1.79825	0.899124	−	0.437694i	$-0.144205\pi$
$89$	16.9646	1.79825	0.899124	+	0.437694i	$0.144205\pi$
$90$	−5.62796	−0.593240
$91$	8.20668	0.860294
$92$	10.1244	1.05554
$93$	−0.912281	−0.0945991
$94$	−3.74225	−0.385984
$95$	2.76332	0.283510
$96$	1.95251	0.199277
$97$	−2.05323	−0.208474	−0.104237	−	0.994552i	$-0.533240\pi$
$97$	−2.05323	−0.208474	−0.104237	+	0.994552i	$0.533240\pi$
$98$	35.6978	3.60603
$99$	−2.93199	−0.294676
$100$	1.68450	0.168450
$101$	2.37103	0.235927	0.117963	−	0.993018i	$-0.462363\pi$
$101$	2.37103	0.235927	0.117963	+	0.993018i	$0.462363\pi$
$102$	−4.02985	−0.399014
$103$	−3.30328	−0.325482	−0.162741	−	0.986669i	$-0.552033\pi$
$103$	−3.30328	−0.325482	−0.162741	+	0.986669i	$0.552033\pi$
$104$	0.982346	0.0963269
$105$	1.31943	0.128763
$106$	17.0908	1.66001
$107$	−0.293542	−0.0283778	−0.0141889	−	0.999899i	$-0.504517\pi$
$107$	−0.293542	−0.0283778	−0.0141889	+	0.999899i	$0.504517\pi$
$108$	2.60591	0.250753
$109$	14.8598	1.42331	0.711655	−	0.702529i	$-0.247946\pi$
$109$	14.8598	1.42331	0.711655	+	0.702529i	$0.247946\pi$
$110$	1.91950	0.183018
$111$	0.717928	0.0681427
$112$	22.9265	2.16635
$113$	7.21829	0.679039	0.339520	−	0.940599i	$-0.389735\pi$
$113$	7.21829	0.679039	0.339520	+	0.940599i	$0.389735\pi$
$114$	−1.38327	−0.129555
$115$	6.01036	0.560469
$116$	15.2513	1.41605
$117$	4.75589	0.439682
$118$	−17.0038	−1.56533
$119$	−40.7295	−3.73367
$120$	0.157937	0.0144176
$121$	1.00000	0.0909091
$122$	16.6178	1.50450
$123$	0.773687	0.0697610
$124$	5.89264	0.529175
$125$	1.00000	0.0894427
$126$	28.4741	2.53667
$127$	14.1325	1.25405	0.627026	−	0.778998i	$-0.284272\pi$
$127$	14.1325	1.25405	0.627026	+	0.778998i	$0.284272\pi$
$128$	4.78462	0.422904
$129$	2.21927	0.195396
$130$	−3.11357	−0.273078
$131$	−22.2478	−1.94380	−0.971899	−	0.235396i	$-0.924361\pi$
$131$	−22.2478	−1.94380	−0.971899	+	0.235396i	$0.924361\pi$
$132$	−0.439297	−0.0382359
$133$	−13.9807	−1.21228
$134$	−7.85577	−0.678635
$135$	1.54700	0.133144
$136$	−4.87535	−0.418058
$137$	−3.39120	−0.289729	−0.144865	−	0.989451i	$-0.546275\pi$
$137$	−3.39120	−0.289729	−0.144865	+	0.989451i	$0.546275\pi$
$138$	−3.00870	−0.256117
$139$	−13.3808	−1.13494	−0.567472	−	0.823393i	$-0.692079\pi$
$139$	−13.3808	−1.13494	−0.567472	+	0.823393i	$0.692079\pi$
$140$	−8.52252	−0.720284
$141$	0.508432	0.0428177
$142$	0.459341	0.0385470
$143$	−1.62207	−0.135644
$144$	13.2862	1.10718
$145$	9.05396	0.751890
$146$	1.91950	0.158859
$147$	−4.85000	−0.400021
$148$	−4.63727	−0.381181
$149$	−12.3339	−1.01043	−0.505214	−	0.862994i	$-0.668587\pi$
$149$	−12.3339	−1.01043	−0.505214	+	0.862994i	$0.668587\pi$
$150$	−0.500585	−0.0408726
$151$	13.3710	1.08811	0.544056	−	0.839049i	$-0.316888\pi$
$151$	13.3710	1.08811	0.544056	+	0.839049i	$0.316888\pi$
$152$	−1.67350	−0.135739
$153$	−23.6033	−1.90822
$154$	−9.71152	−0.782576
$155$	3.49816	0.280979
$156$	0.712570	0.0570513
$157$	−19.5703	−1.56188	−0.780938	−	0.624608i	$-0.785259\pi$
$157$	−19.5703	−1.56188	−0.780938	+	0.624608i	$0.785259\pi$
$158$	0.444765	0.0353836
$159$	−2.32200	−0.184147
$160$	−7.48694	−0.591895
$161$	−30.4088	−2.39655
$162$	16.1095	1.26568
$163$	5.77977	0.452706	0.226353	−	0.974045i	$-0.427320\pi$
$163$	5.77977	0.452706	0.226353	+	0.974045i	$0.427320\pi$
$164$	−4.99743	−0.390233
$165$	−0.260789	−0.0203024
$166$	32.0177	2.48505
$167$	9.08740	0.703204	0.351602	−	0.936150i	$-0.385637\pi$
$167$	9.08740	0.703204	0.351602	+	0.936150i	$0.385637\pi$
$168$	−0.799064	−0.0616491
$169$	−10.3689	−0.797607
$170$	15.4526	1.18516
$171$	−8.10201	−0.619576
$172$	−14.3348	−1.09302
$173$	−22.1123	−1.68116	−0.840582	−	0.541685i	$-0.817787\pi$
$173$	−22.1123	−1.68116	−0.840582	+	0.541685i	$0.817787\pi$
$174$	−4.53227	−0.343591
$175$	−5.05939	−0.382454
$176$	−4.53147	−0.341572
$177$	2.31018	0.173644
$178$	32.5637	2.44075
$179$	18.4166	1.37652	0.688262	−	0.725462i	$-0.258374\pi$
$179$	18.4166	1.37652	0.688262	+	0.725462i	$0.258374\pi$
$180$	−4.93892	−0.368126
$181$	−5.15509	−0.383175	−0.191588	−	0.981476i	$-0.561364\pi$
$181$	−5.15509	−0.383175	−0.191588	+	0.981476i	$0.561364\pi$
$182$	15.7528	1.16767
$183$	−2.25773	−0.166896
$184$	−3.63995	−0.268341
$185$	−2.75291	−0.202398
$186$	−1.75113	−0.128399
$187$	8.05028	0.588695
$188$	−3.28408	−0.239516
$189$	−7.82685	−0.569320
$190$	5.30419	0.384807
$191$	3.36000	0.243121	0.121561	−	0.992584i	$-0.461210\pi$
$191$	3.36000	0.243121	0.121561	+	0.992584i	$0.461210\pi$
$192$	1.38434	0.0999061
$193$	20.2514	1.45773	0.728863	−	0.684660i	$-0.240049\pi$
$193$	20.2514	1.45773	0.728863	+	0.684660i	$0.240049\pi$
$194$	−3.94118	−0.282960
$195$	0.423017	0.0302929
$196$	31.3273	2.23766
$197$	−14.3042	−1.01913	−0.509565	−	0.860432i	$-0.670194\pi$
$197$	−14.3042	−1.01913	−0.509565	+	0.860432i	$0.670194\pi$
$198$	−5.62796	−0.399962
$199$	−10.2846	−0.729058	−0.364529	−	0.931192i	$-0.618770\pi$
$199$	−10.2846	−0.729058	−0.364529	+	0.931192i	$0.618770\pi$
$200$	−0.605613	−0.0428233
$201$	1.06730	0.0752818
$202$	4.55121	0.320222
$203$	−45.8075	−3.21506
$204$	−3.53647	−0.247602
$205$	−2.96672	−0.207205
$206$	−6.34066	−0.441774
$207$	−17.6223	−1.22484
