LMFDB - Embedded newform 4015.2.a.h.1.17

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			1.17
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)

$f(q)$	$=$	$q-0.327392 q^{2} -2.36457 q^{3} -1.89281 q^{4} +1.00000 q^{5} +0.774141 q^{6} +2.46288 q^{7} +1.27448 q^{8} +2.59119 q^{9} +O(q^{10})$	\(q-0.327392 q^{2} -2.36457 q^{3} -1.89281 q^{4} +1.00000 q^{5} +0.774141 q^{6} +2.46288 q^{7} +1.27448 q^{8} +2.59119 q^{9} -0.327392 q^{10} +1.00000 q^{11} +4.47569 q^{12} -0.641298 q^{13} -0.806327 q^{14} -2.36457 q^{15} +3.36838 q^{16} -6.07665 q^{17} -0.848334 q^{18} +8.35139 q^{19} -1.89281 q^{20} -5.82365 q^{21} -0.327392 q^{22} +2.42427 q^{23} -3.01359 q^{24} +1.00000 q^{25} +0.209956 q^{26} +0.966665 q^{27} -4.66177 q^{28} +5.36357 q^{29} +0.774141 q^{30} +7.23441 q^{31} -3.65173 q^{32} -2.36457 q^{33} +1.98945 q^{34} +2.46288 q^{35} -4.90464 q^{36} -5.09224 q^{37} -2.73418 q^{38} +1.51639 q^{39} +1.27448 q^{40} -0.993086 q^{41} +1.90662 q^{42} +5.57472 q^{43} -1.89281 q^{44} +2.59119 q^{45} -0.793687 q^{46} +3.08560 q^{47} -7.96476 q^{48} -0.934228 q^{49} -0.327392 q^{50} +14.3687 q^{51} +1.21386 q^{52} +3.89942 q^{53} -0.316478 q^{54} +1.00000 q^{55} +3.13888 q^{56} -19.7474 q^{57} -1.75599 q^{58} -0.200959 q^{59} +4.47569 q^{60} -10.9562 q^{61} -2.36849 q^{62} +6.38178 q^{63} -5.54120 q^{64} -0.641298 q^{65} +0.774141 q^{66} -10.6466 q^{67} +11.5020 q^{68} -5.73236 q^{69} -0.806327 q^{70} -0.323595 q^{71} +3.30241 q^{72} +1.00000 q^{73} +1.66716 q^{74} -2.36457 q^{75} -15.8076 q^{76} +2.46288 q^{77} -0.496455 q^{78} -10.7550 q^{79} +3.36838 q^{80} -10.0593 q^{81} +0.325128 q^{82} +13.1546 q^{83} +11.0231 q^{84} -6.07665 q^{85} -1.82512 q^{86} -12.6825 q^{87} +1.27448 q^{88} +8.38454 q^{89} -0.848334 q^{90} -1.57944 q^{91} -4.58869 q^{92} -17.1063 q^{93} -1.01020 q^{94} +8.35139 q^{95} +8.63477 q^{96} -1.74254 q^{97} +0.305859 q^{98} +2.59119 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.327392	−0.231501	−0.115751	−	0.993278i	$-0.536927\pi$
$2$	−0.327392	−0.231501	−0.115751	+	0.993278i	$0.536927\pi$
$3$	−2.36457	−1.36518	−0.682592	−	0.730799i	$-0.739148\pi$
$3$	−2.36457	−1.36518	−0.682592	+	0.730799i	$0.739148\pi$
$4$	−1.89281	−0.946407
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.774141	0.316042
$7$	2.46288	0.930881	0.465440	−	0.885079i	$-0.345896\pi$
$7$	2.46288	0.930881	0.465440	+	0.885079i	$0.345896\pi$
$8$	1.27448	0.450595
$9$	2.59119	0.863729
$10$	−0.327392	−0.103530
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	4.47569	1.29202
$13$	−0.641298	−0.177864	−0.0889321	−	0.996038i	$-0.528345\pi$
$13$	−0.641298	−0.177864	−0.0889321	+	0.996038i	$0.528345\pi$
$14$	−0.806327	−0.215500
$15$	−2.36457	−0.610529
$16$	3.36838	0.842094
$17$	−6.07665	−1.47380	−0.736902	−	0.675999i	$-0.763712\pi$
$17$	−6.07665	−1.47380	−0.736902	+	0.675999i	$0.763712\pi$
$18$	−0.848334	−0.199954
$19$	8.35139	1.91594	0.957970	−	0.286869i	$-0.0926144\pi$
$19$	8.35139	1.91594	0.957970	+	0.286869i	$0.0926144\pi$
$20$	−1.89281	−0.423246
$21$	−5.82365	−1.27082
$22$	−0.327392	−0.0698002
$23$	2.42427	0.505495	0.252748	−	0.967532i	$-0.418666\pi$
$23$	2.42427	0.505495	0.252748	+	0.967532i	$0.418666\pi$
$24$	−3.01359	−0.615146
$25$	1.00000	0.200000
$26$	0.209956	0.0411757
$27$	0.966665	0.186035
$28$	−4.66177	−0.880992
$29$	5.36357	0.995991	0.497995	−	0.867180i	$-0.334070\pi$
$29$	5.36357	0.995991	0.497995	+	0.867180i	$0.334070\pi$
$30$	0.774141	0.141338
$31$	7.23441	1.29934	0.649669	−	0.760217i	$-0.274907\pi$
$31$	7.23441	1.29934	0.649669	+	0.760217i	$0.274907\pi$
$32$	−3.65173	−0.645541
$33$	−2.36457	−0.411619
$34$	1.98945	0.341187
$35$	2.46288	0.416302
$36$	−4.90464	−0.817440
$37$	−5.09224	−0.837159	−0.418579	−	0.908180i	$-0.637472\pi$
$37$	−5.09224	−0.837159	−0.418579	+	0.908180i	$0.637472\pi$
$38$	−2.73418	−0.443542
$39$	1.51639	0.242817
$40$	1.27448	0.201512
$41$	−0.993086	−0.155094	−0.0775470	−	0.996989i	$-0.524709\pi$
$41$	−0.993086	−0.155094	−0.0775470	+	0.996989i	$0.524709\pi$
$42$	1.90662	0.294197
$43$	5.57472	0.850136	0.425068	−	0.905161i	$-0.360250\pi$
$43$	5.57472	0.850136	0.425068	+	0.905161i	$0.360250\pi$
$44$	−1.89281	−0.285353
$45$	2.59119	0.386271
$46$	−0.793687	−0.117023
$47$	3.08560	0.450081	0.225040	−	0.974349i	$-0.427749\pi$
$47$	3.08560	0.450081	0.225040	+	0.974349i	$0.427749\pi$
$48$	−7.96476	−1.14961
$49$	−0.934228	−0.133461
$50$	−0.327392	−0.0463002
$51$	14.3687	2.01202
$52$	1.21386	0.168332
$53$	3.89942	0.535626	0.267813	−	0.963471i	$-0.413699\pi$
$53$	3.89942	0.535626	0.267813	+	0.963471i	$0.413699\pi$
$54$	−0.316478	−0.0430672
$55$	1.00000	0.134840
$56$	3.13888	0.419451
$57$	−19.7474	−2.61561
$58$	−1.75599	−0.230573
$59$	−0.200959	−0.0261627	−0.0130813	−	0.999914i	$-0.504164\pi$
$59$	−0.200959	−0.0261627	−0.0130813	+	0.999914i	$0.504164\pi$
$60$	4.47569	0.577809
$61$	−10.9562	−1.40280	−0.701400	−	0.712768i	$-0.747441\pi$
$61$	−10.9562	−1.40280	−0.701400	+	0.712768i	$0.747441\pi$
$62$	−2.36849	−0.300798
$63$	6.38178	0.804029
$64$	−5.54120	−0.692651
$65$	−0.641298	−0.0795432
$66$	0.774141	0.0952902
$67$	−10.6466	−1.30069	−0.650347	−	0.759637i	$-0.725376\pi$
$67$	−10.6466	−1.30069	−0.650347	+	0.759637i	$0.725376\pi$
$68$	11.5020	1.39482
$69$	−5.73236	−0.690095
$70$	−0.806327	−0.0963745
$71$	−0.323595	−0.0384037	−0.0192018	−	0.999816i	$-0.506113\pi$
$71$	−0.323595	−0.0384037	−0.0192018	+	0.999816i	$0.506113\pi$
$72$	3.30241	0.389192
$73$	1.00000	0.117041
$73$	1.00000	0.117041
$74$	1.66716	0.193803
$75$	−2.36457	−0.273037
$76$	−15.8076	−1.81326
$77$	2.46288	0.280671
