LMFDB - Embedded newform 4022.2.a.d.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4022,2,Mod(1,4022)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4022, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4022.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4022 = 2 \cdot 2011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4022.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:	$32.1158316930$
Analytic rank:	$1$
Dimension:	$37$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	4022.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -3.25277 q^{3} +1.00000 q^{4} -3.41922 q^{5} +3.25277 q^{6} +1.95122 q^{7} -1.00000 q^{8} +7.58049 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -3.25277 q^{3} +1.00000 q^{4} -3.41922 q^{5} +3.25277 q^{6} +1.95122 q^{7} -1.00000 q^{8} +7.58049 q^{9} +3.41922 q^{10} +2.17799 q^{11} -3.25277 q^{12} -3.20143 q^{13} -1.95122 q^{14} +11.1219 q^{15} +1.00000 q^{16} -4.06159 q^{17} -7.58049 q^{18} -4.62087 q^{19} -3.41922 q^{20} -6.34688 q^{21} -2.17799 q^{22} +3.12922 q^{23} +3.25277 q^{24} +6.69104 q^{25} +3.20143 q^{26} -14.8993 q^{27} +1.95122 q^{28} +4.13521 q^{29} -11.1219 q^{30} -5.84993 q^{31} -1.00000 q^{32} -7.08449 q^{33} +4.06159 q^{34} -6.67166 q^{35} +7.58049 q^{36} +3.29208 q^{37} +4.62087 q^{38} +10.4135 q^{39} +3.41922 q^{40} +8.39109 q^{41} +6.34688 q^{42} -6.03290 q^{43} +2.17799 q^{44} -25.9193 q^{45} -3.12922 q^{46} +2.62930 q^{47} -3.25277 q^{48} -3.19273 q^{49} -6.69104 q^{50} +13.2114 q^{51} -3.20143 q^{52} -6.37757 q^{53} +14.8993 q^{54} -7.44702 q^{55} -1.95122 q^{56} +15.0306 q^{57} -4.13521 q^{58} -0.661247 q^{59} +11.1219 q^{60} +2.59032 q^{61} +5.84993 q^{62} +14.7912 q^{63} +1.00000 q^{64} +10.9464 q^{65} +7.08449 q^{66} -5.54616 q^{67} -4.06159 q^{68} -10.1786 q^{69} +6.67166 q^{70} +12.0546 q^{71} -7.58049 q^{72} -4.40887 q^{73} -3.29208 q^{74} -21.7644 q^{75} -4.62087 q^{76} +4.24975 q^{77} -10.4135 q^{78} +7.28000 q^{79} -3.41922 q^{80} +25.7224 q^{81} -8.39109 q^{82} +10.6971 q^{83} -6.34688 q^{84} +13.8875 q^{85} +6.03290 q^{86} -13.4509 q^{87} -2.17799 q^{88} +3.25652 q^{89} +25.9193 q^{90} -6.24671 q^{91} +3.12922 q^{92} +19.0284 q^{93} -2.62930 q^{94} +15.7998 q^{95} +3.25277 q^{96} +11.3489 q^{97} +3.19273 q^{98} +16.5102 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q - 37 q^{2} - 5 q^{3} + 37 q^{4} - 13 q^{5} + 5 q^{6} - 22 q^{7} - 37 q^{8} + 32 q^{9}+O(q^{10}) $ 37 * q - 37 * q^2 - 5 * q^3 + 37 * q^4 - 13 * q^5 + 5 * q^6 - 22 * q^7 - 37 * q^8 + 32 * q^9	\( 37 q - 37 q^{2} - 5 q^{3} + 37 q^{4} - 13 q^{5} + 5 q^{6} - 22 q^{7} - 37 q^{8} + 32 q^{9} + 13 q^{10} + 12 q^{11} - 5 q^{12} - 36 q^{13} + 22 q^{14} - 7 q^{15} + 37 q^{16} + 4 q^{17} - 32 q^{18} - 10 q^{19} - 13 q^{20} - 11 q^{21} - 12 q^{22} - q^{23} + 5 q^{24} + 8 q^{25} + 36 q^{26} - 20 q^{27} - 22 q^{28} - 6 q^{29} + 7 q^{30} - 23 q^{31} - 37 q^{32} - 27 q^{33} - 4 q^{34} + 24 q^{35} + 32 q^{36} - 46 q^{37} + 10 q^{38} + 5 q^{39} + 13 q^{40} + 11 q^{41} + 11 q^{42} - 22 q^{43} + 12 q^{44} - 57 q^{45} + q^{46} - 18 q^{47} - 5 q^{48} - q^{49} - 8 q^{50} + 18 q^{51} - 36 q^{52} - 25 q^{53} + 20 q^{54} - 25 q^{55} + 22 q^{56} - 25 q^{57} + 6 q^{58} + 24 q^{59} - 7 q^{60} - 40 q^{61} + 23 q^{62} - 38 q^{63} + 37 q^{64} + 14 q^{65} + 27 q^{66} - 49 q^{67} + 4 q^{68} - 19 q^{69} - 24 q^{70} + 27 q^{71} - 32 q^{72} - 87 q^{73} + 46 q^{74} - 5 q^{75} - 10 q^{76} - 50 q^{77} - 5 q^{78} + 11 q^{79} - 13 q^{80} + 5 q^{81} - 11 q^{82} - 9 q^{83} - 11 q^{84} - 68 q^{85} + 22 q^{86} - 12 q^{87} - 12 q^{88} - 3 q^{89} + 57 q^{90} - 19 q^{91} - q^{92} - 69 q^{93} + 18 q^{94} + 27 q^{95} + 5 q^{96} - 98 q^{97} + q^{98} + 33 q^{99}+O(q^{100}) \) 37 * q - 37 * q^2 - 5 * q^3 + 37 * q^4 - 13 * q^5 + 5 * q^6 - 22 * q^7 - 37 * q^8 + 32 * q^9 + 13 * q^10 + 12 * q^11 - 5 * q^12 - 36 * q^13 + 22 * q^14 - 7 * q^15 + 37 * q^16 + 4 * q^17 - 32 * q^18 - 10 * q^19 - 13 * q^20 - 11 * q^21 - 12 * q^22 - q^23 + 5 * q^24 + 8 * q^25 + 36 * q^26 - 20 * q^27 - 22 * q^28 - 6 * q^29 + 7 * q^30 - 23 * q^31 - 37 * q^32 - 27 * q^33 - 4 * q^34 + 24 * q^35 + 32 * q^36 - 46 * q^37 + 10 * q^38 + 5 * q^39 + 13 * q^40 + 11 * q^41 + 11 * q^42 - 22 * q^43 + 12 * q^44 - 57 * q^45 + q^46 - 18 * q^47 - 5 * q^48 - q^49 - 8 * q^50 + 18 * q^51 - 36 * q^52 - 25 * q^53 + 20 * q^54 - 25 * q^55 + 22 * q^56 - 25 * q^57 + 6 * q^58 + 24 * q^59 - 7 * q^60 - 40 * q^61 + 23 * q^62 - 38 * q^63 + 37 * q^64 + 14 * q^65 + 27 * q^66 - 49 * q^67 + 4 * q^68 - 19 * q^69 - 24 * q^70 + 27 * q^71 - 32 * q^72 - 87 * q^73 + 46 * q^74 - 5 * q^75 - 10 * q^76 - 50 * q^77 - 5 * q^78 + 11 * q^79 - 13 * q^80 + 5 * q^81 - 11 * q^82 - 9 * q^83 - 11 * q^84 - 68 * q^85 + 22 * q^86 - 12 * q^87 - 12 * q^88 - 3 * q^89 + 57 * q^90 - 19 * q^91 - q^92 - 69 * q^93 + 18 * q^94 + 27 * q^95 + 5 * q^96 - 98 * q^97 + q^98 + 33 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−3.25277	−1.87799	−0.938993	−	0.343937i	$-0.888239\pi$
$3$	−3.25277	−1.87799	−0.938993	+	0.343937i	$0.888239\pi$
$4$	1.00000	0.500000
$5$	−3.41922	−1.52912	−0.764560	−	0.644552i	$-0.777044\pi$
$5$	−3.41922	−1.52912	−0.764560	+	0.644552i	$0.777044\pi$
$6$	3.25277	1.32794
$7$	1.95122	0.737493	0.368747	−	0.929530i	$-0.379787\pi$
$7$	1.95122	0.737493	0.368747	+	0.929530i	$0.379787\pi$
$8$	−1.00000	−0.353553
$9$	7.58049	2.52683
$10$	3.41922	1.08125
$11$	2.17799	0.656689	0.328344	−	0.944558i	$-0.393509\pi$
$11$	2.17799	0.656689	0.328344	+	0.944558i	$0.393509\pi$
$12$	−3.25277	−0.938993
$13$	−3.20143	−0.887918	−0.443959	−	0.896047i	$-0.646426\pi$
$13$	−3.20143	−0.887918	−0.443959	+	0.896047i	$0.646426\pi$
$14$	−1.95122	−0.521487
$15$	11.1219	2.87167
$16$	1.00000	0.250000
$17$	−4.06159	−0.985080	−0.492540	−	0.870290i	$-0.663931\pi$
$17$	−4.06159	−0.985080	−0.492540	+	0.870290i	$0.663931\pi$
$18$	−7.58049	−1.78674
$19$	−4.62087	−1.06010	−0.530051	−	0.847966i	$-0.677827\pi$
$19$	−4.62087	−1.06010	−0.530051	+	0.847966i	$0.677827\pi$
$20$	−3.41922	−0.764560
$21$	−6.34688	−1.38500
$22$	−2.17799	−0.464349
$23$	3.12922	0.652488	0.326244	−	0.945286i	$-0.394217\pi$
$23$	3.12922	0.652488	0.326244	+	0.945286i	$0.394217\pi$
$24$	3.25277	0.663968
$25$	6.69104	1.33821
$26$	3.20143	0.627853