$208$	7.35035	0.509655
$209$	2.76332	0.191142
$210$	2.53265	0.174770
$211$	2.08830	0.143764	0.0718822	−	0.997413i	$-0.477099\pi$
$211$	2.08830	0.143764	0.0718822	+	0.997413i	$0.477099\pi$
$212$	14.9984	1.03009
$213$	−0.0624071	−0.00427607
$214$	−0.563455	−0.0385170
$215$	−8.50985	−0.580367
$216$	−0.936880	−0.0637466
$217$	−17.6986	−1.20146
$218$	28.5234	1.93185
$219$	−0.260789	−0.0176225
$220$	1.68450	0.113569
$221$	−13.0581	−0.878384
$222$	1.37807	0.0924897
$223$	26.4461	1.77096	0.885482	−	0.464674i	$-0.153829\pi$
$223$	26.4461	1.77096	0.885482	+	0.464674i	$0.153829\pi$
$224$	37.8794	2.53092
$225$	−2.93199	−0.195466
$226$	13.8555	0.921656
$227$	−11.0178	−0.731276	−0.365638	−	0.930757i	$-0.619149\pi$
$227$	−11.0178	−0.731276	−0.365638	+	0.930757i	$0.619149\pi$
$228$	−1.21392	−0.0803936
$229$	12.8889	0.851719	0.425860	−	0.904789i	$-0.359972\pi$
$229$	12.8889	0.851719	0.425860	+	0.904789i	$0.359972\pi$
$230$	11.5369	0.760721
$231$	1.31943	0.0868122
$232$	−5.48319	−0.359989
$233$	1.64458	0.107740	0.0538700	−	0.998548i	$-0.482844\pi$
$233$	1.64458	0.107740	0.0538700	+	0.998548i	$0.482844\pi$
$234$	9.12895	0.596778
$235$	−1.94959	−0.127177
$236$	−14.9220	−0.971342
$237$	−0.0604269	−0.00392515
$238$	−78.1805	−5.06769
$239$	11.8217	0.764685	0.382343	−	0.924021i	$-0.375117\pi$
$239$	11.8217	0.764685	0.382343	+	0.924021i	$0.375117\pi$
$240$	1.18175	0.0762819
$241$	21.1752	1.36401	0.682007	−	0.731345i	$-0.261107\pi$
$241$	21.1752	1.36401	0.682007	+	0.731345i	$0.261107\pi$
$242$	1.91950	0.123390
$243$	−6.82966	−0.438123
$244$	14.5832	0.933595
$245$	18.5974	1.18815
$246$	1.48510	0.0946862
$247$	−4.48229	−0.285201
$248$	−2.11853	−0.134527
$249$	−4.35000	−0.275670
$250$	1.91950	0.121400
$251$	16.6286	1.04959	0.524794	−	0.851229i	$-0.324142\pi$
$251$	16.6286	1.04959	0.524794	+	0.851229i	$0.324142\pi$
$252$	24.9879	1.57409
$253$	6.01036	0.377868
$254$	27.1273	1.70212
$255$	−2.09942	−0.131471
$256$	19.8007	1.23754
$257$	−29.6351	−1.84859	−0.924294	−	0.381682i	$-0.875345\pi$
$257$	−29.6351	−1.84859	−0.924294	+	0.381682i	$0.875345\pi$
$258$	4.25990	0.265210
$259$	13.9281	0.865447
$260$	−2.73237	−0.169454
$261$	−26.5461	−1.64316
$262$	−42.7047	−2.63831
$263$	−9.47055	−0.583979	−0.291990	−	0.956421i	$-0.594317\pi$
$263$	−9.47055	−0.583979	−0.291990	+	0.956421i	$0.594317\pi$
$264$	0.157937	0.00972034
$265$	8.90378	0.546955
$266$	−26.8360	−1.64542
$267$	−4.42418	−0.270756
$268$	−6.89397	−0.421116
$269$	14.7519	0.899439	0.449719	−	0.893170i	$-0.351524\pi$
$269$	14.7519	0.899439	0.449719	+	0.893170i	$0.351524\pi$
$270$	2.96946	0.180716
$271$	−0.504336	−0.0306362	−0.0153181	−	0.999883i	$-0.504876\pi$
$271$	−0.504336	−0.0306362	−0.0153181	+	0.999883i	$0.504876\pi$
$272$	−36.4796	−2.21190
$273$	−2.14021	−0.129531
$274$	−6.50941	−0.393248
$275$	1.00000	0.0603023
$276$	−2.64033	−0.158929
$277$	3.17052	0.190498	0.0952489	−	0.995453i	$-0.469635\pi$
$277$	3.17052	0.190498	0.0952489	+	0.995453i	$0.469635\pi$
$278$	−25.6845	−1.54045
$279$	−10.2566	−0.614045
$280$	3.06403	0.183111
$281$	−18.6576	−1.11302	−0.556508	−	0.830842i	$-0.687859\pi$
$281$	−18.6576	−1.11302	−0.556508	+	0.830842i	$0.687859\pi$
$282$	0.975936	0.0581162
$283$	−2.36183	−0.140396	−0.0701980	−	0.997533i	$-0.522363\pi$
$283$	−2.36183	−0.140396	−0.0701980	+	0.997533i	$0.522363\pi$
$284$	0.403103	0.0239197
$285$	−0.720641	−0.0426871
$286$	−3.11357	−0.184109
$287$	15.0098	0.886000
$288$	21.9516	1.29351
$289$	47.8071	2.81218
$290$	17.3791	1.02054
$291$	0.535459	0.0313891
$292$	1.68450	0.0985776
$293$	−1.04737	−0.0611879	−0.0305940	−	0.999532i	$-0.509740\pi$
$293$	−1.04737	−0.0611879	−0.0305940	+	0.999532i	$0.509740\pi$
$294$	−9.30959	−0.542946
$295$	−8.85846	−0.515759
$296$	1.66720	0.0969039
$297$	1.54700	0.0897658
$298$	−23.6749	−1.37145
$299$	−9.74922	−0.563812
$300$	−0.439297	−0.0253628
$301$	43.0547	2.48163
$302$	25.6656	1.47689
$303$	−0.618338	−0.0355226
$304$	−12.5219	−0.718178
$305$	8.65733	0.495717
$306$	−45.3067	−2.59001
$307$	17.6897	1.00960	0.504802	−	0.863235i	$-0.331565\pi$
$307$	17.6897	1.00960	0.504802	+	0.863235i	$0.331565\pi$
$308$	−8.52252	−0.485616
$309$	0.861457	0.0490066
$310$	6.71474	0.381372
$311$	12.6987	0.720077	0.360039	−	0.932937i	$-0.382763\pi$
$311$	12.6987	0.720077	0.360039	+	0.932937i	$0.382763\pi$
$312$	−0.256184	−0.0145036
$313$	−6.00541	−0.339446	−0.169723	−	0.985492i	$-0.554287\pi$
$313$	−6.00541	−0.339446	−0.169723	+	0.985492i	$0.554287\pi$
$314$	−37.5652	−2.11993
$315$	14.8341	0.835806
$316$	0.390312	0.0219568
$317$	6.17630	0.346895	0.173448	−	0.984843i	$-0.444509\pi$
$317$	6.17630	0.346895	0.173448	+	0.984843i	$0.444509\pi$
$318$	−4.45709	−0.249941
$319$	9.05396	0.506924
$320$	−5.30828	−0.296742
$321$	0.0765524	0.00427274
$322$	−58.3697	−3.25282
$323$	22.2455	1.23777
$324$	14.1372	0.785399
$325$	−1.62207	−0.0899762
$326$	11.0943	0.614456
$327$	−3.87526	−0.214303
$328$	1.79668	0.0992052
$329$	9.86375	0.543806
$330$	−0.500585	−0.0275563
$331$	−28.4197	−1.56209	−0.781045	−	0.624475i	$-0.785313\pi$
$331$	−28.4197	−1.56209	−0.781045	+	0.624475i	$0.785313\pi$
$332$	28.0977	1.54206
$333$	8.07151	0.442316