$78$	−0.496455	−0.0562125
$79$	−10.7550	−1.21003	−0.605014	−	0.796215i	$-0.706832\pi$
$79$	−10.7550	−1.21003	−0.605014	+	0.796215i	$0.706832\pi$
$80$	3.36838	0.376596
$81$	−10.0593	−1.11770
$82$	0.325128	0.0359044
$83$	13.1546	1.44391	0.721954	−	0.691941i	$-0.243244\pi$
$83$	13.1546	1.44391	0.721954	+	0.691941i	$0.243244\pi$
$84$	11.0231	1.20272
$85$	−6.07665	−0.659106
$86$	−1.82512	−0.196807
$87$	−12.6825	−1.35971
$88$	1.27448	0.135860
$89$	8.38454	0.888760	0.444380	−	0.895838i	$-0.353424\pi$
$89$	8.38454	0.888760	0.444380	+	0.895838i	$0.353424\pi$
$90$	−0.848334	−0.0894223
$91$	−1.57944	−0.165570
$92$	−4.58869	−0.478405
$93$	−17.1063	−1.77384
$94$	−1.01020	−0.104194
$95$	8.35139	0.856834
$96$	8.63477	0.881283
$97$	−1.74254	−0.176928	−0.0884638	−	0.996079i	$-0.528196\pi$
$97$	−1.74254	−0.176928	−0.0884638	+	0.996079i	$0.528196\pi$
$98$	0.305859	0.0308964
$99$	2.59119	0.260424
$100$	−1.89281	−0.189281
$101$	−3.45766	−0.344050	−0.172025	−	0.985093i	$-0.555031\pi$
$101$	−3.45766	−0.344050	−0.172025	+	0.985093i	$0.555031\pi$
$102$	−4.70419	−0.465784
$103$	−15.8333	−1.56010	−0.780051	−	0.625716i	$-0.784807\pi$
$103$	−15.8333	−1.56010	−0.780051	+	0.625716i	$0.784807\pi$
$104$	−0.817319	−0.0801447
$105$	−5.82365	−0.568330
$106$	−1.27664	−0.123998
$107$	−6.58676	−0.636767	−0.318383	−	0.947962i	$-0.603140\pi$
$107$	−6.58676	−0.636767	−0.318383	+	0.947962i	$0.603140\pi$
$108$	−1.82972	−0.176065
$109$	11.4360	1.09537	0.547687	−	0.836683i	$-0.315509\pi$
$109$	11.4360	1.09537	0.547687	+	0.836683i	$0.315509\pi$
$110$	−0.327392	−0.0312156
$111$	12.0409	1.14288
$112$	8.29590	0.783889
$113$	2.18592	0.205634	0.102817	−	0.994700i	$-0.467214\pi$
$113$	2.18592	0.205634	0.102817	+	0.994700i	$0.467214\pi$
$114$	6.46515	0.605517
$115$	2.42427	0.226064
$116$	−10.1522	−0.942613
$117$	−1.66172	−0.153626
$118$	0.0657924	0.00605669
$119$	−14.9661	−1.37194
$120$	−3.01359	−0.275102
$121$	1.00000	0.0909091
$122$	3.58698	0.324750
$123$	2.34822	0.211732
$124$	−13.6934	−1.22970
$125$	1.00000	0.0894427
$126$	−2.08934	−0.186134
$127$	2.14448	0.190292	0.0951459	−	0.995463i	$-0.469668\pi$
$127$	2.14448	0.190292	0.0951459	+	0.995463i	$0.469668\pi$
$128$	9.11761	0.805890
$129$	−13.1818	−1.16059
$130$	0.209956	0.0184143
$131$	13.2584	1.15839	0.579195	−	0.815189i	$-0.303367\pi$
$131$	13.2584	1.15839	0.579195	+	0.815189i	$0.303367\pi$
$132$	4.47569	0.389559
$133$	20.5685	1.78351
$134$	3.48562	0.301112
$135$	0.966665	0.0831973
$136$	−7.74455	−0.664090
$137$	4.52897	0.386936	0.193468	−	0.981107i	$-0.438026\pi$
$137$	4.52897	0.386936	0.193468	+	0.981107i	$0.438026\pi$
$138$	1.87673	0.159758
$139$	−18.8654	−1.60015	−0.800073	−	0.599903i	$-0.795206\pi$
$139$	−18.8654	−1.60015	−0.800073	+	0.599903i	$0.795206\pi$
$140$	−4.66177	−0.393992
$141$	−7.29611	−0.614443
$142$	0.105942	0.00889049
$143$	−0.641298	−0.0536280
$144$	8.72809	0.727341
$145$	5.36357	0.445420
$146$	−0.327392	−0.0270952
$147$	2.20905	0.182199
$148$	9.63866	0.792293
$149$	12.7596	1.04531	0.522653	−	0.852545i	$-0.324942\pi$
$149$	12.7596	1.04531	0.522653	+	0.852545i	$0.324942\pi$
$150$	0.774141	0.0632083
$151$	14.4526	1.17613	0.588066	−	0.808813i	$-0.299889\pi$
$151$	14.4526	1.17613	0.588066	+	0.808813i	$0.299889\pi$
$152$	10.6436	0.863314
$153$	−15.7457	−1.27297
$154$	−0.806327	−0.0649757
$155$	7.23441	0.581082
$156$	−2.87025	−0.229804
$157$	1.71958	0.137237	0.0686187	−	0.997643i	$-0.478141\pi$
$157$	1.71958	0.137237	0.0686187	+	0.997643i	$0.478141\pi$
$158$	3.52109	0.280123
$159$	−9.22044	−0.731228
$160$	−3.65173	−0.288695
$161$	5.97068	0.470556
$162$	3.29334	0.258749
$163$	10.3229	0.808549	0.404275	−	0.914638i	$-0.367524\pi$
$163$	10.3229	0.808549	0.404275	+	0.914638i	$0.367524\pi$
$164$	1.87973	0.146782
$165$	−2.36457	−0.184081
$166$	−4.30672	−0.334266
$167$	−19.0750	−1.47607	−0.738033	−	0.674765i	$-0.764245\pi$
$167$	−19.0750	−1.47607	−0.738033	+	0.674765i	$0.764245\pi$
$168$	−7.42210	−0.572627
$169$	−12.5887	−0.968364
$170$	1.98945	0.152584
$171$	21.6400	1.65485
$172$	−10.5519	−0.804575
$173$	4.87923	0.370961	0.185480	−	0.982648i	$-0.440616\pi$
$173$	4.87923	0.370961	0.185480	+	0.982648i	$0.440616\pi$
$174$	4.15216	0.314775
$175$	2.46288	0.186176
$176$	3.36838	0.253901
$177$	0.475182	0.0357169
$178$	−2.74503	−0.205749
$179$	7.09888	0.530595	0.265298	−	0.964167i	$-0.414530\pi$
$179$	7.09888	0.530595	0.265298	+	0.964167i	$0.414530\pi$
$180$	−4.90464	−0.365570
$181$	4.60092	0.341984	0.170992	−	0.985272i	$-0.445303\pi$
$181$	4.60092	0.341984	0.170992	+	0.985272i	$0.445303\pi$
$182$	0.517096	0.0383297
$183$	25.9067	1.91508
$184$	3.08968	0.227774
$185$	−5.09224	−0.374389
$186$	5.60045	0.410645
$187$	−6.07665	−0.444369
$188$	−5.84047	−0.425960
$189$	2.38078	0.173176
$190$	−2.73418	−0.198358
$191$	−7.01107	−0.507303	−0.253652	−	0.967296i	$-0.581632\pi$
$191$	−7.01107	−0.507303	−0.253652	+	0.967296i	$0.581632\pi$
$192$	13.1026	0.945596
$193$	10.9203	0.786061	0.393030	−	0.919525i	$-0.371427\pi$
$193$	10.9203	0.786061	0.393030	+	0.919525i	$0.371427\pi$
$194$	0.570492	0.0409589
$195$	1.51639	0.108591
$196$	1.76832	0.126309
$197$	−5.70336	−0.406348	−0.203174	−	0.979143i	$-0.565126\pi$
$197$	−5.70336	−0.406348	−0.203174	+	0.979143i	$0.565126\pi$
$198$	−0.848334	−0.0602885
$199$	17.4143	1.23447	0.617233	−	0.786780i	$-0.288253\pi$
$199$	17.4143	1.23447	0.617233	+	0.786780i	$0.288253\pi$
$200$	1.27448	0.0901191
$201$	25.1747	1.77569
$202$	1.13201	0.0796480
$203$	13.2098	0.927148
$204$	−27.1972	−1.90419
$205$	−0.993086	−0.0693601
$206$	5.18369	0.361165
$207$	6.28174	0.436611