$27$	−14.8993	−2.86737
$28$	1.95122	0.368747
$29$	4.13521	0.767890	0.383945	−	0.923356i	$-0.374565\pi$
$29$	4.13521	0.767890	0.383945	+	0.923356i	$0.374565\pi$
$30$	−11.1219	−2.03057
$31$	−5.84993	−1.05068	−0.525339	−	0.850893i	$-0.676061\pi$
$31$	−5.84993	−1.05068	−0.525339	+	0.850893i	$0.676061\pi$
$32$	−1.00000	−0.176777
$33$	−7.08449	−1.23325
$34$	4.06159	0.696557
$35$	−6.67166	−1.12772
$36$	7.58049	1.26342
$37$	3.29208	0.541215	0.270607	−	0.962690i	$-0.412776\pi$
$37$	3.29208	0.541215	0.270607	+	0.962690i	$0.412776\pi$
$38$	4.62087	0.749605
$39$	10.4135	1.66750
$40$	3.41922	0.540626
$41$	8.39109	1.31047	0.655234	−	0.755426i	$-0.272570\pi$
$41$	8.39109	1.31047	0.655234	+	0.755426i	$0.272570\pi$
$42$	6.34688	0.979344
$43$	−6.03290	−0.920009	−0.460004	−	0.887917i	$-0.652152\pi$
$43$	−6.03290	−0.920009	−0.460004	+	0.887917i	$0.652152\pi$
$44$	2.17799	0.328344
$45$	−25.9193	−3.86383
$46$	−3.12922	−0.461379
$47$	2.62930	0.383523	0.191762	−	0.981442i	$-0.438580\pi$
$47$	2.62930	0.383523	0.191762	+	0.981442i	$0.438580\pi$
$48$	−3.25277	−0.469496
$49$	−3.19273	−0.456104
$50$	−6.69104	−0.946256
$51$	13.2114	1.84997
$52$	−3.20143	−0.443959
$53$	−6.37757	−0.876026	−0.438013	−	0.898969i	$-0.644318\pi$
$53$	−6.37757	−0.876026	−0.438013	+	0.898969i	$0.644318\pi$
$54$	14.8993	2.02753
$55$	−7.44702	−1.00416
$56$	−1.95122	−0.260743
$57$	15.0306	1.99086
$58$	−4.13521	−0.542980
$59$	−0.661247	−0.0860870	−0.0430435	−	0.999073i	$-0.513705\pi$
$59$	−0.661247	−0.0860870	−0.0430435	+	0.999073i	$0.513705\pi$
$60$	11.1219	1.43583
$61$	2.59032	0.331657	0.165829	−	0.986155i	$-0.446970\pi$
$61$	2.59032	0.331657	0.165829	+	0.986155i	$0.446970\pi$
$62$	5.84993	0.742942
$63$	14.7912	1.86352
$64$	1.00000	0.125000
$65$	10.9464	1.35773
$66$	7.08449	0.872041
$67$	−5.54616	−0.677572	−0.338786	−	0.940864i	$-0.610016\pi$
$67$	−5.54616	−0.677572	−0.338786	+	0.940864i	$0.610016\pi$
$68$	−4.06159	−0.492540
$69$	−10.1786	−1.22536
$70$	6.67166	0.797416
$71$	12.0546	1.43062	0.715308	−	0.698809i	$-0.246286\pi$
$71$	12.0546	1.43062	0.715308	+	0.698809i	$0.246286\pi$
$72$	−7.58049	−0.893369
$73$	−4.40887	−0.516019	−0.258010	−	0.966142i	$-0.583067\pi$
$73$	−4.40887	−0.516019	−0.258010	+	0.966142i	$0.583067\pi$
$74$	−3.29208	−0.382697
$75$	−21.7644	−2.51314
$76$	−4.62087	−0.530051
$77$	4.24975	0.484303
$78$	−10.4135	−1.17910
$79$	7.28000	0.819064	0.409532	−	0.912296i	$-0.365692\pi$
$79$	7.28000	0.819064	0.409532	+	0.912296i	$0.365692\pi$
$80$	−3.41922	−0.382280
$81$	25.7224	2.85804
$82$	−8.39109	−0.926641
$83$	10.6971	1.17416	0.587082	−	0.809527i	$-0.300277\pi$
$83$	10.6971	1.17416	0.587082	+	0.809527i	$0.300277\pi$
$84$	−6.34688	−0.692501
$85$	13.8875	1.50631
$86$	6.03290	0.650544
$87$	−13.4509	−1.44209
$88$	−2.17799	−0.232174
$89$	3.25652	0.345190	0.172595	−	0.984993i	$-0.444785\pi$
$89$	3.25652	0.345190	0.172595	+	0.984993i	$0.444785\pi$
$90$	25.9193	2.73214
$91$	−6.24671	−0.654834
$92$	3.12922	0.326244
$93$	19.0284	1.97316
$94$	−2.62930	−0.271192
$95$	15.7998	1.62102
$96$	3.25277	0.331984
$97$	11.3489	1.15231	0.576153	−	0.817342i	$-0.304553\pi$
$97$	11.3489	1.15231	0.576153	+	0.817342i	$0.304553\pi$
$98$	3.19273	0.322514
$99$	16.5102	1.65934
$100$	6.69104	0.669104
$101$	5.38776	0.536102	0.268051	−	0.963405i	$-0.413620\pi$
$101$	5.38776	0.536102	0.268051	+	0.963405i	$0.413620\pi$
$102$	−13.2114	−1.30812
$103$	5.00653	0.493308	0.246654	−	0.969104i	$-0.420669\pi$
$103$	5.00653	0.493308	0.246654	+	0.969104i	$0.420669\pi$
$104$	3.20143	0.313926
$105$	21.7013	2.11783
$106$	6.37757	0.619444
$107$	13.0846	1.26494	0.632468	−	0.774586i	$-0.282042\pi$
$107$	13.0846	1.26494	0.632468	+	0.774586i	$0.282042\pi$
$108$	−14.8993	−1.43368
$109$	17.6274	1.68840	0.844199	−	0.536030i	$-0.180077\pi$
$109$	17.6274	1.68840	0.844199	+	0.536030i	$0.180077\pi$
$110$	7.44702	0.710045
$111$	−10.7084	−1.01639
$112$	1.95122	0.184373
$113$	0.898418	0.0845160	0.0422580	−	0.999107i	$-0.486545\pi$
$113$	0.898418	0.0845160	0.0422580	+	0.999107i	$0.486545\pi$
$114$	−15.0306	−1.40775
$115$	−10.6995	−0.997732
$116$	4.13521	0.383945
$117$	−24.2684	−2.24362
$118$	0.661247	0.0608727
$119$	−7.92507	−0.726490
$120$	−11.1219	−1.01529
$121$	−6.25636	−0.568760
$122$	−2.59032	−0.234517
$123$	−27.2942	−2.46104
$124$	−5.84993	−0.525339
$125$	−5.78204	−0.517161
$126$	−14.7912	−1.31771
$127$	−16.3065	−1.44697	−0.723485	−	0.690340i	$-0.757461\pi$
$127$	−16.3065	−1.44697	−0.723485	+	0.690340i	$0.757461\pi$
$128$	−1.00000	−0.0883883
$129$	19.6236	1.72776
$130$	−10.9464	−0.960062
$131$	11.3191	0.988956	0.494478	−	0.869190i	$-0.335359\pi$
$131$	11.3191	0.988956	0.494478	+	0.869190i	$0.335359\pi$
$132$	−7.08449	−0.616626
$133$	−9.01636	−0.781818
$134$	5.54616	0.479115
$135$	50.9438	4.38455
$136$	4.06159	0.348278
$137$	0.0617961	0.00527960	0.00263980	−	0.999997i	$-0.499160\pi$
$137$	0.0617961	0.00527960	0.00263980	+	0.999997i	$0.499160\pi$
$138$	10.1786	0.866463
$139$	7.39225	0.627002	0.313501	−	0.949588i	$-0.398498\pi$
$139$	7.39225	0.627002	0.313501	+	0.949588i	$0.398498\pi$
$140$	−6.67166	−0.563858
$141$	−8.55251	−0.720252
$142$	−12.0546	−1.01160
$143$	−6.97269	−0.583086
$144$	7.58049	0.631708
$145$	−14.1392	−1.17420
$146$	4.40887	0.364881
$147$	10.3852	0.856556
$148$	3.29208	0.270607
$149$	−20.2249	−1.65689	−0.828444	−	0.560072i	$-0.810773\pi$
$149$	−20.2249	−1.65689	−0.828444	+	0.560072i	$0.810773\pi$
$150$	21.7644	1.77706
$151$	−0.818862	−0.0666381	−0.0333190	−	0.999445i	$-0.510608\pi$
$151$	−0.818862	−0.0666381	−0.0333190	+	0.999445i	$0.510608\pi$
$152$	4.62087	0.374802
$153$	−30.7888	−2.48913
$154$	−4.24975	−0.342454
$155$	20.0022	1.60661
$156$	10.4135	0.833749
$157$	16.5448	1.32042	0.660208	−	0.751083i	$-0.270468\pi$
$157$	16.5448	1.32042	0.660208	+	0.751083i	$0.270468\pi$
$158$	−7.28000	−0.579166
$159$	20.7447	1.64516
$160$	3.41922	0.270313
$161$	6.10581	0.481205
$162$	−25.7224	−2.02094
$163$	−6.22369	−0.487477	−0.243738	−	0.969841i	$-0.578374\pi$
$163$	−6.22369	−0.487477	−0.243738	+	0.969841i	$0.578374\pi$
$164$	8.39109	0.655234
$165$	24.2234	1.88579
$166$	−10.6971	−0.830259
$167$	4.50630	0.348708	0.174354	−	0.984683i	$-0.444216\pi$
$167$	4.50630	0.348708	0.174354	+	0.984683i	$0.444216\pi$
$168$	6.34688	0.489672