$334$	17.4433	0.954455
$335$	−4.09260	−0.223603
$336$	−5.97896	−0.326179
$337$	7.52437	0.409879	0.204939	−	0.978775i	$-0.434300\pi$
$337$	7.52437	0.409879	0.204939	+	0.978775i	$0.434300\pi$
$338$	−19.9031	−1.08259
$339$	−1.88245	−0.102240
$340$	13.5607	0.735430
$341$	3.49816	0.189436
$342$	−15.5518	−0.840947
$343$	−58.6759	−3.16820
$344$	5.15367	0.277867
$345$	−1.56743	−0.0843878
$346$	−42.4446	−2.28183
$347$	−14.9875	−0.804572	−0.402286	−	0.915514i	$-0.631784\pi$
$347$	−14.9875	−0.804572	−0.402286	+	0.915514i	$0.631784\pi$
$348$	−3.97738	−0.213210
$349$	2.33812	0.125157	0.0625784	−	0.998040i	$-0.480068\pi$
$349$	2.33812	0.125157	0.0625784	+	0.998040i	$0.480068\pi$
$350$	−9.71152	−0.519103
$351$	−2.50933	−0.133938
$352$	−7.48694	−0.399055
$353$	23.8996	1.27205	0.636024	−	0.771669i	$-0.280578\pi$
$353$	23.8996	1.27205	0.636024	+	0.771669i	$0.280578\pi$
$354$	4.43441	0.235686
$355$	0.239302	0.0127008
$356$	28.5769	1.51457
$357$	10.6218	0.562165
$358$	35.3508	1.86835
$359$	28.4313	1.50055	0.750273	−	0.661128i	$-0.229922\pi$
$359$	28.4313	1.50055	0.750273	+	0.661128i	$0.229922\pi$
$360$	1.77565	0.0935850
$361$	−11.3641	−0.598110
$362$	−9.89522	−0.520081
$363$	−0.260789	−0.0136879
$364$	13.8241	0.724580
$365$	1.00000	0.0523424
$366$	−4.33373	−0.226527
$367$	10.7479	0.561037	0.280519	−	0.959849i	$-0.409494\pi$
$367$	10.7479	0.561037	0.280519	+	0.959849i	$0.409494\pi$
$368$	−27.2358	−1.41976
$369$	8.69839	0.452820
$370$	−5.28422	−0.274714
$371$	−45.0477	−2.33876
$372$	−1.53673	−0.0796759
$373$	−1.85363	−0.0959771	−0.0479885	−	0.998848i	$-0.515281\pi$
$373$	−1.85363	−0.0959771	−0.0479885	+	0.998848i	$0.515281\pi$
$374$	15.4526	0.799032
$375$	−0.260789	−0.0134671
$376$	1.18070	0.0608898
$377$	−14.6861	−0.756375
$378$	−15.0237	−0.772734
$379$	−18.2285	−0.936335	−0.468167	−	0.883640i	$-0.655086\pi$
$379$	−18.2285	−0.936335	−0.468167	+	0.883640i	$0.655086\pi$
$380$	4.65479	0.238786
$381$	−3.68558	−0.188818
$382$	6.44953	0.329987
$383$	−15.9244	−0.813699	−0.406849	−	0.913495i	$-0.633373\pi$
$383$	−15.9244	−0.813699	−0.406849	+	0.913495i	$0.633373\pi$
$384$	−1.24777	−0.0636752
$385$	−5.05939	−0.257850
$386$	38.8726	1.97856
$387$	24.9508	1.26832
$388$	−3.45865	−0.175587
$389$	−0.186606	−0.00946132	−0.00473066	−	0.999989i	$-0.501506\pi$
$389$	−0.186606	−0.00946132	−0.00473066	+	0.999989i	$0.501506\pi$
$390$	0.811983	0.0411164
$391$	48.3851	2.44694
$392$	−11.2628	−0.568859
$393$	5.80197	0.292671
$394$	−27.4569	−1.38326
$395$	0.231708	0.0116585
$396$	−4.93892	−0.248190
$397$	−29.9531	−1.50330	−0.751652	−	0.659560i	$-0.770742\pi$
$397$	−29.9531	−1.50330	−0.751652	+	0.659560i	$0.770742\pi$
$398$	−19.7414	−0.989546
$399$	3.64600	0.182529
$400$	−4.53147	−0.226573
$401$	0.923651	0.0461249	0.0230625	−	0.999734i	$-0.492658\pi$
$401$	0.923651	0.0461249	0.0230625	+	0.999734i	$0.492658\pi$
$402$	2.04869	0.102180
$403$	−5.67426	−0.282655
$404$	3.99399	0.198709
$405$	8.39253	0.417028
$406$	−87.9277	−4.36378
$407$	−2.75291	−0.136457
$408$	1.27144	0.0629455
$409$	17.1161	0.846335	0.423167	−	0.906052i	$-0.360918\pi$
$409$	17.1161	0.846335	0.423167	+	0.906052i	$0.360918\pi$
$410$	−5.69463	−0.281238
$411$	0.884385	0.0436235
$412$	−5.56436	−0.274136
$413$	44.8184	2.20537
$414$	−33.8261	−1.66246
$415$	16.6802	0.818797
$416$	12.1443	0.595425
$417$	3.48956	0.170884
$418$	5.30419	0.259437
$419$	26.1991	1.27991	0.639954	−	0.768413i	$-0.278953\pi$
$419$	26.1991	1.27991	0.639954	+	0.768413i	$0.278953\pi$
$420$	2.22258	0.108451
$421$	−10.0051	−0.487621	−0.243810	−	0.969823i	$-0.578397\pi$
$421$	−10.0051	−0.487621	−0.243810	+	0.969823i	$0.578397\pi$
$422$	4.00850	0.195131
$423$	5.71619	0.277930
$424$	−5.39224	−0.261870
$425$	8.05028	0.390496
$426$	−0.119791	−0.00580388
$427$	−43.8008	−2.11967
$428$	−0.494470	−0.0239011
$429$	0.423017	0.0204235
$430$	−16.3347	−0.787729
$431$	−21.3432	−1.02806	−0.514032	−	0.857771i	$-0.671849\pi$
$431$	−21.3432	−1.02806	−0.514032	+	0.857771i	$0.671849\pi$
$432$	−7.01016	−0.337276
$433$	−21.9708	−1.05585	−0.527925	−	0.849291i	$-0.677030\pi$
$433$	−21.9708	−1.05585	−0.527925	+	0.849291i	$0.677030\pi$
$434$	−33.9725	−1.63073
$435$	−2.36117	−0.113209
$436$	25.0312	1.19878
$437$	16.6085	0.794493
$438$	−0.500585	−0.0239189
$439$	11.0330	0.526575	0.263287	−	0.964717i	$-0.415193\pi$
$439$	11.0330	0.526575	0.263287	+	0.964717i	$0.415193\pi$
$440$	−0.605613	−0.0288714
$441$	−54.5275	−2.59655
$442$	−25.0651	−1.19223
$443$	−12.1571	−0.577599	−0.288800	−	0.957390i	$-0.593256\pi$
$443$	−12.1571	−0.577599	−0.288800	+	0.957390i	$0.593256\pi$
$444$	1.20935	0.0573930
$445$	16.9646	0.804201
$446$	50.7634	2.40372
$447$	3.21653	0.152137
$448$	26.8567	1.26886
$449$	−10.5329	−0.497077	−0.248538	−	0.968622i	$-0.579950\pi$
$449$	−10.5329	−0.497077	−0.248538	+	0.968622i	$0.579950\pi$
$450$	−5.62796	−0.265305
$451$	−2.96672	−0.139697
$452$	12.1592	0.571919
$453$	−3.48699	−0.163833
$454$	−21.1487	−0.992557
$455$	8.20668	0.384735
$456$	0.436429	0.0204377
$457$	−4.23915	−0.198299	−0.0991496	−	0.995073i	$-0.531612\pi$
$457$	−4.23915	−0.198299	−0.0991496	+	0.995073i	$0.531612\pi$
$458$	24.7402	1.15603