$208$	−2.16013	−0.149778
$209$	8.35139	0.577678
$210$	1.90662	0.131569
$211$	26.0862	1.79585	0.897924	−	0.440151i	$-0.145075\pi$
$211$	26.0862	1.79585	0.897924	+	0.440151i	$0.145075\pi$
$212$	−7.38087	−0.506920
$213$	0.765163	0.0524281
$214$	2.15645	0.147412
$215$	5.57472	0.380192
$216$	1.23199	0.0838264
$217$	17.8175	1.20953
$218$	−3.74407	−0.253580
$219$	−2.36457	−0.159783
$220$	−1.89281	−0.127614
$221$	3.89695	0.262137
$222$	−3.94211	−0.264577
$223$	−15.1221	−1.01265	−0.506326	−	0.862342i	$-0.668997\pi$
$223$	−15.1221	−1.01265	−0.506326	+	0.862342i	$0.668997\pi$
$224$	−8.99377	−0.600922
$225$	2.59119	0.172746
$226$	−0.715652	−0.0476045
$227$	−15.3772	−1.02062	−0.510309	−	0.859991i	$-0.670469\pi$
$227$	−15.3772	−1.02062	−0.510309	+	0.859991i	$0.670469\pi$
$228$	37.3782	2.47543
$229$	28.8247	1.90479	0.952394	−	0.304871i	$-0.0986134\pi$
$229$	28.8247	1.90479	0.952394	+	0.304871i	$0.0986134\pi$
$230$	−0.793687	−0.0523342
$231$	−5.82365	−0.383168
$232$	6.83575	0.448789
$233$	21.3999	1.40195	0.700977	−	0.713183i	$-0.252747\pi$
$233$	21.3999	1.40195	0.700977	+	0.713183i	$0.252747\pi$
$234$	0.544035	0.0355647
$235$	3.08560	0.201282
$236$	0.380379	0.0247605
$237$	25.4308	1.65191
$238$	4.89977	0.317605
$239$	−23.2103	−1.50135	−0.750676	−	0.660670i	$-0.770272\pi$
$239$	−23.2103	−1.50135	−0.750676	+	0.660670i	$0.770272\pi$
$240$	−7.96476	−0.514123
$241$	15.7636	1.01543	0.507713	−	0.861526i	$-0.330491\pi$
$241$	15.7636	1.01543	0.507713	+	0.861526i	$0.330491\pi$
$242$	−0.327392	−0.0210456
$243$	20.8859	1.33983
$244$	20.7381	1.32762
$245$	−0.934228	−0.0596857
$246$	−0.768788	−0.0490161
$247$	−5.35573	−0.340777
$248$	9.22008	0.585476
$249$	−31.1050	−1.97120
$250$	−0.327392	−0.0207061
$251$	4.88454	0.308309	0.154155	−	0.988047i	$-0.450735\pi$
$251$	4.88454	0.308309	0.154155	+	0.988047i	$0.450735\pi$
$252$	−12.0795	−0.760939
$253$	2.42427	0.152413
$254$	−0.702085	−0.0440527
$255$	14.3687	0.899801
$256$	8.09738	0.506086
$257$	15.0578	0.939283	0.469641	−	0.882857i	$-0.344383\pi$
$257$	15.0578	0.939283	0.469641	+	0.882857i	$0.344383\pi$
$258$	4.31562	0.268678
$259$	−12.5416	−0.779295
$260$	1.21386	0.0752803
$261$	13.8980	0.860266
$262$	−4.34068	−0.268168
$263$	16.2991	1.00505	0.502524	−	0.864563i	$-0.332405\pi$
$263$	16.2991	1.00505	0.502524	+	0.864563i	$0.332405\pi$
$264$	−3.01359	−0.185473
$265$	3.89942	0.239539
$266$	−6.73395	−0.412885
$267$	−19.8258	−1.21332
$268$	20.1521	1.23099
$269$	23.9598	1.46085	0.730426	−	0.682992i	$-0.239322\pi$
$269$	23.9598	1.46085	0.730426	+	0.682992i	$0.239322\pi$
$270$	−0.316478	−0.0192603
$271$	13.9318	0.846295	0.423148	−	0.906061i	$-0.360925\pi$
$271$	13.9318	0.846295	0.423148	+	0.906061i	$0.360925\pi$
$272$	−20.4685	−1.24108
$273$	3.73469	0.226034
$274$	−1.48275	−0.0895762
$275$	1.00000	0.0603023
$276$	10.8503	0.653111
$277$	−11.7456	−0.705723	−0.352861	−	0.935676i	$-0.614791\pi$
$277$	−11.7456	−0.705723	−0.352861	+	0.935676i	$0.614791\pi$
$278$	6.17639	0.370435
$279$	18.7457	1.12228
$280$	3.13888	0.187584
$281$	−4.89579	−0.292058	−0.146029	−	0.989280i	$-0.546649\pi$
$281$	−4.89579	−0.292058	−0.146029	+	0.989280i	$0.546649\pi$
$282$	2.38869	0.142244
$283$	−6.09546	−0.362338	−0.181169	−	0.983452i	$-0.557988\pi$
$283$	−6.09546	−0.362338	−0.181169	+	0.983452i	$0.557988\pi$
$284$	0.612505	0.0363455
$285$	−19.7474	−1.16974
$286$	0.209956	0.0124150
$287$	−2.44585	−0.144374
$288$	−9.46232	−0.557573
$289$	19.9257	1.17210
$290$	−1.75599	−0.103115
$291$	4.12035	0.241539
$292$	−1.89281	−0.110769
$293$	−2.88854	−0.168750	−0.0843750	−	0.996434i	$-0.526889\pi$
$293$	−2.88854	−0.168750	−0.0843750	+	0.996434i	$0.526889\pi$
$294$	−0.723224	−0.0421793
$295$	−0.200959	−0.0117003
$296$	−6.48993	−0.377220
$297$	0.966665	0.0560916
$298$	−4.17739	−0.241990
$299$	−1.55468	−0.0899095
$300$	4.47569	0.258404
$301$	13.7298	0.791375
$302$	−4.73165	−0.272276
$303$	8.17588	0.469692
$304$	28.1306	1.61340
$305$	−10.9562	−0.627351
$306$	5.15503	0.294694
$307$	−12.1863	−0.695511	−0.347756	−	0.937585i	$-0.613056\pi$
$307$	−12.1863	−0.695511	−0.347756	+	0.937585i	$0.613056\pi$
$308$	−4.66177	−0.265629
$309$	37.4389	2.12983
$310$	−2.36849	−0.134521
$311$	2.83566	0.160795	0.0803977	−	0.996763i	$-0.474381\pi$
$311$	2.83566	0.160795	0.0803977	+	0.996763i	$0.474381\pi$
$312$	1.93261	0.109412
$313$	−8.16184	−0.461334	−0.230667	−	0.973033i	$-0.574091\pi$
$313$	−8.16184	−0.461334	−0.230667	+	0.973033i	$0.574091\pi$
$314$	−0.562976	−0.0317706
$315$	6.38178	0.359573
$316$	20.3571	1.14518
$317$	−6.90411	−0.387773	−0.193887	−	0.981024i	$-0.562109\pi$
$317$	−6.90411	−0.387773	−0.193887	+	0.981024i	$0.562109\pi$
$318$	3.01870	0.169280
$319$	5.36357	0.300302
$320$	−5.54120	−0.309763
$321$	15.5749	0.869304
$322$	−1.95475	−0.108934
$323$	−50.7485	−2.82372
$324$	19.0404	1.05780
$325$	−0.641298	−0.0355728
$326$	−3.37962	−0.187180
$327$	−27.0413	−1.49539
$328$	−1.26566	−0.0698846
$329$	7.59945	0.418971
$330$	0.774141	0.0426151
$331$	−22.3558	−1.22878	−0.614392	−	0.789001i	$-0.710599\pi$
$331$	−22.3558	−1.22878	−0.614392	+	0.789001i	$0.710599\pi$
$332$	−24.8993	−1.36652
$333$	−13.1949	−0.723078
$334$	6.24499	0.341711
$335$	−10.6466	−0.581688
$336$	−19.6162	−1.07015
$337$	−10.0892	−0.549595	−0.274797	−	0.961502i	$-0.588611\pi$
$337$	−10.0892	−0.549595	−0.274797	+	0.961502i	$0.588611\pi$
$338$	4.12145	0.224177
$339$	−5.16876	−0.280728
$340$	11.5020	0.623782
$341$	7.23441	0.391765
$342$	−7.08477	−0.383100
$343$	−19.5410	−1.05512
$344$	7.10484	0.383067
$345$	−5.73236	−0.308620
$346$	−1.59742	−0.0858778