$169$	−2.75082	−0.211602
$170$	−13.8875	−1.06512
$171$	−35.0285	−2.67870
$172$	−6.03290	−0.460004
$173$	8.14175	0.619006	0.309503	−	0.950898i	$-0.399837\pi$
$173$	8.14175	0.619006	0.309503	+	0.950898i	$0.399837\pi$
$174$	13.4509	1.01971
$175$	13.0557	0.986920
$176$	2.17799	0.164172
$177$	2.15088	0.161670
$178$	−3.25652	−0.244086
$179$	3.77829	0.282403	0.141201	−	0.989981i	$-0.454904\pi$
$179$	3.77829	0.282403	0.141201	+	0.989981i	$0.454904\pi$
$180$	−25.9193	−1.93191
$181$	−13.4669	−1.00099	−0.500493	−	0.865741i	$-0.666848\pi$
$181$	−13.4669	−1.00099	−0.500493	+	0.865741i	$0.666848\pi$
$182$	6.24671	0.463037
$183$	−8.42572	−0.622847
$184$	−3.12922	−0.230689
$185$	−11.2563	−0.827582
$186$	−19.0284	−1.39523
$187$	−8.84610	−0.646891
$188$	2.62930	0.191762
$189$	−29.0718	−2.11466
$190$	−15.7998	−1.14624
$191$	7.78638	0.563403	0.281701	−	0.959502i	$-0.409101\pi$
$191$	7.78638	0.563403	0.281701	+	0.959502i	$0.409101\pi$
$192$	−3.25277	−0.234748
$193$	−14.7663	−1.06290	−0.531452	−	0.847089i	$-0.678353\pi$
$193$	−14.7663	−1.06290	−0.531452	+	0.847089i	$0.678353\pi$
$194$	−11.3489	−0.814803
$195$	−35.6061	−2.54980
$196$	−3.19273	−0.228052
$197$	−26.0033	−1.85266	−0.926329	−	0.376714i	$-0.877054\pi$
$197$	−26.0033	−1.85266	−0.926329	+	0.376714i	$0.877054\pi$
$198$	−16.5102	−1.17333
$199$	−10.0493	−0.712379	−0.356190	−	0.934414i	$-0.615924\pi$
$199$	−10.0493	−0.712379	−0.356190	+	0.934414i	$0.615924\pi$
$200$	−6.69104	−0.473128
$201$	18.0404	1.27247
$202$	−5.38776	−0.379082
$203$	8.06872	0.566313
$204$	13.2114	0.924983
$205$	−28.6909	−2.00386
$206$	−5.00653	−0.348822
$207$	23.7210	1.64873
$208$	−3.20143	−0.221979
$209$	−10.0642	−0.696156
$210$	−21.7013	−1.49754
$211$	−15.4297	−1.06222	−0.531111	−	0.847302i	$-0.678225\pi$
$211$	−15.4297	−1.06222	−0.531111	+	0.847302i	$0.678225\pi$
$212$	−6.37757	−0.438013
$213$	−39.2108	−2.68668
$214$	−13.0846	−0.894445
$215$	20.6278	1.40680
$216$	14.8993	1.01377
$217$	−11.4145	−0.774868
$218$	−17.6274	−1.19388
$219$	14.3410	0.969077
$220$	−7.44702	−0.502078
$221$	13.0029	0.874670
$222$	10.7084	0.718699
$223$	−2.85825	−0.191403	−0.0957014	−	0.995410i	$-0.530509\pi$
$223$	−2.85825	−0.191403	−0.0957014	+	0.995410i	$0.530509\pi$
$224$	−1.95122	−0.130372
$225$	50.7214	3.38143
$226$	−0.898418	−0.0597619
$227$	−24.6180	−1.63396	−0.816978	−	0.576669i	$-0.804352\pi$
$227$	−24.6180	−1.63396	−0.816978	+	0.576669i	$0.804352\pi$
$228$	15.0306	0.995428
$229$	−26.0613	−1.72218	−0.861088	−	0.508455i	$-0.830217\pi$
$229$	−26.0613	−1.72218	−0.861088	+	0.508455i	$0.830217\pi$
$230$	10.6995	0.705503
$231$	−13.8234	−0.909515
$232$	−4.13521	−0.271490
$233$	−2.00701	−0.131484	−0.0657418	−	0.997837i	$-0.520941\pi$
$233$	−2.00701	−0.131484	−0.0657418	+	0.997837i	$0.520941\pi$
$234$	24.2684	1.58648
$235$	−8.99016	−0.586453
$236$	−0.661247	−0.0430435
$237$	−23.6802	−1.53819
$238$	7.92507	0.513706
$239$	3.11847	0.201717	0.100859	−	0.994901i	$-0.467841\pi$
$239$	3.11847	0.201717	0.100859	+	0.994901i	$0.467841\pi$
$240$	11.1219	0.717916
$241$	25.1686	1.62125	0.810626	−	0.585564i	$-0.199127\pi$
$241$	25.1686	1.62125	0.810626	+	0.585564i	$0.199127\pi$
$242$	6.25636	0.402174
$243$	−38.9711	−2.50000
$244$	2.59032	0.165829
$245$	10.9166	0.697437
$246$	27.2942	1.74022
$247$	14.7934	0.941283
$248$	5.84993	0.371471
$249$	−34.7953	−2.20506
$250$	5.78204	0.365688
$251$	−13.6442	−0.861215	−0.430607	−	0.902539i	$-0.641701\pi$
$251$	−13.6442	−0.861215	−0.430607	+	0.902539i	$0.641701\pi$
$252$	14.7912	0.931760
$253$	6.81541	0.428481
$254$	16.3065	1.02316
$255$	−45.1726	−2.82882
$256$	1.00000	0.0625000
$257$	−7.50008	−0.467842	−0.233921	−	0.972256i	$-0.575156\pi$
$257$	−7.50008	−0.467842	−0.233921	+	0.972256i	$0.575156\pi$
$258$	−19.6236	−1.22171
$259$	6.42359	0.399142
$260$	10.9464	0.678867
$261$	31.3469	1.94033
$262$	−11.3191	−0.699297
$263$	17.5260	1.08070	0.540351	−	0.841440i	$-0.318291\pi$
$263$	17.5260	1.08070	0.540351	+	0.841440i	$0.318291\pi$
$264$	7.08449	0.436020
$265$	21.8063	1.33955
$266$	9.01636	0.552829
$267$	−10.5927	−0.648263
$268$	−5.54616	−0.338786
$269$	−8.36175	−0.509825	−0.254912	−	0.966964i	$-0.582047\pi$
$269$	−8.36175	−0.509825	−0.254912	+	0.966964i	$0.582047\pi$
$270$	−50.9438	−3.10034
$271$	22.5206	1.36803	0.684014	−	0.729469i	$-0.260233\pi$
$271$	22.5206	1.36803	0.684014	+	0.729469i	$0.260233\pi$
$272$	−4.06159	−0.246270
$273$	20.3191	1.22977
$274$	−0.0617961	−0.00373324
$275$	14.5730	0.878786
$276$	−10.1786	−0.612682
$277$	12.5810	0.755922	0.377961	−	0.925822i	$-0.376625\pi$
$277$	12.5810	0.755922	0.377961	+	0.925822i	$0.376625\pi$
$278$	−7.39225	−0.443358
$279$	−44.3453	−2.65489
$280$	6.67166	0.398708
$281$	1.68418	0.100470	0.0502350	−	0.998737i	$-0.484003\pi$
$281$	1.68418	0.100470	0.0502350	+	0.998737i	$0.484003\pi$
$282$	8.55251	0.509295
$283$	−0.110676	−0.00657899	−0.00328949	−	0.999995i	$-0.501047\pi$
$283$	−0.110676	−0.00657899	−0.00328949	+	0.999995i	$0.501047\pi$
$284$	12.0546	0.715308
$285$	−51.3930	−3.04426
$286$	6.97269	0.412304
$287$	16.3729	0.966461
$288$	−7.58049	−0.446685
$289$	−0.503500	−0.0296176
$290$	14.1392	0.830281
$291$	−36.9153	−2.16401
$292$	−4.40887	−0.258010
$293$	−9.76545	−0.570504	−0.285252	−	0.958453i	$-0.592077\pi$
$293$	−9.76545	−0.570504	−0.285252	+	0.958453i	$0.592077\pi$
$294$	−10.3852	−0.605677
$295$	2.26095	0.131637
$296$	−3.29208	−0.191348
$297$	−32.4505	−1.88297
$298$	20.2249	1.17160
$299$	−10.0180	−0.579356
$300$	−21.7644	−1.25657
$301$	−11.7715	−0.678500
$302$	0.818862	0.0471202
$303$	−17.5251	−1.00679
$304$	−4.62087	−0.265025
$305$	−8.85688	−0.507144
$306$	30.7888	1.76008
$307$	−23.1225	−1.31967	−0.659836	−	0.751410i	$-0.729374\pi$
$307$	−23.1225	−1.31967	−0.659836	+	0.751410i	$0.729374\pi$
$308$	4.24975	0.242152
$309$	−16.2851	−0.926426
$310$	−20.0022	−1.13605
$311$	24.5086	1.38976	0.694878	−	0.719128i	$-0.255458\pi$
$311$	24.5086	1.38976	0.694878	+	0.719128i	$0.255458\pi$
$312$	−10.4135	−0.589549
$313$	0.514781	0.0290971	0.0145486	−	0.999894i	$-0.495369\pi$
$313$	0.514781	0.0290971	0.0145486	+	0.999894i	$0.495369\pi$
$314$	−16.5448	−0.933674
$315$	−50.5744	−2.84955
$316$	7.28000	0.409532
$317$	−5.99957	−0.336969	−0.168485	−	0.985704i	$-0.553887\pi$