$459$	12.4537	0.581291
$460$	10.1244	0.472054
$461$	−4.53169	−0.211062	−0.105531	−	0.994416i	$-0.533654\pi$
$461$	−4.53169	−0.211062	−0.105531	+	0.994416i	$0.533654\pi$
$462$	2.53265	0.117830
$463$	35.5819	1.65363	0.826815	−	0.562473i	$-0.190150\pi$
$463$	35.5819	1.65363	0.826815	+	0.562473i	$0.190150\pi$
$464$	−41.0277	−1.90466
$465$	−0.912281	−0.0423060
$466$	3.15678	0.146235
$467$	−35.5349	−1.64436	−0.822180	−	0.569228i	$-0.807242\pi$
$467$	−35.5349	−1.64436	−0.822180	+	0.569228i	$0.807242\pi$
$468$	8.01127	0.370321
$469$	20.7061	0.956118
$470$	−3.74225	−0.172617
$471$	5.10370	0.235166
$472$	5.36479	0.246935
$473$	−8.50985	−0.391283
$474$	−0.115990	−0.00532758
$475$	2.76332	0.126790
$476$	−68.6087	−3.14467
$477$	−26.1058	−1.19530
$478$	22.6919	1.03790
$479$	−26.0127	−1.18855	−0.594274	−	0.804262i	$-0.702561\pi$
$479$	−26.0127	−1.18855	−0.594274	+	0.804262i	$0.702561\pi$
$480$	1.95251	0.0891194
$481$	4.46541	0.203605
$482$	40.6459	1.85137
$483$	7.93026	0.360839
$484$	1.68450	0.0765680
$485$	−2.05323	−0.0932323
$486$	−13.1096	−0.594662
$487$	−40.5386	−1.83698	−0.918490	−	0.395443i	$-0.870591\pi$
$487$	−40.5386	−1.83698	−0.918490	+	0.395443i	$0.870591\pi$
$488$	−5.24299	−0.237339
$489$	−1.50730	−0.0681624
$490$	35.6978	1.61266
$491$	12.5485	0.566307	0.283153	−	0.959075i	$-0.408619\pi$
$491$	12.5485	0.566307	0.283153	+	0.959075i	$0.408619\pi$
$492$	1.30327	0.0587560
$493$	72.8869	3.28266
$494$	−8.60377	−0.387102
$495$	−2.93199	−0.131783
$496$	−15.8518	−0.711767
$497$	−1.21072	−0.0543082
$498$	−8.34984	−0.374165
$499$	14.2569	0.638228	0.319114	−	0.947716i	$-0.396615\pi$
$499$	14.2569	0.638228	0.319114	+	0.947716i	$0.396615\pi$
$500$	1.68450	0.0753329
$501$	−2.36989	−0.105879
$502$	31.9187	1.42460
$503$	9.76277	0.435300	0.217650	−	0.976027i	$-0.430161\pi$
$503$	9.76277	0.435300	0.217650	+	0.976027i	$0.430161\pi$
$504$	−8.98370	−0.400166
$505$	2.37103	0.105510
$506$	11.5369	0.512878
$507$	2.70409	0.120093
$508$	23.8060	1.05622
$509$	−31.2400	−1.38469	−0.692344	−	0.721567i	$-0.743422\pi$
$509$	−31.2400	−1.38469	−0.692344	+	0.721567i	$0.743422\pi$
$510$	−4.02985	−0.178445
$511$	−5.05939	−0.223814
$512$	28.4382	1.25680
$513$	4.27483	0.188739
$514$	−56.8847	−2.50908
$515$	−3.30328	−0.145560
$516$	3.73835	0.164572
$517$	−1.94959	−0.0857430
$518$	26.7350	1.17467
$519$	5.76662	0.253127
$520$	0.982346	0.0430787
$521$	40.3474	1.76765	0.883826	−	0.467817i	$-0.154959\pi$
$521$	40.3474	1.76765	0.883826	+	0.467817i	$0.154959\pi$
$522$	−50.9554	−2.23026
$523$	36.5074	1.59636	0.798178	−	0.602421i	$-0.205797\pi$
$523$	36.5074	1.59636	0.798178	+	0.602421i	$0.205797\pi$
$524$	−37.4763	−1.63716
$525$	1.31943	0.0575847
$526$	−18.1788	−0.792632
$527$	28.1612	1.22672
$528$	1.18175	0.0514293
$529$	13.1244	0.570628
$530$	17.0908	0.742378
$531$	25.9729	1.12713
$532$	−23.5504	−1.02104
$533$	4.81223	0.208441
$534$	−8.49224	−0.367495
$535$	−0.293542	−0.0126909
$536$	2.47853	0.107056
$537$	−4.80285	−0.207258
$538$	28.3163	1.22080
$539$	18.5974	0.801048
$540$	2.60591	0.112140
$541$	33.3113	1.43216	0.716082	−	0.698016i	$-0.245934\pi$
$541$	33.3113	1.43216	0.716082	+	0.698016i	$0.245934\pi$
$542$	−0.968075	−0.0415824
$543$	1.34439	0.0576933
$544$	−60.2720	−2.58414
$545$	14.8598	0.636523
$546$	−4.10814	−0.175812
$547$	12.0433	0.514935	0.257468	−	0.966287i	$-0.417112\pi$
$547$	12.0433	0.514935	0.257468	+	0.966287i	$0.417112\pi$
$548$	−5.71245	−0.244024
$549$	−25.3832	−1.08333
$550$	1.91950	0.0818479
$551$	25.0189	1.06584
$552$	0.949258	0.0404031
$553$	−1.17230	−0.0498514
$554$	6.08582	0.258562
$555$	0.717928	0.0304743
$556$	−22.5399	−0.955904
$557$	−7.13074	−0.302139	−0.151070	−	0.988523i	$-0.548272\pi$
$557$	−7.13074	−0.302139	−0.151070	+	0.988523i	$0.548272\pi$
$558$	−19.6875	−0.833440
$559$	13.8036	0.583829
$560$	22.9265	0.968820
$561$	−2.09942	−0.0886377
$562$	−35.8132	−1.51069
$563$	6.82712	0.287729	0.143864	−	0.989597i	$-0.454047\pi$
$563$	6.82712	0.287729	0.143864	+	0.989597i	$0.454047\pi$
$564$	0.856451	0.0360631
$565$	7.21829	0.303676
$566$	−4.53353	−0.190559
$567$	−42.4611	−1.78320
$568$	−0.144924	−0.00608088
$569$	34.9467	1.46504	0.732520	−	0.680745i	$-0.238344\pi$
$569$	34.9467	1.46504	0.732520	+	0.680745i	$0.238344\pi$
$570$	−1.38327	−0.0579389
$571$	−28.3733	−1.18739	−0.593694	−	0.804691i	$-0.702331\pi$
$571$	−28.3733	−1.18739	−0.593694	+	0.804691i	$0.702331\pi$
$572$	−2.73237	−0.114246
$573$	−0.876250	−0.0366059
$574$	28.8114	1.20256
$575$	6.01036	0.250649
$576$	15.5638	0.648493
$577$	25.9918	1.08205	0.541027	−	0.841005i	$-0.318036\pi$
$577$	25.9918	1.08205	0.541027	+	0.841005i	$0.318036\pi$
$578$	91.7658	3.81696
$579$	−5.28132	−0.219484
$580$	15.2513	0.633278
$581$	−84.3915	−3.50115
$582$	1.02781	0.0426043
$583$	8.90378	0.368757
$584$	−0.605613	−0.0250604
$585$	4.75589	0.196632
$586$	−2.01043	−0.0830500
$587$	16.3037	0.672924	0.336462	−	0.941697i	$-0.390770\pi$
$587$	16.3037	0.672924	0.336462	+	0.941697i	$0.390770\pi$
$588$	−8.16980	−0.336917
$589$	9.66653	0.398302
$590$	−17.0038	−0.700037
$591$	3.73037	0.153447
$592$	12.4747	0.512708
$593$	29.7094	1.22002	0.610009	−	0.792394i	$-0.291166\pi$