$347$	25.6422	1.37655	0.688274	−	0.725451i	$-0.258369\pi$
$347$	25.6422	1.37655	0.688274	+	0.725451i	$0.258369\pi$
$348$	24.0057	1.28684
$349$	−24.9774	−1.33701	−0.668505	−	0.743707i	$-0.733066\pi$
$349$	−24.9774	−1.33701	−0.668505	+	0.743707i	$0.733066\pi$
$350$	−0.806327	−0.0431000
$351$	−0.619920	−0.0330889
$352$	−3.65173	−0.194638
$353$	7.78170	0.414178	0.207089	−	0.978322i	$-0.433601\pi$
$353$	7.78170	0.414178	0.207089	+	0.978322i	$0.433601\pi$
$354$	−0.155571	−0.00826849
$355$	−0.323595	−0.0171746
$356$	−15.8704	−0.841129
$357$	35.3883	1.87295
$358$	−2.32412	−0.122833
$359$	30.4828	1.60882	0.804411	−	0.594073i	$-0.202481\pi$
$359$	30.4828	1.60882	0.804411	+	0.594073i	$0.202481\pi$
$360$	3.30241	0.174052
$361$	50.7457	2.67083
$362$	−1.50630	−0.0791696
$363$	−2.36457	−0.124108
$364$	2.98959	0.156697
$365$	1.00000	0.0523424
$366$	−8.48166	−0.443343
$367$	2.96163	0.154596	0.0772980	−	0.997008i	$-0.475371\pi$
$367$	2.96163	0.154596	0.0772980	+	0.997008i	$0.475371\pi$
$368$	8.16586	0.425675
$369$	−2.57327	−0.133959
$370$	1.66716	0.0866714
$371$	9.60379	0.498604
$372$	32.3790	1.67877
$373$	−0.746015	−0.0386272	−0.0193136	−	0.999813i	$-0.506148\pi$
$373$	−0.746015	−0.0386272	−0.0193136	+	0.999813i	$0.506148\pi$
$374$	1.98945	0.102872
$375$	−2.36457	−0.122106
$376$	3.93252	0.202804
$377$	−3.43965	−0.177151
$378$	−0.779448	−0.0400905
$379$	6.58248	0.338119	0.169060	−	0.985606i	$-0.445927\pi$
$379$	6.58248	0.338119	0.169060	+	0.985606i	$0.445927\pi$
$380$	−15.8076	−0.810914
$381$	−5.07077	−0.259783
$382$	2.29537	0.117441
$383$	26.6271	1.36058	0.680290	−	0.732943i	$-0.261854\pi$
$383$	26.6271	1.36058	0.680290	+	0.732943i	$0.261854\pi$
$384$	−21.5592	−1.10019
$385$	2.46288	0.125520
$386$	−3.57522	−0.181974
$387$	14.4451	0.734287
$388$	3.29830	0.167446
$389$	−27.7437	−1.40666	−0.703330	−	0.710864i	$-0.748304\pi$
$389$	−27.7437	−1.40666	−0.703330	+	0.710864i	$0.748304\pi$
$390$	−0.496455	−0.0251390
$391$	−14.7315	−0.745002
$392$	−1.19065	−0.0601370
$393$	−31.3503	−1.58142
$394$	1.86723	0.0940699
$395$	−10.7550	−0.541141
$396$	−4.90464	−0.246467
$397$	−0.366934	−0.0184159	−0.00920794	−	0.999958i	$-0.502931\pi$
$397$	−0.366934	−0.0184159	−0.00920794	+	0.999958i	$0.502931\pi$
$398$	−5.70130	−0.285780
$399$	−48.6355	−2.43482
$400$	3.36838	0.168419
$401$	27.6164	1.37909	0.689547	−	0.724240i	$-0.257809\pi$
$401$	27.6164	1.37909	0.689547	+	0.724240i	$0.257809\pi$
$402$	−8.24200	−0.411073
$403$	−4.63941	−0.231106
$404$	6.54471	0.325612
$405$	−10.0593	−0.499851
$406$	−4.32479	−0.214636
$407$	−5.09224	−0.252413
$408$	18.3125	0.906605
$409$	23.3264	1.15342	0.576709	−	0.816950i	$-0.304337\pi$
$409$	23.3264	1.15342	0.576709	+	0.816950i	$0.304337\pi$
$410$	0.325128	0.0160569
$411$	−10.7091	−0.528240
$412$	29.9695	1.47649
$413$	−0.494938	−0.0243543
$414$	−2.05659	−0.101076
$415$	13.1546	0.645735
$416$	2.34185	0.114819
$417$	44.6086	2.18449
$418$	−2.73418	−0.133733
$419$	−28.2163	−1.37846	−0.689229	−	0.724543i	$-0.742051\pi$
$419$	−28.2163	−1.37846	−0.689229	+	0.724543i	$0.742051\pi$
$420$	11.0231	0.537871
$421$	10.3554	0.504691	0.252346	−	0.967637i	$-0.418798\pi$
$421$	10.3554	0.504691	0.252346	+	0.967637i	$0.418798\pi$
$422$	−8.54041	−0.415741
$423$	7.99536	0.388748
$424$	4.96971	0.241351
$425$	−6.07665	−0.294761
$426$	−0.250508	−0.0121372
$427$	−26.9838	−1.30584
$428$	12.4675	0.602640
$429$	1.51639	0.0732122
$430$	−1.82512	−0.0880150
$431$	11.9710	0.576625	0.288312	−	0.957536i	$-0.406906\pi$
$431$	11.9710	0.576625	0.288312	+	0.957536i	$0.406906\pi$
$432$	3.25609	0.156659
$433$	20.1829	0.969927	0.484963	−	0.874534i	$-0.338833\pi$
$433$	20.1829	0.969927	0.484963	+	0.874534i	$0.338833\pi$
$434$	−5.83330	−0.280007
$435$	−12.6825	−0.608081
$436$	−21.6463	−1.03667
$437$	20.2460	0.968499
$438$	0.774141	0.0369899
$439$	0.532483	0.0254140	0.0127070	−	0.999919i	$-0.495955\pi$
$439$	0.532483	0.0254140	0.0127070	+	0.999919i	$0.495955\pi$
$440$	1.27448	0.0607583
$441$	−2.42076	−0.115274
$442$	−1.27583	−0.0606850
$443$	25.8413	1.22776	0.613879	−	0.789400i	$-0.289608\pi$
$443$	25.8413	1.22776	0.613879	+	0.789400i	$0.289608\pi$
$444$	−22.7913	−1.08163
$445$	8.38454	0.397465
$446$	4.95086	0.234430
$447$	−30.1710	−1.42704
$448$	−13.6473	−0.644775
$449$	25.4548	1.20129	0.600643	−	0.799518i	$-0.294911\pi$
$449$	25.4548	1.20129	0.600643	+	0.799518i	$0.294911\pi$
$450$	−0.848334	−0.0399908
$451$	−0.993086	−0.0467626
$452$	−4.13754	−0.194613
$453$	−34.1741	−1.60564
$454$	5.03436	0.236274
$455$	−1.57944	−0.0740453
$456$	−25.1676	−1.17858
$457$	−20.7494	−0.970617	−0.485309	−	0.874343i	$-0.661293\pi$
$457$	−20.7494	−0.970617	−0.485309	+	0.874343i	$0.661293\pi$
$458$	−9.43696	−0.440960
$459$	−5.87409	−0.274179
$460$	−4.58869	−0.213949
$461$	14.7332	0.686196	0.343098	−	0.939300i	$-0.388524\pi$
$461$	14.7332	0.686196	0.343098	+	0.939300i	$0.388524\pi$
$462$	1.90662	0.0887038
$463$	−36.0823	−1.67689	−0.838443	−	0.544989i	$-0.816534\pi$
$463$	−36.0823	−1.67689	−0.838443	+	0.544989i	$0.816534\pi$
$464$	18.0665	0.838718
$465$	−17.1063	−0.793284
$466$	−7.00616	−0.324554
$467$	7.80516	0.361180	0.180590	−	0.983558i	$-0.442199\pi$
$467$	7.80516	0.361180	0.180590	+	0.983558i	$0.442199\pi$
$468$	3.14534	0.145393
$469$	−26.2214	−1.21079
$470$	−1.01020	−0.0465971
$471$	−4.06606	−0.187354
$472$	−0.256118	−0.0117888
$473$	5.57472	0.256326
$474$	−8.32586	−0.382419
$475$	8.35139	0.383188
$476$	28.3280	1.29841
$477$	10.1041	0.462636
$478$	7.59888	0.347565
$479$	38.3255	1.75114	0.875569	−	0.483094i	$-0.160487\pi$
$479$	38.3255	1.75114	0.875569	+	0.483094i	$0.160487\pi$