$317$	−5.99957	−0.336969	−0.168485	+	0.985704i	$0.553887\pi$
$318$	−20.7447	−1.16331
$319$	9.00645	0.504264
$320$	−3.41922	−0.191140
$321$	−42.5612	−2.37553
$322$	−6.10581	−0.340264
$323$	18.7681	1.04428
$324$	25.7224	1.42902
$325$	−21.4209	−1.18822
$326$	6.22369	0.344698
$327$	−57.3378	−3.17079
$328$	−8.39109	−0.463320
$329$	5.13036	0.282846
$330$	−24.2234	−1.33345
$331$	27.5078	1.51197	0.755984	−	0.654590i	$-0.227159\pi$
$331$	27.5078	1.51197	0.755984	+	0.654590i	$0.227159\pi$
$332$	10.6971	0.587082
$333$	24.9556	1.36756
$334$	−4.50630	−0.246574
$335$	18.9635	1.03609
$336$	−6.34688	−0.346250
$337$	31.6121	1.72202	0.861010	−	0.508588i	$-0.169832\pi$
$337$	31.6121	1.72202	0.861010	+	0.508588i	$0.169832\pi$
$338$	2.75082	0.149625
$339$	−2.92234	−0.158720
$340$	13.8875	0.753153
$341$	−12.7411	−0.689968
$342$	35.0285	1.89412
$343$	−19.8883	−1.07387
$344$	6.03290	0.325272
$345$	34.8029	1.87373
$346$	−8.14175	−0.437703
$347$	−26.4559	−1.42023	−0.710113	−	0.704087i	$-0.751356\pi$
$347$	−26.4559	−1.42023	−0.710113	+	0.704087i	$0.751356\pi$
$348$	−13.4509	−0.721043
$349$	−34.5705	−1.85052	−0.925259	−	0.379337i	$-0.876152\pi$
$349$	−34.5705	−1.85052	−0.925259	+	0.379337i	$0.876152\pi$
$350$	−13.0557	−0.697858
$351$	47.6990	2.54599
$352$	−2.17799	−0.116087
$353$	−7.95568	−0.423438	−0.211719	−	0.977331i	$-0.567906\pi$
$353$	−7.95568	−0.423438	−0.211719	+	0.977331i	$0.567906\pi$
$354$	−2.15088	−0.114318
$355$	−41.2173	−2.18759
$356$	3.25652	0.172595
$357$	25.7784	1.36434
$358$	−3.77829	−0.199689
$359$	−14.1995	−0.749418	−0.374709	−	0.927142i	$-0.622257\pi$
$359$	−14.1995	−0.749418	−0.374709	+	0.927142i	$0.622257\pi$
$360$	25.9193	1.36607
$361$	2.35248	0.123815
$362$	13.4669	0.707803
$363$	20.3505	1.06812
$364$	−6.24671	−0.327417
$365$	15.0749	0.789056
$366$	8.42572	0.440420
$367$	−1.32578	−0.0692051	−0.0346026	−	0.999401i	$-0.511017\pi$
$367$	−1.32578	−0.0692051	−0.0346026	+	0.999401i	$0.511017\pi$
$368$	3.12922	0.163122
$369$	63.6086	3.31133
$370$	11.2563	0.585189
$371$	−12.4441	−0.646064
$372$	19.0284	0.986579
$373$	−31.7789	−1.64545	−0.822725	−	0.568440i	$-0.807547\pi$
$373$	−31.7789	−1.64545	−0.822725	+	0.568440i	$0.807547\pi$
$374$	8.84610	0.457421
$375$	18.8076	0.971222
$376$	−2.62930	−0.135596
$377$	−13.2386	−0.681823
$378$	29.0718	1.49529
$379$	29.3730	1.50879	0.754395	−	0.656421i	$-0.227930\pi$
$379$	29.3730	1.50879	0.754395	+	0.656421i	$0.227930\pi$
$380$	15.7998	0.810511
$381$	53.0413	2.71739
$382$	−7.78638	−0.398386
$383$	17.1890	0.878317	0.439158	−	0.898410i	$-0.355277\pi$
$383$	17.1890	0.878317	0.439158	+	0.898410i	$0.355277\pi$
$384$	3.25277	0.165992
$385$	−14.5308	−0.740558
$386$	14.7663	0.751586
$387$	−45.7323	−2.32471
$388$	11.3489	0.576153
$389$	14.1614	0.718010	0.359005	−	0.933336i	$-0.383116\pi$
$389$	14.1614	0.718010	0.359005	+	0.933336i	$0.383116\pi$
$390$	35.6061	1.80298
$391$	−12.7096	−0.642753
$392$	3.19273	0.161257
$393$	−36.8184	−1.85724
$394$	26.0033	1.31003
$395$	−24.8919	−1.25245
$396$	16.5102	0.829670
$397$	2.73482	0.137257	0.0686284	−	0.997642i	$-0.478138\pi$
$397$	2.73482	0.137257	0.0686284	+	0.997642i	$0.478138\pi$
$398$	10.0493	0.503728
$399$	29.3281	1.46824
$400$	6.69104	0.334552
$401$	25.8431	1.29054	0.645271	−	0.763954i	$-0.276745\pi$
$401$	25.8431	1.29054	0.645271	+	0.763954i	$0.276745\pi$
$402$	−18.0404	−0.899772
$403$	18.7282	0.932916
$404$	5.38776	0.268051
$405$	−87.9504	−4.37029
$406$	−8.06872	−0.400444
$407$	7.17012	0.355409
$408$	−13.2114	−0.654062
$409$	−26.4366	−1.30720	−0.653602	−	0.756838i	$-0.726743\pi$
$409$	−26.4366	−1.30720	−0.653602	+	0.756838i	$0.726743\pi$
$410$	28.6909	1.41694
$411$	−0.201008	−0.00991501
$412$	5.00653	0.246654
$413$	−1.29024	−0.0634886
$414$	−23.7210	−1.16583
$415$	−36.5759	−1.79544
$416$	3.20143	0.156963
$417$	−24.0453	−1.17750
$418$	10.0642	0.492257
$419$	−27.1347	−1.32562	−0.662809	−	0.748788i	$-0.730636\pi$
$419$	−27.1347	−1.32562	−0.662809	+	0.748788i	$0.730636\pi$
$420$	21.7013	1.05892
$421$	15.4906	0.754964	0.377482	−	0.926017i	$-0.376790\pi$
$421$	15.4906	0.754964	0.377482	+	0.926017i	$0.376790\pi$
$422$	15.4297	0.751105
$423$	19.9314	0.969099
$424$	6.37757	0.309722
$425$	−27.1763	−1.31824
$426$	39.2108	1.89977
$427$	5.05430	0.244595
$428$	13.0846	0.632468
$429$	22.6805	1.09503
$430$	−20.6278	−0.994760
$431$	0.820468	0.0395206	0.0197603	−	0.999805i	$-0.493710\pi$
$431$	0.820468	0.0395206	0.0197603	+	0.999805i	$0.493710\pi$
$432$	−14.8993	−0.716841
$433$	−16.2787	−0.782302	−0.391151	−	0.920326i	$-0.627923\pi$
$433$	−16.2787	−0.782302	−0.391151	+	0.920326i	$0.627923\pi$
$434$	11.4145	0.547914
$435$	45.9915	2.20512
$436$	17.6274	0.844199
$437$	−14.4597	−0.691703
$438$	−14.3410	−0.685241
$439$	30.0722	1.43527	0.717635	−	0.696420i	$-0.245225\pi$
$439$	30.0722	1.43527	0.717635	+	0.696420i	$0.245225\pi$
$440$	7.44702	0.355023
$441$	−24.2024	−1.15250
$442$	−13.0029	−0.618485
$443$	13.5189	0.642302	0.321151	−	0.947028i	$-0.395930\pi$
$443$	13.5189	0.642302	0.321151	+	0.947028i	$0.395930\pi$
$444$	−10.7084	−0.508197
$445$	−11.1347	−0.527838
$446$	2.85825	0.135342
$447$	65.7869	3.11161
$448$	1.95122	0.0921867
$449$	−35.6385	−1.68188	−0.840942	−	0.541125i	$-0.817998\pi$
$449$	−35.6385	−1.68188	−0.840942	+	0.541125i	$0.817998\pi$
$450$	−50.7214	−2.39103
$451$	18.2757	0.860569
$452$	0.898418	0.0422580
$453$	2.66357	0.125145
$454$	24.6180	1.15538
$455$	21.3589	1.00132
$456$	−15.0306	−0.703874
$457$	−3.41327	−0.159666	−0.0798331	−	0.996808i	$-0.525439\pi$
$457$	−3.41327	−0.159666	−0.0798331	+	0.996808i	$0.525439\pi$
$458$	26.0613	1.21776
$459$	60.5147	2.82458
$460$	−10.6995	−0.498866
$461$	27.6029	1.28560	0.642798	−	0.766036i	$-0.277774\pi$
$461$	27.6029	1.28560	0.642798	+	0.766036i	$0.277774\pi$
$462$	13.8234	0.643124
$463$	2.32107	0.107869	0.0539347	−	0.998544i	$-0.482824\pi$
$463$	2.32107	0.107869	0.0539347	+	0.998544i	$0.482824\pi$
$464$	4.13521	0.191972
$465$	−65.0624	−3.01720
$466$	2.00701	0.0929730
$467$	11.2051	0.518509	0.259254	−	0.965809i	$-0.416523\pi$
$467$	11.2051	0.518509	0.259254	+	0.965809i	$0.416523\pi$
$468$	−24.2684	−1.12181
$469$	−10.8218	−0.499705
$470$	8.99016	0.414685
$471$	−53.8162	−2.47972
$472$	0.661247	0.0304363
$473$	−13.1396	−0.604159
$474$	23.6802	1.08767