$593$	29.7094	1.22002	0.610009	+	0.792394i	$0.291166\pi$
$594$	2.96946	0.121839
$595$	−40.7295	−1.66975
$596$	−20.7763	−0.851031
$597$	2.68211	0.109772
$598$	−18.7137	−0.765259
$599$	29.5739	1.20836	0.604179	−	0.796848i	$-0.293501\pi$
$599$	29.5739	1.20836	0.604179	+	0.796848i	$0.293501\pi$
$600$	0.157937	0.00644774
$601$	33.3005	1.35835	0.679177	−	0.733975i	$-0.262337\pi$
$601$	33.3005	1.35835	0.679177	+	0.733975i	$0.262337\pi$
$602$	82.6436	3.36830
$603$	11.9995	0.488656
$604$	22.5233	0.916460
$605$	1.00000	0.0406558
$606$	−1.18690	−0.0482146
$607$	−43.5409	−1.76727	−0.883635	−	0.468176i	$-0.844911\pi$
$607$	−43.5409	−1.76727	−0.883635	+	0.468176i	$0.844911\pi$
$608$	−20.6888	−0.839041
$609$	11.9461	0.484079
$610$	16.6178	0.672834
$611$	3.16237	0.127936
$612$	−39.7597	−1.60719
$613$	43.0817	1.74005	0.870026	−	0.493006i	$-0.164102\pi$
$613$	43.0817	1.74005	0.870026	+	0.493006i	$0.164102\pi$
$614$	33.9554	1.37033
$615$	0.773687	0.0311981
$616$	3.06403	0.123453
$617$	5.40838	0.217733	0.108867	−	0.994056i	$-0.465278\pi$
$617$	5.40838	0.217733	0.108867	+	0.994056i	$0.465278\pi$
$618$	1.65357	0.0665164
$619$	24.5407	0.986373	0.493186	−	0.869924i	$-0.335832\pi$
$619$	24.5407	0.986373	0.493186	+	0.869924i	$0.335832\pi$
$620$	5.89264	0.236654
$621$	9.29800	0.373116
$622$	24.3752	0.977357
$623$	−85.8307	−3.43874
$624$	−1.91689	−0.0767369
$625$	1.00000	0.0400000
$626$	−11.5274	−0.460728
$627$	−0.720641	−0.0287796
$628$	−32.9660	−1.31549
$629$	−22.1617	−0.883646
$630$	28.4741	1.13443
$631$	5.18828	0.206542	0.103271	−	0.994653i	$-0.467069\pi$
$631$	5.18828	0.206542	0.103271	+	0.994653i	$0.467069\pi$
$632$	−0.140326	−0.00558185
$633$	−0.544605	−0.0216461
$634$	11.8554	0.470839
$635$	14.1325	0.560829
$636$	−3.91140	−0.155097
$637$	−30.1663	−1.19523
$638$	17.3791	0.688045
$639$	−0.701630	−0.0277561
$640$	4.78462	0.189129
$641$	6.78306	0.267915	0.133957	−	0.990987i	$-0.457231\pi$
$641$	6.78306	0.267915	0.133957	+	0.990987i	$0.457231\pi$
$642$	0.146943	0.00579936
$643$	44.0325	1.73647	0.868236	−	0.496151i	$-0.165254\pi$
$643$	44.0325	1.73647	0.868236	+	0.496151i	$0.165254\pi$
$644$	−51.2234	−2.01849
$645$	2.21927	0.0873838
$646$	42.7003	1.68002
$647$	−35.2216	−1.38470	−0.692352	−	0.721560i	$-0.743425\pi$
$647$	−35.2216	−1.38470	−0.692352	+	0.721560i	$0.743425\pi$
$648$	−5.08262	−0.199664
$649$	−8.85846	−0.347725
$650$	−3.11357	−0.122124
$651$	4.61559	0.180899
$652$	9.73599	0.381291
$653$	−12.0554	−0.471765	−0.235882	−	0.971782i	$-0.575798\pi$
$653$	−12.0554	−0.471765	−0.235882	+	0.971782i	$0.575798\pi$
$654$	−7.43858	−0.290872
$655$	−22.2478	−0.869293
$656$	13.4436	0.524884
$657$	−2.93199	−0.114388
$658$	18.9335	0.738105
$659$	−6.40438	−0.249479	−0.124740	−	0.992190i	$-0.539810\pi$
$659$	−6.40438	−0.249479	−0.124740	+	0.992190i	$0.539810\pi$
$660$	−0.439297	−0.0170996
$661$	−32.3306	−1.25751	−0.628757	−	0.777602i	$-0.716436\pi$
$661$	−32.3306	−1.25751	−0.628757	+	0.777602i	$0.716436\pi$
$662$	−54.5518	−2.12021
$663$	3.40541	0.132255
$664$	−10.1017	−0.392023
$665$	−13.9807	−0.542148
$666$	15.4933	0.600353
$667$	54.4176	2.10706
$668$	15.3077	0.592272
$669$	−6.89685	−0.266647
$670$	−7.85577	−0.303495
$671$	8.65733	0.334212
$672$	−9.87850	−0.381072
$673$	−14.0369	−0.541082	−0.270541	−	0.962708i	$-0.587203\pi$
$673$	−14.0369	−0.541082	−0.270541	+	0.962708i	$0.587203\pi$
$674$	14.4431	0.556326
$675$	1.54700	0.0595439
$676$	−17.4663	−0.671783
$677$	19.9621	0.767208	0.383604	−	0.923498i	$-0.374683\pi$
$677$	19.9621	0.767208	0.383604	+	0.923498i	$0.374683\pi$
$678$	−3.61336	−0.138770
$679$	10.3881	0.398658
$680$	−4.87535	−0.186961
$681$	2.87331	0.110106
$682$	6.71474	0.257121
$683$	−6.63806	−0.253998	−0.126999	−	0.991903i	$-0.540535\pi$
$683$	−6.63806	−0.253998	−0.126999	+	0.991903i	$0.540535\pi$
$684$	−13.6478	−0.521837
$685$	−3.39120	−0.129571
$686$	−112.629	−4.30018
$687$	−3.36127	−0.128240
$688$	38.5621	1.47017
$689$	−14.4425	−0.550217
$690$	−3.00870	−0.114539
$691$	6.91495	0.263057	0.131529	−	0.991312i	$-0.458011\pi$
$691$	6.91495	0.263057	0.131529	+	0.991312i	$0.458011\pi$
$692$	−37.2480	−1.41596
$693$	14.8341	0.563500
$694$	−28.7686	−1.09204
$695$	−13.3808	−0.507563
$696$	1.42995	0.0542022
$697$	−23.8829	−0.904631
$698$	4.48804	0.169875
$699$	−0.428888	−0.0162220
$700$	−8.52252	−0.322121
$701$	26.8781	1.01517	0.507585	−	0.861602i	$-0.330538\pi$
$701$	26.8781	1.01517	0.507585	+	0.861602i	$0.330538\pi$
$702$	−4.81667	−0.181794
$703$	−7.60716	−0.286910
$704$	−5.30828	−0.200063
$705$	0.508432	0.0191486
$706$	45.8754	1.72654
$707$	−11.9960	−0.451155
$708$	3.89150	0.146251
$709$	3.08730	0.115946	0.0579729	−	0.998318i	$-0.481536\pi$
$709$	3.08730	0.115946	0.0579729	+	0.998318i	$0.481536\pi$
$710$	0.459341	0.0172387
$711$	−0.679367	−0.0254782
$712$	−10.2740	−0.385034
$713$	21.0252	0.787401
$714$	20.3886	0.763023
$715$	−1.62207	−0.0606619
$716$	31.0227	1.15937
$717$	−3.08298	−0.115136
$718$	54.5740	2.03668
$719$	−5.54758	−0.206890	−0.103445	−	0.994635i	$-0.532987\pi$
$719$	−5.54758	−0.206890	−0.103445	+	0.994635i	$0.532987\pi$
$720$	13.2862	0.495148