$480$	8.63477	0.394122
$481$	3.26564	0.148900
$482$	−5.16089	−0.235072
$483$	−14.1181	−0.642396
$484$	−1.89281	−0.0860370
$485$	−1.74254	−0.0791245
$486$	−6.83789	−0.310173
$487$	1.75485	0.0795197	0.0397598	−	0.999209i	$-0.487341\pi$
$487$	1.75485	0.0795197	0.0397598	+	0.999209i	$0.487341\pi$
$488$	−13.9634	−0.632095
$489$	−24.4091	−1.10382
$490$	0.305859	0.0138173
$491$	−26.6477	−1.20259	−0.601297	−	0.799026i	$-0.705349\pi$
$491$	−26.6477	−1.20259	−0.601297	+	0.799026i	$0.705349\pi$
$492$	−4.44474	−0.200385
$493$	−32.5926	−1.46790
$494$	1.75342	0.0788902
$495$	2.59119	0.116465
$496$	24.3682	1.09417
$497$	−0.796975	−0.0357492
$498$	10.1835	0.456335
$499$	−28.4960	−1.27566	−0.637829	−	0.770178i	$-0.720167\pi$
$499$	−28.4960	−1.27566	−0.637829	+	0.770178i	$0.720167\pi$
$500$	−1.89281	−0.0846492
$501$	45.1041	2.01510
$502$	−1.59916	−0.0713740
$503$	−4.60256	−0.205218	−0.102609	−	0.994722i	$-0.532719\pi$
$503$	−4.60256	−0.205218	−0.102609	+	0.994722i	$0.532719\pi$
$504$	8.13343	0.362292
$505$	−3.45766	−0.153864
$506$	−0.793687	−0.0352837
$507$	29.7669	1.32200
$508$	−4.05910	−0.180093
$509$	6.95620	0.308328	0.154164	−	0.988045i	$-0.450732\pi$
$509$	6.95620	0.308328	0.154164	+	0.988045i	$0.450732\pi$
$510$	−4.70419	−0.208305
$511$	2.46288	0.108951
$512$	−20.8862	−0.923050
$513$	8.07299	0.356431
$514$	−4.92982	−0.217445
$515$	−15.8333	−0.697699
$516$	24.9507	1.09839
$517$	3.08560	0.135704
$518$	4.10601	0.180408
$519$	−11.5373	−0.506430
$520$	−0.817319	−0.0358418
$521$	−8.91754	−0.390685	−0.195342	−	0.980735i	$-0.562582\pi$
$521$	−8.91754	−0.390685	−0.195342	+	0.980735i	$0.562582\pi$
$522$	−4.55010	−0.199153
$523$	−17.4525	−0.763144	−0.381572	−	0.924339i	$-0.624617\pi$
$523$	−17.4525	−0.763144	−0.381572	+	0.924339i	$0.624617\pi$
$524$	−25.0956	−1.09631
$525$	−5.82365	−0.254165
$526$	−5.33621	−0.232670
$527$	−43.9610	−1.91497
$528$	−7.96476	−0.346622
$529$	−17.1229	−0.744474
$530$	−1.27664	−0.0554536
$531$	−0.520723	−0.0225975
$532$	−38.9323	−1.68793
$533$	0.636864	0.0275856
$534$	6.49082	0.280885
$535$	−6.58676	−0.284771
$536$	−13.5689	−0.586087
$537$	−16.7858	−0.724361
$538$	−7.84423	−0.338189
$539$	−0.934228	−0.0402401
$540$	−1.82972	−0.0787385
$541$	−29.6284	−1.27382	−0.636911	−	0.770937i	$-0.719788\pi$
$541$	−29.6284	−1.27382	−0.636911	+	0.770937i	$0.719788\pi$
$542$	−4.56115	−0.195918
$543$	−10.8792	−0.466871
$544$	22.1903	0.951402
$545$	11.4360	0.489866
$546$	−1.22271	−0.0523271
$547$	5.42820	0.232093	0.116046	−	0.993244i	$-0.462978\pi$
$547$	5.42820	0.232093	0.116046	+	0.993244i	$0.462978\pi$
$548$	−8.57251	−0.366199
$549$	−28.3896	−1.21164
$550$	−0.327392	−0.0139600
$551$	44.7933	1.90826
$552$	−7.30575	−0.310953
$553$	−26.4882	−1.12639
$554$	3.84541	0.163376
$555$	12.0409	0.511110
$556$	35.7088	1.51439
$557$	−43.3884	−1.83842	−0.919212	−	0.393762i	$-0.871173\pi$
$557$	−43.3884	−1.83842	−0.919212	+	0.393762i	$0.871173\pi$
$558$	−6.13720	−0.259808
$559$	−3.57505	−0.151209
$560$	8.29590	0.350566
$561$	14.3687	0.606646
$562$	1.60284	0.0676118
$563$	−32.9000	−1.38657	−0.693284	−	0.720665i	$-0.743837\pi$
$563$	−32.9000	−1.38657	−0.693284	+	0.720665i	$0.743837\pi$
$564$	13.8102	0.581514
$565$	2.18592	0.0919623
$566$	1.99561	0.0838816
$567$	−24.7749	−1.04045
$568$	−0.412414	−0.0173045
$569$	−24.0786	−1.00943	−0.504714	−	0.863287i	$-0.668402\pi$
$569$	−24.0786	−1.00943	−0.504714	+	0.863287i	$0.668402\pi$
$570$	6.46515	0.270795
$571$	26.4741	1.10791	0.553953	−	0.832548i	$-0.313119\pi$
$571$	26.4741	1.10791	0.553953	+	0.832548i	$0.313119\pi$
$572$	1.21386	0.0507540
$573$	16.5782	0.692563
$574$	0.800751	0.0334227
$575$	2.42427	0.101099
$576$	−14.3583	−0.598263
$577$	34.5156	1.43690	0.718452	−	0.695577i	$-0.244851\pi$
$577$	34.5156	1.43690	0.718452	+	0.695577i	$0.244851\pi$
$578$	−6.52352	−0.271343
$579$	−25.8218	−1.07312
$580$	−10.1522	−0.421549
$581$	32.3983	1.34411
$582$	−1.34897	−0.0559165
$583$	3.89942	0.161497
$584$	1.27448	0.0527382
$585$	−1.66172	−0.0687038
$586$	0.945683	0.0390658
$587$	37.2797	1.53870	0.769350	−	0.638828i	$-0.220580\pi$
$587$	37.2797	1.53870	0.769350	+	0.638828i	$0.220580\pi$
$588$	−4.18132	−0.172435
$589$	60.4174	2.48945
$590$	0.0657924	0.00270863
$591$	13.4860	0.554739
$592$	−17.1526	−0.704966
$593$	26.6379	1.09389	0.546944	−	0.837169i	$-0.315791\pi$
$593$	26.6379	1.09389	0.546944	+	0.837169i	$0.315791\pi$
$594$	−0.316478	−0.0129853
$595$	−14.9661	−0.613549
$596$	−24.1516	−0.989286
$597$	−41.1773	−1.68527
$598$	0.508990	0.0208141
$599$	43.8011	1.78966	0.894832	−	0.446404i	$-0.147296\pi$
$599$	43.8011	1.78966	0.894832	+	0.446404i	$0.147296\pi$
$600$	−3.01359	−0.123029
$601$	−47.8903	−1.95349	−0.976743	−	0.214412i	$-0.931217\pi$
$601$	−47.8903	−1.95349	−0.976743	+	0.214412i	$0.931217\pi$
$602$	−4.49504	−0.183204
$603$	−27.5874	−1.12345
$604$	−27.3560	−1.11310
$605$	1.00000	0.0406558
$606$	−2.67672	−0.108734
$607$	−0.500138	−0.0203000	−0.0101500	−	0.999948i	$-0.503231\pi$
$607$	−0.500138	−0.0203000	−0.0101500	+	0.999948i	$0.503231\pi$
$608$	−30.4970	−1.23682
$609$	−31.2356	−1.26573
$610$	3.58698	0.145232
$611$	−1.97879	−0.0800532
$612$	29.8038	1.20475
$613$	31.3670	1.26690	0.633450	−	0.773784i	$-0.281638\pi$
$613$	31.3670	1.26690	0.633450	+	0.773784i	$0.281638\pi$
$614$	3.98971	0.161012
$615$	2.34822	0.0946893
$616$	3.13888	0.126469
$617$	−27.1936	−1.09477	−0.547386	−	0.836880i	$-0.684377\pi$
$617$	−27.1936	−1.09477	−0.547386	+	0.836880i	$0.684377\pi$
$618$	−12.2572	−0.493057
$619$	42.6195	1.71302	0.856511	−	0.516130i	$-0.172628\pi$
$619$	42.6195	1.71302	0.856511	+	0.516130i	$0.172628\pi$