$475$	−30.9185	−1.41864
$476$	−7.92507	−0.363245
$477$	−48.3451	−2.21357
$478$	−3.11847	−0.142635
$479$	14.0297	0.641032	0.320516	−	0.947243i	$-0.396144\pi$
$479$	14.0297	0.641032	0.320516	+	0.947243i	$0.396144\pi$
$480$	−11.1219	−0.507644
$481$	−10.5394	−0.480554
$482$	−25.1686	−1.14640
$483$	−19.8608	−0.903697
$484$	−6.25636	−0.284380
$485$	−38.8043	−1.76201
$486$	38.9711	1.76776
$487$	30.8187	1.39653	0.698264	−	0.715840i	$-0.253956\pi$
$487$	30.8187	1.39653	0.698264	+	0.715840i	$0.253956\pi$
$488$	−2.59032	−0.117258
$489$	20.2442	0.915475
$490$	−10.9166	−0.493163
$491$	41.1231	1.85586	0.927929	−	0.372756i	$-0.121587\pi$
$491$	41.1231	1.85586	0.927929	+	0.372756i	$0.121587\pi$
$492$	−27.2942	−1.23052
$493$	−16.7955	−0.756432
$494$	−14.7934	−0.665588
$495$	−56.4521	−2.53733
$496$	−5.84993	−0.262669
$497$	23.5212	1.05507
$498$	34.7953	1.55922
$499$	−0.355755	−0.0159258	−0.00796289	−	0.999968i	$-0.502535\pi$
$499$	−0.355755	−0.0159258	−0.00796289	+	0.999968i	$0.502535\pi$
$500$	−5.78204	−0.258581
$501$	−14.6580	−0.654869
$502$	13.6442	0.608971
$503$	−24.1978	−1.07893	−0.539463	−	0.842009i	$-0.681373\pi$
$503$	−24.1978	−1.07893	−0.539463	+	0.842009i	$0.681373\pi$
$504$	−14.7912	−0.658854
$505$	−18.4219	−0.819765
$506$	−6.81541	−0.302982
$507$	8.94778	0.397385
$508$	−16.3065	−0.723485
$509$	30.2138	1.33920	0.669602	−	0.742720i	$-0.266465\pi$
$509$	30.2138	1.33920	0.669602	+	0.742720i	$0.266465\pi$
$510$	45.1726	2.00028
$511$	−8.60270	−0.380561
$512$	−1.00000	−0.0441942
$513$	68.8477	3.03970
$514$	7.50008	0.330814
$515$	−17.1184	−0.754328
$516$	19.6236	0.863882
$517$	5.72660	0.251855
$518$	−6.42359	−0.282236
$519$	−26.4832	−1.16248
$520$	−10.9464	−0.480031
$521$	−26.4417	−1.15843	−0.579216	−	0.815174i	$-0.696641\pi$
$521$	−26.4417	−1.15843	−0.579216	+	0.815174i	$0.696641\pi$
$522$	−31.3469	−1.37202
$523$	−11.9527	−0.522657	−0.261329	−	0.965250i	$-0.584161\pi$
$523$	−11.9527	−0.522657	−0.261329	+	0.965250i	$0.584161\pi$
$524$	11.3191	0.494478
$525$	−42.4672	−1.85342
$526$	−17.5260	−0.764172
$527$	23.7600	1.03500
$528$	−7.08449	−0.308313
$529$	−13.2080	−0.574260
$530$	−21.8063	−0.947205
$531$	−5.01257	−0.217527
$532$	−9.01636	−0.390909
$533$	−26.8635	−1.16359
$534$	10.5927	0.458391
$535$	−44.7391	−1.93424
$536$	5.54616	0.239558
$537$	−12.2899	−0.530348
$538$	8.36175	0.360501
$539$	−6.95372	−0.299518
$540$	50.9438	2.19227
$541$	−33.0037	−1.41894	−0.709471	−	0.704735i	$-0.751066\pi$
$541$	−33.0037	−1.41894	−0.709471	+	0.704735i	$0.751066\pi$
$542$	−22.5206	−0.967342
$543$	43.8046	1.87984
$544$	4.06159	0.174139
$545$	−60.2719	−2.58176
$546$	−20.3191	−0.869577
$547$	1.17967	0.0504391	0.0252196	−	0.999682i	$-0.491972\pi$
$547$	1.17967	0.0504391	0.0252196	+	0.999682i	$0.491972\pi$
$548$	0.0617961	0.00263980
$549$	19.6359	0.838041
$550$	−14.5730	−0.621396
$551$	−19.1083	−0.814041
$552$	10.1786	0.433231
$553$	14.2049	0.604054
$554$	−12.5810	−0.534517
$555$	36.6142	1.55419
$556$	7.39225	0.313501
$557$	15.5139	0.657343	0.328671	−	0.944444i	$-0.393399\pi$
$557$	15.5139	0.657343	0.328671	+	0.944444i	$0.393399\pi$
$558$	44.3453	1.87729
$559$	19.3139	0.816892
$560$	−6.67166	−0.281929
$561$	28.7743	1.21485
$562$	−1.68418	−0.0710430
$563$	−1.12712	−0.0475024	−0.0237512	−	0.999718i	$-0.507561\pi$
$563$	−1.12712	−0.0475024	−0.0237512	+	0.999718i	$0.507561\pi$
$564$	−8.55251	−0.360126
$565$	−3.07189	−0.129235
$566$	0.110676	0.00465205
$567$	50.1901	2.10779
$568$	−12.0546	−0.505799
$569$	2.17205	0.0910572	0.0455286	−	0.998963i	$-0.485503\pi$
$569$	2.17205	0.0910572	0.0455286	+	0.998963i	$0.485503\pi$
$570$	51.3930	2.15261
$571$	−12.7106	−0.531921	−0.265961	−	0.963984i	$-0.585689\pi$
$571$	−12.7106	−0.531921	−0.265961	+	0.963984i	$0.585689\pi$
$572$	−6.97269	−0.291543
$573$	−25.3273	−1.05806
$574$	−16.3729	−0.683391
$575$	20.9378	0.873165
$576$	7.58049	0.315854
$577$	17.2381	0.717632	0.358816	−	0.933408i	$-0.383181\pi$
$577$	17.2381	0.717632	0.358816	+	0.933408i	$0.383181\pi$
$578$	0.503500	0.0209428
$579$	48.0314	1.99612
$580$	−14.1392	−0.587098
$581$	20.8725	0.865938
$582$	36.9153	1.53019
$583$	−13.8903	−0.575276
$584$	4.40887	0.182440
$585$	82.9791	3.43076
$586$	9.76545	0.403407
$587$	33.6977	1.39085	0.695427	−	0.718596i	$-0.255215\pi$
$587$	33.6977	1.39085	0.695427	+	0.718596i	$0.255215\pi$
$588$	10.3852	0.428278
$589$	27.0318	1.11383
$590$	−2.26095	−0.0930816
$591$	84.5827	3.47927
$592$	3.29208	0.135304
$593$	−40.9006	−1.67959	−0.839793	−	0.542906i	$-0.817324\pi$
$593$	−40.9006	−1.67959	−0.839793	+	0.542906i	$0.817324\pi$
$594$	32.4505	1.33146
$595$	27.0975	1.11089
$596$	−20.2249	−0.828444
$597$	32.6882	1.33784
$598$	10.0180	0.409666
$599$	−2.15533	−0.0880644	−0.0440322	−	0.999030i	$-0.514020\pi$
$599$	−2.15533	−0.0880644	−0.0440322	+	0.999030i	$0.514020\pi$
$600$	21.7644	0.888528
$601$	−42.7923	−1.74553	−0.872767	−	0.488138i	$-0.837676\pi$
$601$	−42.7923	−1.74553	−0.872767	+	0.488138i	$0.837676\pi$
$602$	11.7715	0.479772
$603$	−42.0426	−1.71211
$604$	−0.818862	−0.0333190
$605$	21.3919	0.869703
$606$	17.5251	0.711910
$607$	14.0375	0.569763	0.284881	−	0.958563i	$-0.408046\pi$
$607$	14.0375	0.569763	0.284881	+	0.958563i	$0.408046\pi$
$608$	4.62087	0.187401
$609$	−26.2457	−1.06353
$610$	8.85688	0.358605
$611$	−8.41754	−0.340537
$612$	−30.7888	−1.24456
$613$	−33.4396	−1.35061	−0.675306	−	0.737538i	$-0.735988\pi$
$613$	−33.4396	−1.35061	−0.675306	+	0.737538i	$0.735988\pi$
$614$	23.1225	0.933149
$615$	93.3250	3.76323
$616$	−4.24975	−0.171227
$617$	−25.7892	−1.03824	−0.519118	−	0.854703i	$-0.673739\pi$
$617$	−25.7892	−1.03824	−0.519118	+	0.854703i	$0.673739\pi$
$618$	16.2851	0.655082
$619$	1.06531	0.0428185	0.0214093	−	0.999771i	$-0.493185\pi$
$619$	1.06531	0.0428185	0.0214093	+	0.999771i	$0.493185\pi$
$620$	20.0022	0.803306
$621$	−46.6231	−1.87092
$622$	−24.5086	−0.982706
$623$	6.35420	0.254576
$624$	10.4135	0.416874
$625$	−13.6852	−0.547407
$626$	−0.514781	−0.0205748
$627$	32.7365	1.30737
$628$	16.5448	0.660208
$629$	−13.3711	−0.533140
$630$	50.5744	2.01493
$631$	3.34526	0.133173	0.0665863	−	0.997781i	$-0.478789\pi$
$631$	3.34526	0.133173	0.0665863	+	0.997781i	$0.478789\pi$
$632$	−7.28000	−0.289583
$633$	50.1891	1.99484
$634$	5.99957	0.238273