$721$	16.7126	0.622409
$722$	−21.8134	−0.811811
$723$	−5.52225	−0.205375
$724$	−8.68373	−0.322728
$725$	9.05396	0.336256
$726$	−0.500585	−0.0185784
$727$	−2.51174	−0.0931553	−0.0465777	−	0.998915i	$-0.514831\pi$
$727$	−2.51174	−0.0931553	−0.0465777	+	0.998915i	$0.514831\pi$
$728$	−4.97007	−0.184203
$729$	−23.3965	−0.866537
$730$	1.91950	0.0710440
$731$	−68.5067	−2.53381
$732$	−3.80314	−0.140568
$733$	34.6386	1.27941	0.639704	−	0.768622i	$-0.279057\pi$
$733$	34.6386	1.27941	0.639704	+	0.768622i	$0.279057\pi$
$734$	20.6307	0.761493
$735$	−4.85000	−0.178895
$736$	−44.9992	−1.65869
$737$	−4.09260	−0.150753
$738$	16.6966	0.614610
$739$	−24.1154	−0.887098	−0.443549	−	0.896250i	$-0.646281\pi$
$739$	−24.1154	−0.887098	−0.443549	+	0.896250i	$0.646281\pi$
$740$	−4.63727	−0.170469
$741$	1.16893	0.0429417
$742$	−86.4692	−3.17438
$743$	−34.9553	−1.28239	−0.641193	−	0.767380i	$-0.721560\pi$
$743$	−34.9553	−1.28239	−0.641193	+	0.767380i	$0.721560\pi$
$744$	0.552489	0.0202552
$745$	−12.3339	−0.451877
$746$	−3.55804	−0.130269
$747$	−48.9061	−1.78938
$748$	13.5607	0.495827
$749$	1.48514	0.0542659
$750$	−0.500585	−0.0182788
$751$	−11.1374	−0.406408	−0.203204	−	0.979136i	$-0.565135\pi$
$751$	−11.1374	−0.406408	−0.203204	+	0.979136i	$0.565135\pi$
$752$	8.83451	0.322162
$753$	−4.33655	−0.158033
$754$	−28.1901	−1.02662
$755$	13.3710	0.486619
$756$	−13.1843	−0.479508
$757$	−7.09223	−0.257771	−0.128886	−	0.991659i	$-0.541140\pi$
$757$	−7.09223	−0.257771	−0.128886	+	0.991659i	$0.541140\pi$
$758$	−34.9897	−1.27088
$759$	−1.56743	−0.0568942
$760$	−1.67350	−0.0607042
$761$	8.13384	0.294852	0.147426	−	0.989073i	$-0.452901\pi$
$761$	8.13384	0.294852	0.147426	+	0.989073i	$0.452901\pi$
$762$	−7.07449	−0.256282
$763$	−75.1815	−2.72175
$764$	5.65990	0.204768
$765$	−23.6033	−0.853381
$766$	−30.5669	−1.10443
$767$	14.3690	0.518836
$768$	−5.16378	−0.186332
$769$	1.31148	0.0472932	0.0236466	−	0.999720i	$-0.492472\pi$
$769$	1.31148	0.0472932	0.0236466	+	0.999720i	$0.492472\pi$
$770$	−9.71152	−0.349979
$771$	7.72850	0.278335
$772$	34.1133	1.22777
$773$	−12.7660	−0.459162	−0.229581	−	0.973290i	$-0.573736\pi$
$773$	−12.7660	−0.459162	−0.229581	+	0.973290i	$0.573736\pi$
$774$	47.8932	1.72148
$775$	3.49816	0.125658
$776$	1.24346	0.0446377
$777$	−3.63228	−0.130307
$778$	−0.358192	−0.0128418
$779$	−8.19798	−0.293723
$780$	0.712570	0.0255141
$781$	0.239302	0.00856289
$782$	92.8754	3.32122
$783$	14.0064	0.500549
$784$	−84.2736	−3.00977
$785$	−19.5703	−0.698493
$786$	11.1369	0.397240
$787$	−40.5526	−1.44554	−0.722771	−	0.691087i	$-0.757132\pi$
$787$	−40.5526	−1.44554	−0.722771	+	0.691087i	$0.757132\pi$
$788$	−24.0953	−0.858361
$789$	2.46981	0.0879276
$790$	0.444765	0.0158240
$791$	−36.5201	−1.29851
$792$	1.77565	0.0630950
$793$	−14.0428	−0.498674
$794$	−57.4951	−2.04042
$795$	−2.32200	−0.0823530
$796$	−17.3244	−0.614047
$797$	−23.8325	−0.844191	−0.422096	−	0.906551i	$-0.638705\pi$
$797$	−23.8325	−0.844191	−0.422096	+	0.906551i	$0.638705\pi$
$798$	6.99852	0.247745
$799$	−15.6948	−0.555241
$800$	−7.48694	−0.264703
$801$	−49.7401	−1.75748
$802$	1.77295	0.0626051
$803$	1.00000	0.0352892
$804$	1.79787	0.0634060
$805$	−30.4088	−1.07177
$806$	−10.8918	−0.383646
$807$	−3.84713	−0.135425
$808$	−1.43593	−0.0505157
$809$	16.0244	0.563390	0.281695	−	0.959504i	$-0.409103\pi$
$809$	16.0244	0.563390	0.281695	+	0.959504i	$0.409103\pi$
$810$	16.1095	0.566030
$811$	47.9010	1.68203	0.841015	−	0.541012i	$-0.181959\pi$
$811$	47.9010	1.68203	0.841015	+	0.541012i	$0.181959\pi$
$812$	−77.1625	−2.70787
$813$	0.131525	0.00461279
$814$	−5.28422	−0.185212
$815$	5.77977	0.202457
$816$	9.51346	0.333038
$817$	−23.5154	−0.822700
$818$	32.8543	1.14873
$819$	−24.0619	−0.840791
$820$	−4.99743	−0.174518
$821$	11.4420	0.399327	0.199664	−	0.979865i	$-0.436015\pi$
$821$	11.4420	0.399327	0.199664	+	0.979865i	$0.436015\pi$
$822$	1.69758	0.0592099
$823$	−20.1196	−0.701325	−0.350662	−	0.936502i	$-0.614044\pi$
$823$	−20.1196	−0.701325	−0.350662	+	0.936502i	$0.614044\pi$
$824$	2.00051	0.0696910
$825$	−0.260789	−0.00907949
$826$	86.0291	2.99333
$827$	−16.5886	−0.576843	−0.288422	−	0.957503i	$-0.593130\pi$
$827$	−16.5886	−0.576843	−0.288422	+	0.957503i	$0.593130\pi$
$828$	−29.6847	−1.03161
$829$	42.7293	1.48405	0.742025	−	0.670372i	$-0.233865\pi$
$829$	42.7293	1.48405	0.742025	+	0.670372i	$0.233865\pi$
$830$	32.0177	1.11135
$831$	−0.826834	−0.0286826
$832$	8.61040	0.298512
$833$	149.715	5.18730
$834$	6.69822	0.231940
$835$	9.08740	0.314482
$836$	4.65479	0.160989
$837$	5.41164	0.187054
$838$	50.2892	1.73721
$839$	−28.0798	−0.969422	−0.484711	−	0.874674i	$-0.661075\pi$
$839$	−28.0798	−0.969422	−0.484711	+	0.874674i	$0.661075\pi$
$840$	−0.799064	−0.0275703
$841$	52.9742	1.82669
$842$	−19.2049	−0.661845
$843$	4.86568	0.167583
$844$	3.51773	0.121085
$845$	−10.3689	−0.356701
$846$	10.9722	0.377233
$847$	−5.05939	−0.173843
$848$	−40.3472	−1.38553
$849$	0.615937	0.0211389
$850$	15.4526	0.530018
$851$	−16.5460	−0.567189
$852$	−0.105125	−0.00360151
$853$	31.9888	1.09528	0.547638	−	0.836715i	$-0.315527\pi$
$853$	31.9888	1.09528	0.547638	+	0.836715i	$0.315527\pi$