$620$	−13.6934	−0.549940
$621$	2.34346	0.0940397
$622$	−0.928371	−0.0372243
$623$	20.6501	0.827329
$624$	5.10778	0.204475
$625$	1.00000	0.0400000
$626$	2.67212	0.106799
$627$	−19.7474	−0.788637
$628$	−3.25484	−0.129882
$629$	30.9438	1.23381
$630$	−2.08934	−0.0832414
$631$	−14.5786	−0.580366	−0.290183	−	0.956971i	$-0.593716\pi$
$631$	−14.5786	−0.580366	−0.290183	+	0.956971i	$0.593716\pi$
$632$	−13.7069	−0.545233
$633$	−61.6826	−2.45166
$634$	2.26035	0.0897699
$635$	2.14448	0.0851010
$636$	17.4526	0.692040
$637$	0.599119	0.0237380
$638$	−1.75599	−0.0695203
$639$	−0.838495	−0.0331704
$640$	9.11761	0.360405
$641$	39.1527	1.54644	0.773219	−	0.634139i	$-0.218645\pi$
$641$	39.1527	1.54644	0.773219	+	0.634139i	$0.218645\pi$
$642$	−5.09908	−0.201245
$643$	25.0115	0.986358	0.493179	−	0.869928i	$-0.335835\pi$
$643$	25.0115	0.986358	0.493179	+	0.869928i	$0.335835\pi$
$644$	−11.3014	−0.445338
$645$	−13.1818	−0.519033
$646$	16.6146	0.653695
$647$	−12.8263	−0.504253	−0.252127	−	0.967694i	$-0.581130\pi$
$647$	−12.8263	−0.504253	−0.252127	+	0.967694i	$0.581130\pi$
$648$	−12.8203	−0.503631
$649$	−0.200959	−0.00788834
$650$	0.209956	0.00823515
$651$	−42.1307	−1.65123
$652$	−19.5393	−0.765217
$653$	−29.0871	−1.13827	−0.569133	−	0.822245i	$-0.692721\pi$
$653$	−29.0871	−1.13827	−0.569133	+	0.822245i	$0.692721\pi$
$654$	8.85310	0.346184
$655$	13.2584	0.518047
$656$	−3.34509	−0.130604
$657$	2.59119	0.101092
$658$	−2.48800	−0.0969923
$659$	−23.4984	−0.915366	−0.457683	−	0.889115i	$-0.651321\pi$
$659$	−23.4984	−0.915366	−0.457683	+	0.889115i	$0.651321\pi$
$660$	4.47569	0.174216
$661$	18.5339	0.720886	0.360443	−	0.932781i	$-0.382626\pi$
$661$	18.5339	0.720886	0.360443	+	0.932781i	$0.382626\pi$
$662$	7.31910	0.284465
$663$	−9.21460	−0.357865
$664$	16.7653	0.650618
$665$	20.5685	0.797610
$666$	4.31992	0.167393
$667$	13.0028	0.503469
$668$	36.1054	1.39696
$669$	35.7573	1.38246
$670$	3.48562	0.134661
$671$	−10.9562	−0.422960
$672$	21.2664	0.820369
$673$	−15.2624	−0.588321	−0.294160	−	0.955756i	$-0.595040\pi$
$673$	−15.2624	−0.588321	−0.294160	+	0.955756i	$0.595040\pi$
$674$	3.30313	0.127232
$675$	0.966665	0.0372070
$676$	23.8281	0.916467
$677$	−36.4187	−1.39969	−0.699843	−	0.714297i	$-0.746747\pi$
$677$	−36.4187	−1.39969	−0.699843	+	0.714297i	$0.746747\pi$
$678$	1.69221	0.0649889
$679$	−4.29165	−0.164699
$680$	−7.74455	−0.296990
$681$	36.3603	1.39333
$682$	−2.36849	−0.0906941
$683$	1.68988	0.0646615	0.0323307	−	0.999477i	$-0.489707\pi$
$683$	1.68988	0.0646615	0.0323307	+	0.999477i	$0.489707\pi$
$684$	−40.9605	−1.56617
$685$	4.52897	0.173043
$686$	6.39758	0.244261
$687$	−68.1579	−2.60039
$688$	18.7777	0.715895
$689$	−2.50069	−0.0952686
$690$	1.87673	0.0714458
$691$	−8.73047	−0.332123	−0.166061	−	0.986115i	$-0.553105\pi$
$691$	−8.73047	−0.332123	−0.166061	+	0.986115i	$0.553105\pi$
$692$	−9.23547	−0.351080
$693$	6.38178	0.242424
$694$	−8.39506	−0.318672
$695$	−18.8654	−0.715607
$696$	−16.1636	−0.612679
$697$	6.03464	0.228578
$698$	8.17741	0.309519
$699$	−50.6016	−1.91393
$700$	−4.66177	−0.176198
$701$	−26.8542	−1.01427	−0.507135	−	0.861867i	$-0.669295\pi$
$701$	−26.8542	−1.01427	−0.507135	+	0.861867i	$0.669295\pi$
$702$	0.202957	0.00766012
$703$	−42.5272	−1.60395
$704$	−5.54120	−0.208842
$705$	−7.29611	−0.274787
$706$	−2.54767	−0.0958827
$707$	−8.51580	−0.320270
$708$	−0.899432	−0.0338027
$709$	35.9422	1.34984	0.674919	−	0.737892i	$-0.264178\pi$
$709$	35.9422	1.34984	0.674919	+	0.737892i	$0.264178\pi$
$710$	0.105942	0.00397595
$711$	−27.8681	−1.04514
$712$	10.6859	0.400471
$713$	17.5382	0.656810
$714$	−11.5858	−0.433589
$715$	−0.641298	−0.0239832
$716$	−13.4369	−0.502159
$717$	54.8825	2.04962
$718$	−9.97984	−0.372444
$719$	32.7152	1.22007	0.610036	−	0.792374i	$-0.291155\pi$
$719$	32.7152	1.22007	0.610036	+	0.792374i	$0.291155\pi$
$720$	8.72809	0.325277
$721$	−38.9955	−1.45227
$722$	−16.6137	−0.618299
$723$	−37.2742	−1.38624
$724$	−8.70869	−0.323656
$725$	5.36357	0.199198
$726$	0.774141	0.0287311
$727$	−17.9525	−0.665820	−0.332910	−	0.942959i	$-0.608031\pi$
$727$	−17.9525	−0.665820	−0.332910	+	0.942959i	$0.608031\pi$
$728$	−2.01296	−0.0746052
$729$	−19.2083	−0.711419
$730$	−0.327392	−0.0121173
$731$	−33.8756	−1.25293
$732$	−49.0366	−1.81245
$733$	41.1438	1.51968	0.759840	−	0.650110i	$-0.225277\pi$
$733$	41.1438	1.51968	0.759840	+	0.650110i	$0.225277\pi$
$734$	−0.969614	−0.0357891
$735$	2.20905	0.0814819
$736$	−8.85279	−0.326318
$737$	−10.6466	−0.392174
$738$	0.842468	0.0310117
$739$	11.4091	0.419692	0.209846	−	0.977734i	$-0.432704\pi$
$739$	11.4091	0.419692	0.209846	+	0.977734i	$0.432704\pi$
$740$	9.63866	0.354324
$741$	12.6640	0.465223
$742$	−3.14420	−0.115427
$743$	10.8685	0.398725	0.199362	−	0.979926i	$-0.436113\pi$
$743$	10.8685	0.398725	0.199362	+	0.979926i	$0.436113\pi$
$744$	−21.8015	−0.799283
$745$	12.7596	0.467475
$746$	0.244239	0.00894224
$747$	34.0861	1.24715
$748$	11.5020	0.420554
$749$	−16.2224	−0.592754
$750$	0.774141	0.0282676
$751$	−14.7036	−0.536541	−0.268271	−	0.963344i	$-0.586452\pi$
$751$	−14.7036	−0.536541	−0.268271	+	0.963344i	$0.586452\pi$
$752$	10.3935	0.379010
$753$	−11.5498	−0.420899
$754$	1.12611	0.0410106
$755$	14.4526	0.525983
$756$	−4.50637	−0.163895
$757$	12.3967	0.450565	0.225282	−	0.974294i	$-0.427670\pi$
$757$	12.3967	0.450565	0.225282	+	0.974294i	$0.427670\pi$
$758$	−2.15505	−0.0782750
$759$	−5.73236	−0.208071
$760$	10.6436	0.386086
$761$	25.8774	0.938053	0.469027	−	0.883184i	$-0.344605\pi$
$761$	25.8774	0.938053	0.469027	+	0.883184i	$0.344605\pi$
$762$	1.66013	0.0601401