$635$	55.7556	2.21259
$636$	20.7447	0.822582
$637$	10.2213	0.404983
$638$	−9.00645	−0.356569
$639$	91.3797	3.61493
$640$	3.41922	0.135156
$641$	−14.8086	−0.584905	−0.292453	−	0.956280i	$-0.594471\pi$
$641$	−14.8086	−0.584905	−0.292453	+	0.956280i	$0.594471\pi$
$642$	42.5612	1.67976
$643$	−5.03197	−0.198442	−0.0992208	−	0.995065i	$-0.531635\pi$
$643$	−5.03197	−0.198442	−0.0992208	+	0.995065i	$0.531635\pi$
$644$	6.10581	0.240603
$645$	−67.0974	−2.64196
$646$	−18.7681	−0.738421
$647$	−44.8426	−1.76295	−0.881473	−	0.472234i	$-0.843448\pi$
$647$	−44.8426	−1.76295	−0.881473	+	0.472234i	$0.843448\pi$
$648$	−25.7224	−1.01047
$649$	−1.44019	−0.0565323
$650$	21.4209	0.840198
$651$	37.1288	1.45519
$652$	−6.22369	−0.243738
$653$	−1.45905	−0.0570972	−0.0285486	−	0.999592i	$-0.509089\pi$
$653$	−1.45905	−0.0570972	−0.0285486	+	0.999592i	$0.509089\pi$
$654$	57.3378	2.24209
$655$	−38.7025	−1.51223
$656$	8.39109	0.327617
$657$	−33.4214	−1.30389
$658$	−5.13036	−0.200002
$659$	12.8382	0.500105	0.250052	−	0.968232i	$-0.419552\pi$
$659$	12.8382	0.500105	0.250052	+	0.968232i	$0.419552\pi$
$660$	24.2234	0.942895
$661$	−31.7692	−1.23568	−0.617840	−	0.786304i	$-0.711992\pi$
$661$	−31.7692	−1.23568	−0.617840	+	0.786304i	$0.711992\pi$
$662$	−27.5078	−1.06912
$663$	−42.2954	−1.64262
$664$	−10.6971	−0.415130
$665$	30.8289	1.19549
$666$	−24.9556	−0.967009
$667$	12.9400	0.501039
$668$	4.50630	0.174354
$669$	9.29723	0.359452
$670$	−18.9635	−0.732625
$671$	5.64170	0.217795
$672$	6.34688	0.244836
$673$	−39.4841	−1.52200	−0.761001	−	0.648751i	$-0.775292\pi$
$673$	−39.4841	−1.52200	−0.761001	+	0.648751i	$0.775292\pi$
$674$	−31.6121	−1.21765
$675$	−99.6916	−3.83713
$676$	−2.75082	−0.105801
$677$	8.83845	0.339689	0.169845	−	0.985471i	$-0.445673\pi$
$677$	8.83845	0.339689	0.169845	+	0.985471i	$0.445673\pi$
$678$	2.92234	0.112232
$679$	22.1442	0.849818
$680$	−13.8875	−0.532559
$681$	80.0767	3.06855
$682$	12.7411	0.487881
$683$	2.25808	0.0864029	0.0432014	−	0.999066i	$-0.486244\pi$
$683$	2.25808	0.0864029	0.0432014	+	0.999066i	$0.486244\pi$
$684$	−35.0285	−1.33935
$685$	−0.211294	−0.00807314
$686$	19.8883	0.759338
$687$	84.7712	3.23422
$688$	−6.03290	−0.230002
$689$	20.4174	0.777839
$690$	−34.8029	−1.32493
$691$	−32.0776	−1.22029	−0.610145	−	0.792290i	$-0.708889\pi$
$691$	−32.0776	−1.22029	−0.610145	+	0.792290i	$0.708889\pi$
$692$	8.14175	0.309503
$693$	32.2152	1.22375
$694$	26.4559	1.00425
$695$	−25.2757	−0.958762
$696$	13.4509	0.509854
$697$	−34.0811	−1.29092
$698$	34.5705	1.30851
$699$	6.52834	0.246924
$700$	13.0557	0.493460
$701$	−45.0779	−1.70257	−0.851284	−	0.524705i	$-0.824176\pi$
$701$	−45.0779	−1.70257	−0.851284	+	0.524705i	$0.824176\pi$
$702$	−47.6990	−1.80028
$703$	−15.2123	−0.573742
$704$	2.17799	0.0820861
$705$	29.2429	1.10135
$706$	7.95568	0.299416
$707$	10.5127	0.395372
$708$	2.15088	0.0808350
$709$	−39.1872	−1.47171	−0.735853	−	0.677141i	$-0.763219\pi$
$709$	−39.1872	−1.47171	−0.735853	+	0.677141i	$0.763219\pi$
$710$	41.2173	1.54686
$711$	55.1860	2.06964
$712$	−3.25652	−0.122043
$713$	−18.3057	−0.685555
$714$	−25.7784	−0.964732
$715$	23.8411	0.891608
$716$	3.77829	0.141201
$717$	−10.1437	−0.378822
$718$	14.1995	0.529919
$719$	−48.2647	−1.79997	−0.899985	−	0.435921i	$-0.856423\pi$
$719$	−48.2647	−1.79997	−0.899985	+	0.435921i	$0.856423\pi$
$720$	−25.9193	−0.965957
$721$	9.76886	0.363812
$722$	−2.35248	−0.0875502
$723$	−81.8676	−3.04469
$724$	−13.4669	−0.500493
$725$	27.6689	1.02760
$726$	−20.3505	−0.755277
$727$	−8.70890	−0.322995	−0.161498	−	0.986873i	$-0.551632\pi$
$727$	−8.70890	−0.322995	−0.161498	+	0.986873i	$0.551632\pi$
$728$	6.24671	0.231519
$729$	49.5967	1.83691
$730$	−15.0749	−0.557947
$731$	24.5032	0.906282
$732$	−8.42572	−0.311424
$733$	9.87302	0.364668	0.182334	−	0.983237i	$-0.441635\pi$
$733$	9.87302	0.364668	0.182334	+	0.983237i	$0.441635\pi$
$734$	1.32578	0.0489354
$735$	−35.5092	−1.30978
$736$	−3.12922	−0.115345
$737$	−12.0795	−0.444953
$738$	−63.6086	−2.34146
$739$	35.9484	1.32238	0.661192	−	0.750217i	$-0.270051\pi$
$739$	35.9484	1.32238	0.661192	+	0.750217i	$0.270051\pi$
$740$	−11.2563	−0.413791
$741$	−48.1196	−1.76772
$742$	12.4441	0.456836
$743$	−23.9951	−0.880295	−0.440147	−	0.897926i	$-0.645074\pi$
$743$	−23.9951	−0.880295	−0.440147	+	0.897926i	$0.645074\pi$
$744$	−19.0284	−0.697617
$745$	69.1533	2.53358
$746$	31.7789	1.16351
$747$	81.0896	2.96691
$748$	−8.84610	−0.323445
$749$	25.5310	0.932882
$750$	−18.8076	−0.686757
$751$	−47.1957	−1.72220	−0.861098	−	0.508439i	$-0.830223\pi$
$751$	−47.1957	−1.72220	−0.861098	+	0.508439i	$0.830223\pi$
$752$	2.62930	0.0958809
$753$	44.3814	1.61735
$754$	13.2386	0.482122
$755$	2.79987	0.101898
$756$	−29.0718	−1.05733
$757$	18.5241	0.673270	0.336635	−	0.941635i	$-0.390711\pi$
$757$	18.5241	0.673270	0.336635	+	0.941635i	$0.390711\pi$
$758$	−29.3730	−1.06688
$759$	−22.1689	−0.804682
$760$	−15.7998	−0.573118
$761$	12.3463	0.447552	0.223776	−	0.974641i	$-0.428162\pi$
$761$	12.3463	0.447552	0.223776	+	0.974641i	$0.428162\pi$
$762$	−53.0413	−1.92149
$763$	34.3950	1.24518
$764$	7.78638	0.281701
$765$	105.274	3.80618
$766$	−17.1890	−0.621064
$767$	2.11694	0.0764382
$768$	−3.25277	−0.117374
$769$	44.6215	1.60909	0.804546	−	0.593890i	$-0.202409\pi$
$769$	44.6215	1.60909	0.804546	+	0.593890i	$0.202409\pi$
$770$	14.5308	0.523654
$771$	24.3960	0.878601
$772$	−14.7663	−0.531452
$773$	−7.71786	−0.277592	−0.138796	−	0.990321i	$-0.544323\pi$
$773$	−7.71786	−0.277592	−0.138796	+	0.990321i	$0.544323\pi$
$774$	45.7323	1.64382
$775$	−39.1421	−1.40603
$776$	−11.3489	−0.407402
$777$	−20.8944	−0.749583
$778$	−14.1614	−0.507710
$779$	−38.7742	−1.38923
$780$	−35.6061	−1.27490
$781$	26.2548	0.939470
$782$	12.7096	0.454495
$783$	−61.6116	−2.20182
$784$	−3.19273	−0.114026
$785$	−56.5701	−2.01907
$786$	36.8184	1.31327
$787$	19.8714	0.708339	0.354170	−	0.935181i	$-0.384764\pi$
$787$	19.8714	0.708339	0.354170	+	0.935181i	$0.384764\pi$
$788$	−26.0033	−0.926329
$789$	−57.0081	−2.02954
$790$	24.8919	0.885614
$791$	1.75301	0.0623300
$792$	−16.5102	−0.586665
$793$	−8.29275	−0.294484
$794$	−2.73482	−0.0970552
$795$	−70.9308	−2.51565
$796$	−10.0493	−0.356190
$797$	−39.3603	−1.39421	−0.697106	−	0.716968i	$-0.745529\pi$