$854$	−84.0758	−2.87701
$855$	−8.10201	−0.277083
$856$	0.177773	0.00607615
$857$	36.5653	1.24905	0.624524	−	0.781006i	$-0.285293\pi$
$857$	36.5653	1.24905	0.624524	+	0.781006i	$0.285293\pi$
$858$	0.811983	0.0277206
$859$	−9.29029	−0.316981	−0.158490	−	0.987361i	$-0.550663\pi$
$859$	−9.29029	−0.316981	−0.158490	+	0.987361i	$0.550663\pi$
$860$	−14.3348	−0.488813
$861$	−3.91438	−0.133402
$862$	−40.9683	−1.39539
$863$	−11.2880	−0.384248	−0.192124	−	0.981371i	$-0.561538\pi$
$863$	−11.2880	−0.384248	−0.192124	+	0.981371i	$0.561538\pi$
$864$	−11.5823	−0.394037
$865$	−22.1123	−0.751839
$866$	−42.1731	−1.43310
$867$	−12.4675	−0.423420
$868$	−29.8132	−1.01192
$869$	0.231708	0.00786017
$870$	−4.53227	−0.153658
$871$	6.63849	0.224937
$872$	−8.99928	−0.304754
$873$	6.02004	0.203748
$874$	31.8801	1.07836
$875$	−5.05939	−0.171039
$876$	−0.439297	−0.0148425
$877$	−2.78097	−0.0939067	−0.0469534	−	0.998897i	$-0.514951\pi$
$877$	−2.78097	−0.0939067	−0.0469534	+	0.998897i	$0.514951\pi$
$878$	21.1778	0.714717
$879$	0.273142	0.00921284
$880$	−4.53147	−0.152756
$881$	−7.67817	−0.258684	−0.129342	−	0.991600i	$-0.541287\pi$
$881$	−7.67817	−0.258684	−0.129342	+	0.991600i	$0.541287\pi$
$882$	−104.666	−3.52428
$883$	−8.38796	−0.282277	−0.141139	−	0.989990i	$-0.545076\pi$
$883$	−8.38796	−0.282277	−0.141139	+	0.989990i	$0.545076\pi$
$884$	−21.9963	−0.739817
$885$	2.31018	0.0776560
$886$	−23.3355	−0.783972
$887$	0.678209	0.0227720	0.0113860	−	0.999935i	$-0.496376\pi$
$887$	0.678209	0.0227720	0.0113860	+	0.999935i	$0.496376\pi$
$888$	−0.434786	−0.0145905
$889$	−71.5016	−2.39809
$890$	32.5637	1.09154
$891$	8.39253	0.281160
$892$	44.5484	1.49159
$893$	−5.38734	−0.180280
$894$	6.17414	0.206494
$895$	18.4166	0.615600
$896$	−24.2072	−0.808707
$897$	2.54249	0.0848911
$898$	−20.2179	−0.674679
$899$	31.6722	1.05633
$900$	−4.93892	−0.164631
$901$	71.6779	2.38794
$902$	−5.69463	−0.189611
$903$	−11.2282	−0.373650
$904$	−4.37149	−0.145393
$905$	−5.15509	−0.171361
$906$	−6.69329	−0.222370
$907$	−31.6705	−1.05160	−0.525801	−	0.850608i	$-0.676234\pi$
$907$	−31.6705	−1.05160	−0.525801	+	0.850608i	$0.676234\pi$
$908$	−18.5594	−0.615916
$909$	−6.95184	−0.230578
$910$	15.7528	0.522199
$911$	−22.6435	−0.750213	−0.375107	−	0.926982i	$-0.622394\pi$
$911$	−22.6435	−0.750213	−0.375107	+	0.926982i	$0.622394\pi$
$912$	3.26556	0.108134
$913$	16.6802	0.552033
$914$	−8.13707	−0.269150
$915$	−2.25773	−0.0746383
$916$	21.7112	0.717359
$917$	112.560	3.71707
$918$	23.9050	0.788983
$919$	−20.7185	−0.683439	−0.341720	−	0.939802i	$-0.611009\pi$
$919$	−20.7185	−0.683439	−0.341720	+	0.939802i	$0.611009\pi$
$920$	−3.63995	−0.120006
$921$	−4.61327	−0.152012
$922$	−8.69860	−0.286473
$923$	−0.388164	−0.0127766
$924$	2.22258	0.0731174
$925$	−2.75291	−0.0905152
$926$	68.2996	2.24446
$927$	9.68518	0.318103
$928$	−67.7865	−2.22520
$929$	7.04258	0.231059	0.115530	−	0.993304i	$-0.463143\pi$
$929$	7.04258	0.231059	0.115530	+	0.993304i	$0.463143\pi$
$930$	−1.75113	−0.0574217
$931$	51.3905	1.68426
$932$	2.77029	0.0907438
$933$	−3.31168	−0.108419
$934$	−68.2094	−2.23188
$935$	8.05028	0.263272
$936$	−2.88023	−0.0941432
$937$	30.7631	1.00499	0.502493	−	0.864581i	$-0.332416\pi$
$937$	30.7631	1.00499	0.502493	+	0.864581i	$0.332416\pi$
$938$	39.7454	1.29773
$939$	1.56614	0.0511091
$940$	−3.28408	−0.107115
$941$	−19.5241	−0.636469	−0.318235	−	0.948012i	$-0.603090\pi$
$941$	−19.5241	−0.636469	−0.318235	+	0.948012i	$0.603090\pi$
$942$	9.79657	0.319190
$943$	−17.8311	−0.580659
$944$	40.1418	1.30650
$945$	−7.82685	−0.254607
$946$	−16.3347	−0.531087
$947$	44.0813	1.43245	0.716226	−	0.697869i	$-0.245868\pi$
$947$	44.0813	1.43245	0.716226	+	0.697869i	$0.245868\pi$
$948$	−0.101789	−0.00330595
$949$	−1.62207	−0.0526546
$950$	5.30419	0.172091
$951$	−1.61071	−0.0522308
$952$	24.6663	0.799440
$953$	34.2161	1.10837	0.554185	−	0.832394i	$-0.313030\pi$
$953$	34.2161	1.10837	0.554185	+	0.832394i	$0.313030\pi$
$954$	−50.1101	−1.62238
$955$	3.36000	0.108727
$956$	19.9137	0.644054
$957$	−2.36117	−0.0763257
$958$	−49.9314	−1.61321
$959$	17.1574	0.554041
$960$	1.38434	0.0446794
$961$	−18.7629	−0.605253
$962$	8.57138	0.276352
$963$	0.860662	0.0277344
$964$	35.6695	1.14884
$965$	20.2514	0.651915
$966$	15.2222	0.489765
$967$	−29.8521	−0.959978	−0.479989	−	0.877274i	$-0.659359\pi$
$967$	−29.8521	−0.959978	−0.479989	+	0.877274i	$0.659359\pi$
$968$	−0.605613	−0.0194651
$969$	−5.80136	−0.186367
$970$	−3.94118	−0.126544
$971$	−35.3502	−1.13444	−0.567221	−	0.823565i	$-0.691982\pi$
$971$	−35.3502	−1.13444	−0.567221	+	0.823565i	$0.691982\pi$
$972$	−11.5045	−0.369008
$973$	67.6987	2.17032
$974$	−77.8141	−2.49332
$975$	0.423017	0.0135474
$976$	−39.2304	−1.25573
$977$	−40.1721	−1.28522	−0.642610	−	0.766193i	$-0.722148\pi$
$977$	−40.1721	−1.28522	−0.642610	+	0.766193i	$0.722148\pi$
$978$	−2.89326	−0.0925164
$979$	16.9646	0.542192
$980$	31.3273	1.00071
$981$	−43.5687	−1.39104
$982$	24.0869	0.768645
$983$	−15.6324	−0.498597	−0.249298	−	0.968427i	$-0.580200\pi$
$983$	−15.6324	−0.498597	−0.249298	+	0.968427i	$0.580200\pi$
$984$	−0.468555	−0.0149370
$985$	−14.3042	−0.455769