$763$	28.1656	1.01966
$764$	13.2707	0.480116
$765$	−15.7457	−0.569289
$766$	−8.71749	−0.314976
$767$	0.128875	0.00465340
$768$	−19.1468	−0.690901
$769$	−36.7336	−1.32465	−0.662323	−	0.749218i	$-0.730429\pi$
$769$	−36.7336	−1.32465	−0.662323	+	0.749218i	$0.730429\pi$
$770$	−0.806327	−0.0290580
$771$	−35.6053	−1.28229
$772$	−20.6701	−0.743934
$773$	−50.3884	−1.81235	−0.906173	−	0.422907i	$-0.861010\pi$
$773$	−50.3884	−1.81235	−0.906173	+	0.422907i	$0.861010\pi$
$774$	−4.72922	−0.169988
$775$	7.23441	0.259868
$776$	−2.22082	−0.0797228
$777$	29.6554	1.06388
$778$	9.08305	0.325643
$779$	−8.29364	−0.297151
$780$	−2.87025	−0.102772
$781$	−0.323595	−0.0115791
$782$	4.82296	0.172469
$783$	5.18478	0.185289
$784$	−3.14683	−0.112387
$785$	1.71958	0.0613744
$786$	10.2638	0.366099
$787$	36.6300	1.30572	0.652859	−	0.757479i	$-0.273569\pi$
$787$	36.6300	1.30572	0.652859	+	0.757479i	$0.273569\pi$
$788$	10.7954	0.384570
$789$	−38.5405	−1.37208
$790$	3.52109	0.125275
$791$	5.38365	0.191421
$792$	3.30241	0.117346
$793$	7.02620	0.249508
$794$	0.120131	0.00426329
$795$	−9.22044	−0.327015
$796$	−32.9620	−1.16831
$797$	26.3137	0.932080	0.466040	−	0.884764i	$-0.345680\pi$
$797$	26.3137	0.932080	0.466040	+	0.884764i	$0.345680\pi$
$798$	15.9229	0.563664
$799$	−18.7501	−0.663331
$800$	−3.65173	−0.129108
$801$	21.7259	0.767648
$802$	−9.04137	−0.319262
$803$	1.00000	0.0352892
$804$	−47.6511	−1.68052
$805$	5.97068	0.210439
$806$	1.51891	0.0535012
$807$	−56.6545	−1.99433
$808$	−4.40671	−0.155027
$809$	39.1233	1.37550	0.687751	−	0.725947i	$-0.258598\pi$
$809$	39.1233	1.37550	0.687751	+	0.725947i	$0.258598\pi$
$810$	3.29334	0.115716
$811$	5.79807	0.203598	0.101799	−	0.994805i	$-0.467540\pi$
$811$	5.79807	0.203598	0.101799	+	0.994805i	$0.467540\pi$
$812$	−25.0038	−0.877460
$813$	−32.9427	−1.15535
$814$	1.66716	0.0584338
$815$	10.3229	0.361594
$816$	48.3991	1.69431
$817$	46.5566	1.62881
$818$	−7.63689	−0.267018
$819$	−4.09262	−0.143008
$820$	1.87973	0.0656429
$821$	−3.76985	−0.131569	−0.0657843	−	0.997834i	$-0.520955\pi$
$821$	−3.76985	−0.131569	−0.0657843	+	0.997834i	$0.520955\pi$
$822$	3.50606	0.122288
$823$	−21.5281	−0.750421	−0.375210	−	0.926940i	$-0.622430\pi$
$823$	−21.5281	−0.750421	−0.375210	+	0.926940i	$0.622430\pi$
$824$	−20.1792	−0.702974
$825$	−2.36457	−0.0823237
$826$	0.162039	0.00563805
$827$	9.66591	0.336117	0.168058	−	0.985777i	$-0.446250\pi$
$827$	9.66591	0.336117	0.168058	+	0.985777i	$0.446250\pi$
$828$	−11.8902	−0.413212
$829$	17.5613	0.609929	0.304965	−	0.952364i	$-0.401355\pi$
$829$	17.5613	0.609929	0.304965	+	0.952364i	$0.401355\pi$
$830$	−4.30672	−0.149488
$831$	27.7732	0.963442
$832$	3.55356	0.123198
$833$	5.67698	0.196696
$834$	−14.6045	−0.505713
$835$	−19.0750	−0.660117
$836$	−15.8076	−0.546718
$837$	6.99325	0.241722
$838$	9.23780	0.319115
$839$	−14.8219	−0.511708	−0.255854	−	0.966715i	$-0.582357\pi$
$839$	−14.8219	−0.511708	−0.255854	+	0.966715i	$0.582357\pi$
$840$	−7.42210	−0.256087
$841$	−0.232084	−0.00800289
$842$	−3.39027	−0.116837
$843$	11.5764	0.398714
$844$	−49.3763	−1.69960
$845$	−12.5887	−0.433066
$846$	−2.61762	−0.0899956
$847$	2.46288	0.0846255
$848$	13.1347	0.451047
$849$	14.4131	0.494658
$850$	1.98945	0.0682375
$851$	−12.3450	−0.423180
$852$	−1.44831	−0.0496183
$853$	−17.0110	−0.582445	−0.291223	−	0.956655i	$-0.594062\pi$
$853$	−17.0110	−0.582445	−0.291223	+	0.956655i	$0.594062\pi$
$854$	8.83429	0.302303
$855$	21.6400	0.740073
$856$	−8.39467	−0.286924
$857$	34.9627	1.19430	0.597152	−	0.802128i	$-0.296299\pi$
$857$	34.9627	1.19430	0.597152	+	0.802128i	$0.296299\pi$
$858$	−0.496455	−0.0169487
$859$	35.1109	1.19797	0.598985	−	0.800760i	$-0.295571\pi$
$859$	35.1109	1.19797	0.598985	+	0.800760i	$0.295571\pi$
$860$	−10.5519	−0.359817
$861$	5.78338	0.197097
$862$	−3.91922	−0.133489
$863$	31.4924	1.07201	0.536006	−	0.844214i	$-0.319932\pi$
$863$	31.4924	1.07201	0.536006	+	0.844214i	$0.319932\pi$
$864$	−3.53000	−0.120093
$865$	4.87923	0.165899
$866$	−6.60771	−0.224539
$867$	−47.1157	−1.60013
$868$	−33.7252	−1.14471
$869$	−10.7550	−0.364837
$870$	4.15216	0.140771
$871$	6.82767	0.231347
$872$	14.5750	0.493570
$873$	−4.51524	−0.152818
$874$	−6.62839	−0.224208
$875$	2.46288	0.0832605
$876$	4.47569	0.151220
$877$	−12.9989	−0.438941	−0.219471	−	0.975619i	$-0.570433\pi$
$877$	−12.9989	−0.438941	−0.219471	+	0.975619i	$0.570433\pi$
$878$	−0.174331	−0.00588338
$879$	6.83014	0.230375
$880$	3.36838	0.113548
$881$	18.5787	0.625933	0.312966	−	0.949764i	$-0.398677\pi$
$881$	18.5787	0.625933	0.312966	+	0.949764i	$0.398677\pi$
$882$	0.792538	0.0266861
$883$	−37.9881	−1.27840	−0.639201	−	0.769040i	$-0.720735\pi$
$883$	−37.9881	−1.27840	−0.639201	+	0.769040i	$0.720735\pi$
$884$	−7.37620	−0.248088
$885$	0.475182	0.0159731
$886$	−8.46023	−0.284227
$887$	14.5261	0.487738	0.243869	−	0.969808i	$-0.421583\pi$
$887$	14.5261	0.487738	0.243869	+	0.969808i	$0.421583\pi$
$888$	15.3459	0.514975
$889$	5.28159	0.177139
$890$	−2.74503	−0.0920137
$891$	−10.0593	−0.337000
$892$	28.6234	0.958381
$893$	25.7690	0.862328
$894$	9.87773	0.330361
$895$	7.09888	0.237289
$896$	22.4556	0.750188
$897$	3.67615	0.122743
$898$	−8.33369	−0.278099
$899$	38.8023	1.29413
$900$	−4.90464	−0.163488
$901$	−23.6954	−0.789408
$902$	0.325128	0.0108256
$903$	−32.4652	−1.08037
$904$	2.78590	0.0926577
$905$	4.60092	0.152940
$906$	11.1883	0.371707
$907$	−43.7140	−1.45150	−0.725750	−	0.687959i	$-0.758507\pi$
$907$	−43.7140	−1.45150	−0.725750	+	0.687959i	$0.758507\pi$
$908$	29.1061	0.965920
$909$	−8.95945	−0.297166
$910$	0.517096	0.0171416