$797$	−39.3603	−1.39421	−0.697106	+	0.716968i	$0.745529\pi$
$798$	−29.3281	−1.03820
$799$	−10.6792	−0.377801
$800$	−6.69104	−0.236564
$801$	24.6860	0.872238
$802$	−25.8431	−0.912551
$803$	−9.60248	−0.338864
$804$	18.0404	0.636235
$805$	−20.8771	−0.735821
$806$	−18.7282	−0.659671
$807$	27.1988	0.957444
$808$	−5.38776	−0.189541
$809$	−22.3118	−0.784442	−0.392221	−	0.919871i	$-0.628293\pi$
$809$	−22.3118	−0.784442	−0.392221	+	0.919871i	$0.628293\pi$
$810$	87.9504	3.09026
$811$	8.85288	0.310867	0.155433	−	0.987846i	$-0.450323\pi$
$811$	8.85288	0.310867	0.155433	+	0.987846i	$0.450323\pi$
$812$	8.06872	0.283157
$813$	−73.2542	−2.56914
$814$	−7.17012	−0.251312
$815$	21.2801	0.745411
$816$	13.2114	0.462491
$817$	27.8773	0.975302
$818$	26.4366	0.924333
$819$	−47.3532	−1.65465
$820$	−28.6909	−1.00193
$821$	−36.4023	−1.27045	−0.635224	−	0.772328i	$-0.719092\pi$
$821$	−36.4023	−1.27045	−0.635224	+	0.772328i	$0.719092\pi$
$822$	0.201008	0.00701097
$823$	−32.7752	−1.14247	−0.571235	−	0.820787i	$-0.693536\pi$
$823$	−32.7752	−1.14247	−0.571235	+	0.820787i	$0.693536\pi$
$824$	−5.00653	−0.174411
$825$	−47.4026	−1.65035
$826$	1.29024	0.0448932
$827$	18.6671	0.649120	0.324560	−	0.945865i	$-0.394784\pi$
$827$	18.6671	0.649120	0.324560	+	0.945865i	$0.394784\pi$
$828$	23.7210	0.824363
$829$	−39.2312	−1.36256	−0.681278	−	0.732025i	$-0.738576\pi$
$829$	−39.2312	−1.36256	−0.681278	+	0.732025i	$0.738576\pi$
$830$	36.5759	1.26957
$831$	−40.9232	−1.41961
$832$	−3.20143	−0.110990
$833$	12.9675	0.449298
$834$	24.0453	0.832619
$835$	−15.4080	−0.533217
$836$	−10.0642	−0.348078
$837$	87.1597	3.01268
$838$	27.1347	0.937354
$839$	−17.9160	−0.618529	−0.309264	−	0.950976i	$-0.600083\pi$
$839$	−17.9160	−0.618529	−0.309264	+	0.950976i	$0.600083\pi$
$840$	−21.7013	−0.748768
$841$	−11.9000	−0.410346
$842$	−15.4906	−0.533840
$843$	−5.47826	−0.188681
$844$	−15.4297	−0.531111
$845$	9.40566	0.323564
$846$	−19.9314	−0.685256
$847$	−12.2076	−0.419457
$848$	−6.37757	−0.219007
$849$	0.360002	0.0123552
$850$	27.1763	0.932138
$851$	10.3017	0.353136
$852$	−39.2108	−1.34334
$853$	−14.4134	−0.493504	−0.246752	−	0.969079i	$-0.579363\pi$
$853$	−14.4134	−0.493504	−0.246752	+	0.969079i	$0.579363\pi$
$854$	−5.05430	−0.172955
$855$	119.770	4.09605
$856$	−13.0846	−0.447223
$857$	−30.9779	−1.05819	−0.529093	−	0.848564i	$-0.677468\pi$
$857$	−30.9779	−1.05819	−0.529093	+	0.848564i	$0.677468\pi$
$858$	−22.6805	−0.774301
$859$	24.0623	0.820996	0.410498	−	0.911862i	$-0.365355\pi$
$859$	24.0623	0.820996	0.410498	+	0.911862i	$0.365355\pi$
$860$	20.6278	0.703402
$861$	−53.2572	−1.81500
$862$	−0.820468	−0.0279453
$863$	31.6173	1.07627	0.538133	−	0.842860i	$-0.319130\pi$
$863$	31.6173	1.07627	0.538133	+	0.842860i	$0.319130\pi$
$864$	14.8993	0.506883
$865$	−27.8384	−0.946534
$866$	16.2787	0.553171
$867$	1.63777	0.0556215
$868$	−11.4145	−0.387434
$869$	15.8558	0.537870
$870$	−45.9915	−1.55926
$871$	17.7557	0.601628
$872$	−17.6274	−0.596939
$873$	86.0302	2.91168
$874$	14.4597	0.489108
$875$	−11.2821	−0.381403
$876$	14.3410	0.484539
$877$	42.6544	1.44034	0.720168	−	0.693800i	$-0.244065\pi$
$877$	42.6544	1.44034	0.720168	+	0.693800i	$0.244065\pi$
$878$	−30.0722	−1.01489
$879$	31.7647	1.07140
$880$	−7.44702	−0.251039
$881$	46.1019	1.55321	0.776607	−	0.629986i	$-0.216939\pi$
$881$	46.1019	1.55321	0.776607	+	0.629986i	$0.216939\pi$
$882$	24.2024	0.814938
$883$	−17.8733	−0.601485	−0.300742	−	0.953705i	$-0.597234\pi$
$883$	−17.8733	−0.601485	−0.300742	+	0.953705i	$0.597234\pi$
$884$	13.0029	0.437335
$885$	−7.35433	−0.247213
$886$	−13.5189	−0.454176
$887$	31.6779	1.06364	0.531821	−	0.846857i	$-0.321508\pi$
$887$	31.6779	1.06364	0.531821	+	0.846857i	$0.321508\pi$
$888$	10.7084	0.359349
$889$	−31.8177	−1.06713
$890$	11.1347	0.373238
$891$	56.0231	1.87684
$892$	−2.85825	−0.0957014
$893$	−12.1497	−0.406574
$894$	−65.7869	−2.20024
$895$	−12.9188	−0.431827
$896$	−1.95122	−0.0651858
$897$	32.5862	1.08802
$898$	35.6385	1.18927
$899$	−24.1907	−0.806805
$900$	50.7214	1.69071
$901$	25.9031	0.862956
$902$	−18.2757	−0.608514
$903$	38.2901	1.27421
$904$	−0.898418	−0.0298809
$905$	46.0462	1.53063
$906$	−2.66357	−0.0884911
$907$	59.0551	1.96089	0.980445	−	0.196791i	$-0.0630521\pi$
$907$	59.0551	1.96089	0.980445	+	0.196791i	$0.0630521\pi$
$908$	−24.6180	−0.816978
$909$	40.8419	1.35464
$910$	−21.3589	−0.708040
$911$	−20.4037	−0.676004	−0.338002	−	0.941145i	$-0.609751\pi$
$911$	−20.4037	−0.676004	−0.338002	+	0.941145i	$0.609751\pi$
$912$	15.0306	0.497714
$913$	23.2983	0.771060
$914$	3.41327	0.112901
$915$	28.8094	0.952408
$916$	−26.0613	−0.861088
$917$	22.0861	0.729348
$918$	−60.5147	−1.99728
$919$	47.4406	1.56492	0.782460	−	0.622701i	$-0.213965\pi$
$919$	47.4406	1.56492	0.782460	+	0.622701i	$0.213965\pi$
$920$	10.6995	0.352752
$921$	75.2121	2.47832
$922$	−27.6029	−0.909053
$923$	−38.5920	−1.27027
$924$	−13.8234	−0.454757
$925$	22.0274	0.724258
$926$	−2.32107	−0.0762752
$927$	37.9520	1.24651
$928$	−4.13521	−0.135745
$929$	14.4483	0.474034	0.237017	−	0.971506i	$-0.423830\pi$
$929$	14.4483	0.474034	0.237017	+	0.971506i	$0.423830\pi$
$930$	65.0624	2.13348
$931$	14.7532	0.483516
$932$	−2.00701	−0.0657418
$933$	−79.7208	−2.60994
$934$	−11.2051	−0.366641
$935$	30.2467	0.989174
$936$	24.2684	0.793239
$937$	24.0227	0.784787	0.392394	−	0.919797i	$-0.371647\pi$
$937$	24.0227	0.784787	0.392394	+	0.919797i	$0.371647\pi$
$938$	10.8218	0.353344
$939$	−1.67446	−0.0546440
$940$	−8.99016	−0.293227
$941$	−42.7412	−1.39332	−0.696661	−	0.717400i	$-0.745332\pi$
$941$	−42.7412	−1.39332	−0.696661	+	0.717400i	$0.745332\pi$
$942$	53.8162	1.75343
$943$	26.2576	0.855064
$944$	−0.661247	−0.0215217
$945$	99.4028	3.23357
$946$	13.1396	0.427205
$947$	−15.0717	−0.489763	−0.244882	−	0.969553i	$-0.578749\pi$
$947$	−15.0717	−0.489763	−0.244882	+	0.969553i	$0.578749\pi$
$948$	−23.6802	−0.769096
$949$	14.1147	0.458183
$950$	30.9185	1.00313
$951$	19.5152	0.632824
$952$	7.92507	0.256853
$953$	−7.48348	−0.242414	−0.121207	−	0.992627i	$-0.538676\pi$
$953$	−7.48348	−0.242414	−0.121207	+	0.992627i	$0.538676\pi$
$954$	48.3451	1.56523
$955$	−26.6233	−0.861510
$956$	3.11847	0.100859
$957$	−29.2959	−0.947001
$958$	−14.0297	−0.453278
$959$	0.120578	0.00389367