$986$	139.907	4.45554
$987$	−2.57235	−0.0818789
$988$	−7.55039	−0.240210
$989$	−51.1473	−1.62639
$990$	−5.62796	−0.178868
$991$	−2.27823	−0.0723703	−0.0361852	−	0.999345i	$-0.511521\pi$
$991$	−2.27823	−0.0723703	−0.0361852	+	0.999345i	$0.511521\pi$
$992$	−26.1905	−0.831551
$993$	7.41154	0.235198
$994$	−2.32398	−0.0737123
$995$	−10.2846	−0.326044
$996$	−7.32755	−0.232182
$997$	−12.1301	−0.384163	−0.192082	−	0.981379i	$-0.561524\pi$
$997$	−12.1301	−0.384163	−0.192082	+	0.981379i	$0.561524\pi$
$998$	27.3662	0.866263
$999$	−4.25874	−0.134741

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4015.2.a.h.1.28	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4015.2.a.h.1.28	✓	37	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:	\( N \)	\(=\)	\( 4015 = 5 \cdot 11 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4015.a (trivial)

\(f(q)\)	\(=\)	\(q+1.91950 q^{2} -0.260789 q^{3} +1.68450 q^{4} +1.00000 q^{5} -0.500585 q^{6} -5.05939 q^{7} -0.605613 q^{8} -2.93199 q^{9} +O(q^{10})\)	\(q+1.91950 q^{2} -0.260789 q^{3} +1.68450 q^{4} +1.00000 q^{5} -0.500585 q^{6} -5.05939 q^{7} -0.605613 q^{8} -2.93199 q^{9} +1.91950 q^{10} +1.00000 q^{11} -0.439297 q^{12} -1.62207 q^{13} -9.71152 q^{14} -0.260789 q^{15} -4.53147 q^{16} +8.05028 q^{17} -5.62796 q^{18} +2.76332 q^{19} +1.68450 q^{20} +1.31943 q^{21} +1.91950 q^{22} +6.01036 q^{23} +0.157937 q^{24} +1.00000 q^{25} -3.11357 q^{26} +1.54700 q^{27} -8.52252 q^{28} +9.05396 q^{29} -0.500585 q^{30} +3.49816 q^{31} -7.48694 q^{32} -0.260789 q^{33} +15.4526 q^{34} -5.05939 q^{35} -4.93892 q^{36} -2.75291 q^{37} +5.30419 q^{38} +0.423017 q^{39} -0.605613 q^{40} -2.96672 q^{41} +2.53265 q^{42} -8.50985 q^{43} +1.68450 q^{44} -2.93199 q^{45} +11.5369 q^{46} -1.94959 q^{47} +1.18175 q^{48} +18.5974 q^{49} +1.91950 q^{50} -2.09942 q^{51} -2.73237 q^{52} +8.90378 q^{53} +2.96946 q^{54} +1.00000 q^{55} +3.06403 q^{56} -0.720641 q^{57} +17.3791 q^{58} -8.85846 q^{59} -0.439297 q^{60} +8.65733 q^{61} +6.71474 q^{62} +14.8341 q^{63} -5.30828 q^{64} -1.62207 q^{65} -0.500585 q^{66} -4.09260 q^{67} +13.5607 q^{68} -1.56743 q^{69} -9.71152 q^{70} +0.239302 q^{71} +1.77565 q^{72} +1.00000 q^{73} -5.28422 q^{74} -0.260789 q^{75} +4.65479 q^{76} -5.05939 q^{77} +0.811983 q^{78} +0.231708 q^{79} -4.53147 q^{80} +8.39253 q^{81} -5.69463 q^{82} +16.6802 q^{83} +2.22258 q^{84} +8.05028 q^{85} -16.3347 q^{86} -2.36117 q^{87} -0.605613 q^{88} +16.9646 q^{89} -5.62796 q^{90} +8.20668 q^{91} +10.1244 q^{92} -0.912281 q^{93} -3.74225 q^{94} +2.76332 q^{95} +1.95251 q^{96} -2.05323 q^{97} +35.6978 q^{98} -2.93199 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9}+O(q^{10}) \) 37 * q + 5 * q^2 + 3 * q^3 + 43 * q^4 + 37 * q^5 + 9 * q^6 + 6 * q^7 + 12 * q^8 + 50 * q^9	\( 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9} + 5 q^{10} + 37 q^{11} + 6 q^{12} + 11 q^{13} + 11 q^{14} + 3 q^{15} + 43 q^{16} + 38 q^{17} + 11 q^{18} + 34 q^{19} + 43 q^{20} + 39 q^{21} + 5 q^{22} + 4 q^{23} + 25 q^{24} + 37 q^{25} - 9 q^{26} + 3 q^{27} + 14 q^{28} + 58 q^{29} + 9 q^{30} + 8 q^{31} + 14 q^{32} + 3 q^{33} + 8 q^{34} + 6 q^{35} + 20 q^{36} + 2 q^{37} + 15 q^{38} + 14 q^{39} + 12 q^{40} + 62 q^{41} - 13 q^{42} + 30 q^{43} + 43 q^{44} + 50 q^{45} + 31 q^{46} + 5 q^{47} - 25 q^{48} + 59 q^{49} + 5 q^{50} + 23 q^{51} - q^{52} + 18 q^{53} + 13 q^{54} + 37 q^{55} + 22 q^{56} + 5 q^{57} - 40 q^{58} + 15 q^{59} + 6 q^{60} + 57 q^{61} + 20 q^{62} - 29 q^{63} + 10 q^{64} + 11 q^{65} + 9 q^{66} - 14 q^{67} + 53 q^{68} + 24 q^{69} + 11 q^{70} + 8 q^{71} + 15 q^{72} + 37 q^{73} + 7 q^{74} + 3 q^{75} + 59 q^{76} + 6 q^{77} + q^{78} + 42 q^{79} + 43 q^{80} + 61 q^{81} - 22 q^{82} + 44 q^{83} + 66 q^{84} + 38 q^{85} - q^{86} - 26 q^{87} + 12 q^{88} + 69 q^{89} + 11 q^{90} - 10 q^{91} - 21 q^{92} - 26 q^{93} + 29 q^{94} + 34 q^{95} - 9 q^{96} + 37 q^{97} - 15 q^{98} + 50 q^{99}+O(q^{100}) \) 37 * q + 5 * q^2 + 3 * q^3 + 43 * q^4 + 37 * q^5 + 9 * q^6 + 6 * q^7 + 12 * q^8 + 50 * q^9 + 5 * q^10 + 37 * q^11 + 6 * q^12 + 11 * q^13 + 11 * q^14 + 3 * q^15 + 43 * q^16 + 38 * q^17 + 11 * q^18 + 34 * q^19 + 43 * q^20 + 39 * q^21 + 5 * q^22 + 4 * q^23 + 25 * q^24 + 37 * q^25 - 9 * q^26 + 3 * q^27 + 14 * q^28 + 58 * q^29 + 9 * q^30 + 8 * q^31 + 14 * q^32 + 3 * q^33 + 8 * q^34 + 6 * q^35 + 20 * q^36 + 2 * q^37 + 15 * q^38 + 14 * q^39 + 12 * q^40 + 62 * q^41 - 13 * q^42 + 30 * q^43 + 43 * q^44 + 50 * q^45 + 31 * q^46 + 5 * q^47 - 25 * q^48 + 59 * q^49 + 5 * q^50 + 23 * q^51 - q^52 + 18 * q^53 + 13 * q^54 + 37 * q^55 + 22 * q^56 + 5 * q^57 - 40 * q^58 + 15 * q^59 + 6 * q^60 + 57 * q^61 + 20 * q^62 - 29 * q^63 + 10 * q^64 + 11 * q^65 + 9 * q^66 - 14 * q^67 + 53 * q^68 + 24 * q^69 + 11 * q^70 + 8 * q^71 + 15 * q^72 + 37 * q^73 + 7 * q^74 + 3 * q^75 + 59 * q^76 + 6 * q^77 + q^78 + 42 * q^79 + 43 * q^80 + 61 * q^81 - 22 * q^82 + 44 * q^83 + 66 * q^84 + 38 * q^85 - q^86 - 26 * q^87 + 12 * q^88 + 69 * q^89 + 11 * q^90 - 10 * q^91 - 21 * q^92 - 26 * q^93 + 29 * q^94 + 34 * q^95 - 9 * q^96 + 37 * q^97 - 15 * q^98 + 50 * q^99

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