$911$	−22.0078	−0.729152	−0.364576	−	0.931174i	$-0.618786\pi$
$911$	−22.0078	−0.729152	−0.364576	+	0.931174i	$0.618786\pi$
$912$	−66.5168	−2.20259
$913$	13.1546	0.435355
$914$	6.79319	0.224699
$915$	25.9067	0.856450
$916$	−54.5597	−1.80270
$917$	32.6538	1.07832
$918$	1.92313	0.0634727
$919$	−37.4451	−1.23520	−0.617600	−	0.786492i	$-0.711895\pi$
$919$	−37.4451	−1.23520	−0.617600	+	0.786492i	$0.711895\pi$
$920$	3.08968	0.101864
$921$	28.8154	0.949501
$922$	−4.82355	−0.158855
$923$	0.207521	0.00683063
$924$	11.0231	0.362633
$925$	−5.09224	−0.167432
$926$	11.8130	0.388201
$927$	−41.0271	−1.34751
$928$	−19.5863	−0.642953
$929$	−26.9397	−0.883863	−0.441932	−	0.897049i	$-0.645707\pi$
$929$	−26.9397	−0.883863	−0.441932	+	0.897049i	$0.645707\pi$
$930$	5.60045	0.183646
$931$	−7.80210	−0.255704
$932$	−40.5061	−1.32682
$933$	−6.70511	−0.219515
$934$	−2.55535	−0.0836135
$935$	−6.07665	−0.198728
$936$	−2.11783	−0.0692234
$937$	−0.290083	−0.00947661	−0.00473831	−	0.999989i	$-0.501508\pi$
$937$	−0.290083	−0.00947661	−0.00473831	+	0.999989i	$0.501508\pi$
$938$	8.58467	0.280299
$939$	19.2992	0.629806
$940$	−5.84047	−0.190495
$941$	12.8927	0.420292	0.210146	−	0.977670i	$-0.432606\pi$
$941$	12.8927	0.420292	0.210146	+	0.977670i	$0.432606\pi$
$942$	1.33120	0.0433727
$943$	−2.40751	−0.0783993
$944$	−0.676906	−0.0220314
$945$	2.38078	0.0774467
$946$	−1.82512	−0.0593397
$947$	−14.2277	−0.462337	−0.231168	−	0.972914i	$-0.574255\pi$
$947$	−14.2277	−0.462337	−0.231168	+	0.972914i	$0.574255\pi$
$948$	−48.1359	−1.56338
$949$	−0.641298	−0.0208174
$950$	−2.73418	−0.0887084
$951$	16.3252	0.529382
$952$	−19.0739	−0.618188
$953$	26.5061	0.858618	0.429309	−	0.903158i	$-0.358757\pi$
$953$	26.5061	0.858618	0.429309	+	0.903158i	$0.358757\pi$
$954$	−3.30801	−0.107101
$955$	−7.01107	−0.226873
$956$	43.9329	1.42089
$957$	−12.6825	−0.409968
$958$	−12.5475	−0.405390
$959$	11.1543	0.360192
$960$	13.1026	0.422883
$961$	21.3367	0.688280
$962$	−1.06915	−0.0344706
$963$	−17.0675	−0.549994
$964$	−29.8377	−0.961006
$965$	10.9203	0.351537
$966$	4.62215	0.148715
$967$	34.5708	1.11172	0.555861	−	0.831275i	$-0.312389\pi$
$967$	34.5708	1.11172	0.555861	+	0.831275i	$0.312389\pi$
$968$	1.27448	0.0409632
$969$	119.998	3.85490
$970$	0.570492	0.0183174
$971$	−19.9766	−0.641080	−0.320540	−	0.947235i	$-0.603864\pi$
$971$	−19.9766	−0.641080	−0.320540	+	0.947235i	$0.603864\pi$
$972$	−39.5332	−1.26803
$973$	−46.4633	−1.48954
$974$	−0.574523	−0.0184089
$975$	1.51639	0.0485635
$976$	−36.9047	−1.18129
$977$	13.4085	0.428975	0.214488	−	0.976727i	$-0.431192\pi$
$977$	13.4085	0.428975	0.214488	+	0.976727i	$0.431192\pi$
$978$	7.99135	0.255535
$979$	8.38454	0.267971
$980$	1.76832	0.0564869
$981$	29.6329	0.946106
$982$	8.72424	0.278402
$983$	14.5455	0.463928	0.231964	−	0.972724i	$-0.425485\pi$
$983$	14.5455	0.463928	0.231964	+	0.972724i	$0.425485\pi$
$984$	2.99275	0.0954054
$985$	−5.70336	−0.181724
$986$	10.6705	0.339819
$987$	−17.9694	−0.571973
$988$	10.1374	0.322514
$989$	13.5146	0.429740
$990$	−0.848334	−0.0269618
$991$	34.9445	1.11005	0.555024	−	0.831834i	$-0.312709\pi$
$991$	34.9445	1.11005	0.555024	+	0.831834i	$0.312709\pi$
$992$	−26.4181	−0.838776
$993$	52.8618	1.67752
$994$	0.260923	0.00827598
$995$	17.4143	0.552070
$996$	58.8760	1.86556
$997$	−14.0164	−0.443903	−0.221952	−	0.975058i	$-0.571243\pi$
$997$	−14.0164	−0.443903	−0.221952	+	0.975058i	$0.571243\pi$
$998$	9.32937	0.295316
$999$	−4.92249	−0.155741

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4015.2.a.h.1.17	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4015.2.a.h.1.17	✓	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)

\(f(q)\)	\(=\)	\(q-0.327392 q^{2} -2.36457 q^{3} -1.89281 q^{4} +1.00000 q^{5} +0.774141 q^{6} +2.46288 q^{7} +1.27448 q^{8} +2.59119 q^{9} +O(q^{10})\)	\(q-0.327392 q^{2} -2.36457 q^{3} -1.89281 q^{4} +1.00000 q^{5} +0.774141 q^{6} +2.46288 q^{7} +1.27448 q^{8} +2.59119 q^{9} -0.327392 q^{10} +1.00000 q^{11} +4.47569 q^{12} -0.641298 q^{13} -0.806327 q^{14} -2.36457 q^{15} +3.36838 q^{16} -6.07665 q^{17} -0.848334 q^{18} +8.35139 q^{19} -1.89281 q^{20} -5.82365 q^{21} -0.327392 q^{22} +2.42427 q^{23} -3.01359 q^{24} +1.00000 q^{25} +0.209956 q^{26} +0.966665 q^{27} -4.66177 q^{28} +5.36357 q^{29} +0.774141 q^{30} +7.23441 q^{31} -3.65173 q^{32} -2.36457 q^{33} +1.98945 q^{34} +2.46288 q^{35} -4.90464 q^{36} -5.09224 q^{37} -2.73418 q^{38} +1.51639 q^{39} +1.27448 q^{40} -0.993086 q^{41} +1.90662 q^{42} +5.57472 q^{43} -1.89281 q^{44} +2.59119 q^{45} -0.793687 q^{46} +3.08560 q^{47} -7.96476 q^{48} -0.934228 q^{49} -0.327392 q^{50} +14.3687 q^{51} +1.21386 q^{52} +3.89942 q^{53} -0.316478 q^{54} +1.00000 q^{55} +3.13888 q^{56} -19.7474 q^{57} -1.75599 q^{58} -0.200959 q^{59} +4.47569 q^{60} -10.9562 q^{61} -2.36849 q^{62} +6.38178 q^{63} -5.54120 q^{64} -0.641298 q^{65} +0.774141 q^{66} -10.6466 q^{67} +11.5020 q^{68} -5.73236 q^{69} -0.806327 q^{70} -0.323595 q^{71} +3.30241 q^{72} +1.00000 q^{73} +1.66716 q^{74} -2.36457 q^{75} -15.8076 q^{76} +2.46288 q^{77} -0.496455 q^{78} -10.7550 q^{79} +3.36838 q^{80} -10.0593 q^{81} +0.325128 q^{82} +13.1546 q^{83} +11.0231 q^{84} -6.07665 q^{85} -1.82512 q^{86} -12.6825 q^{87} +1.27448 q^{88} +8.38454 q^{89} -0.848334 q^{90} -1.57944 q^{91} -4.58869 q^{92} -17.1063 q^{93} -1.01020 q^{94} +8.35139 q^{95} +8.63477 q^{96} -1.74254 q^{97} +0.305859 q^{98} +2.59119 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9}+O(q^{10}) \) 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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