$960$	11.1219	0.358958
$961$	3.22165	0.103924
$962$	10.5394	0.339803
$963$	99.1877	3.19628
$964$	25.1686	0.810626
$965$	50.4893	1.62531
$966$	19.8608	0.639010
$967$	4.72733	0.152021	0.0760103	−	0.997107i	$-0.475782\pi$
$967$	4.72733	0.152021	0.0760103	+	0.997107i	$0.475782\pi$
$968$	6.25636	0.201087
$969$	−61.0482	−1.96115
$970$	38.8043	1.24593
$971$	51.8297	1.66329	0.831647	−	0.555304i	$-0.187398\pi$
$971$	51.8297	1.66329	0.831647	+	0.555304i	$0.187398\pi$
$972$	−38.9711	−1.25000
$973$	14.4239	0.462410
$974$	−30.8187	−0.987494
$975$	69.6773	2.23146
$976$	2.59032	0.0829143
$977$	0.847219	0.0271049	0.0135525	−	0.999908i	$-0.495686\pi$
$977$	0.847219	0.0271049	0.0135525	+	0.999908i	$0.495686\pi$
$978$	−20.2442	−0.647338
$979$	7.09267	0.226683
$980$	10.9166	0.348719
$981$	133.624	4.26630
$982$	−41.1231	−1.31229
$983$	−33.1344	−1.05682	−0.528411	−	0.848989i	$-0.677212\pi$
$983$	−33.1344	−1.05682	−0.528411	+	0.848989i	$0.677212\pi$
$984$	27.2942	0.870109
$985$	88.9109	2.83294
$986$	16.7955	0.534879
$987$	−16.6879	−0.531181
$988$	14.7934	0.470641
$989$	−18.8783	−0.600294
$990$	56.4521	1.79416
$991$	−12.3560	−0.392500	−0.196250	−	0.980554i	$-0.562876\pi$
$991$	−12.3560	−0.392500	−0.196250	+	0.980554i	$0.562876\pi$
$992$	5.84993	0.185735
$993$	−89.4766	−2.83945
$994$	−23.5212	−0.746047
$995$	34.3609	1.08931
$996$	−34.7953	−1.10253
$997$	−55.0803	−1.74441	−0.872205	−	0.489140i	$-0.837311\pi$
$997$	−55.0803	−1.74441	−0.872205	+	0.489140i	$0.837311\pi$
$998$	0.355755	0.0112612
$999$	−49.0496	−1.55186

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4022.2.a.d.1.2	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4022.2.a.d.1.2	✓	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:	\( N \)	\(=\)	\( 4022 = 2 \cdot 2011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4022.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -3.25277 q^{3} +1.00000 q^{4} -3.41922 q^{5} +3.25277 q^{6} +1.95122 q^{7} -1.00000 q^{8} +7.58049 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -3.25277 q^{3} +1.00000 q^{4} -3.41922 q^{5} +3.25277 q^{6} +1.95122 q^{7} -1.00000 q^{8} +7.58049 q^{9} +3.41922 q^{10} +2.17799 q^{11} -3.25277 q^{12} -3.20143 q^{13} -1.95122 q^{14} +11.1219 q^{15} +1.00000 q^{16} -4.06159 q^{17} -7.58049 q^{18} -4.62087 q^{19} -3.41922 q^{20} -6.34688 q^{21} -2.17799 q^{22} +3.12922 q^{23} +3.25277 q^{24} +6.69104 q^{25} +3.20143 q^{26} -14.8993 q^{27} +1.95122 q^{28} +4.13521 q^{29} -11.1219 q^{30} -5.84993 q^{31} -1.00000 q^{32} -7.08449 q^{33} +4.06159 q^{34} -6.67166 q^{35} +7.58049 q^{36} +3.29208 q^{37} +4.62087 q^{38} +10.4135 q^{39} +3.41922 q^{40} +8.39109 q^{41} +6.34688 q^{42} -6.03290 q^{43} +2.17799 q^{44} -25.9193 q^{45} -3.12922 q^{46} +2.62930 q^{47} -3.25277 q^{48} -3.19273 q^{49} -6.69104 q^{50} +13.2114 q^{51} -3.20143 q^{52} -6.37757 q^{53} +14.8993 q^{54} -7.44702 q^{55} -1.95122 q^{56} +15.0306 q^{57} -4.13521 q^{58} -0.661247 q^{59} +11.1219 q^{60} +2.59032 q^{61} +5.84993 q^{62} +14.7912 q^{63} +1.00000 q^{64} +10.9464 q^{65} +7.08449 q^{66} -5.54616 q^{67} -4.06159 q^{68} -10.1786 q^{69} +6.67166 q^{70} +12.0546 q^{71} -7.58049 q^{72} -4.40887 q^{73} -3.29208 q^{74} -21.7644 q^{75} -4.62087 q^{76} +4.24975 q^{77} -10.4135 q^{78} +7.28000 q^{79} -3.41922 q^{80} +25.7224 q^{81} -8.39109 q^{82} +10.6971 q^{83} -6.34688 q^{84} +13.8875 q^{85} +6.03290 q^{86} -13.4509 q^{87} -2.17799 q^{88} +3.25652 q^{89} +25.9193 q^{90} -6.24671 q^{91} +3.12922 q^{92} +19.0284 q^{93} -2.62930 q^{94} +15.7998 q^{95} +3.25277 q^{96} +11.3489 q^{97} +3.19273 q^{98} +16.5102 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q - 37 q^{2} - 5 q^{3} + 37 q^{4} - 13 q^{5} + 5 q^{6} - 22 q^{7} - 37 q^{8} + 32 q^{9}+O(q^{10}) \) 37 * q - 37 * q^2 - 5 * q^3 + 37 * q^4 - 13 * q^5 + 5 * q^6 - 22 * q^7 - 37 * q^8 + 32 * q^9	\( 37 q - 37 q^{2} - 5 q^{3} + 37 q^{4} - 13 q^{5} + 5 q^{6} - 22 q^{7} - 37 q^{8} + 32 q^{9} + 13 q^{10} + 12 q^{11} - 5 q^{12} - 36 q^{13} + 22 q^{14} - 7 q^{15} + 37 q^{16} + 4 q^{17} - 32 q^{18} - 10 q^{19} - 13 q^{20} - 11 q^{21} - 12 q^{22} - q^{23} + 5 q^{24} + 8 q^{25} + 36 q^{26} - 20 q^{27} - 22 q^{28} - 6 q^{29} + 7 q^{30} - 23 q^{31} - 37 q^{32} - 27 q^{33} - 4 q^{34} + 24 q^{35} + 32 q^{36} - 46 q^{37} + 10 q^{38} + 5 q^{39} + 13 q^{40} + 11 q^{41} + 11 q^{42} - 22 q^{43} + 12 q^{44} - 57 q^{45} + q^{46} - 18 q^{47} - 5 q^{48} - q^{49} - 8 q^{50} + 18 q^{51} - 36 q^{52} - 25 q^{53} + 20 q^{54} - 25 q^{55} + 22 q^{56} - 25 q^{57} + 6 q^{58} + 24 q^{59} - 7 q^{60} - 40 q^{61} + 23 q^{62} - 38 q^{63} + 37 q^{64} + 14 q^{65} + 27 q^{66} - 49 q^{67} + 4 q^{68} - 19 q^{69} - 24 q^{70} + 27 q^{71} - 32 q^{72} - 87 q^{73} + 46 q^{74} - 5 q^{75} - 10 q^{76} - 50 q^{77} - 5 q^{78} + 11 q^{79} - 13 q^{80} + 5 q^{81} - 11 q^{82} - 9 q^{83} - 11 q^{84} - 68 q^{85} + 22 q^{86} - 12 q^{87} - 12 q^{88} - 3 q^{89} + 57 q^{90} - 19 q^{91} - q^{92} - 69 q^{93} + 18 q^{94} + 27 q^{95} + 5 q^{96} - 98 q^{97} + q^{98} + 33 q^{99}+O(q^{100}) \) 37 * q - 37 * q^2 - 5 * q^3 + 37 * q^4 - 13 * q^5 + 5 * q^6 - 22 * q^7 - 37 * q^8 + 32 * q^9 + 13 * q^10 + 12 * q^11 - 5 * q^12 - 36 * q^13 + 22 * q^14 - 7 * q^15 + 37 * q^16 + 4 * q^17 - 32 * q^18 - 10 * q^19 - 13 * q^20 - 11 * q^21 - 12 * q^22 - q^23 + 5 * q^24 + 8 * q^25 + 36 * q^26 - 20 * q^27 - 22 * q^28 - 6 * q^29 + 7 * q^30 - 23 * q^31 - 37 * q^32 - 27 * q^33 - 4 * q^34 + 24 * q^35 + 32 * q^36 - 46 * q^37 + 10 * q^38 + 5 * q^39 + 13 * q^40 + 11 * q^41 + 11 * q^42 - 22 * q^43 + 12 * q^44 - 57 * q^45 + q^46 - 18 * q^47 - 5 * q^48 - q^49 - 8 * q^50 + 18 * q^51 - 36 * q^52 - 25 * q^53 + 20 * q^54 - 25 * q^55 + 22 * q^56 - 25 * q^57 + 6 * q^58 + 24 * q^59 - 7 * q^60 - 40 * q^61 + 23 * q^62 - 38 * q^63 + 37 * q^64 + 14 * q^65 + 27 * q^66 - 49 * q^67 + 4 * q^68 - 19 * q^69 - 24 * q^70 + 27 * q^71 - 32 * q^72 - 87 * q^73 + 46 * q^74 - 5 * q^75 - 10 * q^76 - 50 * q^77 - 5 * q^78 + 11 * q^79 - 13 * q^80 + 5 * q^81 - 11 * q^82 - 9 * q^83 - 11 * q^84 - 68 * q^85 + 22 * q^86 - 12 * q^87 - 12 * q^88 - 3 * q^89 + 57 * q^90 - 19 * q^91 - q^92 - 69 * q^93 + 18 * q^94 + 27 * q^95 + 5 * q^96 - 98 * q^97 + q^98 + 33 * q^99

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